Subgroups — C₂×C₇×#3564 #13239950

Order 1792.

6598 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3564	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×#563	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#556	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#554	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#552	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#551	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#551	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#544	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#542	C₂	1	2	yes	maximal, complemented
13	C₂×C₇×#541	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#541	C₂	1	2	yes	maximal, complemented
15	C₂×C₇×#539	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#539	C₂	1	2	yes	maximal, complemented
17	C₂×C₇×#538	C₂	1	1	yes	maximal, characteristic
18	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₇×#126	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#563	C₂²	1	32	yes	complemented
22	C₇×#563	C₂²	1	32	yes	complemented
23	C₇×#556	C₂²	1	32	yes	complemented
24	C₇×#554	C₂²	1	32	yes	complemented
25	C₇×#552	C₂²	1	32	yes	complemented
26	C₇×#552	C₂²	1	32	yes	complemented
27	C₇×#551	C₂²	1	32	yes	complemented
28	C₇×#551	C₂²	1	32	yes	complemented
29	C₇×#544	C₂²	1	16	yes	complemented
30	C₇×#543	C₂²	1	16	yes	complemented
31	C₇×#542	C₂²	1	32	yes	complemented
32	C₇×#541	C₂²	1	32	yes	complemented
33	C₇×#541	C₂²	1	32	yes	complemented
34	C₇×#539	C₂²	1	16	yes	complemented
35	C₇×#539	C₂²	1	32	yes	complemented
36	C₇×#538	C₂²	1	16	yes	—
37	C₇×#533	C₂²	1	16	yes	complemented
38	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
41	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
42	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
43	C₇×#529	C₂²	1	16	yes	complemented
44	C₂×C₇×#126	C₂²	1	2	yes	—
45	C₂×C₇×#126	C₂²	1	2	yes	—
46	C₂×C₇×#126	C₂²	1	2	yes	—
47	C₂×C₇×#126	C₂²	1	2	yes	—
48	C₂×C₇×#126	C₂²	1	2	yes	—
49	C₂×C₇×#126	C₂²	1	2	yes	—
50	C₂×C₇×#126	C₂²	1	2	yes	—
51	C₂×C₇×#126	C₂²	1	2	yes	—
52	C₂×C₇×#126	C₂²	1	2	yes	—
53	C₂×C₇×#126	C₂²	1	16	yes	complemented
54	C₂×C₇×#126	C₂²	1	2	yes	complemented
55	C₂×C₇×#126	C₂²	1	2	yes	complemented
56	C₂×C₇×#126	C₂²	1	2	yes	complemented
57	C₂×C₇×#126	C₂²	1	2	yes	complemented
58	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₇×#125	C₂²	1	2	yes	complemented
60	C₂×C₇×#125	C₂²	1	2	yes	complemented
61	C₂×C₇×#125	C₂²	1	2	yes	complemented
62	C₂×C₇×#125	C₂²	1	2	yes	complemented
63	C₂×C₇×#125	C₂²	1	2	yes	complemented
64	C₂×C₇×#125	C₂²	1	2	yes	complemented
65	C₂×C₇×#125	C₂²	1	2	yes	complemented
66	C₂×C₇×#125	C₂²	1	2	yes	complemented
67	C₂×C₇×#125	C₂²	1	2	yes	complemented
68	C₂×C₇×#124	C₂²	1	2	yes	—
69	C₂×C₇×#124	C₂²	1	2	yes	—
70	C₂×C₇×#124	C₂²	1	2	yes	—
71	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₇×#123	C₂²	1	2	yes	—
73	C₂×C₇×#123	C₂²	1	2	yes	—
74	C₂×C₇×#123	C₂²	1	2	yes	—
75	C₂×C₇×#123	C₂²	1	2	yes	—
76	C₂×C₇×#123	C₂²	1	2	yes	—
77	C₂×C₇×#123	C₂²	1	2	yes	—
78	C₂×C₇×#123	C₂²	1	2	yes	—
79	C₂×C₇×#123	C₂²	1	2	yes	complemented
80	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
81	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
82	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
83	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
84	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
85	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
86	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
87	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
88	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
89	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
90	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
91	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
92	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
93	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
94	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
95	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
96	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
97	C₂×C₇×#121	C₂²	1	1	yes	characteristic
98	C₂×C₇×#121	C₂²	1	2	yes	—
99	C₂×C₇×#120	C₂²	1	2	yes	—
100	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
102	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
105	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
106	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
107	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
108	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
109	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
110	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
111	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₇×#117	C₂²	1	2	yes	—
113	C₂×C₇×#117	C₂²	1	2	yes	—
114	C₂×C₇×#117	C₂²	1	2	yes	—
115	C₂×C₇×#117	C₂²	1	2	yes	—
116	C₂×C₇×#117	C₂²	1	2	yes	complemented
117	C₂×C₇×#117	C₂²	1	2	yes	complemented
118	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
122	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
123	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
125	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
126	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
127	C₂×#3564	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂⁵×C₇	C₂³	1	1	yes	characteristic
129	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
130	C₂²×C₇×Q₈	C₂³	1	2	yes	—
131	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
132	C₂²×C₇×Q₈	C₂³	1	2	yes	—
133	C₂²×C₇×Q₈	C₂³	1	2	yes	—
134	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
135	C₂²×C₇×D₄	C₂³	1	2	yes	—
136	C₂²×C₇×D₄	C₂³	1	2	yes	—
137	C₂²×C₇×D₄	C₂³	1	2	yes	—
138	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₇	C₂³	1	2	yes	—
146	C₂³×C₄×C₇	C₂³	1	2	yes	—
147	C₂³×C₄×C₇	C₂³	1	2	yes	—
148	C₂³×C₄×C₇	C₂³	1	2	yes	—
149	C₂³×C₄×C₇	C₂³	1	2	yes	—
150	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
151	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
152	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
153	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
154	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
155	C₇×#126	C₂³	1	16	yes	—
156	C₇×#126	C₂³	1	16	yes	—
157	C₇×#126	C₂³	1	16	yes	—
158	C₇×#126	C₂³	1	16	yes	—
159	C₇×#126	C₂³	1	16	yes	—
160	C₇×#126	C₂³	1	16	yes	—
161	C₇×#126	C₂³	1	16	yes	—
162	C₇×#126	C₂³	1	16	yes	—
163	C₇×#126	C₂³	1	16	yes	—
164	C₇×#126	C₂³	1	16	yes	complemented
165	C₇×#126	C₂³	1	16	yes	complemented
166	C₇×#126	C₂³	1	16	yes	complemented
167	C₇×#126	C₂³	1	16	yes	complemented
168	C₇×#125	C₂³	1	8	yes	complemented
169	C₇×#125	C₂³	1	16	yes	complemented
170	C₇×#125	C₂³	1	16	yes	complemented
171	C₇×#125	C₂³	1	16	yes	complemented
172	C₇×#125	C₂³	1	16	yes	complemented
173	C₇×#125	C₂³	1	16	yes	complemented
174	C₇×#125	C₂³	1	16	yes	complemented
175	C₇×#125	C₂³	1	16	yes	complemented
176	C₇×#125	C₂³	1	16	yes	complemented
177	C₇×#125	C₂³	1	16	yes	complemented
178	C₇×#124	C₂³	1	16	yes	—
179	C₇×#124	C₂³	1	16	yes	—
180	C₇×#124	C₂³	1	16	yes	—
181	C₇×#124	C₂³	1	8	yes	complemented
182	C₇×#123	C₂³	1	16	yes	—
183	C₇×#123	C₂³	1	16	yes	—
184	C₇×#123	C₂³	1	16	yes	—
185	C₇×#123	C₂³	1	16	yes	—
186	C₇×#123	C₂³	1	16	yes	—
187	C₇×#123	C₂³	1	16	yes	—
188	C₇×#123	C₂³	1	16	yes	—
189	C₇×#123	C₂³	1	16	yes	complemented
190	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
191	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
192	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
193	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
194	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
195	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
196	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
197	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
198	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
199	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
200	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
201	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
202	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
203	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
204	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
205	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
206	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
207	C₇×#121	C₂³	1	8	yes	—
208	C₇×#121	C₂³	1	16	yes	—
209	C₇×#120	C₂³	1	16	yes	—
210	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
211	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
212	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
213	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
214	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
215	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
216	C₄×C₇×D₄	C₂³	1	16	yes	—
217	C₄×C₇×D₄	C₂³	1	16	yes	—
218	C₄×C₇×D₄	C₂³	1	16	yes	—
219	C₄×C₇×D₄	C₂³	1	16	yes	—
220	C₄×C₇×D₄	C₂³	1	16	yes	—
221	C₄×C₇×D₄	C₂³	1	8	yes	complemented
222	C₇×#117	C₂³	1	16	yes	—
223	C₇×#117	C₂³	1	16	yes	—
224	C₇×#117	C₂³	1	16	yes	—
225	C₇×#117	C₂³	1	16	yes	—
226	C₇×#117	C₂³	1	16	yes	complemented
227	C₇×#117	C₂³	1	16	yes	complemented
228	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
229	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
230	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
231	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
232	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
233	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
234	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
235	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
236	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
237	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
238	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
239	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
240	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
241	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
242	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
243	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
244	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
245	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
246	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
247	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
248	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
249	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
250	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
251	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
252	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
253	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
254	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
256	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
259	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
261	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
265	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
266	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
267	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
268	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
269	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
270	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
271	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
272	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
273	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
274	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
275	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
276	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
277	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
278	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
279	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
280	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
281	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
282	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
283	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
284	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
285	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
286	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
287	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
288	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
289	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
290	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
293	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₇	C₂³	1	8	yes	—
295	C₂×C₄²×C₇	C₂³	1	2	yes	—
296	C₂×C₄²×C₇	C₂³	1	2	yes	—
297	C₂×C₄²×C₇	C₂³	1	2	yes	—
298	C₂×C₄²×C₇	C₂³	1	2	yes	—
299	C₂×C₄²×C₇	C₂³	1	2	yes	—
300	C₂×C₄²×C₇	C₂³	1	2	yes	—
301	C₂×C₄²×C₇	C₂³	1	2	yes	—
302	#3564	C₂×C₇	1	32	yes	direct product factor
303	C₂×#563	C₂×C₇	1	2	yes	complemented
304	C₂×#563	C₂×C₇	1	2	yes	complemented
305	C₂×#556	C₂×C₇	1	2	yes	complemented
306	C₂×#554	C₂×C₇	1	2	yes	complemented
307	C₂×#552	C₂×C₇	1	2	yes	complemented
308	C₂×#552	C₂×C₇	1	2	yes	complemented
309	C₂×#551	C₂×C₇	1	2	yes	complemented
310	C₂×#551	C₂×C₇	1	2	yes	complemented
311	C₂×#544	C₂×C₇	1	1	yes	characteristic, complemented
312	C₂×#543	C₂×C₇	1	1	yes	characteristic, complemented
313	C₂×#542	C₂×C₇	1	2	yes	complemented
314	C₂×#541	C₂×C₇	1	2	yes	complemented
315	C₂×#541	C₂×C₇	1	2	yes	complemented
316	C₂×#539	C₂×C₇	1	1	yes	characteristic, complemented
317	C₂×#539	C₂×C₇	1	2	yes	complemented
318	C₂×#538	C₂×C₇	1	1	yes	characteristic
319	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
320	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
321	C₂²×#126	C₂×C₇	1	1	yes	characteristic, complemented
322	C₂⁴×C₇	—	2	4	no	—
323	C₂⁴×C₇	—	4	2	no	—
324	C₂⁴×C₇	—	4	2	no	—
325	C₂⁴×C₇	C₂⁴	1	2	yes	—
326	C₂⁴×C₇	C₂⁴	1	2	yes	—
327	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
328	C₂⁴×C₇	C₂⁴	1	4	yes	—
329	C₂×C₇×Q₈	—	4	2	no	—
330	C₂×C₇×Q₈	—	4	4	no	—
331	C₂×C₇×Q₈	—	4	4	no	—
332	C₂×C₇×Q₈	—	4	2	no	—
333	C₂×C₇×Q₈	—	4	4	no	—
334	C₂×C₇×Q₈	—	4	2	no	—
335	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
336	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
337	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
338	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
339	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
340	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
341	C₂×C₇×D₄	—	2	8	no	—
342	C₂×C₇×D₄	—	4	4	no	—
343	C₂×C₇×D₄	—	4	2	no	—
344	C₂×C₇×D₄	—	4	4	no	—
345	C₂×C₇×D₄	C₂⁴	1	8	yes	—
346	C₂×C₇×D₄	C₂⁴	1	8	yes	—
347	C₂×C₇×D₄	C₂⁴	1	8	yes	—
348	C₂×C₇×D₄	C₂⁴	1	4	yes	—
349	C₂²×C₄×C₇	—	2	4	no	—
350	C₂²×C₄×C₇	—	2	4	no	—
351	C₂²×C₄×C₇	—	4	4	no	—
352	C₂²×C₄×C₇	—	4	2	no	—
353	C₂²×C₄×C₇	—	4	2	no	—
354	C₂²×C₄×C₇	—	4	2	no	—
355	C₂²×C₄×C₇	—	4	4	no	—
356	C₂²×C₄×C₇	—	4	4	no	—
357	C₂²×C₄×C₇	—	4	4	no	—
358	C₂²×C₄×C₇	—	4	4	no	—
359	C₂²×C₄×C₇	—	4	2	no	—
360	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
361	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
362	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
365	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
366	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
376	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
377	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
379	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
380	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
381	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
382	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
383	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
384	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
385	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
386	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
387	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
388	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
389	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
390	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
391	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
392	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
393	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
394	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
395	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
396	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
397	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
398	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
399	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
400	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
401	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
402	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
403	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
404	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
405	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
406	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
407	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
408	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
409	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
410	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
411	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
412	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
413	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
414	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
415	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
416	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
417	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
418	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
419	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
420	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
421	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
422	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
423	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
424	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
425	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
426	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
427	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
428	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
429	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
430	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
431	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
432	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
433	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
434	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
435	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
436	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
437	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
438	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
439	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
440	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
441	C₄²×C₇	C₂⁴	1	4	yes	—
442	C₄²×C₇	C₂⁴	1	4	yes	—
443	C₄²×C₇	C₂⁴	1	4	yes	—
444	C₄²×C₇	C₂⁴	1	4	yes	—
445	C₄²×C₇	C₂⁴	1	8	yes	—
446	C₄²×C₇	C₂⁴	1	8	yes	—
447	C₄²×C₇	C₂⁴	1	8	yes	—
448	C₄²×C₇	C₂⁴	1	8	yes	—
449	C₄²×C₇	C₂⁴	1	8	yes	—
450	C₄²×C₇	C₂⁴	1	8	yes	—
451	C₄²×C₇	C₂⁴	1	8	yes	—
452	#563	C₂²×C₇	1	32	yes	complemented
453	#563	C₂²×C₇	1	32	yes	complemented
454	#556	C₂²×C₇	1	32	yes	complemented
455	#554	C₂²×C₇	1	32	yes	complemented
456	#552	C₂²×C₇	1	32	yes	complemented
457	#552	C₂²×C₇	1	32	yes	complemented
458	#551	C₂²×C₇	1	32	yes	complemented
459	#551	C₂²×C₇	1	32	yes	complemented
460	#544	C₂²×C₇	1	16	yes	complemented
461	#543	C₂²×C₇	1	16	yes	complemented
462	#542	C₂²×C₇	1	32	yes	complemented
463	#541	C₂²×C₇	1	32	yes	complemented
464	#541	C₂²×C₇	1	32	yes	complemented
465	#539	C₂²×C₇	1	16	yes	complemented
466	#539	C₂²×C₇	1	32	yes	complemented
467	#538	C₂²×C₇	1	16	yes	—
468	#533	C₂²×C₇	1	16	yes	complemented
469	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
470	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
471	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
472	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
473	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
474	#529	C₂²×C₇	1	16	yes	complemented
475	C₂×#126	C₂²×C₇	1	2	yes	—
476	C₂×#126	C₂²×C₇	1	2	yes	—
477	C₂×#126	C₂²×C₇	1	2	yes	—
478	C₂×#126	C₂²×C₇	1	2	yes	—
479	C₂×#126	C₂²×C₇	1	2	yes	—
480	C₂×#126	C₂²×C₇	1	2	yes	—
481	C₂×#126	C₂²×C₇	1	2	yes	—
482	C₂×#126	C₂²×C₇	1	2	yes	—
483	C₂×#126	C₂²×C₇	1	2	yes	—
484	C₂×#126	C₂²×C₇	1	16	yes	complemented
485	C₂×#126	C₂²×C₇	1	2	yes	complemented
486	C₂×#126	C₂²×C₇	1	2	yes	complemented
487	C₂×#126	C₂²×C₇	1	2	yes	complemented
488	C₂×#126	C₂²×C₇	1	2	yes	complemented
489	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
490	C₂×#125	C₂²×C₇	1	2	yes	complemented
491	C₂×#125	C₂²×C₇	1	2	yes	complemented
492	C₂×#125	C₂²×C₇	1	2	yes	complemented
493	C₂×#125	C₂²×C₇	1	2	yes	complemented
494	C₂×#125	C₂²×C₇	1	2	yes	complemented
495	C₂×#125	C₂²×C₇	1	2	yes	complemented
496	C₂×#125	C₂²×C₇	1	2	yes	complemented
497	C₂×#125	C₂²×C₇	1	2	yes	complemented
498	C₂×#125	C₂²×C₇	1	2	yes	complemented
499	C₂×#124	C₂²×C₇	1	2	yes	—
500	C₂×#124	C₂²×C₇	1	2	yes	—
501	C₂×#124	C₂²×C₇	1	2	yes	—
502	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
503	C₂×#123	C₂²×C₇	1	2	yes	—
504	C₂×#123	C₂²×C₇	1	2	yes	—
505	C₂×#123	C₂²×C₇	1	2	yes	—
506	C₂×#123	C₂²×C₇	1	2	yes	—
507	C₂×#123	C₂²×C₇	1	2	yes	—
508	C₂×#123	C₂²×C₇	1	2	yes	—
509	C₂×#123	C₂²×C₇	1	2	yes	—
510	C₂×#123	C₂²×C₇	1	2	yes	complemented
511	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
512	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
513	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
514	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
515	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
516	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
517	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
518	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
519	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
520	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
521	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
522	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
523	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
524	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
525	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
526	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
527	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
528	C₂×#121	C₂²×C₇	1	1	yes	characteristic
529	C₂×#121	C₂²×C₇	1	2	yes	—
530	C₂×#120	C₂²×C₇	1	2	yes	—
531	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
532	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
533	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
534	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
535	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
536	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
537	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
538	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
539	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
540	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
541	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
542	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
543	C₂×#117	C₂²×C₇	1	2	yes	—
544	C₂×#117	C₂²×C₇	1	2	yes	—
545	C₂×#117	C₂²×C₇	1	2	yes	—
546	C₂×#117	C₂²×C₇	1	2	yes	—
547	C₂×#117	C₂²×C₇	1	2	yes	complemented
548	C₂×#117	C₂²×C₇	1	2	yes	complemented
549	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
550	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
551	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
552	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
553	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
554	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
555	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
556	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
557	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
558	C₂³×C₇	—	2	2	no	—
559	C₂³×C₇	—	2	2	no	—
560	C₂³×C₇	—	2	4	no	—
561	C₂³×C₇	—	2	4	no	—
562	C₂³×C₇	—	2	4	no	—
563	C₂³×C₇	—	2	4	no	—
564	C₂³×C₇	—	2	4	no	—
565	C₂³×C₇	—	2	4	no	—
566	C₂³×C₇	—	2	8	no	—
567	C₂³×C₇	—	4	4	no	—
568	C₂³×C₇	—	4	4	no	—
569	C₂³×C₇	—	8	8	no	—
570	C₂³×C₇	2₋¹⁺⁴	1	4	yes	—
571	C₂³×C₇	C₂⁵	1	4	yes	—
572	C₂³×C₇	C₂⁵	1	4	yes	—
573	C₂³×C₇	C₂⁵	1	2	yes	—
574	C₂³×C₇	C₂⁵	1	1	yes	characteristic
575	C₇×Q₈	—	4	4	no	—
576	C₇×Q₈	—	4	8	no	—
577	C₇×Q₈	—	4	8	no	—
578	C₇×Q₈	—	4	4	no	—
579	C₇×Q₈	—	4	8	no	—
580	C₇×Q₈	—	4	4	no	—
581	C₇×D₄	—	2	16	no	—
582	C₇×D₄	—	4	8	no	—
583	C₇×D₄	—	4	4	no	—
584	C₇×D₄	—	4	8	no	—
585	C₂×C₄×C₇	—	2	8	no	—
586	C₂×C₄×C₇	—	2	8	no	—
587	C₂×C₄×C₇	—	2	2	no	—
588	C₂×C₄×C₇	—	2	2	no	—
589	C₂×C₄×C₇	—	2	4	no	—
590	C₂×C₄×C₇	—	2	4	no	—
591	C₂×C₄×C₇	—	2	2	no	—
592	C₂×C₄×C₇	—	2	4	no	—
593	C₂×C₄×C₇	—	2	4	no	—
594	C₂×C₄×C₇	—	2	4	no	—
595	C₂×C₄×C₇	—	2	4	no	—
596	C₂×C₄×C₇	—	2	4	no	—
597	C₂×C₄×C₇	—	2	2	no	—
598	C₂×C₄×C₇	—	2	2	no	—
599	C₂×C₄×C₇	—	2	4	no	—
600	C₂×C₄×C₇	—	2	4	no	—
601	C₂×C₄×C₇	—	2	2	no	—
602	C₂×C₄×C₇	—	2	4	no	—
603	C₂×C₄×C₇	—	4	8	no	—
604	C₂×C₄×C₇	—	4	4	no	—
605	C₂×C₄×C₇	—	4	4	no	—
606	C₂×C₄×C₇	—	4	4	no	—
607	C₂×C₄×C₇	—	4	8	no	—
608	C₂×C₄×C₇	—	4	8	no	—
609	C₂×C₄×C₇	—	4	8	no	—
610	C₂×C₄×C₇	—	4	8	no	—
611	C₂×C₄×C₇	—	4	4	no	—
612	C₂×C₄×C₇	C₂⁵	1	2	yes	—
613	C₂×C₄×C₇	C₂⁵	1	2	yes	—
614	C₂×C₄×C₇	C₂⁵	1	4	yes	—
615	C₂×C₄×C₇	C₂⁵	1	4	yes	—
616	C₂×C₄×C₇	C₂⁵	1	2	yes	—
617	C₂×C₄×C₇	C₂⁵	1	4	yes	—
618	C₂×C₄×C₇	C₂⁵	1	2	yes	—
619	C₂×C₄×C₇	C₂⁵	1	2	yes	—
620	C₂×C₄×C₇	C₂⁵	1	4	yes	—
621	C₂×C₄×C₇	C₂⁵	1	4	yes	—
622	C₂×C₄×C₇	C₂⁵	1	2	yes	—
623	C₂×C₄×C₇	C₂⁵	1	4	yes	—
624	C₂×C₄×C₇	C₂⁵	1	4	yes	—
625	C₂×C₄×C₇	C₂⁵	1	4	yes	—
626	C₂×C₄×C₇	C₂⁵	1	4	yes	—
627	C₂×C₄×C₇	C₂⁵	1	4	yes	—
628	C₂⁵	C₂³×C₇	1	1	yes	characteristic
629	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
630	C₂²×Q₈	C₂³×C₇	1	2	yes	—
631	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
632	C₂²×Q₈	C₂³×C₇	1	2	yes	—
633	C₂²×Q₈	C₂³×C₇	1	2	yes	—
634	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
635	C₂²×D₄	C₂³×C₇	1	2	yes	—
636	C₂²×D₄	C₂³×C₇	1	2	yes	—
637	C₂²×D₄	C₂³×C₇	1	2	yes	—
638	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
639	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
640	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
641	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
642	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
643	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
644	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
645	C₂³×C₄	C₂³×C₇	1	2	yes	—
646	C₂³×C₄	C₂³×C₇	1	2	yes	—
647	C₂³×C₄	C₂³×C₇	1	2	yes	—
648	C₂³×C₄	C₂³×C₇	1	2	yes	—
649	C₂³×C₄	C₂³×C₇	1	2	yes	—
650	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
651	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
652	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
653	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
654	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
655	#126	C₂³×C₇	1	16	yes	—
656	#126	C₂³×C₇	1	16	yes	—
657	#126	C₂³×C₇	1	16	yes	—
658	#126	C₂³×C₇	1	16	yes	—
659	#126	C₂³×C₇	1	16	yes	—
660	#126	C₂³×C₇	1	16	yes	—
661	#126	C₂³×C₇	1	16	yes	—
662	#126	C₂³×C₇	1	16	yes	—
663	#126	C₂³×C₇	1	16	yes	—
664	#126	C₂³×C₇	1	16	yes	complemented
665	#126	C₂³×C₇	1	16	yes	complemented
666	#126	C₂³×C₇	1	16	yes	complemented
667	#126	C₂³×C₇	1	16	yes	complemented
668	#125	C₂³×C₇	1	8	yes	complemented
669	#125	C₂³×C₇	1	16	yes	complemented
670	#125	C₂³×C₇	1	16	yes	complemented
671	#125	C₂³×C₇	1	16	yes	complemented
672	#125	C₂³×C₇	1	16	yes	complemented
673	#125	C₂³×C₇	1	16	yes	complemented
674	#125	C₂³×C₇	1	16	yes	complemented
675	#125	C₂³×C₇	1	16	yes	complemented
676	#125	C₂³×C₇	1	16	yes	complemented
677	#125	C₂³×C₇	1	16	yes	complemented
678	#124	C₂³×C₇	1	16	yes	—
679	#124	C₂³×C₇	1	16	yes	—
680	#124	C₂³×C₇	1	16	yes	—
681	#124	C₂³×C₇	1	8	yes	complemented
682	#123	C₂³×C₇	1	16	yes	—
683	#123	C₂³×C₇	1	16	yes	—
684	#123	C₂³×C₇	1	16	yes	—
685	#123	C₂³×C₇	1	16	yes	—
686	#123	C₂³×C₇	1	16	yes	—
687	#123	C₂³×C₇	1	16	yes	—
688	#123	C₂³×C₇	1	16	yes	—
689	#123	C₂³×C₇	1	16	yes	complemented
690	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
691	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
692	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
693	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
694	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
695	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
696	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
697	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
698	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
699	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
700	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
701	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
702	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
703	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
704	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
705	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
706	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
707	#121	C₂³×C₇	1	8	yes	—
708	#121	C₂³×C₇	1	16	yes	—
709	#120	C₂³×C₇	1	16	yes	—
710	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
711	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
712	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
713	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
714	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
715	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
716	C₄×D₄	C₂³×C₇	1	16	yes	—
717	C₄×D₄	C₂³×C₇	1	16	yes	—
718	C₄×D₄	C₂³×C₇	1	16	yes	—
719	C₄×D₄	C₂³×C₇	1	16	yes	—
720	C₄×D₄	C₂³×C₇	1	16	yes	—
721	C₄×D₄	C₂³×C₇	1	8	yes	complemented
722	#117	C₂³×C₇	1	16	yes	—
723	#117	C₂³×C₇	1	16	yes	—
724	#117	C₂³×C₇	1	16	yes	—
725	#117	C₂³×C₇	1	16	yes	—
726	#117	C₂³×C₇	1	16	yes	complemented
727	#117	C₂³×C₇	1	16	yes	complemented
728	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
734	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
735	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
736	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
737	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
738	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
739	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
740	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
741	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
745	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
746	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
747	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
748	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
751	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
752	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
755	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
756	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
758	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
759	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
760	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
761	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
762	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
763	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
764	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
765	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
790	C₂×C₄²	C₂³×C₇	1	2	yes	—
791	C₂×C₄²	C₂³×C₇	1	2	yes	—
792	C₂×C₄²	C₂³×C₇	1	2	yes	—
793	C₂×C₄²	C₂³×C₇	1	2	yes	—
794	C₂×C₄²	C₂³×C₇	1	2	yes	—
795	C₂×C₄²	C₂³×C₇	1	2	yes	—
796	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
797	C₂×C₄²	C₂³×C₇	1	2	yes	—
798	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
799	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
800	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
801	C₂×C₄²	C₂³×C₇	1	8	yes	—
802	C₂²×C₇	—	2	2	no	—
803	C₂²×C₇	—	2	2	no	—
804	C₂²×C₇	—	2	8	no	—
805	C₂²×C₇	—	2	4	no	—
806	C₂²×C₇	—	2	4	no	—
807	C₂²×C₇	—	2	4	no	—
808	C₂²×C₇	—	2	4	no	—
809	C₂²×C₇	—	2	4	no	—
810	C₂²×C₇	—	2	4	no	—
811	C₂²×C₇	—	4	8	no	—
812	C₂²×C₇	—	4	8	no	—
813	C₂²×C₇	—	8	8	no	—
814	C₂²×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
815	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
816	C₂²×C₇	#585	1	2	yes	—
817	C₂²×C₇	#585	1	2	yes	—
818	C₂²×C₇	C₂⁶	1	1	yes	characteristic
819	C₄×C₇	—	2	2	no	—
820	C₄×C₇	—	2	2	no	—
821	C₄×C₇	—	2	4	no	—
822	C₄×C₇	—	2	4	no	—
823	C₄×C₇	—	2	2	no	—
824	C₄×C₇	—	2	4	no	—
825	C₄×C₇	—	2	4	no	—
826	C₄×C₇	—	2	4	no	—
827	C₄×C₇	—	2	4	no	—
828	C₄×C₇	—	2	4	no	—
829	C₄×C₇	—	2	2	no	—
830	C₄×C₇	—	2	2	no	—
831	C₄×C₇	—	2	4	no	—
832	C₄×C₇	—	2	4	no	—
833	C₄×C₇	—	2	2	no	—
834	C₄×C₇	—	2	4	no	—
835	C₂⁴	—	2	4	no	—
836	C₂⁴	—	4	2	no	—
837	C₂⁴	—	4	2	no	—
838	C₂⁴	C₂⁴×C₇	1	2	yes	—
839	C₂⁴	C₂⁴×C₇	1	2	yes	—
840	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
841	C₂⁴	C₂⁴×C₇	1	4	yes	—
842	C₂×Q₈	—	4	2	no	—
843	C₂×Q₈	—	4	4	no	—
844	C₂×Q₈	—	4	4	no	—
845	C₂×Q₈	—	4	2	no	—
846	C₂×Q₈	—	4	4	no	—
847	C₂×Q₈	—	4	2	no	—
848	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
849	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
850	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
851	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
852	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
853	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
854	C₂×D₄	—	2	8	no	—
855	C₂×D₄	—	4	4	no	—
856	C₂×D₄	—	4	2	no	—
857	C₂×D₄	—	4	4	no	—
858	C₂×D₄	C₂⁴×C₇	1	8	yes	—
859	C₂×D₄	C₂⁴×C₇	1	8	yes	—
860	C₂×D₄	C₂⁴×C₇	1	8	yes	—
861	C₂×D₄	C₂⁴×C₇	1	4	yes	—
862	C₂²×C₄	—	2	4	no	—
863	C₂²×C₄	—	2	4	no	—
864	C₂²×C₄	—	4	4	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	4	no	—
869	C₂²×C₄	—	4	4	no	—
870	C₂²×C₄	—	4	4	no	—
871	C₂²×C₄	—	4	4	no	—
872	C₂²×C₄	—	4	2	no	—
873	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
886	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
888	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
890	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
891	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
892	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
893	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
894	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
895	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
896	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
897	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
898	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
899	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
900	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
901	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
902	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
903	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
904	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
905	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
906	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
907	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
908	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
909	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
910	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
911	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
912	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
913	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
914	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
915	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
916	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
917	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
918	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
919	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
920	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
921	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
922	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
923	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
924	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
925	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
926	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
927	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
928	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
929	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
930	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
931	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
932	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
933	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
934	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
935	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
936	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
937	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
938	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
939	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
940	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
941	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
942	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
943	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
944	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
945	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
946	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
947	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
948	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
949	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
950	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
951	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
952	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
953	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
954	C₄²	C₂⁴×C₇	1	4	yes	—
955	C₄²	C₂⁴×C₇	1	4	yes	—
956	C₄²	C₂⁴×C₇	1	4	yes	—
957	C₄²	C₂⁴×C₇	1	4	yes	—
958	C₄²	C₂⁴×C₇	1	8	yes	—
959	C₄²	C₂⁴×C₇	1	8	yes	—
960	C₄²	C₂⁴×C₇	1	8	yes	—
961	C₄²	C₂⁴×C₇	1	8	yes	—
962	C₄²	C₂⁴×C₇	1	8	yes	—
963	C₄²	C₂⁴×C₇	1	8	yes	—
964	C₄²	C₂⁴×C₇	1	8	yes	—
965	C₂×C₇	—	2	4	no	—
966	C₂×C₇	—	4	4	no	—
967	C₂×C₇	—	4	4	no	—
968	C₂×C₇	#3564	1	4	yes	direct product factor
969	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
970	C₂×C₇	C₂×#585	1	1	yes	characteristic
971	C₂×C₇	C₂×#585	1	1	yes	characteristic
972	C₂³	—	2	2	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	4	no	—
975	C₂³	—	2	4	no	—
976	C₂³	—	2	4	no	—
977	C₂³	—	2	4	no	—
978	C₂³	—	2	4	no	—
979	C₂³	—	2	4	no	—
980	C₂³	—	2	8	no	—
981	C₂³	—	4	4	no	—
982	C₂³	—	4	4	no	—
983	C₂³	—	8	8	no	—
984	C₂³	C₇×2₋¹⁺⁴	1	4	yes	—
985	C₂³	C₂⁵×C₇	1	4	yes	—
986	C₂³	C₂⁵×C₇	1	4	yes	—
987	C₂³	C₂⁵×C₇	1	2	yes	—
988	C₂³	C₂⁵×C₇	1	1	yes	characteristic
989	Q₈	—	4	4	no	—
990	Q₈	—	4	8	no	—
991	Q₈	—	4	8	no	—
992	Q₈	—	4	4	no	—
993	Q₈	—	4	8	no	—
994	Q₈	—	4	4	no	—
995	D₄	—	2	16	no	—
996	D₄	—	4	8	no	—
997	D₄	—	4	4	no	—
998	D₄	—	4	8	no	—
999	C₂×C₄	—	2	8	no	—
1000	C₂×C₄	—	2	8	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	4	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	4	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	4	no	—
1007	C₂×C₄	—	2	4	no	—
1008	C₂×C₄	—	2	4	no	—
1009	C₂×C₄	—	2	4	no	—
1010	C₂×C₄	—	2	4	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	4	no	—
1014	C₂×C₄	—	2	4	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	4	no	—
1017	C₂×C₄	—	4	8	no	—
1018	C₂×C₄	—	4	4	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	8	no	—
1022	C₂×C₄	—	4	8	no	—
1023	C₂×C₄	—	4	8	no	—
1024	C₂×C₄	—	4	8	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1027	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1028	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1029	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1030	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1031	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1032	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1033	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1034	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1035	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1036	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1037	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1038	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1039	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1040	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1041	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1042	C₇	C₂×#3564	1	1	yes	characteristic, direct product factor, Sylow
1043	C₂²	—	2	8	no	—
1044	C₂²	—	2	2	no	—
1045	C₂²	—	2	2	no	—
1046	C₂²	—	2	4	no	—
1047	C₂²	—	2	4	no	—
1048	C₂²	—	2	4	no	—
1049	C₂²	—	2	4	no	—
1050	C₂²	—	2	4	no	—
1051	C₂²	—	2	4	no	—
1052	C₂²	—	4	8	no	—
1053	C₂²	—	4	8	no	—
1054	C₂²	—	8	8	no	—
1055	C₂²	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
1056	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
1057	C₂²	C₇×#585	1	2	yes	—
1058	C₂²	C₇×#585	1	2	yes	—
1059	C₂²	C₂⁶×C₇	1	1	yes	characteristic
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	4	no	—
1063	C₄	—	2	4	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	4	no	—
1066	C₄	—	2	4	no	—
1067	C₄	—	2	4	no	—
1068	C₄	—	2	4	no	—
1069	C₄	—	2	4	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	4	no	—
1073	C₄	—	2	4	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	4	no	—
1076	C₂	—	2	4	no	—
1077	C₂	—	4	4	no	—
1078	C₂	—	4	4	no	—
1079	C₂	C₇×#3564	1	4	yes	direct product factor
1080	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1081	C₂	C₂×C₇×#585	1	1	yes	characteristic
1082	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×#538	C₂
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×#3564	C₂	direct (N × H)
2. C₂×C₇×#563	C₂	semidirect
3. C₂×C₇×#563	C₂	semidirect
4. C₂×C₇×#556	C₂	semidirect
5. C₂×C₇×#554	C₂	semidirect
6. C₂×C₇×#552	C₂	semidirect
7. C₂×C₇×#552	C₂	semidirect
8. C₂×C₇×#551	C₂	semidirect
9. C₂×C₇×#551	C₂	semidirect
10. C₂×C₇×#544	C₂	semidirect
11. C₂×C₇×#543	C₂	semidirect
12. C₂×C₇×#542	C₂	semidirect
13. C₂×C₇×#541	C₂	semidirect
14. C₂×C₇×#541	C₂	semidirect
15. C₂×C₇×#539	C₂	semidirect
16. C₂×C₇×#539	C₂	semidirect
18. C₂×C₇×#533	C₂	semidirect
19. C₂×C₇×#529	C₂	semidirect
20. C₂²×C₇×#126	C₂	semidirect
21. C₇×#563	C₂²	semidirect
22. C₇×#563	C₂²	semidirect
23. C₇×#556	C₂²	semidirect
24. C₇×#554	C₂²	semidirect
25. C₇×#552	C₂²	semidirect
26. C₇×#552	C₂²	semidirect
27. C₇×#551	C₂²	semidirect
28. C₇×#551	C₂²	semidirect
29. C₇×#544	C₂²	semidirect
30. C₇×#543	C₂²	semidirect
31. C₇×#542	C₂²	semidirect
32. C₇×#541	C₂²	semidirect
33. C₇×#541	C₂²	semidirect
34. C₇×#539	C₂²	semidirect
35. C₇×#539	C₂²	semidirect
37. C₇×#533	C₂²	semidirect
38. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
40. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
43. C₇×#529	C₂²	semidirect
53. C₂×C₇×#126	C₂²	semidirect
54. C₂×C₇×#126	C₂²	semidirect
55. C₂×C₇×#126	C₂²	semidirect
56. C₂×C₇×#126	C₂²	semidirect
57. C₂×C₇×#126	C₂²	semidirect
58. C₂×C₇×#125	C₂²	semidirect
59. C₂×C₇×#125	C₂²	semidirect
60. C₂×C₇×#125	C₂²	semidirect
61. C₂×C₇×#125	C₂²	semidirect
62. C₂×C₇×#125	C₂²	semidirect
63. C₂×C₇×#125	C₂²	semidirect
64. C₂×C₇×#125	C₂²	semidirect
65. C₂×C₇×#125	C₂²	semidirect
66. C₂×C₇×#125	C₂²	semidirect
67. C₂×C₇×#125	C₂²	semidirect
71. C₂×C₇×#124	C₂²	semidirect
79. C₂×C₇×#123	C₂²	semidirect
92. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
93. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
94. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
95. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
96. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
100. C₂×C₄×C₇×Q₈	C₂²	semidirect
101. C₂×C₄×C₇×Q₈	C₂²	semidirect
102. C₂×C₄×C₇×Q₈	C₂²	semidirect
103. C₂×C₄×C₇×Q₈	C₂²	semidirect
104. C₂×C₄×C₇×Q₈	C₂²	semidirect
105. C₂×C₄×C₇×Q₈	C₂²	semidirect
111. C₂×C₄×C₇×D₄	C₂²	semidirect
116. C₂×C₇×#117	C₂²	semidirect
117. C₂×C₇×#117	C₂²	semidirect
121. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
127. C₂×#3564	C₇	direct (N × H)
150. C₇×C₄⋊Q₈	C₂³	semidirect
151. C₇×C₄⋊Q₈	C₂³	semidirect
152. C₇×C₄⋊Q₈	C₂³	semidirect
153. C₇×C₄⋊Q₈	C₂³	semidirect
154. C₇×C₄⋊Q₈	C₂³	semidirect
164. C₇×#126	C₂³	semidirect
165. C₇×#126	C₂³	semidirect
166. C₇×#126	C₂³	semidirect
167. C₇×#126	C₂³	semidirect
168. C₇×#125	C₂³	semidirect
169. C₇×#125	C₂³	semidirect
170. C₇×#125	C₂³	semidirect
171. C₇×#125	C₂³	semidirect
172. C₇×#125	C₂³	semidirect
173. C₇×#125	C₂³	semidirect
174. C₇×#125	C₂³	semidirect
175. C₇×#125	C₂³	semidirect
176. C₇×#125	C₂³	semidirect
177. C₇×#125	C₂³	semidirect
181. C₇×#124	C₂³	semidirect
189. C₇×#123	C₂³	semidirect
202. C₇×C₂²⋊Q₈	C₂³	semidirect
203. C₇×C₂²⋊Q₈	C₂³	semidirect
204. C₇×C₂²⋊Q₈	C₂³	semidirect
205. C₇×C₂²⋊Q₈	C₂³	semidirect
206. C₇×C₂²⋊Q₈	C₂³	semidirect
210. C₄×C₇×Q₈	C₂³	semidirect
211. C₄×C₇×Q₈	C₂³	semidirect
212. C₄×C₇×Q₈	C₂³	semidirect
213. C₄×C₇×Q₈	C₂³	semidirect
214. C₄×C₇×Q₈	C₂³	semidirect
215. C₄×C₇×Q₈	C₂³	semidirect
221. C₄×C₇×D₄	C₂³	semidirect
226. C₇×#117	C₂³	semidirect
227. C₇×#117	C₂³	semidirect
264. C₂×C₇×C₄⋊C₄	C₂³	semidirect
302. #3564	C₂×C₇	direct (N × H)
303. C₂×#563	C₂×C₇	semidirect
304. C₂×#563	C₂×C₇	semidirect
305. C₂×#556	C₂×C₇	semidirect
306. C₂×#554	C₂×C₇	semidirect
307. C₂×#552	C₂×C₇	semidirect
308. C₂×#552	C₂×C₇	semidirect
309. C₂×#551	C₂×C₇	semidirect
310. C₂×#551	C₂×C₇	semidirect
311. C₂×#544	C₂×C₇	semidirect
312. C₂×#543	C₂×C₇	semidirect
313. C₂×#542	C₂×C₇	semidirect
314. C₂×#541	C₂×C₇	semidirect
315. C₂×#541	C₂×C₇	semidirect
316. C₂×#539	C₂×C₇	semidirect
317. C₂×#539	C₂×C₇	semidirect
319. C₂×#533	C₂×C₇	semidirect
320. C₂×#529	C₂×C₇	semidirect
321. C₂²×#126	C₂×C₇	semidirect
452. #563	C₂²×C₇	semidirect
453. #563	C₂²×C₇	semidirect
454. #556	C₂²×C₇	semidirect
455. #554	C₂²×C₇	semidirect
456. #552	C₂²×C₇	semidirect
457. #552	C₂²×C₇	semidirect
458. #551	C₂²×C₇	semidirect
459. #551	C₂²×C₇	semidirect
460. #544	C₂²×C₇	semidirect
461. #543	C₂²×C₇	semidirect
462. #542	C₂²×C₇	semidirect
463. #541	C₂²×C₇	semidirect
464. #541	C₂²×C₇	semidirect
465. #539	C₂²×C₇	semidirect
466. #539	C₂²×C₇	semidirect
468. #533	C₂²×C₇	semidirect
469. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
470. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
471. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
472. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
473. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
474. #529	C₂²×C₇	semidirect
484. C₂×#126	C₂²×C₇	semidirect
485. C₂×#126	C₂²×C₇	semidirect
486. C₂×#126	C₂²×C₇	semidirect
487. C₂×#126	C₂²×C₇	semidirect
488. C₂×#126	C₂²×C₇	semidirect
489. C₂×#125	C₂²×C₇	semidirect
490. C₂×#125	C₂²×C₇	semidirect
491. C₂×#125	C₂²×C₇	semidirect
492. C₂×#125	C₂²×C₇	semidirect
493. C₂×#125	C₂²×C₇	semidirect
494. C₂×#125	C₂²×C₇	semidirect
495. C₂×#125	C₂²×C₇	semidirect
496. C₂×#125	C₂²×C₇	semidirect
497. C₂×#125	C₂²×C₇	semidirect
498. C₂×#125	C₂²×C₇	semidirect
502. C₂×#124	C₂²×C₇	semidirect
510. C₂×#123	C₂²×C₇	semidirect
523. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
524. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
525. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
526. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
527. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
531. C₂×C₄×Q₈	C₂²×C₇	semidirect
532. C₂×C₄×Q₈	C₂²×C₇	semidirect
533. C₂×C₄×Q₈	C₂²×C₇	semidirect
534. C₂×C₄×Q₈	C₂²×C₇	semidirect
535. C₂×C₄×Q₈	C₂²×C₇	semidirect
536. C₂×C₄×Q₈	C₂²×C₇	semidirect
542. C₂×C₄×D₄	C₂²×C₇	semidirect
547. C₂×#117	C₂²×C₇	semidirect
548. C₂×#117	C₂²×C₇	semidirect
552. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
650. C₄⋊Q₈	C₂³×C₇	semidirect
651. C₄⋊Q₈	C₂³×C₇	semidirect
652. C₄⋊Q₈	C₂³×C₇	semidirect
653. C₄⋊Q₈	C₂³×C₇	semidirect
654. C₄⋊Q₈	C₂³×C₇	semidirect
664. #126	C₂³×C₇	semidirect
665. #126	C₂³×C₇	semidirect
666. #126	C₂³×C₇	semidirect
667. #126	C₂³×C₇	semidirect
668. #125	C₂³×C₇	semidirect
669. #125	C₂³×C₇	semidirect
670. #125	C₂³×C₇	semidirect
671. #125	C₂³×C₇	semidirect
672. #125	C₂³×C₇	semidirect
673. #125	C₂³×C₇	semidirect
674. #125	C₂³×C₇	semidirect
675. #125	C₂³×C₇	semidirect
676. #125	C₂³×C₇	semidirect
677. #125	C₂³×C₇	semidirect
681. #124	C₂³×C₇	semidirect
689. #123	C₂³×C₇	semidirect
702. C₂²⋊Q₈	C₂³×C₇	semidirect
703. C₂²⋊Q₈	C₂³×C₇	semidirect
704. C₂²⋊Q₈	C₂³×C₇	semidirect
705. C₂²⋊Q₈	C₂³×C₇	semidirect
706. C₂²⋊Q₈	C₂³×C₇	semidirect
710. C₄×Q₈	C₂³×C₇	semidirect
711. C₄×Q₈	C₂³×C₇	semidirect
712. C₄×Q₈	C₂³×C₇	semidirect
713. C₄×Q₈	C₂³×C₇	semidirect
714. C₄×Q₈	C₂³×C₇	semidirect
715. C₄×Q₈	C₂³×C₇	semidirect
721. C₄×D₄	C₂³×C₇	semidirect
726. #117	C₂³×C₇	semidirect
727. #117	C₂³×C₇	semidirect
764. C₂×C₄⋊C₄	C₂³×C₇	semidirect
968. C₂×C₇	#3564	direct (N × H)
1042. C₇	C₂×#3564	direct (N × H)
1079. C₂	C₇×#3564	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×#3564	2
C₂×C₇×#563	2
C₂×C₇×#556	2
C₂×C₇×#554	2
C₂×C₇×#552	2
C₂×C₇×#551	2
C₂×C₇×#544	2
C₂×C₇×#543	2
C₂×C₇×#542	2
C₂×C₇×#541	2
C₂×C₇×#539	2
C₂×C₇×#538	2
C₂×C₇×#533	2
C₂×C₇×#529	2
C₂²×C₇×#126	2
C₂×#3564	7

Subgroups — C2×C7×#3564 #13239950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3564 #13239950