Subgroups — C₂×C₇×#3515 #13239995

Order 1792.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3515	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#552	C₂	1	4	yes	maximal, complemented
8	C₂×C₇×#552	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#547	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#541	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#539	C₂	1	4	yes	maximal, complemented
13	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#529	C₂	1	2	yes	maximal, complemented
15	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#125	C₂	1	2	yes	maximal, complemented
17	C₂×C₇×#520	C₂	1	2	yes	maximal, complemented
18	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₇×#41	C₂²	1	2	yes	—
21	C₇×#557	C₂²	1	16	yes	complemented
22	C₇×#554	C₂²	1	16	yes	complemented
23	C₇×#554	C₂²	1	16	yes	complemented
24	C₇×#553	C₂²	1	32	yes	complemented
25	C₇×#552	C₂²	1	32	yes	complemented
26	C₇×#552	C₂²	1	64	yes	complemented
27	C₇×#552	C₂²	1	32	yes	complemented
28	C₇×#547	C₂²	1	16	yes	complemented
29	C₇×#547	C₂²	1	32	yes	complemented
30	C₇×#541	C₂²	1	32	yes	complemented
31	C₇×#539	C₂²	1	64	yes	complemented
32	C₇×#533	C₂²	1	16	yes	complemented
33	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
36	C₇×#529	C₂²	1	32	yes	complemented
37	C₇×#529	C₂²	1	16	yes	complemented
38	C₂×C₇×#126	C₂²	1	4	yes	—
39	C₂×C₇×#126	C₂²	1	2	yes	—
40	C₂×C₇×#126	C₂²	1	4	yes	—
41	C₂×C₇×#126	C₂²	1	4	yes	—
42	C₂×C₇×#125	C₂²	1	1	yes	characteristic
43	C₂×C₇×#125	C₂²	1	2	yes	—
44	C₂×C₇×#125	C₂²	1	4	yes	—
45	C₂×C₇×#125	C₂²	1	4	yes	—
46	C₂×C₇×#125	C₂²	1	2	yes	—
47	C₂×C₇×#125	C₂²	1	2	yes	—
48	C₂×C₇×#125	C₂²	1	4	yes	—
49	C₂×C₇×#125	C₂²	1	4	yes	—
50	C₂×C₇×#125	C₂²	1	2	yes	—
51	C₂×C₇×#125	C₂²	1	32	yes	complemented
52	C₂×C₇×#124	C₂²	1	1	yes	characteristic
53	C₂×C₇×#123	C₂²	1	2	yes	—
54	C₂×C₇×#123	C₂²	1	4	yes	—
55	C₂×C₇×#123	C₂²	1	4	yes	—
56	C₂×C₇×#123	C₂²	1	4	yes	—
57	C₂×C₇×#123	C₂²	1	4	yes	—
58	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
60	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
61	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
62	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
63	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
64	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
65	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
66	C₂×C₇×#121	C₂²	1	2	yes	—
67	C₂×C₇×#121	C₂²	1	1	yes	characteristic
68	C₂×C₇×#121	C₂²	1	4	yes	—
69	C₇×#520	C₂²	1	32	yes	complemented
70	C₄×C₇×#41	C₂²	1	16	yes	complemented
71	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
72	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
73	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
74	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
75	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
76	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
77	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
78	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
79	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
80	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
81	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
82	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
83	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
84	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
85	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
86	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
87	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
88	C₂×C₇×#117	C₂²	1	1	yes	characteristic
89	C₂×C₇×#117	C₂²	1	2	yes	—
90	C₂×C₇×#117	C₂²	1	2	yes	—
91	C₂×C₇×#117	C₂²	1	4	yes	—
92	C₂×C₇×#117	C₂²	1	4	yes	—
93	C₂×C₇×#117	C₂²	1	2	yes	—
94	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	—
95	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
96	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
97	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	—
98	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
99	C₂²×C₄²×C₇	C₂²	1	2	yes	—
100	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
101	C₂×#3515	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂×C₇×#41	—	2	8	no	—
103	C₂×C₇×#41	—	2	16	no	—
104	C₂×C₇×#41	C₂³	1	8	yes	—
105	C₂×C₇×#41	C₂³	1	16	yes	—
106	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
107	C₂²×C₇×Q₈	C₂³	1	2	yes	—
108	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
109	C₂²×C₇×Q₈	C₂³	1	2	yes	—
110	C₂²×C₇×D₄	C₂³	1	2	yes	—
111	C₂²×C₇×D₄	C₂³	1	4	yes	—
112	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
113	C₂²×C₇×D₄	C₂³	1	2	yes	—
114	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₇	C₂³	1	2	yes	—
116	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₇	C₂³	1	4	yes	—
118	C₂³×C₄×C₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₇	C₂³	1	4	yes	—
124	C₂³×C₄×C₇	C₂³	1	4	yes	—
125	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
126	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
127	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
128	C₇×#126	C₂³	1	32	yes	—
129	C₇×#126	C₂³	1	16	yes	—
130	C₇×#126	C₂³	1	32	yes	—
131	C₇×#126	C₂³	1	32	yes	—
132	C₇×#125	C₂³	1	8	yes	—
133	C₇×#125	C₂³	1	16	yes	—
134	C₇×#125	C₂³	1	32	yes	—
135	C₇×#125	C₂³	1	32	yes	—
136	C₇×#125	C₂³	1	16	yes	—
137	C₇×#125	C₂³	1	16	yes	—
138	C₇×#125	C₂³	1	32	yes	—
139	C₇×#125	C₂³	1	32	yes	—
140	C₇×#125	C₂³	1	16	yes	—
141	C₇×#124	C₂³	1	8	yes	—
142	C₇×#123	C₂³	1	16	yes	—
143	C₇×#123	C₂³	1	32	yes	—
144	C₇×#123	C₂³	1	32	yes	—
145	C₇×#123	C₂³	1	32	yes	—
146	C₇×#123	C₂³	1	32	yes	—
147	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
148	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
149	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
150	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
151	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
152	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
153	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
154	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
155	C₇×#121	C₂³	1	16	yes	—
156	C₇×#121	C₂³	1	8	yes	—
157	C₇×#121	C₂³	1	32	yes	—
158	C₄×C₇×Q₈	C₂³	1	8	yes	—
159	C₄×C₇×Q₈	C₂³	1	8	yes	—
160	C₄×C₇×Q₈	C₂³	1	16	yes	—
161	C₄×C₇×Q₈	C₂³	1	16	yes	—
162	C₄×C₇×Q₈	C₂³	1	16	yes	—
163	C₄×C₇×Q₈	C₂³	1	8	yes	—
164	C₄×C₇×Q₈	C₂³	1	16	yes	—
165	C₄×C₇×D₄	C₂³	1	8	yes	—
166	C₄×C₇×D₄	C₂³	1	16	yes	—
167	C₄×C₇×D₄	C₂³	1	8	yes	—
168	C₄×C₇×D₄	C₂³	1	16	yes	—
169	C₄×C₇×D₄	C₂³	1	32	yes	—
170	C₄×C₇×D₄	C₂³	1	16	yes	—
171	C₄×C₇×D₄	C₂³	1	32	yes	—
172	C₄×C₇×D₄	C₂³	1	16	yes	—
173	C₄×C₇×D₄	C₂³	1	8	yes	—
174	C₄×C₇×D₄	C₂³	1	16	yes	—
175	C₇×#117	C₂³	1	8	yes	—
176	C₇×#117	C₂³	1	16	yes	—
177	C₇×#117	C₂³	1	16	yes	—
178	C₇×#117	C₂³	1	32	yes	—
179	C₇×#117	C₂³	1	32	yes	—
180	C₇×#117	C₂³	1	16	yes	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
190	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
192	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
193	C₂×C₇×C₄⋊C₄	C₂³	1	32	yes	—
194	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
195	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
196	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
197	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
198	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
199	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
200	C₂×C₇×C₄⋊C₄	C₂³	1	32	yes	—
201	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
202	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
207	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
210	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
214	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
218	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
219	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
220	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₇	C₂³	1	2	yes	—
224	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₇	C₂³	1	2	yes	—
227	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₇	C₂³	1	2	yes	—
229	C₂×C₄²×C₇	C₂³	1	16	yes	—
230	C₂×C₄²×C₇	C₂³	1	8	yes	—
231	C₂×C₄²×C₇	C₂³	1	4	yes	—
232	C₂×C₄²×C₇	C₂³	1	4	yes	—
233	C₂×C₄²×C₇	C₂³	1	2	yes	—
234	#3515	C₂×C₇	1	32	yes	direct product factor
235	C₂×#557	C₂×C₇	1	1	yes	characteristic, complemented
236	C₂×#554	C₂×C₇	1	1	yes	characteristic, complemented
237	C₂×#554	C₂×C₇	1	1	yes	characteristic, complemented
238	C₂×#553	C₂×C₇	1	2	yes	complemented
239	C₂×#552	C₂×C₇	1	2	yes	complemented
240	C₂×#552	C₂×C₇	1	4	yes	complemented
241	C₂×#552	C₂×C₇	1	2	yes	complemented
242	C₂×#547	C₂×C₇	1	1	yes	characteristic, complemented
243	C₂×#547	C₂×C₇	1	2	yes	complemented
244	C₂×#541	C₂×C₇	1	2	yes	complemented
245	C₂×#539	C₂×C₇	1	4	yes	complemented
246	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
247	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
248	C₂×#529	C₂×C₇	1	2	yes	complemented
249	C₂²×#125	C₂×C₇	1	2	yes	complemented
250	C₂×#520	C₂×C₇	1	2	yes	complemented
251	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic, complemented
252	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
253	C₂⁴×C₇	C₂⁴	1	2	yes	—
254	C₂⁴×C₇	C₂⁴	1	2	yes	—
255	C₇×#41	—	2	32	no	—
256	C₇×#41	—	2	64	no	—
257	C₂×C₇×Q₈	—	2	4	no	—
258	C₂×C₇×Q₈	—	2	8	no	—
259	C₂×C₇×Q₈	—	2	4	no	—
260	C₂×C₇×Q₈	—	4	4	no	—
261	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
262	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
263	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
264	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
265	C₂×C₇×D₄	—	2	8	no	—
266	C₂×C₇×D₄	—	2	16	no	—
267	C₂×C₇×D₄	—	2	4	no	—
268	C₂×C₇×D₄	—	4	4	no	—
269	C₂×C₇×D₄	#41	1	8	yes	—
270	C₂×C₇×D₄	C₂⁴	1	4	yes	—
271	C₂×C₇×D₄	C₂⁴	1	8	yes	—
272	C₂×C₇×D₄	C₂⁴	1	16	yes	—
273	C₂×C₇×D₄	C₂⁴	1	8	yes	—
274	C₂×C₇×D₄	C₂⁴	1	4	yes	—
275	C₂²×C₄×C₇	—	2	8	no	—
276	C₂²×C₄×C₇	—	2	16	no	—
277	C₂²×C₄×C₇	—	2	4	no	—
278	C₂²×C₄×C₇	—	2	8	no	—
279	C₂²×C₄×C₇	—	2	8	no	—
280	C₂²×C₄×C₇	—	2	4	no	—
281	C₂²×C₄×C₇	—	4	4	no	—
282	C₂²×C₄×C₇	—	4	8	no	—
283	C₂²×C₄×C₇	—	4	2	no	—
284	C₂²×C₄×C₇	—	4	8	no	—
285	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
286	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
287	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
288	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
298	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
301	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
304	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
305	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
306	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
307	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
309	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
310	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
311	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
312	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
313	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
314	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
315	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
316	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
317	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
318	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
319	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
320	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
321	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
322	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
323	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
324	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
325	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
326	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
327	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
328	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
329	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
330	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
331	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
332	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
333	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
334	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
335	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
336	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
337	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
338	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
339	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
340	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
341	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
342	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
343	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
344	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
345	C₄²×C₇	C₂⁴	1	4	yes	—
346	C₄²×C₇	C₂⁴	1	8	yes	—
347	C₄²×C₇	C₂⁴	1	4	yes	—
348	C₄²×C₇	C₂⁴	1	4	yes	—
349	C₄²×C₇	C₂⁴	1	8	yes	—
350	C₄²×C₇	C₂⁴	1	4	yes	—
351	C₄²×C₇	C₂⁴	1	8	yes	—
352	C₄²×C₇	C₂⁴	1	16	yes	—
353	C₄²×C₇	C₂⁴	1	16	yes	—
354	C₄²×C₇	C₂⁴	1	8	yes	—
355	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
356	C₂²×#41	C₂²×C₇	1	2	yes	—
357	#557	C₂²×C₇	1	16	yes	complemented
358	#554	C₂²×C₇	1	16	yes	complemented
359	#554	C₂²×C₇	1	16	yes	complemented
360	#553	C₂²×C₇	1	32	yes	complemented
361	#552	C₂²×C₇	1	32	yes	complemented
362	#552	C₂²×C₇	1	64	yes	complemented
363	#552	C₂²×C₇	1	32	yes	complemented
364	#547	C₂²×C₇	1	16	yes	complemented
365	#547	C₂²×C₇	1	32	yes	complemented
366	#541	C₂²×C₇	1	32	yes	complemented
367	#539	C₂²×C₇	1	64	yes	complemented
368	#533	C₂²×C₇	1	16	yes	complemented
369	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
370	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
371	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
372	#529	C₂²×C₇	1	32	yes	complemented
373	#529	C₂²×C₇	1	16	yes	complemented
374	C₂×#126	C₂²×C₇	1	4	yes	—
375	C₂×#126	C₂²×C₇	1	2	yes	—
376	C₂×#126	C₂²×C₇	1	4	yes	—
377	C₂×#126	C₂²×C₇	1	4	yes	—
378	C₂×#125	C₂²×C₇	1	1	yes	characteristic
379	C₂×#125	C₂²×C₇	1	2	yes	—
380	C₂×#125	C₂²×C₇	1	4	yes	—
381	C₂×#125	C₂²×C₇	1	4	yes	—
382	C₂×#125	C₂²×C₇	1	2	yes	—
383	C₂×#125	C₂²×C₇	1	2	yes	—
384	C₂×#125	C₂²×C₇	1	4	yes	—
385	C₂×#125	C₂²×C₇	1	4	yes	—
386	C₂×#125	C₂²×C₇	1	2	yes	—
387	C₂×#125	C₂²×C₇	1	32	yes	complemented
388	C₂×#124	C₂²×C₇	1	1	yes	characteristic
389	C₂×#123	C₂²×C₇	1	2	yes	—
390	C₂×#123	C₂²×C₇	1	4	yes	—
391	C₂×#123	C₂²×C₇	1	4	yes	—
392	C₂×#123	C₂²×C₇	1	4	yes	—
393	C₂×#123	C₂²×C₇	1	4	yes	—
394	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
395	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
396	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
397	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
398	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
399	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
400	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
401	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
402	C₂×#121	C₂²×C₇	1	2	yes	—
403	C₂×#121	C₂²×C₇	1	1	yes	characteristic
404	C₂×#121	C₂²×C₇	1	4	yes	—
405	#520	C₂²×C₇	1	32	yes	complemented
406	C₄×#41	C₂²×C₇	1	16	yes	complemented
407	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
408	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
409	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
410	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
411	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
412	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
413	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
414	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
415	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
416	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
418	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
419	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
420	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
421	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
422	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
424	C₂×#117	C₂²×C₇	1	1	yes	characteristic
425	C₂×#117	C₂²×C₇	1	2	yes	—
426	C₂×#117	C₂²×C₇	1	2	yes	—
427	C₂×#117	C₂²×C₇	1	4	yes	—
428	C₂×#117	C₂²×C₇	1	4	yes	—
429	C₂×#117	C₂²×C₇	1	2	yes	—
430	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	—
431	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
432	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
433	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	—
434	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
435	C₂²×C₄²	C₂²×C₇	1	2	yes	—
436	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
437	C₂³×C₇	—	2	4	no	—
438	C₂³×C₇	—	2	4	no	—
439	C₂³×C₇	—	2	2	no	—
440	C₂³×C₇	—	2	4	no	—
441	C₂³×C₇	—	2	2	no	—
442	C₂³×C₇	—	2	4	no	—
443	C₂³×C₇	—	2	4	no	—
444	C₂³×C₇	—	2	2	no	—
445	C₂³×C₇	C₂×#41	1	8	yes	—
446	C₂³×C₇	C₂⁵	1	2	yes	—
447	C₂³×C₇	C₂⁵	1	4	yes	—
448	C₂³×C₇	C₂⁵	1	4	yes	—
449	C₂³×C₇	C₂⁵	1	1	yes	characteristic
450	C₇×Q₈	—	2	8	no	—
451	C₇×Q₈	—	2	16	no	—
452	C₇×Q₈	—	2	8	no	—
453	C₇×Q₈	—	4	8	no	—
454	C₇×D₄	—	2	16	no	—
455	C₇×D₄	—	2	32	no	—
456	C₇×D₄	—	2	8	no	—
457	C₇×D₄	—	4	8	no	—
458	C₇×D₄	C₂×#41	1	16	yes	—
459	C₂×C₄×C₇	—	2	2	no	—
460	C₂×C₄×C₇	—	2	4	no	—
461	C₂×C₄×C₇	—	2	4	no	—
462	C₂×C₄×C₇	—	2	8	no	—
463	C₂×C₄×C₇	—	2	16	no	—
464	C₂×C₄×C₇	—	2	32	no	—
465	C₂×C₄×C₇	—	2	2	no	—
466	C₂×C₄×C₇	—	2	4	no	—
467	C₂×C₄×C₇	—	2	4	no	—
468	C₂×C₄×C₇	—	2	2	no	—
469	C₂×C₄×C₇	—	2	4	no	—
470	C₂×C₄×C₇	—	2	4	no	—
471	C₂×C₄×C₇	—	2	8	no	—
472	C₂×C₄×C₇	—	2	2	no	—
473	C₂×C₄×C₇	—	2	8	no	—
474	C₂×C₄×C₇	—	2	16	no	—
475	C₂×C₄×C₇	—	2	16	no	—
476	C₂×C₄×C₇	—	2	8	no	—
477	C₂×C₄×C₇	—	4	8	no	—
478	C₂×C₄×C₇	—	4	16	no	—
479	C₂×C₄×C₇	—	4	4	no	—
480	C₂×C₄×C₇	—	4	16	no	—
481	C₂×C₄×C₇	C₂×#41	1	4	yes	—
482	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
483	C₂×C₄×C₇	C₂⁵	1	2	yes	—
484	C₂×C₄×C₇	C₂⁵	1	2	yes	—
485	C₂×C₄×C₇	C₂⁵	1	2	yes	—
486	C₂×C₄×C₇	C₂⁵	1	4	yes	—
487	C₂×C₄×C₇	C₂⁵	1	4	yes	—
488	C₂×C₄×C₇	C₂⁵	1	4	yes	—
489	C₂×C₄×C₇	C₂⁵	1	2	yes	—
490	C₂×C₄×C₇	C₂⁵	1	4	yes	—
491	C₂×C₄×C₇	C₂⁵	1	8	yes	—
492	C₂×C₄×C₇	C₂⁵	1	8	yes	—
493	C₂×C₄×C₇	C₂⁵	1	4	yes	—
494	C₂×C₄×C₇	C₂⁵	1	4	yes	—
495	C₂×C₄×C₇	C₂⁵	1	2	yes	—
496	C₂×C₄×C₇	C₂⁵	1	2	yes	—
497	C₂×#41	—	2	8	no	—
498	C₂×#41	—	2	16	no	—
499	C₂×#41	C₂³×C₇	1	8	yes	—
500	C₂×#41	C₂³×C₇	1	16	yes	—
501	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
502	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
503	C₂²×Q₈	C₂³×C₇	1	2	yes	—
504	C₂²×Q₈	C₂³×C₇	1	2	yes	—
505	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
506	C₂²×D₄	C₂³×C₇	1	2	yes	—
507	C₂²×D₄	C₂³×C₇	1	4	yes	—
508	C₂²×D₄	C₂³×C₇	1	2	yes	—
509	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₇	1	4	yes	—
511	C₂³×C₄	C₂³×C₇	1	2	yes	—
512	C₂³×C₄	C₂³×C₇	1	2	yes	—
513	C₂³×C₄	C₂³×C₇	1	2	yes	—
514	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₇	1	4	yes	—
517	C₂³×C₄	C₂³×C₇	1	2	yes	—
518	C₂³×C₄	C₂³×C₇	1	4	yes	—
519	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
520	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
521	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
522	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
523	#126	C₂³×C₇	1	32	yes	—
524	#126	C₂³×C₇	1	16	yes	—
525	#126	C₂³×C₇	1	32	yes	—
526	#126	C₂³×C₇	1	32	yes	—
527	#125	C₂³×C₇	1	8	yes	—
528	#125	C₂³×C₇	1	16	yes	—
529	#125	C₂³×C₇	1	32	yes	—
530	#125	C₂³×C₇	1	32	yes	—
531	#125	C₂³×C₇	1	16	yes	—
532	#125	C₂³×C₇	1	16	yes	—
533	#125	C₂³×C₇	1	32	yes	—
534	#125	C₂³×C₇	1	32	yes	—
535	#125	C₂³×C₇	1	16	yes	—
536	#124	C₂³×C₇	1	8	yes	—
537	#123	C₂³×C₇	1	16	yes	—
538	#123	C₂³×C₇	1	32	yes	—
539	#123	C₂³×C₇	1	32	yes	—
540	#123	C₂³×C₇	1	32	yes	—
541	#123	C₂³×C₇	1	32	yes	—
542	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
543	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
544	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
545	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
546	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
547	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
548	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
549	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
550	#121	C₂³×C₇	1	16	yes	—
551	#121	C₂³×C₇	1	8	yes	—
552	#121	C₂³×C₇	1	32	yes	—
553	C₄×Q₈	C₂³×C₇	1	8	yes	—
554	C₄×Q₈	C₂³×C₇	1	8	yes	—
555	C₄×Q₈	C₂³×C₇	1	16	yes	—
556	C₄×Q₈	C₂³×C₇	1	16	yes	—
557	C₄×Q₈	C₂³×C₇	1	16	yes	—
558	C₄×Q₈	C₂³×C₇	1	8	yes	—
559	C₄×Q₈	C₂³×C₇	1	16	yes	—
560	C₄×D₄	C₂³×C₇	1	8	yes	—
561	C₄×D₄	C₂³×C₇	1	16	yes	—
562	C₄×D₄	C₂³×C₇	1	8	yes	—
563	C₄×D₄	C₂³×C₇	1	16	yes	—
564	C₄×D₄	C₂³×C₇	1	32	yes	—
565	C₄×D₄	C₂³×C₇	1	16	yes	—
566	C₄×D₄	C₂³×C₇	1	32	yes	—
567	C₄×D₄	C₂³×C₇	1	16	yes	—
568	C₄×D₄	C₂³×C₇	1	8	yes	—
569	C₄×D₄	C₂³×C₇	1	16	yes	—
570	#117	C₂³×C₇	1	8	yes	—
571	#117	C₂³×C₇	1	16	yes	—
572	#117	C₂³×C₇	1	16	yes	—
573	#117	C₂³×C₇	1	32	yes	—
574	#117	C₂³×C₇	1	32	yes	—
575	#117	C₂³×C₇	1	16	yes	—
576	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
578	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
585	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
587	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
588	C₂×C₄⋊C₄	C₂³×C₇	1	32	yes	—
589	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
590	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
591	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
592	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
593	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
594	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
595	C₂×C₄⋊C₄	C₂³×C₇	1	32	yes	—
596	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
597	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
602	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
617	C₂×C₄²	C₂³×C₇	1	2	yes	—
618	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₇	1	4	yes	—
620	C₂×C₄²	C₂³×C₇	1	4	yes	—
621	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₇	1	2	yes	—
623	C₂×C₄²	C₂³×C₇	1	2	yes	—
624	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₇	1	2	yes	—
626	C₂×C₄²	C₂³×C₇	1	16	yes	—
627	C₂×C₄²	C₂³×C₇	1	8	yes	—
628	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
629	C₂²×C₇	—	2	4	no	—
630	C₂²×C₇	—	2	4	no	—
631	C₂²×C₇	—	2	16	no	—
632	C₂²×C₇	—	2	2	no	—
633	C₂²×C₇	—	2	4	no	—
634	C₂²×C₇	—	2	2	no	—
635	C₂²×C₇	—	2	4	no	—
636	C₂²×C₇	—	2	4	no	—
637	C₂²×C₇	—	2	2	no	—
638	C₂²×C₇	—	4	4	no	—
639	C₂²×C₇	—	4	8	no	—
640	C₂²×C₇	C₂²×#41	1	8	yes	—
641	C₂²×C₇	C₂²×#41	1	2	yes	—
642	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
643	C₂²×C₇	#585	1	2	yes	—
644	C₂²×C₇	C₂⁶	1	1	yes	characteristic
645	C₄×C₇	—	2	2	no	—
646	C₄×C₇	—	2	4	no	—
647	C₄×C₇	—	2	4	no	—
648	C₄×C₇	—	2	8	no	—
649	C₄×C₇	—	2	2	no	—
650	C₄×C₇	—	2	4	no	—
651	C₄×C₇	—	2	4	no	—
652	C₄×C₇	—	2	2	no	—
653	C₄×C₇	—	2	4	no	—
654	C₄×C₇	—	2	4	no	—
655	C₄×C₇	—	2	8	no	—
656	C₄×C₇	—	2	2	no	—
657	C₄×C₇	C₂²×#41	1	4	yes	—
658	C₄×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
659	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
660	C₂⁴	C₂⁴×C₇	1	2	yes	—
661	C₂⁴	C₂⁴×C₇	1	2	yes	—
662	#41	—	2	32	no	—
663	#41	—	2	64	no	—
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	2	8	no	—
666	C₂×Q₈	—	2	4	no	—
667	C₂×Q₈	—	4	4	no	—
668	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
669	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
670	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
671	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
672	C₂×D₄	—	2	8	no	—
673	C₂×D₄	—	2	16	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	4	4	no	—
676	C₂×D₄	C₇×#41	1	8	yes	—
677	C₂×D₄	C₂⁴×C₇	1	4	yes	—
678	C₂×D₄	C₂⁴×C₇	1	8	yes	—
679	C₂×D₄	C₂⁴×C₇	1	16	yes	—
680	C₂×D₄	C₂⁴×C₇	1	8	yes	—
681	C₂×D₄	C₂⁴×C₇	1	4	yes	—
682	C₂²×C₄	—	2	16	no	—
683	C₂²×C₄	—	2	8	no	—
684	C₂²×C₄	—	2	8	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	2	8	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	4	4	no	—
689	C₂²×C₄	—	4	8	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	8	no	—
692	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
700	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
702	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
703	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
704	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
705	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
706	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
709	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
710	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
711	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
712	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
713	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
714	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
716	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
717	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
718	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
719	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
720	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
721	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
722	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
723	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
724	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
725	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
726	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
727	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
728	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
729	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
730	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
731	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
732	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
733	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
734	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
735	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
736	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
737	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
738	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
739	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
740	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
741	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
742	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
743	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
744	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
745	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
746	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
747	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
748	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
749	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
750	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
751	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
752	C₄²	C₂⁴×C₇	1	4	yes	—
753	C₄²	C₂⁴×C₇	1	8	yes	—
754	C₄²	C₂⁴×C₇	1	4	yes	—
755	C₄²	C₂⁴×C₇	1	4	yes	—
756	C₄²	C₂⁴×C₇	1	8	yes	—
757	C₄²	C₂⁴×C₇	1	4	yes	—
758	C₄²	C₂⁴×C₇	1	8	yes	—
759	C₄²	C₂⁴×C₇	1	16	yes	—
760	C₄²	C₂⁴×C₇	1	16	yes	—
761	C₄²	C₂⁴×C₇	1	8	yes	—
762	C₂×C₇	—	2	8	no	—
763	C₂×C₇	—	4	2	no	—
764	C₂×C₇	—	4	4	no	—
765	C₂×C₇	#3515	1	4	yes	direct product factor
766	C₂×C₇	C₂³×#41	1	1	yes	characteristic
767	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
768	C₂×C₇	C₂×#585	1	1	yes	characteristic
769	C₂³	—	2	4	no	—
770	C₂³	—	2	4	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	4	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	4	no	—
775	C₂³	—	2	4	no	—
776	C₂³	—	2	2	no	—
777	C₂³	C₂×C₇×#41	1	8	yes	—
778	C₂³	C₂⁵×C₇	1	2	yes	—
779	C₂³	C₂⁵×C₇	1	4	yes	—
780	C₂³	C₂⁵×C₇	1	4	yes	—
781	C₂³	C₂⁵×C₇	1	1	yes	characteristic
782	Q₈	—	2	8	no	—
783	Q₈	—	2	16	no	—
784	Q₈	—	2	8	no	—
785	Q₈	—	4	8	no	—
786	D₄	—	2	16	no	—
787	D₄	—	2	32	no	—
788	D₄	—	2	8	no	—
789	D₄	—	4	8	no	—
790	D₄	C₂×C₇×#41	1	16	yes	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	2	8	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	16	no	—
796	C₂×C₄	—	2	32	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	8	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	8	no	—
806	C₂×C₄	—	2	16	no	—
807	C₂×C₄	—	2	16	no	—
808	C₂×C₄	—	2	8	no	—
809	C₂×C₄	—	4	8	no	—
810	C₂×C₄	—	4	16	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	16	no	—
813	C₂×C₄	C₂×C₇×#41	1	4	yes	—
814	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
815	C₂×C₄	C₂⁵×C₇	1	2	yes	—
816	C₂×C₄	C₂⁵×C₇	1	2	yes	—
817	C₂×C₄	C₂⁵×C₇	1	2	yes	—
818	C₂×C₄	C₂⁵×C₇	1	4	yes	—
819	C₂×C₄	C₂⁵×C₇	1	4	yes	—
820	C₂×C₄	C₂⁵×C₇	1	4	yes	—
821	C₂×C₄	C₂⁵×C₇	1	2	yes	—
822	C₂×C₄	C₂⁵×C₇	1	4	yes	—
823	C₂×C₄	C₂⁵×C₇	1	8	yes	—
824	C₂×C₄	C₂⁵×C₇	1	8	yes	—
825	C₂×C₄	C₂⁵×C₇	1	4	yes	—
826	C₂×C₄	C₂⁵×C₇	1	4	yes	—
827	C₂×C₄	C₂⁵×C₇	1	2	yes	—
828	C₂×C₄	C₂⁵×C₇	1	2	yes	—
829	C₇	C₂×#3515	1	1	yes	characteristic, direct product factor, Sylow
830	C₂²	—	2	4	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	2	16	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	4	4	no	—
840	C₂²	—	4	8	no	—
841	C₂²	C₂²×C₇×#41	1	8	yes	—
842	C₂²	C₂²×C₇×#41	1	2	yes	—
843	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
844	C₂²	C₇×#585	1	2	yes	—
845	C₂²	C₂⁶×C₇	1	1	yes	characteristic
846	C₄	—	2	2	no	—
847	C₄	—	2	4	no	—
848	C₄	—	2	4	no	—
849	C₄	—	2	8	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	4	no	—
852	C₄	—	2	4	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	8	no	—
857	C₄	—	2	2	no	—
858	C₄	C₂²×C₇×#41	1	4	yes	—
859	C₄	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
860	C₂	—	2	8	no	—
861	C₂	—	4	2	no	—
862	C₂	—	4	4	no	—
863	C₂	C₇×#3515	1	4	yes	direct product factor
864	C₂	C₂³×C₇×#41	1	1	yes	characteristic
865	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
866	C₂	C₂×C₇×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3515	C₂	direct (N × H)
2. C₂×C₇×#557	C₂	semidirect
3. C₂×C₇×#554	C₂	semidirect
4. C₂×C₇×#554	C₂	semidirect
5. C₂×C₇×#553	C₂	semidirect
6. C₂×C₇×#552	C₂	semidirect
7. C₂×C₇×#552	C₂	semidirect
8. C₂×C₇×#552	C₂	semidirect
9. C₂×C₇×#547	C₂	semidirect
10. C₂×C₇×#547	C₂	semidirect
11. C₂×C₇×#541	C₂	semidirect
12. C₂×C₇×#539	C₂	semidirect
13. C₂×C₇×#533	C₂	semidirect
14. C₂×C₇×#529	C₂	semidirect
15. C₂×C₇×#529	C₂	semidirect
16. C₂²×C₇×#125	C₂	semidirect
17. C₂×C₇×#520	C₂	semidirect
18. C₂×C₄×C₇×#41	C₂	semidirect
21. C₇×#557	C₂²	semidirect
22. C₇×#554	C₂²	semidirect
23. C₇×#554	C₂²	semidirect
24. C₇×#553	C₂²	semidirect
25. C₇×#552	C₂²	semidirect
26. C₇×#552	C₂²	semidirect
27. C₇×#552	C₂²	semidirect
28. C₇×#547	C₂²	semidirect
29. C₇×#547	C₂²	semidirect
30. C₇×#541	C₂²	semidirect
31. C₇×#539	C₂²	semidirect
32. C₇×#533	C₂²	semidirect
36. C₇×#529	C₂²	semidirect
37. C₇×#529	C₂²	semidirect
51. C₂×C₇×#125	C₂²	semidirect
69. C₇×#520	C₂²	semidirect
70. C₄×C₇×#41	C₂²	semidirect
101. C₂×#3515	C₇	direct (N × H)
234. #3515	C₂×C₇	direct (N × H)
235. C₂×#557	C₂×C₇	semidirect
236. C₂×#554	C₂×C₇	semidirect
237. C₂×#554	C₂×C₇	semidirect
238. C₂×#553	C₂×C₇	semidirect
239. C₂×#552	C₂×C₇	semidirect
240. C₂×#552	C₂×C₇	semidirect
241. C₂×#552	C₂×C₇	semidirect
242. C₂×#547	C₂×C₇	semidirect
243. C₂×#547	C₂×C₇	semidirect
244. C₂×#541	C₂×C₇	semidirect
245. C₂×#539	C₂×C₇	semidirect
246. C₂×#533	C₂×C₇	semidirect
247. C₂×#529	C₂×C₇	semidirect
248. C₂×#529	C₂×C₇	semidirect
249. C₂²×#125	C₂×C₇	semidirect
250. C₂×#520	C₂×C₇	semidirect
251. C₂×C₄×#41	C₂×C₇	semidirect
357. #557	C₂²×C₇	semidirect
358. #554	C₂²×C₇	semidirect
359. #554	C₂²×C₇	semidirect
360. #553	C₂²×C₇	semidirect
361. #552	C₂²×C₇	semidirect
362. #552	C₂²×C₇	semidirect
363. #552	C₂²×C₇	semidirect
364. #547	C₂²×C₇	semidirect
365. #547	C₂²×C₇	semidirect
366. #541	C₂²×C₇	semidirect
367. #539	C₂²×C₇	semidirect
368. #533	C₂²×C₇	semidirect
372. #529	C₂²×C₇	semidirect
373. #529	C₂²×C₇	semidirect
387. C₂×#125	C₂²×C₇	semidirect
405. #520	C₂²×C₇	semidirect
406. C₄×#41	C₂²×C₇	semidirect
765. C₂×C₇	#3515	direct (N × H)
829. C₇	C₂×#3515	direct (N × H)
863. C₂	C₇×#3515	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3515	2
C₂×C₇×#557	2
C₂×C₇×#554	2
C₂×C₇×#553	2
C₂×C₇×#552	2
C₂×C₇×#547	2
C₂×C₇×#541	2
C₂×C₇×#539	2
C₂×C₇×#533	2
C₂×C₇×#529	2
C₂²×C₇×#125	2
C₂×C₇×#520	2
C₂×C₄×C₇×#41	2
C₂×#3515	7

Subgroups — C2×C7×#3515 #13239995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3515 #13239995