Subgroups — C₇×#22037 #13199253

Order 1792.

1034 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	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#408	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2388	C₂	1	1	yes	maximal, characteristic
4	C₇×#1955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1924	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1924	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1780	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1753	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	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
23	C₇×#435	—	2	4	no	—
24	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₇×#408	—	2	4	no	—
28	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
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×#97	C₂²	1	1	yes	characteristic
42	C₂×C₇×#97	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
44	C₇×#395	C₄	1	1	yes	characteristic
45	C₇×#394	C₄	1	1	yes	characteristic
46	C₇×#394	C₄	1	1	yes	characteristic
47	C₇×#394	C₄	1	1	yes	characteristic
48	C₇×#393	C₄	1	1	yes	characteristic
49	C₇×#392	C₄	1	1	yes	characteristic
50	C₇×#392	C₄	1	1	yes	characteristic
51	C₇×#392	C₄	1	1	yes	characteristic
52	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₇×C₂²⋊C₄	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	#22037	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂×C₇×#41	—	2	2	no	—
63	C₂×C₇×#41	—	2	2	no	—
64	C₂×C₇×#41	—	4	1	no	—
65	C₂×C₇×#41	—	4	1	no	—
66	C₂×C₇×#41	—	4	1	no	—
67	C₂×C₇×#41	—	4	1	no	—
68	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₇×D₄	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	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
79	C₂×C₇×M₁₆	—	4	1	no	—
80	C₂×C₇×M₁₆	—	4	1	no	—
81	C₂×C₇×M₁₆	D₄	1	4	yes	complemented
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	—	4	1	no	—
86	C₂²×C₇×C₈	—	4	1	no	—
87	C₂²×C₇×C₈	—	4	1	no	—
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	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
94	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
95	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
96	C₄×C₇×D₄	—	2	2	no	—
97	C₄×C₇×D₄	—	2	2	no	—
98	C₄×C₇×D₄	—	4	1	no	—
99	C₄×C₇×D₄	—	4	1	no	—
100	C₄×C₇×D₄	—	4	1	no	—
101	C₄×C₇×D₄	—	4	1	no	—
102	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₂×C₇×C₂²⋊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×C₄²×C₇	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
120	C₇×C₄⋊C₈	—	2	2	no	—
121	C₇×C₄⋊C₈	—	4	1	no	—
122	C₇×C₄⋊C₈	—	4	1	no	—
123	C₇×C₂²⋊C₈	—	2	2	no	—
124	C₇×C₂²⋊C₈	—	2	2	no	—
125	C₇×C₂²⋊C₈	—	2	2	no	—
126	C₇×C₂²⋊C₈	—	2	2	no	—
127	C₇×C₂²⋊C₈	—	2	2	no	—
128	C₇×C₂²⋊C₈	—	2	2	no	—
129	C₇×C₂²⋊C₈	—	2	2	no	—
130	C₇×C₂²⋊C₈	—	4	1	no	—
131	C₇×C₂²⋊C₈	—	4	1	no	—
132	C₇×C₂²⋊C₈	—	4	1	no	—
133	C₇×C₂²⋊C₈	—	4	1	no	—
134	C₇×C₂²⋊C₈	—	4	1	no	—
135	C₇×C₂²⋊C₈	—	4	1	no	—
136	C₇×#97	—	2	2	no	—
137	C₇×#97	—	4	1	no	—
138	C₄×C₇×C₈	—	4	1	no	—
139	C₇×#95	C₂×C₄	1	1	yes	characteristic
140	C₇×#95	C₂×C₄	1	1	yes	characteristic
141	C₇×#95	C₂×C₄	1	1	yes	characteristic
142	C₇×#95	C₂×C₄	1	1	yes	characteristic
143	C₇×#95	C₂×C₄	1	1	yes	characteristic
144	C₇×#95	C₂×C₄	1	1	yes	characteristic
145	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
146	C₂×#408	C₂×C₇	1	1	yes	characteristic, complemented
147	#2388	C₂×C₇	1	1	yes	characteristic
148	#1955	C₂×C₇	1	1	yes	characteristic, complemented
149	#1954	C₂×C₇	1	1	yes	characteristic, complemented
150	#1924	C₂×C₇	1	1	yes	characteristic, complemented
151	#1924	C₂×C₇	1	1	yes	characteristic, complemented
152	#1924	C₂×C₇	1	1	yes	characteristic, complemented
153	#1923	C₂×C₇	1	1	yes	characteristic, complemented
154	#1869	C₂×C₇	1	1	yes	characteristic, complemented
155	#1869	C₂×C₇	1	1	yes	characteristic, complemented
156	#1869	C₂×C₇	1	1	yes	characteristic, complemented
157	#1850	C₂×C₇	1	1	yes	characteristic, complemented
158	#1780	C₂×C₇	1	1	yes	characteristic, complemented
159	#1753	C₂×C₇	1	1	yes	characteristic, complemented
160	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
161	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
162	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
163	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
164	C₇×#41	—	4	4	no	—
165	C₇×#41	—	4	4	no	—
166	C₇×#41	—	4	4	no	—
167	C₇×#41	—	4	4	no	—
168	C₂×C₇×Q₈	—	2	2	no	—
169	C₂×C₇×Q₈	—	4	1	no	—
170	C₂×C₇×Q₈	—	4	1	no	—
171	C₂×C₇×D₄	—	2	2	no	—
172	C₂×C₇×D₄	—	2	2	no	—
173	C₂×C₇×D₄	—	2	2	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	—	2	2	no	—
178	C₂×C₇×D₄	—	2	2	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	—	4	1	no	—
183	C₂×C₇×D₄	—	4	1	no	—
184	C₂×C₇×D₄	—	4	1	no	—
185	C₂×C₇×D₄	—	4	1	no	—
186	C₂×C₇×D₄	—	4	1	no	—
187	C₂×C₇×D₄	—	4	1	no	—
188	C₂×C₇×D₄	—	4	1	no	—
189	C₂²×C₄×C₇	—	2	1	no	—
190	C₂²×C₄×C₇	—	2	1	no	—
191	C₂²×C₄×C₇	—	2	1	no	—
192	C₂²×C₄×C₇	—	2	1	no	—
193	C₂²×C₄×C₇	—	2	1	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	—	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	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	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₇	#41	1	2	yes	—
223	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
224	C₇×M₁₆	—	4	4	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	—	2	1	no	—
245	C₂×C₇×C₈	—	2	1	no	—
246	C₂×C₇×C₈	—	2	1	no	—
247	C₂×C₇×C₈	—	4	4	no	—
248	C₂×C₇×C₈	—	4	4	no	—
249	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
250	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
251	C₇×C₄⋊C₄	—	2	2	no	—
252	C₇×C₄⋊C₄	—	4	1	no	—
253	C₇×C₄⋊C₄	—	4	1	no	—
254	C₇×C₂²⋊C₄	—	2	2	no	—
255	C₇×C₂²⋊C₄	—	2	2	no	—
256	C₇×C₂²⋊C₄	—	2	2	no	—
257	C₇×C₂²⋊C₄	—	2	2	no	—
258	C₇×C₂²⋊C₄	—	4	1	no	—
259	C₇×C₂²⋊C₄	—	4	1	no	—
260	C₇×C₂²⋊C₄	—	4	1	no	—
261	C₇×C₂²⋊C₄	—	4	1	no	—
262	C₇×C₂²⋊C₄	—	4	1	no	—
263	C₇×C₂²⋊C₄	—	4	1	no	—
264	C₇×C₂²⋊C₄	—	4	1	no	—
265	C₇×C₂²⋊C₄	—	4	1	no	—
266	C₄²×C₇	—	2	1	no	—
267	C₄²×C₇	—	2	1	no	—
268	C₄²×C₇	—	2	1	no	—
269	C₄²×C₇	—	2	1	no	—
270	C₄²×C₇	—	2	1	no	—
271	C₄²×C₇	—	2	1	no	—
272	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
273	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
274	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
275	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
277	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
278	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
279	#435	—	2	4	no	—
280	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
283	#408	—	2	4	no	—
284	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
287	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
288	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
290	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
291	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
292	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
293	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
294	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
295	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
296	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
297	C₂×#97	C₂²×C₇	1	1	yes	characteristic
298	C₂×#97	C₂²×C₇	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
300	#395	C₄×C₇	1	1	yes	characteristic
301	#394	C₄×C₇	1	1	yes	characteristic
302	#394	C₄×C₇	1	1	yes	characteristic
303	#394	C₄×C₇	1	1	yes	characteristic
304	#393	C₄×C₇	1	1	yes	characteristic
305	#392	C₄×C₇	1	1	yes	characteristic
306	#392	C₄×C₇	1	1	yes	characteristic
307	#392	C₄×C₇	1	1	yes	characteristic
308	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
309	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
310	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
311	#336	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	C₂³×C₇	—	2	1	no	—
318	C₂³×C₇	—	2	1	no	—
319	C₂³×C₇	—	2	1	no	—
320	C₂³×C₇	—	2	1	no	—
321	C₂³×C₇	—	2	1	no	—
322	C₂³×C₇	—	2	1	no	—
323	C₂³×C₇	—	2	1	no	—
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	C₄×D₄	1	2	yes	—
344	C₂³×C₇	#131	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	C₇×D₄	—	4	4	no	—
351	C₇×D₄	—	4	4	no	—
352	C₇×D₄	—	4	4	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	2	no	—
358	C₂×C₄×C₇	—	2	2	no	—
359	C₂×C₄×C₇	—	2	2	no	—
360	C₂×C₄×C₇	—	2	2	no	—
361	C₂×C₄×C₇	—	2	1	no	—
362	C₂×C₄×C₇	—	2	1	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	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	—	4	1	no	—
386	C₂×C₄×C₇	—	4	1	no	—
387	C₂×C₄×C₇	—	4	1	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	—	4	1	no	—
393	C₂×C₄×C₇	—	4	1	no	—
394	C₂×C₄×C₇	—	4	1	no	—
395	C₂×C₄×C₇	—	4	1	no	—
396	C₂×C₄×C₇	—	4	1	no	—
397	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
398	C₂×C₄×C₇	#131	1	2	yes	—
399	C₂×C₄×C₇	C₂²×D₄	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	H(5,𝔽₂)	1	1	yes	characteristic
403	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
404	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
405	C₇×C₈	—	2	2	no	—
406	C₇×C₈	—	2	2	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	C₇×C₈	—	4	1	no	—
412	C₇×C₈	—	4	1	no	—
413	C₂×#41	—	2	2	no	—
414	C₂×#41	—	2	2	no	—
415	C₂×#41	—	4	1	no	—
416	C₂×#41	—	4	1	no	—
417	C₂×#41	—	4	1	no	—
418	C₂×#41	—	4	1	no	—
419	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
420	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
421	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
422	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
423	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
424	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
425	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
430	C₂×M₁₆	—	4	1	no	—
431	C₂×M₁₆	—	4	1	no	—
432	C₂×M₁₆	C₇×D₄	1	4	yes	complemented
433	C₂²×C₈	—	2	2	no	—
434	C₂²×C₈	—	2	2	no	—
435	C₂²×C₈	—	4	1	no	—
436	C₂²×C₈	—	4	1	no	—
437	C₂²×C₈	—	4	1	no	—
438	C₂²×C₈	—	4	1	no	—
439	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
442	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
443	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
445	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
447	C₄×D₄	—	2	2	no	—
448	C₄×D₄	—	2	2	no	—
449	C₄×D₄	—	4	1	no	—
450	C₄×D₄	—	4	1	no	—
451	C₄×D₄	—	4	1	no	—
452	C₄×D₄	—	4	1	no	—
453	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
457	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
460	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
471	C₄⋊C₈	—	2	2	no	—
472	C₄⋊C₈	—	4	1	no	—
473	C₄⋊C₈	—	4	1	no	—
474	C₂²⋊C₈	—	2	2	no	—
475	C₂²⋊C₈	—	2	2	no	—
476	C₂²⋊C₈	—	2	2	no	—
477	C₂²⋊C₈	—	2	2	no	—
478	C₂²⋊C₈	—	2	2	no	—
479	C₂²⋊C₈	—	2	2	no	—
480	C₂²⋊C₈	—	2	2	no	—
481	C₂²⋊C₈	—	4	1	no	—
482	C₂²⋊C₈	—	4	1	no	—
483	C₂²⋊C₈	—	4	1	no	—
484	C₂²⋊C₈	—	4	1	no	—
485	C₂²⋊C₈	—	4	1	no	—
486	C₂²⋊C₈	—	4	1	no	—
487	#97	—	2	2	no	—
488	#97	—	4	1	no	—
489	C₄×C₈	—	4	1	no	—
490	#95	C₂×C₄×C₇	1	1	yes	characteristic
491	#95	C₂×C₄×C₇	1	1	yes	characteristic
492	#95	C₂×C₄×C₇	1	1	yes	characteristic
493	#95	C₂×C₄×C₇	1	1	yes	characteristic
494	#95	C₂×C₄×C₇	1	1	yes	characteristic
495	#95	C₂×C₄×C₇	1	1	yes	characteristic
496	C₂²×C₇	—	2	2	no	—
497	C₂²×C₇	—	2	2	no	—
498	C₂²×C₇	—	2	2	no	—
499	C₂²×C₇	—	2	2	no	—
500	C₂²×C₇	—	2	2	no	—
501	C₂²×C₇	—	2	2	no	—
502	C₂²×C₇	—	4	1	no	—
503	C₂²×C₇	—	4	1	no	—
504	C₂²×C₇	—	4	1	no	—
505	C₂²×C₇	—	4	1	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	—	4	1	no	—
522	C₂²×C₇	—	4	1	no	—
523	C₂²×C₇	—	4	1	no	—
524	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
525	C₂²×C₇	#518	1	1	yes	characteristic
526	C₂²×C₇	#518	1	1	yes	characteristic
527	C₂²×C₇	C₂×#131	1	1	yes	characteristic
528	C₂²×C₇	C₂×#131	1	1	yes	characteristic
529	C₂²×C₇	#568	1	1	yes	characteristic
530	C₂²×C₇	#568	1	1	yes	characteristic
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	—	4	1	no	—
540	C₄×C₇	—	4	1	no	—
541	C₄×C₇	#534	1	1	yes	characteristic
542	C₄×C₇	#535	1	1	yes	characteristic
543	C₄×C₇	#538	1	1	yes	characteristic
544	C₄×C₇	#538	1	1	yes	characteristic
545	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
546	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
547	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
548	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
549	#41	—	4	4	no	—
550	#41	—	4	4	no	—
551	#41	—	4	4	no	—
552	#41	—	4	4	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	4	1	no	—
555	C₂×Q₈	—	4	1	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	—	4	1	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂×D₄	—	4	1	no	—
568	C₂×D₄	—	4	1	no	—
569	C₂×D₄	—	4	1	no	—
570	C₂×D₄	—	4	1	no	—
571	C₂×D₄	—	4	1	no	—
572	C₂×D₄	—	4	1	no	—
573	C₂×D₄	—	4	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	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	C₂²×C₄×C₇	1	1	yes	characteristic
597	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
598	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
599	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
600	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
601	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
602	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
603	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
604	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
605	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
606	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
607	C₂²×C₄	C₇×#41	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
609	M₁₆	—	4	4	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	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	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	—	4	4	no	—
633	C₂×C₈	—	4	4	no	—
634	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
635	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	4	1	no	—
638	C₄⋊C₄	—	4	1	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	4	1	no	—
644	C₂²⋊C₄	—	4	1	no	—
645	C₂²⋊C₄	—	4	1	no	—
646	C₂²⋊C₄	—	4	1	no	—
647	C₂²⋊C₄	—	4	1	no	—
648	C₂²⋊C₄	—	4	1	no	—
649	C₂²⋊C₄	—	4	1	no	—
650	C₂²⋊C₄	—	4	1	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	1	no	—
654	C₄²	—	2	1	no	—
655	C₄²	—	2	1	no	—
656	C₄²	—	2	1	no	—
657	C₂×C₇	—	4	2	no	—
658	C₂×C₇	—	4	2	no	—
659	C₂×C₇	—	8	1	no	—
660	C₂×C₇	—	8	1	no	—
661	C₂×C₇	#2321	1	1	yes	characteristic
662	C₂×C₇	#2933	1	1	yes	characteristic
663	C₂×C₇	#2935	1	1	yes	characteristic
664	C₂×C₇	#2976	1	1	yes	characteristic
665	C₂×C₇	#2977	1	1	yes	characteristic
666	C₂×C₇	#2980	1	1	yes	characteristic
667	C₂×C₇	#2981	1	1	yes	characteristic
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	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
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	C₄×C₇×D₄	1	2	yes	—
695	C₂³	C₇×#131	1	2	yes	—
696	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
697	Q₈	—	4	4	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	4	no	—
702	D₄	—	4	4	no	—
703	D₄	—	4	4	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	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	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
749	C₂×C₄	C₇×#131	1	2	yes	—
750	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
751	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
752	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
753	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
754	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
755	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
756	C₈	—	2	2	no	—
757	C₈	—	2	2	no	—
758	C₈	—	4	1	no	—
759	C₈	—	4	1	no	—
760	C₈	—	4	1	no	—
761	C₈	—	4	1	no	—
762	C₈	—	4	1	no	—
763	C₈	—	4	1	no	—
764	C₇	#22037	1	1	yes	characteristic, direct product factor, Sylow
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	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	C₂×C₄×C₇×D₄	1	1	yes	characteristic
794	C₂²	C₇×#518	1	1	yes	characteristic
795	C₂²	C₇×#518	1	1	yes	characteristic
796	C₂²	C₂×C₇×#131	1	1	yes	characteristic
797	C₂²	C₂×C₇×#131	1	1	yes	characteristic
798	C₂²	C₇×#568	1	1	yes	characteristic
799	C₂²	C₇×#568	1	1	yes	characteristic
800	C₄	—	2	2	no	—
801	C₄	—	2	2	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	1	no	—
804	C₄	—	4	1	no	—
805	C₄	—	4	1	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	1	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	1	no	—
810	C₄	C₇×#534	1	1	yes	characteristic
811	C₄	C₇×#535	1	1	yes	characteristic
812	C₄	C₇×#538	1	1	yes	characteristic
813	C₄	C₇×#538	1	1	yes	characteristic
814	C₂	—	4	2	no	—
815	C₂	—	4	2	no	—
816	C₂	—	8	1	no	—
817	C₂	—	8	1	no	—
818	C₂	C₇×#2321	1	1	yes	characteristic
819	C₂	C₇×#2933	1	1	yes	characteristic
820	C₂	C₇×#2935	1	1	yes	characteristic
821	C₂	C₇×#2976	1	1	yes	characteristic
822	C₂	C₇×#2977	1	1	yes	characteristic
823	C₂	C₇×#2980	1	1	yes	characteristic
824	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×#435	C₂	semidirect
2. C₂×C₇×#408	C₂	semidirect
4. C₇×#1955	C₂	semidirect
5. C₇×#1954	C₂	semidirect
6. C₇×#1924	C₂	semidirect
7. C₇×#1924	C₂	semidirect
8. C₇×#1924	C₂	semidirect
9. C₇×#1923	C₂	semidirect
10. C₇×#1869	C₂	semidirect
11. C₇×#1869	C₂	semidirect
12. C₇×#1869	C₂	semidirect
13. C₇×#1850	C₂	semidirect
14. C₇×#1780	C₂	semidirect
15. C₇×#1753	C₂	semidirect
61. #22037	C₇	direct (N × H)
81. C₂×C₇×M₁₆	D₄	semidirect
145. C₂×#435	C₂×C₇	semidirect
146. C₂×#408	C₂×C₇	semidirect
148. #1955	C₂×C₇	semidirect
149. #1954	C₂×C₇	semidirect
150. #1924	C₂×C₇	semidirect
151. #1924	C₂×C₇	semidirect
152. #1924	C₂×C₇	semidirect
153. #1923	C₂×C₇	semidirect
154. #1869	C₂×C₇	semidirect
155. #1869	C₂×C₇	semidirect
156. #1869	C₂×C₇	semidirect
157. #1850	C₂×C₇	semidirect
158. #1780	C₂×C₇	semidirect
159. #1753	C₂×C₇	semidirect
432. C₂×M₁₆	C₇×D₄	semidirect
764. C₇	#22037	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×#435	2
C₂×C₇×#408	2
C₇×#2388	2
C₇×#1955	2
C₇×#1954	2
C₇×#1924	2
C₇×#1923	2
C₇×#1869	2
C₇×#1850	2
C₇×#1780	2
C₇×#1753	2
#22037	7

Subgroups — C7×#22037 #13199253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22037 #13199253