Subgroups — C₃₁×#61475 #21518234

Order 7936.

1900 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3514	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3373	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3341	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3324	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3319	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3280	C₂	1	2	yes	maximal, complemented
10	D₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3175	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3118	C₂	1	4	yes	maximal, complemented
14	C₃₁×#3115	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2948	C₂	1	2	yes	maximal, complemented
17	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
20	C₃₁×#559	C₂²	1	2	yes	complemented
21	C₃₁×#556	C₂²	1	2	yes	—
22	C₃₁×#555	C₂²	1	4	yes	complemented
23	C₃₁×#551	—	2	4	no	—
24	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
25	C₃₁×#548	—	2	2	no	—
26	C₃₁×#546	—	2	2	no	—
27	C₃₁×#546	C₂²	1	4	yes	complemented
28	D₄²×C₃₁	C₂²	1	2	yes	—
29	C₃₁×#542	C₂²	1	4	yes	complemented
30	C₃₁×#538	—	2	4	no	—
31	C₃₁×#532	C₂²	1	2	yes	complemented
32	C₃₁×#529	—	2	2	no	—
33	C₃₁×#529	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#124	—	2	2	no	—
35	C₃₁×#518	C₂²	1	4	yes	complemented
36	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
37	C₃₁×#500	C₂²	1	2	yes	complemented
38	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#495	C₂²	1	2	yes	complemented
40	C₃₁×#493	C₂²	1	1	yes	characteristic
41	C₃₁×#489	C₂²	1	4	yes	complemented
42	C₃₁×#486	C₂²	1	2	yes	complemented
43	C₃₁×#485	C₂²	1	4	yes	complemented
44	C₃₁×#482	C₂²	1	4	yes	complemented
45	C₃₁×#482	C₂²	1	4	yes	complemented
46	C₃₁×#476	C₂²	1	4	yes	complemented
47	C₃₁×#475	C₂²	1	2	yes	complemented
48	C₃₁×#474	C₂²	1	2	yes	complemented
49	C₃₁×#474	C₂²	1	4	yes	complemented
50	C₃₁×#468	C₂²	1	4	yes	complemented
51	C₃₁×#467	C₂²	1	2	yes	complemented
52	C₃₁×#466	C₂²	1	2	yes	—
53	C₃₁×#466	C₂²	1	2	yes	complemented
54	C₃₁×#466	C₂²	1	2	yes	complemented
55	C₃₁×#463	C₂²	1	4	yes	complemented
56	C₃₁×#463	C₂²	1	4	yes	complemented
57	C₃₁×#460	C₂²	1	2	yes	complemented
58	C₃₁×#459	C₂²	1	2	yes	—
59	C₃₁×#450	C₂²	1	4	yes	complemented
60	C₃₁×#449	C₂²	1	4	yes	complemented
61	C₃₁×#447	C₂²	1	4	yes	—
62	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#442	C₂²	1	4	yes	complemented
65	C₃₁×#442	C₂²	1	4	yes	complemented
66	C₃₁×#440	C₂²	1	4	yes	complemented
67	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
68	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
69	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
70	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
71	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
72	C₄×D₈×C₃₁	C₂²	1	2	yes	—
73	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
74	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
75	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
76	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
77	C₃₁×#436	C₂²	1	1	yes	characteristic
78	C₃₁×#435	C₂²	1	2	yes	complemented
79	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
81	C₃₁×#433	C₂²	1	2	yes	complemented
82	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#427	C₂²	1	2	yes	complemented
85	C₃₁×#418	C₂²	1	4	yes	complemented
86	C₃₁×#416	C₂²	1	2	yes	complemented
87	C₃₁×#405	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
89	C₂×#41×C₃₁	—	2	2	no	—
90	C₂×#41×C₃₁	C₂³	1	2	yes	—
91	C₂²×Q₈×C₃₁	—	2	2	no	—
92	C₂²×D₄×C₃₁	—	2	2	no	—
93	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
94	C₃₁×#135	—	2	4	no	—
95	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
96	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
97	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
98	C₂×D₈×C₃₁	—	2	8	no	—
99	C₂×D₈×C₃₁	C₂³	1	2	yes	—
100	C₂×D₈×C₃₁	C₂³	1	4	yes	—
101	C₂×D₈×C₃₁	C₂³	1	2	yes	—
102	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
109	C₃₁×#127	C₂³	1	2	yes	—
110	C₃₁×#126	—	2	4	no	—
111	C₃₁×#126	—	2	4	no	—
112	C₃₁×#126	D₄	1	2	yes	—
113	C₃₁×#125	D₄	1	1	yes	characteristic
114	C₃₁×#124	—	2	2	no	—
115	C₃₁×#124	—	2	2	no	—
116	C₃₁×#124	—	2	4	no	—
117	C₃₁×#124	—	2	4	no	—
118	C₃₁×#124	—	2	4	no	—
119	C₃₁×#124	—	2	2	no	—
120	C₃₁×#124	D₄	1	1	yes	characteristic
121	C₃₁×#124	C₂³	1	4	yes	—
122	C₃₁×#123	—	2	4	no	—
123	C₃₁×#123	—	2	4	no	—
124	C₃₁×#123	—	2	4	no	—
125	C₃₁×#123	D₄	1	2	yes	—
126	C₃₁×C₂²⋊Q₈	—	2	2	no	—
127	C₃₁×C₂²⋊Q₈	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	—	2	4	no	—
129	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
130	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₃₁×#121	—	2	4	no	—
132	C₃₁×#121	—	2	2	no	—
133	C₃₁×#121	—	2	2	no	—
134	C₃₁×#121	—	2	4	no	—
135	C₃₁×#121	D₄	1	1	yes	characteristic
136	C₃₁×#121	C₂³	1	4	yes	—
137	C₃₁×#121	C₂³	1	4	yes	—
138	C₃₁×#120	—	2	4	no	—
139	C₃₁×#120	—	2	4	no	—
140	C₄×Q₈×C₃₁	—	2	2	no	—
141	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
142	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
143	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
144	C₄×D₄×C₃₁	—	2	2	no	—
145	C₄×D₄×C₃₁	—	2	2	no	—
146	C₄×D₄×C₃₁	—	2	4	no	—
147	C₄×D₄×C₃₁	—	2	4	no	—
148	C₄×D₄×C₃₁	—	2	2	no	—
149	C₄×D₄×C₃₁	—	2	2	no	—
150	C₄×D₄×C₃₁	C₂³	1	2	yes	—
151	C₄×D₄×C₃₁	C₂³	1	2	yes	—
152	C₄×D₄×C₃₁	C₂³	1	4	yes	—
153	C₄×D₄×C₃₁	C₂³	1	4	yes	—
154	C₄×D₄×C₃₁	C₂³	1	4	yes	—
155	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₄×D₄×C₃₁	C₂³	1	2	yes	—
157	C₃₁×#117	—	2	4	no	—
158	C₃₁×#117	—	2	2	no	—
159	C₃₁×#117	C₂³	1	2	yes	—
160	C₃₁×#117	C₂³	1	4	yes	—
161	C₃₁×#117	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
163	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
164	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
165	C₂×C₄²×C₃₁	—	2	2	no	—
166	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
167	C₃₁×#107	C₂³	1	1	yes	characteristic
168	C₃₁×#107	C₂³	1	2	yes	—
169	C₃₁×#107	C₂³	1	1	yes	characteristic
170	C₃₁×#107	C₂³	1	2	yes	—
171	C₃₁×#107	C₂³	1	4	yes	—
172	C₃₁×#106	C₂³	1	2	yes	—
173	C₃₁×#106	C₂³	1	4	yes	—
174	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
177	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
178	C₃₁×#103	C₂³	1	2	yes	—
179	C₃₁×#103	C₂³	1	2	yes	—
180	C₃₁×#103	C₂³	1	4	yes	—
181	C₃₁×#102	C₂³	1	2	yes	—
182	C₃₁×#102	C₂³	1	2	yes	—
183	C₃₁×#102	C₂³	1	4	yes	—
184	C₃₁×#102	C₂³	1	4	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	4	yes	—
187	C₃₁×#102	C₂³	1	4	yes	—
188	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₃₁×#97	C₂³	1	2	yes	—
192	C₃₁×#97	C₂³	1	2	yes	—
193	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₃₁	C₂³	1	2	yes	—
198	C₂⁴×C₃₁	—	2	4	no	—
199	#41×C₃₁	—	2	4	no	—
200	#41×C₃₁	—	4	2	no	—
201	#41×C₃₁	—	8	4	no	—
202	C₂×Q₈×C₃₁	—	2	2	no	—
203	C₂×Q₈×C₃₁	—	2	4	no	—
204	C₂×Q₈×C₃₁	—	8	4	no	—
205	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
206	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
207	C₂×D₄×C₃₁	—	2	8	no	—
208	C₂×D₄×C₃₁	—	2	2	no	—
209	C₂×D₄×C₃₁	—	2	4	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	4	no	—
212	C₂×D₄×C₃₁	—	2	2	no	—
213	C₂×D₄×C₃₁	—	2	2	no	—
214	C₂×D₄×C₃₁	—	4	4	no	—
215	C₂×D₄×C₃₁	—	8	4	no	—
216	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
219	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₃₁	—	2	2	no	—
221	C₂²×C₄×C₃₁	—	2	2	no	—
222	C₂²×C₄×C₃₁	—	2	2	no	—
223	C₂²×C₄×C₃₁	—	2	4	no	—
224	C₂²×C₄×C₃₁	—	2	4	no	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
230	Q₁₆×C₃₁	—	2	2	no	—
231	SD₁₆×C₃₁	—	2	4	no	—
232	SD₁₆×C₃₁	—	4	4	no	—
233	D₈×C₃₁	—	2	8	no	—
234	D₈×C₃₁	—	2	4	no	—
235	D₈×C₃₁	—	4	2	no	—
236	D₈×C₃₁	#41	1	4	yes	complemented
237	M₁₆×C₃₁	—	4	2	no	—
238	C₂×C₈×C₃₁	—	2	4	no	—
239	C₂×C₈×C₃₁	—	2	2	no	—
240	C₂×C₈×C₃₁	—	4	1	no	—
241	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
245	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
246	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₄⋊C₄×C₃₁	—	2	2	no	—
248	C₄⋊C₄×C₃₁	—	2	2	no	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	2	no	—
251	C₄⋊C₄×C₃₁	—	2	4	no	—
252	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
253	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
256	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
257	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
260	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
261	C₂²⋊C₄×C₃₁	—	2	4	no	—
262	C₂²⋊C₄×C₃₁	—	2	4	no	—
263	C₂²⋊C₄×C₃₁	—	2	2	no	—
264	C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂²⋊C₄×C₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	—	2	4	no	—
273	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
274	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
275	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₄²×C₃₁	—	2	2	no	—
279	C₄²×C₃₁	—	2	2	no	—
280	C₄²×C₃₁	—	2	2	no	—
281	C₄²×C₃₁	—	2	4	no	—
282	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
285	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₄²×C₃₁	C₂⁴	1	2	yes	—
287	#61475	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	2	4	no	—
290	C₂³×C₃₁	—	4	8	no	—
291	C₂³×C₃₁	—	8	4	no	—
292	C₂³×C₃₁	—	8	4	no	—
293	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
294	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₃₁	—	2	2	no	—
296	Q₈×C₃₁	—	2	2	no	—
297	Q₈×C₃₁	—	2	2	no	—
298	Q₈×C₃₁	—	4	4	no	—
299	Q₈×C₃₁	—	8	4	no	—
300	D₄×C₃₁	—	2	2	no	—
301	D₄×C₃₁	—	2	4	no	—
302	D₄×C₃₁	—	2	2	no	—
303	D₄×C₃₁	—	2	4	no	—
304	D₄×C₃₁	—	4	2	no	—
305	D₄×C₃₁	—	4	8	no	—
306	D₄×C₃₁	—	4	4	no	—
307	D₄×C₃₁	—	4	4	no	—
308	D₄×C₃₁	—	8	2	no	—
309	D₄×C₃₁	—	8	4	no	—
310	D₄×C₃₁	—	8	4	no	—
311	D₄×C₃₁	C₂×#41	1	4	yes	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	1	no	—
315	C₂×C₄×C₃₁	—	2	1	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	2	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	4	no	—
321	C₂×C₄×C₃₁	—	4	1	no	—
322	C₂×C₄×C₃₁	—	4	4	no	—
323	C₂×C₄×C₃₁	—	4	4	no	—
324	C₂×C₄×C₃₁	—	8	2	no	—
325	C₂×C₄×C₃₁	—	8	4	no	—
326	C₂×C₄×C₃₁	—	8	4	no	—
327	C₂×C₄×C₃₁	—	8	4	no	—
328	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
337	C₈×C₃₁	—	2	2	no	—
338	C₈×C₃₁	—	2	1	no	—
339	C₈×C₃₁	—	2	1	no	—
340	C₈×C₃₁	—	2	1	no	—
341	C₈×C₃₁	—	2	2	no	—
342	C₈×C₃₁	C₂×#41	1	2	yes	—
343	#3514	C₂×C₃₁	1	2	yes	complemented
344	#3396	C₂×C₃₁	1	1	yes	characteristic, complemented
345	Q₈×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
346	#3373	C₂×C₃₁	1	2	yes	complemented
347	#3342	C₂×C₃₁	1	1	yes	characteristic, complemented
348	#3341	C₂×C₃₁	1	2	yes	complemented
349	#3324	C₂×C₃₁	1	2	yes	complemented
350	#3319	C₂×C₃₁	1	4	yes	complemented
351	#3280	C₂×C₃₁	1	2	yes	complemented
352	D₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
353	#3175	C₂×C₃₁	1	2	yes	complemented
354	#3169	C₂×C₃₁	1	1	yes	characteristic, complemented
355	#3118	C₂×C₃₁	1	4	yes	complemented
356	#3115	C₂×C₃₁	1	2	yes	complemented
357	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
358	#2948	C₂×C₃₁	1	2	yes	complemented
359	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
360	C₂²×C₃₁	—	2	1	no	—
361	C₂²×C₃₁	—	2	2	no	—
362	C₂²×C₃₁	—	2	1	no	—
363	C₂²×C₃₁	—	2	2	no	—
364	C₂²×C₃₁	—	2	4	no	—
365	C₂²×C₃₁	—	2	1	no	—
366	C₂²×C₃₁	—	2	2	no	—
367	C₂²×C₃₁	—	4	2	no	—
368	C₂²×C₃₁	—	4	2	no	—
369	C₂²×C₃₁	—	4	4	no	—
370	C₂²×C₃₁	—	4	4	no	—
371	C₂²×C₃₁	—	4	4	no	—
372	C₂²×C₃₁	—	16	8	no	—
373	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
374	C₄×C₃₁	—	2	1	no	—
375	C₄×C₃₁	—	2	1	no	—
376	C₄×C₃₁	—	2	2	no	—
377	C₄×C₃₁	—	2	1	no	—
378	C₄×C₃₁	—	2	2	no	—
379	C₄×C₃₁	—	2	1	no	—
380	C₄×C₃₁	—	2	2	no	—
381	C₄×C₃₁	—	4	2	no	—
382	C₄×C₃₁	—	4	2	no	—
383	C₄×C₃₁	—	4	2	no	—
384	C₄×C₃₁	—	4	4	no	—
385	C₄×C₃₁	#576	1	2	yes	—
386	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
387	C₄×C₃₁	#585	1	1	yes	characteristic
388	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
389	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
390	#559	C₂²×C₃₁	1	2	yes	complemented
391	#556	C₂²×C₃₁	1	2	yes	—
392	#555	C₂²×C₃₁	1	4	yes	complemented
393	#551	—	2	4	no	—
394	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
395	#548	—	2	2	no	—
396	#546	—	2	2	no	—
397	#546	C₂²×C₃₁	1	4	yes	complemented
398	D₄²	C₂²×C₃₁	1	2	yes	—
399	#542	C₂²×C₃₁	1	4	yes	complemented
400	#538	—	2	4	no	—
401	#532	C₂²×C₃₁	1	2	yes	complemented
402	#529	—	2	2	no	—
403	#529	C₂²×C₃₁	1	1	yes	characteristic
404	C₂×#124	—	2	2	no	—
405	#518	C₂²×C₃₁	1	4	yes	complemented
406	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
407	#500	C₂²×C₃₁	1	2	yes	complemented
408	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
409	#495	C₂²×C₃₁	1	2	yes	complemented
410	#493	C₂²×C₃₁	1	1	yes	characteristic
411	#489	C₂²×C₃₁	1	4	yes	complemented
412	#486	C₂²×C₃₁	1	2	yes	complemented
413	#485	C₂²×C₃₁	1	4	yes	complemented
414	#482	C₂²×C₃₁	1	4	yes	complemented
415	#482	C₂²×C₃₁	1	4	yes	complemented
416	#476	C₂²×C₃₁	1	4	yes	complemented
417	#475	C₂²×C₃₁	1	2	yes	complemented
418	#474	C₂²×C₃₁	1	2	yes	complemented
419	#474	C₂²×C₃₁	1	4	yes	complemented
420	#468	C₂²×C₃₁	1	4	yes	complemented
421	#467	C₂²×C₃₁	1	2	yes	complemented
422	#466	C₂²×C₃₁	1	2	yes	—
423	#466	C₂²×C₃₁	1	2	yes	complemented
424	#466	C₂²×C₃₁	1	2	yes	complemented
425	#463	C₂²×C₃₁	1	4	yes	complemented
426	#463	C₂²×C₃₁	1	4	yes	complemented
427	#460	C₂²×C₃₁	1	2	yes	complemented
428	#459	C₂²×C₃₁	1	2	yes	—
429	#450	C₂²×C₃₁	1	4	yes	complemented
430	#449	C₂²×C₃₁	1	4	yes	complemented
431	#447	C₂²×C₃₁	1	4	yes	—
432	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
433	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
434	#442	C₂²×C₃₁	1	4	yes	complemented
435	#442	C₂²×C₃₁	1	4	yes	complemented
436	#440	C₂²×C₃₁	1	4	yes	complemented
437	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
438	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
439	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
440	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
441	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
442	C₄×D₈	C₂²×C₃₁	1	2	yes	—
443	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
444	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
445	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
446	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
447	#436	C₂²×C₃₁	1	1	yes	characteristic
448	#435	C₂²×C₃₁	1	2	yes	complemented
449	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
450	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
451	#433	C₂²×C₃₁	1	2	yes	complemented
452	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
453	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
454	#427	C₂²×C₃₁	1	2	yes	complemented
455	#418	C₂²×C₃₁	1	4	yes	complemented
456	#416	C₂²×C₃₁	1	2	yes	complemented
457	#405	C₂²×C₃₁	1	2	yes	complemented
458	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
459	C₂×C₃₁	—	4	1	no	—
460	C₂×C₃₁	—	4	2	no	—
461	C₂×C₃₁	—	4	4	no	—
462	C₂×C₃₁	—	8	4	no	—
463	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
464	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
465	C₂×C₃₁	#3584	1	1	yes	characteristic
466	C₂×#41	—	2	2	no	—
467	C₂×#41	C₂³×C₃₁	1	2	yes	—
468	C₂²×Q₈	—	2	2	no	—
469	C₂²×D₄	—	2	2	no	—
470	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
471	#135	—	2	4	no	—
472	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
473	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
474	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
475	C₂×D₈	—	2	8	no	—
476	C₂×D₈	C₂³×C₃₁	1	2	yes	—
477	C₂×D₈	C₂³×C₃₁	1	4	yes	—
478	C₂×D₈	C₂³×C₃₁	1	2	yes	—
479	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
480	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
481	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
482	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
484	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
485	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
486	#127	C₂³×C₃₁	1	2	yes	—
487	#126	—	2	4	no	—
488	#126	—	2	4	no	—
489	#126	D₄×C₃₁	1	2	yes	—
490	#125	D₄×C₃₁	1	1	yes	characteristic
491	#124	—	2	2	no	—
492	#124	—	2	2	no	—
493	#124	—	2	4	no	—
494	#124	—	2	4	no	—
495	#124	—	2	4	no	—
496	#124	—	2	2	no	—
497	#124	D₄×C₃₁	1	1	yes	characteristic
498	#124	C₂³×C₃₁	1	4	yes	—
499	#123	—	2	4	no	—
500	#123	—	2	4	no	—
501	#123	—	2	4	no	—
502	#123	D₄×C₃₁	1	2	yes	—
503	C₂²⋊Q₈	—	2	2	no	—
504	C₂²⋊Q₈	—	2	4	no	—
505	C₂²⋊Q₈	—	2	4	no	—
506	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
507	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
508	#121	—	2	4	no	—
509	#121	—	2	2	no	—
510	#121	—	2	2	no	—
511	#121	—	2	4	no	—
512	#121	D₄×C₃₁	1	1	yes	characteristic
513	#121	C₂³×C₃₁	1	4	yes	—
514	#121	C₂³×C₃₁	1	4	yes	—
515	#120	—	2	4	no	—
516	#120	—	2	4	no	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
519	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
520	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	—	2	4	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	C₂³×C₃₁	1	2	yes	—
528	C₄×D₄	C₂³×C₃₁	1	2	yes	—
529	C₄×D₄	C₂³×C₃₁	1	4	yes	—
530	C₄×D₄	C₂³×C₃₁	1	4	yes	—
531	C₄×D₄	C₂³×C₃₁	1	4	yes	—
532	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
533	C₄×D₄	C₂³×C₃₁	1	2	yes	—
534	#117	—	2	4	no	—
535	#117	—	2	2	no	—
536	#117	C₂³×C₃₁	1	2	yes	—
537	#117	C₂³×C₃₁	1	4	yes	—
538	#117	C₂³×C₃₁	1	2	yes	—
539	C₂×C₂²⋊C₄	—	2	4	no	—
540	C₂×C₂²⋊C₄	—	2	4	no	—
541	C₂×C₂²⋊C₄	—	2	4	no	—
542	C₂×C₄²	—	2	2	no	—
543	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
544	#107	C₂³×C₃₁	1	1	yes	characteristic
545	#107	C₂³×C₃₁	1	2	yes	—
546	#107	C₂³×C₃₁	1	1	yes	characteristic
547	#107	C₂³×C₃₁	1	2	yes	—
548	#107	C₂³×C₃₁	1	4	yes	—
549	#106	C₂³×C₃₁	1	2	yes	—
550	#106	C₂³×C₃₁	1	4	yes	—
551	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
552	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
553	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
554	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
555	#103	C₂³×C₃₁	1	2	yes	—
556	#103	C₂³×C₃₁	1	2	yes	—
557	#103	C₂³×C₃₁	1	4	yes	—
558	#102	C₂³×C₃₁	1	2	yes	—
559	#102	C₂³×C₃₁	1	2	yes	—
560	#102	C₂³×C₃₁	1	4	yes	—
561	#102	C₂³×C₃₁	1	4	yes	—
562	#102	C₂³×C₃₁	1	4	yes	—
563	#102	C₂³×C₃₁	1	4	yes	—
564	#102	C₂³×C₃₁	1	4	yes	—
565	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
566	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
567	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
568	#97	C₂³×C₃₁	1	2	yes	—
569	#97	C₂³×C₃₁	1	2	yes	—
570	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
571	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
572	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
574	C₄×C₈	C₂³×C₃₁	1	2	yes	—
575	C₃₁	#61475	1	1	yes	characteristic, direct product factor, Sylow
576	C₂⁴	—	2	4	no	—
577	#41	—	2	4	no	—
578	#41	—	4	2	no	—
579	#41	—	8	4	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	2	4	no	—
582	C₂×Q₈	—	8	4	no	—
583	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
584	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	4	4	no	—
593	C₂×D₄	—	8	4	no	—
594	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
595	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
596	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
597	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
608	Q₁₆	—	2	2	no	—
609	SD₁₆	—	2	4	no	—
610	SD₁₆	—	4	4	no	—
611	D₈	—	2	8	no	—
612	D₈	—	2	4	no	—
613	D₈	—	4	2	no	—
614	D₈	#41×C₃₁	1	4	yes	complemented
615	M₁₆	—	4	2	no	—
616	C₂×C₈	—	2	4	no	—
617	C₂×C₈	—	2	2	no	—
618	C₂×C₈	—	4	1	no	—
619	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
621	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
622	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
623	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
624	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
631	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
632	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
633	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
634	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
635	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
638	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
652	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
653	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
654	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
655	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	4	no	—
660	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
662	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
663	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
664	C₄²	C₂⁴×C₃₁	1	2	yes	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	4	8	no	—
668	C₂³	—	8	4	no	—
669	C₂³	—	8	4	no	—
670	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
671	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	4	no	—
676	Q₈	—	8	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	4	no	—
681	D₄	—	4	2	no	—
682	D₄	—	4	8	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	4	no	—
685	D₄	—	8	2	no	—
686	D₄	—	8	4	no	—
687	D₄	—	8	4	no	—
688	D₄	C₂×#41×C₃₁	1	4	yes	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	8	2	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	—	8	4	no	—
705	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
708	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
711	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
712	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
713	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
714	C₈	—	2	2	no	—
715	C₈	—	2	1	no	—
716	C₈	—	2	1	no	—
717	C₈	—	2	1	no	—
718	C₈	—	2	2	no	—
719	C₈	C₂×#41×C₃₁	1	2	yes	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	16	8	no	—
733	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
734	C₄	—	2	1	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	1	no	—
739	C₄	—	2	1	no	—
740	C₄	—	2	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	4	no	—
744	C₄	—	4	2	no	—
745	C₄	C₃₁×#576	1	2	yes	—
746	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
747	C₄	C₃₁×#585	1	1	yes	characteristic
748	C₂	—	4	2	no	—
749	C₂	—	4	1	no	—
750	C₂	—	4	4	no	—
751	C₂	—	8	4	no	—
752	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
753	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
754	C₂	C₃₁×#3584	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 ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3514	C₂	semidirect
2. C₃₁×#3396	C₂	semidirect
3. Q₈×D₈×C₃₁	C₂	semidirect
4. C₃₁×#3373	C₂	semidirect
5. C₃₁×#3342	C₂	semidirect
6. C₃₁×#3341	C₂	semidirect
7. C₃₁×#3324	C₂	semidirect
8. C₃₁×#3319	C₂	semidirect
9. C₃₁×#3280	C₂	semidirect
10. D₄×D₈×C₃₁	C₂	semidirect
11. C₃₁×#3175	C₂	semidirect
12. C₃₁×#3169	C₂	semidirect
13. C₃₁×#3118	C₂	semidirect
14. C₃₁×#3115	C₂	semidirect
15. C₃₁×#2966	C₂	semidirect
16. C₃₁×#2948	C₂	semidirect
17. C₄×C₃₁×#135	C₂	semidirect
20. C₃₁×#559	C₂²	semidirect
22. C₃₁×#555	C₂²	semidirect
24. D₄×Q₈×C₃₁	C₂²	semidirect
27. C₃₁×#546	C₂²	semidirect
29. C₃₁×#542	C₂²	semidirect
31. C₃₁×#532	C₂²	semidirect
35. C₃₁×#518	C₂²	semidirect
36. C₄×#41×C₃₁	C₂²	semidirect
37. C₃₁×#500	C₂²	semidirect
38. C₃₁×#500	C₂²	semidirect
39. C₃₁×#495	C₂²	semidirect
41. C₃₁×#489	C₂²	semidirect
42. C₃₁×#486	C₂²	semidirect
43. C₃₁×#485	C₂²	semidirect
44. C₃₁×#482	C₂²	semidirect
45. C₃₁×#482	C₂²	semidirect
46. C₃₁×#476	C₂²	semidirect
47. C₃₁×#475	C₂²	semidirect
48. C₃₁×#474	C₂²	semidirect
49. C₃₁×#474	C₂²	semidirect
50. C₃₁×#468	C₂²	semidirect
51. C₃₁×#467	C₂²	semidirect
53. C₃₁×#466	C₂²	semidirect
54. C₃₁×#466	C₂²	semidirect
55. C₃₁×#463	C₂²	semidirect
56. C₃₁×#463	C₂²	semidirect
57. C₃₁×#460	C₂²	semidirect
59. C₃₁×#450	C₂²	semidirect
60. C₃₁×#449	C₂²	semidirect
62. C₃₁×#446	C₂²	semidirect
63. C₈×Q₈×C₃₁	C₂²	semidirect
64. C₃₁×#442	C₂²	semidirect
65. C₃₁×#442	C₂²	semidirect
66. C₃₁×#440	C₂²	semidirect
67. C₄×Q₁₆×C₃₁	C₂²	semidirect
68. C₄×Q₁₆×C₃₁	C₂²	semidirect
69. C₄×SD₁₆×C₃₁	C₂²	semidirect
70. C₄×SD₁₆×C₃₁	C₂²	semidirect
74. C₄×D₈×C₃₁	C₂²	semidirect
75. C₄×D₈×C₃₁	C₂²	semidirect
76. C₄×D₈×C₃₁	C₂²	semidirect
78. C₃₁×#435	C₂²	semidirect
80. C₈×D₄×C₃₁	C₂²	semidirect
81. C₃₁×#433	C₂²	semidirect
82. C₃₁×#432	C₂²	semidirect
83. C₃₁×#427	C₂²	semidirect
84. C₃₁×#427	C₂²	semidirect
85. C₃₁×#418	C₂²	semidirect
86. C₃₁×#416	C₂²	semidirect
87. C₃₁×#405	C₂²	semidirect
88. C₂×C₄×C₈×C₃₁	C₂²	semidirect
236. D₈×C₃₁	#41	semidirect
287. #61475	C₃₁	direct (N × H)
343. #3514	C₂×C₃₁	semidirect
344. #3396	C₂×C₃₁	semidirect
345. Q₈×D₈	C₂×C₃₁	semidirect
346. #3373	C₂×C₃₁	semidirect
347. #3342	C₂×C₃₁	semidirect
348. #3341	C₂×C₃₁	semidirect
349. #3324	C₂×C₃₁	semidirect
350. #3319	C₂×C₃₁	semidirect
351. #3280	C₂×C₃₁	semidirect
352. D₄×D₈	C₂×C₃₁	semidirect
353. #3175	C₂×C₃₁	semidirect
354. #3169	C₂×C₃₁	semidirect
355. #3118	C₂×C₃₁	semidirect
356. #3115	C₂×C₃₁	semidirect
357. #2966	C₂×C₃₁	semidirect
358. #2948	C₂×C₃₁	semidirect
359. C₄×#135	C₂×C₃₁	semidirect
390. #559	C₂²×C₃₁	semidirect
392. #555	C₂²×C₃₁	semidirect
394. D₄×Q₈	C₂²×C₃₁	semidirect
397. #546	C₂²×C₃₁	semidirect
399. #542	C₂²×C₃₁	semidirect
401. #532	C₂²×C₃₁	semidirect
405. #518	C₂²×C₃₁	semidirect
406. C₄×#41	C₂²×C₃₁	semidirect
407. #500	C₂²×C₃₁	semidirect
408. #500	C₂²×C₃₁	semidirect
409. #495	C₂²×C₃₁	semidirect
411. #489	C₂²×C₃₁	semidirect
412. #486	C₂²×C₃₁	semidirect
413. #485	C₂²×C₃₁	semidirect
414. #482	C₂²×C₃₁	semidirect
415. #482	C₂²×C₃₁	semidirect
416. #476	C₂²×C₃₁	semidirect
417. #475	C₂²×C₃₁	semidirect
418. #474	C₂²×C₃₁	semidirect
419. #474	C₂²×C₃₁	semidirect
420. #468	C₂²×C₃₁	semidirect
421. #467	C₂²×C₃₁	semidirect
423. #466	C₂²×C₃₁	semidirect
424. #466	C₂²×C₃₁	semidirect
425. #463	C₂²×C₃₁	semidirect
426. #463	C₂²×C₃₁	semidirect
427. #460	C₂²×C₃₁	semidirect
429. #450	C₂²×C₃₁	semidirect
430. #449	C₂²×C₃₁	semidirect
432. #446	C₂²×C₃₁	semidirect
433. C₈×Q₈	C₂²×C₃₁	semidirect
434. #442	C₂²×C₃₁	semidirect
435. #442	C₂²×C₃₁	semidirect
436. #440	C₂²×C₃₁	semidirect
437. C₄×Q₁₆	C₂²×C₃₁	semidirect
438. C₄×Q₁₆	C₂²×C₃₁	semidirect
439. C₄×SD₁₆	C₂²×C₃₁	semidirect
440. C₄×SD₁₆	C₂²×C₃₁	semidirect
444. C₄×D₈	C₂²×C₃₁	semidirect
445. C₄×D₈	C₂²×C₃₁	semidirect
446. C₄×D₈	C₂²×C₃₁	semidirect
448. #435	C₂²×C₃₁	semidirect
450. C₈×D₄	C₂²×C₃₁	semidirect
451. #433	C₂²×C₃₁	semidirect
452. #432	C₂²×C₃₁	semidirect
453. #427	C₂²×C₃₁	semidirect
454. #427	C₂²×C₃₁	semidirect
455. #418	C₂²×C₃₁	semidirect
456. #416	C₂²×C₃₁	semidirect
457. #405	C₂²×C₃₁	semidirect
458. C₂×C₄×C₈	C₂²×C₃₁	semidirect
575. C₃₁	#61475	direct (N × H)
614. D₈	#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×#3514	2
C₃₁×#3396	2
Q₈×D₈×C₃₁	2
C₃₁×#3373	2
C₃₁×#3342	2
C₃₁×#3341	2
C₃₁×#3324	2
C₃₁×#3319	2
C₃₁×#3280	2
D₄×D₈×C₃₁	2
C₃₁×#3175	2
C₃₁×#3169	2
C₃₁×#3118	2
C₃₁×#3115	2
C₃₁×#2966	2
C₃₁×#2948	2
C₄×C₃₁×#135	2
#61475	31

Subgroups — C31×#61475 #21518234

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61475 #21518234