Subgroups — C₆₇×#61620 #30740871

Order 17152.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3489	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3331	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3316	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3306	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3298	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3282	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3275	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3270	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3267	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3225	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3204	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3195	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3187	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3125	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3006	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#452×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2976	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
23	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
26	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#562×C₆₇	—	2	2	no	—
29	#554×C₆₇	C₂²	1	2	yes	complemented
30	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
31	#548×C₆₇	C₂²	1	2	yes	—
32	#548×C₆₇	C₂²	1	2	yes	—
33	#547×C₆₇	—	2	2	no	—
34	#547×C₆₇	C₂²	1	2	yes	—
35	#547×C₆₇	C₂²	1	2	yes	—
36	#546×C₆₇	—	2	2	no	—
37	#546×C₆₇	—	2	2	no	—
38	#546×C₆₇	C₂²	1	2	yes	complemented
39	#546×C₆₇	C₂²	1	2	yes	complemented
40	#543×C₆₇	—	2	1	no	—
41	#542×C₆₇	C₂²	1	2	yes	complemented
42	#539×C₆₇	—	2	1	no	—
43	#538×C₆₇	—	2	1	no	—
44	#537×C₆₇	—	2	1	no	—
45	#537×C₆₇	—	2	1	no	—
46	#537×C₆₇	C₂²	1	2	yes	complemented
47	#537×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#536×C₆₇	—	2	1	no	—
49	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#525×C₆₇	—	2	1	no	—
51	#525×C₆₇	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
53	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
56	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#497×C₆₇	C₂²	1	2	yes	complemented
58	#495×C₆₇	C₂²	1	2	yes	complemented
59	#489×C₆₇	C₂²	1	2	yes	complemented
60	#487×C₆₇	C₂²	1	2	yes	complemented
61	#483×C₆₇	C₂²	1	2	yes	complemented
62	#483×C₆₇	C₂²	1	2	yes	complemented
63	#483×C₆₇	C₂²	1	2	yes	complemented
64	#483×C₆₇	C₂²	1	2	yes	complemented
65	#481×C₆₇	C₂²	1	2	yes	complemented
66	#481×C₆₇	C₂²	1	2	yes	complemented
67	#476×C₆₇	C₂²	1	2	yes	complemented
68	#475×C₆₇	C₂²	1	2	yes	complemented
69	#470×C₆₇	C₂²	1	2	yes	complemented
70	#470×C₆₇	C₂²	1	2	yes	complemented
71	#470×C₆₇	C₂²	1	2	yes	complemented
72	#469×C₆₇	C₂²	1	2	yes	complemented
73	#465×C₆₇	C₂²	1	2	yes	—
74	#465×C₆₇	C₂²	1	2	yes	—
75	#465×C₆₇	C₂²	1	2	yes	complemented
76	#465×C₆₇	C₂²	1	2	yes	complemented
77	#464×C₆₇	C₂²	1	2	yes	complemented
78	#464×C₆₇	C₂²	1	2	yes	complemented
79	#463×C₆₇	C₂²	1	2	yes	complemented
80	#463×C₆₇	C₂²	1	2	yes	complemented
81	#462×C₆₇	C₂²	1	2	yes	complemented
82	#461×C₆₇	C₂²	1	2	yes	complemented
83	#452×C₆₇	C₂²	1	2	yes	—
84	#452×C₆₇	C₂²	1	2	yes	—
85	#452×C₆₇	C₂²	1	2	yes	complemented
86	#452×C₆₇	C₂²	1	2	yes	complemented
87	#452×C₆₇	C₂²	1	2	yes	complemented
88	#452×C₆₇	C₂²	1	2	yes	complemented
89	#451×C₆₇	C₂²	1	2	yes	complemented
90	#451×C₆₇	C₂²	1	2	yes	complemented
91	#451×C₆₇	C₂²	1	2	yes	complemented
92	#450×C₆₇	C₂²	1	2	yes	complemented
93	#449×C₆₇	C₂²	1	2	yes	—
94	#449×C₆₇	C₂²	1	2	yes	—
95	#449×C₆₇	C₂²	1	2	yes	complemented
96	#449×C₆₇	C₂²	1	2	yes	complemented
97	#448×C₆₇	C₂²	1	2	yes	—
98	#448×C₆₇	C₂²	1	2	yes	complemented
99	#448×C₆₇	C₂²	1	2	yes	complemented
100	#447×C₆₇	C₂²	1	2	yes	—
101	#442×C₆₇	C₂²	1	2	yes	complemented
102	#441×C₆₇	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
105	#436×C₆₇	C₂²	1	2	yes	complemented
106	#435×C₆₇	C₂²	1	2	yes	complemented
107	#435×C₆₇	C₂²	1	2	yes	complemented
108	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
109	#433×C₆₇	C₂²	1	2	yes	complemented
110	#417×C₆₇	C₂²	1	1	yes	characteristic
111	#417×C₆₇	C₂²	1	1	yes	characteristic
112	#417×C₆₇	C₂²	1	2	yes	complemented
113	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
114	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	#408×C₆₇	C₂²	1	2	yes	complemented
117	#407×C₆₇	C₂²	1	1	yes	characteristic
118	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
119	2₋¹⁺⁴×C₆₇	—	4	2	no	—
120	2₋¹⁺⁴×C₆₇	—	4	2	no	—
121	C₂×#41×C₆₇	—	2	1	no	—
122	C₂×#41×C₆₇	—	2	2	no	—
123	C₂×#41×C₆₇	—	2	2	no	—
124	C₂×#41×C₆₇	—	2	1	no	—
125	C₂×#41×C₆₇	—	2	1	no	—
126	C₂×#41×C₆₇	—	4	2	no	—
127	C₂×#41×C₆₇	—	4	2	no	—
128	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×#41×C₆₇	C₂³	1	2	yes	—
130	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
131	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×#41×C₆₇	C₂³	1	2	yes	—
134	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×Q₈×C₆₇	—	2	1	no	—
136	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
138	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₆₇	—	2	1	no	—
141	C₂²×D₄×C₆₇	—	2	1	no	—
142	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₆₇	—	2	1	no	—
145	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
146	#137×C₆₇	—	4	4	no	—
147	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
148	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
149	#135×C₆₇	—	4	4	no	—
150	C₂×Q₁₆×C₆₇	—	4	2	no	—
151	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₇	—	4	2	no	—
156	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂×D₈×C₆₇	C₂³	1	2	yes	—
163	C₂×D₈×C₆₇	C₂³	1	2	yes	—
164	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
165	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
169	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
170	C₄⋊Q₈×C₆₇	—	2	2	no	—
171	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
172	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
173	#126×C₆₇	—	2	2	no	—
174	#125×C₆₇	—	2	2	no	—
175	#124×C₆₇	—	2	2	no	—
176	#124×C₆₇	—	2	2	no	—
177	#124×C₆₇	—	2	2	no	—
178	#124×C₆₇	C₂³	1	2	yes	—
179	#124×C₆₇	C₂³	1	2	yes	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	—	2	2	no	—
182	#123×C₆₇	—	2	2	no	—
183	#123×C₆₇	—	2	2	no	—
184	#123×C₆₇	—	2	2	no	—
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	D₄	1	2	yes	—
189	C₂²⋊Q₈×C₆₇	—	2	1	no	—
190	C₂²⋊Q₈×C₆₇	—	2	2	no	—
191	C₂²⋊Q₈×C₆₇	—	2	1	no	—
192	C₂²⋊Q₈×C₆₇	—	2	1	no	—
193	C₂²⋊Q₈×C₆₇	—	2	1	no	—
194	C₂²⋊Q₈×C₆₇	—	2	1	no	—
195	C₂²⋊Q₈×C₆₇	—	2	1	no	—
196	C₂²⋊Q₈×C₆₇	—	2	2	no	—
197	C₂²⋊Q₈×C₆₇	—	2	1	no	—
198	C₂²⋊Q₈×C₆₇	—	2	2	no	—
199	C₂²⋊Q₈×C₆₇	—	2	2	no	—
200	C₂²⋊Q₈×C₆₇	—	2	2	no	—
201	C₂²⋊Q₈×C₆₇	—	2	2	no	—
202	C₂²⋊Q₈×C₆₇	—	2	2	no	—
203	C₂²⋊Q₈×C₆₇	—	2	2	no	—
204	C₂²⋊Q₈×C₆₇	—	2	2	no	—
205	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
206	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
207	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
208	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
213	#121×C₆₇	—	2	1	no	—
214	#121×C₆₇	—	2	2	no	—
215	#121×C₆₇	—	2	2	no	—
216	#121×C₆₇	—	2	2	no	—
217	#121×C₆₇	—	2	2	no	—
218	#121×C₆₇	—	2	2	no	—
219	#121×C₆₇	—	2	2	no	—
220	#121×C₆₇	—	2	2	no	—
221	#121×C₆₇	—	2	1	no	—
222	#121×C₆₇	—	2	1	no	—
223	#121×C₆₇	—	2	2	no	—
224	#121×C₆₇	—	2	2	no	—
225	#121×C₆₇	D₄	1	1	yes	characteristic
226	#121×C₆₇	D₄	1	1	yes	characteristic
227	#121×C₆₇	C₂³	1	2	yes	—
228	#121×C₆₇	C₂³	1	2	yes	—
229	#121×C₆₇	C₂³	1	2	yes	—
230	#121×C₆₇	C₂³	1	2	yes	—
231	#120×C₆₇	—	2	2	no	—
232	#120×C₆₇	—	2	2	no	—
233	#120×C₆₇	D₄	1	2	yes	—
234	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
235	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
236	C₄×D₄×C₆₇	—	2	2	no	—
237	C₄×D₄×C₆₇	—	2	2	no	—
238	C₄×D₄×C₆₇	—	2	2	no	—
239	C₄×D₄×C₆₇	—	2	2	no	—
240	C₄×D₄×C₆₇	—	2	2	no	—
241	C₄×D₄×C₆₇	C₂³	1	2	yes	—
242	C₄×D₄×C₆₇	C₂³	1	2	yes	—
243	C₄×D₄×C₆₇	C₂³	1	2	yes	—
244	C₄×D₄×C₆₇	C₂³	1	2	yes	—
245	#117×C₆₇	—	2	1	no	—
246	#117×C₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
248	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
249	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
250	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
251	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
256	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
257	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
258	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
260	#106×C₆₇	C₂³	1	2	yes	—
261	#106×C₆₇	C₂³	1	2	yes	—
262	#106×C₆₇	C₂³	1	2	yes	—
263	#106×C₆₇	C₂³	1	2	yes	—
264	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
265	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
266	#103×C₆₇	C₂³	1	2	yes	—
267	#103×C₆₇	C₂³	1	2	yes	—
268	#103×C₆₇	C₂³	1	2	yes	—
269	#103×C₆₇	C₂³	1	2	yes	—
270	#103×C₆₇	C₂³	1	2	yes	—
271	#103×C₆₇	C₂³	1	2	yes	—
272	#103×C₆₇	C₂³	1	2	yes	—
273	#103×C₆₇	C₂³	1	2	yes	—
274	#103×C₆₇	C₂³	1	2	yes	—
275	#103×C₆₇	C₂³	1	2	yes	—
276	#102×C₆₇	C₂³	1	2	yes	—
277	#102×C₆₇	C₂³	1	2	yes	—
278	#102×C₆₇	C₂³	1	2	yes	—
279	#102×C₆₇	C₂³	1	2	yes	—
280	#102×C₆₇	C₂³	1	2	yes	—
281	#102×C₆₇	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
285	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
286	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
287	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
288	#97×C₆₇	C₂³	1	2	yes	—
289	C₄×C₈×C₆₇	C₂³	1	2	yes	—
290	C₂⁴×C₆₇	—	2	1	no	—
291	C₂⁴×C₆₇	—	2	1	no	—
292	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
293	#41×C₆₇	—	2	2	no	—
294	#41×C₆₇	—	2	2	no	—
295	#41×C₆₇	—	2	2	no	—
296	#41×C₆₇	—	2	4	no	—
297	#41×C₆₇	—	2	2	no	—
298	#41×C₆₇	—	4	1	no	—
299	#41×C₆₇	—	4	1	no	—
300	#41×C₆₇	—	4	1	no	—
301	#41×C₆₇	—	4	1	no	—
302	#41×C₆₇	—	4	1	no	—
303	#41×C₆₇	—	4	1	no	—
304	#41×C₆₇	—	4	2	no	—
305	#41×C₆₇	—	4	4	no	—
306	#41×C₆₇	—	4	4	no	—
307	#41×C₆₇	—	4	2	no	—
308	#41×C₆₇	—	4	2	no	—
309	#41×C₆₇	—	4	4	no	—
310	#41×C₆₇	—	4	8	no	—
311	#41×C₆₇	—	8	4	no	—
312	C₂×Q₈×C₆₇	—	2	1	no	—
313	C₂×Q₈×C₆₇	—	2	2	no	—
314	C₂×Q₈×C₆₇	—	2	1	no	—
315	C₂×Q₈×C₆₇	—	2	1	no	—
316	C₂×Q₈×C₆₇	—	2	2	no	—
317	C₂×Q₈×C₆₇	—	2	2	no	—
318	C₂×Q₈×C₆₇	—	2	4	no	—
319	C₂×Q₈×C₆₇	—	4	1	no	—
320	C₂×Q₈×C₆₇	—	4	2	no	—
321	C₂×Q₈×C₆₇	—	4	1	no	—
322	C₂×Q₈×C₆₇	—	4	1	no	—
323	C₂×Q₈×C₆₇	—	4	4	no	—
324	C₂×Q₈×C₆₇	—	4	1	no	—
325	C₂×Q₈×C₆₇	—	4	1	no	—
326	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₆₇	—	2	1	no	—
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	2	no	—
334	C₂×D₄×C₆₇	—	2	2	no	—
335	C₂×D₄×C₆₇	—	2	1	no	—
336	C₂×D₄×C₆₇	—	2	1	no	—
337	C₂×D₄×C₆₇	—	2	1	no	—
338	C₂×D₄×C₆₇	—	2	2	no	—
339	C₂×D₄×C₆₇	—	2	2	no	—
340	C₂×D₄×C₆₇	—	2	2	no	—
341	C₂×D₄×C₆₇	—	2	2	no	—
342	C₂×D₄×C₆₇	—	2	1	no	—
343	C₂×D₄×C₆₇	—	2	1	no	—
344	C₂×D₄×C₆₇	—	4	1	no	—
345	C₂×D₄×C₆₇	—	4	1	no	—
346	C₂×D₄×C₆₇	—	4	1	no	—
347	C₂×D₄×C₆₇	—	4	4	no	—
348	C₂×D₄×C₆₇	—	8	2	no	—
349	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
353	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
355	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₆₇	—	2	1	no	—
357	C₂²×C₄×C₆₇	—	2	1	no	—
358	C₂²×C₄×C₆₇	—	2	1	no	—
359	C₂²×C₄×C₆₇	—	2	2	no	—
360	C₂²×C₄×C₆₇	—	2	1	no	—
361	C₂²×C₄×C₆₇	—	2	1	no	—
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	1	no	—
364	C₂²×C₄×C₆₇	—	2	2	no	—
365	C₂²×C₄×C₆₇	—	2	2	no	—
366	C₂²×C₄×C₆₇	—	2	1	no	—
367	C₂²×C₄×C₆₇	—	2	1	no	—
368	C₂²×C₄×C₆₇	—	2	1	no	—
369	C₂²×C₄×C₆₇	—	2	2	no	—
370	C₂²×C₄×C₆₇	—	2	2	no	—
371	C₂²×C₄×C₆₇	—	2	2	no	—
372	C₂²×C₄×C₆₇	—	4	1	no	—
373	C₂²×C₄×C₆₇	—	4	1	no	—
374	C₂²×C₄×C₆₇	—	4	4	no	—
375	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
382	Q₁₆×C₆₇	—	2	4	no	—
383	Q₁₆×C₆₇	—	4	2	no	—
384	Q₁₆×C₆₇	—	4	2	no	—
385	Q₁₆×C₆₇	—	4	2	no	—
386	SD₁₆×C₆₇	—	2	4	no	—
387	SD₁₆×C₆₇	—	2	4	no	—
388	SD₁₆×C₆₇	—	4	2	no	—
389	SD₁₆×C₆₇	—	4	2	no	—
390	SD₁₆×C₆₇	—	4	2	no	—
391	SD₁₆×C₆₇	—	4	2	no	—
392	D₈×C₆₇	—	2	4	no	—
393	D₈×C₆₇	—	4	2	no	—
394	M₁₆×C₆₇	—	4	1	no	—
395	M₁₆×C₆₇	—	4	1	no	—
396	M₁₆×C₆₇	—	4	2	no	—
397	C₂×C₈×C₆₇	—	4	1	no	—
398	C₂×C₈×C₆₇	—	4	1	no	—
399	C₂×C₈×C₆₇	—	4	2	no	—
400	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
401	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
402	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
403	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₆₇	—	2	2	no	—
405	C₄⋊C₄×C₆₇	—	2	1	no	—
406	C₄⋊C₄×C₆₇	—	2	2	no	—
407	C₄⋊C₄×C₆₇	—	2	2	no	—
408	C₄⋊C₄×C₆₇	—	2	2	no	—
409	C₄⋊C₄×C₆₇	—	2	2	no	—
410	C₄⋊C₄×C₆₇	—	2	2	no	—
411	C₄⋊C₄×C₆₇	—	2	2	no	—
412	C₄⋊C₄×C₆₇	—	2	1	no	—
413	C₄⋊C₄×C₆₇	—	2	2	no	—
414	C₄⋊C₄×C₆₇	—	2	1	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	—	2	2	no	—
418	C₄⋊C₄×C₆₇	—	2	2	no	—
419	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
422	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
423	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
424	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
426	C₂²⋊C₄×C₆₇	—	2	2	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	2	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	2	no	—
435	C₂²⋊C₄×C₆₇	—	2	2	no	—
436	C₂²⋊C₄×C₆₇	—	2	2	no	—
437	C₂²⋊C₄×C₆₇	—	2	2	no	—
438	C₂²⋊C₄×C₆₇	—	2	2	no	—
439	C₂²⋊C₄×C₆₇	—	2	2	no	—
440	C₂²⋊C₄×C₆₇	—	2	2	no	—
441	C₂²⋊C₄×C₆₇	—	2	2	no	—
442	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
447	C₄²×C₆₇	—	2	2	no	—
448	C₄²×C₆₇	—	2	2	no	—
449	C₄²×C₆₇	C₂⁴	1	2	yes	—
450	C₂³×C₆₇	—	2	1	no	—
451	C₂³×C₆₇	—	2	2	no	—
452	C₂³×C₆₇	—	2	1	no	—
453	C₂³×C₆₇	—	2	2	no	—
454	C₂³×C₆₇	—	4	1	no	—
455	C₂³×C₆₇	—	4	1	no	—
456	C₂³×C₆₇	—	4	2	no	—
457	C₂³×C₆₇	—	4	2	no	—
458	C₂³×C₆₇	—	4	2	no	—
459	C₂³×C₆₇	—	8	1	no	—
460	C₂³×C₆₇	—	8	1	no	—
461	C₂³×C₆₇	—	8	1	no	—
462	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
463	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
464	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
465	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₆₇	—	2	1	no	—
467	Q₈×C₆₇	—	2	2	no	—
468	Q₈×C₆₇	—	2	1	no	—
469	Q₈×C₆₇	—	2	2	no	—
470	Q₈×C₆₇	—	2	2	no	—
471	Q₈×C₆₇	—	2	2	no	—
472	Q₈×C₆₇	—	2	1	no	—
473	Q₈×C₆₇	—	4	1	no	—
474	Q₈×C₆₇	—	4	4	no	—
475	Q₈×C₆₇	—	4	2	no	—
476	Q₈×C₆₇	—	4	2	no	—
477	Q₈×C₆₇	—	8	1	no	—
478	Q₈×C₆₇	—	8	2	no	—
479	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
480	D₄×C₆₇	—	2	4	no	—
481	D₄×C₆₇	—	2	4	no	—
482	D₄×C₆₇	—	2	1	no	—
483	D₄×C₆₇	—	2	2	no	—
484	D₄×C₆₇	—	2	1	no	—
485	D₄×C₆₇	—	2	2	no	—
486	D₄×C₆₇	—	2	1	no	—
487	D₄×C₆₇	—	4	2	no	—
488	D₄×C₆₇	—	4	1	no	—
489	D₄×C₆₇	—	4	2	no	—
490	D₄×C₆₇	—	4	2	no	—
491	D₄×C₆₇	—	4	2	no	—
492	D₄×C₆₇	—	4	2	no	—
493	D₄×C₆₇	—	4	4	no	—
494	D₄×C₆₇	—	4	2	no	—
495	D₄×C₆₇	—	4	4	no	—
496	D₄×C₆₇	—	8	1	no	—
497	D₄×C₆₇	—	8	2	no	—
498	D₄×C₆₇	—	8	2	no	—
499	D₄×C₆₇	—	8	2	no	—
500	D₄×C₆₇	—	8	2	no	—
501	D₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
502	C₂×C₄×C₆₇	—	2	4	no	—
503	C₂×C₄×C₆₇	—	2	1	no	—
504	C₂×C₄×C₆₇	—	2	1	no	—
505	C₂×C₄×C₆₇	—	2	1	no	—
506	C₂×C₄×C₆₇	—	2	2	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	2	1	no	—
509	C₂×C₄×C₆₇	—	2	2	no	—
510	C₂×C₄×C₆₇	—	2	1	no	—
511	C₂×C₄×C₆₇	—	2	1	no	—
512	C₂×C₄×C₆₇	—	2	2	no	—
513	C₂×C₄×C₆₇	—	2	2	no	—
514	C₂×C₄×C₆₇	—	2	2	no	—
515	C₂×C₄×C₆₇	—	2	2	no	—
516	C₂×C₄×C₆₇	—	2	2	no	—
517	C₂×C₄×C₆₇	—	2	1	no	—
518	C₂×C₄×C₆₇	—	4	1	no	—
519	C₂×C₄×C₆₇	—	4	1	no	—
520	C₂×C₄×C₆₇	—	4	1	no	—
521	C₂×C₄×C₆₇	—	4	2	no	—
522	C₂×C₄×C₆₇	—	4	2	no	—
523	C₂×C₄×C₆₇	—	4	2	no	—
524	C₂×C₄×C₆₇	—	4	4	no	—
525	C₂×C₄×C₆₇	—	4	4	no	—
526	C₂×C₄×C₆₇	—	4	2	no	—
527	C₂×C₄×C₆₇	—	4	2	no	—
528	C₂×C₄×C₆₇	—	4	2	no	—
529	C₂×C₄×C₆₇	—	8	2	no	—
530	C₂×C₄×C₆₇	—	8	2	no	—
531	C₂×C₄×C₆₇	—	8	2	no	—
532	C₂×C₄×C₆₇	—	8	1	no	—
533	C₂×C₄×C₆₇	—	8	1	no	—
534	C₂×C₄×C₆₇	—	8	1	no	—
535	C₂×C₄×C₆₇	—	8	2	no	—
536	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
538	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
539	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
543	C₈×C₆₇	—	2	2	no	—
544	C₈×C₆₇	—	2	2	no	—
545	C₈×C₆₇	—	2	2	no	—
546	C₈×C₆₇	—	2	2	no	—
547	C₂²×C₆₇	—	2	1	no	—
548	C₂²×C₆₇	—	2	1	no	—
549	C₂²×C₆₇	—	2	1	no	—
550	C₂²×C₆₇	—	2	1	no	—
551	C₂²×C₆₇	—	2	2	no	—
552	C₂²×C₆₇	—	2	1	no	—
553	C₂²×C₆₇	—	2	2	no	—
554	C₂²×C₆₇	—	2	2	no	—
555	C₂²×C₆₇	—	2	1	no	—
556	C₂²×C₆₇	—	2	2	no	—
557	C₂²×C₆₇	—	2	1	no	—
558	C₂²×C₆₇	—	2	1	no	—
559	C₂²×C₆₇	—	4	1	no	—
560	C₂²×C₆₇	—	4	1	no	—
561	C₂²×C₆₇	—	4	1	no	—
562	C₂²×C₆₇	—	4	2	no	—
563	C₂²×C₆₇	—	4	1	no	—
564	C₂²×C₆₇	—	4	2	no	—
565	C₂²×C₆₇	—	4	2	no	—
566	C₂²×C₆₇	—	4	1	no	—
567	C₂²×C₆₇	—	8	2	no	—
568	C₂²×C₆₇	—	8	4	no	—
569	C₂²×C₆₇	—	16	2	no	—
570	C₂²×C₆₇	#577	1	2	yes	—
571	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
572	C₄×C₆₇	—	2	2	no	—
573	C₄×C₆₇	—	2	1	no	—
574	C₄×C₆₇	—	2	2	no	—
575	C₄×C₆₇	—	2	1	no	—
576	C₄×C₆₇	—	2	2	no	—
577	C₄×C₆₇	—	2	1	no	—
578	C₄×C₆₇	—	2	2	no	—
579	C₄×C₆₇	—	4	2	no	—
580	C₄×C₆₇	—	4	1	no	—
581	C₄×C₆₇	—	4	2	no	—
582	C₄×C₆₇	—	4	2	no	—
583	C₄×C₆₇	—	4	2	no	—
584	C₄×C₆₇	—	4	2	no	—
585	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
586	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
587	#61620	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
588	C₂×C₆₇	—	2	2	no	—
589	C₂×C₆₇	—	4	2	no	—
590	C₂×C₆₇	—	4	1	no	—
591	C₂×C₆₇	—	4	1	no	—
592	C₂×C₆₇	—	4	2	no	—
593	C₂×C₆₇	—	8	1	no	—
594	C₂×C₆₇	—	8	2	no	—
595	C₂×C₆₇	#3484	1	1	yes	characteristic
596	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
597	C₂×C₆₇	#3586	1	1	yes	characteristic
598	#3536	C₂×C₆₇	1	1	yes	characteristic, complemented
599	#3489	C₂×C₆₇	1	1	yes	characteristic, complemented
600	#3331	C₂×C₆₇	1	2	yes	complemented
601	#3316	C₂×C₆₇	1	2	yes	complemented
602	#3306	C₂×C₆₇	1	2	yes	complemented
603	#3298	C₂×C₆₇	1	2	yes	complemented
604	#3282	C₂×C₆₇	1	2	yes	complemented
605	#3275	C₂×C₆₇	1	2	yes	complemented
606	#3270	C₂×C₆₇	1	2	yes	complemented
607	#3267	C₂×C₆₇	1	2	yes	complemented
608	#3225	C₂×C₆₇	1	2	yes	complemented
609	#3204	C₂×C₆₇	1	2	yes	complemented
610	#3195	C₂×C₆₇	1	1	yes	characteristic, complemented
611	#3187	C₂×C₆₇	1	1	yes	characteristic, complemented
612	#3125	C₂×C₆₇	1	2	yes	complemented
613	#3013	C₂×C₆₇	1	2	yes	complemented
614	#3006	C₂×C₆₇	1	1	yes	characteristic, complemented
615	C₂×#452	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#2976	C₂×C₆₇	1	1	yes	characteristic, complemented
617	C₆₇	#61620	1	1	yes	characteristic, direct product factor, Sylow
618	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
619	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
620	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
621	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
622	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
623	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
624	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
626	#562	—	2	2	no	—
627	#554	C₂²×C₆₇	1	2	yes	complemented
628	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
629	#548	C₂²×C₆₇	1	2	yes	—
630	#548	C₂²×C₆₇	1	2	yes	—
631	#547	—	2	2	no	—
632	#547	C₂²×C₆₇	1	2	yes	—
633	#547	C₂²×C₆₇	1	2	yes	—
634	#546	—	2	2	no	—
635	#546	—	2	2	no	—
636	#546	C₂²×C₆₇	1	2	yes	complemented
637	#546	C₂²×C₆₇	1	2	yes	complemented
638	#543	—	2	1	no	—
639	#542	C₂²×C₆₇	1	2	yes	complemented
640	#539	—	2	1	no	—
641	#538	—	2	1	no	—
642	#537	—	2	1	no	—
643	#537	—	2	1	no	—
644	#537	C₂²×C₆₇	1	1	yes	characteristic, complemented
645	#537	C₂²×C₆₇	1	2	yes	complemented
646	#536	—	2	1	no	—
647	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
648	#525	—	2	1	no	—
649	#525	C₂²×C₆₇	1	1	yes	characteristic
650	C₂×C₂²⋊Q₈	—	2	1	no	—
651	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
652	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
653	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
654	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
655	#497	C₂²×C₆₇	1	2	yes	complemented
656	#495	C₂²×C₆₇	1	2	yes	complemented
657	#489	C₂²×C₆₇	1	2	yes	complemented
658	#487	C₂²×C₆₇	1	2	yes	complemented
659	#483	C₂²×C₆₇	1	2	yes	complemented
660	#483	C₂²×C₆₇	1	2	yes	complemented
661	#483	C₂²×C₆₇	1	2	yes	complemented
662	#483	C₂²×C₆₇	1	2	yes	complemented
663	#481	C₂²×C₆₇	1	2	yes	complemented
664	#481	C₂²×C₆₇	1	2	yes	complemented
665	#476	C₂²×C₆₇	1	2	yes	complemented
666	#475	C₂²×C₆₇	1	2	yes	complemented
667	#470	C₂²×C₆₇	1	2	yes	complemented
668	#470	C₂²×C₆₇	1	2	yes	complemented
669	#470	C₂²×C₆₇	1	2	yes	complemented
670	#469	C₂²×C₆₇	1	2	yes	complemented
671	#465	C₂²×C₆₇	1	2	yes	—
672	#465	C₂²×C₆₇	1	2	yes	—
673	#465	C₂²×C₆₇	1	2	yes	complemented
674	#465	C₂²×C₆₇	1	2	yes	complemented
675	#464	C₂²×C₆₇	1	2	yes	complemented
676	#464	C₂²×C₆₇	1	2	yes	complemented
677	#463	C₂²×C₆₇	1	2	yes	complemented
678	#463	C₂²×C₆₇	1	2	yes	complemented
679	#462	C₂²×C₆₇	1	2	yes	complemented
680	#461	C₂²×C₆₇	1	2	yes	complemented
681	#452	C₂²×C₆₇	1	2	yes	—
682	#452	C₂²×C₆₇	1	2	yes	—
683	#452	C₂²×C₆₇	1	2	yes	complemented
684	#452	C₂²×C₆₇	1	2	yes	complemented
685	#452	C₂²×C₆₇	1	2	yes	complemented
686	#452	C₂²×C₆₇	1	2	yes	complemented
687	#451	C₂²×C₆₇	1	2	yes	complemented
688	#451	C₂²×C₆₇	1	2	yes	complemented
689	#451	C₂²×C₆₇	1	2	yes	complemented
690	#450	C₂²×C₆₇	1	2	yes	complemented
691	#449	C₂²×C₆₇	1	2	yes	—
692	#449	C₂²×C₆₇	1	2	yes	—
693	#449	C₂²×C₆₇	1	2	yes	complemented
694	#449	C₂²×C₆₇	1	2	yes	complemented
695	#448	C₂²×C₆₇	1	2	yes	—
696	#448	C₂²×C₆₇	1	2	yes	complemented
697	#448	C₂²×C₆₇	1	2	yes	complemented
698	#447	C₂²×C₆₇	1	2	yes	—
699	#442	C₂²×C₆₇	1	2	yes	complemented
700	#441	C₂²×C₆₇	1	2	yes	complemented
701	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
702	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
703	#436	C₂²×C₆₇	1	2	yes	complemented
704	#435	C₂²×C₆₇	1	2	yes	complemented
705	#435	C₂²×C₆₇	1	2	yes	complemented
706	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
707	#433	C₂²×C₆₇	1	2	yes	complemented
708	#417	C₂²×C₆₇	1	1	yes	characteristic
709	#417	C₂²×C₆₇	1	1	yes	characteristic
710	#417	C₂²×C₆₇	1	2	yes	complemented
711	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
712	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
713	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
714	#408	C₂²×C₆₇	1	2	yes	complemented
715	#407	C₂²×C₆₇	1	1	yes	characteristic
716	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
717	2₋¹⁺⁴	—	4	2	no	—
718	2₋¹⁺⁴	—	4	2	no	—
719	C₂×#41	—	2	1	no	—
720	C₂×#41	—	2	2	no	—
721	C₂×#41	—	2	2	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	2	1	no	—
724	C₂×#41	—	4	2	no	—
725	C₂×#41	—	4	2	no	—
726	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
727	C₂×#41	C₂³×C₆₇	1	2	yes	—
728	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
729	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
731	C₂×#41	C₂³×C₆₇	1	2	yes	—
732	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
733	C₂²×Q₈	—	2	1	no	—
734	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
735	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
736	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
737	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
738	C₂²×D₄	—	2	1	no	—
739	C₂²×D₄	—	2	1	no	—
740	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
741	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
742	C₂³×C₄	—	2	1	no	—
743	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
744	#137	—	4	4	no	—
745	AGL(1,ℤ/8)	—	4	2	no	—
746	AGL(1,ℤ/8)	—	4	2	no	—
747	#135	—	4	4	no	—
748	C₂×Q₁₆	—	4	2	no	—
749	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
750	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
751	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
752	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
753	C₂×SD₁₆	—	4	2	no	—
754	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
755	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
758	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
759	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
760	C₂×D₈	C₂³×C₆₇	1	2	yes	—
761	C₂×D₈	C₂³×C₆₇	1	2	yes	—
762	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
763	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
764	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
765	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
766	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
767	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
768	C₄⋊Q₈	—	2	2	no	—
769	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
770	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
771	#126	—	2	2	no	—
772	#125	—	2	2	no	—
773	#124	—	2	2	no	—
774	#124	—	2	2	no	—
775	#124	—	2	2	no	—
776	#124	C₂³×C₆₇	1	2	yes	—
777	#124	C₂³×C₆₇	1	2	yes	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	D₄×C₆₇	1	2	yes	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	1	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
804	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
805	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
806	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
807	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
808	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
809	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
810	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
811	#121	—	2	1	no	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	—	2	2	no	—
819	#121	—	2	1	no	—
820	#121	—	2	1	no	—
821	#121	—	2	2	no	—
822	#121	—	2	2	no	—
823	#121	D₄×C₆₇	1	1	yes	characteristic
824	#121	D₄×C₆₇	1	1	yes	characteristic
825	#121	C₂³×C₆₇	1	2	yes	—
826	#121	C₂³×C₆₇	1	2	yes	—
827	#121	C₂³×C₆₇	1	2	yes	—
828	#121	C₂³×C₆₇	1	2	yes	—
829	#120	—	2	2	no	—
830	#120	—	2	2	no	—
831	#120	D₄×C₆₇	1	2	yes	—
832	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
833	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	2	no	—
839	C₄×D₄	C₂³×C₆₇	1	2	yes	—
840	C₄×D₄	C₂³×C₆₇	1	2	yes	—
841	C₄×D₄	C₂³×C₆₇	1	2	yes	—
842	C₄×D₄	C₂³×C₆₇	1	2	yes	—
843	#117	—	2	1	no	—
844	#117	C₂³×C₆₇	1	1	yes	characteristic
845	C₂×C₄⋊C₄	—	2	1	no	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	—	2	2	no	—
849	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
850	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
851	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
852	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
853	C₂×C₂²⋊C₄	—	2	1	no	—
854	C₂×C₂²⋊C₄	—	2	1	no	—
855	C₂×C₂²⋊C₄	—	2	1	no	—
856	C₂×C₂²⋊C₄	—	2	2	no	—
857	C₂×C₂²⋊C₄	—	2	2	no	—
858	#106	C₂³×C₆₇	1	2	yes	—
859	#106	C₂³×C₆₇	1	2	yes	—
860	#106	C₂³×C₆₇	1	2	yes	—
861	#106	C₂³×C₆₇	1	2	yes	—
862	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
863	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
864	#103	C₂³×C₆₇	1	2	yes	—
865	#103	C₂³×C₆₇	1	2	yes	—
866	#103	C₂³×C₆₇	1	2	yes	—
867	#103	C₂³×C₆₇	1	2	yes	—
868	#103	C₂³×C₆₇	1	2	yes	—
869	#103	C₂³×C₆₇	1	2	yes	—
870	#103	C₂³×C₆₇	1	2	yes	—
871	#103	C₂³×C₆₇	1	2	yes	—
872	#103	C₂³×C₆₇	1	2	yes	—
873	#103	C₂³×C₆₇	1	2	yes	—
874	#102	C₂³×C₆₇	1	2	yes	—
875	#102	C₂³×C₆₇	1	2	yes	—
876	#102	C₂³×C₆₇	1	2	yes	—
877	#102	C₂³×C₆₇	1	2	yes	—
878	#102	C₂³×C₆₇	1	2	yes	—
879	#102	C₂³×C₆₇	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
886	#97	C₂³×C₆₇	1	2	yes	—
887	C₄×C₈	C₂³×C₆₇	1	2	yes	—
888	C₂⁴	—	2	1	no	—
889	C₂⁴	—	2	1	no	—
890	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
891	#41	—	2	2	no	—
892	#41	—	2	2	no	—
893	#41	—	2	2	no	—
894	#41	—	2	4	no	—
895	#41	—	2	2	no	—
896	#41	—	4	1	no	—
897	#41	—	4	1	no	—
898	#41	—	4	1	no	—
899	#41	—	4	1	no	—
900	#41	—	4	1	no	—
901	#41	—	4	1	no	—
902	#41	—	4	2	no	—
903	#41	—	4	4	no	—
904	#41	—	4	4	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	4	no	—
908	#41	—	4	8	no	—
909	#41	—	8	4	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	—	2	1	no	—
914	C₂×Q₈	—	2	2	no	—
915	C₂×Q₈	—	2	2	no	—
916	C₂×Q₈	—	2	4	no	—
917	C₂×Q₈	—	4	1	no	—
918	C₂×Q₈	—	4	2	no	—
919	C₂×Q₈	—	4	1	no	—
920	C₂×Q₈	—	4	1	no	—
921	C₂×Q₈	—	4	4	no	—
922	C₂×Q₈	—	4	1	no	—
923	C₂×Q₈	—	4	1	no	—
924	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
925	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
926	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
927	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
928	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	1	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	4	1	no	—
943	C₂×D₄	—	4	1	no	—
944	C₂×D₄	—	4	1	no	—
945	C₂×D₄	—	4	4	no	—
946	C₂×D₄	—	8	2	no	—
947	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
948	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
949	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
950	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
951	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
952	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
953	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	4	1	no	—
971	C₂²×C₄	—	4	1	no	—
972	C₂²×C₄	—	4	4	no	—
973	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
974	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
975	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
976	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
977	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
979	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
980	Q₁₆	—	2	4	no	—
981	Q₁₆	—	4	2	no	—
982	Q₁₆	—	4	2	no	—
983	Q₁₆	—	4	2	no	—
984	SD₁₆	—	2	4	no	—
985	SD₁₆	—	2	4	no	—
986	SD₁₆	—	4	2	no	—
987	SD₁₆	—	4	2	no	—
988	SD₁₆	—	4	2	no	—
989	SD₁₆	—	4	2	no	—
990	D₈	—	2	4	no	—
991	D₈	—	4	2	no	—
992	M₁₆	—	4	1	no	—
993	M₁₆	—	4	1	no	—
994	M₁₆	—	4	2	no	—
995	C₂×C₈	—	4	1	no	—
996	C₂×C₈	—	4	1	no	—
997	C₂×C₈	—	4	2	no	—
998	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
999	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1000	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1001	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1018	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1019	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1020	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1021	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1022	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1023	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1041	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1042	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1043	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1044	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1045	C₄²	—	2	2	no	—
1046	C₄²	—	2	2	no	—
1047	C₄²	C₂⁴×C₆₇	1	2	yes	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	2	2	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	—	4	1	no	—
1054	C₂³	—	4	2	no	—
1055	C₂³	—	4	2	no	—
1056	C₂³	—	4	2	no	—
1057	C₂³	—	8	1	no	—
1058	C₂³	—	8	1	no	—
1059	C₂³	—	8	1	no	—
1060	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1061	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1062	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1063	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1064	Q₈	—	2	1	no	—
1065	Q₈	—	2	2	no	—
1066	Q₈	—	2	1	no	—
1067	Q₈	—	2	2	no	—
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	2	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	4	1	no	—
1072	Q₈	—	4	4	no	—
1073	Q₈	—	4	2	no	—
1074	Q₈	—	4	2	no	—
1075	Q₈	—	8	1	no	—
1076	Q₈	—	8	2	no	—
1077	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1078	D₄	—	2	4	no	—
1079	D₄	—	2	4	no	—
1080	D₄	—	2	1	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	4	1	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	4	2	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	4	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	8	1	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	no	—
1097	D₄	—	8	2	no	—
1098	D₄	—	8	2	no	—
1099	D₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1100	C₂×C₄	—	2	4	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	2	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	4	4	no	—
1123	C₂×C₄	—	4	4	no	—
1124	C₂×C₄	—	4	2	no	—
1125	C₂×C₄	—	4	2	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	8	2	no	—
1128	C₂×C₄	—	8	2	no	—
1129	C₂×C₄	—	8	2	no	—
1130	C₂×C₄	—	8	1	no	—
1131	C₂×C₄	—	8	1	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	1	no	—
1134	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1135	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1136	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1137	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1139	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1140	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1141	C₈	—	2	2	no	—
1142	C₈	—	2	2	no	—
1143	C₈	—	2	2	no	—
1144	C₈	—	2	2	no	—
1145	C₂²	—	2	1	no	—
1146	C₂²	—	2	1	no	—
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	1	no	—
1151	C₂²	—	2	1	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	2	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	8	2	no	—
1166	C₂²	—	8	4	no	—
1167	C₂²	—	16	2	no	—
1168	C₂²	#577×C₆₇	1	2	yes	—
1169	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1170	C₄	—	2	2	no	—
1171	C₄	—	2	2	no	—
1172	C₄	—	2	1	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	2	1	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	2	1	no	—
1177	C₄	—	4	2	no	—
1178	C₄	—	4	2	no	—
1179	C₄	—	4	2	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	2	no	—
1182	C₄	—	4	2	no	—
1183	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1184	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1185	C₂	—	2	2	no	—
1186	C₂	—	4	1	no	—
1187	C₂	—	4	1	no	—
1188	C₂	—	4	2	no	—
1189	C₂	—	4	2	no	—
1190	C₂	—	8	1	no	—
1191	C₂	—	8	2	no	—
1192	C₂	C₆₇×#3484	1	1	yes	characteristic
1193	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1194	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 ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3536	C₂	semidirect
2. C₆₇×#3489	C₂	semidirect
3. C₆₇×#3331	C₂	semidirect
4. C₆₇×#3316	C₂	semidirect
5. C₆₇×#3306	C₂	semidirect
6. C₆₇×#3298	C₂	semidirect
7. C₆₇×#3282	C₂	semidirect
8. C₆₇×#3275	C₂	semidirect
9. C₆₇×#3270	C₂	semidirect
10. C₆₇×#3267	C₂	semidirect
11. C₆₇×#3225	C₂	semidirect
12. C₆₇×#3204	C₂	semidirect
13. C₆₇×#3195	C₂	semidirect
14. C₆₇×#3187	C₂	semidirect
15. C₆₇×#3125	C₂	semidirect
16. C₆₇×#3013	C₂	semidirect
17. C₆₇×#3006	C₂	semidirect
18. C₂×#452×C₆₇	C₂	semidirect
19. C₆₇×#2976	C₂	semidirect
20. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
22. C₂×#137×C₆₇	C₂²	semidirect
25. C₂×#135×C₆₇	C₂²	semidirect
26. C₂²×Q₁₆×C₆₇	C₂²	semidirect
27. C₂²×SD₁₆×C₆₇	C₂²	semidirect
29. #554×C₆₇	C₂²	semidirect
30. D₄×Q₈×C₆₇	C₂²	semidirect
38. #546×C₆₇	C₂²	semidirect
39. #546×C₆₇	C₂²	semidirect
41. #542×C₆₇	C₂²	semidirect
46. #537×C₆₇	C₂²	semidirect
47. #537×C₆₇	C₂²	semidirect
49. #536×C₆₇	C₂²	semidirect
56. #520×C₆₇	C₂²	semidirect
57. #497×C₆₇	C₂²	semidirect
58. #495×C₆₇	C₂²	semidirect
59. #489×C₆₇	C₂²	semidirect
60. #487×C₆₇	C₂²	semidirect
61. #483×C₆₇	C₂²	semidirect
62. #483×C₆₇	C₂²	semidirect
63. #483×C₆₇	C₂²	semidirect
64. #483×C₆₇	C₂²	semidirect
65. #481×C₆₇	C₂²	semidirect
66. #481×C₆₇	C₂²	semidirect
67. #476×C₆₇	C₂²	semidirect
68. #475×C₆₇	C₂²	semidirect
69. #470×C₆₇	C₂²	semidirect
70. #470×C₆₇	C₂²	semidirect
71. #470×C₆₇	C₂²	semidirect
72. #469×C₆₇	C₂²	semidirect
75. #465×C₆₇	C₂²	semidirect
76. #465×C₆₇	C₂²	semidirect
77. #464×C₆₇	C₂²	semidirect
78. #464×C₆₇	C₂²	semidirect
79. #463×C₆₇	C₂²	semidirect
80. #463×C₆₇	C₂²	semidirect
81. #462×C₆₇	C₂²	semidirect
82. #461×C₆₇	C₂²	semidirect
85. #452×C₆₇	C₂²	semidirect
86. #452×C₆₇	C₂²	semidirect
87. #452×C₆₇	C₂²	semidirect
88. #452×C₆₇	C₂²	semidirect
89. #451×C₆₇	C₂²	semidirect
90. #451×C₆₇	C₂²	semidirect
91. #451×C₆₇	C₂²	semidirect
92. #450×C₆₇	C₂²	semidirect
95. #449×C₆₇	C₂²	semidirect
96. #449×C₆₇	C₂²	semidirect
98. #448×C₆₇	C₂²	semidirect
99. #448×C₆₇	C₂²	semidirect
101. #442×C₆₇	C₂²	semidirect
102. #441×C₆₇	C₂²	semidirect
103. C₄×SD₁₆×C₆₇	C₂²	semidirect
104. C₄×SD₁₆×C₆₇	C₂²	semidirect
105. #436×C₆₇	C₂²	semidirect
106. #435×C₆₇	C₂²	semidirect
107. #435×C₆₇	C₂²	semidirect
108. C₈×D₄×C₆₇	C₂²	semidirect
109. #433×C₆₇	C₂²	semidirect
112. #417×C₆₇	C₂²	semidirect
113. C₂×#103×C₆₇	C₂²	semidirect
114. C₂×#103×C₆₇	C₂²	semidirect
115. C₂×#102×C₆₇	C₂²	semidirect
116. #408×C₆₇	C₂²	semidirect
587. #61620	C₆₇	direct (N × H)
598. #3536	C₂×C₆₇	semidirect
599. #3489	C₂×C₆₇	semidirect
600. #3331	C₂×C₆₇	semidirect
601. #3316	C₂×C₆₇	semidirect
602. #3306	C₂×C₆₇	semidirect
603. #3298	C₂×C₆₇	semidirect
604. #3282	C₂×C₆₇	semidirect
605. #3275	C₂×C₆₇	semidirect
606. #3270	C₂×C₆₇	semidirect
607. #3267	C₂×C₆₇	semidirect
608. #3225	C₂×C₆₇	semidirect
609. #3204	C₂×C₆₇	semidirect
610. #3195	C₂×C₆₇	semidirect
611. #3187	C₂×C₆₇	semidirect
612. #3125	C₂×C₆₇	semidirect
613. #3013	C₂×C₆₇	semidirect
614. #3006	C₂×C₆₇	semidirect
615. C₂×#452	C₂×C₆₇	semidirect
616. #2976	C₂×C₆₇	semidirect
617. C₆₇	#61620	direct (N × H)
618. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
620. C₂×#137	C₂²×C₆₇	semidirect
623. C₂×#135	C₂²×C₆₇	semidirect
624. C₂²×Q₁₆	C₂²×C₆₇	semidirect
625. C₂²×SD₁₆	C₂²×C₆₇	semidirect
627. #554	C₂²×C₆₇	semidirect
628. D₄×Q₈	C₂²×C₆₇	semidirect
636. #546	C₂²×C₆₇	semidirect
637. #546	C₂²×C₆₇	semidirect
639. #542	C₂²×C₆₇	semidirect
644. #537	C₂²×C₆₇	semidirect
645. #537	C₂²×C₆₇	semidirect
647. #536	C₂²×C₆₇	semidirect
654. #520	C₂²×C₆₇	semidirect
655. #497	C₂²×C₆₇	semidirect
656. #495	C₂²×C₆₇	semidirect
657. #489	C₂²×C₆₇	semidirect
658. #487	C₂²×C₆₇	semidirect
659. #483	C₂²×C₆₇	semidirect
660. #483	C₂²×C₆₇	semidirect
661. #483	C₂²×C₆₇	semidirect
662. #483	C₂²×C₆₇	semidirect
663. #481	C₂²×C₆₇	semidirect
664. #481	C₂²×C₆₇	semidirect
665. #476	C₂²×C₆₇	semidirect
666. #475	C₂²×C₆₇	semidirect
667. #470	C₂²×C₆₇	semidirect
668. #470	C₂²×C₆₇	semidirect
669. #470	C₂²×C₆₇	semidirect
670. #469	C₂²×C₆₇	semidirect
673. #465	C₂²×C₆₇	semidirect
674. #465	C₂²×C₆₇	semidirect
675. #464	C₂²×C₆₇	semidirect
676. #464	C₂²×C₆₇	semidirect
677. #463	C₂²×C₆₇	semidirect
678. #463	C₂²×C₆₇	semidirect
679. #462	C₂²×C₆₇	semidirect
680. #461	C₂²×C₆₇	semidirect
683. #452	C₂²×C₆₇	semidirect
684. #452	C₂²×C₆₇	semidirect
685. #452	C₂²×C₆₇	semidirect
686. #452	C₂²×C₆₇	semidirect
687. #451	C₂²×C₆₇	semidirect
688. #451	C₂²×C₆₇	semidirect
689. #451	C₂²×C₆₇	semidirect
690. #450	C₂²×C₆₇	semidirect
693. #449	C₂²×C₆₇	semidirect
694. #449	C₂²×C₆₇	semidirect
696. #448	C₂²×C₆₇	semidirect
697. #448	C₂²×C₆₇	semidirect
699. #442	C₂²×C₆₇	semidirect
700. #441	C₂²×C₆₇	semidirect
701. C₄×SD₁₆	C₂²×C₆₇	semidirect
702. C₄×SD₁₆	C₂²×C₆₇	semidirect
703. #436	C₂²×C₆₇	semidirect
704. #435	C₂²×C₆₇	semidirect
705. #435	C₂²×C₆₇	semidirect
706. C₈×D₄	C₂²×C₆₇	semidirect
707. #433	C₂²×C₆₇	semidirect
710. #417	C₂²×C₆₇	semidirect
711. C₂×#103	C₂²×C₆₇	semidirect
712. C₂×#103	C₂²×C₆₇	semidirect
713. C₂×#102	C₂²×C₆₇	semidirect
714. #408	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3536	2
C₆₇×#3489	2
C₆₇×#3331	2
C₆₇×#3316	2
C₆₇×#3306	2
C₆₇×#3298	2
C₆₇×#3282	2
C₆₇×#3275	2
C₆₇×#3270	2
C₆₇×#3267	2
C₆₇×#3225	2
C₆₇×#3204	2
C₆₇×#3195	2
C₆₇×#3187	2
C₆₇×#3125	2
C₆₇×#3013	2
C₆₇×#3006	2
C₂×#452×C₆₇	2
C₆₇×#2976	2
#61620	67

Subgroups — C67×#61620 #30740871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61620 #30740871