Subgroups — C₂×C₇×#3318 #13238344

Order 1792.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3318	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#490	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#447	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#442	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	C₂²×C₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×C₇×D₄	—	2	1	no	—
18	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
19	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
21	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
25	C₇×#553	—	2	4	no	—
26	C₇×#553	C₂²	1	8	yes	complemented
27	C₇×D₄²	—	2	4	no	—
28	C₇×D₄²	C₂²	1	8	yes	complemented
29	C₂×C₇×#127	C₂²	1	1	yes	characteristic
30	C₂×C₇×#126	—	2	1	no	—
31	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₇×#123	—	2	1	no	—
33	C₂×C₇×#121	—	2	1	no	—
34	C₂×C₇×#121	—	2	1	no	—
35	C₂×C₇×#121	C₂²	1	1	yes	characteristic
36	C₂×C₇×#121	C₂²	1	1	yes	characteristic
37	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₇×#120	—	2	1	no	—
40	C₂×C₇×#120	—	2	1	no	—
41	C₂×C₄×C₇×D₄	—	2	1	no	—
42	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₇×#490	C₂²	1	8	yes	complemented
48	C₇×#482	C₂²	1	8	yes	complemented
49	C₇×#481	C₂²	1	8	yes	complemented
50	C₇×#478	C₂²	1	8	yes	complemented
51	C₇×#469	C₂²	1	8	yes	complemented
52	C₇×#466	C₂²	1	8	yes	complemented
53	C₇×#459	C₂²	1	8	yes	complemented
54	C₇×#447	C₂²	1	8	yes	complemented
55	C₇×#447	C₂²	1	8	yes	complemented
56	C₇×#442	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	C₂×C₇×#102	C₂²	1	1	yes	characteristic
64	C₂×C₇×#102	C₂²	1	1	yes	characteristic
65	C₂×C₇×#102	C₂²	1	1	yes	characteristic
66	C₂×C₇×#102	C₂²	1	8	yes	complemented
67	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
77	C₂×#3318	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁵×C₇	—	2	1	no	—
79	C₂⁵×C₇	—	2	1	no	—
80	C₂²×C₇×D₄	—	2	4	no	—
81	C₂²×C₇×D₄	—	2	4	no	—
82	C₂²×C₇×D₄	—	2	1	no	—
83	C₂²×C₇×D₄	—	2	1	no	—
84	C₂²×C₇×D₄	—	2	1	no	—
85	C₂²×C₇×D₄	—	2	1	no	—
86	C₂²×C₇×D₄	—	2	8	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	—	2	2	no	—
92	C₂²×C₇×D₄	—	2	1	no	—
93	C₂²×C₇×D₄	—	4	2	no	—
94	C₂²×C₇×D₄	—	4	2	no	—
95	C₂²×C₇×D₄	—	4	8	no	—
96	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
97	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
98	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
99	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
100	C₂²×C₇×D₄	C₂³	1	4	yes	—
101	C₂²×C₇×D₄	C₂³	1	4	yes	—
102	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₇	—	2	1	no	—
104	C₂³×C₄×C₇	—	2	1	no	—
105	C₂³×C₄×C₇	—	2	1	no	—
106	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
108	C₂×C₇×D₈	—	2	4	no	—
109	C₂×C₇×D₈	—	4	2	no	—
110	C₂×C₇×D₈	—	4	2	no	—
111	C₂×C₇×D₈	C₂³	1	4	yes	—
112	C₂×C₇×D₈	C₂³	1	4	yes	complemented
113	C₂×C₇×D₈	C₂³	1	4	yes	complemented
114	C₂×C₇×M₁₆	—	4	2	no	—
115	C₂×C₇×M₁₆	C₂³	1	4	yes	complemented
116	C₂²×C₇×C₈	—	4	2	no	—
117	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
118	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
119	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
120	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
121	C₂²×C₇×C₈	C₂³	1	4	yes	complemented
122	C₇×#127	—	2	2	no	—
123	C₇×#127	C₂³	1	4	yes	—
124	C₇×#126	—	2	8	no	—
125	C₇×#125	—	2	2	no	—
126	C₇×#125	C₂³	1	4	yes	complemented
127	C₇×#123	—	2	8	no	—
128	C₇×#121	—	2	8	no	—
129	C₇×#121	—	2	2	no	—
130	C₇×#121	—	2	2	no	—
131	C₇×#121	—	2	2	no	—
132	C₇×#121	—	2	2	no	—
133	C₇×#121	—	2	8	no	—
134	C₇×#121	C₂³	1	4	yes	—
135	C₇×#121	C₂³	1	4	yes	—
136	C₇×#121	C₂³	1	4	yes	complemented
137	C₇×#121	C₂³	1	4	yes	complemented
138	C₇×#120	—	2	8	no	—
139	C₇×#120	—	2	8	no	—
140	C₄×C₇×D₄	—	2	8	no	—
141	C₄×C₇×D₄	—	2	2	no	—
142	C₄×C₇×D₄	—	2	2	no	—
143	C₄×C₇×D₄	D₄	1	4	yes	—
144	C₄×C₇×D₄	C₂³	1	4	yes	—
145	C₄×C₇×D₄	C₂³	1	4	yes	—
146	C₄×C₇×D₄	C₂³	1	4	yes	complemented
147	C₇×#117	—	2	2	no	—
148	C₇×#117	C₂³	1	4	yes	complemented
149	C₂×C₇×C₄⋊C₄	—	2	1	no	—
150	C₂×C₇×C₄⋊C₄	—	2	2	no	—
151	C₂×C₇×C₄⋊C₄	—	2	1	no	—
152	C₂×C₇×C₄⋊C₄	—	2	1	no	—
153	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
154	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
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	1	no	—
163	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
164	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
165	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
166	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
167	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
168	C₂×C₄²×C₇	—	2	1	no	—
169	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
170	C₇×#107	C₂³	1	4	yes	complemented
171	C₇×#106	C₂³	1	4	yes	complemented
172	C₇×#106	C₂³	1	4	yes	complemented
173	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
174	C₇×#102	C₂³	1	4	yes	—
175	C₇×#102	C₂³	1	4	yes	—
176	C₇×#102	C₂³	1	4	yes	—
177	C₇×#102	C₂³	1	4	yes	complemented
178	C₇×#102	C₂³	1	4	yes	complemented
179	C₇×#102	C₂³	1	4	yes	complemented
180	C₇×#102	C₂³	1	4	yes	complemented
181	C₇×#102	C₂³	1	4	yes	complemented
182	C₇×#102	C₂³	1	4	yes	complemented
183	C₇×#102	C₂³	1	4	yes	complemented
184	C₇×C₂²⋊C₈	C₂³	1	4	yes	complemented
185	C₇×C₂²⋊C₈	C₂³	1	4	yes	complemented
186	C₇×#97	C₂³	1	4	yes	complemented
187	C₂×#553	C₂×C₇	1	1	yes	characteristic, complemented
188	C₂×D₄²	C₂×C₇	1	1	yes	characteristic, complemented
189	#3318	C₂×C₇	1	16	yes	direct product factor
190	C₂×#490	C₂×C₇	1	1	yes	characteristic, complemented
191	C₂×#481	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂×#482	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#478	C₂×C₇	1	1	yes	characteristic, complemented
194	C₂×#469	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×#466	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×#459	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×#447	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂×#447	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂×#442	C₂×C₇	1	1	yes	characteristic, complemented
200	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
201	C₂×#418	C₂×C₇	1	1	yes	characteristic, complemented
202	C₂²×#102	C₂×C₇	1	1	yes	characteristic, complemented
203	C₂⁴×C₇	—	2	1	no	—
204	C₂⁴×C₇	—	2	1	no	—
205	C₂⁴×C₇	—	2	1	no	—
206	C₂⁴×C₇	—	2	1	no	—
207	C₂⁴×C₇	—	2	4	no	—
208	C₂⁴×C₇	—	2	4	no	—
209	C₂⁴×C₇	—	4	4	no	—
210	C₂⁴×C₇	—	4	4	no	—
211	C₂⁴×C₇	—	4	4	no	—
212	C₂⁴×C₇	—	4	4	no	—
213	C₂⁴×C₇	—	8	2	no	—
214	C₂⁴×C₇	—	8	2	no	—
215	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
216	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
217	C₂×C₇×D₄	—	2	4	no	—
218	C₂×C₇×D₄	—	2	8	no	—
219	C₂×C₇×D₄	—	2	8	no	—
220	C₂×C₇×D₄	—	2	4	no	—
221	C₂×C₇×D₄	—	2	4	no	—
222	C₂×C₇×D₄	—	2	4	no	—
223	C₂×C₇×D₄	—	2	4	no	—
224	C₂×C₇×D₄	—	2	1	no	—
225	C₂×C₇×D₄	—	2	1	no	—
226	C₂×C₇×D₄	—	2	4	no	—
227	C₂×C₇×D₄	—	2	4	no	—
228	C₂×C₇×D₄	—	2	1	no	—
229	C₂×C₇×D₄	—	2	1	no	—
230	C₂×C₇×D₄	—	2	4	no	—
231	C₂×C₇×D₄	—	2	4	no	—
232	C₂×C₇×D₄	—	2	2	no	—
233	C₂×C₇×D₄	—	2	2	no	—
234	C₂×C₇×D₄	—	2	2	no	—
235	C₂×C₇×D₄	—	2	2	no	—
236	C₂×C₇×D₄	—	2	2	no	—
237	C₂×C₇×D₄	—	2	2	no	—
238	C₂×C₇×D₄	—	2	2	no	—
239	C₂×C₇×D₄	—	4	4	no	—
240	C₂×C₇×D₄	—	4	4	no	—
241	C₂×C₇×D₄	—	4	8	no	—
242	C₂×C₇×D₄	—	4	8	no	—
243	C₂×C₇×D₄	—	4	4	no	—
244	C₂×C₇×D₄	—	4	4	no	—
245	C₂×C₇×D₄	—	4	4	no	—
246	C₂×C₇×D₄	—	4	32	no	—
247	C₂×C₇×D₄	—	4	4	no	—
248	C₂×C₇×D₄	—	4	4	no	—
249	C₂×C₇×D₄	—	4	4	no	—
250	C₂×C₇×D₄	—	8	2	no	—
251	C₂×C₇×D₄	—	8	2	no	—
252	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
253	C₂×C₇×D₄	#41	1	4	yes	—
254	C₂×C₇×D₄	C₂⁴	1	2	yes	—
255	C₂×C₇×D₄	C₂⁴	1	2	yes	—
256	C₂×C₇×D₄	C₂⁴	1	2	yes	—
257	C₂×C₇×D₄	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₇	—	2	2	no	—
259	C₂²×C₄×C₇	—	2	2	no	—
260	C₂²×C₄×C₇	—	2	2	no	—
261	C₂²×C₄×C₇	—	2	2	no	—
262	C₂²×C₄×C₇	—	2	1	no	—
263	C₂²×C₄×C₇	—	2	1	no	—
264	C₂²×C₄×C₇	—	2	1	no	—
265	C₂²×C₄×C₇	—	2	1	no	—
266	C₂²×C₄×C₇	—	2	4	no	—
267	C₂²×C₄×C₇	—	2	4	no	—
268	C₂²×C₄×C₇	—	2	4	no	—
269	C₂²×C₄×C₇	—	4	4	no	—
270	C₂²×C₄×C₇	—	8	2	no	—
271	C₂²×C₄×C₇	—	8	2	no	—
272	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
281	C₇×D₈	—	2	8	no	—
282	C₇×D₈	—	4	4	no	—
283	C₇×D₈	—	4	4	no	—
284	C₇×M₁₆	—	4	4	no	—
285	C₂×C₇×C₈	—	2	2	no	—
286	C₂×C₇×C₈	—	2	2	no	—
287	C₂×C₇×C₈	—	2	2	no	—
288	C₂×C₇×C₈	—	2	2	no	—
289	C₂×C₇×C₈	—	4	4	no	—
290	C₂×C₇×C₈	C₂⁴	1	2	yes	—
291	C₂×C₇×C₈	C₂⁴	1	2	yes	—
292	C₂×C₇×C₈	C₂⁴	1	2	yes	—
293	C₂×C₇×C₈	C₂⁴	1	2	yes	—
294	C₇×C₄⋊C₄	—	2	1	no	—
295	C₇×C₄⋊C₄	—	2	1	no	—
296	C₇×C₄⋊C₄	—	2	4	no	—
297	C₇×C₄⋊C₄	—	2	4	no	—
298	C₇×C₄⋊C₄	—	2	4	no	—
299	C₇×C₄⋊C₄	—	2	1	no	—
300	C₇×C₄⋊C₄	—	2	1	no	—
301	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
302	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
303	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
305	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
306	C₇×C₂²⋊C₄	—	2	4	no	—
307	C₇×C₂²⋊C₄	—	2	4	no	—
308	C₇×C₂²⋊C₄	—	2	4	no	—
309	C₇×C₂²⋊C₄	—	2	4	no	—
310	C₇×C₂²⋊C₄	—	2	4	no	—
311	C₇×C₂²⋊C₄	—	2	4	no	—
312	C₇×C₂²⋊C₄	—	2	4	no	—
313	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
314	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
315	C₄²×C₇	—	2	4	no	—
316	C₄²×C₇	C₂×D₄	1	2	yes	—
317	C₄²×C₇	C₂⁴	1	2	yes	—
318	C₂³×D₄	—	2	1	no	—
319	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
320	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
321	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
322	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
323	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
324	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
325	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
326	#553	—	2	4	no	—
327	#553	C₂²×C₇	1	8	yes	complemented
328	D₄²	—	2	4	no	—
329	D₄²	C₂²×C₇	1	8	yes	complemented
330	C₂×#127	C₂²×C₇	1	1	yes	characteristic
331	C₂×#126	—	2	1	no	—
332	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
333	C₂×#123	—	2	1	no	—
334	C₂×#121	—	2	1	no	—
335	C₂×#121	—	2	1	no	—
336	C₂×#121	C₂²×C₇	1	1	yes	characteristic
337	C₂×#121	C₂²×C₇	1	1	yes	characteristic
338	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
339	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
340	C₂×#120	—	2	1	no	—
341	C₂×#120	—	2	1	no	—
342	C₂×C₄×D₄	—	2	1	no	—
343	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
344	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
345	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
346	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
347	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
348	#490	C₂²×C₇	1	8	yes	complemented
349	#482	C₂²×C₇	1	8	yes	complemented
350	#481	C₂²×C₇	1	8	yes	complemented
351	#478	C₂²×C₇	1	8	yes	complemented
352	#469	C₂²×C₇	1	8	yes	complemented
353	#466	C₂²×C₇	1	8	yes	complemented
354	#459	C₂²×C₇	1	8	yes	complemented
355	#447	C₂²×C₇	1	8	yes	complemented
356	#447	C₂²×C₇	1	8	yes	complemented
357	#442	C₂²×C₇	1	8	yes	complemented
358	#435	C₂²×C₇	1	8	yes	complemented
359	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
360	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
361	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
362	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
363	#418	C₂²×C₇	1	8	yes	complemented
364	C₂×#102	C₂²×C₇	1	1	yes	characteristic
365	C₂×#102	C₂²×C₇	1	1	yes	characteristic
366	C₂×#102	C₂²×C₇	1	1	yes	characteristic
367	C₂×#102	C₂²×C₇	1	8	yes	complemented
368	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
369	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
370	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
371	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
372	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
373	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
374	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
375	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
376	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
377	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
378	C₂³×C₇	—	2	2	no	—
379	C₂³×C₇	—	2	2	no	—
380	C₂³×C₇	—	2	2	no	—
381	C₂³×C₇	—	2	4	no	—
382	C₂³×C₇	—	2	2	no	—
383	C₂³×C₇	—	2	2	no	—
384	C₂³×C₇	—	2	2	no	—
385	C₂³×C₇	—	2	2	no	—
386	C₂³×C₇	—	2	2	no	—
387	C₂³×C₇	—	2	2	no	—
388	C₂³×C₇	—	4	8	no	—
389	C₂³×C₇	—	4	8	no	—
390	C₂³×C₇	—	4	8	no	—
391	C₂³×C₇	—	4	2	no	—
392	C₂³×C₇	—	4	2	no	—
393	C₂³×C₇	—	4	2	no	—
394	C₂³×C₇	—	4	2	no	—
395	C₂³×C₇	—	4	2	no	—
396	C₂³×C₇	—	4	8	no	—
397	C₂³×C₇	—	4	2	no	—
398	C₂³×C₇	—	4	2	no	—
399	C₂³×C₇	—	4	2	no	—
400	C₂³×C₇	—	4	2	no	—
401	C₂³×C₇	—	4	2	no	—
402	C₂³×C₇	—	4	2	no	—
403	C₂³×C₇	—	8	4	no	—
404	C₂³×C₇	—	8	4	no	—
405	C₂³×C₇	—	8	16	no	—
406	C₂³×C₇	—	8	16	no	—
407	C₂³×C₇	AGL(1,ℤ/8)	1	4	yes	—
408	C₂³×C₇	C₂²×D₄	1	2	yes	—
409	C₂³×C₇	C₂²×D₄	1	2	yes	—
410	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
411	C₇×D₄	—	2	8	no	—
412	C₇×D₄	—	2	4	no	—
413	C₇×D₄	—	2	2	no	—
414	C₇×D₄	—	2	2	no	—
415	C₇×D₄	—	2	2	no	—
416	C₇×D₄	—	2	2	no	—
417	C₇×D₄	—	2	2	no	—
418	C₇×D₄	—	2	2	no	—
419	C₇×D₄	—	2	2	no	—
420	C₇×D₄	—	4	8	no	—
421	C₇×D₄	—	4	8	no	—
422	C₇×D₄	—	4	8	no	—
423	C₇×D₄	—	4	8	no	—
424	C₇×D₄	—	4	8	no	—
425	C₇×D₄	—	4	8	no	—
426	C₇×D₄	—	4	2	no	—
427	C₇×D₄	—	4	2	no	—
428	C₇×D₄	—	4	2	no	—
429	C₇×D₄	—	8	4	no	—
430	C₇×D₄	—	8	4	no	—
431	C₇×D₄	C₂×#41	1	4	yes	—
432	C₂×C₄×C₇	—	2	2	no	—
433	C₂×C₄×C₇	—	2	2	no	—
434	C₂×C₄×C₇	—	2	2	no	—
435	C₂×C₄×C₇	—	2	2	no	—
436	C₂×C₄×C₇	—	2	4	no	—
437	C₂×C₄×C₇	—	2	4	no	—
438	C₂×C₄×C₇	—	2	2	no	—
439	C₂×C₄×C₇	—	2	2	no	—
440	C₂×C₄×C₇	—	2	2	no	—
441	C₂×C₄×C₇	—	2	2	no	—
442	C₂×C₄×C₇	—	2	2	no	—
443	C₂×C₄×C₇	—	2	2	no	—
444	C₂×C₄×C₇	—	2	2	no	—
445	C₂×C₄×C₇	—	2	2	no	—
446	C₂×C₄×C₇	—	4	8	no	—
447	C₂×C₄×C₇	—	4	2	no	—
448	C₂×C₄×C₇	—	4	2	no	—
449	C₂×C₄×C₇	—	4	2	no	—
450	C₂×C₄×C₇	—	4	2	no	—
451	C₂×C₄×C₇	—	8	4	no	—
452	C₂×C₄×C₇	—	8	4	no	—
453	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇	C₂×#41	1	2	yes	—
459	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
460	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
461	C₇×C₈	—	2	2	no	—
462	C₇×C₈	—	2	2	no	—
463	C₇×C₈	—	2	2	no	—
464	C₇×C₈	—	2	2	no	—
465	C₂⁵	—	2	1	no	—
466	C₂⁵	—	2	1	no	—
467	C₂²×D₄	—	2	4	no	—
468	C₂²×D₄	—	2	4	no	—
469	C₂²×D₄	—	2	1	no	—
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	—	2	8	no	—
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	—	2	1	no	—
477	C₂²×D₄	—	2	2	no	—
478	C₂²×D₄	—	2	2	no	—
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	—	4	2	no	—
481	C₂²×D₄	—	4	2	no	—
482	C₂²×D₄	—	4	8	no	—
483	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
484	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
486	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
487	C₂²×D₄	C₂³×C₇	1	4	yes	—
488	C₂²×D₄	C₂³×C₇	1	4	yes	—
489	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
490	C₂³×C₄	—	2	1	no	—
491	C₂³×C₄	—	2	1	no	—
492	C₂³×C₄	—	2	1	no	—
493	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
495	C₂×D₈	—	2	4	no	—
496	C₂×D₈	—	4	2	no	—
497	C₂×D₈	—	4	2	no	—
498	C₂×D₈	C₂³×C₇	1	4	yes	—
499	C₂×D₈	C₂³×C₇	1	4	yes	complemented
500	C₂×D₈	C₂³×C₇	1	4	yes	complemented
501	C₂×M₁₆	—	4	2	no	—
502	C₂×M₁₆	C₂³×C₇	1	4	yes	complemented
503	C₂²×C₈	—	4	2	no	—
504	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
505	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
506	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₇	1	4	yes	complemented
509	#127	—	2	2	no	—
510	#127	C₂³×C₇	1	4	yes	—
511	#126	—	2	8	no	—
512	#125	—	2	2	no	—
513	#125	C₂³×C₇	1	4	yes	complemented
514	#123	—	2	8	no	—
515	#121	—	2	8	no	—
516	#121	—	2	2	no	—
517	#121	—	2	2	no	—
518	#121	—	2	2	no	—
519	#121	—	2	2	no	—
520	#121	—	2	8	no	—
521	#121	C₂³×C₇	1	4	yes	—
522	#121	C₂³×C₇	1	4	yes	—
523	#121	C₂³×C₇	1	4	yes	complemented
524	#121	C₂³×C₇	1	4	yes	complemented
525	#120	—	2	8	no	—
526	#120	—	2	8	no	—
527	C₄×D₄	—	2	8	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	C₇×D₄	1	4	yes	—
531	C₄×D₄	C₂³×C₇	1	4	yes	—
532	C₄×D₄	C₂³×C₇	1	4	yes	—
533	C₄×D₄	C₂³×C₇	1	4	yes	complemented
534	#117	—	2	2	no	—
535	#117	C₂³×C₇	1	4	yes	complemented
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	2	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
555	C₂×C₄²	—	2	1	no	—
556	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
557	#107	C₂³×C₇	1	4	yes	complemented
558	#106	C₂³×C₇	1	4	yes	complemented
559	#106	C₂³×C₇	1	4	yes	complemented
560	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
561	#102	C₂³×C₇	1	4	yes	—
562	#102	C₂³×C₇	1	4	yes	—
563	#102	C₂³×C₇	1	4	yes	—
564	#102	C₂³×C₇	1	4	yes	complemented
565	#102	C₂³×C₇	1	4	yes	complemented
566	#102	C₂³×C₇	1	4	yes	complemented
567	#102	C₂³×C₇	1	4	yes	complemented
568	#102	C₂³×C₇	1	4	yes	complemented
569	#102	C₂³×C₇	1	4	yes	complemented
570	#102	C₂³×C₇	1	4	yes	complemented
571	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
572	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
573	#97	C₂³×C₇	1	4	yes	complemented
574	C₂²×C₇	—	2	2	no	—
575	C₂²×C₇	—	2	8	no	—
576	C₂²×C₇	—	2	2	no	—
577	C₂²×C₇	—	2	2	no	—
578	C₂²×C₇	—	2	4	no	—
579	C₂²×C₇	—	2	2	no	—
580	C₂²×C₇	—	2	2	no	—
581	C₂²×C₇	—	4	4	no	—
582	C₂²×C₇	—	4	8	no	—
583	C₂²×C₇	—	4	2	no	—
584	C₂²×C₇	—	4	2	no	—
585	C₂²×C₇	—	4	2	no	—
586	C₂²×C₇	—	4	2	no	—
587	C₂²×C₇	—	4	2	no	—
588	C₂²×C₇	—	4	2	no	—
589	C₂²×C₇	—	4	2	no	—
590	C₂²×C₇	—	4	2	no	—
591	C₂²×C₇	—	4	2	no	—
592	C₂²×C₇	—	4	2	no	—
593	C₂²×C₇	—	4	2	no	—
594	C₂²×C₇	—	8	16	no	—
595	C₂²×C₇	—	8	16	no	—
596	C₂²×C₇	—	8	4	no	—
597	C₂²×C₇	—	8	4	no	—
598	C₂²×C₇	—	8	4	no	—
599	C₂²×C₇	#546	1	2	yes	—
600	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
601	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
602	C₂²×C₇	#576	1	2	yes	—
603	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
604	C₄×C₇	—	2	2	no	—
605	C₄×C₇	—	2	2	no	—
606	C₄×C₇	—	2	2	no	—
607	C₄×C₇	—	2	2	no	—
608	C₄×C₇	—	4	2	no	—
609	C₄×C₇	—	4	2	no	—
610	C₄×C₇	—	4	2	no	—
611	C₄×C₇	—	4	2	no	—
612	C₄×C₇	#546	1	2	yes	—
613	C₄×C₇	C₂²×#41	1	1	yes	characteristic
614	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂⁴	—	2	1	no	—
616	C₂⁴	—	2	1	no	—
617	C₂⁴	—	2	1	no	—
618	C₂⁴	—	2	1	no	—
619	C₂⁴	—	2	4	no	—
620	C₂⁴	—	2	4	no	—
621	C₂⁴	—	4	4	no	—
622	C₂⁴	—	4	4	no	—
623	C₂⁴	—	4	4	no	—
624	C₂⁴	—	4	4	no	—
625	C₂⁴	—	8	2	no	—
626	C₂⁴	—	8	2	no	—
627	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
628	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	8	no	—
631	C₂×D₄	—	2	8	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	4	4	no	—
652	C₂×D₄	—	4	4	no	—
653	C₂×D₄	—	4	8	no	—
654	C₂×D₄	—	4	8	no	—
655	C₂×D₄	—	4	4	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	4	32	no	—
659	C₂×D₄	—	4	4	no	—
660	C₂×D₄	—	4	4	no	—
661	C₂×D₄	—	4	4	no	—
662	C₂×D₄	—	8	2	no	—
663	C₂×D₄	—	8	2	no	—
664	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
665	C₂×D₄	C₇×#41	1	4	yes	—
666	C₂×D₄	C₂⁴×C₇	1	2	yes	—
667	C₂×D₄	C₂⁴×C₇	1	2	yes	—
668	C₂×D₄	C₂⁴×C₇	1	2	yes	—
669	C₂×D₄	C₂⁴×C₇	1	2	yes	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	4	4	no	—
682	C₂²×C₄	—	8	2	no	—
683	C₂²×C₄	—	8	2	no	—
684	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
685	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
686	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
687	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
688	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
689	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
693	D₈	—	2	8	no	—
694	D₈	—	4	4	no	—
695	D₈	—	4	4	no	—
696	M₁₆	—	4	4	no	—
697	C₂×C₈	—	2	2	no	—
698	C₂×C₈	—	2	2	no	—
699	C₂×C₈	—	2	2	no	—
700	C₂×C₈	—	2	2	no	—
701	C₂×C₈	—	4	4	no	—
702	C₂×C₈	C₂⁴×C₇	1	2	yes	—
703	C₂×C₈	C₂⁴×C₇	1	2	yes	—
704	C₂×C₈	C₂⁴×C₇	1	2	yes	—
705	C₂×C₈	C₂⁴×C₇	1	2	yes	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
714	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
715	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
726	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
727	C₄²	—	2	4	no	—
728	C₄²	C₂×C₇×D₄	1	2	yes	—
729	C₄²	C₂⁴×C₇	1	2	yes	—
730	C₂×C₇	—	2	4	no	—
731	C₂×C₇	—	4	2	no	—
732	C₂×C₇	—	4	4	no	—
733	C₂×C₇	—	8	2	no	—
734	C₂×C₇	—	8	2	no	—
735	C₂×C₇	—	8	2	no	—
736	C₂×C₇	#3318	1	4	yes	direct product factor
737	C₂×C₇	C₂×#546	1	1	yes	characteristic
738	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
739	C₂×C₇	C₂×#576	1	1	yes	characteristic
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	4	8	no	—
751	C₂³	—	4	8	no	—
752	C₂³	—	4	8	no	—
753	C₂³	—	4	2	no	—
754	C₂³	—	4	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	2	no	—
757	C₂³	—	4	2	no	—
758	C₂³	—	4	8	no	—
759	C₂³	—	4	2	no	—
760	C₂³	—	4	2	no	—
761	C₂³	—	4	2	no	—
762	C₂³	—	4	2	no	—
763	C₂³	—	4	2	no	—
764	C₂³	—	4	2	no	—
765	C₂³	—	8	4	no	—
766	C₂³	—	8	4	no	—
767	C₂³	—	8	16	no	—
768	C₂³	—	8	16	no	—
769	C₂³	C₇×AGL(1,ℤ/8)	1	4	yes	—
770	C₂³	C₂²×C₇×D₄	1	2	yes	—
771	C₂³	C₂²×C₇×D₄	1	2	yes	—
772	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
773	D₄	—	2	8	no	—
774	D₄	—	2	2	no	—
775	D₄	—	2	2	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	2	4	no	—
782	D₄	—	4	8	no	—
783	D₄	—	4	8	no	—
784	D₄	—	4	8	no	—
785	D₄	—	4	8	no	—
786	D₄	—	4	8	no	—
787	D₄	—	4	8	no	—
788	D₄	—	4	2	no	—
789	D₄	—	4	2	no	—
790	D₄	—	4	2	no	—
791	D₄	—	8	4	no	—
792	D₄	—	8	4	no	—
793	D₄	C₂×C₇×#41	1	4	yes	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	4	8	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	8	4	no	—
814	C₂×C₄	—	8	4	no	—
815	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
816	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
817	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
818	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
819	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
820	C₂×C₄	C₂×C₇×#41	1	2	yes	—
821	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
822	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
823	C₈	—	2	2	no	—
824	C₈	—	2	2	no	—
825	C₈	—	2	2	no	—
826	C₈	—	2	2	no	—
827	C₇	C₂×#3318	1	1	yes	characteristic, direct product factor, Sylow
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	8	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	4	no	—
838	C₂²	—	4	8	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	8	16	no	—
849	C₂²	—	8	16	no	—
850	C₂²	—	8	4	no	—
851	C₂²	—	8	4	no	—
852	C₂²	—	8	4	no	—
853	C₂²	C₇×#546	1	2	yes	—
854	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
855	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
856	C₂²	C₇×#576	1	2	yes	—
857	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	C₇×#546	1	2	yes	—
867	C₄	C₂²×C₇×#41	1	1	yes	characteristic
868	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
869	C₂	—	2	4	no	—
870	C₂	—	4	2	no	—
871	C₂	—	4	4	no	—
872	C₂	—	8	2	no	—
873	C₂	—	8	2	no	—
874	C₂	—	8	2	no	—
875	C₂	C₇×#3318	1	4	yes	direct product factor
876	C₂	C₂×C₇×#546	1	1	yes	characteristic
877	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
878	C₂	C₂×C₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
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×#553	C₂	semidirect
2. C₂×C₇×D₄²	C₂	semidirect
3. C₇×#3318	C₂	direct (N × H)
4. C₂×C₇×#490	C₂	semidirect
5. C₂×C₇×#481	C₂	semidirect
6. C₂×C₇×#482	C₂	semidirect
7. C₂×C₇×#478	C₂	semidirect
8. C₂×C₇×#469	C₂	semidirect
9. C₂×C₇×#466	C₂	semidirect
10. C₂×C₇×#459	C₂	semidirect
11. C₂×C₇×#447	C₂	semidirect
12. C₂×C₇×#447	C₂	semidirect
13. C₂×C₇×#442	C₂	semidirect
14. C₂×C₇×#435	C₂	semidirect
15. C₂×C₇×#418	C₂	semidirect
16. C₂²×C₇×#102	C₂	semidirect
21. C₂²×C₇×D₈	C₂²	semidirect
22. C₂²×C₇×D₈	C₂²	semidirect
23. C₂²×C₇×M₁₆	C₂²	semidirect
24. C₂³×C₇×C₈	C₂²	semidirect
26. C₇×#553	C₂²	semidirect
28. C₇×D₄²	C₂²	semidirect
31. C₂×C₇×#125	C₂²	semidirect
37. C₂×C₇×#121	C₂²	semidirect
38. C₂×C₇×#121	C₂²	semidirect
44. C₂×C₄×C₇×D₄	C₂²	semidirect
45. C₂×C₇×#117	C₂²	semidirect
46. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
47. C₇×#490	C₂²	semidirect
48. C₇×#482	C₂²	semidirect
49. C₇×#481	C₂²	semidirect
50. C₇×#478	C₂²	semidirect
51. C₇×#469	C₂²	semidirect
52. C₇×#466	C₂²	semidirect
53. C₇×#459	C₂²	semidirect
54. C₇×#447	C₂²	semidirect
55. C₇×#447	C₂²	semidirect
56. C₇×#442	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
66. C₂×C₇×#102	C₂²	semidirect
67. C₂×C₇×#102	C₂²	semidirect
68. C₂×C₇×#102	C₂²	semidirect
69. C₂×C₇×#102	C₂²	semidirect
70. C₂×C₇×#102	C₂²	semidirect
71. C₂×C₇×#102	C₂²	semidirect
72. C₂×C₇×#102	C₂²	semidirect
73. C₂×C₇×#102	C₂²	semidirect
74. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
75. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₇×#97	C₂²	semidirect
77. C₂×#3318	C₇	direct (N × H)
112. C₂×C₇×D₈	C₂³	semidirect
113. C₂×C₇×D₈	C₂³	semidirect
115. C₂×C₇×M₁₆	C₂³	semidirect
121. C₂²×C₇×C₈	C₂³	semidirect
126. C₇×#125	C₂³	semidirect
136. C₇×#121	C₂³	semidirect
137. C₇×#121	C₂³	semidirect
146. C₄×C₇×D₄	C₂³	semidirect
148. C₇×#117	C₂³	semidirect
158. C₂×C₇×C₄⋊C₄	C₂³	semidirect
170. C₇×#107	C₂³	semidirect
171. C₇×#106	C₂³	semidirect
172. C₇×#106	C₂³	semidirect
173. C₇×C₄⋊C₈	C₂³	semidirect
177. C₇×#102	C₂³	semidirect
178. C₇×#102	C₂³	semidirect
179. C₇×#102	C₂³	semidirect
180. C₇×#102	C₂³	semidirect
181. C₇×#102	C₂³	semidirect
182. C₇×#102	C₂³	semidirect
183. C₇×#102	C₂³	semidirect
184. C₇×C₂²⋊C₈	C₂³	semidirect
185. C₇×C₂²⋊C₈	C₂³	semidirect
186. C₇×#97	C₂³	semidirect
187. C₂×#553	C₂×C₇	semidirect
188. C₂×D₄²	C₂×C₇	semidirect
189. #3318	C₂×C₇	direct (N × H)
190. C₂×#490	C₂×C₇	semidirect
191. C₂×#481	C₂×C₇	semidirect
192. C₂×#482	C₂×C₇	semidirect
193. C₂×#478	C₂×C₇	semidirect
194. C₂×#469	C₂×C₇	semidirect
195. C₂×#466	C₂×C₇	semidirect
196. C₂×#459	C₂×C₇	semidirect
197. C₂×#447	C₂×C₇	semidirect
198. C₂×#447	C₂×C₇	semidirect
199. C₂×#442	C₂×C₇	semidirect
200. C₂×#435	C₂×C₇	semidirect
201. C₂×#418	C₂×C₇	semidirect
202. C₂²×#102	C₂×C₇	semidirect
322. C₂²×D₈	C₂²×C₇	semidirect
323. C₂²×D₈	C₂²×C₇	semidirect
324. C₂²×M₁₆	C₂²×C₇	semidirect
325. C₂³×C₈	C₂²×C₇	semidirect
327. #553	C₂²×C₇	semidirect
329. D₄²	C₂²×C₇	semidirect
332. C₂×#125	C₂²×C₇	semidirect
338. C₂×#121	C₂²×C₇	semidirect
339. C₂×#121	C₂²×C₇	semidirect
345. C₂×C₄×D₄	C₂²×C₇	semidirect
346. C₂×#117	C₂²×C₇	semidirect
347. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
348. #490	C₂²×C₇	semidirect
349. #482	C₂²×C₇	semidirect
350. #481	C₂²×C₇	semidirect
351. #478	C₂²×C₇	semidirect
352. #469	C₂²×C₇	semidirect
353. #466	C₂²×C₇	semidirect
354. #459	C₂²×C₇	semidirect
355. #447	C₂²×C₇	semidirect
356. #447	C₂²×C₇	semidirect
357. #442	C₂²×C₇	semidirect
358. #435	C₂²×C₇	semidirect
359. C₂×#107	C₂²×C₇	semidirect
360. C₂×#106	C₂²×C₇	semidirect
361. C₂×#106	C₂²×C₇	semidirect
362. C₂×C₄⋊C₈	C₂²×C₇	semidirect
363. #418	C₂²×C₇	semidirect
367. C₂×#102	C₂²×C₇	semidirect
368. C₂×#102	C₂²×C₇	semidirect
369. C₂×#102	C₂²×C₇	semidirect
370. C₂×#102	C₂²×C₇	semidirect
371. C₂×#102	C₂²×C₇	semidirect
372. C₂×#102	C₂²×C₇	semidirect
373. C₂×#102	C₂²×C₇	semidirect
374. C₂×#102	C₂²×C₇	semidirect
375. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
376. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
377. C₂×#97	C₂²×C₇	semidirect
499. C₂×D₈	C₂³×C₇	semidirect
500. C₂×D₈	C₂³×C₇	semidirect
502. C₂×M₁₆	C₂³×C₇	semidirect
508. C₂²×C₈	C₂³×C₇	semidirect
513. #125	C₂³×C₇	semidirect
523. #121	C₂³×C₇	semidirect
524. #121	C₂³×C₇	semidirect
533. C₄×D₄	C₂³×C₇	semidirect
535. #117	C₂³×C₇	semidirect
545. C₂×C₄⋊C₄	C₂³×C₇	semidirect
557. #107	C₂³×C₇	semidirect
558. #106	C₂³×C₇	semidirect
559. #106	C₂³×C₇	semidirect
560. C₄⋊C₈	C₂³×C₇	semidirect
564. #102	C₂³×C₇	semidirect
565. #102	C₂³×C₇	semidirect
566. #102	C₂³×C₇	semidirect
567. #102	C₂³×C₇	semidirect
568. #102	C₂³×C₇	semidirect
569. #102	C₂³×C₇	semidirect
570. #102	C₂³×C₇	semidirect
571. C₂²⋊C₈	C₂³×C₇	semidirect
572. C₂²⋊C₈	C₂³×C₇	semidirect
573. #97	C₂³×C₇	semidirect
736. C₂×C₇	#3318	direct (N × H)
827. C₇	C₂×#3318	direct (N × H)
875. C₂	C₇×#3318	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×#553	2
C₂×C₇×D₄²	2
C₇×#3318	2
C₂×C₇×#490	2
C₂×C₇×#481	2
C₂×C₇×#482	2
C₂×C₇×#478	2
C₂×C₇×#469	2
C₂×C₇×#466	2
C₂×C₇×#459	2
C₂×C₇×#447	2
C₂×C₇×#442	2
C₂×C₇×#435	2
C₂×C₇×#418	2
C₂²×C₇×#102	2
C₂×#3318	7

Subgroups — C2×C7×#3318 #13238344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3318 #13238344