Subgroups — C₂×C₇×#3311 #13238351

Order 1792.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#546	C₂	1	1	yes	maximal, characteristic
3	C₇×#3311	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#489	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#485	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#470	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#465	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#450	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#418	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#416	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
18	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
23	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
24	C₇×#556	—	2	4	no	—
25	C₇×#556	C₂²	1	8	yes	complemented
26	C₇×#546	—	2	4	no	—
27	C₇×#546	C₂²	1	8	yes	—
28	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₇×#126	—	2	1	no	—
30	C₂×C₇×#126	—	2	1	no	—
31	C₂×C₇×#124	—	2	1	no	—
32	C₂×C₇×#124	C₂²	1	1	yes	characteristic
33	C₂×C₇×#123	—	2	1	no	—
34	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₇×#121	—	2	1	no	—
38	C₂×C₇×#121	C₂²	1	1	yes	characteristic
39	C₂×C₇×#120	—	2	1	no	—
40	C₂×C₄×C₇×Q₈	—	2	1	no	—
41	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₇×#117	C₂²	1	1	yes	characteristic
45	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
47	C₇×#489	C₂²	1	8	yes	complemented
48	C₇×#485	C₂²	1	8	yes	complemented
49	C₇×#482	C₂²	1	8	yes	complemented
50	C₇×#476	C₂²	1	8	yes	complemented
51	C₇×#470	C₂²	1	8	yes	complemented
52	C₇×#465	C₂²	1	8	yes	complemented
53	C₇×#464	C₂²	1	8	yes	complemented
54	C₇×#452	C₂²	1	8	yes	complemented
55	C₇×#450	C₂²	1	8	yes	complemented
56	C₇×#440	C₂²	1	8	yes	complemented
57	C₇×#435	C₂²	1	8	yes	complemented
58	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₇×#418	C₂²	1	8	yes	complemented
63	C₇×#416	C₂²	1	8	yes	complemented
64	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₇×#102	C₂²	1	1	yes	characteristic
69	C₂×C₇×#102	C₂²	1	1	yes	characteristic
70	C₂×C₇×#102	C₂²	1	1	yes	characteristic
71	C₂×C₇×#102	C₂²	1	1	yes	characteristic
72	C₂×C₇×#102	C₂²	1	1	yes	characteristic
73	C₂×C₇×#102	C₂²	1	1	yes	characteristic
74	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
77	C₂×#3311	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁵×C₇	—	2	1	no	—
79	C₂×C₇×#41	—	2	2	no	—
80	C₂×C₇×#41	—	2	4	no	—
81	C₂×C₇×#41	—	4	2	no	—
82	C₂×C₇×#41	C₂³	1	4	yes	—
83	C₂²×C₇×Q₈	—	2	1	no	—
84	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
85	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇×D₄	—	2	4	no	—
87	C₂²×C₇×D₄	—	2	1	no	—
88	C₂²×C₇×D₄	—	2	1	no	—
89	C₂²×C₇×D₄	—	2	1	no	—
90	C₂²×C₇×D₄	—	2	2	no	—
91	C₂²×C₇×D₄	—	4	2	no	—
92	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
93	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
94	C₂²×C₇×D₄	C₂³	1	4	yes	—
95	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₇	—	2	1	no	—
97	C₂³×C₄×C₇	—	2	1	no	—
98	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
100	C₂×C₇×Q₁₆	—	4	2	no	—
101	C₂×C₇×Q₁₆	C₂³	1	4	yes	complemented
102	C₂×C₇×SD₁₆	—	2	4	no	—
103	C₂×C₇×SD₁₆	—	4	2	no	—
104	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₇×M₁₆	—	4	2	no	—
107	C₂×C₇×M₁₆	C₂³	1	4	yes	—
108	C₂²×C₇×C₈	—	4	2	no	—
109	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
111	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
112	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
113	C₂²×C₇×C₈	C₂³	1	4	yes	complemented
114	C₇×C₄⋊Q₈	—	2	2	no	—
115	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
116	C₇×#126	—	2	8	no	—
117	C₇×#126	—	2	8	no	—
118	C₇×#124	—	2	8	no	—
119	C₇×#124	—	2	2	no	—
120	C₇×#124	C₂³	1	4	yes	—
121	C₇×#123	—	2	8	no	—
122	C₇×C₂²⋊Q₈	—	2	2	no	—
123	C₇×C₂²⋊Q₈	—	2	2	no	—
124	C₇×C₂²⋊Q₈	—	2	2	no	—
125	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
127	C₇×C₂²⋊Q₈	C₂³	1	4	yes	complemented
128	C₇×#121	—	2	2	no	—
129	C₇×#121	—	2	8	no	—
130	C₇×#121	C₂³	1	4	yes	—
131	C₇×#120	—	2	8	no	—
132	C₄×C₇×Q₈	—	2	8	no	—
133	C₄×C₇×Q₈	—	2	2	no	—
134	C₄×C₇×Q₈	C₂³	1	4	yes	complemented
135	C₄×C₇×D₄	—	2	2	no	—
136	C₄×C₇×D₄	D₄	1	4	yes	—
137	C₄×C₇×D₄	C₂³	1	4	yes	—
138	C₄×C₇×D₄	C₂³	1	4	yes	—
139	C₇×#117	—	2	2	no	—
140	C₇×#117	—	2	2	no	—
141	C₇×#117	C₂³	1	4	yes	—
142	C₇×#117	C₂³	1	4	yes	complemented
143	C₂×C₇×C₄⋊C₄	—	2	1	no	—
144	C₂×C₇×C₄⋊C₄	—	2	1	no	—
145	C₂×C₇×C₄⋊C₄	—	2	1	no	—
146	C₂×C₇×C₄⋊C₄	—	2	1	no	—
147	C₂×C₇×C₄⋊C₄	—	2	1	no	—
148	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
149	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
154	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
156	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
157	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
158	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
160	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
162	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
163	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
164	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₇	—	2	1	no	—
166	C₂×C₄²×C₇	—	2	1	no	—
167	C₂×C₄²×C₇	—	2	1	no	—
168	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
169	C₇×#107	C₂³	1	4	yes	complemented
170	C₇×#106	C₂³	1	4	yes	complemented
171	C₇×#106	C₂³	1	4	yes	complemented
172	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
173	C₇×#103	C₂³	1	4	yes	complemented
174	C₇×#103	C₂³	1	4	yes	complemented
175	C₇×#103	C₂³	1	4	yes	complemented
176	C₇×#103	C₂³	1	4	yes	complemented
177	C₇×#102	C₂³	1	4	yes	—
178	C₇×#102	C₂³	1	4	yes	—
179	C₇×#102	C₂³	1	4	yes	—
180	C₇×#102	C₂³	1	4	yes	—
181	C₇×#102	C₂³	1	4	yes	—
182	C₇×#102	C₂³	1	4	yes	—
183	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
184	C₇×C₂²⋊C₈	C₂³	1	4	yes	complemented
185	C₇×#97	C₂³	1	4	yes	complemented
186	C₂×#556	C₂×C₇	1	1	yes	characteristic, complemented
187	C₂×#546	C₂×C₇	1	1	yes	characteristic
188	#3311	C₂×C₇	1	16	yes	direct product factor
189	C₂×#489	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂×#485	C₂×C₇	1	1	yes	characteristic, complemented
191	C₂×#482	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#470	C₂×C₇	1	1	yes	characteristic, complemented
194	C₂×#465	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×#452	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×#450	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂×#440	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
200	C₂×#418	C₂×C₇	1	1	yes	characteristic, complemented
201	C₂×#416	C₂×C₇	1	1	yes	characteristic, complemented
202	C₂⁴×C₇	—	2	1	no	—
203	C₂⁴×C₇	—	2	1	no	—
204	C₂⁴×C₇	—	2	4	no	—
205	C₂⁴×C₇	—	4	4	no	—
206	C₂⁴×C₇	—	4	4	no	—
207	C₂⁴×C₇	—	8	2	no	—
208	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
209	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
210	C₇×#41	—	2	8	no	—
211	C₇×#41	—	4	4	no	—
212	C₇×#41	—	4	8	no	—
213	C₂×C₇×Q₈	—	2	1	no	—
214	C₂×C₇×Q₈	—	2	4	no	—
215	C₂×C₇×Q₈	—	2	1	no	—
216	C₂×C₇×Q₈	—	2	2	no	—
217	C₂×C₇×Q₈	—	2	2	no	—
218	C₂×C₇×Q₈	—	2	2	no	—
219	C₂×C₇×Q₈	—	2	2	no	—
220	C₂×C₇×Q₈	—	4	4	no	—
221	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
222	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
223	C₂×C₇×D₄	—	2	8	no	—
224	C₂×C₇×D₄	—	2	4	no	—
225	C₂×C₇×D₄	—	2	4	no	—
226	C₂×C₇×D₄	—	2	1	no	—
227	C₂×C₇×D₄	—	2	4	no	—
228	C₂×C₇×D₄	—	2	1	no	—
229	C₂×C₇×D₄	—	2	2	no	—
230	C₂×C₇×D₄	—	2	2	no	—
231	C₂×C₇×D₄	—	2	2	no	—
232	C₂×C₇×D₄	—	4	4	no	—
233	C₂×C₇×D₄	—	4	8	no	—
234	C₂×C₇×D₄	—	4	2	no	—
235	C₂×C₇×D₄	—	4	4	no	—
236	C₂×C₇×D₄	—	4	4	no	—
237	C₂×C₇×D₄	—	8	2	no	—
238	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
239	C₂×C₇×D₄	#41	1	4	yes	—
240	C₂×C₇×D₄	C₂⁴	1	2	yes	—
241	C₂×C₇×D₄	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₇	—	2	2	no	—
243	C₂²×C₄×C₇	—	2	2	no	—
244	C₂²×C₄×C₇	—	2	2	no	—
245	C₂²×C₄×C₇	—	2	2	no	—
246	C₂²×C₄×C₇	—	2	1	no	—
247	C₂²×C₄×C₇	—	2	1	no	—
248	C₂²×C₄×C₇	—	2	1	no	—
249	C₂²×C₄×C₇	—	2	1	no	—
250	C₂²×C₄×C₇	—	2	1	no	—
251	C₂²×C₄×C₇	—	2	1	no	—
252	C₂²×C₄×C₇	—	2	4	no	—
253	C₂²×C₄×C₇	—	2	4	no	—
254	C₂²×C₄×C₇	—	4	4	no	—
255	C₂²×C₄×C₇	—	8	2	no	—
256	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
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	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
265	C₇×Q₁₆	—	4	4	no	—
266	C₇×SD₁₆	—	2	8	no	—
267	C₇×SD₁₆	—	4	4	no	—
268	C₇×M₁₆	—	4	4	no	—
269	C₂×C₇×C₈	—	2	2	no	—
270	C₂×C₇×C₈	—	2	2	no	—
271	C₂×C₇×C₈	—	2	2	no	—
272	C₂×C₇×C₈	—	2	2	no	—
273	C₂×C₇×C₈	—	4	4	no	—
274	C₂×C₇×C₈	C₂⁴	1	2	yes	—
275	C₂×C₇×C₈	C₂⁴	1	2	yes	—
276	C₂×C₇×C₈	C₂⁴	1	2	yes	—
277	C₂×C₇×C₈	C₂⁴	1	2	yes	—
278	C₇×C₄⋊C₄	—	2	4	no	—
279	C₇×C₄⋊C₄	—	2	4	no	—
280	C₇×C₄⋊C₄	—	2	4	no	—
281	C₇×C₄⋊C₄	—	2	4	no	—
282	C₇×C₄⋊C₄	—	2	4	no	—
283	C₇×C₄⋊C₄	—	2	1	no	—
284	C₇×C₄⋊C₄	—	2	1	no	—
285	C₇×C₄⋊C₄	—	2	1	no	—
286	C₇×C₄⋊C₄	—	2	1	no	—
287	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
288	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
289	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
290	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
291	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
292	C₇×C₂²⋊C₄	—	2	4	no	—
293	C₇×C₂²⋊C₄	—	2	4	no	—
294	C₇×C₂²⋊C₄	—	2	4	no	—
295	C₇×C₂²⋊C₄	—	2	4	no	—
296	C₇×C₂²⋊C₄	—	2	4	no	—
297	C₇×C₂²⋊C₄	—	2	4	no	—
298	C₇×C₂²⋊C₄	—	2	4	no	—
299	C₇×C₂²⋊C₄	—	2	4	no	—
300	C₇×C₂²⋊C₄	—	2	4	no	—
301	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
302	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
303	C₄²×C₇	—	2	4	no	—
304	C₄²×C₇	—	2	4	no	—
305	C₄²×C₇	—	2	4	no	—
306	C₄²×C₇	C₂×D₄	1	2	yes	—
307	C₄²×C₇	C₂⁴	1	2	yes	—
308	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
309	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
310	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
311	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
312	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
313	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
314	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
315	#556	—	2	4	no	—
316	#556	C₂²×C₇	1	8	yes	complemented
317	#546	—	2	4	no	—
318	#546	C₂²×C₇	1	8	yes	—
319	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
320	C₂×#126	—	2	1	no	—
321	C₂×#126	—	2	1	no	—
322	C₂×#124	—	2	1	no	—
323	C₂×#124	C₂²×C₇	1	1	yes	characteristic
324	C₂×#123	—	2	1	no	—
325	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
326	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
327	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
328	C₂×#121	—	2	1	no	—
329	C₂×#121	C₂²×C₇	1	1	yes	characteristic
330	C₂×#120	—	2	1	no	—
331	C₂×C₄×Q₈	—	2	1	no	—
332	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
333	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
334	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
335	C₂×#117	C₂²×C₇	1	1	yes	characteristic
336	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
337	C₂²×C₂²⋊C₄	—	2	1	no	—
338	#489	C₂²×C₇	1	8	yes	complemented
339	#485	C₂²×C₇	1	8	yes	complemented
340	#482	C₂²×C₇	1	8	yes	complemented
341	#476	C₂²×C₇	1	8	yes	complemented
342	#470	C₂²×C₇	1	8	yes	complemented
343	#465	C₂²×C₇	1	8	yes	complemented
344	#464	C₂²×C₇	1	8	yes	complemented
345	#452	C₂²×C₇	1	8	yes	complemented
346	#450	C₂²×C₇	1	8	yes	complemented
347	#440	C₂²×C₇	1	8	yes	complemented
348	#435	C₂²×C₇	1	8	yes	complemented
349	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
350	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
351	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
352	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
353	#418	C₂²×C₇	1	8	yes	complemented
354	#416	C₂²×C₇	1	8	yes	complemented
355	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
356	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
357	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
358	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
359	C₂×#102	C₂²×C₇	1	1	yes	characteristic
360	C₂×#102	C₂²×C₇	1	1	yes	characteristic
361	C₂×#102	C₂²×C₇	1	1	yes	characteristic
362	C₂×#102	C₂²×C₇	1	1	yes	characteristic
363	C₂×#102	C₂²×C₇	1	1	yes	characteristic
364	C₂×#102	C₂²×C₇	1	1	yes	characteristic
365	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
366	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
367	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
368	C₂³×C₇	—	2	2	no	—
369	C₂³×C₇	—	2	2	no	—
370	C₂³×C₇	—	2	4	no	—
371	C₂³×C₇	—	2	2	no	—
372	C₂³×C₇	—	2	2	no	—
373	C₂³×C₇	—	2	2	no	—
374	C₂³×C₇	—	2	2	no	—
375	C₂³×C₇	—	2	2	no	—
376	C₂³×C₇	—	2	2	no	—
377	C₂³×C₇	—	4	8	no	—
378	C₂³×C₇	—	4	8	no	—
379	C₂³×C₇	—	4	2	no	—
380	C₂³×C₇	—	4	2	no	—
381	C₂³×C₇	—	4	2	no	—
382	C₂³×C₇	—	4	2	no	—
383	C₂³×C₇	—	4	2	no	—
384	C₂³×C₇	—	8	4	no	—
385	C₂³×C₇	—	8	16	no	—
386	C₂³×C₇	C₂²×D₄	1	2	yes	—
387	C₂³×C₇	C₂²×D₄	1	2	yes	—
388	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
389	C₇×Q₈	—	2	2	no	—
390	C₇×Q₈	—	2	2	no	—
391	C₇×Q₈	—	2	2	no	—
392	C₇×Q₈	—	2	2	no	—
393	C₇×Q₈	—	4	8	no	—
394	C₇×Q₈	—	4	2	no	—
395	C₇×Q₈	—	4	2	no	—
396	C₇×D₄	—	2	4	no	—
397	C₇×D₄	—	2	2	no	—
398	C₇×D₄	—	2	2	no	—
399	C₇×D₄	—	2	2	no	—
400	C₇×D₄	—	4	4	no	—
401	C₇×D₄	—	4	8	no	—
402	C₇×D₄	—	4	8	no	—
403	C₇×D₄	—	4	2	no	—
404	C₇×D₄	—	8	4	no	—
405	C₇×D₄	C₂×#41	1	4	yes	—
406	C₂×C₄×C₇	—	2	2	no	—
407	C₂×C₄×C₇	—	2	2	no	—
408	C₂×C₄×C₇	—	2	2	no	—
409	C₂×C₄×C₇	—	2	2	no	—
410	C₂×C₄×C₇	—	2	4	no	—
411	C₂×C₄×C₇	—	2	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	—	4	8	no	—
423	C₂×C₄×C₇	—	4	2	no	—
424	C₂×C₄×C₇	—	4	2	no	—
425	C₂×C₄×C₇	—	4	2	no	—
426	C₂×C₄×C₇	—	4	2	no	—
427	C₂×C₄×C₇	—	4	2	no	—
428	C₂×C₄×C₇	—	4	2	no	—
429	C₂×C₄×C₇	—	8	4	no	—
430	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₇	C₂×#41	1	2	yes	—
436	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
437	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
438	C₇×C₈	—	2	2	no	—
439	C₇×C₈	—	2	2	no	—
440	C₇×C₈	—	2	2	no	—
441	C₇×C₈	—	2	2	no	—
442	C₂⁵	—	2	1	no	—
443	C₂×#41	—	2	2	no	—
444	C₂×#41	—	2	4	no	—
445	C₂×#41	—	4	2	no	—
446	C₂×#41	C₂³×C₇	1	4	yes	—
447	C₂²×Q₈	—	2	1	no	—
448	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
449	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
450	C₂²×D₄	—	2	4	no	—
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	—	2	1	no	—
454	C₂²×D₄	—	2	2	no	—
455	C₂²×D₄	—	4	2	no	—
456	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
458	C₂²×D₄	C₂³×C₇	1	4	yes	—
459	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
464	C₂×Q₁₆	—	4	2	no	—
465	C₂×Q₁₆	C₂³×C₇	1	4	yes	complemented
466	C₂×SD₁₆	—	2	4	no	—
467	C₂×SD₁₆	—	4	2	no	—
468	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
469	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
470	C₂×M₁₆	—	4	2	no	—
471	C₂×M₁₆	C₂³×C₇	1	4	yes	—
472	C₂²×C₈	—	4	2	no	—
473	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₇	1	4	yes	complemented
478	C₄⋊Q₈	—	2	2	no	—
479	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
480	#126	—	2	8	no	—
481	#126	—	2	8	no	—
482	#124	—	2	8	no	—
483	#124	—	2	2	no	—
484	#124	C₂³×C₇	1	4	yes	—
485	#123	—	2	8	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
490	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
491	C₂²⋊Q₈	C₂³×C₇	1	4	yes	complemented
492	#121	—	2	2	no	—
493	#121	—	2	8	no	—
494	#121	C₂³×C₇	1	4	yes	—
495	#120	—	2	8	no	—
496	C₄×Q₈	—	2	8	no	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	C₂³×C₇	1	4	yes	complemented
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	C₇×D₄	1	4	yes	—
501	C₄×D₄	C₂³×C₇	1	4	yes	—
502	C₄×D₄	C₂³×C₇	1	4	yes	—
503	#117	—	2	2	no	—
504	#117	—	2	2	no	—
505	#117	C₂³×C₇	1	4	yes	—
506	#117	C₂³×C₇	1	4	yes	complemented
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	8	no	—
527	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	—	2	1	no	—
531	C₂×C₄²	—	2	1	no	—
532	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
533	#107	C₂³×C₇	1	4	yes	complemented
534	#106	C₂³×C₇	1	4	yes	complemented
535	#106	C₂³×C₇	1	4	yes	complemented
536	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
537	#103	C₂³×C₇	1	4	yes	complemented
538	#103	C₂³×C₇	1	4	yes	complemented
539	#103	C₂³×C₇	1	4	yes	complemented
540	#103	C₂³×C₇	1	4	yes	complemented
541	#102	C₂³×C₇	1	4	yes	—
542	#102	C₂³×C₇	1	4	yes	—
543	#102	C₂³×C₇	1	4	yes	—
544	#102	C₂³×C₇	1	4	yes	—
545	#102	C₂³×C₇	1	4	yes	—
546	#102	C₂³×C₇	1	4	yes	—
547	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
548	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
549	#97	C₂³×C₇	1	4	yes	complemented
550	C₂²×C₇	—	2	2	no	—
551	C₂²×C₇	—	2	2	no	—
552	C₂²×C₇	—	2	4	no	—
553	C₂²×C₇	—	2	2	no	—
554	C₂²×C₇	—	2	2	no	—
555	C₂²×C₇	—	2	2	no	—
556	C₂²×C₇	—	2	2	no	—
557	C₂²×C₇	—	4	4	no	—
558	C₂²×C₇	—	4	4	no	—
559	C₂²×C₇	—	4	8	no	—
560	C₂²×C₇	—	4	2	no	—
561	C₂²×C₇	—	4	2	no	—
562	C₂²×C₇	—	4	2	no	—
563	C₂²×C₇	—	4	2	no	—
564	C₂²×C₇	—	4	2	no	—
565	C₂²×C₇	—	8	16	no	—
566	C₂²×C₇	—	8	4	no	—
567	C₂²×C₇	#546	1	2	yes	—
568	C₂²×C₇	#575	1	2	yes	—
569	C₂²×C₇	#577	1	2	yes	—
570	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
571	C₄×C₇	—	2	2	no	—
572	C₄×C₇	—	2	2	no	—
573	C₄×C₇	—	2	2	no	—
574	C₄×C₇	—	2	2	no	—
575	C₄×C₇	—	4	2	no	—
576	C₄×C₇	—	4	2	no	—
577	C₄×C₇	—	4	2	no	—
578	C₄×C₇	—	4	2	no	—
579	C₄×C₇	—	4	2	no	—
580	C₄×C₇	—	4	2	no	—
581	C₄×C₇	#546	1	2	yes	—
582	C₄×C₇	C₂²×#41	1	1	yes	characteristic
583	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
584	C₂⁴	—	2	1	no	—
585	C₂⁴	—	2	1	no	—
586	C₂⁴	—	2	4	no	—
587	C₂⁴	—	4	4	no	—
588	C₂⁴	—	4	4	no	—
589	C₂⁴	—	8	2	no	—
590	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
591	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
592	#41	—	2	8	no	—
593	#41	—	4	4	no	—
594	#41	—	4	8	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	4	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	2	no	—
599	C₂×Q₈	—	2	2	no	—
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	4	4	no	—
603	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
604	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
605	C₂×D₄	—	2	8	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	2	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	—	4	8	no	—
616	C₂×D₄	—	4	2	no	—
617	C₂×D₄	—	4	4	no	—
618	C₂×D₄	—	4	4	no	—
619	C₂×D₄	—	8	2	no	—
620	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
621	C₂×D₄	C₇×#41	1	4	yes	—
622	C₂×D₄	C₂⁴×C₇	1	2	yes	—
623	C₂×D₄	C₂⁴×C₇	1	2	yes	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	4	4	no	—
637	C₂²×C₄	—	8	2	no	—
638	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
639	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
640	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
641	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
642	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
643	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
647	Q₁₆	—	4	4	no	—
648	SD₁₆	—	2	8	no	—
649	SD₁₆	—	4	4	no	—
650	M₁₆	—	4	4	no	—
651	C₂×C₈	—	2	2	no	—
652	C₂×C₈	—	2	2	no	—
653	C₂×C₈	—	2	2	no	—
654	C₂×C₈	—	2	2	no	—
655	C₂×C₈	—	4	4	no	—
656	C₂×C₈	C₂⁴×C₇	1	2	yes	—
657	C₂×C₈	C₂⁴×C₇	1	2	yes	—
658	C₂×C₈	C₂⁴×C₇	1	2	yes	—
659	C₂×C₈	C₂⁴×C₇	1	2	yes	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
670	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
671	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
684	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	4	no	—
688	C₄²	C₂×C₇×D₄	1	2	yes	—
689	C₄²	C₂⁴×C₇	1	2	yes	—
690	C₂×C₇	—	4	2	no	—
691	C₂×C₇	—	4	2	no	—
692	C₂×C₇	—	4	4	no	—
693	C₂×C₇	—	8	2	no	—
694	C₂×C₇	#3311	1	4	yes	direct product factor
695	C₂×C₇	C₂×#546	1	1	yes	characteristic
696	C₂×C₇	C₂×#575	1	1	yes	characteristic
697	C₂×C₇	C₂×#577	1	1	yes	characteristic
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	4	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	4	8	no	—
708	C₂³	—	4	8	no	—
709	C₂³	—	4	2	no	—
710	C₂³	—	4	2	no	—
711	C₂³	—	4	2	no	—
712	C₂³	—	4	2	no	—
713	C₂³	—	4	2	no	—
714	C₂³	—	8	4	no	—
715	C₂³	—	8	16	no	—
716	C₂³	C₂²×C₇×D₄	1	2	yes	—
717	C₂³	C₂²×C₇×D₄	1	2	yes	—
718	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	2	2	no	—
723	Q₈	—	4	8	no	—
724	Q₈	—	4	2	no	—
725	Q₈	—	4	2	no	—
726	D₄	—	2	2	no	—
727	D₄	—	2	2	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	4	no	—
730	D₄	—	4	4	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	8	no	—
733	D₄	—	4	2	no	—
734	D₄	—	8	4	no	—
735	D₄	C₂×C₇×#41	1	4	yes	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	4	8	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	8	4	no	—
760	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
761	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
762	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
763	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
764	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
765	C₂×C₄	C₂×C₇×#41	1	2	yes	—
766	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
767	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
768	C₈	—	2	2	no	—
769	C₈	—	2	2	no	—
770	C₈	—	2	2	no	—
771	C₈	—	2	2	no	—
772	C₇	C₂×#3311	1	1	yes	characteristic, direct product factor, Sylow
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	4	no	—
783	C₂²	—	4	4	no	—
784	C₂²	—	4	8	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	8	16	no	—
789	C₂²	—	8	4	no	—
790	C₂²	C₇×#546	1	2	yes	—
791	C₂²	C₇×#575	1	2	yes	—
792	C₂²	C₇×#577	1	2	yes	—
793	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
794	C₄	—	2	2	no	—
795	C₄	—	2	2	no	—
796	C₄	—	2	2	no	—
797	C₄	—	2	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	2	no	—
804	C₄	C₇×#546	1	2	yes	—
805	C₄	C₂²×C₇×#41	1	1	yes	characteristic
806	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
807	C₂	—	4	2	no	—
808	C₂	—	4	2	no	—
809	C₂	—	4	4	no	—
810	C₂	—	8	2	no	—
811	C₂	C₇×#3311	1	4	yes	direct product factor
812	C₂	C₂×C₇×#546	1	1	yes	characteristic
813	C₂	C₂×C₇×#575	1	1	yes	characteristic
814	C₂	C₂×C₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#556	C₂	semidirect
3. C₇×#3311	C₂	direct (N × H)
4. C₂×C₇×#489	C₂	semidirect
5. C₂×C₇×#485	C₂	semidirect
6. C₂×C₇×#482	C₂	semidirect
7. C₂×C₇×#476	C₂	semidirect
8. C₂×C₇×#470	C₂	semidirect
9. C₂×C₇×#465	C₂	semidirect
10. C₂×C₇×#464	C₂	semidirect
11. C₂×C₇×#452	C₂	semidirect
12. C₂×C₇×#450	C₂	semidirect
13. C₂×C₇×#440	C₂	semidirect
14. C₂×C₇×#435	C₂	semidirect
15. C₂×C₇×#418	C₂	semidirect
16. C₂×C₇×#416	C₂	semidirect
19. C₂²×C₇×Q₁₆	C₂²	semidirect
23. C₂³×C₇×C₈	C₂²	semidirect
25. C₇×#556	C₂²	semidirect
28. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
36. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
41. C₂×C₄×C₇×Q₈	C₂²	semidirect
45. C₂×C₇×#117	C₂²	semidirect
47. C₇×#489	C₂²	semidirect
48. C₇×#485	C₂²	semidirect
49. C₇×#482	C₂²	semidirect
50. C₇×#476	C₂²	semidirect
51. C₇×#470	C₂²	semidirect
52. C₇×#465	C₂²	semidirect
53. C₇×#464	C₂²	semidirect
54. C₇×#452	C₂²	semidirect
55. C₇×#450	C₂²	semidirect
56. C₇×#440	C₂²	semidirect
57. C₇×#435	C₂²	semidirect
58. C₂×C₇×#107	C₂²	semidirect
59. C₂×C₇×#106	C₂²	semidirect
60. C₂×C₇×#106	C₂²	semidirect
61. C₂×C₇×C₄⋊C₈	C₂²	semidirect
62. C₇×#418	C₂²	semidirect
63. C₇×#416	C₂²	semidirect
64. C₂×C₇×#103	C₂²	semidirect
65. C₂×C₇×#103	C₂²	semidirect
66. C₂×C₇×#103	C₂²	semidirect
67. C₂×C₇×#103	C₂²	semidirect
75. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₇×#97	C₂²	semidirect
77. C₂×#3311	C₇	direct (N × H)
101. C₂×C₇×Q₁₆	C₂³	semidirect
113. C₂²×C₇×C₈	C₂³	semidirect
115. C₇×C₄⋊Q₈	C₂³	semidirect
127. C₇×C₂²⋊Q₈	C₂³	semidirect
134. C₄×C₇×Q₈	C₂³	semidirect
142. C₇×#117	C₂³	semidirect
169. C₇×#107	C₂³	semidirect
170. C₇×#106	C₂³	semidirect
171. C₇×#106	C₂³	semidirect
172. C₇×C₄⋊C₈	C₂³	semidirect
173. C₇×#103	C₂³	semidirect
174. C₇×#103	C₂³	semidirect
175. C₇×#103	C₂³	semidirect
176. C₇×#103	C₂³	semidirect
184. C₇×C₂²⋊C₈	C₂³	semidirect
185. C₇×#97	C₂³	semidirect
186. C₂×#556	C₂×C₇	semidirect
188. #3311	C₂×C₇	direct (N × H)
189. C₂×#489	C₂×C₇	semidirect
190. C₂×#485	C₂×C₇	semidirect
191. C₂×#482	C₂×C₇	semidirect
192. C₂×#476	C₂×C₇	semidirect
193. C₂×#470	C₂×C₇	semidirect
194. C₂×#465	C₂×C₇	semidirect
195. C₂×#464	C₂×C₇	semidirect
196. C₂×#452	C₂×C₇	semidirect
197. C₂×#450	C₂×C₇	semidirect
198. C₂×#440	C₂×C₇	semidirect
199. C₂×#435	C₂×C₇	semidirect
200. C₂×#418	C₂×C₇	semidirect
201. C₂×#416	C₂×C₇	semidirect
310. C₂²×Q₁₆	C₂²×C₇	semidirect
314. C₂³×C₈	C₂²×C₇	semidirect
316. #556	C₂²×C₇	semidirect
319. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
327. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
332. C₂×C₄×Q₈	C₂²×C₇	semidirect
336. C₂×#117	C₂²×C₇	semidirect
338. #489	C₂²×C₇	semidirect
339. #485	C₂²×C₇	semidirect
340. #482	C₂²×C₇	semidirect
341. #476	C₂²×C₇	semidirect
342. #470	C₂²×C₇	semidirect
343. #465	C₂²×C₇	semidirect
344. #464	C₂²×C₇	semidirect
345. #452	C₂²×C₇	semidirect
346. #450	C₂²×C₇	semidirect
347. #440	C₂²×C₇	semidirect
348. #435	C₂²×C₇	semidirect
349. C₂×#107	C₂²×C₇	semidirect
350. C₂×#106	C₂²×C₇	semidirect
351. C₂×#106	C₂²×C₇	semidirect
352. C₂×C₄⋊C₈	C₂²×C₇	semidirect
353. #418	C₂²×C₇	semidirect
354. #416	C₂²×C₇	semidirect
355. C₂×#103	C₂²×C₇	semidirect
356. C₂×#103	C₂²×C₇	semidirect
357. C₂×#103	C₂²×C₇	semidirect
358. C₂×#103	C₂²×C₇	semidirect
366. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
367. C₂×#97	C₂²×C₇	semidirect
465. C₂×Q₁₆	C₂³×C₇	semidirect
477. C₂²×C₈	C₂³×C₇	semidirect
479. C₄⋊Q₈	C₂³×C₇	semidirect
491. C₂²⋊Q₈	C₂³×C₇	semidirect
498. C₄×Q₈	C₂³×C₇	semidirect
506. #117	C₂³×C₇	semidirect
533. #107	C₂³×C₇	semidirect
534. #106	C₂³×C₇	semidirect
535. #106	C₂³×C₇	semidirect
536. C₄⋊C₈	C₂³×C₇	semidirect
537. #103	C₂³×C₇	semidirect
538. #103	C₂³×C₇	semidirect
539. #103	C₂³×C₇	semidirect
540. #103	C₂³×C₇	semidirect
548. C₂²⋊C₈	C₂³×C₇	semidirect
549. #97	C₂³×C₇	semidirect
694. C₂×C₇	#3311	direct (N × H)
772. C₇	C₂×#3311	direct (N × H)
811. C₂	C₇×#3311	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×#556	2
C₂×C₇×#546	2
C₇×#3311	2
C₂×C₇×#489	2
C₂×C₇×#485	2
C₂×C₇×#482	2
C₂×C₇×#476	2
C₂×C₇×#470	2
C₂×C₇×#465	2
C₂×C₇×#464	2
C₂×C₇×#452	2
C₂×C₇×#450	2
C₂×C₇×#440	2
C₂×C₇×#435	2
C₂×C₇×#418	2
C₂×C₇×#416	2
C₂×#3311	7

Subgroups — C2×C7×#3311 #13238351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3311 #13238351