Subgroups — C₇×#35007 #13212223

Order 1792.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#538	C₂	1	2	yes	maximal, complemented
2	C₇×#2860	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2856	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2854	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2662	C₂	1	2	yes	maximal, complemented
7	C₇×#2661	C₂	1	2	yes	maximal, complemented
8	C₇×#2555	C₂	1	2	yes	maximal, complemented
9	C₇×#2554	C₂	1	2	yes	maximal, complemented
10	C₇×#2512	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2491	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2472	C₂	1	2	yes	maximal, complemented
13	C₇×#2445	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2428	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2424	C₂	1	2	yes	maximal, complemented
18	C₇×#2416	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2408	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2321	C₂	1	2	yes	maximal, complemented
21	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₇×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
25	C₇×#538	—	2	16	no	—
26	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₇×#127	C₂²	1	1	yes	characteristic
28	C₂×C₇×#127	C₂²	1	1	yes	characteristic
29	C₂×C₇×#126	C₂²	1	2	yes	complemented
30	C₂×C₇×#126	C₂²	1	2	yes	complemented
31	C₂×C₇×#124	C₂²	1	2	yes	complemented
32	C₂×C₇×#124	C₂²	1	2	yes	complemented
33	C₂×C₇×#124	C₂²	1	2	yes	complemented
34	C₂×C₇×#123	C₂²	1	2	yes	complemented
35	C₂×C₇×#123	C₂²	1	2	yes	complemented
36	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₂×C₇×#121	C₂²	1	2	yes	—
38	C₂×C₇×#121	C₂²	1	1	yes	characteristic
39	C₂×C₇×#121	C₂²	1	1	yes	characteristic
40	C₂×C₇×#121	C₂²	1	1	yes	characteristic
41	C₂×C₇×#121	C₂²	1	2	yes	complemented
42	C₂×C₇×#121	C₂²	1	2	yes	complemented
43	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₇×#121	C₂²	1	2	yes	complemented
45	C₂×C₇×#120	C₂²	1	2	yes	—
46	C₂×C₇×#120	C₂²	1	2	yes	—
47	C₂×C₇×#120	C₂²	1	2	yes	—
48	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
51	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
55	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
56	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
57	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
58	C₇×#398	C₂²	1	2	yes	complemented
59	C₇×#397	C₂²	1	2	yes	complemented
60	C₇×#396	C₂²	1	2	yes	complemented
61	C₇×#396	C₂²	1	2	yes	complemented
62	C₇×#395	C₂²	1	2	yes	complemented
63	C₇×#394	C₂²	1	2	yes	—
64	C₇×#394	C₂²	1	2	yes	complemented
65	C₇×#394	C₂²	1	2	yes	complemented
66	C₇×#394	C₂²	1	2	yes	complemented
67	C₇×#394	C₂²	1	2	yes	complemented
68	C₇×#394	C₂²	1	2	yes	complemented
69	C₇×#393	C₂²	1	2	yes	complemented
70	C₇×#392	C₂²	1	2	yes	—
71	C₇×#392	C₂²	1	2	yes	—
72	C₇×#392	C₂²	1	2	yes	—
73	C₇×#392	C₂²	1	2	yes	complemented
74	C₇×#390	C₂²	1	2	yes	—
75	C₇×#390	C₂²	1	1	yes	characteristic
76	C₇×#390	C₂²	1	1	yes	characteristic
77	C₇×#390	C₂²	1	1	yes	characteristic
78	C₇×#390	C₂²	1	1	yes	characteristic
79	C₇×#390	C₂²	1	1	yes	characteristic
80	C₇×#390	C₂²	1	1	yes	characteristic
81	C₇×#390	C₂²	1	2	yes	—
82	C₇×#390	C₂²	1	1	yes	characteristic
83	C₇×#390	C₂²	1	1	yes	characteristic
84	C₇×#390	C₂²	1	2	yes	complemented
85	C₇×#390	C₂²	1	2	yes	complemented
86	C₇×#390	C₂²	1	1	yes	characteristic, complemented
87	C₇×#390	C₂²	1	2	yes	complemented
88	C₇×#390	C₂²	1	2	yes	complemented
89	C₇×#390	C₂²	1	1	yes	characteristic, complemented
90	C₇×#389	C₂²	1	1	yes	characteristic, complemented
91	C₇×#389	C₂²	1	1	yes	characteristic, complemented
92	C₇×#389	C₂²	1	1	yes	characteristic, complemented
93	C₇×#389	C₂²	1	1	yes	characteristic, complemented
94	C₇×#388	C₂²	1	2	yes	complemented
95	C₇×#388	C₂²	1	2	yes	complemented
96	C₇×#388	C₂²	1	2	yes	complemented
97	C₇×#388	C₂²	1	2	yes	complemented
98	C₇×#388	C₂²	1	2	yes	complemented
99	C₇×#388	C₂²	1	2	yes	complemented
100	C₇×#388	C₂²	1	2	yes	complemented
101	C₇×#388	C₂²	1	2	yes	complemented
102	C₇×#386	C₂²	1	2	yes	—
103	C₇×#386	C₂²	1	2	yes	—
104	C₇×#386	C₂²	1	2	yes	complemented
105	C₇×#386	C₂²	1	2	yes	complemented
106	C₇×#386	C₂²	1	2	yes	complemented
107	C₇×#385	C₂²	1	2	yes	—
108	C₇×#384	C₂²	1	1	yes	characteristic, complemented
109	C₇×#380	C₂²	1	1	yes	characteristic
110	C₇×#380	C₂²	1	1	yes	characteristic, complemented
111	C₇×#379	C₂²	1	2	yes	—
112	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₄³×C₇	C₂²	1	1	yes	characteristic, complemented
124	#35007	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁵×C₇	C₂³	1	2	yes	—
126	C₂²×C₇×Q₈	C₂³	1	2	yes	—
127	C₂²×C₇×D₄	—	2	4	no	—
128	C₂²×C₇×D₄	—	4	2	no	—
129	C₂²×C₇×D₄	—	4	2	no	—
130	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
131	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
132	C₂²×C₇×D₄	C₂³	1	2	yes	—
133	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
134	C₂²×C₇×D₄	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	2	yes	—
139	C₂²×C₇×D₄	C₂³	1	2	yes	—
140	C₂²×C₇×D₄	C₂³	1	2	yes	—
141	C₂²×C₇×D₄	C₂³	1	2	yes	—
142	C₂²×C₇×D₄	C₂³	1	2	yes	—
143	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₇	C₂³	1	2	yes	—
148	C₂³×C₄×C₇	C₂³	1	2	yes	—
149	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
151	C₇×C₄⋊Q₈	—	4	2	no	—
152	C₇×#127	—	4	2	no	—
153	C₇×#127	—	4	2	no	—
154	C₇×#126	—	2	8	no	—
155	C₇×#126	—	2	8	no	—
156	C₇×#124	—	2	8	no	—
157	C₇×#124	—	2	8	no	—
158	C₇×#124	—	4	4	no	—
159	C₇×#123	—	2	8	no	—
160	C₇×#123	—	2	8	no	—
161	C₇×C₂²⋊Q₈	—	2	8	no	—
162	C₇×#121	—	2	8	no	—
163	C₇×#121	—	2	8	no	—
164	C₇×#121	—	2	4	no	—
165	C₇×#121	—	2	8	no	—
166	C₇×#121	—	4	4	no	—
167	C₇×#121	—	4	2	no	—
168	C₇×#121	—	4	2	no	—
169	C₇×#121	—	4	2	no	—
170	C₇×#120	—	2	8	no	—
171	C₇×#120	—	2	8	no	—
172	C₇×#120	—	2	8	no	—
173	C₄×C₇×D₄	—	2	8	no	—
174	C₄×C₇×D₄	—	2	4	no	—
175	C₄×C₇×D₄	—	2	4	no	—
176	C₄×C₇×D₄	—	4	2	no	—
177	C₄×C₇×D₄	D₄	1	8	yes	complemented
178	C₂×C₇×C₄⋊C₄	—	4	2	no	—
179	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
190	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
196	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₇	—	4	2	no	—
231	C₂×C₄²×C₇	—	4	2	no	—
232	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₇	C₂³	1	2	yes	—
240	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
241	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
246	C₇×#95	C₂³	1	1	yes	characteristic
247	C₇×#95	C₂³	1	1	yes	characteristic
248	C₇×#95	C₂³	1	1	yes	characteristic
249	C₇×#95	C₂³	1	1	yes	characteristic
250	C₇×#95	C₂³	1	1	yes	characteristic
251	C₇×#95	C₂³	1	1	yes	characteristic
252	C₇×#95	C₂³	1	2	yes	—
253	C₇×#95	C₂³	1	2	yes	—
254	C₇×#95	C₂³	1	2	yes	—
255	C₇×#95	C₂³	1	2	yes	—
256	C₇×#95	C₂³	1	2	yes	—
257	C₇×#95	C₂³	1	2	yes	—
258	C₇×#95	C₂³	1	2	yes	—
259	C₂×#538	C₂×C₇	1	2	yes	complemented
260	#2860	C₂×C₇	1	1	yes	characteristic, complemented
261	#2858	C₂×C₇	1	1	yes	characteristic, complemented
262	#2856	C₂×C₇	1	1	yes	characteristic, complemented
263	#2854	C₂×C₇	1	1	yes	characteristic, complemented
264	#2662	C₂×C₇	1	2	yes	complemented
265	#2661	C₂×C₇	1	2	yes	complemented
266	#2555	C₂×C₇	1	2	yes	complemented
267	#2554	C₂×C₇	1	2	yes	complemented
268	#2512	C₂×C₇	1	1	yes	characteristic, complemented
269	#2491	C₂×C₇	1	1	yes	characteristic, complemented
270	#2472	C₂×C₇	1	2	yes	complemented
271	#2445	C₂×C₇	1	1	yes	characteristic, complemented
272	#2440	C₂×C₇	1	1	yes	characteristic, complemented
273	#2433	C₂×C₇	1	1	yes	characteristic, complemented
274	#2428	C₂×C₇	1	1	yes	characteristic, complemented
275	#2424	C₂×C₇	1	2	yes	complemented
276	#2416	C₂×C₇	1	1	yes	characteristic, complemented
277	#2408	C₂×C₇	1	1	yes	characteristic, complemented
278	#2321	C₂×C₇	1	2	yes	complemented
279	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
280	C₂×#390	C₂×C₇	1	1	yes	characteristic, complemented
281	C₄²×D₄	C₂×C₇	1	1	yes	characteristic, complemented
282	C₂⁴×C₇	—	2	4	no	—
283	C₂⁴×C₇	—	2	4	no	—
284	C₂⁴×C₇	—	2	4	no	—
285	C₂⁴×C₇	—	4	2	no	—
286	C₂⁴×C₇	—	4	2	no	—
287	C₂⁴×C₇	—	4	2	no	—
288	C₂⁴×C₇	—	4	2	no	—
289	C₂⁴×C₇	C₂⁴	1	2	yes	—
290	C₂⁴×C₇	C₂⁴	1	2	yes	—
291	C₂⁴×C₇	C₂⁴	1	2	yes	—
292	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
293	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
294	C₂×C₇×Q₈	—	2	4	no	—
295	C₂×C₇×Q₈	—	4	2	no	—
296	C₂×C₇×Q₈	—	4	2	no	—
297	C₂×C₇×D₄	—	2	2	no	—
298	C₂×C₇×D₄	—	2	2	no	—
299	C₂×C₇×D₄	—	2	4	no	—
300	C₂×C₇×D₄	—	2	4	no	—
301	C₂×C₇×D₄	—	2	4	no	—
302	C₂×C₇×D₄	—	2	4	no	—
303	C₂×C₇×D₄	—	2	4	no	—
304	C₂×C₇×D₄	—	2	4	no	—
305	C₂×C₇×D₄	—	2	4	no	—
306	C₂×C₇×D₄	—	2	4	no	—
307	C₂×C₇×D₄	—	2	2	no	—
308	C₂×C₇×D₄	—	2	4	no	—
309	C₂×C₇×D₄	—	2	2	no	—
310	C₂×C₇×D₄	—	2	2	no	—
311	C₂×C₇×D₄	—	2	4	no	—
312	C₂×C₇×D₄	—	2	4	no	—
313	C₂×C₇×D₄	—	2	2	no	—
314	C₂×C₇×D₄	—	2	2	no	—
315	C₂×C₇×D₄	—	2	2	no	—
316	C₂×C₇×D₄	—	2	2	no	—
317	C₂×C₇×D₄	—	2	2	no	—
318	C₂×C₇×D₄	—	2	2	no	—
319	C₂×C₇×D₄	—	4	2	no	—
320	C₂×C₇×D₄	—	4	2	no	—
321	C₂×C₇×D₄	—	4	16	no	—
322	C₂×C₇×D₄	—	4	2	no	—
323	C₂×C₇×D₄	—	4	2	no	—
324	C₂×C₇×D₄	—	4	2	no	—
325	C₂×C₇×D₄	—	4	2	no	—
326	C₂×C₇×D₄	—	4	2	no	—
327	C₂×C₇×D₄	—	4	2	no	—
328	C₂×C₇×D₄	—	4	2	no	—
329	C₂×C₇×D₄	—	4	2	no	—
330	C₂×C₇×D₄	—	4	2	no	—
331	C₂×C₇×D₄	—	4	2	no	—
332	C₂×C₇×D₄	—	4	2	no	—
333	C₂×C₇×D₄	—	4	2	no	—
334	C₂×C₇×D₄	—	4	2	no	—
335	C₂×C₇×D₄	—	4	2	no	—
336	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
337	C₂²×C₄×C₇	—	2	2	no	—
338	C₂²×C₄×C₇	—	2	2	no	—
339	C₂²×C₄×C₇	—	2	2	no	—
340	C₂²×C₄×C₇	—	2	4	no	—
341	C₂²×C₄×C₇	—	2	2	no	—
342	C₂²×C₄×C₇	—	2	2	no	—
343	C₂²×C₄×C₇	—	2	2	no	—
344	C₂²×C₄×C₇	—	2	2	no	—
345	C₂²×C₄×C₇	—	2	2	no	—
346	C₂²×C₄×C₇	—	2	2	no	—
347	C₂²×C₄×C₇	—	2	4	no	—
348	C₂²×C₄×C₇	—	4	1	no	—
349	C₂²×C₄×C₇	—	4	1	no	—
350	C₂²×C₄×C₇	—	4	1	no	—
351	C₂²×C₄×C₇	—	4	1	no	—
352	C₂²×C₄×C₇	—	4	1	no	—
353	C₂²×C₄×C₇	—	4	1	no	—
354	C₂²×C₄×C₇	—	4	2	no	—
355	C₂²×C₄×C₇	—	4	2	no	—
356	C₂²×C₄×C₇	—	4	2	no	—
357	C₂²×C₄×C₇	—	4	2	no	—
358	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
359	C₂²×C₄×C₇	C₂×D₄	1	4	yes	complemented
360	C₂²×C₄×C₇	#41	1	4	yes	—
361	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
367	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
379	C₇×C₄⋊C₄	—	2	4	no	—
380	C₇×C₄⋊C₄	—	2	4	no	—
381	C₇×C₄⋊C₄	—	2	4	no	—
382	C₇×C₄⋊C₄	—	2	4	no	—
383	C₇×C₄⋊C₄	—	2	4	no	—
384	C₇×C₄⋊C₄	—	2	2	no	—
385	C₇×C₄⋊C₄	—	2	2	no	—
386	C₇×C₄⋊C₄	—	2	2	no	—
387	C₇×C₄⋊C₄	—	2	2	no	—
388	C₇×C₄⋊C₄	—	2	2	no	—
389	C₇×C₄⋊C₄	—	2	2	no	—
390	C₇×C₄⋊C₄	—	2	2	no	—
391	C₇×C₄⋊C₄	—	4	2	no	—
392	C₇×C₄⋊C₄	—	4	2	no	—
393	C₇×C₄⋊C₄	—	4	2	no	—
394	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
395	C₇×C₂²⋊C₄	—	2	4	no	—
396	C₇×C₂²⋊C₄	—	2	4	no	—
397	C₇×C₂²⋊C₄	—	2	2	no	—
398	C₇×C₂²⋊C₄	—	2	4	no	—
399	C₇×C₂²⋊C₄	—	2	4	no	—
400	C₇×C₂²⋊C₄	—	2	4	no	—
401	C₇×C₂²⋊C₄	—	2	4	no	—
402	C₇×C₂²⋊C₄	—	2	4	no	—
403	C₇×C₂²⋊C₄	—	2	4	no	—
404	C₇×C₂²⋊C₄	—	2	4	no	—
405	C₇×C₂²⋊C₄	—	2	4	no	—
406	C₇×C₂²⋊C₄	—	2	4	no	—
407	C₇×C₂²⋊C₄	—	2	4	no	—
408	C₇×C₂²⋊C₄	—	2	2	no	—
409	C₇×C₂²⋊C₄	—	2	2	no	—
410	C₇×C₂²⋊C₄	—	2	4	no	—
411	C₇×C₂²⋊C₄	—	2	4	no	—
412	C₇×C₂²⋊C₄	—	2	4	no	—
413	C₇×C₂²⋊C₄	—	2	4	no	—
414	C₇×C₂²⋊C₄	—	2	4	no	—
415	C₇×C₂²⋊C₄	—	2	4	no	—
416	C₇×C₂²⋊C₄	—	4	2	no	—
417	C₇×C₂²⋊C₄	—	4	2	no	—
418	C₇×C₂²⋊C₄	—	4	2	no	—
419	C₇×C₂²⋊C₄	—	4	2	no	—
420	C₇×C₂²⋊C₄	—	4	2	no	—
421	C₇×C₂²⋊C₄	—	4	2	no	—
422	C₇×C₂²⋊C₄	—	4	2	no	—
423	C₇×C₂²⋊C₄	—	4	2	no	—
424	C₇×C₂²⋊C₄	—	4	2	no	—
425	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
426	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
427	C₇×C₂²⋊C₄	#41	1	4	yes	—
428	C₄²×C₇	—	2	4	no	—
429	C₄²×C₇	—	2	2	no	—
430	C₄²×C₇	—	2	2	no	—
431	C₄²×C₇	—	2	2	no	—
432	C₄²×C₇	—	2	2	no	—
433	C₄²×C₇	—	2	2	no	—
434	C₄²×C₇	—	2	2	no	—
435	C₄²×C₇	—	2	2	no	—
436	C₄²×C₇	—	4	1	no	—
437	C₄²×C₇	—	4	1	no	—
438	C₄²×C₇	—	4	1	no	—
439	C₄²×C₇	—	4	1	no	—
440	C₄²×C₇	—	4	1	no	—
441	C₄²×C₇	C₂×D₄	1	4	yes	complemented
442	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
443	#538	—	2	16	no	—
444	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
445	C₂×#127	C₂²×C₇	1	1	yes	characteristic
446	C₂×#127	C₂²×C₇	1	1	yes	characteristic
447	C₂×#126	C₂²×C₇	1	2	yes	complemented
448	C₂×#126	C₂²×C₇	1	2	yes	complemented
449	C₂×#124	C₂²×C₇	1	2	yes	complemented
450	C₂×#124	C₂²×C₇	1	2	yes	complemented
451	C₂×#124	C₂²×C₇	1	2	yes	complemented
452	C₂×#123	C₂²×C₇	1	2	yes	complemented
453	C₂×#123	C₂²×C₇	1	2	yes	complemented
454	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
455	C₂×#121	C₂²×C₇	1	2	yes	—
456	C₂×#121	C₂²×C₇	1	1	yes	characteristic
457	C₂×#121	C₂²×C₇	1	1	yes	characteristic
458	C₂×#121	C₂²×C₇	1	1	yes	characteristic
459	C₂×#121	C₂²×C₇	1	2	yes	complemented
460	C₂×#121	C₂²×C₇	1	2	yes	complemented
461	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
462	C₂×#121	C₂²×C₇	1	2	yes	complemented
463	C₂×#120	C₂²×C₇	1	2	yes	—
464	C₂×#120	C₂²×C₇	1	2	yes	—
465	C₂×#120	C₂²×C₇	1	2	yes	—
466	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
467	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
468	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
469	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
470	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
471	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
472	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
473	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
474	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
475	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
476	#398	C₂²×C₇	1	2	yes	complemented
477	#397	C₂²×C₇	1	2	yes	complemented
478	#396	C₂²×C₇	1	2	yes	complemented
479	#396	C₂²×C₇	1	2	yes	complemented
480	#395	C₂²×C₇	1	2	yes	complemented
481	#394	C₂²×C₇	1	2	yes	—
482	#394	C₂²×C₇	1	2	yes	complemented
483	#394	C₂²×C₇	1	2	yes	complemented
484	#394	C₂²×C₇	1	2	yes	complemented
485	#394	C₂²×C₇	1	2	yes	complemented
486	#394	C₂²×C₇	1	2	yes	complemented
487	#393	C₂²×C₇	1	2	yes	complemented
488	#392	C₂²×C₇	1	2	yes	—
489	#392	C₂²×C₇	1	2	yes	—
490	#392	C₂²×C₇	1	2	yes	—
491	#392	C₂²×C₇	1	2	yes	complemented
492	#390	C₂²×C₇	1	1	yes	characteristic
493	#390	C₂²×C₇	1	1	yes	characteristic
494	#390	C₂²×C₇	1	1	yes	characteristic
495	#390	C₂²×C₇	1	1	yes	characteristic
496	#390	C₂²×C₇	1	1	yes	characteristic
497	#390	C₂²×C₇	1	1	yes	characteristic
498	#390	C₂²×C₇	1	2	yes	—
499	#390	C₂²×C₇	1	1	yes	characteristic
500	#390	C₂²×C₇	1	1	yes	characteristic
501	#390	C₂²×C₇	1	2	yes	—
502	#390	C₂²×C₇	1	2	yes	complemented
503	#390	C₂²×C₇	1	2	yes	complemented
504	#390	C₂²×C₇	1	1	yes	characteristic, complemented
505	#390	C₂²×C₇	1	2	yes	complemented
506	#390	C₂²×C₇	1	1	yes	characteristic, complemented
507	#390	C₂²×C₇	1	2	yes	complemented
508	#389	C₂²×C₇	1	1	yes	characteristic, complemented
509	#389	C₂²×C₇	1	1	yes	characteristic, complemented
510	#389	C₂²×C₇	1	1	yes	characteristic, complemented
511	#389	C₂²×C₇	1	1	yes	characteristic, complemented
512	#388	C₂²×C₇	1	2	yes	complemented
513	#388	C₂²×C₇	1	2	yes	complemented
514	#388	C₂²×C₇	1	2	yes	complemented
515	#388	C₂²×C₇	1	2	yes	complemented
516	#388	C₂²×C₇	1	2	yes	complemented
517	#388	C₂²×C₇	1	2	yes	complemented
518	#388	C₂²×C₇	1	2	yes	complemented
519	#388	C₂²×C₇	1	2	yes	complemented
520	#386	C₂²×C₇	1	2	yes	—
521	#386	C₂²×C₇	1	2	yes	—
522	#386	C₂²×C₇	1	2	yes	complemented
523	#386	C₂²×C₇	1	2	yes	complemented
524	#386	C₂²×C₇	1	2	yes	complemented
525	#385	C₂²×C₇	1	2	yes	—
526	#384	C₂²×C₇	1	1	yes	characteristic, complemented
527	#380	C₂²×C₇	1	1	yes	characteristic
528	#380	C₂²×C₇	1	1	yes	characteristic, complemented
529	#379	C₂²×C₇	1	2	yes	—
530	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
531	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
532	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
533	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
534	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
535	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
536	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
537	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
538	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
539	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
540	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
541	C₄³	C₂²×C₇	1	1	yes	characteristic, complemented
542	C₂³×C₇	—	2	1	no	—
543	C₂³×C₇	—	2	1	no	—
544	C₂³×C₇	—	2	1	no	—
545	C₂³×C₇	—	2	1	no	—
546	C₂³×C₇	—	2	1	no	—
547	C₂³×C₇	—	2	1	no	—
548	C₂³×C₇	—	2	1	no	—
549	C₂³×C₇	—	2	1	no	—
550	C₂³×C₇	—	2	1	no	—
551	C₂³×C₇	—	2	1	no	—
552	C₂³×C₇	—	2	2	no	—
553	C₂³×C₇	—	2	2	no	—
554	C₂³×C₇	—	2	2	no	—
555	C₂³×C₇	—	2	2	no	—
556	C₂³×C₇	—	2	2	no	—
557	C₂³×C₇	—	2	2	no	—
558	C₂³×C₇	—	2	2	no	—
559	C₂³×C₇	—	2	2	no	—
560	C₂³×C₇	—	2	2	no	—
561	C₂³×C₇	—	2	2	no	—
562	C₂³×C₇	—	2	2	no	—
563	C₂³×C₇	—	2	2	no	—
564	C₂³×C₇	—	2	2	no	—
565	C₂³×C₇	—	2	2	no	—
566	C₂³×C₇	—	2	2	no	—
567	C₂³×C₇	—	2	2	no	—
568	C₂³×C₇	—	2	2	no	—
569	C₂³×C₇	—	2	2	no	—
570	C₂³×C₇	—	2	2	no	—
571	C₂³×C₇	—	2	2	no	—
572	C₂³×C₇	—	2	2	no	—
573	C₂³×C₇	—	4	8	no	—
574	C₂³×C₇	—	4	8	no	—
575	C₂³×C₇	—	4	8	no	—
576	C₂³×C₇	—	8	4	no	—
577	C₂³×C₇	—	8	4	no	—
578	C₂³×C₇	—	8	4	no	—
579	C₂³×C₇	—	8	4	no	—
580	C₂³×C₇	C₂²×D₄	1	2	yes	—
581	C₂³×C₇	C₂²×D₄	1	2	yes	—
582	C₂³×C₇	C₂×#41	1	2	yes	—
583	C₂³×C₇	C₂×#41	1	2	yes	—
584	C₂³×C₇	C₂⁵	1	1	yes	characteristic
585	C₇×Q₈	—	8	4	no	—
586	C₇×D₄	—	2	8	no	—
587	C₇×D₄	—	4	8	no	—
588	C₇×D₄	—	4	8	no	—
589	C₇×D₄	—	4	4	no	—
590	C₇×D₄	—	4	4	no	—
591	C₇×D₄	—	4	4	no	—
592	C₇×D₄	—	8	4	no	—
593	C₇×D₄	—	8	4	no	—
594	C₇×D₄	—	8	4	no	—
595	C₇×D₄	—	8	4	no	—
596	C₇×D₄	—	8	4	no	—
597	C₇×D₄	—	8	4	no	—
598	C₇×D₄	—	8	4	no	—
599	C₂×C₄×C₇	—	2	1	no	—
600	C₂×C₄×C₇	—	2	1	no	—
601	C₂×C₄×C₇	—	2	1	no	—
602	C₂×C₄×C₇	—	2	1	no	—
603	C₂×C₄×C₇	—	2	1	no	—
604	C₂×C₄×C₇	—	2	1	no	—
605	C₂×C₄×C₇	—	2	1	no	—
606	C₂×C₄×C₇	—	2	1	no	—
607	C₂×C₄×C₇	—	2	1	no	—
608	C₂×C₄×C₇	—	2	1	no	—
609	C₂×C₄×C₇	—	2	1	no	—
610	C₂×C₄×C₇	—	2	1	no	—
611	C₂×C₄×C₇	—	2	1	no	—
612	C₂×C₄×C₇	—	2	1	no	—
613	C₂×C₄×C₇	—	2	1	no	—
614	C₂×C₄×C₇	—	2	1	no	—
615	C₂×C₄×C₇	—	2	1	no	—
616	C₂×C₄×C₇	—	2	1	no	—
617	C₂×C₄×C₇	—	2	8	no	—
618	C₂×C₄×C₇	—	2	2	no	—
619	C₂×C₄×C₇	—	2	2	no	—
620	C₂×C₄×C₇	—	2	2	no	—
621	C₂×C₄×C₇	—	2	2	no	—
622	C₂×C₄×C₇	—	2	2	no	—
623	C₂×C₄×C₇	—	2	1	no	—
624	C₂×C₄×C₇	—	2	2	no	—
625	C₂×C₄×C₇	—	2	1	no	—
626	C₂×C₄×C₇	—	2	1	no	—
627	C₂×C₄×C₇	—	2	2	no	—
628	C₂×C₄×C₇	—	2	1	no	—
629	C₂×C₄×C₇	—	2	1	no	—
630	C₂×C₄×C₇	—	2	1	no	—
631	C₂×C₄×C₇	—	2	2	no	—
632	C₂×C₄×C₇	—	2	2	no	—
633	C₂×C₄×C₇	—	2	2	no	—
634	C₂×C₄×C₇	—	2	1	no	—
635	C₂×C₄×C₇	—	2	1	no	—
636	C₂×C₄×C₇	—	2	2	no	—
637	C₂×C₄×C₇	—	2	2	no	—
638	C₂×C₄×C₇	—	2	2	no	—
639	C₂×C₄×C₇	—	2	2	no	—
640	C₂×C₄×C₇	—	2	1	no	—
641	C₂×C₄×C₇	—	2	2	no	—
642	C₂×C₄×C₇	—	4	4	no	—
643	C₂×C₄×C₇	—	4	4	no	—
644	C₂×C₄×C₇	—	4	4	no	—
645	C₂×C₄×C₇	—	4	4	no	—
646	C₂×C₄×C₇	—	4	4	no	—
647	C₂×C₄×C₇	—	8	4	no	—
648	C₂×C₄×C₇	—	8	4	no	—
649	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
650	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
651	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
652	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
653	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
654	C₂×C₄×C₇	C₂×#41	1	2	yes	—
655	C₂×C₄×C₇	C₂×#41	1	2	yes	—
656	C₂×C₄×C₇	C₂×#41	1	2	yes	—
657	C₂×C₄×C₇	C₂×#41	1	2	yes	—
658	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
659	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
660	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
661	C₂⁵	C₂³×C₇	1	2	yes	—
662	C₂²×Q₈	C₂³×C₇	1	2	yes	—
663	C₂²×D₄	—	2	4	no	—
664	C₂²×D₄	—	4	2	no	—
665	C₂²×D₄	—	4	2	no	—
666	C₂²×D₄	C₂³×C₇	1	2	yes	—
667	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
668	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
669	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
670	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
671	C₂²×D₄	C₂³×C₇	1	2	yes	—
672	C₂²×D₄	C₂³×C₇	1	2	yes	—
673	C₂²×D₄	C₂³×C₇	1	2	yes	—
674	C₂²×D₄	C₂³×C₇	1	2	yes	—
675	C₂²×D₄	C₂³×C₇	1	2	yes	—
676	C₂²×D₄	C₂³×C₇	1	2	yes	—
677	C₂²×D₄	C₂³×C₇	1	2	yes	—
678	C₂²×D₄	C₂³×C₇	1	2	yes	—
679	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
680	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
681	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
682	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₇	1	2	yes	—
684	C₂³×C₄	C₂³×C₇	1	2	yes	—
685	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
686	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
687	C₄⋊Q₈	—	4	2	no	—
688	#127	—	4	2	no	—
689	#127	—	4	2	no	—
690	#126	—	2	8	no	—
691	#126	—	2	8	no	—
692	#124	—	2	8	no	—
693	#124	—	2	8	no	—
694	#124	—	4	4	no	—
695	#123	—	2	8	no	—
696	#123	—	2	8	no	—
697	C₂²⋊Q₈	—	2	8	no	—
698	#121	—	2	8	no	—
699	#121	—	2	8	no	—
700	#121	—	2	4	no	—
701	#121	—	2	8	no	—
702	#121	—	4	4	no	—
703	#121	—	4	2	no	—
704	#121	—	4	2	no	—
705	#121	—	4	2	no	—
706	#120	—	2	8	no	—
707	#120	—	2	8	no	—
708	#120	—	2	8	no	—
709	C₄×D₄	—	2	8	no	—
710	C₄×D₄	—	2	4	no	—
711	C₄×D₄	—	2	4	no	—
712	C₄×D₄	—	4	2	no	—
713	C₄×D₄	C₇×D₄	1	8	yes	complemented
714	C₂×C₄⋊C₄	—	4	2	no	—
715	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
718	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
724	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
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	1	yes	characteristic
731	C₂×C₂²⋊C₄	—	2	8	no	—
732	C₂×C₂²⋊C₄	—	4	4	no	—
733	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
744	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
764	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
765	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
766	C₂×C₄²	—	4	2	no	—
767	C₂×C₄²	—	4	2	no	—
768	C₂×C₄²	C₂³×C₇	1	2	yes	—
769	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
774	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
775	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
776	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
777	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
778	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
779	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
780	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
781	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
782	#95	C₂³×C₇	1	1	yes	characteristic
783	#95	C₂³×C₇	1	1	yes	characteristic
784	#95	C₂³×C₇	1	1	yes	characteristic
785	#95	C₂³×C₇	1	1	yes	characteristic
786	#95	C₂³×C₇	1	1	yes	characteristic
787	#95	C₂³×C₇	1	1	yes	characteristic
788	#95	C₂³×C₇	1	2	yes	—
789	#95	C₂³×C₇	1	2	yes	—
790	#95	C₂³×C₇	1	2	yes	—
791	#95	C₂³×C₇	1	2	yes	—
792	#95	C₂³×C₇	1	2	yes	—
793	#95	C₂³×C₇	1	2	yes	—
794	#95	C₂³×C₇	1	2	yes	—
795	C₂²×C₇	—	2	2	no	—
796	C₂²×C₇	—	2	2	no	—
797	C₂²×C₇	—	2	2	no	—
798	C₂²×C₇	—	2	2	no	—
799	C₂²×C₇	—	2	2	no	—
800	C₂²×C₇	—	2	2	no	—
801	C₂²×C₇	—	2	2	no	—
802	C₂²×C₇	—	2	2	no	—
803	C₂²×C₇	—	2	2	no	—
804	C₂²×C₇	—	4	1	no	—
805	C₂²×C₇	—	4	1	no	—
806	C₂²×C₇	—	4	1	no	—
807	C₂²×C₇	—	4	1	no	—
808	C₂²×C₇	—	4	2	no	—
809	C₂²×C₇	—	4	2	no	—
810	C₂²×C₇	—	4	2	no	—
811	C₂²×C₇	—	4	2	no	—
812	C₂²×C₇	—	4	2	no	—
813	C₂²×C₇	—	4	2	no	—
814	C₂²×C₇	—	4	2	no	—
815	C₂²×C₇	—	4	2	no	—
816	C₂²×C₇	—	4	2	no	—
817	C₂²×C₇	—	4	2	no	—
818	C₂²×C₇	—	4	2	no	—
819	C₂²×C₇	—	4	2	no	—
820	C₂²×C₇	—	4	2	no	—
821	C₂²×C₇	—	4	2	no	—
822	C₂²×C₇	—	4	2	no	—
823	C₂²×C₇	—	4	2	no	—
824	C₂²×C₇	—	4	2	no	—
825	C₂²×C₇	—	4	2	no	—
826	C₂²×C₇	—	4	2	no	—
827	C₂²×C₇	—	4	2	no	—
828	C₂²×C₇	—	4	2	no	—
829	C₂²×C₇	—	8	16	no	—
830	C₂²×C₇	#532	1	4	yes	—
831	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
832	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
833	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
834	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
835	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
836	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
837	C₂²×C₇	#585	1	1	yes	characteristic
838	C₄×C₇	—	2	2	no	—
839	C₄×C₇	—	2	2	no	—
840	C₄×C₇	—	2	2	no	—
841	C₄×C₇	—	2	2	no	—
842	C₄×C₇	—	2	2	no	—
843	C₄×C₇	—	2	2	no	—
844	C₄×C₇	—	2	2	no	—
845	C₄×C₇	—	2	2	no	—
846	C₄×C₇	—	2	2	no	—
847	C₄×C₇	—	4	2	no	—
848	C₄×C₇	—	4	1	no	—
849	C₄×C₇	—	4	1	no	—
850	C₄×C₇	—	4	2	no	—
851	C₄×C₇	—	4	2	no	—
852	C₄×C₇	—	4	2	no	—
853	C₄×C₇	—	4	2	no	—
854	C₄×C₇	—	4	1	no	—
855	C₄×C₇	#538	1	4	yes	complemented
856	C₂⁴	—	2	4	no	—
857	C₂⁴	—	2	4	no	—
858	C₂⁴	—	2	4	no	—
859	C₂⁴	—	4	2	no	—
860	C₂⁴	—	4	2	no	—
861	C₂⁴	—	4	2	no	—
862	C₂⁴	—	4	2	no	—
863	C₂⁴	C₂⁴×C₇	1	2	yes	—
864	C₂⁴	C₂⁴×C₇	1	2	yes	—
865	C₂⁴	C₂⁴×C₇	1	2	yes	—
866	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
867	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
868	C₂×Q₈	—	2	4	no	—
869	C₂×Q₈	—	4	2	no	—
870	C₂×Q₈	—	4	2	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	4	no	—
874	C₂×D₄	—	2	4	no	—
875	C₂×D₄	—	2	4	no	—
876	C₂×D₄	—	2	4	no	—
877	C₂×D₄	—	2	4	no	—
878	C₂×D₄	—	2	4	no	—
879	C₂×D₄	—	2	4	no	—
880	C₂×D₄	—	2	4	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	4	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	4	no	—
886	C₂×D₄	—	2	4	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	4	2	no	—
894	C₂×D₄	—	4	2	no	—
895	C₂×D₄	—	4	16	no	—
896	C₂×D₄	—	4	2	no	—
897	C₂×D₄	—	4	2	no	—
898	C₂×D₄	—	4	2	no	—
899	C₂×D₄	—	4	2	no	—
900	C₂×D₄	—	4	2	no	—
901	C₂×D₄	—	4	2	no	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	4	2	no	—
904	C₂×D₄	—	4	2	no	—
905	C₂×D₄	—	4	2	no	—
906	C₂×D₄	—	4	2	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	—	4	2	no	—
909	C₂×D₄	—	4	2	no	—
910	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	4	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	4	no	—
922	C₂²×C₄	—	4	1	no	—
923	C₂²×C₄	—	4	1	no	—
924	C₂²×C₄	—	4	1	no	—
925	C₂²×C₄	—	4	1	no	—
926	C₂²×C₄	—	4	1	no	—
927	C₂²×C₄	—	4	1	no	—
928	C₂²×C₄	—	4	2	no	—
929	C₂²×C₄	—	4	2	no	—
930	C₂²×C₄	—	4	2	no	—
931	C₂²×C₄	—	4	2	no	—
932	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
933	C₂²×C₄	C₂×C₇×D₄	1	4	yes	complemented
934	C₂²×C₄	C₇×#41	1	4	yes	—
935	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
937	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
939	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
940	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
941	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
942	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
943	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
946	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
952	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
953	C₄⋊C₄	—	2	4	no	—
954	C₄⋊C₄	—	2	4	no	—
955	C₄⋊C₄	—	2	4	no	—
956	C₄⋊C₄	—	2	4	no	—
957	C₄⋊C₄	—	2	4	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	4	2	no	—
966	C₄⋊C₄	—	4	2	no	—
967	C₄⋊C₄	—	4	2	no	—
968	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	complemented
969	C₂²⋊C₄	—	2	4	no	—
970	C₂²⋊C₄	—	2	4	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	2	4	no	—
974	C₂²⋊C₄	—	2	4	no	—
975	C₂²⋊C₄	—	2	4	no	—
976	C₂²⋊C₄	—	2	4	no	—
977	C₂²⋊C₄	—	2	4	no	—
978	C₂²⋊C₄	—	2	4	no	—
979	C₂²⋊C₄	—	2	4	no	—
980	C₂²⋊C₄	—	2	4	no	—
981	C₂²⋊C₄	—	2	4	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	4	no	—
985	C₂²⋊C₄	—	2	4	no	—
986	C₂²⋊C₄	—	2	4	no	—
987	C₂²⋊C₄	—	2	4	no	—
988	C₂²⋊C₄	—	2	4	no	—
989	C₂²⋊C₄	—	2	4	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	4	2	no	—
992	C₂²⋊C₄	—	4	2	no	—
993	C₂²⋊C₄	—	4	2	no	—
994	C₂²⋊C₄	—	4	2	no	—
995	C₂²⋊C₄	—	4	2	no	—
996	C₂²⋊C₄	—	4	2	no	—
997	C₂²⋊C₄	—	4	2	no	—
998	C₂²⋊C₄	—	4	2	no	—
999	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
1000	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	complemented
1001	C₂²⋊C₄	C₇×#41	1	4	yes	—
1002	C₄²	—	2	4	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	4	1	no	—
1011	C₄²	—	4	1	no	—
1012	C₄²	—	4	1	no	—
1013	C₄²	—	4	1	no	—
1014	C₄²	—	4	1	no	—
1015	C₄²	C₂×C₇×D₄	1	4	yes	complemented
1016	C₂×C₇	—	2	4	no	—
1017	C₂×C₇	—	4	2	no	—
1018	C₂×C₇	—	8	2	no	—
1019	C₂×C₇	—	8	2	no	—
1020	C₂×C₇	—	8	2	no	—
1021	C₂×C₇	C₂×#532	1	1	yes	characteristic
1022	C₂×C₇	C₂×#538	1	1	yes	characteristic
1023	C₂×C₇	#3460	1	1	yes	characteristic
1024	C₂×C₇	#3496	1	1	yes	characteristic
1025	C₂×C₇	#3498	1	1	yes	characteristic
1026	C₂×C₇	#3514	1	1	yes	characteristic
1027	C₂×C₇	#3519	1	1	yes	characteristic
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	2	2	no	—
1051	C₂³	—	2	2	no	—
1052	C₂³	—	2	2	no	—
1053	C₂³	—	2	2	no	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	2	2	no	—
1059	C₂³	—	4	8	no	—
1060	C₂³	—	4	8	no	—
1061	C₂³	—	4	8	no	—
1062	C₂³	—	8	4	no	—
1063	C₂³	—	8	4	no	—
1064	C₂³	—	8	4	no	—
1065	C₂³	—	8	4	no	—
1066	C₂³	C₂²×C₇×D₄	1	2	yes	—
1067	C₂³	C₂²×C₇×D₄	1	2	yes	—
1068	C₂³	C₂×C₇×#41	1	2	yes	—
1069	C₂³	C₂×C₇×#41	1	2	yes	—
1070	C₂³	C₂⁵×C₇	1	1	yes	characteristic
1071	Q₈	—	8	4	no	—
1072	D₄	—	2	8	no	—
1073	D₄	—	4	8	no	—
1074	D₄	—	4	8	no	—
1075	D₄	—	4	4	no	—
1076	D₄	—	4	4	no	—
1077	D₄	—	4	4	no	—
1078	D₄	—	8	4	no	—
1079	D₄	—	8	4	no	—
1080	D₄	—	8	4	no	—
1081	D₄	—	8	4	no	—
1082	D₄	—	8	4	no	—
1083	D₄	—	8	4	no	—
1084	D₄	—	8	4	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	8	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	4	4	no	—
1129	C₂×C₄	—	4	4	no	—
1130	C₂×C₄	—	4	4	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	8	4	no	—
1134	C₂×C₄	—	8	4	no	—
1135	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1136	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1137	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1138	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1139	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1140	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1141	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1142	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1143	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1144	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1145	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1146	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1147	C₇	#35007	1	1	yes	characteristic, direct product factor, Sylow
1148	C₂²	—	2	2	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	8	16	no	—
1183	C₂²	C₇×#532	1	4	yes	—
1184	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1185	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1186	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1187	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1188	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1189	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1190	C₂²	C₇×#585	1	1	yes	characteristic
1191	C₄	—	2	2	no	—
1192	C₄	—	2	2	no	—
1193	C₄	—	2	2	no	—
1194	C₄	—	2	2	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	2	2	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	4	2	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	2	no	—
1204	C₄	—	4	2	no	—
1205	C₄	—	4	2	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	1	no	—
1208	C₄	C₇×#538	1	4	yes	complemented
1209	C₂	—	2	4	no	—
1210	C₂	—	4	2	no	—
1211	C₂	—	8	2	no	—
1212	C₂	—	8	2	no	—
1213	C₂	—	8	2	no	—
1214	C₂	C₂×C₇×#532	1	1	yes	characteristic
1215	C₂	C₂×C₇×#538	1	1	yes	characteristic
1216	C₂	C₇×#3460	1	1	yes	characteristic
1217	C₂	C₇×#3496	1	1	yes	characteristic
1218	C₂	C₇×#3498	1	1	yes	characteristic
1219	C₂	C₇×#3514	1	1	yes	characteristic
1220	C₂	C₇×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₇×#538	C₂	semidirect
2. C₇×#2860	C₂	semidirect
3. C₇×#2858	C₂	semidirect
4. C₇×#2856	C₂	semidirect
5. C₇×#2854	C₂	semidirect
6. C₇×#2662	C₂	semidirect
7. C₇×#2661	C₂	semidirect
8. C₇×#2555	C₂	semidirect
9. C₇×#2554	C₂	semidirect
10. C₇×#2512	C₂	semidirect
11. C₇×#2491	C₂	semidirect
12. C₇×#2472	C₂	semidirect
13. C₇×#2445	C₂	semidirect
14. C₇×#2440	C₂	semidirect
15. C₇×#2433	C₂	semidirect
16. C₇×#2428	C₂	semidirect
17. C₇×#2424	C₂	semidirect
18. C₇×#2416	C₂	semidirect
19. C₇×#2408	C₂	semidirect
20. C₇×#2321	C₂	semidirect
21. C₄×C₇×#121	C₂	semidirect
22. C₂×C₇×#390	C₂	semidirect
23. C₄²×C₇×D₄	C₂	semidirect
26. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
29. C₂×C₇×#126	C₂²	semidirect
30. C₂×C₇×#126	C₂²	semidirect
31. C₂×C₇×#124	C₂²	semidirect
32. C₂×C₇×#124	C₂²	semidirect
33. C₂×C₇×#124	C₂²	semidirect
34. C₂×C₇×#123	C₂²	semidirect
35. C₂×C₇×#123	C₂²	semidirect
41. C₂×C₇×#121	C₂²	semidirect
42. C₂×C₇×#121	C₂²	semidirect
43. C₂×C₇×#121	C₂²	semidirect
44. C₂×C₇×#121	C₂²	semidirect
52. C₂×C₄×C₇×D₄	C₂²	semidirect
57. C₂²×C₄²×C₇	C₂²	semidirect
58. C₇×#398	C₂²	semidirect
59. C₇×#397	C₂²	semidirect
60. C₇×#396	C₂²	semidirect
61. C₇×#396	C₂²	semidirect
62. C₇×#395	C₂²	semidirect
64. C₇×#394	C₂²	semidirect
65. C₇×#394	C₂²	semidirect
66. C₇×#394	C₂²	semidirect
67. C₇×#394	C₂²	semidirect
68. C₇×#394	C₂²	semidirect
69. C₇×#393	C₂²	semidirect
73. C₇×#392	C₂²	semidirect
84. C₇×#390	C₂²	semidirect
85. C₇×#390	C₂²	semidirect
86. C₇×#390	C₂²	semidirect
87. C₇×#390	C₂²	semidirect
88. C₇×#390	C₂²	semidirect
89. C₇×#390	C₂²	semidirect
90. C₇×#389	C₂²	semidirect
91. C₇×#389	C₂²	semidirect
92. C₇×#389	C₂²	semidirect
93. C₇×#389	C₂²	semidirect
94. C₇×#388	C₂²	semidirect
95. C₇×#388	C₂²	semidirect
96. C₇×#388	C₂²	semidirect
97. C₇×#388	C₂²	semidirect
98. C₇×#388	C₂²	semidirect
99. C₇×#388	C₂²	semidirect
100. C₇×#388	C₂²	semidirect
101. C₇×#388	C₂²	semidirect
104. C₇×#386	C₂²	semidirect
105. C₇×#386	C₂²	semidirect
106. C₇×#386	C₂²	semidirect
108. C₇×#384	C₂²	semidirect
110. C₇×#380	C₂²	semidirect
112. C₄×C₇×C₄⋊C₄	C₂²	semidirect
113. C₄×C₇×C₄⋊C₄	C₂²	semidirect
114. C₄×C₇×C₄⋊C₄	C₂²	semidirect
115. C₄×C₇×C₄⋊C₄	C₂²	semidirect
119. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
120. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
121. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
122. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
123. C₄³×C₇	C₂²	semidirect
124. #35007	C₇	direct (N × H)
177. C₄×C₇×D₄	D₄	semidirect
259. C₂×#538	C₂×C₇	semidirect
260. #2860	C₂×C₇	semidirect
261. #2858	C₂×C₇	semidirect
262. #2856	C₂×C₇	semidirect
263. #2854	C₂×C₇	semidirect
264. #2662	C₂×C₇	semidirect
265. #2661	C₂×C₇	semidirect
266. #2555	C₂×C₇	semidirect
267. #2554	C₂×C₇	semidirect
268. #2512	C₂×C₇	semidirect
269. #2491	C₂×C₇	semidirect
270. #2472	C₂×C₇	semidirect
271. #2445	C₂×C₇	semidirect
272. #2440	C₂×C₇	semidirect
273. #2433	C₂×C₇	semidirect
274. #2428	C₂×C₇	semidirect
275. #2424	C₂×C₇	semidirect
276. #2416	C₂×C₇	semidirect
277. #2408	C₂×C₇	semidirect
278. #2321	C₂×C₇	semidirect
279. C₄×#121	C₂×C₇	semidirect
280. C₂×#390	C₂×C₇	semidirect
281. C₄²×D₄	C₂×C₇	semidirect
359. C₂²×C₄×C₇	C₂×D₄	semidirect
394. C₇×C₄⋊C₄	C₂×D₄	semidirect
426. C₇×C₂²⋊C₄	C₂×D₄	semidirect
441. C₄²×C₇	C₂×D₄	semidirect
444. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
447. C₂×#126	C₂²×C₇	semidirect
448. C₂×#126	C₂²×C₇	semidirect
449. C₂×#124	C₂²×C₇	semidirect
450. C₂×#124	C₂²×C₇	semidirect
451. C₂×#124	C₂²×C₇	semidirect
452. C₂×#123	C₂²×C₇	semidirect
453. C₂×#123	C₂²×C₇	semidirect
459. C₂×#121	C₂²×C₇	semidirect
460. C₂×#121	C₂²×C₇	semidirect
461. C₂×#121	C₂²×C₇	semidirect
462. C₂×#121	C₂²×C₇	semidirect
470. C₂×C₄×D₄	C₂²×C₇	semidirect
475. C₂²×C₄²	C₂²×C₇	semidirect
476. #398	C₂²×C₇	semidirect
477. #397	C₂²×C₇	semidirect
478. #396	C₂²×C₇	semidirect
479. #396	C₂²×C₇	semidirect
480. #395	C₂²×C₇	semidirect
482. #394	C₂²×C₇	semidirect
483. #394	C₂²×C₇	semidirect
484. #394	C₂²×C₇	semidirect
485. #394	C₂²×C₇	semidirect
486. #394	C₂²×C₇	semidirect
487. #393	C₂²×C₇	semidirect
491. #392	C₂²×C₇	semidirect
502. #390	C₂²×C₇	semidirect
503. #390	C₂²×C₇	semidirect
504. #390	C₂²×C₇	semidirect
505. #390	C₂²×C₇	semidirect
506. #390	C₂²×C₇	semidirect
507. #390	C₂²×C₇	semidirect
508. #389	C₂²×C₇	semidirect
509. #389	C₂²×C₇	semidirect
510. #389	C₂²×C₇	semidirect
511. #389	C₂²×C₇	semidirect
512. #388	C₂²×C₇	semidirect
513. #388	C₂²×C₇	semidirect
514. #388	C₂²×C₇	semidirect
515. #388	C₂²×C₇	semidirect
516. #388	C₂²×C₇	semidirect
517. #388	C₂²×C₇	semidirect
518. #388	C₂²×C₇	semidirect
519. #388	C₂²×C₇	semidirect
522. #386	C₂²×C₇	semidirect
523. #386	C₂²×C₇	semidirect
524. #386	C₂²×C₇	semidirect
526. #384	C₂²×C₇	semidirect
528. #380	C₂²×C₇	semidirect
530. C₄×C₄⋊C₄	C₂²×C₇	semidirect
531. C₄×C₄⋊C₄	C₂²×C₇	semidirect
532. C₄×C₄⋊C₄	C₂²×C₇	semidirect
533. C₄×C₄⋊C₄	C₂²×C₇	semidirect
537. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
538. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
539. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
540. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
541. C₄³	C₂²×C₇	semidirect
713. C₄×D₄	C₇×D₄	semidirect
855. C₄×C₇	#538	semidirect
933. C₂²×C₄	C₂×C₇×D₄	semidirect
968. C₄⋊C₄	C₂×C₇×D₄	semidirect
1000. C₂²⋊C₄	C₂×C₇×D₄	semidirect
1015. C₄²	C₂×C₇×D₄	semidirect
1147. C₇	#35007	direct (N × H)
1208. C₄	C₇×#538	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#538	2
C₇×#2860	2
C₇×#2858	2
C₇×#2856	2
C₇×#2854	2
C₇×#2662	2
C₇×#2661	2
C₇×#2555	2
C₇×#2554	2
C₇×#2512	2
C₇×#2491	2
C₇×#2472	2
C₇×#2445	2
C₇×#2440	2
C₇×#2433	2
C₇×#2428	2
C₇×#2424	2
C₇×#2416	2
C₇×#2408	2
C₇×#2321	2
C₄×C₇×#121	2
C₂×C₇×#390	2
C₄²×C₇×D₄	2
#35007	7

Subgroups — C7×#35007 #13212223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#35007 #13212223