Subgroups — C₇×#60952 #13238168

Order 1792.

1802 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3255	C₂	1	2	yes	maximal, complemented
4	C₇×#3254	C₂	1	2	yes	maximal, complemented
5	C₇×#3239	C₂	1	2	yes	maximal, complemented
6	C₇×#3237	C₂	1	2	yes	maximal, complemented
7	C₇×#3218	C₂	1	2	yes	maximal, complemented
8	C₇×#3216	C₂	1	2	yes	maximal, complemented
9	C₇×#3196	C₂	1	4	yes	maximal, complemented
10	C₇×#3172	C₂	1	4	yes	maximal, complemented
11	C₇×#3107	C₂	1	4	yes	maximal, complemented
12	C₇×#3104	C₂	1	2	yes	maximal, complemented
13	C₇×#3103	C₂	1	2	yes	maximal, complemented
14	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#533	—	2	1	no	—
16	C₇×#533	—	2	1	no	—
17	C₇×#533	—	2	1	no	—
18	C₇×#533	—	2	1	no	—
19	C₇×#533	C₂²	1	2	yes	—
20	C₇×#533	C₂²	1	2	yes	—
21	C₇×#533	C₂²	1	2	yes	—
22	C₇×#533	C₂²	1	1	yes	characteristic
23	C₇×#533	C₂²	1	2	yes	—
24	C₇×#533	C₂²	1	1	yes	characteristic
25	C₇×#533	C₂²	1	1	yes	characteristic
26	C₇×#532	C₂²	1	1	yes	characteristic
27	C₇×#532	C₂²	1	1	yes	characteristic
28	C₇×#532	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₇×#529	—	2	1	no	—
32	C₇×#529	—	2	1	no	—
33	C₇×#529	—	2	1	no	—
34	C₇×#529	—	2	1	no	—
35	C₇×#529	C₂²	1	2	yes	—
36	C₇×#529	C₂²	1	2	yes	—
37	C₂×C₇×#125	—	2	1	no	—
38	C₇×#525	—	2	1	no	—
39	C₇×#525	—	2	1	no	—
40	C₇×#525	C₂²	1	2	yes	—
41	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₄×C₇×#41	—	2	1	no	—
44	C₄×C₇×#41	—	2	1	no	—
45	C₄×C₇×#41	C₂²	1	2	yes	—
46	C₂×C₄×C₇×Q₈	—	2	1	no	—
47	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
48	C₂×C₇×#117	—	2	1	no	—
49	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
50	C₇×#501	C₂²	1	4	yes	complemented
51	C₇×#497	C₂²	1	4	yes	complemented
52	C₇×#491	C₂²	1	4	yes	complemented
53	C₇×#489	C₂²	1	4	yes	complemented
54	C₇×#485	C₂²	1	8	yes	—
55	C₇×#484	C₂²	1	4	yes	—
56	C₇×#481	C₂²	1	4	yes	—
57	C₇×#477	C₂²	1	4	yes	complemented
58	C₇×#475	C₂²	1	4	yes	complemented
59	C₇×#475	C₂²	1	4	yes	complemented
60	C₇×#474	C₂²	1	4	yes	complemented
61	C₇×#470	C₂²	1	8	yes	—
62	C₇×#468	C₂²	1	8	yes	—
63	C₇×#462	C₂²	1	4	yes	complemented
64	C₇×#462	C₂²	1	4	yes	complemented
65	C₇×#461	C₂²	1	4	yes	complemented
66	C₇×#460	C₂²	1	4	yes	complemented
67	C₇×#452	C₂²	1	8	yes	—
68	C₇×#451	C₂²	1	4	yes	—
69	C₇×#448	C₂²	1	4	yes	—
70	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
71	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
72	C₇×#432	C₂²	1	2	yes	—
73	C₇×#432	C₂²	1	2	yes	—
74	C₇×#431	C₂²	1	2	yes	—
75	C₇×#431	C₂²	1	2	yes	—
76	C₇×#423	C₂²	1	2	yes	—
77	C₇×#407	C₂²	1	2	yes	—
78	C₄×C₇×M₁₆	C₂²	1	2	yes	—
79	#60952	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂×C₇×#41	—	2	1	no	—
81	C₂×C₇×#41	—	2	1	no	—
82	C₂×C₇×#41	C₂³	1	2	yes	—
83	C₂²×C₇×Q₈	—	2	1	no	—
84	C₂²×C₇×Q₈	C₂³	1	2	yes	—
85	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
88	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
89	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
90	C₂×C₇×M₁₆	C₂³	1	4	yes	—
91	C₇×C₄⋊Q₈	—	2	1	no	—
92	C₇×C₄⋊Q₈	—	2	1	no	—
93	C₇×C₄⋊Q₈	—	2	1	no	—
94	C₇×C₄⋊Q₈	—	2	1	no	—
95	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
98	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
102	C₇×#127	C₂³	1	1	yes	characteristic
103	C₇×#126	—	2	2	no	—
104	C₇×#126	—	2	2	no	—
105	C₇×#125	—	2	2	no	—
106	C₇×#125	—	2	2	no	—
107	C₇×#125	—	2	2	no	—
108	C₇×#125	—	2	2	no	—
109	C₇×#125	—	2	1	no	—
110	C₇×#125	—	2	1	no	—
111	C₇×#125	C₂³	1	2	yes	—
112	C₇×#124	—	2	1	no	—
113	C₇×#124	—	2	1	no	—
114	C₇×#124	C₂³	1	2	yes	—
115	C₇×#123	—	2	2	no	—
116	C₇×#123	—	2	2	no	—
117	C₇×#123	—	2	2	no	—
118	C₇×C₂²⋊Q₈	—	2	2	no	—
119	C₇×C₂²⋊Q₈	—	2	2	no	—
120	C₇×C₂²⋊Q₈	—	2	2	no	—
121	C₇×C₂²⋊Q₈	—	2	2	no	—
122	C₇×C₂²⋊Q₈	—	2	2	no	—
123	C₇×C₂²⋊Q₈	—	2	2	no	—
124	C₇×C₂²⋊Q₈	—	2	1	no	—
125	C₇×C₂²⋊Q₈	—	2	1	no	—
126	C₇×C₂²⋊Q₈	—	2	1	no	—
127	C₇×C₂²⋊Q₈	—	2	1	no	—
128	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
129	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
130	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
131	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
132	C₇×#121	—	2	1	no	—
133	C₇×#121	—	2	1	no	—
134	C₇×#121	—	2	1	no	—
135	C₇×#121	—	2	1	no	—
136	C₇×#121	C₂³	1	2	yes	—
137	C₇×#121	C₂³	1	2	yes	—
138	C₇×#120	—	2	2	no	—
139	C₄×C₇×Q₈	—	2	2	no	—
140	C₄×C₇×Q₈	—	2	2	no	—
141	C₄×C₇×Q₈	—	2	2	no	—
142	C₄×C₇×Q₈	—	2	2	no	—
143	C₄×C₇×Q₈	—	2	2	no	—
144	C₄×C₇×Q₈	—	2	2	no	—
145	C₄×C₇×Q₈	—	2	1	no	—
146	C₄×C₇×Q₈	—	2	1	no	—
147	C₄×C₇×Q₈	—	2	1	no	—
148	C₄×C₇×Q₈	—	2	1	no	—
149	C₄×C₇×Q₈	C₂³	1	2	yes	—
150	C₄×C₇×Q₈	C₂³	1	4	yes	—
151	C₄×C₇×Q₈	C₂³	1	4	yes	—
152	C₄×C₇×Q₈	C₂³	1	2	yes	—
153	C₄×C₇×D₄	—	2	2	no	—
154	C₄×C₇×D₄	—	2	2	no	—
155	C₄×C₇×D₄	—	2	2	no	—
156	C₄×C₇×D₄	—	2	2	no	—
157	C₄×C₇×D₄	—	2	2	no	—
158	C₄×C₇×D₄	—	2	2	no	—
159	C₄×C₇×D₄	—	2	1	no	—
160	C₄×C₇×D₄	—	2	1	no	—
161	C₄×C₇×D₄	—	2	1	no	—
162	C₄×C₇×D₄	—	2	1	no	—
163	C₄×C₇×D₄	C₂³	1	2	yes	—
164	C₄×C₇×D₄	C₂³	1	2	yes	—
165	C₇×#117	—	2	2	no	—
166	C₇×#117	—	2	2	no	—
167	C₇×#117	—	2	2	no	—
168	C₇×#117	—	2	2	no	—
169	C₇×#117	—	2	1	no	—
170	C₇×#117	—	2	1	no	—
171	C₇×#117	—	2	2	no	—
172	C₇×#117	—	2	2	no	—
173	C₇×#117	—	2	2	no	—
174	C₇×#117	C₂³	1	2	yes	—
175	C₂×C₇×C₄⋊C₄	—	2	1	no	—
176	C₂×C₇×C₄⋊C₄	—	2	1	no	—
177	C₂×C₇×C₄⋊C₄	—	2	1	no	—
178	C₂×C₇×C₄⋊C₄	—	2	2	no	—
179	C₂×C₇×C₄⋊C₄	—	2	2	no	—
180	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
182	C₂×C₄²×C₇	—	2	2	no	—
183	C₂×C₄²×C₇	—	2	2	no	—
184	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₇×#107	C₂³	1	8	yes	—
197	C₇×#106	C₂³	1	8	yes	—
198	C₇×C₄⋊C₈	C₂³	1	4	yes	—
199	C₇×C₄⋊C₈	C₂³	1	4	yes	—
200	C₇×#103	C₂³	1	8	yes	—
201	C₇×#103	C₂³	1	8	yes	—
202	C₇×#103	C₂³	1	8	yes	—
203	C₇×#102	C₂³	1	8	yes	—
204	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
205	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
206	C₇×#97	C₂³	1	4	yes	—
207	C₄×C₇×C₈	C₂³	1	4	yes	—
208	#3444	C₂×C₇	1	1	yes	characteristic
209	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
210	#3255	C₂×C₇	1	2	yes	complemented
211	#3254	C₂×C₇	1	2	yes	complemented
212	#3239	C₂×C₇	1	2	yes	complemented
213	#3237	C₂×C₇	1	2	yes	complemented
214	#3218	C₂×C₇	1	2	yes	complemented
215	#3216	C₂×C₇	1	2	yes	complemented
216	#3196	C₂×C₇	1	4	yes	complemented
217	#3172	C₂×C₇	1	4	yes	complemented
218	#3107	C₂×C₇	1	4	yes	complemented
219	#3104	C₂×C₇	1	2	yes	complemented
220	#3103	C₂×C₇	1	2	yes	complemented
221	#2920	C₂×C₇	1	1	yes	characteristic, complemented
222	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
223	C₇×#41	—	4	4	no	—
224	C₇×#41	—	4	4	no	—
225	C₇×#41	—	4	4	no	—
226	C₂×C₇×Q₈	—	2	1	no	—
227	C₂×C₇×Q₈	—	2	1	no	—
228	C₂×C₇×Q₈	—	2	2	no	—
229	C₂×C₇×Q₈	—	2	2	no	—
230	C₂×C₇×Q₈	—	2	2	no	—
231	C₂×C₇×Q₈	—	4	4	no	—
232	C₂×C₇×Q₈	—	4	4	no	—
233	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
234	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
235	C₂×C₇×D₄	—	2	2	no	—
236	C₂×C₇×D₄	—	2	2	no	—
237	C₂×C₇×D₄	—	2	2	no	—
238	C₂×C₇×D₄	—	2	1	no	—
239	C₂×C₇×D₄	—	2	1	no	—
240	C₂×C₇×D₄	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₇	—	2	4	no	—
242	C₂²×C₄×C₇	—	2	2	no	—
243	C₂²×C₄×C₇	—	2	2	no	—
244	C₂²×C₄×C₇	—	2	2	no	—
245	C₂²×C₄×C₇	—	2	2	no	—
246	C₂²×C₄×C₇	—	2	2	no	—
247	C₂²×C₄×C₇	—	4	2	no	—
248	C₂²×C₄×C₇	—	4	2	no	—
249	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
267	C₇×Q₁₆	—	4	8	no	—
268	C₇×SD₁₆	—	4	8	no	—
269	C₇×M₁₆	—	4	4	no	—
270	C₂×C₇×C₈	C₂⁴	1	8	yes	—
271	C₇×C₄⋊C₄	—	2	2	no	—
272	C₇×C₄⋊C₄	—	2	2	no	—
273	C₇×C₄⋊C₄	—	2	2	no	—
274	C₇×C₄⋊C₄	—	2	2	no	—
275	C₇×C₄⋊C₄	—	2	2	no	—
276	C₇×C₄⋊C₄	—	2	2	no	—
277	C₇×C₄⋊C₄	—	2	4	no	—
278	C₇×C₄⋊C₄	—	2	4	no	—
279	C₇×C₄⋊C₄	—	2	4	no	—
280	C₇×C₄⋊C₄	—	2	4	no	—
281	C₇×C₄⋊C₄	—	2	2	no	—
282	C₇×C₄⋊C₄	—	2	1	no	—
283	C₇×C₄⋊C₄	—	2	1	no	—
284	C₇×C₄⋊C₄	—	2	1	no	—
285	C₇×C₄⋊C₄	—	2	1	no	—
286	C₇×C₄⋊C₄	—	2	2	no	—
287	C₇×C₄⋊C₄	—	2	2	no	—
288	C₇×C₄⋊C₄	—	2	2	no	—
289	C₇×C₄⋊C₄	—	2	2	no	—
290	C₇×C₄⋊C₄	—	2	2	no	—
291	C₇×C₄⋊C₄	—	2	2	no	—
292	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
293	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
294	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
295	C₇×C₂²⋊C₄	—	2	4	no	—
296	C₇×C₂²⋊C₄	—	2	4	no	—
297	C₇×C₂²⋊C₄	—	2	2	no	—
298	C₇×C₂²⋊C₄	—	2	2	no	—
299	C₇×C₂²⋊C₄	—	2	2	no	—
300	C₇×C₂²⋊C₄	—	2	2	no	—
301	C₇×C₂²⋊C₄	—	2	2	no	—
302	C₇×C₂²⋊C₄	—	2	2	no	—
303	C₇×C₂²⋊C₄	—	2	2	no	—
304	C₇×C₂²⋊C₄	—	2	2	no	—
305	C₇×C₂²⋊C₄	—	2	2	no	—
306	C₄²×C₇	—	2	2	no	—
307	C₄²×C₇	—	2	4	no	—
308	C₄²×C₇	—	2	2	no	—
309	C₄²×C₇	—	2	2	no	—
310	C₄²×C₇	—	2	4	no	—
311	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₇	C₂⁴	1	1	yes	characteristic
324	C₄²×C₇	C₂⁴	1	1	yes	characteristic
325	C₄²×C₇	C₂⁴	1	1	yes	characteristic
326	C₄²×C₇	C₂⁴	1	1	yes	characteristic
327	#533	—	2	1	no	—
328	#533	—	2	1	no	—
329	#533	—	2	1	no	—
330	#533	—	2	1	no	—
331	#533	C₂²×C₇	1	1	yes	characteristic
332	#533	C₂²×C₇	1	2	yes	—
333	#533	C₂²×C₇	1	2	yes	—
334	#533	C₂²×C₇	1	2	yes	—
335	#533	C₂²×C₇	1	2	yes	—
336	#533	C₂²×C₇	1	1	yes	characteristic
337	#533	C₂²×C₇	1	1	yes	characteristic
338	#532	C₂²×C₇	1	1	yes	characteristic
339	#532	C₂²×C₇	1	1	yes	characteristic
340	#532	C₂²×C₇	1	1	yes	characteristic
341	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
342	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
343	#529	—	2	1	no	—
344	#529	—	2	1	no	—
345	#529	—	2	1	no	—
346	#529	—	2	1	no	—
347	#529	C₂²×C₇	1	2	yes	—
348	#529	C₂²×C₇	1	2	yes	—
349	C₂×#125	—	2	1	no	—
350	#525	—	2	1	no	—
351	#525	—	2	1	no	—
352	#525	C₂²×C₇	1	2	yes	—
353	C₂×C₂²⋊Q₈	—	2	1	no	—
354	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
355	C₄×#41	—	2	1	no	—
356	C₄×#41	—	2	1	no	—
357	C₄×#41	C₂²×C₇	1	2	yes	—
358	C₂×C₄×Q₈	—	2	1	no	—
359	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
360	C₂×#117	—	2	1	no	—
361	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
362	#501	C₂²×C₇	1	4	yes	complemented
363	#497	C₂²×C₇	1	4	yes	complemented
364	#491	C₂²×C₇	1	4	yes	complemented
365	#489	C₂²×C₇	1	4	yes	complemented
366	#485	C₂²×C₇	1	8	yes	—
367	#484	C₂²×C₇	1	4	yes	—
368	#481	C₂²×C₇	1	4	yes	—
369	#477	C₂²×C₇	1	4	yes	complemented
370	#475	C₂²×C₇	1	4	yes	complemented
371	#475	C₂²×C₇	1	4	yes	complemented
372	#474	C₂²×C₇	1	4	yes	complemented
373	#470	C₂²×C₇	1	8	yes	—
374	#468	C₂²×C₇	1	8	yes	—
375	#462	C₂²×C₇	1	4	yes	complemented
376	#462	C₂²×C₇	1	4	yes	complemented
377	#461	C₂²×C₇	1	4	yes	complemented
378	#460	C₂²×C₇	1	4	yes	complemented
379	#452	C₂²×C₇	1	8	yes	—
380	#451	C₂²×C₇	1	4	yes	—
381	#448	C₂²×C₇	1	4	yes	—
382	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
383	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
384	#432	C₂²×C₇	1	2	yes	—
385	#432	C₂²×C₇	1	2	yes	—
386	#431	C₂²×C₇	1	2	yes	—
387	#431	C₂²×C₇	1	2	yes	—
388	#423	C₂²×C₇	1	2	yes	—
389	#407	C₂²×C₇	1	2	yes	—
390	C₄×M₁₆	C₂²×C₇	1	2	yes	—
391	C₂³×C₇	—	2	2	no	—
392	C₂³×C₇	—	2	2	no	—
393	C₂³×C₇	—	4	1	no	—
394	C₂³×C₇	—	4	1	no	—
395	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
396	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
397	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
398	C₇×Q₈	—	2	4	no	—
399	C₇×Q₈	—	2	4	no	—
400	C₇×Q₈	—	2	4	no	—
401	C₇×Q₈	—	4	4	no	—
402	C₇×Q₈	—	4	4	no	—
403	C₇×Q₈	—	4	2	no	—
404	C₇×Q₈	—	4	2	no	—
405	C₇×Q₈	—	4	4	no	—
406	C₇×D₄	—	2	4	no	—
407	C₇×D₄	—	4	2	no	—
408	C₇×D₄	—	4	4	no	—
409	C₇×D₄	—	4	4	no	—
410	C₇×D₄	—	4	4	no	—
411	C₇×D₄	—	4	2	no	—
412	C₂×C₄×C₇	—	2	2	no	—
413	C₂×C₄×C₇	—	2	2	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	2	2	no	—
416	C₂×C₄×C₇	—	2	2	no	—
417	C₂×C₄×C₇	—	2	2	no	—
418	C₂×C₄×C₇	—	2	2	no	—
419	C₂×C₄×C₇	—	2	2	no	—
420	C₂×C₄×C₇	—	2	2	no	—
421	C₂×C₄×C₇	—	2	2	no	—
422	C₂×C₄×C₇	—	2	2	no	—
423	C₂×C₄×C₇	—	2	2	no	—
424	C₂×C₄×C₇	—	2	2	no	—
425	C₂×C₄×C₇	—	2	2	no	—
426	C₂×C₄×C₇	—	2	4	no	—
427	C₂×C₄×C₇	—	2	4	no	—
428	C₂×C₄×C₇	—	4	1	no	—
429	C₂×C₄×C₇	—	4	1	no	—
430	C₂×C₄×C₇	—	4	1	no	—
431	C₂×C₄×C₇	—	4	1	no	—
432	C₂×C₄×C₇	—	4	1	no	—
433	C₂×C₄×C₇	—	4	1	no	—
434	C₂×C₄×C₇	—	4	4	no	—
435	C₂×C₄×C₇	—	4	4	no	—
436	C₂×C₄×C₇	—	4	4	no	—
437	C₂×C₄×C₇	—	4	4	no	—
438	C₂×C₄×C₇	—	4	4	no	—
439	C₂×C₄×C₇	#137	1	4	yes	—
440	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
452	C₇×C₈	—	2	8	no	—
453	C₂×#41	—	2	1	no	—
454	C₂×#41	—	2	1	no	—
455	C₂×#41	C₂³×C₇	1	2	yes	—
456	C₂²×Q₈	—	2	1	no	—
457	C₂²×Q₈	C₂³×C₇	1	2	yes	—
458	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
459	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
461	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
462	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
463	C₂×M₁₆	C₂³×C₇	1	4	yes	—
464	C₄⋊Q₈	—	2	1	no	—
465	C₄⋊Q₈	—	2	1	no	—
466	C₄⋊Q₈	—	2	1	no	—
467	C₄⋊Q₈	—	2	1	no	—
468	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
469	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
470	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
471	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
472	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
473	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
474	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
475	#127	C₂³×C₇	1	1	yes	characteristic
476	#126	—	2	2	no	—
477	#126	—	2	2	no	—
478	#125	—	2	2	no	—
479	#125	—	2	2	no	—
480	#125	—	2	2	no	—
481	#125	—	2	2	no	—
482	#125	—	2	1	no	—
483	#125	—	2	1	no	—
484	#125	C₂³×C₇	1	2	yes	—
485	#124	—	2	1	no	—
486	#124	—	2	1	no	—
487	#124	C₂³×C₇	1	2	yes	—
488	#123	—	2	2	no	—
489	#123	—	2	2	no	—
490	#123	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	1	no	—
498	C₂²⋊Q₈	—	2	1	no	—
499	C₂²⋊Q₈	—	2	1	no	—
500	C₂²⋊Q₈	—	2	1	no	—
501	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
502	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
503	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
504	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
505	#121	—	2	1	no	—
506	#121	—	2	1	no	—
507	#121	—	2	1	no	—
508	#121	—	2	1	no	—
509	#121	C₂³×C₇	1	2	yes	—
510	#121	C₂³×C₇	1	2	yes	—
511	#120	—	2	2	no	—
512	C₄×Q₈	—	2	2	no	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	—	2	1	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×Q₈	—	2	1	no	—
521	C₄×Q₈	—	2	1	no	—
522	C₄×Q₈	C₂³×C₇	1	4	yes	—
523	C₄×Q₈	C₂³×C₇	1	4	yes	—
524	C₄×Q₈	C₂³×C₇	1	2	yes	—
525	C₄×Q₈	C₂³×C₇	1	2	yes	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	—	2	1	no	—
535	C₄×D₄	—	2	1	no	—
536	C₄×D₄	C₂³×C₇	1	2	yes	—
537	C₄×D₄	C₂³×C₇	1	2	yes	—
538	#117	—	2	2	no	—
539	#117	—	2	2	no	—
540	#117	—	2	2	no	—
541	#117	—	2	2	no	—
542	#117	—	2	1	no	—
543	#117	—	2	1	no	—
544	#117	—	2	2	no	—
545	#117	—	2	2	no	—
546	#117	—	2	2	no	—
547	#117	C₂³×C₇	1	2	yes	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	—	2	2	no	—
552	C₂×C₄⋊C₄	—	2	2	no	—
553	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
554	C₂×C₂²⋊C₄	—	2	2	no	—
555	C₂×C₄²	—	2	2	no	—
556	C₂×C₄²	—	2	2	no	—
557	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
558	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
559	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
560	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
561	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
562	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
569	#107	C₂³×C₇	1	8	yes	—
570	#106	C₂³×C₇	1	8	yes	—
571	C₄⋊C₈	C₂³×C₇	1	4	yes	—
572	C₄⋊C₈	C₂³×C₇	1	4	yes	—
573	#103	C₂³×C₇	1	8	yes	—
574	#103	C₂³×C₇	1	8	yes	—
575	#103	C₂³×C₇	1	8	yes	—
576	#102	C₂³×C₇	1	8	yes	—
577	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
578	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
579	#97	C₂³×C₇	1	4	yes	—
580	C₄×C₈	C₂³×C₇	1	4	yes	—
581	C₂²×C₇	—	2	1	no	—
582	C₂²×C₇	—	2	1	no	—
583	C₂²×C₇	—	2	1	no	—
584	C₂²×C₇	—	2	1	no	—
585	C₂²×C₇	—	2	1	no	—
586	C₂²×C₇	—	2	1	no	—
587	C₂²×C₇	—	2	1	no	—
588	C₂²×C₇	—	2	1	no	—
589	C₂²×C₇	—	4	4	no	—
590	C₂²×C₇	—	4	2	no	—
591	C₂²×C₇	—	4	2	no	—
592	C₂²×C₇	—	4	2	no	—
593	C₂²×C₇	C₂×#137	1	2	yes	—
594	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
595	C₄×C₇	—	2	1	no	—
596	C₄×C₇	—	2	1	no	—
597	C₄×C₇	—	2	1	no	—
598	C₄×C₇	—	2	1	no	—
599	C₄×C₇	—	2	1	no	—
600	C₄×C₇	—	2	1	no	—
601	C₄×C₇	—	2	1	no	—
602	C₄×C₇	—	2	1	no	—
603	C₄×C₇	—	4	2	no	—
604	C₄×C₇	—	4	4	no	—
605	C₄×C₇	—	4	2	no	—
606	C₄×C₇	—	4	2	no	—
607	C₄×C₇	—	4	4	no	—
608	C₄×C₇	C₂×#137	1	2	yes	—
609	C₄×C₇	C₂×#137	1	2	yes	—
610	C₄×C₇	#575	1	2	yes	—
611	C₄×C₇	#585	1	2	yes	—
612	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
613	#41	—	4	4	no	—
614	#41	—	4	4	no	—
615	#41	—	4	4	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	—	2	2	no	—
621	C₂×Q₈	—	4	4	no	—
622	C₂×Q₈	—	4	4	no	—
623	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
624	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	C₂⁴×C₇	1	2	yes	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	4	2	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
640	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
641	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
642	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
643	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
644	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
645	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
646	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
647	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
648	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
649	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
650	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
651	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
652	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
653	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
657	Q₁₆	—	4	8	no	—
658	SD₁₆	—	4	8	no	—
659	M₁₆	—	4	4	no	—
660	C₂×C₈	C₂⁴×C₇	1	8	yes	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
683	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₄²	—	2	2	no	—
697	C₄²	—	2	2	no	—
698	C₄²	—	2	4	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	2	no	—
701	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
702	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
703	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
704	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
705	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
706	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
707	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
708	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
709	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
710	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
711	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
712	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
713	C₄²	C₂⁴×C₇	1	1	yes	characteristic
714	C₄²	C₂⁴×C₇	1	1	yes	characteristic
715	C₄²	C₂⁴×C₇	1	1	yes	characteristic
716	C₄²	C₂⁴×C₇	1	1	yes	characteristic
717	C₂×C₇	—	2	2	no	—
718	C₂×C₇	—	4	1	no	—
719	C₂×C₇	—	4	1	no	—
720	C₂×C₇	—	8	2	no	—
721	C₂×C₇	#3449	1	1	yes	characteristic
722	C₂×C₇	C₂²×#137	1	1	yes	characteristic
723	C₂×C₇	C₂×#575	1	1	yes	characteristic
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	4	1	no	—
727	C₂³	—	4	1	no	—
728	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
729	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
730	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
731	Q₈	—	2	4	no	—
732	Q₈	—	2	4	no	—
733	Q₈	—	2	4	no	—
734	Q₈	—	4	4	no	—
735	Q₈	—	4	4	no	—
736	Q₈	—	4	2	no	—
737	Q₈	—	4	2	no	—
738	Q₈	—	4	4	no	—
739	D₄	—	2	4	no	—
740	D₄	—	4	2	no	—
741	D₄	—	4	4	no	—
742	D₄	—	4	4	no	—
743	D₄	—	4	4	no	—
744	D₄	—	4	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	4	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	—	4	4	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	4	no	—
772	C₂×C₄	C₇×#137	1	4	yes	—
773	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
774	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
775	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
776	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
777	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
778	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
779	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
780	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
781	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
782	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
783	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
784	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
785	C₈	—	2	8	no	—
786	C₇	#60952	1	1	yes	characteristic, direct product factor, Sylow
787	C₂²	—	2	1	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	4	4	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	C₂×C₇×#137	1	2	yes	—
800	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	1	no	—
805	C₄	—	2	1	no	—
806	C₄	—	2	1	no	—
807	C₄	—	2	1	no	—
808	C₄	—	2	1	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	4	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	4	no	—
814	C₄	C₂×C₇×#137	1	2	yes	—
815	C₄	C₂×C₇×#137	1	2	yes	—
816	C₄	C₇×#575	1	2	yes	—
817	C₄	C₇×#585	1	2	yes	—
818	C₂	—	2	2	no	—
819	C₂	—	4	1	no	—
820	C₂	—	4	1	no	—
821	C₂	—	8	2	no	—
822	C₂	C₇×#3449	1	1	yes	characteristic
823	C₂	C₂²×C₇×#137	1	1	yes	characteristic
824	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
prime radical	C₇×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#533	C₂	semidirect
3. C₇×#3255	C₂	semidirect
4. C₇×#3254	C₂	semidirect
5. C₇×#3239	C₂	semidirect
6. C₇×#3237	C₂	semidirect
7. C₇×#3218	C₂	semidirect
8. C₇×#3216	C₂	semidirect
9. C₇×#3196	C₂	semidirect
10. C₇×#3172	C₂	semidirect
11. C₇×#3107	C₂	semidirect
12. C₇×#3104	C₂	semidirect
13. C₇×#3103	C₂	semidirect
14. C₇×#2920	C₂	semidirect
50. C₇×#501	C₂²	semidirect
51. C₇×#497	C₂²	semidirect
52. C₇×#491	C₂²	semidirect
53. C₇×#489	C₂²	semidirect
57. C₇×#477	C₂²	semidirect
58. C₇×#475	C₂²	semidirect
59. C₇×#475	C₂²	semidirect
60. C₇×#474	C₂²	semidirect
63. C₇×#462	C₂²	semidirect
64. C₇×#462	C₂²	semidirect
65. C₇×#461	C₂²	semidirect
66. C₇×#460	C₂²	semidirect
70. C₄×C₇×Q₁₆	C₂²	semidirect
71. C₄×C₇×SD₁₆	C₂²	semidirect
79. #60952	C₇	direct (N × H)
209. C₂×#533	C₂×C₇	semidirect
210. #3255	C₂×C₇	semidirect
211. #3254	C₂×C₇	semidirect
212. #3239	C₂×C₇	semidirect
213. #3237	C₂×C₇	semidirect
214. #3218	C₂×C₇	semidirect
215. #3216	C₂×C₇	semidirect
216. #3196	C₂×C₇	semidirect
217. #3172	C₂×C₇	semidirect
218. #3107	C₂×C₇	semidirect
219. #3104	C₂×C₇	semidirect
220. #3103	C₂×C₇	semidirect
221. #2920	C₂×C₇	semidirect
362. #501	C₂²×C₇	semidirect
363. #497	C₂²×C₇	semidirect
364. #491	C₂²×C₇	semidirect
365. #489	C₂²×C₇	semidirect
369. #477	C₂²×C₇	semidirect
370. #475	C₂²×C₇	semidirect
371. #475	C₂²×C₇	semidirect
372. #474	C₂²×C₇	semidirect
375. #462	C₂²×C₇	semidirect
376. #462	C₂²×C₇	semidirect
377. #461	C₂²×C₇	semidirect
378. #460	C₂²×C₇	semidirect
382. C₄×Q₁₆	C₂²×C₇	semidirect
383. C₄×SD₁₆	C₂²×C₇	semidirect
786. C₇	#60952	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×#3444	2
C₂×C₇×#533	2
C₇×#3255	2
C₇×#3254	2
C₇×#3239	2
C₇×#3237	2
C₇×#3218	2
C₇×#3216	2
C₇×#3196	2
C₇×#3172	2
C₇×#3107	2
C₇×#3104	2
C₇×#3103	2
C₇×#2920	2
#60952	7

Subgroups — C7×#60952 #13238168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60952 #13238168