Subgroups — C₃₁×#61767 #21518526

Order 7936.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3492	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3344	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3337	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3336	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3312	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3298	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3190	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3190	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3097	C₂	1	2	yes	maximal, complemented
17	C₂×C₃₁×#484	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#483	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2977	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	2	no	—
21	C₃₁×#554	—	2	1	no	—
22	C₃₁×#554	C₂²	1	2	yes	—
23	C₃₁×#553	—	2	1	no	—
24	C₃₁×#553	C₂²	1	2	yes	—
25	C₃₁×#552	—	2	1	no	—
26	C₃₁×#552	C₂²	1	2	yes	—
27	C₃₁×#552	C₂²	1	2	yes	—
28	C₃₁×#552	C₂²	1	2	yes	—
29	C₃₁×#551	—	2	2	no	—
30	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
31	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
32	C₃₁×#547	—	2	1	no	—
33	C₃₁×#547	C₂²	1	2	yes	—
34	C₃₁×#544	—	2	1	no	—
35	C₃₁×#544	—	2	1	no	—
36	C₃₁×#544	C₂²	1	1	yes	characteristic
37	C₃₁×#541	C₂²	1	2	yes	—
38	C₃₁×#539	—	2	2	no	—
39	C₃₁×#539	—	2	1	no	—
40	C₃₁×#539	—	2	1	no	—
41	C₃₁×#537	C₂²	1	1	yes	characteristic
42	C₃₁×#536	C₂²	1	2	yes	—
43	C₃₁×#525	—	2	2	no	—
44	C₃₁×#525	C₂²	1	1	yes	characteristic
45	C₃₁×#525	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₃₁×#520	C₂²	1	1	yes	characteristic
49	C₃₁×#520	C₂²	1	1	yes	characteristic
50	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	complemented
52	C₃₁×#499	C₂²	1	2	yes	complemented
53	C₃₁×#491	C₂²	1	2	yes	complemented
54	C₃₁×#487	C₂²	1	2	yes	complemented
55	C₃₁×#485	C₂²	1	2	yes	—
56	C₃₁×#485	C₂²	1	2	yes	—
57	C₃₁×#485	C₂²	1	2	yes	complemented
58	C₃₁×#485	C₂²	1	2	yes	complemented
59	C₃₁×#485	C₂²	1	2	yes	complemented
60	C₃₁×#484	C₂²	1	2	yes	—
61	C₃₁×#484	C₂²	1	2	yes	—
62	C₃₁×#484	C₂²	1	2	yes	—
63	C₃₁×#484	C₂²	1	2	yes	—
64	C₃₁×#484	C₂²	1	2	yes	complemented
65	C₃₁×#483	C₂²	1	1	yes	characteristic
66	C₃₁×#483	C₂²	1	2	yes	—
67	C₃₁×#483	C₂²	1	2	yes	—
68	C₃₁×#483	C₂²	1	2	yes	—
69	C₃₁×#483	C₂²	1	2	yes	—
70	C₃₁×#483	C₂²	1	1	yes	characteristic
71	C₃₁×#483	C₂²	1	2	yes	complemented
72	C₃₁×#482	C₂²	1	2	yes	complemented
73	C₃₁×#480	C₂²	1	1	yes	characteristic
74	C₃₁×#480	C₂²	1	1	yes	characteristic
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#479	C₂²	1	2	yes	complemented
77	C₃₁×#479	C₂²	1	2	yes	complemented
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#477	C₂²	1	2	yes	complemented
80	C₃₁×#475	C₂²	1	2	yes	complemented
81	C₃₁×#470	C₂²	1	2	yes	complemented
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#467	C₂²	1	2	yes	—
84	C₃₁×#467	C₂²	1	2	yes	—
85	C₃₁×#467	C₂²	1	2	yes	complemented
86	C₃₁×#465	C₂²	1	2	yes	—
87	C₃₁×#465	C₂²	1	2	yes	—
88	C₃₁×#465	C₂²	1	2	yes	complemented
89	C₃₁×#462	C₂²	1	2	yes	complemented
90	C₃₁×#461	C₂²	1	2	yes	complemented
91	C₃₁×#452	C₂²	1	2	yes	—
92	C₃₁×#452	C₂²	1	2	yes	—
93	C₃₁×#451	C₂²	1	1	yes	characteristic
94	C₃₁×#451	C₂²	1	1	yes	characteristic
95	C₃₁×#451	C₂²	1	2	yes	complemented
96	C₃₁×#448	C₂²	1	1	yes	characteristic
97	C₃₁×#448	C₂²	1	1	yes	characteristic
98	C₃₁×#448	C₂²	1	2	yes	complemented
99	C₃₁×#441	C₂²	1	2	yes	complemented
100	C₃₁×#440	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
103	C₃₁×#435	C₂²	1	2	yes	—
104	C₃₁×#435	C₂²	1	2	yes	—
105	C₈×D₄×C₃₁	C₂²	1	2	yes	—
106	C₈×D₄×C₃₁	C₂²	1	2	yes	—
107	C₃₁×#433	C₂²	1	2	yes	—
108	C₃₁×#428	C₂²	1	2	yes	complemented
109	C₃₁×#427	C₂²	1	2	yes	complemented
110	C₂×C₃₁×#107	C₂²	1	2	yes	—
111	C₂×C₃₁×#106	C₂²	1	2	yes	—
112	C₃₁×#419	C₂²	1	2	yes	complemented
113	C₂×C₃₁×#103	C₂²	1	2	yes	—
114	C₂×C₃₁×#103	C₂²	1	2	yes	—
115	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
116	C₃₁×#408	C₂²	1	2	yes	—
117	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	2	no	—
120	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
125	C₂³×C₄×C₃₁	—	2	1	no	—
126	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
133	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
134	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
135	C₃₁×C₄⋊Q₈	—	2	2	no	—
136	C₃₁×C₄⋊Q₈	—	2	2	no	—
137	C₃₁×C₄⋊Q₈	—	2	2	no	—
138	C₃₁×C₄⋊Q₈	—	2	1	no	—
139	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#125	—	2	2	no	—
148	C₃₁×#125	—	2	2	no	—
149	C₃₁×#125	—	2	2	no	—
150	C₃₁×#125	—	2	2	no	—
151	C₃₁×#125	—	2	2	no	—
152	C₃₁×#125	—	2	2	no	—
153	C₃₁×#125	—	2	1	no	—
154	C₃₁×#125	C₂³	1	2	yes	—
155	C₃₁×#125	C₂³	1	2	yes	—
156	C₃₁×#124	—	2	2	no	—
157	C₃₁×#123	—	2	2	no	—
158	C₃₁×#123	—	2	2	no	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	—	2	2	no	—
161	C₃₁×#123	—	2	2	no	—
162	C₃₁×#123	—	2	1	no	—
163	C₃₁×#123	—	2	2	no	—
164	C₃₁×#123	—	2	2	no	—
165	C₃₁×#123	—	2	2	no	—
166	C₃₁×#123	D₄	1	2	yes	—
167	C₃₁×C₂²⋊Q₈	—	2	1	no	—
168	C₃₁×C₂²⋊Q₈	—	2	1	no	—
169	C₃₁×C₂²⋊Q₈	—	2	1	no	—
170	C₃₁×C₂²⋊Q₈	—	2	1	no	—
171	C₃₁×C₂²⋊Q₈	—	2	1	no	—
172	C₃₁×C₂²⋊Q₈	—	2	2	no	—
173	C₃₁×C₂²⋊Q₈	—	2	2	no	—
174	C₃₁×C₂²⋊Q₈	—	2	2	no	—
175	C₃₁×C₂²⋊Q₈	—	2	2	no	—
176	C₃₁×C₂²⋊Q₈	—	2	2	no	—
177	C₃₁×C₂²⋊Q₈	—	2	2	no	—
178	C₃₁×C₂²⋊Q₈	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	2	no	—
180	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
181	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
182	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
183	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
184	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
185	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
186	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
187	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₃₁×#121	—	2	2	no	—
192	C₃₁×#121	—	2	2	no	—
193	C₃₁×#121	—	2	1	no	—
194	C₃₁×#121	D₄	1	1	yes	characteristic
195	C₃₁×#121	D₄	1	1	yes	characteristic
196	C₃₁×#121	C₂³	1	1	yes	characteristic
197	C₃₁×#121	C₂³	1	1	yes	characteristic
198	C₃₁×#121	C₂³	1	2	yes	—
199	C₃₁×#120	—	2	1	no	—
200	C₃₁×#120	D₄	1	2	yes	—
201	C₄×Q₈×C₃₁	—	2	1	no	—
202	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
203	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
204	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
205	C₄×D₄×C₃₁	—	2	2	no	—
206	C₄×D₄×C₃₁	—	2	1	no	—
207	C₄×D₄×C₃₁	—	2	2	no	—
208	C₄×D₄×C₃₁	—	2	2	no	—
209	C₄×D₄×C₃₁	—	2	2	no	—
210	C₄×D₄×C₃₁	—	2	1	no	—
211	C₄×D₄×C₃₁	—	2	1	no	—
212	C₄×D₄×C₃₁	—	2	2	no	—
213	C₄×D₄×C₃₁	—	2	2	no	—
214	C₄×D₄×C₃₁	C₂³	1	2	yes	—
215	C₄×D₄×C₃₁	C₂³	1	2	yes	—
216	C₄×D₄×C₃₁	C₂³	1	2	yes	—
217	C₃₁×#117	—	2	1	no	—
218	C₃₁×#117	—	2	2	no	—
219	C₃₁×#117	—	2	2	no	—
220	C₃₁×#117	—	2	2	no	—
221	C₃₁×#117	C₂³	1	2	yes	—
222	C₃₁×#117	C₂³	1	2	yes	—
223	C₃₁×#117	C₂³	1	1	yes	characteristic
224	C₃₁×#117	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
226	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
227	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
228	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
229	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
230	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
231	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
240	C₃₁×#107	C₂³	1	2	yes	—
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#107	C₂³	1	2	yes	—
244	C₃₁×#107	C₂³	1	2	yes	—
245	C₃₁×#107	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×#106	C₂³	1	2	yes	—
248	C₃₁×#106	C₂³	1	2	yes	—
249	C₃₁×#106	C₂³	1	2	yes	—
250	C₃₁×#106	C₂³	1	2	yes	—
251	C₃₁×#106	C₂³	1	2	yes	—
252	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#103	C₂³	1	2	yes	—
256	C₃₁×#103	C₂³	1	2	yes	—
257	C₃₁×#103	C₂³	1	2	yes	—
258	C₃₁×#103	C₂³	1	2	yes	—
259	C₃₁×#103	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#103	C₂³	1	2	yes	—
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#103	C₂³	1	2	yes	—
265	C₃₁×#103	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
271	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
272	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₃₁×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
281	#41×C₃₁	—	4	2	no	—
282	#41×C₃₁	—	4	2	no	—
283	#41×C₃₁	—	8	4	no	—
284	C₂×Q₈×C₃₁	—	2	1	no	—
285	C₂×Q₈×C₃₁	—	2	1	no	—
286	C₂×Q₈×C₃₁	—	2	2	no	—
287	C₂×Q₈×C₃₁	—	2	2	no	—
288	C₂×Q₈×C₃₁	—	4	2	no	—
289	C₂×Q₈×C₃₁	—	4	2	no	—
290	C₂×Q₈×C₃₁	—	4	2	no	—
291	C₂×Q₈×C₃₁	—	4	2	no	—
292	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
294	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
295	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂×D₄×C₃₁	—	2	1	no	—
297	C₂×D₄×C₃₁	—	2	1	no	—
298	C₂×D₄×C₃₁	—	2	1	no	—
299	C₂×D₄×C₃₁	—	2	2	no	—
300	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
301	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
302	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
303	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₃₁	—	2	1	no	—
306	C₂²×C₄×C₃₁	—	2	1	no	—
307	C₂²×C₄×C₃₁	—	2	2	no	—
308	C₂²×C₄×C₃₁	—	2	1	no	—
309	C₂²×C₄×C₃₁	—	2	1	no	—
310	C₂²×C₄×C₃₁	—	2	1	no	—
311	C₂²×C₄×C₃₁	—	2	2	no	—
312	C₂²×C₄×C₃₁	—	2	1	no	—
313	C₂²×C₄×C₃₁	—	2	2	no	—
314	C₂²×C₄×C₃₁	—	2	2	no	—
315	C₂²×C₄×C₃₁	—	2	1	no	—
316	C₂²×C₄×C₃₁	—	2	2	no	—
317	C₂²×C₄×C₃₁	—	4	2	no	—
318	C₂²×C₄×C₃₁	—	8	2	no	—
319	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
326	Q₁₆×C₃₁	—	4	2	no	—
327	Q₁₆×C₃₁	—	4	2	no	—
328	SD₁₆×C₃₁	—	4	2	no	—
329	SD₁₆×C₃₁	—	4	2	no	—
330	M₁₆×C₃₁	—	4	2	no	—
331	C₂×C₈×C₃₁	—	4	2	no	—
332	C₂×C₈×C₃₁	—	4	2	no	—
333	C₂×C₈×C₃₁	—	4	2	no	—
334	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
335	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
336	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
337	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₃₁	—	2	1	no	—
339	C₄⋊C₄×C₃₁	—	2	1	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	—	2	2	no	—
343	C₄⋊C₄×C₃₁	—	2	2	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	2	no	—
347	C₄⋊C₄×C₃₁	—	2	2	no	—
348	C₄⋊C₄×C₃₁	—	2	1	no	—
349	C₄⋊C₄×C₃₁	—	2	1	no	—
350	C₄⋊C₄×C₃₁	—	2	2	no	—
351	C₄⋊C₄×C₃₁	—	2	2	no	—
352	C₄⋊C₄×C₃₁	—	2	2	no	—
353	C₄⋊C₄×C₃₁	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	1	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	2	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	2	2	no	—
361	C₄⋊C₄×C₃₁	—	2	1	no	—
362	C₄⋊C₄×C₃₁	—	2	2	no	—
363	C₄⋊C₄×C₃₁	—	2	2	no	—
364	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
366	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
368	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	2	no	—
376	C₂²⋊C₄×C₃₁	—	2	2	no	—
377	C₂²⋊C₄×C₃₁	—	2	2	no	—
378	C₂²⋊C₄×C₃₁	—	2	1	no	—
379	C₂²⋊C₄×C₃₁	—	2	1	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	1	no	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	1	no	—
389	C₂²⋊C₄×C₃₁	—	2	1	no	—
390	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₄²×C₃₁	—	2	2	no	—
396	C₄²×C₃₁	—	2	2	no	—
397	C₄²×C₃₁	—	2	2	no	—
398	C₄²×C₃₁	—	2	2	no	—
399	C₄²×C₃₁	—	2	2	no	—
400	C₄²×C₃₁	—	2	1	no	—
401	C₄²×C₃₁	C₂⁴	1	2	yes	—
402	#61767	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₂³×C₃₁	—	2	2	no	—
404	C₂³×C₃₁	—	2	2	no	—
405	C₂³×C₃₁	—	2	1	no	—
406	C₂³×C₃₁	—	4	1	no	—
407	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
408	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
409	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
410	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
411	Q₈×C₃₁	—	2	2	no	—
412	Q₈×C₃₁	—	2	2	no	—
413	Q₈×C₃₁	—	2	2	no	—
414	Q₈×C₃₁	—	2	2	no	—
415	Q₈×C₃₁	—	2	2	no	—
416	Q₈×C₃₁	—	4	1	no	—
417	Q₈×C₃₁	—	8	1	no	—
418	Q₈×C₃₁	—	8	1	no	—
419	Q₈×C₃₁	—	8	2	no	—
420	Q₈×C₃₁	—	8	2	no	—
421	D₄×C₃₁	—	2	4	no	—
422	D₄×C₃₁	—	2	4	no	—
423	D₄×C₃₁	—	2	2	no	—
424	D₄×C₃₁	—	4	1	no	—
425	D₄×C₃₁	—	4	2	no	—
426	D₄×C₃₁	—	4	2	no	—
427	D₄×C₃₁	—	4	2	no	—
428	D₄×C₃₁	—	4	2	no	—
429	D₄×C₃₁	—	8	2	no	—
430	C₂×C₄×C₃₁	—	2	2	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	2	2	no	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	2	1	no	—
436	C₂×C₄×C₃₁	—	2	2	no	—
437	C₂×C₄×C₃₁	—	2	2	no	—
438	C₂×C₄×C₃₁	—	2	1	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	2	no	—
441	C₂×C₄×C₃₁	—	2	2	no	—
442	C₂×C₄×C₃₁	—	2	1	no	—
443	C₂×C₄×C₃₁	—	2	2	no	—
444	C₂×C₄×C₃₁	—	4	1	no	—
445	C₂×C₄×C₃₁	—	4	1	no	—
446	C₂×C₄×C₃₁	—	4	1	no	—
447	C₂×C₄×C₃₁	—	4	2	no	—
448	C₂×C₄×C₃₁	—	4	2	no	—
449	C₂×C₄×C₃₁	—	4	4	no	—
450	C₂×C₄×C₃₁	—	4	2	no	—
451	C₂×C₄×C₃₁	—	8	2	no	—
452	C₂×C₄×C₃₁	—	8	1	no	—
453	C₂×C₄×C₃₁	—	8	2	no	—
454	C₂×C₄×C₃₁	—	8	1	no	—
455	C₂×C₄×C₃₁	—	8	1	no	—
456	C₂×C₄×C₃₁	—	8	1	no	—
457	C₂×C₄×C₃₁	—	8	2	no	—
458	C₂×C₄×C₃₁	—	8	2	no	—
459	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
466	C₈×C₃₁	—	2	2	no	—
467	C₈×C₃₁	—	2	2	no	—
468	C₈×C₃₁	—	2	2	no	—
469	C₈×C₃₁	—	2	2	no	—
470	#3538	C₂×C₃₁	1	1	yes	characteristic, complemented
471	#3492	C₂×C₃₁	1	1	yes	characteristic
472	#3344	C₂×C₃₁	1	2	yes	complemented
473	#3343	C₂×C₃₁	1	2	yes	complemented
474	#3337	C₂×C₃₁	1	2	yes	complemented
475	#3336	C₂×C₃₁	1	2	yes	complemented
476	#3320	C₂×C₃₁	1	2	yes	complemented
477	#3312	C₂×C₃₁	1	2	yes	complemented
478	#3299	C₂×C₃₁	1	2	yes	complemented
479	#3298	C₂×C₃₁	1	2	yes	complemented
480	#3242	C₂×C₃₁	1	2	yes	complemented
481	#3201	C₂×C₃₁	1	2	yes	complemented
482	#3190	C₂×C₃₁	1	1	yes	characteristic, complemented
483	#3190	C₂×C₃₁	1	1	yes	characteristic, complemented
484	#3120	C₂×C₃₁	1	2	yes	complemented
485	#3097	C₂×C₃₁	1	2	yes	complemented
486	C₂×#484	C₂×C₃₁	1	1	yes	characteristic, complemented
487	C₂×#483	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#2977	C₂×C₃₁	1	1	yes	characteristic, complemented
489	C₂²×C₃₁	—	2	1	no	—
490	C₂²×C₃₁	—	2	1	no	—
491	C₂²×C₃₁	—	2	1	no	—
492	C₂²×C₃₁	—	2	1	no	—
493	C₂²×C₃₁	—	2	1	no	—
494	C₂²×C₃₁	—	2	2	no	—
495	C₂²×C₃₁	—	2	1	no	—
496	C₂²×C₃₁	—	2	2	no	—
497	C₂²×C₃₁	—	2	2	no	—
498	C₂²×C₃₁	—	2	1	no	—
499	C₂²×C₃₁	—	4	4	no	—
500	C₂²×C₃₁	—	4	1	no	—
501	C₂²×C₃₁	—	4	1	no	—
502	C₂²×C₃₁	—	4	1	no	—
503	C₂²×C₃₁	#577	1	2	yes	—
504	C₂²×C₃₁	#578	1	2	yes	—
505	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
506	C₄×C₃₁	—	2	1	no	—
507	C₄×C₃₁	—	2	1	no	—
508	C₄×C₃₁	—	2	1	no	—
509	C₄×C₃₁	—	2	2	no	—
510	C₄×C₃₁	—	2	2	no	—
511	C₄×C₃₁	—	2	2	no	—
512	C₄×C₃₁	—	4	1	no	—
513	C₄×C₃₁	—	4	2	no	—
514	C₄×C₃₁	—	4	2	no	—
515	C₄×C₃₁	—	4	2	no	—
516	C₄×C₃₁	—	4	2	no	—
517	C₄×C₃₁	—	4	2	no	—
518	C₄×C₃₁	—	4	1	no	—
519	C₄×C₃₁	—	4	2	no	—
520	C₄×C₃₁	—	4	1	no	—
521	C₄×C₃₁	#585	1	2	yes	—
522	#563	—	2	2	no	—
523	#554	—	2	1	no	—
524	#554	C₂²×C₃₁	1	2	yes	—
525	#553	—	2	1	no	—
526	#553	C₂²×C₃₁	1	2	yes	—
527	#552	—	2	1	no	—
528	#552	C₂²×C₃₁	1	2	yes	—
529	#552	C₂²×C₃₁	1	2	yes	—
530	#552	C₂²×C₃₁	1	2	yes	—
531	#551	—	2	2	no	—
532	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
533	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
534	#547	—	2	1	no	—
535	#547	C₂²×C₃₁	1	2	yes	—
536	#544	—	2	1	no	—
537	#544	—	2	1	no	—
538	#544	C₂²×C₃₁	1	1	yes	characteristic
539	#541	C₂²×C₃₁	1	2	yes	—
540	#539	—	2	2	no	—
541	#539	—	2	1	no	—
542	#539	—	2	1	no	—
543	#537	C₂²×C₃₁	1	1	yes	characteristic
544	#536	C₂²×C₃₁	1	2	yes	—
545	#525	—	2	2	no	—
546	#525	C₂²×C₃₁	1	1	yes	characteristic
547	#525	C₂²×C₃₁	1	1	yes	characteristic
548	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
549	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
550	#520	C₂²×C₃₁	1	1	yes	characteristic
551	#520	C₂²×C₃₁	1	1	yes	characteristic
552	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
553	#501	C₂²×C₃₁	1	2	yes	complemented
554	#499	C₂²×C₃₁	1	2	yes	complemented
555	#491	C₂²×C₃₁	1	2	yes	complemented
556	#487	C₂²×C₃₁	1	2	yes	complemented
557	#485	C₂²×C₃₁	1	2	yes	—
558	#485	C₂²×C₃₁	1	2	yes	—
559	#485	C₂²×C₃₁	1	2	yes	complemented
560	#485	C₂²×C₃₁	1	2	yes	complemented
561	#485	C₂²×C₃₁	1	2	yes	complemented
562	#484	C₂²×C₃₁	1	2	yes	—
563	#484	C₂²×C₃₁	1	2	yes	—
564	#484	C₂²×C₃₁	1	2	yes	—
565	#484	C₂²×C₃₁	1	2	yes	—
566	#484	C₂²×C₃₁	1	2	yes	complemented
567	#483	C₂²×C₃₁	1	1	yes	characteristic
568	#483	C₂²×C₃₁	1	2	yes	—
569	#483	C₂²×C₃₁	1	2	yes	—
570	#483	C₂²×C₃₁	1	2	yes	—
571	#483	C₂²×C₃₁	1	2	yes	—
572	#483	C₂²×C₃₁	1	1	yes	characteristic
573	#483	C₂²×C₃₁	1	2	yes	complemented
574	#482	C₂²×C₃₁	1	2	yes	complemented
575	#480	C₂²×C₃₁	1	1	yes	characteristic
576	#480	C₂²×C₃₁	1	1	yes	characteristic
577	#479	C₂²×C₃₁	1	2	yes	complemented
578	#479	C₂²×C₃₁	1	2	yes	complemented
579	#479	C₂²×C₃₁	1	2	yes	complemented
580	#478	C₂²×C₃₁	1	2	yes	complemented
581	#477	C₂²×C₃₁	1	2	yes	complemented
582	#475	C₂²×C₃₁	1	2	yes	complemented
583	#470	C₂²×C₃₁	1	2	yes	complemented
584	#468	C₂²×C₃₁	1	2	yes	complemented
585	#467	C₂²×C₃₁	1	2	yes	—
586	#467	C₂²×C₃₁	1	2	yes	—
587	#467	C₂²×C₃₁	1	2	yes	complemented
588	#465	C₂²×C₃₁	1	2	yes	—
589	#465	C₂²×C₃₁	1	2	yes	—
590	#465	C₂²×C₃₁	1	2	yes	complemented
591	#462	C₂²×C₃₁	1	2	yes	complemented
592	#461	C₂²×C₃₁	1	2	yes	complemented
593	#452	C₂²×C₃₁	1	2	yes	—
594	#452	C₂²×C₃₁	1	2	yes	—
595	#451	C₂²×C₃₁	1	1	yes	characteristic
596	#451	C₂²×C₃₁	1	1	yes	characteristic
597	#451	C₂²×C₃₁	1	2	yes	complemented
598	#448	C₂²×C₃₁	1	1	yes	characteristic
599	#448	C₂²×C₃₁	1	1	yes	characteristic
600	#448	C₂²×C₃₁	1	2	yes	complemented
601	#441	C₂²×C₃₁	1	2	yes	complemented
602	#440	C₂²×C₃₁	1	2	yes	complemented
603	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
604	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
605	#435	C₂²×C₃₁	1	2	yes	—
606	#435	C₂²×C₃₁	1	2	yes	—
607	C₈×D₄	C₂²×C₃₁	1	2	yes	—
608	C₈×D₄	C₂²×C₃₁	1	2	yes	—
609	#433	C₂²×C₃₁	1	2	yes	—
610	#428	C₂²×C₃₁	1	2	yes	complemented
611	#427	C₂²×C₃₁	1	2	yes	complemented
612	C₂×#107	C₂²×C₃₁	1	2	yes	—
613	C₂×#106	C₂²×C₃₁	1	2	yes	—
614	#419	C₂²×C₃₁	1	2	yes	complemented
615	C₂×#103	C₂²×C₃₁	1	2	yes	—
616	C₂×#103	C₂²×C₃₁	1	2	yes	—
617	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
618	#408	C₂²×C₃₁	1	2	yes	—
619	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
620	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
621	C₂×C₃₁	—	2	2	no	—
622	C₂×C₃₁	—	2	2	no	—
623	C₂×C₃₁	—	4	2	no	—
624	C₂×C₃₁	—	4	1	no	—
625	C₂×C₃₁	—	8	1	no	—
626	C₂×C₃₁	#3485	1	1	yes	characteristic
627	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
628	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
629	C₂×#41	—	2	2	no	—
630	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
631	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
632	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
633	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
634	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
635	C₂³×C₄	—	2	1	no	—
636	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
637	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
638	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
639	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
640	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
641	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
642	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
643	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
644	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
645	C₄⋊Q₈	—	2	2	no	—
646	C₄⋊Q₈	—	2	2	no	—
647	C₄⋊Q₈	—	2	2	no	—
648	C₄⋊Q₈	—	2	1	no	—
649	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
650	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
651	#126	—	2	2	no	—
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#125	—	2	2	no	—
658	#125	—	2	2	no	—
659	#125	—	2	2	no	—
660	#125	—	2	2	no	—
661	#125	—	2	2	no	—
662	#125	—	2	2	no	—
663	#125	—	2	1	no	—
664	#125	C₂³×C₃₁	1	2	yes	—
665	#125	C₂³×C₃₁	1	2	yes	—
666	#124	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	#123	—	2	2	no	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	—	2	1	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	D₄×C₃₁	1	2	yes	—
677	C₂²⋊Q₈	—	2	1	no	—
678	C₂²⋊Q₈	—	2	1	no	—
679	C₂²⋊Q₈	—	2	1	no	—
680	C₂²⋊Q₈	—	2	1	no	—
681	C₂²⋊Q₈	—	2	1	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
691	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
692	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
693	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
694	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
695	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
696	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
697	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
698	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
699	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
700	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	—	2	1	no	—
704	#121	D₄×C₃₁	1	1	yes	characteristic
705	#121	D₄×C₃₁	1	1	yes	characteristic
706	#121	C₂³×C₃₁	1	1	yes	characteristic
707	#121	C₂³×C₃₁	1	1	yes	characteristic
708	#121	C₂³×C₃₁	1	2	yes	—
709	#120	—	2	1	no	—
710	#120	D₄×C₃₁	1	2	yes	—
711	C₄×Q₈	—	2	1	no	—
712	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
713	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
714	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
715	C₄×D₄	—	2	2	no	—
716	C₄×D₄	—	2	1	no	—
717	C₄×D₄	—	2	2	no	—
718	C₄×D₄	—	2	2	no	—
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	—	2	1	no	—
721	C₄×D₄	—	2	1	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	C₂³×C₃₁	1	2	yes	—
725	C₄×D₄	C₂³×C₃₁	1	2	yes	—
726	C₄×D₄	C₂³×C₃₁	1	2	yes	—
727	#117	—	2	1	no	—
728	#117	—	2	2	no	—
729	#117	—	2	2	no	—
730	#117	—	2	2	no	—
731	#117	C₂³×C₃₁	1	1	yes	characteristic
732	#117	C₂³×C₃₁	1	2	yes	—
733	#117	C₂³×C₃₁	1	2	yes	—
734	#117	C₂³×C₃₁	1	1	yes	characteristic
735	C₂×C₄⋊C₄	—	2	1	no	—
736	C₂×C₄⋊C₄	—	2	1	no	—
737	C₂×C₄⋊C₄	—	2	1	no	—
738	C₂×C₄⋊C₄	—	2	1	no	—
739	C₂×C₄⋊C₄	—	2	1	no	—
740	C₂×C₄⋊C₄	—	2	1	no	—
741	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
742	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
743	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
745	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
746	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
748	C₂×C₂²⋊C₄	—	2	1	no	—
749	C₂×C₂²⋊C₄	—	2	1	no	—
750	#107	C₂³×C₃₁	1	2	yes	—
751	#107	C₂³×C₃₁	1	2	yes	—
752	#107	C₂³×C₃₁	1	2	yes	—
753	#107	C₂³×C₃₁	1	2	yes	—
754	#107	C₂³×C₃₁	1	2	yes	—
755	#107	C₂³×C₃₁	1	2	yes	—
756	#106	C₂³×C₃₁	1	2	yes	—
757	#106	C₂³×C₃₁	1	2	yes	—
758	#106	C₂³×C₃₁	1	2	yes	—
759	#106	C₂³×C₃₁	1	2	yes	—
760	#106	C₂³×C₃₁	1	2	yes	—
761	#106	C₂³×C₃₁	1	2	yes	—
762	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
763	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
764	#103	C₂³×C₃₁	1	2	yes	—
765	#103	C₂³×C₃₁	1	2	yes	—
766	#103	C₂³×C₃₁	1	2	yes	—
767	#103	C₂³×C₃₁	1	2	yes	—
768	#103	C₂³×C₃₁	1	2	yes	—
769	#103	C₂³×C₃₁	1	2	yes	—
770	#103	C₂³×C₃₁	1	2	yes	—
771	#103	C₂³×C₃₁	1	2	yes	—
772	#103	C₂³×C₃₁	1	2	yes	—
773	#103	C₂³×C₃₁	1	2	yes	—
774	#103	C₂³×C₃₁	1	2	yes	—
775	#103	C₂³×C₃₁	1	2	yes	—
776	#103	C₂³×C₃₁	1	2	yes	—
777	#103	C₂³×C₃₁	1	2	yes	—
778	#102	C₂³×C₃₁	1	2	yes	—
779	#102	C₂³×C₃₁	1	2	yes	—
780	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
782	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
783	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
784	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
785	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
788	#97	C₂³×C₃₁	1	2	yes	—
789	C₄×C₈	C₂³×C₃₁	1	2	yes	—
790	C₃₁	#61767	1	1	yes	characteristic, direct product factor, Sylow
791	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
792	#41	—	4	2	no	—
793	#41	—	4	2	no	—
794	#41	—	8	4	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	2	2	no	—
799	C₂×Q₈	—	4	2	no	—
800	C₂×Q₈	—	4	2	no	—
801	C₂×Q₈	—	4	2	no	—
802	C₂×Q₈	—	4	2	no	—
803	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
804	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
805	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
806	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
807	C₂×D₄	—	2	1	no	—
808	C₂×D₄	—	2	1	no	—
809	C₂×D₄	—	2	1	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
812	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
813	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
814	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
815	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	4	2	no	—
829	C₂²×C₄	—	8	2	no	—
830	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
831	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
832	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
837	Q₁₆	—	4	2	no	—
838	Q₁₆	—	4	2	no	—
839	SD₁₆	—	4	2	no	—
840	SD₁₆	—	4	2	no	—
841	M₁₆	—	4	2	no	—
842	C₂×C₈	—	4	2	no	—
843	C₂×C₈	—	4	2	no	—
844	C₂×C₈	—	4	2	no	—
845	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
846	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
847	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
848	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
876	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
877	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
878	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
879	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
880	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
881	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
882	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
883	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
884	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	—	2	1	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	1	no	—
900	C₂²⋊C₄	—	2	1	no	—
901	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
902	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
903	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
904	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
905	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	1	no	—
912	C₄²	C₂⁴×C₃₁	1	2	yes	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	4	1	no	—
917	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
918	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
919	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
920	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
921	Q₈	—	2	2	no	—
922	Q₈	—	2	2	no	—
923	Q₈	—	2	2	no	—
924	Q₈	—	2	2	no	—
925	Q₈	—	2	2	no	—
926	Q₈	—	4	1	no	—
927	Q₈	—	8	1	no	—
928	Q₈	—	8	1	no	—
929	Q₈	—	8	2	no	—
930	Q₈	—	8	2	no	—
931	D₄	—	2	4	no	—
932	D₄	—	2	4	no	—
933	D₄	—	2	2	no	—
934	D₄	—	4	1	no	—
935	D₄	—	4	2	no	—
936	D₄	—	4	2	no	—
937	D₄	—	4	2	no	—
938	D₄	—	4	2	no	—
939	D₄	—	8	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	4	1	no	—
955	C₂×C₄	—	4	1	no	—
956	C₂×C₄	—	4	1	no	—
957	C₂×C₄	—	4	2	no	—
958	C₂×C₄	—	4	2	no	—
959	C₂×C₄	—	4	4	no	—
960	C₂×C₄	—	4	2	no	—
961	C₂×C₄	—	8	2	no	—
962	C₂×C₄	—	8	1	no	—
963	C₂×C₄	—	8	2	no	—
964	C₂×C₄	—	8	1	no	—
965	C₂×C₄	—	8	1	no	—
966	C₂×C₄	—	8	1	no	—
967	C₂×C₄	—	8	2	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
970	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
971	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
972	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
973	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
974	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
975	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
976	C₈	—	2	2	no	—
977	C₈	—	2	2	no	—
978	C₈	—	2	2	no	—
979	C₈	—	2	2	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	1	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	4	4	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	1	no	—
994	C₂²	C₃₁×#577	1	2	yes	—
995	C₂²	C₃₁×#578	1	2	yes	—
996	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	2	no	—
1001	C₄	—	2	2	no	—
1002	C₄	—	2	2	no	—
1003	C₄	—	4	1	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	2	no	—
1009	C₄	—	4	1	no	—
1010	C₄	—	4	2	no	—
1011	C₄	—	4	1	no	—
1012	C₄	C₃₁×#585	1	2	yes	—
1013	C₂	—	2	2	no	—
1014	C₂	—	2	2	no	—
1015	C₂	—	4	1	no	—
1016	C₂	—	4	2	no	—
1017	C₂	—	8	1	no	—
1018	C₂	C₃₁×#3485	1	1	yes	characteristic
1019	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1020	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3492	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3538	C₂	semidirect
3. C₃₁×#3344	C₂	semidirect
4. C₃₁×#3343	C₂	semidirect
5. C₃₁×#3337	C₂	semidirect
6. C₃₁×#3336	C₂	semidirect
7. C₃₁×#3320	C₂	semidirect
8. C₃₁×#3312	C₂	semidirect
9. C₃₁×#3299	C₂	semidirect
10. C₃₁×#3298	C₂	semidirect
11. C₃₁×#3242	C₂	semidirect
12. C₃₁×#3201	C₂	semidirect
13. C₃₁×#3190	C₂	semidirect
14. C₃₁×#3190	C₂	semidirect
15. C₃₁×#3120	C₂	semidirect
16. C₃₁×#3097	C₂	semidirect
17. C₂×C₃₁×#484	C₂	semidirect
18. C₂×C₃₁×#483	C₂	semidirect
19. C₃₁×#2977	C₂	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#499	C₂²	semidirect
53. C₃₁×#491	C₂²	semidirect
54. C₃₁×#487	C₂²	semidirect
57. C₃₁×#485	C₂²	semidirect
58. C₃₁×#485	C₂²	semidirect
59. C₃₁×#485	C₂²	semidirect
64. C₃₁×#484	C₂²	semidirect
71. C₃₁×#483	C₂²	semidirect
72. C₃₁×#482	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
76. C₃₁×#479	C₂²	semidirect
77. C₃₁×#479	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#477	C₂²	semidirect
80. C₃₁×#475	C₂²	semidirect
81. C₃₁×#470	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
85. C₃₁×#467	C₂²	semidirect
88. C₃₁×#465	C₂²	semidirect
89. C₃₁×#462	C₂²	semidirect
90. C₃₁×#461	C₂²	semidirect
95. C₃₁×#451	C₂²	semidirect
98. C₃₁×#448	C₂²	semidirect
99. C₃₁×#441	C₂²	semidirect
100. C₃₁×#440	C₂²	semidirect
101. C₄×Q₁₆×C₃₁	C₂²	semidirect
102. C₄×SD₁₆×C₃₁	C₂²	semidirect
108. C₃₁×#428	C₂²	semidirect
109. C₃₁×#427	C₂²	semidirect
112. C₃₁×#419	C₂²	semidirect
115. C₂×C₃₁×#103	C₂²	semidirect
402. #61767	C₃₁	direct (N × H)
470. #3538	C₂×C₃₁	semidirect
472. #3344	C₂×C₃₁	semidirect
473. #3343	C₂×C₃₁	semidirect
474. #3337	C₂×C₃₁	semidirect
475. #3336	C₂×C₃₁	semidirect
476. #3320	C₂×C₃₁	semidirect
477. #3312	C₂×C₃₁	semidirect
478. #3299	C₂×C₃₁	semidirect
479. #3298	C₂×C₃₁	semidirect
480. #3242	C₂×C₃₁	semidirect
481. #3201	C₂×C₃₁	semidirect
482. #3190	C₂×C₃₁	semidirect
483. #3190	C₂×C₃₁	semidirect
484. #3120	C₂×C₃₁	semidirect
485. #3097	C₂×C₃₁	semidirect
486. C₂×#484	C₂×C₃₁	semidirect
487. C₂×#483	C₂×C₃₁	semidirect
488. #2977	C₂×C₃₁	semidirect
553. #501	C₂²×C₃₁	semidirect
554. #499	C₂²×C₃₁	semidirect
555. #491	C₂²×C₃₁	semidirect
556. #487	C₂²×C₃₁	semidirect
559. #485	C₂²×C₃₁	semidirect
560. #485	C₂²×C₃₁	semidirect
561. #485	C₂²×C₃₁	semidirect
566. #484	C₂²×C₃₁	semidirect
573. #483	C₂²×C₃₁	semidirect
574. #482	C₂²×C₃₁	semidirect
577. #479	C₂²×C₃₁	semidirect
578. #479	C₂²×C₃₁	semidirect
579. #479	C₂²×C₃₁	semidirect
580. #478	C₂²×C₃₁	semidirect
581. #477	C₂²×C₃₁	semidirect
582. #475	C₂²×C₃₁	semidirect
583. #470	C₂²×C₃₁	semidirect
584. #468	C₂²×C₃₁	semidirect
587. #467	C₂²×C₃₁	semidirect
590. #465	C₂²×C₃₁	semidirect
591. #462	C₂²×C₃₁	semidirect
592. #461	C₂²×C₃₁	semidirect
597. #451	C₂²×C₃₁	semidirect
600. #448	C₂²×C₃₁	semidirect
601. #441	C₂²×C₃₁	semidirect
602. #440	C₂²×C₃₁	semidirect
603. C₄×Q₁₆	C₂²×C₃₁	semidirect
604. C₄×SD₁₆	C₂²×C₃₁	semidirect
610. #428	C₂²×C₃₁	semidirect
611. #427	C₂²×C₃₁	semidirect
614. #419	C₂²×C₃₁	semidirect
617. C₂×#103	C₂²×C₃₁	semidirect
790. C₃₁	#61767	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×#3538	2
C₃₁×#3492	2
C₃₁×#3344	2
C₃₁×#3343	2
C₃₁×#3337	2
C₃₁×#3336	2
C₃₁×#3320	2
C₃₁×#3312	2
C₃₁×#3299	2
C₃₁×#3298	2
C₃₁×#3242	2
C₃₁×#3201	2
C₃₁×#3190	2
C₃₁×#3120	2
C₃₁×#3097	2
C₂×C₃₁×#484	2
C₂×C₃₁×#483	2
C₃₁×#2977	2
#61767	31

Subgroups — C31×#61767 #21518526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61767 #21518526