Subgroups — C₂×C₇×#3539 #13239943

Order 1792.

7354 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3539	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#560	C₂	1	4	yes	maximal, complemented
3	C₂×C₇×#553	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#553	C₂	1	4	yes	maximal, complemented
5	C₂×C₇×#552	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#550	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#547	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#541	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#540	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#540	C₂	1	4	yes	maximal, complemented
11	C₂×C₇×#539	C₂	1	4	yes	maximal, complemented
12	C₂×C₇×#537	C₂	1	2	yes	maximal, complemented
13	C₂×C₇×#525	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#525	C₂	1	2	yes	maximal, complemented
15	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
16	C₂²×C₇×#41	C₂²	1	2	yes	—
17	C₂²×C₇×#41	C₂²	1	2	yes	complemented
18	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
19	C₇×#560	C₂²	1	64	yes	complemented
20	C₇×#553	C₂²	1	32	yes	complemented
21	C₇×#553	C₂²	1	64	yes	complemented
22	C₇×#552	C₂²	1	32	yes	complemented
23	C₇×#550	C₂²	1	32	yes	complemented
24	C₇×#547	C₂²	1	32	yes	complemented
25	C₇×#541	C₂²	1	16	yes	complemented
26	C₇×#540	C₂²	1	16	yes	complemented
27	C₇×#540	C₂²	1	64	yes	complemented
28	C₇×#539	C₂²	1	64	yes	complemented
29	C₇×#537	C₂²	1	32	yes	complemented
30	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₇×#127	C₂²	1	4	yes	—
32	C₂×C₇×#127	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₇×#126	C₂²	1	4	yes	—
34	C₂×C₇×#126	C₂²	1	4	yes	—
35	C₂×C₇×#126	C₂²	1	4	yes	complemented
36	C₂×C₇×#125	C₂²	1	4	yes	complemented
37	C₂×C₇×#125	C₂²	1	4	yes	complemented
38	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
40	C₇×#525	C₂²	1	16	yes	complemented
41	C₇×#525	C₂²	1	32	yes	complemented
42	C₂×C₇×#123	C₂²	1	4	yes	—
43	C₂×C₇×#123	C₂²	1	2	yes	—
44	C₂×C₇×#123	C₂²	1	4	yes	—
45	C₂×C₇×#123	C₂²	1	4	yes	—
46	C₂×C₇×#123	C₂²	1	4	yes	—
47	C₂×C₇×#123	C₂²	1	4	yes	complemented
48	C₂×C₇×#123	C₂²	1	4	yes	complemented
49	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
50	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
52	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
53	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
54	C₂×C₇×#121	C₂²	1	2	yes	—
55	C₂×C₇×#121	C₂²	1	2	yes	—
56	C₂×C₇×#121	C₂²	1	2	yes	—
57	C₂×C₇×#121	C₂²	1	4	yes	—
58	C₂×C₇×#121	C₂²	1	4	yes	—
59	C₂×C₇×#121	C₂²	1	4	yes	—
60	C₂×C₇×#121	C₂²	1	4	yes	—
61	C₂×C₇×#121	C₂²	1	4	yes	—
62	C₂×C₇×#121	C₂²	1	4	yes	—
63	C₂×C₇×#121	C₂²	1	4	yes	complemented
64	C₂×C₇×#121	C₂²	1	2	yes	complemented
65	C₂×C₇×#121	C₂²	1	4	yes	complemented
66	C₂×C₇×#120	C₂²	1	2	yes	—
67	C₂×C₇×#120	C₂²	1	4	yes	—
68	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
69	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
70	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
71	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
72	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
73	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
74	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
75	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
76	C₂×C₇×#117	C₂²	1	1	yes	characteristic
77	C₂×C₇×#117	C₂²	1	2	yes	—
78	C₂×C₇×#117	C₂²	1	4	yes	complemented
79	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
80	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	complemented
81	C₂×#3539	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁵×C₇	C₂³	1	1	yes	characteristic
83	C₂×C₇×#41	—	4	4	no	—
84	C₂×C₇×#41	—	4	8	no	—
85	C₂×C₇×#41	—	4	8	no	—
86	C₂×C₇×#41	C₂³	1	8	yes	—
87	C₂×C₇×#41	C₂³	1	16	yes	—
88	C₂×C₇×#41	C₂³	1	16	yes	complemented
89	C₂²×C₇×Q₈	C₂³	1	2	yes	—
90	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
91	C₂²×C₇×D₄	C₂³	1	2	yes	—
92	C₂²×C₇×D₄	C₂³	1	2	yes	—
93	C₂²×C₇×D₄	C₂³	1	4	yes	—
94	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
95	C₂²×C₇×D₄	C₂³	1	4	yes	—
96	C₂²×C₇×D₄	C₂³	1	2	yes	—
97	C₂²×C₇×D₄	C₂³	1	4	yes	—
98	C₂²×C₇×D₄	C₂³	1	4	yes	—
99	C₂²×C₇×D₄	C₂³	1	2	yes	—
100	C₂²×C₇×D₄	C₂³	1	4	yes	—
101	C₂²×C₇×D₄	C₂³	1	4	yes	—
102	C₂³×C₄×C₇	—	4	4	no	—
103	C₂³×C₄×C₇	C₂³	1	2	yes	—
104	C₂³×C₄×C₇	C₂³	1	2	yes	—
105	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₇	C₂³	1	4	yes	—
107	C₂³×C₄×C₇	C₂³	1	4	yes	—
108	C₂³×C₄×C₇	C₂³	1	4	yes	—
109	C₂³×C₄×C₇	C₂³	1	4	yes	—
110	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₇	C₂³	1	2	yes	—
112	C₂³×C₄×C₇	C₂³	1	8	yes	—
113	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
114	C₇×#127	C₂³	1	32	yes	—
115	C₇×#127	C₂³	1	8	yes	complemented
116	C₇×#126	C₂³	1	32	yes	—
117	C₇×#126	C₂³	1	32	yes	—
118	C₇×#126	C₂³	1	32	yes	complemented
119	C₇×#125	C₂³	1	32	yes	complemented
120	C₇×#125	C₂³	1	32	yes	complemented
121	C₇×#125	C₂³	1	8	yes	complemented
122	C₇×#125	C₂³	1	8	yes	complemented
123	C₇×#123	C₂³	1	32	yes	—
124	C₇×#123	C₂³	1	16	yes	—
125	C₇×#123	C₂³	1	32	yes	—
126	C₇×#123	C₂³	1	32	yes	—
127	C₇×#123	C₂³	1	32	yes	—
128	C₇×#123	C₂³	1	32	yes	complemented
129	C₇×#123	C₂³	1	32	yes	complemented
130	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
131	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
132	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
133	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
134	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
135	C₇×#121	C₂³	1	16	yes	—
136	C₇×#121	C₂³	1	16	yes	—
137	C₇×#121	C₂³	1	16	yes	—
138	C₇×#121	C₂³	1	32	yes	—
139	C₇×#121	C₂³	1	32	yes	—
140	C₇×#121	C₂³	1	32	yes	—
141	C₇×#121	C₂³	1	32	yes	—
142	C₇×#121	C₂³	1	32	yes	—
143	C₇×#121	C₂³	1	32	yes	—
144	C₇×#121	C₂³	1	32	yes	complemented
145	C₇×#121	C₂³	1	16	yes	complemented
146	C₇×#121	C₂³	1	32	yes	complemented
147	C₇×#120	C₂³	1	16	yes	—
148	C₇×#120	C₂³	1	32	yes	—
149	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
150	C₄×C₇×D₄	C₂³	1	32	yes	—
151	C₄×C₇×D₄	C₂³	1	16	yes	—
152	C₄×C₇×D₄	C₂³	1	16	yes	—
153	C₄×C₇×D₄	C₂³	1	32	yes	—
154	C₄×C₇×D₄	C₂³	1	32	yes	complemented
155	C₄×C₇×D₄	C₂³	1	16	yes	complemented
156	C₄×C₇×D₄	C₂³	1	32	yes	complemented
157	C₇×#117	C₂³	1	8	yes	—
158	C₇×#117	C₂³	1	16	yes	—
159	C₇×#117	C₂³	1	32	yes	complemented
160	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
164	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
165	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
166	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
169	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
171	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
172	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
174	C₂×C₇×C₄⋊C₄	C₂³	1	32	yes	complemented
175	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
177	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
179	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
180	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
183	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
184	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
186	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
187	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
188	C₂×C₄²×C₇	C₂³	1	4	yes	—
189	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	C₂³	1	4	yes	—
192	#3539	C₂×C₇	1	32	yes	direct product factor
193	C₂×#560	C₂×C₇	1	4	yes	complemented
194	C₂×#553	C₂×C₇	1	2	yes	complemented
195	C₂×#553	C₂×C₇	1	4	yes	complemented
196	C₂×#552	C₂×C₇	1	2	yes	complemented
197	C₂×#550	C₂×C₇	1	2	yes	complemented
198	C₂×#547	C₂×C₇	1	2	yes	complemented
199	C₂×#541	C₂×C₇	1	1	yes	characteristic, complemented
200	C₂×#540	C₂×C₇	1	1	yes	characteristic, complemented
201	C₂×#540	C₂×C₇	1	4	yes	complemented
202	C₂×#539	C₂×C₇	1	4	yes	complemented
203	C₂×#537	C₂×C₇	1	2	yes	complemented
204	C₂×#525	C₂×C₇	1	1	yes	characteristic, complemented
205	C₂×#525	C₂×C₇	1	2	yes	complemented
206	C₂⁴×C₇	—	4	2	no	—
207	C₂⁴×C₇	—	4	4	no	—
208	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
209	C₂⁴×C₇	C₂⁴	1	2	yes	—
210	C₂⁴×C₇	C₂⁴	1	2	yes	—
211	C₂⁴×C₇	C₂⁴	1	4	yes	—
212	C₂⁴×C₇	C₂⁴	1	4	yes	—
213	C₇×#41	—	4	16	no	—
214	C₇×#41	—	4	32	no	—
215	C₇×#41	—	4	32	no	—
216	C₂×C₇×Q₈	—	2	8	no	—
217	C₂×C₇×Q₈	—	4	2	no	—
218	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
219	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
220	C₂×C₇×D₄	—	2	8	no	—
221	C₂×C₇×D₄	—	4	4	no	—
222	C₂×C₇×D₄	—	4	8	no	—
223	C₂×C₇×D₄	—	4	8	no	—
224	C₂×C₇×D₄	—	4	8	no	—
225	C₂×C₇×D₄	—	4	4	no	—
226	C₂×C₇×D₄	—	4	8	no	—
227	C₂×C₇×D₄	—	4	4	no	—
228	C₂×C₇×D₄	—	4	2	no	—
229	C₂×C₇×D₄	—	4	8	no	—
230	C₂×C₇×D₄	—	4	8	no	—
231	C₂×C₇×D₄	C₂⁴	1	8	yes	—
232	C₂×C₇×D₄	C₂⁴	1	8	yes	—
233	C₂×C₇×D₄	C₂⁴	1	16	yes	—
234	C₂×C₇×D₄	C₂⁴	1	16	yes	—
235	C₂×C₇×D₄	C₂⁴	1	8	yes	—
236	C₂×C₇×D₄	C₂⁴	1	16	yes	—
237	C₂×C₇×D₄	C₂⁴	1	16	yes	—
238	C₂×C₇×D₄	C₂⁴	1	8	yes	—
239	C₂×C₇×D₄	C₂⁴	1	16	yes	—
240	C₂×C₇×D₄	C₂⁴	1	4	yes	—
241	C₂×C₇×D₄	C₂⁴	1	16	yes	—
242	C₂²×C₄×C₇	—	2	8	no	—
243	C₂²×C₄×C₇	—	2	4	no	—
244	C₂²×C₄×C₇	—	2	8	no	—
245	C₂²×C₄×C₇	—	4	16	no	—
246	C₂²×C₄×C₇	—	4	2	no	—
247	C₂²×C₄×C₇	—	4	4	no	—
248	C₂²×C₄×C₇	—	4	8	no	—
249	C₂²×C₄×C₇	—	4	8	no	—
250	C₂²×C₄×C₇	—	4	8	no	—
251	C₂²×C₄×C₇	—	4	8	no	—
252	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
253	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
254	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
257	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
264	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
265	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
266	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
267	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
268	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
269	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
270	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
271	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
272	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
273	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
274	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
275	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
276	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
277	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
278	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
279	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
280	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
281	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
282	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
283	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
284	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
285	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
286	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
287	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
288	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
289	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
290	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
291	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
292	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
293	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
294	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
295	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
296	C₄²×C₇	C₂⁴	1	16	yes	—
297	C₄²×C₇	C₂⁴	1	4	yes	—
298	C₄²×C₇	C₂⁴	1	4	yes	—
299	C₄²×C₇	C₂⁴	1	16	yes	—
300	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
301	C₂²×#41	C₂²×C₇	1	2	yes	—
302	C₂²×#41	C₂²×C₇	1	2	yes	complemented
303	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
304	#560	C₂²×C₇	1	64	yes	complemented
305	#553	C₂²×C₇	1	32	yes	complemented
306	#553	C₂²×C₇	1	64	yes	complemented
307	#552	C₂²×C₇	1	32	yes	complemented
308	#550	C₂²×C₇	1	32	yes	complemented
309	#547	C₂²×C₇	1	32	yes	complemented
310	#541	C₂²×C₇	1	16	yes	complemented
311	#540	C₂²×C₇	1	16	yes	complemented
312	#540	C₂²×C₇	1	64	yes	complemented
313	#539	C₂²×C₇	1	64	yes	complemented
314	#537	C₂²×C₇	1	32	yes	complemented
315	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
316	C₂×#127	C₂²×C₇	1	4	yes	—
317	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
318	C₂×#126	C₂²×C₇	1	4	yes	—
319	C₂×#126	C₂²×C₇	1	4	yes	—
320	C₂×#126	C₂²×C₇	1	4	yes	complemented
321	C₂×#125	C₂²×C₇	1	4	yes	complemented
322	C₂×#125	C₂²×C₇	1	4	yes	complemented
323	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
324	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
325	#525	C₂²×C₇	1	16	yes	complemented
326	#525	C₂²×C₇	1	32	yes	complemented
327	C₂×#123	C₂²×C₇	1	4	yes	—
328	C₂×#123	C₂²×C₇	1	2	yes	—
329	C₂×#123	C₂²×C₇	1	4	yes	—
330	C₂×#123	C₂²×C₇	1	4	yes	—
331	C₂×#123	C₂²×C₇	1	4	yes	—
332	C₂×#123	C₂²×C₇	1	4	yes	complemented
333	C₂×#123	C₂²×C₇	1	4	yes	complemented
334	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
335	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
336	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
337	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
338	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
339	C₂×#121	C₂²×C₇	1	2	yes	—
340	C₂×#121	C₂²×C₇	1	2	yes	—
341	C₂×#121	C₂²×C₇	1	2	yes	—
342	C₂×#121	C₂²×C₇	1	4	yes	—
343	C₂×#121	C₂²×C₇	1	4	yes	—
344	C₂×#121	C₂²×C₇	1	4	yes	—
345	C₂×#121	C₂²×C₇	1	4	yes	—
346	C₂×#121	C₂²×C₇	1	4	yes	—
347	C₂×#121	C₂²×C₇	1	4	yes	—
348	C₂×#121	C₂²×C₇	1	4	yes	complemented
349	C₂×#121	C₂²×C₇	1	2	yes	complemented
350	C₂×#121	C₂²×C₇	1	4	yes	complemented
351	C₂×#120	C₂²×C₇	1	2	yes	—
352	C₂×#120	C₂²×C₇	1	4	yes	—
353	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
354	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
355	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
356	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
357	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
358	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
359	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
360	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
361	C₂×#117	C₂²×C₇	1	1	yes	characteristic
362	C₂×#117	C₂²×C₇	1	2	yes	—
363	C₂×#117	C₂²×C₇	1	4	yes	complemented
364	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
365	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	complemented
366	C₂³×C₇	—	2	4	no	—
367	C₂³×C₇	—	2	2	no	—
368	C₂³×C₇	—	2	4	no	—
369	C₂³×C₇	—	2	8	no	—
370	C₂³×C₇	—	2	4	no	—
371	C₂³×C₇	—	2	8	no	—
372	C₂³×C₇	—	2	4	no	—
373	C₂³×C₇	—	2	8	no	—
374	C₂³×C₇	—	2	4	no	—
375	C₂³×C₇	—	2	4	no	—
376	C₂³×C₇	—	2	4	no	—
377	C₂³×C₇	—	4	4	no	—
378	C₂³×C₇	—	4	8	no	—
379	C₂³×C₇	—	4	16	no	—
380	C₂³×C₇	C₂⁵	1	2	yes	—
381	C₂³×C₇	C₂⁵	1	4	yes	—
382	C₂³×C₇	C₂⁵	1	4	yes	—
383	C₂³×C₇	C₂⁵	1	8	yes	—
384	C₂³×C₇	C₂⁵	1	1	yes	characteristic
385	C₇×Q₈	—	2	16	no	—
386	C₇×Q₈	—	4	4	no	—
387	C₇×D₄	—	2	16	no	—
388	C₇×D₄	—	4	8	no	—
389	C₇×D₄	—	4	16	no	—
390	C₇×D₄	—	4	16	no	—
391	C₇×D₄	—	4	16	no	—
392	C₇×D₄	—	4	8	no	—
393	C₇×D₄	—	4	16	no	—
394	C₇×D₄	—	4	8	no	—
395	C₇×D₄	—	4	4	no	—
396	C₇×D₄	—	4	16	no	—
397	C₇×D₄	—	4	16	no	—
398	C₂×C₄×C₇	—	2	4	no	—
399	C₂×C₄×C₇	—	2	2	no	—
400	C₂×C₄×C₇	—	2	4	no	—
401	C₂×C₄×C₇	—	2	8	no	—
402	C₂×C₄×C₇	—	2	4	no	—
403	C₂×C₄×C₇	—	2	8	no	—
404	C₂×C₄×C₇	—	2	8	no	—
405	C₂×C₄×C₇	—	2	4	no	—
406	C₂×C₄×C₇	—	2	16	no	—
407	C₂×C₄×C₇	—	2	8	no	—
408	C₂×C₄×C₇	—	2	16	no	—
409	C₂×C₄×C₇	—	4	4	no	—
410	C₂×C₄×C₇	—	4	8	no	—
411	C₂×C₄×C₇	—	4	16	no	—
412	C₂×C₄×C₇	—	4	16	no	—
413	C₂×C₄×C₇	—	4	16	no	—
414	C₂×C₄×C₇	—	4	16	no	—
415	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
416	C₂×C₄×C₇	C₂⁵	1	4	yes	—
417	C₂×C₄×C₇	C₂⁵	1	8	yes	—
418	C₂×C₄×C₇	C₂⁵	1	4	yes	—
419	C₂×C₄×C₇	C₂⁵	1	8	yes	—
420	C₂×C₄×C₇	C₂⁵	1	4	yes	—
421	C₂×C₄×C₇	C₂⁵	1	8	yes	—
422	C₂×C₄×C₇	C₂⁵	1	4	yes	—
423	C₂×C₄×C₇	C₂⁵	1	2	yes	—
424	C₂×C₄×C₇	C₂⁵	1	2	yes	—
425	C₂⁵	C₂³×C₇	1	1	yes	characteristic
426	C₂×#41	—	4	4	no	—
427	C₂×#41	—	4	8	no	—
428	C₂×#41	—	4	8	no	—
429	C₂×#41	C₂³×C₇	1	8	yes	—
430	C₂×#41	C₂³×C₇	1	16	yes	—
431	C₂×#41	C₂³×C₇	1	16	yes	complemented
432	C₂²×Q₈	C₂³×C₇	1	2	yes	—
433	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
434	C₂²×D₄	C₂³×C₇	1	2	yes	—
435	C₂²×D₄	C₂³×C₇	1	2	yes	—
436	C₂²×D₄	C₂³×C₇	1	4	yes	—
437	C₂²×D₄	C₂³×C₇	1	4	yes	—
438	C₂²×D₄	C₂³×C₇	1	2	yes	—
439	C₂²×D₄	C₂³×C₇	1	4	yes	—
440	C₂²×D₄	C₂³×C₇	1	4	yes	—
441	C₂²×D₄	C₂³×C₇	1	2	yes	—
442	C₂²×D₄	C₂³×C₇	1	4	yes	—
443	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
444	C₂²×D₄	C₂³×C₇	1	4	yes	—
445	C₂³×C₄	—	4	4	no	—
446	C₂³×C₄	C₂³×C₇	1	2	yes	—
447	C₂³×C₄	C₂³×C₇	1	2	yes	—
448	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₇	1	4	yes	—
450	C₂³×C₄	C₂³×C₇	1	4	yes	—
451	C₂³×C₄	C₂³×C₇	1	4	yes	—
452	C₂³×C₄	C₂³×C₇	1	4	yes	—
453	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₇	1	2	yes	—
455	C₂³×C₄	C₂³×C₇	1	8	yes	—
456	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
457	#127	C₂³×C₇	1	32	yes	—
458	#127	C₂³×C₇	1	8	yes	complemented
459	#126	C₂³×C₇	1	32	yes	—
460	#126	C₂³×C₇	1	32	yes	—
461	#126	C₂³×C₇	1	32	yes	complemented
462	#125	C₂³×C₇	1	32	yes	complemented
463	#125	C₂³×C₇	1	32	yes	complemented
464	#125	C₂³×C₇	1	8	yes	complemented
465	#125	C₂³×C₇	1	8	yes	complemented
466	#123	C₂³×C₇	1	32	yes	—
467	#123	C₂³×C₇	1	16	yes	—
468	#123	C₂³×C₇	1	32	yes	—
469	#123	C₂³×C₇	1	32	yes	—
470	#123	C₂³×C₇	1	32	yes	—
471	#123	C₂³×C₇	1	32	yes	complemented
472	#123	C₂³×C₇	1	32	yes	complemented
473	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
474	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
475	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
476	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
477	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
478	#121	C₂³×C₇	1	16	yes	—
479	#121	C₂³×C₇	1	16	yes	—
480	#121	C₂³×C₇	1	16	yes	—
481	#121	C₂³×C₇	1	32	yes	—
482	#121	C₂³×C₇	1	32	yes	—
483	#121	C₂³×C₇	1	32	yes	—
484	#121	C₂³×C₇	1	32	yes	—
485	#121	C₂³×C₇	1	32	yes	—
486	#121	C₂³×C₇	1	32	yes	—
487	#121	C₂³×C₇	1	32	yes	complemented
488	#121	C₂³×C₇	1	16	yes	complemented
489	#121	C₂³×C₇	1	32	yes	complemented
490	#120	C₂³×C₇	1	16	yes	—
491	#120	C₂³×C₇	1	32	yes	—
492	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
493	C₄×D₄	C₂³×C₇	1	32	yes	—
494	C₄×D₄	C₂³×C₇	1	16	yes	—
495	C₄×D₄	C₂³×C₇	1	16	yes	—
496	C₄×D₄	C₂³×C₇	1	32	yes	—
497	C₄×D₄	C₂³×C₇	1	32	yes	complemented
498	C₄×D₄	C₂³×C₇	1	16	yes	complemented
499	C₄×D₄	C₂³×C₇	1	32	yes	complemented
500	#117	C₂³×C₇	1	8	yes	—
501	#117	C₂³×C₇	1	16	yes	—
502	#117	C₂³×C₇	1	32	yes	complemented
503	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
510	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
514	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
515	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
516	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
517	C₂×C₄⋊C₄	C₂³×C₇	1	32	yes	complemented
518	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₇	1	2	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	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₇	1	2	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	2	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	C₂³×C₇	1	4	yes	—
532	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₇	1	4	yes	—
535	C₂²×C₇	—	2	4	no	—
536	C₂²×C₇	—	2	2	no	—
537	C₂²×C₇	—	2	4	no	—
538	C₂²×C₇	—	2	8	no	—
539	C₂²×C₇	—	2	4	no	—
540	C₂²×C₇	—	2	8	no	—
541	C₂²×C₇	—	2	4	no	—
542	C₂²×C₇	—	2	8	no	—
543	C₂²×C₇	—	2	4	no	—
544	C₂²×C₇	—	2	4	no	—
545	C₂²×C₇	—	2	4	no	—
546	C₂²×C₇	—	4	16	no	—
547	C₂²×C₇	—	4	8	no	—
548	C₂²×C₇	—	4	16	no	—
549	C₂²×C₇	—	4	8	no	—
550	C₂²×C₇	—	4	4	no	—
551	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
552	C₂²×C₇	#585	1	4	yes	—
553	C₂²×C₇	C₂⁶	1	1	yes	characteristic
554	C₄×C₇	—	2	4	no	—
555	C₄×C₇	—	2	2	no	—
556	C₄×C₇	—	2	4	no	—
557	C₄×C₇	—	2	8	no	—
558	C₄×C₇	—	2	4	no	—
559	C₄×C₇	—	2	8	no	—
560	C₄×C₇	—	2	8	no	—
561	C₄×C₇	—	2	4	no	—
562	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
563	C₂⁴	—	4	2	no	—
564	C₂⁴	—	4	4	no	—
565	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
566	C₂⁴	C₂⁴×C₇	1	2	yes	—
567	C₂⁴	C₂⁴×C₇	1	2	yes	—
568	C₂⁴	C₂⁴×C₇	1	4	yes	—
569	C₂⁴	C₂⁴×C₇	1	4	yes	—
570	#41	—	4	16	no	—
571	#41	—	4	32	no	—
572	#41	—	4	32	no	—
573	C₂×Q₈	—	2	8	no	—
574	C₂×Q₈	—	4	2	no	—
575	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
576	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
577	C₂×D₄	—	2	8	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂×D₄	—	4	2	no	—
580	C₂×D₄	—	4	8	no	—
581	C₂×D₄	—	4	8	no	—
582	C₂×D₄	—	4	4	no	—
583	C₂×D₄	—	4	8	no	—
584	C₂×D₄	—	4	8	no	—
585	C₂×D₄	—	4	8	no	—
586	C₂×D₄	—	4	4	no	—
587	C₂×D₄	—	4	8	no	—
588	C₂×D₄	C₂⁴×C₇	1	8	yes	—
589	C₂×D₄	C₂⁴×C₇	1	8	yes	—
590	C₂×D₄	C₂⁴×C₇	1	16	yes	—
591	C₂×D₄	C₂⁴×C₇	1	16	yes	—
592	C₂×D₄	C₂⁴×C₇	1	8	yes	—
593	C₂×D₄	C₂⁴×C₇	1	16	yes	—
594	C₂×D₄	C₂⁴×C₇	1	16	yes	—
595	C₂×D₄	C₂⁴×C₇	1	8	yes	—
596	C₂×D₄	C₂⁴×C₇	1	16	yes	—
597	C₂×D₄	C₂⁴×C₇	1	4	yes	—
598	C₂×D₄	C₂⁴×C₇	1	16	yes	—
599	C₂²×C₄	—	2	8	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	8	no	—
602	C₂²×C₄	—	4	16	no	—
603	C₂²×C₄	—	4	2	no	—
604	C₂²×C₄	—	4	4	no	—
605	C₂²×C₄	—	4	8	no	—
606	C₂²×C₄	—	4	8	no	—
607	C₂²×C₄	—	4	8	no	—
608	C₂²×C₄	—	4	8	no	—
609	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
611	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
613	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
615	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
618	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
619	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
620	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
621	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
622	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
623	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
624	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
625	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
626	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
627	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
628	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
629	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
630	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
631	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
632	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
633	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
634	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
635	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
636	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
637	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
638	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
639	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
640	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
641	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
642	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
643	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
644	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
645	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
646	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
647	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
648	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
649	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
650	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
651	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
652	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
653	C₄²	C₂⁴×C₇	1	16	yes	—
654	C₄²	C₂⁴×C₇	1	4	yes	—
655	C₄²	C₂⁴×C₇	1	4	yes	—
656	C₄²	C₂⁴×C₇	1	16	yes	—
657	C₂×C₇	—	4	4	no	—
658	C₂×C₇	—	4	8	no	—
659	C₂×C₇	—	4	4	no	—
660	C₂×C₇	—	4	2	no	—
661	C₂×C₇	#3539	1	4	yes	direct product factor
662	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
663	C₂×C₇	C₂×#585	1	2	yes	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	8	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	8	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	8	no	—
672	C₂³	—	2	4	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	2	4	no	—
675	C₂³	—	4	4	no	—
676	C₂³	—	4	8	no	—
677	C₂³	—	4	16	no	—
678	C₂³	C₂⁵×C₇	1	2	yes	—
679	C₂³	C₂⁵×C₇	1	4	yes	—
680	C₂³	C₂⁵×C₇	1	4	yes	—
681	C₂³	C₂⁵×C₇	1	8	yes	—
682	C₂³	C₂⁵×C₇	1	1	yes	characteristic
683	Q₈	—	2	16	no	—
684	Q₈	—	4	4	no	—
685	D₄	—	2	16	no	—
686	D₄	—	4	8	no	—
687	D₄	—	4	16	no	—
688	D₄	—	4	16	no	—
689	D₄	—	4	16	no	—
690	D₄	—	4	8	no	—
691	D₄	—	4	16	no	—
692	D₄	—	4	8	no	—
693	D₄	—	4	4	no	—
694	D₄	—	4	16	no	—
695	D₄	—	4	16	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	8	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	8	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	16	no	—
705	C₂×C₄	—	2	8	no	—
706	C₂×C₄	—	2	16	no	—
707	C₂×C₄	—	4	4	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	16	no	—
710	C₂×C₄	—	4	16	no	—
711	C₂×C₄	—	4	16	no	—
712	C₂×C₄	—	4	16	no	—
713	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
714	C₂×C₄	C₂⁵×C₇	1	4	yes	—
715	C₂×C₄	C₂⁵×C₇	1	8	yes	—
716	C₂×C₄	C₂⁵×C₇	1	4	yes	—
717	C₂×C₄	C₂⁵×C₇	1	8	yes	—
718	C₂×C₄	C₂⁵×C₇	1	4	yes	—
719	C₂×C₄	C₂⁵×C₇	1	8	yes	—
720	C₂×C₄	C₂⁵×C₇	1	4	yes	—
721	C₂×C₄	C₂⁵×C₇	1	2	yes	—
722	C₂×C₄	C₂⁵×C₇	1	2	yes	—
723	C₇	C₂×#3539	1	1	yes	characteristic, direct product factor, Sylow
724	C₂²	—	2	4	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	8	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	8	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	8	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	4	16	no	—
736	C₂²	—	4	8	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	8	no	—
739	C₂²	—	4	16	no	—
740	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
741	C₂²	C₇×#585	1	4	yes	—
742	C₂²	C₂⁶×C₇	1	1	yes	characteristic
743	C₄	—	2	4	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	4	no	—
746	C₄	—	2	8	no	—
747	C₄	—	2	4	no	—
748	C₄	—	2	8	no	—
749	C₄	—	2	8	no	—
750	C₄	—	2	4	no	—
751	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
752	C₂	—	4	4	no	—
753	C₂	—	4	2	no	—
754	C₂	—	4	4	no	—
755	C₂	—	4	8	no	—
756	C₂	C₇×#3539	1	4	yes	direct product factor
757	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
758	C₂	C₂×C₇×#585	1	2	yes	—

	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×#3539	C₂	direct (N × H)
2. C₂×C₇×#560	C₂	semidirect
3. C₂×C₇×#553	C₂	semidirect
4. C₂×C₇×#553	C₂	semidirect
5. C₂×C₇×#552	C₂	semidirect
6. C₂×C₇×#550	C₂	semidirect
7. C₂×C₇×#547	C₂	semidirect
8. C₂×C₇×#541	C₂	semidirect
9. C₂×C₇×#540	C₂	semidirect
10. C₂×C₇×#540	C₂	semidirect
11. C₂×C₇×#539	C₂	semidirect
12. C₂×C₇×#537	C₂	semidirect
13. C₂×C₇×#525	C₂	semidirect
14. C₂×C₇×#525	C₂	semidirect
17. C₂²×C₇×#41	C₂²	semidirect
19. C₇×#560	C₂²	semidirect
20. C₇×#553	C₂²	semidirect
21. C₇×#553	C₂²	semidirect
22. C₇×#552	C₂²	semidirect
23. C₇×#550	C₂²	semidirect
24. C₇×#547	C₂²	semidirect
25. C₇×#541	C₂²	semidirect
26. C₇×#540	C₂²	semidirect
27. C₇×#540	C₂²	semidirect
28. C₇×#539	C₂²	semidirect
29. C₇×#537	C₂²	semidirect
30. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
32. C₂×C₇×#127	C₂²	semidirect
35. C₂×C₇×#126	C₂²	semidirect
36. C₂×C₇×#125	C₂²	semidirect
37. C₂×C₇×#125	C₂²	semidirect
38. C₂×C₇×#125	C₂²	semidirect
39. C₂×C₇×#125	C₂²	semidirect
40. C₇×#525	C₂²	semidirect
41. C₇×#525	C₂²	semidirect
47. C₂×C₇×#123	C₂²	semidirect
48. C₂×C₇×#123	C₂²	semidirect
52. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
53. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
63. C₂×C₇×#121	C₂²	semidirect
64. C₂×C₇×#121	C₂²	semidirect
65. C₂×C₇×#121	C₂²	semidirect
68. C₂×C₄×C₇×Q₈	C₂²	semidirect
73. C₂×C₄×C₇×D₄	C₂²	semidirect
74. C₂×C₄×C₇×D₄	C₂²	semidirect
75. C₂×C₄×C₇×D₄	C₂²	semidirect
78. C₂×C₇×#117	C₂²	semidirect
79. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
80. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
81. C₂×#3539	C₇	direct (N × H)
88. C₂×C₇×#41	C₂³	semidirect
113. C₇×C₄⋊Q₈	C₂³	semidirect
115. C₇×#127	C₂³	semidirect
118. C₇×#126	C₂³	semidirect
119. C₇×#125	C₂³	semidirect
120. C₇×#125	C₂³	semidirect
121. C₇×#125	C₂³	semidirect
122. C₇×#125	C₂³	semidirect
128. C₇×#123	C₂³	semidirect
129. C₇×#123	C₂³	semidirect
133. C₇×C₂²⋊Q₈	C₂³	semidirect
134. C₇×C₂²⋊Q₈	C₂³	semidirect
144. C₇×#121	C₂³	semidirect
145. C₇×#121	C₂³	semidirect
146. C₇×#121	C₂³	semidirect
149. C₄×C₇×Q₈	C₂³	semidirect
154. C₄×C₇×D₄	C₂³	semidirect
155. C₄×C₇×D₄	C₂³	semidirect
156. C₄×C₇×D₄	C₂³	semidirect
159. C₇×#117	C₂³	semidirect
173. C₂×C₇×C₄⋊C₄	C₂³	semidirect
174. C₂×C₇×C₄⋊C₄	C₂³	semidirect
192. #3539	C₂×C₇	direct (N × H)
193. C₂×#560	C₂×C₇	semidirect
194. C₂×#553	C₂×C₇	semidirect
195. C₂×#553	C₂×C₇	semidirect
196. C₂×#552	C₂×C₇	semidirect
197. C₂×#550	C₂×C₇	semidirect
198. C₂×#547	C₂×C₇	semidirect
199. C₂×#541	C₂×C₇	semidirect
200. C₂×#540	C₂×C₇	semidirect
201. C₂×#540	C₂×C₇	semidirect
202. C₂×#539	C₂×C₇	semidirect
203. C₂×#537	C₂×C₇	semidirect
204. C₂×#525	C₂×C₇	semidirect
205. C₂×#525	C₂×C₇	semidirect
302. C₂²×#41	C₂²×C₇	semidirect
304. #560	C₂²×C₇	semidirect
305. #553	C₂²×C₇	semidirect
306. #553	C₂²×C₇	semidirect
307. #552	C₂²×C₇	semidirect
308. #550	C₂²×C₇	semidirect
309. #547	C₂²×C₇	semidirect
310. #541	C₂²×C₇	semidirect
311. #540	C₂²×C₇	semidirect
312. #540	C₂²×C₇	semidirect
313. #539	C₂²×C₇	semidirect
314. #537	C₂²×C₇	semidirect
315. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
317. C₂×#127	C₂²×C₇	semidirect
320. C₂×#126	C₂²×C₇	semidirect
321. C₂×#125	C₂²×C₇	semidirect
322. C₂×#125	C₂²×C₇	semidirect
323. C₂×#125	C₂²×C₇	semidirect
324. C₂×#125	C₂²×C₇	semidirect
325. #525	C₂²×C₇	semidirect
326. #525	C₂²×C₇	semidirect
332. C₂×#123	C₂²×C₇	semidirect
333. C₂×#123	C₂²×C₇	semidirect
337. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
338. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
348. C₂×#121	C₂²×C₇	semidirect
349. C₂×#121	C₂²×C₇	semidirect
350. C₂×#121	C₂²×C₇	semidirect
353. C₂×C₄×Q₈	C₂²×C₇	semidirect
358. C₂×C₄×D₄	C₂²×C₇	semidirect
359. C₂×C₄×D₄	C₂²×C₇	semidirect
360. C₂×C₄×D₄	C₂²×C₇	semidirect
363. C₂×#117	C₂²×C₇	semidirect
364. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
365. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
431. C₂×#41	C₂³×C₇	semidirect
456. C₄⋊Q₈	C₂³×C₇	semidirect
458. #127	C₂³×C₇	semidirect
461. #126	C₂³×C₇	semidirect
462. #125	C₂³×C₇	semidirect
463. #125	C₂³×C₇	semidirect
464. #125	C₂³×C₇	semidirect
465. #125	C₂³×C₇	semidirect
471. #123	C₂³×C₇	semidirect
472. #123	C₂³×C₇	semidirect
476. C₂²⋊Q₈	C₂³×C₇	semidirect
477. C₂²⋊Q₈	C₂³×C₇	semidirect
487. #121	C₂³×C₇	semidirect
488. #121	C₂³×C₇	semidirect
489. #121	C₂³×C₇	semidirect
492. C₄×Q₈	C₂³×C₇	semidirect
497. C₄×D₄	C₂³×C₇	semidirect
498. C₄×D₄	C₂³×C₇	semidirect
499. C₄×D₄	C₂³×C₇	semidirect
502. #117	C₂³×C₇	semidirect
516. C₂×C₄⋊C₄	C₂³×C₇	semidirect
517. C₂×C₄⋊C₄	C₂³×C₇	semidirect
661. C₂×C₇	#3539	direct (N × H)
723. C₇	C₂×#3539	direct (N × H)
756. C₂	C₇×#3539	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×#3539	2
C₂×C₇×#560	2
C₂×C₇×#553	2
C₂×C₇×#552	2
C₂×C₇×#550	2
C₂×C₇×#547	2
C₂×C₇×#541	2
C₂×C₇×#540	2
C₂×C₇×#539	2
C₂×C₇×#537	2
C₂×C₇×#525	2
C₂×#3539	7

Subgroups — C2×C7×#3539 #13239943

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3539 #13239943