Subgroups — C₂×C₇×#3559 #13239948

Order 1792.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3559	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×#562	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#554	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#553	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#547	C₂	1	4	yes	maximal, complemented
8	C₂×C₇×#547	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#544	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#540	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#539	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#539	C₂	1	4	yes	maximal, complemented
13	C₂×C₇×#537	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₇×#41	C₂²	1	2	yes	—
18	C₂²×C₇×#41	C₂²	1	4	yes	—
19	C₇×#563	C₂²	1	32	yes	complemented
20	C₇×#562	C₂²	1	32	yes	complemented
21	C₇×#554	C₂²	1	32	yes	complemented
22	C₇×#553	C₂²	1	32	yes	complemented
23	C₇×#553	C₂²	1	32	yes	complemented
24	C₇×#547	C₂²	1	64	yes	complemented
25	C₇×#547	C₂²	1	32	yes	complemented
26	C₇×#544	C₂²	1	32	yes	complemented
27	C₇×#540	C₂²	1	32	yes	complemented
28	C₇×#539	C₂²	1	32	yes	complemented
29	C₇×#539	C₂²	1	64	yes	complemented
30	C₇×#537	C₂²	1	32	yes	complemented
31	C₇×#532	C₂²	1	16	yes	complemented
32	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	—
35	C₂×C₇×#127	C₂²	1	1	yes	characteristic
36	C₇×#529	C₂²	1	16	yes	complemented
37	C₂×C₇×#126	C₂²	1	2	yes	—
38	C₂×C₇×#126	C₂²	1	4	yes	—
39	C₂×C₇×#126	C₂²	1	4	yes	—
40	C₂×C₇×#125	C₂²	1	2	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	1	yes	characteristic
45	C₂×C₇×#125	C₂²	1	4	yes	—
46	C₂×C₇×#125	C₂²	1	2	yes	—
47	C₂×C₇×#125	C₂²	1	16	yes	complemented
48	C₂×C₇×#124	C₂²	1	1	yes	characteristic
49	C₂×C₇×#124	C₂²	1	2	yes	—
50	C₂×C₇×#123	C₂²	1	2	yes	—
51	C₂×C₇×#123	C₂²	1	4	yes	—
52	C₂×C₇×#123	C₂²	1	4	yes	—
53	C₂×C₇×#123	C₂²	1	4	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×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
59	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
60	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
61	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
62	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
63	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
64	C₂×C₇×#121	C₂²	1	1	yes	characteristic
65	C₂×C₇×#121	C₂²	1	2	yes	—
66	C₂×C₇×#121	C₂²	1	2	yes	—
67	C₂×C₇×#121	C₂²	1	4	yes	—
68	C₂×C₇×#121	C₂²	1	4	yes	—
69	C₂×C₇×#121	C₂²	1	4	yes	—
70	C₂×C₇×#121	C₂²	1	2	yes	—
71	C₂×C₇×#121	C₂²	1	4	yes	—
72	C₂×C₇×#121	C₂²	1	2	yes	—
73	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
74	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
75	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
77	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
78	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
79	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
80	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
81	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
82	C₂×C₇×#117	C₂²	1	2	yes	—
83	C₂×C₇×#117	C₂²	1	2	yes	—
84	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
85	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
86	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
87	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
88	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	—
89	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
90	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
91	C₂×#3559	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂×C₇×#41	—	4	8	no	—
93	C₂×C₇×#41	—	4	16	no	—
94	C₂×C₇×#41	C₂³	1	16	yes	—
95	C₂×C₇×#41	C₂³	1	32	yes	—
96	C₂²×C₇×Q₈	C₂³	1	4	yes	—
97	C₂²×C₇×Q₈	C₂³	1	2	yes	—
98	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
99	C₂²×C₇×D₄	C₂³	1	4	yes	—
100	C₂²×C₇×D₄	C₂³	1	2	yes	—
101	C₂²×C₇×D₄	C₂³	1	2	yes	—
102	C₂²×C₇×D₄	C₂³	1	4	yes	—
103	C₂²×C₇×D₄	C₂³	1	2	yes	—
104	C₂²×C₇×D₄	C₂³	1	4	yes	—
105	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
106	C₂²×C₇×D₄	C₂³	1	2	yes	—
107	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₇	C₂³	1	2	yes	—
109	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₇	C₂³	1	4	yes	—
114	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₇	C₂³	1	2	yes	—
116	C₂³×C₄×C₇	C₂³	1	4	yes	—
117	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
118	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
119	C₇×C₄⋊Q₈	C₂³	1	32	yes	—
120	C₇×#127	C₂³	1	8	yes	—
121	C₇×#126	C₂³	1	16	yes	—
122	C₇×#126	C₂³	1	32	yes	—
123	C₇×#126	C₂³	1	32	yes	—
124	C₇×#125	C₂³	1	16	yes	—
125	C₇×#125	C₂³	1	16	yes	—
126	C₇×#125	C₂³	1	16	yes	—
127	C₇×#125	C₂³	1	16	yes	—
128	C₇×#125	C₂³	1	8	yes	—
129	C₇×#125	C₂³	1	32	yes	—
130	C₇×#125	C₂³	1	16	yes	—
131	C₇×#124	C₂³	1	8	yes	—
132	C₇×#124	C₂³	1	16	yes	—
133	C₇×#123	C₂³	1	16	yes	—
134	C₇×#123	C₂³	1	32	yes	—
135	C₇×#123	C₂³	1	32	yes	—
136	C₇×#123	C₂³	1	32	yes	—
137	C₇×#123	C₂³	1	32	yes	—
138	C₇×#123	C₂³	1	32	yes	—
139	C₇×#123	C₂³	1	32	yes	—
140	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
141	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
142	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
143	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
144	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
145	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
146	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
147	C₇×#121	C₂³	1	8	yes	—
148	C₇×#121	C₂³	1	16	yes	—
149	C₇×#121	C₂³	1	16	yes	—
150	C₇×#121	C₂³	1	32	yes	—
151	C₇×#121	C₂³	1	32	yes	—
152	C₇×#121	C₂³	1	32	yes	—
153	C₇×#121	C₂³	1	16	yes	—
154	C₇×#121	C₂³	1	32	yes	—
155	C₇×#121	C₂³	1	16	yes	—
156	C₄×C₇×Q₈	C₂³	1	8	yes	—
157	C₄×C₇×D₄	C₂³	1	16	yes	—
158	C₄×C₇×D₄	C₂³	1	8	yes	—
159	C₄×C₇×D₄	C₂³	1	16	yes	—
160	C₄×C₇×D₄	C₂³	1	16	yes	—
161	C₄×C₇×D₄	C₂³	1	32	yes	—
162	C₄×C₇×D₄	C₂³	1	32	yes	—
163	C₄×C₇×D₄	C₂³	1	16	yes	—
164	C₄×C₇×D₄	C₂³	1	16	yes	—
165	C₇×#117	C₂³	1	16	yes	—
166	C₇×#117	C₂³	1	16	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	2	yes	—
171	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	4	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	4	yes	—
179	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
184	C₂×C₇×C₄⋊C₄	C₂³	1	32	yes	—
185	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
186	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
192	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
195	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
199	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
200	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
201	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
202	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
203	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₇	C₂³	1	8	yes	—
210	C₂×C₄²×C₇	C₂³	1	2	yes	—
211	C₂×C₄²×C₇	C₂³	1	4	yes	—
212	#3559	C₂×C₇	1	32	yes	direct product factor
213	C₂×#563	C₂×C₇	1	2	yes	complemented
214	C₂×#562	C₂×C₇	1	2	yes	complemented
215	C₂×#554	C₂×C₇	1	2	yes	complemented
216	C₂×#553	C₂×C₇	1	2	yes	complemented
217	C₂×#553	C₂×C₇	1	2	yes	complemented
218	C₂×#547	C₂×C₇	1	4	yes	complemented
219	C₂×#547	C₂×C₇	1	2	yes	complemented
220	C₂×#544	C₂×C₇	1	2	yes	complemented
221	C₂×#540	C₂×C₇	1	2	yes	complemented
222	C₂×#539	C₂×C₇	1	2	yes	complemented
223	C₂×#539	C₂×C₇	1	4	yes	complemented
224	C₂×#537	C₂×C₇	1	2	yes	complemented
225	C₂×#532	C₂×C₇	1	1	yes	characteristic, complemented
226	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
227	C₂²×#125	C₂×C₇	1	1	yes	characteristic, complemented
228	C₂⁴×C₇	C₂⁴	1	2	yes	—
229	C₂⁴×C₇	C₂⁴	1	4	yes	—
230	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
231	C₇×#41	—	4	32	no	—
232	C₇×#41	—	4	64	no	—
233	C₂×C₇×Q₈	—	4	2	no	—
234	C₂×C₇×Q₈	—	4	8	no	—
235	C₂×C₇×Q₈	—	4	4	no	—
236	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
237	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
238	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
239	C₂×C₇×D₄	—	2	16	no	—
240	C₂×C₇×D₄	—	2	8	no	—
241	C₂×C₇×D₄	—	2	8	no	—
242	C₂×C₇×D₄	—	4	8	no	—
243	C₂×C₇×D₄	—	4	4	no	—
244	C₂×C₇×D₄	—	4	2	no	—
245	C₂×C₇×D₄	—	4	8	no	—
246	C₂×C₇×D₄	—	4	4	no	—
247	C₂×C₇×D₄	C₂⁴	1	8	yes	—
248	C₂×C₇×D₄	C₂⁴	1	8	yes	—
249	C₂×C₇×D₄	C₂⁴	1	16	yes	—
250	C₂×C₇×D₄	C₂⁴	1	16	yes	—
251	C₂×C₇×D₄	C₂⁴	1	4	yes	—
252	C₂×C₇×D₄	C₂⁴	1	8	yes	—
253	C₂×C₇×D₄	C₂⁴	1	16	yes	—
254	C₂×C₇×D₄	C₂⁴	1	8	yes	—
255	C₂²×C₄×C₇	—	2	4	no	—
256	C₂²×C₄×C₇	—	2	8	no	—
257	C₂²×C₄×C₇	—	2	4	no	—
258	C₂²×C₄×C₇	—	2	8	no	—
259	C₂²×C₄×C₇	—	4	4	no	—
260	C₂²×C₄×C₇	—	4	8	no	—
261	C₂²×C₄×C₇	—	4	2	no	—
262	C₂²×C₄×C₇	—	4	8	no	—
263	C₂²×C₄×C₇	—	4	8	no	—
264	C₂²×C₄×C₇	—	4	8	no	—
265	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
268	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
269	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
277	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
279	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
280	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
282	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
283	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
284	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
285	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
286	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
287	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
288	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
289	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
290	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
291	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
292	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
293	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
294	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
295	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
296	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
297	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
298	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
299	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
300	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
301	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
302	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
303	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
304	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
305	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
306	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
307	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
308	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
309	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
310	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
311	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
312	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
313	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
314	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
315	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
316	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
317	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
318	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
319	C₄²×C₇	C₂⁴	1	4	yes	—
320	C₄²×C₇	C₂⁴	1	4	yes	—
321	C₄²×C₇	C₂⁴	1	4	yes	—
322	C₄²×C₇	C₂⁴	1	4	yes	—
323	C₄²×C₇	C₂⁴	1	8	yes	—
324	C₄²×C₇	C₂⁴	1	16	yes	—
325	C₂²×#41	C₂²×C₇	1	2	yes	—
326	C₂²×#41	C₂²×C₇	1	4	yes	—
327	#563	C₂²×C₇	1	32	yes	complemented
328	#562	C₂²×C₇	1	32	yes	complemented
329	#554	C₂²×C₇	1	32	yes	complemented
330	#553	C₂²×C₇	1	32	yes	complemented
331	#553	C₂²×C₇	1	32	yes	complemented
332	#547	C₂²×C₇	1	64	yes	complemented
333	#547	C₂²×C₇	1	32	yes	complemented
334	#544	C₂²×C₇	1	32	yes	complemented
335	#540	C₂²×C₇	1	32	yes	complemented
336	#539	C₂²×C₇	1	32	yes	complemented
337	#539	C₂²×C₇	1	64	yes	complemented
338	#537	C₂²×C₇	1	32	yes	complemented
339	#532	C₂²×C₇	1	16	yes	complemented
340	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
341	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
342	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	—
343	C₂×#127	C₂²×C₇	1	1	yes	characteristic
344	#529	C₂²×C₇	1	16	yes	complemented
345	C₂×#126	C₂²×C₇	1	2	yes	—
346	C₂×#126	C₂²×C₇	1	4	yes	—
347	C₂×#126	C₂²×C₇	1	4	yes	—
348	C₂×#125	C₂²×C₇	1	2	yes	—
349	C₂×#125	C₂²×C₇	1	2	yes	—
350	C₂×#125	C₂²×C₇	1	2	yes	—
351	C₂×#125	C₂²×C₇	1	2	yes	—
352	C₂×#125	C₂²×C₇	1	1	yes	characteristic
353	C₂×#125	C₂²×C₇	1	4	yes	—
354	C₂×#125	C₂²×C₇	1	2	yes	—
355	C₂×#125	C₂²×C₇	1	16	yes	complemented
356	C₂×#124	C₂²×C₇	1	1	yes	characteristic
357	C₂×#124	C₂²×C₇	1	2	yes	—
358	C₂×#123	C₂²×C₇	1	2	yes	—
359	C₂×#123	C₂²×C₇	1	4	yes	—
360	C₂×#123	C₂²×C₇	1	4	yes	—
361	C₂×#123	C₂²×C₇	1	4	yes	—
362	C₂×#123	C₂²×C₇	1	4	yes	—
363	C₂×#123	C₂²×C₇	1	4	yes	—
364	C₂×#123	C₂²×C₇	1	4	yes	—
365	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
366	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
367	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
368	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
369	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
370	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
371	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
372	C₂×#121	C₂²×C₇	1	1	yes	characteristic
373	C₂×#121	C₂²×C₇	1	2	yes	—
374	C₂×#121	C₂²×C₇	1	2	yes	—
375	C₂×#121	C₂²×C₇	1	4	yes	—
376	C₂×#121	C₂²×C₇	1	4	yes	—
377	C₂×#121	C₂²×C₇	1	4	yes	—
378	C₂×#121	C₂²×C₇	1	2	yes	—
379	C₂×#121	C₂²×C₇	1	4	yes	—
380	C₂×#121	C₂²×C₇	1	2	yes	—
381	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
383	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
385	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
386	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
387	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
388	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
389	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
390	C₂×#117	C₂²×C₇	1	2	yes	—
391	C₂×#117	C₂²×C₇	1	2	yes	—
392	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
393	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
394	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
395	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
396	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	—
397	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
398	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
399	C₂³×C₇	—	2	2	no	—
400	C₂³×C₇	—	2	2	no	—
401	C₂³×C₇	—	2	4	no	—
402	C₂³×C₇	—	2	8	no	—
403	C₂³×C₇	—	2	4	no	—
404	C₂³×C₇	—	2	8	no	—
405	C₂³×C₇	—	2	8	no	—
406	C₂³×C₇	—	2	4	no	—
407	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
408	C₂³×C₇	C₂⁵	1	4	yes	—
409	C₂³×C₇	C₂⁵	1	8	yes	—
410	C₂³×C₇	C₂⁵	1	2	yes	—
411	C₂³×C₇	C₂⁵	1	1	yes	characteristic
412	C₇×Q₈	—	4	4	no	—
413	C₇×Q₈	—	4	16	no	—
414	C₇×Q₈	—	4	8	no	—
415	C₇×D₄	—	2	16	no	—
416	C₇×D₄	—	2	32	no	—
417	C₇×D₄	—	2	16	no	—
418	C₇×D₄	—	4	16	no	—
419	C₇×D₄	—	4	8	no	—
420	C₇×D₄	—	4	4	no	—
421	C₇×D₄	—	4	16	no	—
422	C₇×D₄	—	4	8	no	—
423	C₂×C₄×C₇	—	2	2	no	—
424	C₂×C₄×C₇	—	2	8	no	—
425	C₂×C₄×C₇	—	2	2	no	—
426	C₂×C₄×C₇	—	2	8	no	—
427	C₂×C₄×C₇	—	2	16	no	—
428	C₂×C₄×C₇	—	2	8	no	—
429	C₂×C₄×C₇	—	2	4	no	—
430	C₂×C₄×C₇	—	2	2	no	—
431	C₂×C₄×C₇	—	2	4	no	—
432	C₂×C₄×C₇	—	2	8	no	—
433	C₂×C₄×C₇	—	2	4	no	—
434	C₂×C₄×C₇	—	2	2	no	—
435	C₂×C₄×C₇	—	2	2	no	—
436	C₂×C₄×C₇	—	2	8	no	—
437	C₂×C₄×C₇	—	2	16	no	—
438	C₂×C₄×C₇	—	4	8	no	—
439	C₂×C₄×C₇	—	4	16	no	—
440	C₂×C₄×C₇	—	4	4	no	—
441	C₂×C₄×C₇	—	4	16	no	—
442	C₂×C₄×C₇	—	4	16	no	—
443	C₂×C₄×C₇	—	4	16	no	—
444	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
445	C₂×C₄×C₇	C₂⁵	1	2	yes	—
446	C₂×C₄×C₇	C₂⁵	1	4	yes	—
447	C₂×C₄×C₇	C₂⁵	1	2	yes	—
448	C₂×C₄×C₇	C₂⁵	1	2	yes	—
449	C₂×C₄×C₇	C₂⁵	1	2	yes	—
450	C₂×C₄×C₇	C₂⁵	1	2	yes	—
451	C₂×C₄×C₇	C₂⁵	1	4	yes	—
452	C₂×C₄×C₇	C₂⁵	1	8	yes	—
453	C₂×C₄×C₇	C₂⁵	1	4	yes	—
454	C₂×C₄×C₇	C₂⁵	1	8	yes	—
455	C₂×C₄×C₇	C₂⁵	1	8	yes	—
456	C₂×C₄×C₇	C₂⁵	1	2	yes	—
457	C₂×#41	—	4	8	no	—
458	C₂×#41	—	4	16	no	—
459	C₂×#41	C₂³×C₇	1	16	yes	—
460	C₂×#41	C₂³×C₇	1	32	yes	—
461	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
462	C₂²×Q₈	C₂³×C₇	1	4	yes	—
463	C₂²×Q₈	C₂³×C₇	1	2	yes	—
464	C₂²×D₄	C₂³×C₇	1	2	yes	—
465	C₂²×D₄	C₂³×C₇	1	2	yes	—
466	C₂²×D₄	C₂³×C₇	1	4	yes	—
467	C₂²×D₄	C₂³×C₇	1	4	yes	—
468	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₇	1	2	yes	—
470	C₂²×D₄	C₂³×C₇	1	4	yes	—
471	C₂²×D₄	C₂³×C₇	1	2	yes	—
472	C₂³×C₄	C₂³×C₇	1	2	yes	—
473	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₇	1	2	yes	—
476	C₂³×C₄	C₂³×C₇	1	2	yes	—
477	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₇	1	4	yes	—
479	C₂³×C₄	C₂³×C₇	1	4	yes	—
480	C₂³×C₄	C₂³×C₇	1	4	yes	—
481	C₂³×C₄	C₂³×C₇	1	4	yes	—
482	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
483	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
484	C₄⋊Q₈	C₂³×C₇	1	32	yes	—
485	#127	C₂³×C₇	1	8	yes	—
486	#126	C₂³×C₇	1	16	yes	—
487	#126	C₂³×C₇	1	32	yes	—
488	#126	C₂³×C₇	1	32	yes	—
489	#125	C₂³×C₇	1	16	yes	—
490	#125	C₂³×C₇	1	16	yes	—
491	#125	C₂³×C₇	1	16	yes	—
492	#125	C₂³×C₇	1	16	yes	—
493	#125	C₂³×C₇	1	8	yes	—
494	#125	C₂³×C₇	1	32	yes	—
495	#125	C₂³×C₇	1	16	yes	—
496	#124	C₂³×C₇	1	8	yes	—
497	#124	C₂³×C₇	1	16	yes	—
498	#123	C₂³×C₇	1	16	yes	—
499	#123	C₂³×C₇	1	32	yes	—
500	#123	C₂³×C₇	1	32	yes	—
501	#123	C₂³×C₇	1	32	yes	—
502	#123	C₂³×C₇	1	32	yes	—
503	#123	C₂³×C₇	1	32	yes	—
504	#123	C₂³×C₇	1	32	yes	—
505	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
506	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
507	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
508	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
509	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
510	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
511	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
512	#121	C₂³×C₇	1	8	yes	—
513	#121	C₂³×C₇	1	16	yes	—
514	#121	C₂³×C₇	1	16	yes	—
515	#121	C₂³×C₇	1	32	yes	—
516	#121	C₂³×C₇	1	32	yes	—
517	#121	C₂³×C₇	1	32	yes	—
518	#121	C₂³×C₇	1	16	yes	—
519	#121	C₂³×C₇	1	32	yes	—
520	#121	C₂³×C₇	1	16	yes	—
521	C₄×Q₈	C₂³×C₇	1	8	yes	—
522	C₄×D₄	C₂³×C₇	1	16	yes	—
523	C₄×D₄	C₂³×C₇	1	8	yes	—
524	C₄×D₄	C₂³×C₇	1	16	yes	—
525	C₄×D₄	C₂³×C₇	1	16	yes	—
526	C₄×D₄	C₂³×C₇	1	32	yes	—
527	C₄×D₄	C₂³×C₇	1	32	yes	—
528	C₄×D₄	C₂³×C₇	1	16	yes	—
529	C₄×D₄	C₂³×C₇	1	16	yes	—
530	#117	C₂³×C₇	1	16	yes	—
531	#117	C₂³×C₇	1	16	yes	—
532	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
538	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
539	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
540	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
541	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
543	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
544	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
546	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
547	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
548	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
549	C₂×C₄⋊C₄	C₂³×C₇	1	32	yes	—
550	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
551	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
555	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
570	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₇	1	2	yes	—
572	C₂×C₄²	C₂³×C₇	1	4	yes	—
573	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
574	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₇	1	8	yes	—
577	C₂²×C₇	—	2	2	no	—
578	C₂²×C₇	—	2	2	no	—
579	C₂²×C₇	—	2	8	no	—
580	C₂²×C₇	—	2	4	no	—
581	C₂²×C₇	—	2	8	no	—
582	C₂²×C₇	—	2	4	no	—
583	C₂²×C₇	—	2	8	no	—
584	C₂²×C₇	—	2	8	no	—
585	C₂²×C₇	—	2	4	no	—
586	C₂²×C₇	—	4	8	no	—
587	C₂²×C₇	—	4	16	no	—
588	C₂²×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
589	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
590	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
591	C₂²×C₇	#585	1	2	yes	—
592	C₂²×C₇	C₂⁶	1	1	yes	characteristic
593	C₄×C₇	—	2	2	no	—
594	C₄×C₇	—	2	8	no	—
595	C₄×C₇	—	2	2	no	—
596	C₄×C₇	—	2	8	no	—
597	C₄×C₇	—	2	4	no	—
598	C₄×C₇	—	2	2	no	—
599	C₄×C₇	—	2	4	no	—
600	C₄×C₇	—	2	8	no	—
601	C₄×C₇	—	2	4	no	—
602	C₄×C₇	—	2	2	no	—
603	C₄×C₇	—	2	2	no	—
604	C₄×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
605	C₂⁴	C₂⁴×C₇	1	2	yes	—
606	C₂⁴	C₂⁴×C₇	1	4	yes	—
607	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
608	#41	—	4	32	no	—
609	#41	—	4	64	no	—
610	C₂×Q₈	—	4	8	no	—
611	C₂×Q₈	—	4	4	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
614	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
615	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
616	C₂×D₄	—	2	8	no	—
617	C₂×D₄	—	2	16	no	—
618	C₂×D₄	—	2	8	no	—
619	C₂×D₄	—	4	8	no	—
620	C₂×D₄	—	4	4	no	—
621	C₂×D₄	—	4	8	no	—
622	C₂×D₄	—	4	4	no	—
623	C₂×D₄	—	4	2	no	—
624	C₂×D₄	C₂⁴×C₇	1	8	yes	—
625	C₂×D₄	C₂⁴×C₇	1	8	yes	—
626	C₂×D₄	C₂⁴×C₇	1	16	yes	—
627	C₂×D₄	C₂⁴×C₇	1	16	yes	—
628	C₂×D₄	C₂⁴×C₇	1	4	yes	—
629	C₂×D₄	C₂⁴×C₇	1	8	yes	—
630	C₂×D₄	C₂⁴×C₇	1	16	yes	—
631	C₂×D₄	C₂⁴×C₇	1	8	yes	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	8	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	8	no	—
636	C₂²×C₄	—	4	4	no	—
637	C₂²×C₄	—	4	8	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	8	no	—
640	C₂²×C₄	—	4	8	no	—
641	C₂²×C₄	—	4	8	no	—
642	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
649	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
650	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
652	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
654	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
655	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
656	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
657	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
658	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
659	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
660	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
661	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
662	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
663	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
664	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
665	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
666	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
667	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
668	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
669	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
670	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
671	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
672	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
673	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
674	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
675	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
676	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
677	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
678	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
679	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
680	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
681	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
682	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
683	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
684	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
685	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
686	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
687	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
688	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
689	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
690	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
691	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
692	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
693	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
694	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
695	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
696	C₄²	C₂⁴×C₇	1	4	yes	—
697	C₄²	C₂⁴×C₇	1	4	yes	—
698	C₄²	C₂⁴×C₇	1	4	yes	—
699	C₄²	C₂⁴×C₇	1	4	yes	—
700	C₄²	C₂⁴×C₇	1	8	yes	—
701	C₄²	C₂⁴×C₇	1	16	yes	—
702	C₂×C₇	—	2	4	no	—
703	C₂×C₇	—	4	4	no	—
704	C₂×C₇	—	4	8	no	—
705	C₂×C₇	#3559	1	4	yes	direct product factor
706	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
707	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
708	C₂×C₇	C₂×#585	1	1	yes	characteristic
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	2	8	no	—
713	C₂³	—	2	4	no	—
714	C₂³	—	2	8	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	2	4	no	—
717	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
718	C₂³	C₂⁵×C₇	1	4	yes	—
719	C₂³	C₂⁵×C₇	1	8	yes	—
720	C₂³	C₂⁵×C₇	1	2	yes	—
721	C₂³	C₂⁵×C₇	1	1	yes	characteristic
722	Q₈	—	4	4	no	—
723	Q₈	—	4	16	no	—
724	Q₈	—	4	8	no	—
725	D₄	—	2	16	no	—
726	D₄	—	2	32	no	—
727	D₄	—	2	16	no	—
728	D₄	—	4	16	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	4	no	—
731	D₄	—	4	16	no	—
732	D₄	—	4	8	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	8	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	8	no	—
737	C₂×C₄	—	2	16	no	—
738	C₂×C₄	—	2	8	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	8	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	8	no	—
747	C₂×C₄	—	2	16	no	—
748	C₂×C₄	—	4	8	no	—
749	C₂×C₄	—	4	16	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	16	no	—
752	C₂×C₄	—	4	16	no	—
753	C₂×C₄	—	4	16	no	—
754	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
755	C₂×C₄	C₂⁵×C₇	1	2	yes	—
756	C₂×C₄	C₂⁵×C₇	1	4	yes	—
757	C₂×C₄	C₂⁵×C₇	1	2	yes	—
758	C₂×C₄	C₂⁵×C₇	1	2	yes	—
759	C₂×C₄	C₂⁵×C₇	1	2	yes	—
760	C₂×C₄	C₂⁵×C₇	1	2	yes	—
761	C₂×C₄	C₂⁵×C₇	1	4	yes	—
762	C₂×C₄	C₂⁵×C₇	1	8	yes	—
763	C₂×C₄	C₂⁵×C₇	1	4	yes	—
764	C₂×C₄	C₂⁵×C₇	1	8	yes	—
765	C₂×C₄	C₂⁵×C₇	1	8	yes	—
766	C₂×C₄	C₂⁵×C₇	1	2	yes	—
767	C₇	C₂×#3559	1	1	yes	characteristic, direct product factor, Sylow
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	8	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	8	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	8	no	—
775	C₂²	—	2	8	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	4	8	no	—
778	C₂²	—	4	16	no	—
779	C₂²	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
780	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
781	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
782	C₂²	C₇×#585	1	2	yes	—
783	C₂²	C₂⁶×C₇	1	1	yes	characteristic
784	C₄	—	2	2	no	—
785	C₄	—	2	8	no	—
786	C₄	—	2	2	no	—
787	C₄	—	2	8	no	—
788	C₄	—	2	4	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	4	no	—
791	C₄	—	2	8	no	—
792	C₄	—	2	4	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
796	C₂	—	2	4	no	—
797	C₂	—	4	4	no	—
798	C₂	—	4	8	no	—
799	C₂	C₇×#3559	1	4	yes	direct product factor
800	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
801	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
802	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×#3559	C₂	direct (N × H)
2. C₂×C₇×#563	C₂	semidirect
3. C₂×C₇×#562	C₂	semidirect
4. C₂×C₇×#554	C₂	semidirect
5. C₂×C₇×#553	C₂	semidirect
6. C₂×C₇×#553	C₂	semidirect
7. C₂×C₇×#547	C₂	semidirect
8. C₂×C₇×#547	C₂	semidirect
9. C₂×C₇×#544	C₂	semidirect
10. C₂×C₇×#540	C₂	semidirect
11. C₂×C₇×#539	C₂	semidirect
12. C₂×C₇×#539	C₂	semidirect
13. C₂×C₇×#537	C₂	semidirect
14. C₂×C₇×#532	C₂	semidirect
15. C₂×C₇×#529	C₂	semidirect
16. C₂²×C₇×#125	C₂	semidirect
19. C₇×#563	C₂²	semidirect
20. C₇×#562	C₂²	semidirect
21. C₇×#554	C₂²	semidirect
22. C₇×#553	C₂²	semidirect
23. C₇×#553	C₂²	semidirect
24. C₇×#547	C₂²	semidirect
25. C₇×#547	C₂²	semidirect
26. C₇×#544	C₂²	semidirect
27. C₇×#540	C₂²	semidirect
28. C₇×#539	C₂²	semidirect
29. C₇×#539	C₂²	semidirect
30. C₇×#537	C₂²	semidirect
31. C₇×#532	C₂²	semidirect
36. C₇×#529	C₂²	semidirect
47. C₂×C₇×#125	C₂²	semidirect
91. C₂×#3559	C₇	direct (N × H)
212. #3559	C₂×C₇	direct (N × H)
213. C₂×#563	C₂×C₇	semidirect
214. C₂×#562	C₂×C₇	semidirect
215. C₂×#554	C₂×C₇	semidirect
216. C₂×#553	C₂×C₇	semidirect
217. C₂×#553	C₂×C₇	semidirect
218. C₂×#547	C₂×C₇	semidirect
219. C₂×#547	C₂×C₇	semidirect
220. C₂×#544	C₂×C₇	semidirect
221. C₂×#540	C₂×C₇	semidirect
222. C₂×#539	C₂×C₇	semidirect
223. C₂×#539	C₂×C₇	semidirect
224. C₂×#537	C₂×C₇	semidirect
225. C₂×#532	C₂×C₇	semidirect
226. C₂×#529	C₂×C₇	semidirect
227. C₂²×#125	C₂×C₇	semidirect
327. #563	C₂²×C₇	semidirect
328. #562	C₂²×C₇	semidirect
329. #554	C₂²×C₇	semidirect
330. #553	C₂²×C₇	semidirect
331. #553	C₂²×C₇	semidirect
332. #547	C₂²×C₇	semidirect
333. #547	C₂²×C₇	semidirect
334. #544	C₂²×C₇	semidirect
335. #540	C₂²×C₇	semidirect
336. #539	C₂²×C₇	semidirect
337. #539	C₂²×C₇	semidirect
338. #537	C₂²×C₇	semidirect
339. #532	C₂²×C₇	semidirect
344. #529	C₂²×C₇	semidirect
355. C₂×#125	C₂²×C₇	semidirect
705. C₂×C₇	#3559	direct (N × H)
767. C₇	C₂×#3559	direct (N × H)
799. C₂	C₇×#3559	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×#3559	2
C₂×C₇×#563	2
C₂×C₇×#562	2
C₂×C₇×#554	2
C₂×C₇×#553	2
C₂×C₇×#547	2
C₂×C₇×#544	2
C₂×C₇×#540	2
C₂×C₇×#539	2
C₂×C₇×#537	2
C₂×C₇×#532	2
C₂×C₇×#529	2
C₂²×C₇×#125	2
C₂×#3559	7

Subgroups — C2×C7×#3559 #13239948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3559 #13239948