Subgroups — C₂×C₇×#3306 #13238341

Order 1792.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3306	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#489	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#483	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#465	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×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₇×#41	—	2	1	no	—
18	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
19	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
22	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
23	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
25	C₇×#547	—	2	4	no	—
26	C₇×#547	C₂²	1	8	yes	complemented
27	C₇×#546	—	2	4	no	—
28	C₇×#546	C₂²	1	8	yes	complemented
29	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₇×#124	C₂²	1	1	yes	characteristic
31	C₂×C₇×#123	—	2	1	no	—
32	C₂×C₇×#123	—	2	1	no	—
33	C₂×C₇×#123	—	2	1	no	—
34	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
35	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×#121	—	2	1	no	—
37	C₂×C₇×#121	C₂²	1	1	yes	characteristic
38	C₂×C₇×#121	C₂²	1	1	yes	characteristic
39	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₇×#120	—	2	1	no	—
41	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
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×#483	C₂²	1	8	yes	complemented
49	C₇×#481	C₂²	1	8	yes	complemented
50	C₇×#476	C₂²	1	8	yes	complemented
51	C₇×#469	C₂²	1	8	yes	complemented
52	C₇×#465	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×#106	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×#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×#102	C₂²	1	1	yes	characteristic
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	8	yes	complemented
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×#3306	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁵×C₇	—	2	1	no	—
79	C₂×C₇×#41	—	2	8	no	—
80	C₂×C₇×#41	—	2	2	no	—
81	C₂×C₇×#41	—	2	4	no	—
82	C₂×C₇×#41	—	4	2	no	—
83	C₂×C₇×#41	—	4	8	no	—
84	C₂×C₇×#41	C₂³	1	4	yes	—
85	C₂²×C₇×Q₈	—	2	1	no	—
86	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×D₄	—	2	4	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	1	no	—
92	C₂²×C₇×D₄	—	2	1	no	—
93	C₂²×C₇×D₄	—	2	2	no	—
94	C₂²×C₇×D₄	—	4	2	no	—
95	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
96	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
97	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
98	C₂²×C₇×D₄	C₂³	1	4	yes	—
99	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₇	—	2	1	no	—
101	C₂³×C₄×C₇	—	2	1	no	—
102	C₂³×C₄×C₇	—	2	1	no	—
103	C₂³×C₄×C₇	—	2	1	no	—
104	C₂³×C₄×C₇	—	2	1	no	—
105	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
107	C₂×C₇×SD₁₆	—	4	2	no	—
108	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
109	C₂×C₇×D₈	—	2	4	no	—
110	C₂×C₇×D₈	—	4	2	no	—
111	C₂×C₇×D₈	C₂³	1	4	yes	—
112	C₂×C₇×D₈	C₂³	1	4	yes	—
113	C₂×C₇×M₁₆	—	4	2	no	—
114	C₂×C₇×M₁₆	C₂³	1	4	yes	complemented
115	C₂²×C₇×C₈	—	4	2	no	—
116	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
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	4	yes	—
121	C₇×C₄⋊Q₈	—	2	2	no	—
122	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
123	C₇×#124	—	2	2	no	—
124	C₇×#124	C₂³	1	4	yes	—
125	C₇×#123	—	2	8	no	—
126	C₇×#123	—	2	8	no	—
127	C₇×#123	—	2	8	no	—
128	C₇×C₂²⋊Q₈	—	2	2	no	—
129	C₇×C₂²⋊Q₈	—	2	8	no	—
130	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₇×#121	—	2	2	no	—
132	C₇×#121	—	2	2	no	—
133	C₇×#121	—	2	2	no	—
134	C₇×#121	—	2	8	no	—
135	C₇×#121	C₂³	1	4	yes	—
136	C₇×#121	C₂³	1	4	yes	—
137	C₇×#121	C₂³	1	4	yes	complemented
138	C₇×#120	—	2	8	no	—
139	C₄×C₇×D₄	—	2	2	no	—
140	C₄×C₇×D₄	—	2	2	no	—
141	C₄×C₇×D₄	D₄	1	4	yes	—
142	C₄×C₇×D₄	C₂³	1	4	yes	—
143	C₄×C₇×D₄	C₂³	1	4	yes	—
144	C₄×C₇×D₄	C₂³	1	4	yes	complemented
145	C₂×C₇×C₄⋊C₄	—	2	1	no	—
146	C₂×C₇×C₄⋊C₄	—	2	2	no	—
147	C₂×C₇×C₄⋊C₄	—	2	1	no	—
148	C₂×C₇×C₄⋊C₄	—	2	2	no	—
149	C₂×C₇×C₄⋊C₄	—	2	1	no	—
150	C₂×C₇×C₄⋊C₄	—	2	1	no	—
151	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
152	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
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	1	yes	characteristic
157	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
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	1	no	—
165	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
166	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
167	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
168	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
169	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
170	C₇×#106	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×#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×#102	C₂³	1	4	yes	complemented
184	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
185	C₇×C₂²⋊C₈	C₂³	1	4	yes	complemented
186	C₇×#97	C₂³	1	4	yes	complemented
187	C₂×#547	C₂×C₇	1	1	yes	characteristic, complemented
188	C₂×#546	C₂×C₇	1	1	yes	characteristic, complemented
189	#3306	C₂×C₇	1	16	yes	direct product factor
190	C₂×#489	C₂×C₇	1	1	yes	characteristic, complemented
191	C₂×#481	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂×#483	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
194	C₂×#469	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×#465	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×#463	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×#449	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×#417	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	4	no	—
207	C₂⁴×C₇	—	4	4	no	—
208	C₂⁴×C₇	—	4	4	no	—
209	C₂⁴×C₇	—	8	2	no	—
210	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
211	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
212	C₇×#41	—	2	8	no	—
213	C₇×#41	—	4	4	no	—
214	C₇×#41	—	4	8	no	—
215	C₇×#41	—	4	32	no	—
216	C₂×C₇×Q₈	—	2	1	no	—
217	C₂×C₇×Q₈	—	2	4	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×D₄	—	2	4	no	—
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	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	1	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	—	4	4	no	—
238	C₂×C₇×D₄	—	4	8	no	—
239	C₂×C₇×D₄	—	4	4	no	—
240	C₂×C₇×D₄	—	4	4	no	—
241	C₂×C₇×D₄	—	4	4	no	—
242	C₂×C₇×D₄	—	4	4	no	—
243	C₂×C₇×D₄	—	8	2	no	—
244	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
245	C₂×C₇×D₄	#41	1	4	yes	complemented
246	C₂×C₇×D₄	C₂⁴	1	2	yes	—
247	C₂×C₇×D₄	C₂⁴	1	2	yes	—
248	C₂×C₇×D₄	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₇	—	2	2	no	—
250	C₂²×C₄×C₇	—	2	2	no	—
251	C₂²×C₄×C₇	—	2	2	no	—
252	C₂²×C₄×C₇	—	2	2	no	—
253	C₂²×C₄×C₇	—	2	4	no	—
254	C₂²×C₄×C₇	—	2	4	no	—
255	C₂²×C₄×C₇	—	2	1	no	—
256	C₂²×C₄×C₇	—	2	1	no	—
257	C₂²×C₄×C₇	—	2	1	no	—
258	C₂²×C₄×C₇	—	2	1	no	—
259	C₂²×C₄×C₇	—	2	1	no	—
260	C₂²×C₄×C₇	—	2	4	no	—
261	C₂²×C₄×C₇	—	2	4	no	—
262	C₂²×C₄×C₇	—	2	4	no	—
263	C₂²×C₄×C₇	—	4	4	no	—
264	C₂²×C₄×C₇	—	4	4	no	—
265	C₂²×C₄×C₇	—	4	4	no	—
266	C₂²×C₄×C₇	—	4	4	no	—
267	C₂²×C₄×C₇	—	8	2	no	—
268	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
277	C₇×SD₁₆	—	4	4	no	—
278	C₇×D₈	—	2	8	no	—
279	C₇×D₈	—	4	4	no	—
280	C₇×M₁₆	—	4	4	no	—
281	C₂×C₇×C₈	—	2	2	no	—
282	C₂×C₇×C₈	—	2	2	no	—
283	C₂×C₇×C₈	—	2	2	no	—
284	C₂×C₇×C₈	—	2	2	no	—
285	C₂×C₇×C₈	—	4	4	no	—
286	C₂×C₇×C₈	C₂⁴	1	2	yes	—
287	C₂×C₇×C₈	C₂⁴	1	2	yes	—
288	C₂×C₇×C₈	C₂⁴	1	2	yes	—
289	C₂×C₇×C₈	C₂⁴	1	2	yes	—
290	C₇×C₄⋊C₄	—	2	1	no	—
291	C₇×C₄⋊C₄	—	2	1	no	—
292	C₇×C₄⋊C₄	—	2	1	no	—
293	C₇×C₄⋊C₄	—	2	4	no	—
294	C₇×C₄⋊C₄	—	2	4	no	—
295	C₇×C₄⋊C₄	—	2	4	no	—
296	C₇×C₄⋊C₄	—	2	4	no	—
297	C₇×C₄⋊C₄	—	2	1	no	—
298	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
299	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
300	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
301	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
303	C₇×C₂²⋊C₄	—	2	4	no	—
304	C₇×C₂²⋊C₄	—	2	4	no	—
305	C₇×C₂²⋊C₄	—	2	4	no	—
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	C₂×D₄	1	4	yes	—
312	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
313	C₄²×C₇	C₂×D₄	1	2	yes	—
314	C₄²×C₇	C₂⁴	1	2	yes	—
315	C₂²×#41	—	2	1	no	—
316	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
317	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
318	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
319	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
320	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
321	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
322	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
323	#547	—	2	4	no	—
324	#547	C₂²×C₇	1	8	yes	complemented
325	#546	—	2	4	no	—
326	#546	C₂²×C₇	1	8	yes	complemented
327	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
328	C₂×#124	C₂²×C₇	1	1	yes	characteristic
329	C₂×#123	—	2	1	no	—
330	C₂×#123	—	2	1	no	—
331	C₂×#123	—	2	1	no	—
332	C₂×C₂²⋊Q₈	—	2	1	no	—
333	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
334	C₂×#121	—	2	1	no	—
335	C₂×#121	C₂²×C₇	1	1	yes	characteristic
336	C₂×#121	C₂²×C₇	1	1	yes	characteristic
337	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
338	C₂×#120	—	2	1	no	—
339	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
340	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
341	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
342	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
343	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
344	C₂²×C₂²⋊C₄	—	2	1	no	—
345	#489	C₂²×C₇	1	8	yes	complemented
346	#483	C₂²×C₇	1	8	yes	complemented
347	#481	C₂²×C₇	1	8	yes	complemented
348	#476	C₂²×C₇	1	8	yes	complemented
349	#469	C₂²×C₇	1	8	yes	complemented
350	#465	C₂²×C₇	1	8	yes	complemented
351	#463	C₂²×C₇	1	8	yes	complemented
352	#449	C₂²×C₇	1	8	yes	complemented
353	#447	C₂²×C₇	1	8	yes	complemented
354	#442	C₂²×C₇	1	8	yes	complemented
355	#435	C₂²×C₇	1	8	yes	complemented
356	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
357	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
358	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
359	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
360	#417	C₂²×C₇	1	8	yes	complemented
361	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
362	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
363	C₂×#103	C₂²×C₇	1	1	yes	characteristic, 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	1	yes	characteristic
368	C₂×#102	C₂²×C₇	1	1	yes	characteristic
369	C₂×#102	C₂²×C₇	1	1	yes	characteristic
370	C₂×#102	C₂²×C₇	1	8	yes	complemented
371	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
372	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
373	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
374	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
375	C₂³×C₇	—	2	2	no	—
376	C₂³×C₇	—	2	2	no	—
377	C₂³×C₇	—	2	2	no	—
378	C₂³×C₇	—	2	4	no	—
379	C₂³×C₇	—	2	2	no	—
380	C₂³×C₇	—	2	2	no	—
381	C₂³×C₇	—	2	2	no	—
382	C₂³×C₇	—	2	2	no	—
383	C₂³×C₇	—	2	2	no	—
384	C₂³×C₇	—	4	8	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	8	no	—
391	C₂³×C₇	—	4	2	no	—
392	C₂³×C₇	—	4	2	no	—
393	C₂³×C₇	—	4	2	no	—
394	C₂³×C₇	—	8	4	no	—
395	C₂³×C₇	—	8	16	no	—
396	C₂³×C₇	AGL(1,ℤ/8)	1	4	yes	—
397	C₂³×C₇	C₂²×D₄	1	2	yes	—
398	C₂³×C₇	C₂²×D₄	1	2	yes	—
399	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
400	C₇×Q₈	—	2	2	no	—
401	C₇×Q₈	—	2	2	no	—
402	C₇×Q₈	—	4	8	no	—
403	C₇×Q₈	—	4	2	no	—
404	C₇×D₄	—	2	8	no	—
405	C₇×D₄	—	2	4	no	—
406	C₇×D₄	—	2	2	no	—
407	C₇×D₄	—	2	2	no	—
408	C₇×D₄	—	2	2	no	—
409	C₇×D₄	—	2	2	no	—
410	C₇×D₄	—	2	2	no	—
411	C₇×D₄	—	4	8	no	—
412	C₇×D₄	—	4	8	no	—
413	C₇×D₄	—	4	8	no	—
414	C₇×D₄	—	4	8	no	—
415	C₇×D₄	—	4	2	no	—
416	C₇×D₄	—	4	2	no	—
417	C₇×D₄	—	8	4	no	—
418	C₇×D₄	C₂×#41	1	4	yes	complemented
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	4	no	—
424	C₂×C₄×C₇	—	2	4	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	—	2	2	no	—
431	C₂×C₄×C₇	—	2	2	no	—
432	C₂×C₄×C₇	—	2	2	no	—
433	C₂×C₄×C₇	—	2	2	no	—
434	C₂×C₄×C₇	—	4	8	no	—
435	C₂×C₄×C₇	—	4	8	no	—
436	C₂×C₄×C₇	—	4	8	no	—
437	C₂×C₄×C₇	—	4	2	no	—
438	C₂×C₄×C₇	—	4	2	no	—
439	C₂×C₄×C₇	—	4	2	no	—
440	C₂×C₄×C₇	—	4	2	no	—
441	C₂×C₄×C₇	—	4	8	no	—
442	C₂×C₄×C₇	—	4	2	no	—
443	C₂×C₄×C₇	—	8	4	no	—
444	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
447	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
448	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₇	C₂×#41	1	2	yes	—
450	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
451	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
452	C₇×C₈	—	2	2	no	—
453	C₇×C₈	—	2	2	no	—
454	C₇×C₈	—	2	2	no	—
455	C₇×C₈	—	2	2	no	—
456	C₂⁵	—	2	1	no	—
457	C₂×#41	—	2	8	no	—
458	C₂×#41	—	2	2	no	—
459	C₂×#41	—	2	4	no	—
460	C₂×#41	—	4	2	no	—
461	C₂×#41	—	4	8	no	—
462	C₂×#41	C₂³×C₇	1	4	yes	—
463	C₂²×Q₈	—	2	1	no	—
464	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
465	C₂²×D₄	—	2	4	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	—	2	1	no	—
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	—	2	2	no	—
472	C₂²×D₄	—	4	2	no	—
473	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
474	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
476	C₂²×D₄	C₂³×C₇	1	4	yes	—
477	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	—	2	1	no	—
480	C₂³×C₄	—	2	1	no	—
481	C₂³×C₄	—	2	1	no	—
482	C₂³×C₄	—	2	1	no	—
483	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
485	C₂×SD₁₆	—	4	2	no	—
486	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
487	C₂×D₈	—	2	4	no	—
488	C₂×D₈	—	4	2	no	—
489	C₂×D₈	C₂³×C₇	1	4	yes	—
490	C₂×D₈	C₂³×C₇	1	4	yes	—
491	C₂×M₁₆	—	4	2	no	—
492	C₂×M₁₆	C₂³×C₇	1	4	yes	complemented
493	C₂²×C₈	—	4	2	no	—
494	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
497	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
498	C₂²×C₈	C₂³×C₇	1	4	yes	—
499	C₄⋊Q₈	—	2	2	no	—
500	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
501	#124	—	2	2	no	—
502	#124	C₂³×C₇	1	4	yes	—
503	#123	—	2	8	no	—
504	#123	—	2	8	no	—
505	#123	—	2	8	no	—
506	C₂²⋊Q₈	—	2	2	no	—
507	C₂²⋊Q₈	—	2	8	no	—
508	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
509	#121	—	2	2	no	—
510	#121	—	2	2	no	—
511	#121	—	2	2	no	—
512	#121	—	2	8	no	—
513	#121	C₂³×C₇	1	4	yes	—
514	#121	C₂³×C₇	1	4	yes	—
515	#121	C₂³×C₇	1	4	yes	complemented
516	#120	—	2	8	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	C₇×D₄	1	4	yes	—
520	C₄×D₄	C₂³×C₇	1	4	yes	—
521	C₄×D₄	C₂³×C₇	1	4	yes	—
522	C₄×D₄	C₂³×C₇	1	4	yes	complemented
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	—	2	2	no	—
525	C₂×C₄⋊C₄	—	2	1	no	—
526	C₂×C₄⋊C₄	—	2	2	no	—
527	C₂×C₄⋊C₄	—	2	1	no	—
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
533	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	—	2	1	no	—
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	8	no	—
545	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
548	#106	C₂³×C₇	1	4	yes	complemented
549	#106	C₂³×C₇	1	4	yes	complemented
550	#106	C₂³×C₇	1	4	yes	complemented
551	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
552	#103	C₂³×C₇	1	4	yes	complemented
553	#103	C₂³×C₇	1	4	yes	complemented
554	#103	C₂³×C₇	1	4	yes	complemented
555	#102	C₂³×C₇	1	4	yes	—
556	#102	C₂³×C₇	1	4	yes	—
557	#102	C₂³×C₇	1	4	yes	—
558	#102	C₂³×C₇	1	4	yes	—
559	#102	C₂³×C₇	1	4	yes	—
560	#102	C₂³×C₇	1	4	yes	—
561	#102	C₂³×C₇	1	4	yes	complemented
562	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
563	C₂²⋊C₈	C₂³×C₇	1	4	yes	complemented
564	#97	C₂³×C₇	1	4	yes	complemented
565	C₂²×C₇	—	2	2	no	—
566	C₂²×C₇	—	2	8	no	—
567	C₂²×C₇	—	2	2	no	—
568	C₂²×C₇	—	2	2	no	—
569	C₂²×C₇	—	2	4	no	—
570	C₂²×C₇	—	2	2	no	—
571	C₂²×C₇	—	2	2	no	—
572	C₂²×C₇	—	4	4	no	—
573	C₂²×C₇	—	4	8	no	—
574	C₂²×C₇	—	4	2	no	—
575	C₂²×C₇	—	4	2	no	—
576	C₂²×C₇	—	4	2	no	—
577	C₂²×C₇	—	4	2	no	—
578	C₂²×C₇	—	4	2	no	—
579	C₂²×C₇	—	4	2	no	—
580	C₂²×C₇	—	4	2	no	—
581	C₂²×C₇	—	4	2	no	—
582	C₂²×C₇	—	8	16	no	—
583	C₂²×C₇	—	8	4	no	—
584	C₂²×C₇	—	8	4	no	—
585	C₂²×C₇	#546	1	2	yes	—
586	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
587	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
588	C₂²×C₇	#577	1	2	yes	—
589	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
590	C₄×C₇	—	2	2	no	—
591	C₄×C₇	—	2	2	no	—
592	C₄×C₇	—	2	2	no	—
593	C₄×C₇	—	2	2	no	—
594	C₄×C₇	—	4	2	no	—
595	C₄×C₇	—	4	2	no	—
596	C₄×C₇	—	4	2	no	—
597	C₄×C₇	—	4	2	no	—
598	C₄×C₇	—	4	2	no	—
599	C₄×C₇	#546	1	2	yes	—
600	C₄×C₇	C₂²×#41	1	1	yes	characteristic
601	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
602	C₂⁴	—	2	1	no	—
603	C₂⁴	—	2	1	no	—
604	C₂⁴	—	2	1	no	—
605	C₂⁴	—	2	4	no	—
606	C₂⁴	—	4	4	no	—
607	C₂⁴	—	4	4	no	—
608	C₂⁴	—	8	2	no	—
609	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
610	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
611	#41	—	2	8	no	—
612	#41	—	4	4	no	—
613	#41	—	4	8	no	—
614	#41	—	4	32	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	4	no	—
617	C₂×Q₈	—	2	2	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	4	4	no	—
620	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	8	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	4	4	no	—
637	C₂×D₄	—	4	8	no	—
638	C₂×D₄	—	4	4	no	—
639	C₂×D₄	—	4	4	no	—
640	C₂×D₄	—	4	4	no	—
641	C₂×D₄	—	4	4	no	—
642	C₂×D₄	—	8	2	no	—
643	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
644	C₂×D₄	C₇×#41	1	4	yes	complemented
645	C₂×D₄	C₂⁴×C₇	1	2	yes	—
646	C₂×D₄	C₂⁴×C₇	1	2	yes	—
647	C₂×D₄	C₂⁴×C₇	1	2	yes	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	4	4	no	—
663	C₂²×C₄	—	4	4	no	—
664	C₂²×C₄	—	4	4	no	—
665	C₂²×C₄	—	4	4	no	—
666	C₂²×C₄	—	8	2	no	—
667	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
668	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
669	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
670	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
671	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
672	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
676	SD₁₆	—	4	4	no	—
677	D₈	—	2	8	no	—
678	D₈	—	4	4	no	—
679	M₁₆	—	4	4	no	—
680	C₂×C₈	—	2	2	no	—
681	C₂×C₈	—	2	2	no	—
682	C₂×C₈	—	2	2	no	—
683	C₂×C₈	—	2	2	no	—
684	C₂×C₈	—	4	4	no	—
685	C₂×C₈	C₂⁴×C₇	1	2	yes	—
686	C₂×C₈	C₂⁴×C₇	1	2	yes	—
687	C₂×C₈	C₂⁴×C₇	1	2	yes	—
688	C₂×C₈	C₂⁴×C₇	1	2	yes	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
698	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
699	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
700	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
701	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
711	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
712	C₄²	C₂×C₇×D₄	1	2	yes	—
713	C₄²	C₂⁴×C₇	1	2	yes	—
714	C₂×C₇	—	2	4	no	—
715	C₂×C₇	—	4	2	no	—
716	C₂×C₇	—	4	4	no	—
717	C₂×C₇	—	8	2	no	—
718	C₂×C₇	—	8	2	no	—
719	C₂×C₇	#3306	1	4	yes	direct product factor
720	C₂×C₇	C₂×#546	1	1	yes	characteristic
721	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
722	C₂×C₇	C₂×#577	1	1	yes	characteristic
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	4	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	4	8	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	4	2	no	—
736	C₂³	—	4	2	no	—
737	C₂³	—	4	2	no	—
738	C₂³	—	4	8	no	—
739	C₂³	—	4	2	no	—
740	C₂³	—	4	2	no	—
741	C₂³	—	4	2	no	—
742	C₂³	—	8	4	no	—
743	C₂³	—	8	16	no	—
744	C₂³	C₇×AGL(1,ℤ/8)	1	4	yes	—
745	C₂³	C₂²×C₇×D₄	1	2	yes	—
746	C₂³	C₂²×C₇×D₄	1	2	yes	—
747	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
748	Q₈	—	2	2	no	—
749	Q₈	—	2	2	no	—
750	Q₈	—	4	8	no	—
751	Q₈	—	4	2	no	—
752	D₄	—	2	8	no	—
753	D₄	—	2	2	no	—
754	D₄	—	2	2	no	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	4	no	—
759	D₄	—	4	8	no	—
760	D₄	—	4	8	no	—
761	D₄	—	4	8	no	—
762	D₄	—	4	8	no	—
763	D₄	—	4	2	no	—
764	D₄	—	4	2	no	—
765	D₄	—	8	4	no	—
766	D₄	C₂×C₇×#41	1	4	yes	complemented
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	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	4	8	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	8	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	8	4	no	—
792	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
793	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
794	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
795	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
796	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
797	C₂×C₄	C₂×C₇×#41	1	2	yes	—
798	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
799	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
800	C₈	—	2	2	no	—
801	C₈	—	2	2	no	—
802	C₈	—	2	2	no	—
803	C₈	—	2	2	no	—
804	C₇	C₂×#3306	1	1	yes	characteristic, direct product factor, Sylow
805	C₂²	—	2	2	no	—
806	C₂²	—	2	8	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	4	no	—
815	C₂²	—	4	8	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	8	16	no	—
823	C₂²	—	8	4	no	—
824	C₂²	—	8	4	no	—
825	C₂²	C₇×#546	1	2	yes	—
826	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
827	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
828	C₂²	C₇×#577	1	2	yes	—
829	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
830	C₄	—	2	2	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	C₇×#546	1	2	yes	—
840	C₄	C₂²×C₇×#41	1	1	yes	characteristic
841	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
842	C₂	—	2	4	no	—
843	C₂	—	4	2	no	—
844	C₂	—	4	4	no	—
845	C₂	—	8	2	no	—
846	C₂	—	8	2	no	—
847	C₂	C₇×#3306	1	4	yes	direct product factor
848	C₂	C₂×C₇×#546	1	1	yes	characteristic
849	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
850	C₂	C₂×C₇×#577	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×#547	C₂	semidirect
2. C₂×C₇×#546	C₂	semidirect
3. C₇×#3306	C₂	direct (N × H)
4. C₂×C₇×#489	C₂	semidirect
5. C₂×C₇×#481	C₂	semidirect
6. C₂×C₇×#483	C₂	semidirect
7. C₂×C₇×#476	C₂	semidirect
8. C₂×C₇×#469	C₂	semidirect
9. C₂×C₇×#465	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×#417	C₂	semidirect
16. C₂²×C₇×#102	C₂	semidirect
20. C₂²×C₇×SD₁₆	C₂²	semidirect
23. C₂²×C₇×M₁₆	C₂²	semidirect
26. C₇×#547	C₂²	semidirect
28. C₇×#546	C₂²	semidirect
29. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₇×#121	C₂²	semidirect
43. C₂×C₄×C₇×D₄	C₂²	semidirect
45. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
47. C₇×#489	C₂²	semidirect
48. C₇×#483	C₂²	semidirect
49. C₇×#481	C₂²	semidirect
50. C₇×#476	C₂²	semidirect
51. C₇×#469	C₂²	semidirect
52. C₇×#465	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×#106	C₂²	semidirect
59. C₂×C₇×#106	C₂²	semidirect
60. C₂×C₇×#106	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
72. C₂×C₇×#102	C₂²	semidirect
73. C₂×C₇×#102	C₂²	semidirect
75. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₇×#97	C₂²	semidirect
77. C₂×#3306	C₇	direct (N × H)
108. C₂×C₇×SD₁₆	C₂³	semidirect
114. C₂×C₇×M₁₆	C₂³	semidirect
122. C₇×C₄⋊Q₈	C₂³	semidirect
137. C₇×#121	C₂³	semidirect
144. C₄×C₇×D₄	C₂³	semidirect
157. C₂×C₇×C₄⋊C₄	C₂³	semidirect
170. C₇×#106	C₂³	semidirect
171. C₇×#106	C₂³	semidirect
172. C₇×#106	C₂³	semidirect
173. C₇×C₄⋊C₈	C₂³	semidirect
174. C₇×#103	C₂³	semidirect
175. C₇×#103	C₂³	semidirect
176. C₇×#103	C₂³	semidirect
183. C₇×#102	C₂³	semidirect
185. C₇×C₂²⋊C₈	C₂³	semidirect
186. C₇×#97	C₂³	semidirect
187. C₂×#547	C₂×C₇	semidirect
188. C₂×#546	C₂×C₇	semidirect
189. #3306	C₂×C₇	direct (N × H)
190. C₂×#489	C₂×C₇	semidirect
191. C₂×#481	C₂×C₇	semidirect
192. C₂×#483	C₂×C₇	semidirect
193. C₂×#476	C₂×C₇	semidirect
194. C₂×#469	C₂×C₇	semidirect
195. C₂×#465	C₂×C₇	semidirect
196. C₂×#463	C₂×C₇	semidirect
197. C₂×#449	C₂×C₇	semidirect
198. C₂×#447	C₂×C₇	semidirect
199. C₂×#442	C₂×C₇	semidirect
200. C₂×#435	C₂×C₇	semidirect
201. C₂×#417	C₂×C₇	semidirect
202. C₂²×#102	C₂×C₇	semidirect
245. C₂×C₇×D₄	#41	semidirect
318. C₂²×SD₁₆	C₂²×C₇	semidirect
321. C₂²×M₁₆	C₂²×C₇	semidirect
324. #547	C₂²×C₇	semidirect
326. #546	C₂²×C₇	semidirect
327. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
337. C₂×#121	C₂²×C₇	semidirect
341. C₂×C₄×D₄	C₂²×C₇	semidirect
343. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
345. #489	C₂²×C₇	semidirect
346. #483	C₂²×C₇	semidirect
347. #481	C₂²×C₇	semidirect
348. #476	C₂²×C₇	semidirect
349. #469	C₂²×C₇	semidirect
350. #465	C₂²×C₇	semidirect
351. #463	C₂²×C₇	semidirect
352. #449	C₂²×C₇	semidirect
353. #447	C₂²×C₇	semidirect
354. #442	C₂²×C₇	semidirect
355. #435	C₂²×C₇	semidirect
356. C₂×#106	C₂²×C₇	semidirect
357. C₂×#106	C₂²×C₇	semidirect
358. C₂×#106	C₂²×C₇	semidirect
359. C₂×C₄⋊C₈	C₂²×C₇	semidirect
360. #417	C₂²×C₇	semidirect
361. C₂×#103	C₂²×C₇	semidirect
362. C₂×#103	C₂²×C₇	semidirect
363. C₂×#103	C₂²×C₇	semidirect
370. C₂×#102	C₂²×C₇	semidirect
371. C₂×#102	C₂²×C₇	semidirect
373. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
374. C₂×#97	C₂²×C₇	semidirect
418. C₇×D₄	C₂×#41	semidirect
486. C₂×SD₁₆	C₂³×C₇	semidirect
492. C₂×M₁₆	C₂³×C₇	semidirect
500. C₄⋊Q₈	C₂³×C₇	semidirect
515. #121	C₂³×C₇	semidirect
522. C₄×D₄	C₂³×C₇	semidirect
535. C₂×C₄⋊C₄	C₂³×C₇	semidirect
548. #106	C₂³×C₇	semidirect
549. #106	C₂³×C₇	semidirect
550. #106	C₂³×C₇	semidirect
551. C₄⋊C₈	C₂³×C₇	semidirect
552. #103	C₂³×C₇	semidirect
553. #103	C₂³×C₇	semidirect
554. #103	C₂³×C₇	semidirect
561. #102	C₂³×C₇	semidirect
563. C₂²⋊C₈	C₂³×C₇	semidirect
564. #97	C₂³×C₇	semidirect
644. C₂×D₄	C₇×#41	semidirect
719. C₂×C₇	#3306	direct (N × H)
766. D₄	C₂×C₇×#41	semidirect
804. C₇	C₂×#3306	direct (N × H)
847. C₂	C₇×#3306	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×#547	2
C₂×C₇×#546	2
C₇×#3306	2
C₂×C₇×#489	2
C₂×C₇×#481	2
C₂×C₇×#483	2
C₂×C₇×#476	2
C₂×C₇×#469	2
C₂×C₇×#465	2
C₂×C₇×#463	2
C₂×C₇×#449	2
C₂×C₇×#447	2
C₂×C₇×#442	2
C₂×C₇×#435	2
C₂×C₇×#417	2
C₂²×C₇×#102	2
C₂×#3306	7

Subgroups — C2×C7×#3306 #13238341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3306 #13238341