Subgroups — C₇×#62887 #13240103

Order 1792.

6910 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3562	C₂	1	8	yes	maximal, complemented
2	C₇×#3561	C₂	1	8	yes	maximal, complemented
3	C₇×#3554	C₂	1	8	yes	maximal, complemented
4	C₇×#3552	C₂	1	8	yes	maximal, complemented
5	C₇×#3535	C₂	1	8	yes	maximal, complemented
6	C₇×#3533	C₂	1	8	yes	maximal, complemented
7	C₇×#3510	C₂	1	2	yes	maximal, complemented
8	C₇×#3509	C₂	1	2	yes	maximal, complemented
9	C₇×#3500	C₂	1	2	yes	maximal, complemented
10	C₇×#3499	C₂	1	2	yes	maximal, complemented
11	C₇×#3487	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3486	C₂	1	2	yes	maximal, complemented
13	C₇×#3485	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3455	C₂	1	2	yes	maximal, complemented
15	C₂×C₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×2₋¹⁺⁴	C₂²	1	2	yes	—
17	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
19	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
20	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₇×#563	C₂²	1	16	yes	complemented
22	C₇×#563	C₂²	1	8	yes	complemented
23	C₇×#562	C₂²	1	16	yes	complemented
24	C₇×#562	C₂²	1	16	yes	complemented
25	C₇×#560	C₂²	1	8	yes	complemented
26	C₇×#559	C₂²	1	8	yes	complemented
27	C₇×#559	C₂²	1	8	yes	complemented
28	C₇×#557	C₂²	1	8	yes	complemented
29	C₇×#556	C₂²	1	8	yes	complemented
30	C₇×#556	C₂²	1	8	yes	complemented
31	C₇×#554	C₂²	1	16	yes	complemented
32	C₇×#553	C₂²	1	16	yes	complemented
33	C₇×#552	C₂²	1	16	yes	complemented
34	C₇×#551	C₂²	1	8	yes	complemented
35	C₇×#551	C₂²	1	16	yes	complemented
36	C₇×#551	C₂²	1	16	yes	complemented
37	C₇×#550	C₂²	1	8	yes	complemented
38	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
39	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
40	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
41	C₇×#548	C₂²	1	8	yes	complemented
42	C₇×#548	C₂²	1	8	yes	complemented
43	C₇×#548	C₂²	1	8	yes	complemented
44	C₇×#548	C₂²	1	8	yes	complemented
45	C₇×#547	C₂²	1	8	yes	—
46	C₇×#547	C₂²	1	8	yes	complemented
47	C₇×#547	C₂²	1	16	yes	complemented
48	C₇×#546	C₂²	1	8	yes	—
49	C₇×#546	C₂²	1	16	yes	—
50	C₇×#546	C₂²	1	8	yes	complemented
51	C₇×#544	C₂²	1	8	yes	complemented
52	C₇×#543	C₂²	1	8	yes	complemented
53	C₇×#542	C₂²	1	4	yes	complemented
54	C₇×#542	C₂²	1	8	yes	complemented
55	C₇×#542	C₂²	1	16	yes	complemented
56	C₇×#542	C₂²	1	16	yes	complemented
57	C₇×#542	C₂²	1	4	yes	complemented
58	C₇×#541	C₂²	1	8	yes	complemented
59	C₇×#541	C₂²	1	4	yes	complemented
60	C₇×#540	C₂²	1	4	yes	complemented
61	C₇×#540	C₂²	1	16	yes	complemented
62	C₇×#539	C₂²	1	16	yes	complemented
63	C₇×#539	C₂²	1	8	yes	complemented
64	C₇×#539	C₂²	1	16	yes	complemented
65	C₇×#539	C₂²	1	8	yes	complemented
66	C₇×#538	C₂²	1	16	yes	complemented
67	C₇×#538	C₂²	1	8	yes	complemented
68	C₇×#538	C₂²	1	8	yes	complemented
69	C₇×#536	C₂²	1	2	yes	—
70	C₇×#536	C₂²	1	2	yes	—
71	C₇×#536	C₂²	1	4	yes	complemented
72	C₇×#536	C₂²	1	8	yes	complemented
73	C₇×#536	C₂²	1	8	yes	complemented
74	C₇×#536	C₂²	1	2	yes	complemented
75	C₇×#536	C₂²	1	8	yes	complemented
76	C₇×#536	C₂²	1	4	yes	complemented
77	C₇×#536	C₂²	1	4	yes	complemented
78	C₇×#535	C₂²	1	2	yes	—
79	C₇×#535	C₂²	1	4	yes	complemented
80	C₇×#535	C₂²	1	4	yes	complemented
81	C₇×#534	C₂²	1	4	yes	—
82	C₇×#533	C₂²	1	8	yes	complemented
83	C₇×#533	C₂²	1	2	yes	complemented
84	C₇×#532	C₂²	1	2	yes	—
85	C₇×#532	C₂²	1	4	yes	complemented
86	C₇×#532	C₂²	1	4	yes	complemented
87	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
88	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	complemented
89	C₇×#529	C₂²	1	8	yes	complemented
90	C₇×#529	C₂²	1	8	yes	complemented
91	C₇×#529	C₂²	1	8	yes	complemented
92	C₂×C₇×#124	C₂²	1	2	yes	—
93	C₂×C₇×#124	C₂²	1	4	yes	complemented
94	C₇×#525	C₂²	1	2	yes	—
95	C₇×#525	C₂²	1	2	yes	complemented
96	C₇×#525	C₂²	1	8	yes	complemented
97	C₇×#525	C₂²	1	4	yes	complemented
98	C₂×C₇×#123	C₂²	1	4	yes	—
99	C₂×C₇×#123	C₂²	1	4	yes	complemented
100	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
101	C₇×#519	C₂²	1	2	yes	complemented
102	C₇×#519	C₂²	1	1	yes	characteristic, complemented
103	C₇×#518	C₂²	1	1	yes	characteristic
104	C₄×C₇×#41	C₂²	1	2	yes	—
105	C₄×C₇×#41	C₂²	1	2	yes	complemented
106	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
107	#62887	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₇×2₋¹⁺⁴	—	4	8	no	—
109	C₇×2₋¹⁺⁴	—	4	4	no	—
110	C₇×H(5,𝔽₂)	—	4	4	no	—
111	C₂×C₇×#41	—	4	4	no	—
112	C₂×C₇×#41	C₂³	1	2	yes	—
113	C₂×C₇×#41	C₂³	1	2	yes	—
114	C₂×C₇×#41	C₂³	1	8	yes	—
115	C₂×C₇×#41	C₂³	1	4	yes	—
116	C₂×C₇×#41	C₂³	1	8	yes	—
117	C₂×C₇×#41	C₂³	1	4	yes	—
118	C₂×C₇×#41	C₂³	1	4	yes	—
119	C₂×C₇×#41	C₂³	1	4	yes	—
120	C₂×C₇×#41	C₂³	1	4	yes	—
121	C₂²×C₇×Q₈	—	4	4	no	—
122	C₂²×C₇×Q₈	C₂³	1	2	yes	—
123	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
124	C₂²×C₇×Q₈	C₂³	1	2	yes	—
125	C₂²×C₇×Q₈	C₂³	1	8	yes	—
126	C₂²×C₇×Q₈	C₂³	1	4	yes	—
127	C₂²×C₇×Q₈	C₂³	1	4	yes	—
128	C₂²×C₇×Q₈	C₂³	1	4	yes	—
129	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
130	C₂²×C₇×D₄	C₂³	1	2	yes	—
131	C₂²×C₇×D₄	C₂³	1	4	yes	—
132	C₂²×C₇×D₄	C₂³	1	4	yes	—
133	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₇	C₂³	1	2	yes	—
136	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
138	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
139	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
140	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
141	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
142	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
143	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
144	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
145	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
146	C₇×#127	C₂³	1	2	yes	—
147	C₇×#127	C₂³	1	4	yes	—
148	C₇×#127	C₂³	1	8	yes	—
149	C₇×#126	C₂³	1	8	yes	—
150	C₇×#126	C₂³	1	16	yes	—
151	C₇×#126	C₂³	1	8	yes	—
152	C₇×#126	C₂³	1	8	yes	—
153	C₇×#126	C₂³	1	8	yes	—
154	C₇×#126	C₂³	1	16	yes	—
155	C₇×#126	C₂³	1	16	yes	—
156	C₇×#126	C₂³	1	16	yes	—
157	C₇×#125	C₂³	1	4	yes	—
158	C₇×#125	C₂³	1	8	yes	—
159	C₇×#125	C₂³	1	8	yes	—
160	C₇×#125	C₂³	1	16	yes	—
161	C₇×#125	C₂³	1	16	yes	—
162	C₇×#125	C₂³	1	16	yes	—
163	C₇×#124	C₂³	1	4	yes	—
164	C₇×#124	C₂³	1	4	yes	—
165	C₇×#124	C₂³	1	8	yes	—
166	C₇×#124	C₂³	1	2	yes	—
167	C₇×#124	C₂³	1	4	yes	—
168	C₇×#124	C₂³	1	4	yes	—
169	C₇×#124	C₂³	1	16	yes	—
170	C₇×#124	C₂³	1	8	yes	—
171	C₇×#124	C₂³	1	8	yes	—
172	C₇×#124	C₂³	1	2	yes	—
173	C₇×#124	C₂³	1	4	yes	—
174	C₇×#124	C₂³	1	4	yes	—
175	C₇×#124	C₂³	1	8	yes	—
176	C₇×#124	C₂³	1	16	yes	—
177	C₇×#124	C₂³	1	16	yes	—
178	C₇×#123	C₂³	1	4	yes	—
179	C₇×#123	C₂³	1	8	yes	—
180	C₇×#123	C₂³	1	16	yes	—
181	C₇×#123	C₂³	1	16	yes	—
182	C₇×#123	C₂³	1	8	yes	—
183	C₇×#123	C₂³	1	8	yes	—
184	C₇×#123	C₂³	1	4	yes	—
185	C₇×#123	C₂³	1	8	yes	—
186	C₇×#123	C₂³	1	8	yes	—
187	C₇×#123	C₂³	1	8	yes	—
188	C₇×#123	C₂³	1	8	yes	—
189	C₇×#123	C₂³	1	8	yes	—
190	C₇×#123	C₂³	1	16	yes	—
191	C₇×#123	C₂³	1	8	yes	—
192	C₇×#123	C₂³	1	8	yes	—
193	C₇×#123	C₂³	1	16	yes	—
194	C₇×#123	C₂³	1	16	yes	—
195	C₇×#123	C₂³	1	16	yes	—
196	C₇×#123	C₂³	1	16	yes	—
197	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
198	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
199	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
200	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
201	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
202	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
203	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
204	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
205	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
206	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
207	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
208	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
209	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
210	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
211	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
212	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
213	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
214	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
215	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
216	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
217	C₇×#121	C₂³	1	4	yes	—
218	C₇×#121	C₂³	1	8	yes	—
219	C₇×#121	C₂³	1	16	yes	—
220	C₇×#121	C₂³	1	4	yes	—
221	C₇×#121	C₂³	1	8	yes	—
222	C₇×#121	C₂³	1	8	yes	—
223	C₇×#121	C₂³	1	8	yes	—
224	C₇×#121	C₂³	1	8	yes	—
225	C₇×#121	C₂³	1	16	yes	—
226	C₇×#121	C₂³	1	16	yes	—
227	C₇×#121	C₂³	1	16	yes	—
228	C₇×#121	C₂³	1	16	yes	—
229	C₇×#121	C₂³	1	16	yes	—
230	C₇×#120	C₂³	1	4	yes	—
231	C₇×#120	C₂³	1	4	yes	—
232	C₇×#120	C₂³	1	8	yes	—
233	C₇×#120	C₂³	1	8	yes	—
234	C₇×#120	C₂³	1	16	yes	—
235	C₄×C₇×Q₈	C₂³	1	4	yes	—
236	C₄×C₇×Q₈	C₂³	1	4	yes	—
237	C₄×C₇×Q₈	C₂³	1	8	yes	—
238	C₄×C₇×Q₈	C₂³	1	8	yes	—
239	C₄×C₇×Q₈	C₂³	1	8	yes	—
240	C₄×C₇×Q₈	C₂³	1	8	yes	—
241	C₄×C₇×Q₈	C₂³	1	16	yes	—
242	C₄×C₇×D₄	C₂³	1	8	yes	—
243	C₄×C₇×D₄	C₂³	1	4	yes	—
244	C₄×C₇×D₄	C₂³	1	8	yes	—
245	C₄×C₇×D₄	C₂³	1	4	yes	—
246	C₄×C₇×D₄	C₂³	1	8	yes	—
247	C₄×C₇×D₄	C₂³	1	8	yes	—
248	C₄×C₇×D₄	C₂³	1	8	yes	—
249	C₄×C₇×D₄	C₂³	1	16	yes	—
250	C₄×C₇×D₄	C₂³	1	16	yes	—
251	C₄×C₇×D₄	C₂³	1	16	yes	—
252	C₄×C₇×D₄	C₂³	1	8	yes	—
253	C₄×C₇×D₄	C₂³	1	16	yes	—
254	C₄×C₇×D₄	C₂³	1	16	yes	—
255	C₄×C₇×D₄	C₂³	1	16	yes	—
256	C₇×#117	C₂³	1	4	yes	—
257	C₇×#117	C₂³	1	4	yes	—
258	C₇×#117	C₂³	1	2	yes	—
259	C₇×#117	C₂³	1	4	yes	—
260	C₇×#117	C₂³	1	2	yes	—
261	C₇×#117	C₂³	1	4	yes	—
262	C₇×#117	C₂³	1	4	yes	—
263	C₇×#117	C₂³	1	8	yes	—
264	C₇×#117	C₂³	1	16	yes	—
265	C₇×#117	C₂³	1	16	yes	—
266	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
267	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
268	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
269	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
270	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
271	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
272	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
273	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
274	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
275	C₂×C₄²×C₇	C₂³	1	2	yes	—
276	C₂×C₄²×C₇	C₂³	1	4	yes	—
277	C₂×C₄²×C₇	C₂³	1	4	yes	—
278	#3562	C₂×C₇	1	8	yes	complemented
279	#3561	C₂×C₇	1	8	yes	complemented
280	#3554	C₂×C₇	1	8	yes	complemented
281	#3552	C₂×C₇	1	8	yes	complemented
282	#3535	C₂×C₇	1	8	yes	complemented
283	#3533	C₂×C₇	1	8	yes	complemented
284	#3510	C₂×C₇	1	2	yes	complemented
285	#3509	C₂×C₇	1	2	yes	complemented
286	#3500	C₂×C₇	1	2	yes	complemented
287	#3499	C₂×C₇	1	2	yes	complemented
288	#3487	C₂×C₇	1	1	yes	characteristic, complemented
289	#3486	C₂×C₇	1	2	yes	complemented
290	#3485	C₂×C₇	1	1	yes	characteristic, complemented
291	#3455	C₂×C₇	1	2	yes	complemented
292	C₂×#536	C₂×C₇	1	1	yes	characteristic, complemented
293	C₂⁴×C₇	C₂⁴	1	2	yes	—
294	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
295	C₂⁴×C₇	C₂⁴	1	4	yes	—
296	C₇×#41	—	2	8	no	—
297	C₇×#41	—	2	8	no	—
298	C₇×#41	—	4	8	no	—
299	C₇×#41	—	4	16	no	—
300	C₇×#41	—	4	16	no	—
301	C₇×#41	—	4	8	no	—
302	C₇×#41	—	4	8	no	—
303	C₇×#41	—	4	8	no	—
304	C₇×#41	—	4	8	no	—
305	C₂×C₇×Q₈	—	2	8	no	—
306	C₂×C₇×Q₈	—	2	4	no	—
307	C₂×C₇×Q₈	—	4	4	no	—
308	C₂×C₇×Q₈	—	4	16	no	—
309	C₂×C₇×Q₈	—	4	8	no	—
310	C₂×C₇×Q₈	—	4	8	no	—
311	C₂×C₇×Q₈	—	4	8	no	—
312	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
313	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
314	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
315	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
316	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
317	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
318	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
319	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
320	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
321	C₂×C₇×D₄	—	2	4	no	—
322	C₂×C₇×D₄	—	4	8	no	—
323	C₂×C₇×D₄	—	4	4	no	—
324	C₂×C₇×D₄	—	4	8	no	—
325	C₂×C₇×D₄	C₂⁴	1	4	yes	—
326	C₂×C₇×D₄	C₂⁴	1	4	yes	—
327	C₂×C₇×D₄	C₂⁴	1	4	yes	—
328	C₂×C₇×D₄	C₂⁴	1	2	yes	—
329	C₂×C₇×D₄	C₂⁴	1	2	yes	—
330	C₂×C₇×D₄	C₂⁴	1	8	yes	—
331	C₂×C₇×D₄	C₂⁴	1	8	yes	—
332	C₂×C₇×D₄	C₂⁴	1	16	yes	—
333	C₂×C₇×D₄	C₂⁴	1	8	yes	—
334	C₂×C₇×D₄	C₂⁴	1	8	yes	—
335	C₂×C₇×D₄	C₂⁴	1	8	yes	—
336	C₂×C₇×D₄	C₂⁴	1	8	yes	—
337	C₂×C₇×D₄	C₂⁴	1	4	yes	—
338	C₂²×C₄×C₇	—	2	4	no	—
339	C₂²×C₄×C₇	—	4	4	no	—
340	C₂²×C₄×C₇	—	4	4	no	—
341	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
342	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
343	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
344	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
347	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
348	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
349	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
350	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
351	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
352	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
353	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
354	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
355	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
356	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
357	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
358	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
359	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
360	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
361	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
362	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
363	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
364	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
365	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
366	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
367	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
368	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
369	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
370	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
371	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
372	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
373	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
374	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
375	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
376	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
377	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
378	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
379	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
380	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
381	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
382	C₇×C₂²⋊C₄	C₂⁴	1	2	yes	—
383	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
384	C₇×C₂²⋊C₄	C₂⁴	1	2	yes	—
385	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
386	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
387	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
388	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
389	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
390	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
391	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
392	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
393	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
394	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
395	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
396	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
397	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
398	C₄²×C₇	C₂⁴	1	2	yes	—
399	C₄²×C₇	C₂⁴	1	2	yes	—
400	C₄²×C₇	C₂⁴	1	4	yes	—
401	C₄²×C₇	C₂⁴	1	4	yes	—
402	C₄²×C₇	C₂⁴	1	8	yes	—
403	C₄²×C₇	C₂⁴	1	4	yes	—
404	C₄²×C₇	C₂⁴	1	8	yes	—
405	C₄²×C₇	C₂⁴	1	16	yes	—
406	C₄²×C₇	C₂⁴	1	8	yes	—
407	C₂×2₋¹⁺⁴	C₂²×C₇	1	2	yes	—
408	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic, complemented
409	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
410	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
411	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
412	#563	C₂²×C₇	1	8	yes	complemented
413	#563	C₂²×C₇	1	16	yes	complemented
414	#562	C₂²×C₇	1	16	yes	complemented
415	#562	C₂²×C₇	1	16	yes	complemented
416	#560	C₂²×C₇	1	8	yes	complemented
417	#559	C₂²×C₇	1	8	yes	complemented
418	#559	C₂²×C₇	1	8	yes	complemented
419	#557	C₂²×C₇	1	8	yes	complemented
420	#556	C₂²×C₇	1	8	yes	complemented
421	#556	C₂²×C₇	1	8	yes	complemented
422	#554	C₂²×C₇	1	16	yes	complemented
423	#553	C₂²×C₇	1	16	yes	complemented
424	#552	C₂²×C₇	1	16	yes	complemented
425	#551	C₂²×C₇	1	16	yes	complemented
426	#551	C₂²×C₇	1	8	yes	complemented
427	#551	C₂²×C₇	1	16	yes	complemented
428	#550	C₂²×C₇	1	8	yes	complemented
429	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
430	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
431	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
432	#548	C₂²×C₇	1	8	yes	complemented
433	#548	C₂²×C₇	1	8	yes	complemented
434	#548	C₂²×C₇	1	8	yes	complemented
435	#548	C₂²×C₇	1	8	yes	complemented
436	#547	C₂²×C₇	1	8	yes	—
437	#547	C₂²×C₇	1	16	yes	complemented
438	#547	C₂²×C₇	1	8	yes	complemented
439	#546	C₂²×C₇	1	8	yes	—
440	#546	C₂²×C₇	1	16	yes	—
441	#546	C₂²×C₇	1	8	yes	complemented
442	#544	C₂²×C₇	1	8	yes	complemented
443	#543	C₂²×C₇	1	8	yes	complemented
444	#542	C₂²×C₇	1	4	yes	complemented
445	#542	C₂²×C₇	1	4	yes	complemented
446	#542	C₂²×C₇	1	8	yes	complemented
447	#542	C₂²×C₇	1	16	yes	complemented
448	#542	C₂²×C₇	1	16	yes	complemented
449	#541	C₂²×C₇	1	4	yes	complemented
450	#541	C₂²×C₇	1	8	yes	complemented
451	#540	C₂²×C₇	1	4	yes	complemented
452	#540	C₂²×C₇	1	16	yes	complemented
453	#539	C₂²×C₇	1	8	yes	complemented
454	#539	C₂²×C₇	1	16	yes	complemented
455	#539	C₂²×C₇	1	16	yes	complemented
456	#539	C₂²×C₇	1	8	yes	complemented
457	#538	C₂²×C₇	1	8	yes	complemented
458	#538	C₂²×C₇	1	16	yes	complemented
459	#538	C₂²×C₇	1	8	yes	complemented
460	#536	C₂²×C₇	1	2	yes	—
461	#536	C₂²×C₇	1	2	yes	—
462	#536	C₂²×C₇	1	8	yes	complemented
463	#536	C₂²×C₇	1	8	yes	complemented
464	#536	C₂²×C₇	1	2	yes	complemented
465	#536	C₂²×C₇	1	8	yes	complemented
466	#536	C₂²×C₇	1	4	yes	complemented
467	#536	C₂²×C₇	1	4	yes	complemented
468	#536	C₂²×C₇	1	4	yes	complemented
469	#535	C₂²×C₇	1	2	yes	—
470	#535	C₂²×C₇	1	4	yes	complemented
471	#535	C₂²×C₇	1	4	yes	complemented
472	#534	C₂²×C₇	1	4	yes	—
473	#533	C₂²×C₇	1	2	yes	complemented
474	#533	C₂²×C₇	1	8	yes	complemented
475	#532	C₂²×C₇	1	2	yes	—
476	#532	C₂²×C₇	1	4	yes	complemented
477	#532	C₂²×C₇	1	4	yes	complemented
478	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
479	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	complemented
480	#529	C₂²×C₇	1	8	yes	complemented
481	#529	C₂²×C₇	1	8	yes	complemented
482	#529	C₂²×C₇	1	8	yes	complemented
483	C₂×#124	C₂²×C₇	1	2	yes	—
484	C₂×#124	C₂²×C₇	1	4	yes	complemented
485	#525	C₂²×C₇	1	2	yes	—
486	#525	C₂²×C₇	1	2	yes	complemented
487	#525	C₂²×C₇	1	8	yes	complemented
488	#525	C₂²×C₇	1	4	yes	complemented
489	C₂×#123	C₂²×C₇	1	4	yes	—
490	C₂×#123	C₂²×C₇	1	4	yes	complemented
491	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
492	#519	C₂²×C₇	1	2	yes	complemented
493	#519	C₂²×C₇	1	1	yes	characteristic, complemented
494	#518	C₂²×C₇	1	1	yes	characteristic
495	C₄×#41	C₂²×C₇	1	2	yes	—
496	C₄×#41	C₂²×C₇	1	2	yes	complemented
497	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
498	C₂³×C₇	—	2	2	no	—
499	C₂³×C₇	—	2	4	no	—
500	C₂³×C₇	—	4	2	no	—
501	C₂³×C₇	—	4	4	no	—
502	C₂³×C₇	—	4	4	no	—
503	C₂³×C₇	—	4	8	no	—
504	C₂³×C₇	C₂⁵	1	4	yes	—
505	C₂³×C₇	C₂⁵	1	4	yes	—
506	C₂³×C₇	C₂⁵	1	2	yes	—
507	C₂³×C₇	C₂⁵	1	4	yes	—
508	C₂³×C₇	C₂⁵	1	1	yes	characteristic
509	C₇×Q₈	—	2	8	no	—
510	C₇×Q₈	—	2	8	no	—
511	C₇×Q₈	—	2	8	no	—
512	C₇×Q₈	—	2	4	no	—
513	C₇×Q₈	—	2	4	no	—
514	C₇×Q₈	—	4	8	no	—
515	C₇×Q₈	—	4	8	no	—
516	C₇×Q₈	—	4	4	no	—
517	C₇×Q₈	—	4	8	no	—
518	C₇×D₄	—	2	8	no	—
519	C₇×D₄	—	2	8	no	—
520	C₇×D₄	—	2	8	no	—
521	C₇×D₄	—	2	4	no	—
522	C₇×D₄	—	2	4	no	—
523	C₇×D₄	—	4	8	no	—
524	C₇×D₄	—	4	8	no	—
525	C₇×D₄	—	4	8	no	—
526	C₇×D₄	—	4	8	no	—
527	C₇×D₄	—	4	16	no	—
528	C₇×D₄	—	4	8	no	—
529	C₇×D₄	—	4	4	no	—
530	C₇×D₄	—	4	8	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	4	no	—
533	C₂×C₄×C₇	—	2	8	no	—
534	C₂×C₄×C₇	—	2	8	no	—
535	C₂×C₄×C₇	—	2	8	no	—
536	C₂×C₄×C₇	—	2	8	no	—
537	C₂×C₄×C₇	—	4	8	no	—
538	C₂×C₄×C₇	—	4	8	no	—
539	C₂×C₄×C₇	—	4	8	no	—
540	C₂×C₄×C₇	—	4	4	no	—
541	C₂×C₄×C₇	—	4	8	no	—
542	C₂×C₄×C₇	—	4	8	no	—
543	C₂×C₄×C₇	—	4	4	no	—
544	C₂×C₄×C₇	—	4	8	no	—
545	C₂×C₄×C₇	—	4	8	no	—
546	C₂×C₄×C₇	—	4	8	no	—
547	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
548	C₂×C₄×C₇	C₂⁵	1	8	yes	—
549	C₂×C₄×C₇	C₂⁵	1	4	yes	—
550	C₂×C₄×C₇	C₂⁵	1	8	yes	—
551	C₂×C₄×C₇	C₂⁵	1	4	yes	—
552	C₂×C₄×C₇	C₂⁵	1	4	yes	—
553	C₂×C₄×C₇	C₂⁵	1	8	yes	—
554	C₂×C₄×C₇	C₂⁵	1	4	yes	—
555	C₂×C₄×C₇	C₂⁵	1	4	yes	—
556	C₂×C₄×C₇	C₂⁵	1	2	yes	—
557	C₂×C₄×C₇	C₂⁵	1	2	yes	—
558	2₋¹⁺⁴	—	4	8	no	—
559	2₋¹⁺⁴	—	4	4	no	—
560	H(5,𝔽₂)	—	4	4	no	—
561	C₂×#41	—	4	4	no	—
562	C₂×#41	C₂³×C₇	1	2	yes	—
563	C₂×#41	C₂³×C₇	1	2	yes	—
564	C₂×#41	C₂³×C₇	1	4	yes	—
565	C₂×#41	C₂³×C₇	1	8	yes	—
566	C₂×#41	C₂³×C₇	1	4	yes	—
567	C₂×#41	C₂³×C₇	1	4	yes	—
568	C₂×#41	C₂³×C₇	1	4	yes	—
569	C₂×#41	C₂³×C₇	1	4	yes	—
570	C₂×#41	C₂³×C₇	1	8	yes	—
571	C₂²×Q₈	—	4	4	no	—
572	C₂²×Q₈	C₂³×C₇	1	2	yes	—
573	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
574	C₂²×Q₈	C₂³×C₇	1	2	yes	—
575	C₂²×Q₈	C₂³×C₇	1	4	yes	—
576	C₂²×Q₈	C₂³×C₇	1	4	yes	—
577	C₂²×Q₈	C₂³×C₇	1	4	yes	—
578	C₂²×Q₈	C₂³×C₇	1	8	yes	—
579	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
580	C₂²×D₄	C₂³×C₇	1	4	yes	—
581	C₂²×D₄	C₂³×C₇	1	2	yes	—
582	C₂²×D₄	C₂³×C₇	1	4	yes	—
583	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
584	C₂³×C₄	C₂³×C₇	1	2	yes	—
585	C₂³×C₄	C₂³×C₇	1	2	yes	—
586	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
587	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
588	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
589	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
590	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
591	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
592	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
593	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
594	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
595	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
596	#127	C₂³×C₇	1	2	yes	—
597	#127	C₂³×C₇	1	4	yes	—
598	#127	C₂³×C₇	1	8	yes	—
599	#126	C₂³×C₇	1	8	yes	—
600	#126	C₂³×C₇	1	16	yes	—
601	#126	C₂³×C₇	1	8	yes	—
602	#126	C₂³×C₇	1	8	yes	—
603	#126	C₂³×C₇	1	8	yes	—
604	#126	C₂³×C₇	1	16	yes	—
605	#126	C₂³×C₇	1	16	yes	—
606	#126	C₂³×C₇	1	16	yes	—
607	#125	C₂³×C₇	1	4	yes	—
608	#125	C₂³×C₇	1	8	yes	—
609	#125	C₂³×C₇	1	8	yes	—
610	#125	C₂³×C₇	1	16	yes	—
611	#125	C₂³×C₇	1	16	yes	—
612	#125	C₂³×C₇	1	16	yes	—
613	#124	C₂³×C₇	1	4	yes	—
614	#124	C₂³×C₇	1	4	yes	—
615	#124	C₂³×C₇	1	8	yes	—
616	#124	C₂³×C₇	1	2	yes	—
617	#124	C₂³×C₇	1	4	yes	—
618	#124	C₂³×C₇	1	4	yes	—
619	#124	C₂³×C₇	1	16	yes	—
620	#124	C₂³×C₇	1	8	yes	—
621	#124	C₂³×C₇	1	8	yes	—
622	#124	C₂³×C₇	1	2	yes	—
623	#124	C₂³×C₇	1	4	yes	—
624	#124	C₂³×C₇	1	4	yes	—
625	#124	C₂³×C₇	1	8	yes	—
626	#124	C₂³×C₇	1	16	yes	—
627	#124	C₂³×C₇	1	16	yes	—
628	#123	C₂³×C₇	1	4	yes	—
629	#123	C₂³×C₇	1	8	yes	—
630	#123	C₂³×C₇	1	16	yes	—
631	#123	C₂³×C₇	1	16	yes	—
632	#123	C₂³×C₇	1	8	yes	—
633	#123	C₂³×C₇	1	8	yes	—
634	#123	C₂³×C₇	1	4	yes	—
635	#123	C₂³×C₇	1	8	yes	—
636	#123	C₂³×C₇	1	8	yes	—
637	#123	C₂³×C₇	1	8	yes	—
638	#123	C₂³×C₇	1	8	yes	—
639	#123	C₂³×C₇	1	8	yes	—
640	#123	C₂³×C₇	1	16	yes	—
641	#123	C₂³×C₇	1	8	yes	—
642	#123	C₂³×C₇	1	8	yes	—
643	#123	C₂³×C₇	1	16	yes	—
644	#123	C₂³×C₇	1	16	yes	—
645	#123	C₂³×C₇	1	16	yes	—
646	#123	C₂³×C₇	1	16	yes	—
647	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
648	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
649	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
650	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
651	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
652	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
653	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
654	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
655	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
656	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
657	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
658	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
659	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
660	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
661	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
662	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
663	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
664	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
665	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
666	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
667	#121	C₂³×C₇	1	4	yes	—
668	#121	C₂³×C₇	1	8	yes	—
669	#121	C₂³×C₇	1	16	yes	—
670	#121	C₂³×C₇	1	4	yes	—
671	#121	C₂³×C₇	1	8	yes	—
672	#121	C₂³×C₇	1	8	yes	—
673	#121	C₂³×C₇	1	8	yes	—
674	#121	C₂³×C₇	1	8	yes	—
675	#121	C₂³×C₇	1	16	yes	—
676	#121	C₂³×C₇	1	16	yes	—
677	#121	C₂³×C₇	1	16	yes	—
678	#121	C₂³×C₇	1	16	yes	—
679	#121	C₂³×C₇	1	16	yes	—
680	#120	C₂³×C₇	1	4	yes	—
681	#120	C₂³×C₇	1	4	yes	—
682	#120	C₂³×C₇	1	8	yes	—
683	#120	C₂³×C₇	1	8	yes	—
684	#120	C₂³×C₇	1	16	yes	—
685	C₄×Q₈	C₂³×C₇	1	4	yes	—
686	C₄×Q₈	C₂³×C₇	1	4	yes	—
687	C₄×Q₈	C₂³×C₇	1	8	yes	—
688	C₄×Q₈	C₂³×C₇	1	8	yes	—
689	C₄×Q₈	C₂³×C₇	1	8	yes	—
690	C₄×Q₈	C₂³×C₇	1	8	yes	—
691	C₄×Q₈	C₂³×C₇	1	16	yes	—
692	C₄×D₄	C₂³×C₇	1	8	yes	—
693	C₄×D₄	C₂³×C₇	1	4	yes	—
694	C₄×D₄	C₂³×C₇	1	8	yes	—
695	C₄×D₄	C₂³×C₇	1	4	yes	—
696	C₄×D₄	C₂³×C₇	1	8	yes	—
697	C₄×D₄	C₂³×C₇	1	8	yes	—
698	C₄×D₄	C₂³×C₇	1	8	yes	—
699	C₄×D₄	C₂³×C₇	1	16	yes	—
700	C₄×D₄	C₂³×C₇	1	16	yes	—
701	C₄×D₄	C₂³×C₇	1	16	yes	—
702	C₄×D₄	C₂³×C₇	1	8	yes	—
703	C₄×D₄	C₂³×C₇	1	16	yes	—
704	C₄×D₄	C₂³×C₇	1	16	yes	—
705	C₄×D₄	C₂³×C₇	1	16	yes	—
706	#117	C₂³×C₇	1	4	yes	—
707	#117	C₂³×C₇	1	4	yes	—
708	#117	C₂³×C₇	1	2	yes	—
709	#117	C₂³×C₇	1	4	yes	—
710	#117	C₂³×C₇	1	2	yes	—
711	#117	C₂³×C₇	1	4	yes	—
712	#117	C₂³×C₇	1	4	yes	—
713	#117	C₂³×C₇	1	8	yes	—
714	#117	C₂³×C₇	1	16	yes	—
715	#117	C₂³×C₇	1	16	yes	—
716	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
718	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
719	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
725	C₂×C₄²	C₂³×C₇	1	2	yes	—
726	C₂×C₄²	C₂³×C₇	1	4	yes	—
727	C₂×C₄²	C₂³×C₇	1	4	yes	—
728	C₂²×C₇	—	2	2	no	—
729	C₂²×C₇	—	2	2	no	—
730	C₂²×C₇	—	2	4	no	—
731	C₂²×C₇	—	2	4	no	—
732	C₂²×C₇	—	2	4	no	—
733	C₂²×C₇	—	2	8	no	—
734	C₂²×C₇	—	2	8	no	—
735	C₂²×C₇	—	2	8	no	—
736	C₂²×C₇	—	2	4	no	—
737	C₂²×C₇	—	4	4	no	—
738	C₂²×C₇	—	8	4	no	—
739	C₂²×C₇	—	16	4	no	—
740	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
741	C₂²×C₇	C₂⁶	1	1	yes	characteristic
742	C₄×C₇	—	2	2	no	—
743	C₄×C₇	—	2	4	no	—
744	C₄×C₇	—	2	4	no	—
745	C₄×C₇	—	2	4	no	—
746	C₄×C₇	—	2	8	no	—
747	C₄×C₇	—	2	4	no	—
748	C₄×C₇	—	2	8	no	—
749	C₄×C₇	—	2	4	no	—
750	C₄×C₇	—	2	8	no	—
751	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
752	C₂⁴	C₂⁴×C₇	1	2	yes	—
753	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
754	C₂⁴	C₂⁴×C₇	1	4	yes	—
755	#41	—	2	8	no	—
756	#41	—	2	8	no	—
757	#41	—	4	8	no	—
758	#41	—	4	16	no	—
759	#41	—	4	16	no	—
760	#41	—	4	8	no	—
761	#41	—	4	8	no	—
762	#41	—	4	8	no	—
763	#41	—	4	8	no	—
764	C₂×Q₈	—	2	8	no	—
765	C₂×Q₈	—	2	4	no	—
766	C₂×Q₈	—	4	4	no	—
767	C₂×Q₈	—	4	16	no	—
768	C₂×Q₈	—	4	8	no	—
769	C₂×Q₈	—	4	8	no	—
770	C₂×Q₈	—	4	8	no	—
771	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
772	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
773	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
774	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
775	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
776	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
777	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
778	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
779	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	4	8	no	—
782	C₂×D₄	—	4	4	no	—
783	C₂×D₄	—	4	8	no	—
784	C₂×D₄	C₂⁴×C₇	1	4	yes	—
785	C₂×D₄	C₂⁴×C₇	1	4	yes	—
786	C₂×D₄	C₂⁴×C₇	1	4	yes	—
787	C₂×D₄	C₂⁴×C₇	1	2	yes	—
788	C₂×D₄	C₂⁴×C₇	1	2	yes	—
789	C₂×D₄	C₂⁴×C₇	1	8	yes	—
790	C₂×D₄	C₂⁴×C₇	1	8	yes	—
791	C₂×D₄	C₂⁴×C₇	1	16	yes	—
792	C₂×D₄	C₂⁴×C₇	1	8	yes	—
793	C₂×D₄	C₂⁴×C₇	1	8	yes	—
794	C₂×D₄	C₂⁴×C₇	1	8	yes	—
795	C₂×D₄	C₂⁴×C₇	1	8	yes	—
796	C₂×D₄	C₂⁴×C₇	1	4	yes	—
797	C₂²×C₄	—	2	4	no	—
798	C₂²×C₄	—	4	4	no	—
799	C₂²×C₄	—	4	4	no	—
800	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
801	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
802	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
803	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
806	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
807	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
808	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
809	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
810	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
811	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
812	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
813	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
814	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
815	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
816	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
817	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
818	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
819	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
820	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
821	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
822	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
823	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
824	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
825	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
826	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
827	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
828	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
829	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
830	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
831	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
832	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
833	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
834	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
835	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
836	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
837	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
838	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
839	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
840	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
841	C₂²⋊C₄	C₂⁴×C₇	1	2	yes	—
842	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
843	C₂²⋊C₄	C₂⁴×C₇	1	2	yes	—
844	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
845	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
846	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
847	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
848	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
849	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
850	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
851	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
852	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
853	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
854	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
855	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
856	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
857	C₄²	C₂⁴×C₇	1	2	yes	—
858	C₄²	C₂⁴×C₇	1	2	yes	—
859	C₄²	C₂⁴×C₇	1	4	yes	—
860	C₄²	C₂⁴×C₇	1	4	yes	—
861	C₄²	C₂⁴×C₇	1	8	yes	—
862	C₄²	C₂⁴×C₇	1	4	yes	—
863	C₄²	C₂⁴×C₇	1	8	yes	—
864	C₄²	C₂⁴×C₇	1	16	yes	—
865	C₄²	C₂⁴×C₇	1	8	yes	—
866	C₂×C₇	—	2	2	no	—
867	C₂×C₇	—	4	4	no	—
868	C₂×C₇	—	4	2	no	—
869	C₂×C₇	—	4	4	no	—
870	C₂×C₇	—	4	4	no	—
871	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
872	C₂×C₇	2₋¹⁺⁶	1	2	yes	—
873	C₂³	—	2	2	no	—
874	C₂³	—	2	4	no	—
875	C₂³	—	4	2	no	—
876	C₂³	—	4	4	no	—
877	C₂³	—	4	4	no	—
878	C₂³	—	4	8	no	—
879	C₂³	C₂⁵×C₇	1	4	yes	—
880	C₂³	C₂⁵×C₇	1	4	yes	—
881	C₂³	C₂⁵×C₇	1	2	yes	—
882	C₂³	C₂⁵×C₇	1	4	yes	—
883	C₂³	C₂⁵×C₇	1	1	yes	characteristic
884	Q₈	—	2	8	no	—
885	Q₈	—	2	8	no	—
886	Q₈	—	2	8	no	—
887	Q₈	—	2	4	no	—
888	Q₈	—	2	4	no	—
889	Q₈	—	4	8	no	—
890	Q₈	—	4	8	no	—
891	Q₈	—	4	4	no	—
892	Q₈	—	4	8	no	—
893	D₄	—	2	8	no	—
894	D₄	—	2	8	no	—
895	D₄	—	2	8	no	—
896	D₄	—	2	4	no	—
897	D₄	—	2	4	no	—
898	D₄	—	4	8	no	—
899	D₄	—	4	8	no	—
900	D₄	—	4	8	no	—
901	D₄	—	4	8	no	—
902	D₄	—	4	16	no	—
903	D₄	—	4	8	no	—
904	D₄	—	4	4	no	—
905	D₄	—	4	8	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	4	no	—
908	C₂×C₄	—	2	8	no	—
909	C₂×C₄	—	2	8	no	—
910	C₂×C₄	—	2	8	no	—
911	C₂×C₄	—	2	8	no	—
912	C₂×C₄	—	4	8	no	—
913	C₂×C₄	—	4	8	no	—
914	C₂×C₄	—	4	8	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	8	no	—
917	C₂×C₄	—	4	8	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	8	no	—
920	C₂×C₄	—	4	8	no	—
921	C₂×C₄	—	4	8	no	—
922	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
923	C₂×C₄	C₂⁵×C₇	1	8	yes	—
924	C₂×C₄	C₂⁵×C₇	1	4	yes	—
925	C₂×C₄	C₂⁵×C₇	1	8	yes	—
926	C₂×C₄	C₂⁵×C₇	1	4	yes	—
927	C₂×C₄	C₂⁵×C₇	1	4	yes	—
928	C₂×C₄	C₂⁵×C₇	1	8	yes	—
929	C₂×C₄	C₂⁵×C₇	1	4	yes	—
930	C₂×C₄	C₂⁵×C₇	1	4	yes	—
931	C₂×C₄	C₂⁵×C₇	1	2	yes	—
932	C₂×C₄	C₂⁵×C₇	1	2	yes	—
933	C₇	#62887	1	1	yes	characteristic, direct product factor, Sylow
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	2	4	no	—
939	C₂²	—	2	8	no	—
940	C₂²	—	2	8	no	—
941	C₂²	—	2	8	no	—
942	C₂²	—	2	4	no	—
943	C₂²	—	4	4	no	—
944	C₂²	—	8	4	no	—
945	C₂²	—	16	4	no	—
946	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
947	C₂²	C₂⁶×C₇	1	1	yes	characteristic
948	C₄	—	2	2	no	—
949	C₄	—	2	4	no	—
950	C₄	—	2	4	no	—
951	C₄	—	2	4	no	—
952	C₄	—	2	8	no	—
953	C₄	—	2	4	no	—
954	C₄	—	2	8	no	—
955	C₄	—	2	4	no	—
956	C₄	—	2	8	no	—
957	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
958	C₂	—	2	2	no	—
959	C₂	—	4	2	no	—
960	C₂	—	4	4	no	—
961	C₂	—	4	4	no	—
962	C₂	—	4	4	no	—
963	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
964	C₂	C₇×2₋¹⁺⁶	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3562	C₂	semidirect
2. C₇×#3561	C₂	semidirect
3. C₇×#3554	C₂	semidirect
4. C₇×#3552	C₂	semidirect
5. C₇×#3535	C₂	semidirect
6. C₇×#3533	C₂	semidirect
7. C₇×#3510	C₂	semidirect
8. C₇×#3509	C₂	semidirect
9. C₇×#3500	C₂	semidirect
10. C₇×#3499	C₂	semidirect
11. C₇×#3487	C₂	semidirect
12. C₇×#3486	C₂	semidirect
13. C₇×#3485	C₂	semidirect
14. C₇×#3455	C₂	semidirect
15. C₂×C₇×#536	C₂	semidirect
17. C₂×C₇×2₋¹⁺⁴	C₂²	semidirect
20. C₂³×C₇×Q₈	C₂²	semidirect
21. C₇×#563	C₂²	semidirect
22. C₇×#563	C₂²	semidirect
23. C₇×#562	C₂²	semidirect
24. C₇×#562	C₂²	semidirect
25. C₇×#560	C₂²	semidirect
26. C₇×#559	C₂²	semidirect
27. C₇×#559	C₂²	semidirect
28. C₇×#557	C₂²	semidirect
29. C₇×#556	C₂²	semidirect
30. C₇×#556	C₂²	semidirect
31. C₇×#554	C₂²	semidirect
32. C₇×#553	C₂²	semidirect
33. C₇×#552	C₂²	semidirect
34. C₇×#551	C₂²	semidirect
35. C₇×#551	C₂²	semidirect
36. C₇×#551	C₂²	semidirect
37. C₇×#550	C₂²	semidirect
38. C₇×D₄×Q₈	C₂²	semidirect
39. C₇×D₄×Q₈	C₂²	semidirect
40. C₇×D₄×Q₈	C₂²	semidirect
41. C₇×#548	C₂²	semidirect
42. C₇×#548	C₂²	semidirect
43. C₇×#548	C₂²	semidirect
44. C₇×#548	C₂²	semidirect
46. C₇×#547	C₂²	semidirect
47. C₇×#547	C₂²	semidirect
50. C₇×#546	C₂²	semidirect
51. C₇×#544	C₂²	semidirect
52. C₇×#543	C₂²	semidirect
53. C₇×#542	C₂²	semidirect
54. C₇×#542	C₂²	semidirect
55. C₇×#542	C₂²	semidirect
56. C₇×#542	C₂²	semidirect
57. C₇×#542	C₂²	semidirect
58. C₇×#541	C₂²	semidirect
59. C₇×#541	C₂²	semidirect
60. C₇×#540	C₂²	semidirect
61. C₇×#540	C₂²	semidirect
62. C₇×#539	C₂²	semidirect
63. C₇×#539	C₂²	semidirect
64. C₇×#539	C₂²	semidirect
65. C₇×#539	C₂²	semidirect
66. C₇×#538	C₂²	semidirect
67. C₇×#538	C₂²	semidirect
68. C₇×#538	C₂²	semidirect
71. C₇×#536	C₂²	semidirect
72. C₇×#536	C₂²	semidirect
73. C₇×#536	C₂²	semidirect
74. C₇×#536	C₂²	semidirect
75. C₇×#536	C₂²	semidirect
76. C₇×#536	C₂²	semidirect
77. C₇×#536	C₂²	semidirect
79. C₇×#535	C₂²	semidirect
80. C₇×#535	C₂²	semidirect
82. C₇×#533	C₂²	semidirect
83. C₇×#533	C₂²	semidirect
85. C₇×#532	C₂²	semidirect
86. C₇×#532	C₂²	semidirect
87. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
88. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
89. C₇×#529	C₂²	semidirect
90. C₇×#529	C₂²	semidirect
91. C₇×#529	C₂²	semidirect
93. C₂×C₇×#124	C₂²	semidirect
95. C₇×#525	C₂²	semidirect
96. C₇×#525	C₂²	semidirect
97. C₇×#525	C₂²	semidirect
99. C₂×C₇×#123	C₂²	semidirect
100. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
101. C₇×#519	C₂²	semidirect
102. C₇×#519	C₂²	semidirect
105. C₄×C₇×#41	C₂²	semidirect
106. C₂×C₇×#117	C₂²	semidirect
107. #62887	C₇	direct (N × H)
278. #3562	C₂×C₇	semidirect
279. #3561	C₂×C₇	semidirect
280. #3554	C₂×C₇	semidirect
281. #3552	C₂×C₇	semidirect
282. #3535	C₂×C₇	semidirect
283. #3533	C₂×C₇	semidirect
284. #3510	C₂×C₇	semidirect
285. #3509	C₂×C₇	semidirect
286. #3500	C₂×C₇	semidirect
287. #3499	C₂×C₇	semidirect
288. #3487	C₂×C₇	semidirect
289. #3486	C₂×C₇	semidirect
290. #3485	C₂×C₇	semidirect
291. #3455	C₂×C₇	semidirect
292. C₂×#536	C₂×C₇	semidirect
408. C₂×2₋¹⁺⁴	C₂²×C₇	semidirect
411. C₂³×Q₈	C₂²×C₇	semidirect
412. #563	C₂²×C₇	semidirect
413. #563	C₂²×C₇	semidirect
414. #562	C₂²×C₇	semidirect
415. #562	C₂²×C₇	semidirect
416. #560	C₂²×C₇	semidirect
417. #559	C₂²×C₇	semidirect
418. #559	C₂²×C₇	semidirect
419. #557	C₂²×C₇	semidirect
420. #556	C₂²×C₇	semidirect
421. #556	C₂²×C₇	semidirect
422. #554	C₂²×C₇	semidirect
423. #553	C₂²×C₇	semidirect
424. #552	C₂²×C₇	semidirect
425. #551	C₂²×C₇	semidirect
426. #551	C₂²×C₇	semidirect
427. #551	C₂²×C₇	semidirect
428. #550	C₂²×C₇	semidirect
429. D₄×Q₈	C₂²×C₇	semidirect
430. D₄×Q₈	C₂²×C₇	semidirect
431. D₄×Q₈	C₂²×C₇	semidirect
432. #548	C₂²×C₇	semidirect
433. #548	C₂²×C₇	semidirect
434. #548	C₂²×C₇	semidirect
435. #548	C₂²×C₇	semidirect
437. #547	C₂²×C₇	semidirect
438. #547	C₂²×C₇	semidirect
441. #546	C₂²×C₇	semidirect
442. #544	C₂²×C₇	semidirect
443. #543	C₂²×C₇	semidirect
444. #542	C₂²×C₇	semidirect
445. #542	C₂²×C₇	semidirect
446. #542	C₂²×C₇	semidirect
447. #542	C₂²×C₇	semidirect
448. #542	C₂²×C₇	semidirect
449. #541	C₂²×C₇	semidirect
450. #541	C₂²×C₇	semidirect
451. #540	C₂²×C₇	semidirect
452. #540	C₂²×C₇	semidirect
453. #539	C₂²×C₇	semidirect
454. #539	C₂²×C₇	semidirect
455. #539	C₂²×C₇	semidirect
456. #539	C₂²×C₇	semidirect
457. #538	C₂²×C₇	semidirect
458. #538	C₂²×C₇	semidirect
459. #538	C₂²×C₇	semidirect
462. #536	C₂²×C₇	semidirect
463. #536	C₂²×C₇	semidirect
464. #536	C₂²×C₇	semidirect
465. #536	C₂²×C₇	semidirect
466. #536	C₂²×C₇	semidirect
467. #536	C₂²×C₇	semidirect
468. #536	C₂²×C₇	semidirect
470. #535	C₂²×C₇	semidirect
471. #535	C₂²×C₇	semidirect
473. #533	C₂²×C₇	semidirect
474. #533	C₂²×C₇	semidirect
476. #532	C₂²×C₇	semidirect
477. #532	C₂²×C₇	semidirect
478. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
479. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
480. #529	C₂²×C₇	semidirect
481. #529	C₂²×C₇	semidirect
482. #529	C₂²×C₇	semidirect
484. C₂×#124	C₂²×C₇	semidirect
486. #525	C₂²×C₇	semidirect
487. #525	C₂²×C₇	semidirect
488. #525	C₂²×C₇	semidirect
490. C₂×#123	C₂²×C₇	semidirect
491. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
492. #519	C₂²×C₇	semidirect
493. #519	C₂²×C₇	semidirect
496. C₄×#41	C₂²×C₇	semidirect
497. C₂×#117	C₂²×C₇	semidirect
933. C₇	#62887	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3562	2
C₇×#3561	2
C₇×#3554	2
C₇×#3552	2
C₇×#3535	2
C₇×#3533	2
C₇×#3510	2
C₇×#3509	2
C₇×#3500	2
C₇×#3499	2
C₇×#3487	2
C₇×#3486	2
C₇×#3485	2
C₇×#3455	2
C₂×C₇×#536	2
#62887	7

Subgroups — C7×#62887 #13240103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62887 #13240103