Subgroups — C₂×C₇×#2472 #13211874

Order 1792.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₇×#120	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2472	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₇×#397	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#393	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#390	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#388	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#388	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#379	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁶×C₇	C₂²	1	1	yes	characteristic
18	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
24	C₂×C₇×#124	—	2	8	no	—
25	C₂×C₇×#124	C₂²	1	8	yes	complemented
26	C₂×C₇×C₂²⋊Q₈	—	2	8	no	—
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	complemented
28	C₂×C₇×#120	—	2	8	no	—
29	C₂×C₇×#120	C₂²	1	8	yes	—
30	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₇×C₂²⋊C₄	—	2	8	no	—
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×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×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂²×C₇×C₂²⋊C₄	C₂²	1	8	yes	complemented
48	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
54	C₇×#397	C₂²	1	8	yes	complemented
55	C₇×#394	C₂²	1	8	yes	complemented
56	C₇×#394	C₂²	1	8	yes	complemented
57	C₇×#393	C₂²	1	8	yes	complemented
58	C₇×#390	C₂²	1	8	yes	complemented
59	C₇×#388	C₂²	1	8	yes	complemented
60	C₇×#388	C₂²	1	8	yes	complemented
61	C₇×#386	C₂²	1	8	yes	complemented
62	C₇×#386	C₂²	1	8	yes	complemented
63	C₇×#379	C₂²	1	8	yes	complemented
64	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	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×C₇×#95	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₇×#95	C₂²	1	1	yes	characteristic, complemented
71	C₂×#2472	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂⁵×C₇	—	2	4	no	—
73	C₂⁵×C₇	—	2	4	no	—
74	C₂⁵×C₇	—	2	4	no	—
75	C₂⁵×C₇	—	2	4	no	—
76	C₂⁵×C₇	—	2	4	no	—
77	C₂⁵×C₇	—	4	2	no	—
78	C₂⁵×C₇	—	4	2	no	—
79	C₂⁵×C₇	C₂³	1	1	yes	characteristic
80	C₂⁵×C₇	C₂³	1	1	yes	characteristic
81	C₂⁵×C₇	C₂³	1	1	yes	characteristic
82	C₂⁵×C₇	C₂³	1	4	yes	—
83	C₂⁵×C₇	C₂³	1	1	yes	characteristic
84	C₂²×C₇×Q₈	—	2	4	no	—
85	C₂²×C₇×Q₈	—	2	4	no	—
86	C₂²×C₇×Q₈	—	4	2	no	—
87	C₂²×C₇×Q₈	C₂³	1	4	yes	complemented
88	C₂²×C₇×D₄	—	2	4	no	—
89	C₂²×C₇×D₄	—	2	4	no	—
90	C₂²×C₇×D₄	—	2	4	no	—
91	C₂²×C₇×D₄	—	2	4	no	—
92	C₂²×C₇×D₄	—	2	4	no	—
93	C₂²×C₇×D₄	—	2	4	no	—
94	C₂²×C₇×D₄	—	2	4	no	—
95	C₂²×C₇×D₄	—	4	2	no	—
96	C₂²×C₇×D₄	—	4	2	no	—
97	C₂²×C₇×D₄	C₂³	1	4	yes	—
98	C₂²×C₇×D₄	C₂³	1	4	yes	—
99	C₂²×C₇×D₄	C₂³	1	4	yes	—
100	C₂³×C₄×C₇	—	2	4	no	—
101	C₂³×C₄×C₇	—	2	4	no	—
102	C₂³×C₄×C₇	—	2	4	no	—
103	C₂³×C₄×C₇	—	2	4	no	—
104	C₂³×C₄×C₇	—	4	2	no	—
105	C₂³×C₄×C₇	—	4	2	no	—
106	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₇	C₂³	1	4	yes	—
114	C₂³×C₄×C₇	C₂³	1	4	yes	—
115	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
119	C₇×#124	—	2	32	no	—
120	C₇×C₂²⋊Q₈	—	2	32	no	—
121	C₇×#120	—	2	32	no	—
122	C₂×C₇×C₄⋊C₄	—	2	4	no	—
123	C₂×C₇×C₄⋊C₄	—	2	4	no	—
124	C₂×C₇×C₄⋊C₄	—	2	4	no	—
125	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
126	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
127	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
128	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
129	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
130	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
131	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
132	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
133	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
134	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
135	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
136	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
137	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
138	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
139	C₂×C₇×C₂²⋊C₄	—	2	32	no	—
140	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
141	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
142	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
143	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
144	C₂×C₇×C₂²⋊C₄	D₄	1	8	yes	—
145	C₂×C₇×C₂²⋊C₄	D₄	1	8	yes	complemented
146	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
159	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	complemented
160	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	complemented
161	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	complemented
162	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	complemented
163	C₂×C₄²×C₇	—	2	4	no	—
164	C₂×C₄²×C₇	—	4	2	no	—
165	C₂×C₄²×C₇	C₂³	1	4	yes	complemented
166	C₂×C₄²×C₇	C₂³	1	4	yes	complemented
167	C₇×#95	C₂³	1	4	yes	complemented
168	C₇×#95	C₂³	1	4	yes	complemented
169	C₇×#95	C₂³	1	4	yes	complemented
170	C₇×#95	C₂³	1	4	yes	complemented
171	C₇×#95	C₂³	1	4	yes	complemented
172	C₇×#95	C₂³	1	4	yes	complemented
173	C₂²×#124	C₂×C₇	1	1	yes	characteristic, complemented
174	C₂²×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
175	C₂²×#120	C₂×C₇	1	1	yes	characteristic
176	C₂³×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
177	#2472	C₂×C₇	1	16	yes	direct product factor
178	C₂×#397	C₂×C₇	1	1	yes	characteristic, complemented
179	C₂×#394	C₂×C₇	1	1	yes	characteristic, complemented
180	C₂×#394	C₂×C₇	1	1	yes	characteristic, complemented
181	C₂×#393	C₂×C₇	1	1	yes	characteristic, complemented
182	C₂×#390	C₂×C₇	1	1	yes	characteristic, complemented
183	C₂×#388	C₂×C₇	1	1	yes	characteristic, complemented
184	C₂×#388	C₂×C₇	1	1	yes	characteristic, complemented
185	C₂×#386	C₂×C₇	1	1	yes	characteristic, complemented
186	C₂×#386	C₂×C₇	1	1	yes	characteristic, complemented
187	C₂×#379	C₂×C₇	1	1	yes	characteristic, complemented
188	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
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	32	no	—
194	C₂⁴×C₇	—	2	8	no	—
195	C₂⁴×C₇	—	2	2	no	—
196	C₂⁴×C₇	—	2	2	no	—
197	C₂⁴×C₇	—	2	2	no	—
198	C₂⁴×C₇	—	2	8	no	—
199	C₂⁴×C₇	—	2	8	no	—
200	C₂⁴×C₇	—	2	2	no	—
201	C₂⁴×C₇	—	2	2	no	—
202	C₂⁴×C₇	—	2	2	no	—
203	C₂⁴×C₇	—	2	2	no	—
204	C₂⁴×C₇	—	2	2	no	—
205	C₂⁴×C₇	—	2	2	no	—
206	C₂⁴×C₇	—	2	2	no	—
207	C₂⁴×C₇	—	2	2	no	—
208	C₂⁴×C₇	—	2	2	no	—
209	C₂⁴×C₇	—	2	2	no	—
210	C₂⁴×C₇	—	2	8	no	—
211	C₂⁴×C₇	—	2	2	no	—
212	C₂⁴×C₇	—	2	2	no	—
213	C₂⁴×C₇	—	2	2	no	—
214	C₂⁴×C₇	—	2	2	no	—
215	C₂⁴×C₇	—	2	8	no	—
216	C₂⁴×C₇	—	2	2	no	—
217	C₂⁴×C₇	—	2	2	no	—
218	C₂⁴×C₇	—	4	4	no	—
219	C₂⁴×C₇	—	4	4	no	—
220	C₂⁴×C₇	—	4	16	no	—
221	C₂⁴×C₇	—	4	16	no	—
222	C₂⁴×C₇	—	4	16	no	—
223	C₂⁴×C₇	—	4	16	no	—
224	C₂⁴×C₇	—	4	16	no	—
225	C₂⁴×C₇	—	4	16	no	—
226	C₂⁴×C₇	C₂×D₄	1	4	yes	—
227	C₂⁴×C₇	C₂×D₄	1	4	yes	—
228	C₂⁴×C₇	#41	1	4	yes	—
229	C₂⁴×C₇	#41	1	4	yes	—
230	C₂⁴×C₇	#41	1	4	yes	—
231	C₂⁴×C₇	C₂⁴	1	2	yes	—
232	C₂⁴×C₇	C₂⁴	1	2	yes	—
233	C₂⁴×C₇	C₂⁴	1	2	yes	—
234	C₂⁴×C₇	C₂⁴	1	2	yes	—
235	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
236	C₂×C₇×Q₈	—	2	8	no	—
237	C₂×C₇×Q₈	—	2	8	no	—
238	C₂×C₇×Q₈	—	4	4	no	—
239	C₂×C₇×Q₈	—	4	16	no	—
240	C₂×C₇×D₄	—	2	8	no	—
241	C₂×C₇×D₄	—	2	8	no	—
242	C₂×C₇×D₄	—	2	8	no	—
243	C₂×C₇×D₄	—	2	8	no	—
244	C₂×C₇×D₄	—	2	8	no	—
245	C₂×C₇×D₄	—	2	8	no	—
246	C₂×C₇×D₄	—	2	8	no	—
247	C₂×C₇×D₄	—	4	4	no	—
248	C₂×C₇×D₄	—	4	4	no	—
249	C₂×C₇×D₄	—	4	16	no	—
250	C₂×C₇×D₄	—	4	16	no	—
251	C₂×C₇×D₄	—	4	16	no	—
252	C₂²×C₄×C₇	—	2	2	no	—
253	C₂²×C₄×C₇	—	2	2	no	—
254	C₂²×C₄×C₇	—	2	2	no	—
255	C₂²×C₄×C₇	—	2	2	no	—
256	C₂²×C₄×C₇	—	2	2	no	—
257	C₂²×C₄×C₇	—	2	2	no	—
258	C₂²×C₄×C₇	—	2	2	no	—
259	C₂²×C₄×C₇	—	2	2	no	—
260	C₂²×C₄×C₇	—	2	2	no	—
261	C₂²×C₄×C₇	—	2	2	no	—
262	C₂²×C₄×C₇	—	2	2	no	—
263	C₂²×C₄×C₇	—	2	2	no	—
264	C₂²×C₄×C₇	—	2	2	no	—
265	C₂²×C₄×C₇	—	2	2	no	—
266	C₂²×C₄×C₇	—	2	2	no	—
267	C₂²×C₄×C₇	—	2	2	no	—
268	C₂²×C₄×C₇	—	2	8	no	—
269	C₂²×C₄×C₇	—	2	2	no	—
270	C₂²×C₄×C₇	—	2	2	no	—
271	C₂²×C₄×C₇	—	2	2	no	—
272	C₂²×C₄×C₇	—	2	2	no	—
273	C₂²×C₄×C₇	—	2	8	no	—
274	C₂²×C₄×C₇	—	2	2	no	—
275	C₂²×C₄×C₇	—	2	2	no	—
276	C₂²×C₄×C₇	—	2	2	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	2	2	no	—
279	C₂²×C₄×C₇	—	2	2	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	2	2	no	—
282	C₂²×C₄×C₇	—	2	2	no	—
283	C₂²×C₄×C₇	—	2	8	no	—
284	C₂²×C₄×C₇	—	2	8	no	—
285	C₂²×C₄×C₇	—	4	4	no	—
286	C₂²×C₄×C₇	—	4	4	no	—
287	C₂²×C₄×C₇	—	4	16	no	—
288	C₂²×C₄×C₇	—	4	16	no	—
289	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
290	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
291	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
292	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
293	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
304	C₇×C₄⋊C₄	—	2	8	no	—
305	C₇×C₄⋊C₄	—	2	8	no	—
306	C₇×C₄⋊C₄	—	2	8	no	—
307	C₇×C₂²⋊C₄	—	2	8	no	—
308	C₇×C₂²⋊C₄	—	2	8	no	—
309	C₇×C₂²⋊C₄	—	2	8	no	—
310	C₇×C₂²⋊C₄	—	2	8	no	—
311	C₇×C₂²⋊C₄	—	2	8	no	—
312	C₇×C₂²⋊C₄	—	2	8	no	—
313	C₇×C₂²⋊C₄	—	2	8	no	—
314	C₇×C₂²⋊C₄	—	2	8	no	—
315	C₇×C₂²⋊C₄	—	2	8	no	—
316	C₇×C₂²⋊C₄	—	2	8	no	—
317	C₇×C₂²⋊C₄	—	2	8	no	—
318	C₇×C₂²⋊C₄	—	4	4	no	—
319	C₇×C₂²⋊C₄	—	4	4	no	—
320	C₇×C₂²⋊C₄	—	4	4	no	—
321	C₇×C₂²⋊C₄	—	4	4	no	—
322	C₇×C₂²⋊C₄	C₂×D₄	1	16	yes	—
323	C₇×C₂²⋊C₄	C₂×D₄	1	16	yes	complemented
324	C₄²×C₇	—	2	8	no	—
325	C₄²×C₇	—	4	4	no	—
326	C₂⁶	C₂²×C₇	1	1	yes	characteristic
327	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
328	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
329	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
330	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
331	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
332	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
333	C₂×#124	—	2	8	no	—
334	C₂×#124	C₂²×C₇	1	8	yes	complemented
335	C₂×C₂²⋊Q₈	—	2	8	no	—
336	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	complemented
337	C₂×#120	—	2	8	no	—
338	C₂×#120	C₂²×C₇	1	8	yes	—
339	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
340	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
341	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
342	C₂²×C₂²⋊C₄	—	2	8	no	—
343	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
344	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
347	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
348	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
349	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
350	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
351	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
352	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
353	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
354	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
355	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
356	C₂²×C₂²⋊C₄	C₂²×C₇	1	8	yes	complemented
357	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
358	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
359	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
360	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
361	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
362	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
363	#397	C₂²×C₇	1	8	yes	complemented
364	#394	C₂²×C₇	1	8	yes	complemented
365	#394	C₂²×C₇	1	8	yes	complemented
366	#393	C₂²×C₇	1	8	yes	complemented
367	#390	C₂²×C₇	1	8	yes	complemented
368	#388	C₂²×C₇	1	8	yes	complemented
369	#388	C₂²×C₇	1	8	yes	complemented
370	#386	C₂²×C₇	1	8	yes	complemented
371	#386	C₂²×C₇	1	8	yes	complemented
372	#379	C₂²×C₇	1	8	yes	complemented
373	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	complemented
374	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
375	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
376	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
377	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
378	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
379	C₂×#95	C₂²×C₇	1	1	yes	characteristic, complemented
380	C₂³×C₇	—	2	8	no	—
381	C₂³×C₇	—	2	8	no	—
382	C₂³×C₇	—	2	8	no	—
383	C₂³×C₇	—	2	8	no	—
384	C₂³×C₇	—	2	8	no	—
385	C₂³×C₇	—	2	8	no	—
386	C₂³×C₇	—	2	2	no	—
387	C₂³×C₇	—	2	2	no	—
388	C₂³×C₇	—	2	2	no	—
389	C₂³×C₇	—	2	2	no	—
390	C₂³×C₇	—	2	32	no	—
391	C₂³×C₇	—	2	8	no	—
392	C₂³×C₇	—	2	8	no	—
393	C₂³×C₇	—	2	8	no	—
394	C₂³×C₇	—	2	8	no	—
395	C₂³×C₇	—	2	8	no	—
396	C₂³×C₇	—	2	8	no	—
397	C₂³×C₇	—	2	2	no	—
398	C₂³×C₇	—	2	2	no	—
399	C₂³×C₇	—	2	2	no	—
400	C₂³×C₇	—	2	2	no	—
401	C₂³×C₇	—	2	2	no	—
402	C₂³×C₇	—	2	2	no	—
403	C₂³×C₇	—	2	2	no	—
404	C₂³×C₇	—	2	2	no	—
405	C₂³×C₇	—	2	2	no	—
406	C₂³×C₇	—	2	2	no	—
407	C₂³×C₇	—	2	2	no	—
408	C₂³×C₇	—	2	2	no	—
409	C₂³×C₇	—	2	2	no	—
410	C₂³×C₇	—	2	2	no	—
411	C₂³×C₇	—	2	2	no	—
412	C₂³×C₇	—	2	2	no	—
413	C₂³×C₇	—	2	2	no	—
414	C₂³×C₇	—	2	2	no	—
415	C₂³×C₇	—	2	2	no	—
416	C₂³×C₇	—	4	16	no	—
417	C₂³×C₇	—	4	16	no	—
418	C₂³×C₇	—	4	16	no	—
419	C₂³×C₇	—	4	16	no	—
420	C₂³×C₇	—	4	16	no	—
421	C₂³×C₇	—	4	128	no	—
422	C₂³×C₇	—	4	4	no	—
423	C₂³×C₇	—	4	4	no	—
424	C₂³×C₇	—	4	16	no	—
425	C₂³×C₇	—	4	4	no	—
426	C₂³×C₇	—	4	4	no	—
427	C₂³×C₇	—	4	4	no	—
428	C₂³×C₇	—	4	4	no	—
429	C₂³×C₇	—	4	4	no	—
430	C₂³×C₇	—	4	4	no	—
431	C₂³×C₇	—	4	4	no	—
432	C₂³×C₇	—	4	4	no	—
433	C₂³×C₇	—	4	4	no	—
434	C₂³×C₇	—	4	4	no	—
435	C₂³×C₇	—	4	4	no	—
436	C₂³×C₇	—	4	4	no	—
437	C₂³×C₇	—	4	4	no	—
438	C₂³×C₇	#124	1	16	yes	complemented
439	C₂³×C₇	C₂²×D₄	1	4	yes	—
440	C₂³×C₇	C₂²×D₄	1	4	yes	—
441	C₂³×C₇	C₂²×D₄	1	2	yes	—
442	C₂³×C₇	C₂²×D₄	1	2	yes	—
443	C₂³×C₇	C₂×#41	1	4	yes	—
444	C₂³×C₇	C₂×#41	1	4	yes	—
445	C₂³×C₇	C₂×#41	1	4	yes	—
446	C₂³×C₇	C₂×#41	1	2	yes	—
447	C₂³×C₇	C₂×#41	1	2	yes	—
448	C₂³×C₇	C₂×#41	1	2	yes	—
449	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
450	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
451	C₂³×C₇	C₂⁵	1	1	yes	characteristic
452	C₇×Q₈	—	4	16	no	—
453	C₇×D₄	—	4	16	no	—
454	C₇×D₄	—	4	16	no	—
455	C₇×D₄	—	4	16	no	—
456	C₂×C₄×C₇	—	2	8	no	—
457	C₂×C₄×C₇	—	2	8	no	—
458	C₂×C₄×C₇	—	2	8	no	—
459	C₂×C₄×C₇	—	2	8	no	—
460	C₂×C₄×C₇	—	2	2	no	—
461	C₂×C₄×C₇	—	2	2	no	—
462	C₂×C₄×C₇	—	2	2	no	—
463	C₂×C₄×C₇	—	2	2	no	—
464	C₂×C₄×C₇	—	2	2	no	—
465	C₂×C₄×C₇	—	2	2	no	—
466	C₂×C₄×C₇	—	2	2	no	—
467	C₂×C₄×C₇	—	2	2	no	—
468	C₂×C₄×C₇	—	2	2	no	—
469	C₂×C₄×C₇	—	2	2	no	—
470	C₂×C₄×C₇	—	2	2	no	—
471	C₂×C₄×C₇	—	2	2	no	—
472	C₂×C₄×C₇	—	2	2	no	—
473	C₂×C₄×C₇	—	2	2	no	—
474	C₂×C₄×C₇	—	2	2	no	—
475	C₂×C₄×C₇	—	2	2	no	—
476	C₂×C₄×C₇	—	2	2	no	—
477	C₂×C₄×C₇	—	2	2	no	—
478	C₂×C₄×C₇	—	2	2	no	—
479	C₂×C₄×C₇	—	2	2	no	—
480	C₂×C₄×C₇	—	2	2	no	—
481	C₂×C₄×C₇	—	2	2	no	—
482	C₂×C₄×C₇	—	2	2	no	—
483	C₂×C₄×C₇	—	2	2	no	—
484	C₂×C₄×C₇	—	2	2	no	—
485	C₂×C₄×C₇	—	2	2	no	—
486	C₂×C₄×C₇	—	2	2	no	—
487	C₂×C₄×C₇	—	2	2	no	—
488	C₂×C₄×C₇	—	2	2	no	—
489	C₂×C₄×C₇	—	4	16	no	—
490	C₂×C₄×C₇	—	4	16	no	—
491	C₂×C₄×C₇	—	4	4	no	—
492	C₂×C₄×C₇	—	4	4	no	—
493	C₂×C₄×C₇	—	4	4	no	—
494	C₂×C₄×C₇	—	4	4	no	—
495	C₂×C₄×C₇	—	4	4	no	—
496	C₂×C₄×C₇	—	4	4	no	—
497	C₂×C₄×C₇	—	4	4	no	—
498	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
499	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
500	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
501	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
502	C₂⁵	—	2	4	no	—
503	C₂⁵	—	2	4	no	—
504	C₂⁵	—	2	4	no	—
505	C₂⁵	—	2	4	no	—
506	C₂⁵	—	2	4	no	—
507	C₂⁵	—	4	2	no	—
508	C₂⁵	—	4	2	no	—
509	C₂⁵	C₂³×C₇	1	1	yes	characteristic
510	C₂⁵	C₂³×C₇	1	1	yes	characteristic
511	C₂⁵	C₂³×C₇	1	1	yes	characteristic
512	C₂⁵	C₂³×C₇	1	4	yes	—
513	C₂⁵	C₂³×C₇	1	1	yes	characteristic
514	C₂²×Q₈	—	2	4	no	—
515	C₂²×Q₈	—	2	4	no	—
516	C₂²×Q₈	—	4	2	no	—
517	C₂²×Q₈	C₂³×C₇	1	4	yes	complemented
518	C₂²×D₄	—	2	4	no	—
519	C₂²×D₄	—	2	4	no	—
520	C₂²×D₄	—	2	4	no	—
521	C₂²×D₄	—	2	4	no	—
522	C₂²×D₄	—	2	4	no	—
523	C₂²×D₄	—	2	4	no	—
524	C₂²×D₄	—	2	4	no	—
525	C₂²×D₄	—	4	2	no	—
526	C₂²×D₄	—	4	2	no	—
527	C₂²×D₄	C₂³×C₇	1	4	yes	—
528	C₂²×D₄	C₂³×C₇	1	4	yes	—
529	C₂²×D₄	C₂³×C₇	1	4	yes	—
530	C₂³×C₄	—	2	4	no	—
531	C₂³×C₄	—	2	4	no	—
532	C₂³×C₄	—	2	4	no	—
533	C₂³×C₄	—	2	4	no	—
534	C₂³×C₄	—	4	2	no	—
535	C₂³×C₄	—	4	2	no	—
536	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₇	1	4	yes	—
544	C₂³×C₄	C₂³×C₇	1	4	yes	—
545	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
549	#124	—	2	32	no	—
550	C₂²⋊Q₈	—	2	32	no	—
551	#120	—	2	32	no	—
552	C₂×C₄⋊C₄	—	2	4	no	—
553	C₂×C₄⋊C₄	—	2	4	no	—
554	C₂×C₄⋊C₄	—	2	4	no	—
555	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
556	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
557	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
558	C₂×C₂²⋊C₄	—	2	4	no	—
559	C₂×C₂²⋊C₄	—	2	4	no	—
560	C₂×C₂²⋊C₄	—	2	4	no	—
561	C₂×C₂²⋊C₄	—	2	4	no	—
562	C₂×C₂²⋊C₄	—	2	4	no	—
563	C₂×C₂²⋊C₄	—	2	4	no	—
564	C₂×C₂²⋊C₄	—	2	4	no	—
565	C₂×C₂²⋊C₄	—	2	4	no	—
566	C₂×C₂²⋊C₄	—	2	4	no	—
567	C₂×C₂²⋊C₄	—	2	4	no	—
568	C₂×C₂²⋊C₄	—	2	4	no	—
569	C₂×C₂²⋊C₄	—	2	32	no	—
570	C₂×C₂²⋊C₄	—	4	2	no	—
571	C₂×C₂²⋊C₄	—	4	2	no	—
572	C₂×C₂²⋊C₄	—	4	2	no	—
573	C₂×C₂²⋊C₄	—	4	2	no	—
574	C₂×C₂²⋊C₄	C₇×D₄	1	8	yes	—
575	C₂×C₂²⋊C₄	C₇×D₄	1	8	yes	complemented
576	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	complemented
590	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	complemented
591	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	complemented
592	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	complemented
593	C₂×C₄²	—	2	4	no	—
594	C₂×C₄²	—	4	2	no	—
595	C₂×C₄²	C₂³×C₇	1	4	yes	complemented
596	C₂×C₄²	C₂³×C₇	1	4	yes	complemented
597	#95	C₂³×C₇	1	4	yes	complemented
598	#95	C₂³×C₇	1	4	yes	complemented
599	#95	C₂³×C₇	1	4	yes	complemented
600	#95	C₂³×C₇	1	4	yes	complemented
601	#95	C₂³×C₇	1	4	yes	complemented
602	#95	C₂³×C₇	1	4	yes	complemented
603	C₂²×C₇	—	2	4	no	—
604	C₂²×C₇	—	2	4	no	—
605	C₂²×C₇	—	2	4	no	—
606	C₂²×C₇	—	2	4	no	—
607	C₂²×C₇	—	2	4	no	—
608	C₂²×C₇	—	2	4	no	—
609	C₂²×C₇	—	2	32	no	—
610	C₂²×C₇	—	2	4	no	—
611	C₂²×C₇	—	2	4	no	—
612	C₂²×C₇	—	2	4	no	—
613	C₂²×C₇	—	2	4	no	—
614	C₂²×C₇	—	2	4	no	—
615	C₂²×C₇	—	2	4	no	—
616	C₂²×C₇	—	4	64	no	—
617	C₂²×C₇	—	4	2	no	—
618	C₂²×C₇	—	4	2	no	—
619	C₂²×C₇	—	4	2	no	—
620	C₂²×C₇	—	4	2	no	—
621	C₂²×C₇	—	4	2	no	—
622	C₂²×C₇	—	4	2	no	—
623	C₂²×C₇	—	4	2	no	—
624	C₂²×C₇	—	4	2	no	—
625	C₂²×C₇	—	4	16	no	—
626	C₂²×C₇	—	4	16	no	—
627	C₂²×C₇	—	4	2	no	—
628	C₂²×C₇	—	4	2	no	—
629	C₂²×C₇	—	4	2	no	—
630	C₂²×C₇	—	4	2	no	—
631	C₂²×C₇	—	4	2	no	—
632	C₂²×C₇	—	4	2	no	—
633	C₂²×C₇	—	4	2	no	—
634	C₂²×C₇	—	8	8	no	—
635	C₂²×C₇	#525	1	4	yes	—
636	C₂²×C₇	C₂×#124	1	4	yes	—
637	C₂²×C₇	C₂×#124	1	8	yes	complemented
638	C₂²×C₇	#538	1	4	yes	—
639	C₂²×C₇	D₄²	1	4	yes	—
640	C₂²×C₇	#546	1	4	yes	—
641	C₂²×C₇	#546	1	4	yes	—
642	C₂²×C₇	#551	1	4	yes	—
643	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
644	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
645	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
646	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
647	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
648	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
649	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
650	C₄×C₇	—	2	4	no	—
651	C₄×C₇	—	2	4	no	—
652	C₄×C₇	—	2	4	no	—
653	C₄×C₇	—	2	4	no	—
654	C₄×C₇	—	4	2	no	—
655	C₄×C₇	—	4	2	no	—
656	C₄×C₇	—	4	2	no	—
657	C₄×C₇	—	4	2	no	—
658	C₄×C₇	—	4	2	no	—
659	C₄×C₇	—	4	2	no	—
660	C₄×C₇	—	4	2	no	—
661	C₂⁴	—	2	2	no	—
662	C₂⁴	—	2	2	no	—
663	C₂⁴	—	2	2	no	—
664	C₂⁴	—	2	2	no	—
665	C₂⁴	—	2	32	no	—
666	C₂⁴	—	2	8	no	—
667	C₂⁴	—	2	2	no	—
668	C₂⁴	—	2	2	no	—
669	C₂⁴	—	2	2	no	—
670	C₂⁴	—	2	8	no	—
671	C₂⁴	—	2	8	no	—
672	C₂⁴	—	2	2	no	—
673	C₂⁴	—	2	2	no	—
674	C₂⁴	—	2	2	no	—
675	C₂⁴	—	2	2	no	—
676	C₂⁴	—	2	2	no	—
677	C₂⁴	—	2	2	no	—
678	C₂⁴	—	2	2	no	—
679	C₂⁴	—	2	2	no	—
680	C₂⁴	—	2	2	no	—
681	C₂⁴	—	2	2	no	—
682	C₂⁴	—	2	8	no	—
683	C₂⁴	—	2	2	no	—
684	C₂⁴	—	2	2	no	—
685	C₂⁴	—	2	2	no	—
686	C₂⁴	—	2	2	no	—
687	C₂⁴	—	2	8	no	—
688	C₂⁴	—	2	2	no	—
689	C₂⁴	—	2	2	no	—
690	C₂⁴	—	4	4	no	—
691	C₂⁴	—	4	4	no	—
692	C₂⁴	—	4	16	no	—
693	C₂⁴	—	4	16	no	—
694	C₂⁴	—	4	16	no	—
695	C₂⁴	—	4	16	no	—
696	C₂⁴	—	4	16	no	—
697	C₂⁴	—	4	16	no	—
698	C₂⁴	C₂×C₇×D₄	1	4	yes	—
699	C₂⁴	C₂×C₇×D₄	1	4	yes	—
700	C₂⁴	C₇×#41	1	4	yes	—
701	C₂⁴	C₇×#41	1	4	yes	—
702	C₂⁴	C₇×#41	1	4	yes	—
703	C₂⁴	C₂⁴×C₇	1	2	yes	—
704	C₂⁴	C₂⁴×C₇	1	2	yes	—
705	C₂⁴	C₂⁴×C₇	1	2	yes	—
706	C₂⁴	C₂⁴×C₇	1	2	yes	—
707	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
708	C₂×Q₈	—	2	8	no	—
709	C₂×Q₈	—	2	8	no	—
710	C₂×Q₈	—	4	4	no	—
711	C₂×Q₈	—	4	16	no	—
712	C₂×D₄	—	2	8	no	—
713	C₂×D₄	—	2	8	no	—
714	C₂×D₄	—	2	8	no	—
715	C₂×D₄	—	2	8	no	—
716	C₂×D₄	—	2	8	no	—
717	C₂×D₄	—	2	8	no	—
718	C₂×D₄	—	2	8	no	—
719	C₂×D₄	—	4	4	no	—
720	C₂×D₄	—	4	4	no	—
721	C₂×D₄	—	4	16	no	—
722	C₂×D₄	—	4	16	no	—
723	C₂×D₄	—	4	16	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	8	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	8	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	8	no	—
756	C₂²×C₄	—	2	8	no	—
757	C₂²×C₄	—	4	4	no	—
758	C₂²×C₄	—	4	4	no	—
759	C₂²×C₄	—	4	16	no	—
760	C₂²×C₄	—	4	16	no	—
761	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
762	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
763	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
764	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
765	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
776	C₄⋊C₄	—	2	8	no	—
777	C₄⋊C₄	—	2	8	no	—
778	C₄⋊C₄	—	2	8	no	—
779	C₂²⋊C₄	—	2	8	no	—
780	C₂²⋊C₄	—	2	8	no	—
781	C₂²⋊C₄	—	2	8	no	—
782	C₂²⋊C₄	—	2	8	no	—
783	C₂²⋊C₄	—	2	8	no	—
784	C₂²⋊C₄	—	2	8	no	—
785	C₂²⋊C₄	—	2	8	no	—
786	C₂²⋊C₄	—	2	8	no	—
787	C₂²⋊C₄	—	2	8	no	—
788	C₂²⋊C₄	—	2	8	no	—
789	C₂²⋊C₄	—	2	8	no	—
790	C₂²⋊C₄	—	4	4	no	—
791	C₂²⋊C₄	—	4	4	no	—
792	C₂²⋊C₄	—	4	4	no	—
793	C₂²⋊C₄	—	4	4	no	—
794	C₂²⋊C₄	C₂×C₇×D₄	1	16	yes	—
795	C₂²⋊C₄	C₂×C₇×D₄	1	16	yes	complemented
796	C₄²	—	2	8	no	—
797	C₄²	—	4	4	no	—
798	C₂×C₇	—	2	8	no	—
799	C₂×C₇	—	4	4	no	—
800	C₂×C₇	—	4	4	no	—
801	C₂×C₇	—	8	2	no	—
802	C₂×C₇	#2472	1	8	yes	direct product factor
803	C₂×C₇	C₂×#525	1	1	yes	characteristic
804	C₂×C₇	C₂²×#124	1	1	yes	characteristic
805	C₂×C₇	C₂×#538	1	1	yes	characteristic
806	C₂×C₇	C₂×D₄²	1	1	yes	characteristic
807	C₂×C₇	C₂×#546	1	1	yes	characteristic
808	C₂×C₇	C₂×#546	1	1	yes	characteristic
809	C₂×C₇	C₂×#551	1	1	yes	characteristic
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	8	no	—
815	C₂³	—	2	8	no	—
816	C₂³	—	2	8	no	—
817	C₂³	—	2	8	no	—
818	C₂³	—	2	8	no	—
819	C₂³	—	2	8	no	—
820	C₂³	—	2	32	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	8	no	—
834	C₂³	—	2	8	no	—
835	C₂³	—	2	8	no	—
836	C₂³	—	2	8	no	—
837	C₂³	—	2	8	no	—
838	C₂³	—	2	8	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	4	16	no	—
847	C₂³	—	4	16	no	—
848	C₂³	—	4	16	no	—
849	C₂³	—	4	16	no	—
850	C₂³	—	4	128	no	—
851	C₂³	—	4	16	no	—
852	C₂³	—	4	4	no	—
853	C₂³	—	4	4	no	—
854	C₂³	—	4	16	no	—
855	C₂³	—	4	4	no	—
856	C₂³	—	4	4	no	—
857	C₂³	—	4	4	no	—
858	C₂³	—	4	4	no	—
859	C₂³	—	4	4	no	—
860	C₂³	—	4	4	no	—
861	C₂³	—	4	4	no	—
862	C₂³	—	4	4	no	—
863	C₂³	—	4	4	no	—
864	C₂³	—	4	4	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	4	4	no	—
867	C₂³	—	4	4	no	—
868	C₂³	C₇×#124	1	16	yes	complemented
869	C₂³	C₂²×C₇×D₄	1	4	yes	—
870	C₂³	C₂²×C₇×D₄	1	4	yes	—
871	C₂³	C₂²×C₇×D₄	1	2	yes	—
872	C₂³	C₂²×C₇×D₄	1	2	yes	—
873	C₂³	C₂×C₇×#41	1	4	yes	—
874	C₂³	C₂×C₇×#41	1	4	yes	—
875	C₂³	C₂×C₇×#41	1	4	yes	—
876	C₂³	C₂×C₇×#41	1	2	yes	—
877	C₂³	C₂×C₇×#41	1	2	yes	—
878	C₂³	C₂×C₇×#41	1	2	yes	—
879	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
880	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
881	C₂³	C₂⁵×C₇	1	1	yes	characteristic
882	Q₈	—	4	16	no	—
883	D₄	—	4	16	no	—
884	D₄	—	4	16	no	—
885	D₄	—	4	16	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	8	no	—
895	C₂×C₄	—	2	8	no	—
896	C₂×C₄	—	2	8	no	—
897	C₂×C₄	—	2	8	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	4	16	no	—
920	C₂×C₄	—	4	16	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
929	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
930	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
931	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
932	C₇	C₂×#2472	1	1	yes	characteristic, direct product factor, Sylow
933	C₂²	—	2	32	no	—
934	C₂²	—	2	4	no	—
935	C₂²	—	2	4	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	2	4	no	—
939	C₂²	—	2	4	no	—
940	C₂²	—	2	4	no	—
941	C₂²	—	2	4	no	—
942	C₂²	—	2	4	no	—
943	C₂²	—	2	4	no	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	4	64	no	—
947	C₂²	—	4	16	no	—
948	C₂²	—	4	16	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	8	8	no	—
965	C₂²	C₇×#525	1	4	yes	—
966	C₂²	C₂×C₇×#124	1	4	yes	—
967	C₂²	C₂×C₇×#124	1	8	yes	complemented
968	C₂²	C₇×#538	1	4	yes	—
969	C₂²	C₇×D₄²	1	4	yes	—
970	C₂²	C₇×#546	1	4	yes	—
971	C₂²	C₇×#546	1	4	yes	—
972	C₂²	C₇×#551	1	4	yes	—
973	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
974	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
975	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
976	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
977	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
978	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
979	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
980	C₄	—	2	4	no	—
981	C₄	—	2	4	no	—
982	C₄	—	2	4	no	—
983	C₄	—	2	4	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₂	—	2	8	no	—
992	C₂	—	4	4	no	—
993	C₂	—	4	4	no	—
994	C₂	—	8	2	no	—
995	C₂	C₇×#2472	1	8	yes	direct product factor
996	C₂	C₂×C₇×#525	1	1	yes	characteristic
997	C₂	C₂²×C₇×#124	1	1	yes	characteristic
998	C₂	C₂×C₇×#538	1	1	yes	characteristic
999	C₂	C₂×C₇×D₄²	1	1	yes	characteristic
1000	C₂	C₂×C₇×#546	1	1	yes	characteristic
1001	C₂	C₂×C₇×#546	1	1	yes	characteristic
1002	C₂	C₂×C₇×#551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂²×C₇×#120	C₂
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×#124	C₂	semidirect
2. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
4. C₂³×C₇×C₂²⋊C₄	C₂	semidirect
5. C₇×#2472	C₂	direct (N × H)
6. C₂×C₇×#397	C₂	semidirect
7. C₂×C₇×#394	C₂	semidirect
8. C₂×C₇×#394	C₂	semidirect
9. C₂×C₇×#393	C₂	semidirect
10. C₂×C₇×#390	C₂	semidirect
11. C₂×C₇×#388	C₂	semidirect
12. C₂×C₇×#388	C₂	semidirect
13. C₂×C₇×#386	C₂	semidirect
14. C₂×C₇×#386	C₂	semidirect
15. C₂×C₇×#379	C₂	semidirect
16. C₂×C₄×C₇×C₂²⋊C₄	C₂	semidirect
18. C₂³×C₇×Q₈	C₂²	semidirect
25. C₂×C₇×#124	C₂²	semidirect
27. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
30. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
31. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
32. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
47. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
48. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
49. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
50. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
51. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
52. C₂²×C₄²×C₇	C₂²	semidirect
53. C₂²×C₄²×C₇	C₂²	semidirect
54. C₇×#397	C₂²	semidirect
55. C₇×#394	C₂²	semidirect
56. C₇×#394	C₂²	semidirect
57. C₇×#393	C₂²	semidirect
58. C₇×#390	C₂²	semidirect
59. C₇×#388	C₂²	semidirect
60. C₇×#388	C₂²	semidirect
61. C₇×#386	C₂²	semidirect
62. C₇×#386	C₂²	semidirect
63. C₇×#379	C₂²	semidirect
64. C₄×C₇×C₂²⋊C₄	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×C₇×#95	C₂²	semidirect
70. C₂×C₇×#95	C₂²	semidirect
71. C₂×#2472	C₇	direct (N × H)
87. C₂²×C₇×Q₈	C₂³	semidirect
125. C₂×C₇×C₄⋊C₄	C₂³	semidirect
126. C₂×C₇×C₄⋊C₄	C₂³	semidirect
127. C₂×C₇×C₄⋊C₄	C₂³	semidirect
145. C₂×C₇×C₂²⋊C₄	D₄	semidirect
159. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
160. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
161. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
162. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
165. C₂×C₄²×C₇	C₂³	semidirect
166. C₂×C₄²×C₇	C₂³	semidirect
167. C₇×#95	C₂³	semidirect
168. C₇×#95	C₂³	semidirect
169. C₇×#95	C₂³	semidirect
170. C₇×#95	C₂³	semidirect
171. C₇×#95	C₂³	semidirect
172. C₇×#95	C₂³	semidirect
173. C₂²×#124	C₂×C₇	semidirect
174. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
176. C₂³×C₂²⋊C₄	C₂×C₇	semidirect
177. #2472	C₂×C₇	direct (N × H)
178. C₂×#397	C₂×C₇	semidirect
179. C₂×#394	C₂×C₇	semidirect
180. C₂×#394	C₂×C₇	semidirect
181. C₂×#393	C₂×C₇	semidirect
182. C₂×#390	C₂×C₇	semidirect
183. C₂×#388	C₂×C₇	semidirect
184. C₂×#388	C₂×C₇	semidirect
185. C₂×#386	C₂×C₇	semidirect
186. C₂×#386	C₂×C₇	semidirect
187. C₂×#379	C₂×C₇	semidirect
188. C₂×C₄×C₂²⋊C₄	C₂×C₇	semidirect
323. C₇×C₂²⋊C₄	C₂×D₄	semidirect
327. C₂³×Q₈	C₂²×C₇	semidirect
334. C₂×#124	C₂²×C₇	semidirect
336. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
339. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
340. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
341. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
356. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
357. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
358. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
359. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
360. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
361. C₂²×C₄²	C₂²×C₇	semidirect
362. C₂²×C₄²	C₂²×C₇	semidirect
363. #397	C₂²×C₇	semidirect
364. #394	C₂²×C₇	semidirect
365. #394	C₂²×C₇	semidirect
366. #393	C₂²×C₇	semidirect
367. #390	C₂²×C₇	semidirect
368. #388	C₂²×C₇	semidirect
369. #388	C₂²×C₇	semidirect
370. #386	C₂²×C₇	semidirect
371. #386	C₂²×C₇	semidirect
372. #379	C₂²×C₇	semidirect
373. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
374. C₂×#95	C₂²×C₇	semidirect
375. C₂×#95	C₂²×C₇	semidirect
376. C₂×#95	C₂²×C₇	semidirect
377. C₂×#95	C₂²×C₇	semidirect
378. C₂×#95	C₂²×C₇	semidirect
379. C₂×#95	C₂²×C₇	semidirect
438. C₂³×C₇	#124	semidirect
517. C₂²×Q₈	C₂³×C₇	semidirect
555. C₂×C₄⋊C₄	C₂³×C₇	semidirect
556. C₂×C₄⋊C₄	C₂³×C₇	semidirect
557. C₂×C₄⋊C₄	C₂³×C₇	semidirect
575. C₂×C₂²⋊C₄	C₇×D₄	semidirect
589. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
590. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
591. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
592. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
595. C₂×C₄²	C₂³×C₇	semidirect
596. C₂×C₄²	C₂³×C₇	semidirect
597. #95	C₂³×C₇	semidirect
598. #95	C₂³×C₇	semidirect
599. #95	C₂³×C₇	semidirect
600. #95	C₂³×C₇	semidirect
601. #95	C₂³×C₇	semidirect
602. #95	C₂³×C₇	semidirect
637. C₂²×C₇	C₂×#124	semidirect
795. C₂²⋊C₄	C₂×C₇×D₄	semidirect
802. C₂×C₇	#2472	direct (N × H)
868. C₂³	C₇×#124	semidirect
932. C₇	C₂×#2472	direct (N × H)
967. C₂²	C₂×C₇×#124	semidirect
995. C₂	C₇×#2472	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×#124	2
C₂²×C₇×C₂²⋊Q₈	2
C₂²×C₇×#120	2
C₂³×C₇×C₂²⋊C₄	2
C₇×#2472	2
C₂×C₇×#397	2
C₂×C₇×#394	2
C₂×C₇×#393	2
C₂×C₇×#390	2
C₂×C₇×#388	2
C₂×C₇×#386	2
C₂×C₇×#379	2
C₂×C₄×C₇×C₂²⋊C₄	2
C₂×#2472	7

Subgroups — C2×C7×#2472 #13211874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2472 #13211874