Subgroups — C₇×#22472 #13199688

Order 1792.

1162 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1818	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1817	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1750	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1729	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1728	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
20	C₇×#529	—	2	4	no	—
21	C₇×#529	—	2	4	no	—
22	C₂×C₇×#126	C₄	1	1	yes	characteristic
23	C₂×C₇×#126	C₄	1	1	yes	characteristic
24	C₂×C₇×#125	C₄	1	1	yes	characteristic
25	C₂×C₇×#124	C₄	1	1	yes	characteristic
26	C₂×C₇×#123	C₄	1	1	yes	characteristic
27	C₂×C₇×#123	C₄	1	1	yes	characteristic
28	C₂×C₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
29	C₂×C₇×#121	C₄	1	1	yes	characteristic
30	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₇×#117	C₂²	1	1	yes	characteristic
35	C₂×C₇×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
37	C₇×#436	—	2	4	no	—
38	C₇×#435	—	2	4	no	—
39	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₇×#97	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
51	C₇×#336	C₂²	1	1	yes	characteristic
52	C₇×#336	C₂²	1	1	yes	characteristic
53	C₇×#336	C₂²	1	1	yes	characteristic
54	C₇×#336	C₂²	1	1	yes	characteristic
55	C₇×#336	C₂²	1	1	yes	characteristic
56	C₇×#336	C₂²	1	1	yes	characteristic
57	C₇×#336	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	C₇×#336	C₂²	1	1	yes	characteristic
60	C₇×#336	C₂²	1	1	yes	characteristic
61	C₇×#336	C₂²	1	1	yes	characteristic
62	C₇×#336	C₂²	1	1	yes	characteristic
63	#22472	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
73	C₂×C₇×M₁₆	—	2	2	no	—
74	C₂×C₇×M₁₆	—	2	2	no	—
75	C₂×C₇×M₁₆	—	2	2	no	—
76	C₂×C₇×M₁₆	—	2	2	no	—
77	C₂×C₇×M₁₆	—	2	2	no	—
78	C₂×C₇×M₁₆	—	2	2	no	—
79	C₂×C₇×M₁₆	—	4	1	no	—
80	C₂×C₇×M₁₆	—	4	1	no	—
81	C₂×C₇×M₁₆	—	4	1	no	—
82	C₂²×C₇×C₈	—	2	2	no	—
83	C₂²×C₇×C₈	—	2	2	no	—
84	C₂²×C₇×C₈	—	4	1	no	—
85	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
91	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
92	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
93	C₇×#126	—	2	4	no	—
94	C₇×#126	—	2	4	no	—
95	C₇×#125	—	2	4	no	—
96	C₇×#124	—	2	4	no	—
97	C₇×#123	—	2	4	no	—
98	C₇×#123	—	2	4	no	—
99	C₇×C₂²⋊Q₈	—	2	4	no	—
100	C₇×#121	—	2	4	no	—
101	C₄×C₇×Q₈	—	2	2	no	—
102	C₄×C₇×Q₈	—	2	2	no	—
103	C₄×C₇×D₄	—	2	2	no	—
104	C₄×C₇×D₄	—	2	2	no	—
105	C₄×C₇×D₄	—	2	2	no	—
106	C₄×C₇×D₄	—	2	2	no	—
107	C₄×C₇×D₄	D₄	1	4	yes	—
108	C₄×C₇×D₄	D₄	1	4	yes	—
109	C₇×#117	—	2	2	no	—
110	C₇×#117	—	2	2	no	—
111	C₇×#117	—	2	2	no	—
112	C₇×#117	—	2	2	no	—
113	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
121	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
122	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
123	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
124	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
125	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
126	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
127	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
128	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
129	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
130	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
131	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
132	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
133	C₂×C₄²×C₇	—	2	2	no	—
134	C₂×C₄²×C₇	—	2	2	no	—
135	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
136	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
137	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
141	C₇×C₄⋊C₈	—	2	2	no	—
142	C₇×C₄⋊C₈	—	2	2	no	—
143	C₇×C₂²⋊C₈	—	2	2	no	—
144	C₇×C₂²⋊C₈	—	2	2	no	—
145	C₇×C₂²⋊C₈	—	2	2	no	—
146	C₇×C₂²⋊C₈	—	2	2	no	—
147	C₇×C₂²⋊C₈	—	2	2	no	—
148	C₇×C₂²⋊C₈	—	2	2	no	—
149	C₇×C₂²⋊C₈	—	4	1	no	—
150	C₇×C₂²⋊C₈	—	4	1	no	—
151	C₇×#97	—	2	2	no	—
152	C₄×C₇×C₈	—	2	2	no	—
153	C₂×#529	C₂×C₇	1	1	yes	characteristic
154	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
155	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
156	#1985	C₂×C₇	1	1	yes	characteristic, complemented
157	#1984	C₂×C₇	1	1	yes	characteristic, complemented
158	#1870	C₂×C₇	1	1	yes	characteristic, complemented
159	#1870	C₂×C₇	1	1	yes	characteristic, complemented
160	#1870	C₂×C₇	1	1	yes	characteristic, complemented
161	#1869	C₂×C₇	1	1	yes	characteristic, complemented
162	#1818	C₂×C₇	1	1	yes	characteristic, complemented
163	#1817	C₂×C₇	1	1	yes	characteristic, complemented
164	#1798	C₂×C₇	1	1	yes	characteristic, complemented
165	#1750	C₂×C₇	1	1	yes	characteristic, complemented
166	#1729	C₂×C₇	1	1	yes	characteristic, complemented
167	#1728	C₂×C₇	1	1	yes	characteristic, complemented
168	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
169	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
170	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₇×Q₈	—	2	2	no	—
172	C₂×C₇×Q₈	—	2	2	no	—
173	C₂×C₇×Q₈	—	4	1	no	—
174	C₂×C₇×D₄	—	2	2	no	—
175	C₂×C₇×D₄	—	2	2	no	—
176	C₂×C₇×D₄	—	2	2	no	—
177	C₂×C₇×D₄	—	4	1	no	—
178	C₂×C₇×D₄	—	4	1	no	—
179	C₂×C₇×D₄	—	4	1	no	—
180	C₂×C₇×D₄	—	4	1	no	—
181	C₂×C₇×D₄	—	4	1	no	—
182	C₂×C₇×D₄	C₂²⋊C₄	1	4	yes	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	2	1	no	—
188	C₂²×C₄×C₇	—	2	1	no	—
189	C₂²×C₄×C₇	—	2	1	no	—
190	C₂²×C₄×C₇	—	2	1	no	—
191	C₂²×C₄×C₇	—	2	2	no	—
192	C₂²×C₄×C₇	—	2	2	no	—
193	C₂²×C₄×C₇	—	2	2	no	—
194	C₂²×C₄×C₇	—	2	1	no	—
195	C₂²×C₄×C₇	—	2	1	no	—
196	C₂²×C₄×C₇	—	2	1	no	—
197	C₂²×C₄×C₇	—	2	1	no	—
198	C₂²×C₄×C₇	—	2	1	no	—
199	C₂²×C₄×C₇	—	2	1	no	—
200	C₂²×C₄×C₇	—	4	1	no	—
201	C₂²×C₄×C₇	—	4	1	no	—
202	C₂²×C₄×C₇	—	4	1	no	—
203	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
215	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
216	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
217	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
219	C₇×M₁₆	—	4	4	no	—
220	C₇×M₁₆	—	4	4	no	—
221	C₇×M₁₆	—	4	4	no	—
222	C₂×C₇×C₈	—	2	1	no	—
223	C₂×C₇×C₈	—	2	1	no	—
224	C₂×C₇×C₈	—	2	1	no	—
225	C₂×C₇×C₈	—	2	1	no	—
226	C₂×C₇×C₈	—	2	1	no	—
227	C₂×C₇×C₈	—	2	1	no	—
228	C₂×C₇×C₈	—	2	1	no	—
229	C₂×C₇×C₈	—	2	1	no	—
230	C₂×C₇×C₈	—	2	1	no	—
231	C₂×C₇×C₈	—	2	1	no	—
232	C₂×C₇×C₈	—	2	1	no	—
233	C₂×C₇×C₈	—	2	1	no	—
234	C₂×C₇×C₈	—	2	1	no	—
235	C₂×C₇×C₈	—	2	1	no	—
236	C₂×C₇×C₈	—	2	1	no	—
237	C₂×C₇×C₈	—	2	1	no	—
238	C₂×C₇×C₈	—	2	1	no	—
239	C₂×C₇×C₈	—	2	1	no	—
240	C₂×C₇×C₈	—	2	1	no	—
241	C₂×C₇×C₈	—	2	1	no	—
242	C₂×C₇×C₈	—	2	1	no	—
243	C₂×C₇×C₈	—	2	1	no	—
244	C₂×C₇×C₈	—	4	4	no	—
245	C₂×C₇×C₈	#41	1	2	yes	—
246	C₂×C₇×C₈	#41	1	2	yes	—
247	C₇×C₄⋊C₄	—	2	2	no	—
248	C₇×C₄⋊C₄	—	2	2	no	—
249	C₇×C₄⋊C₄	—	2	2	no	—
250	C₇×C₄⋊C₄	—	2	2	no	—
251	C₇×C₄⋊C₄	—	2	2	no	—
252	C₇×C₄⋊C₄	—	2	2	no	—
253	C₇×C₄⋊C₄	—	2	2	no	—
254	C₇×C₄⋊C₄	—	2	2	no	—
255	C₇×C₄⋊C₄	—	2	2	no	—
256	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
257	C₇×C₂²⋊C₄	—	2	2	no	—
258	C₇×C₂²⋊C₄	—	2	2	no	—
259	C₇×C₂²⋊C₄	—	2	2	no	—
260	C₇×C₂²⋊C₄	—	2	2	no	—
261	C₇×C₂²⋊C₄	—	2	2	no	—
262	C₇×C₂²⋊C₄	—	2	2	no	—
263	C₇×C₂²⋊C₄	—	2	2	no	—
264	C₇×C₂²⋊C₄	—	2	2	no	—
265	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
266	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
267	C₄²×C₇	—	2	2	no	—
268	C₄²×C₇	—	2	2	no	—
269	C₄²×C₇	—	2	1	no	—
270	C₄²×C₇	—	2	1	no	—
271	C₄²×C₇	—	2	1	no	—
272	C₄²×C₇	—	2	1	no	—
273	C₄²×C₇	—	2	1	no	—
274	C₄²×C₇	—	2	1	no	—
275	C₄²×C₇	C₂×D₄	1	2	yes	—
276	C₄²×C₇	C₂×D₄	1	2	yes	—
277	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
278	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
279	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
280	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
281	#529	—	2	4	no	—
282	#529	—	2	4	no	—
283	C₂×#126	C₄×C₇	1	1	yes	characteristic
284	C₂×#126	C₄×C₇	1	1	yes	characteristic
285	C₂×#125	C₄×C₇	1	1	yes	characteristic
286	C₂×#124	C₄×C₇	1	1	yes	characteristic
287	C₂×#123	C₄×C₇	1	1	yes	characteristic
288	C₂×#123	C₄×C₇	1	1	yes	characteristic
289	C₂×C₂²⋊Q₈	C₄×C₇	1	1	yes	characteristic
290	C₂×#121	C₄×C₇	1	1	yes	characteristic
291	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
292	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
293	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
294	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
295	C₂×#117	C₂²×C₇	1	1	yes	characteristic
296	C₂×#117	C₂²×C₇	1	1	yes	characteristic
297	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
298	#436	—	2	4	no	—
299	#435	—	2	4	no	—
300	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
301	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
302	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
303	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
304	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
305	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
306	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
307	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
308	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
309	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
310	C₂×#97	C₂²×C₇	1	1	yes	characteristic
311	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
312	#336	C₂²×C₇	1	1	yes	characteristic
313	#336	C₂²×C₇	1	1	yes	characteristic
314	#336	C₂²×C₇	1	1	yes	characteristic
315	#336	C₂²×C₇	1	1	yes	characteristic
316	#336	C₂²×C₇	1	1	yes	characteristic
317	#336	C₂²×C₇	1	1	yes	characteristic
318	#336	C₂²×C₇	1	1	yes	characteristic
319	#336	C₂²×C₇	1	1	yes	characteristic
320	#336	C₂²×C₇	1	1	yes	characteristic
321	#336	C₂²×C₇	1	1	yes	characteristic
322	#336	C₂²×C₇	1	1	yes	characteristic
323	#336	C₂²×C₇	1	1	yes	characteristic
324	C₂³×C₇	—	2	1	no	—
325	C₂³×C₇	—	2	1	no	—
326	C₂³×C₇	—	2	1	no	—
327	C₂³×C₇	—	2	1	no	—
328	C₂³×C₇	—	2	1	no	—
329	C₂³×C₇	—	2	1	no	—
330	C₂³×C₇	—	2	1	no	—
331	C₂³×C₇	—	2	1	no	—
332	C₂³×C₇	—	2	1	no	—
333	C₂³×C₇	—	2	1	no	—
334	C₂³×C₇	—	2	1	no	—
335	C₂³×C₇	—	2	1	no	—
336	C₂³×C₇	—	2	1	no	—
337	C₂³×C₇	—	2	1	no	—
338	C₂³×C₇	—	2	1	no	—
339	C₂³×C₇	—	2	1	no	—
340	C₂³×C₇	—	2	1	no	—
341	C₂³×C₇	—	2	1	no	—
342	C₂³×C₇	—	2	1	no	—
343	C₂³×C₇	C₂×C₂²⋊C₄	1	2	yes	—
344	C₂³×C₇	C₂×C₂²⋊C₄	1	2	yes	—
345	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
346	C₇×Q₈	—	4	4	no	—
347	C₇×D₄	—	4	4	no	—
348	C₇×D₄	—	4	4	no	—
349	C₇×D₄	—	4	4	no	—
350	C₂×C₄×C₇	—	2	1	no	—
351	C₂×C₄×C₇	—	2	1	no	—
352	C₂×C₄×C₇	—	2	1	no	—
353	C₂×C₄×C₇	—	2	1	no	—
354	C₂×C₄×C₇	—	2	1	no	—
355	C₂×C₄×C₇	—	2	1	no	—
356	C₂×C₄×C₇	—	2	1	no	—
357	C₂×C₄×C₇	—	2	1	no	—
358	C₂×C₄×C₇	—	2	1	no	—
359	C₂×C₄×C₇	—	2	1	no	—
360	C₂×C₄×C₇	—	2	2	no	—
361	C₂×C₄×C₇	—	2	2	no	—
362	C₂×C₄×C₇	—	2	2	no	—
363	C₂×C₄×C₇	—	2	2	no	—
364	C₂×C₄×C₇	—	2	2	no	—
365	C₂×C₄×C₇	—	2	2	no	—
366	C₂×C₄×C₇	—	2	2	no	—
367	C₂×C₄×C₇	—	2	2	no	—
368	C₂×C₄×C₇	—	2	1	no	—
369	C₂×C₄×C₇	—	2	1	no	—
370	C₂×C₄×C₇	—	2	1	no	—
371	C₂×C₄×C₇	—	2	1	no	—
372	C₂×C₄×C₇	—	2	1	no	—
373	C₂×C₄×C₇	—	2	1	no	—
374	C₂×C₄×C₇	—	2	1	no	—
375	C₂×C₄×C₇	—	2	1	no	—
376	C₂×C₄×C₇	—	2	1	no	—
377	C₂×C₄×C₇	—	2	1	no	—
378	C₂×C₄×C₇	—	2	1	no	—
379	C₂×C₄×C₇	—	2	1	no	—
380	C₂×C₄×C₇	—	2	1	no	—
381	C₂×C₄×C₇	—	2	1	no	—
382	C₂×C₄×C₇	—	2	1	no	—
383	C₂×C₄×C₇	—	2	1	no	—
384	C₂×C₄×C₇	—	2	1	no	—
385	C₂×C₄×C₇	—	2	1	no	—
386	C₂×C₄×C₇	—	4	4	no	—
387	C₂×C₄×C₇	—	4	4	no	—
388	C₂×C₄×C₇	—	4	1	no	—
389	C₂×C₄×C₇	—	4	1	no	—
390	C₂×C₄×C₇	—	4	1	no	—
391	C₂×C₄×C₇	—	4	1	no	—
392	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
393	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
394	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
395	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
396	C₂×C₄×C₇	#131	1	2	yes	—
397	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
400	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
401	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
402	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
403	C₇×C₈	—	2	2	no	—
404	C₇×C₈	—	2	2	no	—
405	C₇×C₈	—	4	1	no	—
406	C₇×C₈	—	4	1	no	—
407	C₇×C₈	—	4	1	no	—
408	C₇×C₈	—	4	1	no	—
409	C₇×C₈	—	4	1	no	—
410	C₇×C₈	—	4	1	no	—
411	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
412	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
413	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
414	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
415	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
416	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
420	C₂×M₁₆	—	2	2	no	—
421	C₂×M₁₆	—	2	2	no	—
422	C₂×M₁₆	—	2	2	no	—
423	C₂×M₁₆	—	2	2	no	—
424	C₂×M₁₆	—	2	2	no	—
425	C₂×M₁₆	—	2	2	no	—
426	C₂×M₁₆	—	4	1	no	—
427	C₂×M₁₆	—	4	1	no	—
428	C₂×M₁₆	—	4	1	no	—
429	C₂²×C₈	—	2	2	no	—
430	C₂²×C₈	—	2	2	no	—
431	C₂²×C₈	—	4	1	no	—
432	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
434	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
435	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
436	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
440	#126	—	2	4	no	—
441	#126	—	2	4	no	—
442	#125	—	2	4	no	—
443	#124	—	2	4	no	—
444	#123	—	2	4	no	—
445	#123	—	2	4	no	—
446	C₂²⋊Q₈	—	2	4	no	—
447	#121	—	2	4	no	—
448	C₄×Q₈	—	2	2	no	—
449	C₄×Q₈	—	2	2	no	—
450	C₄×D₄	—	2	2	no	—
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	2	2	no	—
454	C₄×D₄	C₇×D₄	1	4	yes	—
455	C₄×D₄	C₇×D₄	1	4	yes	—
456	#117	—	2	2	no	—
457	#117	—	2	2	no	—
458	#117	—	2	2	no	—
459	#117	—	2	2	no	—
460	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
475	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
480	C₂×C₄²	—	2	2	no	—
481	C₂×C₄²	—	2	2	no	—
482	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
483	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
484	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
485	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
487	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
488	C₄⋊C₈	—	2	2	no	—
489	C₄⋊C₈	—	2	2	no	—
490	C₂²⋊C₈	—	2	2	no	—
491	C₂²⋊C₈	—	2	2	no	—
492	C₂²⋊C₈	—	2	2	no	—
493	C₂²⋊C₈	—	2	2	no	—
494	C₂²⋊C₈	—	2	2	no	—
495	C₂²⋊C₈	—	2	2	no	—
496	C₂²⋊C₈	—	4	1	no	—
497	C₂²⋊C₈	—	4	1	no	—
498	#97	—	2	2	no	—
499	C₄×C₈	—	2	2	no	—
500	C₂²×C₇	—	2	2	no	—
501	C₂²×C₇	—	2	2	no	—
502	C₂²×C₇	—	2	2	no	—
503	C₂²×C₇	—	2	2	no	—
504	C₂²×C₇	—	2	2	no	—
505	C₂²×C₇	—	2	2	no	—
506	C₂²×C₇	—	4	1	no	—
507	C₂²×C₇	—	4	1	no	—
508	C₂²×C₇	—	4	1	no	—
509	C₂²×C₇	—	4	1	no	—
510	C₂²×C₇	—	4	1	no	—
511	C₂²×C₇	—	4	1	no	—
512	C₂²×C₇	—	4	1	no	—
513	C₂²×C₇	—	4	1	no	—
514	C₂²×C₇	—	4	1	no	—
515	C₂²×C₇	—	4	1	no	—
516	C₂²×C₇	—	4	1	no	—
517	C₂²×C₇	—	4	1	no	—
518	C₂²×C₇	—	4	1	no	—
519	C₂²×C₇	—	4	1	no	—
520	C₂²×C₇	—	4	1	no	—
521	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
522	C₂²×C₇	C₄×#41	1	1	yes	characteristic
523	C₂²×C₇	#520	1	1	yes	characteristic
524	C₂²×C₇	C₂×#131	1	1	yes	characteristic
525	C₂²×C₇	#568	1	1	yes	characteristic
526	C₂²×C₇	#568	1	1	yes	characteristic
527	C₂²×C₇	#568	1	1	yes	characteristic
528	C₄×C₇	—	2	2	no	—
529	C₄×C₇	—	2	2	no	—
530	C₄×C₇	—	2	2	no	—
531	C₄×C₇	—	2	2	no	—
532	C₄×C₇	—	2	2	no	—
533	C₄×C₇	—	4	1	no	—
534	C₄×C₇	—	4	1	no	—
535	C₄×C₇	—	4	1	no	—
536	C₄×C₇	—	4	1	no	—
537	C₄×C₇	—	4	1	no	—
538	C₄×C₇	—	4	1	no	—
539	C₄×C₇	#546	1	1	yes	characteristic
540	C₄×C₇	#546	1	1	yes	characteristic
541	C₄×C₇	#547	1	1	yes	characteristic
542	C₄×C₇	#547	1	1	yes	characteristic
543	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
544	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
545	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	4	1	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	4	1	no	—
553	C₂×D₄	—	4	1	no	—
554	C₂×D₄	—	4	1	no	—
555	C₂×D₄	—	4	1	no	—
556	C₂×D₄	—	4	1	no	—
557	C₂×D₄	C₇×C₂²⋊C₄	1	4	yes	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	4	1	no	—
576	C₂²×C₄	—	4	1	no	—
577	C₂²×C₄	—	4	1	no	—
578	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
579	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
580	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
581	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
582	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
583	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
584	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
585	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
586	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
587	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
588	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
589	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
590	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
591	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
592	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
594	M₁₆	—	4	4	no	—
595	M₁₆	—	4	4	no	—
596	M₁₆	—	4	4	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	4	4	no	—
620	C₂×C₈	C₇×#41	1	2	yes	—
621	C₂×C₈	C₇×#41	1	2	yes	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
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	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
641	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	2	no	—
644	C₄²	—	2	1	no	—
645	C₄²	—	2	1	no	—
646	C₄²	—	2	1	no	—
647	C₄²	—	2	1	no	—
648	C₄²	—	2	1	no	—
649	C₄²	—	2	1	no	—
650	C₄²	C₂×C₇×D₄	1	2	yes	—
651	C₄²	C₂×C₇×D₄	1	2	yes	—
652	C₂×C₇	—	4	2	no	—
653	C₂×C₇	—	4	2	no	—
654	C₂×C₇	—	8	1	no	—
655	C₂×C₇	#2339	1	1	yes	characteristic
656	C₂×C₇	#2879	1	1	yes	characteristic
657	C₂×C₇	#2880	1	1	yes	characteristic
658	C₂×C₇	#2967	1	1	yes	characteristic
659	C₂×C₇	#2969	1	1	yes	characteristic
660	C₂×C₇	#2993	1	1	yes	characteristic
661	C₂×C₇	#2995	1	1	yes	characteristic
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	C₂×C₇×C₂²⋊C₄	1	2	yes	—
682	C₂³	C₂×C₇×C₂²⋊C₄	1	2	yes	—
683	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
684	Q₈	—	4	4	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	4	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	4	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
731	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
732	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
733	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
734	C₂×C₄	C₇×#131	1	2	yes	—
735	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
736	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
737	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
738	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
739	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
740	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
741	C₈	—	2	2	no	—
742	C₈	—	2	2	no	—
743	C₈	—	4	1	no	—
744	C₈	—	4	1	no	—
745	C₈	—	4	1	no	—
746	C₈	—	4	1	no	—
747	C₈	—	4	1	no	—
748	C₈	—	4	1	no	—
749	C₇	#22472	1	1	yes	characteristic, direct product factor, Sylow
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
772	C₂²	C₄×C₇×#41	1	1	yes	characteristic
773	C₂²	C₇×#520	1	1	yes	characteristic
774	C₂²	C₂×C₇×#131	1	1	yes	characteristic
775	C₂²	C₇×#568	1	1	yes	characteristic
776	C₂²	C₇×#568	1	1	yes	characteristic
777	C₂²	C₇×#568	1	1	yes	characteristic
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	1	no	—
789	C₄	C₇×#546	1	1	yes	characteristic
790	C₄	C₇×#546	1	1	yes	characteristic
791	C₄	C₇×#547	1	1	yes	characteristic
792	C₄	C₇×#547	1	1	yes	characteristic
793	C₂	—	4	2	no	—
794	C₂	—	4	2	no	—
795	C₂	—	8	1	no	—
796	C₂	C₇×#2339	1	1	yes	characteristic
797	C₂	C₇×#2879	1	1	yes	characteristic
798	C₂	C₇×#2880	1	1	yes	characteristic
799	C₂	C₇×#2967	1	1	yes	characteristic
800	C₂	C₇×#2969	1	1	yes	characteristic
801	C₂	C₇×#2993	1	1	yes	characteristic
802	C₂	C₇×#2995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂×C₇×#121	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#436	C₂	semidirect
3. C₂×C₇×#435	C₂	semidirect
4. C₇×#1985	C₂	semidirect
5. C₇×#1984	C₂	semidirect
6. C₇×#1870	C₂	semidirect
7. C₇×#1870	C₂	semidirect
8. C₇×#1870	C₂	semidirect
9. C₇×#1869	C₂	semidirect
10. C₇×#1818	C₂	semidirect
11. C₇×#1817	C₂	semidirect
12. C₇×#1798	C₂	semidirect
13. C₇×#1750	C₂	semidirect
14. C₇×#1729	C₂	semidirect
15. C₇×#1728	C₂	semidirect
63. #22472	C₇	direct (N × H)
154. C₂×#436	C₂×C₇	semidirect
155. C₂×#435	C₂×C₇	semidirect
156. #1985	C₂×C₇	semidirect
157. #1984	C₂×C₇	semidirect
158. #1870	C₂×C₇	semidirect
159. #1870	C₂×C₇	semidirect
160. #1870	C₂×C₇	semidirect
161. #1869	C₂×C₇	semidirect
162. #1818	C₂×C₇	semidirect
163. #1817	C₂×C₇	semidirect
164. #1798	C₂×C₇	semidirect
165. #1750	C₂×C₇	semidirect
166. #1729	C₂×C₇	semidirect
167. #1728	C₂×C₇	semidirect
749. C₇	#22472	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×#529	2
C₂×C₇×#436	2
C₂×C₇×#435	2
C₇×#1985	2
C₇×#1984	2
C₇×#1870	2
C₇×#1869	2
C₇×#1818	2
C₇×#1817	2
C₇×#1798	2
C₇×#1750	2
C₇×#1729	2
C₇×#1728	2
#22472	7

Subgroups — C7×#22472 #13199688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22472 #13199688