Subgroups — C₂×C₇×#3320 #13238348

Order 1792.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 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
2	C₂×C₇×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3320	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#491	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#465	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#448	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#448	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×#419	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
19	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
23	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
24	C₇×#553	—	2	4	no	—
25	C₇×#553	C₂²	1	8	yes	—
26	C₇×D₄×Q₈	—	2	4	no	—
27	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
28	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
29	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×#126	—	2	1	no	—
31	C₂×C₇×#125	C₂²	1	1	yes	characteristic
32	C₂×C₇×#123	—	2	1	no	—
33	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
34	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
35	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×#121	—	2	1	no	—
38	C₂×C₇×#121	C₂²	1	1	yes	characteristic
39	C₂×C₇×#121	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×D₄	—	2	1	no	—
42	C₂×C₄×C₇×D₄	—	2	1	no	—
43	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₇×#117	C₂²	1	1	yes	characteristic
46	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₇×#491	C₂²	1	8	yes	complemented
48	C₇×#485	C₂²	1	8	yes	complemented
49	C₇×#484	C₂²	1	8	yes	complemented
50	C₇×#479	C₂²	1	8	yes	complemented
51	C₇×#468	C₂²	1	8	yes	complemented
52	C₇×#465	C₂²	1	8	yes	complemented
53	C₇×#461	C₂²	1	8	yes	complemented
54	C₇×#448	C₂²	1	8	yes	complemented
55	C₇×#448	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
59	C₂×C₇×#107	C₂²	1	1	yes	characteristic
60	C₂×C₇×#106	C₂²	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₇×#419	C₂²	1	8	yes	complemented
63	C₂×C₇×#103	C₂²	1	1	yes	characteristic
64	C₂×C₇×#103	C₂²	1	1	yes	characteristic
65	C₂×C₇×#103	C₂²	1	1	yes	characteristic
66	C₂×C₇×#103	C₂²	1	1	yes	characteristic
67	C₂×C₇×#103	C₂²	1	1	yes	characteristic
68	C₂×C₇×#103	C₂²	1	1	yes	characteristic
69	C₂×C₇×#103	C₂²	1	1	yes	characteristic
70	C₂×C₇×#103	C₂²	1	1	yes	characteristic
71	C₂×C₇×#103	C₂²	1	1	yes	characteristic
72	C₂×C₇×#103	C₂²	1	8	yes	complemented
73	C₂×C₇×#102	C₂²	1	1	yes	characteristic
74	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₇×#97	C₂²	1	1	yes	characteristic
77	C₂×#3320	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂²×C₇×Q₈	—	2	1	no	—
79	C₂²×C₇×Q₈	—	2	1	no	—
80	C₂²×C₇×Q₈	—	2	2	no	—
81	C₂²×C₇×Q₈	—	2	2	no	—
82	C₂²×C₇×Q₈	—	2	4	no	—
83	C₂²×C₇×Q₈	—	2	4	no	—
84	C₂²×C₇×Q₈	—	4	2	no	—
85	C₂²×C₇×Q₈	—	4	2	no	—
86	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×Q₈	C₂³	1	4	yes	—
89	C₂²×C₇×Q₈	C₂³	1	4	yes	—
90	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
91	C₂²×C₇×D₄	—	2	1	no	—
92	C₂²×C₇×D₄	—	2	1	no	—
93	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
94	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₇	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
101	C₂×C₇×SD₁₆	—	2	4	no	—
102	C₂×C₇×SD₁₆	—	4	2	no	—
103	C₂×C₇×SD₁₆	—	4	2	no	—
104	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₇×M₁₆	—	4	2	no	—
108	C₂×C₇×M₁₆	C₂³	1	4	yes	—
109	C₂²×C₇×C₈	—	4	2	no	—
110	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
111	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
112	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
113	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
114	C₂²×C₇×C₈	C₂³	1	4	yes	—
115	C₇×C₄⋊Q₈	—	2	8	no	—
116	C₇×C₄⋊Q₈	—	2	2	no	—
117	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
118	C₇×#126	—	2	8	no	—
119	C₇×#125	—	2	2	no	—
120	C₇×#125	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	8	no	—
125	C₇×C₂²⋊Q₈	—	2	8	no	—
126	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
127	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₇×#121	—	2	8	no	—
129	C₇×#121	—	2	2	no	—
130	C₇×#121	—	2	2	no	—
131	C₇×#121	C₂³	1	4	yes	—
132	C₇×#121	C₂³	1	4	yes	—
133	C₄×C₇×Q₈	—	2	2	no	—
134	C₄×C₇×Q₈	C₂³	1	4	yes	—
135	C₄×C₇×D₄	—	2	8	no	—
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	C₇×#117	—	2	2	no	—
142	C₇×#117	C₂³	1	4	yes	—
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	—	2	1	no	—
151	C₂×C₇×C₄⋊C₄	—	2	1	no	—
152	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
153	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
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×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	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	—
170	C₇×#107	C₂³	1	4	yes	—
171	C₇×#106	C₂³	1	4	yes	—
172	C₇×C₄⋊C₈	C₂³	1	4	yes	—
173	C₇×#103	C₂³	1	4	yes	—
174	C₇×#103	C₂³	1	4	yes	—
175	C₇×#103	C₂³	1	4	yes	—
176	C₇×#103	C₂³	1	4	yes	—
177	C₇×#103	C₂³	1	4	yes	—
178	C₇×#103	C₂³	1	4	yes	—
179	C₇×#103	C₂³	1	4	yes	—
180	C₇×#103	C₂³	1	4	yes	—
181	C₇×#103	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	—
185	C₇×#97	C₂³	1	4	yes	—
186	C₂×#553	C₂×C₇	1	1	yes	characteristic
187	C₂×D₄×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
188	#3320	C₂×C₇	1	16	yes	direct product factor
189	C₂×#491	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂×#484	C₂×C₇	1	1	yes	characteristic, complemented
191	C₂×#485	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂×#479	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#468	C₂×C₇	1	1	yes	characteristic, complemented
194	C₂×#465	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×#461	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×#448	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×#448	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×#419	C₂×C₇	1	1	yes	characteristic, complemented
201	C₂²×#103	C₂×C₇	1	1	yes	characteristic, complemented
202	C₂⁴×C₇	—	2	1	no	—
203	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
204	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
205	C₂×C₇×Q₈	—	2	1	no	—
206	C₂×C₇×Q₈	—	2	4	no	—
207	C₂×C₇×Q₈	—	2	4	no	—
208	C₂×C₇×Q₈	—	2	1	no	—
209	C₂×C₇×Q₈	—	2	1	no	—
210	C₂×C₇×Q₈	—	2	2	no	—
211	C₂×C₇×Q₈	—	2	8	no	—
212	C₂×C₇×Q₈	—	2	8	no	—
213	C₂×C₇×Q₈	—	2	2	no	—
214	C₂×C₇×Q₈	—	2	2	no	—
215	C₂×C₇×Q₈	—	2	2	no	—
216	C₂×C₇×Q₈	—	2	2	no	—
217	C₂×C₇×Q₈	—	4	4	no	—
218	C₂×C₇×Q₈	—	4	4	no	—
219	C₂×C₇×Q₈	—	4	4	no	—
220	C₂×C₇×Q₈	—	4	4	no	—
221	C₂×C₇×Q₈	—	4	8	no	—
222	C₂×C₇×Q₈	—	4	8	no	—
223	C₂×C₇×Q₈	#41	1	4	yes	—
224	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
225	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
226	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
227	C₂×C₇×D₄	—	2	4	no	—
228	C₂×C₇×D₄	—	2	4	no	—
229	C₂×C₇×D₄	—	2	4	no	—
230	C₂×C₇×D₄	—	2	1	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	—	8	2	no	—
235	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
236	C₂×C₇×D₄	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₇	—	2	1	no	—
238	C₂²×C₄×C₇	—	2	2	no	—
239	C₂²×C₄×C₇	—	2	2	no	—
240	C₂²×C₄×C₇	—	2	2	no	—
241	C₂²×C₄×C₇	—	2	2	no	—
242	C₂²×C₄×C₇	—	2	4	no	—
243	C₂²×C₄×C₇	—	2	4	no	—
244	C₂²×C₄×C₇	—	2	1	no	—
245	C₂²×C₄×C₇	—	2	1	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	4	no	—
251	C₂²×C₄×C₇	—	2	4	no	—
252	C₂²×C₄×C₇	—	4	4	no	—
253	C₂²×C₄×C₇	—	4	4	no	—
254	C₂²×C₄×C₇	—	8	2	no	—
255	C₂²×C₄×C₇	—	8	2	no	—
256	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
265	C₇×SD₁₆	—	2	8	no	—
266	C₇×SD₁₆	—	4	4	no	—
267	C₇×SD₁₆	—	4	4	no	—
268	C₇×M₁₆	—	4	4	no	—
269	C₂×C₇×C₈	—	2	2	no	—
270	C₂×C₇×C₈	—	2	2	no	—
271	C₂×C₇×C₈	—	2	2	no	—
272	C₂×C₇×C₈	—	2	2	no	—
273	C₂×C₇×C₈	—	4	4	no	—
274	C₂×C₇×C₈	C₂⁴	1	2	yes	—
275	C₂×C₇×C₈	C₂⁴	1	2	yes	—
276	C₂×C₇×C₈	C₂⁴	1	2	yes	—
277	C₂×C₇×C₈	C₂⁴	1	2	yes	—
278	C₇×C₄⋊C₄	—	2	1	no	—
279	C₇×C₄⋊C₄	—	2	1	no	—
280	C₇×C₄⋊C₄	—	2	4	no	—
281	C₇×C₄⋊C₄	—	2	4	no	—
282	C₇×C₄⋊C₄	—	2	4	no	—
283	C₇×C₄⋊C₄	—	2	4	no	—
284	C₇×C₄⋊C₄	—	2	4	no	—
285	C₇×C₄⋊C₄	—	2	4	no	—
286	C₇×C₄⋊C₄	—	2	4	no	—
287	C₇×C₄⋊C₄	—	2	4	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	C₂×D₄	1	4	yes	—
302	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
303	C₄²×C₇	—	2	4	no	—
304	C₄²×C₇	—	2	4	no	—
305	C₄²×C₇	C₂×D₄	1	2	yes	—
306	C₄²×C₇	C₂⁴	1	2	yes	—
307	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
308	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
309	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
310	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
311	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
312	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
313	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
314	#553	—	2	4	no	—
315	#553	C₂²×C₇	1	8	yes	—
316	D₄×Q₈	—	2	4	no	—
317	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
318	C₂×C₄⋊Q₈	—	2	1	no	—
319	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
320	C₂×#126	—	2	1	no	—
321	C₂×#125	C₂²×C₇	1	1	yes	characteristic
322	C₂×#123	—	2	1	no	—
323	C₂×C₂²⋊Q₈	—	2	1	no	—
324	C₂×C₂²⋊Q₈	—	2	1	no	—
325	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
326	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
327	C₂×#121	—	2	1	no	—
328	C₂×#121	C₂²×C₇	1	1	yes	characteristic
329	C₂×#121	C₂²×C₇	1	1	yes	characteristic
330	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
331	C₂×C₄×D₄	—	2	1	no	—
332	C₂×C₄×D₄	—	2	1	no	—
333	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
334	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
335	C₂×#117	C₂²×C₇	1	1	yes	characteristic
336	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
337	#491	C₂²×C₇	1	8	yes	complemented
338	#485	C₂²×C₇	1	8	yes	complemented
339	#484	C₂²×C₇	1	8	yes	complemented
340	#479	C₂²×C₇	1	8	yes	complemented
341	#468	C₂²×C₇	1	8	yes	complemented
342	#465	C₂²×C₇	1	8	yes	complemented
343	#461	C₂²×C₇	1	8	yes	complemented
344	#448	C₂²×C₇	1	8	yes	complemented
345	#448	C₂²×C₇	1	8	yes	complemented
346	#440	C₂²×C₇	1	8	yes	complemented
347	#435	C₂²×C₇	1	8	yes	complemented
348	C₂×#107	C₂²×C₇	1	1	yes	characteristic
349	C₂×#107	C₂²×C₇	1	1	yes	characteristic
350	C₂×#106	C₂²×C₇	1	1	yes	characteristic
351	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
352	#419	C₂²×C₇	1	8	yes	complemented
353	C₂×#103	C₂²×C₇	1	1	yes	characteristic
354	C₂×#103	C₂²×C₇	1	1	yes	characteristic
355	C₂×#103	C₂²×C₇	1	1	yes	characteristic
356	C₂×#103	C₂²×C₇	1	1	yes	characteristic
357	C₂×#103	C₂²×C₇	1	1	yes	characteristic
358	C₂×#103	C₂²×C₇	1	1	yes	characteristic
359	C₂×#103	C₂²×C₇	1	1	yes	characteristic
360	C₂×#103	C₂²×C₇	1	1	yes	characteristic
361	C₂×#103	C₂²×C₇	1	1	yes	characteristic
362	C₂×#103	C₂²×C₇	1	8	yes	complemented
363	C₂×#102	C₂²×C₇	1	1	yes	characteristic
364	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
365	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
366	C₂×#97	C₂²×C₇	1	1	yes	characteristic
367	C₂³×C₇	—	2	2	no	—
368	C₂³×C₇	—	2	2	no	—
369	C₂³×C₇	—	2	2	no	—
370	C₂³×C₇	—	2	2	no	—
371	C₂³×C₇	—	2	2	no	—
372	C₂³×C₇	—	2	2	no	—
373	C₂³×C₇	—	4	2	no	—
374	C₂³×C₇	—	4	2	no	—
375	C₂³×C₇	—	4	2	no	—
376	C₂³×C₇	#137	1	4	yes	—
377	C₂³×C₇	C₂²×D₄	1	2	yes	—
378	C₂³×C₇	C₂²×D₄	1	2	yes	—
379	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
380	C₇×Q₈	—	2	4	no	—
381	C₇×Q₈	—	2	2	no	—
382	C₇×Q₈	—	2	2	no	—
383	C₇×Q₈	—	2	2	no	—
384	C₇×Q₈	—	2	2	no	—
385	C₇×Q₈	—	2	2	no	—
386	C₇×Q₈	—	4	8	no	—
387	C₇×Q₈	—	4	8	no	—
388	C₇×Q₈	—	4	2	no	—
389	C₇×Q₈	—	4	2	no	—
390	C₇×Q₈	C₂×#41	1	4	yes	—
391	C₇×D₄	—	2	8	no	—
392	C₇×D₄	—	2	2	no	—
393	C₇×D₄	—	2	2	no	—
394	C₇×D₄	—	4	8	no	—
395	C₇×D₄	—	4	2	no	—
396	C₇×D₄	—	8	4	no	—
397	C₂×C₄×C₇	—	2	2	no	—
398	C₂×C₄×C₇	—	2	2	no	—
399	C₂×C₄×C₇	—	2	4	no	—
400	C₂×C₄×C₇	—	2	2	no	—
401	C₂×C₄×C₇	—	2	2	no	—
402	C₂×C₄×C₇	—	2	2	no	—
403	C₂×C₄×C₇	—	2	4	no	—
404	C₂×C₄×C₇	—	2	4	no	—
405	C₂×C₄×C₇	—	2	2	no	—
406	C₂×C₄×C₇	—	2	2	no	—
407	C₂×C₄×C₇	—	2	2	no	—
408	C₂×C₄×C₇	—	2	2	no	—
409	C₂×C₄×C₇	—	2	2	no	—
410	C₂×C₄×C₇	—	2	2	no	—
411	C₂×C₄×C₇	—	2	2	no	—
412	C₂×C₄×C₇	—	2	2	no	—
413	C₂×C₄×C₇	—	2	2	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	4	8	no	—
416	C₂×C₄×C₇	—	4	8	no	—
417	C₂×C₄×C₇	—	4	2	no	—
418	C₂×C₄×C₇	—	4	2	no	—
419	C₂×C₄×C₇	—	4	2	no	—
420	C₂×C₄×C₇	—	4	2	no	—
421	C₂×C₄×C₇	—	4	2	no	—
422	C₂×C₄×C₇	—	4	2	no	—
423	C₂×C₄×C₇	—	8	4	no	—
424	C₂×C₄×C₇	—	8	4	no	—
425	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₇	C₂×#41	1	2	yes	—
431	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
432	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
433	C₇×C₈	—	2	2	no	—
434	C₇×C₈	—	2	2	no	—
435	C₇×C₈	—	2	2	no	—
436	C₇×C₈	—	2	2	no	—
437	C₂²×Q₈	—	2	1	no	—
438	C₂²×Q₈	—	2	1	no	—
439	C₂²×Q₈	—	2	2	no	—
440	C₂²×Q₈	—	2	2	no	—
441	C₂²×Q₈	—	2	4	no	—
442	C₂²×Q₈	—	2	4	no	—
443	C₂²×Q₈	—	4	2	no	—
444	C₂²×Q₈	—	4	2	no	—
445	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
446	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
447	C₂²×Q₈	C₂³×C₇	1	4	yes	—
448	C₂²×Q₈	C₂³×C₇	1	4	yes	—
449	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
450	C₂²×D₄	—	2	1	no	—
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
453	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
454	C₂³×C₄	—	2	1	no	—
455	C₂³×C₄	—	2	1	no	—
456	C₂³×C₄	—	2	1	no	—
457	C₂³×C₄	—	2	1	no	—
458	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
460	C₂×SD₁₆	—	2	4	no	—
461	C₂×SD₁₆	—	4	2	no	—
462	C₂×SD₁₆	—	4	2	no	—
463	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
464	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
465	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
466	C₂×M₁₆	—	4	2	no	—
467	C₂×M₁₆	C₂³×C₇	1	4	yes	—
468	C₂²×C₈	—	4	2	no	—
469	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₇	1	4	yes	—
474	C₄⋊Q₈	—	2	8	no	—
475	C₄⋊Q₈	—	2	2	no	—
476	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
477	#126	—	2	8	no	—
478	#125	—	2	2	no	—
479	#125	C₂³×C₇	1	4	yes	—
480	#123	—	2	8	no	—
481	C₂²⋊Q₈	—	2	2	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	8	no	—
484	C₂²⋊Q₈	—	2	8	no	—
485	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
486	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
487	#121	—	2	8	no	—
488	#121	—	2	2	no	—
489	#121	—	2	2	no	—
490	#121	C₂³×C₇	1	4	yes	—
491	#121	C₂³×C₇	1	4	yes	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	C₂³×C₇	1	4	yes	—
494	C₄×D₄	—	2	8	no	—
495	C₄×D₄	—	2	8	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	C₇×D₄	1	4	yes	—
498	C₄×D₄	C₂³×C₇	1	4	yes	—
499	C₄×D₄	C₂³×C₇	1	4	yes	—
500	#117	—	2	2	no	—
501	#117	C₂³×C₇	1	4	yes	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	2	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
515	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
525	C₂×C₄²	—	2	1	no	—
526	C₂×C₄²	—	2	1	no	—
527	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
528	#107	C₂³×C₇	1	4	yes	—
529	#107	C₂³×C₇	1	4	yes	—
530	#106	C₂³×C₇	1	4	yes	—
531	C₄⋊C₈	C₂³×C₇	1	4	yes	—
532	#103	C₂³×C₇	1	4	yes	—
533	#103	C₂³×C₇	1	4	yes	—
534	#103	C₂³×C₇	1	4	yes	—
535	#103	C₂³×C₇	1	4	yes	—
536	#103	C₂³×C₇	1	4	yes	—
537	#103	C₂³×C₇	1	4	yes	—
538	#103	C₂³×C₇	1	4	yes	—
539	#103	C₂³×C₇	1	4	yes	—
540	#103	C₂³×C₇	1	4	yes	—
541	#102	C₂³×C₇	1	4	yes	—
542	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
543	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
544	#97	C₂³×C₇	1	4	yes	—
545	C₂²×C₇	—	2	2	no	—
546	C₂²×C₇	—	2	8	no	—
547	C₂²×C₇	—	2	2	no	—
548	C₂²×C₇	—	2	2	no	—
549	C₂²×C₇	—	2	2	no	—
550	C₂²×C₇	—	2	2	no	—
551	C₂²×C₇	—	4	4	no	—
552	C₂²×C₇	—	4	2	no	—
553	C₂²×C₇	—	4	2	no	—
554	C₂²×C₇	—	4	2	no	—
555	C₂²×C₇	—	8	4	no	—
556	C₂²×C₇	#546	1	2	yes	—
557	C₂²×C₇	C₂×#137	1	4	yes	—
558	C₂²×C₇	C₂×#137	1	2	yes	—
559	C₂²×C₇	#577	1	2	yes	—
560	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
561	C₄×C₇	—	2	2	no	—
562	C₄×C₇	—	2	2	no	—
563	C₄×C₇	—	2	4	no	—
564	C₄×C₇	—	2	2	no	—
565	C₄×C₇	—	2	2	no	—
566	C₄×C₇	—	4	2	no	—
567	C₄×C₇	—	4	2	no	—
568	C₄×C₇	—	4	2	no	—
569	C₄×C₇	—	4	2	no	—
570	C₄×C₇	—	4	2	no	—
571	C₄×C₇	—	4	2	no	—
572	C₄×C₇	#546	1	2	yes	—
573	C₄×C₇	C₂²×#41	1	1	yes	characteristic
574	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
575	C₂⁴	—	2	1	no	—
576	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
577	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	4	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	8	no	—
585	C₂×Q₈	—	2	8	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	2	2	no	—
588	C₂×Q₈	—	2	2	no	—
589	C₂×Q₈	—	2	2	no	—
590	C₂×Q₈	—	4	4	no	—
591	C₂×Q₈	—	4	4	no	—
592	C₂×Q₈	—	4	4	no	—
593	C₂×Q₈	—	4	4	no	—
594	C₂×Q₈	—	4	8	no	—
595	C₂×Q₈	—	4	8	no	—
596	C₂×Q₈	C₇×#41	1	4	yes	—
597	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
598	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
599	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	—	8	2	no	—
608	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
609	C₂×D₄	C₂⁴×C₇	1	2	yes	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	4	4	no	—
626	C₂²×C₄	—	4	4	no	—
627	C₂²×C₄	—	8	2	no	—
628	C₂²×C₄	—	8	2	no	—
629	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
630	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
631	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
632	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
633	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
634	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
638	SD₁₆	—	2	8	no	—
639	SD₁₆	—	4	4	no	—
640	SD₁₆	—	4	4	no	—
641	M₁₆	—	4	4	no	—
642	C₂×C₈	—	2	2	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	2	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	—	4	4	no	—
647	C₂×C₈	C₂⁴×C₇	1	2	yes	—
648	C₂×C₈	C₂⁴×C₇	1	2	yes	—
649	C₂×C₈	C₂⁴×C₇	1	2	yes	—
650	C₂×C₈	C₂⁴×C₇	1	2	yes	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
664	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
665	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
675	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
676	C₄²	—	2	4	no	—
677	C₄²	—	2	4	no	—
678	C₄²	C₂×C₇×D₄	1	2	yes	—
679	C₄²	C₂⁴×C₇	1	2	yes	—
680	C₂×C₇	—	2	4	no	—
681	C₂×C₇	—	4	2	no	—
682	C₂×C₇	—	8	2	no	—
683	C₂×C₇	#3320	1	4	yes	direct product factor
684	C₂×C₇	C₂×#546	1	1	yes	characteristic
685	C₂×C₇	C₂²×#137	1	1	yes	characteristic
686	C₂×C₇	C₂×#577	1	1	yes	characteristic
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	4	2	no	—
694	C₂³	—	4	2	no	—
695	C₂³	—	4	2	no	—
696	C₂³	C₇×#137	1	4	yes	—
697	C₂³	C₂²×C₇×D₄	1	2	yes	—
698	C₂³	C₂²×C₇×D₄	1	2	yes	—
699	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
700	Q₈	—	2	2	no	—
701	Q₈	—	2	4	no	—
702	Q₈	—	2	2	no	—
703	Q₈	—	2	2	no	—
704	Q₈	—	2	2	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	4	8	no	—
707	Q₈	—	4	8	no	—
708	Q₈	—	4	2	no	—
709	Q₈	—	4	2	no	—
710	Q₈	C₂×C₇×#41	1	4	yes	—
711	D₄	—	2	8	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	2	no	—
714	D₄	—	4	8	no	—
715	D₄	—	4	2	no	—
716	D₄	—	8	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	4	8	no	—
736	C₂×C₄	—	4	8	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	4	2	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	8	4	no	—
744	C₂×C₄	—	8	4	no	—
745	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
746	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
747	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
748	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
749	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
750	C₂×C₄	C₂×C₇×#41	1	2	yes	—
751	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
752	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
753	C₈	—	2	2	no	—
754	C₈	—	2	2	no	—
755	C₈	—	2	2	no	—
756	C₈	—	2	2	no	—
757	C₇	C₂×#3320	1	1	yes	characteristic, direct product factor, Sylow
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	8	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	4	4	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	8	4	no	—
769	C₂²	C₇×#546	1	2	yes	—
770	C₂²	C₂×C₇×#137	1	4	yes	—
771	C₂²	C₂×C₇×#137	1	2	yes	—
772	C₂²	C₇×#577	1	2	yes	—
773	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	4	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	C₇×#546	1	2	yes	—
786	C₄	C₂²×C₇×#41	1	1	yes	characteristic
787	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
788	C₂	—	2	4	no	—
789	C₂	—	4	2	no	—
790	C₂	—	8	2	no	—
791	C₂	C₇×#3320	1	4	yes	direct product factor
792	C₂	C₂×C₇×#546	1	1	yes	characteristic
793	C₂	C₂²×C₇×#137	1	1	yes	characteristic
794	C₂	C₂×C₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#553	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
2. C₂×C₇×D₄×Q₈	C₂	semidirect
3. C₇×#3320	C₂	direct (N × H)
4. C₂×C₇×#491	C₂	semidirect
5. C₂×C₇×#484	C₂	semidirect
6. C₂×C₇×#485	C₂	semidirect
7. C₂×C₇×#479	C₂	semidirect
8. C₂×C₇×#468	C₂	semidirect
9. C₂×C₇×#465	C₂	semidirect
10. C₂×C₇×#461	C₂	semidirect
11. C₂×C₇×#448	C₂	semidirect
12. C₂×C₇×#448	C₂	semidirect
13. C₂×C₇×#440	C₂	semidirect
14. C₂×C₇×#435	C₂	semidirect
15. C₂×C₇×#419	C₂	semidirect
16. C₂²×C₇×#103	C₂	semidirect
27. C₇×D₄×Q₈	C₂²	semidirect
47. C₇×#491	C₂²	semidirect
48. C₇×#485	C₂²	semidirect
49. C₇×#484	C₂²	semidirect
50. C₇×#479	C₂²	semidirect
51. C₇×#468	C₂²	semidirect
52. C₇×#465	C₂²	semidirect
53. C₇×#461	C₂²	semidirect
54. C₇×#448	C₂²	semidirect
55. C₇×#448	C₂²	semidirect
56. C₇×#440	C₂²	semidirect
57. C₇×#435	C₂²	semidirect
62. C₇×#419	C₂²	semidirect
72. C₂×C₇×#103	C₂²	semidirect
77. C₂×#3320	C₇	direct (N × H)
187. C₂×D₄×Q₈	C₂×C₇	semidirect
188. #3320	C₂×C₇	direct (N × H)
189. C₂×#491	C₂×C₇	semidirect
190. C₂×#484	C₂×C₇	semidirect
191. C₂×#485	C₂×C₇	semidirect
192. C₂×#479	C₂×C₇	semidirect
193. C₂×#468	C₂×C₇	semidirect
194. C₂×#465	C₂×C₇	semidirect
195. C₂×#461	C₂×C₇	semidirect
196. C₂×#448	C₂×C₇	semidirect
197. C₂×#448	C₂×C₇	semidirect
198. C₂×#440	C₂×C₇	semidirect
199. C₂×#435	C₂×C₇	semidirect
200. C₂×#419	C₂×C₇	semidirect
201. C₂²×#103	C₂×C₇	semidirect
317. D₄×Q₈	C₂²×C₇	semidirect
337. #491	C₂²×C₇	semidirect
338. #485	C₂²×C₇	semidirect
339. #484	C₂²×C₇	semidirect
340. #479	C₂²×C₇	semidirect
341. #468	C₂²×C₇	semidirect
342. #465	C₂²×C₇	semidirect
343. #461	C₂²×C₇	semidirect
344. #448	C₂²×C₇	semidirect
345. #448	C₂²×C₇	semidirect
346. #440	C₂²×C₇	semidirect
347. #435	C₂²×C₇	semidirect
352. #419	C₂²×C₇	semidirect
362. C₂×#103	C₂²×C₇	semidirect
683. C₂×C₇	#3320	direct (N × H)
757. C₇	C₂×#3320	direct (N × H)
791. C₂	C₇×#3320	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×D₄×Q₈	2
C₇×#3320	2
C₂×C₇×#491	2
C₂×C₇×#484	2
C₂×C₇×#485	2
C₂×C₇×#479	2
C₂×C₇×#468	2
C₂×C₇×#465	2
C₂×C₇×#461	2
C₂×C₇×#448	2
C₂×C₇×#440	2
C₂×C₇×#435	2
C₂×C₇×#419	2
C₂²×C₇×#103	2
C₂×#3320	7

Subgroups — C2×C7×#3320 #13238348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3320 #13238348