Subgroups — C₆₇×#61096 #30740347

Order 17152.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#578×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#577×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3497	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×#3268	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3266	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3153	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#464×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3012	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3010	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
28	#578×C₆₇	—	2	8	no	—
29	#577×C₆₇	—	2	8	no	—
30	C₂×#137×C₆₇	C₂²	1	2	yes	—
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	1	yes	characteristic, complemented
35	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
37	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#135×C₆₇	C₂²	1	2	yes	—
42	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
43	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
45	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
46	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
47	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#550×C₆₇	—	2	1	no	—
50	#550×C₆₇	C₂²	1	2	yes	complemented
51	D₄×Q₈×C₆₇	—	2	1	no	—
52	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
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	—
57	#548×C₆₇	C₂²	1	2	yes	complemented
58	#548×C₆₇	C₂²	1	2	yes	complemented
59	#546×C₆₇	—	2	2	no	—
60	#546×C₆₇	—	2	2	no	—
61	#546×C₆₇	C₂²	1	2	yes	—
62	#546×C₆₇	C₂²	1	2	yes	—
63	#537×C₆₇	—	2	2	no	—
64	#537×C₆₇	C₂²	1	1	yes	characteristic
65	#537×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#536×C₆₇	—	2	1	no	—
67	#536×C₆₇	C₂²	1	1	yes	characteristic
68	#535×C₆₇	—	2	1	no	—
69	#535×C₆₇	C₂²	1	1	yes	characteristic
70	#532×C₆₇	—	2	1	no	—
71	#532×C₆₇	—	2	2	no	—
72	#532×C₆₇	C₂²	1	1	yes	characteristic
73	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	C₂×#124×C₆₇	—	2	1	no	—
75	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
76	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
77	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#497×C₆₇	C₂²	1	2	yes	complemented
79	#496×C₆₇	C₂²	1	2	yes	complemented
80	#495×C₆₇	C₂²	1	2	yes	complemented
81	#495×C₆₇	C₂²	1	2	yes	complemented
82	#470×C₆₇	C₂²	1	2	yes	complemented
83	#469×C₆₇	C₂²	1	2	yes	complemented
84	#468×C₆₇	C₂²	1	2	yes	complemented
85	#468×C₆₇	C₂²	1	2	yes	complemented
86	#467×C₆₇	C₂²	1	2	yes	complemented
87	#466×C₆₇	C₂²	1	2	yes	complemented
88	#465×C₆₇	C₂²	1	2	yes	complemented
89	#465×C₆₇	C₂²	1	2	yes	complemented
90	#464×C₆₇	C₂²	1	2	yes	complemented
91	#464×C₆₇	C₂²	1	2	yes	complemented
92	#464×C₆₇	C₂²	1	2	yes	complemented
93	#464×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#464×C₆₇	C₂²	1	2	yes	complemented
95	#464×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#463×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#463×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#452×C₆₇	C₂²	1	2	yes	—
103	#452×C₆₇	C₂²	1	2	yes	complemented
104	#452×C₆₇	C₂²	1	2	yes	complemented
105	#452×C₆₇	C₂²	1	2	yes	complemented
106	#451×C₆₇	C₂²	1	2	yes	complemented
107	#451×C₆₇	C₂²	1	2	yes	complemented
108	#451×C₆₇	C₂²	1	2	yes	complemented
109	#450×C₆₇	C₂²	1	2	yes	—
110	#449×C₆₇	C₂²	1	2	yes	—
111	#449×C₆₇	C₂²	1	2	yes	complemented
112	#449×C₆₇	C₂²	1	2	yes	complemented
113	#449×C₆₇	C₂²	1	2	yes	complemented
114	#448×C₆₇	C₂²	1	2	yes	complemented
115	#448×C₆₇	C₂²	1	2	yes	complemented
116	#448×C₆₇	C₂²	1	2	yes	complemented
117	#447×C₆₇	C₂²	1	2	yes	—
118	#441×C₆₇	C₂²	1	2	yes	complemented
119	#440×C₆₇	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
122	#436×C₆₇	C₂²	1	2	yes	complemented
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	#435×C₆₇	C₂²	1	2	yes	complemented
125	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
126	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#417×C₆₇	C₂²	1	1	yes	characteristic
130	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
134	#408×C₆₇	C₂²	1	1	yes	characteristic
135	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
136	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	2₋¹⁺⁴×C₆₇	—	2	4	no	—
138	2₋¹⁺⁴×C₆₇	—	2	4	no	—
139	2₋¹⁺⁴×C₆₇	—	2	4	no	—
140	2₋¹⁺⁴×C₆₇	—	4	2	no	—
141	2₋¹⁺⁴×C₆₇	—	4	2	no	—
142	2₋¹⁺⁴×C₆₇	—	4	2	no	—
143	H(5,𝔽₂)×C₆₇	—	2	4	no	—
144	H(5,𝔽₂)×C₆₇	—	4	2	no	—
145	C₂×#41×C₆₇	—	2	1	no	—
146	C₂×#41×C₆₇	—	2	1	no	—
147	C₂×#41×C₆₇	—	2	2	no	—
148	C₂×#41×C₆₇	—	2	2	no	—
149	C₂×#41×C₆₇	—	2	2	no	—
150	C₂×#41×C₆₇	—	2	1	no	—
151	C₂×#41×C₆₇	—	2	1	no	—
152	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×#41×C₆₇	C₂³	1	2	yes	—
155	C₂×#41×C₆₇	C₂³	1	2	yes	—
156	C₂×#41×C₆₇	C₂³	1	2	yes	—
157	C₂×#41×C₆₇	C₂³	1	2	yes	—
158	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
161	C₂²×Q₈×C₆₇	—	2	1	no	—
162	C₂²×Q₈×C₆₇	—	2	1	no	—
163	C₂²×Q₈×C₆₇	—	2	1	no	—
164	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
166	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
167	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
168	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
169	C₂²×D₄×C₆₇	—	2	1	no	—
170	C₂²×D₄×C₆₇	—	2	2	no	—
171	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
173	#137×C₆₇	—	2	8	no	—
174	#137×C₆₇	—	2	8	no	—
175	#137×C₆₇	—	2	8	no	—
176	#137×C₆₇	—	2	4	no	—
177	#137×C₆₇	—	4	2	no	—
178	#137×C₆₇	D₄	1	8	yes	complemented
179	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
180	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
181	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
182	#135×C₆₇	—	2	4	no	—
183	#135×C₆₇	—	2	4	no	—
184	#135×C₆₇	—	2	8	no	—
185	#135×C₆₇	—	2	8	no	—
186	C₂×Q₁₆×C₆₇	—	2	4	no	—
187	C₂×Q₁₆×C₆₇	—	2	8	no	—
188	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
190	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
191	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
193	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
194	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
195	C₂×SD₁₆×C₆₇	—	2	4	no	—
196	C₂×SD₁₆×C₆₇	—	2	8	no	—
197	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
199	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
200	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
204	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
205	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
206	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
207	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
208	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×D₈×C₆₇	C₂³	1	2	yes	—
211	C₂×D₈×C₆₇	C₂³	1	2	yes	—
212	#131×C₆₇	—	2	4	no	—
213	#131×C₆₇	—	2	4	no	—
214	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
215	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
216	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
218	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
219	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
220	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
221	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
222	C₄⋊Q₈×C₆₇	—	2	1	no	—
223	C₄⋊Q₈×C₆₇	—	2	2	no	—
224	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
225	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
226	#127×C₆₇	—	2	1	no	—
227	#127×C₆₇	—	2	2	no	—
228	#127×C₆₇	D₄	1	1	yes	characteristic
229	#127×C₆₇	C₂³	1	1	yes	characteristic
230	#124×C₆₇	—	2	1	no	—
231	#124×C₆₇	—	2	1	no	—
232	#124×C₆₇	—	2	2	no	—
233	#124×C₆₇	—	2	2	no	—
234	#124×C₆₇	—	2	2	no	—
235	#124×C₆₇	—	2	2	no	—
236	#124×C₆₇	—	2	1	no	—
237	#124×C₆₇	—	2	1	no	—
238	#124×C₆₇	D₄	1	1	yes	characteristic
239	#124×C₆₇	D₄	1	1	yes	characteristic
240	#124×C₆₇	C₂³	1	1	yes	characteristic
241	#124×C₆₇	C₂³	1	1	yes	characteristic
242	#124×C₆₇	C₂³	1	2	yes	—
243	#124×C₆₇	C₂³	1	2	yes	—
244	#123×C₆₇	—	2	2	no	—
245	#123×C₆₇	—	2	2	no	—
246	#123×C₆₇	—	2	2	no	—
247	C₂²⋊Q₈×C₆₇	—	2	1	no	—
248	C₂²⋊Q₈×C₆₇	—	2	1	no	—
249	C₂²⋊Q₈×C₆₇	—	2	2	no	—
250	C₂²⋊Q₈×C₆₇	—	2	2	no	—
251	C₂²⋊Q₈×C₆₇	—	2	2	no	—
252	C₂²⋊Q₈×C₆₇	—	2	2	no	—
253	C₂²⋊Q₈×C₆₇	—	2	2	no	—
254	C₂²⋊Q₈×C₆₇	—	2	2	no	—
255	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
256	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
257	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
258	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
259	#121×C₆₇	—	2	2	no	—
260	#121×C₆₇	—	2	2	no	—
261	#121×C₆₇	—	2	2	no	—
262	#121×C₆₇	—	2	2	no	—
263	#121×C₆₇	—	2	2	no	—
264	#121×C₆₇	—	2	2	no	—
265	#121×C₆₇	—	2	1	no	—
266	#121×C₆₇	—	2	1	no	—
267	#121×C₆₇	—	2	1	no	—
268	#121×C₆₇	—	2	1	no	—
269	#121×C₆₇	—	2	2	no	—
270	#121×C₆₇	—	2	2	no	—
271	#121×C₆₇	—	2	2	no	—
272	#121×C₆₇	—	2	2	no	—
273	#121×C₆₇	D₄	1	2	yes	—
274	#121×C₆₇	D₄	1	2	yes	—
275	#121×C₆₇	C₂³	1	2	yes	—
276	#121×C₆₇	C₂³	1	2	yes	—
277	#121×C₆₇	C₂³	1	2	yes	—
278	#121×C₆₇	C₂³	1	2	yes	—
279	#120×C₆₇	—	2	2	no	—
280	#120×C₆₇	—	2	2	no	—
281	#120×C₆₇	—	2	2	no	—
282	C₄×Q₈×C₆₇	—	2	1	no	—
283	C₄×Q₈×C₆₇	—	2	1	no	—
284	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
286	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
287	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₆₇	—	2	2	no	—
289	C₄×D₄×C₆₇	—	2	1	no	—
290	C₄×D₄×C₆₇	—	2	1	no	—
291	C₄×D₄×C₆₇	—	2	2	no	—
292	C₄×D₄×C₆₇	—	2	2	no	—
293	C₄×D₄×C₆₇	—	2	2	no	—
294	C₄×D₄×C₆₇	—	2	2	no	—
295	C₄×D₄×C₆₇	—	2	2	no	—
296	C₄×D₄×C₆₇	—	2	1	no	—
297	C₄×D₄×C₆₇	—	2	1	no	—
298	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
299	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
300	C₄×D₄×C₆₇	C₂³	1	2	yes	—
301	C₄×D₄×C₆₇	C₂³	1	2	yes	—
302	#117×C₆₇	—	2	1	no	—
303	#117×C₆₇	C₂³	1	1	yes	characteristic
304	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
305	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
307	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
308	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
309	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
310	C₂×C₄²×C₆₇	—	2	1	no	—
311	C₂×C₄²×C₆₇	—	2	1	no	—
312	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
313	#107×C₆₇	C₂³	1	2	yes	—
314	#106×C₆₇	C₂³	1	2	yes	—
315	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
318	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
319	#103×C₆₇	C₂³	1	1	yes	characteristic
320	#103×C₆₇	C₂³	1	1	yes	characteristic
321	#103×C₆₇	C₂³	1	2	yes	—
322	#103×C₆₇	C₂³	1	2	yes	—
323	#103×C₆₇	C₂³	1	2	yes	—
324	#103×C₆₇	C₂³	1	2	yes	—
325	#103×C₆₇	C₂³	1	2	yes	—
326	#103×C₆₇	C₂³	1	1	yes	characteristic
327	#103×C₆₇	C₂³	1	1	yes	characteristic
328	#102×C₆₇	C₂³	1	2	yes	—
329	#102×C₆₇	C₂³	1	1	yes	characteristic
330	#102×C₆₇	C₂³	1	1	yes	characteristic
331	#102×C₆₇	C₂³	1	2	yes	—
332	#102×C₆₇	C₂³	1	2	yes	—
333	#102×C₆₇	C₂³	1	1	yes	characteristic
334	#102×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
336	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
337	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
338	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
339	#97×C₆₇	C₂³	1	2	yes	—
340	C₄×C₈×C₆₇	C₂³	1	2	yes	—
341	C₂⁴×C₆₇	—	2	2	no	—
342	C₂⁴×C₆₇	—	2	1	no	—
343	#41×C₆₇	—	2	2	no	—
344	#41×C₆₇	—	2	2	no	—
345	#41×C₆₇	—	2	2	no	—
346	#41×C₆₇	—	2	2	no	—
347	#41×C₆₇	—	2	2	no	—
348	#41×C₆₇	—	2	4	no	—
349	#41×C₆₇	—	2	4	no	—
350	#41×C₆₇	—	2	4	no	—
351	#41×C₆₇	—	2	4	no	—
352	#41×C₆₇	—	2	2	no	—
353	#41×C₆₇	—	2	2	no	—
354	#41×C₆₇	—	2	2	no	—
355	#41×C₆₇	—	2	2	no	—
356	#41×C₆₇	—	4	2	no	—
357	#41×C₆₇	—	4	2	no	—
358	#41×C₆₇	—	4	2	no	—
359	#41×C₆₇	—	4	2	no	—
360	#41×C₆₇	—	4	8	no	—
361	#41×C₆₇	—	4	8	no	—
362	#41×C₆₇	—	4	4	no	—
363	#41×C₆₇	—	4	4	no	—
364	#41×C₆₇	—	4	8	no	—
365	#41×C₆₇	—	4	4	no	—
366	#41×C₆₇	—	4	4	no	—
367	#41×C₆₇	C₂×D₄	1	4	yes	—
368	C₂×Q₈×C₆₇	—	2	1	no	—
369	C₂×Q₈×C₆₇	—	2	2	no	—
370	C₂×Q₈×C₆₇	—	2	2	no	—
371	C₂×Q₈×C₆₇	—	2	2	no	—
372	C₂×Q₈×C₆₇	—	2	1	no	—
373	C₂×Q₈×C₆₇	—	2	2	no	—
374	C₂×Q₈×C₆₇	—	2	4	no	—
375	C₂×Q₈×C₆₇	—	2	4	no	—
376	C₂×Q₈×C₆₇	—	2	4	no	—
377	C₂×Q₈×C₆₇	—	2	2	no	—
378	C₂×Q₈×C₆₇	—	2	2	no	—
379	C₂×Q₈×C₆₇	—	4	2	no	—
380	C₂×Q₈×C₆₇	—	4	2	no	—
381	C₂×Q₈×C₆₇	—	4	2	no	—
382	C₂×Q₈×C₆₇	—	4	4	no	—
383	C₂×Q₈×C₆₇	—	4	4	no	—
384	C₂×Q₈×C₆₇	—	4	4	no	—
385	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
386	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
387	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
388	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
389	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
390	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
391	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
392	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
393	C₂×D₄×C₆₇	—	2	1	no	—
394	C₂×D₄×C₆₇	—	2	4	no	—
395	C₂×D₄×C₆₇	—	2	2	no	—
396	C₂×D₄×C₆₇	—	2	1	no	—
397	C₂×D₄×C₆₇	—	2	1	no	—
398	C₂×D₄×C₆₇	—	2	2	no	—
399	C₂×D₄×C₆₇	—	2	2	no	—
400	C₂×D₄×C₆₇	—	2	2	no	—
401	C₂×D₄×C₆₇	—	2	2	no	—
402	C₂×D₄×C₆₇	—	2	2	no	—
403	C₂×D₄×C₆₇	—	2	2	no	—
404	C₂×D₄×C₆₇	—	2	2	no	—
405	C₂×D₄×C₆₇	—	2	2	no	—
406	C₂×D₄×C₆₇	—	2	1	no	—
407	C₂×D₄×C₆₇	—	2	2	no	—
408	C₂×D₄×C₆₇	—	2	1	no	—
409	C₂×D₄×C₆₇	—	2	1	no	—
410	C₂×D₄×C₆₇	—	2	2	no	—
411	C₂×D₄×C₆₇	—	4	2	no	—
412	C₂×D₄×C₆₇	—	4	4	no	—
413	C₂×D₄×C₆₇	—	4	8	no	—
414	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
415	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
416	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
417	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
418	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
419	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
420	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
421	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
423	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₆₇	—	2	1	no	—
425	C₂²×C₄×C₆₇	—	2	1	no	—
426	C₂²×C₄×C₆₇	—	2	1	no	—
427	C₂²×C₄×C₆₇	—	2	2	no	—
428	C₂²×C₄×C₆₇	—	2	2	no	—
429	C₂²×C₄×C₆₇	—	2	2	no	—
430	C₂²×C₄×C₆₇	—	2	1	no	—
431	C₂²×C₄×C₆₇	—	2	2	no	—
432	C₂²×C₄×C₆₇	—	2	2	no	—
433	C₂²×C₄×C₆₇	—	2	2	no	—
434	C₂²×C₄×C₆₇	—	2	1	no	—
435	C₂²×C₄×C₆₇	—	2	1	no	—
436	C₂²×C₄×C₆₇	—	2	2	no	—
437	C₂²×C₄×C₆₇	—	2	1	no	—
438	C₂²×C₄×C₆₇	—	2	1	no	—
439	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
440	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
441	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
442	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
443	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
444	Q₁₆×C₆₇	—	2	4	no	—
445	Q₁₆×C₆₇	—	2	2	no	—
446	Q₁₆×C₆₇	—	2	4	no	—
447	Q₁₆×C₆₇	—	2	2	no	—
448	Q₁₆×C₆₇	—	2	4	no	—
449	Q₁₆×C₆₇	—	4	2	no	—
450	Q₁₆×C₆₇	C₂×D₄	1	8	yes	—
451	SD₁₆×C₆₇	—	2	4	no	—
452	SD₁₆×C₆₇	—	2	4	no	—
453	SD₁₆×C₆₇	—	2	2	no	—
454	SD₁₆×C₆₇	—	2	2	no	—
455	SD₁₆×C₆₇	—	2	2	no	—
456	SD₁₆×C₆₇	—	2	2	no	—
457	SD₁₆×C₆₇	—	2	4	no	—
458	SD₁₆×C₆₇	—	2	4	no	—
459	SD₁₆×C₆₇	—	4	2	no	—
460	SD₁₆×C₆₇	—	4	2	no	—
461	SD₁₆×C₆₇	C₂×D₄	1	8	yes	—
462	D₈×C₆₇	—	2	2	no	—
463	D₈×C₆₇	—	2	2	no	—
464	D₈×C₆₇	—	2	4	no	—
465	D₈×C₆₇	—	4	2	no	—
466	M₁₆×C₆₇	—	2	2	no	—
467	M₁₆×C₆₇	—	2	4	no	—
468	M₁₆×C₆₇	—	2	4	no	—
469	M₁₆×C₆₇	C₂×D₄	1	4	yes	—
470	C₂×C₈×C₆₇	—	2	2	no	—
471	C₂×C₈×C₆₇	—	2	2	no	—
472	C₂×C₈×C₆₇	—	2	4	no	—
473	C₂×C₈×C₆₇	—	2	4	no	—
474	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
475	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
476	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
477	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
478	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
479	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
480	C₄⋊C₄×C₆₇	—	2	2	no	—
481	C₄⋊C₄×C₆₇	—	2	2	no	—
482	C₄⋊C₄×C₆₇	—	2	1	no	—
483	C₄⋊C₄×C₆₇	—	2	1	no	—
484	C₄⋊C₄×C₆₇	—	2	1	no	—
485	C₄⋊C₄×C₆₇	—	2	1	no	—
486	C₄⋊C₄×C₆₇	—	2	1	no	—
487	C₄⋊C₄×C₆₇	—	2	2	no	—
488	C₄⋊C₄×C₆₇	—	2	2	no	—
489	C₄⋊C₄×C₆₇	—	2	2	no	—
490	C₄⋊C₄×C₆₇	—	2	2	no	—
491	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
492	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
493	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
494	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
495	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₂²⋊C₄×C₆₇	—	2	2	no	—
497	C₂²⋊C₄×C₆₇	—	2	2	no	—
498	C₂²⋊C₄×C₆₇	—	2	1	no	—
499	C₂²⋊C₄×C₆₇	—	2	2	no	—
500	C₂²⋊C₄×C₆₇	—	2	2	no	—
501	C₂²⋊C₄×C₆₇	—	2	2	no	—
502	C₂²⋊C₄×C₆₇	—	2	2	no	—
503	C₂²⋊C₄×C₆₇	—	2	2	no	—
504	C₂²⋊C₄×C₆₇	—	2	2	no	—
505	C₂²⋊C₄×C₆₇	—	2	2	no	—
506	C₂²⋊C₄×C₆₇	—	2	2	no	—
507	C₂²⋊C₄×C₆₇	—	2	1	no	—
508	C₂²⋊C₄×C₆₇	—	2	1	no	—
509	C₂²⋊C₄×C₆₇	—	2	1	no	—
510	C₂²⋊C₄×C₆₇	—	2	1	no	—
511	C₂²⋊C₄×C₆₇	—	2	1	no	—
512	C₂²⋊C₄×C₆₇	—	2	1	no	—
513	C₂²⋊C₄×C₆₇	—	2	2	no	—
514	C₂²⋊C₄×C₆₇	—	2	2	no	—
515	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
516	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
517	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
518	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
519	C₄²×C₆₇	—	2	1	no	—
520	C₄²×C₆₇	—	2	1	no	—
521	C₄²×C₆₇	—	2	1	no	—
522	C₄²×C₆₇	—	2	2	no	—
523	C₄²×C₆₇	—	2	2	no	—
524	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
525	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
526	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
527	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
528	C₂³×C₆₇	—	2	1	no	—
529	C₂³×C₆₇	—	2	2	no	—
530	C₂³×C₆₇	—	2	1	no	—
531	C₂³×C₆₇	—	2	1	no	—
532	C₂³×C₆₇	—	4	4	no	—
533	C₂³×C₆₇	—	4	2	no	—
534	C₂³×C₆₇	—	8	1	no	—
535	C₂³×C₆₇	—	8	1	no	—
536	C₂³×C₆₇	—	8	2	no	—
537	C₂³×C₆₇	—	8	2	no	—
538	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
539	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
540	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
541	Q₈×C₆₇	—	2	4	no	—
542	Q₈×C₆₇	—	2	2	no	—
543	Q₈×C₆₇	—	2	2	no	—
544	Q₈×C₆₇	—	2	2	no	—
545	Q₈×C₆₇	—	2	1	no	—
546	Q₈×C₆₇	—	2	1	no	—
547	Q₈×C₆₇	—	2	1	no	—
548	Q₈×C₆₇	—	2	2	no	—
549	Q₈×C₆₇	—	2	1	no	—
550	Q₈×C₆₇	—	2	2	no	—
551	Q₈×C₆₇	—	2	1	no	—
552	Q₈×C₆₇	—	4	4	no	—
553	Q₈×C₆₇	—	4	4	no	—
554	Q₈×C₆₇	—	4	4	no	—
555	Q₈×C₆₇	—	4	2	no	—
556	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
557	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
558	D₄×C₆₇	—	2	4	no	—
559	D₄×C₆₇	—	2	4	no	—
560	D₄×C₆₇	—	2	4	no	—
561	D₄×C₆₇	—	2	2	no	—
562	D₄×C₆₇	—	2	2	no	—
563	D₄×C₆₇	—	2	1	no	—
564	D₄×C₆₇	—	2	2	no	—
565	D₄×C₆₇	—	2	1	no	—
566	D₄×C₆₇	—	2	1	no	—
567	D₄×C₆₇	—	2	1	no	—
568	D₄×C₆₇	—	2	2	no	—
569	D₄×C₆₇	—	2	1	no	—
570	D₄×C₆₇	—	4	2	no	—
571	D₄×C₆₇	—	4	2	no	—
572	D₄×C₆₇	—	4	4	no	—
573	D₄×C₆₇	—	4	4	no	—
574	D₄×C₆₇	—	4	4	no	—
575	D₄×C₆₇	—	4	4	no	—
576	D₄×C₆₇	—	4	2	no	—
577	D₄×C₆₇	—	4	4	no	—
578	D₄×C₆₇	—	4	2	no	—
579	D₄×C₆₇	—	4	2	no	—
580	D₄×C₆₇	—	4	2	no	—
581	D₄×C₆₇	—	8	1	no	—
582	D₄×C₆₇	—	8	2	no	—
583	D₄×C₆₇	—	8	2	no	—
584	D₄×C₆₇	—	8	2	no	—
585	D₄×C₆₇	—	8	2	no	—
586	D₄×C₆₇	C₂²×D₄	1	2	yes	—
587	C₂×C₄×C₆₇	—	2	4	no	—
588	C₂×C₄×C₆₇	—	2	1	no	—
589	C₂×C₄×C₆₇	—	2	2	no	—
590	C₂×C₄×C₆₇	—	2	4	no	—
591	C₂×C₄×C₆₇	—	2	2	no	—
592	C₂×C₄×C₆₇	—	2	2	no	—
593	C₂×C₄×C₆₇	—	2	2	no	—
594	C₂×C₄×C₆₇	—	2	2	no	—
595	C₂×C₄×C₆₇	—	2	1	no	—
596	C₂×C₄×C₆₇	—	2	1	no	—
597	C₂×C₄×C₆₇	—	2	2	no	—
598	C₂×C₄×C₆₇	—	2	2	no	—
599	C₂×C₄×C₆₇	—	2	1	no	—
600	C₂×C₄×C₆₇	—	2	1	no	—
601	C₂×C₄×C₆₇	—	4	1	no	—
602	C₂×C₄×C₆₇	—	4	1	no	—
603	C₂×C₄×C₆₇	—	4	4	no	—
604	C₂×C₄×C₆₇	—	4	4	no	—
605	C₂×C₄×C₆₇	—	4	4	no	—
606	C₂×C₄×C₆₇	—	4	4	no	—
607	C₂×C₄×C₆₇	—	4	4	no	—
608	C₂×C₄×C₆₇	—	4	4	no	—
609	C₂×C₄×C₆₇	—	4	4	no	—
610	C₂×C₄×C₆₇	—	4	2	no	—
611	C₂×C₄×C₆₇	—	4	2	no	—
612	C₂×C₄×C₆₇	—	4	2	no	—
613	C₂×C₄×C₆₇	—	8	1	no	—
614	C₂×C₄×C₆₇	—	8	1	no	—
615	C₂×C₄×C₆₇	—	8	1	no	—
616	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
617	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
618	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
619	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
620	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
621	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
622	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
623	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
624	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
625	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
626	C₈×C₆₇	—	2	1	no	—
627	C₈×C₆₇	—	2	1	no	—
628	C₈×C₆₇	—	2	1	no	—
629	C₈×C₆₇	—	2	1	no	—
630	C₈×C₆₇	—	2	2	no	—
631	C₈×C₆₇	C₂²×D₄	1	4	yes	—
632	C₂²×C₆₇	—	2	1	no	—
633	C₂²×C₆₇	—	2	1	no	—
634	C₂²×C₆₇	—	2	2	no	—
635	C₂²×C₆₇	—	2	2	no	—
636	C₂²×C₆₇	—	2	2	no	—
637	C₂²×C₆₇	—	2	2	no	—
638	C₂²×C₆₇	—	2	2	no	—
639	C₂²×C₆₇	—	2	2	no	—
640	C₂²×C₆₇	—	2	2	no	—
641	C₂²×C₆₇	—	4	1	no	—
642	C₂²×C₆₇	—	4	1	no	—
643	C₂²×C₆₇	—	4	1	no	—
644	C₂²×C₆₇	—	4	1	no	—
645	C₂²×C₆₇	—	4	2	no	—
646	C₂²×C₆₇	—	4	1	no	—
647	C₂²×C₆₇	—	4	1	no	—
648	C₂²×C₆₇	—	4	2	no	—
649	C₂²×C₆₇	—	4	1	no	—
650	C₂²×C₆₇	—	4	1	no	—
651	C₂²×C₆₇	—	4	2	no	—
652	C₂²×C₆₇	—	16	2	no	—
653	C₂²×C₆₇	—	16	4	no	—
654	C₂²×C₆₇	D₄²	1	2	yes	—
655	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
656	C₄×C₆₇	—	2	1	no	—
657	C₄×C₆₇	—	2	1	no	—
658	C₄×C₆₇	—	2	1	no	—
659	C₄×C₆₇	—	2	1	no	—
660	C₄×C₆₇	—	2	2	no	—
661	C₄×C₆₇	—	2	4	no	—
662	C₄×C₆₇	—	2	2	no	—
663	C₄×C₆₇	—	2	2	no	—
664	C₄×C₆₇	—	4	1	no	—
665	C₄×C₆₇	—	4	2	no	—
666	C₄×C₆₇	—	4	1	no	—
667	C₄×C₆₇	—	4	2	no	—
668	C₄×C₆₇	—	4	1	no	—
669	C₄×C₆₇	—	4	1	no	—
670	C₄×C₆₇	D₄²	1	2	yes	—
671	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
672	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
673	#61096	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
674	C₂×C₆₇	—	2	2	no	—
675	C₂×C₆₇	—	4	2	no	—
676	C₂×C₆₇	—	4	2	no	—
677	C₂×C₆₇	—	4	2	no	—
678	C₂×C₆₇	—	8	1	no	—
679	C₂×C₆₇	—	8	1	no	—
680	C₂×C₆₇	—	8	2	no	—
681	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
682	C₂×C₆₇	#3584	1	1	yes	characteristic
683	C₂×C₆₇	#3586	1	1	yes	characteristic
684	C₂×#578	C₂×C₆₇	1	1	yes	characteristic, complemented
685	C₂×#577	C₂×C₆₇	1	1	yes	characteristic, complemented
686	#3500	C₂×C₆₇	1	1	yes	characteristic, complemented
687	#3497	C₂×C₆₇	1	1	yes	characteristic, complemented
688	#3285	C₂×C₆₇	1	2	yes	complemented
689	#3282	C₂×C₆₇	1	2	yes	complemented
690	#3277	C₂×C₆₇	1	2	yes	complemented
691	#3275	C₂×C₆₇	1	2	yes	complemented
692	#3271	C₂×C₆₇	1	2	yes	complemented
693	#3270	C₂×C₆₇	1	2	yes	complemented
694	#3268	C₂×C₆₇	1	2	yes	complemented
695	#3266	C₂×C₆₇	1	2	yes	complemented
696	#3153	C₂×C₆₇	1	1	yes	characteristic, complemented
697	#3063	C₂×C₆₇	1	1	yes	characteristic, complemented
698	#3062	C₂×C₆₇	1	1	yes	characteristic, complemented
699	#3035	C₂×C₆₇	1	1	yes	characteristic, complemented
700	C₂×#464	C₂×C₆₇	1	1	yes	characteristic, complemented
701	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
702	#3012	C₂×C₆₇	1	1	yes	characteristic, complemented
703	#3011	C₂×C₆₇	1	1	yes	characteristic, complemented
704	#3010	C₂×C₆₇	1	1	yes	characteristic, complemented
705	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
706	#2935	C₂×C₆₇	1	1	yes	characteristic, complemented
707	C₆₇	#61096	1	1	yes	characteristic, direct product factor, Sylow
708	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
709	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
710	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
712	#578	—	2	8	no	—
713	#577	—	2	8	no	—
714	C₂×#137	C₂²×C₆₇	1	2	yes	—
715	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
716	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
717	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
718	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
719	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
720	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
721	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
722	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
723	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
724	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
725	C₂×#135	C₂²×C₆₇	1	2	yes	—
726	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
727	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
728	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
729	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
730	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
731	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
732	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
733	#550	—	2	1	no	—
734	#550	C₂²×C₆₇	1	2	yes	complemented
735	D₄×Q₈	—	2	1	no	—
736	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
737	#548	—	2	1	no	—
738	#548	—	2	1	no	—
739	#548	C₂²×C₆₇	1	2	yes	—
740	#548	C₂²×C₆₇	1	2	yes	—
741	#548	C₂²×C₆₇	1	2	yes	complemented
742	#548	C₂²×C₆₇	1	2	yes	complemented
743	#546	—	2	2	no	—
744	#546	—	2	2	no	—
745	#546	C₂²×C₆₇	1	2	yes	—
746	#546	C₂²×C₆₇	1	2	yes	—
747	#537	—	2	2	no	—
748	#537	C₂²×C₆₇	1	1	yes	characteristic
749	#537	C₂²×C₆₇	1	1	yes	characteristic, complemented
750	#536	—	2	1	no	—
751	#536	C₂²×C₆₇	1	1	yes	characteristic
752	#535	—	2	1	no	—
753	#535	C₂²×C₆₇	1	1	yes	characteristic
754	#532	—	2	1	no	—
755	#532	—	2	2	no	—
756	#532	C₂²×C₆₇	1	1	yes	characteristic
757	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
758	C₂×#124	—	2	1	no	—
759	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
760	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
761	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
762	#497	C₂²×C₆₇	1	2	yes	complemented
763	#496	C₂²×C₆₇	1	2	yes	complemented
764	#495	C₂²×C₆₇	1	2	yes	complemented
765	#495	C₂²×C₆₇	1	2	yes	complemented
766	#470	C₂²×C₆₇	1	2	yes	complemented
767	#469	C₂²×C₆₇	1	2	yes	complemented
768	#468	C₂²×C₆₇	1	2	yes	complemented
769	#468	C₂²×C₆₇	1	2	yes	complemented
770	#467	C₂²×C₆₇	1	2	yes	complemented
771	#466	C₂²×C₆₇	1	2	yes	complemented
772	#465	C₂²×C₆₇	1	2	yes	complemented
773	#465	C₂²×C₆₇	1	2	yes	complemented
774	#464	C₂²×C₆₇	1	2	yes	complemented
775	#464	C₂²×C₆₇	1	2	yes	complemented
776	#464	C₂²×C₆₇	1	2	yes	complemented
777	#464	C₂²×C₆₇	1	1	yes	characteristic, complemented
778	#464	C₂²×C₆₇	1	2	yes	complemented
779	#464	C₂²×C₆₇	1	1	yes	characteristic, complemented
780	#463	C₂²×C₆₇	1	1	yes	characteristic, complemented
781	#463	C₂²×C₆₇	1	1	yes	characteristic, complemented
782	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
783	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
784	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
785	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
786	#452	C₂²×C₆₇	1	2	yes	—
787	#452	C₂²×C₆₇	1	2	yes	complemented
788	#452	C₂²×C₆₇	1	2	yes	complemented
789	#452	C₂²×C₆₇	1	2	yes	complemented
790	#451	C₂²×C₆₇	1	2	yes	complemented
791	#451	C₂²×C₆₇	1	2	yes	complemented
792	#451	C₂²×C₆₇	1	2	yes	complemented
793	#450	C₂²×C₆₇	1	2	yes	—
794	#449	C₂²×C₆₇	1	2	yes	—
795	#449	C₂²×C₆₇	1	2	yes	complemented
796	#449	C₂²×C₆₇	1	2	yes	complemented
797	#449	C₂²×C₆₇	1	2	yes	complemented
798	#448	C₂²×C₆₇	1	2	yes	complemented
799	#448	C₂²×C₆₇	1	2	yes	complemented
800	#448	C₂²×C₆₇	1	2	yes	complemented
801	#447	C₂²×C₆₇	1	2	yes	—
802	#441	C₂²×C₆₇	1	2	yes	complemented
803	#440	C₂²×C₆₇	1	2	yes	complemented
804	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
805	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
806	#436	C₂²×C₆₇	1	2	yes	complemented
807	#435	C₂²×C₆₇	1	2	yes	complemented
808	#435	C₂²×C₆₇	1	2	yes	complemented
809	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
810	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
811	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
812	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
813	#417	C₂²×C₆₇	1	1	yes	characteristic
814	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
815	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
816	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
817	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
818	#408	C₂²×C₆₇	1	1	yes	characteristic
819	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
820	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
821	2₋¹⁺⁴	—	2	4	no	—
822	2₋¹⁺⁴	—	2	4	no	—
823	2₋¹⁺⁴	—	2	4	no	—
824	2₋¹⁺⁴	—	4	2	no	—
825	2₋¹⁺⁴	—	4	2	no	—
826	2₋¹⁺⁴	—	4	2	no	—
827	H(5,𝔽₂)	—	2	4	no	—
828	H(5,𝔽₂)	—	4	2	no	—
829	C₂×#41	—	2	1	no	—
830	C₂×#41	—	2	1	no	—
831	C₂×#41	—	2	2	no	—
832	C₂×#41	—	2	2	no	—
833	C₂×#41	—	2	2	no	—
834	C₂×#41	—	2	1	no	—
835	C₂×#41	—	2	1	no	—
836	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
837	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
838	C₂×#41	C₂³×C₆₇	1	2	yes	—
839	C₂×#41	C₂³×C₆₇	1	2	yes	—
840	C₂×#41	C₂³×C₆₇	1	2	yes	—
841	C₂×#41	C₂³×C₆₇	1	2	yes	—
842	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
843	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
844	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
845	C₂²×Q₈	—	2	1	no	—
846	C₂²×Q₈	—	2	1	no	—
847	C₂²×Q₈	—	2	1	no	—
848	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
849	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
850	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
851	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
852	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
853	C₂²×D₄	—	2	1	no	—
854	C₂²×D₄	—	2	2	no	—
855	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
856	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
857	#137	—	2	8	no	—
858	#137	—	2	8	no	—
859	#137	—	2	8	no	—
860	#137	—	2	4	no	—
861	#137	—	4	2	no	—
862	#137	D₄×C₆₇	1	8	yes	complemented
863	AGL(1,ℤ/8)	—	2	8	no	—
864	AGL(1,ℤ/8)	—	2	4	no	—
865	AGL(1,ℤ/8)	—	4	2	no	—
866	#135	—	2	4	no	—
867	#135	—	2	4	no	—
868	#135	—	2	8	no	—
869	#135	—	2	8	no	—
870	C₂×Q₁₆	—	2	4	no	—
871	C₂×Q₁₆	—	2	8	no	—
872	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
873	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
874	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
875	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
876	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
877	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
878	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
879	C₂×SD₁₆	—	2	4	no	—
880	C₂×SD₁₆	—	2	8	no	—
881	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
882	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
883	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
884	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
885	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
886	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
887	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
888	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
889	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
890	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
891	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
892	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
893	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
894	C₂×D₈	C₂³×C₆₇	1	2	yes	—
895	C₂×D₈	C₂³×C₆₇	1	2	yes	—
896	#131	—	2	4	no	—
897	#131	—	2	4	no	—
898	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
899	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
900	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
901	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
902	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
903	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
904	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
905	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
906	C₄⋊Q₈	—	2	1	no	—
907	C₄⋊Q₈	—	2	2	no	—
908	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
909	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
910	#127	—	2	1	no	—
911	#127	—	2	2	no	—
912	#127	D₄×C₆₇	1	1	yes	characteristic
913	#127	C₂³×C₆₇	1	1	yes	characteristic
914	#124	—	2	1	no	—
915	#124	—	2	1	no	—
916	#124	—	2	2	no	—
917	#124	—	2	2	no	—
918	#124	—	2	2	no	—
919	#124	—	2	2	no	—
920	#124	—	2	1	no	—
921	#124	—	2	1	no	—
922	#124	D₄×C₆₇	1	1	yes	characteristic
923	#124	D₄×C₆₇	1	1	yes	characteristic
924	#124	C₂³×C₆₇	1	2	yes	—
925	#124	C₂³×C₆₇	1	2	yes	—
926	#124	C₂³×C₆₇	1	1	yes	characteristic
927	#124	C₂³×C₆₇	1	1	yes	characteristic
928	#123	—	2	2	no	—
929	#123	—	2	2	no	—
930	#123	—	2	2	no	—
931	C₂²⋊Q₈	—	2	1	no	—
932	C₂²⋊Q₈	—	2	1	no	—
933	C₂²⋊Q₈	—	2	2	no	—
934	C₂²⋊Q₈	—	2	2	no	—
935	C₂²⋊Q₈	—	2	2	no	—
936	C₂²⋊Q₈	—	2	2	no	—
937	C₂²⋊Q₈	—	2	2	no	—
938	C₂²⋊Q₈	—	2	2	no	—
939	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
940	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
941	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
942	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
943	#121	—	2	2	no	—
944	#121	—	2	2	no	—
945	#121	—	2	2	no	—
946	#121	—	2	2	no	—
947	#121	—	2	2	no	—
948	#121	—	2	2	no	—
949	#121	—	2	1	no	—
950	#121	—	2	1	no	—
951	#121	—	2	1	no	—
952	#121	—	2	1	no	—
953	#121	—	2	2	no	—
954	#121	—	2	2	no	—
955	#121	—	2	2	no	—
956	#121	—	2	2	no	—
957	#121	D₄×C₆₇	1	2	yes	—
958	#121	D₄×C₆₇	1	2	yes	—
959	#121	C₂³×C₆₇	1	2	yes	—
960	#121	C₂³×C₆₇	1	2	yes	—
961	#121	C₂³×C₆₇	1	2	yes	—
962	#121	C₂³×C₆₇	1	2	yes	—
963	#120	—	2	2	no	—
964	#120	—	2	2	no	—
965	#120	—	2	2	no	—
966	C₄×Q₈	—	2	1	no	—
967	C₄×Q₈	—	2	1	no	—
968	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
969	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
970	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
971	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
972	C₄×D₄	—	2	2	no	—
973	C₄×D₄	—	2	1	no	—
974	C₄×D₄	—	2	1	no	—
975	C₄×D₄	—	2	2	no	—
976	C₄×D₄	—	2	2	no	—
977	C₄×D₄	—	2	2	no	—
978	C₄×D₄	—	2	2	no	—
979	C₄×D₄	—	2	2	no	—
980	C₄×D₄	—	2	1	no	—
981	C₄×D₄	—	2	1	no	—
982	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
983	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
984	C₄×D₄	C₂³×C₆₇	1	2	yes	—
985	C₄×D₄	C₂³×C₆₇	1	2	yes	—
986	#117	—	2	1	no	—
987	#117	C₂³×C₆₇	1	1	yes	characteristic
988	C₂×C₄⋊C₄	—	2	1	no	—
989	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
990	C₂×C₂²⋊C₄	—	2	1	no	—
991	C₂×C₂²⋊C₄	—	2	1	no	—
992	C₂×C₂²⋊C₄	—	2	2	no	—
993	C₂×C₂²⋊C₄	—	2	2	no	—
994	C₂×C₄²	—	2	1	no	—
995	C₂×C₄²	—	2	1	no	—
996	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
997	#107	C₂³×C₆₇	1	2	yes	—
998	#106	C₂³×C₆₇	1	2	yes	—
999	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1000	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1001	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1002	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1003	#103	C₂³×C₆₇	1	2	yes	—
1004	#103	C₂³×C₆₇	1	2	yes	—
1005	#103	C₂³×C₆₇	1	1	yes	characteristic
1006	#103	C₂³×C₆₇	1	1	yes	characteristic
1007	#103	C₂³×C₆₇	1	1	yes	characteristic
1008	#103	C₂³×C₆₇	1	1	yes	characteristic
1009	#103	C₂³×C₆₇	1	2	yes	—
1010	#103	C₂³×C₆₇	1	2	yes	—
1011	#103	C₂³×C₆₇	1	2	yes	—
1012	#102	C₂³×C₆₇	1	2	yes	—
1013	#102	C₂³×C₆₇	1	2	yes	—
1014	#102	C₂³×C₆₇	1	1	yes	characteristic
1015	#102	C₂³×C₆₇	1	1	yes	characteristic
1016	#102	C₂³×C₆₇	1	1	yes	characteristic
1017	#102	C₂³×C₆₇	1	1	yes	characteristic
1018	#102	C₂³×C₆₇	1	2	yes	—
1019	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1020	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1021	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1022	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1023	#97	C₂³×C₆₇	1	2	yes	—
1024	C₄×C₈	C₂³×C₆₇	1	2	yes	—
1025	C₂⁴	—	2	2	no	—
1026	C₂⁴	—	2	1	no	—
1027	#41	—	2	2	no	—
1028	#41	—	2	2	no	—
1029	#41	—	2	2	no	—
1030	#41	—	2	2	no	—
1031	#41	—	2	2	no	—
1032	#41	—	2	4	no	—
1033	#41	—	2	4	no	—
1034	#41	—	2	4	no	—
1035	#41	—	2	4	no	—
1036	#41	—	2	2	no	—
1037	#41	—	2	2	no	—
1038	#41	—	2	2	no	—
1039	#41	—	2	2	no	—
1040	#41	—	4	2	no	—
1041	#41	—	4	2	no	—
1042	#41	—	4	2	no	—
1043	#41	—	4	2	no	—
1044	#41	—	4	8	no	—
1045	#41	—	4	8	no	—
1046	#41	—	4	4	no	—
1047	#41	—	4	4	no	—
1048	#41	—	4	8	no	—
1049	#41	—	4	4	no	—
1050	#41	—	4	4	no	—
1051	#41	C₂×D₄×C₆₇	1	4	yes	—
1052	C₂×Q₈	—	2	1	no	—
1053	C₂×Q₈	—	2	2	no	—
1054	C₂×Q₈	—	2	2	no	—
1055	C₂×Q₈	—	2	2	no	—
1056	C₂×Q₈	—	2	1	no	—
1057	C₂×Q₈	—	2	2	no	—
1058	C₂×Q₈	—	2	4	no	—
1059	C₂×Q₈	—	2	4	no	—
1060	C₂×Q₈	—	2	4	no	—
1061	C₂×Q₈	—	2	2	no	—
1062	C₂×Q₈	—	2	2	no	—
1063	C₂×Q₈	—	4	2	no	—
1064	C₂×Q₈	—	4	2	no	—
1065	C₂×Q₈	—	4	2	no	—
1066	C₂×Q₈	—	4	4	no	—
1067	C₂×Q₈	—	4	4	no	—
1068	C₂×Q₈	—	4	4	no	—
1069	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
1070	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1071	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1072	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1073	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1074	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1075	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1076	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1077	C₂×D₄	—	2	1	no	—
1078	C₂×D₄	—	2	4	no	—
1079	C₂×D₄	—	2	2	no	—
1080	C₂×D₄	—	2	1	no	—
1081	C₂×D₄	—	2	1	no	—
1082	C₂×D₄	—	2	2	no	—
1083	C₂×D₄	—	2	2	no	—
1084	C₂×D₄	—	2	2	no	—
1085	C₂×D₄	—	2	2	no	—
1086	C₂×D₄	—	2	2	no	—
1087	C₂×D₄	—	2	2	no	—
1088	C₂×D₄	—	2	2	no	—
1089	C₂×D₄	—	2	2	no	—
1090	C₂×D₄	—	2	1	no	—
1091	C₂×D₄	—	2	2	no	—
1092	C₂×D₄	—	2	1	no	—
1093	C₂×D₄	—	2	1	no	—
1094	C₂×D₄	—	2	2	no	—
1095	C₂×D₄	—	4	2	no	—
1096	C₂×D₄	—	4	4	no	—
1097	C₂×D₄	—	4	8	no	—
1098	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1099	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1100	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1101	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1102	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1103	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1104	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1105	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1106	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1107	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1108	C₂²×C₄	—	2	1	no	—
1109	C₂²×C₄	—	2	1	no	—
1110	C₂²×C₄	—	2	1	no	—
1111	C₂²×C₄	—	2	2	no	—
1112	C₂²×C₄	—	2	2	no	—
1113	C₂²×C₄	—	2	2	no	—
1114	C₂²×C₄	—	2	1	no	—
1115	C₂²×C₄	—	2	2	no	—
1116	C₂²×C₄	—	2	2	no	—
1117	C₂²×C₄	—	2	2	no	—
1118	C₂²×C₄	—	2	1	no	—
1119	C₂²×C₄	—	2	1	no	—
1120	C₂²×C₄	—	2	2	no	—
1121	C₂²×C₄	—	2	1	no	—
1122	C₂²×C₄	—	2	1	no	—
1123	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1124	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1125	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1126	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1127	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1128	Q₁₆	—	2	4	no	—
1129	Q₁₆	—	2	2	no	—
1130	Q₁₆	—	2	4	no	—
1131	Q₁₆	—	2	2	no	—
1132	Q₁₆	—	2	4	no	—
1133	Q₁₆	—	4	2	no	—
1134	Q₁₆	C₂×D₄×C₆₇	1	8	yes	—
1135	SD₁₆	—	2	4	no	—
1136	SD₁₆	—	2	4	no	—
1137	SD₁₆	—	2	2	no	—
1138	SD₁₆	—	2	2	no	—
1139	SD₁₆	—	2	2	no	—
1140	SD₁₆	—	2	2	no	—
1141	SD₁₆	—	2	4	no	—
1142	SD₁₆	—	2	4	no	—
1143	SD₁₆	—	4	2	no	—
1144	SD₁₆	—	4	2	no	—
1145	SD₁₆	C₂×D₄×C₆₇	1	8	yes	—
1146	D₈	—	2	2	no	—
1147	D₈	—	2	2	no	—
1148	D₈	—	2	4	no	—
1149	D₈	—	4	2	no	—
1150	M₁₆	—	2	2	no	—
1151	M₁₆	—	2	4	no	—
1152	M₁₆	—	2	4	no	—
1153	M₁₆	C₂×D₄×C₆₇	1	4	yes	—
1154	C₂×C₈	—	2	2	no	—
1155	C₂×C₈	—	2	2	no	—
1156	C₂×C₈	—	2	4	no	—
1157	C₂×C₈	—	2	4	no	—
1158	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1159	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1160	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1161	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1162	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1163	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1164	C₄⋊C₄	—	2	2	no	—
1165	C₄⋊C₄	—	2	2	no	—
1166	C₄⋊C₄	—	2	1	no	—
1167	C₄⋊C₄	—	2	1	no	—
1168	C₄⋊C₄	—	2	1	no	—
1169	C₄⋊C₄	—	2	1	no	—
1170	C₄⋊C₄	—	2	1	no	—
1171	C₄⋊C₄	—	2	2	no	—
1172	C₄⋊C₄	—	2	2	no	—
1173	C₄⋊C₄	—	2	2	no	—
1174	C₄⋊C₄	—	2	2	no	—
1175	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1176	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1177	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1178	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1179	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1180	C₂²⋊C₄	—	2	2	no	—
1181	C₂²⋊C₄	—	2	2	no	—
1182	C₂²⋊C₄	—	2	1	no	—
1183	C₂²⋊C₄	—	2	2	no	—
1184	C₂²⋊C₄	—	2	2	no	—
1185	C₂²⋊C₄	—	2	2	no	—
1186	C₂²⋊C₄	—	2	2	no	—
1187	C₂²⋊C₄	—	2	2	no	—
1188	C₂²⋊C₄	—	2	2	no	—
1189	C₂²⋊C₄	—	2	2	no	—
1190	C₂²⋊C₄	—	2	2	no	—
1191	C₂²⋊C₄	—	2	1	no	—
1192	C₂²⋊C₄	—	2	1	no	—
1193	C₂²⋊C₄	—	2	1	no	—
1194	C₂²⋊C₄	—	2	1	no	—
1195	C₂²⋊C₄	—	2	1	no	—
1196	C₂²⋊C₄	—	2	1	no	—
1197	C₂²⋊C₄	—	2	2	no	—
1198	C₂²⋊C₄	—	2	2	no	—
1199	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1200	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1201	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1202	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1203	C₄²	—	2	1	no	—
1204	C₄²	—	2	1	no	—
1205	C₄²	—	2	1	no	—
1206	C₄²	—	2	2	no	—
1207	C₄²	—	2	2	no	—
1208	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1209	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1210	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1211	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1212	C₂³	—	2	1	no	—
1213	C₂³	—	2	2	no	—
1214	C₂³	—	2	1	no	—
1215	C₂³	—	2	1	no	—
1216	C₂³	—	4	4	no	—
1217	C₂³	—	4	2	no	—
1218	C₂³	—	8	1	no	—
1219	C₂³	—	8	1	no	—
1220	C₂³	—	8	2	no	—
1221	C₂³	—	8	2	no	—
1222	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1223	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1224	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1225	Q₈	—	2	4	no	—
1226	Q₈	—	2	2	no	—
1227	Q₈	—	2	2	no	—
1228	Q₈	—	2	2	no	—
1229	Q₈	—	2	1	no	—
1230	Q₈	—	2	1	no	—
1231	Q₈	—	2	1	no	—
1232	Q₈	—	2	2	no	—
1233	Q₈	—	2	1	no	—
1234	Q₈	—	2	2	no	—
1235	Q₈	—	2	1	no	—
1236	Q₈	—	4	4	no	—
1237	Q₈	—	4	4	no	—
1238	Q₈	—	4	4	no	—
1239	Q₈	—	4	2	no	—
1240	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
1241	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1242	D₄	—	2	4	no	—
1243	D₄	—	2	4	no	—
1244	D₄	—	2	4	no	—
1245	D₄	—	2	2	no	—
1246	D₄	—	2	2	no	—
1247	D₄	—	2	1	no	—
1248	D₄	—	2	2	no	—
1249	D₄	—	2	1	no	—
1250	D₄	—	2	1	no	—
1251	D₄	—	2	1	no	—
1252	D₄	—	2	2	no	—
1253	D₄	—	2	1	no	—
1254	D₄	—	4	2	no	—
1255	D₄	—	4	2	no	—
1256	D₄	—	4	4	no	—
1257	D₄	—	4	4	no	—
1258	D₄	—	4	4	no	—
1259	D₄	—	4	4	no	—
1260	D₄	—	4	2	no	—
1261	D₄	—	4	4	no	—
1262	D₄	—	4	2	no	—
1263	D₄	—	4	2	no	—
1264	D₄	—	4	2	no	—
1265	D₄	—	8	1	no	—
1266	D₄	—	8	2	no	—
1267	D₄	—	8	2	no	—
1268	D₄	—	8	2	no	—
1269	D₄	—	8	2	no	—
1270	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1271	C₂×C₄	—	2	4	no	—
1272	C₂×C₄	—	2	1	no	—
1273	C₂×C₄	—	2	2	no	—
1274	C₂×C₄	—	2	4	no	—
1275	C₂×C₄	—	2	2	no	—
1276	C₂×C₄	—	2	2	no	—
1277	C₂×C₄	—	2	2	no	—
1278	C₂×C₄	—	2	2	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	2	2	no	—
1282	C₂×C₄	—	2	2	no	—
1283	C₂×C₄	—	2	1	no	—
1284	C₂×C₄	—	2	1	no	—
1285	C₂×C₄	—	4	1	no	—
1286	C₂×C₄	—	4	1	no	—
1287	C₂×C₄	—	4	4	no	—
1288	C₂×C₄	—	4	4	no	—
1289	C₂×C₄	—	4	4	no	—
1290	C₂×C₄	—	4	4	no	—
1291	C₂×C₄	—	4	4	no	—
1292	C₂×C₄	—	4	4	no	—
1293	C₂×C₄	—	4	4	no	—
1294	C₂×C₄	—	4	2	no	—
1295	C₂×C₄	—	4	2	no	—
1296	C₂×C₄	—	4	2	no	—
1297	C₂×C₄	—	8	1	no	—
1298	C₂×C₄	—	8	1	no	—
1299	C₂×C₄	—	8	1	no	—
1300	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1301	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1302	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1303	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1304	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1305	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1306	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1307	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1308	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1309	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1310	C₈	—	2	1	no	—
1311	C₈	—	2	1	no	—
1312	C₈	—	2	1	no	—
1313	C₈	—	2	1	no	—
1314	C₈	—	2	2	no	—
1315	C₈	C₂²×D₄×C₆₇	1	4	yes	—
1316	C₂²	—	2	1	no	—
1317	C₂²	—	2	1	no	—
1318	C₂²	—	2	2	no	—
1319	C₂²	—	2	2	no	—
1320	C₂²	—	2	2	no	—
1321	C₂²	—	2	2	no	—
1322	C₂²	—	2	2	no	—
1323	C₂²	—	2	2	no	—
1324	C₂²	—	2	2	no	—
1325	C₂²	—	4	1	no	—
1326	C₂²	—	4	1	no	—
1327	C₂²	—	4	1	no	—
1328	C₂²	—	4	1	no	—
1329	C₂²	—	4	2	no	—
1330	C₂²	—	4	1	no	—
1331	C₂²	—	4	1	no	—
1332	C₂²	—	4	2	no	—
1333	C₂²	—	4	1	no	—
1334	C₂²	—	4	1	no	—
1335	C₂²	—	4	2	no	—
1336	C₂²	—	16	2	no	—
1337	C₂²	—	16	4	no	—
1338	C₂²	D₄²×C₆₇	1	2	yes	—
1339	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1340	C₄	—	2	1	no	—
1341	C₄	—	2	1	no	—
1342	C₄	—	2	1	no	—
1343	C₄	—	2	1	no	—
1344	C₄	—	2	2	no	—
1345	C₄	—	2	4	no	—
1346	C₄	—	2	2	no	—
1347	C₄	—	2	2	no	—
1348	C₄	—	4	1	no	—
1349	C₄	—	4	2	no	—
1350	C₄	—	4	1	no	—
1351	C₄	—	4	2	no	—
1352	C₄	—	4	1	no	—
1353	C₄	—	4	1	no	—
1354	C₄	D₄²×C₆₇	1	2	yes	—
1355	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1356	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1357	C₂	—	2	2	no	—
1358	C₂	—	4	2	no	—
1359	C₂	—	4	2	no	—
1360	C₂	—	4	2	no	—
1361	C₂	—	8	2	no	—
1362	C₂	—	8	1	no	—
1363	C₂	—	8	1	no	—
1364	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1365	C₂	C₆₇×#3584	1	1	yes	characteristic
1366	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 ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#578×C₆₇	C₂	semidirect
2. C₂×#577×C₆₇	C₂	semidirect
3. C₆₇×#3500	C₂	semidirect
4. C₆₇×#3497	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×#3268	C₂	semidirect
12. C₆₇×#3266	C₂	semidirect
13. C₆₇×#3153	C₂	semidirect
14. C₆₇×#3063	C₂	semidirect
15. C₆₇×#3062	C₂	semidirect
16. C₆₇×#3035	C₂	semidirect
17. C₂×#464×C₆₇	C₂	semidirect
18. C₆₇×#3013	C₂	semidirect
19. C₆₇×#3012	C₂	semidirect
20. C₆₇×#3011	C₂	semidirect
21. C₆₇×#3010	C₂	semidirect
22. C₄×#137×C₆₇	C₂	semidirect
23. C₆₇×#2935	C₂	semidirect
26. C₂×2₋¹⁺⁴×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
42. C₂×#135×C₆₇	C₂²	semidirect
43. C₂²×Q₁₆×C₆₇	C₂²	semidirect
44. C₂²×Q₁₆×C₆₇	C₂²	semidirect
48. C₂×#131×C₆₇	C₂²	semidirect
50. #550×C₆₇	C₂²	semidirect
52. D₄×Q₈×C₆₇	C₂²	semidirect
57. #548×C₆₇	C₂²	semidirect
58. #548×C₆₇	C₂²	semidirect
65. #537×C₆₇	C₂²	semidirect
73. #532×C₆₇	C₂²	semidirect
77. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
78. #497×C₆₇	C₂²	semidirect
79. #496×C₆₇	C₂²	semidirect
80. #495×C₆₇	C₂²	semidirect
81. #495×C₆₇	C₂²	semidirect
82. #470×C₆₇	C₂²	semidirect
83. #469×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #468×C₆₇	C₂²	semidirect
86. #467×C₆₇	C₂²	semidirect
87. #466×C₆₇	C₂²	semidirect
88. #465×C₆₇	C₂²	semidirect
89. #465×C₆₇	C₂²	semidirect
90. #464×C₆₇	C₂²	semidirect
91. #464×C₆₇	C₂²	semidirect
92. #464×C₆₇	C₂²	semidirect
93. #464×C₆₇	C₂²	semidirect
94. #464×C₆₇	C₂²	semidirect
95. #464×C₆₇	C₂²	semidirect
96. #463×C₆₇	C₂²	semidirect
97. #463×C₆₇	C₂²	semidirect
98. #462×C₆₇	C₂²	semidirect
99. #461×C₆₇	C₂²	semidirect
100. #460×C₆₇	C₂²	semidirect
101. #459×C₆₇	C₂²	semidirect
103. #452×C₆₇	C₂²	semidirect
104. #452×C₆₇	C₂²	semidirect
105. #452×C₆₇	C₂²	semidirect
106. #451×C₆₇	C₂²	semidirect
107. #451×C₆₇	C₂²	semidirect
108. #451×C₆₇	C₂²	semidirect
111. #449×C₆₇	C₂²	semidirect
112. #449×C₆₇	C₂²	semidirect
113. #449×C₆₇	C₂²	semidirect
114. #448×C₆₇	C₂²	semidirect
115. #448×C₆₇	C₂²	semidirect
116. #448×C₆₇	C₂²	semidirect
118. #441×C₆₇	C₂²	semidirect
119. #440×C₆₇	C₂²	semidirect
120. C₄×Q₁₆×C₆₇	C₂²	semidirect
121. C₄×SD₁₆×C₆₇	C₂²	semidirect
122. #436×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. #435×C₆₇	C₂²	semidirect
125. C₈×D₄×C₆₇	C₂²	semidirect
126. #428×C₆₇	C₂²	semidirect
127. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
128. #419×C₆₇	C₂²	semidirect
130. #416×C₆₇	C₂²	semidirect
131. #416×C₆₇	C₂²	semidirect
132. C₂×#103×C₆₇	C₂²	semidirect
135. #408×C₆₇	C₂²	semidirect
136. C₄×M₁₆×C₆₇	C₂²	semidirect
178. #137×C₆₇	D₄	semidirect
673. #61096	C₆₇	direct (N × H)
684. C₂×#578	C₂×C₆₇	semidirect
685. C₂×#577	C₂×C₆₇	semidirect
686. #3500	C₂×C₆₇	semidirect
687. #3497	C₂×C₆₇	semidirect
688. #3285	C₂×C₆₇	semidirect
689. #3282	C₂×C₆₇	semidirect
690. #3277	C₂×C₆₇	semidirect
691. #3275	C₂×C₆₇	semidirect
692. #3271	C₂×C₆₇	semidirect
693. #3270	C₂×C₆₇	semidirect
694. #3268	C₂×C₆₇	semidirect
695. #3266	C₂×C₆₇	semidirect
696. #3153	C₂×C₆₇	semidirect
697. #3063	C₂×C₆₇	semidirect
698. #3062	C₂×C₆₇	semidirect
699. #3035	C₂×C₆₇	semidirect
700. C₂×#464	C₂×C₆₇	semidirect
701. #3013	C₂×C₆₇	semidirect
702. #3012	C₂×C₆₇	semidirect
703. #3011	C₂×C₆₇	semidirect
704. #3010	C₂×C₆₇	semidirect
705. C₄×#137	C₂×C₆₇	semidirect
706. #2935	C₂×C₆₇	semidirect
707. C₆₇	#61096	direct (N × H)
710. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
716. C₂×#137	C₂²×C₆₇	semidirect
717. C₂×#137	C₂²×C₆₇	semidirect
718. C₂×#137	C₂²×C₆₇	semidirect
719. C₂×#137	C₂²×C₆₇	semidirect
726. C₂×#135	C₂²×C₆₇	semidirect
727. C₂²×Q₁₆	C₂²×C₆₇	semidirect
728. C₂²×Q₁₆	C₂²×C₆₇	semidirect
732. C₂×#131	C₂²×C₆₇	semidirect
734. #550	C₂²×C₆₇	semidirect
736. D₄×Q₈	C₂²×C₆₇	semidirect
741. #548	C₂²×C₆₇	semidirect
742. #548	C₂²×C₆₇	semidirect
749. #537	C₂²×C₆₇	semidirect
757. #532	C₂²×C₆₇	semidirect
761. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
762. #497	C₂²×C₆₇	semidirect
763. #496	C₂²×C₆₇	semidirect
764. #495	C₂²×C₆₇	semidirect
765. #495	C₂²×C₆₇	semidirect
766. #470	C₂²×C₆₇	semidirect
767. #469	C₂²×C₆₇	semidirect
768. #468	C₂²×C₆₇	semidirect
769. #468	C₂²×C₆₇	semidirect
770. #467	C₂²×C₆₇	semidirect
771. #466	C₂²×C₆₇	semidirect
772. #465	C₂²×C₆₇	semidirect
773. #465	C₂²×C₆₇	semidirect
774. #464	C₂²×C₆₇	semidirect
775. #464	C₂²×C₆₇	semidirect
776. #464	C₂²×C₆₇	semidirect
777. #464	C₂²×C₆₇	semidirect
778. #464	C₂²×C₆₇	semidirect
779. #464	C₂²×C₆₇	semidirect
780. #463	C₂²×C₆₇	semidirect
781. #463	C₂²×C₆₇	semidirect
782. #462	C₂²×C₆₇	semidirect
783. #461	C₂²×C₆₇	semidirect
784. #460	C₂²×C₆₇	semidirect
785. #459	C₂²×C₆₇	semidirect
787. #452	C₂²×C₆₇	semidirect
788. #452	C₂²×C₆₇	semidirect
789. #452	C₂²×C₆₇	semidirect
790. #451	C₂²×C₆₇	semidirect
791. #451	C₂²×C₆₇	semidirect
792. #451	C₂²×C₆₇	semidirect
795. #449	C₂²×C₆₇	semidirect
796. #449	C₂²×C₆₇	semidirect
797. #449	C₂²×C₆₇	semidirect
798. #448	C₂²×C₆₇	semidirect
799. #448	C₂²×C₆₇	semidirect
800. #448	C₂²×C₆₇	semidirect
802. #441	C₂²×C₆₇	semidirect
803. #440	C₂²×C₆₇	semidirect
804. C₄×Q₁₆	C₂²×C₆₇	semidirect
805. C₄×SD₁₆	C₂²×C₆₇	semidirect
806. #436	C₂²×C₆₇	semidirect
807. #435	C₂²×C₆₇	semidirect
808. #435	C₂²×C₆₇	semidirect
809. C₈×D₄	C₂²×C₆₇	semidirect
810. #428	C₂²×C₆₇	semidirect
811. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
812. #419	C₂²×C₆₇	semidirect
814. #416	C₂²×C₆₇	semidirect
815. #416	C₂²×C₆₇	semidirect
816. C₂×#103	C₂²×C₆₇	semidirect
819. #408	C₂²×C₆₇	semidirect
820. C₄×M₁₆	C₂²×C₆₇	semidirect
862. #137	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#578×C₆₇	2
C₂×#577×C₆₇	2
C₆₇×#3500	2
C₆₇×#3497	2
C₆₇×#3285	2
C₆₇×#3282	2
C₆₇×#3277	2
C₆₇×#3275	2
C₆₇×#3271	2
C₆₇×#3270	2
C₆₇×#3268	2
C₆₇×#3266	2
C₆₇×#3153	2
C₆₇×#3063	2
C₆₇×#3062	2
C₆₇×#3035	2
C₂×#464×C₆₇	2
C₆₇×#3013	2
C₆₇×#3012	2
C₆₇×#3011	2
C₆₇×#3010	2
C₄×#137×C₆₇	2
C₆₇×#2935	2
#61096	67

Subgroups — C67×#61096 #30740347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61096 #30740347