Subgroups — #32863414

Order 18176.

1894 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597510	C₂	1	2	yes	maximal, complemented
2	#22597500	C₂	1	1	yes	maximal, characteristic, complemented
3	#22597489	C₂	1	1	yes	maximal, characteristic, complemented
4	#22597465	C₂	1	1	yes	maximal, characteristic, complemented
5	#22597457	C₂	1	1	yes	maximal, characteristic, complemented
6	#22597416	C₂	1	1	yes	maximal, characteristic, complemented
7	#22597402	C₂	1	2	yes	maximal, complemented
8	#22597388	C₂	1	2	yes	maximal, complemented
9	#22597381	C₂	1	1	yes	maximal, characteristic, complemented
10	#22597375	C₂	1	1	yes	maximal, characteristic, complemented
11	#22597369	C₂	1	2	yes	maximal, complemented
12	#22597360	C₂	1	1	yes	maximal, characteristic, complemented
13	#22597345	C₂	1	1	yes	maximal, characteristic, complemented
14	#22597327	C₂	1	2	yes	maximal, complemented
15	#22597316	C₂	1	1	yes	maximal, characteristic, complemented
16	#22597307	C₂	1	1	yes	maximal, characteristic, complemented
17	#22597084	C₂	1	1	yes	maximal, characteristic, complemented
18	D₄×#11765849	C₂	1	2	yes	maximal, complemented
19	D₄×#11765849	C₂	1	1	yes	maximal, characteristic, complemented
20	#22597067	C₂	1	2	yes	maximal, complemented
21	#22597044	C₂	1	2	yes	maximal, complemented
22	C₂×#17986077	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₁×#3481	C₂	1	1	yes	maximal, characteristic
24	C₂×#14556135	C₂²	1	2	yes	complemented
25	C₂²×#11765849	C₂²	1	2	yes	complemented
26	C₂²×#11765849	C₂²	1	2	yes	complemented
27	#17986130	C₂²	1	1	yes	characteristic, complemented
28	#17986130	C₂²	1	1	yes	characteristic, complemented
29	#17986130	C₂²	1	2	yes	complemented
30	#17986130	C₂²	1	1	yes	characteristic, complemented
31	#17986130	C₂²	1	1	yes	characteristic, complemented
32	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	#17986077	C₂²	1	1	yes	characteristic
35	#17986077	C₂²	1	1	yes	characteristic
36	#17986077	C₂²	1	1	yes	characteristic
37	#17986077	C₂²	1	1	yes	characteristic
38	#17986077	C₂²	1	2	yes	complemented
39	#17986077	C₂²	1	1	yes	characteristic, complemented
40	#17986077	C₂²	1	1	yes	characteristic, complemented
41	#17986077	C₂²	1	2	yes	complemented
42	#17986077	C₂²	1	2	yes	complemented
43	#17986077	C₂²	1	1	yes	characteristic, complemented
44	#17986077	C₂²	1	2	yes	complemented
45	#17986077	C₂²	1	2	yes	complemented
46	#17986077	C₂²	1	1	yes	characteristic, complemented
47	#17986077	C₂²	1	2	yes	complemented
48	#17986077	C₂²	1	1	yes	characteristic, complemented
49	#17986077	C₂²	1	1	yes	characteristic, complemented
50	#17986077	C₂²	1	2	yes	complemented
51	#17986077	C₂²	1	2	yes	complemented
52	#17986071	C₂²	1	2	yes	—
53	#17986071	C₂²	1	1	yes	characteristic
54	#17986071	C₂²	1	1	yes	characteristic
55	#17986071	C₂²	1	1	yes	characteristic, complemented
56	#17986071	C₂²	1	2	yes	complemented
57	#17986071	C₂²	1	2	yes	complemented
58	#17986071	C₂²	1	2	yes	complemented
59	#17986071	C₂²	1	2	yes	complemented
60	#17986071	C₂²	1	2	yes	complemented
61	#17986071	C₂²	1	2	yes	complemented
62	#17986071	C₂²	1	2	yes	complemented
63	#17986071	C₂²	1	2	yes	complemented
64	#17986071	C₂²	1	2	yes	complemented
65	#17986071	C₂²	1	2	yes	complemented
66	#17986071	C₂²	1	2	yes	complemented
67	#17986071	C₂²	1	2	yes	complemented
68	#17986071	C₂²	1	2	yes	complemented
69	#17986071	C₂²	1	1	yes	characteristic, complemented
70	#17986071	C₂²	1	2	yes	complemented
71	#17986071	C₂²	1	2	yes	complemented
72	D₄×C₇₁⋊C₈	C₂²	1	2	yes	complemented
73	D₄×C₇₁⋊C₈	C₂²	1	2	yes	complemented
74	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
75	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
76	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
77	D₄×C₇₁⋊C₈	C₂²	1	2	yes	complemented
78	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
79	#17986060	C₂²	1	2	yes	complemented
80	#17986060	C₂²	1	2	yes	complemented
81	#17986060	C₂²	1	2	yes	complemented
82	#17986060	C₂²	1	2	yes	complemented
83	#17986056	C₂²	1	1	yes	characteristic, complemented
84	#17986056	C₂²	1	2	yes	complemented
85	#17986056	C₂²	1	1	yes	characteristic, complemented
86	#17986056	C₂²	1	2	yes	complemented
87	#17986052	C₂²	1	1	yes	characteristic, complemented
88	#17986052	C₂²	1	1	yes	characteristic, complemented
89	#17986052	C₂²	1	1	yes	characteristic, complemented
90	#17986052	C₂²	1	1	yes	characteristic, complemented
91	#17986026	C₂²	1	2	yes	complemented
92	#17986026	C₂²	1	2	yes	complemented
93	#17986023	C₂²	1	2	yes	complemented
94	#17986023	C₂²	1	1	yes	characteristic, complemented
95	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
97	#17985966	C₂²	1	2	yes	complemented
98	#17985966	C₂²	1	2	yes	complemented
99	#17985966	C₂²	1	2	yes	complemented
100	#17985963	C₂²	1	2	yes	complemented
101	#17985963	C₂²	1	2	yes	complemented
102	#17985963	C₂²	1	2	yes	complemented
103	#17985963	C₂²	1	2	yes	complemented
104	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	2	yes	complemented
105	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	2	yes	complemented
106	#17985955	C₂²	1	2	yes	complemented
107	#17985955	C₂²	1	2	yes	complemented
108	C₄×#11765849	C₂²	1	1	yes	characteristic, complemented
109	C₄×#11765849	C₂²	1	1	yes	characteristic, complemented
110	C₄×#11765849	C₂²	1	2	yes	complemented
111	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
112	#559×C₇₁	C₄	1	1	yes	characteristic
113	#554×C₇₁	C₄	1	1	yes	characteristic
114	#554×C₇₁	C₄	1	1	yes	characteristic
115	#553×C₇₁	C₄	1	1	yes	characteristic
116	#553×C₇₁	C₄	1	1	yes	characteristic
117	#553×C₇₁	C₄	1	2	yes	—
118	#551×C₇₁	C₄	1	2	yes	—
119	#551×C₇₁	C₄	1	2	yes	—
120	#546×C₇₁	C₄	1	2	yes	—
121	#546×C₇₁	C₄	1	1	yes	characteristic
122	#546×C₇₁	C₄	1	1	yes	characteristic
123	D₄²×C₇₁	C₄	1	1	yes	characteristic
124	#532×C₇₁	C₂²	1	1	yes	characteristic
125	#529×C₇₁	C₂²	1	1	yes	characteristic
126	#529×C₇₁	C₂²	1	1	yes	characteristic
127	#529×C₇₁	C₂²	1	2	yes	—
128	#525×C₇₁	C₂²	1	2	yes	—
129	#525×C₇₁	C₂²	1	2	yes	—
130	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
131	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
132	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
133	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
134	C₂×C₄×D₄×C₇₁	C₂²	1	2	yes	—
135	#14556135	—	4	4	no	—
136	C₂×#11765849	—	4	4	no	—
137	C₂×#11765849	—	4	4	no	—
138	C₂×#11765849	C₂³	1	1	yes	characteristic
139	C₂×#11765849	C₂³	1	2	yes	—
140	C₂×#11765849	C₂³	1	1	yes	characteristic
141	C₂×#11765849	C₂³	1	2	yes	—
142	C₂×#11765849	C₂³	1	1	yes	characteristic
143	C₂×#11765849	C₂³	1	2	yes	—
144	C₂×#11765849	C₂³	1	2	yes	—
145	C₂×#11765849	C₂³	1	2	yes	—
146	C₂×#11765849	C₂³	1	2	yes	—
147	C₂×#11765849	C₂³	1	2	yes	—
148	C₂×#11765849	C₂³	1	2	yes	—
149	C₂×#11765849	C₂³	1	1	yes	characteristic
150	C₂×#11765849	C₂³	1	2	yes	—
151	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
152	C₂²×C₇₁⋊C₈	C₂³	1	2	yes	—
153	C₂²×C₇₁⋊C₈	C₂³	1	2	yes	—
154	C₂²×C₇₁⋊C₈	C₂³	1	2	yes	—
155	C₂²×C₇₁⋊C₈	C₂³	1	2	yes	—
156	C₂²×C₇₁⋊C₈	C₂³	1	2	yes	—
157	C₂²×C₇₁⋊C₈	C₂³	1	2	yes	—
158	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
159	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
160	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
161	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
162	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
163	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
164	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
165	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
166	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
167	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
168	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
169	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
170	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
171	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
172	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
173	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
174	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
175	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
176	C₂²⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
177	C₂²⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
178	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
179	C₂²⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
180	C₂²⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
181	C₂²⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
182	C₂²⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
183	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
184	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
185	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
186	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
187	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
188	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
189	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
190	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
191	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
192	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
193	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
194	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
195	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
196	C₂²⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
197	#14556039	C₂³	1	2	yes	—
198	#14556039	C₂³	1	1	yes	characteristic
199	#14556039	C₂³	1	2	yes	—
200	#14556039	C₂³	1	2	yes	—
201	#14556039	C₂³	1	2	yes	—
202	#14556039	C₂³	1	1	yes	characteristic
203	#14556039	C₂³	1	1	yes	characteristic
204	#14556039	C₂³	1	1	yes	characteristic
205	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
206	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
207	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
208	C₄×C₇₁⋊C₈	C₂³	1	2	yes	—
209	C₄×C₇₁⋊C₈	C₂³	1	2	yes	—
210	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
211	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
212	C₄×C₇₁⋊C₈	C₂³	1	2	yes	—
213	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
214	C₂×#41×C₇₁	C₂×C₄	1	1	yes	characteristic
215	C₂×#41×C₇₁	C₂×C₄	1	1	yes	characteristic
216	C₂×#41×C₇₁	C₂³	1	2	yes	—
217	C₂²×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
218	C₂²×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
219	C₂²×D₄×C₇₁	C₂×C₄	1	2	yes	—
220	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
221	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
222	C₄⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
223	#127×C₇₁	C₂×C₄	1	1	yes	characteristic
224	#126×C₇₁	C₂×C₄	1	2	yes	—
225	#126×C₇₁	C₂×C₄	1	2	yes	—
226	#126×C₇₁	C₂×C₄	1	2	yes	—
227	#126×C₇₁	C₂×C₄	1	2	yes	—
228	#125×C₇₁	C₂×C₄	1	1	yes	characteristic
229	#125×C₇₁	C₂×C₄	1	1	yes	characteristic
230	#125×C₇₁	C₂×C₄	1	2	yes	—
231	#124×C₇₁	C₂×C₄	1	1	yes	characteristic
232	#124×C₇₁	C₂×C₄	1	1	yes	characteristic
233	#124×C₇₁	C₂×C₄	1	2	yes	—
234	#124×C₇₁	C₂×C₄	1	2	yes	—
235	#123×C₇₁	C₂×C₄	1	2	yes	—
236	#123×C₇₁	C₂×C₄	1	2	yes	—
237	#123×C₇₁	C₂×C₄	1	2	yes	—
238	#123×C₇₁	C₂×C₄	1	2	yes	—
239	#123×C₇₁	C₂×C₄	1	2	yes	—
240	#123×C₇₁	C₂×C₄	1	2	yes	—
241	#123×C₇₁	C₂×C₄	1	2	yes	—
242	#123×C₇₁	C₂×C₄	1	2	yes	—
243	C₂²⋊Q₈×C₇₁	C₂×C₄	1	2	yes	—
244	C₂²⋊Q₈×C₇₁	C₂×C₄	1	2	yes	—
245	C₂²⋊Q₈×C₇₁	C₂×C₄	1	2	yes	—
246	C₂²⋊Q₈×C₇₁	C₂×C₄	1	2	yes	—
247	C₂²⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
248	C₂²⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
249	C₂²⋊Q₈×C₇₁	C₂×C₄	1	2	yes	—
250	#121×C₇₁	C₂×C₄	1	2	yes	—
251	#121×C₇₁	C₂×C₄	1	2	yes	—
252	#121×C₇₁	C₂×C₄	1	2	yes	—
253	#121×C₇₁	C₂×C₄	1	2	yes	—
254	#121×C₇₁	C₂×C₄	1	1	yes	characteristic
255	#121×C₇₁	C₂×C₄	1	1	yes	characteristic
256	#121×C₇₁	C₂×C₄	1	2	yes	—
257	#121×C₇₁	C₂×C₄	1	1	yes	characteristic
258	#121×C₇₁	C₂×C₄	1	1	yes	characteristic
259	#121×C₇₁	C₂×C₄	1	2	yes	—
260	#120×C₇₁	C₂×C₄	1	2	yes	—
261	#120×C₇₁	C₂×C₄	1	2	yes	—
262	#120×C₇₁	C₂×C₄	1	2	yes	—
263	#120×C₇₁	C₂×C₄	1	2	yes	—
264	C₄×Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
265	C₄×Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
266	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
267	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
268	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
269	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
270	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
271	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
272	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
273	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
274	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
275	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
276	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
277	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
278	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
279	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
280	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
281	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
282	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
283	C₄×D₄×C₇₁	C₂³	1	2	yes	—
284	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
285	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₇₁	C₂³	1	2	yes	—
289	C₄×D₄×C₇₁	C₂³	1	2	yes	—
290	C₄×D₄×C₇₁	C₂³	1	2	yes	—
291	C₄×D₄×C₇₁	C₂³	1	2	yes	—
292	C₄×D₄×C₇₁	C₂³	1	2	yes	—
293	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
295	#117×C₇₁	C₂×C₄	1	1	yes	characteristic
296	#117×C₇₁	C₂×C₄	1	2	yes	—
297	#117×C₇₁	C₂×C₄	1	1	yes	characteristic
298	#117×C₇₁	C₂×C₄	1	1	yes	characteristic
299	#117×C₇₁	C₂×C₄	1	1	yes	characteristic
300	#117×C₇₁	C₂³	1	2	yes	—
301	#117×C₇₁	C₂³	1	2	yes	—
302	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
303	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
304	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
305	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
306	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
307	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
308	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
309	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
313	#11765849	—	2	2	no	—
314	#11765849	—	2	4	no	—
315	#11765849	—	2	4	no	—
316	#11765849	—	2	2	no	—
317	#11765849	—	4	2	no	—
318	#11765849	—	4	2	no	—
319	#11765849	—	4	2	no	—
320	#11765849	—	4	2	no	—
321	#11765849	—	4	1	no	—
322	#11765849	—	4	2	no	—
323	#11765849	—	4	2	no	—
324	#11765849	—	4	1	no	—
325	#11765849	—	4	2	no	—
326	C₂×C₇₁⋊C₈	—	2	2	no	—
327	C₂×C₇₁⋊C₈	—	2	4	no	—
328	C₂×C₇₁⋊C₈	—	4	2	no	—
329	C₂×C₇₁⋊C₈	—	4	1	no	—
330	C₂×C₇₁⋊C₈	—	4	2	no	—
331	C₂×C₇₁⋊C₈	—	4	2	no	—
332	C₂×C₇₁⋊C₈	—	4	2	no	—
333	C₂×C₇₁⋊C₈	—	4	2	no	—
334	C₂×C₇₁⋊C₈	C₂⁴	1	1	yes	characteristic
335	C₂×C₇₁⋊C₈	C₂⁴	1	1	yes	characteristic
336	C₂×C₇₁⋊C₈	C₂⁴	1	2	yes	—
337	C₂×C₇₁⋊C₈	C₂⁴	1	1	yes	characteristic
338	C₂×C₇₁⋊C₈	C₂⁴	1	1	yes	characteristic
339	C₂×C₇₁⋊C₈	C₂⁴	1	1	yes	characteristic
340	C₂×C₇₁⋊C₈	C₂⁴	1	1	yes	characteristic
341	C₂×C₇₁⋊C₈	C₂⁴	1	1	yes	characteristic
342	C₂×C₇₁⋊C₈	C₂⁴	1	2	yes	—
343	C₂×C₇₁⋊C₈	C₂⁴	1	2	yes	—
344	C₂×C₇₁⋊C₈	C₂⁴	1	2	yes	—
345	C₂×C₇₁⋊C₈	C₂⁴	1	1	yes	characteristic
346	C₂⁴×C₇₁	C₂²×C₄	1	2	yes	—
347	C₂⁴×C₇₁	C₂²×C₄	1	2	yes	—
348	#41×C₇₁	—	4	2	no	—
349	#41×C₇₁	—	4	2	no	—
350	#41×C₇₁	—	4	2	no	—
351	#41×C₇₁	—	4	2	no	—
352	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
353	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
354	C₂×Q₈×C₇₁	C₂²×C₄	1	2	yes	—
355	C₂×D₄×C₇₁	—	4	2	no	—
356	C₂×D₄×C₇₁	—	4	2	no	—
357	C₂×D₄×C₇₁	—	4	4	no	—
358	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
359	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
360	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
361	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
362	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
363	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
364	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
365	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
366	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
367	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
368	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
369	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
370	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
371	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
372	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
373	C₂²×C₄×C₇₁	—	4	2	no	—
374	C₂²×C₄×C₇₁	—	4	2	no	—
375	C₂²×C₄×C₇₁	—	4	2	no	—
376	C₂²×C₄×C₇₁	—	4	2	no	—
377	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
378	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
379	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
380	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
381	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
382	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
383	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
384	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
385	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
386	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
387	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
388	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
389	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
390	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
391	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
394	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
396	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
397	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
398	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
399	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
400	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
403	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
404	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
405	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
406	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
407	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
408	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
409	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
410	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
411	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
412	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
413	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
414	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
415	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
416	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
417	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
419	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
420	C₂²⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
421	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
422	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
424	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
425	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
426	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
427	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
428	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
429	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
430	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
431	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
432	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
433	C₂²⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
434	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
435	C₂²⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
436	C₂²⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
437	C₂²⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
438	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
441	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
442	C₂²⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
443	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
444	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
445	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
446	C₄²×C₇₁	C₂²×C₄	1	2	yes	—
447	C₄²×C₇₁	C₂²×C₄	1	2	yes	—
448	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
449	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
450	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
451	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
452	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
454	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
455	C₄²×C₇₁	C₂⁴	1	2	yes	—
456	C₂³×C₇₁	—	2	4	no	—
457	C₂³×C₇₁	—	4	2	no	—
458	C₂³×C₇₁	—	4	2	no	—
459	C₂³×C₇₁	—	4	2	no	—
460	C₂³×C₇₁	—	4	2	no	—
461	C₂³×C₇₁	—	4	2	no	—
462	C₂³×C₇₁	C₂³×C₄	1	2	yes	—
463	C₂³×C₇₁	C₂³×C₄	1	2	yes	—
464	C₂³×C₇₁	C₂³×C₄	1	1	yes	characteristic
465	C₂³×C₇₁	C₂³×C₄	1	2	yes	—
466	C₂³×C₇₁	C₂³×C₄	1	1	yes	characteristic
467	C₂³×C₇₁	C₂³×C₄	1	1	yes	characteristic
468	Q₈×C₇₁	—	2	2	no	—
469	Q₈×C₇₁	—	4	2	no	—
470	Q₈×C₇₁	—	4	1	no	—
471	D₄×C₇₁	—	2	2	no	—
472	D₄×C₇₁	—	2	4	no	—
473	D₄×C₇₁	—	2	2	no	—
474	D₄×C₇₁	—	2	2	no	—
475	D₄×C₇₁	—	2	2	no	—
476	D₄×C₇₁	—	2	2	no	—
477	D₄×C₇₁	—	4	2	no	—
478	D₄×C₇₁	—	4	2	no	—
479	D₄×C₇₁	—	4	2	no	—
480	D₄×C₇₁	—	4	2	no	—
481	D₄×C₇₁	—	4	2	no	—
482	D₄×C₇₁	—	4	2	no	—
483	D₄×C₇₁	—	4	2	no	—
484	D₄×C₇₁	—	4	1	no	—
485	D₄×C₇₁	—	4	2	no	—
486	C₂×C₄×C₇₁	—	2	2	no	—
487	C₂×C₄×C₇₁	—	2	2	no	—
488	C₂×C₄×C₇₁	—	2	2	no	—
489	C₂×C₄×C₇₁	—	2	2	no	—
490	C₂×C₄×C₇₁	—	2	1	no	—
491	C₂×C₄×C₇₁	—	2	2	no	—
492	C₂×C₄×C₇₁	—	2	1	no	—
493	C₂×C₄×C₇₁	—	2	2	no	—
494	C₂×C₄×C₇₁	—	2	2	no	—
495	C₂×C₄×C₇₁	—	2	1	no	—
496	C₂×C₄×C₇₁	—	2	1	no	—
497	C₂×C₄×C₇₁	—	2	2	no	—
498	C₂×C₄×C₇₁	—	2	1	no	—
499	C₂×C₄×C₇₁	—	2	2	no	—
500	C₂×C₄×C₇₁	—	2	2	no	—
501	C₂×C₄×C₇₁	—	2	1	no	—
502	C₂×C₄×C₇₁	—	4	2	no	—
503	C₂×C₄×C₇₁	—	4	2	no	—
504	C₂×C₄×C₇₁	—	4	2	no	—
505	C₂×C₄×C₇₁	—	4	2	no	—
506	C₂×C₄×C₇₁	—	4	2	no	—
507	C₂×C₄×C₇₁	—	4	2	no	—
508	C₂×C₄×C₇₁	—	4	2	no	—
509	C₂×C₄×C₇₁	—	4	1	no	—
510	C₂×C₄×C₇₁	—	4	1	no	—
511	C₂×C₄×C₇₁	—	4	2	no	—
512	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
513	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
514	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
515	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
516	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
517	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
518	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
519	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
520	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
521	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
522	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
523	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
524	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
525	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
526	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
527	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
528	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
529	C₇₁⋊C₈	—	2	2	no	—
530	C₇₁⋊C₈	—	2	1	no	—
531	C₇₁⋊C₈	—	2	2	no	—
532	C₇₁⋊C₈	—	2	1	no	—
533	C₇₁⋊C₈	—	2	2	no	—
534	C₇₁⋊C₈	—	2	1	no	—
535	C₇₁⋊C₈	—	2	1	no	—
536	C₇₁⋊C₈	—	2	2	no	—
537	C₇₁⋊C₈	—	2	1	no	—
538	C₇₁⋊C₈	—	2	1	no	—
539	C₇₁⋊C₈	—	2	1	no	—
540	C₇₁⋊C₈	H(5,𝔽₂)	1	2	yes	—
541	C₂²×C₇₁	—	2	1	no	—
542	C₂²×C₇₁	—	2	1	no	—
543	C₂²×C₇₁	—	2	1	no	—
544	C₂²×C₇₁	—	2	2	no	—
545	C₂²×C₇₁	—	2	2	no	—
546	C₂²×C₇₁	—	2	2	no	—
547	C₂²×C₇₁	—	2	1	no	—
548	C₂²×C₇₁	—	2	1	no	—
549	C₂²×C₇₁	—	2	1	no	—
550	C₂²×C₇₁	—	2	1	no	—
551	C₂²×C₇₁	—	2	2	no	—
552	C₂²×C₇₁	—	2	1	no	—
553	C₂²×C₇₁	—	2	2	no	—
554	C₂²×C₇₁	—	2	2	no	—
555	C₂²×C₇₁	—	2	2	no	—
556	C₂²×C₇₁	—	2	2	no	—
557	C₂²×C₇₁	—	2	2	no	—
558	C₂²×C₇₁	—	8	4	no	—
559	C₂²×C₇₁	—	8	4	no	—
560	C₂²×C₇₁	#568	1	2	yes	—
561	C₂²×C₇₁	C₂⁴×C₄	1	1	yes	characteristic
562	C₄×C₇₁	—	2	1	no	—
563	C₄×C₇₁	—	2	2	no	—
564	C₄×C₇₁	—	2	1	no	—
565	C₄×C₇₁	—	2	2	no	—
566	C₄×C₇₁	—	2	2	no	—
567	C₄×C₇₁	—	2	1	no	—
568	C₄×C₇₁	—	2	1	no	—
569	C₄×C₇₁	—	2	1	no	—
570	C₄×C₇₁	—	2	1	no	—
571	C₄×C₇₁	—	2	1	no	—
572	C₄×C₇₁	—	2	1	no	—
573	C₄×C₇₁	—	2	1	no	—
574	C₄×C₇₁	—	2	2	no	—
575	C₄×C₇₁	—	2	1	no	—
576	C₄×C₇₁	—	2	2	no	—
577	C₄×C₇₁	#568	1	2	yes	—
578	C₄×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₄×C₇₁	#585	1	1	yes	characteristic
580	#60324	—	71	1	no	maximal, Sylow
581	C₂×C₇₁	—	2	2	no	—
582	C₂×C₇₁	—	4	1	no	—
583	C₂×C₇₁	—	4	2	no	—
584	C₂×C₇₁	—	4	2	no	—
585	C₂×C₇₁	—	4	1	no	—
586	C₂×C₇₁	—	4	2	no	—
587	C₂×C₇₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
588	C₂×C₇₁	C₂×#568	1	1	yes	characteristic
589	C₂×C₇₁	C₂×#568	1	1	yes	characteristic
590	#3481	D₇₁	1	1	yes	characteristic
591	#2995	—	71	2	no	—
592	#2994	—	71	1	no	—
593	#2993	—	71	1	no	—
594	#2990	—	71	1	no	—
595	#2989	—	71	1	no	—
596	#2981	—	71	1	no	—
597	#2978	—	71	2	no	—
598	#2976	—	71	2	no	—
599	#2975	—	71	1	no	—
600	#2974	—	71	1	no	—
601	#2973	—	71	2	no	—
602	#2971	—	71	1	no	—
603	#2969	—	71	1	no	—
604	#2967	—	71	2	no	—
605	#2966	—	71	1	no	—
606	#2965	—	71	1	no	—
607	#2935	—	71	1	no	—
608	D₄×M₁₆	—	71	2	no	—
609	D₄×M₁₆	—	71	1	no	—
610	#2933	—	71	2	no	—
611	#2930	—	71	2	no	—
612	C₂×#436	—	71	1	no	—
613	C₇₁	#60324	1	1	yes	characteristic, complemented, Sylow
614	C₂×#131	—	71	2	no	—
615	C₂²×M₁₆	—	71	2	no	—
616	C₂²×M₁₆	—	71	2	no	—
617	#559	Dic₇₁	1	1	yes	characteristic
618	#554	Dic₇₁	1	1	yes	characteristic
619	#554	Dic₇₁	1	1	yes	characteristic
620	#553	Dic₇₁	1	1	yes	characteristic
621	#553	Dic₇₁	1	1	yes	characteristic
622	#553	Dic₇₁	1	2	yes	—
623	#551	Dic₇₁	1	2	yes	—
624	#551	Dic₇₁	1	2	yes	—
625	#546	Dic₇₁	1	2	yes	—
626	#546	Dic₇₁	1	1	yes	characteristic
627	#546	Dic₇₁	1	1	yes	characteristic
628	D₄²	Dic₇₁	1	1	yes	characteristic
629	#532	C₂×D₇₁	1	1	yes	characteristic
630	#529	C₂×D₇₁	1	1	yes	characteristic
631	#529	C₂×D₇₁	1	2	yes	—
632	#529	C₂×D₇₁	1	1	yes	characteristic
633	#525	C₂×D₇₁	1	2	yes	—
634	#525	C₂×D₇₁	1	2	yes	—
635	C₄×#41	C₂×D₇₁	1	1	yes	characteristic
636	C₄×#41	C₂×D₇₁	1	1	yes	characteristic
637	C₂×C₄×D₄	C₂×D₇₁	1	1	yes	characteristic
638	C₂×C₄×D₄	C₂×D₇₁	1	2	yes	—
639	C₂×C₄×D₄	C₂×D₇₁	1	1	yes	characteristic
640	#446	—	71	1	no	—
641	#446	—	71	1	no	—
642	#446	—	71	1	no	—
643	#446	—	71	2	no	—
644	#446	—	71	1	no	—
645	C₈×Q₈	—	71	1	no	—
646	C₈×Q₈	—	71	1	no	—
647	#436	—	71	1	no	—
648	#436	—	71	1	no	—
649	#436	—	71	1	no	—
650	#436	—	71	1	no	—
651	#436	—	71	2	no	—
652	#436	—	71	1	no	—
653	#436	—	71	2	no	—
654	#436	—	71	1	no	—
655	#436	—	71	1	no	—
656	#436	—	71	2	no	—
657	#436	—	71	2	no	—
658	#436	—	71	2	no	—
659	#436	—	71	2	no	—
660	#436	—	71	1	no	—
661	#436	—	71	1	no	—
662	#436	—	71	1	no	—
663	#436	—	71	2	no	—
664	#436	—	71	2	no	—
665	#435	—	71	1	no	—
666	#435	—	71	2	no	—
667	#435	—	71	1	no	—
668	#435	—	71	2	no	—
669	#435	—	71	2	no	—
670	#435	—	71	2	no	—
671	#435	—	71	2	no	—
672	#435	—	71	1	no	—
673	#435	—	71	2	no	—
674	#435	—	71	2	no	—
675	#435	—	71	2	no	—
676	#435	—	71	2	no	—
677	#435	—	71	2	no	—
678	#435	—	71	2	no	—
679	#435	—	71	2	no	—
680	#435	—	71	1	no	—
681	#435	—	71	2	no	—
682	#435	—	71	2	no	—
683	#435	—	71	2	no	—
684	#435	—	71	2	no	—
685	C₈×D₄	—	71	2	no	—
686	C₈×D₄	—	71	2	no	—
687	C₈×D₄	—	71	1	no	—
688	C₈×D₄	—	71	2	no	—
689	C₈×D₄	—	71	1	no	—
690	C₈×D₄	—	71	1	no	—
691	C₈×D₄	—	71	1	no	—
692	#433	—	71	2	no	—
693	#433	—	71	2	no	—
694	#433	—	71	2	no	—
695	#433	—	71	2	no	—
696	#432	—	71	1	no	—
697	#432	—	71	2	no	—
698	#432	—	71	2	no	—
699	#432	—	71	1	no	—
700	#431	—	71	1	no	—
701	#431	—	71	1	no	—
702	#431	—	71	1	no	—
703	#431	—	71	1	no	—
704	#424	—	71	2	no	—
705	#424	—	71	2	no	—
706	#423	—	71	2	no	—
707	#423	—	71	1	no	—
708	C₂×C₄⋊C₈	—	71	1	no	—
709	C₂×C₄⋊C₈	—	71	1	no	—
710	#408	—	71	2	no	—
711	#408	—	71	2	no	—
712	#408	—	71	2	no	—
713	#407	—	71	2	no	—
714	#407	—	71	2	no	—
715	#407	—	71	2	no	—
716	#407	—	71	2	no	—
717	C₂×C₂²⋊C₈	—	71	2	no	—
718	C₂×C₂²⋊C₈	—	71	2	no	—
719	#405	—	71	2	no	—
720	#405	—	71	2	no	—
721	C₄×M₁₆	—	71	1	no	—
722	C₄×M₁₆	—	71	2	no	—
723	C₄×M₁₆	—	71	1	no	—
724	C₂×C₄×C₈	—	71	1	no	—
725	C₂×#41	C₂×Dic₇₁	1	1	yes	characteristic
726	C₂×#41	C₂×Dic₇₁	1	1	yes	characteristic
727	C₂×#41	C₂²×D₇₁	1	2	yes	—
728	C₂²×D₄	C₂×Dic₇₁	1	1	yes	characteristic
729	C₂²×D₄	C₂×Dic₇₁	1	1	yes	characteristic
730	C₂²×D₄	C₂×Dic₇₁	1	2	yes	—
731	C₂³×C₄	C₂²×D₇₁	1	2	yes	—
732	C₂³×C₄	C₂²×D₇₁	1	2	yes	—
733	#131	—	284	4	no	—
734	C₂×M₁₆	—	284	4	no	—
735	C₂×M₁₆	—	284	4	no	—
736	C₂×M₁₆	—	71	2	no	—
737	C₂×M₁₆	—	71	2	no	—
738	C₂×M₁₆	—	71	2	no	—
739	C₂×M₁₆	—	71	2	no	—
740	C₂×M₁₆	—	71	2	no	—
741	C₂×M₁₆	—	71	1	no	—
742	C₂×M₁₆	—	71	2	no	—
743	C₂×M₁₆	—	71	1	no	—
744	C₂×M₁₆	—	71	2	no	—
745	C₂×M₁₆	—	71	2	no	—
746	C₂×M₁₆	—	71	1	no	—
747	C₂×M₁₆	—	71	2	no	—
748	C₂×M₁₆	—	71	1	no	—
749	C₂²×C₈	—	71	2	no	—
750	C₂²×C₈	—	71	2	no	—
751	C₂²×C₈	—	71	2	no	—
752	C₂²×C₈	—	71	2	no	—
753	C₂²×C₈	—	71	1	no	—
754	C₂²×C₈	—	71	2	no	—
755	C₂²×C₈	—	71	1	no	—
756	C₂²×C₈	—	71	2	no	—
757	C₄⋊Q₈	C₂×Dic₇₁	1	1	yes	characteristic
758	#127	C₂×Dic₇₁	1	1	yes	characteristic
759	#126	C₂×Dic₇₁	1	2	yes	—
760	#126	C₂×Dic₇₁	1	2	yes	—
761	#126	C₂×Dic₇₁	1	2	yes	—
762	#126	C₂×Dic₇₁	1	2	yes	—
763	#125	C₂×Dic₇₁	1	1	yes	characteristic
764	#125	C₂×Dic₇₁	1	2	yes	—
765	#125	C₂×Dic₇₁	1	1	yes	characteristic
766	#124	C₂×Dic₇₁	1	1	yes	characteristic
767	#124	C₂×Dic₇₁	1	1	yes	characteristic
768	#124	C₂×Dic₇₁	1	2	yes	—
769	#124	C₂×Dic₇₁	1	2	yes	—
770	#123	C₂×Dic₇₁	1	2	yes	—
771	#123	C₂×Dic₇₁	1	2	yes	—
772	#123	C₂×Dic₇₁	1	2	yes	—
773	#123	C₂×Dic₇₁	1	2	yes	—
774	#123	C₂×Dic₇₁	1	2	yes	—
775	#123	C₂×Dic₇₁	1	2	yes	—
776	#123	C₂×Dic₇₁	1	2	yes	—
777	#123	C₂×Dic₇₁	1	2	yes	—
778	C₂²⋊Q₈	C₂×Dic₇₁	1	2	yes	—
779	C₂²⋊Q₈	C₂×Dic₇₁	1	2	yes	—
780	C₂²⋊Q₈	C₂×Dic₇₁	1	2	yes	—
781	C₂²⋊Q₈	C₂×Dic₇₁	1	2	yes	—
782	C₂²⋊Q₈	C₂×Dic₇₁	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂×Dic₇₁	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂×Dic₇₁	1	2	yes	—
785	#121	C₂×Dic₇₁	1	2	yes	—
786	#121	C₂×Dic₇₁	1	2	yes	—
787	#121	C₂×Dic₇₁	1	2	yes	—
788	#121	C₂×Dic₇₁	1	2	yes	—
789	#121	C₂×Dic₇₁	1	1	yes	characteristic
790	#121	C₂×Dic₇₁	1	1	yes	characteristic
791	#121	C₂×Dic₇₁	1	2	yes	—
792	#121	C₂×Dic₇₁	1	1	yes	characteristic
793	#121	C₂×Dic₇₁	1	1	yes	characteristic
794	#121	C₂×Dic₇₁	1	2	yes	—
795	#120	C₂×Dic₇₁	1	2	yes	—
796	#120	C₂×Dic₇₁	1	2	yes	—
797	#120	C₂×Dic₇₁	1	2	yes	—
798	#120	C₂×Dic₇₁	1	2	yes	—
799	C₄×Q₈	C₂×Dic₇₁	1	1	yes	characteristic
800	C₄×Q₈	C₂×Dic₇₁	1	1	yes	characteristic
801	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
802	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
803	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
804	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
805	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
806	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
807	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
808	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
809	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
810	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
811	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
812	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
813	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
814	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
815	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
816	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
817	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
818	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
819	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
820	C₄×D₄	C₂²×D₇₁	1	2	yes	—
821	C₄×D₄	C₂²×D₇₁	1	2	yes	—
822	C₄×D₄	C₂²×D₇₁	1	2	yes	—
823	C₄×D₄	C₂²×D₇₁	1	2	yes	—
824	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
825	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
826	C₄×D₄	C₂²×D₇₁	1	2	yes	—
827	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
828	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
829	C₄×D₄	C₂²×D₇₁	1	2	yes	—
830	#117	C₂×Dic₇₁	1	1	yes	characteristic
831	#117	C₂×Dic₇₁	1	1	yes	characteristic
832	#117	C₂×Dic₇₁	1	2	yes	—
833	#117	C₂×Dic₇₁	1	1	yes	characteristic
834	#117	C₂×Dic₇₁	1	1	yes	characteristic
835	#117	C₂²×D₇₁	1	2	yes	—
836	#117	C₂²×D₇₁	1	2	yes	—
837	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
838	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂×Dic₇₁	1	2	yes	—
840	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	2	yes	—
841	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	2	yes	—
842	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	2	yes	—
843	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	2	yes	—
844	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
845	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
846	C₂×C₄²	C₂²×D₇₁	1	2	yes	—
847	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
848	C₄⋊C₈	—	71	1	no	—
849	C₄⋊C₈	—	71	1	no	—
850	C₄⋊C₈	—	71	1	no	—
851	C₄⋊C₈	—	71	2	no	—
852	C₄⋊C₈	—	71	2	no	—
853	C₄⋊C₈	—	71	1	no	—
854	C₄⋊C₈	—	71	2	no	—
855	C₄⋊C₈	—	71	2	no	—
856	C₄⋊C₈	—	71	2	no	—
857	C₄⋊C₈	—	71	1	no	—
858	C₄⋊C₈	—	71	1	no	—
859	C₄⋊C₈	—	71	2	no	—
860	C₄⋊C₈	—	71	1	no	—
861	C₄⋊C₈	—	71	1	no	—
862	C₄⋊C₈	—	71	1	no	—
863	C₄⋊C₈	—	71	1	no	—
864	C₄⋊C₈	—	71	2	no	—
865	C₂²⋊C₈	—	71	1	no	—
866	C₂²⋊C₈	—	71	2	no	—
867	C₂²⋊C₈	—	71	2	no	—
868	C₂²⋊C₈	—	71	2	no	—
869	C₂²⋊C₈	—	71	2	no	—
870	C₂²⋊C₈	—	71	2	no	—
871	C₂²⋊C₈	—	71	2	no	—
872	C₂²⋊C₈	—	71	2	no	—
873	C₂²⋊C₈	—	71	1	no	—
874	C₂²⋊C₈	—	71	1	no	—
875	C₂²⋊C₈	—	71	2	no	—
876	C₂²⋊C₈	—	71	1	no	—
877	C₂²⋊C₈	—	71	2	no	—
878	C₂²⋊C₈	—	71	2	no	—
879	C₂²⋊C₈	—	71	2	no	—
880	C₂²⋊C₈	—	71	2	no	—
881	C₂²⋊C₈	—	71	2	no	—
882	C₂²⋊C₈	—	71	2	no	—
883	C₂²⋊C₈	—	71	1	no	—
884	C₂²⋊C₈	—	71	1	no	—
885	C₂²⋊C₈	—	71	2	no	—
886	#97	—	71	1	no	—
887	#97	—	71	1	no	—
888	#97	—	71	2	no	—
889	#97	—	71	1	no	—
890	#97	—	71	1	no	—
891	#97	—	71	2	no	—
892	#97	—	71	2	no	—
893	#97	—	71	2	no	—
894	C₄×C₈	—	71	1	no	—
895	C₄×C₈	—	71	1	no	—
896	C₄×C₈	—	71	1	no	—
897	C₄×C₈	—	71	1	no	—
898	C₄×C₈	—	71	2	no	—
899	C₄×C₈	—	71	1	no	—
900	C₄×C₈	—	71	1	no	—
901	C₄×C₈	—	71	2	no	—
902	C₄×C₈	—	71	2	no	—
903	C₂⁴	C₂²×Dic₇₁	1	2	yes	—
904	C₂⁴	C₂²×Dic₇₁	1	2	yes	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	2	no	—
908	#41	—	4	2	no	—
909	C₂×Q₈	C₂²×Dic₇₁	1	1	yes	characteristic
910	C₂×Q₈	C₂²×Dic₇₁	1	1	yes	characteristic
911	C₂×Q₈	C₂²×Dic₇₁	1	2	yes	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	4	4	no	—
915	C₂×D₄	C₂²×Dic₇₁	1	1	yes	characteristic
916	C₂×D₄	C₂²×Dic₇₁	1	1	yes	characteristic
917	C₂×D₄	C₂²×Dic₇₁	1	1	yes	characteristic
918	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
919	C₂×D₄	C₂²×Dic₇₁	1	1	yes	characteristic
920	C₂×D₄	C₂²×Dic₇₁	1	1	yes	characteristic
921	C₂×D₄	C₂²×Dic₇₁	1	1	yes	characteristic
922	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
923	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
924	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
925	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
926	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
927	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
928	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
929	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
930	C₂²×C₄	—	4	2	no	—
931	C₂²×C₄	—	4	2	no	—
932	C₂²×C₄	—	4	2	no	—
933	C₂²×C₄	—	4	2	no	—
934	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
935	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
936	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
937	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
938	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
939	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
940	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
941	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
942	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
943	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
944	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
945	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
946	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
947	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
948	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
949	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
950	C₂²×C₄	C₂³×D₇₁	1	2	yes	—
951	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
952	C₂²×C₄	C₂³×D₇₁	1	2	yes	—
953	C₂²×C₄	C₂³×D₇₁	1	2	yes	—
954	M₁₆	—	284	2	no	—
955	M₁₆	—	284	2	no	—
956	M₁₆	—	284	2	no	—
957	M₁₆	—	284	2	no	—
958	M₁₆	—	284	1	no	—
959	M₁₆	—	284	2	no	—
960	M₁₆	—	284	2	no	—
961	M₁₆	—	284	1	no	—
962	M₁₆	—	284	2	no	—
963	M₁₆	—	142	2	no	—
964	M₁₆	—	142	4	no	—
965	M₁₆	—	142	4	no	—
966	M₁₆	—	142	2	no	—
967	C₂×C₈	—	284	2	no	—
968	C₂×C₈	—	284	1	no	—
969	C₂×C₈	—	284	2	no	—
970	C₂×C₈	—	284	2	no	—
971	C₂×C₈	—	284	2	no	—
972	C₂×C₈	—	284	2	no	—
973	C₂×C₈	—	71	1	no	—
974	C₂×C₈	—	71	1	no	—
975	C₂×C₈	—	71	1	no	—
976	C₂×C₈	—	71	1	no	—
977	C₂×C₈	—	71	2	no	—
978	C₂×C₈	—	71	1	no	—
979	C₂×C₈	—	71	1	no	—
980	C₂×C₈	—	71	1	no	—
981	C₂×C₈	—	71	1	no	—
982	C₂×C₈	—	71	2	no	—
983	C₂×C₈	—	71	2	no	—
984	C₂×C₈	—	71	2	no	—
985	C₂×C₈	—	142	2	no	—
986	C₂×C₈	—	142	4	no	—
987	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
988	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
990	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
991	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
992	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
993	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
994	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
995	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
996	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
999	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
1001	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
1002	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
1003	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1004	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1005	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1006	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1007	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1008	C₂²⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
1009	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1010	C₂²⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
1011	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1012	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1013	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1014	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1015	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1016	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1017	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1018	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1019	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1020	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1021	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1022	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1023	C₂²⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
1024	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1025	C₂²⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
1026	C₂²⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
1027	C₂²⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
1028	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1029	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1030	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1031	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1032	C₂²⋊C₄	C₂²×Dic₇₁	1	2	yes	—
1033	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
1034	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
1035	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
1036	C₄²	C₂²×Dic₇₁	1	2	yes	—
1037	C₄²	C₂²×Dic₇₁	1	2	yes	—
1038	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
1039	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
1040	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
1041	C₄²	C₂³×D₇₁	1	1	yes	characteristic
1042	C₄²	C₂³×D₇₁	1	1	yes	characteristic
1043	C₄²	C₂³×D₇₁	1	2	yes	—
1044	C₄²	C₂³×D₇₁	1	1	yes	characteristic
1045	C₄²	C₂³×D₇₁	1	1	yes	characteristic
1046	C₂³	—	2	4	no	—
1047	C₂³	—	4	2	no	—
1048	C₂³	—	4	2	no	—
1049	C₂³	—	4	2	no	—
1050	C₂³	—	4	2	no	—
1051	C₂³	—	4	2	no	—
1052	C₂³	C₂³×Dic₇₁	1	2	yes	—
1053	C₂³	C₂³×Dic₇₁	1	2	yes	—
1054	C₂³	C₂³×Dic₇₁	1	1	yes	characteristic
1055	C₂³	C₂³×Dic₇₁	1	2	yes	—
1056	C₂³	C₂³×Dic₇₁	1	1	yes	characteristic
1057	C₂³	C₂³×Dic₇₁	1	1	yes	characteristic
1058	Q₈	—	2	2	no	—
1059	Q₈	—	4	1	no	—
1060	Q₈	—	4	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	4	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	1	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	4	2	no	—
1075	D₄	—	4	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
1103	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
1104	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
1105	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
1106	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
1107	C₂×C₄	C₂³×Dic₇₁	1	2	yes	—
1108	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
1109	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
1110	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
1111	C₂×C₄	C₂³×Dic₇₁	1	2	yes	—
1112	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
1113	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
1114	C₂×C₄	C₂³×Dic₇₁	1	2	yes	—
1115	C₂×C₄	C₂³×Dic₇₁	1	2	yes	—
1116	C₂×C₄	C₂³×Dic₇₁	1	2	yes	—
1117	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
1118	C₂×C₄	C₂⁴×D₇₁	1	1	yes	characteristic
1119	C₈	—	71	2	no	—
1120	C₈	—	142	2	no	—
1121	C₈	—	142	2	no	—
1122	C₈	—	142	1	no	—
1123	C₈	—	142	2	no	—
1124	C₈	—	142	1	no	—
1125	C₈	—	142	1	no	—
1126	C₈	—	142	1	no	—
1127	C₈	—	142	2	no	—
1128	C₈	—	142	1	no	—
1129	C₈	—	142	1	no	—
1130	C₈	—	142	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	2	2	no	—
1146	C₂²	—	2	2	no	—
1147	C₂²	—	2	1	no	—
1148	C₂²	—	8	4	no	—
1149	C₂²	—	8	4	no	—
1150	C₂²	#17986766	1	2	yes	—
1151	C₂²	C₂⁴×Dic₇₁	1	1	yes	characteristic
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	2	1	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	1	no	—
1167	C₄	#17986766	1	2	yes	—
1168	C₄	H(5,𝔽₂)×D₇₁	1	1	yes	characteristic
1169	C₄	#17986834	1	1	yes	characteristic
1170	C₂	—	2	2	no	—
1171	C₂	—	4	1	no	—
1172	C₂	—	4	2	no	—
1173	C₂	—	4	2	no	—
1174	C₂	—	4	2	no	—
1175	C₂	—	4	1	no	—
1176	C₂	H(5,𝔽₂)×Dic₇₁	1	1	yes	characteristic
1177	C₂	C₂×#17986766	1	1	yes	characteristic
1178	C₂	C₂×#17986766	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₇₁
commutator, socle	C₂²×C₇₁	C₂⁴×C₄
Fitting, prime radical	C₇₁×#3481	C₂
cosocle	C₂×C₄×C₇₁	C₂⁵
hypercenter	#3481	D₇₁
hypocenter	C₇₁	#60324
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ #3481

Complements

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

N	H ≅ G/N	type
1. #22597510	C₂	semidirect
2. #22597500	C₂	semidirect
3. #22597489	C₂	semidirect
4. #22597465	C₂	semidirect
5. #22597457	C₂	semidirect
6. #22597416	C₂	semidirect
7. #22597402	C₂	semidirect
8. #22597388	C₂	semidirect
9. #22597381	C₂	semidirect
10. #22597375	C₂	semidirect
11. #22597369	C₂	semidirect
12. #22597360	C₂	semidirect
13. #22597345	C₂	semidirect
14. #22597327	C₂	semidirect
15. #22597316	C₂	semidirect
16. #22597307	C₂	semidirect
17. #22597084	C₂	semidirect
18. D₄×#11765849	C₂	semidirect
19. D₄×#11765849	C₂	semidirect
20. #22597067	C₂	semidirect
21. #22597044	C₂	semidirect
22. C₂×#17986077	C₂	semidirect
24. C₂×#14556135	C₂²	semidirect
25. C₂²×#11765849	C₂²	semidirect
26. C₂²×#11765849	C₂²	semidirect
27. #17986130	C₂²	semidirect
28. #17986130	C₂²	semidirect
29. #17986130	C₂²	semidirect
30. #17986130	C₂²	semidirect
31. #17986130	C₂²	semidirect
32. Q₈×C₇₁⋊C₈	C₂²	semidirect
33. Q₈×C₇₁⋊C₈	C₂²	semidirect
38. #17986077	C₂²	semidirect
39. #17986077	C₂²	semidirect
40. #17986077	C₂²	semidirect
41. #17986077	C₂²	semidirect
42. #17986077	C₂²	semidirect
43. #17986077	C₂²	semidirect
44. #17986077	C₂²	semidirect
45. #17986077	C₂²	semidirect
46. #17986077	C₂²	semidirect
47. #17986077	C₂²	semidirect
48. #17986077	C₂²	semidirect
49. #17986077	C₂²	semidirect
50. #17986077	C₂²	semidirect
51. #17986077	C₂²	semidirect
55. #17986071	C₂²	semidirect
56. #17986071	C₂²	semidirect
57. #17986071	C₂²	semidirect
58. #17986071	C₂²	semidirect
59. #17986071	C₂²	semidirect
60. #17986071	C₂²	semidirect
61. #17986071	C₂²	semidirect
62. #17986071	C₂²	semidirect
63. #17986071	C₂²	semidirect
64. #17986071	C₂²	semidirect
65. #17986071	C₂²	semidirect
66. #17986071	C₂²	semidirect
67. #17986071	C₂²	semidirect
68. #17986071	C₂²	semidirect
69. #17986071	C₂²	semidirect
70. #17986071	C₂²	semidirect
71. #17986071	C₂²	semidirect
72. D₄×C₇₁⋊C₈	C₂²	semidirect
73. D₄×C₇₁⋊C₈	C₂²	semidirect
74. D₄×C₇₁⋊C₈	C₂²	semidirect
75. D₄×C₇₁⋊C₈	C₂²	semidirect
76. D₄×C₇₁⋊C₈	C₂²	semidirect
77. D₄×C₇₁⋊C₈	C₂²	semidirect
78. D₄×C₇₁⋊C₈	C₂²	semidirect
79. #17986060	C₂²	semidirect
80. #17986060	C₂²	semidirect
81. #17986060	C₂²	semidirect
82. #17986060	C₂²	semidirect
83. #17986056	C₂²	semidirect
84. #17986056	C₂²	semidirect
85. #17986056	C₂²	semidirect
86. #17986056	C₂²	semidirect
87. #17986052	C₂²	semidirect
88. #17986052	C₂²	semidirect
89. #17986052	C₂²	semidirect
90. #17986052	C₂²	semidirect
91. #17986026	C₂²	semidirect
92. #17986026	C₂²	semidirect
93. #17986023	C₂²	semidirect
94. #17986023	C₂²	semidirect
95. C₂×C₄⋊(C₇₁⋊C₈)	C₂²	semidirect
96. C₂×C₄⋊(C₇₁⋊C₈)	C₂²	semidirect
97. #17985966	C₂²	semidirect
98. #17985966	C₂²	semidirect
99. #17985966	C₂²	semidirect
100. #17985963	C₂²	semidirect
101. #17985963	C₂²	semidirect
102. #17985963	C₂²	semidirect
103. #17985963	C₂²	semidirect
104. C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	semidirect
105. C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	semidirect
106. #17985955	C₂²	semidirect
107. #17985955	C₂²	semidirect
108. C₄×#11765849	C₂²	semidirect
109. C₄×#11765849	C₂²	semidirect
110. C₄×#11765849	C₂²	semidirect
111. C₂×C₄×C₇₁⋊C₈	C₂²	semidirect
613. C₇₁	#60324	semidirect

Maximal subgroups

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

subgroup	index
#22597510	2
#22597500	2
#22597489	2
#22597465	2
#22597457	2
#22597416	2
#22597402	2
#22597388	2
#22597381	2
#22597375	2
#22597369	2
#22597360	2
#22597345	2
#22597327	2
#22597316	2
#22597307	2
#22597084	2
D₄×#11765849	2
#22597067	2
#22597044	2
C₂×#17986077	2
C₇₁×#3481	2
#60324	71