Subgroups — C₇×#61386 #13238602

Order 1792.

1690 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3504	C₂	1	1	yes	maximal, characteristic
2	C₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3390	C₂	1	2	yes	maximal, complemented
4	C₇×#3390	C₂	1	2	yes	maximal, complemented
5	C₇×#3388	C₂	1	2	yes	maximal, complemented
6	C₇×#3388	C₂	1	2	yes	maximal, complemented
7	C₇×#3387	C₂	1	2	yes	maximal, complemented
8	C₇×#3385	C₂	1	2	yes	maximal, complemented
9	C₇×#3383	C₂	1	2	yes	maximal, complemented
10	C₇×#3381	C₂	1	2	yes	maximal, complemented
11	C₇×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3164	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3163	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3084	C₂	1	1	yes	maximal, characteristic
15	C₇×#3083	C₂	1	1	yes	maximal, characteristic
16	C₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3076	C₂	1	1	yes	maximal, characteristic
19	C₂×C₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2947	C₂	1	1	yes	maximal, characteristic
22	C₇×#2947	C₂	1	1	yes	maximal, characteristic
23	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic
24	C₂×C₇×#137	C₂²	1	1	yes	characteristic
25	C₇×Q₈²	—	2	1	no	—
26	C₇×Q₈²	C₂²	1	2	yes	—
27	C₇×#557	—	2	1	no	—
28	C₇×#557	—	2	1	no	—
29	C₇×#557	—	2	1	no	—
30	C₇×#557	C₂²	1	2	yes	—
31	C₇×#557	C₂²	1	2	yes	—
32	C₇×#557	C₂²	1	2	yes	—
33	C₇×#557	C₂²	1	2	yes	—
34	C₇×#557	C₂²	1	2	yes	—
35	C₇×#554	—	2	2	no	—
36	C₇×#554	—	2	2	no	—
37	C₇×#554	C₂²	1	2	yes	—
38	C₇×#554	C₂²	1	2	yes	—
39	C₇×#544	—	2	1	no	—
40	C₇×#544	—	2	1	no	—
41	C₇×#544	—	2	2	no	—
42	C₇×#544	C₂²	1	1	yes	characteristic
43	C₇×#544	C₂²	1	1	yes	characteristic
44	C₇×#544	C₂²	1	1	yes	characteristic
45	C₇×#544	C₂²	1	1	yes	characteristic
46	C₇×#533	—	2	1	no	—
47	C₇×#533	—	2	2	no	—
48	C₇×#533	C₂²	1	1	yes	characteristic
49	C₇×#533	C₂²	1	1	yes	characteristic
50	C₂×C₇×#125	—	2	1	no	—
51	C₂×C₇×#125	C₂²	1	1	yes	characteristic
52	C₇×#520	C₂²	1	1	yes	characteristic
53	C₇×#520	C₂²	1	1	yes	characteristic
54	C₇×#519	C₂²	1	1	yes	characteristic
55	C₇×#519	C₂²	1	1	yes	characteristic
56	C₄×C₇×#41	C₂²	1	1	yes	characteristic
57	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
58	C₇×#501	C₂²	1	2	yes	—
59	C₇×#501	C₂²	1	2	yes	—
60	C₇×#501	C₂²	1	2	yes	—
61	C₇×#501	C₂²	1	2	yes	—
62	C₇×#501	C₂²	1	2	yes	—
63	C₇×#501	C₂²	1	2	yes	—
64	C₇×#500	C₂²	1	2	yes	—
65	C₇×#499	C₂²	1	2	yes	—
66	C₇×#499	C₂²	1	2	yes	—
67	C₇×#499	C₂²	1	2	yes	—
68	C₇×#499	C₂²	1	2	yes	—
69	C₇×#498	C₂²	1	2	yes	—
70	C₇×#479	C₂²	1	2	yes	—
71	C₇×#479	C₂²	1	2	yes	—
72	C₇×#479	C₂²	1	2	yes	—
73	C₇×#479	C₂²	1	2	yes	—
74	C₇×#479	C₂²	1	1	yes	characteristic
75	C₇×#479	C₂²	1	1	yes	characteristic
76	C₇×#479	C₂²	1	2	yes	—
77	C₇×#479	C₂²	1	2	yes	—
78	C₇×#479	C₂²	1	2	yes	—
79	C₇×#479	C₂²	1	2	yes	—
80	C₇×#479	C₂²	1	2	yes	—
81	C₇×#479	C₂²	1	2	yes	—
82	C₇×#478	C₂²	1	1	yes	characteristic
83	C₇×#478	C₂²	1	1	yes	characteristic
84	C₇×#478	C₂²	1	2	yes	—
85	C₇×#478	C₂²	1	2	yes	—
86	C₇×#477	C₂²	1	1	yes	characteristic
87	C₇×#477	C₂²	1	2	yes	—
88	C₇×#477	C₂²	1	2	yes	—
89	C₇×#477	C₂²	1	2	yes	—
90	C₇×#476	C₂²	1	1	yes	characteristic
91	C₇×#476	C₂²	1	2	yes	—
92	C₇×#475	C₂²	1	1	yes	characteristic
93	C₇×#475	C₂²	1	2	yes	—
94	C₇×#475	C₂²	1	2	yes	—
95	C₇×#475	C₂²	1	2	yes	—
96	C₇×#474	C₂²	1	1	yes	characteristic
97	C₇×#474	C₂²	1	2	yes	—
98	C₇×#446	C₂²	1	2	yes	—
99	C₇×#446	C₂²	1	2	yes	—
100	C₇×#446	C₂²	1	2	yes	—
101	C₇×C₈×Q₈	C₂²	1	2	yes	—
102	C₇×#441	C₂²	1	2	yes	—
103	C₇×#441	C₂²	1	2	yes	—
104	C₇×#441	C₂²	1	2	yes	—
105	C₇×#440	C₂²	1	2	yes	—
106	C₇×#440	C₂²	1	2	yes	—
107	C₇×#440	C₂²	1	2	yes	—
108	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
109	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
110	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
111	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
112	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
113	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
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×#428	C₂²	1	1	yes	characteristic
118	C₇×#428	C₂²	1	1	yes	characteristic
119	C₇×#427	C₂²	1	1	yes	characteristic
120	C₇×#427	C₂²	1	1	yes	characteristic
121	C₂×C₇×#107	C₂²	1	1	yes	characteristic
122	C₂×C₇×#106	C₂²	1	1	yes	characteristic
123	C₇×#424	C₂²	1	1	yes	characteristic
124	C₇×#424	C₂²	1	1	yes	characteristic
125	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₇×#419	C₂²	1	1	yes	characteristic
127	C₇×#417	C₂²	1	1	yes	characteristic
128	C₇×#416	C₂²	1	1	yes	characteristic
129	C₇×#416	C₂²	1	1	yes	characteristic
130	C₂×C₇×#103	C₂²	1	1	yes	characteristic
131	C₂×C₇×#103	C₂²	1	1	yes	characteristic
132	C₇×#405	C₂²	1	1	yes	characteristic
133	C₇×#405	C₂²	1	1	yes	characteristic
134	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
135	#61386	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	C₇×#137	Q₈	1	8	yes	complemented
139	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
140	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
141	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
142	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
143	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
144	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
145	C₇×C₄⋊Q₈	—	2	2	no	—
146	C₇×C₄⋊Q₈	—	2	2	no	—
147	C₇×C₄⋊Q₈	—	2	2	no	—
148	C₇×C₄⋊Q₈	—	2	2	no	—
149	C₇×C₄⋊Q₈	—	2	2	no	—
150	C₇×C₄⋊Q₈	—	2	1	no	—
151	C₇×C₄⋊Q₈	—	2	1	no	—
152	C₇×C₄⋊Q₈	—	2	2	no	—
153	C₇×C₄⋊Q₈	—	2	2	no	—
154	C₇×C₄⋊Q₈	—	2	2	no	—
155	C₇×C₄⋊Q₈	—	2	1	no	—
156	C₇×C₄⋊Q₈	—	2	1	no	—
157	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
158	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
159	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₇×#125	—	2	1	no	—
166	C₇×#125	—	2	1	no	—
167	C₇×#125	—	2	2	no	—
168	C₇×#125	—	2	2	no	—
169	C₇×#125	—	2	2	no	—
170	C₇×#125	—	2	2	no	—
171	C₇×#125	—	2	2	no	—
172	C₇×#125	—	2	2	no	—
173	C₇×#125	—	2	2	no	—
174	C₇×#125	—	2	2	no	—
175	C₇×#125	—	2	2	no	—
176	C₇×#125	—	2	2	no	—
177	C₇×#125	—	2	1	no	—
178	C₇×#125	—	2	1	no	—
179	C₇×#125	—	2	1	no	—
180	C₇×#125	—	2	1	no	—
181	C₇×#125	D₄	1	1	yes	characteristic
182	C₇×#125	D₄	1	1	yes	characteristic
183	C₇×#125	C₂³	1	1	yes	characteristic
184	C₇×#125	C₂³	1	1	yes	characteristic
185	C₇×#125	C₂³	1	2	yes	—
186	C₇×#125	C₂³	1	2	yes	—
187	C₇×#125	C₂³	1	2	yes	—
188	C₇×#125	C₂³	1	2	yes	—
189	C₇×#125	C₂³	1	2	yes	—
190	C₇×#125	C₂³	1	2	yes	—
191	C₇×C₂²⋊Q₈	—	2	2	no	—
192	C₇×C₂²⋊Q₈	—	2	2	no	—
193	C₇×C₂²⋊Q₈	—	2	1	no	—
194	C₇×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
201	C₇×C₂²⋊Q₈	—	2	2	no	—
202	C₇×C₂²⋊Q₈	—	2	2	no	—
203	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
204	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
205	C₄×C₇×Q₈	—	2	2	no	—
206	C₄×C₇×Q₈	—	2	1	no	—
207	C₄×C₇×Q₈	—	2	1	no	—
208	C₄×C₇×Q₈	—	2	1	no	—
209	C₄×C₇×Q₈	—	2	1	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	—	2	2	no	—
215	C₄×C₇×Q₈	—	2	1	no	—
216	C₄×C₇×Q₈	—	2	1	no	—
217	C₄×C₇×Q₈	—	2	1	no	—
218	C₄×C₇×Q₈	—	2	1	no	—
219	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
220	C₄×C₇×Q₈	C₂³	1	2	yes	—
221	C₄×C₇×Q₈	C₂³	1	2	yes	—
222	C₄×C₇×Q₈	C₂³	1	2	yes	—
223	C₄×C₇×Q₈	C₂³	1	2	yes	—
224	C₄×C₇×Q₈	C₂³	1	2	yes	—
225	C₄×C₇×Q₈	C₂³	1	2	yes	—
226	C₄×C₇×Q₈	C₂³	1	2	yes	—
227	C₄×C₇×Q₈	C₂³	1	2	yes	—
228	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
229	C₄×C₇×Q₈	C₂³	1	2	yes	—
230	C₄×C₇×Q₈	C₂³	1	2	yes	—
231	C₄×C₇×D₄	—	2	1	no	—
232	C₄×C₇×D₄	—	2	1	no	—
233	C₄×C₇×D₄	—	2	2	no	—
234	C₄×C₇×D₄	—	2	2	no	—
235	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
236	C₄×C₇×D₄	C₂³	1	2	yes	—
237	C₄×C₇×D₄	C₂³	1	2	yes	—
238	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
239	C₇×#117	—	2	1	no	—
240	C₇×#117	—	2	1	no	—
241	C₇×#117	—	2	2	no	—
242	C₇×#117	—	2	2	no	—
243	C₇×#117	—	2	1	no	—
244	C₇×#117	C₂³	1	1	yes	characteristic
245	C₇×#117	C₂³	1	1	yes	characteristic
246	C₇×#117	C₂³	1	1	yes	characteristic
247	C₇×#117	C₂³	1	1	yes	characteristic
248	C₇×#117	C₂³	1	1	yes	characteristic
249	C₂×C₇×C₄⋊C₄	—	2	1	no	—
250	C₂×C₇×C₄⋊C₄	—	2	1	no	—
251	C₂×C₇×C₄⋊C₄	—	2	1	no	—
252	C₂×C₇×C₄⋊C₄	—	2	1	no	—
253	C₂×C₇×C₄⋊C₄	—	2	1	no	—
254	C₂×C₇×C₄⋊C₄	—	2	2	no	—
255	C₂×C₇×C₄⋊C₄	—	2	2	no	—
256	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₇	—	2	1	no	—
260	C₂×C₄²×C₇	—	2	1	no	—
261	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
262	C₇×#107	C₂³	1	2	yes	—
263	C₇×#107	C₂³	1	1	yes	characteristic
264	C₇×#107	C₂³	1	2	yes	—
265	C₇×#107	C₂³	1	1	yes	characteristic
266	C₇×#107	C₂³	1	1	yes	characteristic
267	C₇×#107	C₂³	1	2	yes	—
268	C₇×#107	C₂³	1	2	yes	—
269	C₇×#107	C₂³	1	1	yes	characteristic
270	C₇×#107	C₂³	1	2	yes	—
271	C₇×#107	C₂³	1	2	yes	—
272	C₇×#107	C₂³	1	2	yes	—
273	C₇×#106	C₂³	1	1	yes	characteristic
274	C₇×#106	C₂³	1	1	yes	characteristic
275	C₇×#106	C₂³	1	2	yes	—
276	C₇×#106	C₂³	1	1	yes	characteristic
277	C₇×#106	C₂³	1	2	yes	—
278	C₇×#106	C₂³	1	2	yes	—
279	C₇×#106	C₂³	1	2	yes	—
280	C₇×#106	C₂³	1	1	yes	characteristic
281	C₇×#106	C₂³	1	2	yes	—
282	C₇×#106	C₂³	1	2	yes	—
283	C₇×#106	C₂³	1	2	yes	—
284	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₇×C₄⋊C₈	C₂³	1	2	yes	—
286	C₇×C₄⋊C₈	C₂³	1	2	yes	—
287	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₇×C₄⋊C₈	C₂³	1	2	yes	—
289	C₇×C₄⋊C₈	C₂³	1	2	yes	—
290	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₇×#103	C₂³	1	1	yes	characteristic
293	C₇×#103	C₂³	1	1	yes	characteristic
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#103	C₂³	1	2	yes	—
297	C₇×#103	C₂³	1	2	yes	—
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#103	C₂³	1	2	yes	—
300	C₇×#103	C₂³	1	2	yes	—
301	C₇×#103	C₂³	1	1	yes	characteristic
302	C₇×#103	C₂³	1	1	yes	characteristic
303	C₇×#102	C₂³	1	1	yes	characteristic
304	C₇×#102	C₂³	1	1	yes	characteristic
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	1	yes	characteristic
307	C₇×#102	C₂³	1	1	yes	characteristic
308	C₇×#97	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	C₄×C₇×C₈	C₂³	1	2	yes	—
314	#3504	C₂×C₇	1	1	yes	characteristic
315	#3502	C₂×C₇	1	1	yes	characteristic, complemented
316	#3390	C₂×C₇	1	2	yes	complemented
317	#3390	C₂×C₇	1	2	yes	complemented
318	#3388	C₂×C₇	1	2	yes	complemented
319	#3388	C₂×C₇	1	2	yes	complemented
320	#3387	C₂×C₇	1	2	yes	complemented
321	#3385	C₂×C₇	1	2	yes	complemented
322	#3383	C₂×C₇	1	2	yes	complemented
323	#3381	C₂×C₇	1	2	yes	complemented
324	#3166	C₂×C₇	1	1	yes	characteristic, complemented
325	#3164	C₂×C₇	1	1	yes	characteristic, complemented
326	#3163	C₂×C₇	1	1	yes	characteristic, complemented
327	#3084	C₂×C₇	1	1	yes	characteristic
328	#3083	C₂×C₇	1	1	yes	characteristic
329	#3082	C₂×C₇	1	1	yes	characteristic, complemented
330	#3082	C₂×C₇	1	1	yes	characteristic, complemented
331	#3076	C₂×C₇	1	1	yes	characteristic
332	C₂×#479	C₂×C₇	1	1	yes	characteristic, complemented
333	#2962	C₂×C₇	1	1	yes	characteristic, complemented
334	#2947	C₂×C₇	1	1	yes	characteristic
335	#2947	C₂×C₇	1	1	yes	characteristic
336	C₄×#137	C₂×C₇	1	1	yes	characteristic
337	C₇×#41	—	2	2	no	—
338	C₇×#41	C₂×Q₈	1	4	yes	—
339	C₂×C₇×Q₈	—	2	1	no	—
340	C₂×C₇×Q₈	—	2	1	no	—
341	C₂×C₇×Q₈	—	2	2	no	—
342	C₂×C₇×Q₈	—	2	2	no	—
343	C₂×C₇×Q₈	—	2	1	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	C₂×D₄	1	2	yes	—
348	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
349	C₂×C₇×Q₈	C₂×Q₈	1	4	yes	—
350	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
351	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
352	C₂×C₇×D₄	—	2	1	no	—
353	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₇	—	2	1	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	2	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	C₂⁴	1	1	yes	characteristic
366	C₇×Q₁₆	C₂×Q₈	1	8	yes	—
367	C₇×SD₁₆	C₂×Q₈	1	8	yes	—
368	C₇×M₁₆	—	2	2	no	—
369	C₇×M₁₆	C₂×Q₈	1	4	yes	—
370	C₂×C₇×C₈	—	2	2	no	—
371	C₂×C₇×C₈	—	2	2	no	—
372	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
373	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₇×C₈	C₂⁴	1	2	yes	—
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	C₇×C₄⋊C₄	—	2	2	no	—
379	C₇×C₄⋊C₄	—	2	2	no	—
380	C₇×C₄⋊C₄	—	2	1	no	—
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	2	no	—
386	C₇×C₄⋊C₄	—	2	2	no	—
387	C₇×C₄⋊C₄	—	2	2	no	—
388	C₇×C₄⋊C₄	—	2	2	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	1	no	—
393	C₇×C₄⋊C₄	—	2	1	no	—
394	C₇×C₄⋊C₄	—	2	1	no	—
395	C₇×C₄⋊C₄	—	2	2	no	—
396	C₇×C₄⋊C₄	—	2	2	no	—
397	C₇×C₄⋊C₄	—	2	2	no	—
398	C₇×C₄⋊C₄	—	2	2	no	—
399	C₇×C₄⋊C₄	—	2	1	no	—
400	C₇×C₄⋊C₄	—	2	1	no	—
401	C₇×C₄⋊C₄	—	2	1	no	—
402	C₇×C₄⋊C₄	—	2	2	no	—
403	C₇×C₄⋊C₄	—	2	2	no	—
404	C₇×C₄⋊C₄	—	2	1	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	1	no	—
410	C₇×C₄⋊C₄	—	2	1	no	—
411	C₇×C₄⋊C₄	—	2	2	no	—
412	C₇×C₄⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
417	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
418	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
419	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
420	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
421	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
422	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
423	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
424	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
425	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
426	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
427	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
428	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
429	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
430	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
431	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
432	C₇×C₂²⋊C₄	—	2	1	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	C₂×D₄	1	2	yes	—
440	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
441	C₄²×C₇	—	2	1	no	—
442	C₄²×C₇	—	2	1	no	—
443	C₄²×C₇	—	2	1	no	—
444	C₄²×C₇	—	2	2	no	—
445	C₄²×C₇	—	2	2	no	—
446	C₄²×C₇	—	2	2	no	—
447	C₄²×C₇	—	2	2	no	—
448	C₄²×C₇	—	2	2	no	—
449	C₄²×C₇	—	2	2	no	—
450	C₄²×C₇	—	2	2	no	—
451	C₄²×C₇	—	2	2	no	—
452	C₄²×C₇	—	2	1	no	—
453	C₄²×C₇	—	2	1	no	—
454	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₇	C₂⁴	1	1	yes	characteristic
457	C₄²×C₇	C₂⁴	1	2	yes	—
458	C₄²×C₇	C₂⁴	1	2	yes	—
459	C₄²×C₇	C₂⁴	1	1	yes	characteristic
460	C₂×#137	C₂²×C₇	1	1	yes	characteristic
461	Q₈²	—	2	1	no	—
462	Q₈²	C₂²×C₇	1	2	yes	—
463	#557	—	2	1	no	—
464	#557	—	2	1	no	—
465	#557	—	2	1	no	—
466	#557	C₂²×C₇	1	2	yes	—
467	#557	C₂²×C₇	1	2	yes	—
468	#557	C₂²×C₇	1	2	yes	—
469	#557	C₂²×C₇	1	2	yes	—
470	#557	C₂²×C₇	1	2	yes	—
471	#554	—	2	2	no	—
472	#554	—	2	2	no	—
473	#554	C₂²×C₇	1	2	yes	—
474	#554	C₂²×C₇	1	2	yes	—
475	#544	—	2	1	no	—
476	#544	—	2	1	no	—
477	#544	—	2	2	no	—
478	#544	C₂²×C₇	1	1	yes	characteristic
479	#544	C₂²×C₇	1	1	yes	characteristic
480	#544	C₂²×C₇	1	1	yes	characteristic
481	#544	C₂²×C₇	1	1	yes	characteristic
482	#533	—	2	1	no	—
483	#533	—	2	2	no	—
484	#533	C₂²×C₇	1	1	yes	characteristic
485	#533	C₂²×C₇	1	1	yes	characteristic
486	C₂×#125	—	2	1	no	—
487	C₂×#125	C₂²×C₇	1	1	yes	characteristic
488	#520	C₂²×C₇	1	1	yes	characteristic
489	#520	C₂²×C₇	1	1	yes	characteristic
490	#519	C₂²×C₇	1	1	yes	characteristic
491	#519	C₂²×C₇	1	1	yes	characteristic
492	C₄×#41	C₂²×C₇	1	1	yes	characteristic
493	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
494	#501	C₂²×C₇	1	2	yes	—
495	#501	C₂²×C₇	1	2	yes	—
496	#501	C₂²×C₇	1	2	yes	—
497	#501	C₂²×C₇	1	2	yes	—
498	#501	C₂²×C₇	1	2	yes	—
499	#501	C₂²×C₇	1	2	yes	—
500	#500	C₂²×C₇	1	2	yes	—
501	#499	C₂²×C₇	1	2	yes	—
502	#499	C₂²×C₇	1	2	yes	—
503	#499	C₂²×C₇	1	2	yes	—
504	#499	C₂²×C₇	1	2	yes	—
505	#498	C₂²×C₇	1	2	yes	—
506	#479	C₂²×C₇	1	2	yes	—
507	#479	C₂²×C₇	1	2	yes	—
508	#479	C₂²×C₇	1	2	yes	—
509	#479	C₂²×C₇	1	2	yes	—
510	#479	C₂²×C₇	1	1	yes	characteristic
511	#479	C₂²×C₇	1	1	yes	characteristic
512	#479	C₂²×C₇	1	2	yes	—
513	#479	C₂²×C₇	1	2	yes	—
514	#479	C₂²×C₇	1	2	yes	—
515	#479	C₂²×C₇	1	2	yes	—
516	#479	C₂²×C₇	1	2	yes	—
517	#479	C₂²×C₇	1	2	yes	—
518	#478	C₂²×C₇	1	1	yes	characteristic
519	#478	C₂²×C₇	1	1	yes	characteristic
520	#478	C₂²×C₇	1	2	yes	—
521	#478	C₂²×C₇	1	2	yes	—
522	#477	C₂²×C₇	1	1	yes	characteristic
523	#477	C₂²×C₇	1	2	yes	—
524	#477	C₂²×C₇	1	2	yes	—
525	#477	C₂²×C₇	1	2	yes	—
526	#476	C₂²×C₇	1	1	yes	characteristic
527	#476	C₂²×C₇	1	2	yes	—
528	#475	C₂²×C₇	1	1	yes	characteristic
529	#475	C₂²×C₇	1	2	yes	—
530	#475	C₂²×C₇	1	2	yes	—
531	#475	C₂²×C₇	1	2	yes	—
532	#474	C₂²×C₇	1	1	yes	characteristic
533	#474	C₂²×C₇	1	2	yes	—
534	#446	C₂²×C₇	1	2	yes	—
535	#446	C₂²×C₇	1	2	yes	—
536	#446	C₂²×C₇	1	2	yes	—
537	C₈×Q₈	C₂²×C₇	1	2	yes	—
538	#441	C₂²×C₇	1	2	yes	—
539	#441	C₂²×C₇	1	2	yes	—
540	#441	C₂²×C₇	1	2	yes	—
541	#440	C₂²×C₇	1	2	yes	—
542	#440	C₂²×C₇	1	2	yes	—
543	#440	C₂²×C₇	1	2	yes	—
544	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
545	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
546	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
547	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
548	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
549	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
550	#428	C₂²×C₇	1	1	yes	characteristic
551	#428	C₂²×C₇	1	1	yes	characteristic
552	#428	C₂²×C₇	1	1	yes	characteristic
553	#428	C₂²×C₇	1	1	yes	characteristic
554	#428	C₂²×C₇	1	1	yes	characteristic
555	#427	C₂²×C₇	1	1	yes	characteristic
556	#427	C₂²×C₇	1	1	yes	characteristic
557	C₂×#107	C₂²×C₇	1	1	yes	characteristic
558	C₂×#106	C₂²×C₇	1	1	yes	characteristic
559	#424	C₂²×C₇	1	1	yes	characteristic
560	#424	C₂²×C₇	1	1	yes	characteristic
561	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
562	#419	C₂²×C₇	1	1	yes	characteristic
563	#417	C₂²×C₇	1	1	yes	characteristic
564	#416	C₂²×C₇	1	1	yes	characteristic
565	#416	C₂²×C₇	1	1	yes	characteristic
566	C₂×#103	C₂²×C₇	1	1	yes	characteristic
567	C₂×#103	C₂²×C₇	1	1	yes	characteristic
568	#405	C₂²×C₇	1	1	yes	characteristic
569	#405	C₂²×C₇	1	1	yes	characteristic
570	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
571	C₂³×C₇	—	2	1	no	—
572	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
573	C₇×Q₈	—	2	4	no	—
574	C₇×Q₈	—	2	2	no	—
575	C₇×Q₈	—	2	1	no	—
576	C₇×Q₈	—	4	2	no	—
577	C₇×Q₈	—	4	2	no	—
578	C₇×Q₈	—	4	2	no	—
579	C₇×Q₈	—	8	1	no	—
580	C₇×Q₈	—	8	2	no	—
581	C₇×Q₈	—	8	2	no	—
582	C₇×Q₈	—	8	2	no	—
583	C₇×Q₈	—	8	2	no	—
584	C₇×Q₈	C₂²×Q₈	1	4	yes	—
585	C₇×Q₈	C₂²×Q₈	1	2	yes	—
586	C₇×D₄	—	2	4	no	—
587	C₇×D₄	—	2	1	no	—
588	C₇×D₄	C₂²×Q₈	1	2	yes	—
589	C₂×C₄×C₇	—	2	4	no	—
590	C₂×C₄×C₇	—	2	1	no	—
591	C₂×C₄×C₇	—	2	2	no	—
592	C₂×C₄×C₇	—	2	4	no	—
593	C₂×C₄×C₇	—	2	1	no	—
594	C₂×C₄×C₇	—	2	1	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	2	no	—
600	C₂×C₄×C₇	—	2	2	no	—
601	C₂×C₄×C₇	—	2	2	no	—
602	C₂×C₄×C₇	—	4	1	no	—
603	C₂×C₄×C₇	—	4	1	no	—
604	C₂×C₄×C₇	—	8	1	no	—
605	C₂×C₄×C₇	—	8	2	no	—
606	C₂×C₄×C₇	—	8	1	no	—
607	C₂×C₄×C₇	—	8	2	no	—
608	C₂×C₄×C₇	—	8	1	no	—
609	C₂×C₄×C₇	—	8	1	no	—
610	C₂×C₄×C₇	—	8	1	no	—
611	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
612	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
613	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
614	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
615	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
616	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
617	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
618	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
619	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
620	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
621	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
622	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
623	C₇×C₈	—	2	1	no	—
624	C₇×C₈	—	2	1	no	—
625	C₇×C₈	—	2	1	no	—
626	C₇×C₈	—	2	1	no	—
627	C₇×C₈	—	2	2	no	—
628	C₇×C₈	C₂²×Q₈	1	4	yes	—
629	C₂×#41	C₂³×C₇	1	1	yes	characteristic
630	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
631	#137	C₇×Q₈	1	8	yes	complemented
632	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
634	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
635	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
636	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
637	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
638	C₄⋊Q₈	—	2	2	no	—
639	C₄⋊Q₈	—	2	2	no	—
640	C₄⋊Q₈	—	2	2	no	—
641	C₄⋊Q₈	—	2	2	no	—
642	C₄⋊Q₈	—	2	2	no	—
643	C₄⋊Q₈	—	2	1	no	—
644	C₄⋊Q₈	—	2	1	no	—
645	C₄⋊Q₈	—	2	2	no	—
646	C₄⋊Q₈	—	2	2	no	—
647	C₄⋊Q₈	—	2	2	no	—
648	C₄⋊Q₈	—	2	1	no	—
649	C₄⋊Q₈	—	2	1	no	—
650	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
651	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
653	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
654	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
655	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
656	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
657	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
658	#125	—	2	1	no	—
659	#125	—	2	1	no	—
660	#125	—	2	2	no	—
661	#125	—	2	2	no	—
662	#125	—	2	2	no	—
663	#125	—	2	2	no	—
664	#125	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	—	2	2	no	—
667	#125	—	2	2	no	—
668	#125	—	2	2	no	—
669	#125	—	2	2	no	—
670	#125	—	2	1	no	—
671	#125	—	2	1	no	—
672	#125	—	2	1	no	—
673	#125	—	2	1	no	—
674	#125	C₇×D₄	1	1	yes	characteristic
675	#125	C₇×D₄	1	1	yes	characteristic
676	#125	C₂³×C₇	1	2	yes	—
677	#125	C₂³×C₇	1	2	yes	—
678	#125	C₂³×C₇	1	1	yes	characteristic
679	#125	C₂³×C₇	1	1	yes	characteristic
680	#125	C₂³×C₇	1	2	yes	—
681	#125	C₂³×C₇	1	2	yes	—
682	#125	C₂³×C₇	1	2	yes	—
683	#125	C₂³×C₇	1	2	yes	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	1	no	—
687	C₂²⋊Q₈	—	2	1	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	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	C₇×D₄	1	2	yes	—
697	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
698	C₄×Q₈	—	2	2	no	—
699	C₄×Q₈	—	2	1	no	—
700	C₄×Q₈	—	2	1	no	—
701	C₄×Q₈	—	2	1	no	—
702	C₄×Q₈	—	2	1	no	—
703	C₄×Q₈	—	2	2	no	—
704	C₄×Q₈	—	2	2	no	—
705	C₄×Q₈	—	2	2	no	—
706	C₄×Q₈	—	2	2	no	—
707	C₄×Q₈	—	2	2	no	—
708	C₄×Q₈	—	2	1	no	—
709	C₄×Q₈	—	2	1	no	—
710	C₄×Q₈	—	2	1	no	—
711	C₄×Q₈	—	2	1	no	—
712	C₄×Q₈	C₂³×C₇	1	2	yes	—
713	C₄×Q₈	C₂³×C₇	1	2	yes	—
714	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
715	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
716	C₄×Q₈	C₂³×C₇	1	2	yes	—
717	C₄×Q₈	C₂³×C₇	1	2	yes	—
718	C₄×Q₈	C₂³×C₇	1	2	yes	—
719	C₄×Q₈	C₂³×C₇	1	2	yes	—
720	C₄×Q₈	C₂³×C₇	1	2	yes	—
721	C₄×Q₈	C₂³×C₇	1	2	yes	—
722	C₄×Q₈	C₂³×C₇	1	2	yes	—
723	C₄×Q₈	C₂³×C₇	1	2	yes	—
724	C₄×D₄	—	2	1	no	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	—	2	2	no	—
727	C₄×D₄	—	2	2	no	—
728	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
729	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
730	C₄×D₄	C₂³×C₇	1	2	yes	—
731	C₄×D₄	C₂³×C₇	1	2	yes	—
732	#117	—	2	1	no	—
733	#117	—	2	1	no	—
734	#117	—	2	2	no	—
735	#117	—	2	2	no	—
736	#117	—	2	1	no	—
737	#117	C₂³×C₇	1	1	yes	characteristic
738	#117	C₂³×C₇	1	1	yes	characteristic
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	C₂×C₄⋊C₄	—	2	1	no	—
743	C₂×C₄⋊C₄	—	2	1	no	—
744	C₂×C₄⋊C₄	—	2	1	no	—
745	C₂×C₄⋊C₄	—	2	1	no	—
746	C₂×C₄⋊C₄	—	2	1	no	—
747	C₂×C₄⋊C₄	—	2	2	no	—
748	C₂×C₄⋊C₄	—	2	2	no	—
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×C₄²	—	2	1	no	—
753	C₂×C₄²	—	2	1	no	—
754	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
755	#107	C₂³×C₇	1	2	yes	—
756	#107	C₂³×C₇	1	2	yes	—
757	#107	C₂³×C₇	1	1	yes	characteristic
758	#107	C₂³×C₇	1	1	yes	characteristic
759	#107	C₂³×C₇	1	1	yes	characteristic
760	#107	C₂³×C₇	1	1	yes	characteristic
761	#107	C₂³×C₇	1	2	yes	—
762	#107	C₂³×C₇	1	2	yes	—
763	#107	C₂³×C₇	1	2	yes	—
764	#107	C₂³×C₇	1	2	yes	—
765	#107	C₂³×C₇	1	2	yes	—
766	#106	C₂³×C₇	1	2	yes	—
767	#106	C₂³×C₇	1	2	yes	—
768	#106	C₂³×C₇	1	1	yes	characteristic
769	#106	C₂³×C₇	1	1	yes	characteristic
770	#106	C₂³×C₇	1	1	yes	characteristic
771	#106	C₂³×C₇	1	1	yes	characteristic
772	#106	C₂³×C₇	1	2	yes	—
773	#106	C₂³×C₇	1	2	yes	—
774	#106	C₂³×C₇	1	2	yes	—
775	#106	C₂³×C₇	1	2	yes	—
776	#106	C₂³×C₇	1	2	yes	—
777	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
778	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
779	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
780	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
781	C₄⋊C₈	C₂³×C₇	1	2	yes	—
782	C₄⋊C₈	C₂³×C₇	1	2	yes	—
783	C₄⋊C₈	C₂³×C₇	1	2	yes	—
784	C₄⋊C₈	C₂³×C₇	1	2	yes	—
785	#103	C₂³×C₇	1	2	yes	—
786	#103	C₂³×C₇	1	2	yes	—
787	#103	C₂³×C₇	1	2	yes	—
788	#103	C₂³×C₇	1	2	yes	—
789	#103	C₂³×C₇	1	1	yes	characteristic
790	#103	C₂³×C₇	1	1	yes	characteristic
791	#103	C₂³×C₇	1	1	yes	characteristic
792	#103	C₂³×C₇	1	1	yes	characteristic
793	#103	C₂³×C₇	1	2	yes	—
794	#103	C₂³×C₇	1	2	yes	—
795	#103	C₂³×C₇	1	2	yes	—
796	#102	C₂³×C₇	1	1	yes	characteristic
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	2	yes	—
801	#97	C₂³×C₇	1	2	yes	—
802	#97	C₂³×C₇	1	2	yes	—
803	#97	C₂³×C₇	1	2	yes	—
804	C₄×C₈	C₂³×C₇	1	2	yes	—
805	C₄×C₈	C₂³×C₇	1	2	yes	—
806	C₄×C₈	C₂³×C₇	1	2	yes	—
807	C₂²×C₇	—	2	1	no	—
808	C₂²×C₇	—	2	1	no	—
809	C₂²×C₇	—	2	2	no	—
810	C₂²×C₇	—	4	1	no	—
811	C₂²×C₇	—	4	1	no	—
812	C₂²×C₇	D₄×Q₈	1	2	yes	—
813	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
814	C₄×C₇	—	2	1	no	—
815	C₄×C₇	—	2	1	no	—
816	C₄×C₇	—	2	2	no	—
817	C₄×C₇	—	2	2	no	—
818	C₄×C₇	—	2	1	no	—
819	C₄×C₇	—	2	1	no	—
820	C₄×C₇	—	2	2	no	—
821	C₄×C₇	—	2	2	no	—
822	C₄×C₇	—	2	2	no	—
823	C₄×C₇	—	2	4	no	—
824	C₄×C₇	—	4	2	no	—
825	C₄×C₇	—	4	1	no	—
826	C₄×C₇	—	4	2	no	—
827	C₄×C₇	—	4	1	no	—
828	C₄×C₇	—	4	1	no	—
829	C₄×C₇	—	4	2	no	—
830	C₄×C₇	—	4	1	no	—
831	C₄×C₇	—	4	1	no	—
832	C₄×C₇	—	4	1	no	—
833	C₄×C₇	D₄×Q₈	1	2	yes	—
834	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
835	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
836	#41	—	2	2	no	—
837	#41	C₂×C₇×Q₈	1	4	yes	—
838	C₂×Q₈	—	2	1	no	—
839	C₂×Q₈	—	2	1	no	—
840	C₂×Q₈	—	2	2	no	—
841	C₂×Q₈	—	2	2	no	—
842	C₂×Q₈	—	2	1	no	—
843	C₂×Q₈	—	2	2	no	—
844	C₂×Q₈	—	2	2	no	—
845	C₂×Q₈	—	2	2	no	—
846	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
847	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
848	C₂×Q₈	C₂×C₇×Q₈	1	4	yes	—
849	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
850	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
851	C₂×D₄	—	2	1	no	—
852	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
863	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
865	Q₁₆	C₂×C₇×Q₈	1	8	yes	—
866	SD₁₆	C₂×C₇×Q₈	1	8	yes	—
867	M₁₆	—	2	2	no	—
868	M₁₆	C₂×C₇×Q₈	1	4	yes	—
869	C₂×C₈	—	2	2	no	—
870	C₂×C₈	—	2	2	no	—
871	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
872	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
873	C₂×C₈	C₂⁴×C₇	1	2	yes	—
874	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
875	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
876	C₂×C₈	C₂⁴×C₇	1	2	yes	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	1	no	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
913	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
914	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
915	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
916	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
917	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
918	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
919	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
920	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
921	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
922	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
923	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
924	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
925	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
926	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
927	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
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	C₂²⋊C₄	—	2	1	no	—
932	C₂²⋊C₄	—	2	1	no	—
933	C₂²⋊C₄	—	2	1	no	—
934	C₂²⋊C₄	—	2	1	no	—
935	C₂²⋊C₄	—	2	1	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
939	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
940	C₄²	—	2	1	no	—
941	C₄²	—	2	1	no	—
942	C₄²	—	2	1	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	—	2	2	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	1	no	—
952	C₄²	—	2	1	no	—
953	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
954	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
955	C₄²	C₂⁴×C₇	1	1	yes	characteristic
956	C₄²	C₂⁴×C₇	1	2	yes	—
957	C₄²	C₂⁴×C₇	1	2	yes	—
958	C₄²	C₂⁴×C₇	1	1	yes	characteristic
959	C₂×C₇	—	2	2	no	—
960	C₂×C₇	—	4	2	no	—
961	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
962	C₂×C₇	#3584	1	1	yes	characteristic
963	C₂×C₇	#3586	1	1	yes	characteristic
964	C₂³	—	2	1	no	—
965	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
966	Q₈	—	2	2	no	—
967	Q₈	—	2	1	no	—
968	Q₈	—	2	4	no	—
969	Q₈	—	4	2	no	—
970	Q₈	—	4	2	no	—
971	Q₈	—	4	2	no	—
972	Q₈	—	8	1	no	—
973	Q₈	—	8	2	no	—
974	Q₈	—	8	2	no	—
975	Q₈	—	8	2	no	—
976	Q₈	—	8	2	no	—
977	Q₈	C₂²×C₇×Q₈	1	4	yes	—
978	Q₈	C₂²×C₇×Q₈	1	2	yes	—
979	D₄	—	2	4	no	—
980	D₄	—	2	1	no	—
981	D₄	C₂²×C₇×Q₈	1	2	yes	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	4	no	—
985	C₂×C₄	—	2	4	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	4	1	no	—
996	C₂×C₄	—	4	1	no	—
997	C₂×C₄	—	8	1	no	—
998	C₂×C₄	—	8	2	no	—
999	C₂×C₄	—	8	1	no	—
1000	C₂×C₄	—	8	2	no	—
1001	C₂×C₄	—	8	1	no	—
1002	C₂×C₄	—	8	1	no	—
1003	C₂×C₄	—	8	1	no	—
1004	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1005	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1006	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1007	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1008	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1009	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1010	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1011	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1012	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1013	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
1014	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1015	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1016	C₈	—	2	1	no	—
1017	C₈	—	2	1	no	—
1018	C₈	—	2	1	no	—
1019	C₈	—	2	1	no	—
1020	C₈	—	2	2	no	—
1021	C₈	C₂²×C₇×Q₈	1	4	yes	—
1022	C₇	#61386	1	1	yes	characteristic, direct product factor, Sylow
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	C₇×D₄×Q₈	1	2	yes	—
1029	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1030	C₄	—	2	1	no	—
1031	C₄	—	2	1	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	2	1	no	—
1035	C₄	—	2	1	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	4	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	1	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	1	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	C₇×D₄×Q₈	1	2	yes	—
1050	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
1051	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1052	C₂	—	2	2	no	—
1053	C₂	—	4	2	no	—
1054	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
1055	C₂	C₇×#3584	1	1	yes	characteristic
1056	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	C₂×C₇×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3502	C₂	semidirect
3. C₇×#3390	C₂	semidirect
4. C₇×#3390	C₂	semidirect
5. C₇×#3388	C₂	semidirect
6. C₇×#3388	C₂	semidirect
7. C₇×#3387	C₂	semidirect
8. C₇×#3385	C₂	semidirect
9. C₇×#3383	C₂	semidirect
10. C₇×#3381	C₂	semidirect
11. C₇×#3166	C₂	semidirect
12. C₇×#3164	C₂	semidirect
13. C₇×#3163	C₂	semidirect
16. C₇×#3082	C₂	semidirect
17. C₇×#3082	C₂	semidirect
19. C₂×C₇×#479	C₂	semidirect
20. C₇×#2962	C₂	semidirect
135. #61386	C₇	direct (N × H)
138. C₇×#137	Q₈	semidirect
315. #3502	C₂×C₇	semidirect
316. #3390	C₂×C₇	semidirect
317. #3390	C₂×C₇	semidirect
318. #3388	C₂×C₇	semidirect
319. #3388	C₂×C₇	semidirect
320. #3387	C₂×C₇	semidirect
321. #3385	C₂×C₇	semidirect
322. #3383	C₂×C₇	semidirect
323. #3381	C₂×C₇	semidirect
324. #3166	C₂×C₇	semidirect
325. #3164	C₂×C₇	semidirect
326. #3163	C₂×C₇	semidirect
329. #3082	C₂×C₇	semidirect
330. #3082	C₂×C₇	semidirect
332. C₂×#479	C₂×C₇	semidirect
333. #2962	C₂×C₇	semidirect
631. #137	C₇×Q₈	semidirect
1022. C₇	#61386	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×#3504	2
C₇×#3502	2
C₇×#3390	2
C₇×#3388	2
C₇×#3387	2
C₇×#3385	2
C₇×#3383	2
C₇×#3381	2
C₇×#3166	2
C₇×#3164	2
C₇×#3163	2
C₇×#3084	2
C₇×#3083	2
C₇×#3082	2
C₇×#3076	2
C₂×C₇×#479	2
C₇×#2962	2
C₇×#2947	2
C₄×C₇×#137	2
#61386	7

Subgroups — C7×#61386 #13238602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61386 #13238602