Subgroups — C₇×#22849 #13200065

Order 1792.

1144 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#408	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2388	C₂	1	1	yes	maximal, characteristic
6	C₇×#1955	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1924	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1752	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
20	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
21	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
25	C₇×#436	—	2	4	no	—
26	C₇×#435	—	2	4	no	—
27	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₇×#408	—	2	4	no	—
31	C₇×#408	—	2	4	no	—
32	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₇×C₂²⋊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×#97	C₂²	1	1	yes	characteristic
44	C₂×C₇×#97	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
46	C₇×#395	C₄	1	1	yes	characteristic
47	C₇×#394	C₄	1	1	yes	characteristic
48	C₇×#394	C₄	1	1	yes	characteristic
49	C₇×#394	C₄	1	1	yes	characteristic
50	C₇×#393	C₄	1	1	yes	characteristic
51	C₇×#392	C₄	1	1	yes	characteristic
52	C₇×#392	C₄	1	1	yes	characteristic
53	C₇×#392	C₄	1	1	yes	characteristic
54	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
56	C₄×C₇×C₂²⋊C₄	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	#22849	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂×C₇×#41	—	2	2	no	—
65	C₂×C₇×#41	—	2	2	no	—
66	C₂×C₇×#41	—	2	2	no	—
67	C₂×C₇×#41	—	2	2	no	—
68	C₂×C₇×#41	—	4	1	no	—
69	C₂×C₇×#41	—	4	1	no	—
70	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
77	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
81	C₂×C₇×M₁₆	—	2	2	no	—
82	C₂×C₇×M₁₆	—	2	2	no	—
83	C₂×C₇×M₁₆	—	2	2	no	—
84	C₂×C₇×M₁₆	—	2	2	no	—
85	C₂×C₇×M₁₆	—	2	2	no	—
86	C₂×C₇×M₁₆	—	2	2	no	—
87	C₂×C₇×M₁₆	—	4	1	no	—
88	C₂×C₇×M₁₆	—	4	1	no	—
89	C₂×C₇×M₁₆	—	4	1	no	—
90	C₂²×C₇×C₈	—	2	2	no	—
91	C₂²×C₇×C₈	—	2	2	no	—
92	C₂²×C₇×C₈	—	2	2	no	—
93	C₂²×C₇×C₈	—	2	2	no	—
94	C₂²×C₇×C₈	—	4	1	no	—
95	C₂²×C₇×C₈	—	4	1	no	—
96	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
97	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
98	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
99	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
100	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
101	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
102	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
103	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
108	C₄×C₇×D₄	—	4	1	no	—
109	C₄×C₇×D₄	—	4	1	no	—
110	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
121	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
122	C₂×C₇×C₂²⋊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×C₄²×C₇	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
128	C₇×C₄⋊C₈	—	2	2	no	—
129	C₇×C₄⋊C₈	—	2	2	no	—
130	C₇×C₄⋊C₈	—	4	1	no	—
131	C₇×C₂²⋊C₈	—	2	2	no	—
132	C₇×C₂²⋊C₈	—	2	2	no	—
133	C₇×C₂²⋊C₈	—	2	2	no	—
134	C₇×C₂²⋊C₈	—	2	2	no	—
135	C₇×C₂²⋊C₈	—	2	2	no	—
136	C₇×C₂²⋊C₈	—	2	2	no	—
137	C₇×C₂²⋊C₈	—	2	2	no	—
138	C₇×C₂²⋊C₈	—	2	2	no	—
139	C₇×C₂²⋊C₈	—	4	1	no	—
140	C₇×C₂²⋊C₈	D₄	1	4	yes	complemented
141	C₇×C₂²⋊C₈	D₄	1	4	yes	complemented
142	C₇×#97	—	2	2	no	—
143	C₇×#97	—	4	1	no	—
144	C₄×C₇×C₈	—	2	2	no	—
145	C₇×#95	C₂×C₄	1	1	yes	characteristic
146	C₇×#95	C₂×C₄	1	1	yes	characteristic
147	C₇×#95	C₂×C₄	1	1	yes	characteristic
148	C₇×#95	C₂×C₄	1	1	yes	characteristic
149	C₇×#95	C₂×C₄	1	1	yes	characteristic
150	C₇×#95	C₂×C₄	1	1	yes	characteristic
151	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
152	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
153	C₂×#408	C₂×C₇	1	1	yes	characteristic, complemented
154	C₂×#408	C₂×C₇	1	1	yes	characteristic, complemented
155	#2388	C₂×C₇	1	1	yes	characteristic
156	#1955	C₂×C₇	1	1	yes	characteristic, complemented
157	#1924	C₂×C₇	1	1	yes	characteristic, complemented
158	#1923	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	#1851	C₂×C₇	1	1	yes	characteristic, complemented
163	#1850	C₂×C₇	1	1	yes	characteristic, complemented
164	#1753	C₂×C₇	1	1	yes	characteristic, complemented
165	#1752	C₂×C₇	1	1	yes	characteristic, complemented
166	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
167	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
168	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
169	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
170	C₇×#41	—	4	4	no	—
171	C₇×#41	—	4	4	no	—
172	C₇×#41	—	4	4	no	—
173	C₇×#41	—	4	4	no	—
174	C₂×C₇×Q₈	—	2	2	no	—
175	C₂×C₇×Q₈	—	2	2	no	—
176	C₂×C₇×Q₈	—	4	1	no	—
177	C₂×C₇×D₄	—	2	2	no	—
178	C₂×C₇×D₄	—	2	2	no	—
179	C₂×C₇×D₄	—	2	2	no	—
180	C₂×C₇×D₄	—	2	2	no	—
181	C₂×C₇×D₄	—	2	2	no	—
182	C₂×C₇×D₄	—	2	2	no	—
183	C₂×C₇×D₄	—	2	2	no	—
184	C₂×C₇×D₄	—	2	2	no	—
185	C₂×C₇×D₄	—	2	2	no	—
186	C₂×C₇×D₄	—	4	1	no	—
187	C₂×C₇×D₄	—	4	1	no	—
188	C₂×C₇×D₄	—	4	1	no	—
189	C₂×C₇×D₄	—	4	1	no	—
190	C₂×C₇×D₄	—	4	1	no	—
191	C₂×C₇×D₄	—	4	1	no	—
192	C₂×C₇×D₄	—	4	1	no	—
193	C₂×C₇×D₄	—	4	1	no	—
194	C₂×C₇×D₄	—	4	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	—	2	1	no	—
201	C₂²×C₄×C₇	—	2	1	no	—
202	C₂²×C₄×C₇	—	2	1	no	—
203	C₂²×C₄×C₇	—	2	1	no	—
204	C₂²×C₄×C₇	—	2	1	no	—
205	C₂²×C₄×C₇	—	2	1	no	—
206	C₂²×C₄×C₇	—	2	1	no	—
207	C₂²×C₄×C₇	—	2	1	no	—
208	C₂²×C₄×C₇	—	2	1	no	—
209	C₂²×C₄×C₇	—	2	1	no	—
210	C₂²×C₄×C₇	—	2	1	no	—
211	C₂²×C₄×C₇	—	2	1	no	—
212	C₂²×C₄×C₇	—	2	1	no	—
213	C₂²×C₄×C₇	—	2	1	no	—
214	C₂²×C₄×C₇	—	2	1	no	—
215	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
216	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
217	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
218	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
219	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
220	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
221	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
222	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
223	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
224	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
225	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₇	#41	1	2	yes	—
228	C₂²×C₄×C₇	#41	1	2	yes	—
229	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
230	C₇×M₁₆	—	4	4	no	—
231	C₇×M₁₆	—	4	4	no	—
232	C₇×M₁₆	—	4	4	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	—	2	1	no	—
245	C₂×C₇×C₈	—	2	1	no	—
246	C₂×C₇×C₈	—	2	1	no	—
247	C₂×C₇×C₈	—	2	1	no	—
248	C₂×C₇×C₈	—	2	1	no	—
249	C₂×C₇×C₈	—	2	1	no	—
250	C₂×C₇×C₈	—	2	1	no	—
251	C₂×C₇×C₈	—	2	1	no	—
252	C₂×C₇×C₈	—	2	1	no	—
253	C₂×C₇×C₈	—	4	4	no	—
254	C₂×C₇×C₈	—	4	4	no	—
255	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
256	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
257	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
258	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
259	C₇×C₄⋊C₄	—	2	2	no	—
260	C₇×C₄⋊C₄	—	2	2	no	—
261	C₇×C₄⋊C₄	—	4	1	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	—	2	2	no	—
266	C₇×C₂²⋊C₄	—	2	2	no	—
267	C₇×C₂²⋊C₄	—	2	2	no	—
268	C₇×C₂²⋊C₄	—	4	1	no	—
269	C₇×C₂²⋊C₄	—	4	1	no	—
270	C₇×C₂²⋊C₄	—	4	1	no	—
271	C₇×C₂²⋊C₄	—	4	1	no	—
272	C₇×C₂²⋊C₄	—	4	1	no	—
273	C₇×C₂²⋊C₄	—	4	1	no	—
274	C₄²×C₇	—	2	1	no	—
275	C₄²×C₇	—	2	1	no	—
276	C₄²×C₇	—	2	1	no	—
277	C₄²×C₇	—	2	1	no	—
278	C₄²×C₇	—	2	1	no	—
279	C₄²×C₇	—	2	1	no	—
280	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
281	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
282	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
283	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
284	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
285	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
287	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
288	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
289	#436	—	2	4	no	—
290	#435	—	2	4	no	—
291	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
292	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
293	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
294	#408	—	2	4	no	—
295	#408	—	2	4	no	—
296	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
297	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
298	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
299	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
300	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
301	C₂×C₂²⋊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×#97	C₂²×C₇	1	1	yes	characteristic
308	C₂×#97	C₂²×C₇	1	1	yes	characteristic
309	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
310	#395	C₄×C₇	1	1	yes	characteristic
311	#394	C₄×C₇	1	1	yes	characteristic
312	#394	C₄×C₇	1	1	yes	characteristic
313	#394	C₄×C₇	1	1	yes	characteristic
314	#393	C₄×C₇	1	1	yes	characteristic
315	#392	C₄×C₇	1	1	yes	characteristic
316	#392	C₄×C₇	1	1	yes	characteristic
317	#392	C₄×C₇	1	1	yes	characteristic
318	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
319	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
320	C₄×C₂²⋊C₄	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	#336	C₂²×C₇	1	1	yes	characteristic
325	#336	C₂²×C₇	1	1	yes	characteristic
326	#336	C₂²×C₇	1	1	yes	characteristic
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	—	2	1	no	—
344	C₂³×C₇	—	2	1	no	—
345	C₂³×C₇	—	2	1	no	—
346	C₂³×C₇	—	2	1	no	—
347	C₂³×C₇	—	2	1	no	—
348	C₂³×C₇	—	2	1	no	—
349	C₂³×C₇	—	2	1	no	—
350	C₂³×C₇	—	2	1	no	—
351	C₂³×C₇	—	2	1	no	—
352	C₂³×C₇	—	2	1	no	—
353	C₂³×C₇	C₄×D₄	1	2	yes	—
354	C₂³×C₇	C₄×D₄	1	2	yes	—
355	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
356	C₇×Q₈	—	4	4	no	—
357	C₇×D₄	—	4	4	no	—
358	C₇×D₄	—	4	4	no	—
359	C₇×D₄	—	4	4	no	—
360	C₇×D₄	—	4	4	no	—
361	C₇×D₄	—	4	4	no	—
362	C₇×D₄	—	4	4	no	—
363	C₂×C₄×C₇	—	2	1	no	—
364	C₂×C₄×C₇	—	2	1	no	—
365	C₂×C₄×C₇	—	2	1	no	—
366	C₂×C₄×C₇	—	2	1	no	—
367	C₂×C₄×C₇	—	2	1	no	—
368	C₂×C₄×C₇	—	2	1	no	—
369	C₂×C₄×C₇	—	2	2	no	—
370	C₂×C₄×C₇	—	2	2	no	—
371	C₂×C₄×C₇	—	2	2	no	—
372	C₂×C₄×C₇	—	2	2	no	—
373	C₂×C₄×C₇	—	2	2	no	—
374	C₂×C₄×C₇	—	2	2	no	—
375	C₂×C₄×C₇	—	2	2	no	—
376	C₂×C₄×C₇	—	2	2	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	—	2	1	no	—
387	C₂×C₄×C₇	—	2	1	no	—
388	C₂×C₄×C₇	—	2	1	no	—
389	C₂×C₄×C₇	—	2	1	no	—
390	C₂×C₄×C₇	—	2	1	no	—
391	C₂×C₄×C₇	—	2	1	no	—
392	C₂×C₄×C₇	—	2	1	no	—
393	C₂×C₄×C₇	—	2	1	no	—
394	C₂×C₄×C₇	—	2	1	no	—
395	C₂×C₄×C₇	—	2	1	no	—
396	C₂×C₄×C₇	—	2	1	no	—
397	C₂×C₄×C₇	—	2	1	no	—
398	C₂×C₄×C₇	—	4	1	no	—
399	C₂×C₄×C₇	—	4	1	no	—
400	C₂×C₄×C₇	—	4	1	no	—
401	C₂×C₄×C₇	—	4	1	no	—
402	C₂×C₄×C₇	—	4	1	no	—
403	C₂×C₄×C₇	—	4	1	no	—
404	C₂×C₄×C₇	—	4	1	no	—
405	C₂×C₄×C₇	—	4	1	no	—
406	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
407	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
408	C₂×C₄×C₇	#131	1	2	yes	—
409	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
412	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
413	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
414	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
415	C₇×C₈	—	2	2	no	—
416	C₇×C₈	—	2	2	no	—
417	C₇×C₈	—	2	2	no	—
418	C₇×C₈	—	2	2	no	—
419	C₇×C₈	—	4	1	no	—
420	C₇×C₈	—	4	1	no	—
421	C₇×C₈	—	4	1	no	—
422	C₇×C₈	—	4	1	no	—
423	C₂×#41	—	2	2	no	—
424	C₂×#41	—	2	2	no	—
425	C₂×#41	—	2	2	no	—
426	C₂×#41	—	2	2	no	—
427	C₂×#41	—	4	1	no	—
428	C₂×#41	—	4	1	no	—
429	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
430	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
431	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
432	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
433	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
434	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
435	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
440	C₂×M₁₆	—	2	2	no	—
441	C₂×M₁₆	—	2	2	no	—
442	C₂×M₁₆	—	2	2	no	—
443	C₂×M₁₆	—	2	2	no	—
444	C₂×M₁₆	—	2	2	no	—
445	C₂×M₁₆	—	2	2	no	—
446	C₂×M₁₆	—	4	1	no	—
447	C₂×M₁₆	—	4	1	no	—
448	C₂×M₁₆	—	4	1	no	—
449	C₂²×C₈	—	2	2	no	—
450	C₂²×C₈	—	2	2	no	—
451	C₂²×C₈	—	2	2	no	—
452	C₂²×C₈	—	2	2	no	—
453	C₂²×C₈	—	4	1	no	—
454	C₂²×C₈	—	4	1	no	—
455	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
456	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
460	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
461	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
463	C₄×D₄	—	2	2	no	—
464	C₄×D₄	—	2	2	no	—
465	C₄×D₄	—	2	2	no	—
466	C₄×D₄	—	2	2	no	—
467	C₄×D₄	—	4	1	no	—
468	C₄×D₄	—	4	1	no	—
469	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
471	C₂×C₄⋊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×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
481	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	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	C₄⋊C₈	—	2	2	no	—
488	C₄⋊C₈	—	2	2	no	—
489	C₄⋊C₈	—	4	1	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	—	2	2	no	—
497	C₂²⋊C₈	—	2	2	no	—
498	C₂²⋊C₈	—	4	1	no	—
499	C₂²⋊C₈	C₇×D₄	1	4	yes	complemented
500	C₂²⋊C₈	C₇×D₄	1	4	yes	complemented
501	#97	—	2	2	no	—
502	#97	—	4	1	no	—
503	C₄×C₈	—	2	2	no	—
504	#95	C₂×C₄×C₇	1	1	yes	characteristic
505	#95	C₂×C₄×C₇	1	1	yes	characteristic
506	#95	C₂×C₄×C₇	1	1	yes	characteristic
507	#95	C₂×C₄×C₇	1	1	yes	characteristic
508	#95	C₂×C₄×C₇	1	1	yes	characteristic
509	#95	C₂×C₄×C₇	1	1	yes	characteristic
510	C₂²×C₇	—	2	2	no	—
511	C₂²×C₇	—	2	2	no	—
512	C₂²×C₇	—	2	2	no	—
513	C₂²×C₇	—	2	2	no	—
514	C₂²×C₇	—	2	2	no	—
515	C₂²×C₇	—	2	2	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	—	4	1	no	—
522	C₂²×C₇	—	4	1	no	—
523	C₂²×C₇	—	4	1	no	—
524	C₂²×C₇	—	4	1	no	—
525	C₂²×C₇	—	4	1	no	—
526	C₂²×C₇	—	4	1	no	—
527	C₂²×C₇	—	4	1	no	—
528	C₂²×C₇	—	4	1	no	—
529	C₂²×C₇	—	4	1	no	—
530	C₂²×C₇	—	4	1	no	—
531	C₂²×C₇	—	4	1	no	—
532	C₂²×C₇	—	4	1	no	—
533	C₂²×C₇	—	4	1	no	—
534	C₂²×C₇	—	4	1	no	—
535	C₂²×C₇	—	4	1	no	—
536	C₂²×C₇	—	4	1	no	—
537	C₂²×C₇	—	4	1	no	—
538	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
539	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
540	C₂²×C₇	#518	1	1	yes	characteristic
541	C₂²×C₇	C₂×#131	1	1	yes	characteristic
542	C₂²×C₇	#568	1	1	yes	characteristic
543	C₂²×C₇	#568	1	1	yes	characteristic
544	C₂²×C₇	#568	1	1	yes	characteristic
545	C₄×C₇	—	2	2	no	—
546	C₄×C₇	—	2	2	no	—
547	C₄×C₇	—	2	2	no	—
548	C₄×C₇	—	4	1	no	—
549	C₄×C₇	—	4	1	no	—
550	C₄×C₇	—	4	1	no	—
551	C₄×C₇	—	4	1	no	—
552	C₄×C₇	—	4	1	no	—
553	C₄×C₇	—	4	1	no	—
554	C₄×C₇	—	4	1	no	—
555	C₄×C₇	D₄²	1	1	yes	characteristic
556	C₄×C₇	#546	1	1	yes	characteristic
557	C₄×C₇	#546	1	1	yes	characteristic
558	C₄×C₇	#551	1	1	yes	characteristic
559	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
560	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
561	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
562	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
563	#41	—	4	4	no	—
564	#41	—	4	4	no	—
565	#41	—	4	4	no	—
566	#41	—	4	4	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	4	1	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	4	1	no	—
580	C₂×D₄	—	4	1	no	—
581	C₂×D₄	—	4	1	no	—
582	C₂×D₄	—	4	1	no	—
583	C₂×D₄	—	4	1	no	—
584	C₂×D₄	—	4	1	no	—
585	C₂×D₄	—	4	1	no	—
586	C₂×D₄	—	4	1	no	—
587	C₂×D₄	—	4	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
609	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
610	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
611	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
612	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
613	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
614	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
615	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
616	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
617	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
618	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
619	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
620	C₂²×C₄	C₇×#41	1	2	yes	—
621	C₂²×C₄	C₇×#41	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
623	M₁₆	—	4	4	no	—
624	M₁₆	—	4	4	no	—
625	M₁₆	—	4	4	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	2	1	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	—	2	1	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	1	no	—
642	C₂×C₈	—	2	1	no	—
643	C₂×C₈	—	2	1	no	—
644	C₂×C₈	—	2	1	no	—
645	C₂×C₈	—	2	1	no	—
646	C₂×C₈	—	4	4	no	—
647	C₂×C₈	—	4	4	no	—
648	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
649	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
650	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
651	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	4	1	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	4	1	no	—
662	C₂²⋊C₄	—	4	1	no	—
663	C₂²⋊C₄	—	4	1	no	—
664	C₂²⋊C₄	—	4	1	no	—
665	C₂²⋊C₄	—	4	1	no	—
666	C₂²⋊C₄	—	4	1	no	—
667	C₄²	—	2	1	no	—
668	C₄²	—	2	1	no	—
669	C₄²	—	2	1	no	—
670	C₄²	—	2	1	no	—
671	C₄²	—	2	1	no	—
672	C₄²	—	2	1	no	—
673	C₂×C₇	—	4	2	no	—
674	C₂×C₇	—	4	2	no	—
675	C₂×C₇	—	8	1	no	—
676	C₂×C₇	—	8	1	no	—
677	C₂×C₇	#2358	1	1	yes	characteristic
678	C₂×C₇	#2930	1	1	yes	characteristic
679	C₂×C₇	#2932	1	1	yes	characteristic
680	C₂×C₇	#2933	1	1	yes	characteristic
681	C₂×C₇	#2935	1	1	yes	characteristic
682	C₂×C₇	#2978	1	1	yes	characteristic
683	C₂×C₇	#2981	1	1	yes	characteristic
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	C₄×C₇×D₄	1	2	yes	—
711	C₂³	C₄×C₇×D₄	1	2	yes	—
712	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
713	Q₈	—	4	4	no	—
714	D₄	—	4	4	no	—
715	D₄	—	4	4	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	4	no	—
719	D₄	—	4	4	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	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
764	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
765	C₂×C₄	C₇×#131	1	2	yes	—
766	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
767	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
768	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
769	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
770	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
771	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
772	C₈	—	2	2	no	—
773	C₈	—	2	2	no	—
774	C₈	—	2	2	no	—
775	C₈	—	2	2	no	—
776	C₈	—	4	1	no	—
777	C₈	—	4	1	no	—
778	C₈	—	4	1	no	—
779	C₈	—	4	1	no	—
780	C₇	#22849	1	1	yes	characteristic, direct product factor, Sylow
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
810	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
811	C₂²	C₇×#518	1	1	yes	characteristic
812	C₂²	C₂×C₇×#131	1	1	yes	characteristic
813	C₂²	C₇×#568	1	1	yes	characteristic
814	C₂²	C₇×#568	1	1	yes	characteristic
815	C₂²	C₇×#568	1	1	yes	characteristic
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	4	1	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	1	no	—
826	C₄	C₇×D₄²	1	1	yes	characteristic
827	C₄	C₇×#546	1	1	yes	characteristic
828	C₄	C₇×#546	1	1	yes	characteristic
829	C₄	C₇×#551	1	1	yes	characteristic
830	C₂	—	4	2	no	—
831	C₂	—	4	2	no	—
832	C₂	—	8	1	no	—
833	C₂	—	8	1	no	—
834	C₂	C₇×#2358	1	1	yes	characteristic
835	C₂	C₇×#2930	1	1	yes	characteristic
836	C₂	C₇×#2932	1	1	yes	characteristic
837	C₂	C₇×#2933	1	1	yes	characteristic
838	C₂	C₇×#2935	1	1	yes	characteristic
839	C₂	C₇×#2978	1	1	yes	characteristic
840	C₂	C₇×#2981	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	C₇×#2388	C₂
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
1. C₂×C₇×#436	C₂	semidirect
2. C₂×C₇×#435	C₂	semidirect
3. C₂×C₇×#408	C₂	semidirect
4. C₂×C₇×#408	C₂	semidirect
6. C₇×#1955	C₂	semidirect
7. C₇×#1924	C₂	semidirect
8. C₇×#1923	C₂	semidirect
9. C₇×#1870	C₂	semidirect
10. C₇×#1870	C₂	semidirect
11. C₇×#1869	C₂	semidirect
12. C₇×#1851	C₂	semidirect
13. C₇×#1850	C₂	semidirect
14. C₇×#1753	C₂	semidirect
15. C₇×#1752	C₂	semidirect
63. #22849	C₇	direct (N × H)
140. C₇×C₂²⋊C₈	D₄	semidirect
141. C₇×C₂²⋊C₈	D₄	semidirect
151. C₂×#436	C₂×C₇	semidirect
152. C₂×#435	C₂×C₇	semidirect
153. C₂×#408	C₂×C₇	semidirect
154. C₂×#408	C₂×C₇	semidirect
156. #1955	C₂×C₇	semidirect
157. #1924	C₂×C₇	semidirect
158. #1923	C₂×C₇	semidirect
159. #1870	C₂×C₇	semidirect
160. #1870	C₂×C₇	semidirect
161. #1869	C₂×C₇	semidirect
162. #1851	C₂×C₇	semidirect
163. #1850	C₂×C₇	semidirect
164. #1753	C₂×C₇	semidirect
165. #1752	C₂×C₇	semidirect
499. C₂²⋊C₈	C₇×D₄	semidirect
500. C₂²⋊C₈	C₇×D₄	semidirect
780. C₇	#22849	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×#436	2
C₂×C₇×#435	2
C₂×C₇×#408	2
C₇×#2388	2
C₇×#1955	2
C₇×#1924	2
C₇×#1923	2
C₇×#1870	2
C₇×#1869	2
C₇×#1851	2
C₇×#1850	2
C₇×#1753	2
C₇×#1752	2
#22849	7

Subgroups — C7×#22849 #13200065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22849 #13200065