Subgroups — C₂×C₇×#3545 #13239969

Order 1792.

7430 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×#3545	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#563	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#562	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#555	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#551	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#551	C₂	1	4	yes	maximal, complemented
8	C₂×C₇×#546	C₂	1	4	yes	maximal, complemented
9	C₂×C₇×#542	C₂	1	4	yes	maximal, complemented
10	C₂×C₇×#538	C₂	1	4	yes	maximal, complemented
11	C₂×C₇×#536	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#534	C₂	1	2	yes	maximal, complemented
13	C₂×C₇×#529	C₂	1	2	yes	maximal, complemented
14	C₂²×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₇×#41	C₂²	1	2	yes	—
16	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
18	C₂³×C₇×D₄	C₂²	1	2	yes	complemented
19	C₇×#563	C₂²	1	16	yes	complemented
20	C₇×#562	C₂²	1	32	yes	complemented
21	C₇×H(3,𝔽₄)	C₂²	1	16	yes	complemented
22	C₇×#555	C₂²	1	32	yes	complemented
23	C₇×#551	C₂²	1	32	yes	complemented
24	C₇×#551	C₂²	1	64	yes	complemented
25	C₇×#546	C₂²	1	64	yes	complemented
26	C₇×#542	C₂²	1	64	yes	complemented
27	C₇×#538	C₂²	1	64	yes	complemented
28	C₇×#536	C₂²	1	32	yes	complemented
29	C₇×#534	C₂²	1	32	yes	complemented
30	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
31	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
32	C₇×#529	C₂²	1	32	yes	complemented
33	C₂×C₇×#126	C₂²	1	4	yes	complemented
34	C₂×C₇×#126	C₂²	1	4	yes	complemented
35	C₂×C₇×#126	C₂²	1	4	yes	complemented
36	C₂×C₇×#125	C₂²	1	2	yes	complemented
37	C₂×C₇×#124	C₂²	1	1	yes	characteristic
38	C₂×C₇×#124	C₂²	1	1	yes	characteristic
39	C₂×C₇×#124	C₂²	1	4	yes	complemented
40	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₇×#124	C₂²	1	2	yes	complemented
43	C₂×C₇×#124	C₂²	1	2	yes	complemented
44	C₂×C₇×#124	C₂²	1	2	yes	complemented
45	C₂×C₇×#124	C₂²	1	4	yes	complemented
46	C₂×C₇×#124	C₂²	1	4	yes	complemented
47	C₂×C₇×#124	C₂²	1	16	yes	complemented
48	C₂×C₇×#123	C₂²	1	2	yes	—
49	C₂×C₇×#123	C₂²	1	4	yes	complemented
50	C₂×C₇×#123	C₂²	1	2	yes	complemented
51	C₂×C₇×#123	C₂²	1	4	yes	complemented
52	C₂×C₇×#123	C₂²	1	4	yes	complemented
53	C₂×C₇×#123	C₂²	1	4	yes	complemented
54	C₂×C₇×#123	C₂²	1	4	yes	complemented
55	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
57	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
58	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
59	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂×C₇×#121	C₂²	1	2	yes	—
61	C₂×C₇×#121	C₂²	1	4	yes	—
62	C₂×C₇×#121	C₂²	1	4	yes	complemented
63	C₂×C₇×#121	C₂²	1	4	yes	complemented
64	C₂×C₇×#121	C₂²	1	4	yes	complemented
65	C₂×C₇×#120	C₂²	1	4	yes	—
66	C₂×C₇×#120	C₂²	1	2	yes	—
67	C₂×C₇×#120	C₂²	1	2	yes	complemented
68	C₂×C₇×#120	C₂²	1	4	yes	complemented
69	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
70	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
71	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
72	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
73	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
74	C₂×C₇×#117	C₂²	1	4	yes	complemented
75	C₂×C₇×#117	C₂²	1	2	yes	complemented
76	C₂×C₇×#117	C₂²	1	4	yes	complemented
77	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	complemented
78	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
79	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	complemented
80	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
81	C₂×#3545	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁵×C₇	C₂³	1	2	yes	—
83	C₂⁵×C₇	C₂³	1	2	yes	—
84	C₂×C₇×#41	—	4	8	no	—
85	C₂×C₇×#41	C₂³	1	16	yes	—
86	C₂²×C₇×Q₈	—	4	4	no	—
87	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×Q₈	C₂³	1	2	yes	—
89	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
90	C₂²×C₇×Q₈	C₂³	1	2	yes	—
91	C₂²×C₇×Q₈	C₂³	1	2	yes	—
92	C₂²×C₇×Q₈	C₂³	1	8	yes	complemented
93	C₂²×C₇×D₄	—	4	4	no	—
94	C₂²×C₇×D₄	—	4	8	no	—
95	C₂²×C₇×D₄	C₂³	1	4	yes	—
96	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
97	C₂²×C₇×D₄	C₂³	1	2	yes	—
98	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
99	C₂²×C₇×D₄	C₂³	1	8	yes	—
100	C₂²×C₇×D₄	C₂³	1	4	yes	—
101	C₂²×C₇×D₄	C₂³	1	2	yes	—
102	C₂²×C₇×D₄	C₂³	1	4	yes	—
103	C₂²×C₇×D₄	C₂³	1	4	yes	—
104	C₂²×C₇×D₄	C₂³	1	2	yes	—
105	C₂²×C₇×D₄	C₂³	1	16	yes	complemented
106	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₇	C₂³	1	2	yes	—
108	C₂³×C₄×C₇	C₂³	1	2	yes	—
109	C₂³×C₄×C₇	C₂³	1	4	yes	—
110	C₂³×C₄×C₇	C₂³	1	2	yes	—
111	C₂³×C₄×C₇	C₂³	1	4	yes	—
112	C₂³×C₄×C₇	C₂³	1	4	yes	—
113	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
114	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
115	C₇×#126	C₂³	1	32	yes	complemented
116	C₇×#126	C₂³	1	32	yes	complemented
117	C₇×#126	C₂³	1	32	yes	complemented
118	C₇×#125	C₂³	1	16	yes	complemented
119	C₇×#124	C₂³	1	8	yes	—
120	C₇×#124	C₂³	1	8	yes	—
121	C₇×#124	C₂³	1	32	yes	complemented
122	C₇×#124	C₂³	1	8	yes	complemented
123	C₇×#124	C₂³	1	8	yes	complemented
124	C₇×#124	C₂³	1	16	yes	complemented
125	C₇×#124	C₂³	1	16	yes	complemented
126	C₇×#124	C₂³	1	16	yes	complemented
127	C₇×#124	C₂³	1	32	yes	complemented
128	C₇×#124	C₂³	1	32	yes	complemented
129	C₇×#123	C₂³	1	16	yes	—
130	C₇×#123	C₂³	1	32	yes	complemented
131	C₇×#123	C₂³	1	16	yes	complemented
132	C₇×#123	C₂³	1	32	yes	complemented
133	C₇×#123	C₂³	1	32	yes	complemented
134	C₇×#123	C₂³	1	32	yes	complemented
135	C₇×#123	C₂³	1	32	yes	complemented
136	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
137	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
138	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
139	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
140	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
141	C₇×#121	C₂³	1	16	yes	—
142	C₇×#121	C₂³	1	32	yes	—
143	C₇×#121	C₂³	1	32	yes	complemented
144	C₇×#121	C₂³	1	32	yes	complemented
145	C₇×#121	C₂³	1	32	yes	complemented
146	C₇×#120	C₂³	1	32	yes	—
147	C₇×#120	C₂³	1	16	yes	—
148	C₇×#120	C₂³	1	16	yes	complemented
149	C₇×#120	C₂³	1	32	yes	complemented
150	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
151	C₄×C₇×D₄	C₂³	1	16	yes	complemented
152	C₄×C₇×D₄	C₂³	1	32	yes	complemented
153	C₄×C₇×D₄	C₂³	1	32	yes	complemented
154	C₄×C₇×D₄	C₂³	1	32	yes	complemented
155	C₇×#117	C₂³	1	32	yes	complemented
156	C₇×#117	C₂³	1	16	yes	complemented
157	C₇×#117	C₂³	1	32	yes	complemented
158	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
159	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
160	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
162	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
163	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
164	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
167	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
168	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
169	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
170	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
171	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
172	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
176	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
177	C₂×C₇×C₂²⋊C₄	C₂³	1	4	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	4	yes	—
181	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
182	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	complemented
183	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	complemented
184	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	complemented
185	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₇	C₂³	1	4	yes	—
190	C₂×C₄²×C₇	C₂³	1	2	yes	—
191	C₂×C₄²×C₇	C₂³	1	8	yes	complemented
192	#3545	C₂×C₇	1	32	yes	direct product factor
193	C₂×#563	C₂×C₇	1	1	yes	characteristic, complemented
194	C₂×#562	C₂×C₇	1	2	yes	complemented
195	C₂×H(3,𝔽₄)	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×#555	C₂×C₇	1	2	yes	complemented
197	C₂×#551	C₂×C₇	1	2	yes	complemented
198	C₂×#551	C₂×C₇	1	4	yes	complemented
199	C₂×#546	C₂×C₇	1	4	yes	complemented
200	C₂×#542	C₂×C₇	1	4	yes	complemented
201	C₂×#538	C₂×C₇	1	4	yes	complemented
202	C₂×#536	C₂×C₇	1	2	yes	complemented
203	C₂×#534	C₂×C₇	1	2	yes	complemented
204	C₂×#529	C₂×C₇	1	2	yes	complemented
205	C₂²×#124	C₂×C₇	1	1	yes	characteristic, complemented
206	C₂⁴×C₇	—	2	8	no	—
207	C₂⁴×C₇	—	4	4	no	—
208	C₂⁴×C₇	—	4	8	no	—
209	C₂⁴×C₇	—	4	8	no	—
210	C₂⁴×C₇	C₂⁴	1	2	yes	—
211	C₂⁴×C₇	C₂⁴	1	4	yes	—
212	C₂⁴×C₇	C₂⁴	1	2	yes	—
213	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₇	C₂⁴	1	8	yes	—
215	C₂⁴×C₇	C₂⁴	1	8	yes	—
216	C₇×#41	—	4	32	no	—
217	C₂×C₇×Q₈	—	4	2	no	—
218	C₂×C₇×Q₈	—	4	4	no	—
219	C₂×C₇×Q₈	—	4	2	no	—
220	C₂×C₇×Q₈	—	4	16	no	—
221	C₂×C₇×Q₈	—	4	4	no	—
222	C₂×C₇×Q₈	—	4	4	no	—
223	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
224	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
225	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
226	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
227	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
228	C₂×C₇×D₄	—	2	16	no	—
229	C₂×C₇×D₄	—	4	2	no	—
230	C₂×C₇×D₄	—	4	4	no	—
231	C₂×C₇×D₄	—	4	2	no	—
232	C₂×C₇×D₄	—	4	16	no	—
233	C₂×C₇×D₄	—	4	8	no	—
234	C₂×C₇×D₄	—	4	8	no	—
235	C₂×C₇×D₄	—	4	8	no	—
236	C₂×C₇×D₄	—	4	4	no	—
237	C₂×C₇×D₄	—	4	4	no	—
238	C₂×C₇×D₄	—	4	32	no	—
239	C₂×C₇×D₄	C₂⁴	1	16	yes	—
240	C₂×C₇×D₄	C₂⁴	1	16	yes	—
241	C₂×C₇×D₄	C₂⁴	1	16	yes	—
242	C₂×C₇×D₄	C₂⁴	1	8	yes	—
243	C₂×C₇×D₄	C₂⁴	1	4	yes	—
244	C₂×C₇×D₄	C₂⁴	1	8	yes	—
245	C₂×C₇×D₄	C₂⁴	1	8	yes	—
246	C₂×C₇×D₄	C₂⁴	1	16	yes	—
247	C₂×C₇×D₄	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₇	—	2	4	no	—
249	C₂²×C₄×C₇	—	2	8	no	—
250	C₂²×C₄×C₇	—	4	8	no	—
251	C₂²×C₄×C₇	—	4	4	no	—
252	C₂²×C₄×C₇	—	4	8	no	—
253	C₂²×C₄×C₇	—	4	4	no	—
254	C₂²×C₄×C₇	—	4	8	no	—
255	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
257	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
260	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
265	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
267	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
268	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
269	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
270	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
271	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
272	C₇×C₄⋊C₄	C₂⁴	1	16	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	8	yes	—
279	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
280	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
281	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
282	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
283	C₇×C₂²⋊C₄	C₂⁴	1	16	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	8	yes	—
288	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
289	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
290	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
291	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
292	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
293	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
294	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
295	C₄²×C₇	C₂⁴	1	4	yes	—
296	C₄²×C₇	C₂⁴	1	8	yes	—
297	C₄²×C₇	C₂⁴	1	4	yes	—
298	C₄²×C₇	C₂⁴	1	8	yes	—
299	C₄²×C₇	C₂⁴	1	16	yes	—
300	C₄²×C₇	C₂⁴	1	8	yes	—
301	C₂²×#41	C₂²×C₇	1	2	yes	—
302	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
303	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
304	C₂³×D₄	C₂²×C₇	1	2	yes	complemented
305	#563	C₂²×C₇	1	16	yes	complemented
306	#562	C₂²×C₇	1	32	yes	complemented
307	H(3,𝔽₄)	C₂²×C₇	1	16	yes	complemented
308	#555	C₂²×C₇	1	32	yes	complemented
309	#551	C₂²×C₇	1	32	yes	complemented
310	#551	C₂²×C₇	1	64	yes	complemented
311	#546	C₂²×C₇	1	64	yes	complemented
312	#542	C₂²×C₇	1	64	yes	complemented
313	#538	C₂²×C₇	1	64	yes	complemented
314	#536	C₂²×C₇	1	32	yes	complemented
315	#534	C₂²×C₇	1	32	yes	complemented
316	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
317	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
318	#529	C₂²×C₇	1	32	yes	complemented
319	C₂×#126	C₂²×C₇	1	4	yes	complemented
320	C₂×#126	C₂²×C₇	1	4	yes	complemented
321	C₂×#126	C₂²×C₇	1	4	yes	complemented
322	C₂×#125	C₂²×C₇	1	2	yes	complemented
323	C₂×#124	C₂²×C₇	1	1	yes	characteristic
324	C₂×#124	C₂²×C₇	1	1	yes	characteristic
325	C₂×#124	C₂²×C₇	1	4	yes	complemented
326	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
327	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
328	C₂×#124	C₂²×C₇	1	2	yes	complemented
329	C₂×#124	C₂²×C₇	1	2	yes	complemented
330	C₂×#124	C₂²×C₇	1	2	yes	complemented
331	C₂×#124	C₂²×C₇	1	4	yes	complemented
332	C₂×#124	C₂²×C₇	1	4	yes	complemented
333	C₂×#124	C₂²×C₇	1	16	yes	complemented
334	C₂×#123	C₂²×C₇	1	2	yes	—
335	C₂×#123	C₂²×C₇	1	4	yes	complemented
336	C₂×#123	C₂²×C₇	1	2	yes	complemented
337	C₂×#123	C₂²×C₇	1	4	yes	complemented
338	C₂×#123	C₂²×C₇	1	4	yes	complemented
339	C₂×#123	C₂²×C₇	1	4	yes	complemented
340	C₂×#123	C₂²×C₇	1	4	yes	complemented
341	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
342	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
343	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
344	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
345	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
346	C₂×#121	C₂²×C₇	1	2	yes	—
347	C₂×#121	C₂²×C₇	1	4	yes	—
348	C₂×#121	C₂²×C₇	1	4	yes	complemented
349	C₂×#121	C₂²×C₇	1	4	yes	complemented
350	C₂×#121	C₂²×C₇	1	4	yes	complemented
351	C₂×#120	C₂²×C₇	1	4	yes	—
352	C₂×#120	C₂²×C₇	1	2	yes	—
353	C₂×#120	C₂²×C₇	1	2	yes	complemented
354	C₂×#120	C₂²×C₇	1	4	yes	complemented
355	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
356	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
357	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
358	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
359	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
360	C₂×#117	C₂²×C₇	1	4	yes	complemented
361	C₂×#117	C₂²×C₇	1	2	yes	complemented
362	C₂×#117	C₂²×C₇	1	4	yes	complemented
363	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	complemented
364	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
365	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	complemented
366	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
367	C₂³×C₇	—	2	4	no	—
368	C₂³×C₇	—	2	8	no	—
369	C₂³×C₇	—	2	4	no	—
370	C₂³×C₇	—	2	4	no	—
371	C₂³×C₇	—	2	8	no	—
372	C₂³×C₇	—	2	8	no	—
373	C₂³×C₇	—	2	8	no	—
374	C₂³×C₇	—	2	8	no	—
375	C₂³×C₇	—	2	16	no	—
376	C₂³×C₇	—	4	8	no	—
377	C₂³×C₇	—	4	16	no	—
378	C₂³×C₇	—	4	16	no	—
379	C₂³×C₇	—	8	16	no	—
380	C₂³×C₇	—	8	16	no	—
381	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
382	C₂³×C₇	C₂⁵	1	4	yes	—
383	C₂³×C₇	C₂⁵	1	8	yes	—
384	C₂³×C₇	C₂⁵	1	4	yes	—
385	C₂³×C₇	C₂⁵	1	2	yes	—
386	C₂³×C₇	C₂⁵	1	1	yes	characteristic
387	C₇×Q₈	—	4	4	no	—
388	C₇×Q₈	—	4	8	no	—
389	C₇×Q₈	—	4	4	no	—
390	C₇×Q₈	—	4	8	no	—
391	C₇×Q₈	—	4	8	no	—
392	C₇×D₄	—	2	32	no	—
393	C₇×D₄	—	4	4	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	C₇×D₄	—	4	16	no	—
399	C₇×D₄	—	4	8	no	—
400	C₇×D₄	—	4	8	no	—
401	C₂×C₄×C₇	—	2	4	no	—
402	C₂×C₄×C₇	—	2	8	no	—
403	C₂×C₄×C₇	—	2	2	no	—
404	C₂×C₄×C₇	—	2	2	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	4	no	—
409	C₂×C₄×C₇	—	2	8	no	—
410	C₂×C₄×C₇	—	2	4	no	—
411	C₂×C₄×C₇	—	2	8	no	—
412	C₂×C₄×C₇	—	4	16	no	—
413	C₂×C₄×C₇	—	4	8	no	—
414	C₂×C₄×C₇	—	4	16	no	—
415	C₂×C₄×C₇	—	4	8	no	—
416	C₂×C₄×C₇	—	4	16	no	—
417	C₂×C₄×C₇	C₂⁵	1	4	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	2	yes	—
422	C₂×C₄×C₇	C₂⁵	1	2	yes	—
423	C₂×C₄×C₇	C₂⁵	1	8	yes	—
424	C₂×C₄×C₇	C₂⁵	1	8	yes	—
425	C₂×C₄×C₇	C₂⁵	1	4	yes	—
426	C₂⁵	C₂³×C₇	1	2	yes	—
427	C₂⁵	C₂³×C₇	1	2	yes	—
428	C₂×#41	—	4	8	no	—
429	C₂×#41	C₂³×C₇	1	16	yes	—
430	C₂²×Q₈	—	4	4	no	—
431	C₂²×Q₈	C₂³×C₇	1	2	yes	—
432	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
433	C₂²×Q₈	C₂³×C₇	1	2	yes	—
434	C₂²×Q₈	C₂³×C₇	1	2	yes	—
435	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
436	C₂²×Q₈	C₂³×C₇	1	8	yes	complemented
437	C₂²×D₄	—	4	4	no	—
438	C₂²×D₄	—	4	8	no	—
439	C₂²×D₄	C₂³×C₇	1	4	yes	—
440	C₂²×D₄	C₂³×C₇	1	4	yes	—
441	C₂²×D₄	C₂³×C₇	1	4	yes	—
442	C₂²×D₄	C₂³×C₇	1	2	yes	—
443	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
444	C₂²×D₄	C₂³×C₇	1	2	yes	—
445	C₂²×D₄	C₂³×C₇	1	2	yes	—
446	C₂²×D₄	C₂³×C₇	1	4	yes	—
447	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
448	C₂²×D₄	C₂³×C₇	1	8	yes	—
449	C₂²×D₄	C₂³×C₇	1	16	yes	complemented
450	C₂³×C₄	C₂³×C₇	1	2	yes	—
451	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₇	1	2	yes	—
453	C₂³×C₄	C₂³×C₇	1	4	yes	—
454	C₂³×C₄	C₂³×C₇	1	4	yes	—
455	C₂³×C₄	C₂³×C₇	1	4	yes	—
456	C₂³×C₄	C₂³×C₇	1	2	yes	—
457	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
458	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
459	#126	C₂³×C₇	1	32	yes	complemented
460	#126	C₂³×C₇	1	32	yes	complemented
461	#126	C₂³×C₇	1	32	yes	complemented
462	#125	C₂³×C₇	1	16	yes	complemented
463	#124	C₂³×C₇	1	8	yes	—
464	#124	C₂³×C₇	1	8	yes	—
465	#124	C₂³×C₇	1	32	yes	complemented
466	#124	C₂³×C₇	1	8	yes	complemented
467	#124	C₂³×C₇	1	8	yes	complemented
468	#124	C₂³×C₇	1	16	yes	complemented
469	#124	C₂³×C₇	1	16	yes	complemented
470	#124	C₂³×C₇	1	16	yes	complemented
471	#124	C₂³×C₇	1	32	yes	complemented
472	#124	C₂³×C₇	1	32	yes	complemented
473	#123	C₂³×C₇	1	16	yes	—
474	#123	C₂³×C₇	1	32	yes	complemented
475	#123	C₂³×C₇	1	16	yes	complemented
476	#123	C₂³×C₇	1	32	yes	complemented
477	#123	C₂³×C₇	1	32	yes	complemented
478	#123	C₂³×C₇	1	32	yes	complemented
479	#123	C₂³×C₇	1	32	yes	complemented
480	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
481	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
482	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
483	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
484	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
485	#121	C₂³×C₇	1	16	yes	—
486	#121	C₂³×C₇	1	32	yes	—
487	#121	C₂³×C₇	1	32	yes	complemented
488	#121	C₂³×C₇	1	32	yes	complemented
489	#121	C₂³×C₇	1	32	yes	complemented
490	#120	C₂³×C₇	1	32	yes	—
491	#120	C₂³×C₇	1	16	yes	—
492	#120	C₂³×C₇	1	16	yes	complemented
493	#120	C₂³×C₇	1	32	yes	complemented
494	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
495	C₄×D₄	C₂³×C₇	1	16	yes	complemented
496	C₄×D₄	C₂³×C₇	1	32	yes	complemented
497	C₄×D₄	C₂³×C₇	1	32	yes	complemented
498	C₄×D₄	C₂³×C₇	1	32	yes	complemented
499	#117	C₂³×C₇	1	32	yes	complemented
500	#117	C₂³×C₇	1	16	yes	complemented
501	#117	C₂³×C₇	1	32	yes	complemented
502	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₇	1	4	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	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
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	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	32	yes	complemented
527	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	complemented
528	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	complemented
529	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₇	1	2	yes	—
531	C₂×C₄²	C₂³×C₇	1	4	yes	—
532	C₂×C₄²	C₂³×C₇	1	2	yes	—
533	C₂×C₄²	C₂³×C₇	1	2	yes	—
534	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₇	1	8	yes	complemented
536	C₂²×C₇	—	2	4	no	—
537	C₂²×C₇	—	2	8	no	—
538	C₂²×C₇	—	2	8	no	—
539	C₂²×C₇	—	2	4	no	—
540	C₂²×C₇	—	2	4	no	—
541	C₂²×C₇	—	2	8	no	—
542	C₂²×C₇	—	2	8	no	—
543	C₂²×C₇	—	2	8	no	—
544	C₂²×C₇	—	2	8	no	—
545	C₂²×C₇	—	4	16	no	—
546	C₂²×C₇	—	4	8	no	—
547	C₂²×C₇	—	4	8	no	—
548	C₂²×C₇	—	8	16	no	—
549	C₂²×C₇	—	8	16	no	—
550	C₂²×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
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	2	no	—
557	C₄×C₇	—	2	4	no	—
558	C₄×C₇	—	2	8	no	—
559	C₄×C₇	—	2	4	no	—
560	C₄×C₇	—	2	8	no	—
561	C₄×C₇	—	2	4	no	—
562	C₄×C₇	—	2	8	no	—
563	C₂⁴	—	2	8	no	—
564	C₂⁴	—	4	4	no	—
565	C₂⁴	—	4	8	no	—
566	C₂⁴	—	4	8	no	—
567	C₂⁴	C₂⁴×C₇	1	2	yes	—
568	C₂⁴	C₂⁴×C₇	1	4	yes	—
569	C₂⁴	C₂⁴×C₇	1	2	yes	—
570	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
571	C₂⁴	C₂⁴×C₇	1	8	yes	—
572	C₂⁴	C₂⁴×C₇	1	8	yes	—
573	#41	—	4	32	no	—
574	C₂×Q₈	—	4	2	no	—
575	C₂×Q₈	—	4	4	no	—
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	—	4	16	no	—
578	C₂×Q₈	—	4	4	no	—
579	C₂×Q₈	—	4	4	no	—
580	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
581	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
582	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
583	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
584	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
585	C₂×D₄	—	2	16	no	—
586	C₂×D₄	—	4	2	no	—
587	C₂×D₄	—	4	4	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	—	4	16	no	—
590	C₂×D₄	—	4	8	no	—
591	C₂×D₄	—	4	4	no	—
592	C₂×D₄	—	4	8	no	—
593	C₂×D₄	—	4	8	no	—
594	C₂×D₄	—	4	4	no	—
595	C₂×D₄	—	4	32	no	—
596	C₂×D₄	C₂⁴×C₇	1	16	yes	—
597	C₂×D₄	C₂⁴×C₇	1	16	yes	—
598	C₂×D₄	C₂⁴×C₇	1	16	yes	—
599	C₂×D₄	C₂⁴×C₇	1	8	yes	—
600	C₂×D₄	C₂⁴×C₇	1	4	yes	—
601	C₂×D₄	C₂⁴×C₇	1	8	yes	—
602	C₂×D₄	C₂⁴×C₇	1	8	yes	—
603	C₂×D₄	C₂⁴×C₇	1	16	yes	—
604	C₂×D₄	C₂⁴×C₇	1	4	yes	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	8	no	—
607	C₂²×C₄	—	4	4	no	—
608	C₂²×C₄	—	4	8	no	—
609	C₂²×C₄	—	4	4	no	—
610	C₂²×C₄	—	4	8	no	—
611	C₂²×C₄	—	4	8	no	—
612	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
614	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
619	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
620	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
621	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
623	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
624	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
625	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
626	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
627	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
628	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
629	C₄⋊C₄	C₂⁴×C₇	1	16	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	8	yes	—
636	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
637	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
638	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
639	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
640	C₂²⋊C₄	C₂⁴×C₇	1	16	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	8	yes	—
645	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
646	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
647	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
648	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
649	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
650	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
651	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
652	C₄²	C₂⁴×C₇	1	4	yes	—
653	C₄²	C₂⁴×C₇	1	8	yes	—
654	C₄²	C₂⁴×C₇	1	4	yes	—
655	C₄²	C₂⁴×C₇	1	8	yes	—
656	C₄²	C₂⁴×C₇	1	16	yes	—
657	C₄²	C₂⁴×C₇	1	8	yes	—
658	C₂×C₇	—	2	4	no	—
659	C₂×C₇	—	4	8	no	—
660	C₂×C₇	—	4	4	no	—
661	C₂×C₇	—	4	4	no	—
662	C₂×C₇	#3545	1	4	yes	direct product factor
663	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
664	C₂×C₇	C₂×#585	1	2	yes	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	8	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	8	no	—
670	C₂³	—	2	8	no	—
671	C₂³	—	2	8	no	—
672	C₂³	—	2	8	no	—
673	C₂³	—	2	16	no	—
674	C₂³	—	4	8	no	—
675	C₂³	—	4	16	no	—
676	C₂³	—	4	16	no	—
677	C₂³	—	8	16	no	—
678	C₂³	—	8	16	no	—
679	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
680	C₂³	C₂⁵×C₇	1	4	yes	—
681	C₂³	C₂⁵×C₇	1	8	yes	—
682	C₂³	C₂⁵×C₇	1	4	yes	—
683	C₂³	C₂⁵×C₇	1	2	yes	—
684	C₂³	C₂⁵×C₇	1	1	yes	characteristic
685	Q₈	—	4	4	no	—
686	Q₈	—	4	8	no	—
687	Q₈	—	4	4	no	—
688	Q₈	—	4	8	no	—
689	Q₈	—	4	8	no	—
690	D₄	—	2	32	no	—
691	D₄	—	4	4	no	—
692	D₄	—	4	8	no	—
693	D₄	—	4	4	no	—
694	D₄	—	4	16	no	—
695	D₄	—	4	16	no	—
696	D₄	—	4	16	no	—
697	D₄	—	4	8	no	—
698	D₄	—	4	8	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	16	no	—
705	C₂×C₄	—	2	8	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	8	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	8	no	—
710	C₂×C₄	—	4	16	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	16	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	4	16	no	—
715	C₂×C₄	C₂⁵×C₇	1	4	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	2	yes	—
720	C₂×C₄	C₂⁵×C₇	1	2	yes	—
721	C₂×C₄	C₂⁵×C₇	1	8	yes	—
722	C₂×C₄	C₂⁵×C₇	1	8	yes	—
723	C₂×C₄	C₂⁵×C₇	1	4	yes	—
724	C₇	C₂×#3545	1	1	yes	characteristic, direct product factor, Sylow
725	C₂²	—	2	4	no	—
726	C₂²	—	2	8	no	—
727	C₂²	—	2	8	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	8	no	—
731	C₂²	—	2	8	no	—
732	C₂²	—	2	8	no	—
733	C₂²	—	2	8	no	—
734	C₂²	—	4	8	no	—
735	C₂²	—	4	16	no	—
736	C₂²	—	4	8	no	—
737	C₂²	—	8	16	no	—
738	C₂²	—	8	16	no	—
739	C₂²	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
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	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	8	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	8	no	—
750	C₄	—	2	4	no	—
751	C₄	—	2	8	no	—
752	C₂	—	2	4	no	—
753	C₂	—	4	4	no	—
754	C₂	—	4	8	no	—
755	C₂	—	4	4	no	—
756	C₂	C₇×#3545	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×#3545	C₂	direct (N × H)
2. C₂×C₇×#563	C₂	semidirect
3. C₂×C₇×#562	C₂	semidirect
4. C₂×C₇×H(3,𝔽₄)	C₂	semidirect
5. C₂×C₇×#555	C₂	semidirect
6. C₂×C₇×#551	C₂	semidirect
7. C₂×C₇×#551	C₂	semidirect
8. C₂×C₇×#546	C₂	semidirect
9. C₂×C₇×#542	C₂	semidirect
10. C₂×C₇×#538	C₂	semidirect
11. C₂×C₇×#536	C₂	semidirect
12. C₂×C₇×#534	C₂	semidirect
13. C₂×C₇×#529	C₂	semidirect
14. C₂²×C₇×#124	C₂	semidirect
16. C₂³×C₇×Q₈	C₂²	semidirect
18. C₂³×C₇×D₄	C₂²	semidirect
19. C₇×#563	C₂²	semidirect
20. C₇×#562	C₂²	semidirect
21. C₇×H(3,𝔽₄)	C₂²	semidirect
22. C₇×#555	C₂²	semidirect
23. C₇×#551	C₂²	semidirect
24. C₇×#551	C₂²	semidirect
25. C₇×#546	C₂²	semidirect
26. C₇×#542	C₂²	semidirect
27. C₇×#538	C₂²	semidirect
28. C₇×#536	C₂²	semidirect
29. C₇×#534	C₂²	semidirect
30. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
32. C₇×#529	C₂²	semidirect
33. C₂×C₇×#126	C₂²	semidirect
34. C₂×C₇×#126	C₂²	semidirect
35. C₂×C₇×#126	C₂²	semidirect
36. C₂×C₇×#125	C₂²	semidirect
39. C₂×C₇×#124	C₂²	semidirect
40. C₂×C₇×#124	C₂²	semidirect
41. C₂×C₇×#124	C₂²	semidirect
42. C₂×C₇×#124	C₂²	semidirect
43. C₂×C₇×#124	C₂²	semidirect
44. C₂×C₇×#124	C₂²	semidirect
45. C₂×C₇×#124	C₂²	semidirect
46. C₂×C₇×#124	C₂²	semidirect
47. C₂×C₇×#124	C₂²	semidirect
49. C₂×C₇×#123	C₂²	semidirect
50. C₂×C₇×#123	C₂²	semidirect
51. C₂×C₇×#123	C₂²	semidirect
52. C₂×C₇×#123	C₂²	semidirect
53. C₂×C₇×#123	C₂²	semidirect
54. C₂×C₇×#123	C₂²	semidirect
55. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
56. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
57. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
58. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
59. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₇×#121	C₂²	semidirect
63. C₂×C₇×#121	C₂²	semidirect
64. C₂×C₇×#121	C₂²	semidirect
67. C₂×C₇×#120	C₂²	semidirect
68. C₂×C₇×#120	C₂²	semidirect
69. C₂×C₄×C₇×Q₈	C₂²	semidirect
70. C₂×C₄×C₇×D₄	C₂²	semidirect
71. C₂×C₄×C₇×D₄	C₂²	semidirect
72. C₂×C₄×C₇×D₄	C₂²	semidirect
73. C₂×C₄×C₇×D₄	C₂²	semidirect
74. C₂×C₇×#117	C₂²	semidirect
75. C₂×C₇×#117	C₂²	semidirect
76. C₂×C₇×#117	C₂²	semidirect
77. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
78. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
79. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
80. C₂²×C₄²×C₇	C₂²	semidirect
81. C₂×#3545	C₇	direct (N × H)
92. C₂²×C₇×Q₈	C₂³	semidirect
105. C₂²×C₇×D₄	C₂³	semidirect
113. C₇×C₄⋊Q₈	C₂³	semidirect
114. C₇×C₄⋊Q₈	C₂³	semidirect
115. C₇×#126	C₂³	semidirect
116. C₇×#126	C₂³	semidirect
117. C₇×#126	C₂³	semidirect
118. C₇×#125	C₂³	semidirect
121. C₇×#124	C₂³	semidirect
122. C₇×#124	C₂³	semidirect
123. C₇×#124	C₂³	semidirect
124. C₇×#124	C₂³	semidirect
125. C₇×#124	C₂³	semidirect
126. C₇×#124	C₂³	semidirect
127. C₇×#124	C₂³	semidirect
128. C₇×#124	C₂³	semidirect
130. C₇×#123	C₂³	semidirect
131. C₇×#123	C₂³	semidirect
132. C₇×#123	C₂³	semidirect
133. C₇×#123	C₂³	semidirect
134. C₇×#123	C₂³	semidirect
135. C₇×#123	C₂³	semidirect
136. C₇×C₂²⋊Q₈	C₂³	semidirect
137. C₇×C₂²⋊Q₈	C₂³	semidirect
138. C₇×C₂²⋊Q₈	C₂³	semidirect
139. C₇×C₂²⋊Q₈	C₂³	semidirect
140. C₇×C₂²⋊Q₈	C₂³	semidirect
143. C₇×#121	C₂³	semidirect
144. C₇×#121	C₂³	semidirect
145. C₇×#121	C₂³	semidirect
148. C₇×#120	C₂³	semidirect
149. C₇×#120	C₂³	semidirect
150. C₄×C₇×Q₈	C₂³	semidirect
151. C₄×C₇×D₄	C₂³	semidirect
152. C₄×C₇×D₄	C₂³	semidirect
153. C₄×C₇×D₄	C₂³	semidirect
154. C₄×C₇×D₄	C₂³	semidirect
155. C₇×#117	C₂³	semidirect
156. C₇×#117	C₂³	semidirect
157. C₇×#117	C₂³	semidirect
182. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
183. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
184. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
191. C₂×C₄²×C₇	C₂³	semidirect
192. #3545	C₂×C₇	direct (N × H)
193. C₂×#563	C₂×C₇	semidirect
194. C₂×#562	C₂×C₇	semidirect
195. C₂×H(3,𝔽₄)	C₂×C₇	semidirect
196. C₂×#555	C₂×C₇	semidirect
197. C₂×#551	C₂×C₇	semidirect
198. C₂×#551	C₂×C₇	semidirect
199. C₂×#546	C₂×C₇	semidirect
200. C₂×#542	C₂×C₇	semidirect
201. C₂×#538	C₂×C₇	semidirect
202. C₂×#536	C₂×C₇	semidirect
203. C₂×#534	C₂×C₇	semidirect
204. C₂×#529	C₂×C₇	semidirect
205. C₂²×#124	C₂×C₇	semidirect
302. C₂³×Q₈	C₂²×C₇	semidirect
304. C₂³×D₄	C₂²×C₇	semidirect
305. #563	C₂²×C₇	semidirect
306. #562	C₂²×C₇	semidirect
307. H(3,𝔽₄)	C₂²×C₇	semidirect
308. #555	C₂²×C₇	semidirect
309. #551	C₂²×C₇	semidirect
310. #551	C₂²×C₇	semidirect
311. #546	C₂²×C₇	semidirect
312. #542	C₂²×C₇	semidirect
313. #538	C₂²×C₇	semidirect
314. #536	C₂²×C₇	semidirect
315. #534	C₂²×C₇	semidirect
316. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
317. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
318. #529	C₂²×C₇	semidirect
319. C₂×#126	C₂²×C₇	semidirect
320. C₂×#126	C₂²×C₇	semidirect
321. C₂×#126	C₂²×C₇	semidirect
322. C₂×#125	C₂²×C₇	semidirect
325. C₂×#124	C₂²×C₇	semidirect
326. C₂×#124	C₂²×C₇	semidirect
327. C₂×#124	C₂²×C₇	semidirect
328. C₂×#124	C₂²×C₇	semidirect
329. C₂×#124	C₂²×C₇	semidirect
330. C₂×#124	C₂²×C₇	semidirect
331. C₂×#124	C₂²×C₇	semidirect
332. C₂×#124	C₂²×C₇	semidirect
333. C₂×#124	C₂²×C₇	semidirect
335. C₂×#123	C₂²×C₇	semidirect
336. C₂×#123	C₂²×C₇	semidirect
337. C₂×#123	C₂²×C₇	semidirect
338. C₂×#123	C₂²×C₇	semidirect
339. C₂×#123	C₂²×C₇	semidirect
340. C₂×#123	C₂²×C₇	semidirect
341. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
342. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
343. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
344. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
345. 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×#120	C₂²×C₇	semidirect
354. C₂×#120	C₂²×C₇	semidirect
355. C₂×C₄×Q₈	C₂²×C₇	semidirect
356. C₂×C₄×D₄	C₂²×C₇	semidirect
357. C₂×C₄×D₄	C₂²×C₇	semidirect
358. C₂×C₄×D₄	C₂²×C₇	semidirect
359. C₂×C₄×D₄	C₂²×C₇	semidirect
360. C₂×#117	C₂²×C₇	semidirect
361. C₂×#117	C₂²×C₇	semidirect
362. C₂×#117	C₂²×C₇	semidirect
363. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
364. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
365. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
366. C₂²×C₄²	C₂²×C₇	semidirect
436. C₂²×Q₈	C₂³×C₇	semidirect
449. C₂²×D₄	C₂³×C₇	semidirect
457. C₄⋊Q₈	C₂³×C₇	semidirect
458. C₄⋊Q₈	C₂³×C₇	semidirect
459. #126	C₂³×C₇	semidirect
460. #126	C₂³×C₇	semidirect
461. #126	C₂³×C₇	semidirect
462. #125	C₂³×C₇	semidirect
465. #124	C₂³×C₇	semidirect
466. #124	C₂³×C₇	semidirect
467. #124	C₂³×C₇	semidirect
468. #124	C₂³×C₇	semidirect
469. #124	C₂³×C₇	semidirect
470. #124	C₂³×C₇	semidirect
471. #124	C₂³×C₇	semidirect
472. #124	C₂³×C₇	semidirect
474. #123	C₂³×C₇	semidirect
475. #123	C₂³×C₇	semidirect
476. #123	C₂³×C₇	semidirect
477. #123	C₂³×C₇	semidirect
478. #123	C₂³×C₇	semidirect
479. #123	C₂³×C₇	semidirect
480. C₂²⋊Q₈	C₂³×C₇	semidirect
481. C₂²⋊Q₈	C₂³×C₇	semidirect
482. C₂²⋊Q₈	C₂³×C₇	semidirect
483. C₂²⋊Q₈	C₂³×C₇	semidirect
484. C₂²⋊Q₈	C₂³×C₇	semidirect
487. #121	C₂³×C₇	semidirect
488. #121	C₂³×C₇	semidirect
489. #121	C₂³×C₇	semidirect
492. #120	C₂³×C₇	semidirect
493. #120	C₂³×C₇	semidirect
494. C₄×Q₈	C₂³×C₇	semidirect
495. C₄×D₄	C₂³×C₇	semidirect
496. C₄×D₄	C₂³×C₇	semidirect
497. C₄×D₄	C₂³×C₇	semidirect
498. C₄×D₄	C₂³×C₇	semidirect
499. #117	C₂³×C₇	semidirect
500. #117	C₂³×C₇	semidirect
501. #117	C₂³×C₇	semidirect
526. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
527. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
528. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
535. C₂×C₄²	C₂³×C₇	semidirect
662. C₂×C₇	#3545	direct (N × H)
724. C₇	C₂×#3545	direct (N × H)
756. C₂	C₇×#3545	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×#3545	2
C₂×C₇×#563	2
C₂×C₇×#562	2
C₂×C₇×H(3,𝔽₄)	2
C₂×C₇×#555	2
C₂×C₇×#551	2
C₂×C₇×#546	2
C₂×C₇×#542	2
C₂×C₇×#538	2
C₂×C₇×#536	2
C₂×C₇×#534	2
C₂×C₇×#529	2
C₂²×C₇×#124	2
C₂×#3545	7

Subgroups — C2×C7×#3545 #13239969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3545 #13239969