Subgroups — C₆₇×#61068 #30740319

Order 17152.

2772 conjugacy classes of subgroups.

The subgroup lattice has 1580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#548×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3285	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3282	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3277	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3275	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3271	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3270	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3269	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3265	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3153	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3055	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3040	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3006	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3005	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3004	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#575×C₆₇	—	2	8	no	—
29	C₂×#137×C₆₇	—	2	8	no	—
30	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
33	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
34	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
35	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
41	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
44	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
45	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
46	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
47	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#550×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#548×C₆₇	—	2	1	no	—
52	#548×C₆₇	—	2	1	no	—
53	#548×C₆₇	—	2	1	no	—
54	#548×C₆₇	—	2	1	no	—
55	#548×C₆₇	C₂²	1	2	yes	—
56	#548×C₆₇	C₂²	1	2	yes	complemented
57	#548×C₆₇	C₂²	1	2	yes	complemented
58	#548×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#548×C₆₇	C₂²	1	2	yes	complemented
60	#548×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#547×C₆₇	—	2	1	no	—
62	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#546×C₆₇	—	2	1	no	—
64	#546×C₆₇	—	2	1	no	—
65	#546×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#546×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	D₄²×C₆₇	—	2	1	no	—
68	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#532×C₆₇	—	2	1	no	—
70	#532×C₆₇	C₂²	1	1	yes	characteristic
71	C₂×#124×C₆₇	—	2	1	no	—
72	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#525×C₆₇	—	2	1	no	—
74	#525×C₆₇	—	2	1	no	—
75	#525×C₆₇	C₂²	1	1	yes	characteristic
76	#525×C₆₇	C₂²	1	1	yes	characteristic
77	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
78	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	C₂×#121×C₆₇	—	2	1	no	—
80	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
82	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄×D₄×C₆₇	—	2	1	no	—
84	C₂×C₄×D₄×C₆₇	—	2	1	no	—
85	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
86	#497×C₆₇	C₂²	1	2	yes	complemented
87	#496×C₆₇	C₂²	1	2	yes	complemented
88	#495×C₆₇	C₂²	1	2	yes	complemented
89	#495×C₆₇	C₂²	1	2	yes	complemented
90	#470×C₆₇	C₂²	1	2	yes	complemented
91	#469×C₆₇	C₂²	1	2	yes	complemented
92	#468×C₆₇	C₂²	1	2	yes	complemented
93	#468×C₆₇	C₂²	1	2	yes	complemented
94	#467×C₆₇	C₂²	1	2	yes	complemented
95	#466×C₆₇	C₂²	1	2	yes	complemented
96	#465×C₆₇	C₂²	1	2	yes	complemented
97	#465×C₆₇	C₂²	1	2	yes	complemented
98	#464×C₆₇	C₂²	1	2	yes	complemented
99	#464×C₆₇	C₂²	1	2	yes	complemented
100	#464×C₆₇	C₂²	1	2	yes	complemented
101	#464×C₆₇	C₂²	1	2	yes	complemented
102	#463×C₆₇	C₂²	1	2	yes	complemented
103	#463×C₆₇	C₂²	1	2	yes	complemented
104	#462×C₆₇	C₂²	1	2	yes	complemented
105	#460×C₆₇	C₂²	1	2	yes	complemented
106	#452×C₆₇	C₂²	1	2	yes	complemented
107	#452×C₆₇	C₂²	1	2	yes	complemented
108	#452×C₆₇	C₂²	1	2	yes	complemented
109	#452×C₆₇	C₂²	1	2	yes	complemented
110	#451×C₆₇	C₂²	1	2	yes	complemented
111	#451×C₆₇	C₂²	1	2	yes	complemented
112	#451×C₆₇	C₂²	1	2	yes	complemented
113	#450×C₆₇	C₂²	1	2	yes	complemented
114	#449×C₆₇	C₂²	1	2	yes	complemented
115	#449×C₆₇	C₂²	1	2	yes	complemented
116	#449×C₆₇	C₂²	1	2	yes	complemented
117	#449×C₆₇	C₂²	1	2	yes	complemented
118	#448×C₆₇	C₂²	1	2	yes	complemented
119	#448×C₆₇	C₂²	1	2	yes	complemented
120	#448×C₆₇	C₂²	1	2	yes	complemented
121	#447×C₆₇	C₂²	1	2	yes	complemented
122	#441×C₆₇	C₂²	1	2	yes	complemented
123	#440×C₆₇	C₂²	1	2	yes	complemented
124	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
125	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
126	#436×C₆₇	C₂²	1	2	yes	complemented
127	#435×C₆₇	C₂²	1	2	yes	complemented
128	#435×C₆₇	C₂²	1	2	yes	complemented
129	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
130	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	#417×C₆₇	C₂²	1	1	yes	characteristic
136	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
138	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
139	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
140	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
141	C₂×#41×C₆₇	—	2	1	no	—
142	C₂×#41×C₆₇	—	2	1	no	—
143	C₂×#41×C₆₇	—	2	1	no	—
144	C₂×#41×C₆₇	—	2	1	no	—
145	C₂×#41×C₆₇	—	2	1	no	—
146	C₂×#41×C₆₇	—	2	1	no	—
147	C₂×#41×C₆₇	—	2	4	no	—
148	C₂×#41×C₆₇	—	2	4	no	—
149	C₂×#41×C₆₇	—	2	4	no	—
150	C₂×#41×C₆₇	—	4	2	no	—
151	C₂×#41×C₆₇	—	4	2	no	—
152	C₂×#41×C₆₇	—	4	2	no	—
153	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×#41×C₆₇	C₂³	1	2	yes	—
158	C₂×#41×C₆₇	C₂³	1	2	yes	—
159	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
162	C₂²×Q₈×C₆₇	—	2	1	no	—
163	C₂²×Q₈×C₆₇	—	2	1	no	—
164	C₂²×Q₈×C₆₇	—	2	1	no	—
165	C₂²×Q₈×C₆₇	—	2	4	no	—
166	C₂²×Q₈×C₆₇	—	4	2	no	—
167	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
168	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
169	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
170	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
171	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
172	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
173	C₂²×D₄×C₆₇	—	2	1	no	—
174	C₂²×D₄×C₆₇	—	2	1	no	—
175	C₂²×D₄×C₆₇	—	2	1	no	—
176	C₂²×D₄×C₆₇	—	2	1	no	—
177	C₂²×D₄×C₆₇	—	2	1	no	—
178	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
179	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂³×C₄×C₆₇	—	2	1	no	—
183	C₂³×C₄×C₆₇	—	2	1	no	—
184	C₂³×C₄×C₆₇	—	2	1	no	—
185	C₂³×C₄×C₆₇	—	2	1	no	—
186	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
188	#137×C₆₇	—	2	4	no	—
189	#137×C₆₇	—	2	4	no	—
190	#137×C₆₇	—	2	4	no	—
191	#137×C₆₇	—	2	8	no	—
192	#137×C₆₇	—	2	8	no	—
193	#137×C₆₇	—	2	8	no	—
194	#137×C₆₇	—	2	4	no	—
195	#137×C₆₇	—	4	2	no	—
196	#137×C₆₇	D₄	1	8	yes	complemented
197	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
198	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
199	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
200	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
201	#135×C₆₇	—	2	8	no	—
202	#135×C₆₇	—	2	8	no	—
203	C₂×Q₁₆×C₆₇	—	2	8	no	—
204	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
205	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
206	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
207	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
208	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
209	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
210	C₂×SD₁₆×C₆₇	—	2	8	no	—
211	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
212	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
213	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
214	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
215	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
216	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
217	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
218	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
219	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
220	C₂×D₈×C₆₇	C₂³	1	2	yes	—
221	C₂×D₈×C₆₇	C₂³	1	2	yes	—
222	C₂×D₈×C₆₇	C₂³	1	2	yes	—
223	C₂×M₁₆×C₆₇	—	2	4	no	—
224	C₂×M₁₆×C₆₇	—	2	4	no	—
225	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
226	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
227	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
228	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
231	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
232	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
233	C₄⋊Q₈×C₆₇	—	2	1	no	—
234	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
235	#127×C₆₇	—	2	1	no	—
236	#127×C₆₇	C₂³	1	1	yes	characteristic
237	#124×C₆₇	—	2	2	no	—
238	#124×C₆₇	—	2	2	no	—
239	#124×C₆₇	—	2	2	no	—
240	#124×C₆₇	—	2	2	no	—
241	#124×C₆₇	—	2	1	no	—
242	#124×C₆₇	—	2	1	no	—
243	#124×C₆₇	—	2	1	no	—
244	#124×C₆₇	—	2	1	no	—
245	#124×C₆₇	C₂³	1	2	yes	—
246	#124×C₆₇	C₂³	1	2	yes	—
247	#124×C₆₇	C₂³	1	1	yes	characteristic
248	#124×C₆₇	C₂³	1	1	yes	characteristic
249	#123×C₆₇	—	2	1	no	—
250	#123×C₆₇	—	2	1	no	—
251	#123×C₆₇	—	2	1	no	—
252	#123×C₆₇	—	2	1	no	—
253	#123×C₆₇	—	2	1	no	—
254	#123×C₆₇	—	2	1	no	—
255	C₂²⋊Q₈×C₆₇	—	2	1	no	—
256	C₂²⋊Q₈×C₆₇	—	2	1	no	—
257	C₂²⋊Q₈×C₆₇	—	2	2	no	—
258	C₂²⋊Q₈×C₆₇	—	2	2	no	—
259	C₂²⋊Q₈×C₆₇	—	2	2	no	—
260	C₂²⋊Q₈×C₆₇	—	2	2	no	—
261	C₂²⋊Q₈×C₆₇	—	2	1	no	—
262	C₂²⋊Q₈×C₆₇	—	2	1	no	—
263	C₂²⋊Q₈×C₆₇	—	2	1	no	—
264	C₂²⋊Q₈×C₆₇	—	2	1	no	—
265	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
266	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
267	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
268	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
269	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
270	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
271	#121×C₆₇	—	2	2	no	—
272	#121×C₆₇	—	2	2	no	—
273	#121×C₆₇	—	2	2	no	—
274	#121×C₆₇	—	2	2	no	—
275	#121×C₆₇	—	2	1	no	—
276	#121×C₆₇	—	2	1	no	—
277	#121×C₆₇	—	2	1	no	—
278	#121×C₆₇	—	2	1	no	—
279	#121×C₆₇	—	2	1	no	—
280	#121×C₆₇	—	2	1	no	—
281	#121×C₆₇	—	2	1	no	—
282	#121×C₆₇	—	2	1	no	—
283	#121×C₆₇	—	2	1	no	—
284	#121×C₆₇	—	2	1	no	—
285	#121×C₆₇	—	2	1	no	—
286	#121×C₆₇	—	2	1	no	—
287	#121×C₆₇	C₂³	1	1	yes	characteristic
288	#121×C₆₇	C₂³	1	1	yes	characteristic
289	#121×C₆₇	C₂³	1	2	yes	—
290	#121×C₆₇	C₂³	1	1	yes	characteristic
291	#121×C₆₇	C₂³	1	1	yes	characteristic
292	#121×C₆₇	C₂³	1	2	yes	—
293	#120×C₆₇	—	2	1	no	—
294	#120×C₆₇	—	2	1	no	—
295	#120×C₆₇	—	2	1	no	—
296	#120×C₆₇	—	2	1	no	—
297	#120×C₆₇	—	2	1	no	—
298	#120×C₆₇	—	2	1	no	—
299	C₄×Q₈×C₆₇	—	2	1	no	—
300	C₄×Q₈×C₆₇	—	2	1	no	—
301	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
302	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
303	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
304	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
305	C₄×D₄×C₆₇	—	2	1	no	—
306	C₄×D₄×C₆₇	—	2	1	no	—
307	C₄×D₄×C₆₇	—	2	1	no	—
308	C₄×D₄×C₆₇	—	2	1	no	—
309	C₄×D₄×C₆₇	—	2	1	no	—
310	C₄×D₄×C₆₇	—	2	1	no	—
311	C₄×D₄×C₆₇	—	2	1	no	—
312	C₄×D₄×C₆₇	—	2	1	no	—
313	C₄×D₄×C₆₇	—	2	1	no	—
314	C₄×D₄×C₆₇	—	2	1	no	—
315	C₄×D₄×C₆₇	—	2	2	no	—
316	C₄×D₄×C₆₇	—	2	2	no	—
317	C₄×D₄×C₆₇	—	2	2	no	—
318	C₄×D₄×C₆₇	—	2	2	no	—
319	C₄×D₄×C₆₇	—	2	1	no	—
320	C₄×D₄×C₆₇	—	2	1	no	—
321	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
322	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
323	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
324	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
325	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
326	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
327	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
328	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
329	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
330	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
331	#117×C₆₇	—	2	1	no	—
332	#117×C₆₇	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
334	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
335	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
336	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
337	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
339	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
340	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
341	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
342	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
343	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
344	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
346	C₂×C₄²×C₆₇	—	2	1	no	—
347	C₂×C₄²×C₆₇	—	2	1	no	—
348	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
349	#107×C₆₇	C₂³	1	2	yes	—
350	#106×C₆₇	C₂³	1	2	yes	—
351	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
352	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
353	#103×C₆₇	C₂³	1	2	yes	—
354	#103×C₆₇	C₂³	1	2	yes	—
355	#103×C₆₇	C₂³	1	2	yes	—
356	#103×C₆₇	C₂³	1	2	yes	—
357	#103×C₆₇	C₂³	1	2	yes	—
358	#103×C₆₇	C₂³	1	2	yes	—
359	#103×C₆₇	C₂³	1	2	yes	—
360	#102×C₆₇	C₂³	1	2	yes	—
361	#102×C₆₇	C₂³	1	2	yes	—
362	#102×C₆₇	C₂³	1	2	yes	—
363	#102×C₆₇	C₂³	1	2	yes	—
364	#102×C₆₇	C₂³	1	2	yes	—
365	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
366	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
367	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
368	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
369	#97×C₆₇	C₂³	1	2	yes	—
370	C₄×C₈×C₆₇	C₂³	1	2	yes	—
371	C₂⁴×C₆₇	—	2	1	no	—
372	C₂⁴×C₆₇	—	2	1	no	—
373	C₂⁴×C₆₇	—	2	1	no	—
374	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
376	#41×C₆₇	—	2	2	no	—
377	#41×C₆₇	—	2	4	no	—
378	#41×C₆₇	—	2	2	no	—
379	#41×C₆₇	—	2	4	no	—
380	#41×C₆₇	—	2	2	no	—
381	#41×C₆₇	—	2	2	no	—
382	#41×C₆₇	—	2	2	no	—
383	#41×C₆₇	—	2	2	no	—
384	#41×C₆₇	—	2	2	no	—
385	#41×C₆₇	—	2	2	no	—
386	#41×C₆₇	—	2	2	no	—
387	#41×C₆₇	—	4	4	no	—
388	#41×C₆₇	—	4	4	no	—
389	#41×C₆₇	—	4	2	no	—
390	#41×C₆₇	—	4	1	no	—
391	#41×C₆₇	—	4	1	no	—
392	#41×C₆₇	—	4	2	no	—
393	#41×C₆₇	—	4	1	no	—
394	#41×C₆₇	—	4	1	no	—
395	#41×C₆₇	—	4	4	no	—
396	#41×C₆₇	—	4	4	no	—
397	#41×C₆₇	—	4	4	no	—
398	#41×C₆₇	—	4	4	no	—
399	#41×C₆₇	C₂×D₄	1	4	yes	—
400	C₂×Q₈×C₆₇	—	2	1	no	—
401	C₂×Q₈×C₆₇	—	2	2	no	—
402	C₂×Q₈×C₆₇	—	2	2	no	—
403	C₂×Q₈×C₆₇	—	2	1	no	—
404	C₂×Q₈×C₆₇	—	2	1	no	—
405	C₂×Q₈×C₆₇	—	2	1	no	—
406	C₂×Q₈×C₆₇	—	2	2	no	—
407	C₂×Q₈×C₆₇	—	2	4	no	—
408	C₂×Q₈×C₆₇	—	2	2	no	—
409	C₂×Q₈×C₆₇	—	2	4	no	—
410	C₂×Q₈×C₆₇	—	2	2	no	—
411	C₂×Q₈×C₆₇	—	2	2	no	—
412	C₂×Q₈×C₆₇	—	2	2	no	—
413	C₂×Q₈×C₆₇	—	4	4	no	—
414	C₂×Q₈×C₆₇	—	4	2	no	—
415	C₂×Q₈×C₆₇	—	4	2	no	—
416	C₂×Q₈×C₆₇	—	4	1	no	—
417	C₂×Q₈×C₆₇	—	4	1	no	—
418	C₂×Q₈×C₆₇	—	4	4	no	—
419	C₂×Q₈×C₆₇	—	4	4	no	—
420	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	complemented
421	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
422	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
423	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
425	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₂×D₄×C₆₇	—	2	1	no	—
427	C₂×D₄×C₆₇	—	2	2	no	—
428	C₂×D₄×C₆₇	—	2	2	no	—
429	C₂×D₄×C₆₇	—	2	1	no	—
430	C₂×D₄×C₆₇	—	2	1	no	—
431	C₂×D₄×C₆₇	—	2	2	no	—
432	C₂×D₄×C₆₇	—	2	2	no	—
433	C₂×D₄×C₆₇	—	2	1	no	—
434	C₂×D₄×C₆₇	—	2	1	no	—
435	C₂×D₄×C₆₇	—	2	1	no	—
436	C₂×D₄×C₆₇	—	2	1	no	—
437	C₂×D₄×C₆₇	—	2	2	no	—
438	C₂×D₄×C₆₇	—	2	2	no	—
439	C₂×D₄×C₆₇	—	2	1	no	—
440	C₂×D₄×C₆₇	—	2	1	no	—
441	C₂×D₄×C₆₇	—	2	1	no	—
442	C₂×D₄×C₆₇	—	2	1	no	—
443	C₂×D₄×C₆₇	—	2	2	no	—
444	C₂×D₄×C₆₇	—	2	1	no	—
445	C₂×D₄×C₆₇	—	2	1	no	—
446	C₂×D₄×C₆₇	—	2	1	no	—
447	C₂×D₄×C₆₇	—	2	1	no	—
448	C₂×D₄×C₆₇	—	2	1	no	—
449	C₂×D₄×C₆₇	—	2	2	no	—
450	C₂×D₄×C₆₇	—	4	1	no	—
451	C₂×D₄×C₆₇	—	4	1	no	—
452	C₂×D₄×C₆₇	—	4	4	no	—
453	C₂×D₄×C₆₇	—	4	2	no	—
454	C₂×D₄×C₆₇	—	4	4	no	—
455	C₂×D₄×C₆₇	—	4	4	no	—
456	C₂×D₄×C₆₇	—	4	4	no	—
457	C₂×D₄×C₆₇	—	4	4	no	—
458	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
459	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
460	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
461	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
462	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
463	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
464	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
465	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
466	C₂²×C₄×C₆₇	—	2	1	no	—
467	C₂²×C₄×C₆₇	—	2	1	no	—
468	C₂²×C₄×C₆₇	—	2	2	no	—
469	C₂²×C₄×C₆₇	—	2	2	no	—
470	C₂²×C₄×C₆₇	—	2	2	no	—
471	C₂²×C₄×C₆₇	—	2	2	no	—
472	C₂²×C₄×C₆₇	—	2	1	no	—
473	C₂²×C₄×C₆₇	—	2	1	no	—
474	C₂²×C₄×C₆₇	—	2	2	no	—
475	C₂²×C₄×C₆₇	—	2	2	no	—
476	C₂²×C₄×C₆₇	—	2	1	no	—
477	C₂²×C₄×C₆₇	—	2	1	no	—
478	C₂²×C₄×C₆₇	—	2	1	no	—
479	C₂²×C₄×C₆₇	—	2	1	no	—
480	C₂²×C₄×C₆₇	—	2	1	no	—
481	C₂²×C₄×C₆₇	—	2	1	no	—
482	C₂²×C₄×C₆₇	—	2	1	no	—
483	C₂²×C₄×C₆₇	—	2	1	no	—
484	C₂²×C₄×C₆₇	—	2	1	no	—
485	C₂²×C₄×C₆₇	—	2	2	no	—
486	C₂²×C₄×C₆₇	—	2	2	no	—
487	C₂²×C₄×C₆₇	—	2	1	no	—
488	C₂²×C₄×C₆₇	—	4	4	no	—
489	C₂²×C₄×C₆₇	—	4	4	no	—
490	C₂²×C₄×C₆₇	—	4	4	no	—
491	C₂²×C₄×C₆₇	—	4	4	no	—
492	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
493	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
494	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
495	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
496	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
497	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
498	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
499	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
500	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
501	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
502	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
503	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
504	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
505	Q₁₆×C₆₇	—	2	4	no	—
506	Q₁₆×C₆₇	—	2	4	no	—
507	Q₁₆×C₆₇	—	2	4	no	—
508	Q₁₆×C₆₇	—	2	4	no	—
509	Q₁₆×C₆₇	—	4	2	no	—
510	Q₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
511	SD₁₆×C₆₇	—	2	4	no	—
512	SD₁₆×C₆₇	—	2	4	no	—
513	SD₁₆×C₆₇	—	2	4	no	—
514	SD₁₆×C₆₇	—	2	4	no	—
515	SD₁₆×C₆₇	—	2	4	no	—
516	SD₁₆×C₆₇	—	2	4	no	—
517	SD₁₆×C₆₇	—	4	2	no	—
518	SD₁₆×C₆₇	—	4	2	no	—
519	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
520	D₈×C₆₇	—	2	4	no	—
521	D₈×C₆₇	—	2	4	no	—
522	D₈×C₆₇	—	4	2	no	—
523	M₁₆×C₆₇	—	2	2	no	—
524	M₁₆×C₆₇	—	2	2	no	—
525	M₁₆×C₆₇	—	2	2	no	—
526	M₁₆×C₆₇	—	2	4	no	—
527	M₁₆×C₆₇	—	2	4	no	—
528	M₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
529	C₂×C₈×C₆₇	—	2	4	no	—
530	C₂×C₈×C₆₇	—	2	4	no	—
531	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
532	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
533	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
534	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
535	C₄⋊C₄×C₆₇	—	2	1	no	—
536	C₄⋊C₄×C₆₇	—	2	2	no	—
537	C₄⋊C₄×C₆₇	—	2	2	no	—
538	C₄⋊C₄×C₆₇	—	2	1	no	—
539	C₄⋊C₄×C₆₇	—	2	1	no	—
540	C₄⋊C₄×C₆₇	—	2	2	no	—
541	C₄⋊C₄×C₆₇	—	2	2	no	—
542	C₄⋊C₄×C₆₇	—	2	1	no	—
543	C₄⋊C₄×C₆₇	—	2	1	no	—
544	C₄⋊C₄×C₆₇	—	2	1	no	—
545	C₄⋊C₄×C₆₇	—	2	1	no	—
546	C₄⋊C₄×C₆₇	—	2	1	no	—
547	C₄⋊C₄×C₆₇	—	2	1	no	—
548	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
549	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
550	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
551	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
552	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
553	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
554	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
555	C₂²⋊C₄×C₆₇	—	2	1	no	—
556	C₂²⋊C₄×C₆₇	—	2	1	no	—
557	C₂²⋊C₄×C₆₇	—	2	2	no	—
558	C₂²⋊C₄×C₆₇	—	2	2	no	—
559	C₂²⋊C₄×C₆₇	—	2	1	no	—
560	C₂²⋊C₄×C₆₇	—	2	1	no	—
561	C₂²⋊C₄×C₆₇	—	2	1	no	—
562	C₂²⋊C₄×C₆₇	—	2	1	no	—
563	C₂²⋊C₄×C₆₇	—	2	1	no	—
564	C₂²⋊C₄×C₆₇	—	2	1	no	—
565	C₂²⋊C₄×C₆₇	—	2	1	no	—
566	C₂²⋊C₄×C₆₇	—	2	2	no	—
567	C₂²⋊C₄×C₆₇	—	2	2	no	—
568	C₂²⋊C₄×C₆₇	—	2	2	no	—
569	C₂²⋊C₄×C₆₇	—	2	2	no	—
570	C₂²⋊C₄×C₆₇	—	2	2	no	—
571	C₂²⋊C₄×C₆₇	—	2	2	no	—
572	C₂²⋊C₄×C₆₇	—	2	1	no	—
573	C₂²⋊C₄×C₆₇	—	2	1	no	—
574	C₂²⋊C₄×C₆₇	—	2	1	no	—
575	C₂²⋊C₄×C₆₇	—	2	1	no	—
576	C₂²⋊C₄×C₆₇	—	2	1	no	—
577	C₂²⋊C₄×C₆₇	—	2	1	no	—
578	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
579	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
580	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
581	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
582	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
583	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
584	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
585	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
586	C₄²×C₆₇	—	2	1	no	—
587	C₄²×C₆₇	—	2	1	no	—
588	C₄²×C₆₇	—	2	1	no	—
589	C₄²×C₆₇	—	2	2	no	—
590	C₄²×C₆₇	—	2	2	no	—
591	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
592	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
593	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
594	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
595	C₂³×C₆₇	—	2	2	no	—
596	C₂³×C₆₇	—	2	2	no	—
597	C₂³×C₆₇	—	2	1	no	—
598	C₂³×C₆₇	—	2	2	no	—
599	C₂³×C₆₇	—	2	2	no	—
600	C₂³×C₆₇	—	2	1	no	—
601	C₂³×C₆₇	—	2	1	no	—
602	C₂³×C₆₇	—	4	1	no	—
603	C₂³×C₆₇	—	4	1	no	—
604	C₂³×C₆₇	—	4	1	no	—
605	C₂³×C₆₇	—	4	2	no	—
606	C₂³×C₆₇	—	4	2	no	—
607	C₂³×C₆₇	—	4	2	no	—
608	C₂³×C₆₇	—	4	2	no	—
609	C₂³×C₆₇	—	4	2	no	—
610	C₂³×C₆₇	—	4	2	no	—
611	C₂³×C₆₇	—	4	2	no	—
612	C₂³×C₆₇	—	8	1	no	—
613	C₂³×C₆₇	—	8	1	no	—
614	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
615	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
616	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
617	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
618	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
619	Q₈×C₆₇	—	2	4	no	—
620	Q₈×C₆₇	—	2	2	no	—
621	Q₈×C₆₇	—	2	1	no	—
622	Q₈×C₆₇	—	2	2	no	—
623	Q₈×C₆₇	—	2	1	no	—
624	Q₈×C₆₇	—	2	1	no	—
625	Q₈×C₆₇	—	2	1	no	—
626	Q₈×C₆₇	—	2	2	no	—
627	Q₈×C₆₇	—	2	1	no	—
628	Q₈×C₆₇	—	4	4	no	—
629	Q₈×C₆₇	—	4	4	no	—
630	Q₈×C₆₇	—	4	2	no	—
631	Q₈×C₆₇	—	4	2	no	—
632	Q₈×C₆₇	—	4	2	no	—
633	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
634	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
635	D₄×C₆₇	—	2	4	no	—
636	D₄×C₆₇	—	2	2	no	—
637	D₄×C₆₇	—	2	2	no	—
638	D₄×C₆₇	—	2	2	no	—
639	D₄×C₆₇	—	2	1	no	—
640	D₄×C₆₇	—	2	1	no	—
641	D₄×C₆₇	—	2	1	no	—
642	D₄×C₆₇	—	2	1	no	—
643	D₄×C₆₇	—	2	2	no	—
644	D₄×C₆₇	—	2	1	no	—
645	D₄×C₆₇	—	4	1	no	—
646	D₄×C₆₇	—	4	1	no	—
647	D₄×C₆₇	—	4	2	no	—
648	D₄×C₆₇	—	4	2	no	—
649	D₄×C₆₇	—	4	2	no	—
650	D₄×C₆₇	—	4	2	no	—
651	D₄×C₆₇	—	4	4	no	—
652	D₄×C₆₇	—	4	4	no	—
653	D₄×C₆₇	—	4	2	no	—
654	D₄×C₆₇	—	4	2	no	—
655	D₄×C₆₇	—	4	2	no	—
656	D₄×C₆₇	—	4	2	no	—
657	D₄×C₆₇	—	4	4	no	—
658	D₄×C₆₇	—	4	2	no	—
659	D₄×C₆₇	—	4	2	no	—
660	D₄×C₆₇	—	4	2	no	—
661	D₄×C₆₇	—	4	4	no	—
662	D₄×C₆₇	—	4	2	no	—
663	D₄×C₆₇	—	8	1	no	—
664	D₄×C₆₇	—	8	1	no	—
665	D₄×C₆₇	—	8	1	no	—
666	D₄×C₆₇	C₂²×D₄	1	2	yes	—
667	C₂×C₄×C₆₇	—	2	2	no	—
668	C₂×C₄×C₆₇	—	2	2	no	—
669	C₂×C₄×C₆₇	—	2	4	no	—
670	C₂×C₄×C₆₇	—	2	1	no	—
671	C₂×C₄×C₆₇	—	2	2	no	—
672	C₂×C₄×C₆₇	—	2	2	no	—
673	C₂×C₄×C₆₇	—	2	2	no	—
674	C₂×C₄×C₆₇	—	2	2	no	—
675	C₂×C₄×C₆₇	—	2	2	no	—
676	C₂×C₄×C₆₇	—	2	4	no	—
677	C₂×C₄×C₆₇	—	2	1	no	—
678	C₂×C₄×C₆₇	—	2	1	no	—
679	C₂×C₄×C₆₇	—	2	1	no	—
680	C₂×C₄×C₆₇	—	2	1	no	—
681	C₂×C₄×C₆₇	—	2	1	no	—
682	C₂×C₄×C₆₇	—	2	1	no	—
683	C₂×C₄×C₆₇	—	2	1	no	—
684	C₂×C₄×C₆₇	—	2	1	no	—
685	C₂×C₄×C₆₇	—	2	1	no	—
686	C₂×C₄×C₆₇	—	2	1	no	—
687	C₂×C₄×C₆₇	—	2	2	no	—
688	C₂×C₄×C₆₇	—	2	2	no	—
689	C₂×C₄×C₆₇	—	2	1	no	—
690	C₂×C₄×C₆₇	—	2	1	no	—
691	C₂×C₄×C₆₇	—	4	1	no	—
692	C₂×C₄×C₆₇	—	4	1	no	—
693	C₂×C₄×C₆₇	—	4	2	no	—
694	C₂×C₄×C₆₇	—	4	4	no	—
695	C₂×C₄×C₆₇	—	4	4	no	—
696	C₂×C₄×C₆₇	—	4	2	no	—
697	C₂×C₄×C₆₇	—	4	2	no	—
698	C₂×C₄×C₆₇	—	4	2	no	—
699	C₂×C₄×C₆₇	—	4	4	no	—
700	C₂×C₄×C₆₇	—	4	4	no	—
701	C₂×C₄×C₆₇	—	4	2	no	—
702	C₂×C₄×C₆₇	—	4	2	no	—
703	C₂×C₄×C₆₇	—	4	2	no	—
704	C₂×C₄×C₆₇	—	4	2	no	—
705	C₂×C₄×C₆₇	—	4	2	no	—
706	C₂×C₄×C₆₇	—	4	2	no	—
707	C₂×C₄×C₆₇	—	4	2	no	—
708	C₂×C₄×C₆₇	—	8	1	no	—
709	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
710	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
711	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
712	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
713	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
714	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
715	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
716	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
717	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
718	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
719	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
720	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
721	C₈×C₆₇	—	2	2	no	—
722	C₈×C₆₇	—	2	2	no	—
723	C₈×C₆₇	—	2	2	no	—
724	C₈×C₆₇	C₂²×D₄	1	4	yes	—
725	C₂²×C₆₇	—	2	1	no	—
726	C₂²×C₆₇	—	2	1	no	—
727	C₂²×C₆₇	—	2	1	no	—
728	C₂²×C₆₇	—	2	1	no	—
729	C₂²×C₆₇	—	2	1	no	—
730	C₂²×C₆₇	—	2	1	no	—
731	C₂²×C₆₇	—	2	1	no	—
732	C₂²×C₆₇	—	2	1	no	—
733	C₂²×C₆₇	—	2	1	no	—
734	C₂²×C₆₇	—	2	1	no	—
735	C₂²×C₆₇	—	2	2	no	—
736	C₂²×C₆₇	—	2	1	no	—
737	C₂²×C₆₇	—	2	1	no	—
738	C₂²×C₆₇	—	2	1	no	—
739	C₂²×C₆₇	—	4	4	no	—
740	C₂²×C₆₇	—	4	1	no	—
741	C₂²×C₆₇	—	4	1	no	—
742	C₂²×C₆₇	—	4	1	no	—
743	C₂²×C₆₇	—	4	1	no	—
744	C₂²×C₆₇	—	4	2	no	—
745	C₂²×C₆₇	—	4	2	no	—
746	C₂²×C₆₇	—	4	1	no	—
747	C₂²×C₆₇	—	4	1	no	—
748	C₂²×C₆₇	—	4	1	no	—
749	C₂²×C₆₇	—	4	1	no	—
750	C₂²×C₆₇	—	4	2	no	—
751	C₂²×C₆₇	—	8	2	no	—
752	C₂²×C₆₇	—	8	4	no	—
753	C₂²×C₆₇	—	8	4	no	—
754	C₂²×C₆₇	—	8	4	no	—
755	C₂²×C₆₇	D₄²	1	2	yes	—
756	C₂²×C₆₇	#575	1	2	yes	complemented
757	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
758	C₄×C₆₇	—	2	1	no	—
759	C₄×C₆₇	—	2	1	no	—
760	C₄×C₆₇	—	2	1	no	—
761	C₄×C₆₇	—	2	1	no	—
762	C₄×C₆₇	—	2	1	no	—
763	C₄×C₆₇	—	2	1	no	—
764	C₄×C₆₇	—	2	2	no	—
765	C₄×C₆₇	—	2	4	no	—
766	C₄×C₆₇	—	2	1	no	—
767	C₄×C₆₇	—	2	1	no	—
768	C₄×C₆₇	—	4	1	no	—
769	C₄×C₆₇	—	4	1	no	—
770	C₄×C₆₇	—	4	1	no	—
771	C₄×C₆₇	—	4	2	no	—
772	C₄×C₆₇	—	4	1	no	—
773	C₄×C₆₇	—	4	2	no	—
774	C₄×C₆₇	D₄²	1	2	yes	—
775	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
776	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
777	#61068	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
778	C₂×C₆₇	—	2	2	no	—
779	C₂×C₆₇	—	2	2	no	—
780	C₂×C₆₇	—	4	1	no	—
781	C₂×C₆₇	—	4	1	no	—
782	C₂×C₆₇	—	4	1	no	—
783	C₂×C₆₇	—	4	2	no	—
784	C₂×C₆₇	—	8	1	no	—
785	C₂×C₆₇	—	8	1	no	—
786	C₂×C₆₇	—	8	2	no	—
787	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
788	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
789	C₂×C₆₇	#3586	1	1	yes	characteristic
790	C₂×#575	C₂×C₆₇	1	1	yes	characteristic, complemented
791	C₂²×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
792	D₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
793	C₂×#548	C₂×C₆₇	1	1	yes	characteristic, complemented
794	#3285	C₂×C₆₇	1	2	yes	complemented
795	#3282	C₂×C₆₇	1	2	yes	complemented
796	#3277	C₂×C₆₇	1	2	yes	complemented
797	#3275	C₂×C₆₇	1	2	yes	complemented
798	#3271	C₂×C₆₇	1	2	yes	complemented
799	#3270	C₂×C₆₇	1	2	yes	complemented
800	#3269	C₂×C₆₇	1	2	yes	complemented
801	#3265	C₂×C₆₇	1	2	yes	complemented
802	#3153	C₂×C₆₇	1	1	yes	characteristic, complemented
803	#3056	C₂×C₆₇	1	1	yes	characteristic, complemented
804	#3055	C₂×C₆₇	1	1	yes	characteristic, complemented
805	#3040	C₂×C₆₇	1	1	yes	characteristic, complemented
806	#3037	C₂×C₆₇	1	1	yes	characteristic, complemented
807	#3007	C₂×C₆₇	1	1	yes	characteristic, complemented
808	#3006	C₂×C₆₇	1	1	yes	characteristic, complemented
809	#3005	C₂×C₆₇	1	1	yes	characteristic, complemented
810	#3004	C₂×C₆₇	1	1	yes	characteristic, complemented
811	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
812	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
813	C₆₇	#61068	1	1	yes	characteristic, direct product factor, Sylow
814	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
815	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
816	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
817	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
818	#575	—	2	8	no	—
819	C₂×#137	—	2	8	no	—
820	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
821	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
822	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
823	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
824	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
825	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
826	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
827	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
828	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
829	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
830	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
831	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
832	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
833	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
834	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
835	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
836	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
837	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
838	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
839	#550	C₂²×C₆₇	1	1	yes	characteristic, complemented
840	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
841	#548	—	2	1	no	—
842	#548	—	2	1	no	—
843	#548	—	2	1	no	—
844	#548	—	2	1	no	—
845	#548	C₂²×C₆₇	1	2	yes	—
846	#548	C₂²×C₆₇	1	2	yes	complemented
847	#548	C₂²×C₆₇	1	2	yes	complemented
848	#548	C₂²×C₆₇	1	2	yes	complemented
849	#548	C₂²×C₆₇	1	1	yes	characteristic, complemented
850	#548	C₂²×C₆₇	1	1	yes	characteristic, complemented
851	#547	—	2	1	no	—
852	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
853	#546	—	2	1	no	—
854	#546	—	2	1	no	—
855	#546	C₂²×C₆₇	1	1	yes	characteristic, complemented
856	#546	C₂²×C₆₇	1	1	yes	characteristic, complemented
857	D₄²	—	2	1	no	—
858	D₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
859	#532	—	2	1	no	—
860	#532	C₂²×C₆₇	1	1	yes	characteristic
861	C₂×#124	—	2	1	no	—
862	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
863	#525	—	2	1	no	—
864	#525	—	2	1	no	—
865	#525	C₂²×C₆₇	1	1	yes	characteristic
866	#525	C₂²×C₆₇	1	1	yes	characteristic
867	C₂×C₂²⋊Q₈	—	2	1	no	—
868	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
869	C₂×#121	—	2	1	no	—
870	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
871	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
872	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
873	C₂×C₄×D₄	—	2	1	no	—
874	C₂×C₄×D₄	—	2	1	no	—
875	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
876	#497	C₂²×C₆₇	1	2	yes	complemented
877	#496	C₂²×C₆₇	1	2	yes	complemented
878	#495	C₂²×C₆₇	1	2	yes	complemented
879	#495	C₂²×C₆₇	1	2	yes	complemented
880	#470	C₂²×C₆₇	1	2	yes	complemented
881	#469	C₂²×C₆₇	1	2	yes	complemented
882	#468	C₂²×C₆₇	1	2	yes	complemented
883	#468	C₂²×C₆₇	1	2	yes	complemented
884	#467	C₂²×C₆₇	1	2	yes	complemented
885	#466	C₂²×C₆₇	1	2	yes	complemented
886	#465	C₂²×C₆₇	1	2	yes	complemented
887	#465	C₂²×C₆₇	1	2	yes	complemented
888	#464	C₂²×C₆₇	1	2	yes	complemented
889	#464	C₂²×C₆₇	1	2	yes	complemented
890	#464	C₂²×C₆₇	1	2	yes	complemented
891	#464	C₂²×C₆₇	1	2	yes	complemented
892	#463	C₂²×C₆₇	1	2	yes	complemented
893	#463	C₂²×C₆₇	1	2	yes	complemented
894	#462	C₂²×C₆₇	1	2	yes	complemented
895	#460	C₂²×C₆₇	1	2	yes	complemented
896	#452	C₂²×C₆₇	1	2	yes	complemented
897	#452	C₂²×C₆₇	1	2	yes	complemented
898	#452	C₂²×C₆₇	1	2	yes	complemented
899	#452	C₂²×C₆₇	1	2	yes	complemented
900	#451	C₂²×C₆₇	1	2	yes	complemented
901	#451	C₂²×C₆₇	1	2	yes	complemented
902	#451	C₂²×C₆₇	1	2	yes	complemented
903	#450	C₂²×C₆₇	1	2	yes	complemented
904	#449	C₂²×C₆₇	1	2	yes	complemented
905	#449	C₂²×C₆₇	1	2	yes	complemented
906	#449	C₂²×C₆₇	1	2	yes	complemented
907	#449	C₂²×C₆₇	1	2	yes	complemented
908	#448	C₂²×C₆₇	1	2	yes	complemented
909	#448	C₂²×C₆₇	1	2	yes	complemented
910	#448	C₂²×C₆₇	1	2	yes	complemented
911	#447	C₂²×C₆₇	1	2	yes	complemented
912	#441	C₂²×C₆₇	1	2	yes	complemented
913	#440	C₂²×C₆₇	1	2	yes	complemented
914	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
915	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
916	#436	C₂²×C₆₇	1	2	yes	complemented
917	#435	C₂²×C₆₇	1	2	yes	complemented
918	#435	C₂²×C₆₇	1	2	yes	complemented
919	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
920	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
921	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
922	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
923	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
924	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
925	#417	C₂²×C₆₇	1	1	yes	characteristic
926	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
927	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
928	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
929	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
930	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
931	C₂×#41	—	2	1	no	—
932	C₂×#41	—	2	1	no	—
933	C₂×#41	—	2	1	no	—
934	C₂×#41	—	2	1	no	—
935	C₂×#41	—	2	1	no	—
936	C₂×#41	—	2	1	no	—
937	C₂×#41	—	2	4	no	—
938	C₂×#41	—	2	4	no	—
939	C₂×#41	—	2	4	no	—
940	C₂×#41	—	4	2	no	—
941	C₂×#41	—	4	2	no	—
942	C₂×#41	—	4	2	no	—
943	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
944	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
945	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
946	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
947	C₂×#41	C₂³×C₆₇	1	2	yes	—
948	C₂×#41	C₂³×C₆₇	1	2	yes	—
949	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
950	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
951	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
952	C₂²×Q₈	—	2	1	no	—
953	C₂²×Q₈	—	2	1	no	—
954	C₂²×Q₈	—	2	1	no	—
955	C₂²×Q₈	—	2	4	no	—
956	C₂²×Q₈	—	4	2	no	—
957	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
958	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
959	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
960	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
961	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
962	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
963	C₂²×D₄	—	2	1	no	—
964	C₂²×D₄	—	2	1	no	—
965	C₂²×D₄	—	2	1	no	—
966	C₂²×D₄	—	2	1	no	—
967	C₂²×D₄	—	2	1	no	—
968	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
969	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
970	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
971	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
972	C₂³×C₄	—	2	1	no	—
973	C₂³×C₄	—	2	1	no	—
974	C₂³×C₄	—	2	1	no	—
975	C₂³×C₄	—	2	1	no	—
976	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
977	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
978	#137	—	2	4	no	—
979	#137	—	2	4	no	—
980	#137	—	2	4	no	—
981	#137	—	2	8	no	—
982	#137	—	2	8	no	—
983	#137	—	2	8	no	—
984	#137	—	2	4	no	—
985	#137	—	4	2	no	—
986	#137	D₄×C₆₇	1	8	yes	complemented
987	AGL(1,ℤ/8)	—	2	4	no	—
988	AGL(1,ℤ/8)	—	2	8	no	—
989	AGL(1,ℤ/8)	—	2	4	no	—
990	AGL(1,ℤ/8)	—	4	2	no	—
991	#135	—	2	8	no	—
992	#135	—	2	8	no	—
993	C₂×Q₁₆	—	2	8	no	—
994	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
995	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
996	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
997	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
998	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
999	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
1000	C₂×SD₁₆	—	2	8	no	—
1001	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
1002	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
1003	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
1004	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
1005	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
1006	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
1007	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
1008	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
1009	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
1010	C₂×D₈	C₂³×C₆₇	1	2	yes	—
1011	C₂×D₈	C₂³×C₆₇	1	2	yes	—
1012	C₂×D₈	C₂³×C₆₇	1	2	yes	—
1013	C₂×M₁₆	—	2	4	no	—
1014	C₂×M₁₆	—	2	4	no	—
1015	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
1016	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
1017	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
1018	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
1019	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
1020	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
1021	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
1022	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
1023	C₄⋊Q₈	—	2	1	no	—
1024	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
1025	#127	—	2	1	no	—
1026	#127	C₂³×C₆₇	1	1	yes	characteristic
1027	#124	—	2	2	no	—
1028	#124	—	2	2	no	—
1029	#124	—	2	2	no	—
1030	#124	—	2	2	no	—
1031	#124	—	2	1	no	—
1032	#124	—	2	1	no	—
1033	#124	—	2	1	no	—
1034	#124	—	2	1	no	—
1035	#124	C₂³×C₆₇	1	2	yes	—
1036	#124	C₂³×C₆₇	1	2	yes	—
1037	#124	C₂³×C₆₇	1	1	yes	characteristic
1038	#124	C₂³×C₆₇	1	1	yes	characteristic
1039	#123	—	2	1	no	—
1040	#123	—	2	1	no	—
1041	#123	—	2	1	no	—
1042	#123	—	2	1	no	—
1043	#123	—	2	1	no	—
1044	#123	—	2	1	no	—
1045	C₂²⋊Q₈	—	2	1	no	—
1046	C₂²⋊Q₈	—	2	1	no	—
1047	C₂²⋊Q₈	—	2	2	no	—
1048	C₂²⋊Q₈	—	2	2	no	—
1049	C₂²⋊Q₈	—	2	2	no	—
1050	C₂²⋊Q₈	—	2	2	no	—
1051	C₂²⋊Q₈	—	2	1	no	—
1052	C₂²⋊Q₈	—	2	1	no	—
1053	C₂²⋊Q₈	—	2	1	no	—
1054	C₂²⋊Q₈	—	2	1	no	—
1055	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
1056	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
1057	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
1058	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
1059	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
1060	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
1061	#121	—	2	2	no	—
1062	#121	—	2	2	no	—
1063	#121	—	2	2	no	—
1064	#121	—	2	2	no	—
1065	#121	—	2	1	no	—
1066	#121	—	2	1	no	—
1067	#121	—	2	1	no	—
1068	#121	—	2	1	no	—
1069	#121	—	2	1	no	—
1070	#121	—	2	1	no	—
1071	#121	—	2	1	no	—
1072	#121	—	2	1	no	—
1073	#121	—	2	1	no	—
1074	#121	—	2	1	no	—
1075	#121	—	2	1	no	—
1076	#121	—	2	1	no	—
1077	#121	C₂³×C₆₇	1	2	yes	—
1078	#121	C₂³×C₆₇	1	2	yes	—
1079	#121	C₂³×C₆₇	1	1	yes	characteristic
1080	#121	C₂³×C₆₇	1	1	yes	characteristic
1081	#121	C₂³×C₆₇	1	1	yes	characteristic
1082	#121	C₂³×C₆₇	1	1	yes	characteristic
1083	#120	—	2	1	no	—
1084	#120	—	2	1	no	—
1085	#120	—	2	1	no	—
1086	#120	—	2	1	no	—
1087	#120	—	2	1	no	—
1088	#120	—	2	1	no	—
1089	C₄×Q₈	—	2	1	no	—
1090	C₄×Q₈	—	2	1	no	—
1091	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
1092	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
1093	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
1094	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
1095	C₄×D₄	—	2	1	no	—
1096	C₄×D₄	—	2	1	no	—
1097	C₄×D₄	—	2	1	no	—
1098	C₄×D₄	—	2	1	no	—
1099	C₄×D₄	—	2	1	no	—
1100	C₄×D₄	—	2	1	no	—
1101	C₄×D₄	—	2	1	no	—
1102	C₄×D₄	—	2	1	no	—
1103	C₄×D₄	—	2	1	no	—
1104	C₄×D₄	—	2	1	no	—
1105	C₄×D₄	—	2	2	no	—
1106	C₄×D₄	—	2	2	no	—
1107	C₄×D₄	—	2	2	no	—
1108	C₄×D₄	—	2	2	no	—
1109	C₄×D₄	—	2	1	no	—
1110	C₄×D₄	—	2	1	no	—
1111	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
1112	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
1113	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
1114	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
1115	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
1116	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
1117	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
1118	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
1119	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
1120	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
1121	#117	—	2	1	no	—
1122	#117	C₂³×C₆₇	1	1	yes	characteristic
1123	C₂×C₄⋊C₄	—	2	1	no	—
1124	C₂×C₄⋊C₄	—	2	1	no	—
1125	C₂×C₄⋊C₄	—	2	1	no	—
1126	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
1127	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1128	C₂×C₂²⋊C₄	—	2	1	no	—
1129	C₂×C₂²⋊C₄	—	2	1	no	—
1130	C₂×C₂²⋊C₄	—	2	1	no	—
1131	C₂×C₂²⋊C₄	—	2	1	no	—
1132	C₂×C₂²⋊C₄	—	2	1	no	—
1133	C₂×C₂²⋊C₄	—	2	1	no	—
1134	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
1135	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
1136	C₂×C₄²	—	2	1	no	—
1137	C₂×C₄²	—	2	1	no	—
1138	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1139	#107	C₂³×C₆₇	1	2	yes	—
1140	#106	C₂³×C₆₇	1	2	yes	—
1141	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
1142	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
1143	#103	C₂³×C₆₇	1	2	yes	—
1144	#103	C₂³×C₆₇	1	2	yes	—
1145	#103	C₂³×C₆₇	1	2	yes	—
1146	#103	C₂³×C₆₇	1	2	yes	—
1147	#103	C₂³×C₆₇	1	2	yes	—
1148	#103	C₂³×C₆₇	1	2	yes	—
1149	#103	C₂³×C₆₇	1	2	yes	—
1150	#102	C₂³×C₆₇	1	2	yes	—
1151	#102	C₂³×C₆₇	1	2	yes	—
1152	#102	C₂³×C₆₇	1	2	yes	—
1153	#102	C₂³×C₆₇	1	2	yes	—
1154	#102	C₂³×C₆₇	1	2	yes	—
1155	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1156	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1157	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1158	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1159	#97	C₂³×C₆₇	1	2	yes	—
1160	C₄×C₈	C₂³×C₆₇	1	2	yes	—
1161	C₂⁴	—	2	1	no	—
1162	C₂⁴	—	2	1	no	—
1163	C₂⁴	—	2	1	no	—
1164	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1165	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1166	#41	—	2	2	no	—
1167	#41	—	2	4	no	—
1168	#41	—	2	2	no	—
1169	#41	—	2	4	no	—
1170	#41	—	2	2	no	—
1171	#41	—	2	2	no	—
1172	#41	—	2	2	no	—
1173	#41	—	2	2	no	—
1174	#41	—	2	2	no	—
1175	#41	—	2	2	no	—
1176	#41	—	2	2	no	—
1177	#41	—	4	4	no	—
1178	#41	—	4	4	no	—
1179	#41	—	4	2	no	—
1180	#41	—	4	1	no	—
1181	#41	—	4	1	no	—
1182	#41	—	4	2	no	—
1183	#41	—	4	1	no	—
1184	#41	—	4	1	no	—
1185	#41	—	4	4	no	—
1186	#41	—	4	4	no	—
1187	#41	—	4	4	no	—
1188	#41	—	4	4	no	—
1189	#41	C₂×D₄×C₆₇	1	4	yes	—
1190	C₂×Q₈	—	2	1	no	—
1191	C₂×Q₈	—	2	2	no	—
1192	C₂×Q₈	—	2	2	no	—
1193	C₂×Q₈	—	2	1	no	—
1194	C₂×Q₈	—	2	1	no	—
1195	C₂×Q₈	—	2	1	no	—
1196	C₂×Q₈	—	2	2	no	—
1197	C₂×Q₈	—	2	4	no	—
1198	C₂×Q₈	—	2	2	no	—
1199	C₂×Q₈	—	2	4	no	—
1200	C₂×Q₈	—	2	2	no	—
1201	C₂×Q₈	—	2	2	no	—
1202	C₂×Q₈	—	2	2	no	—
1203	C₂×Q₈	—	4	4	no	—
1204	C₂×Q₈	—	4	2	no	—
1205	C₂×Q₈	—	4	2	no	—
1206	C₂×Q₈	—	4	1	no	—
1207	C₂×Q₈	—	4	1	no	—
1208	C₂×Q₈	—	4	4	no	—
1209	C₂×Q₈	—	4	4	no	—
1210	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	complemented
1211	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1212	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1213	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1214	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1215	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1216	C₂×D₄	—	2	1	no	—
1217	C₂×D₄	—	2	2	no	—
1218	C₂×D₄	—	2	2	no	—
1219	C₂×D₄	—	2	1	no	—
1220	C₂×D₄	—	2	1	no	—
1221	C₂×D₄	—	2	2	no	—
1222	C₂×D₄	—	2	2	no	—
1223	C₂×D₄	—	2	1	no	—
1224	C₂×D₄	—	2	1	no	—
1225	C₂×D₄	—	2	1	no	—
1226	C₂×D₄	—	2	1	no	—
1227	C₂×D₄	—	2	2	no	—
1228	C₂×D₄	—	2	2	no	—
1229	C₂×D₄	—	2	1	no	—
1230	C₂×D₄	—	2	1	no	—
1231	C₂×D₄	—	2	1	no	—
1232	C₂×D₄	—	2	1	no	—
1233	C₂×D₄	—	2	2	no	—
1234	C₂×D₄	—	2	1	no	—
1235	C₂×D₄	—	2	1	no	—
1236	C₂×D₄	—	2	1	no	—
1237	C₂×D₄	—	2	1	no	—
1238	C₂×D₄	—	2	1	no	—
1239	C₂×D₄	—	2	2	no	—
1240	C₂×D₄	—	4	1	no	—
1241	C₂×D₄	—	4	1	no	—
1242	C₂×D₄	—	4	4	no	—
1243	C₂×D₄	—	4	2	no	—
1244	C₂×D₄	—	4	4	no	—
1245	C₂×D₄	—	4	4	no	—
1246	C₂×D₄	—	4	4	no	—
1247	C₂×D₄	—	4	4	no	—
1248	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1249	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1250	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1251	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1252	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1253	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1254	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1255	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1256	C₂²×C₄	—	2	1	no	—
1257	C₂²×C₄	—	2	1	no	—
1258	C₂²×C₄	—	2	2	no	—
1259	C₂²×C₄	—	2	2	no	—
1260	C₂²×C₄	—	2	2	no	—
1261	C₂²×C₄	—	2	2	no	—
1262	C₂²×C₄	—	2	1	no	—
1263	C₂²×C₄	—	2	1	no	—
1264	C₂²×C₄	—	2	2	no	—
1265	C₂²×C₄	—	2	2	no	—
1266	C₂²×C₄	—	2	1	no	—
1267	C₂²×C₄	—	2	1	no	—
1268	C₂²×C₄	—	2	1	no	—
1269	C₂²×C₄	—	2	1	no	—
1270	C₂²×C₄	—	2	1	no	—
1271	C₂²×C₄	—	2	1	no	—
1272	C₂²×C₄	—	2	1	no	—
1273	C₂²×C₄	—	2	1	no	—
1274	C₂²×C₄	—	2	1	no	—
1275	C₂²×C₄	—	2	2	no	—
1276	C₂²×C₄	—	2	2	no	—
1277	C₂²×C₄	—	2	1	no	—
1278	C₂²×C₄	—	4	4	no	—
1279	C₂²×C₄	—	4	4	no	—
1280	C₂²×C₄	—	4	4	no	—
1281	C₂²×C₄	—	4	4	no	—
1282	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1283	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1284	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1285	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1286	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1287	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1288	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1289	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1290	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1291	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1292	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1293	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1294	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1295	Q₁₆	—	2	4	no	—
1296	Q₁₆	—	2	4	no	—
1297	Q₁₆	—	2	4	no	—
1298	Q₁₆	—	2	4	no	—
1299	Q₁₆	—	4	2	no	—
1300	Q₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
1301	SD₁₆	—	2	4	no	—
1302	SD₁₆	—	2	4	no	—
1303	SD₁₆	—	2	4	no	—
1304	SD₁₆	—	2	4	no	—
1305	SD₁₆	—	2	4	no	—
1306	SD₁₆	—	2	4	no	—
1307	SD₁₆	—	4	2	no	—
1308	SD₁₆	—	4	2	no	—
1309	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
1310	D₈	—	2	4	no	—
1311	D₈	—	2	4	no	—
1312	D₈	—	4	2	no	—
1313	M₁₆	—	2	2	no	—
1314	M₁₆	—	2	2	no	—
1315	M₁₆	—	2	2	no	—
1316	M₁₆	—	2	4	no	—
1317	M₁₆	—	2	4	no	—
1318	M₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
1319	C₂×C₈	—	2	4	no	—
1320	C₂×C₈	—	2	4	no	—
1321	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1322	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1323	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1324	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1325	C₄⋊C₄	—	2	1	no	—
1326	C₄⋊C₄	—	2	2	no	—
1327	C₄⋊C₄	—	2	2	no	—
1328	C₄⋊C₄	—	2	1	no	—
1329	C₄⋊C₄	—	2	1	no	—
1330	C₄⋊C₄	—	2	2	no	—
1331	C₄⋊C₄	—	2	2	no	—
1332	C₄⋊C₄	—	2	1	no	—
1333	C₄⋊C₄	—	2	1	no	—
1334	C₄⋊C₄	—	2	1	no	—
1335	C₄⋊C₄	—	2	1	no	—
1336	C₄⋊C₄	—	2	1	no	—
1337	C₄⋊C₄	—	2	1	no	—
1338	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1339	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1340	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1341	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1342	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1343	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1344	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1345	C₂²⋊C₄	—	2	1	no	—
1346	C₂²⋊C₄	—	2	1	no	—
1347	C₂²⋊C₄	—	2	2	no	—
1348	C₂²⋊C₄	—	2	2	no	—
1349	C₂²⋊C₄	—	2	1	no	—
1350	C₂²⋊C₄	—	2	1	no	—
1351	C₂²⋊C₄	—	2	1	no	—
1352	C₂²⋊C₄	—	2	1	no	—
1353	C₂²⋊C₄	—	2	1	no	—
1354	C₂²⋊C₄	—	2	1	no	—
1355	C₂²⋊C₄	—	2	1	no	—
1356	C₂²⋊C₄	—	2	2	no	—
1357	C₂²⋊C₄	—	2	2	no	—
1358	C₂²⋊C₄	—	2	2	no	—
1359	C₂²⋊C₄	—	2	2	no	—
1360	C₂²⋊C₄	—	2	2	no	—
1361	C₂²⋊C₄	—	2	2	no	—
1362	C₂²⋊C₄	—	2	1	no	—
1363	C₂²⋊C₄	—	2	1	no	—
1364	C₂²⋊C₄	—	2	1	no	—
1365	C₂²⋊C₄	—	2	1	no	—
1366	C₂²⋊C₄	—	2	1	no	—
1367	C₂²⋊C₄	—	2	1	no	—
1368	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1369	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1370	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1371	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1372	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1373	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1374	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1375	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1376	C₄²	—	2	1	no	—
1377	C₄²	—	2	1	no	—
1378	C₄²	—	2	1	no	—
1379	C₄²	—	2	2	no	—
1380	C₄²	—	2	2	no	—
1381	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1382	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1383	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1384	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1385	C₂³	—	2	2	no	—
1386	C₂³	—	2	2	no	—
1387	C₂³	—	2	1	no	—
1388	C₂³	—	2	2	no	—
1389	C₂³	—	2	2	no	—
1390	C₂³	—	2	1	no	—
1391	C₂³	—	2	1	no	—
1392	C₂³	—	4	1	no	—
1393	C₂³	—	4	1	no	—
1394	C₂³	—	4	1	no	—
1395	C₂³	—	4	2	no	—
1396	C₂³	—	4	2	no	—
1397	C₂³	—	4	2	no	—
1398	C₂³	—	4	2	no	—
1399	C₂³	—	4	2	no	—
1400	C₂³	—	4	2	no	—
1401	C₂³	—	4	2	no	—
1402	C₂³	—	8	1	no	—
1403	C₂³	—	8	1	no	—
1404	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1405	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1406	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1407	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1408	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1409	Q₈	—	2	4	no	—
1410	Q₈	—	2	2	no	—
1411	Q₈	—	2	1	no	—
1412	Q₈	—	2	2	no	—
1413	Q₈	—	2	1	no	—
1414	Q₈	—	2	1	no	—
1415	Q₈	—	2	1	no	—
1416	Q₈	—	2	2	no	—
1417	Q₈	—	2	1	no	—
1418	Q₈	—	4	4	no	—
1419	Q₈	—	4	4	no	—
1420	Q₈	—	4	2	no	—
1421	Q₈	—	4	2	no	—
1422	Q₈	—	4	2	no	—
1423	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
1424	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1425	D₄	—	2	4	no	—
1426	D₄	—	2	2	no	—
1427	D₄	—	2	2	no	—
1428	D₄	—	2	2	no	—
1429	D₄	—	2	1	no	—
1430	D₄	—	2	1	no	—
1431	D₄	—	2	1	no	—
1432	D₄	—	2	1	no	—
1433	D₄	—	2	2	no	—
1434	D₄	—	2	1	no	—
1435	D₄	—	4	1	no	—
1436	D₄	—	4	1	no	—
1437	D₄	—	4	2	no	—
1438	D₄	—	4	2	no	—
1439	D₄	—	4	2	no	—
1440	D₄	—	4	2	no	—
1441	D₄	—	4	4	no	—
1442	D₄	—	4	4	no	—
1443	D₄	—	4	2	no	—
1444	D₄	—	4	2	no	—
1445	D₄	—	4	2	no	—
1446	D₄	—	4	2	no	—
1447	D₄	—	4	4	no	—
1448	D₄	—	4	2	no	—
1449	D₄	—	4	2	no	—
1450	D₄	—	4	2	no	—
1451	D₄	—	4	4	no	—
1452	D₄	—	4	2	no	—
1453	D₄	—	8	1	no	—
1454	D₄	—	8	1	no	—
1455	D₄	—	8	1	no	—
1456	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1457	C₂×C₄	—	2	2	no	—
1458	C₂×C₄	—	2	2	no	—
1459	C₂×C₄	—	2	4	no	—
1460	C₂×C₄	—	2	1	no	—
1461	C₂×C₄	—	2	2	no	—
1462	C₂×C₄	—	2	2	no	—
1463	C₂×C₄	—	2	2	no	—
1464	C₂×C₄	—	2	2	no	—
1465	C₂×C₄	—	2	2	no	—
1466	C₂×C₄	—	2	4	no	—
1467	C₂×C₄	—	2	1	no	—
1468	C₂×C₄	—	2	1	no	—
1469	C₂×C₄	—	2	1	no	—
1470	C₂×C₄	—	2	1	no	—
1471	C₂×C₄	—	2	1	no	—
1472	C₂×C₄	—	2	1	no	—
1473	C₂×C₄	—	2	1	no	—
1474	C₂×C₄	—	2	1	no	—
1475	C₂×C₄	—	2	1	no	—
1476	C₂×C₄	—	2	1	no	—
1477	C₂×C₄	—	2	2	no	—
1478	C₂×C₄	—	2	2	no	—
1479	C₂×C₄	—	2	1	no	—
1480	C₂×C₄	—	2	1	no	—
1481	C₂×C₄	—	4	1	no	—
1482	C₂×C₄	—	4	1	no	—
1483	C₂×C₄	—	4	2	no	—
1484	C₂×C₄	—	4	4	no	—
1485	C₂×C₄	—	4	4	no	—
1486	C₂×C₄	—	4	2	no	—
1487	C₂×C₄	—	4	2	no	—
1488	C₂×C₄	—	4	2	no	—
1489	C₂×C₄	—	4	4	no	—
1490	C₂×C₄	—	4	4	no	—
1491	C₂×C₄	—	4	2	no	—
1492	C₂×C₄	—	4	2	no	—
1493	C₂×C₄	—	4	2	no	—
1494	C₂×C₄	—	4	2	no	—
1495	C₂×C₄	—	4	2	no	—
1496	C₂×C₄	—	4	2	no	—
1497	C₂×C₄	—	4	2	no	—
1498	C₂×C₄	—	8	1	no	—
1499	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1500	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1501	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1502	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1503	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1504	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1505	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1506	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1507	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1508	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1509	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1510	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1511	C₈	—	2	2	no	—
1512	C₈	—	2	2	no	—
1513	C₈	—	2	2	no	—
1514	C₈	C₂²×D₄×C₆₇	1	4	yes	—
1515	C₂²	—	2	1	no	—
1516	C₂²	—	2	1	no	—
1517	C₂²	—	2	1	no	—
1518	C₂²	—	2	1	no	—
1519	C₂²	—	2	1	no	—
1520	C₂²	—	2	1	no	—
1521	C₂²	—	2	1	no	—
1522	C₂²	—	2	1	no	—
1523	C₂²	—	2	1	no	—
1524	C₂²	—	2	1	no	—
1525	C₂²	—	2	1	no	—
1526	C₂²	—	2	1	no	—
1527	C₂²	—	2	1	no	—
1528	C₂²	—	2	2	no	—
1529	C₂²	—	4	4	no	—
1530	C₂²	—	4	1	no	—
1531	C₂²	—	4	1	no	—
1532	C₂²	—	4	1	no	—
1533	C₂²	—	4	1	no	—
1534	C₂²	—	4	2	no	—
1535	C₂²	—	4	1	no	—
1536	C₂²	—	4	1	no	—
1537	C₂²	—	4	2	no	—
1538	C₂²	—	4	2	no	—
1539	C₂²	—	4	1	no	—
1540	C₂²	—	4	1	no	—
1541	C₂²	—	8	2	no	—
1542	C₂²	—	8	4	no	—
1543	C₂²	—	8	4	no	—
1544	C₂²	—	8	4	no	—
1545	C₂²	D₄²×C₆₇	1	2	yes	—
1546	C₂²	#575×C₆₇	1	2	yes	complemented
1547	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1548	C₄	—	2	1	no	—
1549	C₄	—	2	1	no	—
1550	C₄	—	2	1	no	—
1551	C₄	—	2	1	no	—
1552	C₄	—	2	1	no	—
1553	C₄	—	2	1	no	—
1554	C₄	—	2	1	no	—
1555	C₄	—	2	1	no	—
1556	C₄	—	2	2	no	—
1557	C₄	—	2	4	no	—
1558	C₄	—	4	1	no	—
1559	C₄	—	4	2	no	—
1560	C₄	—	4	1	no	—
1561	C₄	—	4	1	no	—
1562	C₄	—	4	1	no	—
1563	C₄	—	4	2	no	—
1564	C₄	D₄²×C₆₇	1	2	yes	—
1565	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1566	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1567	C₂	—	2	2	no	—
1568	C₂	—	2	2	no	—
1569	C₂	—	4	1	no	—
1570	C₂	—	4	1	no	—
1571	C₂	—	4	1	no	—
1572	C₂	—	4	2	no	—
1573	C₂	—	8	1	no	—
1574	C₂	—	8	1	no	—
1575	C₂	—	8	2	no	—
1576	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1577	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
1578	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#575×C₆₇	C₂	semidirect
2. C₂²×#137×C₆₇	C₂	semidirect
3. D₄×#41×C₆₇	C₂	semidirect
4. C₂×#548×C₆₇	C₂	semidirect
5. C₆₇×#3285	C₂	semidirect
6. C₆₇×#3282	C₂	semidirect
7. C₆₇×#3277	C₂	semidirect
8. C₆₇×#3275	C₂	semidirect
9. C₆₇×#3271	C₂	semidirect
10. C₆₇×#3270	C₂	semidirect
11. C₆₇×#3269	C₂	semidirect
12. C₆₇×#3265	C₂	semidirect
13. C₆₇×#3153	C₂	semidirect
14. C₆₇×#3056	C₂	semidirect
15. C₆₇×#3055	C₂	semidirect
16. C₆₇×#3040	C₂	semidirect
17. C₆₇×#3037	C₂	semidirect
18. C₆₇×#3007	C₂	semidirect
19. C₆₇×#3006	C₂	semidirect
20. C₆₇×#3005	C₂	semidirect
21. C₆₇×#3004	C₂	semidirect
22. C₄×#137×C₆₇	C₂	semidirect
23. D₄×M₁₆×C₆₇	C₂	semidirect
26. C₂²×#41×C₆₇	C₂²	semidirect
27. C₂³×Q₈×C₆₇	C₂²	semidirect
32. C₂×#137×C₆₇	C₂²	semidirect
33. C₂×#137×C₆₇	C₂²	semidirect
34. C₂×#137×C₆₇	C₂²	semidirect
35. C₂×#137×C₆₇	C₂²	semidirect
36. C₂×#137×C₆₇	C₂²	semidirect
37. C₂×#137×C₆₇	C₂²	semidirect
38. C₂×#137×C₆₇	C₂²	semidirect
40. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
41. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
42. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
43. C₂×#135×C₆₇	C₂²	semidirect
44. C₂×#135×C₆₇	C₂²	semidirect
45. C₂²×Q₁₆×C₆₇	C₂²	semidirect
46. C₂²×SD₁₆×C₆₇	C₂²	semidirect
47. C₂²×M₁₆×C₆₇	C₂²	semidirect
48. C₂²×M₁₆×C₆₇	C₂²	semidirect
49. #550×C₆₇	C₂²	semidirect
50. D₄×Q₈×C₆₇	C₂²	semidirect
56. #548×C₆₇	C₂²	semidirect
57. #548×C₆₇	C₂²	semidirect
58. #548×C₆₇	C₂²	semidirect
59. #548×C₆₇	C₂²	semidirect
60. #548×C₆₇	C₂²	semidirect
62. #547×C₆₇	C₂²	semidirect
65. #546×C₆₇	C₂²	semidirect
66. #546×C₆₇	C₂²	semidirect
68. D₄²×C₆₇	C₂²	semidirect
72. C₂×#124×C₆₇	C₂²	semidirect
78. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
80. C₂×#121×C₆₇	C₂²	semidirect
82. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
86. #497×C₆₇	C₂²	semidirect
87. #496×C₆₇	C₂²	semidirect
88. #495×C₆₇	C₂²	semidirect
89. #495×C₆₇	C₂²	semidirect
90. #470×C₆₇	C₂²	semidirect
91. #469×C₆₇	C₂²	semidirect
92. #468×C₆₇	C₂²	semidirect
93. #468×C₆₇	C₂²	semidirect
94. #467×C₆₇	C₂²	semidirect
95. #466×C₆₇	C₂²	semidirect
96. #465×C₆₇	C₂²	semidirect
97. #465×C₆₇	C₂²	semidirect
98. #464×C₆₇	C₂²	semidirect
99. #464×C₆₇	C₂²	semidirect
100. #464×C₆₇	C₂²	semidirect
101. #464×C₆₇	C₂²	semidirect
102. #463×C₆₇	C₂²	semidirect
103. #463×C₆₇	C₂²	semidirect
104. #462×C₆₇	C₂²	semidirect
105. #460×C₆₇	C₂²	semidirect
106. #452×C₆₇	C₂²	semidirect
107. #452×C₆₇	C₂²	semidirect
108. #452×C₆₇	C₂²	semidirect
109. #452×C₆₇	C₂²	semidirect
110. #451×C₆₇	C₂²	semidirect
111. #451×C₆₇	C₂²	semidirect
112. #451×C₆₇	C₂²	semidirect
113. #450×C₆₇	C₂²	semidirect
114. #449×C₆₇	C₂²	semidirect
115. #449×C₆₇	C₂²	semidirect
116. #449×C₆₇	C₂²	semidirect
117. #449×C₆₇	C₂²	semidirect
118. #448×C₆₇	C₂²	semidirect
119. #448×C₆₇	C₂²	semidirect
120. #448×C₆₇	C₂²	semidirect
121. #447×C₆₇	C₂²	semidirect
122. #441×C₆₇	C₂²	semidirect
123. #440×C₆₇	C₂²	semidirect
124. C₄×Q₁₆×C₆₇	C₂²	semidirect
125. C₄×SD₁₆×C₆₇	C₂²	semidirect
126. #436×C₆₇	C₂²	semidirect
127. #435×C₆₇	C₂²	semidirect
128. #435×C₆₇	C₂²	semidirect
129. C₈×D₄×C₆₇	C₂²	semidirect
130. #428×C₆₇	C₂²	semidirect
131. #423×C₆₇	C₂²	semidirect
132. #419×C₆₇	C₂²	semidirect
133. #419×C₆₇	C₂²	semidirect
134. #418×C₆₇	C₂²	semidirect
136. #417×C₆₇	C₂²	semidirect
137. #417×C₆₇	C₂²	semidirect
138. #407×C₆₇	C₂²	semidirect
139. #407×C₆₇	C₂²	semidirect
140. C₄×M₁₆×C₆₇	C₂²	semidirect
196. #137×C₆₇	D₄	semidirect
420. C₂×Q₈×C₆₇	C₂×D₄	semidirect
510. Q₁₆×C₆₇	C₂×D₄	semidirect
519. SD₁₆×C₆₇	C₂×D₄	semidirect
528. M₁₆×C₆₇	C₂×D₄	semidirect
756. C₂²×C₆₇	#575	semidirect
777. #61068	C₆₇	direct (N × H)
790. C₂×#575	C₂×C₆₇	semidirect
791. C₂²×#137	C₂×C₆₇	semidirect
792. D₄×#41	C₂×C₆₇	semidirect
793. C₂×#548	C₂×C₆₇	semidirect
794. #3285	C₂×C₆₇	semidirect
795. #3282	C₂×C₆₇	semidirect
796. #3277	C₂×C₆₇	semidirect
797. #3275	C₂×C₆₇	semidirect
798. #3271	C₂×C₆₇	semidirect
799. #3270	C₂×C₆₇	semidirect
800. #3269	C₂×C₆₇	semidirect
801. #3265	C₂×C₆₇	semidirect
802. #3153	C₂×C₆₇	semidirect
803. #3056	C₂×C₆₇	semidirect
804. #3055	C₂×C₆₇	semidirect
805. #3040	C₂×C₆₇	semidirect
806. #3037	C₂×C₆₇	semidirect
807. #3007	C₂×C₆₇	semidirect
808. #3006	C₂×C₆₇	semidirect
809. #3005	C₂×C₆₇	semidirect
810. #3004	C₂×C₆₇	semidirect
811. C₄×#137	C₂×C₆₇	semidirect
812. D₄×M₁₆	C₂×C₆₇	semidirect
813. C₆₇	#61068	direct (N × H)
816. C₂²×#41	C₂²×C₆₇	semidirect
817. C₂³×Q₈	C₂²×C₆₇	semidirect
822. C₂×#137	C₂²×C₆₇	semidirect
823. C₂×#137	C₂²×C₆₇	semidirect
824. C₂×#137	C₂²×C₆₇	semidirect
825. C₂×#137	C₂²×C₆₇	semidirect
826. C₂×#137	C₂²×C₆₇	semidirect
827. C₂×#137	C₂²×C₆₇	semidirect
828. C₂×#137	C₂²×C₆₇	semidirect
830. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
831. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
832. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
833. C₂×#135	C₂²×C₆₇	semidirect
834. C₂×#135	C₂²×C₆₇	semidirect
835. C₂²×Q₁₆	C₂²×C₆₇	semidirect
836. C₂²×SD₁₆	C₂²×C₆₇	semidirect
837. C₂²×M₁₆	C₂²×C₆₇	semidirect
838. C₂²×M₁₆	C₂²×C₆₇	semidirect
839. #550	C₂²×C₆₇	semidirect
840. D₄×Q₈	C₂²×C₆₇	semidirect
846. #548	C₂²×C₆₇	semidirect
847. #548	C₂²×C₆₇	semidirect
848. #548	C₂²×C₆₇	semidirect
849. #548	C₂²×C₆₇	semidirect
850. #548	C₂²×C₆₇	semidirect
852. #547	C₂²×C₆₇	semidirect
855. #546	C₂²×C₆₇	semidirect
856. #546	C₂²×C₆₇	semidirect
858. D₄²	C₂²×C₆₇	semidirect
862. C₂×#124	C₂²×C₆₇	semidirect
868. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
870. C₂×#121	C₂²×C₆₇	semidirect
872. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
876. #497	C₂²×C₆₇	semidirect
877. #496	C₂²×C₆₇	semidirect
878. #495	C₂²×C₆₇	semidirect
879. #495	C₂²×C₆₇	semidirect
880. #470	C₂²×C₆₇	semidirect
881. #469	C₂²×C₆₇	semidirect
882. #468	C₂²×C₆₇	semidirect
883. #468	C₂²×C₆₇	semidirect
884. #467	C₂²×C₆₇	semidirect
885. #466	C₂²×C₆₇	semidirect
886. #465	C₂²×C₆₇	semidirect
887. #465	C₂²×C₆₇	semidirect
888. #464	C₂²×C₆₇	semidirect
889. #464	C₂²×C₆₇	semidirect
890. #464	C₂²×C₆₇	semidirect
891. #464	C₂²×C₆₇	semidirect
892. #463	C₂²×C₆₇	semidirect
893. #463	C₂²×C₆₇	semidirect
894. #462	C₂²×C₆₇	semidirect
895. #460	C₂²×C₆₇	semidirect
896. #452	C₂²×C₆₇	semidirect
897. #452	C₂²×C₆₇	semidirect
898. #452	C₂²×C₆₇	semidirect
899. #452	C₂²×C₆₇	semidirect
900. #451	C₂²×C₆₇	semidirect
901. #451	C₂²×C₆₇	semidirect
902. #451	C₂²×C₆₇	semidirect
903. #450	C₂²×C₆₇	semidirect
904. #449	C₂²×C₆₇	semidirect
905. #449	C₂²×C₆₇	semidirect
906. #449	C₂²×C₆₇	semidirect
907. #449	C₂²×C₆₇	semidirect
908. #448	C₂²×C₆₇	semidirect
909. #448	C₂²×C₆₇	semidirect
910. #448	C₂²×C₆₇	semidirect
911. #447	C₂²×C₆₇	semidirect
912. #441	C₂²×C₆₇	semidirect
913. #440	C₂²×C₆₇	semidirect
914. C₄×Q₁₆	C₂²×C₆₇	semidirect
915. C₄×SD₁₆	C₂²×C₆₇	semidirect
916. #436	C₂²×C₆₇	semidirect
917. #435	C₂²×C₆₇	semidirect
918. #435	C₂²×C₆₇	semidirect
919. C₈×D₄	C₂²×C₆₇	semidirect
920. #428	C₂²×C₆₇	semidirect
921. #423	C₂²×C₆₇	semidirect
922. #419	C₂²×C₆₇	semidirect
923. #419	C₂²×C₆₇	semidirect
924. #418	C₂²×C₆₇	semidirect
926. #417	C₂²×C₆₇	semidirect
927. #417	C₂²×C₆₇	semidirect
928. #407	C₂²×C₆₇	semidirect
929. #407	C₂²×C₆₇	semidirect
930. C₄×M₁₆	C₂²×C₆₇	semidirect
986. #137	D₄×C₆₇	semidirect
1210. C₂×Q₈	C₂×D₄×C₆₇	semidirect
1300. Q₁₆	C₂×D₄×C₆₇	semidirect
1309. SD₁₆	C₂×D₄×C₆₇	semidirect
1318. M₁₆	C₂×D₄×C₆₇	semidirect
1546. C₂²	#575×C₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#575×C₆₇	2
C₂²×#137×C₆₇	2
D₄×#41×C₆₇	2
C₂×#548×C₆₇	2
C₆₇×#3285	2
C₆₇×#3282	2
C₆₇×#3277	2
C₆₇×#3275	2
C₆₇×#3271	2
C₆₇×#3270	2
C₆₇×#3269	2
C₆₇×#3265	2
C₆₇×#3153	2
C₆₇×#3056	2
C₆₇×#3055	2
C₆₇×#3040	2
C₆₇×#3037	2
C₆₇×#3007	2
C₆₇×#3006	2
C₆₇×#3005	2
C₆₇×#3004	2
C₄×#137×C₆₇	2
D₄×M₁₆×C₆₇	2
#61068	67

Subgroups — C67×#61068 #30740319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61068 #30740319