Subgroups — C₇×#61858 #13239074

Order 1792.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3388	C₂	1	2	yes	maximal, complemented
4	C₇×#3387	C₂	1	2	yes	maximal, complemented
5	C₇×#3387	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3384	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3381	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×Q₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3376	C₂	1	2	yes	maximal, complemented
10	C₇×#3374	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3369	C₂	1	2	yes	maximal, complemented
12	C₇×#3367	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3364	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3359	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3244	C₂	1	2	yes	maximal, complemented
16	C₇×#3242	C₂	1	2	yes	maximal, complemented
17	C₇×#3239	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3229	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3125	C₂	1	2	yes	maximal
20	C₇×#3120	C₂	1	2	yes	maximal, complemented
21	C₇×#3116	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#3102	C₂	1	1	yes	maximal, characteristic
23	C₇×#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#563	—	2	2	no	—
25	C₇×Q₈²	C₂²	1	2	yes	—
26	C₇×Q₈²	C₂²	1	1	yes	characteristic
27	C₇×#557	C₂²	1	1	yes	characteristic
28	C₇×#557	C₂²	1	1	yes	characteristic
29	C₇×#557	C₂²	1	1	yes	characteristic
30	C₇×#557	C₂²	1	2	yes	—
31	C₇×#556	—	2	1	no	—
32	C₇×#556	C₂²	1	1	yes	characteristic
33	C₇×#556	C₂²	1	2	yes	—
34	C₇×#554	—	2	2	no	—
35	C₇×#554	C₂²	1	2	yes	—
36	C₇×#554	C₂²	1	1	yes	characteristic
37	C₇×#552	—	2	1	no	—
38	C₇×D₄×Q₈	—	2	1	no	—
39	C₇×D₄×Q₈	—	2	1	no	—
40	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
41	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
42	C₇×#544	—	2	1	no	—
43	C₇×#544	—	2	2	no	—
44	C₇×#544	C₂²	1	2	yes	—
45	C₇×#542	C₂²	1	2	yes	—
46	C₇×#541	—	2	1	no	—
47	C₇×#541	—	2	2	no	—
48	C₇×#541	C₂²	1	2	yes	—
49	C₇×#533	—	2	1	no	—
50	C₇×#533	C₂²	1	1	yes	characteristic
51	C₇×#533	C₂²	1	1	yes	characteristic
52	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
53	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
54	C₇×#529	C₂²	1	1	yes	characteristic
55	C₇×#520	C₂²	1	2	yes	—
56	C₄×C₇×#41	C₂²	1	1	yes	characteristic
57	C₇×#501	C₂²	1	2	yes	—
58	C₇×#501	C₂²	1	2	yes	—
59	C₇×#501	C₂²	1	2	yes	—
60	C₇×#499	C₂²	1	2	yes	—
61	C₇×#498	C₂²	1	1	yes	characteristic
62	C₇×#498	C₂²	1	1	yes	characteristic
63	C₇×#498	C₂²	1	2	yes	—
64	C₇×#491	C₂²	1	2	yes	—
65	C₇×#489	C₂²	1	2	yes	—
66	C₇×#489	C₂²	1	2	yes	—
67	C₇×#488	C₂²	1	2	yes	—
68	C₇×#487	C₂²	1	1	yes	characteristic
69	C₇×#487	C₂²	1	1	yes	characteristic
70	C₇×#487	C₂²	1	2	yes	—
71	C₇×#485	C₂²	1	1	yes	characteristic
72	C₇×#485	C₂²	1	2	yes	—
73	C₇×#484	C₂²	1	2	yes	—
74	C₇×#483	C₂²	1	2	yes	—
75	C₇×#483	C₂²	1	2	yes	—
76	C₇×#482	C₂²	1	1	yes	characteristic
77	C₇×#481	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	1	yes	characteristic
82	C₇×#479	C₂²	1	2	yes	—
83	C₇×#478	C₂²	1	2	yes	—
84	C₇×#478	C₂²	1	1	yes	characteristic
85	C₇×#478	C₂²	1	2	yes	—
86	C₇×#477	C₂²	1	2	yes	—
87	C₇×#477	C₂²	1	1	yes	characteristic
88	C₇×#476	C₂²	1	2	yes	—
89	C₇×#476	C₂²	1	1	yes	characteristic
90	C₇×#476	C₂²	1	2	yes	—
91	C₇×#475	C₂²	1	2	yes	—
92	C₇×#475	C₂²	1	2	yes	—
93	C₇×#475	C₂²	1	1	yes	characteristic
94	C₇×#475	C₂²	1	1	yes	characteristic
95	C₇×#475	C₂²	1	2	yes	—
96	C₇×#475	C₂²	1	2	yes	—
97	C₇×#475	C₂²	1	2	yes	—
98	C₇×#474	C₂²	1	1	yes	characteristic
99	C₇×#474	C₂²	1	1	yes	characteristic
100	C₇×#464	C₂²	1	1	yes	characteristic
101	C₇×#464	C₂²	1	2	yes	—
102	C₇×#463	C₂²	1	1	yes	characteristic
103	C₇×#463	C₂²	1	2	yes	—
104	C₇×#462	C₂²	1	1	yes	characteristic
105	C₇×#462	C₂²	1	2	yes	—
106	C₇×#461	C₂²	1	1	yes	characteristic
107	C₇×#461	C₂²	1	2	yes	—
108	C₇×#452	C₂²	1	1	yes	characteristic
109	C₇×#452	C₂²	1	2	yes	—
110	C₇×#449	C₂²	1	1	yes	characteristic
111	C₇×#446	C₂²	1	1	yes	characteristic
112	C₇×#446	C₂²	1	2	yes	—
113	C₇×#446	C₂²	1	1	yes	characteristic
114	C₇×#446	C₂²	1	2	yes	—
115	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
116	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
117	C₇×#442	C₂²	1	2	yes	—
118	C₇×#441	C₂²	1	2	yes	—
119	C₇×#441	C₂²	1	2	yes	—
120	C₇×#441	C₂²	1	2	yes	—
121	C₇×#440	C₂²	1	2	yes	—
122	C₇×#440	C₂²	1	2	yes	—
123	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
124	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
125	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
126	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
127	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
128	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
129	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
130	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
131	C₇×#433	C₂²	1	2	yes	—
132	C₇×#433	C₂²	1	2	yes	—
133	C₇×#432	C₂²	1	1	yes	characteristic
134	C₇×#431	C₂²	1	1	yes	characteristic
135	#61858	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	C₂³	1	1	yes	characteristic
137	C₂²×C₇×Q₈	—	2	1	no	—
138	C₂²×C₇×Q₈	—	2	1	no	—
139	C₂²×C₇×Q₈	—	2	1	no	—
140	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
141	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
142	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
145	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
146	C₇×C₄⋊Q₈	—	2	1	no	—
147	C₇×C₄⋊Q₈	—	2	1	no	—
148	C₇×C₄⋊Q₈	—	2	2	no	—
149	C₇×C₄⋊Q₈	—	2	2	no	—
150	C₇×C₄⋊Q₈	—	2	2	no	—
151	C₇×C₄⋊Q₈	—	2	2	no	—
152	C₇×C₄⋊Q₈	—	2	2	no	—
153	C₇×C₄⋊Q₈	—	2	2	no	—
154	C₇×C₄⋊Q₈	—	2	1	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	1	yes	characteristic
162	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₇×#126	—	2	2	no	—
169	C₇×#126	—	2	2	no	—
170	C₇×#126	—	2	2	no	—
171	C₇×#126	—	2	2	no	—
172	C₇×#126	—	2	2	no	—
173	C₇×#126	—	2	2	no	—
174	C₇×#126	—	2	1	no	—
175	C₇×#125	—	2	2	no	—
176	C₇×#125	—	2	2	no	—
177	C₇×#125	—	2	2	no	—
178	C₇×#125	—	2	2	no	—
179	C₇×#125	—	2	2	no	—
180	C₇×#125	—	2	2	no	—
181	C₇×#125	—	2	1	no	—
182	C₇×#125	—	2	2	no	—
183	C₇×#125	—	2	2	no	—
184	C₇×#125	—	2	1	no	—
185	C₇×#125	D₄	1	2	yes	—
186	C₇×#125	C₂³	1	2	yes	—
187	C₇×#125	C₂³	1	2	yes	—
188	C₇×#125	C₂³	1	1	yes	characteristic
189	C₇×#125	C₂³	1	2	yes	—
190	C₇×#124	—	2	2	no	—
191	C₇×#124	C₂³	1	2	yes	—
192	C₇×#124	C₂³	1	1	yes	characteristic
193	C₇×#123	—	2	1	no	—
194	C₇×#123	—	2	2	no	—
195	C₇×C₂²⋊Q₈	—	2	2	no	—
196	C₇×C₂²⋊Q₈	—	2	1	no	—
197	C₇×C₂²⋊Q₈	—	2	1	no	—
198	C₇×C₂²⋊Q₈	—	2	2	no	—
199	C₇×C₂²⋊Q₈	—	2	1	no	—
200	C₇×C₂²⋊Q₈	—	2	1	no	—
201	C₇×C₂²⋊Q₈	—	2	1	no	—
202	C₇×C₂²⋊Q₈	—	2	2	no	—
203	C₇×C₂²⋊Q₈	—	2	2	no	—
204	C₇×C₂²⋊Q₈	—	2	2	no	—
205	C₇×C₂²⋊Q₈	—	2	2	no	—
206	C₇×C₂²⋊Q₈	—	2	2	no	—
207	C₇×C₂²⋊Q₈	—	2	2	no	—
208	C₇×C₂²⋊Q₈	—	2	2	no	—
209	C₇×C₂²⋊Q₈	—	2	2	no	—
210	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
212	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
213	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₇×#121	C₂³	1	1	yes	characteristic
216	C₄×C₇×Q₈	—	2	2	no	—
217	C₄×C₇×Q₈	—	2	1	no	—
218	C₄×C₇×Q₈	—	2	1	no	—
219	C₄×C₇×Q₈	—	2	1	no	—
220	C₄×C₇×Q₈	—	2	1	no	—
221	C₄×C₇×Q₈	—	2	2	no	—
222	C₄×C₇×Q₈	—	2	1	no	—
223	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
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	2	yes	—
229	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
230	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
231	C₄×C₇×Q₈	C₂³	1	2	yes	—
232	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
233	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
234	C₄×C₇×Q₈	C₂³	1	2	yes	—
235	C₄×C₇×D₄	—	2	1	no	—
236	C₄×C₇×D₄	—	2	1	no	—
237	C₄×C₇×D₄	—	2	1	no	—
238	C₄×C₇×D₄	—	2	2	no	—
239	C₄×C₇×D₄	—	2	2	no	—
240	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
241	C₄×C₇×D₄	C₂³	1	2	yes	—
242	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
243	C₄×C₇×D₄	C₂³	1	2	yes	—
244	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
245	C₄×C₇×D₄	C₂³	1	2	yes	—
246	C₇×#117	—	2	1	no	—
247	C₇×#117	—	2	2	no	—
248	C₇×#117	—	2	2	no	—
249	C₇×#117	—	2	1	no	—
250	C₇×#117	—	2	1	no	—
251	C₇×#117	—	2	1	no	—
252	C₇×#117	C₂³	1	1	yes	characteristic
253	C₇×#117	C₂³	1	2	yes	—
254	C₂×C₇×C₄⋊C₄	—	2	1	no	—
255	C₂×C₇×C₄⋊C₄	—	2	2	no	—
256	C₂×C₇×C₄⋊C₄	—	2	2	no	—
257	C₂×C₇×C₄⋊C₄	—	2	1	no	—
258	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
259	C₂×C₄²×C₇	—	2	1	no	—
260	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
261	C₇×#107	C₂³	1	2	yes	—
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×#106	C₂³	1	2	yes	—
267	C₇×#106	C₂³	1	2	yes	—
268	C₇×#106	C₂³	1	1	yes	characteristic
269	C₇×#106	C₂³	1	2	yes	—
270	C₇×#106	C₂³	1	2	yes	—
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	1	yes	characteristic
275	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₇×C₄⋊C₈	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	1	yes	characteristic
287	C₇×#103	C₂³	1	2	yes	—
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	2	yes	—
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×#102	C₂³	1	2	yes	—
297	C₇×#102	C₂³	1	2	yes	—
298	C₇×#102	C₂³	1	1	yes	characteristic
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	1	yes	characteristic
301	C₇×#102	C₂³	1	1	yes	characteristic
302	C₇×#102	C₂³	1	1	yes	characteristic
303	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₇×#97	C₂³	1	2	yes	—
307	C₇×#97	C₂³	1	2	yes	—
308	C₇×#97	C₂³	1	2	yes	—
309	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
310	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
311	C₄×C₇×C₈	C₂³	1	2	yes	—
312	C₄×C₇×C₈	C₂³	1	2	yes	—
313	#3555	C₂×C₇	1	1	yes	characteristic, complemented
314	#3503	C₂×C₇	1	1	yes	characteristic, complemented
315	#3388	C₂×C₇	1	2	yes	complemented
316	#3387	C₂×C₇	1	1	yes	characteristic, complemented
317	#3387	C₂×C₇	1	2	yes	complemented
318	#3384	C₂×C₇	1	1	yes	characteristic, complemented
319	#3381	C₂×C₇	1	1	yes	characteristic, complemented
320	Q₈×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
321	#3376	C₂×C₇	1	2	yes	complemented
322	#3374	C₂×C₇	1	1	yes	characteristic, complemented
323	#3369	C₂×C₇	1	2	yes	complemented
324	#3367	C₂×C₇	1	1	yes	characteristic, complemented
325	#3364	C₂×C₇	1	1	yes	characteristic, complemented
326	#3359	C₂×C₇	1	1	yes	characteristic, complemented
327	#3244	C₂×C₇	1	2	yes	complemented
328	#3242	C₂×C₇	1	2	yes	complemented
329	#3239	C₂×C₇	1	1	yes	characteristic, complemented
330	#3229	C₂×C₇	1	1	yes	characteristic, complemented
331	#3125	C₂×C₇	1	2	yes	—
332	#3120	C₂×C₇	1	2	yes	complemented
333	#3116	C₂×C₇	1	1	yes	characteristic, complemented
334	#3102	C₂×C₇	1	1	yes	characteristic
335	#2985	C₂×C₇	1	1	yes	characteristic, complemented
336	C₇×#41	—	2	2	no	—
337	C₇×#41	—	2	2	no	—
338	C₂×C₇×Q₈	—	2	1	no	—
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	2	no	—
344	C₂×C₇×Q₈	—	2	2	no	—
345	C₂×C₇×Q₈	—	8	2	no	—
346	C₂×C₇×Q₈	—	8	2	no	—
347	C₂×C₇×Q₈	—	8	2	no	—
348	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
349	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
350	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
351	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
352	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
353	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
354	C₂×C₇×D₄	—	2	1	no	—
355	C₂×C₇×D₄	—	2	1	no	—
356	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
357	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₇	—	2	1	no	—
359	C₂²×C₄×C₇	—	2	2	no	—
360	C₂²×C₄×C₇	—	2	1	no	—
361	C₂²×C₄×C₇	—	2	1	no	—
362	C₂²×C₄×C₇	—	2	1	no	—
363	C₂²×C₄×C₇	—	2	2	no	—
364	C₂²×C₄×C₇	—	2	2	no	—
365	C₂²×C₄×C₇	—	2	2	no	—
366	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
369	C₇×Q₁₆	—	2	2	no	—
370	C₇×Q₁₆	—	2	4	no	—
371	C₇×SD₁₆	—	2	2	no	—
372	C₇×SD₁₆	—	2	2	no	—
373	C₇×SD₁₆	—	2	4	no	—
374	C₇×D₈	—	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	1	yes	characteristic
378	C₂×C₇×C₈	C₂⁴	1	2	yes	—
379	C₂×C₇×C₈	C₂⁴	1	2	yes	—
380	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
381	C₇×C₄⋊C₄	—	2	2	no	—
382	C₇×C₄⋊C₄	—	2	2	no	—
383	C₇×C₄⋊C₄	—	2	1	no	—
384	C₇×C₄⋊C₄	—	2	2	no	—
385	C₇×C₄⋊C₄	—	2	2	no	—
386	C₇×C₄⋊C₄	—	2	1	no	—
387	C₇×C₄⋊C₄	—	2	1	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	1	no	—
392	C₇×C₄⋊C₄	—	2	1	no	—
393	C₇×C₄⋊C₄	—	2	1	no	—
394	C₇×C₄⋊C₄	—	2	2	no	—
395	C₇×C₄⋊C₄	—	2	1	no	—
396	C₇×C₄⋊C₄	—	2	1	no	—
397	C₇×C₄⋊C₄	—	2	1	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	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	2	no	—
410	C₇×C₄⋊C₄	—	2	2	no	—
411	C₇×C₄⋊C₄	—	2	1	no	—
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	2	yes	—
415	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
416	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
417	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
418	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
419	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
420	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
421	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
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×C₄⋊C₄	C₂⁴	1	2	yes	—
426	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
427	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	no	—
432	C₇×C₂²⋊C₄	—	2	1	no	—
433	C₇×C₂²⋊C₄	—	2	1	no	—
434	C₇×C₂²⋊C₄	—	2	2	no	—
435	C₇×C₂²⋊C₄	—	2	2	no	—
436	C₇×C₂²⋊C₄	—	2	1	no	—
437	C₇×C₂²⋊C₄	—	2	1	no	—
438	C₇×C₂²⋊C₄	—	2	2	no	—
439	C₇×C₂²⋊C₄	—	2	2	no	—
440	C₇×C₂²⋊C₄	—	2	1	no	—
441	C₇×C₂²⋊C₄	—	2	2	no	—
442	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
443	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
444	C₄²×C₇	—	2	1	no	—
445	C₄²×C₇	—	2	1	no	—
446	C₄²×C₇	—	2	1	no	—
447	C₄²×C₇	—	2	2	no	—
448	C₄²×C₇	—	2	2	no	—
449	C₄²×C₇	—	2	2	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	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	#563	—	2	2	no	—
461	Q₈²	C₂²×C₇	1	2	yes	—
462	Q₈²	C₂²×C₇	1	1	yes	characteristic
463	#557	C₂²×C₇	1	1	yes	characteristic
464	#557	C₂²×C₇	1	1	yes	characteristic
465	#557	C₂²×C₇	1	1	yes	characteristic
466	#557	C₂²×C₇	1	2	yes	—
467	#556	—	2	1	no	—
468	#556	C₂²×C₇	1	1	yes	characteristic
469	#556	C₂²×C₇	1	2	yes	—
470	#554	—	2	2	no	—
471	#554	C₂²×C₇	1	2	yes	—
472	#554	C₂²×C₇	1	1	yes	characteristic
473	#552	—	2	1	no	—
474	D₄×Q₈	—	2	1	no	—
475	D₄×Q₈	—	2	1	no	—
476	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
477	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
478	#544	—	2	1	no	—
479	#544	—	2	2	no	—
480	#544	C₂²×C₇	1	2	yes	—
481	#542	C₂²×C₇	1	2	yes	—
482	#541	—	2	1	no	—
483	#541	—	2	2	no	—
484	#541	C₂²×C₇	1	2	yes	—
485	#533	—	2	1	no	—
486	#533	C₂²×C₇	1	1	yes	characteristic
487	#533	C₂²×C₇	1	1	yes	characteristic
488	C₂×C₄⋊Q₈	—	2	1	no	—
489	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
490	#529	C₂²×C₇	1	1	yes	characteristic
491	#520	C₂²×C₇	1	2	yes	—
492	C₄×#41	C₂²×C₇	1	1	yes	characteristic
493	#501	C₂²×C₇	1	2	yes	—
494	#501	C₂²×C₇	1	2	yes	—
495	#501	C₂²×C₇	1	2	yes	—
496	#499	C₂²×C₇	1	2	yes	—
497	#498	C₂²×C₇	1	1	yes	characteristic
498	#498	C₂²×C₇	1	2	yes	—
499	#498	C₂²×C₇	1	1	yes	characteristic
500	#491	C₂²×C₇	1	2	yes	—
501	#489	C₂²×C₇	1	2	yes	—
502	#489	C₂²×C₇	1	2	yes	—
503	#488	C₂²×C₇	1	2	yes	—
504	#487	C₂²×C₇	1	1	yes	characteristic
505	#487	C₂²×C₇	1	2	yes	—
506	#487	C₂²×C₇	1	1	yes	characteristic
507	#485	C₂²×C₇	1	1	yes	characteristic
508	#485	C₂²×C₇	1	2	yes	—
509	#484	C₂²×C₇	1	2	yes	—
510	#483	C₂²×C₇	1	2	yes	—
511	#483	C₂²×C₇	1	2	yes	—
512	#482	C₂²×C₇	1	1	yes	characteristic
513	#481	C₂²×C₇	1	2	yes	—
514	#479	C₂²×C₇	1	1	yes	characteristic
515	#479	C₂²×C₇	1	2	yes	—
516	#479	C₂²×C₇	1	2	yes	—
517	#479	C₂²×C₇	1	2	yes	—
518	#479	C₂²×C₇	1	2	yes	—
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	2	yes	—
523	#477	C₂²×C₇	1	1	yes	characteristic
524	#476	C₂²×C₇	1	2	yes	—
525	#476	C₂²×C₇	1	1	yes	characteristic
526	#476	C₂²×C₇	1	2	yes	—
527	#475	C₂²×C₇	1	1	yes	characteristic
528	#475	C₂²×C₇	1	2	yes	—
529	#475	C₂²×C₇	1	2	yes	—
530	#475	C₂²×C₇	1	2	yes	—
531	#475	C₂²×C₇	1	1	yes	characteristic
532	#475	C₂²×C₇	1	2	yes	—
533	#475	C₂²×C₇	1	2	yes	—
534	#474	C₂²×C₇	1	1	yes	characteristic
535	#474	C₂²×C₇	1	1	yes	characteristic
536	#464	C₂²×C₇	1	1	yes	characteristic
537	#464	C₂²×C₇	1	2	yes	—
538	#463	C₂²×C₇	1	1	yes	characteristic
539	#463	C₂²×C₇	1	2	yes	—
540	#462	C₂²×C₇	1	1	yes	characteristic
541	#462	C₂²×C₇	1	2	yes	—
542	#461	C₂²×C₇	1	1	yes	characteristic
543	#461	C₂²×C₇	1	2	yes	—
544	#452	C₂²×C₇	1	1	yes	characteristic
545	#452	C₂²×C₇	1	2	yes	—
546	#449	C₂²×C₇	1	1	yes	characteristic
547	#446	C₂²×C₇	1	1	yes	characteristic
548	#446	C₂²×C₇	1	2	yes	—
549	#446	C₂²×C₇	1	1	yes	characteristic
550	#446	C₂²×C₇	1	2	yes	—
551	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
552	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
553	#442	C₂²×C₇	1	2	yes	—
554	#441	C₂²×C₇	1	2	yes	—
555	#441	C₂²×C₇	1	2	yes	—
556	#441	C₂²×C₇	1	2	yes	—
557	#440	C₂²×C₇	1	2	yes	—
558	#440	C₂²×C₇	1	2	yes	—
559	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
560	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
561	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
562	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
563	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
564	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
565	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
566	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
567	#433	C₂²×C₇	1	2	yes	—
568	#433	C₂²×C₇	1	2	yes	—
569	#432	C₂²×C₇	1	1	yes	characteristic
570	#431	C₂²×C₇	1	1	yes	characteristic
571	C₂³×C₇	—	2	1	no	—
572	C₂³×C₇	—	2	1	no	—
573	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
574	C₇×Q₈	—	2	2	no	—
575	C₇×Q₈	—	2	2	no	—
576	C₇×Q₈	—	2	1	no	—
577	C₇×Q₈	—	2	1	no	—
578	C₇×Q₈	—	2	2	no	—
579	C₇×Q₈	—	2	2	no	—
580	C₇×Q₈	—	2	1	no	—
581	C₇×Q₈	—	4	2	no	—
582	C₇×Q₈	—	4	2	no	—
583	C₇×Q₈	—	4	2	no	—
584	C₇×Q₈	—	8	1	no	—
585	C₇×Q₈	—	8	2	no	—
586	C₇×Q₈	—	8	2	no	—
587	C₇×Q₈	—	8	2	no	—
588	C₇×Q₈	—	8	2	no	—
589	C₇×Q₈	2₋¹⁺⁴	1	2	yes	—
590	C₇×D₄	—	2	4	no	—
591	C₇×D₄	—	2	1	no	—
592	C₇×D₄	—	2	1	no	—
593	C₇×D₄	—	2	1	no	—
594	C₇×D₄	—	8	1	no	—
595	C₇×D₄	2₋¹⁺⁴	1	2	yes	—
596	C₂×C₄×C₇	—	2	4	no	—
597	C₂×C₄×C₇	—	2	1	no	—
598	C₂×C₄×C₇	—	2	2	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	1	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	2	no	—
609	C₂×C₄×C₇	—	2	2	no	—
610	C₂×C₄×C₇	—	4	1	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	2	no	—
616	C₂×C₄×C₇	—	8	2	no	—
617	C₂×C₄×C₇	—	8	2	no	—
618	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
619	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
620	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
621	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
622	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
626	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
627	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
628	C₇×C₈	—	2	1	no	—
629	C₇×C₈	—	2	1	no	—
630	C₇×C₈	—	2	1	no	—
631	C₇×C₈	—	2	2	no	—
632	C₇×C₈	—	2	1	no	—
633	C₇×C₈	—	2	2	no	—
634	C₂×#41	C₂³×C₇	1	1	yes	characteristic
635	C₂²×Q₈	—	2	1	no	—
636	C₂²×Q₈	—	2	1	no	—
637	C₂²×Q₈	—	2	1	no	—
638	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
639	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
640	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
641	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
642	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
643	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
644	C₄⋊Q₈	—	2	1	no	—
645	C₄⋊Q₈	—	2	1	no	—
646	C₄⋊Q₈	—	2	2	no	—
647	C₄⋊Q₈	—	2	2	no	—
648	C₄⋊Q₈	—	2	2	no	—
649	C₄⋊Q₈	—	2	2	no	—
650	C₄⋊Q₈	—	2	2	no	—
651	C₄⋊Q₈	—	2	2	no	—
652	C₄⋊Q₈	—	2	1	no	—
653	C₄⋊Q₈	—	2	1	no	—
654	C₄⋊Q₈	—	2	1	no	—
655	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
656	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
657	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
658	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
659	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
660	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
661	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
662	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
663	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
664	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
665	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
666	#126	—	2	2	no	—
667	#126	—	2	2	no	—
668	#126	—	2	2	no	—
669	#126	—	2	2	no	—
670	#126	—	2	2	no	—
671	#126	—	2	2	no	—
672	#126	—	2	1	no	—
673	#125	—	2	2	no	—
674	#125	—	2	2	no	—
675	#125	—	2	2	no	—
676	#125	—	2	2	no	—
677	#125	—	2	2	no	—
678	#125	—	2	2	no	—
679	#125	—	2	1	no	—
680	#125	—	2	2	no	—
681	#125	—	2	2	no	—
682	#125	—	2	1	no	—
683	#125	C₇×D₄	1	2	yes	—
684	#125	C₂³×C₇	1	1	yes	characteristic
685	#125	C₂³×C₇	1	2	yes	—
686	#125	C₂³×C₇	1	2	yes	—
687	#125	C₂³×C₇	1	2	yes	—
688	#124	—	2	2	no	—
689	#124	C₂³×C₇	1	1	yes	characteristic
690	#124	C₂³×C₇	1	2	yes	—
691	#123	—	2	1	no	—
692	#123	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	1	no	—
695	C₂²⋊Q₈	—	2	1	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	1	no	—
698	C₂²⋊Q₈	—	2	1	no	—
699	C₂²⋊Q₈	—	2	1	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	—	2	2	no	—
705	C₂²⋊Q₈	—	2	2	no	—
706	C₂²⋊Q₈	—	2	2	no	—
707	C₂²⋊Q₈	—	2	2	no	—
708	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
709	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
710	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
711	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
712	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
713	#121	C₂³×C₇	1	1	yes	characteristic
714	C₄×Q₈	—	2	2	no	—
715	C₄×Q₈	—	2	1	no	—
716	C₄×Q₈	—	2	1	no	—
717	C₄×Q₈	—	2	1	no	—
718	C₄×Q₈	—	2	1	no	—
719	C₄×Q₈	—	2	2	no	—
720	C₄×Q₈	—	2	1	no	—
721	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
722	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
723	C₄×Q₈	C₂³×C₇	1	2	yes	—
724	C₄×Q₈	C₂³×C₇	1	2	yes	—
725	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
726	C₄×Q₈	C₂³×C₇	1	2	yes	—
727	C₄×Q₈	C₂³×C₇	1	2	yes	—
728	C₄×Q₈	C₂³×C₇	1	2	yes	—
729	C₄×Q₈	C₂³×C₇	1	2	yes	—
730	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
731	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
732	C₄×Q₈	C₂³×C₇	1	2	yes	—
733	C₄×D₄	—	2	1	no	—
734	C₄×D₄	—	2	1	no	—
735	C₄×D₄	—	2	1	no	—
736	C₄×D₄	—	2	2	no	—
737	C₄×D₄	—	2	2	no	—
738	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
739	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
740	C₄×D₄	C₂³×C₇	1	2	yes	—
741	C₄×D₄	C₂³×C₇	1	2	yes	—
742	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
743	C₄×D₄	C₂³×C₇	1	2	yes	—
744	#117	—	2	1	no	—
745	#117	—	2	2	no	—
746	#117	—	2	2	no	—
747	#117	—	2	1	no	—
748	#117	—	2	1	no	—
749	#117	—	2	1	no	—
750	#117	C₂³×C₇	1	1	yes	characteristic
751	#117	C₂³×C₇	1	2	yes	—
752	C₂×C₄⋊C₄	—	2	1	no	—
753	C₂×C₄⋊C₄	—	2	2	no	—
754	C₂×C₄⋊C₄	—	2	2	no	—
755	C₂×C₄⋊C₄	—	2	1	no	—
756	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
757	C₂×C₄²	—	2	1	no	—
758	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
759	#107	C₂³×C₇	1	1	yes	characteristic
760	#107	C₂³×C₇	1	2	yes	—
761	#107	C₂³×C₇	1	1	yes	characteristic
762	#107	C₂³×C₇	1	2	yes	—
763	#107	C₂³×C₇	1	2	yes	—
764	#106	C₂³×C₇	1	2	yes	—
765	#106	C₂³×C₇	1	2	yes	—
766	#106	C₂³×C₇	1	1	yes	characteristic
767	#106	C₂³×C₇	1	2	yes	—
768	#106	C₂³×C₇	1	1	yes	characteristic
769	#106	C₂³×C₇	1	2	yes	—
770	#106	C₂³×C₇	1	2	yes	—
771	#106	C₂³×C₇	1	2	yes	—
772	#106	C₂³×C₇	1	2	yes	—
773	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
774	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
775	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
776	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
777	C₄⋊C₈	C₂³×C₇	1	2	yes	—
778	C₄⋊C₈	C₂³×C₇	1	2	yes	—
779	C₄⋊C₈	C₂³×C₇	1	2	yes	—
780	C₄⋊C₈	C₂³×C₇	1	2	yes	—
781	#103	C₂³×C₇	1	1	yes	characteristic
782	#103	C₂³×C₇	1	2	yes	—
783	#103	C₂³×C₇	1	2	yes	—
784	#103	C₂³×C₇	1	1	yes	characteristic
785	#103	C₂³×C₇	1	2	yes	—
786	#103	C₂³×C₇	1	1	yes	characteristic
787	#103	C₂³×C₇	1	2	yes	—
788	#103	C₂³×C₇	1	1	yes	characteristic
789	#103	C₂³×C₇	1	2	yes	—
790	#103	C₂³×C₇	1	2	yes	—
791	#103	C₂³×C₇	1	2	yes	—
792	#103	C₂³×C₇	1	2	yes	—
793	#103	C₂³×C₇	1	2	yes	—
794	#102	C₂³×C₇	1	1	yes	characteristic
795	#102	C₂³×C₇	1	1	yes	characteristic
796	#102	C₂³×C₇	1	1	yes	characteristic
797	#102	C₂³×C₇	1	2	yes	—
798	#102	C₂³×C₇	1	2	yes	—
799	#102	C₂³×C₇	1	1	yes	characteristic
800	#102	C₂³×C₇	1	2	yes	—
801	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
802	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
803	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
804	#97	C₂³×C₇	1	2	yes	—
805	#97	C₂³×C₇	1	2	yes	—
806	#97	C₂³×C₇	1	2	yes	—
807	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
808	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
809	C₄×C₈	C₂³×C₇	1	2	yes	—
810	C₄×C₈	C₂³×C₇	1	2	yes	—
811	C₂²×C₇	—	2	1	no	—
812	C₂²×C₇	—	2	1	no	—
813	C₂²×C₇	—	2	2	no	—
814	C₂²×C₇	—	2	1	no	—
815	C₂²×C₇	—	4	1	no	—
816	C₂²×C₇	—	4	1	no	—
817	C₂²×C₇	—	4	1	no	—
818	C₂²×C₇	—	4	1	no	—
819	C₂²×C₇	—	4	1	no	—
820	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
821	C₄×C₇	—	2	1	no	—
822	C₄×C₇	—	2	1	no	—
823	C₄×C₇	—	2	2	no	—
824	C₄×C₇	—	2	2	no	—
825	C₄×C₇	—	2	1	no	—
826	C₄×C₇	—	2	2	no	—
827	C₄×C₇	—	2	1	no	—
828	C₄×C₇	—	2	2	no	—
829	C₄×C₇	—	2	2	no	—
830	C₄×C₇	—	4	1	no	—
831	C₄×C₇	—	4	2	no	—
832	C₄×C₇	—	4	1	no	—
833	C₄×C₇	—	4	2	no	—
834	C₄×C₇	—	4	1	no	—
835	C₄×C₇	—	4	1	no	—
836	C₄×C₇	—	4	1	no	—
837	C₄×C₇	—	4	2	no	—
838	C₄×C₇	—	4	2	no	—
839	C₄×C₇	#577	1	2	yes	—
840	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
841	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
842	#41	—	2	2	no	—
843	#41	—	2	2	no	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	2	2	no	—
848	C₂×Q₈	—	2	2	no	—
849	C₂×Q₈	—	2	2	no	—
850	C₂×Q₈	—	2	2	no	—
851	C₂×Q₈	—	8	2	no	—
852	C₂×Q₈	—	8	2	no	—
853	C₂×Q₈	—	8	2	no	—
854	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
855	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
856	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
857	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
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	C₂⁴×C₇	1	1	yes	characteristic
863	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
864	C₂²×C₄	—	2	1	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	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
873	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
875	Q₁₆	—	2	2	no	—
876	Q₁₆	—	2	4	no	—
877	SD₁₆	—	2	2	no	—
878	SD₁₆	—	2	2	no	—
879	SD₁₆	—	2	4	no	—
880	D₈	—	2	2	no	—
881	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
882	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
883	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
884	C₂×C₈	C₂⁴×C₇	1	2	yes	—
885	C₂×C₈	C₂⁴×C₇	1	2	yes	—
886	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	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	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	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	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	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	1	no	—
918	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
919	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
920	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
921	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
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	2	yes	—
925	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
926	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
927	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
928	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
930	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
931	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
932	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	1	no	—
936	C₂²⋊C₄	—	2	1	no	—
937	C₂²⋊C₄	—	2	1	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	1	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	1	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
949	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
950	C₄²	—	2	1	no	—
951	C₄²	—	2	1	no	—
952	C₄²	—	2	1	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	2	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	1	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
961	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
962	C₄²	C₂⁴×C₇	1	1	yes	characteristic
963	C₄²	C₂⁴×C₇	1	2	yes	—
964	C₄²	C₂⁴×C₇	1	2	yes	—
965	C₄²	C₂⁴×C₇	1	1	yes	characteristic
966	C₂×C₇	—	4	1	no	—
967	C₂×C₇	—	4	2	no	—
968	C₂×C₇	—	8	1	no	—
969	C₂×C₇	#3486	1	1	yes	characteristic
970	C₂×C₇	C₂×#577	1	1	yes	characteristic
971	C₂×C₇	#3586	1	1	yes	characteristic
972	C₂³	—	2	1	no	—
973	C₂³	—	2	1	no	—
974	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
975	Q₈	—	2	1	no	—
976	Q₈	—	2	2	no	—
977	Q₈	—	2	2	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	2	2	no	—
980	Q₈	—	2	1	no	—
981	Q₈	—	2	2	no	—
982	Q₈	—	4	2	no	—
983	Q₈	—	4	2	no	—
984	Q₈	—	4	2	no	—
985	Q₈	—	8	1	no	—
986	Q₈	—	8	2	no	—
987	Q₈	—	8	2	no	—
988	Q₈	—	8	2	no	—
989	Q₈	—	8	2	no	—
990	Q₈	C₇×2₋¹⁺⁴	1	2	yes	—
991	D₄	—	2	4	no	—
992	D₄	—	2	1	no	—
993	D₄	—	2	1	no	—
994	D₄	—	2	1	no	—
995	D₄	—	8	1	no	—
996	D₄	C₇×2₋¹⁺⁴	1	2	yes	—
997	C₂×C₄	—	2	4	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	4	2	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	—	8	2	no	—
1019	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1020	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1021	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1022	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1023	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1024	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1025	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1026	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1027	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1028	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	2	no	—
1033	C₈	—	2	1	no	—
1034	C₈	—	2	2	no	—
1035	C₇	#61858	1	1	yes	characteristic, direct product factor, Sylow
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1046	C₄	—	2	1	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	4	1	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	1	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	1	no	—
1064	C₄	C₇×#577	1	2	yes	—
1065	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1066	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1067	C₂	—	4	1	no	—
1068	C₂	—	4	2	no	—
1069	C₂	—	8	1	no	—
1070	C₂	C₇×#3486	1	1	yes	characteristic
1071	C₂	C₂×C₇×#577	1	1	yes	characteristic
1072	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×#449	C₂²
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
1. C₇×#3555	C₂	semidirect
2. C₇×#3503	C₂	semidirect
3. C₇×#3388	C₂	semidirect
4. C₇×#3387	C₂	semidirect
5. C₇×#3387	C₂	semidirect
6. C₇×#3384	C₂	semidirect
7. C₇×#3381	C₂	semidirect
8. C₇×Q₈×SD₁₆	C₂	semidirect
9. C₇×#3376	C₂	semidirect
10. C₇×#3374	C₂	semidirect
11. C₇×#3369	C₂	semidirect
12. C₇×#3367	C₂	semidirect
13. C₇×#3364	C₂	semidirect
14. C₇×#3359	C₂	semidirect
15. C₇×#3244	C₂	semidirect
16. C₇×#3242	C₂	semidirect
17. C₇×#3239	C₂	semidirect
18. C₇×#3229	C₂	semidirect
20. C₇×#3120	C₂	semidirect
21. C₇×#3116	C₂	semidirect
23. C₇×#2985	C₂	semidirect
135. #61858	C₇	direct (N × H)
313. #3555	C₂×C₇	semidirect
314. #3503	C₂×C₇	semidirect
315. #3388	C₂×C₇	semidirect
316. #3387	C₂×C₇	semidirect
317. #3387	C₂×C₇	semidirect
318. #3384	C₂×C₇	semidirect
319. #3381	C₂×C₇	semidirect
320. Q₈×SD₁₆	C₂×C₇	semidirect
321. #3376	C₂×C₇	semidirect
322. #3374	C₂×C₇	semidirect
323. #3369	C₂×C₇	semidirect
324. #3367	C₂×C₇	semidirect
325. #3364	C₂×C₇	semidirect
326. #3359	C₂×C₇	semidirect
327. #3244	C₂×C₇	semidirect
328. #3242	C₂×C₇	semidirect
329. #3239	C₂×C₇	semidirect
330. #3229	C₂×C₇	semidirect
332. #3120	C₂×C₇	semidirect
333. #3116	C₂×C₇	semidirect
335. #2985	C₂×C₇	semidirect
1035. C₇	#61858	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×#3555	2
C₇×#3503	2
C₇×#3388	2
C₇×#3387	2
C₇×#3384	2
C₇×#3381	2
C₇×Q₈×SD₁₆	2
C₇×#3376	2
C₇×#3374	2
C₇×#3369	2
C₇×#3367	2
C₇×#3364	2
C₇×#3359	2
C₇×#3244	2
C₇×#3242	2
C₇×#3239	2
C₇×#3229	2
C₇×#3125	2
C₇×#3120	2
C₇×#3116	2
C₇×#3102	2
C₇×#2985	2
#61858	7

Subgroups — C7×#61858 #13239074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61858 #13239074