Subgroups — C₂×C₇×#2481 #13211877

Order 1792.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2481	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#400	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#397	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#396	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#388	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#387	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#386	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#386	C₂	1	1	yes	maximal, characteristic
13	C₂×C₇×#386	C₂	1	1	yes	maximal, characteristic
14	C₂×C₇×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
21	C₂×C₇×#126	—	2	8	no	—
22	C₂×C₇×#126	C₂²	1	8	yes	complemented
23	C₂²×C₇×C₄⋊C₄	—	2	8	no	—
24	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₇×C₄⋊C₄	C₂²	1	8	yes	complemented
33	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
44	C₇×#400	C₂²	1	8	yes	complemented
45	C₇×#400	C₂²	1	8	yes	complemented
46	C₇×#397	C₂²	1	8	yes	complemented
47	C₇×#396	C₂²	1	8	yes	complemented
48	C₇×#388	C₂²	1	8	yes	complemented
49	C₇×#387	C₂²	1	8	yes	complemented
50	C₇×#387	C₂²	1	8	yes	complemented
51	C₇×#386	C₂²	1	8	yes	—
52	C₇×#386	C₂²	1	8	yes	—
53	C₇×#386	C₂²	1	8	yes	—
54	C₇×#385	C₂²	1	8	yes	complemented
55	C₇×#380	C₂²	1	8	yes	complemented
56	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	complemented
57	C₂×C₇×#95	C₂²	1	1	yes	characteristic
58	C₂×C₇×#95	C₂²	1	1	yes	characteristic
59	C₂×C₇×#95	C₂²	1	1	yes	characteristic
60	C₂×C₇×#95	C₂²	1	1	yes	characteristic
61	C₂×C₇×#95	C₂²	1	1	yes	characteristic
62	C₂×C₇×#95	C₂²	1	1	yes	characteristic
63	C₂×C₇×#95	C₂²	1	1	yes	characteristic
64	C₂×C₇×#95	C₂²	1	1	yes	characteristic
65	C₂×C₇×#95	C₂²	1	1	yes	characteristic
66	C₂×C₇×#95	C₂²	1	1	yes	characteristic
67	C₂×C₇×#95	C₂²	1	1	yes	characteristic
68	C₂×C₇×#95	C₂²	1	1	yes	characteristic
69	C₂×#2481	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂⁵×C₇	C₂³	1	1	yes	characteristic
71	C₂⁵×C₇	C₂³	1	1	yes	characteristic
72	C₂²×C₇×D₄	—	2	4	no	—
73	C₂²×C₇×D₄	—	2	4	no	—
74	C₂²×C₇×D₄	—	2	4	no	—
75	C₂²×C₇×D₄	C₂³	1	4	yes	—
76	C₂³×C₄×C₇	—	2	4	no	—
77	C₂³×C₄×C₇	—	2	4	no	—
78	C₂³×C₄×C₇	—	2	4	no	—
79	C₂³×C₄×C₇	—	2	4	no	—
80	C₂³×C₄×C₇	—	2	4	no	—
81	C₂³×C₄×C₇	—	2	4	no	—
82	C₂³×C₄×C₇	—	2	4	no	—
83	C₂³×C₄×C₇	—	4	2	no	—
84	C₂³×C₄×C₇	—	4	2	no	—
85	C₂³×C₄×C₇	C₂³	1	4	yes	—
86	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₇	C₂³	1	4	yes	—
96	C₂³×C₄×C₇	C₂³	1	4	yes	—
97	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
101	C₇×#126	—	2	32	no	—
102	C₂×C₇×C₄⋊C₄	—	2	4	no	—
103	C₂×C₇×C₄⋊C₄	—	2	4	no	—
104	C₂×C₇×C₄⋊C₄	—	2	4	no	—
105	C₂×C₇×C₄⋊C₄	—	2	4	no	—
106	C₂×C₇×C₄⋊C₄	—	2	4	no	—
107	C₂×C₇×C₄⋊C₄	—	2	4	no	—
108	C₂×C₇×C₄⋊C₄	—	2	32	no	—
109	C₂×C₇×C₄⋊C₄	—	4	2	no	—
110	C₂×C₇×C₄⋊C₄	D₄	1	8	yes	complemented
111	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
120	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
121	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
122	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
123	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
124	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
125	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
126	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
127	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
128	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₄²×C₇	—	2	4	no	—
138	C₂×C₄²×C₇	—	4	2	no	—
139	C₂×C₄²×C₇	C₂³	1	4	yes	—
140	C₂×C₄²×C₇	C₂³	1	4	yes	—
141	C₇×#95	C₂³	1	4	yes	—
142	C₇×#95	C₂³	1	4	yes	—
143	C₇×#95	C₂³	1	4	yes	—
144	C₇×#95	C₂³	1	4	yes	—
145	C₇×#95	C₂³	1	4	yes	—
146	C₇×#95	C₂³	1	4	yes	—
147	C₇×#95	C₂³	1	4	yes	—
148	C₇×#95	C₂³	1	4	yes	—
149	C₇×#95	C₂³	1	4	yes	—
150	C₇×#95	C₂³	1	4	yes	—
151	C₇×#95	C₂³	1	4	yes	—
152	C₇×#95	C₂³	1	4	yes	—
153	C₂²×#126	C₂×C₇	1	1	yes	characteristic, complemented
154	C₂³×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
155	#2481	C₂×C₇	1	16	yes	direct product factor
156	C₂×#400	C₂×C₇	1	1	yes	characteristic, complemented
157	C₂×#400	C₂×C₇	1	1	yes	characteristic, complemented
158	C₂×#397	C₂×C₇	1	1	yes	characteristic, complemented
159	C₂×#396	C₂×C₇	1	1	yes	characteristic, complemented
160	C₂×#388	C₂×C₇	1	1	yes	characteristic, complemented
161	C₂×#387	C₂×C₇	1	1	yes	characteristic, complemented
162	C₂×#387	C₂×C₇	1	1	yes	characteristic, complemented
163	C₂×#386	C₂×C₇	1	1	yes	characteristic
164	C₂×#386	C₂×C₇	1	1	yes	characteristic
165	C₂×#386	C₂×C₇	1	1	yes	characteristic
166	C₂×#385	C₂×C₇	1	1	yes	characteristic, complemented
167	C₂×#380	C₂×C₇	1	1	yes	characteristic, complemented
168	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
169	C₂⁴×C₇	—	2	2	no	—
170	C₂⁴×C₇	—	2	2	no	—
171	C₂⁴×C₇	—	2	2	no	—
172	C₂⁴×C₇	—	2	2	no	—
173	C₂⁴×C₇	—	2	2	no	—
174	C₂⁴×C₇	—	2	2	no	—
175	C₂⁴×C₇	—	2	2	no	—
176	C₂⁴×C₇	—	2	2	no	—
177	C₂⁴×C₇	—	2	2	no	—
178	C₂⁴×C₇	—	2	2	no	—
179	C₂⁴×C₇	—	2	2	no	—
180	C₂⁴×C₇	#41	1	4	yes	—
181	C₂⁴×C₇	#41	1	4	yes	—
182	C₂⁴×C₇	#41	1	4	yes	—
183	C₂⁴×C₇	C₂⁴	1	2	yes	—
184	C₂⁴×C₇	C₂⁴	1	2	yes	—
185	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
186	C₂×C₇×D₄	—	2	8	no	—
187	C₂×C₇×D₄	—	2	8	no	—
188	C₂×C₇×D₄	—	2	8	no	—
189	C₂×C₇×D₄	—	4	16	no	—
190	C₂²×C₄×C₇	—	2	32	no	—
191	C₂²×C₄×C₇	—	2	2	no	—
192	C₂²×C₄×C₇	—	2	8	no	—
193	C₂²×C₄×C₇	—	2	2	no	—
194	C₂²×C₄×C₇	—	2	2	no	—
195	C₂²×C₄×C₇	—	2	2	no	—
196	C₂²×C₄×C₇	—	2	2	no	—
197	C₂²×C₄×C₇	—	2	2	no	—
198	C₂²×C₄×C₇	—	2	2	no	—
199	C₂²×C₄×C₇	—	2	2	no	—
200	C₂²×C₄×C₇	—	2	8	no	—
201	C₂²×C₄×C₇	—	2	8	no	—
202	C₂²×C₄×C₇	—	2	2	no	—
203	C₂²×C₄×C₇	—	2	2	no	—
204	C₂²×C₄×C₇	—	2	2	no	—
205	C₂²×C₄×C₇	—	2	2	no	—
206	C₂²×C₄×C₇	—	2	2	no	—
207	C₂²×C₄×C₇	—	2	2	no	—
208	C₂²×C₄×C₇	—	2	2	no	—
209	C₂²×C₄×C₇	—	2	2	no	—
210	C₂²×C₄×C₇	—	2	2	no	—
211	C₂²×C₄×C₇	—	2	2	no	—
212	C₂²×C₄×C₇	—	2	2	no	—
213	C₂²×C₄×C₇	—	2	2	no	—
214	C₂²×C₄×C₇	—	2	2	no	—
215	C₂²×C₄×C₇	—	2	2	no	—
216	C₂²×C₄×C₇	—	2	8	no	—
217	C₂²×C₄×C₇	—	2	8	no	—
218	C₂²×C₄×C₇	—	2	2	no	—
219	C₂²×C₄×C₇	—	2	2	no	—
220	C₂²×C₄×C₇	—	2	2	no	—
221	C₂²×C₄×C₇	—	2	2	no	—
222	C₂²×C₄×C₇	—	2	2	no	—
223	C₂²×C₄×C₇	—	2	2	no	—
224	C₂²×C₄×C₇	—	2	2	no	—
225	C₂²×C₄×C₇	—	2	2	no	—
226	C₂²×C₄×C₇	—	2	2	no	—
227	C₂²×C₄×C₇	—	2	2	no	—
228	C₂²×C₄×C₇	—	2	2	no	—
229	C₂²×C₄×C₇	—	2	2	no	—
230	C₂²×C₄×C₇	—	2	2	no	—
231	C₂²×C₄×C₇	—	2	8	no	—
232	C₂²×C₄×C₇	—	2	8	no	—
233	C₂²×C₄×C₇	—	4	4	no	—
234	C₂²×C₄×C₇	—	4	4	no	—
235	C₂²×C₄×C₇	—	4	16	no	—
236	C₂²×C₄×C₇	—	4	16	no	—
237	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
238	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₇	#41	1	4	yes	—
241	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
254	C₇×C₄⋊C₄	—	2	8	no	—
255	C₇×C₄⋊C₄	—	2	8	no	—
256	C₇×C₄⋊C₄	—	2	8	no	—
257	C₇×C₄⋊C₄	—	2	8	no	—
258	C₇×C₄⋊C₄	—	2	8	no	—
259	C₇×C₄⋊C₄	—	2	8	no	—
260	C₇×C₄⋊C₄	—	4	4	no	—
261	C₇×C₄⋊C₄	C₂×D₄	1	16	yes	complemented
262	C₇×C₂²⋊C₄	—	2	8	no	—
263	C₇×C₂²⋊C₄	—	2	8	no	—
264	C₇×C₂²⋊C₄	—	2	8	no	—
265	C₇×C₂²⋊C₄	—	2	8	no	—
266	C₇×C₂²⋊C₄	—	2	8	no	—
267	C₇×C₂²⋊C₄	—	2	8	no	—
268	C₇×C₂²⋊C₄	—	2	8	no	—
269	C₇×C₂²⋊C₄	—	4	4	no	—
270	C₇×C₂²⋊C₄	—	4	4	no	—
271	C₄²×C₇	—	2	8	no	—
272	C₄²×C₇	—	4	4	no	—
273	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
274	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
275	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
276	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
277	C₂×#126	—	2	8	no	—
278	C₂×#126	C₂²×C₇	1	8	yes	complemented
279	C₂²×C₄⋊C₄	—	2	8	no	—
280	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
282	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
283	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
284	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
285	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
286	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
287	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
288	C₂²×C₄⋊C₄	C₂²×C₇	1	8	yes	complemented
289	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
290	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
291	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
292	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
293	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
294	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
295	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
296	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
297	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
298	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
299	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
300	#400	C₂²×C₇	1	8	yes	complemented
301	#400	C₂²×C₇	1	8	yes	complemented
302	#397	C₂²×C₇	1	8	yes	complemented
303	#396	C₂²×C₇	1	8	yes	complemented
304	#388	C₂²×C₇	1	8	yes	complemented
305	#387	C₂²×C₇	1	8	yes	complemented
306	#387	C₂²×C₇	1	8	yes	complemented
307	#386	C₂²×C₇	1	8	yes	—
308	#386	C₂²×C₇	1	8	yes	—
309	#386	C₂²×C₇	1	8	yes	—
310	#385	C₂²×C₇	1	8	yes	complemented
311	#380	C₂²×C₇	1	8	yes	complemented
312	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	complemented
313	C₂×#95	C₂²×C₇	1	1	yes	characteristic
314	C₂×#95	C₂²×C₇	1	1	yes	characteristic
315	C₂×#95	C₂²×C₇	1	1	yes	characteristic
316	C₂×#95	C₂²×C₇	1	1	yes	characteristic
317	C₂×#95	C₂²×C₇	1	1	yes	characteristic
318	C₂×#95	C₂²×C₇	1	1	yes	characteristic
319	C₂×#95	C₂²×C₇	1	1	yes	characteristic
320	C₂×#95	C₂²×C₇	1	1	yes	characteristic
321	C₂×#95	C₂²×C₇	1	1	yes	characteristic
322	C₂×#95	C₂²×C₇	1	1	yes	characteristic
323	C₂×#95	C₂²×C₇	1	1	yes	characteristic
324	C₂×#95	C₂²×C₇	1	1	yes	characteristic
325	C₂³×C₇	—	2	8	no	—
326	C₂³×C₇	—	2	8	no	—
327	C₂³×C₇	—	2	8	no	—
328	C₂³×C₇	—	2	8	no	—
329	C₂³×C₇	—	2	8	no	—
330	C₂³×C₇	—	2	8	no	—
331	C₂³×C₇	—	2	2	no	—
332	C₂³×C₇	—	2	2	no	—
333	C₂³×C₇	—	2	2	no	—
334	C₂³×C₇	—	2	2	no	—
335	C₂³×C₇	—	2	2	no	—
336	C₂³×C₇	—	2	2	no	—
337	C₂³×C₇	—	2	2	no	—
338	C₂³×C₇	—	2	2	no	—
339	C₂³×C₇	—	2	2	no	—
340	C₂³×C₇	—	2	2	no	—
341	C₂³×C₇	—	2	2	no	—
342	C₂³×C₇	—	4	4	no	—
343	C₂³×C₇	—	4	4	no	—
344	C₂³×C₇	—	4	4	no	—
345	C₂³×C₇	—	4	4	no	—
346	C₂³×C₇	—	4	4	no	—
347	C₂³×C₇	—	4	4	no	—
348	C₂³×C₇	—	4	4	no	—
349	C₂³×C₇	#126	1	16	yes	complemented
350	C₂³×C₇	C₂²×D₄	1	2	yes	—
351	C₂³×C₇	C₂×#41	1	4	yes	—
352	C₂³×C₇	C₂×#41	1	4	yes	—
353	C₂³×C₇	C₂×#41	1	4	yes	—
354	C₂³×C₇	C₂×#41	1	2	yes	—
355	C₂³×C₇	C₂×#41	1	2	yes	—
356	C₂³×C₇	C₂×#41	1	2	yes	—
357	C₂³×C₇	C₂×#41	1	2	yes	—
358	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
359	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
360	C₂³×C₇	C₂⁵	1	1	yes	characteristic
361	C₇×D₄	—	4	16	no	—
362	C₂×C₄×C₇	—	2	32	no	—
363	C₂×C₄×C₇	—	2	8	no	—
364	C₂×C₄×C₇	—	2	8	no	—
365	C₂×C₄×C₇	—	2	8	no	—
366	C₂×C₄×C₇	—	2	8	no	—
367	C₂×C₄×C₇	—	2	2	no	—
368	C₂×C₄×C₇	—	2	2	no	—
369	C₂×C₄×C₇	—	2	2	no	—
370	C₂×C₄×C₇	—	2	2	no	—
371	C₂×C₄×C₇	—	2	2	no	—
372	C₂×C₄×C₇	—	2	2	no	—
373	C₂×C₄×C₇	—	2	2	no	—
374	C₂×C₄×C₇	—	2	2	no	—
375	C₂×C₄×C₇	—	2	2	no	—
376	C₂×C₄×C₇	—	2	2	no	—
377	C₂×C₄×C₇	—	2	2	no	—
378	C₂×C₄×C₇	—	2	2	no	—
379	C₂×C₄×C₇	—	2	2	no	—
380	C₂×C₄×C₇	—	2	2	no	—
381	C₂×C₄×C₇	—	2	2	no	—
382	C₂×C₄×C₇	—	2	2	no	—
383	C₂×C₄×C₇	—	2	2	no	—
384	C₂×C₄×C₇	—	2	2	no	—
385	C₂×C₄×C₇	—	2	2	no	—
386	C₂×C₄×C₇	—	2	2	no	—
387	C₂×C₄×C₇	—	2	2	no	—
388	C₂×C₄×C₇	—	2	2	no	—
389	C₂×C₄×C₇	—	2	2	no	—
390	C₂×C₄×C₇	—	2	2	no	—
391	C₂×C₄×C₇	—	2	2	no	—
392	C₂×C₄×C₇	—	2	2	no	—
393	C₂×C₄×C₇	—	2	2	no	—
394	C₂×C₄×C₇	—	2	2	no	—
395	C₂×C₄×C₇	—	2	2	no	—
396	C₂×C₄×C₇	—	2	2	no	—
397	C₂×C₄×C₇	—	2	2	no	—
398	C₂×C₄×C₇	—	2	2	no	—
399	C₂×C₄×C₇	—	2	2	no	—
400	C₂×C₄×C₇	—	2	2	no	—
401	C₂×C₄×C₇	—	2	2	no	—
402	C₂×C₄×C₇	—	4	16	no	—
403	C₂×C₄×C₇	—	4	16	no	—
404	C₂×C₄×C₇	—	4	4	no	—
405	C₂×C₄×C₇	—	4	4	no	—
406	C₂×C₄×C₇	—	4	4	no	—
407	C₂×C₄×C₇	—	4	4	no	—
408	C₂×C₄×C₇	—	4	4	no	—
409	C₂×C₄×C₇	—	4	4	no	—
410	C₂×C₄×C₇	—	4	4	no	—
411	C₂×C₄×C₇	—	4	4	no	—
412	C₂×C₄×C₇	—	4	4	no	—
413	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
414	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
415	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
416	C₂×C₄×C₇	C₂×#41	1	4	yes	—
417	C₂⁵	C₂³×C₇	1	1	yes	characteristic
418	C₂⁵	C₂³×C₇	1	1	yes	characteristic
419	C₂²×D₄	—	2	4	no	—
420	C₂²×D₄	—	2	4	no	—
421	C₂²×D₄	—	2	4	no	—
422	C₂²×D₄	C₂³×C₇	1	4	yes	—
423	C₂³×C₄	—	2	4	no	—
424	C₂³×C₄	—	2	4	no	—
425	C₂³×C₄	—	2	4	no	—
426	C₂³×C₄	—	2	4	no	—
427	C₂³×C₄	—	2	4	no	—
428	C₂³×C₄	—	2	4	no	—
429	C₂³×C₄	—	2	4	no	—
430	C₂³×C₄	—	4	2	no	—
431	C₂³×C₄	—	4	2	no	—
432	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₇	1	4	yes	—
441	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₇	1	4	yes	—
443	C₂³×C₄	C₂³×C₇	1	4	yes	—
444	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
448	#126	—	2	32	no	—
449	C₂×C₄⋊C₄	—	2	4	no	—
450	C₂×C₄⋊C₄	—	2	4	no	—
451	C₂×C₄⋊C₄	—	2	4	no	—
452	C₂×C₄⋊C₄	—	2	4	no	—
453	C₂×C₄⋊C₄	—	2	4	no	—
454	C₂×C₄⋊C₄	—	2	4	no	—
455	C₂×C₄⋊C₄	—	2	32	no	—
456	C₂×C₄⋊C₄	—	4	2	no	—
457	C₂×C₄⋊C₄	C₇×D₄	1	8	yes	complemented
458	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
459	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
460	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
461	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
464	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
465	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
466	C₂×C₂²⋊C₄	—	2	4	no	—
467	C₂×C₂²⋊C₄	—	2	4	no	—
468	C₂×C₂²⋊C₄	—	2	4	no	—
469	C₂×C₂²⋊C₄	—	2	4	no	—
470	C₂×C₂²⋊C₄	—	2	4	no	—
471	C₂×C₂²⋊C₄	—	2	4	no	—
472	C₂×C₂²⋊C₄	—	2	4	no	—
473	C₂×C₂²⋊C₄	—	4	2	no	—
474	C₂×C₂²⋊C₄	—	4	2	no	—
475	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
484	C₂×C₄²	—	2	4	no	—
485	C₂×C₄²	—	4	2	no	—
486	C₂×C₄²	C₂³×C₇	1	4	yes	—
487	C₂×C₄²	C₂³×C₇	1	4	yes	—
488	#95	C₂³×C₇	1	4	yes	—
489	#95	C₂³×C₇	1	4	yes	—
490	#95	C₂³×C₇	1	4	yes	—
491	#95	C₂³×C₇	1	4	yes	—
492	#95	C₂³×C₇	1	4	yes	—
493	#95	C₂³×C₇	1	4	yes	—
494	#95	C₂³×C₇	1	4	yes	—
495	#95	C₂³×C₇	1	4	yes	—
496	#95	C₂³×C₇	1	4	yes	—
497	#95	C₂³×C₇	1	4	yes	—
498	#95	C₂³×C₇	1	4	yes	—
499	#95	C₂³×C₇	1	4	yes	—
500	C₂²×C₇	—	2	4	no	—
501	C₂²×C₇	—	2	4	no	—
502	C₂²×C₇	—	2	4	no	—
503	C₂²×C₇	—	2	4	no	—
504	C₂²×C₇	—	2	4	no	—
505	C₂²×C₇	—	2	4	no	—
506	C₂²×C₇	—	2	32	no	—
507	C₂²×C₇	—	4	2	no	—
508	C₂²×C₇	—	4	2	no	—
509	C₂²×C₇	—	4	2	no	—
510	C₂²×C₇	—	4	2	no	—
511	C₂²×C₇	—	4	2	no	—
512	C₂²×C₇	—	4	2	no	—
513	C₂²×C₇	—	4	2	no	—
514	C₂²×C₇	—	8	8	no	—
515	C₂²×C₇	#525	1	4	yes	—
516	C₂²×C₇	C₂×#126	1	4	yes	—
517	C₂²×C₇	C₂×#126	1	8	yes	complemented
518	C₂²×C₇	#539	1	4	yes	—
519	C₂²×C₇	#546	1	4	yes	—
520	C₂²×C₇	#548	1	4	yes	—
521	C₂²×C₇	#552	1	4	yes	—
522	C₂²×C₇	#553	1	4	yes	—
523	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
524	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
525	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
526	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
527	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
528	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
529	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	C₄×C₇	—	2	4	no	—
531	C₄×C₇	—	2	4	no	—
532	C₄×C₇	—	2	4	no	—
533	C₄×C₇	—	2	4	no	—
534	C₄×C₇	—	4	2	no	—
535	C₄×C₇	—	4	2	no	—
536	C₄×C₇	—	4	2	no	—
537	C₄×C₇	—	4	2	no	—
538	C₄×C₇	—	4	2	no	—
539	C₄×C₇	—	4	2	no	—
540	C₄×C₇	—	4	2	no	—
541	C₄×C₇	—	4	2	no	—
542	C₄×C₇	—	4	2	no	—
543	C₂⁴	—	2	2	no	—
544	C₂⁴	—	2	2	no	—
545	C₂⁴	—	2	2	no	—
546	C₂⁴	—	2	2	no	—
547	C₂⁴	—	2	2	no	—
548	C₂⁴	—	2	2	no	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	2	2	no	—
553	C₂⁴	—	2	2	no	—
554	C₂⁴	C₇×#41	1	4	yes	—
555	C₂⁴	C₇×#41	1	4	yes	—
556	C₂⁴	C₇×#41	1	4	yes	—
557	C₂⁴	C₂⁴×C₇	1	2	yes	—
558	C₂⁴	C₂⁴×C₇	1	2	yes	—
559	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
560	C₂×D₄	—	2	8	no	—
561	C₂×D₄	—	2	8	no	—
562	C₂×D₄	—	2	8	no	—
563	C₂×D₄	—	4	16	no	—
564	C₂²×C₄	—	2	32	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	8	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	8	no	—
575	C₂²×C₄	—	2	8	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	8	no	—
591	C₂²×C₄	—	2	8	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	8	no	—
606	C₂²×C₄	—	2	8	no	—
607	C₂²×C₄	—	4	4	no	—
608	C₂²×C₄	—	4	4	no	—
609	C₂²×C₄	—	4	16	no	—
610	C₂²×C₄	—	4	16	no	—
611	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
612	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
613	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
614	C₂²×C₄	C₇×#41	1	4	yes	—
615	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
628	C₄⋊C₄	—	2	8	no	—
629	C₄⋊C₄	—	2	8	no	—
630	C₄⋊C₄	—	2	8	no	—
631	C₄⋊C₄	—	2	8	no	—
632	C₄⋊C₄	—	2	8	no	—
633	C₄⋊C₄	—	2	8	no	—
634	C₄⋊C₄	—	4	4	no	—
635	C₄⋊C₄	C₂×C₇×D₄	1	16	yes	complemented
636	C₂²⋊C₄	—	2	8	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	2	8	no	—
639	C₂²⋊C₄	—	2	8	no	—
640	C₂²⋊C₄	—	2	8	no	—
641	C₂²⋊C₄	—	2	8	no	—
642	C₂²⋊C₄	—	2	8	no	—
643	C₂²⋊C₄	—	4	4	no	—
644	C₂²⋊C₄	—	4	4	no	—
645	C₄²	—	2	8	no	—
646	C₄²	—	4	4	no	—
647	C₂×C₇	—	2	8	no	—
648	C₂×C₇	—	8	2	no	—
649	C₂×C₇	#2481	1	8	yes	direct product factor
650	C₂×C₇	C₂×#525	1	1	yes	characteristic
651	C₂×C₇	C₂²×#126	1	1	yes	characteristic
652	C₂×C₇	C₂×#539	1	1	yes	characteristic
653	C₂×C₇	C₂×#546	1	1	yes	characteristic
654	C₂×C₇	C₂×#548	1	1	yes	characteristic
655	C₂×C₇	C₂×#552	1	1	yes	characteristic
656	C₂×C₇	C₂×#553	1	1	yes	characteristic
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	8	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	8	no	—
664	C₂³	—	2	8	no	—
665	C₂³	—	2	8	no	—
666	C₂³	—	2	8	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	4	4	no	—
675	C₂³	—	4	4	no	—
676	C₂³	—	4	4	no	—
677	C₂³	—	4	4	no	—
678	C₂³	—	4	4	no	—
679	C₂³	—	4	4	no	—
680	C₂³	—	4	4	no	—
681	C₂³	C₇×#126	1	16	yes	complemented
682	C₂³	C₂²×C₇×D₄	1	2	yes	—
683	C₂³	C₂×C₇×#41	1	4	yes	—
684	C₂³	C₂×C₇×#41	1	4	yes	—
685	C₂³	C₂×C₇×#41	1	4	yes	—
686	C₂³	C₂×C₇×#41	1	2	yes	—
687	C₂³	C₂×C₇×#41	1	2	yes	—
688	C₂³	C₂×C₇×#41	1	2	yes	—
689	C₂³	C₂×C₇×#41	1	2	yes	—
690	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
691	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
692	C₂³	C₂⁵×C₇	1	1	yes	characteristic
693	D₄	—	4	16	no	—
694	C₂×C₄	—	2	32	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	8	no	—
704	C₂×C₄	—	2	8	no	—
705	C₂×C₄	—	2	8	no	—
706	C₂×C₄	—	2	8	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	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	2	no	—
728	C₂×C₄	—	2	2	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	—	4	16	no	—
735	C₂×C₄	—	4	16	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	4	4	no	—
738	C₂×C₄	—	4	4	no	—
739	C₂×C₄	—	4	4	no	—
740	C₂×C₄	—	4	4	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	4	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
746	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
747	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
748	C₂×C₄	C₂×C₇×#41	1	4	yes	—
749	C₇	C₂×#2481	1	1	yes	characteristic, direct product factor, Sylow
750	C₂²	—	2	32	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	8	8	no	—
765	C₂²	C₇×#525	1	4	yes	—
766	C₂²	C₂×C₇×#126	1	4	yes	—
767	C₂²	C₂×C₇×#126	1	8	yes	complemented
768	C₂²	C₇×#539	1	4	yes	—
769	C₂²	C₇×#546	1	4	yes	—
770	C₂²	C₇×#548	1	4	yes	—
771	C₂²	C₇×#552	1	4	yes	—
772	C₂²	C₇×#553	1	4	yes	—
773	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
774	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
775	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
776	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
777	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
778	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
779	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
780	C₄	—	2	4	no	—
781	C₄	—	2	4	no	—
782	C₄	—	2	4	no	—
783	C₄	—	2	4	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₂	—	2	8	no	—
794	C₂	—	8	2	no	—
795	C₂	C₇×#2481	1	8	yes	direct product factor
796	C₂	C₂×C₇×#525	1	1	yes	characteristic
797	C₂	C₂²×C₇×#126	1	1	yes	characteristic
798	C₂	C₂×C₇×#539	1	1	yes	characteristic
799	C₂	C₂×C₇×#546	1	1	yes	characteristic
800	C₂	C₂×C₇×#548	1	1	yes	characteristic
801	C₂	C₂×C₇×#552	1	1	yes	characteristic
802	C₂	C₂×C₇×#553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂³×C₇×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂²×C₇×#126	C₂	semidirect
2. C₂³×C₇×C₄⋊C₄	C₂	semidirect
3. C₇×#2481	C₂	direct (N × H)
4. C₂×C₇×#400	C₂	semidirect
5. C₂×C₇×#400	C₂	semidirect
6. C₂×C₇×#397	C₂	semidirect
7. C₂×C₇×#396	C₂	semidirect
8. C₂×C₇×#388	C₂	semidirect
9. C₂×C₇×#387	C₂	semidirect
10. C₂×C₇×#387	C₂	semidirect
14. C₂×C₇×#385	C₂	semidirect
15. C₂×C₇×#380	C₂	semidirect
16. C₂×C₄×C₇×C₂²⋊C₄	C₂	semidirect
22. C₂×C₇×#126	C₂²	semidirect
32. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
44. C₇×#400	C₂²	semidirect
45. C₇×#400	C₂²	semidirect
46. C₇×#397	C₂²	semidirect
47. C₇×#396	C₂²	semidirect
48. C₇×#388	C₂²	semidirect
49. C₇×#387	C₂²	semidirect
50. C₇×#387	C₂²	semidirect
54. C₇×#385	C₂²	semidirect
55. C₇×#380	C₂²	semidirect
56. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
69. C₂×#2481	C₇	direct (N × H)
110. C₂×C₇×C₄⋊C₄	D₄	semidirect
153. C₂²×#126	C₂×C₇	semidirect
154. C₂³×C₄⋊C₄	C₂×C₇	semidirect
155. #2481	C₂×C₇	direct (N × H)
156. C₂×#400	C₂×C₇	semidirect
157. C₂×#400	C₂×C₇	semidirect
158. C₂×#397	C₂×C₇	semidirect
159. C₂×#396	C₂×C₇	semidirect
160. C₂×#388	C₂×C₇	semidirect
161. C₂×#387	C₂×C₇	semidirect
162. C₂×#387	C₂×C₇	semidirect
166. C₂×#385	C₂×C₇	semidirect
167. C₂×#380	C₂×C₇	semidirect
168. C₂×C₄×C₂²⋊C₄	C₂×C₇	semidirect
261. C₇×C₄⋊C₄	C₂×D₄	semidirect
278. C₂×#126	C₂²×C₇	semidirect
288. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
300. #400	C₂²×C₇	semidirect
301. #400	C₂²×C₇	semidirect
302. #397	C₂²×C₇	semidirect
303. #396	C₂²×C₇	semidirect
304. #388	C₂²×C₇	semidirect
305. #387	C₂²×C₇	semidirect
306. #387	C₂²×C₇	semidirect
310. #385	C₂²×C₇	semidirect
311. #380	C₂²×C₇	semidirect
312. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
349. C₂³×C₇	#126	semidirect
457. C₂×C₄⋊C₄	C₇×D₄	semidirect
517. C₂²×C₇	C₂×#126	semidirect
635. C₄⋊C₄	C₂×C₇×D₄	semidirect
649. C₂×C₇	#2481	direct (N × H)
681. C₂³	C₇×#126	semidirect
749. C₇	C₂×#2481	direct (N × H)
767. C₂²	C₂×C₇×#126	semidirect
795. C₂	C₇×#2481	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₇×#126	2
C₂³×C₇×C₄⋊C₄	2
C₇×#2481	2
C₂×C₇×#400	2
C₂×C₇×#397	2
C₂×C₇×#396	2
C₂×C₇×#388	2
C₂×C₇×#387	2
C₂×C₇×#386	2
C₂×C₇×#385	2
C₂×C₇×#380	2
C₂×C₄×C₇×C₂²⋊C₄	2
C₂×#2481	7

Subgroups — C2×C7×#2481 #13211877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2481 #13211877