Subgroups — C₇×#62755 #13239971

Order 1792.

6644 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3566	C₂	1	8	yes	maximal, complemented
2	C₇×#3564	C₂	1	4	yes	maximal, complemented
3	C₇×#3560	C₂	1	4	yes	maximal, complemented
4	C₇×#3553	C₂	1	4	yes	maximal, complemented
5	C₇×#3545	C₂	1	4	yes	maximal, complemented
6	C₇×#3535	C₂	1	4	yes	maximal, complemented
7	C₇×#3534	C₂	1	4	yes	maximal, complemented
8	C₇×#3531	C₂	1	2	yes	maximal, complemented
9	C₇×#3529	C₂	1	2	yes	maximal, complemented
10	C₇×#3481	C₂	1	4	yes	maximal, complemented
11	C₇×#3475	C₂	1	8	yes	maximal, complemented
12	C₇×#3461	C₂	1	4	yes	maximal, complemented
13	C₇×#3459	C₂	1	4	yes	maximal, complemented
14	C₇×#3455	C₂	1	4	yes	maximal, complemented
15	C₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#529	C₂	1	2	yes	maximal, complemented
17	C₇×#564	C₂²	1	2	yes	complemented
18	C₇×#563	C₂²	1	8	yes	complemented
19	C₇×#563	C₂²	1	4	yes	complemented
20	C₇×#563	C₂²	1	8	yes	complemented
21	C₇×#563	C₂²	1	2	yes	complemented
22	C₇×#563	C₂²	1	4	yes	complemented
23	C₇×#562	C₂²	1	8	yes	complemented
24	C₇×#562	C₂²	1	8	yes	complemented
25	C₇×#562	C₂²	1	4	yes	complemented
26	C₇×#562	C₂²	1	2	yes	complemented
27	C₇×H(3,𝔽₄)	C₂²	1	2	yes	complemented
28	C₇×#560	C₂²	1	4	yes	complemented
29	C₇×#560	C₂²	1	8	yes	complemented
30	C₇×#559	C₂²	1	4	yes	complemented
31	C₇×#556	C₂²	1	8	yes	complemented
32	C₇×#555	C₂²	1	8	yes	complemented
33	C₇×#554	C₂²	1	8	yes	complemented
34	C₇×#554	C₂²	1	8	yes	complemented
35	C₇×#553	C₂²	1	8	yes	complemented
36	C₇×#553	C₂²	1	8	yes	complemented
37	C₇×#553	C₂²	1	8	yes	complemented
38	C₇×#553	C₂²	1	8	yes	complemented
39	C₇×#552	C₂²	1	8	yes	complemented
40	C₇×#552	C₂²	1	8	yes	complemented
41	C₇×#552	C₂²	1	8	yes	complemented
42	C₇×#552	C₂²	1	8	yes	complemented
43	C₇×#551	C₂²	1	8	yes	complemented
44	C₇×#551	C₂²	1	8	yes	complemented
45	C₇×#551	C₂²	1	8	yes	complemented
46	C₇×#551	C₂²	1	4	yes	complemented
47	C₇×#551	C₂²	1	8	yes	complemented
48	C₇×#551	C₂²	1	8	yes	complemented
49	C₇×#551	C₂²	1	4	yes	complemented
50	C₇×#547	C₂²	1	8	yes	complemented
51	C₇×#546	C₂²	1	8	yes	complemented
52	C₇×#546	C₂²	1	8	yes	complemented
53	C₇×#546	C₂²	1	8	yes	complemented
54	C₇×#546	C₂²	1	8	yes	complemented
55	C₇×D₄²	C₂²	1	4	yes	complemented
56	C₇×#544	C₂²	1	4	yes	complemented
57	C₇×#543	C₂²	1	4	yes	complemented
58	C₇×#542	C₂²	1	8	yes	complemented
59	C₇×#542	C₂²	1	8	yes	complemented
60	C₇×#542	C₂²	1	8	yes	complemented
61	C₇×#542	C₂²	1	8	yes	complemented
62	C₇×#541	C₂²	1	8	yes	complemented
63	C₇×#541	C₂²	1	8	yes	complemented
64	C₇×#541	C₂²	1	8	yes	complemented
65	C₇×#540	C₂²	1	8	yes	complemented
66	C₇×#539	C₂²	1	8	yes	complemented
67	C₇×#539	C₂²	1	4	yes	complemented
68	C₇×#539	C₂²	1	8	yes	complemented
69	C₇×#539	C₂²	1	4	yes	complemented
70	C₇×#539	C₂²	1	8	yes	complemented
71	C₇×#539	C₂²	1	8	yes	complemented
72	C₇×#539	C₂²	1	8	yes	complemented
73	C₇×#539	C₂²	1	8	yes	complemented
74	C₇×#538	C₂²	1	4	yes	—
75	C₇×#538	C₂²	1	8	yes	complemented
76	C₇×#538	C₂²	1	8	yes	complemented
77	C₇×#538	C₂²	1	4	yes	complemented
78	C₇×#538	C₂²	1	8	yes	complemented
79	C₇×#538	C₂²	1	8	yes	complemented
80	C₇×#537	C₂²	1	4	yes	—
81	C₇×#536	C₂²	1	8	yes	complemented
82	C₇×#534	C₂²	1	4	yes	complemented
83	C₇×#534	C₂²	1	8	yes	complemented
84	C₇×#533	C₂²	1	2	yes	complemented
85	C₇×#533	C₂²	1	1	yes	characteristic, complemented
86	C₇×#533	C₂²	1	4	yes	complemented
87	C₇×#533	C₂²	1	8	yes	complemented
88	C₇×#532	C₂²	1	2	yes	complemented
89	C₇×#532	C₂²	1	1	yes	characteristic, complemented
90	C₇×#532	C₂²	1	4	yes	complemented
91	C₇×#529	C₂²	1	4	yes	complemented
92	C₇×#529	C₂²	1	4	yes	complemented
93	C₇×#529	C₂²	1	4	yes	complemented
94	C₇×#529	C₂²	1	4	yes	complemented
95	C₇×#529	C₂²	1	4	yes	complemented
96	C₇×#529	C₂²	1	4	yes	complemented
97	C₇×#529	C₂²	1	4	yes	complemented
98	C₇×#529	C₂²	1	4	yes	complemented
99	C₇×#529	C₂²	1	4	yes	complemented
100	C₇×#529	C₂²	1	4	yes	complemented
101	C₇×#529	C₂²	1	4	yes	complemented
102	C₇×#529	C₂²	1	8	yes	complemented
103	C₇×#529	C₂²	1	8	yes	complemented
104	C₇×#529	C₂²	1	8	yes	complemented
105	C₇×#529	C₂²	1	8	yes	complemented
106	C₇×#529	C₂²	1	8	yes	complemented
107	C₇×#529	C₂²	1	8	yes	complemented
108	C₂×C₇×#126	C₂²	1	4	yes	complemented
109	C₂×C₇×#125	C₂²	1	2	yes	complemented
110	C₂×C₇×#124	C₂²	1	2	yes	complemented
111	C₇×#525	C₂²	1	2	yes	complemented
112	C₇×#525	C₂²	1	4	yes	complemented
113	C₇×#525	C₂²	1	4	yes	complemented
114	C₇×#525	C₂²	1	4	yes	complemented
115	C₇×#525	C₂²	1	8	yes	complemented
116	C₇×#525	C₂²	1	8	yes	complemented
117	C₂×C₇×#123	C₂²	1	4	yes	complemented
118	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
119	C₂×C₇×#121	C₂²	1	2	yes	—
120	C₄×C₇×#41	C₂²	1	2	yes	complemented
121	C₄×C₇×#41	C₂²	1	4	yes	complemented
122	C₄×C₇×#41	C₂²	1	4	yes	complemented
123	C₄×C₇×#41	C₂²	1	8	yes	complemented
124	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
125	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
126	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
127	C₂×C₄×C₇×D₄	C₂²	1	8	yes	complemented
128	C₂×C₇×#117	C₂²	1	4	yes	complemented
129	C₂×C₇×#117	C₂²	1	4	yes	complemented
130	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
131	#62755	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂×C₇×#41	C₂³	1	4	yes	—
133	C₂×C₇×#41	C₂³	1	2	yes	—
134	C₂×C₇×#41	C₂³	1	4	yes	—
135	C₂×C₇×#41	C₂³	1	8	yes	—
136	C₂²×C₇×Q₈	C₂³	1	2	yes	—
137	C₂²×C₇×D₄	C₂³	1	4	yes	—
138	C₂²×C₇×D₄	C₂³	1	2	yes	—
139	C₂²×C₇×D₄	C₂³	1	8	yes	—
140	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₇	C₂³	1	2	yes	—
142	C₂³×C₄×C₇	C₂³	1	4	yes	—
143	C₂³×C₄×C₇	C₂³	1	4	yes	—
144	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
145	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
146	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
147	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
148	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
149	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
150	C₇×#127	C₂³	1	1	yes	characteristic
151	C₇×#127	C₂³	1	4	yes	—
152	C₇×#126	C₂³	1	8	yes	—
153	C₇×#126	C₂³	1	8	yes	—
154	C₇×#126	C₂³	1	8	yes	—
155	C₇×#126	C₂³	1	8	yes	—
156	C₇×#126	C₂³	1	8	yes	—
157	C₇×#126	C₂³	1	8	yes	—
158	C₇×#126	C₂³	1	8	yes	—
159	C₇×#126	C₂³	1	8	yes	—
160	C₇×#126	C₂³	1	8	yes	—
161	C₇×#126	C₂³	1	8	yes	—
162	C₇×#126	C₂³	1	8	yes	—
163	C₇×#126	C₂³	1	8	yes	—
164	C₇×#126	C₂³	1	8	yes	—
165	C₇×#126	C₂³	1	8	yes	—
166	C₇×#126	C₂³	1	8	yes	—
167	C₇×#126	C₂³	1	8	yes	—
168	C₇×#126	C₂³	1	8	yes	—
169	C₇×#125	C₂³	1	4	yes	—
170	C₇×#125	C₂³	1	4	yes	—
171	C₇×#125	C₂³	1	4	yes	—
172	C₇×#125	C₂³	1	4	yes	—
173	C₇×#125	C₂³	1	4	yes	—
174	C₇×#125	C₂³	1	2	yes	—
175	C₇×#125	C₂³	1	8	yes	—
176	C₇×#125	C₂³	1	8	yes	—
177	C₇×#125	C₂³	1	8	yes	—
178	C₇×#125	C₂³	1	8	yes	—
179	C₇×#125	C₂³	1	8	yes	—
180	C₇×#125	C₂³	1	8	yes	—
181	C₇×#125	C₂³	1	8	yes	—
182	C₇×#125	C₂³	1	8	yes	—
183	C₇×#125	C₂³	1	8	yes	—
184	C₇×#124	C₂³	1	4	yes	—
185	C₇×#124	C₂³	1	4	yes	—
186	C₇×#124	C₂³	1	4	yes	—
187	C₇×#124	C₂³	1	4	yes	—
188	C₇×#124	C₂³	1	4	yes	—
189	C₇×#124	C₂³	1	2	yes	—
190	C₇×#124	C₂³	1	8	yes	—
191	C₇×#124	C₂³	1	8	yes	—
192	C₇×#124	C₂³	1	8	yes	—
193	C₇×#124	C₂³	1	8	yes	—
194	C₇×#124	C₂³	1	8	yes	—
195	C₇×#124	C₂³	1	8	yes	—
196	C₇×#124	C₂³	1	4	yes	—
197	C₇×#124	C₂³	1	4	yes	—
198	C₇×#123	C₂³	1	8	yes	—
199	C₇×#123	C₂³	1	8	yes	—
200	C₇×#123	C₂³	1	8	yes	—
201	C₇×#123	C₂³	1	8	yes	—
202	C₇×#123	C₂³	1	8	yes	—
203	C₇×#123	C₂³	1	4	yes	—
204	C₇×#123	C₂³	1	8	yes	—
205	C₇×#123	C₂³	1	8	yes	—
206	C₇×#123	C₂³	1	8	yes	—
207	C₇×#123	C₂³	1	8	yes	—
208	C₇×#123	C₂³	1	8	yes	—
209	C₇×#123	C₂³	1	4	yes	—
210	C₇×#123	C₂³	1	4	yes	—
211	C₇×#123	C₂³	1	8	yes	—
212	C₇×#123	C₂³	1	8	yes	—
213	C₇×#123	C₂³	1	8	yes	—
214	C₇×#123	C₂³	1	8	yes	—
215	C₇×#123	C₂³	1	8	yes	—
216	C₇×#123	C₂³	1	8	yes	—
217	C₇×#123	C₂³	1	8	yes	—
218	C₇×#123	C₂³	1	8	yes	—
219	C₇×#123	C₂³	1	8	yes	—
220	C₇×#123	C₂³	1	8	yes	—
221	C₇×#123	C₂³	1	8	yes	—
222	C₇×#123	C₂³	1	8	yes	—
223	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
224	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
225	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
226	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
227	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
228	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
229	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
230	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
231	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
232	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
233	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
234	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
235	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
236	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
237	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
238	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
239	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
240	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
241	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
242	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
243	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
244	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
245	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
246	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
247	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
248	C₇×#121	C₂³	1	4	yes	—
249	C₇×#121	C₂³	1	4	yes	—
250	C₇×#121	C₂³	1	4	yes	—
251	C₇×#121	C₂³	1	4	yes	—
252	C₇×#121	C₂³	1	4	yes	—
253	C₇×#121	C₂³	1	4	yes	—
254	C₇×#121	C₂³	1	4	yes	—
255	C₇×#121	C₂³	1	8	yes	—
256	C₇×#121	C₂³	1	8	yes	—
257	C₇×#121	C₂³	1	8	yes	—
258	C₇×#121	C₂³	1	8	yes	—
259	C₇×#121	C₂³	1	8	yes	—
260	C₇×#121	C₂³	1	8	yes	—
261	C₇×#121	C₂³	1	8	yes	—
262	C₇×#121	C₂³	1	8	yes	—
263	C₇×#121	C₂³	1	8	yes	—
264	C₇×#121	C₂³	1	8	yes	—
265	C₇×#121	C₂³	1	8	yes	—
266	C₇×#121	C₂³	1	8	yes	—
267	C₇×#121	C₂³	1	8	yes	—
268	C₇×#121	C₂³	1	8	yes	—
269	C₇×#120	C₂³	1	4	yes	—
270	C₇×#120	C₂³	1	8	yes	—
271	C₇×#120	C₂³	1	8	yes	—
272	C₇×#120	C₂³	1	8	yes	—
273	C₇×#120	C₂³	1	8	yes	—
274	C₇×#120	C₂³	1	8	yes	—
275	C₇×#120	C₂³	1	4	yes	—
276	C₇×#120	C₂³	1	4	yes	—
277	C₄×C₇×Q₈	C₂³	1	4	yes	—
278	C₄×C₇×Q₈	C₂³	1	4	yes	—
279	C₄×C₇×Q₈	C₂³	1	4	yes	—
280	C₄×C₇×Q₈	C₂³	1	4	yes	—
281	C₄×C₇×Q₈	C₂³	1	8	yes	—
282	C₄×C₇×Q₈	C₂³	1	4	yes	—
283	C₄×C₇×Q₈	C₂³	1	4	yes	—
284	C₄×C₇×Q₈	C₂³	1	4	yes	—
285	C₄×C₇×Q₈	C₂³	1	8	yes	—
286	C₄×C₇×Q₈	C₂³	1	8	yes	—
287	C₄×C₇×D₄	C₂³	1	8	yes	—
288	C₄×C₇×D₄	C₂³	1	8	yes	—
289	C₄×C₇×D₄	C₂³	1	4	yes	—
290	C₄×C₇×D₄	C₂³	1	4	yes	—
291	C₄×C₇×D₄	C₂³	1	8	yes	—
292	C₄×C₇×D₄	C₂³	1	8	yes	—
293	C₄×C₇×D₄	C₂³	1	8	yes	—
294	C₄×C₇×D₄	C₂³	1	4	yes	—
295	C₄×C₇×D₄	C₂³	1	4	yes	—
296	C₄×C₇×D₄	C₂³	1	8	yes	—
297	C₄×C₇×D₄	C₂³	1	8	yes	—
298	C₄×C₇×D₄	C₂³	1	8	yes	—
299	C₄×C₇×D₄	C₂³	1	8	yes	—
300	C₄×C₇×D₄	C₂³	1	8	yes	—
301	C₄×C₇×D₄	C₂³	1	8	yes	—
302	C₄×C₇×D₄	C₂³	1	8	yes	—
303	C₄×C₇×D₄	C₂³	1	4	yes	—
304	C₄×C₇×D₄	C₂³	1	8	yes	—
305	C₄×C₇×D₄	C₂³	1	8	yes	—
306	C₄×C₇×D₄	C₂³	1	4	yes	—
307	C₄×C₇×D₄	C₂³	1	4	yes	—
308	C₄×C₇×D₄	C₂³	1	8	yes	—
309	C₄×C₇×D₄	C₂³	1	8	yes	—
310	C₄×C₇×D₄	C₂³	1	8	yes	—
311	C₄×C₇×D₄	C₂³	1	8	yes	—
312	C₄×C₇×D₄	C₂³	1	8	yes	—
313	C₄×C₇×D₄	C₂³	1	8	yes	—
314	C₇×#117	C₂³	1	8	yes	—
315	C₇×#117	C₂³	1	8	yes	—
316	C₇×#117	C₂³	1	8	yes	—
317	C₇×#117	C₂³	1	8	yes	—
318	C₇×#117	C₂³	1	8	yes	—
319	C₇×#117	C₂³	1	8	yes	—
320	C₇×#117	C₂³	1	8	yes	—
321	C₇×#117	C₂³	1	4	yes	—
322	C₇×#117	C₂³	1	2	yes	—
323	C₇×#117	C₂³	1	4	yes	—
324	C₇×#117	C₂³	1	4	yes	—
325	C₇×#117	C₂³	1	8	yes	—
326	C₇×#117	C₂³	1	8	yes	—
327	C₇×#117	C₂³	1	8	yes	—
328	C₇×#117	C₂³	1	8	yes	—
329	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
330	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
331	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
332	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
333	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
334	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
335	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
336	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
337	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
338	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
339	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
340	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
341	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
342	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
343	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
344	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
345	C₂×C₄²×C₇	C₂³	1	2	yes	—
346	C₂×C₄²×C₇	C₂³	1	2	yes	—
347	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
348	C₂×C₄²×C₇	C₂³	1	2	yes	—
349	C₂×C₄²×C₇	C₂³	1	2	yes	—
350	C₂×C₄²×C₇	C₂³	1	2	yes	—
351	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
352	C₂×C₄²×C₇	C₂³	1	4	yes	—
353	C₂×C₄²×C₇	C₂³	1	4	yes	—
354	C₂×C₄²×C₇	C₂³	1	4	yes	—
355	C₂×C₄²×C₇	C₂³	1	8	yes	—
356	#3566	C₂×C₇	1	8	yes	complemented
357	#3564	C₂×C₇	1	4	yes	complemented
358	#3560	C₂×C₇	1	4	yes	complemented
359	#3553	C₂×C₇	1	4	yes	complemented
360	#3545	C₂×C₇	1	4	yes	complemented
361	#3535	C₂×C₇	1	4	yes	complemented
362	#3534	C₂×C₇	1	4	yes	complemented
363	#3531	C₂×C₇	1	2	yes	complemented
364	#3529	C₂×C₇	1	2	yes	complemented
365	#3481	C₂×C₇	1	4	yes	complemented
366	#3475	C₂×C₇	1	8	yes	complemented
367	#3461	C₂×C₇	1	4	yes	complemented
368	#3459	C₂×C₇	1	4	yes	complemented
369	#3455	C₂×C₇	1	4	yes	complemented
370	#3444	C₂×C₇	1	1	yes	characteristic, complemented
371	C₂×#529	C₂×C₇	1	2	yes	complemented
372	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
373	C₂⁴×C₇	C₂⁴	1	4	yes	—
374	C₂⁴×C₇	C₂⁴	1	4	yes	—
375	C₇×#41	—	4	8	no	—
376	C₇×#41	—	4	4	no	—
377	C₇×#41	—	4	8	no	—
378	C₇×#41	—	4	16	no	—
379	C₂×C₇×Q₈	—	4	4	no	—
380	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
381	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
382	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
383	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
384	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
385	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
386	C₂×C₇×D₄	—	4	4	no	—
387	C₂×C₇×D₄	—	4	8	no	—
388	C₂×C₇×D₄	—	4	16	no	—
389	C₂×C₇×D₄	C₂⁴	1	8	yes	—
390	C₂×C₇×D₄	C₂⁴	1	8	yes	—
391	C₂×C₇×D₄	C₂⁴	1	4	yes	—
392	C₂×C₇×D₄	C₂⁴	1	8	yes	—
393	C₂×C₇×D₄	C₂⁴	1	8	yes	—
394	C₂×C₇×D₄	C₂⁴	1	4	yes	—
395	C₂×C₇×D₄	C₂⁴	1	4	yes	—
396	C₂×C₇×D₄	C₂⁴	1	8	yes	—
397	C₂×C₇×D₄	C₂⁴	1	4	yes	—
398	C₂×C₇×D₄	C₂⁴	1	4	yes	—
399	C₂×C₇×D₄	C₂⁴	1	2	yes	—
400	C₂×C₇×D₄	C₂⁴	1	8	yes	—
401	C₂×C₇×D₄	C₂⁴	1	8	yes	—
402	C₂²×C₄×C₇	—	4	2	no	—
403	C₂²×C₄×C₇	—	4	8	no	—
404	C₂²×C₄×C₇	—	4	8	no	—
405	C₂²×C₄×C₇	—	4	4	no	—
406	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
408	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
409	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
410	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
412	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
413	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
414	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
415	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
416	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
418	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
419	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
420	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
421	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
422	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
423	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
424	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
425	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
426	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
427	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
428	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
429	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
430	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
431	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
432	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
433	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
434	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
435	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
436	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
437	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
438	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
439	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
440	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
441	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
442	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
443	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
444	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
445	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
446	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
447	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
448	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
449	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
450	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
451	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
452	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
453	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
454	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
455	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
456	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
457	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
458	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
459	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
460	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
461	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
462	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
463	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
464	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
465	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
466	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
467	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
468	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
469	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
470	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
471	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
472	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
473	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
474	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
475	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
476	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
477	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
478	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
479	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
480	C₄²×C₇	C₂⁴	1	2	yes	—
481	C₄²×C₇	C₂⁴	1	2	yes	—
482	C₄²×C₇	C₂⁴	1	2	yes	—
483	C₄²×C₇	C₂⁴	1	2	yes	—
484	C₄²×C₇	C₂⁴	1	2	yes	—
485	C₄²×C₇	C₂⁴	1	1	yes	characteristic
486	C₄²×C₇	C₂⁴	1	1	yes	characteristic
487	C₄²×C₇	C₂⁴	1	4	yes	—
488	C₄²×C₇	C₂⁴	1	8	yes	—
489	C₄²×C₇	C₂⁴	1	8	yes	—
490	C₄²×C₇	C₂⁴	1	8	yes	—
491	C₄²×C₇	C₂⁴	1	4	yes	—
492	C₄²×C₇	C₂⁴	1	8	yes	—
493	C₄²×C₇	C₂⁴	1	1	yes	characteristic
494	C₄²×C₇	C₂⁴	1	8	yes	—
495	C₄²×C₇	C₂⁴	1	2	yes	—
496	C₄²×C₇	C₂⁴	1	1	yes	characteristic
497	C₄²×C₇	C₂⁴	1	4	yes	—
498	#564	C₂²×C₇	1	2	yes	complemented
499	#563	C₂²×C₇	1	2	yes	complemented
500	#563	C₂²×C₇	1	4	yes	complemented
501	#563	C₂²×C₇	1	8	yes	complemented
502	#563	C₂²×C₇	1	4	yes	complemented
503	#563	C₂²×C₇	1	8	yes	complemented
504	#562	C₂²×C₇	1	8	yes	complemented
505	#562	C₂²×C₇	1	4	yes	complemented
506	#562	C₂²×C₇	1	8	yes	complemented
507	#562	C₂²×C₇	1	2	yes	complemented
508	H(3,𝔽₄)	C₂²×C₇	1	2	yes	complemented
509	#560	C₂²×C₇	1	8	yes	complemented
510	#560	C₂²×C₇	1	4	yes	complemented
511	#559	C₂²×C₇	1	4	yes	complemented
512	#556	C₂²×C₇	1	8	yes	complemented
513	#555	C₂²×C₇	1	8	yes	complemented
514	#554	C₂²×C₇	1	8	yes	complemented
515	#554	C₂²×C₇	1	8	yes	complemented
516	#553	C₂²×C₇	1	8	yes	complemented
517	#553	C₂²×C₇	1	8	yes	complemented
518	#553	C₂²×C₇	1	8	yes	complemented
519	#553	C₂²×C₇	1	8	yes	complemented
520	#552	C₂²×C₇	1	8	yes	complemented
521	#552	C₂²×C₇	1	8	yes	complemented
522	#552	C₂²×C₇	1	8	yes	complemented
523	#552	C₂²×C₇	1	8	yes	complemented
524	#551	C₂²×C₇	1	8	yes	complemented
525	#551	C₂²×C₇	1	8	yes	complemented
526	#551	C₂²×C₇	1	8	yes	complemented
527	#551	C₂²×C₇	1	8	yes	complemented
528	#551	C₂²×C₇	1	4	yes	complemented
529	#551	C₂²×C₇	1	8	yes	complemented
530	#551	C₂²×C₇	1	4	yes	complemented
531	#547	C₂²×C₇	1	8	yes	complemented
532	#546	C₂²×C₇	1	8	yes	complemented
533	#546	C₂²×C₇	1	8	yes	complemented
534	#546	C₂²×C₇	1	8	yes	complemented
535	#546	C₂²×C₇	1	8	yes	complemented
536	D₄²	C₂²×C₇	1	4	yes	complemented
537	#544	C₂²×C₇	1	4	yes	complemented
538	#543	C₂²×C₇	1	4	yes	complemented
539	#542	C₂²×C₇	1	8	yes	complemented
540	#542	C₂²×C₇	1	8	yes	complemented
541	#542	C₂²×C₇	1	8	yes	complemented
542	#542	C₂²×C₇	1	8	yes	complemented
543	#541	C₂²×C₇	1	8	yes	complemented
544	#541	C₂²×C₇	1	8	yes	complemented
545	#541	C₂²×C₇	1	8	yes	complemented
546	#540	C₂²×C₇	1	8	yes	complemented
547	#539	C₂²×C₇	1	8	yes	complemented
548	#539	C₂²×C₇	1	8	yes	complemented
549	#539	C₂²×C₇	1	8	yes	complemented
550	#539	C₂²×C₇	1	8	yes	complemented
551	#539	C₂²×C₇	1	8	yes	complemented
552	#539	C₂²×C₇	1	8	yes	complemented
553	#539	C₂²×C₇	1	4	yes	complemented
554	#539	C₂²×C₇	1	4	yes	complemented
555	#538	C₂²×C₇	1	4	yes	—
556	#538	C₂²×C₇	1	8	yes	complemented
557	#538	C₂²×C₇	1	8	yes	complemented
558	#538	C₂²×C₇	1	4	yes	complemented
559	#538	C₂²×C₇	1	8	yes	complemented
560	#538	C₂²×C₇	1	8	yes	complemented
561	#537	C₂²×C₇	1	4	yes	—
562	#536	C₂²×C₇	1	8	yes	complemented
563	#534	C₂²×C₇	1	8	yes	complemented
564	#534	C₂²×C₇	1	4	yes	complemented
565	#533	C₂²×C₇	1	1	yes	characteristic, complemented
566	#533	C₂²×C₇	1	2	yes	complemented
567	#533	C₂²×C₇	1	4	yes	complemented
568	#533	C₂²×C₇	1	8	yes	complemented
569	#532	C₂²×C₇	1	1	yes	characteristic, complemented
570	#532	C₂²×C₇	1	2	yes	complemented
571	#532	C₂²×C₇	1	4	yes	complemented
572	#529	C₂²×C₇	1	4	yes	complemented
573	#529	C₂²×C₇	1	4	yes	complemented
574	#529	C₂²×C₇	1	4	yes	complemented
575	#529	C₂²×C₇	1	4	yes	complemented
576	#529	C₂²×C₇	1	4	yes	complemented
577	#529	C₂²×C₇	1	4	yes	complemented
578	#529	C₂²×C₇	1	4	yes	complemented
579	#529	C₂²×C₇	1	4	yes	complemented
580	#529	C₂²×C₇	1	4	yes	complemented
581	#529	C₂²×C₇	1	4	yes	complemented
582	#529	C₂²×C₇	1	4	yes	complemented
583	#529	C₂²×C₇	1	8	yes	complemented
584	#529	C₂²×C₇	1	8	yes	complemented
585	#529	C₂²×C₇	1	8	yes	complemented
586	#529	C₂²×C₇	1	8	yes	complemented
587	#529	C₂²×C₇	1	8	yes	complemented
588	#529	C₂²×C₇	1	8	yes	complemented
589	C₂×#126	C₂²×C₇	1	4	yes	complemented
590	C₂×#125	C₂²×C₇	1	2	yes	complemented
591	C₂×#124	C₂²×C₇	1	2	yes	complemented
592	#525	C₂²×C₇	1	2	yes	complemented
593	#525	C₂²×C₇	1	4	yes	complemented
594	#525	C₂²×C₇	1	4	yes	complemented
595	#525	C₂²×C₇	1	4	yes	complemented
596	#525	C₂²×C₇	1	8	yes	complemented
597	#525	C₂²×C₇	1	8	yes	complemented
598	C₂×#123	C₂²×C₇	1	4	yes	complemented
599	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
600	C₂×#121	C₂²×C₇	1	2	yes	—
601	C₄×#41	C₂²×C₇	1	2	yes	complemented
602	C₄×#41	C₂²×C₇	1	4	yes	complemented
603	C₄×#41	C₂²×C₇	1	4	yes	complemented
604	C₄×#41	C₂²×C₇	1	8	yes	complemented
605	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
606	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
607	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
608	C₂×C₄×D₄	C₂²×C₇	1	8	yes	complemented
609	C₂×#117	C₂²×C₇	1	4	yes	complemented
610	C₂×#117	C₂²×C₇	1	4	yes	complemented
611	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
612	C₂³×C₇	—	2	4	no	—
613	C₂³×C₇	—	2	8	no	—
614	C₂³×C₇	—	4	1	no	—
615	C₂³×C₇	—	4	4	no	—
616	C₂³×C₇	—	4	4	no	—
617	C₂³×C₇	—	4	4	no	—
618	C₂³×C₇	—	4	8	no	—
619	C₂³×C₇	C₂⁵	1	8	yes	—
620	C₂³×C₇	C₂⁵	1	4	yes	—
621	C₂³×C₇	C₂⁵	1	1	yes	characteristic
622	C₂³×C₇	C₂⁵	1	2	yes	—
623	C₇×Q₈	—	4	4	no	—
624	C₇×Q₈	—	4	4	no	—
625	C₇×Q₈	—	4	4	no	—
626	C₇×Q₈	—	4	2	no	—
627	C₇×Q₈	—	4	4	no	—
628	C₇×Q₈	—	4	8	no	—
629	C₇×D₄	—	2	16	no	—
630	C₇×D₄	—	2	16	no	—
631	C₇×D₄	—	4	4	no	—
632	C₇×D₄	—	4	4	no	—
633	C₇×D₄	—	4	8	no	—
634	C₇×D₄	—	4	8	no	—
635	C₇×D₄	—	4	8	no	—
636	C₇×D₄	—	4	8	no	—
637	C₇×D₄	—	4	4	no	—
638	C₇×D₄	—	4	4	no	—
639	C₇×D₄	—	4	2	no	—
640	C₇×D₄	—	4	4	no	—
641	C₇×D₄	—	4	8	no	—
642	C₂×C₄×C₇	—	2	4	no	—
643	C₂×C₄×C₇	—	2	4	no	—
644	C₂×C₄×C₇	—	2	8	no	—
645	C₂×C₄×C₇	—	2	4	no	—
646	C₂×C₄×C₇	—	2	16	no	—
647	C₂×C₄×C₇	—	2	2	no	—
648	C₂×C₄×C₇	—	2	8	no	—
649	C₂×C₄×C₇	—	4	1	no	—
650	C₂×C₄×C₇	—	4	8	no	—
651	C₂×C₄×C₇	—	4	2	no	—
652	C₂×C₄×C₇	—	4	2	no	—
653	C₂×C₄×C₇	—	4	2	no	—
654	C₂×C₄×C₇	—	4	4	no	—
655	C₂×C₄×C₇	—	4	4	no	—
656	C₂×C₄×C₇	—	4	8	no	—
657	C₂×C₄×C₇	—	4	2	no	—
658	C₂×C₄×C₇	—	4	2	no	—
659	C₂×C₄×C₇	—	4	4	no	—
660	C₂×C₄×C₇	—	4	8	no	—
661	C₂×C₄×C₇	—	4	8	no	—
662	C₂×C₄×C₇	—	4	8	no	—
663	C₂×C₄×C₇	—	4	8	no	—
664	C₂×C₄×C₇	C₂⁵	1	2	yes	—
665	C₂×C₄×C₇	C₂⁵	1	2	yes	—
666	C₂×C₄×C₇	C₂⁵	1	8	yes	—
667	C₂×C₄×C₇	C₂⁵	1	2	yes	—
668	C₂×C₄×C₇	C₂⁵	1	2	yes	—
669	C₂×C₄×C₇	C₂⁵	1	2	yes	—
670	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
671	C₂×C₄×C₇	C₂⁵	1	4	yes	—
672	C₂×C₄×C₇	C₂⁵	1	8	yes	—
673	C₂×C₄×C₇	C₂⁵	1	8	yes	—
674	C₂×C₄×C₇	C₂⁵	1	8	yes	—
675	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
676	C₂×#41	C₂³×C₇	1	4	yes	—
677	C₂×#41	C₂³×C₇	1	2	yes	—
678	C₂×#41	C₂³×C₇	1	4	yes	—
679	C₂×#41	C₂³×C₇	1	8	yes	—
680	C₂²×Q₈	C₂³×C₇	1	2	yes	—
681	C₂²×D₄	C₂³×C₇	1	4	yes	—
682	C₂²×D₄	C₂³×C₇	1	2	yes	—
683	C₂²×D₄	C₂³×C₇	1	8	yes	—
684	C₂³×C₄	C₂³×C₇	1	4	yes	—
685	C₂³×C₄	C₂³×C₇	1	4	yes	—
686	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
687	C₂³×C₄	C₂³×C₇	1	2	yes	—
688	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
689	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
690	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
691	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
692	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
693	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
694	#127	C₂³×C₇	1	1	yes	characteristic
695	#127	C₂³×C₇	1	4	yes	—
696	#126	C₂³×C₇	1	8	yes	—
697	#126	C₂³×C₇	1	8	yes	—
698	#126	C₂³×C₇	1	8	yes	—
699	#126	C₂³×C₇	1	8	yes	—
700	#126	C₂³×C₇	1	8	yes	—
701	#126	C₂³×C₇	1	8	yes	—
702	#126	C₂³×C₇	1	8	yes	—
703	#126	C₂³×C₇	1	8	yes	—
704	#126	C₂³×C₇	1	8	yes	—
705	#126	C₂³×C₇	1	8	yes	—
706	#126	C₂³×C₇	1	8	yes	—
707	#126	C₂³×C₇	1	8	yes	—
708	#126	C₂³×C₇	1	8	yes	—
709	#126	C₂³×C₇	1	8	yes	—
710	#126	C₂³×C₇	1	8	yes	—
711	#126	C₂³×C₇	1	8	yes	—
712	#126	C₂³×C₇	1	8	yes	—
713	#125	C₂³×C₇	1	4	yes	—
714	#125	C₂³×C₇	1	4	yes	—
715	#125	C₂³×C₇	1	4	yes	—
716	#125	C₂³×C₇	1	4	yes	—
717	#125	C₂³×C₇	1	4	yes	—
718	#125	C₂³×C₇	1	2	yes	—
719	#125	C₂³×C₇	1	8	yes	—
720	#125	C₂³×C₇	1	8	yes	—
721	#125	C₂³×C₇	1	8	yes	—
722	#125	C₂³×C₇	1	8	yes	—
723	#125	C₂³×C₇	1	8	yes	—
724	#125	C₂³×C₇	1	8	yes	—
725	#125	C₂³×C₇	1	8	yes	—
726	#125	C₂³×C₇	1	8	yes	—
727	#125	C₂³×C₇	1	8	yes	—
728	#124	C₂³×C₇	1	4	yes	—
729	#124	C₂³×C₇	1	4	yes	—
730	#124	C₂³×C₇	1	4	yes	—
731	#124	C₂³×C₇	1	4	yes	—
732	#124	C₂³×C₇	1	4	yes	—
733	#124	C₂³×C₇	1	2	yes	—
734	#124	C₂³×C₇	1	8	yes	—
735	#124	C₂³×C₇	1	8	yes	—
736	#124	C₂³×C₇	1	8	yes	—
737	#124	C₂³×C₇	1	8	yes	—
738	#124	C₂³×C₇	1	8	yes	—
739	#124	C₂³×C₇	1	8	yes	—
740	#124	C₂³×C₇	1	4	yes	—
741	#124	C₂³×C₇	1	4	yes	—
742	#123	C₂³×C₇	1	8	yes	—
743	#123	C₂³×C₇	1	8	yes	—
744	#123	C₂³×C₇	1	8	yes	—
745	#123	C₂³×C₇	1	8	yes	—
746	#123	C₂³×C₇	1	8	yes	—
747	#123	C₂³×C₇	1	4	yes	—
748	#123	C₂³×C₇	1	8	yes	—
749	#123	C₂³×C₇	1	8	yes	—
750	#123	C₂³×C₇	1	8	yes	—
751	#123	C₂³×C₇	1	8	yes	—
752	#123	C₂³×C₇	1	8	yes	—
753	#123	C₂³×C₇	1	4	yes	—
754	#123	C₂³×C₇	1	4	yes	—
755	#123	C₂³×C₇	1	8	yes	—
756	#123	C₂³×C₇	1	8	yes	—
757	#123	C₂³×C₇	1	8	yes	—
758	#123	C₂³×C₇	1	8	yes	—
759	#123	C₂³×C₇	1	8	yes	—
760	#123	C₂³×C₇	1	8	yes	—
761	#123	C₂³×C₇	1	8	yes	—
762	#123	C₂³×C₇	1	8	yes	—
763	#123	C₂³×C₇	1	8	yes	—
764	#123	C₂³×C₇	1	8	yes	—
765	#123	C₂³×C₇	1	8	yes	—
766	#123	C₂³×C₇	1	8	yes	—
767	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
768	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
769	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
770	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
771	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
772	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
773	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
774	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
775	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
776	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
777	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
778	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
779	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
780	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
781	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
782	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
783	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
784	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
785	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
786	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
787	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
788	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
789	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
790	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
791	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
792	#121	C₂³×C₇	1	4	yes	—
793	#121	C₂³×C₇	1	4	yes	—
794	#121	C₂³×C₇	1	4	yes	—
795	#121	C₂³×C₇	1	4	yes	—
796	#121	C₂³×C₇	1	4	yes	—
797	#121	C₂³×C₇	1	4	yes	—
798	#121	C₂³×C₇	1	4	yes	—
799	#121	C₂³×C₇	1	8	yes	—
800	#121	C₂³×C₇	1	8	yes	—
801	#121	C₂³×C₇	1	8	yes	—
802	#121	C₂³×C₇	1	8	yes	—
803	#121	C₂³×C₇	1	8	yes	—
804	#121	C₂³×C₇	1	8	yes	—
805	#121	C₂³×C₇	1	8	yes	—
806	#121	C₂³×C₇	1	8	yes	—
807	#121	C₂³×C₇	1	8	yes	—
808	#121	C₂³×C₇	1	8	yes	—
809	#121	C₂³×C₇	1	8	yes	—
810	#121	C₂³×C₇	1	8	yes	—
811	#121	C₂³×C₇	1	8	yes	—
812	#121	C₂³×C₇	1	8	yes	—
813	#120	C₂³×C₇	1	4	yes	—
814	#120	C₂³×C₇	1	8	yes	—
815	#120	C₂³×C₇	1	8	yes	—
816	#120	C₂³×C₇	1	8	yes	—
817	#120	C₂³×C₇	1	8	yes	—
818	#120	C₂³×C₇	1	8	yes	—
819	#120	C₂³×C₇	1	4	yes	—
820	#120	C₂³×C₇	1	4	yes	—
821	C₄×Q₈	C₂³×C₇	1	4	yes	—
822	C₄×Q₈	C₂³×C₇	1	4	yes	—
823	C₄×Q₈	C₂³×C₇	1	4	yes	—
824	C₄×Q₈	C₂³×C₇	1	4	yes	—
825	C₄×Q₈	C₂³×C₇	1	8	yes	—
826	C₄×Q₈	C₂³×C₇	1	4	yes	—
827	C₄×Q₈	C₂³×C₇	1	4	yes	—
828	C₄×Q₈	C₂³×C₇	1	4	yes	—
829	C₄×Q₈	C₂³×C₇	1	8	yes	—
830	C₄×Q₈	C₂³×C₇	1	8	yes	—
831	C₄×D₄	C₂³×C₇	1	8	yes	—
832	C₄×D₄	C₂³×C₇	1	8	yes	—
833	C₄×D₄	C₂³×C₇	1	4	yes	—
834	C₄×D₄	C₂³×C₇	1	4	yes	—
835	C₄×D₄	C₂³×C₇	1	8	yes	—
836	C₄×D₄	C₂³×C₇	1	8	yes	—
837	C₄×D₄	C₂³×C₇	1	8	yes	—
838	C₄×D₄	C₂³×C₇	1	4	yes	—
839	C₄×D₄	C₂³×C₇	1	4	yes	—
840	C₄×D₄	C₂³×C₇	1	8	yes	—
841	C₄×D₄	C₂³×C₇	1	8	yes	—
842	C₄×D₄	C₂³×C₇	1	8	yes	—
843	C₄×D₄	C₂³×C₇	1	8	yes	—
844	C₄×D₄	C₂³×C₇	1	8	yes	—
845	C₄×D₄	C₂³×C₇	1	8	yes	—
846	C₄×D₄	C₂³×C₇	1	8	yes	—
847	C₄×D₄	C₂³×C₇	1	4	yes	—
848	C₄×D₄	C₂³×C₇	1	8	yes	—
849	C₄×D₄	C₂³×C₇	1	8	yes	—
850	C₄×D₄	C₂³×C₇	1	4	yes	—
851	C₄×D₄	C₂³×C₇	1	4	yes	—
852	C₄×D₄	C₂³×C₇	1	8	yes	—
853	C₄×D₄	C₂³×C₇	1	8	yes	—
854	C₄×D₄	C₂³×C₇	1	8	yes	—
855	C₄×D₄	C₂³×C₇	1	8	yes	—
856	C₄×D₄	C₂³×C₇	1	8	yes	—
857	C₄×D₄	C₂³×C₇	1	8	yes	—
858	#117	C₂³×C₇	1	8	yes	—
859	#117	C₂³×C₇	1	8	yes	—
860	#117	C₂³×C₇	1	8	yes	—
861	#117	C₂³×C₇	1	8	yes	—
862	#117	C₂³×C₇	1	8	yes	—
863	#117	C₂³×C₇	1	8	yes	—
864	#117	C₂³×C₇	1	8	yes	—
865	#117	C₂³×C₇	1	4	yes	—
866	#117	C₂³×C₇	1	2	yes	—
867	#117	C₂³×C₇	1	4	yes	—
868	#117	C₂³×C₇	1	4	yes	—
869	#117	C₂³×C₇	1	8	yes	—
870	#117	C₂³×C₇	1	8	yes	—
871	#117	C₂³×C₇	1	8	yes	—
872	#117	C₂³×C₇	1	8	yes	—
873	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
874	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
875	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
876	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
877	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
878	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
879	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
880	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
881	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
882	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
883	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
884	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
885	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
886	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
887	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
888	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
889	C₂×C₄²	C₂³×C₇	1	2	yes	—
890	C₂×C₄²	C₂³×C₇	1	4	yes	—
891	C₂×C₄²	C₂³×C₇	1	4	yes	—
892	C₂×C₄²	C₂³×C₇	1	4	yes	—
893	C₂×C₄²	C₂³×C₇	1	2	yes	—
894	C₂×C₄²	C₂³×C₇	1	8	yes	—
895	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
896	C₂×C₄²	C₂³×C₇	1	2	yes	—
897	C₂×C₄²	C₂³×C₇	1	2	yes	—
898	C₂×C₄²	C₂³×C₇	1	2	yes	—
899	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
900	C₂²×C₇	—	2	2	no	—
901	C₂²×C₇	—	2	2	no	—
902	C₂²×C₇	—	2	8	no	—
903	C₂²×C₇	—	2	1	no	—
904	C₂²×C₇	—	2	4	no	—
905	C₂²×C₇	—	2	8	no	—
906	C₂²×C₇	—	2	2	no	—
907	C₂²×C₇	—	2	8	no	—
908	C₂²×C₇	—	2	8	no	—
909	C₂²×C₇	—	4	4	no	—
910	C₂²×C₇	—	8	8	no	—
911	C₂²×C₇	—	8	8	no	—
912	C₂²×C₇	#585	1	4	yes	—
913	C₂²×C₇	C₂⁶	1	1	yes	characteristic
914	C₄×C₇	—	2	2	no	—
915	C₄×C₇	—	2	2	no	—
916	C₄×C₇	—	2	8	no	—
917	C₄×C₇	—	2	2	no	—
918	C₄×C₇	—	2	2	no	—
919	C₄×C₇	—	2	2	no	—
920	C₄×C₇	—	2	1	no	—
921	C₄×C₇	—	2	4	no	—
922	C₄×C₇	—	2	8	no	—
923	C₄×C₇	—	2	8	no	—
924	C₄×C₇	—	2	8	no	—
925	C₄×C₇	#585	1	2	yes	—
926	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
927	C₂⁴	C₂⁴×C₇	1	4	yes	—
928	C₂⁴	C₂⁴×C₇	1	4	yes	—
929	#41	—	4	8	no	—
930	#41	—	4	4	no	—
931	#41	—	4	8	no	—
932	#41	—	4	16	no	—
933	C₂×Q₈	—	4	4	no	—
934	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
935	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
936	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
937	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
938	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
939	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
940	C₂×D₄	—	4	4	no	—
941	C₂×D₄	—	4	8	no	—
942	C₂×D₄	—	4	16	no	—
943	C₂×D₄	C₂⁴×C₇	1	8	yes	—
944	C₂×D₄	C₂⁴×C₇	1	8	yes	—
945	C₂×D₄	C₂⁴×C₇	1	4	yes	—
946	C₂×D₄	C₂⁴×C₇	1	8	yes	—
947	C₂×D₄	C₂⁴×C₇	1	8	yes	—
948	C₂×D₄	C₂⁴×C₇	1	4	yes	—
949	C₂×D₄	C₂⁴×C₇	1	4	yes	—
950	C₂×D₄	C₂⁴×C₇	1	8	yes	—
951	C₂×D₄	C₂⁴×C₇	1	4	yes	—
952	C₂×D₄	C₂⁴×C₇	1	4	yes	—
953	C₂×D₄	C₂⁴×C₇	1	2	yes	—
954	C₂×D₄	C₂⁴×C₇	1	8	yes	—
955	C₂×D₄	C₂⁴×C₇	1	8	yes	—
956	C₂²×C₄	—	4	2	no	—
957	C₂²×C₄	—	4	8	no	—
958	C₂²×C₄	—	4	8	no	—
959	C₂²×C₄	—	4	4	no	—
960	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
961	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
962	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
963	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
964	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
966	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
967	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
968	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
969	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
970	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
971	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
972	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
973	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
974	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
975	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
976	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
977	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
978	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
979	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
980	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
981	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
982	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
983	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
984	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
985	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
986	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
987	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
988	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
989	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
990	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
991	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
992	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
993	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
994	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
995	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
996	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
997	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
998	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
999	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
1000	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
1001	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
1002	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
1003	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
1004	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
1005	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
1006	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
1007	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
1008	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
1009	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1010	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1011	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1012	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1013	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1014	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1015	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1016	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1017	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1018	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1019	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1020	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1021	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1022	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1023	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1024	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1025	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1026	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1027	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1028	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
1029	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1030	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
1031	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1032	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
1033	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
1034	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₇	1	2	yes	—
1036	C₄²	C₂⁴×C₇	1	8	yes	—
1037	C₄²	C₂⁴×C₇	1	2	yes	—
1038	C₄²	C₂⁴×C₇	1	4	yes	—
1039	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1040	C₄²	C₂⁴×C₇	1	2	yes	—
1041	C₄²	C₂⁴×C₇	1	2	yes	—
1042	C₄²	C₂⁴×C₇	1	2	yes	—
1043	C₄²	C₂⁴×C₇	1	2	yes	—
1044	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1045	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1046	C₄²	C₂⁴×C₇	1	4	yes	—
1047	C₄²	C₂⁴×C₇	1	8	yes	—
1048	C₄²	C₂⁴×C₇	1	8	yes	—
1049	C₄²	C₂⁴×C₇	1	8	yes	—
1050	C₄²	C₂⁴×C₇	1	4	yes	—
1051	C₄²	C₂⁴×C₇	1	8	yes	—
1052	C₂×C₇	—	2	4	no	—
1053	C₂×C₇	—	4	1	no	—
1054	C₂×C₇	—	4	4	no	—
1055	C₂×C₇	—	4	8	no	—
1056	C₂×C₇	C₂×#585	1	2	yes	—
1057	C₂×C₇	C₂×#585	1	1	yes	characteristic
1058	C₂³	—	2	4	no	—
1059	C₂³	—	2	8	no	—
1060	C₂³	—	4	1	no	—
1061	C₂³	—	4	4	no	—
1062	C₂³	—	4	4	no	—
1063	C₂³	—	4	4	no	—
1064	C₂³	—	4	8	no	—
1065	C₂³	C₂⁵×C₇	1	8	yes	—
1066	C₂³	C₂⁵×C₇	1	4	yes	—
1067	C₂³	C₂⁵×C₇	1	1	yes	characteristic
1068	C₂³	C₂⁵×C₇	1	2	yes	—
1069	Q₈	—	4	4	no	—
1070	Q₈	—	4	4	no	—
1071	Q₈	—	4	4	no	—
1072	Q₈	—	4	2	no	—
1073	Q₈	—	4	4	no	—
1074	Q₈	—	4	8	no	—
1075	D₄	—	2	16	no	—
1076	D₄	—	2	16	no	—
1077	D₄	—	4	4	no	—
1078	D₄	—	4	4	no	—
1079	D₄	—	4	8	no	—
1080	D₄	—	4	8	no	—
1081	D₄	—	4	8	no	—
1082	D₄	—	4	8	no	—
1083	D₄	—	4	4	no	—
1084	D₄	—	4	4	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	4	no	—
1087	D₄	—	4	8	no	—
1088	C₂×C₄	—	2	4	no	—
1089	C₂×C₄	—	2	4	no	—
1090	C₂×C₄	—	2	8	no	—
1091	C₂×C₄	—	2	4	no	—
1092	C₂×C₄	—	2	16	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	8	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	8	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	4	no	—
1101	C₂×C₄	—	4	4	no	—
1102	C₂×C₄	—	4	8	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	4	no	—
1106	C₂×C₄	—	4	8	no	—
1107	C₂×C₄	—	4	8	no	—
1108	C₂×C₄	—	4	8	no	—
1109	C₂×C₄	—	4	8	no	—
1110	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1111	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1112	C₂×C₄	C₂⁵×C₇	1	8	yes	—
1113	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1114	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1115	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1116	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1117	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1118	C₂×C₄	C₂⁵×C₇	1	8	yes	—
1119	C₂×C₄	C₂⁵×C₇	1	8	yes	—
1120	C₂×C₄	C₂⁵×C₇	1	8	yes	—
1121	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1122	C₇	#62755	1	1	yes	characteristic, direct product factor, Sylow
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	8	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	4	no	—
1128	C₂²	—	2	8	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	8	no	—
1131	C₂²	—	2	8	no	—
1132	C₂²	—	4	4	no	—
1133	C₂²	—	8	8	no	—
1134	C₂²	—	8	8	no	—
1135	C₂²	C₇×#585	1	4	yes	—
1136	C₂²	C₂⁶×C₇	1	1	yes	characteristic
1137	C₄	—	2	2	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	8	no	—
1140	C₄	—	2	2	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	4	no	—
1145	C₄	—	2	8	no	—
1146	C₄	—	2	8	no	—
1147	C₄	—	2	8	no	—
1148	C₄	C₇×#585	1	2	yes	—
1149	C₂	—	2	4	no	—
1150	C₂	—	4	1	no	—
1151	C₂	—	4	8	no	—
1152	C₂	—	4	4	no	—
1153	C₂	C₂×C₇×#585	1	2	yes	—
1154	C₂	C₂×C₇×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
socle	C₂²×C₇	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3566	C₂	semidirect
2. C₇×#3564	C₂	semidirect
3. C₇×#3560	C₂	semidirect
4. C₇×#3553	C₂	semidirect
5. C₇×#3545	C₂	semidirect
6. C₇×#3535	C₂	semidirect
7. C₇×#3534	C₂	semidirect
8. C₇×#3531	C₂	semidirect
9. C₇×#3529	C₂	semidirect
10. C₇×#3481	C₂	semidirect
11. C₇×#3475	C₂	semidirect
12. C₇×#3461	C₂	semidirect
13. C₇×#3459	C₂	semidirect
14. C₇×#3455	C₂	semidirect
15. C₇×#3444	C₂	semidirect
16. C₂×C₇×#529	C₂	semidirect
17. C₇×#564	C₂²	semidirect
18. C₇×#563	C₂²	semidirect
19. C₇×#563	C₂²	semidirect
20. C₇×#563	C₂²	semidirect
21. C₇×#563	C₂²	semidirect
22. C₇×#563	C₂²	semidirect
23. C₇×#562	C₂²	semidirect
24. C₇×#562	C₂²	semidirect
25. C₇×#562	C₂²	semidirect
26. C₇×#562	C₂²	semidirect
27. C₇×H(3,𝔽₄)	C₂²	semidirect
28. C₇×#560	C₂²	semidirect
29. C₇×#560	C₂²	semidirect
30. C₇×#559	C₂²	semidirect
31. C₇×#556	C₂²	semidirect
32. C₇×#555	C₂²	semidirect
33. C₇×#554	C₂²	semidirect
34. C₇×#554	C₂²	semidirect
35. C₇×#553	C₂²	semidirect
36. C₇×#553	C₂²	semidirect
37. C₇×#553	C₂²	semidirect
38. C₇×#553	C₂²	semidirect
39. C₇×#552	C₂²	semidirect
40. C₇×#552	C₂²	semidirect
41. C₇×#552	C₂²	semidirect
42. C₇×#552	C₂²	semidirect
43. C₇×#551	C₂²	semidirect
44. C₇×#551	C₂²	semidirect
45. C₇×#551	C₂²	semidirect
46. C₇×#551	C₂²	semidirect
47. C₇×#551	C₂²	semidirect
48. C₇×#551	C₂²	semidirect
49. C₇×#551	C₂²	semidirect
50. C₇×#547	C₂²	semidirect
51. C₇×#546	C₂²	semidirect
52. C₇×#546	C₂²	semidirect
53. C₇×#546	C₂²	semidirect
54. C₇×#546	C₂²	semidirect
55. C₇×D₄²	C₂²	semidirect
56. C₇×#544	C₂²	semidirect
57. C₇×#543	C₂²	semidirect
58. C₇×#542	C₂²	semidirect
59. C₇×#542	C₂²	semidirect
60. C₇×#542	C₂²	semidirect
61. C₇×#542	C₂²	semidirect
62. C₇×#541	C₂²	semidirect
63. C₇×#541	C₂²	semidirect
64. C₇×#541	C₂²	semidirect
65. C₇×#540	C₂²	semidirect
66. C₇×#539	C₂²	semidirect
67. C₇×#539	C₂²	semidirect
68. C₇×#539	C₂²	semidirect
69. C₇×#539	C₂²	semidirect
70. C₇×#539	C₂²	semidirect
71. C₇×#539	C₂²	semidirect
72. C₇×#539	C₂²	semidirect
73. C₇×#539	C₂²	semidirect
75. C₇×#538	C₂²	semidirect
76. C₇×#538	C₂²	semidirect
77. C₇×#538	C₂²	semidirect
78. C₇×#538	C₂²	semidirect
79. C₇×#538	C₂²	semidirect
81. C₇×#536	C₂²	semidirect
82. C₇×#534	C₂²	semidirect
83. C₇×#534	C₂²	semidirect
84. C₇×#533	C₂²	semidirect
85. C₇×#533	C₂²	semidirect
86. C₇×#533	C₂²	semidirect
87. C₇×#533	C₂²	semidirect
88. C₇×#532	C₂²	semidirect
89. C₇×#532	C₂²	semidirect
90. C₇×#532	C₂²	semidirect
91. C₇×#529	C₂²	semidirect
92. C₇×#529	C₂²	semidirect
93. C₇×#529	C₂²	semidirect
94. C₇×#529	C₂²	semidirect
95. C₇×#529	C₂²	semidirect
96. C₇×#529	C₂²	semidirect
97. C₇×#529	C₂²	semidirect
98. C₇×#529	C₂²	semidirect
99. C₇×#529	C₂²	semidirect
100. C₇×#529	C₂²	semidirect
101. C₇×#529	C₂²	semidirect
102. C₇×#529	C₂²	semidirect
103. C₇×#529	C₂²	semidirect
104. C₇×#529	C₂²	semidirect
105. C₇×#529	C₂²	semidirect
106. C₇×#529	C₂²	semidirect
107. C₇×#529	C₂²	semidirect
108. C₂×C₇×#126	C₂²	semidirect
109. C₂×C₇×#125	C₂²	semidirect
110. C₂×C₇×#124	C₂²	semidirect
111. C₇×#525	C₂²	semidirect
112. C₇×#525	C₂²	semidirect
113. C₇×#525	C₂²	semidirect
114. C₇×#525	C₂²	semidirect
115. C₇×#525	C₂²	semidirect
116. C₇×#525	C₂²	semidirect
117. C₂×C₇×#123	C₂²	semidirect
118. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
120. C₄×C₇×#41	C₂²	semidirect
121. C₄×C₇×#41	C₂²	semidirect
122. C₄×C₇×#41	C₂²	semidirect
123. C₄×C₇×#41	C₂²	semidirect
124. C₂×C₄×C₇×Q₈	C₂²	semidirect
125. C₂×C₄×C₇×D₄	C₂²	semidirect
126. C₂×C₄×C₇×D₄	C₂²	semidirect
127. C₂×C₄×C₇×D₄	C₂²	semidirect
128. C₂×C₇×#117	C₂²	semidirect
129. C₂×C₇×#117	C₂²	semidirect
130. C₂²×C₄²×C₇	C₂²	semidirect
131. #62755	C₇	direct (N × H)
356. #3566	C₂×C₇	semidirect
357. #3564	C₂×C₇	semidirect
358. #3560	C₂×C₇	semidirect
359. #3553	C₂×C₇	semidirect
360. #3545	C₂×C₇	semidirect
361. #3535	C₂×C₇	semidirect
362. #3534	C₂×C₇	semidirect
363. #3531	C₂×C₇	semidirect
364. #3529	C₂×C₇	semidirect
365. #3481	C₂×C₇	semidirect
366. #3475	C₂×C₇	semidirect
367. #3461	C₂×C₇	semidirect
368. #3459	C₂×C₇	semidirect
369. #3455	C₂×C₇	semidirect
370. #3444	C₂×C₇	semidirect
371. C₂×#529	C₂×C₇	semidirect
498. #564	C₂²×C₇	semidirect
499. #563	C₂²×C₇	semidirect
500. #563	C₂²×C₇	semidirect
501. #563	C₂²×C₇	semidirect
502. #563	C₂²×C₇	semidirect
503. #563	C₂²×C₇	semidirect
504. #562	C₂²×C₇	semidirect
505. #562	C₂²×C₇	semidirect
506. #562	C₂²×C₇	semidirect
507. #562	C₂²×C₇	semidirect
508. H(3,𝔽₄)	C₂²×C₇	semidirect
509. #560	C₂²×C₇	semidirect
510. #560	C₂²×C₇	semidirect
511. #559	C₂²×C₇	semidirect
512. #556	C₂²×C₇	semidirect
513. #555	C₂²×C₇	semidirect
514. #554	C₂²×C₇	semidirect
515. #554	C₂²×C₇	semidirect
516. #553	C₂²×C₇	semidirect
517. #553	C₂²×C₇	semidirect
518. #553	C₂²×C₇	semidirect
519. #553	C₂²×C₇	semidirect
520. #552	C₂²×C₇	semidirect
521. #552	C₂²×C₇	semidirect
522. #552	C₂²×C₇	semidirect
523. #552	C₂²×C₇	semidirect
524. #551	C₂²×C₇	semidirect
525. #551	C₂²×C₇	semidirect
526. #551	C₂²×C₇	semidirect
527. #551	C₂²×C₇	semidirect
528. #551	C₂²×C₇	semidirect
529. #551	C₂²×C₇	semidirect
530. #551	C₂²×C₇	semidirect
531. #547	C₂²×C₇	semidirect
532. #546	C₂²×C₇	semidirect
533. #546	C₂²×C₇	semidirect
534. #546	C₂²×C₇	semidirect
535. #546	C₂²×C₇	semidirect
536. D₄²	C₂²×C₇	semidirect
537. #544	C₂²×C₇	semidirect
538. #543	C₂²×C₇	semidirect
539. #542	C₂²×C₇	semidirect
540. #542	C₂²×C₇	semidirect
541. #542	C₂²×C₇	semidirect
542. #542	C₂²×C₇	semidirect
543. #541	C₂²×C₇	semidirect
544. #541	C₂²×C₇	semidirect
545. #541	C₂²×C₇	semidirect
546. #540	C₂²×C₇	semidirect
547. #539	C₂²×C₇	semidirect
548. #539	C₂²×C₇	semidirect
549. #539	C₂²×C₇	semidirect
550. #539	C₂²×C₇	semidirect
551. #539	C₂²×C₇	semidirect
552. #539	C₂²×C₇	semidirect
553. #539	C₂²×C₇	semidirect
554. #539	C₂²×C₇	semidirect
556. #538	C₂²×C₇	semidirect
557. #538	C₂²×C₇	semidirect
558. #538	C₂²×C₇	semidirect
559. #538	C₂²×C₇	semidirect
560. #538	C₂²×C₇	semidirect
562. #536	C₂²×C₇	semidirect
563. #534	C₂²×C₇	semidirect
564. #534	C₂²×C₇	semidirect
565. #533	C₂²×C₇	semidirect
566. #533	C₂²×C₇	semidirect
567. #533	C₂²×C₇	semidirect
568. #533	C₂²×C₇	semidirect
569. #532	C₂²×C₇	semidirect
570. #532	C₂²×C₇	semidirect
571. #532	C₂²×C₇	semidirect
572. #529	C₂²×C₇	semidirect
573. #529	C₂²×C₇	semidirect
574. #529	C₂²×C₇	semidirect
575. #529	C₂²×C₇	semidirect
576. #529	C₂²×C₇	semidirect
577. #529	C₂²×C₇	semidirect
578. #529	C₂²×C₇	semidirect
579. #529	C₂²×C₇	semidirect
580. #529	C₂²×C₇	semidirect
581. #529	C₂²×C₇	semidirect
582. #529	C₂²×C₇	semidirect
583. #529	C₂²×C₇	semidirect
584. #529	C₂²×C₇	semidirect
585. #529	C₂²×C₇	semidirect
586. #529	C₂²×C₇	semidirect
587. #529	C₂²×C₇	semidirect
588. #529	C₂²×C₇	semidirect
589. C₂×#126	C₂²×C₇	semidirect
590. C₂×#125	C₂²×C₇	semidirect
591. C₂×#124	C₂²×C₇	semidirect
592. #525	C₂²×C₇	semidirect
593. #525	C₂²×C₇	semidirect
594. #525	C₂²×C₇	semidirect
595. #525	C₂²×C₇	semidirect
596. #525	C₂²×C₇	semidirect
597. #525	C₂²×C₇	semidirect
598. C₂×#123	C₂²×C₇	semidirect
599. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
601. C₄×#41	C₂²×C₇	semidirect
602. C₄×#41	C₂²×C₇	semidirect
603. C₄×#41	C₂²×C₇	semidirect
604. C₄×#41	C₂²×C₇	semidirect
605. C₂×C₄×Q₈	C₂²×C₇	semidirect
606. C₂×C₄×D₄	C₂²×C₇	semidirect
607. C₂×C₄×D₄	C₂²×C₇	semidirect
608. C₂×C₄×D₄	C₂²×C₇	semidirect
609. C₂×#117	C₂²×C₇	semidirect
610. C₂×#117	C₂²×C₇	semidirect
611. C₂²×C₄²	C₂²×C₇	semidirect
1122. C₇	#62755	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×#3566	2
C₇×#3564	2
C₇×#3560	2
C₇×#3553	2
C₇×#3545	2
C₇×#3535	2
C₇×#3534	2
C₇×#3531	2
C₇×#3529	2
C₇×#3481	2
C₇×#3475	2
C₇×#3461	2
C₇×#3459	2
C₇×#3455	2
C₇×#3444	2
C₂×C₇×#529	2
#62755	7

Subgroups — C7×#62755 #13239971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62755 #13239971