Subgroups — C₃₁×#60696 #21517455

Order 7936.

1850 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3461	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3178	C₂	1	4	yes	maximal, complemented
3	C₃₁×#3177	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3175	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3172	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3170	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3168	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3156	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3137	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3063	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3061	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#3059	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₃₁×#137	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₃₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#137	C₂²	1	2	yes	—
19	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
23	C₃₁×#544	C₂²	1	2	yes	—
24	C₃₁×#542	—	2	2	no	—
25	C₃₁×#542	C₂²	1	4	yes	—
26	C₃₁×#541	—	2	2	no	—
27	C₃₁×#541	C₂²	1	4	yes	—
28	C₃₁×#539	—	2	4	no	—
29	C₃₁×#537	C₂²	1	2	yes	—
30	C₃₁×#536	C₂²	1	2	yes	—
31	C₃₁×#536	C₂²	1	2	yes	—
32	C₃₁×#533	—	2	2	no	—
33	C₃₁×#533	C₂²	1	4	yes	—
34	C₃₁×#529	—	2	4	no	—
35	C₃₁×#529	—	2	2	no	—
36	C₃₁×#529	C₂²	1	4	yes	—
37	C₄×#41×C₃₁	C₂²	1	2	yes	—
38	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
40	C₃₁×#501	C₂²	1	4	yes	—
41	C₃₁×#500	C₂²	1	2	yes	—
42	C₃₁×#499	C₂²	1	2	yes	—
43	C₃₁×#497	C₂²	1	4	yes	—
44	C₃₁×#495	C₂²	1	2	yes	—
45	C₃₁×#494	C₂²	1	2	yes	—
46	C₃₁×#491	C₂²	1	4	yes	—
47	C₃₁×#489	C₂²	1	4	yes	—
48	C₃₁×#488	C₂²	1	4	yes	—
49	C₃₁×#487	C₂²	1	4	yes	—
50	C₃₁×#470	C₂²	1	4	yes	—
51	C₃₁×#470	C₂²	1	4	yes	—
52	C₃₁×#468	C₂²	1	4	yes	—
53	C₃₁×#468	C₂²	1	4	yes	—
54	C₃₁×#467	C₂²	1	2	yes	—
55	C₃₁×#467	C₂²	1	2	yes	—
56	C₃₁×#467	C₂²	1	2	yes	—
57	C₃₁×#467	C₂²	1	4	yes	—
58	C₃₁×#466	C₂²	1	2	yes	—
59	C₃₁×#465	C₂²	1	4	yes	—
60	C₃₁×#441	C₂²	1	4	yes	—
61	C₃₁×#440	C₂²	1	4	yes	—
62	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
63	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
64	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	—
65	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
66	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
67	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
68	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
69	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
70	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
71	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
72	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
73	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
74	C₃₁×#428	C₂²	1	2	yes	—
75	C₃₁×#427	C₂²	1	1	yes	characteristic
76	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
77	C₃₁×#419	C₂²	1	2	yes	—
78	C₃₁×#417	C₂²	1	2	yes	—
79	C₃₁×#416	C₂²	1	2	yes	—
80	C₂×C₃₁×#103	C₂²	1	2	yes	—
81	C₃₁×#405	C₂²	1	1	yes	characteristic
82	C₃₁×#405	C₂²	1	1	yes	characteristic
83	C₃₁×#405	C₂²	1	2	yes	—
84	C₃₁×#405	C₂²	1	2	yes	—
85	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
86	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
87	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
89	C₂×#41×C₃₁	C₂³	1	2	yes	—
90	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
92	C₃₁×#137	—	2	8	no	—
93	C₃₁×#135	—	2	4	no	—
94	C₂×Q₁₆×C₃₁	—	2	4	no	—
95	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
96	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
98	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
101	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
102	C₃₁×#131	—	2	4	no	—
103	C₃₁×#131	—	2	4	no	—
104	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
106	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
110	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
111	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	—	2	2	no	—
113	C₃₁×C₄⋊Q₈	—	2	2	no	—
114	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₃₁×#126	—	2	4	no	—
117	C₃₁×#126	—	2	4	no	—
118	C₃₁×#126	—	2	4	no	—
119	C₃₁×#126	—	2	4	no	—
120	C₃₁×#125	—	2	4	no	—
121	C₃₁×#125	—	2	2	no	—
122	C₃₁×#125	—	2	4	no	—
123	C₃₁×#125	—	2	4	no	—
124	C₃₁×#125	C₂³	1	4	yes	—
125	C₃₁×#124	—	2	2	no	—
126	C₃₁×#124	—	2	4	no	—
127	C₃₁×#124	C₂³	1	4	yes	—
128	C₃₁×#123	—	2	4	no	—
129	C₃₁×#123	—	2	4	no	—
130	C₃₁×#123	—	2	4	no	—
131	C₃₁×#123	—	2	4	no	—
132	C₃₁×C₂²⋊Q₈	—	2	2	no	—
133	C₃₁×C₂²⋊Q₈	—	2	4	no	—
134	C₃₁×C₂²⋊Q₈	—	2	2	no	—
135	C₃₁×C₂²⋊Q₈	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₃₁×#121	—	2	4	no	—
142	C₃₁×#121	—	2	2	no	—
143	C₃₁×#121	C₂³	1	4	yes	—
144	C₄×Q₈×C₃₁	—	2	2	no	—
145	C₄×Q₈×C₃₁	—	2	2	no	—
146	C₄×Q₈×C₃₁	—	2	4	no	—
147	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
148	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
149	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
150	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
151	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
152	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
153	C₄×D₄×C₃₁	—	2	2	no	—
154	C₄×D₄×C₃₁	—	2	2	no	—
155	C₄×D₄×C₃₁	—	2	4	no	—
156	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
157	C₄×D₄×C₃₁	D₄	1	2	yes	—
158	C₄×D₄×C₃₁	D₄	1	2	yes	—
159	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
160	C₄×D₄×C₃₁	C₂³	1	2	yes	—
161	C₄×D₄×C₃₁	C₂³	1	2	yes	—
162	C₃₁×#117	—	2	4	no	—
163	C₃₁×#117	—	2	2	no	—
164	C₃₁×#117	—	2	4	no	—
165	C₃₁×#117	C₂³	1	2	yes	—
166	C₃₁×#117	C₂³	1	1	yes	characteristic
167	C₃₁×#117	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄²×C₃₁	—	2	2	no	—
171	C₂×C₄²×C₃₁	—	2	2	no	—
172	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
174	C₃₁×#107	C₂³	1	2	yes	—
175	C₃₁×#107	C₂³	1	2	yes	—
176	C₃₁×#107	C₂³	1	1	yes	characteristic
177	C₃₁×#107	C₂³	1	1	yes	characteristic
178	C₃₁×#107	C₂³	1	4	yes	—
179	C₃₁×#106	C₂³	1	2	yes	—
180	C₃₁×#106	C₂³	1	4	yes	—
181	C₃₁×#103	C₂³	1	4	yes	—
182	C₃₁×#103	C₂³	1	4	yes	—
183	C₃₁×#103	C₂³	1	2	yes	—
184	C₃₁×#103	C₂³	1	2	yes	—
185	C₃₁×#103	C₂³	1	4	yes	—
186	C₃₁×#103	C₂³	1	4	yes	—
187	C₃₁×#103	C₂³	1	4	yes	—
188	C₃₁×#102	C₂³	1	2	yes	—
189	C₃₁×#102	C₂³	1	2	yes	—
190	C₃₁×#102	C₂³	1	4	yes	—
191	C₃₁×#97	C₂³	1	2	yes	—
192	C₃₁×#97	C₂³	1	2	yes	—
193	C₃₁×#97	C₂³	1	2	yes	—
194	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₃₁	C₂³	1	2	yes	—
196	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₃₁	C₂³	1	2	yes	—
200	C₄×C₈×C₃₁	C₂³	1	2	yes	—
201	#41×C₃₁	—	2	2	no	—
202	#41×C₃₁	—	2	2	no	—
203	#41×C₃₁	—	2	4	no	—
204	#41×C₃₁	—	2	4	no	—
205	C₂×Q₈×C₃₁	—	2	2	no	—
206	C₂×Q₈×C₃₁	—	2	4	no	—
207	C₂×Q₈×C₃₁	—	2	4	no	—
208	C₂×Q₈×C₃₁	—	2	4	no	—
209	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
210	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
211	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
212	C₂×D₄×C₃₁	—	2	2	no	—
213	C₂×D₄×C₃₁	—	2	4	no	—
214	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₃₁	—	2	2	no	—
218	C₂²×C₄×C₃₁	—	2	2	no	—
219	C₂²×C₄×C₃₁	—	2	2	no	—
220	C₂²×C₄×C₃₁	—	2	2	no	—
221	C₂²×C₄×C₃₁	—	2	2	no	—
222	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
228	Q₁₆×C₃₁	—	2	4	no	—
229	Q₁₆×C₃₁	—	2	4	no	—
230	Q₁₆×C₃₁	—	2	2	no	—
231	Q₁₆×C₃₁	—	2	8	no	—
232	SD₁₆×C₃₁	—	2	4	no	—
233	SD₁₆×C₃₁	—	2	8	no	—
234	D₈×C₃₁	—	2	2	no	—
235	M₁₆×C₃₁	—	2	2	no	—
236	M₁₆×C₃₁	—	2	4	no	—
237	M₁₆×C₃₁	—	2	4	no	—
238	M₁₆×C₃₁	#41	1	4	yes	—
239	C₂×C₈×C₃₁	—	2	2	no	—
240	C₂×C₈×C₃₁	—	2	4	no	—
241	C₂×C₈×C₃₁	—	2	4	no	—
242	C₂×C₈×C₃₁	#41	1	4	yes	—
243	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
246	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
248	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	4	no	—
251	C₄⋊C₄×C₃₁	—	2	2	no	—
252	C₄⋊C₄×C₃₁	—	2	2	no	—
253	C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₄⋊C₄×C₃₁	—	2	4	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	—	2	4	no	—
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	—	2	4	no	—
259	C₄⋊C₄×C₃₁	—	2	4	no	—
260	C₄⋊C₄×C₃₁	—	2	4	no	—
261	C₄⋊C₄×C₃₁	—	2	4	no	—
262	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
264	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
265	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
266	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
268	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	4	no	—
271	C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂²⋊C₄×C₃₁	—	2	4	no	—
273	C₂²⋊C₄×C₃₁	—	2	2	no	—
274	C₂²⋊C₄×C₃₁	—	2	2	no	—
275	C₂²⋊C₄×C₃₁	—	2	4	no	—
276	C₂²⋊C₄×C₃₁	—	2	4	no	—
277	C₂²⋊C₄×C₃₁	—	2	4	no	—
278	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
279	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
281	C₄²×C₃₁	—	2	2	no	—
282	C₄²×C₃₁	—	2	2	no	—
283	C₄²×C₃₁	—	2	4	no	—
284	C₄²×C₃₁	—	2	4	no	—
285	C₄²×C₃₁	—	2	2	no	—
286	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
287	C₄²×C₃₁	C₂×D₄	1	2	yes	—
288	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
289	C₄²×C₃₁	C₂×D₄	1	2	yes	—
290	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
291	C₄²×C₃₁	C₂⁴	1	2	yes	—
292	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
293	#60696	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
294	C₂³×C₃₁	—	2	2	no	—
295	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
296	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
297	Q₈×C₃₁	—	2	2	no	—
298	Q₈×C₃₁	—	2	4	no	—
299	Q₈×C₃₁	—	2	2	no	—
300	Q₈×C₃₁	—	2	4	no	—
301	Q₈×C₃₁	—	2	2	no	—
302	Q₈×C₃₁	—	4	4	no	—
303	Q₈×C₃₁	—	8	4	no	—
304	D₄×C₃₁	—	2	4	no	—
305	D₄×C₃₁	—	2	2	no	—
306	D₄×C₃₁	—	2	2	no	—
307	D₄×C₃₁	—	2	2	no	—
308	D₄×C₃₁	—	4	4	no	—
309	D₄×C₃₁	—	8	4	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	4	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	4	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	4	no	—
319	C₂×C₄×C₃₁	—	4	1	no	—
320	C₂×C₄×C₃₁	—	4	2	no	—
321	C₂×C₄×C₃₁	—	4	4	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	2	no	—
326	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
335	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
336	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
337	C₈×C₃₁	—	2	1	no	—
338	C₈×C₃₁	—	2	1	no	—
339	C₈×C₃₁	—	2	2	no	—
340	C₈×C₃₁	C₂×#41	1	2	yes	—
341	C₈×C₃₁	C₂×#41	1	4	yes	—
342	C₈×C₃₁	C₂×#41	1	2	yes	—
343	#3461	C₂×C₃₁	1	2	yes	complemented
344	#3178	C₂×C₃₁	1	4	yes	complemented
345	#3177	C₂×C₃₁	1	2	yes	complemented
346	#3175	C₂×C₃₁	1	2	yes	complemented
347	#3172	C₂×C₃₁	1	4	yes	complemented
348	#3170	C₂×C₃₁	1	2	yes	complemented
349	#3168	C₂×C₃₁	1	2	yes	complemented
350	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
351	#3156	C₂×C₃₁	1	1	yes	characteristic, complemented
352	#3137	C₂×C₃₁	1	2	yes	complemented
353	#3063	C₂×C₃₁	1	2	yes	complemented
354	#3061	C₂×C₃₁	1	1	yes	characteristic
355	#3059	C₂×C₃₁	1	1	yes	characteristic, complemented
356	C₄×#137	C₂×C₃₁	1	2	yes	complemented
357	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
358	C₂×C₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
359	C₄×#131	C₂×C₃₁	1	1	yes	characteristic, complemented
360	C₂²×C₃₁	—	2	1	no	—
361	C₂²×C₃₁	—	2	1	no	—
362	C₂²×C₃₁	—	2	2	no	—
363	C₂²×C₃₁	—	2	2	no	—
364	C₂²×C₃₁	—	2	2	no	—
365	C₂²×C₃₁	—	4	2	no	—
366	C₂²×C₃₁	—	4	2	no	—
367	C₂²×C₃₁	—	4	2	no	—
368	C₂²×C₃₁	#532	1	2	yes	—
369	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
370	C₄×C₃₁	—	2	1	no	—
371	C₄×C₃₁	—	2	1	no	—
372	C₄×C₃₁	—	2	2	no	—
373	C₄×C₃₁	—	2	2	no	—
374	C₄×C₃₁	—	2	1	no	—
375	C₄×C₃₁	—	2	2	no	—
376	C₄×C₃₁	—	4	4	no	—
377	C₄×C₃₁	—	4	2	no	—
378	C₄×C₃₁	—	4	2	no	—
379	C₄×C₃₁	—	4	4	no	—
380	C₄×C₃₁	—	4	2	no	—
381	C₄×C₃₁	#532	1	2	yes	—
382	C₄×C₃₁	#578	1	2	yes	—
383	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
384	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
385	C₂×#137	C₂²×C₃₁	1	2	yes	—
386	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
387	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
388	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
389	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
390	#544	C₂²×C₃₁	1	2	yes	—
391	#542	—	2	2	no	—
392	#542	C₂²×C₃₁	1	4	yes	—
393	#541	—	2	2	no	—
394	#541	C₂²×C₃₁	1	4	yes	—
395	#539	—	2	4	no	—
396	#537	C₂²×C₃₁	1	2	yes	—
397	#536	C₂²×C₃₁	1	2	yes	—
398	#536	C₂²×C₃₁	1	2	yes	—
399	#533	—	2	2	no	—
400	#533	C₂²×C₃₁	1	4	yes	—
401	#529	—	2	4	no	—
402	#529	—	2	2	no	—
403	#529	C₂²×C₃₁	1	4	yes	—
404	C₄×#41	C₂²×C₃₁	1	2	yes	—
405	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
407	#501	C₂²×C₃₁	1	4	yes	—
408	#500	C₂²×C₃₁	1	2	yes	—
409	#499	C₂²×C₃₁	1	2	yes	—
410	#497	C₂²×C₃₁	1	4	yes	—
411	#495	C₂²×C₃₁	1	2	yes	—
412	#494	C₂²×C₃₁	1	2	yes	—
413	#491	C₂²×C₃₁	1	4	yes	—
414	#489	C₂²×C₃₁	1	4	yes	—
415	#488	C₂²×C₃₁	1	4	yes	—
416	#487	C₂²×C₃₁	1	4	yes	—
417	#470	C₂²×C₃₁	1	4	yes	—
418	#470	C₂²×C₃₁	1	4	yes	—
419	#468	C₂²×C₃₁	1	4	yes	—
420	#468	C₂²×C₃₁	1	4	yes	—
421	#467	C₂²×C₃₁	1	2	yes	—
422	#467	C₂²×C₃₁	1	2	yes	—
423	#467	C₂²×C₃₁	1	2	yes	—
424	#467	C₂²×C₃₁	1	4	yes	—
425	#466	C₂²×C₃₁	1	2	yes	—
426	#465	C₂²×C₃₁	1	4	yes	—
427	#441	C₂²×C₃₁	1	4	yes	—
428	#440	C₂²×C₃₁	1	4	yes	—
429	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
430	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
431	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	—
432	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
433	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
434	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
435	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
436	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
437	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
438	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
439	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
440	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
441	#428	C₂²×C₃₁	1	2	yes	—
442	#427	C₂²×C₃₁	1	1	yes	characteristic
443	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
444	#419	C₂²×C₃₁	1	2	yes	—
445	#417	C₂²×C₃₁	1	2	yes	—
446	#416	C₂²×C₃₁	1	2	yes	—
447	C₂×#103	C₂²×C₃₁	1	2	yes	—
448	#405	C₂²×C₃₁	1	1	yes	characteristic
449	#405	C₂²×C₃₁	1	1	yes	characteristic
450	#405	C₂²×C₃₁	1	2	yes	—
451	#405	C₂²×C₃₁	1	2	yes	—
452	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
453	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
454	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
455	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
456	C₂×C₃₁	—	2	2	no	—
457	C₂×C₃₁	—	4	2	no	—
458	C₂×C₃₁	—	8	2	no	—
459	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
460	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
461	C₂×C₃₁	#3584	1	1	yes	characteristic
462	C₂×#41	C₂³×C₃₁	1	2	yes	—
463	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
464	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
465	#137	—	2	8	no	—
466	#135	—	2	4	no	—
467	C₂×Q₁₆	—	2	4	no	—
468	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
469	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
470	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
471	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
472	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
473	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
474	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
475	#131	—	2	4	no	—
476	#131	—	2	4	no	—
477	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
478	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
479	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
480	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
482	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
483	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
484	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
485	C₄⋊Q₈	—	2	2	no	—
486	C₄⋊Q₈	—	2	2	no	—
487	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
488	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
489	#126	—	2	4	no	—
490	#126	—	2	4	no	—
491	#126	—	2	4	no	—
492	#126	—	2	4	no	—
493	#125	—	2	4	no	—
494	#125	—	2	2	no	—
495	#125	—	2	4	no	—
496	#125	—	2	4	no	—
497	#125	C₂³×C₃₁	1	4	yes	—
498	#124	—	2	2	no	—
499	#124	—	2	4	no	—
500	#124	C₂³×C₃₁	1	4	yes	—
501	#123	—	2	4	no	—
502	#123	—	2	4	no	—
503	#123	—	2	4	no	—
504	#123	—	2	4	no	—
505	C₂²⋊Q₈	—	2	2	no	—
506	C₂²⋊Q₈	—	2	4	no	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	4	no	—
510	C₂²⋊Q₈	—	2	4	no	—
511	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
512	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
513	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
514	#121	—	2	4	no	—
515	#121	—	2	2	no	—
516	#121	C₂³×C₃₁	1	4	yes	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	—	2	4	no	—
520	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
521	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
522	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
523	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
524	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
525	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	4	no	—
529	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
530	C₄×D₄	D₄×C₃₁	1	2	yes	—
531	C₄×D₄	D₄×C₃₁	1	2	yes	—
532	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
533	C₄×D₄	C₂³×C₃₁	1	2	yes	—
534	C₄×D₄	C₂³×C₃₁	1	2	yes	—
535	#117	—	2	4	no	—
536	#117	—	2	2	no	—
537	#117	—	2	4	no	—
538	#117	C₂³×C₃₁	1	2	yes	—
539	#117	C₂³×C₃₁	1	1	yes	characteristic
540	#117	C₂³×C₃₁	1	2	yes	—
541	C₂×C₄⋊C₄	—	2	2	no	—
542	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
543	C₂×C₄²	—	2	2	no	—
544	C₂×C₄²	—	2	2	no	—
545	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
547	#107	C₂³×C₃₁	1	2	yes	—
548	#107	C₂³×C₃₁	1	2	yes	—
549	#107	C₂³×C₃₁	1	1	yes	characteristic
550	#107	C₂³×C₃₁	1	1	yes	characteristic
551	#107	C₂³×C₃₁	1	4	yes	—
552	#106	C₂³×C₃₁	1	2	yes	—
553	#106	C₂³×C₃₁	1	4	yes	—
554	#103	C₂³×C₃₁	1	4	yes	—
555	#103	C₂³×C₃₁	1	4	yes	—
556	#103	C₂³×C₃₁	1	2	yes	—
557	#103	C₂³×C₃₁	1	2	yes	—
558	#103	C₂³×C₃₁	1	4	yes	—
559	#103	C₂³×C₃₁	1	4	yes	—
560	#103	C₂³×C₃₁	1	4	yes	—
561	#102	C₂³×C₃₁	1	2	yes	—
562	#102	C₂³×C₃₁	1	2	yes	—
563	#102	C₂³×C₃₁	1	4	yes	—
564	#97	C₂³×C₃₁	1	2	yes	—
565	#97	C₂³×C₃₁	1	2	yes	—
566	#97	C₂³×C₃₁	1	2	yes	—
567	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
568	C₄×C₈	C₂³×C₃₁	1	2	yes	—
569	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
570	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
571	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
572	C₄×C₈	C₂³×C₃₁	1	2	yes	—
573	C₄×C₈	C₂³×C₃₁	1	2	yes	—
574	C₃₁	#60696	1	1	yes	characteristic, direct product factor, Sylow
575	#41	—	2	2	no	—
576	#41	—	2	2	no	—
577	#41	—	2	4	no	—
578	#41	—	2	4	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	—	2	4	no	—
582	C₂×Q₈	—	2	4	no	—
583	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
584	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
585	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
589	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
590	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
598	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
602	Q₁₆	—	2	4	no	—
603	Q₁₆	—	2	4	no	—
604	Q₁₆	—	2	2	no	—
605	Q₁₆	—	2	8	no	—
606	SD₁₆	—	2	4	no	—
607	SD₁₆	—	2	8	no	—
608	D₈	—	2	2	no	—
609	M₁₆	—	2	2	no	—
610	M₁₆	—	2	4	no	—
611	M₁₆	—	2	4	no	—
612	M₁₆	#41×C₃₁	1	4	yes	—
613	C₂×C₈	—	2	2	no	—
614	C₂×C₈	—	2	4	no	—
615	C₂×C₈	—	2	4	no	—
616	C₂×C₈	#41×C₃₁	1	4	yes	—
617	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
618	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
619	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
620	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
621	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
622	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
637	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
638	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
639	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
642	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
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	C₄²	—	2	4	no	—
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	C₂×D₄×C₃₁	1	2	yes	—
663	C₄²	C₂×D₄×C₃₁	1	2	yes	—
664	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
665	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
666	C₄²	C₂⁴×C₃₁	1	2	yes	—
667	C₂³	—	2	2	no	—
668	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
669	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
670	Q₈	—	2	2	no	—
671	Q₈	—	2	4	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	2	4	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	4	no	—
676	Q₈	—	8	4	no	—
677	D₄	—	2	4	no	—
678	D₄	—	2	2	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	2	no	—
681	D₄	—	4	4	no	—
682	D₄	—	8	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	8	2	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
701	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
702	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
704	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
707	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
708	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
709	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
710	C₈	—	2	1	no	—
711	C₈	—	2	1	no	—
712	C₈	—	2	2	no	—
713	C₈	C₂×#41×C₃₁	1	2	yes	—
714	C₈	C₂×#41×C₃₁	1	4	yes	—
715	C₈	C₂×#41×C₃₁	1	2	yes	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	C₃₁×#532	1	2	yes	—
725	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
726	C₄	—	2	2	no	—
727	C₄	—	2	1	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	4	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	2	no	—
737	C₄	C₃₁×#532	1	2	yes	—
738	C₄	C₃₁×#578	1	2	yes	—
739	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
740	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
741	C₂	—	2	2	no	—
742	C₂	—	4	2	no	—
743	C₂	—	8	2	no	—
744	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
745	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
746	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
prime radical	C₃₁×#3061	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3461	C₂	semidirect
2. C₃₁×#3178	C₂	semidirect
3. C₃₁×#3177	C₂	semidirect
4. C₃₁×#3175	C₂	semidirect
5. C₃₁×#3172	C₂	semidirect
6. C₃₁×#3170	C₂	semidirect
7. C₃₁×#3168	C₂	semidirect
8. C₃₁×#3164	C₂	semidirect
9. C₃₁×#3156	C₂	semidirect
10. C₃₁×#3137	C₂	semidirect
11. C₃₁×#3063	C₂	semidirect
13. C₃₁×#3059	C₂	semidirect
14. C₄×C₃₁×#137	C₂	semidirect
15. C₄×C₃₁×#135	C₂	semidirect
16. C₂×C₄×Q₁₆×C₃₁	C₂	semidirect
17. C₄×C₃₁×#131	C₂	semidirect
293. #60696	C₃₁	direct (N × H)
343. #3461	C₂×C₃₁	semidirect
344. #3178	C₂×C₃₁	semidirect
345. #3177	C₂×C₃₁	semidirect
346. #3175	C₂×C₃₁	semidirect
347. #3172	C₂×C₃₁	semidirect
348. #3170	C₂×C₃₁	semidirect
349. #3168	C₂×C₃₁	semidirect
350. #3164	C₂×C₃₁	semidirect
351. #3156	C₂×C₃₁	semidirect
352. #3137	C₂×C₃₁	semidirect
353. #3063	C₂×C₃₁	semidirect
355. #3059	C₂×C₃₁	semidirect
356. C₄×#137	C₂×C₃₁	semidirect
357. C₄×#135	C₂×C₃₁	semidirect
358. C₂×C₄×Q₁₆	C₂×C₃₁	semidirect
359. C₄×#131	C₂×C₃₁	semidirect
574. C₃₁	#60696	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×#3461	2
C₃₁×#3178	2
C₃₁×#3177	2
C₃₁×#3175	2
C₃₁×#3172	2
C₃₁×#3170	2
C₃₁×#3168	2
C₃₁×#3164	2
C₃₁×#3156	2
C₃₁×#3137	2
C₃₁×#3063	2
C₃₁×#3061	2
C₃₁×#3059	2
C₄×C₃₁×#137	2
C₄×C₃₁×#135	2
C₂×C₄×Q₁₆×C₃₁	2
C₄×C₃₁×#131	2
#60696	31

Subgroups — C31×#60696 #21517455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60696 #21517455