Subgroups — C₂×C₇×#3319 #13238352

Order 1792.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3319	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×#474	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#449	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	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×SD₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
21	C₂²×C₇×D₈	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×#555	—	2	4	no	—
25	C₇×#555	C₂²	1	8	yes	complemented
26	C₇×#546	—	2	4	no	—
27	C₇×#546	C₂²	1	8	yes	complemented
28	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₇×#124	—	2	1	no	—
30	C₂×C₇×#124	—	2	1	no	—
31	C₂×C₇×#124	C₂²	1	1	yes	characteristic
32	C₂×C₇×#123	—	2	1	no	—
33	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×#121	—	2	1	no	—
35	C₂×C₇×#121	—	2	1	no	—
36	C₂×C₇×#121	C₂²	1	1	yes	characteristic
37	C₂×C₇×#121	C₂²	1	1	yes	characteristic
38	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₇×#120	—	2	1	no	—
40	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₇×#117	—	2	1	no	—
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×#474	C₂²	1	8	yes	complemented
51	C₇×#468	C₂²	1	8	yes	complemented
52	C₇×#466	C₂²	1	8	yes	complemented
53	C₇×#463	C₂²	1	8	yes	complemented
54	C₇×#449	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×#107	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×#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	1	yes	characteristic, 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×#3319	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×D₄	—	2	4	no	—
86	C₂²×C₇×D₄	—	2	1	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	1	no	—
91	C₂²×C₇×D₄	—	2	2	no	—
92	C₂²×C₇×D₄	—	4	2	no	—
93	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
94	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
95	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
96	C₂²×C₇×D₄	C₂³	1	4	yes	—
97	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇	—	2	1	no	—
99	C₂³×C₄×C₇	—	2	1	no	—
100	C₂³×C₄×C₇	—	2	1	no	—
101	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
103	C₂×C₇×SD₁₆	—	4	2	no	—
104	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
105	C₂×C₇×D₈	—	2	4	no	—
106	C₂×C₇×D₈	—	4	2	no	—
107	C₂×C₇×D₈	C₂³	1	4	yes	—
108	C₂×C₇×D₈	C₂³	1	4	yes	—
109	C₂×C₇×M₁₆	—	4	2	no	—
110	C₂×C₇×M₁₆	C₂³	1	4	yes	—
111	C₂²×C₇×C₈	—	4	2	no	—
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	1	yes	characteristic
116	C₂²×C₇×C₈	C₂³	1	4	yes	complemented
117	C₇×C₄⋊Q₈	—	2	2	no	—
118	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
119	C₇×#124	—	2	8	no	—
120	C₇×#124	—	2	8	no	—
121	C₇×#124	—	2	2	no	—
122	C₇×#124	C₂³	1	4	yes	—
123	C₇×#123	—	2	8	no	—
124	C₇×C₂²⋊Q₈	—	2	2	no	—
125	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₇×#121	—	2	8	no	—
127	C₇×#121	—	2	2	no	—
128	C₇×#121	—	2	2	no	—
129	C₇×#121	—	2	2	no	—
130	C₇×#121	—	2	8	no	—
131	C₇×#121	C₂³	1	4	yes	—
132	C₇×#121	C₂³	1	4	yes	—
133	C₇×#121	C₂³	1	4	yes	complemented
134	C₇×#120	—	2	8	no	—
135	C₄×C₇×D₄	—	2	2	no	—
136	C₄×C₇×D₄	—	2	2	no	—
137	C₄×C₇×D₄	D₄	1	4	yes	—
138	C₄×C₇×D₄	C₂³	1	4	yes	—
139	C₄×C₇×D₄	C₂³	1	4	yes	—
140	C₄×C₇×D₄	C₂³	1	4	yes	complemented
141	C₇×#117	—	2	2	no	—
142	C₇×#117	—	2	2	no	—
143	C₇×#117	—	2	8	no	—
144	C₇×#117	C₂³	1	4	yes	—
145	C₇×#117	C₂³	1	4	yes	complemented
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	1	no	—
163	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
164	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
165	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
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×#107	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×#102	C₂³	1	4	yes	—
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	complemented
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×#555	C₂×C₇	1	1	yes	characteristic, complemented
187	C₂×#546	C₂×C₇	1	1	yes	characteristic, complemented
188	#3319	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×#474	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#468	C₂×C₇	1	1	yes	characteristic, complemented
194	C₂×#466	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×#463	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×#449	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×#447	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂×#442	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	1	no	—
205	C₂⁴×C₇	—	2	4	no	—
206	C₂⁴×C₇	—	4	4	no	—
207	C₂⁴×C₇	—	4	4	no	—
208	C₂⁴×C₇	—	8	2	no	—
209	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
210	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
211	C₇×#41	—	2	8	no	—
212	C₇×#41	—	4	4	no	—
213	C₇×#41	—	4	8	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	—	8	2	no	—
219	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
220	C₂×C₇×D₄	—	2	8	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	4	no	—
225	C₂×C₇×D₄	—	2	1	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	—	2	2	no	—
233	C₂×C₇×D₄	—	2	2	no	—
234	C₂×C₇×D₄	—	4	4	no	—
235	C₂×C₇×D₄	—	4	8	no	—
236	C₂×C₇×D₄	—	4	2	no	—
237	C₂×C₇×D₄	—	4	4	no	—
238	C₂×C₇×D₄	—	4	4	no	—
239	C₂×C₇×D₄	—	8	2	no	—
240	C₂×C₇×D₄	—	8	2	no	—
241	C₂×C₇×D₄	—	8	2	no	—
242	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
243	C₂×C₇×D₄	#41	1	4	yes	—
244	C₂×C₇×D₄	C₂⁴	1	2	yes	—
245	C₂×C₇×D₄	C₂⁴	1	2	yes	—
246	C₂×C₇×D₄	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₇	—	2	2	no	—
248	C₂²×C₄×C₇	—	2	2	no	—
249	C₂²×C₄×C₇	—	2	2	no	—
250	C₂²×C₄×C₇	—	2	2	no	—
251	C₂²×C₄×C₇	—	2	1	no	—
252	C₂²×C₄×C₇	—	2	1	no	—
253	C₂²×C₄×C₇	—	2	1	no	—
254	C₂²×C₄×C₇	—	2	1	no	—
255	C₂²×C₄×C₇	—	2	1	no	—
256	C₂²×C₄×C₇	—	2	4	no	—
257	C₂²×C₄×C₇	—	2	4	no	—
258	C₂²×C₄×C₇	—	2	4	no	—
259	C₂²×C₄×C₇	—	4	4	no	—
260	C₂²×C₄×C₇	—	4	4	no	—
261	C₂²×C₄×C₇	—	8	2	no	—
262	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
271	C₇×SD₁₆	—	4	4	no	—
272	C₇×D₈	—	2	8	no	—
273	C₇×D₈	—	4	4	no	—
274	C₇×M₁₆	—	4	4	no	—
275	C₂×C₇×C₈	—	2	2	no	—
276	C₂×C₇×C₈	—	2	2	no	—
277	C₂×C₇×C₈	—	2	2	no	—
278	C₂×C₇×C₈	—	2	2	no	—
279	C₂×C₇×C₈	—	4	4	no	—
280	C₂×C₇×C₈	C₂⁴	1	2	yes	—
281	C₂×C₇×C₈	C₂⁴	1	2	yes	—
282	C₂×C₇×C₈	C₂⁴	1	2	yes	—
283	C₂×C₇×C₈	C₂⁴	1	2	yes	—
284	C₇×C₄⋊C₄	—	2	4	no	—
285	C₇×C₄⋊C₄	—	2	4	no	—
286	C₇×C₄⋊C₄	—	2	1	no	—
287	C₇×C₄⋊C₄	—	2	1	no	—
288	C₇×C₄⋊C₄	—	2	1	no	—
289	C₇×C₄⋊C₄	—	2	1	no	—
290	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
291	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
292	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
293	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
294	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
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	—	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	—	2	4	no	—
309	C₄²×C₇	C₂×D₄	1	2	yes	—
310	C₄²×C₇	C₂⁴	1	2	yes	—
311	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
312	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
313	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
314	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
315	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
316	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
317	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
318	#555	—	2	4	no	—
319	#555	C₂²×C₇	1	8	yes	complemented
320	#546	—	2	4	no	—
321	#546	C₂²×C₇	1	8	yes	complemented
322	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
323	C₂×#124	—	2	1	no	—
324	C₂×#124	—	2	1	no	—
325	C₂×#124	C₂²×C₇	1	1	yes	characteristic
326	C₂×#123	—	2	1	no	—
327	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
328	C₂×#121	—	2	1	no	—
329	C₂×#121	—	2	1	no	—
330	C₂×#121	C₂²×C₇	1	1	yes	characteristic
331	C₂×#121	C₂²×C₇	1	1	yes	characteristic
332	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
333	C₂×#120	—	2	1	no	—
334	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
335	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
336	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
337	C₂×#117	—	2	1	no	—
338	C₂×#117	C₂²×C₇	1	1	yes	characteristic
339	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
340	C₂²×C₂²⋊C₄	—	2	1	no	—
341	#489	C₂²×C₇	1	8	yes	complemented
342	#485	C₂²×C₇	1	8	yes	complemented
343	#482	C₂²×C₇	1	8	yes	complemented
344	#474	C₂²×C₇	1	8	yes	complemented
345	#468	C₂²×C₇	1	8	yes	complemented
346	#466	C₂²×C₇	1	8	yes	complemented
347	#463	C₂²×C₇	1	8	yes	complemented
348	#449	C₂²×C₇	1	8	yes	complemented
349	#447	C₂²×C₇	1	8	yes	complemented
350	#442	C₂²×C₇	1	8	yes	complemented
351	#435	C₂²×C₇	1	8	yes	complemented
352	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
353	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
354	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
355	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
356	#418	C₂²×C₇	1	8	yes	complemented
357	#416	C₂²×C₇	1	8	yes	complemented
358	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
359	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
360	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
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	1	yes	characteristic
367	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
368	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
369	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
370	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
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	—	2	2	no	—
379	C₂³×C₇	—	2	2	no	—
380	C₂³×C₇	—	2	2	no	—
381	C₂³×C₇	—	4	8	no	—
382	C₂³×C₇	—	4	8	no	—
383	C₂³×C₇	—	4	2	no	—
384	C₂³×C₇	—	4	2	no	—
385	C₂³×C₇	—	4	2	no	—
386	C₂³×C₇	—	4	2	no	—
387	C₂³×C₇	—	4	2	no	—
388	C₂³×C₇	—	4	2	no	—
389	C₂³×C₇	—	4	2	no	—
390	C₂³×C₇	—	4	2	no	—
391	C₂³×C₇	—	8	4	no	—
392	C₂³×C₇	—	8	16	no	—
393	C₂³×C₇	C₂²×D₄	1	2	yes	—
394	C₂³×C₇	C₂²×D₄	1	2	yes	—
395	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
396	C₇×Q₈	—	2	2	no	—
397	C₇×Q₈	—	2	2	no	—
398	C₇×Q₈	—	4	2	no	—
399	C₇×Q₈	—	8	4	no	—
400	C₇×D₄	—	2	4	no	—
401	C₇×D₄	—	2	2	no	—
402	C₇×D₄	—	2	2	no	—
403	C₇×D₄	—	2	2	no	—
404	C₇×D₄	—	2	2	no	—
405	C₇×D₄	—	2	2	no	—
406	C₇×D₄	—	4	4	no	—
407	C₇×D₄	—	4	8	no	—
408	C₇×D₄	—	4	8	no	—
409	C₇×D₄	—	4	2	no	—
410	C₇×D₄	—	4	2	no	—
411	C₇×D₄	—	8	4	no	—
412	C₇×D₄	—	8	4	no	—
413	C₇×D₄	—	8	4	no	—
414	C₇×D₄	C₂×#41	1	4	yes	—
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	4	no	—
420	C₂×C₄×C₇	—	2	4	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	—	2	2	no	—
425	C₂×C₄×C₇	—	2	2	no	—
426	C₂×C₄×C₇	—	2	2	no	—
427	C₂×C₄×C₇	—	2	2	no	—
428	C₂×C₄×C₇	—	2	2	no	—
429	C₂×C₄×C₇	—	2	2	no	—
430	C₂×C₄×C₇	—	4	8	no	—
431	C₂×C₄×C₇	—	4	8	no	—
432	C₂×C₄×C₇	—	4	2	no	—
433	C₂×C₄×C₇	—	4	2	no	—
434	C₂×C₄×C₇	—	4	2	no	—
435	C₂×C₄×C₇	—	4	2	no	—
436	C₂×C₄×C₇	—	4	2	no	—
437	C₂×C₄×C₇	—	8	4	no	—
438	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
442	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₇	C₂×#41	1	2	yes	—
444	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
445	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
446	C₇×C₈	—	2	2	no	—
447	C₇×C₈	—	2	2	no	—
448	C₇×C₈	—	2	2	no	—
449	C₇×C₈	—	2	2	no	—
450	C₂⁵	—	2	1	no	—
451	C₂×#41	—	2	2	no	—
452	C₂×#41	—	2	4	no	—
453	C₂×#41	—	4	2	no	—
454	C₂×#41	C₂³×C₇	1	4	yes	—
455	C₂²×Q₈	—	2	1	no	—
456	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
457	C₂²×D₄	—	2	4	no	—
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	2	no	—
464	C₂²×D₄	—	4	2	no	—
465	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
466	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₇	1	4	yes	—
469	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
470	C₂³×C₄	—	2	1	no	—
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
475	C₂×SD₁₆	—	4	2	no	—
476	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
477	C₂×D₈	—	2	4	no	—
478	C₂×D₈	—	4	2	no	—
479	C₂×D₈	C₂³×C₇	1	4	yes	—
480	C₂×D₈	C₂³×C₇	1	4	yes	—
481	C₂×M₁₆	—	4	2	no	—
482	C₂×M₁₆	C₂³×C₇	1	4	yes	—
483	C₂²×C₈	—	4	2	no	—
484	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₇	1	4	yes	complemented
489	C₄⋊Q₈	—	2	2	no	—
490	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
491	#124	—	2	8	no	—
492	#124	—	2	8	no	—
493	#124	—	2	2	no	—
494	#124	C₂³×C₇	1	4	yes	—
495	#123	—	2	8	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
498	#121	—	2	8	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	2	no	—
502	#121	—	2	8	no	—
503	#121	C₂³×C₇	1	4	yes	—
504	#121	C₂³×C₇	1	4	yes	—
505	#121	C₂³×C₇	1	4	yes	complemented
506	#120	—	2	8	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	C₇×D₄	1	4	yes	—
510	C₄×D₄	C₂³×C₇	1	4	yes	—
511	C₄×D₄	C₂³×C₇	1	4	yes	—
512	C₄×D₄	C₂³×C₇	1	4	yes	complemented
513	#117	—	2	2	no	—
514	#117	—	2	2	no	—
515	#117	—	2	8	no	—
516	#117	C₂³×C₇	1	4	yes	—
517	#117	C₂³×C₇	1	4	yes	complemented
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
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	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	8	no	—
536	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
538	C₂×C₄²	—	2	1	no	—
539	C₂×C₄²	—	2	1	no	—
540	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
541	#107	C₂³×C₇	1	4	yes	complemented
542	#107	C₂³×C₇	1	4	yes	complemented
543	#106	C₂³×C₇	1	4	yes	complemented
544	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
545	#103	C₂³×C₇	1	4	yes	complemented
546	#103	C₂³×C₇	1	4	yes	complemented
547	#103	C₂³×C₇	1	4	yes	complemented
548	#102	C₂³×C₇	1	4	yes	—
549	#102	C₂³×C₇	1	4	yes	—
550	#102	C₂³×C₇	1	4	yes	—
551	#102	C₂³×C₇	1	4	yes	—
552	#102	C₂³×C₇	1	4	yes	—
553	#102	C₂³×C₇	1	4	yes	—
554	#102	C₂³×C₇	1	4	yes	complemented
555	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
556	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
557	#97	C₂³×C₇	1	4	yes	complemented
558	C₂²×C₇	—	2	2	no	—
559	C₂²×C₇	—	2	2	no	—
560	C₂²×C₇	—	2	4	no	—
561	C₂²×C₇	—	2	2	no	—
562	C₂²×C₇	—	2	2	no	—
563	C₂²×C₇	—	2	2	no	—
564	C₂²×C₇	—	2	2	no	—
565	C₂²×C₇	—	4	4	no	—
566	C₂²×C₇	—	4	4	no	—
567	C₂²×C₇	—	4	8	no	—
568	C₂²×C₇	—	4	2	no	—
569	C₂²×C₇	—	4	2	no	—
570	C₂²×C₇	—	4	2	no	—
571	C₂²×C₇	—	4	2	no	—
572	C₂²×C₇	—	4	2	no	—
573	C₂²×C₇	—	4	2	no	—
574	C₂²×C₇	—	4	2	no	—
575	C₂²×C₇	—	4	2	no	—
576	C₂²×C₇	—	8	16	no	—
577	C₂²×C₇	—	8	4	no	—
578	C₂²×C₇	—	8	4	no	—
579	C₂²×C₇	#546	1	2	yes	—
580	C₂²×C₇	#575	1	2	yes	—
581	C₂²×C₇	#576	1	2	yes	—
582	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
583	C₄×C₇	—	2	2	no	—
584	C₄×C₇	—	2	2	no	—
585	C₄×C₇	—	2	2	no	—
586	C₄×C₇	—	2	2	no	—
587	C₄×C₇	—	4	2	no	—
588	C₄×C₇	—	4	2	no	—
589	C₄×C₇	—	4	2	no	—
590	C₄×C₇	—	4	2	no	—
591	C₄×C₇	—	4	2	no	—
592	C₄×C₇	#546	1	2	yes	—
593	C₄×C₇	C₂²×#41	1	1	yes	characteristic
594	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
595	C₂⁴	—	2	1	no	—
596	C₂⁴	—	2	1	no	—
597	C₂⁴	—	2	1	no	—
598	C₂⁴	—	2	4	no	—
599	C₂⁴	—	4	4	no	—
600	C₂⁴	—	4	4	no	—
601	C₂⁴	—	8	2	no	—
602	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
603	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
604	#41	—	2	8	no	—
605	#41	—	4	4	no	—
606	#41	—	4	8	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	8	2	no	—
612	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
613	C₂×D₄	—	2	8	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	—	4	8	no	—
629	C₂×D₄	—	4	2	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	—	4	4	no	—
632	C₂×D₄	—	8	2	no	—
633	C₂×D₄	—	8	2	no	—
634	C₂×D₄	—	8	2	no	—
635	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
636	C₂×D₄	C₇×#41	1	4	yes	—
637	C₂×D₄	C₂⁴×C₇	1	2	yes	—
638	C₂×D₄	C₂⁴×C₇	1	2	yes	—
639	C₂×D₄	C₂⁴×C₇	1	2	yes	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	4	4	no	—
653	C₂²×C₄	—	4	4	no	—
654	C₂²×C₄	—	8	2	no	—
655	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
656	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
657	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
658	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
659	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
660	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
664	SD₁₆	—	4	4	no	—
665	D₈	—	2	8	no	—
666	D₈	—	4	4	no	—
667	M₁₆	—	4	4	no	—
668	C₂×C₈	—	2	2	no	—
669	C₂×C₈	—	2	2	no	—
670	C₂×C₈	—	2	2	no	—
671	C₂×C₈	—	2	2	no	—
672	C₂×C₈	—	4	4	no	—
673	C₂×C₈	C₂⁴×C₇	1	2	yes	—
674	C₂×C₈	C₂⁴×C₇	1	2	yes	—
675	C₂×C₈	C₂⁴×C₇	1	2	yes	—
676	C₂×C₈	C₂⁴×C₇	1	2	yes	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
684	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
685	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
686	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
687	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
699	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	4	no	—
702	C₄²	C₂×C₇×D₄	1	2	yes	—
703	C₄²	C₂⁴×C₇	1	2	yes	—
704	C₂×C₇	—	4	2	no	—
705	C₂×C₇	—	4	2	no	—
706	C₂×C₇	—	4	4	no	—
707	C₂×C₇	—	8	2	no	—
708	C₂×C₇	—	8	2	no	—
709	C₂×C₇	#3319	1	4	yes	direct product factor
710	C₂×C₇	C₂×#546	1	1	yes	characteristic
711	C₂×C₇	C₂×#575	1	1	yes	characteristic
712	C₂×C₇	C₂×#576	1	1	yes	characteristic
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	4	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	4	8	no	—
724	C₂³	—	4	8	no	—
725	C₂³	—	4	2	no	—
726	C₂³	—	4	2	no	—
727	C₂³	—	4	2	no	—
728	C₂³	—	4	2	no	—
729	C₂³	—	4	2	no	—
730	C₂³	—	4	2	no	—
731	C₂³	—	4	2	no	—
732	C₂³	—	4	2	no	—
733	C₂³	—	8	4	no	—
734	C₂³	—	8	16	no	—
735	C₂³	C₂²×C₇×D₄	1	2	yes	—
736	C₂³	C₂²×C₇×D₄	1	2	yes	—
737	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
738	Q₈	—	2	2	no	—
739	Q₈	—	2	2	no	—
740	Q₈	—	4	2	no	—
741	Q₈	—	8	4	no	—
742	D₄	—	2	2	no	—
743	D₄	—	2	2	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	2	no	—
746	D₄	—	2	2	no	—
747	D₄	—	2	4	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	8	no	—
750	D₄	—	4	8	no	—
751	D₄	—	4	2	no	—
752	D₄	—	4	2	no	—
753	D₄	—	8	4	no	—
754	D₄	—	8	4	no	—
755	D₄	—	8	4	no	—
756	D₄	C₂×C₇×#41	1	4	yes	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	4	8	no	—
773	C₂×C₄	—	4	8	no	—
774	C₂×C₄	—	4	2	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	4	2	no	—
779	C₂×C₄	—	8	4	no	—
780	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
781	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
782	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
783	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
784	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
785	C₂×C₄	C₂×C₇×#41	1	2	yes	—
786	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
787	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
788	C₈	—	2	2	no	—
789	C₈	—	2	2	no	—
790	C₈	—	2	2	no	—
791	C₈	—	2	2	no	—
792	C₇	C₂×#3319	1	1	yes	characteristic, direct product factor, Sylow
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	4	no	—
803	C₂²	—	4	4	no	—
804	C₂²	—	4	8	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	8	16	no	—
812	C₂²	—	8	4	no	—
813	C₂²	—	8	4	no	—
814	C₂²	C₇×#546	1	2	yes	—
815	C₂²	C₇×#575	1	2	yes	—
816	C₂²	C₇×#576	1	2	yes	—
817	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	C₇×#546	1	2	yes	—
828	C₄	C₂²×C₇×#41	1	1	yes	characteristic
829	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂	—	4	2	no	—
831	C₂	—	4	2	no	—
832	C₂	—	4	4	no	—
833	C₂	—	8	2	no	—
834	C₂	—	8	2	no	—
835	C₂	C₇×#3319	1	4	yes	direct product factor
836	C₂	C₂×C₇×#546	1	1	yes	characteristic
837	C₂	C₂×C₇×#575	1	1	yes	characteristic
838	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×#555	C₂	semidirect
2. C₂×C₇×#546	C₂	semidirect
3. C₇×#3319	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×#474	C₂	semidirect
8. C₂×C₇×#468	C₂	semidirect
9. C₂×C₇×#466	C₂	semidirect
10. C₂×C₇×#463	C₂	semidirect
11. C₂×C₇×#449	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. C₂×C₇×#416	C₂	semidirect
19. C₂²×C₇×SD₁₆	C₂²	semidirect
23. C₂³×C₇×C₈	C₂²	semidirect
25. C₇×#555	C₂²	semidirect
27. C₇×#546	C₂²	semidirect
28. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
38. C₂×C₇×#121	C₂²	semidirect
42. C₂×C₄×C₇×D₄	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×#474	C₂²	semidirect
51. C₇×#468	C₂²	semidirect
52. C₇×#466	C₂²	semidirect
53. C₇×#463	C₂²	semidirect
54. C₇×#449	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×#107	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
73. C₂×C₇×#102	C₂²	semidirect
75. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₇×#97	C₂²	semidirect
77. C₂×#3319	C₇	direct (N × H)
104. C₂×C₇×SD₁₆	C₂³	semidirect
116. C₂²×C₇×C₈	C₂³	semidirect
118. C₇×C₄⋊Q₈	C₂³	semidirect
133. C₇×#121	C₂³	semidirect
140. C₄×C₇×D₄	C₂³	semidirect
145. C₇×#117	C₂³	semidirect
169. C₇×#107	C₂³	semidirect
170. C₇×#107	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
182. C₇×#102	C₂³	semidirect
184. C₇×C₂²⋊C₈	C₂³	semidirect
185. C₇×#97	C₂³	semidirect
186. C₂×#555	C₂×C₇	semidirect
187. C₂×#546	C₂×C₇	semidirect
188. #3319	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×#474	C₂×C₇	semidirect
193. C₂×#468	C₂×C₇	semidirect
194. C₂×#466	C₂×C₇	semidirect
195. C₂×#463	C₂×C₇	semidirect
196. C₂×#449	C₂×C₇	semidirect
197. C₂×#447	C₂×C₇	semidirect
198. C₂×#442	C₂×C₇	semidirect
199. C₂×#435	C₂×C₇	semidirect
200. C₂×#418	C₂×C₇	semidirect
201. C₂×#416	C₂×C₇	semidirect
313. C₂²×SD₁₆	C₂²×C₇	semidirect
317. C₂³×C₈	C₂²×C₇	semidirect
319. #555	C₂²×C₇	semidirect
321. #546	C₂²×C₇	semidirect
322. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
332. C₂×#121	C₂²×C₇	semidirect
336. C₂×C₄×D₄	C₂²×C₇	semidirect
339. C₂×#117	C₂²×C₇	semidirect
341. #489	C₂²×C₇	semidirect
342. #485	C₂²×C₇	semidirect
343. #482	C₂²×C₇	semidirect
344. #474	C₂²×C₇	semidirect
345. #468	C₂²×C₇	semidirect
346. #466	C₂²×C₇	semidirect
347. #463	C₂²×C₇	semidirect
348. #449	C₂²×C₇	semidirect
349. #447	C₂²×C₇	semidirect
350. #442	C₂²×C₇	semidirect
351. #435	C₂²×C₇	semidirect
352. C₂×#107	C₂²×C₇	semidirect
353. C₂×#107	C₂²×C₇	semidirect
354. C₂×#106	C₂²×C₇	semidirect
355. C₂×C₄⋊C₈	C₂²×C₇	semidirect
356. #418	C₂²×C₇	semidirect
357. #416	C₂²×C₇	semidirect
358. C₂×#103	C₂²×C₇	semidirect
359. C₂×#103	C₂²×C₇	semidirect
360. C₂×#103	C₂²×C₇	semidirect
367. C₂×#102	C₂²×C₇	semidirect
369. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
370. C₂×#97	C₂²×C₇	semidirect
476. C₂×SD₁₆	C₂³×C₇	semidirect
488. C₂²×C₈	C₂³×C₇	semidirect
490. C₄⋊Q₈	C₂³×C₇	semidirect
505. #121	C₂³×C₇	semidirect
512. C₄×D₄	C₂³×C₇	semidirect
517. #117	C₂³×C₇	semidirect
541. #107	C₂³×C₇	semidirect
542. #107	C₂³×C₇	semidirect
543. #106	C₂³×C₇	semidirect
544. C₄⋊C₈	C₂³×C₇	semidirect
545. #103	C₂³×C₇	semidirect
546. #103	C₂³×C₇	semidirect
547. #103	C₂³×C₇	semidirect
554. #102	C₂³×C₇	semidirect
556. C₂²⋊C₈	C₂³×C₇	semidirect
557. #97	C₂³×C₇	semidirect
709. C₂×C₇	#3319	direct (N × H)
792. C₇	C₂×#3319	direct (N × H)
835. C₂	C₇×#3319	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×#555	2
C₂×C₇×#546	2
C₇×#3319	2
C₂×C₇×#489	2
C₂×C₇×#485	2
C₂×C₇×#482	2
C₂×C₇×#474	2
C₂×C₇×#468	2
C₂×C₇×#466	2
C₂×C₇×#463	2
C₂×C₇×#449	2
C₂×C₇×#447	2
C₂×C₇×#442	2
C₂×C₇×#435	2
C₂×C₇×#418	2
C₂×C₇×#416	2
C₂×#3319	7

Subgroups — C2×C7×#3319 #13238352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3319 #13238352