Subgroups — C₇×#61008 #13238224

Order 1792.

1712 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3511	C₂	1	1	yes	maximal, characteristic
2	C₇×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3258	C₂	1	4	yes	maximal, complemented
4	C₇×#3231	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3229	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3228	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3209	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3201	C₂	1	4	yes	maximal, complemented
13	C₇×#3185	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3182	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3121	C₂	1	4	yes	maximal, complemented
18	C₇×#3120	C₂	1	4	yes	maximal, complemented
19	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#557	—	2	1	no	—
21	C₇×#557	—	2	1	no	—
22	C₇×#556	—	2	1	no	—
23	C₇×#556	—	2	1	no	—
24	C₇×#556	—	2	1	no	—
25	C₇×#555	—	2	1	no	—
26	C₇×#554	—	2	1	no	—
27	C₇×#553	—	2	1	no	—
28	C₇×#553	—	2	1	no	—
29	C₇×#552	—	2	1	no	—
30	C₇×#552	—	2	1	no	—
31	C₇×#552	—	2	1	no	—
32	C₇×#552	—	2	1	no	—
33	C₇×#548	—	2	1	no	—
34	C₇×#548	—	2	1	no	—
35	C₇×#547	—	2	1	no	—
36	C₇×#542	C₂²	1	2	yes	—
37	C₇×#542	C₂²	1	2	yes	—
38	C₇×#541	C₂²	1	2	yes	—
39	C₇×#541	C₂²	1	2	yes	—
40	C₇×#537	C₂²	1	2	yes	—
41	C₇×#536	C₂²	1	2	yes	—
42	C₇×#533	C₂²	1	1	yes	characteristic
43	C₇×#533	C₂²	1	1	yes	characteristic
44	C₇×#533	C₂²	1	1	yes	characteristic
45	C₇×#533	C₂²	1	1	yes	characteristic
46	C₇×#533	C₂²	1	1	yes	characteristic
47	C₇×#533	C₂²	1	1	yes	characteristic
48	C₇×#533	C₂²	1	1	yes	characteristic
49	C₇×#532	C₂²	1	1	yes	characteristic
50	C₇×#532	C₂²	1	1	yes	characteristic
51	C₇×#532	C₂²	1	1	yes	characteristic
52	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
53	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
54	C₇×#520	C₂²	1	2	yes	—
55	C₇×#519	C₂²	1	2	yes	—
56	C₄×C₇×#41	C₂²	1	1	yes	characteristic
57	C₇×#500	C₂²	1	1	yes	characteristic
58	C₇×#500	C₂²	1	1	yes	characteristic
59	C₇×#498	C₂²	1	1	yes	characteristic
60	C₇×#498	C₂²	1	1	yes	characteristic
61	C₇×#494	C₂²	1	1	yes	characteristic
62	C₇×#494	C₂²	1	1	yes	characteristic
63	C₇×#492	C₂²	1	1	yes	characteristic
64	C₇×#492	C₂²	1	1	yes	characteristic
65	C₇×#487	C₂²	1	1	yes	characteristic
66	C₇×#487	C₂²	1	1	yes	characteristic
67	C₇×#487	C₂²	1	1	yes	characteristic
68	C₇×#487	C₂²	1	1	yes	characteristic
69	C₇×#487	C₂²	1	1	yes	characteristic
70	C₇×#487	C₂²	1	1	yes	characteristic
71	C₇×#486	C₂²	1	1	yes	characteristic
72	C₇×#486	C₂²	1	1	yes	characteristic
73	C₇×#485	C₂²	1	4	yes	—
74	C₇×#484	C₂²	1	4	yes	—
75	C₇×#483	C₂²	1	4	yes	—
76	C₇×#482	C₂²	1	4	yes	—
77	C₇×#479	C₂²	1	4	yes	—
78	C₇×#478	C₂²	1	4	yes	—
79	C₇×#477	C₂²	1	4	yes	—
80	C₇×#475	C₂²	1	4	yes	—
81	C₇×#470	C₂²	1	4	yes	—
82	C₇×#468	C₂²	1	4	yes	—
83	C₇×#467	C₂²	1	4	yes	—
84	C₇×#465	C₂²	1	4	yes	—
85	C₇×#464	C₂²	1	4	yes	—
86	C₇×#464	C₂²	1	4	yes	—
87	C₇×#462	C₂²	1	4	yes	—
88	C₇×#461	C₂²	1	4	yes	—
89	C₇×#452	C₂²	1	4	yes	—
90	C₇×#452	C₂²	1	4	yes	—
91	C₇×#451	C₂²	1	4	yes	—
92	C₇×#448	C₂²	1	4	yes	—
93	C₇×#441	C₂²	1	4	yes	—
94	C₇×#440	C₂²	1	4	yes	—
95	C₄×C₇×Q₁₆	C₂²	1	4	yes	—
96	C₄×C₇×SD₁₆	C₂²	1	4	yes	—
97	C₇×#433	C₂²	1	2	yes	—
98	C₇×#433	C₂²	1	2	yes	—
99	C₇×#431	C₂²	1	1	yes	characteristic
100	C₇×#431	C₂²	1	1	yes	characteristic
101	C₇×#431	C₂²	1	1	yes	characteristic
102	C₇×#431	C₂²	1	1	yes	characteristic
103	C₇×#424	C₂²	1	2	yes	—
104	C₇×#408	C₂²	1	2	yes	—
105	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
106	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
107	#61008	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂×C₇×#41	—	2	1	no	—
109	C₂×C₇×#41	—	2	1	no	—
110	C₂×C₇×#41	C₂³	1	2	yes	—
111	C₂×C₇×#41	C₂³	1	1	yes	characteristic
112	C₂²×C₇×Q₈	—	2	1	no	—
113	C₂²×C₇×Q₈	C₂³	1	2	yes	—
114	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
115	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
116	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₇×M₁₆	C₂³	1	2	yes	—
119	C₂²×C₇×C₈	C₂³	1	2	yes	—
120	C₇×C₄⋊Q₈	—	2	2	no	—
121	C₇×C₄⋊Q₈	—	2	1	no	—
122	C₇×C₄⋊Q₈	—	2	1	no	—
123	C₇×C₄⋊Q₈	—	2	1	no	—
124	C₇×C₄⋊Q₈	—	2	1	no	—
125	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
131	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
132	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
133	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
134	C₇×#127	C₂³	1	1	yes	characteristic
135	C₇×#126	—	2	2	no	—
136	C₇×#126	—	2	2	no	—
137	C₇×#126	—	2	2	no	—
138	C₇×#126	—	2	2	no	—
139	C₇×#126	—	2	2	no	—
140	C₇×#126	—	2	2	no	—
141	C₇×#125	—	2	2	no	—
142	C₇×#125	—	2	2	no	—
143	C₇×#125	—	2	2	no	—
144	C₇×#125	—	2	2	no	—
145	C₇×#125	—	2	1	no	—
146	C₇×#125	—	2	1	no	—
147	C₇×#125	—	2	1	no	—
148	C₇×#125	—	2	1	no	—
149	C₇×#125	—	2	1	no	—
150	C₇×#125	—	2	1	no	—
151	C₇×#125	C₂³	1	2	yes	—
152	C₇×#124	—	2	2	no	—
153	C₇×#124	—	2	2	no	—
154	C₇×#124	—	2	2	no	—
155	C₇×#124	—	2	1	no	—
156	C₇×#124	—	2	1	no	—
157	C₇×#124	C₂³	1	2	yes	—
158	C₇×#123	—	2	2	no	—
159	C₇×#123	—	2	2	no	—
160	C₇×#123	—	2	2	no	—
161	C₇×#123	—	2	2	no	—
162	C₇×C₂²⋊Q₈	—	2	2	no	—
163	C₇×C₂²⋊Q₈	—	2	1	no	—
164	C₇×C₂²⋊Q₈	—	2	1	no	—
165	C₇×C₂²⋊Q₈	—	2	1	no	—
166	C₇×C₂²⋊Q₈	—	2	1	no	—
167	C₇×C₂²⋊Q₈	—	2	1	no	—
168	C₇×C₂²⋊Q₈	—	2	1	no	—
169	C₇×C₂²⋊Q₈	—	2	1	no	—
170	C₇×C₂²⋊Q₈	—	2	1	no	—
171	C₇×C₂²⋊Q₈	—	2	2	no	—
172	C₇×C₂²⋊Q₈	—	2	2	no	—
173	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
174	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
175	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
176	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₇×#121	—	2	2	no	—
180	C₇×#121	—	2	2	no	—
181	C₇×#121	—	2	2	no	—
182	C₇×#121	—	2	1	no	—
183	C₇×#121	—	2	1	no	—
184	C₇×#121	—	2	1	no	—
185	C₇×#121	—	2	1	no	—
186	C₇×#121	C₂³	1	2	yes	—
187	C₇×#121	C₂³	1	2	yes	—
188	C₄×C₇×Q₈	—	2	2	no	—
189	C₄×C₇×Q₈	—	2	2	no	—
190	C₄×C₇×Q₈	—	2	1	no	—
191	C₄×C₇×Q₈	—	2	1	no	—
192	C₄×C₇×Q₈	—	2	1	no	—
193	C₄×C₇×Q₈	—	2	1	no	—
194	C₄×C₇×Q₈	—	2	1	no	—
195	C₄×C₇×Q₈	—	2	1	no	—
196	C₄×C₇×Q₈	—	2	1	no	—
197	C₄×C₇×Q₈	—	2	1	no	—
198	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
199	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
200	C₄×C₇×Q₈	C₂³	1	2	yes	—
201	C₄×C₇×Q₈	C₂³	1	2	yes	—
202	C₄×C₇×Q₈	C₂³	1	2	yes	—
203	C₄×C₇×Q₈	C₂³	1	2	yes	—
204	C₄×C₇×Q₈	C₂³	1	2	yes	—
205	C₄×C₇×Q₈	C₂³	1	2	yes	—
206	C₄×C₇×D₄	—	2	2	no	—
207	C₄×C₇×D₄	—	2	2	no	—
208	C₄×C₇×D₄	—	2	1	no	—
209	C₄×C₇×D₄	—	2	1	no	—
210	C₄×C₇×D₄	—	2	1	no	—
211	C₄×C₇×D₄	—	2	1	no	—
212	C₄×C₇×D₄	D₄	1	1	yes	characteristic
213	C₄×C₇×D₄	D₄	1	1	yes	characteristic
214	C₄×C₇×D₄	D₄	1	1	yes	characteristic
215	C₄×C₇×D₄	D₄	1	1	yes	characteristic
216	C₄×C₇×D₄	D₄	1	1	yes	characteristic
217	C₄×C₇×D₄	D₄	1	1	yes	characteristic
218	C₄×C₇×D₄	C₂³	1	2	yes	—
219	C₄×C₇×D₄	C₂³	1	2	yes	—
220	C₇×#117	—	2	1	no	—
221	C₇×#117	—	2	1	no	—
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	2	no	—
228	C₇×#117	—	2	2	no	—
229	C₇×#117	C₂³	1	2	yes	—
230	C₇×#117	C₂³	1	1	yes	characteristic
231	C₇×#117	C₂³	1	1	yes	characteristic
232	C₇×#117	C₂³	1	1	yes	characteristic
233	C₂×C₇×C₄⋊C₄	—	2	1	no	—
234	C₂×C₇×C₄⋊C₄	—	2	1	no	—
235	C₂×C₇×C₄⋊C₄	—	2	1	no	—
236	C₂×C₇×C₄⋊C₄	—	2	2	no	—
237	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
238	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
241	C₇×#107	C₂³	1	4	yes	—
242	C₇×#107	C₂³	1	4	yes	—
243	C₇×#106	C₂³	1	4	yes	—
244	C₇×#106	C₂³	1	4	yes	—
245	C₇×C₄⋊C₈	C₂³	1	2	yes	—
246	C₇×C₄⋊C₈	C₂³	1	2	yes	—
247	C₇×C₄⋊C₈	C₂³	1	2	yes	—
248	C₇×C₄⋊C₈	C₂³	1	2	yes	—
249	C₇×#103	C₂³	1	4	yes	—
250	C₇×#103	C₂³	1	4	yes	—
251	C₇×#103	C₂³	1	4	yes	—
252	C₇×#103	C₂³	1	4	yes	—
253	C₇×#103	C₂³	1	4	yes	—
254	C₇×#103	C₂³	1	4	yes	—
255	C₇×#102	C₂³	1	4	yes	—
256	C₇×#102	C₂³	1	4	yes	—
257	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
261	C₇×#97	C₂³	1	2	yes	—
262	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
263	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
264	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
265	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
266	C₄×C₇×C₈	C₂³	1	2	yes	—
267	#3511	C₂×C₇	1	1	yes	characteristic
268	#3509	C₂×C₇	1	1	yes	characteristic, complemented
269	#3258	C₂×C₇	1	4	yes	complemented
270	#3231	C₂×C₇	1	1	yes	characteristic, complemented
271	#3230	C₂×C₇	1	1	yes	characteristic, complemented
272	#3229	C₂×C₇	1	1	yes	characteristic, complemented
273	#3228	C₂×C₇	1	1	yes	characteristic, complemented
274	#3210	C₂×C₇	1	1	yes	characteristic, complemented
275	#3210	C₂×C₇	1	1	yes	characteristic, complemented
276	#3209	C₂×C₇	1	1	yes	characteristic, complemented
277	#3206	C₂×C₇	1	1	yes	characteristic, complemented
278	#3201	C₂×C₇	1	4	yes	complemented
279	#3185	C₂×C₇	1	1	yes	characteristic, complemented
280	#3182	C₂×C₇	1	1	yes	characteristic, complemented
281	#3170	C₂×C₇	1	1	yes	characteristic, complemented
282	#3167	C₂×C₇	1	1	yes	characteristic, complemented
283	#3121	C₂×C₇	1	4	yes	complemented
284	#3120	C₂×C₇	1	4	yes	complemented
285	#2922	C₂×C₇	1	1	yes	characteristic, complemented
286	C₇×#41	—	4	2	no	—
287	C₇×#41	—	4	4	no	—
288	C₇×#41	—	8	2	no	—
289	C₇×#41	—	8	2	no	—
290	C₂×C₇×Q₈	—	2	1	no	—
291	C₂×C₇×Q₈	—	2	1	no	—
292	C₂×C₇×Q₈	—	2	2	no	—
293	C₂×C₇×Q₈	—	2	1	no	—
294	C₂×C₇×Q₈	—	2	1	no	—
295	C₂×C₇×Q₈	—	2	2	no	—
296	C₂×C₇×Q₈	—	4	4	no	—
297	C₂×C₇×Q₈	—	8	2	no	—
298	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
299	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
300	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
301	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
302	C₂×C₇×D₄	—	2	2	no	—
303	C₂×C₇×D₄	—	2	2	no	—
304	C₂×C₇×D₄	—	2	2	no	—
305	C₂×C₇×D₄	—	2	1	no	—
306	C₂×C₇×D₄	—	2	1	no	—
307	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
308	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
309	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
310	C₂×C₇×D₄	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₇	—	2	2	no	—
312	C₂²×C₄×C₇	—	2	2	no	—
313	C₂²×C₄×C₇	—	2	2	no	—
314	C₂²×C₄×C₇	—	2	2	no	—
315	C₂²×C₄×C₇	—	2	2	no	—
316	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
325	C₇×Q₁₆	—	4	4	no	—
326	C₇×Q₁₆	—	4	4	no	—
327	C₇×SD₁₆	—	4	4	no	—
328	C₇×SD₁₆	—	4	4	no	—
329	C₇×M₁₆	—	4	2	no	—
330	C₂×C₇×C₈	—	4	2	no	—
331	C₂×C₇×C₈	C₂⁴	1	2	yes	—
332	C₂×C₇×C₈	C₂⁴	1	2	yes	—
333	C₂×C₇×C₈	C₂⁴	1	2	yes	—
334	C₂×C₇×C₈	C₂⁴	1	2	yes	—
335	C₇×C₄⋊C₄	—	2	2	no	—
336	C₇×C₄⋊C₄	—	2	1	no	—
337	C₇×C₄⋊C₄	—	2	1	no	—
338	C₇×C₄⋊C₄	—	2	1	no	—
339	C₇×C₄⋊C₄	—	2	1	no	—
340	C₇×C₄⋊C₄	—	2	1	no	—
341	C₇×C₄⋊C₄	—	2	1	no	—
342	C₇×C₄⋊C₄	—	2	2	no	—
343	C₇×C₄⋊C₄	—	2	2	no	—
344	C₇×C₄⋊C₄	—	2	2	no	—
345	C₇×C₄⋊C₄	—	2	2	no	—
346	C₇×C₄⋊C₄	—	2	2	no	—
347	C₇×C₄⋊C₄	—	2	1	no	—
348	C₇×C₄⋊C₄	—	2	1	no	—
349	C₇×C₄⋊C₄	—	2	1	no	—
350	C₇×C₄⋊C₄	—	2	2	no	—
351	C₇×C₄⋊C₄	—	2	2	no	—
352	C₇×C₄⋊C₄	—	2	2	no	—
353	C₇×C₄⋊C₄	—	2	2	no	—
354	C₇×C₄⋊C₄	—	2	1	no	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	2	no	—
357	C₇×C₄⋊C₄	—	2	2	no	—
358	C₇×C₄⋊C₄	—	2	2	no	—
359	C₇×C₄⋊C₄	—	2	2	no	—
360	C₇×C₄⋊C₄	—	2	2	no	—
361	C₇×C₄⋊C₄	—	2	2	no	—
362	C₇×C₄⋊C₄	—	2	2	no	—
363	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
364	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
365	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
366	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
367	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
368	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
369	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
370	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
371	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
372	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
373	C₇×C₂²⋊C₄	—	2	2	no	—
374	C₇×C₂²⋊C₄	—	2	2	no	—
375	C₇×C₂²⋊C₄	—	2	2	no	—
376	C₇×C₂²⋊C₄	—	2	2	no	—
377	C₇×C₂²⋊C₄	—	2	2	no	—
378	C₇×C₂²⋊C₄	—	2	2	no	—
379	C₇×C₂²⋊C₄	—	2	2	no	—
380	C₇×C₂²⋊C₄	—	2	2	no	—
381	C₇×C₂²⋊C₄	—	2	2	no	—
382	C₇×C₂²⋊C₄	—	2	2	no	—
383	C₇×C₂²⋊C₄	—	2	2	no	—
384	C₇×C₂²⋊C₄	—	2	2	no	—
385	C₇×C₂²⋊C₄	—	2	2	no	—
386	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
387	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
388	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
389	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
390	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
391	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₇	—	2	2	no	—
393	C₄²×C₇	—	2	2	no	—
394	C₄²×C₇	—	2	2	no	—
395	C₄²×C₇	—	2	2	no	—
396	C₄²×C₇	—	2	2	no	—
397	C₄²×C₇	—	2	2	no	—
398	C₄²×C₇	—	2	2	no	—
399	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
403	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
404	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
405	C₄²×C₇	C₂⁴	1	1	yes	characteristic
406	C₄²×C₇	C₂⁴	1	1	yes	characteristic
407	C₄²×C₇	C₂⁴	1	1	yes	characteristic
408	C₄²×C₇	C₂⁴	1	1	yes	characteristic
409	#557	—	2	1	no	—
410	#557	—	2	1	no	—
411	#556	—	2	1	no	—
412	#556	—	2	1	no	—
413	#556	—	2	1	no	—
414	#555	—	2	1	no	—
415	#554	—	2	1	no	—
416	#553	—	2	1	no	—
417	#553	—	2	1	no	—
418	#552	—	2	1	no	—
419	#552	—	2	1	no	—
420	#552	—	2	1	no	—
421	#552	—	2	1	no	—
422	#548	—	2	1	no	—
423	#548	—	2	1	no	—
424	#547	—	2	1	no	—
425	#542	C₂²×C₇	1	2	yes	—
426	#542	C₂²×C₇	1	2	yes	—
427	#541	C₂²×C₇	1	2	yes	—
428	#541	C₂²×C₇	1	2	yes	—
429	#537	C₂²×C₇	1	2	yes	—
430	#536	C₂²×C₇	1	2	yes	—
431	#533	C₂²×C₇	1	1	yes	characteristic
432	#533	C₂²×C₇	1	1	yes	characteristic
433	#533	C₂²×C₇	1	1	yes	characteristic
434	#533	C₂²×C₇	1	1	yes	characteristic
435	#533	C₂²×C₇	1	1	yes	characteristic
436	#533	C₂²×C₇	1	1	yes	characteristic
437	#533	C₂²×C₇	1	1	yes	characteristic
438	#532	C₂²×C₇	1	1	yes	characteristic
439	#532	C₂²×C₇	1	1	yes	characteristic
440	#532	C₂²×C₇	1	1	yes	characteristic
441	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
442	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
443	#520	C₂²×C₇	1	2	yes	—
444	#519	C₂²×C₇	1	2	yes	—
445	C₄×#41	C₂²×C₇	1	1	yes	characteristic
446	#500	C₂²×C₇	1	1	yes	characteristic
447	#500	C₂²×C₇	1	1	yes	characteristic
448	#498	C₂²×C₇	1	1	yes	characteristic
449	#498	C₂²×C₇	1	1	yes	characteristic
450	#494	C₂²×C₇	1	1	yes	characteristic
451	#494	C₂²×C₇	1	1	yes	characteristic
452	#492	C₂²×C₇	1	1	yes	characteristic
453	#492	C₂²×C₇	1	1	yes	characteristic
454	#487	C₂²×C₇	1	1	yes	characteristic
455	#487	C₂²×C₇	1	1	yes	characteristic
456	#487	C₂²×C₇	1	1	yes	characteristic
457	#487	C₂²×C₇	1	1	yes	characteristic
458	#487	C₂²×C₇	1	1	yes	characteristic
459	#487	C₂²×C₇	1	1	yes	characteristic
460	#486	C₂²×C₇	1	1	yes	characteristic
461	#486	C₂²×C₇	1	1	yes	characteristic
462	#485	C₂²×C₇	1	4	yes	—
463	#484	C₂²×C₇	1	4	yes	—
464	#483	C₂²×C₇	1	4	yes	—
465	#482	C₂²×C₇	1	4	yes	—
466	#479	C₂²×C₇	1	4	yes	—
467	#478	C₂²×C₇	1	4	yes	—
468	#477	C₂²×C₇	1	4	yes	—
469	#475	C₂²×C₇	1	4	yes	—
470	#470	C₂²×C₇	1	4	yes	—
471	#468	C₂²×C₇	1	4	yes	—
472	#467	C₂²×C₇	1	4	yes	—
473	#465	C₂²×C₇	1	4	yes	—
474	#464	C₂²×C₇	1	4	yes	—
475	#464	C₂²×C₇	1	4	yes	—
476	#462	C₂²×C₇	1	4	yes	—
477	#461	C₂²×C₇	1	4	yes	—
478	#452	C₂²×C₇	1	4	yes	—
479	#452	C₂²×C₇	1	4	yes	—
480	#451	C₂²×C₇	1	4	yes	—
481	#448	C₂²×C₇	1	4	yes	—
482	#441	C₂²×C₇	1	4	yes	—
483	#440	C₂²×C₇	1	4	yes	—
484	C₄×Q₁₆	C₂²×C₇	1	4	yes	—
485	C₄×SD₁₆	C₂²×C₇	1	4	yes	—
486	#433	C₂²×C₇	1	2	yes	—
487	#433	C₂²×C₇	1	2	yes	—
488	#431	C₂²×C₇	1	1	yes	characteristic
489	#431	C₂²×C₇	1	1	yes	characteristic
490	#431	C₂²×C₇	1	1	yes	characteristic
491	#431	C₂²×C₇	1	1	yes	characteristic
492	#424	C₂²×C₇	1	2	yes	—
493	#408	C₂²×C₇	1	2	yes	—
494	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
495	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
496	C₂³×C₇	—	2	2	no	—
497	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
498	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
499	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
500	C₇×Q₈	—	2	4	no	—
501	C₇×Q₈	—	2	4	no	—
502	C₇×Q₈	—	2	4	no	—
503	C₇×Q₈	—	4	1	no	—
504	C₇×Q₈	—	4	4	no	—
505	C₇×Q₈	—	4	2	no	—
506	C₇×Q₈	—	4	2	no	—
507	C₇×Q₈	—	4	2	no	—
508	C₇×Q₈	—	4	2	no	—
509	C₇×Q₈	—	8	2	no	—
510	C₇×D₄	—	2	4	no	—
511	C₇×D₄	—	4	1	no	—
512	C₇×D₄	—	4	1	no	—
513	C₇×D₄	—	4	1	no	—
514	C₇×D₄	—	4	4	no	—
515	C₇×D₄	—	4	2	no	—
516	C₇×D₄	—	4	2	no	—
517	C₇×D₄	—	8	2	no	—
518	C₇×D₄	—	8	2	no	—
519	C₂×C₄×C₇	—	2	2	no	—
520	C₂×C₄×C₇	—	2	2	no	—
521	C₂×C₄×C₇	—	2	2	no	—
522	C₂×C₄×C₇	—	2	2	no	—
523	C₂×C₄×C₇	—	2	2	no	—
524	C₂×C₄×C₇	—	2	2	no	—
525	C₂×C₄×C₇	—	2	2	no	—
526	C₂×C₄×C₇	—	2	2	no	—
527	C₂×C₄×C₇	—	2	2	no	—
528	C₂×C₄×C₇	—	2	2	no	—
529	C₂×C₄×C₇	—	2	2	no	—
530	C₂×C₄×C₇	—	2	2	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	2	2	no	—
534	C₂×C₄×C₇	—	2	2	no	—
535	C₂×C₄×C₇	—	4	4	no	—
536	C₂×C₄×C₇	—	4	4	no	—
537	C₂×C₄×C₇	—	8	2	no	—
538	C₂×C₄×C₇	—	8	2	no	—
539	C₂×C₄×C₇	—	8	2	no	—
540	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
552	C₇×C₈	—	2	2	no	—
553	C₇×C₈	—	2	2	no	—
554	C₇×C₈	—	2	2	no	—
555	C₇×C₈	—	2	2	no	—
556	C₂×#41	—	2	1	no	—
557	C₂×#41	—	2	1	no	—
558	C₂×#41	C₂³×C₇	1	2	yes	—
559	C₂×#41	C₂³×C₇	1	1	yes	characteristic
560	C₂²×Q₈	—	2	1	no	—
561	C₂²×Q₈	C₂³×C₇	1	2	yes	—
562	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
563	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
564	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
565	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
566	C₂×M₁₆	C₂³×C₇	1	2	yes	—
567	C₂²×C₈	C₂³×C₇	1	2	yes	—
568	C₄⋊Q₈	—	2	2	no	—
569	C₄⋊Q₈	—	2	1	no	—
570	C₄⋊Q₈	—	2	1	no	—
571	C₄⋊Q₈	—	2	1	no	—
572	C₄⋊Q₈	—	2	1	no	—
573	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
574	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
575	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
576	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
577	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
578	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
579	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
580	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
581	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
582	#127	C₂³×C₇	1	1	yes	characteristic
583	#126	—	2	2	no	—
584	#126	—	2	2	no	—
585	#126	—	2	2	no	—
586	#126	—	2	2	no	—
587	#126	—	2	2	no	—
588	#126	—	2	2	no	—
589	#125	—	2	2	no	—
590	#125	—	2	2	no	—
591	#125	—	2	2	no	—
592	#125	—	2	2	no	—
593	#125	—	2	1	no	—
594	#125	—	2	1	no	—
595	#125	—	2	1	no	—
596	#125	—	2	1	no	—
597	#125	—	2	1	no	—
598	#125	—	2	1	no	—
599	#125	C₂³×C₇	1	2	yes	—
600	#124	—	2	2	no	—
601	#124	—	2	2	no	—
602	#124	—	2	2	no	—
603	#124	—	2	1	no	—
604	#124	—	2	1	no	—
605	#124	C₂³×C₇	1	2	yes	—
606	#123	—	2	2	no	—
607	#123	—	2	2	no	—
608	#123	—	2	2	no	—
609	#123	—	2	2	no	—
610	C₂²⋊Q₈	—	2	2	no	—
611	C₂²⋊Q₈	—	2	1	no	—
612	C₂²⋊Q₈	—	2	1	no	—
613	C₂²⋊Q₈	—	2	1	no	—
614	C₂²⋊Q₈	—	2	1	no	—
615	C₂²⋊Q₈	—	2	1	no	—
616	C₂²⋊Q₈	—	2	1	no	—
617	C₂²⋊Q₈	—	2	1	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	2	no	—
620	C₂²⋊Q₈	—	2	2	no	—
621	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
622	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
623	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
624	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
625	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
626	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
627	#121	—	2	2	no	—
628	#121	—	2	2	no	—
629	#121	—	2	2	no	—
630	#121	—	2	1	no	—
631	#121	—	2	1	no	—
632	#121	—	2	1	no	—
633	#121	—	2	1	no	—
634	#121	C₂³×C₇	1	2	yes	—
635	#121	C₂³×C₇	1	2	yes	—
636	C₄×Q₈	—	2	2	no	—
637	C₄×Q₈	—	2	2	no	—
638	C₄×Q₈	—	2	1	no	—
639	C₄×Q₈	—	2	1	no	—
640	C₄×Q₈	—	2	1	no	—
641	C₄×Q₈	—	2	1	no	—
642	C₄×Q₈	—	2	1	no	—
643	C₄×Q₈	—	2	1	no	—
644	C₄×Q₈	—	2	1	no	—
645	C₄×Q₈	—	2	1	no	—
646	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
647	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
648	C₄×Q₈	C₂³×C₇	1	2	yes	—
649	C₄×Q₈	C₂³×C₇	1	2	yes	—
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×D₄	—	2	2	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	—	2	1	no	—
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	1	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	C₇×D₄	1	1	yes	characteristic
661	C₄×D₄	C₇×D₄	1	1	yes	characteristic
662	C₄×D₄	C₇×D₄	1	1	yes	characteristic
663	C₄×D₄	C₇×D₄	1	1	yes	characteristic
664	C₄×D₄	C₇×D₄	1	1	yes	characteristic
665	C₄×D₄	C₇×D₄	1	1	yes	characteristic
666	C₄×D₄	C₂³×C₇	1	2	yes	—
667	C₄×D₄	C₂³×C₇	1	2	yes	—
668	#117	—	2	1	no	—
669	#117	—	2	1	no	—
670	#117	—	2	1	no	—
671	#117	—	2	1	no	—
672	#117	—	2	1	no	—
673	#117	—	2	1	no	—
674	#117	—	2	2	no	—
675	#117	—	2	2	no	—
676	#117	—	2	2	no	—
677	#117	C₂³×C₇	1	2	yes	—
678	#117	C₂³×C₇	1	1	yes	characteristic
679	#117	C₂³×C₇	1	1	yes	characteristic
680	#117	C₂³×C₇	1	1	yes	characteristic
681	C₂×C₄⋊C₄	—	2	1	no	—
682	C₂×C₄⋊C₄	—	2	1	no	—
683	C₂×C₄⋊C₄	—	2	1	no	—
684	C₂×C₄⋊C₄	—	2	2	no	—
685	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
686	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
689	#107	C₂³×C₇	1	4	yes	—
690	#107	C₂³×C₇	1	4	yes	—
691	#106	C₂³×C₇	1	4	yes	—
692	#106	C₂³×C₇	1	4	yes	—
693	C₄⋊C₈	C₂³×C₇	1	2	yes	—
694	C₄⋊C₈	C₂³×C₇	1	2	yes	—
695	C₄⋊C₈	C₂³×C₇	1	2	yes	—
696	C₄⋊C₈	C₂³×C₇	1	2	yes	—
697	#103	C₂³×C₇	1	4	yes	—
698	#103	C₂³×C₇	1	4	yes	—
699	#103	C₂³×C₇	1	4	yes	—
700	#103	C₂³×C₇	1	4	yes	—
701	#103	C₂³×C₇	1	4	yes	—
702	#103	C₂³×C₇	1	4	yes	—
703	#102	C₂³×C₇	1	4	yes	—
704	#102	C₂³×C₇	1	4	yes	—
705	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
706	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
707	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
708	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
709	#97	C₂³×C₇	1	2	yes	—
710	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
711	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
712	C₄×C₈	C₂³×C₇	1	2	yes	—
713	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
714	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
715	C₂²×C₇	—	2	1	no	—
716	C₂²×C₇	—	2	1	no	—
717	C₂²×C₇	—	2	1	no	—
718	C₂²×C₇	—	2	1	no	—
719	C₂²×C₇	—	2	1	no	—
720	C₂²×C₇	—	2	1	no	—
721	C₂²×C₇	—	2	1	no	—
722	C₂²×C₇	—	2	1	no	—
723	C₂²×C₇	—	2	1	no	—
724	C₂²×C₇	—	4	2	no	—
725	C₂²×C₇	—	4	2	no	—
726	C₂²×C₇	—	4	2	no	—
727	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
728	C₄×C₇	—	2	1	no	—
729	C₄×C₇	—	2	1	no	—
730	C₄×C₇	—	2	1	no	—
731	C₄×C₇	—	2	1	no	—
732	C₄×C₇	—	2	1	no	—
733	C₄×C₇	—	2	1	no	—
734	C₄×C₇	—	2	1	no	—
735	C₄×C₇	—	2	1	no	—
736	C₄×C₇	—	2	1	no	—
737	C₄×C₇	—	4	2	no	—
738	C₄×C₇	—	4	2	no	—
739	C₄×C₇	—	4	2	no	—
740	C₄×C₇	—	4	2	no	—
741	C₄×C₇	—	4	2	no	—
742	C₄×C₇	—	4	2	no	—
743	C₄×C₇	—	4	2	no	—
744	C₄×C₇	#577	1	2	yes	—
745	C₄×C₇	#578	1	2	yes	—
746	C₄×C₇	#585	1	2	yes	—
747	#41	—	4	2	no	—
748	#41	—	4	4	no	—
749	#41	—	8	2	no	—
750	#41	—	8	2	no	—
751	C₂×Q₈	—	2	1	no	—
752	C₂×Q₈	—	2	1	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	—	2	1	no	—
755	C₂×Q₈	—	2	1	no	—
756	C₂×Q₈	—	2	2	no	—
757	C₂×Q₈	—	4	4	no	—
758	C₂×Q₈	—	8	2	no	—
759	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
760	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
761	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
762	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	1	no	—
767	C₂×D₄	—	2	1	no	—
768	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
769	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
770	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
771	C₂×D₄	C₂⁴×C₇	1	2	yes	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
778	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
779	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
780	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
781	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
782	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
786	Q₁₆	—	4	4	no	—
787	Q₁₆	—	4	4	no	—
788	SD₁₆	—	4	4	no	—
789	SD₁₆	—	4	4	no	—
790	M₁₆	—	4	2	no	—
791	C₂×C₈	—	4	2	no	—
792	C₂×C₈	C₂⁴×C₇	1	2	yes	—
793	C₂×C₈	C₂⁴×C₇	1	2	yes	—
794	C₂×C₈	C₂⁴×C₇	1	2	yes	—
795	C₂×C₈	C₂⁴×C₇	1	2	yes	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	1	no	—
799	C₄⋊C₄	—	2	1	no	—
800	C₄⋊C₄	—	2	1	no	—
801	C₄⋊C₄	—	2	1	no	—
802	C₄⋊C₄	—	2	1	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
825	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
826	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
827	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
828	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
829	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
830	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
831	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
832	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
833	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
848	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
849	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
850	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
851	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
852	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	—	2	2	no	—
856	C₄²	—	2	2	no	—
857	C₄²	—	2	2	no	—
858	C₄²	—	2	2	no	—
859	C₄²	—	2	2	no	—
860	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
861	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
862	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
863	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
864	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
865	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
866	C₄²	C₂⁴×C₇	1	1	yes	characteristic
867	C₄²	C₂⁴×C₇	1	1	yes	characteristic
868	C₄²	C₂⁴×C₇	1	1	yes	characteristic
869	C₄²	C₂⁴×C₇	1	1	yes	characteristic
870	C₂×C₇	—	4	1	no	—
871	C₂×C₇	—	4	1	no	—
872	C₂×C₇	—	4	1	no	—
873	C₂×C₇	—	8	2	no	—
874	C₂×C₇	#3449	1	1	yes	characteristic
875	C₂×C₇	C₂×#577	1	1	yes	characteristic
876	C₂×C₇	C₂×#578	1	1	yes	characteristic
877	C₂³	—	2	2	no	—
878	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
879	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
880	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
881	Q₈	—	2	4	no	—
882	Q₈	—	2	4	no	—
883	Q₈	—	2	4	no	—
884	Q₈	—	4	1	no	—
885	Q₈	—	4	4	no	—
886	Q₈	—	4	2	no	—
887	Q₈	—	4	2	no	—
888	Q₈	—	4	2	no	—
889	Q₈	—	4	2	no	—
890	Q₈	—	8	2	no	—
891	D₄	—	2	4	no	—
892	D₄	—	4	1	no	—
893	D₄	—	4	1	no	—
894	D₄	—	4	1	no	—
895	D₄	—	4	4	no	—
896	D₄	—	4	2	no	—
897	D₄	—	4	2	no	—
898	D₄	—	8	2	no	—
899	D₄	—	8	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	8	2	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
922	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
923	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
924	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
925	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
926	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
927	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
928	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
929	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
930	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
931	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
932	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
933	C₈	—	2	2	no	—
934	C₈	—	2	2	no	—
935	C₈	—	2	2	no	—
936	C₈	—	2	2	no	—
937	C₇	#61008	1	1	yes	characteristic, direct product factor, Sylow
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	1	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	C₇×#577	1	2	yes	—
968	C₄	C₇×#578	1	2	yes	—
969	C₄	C₇×#585	1	2	yes	—
970	C₂	—	4	1	no	—
971	C₂	—	4	1	no	—
972	C₂	—	4	1	no	—
973	C₂	—	8	2	no	—
974	C₂	C₇×#3449	1	1	yes	characteristic
975	C₂	C₂×C₇×#577	1	1	yes	characteristic
976	C₂	C₂×C₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3511	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3509	C₂	semidirect
3. C₇×#3258	C₂	semidirect
4. C₇×#3231	C₂	semidirect
5. C₇×#3230	C₂	semidirect
6. C₇×#3229	C₂	semidirect
7. C₇×#3228	C₂	semidirect
8. C₇×#3210	C₂	semidirect
9. C₇×#3210	C₂	semidirect
10. C₇×#3209	C₂	semidirect
11. C₇×#3206	C₂	semidirect
12. C₇×#3201	C₂	semidirect
13. C₇×#3185	C₂	semidirect
14. C₇×#3182	C₂	semidirect
15. C₇×#3170	C₂	semidirect
16. C₇×#3167	C₂	semidirect
17. C₇×#3121	C₂	semidirect
18. C₇×#3120	C₂	semidirect
19. C₇×#2922	C₂	semidirect
107. #61008	C₇	direct (N × H)
268. #3509	C₂×C₇	semidirect
269. #3258	C₂×C₇	semidirect
270. #3231	C₂×C₇	semidirect
271. #3230	C₂×C₇	semidirect
272. #3229	C₂×C₇	semidirect
273. #3228	C₂×C₇	semidirect
274. #3210	C₂×C₇	semidirect
275. #3210	C₂×C₇	semidirect
276. #3209	C₂×C₇	semidirect
277. #3206	C₂×C₇	semidirect
278. #3201	C₂×C₇	semidirect
279. #3185	C₂×C₇	semidirect
280. #3182	C₂×C₇	semidirect
281. #3170	C₂×C₇	semidirect
282. #3167	C₂×C₇	semidirect
283. #3121	C₂×C₇	semidirect
284. #3120	C₂×C₇	semidirect
285. #2922	C₂×C₇	semidirect
937. C₇	#61008	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×#3511	2
C₇×#3509	2
C₇×#3258	2
C₇×#3231	2
C₇×#3230	2
C₇×#3229	2
C₇×#3228	2
C₇×#3210	2
C₇×#3209	2
C₇×#3206	2
C₇×#3201	2
C₇×#3185	2
C₇×#3182	2
C₇×#3170	2
C₇×#3167	2
C₇×#3121	2
C₇×#3120	2
C₇×#2922	2
#61008	7

Subgroups — C7×#61008 #13238224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61008 #13238224