Subgroups — C₇×#34681 #13211897

Order 1792.

3700 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#525	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2472	C₂	1	2	yes	maximal, complemented
5	C₇×#2464	C₂	1	2	yes	maximal, complemented
6	C₇×#2461	C₂	1	2	yes	maximal, complemented
7	C₇×#2452	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2445	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2440	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2433	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2428	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2424	C₂	1	2	yes	maximal, complemented
13	C₇×#2422	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2416	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2392	C₂	1	2	yes	maximal, complemented
17	C₇×#2388	C₂	1	2	yes	maximal, complemented
18	C₄×C₇×#127	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₇×#120	C₂	1	2	yes	maximal, complemented
22	C₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₇×#41	C₂²	1	2	yes	complemented
25	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
27	C₇×#532	—	2	8	no	—
28	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₇×#127	C₂²	1	1	yes	characteristic
30	C₂×C₇×#127	C₂²	1	1	yes	characteristic
31	C₂×C₇×#124	C₂²	1	2	yes	complemented
32	C₇×#525	—	2	16	no	—
33	C₂×C₇×#123	C₂²	1	2	yes	complemented
34	C₂×C₇×#123	C₂²	1	2	yes	complemented
35	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×C₇×#121	C₂²	1	1	yes	characteristic
38	C₂×C₇×#121	C₂²	1	1	yes	characteristic
39	C₂×C₇×#121	C₂²	1	2	yes	—
40	C₂×C₇×#121	C₂²	1	1	yes	characteristic
41	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₇×#121	C₂²	1	2	yes	complemented
43	C₂×C₇×#121	C₂²	1	2	yes	complemented
44	C₂×C₇×#120	C₂²	1	2	yes	—
45	C₂×C₇×#120	C₂²	1	2	yes	—
46	C₂×C₇×#120	C₂²	1	2	yes	—
47	C₂×C₄×C₇×D₄	—	2	8	no	—
48	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
49	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
54	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
56	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
57	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
59	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
60	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
61	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
63	C₂×C₇×#117	C₂²	1	2	yes	complemented
64	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
66	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
67	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
68	C₇×#398	C₂²	1	2	yes	complemented
69	C₇×#397	C₂²	1	2	yes	complemented
70	C₇×#396	C₂²	1	2	yes	complemented
71	C₇×#396	C₂²	1	2	yes	complemented
72	C₇×#395	C₂²	1	2	yes	complemented
73	C₇×#394	C₂²	1	2	yes	—
74	C₇×#394	C₂²	1	2	yes	complemented
75	C₇×#394	C₂²	1	2	yes	complemented
76	C₇×#394	C₂²	1	2	yes	complemented
77	C₇×#394	C₂²	1	2	yes	complemented
78	C₇×#394	C₂²	1	2	yes	complemented
79	C₇×#393	C₂²	1	2	yes	complemented
80	C₇×#392	C₂²	1	2	yes	—
81	C₇×#392	C₂²	1	2	yes	—
82	C₇×#392	C₂²	1	2	yes	—
83	C₇×#392	C₂²	1	2	yes	complemented
84	C₇×#390	C₂²	1	1	yes	characteristic
85	C₇×#390	C₂²	1	1	yes	characteristic
86	C₇×#390	C₂²	1	1	yes	characteristic
87	C₇×#390	C₂²	1	1	yes	characteristic
88	C₇×#390	C₂²	1	1	yes	characteristic, complemented
89	C₇×#390	C₂²	1	2	yes	complemented
90	C₇×#390	C₂²	1	1	yes	characteristic, complemented
91	C₇×#390	C₂²	1	2	yes	complemented
92	C₇×#389	C₂²	1	1	yes	characteristic, complemented
93	C₇×#389	C₂²	1	1	yes	characteristic, complemented
94	C₇×#389	C₂²	1	1	yes	characteristic, complemented
95	C₇×#389	C₂²	1	1	yes	characteristic, 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×#386	C₂²	1	2	yes	—
101	C₇×#386	C₂²	1	2	yes	—
102	C₇×#386	C₂²	1	2	yes	complemented
103	C₇×#386	C₂²	1	2	yes	complemented
104	C₇×#386	C₂²	1	2	yes	complemented
105	C₇×#385	C₂²	1	2	yes	—
106	C₇×#385	C₂²	1	2	yes	complemented
107	C₇×#385	C₂²	1	2	yes	complemented
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	2	yes	complemented
121	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
124	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
125	C₄³×C₇	C₂²	1	1	yes	characteristic, complemented
126	#34681	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁵×C₇	C₂³	1	2	yes	—
128	C₂×C₇×#41	—	2	8	no	—
129	C₂×C₇×#41	—	2	8	no	—
130	C₂×C₇×#41	—	4	4	no	—
131	C₂²×C₇×Q₈	C₂³	1	2	yes	—
132	C₂²×C₇×D₄	—	2	4	no	—
133	C₂²×C₇×D₄	—	2	4	no	—
134	C₂²×C₇×D₄	—	2	4	no	—
135	C₂²×C₇×D₄	C₂³	1	2	yes	—
136	C₂²×C₇×D₄	C₂³	1	2	yes	—
137	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
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	C₂²×C₇×D₄	C₂³	1	2	yes	—
144	C₂²×C₇×D₄	C₂³	1	2	yes	—
145	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
146	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
147	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₇	—	2	8	no	—
149	C₂³×C₄×C₇	—	2	8	no	—
150	C₂³×C₄×C₇	—	4	4	no	—
151	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
152	C₂³×C₄×C₇	C₂³	1	2	yes	—
153	C₂³×C₄×C₇	C₂³	1	2	yes	—
154	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₇	C₂³	1	2	yes	—
157	C₂³×C₄×C₇	C₂³	1	2	yes	—
158	C₂³×C₄×C₇	C₂³	1	2	yes	—
159	C₂³×C₄×C₇	C₂³	1	2	yes	—
160	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
161	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
162	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
163	C₇×C₄⋊Q₈	—	2	4	no	—
164	C₇×#127	—	2	4	no	—
165	C₇×#127	—	2	4	no	—
166	C₇×#124	—	2	8	no	—
167	C₇×#123	—	2	8	no	—
168	C₇×#123	—	2	8	no	—
169	C₇×C₂²⋊Q₈	—	2	8	no	—
170	C₇×C₂²⋊Q₈	—	2	8	no	—
171	C₇×#121	—	2	8	no	—
172	C₇×#121	—	2	4	no	—
173	C₇×#121	—	2	4	no	—
174	C₇×#121	—	2	4	no	—
175	C₇×#121	—	2	4	no	—
176	C₇×#121	—	2	8	no	—
177	C₇×#121	—	2	8	no	—
178	C₇×#120	—	2	8	no	—
179	C₇×#120	—	2	8	no	—
180	C₇×#120	—	2	8	no	—
181	C₄×C₇×D₄	—	2	4	no	—
182	C₄×C₇×D₄	—	2	8	no	—
183	C₄×C₇×D₄	—	2	8	no	—
184	C₄×C₇×D₄	—	2	8	no	—
185	C₄×C₇×D₄	—	2	8	no	—
186	C₄×C₇×D₄	—	2	4	no	—
187	C₄×C₇×D₄	—	2	4	no	—
188	C₄×C₇×D₄	—	2	8	no	—
189	C₄×C₇×D₄	—	2	4	no	—
190	C₄×C₇×D₄	—	2	4	no	—
191	C₄×C₇×D₄	—	2	4	no	—
192	C₄×C₇×D₄	—	2	8	no	—
193	C₄×C₇×D₄	—	4	4	no	—
194	C₄×C₇×D₄	D₄	1	8	yes	complemented
195	C₄×C₇×D₄	D₄	1	8	yes	complemented
196	C₇×#117	—	2	8	no	—
197	C₂×C₇×C₄⋊C₄	—	2	4	no	—
198	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
212	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
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	1	yes	characteristic
219	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
228	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
239	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
240	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₇	—	2	4	no	—
245	C₂×C₄²×C₇	—	2	4	no	—
246	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
247	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
248	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
249	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
250	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
251	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
252	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
253	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
254	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
255	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
256	C₂×C₄²×C₇	C₂³	1	2	yes	—
257	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
258	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
260	C₇×#95	C₂³	1	1	yes	characteristic
261	C₇×#95	C₂³	1	1	yes	characteristic
262	C₇×#95	C₂³	1	1	yes	characteristic
263	C₇×#95	C₂³	1	1	yes	characteristic
264	C₇×#95	C₂³	1	1	yes	characteristic
265	C₇×#95	C₂³	1	1	yes	characteristic
266	C₇×#95	C₂³	1	2	yes	—
267	C₇×#95	C₂³	1	2	yes	—
268	C₇×#95	C₂³	1	2	yes	—
269	C₇×#95	C₂³	1	2	yes	—
270	C₇×#95	C₂³	1	2	yes	—
271	C₇×#95	C₂³	1	2	yes	—
272	C₇×#95	C₂³	1	2	yes	—
273	C₂×#532	C₂×C₇	1	1	yes	characteristic, complemented
274	C₂×#525	C₂×C₇	1	2	yes	complemented
275	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic, complemented
276	#2472	C₂×C₇	1	2	yes	complemented
277	#2464	C₂×C₇	1	2	yes	complemented
278	#2461	C₂×C₇	1	2	yes	complemented
279	#2452	C₂×C₇	1	1	yes	characteristic, complemented
280	#2445	C₂×C₇	1	1	yes	characteristic, complemented
281	#2440	C₂×C₇	1	1	yes	characteristic, complemented
282	#2433	C₂×C₇	1	1	yes	characteristic, complemented
283	#2428	C₂×C₇	1	1	yes	characteristic, complemented
284	#2424	C₂×C₇	1	2	yes	complemented
285	#2422	C₂×C₇	1	1	yes	characteristic, complemented
286	#2416	C₂×C₇	1	1	yes	characteristic, complemented
287	#2408	C₂×C₇	1	1	yes	characteristic, complemented
288	#2392	C₂×C₇	1	2	yes	complemented
289	#2388	C₂×C₇	1	2	yes	complemented
290	C₄×#127	C₂×C₇	1	1	yes	characteristic, complemented
291	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
292	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
293	C₄×#120	C₂×C₇	1	2	yes	complemented
294	#2293	C₂×C₇	1	1	yes	characteristic, complemented
295	C₄²×D₄	C₂×C₇	1	1	yes	characteristic, complemented
296	C₂⁴×C₇	—	2	4	no	—
297	C₂⁴×C₇	—	2	4	no	—
298	C₂⁴×C₇	—	2	4	no	—
299	C₂⁴×C₇	—	2	4	no	—
300	C₂⁴×C₇	—	2	4	no	—
301	C₂⁴×C₇	—	4	2	no	—
302	C₂⁴×C₇	—	4	2	no	—
303	C₂⁴×C₇	C₂⁴	1	2	yes	—
304	C₂⁴×C₇	C₂⁴	1	2	yes	—
305	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
306	C₂⁴×C₇	C₂⁴	1	2	yes	—
307	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
308	C₇×#41	—	4	32	no	—
309	C₂×C₇×Q₈	—	2	4	no	—
310	C₂×C₇×Q₈	—	2	4	no	—
311	C₂×C₇×Q₈	—	4	2	no	—
312	C₂×C₇×D₄	—	2	32	no	—
313	C₂×C₇×D₄	—	2	4	no	—
314	C₂×C₇×D₄	—	2	2	no	—
315	C₂×C₇×D₄	—	2	2	no	—
316	C₂×C₇×D₄	—	2	4	no	—
317	C₂×C₇×D₄	—	2	4	no	—
318	C₂×C₇×D₄	—	2	4	no	—
319	C₂×C₇×D₄	—	2	4	no	—
320	C₂×C₇×D₄	—	2	4	no	—
321	C₂×C₇×D₄	—	2	4	no	—
322	C₂×C₇×D₄	—	2	4	no	—
323	C₂×C₇×D₄	—	2	4	no	—
324	C₂×C₇×D₄	—	2	4	no	—
325	C₂×C₇×D₄	—	2	4	no	—
326	C₂×C₇×D₄	—	2	4	no	—
327	C₂×C₇×D₄	—	2	4	no	—
328	C₂×C₇×D₄	—	2	4	no	—
329	C₂×C₇×D₄	—	2	2	no	—
330	C₂×C₇×D₄	—	2	4	no	—
331	C₂×C₇×D₄	—	2	2	no	—
332	C₂×C₇×D₄	—	2	4	no	—
333	C₂×C₇×D₄	—	2	4	no	—
334	C₂×C₇×D₄	—	2	4	no	—
335	C₂×C₇×D₄	—	2	2	no	—
336	C₂×C₇×D₄	—	2	2	no	—
337	C₂×C₇×D₄	—	2	2	no	—
338	C₂×C₇×D₄	—	2	4	no	—
339	C₂×C₇×D₄	—	2	4	no	—
340	C₂×C₇×D₄	—	2	2	no	—
341	C₂×C₇×D₄	—	2	2	no	—
342	C₂×C₇×D₄	—	4	2	no	—
343	C₂×C₇×D₄	—	4	2	no	—
344	C₂×C₇×D₄	—	4	2	no	—
345	C₂×C₇×D₄	—	4	2	no	—
346	C₂×C₇×D₄	—	4	2	no	—
347	C₂×C₇×D₄	—	4	2	no	—
348	C₂×C₇×D₄	—	4	2	no	—
349	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
350	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
351	C₂×C₇×D₄	#41	1	4	yes	complemented
352	C₂²×C₄×C₇	—	2	2	no	—
353	C₂²×C₄×C₇	—	2	2	no	—
354	C₂²×C₄×C₇	—	2	2	no	—
355	C₂²×C₄×C₇	—	2	4	no	—
356	C₂²×C₄×C₇	—	2	2	no	—
357	C₂²×C₄×C₇	—	2	2	no	—
358	C₂²×C₄×C₇	—	2	4	no	—
359	C₂²×C₄×C₇	—	2	2	no	—
360	C₂²×C₄×C₇	—	2	4	no	—
361	C₂²×C₄×C₇	—	2	4	no	—
362	C₂²×C₄×C₇	—	2	2	no	—
363	C₂²×C₄×C₇	—	2	2	no	—
364	C₂²×C₄×C₇	—	2	2	no	—
365	C₂²×C₄×C₇	—	2	2	no	—
366	C₂²×C₄×C₇	—	2	4	no	—
367	C₂²×C₄×C₇	—	2	4	no	—
368	C₂²×C₄×C₇	—	2	4	no	—
369	C₂²×C₄×C₇	—	2	4	no	—
370	C₂²×C₄×C₇	—	2	4	no	—
371	C₂²×C₄×C₇	—	2	4	no	—
372	C₂²×C₄×C₇	—	2	4	no	—
373	C₂²×C₄×C₇	—	2	4	no	—
374	C₂²×C₄×C₇	—	2	2	no	—
375	C₂²×C₄×C₇	—	2	2	no	—
376	C₂²×C₄×C₇	—	2	2	no	—
377	C₂²×C₄×C₇	—	2	4	no	—
378	C₂²×C₄×C₇	—	2	4	no	—
379	C₂²×C₄×C₇	—	4	2	no	—
380	C₂²×C₄×C₇	—	4	2	no	—
381	C₂²×C₄×C₇	—	4	2	no	—
382	C₂²×C₄×C₇	—	4	1	no	—
383	C₂²×C₄×C₇	—	4	1	no	—
384	C₂²×C₄×C₇	—	4	32	no	—
385	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
386	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
387	C₂²×C₄×C₇	C₂×D₄	1	4	yes	complemented
388	C₂²×C₄×C₇	#41	1	4	yes	complemented
389	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
393	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
394	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
395	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
396	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
401	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
407	C₇×C₄⋊C₄	—	2	4	no	—
408	C₇×C₄⋊C₄	—	2	2	no	—
409	C₇×C₄⋊C₄	—	2	4	no	—
410	C₇×C₄⋊C₄	—	2	4	no	—
411	C₇×C₄⋊C₄	—	2	4	no	—
412	C₇×C₄⋊C₄	—	2	2	no	—
413	C₇×C₄⋊C₄	—	2	4	no	—
414	C₇×C₄⋊C₄	—	2	4	no	—
415	C₇×C₄⋊C₄	—	2	4	no	—
416	C₇×C₄⋊C₄	—	2	2	no	—
417	C₇×C₄⋊C₄	—	2	2	no	—
418	C₇×C₄⋊C₄	—	2	2	no	—
419	C₇×C₄⋊C₄	—	2	2	no	—
420	C₇×C₄⋊C₄	—	4	2	no	—
421	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
422	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
423	C₇×C₂²⋊C₄	—	2	4	no	—
424	C₇×C₂²⋊C₄	—	2	4	no	—
425	C₇×C₂²⋊C₄	—	2	4	no	—
426	C₇×C₂²⋊C₄	—	2	4	no	—
427	C₇×C₂²⋊C₄	—	2	2	no	—
428	C₇×C₂²⋊C₄	—	2	4	no	—
429	C₇×C₂²⋊C₄	—	2	4	no	—
430	C₇×C₂²⋊C₄	—	2	4	no	—
431	C₇×C₂²⋊C₄	—	2	4	no	—
432	C₇×C₂²⋊C₄	—	2	4	no	—
433	C₇×C₂²⋊C₄	—	2	4	no	—
434	C₇×C₂²⋊C₄	—	2	4	no	—
435	C₇×C₂²⋊C₄	—	2	4	no	—
436	C₇×C₂²⋊C₄	—	2	4	no	—
437	C₇×C₂²⋊C₄	—	2	4	no	—
438	C₇×C₂²⋊C₄	—	2	4	no	—
439	C₇×C₂²⋊C₄	—	2	2	no	—
440	C₇×C₂²⋊C₄	—	2	2	no	—
441	C₇×C₂²⋊C₄	—	2	4	no	—
442	C₇×C₂²⋊C₄	—	2	4	no	—
443	C₇×C₂²⋊C₄	—	2	4	no	—
444	C₇×C₂²⋊C₄	—	4	2	no	—
445	C₇×C₂²⋊C₄	—	4	2	no	—
446	C₇×C₂²⋊C₄	—	4	2	no	—
447	C₇×C₂²⋊C₄	—	4	2	no	—
448	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
449	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
450	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
451	C₇×C₂²⋊C₄	#41	1	4	yes	complemented
452	C₄²×C₇	—	2	2	no	—
453	C₄²×C₇	—	2	2	no	—
454	C₄²×C₇	—	2	2	no	—
455	C₄²×C₇	—	2	2	no	—
456	C₄²×C₇	—	2	2	no	—
457	C₄²×C₇	—	2	2	no	—
458	C₄²×C₇	—	2	4	no	—
459	C₄²×C₇	—	2	2	no	—
460	C₄²×C₇	—	2	2	no	—
461	C₄²×C₇	—	2	2	no	—
462	C₄²×C₇	—	2	2	no	—
463	C₄²×C₇	—	4	1	no	—
464	C₄²×C₇	C₂×D₄	1	4	yes	—
465	C₄²×C₇	C₂×D₄	1	4	yes	complemented
466	C₂²×#41	C₂²×C₇	1	2	yes	complemented
467	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
468	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
469	#532	—	2	8	no	—
470	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
471	C₂×#127	C₂²×C₇	1	1	yes	characteristic
472	C₂×#127	C₂²×C₇	1	1	yes	characteristic
473	C₂×#124	C₂²×C₇	1	2	yes	complemented
474	#525	—	2	16	no	—
475	C₂×#123	C₂²×C₇	1	2	yes	complemented
476	C₂×#123	C₂²×C₇	1	2	yes	complemented
477	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
478	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
479	C₂×#121	C₂²×C₇	1	1	yes	characteristic
480	C₂×#121	C₂²×C₇	1	1	yes	characteristic
481	C₂×#121	C₂²×C₇	1	2	yes	—
482	C₂×#121	C₂²×C₇	1	1	yes	characteristic
483	C₂×#121	C₂²×C₇	1	2	yes	complemented
484	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
485	C₂×#121	C₂²×C₇	1	2	yes	complemented
486	C₂×#120	C₂²×C₇	1	2	yes	—
487	C₂×#120	C₂²×C₇	1	2	yes	—
488	C₂×#120	C₂²×C₇	1	2	yes	—
489	C₂×C₄×D₄	—	2	8	no	—
490	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
491	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
492	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
493	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
494	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
495	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
496	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
497	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
498	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
499	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
501	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
502	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
503	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
504	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
505	C₂×#117	C₂²×C₇	1	2	yes	complemented
506	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
507	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
508	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
509	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
510	#398	C₂²×C₇	1	2	yes	complemented
511	#397	C₂²×C₇	1	2	yes	complemented
512	#396	C₂²×C₇	1	2	yes	complemented
513	#396	C₂²×C₇	1	2	yes	complemented
514	#395	C₂²×C₇	1	2	yes	complemented
515	#394	C₂²×C₇	1	2	yes	—
516	#394	C₂²×C₇	1	2	yes	complemented
517	#394	C₂²×C₇	1	2	yes	complemented
518	#394	C₂²×C₇	1	2	yes	complemented
519	#394	C₂²×C₇	1	2	yes	complemented
520	#394	C₂²×C₇	1	2	yes	complemented
521	#393	C₂²×C₇	1	2	yes	complemented
522	#392	C₂²×C₇	1	2	yes	—
523	#392	C₂²×C₇	1	2	yes	—
524	#392	C₂²×C₇	1	2	yes	—
525	#392	C₂²×C₇	1	2	yes	complemented
526	#390	C₂²×C₇	1	1	yes	characteristic
527	#390	C₂²×C₇	1	1	yes	characteristic
528	#390	C₂²×C₇	1	1	yes	characteristic
529	#390	C₂²×C₇	1	1	yes	characteristic
530	#390	C₂²×C₇	1	1	yes	characteristic, complemented
531	#390	C₂²×C₇	1	2	yes	complemented
532	#390	C₂²×C₇	1	2	yes	complemented
533	#390	C₂²×C₇	1	1	yes	characteristic, complemented
534	#389	C₂²×C₇	1	1	yes	characteristic, complemented
535	#389	C₂²×C₇	1	1	yes	characteristic, complemented
536	#389	C₂²×C₇	1	1	yes	characteristic, complemented
537	#389	C₂²×C₇	1	1	yes	characteristic, complemented
538	#388	C₂²×C₇	1	2	yes	complemented
539	#388	C₂²×C₇	1	2	yes	complemented
540	#388	C₂²×C₇	1	2	yes	complemented
541	#388	C₂²×C₇	1	2	yes	complemented
542	#386	C₂²×C₇	1	2	yes	—
543	#386	C₂²×C₇	1	2	yes	—
544	#386	C₂²×C₇	1	2	yes	complemented
545	#386	C₂²×C₇	1	2	yes	complemented
546	#386	C₂²×C₇	1	2	yes	complemented
547	#385	C₂²×C₇	1	2	yes	—
548	#385	C₂²×C₇	1	2	yes	complemented
549	#385	C₂²×C₇	1	2	yes	complemented
550	#384	C₂²×C₇	1	1	yes	characteristic, complemented
551	#380	C₂²×C₇	1	1	yes	characteristic
552	#380	C₂²×C₇	1	1	yes	characteristic, complemented
553	#379	C₂²×C₇	1	2	yes	—
554	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
555	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
556	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
557	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
558	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
559	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
560	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
561	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
562	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
563	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
564	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
565	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
566	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
567	C₄³	C₂²×C₇	1	1	yes	characteristic, complemented
568	C₂³×C₇	—	2	1	no	—
569	C₂³×C₇	—	2	1	no	—
570	C₂³×C₇	—	2	1	no	—
571	C₂³×C₇	—	2	1	no	—
572	C₂³×C₇	—	2	16	no	—
573	C₂³×C₇	—	2	2	no	—
574	C₂³×C₇	—	2	2	no	—
575	C₂³×C₇	—	2	2	no	—
576	C₂³×C₇	—	2	1	no	—
577	C₂³×C₇	—	2	1	no	—
578	C₂³×C₇	—	2	1	no	—
579	C₂³×C₇	—	2	2	no	—
580	C₂³×C₇	—	2	2	no	—
581	C₂³×C₇	—	2	1	no	—
582	C₂³×C₇	—	2	2	no	—
583	C₂³×C₇	—	2	2	no	—
584	C₂³×C₇	—	2	2	no	—
585	C₂³×C₇	—	2	2	no	—
586	C₂³×C₇	—	2	2	no	—
587	C₂³×C₇	—	2	1	no	—
588	C₂³×C₇	—	2	2	no	—
589	C₂³×C₇	—	2	1	no	—
590	C₂³×C₇	—	2	2	no	—
591	C₂³×C₇	—	2	2	no	—
592	C₂³×C₇	—	2	2	no	—
593	C₂³×C₇	—	2	2	no	—
594	C₂³×C₇	—	2	2	no	—
595	C₂³×C₇	—	2	2	no	—
596	C₂³×C₇	—	2	2	no	—
597	C₂³×C₇	—	2	2	no	—
598	C₂³×C₇	—	4	8	no	—
599	C₂³×C₇	—	4	8	no	—
600	C₂³×C₇	—	4	8	no	—
601	C₂³×C₇	—	4	8	no	—
602	C₂³×C₇	—	4	8	no	—
603	C₂³×C₇	—	4	8	no	—
604	C₂³×C₇	C₂²×D₄	1	4	yes	—
605	C₂³×C₇	C₂²×D₄	1	2	yes	—
606	C₂³×C₇	C₂²×D₄	1	2	yes	—
607	C₂³×C₇	C₂×#41	1	4	yes	—
608	C₂³×C₇	C₂×#41	1	2	yes	—
609	C₂³×C₇	C₂×#41	1	2	yes	—
610	C₂³×C₇	C₂⁵	1	1	yes	characteristic
611	C₇×Q₈	—	4	8	no	—
612	C₇×D₄	—	2	16	no	—
613	C₇×D₄	—	2	8	no	—
614	C₇×D₄	—	2	8	no	—
615	C₇×D₄	—	2	8	no	—
616	C₇×D₄	—	4	8	no	—
617	C₇×D₄	—	4	8	no	—
618	C₇×D₄	—	4	8	no	—
619	C₇×D₄	—	4	8	no	—
620	C₇×D₄	—	4	8	no	—
621	C₇×D₄	—	4	8	no	—
622	C₇×D₄	—	4	8	no	—
623	C₇×D₄	—	4	8	no	—
624	C₇×D₄	—	4	4	no	—
625	C₂×C₄×C₇	—	2	1	no	—
626	C₂×C₄×C₇	—	2	1	no	—
627	C₂×C₄×C₇	—	2	1	no	—
628	C₂×C₄×C₇	—	2	1	no	—
629	C₂×C₄×C₇	—	2	2	no	—
630	C₂×C₄×C₇	—	2	1	no	—
631	C₂×C₄×C₇	—	2	1	no	—
632	C₂×C₄×C₇	—	2	1	no	—
633	C₂×C₄×C₇	—	2	1	no	—
634	C₂×C₄×C₇	—	2	1	no	—
635	C₂×C₄×C₇	—	2	1	no	—
636	C₂×C₄×C₇	—	2	1	no	—
637	C₂×C₄×C₇	—	2	1	no	—
638	C₂×C₄×C₇	—	2	2	no	—
639	C₂×C₄×C₇	—	2	1	no	—
640	C₂×C₄×C₇	—	2	1	no	—
641	C₂×C₄×C₇	—	2	1	no	—
642	C₂×C₄×C₇	—	2	1	no	—
643	C₂×C₄×C₇	—	2	8	no	—
644	C₂×C₄×C₇	—	2	8	no	—
645	C₂×C₄×C₇	—	2	16	no	—
646	C₂×C₄×C₇	—	2	8	no	—
647	C₂×C₄×C₇	—	2	1	no	—
648	C₂×C₄×C₇	—	2	1	no	—
649	C₂×C₄×C₇	—	2	2	no	—
650	C₂×C₄×C₇	—	2	2	no	—
651	C₂×C₄×C₇	—	2	2	no	—
652	C₂×C₄×C₇	—	2	2	no	—
653	C₂×C₄×C₇	—	2	2	no	—
654	C₂×C₄×C₇	—	2	2	no	—
655	C₂×C₄×C₇	—	2	1	no	—
656	C₂×C₄×C₇	—	2	1	no	—
657	C₂×C₄×C₇	—	2	2	no	—
658	C₂×C₄×C₇	—	2	1	no	—
659	C₂×C₄×C₇	—	2	1	no	—
660	C₂×C₄×C₇	—	2	2	no	—
661	C₂×C₄×C₇	—	2	2	no	—
662	C₂×C₄×C₇	—	2	1	no	—
663	C₂×C₄×C₇	—	2	2	no	—
664	C₂×C₄×C₇	—	2	2	no	—
665	C₂×C₄×C₇	—	2	1	no	—
666	C₂×C₄×C₇	—	2	1	no	—
667	C₂×C₄×C₇	—	2	2	no	—
668	C₂×C₄×C₇	—	4	4	no	—
669	C₂×C₄×C₇	—	4	8	no	—
670	C₂×C₄×C₇	—	4	4	no	—
671	C₂×C₄×C₇	—	4	8	no	—
672	C₂×C₄×C₇	—	4	8	no	—
673	C₂×C₄×C₇	—	4	4	no	—
674	C₂×C₄×C₇	—	4	8	no	—
675	C₂×C₄×C₇	—	4	8	no	—
676	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
677	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
678	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
679	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
680	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
681	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
682	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
683	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
684	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
685	C₂×C₄×C₇	C₂×#41	1	2	yes	—
686	C₂×C₄×C₇	C₂×#41	1	2	yes	—
687	C₂×C₄×C₇	C₂×#41	1	2	yes	—
688	C₂×C₄×C₇	C₂×#41	1	2	yes	—
689	C₂×C₄×C₇	C₂×#41	1	2	yes	—
690	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
691	C₂⁵	C₂³×C₇	1	2	yes	—
692	C₂×#41	—	2	8	no	—
693	C₂×#41	—	2	8	no	—
694	C₂×#41	—	4	4	no	—
695	C₂²×Q₈	C₂³×C₇	1	2	yes	—
696	C₂²×D₄	—	2	4	no	—
697	C₂²×D₄	—	2	4	no	—
698	C₂²×D₄	—	2	4	no	—
699	C₂²×D₄	C₂³×C₇	1	2	yes	—
700	C₂²×D₄	C₂³×C₇	1	2	yes	—
701	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
702	C₂²×D₄	C₂³×C₇	1	2	yes	—
703	C₂²×D₄	C₂³×C₇	1	2	yes	—
704	C₂²×D₄	C₂³×C₇	1	2	yes	—
705	C₂²×D₄	C₂³×C₇	1	2	yes	—
706	C₂²×D₄	C₂³×C₇	1	2	yes	—
707	C₂²×D₄	C₂³×C₇	1	2	yes	—
708	C₂²×D₄	C₂³×C₇	1	2	yes	—
709	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
710	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
711	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
712	C₂³×C₄	—	2	8	no	—
713	C₂³×C₄	—	2	8	no	—
714	C₂³×C₄	—	4	4	no	—
715	C₂³×C₄	C₂³×C₇	1	2	yes	—
716	C₂³×C₄	C₂³×C₇	1	2	yes	—
717	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
718	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
719	C₂³×C₄	C₂³×C₇	1	2	yes	—
720	C₂³×C₄	C₂³×C₇	1	2	yes	—
721	C₂³×C₄	C₂³×C₇	1	2	yes	—
722	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
723	C₂³×C₄	C₂³×C₇	1	2	yes	—
724	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
725	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
726	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
727	C₄⋊Q₈	—	2	4	no	—
728	#127	—	2	4	no	—
729	#127	—	2	4	no	—
730	#124	—	2	8	no	—
731	#123	—	2	8	no	—
732	#123	—	2	8	no	—
733	C₂²⋊Q₈	—	2	8	no	—
734	C₂²⋊Q₈	—	2	8	no	—
735	#121	—	2	8	no	—
736	#121	—	2	4	no	—
737	#121	—	2	4	no	—
738	#121	—	2	4	no	—
739	#121	—	2	4	no	—
740	#121	—	2	8	no	—
741	#121	—	2	8	no	—
742	#120	—	2	8	no	—
743	#120	—	2	8	no	—
744	#120	—	2	8	no	—
745	C₄×D₄	—	2	4	no	—
746	C₄×D₄	—	2	8	no	—
747	C₄×D₄	—	2	8	no	—
748	C₄×D₄	—	2	8	no	—
749	C₄×D₄	—	2	8	no	—
750	C₄×D₄	—	2	4	no	—
751	C₄×D₄	—	2	4	no	—
752	C₄×D₄	—	2	8	no	—
753	C₄×D₄	—	2	4	no	—
754	C₄×D₄	—	2	4	no	—
755	C₄×D₄	—	2	4	no	—
756	C₄×D₄	—	2	8	no	—
757	C₄×D₄	—	4	4	no	—
758	C₄×D₄	C₇×D₄	1	8	yes	complemented
759	C₄×D₄	C₇×D₄	1	8	yes	complemented
760	#117	—	2	8	no	—
761	C₂×C₄⋊C₄	—	2	4	no	—
762	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
763	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
764	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
765	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
766	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
767	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
768	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
769	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
770	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
771	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
772	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
773	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
774	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
775	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
776	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
777	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
778	C₂×C₂²⋊C₄	—	2	8	no	—
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	1	yes	characteristic
787	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
788	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
789	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
796	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
800	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
801	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
802	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
803	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
804	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
805	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
806	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
807	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
808	C₂×C₄²	—	2	4	no	—
809	C₂×C₄²	—	2	4	no	—
810	C₂×C₄²	C₂³×C₇	1	2	yes	—
811	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
812	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
813	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
814	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
815	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
816	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
817	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
818	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
819	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
820	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
821	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
822	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
823	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
824	#95	C₂³×C₇	1	1	yes	characteristic
825	#95	C₂³×C₇	1	1	yes	characteristic
826	#95	C₂³×C₇	1	1	yes	characteristic
827	#95	C₂³×C₇	1	1	yes	characteristic
828	#95	C₂³×C₇	1	1	yes	characteristic
829	#95	C₂³×C₇	1	1	yes	characteristic
830	#95	C₂³×C₇	1	2	yes	—
831	#95	C₂³×C₇	1	2	yes	—
832	#95	C₂³×C₇	1	2	yes	—
833	#95	C₂³×C₇	1	2	yes	—
834	#95	C₂³×C₇	1	2	yes	—
835	#95	C₂³×C₇	1	2	yes	—
836	#95	C₂³×C₇	1	2	yes	—
837	C₂²×C₇	—	2	2	no	—
838	C₂²×C₇	—	2	2	no	—
839	C₂²×C₇	—	2	2	no	—
840	C₂²×C₇	—	2	2	no	—
841	C₂²×C₇	—	2	2	no	—
842	C₂²×C₇	—	2	2	no	—
843	C₂²×C₇	—	2	4	no	—
844	C₂²×C₇	—	2	4	no	—
845	C₂²×C₇	—	2	2	no	—
846	C₂²×C₇	—	2	4	no	—
847	C₂²×C₇	—	2	2	no	—
848	C₂²×C₇	—	2	4	no	—
849	C₂²×C₇	—	2	2	no	—
850	C₂²×C₇	—	2	4	no	—
851	C₂²×C₇	—	2	4	no	—
852	C₂²×C₇	—	4	32	no	—
853	C₂²×C₇	—	4	1	no	—
854	C₂²×C₇	—	4	2	no	—
855	C₂²×C₇	—	4	2	no	—
856	C₂²×C₇	—	4	1	no	—
857	C₂²×C₇	—	4	2	no	—
858	C₂²×C₇	—	4	2	no	—
859	C₂²×C₇	—	4	2	no	—
860	C₂²×C₇	—	4	1	no	—
861	C₂²×C₇	—	4	2	no	—
862	C₂²×C₇	—	4	2	no	—
863	C₂²×C₇	—	4	1	no	—
864	C₂²×C₇	—	4	2	no	—
865	C₂²×C₇	—	4	2	no	—
866	C₂²×C₇	—	4	2	no	—
867	C₂²×C₇	—	4	2	no	—
868	C₂²×C₇	—	4	2	no	—
869	C₂²×C₇	—	4	2	no	—
870	C₂²×C₇	—	4	2	no	—
871	C₂²×C₇	—	4	2	no	—
872	C₂²×C₇	#532	1	4	yes	complemented
873	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
874	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
875	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
876	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
877	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
878	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
879	C₂²×C₇	#585	1	1	yes	characteristic
880	C₄×C₇	—	2	2	no	—
881	C₄×C₇	—	2	2	no	—
882	C₄×C₇	—	2	2	no	—
883	C₄×C₇	—	2	4	no	—
884	C₄×C₇	—	2	2	no	—
885	C₄×C₇	—	2	2	no	—
886	C₄×C₇	—	2	2	no	—
887	C₄×C₇	—	2	2	no	—
888	C₄×C₇	—	2	2	no	—
889	C₄×C₇	—	4	1	no	—
890	C₄×C₇	—	4	2	no	—
891	C₄×C₇	—	4	1	no	—
892	C₄×C₇	—	4	2	no	—
893	C₄×C₇	—	4	2	no	—
894	C₄×C₇	—	4	1	no	—
895	C₄×C₇	—	4	2	no	—
896	C₄×C₇	#525	1	4	yes	complemented
897	C₄×C₇	D₄²	1	4	yes	—
898	C₂⁴	—	2	4	no	—
899	C₂⁴	—	2	4	no	—
900	C₂⁴	—	2	4	no	—
901	C₂⁴	—	2	4	no	—
902	C₂⁴	—	2	4	no	—
903	C₂⁴	—	4	2	no	—
904	C₂⁴	—	4	2	no	—
905	C₂⁴	C₂⁴×C₇	1	2	yes	—
906	C₂⁴	C₂⁴×C₇	1	2	yes	—
907	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
908	C₂⁴	C₂⁴×C₇	1	2	yes	—
909	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
910	#41	—	4	32	no	—
911	C₂×Q₈	—	2	4	no	—
912	C₂×Q₈	—	2	4	no	—
913	C₂×Q₈	—	4	2	no	—
914	C₂×D₄	—	2	32	no	—
915	C₂×D₄	—	2	4	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	4	no	—
919	C₂×D₄	—	2	4	no	—
920	C₂×D₄	—	2	4	no	—
921	C₂×D₄	—	2	4	no	—
922	C₂×D₄	—	2	4	no	—
923	C₂×D₄	—	2	4	no	—
924	C₂×D₄	—	2	4	no	—
925	C₂×D₄	—	2	4	no	—
926	C₂×D₄	—	2	4	no	—
927	C₂×D₄	—	2	4	no	—
928	C₂×D₄	—	2	4	no	—
929	C₂×D₄	—	2	4	no	—
930	C₂×D₄	—	2	4	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	4	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	4	no	—
935	C₂×D₄	—	2	4	no	—
936	C₂×D₄	—	2	4	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	4	no	—
941	C₂×D₄	—	2	4	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	4	2	no	—
945	C₂×D₄	—	4	2	no	—
946	C₂×D₄	—	4	2	no	—
947	C₂×D₄	—	4	2	no	—
948	C₂×D₄	—	4	2	no	—
949	C₂×D₄	—	4	2	no	—
950	C₂×D₄	—	4	2	no	—
951	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
952	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
953	C₂×D₄	C₇×#41	1	4	yes	complemented
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	4	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	4	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	4	no	—
963	C₂²×C₄	—	2	4	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	4	no	—
969	C₂²×C₄	—	2	4	no	—
970	C₂²×C₄	—	2	4	no	—
971	C₂²×C₄	—	2	4	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	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	—	2	4	no	—
980	C₂²×C₄	—	2	4	no	—
981	C₂²×C₄	—	4	2	no	—
982	C₂²×C₄	—	4	2	no	—
983	C₂²×C₄	—	4	2	no	—
984	C₂²×C₄	—	4	1	no	—
985	C₂²×C₄	—	4	1	no	—
986	C₂²×C₄	—	4	32	no	—
987	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
988	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
989	C₂²×C₄	C₂×C₇×D₄	1	4	yes	complemented
990	C₂²×C₄	C₇×#41	1	4	yes	complemented
991	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
992	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
993	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
994	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
995	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
996	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
997	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
998	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1000	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1001	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1002	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
1003	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1004	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1006	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1007	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1008	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1009	C₄⋊C₄	—	2	4	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	4	no	—
1012	C₄⋊C₄	—	2	4	no	—
1013	C₄⋊C₄	—	2	4	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	4	no	—
1016	C₄⋊C₄	—	2	4	no	—
1017	C₄⋊C₄	—	2	4	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	4	2	no	—
1023	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
1024	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	complemented
1025	C₂²⋊C₄	—	2	4	no	—
1026	C₂²⋊C₄	—	2	4	no	—
1027	C₂²⋊C₄	—	2	4	no	—
1028	C₂²⋊C₄	—	2	4	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	4	no	—
1031	C₂²⋊C₄	—	2	4	no	—
1032	C₂²⋊C₄	—	2	4	no	—
1033	C₂²⋊C₄	—	2	4	no	—
1034	C₂²⋊C₄	—	2	4	no	—
1035	C₂²⋊C₄	—	2	4	no	—
1036	C₂²⋊C₄	—	2	4	no	—
1037	C₂²⋊C₄	—	2	4	no	—
1038	C₂²⋊C₄	—	2	4	no	—
1039	C₂²⋊C₄	—	2	4	no	—
1040	C₂²⋊C₄	—	2	4	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	4	no	—
1044	C₂²⋊C₄	—	2	4	no	—
1045	C₂²⋊C₄	—	2	4	no	—
1046	C₂²⋊C₄	—	4	2	no	—
1047	C₂²⋊C₄	—	4	2	no	—
1048	C₂²⋊C₄	—	4	2	no	—
1049	C₂²⋊C₄	—	4	2	no	—
1050	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
1051	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
1052	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	complemented
1053	C₂²⋊C₄	C₇×#41	1	4	yes	complemented
1054	C₄²	—	2	2	no	—
1055	C₄²	—	2	2	no	—
1056	C₄²	—	2	2	no	—
1057	C₄²	—	2	2	no	—
1058	C₄²	—	2	2	no	—
1059	C₄²	—	2	2	no	—
1060	C₄²	—	2	4	no	—
1061	C₄²	—	2	2	no	—
1062	C₄²	—	2	2	no	—
1063	C₄²	—	2	2	no	—
1064	C₄²	—	2	2	no	—
1065	C₄²	—	4	1	no	—
1066	C₄²	C₂×C₇×D₄	1	4	yes	—
1067	C₄²	C₂×C₇×D₄	1	4	yes	complemented
1068	C₂×C₇	—	2	4	no	—
1069	C₂×C₇	—	4	2	no	—
1070	C₂×C₇	—	4	4	no	—
1071	C₂×C₇	—	4	4	no	—
1072	C₂×C₇	—	8	2	no	—
1073	C₂×C₇	C₂×#525	1	1	yes	characteristic
1074	C₂×C₇	C₂×#532	1	1	yes	characteristic
1075	C₂×C₇	#3460	1	1	yes	characteristic
1076	C₂×C₇	C₂×D₄²	1	1	yes	characteristic
1077	C₂×C₇	D₄×#41	1	1	yes	characteristic
1078	C₂×C₇	D₄×#41	1	1	yes	characteristic
1079	C₂×C₇	#3481	1	1	yes	characteristic
1080	C₂³	—	2	1	no	—
1081	C₂³	—	2	1	no	—
1082	C₂³	—	2	1	no	—
1083	C₂³	—	2	1	no	—
1084	C₂³	—	2	16	no	—
1085	C₂³	—	2	2	no	—
1086	C₂³	—	2	2	no	—
1087	C₂³	—	2	2	no	—
1088	C₂³	—	2	1	no	—
1089	C₂³	—	2	1	no	—
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	2	no	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	2	1	no	—
1094	C₂³	—	2	2	no	—
1095	C₂³	—	2	2	no	—
1096	C₂³	—	2	2	no	—
1097	C₂³	—	2	2	no	—
1098	C₂³	—	2	2	no	—
1099	C₂³	—	2	1	no	—
1100	C₂³	—	2	2	no	—
1101	C₂³	—	2	1	no	—
1102	C₂³	—	2	2	no	—
1103	C₂³	—	2	2	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	2	2	no	—
1107	C₂³	—	2	2	no	—
1108	C₂³	—	2	2	no	—
1109	C₂³	—	2	2	no	—
1110	C₂³	—	4	8	no	—
1111	C₂³	—	4	8	no	—
1112	C₂³	—	4	8	no	—
1113	C₂³	—	4	8	no	—
1114	C₂³	—	4	8	no	—
1115	C₂³	—	4	8	no	—
1116	C₂³	C₂²×C₇×D₄	1	4	yes	—
1117	C₂³	C₂²×C₇×D₄	1	2	yes	—
1118	C₂³	C₂²×C₇×D₄	1	2	yes	—
1119	C₂³	C₂×C₇×#41	1	4	yes	—
1120	C₂³	C₂×C₇×#41	1	2	yes	—
1121	C₂³	C₂×C₇×#41	1	2	yes	—
1122	C₂³	C₂⁵×C₇	1	1	yes	characteristic
1123	Q₈	—	4	8	no	—
1124	D₄	—	2	16	no	—
1125	D₄	—	2	8	no	—
1126	D₄	—	2	8	no	—
1127	D₄	—	2	8	no	—
1128	D₄	—	4	8	no	—
1129	D₄	—	4	8	no	—
1130	D₄	—	4	8	no	—
1131	D₄	—	4	8	no	—
1132	D₄	—	4	8	no	—
1133	D₄	—	4	8	no	—
1134	D₄	—	4	8	no	—
1135	D₄	—	4	8	no	—
1136	D₄	—	4	4	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	8	no	—
1156	C₂×C₄	—	2	8	no	—
1157	C₂×C₄	—	2	16	no	—
1158	C₂×C₄	—	2	8	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	2	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	4	4	no	—
1181	C₂×C₄	—	4	8	no	—
1182	C₂×C₄	—	4	4	no	—
1183	C₂×C₄	—	4	8	no	—
1184	C₂×C₄	—	4	8	no	—
1185	C₂×C₄	—	4	4	no	—
1186	C₂×C₄	—	4	8	no	—
1187	C₂×C₄	—	4	8	no	—
1188	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1189	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1190	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1191	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
1192	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1193	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1194	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1195	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1196	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1197	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1198	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1199	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1200	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1201	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1202	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1203	C₇	#34681	1	1	yes	characteristic, direct product factor, Sylow
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	2	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	2	no	—
1210	C₂²	—	2	4	no	—
1211	C₂²	—	2	4	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	2	4	no	—
1214	C₂²	—	2	2	no	—
1215	C₂²	—	2	4	no	—
1216	C₂²	—	2	2	no	—
1217	C₂²	—	2	4	no	—
1218	C₂²	—	2	4	no	—
1219	C₂²	—	4	32	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	2	no	—
1222	C₂²	—	4	2	no	—
1223	C₂²	—	4	2	no	—
1224	C₂²	—	4	2	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	2	no	—
1227	C₂²	—	4	1	no	—
1228	C₂²	—	4	2	no	—
1229	C₂²	—	4	2	no	—
1230	C₂²	—	4	2	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	4	2	no	—
1233	C₂²	—	4	2	no	—
1234	C₂²	—	4	2	no	—
1235	C₂²	—	4	2	no	—
1236	C₂²	—	4	2	no	—
1237	C₂²	—	4	2	no	—
1238	C₂²	—	4	2	no	—
1239	C₂²	C₇×#532	1	4	yes	complemented
1240	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1241	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1242	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1243	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1244	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1245	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1246	C₂²	C₇×#585	1	1	yes	characteristic
1247	C₄	—	2	2	no	—
1248	C₄	—	2	2	no	—
1249	C₄	—	2	2	no	—
1250	C₄	—	2	4	no	—
1251	C₄	—	2	2	no	—
1252	C₄	—	2	2	no	—
1253	C₄	—	2	2	no	—
1254	C₄	—	2	2	no	—
1255	C₄	—	2	2	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	2	no	—
1258	C₄	—	4	1	no	—
1259	C₄	—	4	2	no	—
1260	C₄	—	4	2	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	4	2	no	—
1263	C₄	C₇×#525	1	4	yes	complemented
1264	C₄	C₇×D₄²	1	4	yes	—
1265	C₂	—	2	4	no	—
1266	C₂	—	4	4	no	—
1267	C₂	—	4	4	no	—
1268	C₂	—	4	2	no	—
1269	C₂	—	8	2	no	—
1270	C₂	C₂×C₇×#525	1	1	yes	characteristic
1271	C₂	C₂×C₇×#532	1	1	yes	characteristic
1272	C₂	C₇×#3460	1	1	yes	characteristic
1273	C₂	C₂×C₇×D₄²	1	1	yes	characteristic
1274	C₂	C₇×D₄×#41	1	1	yes	characteristic
1275	C₂	C₇×D₄×#41	1	1	yes	characteristic
1276	C₂	C₇×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#532	C₂	semidirect
2. C₂×C₇×#525	C₂	semidirect
3. C₂²×C₄×C₇×D₄	C₂	semidirect
4. C₇×#2472	C₂	semidirect
5. C₇×#2464	C₂	semidirect
6. C₇×#2461	C₂	semidirect
7. C₇×#2452	C₂	semidirect
8. C₇×#2445	C₂	semidirect
9. C₇×#2440	C₂	semidirect
10. C₇×#2433	C₂	semidirect
11. C₇×#2428	C₂	semidirect
12. C₇×#2424	C₂	semidirect
13. C₇×#2422	C₂	semidirect
14. C₇×#2416	C₂	semidirect
15. C₇×#2408	C₂	semidirect
16. C₇×#2392	C₂	semidirect
17. C₇×#2388	C₂	semidirect
18. C₄×C₇×#127	C₂	semidirect
19. C₄×C₇×#121	C₂	semidirect
20. C₄×C₇×#121	C₂	semidirect
21. C₄×C₇×#120	C₂	semidirect
22. C₇×#2293	C₂	semidirect
23. C₄²×C₇×D₄	C₂	semidirect
24. C₂²×C₇×#41	C₂²	semidirect
28. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₇×#124	C₂²	semidirect
33. C₂×C₇×#123	C₂²	semidirect
34. C₂×C₇×#123	C₂²	semidirect
36. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
41. C₂×C₇×#121	C₂²	semidirect
42. C₂×C₇×#121	C₂²	semidirect
43. C₂×C₇×#121	C₂²	semidirect
58. C₂×C₄×C₇×D₄	C₂²	semidirect
59. C₂×C₄×C₇×D₄	C₂²	semidirect
60. C₂×C₄×C₇×D₄	C₂²	semidirect
61. C₂×C₄×C₇×D₄	C₂²	semidirect
62. C₂×C₄×C₇×D₄	C₂²	semidirect
63. C₂×C₇×#117	C₂²	semidirect
67. C₂²×C₄²×C₇	C₂²	semidirect
68. C₇×#398	C₂²	semidirect
69. C₇×#397	C₂²	semidirect
70. C₇×#396	C₂²	semidirect
71. C₇×#396	C₂²	semidirect
72. C₇×#395	C₂²	semidirect
74. C₇×#394	C₂²	semidirect
75. C₇×#394	C₂²	semidirect
76. C₇×#394	C₂²	semidirect
77. C₇×#394	C₂²	semidirect
78. C₇×#394	C₂²	semidirect
79. C₇×#393	C₂²	semidirect
83. C₇×#392	C₂²	semidirect
88. C₇×#390	C₂²	semidirect
89. C₇×#390	C₂²	semidirect
90. C₇×#390	C₂²	semidirect
91. C₇×#390	C₂²	semidirect
92. C₇×#389	C₂²	semidirect
93. C₇×#389	C₂²	semidirect
94. C₇×#389	C₂²	semidirect
95. C₇×#389	C₂²	semidirect
96. C₇×#388	C₂²	semidirect
97. C₇×#388	C₂²	semidirect
98. C₇×#388	C₂²	semidirect
99. C₇×#388	C₂²	semidirect
102. C₇×#386	C₂²	semidirect
103. C₇×#386	C₂²	semidirect
104. C₇×#386	C₂²	semidirect
106. C₇×#385	C₂²	semidirect
107. C₇×#385	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. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
124. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
125. C₄³×C₇	C₂²	semidirect
126. #34681	C₇	direct (N × H)
194. C₄×C₇×D₄	D₄	semidirect
195. C₄×C₇×D₄	D₄	semidirect
273. C₂×#532	C₂×C₇	semidirect
274. C₂×#525	C₂×C₇	semidirect
275. C₂²×C₄×D₄	C₂×C₇	semidirect
276. #2472	C₂×C₇	semidirect
277. #2464	C₂×C₇	semidirect
278. #2461	C₂×C₇	semidirect
279. #2452	C₂×C₇	semidirect
280. #2445	C₂×C₇	semidirect
281. #2440	C₂×C₇	semidirect
282. #2433	C₂×C₇	semidirect
283. #2428	C₂×C₇	semidirect
284. #2424	C₂×C₇	semidirect
285. #2422	C₂×C₇	semidirect
286. #2416	C₂×C₇	semidirect
287. #2408	C₂×C₇	semidirect
288. #2392	C₂×C₇	semidirect
289. #2388	C₂×C₇	semidirect
290. C₄×#127	C₂×C₇	semidirect
291. C₄×#121	C₂×C₇	semidirect
292. C₄×#121	C₂×C₇	semidirect
293. C₄×#120	C₂×C₇	semidirect
294. #2293	C₂×C₇	semidirect
295. C₄²×D₄	C₂×C₇	semidirect
351. C₂×C₇×D₄	#41	semidirect
387. C₂²×C₄×C₇	C₂×D₄	semidirect
388. C₂²×C₄×C₇	#41	semidirect
422. C₇×C₄⋊C₄	C₂×D₄	semidirect
450. C₇×C₂²⋊C₄	C₂×D₄	semidirect
451. C₇×C₂²⋊C₄	#41	semidirect
465. C₄²×C₇	C₂×D₄	semidirect
466. C₂²×#41	C₂²×C₇	semidirect
470. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
473. C₂×#124	C₂²×C₇	semidirect
475. C₂×#123	C₂²×C₇	semidirect
476. C₂×#123	C₂²×C₇	semidirect
478. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
483. C₂×#121	C₂²×C₇	semidirect
484. C₂×#121	C₂²×C₇	semidirect
485. C₂×#121	C₂²×C₇	semidirect
500. C₂×C₄×D₄	C₂²×C₇	semidirect
501. C₂×C₄×D₄	C₂²×C₇	semidirect
502. C₂×C₄×D₄	C₂²×C₇	semidirect
503. C₂×C₄×D₄	C₂²×C₇	semidirect
504. C₂×C₄×D₄	C₂²×C₇	semidirect
505. C₂×#117	C₂²×C₇	semidirect
509. C₂²×C₄²	C₂²×C₇	semidirect
510. #398	C₂²×C₇	semidirect
511. #397	C₂²×C₇	semidirect
512. #396	C₂²×C₇	semidirect
513. #396	C₂²×C₇	semidirect
514. #395	C₂²×C₇	semidirect
516. #394	C₂²×C₇	semidirect
517. #394	C₂²×C₇	semidirect
518. #394	C₂²×C₇	semidirect
519. #394	C₂²×C₇	semidirect
520. #394	C₂²×C₇	semidirect
521. #393	C₂²×C₇	semidirect
525. #392	C₂²×C₇	semidirect
530. #390	C₂²×C₇	semidirect
531. #390	C₂²×C₇	semidirect
532. #390	C₂²×C₇	semidirect
533. #390	C₂²×C₇	semidirect
534. #389	C₂²×C₇	semidirect
535. #389	C₂²×C₇	semidirect
536. #389	C₂²×C₇	semidirect
537. #389	C₂²×C₇	semidirect
538. #388	C₂²×C₇	semidirect
539. #388	C₂²×C₇	semidirect
540. #388	C₂²×C₇	semidirect
541. #388	C₂²×C₇	semidirect
544. #386	C₂²×C₇	semidirect
545. #386	C₂²×C₇	semidirect
546. #386	C₂²×C₇	semidirect
548. #385	C₂²×C₇	semidirect
549. #385	C₂²×C₇	semidirect
550. #384	C₂²×C₇	semidirect
552. #380	C₂²×C₇	semidirect
554. C₄×C₄⋊C₄	C₂²×C₇	semidirect
555. C₄×C₄⋊C₄	C₂²×C₇	semidirect
556. C₄×C₄⋊C₄	C₂²×C₇	semidirect
557. C₄×C₄⋊C₄	C₂²×C₇	semidirect
561. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
562. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
563. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
564. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
565. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
566. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
567. C₄³	C₂²×C₇	semidirect
758. C₄×D₄	C₇×D₄	semidirect
759. C₄×D₄	C₇×D₄	semidirect
872. C₂²×C₇	#532	semidirect
896. C₄×C₇	#525	semidirect
953. C₂×D₄	C₇×#41	semidirect
989. C₂²×C₄	C₂×C₇×D₄	semidirect
990. C₂²×C₄	C₇×#41	semidirect
1024. C₄⋊C₄	C₂×C₇×D₄	semidirect
1052. C₂²⋊C₄	C₂×C₇×D₄	semidirect
1053. C₂²⋊C₄	C₇×#41	semidirect
1067. C₄²	C₂×C₇×D₄	semidirect
1203. C₇	#34681	direct (N × H)
1239. C₂²	C₇×#532	semidirect
1263. C₄	C₇×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#532	2
C₂×C₇×#525	2
C₂²×C₄×C₇×D₄	2
C₇×#2472	2
C₇×#2464	2
C₇×#2461	2
C₇×#2452	2
C₇×#2445	2
C₇×#2440	2
C₇×#2433	2
C₇×#2428	2
C₇×#2424	2
C₇×#2422	2
C₇×#2416	2
C₇×#2408	2
C₇×#2392	2
C₇×#2388	2
C₄×C₇×#127	2
C₄×C₇×#121	2
C₄×C₇×#120	2
C₇×#2293	2
C₄²×C₇×D₄	2
#34681	7

Subgroups — C7×#34681 #13211897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34681 #13211897