Subgroups — C₇×#60876 #13238092

Order 1792.

1640 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3495	C₂	1	1	yes	maximal, characteristic
2	C₇×#3458	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3244	C₂	1	2	yes	maximal, complemented
4	C₇×#3243	C₂	1	2	yes	maximal, complemented
5	C₇×#3242	C₂	1	2	yes	maximal, complemented
6	C₇×#3242	C₂	1	2	yes	maximal, complemented
7	C₇×#3240	C₂	1	2	yes	maximal, complemented
8	C₇×#3237	C₂	1	2	yes	maximal, complemented
9	C₇×#3233	C₂	1	2	yes	maximal, complemented
10	C₇×#3231	C₂	1	2	yes	maximal, complemented
11	C₇×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3163	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3095	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3093	C₂	1	1	yes	maximal, characteristic
17	C₇×#3091	C₂	1	1	yes	maximal, characteristic
18	C₂×C₇×#485	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3084	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#556	—	2	1	no	—
25	C₇×#554	—	2	1	no	—
26	C₇×#552	—	2	2	no	—
27	C₇×#552	—	2	1	no	—
28	C₇×#552	—	2	1	no	—
29	C₇×#551	—	2	2	no	—
30	C₇×#544	—	2	1	no	—
31	C₇×#544	—	2	1	no	—
32	C₇×#544	C₂²	1	1	yes	characteristic
33	C₇×#544	C₂²	1	1	yes	characteristic
34	C₇×#544	C₂²	1	1	yes	characteristic
35	C₇×#544	C₂²	1	2	yes	—
36	C₇×#544	C₂²	1	2	yes	—
37	C₇×#544	C₂²	1	1	yes	characteristic
38	C₇×#544	C₂²	1	1	yes	characteristic
39	C₇×#543	—	2	2	no	—
40	C₇×#542	C₂²	1	2	yes	—
41	C₇×#541	C₂²	1	2	yes	—
42	C₇×#536	C₂²	1	1	yes	characteristic
43	C₇×#533	—	2	2	no	—
44	C₇×#533	—	2	1	no	—
45	C₇×#533	—	2	1	no	—
46	C₇×#533	C₂²	1	2	yes	—
47	C₇×#533	C₂²	1	2	yes	—
48	C₇×#533	C₂²	1	2	yes	—
49	C₇×#529	C₂²	1	2	yes	—
50	C₇×#525	C₂²	1	1	yes	characteristic
51	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
52	C₇×#520	C₂²	1	1	yes	characteristic
53	C₇×#519	C₂²	1	1	yes	characteristic
54	C₂×C₇×#117	C₂²	1	1	yes	characteristic
55	C₂×C₇×#117	C₂²	1	1	yes	characteristic
56	C₂×C₇×#117	C₂²	1	1	yes	characteristic
57	C₇×#501	C₂²	1	2	yes	complemented
58	C₇×#501	C₂²	1	2	yes	complemented
59	C₇×#501	C₂²	1	2	yes	complemented
60	C₇×#501	C₂²	1	2	yes	complemented
61	C₇×#500	C₂²	1	2	yes	complemented
62	C₇×#499	C₂²	1	2	yes	complemented
63	C₇×#499	C₂²	1	2	yes	complemented
64	C₇×#498	C₂²	1	2	yes	complemented
65	C₇×#491	C₂²	1	2	yes	complemented
66	C₇×#491	C₂²	1	2	yes	complemented
67	C₇×#489	C₂²	1	2	yes	complemented
68	C₇×#489	C₂²	1	2	yes	complemented
69	C₇×#488	C₂²	1	2	yes	complemented
70	C₇×#488	C₂²	1	2	yes	complemented
71	C₇×#487	C₂²	1	2	yes	complemented
72	C₇×#487	C₂²	1	2	yes	complemented
73	C₇×#485	C₂²	1	1	yes	characteristic
74	C₇×#485	C₂²	1	2	yes	—
75	C₇×#485	C₂²	1	2	yes	—
76	C₇×#485	C₂²	1	2	yes	—
77	C₇×#485	C₂²	1	2	yes	—
78	C₇×#485	C₂²	1	1	yes	characteristic
79	C₇×#485	C₂²	1	2	yes	—
80	C₇×#485	C₂²	1	2	yes	—
81	C₇×#485	C₂²	1	2	yes	—
82	C₇×#485	C₂²	1	2	yes	—
83	C₇×#484	C₂²	1	1	yes	characteristic
84	C₇×#484	C₂²	1	2	yes	—
85	C₇×#483	C₂²	1	1	yes	characteristic
86	C₇×#483	C₂²	1	2	yes	—
87	C₇×#482	C₂²	1	1	yes	characteristic
88	C₇×#482	C₂²	1	2	yes	—
89	C₇×#482	C₂²	1	1	yes	characteristic
90	C₇×#482	C₂²	1	2	yes	—
91	C₇×#481	C₂²	1	1	yes	characteristic
92	C₇×#480	C₂²	1	1	yes	characteristic
93	C₇×#479	C₂²	1	2	yes	complemented
94	C₇×#479	C₂²	1	2	yes	complemented
95	C₇×#479	C₂²	1	2	yes	complemented
96	C₇×#479	C₂²	1	2	yes	complemented
97	C₇×#479	C₂²	1	2	yes	complemented
98	C₇×#479	C₂²	1	2	yes	complemented
99	C₇×#478	C₂²	1	2	yes	complemented
100	C₇×#478	C₂²	1	2	yes	complemented
101	C₇×#477	C₂²	1	2	yes	complemented
102	C₇×#477	C₂²	1	2	yes	complemented
103	C₇×#477	C₂²	1	2	yes	complemented
104	C₇×#476	C₂²	1	2	yes	complemented
105	C₇×#475	C₂²	1	2	yes	complemented
106	C₇×#475	C₂²	1	2	yes	complemented
107	C₇×#475	C₂²	1	2	yes	complemented
108	C₇×#474	C₂²	1	2	yes	complemented
109	C₇×#433	C₂²	1	2	yes	—
110	C₇×#433	C₂²	1	2	yes	—
111	C₇×#432	C₂²	1	2	yes	—
112	C₇×#431	C₂²	1	2	yes	—
113	C₇×#428	C₂²	1	1	yes	characteristic
114	C₇×#428	C₂²	1	1	yes	characteristic
115	C₇×#428	C₂²	1	1	yes	characteristic
116	C₇×#428	C₂²	1	1	yes	characteristic
117	C₇×#427	C₂²	1	1	yes	characteristic
118	C₇×#427	C₂²	1	1	yes	characteristic
119	C₂×C₇×#107	C₂²	1	1	yes	characteristic
120	C₂×C₇×#106	C₂²	1	1	yes	characteristic
121	C₇×#424	C₂²	1	1	yes	characteristic
122	C₇×#424	C₂²	1	1	yes	characteristic
123	C₇×#419	C₂²	1	1	yes	characteristic
124	C₇×#419	C₂²	1	1	yes	characteristic
125	C₇×#417	C₂²	1	1	yes	characteristic
126	C₇×#417	C₂²	1	1	yes	characteristic
127	C₇×#416	C₂²	1	1	yes	characteristic
128	C₇×#416	C₂²	1	1	yes	characteristic
129	C₂×C₇×#103	C₂²	1	1	yes	characteristic
130	C₂×C₇×#103	C₂²	1	1	yes	characteristic
131	C₇×#407	C₂²	1	1	yes	characteristic
132	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
133	C₇×#405	C₂²	1	1	yes	characteristic
134	C₇×#405	C₂²	1	1	yes	characteristic
135	#60876	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	C₂³	1	1	yes	characteristic
137	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
139	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
141	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
142	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
143	C₇×C₄⋊Q₈	—	2	1	no	—
144	C₇×C₄⋊Q₈	—	2	1	no	—
145	C₇×C₄⋊Q₈	—	2	1	no	—
146	C₇×C₄⋊Q₈	—	2	2	no	—
147	C₇×C₄⋊Q₈	—	2	1	no	—
148	C₇×C₄⋊Q₈	—	2	2	no	—
149	C₇×C₄⋊Q₈	—	2	1	no	—
150	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
151	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
153	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₇×#126	—	2	2	no	—
157	C₇×#126	—	2	2	no	—
158	C₇×#126	—	2	2	no	—
159	C₇×#126	—	2	2	no	—
160	C₇×#125	—	2	1	no	—
161	C₇×#125	—	2	1	no	—
162	C₇×#125	—	2	1	no	—
163	C₇×#125	—	2	2	no	—
164	C₇×#125	—	2	1	no	—
165	C₇×#125	—	2	2	no	—
166	C₇×#125	—	2	2	no	—
167	C₇×#125	—	2	2	no	—
168	C₇×#125	—	2	1	no	—
169	C₇×#125	—	2	2	no	—
170	C₇×#125	C₂³	1	2	yes	—
171	C₇×#125	C₂³	1	2	yes	—
172	C₇×#125	C₂³	1	2	yes	—
173	C₇×#125	C₂³	1	2	yes	—
174	C₇×#125	C₂³	1	2	yes	—
175	C₇×#124	—	2	2	no	—
176	C₇×#124	C₂³	1	2	yes	—
177	C₇×#123	—	2	1	no	—
178	C₇×#123	—	2	2	no	—
179	C₇×#123	—	2	2	no	—
180	C₇×#123	—	2	2	no	—
181	C₇×C₂²⋊Q₈	—	2	1	no	—
182	C₇×C₂²⋊Q₈	—	2	1	no	—
183	C₇×C₂²⋊Q₈	—	2	2	no	—
184	C₇×C₂²⋊Q₈	—	2	2	no	—
185	C₇×C₂²⋊Q₈	—	2	2	no	—
186	C₇×C₂²⋊Q₈	—	2	2	no	—
187	C₇×C₂²⋊Q₈	—	2	2	no	—
188	C₇×C₂²⋊Q₈	—	2	1	no	—
189	C₇×C₂²⋊Q₈	—	2	1	no	—
190	C₇×C₂²⋊Q₈	—	2	2	no	—
191	C₇×C₂²⋊Q₈	—	2	2	no	—
192	C₇×C₂²⋊Q₈	—	2	2	no	—
193	C₇×C₂²⋊Q₈	—	2	2	no	—
194	C₇×C₂²⋊Q₈	—	2	2	no	—
195	C₇×C₂²⋊Q₈	—	2	2	no	—
196	C₇×C₂²⋊Q₈	—	2	2	no	—
197	C₇×C₂²⋊Q₈	—	2	2	no	—
198	C₇×C₂²⋊Q₈	—	2	2	no	—
199	C₇×C₂²⋊Q₈	—	2	2	no	—
200	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
202	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
204	C₇×#121	C₂³	1	1	yes	characteristic
205	C₇×#121	C₂³	1	1	yes	characteristic
206	C₇×#120	—	2	1	no	—
207	C₄×C₇×Q₈	—	2	1	no	—
208	C₄×C₇×Q₈	—	2	1	no	—
209	C₄×C₇×Q₈	—	2	2	no	—
210	C₄×C₇×Q₈	—	2	2	no	—
211	C₄×C₇×Q₈	—	2	2	no	—
212	C₄×C₇×Q₈	—	2	2	no	—
213	C₄×C₇×Q₈	—	2	2	no	—
214	C₄×C₇×Q₈	C₂³	1	2	yes	—
215	C₄×C₇×Q₈	C₂³	1	2	yes	—
216	C₄×C₇×Q₈	C₂³	1	2	yes	—
217	C₄×C₇×D₄	—	2	1	no	—
218	C₄×C₇×D₄	—	2	1	no	—
219	C₄×C₇×D₄	—	2	2	no	—
220	C₄×C₇×D₄	—	2	2	no	—
221	C₄×C₇×D₄	C₂³	1	2	yes	—
222	C₇×#117	—	2	1	no	—
223	C₇×#117	—	2	1	no	—
224	C₇×#117	—	2	1	no	—
225	C₇×#117	—	2	1	no	—
226	C₇×#117	—	2	2	no	—
227	C₇×#117	—	2	1	no	—
228	C₇×#117	—	2	2	no	—
229	C₇×#117	—	2	2	no	—
230	C₇×#117	D₄	1	1	yes	characteristic
231	C₇×#117	D₄	1	2	yes	—
232	C₇×#117	D₄	1	1	yes	characteristic
233	C₇×#117	C₂³	1	1	yes	characteristic
234	C₇×#117	C₂³	1	2	yes	—
235	C₇×#117	C₂³	1	1	yes	characteristic
236	C₇×#117	C₂³	1	2	yes	—
237	C₇×#117	C₂³	1	1	yes	characteristic
238	C₇×#117	C₂³	1	1	yes	characteristic
239	C₇×#117	C₂³	1	1	yes	characteristic
240	C₇×#117	C₂³	1	1	yes	characteristic
241	C₇×#117	C₂³	1	1	yes	characteristic
242	C₇×#117	C₂³	1	2	yes	—
243	C₂×C₇×C₄⋊C₄	—	2	1	no	—
244	C₂×C₇×C₄⋊C₄	—	2	1	no	—
245	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
246	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
247	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
256	C₂×C₄²×C₇	—	2	1	no	—
257	C₂×C₄²×C₇	—	2	1	no	—
258	C₂×C₄²×C₇	C₂³	1	2	yes	—
259	C₇×#107	C₂³	1	2	yes	—
260	C₇×#107	C₂³	1	2	yes	—
261	C₇×#107	C₂³	1	1	yes	characteristic
262	C₇×#107	C₂³	1	1	yes	characteristic
263	C₇×#107	C₂³	1	2	yes	—
264	C₇×#107	C₂³	1	2	yes	—
265	C₇×#107	C₂³	1	2	yes	—
266	C₇×#107	C₂³	1	2	yes	—
267	C₇×#107	C₂³	1	1	yes	characteristic
268	C₇×#107	C₂³	1	1	yes	characteristic
269	C₇×#106	C₂³	1	1	yes	characteristic
270	C₇×#106	C₂³	1	1	yes	characteristic
271	C₇×#106	C₂³	1	2	yes	—
272	C₇×#106	C₂³	1	2	yes	—
273	C₇×#106	C₂³	1	2	yes	—
274	C₇×#106	C₂³	1	2	yes	—
275	C₇×#106	C₂³	1	2	yes	—
276	C₇×#106	C₂³	1	2	yes	—
277	C₇×#106	C₂³	1	1	yes	characteristic
278	C₇×#106	C₂³	1	1	yes	characteristic
279	C₇×C₄⋊C₈	C₂³	1	2	yes	—
280	C₇×C₄⋊C₈	C₂³	1	2	yes	—
281	C₇×C₄⋊C₈	C₂³	1	2	yes	—
282	C₇×C₄⋊C₈	C₂³	1	2	yes	—
283	C₇×#103	C₂³	1	1	yes	characteristic
284	C₇×#103	C₂³	1	2	yes	—
285	C₇×#103	C₂³	1	2	yes	—
286	C₇×#103	C₂³	1	2	yes	—
287	C₇×#103	C₂³	1	2	yes	—
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	1	yes	characteristic
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	1	yes	characteristic
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	2	yes	—
297	C₇×#102	C₂³	1	1	yes	characteristic
298	C₇×#102	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	1	yes	characteristic
300	C₇×#102	C₂³	1	2	yes	—
301	C₇×#102	C₂³	1	1	yes	characteristic
302	C₇×#102	C₂³	1	1	yes	characteristic
303	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
307	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₇×#97	C₂³	1	2	yes	—
310	C₇×#97	C₂³	1	2	yes	—
311	C₄×C₇×C₈	C₂³	1	2	yes	—
312	C₄×C₇×C₈	C₂³	1	2	yes	—
313	#3495	C₂×C₇	1	1	yes	characteristic
314	#3458	C₂×C₇	1	1	yes	characteristic, complemented
315	#3244	C₂×C₇	1	2	yes	complemented
316	#3243	C₂×C₇	1	2	yes	complemented
317	#3242	C₂×C₇	1	2	yes	complemented
318	#3242	C₂×C₇	1	2	yes	complemented
319	#3240	C₂×C₇	1	2	yes	complemented
320	#3237	C₂×C₇	1	2	yes	complemented
321	#3233	C₂×C₇	1	2	yes	complemented
322	#3231	C₂×C₇	1	2	yes	complemented
323	#3164	C₂×C₇	1	1	yes	characteristic, complemented
324	#3163	C₂×C₇	1	1	yes	characteristic, complemented
325	#3137	C₂×C₇	1	1	yes	characteristic, complemented
326	#3137	C₂×C₇	1	1	yes	characteristic, complemented
327	#3095	C₂×C₇	1	1	yes	characteristic, complemented
328	#3093	C₂×C₇	1	1	yes	characteristic
329	#3091	C₂×C₇	1	1	yes	characteristic
330	C₂×#485	C₂×C₇	1	1	yes	characteristic, complemented
331	#3084	C₂×C₇	1	1	yes	characteristic, complemented
332	#3083	C₂×C₇	1	1	yes	characteristic, complemented
333	#3082	C₂×C₇	1	1	yes	characteristic, complemented
334	#3082	C₂×C₇	1	1	yes	characteristic, complemented
335	#2924	C₂×C₇	1	1	yes	characteristic, complemented
336	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
337	C₇×#41	—	2	2	no	—
338	C₇×#41	—	2	2	no	—
339	C₂×C₇×Q₈	—	2	1	no	—
340	C₂×C₇×Q₈	—	2	2	no	—
341	C₂×C₇×Q₈	—	2	2	no	—
342	C₂×C₇×Q₈	—	2	2	no	—
343	C₂×C₇×Q₈	—	2	2	no	—
344	C₂×C₇×Q₈	—	2	2	no	—
345	C₂×C₇×Q₈	—	2	2	no	—
346	C₂×C₇×Q₈	—	2	2	no	—
347	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
348	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
349	C₂×C₇×D₄	—	2	1	no	—
350	C₂×C₇×D₄	—	2	1	no	—
351	C₂×C₇×D₄	—	2	1	no	—
352	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₇	—	2	2	no	—
354	C₂²×C₄×C₇	—	2	2	no	—
355	C₂²×C₄×C₇	—	2	1	no	—
356	C₂²×C₄×C₇	—	2	1	no	—
357	C₂²×C₄×C₇	—	2	1	no	—
358	C₂²×C₄×C₇	—	2	1	no	—
359	C₂²×C₄×C₇	—	2	1	no	—
360	C₂²×C₄×C₇	—	2	1	no	—
361	C₂²×C₄×C₇	—	2	1	no	—
362	C₂²×C₄×C₇	—	2	2	no	—
363	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
371	C₇×M₁₆	—	2	2	no	—
372	C₇×M₁₆	—	2	2	no	—
373	C₂×C₇×C₈	—	2	2	no	—
374	C₂×C₇×C₈	—	2	2	no	—
375	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
376	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₇×C₈	C₂⁴	1	2	yes	—
378	C₂×C₇×C₈	C₂⁴	1	2	yes	—
379	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
380	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
381	C₇×C₄⋊C₄	—	2	1	no	—
382	C₇×C₄⋊C₄	—	2	2	no	—
383	C₇×C₄⋊C₄	—	2	2	no	—
384	C₇×C₄⋊C₄	—	2	2	no	—
385	C₇×C₄⋊C₄	—	2	1	no	—
386	C₇×C₄⋊C₄	—	2	1	no	—
387	C₇×C₄⋊C₄	—	2	1	no	—
388	C₇×C₄⋊C₄	—	2	1	no	—
389	C₇×C₄⋊C₄	—	2	2	no	—
390	C₇×C₄⋊C₄	—	2	2	no	—
391	C₇×C₄⋊C₄	—	2	2	no	—
392	C₇×C₄⋊C₄	—	2	2	no	—
393	C₇×C₄⋊C₄	—	2	2	no	—
394	C₇×C₄⋊C₄	—	2	1	no	—
395	C₇×C₄⋊C₄	—	2	2	no	—
396	C₇×C₄⋊C₄	—	2	1	no	—
397	C₇×C₄⋊C₄	—	2	2	no	—
398	C₇×C₄⋊C₄	—	2	2	no	—
399	C₇×C₄⋊C₄	—	2	2	no	—
400	C₇×C₄⋊C₄	—	2	2	no	—
401	C₇×C₄⋊C₄	—	2	2	no	—
402	C₇×C₄⋊C₄	—	2	2	no	—
403	C₇×C₄⋊C₄	—	2	2	no	—
404	C₇×C₄⋊C₄	—	2	2	no	—
405	C₇×C₄⋊C₄	—	2	2	no	—
406	C₇×C₄⋊C₄	—	2	2	no	—
407	C₇×C₄⋊C₄	—	2	2	no	—
408	C₇×C₄⋊C₄	—	2	2	no	—
409	C₇×C₄⋊C₄	—	2	2	no	—
410	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
412	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
413	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
414	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
415	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
416	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
418	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
419	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
420	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
421	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
422	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
423	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
424	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
425	C₇×C₂²⋊C₄	—	2	2	no	—
426	C₇×C₂²⋊C₄	—	2	1	no	—
427	C₇×C₂²⋊C₄	—	2	1	no	—
428	C₇×C₂²⋊C₄	—	2	2	no	—
429	C₇×C₂²⋊C₄	—	2	1	no	—
430	C₇×C₂²⋊C₄	—	2	1	no	—
431	C₇×C₂²⋊C₄	—	2	2	no	—
432	C₇×C₂²⋊C₄	—	2	2	no	—
433	C₇×C₂²⋊C₄	—	2	1	no	—
434	C₇×C₂²⋊C₄	—	2	1	no	—
435	C₇×C₂²⋊C₄	—	2	1	no	—
436	C₇×C₂²⋊C₄	—	2	1	no	—
437	C₇×C₂²⋊C₄	—	2	2	no	—
438	C₇×C₂²⋊C₄	—	2	2	no	—
439	C₇×C₂²⋊C₄	—	2	1	no	—
440	C₇×C₂²⋊C₄	—	2	2	no	—
441	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
442	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
443	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
444	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
445	C₄²×C₇	—	2	2	no	—
446	C₄²×C₇	—	2	1	no	—
447	C₄²×C₇	—	2	1	no	—
448	C₄²×C₇	—	2	2	no	—
449	C₄²×C₇	—	2	1	no	—
450	C₄²×C₇	—	2	1	no	—
451	C₄²×C₇	—	2	2	no	—
452	C₄²×C₇	—	2	2	no	—
453	C₄²×C₇	—	2	2	no	—
454	C₄²×C₇	—	2	1	no	—
455	C₄²×C₇	C₂×D₄	1	2	yes	—
456	C₄²×C₇	C₂×D₄	1	2	yes	—
457	C₄²×C₇	C₂⁴	1	2	yes	—
458	C₄²×C₇	C₂⁴	1	2	yes	—
459	#556	—	2	1	no	—
460	#554	—	2	1	no	—
461	#552	—	2	2	no	—
462	#552	—	2	1	no	—
463	#552	—	2	1	no	—
464	#551	—	2	2	no	—
465	#544	—	2	1	no	—
466	#544	—	2	1	no	—
467	#544	C₂²×C₇	1	1	yes	characteristic
468	#544	C₂²×C₇	1	1	yes	characteristic
469	#544	C₂²×C₇	1	1	yes	characteristic
470	#544	C₂²×C₇	1	1	yes	characteristic
471	#544	C₂²×C₇	1	1	yes	characteristic
472	#544	C₂²×C₇	1	2	yes	—
473	#544	C₂²×C₇	1	2	yes	—
474	#543	—	2	2	no	—
475	#542	C₂²×C₇	1	2	yes	—
476	#541	C₂²×C₇	1	2	yes	—
477	#536	C₂²×C₇	1	1	yes	characteristic
478	#533	—	2	2	no	—
479	#533	—	2	1	no	—
480	#533	—	2	1	no	—
481	#533	C₂²×C₇	1	2	yes	—
482	#533	C₂²×C₇	1	2	yes	—
483	#533	C₂²×C₇	1	2	yes	—
484	#529	C₂²×C₇	1	2	yes	—
485	#525	C₂²×C₇	1	1	yes	characteristic
486	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
487	#520	C₂²×C₇	1	1	yes	characteristic
488	#519	C₂²×C₇	1	1	yes	characteristic
489	C₂×#117	C₂²×C₇	1	1	yes	characteristic
490	C₂×#117	C₂²×C₇	1	1	yes	characteristic
491	C₂×#117	C₂²×C₇	1	1	yes	characteristic
492	#501	C₂²×C₇	1	2	yes	complemented
493	#501	C₂²×C₇	1	2	yes	complemented
494	#501	C₂²×C₇	1	2	yes	complemented
495	#501	C₂²×C₇	1	2	yes	complemented
496	#500	C₂²×C₇	1	2	yes	complemented
497	#499	C₂²×C₇	1	2	yes	complemented
498	#499	C₂²×C₇	1	2	yes	complemented
499	#498	C₂²×C₇	1	2	yes	complemented
500	#491	C₂²×C₇	1	2	yes	complemented
501	#491	C₂²×C₇	1	2	yes	complemented
502	#489	C₂²×C₇	1	2	yes	complemented
503	#489	C₂²×C₇	1	2	yes	complemented
504	#488	C₂²×C₇	1	2	yes	complemented
505	#488	C₂²×C₇	1	2	yes	complemented
506	#487	C₂²×C₇	1	2	yes	complemented
507	#487	C₂²×C₇	1	2	yes	complemented
508	#485	C₂²×C₇	1	2	yes	—
509	#485	C₂²×C₇	1	2	yes	—
510	#485	C₂²×C₇	1	2	yes	—
511	#485	C₂²×C₇	1	2	yes	—
512	#485	C₂²×C₇	1	1	yes	characteristic
513	#485	C₂²×C₇	1	1	yes	characteristic
514	#485	C₂²×C₇	1	2	yes	—
515	#485	C₂²×C₇	1	2	yes	—
516	#485	C₂²×C₇	1	2	yes	—
517	#485	C₂²×C₇	1	2	yes	—
518	#484	C₂²×C₇	1	1	yes	characteristic
519	#484	C₂²×C₇	1	2	yes	—
520	#483	C₂²×C₇	1	1	yes	characteristic
521	#483	C₂²×C₇	1	2	yes	—
522	#482	C₂²×C₇	1	1	yes	characteristic
523	#482	C₂²×C₇	1	1	yes	characteristic
524	#482	C₂²×C₇	1	2	yes	—
525	#482	C₂²×C₇	1	2	yes	—
526	#481	C₂²×C₇	1	1	yes	characteristic
527	#480	C₂²×C₇	1	1	yes	characteristic
528	#479	C₂²×C₇	1	2	yes	complemented
529	#479	C₂²×C₇	1	2	yes	complemented
530	#479	C₂²×C₇	1	2	yes	complemented
531	#479	C₂²×C₇	1	2	yes	complemented
532	#479	C₂²×C₇	1	2	yes	complemented
533	#479	C₂²×C₇	1	2	yes	complemented
534	#478	C₂²×C₇	1	2	yes	complemented
535	#478	C₂²×C₇	1	2	yes	complemented
536	#477	C₂²×C₇	1	2	yes	complemented
537	#477	C₂²×C₇	1	2	yes	complemented
538	#477	C₂²×C₇	1	2	yes	complemented
539	#476	C₂²×C₇	1	2	yes	complemented
540	#475	C₂²×C₇	1	2	yes	complemented
541	#475	C₂²×C₇	1	2	yes	complemented
542	#475	C₂²×C₇	1	2	yes	complemented
543	#474	C₂²×C₇	1	2	yes	complemented
544	#433	C₂²×C₇	1	2	yes	—
545	#433	C₂²×C₇	1	2	yes	—
546	#432	C₂²×C₇	1	2	yes	—
547	#431	C₂²×C₇	1	2	yes	—
548	#428	C₂²×C₇	1	1	yes	characteristic
549	#428	C₂²×C₇	1	1	yes	characteristic
550	#428	C₂²×C₇	1	1	yes	characteristic
551	#428	C₂²×C₇	1	1	yes	characteristic
552	#427	C₂²×C₇	1	1	yes	characteristic
553	#427	C₂²×C₇	1	1	yes	characteristic
554	C₂×#107	C₂²×C₇	1	1	yes	characteristic
555	C₂×#106	C₂²×C₇	1	1	yes	characteristic
556	#424	C₂²×C₇	1	1	yes	characteristic
557	#424	C₂²×C₇	1	1	yes	characteristic
558	#419	C₂²×C₇	1	1	yes	characteristic
559	#419	C₂²×C₇	1	1	yes	characteristic
560	#417	C₂²×C₇	1	1	yes	characteristic
561	#417	C₂²×C₇	1	1	yes	characteristic
562	#416	C₂²×C₇	1	1	yes	characteristic
563	#416	C₂²×C₇	1	1	yes	characteristic
564	C₂×#103	C₂²×C₇	1	1	yes	characteristic
565	C₂×#103	C₂²×C₇	1	1	yes	characteristic
566	#407	C₂²×C₇	1	1	yes	characteristic
567	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
568	#405	C₂²×C₇	1	1	yes	characteristic
569	#405	C₂²×C₇	1	1	yes	characteristic
570	C₂³×C₇	—	2	2	no	—
571	C₂³×C₇	—	2	1	no	—
572	C₂³×C₇	—	4	1	no	—
573	C₂³×C₇	—	4	1	no	—
574	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
575	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
576	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
577	C₇×Q₈	—	2	2	no	—
578	C₇×Q₈	—	2	2	no	—
579	C₇×Q₈	—	2	1	no	—
580	C₇×Q₈	—	2	1	no	—
581	C₇×Q₈	—	4	2	no	—
582	C₇×Q₈	—	8	2	no	—
583	C₇×Q₈	—	8	2	no	—
584	C₇×Q₈	—	8	2	no	—
585	C₇×Q₈	—	8	2	no	—
586	C₇×Q₈	—	8	2	no	—
587	C₇×D₄	—	2	1	no	—
588	C₇×D₄	—	2	1	no	—
589	C₇×D₄	—	4	2	no	—
590	C₇×D₄	—	4	2	no	—
591	C₇×D₄	—	8	1	no	—
592	C₂×C₄×C₇	—	2	2	no	—
593	C₂×C₄×C₇	—	2	2	no	—
594	C₂×C₄×C₇	—	2	2	no	—
595	C₂×C₄×C₇	—	2	1	no	—
596	C₂×C₄×C₇	—	2	1	no	—
597	C₂×C₄×C₇	—	2	1	no	—
598	C₂×C₄×C₇	—	2	1	no	—
599	C₂×C₄×C₇	—	2	1	no	—
600	C₂×C₄×C₇	—	2	1	no	—
601	C₂×C₄×C₇	—	2	2	no	—
602	C₂×C₄×C₇	—	2	1	no	—
603	C₂×C₄×C₇	—	2	2	no	—
604	C₂×C₄×C₇	—	2	1	no	—
605	C₂×C₄×C₇	—	2	1	no	—
606	C₂×C₄×C₇	—	2	2	no	—
607	C₂×C₄×C₇	—	2	1	no	—
608	C₂×C₄×C₇	—	2	1	no	—
609	C₂×C₄×C₇	—	2	2	no	—
610	C₂×C₄×C₇	—	4	2	no	—
611	C₂×C₄×C₇	—	4	2	no	—
612	C₂×C₄×C₇	—	4	2	no	—
613	C₂×C₄×C₇	—	4	2	no	—
614	C₂×C₄×C₇	—	8	2	no	—
615	C₂×C₄×C₇	—	8	1	no	—
616	C₂×C₄×C₇	—	8	1	no	—
617	C₂×C₄×C₇	—	8	1	no	—
618	C₂×C₄×C₇	—	8	1	no	—
619	C₂×C₄×C₇	—	8	1	no	—
620	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
621	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
622	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
623	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
624	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
625	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
626	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
627	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
628	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
629	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
630	C₇×C₈	—	2	1	no	—
631	C₇×C₈	—	2	1	no	—
632	C₇×C₈	—	2	1	no	—
633	C₇×C₈	—	2	1	no	—
634	C₇×C₈	—	2	2	no	—
635	C₇×C₈	—	2	2	no	—
636	C₂×#41	C₂³×C₇	1	1	yes	characteristic
637	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
638	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
639	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
640	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
641	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
642	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
643	C₄⋊Q₈	—	2	1	no	—
644	C₄⋊Q₈	—	2	1	no	—
645	C₄⋊Q₈	—	2	1	no	—
646	C₄⋊Q₈	—	2	2	no	—
647	C₄⋊Q₈	—	2	1	no	—
648	C₄⋊Q₈	—	2	2	no	—
649	C₄⋊Q₈	—	2	1	no	—
650	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
651	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
652	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
653	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
654	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
655	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#125	—	2	1	no	—
661	#125	—	2	1	no	—
662	#125	—	2	1	no	—
663	#125	—	2	2	no	—
664	#125	—	2	1	no	—
665	#125	—	2	2	no	—
666	#125	—	2	2	no	—
667	#125	—	2	2	no	—
668	#125	—	2	1	no	—
669	#125	—	2	2	no	—
670	#125	C₂³×C₇	1	2	yes	—
671	#125	C₂³×C₇	1	2	yes	—
672	#125	C₂³×C₇	1	2	yes	—
673	#125	C₂³×C₇	1	2	yes	—
674	#125	C₂³×C₇	1	2	yes	—
675	#124	—	2	2	no	—
676	#124	C₂³×C₇	1	2	yes	—
677	#123	—	2	1	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	C₂²⋊Q₈	—	2	1	no	—
682	C₂²⋊Q₈	—	2	1	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	1	no	—
689	C₂²⋊Q₈	—	2	1	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
701	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
702	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
703	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
704	#121	C₂³×C₇	1	1	yes	characteristic
705	#121	C₂³×C₇	1	1	yes	characteristic
706	#120	—	2	1	no	—
707	C₄×Q₈	—	2	1	no	—
708	C₄×Q₈	—	2	1	no	—
709	C₄×Q₈	—	2	2	no	—
710	C₄×Q₈	—	2	2	no	—
711	C₄×Q₈	—	2	2	no	—
712	C₄×Q₈	—	2	2	no	—
713	C₄×Q₈	—	2	2	no	—
714	C₄×Q₈	C₂³×C₇	1	2	yes	—
715	C₄×Q₈	C₂³×C₇	1	2	yes	—
716	C₄×Q₈	C₂³×C₇	1	2	yes	—
717	C₄×D₄	—	2	1	no	—
718	C₄×D₄	—	2	1	no	—
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	C₂³×C₇	1	2	yes	—
722	#117	—	2	1	no	—
723	#117	—	2	1	no	—
724	#117	—	2	1	no	—
725	#117	—	2	1	no	—
726	#117	—	2	2	no	—
727	#117	—	2	1	no	—
728	#117	—	2	2	no	—
729	#117	—	2	2	no	—
730	#117	C₇×D₄	1	1	yes	characteristic
731	#117	C₇×D₄	1	2	yes	—
732	#117	C₇×D₄	1	1	yes	characteristic
733	#117	C₂³×C₇	1	2	yes	—
734	#117	C₂³×C₇	1	1	yes	characteristic
735	#117	C₂³×C₇	1	1	yes	characteristic
736	#117	C₂³×C₇	1	1	yes	characteristic
737	#117	C₂³×C₇	1	1	yes	characteristic
738	#117	C₂³×C₇	1	2	yes	—
739	#117	C₂³×C₇	1	1	yes	characteristic
740	#117	C₂³×C₇	1	1	yes	characteristic
741	#117	C₂³×C₇	1	1	yes	characteristic
742	#117	C₂³×C₇	1	2	yes	—
743	C₂×C₄⋊C₄	—	2	1	no	—
744	C₂×C₄⋊C₄	—	2	1	no	—
745	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
752	C₂×C₂²⋊C₄	—	2	1	no	—
753	C₂×C₂²⋊C₄	—	2	1	no	—
754	C₂×C₂²⋊C₄	—	2	1	no	—
755	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
756	C₂×C₄²	—	2	1	no	—
757	C₂×C₄²	—	2	1	no	—
758	C₂×C₄²	C₂³×C₇	1	2	yes	—
759	#107	C₂³×C₇	1	2	yes	—
760	#107	C₂³×C₇	1	2	yes	—
761	#107	C₂³×C₇	1	1	yes	characteristic
762	#107	C₂³×C₇	1	1	yes	characteristic
763	#107	C₂³×C₇	1	1	yes	characteristic
764	#107	C₂³×C₇	1	1	yes	characteristic
765	#107	C₂³×C₇	1	2	yes	—
766	#107	C₂³×C₇	1	2	yes	—
767	#107	C₂³×C₇	1	2	yes	—
768	#107	C₂³×C₇	1	2	yes	—
769	#106	C₂³×C₇	1	2	yes	—
770	#106	C₂³×C₇	1	2	yes	—
771	#106	C₂³×C₇	1	1	yes	characteristic
772	#106	C₂³×C₇	1	1	yes	characteristic
773	#106	C₂³×C₇	1	1	yes	characteristic
774	#106	C₂³×C₇	1	1	yes	characteristic
775	#106	C₂³×C₇	1	2	yes	—
776	#106	C₂³×C₇	1	2	yes	—
777	#106	C₂³×C₇	1	2	yes	—
778	#106	C₂³×C₇	1	2	yes	—
779	C₄⋊C₈	C₂³×C₇	1	2	yes	—
780	C₄⋊C₈	C₂³×C₇	1	2	yes	—
781	C₄⋊C₈	C₂³×C₇	1	2	yes	—
782	C₄⋊C₈	C₂³×C₇	1	2	yes	—
783	#103	C₂³×C₇	1	2	yes	—
784	#103	C₂³×C₇	1	2	yes	—
785	#103	C₂³×C₇	1	2	yes	—
786	#103	C₂³×C₇	1	2	yes	—
787	#103	C₂³×C₇	1	1	yes	characteristic
788	#103	C₂³×C₇	1	1	yes	characteristic
789	#103	C₂³×C₇	1	1	yes	characteristic
790	#103	C₂³×C₇	1	1	yes	characteristic
791	#103	C₂³×C₇	1	2	yes	—
792	#103	C₂³×C₇	1	2	yes	—
793	#103	C₂³×C₇	1	2	yes	—
794	#103	C₂³×C₇	1	2	yes	—
795	#103	C₂³×C₇	1	2	yes	—
796	#103	C₂³×C₇	1	2	yes	—
797	#102	C₂³×C₇	1	1	yes	characteristic
798	#102	C₂³×C₇	1	1	yes	characteristic
799	#102	C₂³×C₇	1	1	yes	characteristic
800	#102	C₂³×C₇	1	1	yes	characteristic
801	#102	C₂³×C₇	1	2	yes	—
802	#102	C₂³×C₇	1	2	yes	—
803	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
804	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
805	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
806	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
807	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
808	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
809	#97	C₂³×C₇	1	2	yes	—
810	#97	C₂³×C₇	1	2	yes	—
811	C₄×C₈	C₂³×C₇	1	2	yes	—
812	C₄×C₈	C₂³×C₇	1	2	yes	—
813	C₂²×C₇	—	2	1	no	—
814	C₂²×C₇	—	2	1	no	—
815	C₂²×C₇	—	2	1	no	—
816	C₂²×C₇	—	2	1	no	—
817	C₂²×C₇	—	2	1	no	—
818	C₂²×C₇	—	2	1	no	—
819	C₂²×C₇	—	2	1	no	—
820	C₂²×C₇	—	2	1	no	—
821	C₂²×C₇	—	4	1	no	—
822	C₂²×C₇	—	4	1	no	—
823	C₂²×C₇	—	4	1	no	—
824	C₂²×C₇	—	8	2	no	—
825	C₂²×C₇	#536	1	2	yes	—
826	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
827	C₄×C₇	—	2	2	no	—
828	C₄×C₇	—	2	2	no	—
829	C₄×C₇	—	2	2	no	—
830	C₄×C₇	—	2	2	no	—
831	C₄×C₇	—	2	1	no	—
832	C₄×C₇	—	2	1	no	—
833	C₄×C₇	—	4	2	no	—
834	C₄×C₇	—	4	2	no	—
835	C₄×C₇	—	4	1	no	—
836	C₄×C₇	—	4	1	no	—
837	C₄×C₇	—	4	1	no	—
838	C₄×C₇	—	4	2	no	—
839	C₄×C₇	—	4	1	no	—
840	C₄×C₇	—	4	1	no	—
841	C₄×C₇	—	4	1	no	—
842	C₄×C₇	—	4	1	no	—
843	C₄×C₇	—	4	2	no	—
844	C₄×C₇	#536	1	2	yes	—
845	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
846	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
847	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
848	#41	—	2	2	no	—
849	#41	—	2	2	no	—
850	C₂×Q₈	—	2	1	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	—	2	2	no	—
853	C₂×Q₈	—	2	2	no	—
854	C₂×Q₈	—	2	2	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	2	no	—
858	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
859	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
860	C₂×D₄	—	2	1	no	—
861	C₂×D₄	—	2	1	no	—
862	C₂×D₄	—	2	1	no	—
863	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
875	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
876	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
877	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
878	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
879	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
882	M₁₆	—	2	2	no	—
883	M₁₆	—	2	2	no	—
884	C₂×C₈	—	2	2	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
887	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
888	C₂×C₈	C₂⁴×C₇	1	2	yes	—
889	C₂×C₈	C₂⁴×C₇	1	2	yes	—
890	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
891	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
922	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
923	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
924	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
925	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
926	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
927	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
928	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
929	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
930	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
931	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
932	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
933	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
935	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	1	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	1	no	—
946	C₂²⋊C₄	—	2	1	no	—
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
953	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
954	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
955	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	1	no	—
958	C₄²	—	2	1	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	1	no	—
966	C₄²	C₂×C₇×D₄	1	2	yes	—
967	C₄²	C₂×C₇×D₄	1	2	yes	—
968	C₄²	C₂⁴×C₇	1	2	yes	—
969	C₄²	C₂⁴×C₇	1	2	yes	—
970	C₂×C₇	—	2	2	no	—
971	C₂×C₇	—	4	1	no	—
972	C₂×C₇	—	4	1	no	—
973	C₂×C₇	—	8	1	no	—
974	C₂×C₇	C₂×#536	1	1	yes	characteristic
975	C₂×C₇	#3584	1	1	yes	characteristic
976	C₂×C₇	#3586	1	1	yes	characteristic
977	C₂³	—	2	2	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	4	1	no	—
980	C₂³	—	4	1	no	—
981	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
982	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
983	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
984	Q₈	—	2	2	no	—
985	Q₈	—	2	2	no	—
986	Q₈	—	2	1	no	—
987	Q₈	—	2	1	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	8	2	no	—
990	Q₈	—	8	2	no	—
991	Q₈	—	8	2	no	—
992	Q₈	—	8	2	no	—
993	Q₈	—	8	2	no	—
994	D₄	—	2	1	no	—
995	D₄	—	2	1	no	—
996	D₄	—	4	2	no	—
997	D₄	—	4	2	no	—
998	D₄	—	8	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	4	2	no	—
1018	C₂×C₄	—	4	2	no	—
1019	C₂×C₄	—	4	2	no	—
1020	C₂×C₄	—	4	2	no	—
1021	C₂×C₄	—	8	2	no	—
1022	C₂×C₄	—	8	1	no	—
1023	C₂×C₄	—	8	1	no	—
1024	C₂×C₄	—	8	1	no	—
1025	C₂×C₄	—	8	1	no	—
1026	C₂×C₄	—	8	1	no	—
1027	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1028	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1029	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1030	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1031	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1032	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1033	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1034	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1035	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1036	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1037	C₈	—	2	1	no	—
1038	C₈	—	2	1	no	—
1039	C₈	—	2	1	no	—
1040	C₈	—	2	1	no	—
1041	C₈	—	2	2	no	—
1042	C₈	—	2	2	no	—
1043	C₇	#60876	1	1	yes	characteristic, direct product factor, Sylow
1044	C₂²	—	2	1	no	—
1045	C₂²	—	2	1	no	—
1046	C₂²	—	2	1	no	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	8	2	no	—
1056	C₂²	C₇×#536	1	2	yes	—
1057	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1058	C₄	—	2	2	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	2	no	—
1075	C₄	C₇×#536	1	2	yes	—
1076	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1077	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1078	C₂	—	2	2	no	—
1079	C₂	—	4	1	no	—
1080	C₂	—	4	1	no	—
1081	C₂	—	8	1	no	—
1082	C₂	C₂×C₇×#536	1	1	yes	characteristic
1083	C₂	C₇×#3584	1	1	yes	characteristic
1084	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3458	C₂	semidirect
3. C₇×#3244	C₂	semidirect
4. C₇×#3243	C₂	semidirect
5. C₇×#3242	C₂	semidirect
6. C₇×#3242	C₂	semidirect
7. C₇×#3240	C₂	semidirect
8. C₇×#3237	C₂	semidirect
9. C₇×#3233	C₂	semidirect
10. C₇×#3231	C₂	semidirect
11. C₇×#3164	C₂	semidirect
12. C₇×#3163	C₂	semidirect
13. C₇×#3137	C₂	semidirect
14. C₇×#3137	C₂	semidirect
15. C₇×#3095	C₂	semidirect
18. C₂×C₇×#485	C₂	semidirect
19. C₇×#3084	C₂	semidirect
20. C₇×#3083	C₂	semidirect
21. C₇×#3082	C₂	semidirect
22. C₇×#3082	C₂	semidirect
23. C₇×#2924	C₂	semidirect
57. C₇×#501	C₂²	semidirect
58. C₇×#501	C₂²	semidirect
59. C₇×#501	C₂²	semidirect
60. C₇×#501	C₂²	semidirect
61. C₇×#500	C₂²	semidirect
62. C₇×#499	C₂²	semidirect
63. C₇×#499	C₂²	semidirect
64. C₇×#498	C₂²	semidirect
65. C₇×#491	C₂²	semidirect
66. C₇×#491	C₂²	semidirect
67. C₇×#489	C₂²	semidirect
68. C₇×#489	C₂²	semidirect
69. C₇×#488	C₂²	semidirect
70. C₇×#488	C₂²	semidirect
71. C₇×#487	C₂²	semidirect
72. C₇×#487	C₂²	semidirect
93. C₇×#479	C₂²	semidirect
94. C₇×#479	C₂²	semidirect
95. C₇×#479	C₂²	semidirect
96. C₇×#479	C₂²	semidirect
97. C₇×#479	C₂²	semidirect
98. C₇×#479	C₂²	semidirect
99. C₇×#478	C₂²	semidirect
100. C₇×#478	C₂²	semidirect
101. C₇×#477	C₂²	semidirect
102. C₇×#477	C₂²	semidirect
103. C₇×#477	C₂²	semidirect
104. C₇×#476	C₂²	semidirect
105. C₇×#475	C₂²	semidirect
106. C₇×#475	C₂²	semidirect
107. C₇×#475	C₂²	semidirect
108. C₇×#474	C₂²	semidirect
135. #60876	C₇	direct (N × H)
314. #3458	C₂×C₇	semidirect
315. #3244	C₂×C₇	semidirect
316. #3243	C₂×C₇	semidirect
317. #3242	C₂×C₇	semidirect
318. #3242	C₂×C₇	semidirect
319. #3240	C₂×C₇	semidirect
320. #3237	C₂×C₇	semidirect
321. #3233	C₂×C₇	semidirect
322. #3231	C₂×C₇	semidirect
323. #3164	C₂×C₇	semidirect
324. #3163	C₂×C₇	semidirect
325. #3137	C₂×C₇	semidirect
326. #3137	C₂×C₇	semidirect
327. #3095	C₂×C₇	semidirect
330. C₂×#485	C₂×C₇	semidirect
331. #3084	C₂×C₇	semidirect
332. #3083	C₂×C₇	semidirect
333. #3082	C₂×C₇	semidirect
334. #3082	C₂×C₇	semidirect
335. #2924	C₂×C₇	semidirect
492. #501	C₂²×C₇	semidirect
493. #501	C₂²×C₇	semidirect
494. #501	C₂²×C₇	semidirect
495. #501	C₂²×C₇	semidirect
496. #500	C₂²×C₇	semidirect
497. #499	C₂²×C₇	semidirect
498. #499	C₂²×C₇	semidirect
499. #498	C₂²×C₇	semidirect
500. #491	C₂²×C₇	semidirect
501. #491	C₂²×C₇	semidirect
502. #489	C₂²×C₇	semidirect
503. #489	C₂²×C₇	semidirect
504. #488	C₂²×C₇	semidirect
505. #488	C₂²×C₇	semidirect
506. #487	C₂²×C₇	semidirect
507. #487	C₂²×C₇	semidirect
528. #479	C₂²×C₇	semidirect
529. #479	C₂²×C₇	semidirect
530. #479	C₂²×C₇	semidirect
531. #479	C₂²×C₇	semidirect
532. #479	C₂²×C₇	semidirect
533. #479	C₂²×C₇	semidirect
534. #478	C₂²×C₇	semidirect
535. #478	C₂²×C₇	semidirect
536. #477	C₂²×C₇	semidirect
537. #477	C₂²×C₇	semidirect
538. #477	C₂²×C₇	semidirect
539. #476	C₂²×C₇	semidirect
540. #475	C₂²×C₇	semidirect
541. #475	C₂²×C₇	semidirect
542. #475	C₂²×C₇	semidirect
543. #474	C₂²×C₇	semidirect
1043. C₇	#60876	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×#3495	2
C₇×#3458	2
C₇×#3244	2
C₇×#3243	2
C₇×#3242	2
C₇×#3240	2
C₇×#3237	2
C₇×#3233	2
C₇×#3231	2
C₇×#3164	2
C₇×#3163	2
C₇×#3137	2
C₇×#3095	2
C₇×#3093	2
C₇×#3091	2
C₂×C₇×#485	2
C₇×#3084	2
C₇×#3083	2
C₇×#3082	2
C₇×#2924	2
#60876	7

Subgroups — C7×#60876 #13238092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60876 #13238092