Subgroups — C₂×C₇×#3314 #13238342

Order 1792.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#546	C₂	1	1	yes	maximal, characteristic
3	C₇×#3314	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#489	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#467	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×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#102	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, complemented
23	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
24	C₇×#554	—	2	4	no	—
25	C₇×#554	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×#125	—	2	1	no	—
30	C₂×C₇×#124	C₂²	1	1	yes	characteristic
31	C₂×C₇×#123	—	2	1	no	—
32	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
33	C₂×C₇×C₂²⋊Q₈	—	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	C₂²	1	1	yes	characteristic, complemented
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	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
47	C₇×#489	C₂²	1	8	yes	complemented
48	C₇×#484	C₂²	1	8	yes	complemented
49	C₇×#480	C₂²	1	8	yes	complemented
50	C₇×#474	C₂²	1	8	yes	complemented
51	C₇×#468	C₂²	1	8	yes	complemented
52	C₇×#467	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×#107	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₇×#417	C₂²	1	8	yes	complemented
63	C₂×C₇×#103	C₂²	1	1	yes	characteristic, 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×#102	C₂²	1	1	yes	characteristic
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	8	yes	complemented
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×#3314	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	—	2	1	no	—
99	C₂³×C₄×C₇	—	2	1	no	—
100	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
102	C₂×C₇×Q₁₆	—	4	2	no	—
103	C₂×C₇×Q₁₆	C₂³	1	4	yes	complemented
104	C₂×C₇×SD₁₆	—	2	4	no	—
105	C₂×C₇×SD₁₆	—	4	2	no	—
106	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
108	C₂×C₇×M₁₆	—	4	2	no	—
109	C₂×C₇×M₁₆	C₂³	1	4	yes	complemented
110	C₂²×C₇×C₈	—	4	2	no	—
111	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
112	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
113	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
114	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
115	C₂²×C₇×C₈	C₂³	1	4	yes	—
116	C₇×C₄⋊Q₈	—	2	2	no	—
117	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
118	C₇×#125	—	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	—	2	8	no	—
126	C₇×C₂²⋊Q₈	—	2	8	no	—
127	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
129	C₇×C₂²⋊Q₈	C₂³	1	4	yes	complemented
130	C₇×#121	—	2	2	no	—
131	C₇×#121	—	2	8	no	—
132	C₇×#121	C₂³	1	4	yes	—
133	C₇×#120	—	2	8	no	—
134	C₄×C₇×Q₈	—	2	2	no	—
135	C₄×C₇×Q₈	C₂³	1	4	yes	complemented
136	C₄×C₇×D₄	—	2	8	no	—
137	C₄×C₇×D₄	—	2	2	no	—
138	C₄×C₇×D₄	D₄	1	4	yes	—
139	C₄×C₇×D₄	C₂³	1	4	yes	—
140	C₄×C₇×D₄	C₂³	1	4	yes	—
141	C₂×C₇×C₄⋊C₄	—	2	1	no	—
142	C₂×C₇×C₄⋊C₄	—	2	2	no	—
143	C₂×C₇×C₄⋊C₄	—	2	1	no	—
144	C₂×C₇×C₄⋊C₄	—	2	2	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	—	2	1	no	—
149	C₂×C₇×C₄⋊C₄	—	2	1	no	—
150	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
151	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
152	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₇×C₄⋊C₄	C₂³	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	4	yes	complemented
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	1	no	—
163	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
164	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
165	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
166	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
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×#107	C₂³	1	4	yes	complemented
171	C₇×#107	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×#554	C₂×C₇	1	1	yes	characteristic, complemented
187	C₂×#546	C₂×C₇	1	1	yes	characteristic
188	#3314	C₂×C₇	1	16	yes	direct product factor
189	C₂×#489	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂×#484	C₂×C₇	1	1	yes	characteristic, complemented
191	C₂×#480	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂×#474	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#468	C₂×C₇	1	1	yes	characteristic, complemented
194	C₂×#467	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×#417	C₂×C₇	1	1	yes	characteristic, complemented
201	C₂²×#102	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	1	no	—
215	C₂×C₇×Q₈	—	2	4	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	—	8	2	no	—
221	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
222	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
223	C₂×C₇×D₄	—	2	4	no	—
224	C₂×C₇×D₄	—	2	8	no	—
225	C₂×C₇×D₄	—	2	4	no	—
226	C₂×C₇×D₄	—	2	4	no	—
227	C₂×C₇×D₄	—	2	1	no	—
228	C₂×C₇×D₄	—	2	4	no	—
229	C₂×C₇×D₄	—	2	1	no	—
230	C₂×C₇×D₄	—	2	2	no	—
231	C₂×C₇×D₄	—	2	2	no	—
232	C₂×C₇×D₄	—	2	2	no	—
233	C₂×C₇×D₄	—	4	4	no	—
234	C₂×C₇×D₄	—	4	8	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	—	2	4	no	—
255	C₂²×C₄×C₇	—	2	4	no	—
256	C₂²×C₄×C₇	—	4	4	no	—
257	C₂²×C₄×C₇	—	8	2	no	—
258	C₂²×C₄×C₇	—	8	2	no	—
259	C₂²×C₄×C₇	—	8	2	no	—
260	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
269	C₇×Q₁₆	—	4	4	no	—
270	C₇×SD₁₆	—	2	8	no	—
271	C₇×SD₁₆	—	4	4	no	—
272	C₇×M₁₆	—	4	4	no	—
273	C₂×C₇×C₈	—	2	2	no	—
274	C₂×C₇×C₈	—	2	2	no	—
275	C₂×C₇×C₈	—	2	2	no	—
276	C₂×C₇×C₈	—	2	2	no	—
277	C₂×C₇×C₈	—	4	4	no	—
278	C₂×C₇×C₈	C₂⁴	1	2	yes	—
279	C₂×C₇×C₈	C₂⁴	1	2	yes	—
280	C₂×C₇×C₈	C₂⁴	1	2	yes	—
281	C₂×C₇×C₈	C₂⁴	1	2	yes	—
282	C₇×C₄⋊C₄	—	2	1	no	—
283	C₇×C₄⋊C₄	—	2	4	no	—
284	C₇×C₄⋊C₄	—	2	1	no	—
285	C₇×C₄⋊C₄	—	2	1	no	—
286	C₇×C₄⋊C₄	—	2	4	no	—
287	C₇×C₄⋊C₄	—	2	4	no	—
288	C₇×C₄⋊C₄	—	2	4	no	—
289	C₇×C₄⋊C₄	—	2	4	no	—
290	C₇×C₄⋊C₄	—	2	4	no	—
291	C₇×C₄⋊C₄	—	2	4	no	—
292	C₇×C₄⋊C₄	—	2	1	no	—
293	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
294	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
295	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
296	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
297	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
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	—	2	4	no	—
302	C₇×C₂²⋊C₄	—	2	4	no	—
303	C₇×C₂²⋊C₄	—	2	4	no	—
304	C₇×C₂²⋊C₄	—	2	4	no	—
305	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
306	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
307	C₄²×C₇	—	2	4	no	—
308	C₄²×C₇	C₂×D₄	1	2	yes	—
309	C₄²×C₇	C₂⁴	1	2	yes	—
310	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
311	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
312	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
313	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
314	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
315	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
316	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
317	#554	—	2	4	no	—
318	#554	C₂²×C₇	1	8	yes	complemented
319	#546	—	2	4	no	—
320	#546	C₂²×C₇	1	8	yes	—
321	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
322	C₂×#125	—	2	1	no	—
323	C₂×#124	C₂²×C₇	1	1	yes	characteristic
324	C₂×#123	—	2	1	no	—
325	C₂×C₂²⋊Q₈	—	2	1	no	—
326	C₂×C₂²⋊Q₈	—	2	1	no	—
327	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
328	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
329	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
330	C₂×#121	—	2	1	no	—
331	C₂×#121	C₂²×C₇	1	1	yes	characteristic
332	C₂×#120	—	2	1	no	—
333	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
334	C₂×C₄×D₄	—	2	1	no	—
335	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
336	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
337	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
338	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
339	C₂²×C₂²⋊C₄	—	2	1	no	—
340	#489	C₂²×C₇	1	8	yes	complemented
341	#484	C₂²×C₇	1	8	yes	complemented
342	#480	C₂²×C₇	1	8	yes	complemented
343	#474	C₂²×C₇	1	8	yes	complemented
344	#468	C₂²×C₇	1	8	yes	complemented
345	#467	C₂²×C₇	1	8	yes	complemented
346	#464	C₂²×C₇	1	8	yes	complemented
347	#452	C₂²×C₇	1	8	yes	complemented
348	#450	C₂²×C₇	1	8	yes	complemented
349	#440	C₂²×C₇	1	8	yes	complemented
350	#435	C₂²×C₇	1	8	yes	complemented
351	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
352	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
353	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
354	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
355	#417	C₂²×C₇	1	8	yes	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×#103	C₂²×C₇	1	1	yes	characteristic, complemented
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×#102	C₂²×C₇	1	1	yes	characteristic
366	C₂×#102	C₂²×C₇	1	8	yes	complemented
367	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
368	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
369	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
370	C₂³×C₇	—	2	2	no	—
371	C₂³×C₇	—	2	2	no	—
372	C₂³×C₇	—	2	2	no	—
373	C₂³×C₇	—	2	4	no	—
374	C₂³×C₇	—	2	2	no	—
375	C₂³×C₇	—	2	2	no	—
376	C₂³×C₇	—	2	2	no	—
377	C₂³×C₇	—	2	2	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	8	no	—
383	C₂³×C₇	—	4	2	no	—
384	C₂³×C₇	—	4	2	no	—
385	C₂³×C₇	—	8	4	no	—
386	C₂³×C₇	—	8	16	no	—
387	C₂³×C₇	#137	1	4	yes	—
388	C₂³×C₇	C₂²×D₄	1	2	yes	—
389	C₂³×C₇	C₂²×D₄	1	2	yes	—
390	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
391	C₇×Q₈	—	2	2	no	—
392	C₇×Q₈	—	2	2	no	—
393	C₇×Q₈	—	2	2	no	—
394	C₇×Q₈	—	2	2	no	—
395	C₇×Q₈	—	4	2	no	—
396	C₇×Q₈	—	4	2	no	—
397	C₇×Q₈	—	8	4	no	—
398	C₇×D₄	—	2	8	no	—
399	C₇×D₄	—	2	4	no	—
400	C₇×D₄	—	2	2	no	—
401	C₇×D₄	—	2	2	no	—
402	C₇×D₄	—	2	2	no	—
403	C₇×D₄	—	4	8	no	—
404	C₇×D₄	—	4	8	no	—
405	C₇×D₄	—	4	2	no	—
406	C₇×D₄	—	8	4	no	—
407	C₇×D₄	C₂×#41	1	4	yes	—
408	C₂×C₄×C₇	—	2	2	no	—
409	C₂×C₄×C₇	—	2	2	no	—
410	C₂×C₄×C₇	—	2	2	no	—
411	C₂×C₄×C₇	—	2	2	no	—
412	C₂×C₄×C₇	—	2	4	no	—
413	C₂×C₄×C₇	—	2	4	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	—	2	2	no	—
423	C₂×C₄×C₇	—	2	2	no	—
424	C₂×C₄×C₇	—	4	8	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	—	4	2	no	—
430	C₂×C₄×C₇	—	4	2	no	—
431	C₂×C₄×C₇	—	8	4	no	—
432	C₂×C₄×C₇	—	8	4	no	—
433	C₂×C₄×C₇	—	8	4	no	—
434	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₇	C₂×#41	1	2	yes	—
440	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
441	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
442	C₇×C₈	—	2	2	no	—
443	C₇×C₈	—	2	2	no	—
444	C₇×C₈	—	2	2	no	—
445	C₇×C₈	—	2	2	no	—
446	C₂⁵	—	2	1	no	—
447	C₂×#41	—	2	2	no	—
448	C₂×#41	—	2	4	no	—
449	C₂×#41	—	4	2	no	—
450	C₂×#41	C₂³×C₇	1	4	yes	—
451	C₂²×Q₈	—	2	1	no	—
452	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
453	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
454	C₂²×D₄	—	2	4	no	—
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	—	2	1	no	—
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	—	2	2	no	—
459	C₂²×D₄	—	4	2	no	—
460	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
461	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
462	C₂²×D₄	C₂³×C₇	1	4	yes	—
463	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
464	C₂³×C₄	—	2	1	no	—
465	C₂³×C₄	—	2	1	no	—
466	C₂³×C₄	—	2	1	no	—
467	C₂³×C₄	—	2	1	no	—
468	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
470	C₂×Q₁₆	—	4	2	no	—
471	C₂×Q₁₆	C₂³×C₇	1	4	yes	complemented
472	C₂×SD₁₆	—	2	4	no	—
473	C₂×SD₁₆	—	4	2	no	—
474	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
475	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
476	C₂×M₁₆	—	4	2	no	—
477	C₂×M₁₆	C₂³×C₇	1	4	yes	complemented
478	C₂²×C₈	—	4	2	no	—
479	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
482	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₇	1	4	yes	—
484	C₄⋊Q₈	—	2	2	no	—
485	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
486	#125	—	2	8	no	—
487	#124	—	2	2	no	—
488	#124	C₂³×C₇	1	4	yes	—
489	#123	—	2	8	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	2	8	no	—
494	C₂²⋊Q₈	—	2	8	no	—
495	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
496	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
497	C₂²⋊Q₈	C₂³×C₇	1	4	yes	complemented
498	#121	—	2	2	no	—
499	#121	—	2	8	no	—
500	#121	C₂³×C₇	1	4	yes	—
501	#120	—	2	8	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	C₂³×C₇	1	4	yes	complemented
504	C₄×D₄	—	2	8	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	C₇×D₄	1	4	yes	—
507	C₄×D₄	C₂³×C₇	1	4	yes	—
508	C₄×D₄	C₂³×C₇	1	4	yes	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	2	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	2	no	—
513	C₂×C₄⋊C₄	—	2	1	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
522	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	8	no	—
533	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
535	C₂×C₄²	—	2	1	no	—
536	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
537	#107	C₂³×C₇	1	4	yes	complemented
538	#107	C₂³×C₇	1	4	yes	complemented
539	#107	C₂³×C₇	1	4	yes	complemented
540	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
541	#103	C₂³×C₇	1	4	yes	complemented
542	#103	C₂³×C₇	1	4	yes	complemented
543	#103	C₂³×C₇	1	4	yes	complemented
544	#103	C₂³×C₇	1	4	yes	complemented
545	#102	C₂³×C₇	1	4	yes	—
546	#102	C₂³×C₇	1	4	yes	—
547	#102	C₂³×C₇	1	4	yes	—
548	#102	C₂³×C₇	1	4	yes	—
549	#102	C₂³×C₇	1	4	yes	—
550	#102	C₂³×C₇	1	4	yes	—
551	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
552	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
553	#97	C₂³×C₇	1	4	yes	complemented
554	C₂²×C₇	—	2	2	no	—
555	C₂²×C₇	—	2	8	no	—
556	C₂²×C₇	—	2	2	no	—
557	C₂²×C₇	—	2	2	no	—
558	C₂²×C₇	—	2	4	no	—
559	C₂²×C₇	—	2	2	no	—
560	C₂²×C₇	—	2	2	no	—
561	C₂²×C₇	—	4	4	no	—
562	C₂²×C₇	—	4	8	no	—
563	C₂²×C₇	—	4	2	no	—
564	C₂²×C₇	—	4	2	no	—
565	C₂²×C₇	—	4	2	no	—
566	C₂²×C₇	—	4	2	no	—
567	C₂²×C₇	—	4	2	no	—
568	C₂²×C₇	—	8	16	no	—
569	C₂²×C₇	—	8	4	no	—
570	C₂²×C₇	#546	1	2	yes	—
571	C₂²×C₇	C₂×#137	1	4	yes	—
572	C₂²×C₇	C₂×#137	1	2	yes	—
573	C₂²×C₇	#576	1	2	yes	—
574	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
575	C₄×C₇	—	2	2	no	—
576	C₄×C₇	—	2	2	no	—
577	C₄×C₇	—	2	2	no	—
578	C₄×C₇	—	2	2	no	—
579	C₄×C₇	—	4	2	no	—
580	C₄×C₇	—	4	2	no	—
581	C₄×C₇	—	4	2	no	—
582	C₄×C₇	—	4	2	no	—
583	C₄×C₇	—	4	2	no	—
584	C₄×C₇	—	4	2	no	—
585	C₄×C₇	#546	1	2	yes	—
586	C₄×C₇	C₂²×#41	1	1	yes	characteristic
587	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
588	C₂⁴	—	2	1	no	—
589	C₂⁴	—	2	1	no	—
590	C₂⁴	—	2	4	no	—
591	C₂⁴	—	4	4	no	—
592	C₂⁴	—	4	4	no	—
593	C₂⁴	—	8	2	no	—
594	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
595	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
596	#41	—	2	8	no	—
597	#41	—	4	4	no	—
598	#41	—	4	8	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	4	no	—
602	C₂×Q₈	—	2	2	no	—
603	C₂×Q₈	—	2	2	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	8	2	no	—
607	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
608	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	8	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	—	4	8	no	—
621	C₂×D₄	—	4	4	no	—
622	C₂×D₄	—	4	4	no	—
623	C₂×D₄	—	8	2	no	—
624	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
625	C₂×D₄	C₇×#41	1	4	yes	—
626	C₂×D₄	C₂⁴×C₇	1	2	yes	—
627	C₂×D₄	C₂⁴×C₇	1	2	yes	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	4	4	no	—
643	C₂²×C₄	—	8	2	no	—
644	C₂²×C₄	—	8	2	no	—
645	C₂²×C₄	—	8	2	no	—
646	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
647	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
648	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
649	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
650	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
651	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
655	Q₁₆	—	4	4	no	—
656	SD₁₆	—	2	8	no	—
657	SD₁₆	—	4	4	no	—
658	M₁₆	—	4	4	no	—
659	C₂×C₈	—	2	2	no	—
660	C₂×C₈	—	2	2	no	—
661	C₂×C₈	—	2	2	no	—
662	C₂×C₈	—	2	2	no	—
663	C₂×C₈	—	4	4	no	—
664	C₂×C₈	C₂⁴×C₇	1	2	yes	—
665	C₂×C₈	C₂⁴×C₇	1	2	yes	—
666	C₂×C₈	C₂⁴×C₇	1	2	yes	—
667	C₂×C₈	C₂⁴×C₇	1	2	yes	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
680	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
681	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
682	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
692	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
693	C₄²	—	2	4	no	—
694	C₄²	C₂×C₇×D₄	1	2	yes	—
695	C₄²	C₂⁴×C₇	1	2	yes	—
696	C₂×C₇	—	2	4	no	—
697	C₂×C₇	—	4	2	no	—
698	C₂×C₇	—	4	4	no	—
699	C₂×C₇	—	8	2	no	—
700	C₂×C₇	#3314	1	4	yes	direct product factor
701	C₂×C₇	C₂×#546	1	1	yes	characteristic
702	C₂×C₇	C₂²×#137	1	1	yes	characteristic
703	C₂×C₇	C₂×#576	1	1	yes	characteristic
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	4	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	4	8	no	—
713	C₂³	—	4	2	no	—
714	C₂³	—	4	2	no	—
715	C₂³	—	4	2	no	—
716	C₂³	—	4	8	no	—
717	C₂³	—	4	2	no	—
718	C₂³	—	4	2	no	—
719	C₂³	—	8	4	no	—
720	C₂³	—	8	16	no	—
721	C₂³	C₇×#137	1	4	yes	—
722	C₂³	C₂²×C₇×D₄	1	2	yes	—
723	C₂³	C₂²×C₇×D₄	1	2	yes	—
724	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
725	Q₈	—	2	2	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	2	2	no	—
728	Q₈	—	2	2	no	—
729	Q₈	—	4	2	no	—
730	Q₈	—	4	2	no	—
731	Q₈	—	8	4	no	—
732	D₄	—	2	8	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	2	4	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	8	no	—
739	D₄	—	4	2	no	—
740	D₄	—	8	4	no	—
741	D₄	C₂×C₇×#41	1	4	yes	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	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	4	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	4	8	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	2	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	8	4	no	—
766	C₂×C₄	—	8	4	no	—
767	C₂×C₄	—	8	4	no	—
768	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
769	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
770	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
771	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
772	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
773	C₂×C₄	C₂×C₇×#41	1	2	yes	—
774	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
775	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
776	C₈	—	2	2	no	—
777	C₈	—	2	2	no	—
778	C₈	—	2	2	no	—
779	C₈	—	2	2	no	—
780	C₇	C₂×#3314	1	1	yes	characteristic, direct product factor, Sylow
781	C₂²	—	2	2	no	—
782	C₂²	—	2	8	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	8	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	8	16	no	—
796	C₂²	—	8	4	no	—
797	C₂²	C₇×#546	1	2	yes	—
798	C₂²	C₂×C₇×#137	1	4	yes	—
799	C₂²	C₂×C₇×#137	1	2	yes	—
800	C₂²	C₇×#576	1	2	yes	—
801	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
802	C₄	—	2	2	no	—
803	C₄	—	2	2	no	—
804	C₄	—	2	2	no	—
805	C₄	—	2	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	C₇×#546	1	2	yes	—
813	C₄	C₂²×C₇×#41	1	1	yes	characteristic
814	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
815	C₂	—	2	4	no	—
816	C₂	—	4	2	no	—
817	C₂	—	4	4	no	—
818	C₂	—	8	2	no	—
819	C₂	C₇×#3314	1	4	yes	direct product factor
820	C₂	C₂×C₇×#546	1	1	yes	characteristic
821	C₂	C₂²×C₇×#137	1	1	yes	characteristic
822	C₂	C₂×C₇×#576	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×#554	C₂	semidirect
3. C₇×#3314	C₂	direct (N × H)
4. C₂×C₇×#489	C₂	semidirect
5. C₂×C₇×#484	C₂	semidirect
6. C₂×C₇×#480	C₂	semidirect
7. C₂×C₇×#474	C₂	semidirect
8. C₂×C₇×#468	C₂	semidirect
9. C₂×C₇×#467	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×#417	C₂	semidirect
16. C₂²×C₇×#102	C₂	semidirect
19. C₂²×C₇×Q₁₆	C₂²	semidirect
22. C₂²×C₇×M₁₆	C₂²	semidirect
25. C₇×#554	C₂²	semidirect
28. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
36. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
40. C₂×C₄×C₇×Q₈	C₂²	semidirect
45. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
47. C₇×#489	C₂²	semidirect
48. C₇×#484	C₂²	semidirect
49. C₇×#480	C₂²	semidirect
50. C₇×#474	C₂²	semidirect
51. C₇×#468	C₂²	semidirect
52. C₇×#467	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×#107	C₂²	semidirect
60. C₂×C₇×#107	C₂²	semidirect
61. C₂×C₇×C₄⋊C₈	C₂²	semidirect
62. C₇×#417	C₂²	semidirect
63. C₂×C₇×#103	C₂²	semidirect
64. C₂×C₇×#103	C₂²	semidirect
65. C₂×C₇×#103	C₂²	semidirect
66. C₂×C₇×#103	C₂²	semidirect
73. C₂×C₇×#102	C₂²	semidirect
75. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₇×#97	C₂²	semidirect
77. C₂×#3314	C₇	direct (N × H)
103. C₂×C₇×Q₁₆	C₂³	semidirect
109. C₂×C₇×M₁₆	C₂³	semidirect
117. C₇×C₄⋊Q₈	C₂³	semidirect
129. C₇×C₂²⋊Q₈	C₂³	semidirect
135. C₄×C₇×Q₈	C₂³	semidirect
156. C₂×C₇×C₄⋊C₄	C₂³	semidirect
169. C₇×#107	C₂³	semidirect
170. C₇×#107	C₂³	semidirect
171. C₇×#107	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×#554	C₂×C₇	semidirect
188. #3314	C₂×C₇	direct (N × H)
189. C₂×#489	C₂×C₇	semidirect
190. C₂×#484	C₂×C₇	semidirect
191. C₂×#480	C₂×C₇	semidirect
192. C₂×#474	C₂×C₇	semidirect
193. C₂×#468	C₂×C₇	semidirect
194. C₂×#467	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×#417	C₂×C₇	semidirect
201. C₂²×#102	C₂×C₇	semidirect
312. C₂²×Q₁₆	C₂²×C₇	semidirect
315. C₂²×M₁₆	C₂²×C₇	semidirect
318. #554	C₂²×C₇	semidirect
321. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
329. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
333. C₂×C₄×Q₈	C₂²×C₇	semidirect
338. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
340. #489	C₂²×C₇	semidirect
341. #484	C₂²×C₇	semidirect
342. #480	C₂²×C₇	semidirect
343. #474	C₂²×C₇	semidirect
344. #468	C₂²×C₇	semidirect
345. #467	C₂²×C₇	semidirect
346. #464	C₂²×C₇	semidirect
347. #452	C₂²×C₇	semidirect
348. #450	C₂²×C₇	semidirect
349. #440	C₂²×C₇	semidirect
350. #435	C₂²×C₇	semidirect
351. C₂×#107	C₂²×C₇	semidirect
352. C₂×#107	C₂²×C₇	semidirect
353. C₂×#107	C₂²×C₇	semidirect
354. C₂×C₄⋊C₈	C₂²×C₇	semidirect
355. #417	C₂²×C₇	semidirect
356. C₂×#103	C₂²×C₇	semidirect
357. C₂×#103	C₂²×C₇	semidirect
358. C₂×#103	C₂²×C₇	semidirect
359. C₂×#103	C₂²×C₇	semidirect
366. C₂×#102	C₂²×C₇	semidirect
368. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
369. C₂×#97	C₂²×C₇	semidirect
471. C₂×Q₁₆	C₂³×C₇	semidirect
477. C₂×M₁₆	C₂³×C₇	semidirect
485. C₄⋊Q₈	C₂³×C₇	semidirect
497. C₂²⋊Q₈	C₂³×C₇	semidirect
503. C₄×Q₈	C₂³×C₇	semidirect
524. C₂×C₄⋊C₄	C₂³×C₇	semidirect
537. #107	C₂³×C₇	semidirect
538. #107	C₂³×C₇	semidirect
539. #107	C₂³×C₇	semidirect
540. C₄⋊C₈	C₂³×C₇	semidirect
541. #103	C₂³×C₇	semidirect
542. #103	C₂³×C₇	semidirect
543. #103	C₂³×C₇	semidirect
544. #103	C₂³×C₇	semidirect
552. C₂²⋊C₈	C₂³×C₇	semidirect
553. #97	C₂³×C₇	semidirect
700. C₂×C₇	#3314	direct (N × H)
780. C₇	C₂×#3314	direct (N × H)
819. C₂	C₇×#3314	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×#554	2
C₂×C₇×#546	2
C₇×#3314	2
C₂×C₇×#489	2
C₂×C₇×#484	2
C₂×C₇×#480	2
C₂×C₇×#474	2
C₂×C₇×#468	2
C₂×C₇×#467	2
C₂×C₇×#464	2
C₂×C₇×#452	2
C₂×C₇×#450	2
C₂×C₇×#440	2
C₂×C₇×#435	2
C₂×C₇×#417	2
C₂²×C₇×#102	2
C₂×#3314	7

Subgroups — C2×C7×#3314 #13238342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3314 #13238342