Subgroups — C₂×C₇×#2480 #13211876

Order 1792.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 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×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₇×#2480	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#397	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×#388	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#388	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#385	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#385	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#380	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#379	C₂	1	1	yes	maximal, characteristic
15	C₂×C₇×#379	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁶×C₇	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
20	C₂×C₇×#126	—	2	8	no	—
21	C₂×C₇×#126	C₂²	1	8	yes	complemented
22	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₇×C₂²⋊C₄	—	2	8	no	—
29	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	8	yes	—
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×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
48	C₇×#397	C₂²	1	8	yes	complemented
49	C₇×#397	C₂²	1	8	yes	complemented
50	C₇×#397	C₂²	1	8	yes	complemented
51	C₇×#396	C₂²	1	8	yes	complemented
52	C₇×#388	C₂²	1	8	yes	complemented
53	C₇×#388	C₂²	1	8	yes	complemented
54	C₇×#388	C₂²	1	8	yes	complemented
55	C₇×#385	C₂²	1	8	yes	complemented
56	C₇×#385	C₂²	1	8	yes	complemented
57	C₇×#380	C₂²	1	8	yes	complemented
58	C₇×#379	C₂²	1	8	yes	—
59	C₇×#379	C₂²	1	8	yes	—
60	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	complemented
61	C₂×C₇×#95	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₇×#95	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₇×#95	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₇×#95	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₇×#95	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₇×#95	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₇×#95	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₇×#95	C₂²	1	1	yes	characteristic, complemented
69	C₂×#2480	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂⁵×C₇	—	2	4	no	—
71	C₂⁵×C₇	—	2	4	no	—
72	C₂⁵×C₇	—	2	4	no	—
73	C₂⁵×C₇	—	2	4	no	—
74	C₂⁵×C₇	—	2	4	no	—
75	C₂⁵×C₇	—	4	2	no	—
76	C₂⁵×C₇	—	4	2	no	—
77	C₂⁵×C₇	C₂³	1	1	yes	characteristic
78	C₂⁵×C₇	C₂³	1	1	yes	characteristic
79	C₂⁵×C₇	C₂³	1	4	yes	—
80	C₂⁵×C₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₇	—	2	4	no	—
82	C₂³×C₄×C₇	—	2	4	no	—
83	C₂³×C₄×C₇	—	2	4	no	—
84	C₂³×C₄×C₇	—	2	4	no	—
85	C₂³×C₄×C₇	—	4	2	no	—
86	C₂³×C₄×C₇	—	4	2	no	—
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	1	yes	characteristic
96	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₇	C₂³	1	4	yes	—
98	C₂³×C₄×C₇	C₂³	1	4	yes	—
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	—	4	2	no	—
106	C₂×C₇×C₄⋊C₄	—	4	2	no	—
107	C₂×C₇×C₄⋊C₄	—	4	2	no	—
108	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
109	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
110	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
111	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
112	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
113	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
114	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
115	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
116	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
117	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
118	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
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	32	no	—
126	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
127	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
128	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
129	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
130	C₂×C₇×C₂²⋊C₄	D₄	1	8	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×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₄²×C₇	—	2	4	no	—
148	C₂×C₄²×C₇	—	4	2	no	—
149	C₂×C₄²×C₇	C₂³	1	4	yes	complemented
150	C₂×C₄²×C₇	C₂³	1	4	yes	complemented
151	C₇×#95	C₂³	1	4	yes	complemented
152	C₇×#95	C₂³	1	4	yes	complemented
153	C₇×#95	C₂³	1	4	yes	complemented
154	C₇×#95	C₂³	1	4	yes	complemented
155	C₇×#95	C₂³	1	4	yes	complemented
156	C₇×#95	C₂³	1	4	yes	complemented
157	C₇×#95	C₂³	1	4	yes	complemented
158	C₇×#95	C₂³	1	4	yes	complemented
159	C₂²×#126	C₂×C₇	1	1	yes	characteristic, complemented
160	C₂³×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
161	#2480	C₂×C₇	1	16	yes	direct product factor
162	C₂×#397	C₂×C₇	1	1	yes	characteristic, complemented
163	C₂×#397	C₂×C₇	1	1	yes	characteristic, complemented
164	C₂×#397	C₂×C₇	1	1	yes	characteristic, complemented
165	C₂×#396	C₂×C₇	1	1	yes	characteristic, complemented
166	C₂×#388	C₂×C₇	1	1	yes	characteristic, complemented
167	C₂×#388	C₂×C₇	1	1	yes	characteristic, complemented
168	C₂×#388	C₂×C₇	1	1	yes	characteristic, complemented
169	C₂×#385	C₂×C₇	1	1	yes	characteristic, complemented
170	C₂×#385	C₂×C₇	1	1	yes	characteristic, complemented
171	C₂×#380	C₂×C₇	1	1	yes	characteristic, complemented
172	C₂×#379	C₂×C₇	1	1	yes	characteristic
173	C₂×#379	C₂×C₇	1	1	yes	characteristic
174	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
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	32	no	—
180	C₂⁴×C₇	—	2	8	no	—
181	C₂⁴×C₇	—	2	2	no	—
182	C₂⁴×C₇	—	2	8	no	—
183	C₂⁴×C₇	—	2	8	no	—
184	C₂⁴×C₇	—	2	2	no	—
185	C₂⁴×C₇	—	2	2	no	—
186	C₂⁴×C₇	—	2	2	no	—
187	C₂⁴×C₇	—	2	2	no	—
188	C₂⁴×C₇	—	2	2	no	—
189	C₂⁴×C₇	—	2	2	no	—
190	C₂⁴×C₇	—	2	2	no	—
191	C₂⁴×C₇	—	2	2	no	—
192	C₂⁴×C₇	—	2	2	no	—
193	C₂⁴×C₇	—	2	2	no	—
194	C₂⁴×C₇	—	2	2	no	—
195	C₂⁴×C₇	—	2	8	no	—
196	C₂⁴×C₇	—	2	8	no	—
197	C₂⁴×C₇	—	4	4	no	—
198	C₂⁴×C₇	—	4	4	no	—
199	C₂⁴×C₇	—	4	16	no	—
200	C₂⁴×C₇	—	4	16	no	—
201	C₂⁴×C₇	—	4	16	no	—
202	C₂⁴×C₇	—	4	16	no	—
203	C₂⁴×C₇	—	4	16	no	—
204	C₂⁴×C₇	—	4	16	no	—
205	C₂⁴×C₇	C₂×D₄	1	4	yes	—
206	C₂⁴×C₇	#41	1	4	yes	—
207	C₂⁴×C₇	#41	1	4	yes	—
208	C₂⁴×C₇	#41	1	4	yes	—
209	C₂⁴×C₇	#41	1	4	yes	—
210	C₂⁴×C₇	C₂⁴	1	2	yes	—
211	C₂⁴×C₇	C₂⁴	1	2	yes	—
212	C₂⁴×C₇	C₂⁴	1	2	yes	—
213	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₇	—	2	2	no	—
215	C₂²×C₄×C₇	—	2	2	no	—
216	C₂²×C₄×C₇	—	2	2	no	—
217	C₂²×C₄×C₇	—	2	2	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	2	no	—
232	C₂²×C₄×C₇	—	2	2	no	—
233	C₂²×C₄×C₇	—	2	2	no	—
234	C₂²×C₄×C₇	—	2	2	no	—
235	C₂²×C₄×C₇	—	2	2	no	—
236	C₂²×C₄×C₇	—	2	8	no	—
237	C₂²×C₄×C₇	—	2	8	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	2	no	—
243	C₂²×C₄×C₇	—	2	2	no	—
244	C₂²×C₄×C₇	—	2	2	no	—
245	C₂²×C₄×C₇	—	2	2	no	—
246	C₂²×C₄×C₇	—	2	2	no	—
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	8	no	—
251	C₂²×C₄×C₇	—	2	8	no	—
252	C₂²×C₄×C₇	—	4	4	no	—
253	C₂²×C₄×C₇	—	4	4	no	—
254	C₂²×C₄×C₇	—	4	16	no	—
255	C₂²×C₄×C₇	—	4	16	no	—
256	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
257	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
258	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
270	C₇×C₄⋊C₄	—	2	8	no	—
271	C₇×C₄⋊C₄	—	2	8	no	—
272	C₇×C₄⋊C₄	—	2	8	no	—
273	C₇×C₄⋊C₄	—	4	4	no	—
274	C₇×C₄⋊C₄	—	4	4	no	—
275	C₇×C₄⋊C₄	—	4	4	no	—
276	C₇×C₂²⋊C₄	—	2	8	no	—
277	C₇×C₂²⋊C₄	—	2	8	no	—
278	C₇×C₂²⋊C₄	—	2	8	no	—
279	C₇×C₂²⋊C₄	—	2	8	no	—
280	C₇×C₂²⋊C₄	—	2	8	no	—
281	C₇×C₂²⋊C₄	—	2	8	no	—
282	C₇×C₂²⋊C₄	—	2	8	no	—
283	C₇×C₂²⋊C₄	—	2	8	no	—
284	C₇×C₂²⋊C₄	—	2	8	no	—
285	C₇×C₂²⋊C₄	—	2	8	no	—
286	C₇×C₂²⋊C₄	—	2	8	no	—
287	C₇×C₂²⋊C₄	—	4	4	no	—
288	C₇×C₂²⋊C₄	—	4	4	no	—
289	C₇×C₂²⋊C₄	—	4	4	no	—
290	C₇×C₂²⋊C₄	—	4	4	no	—
291	C₇×C₂²⋊C₄	C₂×D₄	1	16	yes	—
292	C₄²×C₇	—	2	8	no	—
293	C₄²×C₇	—	4	4	no	—
294	C₂⁶	C₂²×C₇	1	1	yes	characteristic
295	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
296	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
297	C₂×#126	—	2	8	no	—
298	C₂×#126	C₂²×C₇	1	8	yes	complemented
299	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
300	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
301	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
302	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
303	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
304	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
305	C₂²×C₂²⋊C₄	—	2	8	no	—
306	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
307	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
308	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
309	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
310	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
311	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
312	C₂²×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
313	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
315	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
316	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
317	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
318	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
319	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
320	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
321	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
322	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
323	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
324	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
325	#397	C₂²×C₇	1	8	yes	complemented
326	#397	C₂²×C₇	1	8	yes	complemented
327	#397	C₂²×C₇	1	8	yes	complemented
328	#396	C₂²×C₇	1	8	yes	complemented
329	#388	C₂²×C₇	1	8	yes	complemented
330	#388	C₂²×C₇	1	8	yes	complemented
331	#388	C₂²×C₇	1	8	yes	complemented
332	#385	C₂²×C₇	1	8	yes	complemented
333	#385	C₂²×C₇	1	8	yes	complemented
334	#380	C₂²×C₇	1	8	yes	complemented
335	#379	C₂²×C₇	1	8	yes	—
336	#379	C₂²×C₇	1	8	yes	—
337	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	complemented
338	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
339	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
340	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
341	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
342	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
343	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
344	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
345	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
346	C₂³×C₇	—	2	8	no	—
347	C₂³×C₇	—	2	8	no	—
348	C₂³×C₇	—	2	8	no	—
349	C₂³×C₇	—	2	8	no	—
350	C₂³×C₇	—	2	8	no	—
351	C₂³×C₇	—	2	8	no	—
352	C₂³×C₇	—	2	2	no	—
353	C₂³×C₇	—	2	2	no	—
354	C₂³×C₇	—	2	2	no	—
355	C₂³×C₇	—	2	2	no	—
356	C₂³×C₇	—	2	32	no	—
357	C₂³×C₇	—	2	8	no	—
358	C₂³×C₇	—	2	8	no	—
359	C₂³×C₇	—	2	8	no	—
360	C₂³×C₇	—	2	8	no	—
361	C₂³×C₇	—	2	8	no	—
362	C₂³×C₇	—	2	8	no	—
363	C₂³×C₇	—	2	2	no	—
364	C₂³×C₇	—	2	2	no	—
365	C₂³×C₇	—	2	2	no	—
366	C₂³×C₇	—	2	2	no	—
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	—	2	2	no	—
374	C₂³×C₇	—	2	2	no	—
375	C₂³×C₇	—	4	16	no	—
376	C₂³×C₇	—	4	16	no	—
377	C₂³×C₇	—	4	16	no	—
378	C₂³×C₇	—	4	16	no	—
379	C₂³×C₇	—	4	16	no	—
380	C₂³×C₇	—	4	128	no	—
381	C₂³×C₇	—	4	4	no	—
382	C₂³×C₇	—	4	4	no	—
383	C₂³×C₇	—	4	16	no	—
384	C₂³×C₇	—	4	4	no	—
385	C₂³×C₇	—	4	4	no	—
386	C₂³×C₇	—	4	4	no	—
387	C₂³×C₇	—	4	4	no	—
388	C₂³×C₇	—	4	4	no	—
389	C₂³×C₇	—	4	4	no	—
390	C₂³×C₇	#126	1	16	yes	complemented
391	C₂³×C₇	C₂²×D₄	1	4	yes	—
392	C₂³×C₇	C₂²×D₄	1	2	yes	—
393	C₂³×C₇	C₂×#41	1	4	yes	—
394	C₂³×C₇	C₂×#41	1	4	yes	—
395	C₂³×C₇	C₂×#41	1	4	yes	—
396	C₂³×C₇	C₂×#41	1	4	yes	—
397	C₂³×C₇	C₂×#41	1	2	yes	—
398	C₂³×C₇	C₂×#41	1	2	yes	—
399	C₂³×C₇	C₂×#41	1	2	yes	—
400	C₂³×C₇	C₂×#41	1	2	yes	—
401	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
402	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
403	C₂³×C₇	C₂⁵	1	1	yes	characteristic
404	C₂×C₄×C₇	—	2	8	no	—
405	C₂×C₄×C₇	—	2	8	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	—	2	2	no	—
416	C₂×C₄×C₇	—	2	2	no	—
417	C₂×C₄×C₇	—	2	2	no	—
418	C₂×C₄×C₇	—	2	2	no	—
419	C₂×C₄×C₇	—	2	2	no	—
420	C₂×C₄×C₇	—	2	2	no	—
421	C₂×C₄×C₇	—	2	2	no	—
422	C₂×C₄×C₇	—	2	2	no	—
423	C₂×C₄×C₇	—	2	2	no	—
424	C₂×C₄×C₇	—	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	—	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	—	2	2	no	—
435	C₂×C₄×C₇	—	2	2	no	—
436	C₂×C₄×C₇	—	2	2	no	—
437	C₂×C₄×C₇	—	2	2	no	—
438	C₂×C₄×C₇	—	2	2	no	—
439	C₂×C₄×C₇	—	2	2	no	—
440	C₂×C₄×C₇	—	4	16	no	—
441	C₂×C₄×C₇	—	4	16	no	—
442	C₂×C₄×C₇	—	4	4	no	—
443	C₂×C₄×C₇	—	4	4	no	—
444	C₂×C₄×C₇	—	4	4	no	—
445	C₂×C₄×C₇	—	4	4	no	—
446	C₂×C₄×C₇	—	4	4	no	—
447	C₂×C₄×C₇	—	4	4	no	—
448	C₂×C₄×C₇	—	4	4	no	—
449	C₂×C₄×C₇	—	4	4	no	—
450	C₂×C₄×C₇	—	4	4	no	—
451	C₂×C₄×C₇	—	4	4	no	—
452	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
453	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
454	C₂⁵	—	2	4	no	—
455	C₂⁵	—	2	4	no	—
456	C₂⁵	—	2	4	no	—
457	C₂⁵	—	2	4	no	—
458	C₂⁵	—	2	4	no	—
459	C₂⁵	—	4	2	no	—
460	C₂⁵	—	4	2	no	—
461	C₂⁵	C₂³×C₇	1	1	yes	characteristic
462	C₂⁵	C₂³×C₇	1	1	yes	characteristic
463	C₂⁵	C₂³×C₇	1	4	yes	—
464	C₂⁵	C₂³×C₇	1	1	yes	characteristic
465	C₂³×C₄	—	2	4	no	—
466	C₂³×C₄	—	2	4	no	—
467	C₂³×C₄	—	2	4	no	—
468	C₂³×C₄	—	2	4	no	—
469	C₂³×C₄	—	4	2	no	—
470	C₂³×C₄	—	4	2	no	—
471	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₇	1	4	yes	—
482	C₂³×C₄	C₂³×C₇	1	4	yes	—
483	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
485	#126	—	2	32	no	—
486	C₂×C₄⋊C₄	—	2	4	no	—
487	C₂×C₄⋊C₄	—	2	4	no	—
488	C₂×C₄⋊C₄	—	2	4	no	—
489	C₂×C₄⋊C₄	—	4	2	no	—
490	C₂×C₄⋊C₄	—	4	2	no	—
491	C₂×C₄⋊C₄	—	4	2	no	—
492	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
493	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
494	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
495	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
496	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
497	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
498	C₂×C₂²⋊C₄	—	2	4	no	—
499	C₂×C₂²⋊C₄	—	2	4	no	—
500	C₂×C₂²⋊C₄	—	2	4	no	—
501	C₂×C₂²⋊C₄	—	2	4	no	—
502	C₂×C₂²⋊C₄	—	2	4	no	—
503	C₂×C₂²⋊C₄	—	2	4	no	—
504	C₂×C₂²⋊C₄	—	2	4	no	—
505	C₂×C₂²⋊C₄	—	2	4	no	—
506	C₂×C₂²⋊C₄	—	2	4	no	—
507	C₂×C₂²⋊C₄	—	2	4	no	—
508	C₂×C₂²⋊C₄	—	2	4	no	—
509	C₂×C₂²⋊C₄	—	2	32	no	—
510	C₂×C₂²⋊C₄	—	4	2	no	—
511	C₂×C₂²⋊C₄	—	4	2	no	—
512	C₂×C₂²⋊C₄	—	4	2	no	—
513	C₂×C₂²⋊C₄	—	4	2	no	—
514	C₂×C₂²⋊C₄	C₇×D₄	1	8	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
531	C₂×C₄²	—	2	4	no	—
532	C₂×C₄²	—	4	2	no	—
533	C₂×C₄²	C₂³×C₇	1	4	yes	complemented
534	C₂×C₄²	C₂³×C₇	1	4	yes	complemented
535	#95	C₂³×C₇	1	4	yes	complemented
536	#95	C₂³×C₇	1	4	yes	complemented
537	#95	C₂³×C₇	1	4	yes	complemented
538	#95	C₂³×C₇	1	4	yes	complemented
539	#95	C₂³×C₇	1	4	yes	complemented
540	#95	C₂³×C₇	1	4	yes	complemented
541	#95	C₂³×C₇	1	4	yes	complemented
542	#95	C₂³×C₇	1	4	yes	complemented
543	C₂²×C₇	—	2	4	no	—
544	C₂²×C₇	—	2	4	no	—
545	C₂²×C₇	—	2	4	no	—
546	C₂²×C₇	—	2	4	no	—
547	C₂²×C₇	—	2	4	no	—
548	C₂²×C₇	—	2	4	no	—
549	C₂²×C₇	—	2	32	no	—
550	C₂²×C₇	—	2	4	no	—
551	C₂²×C₇	—	2	4	no	—
552	C₂²×C₇	—	2	4	no	—
553	C₂²×C₇	—	2	4	no	—
554	C₂²×C₇	—	2	4	no	—
555	C₂²×C₇	—	2	4	no	—
556	C₂²×C₇	—	4	64	no	—
557	C₂²×C₇	—	4	2	no	—
558	C₂²×C₇	—	4	2	no	—
559	C₂²×C₇	—	4	2	no	—
560	C₂²×C₇	—	4	2	no	—
561	C₂²×C₇	—	4	2	no	—
562	C₂²×C₇	—	4	2	no	—
563	C₂²×C₇	—	4	2	no	—
564	C₂²×C₇	—	4	2	no	—
565	C₂²×C₇	—	4	16	no	—
566	C₂²×C₇	—	4	16	no	—
567	C₂²×C₇	#525	1	4	yes	—
568	C₂²×C₇	C₂×#126	1	4	yes	—
569	C₂²×C₇	C₂×#126	1	8	yes	complemented
570	C₂²×C₇	#538	1	4	yes	—
571	C₂²×C₇	#546	1	4	yes	—
572	C₂²×C₇	#546	1	4	yes	—
573	C₂²×C₇	#551	1	4	yes	—
574	C₂²×C₇	#551	1	4	yes	—
575	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
576	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
577	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
578	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
579	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
580	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
582	C₄×C₇	—	2	4	no	—
583	C₄×C₇	—	2	4	no	—
584	C₄×C₇	—	4	2	no	—
585	C₄×C₇	—	4	2	no	—
586	C₄×C₇	—	4	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	—	4	2	no	—
593	C₄×C₇	—	4	2	no	—
594	C₂⁴	—	2	2	no	—
595	C₂⁴	—	2	2	no	—
596	C₂⁴	—	2	2	no	—
597	C₂⁴	—	2	2	no	—
598	C₂⁴	—	2	32	no	—
599	C₂⁴	—	2	8	no	—
600	C₂⁴	—	2	2	no	—
601	C₂⁴	—	2	8	no	—
602	C₂⁴	—	2	8	no	—
603	C₂⁴	—	2	2	no	—
604	C₂⁴	—	2	2	no	—
605	C₂⁴	—	2	2	no	—
606	C₂⁴	—	2	2	no	—
607	C₂⁴	—	2	2	no	—
608	C₂⁴	—	2	2	no	—
609	C₂⁴	—	2	2	no	—
610	C₂⁴	—	2	2	no	—
611	C₂⁴	—	2	2	no	—
612	C₂⁴	—	2	2	no	—
613	C₂⁴	—	2	2	no	—
614	C₂⁴	—	2	8	no	—
615	C₂⁴	—	2	8	no	—
616	C₂⁴	—	4	4	no	—
617	C₂⁴	—	4	4	no	—
618	C₂⁴	—	4	16	no	—
619	C₂⁴	—	4	16	no	—
620	C₂⁴	—	4	16	no	—
621	C₂⁴	—	4	16	no	—
622	C₂⁴	—	4	16	no	—
623	C₂⁴	—	4	16	no	—
624	C₂⁴	C₂×C₇×D₄	1	4	yes	—
625	C₂⁴	C₇×#41	1	4	yes	—
626	C₂⁴	C₇×#41	1	4	yes	—
627	C₂⁴	C₇×#41	1	4	yes	—
628	C₂⁴	C₇×#41	1	4	yes	—
629	C₂⁴	C₂⁴×C₇	1	2	yes	—
630	C₂⁴	C₂⁴×C₇	1	2	yes	—
631	C₂⁴	C₂⁴×C₇	1	2	yes	—
632	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
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	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
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	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	8	no	—
656	C₂²×C₄	—	2	8	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	8	no	—
670	C₂²×C₄	—	2	8	no	—
671	C₂²×C₄	—	4	4	no	—
672	C₂²×C₄	—	4	4	no	—
673	C₂²×C₄	—	4	16	no	—
674	C₂²×C₄	—	4	16	no	—
675	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
676	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
677	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
689	C₄⋊C₄	—	2	8	no	—
690	C₄⋊C₄	—	2	8	no	—
691	C₄⋊C₄	—	2	8	no	—
692	C₄⋊C₄	—	4	4	no	—
693	C₄⋊C₄	—	4	4	no	—
694	C₄⋊C₄	—	4	4	no	—
695	C₂²⋊C₄	—	2	8	no	—
696	C₂²⋊C₄	—	2	8	no	—
697	C₂²⋊C₄	—	2	8	no	—
698	C₂²⋊C₄	—	2	8	no	—
699	C₂²⋊C₄	—	2	8	no	—
700	C₂²⋊C₄	—	2	8	no	—
701	C₂²⋊C₄	—	2	8	no	—
702	C₂²⋊C₄	—	2	8	no	—
703	C₂²⋊C₄	—	2	8	no	—
704	C₂²⋊C₄	—	2	8	no	—
705	C₂²⋊C₄	—	2	8	no	—
706	C₂²⋊C₄	—	4	4	no	—
707	C₂²⋊C₄	—	4	4	no	—
708	C₂²⋊C₄	—	4	4	no	—
709	C₂²⋊C₄	—	4	4	no	—
710	C₂²⋊C₄	C₂×C₇×D₄	1	16	yes	—
711	C₄²	—	2	8	no	—
712	C₄²	—	4	4	no	—
713	C₂×C₇	—	2	8	no	—
714	C₂×C₇	—	4	4	no	—
715	C₂×C₇	—	4	4	no	—
716	C₂×C₇	#2480	1	8	yes	direct product factor
717	C₂×C₇	C₂×#525	1	1	yes	characteristic
718	C₂×C₇	C₂²×#126	1	1	yes	characteristic
719	C₂×C₇	C₂×#538	1	1	yes	characteristic
720	C₂×C₇	C₂×#546	1	1	yes	characteristic
721	C₂×C₇	C₂×#546	1	1	yes	characteristic
722	C₂×C₇	C₂×#551	1	1	yes	characteristic
723	C₂×C₇	C₂×#551	1	1	yes	characteristic
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	8	no	—
729	C₂³	—	2	8	no	—
730	C₂³	—	2	8	no	—
731	C₂³	—	2	8	no	—
732	C₂³	—	2	8	no	—
733	C₂³	—	2	8	no	—
734	C₂³	—	2	32	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	8	no	—
748	C₂³	—	2	8	no	—
749	C₂³	—	2	8	no	—
750	C₂³	—	2	8	no	—
751	C₂³	—	2	8	no	—
752	C₂³	—	2	8	no	—
753	C₂³	—	4	16	no	—
754	C₂³	—	4	16	no	—
755	C₂³	—	4	16	no	—
756	C₂³	—	4	16	no	—
757	C₂³	—	4	128	no	—
758	C₂³	—	4	16	no	—
759	C₂³	—	4	4	no	—
760	C₂³	—	4	4	no	—
761	C₂³	—	4	16	no	—
762	C₂³	—	4	4	no	—
763	C₂³	—	4	4	no	—
764	C₂³	—	4	4	no	—
765	C₂³	—	4	4	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	4	4	no	—
768	C₂³	C₇×#126	1	16	yes	complemented
769	C₂³	C₂²×C₇×D₄	1	4	yes	—
770	C₂³	C₂²×C₇×D₄	1	2	yes	—
771	C₂³	C₂×C₇×#41	1	4	yes	—
772	C₂³	C₂×C₇×#41	1	4	yes	—
773	C₂³	C₂×C₇×#41	1	4	yes	—
774	C₂³	C₂×C₇×#41	1	4	yes	—
775	C₂³	C₂×C₇×#41	1	2	yes	—
776	C₂³	C₂×C₇×#41	1	2	yes	—
777	C₂³	C₂×C₇×#41	1	2	yes	—
778	C₂³	C₂×C₇×#41	1	2	yes	—
779	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
780	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
781	C₂³	C₂⁵×C₇	1	1	yes	characteristic
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	8	no	—
787	C₂×C₄	—	2	8	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	4	16	no	—
819	C₂×C₄	—	4	16	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	4	no	—
823	C₂×C₄	—	4	4	no	—
824	C₂×C₄	—	4	4	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
831	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
832	C₇	C₂×#2480	1	1	yes	characteristic, direct product factor, Sylow
833	C₂²	—	2	32	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	4	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	2	4	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	2	4	no	—
846	C₂²	—	4	64	no	—
847	C₂²	—	4	16	no	—
848	C₂²	—	4	16	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	C₇×#525	1	4	yes	—
858	C₂²	C₂×C₇×#126	1	4	yes	—
859	C₂²	C₂×C₇×#126	1	8	yes	complemented
860	C₂²	C₇×#538	1	4	yes	—
861	C₂²	C₇×#546	1	4	yes	—
862	C₂²	C₇×#546	1	4	yes	—
863	C₂²	C₇×#551	1	4	yes	—
864	C₂²	C₇×#551	1	4	yes	—
865	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
866	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
867	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
868	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
869	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
870	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
871	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
872	C₄	—	2	4	no	—
873	C₄	—	2	4	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₂	—	2	8	no	—
885	C₂	—	4	4	no	—
886	C₂	—	4	4	no	—
887	C₂	C₇×#2480	1	8	yes	direct product factor
888	C₂	C₂×C₇×#525	1	1	yes	characteristic
889	C₂	C₂²×C₇×#126	1	1	yes	characteristic
890	C₂	C₂×C₇×#538	1	1	yes	characteristic
891	C₂	C₂×C₇×#546	1	1	yes	characteristic
892	C₂	C₂×C₇×#546	1	1	yes	characteristic
893	C₂	C₂×C₇×#551	1	1	yes	characteristic
894	C₂	C₂×C₇×#551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁶×C₇	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
3. C₇×#2480	C₂	direct (N × H)
4. C₂×C₇×#397	C₂	semidirect
5. C₂×C₇×#397	C₂	semidirect
6. C₂×C₇×#397	C₂	semidirect
7. C₂×C₇×#396	C₂	semidirect
8. C₂×C₇×#388	C₂	semidirect
9. C₂×C₇×#388	C₂	semidirect
10. C₂×C₇×#388	C₂	semidirect
11. C₂×C₇×#385	C₂	semidirect
12. C₂×C₇×#385	C₂	semidirect
13. C₂×C₇×#380	C₂	semidirect
16. C₂×C₄×C₇×C₂²⋊C₄	C₂	semidirect
21. C₂×C₇×#126	C₂²	semidirect
22. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
23. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
24. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
25. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
26. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
27. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
46. C₂²×C₄²×C₇	C₂²	semidirect
47. C₂²×C₄²×C₇	C₂²	semidirect
48. C₇×#397	C₂²	semidirect
49. C₇×#397	C₂²	semidirect
50. C₇×#397	C₂²	semidirect
51. C₇×#396	C₂²	semidirect
52. C₇×#388	C₂²	semidirect
53. C₇×#388	C₂²	semidirect
54. C₇×#388	C₂²	semidirect
55. C₇×#385	C₂²	semidirect
56. C₇×#385	C₂²	semidirect
57. C₇×#380	C₂²	semidirect
60. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
61. C₂×C₇×#95	C₂²	semidirect
62. C₂×C₇×#95	C₂²	semidirect
63. C₂×C₇×#95	C₂²	semidirect
64. C₂×C₇×#95	C₂²	semidirect
65. C₂×C₇×#95	C₂²	semidirect
66. C₂×C₇×#95	C₂²	semidirect
67. C₂×C₇×#95	C₂²	semidirect
68. C₂×C₇×#95	C₂²	semidirect
69. C₂×#2480	C₇	direct (N × H)
108. C₂×C₇×C₄⋊C₄	C₂³	semidirect
109. C₂×C₇×C₄⋊C₄	C₂³	semidirect
110. C₂×C₇×C₄⋊C₄	C₂³	semidirect
111. C₂×C₇×C₄⋊C₄	C₂³	semidirect
112. C₂×C₇×C₄⋊C₄	C₂³	semidirect
113. C₂×C₇×C₄⋊C₄	C₂³	semidirect
149. C₂×C₄²×C₇	C₂³	semidirect
150. C₂×C₄²×C₇	C₂³	semidirect
151. C₇×#95	C₂³	semidirect
152. C₇×#95	C₂³	semidirect
153. C₇×#95	C₂³	semidirect
154. C₇×#95	C₂³	semidirect
155. C₇×#95	C₂³	semidirect
156. C₇×#95	C₂³	semidirect
157. C₇×#95	C₂³	semidirect
158. C₇×#95	C₂³	semidirect
159. C₂²×#126	C₂×C₇	semidirect
161. #2480	C₂×C₇	direct (N × H)
162. C₂×#397	C₂×C₇	semidirect
163. C₂×#397	C₂×C₇	semidirect
164. C₂×#397	C₂×C₇	semidirect
165. C₂×#396	C₂×C₇	semidirect
166. C₂×#388	C₂×C₇	semidirect
167. C₂×#388	C₂×C₇	semidirect
168. C₂×#388	C₂×C₇	semidirect
169. C₂×#385	C₂×C₇	semidirect
170. C₂×#385	C₂×C₇	semidirect
171. C₂×#380	C₂×C₇	semidirect
174. C₂×C₄×C₂²⋊C₄	C₂×C₇	semidirect
298. C₂×#126	C₂²×C₇	semidirect
299. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
300. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
301. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
302. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
303. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
304. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
323. C₂²×C₄²	C₂²×C₇	semidirect
324. C₂²×C₄²	C₂²×C₇	semidirect
325. #397	C₂²×C₇	semidirect
326. #397	C₂²×C₇	semidirect
327. #397	C₂²×C₇	semidirect
328. #396	C₂²×C₇	semidirect
329. #388	C₂²×C₇	semidirect
330. #388	C₂²×C₇	semidirect
331. #388	C₂²×C₇	semidirect
332. #385	C₂²×C₇	semidirect
333. #385	C₂²×C₇	semidirect
334. #380	C₂²×C₇	semidirect
337. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
338. C₂×#95	C₂²×C₇	semidirect
339. C₂×#95	C₂²×C₇	semidirect
340. C₂×#95	C₂²×C₇	semidirect
341. C₂×#95	C₂²×C₇	semidirect
342. C₂×#95	C₂²×C₇	semidirect
343. C₂×#95	C₂²×C₇	semidirect
344. C₂×#95	C₂²×C₇	semidirect
345. C₂×#95	C₂²×C₇	semidirect
390. C₂³×C₇	#126	semidirect
492. C₂×C₄⋊C₄	C₂³×C₇	semidirect
493. C₂×C₄⋊C₄	C₂³×C₇	semidirect
494. C₂×C₄⋊C₄	C₂³×C₇	semidirect
495. C₂×C₄⋊C₄	C₂³×C₇	semidirect
496. C₂×C₄⋊C₄	C₂³×C₇	semidirect
497. C₂×C₄⋊C₄	C₂³×C₇	semidirect
533. C₂×C₄²	C₂³×C₇	semidirect
534. C₂×C₄²	C₂³×C₇	semidirect
535. #95	C₂³×C₇	semidirect
536. #95	C₂³×C₇	semidirect
537. #95	C₂³×C₇	semidirect
538. #95	C₂³×C₇	semidirect
539. #95	C₂³×C₇	semidirect
540. #95	C₂³×C₇	semidirect
541. #95	C₂³×C₇	semidirect
542. #95	C₂³×C₇	semidirect
569. C₂²×C₇	C₂×#126	semidirect
716. C₂×C₇	#2480	direct (N × H)
768. C₂³	C₇×#126	semidirect
832. C₇	C₂×#2480	direct (N × H)
859. C₂²	C₂×C₇×#126	semidirect
887. C₂	C₇×#2480	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×C₂²⋊C₄	2
C₇×#2480	2
C₂×C₇×#397	2
C₂×C₇×#396	2
C₂×C₇×#388	2
C₂×C₇×#385	2
C₂×C₇×#380	2
C₂×C₇×#379	2
C₂×C₄×C₇×C₂²⋊C₄	2
C₂×#2480	7

Subgroups — C2×C7×#2480 #13211876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2480 #13211876