Subgroups — C₃₁×#61243 #21518002

Order 7936.

1848 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3475	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3350	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3349	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3347	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3346	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3345	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3344	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3162	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3091	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3091	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3076	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3054	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2943	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2911	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×#556	C₂²	1	2	yes	—
24	C₃₁×#555	C₂²	1	2	yes	—
25	C₃₁×#554	C₂²	1	2	yes	—
26	C₃₁×#553	C₂²	1	2	yes	—
27	C₃₁×#553	C₂²	1	2	yes	—
28	C₃₁×#552	—	2	2	no	—
29	C₃₁×#552	C₂²	1	2	yes	—
30	C₃₁×#552	C₂²	1	2	yes	—
31	C₃₁×#551	—	2	2	no	—
32	C₃₁×#551	—	2	2	no	—
33	C₃₁×#547	C₂²	1	2	yes	—
34	C₃₁×#546	—	2	2	no	—
35	C₃₁×#533	C₂²	1	2	yes	—
36	C₃₁×#529	—	2	2	no	—
37	C₃₁×#529	—	2	2	no	—
38	C₃₁×#529	—	2	2	no	—
39	C₃₁×#525	C₂²	1	2	yes	—
40	C₃₁×#525	C₂²	1	2	yes	—
41	C₄×#41×C₃₁	—	2	2	no	—
42	C₄×#41×C₃₁	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₃₁×#117	C₂²	1	2	yes	—
45	C₂×C₃₁×#117	C₂²	1	2	yes	—
46	C₃₁×#501	C₂²	1	2	yes	complemented
47	C₃₁×#501	C₂²	1	2	yes	complemented
48	C₃₁×#501	C₂²	1	2	yes	complemented
49	C₃₁×#501	C₂²	1	2	yes	complemented
50	C₃₁×#485	C₂²	1	2	yes	complemented
51	C₃₁×#485	C₂²	1	2	yes	complemented
52	C₃₁×#485	C₂²	1	2	yes	complemented
53	C₃₁×#485	C₂²	1	2	yes	complemented
54	C₃₁×#484	C₂²	1	2	yes	complemented
55	C₃₁×#484	C₂²	1	2	yes	complemented
56	C₃₁×#483	C₂²	1	2	yes	complemented
57	C₃₁×#483	C₂²	1	2	yes	complemented
58	C₃₁×#482	C₂²	1	2	yes	complemented
59	C₃₁×#482	C₂²	1	2	yes	complemented
60	C₃₁×#482	C₂²	1	2	yes	complemented
61	C₃₁×#482	C₂²	1	2	yes	complemented
62	C₃₁×#481	C₂²	1	2	yes	complemented
63	C₃₁×#481	C₂²	1	2	yes	complemented
64	C₃₁×#480	C₂²	1	2	yes	complemented
65	C₃₁×#480	C₂²	1	2	yes	complemented
66	C₃₁×#479	C₂²	1	2	yes	complemented
67	C₃₁×#479	C₂²	1	2	yes	complemented
68	C₃₁×#478	C₂²	1	2	yes	complemented
69	C₃₁×#478	C₂²	1	2	yes	complemented
70	C₃₁×#477	C₂²	1	2	yes	complemented
71	C₃₁×#476	C₂²	1	2	yes	complemented
72	C₃₁×#475	C₂²	1	2	yes	complemented
73	C₃₁×#474	C₂²	1	2	yes	complemented
74	C₃₁×#470	C₂²	1	2	yes	complemented
75	C₃₁×#469	C₂²	1	2	yes	complemented
76	C₃₁×#468	C₂²	1	2	yes	complemented
77	C₃₁×#468	C₂²	1	2	yes	complemented
78	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#465	C₂²	1	2	yes	complemented
83	C₃₁×#465	C₂²	1	2	yes	complemented
84	C₃₁×#442	C₂²	1	2	yes	complemented
85	C₃₁×#441	C₂²	1	2	yes	complemented
86	C₃₁×#440	C₂²	1	2	yes	complemented
87	C₃₁×#440	C₂²	1	2	yes	complemented
88	C₃₁×#435	C₂²	1	2	yes	—
89	C₃₁×#435	C₂²	1	2	yes	—
90	C₃₁×#435	C₂²	1	2	yes	—
91	C₃₁×#435	C₂²	1	2	yes	—
92	C₃₁×#428	C₂²	1	2	yes	complemented
93	C₃₁×#428	C₂²	1	2	yes	complemented
94	C₃₁×#428	C₂²	1	2	yes	complemented
95	C₃₁×#428	C₂²	1	2	yes	complemented
96	C₃₁×#427	C₂²	1	2	yes	—
97	C₃₁×#427	C₂²	1	2	yes	—
98	C₃₁×#427	C₂²	1	2	yes	—
99	C₃₁×#427	C₂²	1	1	yes	characteristic
100	C₃₁×#427	C₂²	1	1	yes	characteristic
101	C₃₁×#427	C₂²	1	1	yes	characteristic
102	C₃₁×#427	C₂²	1	2	yes	complemented
103	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
108	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
109	C₃₁×#416	C₂²	1	2	yes	—
110	C₃₁×#416	C₂²	1	2	yes	—
111	C₃₁×#416	C₂²	1	2	yes	—
112	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
113	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
114	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
115	C₂×#41×C₃₁	—	2	2	no	—
116	C₂×#41×C₃₁	C₂³	1	2	yes	—
117	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
118	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₃₁×#135	—	2	4	no	—
121	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
122	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂×M₁₆×C₃₁	—	2	4	no	—
125	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂²×C₈×C₃₁	—	2	4	no	—
128	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
136	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×#126	—	2	2	no	—
139	C₃₁×#126	—	2	2	no	—
140	C₃₁×#126	—	2	2	no	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#125	—	2	2	no	—
145	C₃₁×#125	—	2	2	no	—
146	C₃₁×#125	—	2	2	no	—
147	C₃₁×#125	C₂³	1	2	yes	—
148	C₃₁×#125	C₂³	1	2	yes	—
149	C₃₁×#124	—	2	2	no	—
150	C₃₁×#124	—	2	2	no	—
151	C₃₁×#124	—	2	2	no	—
152	C₃₁×#123	—	2	2	no	—
153	C₃₁×#123	—	2	2	no	—
154	C₃₁×#123	—	2	2	no	—
155	C₃₁×#123	—	2	2	no	—
156	C₃₁×#123	—	2	2	no	—
157	C₃₁×#123	—	2	2	no	—
158	C₃₁×#123	—	2	2	no	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×C₂²⋊Q₈	—	2	2	no	—
161	C₃₁×C₂²⋊Q₈	—	2	2	no	—
162	C₃₁×C₂²⋊Q₈	—	2	2	no	—
163	C₃₁×C₂²⋊Q₈	—	2	2	no	—
164	C₃₁×C₂²⋊Q₈	—	2	2	no	—
165	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
167	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₃₁×#121	—	2	2	no	—
170	C₃₁×#121	—	2	2	no	—
171	C₃₁×#121	—	2	2	no	—
172	C₃₁×#121	C₂³	1	2	yes	—
173	C₃₁×#121	C₂³	1	2	yes	—
174	C₃₁×#121	C₂³	1	2	yes	—
175	C₃₁×#121	C₂³	1	2	yes	—
176	C₃₁×#120	—	2	2	no	—
177	C₃₁×#120	—	2	2	no	—
178	C₄×Q₈×C₃₁	—	2	2	no	—
179	C₄×Q₈×C₃₁	—	2	2	no	—
180	C₄×Q₈×C₃₁	—	2	2	no	—
181	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
182	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
183	C₄×D₄×C₃₁	—	2	2	no	—
184	C₄×D₄×C₃₁	—	2	2	no	—
185	C₄×D₄×C₃₁	—	2	2	no	—
186	C₄×D₄×C₃₁	—	2	2	no	—
187	C₄×D₄×C₃₁	—	2	2	no	—
188	C₄×D₄×C₃₁	—	2	2	no	—
189	C₄×D₄×C₃₁	—	2	2	no	—
190	C₄×D₄×C₃₁	—	2	2	no	—
191	C₄×D₄×C₃₁	—	2	2	no	—
192	C₄×D₄×C₃₁	D₄	1	2	yes	—
193	C₄×D₄×C₃₁	D₄	1	2	yes	—
194	C₄×D₄×C₃₁	C₂³	1	2	yes	—
195	C₄×D₄×C₃₁	C₂³	1	2	yes	—
196	C₄×D₄×C₃₁	C₂³	1	2	yes	—
197	C₄×D₄×C₃₁	C₂³	1	2	yes	—
198	C₃₁×#117	—	2	2	no	—
199	C₃₁×#117	—	2	2	no	—
200	C₃₁×#117	—	2	2	no	—
201	C₃₁×#117	—	2	2	no	—
202	C₃₁×#117	—	2	2	no	—
203	C₃₁×#117	—	2	2	no	—
204	C₃₁×#117	—	2	2	no	—
205	C₃₁×#117	—	2	2	no	—
206	C₃₁×#117	C₂³	1	2	yes	—
207	C₃₁×#117	C₂³	1	2	yes	—
208	C₃₁×#117	C₂³	1	2	yes	—
209	C₃₁×#117	C₂³	1	2	yes	—
210	C₃₁×#117	C₂³	1	2	yes	—
211	C₃₁×#117	C₂³	1	2	yes	—
212	C₃₁×#117	C₂³	1	2	yes	—
213	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
214	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
215	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
216	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
217	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
219	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
220	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₃₁	—	2	2	no	—
223	C₂×C₄²×C₃₁	—	2	2	no	—
224	C₂×C₄²×C₃₁	—	2	2	no	—
225	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
226	C₃₁×#107	C₂³	1	1	yes	characteristic
227	C₃₁×#107	C₂³	1	1	yes	characteristic
228	C₃₁×#107	C₂³	1	1	yes	characteristic
229	C₃₁×#107	C₂³	1	1	yes	characteristic
230	C₃₁×#107	C₂³	1	2	yes	—
231	C₃₁×#107	C₂³	1	2	yes	—
232	C₃₁×#107	C₂³	1	1	yes	characteristic
233	C₃₁×#107	C₂³	1	1	yes	characteristic
234	C₃₁×#107	C₂³	1	2	yes	—
235	C₃₁×#107	C₂³	1	2	yes	—
236	C₃₁×#107	C₂³	1	2	yes	—
237	C₃₁×#107	C₂³	1	2	yes	—
238	C₃₁×#106	C₂³	1	2	yes	—
239	C₃₁×#106	C₂³	1	2	yes	—
240	C₃₁×#106	C₂³	1	2	yes	—
241	C₃₁×#106	C₂³	1	2	yes	—
242	C₃₁×#106	C₂³	1	2	yes	—
243	C₃₁×#106	C₂³	1	2	yes	—
244	C₃₁×#106	C₂³	1	2	yes	—
245	C₃₁×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
249	C₃₁×#103	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#103	C₂³	1	2	yes	—
253	C₃₁×#103	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#102	C₂³	1	2	yes	—
256	C₃₁×#102	C₂³	1	2	yes	—
257	C₃₁×#102	C₂³	1	2	yes	—
258	C₃₁×#102	C₂³	1	2	yes	—
259	C₃₁×#102	C₂³	1	2	yes	—
260	C₃₁×#102	C₂³	1	2	yes	—
261	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
262	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
263	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
264	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
265	C₃₁×#97	C₂³	1	2	yes	—
266	C₃₁×#97	C₂³	1	2	yes	—
267	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
268	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
269	#41×C₃₁	—	2	4	no	—
270	#41×C₃₁	—	2	4	no	—
271	#41×C₃₁	—	4	8	no	—
272	C₂×Q₈×C₃₁	—	2	2	no	—
273	C₂×Q₈×C₃₁	—	2	2	no	—
274	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
275	C₂×D₄×C₃₁	—	2	2	no	—
276	C₂×D₄×C₃₁	—	2	2	no	—
277	C₂×D₄×C₃₁	—	2	2	no	—
278	C₂×D₄×C₃₁	—	2	2	no	—
279	C₂×D₄×C₃₁	—	2	2	no	—
280	C₂×D₄×C₃₁	—	4	2	no	—
281	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₃₁	—	2	2	no	—
285	C₂²×C₄×C₃₁	—	2	2	no	—
286	C₂²×C₄×C₃₁	—	2	2	no	—
287	C₂²×C₄×C₃₁	—	2	2	no	—
288	C₂²×C₄×C₃₁	—	2	2	no	—
289	C₂²×C₄×C₃₁	—	2	2	no	—
290	C₂²×C₄×C₃₁	—	2	2	no	—
291	C₂²×C₄×C₃₁	—	2	2	no	—
292	C₂²×C₄×C₃₁	—	2	2	no	—
293	C₂²×C₄×C₃₁	—	2	2	no	—
294	C₂²×C₄×C₃₁	—	2	2	no	—
295	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
306	Q₁₆×C₃₁	—	2	2	no	—
307	SD₁₆×C₃₁	—	2	4	no	—
308	D₈×C₃₁	—	2	2	no	—
309	M₁₆×C₃₁	—	2	4	no	—
310	M₁₆×C₃₁	—	2	4	no	—
311	C₂×C₈×C₃₁	—	2	2	no	—
312	C₂×C₈×C₃₁	—	2	2	no	—
313	C₂×C₈×C₃₁	—	2	2	no	—
314	C₂×C₈×C₃₁	—	2	2	no	—
315	C₂×C₈×C₃₁	—	2	2	no	—
316	C₂×C₈×C₃₁	—	2	2	no	—
317	C₂×C₈×C₃₁	—	2	2	no	—
318	C₂×C₈×C₃₁	#41	1	4	yes	complemented
319	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
320	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
322	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₄⋊C₄×C₃₁	—	2	2	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	2	no	—
328	C₄⋊C₄×C₃₁	—	2	2	no	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	2	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	—	2	2	no	—
336	C₄⋊C₄×C₃₁	—	2	2	no	—
337	C₄⋊C₄×C₃₁	—	2	2	no	—
338	C₄⋊C₄×C₃₁	—	2	2	no	—
339	C₄⋊C₄×C₃₁	—	2	2	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
342	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
349	C₂²⋊C₄×C₃₁	—	2	2	no	—
350	C₂²⋊C₄×C₃₁	—	2	2	no	—
351	C₂²⋊C₄×C₃₁	—	2	2	no	—
352	C₂²⋊C₄×C₃₁	—	2	2	no	—
353	C₂²⋊C₄×C₃₁	—	2	2	no	—
354	C₂²⋊C₄×C₃₁	—	2	2	no	—
355	C₂²⋊C₄×C₃₁	—	2	2	no	—
356	C₂²⋊C₄×C₃₁	—	2	2	no	—
357	C₂²⋊C₄×C₃₁	—	2	2	no	—
358	C₂²⋊C₄×C₃₁	—	2	2	no	—
359	C₂²⋊C₄×C₃₁	—	2	2	no	—
360	C₂²⋊C₄×C₃₁	—	2	2	no	—
361	C₂²⋊C₄×C₃₁	—	2	2	no	—
362	C₂²⋊C₄×C₃₁	—	2	2	no	—
363	C₂²⋊C₄×C₃₁	—	2	2	no	—
364	C₂²⋊C₄×C₃₁	—	2	2	no	—
365	C₂²⋊C₄×C₃₁	—	2	2	no	—
366	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
368	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
369	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
370	C₄²×C₃₁	—	2	2	no	—
371	C₄²×C₃₁	—	2	2	no	—
372	C₄²×C₃₁	—	2	2	no	—
373	C₄²×C₃₁	—	2	2	no	—
374	C₄²×C₃₁	—	2	2	no	—
375	C₄²×C₃₁	—	2	2	no	—
376	C₄²×C₃₁	—	2	2	no	—
377	C₄²×C₃₁	—	2	2	no	—
378	C₄²×C₃₁	—	2	2	no	—
379	C₄²×C₃₁	C₂×D₄	1	2	yes	—
380	C₄²×C₃₁	C₂⁴	1	2	yes	—
381	#61243	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₂³×C₃₁	—	2	2	no	—
383	C₂³×C₃₁	—	2	2	no	—
384	C₂³×C₃₁	—	2	2	no	—
385	C₂³×C₃₁	—	2	2	no	—
386	C₂³×C₃₁	—	4	1	no	—
387	C₂³×C₃₁	—	4	1	no	—
388	C₂³×C₃₁	—	4	1	no	—
389	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
390	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
391	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
392	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
393	Q₈×C₃₁	—	2	2	no	—
394	Q₈×C₃₁	—	2	2	no	—
395	Q₈×C₃₁	—	4	4	no	—
396	Q₈×C₃₁	—	8	2	no	—
397	D₄×C₃₁	—	2	4	no	—
398	D₄×C₃₁	—	2	2	no	—
399	D₄×C₃₁	—	2	2	no	—
400	D₄×C₃₁	—	4	2	no	—
401	D₄×C₃₁	—	4	4	no	—
402	D₄×C₃₁	—	4	4	no	—
403	D₄×C₃₁	—	4	4	no	—
404	D₄×C₃₁	—	8	2	no	—
405	D₄×C₃₁	—	8	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	4	no	—
411	C₂×C₄×C₃₁	—	2	1	no	—
412	C₂×C₄×C₃₁	—	2	1	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	1	no	—
415	C₂×C₄×C₃₁	—	2	2	no	—
416	C₂×C₄×C₃₁	—	2	1	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	2	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	2	no	—
424	C₂×C₄×C₃₁	—	4	1	no	—
425	C₂×C₄×C₃₁	—	4	1	no	—
426	C₂×C₄×C₃₁	—	4	4	no	—
427	C₂×C₄×C₃₁	—	4	4	no	—
428	C₂×C₄×C₃₁	—	4	4	no	—
429	C₂×C₄×C₃₁	—	4	4	no	—
430	C₂×C₄×C₃₁	—	8	2	no	—
431	C₂×C₄×C₃₁	—	8	2	no	—
432	C₂×C₄×C₃₁	—	8	2	no	—
433	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
440	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
441	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
442	C₈×C₃₁	—	2	1	no	—
443	C₈×C₃₁	—	2	1	no	—
444	C₈×C₃₁	—	2	2	no	—
445	C₈×C₃₁	—	2	2	no	—
446	C₈×C₃₁	C₂×#41	1	2	yes	—
447	C₈×C₃₁	C₂×#41	1	2	yes	—
448	#3475	C₂×C₃₁	1	2	yes	complemented
449	#3350	C₂×C₃₁	1	2	yes	complemented
450	#3349	C₂×C₃₁	1	2	yes	complemented
451	#3348	C₂×C₃₁	1	2	yes	complemented
452	#3347	C₂×C₃₁	1	2	yes	complemented
453	#3346	C₂×C₃₁	1	2	yes	complemented
454	#3345	C₂×C₃₁	1	2	yes	complemented
455	#3344	C₂×C₃₁	1	2	yes	complemented
456	#3343	C₂×C₃₁	1	2	yes	complemented
457	#3162	C₂×C₃₁	1	1	yes	characteristic, complemented
458	#3091	C₂×C₃₁	1	2	yes	complemented
459	#3091	C₂×C₃₁	1	2	yes	complemented
460	#3076	C₂×C₃₁	1	2	yes	complemented
461	#3054	C₂×C₃₁	1	1	yes	characteristic, complemented
462	#3050	C₂×C₃₁	1	1	yes	characteristic, complemented
463	#2943	C₂×C₃₁	1	1	yes	characteristic, complemented
464	C₂×#435	C₂×C₃₁	1	1	yes	characteristic, complemented
465	#2911	C₂×C₃₁	1	1	yes	characteristic, complemented
466	C₂×#427	C₂×C₃₁	1	1	yes	characteristic, complemented
467	C₂²×C₃₁	—	2	1	no	—
468	C₂²×C₃₁	—	2	1	no	—
469	C₂²×C₃₁	—	2	1	no	—
470	C₂²×C₃₁	—	2	1	no	—
471	C₂²×C₃₁	—	2	2	no	—
472	C₂²×C₃₁	—	2	1	no	—
473	C₂²×C₃₁	—	2	1	no	—
474	C₂²×C₃₁	—	2	2	no	—
475	C₂²×C₃₁	—	2	2	no	—
476	C₂²×C₃₁	—	2	1	no	—
477	C₂²×C₃₁	—	4	4	no	—
478	C₂²×C₃₁	—	4	2	no	—
479	C₂²×C₃₁	—	4	2	no	—
480	C₂²×C₃₁	—	4	2	no	—
481	C₂²×C₃₁	—	8	2	no	—
482	C₂²×C₃₁	#547	1	2	yes	—
483	C₂²×C₃₁	#575	1	2	yes	—
484	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
485	C₄×C₃₁	—	2	2	no	—
486	C₄×C₃₁	—	2	1	no	—
487	C₄×C₃₁	—	2	1	no	—
488	C₄×C₃₁	—	2	2	no	—
489	C₄×C₃₁	—	2	2	no	—
490	C₄×C₃₁	—	4	2	no	—
491	C₄×C₃₁	—	4	2	no	—
492	C₄×C₃₁	—	4	2	no	—
493	C₄×C₃₁	—	4	2	no	—
494	C₄×C₃₁	—	4	2	no	—
495	C₄×C₃₁	—	4	2	no	—
496	C₄×C₃₁	—	4	2	no	—
497	C₄×C₃₁	#547	1	2	yes	—
498	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
499	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
500	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
501	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
502	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
503	#556	C₂²×C₃₁	1	2	yes	—
504	#555	C₂²×C₃₁	1	2	yes	—
505	#554	C₂²×C₃₁	1	2	yes	—
506	#553	C₂²×C₃₁	1	2	yes	—
507	#553	C₂²×C₃₁	1	2	yes	—
508	#552	—	2	2	no	—
509	#552	C₂²×C₃₁	1	2	yes	—
510	#552	C₂²×C₃₁	1	2	yes	—
511	#551	—	2	2	no	—
512	#551	—	2	2	no	—
513	#547	C₂²×C₃₁	1	2	yes	—
514	#546	—	2	2	no	—
515	#533	C₂²×C₃₁	1	2	yes	—
516	#529	—	2	2	no	—
517	#529	—	2	2	no	—
518	#529	—	2	2	no	—
519	#525	C₂²×C₃₁	1	2	yes	—
520	#525	C₂²×C₃₁	1	2	yes	—
521	C₄×#41	—	2	2	no	—
522	C₄×#41	C₂²×C₃₁	1	2	yes	—
523	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
524	C₂×#117	C₂²×C₃₁	1	2	yes	—
525	C₂×#117	C₂²×C₃₁	1	2	yes	—
526	#501	C₂²×C₃₁	1	2	yes	complemented
527	#501	C₂²×C₃₁	1	2	yes	complemented
528	#501	C₂²×C₃₁	1	2	yes	complemented
529	#501	C₂²×C₃₁	1	2	yes	complemented
530	#485	C₂²×C₃₁	1	2	yes	complemented
531	#485	C₂²×C₃₁	1	2	yes	complemented
532	#485	C₂²×C₃₁	1	2	yes	complemented
533	#485	C₂²×C₃₁	1	2	yes	complemented
534	#484	C₂²×C₃₁	1	2	yes	complemented
535	#484	C₂²×C₃₁	1	2	yes	complemented
536	#483	C₂²×C₃₁	1	2	yes	complemented
537	#483	C₂²×C₃₁	1	2	yes	complemented
538	#482	C₂²×C₃₁	1	2	yes	complemented
539	#482	C₂²×C₃₁	1	2	yes	complemented
540	#482	C₂²×C₃₁	1	2	yes	complemented
541	#482	C₂²×C₃₁	1	2	yes	complemented
542	#481	C₂²×C₃₁	1	2	yes	complemented
543	#481	C₂²×C₃₁	1	2	yes	complemented
544	#480	C₂²×C₃₁	1	2	yes	complemented
545	#480	C₂²×C₃₁	1	2	yes	complemented
546	#479	C₂²×C₃₁	1	2	yes	complemented
547	#479	C₂²×C₃₁	1	2	yes	complemented
548	#478	C₂²×C₃₁	1	2	yes	complemented
549	#478	C₂²×C₃₁	1	2	yes	complemented
550	#477	C₂²×C₃₁	1	2	yes	complemented
551	#476	C₂²×C₃₁	1	2	yes	complemented
552	#475	C₂²×C₃₁	1	2	yes	complemented
553	#474	C₂²×C₃₁	1	2	yes	complemented
554	#470	C₂²×C₃₁	1	2	yes	complemented
555	#469	C₂²×C₃₁	1	2	yes	complemented
556	#468	C₂²×C₃₁	1	2	yes	complemented
557	#468	C₂²×C₃₁	1	2	yes	complemented
558	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
559	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
560	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
561	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
562	#465	C₂²×C₃₁	1	2	yes	complemented
563	#465	C₂²×C₃₁	1	2	yes	complemented
564	#442	C₂²×C₃₁	1	2	yes	complemented
565	#441	C₂²×C₃₁	1	2	yes	complemented
566	#440	C₂²×C₃₁	1	2	yes	complemented
567	#440	C₂²×C₃₁	1	2	yes	complemented
568	#435	C₂²×C₃₁	1	2	yes	—
569	#435	C₂²×C₃₁	1	2	yes	—
570	#435	C₂²×C₃₁	1	2	yes	—
571	#435	C₂²×C₃₁	1	2	yes	—
572	#428	C₂²×C₃₁	1	2	yes	complemented
573	#428	C₂²×C₃₁	1	2	yes	complemented
574	#428	C₂²×C₃₁	1	2	yes	complemented
575	#428	C₂²×C₃₁	1	2	yes	complemented
576	#427	C₂²×C₃₁	1	2	yes	—
577	#427	C₂²×C₃₁	1	2	yes	—
578	#427	C₂²×C₃₁	1	2	yes	—
579	#427	C₂²×C₃₁	1	1	yes	characteristic
580	#427	C₂²×C₃₁	1	1	yes	characteristic
581	#427	C₂²×C₃₁	1	1	yes	characteristic
582	#427	C₂²×C₃₁	1	2	yes	complemented
583	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
584	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
585	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
586	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
587	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
588	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
589	#416	C₂²×C₃₁	1	2	yes	—
590	#416	C₂²×C₃₁	1	2	yes	—
591	#416	C₂²×C₃₁	1	2	yes	—
592	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
593	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
594	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
595	C₂×C₃₁	—	2	2	no	—
596	C₂×C₃₁	—	2	2	no	—
597	C₂×C₃₁	—	4	1	no	—
598	C₂×C₃₁	—	4	2	no	—
599	C₂×C₃₁	—	8	2	no	—
600	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
601	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
602	C₂×C₃₁	#3584	1	1	yes	characteristic
603	C₂×#41	—	2	2	no	—
604	C₂×#41	C₂³×C₃₁	1	2	yes	—
605	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
608	#135	—	2	4	no	—
609	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
610	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
611	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
612	C₂×M₁₆	—	2	4	no	—
613	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
614	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
615	C₂²×C₈	—	2	4	no	—
616	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
617	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
618	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
619	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
620	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
621	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
622	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
623	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
625	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
626	#126	—	2	2	no	—
627	#126	—	2	2	no	—
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#125	—	2	2	no	—
633	#125	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	C₂³×C₃₁	1	2	yes	—
636	#125	C₂³×C₃₁	1	2	yes	—
637	#124	—	2	2	no	—
638	#124	—	2	2	no	—
639	#124	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	#123	—	2	2	no	—
643	#123	—	2	2	no	—
644	#123	—	2	2	no	—
645	#123	—	2	2	no	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	C₂²⋊Q₈	—	2	2	no	—
649	C₂²⋊Q₈	—	2	2	no	—
650	C₂²⋊Q₈	—	2	2	no	—
651	C₂²⋊Q₈	—	2	2	no	—
652	C₂²⋊Q₈	—	2	2	no	—
653	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
654	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
655	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
656	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
657	#121	—	2	2	no	—
658	#121	—	2	2	no	—
659	#121	—	2	2	no	—
660	#121	C₂³×C₃₁	1	2	yes	—
661	#121	C₂³×C₃₁	1	2	yes	—
662	#121	C₂³×C₃₁	1	2	yes	—
663	#121	C₂³×C₃₁	1	2	yes	—
664	#120	—	2	2	no	—
665	#120	—	2	2	no	—
666	C₄×Q₈	—	2	2	no	—
667	C₄×Q₈	—	2	2	no	—
668	C₄×Q₈	—	2	2	no	—
669	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
670	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	D₄×C₃₁	1	2	yes	—
681	C₄×D₄	D₄×C₃₁	1	2	yes	—
682	C₄×D₄	C₂³×C₃₁	1	2	yes	—
683	C₄×D₄	C₂³×C₃₁	1	2	yes	—
684	C₄×D₄	C₂³×C₃₁	1	2	yes	—
685	C₄×D₄	C₂³×C₃₁	1	2	yes	—
686	#117	—	2	2	no	—
687	#117	—	2	2	no	—
688	#117	—	2	2	no	—
689	#117	—	2	2	no	—
690	#117	—	2	2	no	—
691	#117	—	2	2	no	—
692	#117	—	2	2	no	—
693	#117	—	2	2	no	—
694	#117	C₂³×C₃₁	1	2	yes	—
695	#117	C₂³×C₃₁	1	2	yes	—
696	#117	C₂³×C₃₁	1	2	yes	—
697	#117	C₂³×C₃₁	1	2	yes	—
698	#117	C₂³×C₃₁	1	2	yes	—
699	#117	C₂³×C₃₁	1	2	yes	—
700	#117	C₂³×C₃₁	1	2	yes	—
701	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
706	C₂×C₂²⋊C₄	—	2	2	no	—
707	C₂×C₂²⋊C₄	—	2	2	no	—
708	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
709	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
710	C₂×C₄²	—	2	2	no	—
711	C₂×C₄²	—	2	2	no	—
712	C₂×C₄²	—	2	2	no	—
713	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
714	#107	C₂³×C₃₁	1	1	yes	characteristic
715	#107	C₂³×C₃₁	1	1	yes	characteristic
716	#107	C₂³×C₃₁	1	1	yes	characteristic
717	#107	C₂³×C₃₁	1	1	yes	characteristic
718	#107	C₂³×C₃₁	1	2	yes	—
719	#107	C₂³×C₃₁	1	2	yes	—
720	#107	C₂³×C₃₁	1	1	yes	characteristic
721	#107	C₂³×C₃₁	1	1	yes	characteristic
722	#107	C₂³×C₃₁	1	2	yes	—
723	#107	C₂³×C₃₁	1	2	yes	—
724	#107	C₂³×C₃₁	1	2	yes	—
725	#107	C₂³×C₃₁	1	2	yes	—
726	#106	C₂³×C₃₁	1	2	yes	—
727	#106	C₂³×C₃₁	1	2	yes	—
728	#106	C₂³×C₃₁	1	2	yes	—
729	#106	C₂³×C₃₁	1	2	yes	—
730	#106	C₂³×C₃₁	1	2	yes	—
731	#106	C₂³×C₃₁	1	2	yes	—
732	#106	C₂³×C₃₁	1	2	yes	—
733	#106	C₂³×C₃₁	1	2	yes	—
734	#106	C₂³×C₃₁	1	2	yes	—
735	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
736	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
737	#103	C₂³×C₃₁	1	2	yes	—
738	#103	C₂³×C₃₁	1	2	yes	—
739	#103	C₂³×C₃₁	1	2	yes	—
740	#103	C₂³×C₃₁	1	2	yes	—
741	#103	C₂³×C₃₁	1	2	yes	—
742	#103	C₂³×C₃₁	1	2	yes	—
743	#102	C₂³×C₃₁	1	2	yes	—
744	#102	C₂³×C₃₁	1	2	yes	—
745	#102	C₂³×C₃₁	1	2	yes	—
746	#102	C₂³×C₃₁	1	2	yes	—
747	#102	C₂³×C₃₁	1	2	yes	—
748	#102	C₂³×C₃₁	1	2	yes	—
749	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
750	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
751	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
752	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
753	#97	C₂³×C₃₁	1	2	yes	—
754	#97	C₂³×C₃₁	1	2	yes	—
755	C₃₁	#61243	1	1	yes	characteristic, direct product factor, Sylow
756	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
757	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
758	#41	—	2	4	no	—
759	#41	—	2	4	no	—
760	#41	—	4	8	no	—
761	C₂×Q₈	—	2	2	no	—
762	C₂×Q₈	—	2	2	no	—
763	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
771	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
772	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
785	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
786	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
790	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
795	Q₁₆	—	2	2	no	—
796	SD₁₆	—	2	4	no	—
797	D₈	—	2	2	no	—
798	M₁₆	—	2	4	no	—
799	M₁₆	—	2	4	no	—
800	C₂×C₈	—	2	2	no	—
801	C₂×C₈	—	2	2	no	—
802	C₂×C₈	—	2	2	no	—
803	C₂×C₈	—	2	2	no	—
804	C₂×C₈	—	2	2	no	—
805	C₂×C₈	—	2	2	no	—
806	C₂×C₈	—	2	2	no	—
807	C₂×C₈	#41×C₃₁	1	4	yes	complemented
808	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
809	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
810	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
811	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
812	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
813	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
831	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
832	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
833	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
834	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
835	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
836	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
837	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
856	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
857	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
858	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
859	C₄²	—	2	2	no	—
860	C₄²	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	C₂×D₄×C₃₁	1	2	yes	—
869	C₄²	C₂⁴×C₃₁	1	2	yes	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	4	1	no	—
875	C₂³	—	4	1	no	—
876	C₂³	—	4	1	no	—
877	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
878	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
879	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
880	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
881	Q₈	—	2	2	no	—
882	Q₈	—	2	2	no	—
883	Q₈	—	4	4	no	—
884	Q₈	—	8	2	no	—
885	D₄	—	2	4	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	2	no	—
888	D₄	—	4	2	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	4	no	—
891	D₄	—	4	4	no	—
892	D₄	—	8	2	no	—
893	D₄	—	8	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	4	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	4	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	4	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	8	2	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
922	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
923	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
924	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
925	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
926	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
927	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
928	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
929	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
930	C₈	—	2	1	no	—
931	C₈	—	2	1	no	—
932	C₈	—	2	2	no	—
933	C₈	—	2	2	no	—
934	C₈	C₂×#41×C₃₁	1	2	yes	—
935	C₈	C₂×#41×C₃₁	1	2	yes	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	4	4	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	8	2	no	—
951	C₂²	C₃₁×#547	1	2	yes	—
952	C₂²	C₃₁×#575	1	2	yes	—
953	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	2	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	4	2	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	C₃₁×#547	1	2	yes	—
967	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
968	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
969	C₂	—	2	2	no	—
970	C₂	—	2	2	no	—
971	C₂	—	4	1	no	—
972	C₂	—	4	2	no	—
973	C₂	—	8	2	no	—
974	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
975	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
976	C₂	C₃₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3475	C₂	semidirect
2. C₃₁×#3350	C₂	semidirect
3. C₃₁×#3349	C₂	semidirect
4. C₃₁×#3348	C₂	semidirect
5. C₃₁×#3347	C₂	semidirect
6. C₃₁×#3346	C₂	semidirect
7. C₃₁×#3345	C₂	semidirect
8. C₃₁×#3344	C₂	semidirect
9. C₃₁×#3343	C₂	semidirect
10. C₃₁×#3162	C₂	semidirect
11. C₃₁×#3091	C₂	semidirect
12. C₃₁×#3091	C₂	semidirect
13. C₃₁×#3076	C₂	semidirect
14. C₃₁×#3054	C₂	semidirect
15. C₃₁×#3050	C₂	semidirect
16. C₃₁×#2943	C₂	semidirect
17. C₂×C₃₁×#435	C₂	semidirect
18. C₃₁×#2911	C₂	semidirect
19. C₂×C₃₁×#427	C₂	semidirect
46. C₃₁×#501	C₂²	semidirect
47. C₃₁×#501	C₂²	semidirect
48. C₃₁×#501	C₂²	semidirect
49. C₃₁×#501	C₂²	semidirect
50. C₃₁×#485	C₂²	semidirect
51. C₃₁×#485	C₂²	semidirect
52. C₃₁×#485	C₂²	semidirect
53. C₃₁×#485	C₂²	semidirect
54. C₃₁×#484	C₂²	semidirect
55. C₃₁×#484	C₂²	semidirect
56. C₃₁×#483	C₂²	semidirect
57. C₃₁×#483	C₂²	semidirect
58. C₃₁×#482	C₂²	semidirect
59. C₃₁×#482	C₂²	semidirect
60. C₃₁×#482	C₂²	semidirect
61. C₃₁×#482	C₂²	semidirect
62. C₃₁×#481	C₂²	semidirect
63. C₃₁×#481	C₂²	semidirect
64. C₃₁×#480	C₂²	semidirect
65. C₃₁×#480	C₂²	semidirect
66. C₃₁×#479	C₂²	semidirect
67. C₃₁×#479	C₂²	semidirect
68. C₃₁×#478	C₂²	semidirect
69. C₃₁×#478	C₂²	semidirect
70. C₃₁×#477	C₂²	semidirect
71. C₃₁×#476	C₂²	semidirect
72. C₃₁×#475	C₂²	semidirect
73. C₃₁×#474	C₂²	semidirect
74. C₃₁×#470	C₂²	semidirect
75. C₃₁×#469	C₂²	semidirect
76. C₃₁×#468	C₂²	semidirect
77. C₃₁×#468	C₂²	semidirect
78. C₃₁×#467	C₂²	semidirect
79. C₃₁×#467	C₂²	semidirect
80. C₃₁×#466	C₂²	semidirect
81. C₃₁×#466	C₂²	semidirect
82. C₃₁×#465	C₂²	semidirect
83. C₃₁×#465	C₂²	semidirect
84. C₃₁×#442	C₂²	semidirect
85. C₃₁×#441	C₂²	semidirect
86. C₃₁×#440	C₂²	semidirect
87. C₃₁×#440	C₂²	semidirect
92. C₃₁×#428	C₂²	semidirect
93. C₃₁×#428	C₂²	semidirect
94. C₃₁×#428	C₂²	semidirect
95. C₃₁×#428	C₂²	semidirect
102. C₃₁×#427	C₂²	semidirect
103. C₃₁×#427	C₂²	semidirect
104. C₃₁×#427	C₂²	semidirect
105. C₂×C₃₁×#107	C₂²	semidirect
106. C₂×C₃₁×#107	C₂²	semidirect
107. C₂×C₃₁×#106	C₂²	semidirect
318. C₂×C₈×C₃₁	#41	semidirect
381. #61243	C₃₁	direct (N × H)
448. #3475	C₂×C₃₁	semidirect
449. #3350	C₂×C₃₁	semidirect
450. #3349	C₂×C₃₁	semidirect
451. #3348	C₂×C₃₁	semidirect
452. #3347	C₂×C₃₁	semidirect
453. #3346	C₂×C₃₁	semidirect
454. #3345	C₂×C₃₁	semidirect
455. #3344	C₂×C₃₁	semidirect
456. #3343	C₂×C₃₁	semidirect
457. #3162	C₂×C₃₁	semidirect
458. #3091	C₂×C₃₁	semidirect
459. #3091	C₂×C₃₁	semidirect
460. #3076	C₂×C₃₁	semidirect
461. #3054	C₂×C₃₁	semidirect
462. #3050	C₂×C₃₁	semidirect
463. #2943	C₂×C₃₁	semidirect
464. C₂×#435	C₂×C₃₁	semidirect
465. #2911	C₂×C₃₁	semidirect
466. C₂×#427	C₂×C₃₁	semidirect
526. #501	C₂²×C₃₁	semidirect
527. #501	C₂²×C₃₁	semidirect
528. #501	C₂²×C₃₁	semidirect
529. #501	C₂²×C₃₁	semidirect
530. #485	C₂²×C₃₁	semidirect
531. #485	C₂²×C₃₁	semidirect
532. #485	C₂²×C₃₁	semidirect
533. #485	C₂²×C₃₁	semidirect
534. #484	C₂²×C₃₁	semidirect
535. #484	C₂²×C₃₁	semidirect
536. #483	C₂²×C₃₁	semidirect
537. #483	C₂²×C₃₁	semidirect
538. #482	C₂²×C₃₁	semidirect
539. #482	C₂²×C₃₁	semidirect
540. #482	C₂²×C₃₁	semidirect
541. #482	C₂²×C₃₁	semidirect
542. #481	C₂²×C₃₁	semidirect
543. #481	C₂²×C₃₁	semidirect
544. #480	C₂²×C₃₁	semidirect
545. #480	C₂²×C₃₁	semidirect
546. #479	C₂²×C₃₁	semidirect
547. #479	C₂²×C₃₁	semidirect
548. #478	C₂²×C₃₁	semidirect
549. #478	C₂²×C₃₁	semidirect
550. #477	C₂²×C₃₁	semidirect
551. #476	C₂²×C₃₁	semidirect
552. #475	C₂²×C₃₁	semidirect
553. #474	C₂²×C₃₁	semidirect
554. #470	C₂²×C₃₁	semidirect
555. #469	C₂²×C₃₁	semidirect
556. #468	C₂²×C₃₁	semidirect
557. #468	C₂²×C₃₁	semidirect
558. #467	C₂²×C₃₁	semidirect
559. #467	C₂²×C₃₁	semidirect
560. #466	C₂²×C₃₁	semidirect
561. #466	C₂²×C₃₁	semidirect
562. #465	C₂²×C₃₁	semidirect
563. #465	C₂²×C₃₁	semidirect
564. #442	C₂²×C₃₁	semidirect
565. #441	C₂²×C₃₁	semidirect
566. #440	C₂²×C₃₁	semidirect
567. #440	C₂²×C₃₁	semidirect
572. #428	C₂²×C₃₁	semidirect
573. #428	C₂²×C₃₁	semidirect
574. #428	C₂²×C₃₁	semidirect
575. #428	C₂²×C₃₁	semidirect
582. #427	C₂²×C₃₁	semidirect
583. #427	C₂²×C₃₁	semidirect
584. #427	C₂²×C₃₁	semidirect
585. C₂×#107	C₂²×C₃₁	semidirect
586. C₂×#107	C₂²×C₃₁	semidirect
587. C₂×#106	C₂²×C₃₁	semidirect
755. C₃₁	#61243	direct (N × H)
807. C₂×C₈	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3475	2
C₃₁×#3350	2
C₃₁×#3349	2
C₃₁×#3348	2
C₃₁×#3347	2
C₃₁×#3346	2
C₃₁×#3345	2
C₃₁×#3344	2
C₃₁×#3343	2
C₃₁×#3162	2
C₃₁×#3091	2
C₃₁×#3076	2
C₃₁×#3054	2
C₃₁×#3050	2
C₃₁×#2943	2
C₂×C₃₁×#435	2
C₃₁×#2911	2
C₂×C₃₁×#427	2
#61243	31

Subgroups — C31×#61243 #21518002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61243 #21518002