Subgroups — C₃₁×#61954 #21518713

Order 7936.

1868 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3394	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3364	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3302	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3301	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3285	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3284	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3248	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3212	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3107	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3035	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#135	C₂²	1	4	yes	—
19	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
20	C₃₁×#559	—	2	1	no	—
21	C₃₁×#559	C₂²	1	1	yes	characteristic
22	C₃₁×#557	C₂²	1	1	yes	characteristic
23	C₃₁×#556	—	2	1	no	—
24	C₃₁×#556	C₂²	1	2	yes	—
25	C₃₁×#556	C₂²	1	1	yes	characteristic
26	C₃₁×#555	—	2	1	no	—
27	C₃₁×#554	—	2	1	no	—
28	C₃₁×#553	—	2	2	no	—
29	C₃₁×#553	—	2	2	no	—
30	C₃₁×#553	C₂²	1	2	yes	—
31	C₃₁×#550	C₂²	1	1	yes	characteristic
32	C₃₁×#548	C₂²	1	2	yes	—
33	C₃₁×#548	C₂²	1	4	yes	—
34	C₃₁×#547	C₂²	1	2	yes	—
35	C₃₁×#542	—	2	2	no	—
36	C₃₁×#537	—	2	1	no	—
37	C₃₁×#533	C₂²	1	2	yes	—
38	C₃₁×#532	—	2	1	no	—
39	C₃₁×#532	C₂²	1	2	yes	—
40	C₃₁×#532	C₂²	1	1	yes	characteristic
41	C₃₁×#532	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃₁×#529	—	2	2	no	—
44	C₃₁×#529	C₂²	1	2	yes	—
45	C₃₁×#520	—	2	1	no	—
46	C₄×#41×C₃₁	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	2	yes	—
48	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
50	C₃₁×#495	C₂²	1	4	yes	—
51	C₃₁×#492	C₂²	1	2	yes	—
52	C₃₁×#488	C₂²	1	4	yes	—
53	C₃₁×#487	C₂²	1	2	yes	—
54	C₃₁×#485	C₂²	1	4	yes	—
55	C₃₁×#481	C₂²	1	2	yes	—
56	C₃₁×#479	C₂²	1	4	yes	—
57	C₃₁×#475	C₂²	1	1	yes	characteristic
58	C₃₁×#475	C₂²	1	1	yes	characteristic
59	C₃₁×#474	C₂²	1	2	yes	—
60	C₃₁×#474	C₂²	1	2	yes	—
61	C₃₁×#467	C₂²	1	4	yes	—
62	C₃₁×#466	C₂²	1	4	yes	—
63	C₃₁×#465	C₂²	1	4	yes	—
64	C₃₁×#464	C₂²	1	4	yes	—
65	C₃₁×#464	C₂²	1	4	yes	—
66	C₃₁×#463	C₂²	1	4	yes	—
67	C₃₁×#462	C₂²	1	2	yes	—
68	C₃₁×#462	C₂²	1	2	yes	—
69	C₃₁×#462	C₂²	1	2	yes	—
70	C₃₁×#462	C₂²	1	2	yes	—
71	C₃₁×#461	C₂²	1	2	yes	—
72	C₃₁×#461	C₂²	1	2	yes	—
73	C₃₁×#460	C₂²	1	1	yes	characteristic
74	C₃₁×#460	C₂²	1	1	yes	characteristic
75	C₃₁×#459	C₂²	1	2	yes	—
76	C₃₁×#459	C₂²	1	2	yes	—
77	C₃₁×#452	C₂²	1	4	yes	—
78	C₃₁×#452	C₂²	1	4	yes	—
79	C₃₁×#449	C₂²	1	4	yes	—
80	C₃₁×#448	C₂²	1	2	yes	—
81	C₃₁×#448	C₂²	1	4	yes	—
82	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
83	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	—
84	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
85	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
86	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
87	C₈×D₄×C₃₁	C₂²	1	2	yes	—
88	C₈×D₄×C₃₁	C₂²	1	4	yes	—
89	C₃₁×#431	C₂²	1	1	yes	characteristic
90	C₃₁×#431	C₂²	1	2	yes	—
91	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
93	C₃₁×#416	C₂²	1	4	yes	—
94	C₂×C₃₁×#103	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	1	no	—
97	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
98	C₂×#41×C₃₁	C₂³	1	2	yes	—
99	C₂×#41×C₃₁	C₂³	1	4	yes	—
100	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
102	C₃₁×#135	—	4	8	no	—
103	C₂×Q₁₆×C₃₁	—	4	4	no	—
104	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
105	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂×D₈×C₃₁	C₂³	1	4	yes	—
111	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
112	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
113	C₃₁×C₄⋊Q₈	—	2	1	no	—
114	C₃₁×C₄⋊Q₈	—	2	1	no	—
115	C₃₁×C₄⋊Q₈	—	2	1	no	—
116	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃₁×#127	—	2	1	no	—
121	C₃₁×#127	C₂³	1	1	yes	characteristic
122	C₃₁×#127	C₂³	1	1	yes	characteristic
123	C₃₁×#126	—	2	2	no	—
124	C₃₁×#126	—	2	4	no	—
125	C₃₁×#126	—	2	2	no	—
126	C₃₁×#126	—	2	2	no	—
127	C₃₁×#125	—	2	2	no	—
128	C₃₁×#125	—	2	2	no	—
129	C₃₁×#125	C₂³	1	2	yes	—
130	C₃₁×#124	—	2	1	no	—
131	C₃₁×#124	—	2	1	no	—
132	C₃₁×#124	—	2	2	no	—
133	C₃₁×#124	—	2	4	no	—
134	C₃₁×#124	—	2	1	no	—
135	C₃₁×#124	—	2	1	no	—
136	C₃₁×#124	C₂³	1	4	yes	—
137	C₃₁×#124	C₂³	1	2	yes	—
138	C₃₁×#123	—	2	2	no	—
139	C₃₁×#123	—	2	2	no	—
140	C₃₁×#123	—	2	2	no	—
141	C₃₁×#123	—	2	4	no	—
142	C₃₁×C₂²⋊Q₈	—	2	2	no	—
143	C₃₁×C₂²⋊Q₈	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	2	no	—
145	C₃₁×C₂²⋊Q₈	—	2	4	no	—
146	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₃₁×#121	—	2	2	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	—	2	2	no	—
151	C₃₁×#121	—	2	4	no	—
152	C₃₁×#121	—	2	2	no	—
153	C₃₁×#121	—	2	1	no	—
154	C₃₁×#121	—	2	1	no	—
155	C₃₁×#121	—	2	2	no	—
156	C₃₁×#121	—	2	2	no	—
157	C₃₁×#121	C₂³	1	2	yes	—
158	C₃₁×#121	C₂³	1	2	yes	—
159	C₃₁×#121	C₂³	1	2	yes	—
160	C₄×Q₈×C₃₁	—	2	1	no	—
161	C₄×Q₈×C₃₁	—	2	1	no	—
162	C₄×Q₈×C₃₁	—	2	1	no	—
163	C₄×Q₈×C₃₁	—	2	1	no	—
164	C₄×Q₈×C₃₁	—	2	2	no	—
165	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
169	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
170	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₃₁	—	2	2	no	—
174	C₄×D₄×C₃₁	—	2	2	no	—
175	C₄×D₄×C₃₁	—	2	2	no	—
176	C₄×D₄×C₃₁	—	2	1	no	—
177	C₄×D₄×C₃₁	—	2	1	no	—
178	C₄×D₄×C₃₁	—	2	2	no	—
179	C₄×D₄×C₃₁	—	2	2	no	—
180	C₄×D₄×C₃₁	—	2	4	no	—
181	C₄×D₄×C₃₁	—	2	2	no	—
182	C₄×D₄×C₃₁	—	2	1	no	—
183	C₄×D₄×C₃₁	—	2	2	no	—
184	C₄×D₄×C₃₁	—	2	1	no	—
185	C₄×D₄×C₃₁	D₄	1	2	yes	—
186	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
187	C₄×D₄×C₃₁	C₂³	1	2	yes	—
188	C₄×D₄×C₃₁	C₂³	1	2	yes	—
189	C₄×D₄×C₃₁	C₂³	1	2	yes	—
190	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₃₁	C₂³	1	2	yes	—
192	C₃₁×#117	—	2	2	no	—
193	C₃₁×#117	—	2	2	no	—
194	C₃₁×#117	—	2	2	no	—
195	C₃₁×#117	—	2	2	no	—
196	C₃₁×#117	D₄	1	1	yes	characteristic
197	C₃₁×#117	D₄	1	2	yes	—
198	C₃₁×#117	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
200	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
201	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
202	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
203	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₃₁	—	2	1	no	—
205	C₂×C₄²×C₃₁	—	2	2	no	—
206	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₃₁×#107	C₂³	1	4	yes	—
209	C₃₁×#106	C₂³	1	2	yes	—
210	C₃₁×#106	C₂³	1	2	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
215	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₃₁×#103	C₂³	1	4	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#103	C₂³	1	4	yes	—
219	C₃₁×#103	C₂³	1	2	yes	—
220	C₃₁×#103	C₂³	1	2	yes	—
221	C₃₁×#103	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	2	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×#102	C₂³	1	2	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₄×C₈×C₃₁	C₂³	1	2	yes	—
229	C₄×C₈×C₃₁	C₂³	1	4	yes	—
230	#41×C₃₁	—	2	4	no	—
231	#41×C₃₁	—	2	4	no	—
232	#41×C₃₁	—	4	2	no	—
233	#41×C₃₁	—	4	4	no	—
234	#41×C₃₁	—	4	4	no	—
235	#41×C₃₁	—	4	4	no	—
236	#41×C₃₁	—	4	4	no	—
237	C₂×Q₈×C₃₁	—	2	1	no	—
238	C₂×Q₈×C₃₁	—	2	1	no	—
239	C₂×Q₈×C₃₁	—	2	1	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	2	2	no	—
242	C₂×Q₈×C₃₁	—	4	1	no	—
243	C₂×Q₈×C₃₁	—	4	2	no	—
244	C₂×Q₈×C₃₁	—	4	2	no	—
245	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	4	no	—
254	C₂×D₄×C₃₁	—	2	1	no	—
255	C₂×D₄×C₃₁	—	2	1	no	—
256	C₂×D₄×C₃₁	—	2	1	no	—
257	C₂×D₄×C₃₁	—	2	1	no	—
258	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
261	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₃₁	—	2	1	no	—
263	C₂²×C₄×C₃₁	—	2	1	no	—
264	C₂²×C₄×C₃₁	—	2	2	no	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	2	2	no	—
267	C₂²×C₄×C₃₁	—	2	2	no	—
268	C₂²×C₄×C₃₁	—	2	2	no	—
269	C₂²×C₄×C₃₁	—	2	4	no	—
270	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
276	Q₁₆×C₃₁	—	2	8	no	—
277	Q₁₆×C₃₁	—	4	4	no	—
278	SD₁₆×C₃₁	—	2	4	no	—
279	SD₁₆×C₃₁	—	4	4	no	—
280	SD₁₆×C₃₁	—	4	2	no	—
281	SD₁₆×C₃₁	—	4	4	no	—
282	D₈×C₃₁	—	4	4	no	—
283	C₂×C₈×C₃₁	—	4	2	no	—
284	C₂×C₈×C₃₁	—	4	4	no	—
285	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
286	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
287	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	4	no	—
293	C₄⋊C₄×C₃₁	—	2	1	no	—
294	C₄⋊C₄×C₃₁	—	2	1	no	—
295	C₄⋊C₄×C₃₁	—	2	1	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	1	no	—
298	C₄⋊C₄×C₃₁	—	2	1	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	2	no	—
302	C₄⋊C₄×C₃₁	—	2	1	no	—
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	4	no	—
305	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
306	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
313	C₂²⋊C₄×C₃₁	—	2	4	no	—
314	C₂²⋊C₄×C₃₁	—	2	2	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	4	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	2	no	—
320	C₂²⋊C₄×C₃₁	—	2	2	no	—
321	C₂²⋊C₄×C₃₁	—	2	4	no	—
322	C₂²⋊C₄×C₃₁	—	2	2	no	—
323	C₂²⋊C₄×C₃₁	—	2	2	no	—
324	C₂²⋊C₄×C₃₁	—	2	2	no	—
325	C₂²⋊C₄×C₃₁	—	2	2	no	—
326	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
329	C₄²×C₃₁	—	2	1	no	—
330	C₄²×C₃₁	—	2	1	no	—
331	C₄²×C₃₁	—	2	2	no	—
332	C₄²×C₃₁	—	2	2	no	—
333	C₄²×C₃₁	—	2	1	no	—
334	C₄²×C₃₁	—	2	1	no	—
335	C₄²×C₃₁	—	2	4	no	—
336	C₄²×C₃₁	C₂×D₄	1	2	yes	—
337	C₄²×C₃₁	C₂×D₄	1	2	yes	—
338	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₄²×C₃₁	C₂⁴	1	2	yes	—
342	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
343	#61954	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂³×C₃₁	—	2	2	no	—
345	C₂³×C₃₁	—	2	2	no	—
346	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
347	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
348	Q₈×C₃₁	—	2	2	no	—
349	Q₈×C₃₁	—	2	1	no	—
350	Q₈×C₃₁	—	2	4	no	—
351	Q₈×C₃₁	—	2	1	no	—
352	Q₈×C₃₁	—	2	1	no	—
353	Q₈×C₃₁	—	2	4	no	—
354	Q₈×C₃₁	—	4	2	no	—
355	Q₈×C₃₁	—	4	2	no	—
356	Q₈×C₃₁	—	4	2	no	—
357	Q₈×C₃₁	—	8	2	no	—
358	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
359	D₄×C₃₁	—	2	4	no	—
360	D₄×C₃₁	—	2	2	no	—
361	D₄×C₃₁	—	2	2	no	—
362	D₄×C₃₁	—	2	2	no	—
363	D₄×C₃₁	—	2	2	no	—
364	D₄×C₃₁	—	2	2	no	—
365	D₄×C₃₁	—	4	4	no	—
366	D₄×C₃₁	—	4	2	no	—
367	D₄×C₃₁	—	4	4	no	—
368	D₄×C₃₁	—	4	4	no	—
369	D₄×C₃₁	—	4	2	no	—
370	D₄×C₃₁	—	4	2	no	—
371	D₄×C₃₁	—	8	1	no	—
372	D₄×C₃₁	—	8	2	no	—
373	D₄×C₃₁	—	8	4	no	—
374	C₂×C₄×C₃₁	—	2	1	no	—
375	C₂×C₄×C₃₁	—	2	4	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	1	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	1	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	4	no	—
386	C₂×C₄×C₃₁	—	4	2	no	—
387	C₂×C₄×C₃₁	—	4	1	no	—
388	C₂×C₄×C₃₁	—	4	4	no	—
389	C₂×C₄×C₃₁	—	4	2	no	—
390	C₂×C₄×C₃₁	—	4	4	no	—
391	C₂×C₄×C₃₁	—	4	4	no	—
392	C₂×C₄×C₃₁	—	8	2	no	—
393	C₂×C₄×C₃₁	—	8	4	no	—
394	C₂×C₄×C₃₁	—	8	1	no	—
395	C₂×C₄×C₃₁	—	8	2	no	—
396	C₂×C₄×C₃₁	#135	1	4	yes	complemented
397	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
406	C₈×C₃₁	—	2	4	no	—
407	C₈×C₃₁	—	2	2	no	—
408	C₈×C₃₁	—	2	2	no	—
409	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
410	#3480	C₂×C₃₁	1	1	yes	characteristic, complemented
411	#3394	C₂×C₃₁	1	2	yes	complemented
412	#3364	C₂×C₃₁	1	2	yes	complemented
413	#3302	C₂×C₃₁	1	2	yes	complemented
414	#3301	C₂×C₃₁	1	4	yes	complemented
415	#3285	C₂×C₃₁	1	4	yes	complemented
416	#3284	C₂×C₃₁	1	2	yes	complemented
417	#3248	C₂×C₃₁	1	2	yes	complemented
418	#3245	C₂×C₃₁	1	1	yes	characteristic, complemented
419	#3212	C₂×C₃₁	1	2	yes	complemented
420	#3206	C₂×C₃₁	1	1	yes	characteristic, complemented
421	#3107	C₂×C₃₁	1	2	yes	complemented
422	#3103	C₂×C₃₁	1	1	yes	characteristic, complemented
423	#3035	C₂×C₃₁	1	2	yes	complemented
424	C₂×#462	C₂×C₃₁	1	1	yes	characteristic, complemented
425	#2988	C₂×C₃₁	1	1	yes	characteristic, complemented
426	C₂²×C₃₁	—	2	1	no	—
427	C₂²×C₃₁	—	2	1	no	—
428	C₂²×C₃₁	—	2	2	no	—
429	C₂²×C₃₁	—	2	2	no	—
430	C₂²×C₃₁	—	2	2	no	—
431	C₂²×C₃₁	—	4	2	no	—
432	C₂²×C₃₁	—	4	2	no	—
433	C₂²×C₃₁	—	4	2	no	—
434	C₂²×C₃₁	—	4	2	no	—
435	C₂²×C₃₁	—	4	2	no	—
436	C₂²×C₃₁	—	4	2	no	—
437	C₂²×C₃₁	C₂×#135	1	2	yes	—
438	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₃₁	—	2	1	no	—
440	C₄×C₃₁	—	2	2	no	—
441	C₄×C₃₁	—	2	1	no	—
442	C₄×C₃₁	—	2	2	no	—
443	C₄×C₃₁	—	2	1	no	—
444	C₄×C₃₁	—	2	2	no	—
445	C₄×C₃₁	—	2	2	no	—
446	C₄×C₃₁	—	4	1	no	—
447	C₄×C₃₁	—	4	1	no	—
448	C₄×C₃₁	—	4	1	no	—
449	C₄×C₃₁	—	4	4	no	—
450	C₄×C₃₁	—	4	2	no	—
451	C₄×C₃₁	—	4	2	no	—
452	C₄×C₃₁	C₂×#135	1	2	yes	—
453	C₄×C₃₁	C₂×#135	1	2	yes	—
454	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
455	C₄×C₃₁	#585	1	1	yes	characteristic
456	C₂×#135	C₂²×C₃₁	1	4	yes	—
457	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
458	#559	—	2	1	no	—
459	#559	C₂²×C₃₁	1	1	yes	characteristic
460	#557	C₂²×C₃₁	1	1	yes	characteristic
461	#556	—	2	1	no	—
462	#556	C₂²×C₃₁	1	2	yes	—
463	#556	C₂²×C₃₁	1	1	yes	characteristic
464	#555	—	2	1	no	—
465	#554	—	2	1	no	—
466	#553	—	2	2	no	—
467	#553	—	2	2	no	—
468	#553	C₂²×C₃₁	1	2	yes	—
469	#550	C₂²×C₃₁	1	1	yes	characteristic
470	#548	C₂²×C₃₁	1	2	yes	—
471	#548	C₂²×C₃₁	1	4	yes	—
472	#547	C₂²×C₃₁	1	2	yes	—
473	#542	—	2	2	no	—
474	#537	—	2	1	no	—
475	#533	C₂²×C₃₁	1	2	yes	—
476	#532	—	2	1	no	—
477	#532	C₂²×C₃₁	1	2	yes	—
478	#532	C₂²×C₃₁	1	1	yes	characteristic
479	#532	C₂²×C₃₁	1	1	yes	characteristic
480	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
481	#529	—	2	2	no	—
482	#529	C₂²×C₃₁	1	2	yes	—
483	#520	—	2	1	no	—
484	C₄×#41	—	2	1	no	—
485	C₄×#41	C₂²×C₃₁	1	2	yes	—
486	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
487	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
488	#495	C₂²×C₃₁	1	4	yes	—
489	#492	C₂²×C₃₁	1	2	yes	—
490	#488	C₂²×C₃₁	1	4	yes	—
491	#487	C₂²×C₃₁	1	2	yes	—
492	#485	C₂²×C₃₁	1	4	yes	—
493	#481	C₂²×C₃₁	1	2	yes	—
494	#479	C₂²×C₃₁	1	4	yes	—
495	#475	C₂²×C₃₁	1	1	yes	characteristic
496	#475	C₂²×C₃₁	1	1	yes	characteristic
497	#474	C₂²×C₃₁	1	2	yes	—
498	#474	C₂²×C₃₁	1	2	yes	—
499	#467	C₂²×C₃₁	1	4	yes	—
500	#466	C₂²×C₃₁	1	4	yes	—
501	#465	C₂²×C₃₁	1	4	yes	—
502	#464	C₂²×C₃₁	1	4	yes	—
503	#464	C₂²×C₃₁	1	4	yes	—
504	#463	C₂²×C₃₁	1	4	yes	—
505	#462	C₂²×C₃₁	1	2	yes	—
506	#462	C₂²×C₃₁	1	2	yes	—
507	#462	C₂²×C₃₁	1	2	yes	—
508	#462	C₂²×C₃₁	1	2	yes	—
509	#461	C₂²×C₃₁	1	2	yes	—
510	#461	C₂²×C₃₁	1	2	yes	—
511	#460	C₂²×C₃₁	1	1	yes	characteristic
512	#460	C₂²×C₃₁	1	1	yes	characteristic
513	#459	C₂²×C₃₁	1	2	yes	—
514	#459	C₂²×C₃₁	1	2	yes	—
515	#452	C₂²×C₃₁	1	4	yes	—
516	#452	C₂²×C₃₁	1	4	yes	—
517	#449	C₂²×C₃₁	1	4	yes	—
518	#448	C₂²×C₃₁	1	2	yes	—
519	#448	C₂²×C₃₁	1	4	yes	—
520	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
521	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	—
522	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
523	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
524	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
525	C₈×D₄	C₂²×C₃₁	1	2	yes	—
526	C₈×D₄	C₂²×C₃₁	1	4	yes	—
527	#431	C₂²×C₃₁	1	1	yes	characteristic
528	#431	C₂²×C₃₁	1	2	yes	—
529	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
530	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
531	#416	C₂²×C₃₁	1	4	yes	—
532	C₂×#103	C₂²×C₃₁	1	2	yes	—
533	C₂×C₃₁	—	2	2	no	—
534	C₂×C₃₁	—	4	2	no	—
535	C₂×C₃₁	—	8	2	no	—
536	C₂×C₃₁	—	8	2	no	—
537	C₂×C₃₁	#3488	1	1	yes	characteristic
538	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
539	C₂×C₃₁	#3586	1	1	yes	characteristic
540	C₂×#41	—	2	1	no	—
541	C₂×#41	—	2	1	no	—
542	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
543	C₂×#41	C₂³×C₃₁	1	2	yes	—
544	C₂×#41	C₂³×C₃₁	1	4	yes	—
545	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
546	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
547	#135	—	4	8	no	—
548	C₂×Q₁₆	—	4	4	no	—
549	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
550	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
551	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
552	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
553	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
554	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
555	C₂×D₈	C₂³×C₃₁	1	4	yes	—
556	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
557	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
558	C₄⋊Q₈	—	2	1	no	—
559	C₄⋊Q₈	—	2	1	no	—
560	C₄⋊Q₈	—	2	1	no	—
561	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
562	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
563	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
564	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
565	#127	—	2	1	no	—
566	#127	C₂³×C₃₁	1	1	yes	characteristic
567	#127	C₂³×C₃₁	1	1	yes	characteristic
568	#126	—	2	2	no	—
569	#126	—	2	4	no	—
570	#126	—	2	2	no	—
571	#126	—	2	2	no	—
572	#125	—	2	2	no	—
573	#125	—	2	2	no	—
574	#125	C₂³×C₃₁	1	2	yes	—
575	#124	—	2	1	no	—
576	#124	—	2	1	no	—
577	#124	—	2	2	no	—
578	#124	—	2	4	no	—
579	#124	—	2	1	no	—
580	#124	—	2	1	no	—
581	#124	C₂³×C₃₁	1	2	yes	—
582	#124	C₂³×C₃₁	1	4	yes	—
583	#123	—	2	2	no	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	#123	—	2	4	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	4	no	—
591	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
592	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	—	2	4	no	—
597	#121	—	2	2	no	—
598	#121	—	2	1	no	—
599	#121	—	2	1	no	—
600	#121	—	2	2	no	—
601	#121	—	2	2	no	—
602	#121	C₂³×C₃₁	1	2	yes	—
603	#121	C₂³×C₃₁	1	2	yes	—
604	#121	C₂³×C₃₁	1	2	yes	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	—	2	1	no	—
608	C₄×Q₈	—	2	1	no	—
609	C₄×Q₈	—	2	2	no	—
610	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
611	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
612	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
613	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
614	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
615	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
616	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
617	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	4	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	D₄×C₃₁	1	2	yes	—
631	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
632	C₄×D₄	C₂³×C₃₁	1	2	yes	—
633	C₄×D₄	C₂³×C₃₁	1	2	yes	—
634	C₄×D₄	C₂³×C₃₁	1	2	yes	—
635	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
636	C₄×D₄	C₂³×C₃₁	1	2	yes	—
637	#117	—	2	2	no	—
638	#117	—	2	2	no	—
639	#117	—	2	2	no	—
640	#117	—	2	2	no	—
641	#117	D₄×C₃₁	1	1	yes	characteristic
642	#117	D₄×C₃₁	1	2	yes	—
643	#117	C₂³×C₃₁	1	2	yes	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	—	2	2	no	—
648	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
649	C₂×C₄²	—	2	1	no	—
650	C₂×C₄²	—	2	2	no	—
651	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
653	#107	C₂³×C₃₁	1	4	yes	—
654	#106	C₂³×C₃₁	1	2	yes	—
655	#106	C₂³×C₃₁	1	2	yes	—
656	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
657	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
658	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
659	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
660	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
661	#103	C₂³×C₃₁	1	4	yes	—
662	#103	C₂³×C₃₁	1	4	yes	—
663	#103	C₂³×C₃₁	1	4	yes	—
664	#103	C₂³×C₃₁	1	2	yes	—
665	#103	C₂³×C₃₁	1	2	yes	—
666	#103	C₂³×C₃₁	1	4	yes	—
667	#102	C₂³×C₃₁	1	2	yes	—
668	#102	C₂³×C₃₁	1	4	yes	—
669	#102	C₂³×C₃₁	1	2	yes	—
670	#102	C₂³×C₃₁	1	4	yes	—
671	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
672	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
673	C₄×C₈	C₂³×C₃₁	1	2	yes	—
674	C₄×C₈	C₂³×C₃₁	1	4	yes	—
675	C₃₁	#61954	1	1	yes	characteristic, direct product factor, Sylow
676	#41	—	2	4	no	—
677	#41	—	2	4	no	—
678	#41	—	4	2	no	—
679	#41	—	4	4	no	—
680	#41	—	4	4	no	—
681	#41	—	4	4	no	—
682	#41	—	4	4	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	1	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	4	1	no	—
689	C₂×Q₈	—	4	2	no	—
690	C₂×Q₈	—	4	2	no	—
691	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
692	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
693	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
694	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
705	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
706	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
707	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
717	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
719	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
722	Q₁₆	—	2	8	no	—
723	Q₁₆	—	4	4	no	—
724	SD₁₆	—	2	4	no	—
725	SD₁₆	—	4	4	no	—
726	SD₁₆	—	4	2	no	—
727	SD₁₆	—	4	4	no	—
728	D₈	—	4	4	no	—
729	C₂×C₈	—	4	2	no	—
730	C₂×C₈	—	4	4	no	—
731	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
732	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
733	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
752	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
753	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
754	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
755	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
756	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
757	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
758	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
773	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
774	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	1	no	—
780	C₄²	—	2	1	no	—
781	C₄²	—	2	4	no	—
782	C₄²	C₂×D₄×C₃₁	1	2	yes	—
783	C₄²	C₂×D₄×C₃₁	1	2	yes	—
784	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
785	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
786	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
787	C₄²	C₂⁴×C₃₁	1	2	yes	—
788	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
792	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
793	Q₈	—	2	2	no	—
794	Q₈	—	2	1	no	—
795	Q₈	—	2	4	no	—
796	Q₈	—	2	1	no	—
797	Q₈	—	2	1	no	—
798	Q₈	—	2	4	no	—
799	Q₈	—	4	2	no	—
800	Q₈	—	4	2	no	—
801	Q₈	—	4	2	no	—
802	Q₈	—	8	2	no	—
803	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
804	D₄	—	2	4	no	—
805	D₄	—	2	2	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	2	no	—
808	D₄	—	2	2	no	—
809	D₄	—	2	2	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	2	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	4	no	—
814	D₄	—	4	2	no	—
815	D₄	—	4	2	no	—
816	D₄	—	8	1	no	—
817	D₄	—	8	2	no	—
818	D₄	—	8	4	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	4	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	2	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	—	8	4	no	—
839	C₂×C₄	—	8	1	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	C₃₁×#135	1	4	yes	complemented
842	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
844	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
850	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
851	C₈	—	2	4	no	—
852	C₈	—	2	2	no	—
853	C₈	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	C₂×C₃₁×#135	1	2	yes	—
866	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
867	C₄	—	2	2	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	4	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	1	no	—
880	C₄	C₂×C₃₁×#135	1	2	yes	—
881	C₄	C₂×C₃₁×#135	1	2	yes	—
882	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
883	C₄	C₃₁×#585	1	1	yes	characteristic
884	C₂	—	2	2	no	—
885	C₂	—	4	2	no	—
886	C₂	—	8	2	no	—
887	C₂	—	8	2	no	—
888	C₂	C₃₁×#3488	1	1	yes	characteristic
889	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
890	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3511	C₂	semidirect
2. C₃₁×#3480	C₂	semidirect
3. C₃₁×#3394	C₂	semidirect
4. C₃₁×#3364	C₂	semidirect
5. C₃₁×#3302	C₂	semidirect
6. C₃₁×#3301	C₂	semidirect
7. C₃₁×#3285	C₂	semidirect
8. C₃₁×#3284	C₂	semidirect
9. C₃₁×#3248	C₂	semidirect
10. C₃₁×#3245	C₂	semidirect
11. C₃₁×#3212	C₂	semidirect
12. C₃₁×#3206	C₂	semidirect
13. C₃₁×#3107	C₂	semidirect
14. C₃₁×#3103	C₂	semidirect
15. C₃₁×#3035	C₂	semidirect
16. C₂×C₃₁×#462	C₂	semidirect
17. C₃₁×#2988	C₂	semidirect
343. #61954	C₃₁	direct (N × H)
396. C₂×C₄×C₃₁	#135	semidirect
409. #3511	C₂×C₃₁	semidirect
410. #3480	C₂×C₃₁	semidirect
411. #3394	C₂×C₃₁	semidirect
412. #3364	C₂×C₃₁	semidirect
413. #3302	C₂×C₃₁	semidirect
414. #3301	C₂×C₃₁	semidirect
415. #3285	C₂×C₃₁	semidirect
416. #3284	C₂×C₃₁	semidirect
417. #3248	C₂×C₃₁	semidirect
418. #3245	C₂×C₃₁	semidirect
419. #3212	C₂×C₃₁	semidirect
420. #3206	C₂×C₃₁	semidirect
421. #3107	C₂×C₃₁	semidirect
422. #3103	C₂×C₃₁	semidirect
423. #3035	C₂×C₃₁	semidirect
424. C₂×#462	C₂×C₃₁	semidirect
425. #2988	C₂×C₃₁	semidirect
675. C₃₁	#61954	direct (N × H)
841. C₂×C₄	C₃₁×#135	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3511	2
C₃₁×#3480	2
C₃₁×#3394	2
C₃₁×#3364	2
C₃₁×#3302	2
C₃₁×#3301	2
C₃₁×#3285	2
C₃₁×#3284	2
C₃₁×#3248	2
C₃₁×#3245	2
C₃₁×#3212	2
C₃₁×#3206	2
C₃₁×#3107	2
C₃₁×#3103	2
C₃₁×#3035	2
C₂×C₃₁×#462	2
C₃₁×#2988	2
#61954	31

Subgroups — C31×#61954 #21518713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61954 #21518713