Subgroups — C₇×#60950 #13238166

Order 1792.

1812 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic
3	C₇×#3252	C₂	1	4	yes	maximal, complemented
4	C₇×#3238	C₂	1	2	yes	maximal, complemented
5	C₇×#3236	C₂	1	2	yes	maximal, complemented
6	C₇×#3218	C₂	1	2	yes	maximal, complemented
7	C₇×#3215	C₂	1	2	yes	maximal, complemented
8	C₇×#3195	C₂	1	2	yes	maximal, complemented
9	C₇×#3193	C₂	1	2	yes	maximal
10	C₇×#3172	C₂	1	4	yes	maximal, complemented
11	C₇×#3108	C₂	1	4	yes	maximal, complemented
12	C₇×#3104	C₂	1	2	yes	maximal, complemented
13	C₇×#3101	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	complemented
22	C₇×#533	C₂²	1	2	yes	complemented
23	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₇×#529	—	2	1	no	—
26	C₇×#529	—	2	1	no	—
27	C₇×#529	—	2	1	no	—
28	C₇×#529	—	2	1	no	—
29	C₇×#529	C₂²	1	2	yes	—
30	C₇×#529	C₂²	1	2	yes	—
31	C₇×#529	C₂²	1	2	yes	—
32	C₇×#529	C₂²	1	2	yes	—
33	C₂×C₇×#126	—	2	1	no	—
34	C₂×C₇×#125	—	2	1	no	—
35	C₂×C₇×#125	C₂²	1	1	yes	characteristic
36	C₂×C₇×#124	C₂²	1	1	yes	characteristic
37	C₂×C₇×#123	—	2	1	no	—
38	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
39	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
40	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₇×#121	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×Q₈	—	2	1	no	—
43	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
45	C₂×C₄×C₇×D₄	—	2	1	no	—
46	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₇×#117	—	2	1	no	—
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×#484	C₂²	1	4	yes	—
55	C₇×#483	C₂²	1	4	yes	—
56	C₇×#483	C₂²	1	4	yes	complemented
57	C₇×#480	C₂²	1	4	yes	—
58	C₇×#479	C₂²	1	8	yes	complemented
59	C₇×#477	C₂²	1	4	yes	complemented
60	C₇×#476	C₂²	1	4	yes	complemented
61	C₇×#470	C₂²	1	8	yes	complemented
62	C₇×#468	C₂²	1	8	yes	—
63	C₇×#464	C₂²	1	8	yes	complemented
64	C₇×#462	C₂²	1	4	yes	complemented
65	C₇×#461	C₂²	1	4	yes	complemented
66	C₇×#451	C₂²	1	4	yes	—
67	C₇×#451	C₂²	1	4	yes	complemented
68	C₇×#450	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	complemented
74	C₇×#431	C₂²	1	2	yes	—
75	C₇×#431	C₂²	1	2	yes	complemented
76	C₇×#423	C₂²	1	2	yes	complemented
77	C₇×#407	C₂²	1	2	yes	—
78	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
79	#60950	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂²×C₇×Q₈	—	2	1	no	—
81	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
82	C₂²×C₇×Q₈	C₂³	1	2	yes	—
83	C₂²×C₇×D₄	—	2	1	no	—
84	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₇	—	2	1	no	—
86	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
88	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
89	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
90	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
91	C₂×C₇×M₁₆	C₂³	1	4	yes	—
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	—	2	1	no	—
96	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
100	C₇×#126	—	2	2	no	—
101	C₇×#126	—	2	2	no	—
102	C₇×#126	—	2	2	no	—
103	C₇×#126	—	2	2	no	—
104	C₇×#125	—	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	1	no	—
109	C₇×#125	—	2	1	no	—
110	C₇×#125	C₂³	1	2	yes	—
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×#124	C₂³	1	2	yes	—
116	C₇×#123	—	2	2	no	—
117	C₇×#123	—	2	2	no	—
118	C₇×#123	—	2	2	no	—
119	C₇×#123	—	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	2	no	—
127	C₇×C₂²⋊Q₈	—	2	2	no	—
128	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
129	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
130	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₇×#121	—	2	1	no	—
133	C₇×#121	—	2	1	no	—
134	C₇×#121	C₂³	1	2	yes	—
135	C₇×#121	C₂³	1	2	yes	—
136	C₄×C₇×Q₈	—	2	2	no	—
137	C₄×C₇×Q₈	—	2	2	no	—
138	C₄×C₇×Q₈	—	2	2	no	—
139	C₄×C₇×Q₈	—	2	2	no	—
140	C₄×C₇×Q₈	—	2	1	no	—
141	C₄×C₇×Q₈	—	2	1	no	—
142	C₄×C₇×Q₈	—	2	2	no	—
143	C₄×C₇×Q₈	—	2	2	no	—
144	C₄×C₇×Q₈	C₂³	1	2	yes	—
145	C₄×C₇×Q₈	C₂³	1	4	yes	—
146	C₄×C₇×Q₈	C₂³	1	2	yes	—
147	C₄×C₇×Q₈	C₂³	1	4	yes	—
148	C₄×C₇×D₄	—	2	2	no	—
149	C₄×C₇×D₄	—	2	2	no	—
150	C₄×C₇×D₄	—	2	2	no	—
151	C₄×C₇×D₄	—	2	2	no	—
152	C₄×C₇×D₄	—	2	1	no	—
153	C₄×C₇×D₄	—	2	1	no	—
154	C₄×C₇×D₄	C₂³	1	2	yes	—
155	C₄×C₇×D₄	C₂³	1	2	yes	—
156	C₇×#117	—	2	2	no	—
157	C₇×#117	—	2	2	no	—
158	C₇×#117	—	2	2	no	—
159	C₇×#117	—	2	2	no	—
160	C₇×#117	—	2	2	no	—
161	C₇×#117	—	2	2	no	—
162	C₇×#117	—	2	2	no	—
163	C₇×#117	—	2	2	no	—
164	C₂×C₇×C₄⋊C₄	—	2	1	no	—
165	C₂×C₇×C₄⋊C₄	—	2	1	no	—
166	C₂×C₇×C₄⋊C₄	—	2	1	no	—
167	C₂×C₇×C₄⋊C₄	—	2	1	no	—
168	C₂×C₇×C₄⋊C₄	—	2	1	no	—
169	C₂×C₇×C₄⋊C₄	—	2	1	no	—
170	C₂×C₇×C₄⋊C₄	—	2	2	no	—
171	C₂×C₇×C₄⋊C₄	—	2	1	no	—
172	C₂×C₇×C₄⋊C₄	—	2	2	no	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
177	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
178	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
179	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
180	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₄²×C₇	—	2	1	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	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
209	C₂×#529	C₂×C₇	1	1	yes	characteristic
210	#3252	C₂×C₇	1	4	yes	complemented
211	#3238	C₂×C₇	1	2	yes	complemented
212	#3236	C₂×C₇	1	2	yes	complemented
213	#3218	C₂×C₇	1	2	yes	complemented
214	#3215	C₂×C₇	1	2	yes	complemented
215	#3195	C₂×C₇	1	2	yes	complemented
216	#3193	C₂×C₇	1	2	yes	—
217	#3172	C₂×C₇	1	4	yes	complemented
218	#3108	C₂×C₇	1	4	yes	complemented
219	#3104	C₂×C₇	1	2	yes	complemented
220	#3101	C₂×C₇	1	2	yes	complemented
221	#2920	C₂×C₇	1	1	yes	characteristic, complemented
222	C₂⁴×C₇	—	2	1	no	—
223	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
224	C₂×C₇×Q₈	—	2	1	no	—
225	C₂×C₇×Q₈	—	2	2	no	—
226	C₂×C₇×Q₈	—	2	2	no	—
227	C₂×C₇×Q₈	—	2	2	no	—
228	C₂×C₇×Q₈	—	4	2	no	—
229	C₂×C₇×Q₈	—	4	4	no	—
230	C₂×C₇×Q₈	—	4	4	no	—
231	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
232	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
233	C₂×C₇×D₄	—	2	2	no	—
234	C₂×C₇×D₄	—	2	2	no	—
235	C₂×C₇×D₄	—	2	1	no	—
236	C₂×C₇×D₄	—	4	2	no	—
237	C₂×C₇×D₄	—	4	4	no	—
238	C₂×C₇×D₄	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₇	—	2	4	no	—
240	C₂²×C₄×C₇	—	2	1	no	—
241	C₂²×C₄×C₇	—	2	2	no	—
242	C₂²×C₄×C₇	—	2	1	no	—
243	C₂²×C₄×C₇	—	2	2	no	—
244	C₂²×C₄×C₇	—	2	1	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	—	4	4	no	—
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	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
268	C₇×Q₁₆	—	4	8	no	—
269	C₇×SD₁₆	—	4	8	no	—
270	C₇×M₁₆	—	4	4	no	—
271	C₂×C₇×C₈	C₂⁴	1	8	yes	—
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	2	no	—
278	C₇×C₄⋊C₄	—	2	2	no	—
279	C₇×C₄⋊C₄	—	2	2	no	—
280	C₇×C₄⋊C₄	—	2	2	no	—
281	C₇×C₄⋊C₄	—	2	2	no	—
282	C₇×C₄⋊C₄	—	2	2	no	—
283	C₇×C₄⋊C₄	—	2	2	no	—
284	C₇×C₄⋊C₄	—	2	4	no	—
285	C₇×C₄⋊C₄	—	2	4	no	—
286	C₇×C₄⋊C₄	—	2	4	no	—
287	C₇×C₄⋊C₄	—	2	4	no	—
288	C₇×C₄⋊C₄	—	2	2	no	—
289	C₇×C₄⋊C₄	—	2	2	no	—
290	C₇×C₄⋊C₄	—	2	1	no	—
291	C₇×C₄⋊C₄	—	2	1	no	—
292	C₇×C₄⋊C₄	—	2	2	no	—
293	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
294	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
295	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
296	C₇×C₂²⋊C₄	—	2	4	no	—
297	C₇×C₂²⋊C₄	—	2	4	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	C₇×C₂²⋊C₄	—	2	2	no	—
307	C₇×C₂²⋊C₄	—	2	2	no	—
308	C₄²×C₇	—	2	2	no	—
309	C₄²×C₇	—	2	4	no	—
310	C₄²×C₇	—	2	2	no	—
311	C₄²×C₇	—	2	4	no	—
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	C₂×D₄	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	C₄²×C₇	C₂⁴	1	1	yes	characteristic
328	#533	—	2	1	no	—
329	#533	—	2	1	no	—
330	#533	—	2	1	no	—
331	#533	—	2	1	no	—
332	#533	C₂²×C₇	1	2	yes	—
333	#533	C₂²×C₇	1	2	yes	—
334	#533	C₂²×C₇	1	2	yes	complemented
335	#533	C₂²×C₇	1	2	yes	complemented
336	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
337	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
338	#529	—	2	1	no	—
339	#529	—	2	1	no	—
340	#529	—	2	1	no	—
341	#529	—	2	1	no	—
342	#529	C₂²×C₇	1	2	yes	—
343	#529	C₂²×C₇	1	2	yes	—
344	#529	C₂²×C₇	1	2	yes	—
345	#529	C₂²×C₇	1	2	yes	—
346	C₂×#126	—	2	1	no	—
347	C₂×#125	—	2	1	no	—
348	C₂×#125	C₂²×C₇	1	1	yes	characteristic
349	C₂×#124	C₂²×C₇	1	1	yes	characteristic
350	C₂×#123	—	2	1	no	—
351	C₂×C₂²⋊Q₈	—	2	1	no	—
352	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
353	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
354	C₂×#121	C₂²×C₇	1	1	yes	characteristic
355	C₂×C₄×Q₈	—	2	1	no	—
356	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
357	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
358	C₂×C₄×D₄	—	2	1	no	—
359	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
360	C₂×#117	—	2	1	no	—
361	C₂×#117	—	2	1	no	—
362	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
363	#501	C₂²×C₇	1	4	yes	complemented
364	#497	C₂²×C₇	1	4	yes	complemented
365	#491	C₂²×C₇	1	4	yes	complemented
366	#489	C₂²×C₇	1	4	yes	complemented
367	#484	C₂²×C₇	1	4	yes	—
368	#483	C₂²×C₇	1	4	yes	—
369	#483	C₂²×C₇	1	4	yes	complemented
370	#480	C₂²×C₇	1	4	yes	—
371	#479	C₂²×C₇	1	8	yes	complemented
372	#477	C₂²×C₇	1	4	yes	complemented
373	#476	C₂²×C₇	1	4	yes	complemented
374	#470	C₂²×C₇	1	8	yes	complemented
375	#468	C₂²×C₇	1	8	yes	—
376	#464	C₂²×C₇	1	8	yes	complemented
377	#462	C₂²×C₇	1	4	yes	complemented
378	#461	C₂²×C₇	1	4	yes	complemented
379	#451	C₂²×C₇	1	4	yes	—
380	#451	C₂²×C₇	1	4	yes	complemented
381	#450	C₂²×C₇	1	4	yes	—
382	#448	C₂²×C₇	1	4	yes	—
383	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
384	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
385	#432	C₂²×C₇	1	2	yes	—
386	#432	C₂²×C₇	1	2	yes	complemented
387	#431	C₂²×C₇	1	2	yes	—
388	#431	C₂²×C₇	1	2	yes	complemented
389	#423	C₂²×C₇	1	2	yes	complemented
390	#407	C₂²×C₇	1	2	yes	—
391	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
392	C₂³×C₇	—	2	2	no	—
393	C₂³×C₇	—	2	2	no	—
394	C₂³×C₇	—	2	2	no	—
395	C₂³×C₇	—	4	1	no	—
396	C₂³×C₇	—	4	2	no	—
397	C₂³×C₇	—	4	2	no	—
398	C₂³×C₇	—	4	2	no	—
399	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
400	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
401	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
402	C₇×Q₈	—	2	8	no	—
403	C₇×Q₈	—	2	4	no	—
404	C₇×Q₈	—	4	2	no	—
405	C₇×Q₈	—	4	4	no	—
406	C₇×Q₈	—	4	4	no	—
407	C₇×Q₈	—	4	4	no	—
408	C₇×D₄	—	2	4	no	—
409	C₇×D₄	—	4	2	no	—
410	C₇×D₄	—	4	4	no	—
411	C₇×D₄	—	4	4	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	4	no	—
424	C₂×C₄×C₇	—	2	2	no	—
425	C₂×C₄×C₇	—	2	4	no	—
426	C₂×C₄×C₇	—	2	2	no	—
427	C₂×C₄×C₇	—	4	1	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	2	no	—
435	C₂×C₄×C₇	—	4	4	no	—
436	C₂×C₄×C₇	—	4	2	no	—
437	C₂×C₄×C₇	—	4	2	no	—
438	C₂×C₄×C₇	—	4	4	no	—
439	C₂×C₄×C₇	—	4	4	no	—
440	C₂×C₄×C₇	—	4	4	no	—
441	C₂×C₄×C₇	#137	1	4	yes	—
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	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
454	C₇×C₈	—	2	8	no	—
455	C₂²×Q₈	—	2	1	no	—
456	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
457	C₂²×Q₈	C₂³×C₇	1	2	yes	—
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
462	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
464	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
465	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
466	C₂×M₁₆	C₂³×C₇	1	4	yes	—
467	C₄⋊Q₈	—	2	1	no	—
468	C₄⋊Q₈	—	2	1	no	—
469	C₄⋊Q₈	—	2	1	no	—
470	C₄⋊Q₈	—	2	1	no	—
471	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
472	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
473	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
474	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
475	#126	—	2	2	no	—
476	#126	—	2	2	no	—
477	#126	—	2	2	no	—
478	#126	—	2	2	no	—
479	#125	—	2	2	no	—
480	#125	—	2	2	no	—
481	#125	—	2	2	no	—
482	#125	—	2	2	no	—
483	#125	—	2	1	no	—
484	#125	—	2	1	no	—
485	#125	C₂³×C₇	1	2	yes	—
486	#125	C₂³×C₇	1	2	yes	—
487	#124	—	2	1	no	—
488	#124	—	2	1	no	—
489	#124	C₂³×C₇	1	2	yes	—
490	#124	C₂³×C₇	1	2	yes	—
491	#123	—	2	2	no	—
492	#123	—	2	2	no	—
493	#123	—	2	2	no	—
494	#123	—	2	2	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	2	1	no	—
500	C₂²⋊Q₈	—	2	1	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
504	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
505	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
506	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
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	C₄×Q₈	—	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	1	no	—
516	C₄×Q₈	—	2	1	no	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	C₂³×C₇	1	2	yes	—
520	C₄×Q₈	C₂³×C₇	1	2	yes	—
521	C₄×Q₈	C₂³×C₇	1	4	yes	—
522	C₄×Q₈	C₂³×C₇	1	4	yes	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	1	no	—
528	C₄×D₄	—	2	1	no	—
529	C₄×D₄	C₂³×C₇	1	2	yes	—
530	C₄×D₄	C₂³×C₇	1	2	yes	—
531	#117	—	2	2	no	—
532	#117	—	2	2	no	—
533	#117	—	2	2	no	—
534	#117	—	2	2	no	—
535	#117	—	2	2	no	—
536	#117	—	2	2	no	—
537	#117	—	2	2	no	—
538	#117	—	2	2	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	2	1	no	—
542	C₂×C₄⋊C₄	—	2	1	no	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	—	2	2	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	—	2	2	no	—
548	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
551	C₂×C₂²⋊C₄	—	2	2	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₂²⋊C₄	—	2	1	no	—
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	—	2	2	no	—
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	C₇×D₄	1	1	yes	characteristic
564	C₂×C₄²	C₇×D₄	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	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
571	#107	C₂³×C₇	1	8	yes	—
572	#106	C₂³×C₇	1	8	yes	—
573	C₄⋊C₈	C₂³×C₇	1	4	yes	—
574	C₄⋊C₈	C₂³×C₇	1	4	yes	—
575	#103	C₂³×C₇	1	8	yes	—
576	#103	C₂³×C₇	1	8	yes	—
577	#103	C₂³×C₇	1	8	yes	—
578	#102	C₂³×C₇	1	8	yes	—
579	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
580	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
581	#97	C₂³×C₇	1	4	yes	—
582	C₄×C₈	C₂³×C₇	1	4	yes	—
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	—	2	1	no	—
590	C₂²×C₇	—	4	4	no	—
591	C₂²×C₇	—	4	2	no	—
592	C₂²×C₇	—	4	2	no	—
593	C₂²×C₇	—	4	2	no	—
594	C₂²×C₇	—	8	4	no	—
595	C₂²×C₇	C₂×#137	1	2	yes	—
596	C₂²×C₇	#575	1	2	yes	—
597	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
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	—	2	1	no	—
604	C₄×C₇	—	2	1	no	—
605	C₄×C₇	—	2	1	no	—
606	C₄×C₇	—	2	1	no	—
607	C₄×C₇	—	4	2	no	—
608	C₄×C₇	—	4	4	no	—
609	C₄×C₇	—	4	2	no	—
610	C₄×C₇	—	4	2	no	—
611	C₄×C₇	—	4	4	no	—
612	C₄×C₇	C₂×#137	1	2	yes	—
613	C₄×C₇	C₂×#137	1	2	yes	—
614	C₄×C₇	#585	1	2	yes	—
615	C₂⁴	—	2	1	no	—
616	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
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	2	no	—
622	C₂×Q₈	—	4	4	no	—
623	C₂×Q₈	—	4	4	no	—
624	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	4	2	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	C₂⁴×C₇	1	2	yes	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	4	no	—
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	C₂×C₇×D₄	1	1	yes	characteristic
655	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
656	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
657	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
661	Q₁₆	—	4	8	no	—
662	SD₁₆	—	4	8	no	—
663	M₁₆	—	4	4	no	—
664	C₂×C₈	C₂⁴×C₇	1	8	yes	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
687	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
688	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	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	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	4	no	—
704	C₄²	—	2	4	no	—
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	C₂×C₇×D₄	1	1	yes	characteristic
714	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
715	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
716	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
717	C₄²	C₂⁴×C₇	1	1	yes	characteristic
718	C₄²	C₂⁴×C₇	1	1	yes	characteristic
719	C₄²	C₂⁴×C₇	1	1	yes	characteristic
720	C₄²	C₂⁴×C₇	1	1	yes	characteristic
721	C₂×C₇	—	2	2	no	—
722	C₂×C₇	—	2	2	no	—
723	C₂×C₇	—	4	1	no	—
724	C₂×C₇	—	8	2	no	—
725	C₂×C₇	#3449	1	1	yes	characteristic
726	C₂×C₇	C₂²×#137	1	1	yes	characteristic
727	C₂×C₇	C₂×#575	1	1	yes	characteristic
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	4	1	no	—
732	C₂³	—	4	2	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	4	2	no	—
735	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
736	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
737	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
738	Q₈	—	2	8	no	—
739	Q₈	—	2	4	no	—
740	Q₈	—	4	4	no	—
741	Q₈	—	4	4	no	—
742	Q₈	—	4	2	no	—
743	Q₈	—	4	4	no	—
744	D₄	—	2	4	no	—
745	D₄	—	4	2	no	—
746	D₄	—	4	4	no	—
747	D₄	—	4	4	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	2	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	2	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	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	2	no	—
771	C₂×C₄	—	4	4	no	—
772	C₂×C₄	—	4	2	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	C₇×#137	1	4	yes	—
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	C₂²×C₇×D₄	1	1	yes	characteristic
785	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
786	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
787	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
788	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
789	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
790	C₈	—	2	8	no	—
791	C₇	#60950	1	1	yes	characteristic, direct product factor, Sylow
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	4	4	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	8	4	no	—
804	C₂²	C₂×C₇×#137	1	2	yes	—
805	C₂²	C₇×#575	1	2	yes	—
806	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
807	C₄	—	2	1	no	—
808	C₄	—	2	1	no	—
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	4	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	4	no	—
821	C₄	C₂×C₇×#137	1	2	yes	—
822	C₄	C₂×C₇×#137	1	2	yes	—
823	C₄	C₇×#585	1	2	yes	—
824	C₂	—	2	2	no	—
825	C₂	—	2	2	no	—
826	C₂	—	4	1	no	—
827	C₂	—	8	2	no	—
828	C₂	C₇×#3449	1	1	yes	characteristic
829	C₂	C₂²×C₇×#137	1	1	yes	characteristic
830	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	C₂×C₇×#121	C₂²
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
1. C₂×C₇×#533	C₂	semidirect
3. C₇×#3252	C₂	semidirect
4. C₇×#3238	C₂	semidirect
5. C₇×#3236	C₂	semidirect
6. C₇×#3218	C₂	semidirect
7. C₇×#3215	C₂	semidirect
8. C₇×#3195	C₂	semidirect
10. C₇×#3172	C₂	semidirect
11. C₇×#3108	C₂	semidirect
12. C₇×#3104	C₂	semidirect
13. C₇×#3101	C₂	semidirect
14. C₇×#2920	C₂	semidirect
21. C₇×#533	C₂²	semidirect
22. C₇×#533	C₂²	semidirect
23. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
44. C₂×C₄×C₇×Q₈	C₂²	semidirect
50. C₇×#501	C₂²	semidirect
51. C₇×#497	C₂²	semidirect
52. C₇×#491	C₂²	semidirect
53. C₇×#489	C₂²	semidirect
56. C₇×#483	C₂²	semidirect
58. C₇×#479	C₂²	semidirect
59. C₇×#477	C₂²	semidirect
60. C₇×#476	C₂²	semidirect
61. C₇×#470	C₂²	semidirect
63. C₇×#464	C₂²	semidirect
64. C₇×#462	C₂²	semidirect
65. C₇×#461	C₂²	semidirect
67. C₇×#451	C₂²	semidirect
70. C₄×C₇×Q₁₆	C₂²	semidirect
71. C₄×C₇×SD₁₆	C₂²	semidirect
73. C₇×#432	C₂²	semidirect
75. C₇×#431	C₂²	semidirect
76. C₇×#423	C₂²	semidirect
78. C₄×C₇×M₁₆	C₂²	semidirect
79. #60950	C₇	direct (N × H)
208. C₂×#533	C₂×C₇	semidirect
210. #3252	C₂×C₇	semidirect
211. #3238	C₂×C₇	semidirect
212. #3236	C₂×C₇	semidirect
213. #3218	C₂×C₇	semidirect
214. #3215	C₂×C₇	semidirect
215. #3195	C₂×C₇	semidirect
217. #3172	C₂×C₇	semidirect
218. #3108	C₂×C₇	semidirect
219. #3104	C₂×C₇	semidirect
220. #3101	C₂×C₇	semidirect
221. #2920	C₂×C₇	semidirect
334. #533	C₂²×C₇	semidirect
335. #533	C₂²×C₇	semidirect
336. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
337. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
357. C₂×C₄×Q₈	C₂²×C₇	semidirect
363. #501	C₂²×C₇	semidirect
364. #497	C₂²×C₇	semidirect
365. #491	C₂²×C₇	semidirect
366. #489	C₂²×C₇	semidirect
369. #483	C₂²×C₇	semidirect
371. #479	C₂²×C₇	semidirect
372. #477	C₂²×C₇	semidirect
373. #476	C₂²×C₇	semidirect
374. #470	C₂²×C₇	semidirect
376. #464	C₂²×C₇	semidirect
377. #462	C₂²×C₇	semidirect
378. #461	C₂²×C₇	semidirect
380. #451	C₂²×C₇	semidirect
383. C₄×Q₁₆	C₂²×C₇	semidirect
384. C₄×SD₁₆	C₂²×C₇	semidirect
386. #432	C₂²×C₇	semidirect
388. #431	C₂²×C₇	semidirect
389. #423	C₂²×C₇	semidirect
391. C₄×M₁₆	C₂²×C₇	semidirect
791. C₇	#60950	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#533	2
C₂×C₇×#529	2
C₇×#3252	2
C₇×#3238	2
C₇×#3236	2
C₇×#3218	2
C₇×#3215	2
C₇×#3195	2
C₇×#3193	2
C₇×#3172	2
C₇×#3108	2
C₇×#3104	2
C₇×#3101	2
C₇×#2920	2
#60950	7

Subgroups — C7×#60950 #13238166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60950 #13238166