Subgroups — C₂×C₇×#3563 #13239949

Order 1792.

6458 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3563	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#564	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×#563	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#557	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#554	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#552	C₂	1	4	yes	maximal, complemented
7	C₂×C₇×#552	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#552	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#544	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#544	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#541	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#541	C₂	1	4	yes	maximal, complemented
13	C₂×C₇×#539	C₂	1	2	yes	maximal
14	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#564	C₂²	1	32	yes	complemented
18	C₇×#563	C₂²	1	32	yes	complemented
19	C₇×#557	C₂²	1	32	yes	complemented
20	C₇×#554	C₂²	1	32	yes	complemented
21	C₇×#552	C₂²	1	64	yes	complemented
22	C₇×#552	C₂²	1	32	yes	complemented
23	C₇×#552	C₂²	1	32	yes	complemented
24	C₇×#544	C₂²	1	32	yes	complemented
25	C₇×#544	C₂²	1	32	yes	complemented
26	C₇×#541	C₂²	1	32	yes	complemented
27	C₇×#541	C₂²	1	64	yes	complemented
28	C₇×#539	C₂²	1	32	yes	—
29	C₇×#533	C₂²	1	16	yes	complemented
30	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	—
33	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	—
35	C₇×#529	C₂²	1	16	yes	—
36	C₂×C₇×#126	C₂²	1	2	yes	—
37	C₂×C₇×#126	C₂²	1	4	yes	—
38	C₂×C₇×#126	C₂²	1	4	yes	—
39	C₂×C₇×#126	C₂²	1	4	yes	—
40	C₂×C₇×#126	C₂²	1	4	yes	—
41	C₂×C₇×#125	C₂²	1	2	yes	—
42	C₂×C₇×#125	C₂²	1	2	yes	—
43	C₂×C₇×#125	C₂²	1	2	yes	—
44	C₂×C₇×#125	C₂²	1	2	yes	—
45	C₂×C₇×#125	C₂²	1	1	yes	characteristic
46	C₂×C₇×#125	C₂²	1	2	yes	—
47	C₂×C₇×#125	C₂²	1	4	yes	—
48	C₂×C₇×#125	C₂²	1	4	yes	—
49	C₂×C₇×#125	C₂²	1	4	yes	—
50	C₂×C₇×#125	C₂²	1	4	yes	—
51	C₂×C₇×#125	C₂²	1	4	yes	—
52	C₂×C₇×#125	C₂²	1	4	yes	—
53	C₂×C₇×#125	C₂²	1	2	yes	—
54	C₂×C₇×#125	C₂²	1	4	yes	—
55	C₂×C₇×#125	C₂²	1	4	yes	—
56	C₂×C₇×#125	C₂²	1	16	yes	complemented
57	C₂×C₇×#124	C₂²	1	1	yes	characteristic
58	C₂×C₇×#123	C₂²	1	2	yes	—
59	C₂×C₇×#123	C₂²	1	4	yes	—
60	C₂×C₇×#123	C₂²	1	4	yes	—
61	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
62	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
63	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
64	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
65	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
66	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
67	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
68	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
69	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
70	C₂×C₇×#121	C₂²	1	1	yes	characteristic
71	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
72	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
73	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
74	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	—
75	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
76	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
77	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
78	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
79	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
80	C₂×C₇×#117	C₂²	1	2	yes	—
81	C₂×C₇×#117	C₂²	1	2	yes	—
82	C₂×C₇×#117	C₂²	1	4	yes	—
83	C₂×C₇×#117	C₂²	1	2	yes	—
84	C₂×C₇×#117	C₂²	1	4	yes	—
85	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
86	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
87	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
88	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
89	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
90	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
91	C₂×#3563	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂²×C₇×Q₈	C₂³	1	2	yes	—
93	C₂²×C₇×Q₈	C₂³	1	4	yes	—
94	C₂²×C₇×Q₈	C₂³	1	2	yes	—
95	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
96	C₂²×C₇×D₄	C₂³	1	2	yes	—
97	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₇	C₂³	1	2	yes	—
101	C₂³×C₄×C₇	C₂³	1	2	yes	—
102	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₇	C₂³	1	2	yes	—
104	C₂³×C₄×C₇	C₂³	1	4	yes	—
105	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
106	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
107	C₇×C₄⋊Q₈	C₂³	1	32	yes	—
108	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
109	C₇×C₄⋊Q₈	C₂³	1	32	yes	—
110	C₇×#126	C₂³	1	16	yes	—
111	C₇×#126	C₂³	1	32	yes	—
112	C₇×#126	C₂³	1	32	yes	—
113	C₇×#126	C₂³	1	32	yes	—
114	C₇×#126	C₂³	1	32	yes	—
115	C₇×#125	C₂³	1	16	yes	—
116	C₇×#125	C₂³	1	16	yes	—
117	C₇×#125	C₂³	1	16	yes	—
118	C₇×#125	C₂³	1	16	yes	—
119	C₇×#125	C₂³	1	8	yes	—
120	C₇×#125	C₂³	1	16	yes	—
121	C₇×#125	C₂³	1	32	yes	—
122	C₇×#125	C₂³	1	32	yes	—
123	C₇×#125	C₂³	1	32	yes	—
124	C₇×#125	C₂³	1	32	yes	—
125	C₇×#125	C₂³	1	32	yes	—
126	C₇×#125	C₂³	1	32	yes	—
127	C₇×#125	C₂³	1	16	yes	—
128	C₇×#125	C₂³	1	32	yes	—
129	C₇×#125	C₂³	1	32	yes	—
130	C₇×#124	C₂³	1	8	yes	—
131	C₇×#123	C₂³	1	16	yes	—
132	C₇×#123	C₂³	1	32	yes	—
133	C₇×#123	C₂³	1	32	yes	—
134	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
135	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
136	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
137	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
138	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
139	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
140	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
141	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
142	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
143	C₇×#121	C₂³	1	8	yes	—
144	C₄×C₇×Q₈	C₂³	1	8	yes	—
145	C₄×C₇×Q₈	C₂³	1	16	yes	—
146	C₄×C₇×Q₈	C₂³	1	16	yes	—
147	C₄×C₇×Q₈	C₂³	1	32	yes	—
148	C₄×C₇×Q₈	C₂³	1	16	yes	—
149	C₄×C₇×Q₈	C₂³	1	16	yes	—
150	C₄×C₇×D₄	C₂³	1	8	yes	—
151	C₄×C₇×D₄	C₂³	1	16	yes	—
152	C₄×C₇×D₄	C₂³	1	32	yes	—
153	C₇×#117	C₂³	1	16	yes	—
154	C₇×#117	C₂³	1	16	yes	—
155	C₇×#117	C₂³	1	32	yes	—
156	C₇×#117	C₂³	1	16	yes	—
157	C₇×#117	C₂³	1	32	yes	—
158	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	4	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	16	yes	—
169	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
170	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
171	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
172	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
176	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
178	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	2	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	4	yes	—
186	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
188	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
189	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
191	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
192	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
196	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
199	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇	C₂³	1	8	yes	—
205	C₂×C₄²×C₇	C₂³	1	4	yes	—
206	C₂×C₄²×C₇	C₂³	1	4	yes	—
207	C₂×C₄²×C₇	C₂³	1	2	yes	—
208	C₂×C₄²×C₇	C₂³	1	4	yes	—
209	C₂×C₄²×C₇	C₂³	1	4	yes	—
210	#3563	C₂×C₇	1	32	yes	direct product factor
211	C₂×#564	C₂×C₇	1	2	yes	complemented
212	C₂×#563	C₂×C₇	1	2	yes	complemented
213	C₂×#557	C₂×C₇	1	2	yes	complemented
214	C₂×#554	C₂×C₇	1	2	yes	complemented
215	C₂×#552	C₂×C₇	1	4	yes	complemented
216	C₂×#552	C₂×C₇	1	2	yes	complemented
217	C₂×#552	C₂×C₇	1	2	yes	complemented
218	C₂×#544	C₂×C₇	1	2	yes	complemented
219	C₂×#544	C₂×C₇	1	2	yes	complemented
220	C₂×#541	C₂×C₇	1	2	yes	complemented
221	C₂×#541	C₂×C₇	1	4	yes	complemented
222	C₂×#539	C₂×C₇	1	2	yes	—
223	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
224	C₂×#529	C₂×C₇	1	1	yes	characteristic
225	C₂²×#125	C₂×C₇	1	1	yes	characteristic, complemented
226	C₂⁴×C₇	C₂⁴	1	2	yes	—
227	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
228	C₂×C₇×Q₈	—	2	8	no	—
229	C₂×C₇×Q₈	—	4	8	no	—
230	C₂×C₇×Q₈	—	4	2	no	—
231	C₂×C₇×Q₈	—	4	4	no	—
232	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
233	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
234	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
235	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
236	C₂×C₇×D₄	—	2	8	no	—
237	C₂×C₇×D₄	—	4	2	no	—
238	C₂×C₇×D₄	C₂⁴	1	8	yes	—
239	C₂×C₇×D₄	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₇	—	2	4	no	—
241	C₂²×C₄×C₇	—	2	8	no	—
242	C₂²×C₄×C₇	—	2	4	no	—
243	C₂²×C₄×C₇	—	2	8	no	—
244	C₂²×C₄×C₇	—	4	4	no	—
245	C₂²×C₄×C₇	—	4	8	no	—
246	C₂²×C₄×C₇	—	4	2	no	—
247	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
250	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
251	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
265	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
266	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
267	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
268	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
269	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
270	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
271	C₇×C₄⋊C₄	C₂⁴	1	8	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	8	yes	—
277	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
278	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
279	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
280	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
281	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
282	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
283	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
284	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
285	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
286	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
287	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
288	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
289	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
290	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
291	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
292	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
293	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
294	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
295	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
296	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
297	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
298	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
299	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
300	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
301	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
302	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
303	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
304	C₄²×C₇	C₂⁴	1	4	yes	—
305	C₄²×C₇	C₂⁴	1	4	yes	—
306	C₄²×C₇	C₂⁴	1	4	yes	—
307	C₄²×C₇	C₂⁴	1	4	yes	—
308	C₄²×C₇	C₂⁴	1	16	yes	—
309	C₄²×C₇	C₂⁴	1	16	yes	—
310	C₄²×C₇	C₂⁴	1	8	yes	—
311	C₄²×C₇	C₂⁴	1	16	yes	—
312	C₄²×C₇	C₂⁴	1	16	yes	—
313	#564	C₂²×C₇	1	32	yes	complemented
314	#563	C₂²×C₇	1	32	yes	complemented
315	#557	C₂²×C₇	1	32	yes	complemented
316	#554	C₂²×C₇	1	32	yes	complemented
317	#552	C₂²×C₇	1	64	yes	complemented
318	#552	C₂²×C₇	1	32	yes	complemented
319	#552	C₂²×C₇	1	32	yes	complemented
320	#544	C₂²×C₇	1	32	yes	complemented
321	#544	C₂²×C₇	1	32	yes	complemented
322	#541	C₂²×C₇	1	32	yes	complemented
323	#541	C₂²×C₇	1	64	yes	complemented
324	#539	C₂²×C₇	1	32	yes	—
325	#533	C₂²×C₇	1	16	yes	complemented
326	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
327	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
328	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	—
329	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
330	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	—
331	#529	C₂²×C₇	1	16	yes	—
332	C₂×#126	C₂²×C₇	1	2	yes	—
333	C₂×#126	C₂²×C₇	1	4	yes	—
334	C₂×#126	C₂²×C₇	1	4	yes	—
335	C₂×#126	C₂²×C₇	1	4	yes	—
336	C₂×#126	C₂²×C₇	1	4	yes	—
337	C₂×#125	C₂²×C₇	1	2	yes	—
338	C₂×#125	C₂²×C₇	1	2	yes	—
339	C₂×#125	C₂²×C₇	1	2	yes	—
340	C₂×#125	C₂²×C₇	1	2	yes	—
341	C₂×#125	C₂²×C₇	1	1	yes	characteristic
342	C₂×#125	C₂²×C₇	1	2	yes	—
343	C₂×#125	C₂²×C₇	1	4	yes	—
344	C₂×#125	C₂²×C₇	1	4	yes	—
345	C₂×#125	C₂²×C₇	1	4	yes	—
346	C₂×#125	C₂²×C₇	1	4	yes	—
347	C₂×#125	C₂²×C₇	1	4	yes	—
348	C₂×#125	C₂²×C₇	1	4	yes	—
349	C₂×#125	C₂²×C₇	1	2	yes	—
350	C₂×#125	C₂²×C₇	1	4	yes	—
351	C₂×#125	C₂²×C₇	1	4	yes	—
352	C₂×#125	C₂²×C₇	1	16	yes	complemented
353	C₂×#124	C₂²×C₇	1	1	yes	characteristic
354	C₂×#123	C₂²×C₇	1	2	yes	—
355	C₂×#123	C₂²×C₇	1	4	yes	—
356	C₂×#123	C₂²×C₇	1	4	yes	—
357	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
358	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
359	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
360	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
361	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
362	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
363	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
364	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
365	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
366	C₂×#121	C₂²×C₇	1	1	yes	characteristic
367	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
368	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
369	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
370	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	—
371	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
372	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
373	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
375	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
376	C₂×#117	C₂²×C₇	1	2	yes	—
377	C₂×#117	C₂²×C₇	1	2	yes	—
378	C₂×#117	C₂²×C₇	1	4	yes	—
379	C₂×#117	C₂²×C₇	1	2	yes	—
380	C₂×#117	C₂²×C₇	1	4	yes	—
381	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
382	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
383	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
384	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
385	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
386	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
387	C₂³×C₇	—	2	2	no	—
388	C₂³×C₇	—	2	2	no	—
389	C₂³×C₇	—	2	4	no	—
390	C₂³×C₇	—	2	4	no	—
391	C₂³×C₇	—	2	4	no	—
392	C₂³×C₇	2₋¹⁺⁴	1	4	yes	—
393	C₂³×C₇	C₂⁵	1	4	yes	—
394	C₂³×C₇	C₂⁵	1	2	yes	—
395	C₂³×C₇	C₂⁵	1	1	yes	characteristic
396	C₇×Q₈	—	2	16	no	—
397	C₇×Q₈	—	4	16	no	—
398	C₇×Q₈	—	4	4	no	—
399	C₇×Q₈	—	4	8	no	—
400	C₇×D₄	—	2	16	no	—
401	C₇×D₄	—	4	4	no	—
402	C₂×C₄×C₇	—	2	8	no	—
403	C₂×C₄×C₇	—	2	16	no	—
404	C₂×C₄×C₇	—	2	2	no	—
405	C₂×C₄×C₇	—	2	2	no	—
406	C₂×C₄×C₇	—	2	8	no	—
407	C₂×C₄×C₇	—	2	2	no	—
408	C₂×C₄×C₇	—	2	4	no	—
409	C₂×C₄×C₇	—	2	4	no	—
410	C₂×C₄×C₇	—	2	8	no	—
411	C₂×C₄×C₇	—	2	8	no	—
412	C₂×C₄×C₇	—	2	2	no	—
413	C₂×C₄×C₇	—	2	8	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	2	4	no	—
416	C₂×C₄×C₇	—	2	8	no	—
417	C₂×C₄×C₇	—	2	16	no	—
418	C₂×C₄×C₇	—	4	8	no	—
419	C₂×C₄×C₇	—	4	16	no	—
420	C₂×C₄×C₇	—	4	4	no	—
421	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
422	C₂×C₄×C₇	C₂⁵	1	2	yes	—
423	C₂×C₄×C₇	C₂⁵	1	8	yes	—
424	C₂×C₄×C₇	C₂⁵	1	4	yes	—
425	C₂×C₄×C₇	C₂⁵	1	4	yes	—
426	C₂×C₄×C₇	C₂⁵	1	2	yes	—
427	C₂×C₄×C₇	C₂⁵	1	2	yes	—
428	C₂×C₄×C₇	C₂⁵	1	4	yes	—
429	C₂×C₄×C₇	C₂⁵	1	8	yes	—
430	C₂×C₄×C₇	C₂⁵	1	2	yes	—
431	C₂×C₄×C₇	C₂⁵	1	8	yes	—
432	C₂×C₄×C₇	C₂⁵	1	2	yes	—
433	C₂×C₄×C₇	C₂⁵	1	8	yes	—
434	C₂×C₄×C₇	C₂⁵	1	2	yes	—
435	C₂²×Q₈	C₂³×C₇	1	2	yes	—
436	C₂²×Q₈	C₂³×C₇	1	4	yes	—
437	C₂²×Q₈	C₂³×C₇	1	2	yes	—
438	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
439	C₂²×D₄	C₂³×C₇	1	2	yes	—
440	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₇	1	2	yes	—
442	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₇	1	2	yes	—
445	C₂³×C₄	C₂³×C₇	1	2	yes	—
446	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₇	1	4	yes	—
448	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
449	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
450	C₄⋊Q₈	C₂³×C₇	1	32	yes	—
451	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
452	C₄⋊Q₈	C₂³×C₇	1	32	yes	—
453	#126	C₂³×C₇	1	16	yes	—
454	#126	C₂³×C₇	1	32	yes	—
455	#126	C₂³×C₇	1	32	yes	—
456	#126	C₂³×C₇	1	32	yes	—
457	#126	C₂³×C₇	1	32	yes	—
458	#125	C₂³×C₇	1	16	yes	—
459	#125	C₂³×C₇	1	16	yes	—
460	#125	C₂³×C₇	1	16	yes	—
461	#125	C₂³×C₇	1	16	yes	—
462	#125	C₂³×C₇	1	8	yes	—
463	#125	C₂³×C₇	1	16	yes	—
464	#125	C₂³×C₇	1	32	yes	—
465	#125	C₂³×C₇	1	32	yes	—
466	#125	C₂³×C₇	1	32	yes	—
467	#125	C₂³×C₇	1	32	yes	—
468	#125	C₂³×C₇	1	32	yes	—
469	#125	C₂³×C₇	1	32	yes	—
470	#125	C₂³×C₇	1	16	yes	—
471	#125	C₂³×C₇	1	32	yes	—
472	#125	C₂³×C₇	1	32	yes	—
473	#124	C₂³×C₇	1	8	yes	—
474	#123	C₂³×C₇	1	16	yes	—
475	#123	C₂³×C₇	1	32	yes	—
476	#123	C₂³×C₇	1	32	yes	—
477	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
478	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
479	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
480	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
481	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
482	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
483	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
484	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
485	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
486	#121	C₂³×C₇	1	8	yes	—
487	C₄×Q₈	C₂³×C₇	1	8	yes	—
488	C₄×Q₈	C₂³×C₇	1	16	yes	—
489	C₄×Q₈	C₂³×C₇	1	16	yes	—
490	C₄×Q₈	C₂³×C₇	1	32	yes	—
491	C₄×Q₈	C₂³×C₇	1	16	yes	—
492	C₄×Q₈	C₂³×C₇	1	16	yes	—
493	C₄×D₄	C₂³×C₇	1	8	yes	—
494	C₄×D₄	C₂³×C₇	1	16	yes	—
495	C₄×D₄	C₂³×C₇	1	32	yes	—
496	#117	C₂³×C₇	1	16	yes	—
497	#117	C₂³×C₇	1	16	yes	—
498	#117	C₂³×C₇	1	32	yes	—
499	#117	C₂³×C₇	1	16	yes	—
500	#117	C₂³×C₇	1	32	yes	—
501	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₇	1	4	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	16	yes	—
512	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
513	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
514	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
515	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
516	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
517	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
519	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
521	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
525	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
529	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
530	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
531	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
532	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
543	C₂×C₄²	C₂³×C₇	1	4	yes	—
544	C₂×C₄²	C₂³×C₇	1	4	yes	—
545	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₇	1	2	yes	—
547	C₂×C₄²	C₂³×C₇	1	4	yes	—
548	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₇	1	4	yes	—
550	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₇	1	8	yes	—
553	C₂²×C₇	—	2	2	no	—
554	C₂²×C₇	—	2	2	no	—
555	C₂²×C₇	—	2	8	no	—
556	C₂²×C₇	—	2	4	no	—
557	C₂²×C₇	—	2	4	no	—
558	C₂²×C₇	—	2	4	no	—
559	C₂²×C₇	—	4	8	no	—
560	C₂²×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
561	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
562	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
563	C₂²×C₇	#585	1	2	yes	—
564	C₂²×C₇	C₂⁶	1	1	yes	characteristic
565	C₄×C₇	—	2	2	no	—
566	C₄×C₇	—	2	2	no	—
567	C₄×C₇	—	2	8	no	—
568	C₄×C₇	—	2	2	no	—
569	C₄×C₇	—	2	4	no	—
570	C₄×C₇	—	2	4	no	—
571	C₄×C₇	—	2	8	no	—
572	C₄×C₇	—	2	8	no	—
573	C₄×C₇	—	2	2	no	—
574	C₄×C₇	—	2	8	no	—
575	C₄×C₇	—	2	2	no	—
576	C₄×C₇	—	2	4	no	—
577	C₄×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
578	C₂⁴	C₂⁴×C₇	1	2	yes	—
579	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
580	C₂×Q₈	—	2	8	no	—
581	C₂×Q₈	—	4	8	no	—
582	C₂×Q₈	—	4	2	no	—
583	C₂×Q₈	—	4	4	no	—
584	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
585	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
586	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
587	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
588	C₂×D₄	—	2	8	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	C₂⁴×C₇	1	8	yes	—
591	C₂×D₄	C₂⁴×C₇	1	4	yes	—
592	C₂²×C₄	—	2	8	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	8	no	—
596	C₂²×C₄	—	4	4	no	—
597	C₂²×C₄	—	4	8	no	—
598	C₂²×C₄	—	4	2	no	—
599	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
601	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
605	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
608	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
611	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
612	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
613	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
614	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
615	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
616	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
617	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
618	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
619	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
620	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
621	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
622	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
623	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
624	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
625	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
626	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
627	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
628	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
629	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
630	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
631	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
632	C₄⋊C₄	C₂⁴×C₇	1	8	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	4	yes	—
637	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
638	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
639	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
640	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
641	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
642	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
643	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
644	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
645	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
646	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
647	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
648	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
649	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
650	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
651	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
652	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
653	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
654	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
655	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
656	C₄²	C₂⁴×C₇	1	4	yes	—
657	C₄²	C₂⁴×C₇	1	4	yes	—
658	C₄²	C₂⁴×C₇	1	4	yes	—
659	C₄²	C₂⁴×C₇	1	4	yes	—
660	C₄²	C₂⁴×C₇	1	16	yes	—
661	C₄²	C₂⁴×C₇	1	16	yes	—
662	C₄²	C₂⁴×C₇	1	8	yes	—
663	C₄²	C₂⁴×C₇	1	16	yes	—
664	C₄²	C₂⁴×C₇	1	16	yes	—
665	C₂×C₇	—	2	4	no	—
666	C₂×C₇	—	4	4	no	—
667	C₂×C₇	#3563	1	4	yes	direct product factor
668	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
669	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
670	C₂×C₇	C₂×#585	1	1	yes	characteristic
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	2	4	no	—
675	C₂³	—	2	4	no	—
676	C₂³	C₇×2₋¹⁺⁴	1	4	yes	—
677	C₂³	C₂⁵×C₇	1	4	yes	—
678	C₂³	C₂⁵×C₇	1	2	yes	—
679	C₂³	C₂⁵×C₇	1	1	yes	characteristic
680	Q₈	—	2	16	no	—
681	Q₈	—	4	16	no	—
682	Q₈	—	4	4	no	—
683	Q₈	—	4	8	no	—
684	D₄	—	2	16	no	—
685	D₄	—	4	4	no	—
686	C₂×C₄	—	2	8	no	—
687	C₂×C₄	—	2	16	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	8	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	8	no	—
695	C₂×C₄	—	2	8	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	8	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	16	no	—
702	C₂×C₄	—	4	8	no	—
703	C₂×C₄	—	4	16	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
706	C₂×C₄	C₂⁵×C₇	1	2	yes	—
707	C₂×C₄	C₂⁵×C₇	1	8	yes	—
708	C₂×C₄	C₂⁵×C₇	1	4	yes	—
709	C₂×C₄	C₂⁵×C₇	1	4	yes	—
710	C₂×C₄	C₂⁵×C₇	1	2	yes	—
711	C₂×C₄	C₂⁵×C₇	1	2	yes	—
712	C₂×C₄	C₂⁵×C₇	1	4	yes	—
713	C₂×C₄	C₂⁵×C₇	1	8	yes	—
714	C₂×C₄	C₂⁵×C₇	1	2	yes	—
715	C₂×C₄	C₂⁵×C₇	1	8	yes	—
716	C₂×C₄	C₂⁵×C₇	1	2	yes	—
717	C₂×C₄	C₂⁵×C₇	1	8	yes	—
718	C₂×C₄	C₂⁵×C₇	1	2	yes	—
719	C₇	C₂×#3563	1	1	yes	characteristic, direct product factor, Sylow
720	C₂²	—	2	8	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	4	8	no	—
727	C₂²	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
728	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
729	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
730	C₂²	C₇×#585	1	2	yes	—
731	C₂²	C₂⁶×C₇	1	1	yes	characteristic
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	8	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	4	no	—
738	C₄	—	2	8	no	—
739	C₄	—	2	8	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	8	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	4	no	—
744	C₄	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
745	C₂	—	2	4	no	—
746	C₂	—	4	4	no	—
747	C₂	C₇×#3563	1	4	yes	direct product factor
748	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
749	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
750	C₂	C₂×C₇×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
prime radical	C₂×C₇×#121	C₂²
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×#3563	C₂	direct (N × H)
2. C₂×C₇×#564	C₂	semidirect
3. C₂×C₇×#563	C₂	semidirect
4. C₂×C₇×#557	C₂	semidirect
5. C₂×C₇×#554	C₂	semidirect
6. C₂×C₇×#552	C₂	semidirect
7. C₂×C₇×#552	C₂	semidirect
8. C₂×C₇×#552	C₂	semidirect
9. C₂×C₇×#544	C₂	semidirect
10. C₂×C₇×#544	C₂	semidirect
11. C₂×C₇×#541	C₂	semidirect
12. C₂×C₇×#541	C₂	semidirect
14. C₂×C₇×#533	C₂	semidirect
16. C₂²×C₇×#125	C₂	semidirect
17. C₇×#564	C₂²	semidirect
18. C₇×#563	C₂²	semidirect
19. C₇×#557	C₂²	semidirect
20. C₇×#554	C₂²	semidirect
21. C₇×#552	C₂²	semidirect
22. C₇×#552	C₂²	semidirect
23. C₇×#552	C₂²	semidirect
24. C₇×#544	C₂²	semidirect
25. C₇×#544	C₂²	semidirect
26. C₇×#541	C₂²	semidirect
27. C₇×#541	C₂²	semidirect
29. C₇×#533	C₂²	semidirect
56. C₂×C₇×#125	C₂²	semidirect
91. C₂×#3563	C₇	direct (N × H)
210. #3563	C₂×C₇	direct (N × H)
211. C₂×#564	C₂×C₇	semidirect
212. C₂×#563	C₂×C₇	semidirect
213. C₂×#557	C₂×C₇	semidirect
214. C₂×#554	C₂×C₇	semidirect
215. C₂×#552	C₂×C₇	semidirect
216. C₂×#552	C₂×C₇	semidirect
217. C₂×#552	C₂×C₇	semidirect
218. C₂×#544	C₂×C₇	semidirect
219. C₂×#544	C₂×C₇	semidirect
220. C₂×#541	C₂×C₇	semidirect
221. C₂×#541	C₂×C₇	semidirect
223. C₂×#533	C₂×C₇	semidirect
225. C₂²×#125	C₂×C₇	semidirect
313. #564	C₂²×C₇	semidirect
314. #563	C₂²×C₇	semidirect
315. #557	C₂²×C₇	semidirect
316. #554	C₂²×C₇	semidirect
317. #552	C₂²×C₇	semidirect
318. #552	C₂²×C₇	semidirect
319. #552	C₂²×C₇	semidirect
320. #544	C₂²×C₇	semidirect
321. #544	C₂²×C₇	semidirect
322. #541	C₂²×C₇	semidirect
323. #541	C₂²×C₇	semidirect
325. #533	C₂²×C₇	semidirect
352. C₂×#125	C₂²×C₇	semidirect
667. C₂×C₇	#3563	direct (N × H)
719. C₇	C₂×#3563	direct (N × H)
747. C₂	C₇×#3563	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×#3563	2
C₂×C₇×#564	2
C₂×C₇×#563	2
C₂×C₇×#557	2
C₂×C₇×#554	2
C₂×C₇×#552	2
C₂×C₇×#544	2
C₂×C₇×#541	2
C₂×C₇×#539	2
C₂×C₇×#533	2
C₂×C₇×#529	2
C₂²×C₇×#125	2
C₂×#3563	7

Subgroups — C2×C7×#3563 #13239949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3563 #13239949