Subgroups — C₃₁×#60766 #21517525

Order 7936.

2140 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3202	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3200	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3197	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3196	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3191	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3190	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3099	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×#485	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3061	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3060	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3013	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3007	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3002	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2880	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic, complemented
33	D₄×Q₈×C₃₁	—	2	1	no	—
34	C₃₁×#548	—	2	1	no	—
35	C₃₁×#547	—	2	2	no	—
36	C₃₁×#547	—	2	1	no	—
37	C₃₁×#546	—	2	2	no	—
38	C₃₁×#546	—	2	1	no	—
39	C₃₁×#537	C₂²	1	1	yes	characteristic
40	C₃₁×#537	C₂²	1	1	yes	characteristic
41	C₃₁×#537	C₂²	1	1	yes	characteristic
42	C₃₁×#537	C₂²	1	1	yes	characteristic
43	C₃₁×#537	C₂²	1	2	yes	—
44	C₃₁×#537	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#536	—	2	1	no	—
46	C₃₁×#536	C₂²	1	2	yes	—
47	C₃₁×#536	C₂²	1	2	yes	—
48	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#535	—	2	1	no	—
50	C₃₁×#535	C₂²	1	2	yes	—
51	C₃₁×#534	—	2	2	no	—
52	C₃₁×#532	—	2	2	no	—
53	C₃₁×#525	—	2	1	no	—
54	C₃₁×#525	—	2	1	no	—
55	C₃₁×#525	C₂²	1	1	yes	characteristic
56	C₃₁×#525	C₂²	1	2	yes	—
57	C₃₁×#525	C₂²	1	2	yes	—
58	C₃₁×#525	C₂²	1	2	yes	complemented
59	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
60	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
63	C₃₁×#485	C₂²	1	2	yes	complemented
64	C₃₁×#485	C₂²	1	2	yes	complemented
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#485	C₂²	1	2	yes	complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#485	C₂²	1	2	yes	complemented
69	C₃₁×#485	C₂²	1	2	yes	complemented
70	C₃₁×#485	C₂²	1	2	yes	complemented
71	C₃₁×#484	C₂²	1	2	yes	complemented
72	C₃₁×#483	C₂²	1	2	yes	complemented
73	C₃₁×#482	C₂²	1	2	yes	complemented
74	C₃₁×#482	C₂²	1	2	yes	complemented
75	C₃₁×#482	C₂²	1	2	yes	complemented
76	C₃₁×#482	C₂²	1	2	yes	complemented
77	C₃₁×#481	C₂²	1	2	yes	complemented
78	C₃₁×#480	C₂²	1	2	yes	complemented
79	C₃₁×#470	C₂²	1	2	yes	complemented
80	C₃₁×#470	C₂²	1	2	yes	complemented
81	C₃₁×#470	C₂²	1	2	yes	complemented
82	C₃₁×#469	C₂²	1	2	yes	complemented
83	C₃₁×#468	C₂²	1	2	yes	complemented
84	C₃₁×#468	C₂²	1	2	yes	complemented
85	C₃₁×#468	C₂²	1	2	yes	complemented
86	C₃₁×#468	C₂²	1	2	yes	complemented
87	C₃₁×#467	C₂²	1	2	yes	complemented
88	C₃₁×#467	C₂²	1	2	yes	complemented
89	C₃₁×#467	C₂²	1	2	yes	complemented
90	C₃₁×#466	C₂²	1	2	yes	complemented
91	C₃₁×#465	C₂²	1	2	yes	complemented
92	C₃₁×#465	C₂²	1	2	yes	complemented
93	C₃₁×#465	C₂²	1	2	yes	complemented
94	C₃₁×#465	C₂²	1	2	yes	complemented
95	C₃₁×#452	C₂²	1	1	yes	characteristic
96	C₃₁×#452	C₂²	1	2	yes	—
97	C₃₁×#452	C₂²	1	2	yes	—
98	C₃₁×#452	C₂²	1	1	yes	characteristic
99	C₃₁×#452	C₂²	1	2	yes	complemented
100	C₃₁×#452	C₂²	1	2	yes	complemented
101	C₃₁×#451	C₂²	1	2	yes	complemented
102	C₃₁×#451	C₂²	1	2	yes	complemented
103	C₃₁×#451	C₂²	1	2	yes	complemented
104	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#450	C₂²	1	2	yes	complemented
106	C₃₁×#450	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#449	C₂²	1	1	yes	characteristic
108	C₃₁×#449	C₂²	1	1	yes	characteristic
109	C₃₁×#449	C₂²	1	2	yes	complemented
110	C₃₁×#449	C₂²	1	2	yes	complemented
111	C₃₁×#448	C₂²	1	2	yes	complemented
112	C₃₁×#448	C₂²	1	2	yes	complemented
113	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#447	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
120	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#408	C₂²	1	2	yes	—
128	C₃₁×#408	C₂²	1	2	yes	—
129	C₃₁×#408	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#408	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#407	C₂²	1	1	yes	characteristic
132	C₃₁×#407	C₂²	1	2	yes	complemented
133	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	C₃₁×2₋¹⁺⁴	—	4	2	no	—
136	C₃₁×2₋¹⁺⁴	—	4	2	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	—	2	2	no	—
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	—	4	2	no	—
142	C₂×#41×C₃₁	—	4	2	no	—
143	C₂×#41×C₃₁	—	4	2	no	—
144	C₂×#41×C₃₁	—	4	2	no	—
145	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
146	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
147	C₂×#41×C₃₁	D₄	1	2	yes	—
148	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×#41×C₃₁	C₂³	1	2	yes	—
154	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×#41×C₃₁	C₂³	1	2	yes	—
157	C₂²×Q₈×C₃₁	—	2	1	no	—
158	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
159	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
160	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
161	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
162	C₂²×D₄×C₃₁	—	2	1	no	—
163	C₂²×D₄×C₃₁	D₄	1	2	yes	—
164	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
165	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₂³×C₄×C₃₁	—	2	1	no	—
167	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
169	C₃₁×#137	—	4	2	no	—
170	C₃₁×#137	—	4	2	no	—
171	C₃₁×#135	—	4	2	no	—
172	C₃₁×#135	—	4	2	no	—
173	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
176	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
177	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
182	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
183	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
185	C₃₁×#131	—	4	2	no	—
186	C₃₁×#131	—	4	2	no	—
187	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
188	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
190	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
191	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
192	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
193	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
194	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
195	C₃₁×C₄⋊Q₈	—	2	2	no	—
196	C₃₁×C₄⋊Q₈	—	2	2	no	—
197	C₃₁×C₄⋊Q₈	—	2	1	no	—
198	C₃₁×#127	—	2	2	no	—
199	C₃₁×#124	—	2	2	no	—
200	C₃₁×#124	—	2	2	no	—
201	C₃₁×#124	—	2	2	no	—
202	C₃₁×#124	—	2	1	no	—
203	C₃₁×#123	—	2	2	no	—
204	C₃₁×#123	—	2	2	no	—
205	C₃₁×#123	—	2	2	no	—
206	C₃₁×#123	—	2	2	no	—
207	C₃₁×#123	—	2	2	no	—
208	C₃₁×#123	—	2	2	no	—
209	C₃₁×#123	—	2	2	no	—
210	C₃₁×#123	—	2	1	no	—
211	C₃₁×#123	—	2	2	no	—
212	C₃₁×C₂²⋊Q₈	—	2	1	no	—
213	C₃₁×C₂²⋊Q₈	—	2	1	no	—
214	C₃₁×C₂²⋊Q₈	—	2	1	no	—
215	C₃₁×C₂²⋊Q₈	—	2	1	no	—
216	C₃₁×C₂²⋊Q₈	—	2	2	no	—
217	C₃₁×C₂²⋊Q₈	—	2	1	no	—
218	C₃₁×C₂²⋊Q₈	—	2	1	no	—
219	C₃₁×C₂²⋊Q₈	—	2	1	no	—
220	C₃₁×C₂²⋊Q₈	—	2	2	no	—
221	C₃₁×C₂²⋊Q₈	—	2	2	no	—
222	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
227	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
229	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
230	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
231	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
232	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
233	C₃₁×#121	—	2	1	no	—
234	C₃₁×#121	—	2	1	no	—
235	C₃₁×#121	—	2	1	no	—
236	C₃₁×#121	—	2	1	no	—
237	C₃₁×#121	—	2	2	no	—
238	C₃₁×#121	—	2	2	no	—
239	C₃₁×#121	—	2	2	no	—
240	C₃₁×#121	—	2	2	no	—
241	C₃₁×#121	—	2	2	no	—
242	C₃₁×#121	—	2	2	no	—
243	C₃₁×#121	—	2	2	no	—
244	C₃₁×#121	—	2	2	no	—
245	C₃₁×#121	—	2	1	no	—
246	C₃₁×#121	C₂³	1	1	yes	characteristic
247	C₃₁×#121	C₂³	1	2	yes	—
248	C₃₁×#121	C₂³	1	2	yes	—
249	C₃₁×#121	C₂³	1	1	yes	characteristic
250	C₃₁×#121	C₂³	1	2	yes	—
251	C₃₁×#121	C₂³	1	2	yes	—
252	C₃₁×#121	C₂³	1	2	yes	—
253	C₃₁×#120	—	2	2	no	—
254	C₃₁×#120	—	2	2	no	—
255	C₃₁×#120	—	2	1	no	—
256	C₃₁×#120	—	2	2	no	—
257	C₃₁×#120	—	2	2	no	—
258	C₃₁×#120	—	2	2	no	—
259	C₄×Q₈×C₃₁	—	2	1	no	—
260	C₄×D₄×C₃₁	—	2	2	no	—
261	C₄×D₄×C₃₁	—	2	1	no	—
262	C₄×D₄×C₃₁	—	2	2	no	—
263	C₄×D₄×C₃₁	—	2	2	no	—
264	C₄×D₄×C₃₁	—	2	2	no	—
265	C₄×D₄×C₃₁	—	2	2	no	—
266	C₄×D₄×C₃₁	—	2	1	no	—
267	C₄×D₄×C₃₁	—	2	1	no	—
268	C₄×D₄×C₃₁	—	2	2	no	—
269	C₄×D₄×C₃₁	—	2	2	no	—
270	C₃₁×#117	—	2	1	no	—
271	C₃₁×#117	—	2	1	no	—
272	C₃₁×#117	C₂³	1	1	yes	characteristic
273	C₃₁×#117	C₂³	1	2	yes	—
274	C₃₁×#117	C₂³	1	2	yes	—
275	C₃₁×#117	C₂³	1	2	yes	—
276	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
277	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
282	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
283	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
284	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
285	C₂×C₄²×C₃₁	—	2	1	no	—
286	C₃₁×#107	C₂³	1	2	yes	—
287	C₃₁×#107	C₂³	1	2	yes	—
288	C₃₁×#107	C₂³	1	2	yes	—
289	C₃₁×#107	C₂³	1	2	yes	—
290	C₃₁×#106	C₂³	1	2	yes	—
291	C₃₁×#106	C₂³	1	2	yes	—
292	C₃₁×#106	C₂³	1	2	yes	—
293	C₃₁×#106	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#103	C₂³	1	1	yes	characteristic
299	C₃₁×#103	C₂³	1	1	yes	characteristic
300	C₃₁×#103	C₂³	1	1	yes	characteristic
301	C₃₁×#103	C₂³	1	1	yes	characteristic
302	C₃₁×#103	C₂³	1	2	yes	—
303	C₃₁×#103	C₂³	1	2	yes	—
304	C₃₁×#103	C₂³	1	2	yes	—
305	C₃₁×#103	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	1	yes	characteristic
307	C₃₁×#102	C₂³	1	1	yes	characteristic
308	C₃₁×#102	C₂³	1	1	yes	characteristic
309	C₃₁×#102	C₂³	1	1	yes	characteristic
310	C₃₁×#102	C₂³	1	2	yes	—
311	C₃₁×#102	C₂³	1	2	yes	—
312	C₃₁×#102	C₂³	1	2	yes	—
313	C₃₁×#102	C₂³	1	2	yes	—
314	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
315	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
316	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
317	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
318	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
321	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
322	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
323	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
324	C₂⁴×C₃₁	—	2	1	no	—
325	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
327	#41×C₃₁	—	2	2	no	—
328	#41×C₃₁	—	2	2	no	—
329	#41×C₃₁	—	2	2	no	—
330	#41×C₃₁	—	2	2	no	—
331	#41×C₃₁	—	2	2	no	—
332	#41×C₃₁	—	2	2	no	—
333	#41×C₃₁	—	2	2	no	—
334	#41×C₃₁	—	2	2	no	—
335	#41×C₃₁	—	2	2	no	—
336	#41×C₃₁	—	2	2	no	—
337	#41×C₃₁	—	4	2	no	—
338	#41×C₃₁	—	4	2	no	—
339	#41×C₃₁	—	4	4	no	—
340	#41×C₃₁	—	4	2	no	—
341	#41×C₃₁	—	4	2	no	—
342	#41×C₃₁	—	4	1	no	—
343	#41×C₃₁	—	4	1	no	—
344	#41×C₃₁	—	4	1	no	—
345	#41×C₃₁	—	4	1	no	—
346	#41×C₃₁	—	4	2	no	—
347	#41×C₃₁	—	4	2	no	—
348	#41×C₃₁	—	4	4	no	—
349	#41×C₃₁	—	4	4	no	—
350	#41×C₃₁	—	4	8	no	—
351	#41×C₃₁	—	4	4	no	—
352	C₂×Q₈×C₃₁	—	2	2	no	—
353	C₂×Q₈×C₃₁	—	2	1	no	—
354	C₂×Q₈×C₃₁	—	2	1	no	—
355	C₂×Q₈×C₃₁	—	2	2	no	—
356	C₂×Q₈×C₃₁	—	2	2	no	—
357	C₂×Q₈×C₃₁	—	4	2	no	—
358	C₂×Q₈×C₃₁	—	4	1	no	—
359	C₂×Q₈×C₃₁	—	4	1	no	—
360	C₂×Q₈×C₃₁	—	4	2	no	—
361	C₂×Q₈×C₃₁	—	4	2	no	—
362	C₂×Q₈×C₃₁	—	4	4	no	—
363	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
364	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
365	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
366	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
367	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂×D₄×C₃₁	—	2	1	no	—
371	C₂×D₄×C₃₁	—	2	1	no	—
372	C₂×D₄×C₃₁	—	2	1	no	—
373	C₂×D₄×C₃₁	—	2	2	no	—
374	C₂×D₄×C₃₁	—	2	1	no	—
375	C₂×D₄×C₃₁	—	2	1	no	—
376	C₂×D₄×C₃₁	—	2	1	no	—
377	C₂×D₄×C₃₁	—	2	2	no	—
378	C₂×D₄×C₃₁	—	2	2	no	—
379	C₂×D₄×C₃₁	—	2	2	no	—
380	C₂×D₄×C₃₁	—	2	2	no	—
381	C₂×D₄×C₃₁	—	2	1	no	—
382	C₂×D₄×C₃₁	—	2	2	no	—
383	C₂×D₄×C₃₁	—	2	1	no	—
384	C₂×D₄×C₃₁	—	4	2	no	—
385	C₂×D₄×C₃₁	—	4	1	no	—
386	C₂×D₄×C₃₁	—	4	1	no	—
387	C₂×D₄×C₃₁	—	4	4	no	—
388	C₂×D₄×C₃₁	—	4	4	no	—
389	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
390	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
391	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
392	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
393	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
394	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₃₁	—	2	2	no	—
400	C₂²×C₄×C₃₁	—	2	2	no	—
401	C₂²×C₄×C₃₁	—	2	2	no	—
402	C₂²×C₄×C₃₁	—	2	1	no	—
403	C₂²×C₄×C₃₁	—	2	1	no	—
404	C₂²×C₄×C₃₁	—	2	1	no	—
405	C₂²×C₄×C₃₁	—	2	1	no	—
406	C₂²×C₄×C₃₁	—	2	2	no	—
407	C₂²×C₄×C₃₁	—	2	1	no	—
408	C₂²×C₄×C₃₁	—	2	1	no	—
409	C₂²×C₄×C₃₁	—	2	1	no	—
410	C₂²×C₄×C₃₁	—	2	2	no	—
411	C₂²×C₄×C₃₁	—	2	1	no	—
412	C₂²×C₄×C₃₁	—	2	1	no	—
413	C₂²×C₄×C₃₁	—	2	1	no	—
414	C₂²×C₄×C₃₁	—	4	2	no	—
415	C₂²×C₄×C₃₁	—	4	2	no	—
416	C₂²×C₄×C₃₁	—	4	4	no	—
417	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
418	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
419	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
420	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
421	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
422	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
423	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
424	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
427	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
428	Q₁₆×C₃₁	—	4	1	no	—
429	Q₁₆×C₃₁	—	4	1	no	—
430	Q₁₆×C₃₁	—	4	2	no	—
431	Q₁₆×C₃₁	—	4	2	no	—
432	SD₁₆×C₃₁	—	4	1	no	—
433	SD₁₆×C₃₁	—	4	1	no	—
434	SD₁₆×C₃₁	—	4	1	no	—
435	SD₁₆×C₃₁	—	4	1	no	—
436	SD₁₆×C₃₁	—	4	2	no	—
437	SD₁₆×C₃₁	—	4	2	no	—
438	D₈×C₃₁	—	4	1	no	—
439	D₈×C₃₁	—	4	1	no	—
440	M₁₆×C₃₁	—	2	2	no	—
441	M₁₆×C₃₁	—	2	2	no	—
442	M₁₆×C₃₁	—	4	2	no	—
443	M₁₆×C₃₁	—	4	2	no	—
444	C₂×C₈×C₃₁	—	2	2	no	—
445	C₂×C₈×C₃₁	—	2	2	no	—
446	C₂×C₈×C₃₁	—	4	2	no	—
447	C₂×C₈×C₃₁	—	4	2	no	—
448	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
449	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
450	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
451	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
452	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
453	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₃₁	—	2	2	no	—
455	C₄⋊C₄×C₃₁	—	2	1	no	—
456	C₄⋊C₄×C₃₁	—	2	2	no	—
457	C₄⋊C₄×C₃₁	—	2	2	no	—
458	C₄⋊C₄×C₃₁	—	2	2	no	—
459	C₄⋊C₄×C₃₁	—	2	1	no	—
460	C₄⋊C₄×C₃₁	—	2	1	no	—
461	C₄⋊C₄×C₃₁	—	2	2	no	—
462	C₄⋊C₄×C₃₁	—	2	1	no	—
463	C₄⋊C₄×C₃₁	—	2	2	no	—
464	C₄⋊C₄×C₃₁	—	2	2	no	—
465	C₄⋊C₄×C₃₁	—	2	2	no	—
466	C₄⋊C₄×C₃₁	—	2	2	no	—
467	C₄⋊C₄×C₃₁	—	2	1	no	—
468	C₄⋊C₄×C₃₁	—	2	2	no	—
469	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
470	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
471	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
472	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
473	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
474	C₂²⋊C₄×C₃₁	—	2	2	no	—
475	C₂²⋊C₄×C₃₁	—	2	1	no	—
476	C₂²⋊C₄×C₃₁	—	2	2	no	—
477	C₂²⋊C₄×C₃₁	—	2	2	no	—
478	C₂²⋊C₄×C₃₁	—	2	2	no	—
479	C₂²⋊C₄×C₃₁	—	2	2	no	—
480	C₂²⋊C₄×C₃₁	—	2	2	no	—
481	C₂²⋊C₄×C₃₁	—	2	2	no	—
482	C₂²⋊C₄×C₃₁	—	2	1	no	—
483	C₂²⋊C₄×C₃₁	—	2	2	no	—
484	C₂²⋊C₄×C₃₁	—	2	2	no	—
485	C₂²⋊C₄×C₃₁	—	2	2	no	—
486	C₂²⋊C₄×C₃₁	—	2	2	no	—
487	C₂²⋊C₄×C₃₁	—	2	1	no	—
488	C₂²⋊C₄×C₃₁	—	2	2	no	—
489	C₂²⋊C₄×C₃₁	—	2	1	no	—
490	C₂²⋊C₄×C₃₁	—	2	2	no	—
491	C₂²⋊C₄×C₃₁	—	2	2	no	—
492	C₂²⋊C₄×C₃₁	—	2	2	no	—
493	C₂²⋊C₄×C₃₁	—	2	2	no	—
494	C₂²⋊C₄×C₃₁	—	2	1	no	—
495	C₂²⋊C₄×C₃₁	—	2	2	no	—
496	C₄²×C₃₁	—	2	2	no	—
497	C₄²×C₃₁	—	2	2	no	—
498	C₄²×C₃₁	—	2	2	no	—
499	C₄²×C₃₁	—	2	1	no	—
500	#60766	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
501	C₂³×C₃₁	—	2	2	no	—
502	C₂³×C₃₁	—	2	1	no	—
503	C₂³×C₃₁	—	2	1	no	—
504	C₂³×C₃₁	—	2	1	no	—
505	C₂³×C₃₁	—	4	2	no	—
506	C₂³×C₃₁	—	4	1	no	—
507	C₂³×C₃₁	—	4	1	no	—
508	C₂³×C₃₁	—	4	2	no	—
509	C₂³×C₃₁	—	4	2	no	—
510	C₂³×C₃₁	—	4	2	no	—
511	C₂³×C₃₁	—	8	1	no	—
512	C₂³×C₃₁	—	8	1	no	—
513	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
516	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
517	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
518	Q₈×C₃₁	—	2	2	no	—
519	Q₈×C₃₁	—	2	2	no	—
520	Q₈×C₃₁	—	2	2	no	—
521	Q₈×C₃₁	—	2	2	no	—
522	Q₈×C₃₁	—	2	1	no	—
523	Q₈×C₃₁	—	2	1	no	—
524	Q₈×C₃₁	—	2	1	no	—
525	Q₈×C₃₁	—	2	1	no	—
526	Q₈×C₃₁	—	2	1	no	—
527	Q₈×C₃₁	—	2	1	no	—
528	Q₈×C₃₁	—	4	2	no	—
529	Q₈×C₃₁	—	4	4	no	—
530	Q₈×C₃₁	—	4	2	no	—
531	Q₈×C₃₁	—	4	2	no	—
532	D₄×C₃₁	—	2	4	no	—
533	D₄×C₃₁	—	2	4	no	—
534	D₄×C₃₁	—	2	2	no	—
535	D₄×C₃₁	—	2	2	no	—
536	D₄×C₃₁	—	2	1	no	—
537	D₄×C₃₁	—	2	1	no	—
538	D₄×C₃₁	—	2	1	no	—
539	D₄×C₃₁	—	2	1	no	—
540	D₄×C₃₁	—	2	1	no	—
541	D₄×C₃₁	—	2	1	no	—
542	D₄×C₃₁	—	4	2	no	—
543	D₄×C₃₁	—	4	2	no	—
544	D₄×C₃₁	—	4	2	no	—
545	D₄×C₃₁	—	4	2	no	—
546	D₄×C₃₁	—	4	2	no	—
547	D₄×C₃₁	—	4	2	no	—
548	D₄×C₃₁	—	4	2	no	—
549	D₄×C₃₁	—	4	4	no	—
550	D₄×C₃₁	—	4	2	no	—
551	D₄×C₃₁	—	4	2	no	—
552	D₄×C₃₁	—	4	2	no	—
553	D₄×C₃₁	—	8	2	no	—
554	D₄×C₃₁	—	8	1	no	—
555	D₄×C₃₁	—	8	2	no	—
556	D₄×C₃₁	—	8	2	no	—
557	D₄×C₃₁	—	8	2	no	—
558	D₄×C₃₁	—	8	2	no	—
559	C₂×C₄×C₃₁	—	2	2	no	—
560	C₂×C₄×C₃₁	—	2	2	no	—
561	C₂×C₄×C₃₁	—	2	2	no	—
562	C₂×C₄×C₃₁	—	2	2	no	—
563	C₂×C₄×C₃₁	—	2	2	no	—
564	C₂×C₄×C₃₁	—	2	1	no	—
565	C₂×C₄×C₃₁	—	2	1	no	—
566	C₂×C₄×C₃₁	—	2	1	no	—
567	C₂×C₄×C₃₁	—	2	1	no	—
568	C₂×C₄×C₃₁	—	2	2	no	—
569	C₂×C₄×C₃₁	—	2	2	no	—
570	C₂×C₄×C₃₁	—	2	1	no	—
571	C₂×C₄×C₃₁	—	2	2	no	—
572	C₂×C₄×C₃₁	—	2	2	no	—
573	C₂×C₄×C₃₁	—	2	2	no	—
574	C₂×C₄×C₃₁	—	2	1	no	—
575	C₂×C₄×C₃₁	—	2	1	no	—
576	C₂×C₄×C₃₁	—	2	1	no	—
577	C₂×C₄×C₃₁	—	2	2	no	—
578	C₂×C₄×C₃₁	—	2	1	no	—
579	C₂×C₄×C₃₁	—	4	2	no	—
580	C₂×C₄×C₃₁	—	4	2	no	—
581	C₂×C₄×C₃₁	—	4	2	no	—
582	C₂×C₄×C₃₁	—	4	2	no	—
583	C₂×C₄×C₃₁	—	4	2	no	—
584	C₂×C₄×C₃₁	—	4	4	no	—
585	C₂×C₄×C₃₁	—	4	2	no	—
586	C₂×C₄×C₃₁	—	4	4	no	—
587	C₂×C₄×C₃₁	—	4	2	no	—
588	C₂×C₄×C₃₁	—	4	2	no	—
589	C₂×C₄×C₃₁	—	4	2	no	—
590	C₂×C₄×C₃₁	—	4	2	no	—
591	C₂×C₄×C₃₁	—	8	1	no	—
592	C₂×C₄×C₃₁	—	8	2	no	—
593	C₂×C₄×C₃₁	—	8	1	no	—
594	C₂×C₄×C₃₁	—	8	1	no	—
595	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
597	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
598	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
599	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
600	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
601	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
602	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
603	C₈×C₃₁	—	2	1	no	—
604	C₈×C₃₁	—	2	1	no	—
605	C₈×C₃₁	—	2	1	no	—
606	C₈×C₃₁	—	2	1	no	—
607	C₈×C₃₁	—	2	2	no	—
608	C₈×C₃₁	—	2	2	no	—
609	#3489	C₂×C₃₁	1	1	yes	characteristic, complemented
610	#3449	C₂×C₃₁	1	1	yes	characteristic, complemented
611	#3202	C₂×C₃₁	1	2	yes	complemented
612	#3201	C₂×C₃₁	1	2	yes	complemented
613	#3200	C₂×C₃₁	1	2	yes	complemented
614	#3198	C₂×C₃₁	1	2	yes	complemented
615	#3197	C₂×C₃₁	1	2	yes	complemented
616	#3196	C₂×C₃₁	1	2	yes	complemented
617	#3191	C₂×C₃₁	1	2	yes	complemented
618	#3190	C₂×C₃₁	1	2	yes	complemented
619	#3099	C₂×C₃₁	1	1	yes	characteristic, complemented
620	#3098	C₂×C₃₁	1	1	yes	characteristic, complemented
621	#3093	C₂×C₃₁	1	1	yes	characteristic, complemented
622	C₂×#485	C₂×C₃₁	1	1	yes	characteristic, complemented
623	#3063	C₂×C₃₁	1	1	yes	characteristic, complemented
624	#3063	C₂×C₃₁	1	1	yes	characteristic, complemented
625	#3061	C₂×C₃₁	1	1	yes	characteristic, complemented
626	#3060	C₂×C₃₁	1	1	yes	characteristic, complemented
627	#3013	C₂×C₃₁	1	1	yes	characteristic, complemented
628	#3013	C₂×C₃₁	1	1	yes	characteristic, complemented
629	#3007	C₂×C₃₁	1	1	yes	characteristic, complemented
630	#3002	C₂×C₃₁	1	1	yes	characteristic, complemented
631	#2880	C₂×C₃₁	1	1	yes	characteristic, complemented
632	C₂²×C₃₁	—	2	1	no	—
633	C₂²×C₃₁	—	2	1	no	—
634	C₂²×C₃₁	—	2	2	no	—
635	C₂²×C₃₁	—	2	2	no	—
636	C₂²×C₃₁	—	2	1	no	—
637	C₂²×C₃₁	—	2	1	no	—
638	C₂²×C₃₁	—	2	1	no	—
639	C₂²×C₃₁	—	2	2	no	—
640	C₂²×C₃₁	—	2	2	no	—
641	C₂²×C₃₁	—	2	1	no	—
642	C₂²×C₃₁	—	2	1	no	—
643	C₂²×C₃₁	—	2	1	no	—
644	C₂²×C₃₁	—	2	2	no	—
645	C₂²×C₃₁	—	2	2	no	—
646	C₂²×C₃₁	—	4	1	no	—
647	C₂²×C₃₁	—	4	1	no	—
648	C₂²×C₃₁	—	4	1	no	—
649	C₂²×C₃₁	—	4	1	no	—
650	C₂²×C₃₁	—	4	1	no	—
651	C₂²×C₃₁	—	4	1	no	—
652	C₂²×C₃₁	—	4	1	no	—
653	C₂²×C₃₁	—	4	1	no	—
654	C₂²×C₃₁	—	4	1	no	—
655	C₂²×C₃₁	—	8	2	no	—
656	C₂²×C₃₁	—	8	4	no	—
657	C₂²×C₃₁	—	8	4	no	—
658	C₂²×C₃₁	#534	1	2	yes	—
659	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
660	C₄×C₃₁	—	2	1	no	—
661	C₄×C₃₁	—	2	1	no	—
662	C₄×C₃₁	—	2	2	no	—
663	C₄×C₃₁	—	2	2	no	—
664	C₄×C₃₁	—	4	2	no	—
665	C₄×C₃₁	—	4	1	no	—
666	C₄×C₃₁	—	4	2	no	—
667	C₄×C₃₁	—	4	2	no	—
668	C₄×C₃₁	—	4	1	no	—
669	C₄×C₃₁	—	4	1	no	—
670	C₄×C₃₁	—	4	1	no	—
671	C₄×C₃₁	—	4	2	no	—
672	C₄×C₃₁	—	4	1	no	—
673	C₄×C₃₁	#534	1	2	yes	—
674	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
675	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
678	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
679	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic, complemented
685	D₄×Q₈	—	2	1	no	—
686	#548	—	2	1	no	—
687	#547	—	2	2	no	—
688	#547	—	2	1	no	—
689	#546	—	2	2	no	—
690	#546	—	2	1	no	—
691	#537	C₂²×C₃₁	1	1	yes	characteristic
692	#537	C₂²×C₃₁	1	1	yes	characteristic
693	#537	C₂²×C₃₁	1	1	yes	characteristic
694	#537	C₂²×C₃₁	1	1	yes	characteristic
695	#537	C₂²×C₃₁	1	2	yes	—
696	#537	C₂²×C₃₁	1	1	yes	characteristic, complemented
697	#536	—	2	1	no	—
698	#536	C₂²×C₃₁	1	2	yes	—
699	#536	C₂²×C₃₁	1	2	yes	—
700	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	#535	—	2	1	no	—
702	#535	C₂²×C₃₁	1	2	yes	—
703	#534	—	2	2	no	—
704	#532	—	2	2	no	—
705	#525	—	2	1	no	—
706	#525	—	2	1	no	—
707	#525	C₂²×C₃₁	1	1	yes	characteristic
708	#525	C₂²×C₃₁	1	2	yes	—
709	#525	C₂²×C₃₁	1	2	yes	—
710	#525	C₂²×C₃₁	1	2	yes	complemented
711	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
712	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
713	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
715	#485	C₂²×C₃₁	1	2	yes	complemented
716	#485	C₂²×C₃₁	1	2	yes	complemented
717	#485	C₂²×C₃₁	1	2	yes	complemented
718	#485	C₂²×C₃₁	1	2	yes	complemented
719	#485	C₂²×C₃₁	1	2	yes	complemented
720	#485	C₂²×C₃₁	1	2	yes	complemented
721	#485	C₂²×C₃₁	1	2	yes	complemented
722	#485	C₂²×C₃₁	1	2	yes	complemented
723	#484	C₂²×C₃₁	1	2	yes	complemented
724	#483	C₂²×C₃₁	1	2	yes	complemented
725	#482	C₂²×C₃₁	1	2	yes	complemented
726	#482	C₂²×C₃₁	1	2	yes	complemented
727	#482	C₂²×C₃₁	1	2	yes	complemented
728	#482	C₂²×C₃₁	1	2	yes	complemented
729	#481	C₂²×C₃₁	1	2	yes	complemented
730	#480	C₂²×C₃₁	1	2	yes	complemented
731	#470	C₂²×C₃₁	1	2	yes	complemented
732	#470	C₂²×C₃₁	1	2	yes	complemented
733	#470	C₂²×C₃₁	1	2	yes	complemented
734	#469	C₂²×C₃₁	1	2	yes	complemented
735	#468	C₂²×C₃₁	1	2	yes	complemented
736	#468	C₂²×C₃₁	1	2	yes	complemented
737	#468	C₂²×C₃₁	1	2	yes	complemented
738	#468	C₂²×C₃₁	1	2	yes	complemented
739	#467	C₂²×C₃₁	1	2	yes	complemented
740	#467	C₂²×C₃₁	1	2	yes	complemented
741	#467	C₂²×C₃₁	1	2	yes	complemented
742	#466	C₂²×C₃₁	1	2	yes	complemented
743	#465	C₂²×C₃₁	1	2	yes	complemented
744	#465	C₂²×C₃₁	1	2	yes	complemented
745	#465	C₂²×C₃₁	1	2	yes	complemented
746	#465	C₂²×C₃₁	1	2	yes	complemented
747	#452	C₂²×C₃₁	1	1	yes	characteristic
748	#452	C₂²×C₃₁	1	2	yes	—
749	#452	C₂²×C₃₁	1	2	yes	—
750	#452	C₂²×C₃₁	1	1	yes	characteristic
751	#452	C₂²×C₃₁	1	2	yes	complemented
752	#452	C₂²×C₃₁	1	2	yes	complemented
753	#451	C₂²×C₃₁	1	2	yes	complemented
754	#451	C₂²×C₃₁	1	2	yes	complemented
755	#451	C₂²×C₃₁	1	2	yes	complemented
756	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
757	#450	C₂²×C₃₁	1	2	yes	complemented
758	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
759	#449	C₂²×C₃₁	1	1	yes	characteristic
760	#449	C₂²×C₃₁	1	1	yes	characteristic
761	#449	C₂²×C₃₁	1	2	yes	complemented
762	#449	C₂²×C₃₁	1	2	yes	complemented
763	#448	C₂²×C₃₁	1	2	yes	complemented
764	#448	C₂²×C₃₁	1	2	yes	complemented
765	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
766	#447	C₂²×C₃₁	1	1	yes	characteristic, complemented
767	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
768	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
769	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
770	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
771	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
772	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
773	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
774	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
775	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
776	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
777	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
778	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
779	#408	C₂²×C₃₁	1	2	yes	—
780	#408	C₂²×C₃₁	1	2	yes	—
781	#408	C₂²×C₃₁	1	1	yes	characteristic, complemented
782	#408	C₂²×C₃₁	1	1	yes	characteristic, complemented
783	#407	C₂²×C₃₁	1	1	yes	characteristic
784	#407	C₂²×C₃₁	1	2	yes	complemented
785	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
786	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
787	C₂×C₃₁	—	2	2	no	—
788	C₂×C₃₁	—	4	2	no	—
789	C₂×C₃₁	—	4	2	no	—
790	C₂×C₃₁	—	4	1	no	—
791	C₂×C₃₁	—	4	1	no	—
792	C₂×C₃₁	—	8	1	no	—
793	C₂×C₃₁	—	8	1	no	—
794	C₂×C₃₁	—	8	1	no	—
795	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
796	C₂×C₃₁	#3584	1	1	yes	characteristic
797	C₂×C₃₁	#3586	1	1	yes	characteristic
798	2₋¹⁺⁴	—	4	2	no	—
799	2₋¹⁺⁴	—	4	2	no	—
800	C₂×#41	—	2	1	no	—
801	C₂×#41	—	2	2	no	—
802	C₂×#41	—	2	1	no	—
803	C₂×#41	—	2	1	no	—
804	C₂×#41	—	4	2	no	—
805	C₂×#41	—	4	2	no	—
806	C₂×#41	—	4	2	no	—
807	C₂×#41	—	4	2	no	—
808	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
809	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
810	C₂×#41	D₄×C₃₁	1	2	yes	—
811	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
812	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
813	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
814	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
815	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
816	C₂×#41	C₂³×C₃₁	1	2	yes	—
817	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
818	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
819	C₂×#41	C₂³×C₃₁	1	2	yes	—
820	C₂²×Q₈	—	2	1	no	—
821	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
822	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
823	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
824	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
825	C₂²×D₄	—	2	1	no	—
826	C₂²×D₄	D₄×C₃₁	1	2	yes	—
827	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
828	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
829	C₂³×C₄	—	2	1	no	—
830	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
831	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
832	#137	—	4	2	no	—
833	#137	—	4	2	no	—
834	#135	—	4	2	no	—
835	#135	—	4	2	no	—
836	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
837	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
838	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
839	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
840	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
841	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
842	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
843	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
844	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
845	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
846	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
847	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
848	#131	—	4	2	no	—
849	#131	—	4	2	no	—
850	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
851	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
852	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
853	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
854	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
855	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
856	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
857	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
858	C₄⋊Q₈	—	2	2	no	—
859	C₄⋊Q₈	—	2	2	no	—
860	C₄⋊Q₈	—	2	1	no	—
861	#127	—	2	2	no	—
862	#124	—	2	2	no	—
863	#124	—	2	2	no	—
864	#124	—	2	2	no	—
865	#124	—	2	1	no	—
866	#123	—	2	2	no	—
867	#123	—	2	2	no	—
868	#123	—	2	2	no	—
869	#123	—	2	2	no	—
870	#123	—	2	2	no	—
871	#123	—	2	2	no	—
872	#123	—	2	2	no	—
873	#123	—	2	1	no	—
874	#123	—	2	2	no	—
875	C₂²⋊Q₈	—	2	1	no	—
876	C₂²⋊Q₈	—	2	1	no	—
877	C₂²⋊Q₈	—	2	1	no	—
878	C₂²⋊Q₈	—	2	1	no	—
879	C₂²⋊Q₈	—	2	2	no	—
880	C₂²⋊Q₈	—	2	1	no	—
881	C₂²⋊Q₈	—	2	1	no	—
882	C₂²⋊Q₈	—	2	1	no	—
883	C₂²⋊Q₈	—	2	2	no	—
884	C₂²⋊Q₈	—	2	2	no	—
885	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
886	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
887	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
888	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
889	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
890	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
891	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
892	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
893	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
894	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
895	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
896	#121	—	2	1	no	—
897	#121	—	2	1	no	—
898	#121	—	2	1	no	—
899	#121	—	2	1	no	—
900	#121	—	2	2	no	—
901	#121	—	2	2	no	—
902	#121	—	2	2	no	—
903	#121	—	2	2	no	—
904	#121	—	2	2	no	—
905	#121	—	2	2	no	—
906	#121	—	2	2	no	—
907	#121	—	2	2	no	—
908	#121	—	2	1	no	—
909	#121	C₂³×C₃₁	1	1	yes	characteristic
910	#121	C₂³×C₃₁	1	2	yes	—
911	#121	C₂³×C₃₁	1	2	yes	—
912	#121	C₂³×C₃₁	1	2	yes	—
913	#121	C₂³×C₃₁	1	2	yes	—
914	#121	C₂³×C₃₁	1	1	yes	characteristic
915	#121	C₂³×C₃₁	1	2	yes	—
916	#120	—	2	2	no	—
917	#120	—	2	2	no	—
918	#120	—	2	1	no	—
919	#120	—	2	2	no	—
920	#120	—	2	2	no	—
921	#120	—	2	2	no	—
922	C₄×Q₈	—	2	1	no	—
923	C₄×D₄	—	2	2	no	—
924	C₄×D₄	—	2	1	no	—
925	C₄×D₄	—	2	2	no	—
926	C₄×D₄	—	2	2	no	—
927	C₄×D₄	—	2	2	no	—
928	C₄×D₄	—	2	2	no	—
929	C₄×D₄	—	2	1	no	—
930	C₄×D₄	—	2	1	no	—
931	C₄×D₄	—	2	2	no	—
932	C₄×D₄	—	2	2	no	—
933	#117	—	2	1	no	—
934	#117	—	2	1	no	—
935	#117	C₂³×C₃₁	1	2	yes	—
936	#117	C₂³×C₃₁	1	2	yes	—
937	#117	C₂³×C₃₁	1	1	yes	characteristic
938	#117	C₂³×C₃₁	1	2	yes	—
939	C₂×C₄⋊C₄	—	2	1	no	—
940	C₂×C₄⋊C₄	—	2	2	no	—
941	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
945	C₂×C₂²⋊C₄	—	2	1	no	—
946	C₂×C₂²⋊C₄	—	2	1	no	—
947	C₂×C₂²⋊C₄	—	2	2	no	—
948	C₂×C₄²	—	2	1	no	—
949	#107	C₂³×C₃₁	1	2	yes	—
950	#107	C₂³×C₃₁	1	2	yes	—
951	#107	C₂³×C₃₁	1	2	yes	—
952	#107	C₂³×C₃₁	1	2	yes	—
953	#106	C₂³×C₃₁	1	2	yes	—
954	#106	C₂³×C₃₁	1	2	yes	—
955	#106	C₂³×C₃₁	1	2	yes	—
956	#106	C₂³×C₃₁	1	2	yes	—
957	#103	C₂³×C₃₁	1	2	yes	—
958	#103	C₂³×C₃₁	1	2	yes	—
959	#103	C₂³×C₃₁	1	2	yes	—
960	#103	C₂³×C₃₁	1	2	yes	—
961	#103	C₂³×C₃₁	1	1	yes	characteristic
962	#103	C₂³×C₃₁	1	1	yes	characteristic
963	#103	C₂³×C₃₁	1	1	yes	characteristic
964	#103	C₂³×C₃₁	1	1	yes	characteristic
965	#103	C₂³×C₃₁	1	2	yes	—
966	#103	C₂³×C₃₁	1	2	yes	—
967	#103	C₂³×C₃₁	1	2	yes	—
968	#103	C₂³×C₃₁	1	2	yes	—
969	#102	C₂³×C₃₁	1	1	yes	characteristic
970	#102	C₂³×C₃₁	1	1	yes	characteristic
971	#102	C₂³×C₃₁	1	1	yes	characteristic
972	#102	C₂³×C₃₁	1	1	yes	characteristic
973	#102	C₂³×C₃₁	1	2	yes	—
974	#102	C₂³×C₃₁	1	2	yes	—
975	#102	C₂³×C₃₁	1	2	yes	—
976	#102	C₂³×C₃₁	1	2	yes	—
977	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
978	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
979	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
980	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
981	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
982	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
983	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
984	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
985	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
986	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
987	C₃₁	#60766	1	1	yes	characteristic, direct product factor, Sylow
988	C₂⁴	—	2	1	no	—
989	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
990	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
991	#41	—	2	2	no	—
992	#41	—	2	2	no	—
993	#41	—	2	2	no	—
994	#41	—	2	2	no	—
995	#41	—	2	2	no	—
996	#41	—	2	2	no	—
997	#41	—	2	2	no	—
998	#41	—	2	2	no	—
999	#41	—	2	2	no	—
1000	#41	—	2	2	no	—
1001	#41	—	4	2	no	—
1002	#41	—	4	2	no	—
1003	#41	—	4	4	no	—
1004	#41	—	4	2	no	—
1005	#41	—	4	2	no	—
1006	#41	—	4	1	no	—
1007	#41	—	4	1	no	—
1008	#41	—	4	1	no	—
1009	#41	—	4	1	no	—
1010	#41	—	4	2	no	—
1011	#41	—	4	2	no	—
1012	#41	—	4	4	no	—
1013	#41	—	4	4	no	—
1014	#41	—	4	8	no	—
1015	#41	—	4	4	no	—
1016	C₂×Q₈	—	2	2	no	—
1017	C₂×Q₈	—	2	1	no	—
1018	C₂×Q₈	—	2	1	no	—
1019	C₂×Q₈	—	2	2	no	—
1020	C₂×Q₈	—	2	2	no	—
1021	C₂×Q₈	—	4	2	no	—
1022	C₂×Q₈	—	4	1	no	—
1023	C₂×Q₈	—	4	1	no	—
1024	C₂×Q₈	—	4	2	no	—
1025	C₂×Q₈	—	4	2	no	—
1026	C₂×Q₈	—	4	4	no	—
1027	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1028	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1029	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
1030	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1031	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1032	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1033	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1034	C₂×D₄	—	2	1	no	—
1035	C₂×D₄	—	2	1	no	—
1036	C₂×D₄	—	2	1	no	—
1037	C₂×D₄	—	2	2	no	—
1038	C₂×D₄	—	2	1	no	—
1039	C₂×D₄	—	2	1	no	—
1040	C₂×D₄	—	2	1	no	—
1041	C₂×D₄	—	2	2	no	—
1042	C₂×D₄	—	2	2	no	—
1043	C₂×D₄	—	2	2	no	—
1044	C₂×D₄	—	2	2	no	—
1045	C₂×D₄	—	2	1	no	—
1046	C₂×D₄	—	2	2	no	—
1047	C₂×D₄	—	2	1	no	—
1048	C₂×D₄	—	4	2	no	—
1049	C₂×D₄	—	4	1	no	—
1050	C₂×D₄	—	4	1	no	—
1051	C₂×D₄	—	4	4	no	—
1052	C₂×D₄	—	4	4	no	—
1053	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1054	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1055	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1056	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1057	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1058	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1059	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1060	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1061	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1062	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1063	C₂²×C₄	—	2	2	no	—
1064	C₂²×C₄	—	2	2	no	—
1065	C₂²×C₄	—	2	2	no	—
1066	C₂²×C₄	—	2	1	no	—
1067	C₂²×C₄	—	2	1	no	—
1068	C₂²×C₄	—	2	1	no	—
1069	C₂²×C₄	—	2	1	no	—
1070	C₂²×C₄	—	2	2	no	—
1071	C₂²×C₄	—	2	1	no	—
1072	C₂²×C₄	—	2	1	no	—
1073	C₂²×C₄	—	2	1	no	—
1074	C₂²×C₄	—	2	2	no	—
1075	C₂²×C₄	—	2	1	no	—
1076	C₂²×C₄	—	2	1	no	—
1077	C₂²×C₄	—	2	1	no	—
1078	C₂²×C₄	—	4	2	no	—
1079	C₂²×C₄	—	4	2	no	—
1080	C₂²×C₄	—	4	4	no	—
1081	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1082	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1083	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1084	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1085	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1086	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1087	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1088	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1089	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1090	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1091	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1092	Q₁₆	—	4	1	no	—
1093	Q₁₆	—	4	1	no	—
1094	Q₁₆	—	4	2	no	—
1095	Q₁₆	—	4	2	no	—
1096	SD₁₆	—	4	1	no	—
1097	SD₁₆	—	4	1	no	—
1098	SD₁₆	—	4	1	no	—
1099	SD₁₆	—	4	1	no	—
1100	SD₁₆	—	4	2	no	—
1101	SD₁₆	—	4	2	no	—
1102	D₈	—	4	1	no	—
1103	D₈	—	4	1	no	—
1104	M₁₆	—	2	2	no	—
1105	M₁₆	—	2	2	no	—
1106	M₁₆	—	4	2	no	—
1107	M₁₆	—	4	2	no	—
1108	C₂×C₈	—	2	2	no	—
1109	C₂×C₈	—	2	2	no	—
1110	C₂×C₈	—	4	2	no	—
1111	C₂×C₈	—	4	2	no	—
1112	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1113	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1114	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1115	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1116	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1117	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1118	C₄⋊C₄	—	2	2	no	—
1119	C₄⋊C₄	—	2	1	no	—
1120	C₄⋊C₄	—	2	2	no	—
1121	C₄⋊C₄	—	2	2	no	—
1122	C₄⋊C₄	—	2	2	no	—
1123	C₄⋊C₄	—	2	1	no	—
1124	C₄⋊C₄	—	2	1	no	—
1125	C₄⋊C₄	—	2	2	no	—
1126	C₄⋊C₄	—	2	1	no	—
1127	C₄⋊C₄	—	2	2	no	—
1128	C₄⋊C₄	—	2	2	no	—
1129	C₄⋊C₄	—	2	2	no	—
1130	C₄⋊C₄	—	2	2	no	—
1131	C₄⋊C₄	—	2	1	no	—
1132	C₄⋊C₄	—	2	2	no	—
1133	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1134	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1135	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1136	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1137	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1138	C₂²⋊C₄	—	2	2	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	2	no	—
1141	C₂²⋊C₄	—	2	2	no	—
1142	C₂²⋊C₄	—	2	2	no	—
1143	C₂²⋊C₄	—	2	2	no	—
1144	C₂²⋊C₄	—	2	2	no	—
1145	C₂²⋊C₄	—	2	2	no	—
1146	C₂²⋊C₄	—	2	1	no	—
1147	C₂²⋊C₄	—	2	2	no	—
1148	C₂²⋊C₄	—	2	2	no	—
1149	C₂²⋊C₄	—	2	2	no	—
1150	C₂²⋊C₄	—	2	2	no	—
1151	C₂²⋊C₄	—	2	1	no	—
1152	C₂²⋊C₄	—	2	2	no	—
1153	C₂²⋊C₄	—	2	1	no	—
1154	C₂²⋊C₄	—	2	2	no	—
1155	C₂²⋊C₄	—	2	2	no	—
1156	C₂²⋊C₄	—	2	2	no	—
1157	C₂²⋊C₄	—	2	2	no	—
1158	C₂²⋊C₄	—	2	1	no	—
1159	C₂²⋊C₄	—	2	2	no	—
1160	C₄²	—	2	2	no	—
1161	C₄²	—	2	2	no	—
1162	C₄²	—	2	2	no	—
1163	C₄²	—	2	1	no	—
1164	C₂³	—	2	2	no	—
1165	C₂³	—	2	1	no	—
1166	C₂³	—	2	1	no	—
1167	C₂³	—	2	1	no	—
1168	C₂³	—	4	2	no	—
1169	C₂³	—	4	1	no	—
1170	C₂³	—	4	1	no	—
1171	C₂³	—	4	2	no	—
1172	C₂³	—	4	2	no	—
1173	C₂³	—	4	2	no	—
1174	C₂³	—	8	1	no	—
1175	C₂³	—	8	1	no	—
1176	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1177	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1178	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1179	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1180	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1181	Q₈	—	2	2	no	—
1182	Q₈	—	2	2	no	—
1183	Q₈	—	2	2	no	—
1184	Q₈	—	2	2	no	—
1185	Q₈	—	2	1	no	—
1186	Q₈	—	2	1	no	—
1187	Q₈	—	2	1	no	—
1188	Q₈	—	2	1	no	—
1189	Q₈	—	2	1	no	—
1190	Q₈	—	2	1	no	—
1191	Q₈	—	4	2	no	—
1192	Q₈	—	4	4	no	—
1193	Q₈	—	4	2	no	—
1194	Q₈	—	4	2	no	—
1195	D₄	—	2	4	no	—
1196	D₄	—	2	4	no	—
1197	D₄	—	2	2	no	—
1198	D₄	—	2	2	no	—
1199	D₄	—	2	1	no	—
1200	D₄	—	2	1	no	—
1201	D₄	—	2	1	no	—
1202	D₄	—	2	1	no	—
1203	D₄	—	2	1	no	—
1204	D₄	—	2	1	no	—
1205	D₄	—	4	2	no	—
1206	D₄	—	4	2	no	—
1207	D₄	—	4	2	no	—
1208	D₄	—	4	2	no	—
1209	D₄	—	4	2	no	—
1210	D₄	—	4	2	no	—
1211	D₄	—	4	2	no	—
1212	D₄	—	4	4	no	—
1213	D₄	—	4	2	no	—
1214	D₄	—	4	2	no	—
1215	D₄	—	4	2	no	—
1216	D₄	—	8	2	no	—
1217	D₄	—	8	1	no	—
1218	D₄	—	8	2	no	—
1219	D₄	—	8	2	no	—
1220	D₄	—	8	2	no	—
1221	D₄	—	8	2	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	2	no	—
1224	C₂×C₄	—	2	2	no	—
1225	C₂×C₄	—	2	2	no	—
1226	C₂×C₄	—	2	2	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	1	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	2	no	—
1232	C₂×C₄	—	2	2	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	2	no	—
1235	C₂×C₄	—	2	2	no	—
1236	C₂×C₄	—	2	2	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	2	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	4	2	no	—
1243	C₂×C₄	—	4	2	no	—
1244	C₂×C₄	—	4	2	no	—
1245	C₂×C₄	—	4	2	no	—
1246	C₂×C₄	—	4	2	no	—
1247	C₂×C₄	—	4	4	no	—
1248	C₂×C₄	—	4	2	no	—
1249	C₂×C₄	—	4	4	no	—
1250	C₂×C₄	—	4	2	no	—
1251	C₂×C₄	—	4	2	no	—
1252	C₂×C₄	—	4	2	no	—
1253	C₂×C₄	—	4	2	no	—
1254	C₂×C₄	—	8	1	no	—
1255	C₂×C₄	—	8	2	no	—
1256	C₂×C₄	—	8	1	no	—
1257	C₂×C₄	—	8	1	no	—
1258	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1259	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1260	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1261	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1262	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1263	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1264	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1265	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1266	C₈	—	2	1	no	—
1267	C₈	—	2	1	no	—
1268	C₈	—	2	1	no	—
1269	C₈	—	2	1	no	—
1270	C₈	—	2	2	no	—
1271	C₈	—	2	2	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	1	no	—
1275	C₂²	—	2	1	no	—
1276	C₂²	—	2	2	no	—
1277	C₂²	—	2	2	no	—
1278	C₂²	—	2	2	no	—
1279	C₂²	—	2	2	no	—
1280	C₂²	—	2	1	no	—
1281	C₂²	—	2	1	no	—
1282	C₂²	—	2	1	no	—
1283	C₂²	—	2	2	no	—
1284	C₂²	—	2	2	no	—
1285	C₂²	—	2	1	no	—
1286	C₂²	—	4	1	no	—
1287	C₂²	—	4	1	no	—
1288	C₂²	—	4	1	no	—
1289	C₂²	—	4	1	no	—
1290	C₂²	—	4	1	no	—
1291	C₂²	—	4	1	no	—
1292	C₂²	—	4	1	no	—
1293	C₂²	—	4	1	no	—
1294	C₂²	—	4	1	no	—
1295	C₂²	—	8	2	no	—
1296	C₂²	—	8	4	no	—
1297	C₂²	—	8	4	no	—
1298	C₂²	C₃₁×#534	1	2	yes	—
1299	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1300	C₄	—	2	1	no	—
1301	C₄	—	2	1	no	—
1302	C₄	—	2	2	no	—
1303	C₄	—	2	2	no	—
1304	C₄	—	4	1	no	—
1305	C₄	—	4	1	no	—
1306	C₄	—	4	2	no	—
1307	C₄	—	4	1	no	—
1308	C₄	—	4	2	no	—
1309	C₄	—	4	1	no	—
1310	C₄	—	4	2	no	—
1311	C₄	—	4	2	no	—
1312	C₄	—	4	1	no	—
1313	C₄	C₃₁×#534	1	2	yes	—
1314	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1315	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1316	C₂	—	2	2	no	—
1317	C₂	—	4	1	no	—
1318	C₂	—	4	1	no	—
1319	C₂	—	4	2	no	—
1320	C₂	—	4	2	no	—
1321	C₂	—	8	1	no	—
1322	C₂	—	8	1	no	—
1323	C₂	—	8	1	no	—
1324	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
1325	C₂	C₃₁×#3584	1	1	yes	characteristic
1326	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3489	C₂	semidirect
2. C₃₁×#3449	C₂	semidirect
3. C₃₁×#3202	C₂	semidirect
4. C₃₁×#3201	C₂	semidirect
5. C₃₁×#3200	C₂	semidirect
6. C₃₁×#3198	C₂	semidirect
7. C₃₁×#3197	C₂	semidirect
8. C₃₁×#3196	C₂	semidirect
9. C₃₁×#3191	C₂	semidirect
10. C₃₁×#3190	C₂	semidirect
11. C₃₁×#3099	C₂	semidirect
12. C₃₁×#3098	C₂	semidirect
13. C₃₁×#3093	C₂	semidirect
14. C₂×C₃₁×#485	C₂	semidirect
15. C₃₁×#3063	C₂	semidirect
16. C₃₁×#3063	C₂	semidirect
17. C₃₁×#3061	C₂	semidirect
18. C₃₁×#3060	C₂	semidirect
19. C₃₁×#3013	C₂	semidirect
20. C₃₁×#3013	C₂	semidirect
21. C₃₁×#3007	C₂	semidirect
22. C₃₁×#3002	C₂	semidirect
23. C₃₁×#2880	C₂	semidirect
24. C₂×C₃₁×2₋¹⁺⁴	C₂²	semidirect
27. C₂×C₃₁×#137	C₂²	semidirect
28. C₂×C₃₁×#137	C₂²	semidirect
29. C₂×C₃₁×#135	C₂²	semidirect
30. C₂×C₃₁×#135	C₂²	semidirect
31. C₂×C₃₁×#131	C₂²	semidirect
32. C₂×C₃₁×#131	C₂²	semidirect
44. C₃₁×#537	C₂²	semidirect
48. C₃₁×#536	C₂²	semidirect
58. C₃₁×#525	C₂²	semidirect
60. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
61. C₃₁×#520	C₂²	semidirect
63. C₃₁×#485	C₂²	semidirect
64. C₃₁×#485	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
66. C₃₁×#485	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
69. C₃₁×#485	C₂²	semidirect
70. C₃₁×#485	C₂²	semidirect
71. C₃₁×#484	C₂²	semidirect
72. C₃₁×#483	C₂²	semidirect
73. C₃₁×#482	C₂²	semidirect
74. C₃₁×#482	C₂²	semidirect
75. C₃₁×#482	C₂²	semidirect
76. C₃₁×#482	C₂²	semidirect
77. C₃₁×#481	C₂²	semidirect
78. C₃₁×#480	C₂²	semidirect
79. C₃₁×#470	C₂²	semidirect
80. C₃₁×#470	C₂²	semidirect
81. C₃₁×#470	C₂²	semidirect
82. C₃₁×#469	C₂²	semidirect
83. C₃₁×#468	C₂²	semidirect
84. C₃₁×#468	C₂²	semidirect
85. C₃₁×#468	C₂²	semidirect
86. C₃₁×#468	C₂²	semidirect
87. C₃₁×#467	C₂²	semidirect
88. C₃₁×#467	C₂²	semidirect
89. C₃₁×#467	C₂²	semidirect
90. C₃₁×#466	C₂²	semidirect
91. C₃₁×#465	C₂²	semidirect
92. C₃₁×#465	C₂²	semidirect
93. C₃₁×#465	C₂²	semidirect
94. C₃₁×#465	C₂²	semidirect
99. C₃₁×#452	C₂²	semidirect
100. C₃₁×#452	C₂²	semidirect
101. C₃₁×#451	C₂²	semidirect
102. C₃₁×#451	C₂²	semidirect
103. C₃₁×#451	C₂²	semidirect
104. C₃₁×#451	C₂²	semidirect
105. C₃₁×#450	C₂²	semidirect
106. C₃₁×#450	C₂²	semidirect
109. C₃₁×#449	C₂²	semidirect
110. C₃₁×#449	C₂²	semidirect
111. C₃₁×#448	C₂²	semidirect
112. C₃₁×#448	C₂²	semidirect
113. C₃₁×#448	C₂²	semidirect
114. C₃₁×#447	C₂²	semidirect
115. C₃₁×#428	C₂²	semidirect
116. C₃₁×#428	C₂²	semidirect
117. C₂×C₃₁×#107	C₂²	semidirect
118. C₂×C₃₁×#106	C₂²	semidirect
119. C₃₁×#417	C₂²	semidirect
120. C₃₁×#417	C₂²	semidirect
121. C₃₁×#417	C₂²	semidirect
122. C₃₁×#417	C₂²	semidirect
123. C₃₁×#416	C₂²	semidirect
124. C₃₁×#416	C₂²	semidirect
125. C₂×C₃₁×#103	C₂²	semidirect
126. C₂×C₃₁×#103	C₂²	semidirect
129. C₃₁×#408	C₂²	semidirect
130. C₃₁×#408	C₂²	semidirect
132. C₃₁×#407	C₂²	semidirect
134. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
500. #60766	C₃₁	direct (N × H)
609. #3489	C₂×C₃₁	semidirect
610. #3449	C₂×C₃₁	semidirect
611. #3202	C₂×C₃₁	semidirect
612. #3201	C₂×C₃₁	semidirect
613. #3200	C₂×C₃₁	semidirect
614. #3198	C₂×C₃₁	semidirect
615. #3197	C₂×C₃₁	semidirect
616. #3196	C₂×C₃₁	semidirect
617. #3191	C₂×C₃₁	semidirect
618. #3190	C₂×C₃₁	semidirect
619. #3099	C₂×C₃₁	semidirect
620. #3098	C₂×C₃₁	semidirect
621. #3093	C₂×C₃₁	semidirect
622. C₂×#485	C₂×C₃₁	semidirect
623. #3063	C₂×C₃₁	semidirect
624. #3063	C₂×C₃₁	semidirect
625. #3061	C₂×C₃₁	semidirect
626. #3060	C₂×C₃₁	semidirect
627. #3013	C₂×C₃₁	semidirect
628. #3013	C₂×C₃₁	semidirect
629. #3007	C₂×C₃₁	semidirect
630. #3002	C₂×C₃₁	semidirect
631. #2880	C₂×C₃₁	semidirect
676. C₂×2₋¹⁺⁴	C₂²×C₃₁	semidirect
679. C₂×#137	C₂²×C₃₁	semidirect
680. C₂×#137	C₂²×C₃₁	semidirect
681. C₂×#135	C₂²×C₃₁	semidirect
682. C₂×#135	C₂²×C₃₁	semidirect
683. C₂×#131	C₂²×C₃₁	semidirect
684. C₂×#131	C₂²×C₃₁	semidirect
696. #537	C₂²×C₃₁	semidirect
700. #536	C₂²×C₃₁	semidirect
710. #525	C₂²×C₃₁	semidirect
712. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
713. #520	C₂²×C₃₁	semidirect
715. #485	C₂²×C₃₁	semidirect
716. #485	C₂²×C₃₁	semidirect
717. #485	C₂²×C₃₁	semidirect
718. #485	C₂²×C₃₁	semidirect
719. #485	C₂²×C₃₁	semidirect
720. #485	C₂²×C₃₁	semidirect
721. #485	C₂²×C₃₁	semidirect
722. #485	C₂²×C₃₁	semidirect
723. #484	C₂²×C₃₁	semidirect
724. #483	C₂²×C₃₁	semidirect
725. #482	C₂²×C₃₁	semidirect
726. #482	C₂²×C₃₁	semidirect
727. #482	C₂²×C₃₁	semidirect
728. #482	C₂²×C₃₁	semidirect
729. #481	C₂²×C₃₁	semidirect
730. #480	C₂²×C₃₁	semidirect
731. #470	C₂²×C₃₁	semidirect
732. #470	C₂²×C₃₁	semidirect
733. #470	C₂²×C₃₁	semidirect
734. #469	C₂²×C₃₁	semidirect
735. #468	C₂²×C₃₁	semidirect
736. #468	C₂²×C₃₁	semidirect
737. #468	C₂²×C₃₁	semidirect
738. #468	C₂²×C₃₁	semidirect
739. #467	C₂²×C₃₁	semidirect
740. #467	C₂²×C₃₁	semidirect
741. #467	C₂²×C₃₁	semidirect
742. #466	C₂²×C₃₁	semidirect
743. #465	C₂²×C₃₁	semidirect
744. #465	C₂²×C₃₁	semidirect
745. #465	C₂²×C₃₁	semidirect
746. #465	C₂²×C₃₁	semidirect
751. #452	C₂²×C₃₁	semidirect
752. #452	C₂²×C₃₁	semidirect
753. #451	C₂²×C₃₁	semidirect
754. #451	C₂²×C₃₁	semidirect
755. #451	C₂²×C₃₁	semidirect
756. #451	C₂²×C₃₁	semidirect
757. #450	C₂²×C₃₁	semidirect
758. #450	C₂²×C₃₁	semidirect
761. #449	C₂²×C₃₁	semidirect
762. #449	C₂²×C₃₁	semidirect
763. #448	C₂²×C₃₁	semidirect
764. #448	C₂²×C₃₁	semidirect
765. #448	C₂²×C₃₁	semidirect
766. #447	C₂²×C₃₁	semidirect
767. #428	C₂²×C₃₁	semidirect
768. #428	C₂²×C₃₁	semidirect
769. C₂×#107	C₂²×C₃₁	semidirect
770. C₂×#106	C₂²×C₃₁	semidirect
771. #417	C₂²×C₃₁	semidirect
772. #417	C₂²×C₃₁	semidirect
773. #417	C₂²×C₃₁	semidirect
774. #417	C₂²×C₃₁	semidirect
775. #416	C₂²×C₃₁	semidirect
776. #416	C₂²×C₃₁	semidirect
777. C₂×#103	C₂²×C₃₁	semidirect
778. C₂×#103	C₂²×C₃₁	semidirect
781. #408	C₂²×C₃₁	semidirect
782. #408	C₂²×C₃₁	semidirect
784. #407	C₂²×C₃₁	semidirect
786. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
987. C₃₁	#60766	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3489	2
C₃₁×#3449	2
C₃₁×#3202	2
C₃₁×#3201	2
C₃₁×#3200	2
C₃₁×#3198	2
C₃₁×#3197	2
C₃₁×#3196	2
C₃₁×#3191	2
C₃₁×#3190	2
C₃₁×#3099	2
C₃₁×#3098	2
C₃₁×#3093	2
C₂×C₃₁×#485	2
C₃₁×#3063	2
C₃₁×#3061	2
C₃₁×#3060	2
C₃₁×#3013	2
C₃₁×#3007	2
C₃₁×#3002	2
C₃₁×#2880	2
#60766	31

Subgroups — C31×#60766 #21517525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60766 #21517525