Subgroups — C₃₁×#61328 #21518087

Order 7936.

1738 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3507	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3377	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3375	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3374	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3364	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3363	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3137	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3131	C₂	1	1	yes	maximal, characteristic
11	C₃₁×#3083	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3044	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic
15	C₃₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2947	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#137	C₂²	1	2	yes	—
19	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#559	C₂²	1	2	yes	—
21	Q₈²×C₃₁	—	2	1	no	—
22	Q₈²×C₃₁	C₂²	1	2	yes	—
23	C₃₁×#557	—	2	1	no	—
24	C₃₁×#557	—	2	2	no	—
25	C₃₁×#557	C₂²	1	2	yes	—
26	C₃₁×#557	C₂²	1	4	yes	—
27	C₃₁×#557	C₂²	1	2	yes	—
28	C₃₁×#556	—	2	1	no	—
29	C₃₁×#556	C₂²	1	4	yes	—
30	C₃₁×#554	—	2	1	no	—
31	C₃₁×#552	—	2	2	no	—
32	C₃₁×#544	—	2	2	no	—
33	C₃₁×#544	C₂²	1	2	yes	—
34	C₃₁×#539	—	2	2	no	—
35	C₃₁×#536	C₂²	1	2	yes	—
36	C₃₁×#533	—	2	2	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#533	C₂²	1	1	yes	characteristic
39	C₃₁×#532	C₂²	1	1	yes	characteristic
40	C₃₁×#529	—	2	2	no	—
41	C₃₁×#520	C₂²	1	2	yes	—
42	C₃₁×#519	C₂²	1	2	yes	—
43	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#491	C₂²	1	4	yes	—
46	C₃₁×#489	C₂²	1	4	yes	—
47	C₃₁×#488	C₂²	1	2	yes	—
48	C₃₁×#488	C₂²	1	4	yes	—
49	C₃₁×#488	C₂²	1	2	yes	—
50	C₃₁×#487	C₂²	1	1	yes	characteristic
51	C₃₁×#487	C₂²	1	4	yes	—
52	C₃₁×#487	C₂²	1	1	yes	characteristic
53	C₃₁×#486	C₂²	1	1	yes	characteristic
54	C₃₁×#486	C₂²	1	1	yes	characteristic
55	C₃₁×#479	C₂²	1	4	yes	—
56	C₃₁×#479	C₂²	1	4	yes	—
57	C₃₁×#478	C₂²	1	4	yes	—
58	C₃₁×#477	C₂²	1	2	yes	—
59	C₃₁×#477	C₂²	1	4	yes	—
60	C₃₁×#475	C₂²	1	2	yes	—
61	C₃₁×#474	C₂²	1	4	yes	—
62	C₃₁×#464	C₂²	1	4	yes	—
63	C₃₁×#464	C₂²	1	4	yes	—
64	C₃₁×#464	C₂²	1	4	yes	—
65	C₃₁×#462	C₂²	1	2	yes	—
66	C₃₁×#462	C₂²	1	4	yes	—
67	C₃₁×#462	C₂²	1	4	yes	—
68	C₃₁×#460	C₂²	1	2	yes	—
69	C₃₁×#446	C₂²	1	2	yes	—
70	C₃₁×#446	C₂²	1	2	yes	—
71	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
72	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
73	C₃₁×#441	C₂²	1	4	yes	—
74	C₃₁×#440	C₂²	1	4	yes	—
75	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	—
76	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
77	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
78	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
79	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
80	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
81	C₃₁×#428	C₂²	1	2	yes	—
82	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
83	C₃₁×#424	C₂²	1	2	yes	—
84	C₃₁×#423	C₂²	1	1	yes	characteristic
85	C₃₁×#419	C₂²	1	2	yes	—
86	C₃₁×#417	C₂²	1	2	yes	—
87	C₃₁×#416	C₂²	1	2	yes	—
88	C₃₁×#416	C₂²	1	2	yes	—
89	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
90	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
91	C₃₁×#405	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
93	C₂×#41×C₃₁	C₂³	1	2	yes	—
94	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
96	C₃₁×#137	—	2	8	no	—
97	C₂×Q₁₆×C₃₁	—	2	4	no	—
98	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
99	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
102	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₃₁×C₄⋊Q₈	—	2	2	no	—
106	C₃₁×C₄⋊Q₈	—	2	4	no	—
107	C₃₁×C₄⋊Q₈	—	2	2	no	—
108	C₃₁×C₄⋊Q₈	—	2	4	no	—
109	C₃₁×C₄⋊Q₈	—	2	2	no	—
110	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
114	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₃₁×#127	C₂³	1	1	yes	characteristic
118	C₃₁×#126	—	2	4	no	—
119	C₃₁×#126	—	2	4	no	—
120	C₃₁×#125	—	2	2	no	—
121	C₃₁×#125	—	2	4	no	—
122	C₃₁×#125	—	2	4	no	—
123	C₃₁×#125	—	2	4	no	—
124	C₃₁×#125	—	2	4	no	—
125	C₃₁×#125	—	2	2	no	—
126	C₃₁×#125	D₄	1	2	yes	—
127	C₃₁×#125	C₂³	1	4	yes	—
128	C₃₁×#125	C₂³	1	2	yes	—
129	C₃₁×#124	—	2	2	no	—
130	C₃₁×#124	C₂³	1	2	yes	—
131	C₃₁×#124	C₂³	1	4	yes	—
132	C₃₁×#123	—	2	4	no	—
133	C₃₁×#123	—	2	4	no	—
134	C₃₁×C₂²⋊Q₈	—	2	4	no	—
135	C₃₁×C₂²⋊Q₈	—	2	1	no	—
136	C₃₁×C₂²⋊Q₈	—	2	1	no	—
137	C₃₁×C₂²⋊Q₈	—	2	2	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	4	no	—
140	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
141	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
142	C₃₁×#121	—	2	1	no	—
143	C₃₁×#121	—	2	1	no	—
144	C₄×Q₈×C₃₁	—	2	2	no	—
145	C₄×Q₈×C₃₁	—	2	2	no	—
146	C₄×Q₈×C₃₁	—	2	2	no	—
147	C₄×Q₈×C₃₁	—	2	2	no	—
148	C₄×Q₈×C₃₁	—	2	4	no	—
149	C₄×Q₈×C₃₁	—	2	2	no	—
150	C₄×Q₈×C₃₁	—	2	1	no	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	—	2	1	no	—
154	C₄×Q₈×C₃₁	—	2	1	no	—
155	C₄×Q₈×C₃₁	—	2	1	no	—
156	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
157	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
158	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
159	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
160	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
161	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
162	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
163	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
164	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
165	C₄×D₄×C₃₁	—	2	2	no	—
166	C₄×D₄×C₃₁	—	2	4	no	—
167	C₄×D₄×C₃₁	—	2	1	no	—
168	C₄×D₄×C₃₁	—	2	1	no	—
169	C₄×D₄×C₃₁	C₂³	1	4	yes	—
170	C₃₁×#117	—	2	2	no	—
171	C₃₁×#117	—	2	4	no	—
172	C₃₁×#117	—	2	4	no	—
173	C₃₁×#117	C₂³	1	2	yes	—
174	C₃₁×#117	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
176	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
177	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₃₁	—	2	1	no	—
181	C₂×C₄²×C₃₁	—	2	1	no	—
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₃₁×#107	C₂³	1	2	yes	—
184	C₃₁×#107	C₂³	1	2	yes	—
185	C₃₁×#107	C₂³	1	4	yes	—
186	C₃₁×#106	C₂³	1	4	yes	—
187	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
188	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
189	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
190	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
191	C₃₁×#103	C₂³	1	2	yes	—
192	C₃₁×#103	C₂³	1	2	yes	—
193	C₃₁×#103	C₂³	1	2	yes	—
194	C₃₁×#103	C₂³	1	2	yes	—
195	C₃₁×#103	C₂³	1	2	yes	—
196	C₃₁×#103	C₂³	1	2	yes	—
197	C₃₁×#103	C₂³	1	2	yes	—
198	C₃₁×#103	C₂³	1	2	yes	—
199	C₃₁×#103	C₂³	1	4	yes	—
200	C₃₁×#103	C₂³	1	4	yes	—
201	C₃₁×#103	C₂³	1	4	yes	—
202	C₃₁×#102	C₂³	1	2	yes	—
203	C₃₁×#102	C₂³	1	2	yes	—
204	C₃₁×#102	C₂³	1	2	yes	—
205	C₃₁×#102	C₂³	1	2	yes	—
206	C₃₁×#102	C₂³	1	4	yes	—
207	C₃₁×#97	C₂³	1	4	yes	—
208	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₃₁	C₂³	1	4	yes	—
213	#41×C₃₁	—	2	4	no	—
214	#41×C₃₁	—	2	4	no	—
215	C₂×Q₈×C₃₁	—	2	1	no	—
216	C₂×Q₈×C₃₁	—	2	1	no	—
217	C₂×Q₈×C₃₁	—	2	1	no	—
218	C₂×Q₈×C₃₁	—	2	1	no	—
219	C₂×Q₈×C₃₁	—	2	4	no	—
220	C₂×Q₈×C₃₁	—	2	2	no	—
221	C₂×Q₈×C₃₁	—	2	2	no	—
222	C₂×Q₈×C₃₁	—	2	2	no	—
223	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₃₁	#41	1	4	yes	—
226	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
227	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
229	C₂×D₄×C₃₁	—	2	2	no	—
230	C₂×D₄×C₃₁	—	2	1	no	—
231	C₂×D₄×C₃₁	—	2	1	no	—
232	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₃₁	—	2	1	no	—
234	C₂²×C₄×C₃₁	—	2	1	no	—
235	C₂²×C₄×C₃₁	—	2	1	no	—
236	C₂²×C₄×C₃₁	—	2	1	no	—
237	C₂²×C₄×C₃₁	—	2	2	no	—
238	C₂²×C₄×C₃₁	—	2	4	no	—
239	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
242	Q₁₆×C₃₁	—	2	4	no	—
243	Q₁₆×C₃₁	—	2	4	no	—
244	Q₁₆×C₃₁	—	2	8	no	—
245	SD₁₆×C₃₁	—	2	8	no	—
246	M₁₆×C₃₁	—	2	4	no	—
247	C₂×C₈×C₃₁	—	2	2	no	—
248	C₂×C₈×C₃₁	—	2	2	no	—
249	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
254	C₄⋊C₄×C₃₁	—	2	1	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₄⋊C₄×C₃₁	—	2	4	no	—
262	C₄⋊C₄×C₃₁	—	2	4	no	—
263	C₄⋊C₄×C₃₁	—	2	4	no	—
264	C₄⋊C₄×C₃₁	—	2	1	no	—
265	C₄⋊C₄×C₃₁	—	2	1	no	—
266	C₄⋊C₄×C₃₁	—	2	2	no	—
267	C₄⋊C₄×C₃₁	—	2	1	no	—
268	C₄⋊C₄×C₃₁	—	2	4	no	—
269	C₄⋊C₄×C₃₁	—	2	1	no	—
270	C₄⋊C₄×C₃₁	—	2	4	no	—
271	C₄⋊C₄×C₃₁	—	2	4	no	—
272	C₄⋊C₄×C₃₁	—	2	2	no	—
273	C₄⋊C₄×C₃₁	—	2	4	no	—
274	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
277	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
279	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂²⋊C₄×C₃₁	—	2	2	no	—
285	C₂²⋊C₄×C₃₁	—	2	2	no	—
286	C₂²⋊C₄×C₃₁	—	2	4	no	—
287	C₂²⋊C₄×C₃₁	—	2	4	no	—
288	C₂²⋊C₄×C₃₁	—	2	2	no	—
289	C₂²⋊C₄×C₃₁	—	2	4	no	—
290	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
291	C₄²×C₃₁	—	2	2	no	—
292	C₄²×C₃₁	—	2	2	no	—
293	C₄²×C₃₁	—	2	2	no	—
294	C₄²×C₃₁	—	2	2	no	—
295	C₄²×C₃₁	—	2	4	no	—
296	C₄²×C₃₁	—	2	4	no	—
297	C₄²×C₃₁	—	2	4	no	—
298	C₄²×C₃₁	—	2	2	no	—
299	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₄²×C₃₁	C₂⁴	1	4	yes	—
304	#61328	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
305	C₂³×C₃₁	—	2	2	no	—
306	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
307	Q₈×C₃₁	—	2	4	no	—
308	Q₈×C₃₁	—	2	4	no	—
309	Q₈×C₃₁	—	2	2	no	—
310	Q₈×C₃₁	—	2	2	no	—
311	Q₈×C₃₁	—	2	2	no	—
312	Q₈×C₃₁	—	2	2	no	—
313	Q₈×C₃₁	—	2	2	no	—
314	Q₈×C₃₁	—	4	2	no	—
315	Q₈×C₃₁	—	4	2	no	—
316	Q₈×C₃₁	—	4	2	no	—
317	Q₈×C₃₁	—	8	1	no	—
318	Q₈×C₃₁	—	8	4	no	—
319	Q₈×C₃₁	C₂×#41	1	4	yes	—
320	D₄×C₃₁	—	2	2	no	—
321	D₄×C₃₁	—	2	2	no	—
322	D₄×C₃₁	—	4	4	no	—
323	D₄×C₃₁	—	4	2	no	—
324	D₄×C₃₁	—	8	1	no	—
325	C₂×C₄×C₃₁	—	2	4	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	4	1	no	—
335	C₂×C₄×C₃₁	—	4	2	no	—
336	C₂×C₄×C₃₁	—	4	4	no	—
337	C₂×C₄×C₃₁	—	8	4	no	—
338	C₂×C₄×C₃₁	—	8	1	no	—
339	C₂×C₄×C₃₁	—	8	1	no	—
340	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
342	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
343	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
348	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
349	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
350	C₈×C₃₁	—	2	1	no	—
351	C₈×C₃₁	—	2	1	no	—
352	C₈×C₃₁	—	2	4	no	—
353	C₈×C₃₁	—	2	1	no	—
354	C₈×C₃₁	—	2	1	no	—
355	#3507	C₂×C₃₁	1	1	yes	characteristic
356	#3502	C₂×C₃₁	1	1	yes	characteristic, complemented
357	#3377	C₂×C₃₁	1	4	yes	complemented
358	#3375	C₂×C₃₁	1	2	yes	complemented
359	#3374	C₂×C₃₁	1	2	yes	complemented
360	#3365	C₂×C₃₁	1	2	yes	complemented
361	#3364	C₂×C₃₁	1	4	yes	complemented
362	#3363	C₂×C₃₁	1	2	yes	complemented
363	#3137	C₂×C₃₁	1	2	yes	complemented
364	#3131	C₂×C₃₁	1	1	yes	characteristic
365	#3083	C₂×C₃₁	1	2	yes	complemented
366	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
367	#3044	C₂×C₃₁	1	2	yes	complemented
368	#3037	C₂×C₃₁	1	1	yes	characteristic
369	#2960	C₂×C₃₁	1	1	yes	characteristic, complemented
370	#2947	C₂×C₃₁	1	2	yes	complemented
371	C₂×C₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
372	C₂²×C₃₁	—	2	1	no	—
373	C₂²×C₃₁	—	2	1	no	—
374	C₂²×C₃₁	—	4	2	no	—
375	C₂²×C₃₁	—	4	2	no	—
376	C₂²×C₃₁	—	4	2	no	—
377	C₂²×C₃₁	#548	1	2	yes	—
378	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₃₁	—	2	1	no	—
380	C₄×C₃₁	—	2	1	no	—
381	C₄×C₃₁	—	2	4	no	—
382	C₄×C₃₁	—	2	4	no	—
383	C₄×C₃₁	—	2	1	no	—
384	C₄×C₃₁	—	2	4	no	—
385	C₄×C₃₁	—	4	2	no	—
386	C₄×C₃₁	—	4	2	no	—
387	C₄×C₃₁	—	4	2	no	—
388	C₄×C₃₁	—	4	2	no	—
389	C₄×C₃₁	—	4	2	no	—
390	C₄×C₃₁	—	4	2	no	—
391	C₄×C₃₁	#548	1	2	yes	—
392	C₄×C₃₁	#578	1	2	yes	—
393	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
394	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
395	C₂×#137	C₂²×C₃₁	1	2	yes	—
396	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
397	#559	C₂²×C₃₁	1	2	yes	—
398	Q₈²	—	2	1	no	—
399	Q₈²	C₂²×C₃₁	1	2	yes	—
400	#557	—	2	1	no	—
401	#557	—	2	2	no	—
402	#557	C₂²×C₃₁	1	2	yes	—
403	#557	C₂²×C₃₁	1	4	yes	—
404	#557	C₂²×C₃₁	1	2	yes	—
405	#556	—	2	1	no	—
406	#556	C₂²×C₃₁	1	4	yes	—
407	#554	—	2	1	no	—
408	#552	—	2	2	no	—
409	#544	—	2	2	no	—
410	#544	C₂²×C₃₁	1	2	yes	—
411	#539	—	2	2	no	—
412	#536	C₂²×C₃₁	1	2	yes	—
413	#533	—	2	2	no	—
414	#533	C₂²×C₃₁	1	1	yes	characteristic
415	#533	C₂²×C₃₁	1	1	yes	characteristic
416	#532	C₂²×C₃₁	1	1	yes	characteristic
417	#529	—	2	2	no	—
418	#520	C₂²×C₃₁	1	2	yes	—
419	#519	C₂²×C₃₁	1	2	yes	—
420	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
421	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
422	#491	C₂²×C₃₁	1	4	yes	—
423	#489	C₂²×C₃₁	1	4	yes	—
424	#488	C₂²×C₃₁	1	2	yes	—
425	#488	C₂²×C₃₁	1	4	yes	—
426	#488	C₂²×C₃₁	1	2	yes	—
427	#487	C₂²×C₃₁	1	1	yes	characteristic
428	#487	C₂²×C₃₁	1	4	yes	—
429	#487	C₂²×C₃₁	1	1	yes	characteristic
430	#486	C₂²×C₃₁	1	1	yes	characteristic
431	#486	C₂²×C₃₁	1	1	yes	characteristic
432	#479	C₂²×C₃₁	1	4	yes	—
433	#479	C₂²×C₃₁	1	4	yes	—
434	#478	C₂²×C₃₁	1	4	yes	—
435	#477	C₂²×C₃₁	1	2	yes	—
436	#477	C₂²×C₃₁	1	4	yes	—
437	#475	C₂²×C₃₁	1	2	yes	—
438	#474	C₂²×C₃₁	1	4	yes	—
439	#464	C₂²×C₃₁	1	4	yes	—
440	#464	C₂²×C₃₁	1	4	yes	—
441	#464	C₂²×C₃₁	1	4	yes	—
442	#462	C₂²×C₃₁	1	2	yes	—
443	#462	C₂²×C₃₁	1	4	yes	—
444	#462	C₂²×C₃₁	1	4	yes	—
445	#460	C₂²×C₃₁	1	2	yes	—
446	#446	C₂²×C₃₁	1	2	yes	—
447	#446	C₂²×C₃₁	1	2	yes	—
448	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
449	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
450	#441	C₂²×C₃₁	1	4	yes	—
451	#440	C₂²×C₃₁	1	4	yes	—
452	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	—
453	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
454	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
455	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
456	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
457	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
458	#428	C₂²×C₃₁	1	2	yes	—
459	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
460	#424	C₂²×C₃₁	1	2	yes	—
461	#423	C₂²×C₃₁	1	1	yes	characteristic
462	#419	C₂²×C₃₁	1	2	yes	—
463	#417	C₂²×C₃₁	1	2	yes	—
464	#416	C₂²×C₃₁	1	2	yes	—
465	#416	C₂²×C₃₁	1	2	yes	—
466	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
467	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
468	#405	C₂²×C₃₁	1	2	yes	—
469	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
470	C₂×C₃₁	—	2	2	no	—
471	C₂×C₃₁	—	8	2	no	—
472	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
473	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
474	C₂×C₃₁	#3584	1	1	yes	characteristic
475	C₂×#41	C₂³×C₃₁	1	2	yes	—
476	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
477	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
478	#137	—	2	8	no	—
479	C₂×Q₁₆	—	2	4	no	—
480	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
481	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
482	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
483	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
484	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
485	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
487	C₄⋊Q₈	—	2	2	no	—
488	C₄⋊Q₈	—	2	4	no	—
489	C₄⋊Q₈	—	2	2	no	—
490	C₄⋊Q₈	—	2	4	no	—
491	C₄⋊Q₈	—	2	2	no	—
492	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
493	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
494	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
495	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
496	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
497	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
498	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
499	#127	C₂³×C₃₁	1	1	yes	characteristic
500	#126	—	2	4	no	—
501	#126	—	2	4	no	—
502	#125	—	2	2	no	—
503	#125	—	2	4	no	—
504	#125	—	2	4	no	—
505	#125	—	2	4	no	—
506	#125	—	2	4	no	—
507	#125	—	2	2	no	—
508	#125	D₄×C₃₁	1	2	yes	—
509	#125	C₂³×C₃₁	1	2	yes	—
510	#125	C₂³×C₃₁	1	4	yes	—
511	#124	—	2	2	no	—
512	#124	C₂³×C₃₁	1	2	yes	—
513	#124	C₂³×C₃₁	1	4	yes	—
514	#123	—	2	4	no	—
515	#123	—	2	4	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	—	2	1	no	—
518	C₂²⋊Q₈	—	2	1	no	—
519	C₂²⋊Q₈	—	2	2	no	—
520	C₂²⋊Q₈	—	2	2	no	—
521	C₂²⋊Q₈	—	2	4	no	—
522	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
523	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
524	#121	—	2	1	no	—
525	#121	—	2	1	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	—	2	2	no	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×Q₈	—	2	4	no	—
531	C₄×Q₈	—	2	2	no	—
532	C₄×Q₈	—	2	1	no	—
533	C₄×Q₈	—	2	1	no	—
534	C₄×Q₈	—	2	1	no	—
535	C₄×Q₈	—	2	1	no	—
536	C₄×Q₈	—	2	1	no	—
537	C₄×Q₈	—	2	1	no	—
538	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
539	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
540	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
541	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
542	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
543	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
544	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
545	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
546	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	4	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	C₂³×C₃₁	1	4	yes	—
552	#117	—	2	2	no	—
553	#117	—	2	4	no	—
554	#117	—	2	4	no	—
555	#117	C₂³×C₃₁	1	2	yes	—
556	#117	C₂³×C₃₁	1	2	yes	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	2	no	—
560	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
562	C₂×C₄²	—	2	1	no	—
563	C₂×C₄²	—	2	1	no	—
564	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
565	#107	C₂³×C₃₁	1	2	yes	—
566	#107	C₂³×C₃₁	1	2	yes	—
567	#107	C₂³×C₃₁	1	4	yes	—
568	#106	C₂³×C₃₁	1	4	yes	—
569	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
570	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
571	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
572	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
573	#103	C₂³×C₃₁	1	2	yes	—
574	#103	C₂³×C₃₁	1	2	yes	—
575	#103	C₂³×C₃₁	1	2	yes	—
576	#103	C₂³×C₃₁	1	2	yes	—
577	#103	C₂³×C₃₁	1	2	yes	—
578	#103	C₂³×C₃₁	1	2	yes	—
579	#103	C₂³×C₃₁	1	2	yes	—
580	#103	C₂³×C₃₁	1	2	yes	—
581	#103	C₂³×C₃₁	1	4	yes	—
582	#103	C₂³×C₃₁	1	4	yes	—
583	#103	C₂³×C₃₁	1	4	yes	—
584	#102	C₂³×C₃₁	1	2	yes	—
585	#102	C₂³×C₃₁	1	2	yes	—
586	#102	C₂³×C₃₁	1	2	yes	—
587	#102	C₂³×C₃₁	1	2	yes	—
588	#102	C₂³×C₃₁	1	4	yes	—
589	#97	C₂³×C₃₁	1	4	yes	—
590	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
591	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
592	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
593	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
594	C₄×C₈	C₂³×C₃₁	1	4	yes	—
595	C₃₁	#61328	1	1	yes	characteristic, direct product factor, Sylow
596	#41	—	2	4	no	—
597	#41	—	2	4	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	4	no	—
603	C₂×Q₈	—	2	2	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
607	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
608	C₂×Q₈	#41×C₃₁	1	4	yes	—
609	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
610	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
611	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
612	C₂×D₄	—	2	2	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
625	Q₁₆	—	2	4	no	—
626	Q₁₆	—	2	4	no	—
627	Q₁₆	—	2	8	no	—
628	SD₁₆	—	2	8	no	—
629	M₁₆	—	2	4	no	—
630	C₂×C₈	—	2	2	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
633	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
634	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
635	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
636	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
658	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
659	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
660	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
661	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
662	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
663	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
664	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
665	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	2	no	—
676	C₄²	—	2	2	no	—
677	C₄²	—	2	2	no	—
678	C₄²	—	2	4	no	—
679	C₄²	—	2	4	no	—
680	C₄²	—	2	4	no	—
681	C₄²	—	2	2	no	—
682	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
683	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
684	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
685	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
686	C₄²	C₂⁴×C₃₁	1	4	yes	—
687	C₂³	—	2	2	no	—
688	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
689	Q₈	—	2	4	no	—
690	Q₈	—	2	4	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	2	2	no	—
694	Q₈	—	2	2	no	—
695	Q₈	—	2	2	no	—
696	Q₈	—	4	2	no	—
697	Q₈	—	4	2	no	—
698	Q₈	—	4	2	no	—
699	Q₈	—	8	1	no	—
700	Q₈	—	8	4	no	—
701	Q₈	C₂×#41×C₃₁	1	4	yes	—
702	D₄	—	2	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	4	4	no	—
705	D₄	—	4	2	no	—
706	D₄	—	8	1	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	—	8	1	no	—
721	C₂×C₄	—	8	1	no	—
722	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
723	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
724	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
725	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
729	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
730	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
731	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
732	C₈	—	2	1	no	—
733	C₈	—	2	1	no	—
734	C₈	—	2	4	no	—
735	C₈	—	2	1	no	—
736	C₈	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	C₃₁×#548	1	2	yes	—
743	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
744	C₄	—	2	4	no	—
745	C₄	—	2	1	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	4	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	C₃₁×#548	1	2	yes	—
757	C₄	C₃₁×#578	1	2	yes	—
758	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
759	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
760	C₂	—	2	2	no	—
761	C₂	—	8	2	no	—
762	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
763	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
764	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3502	C₂	semidirect
3. C₃₁×#3377	C₂	semidirect
4. C₃₁×#3375	C₂	semidirect
5. C₃₁×#3374	C₂	semidirect
6. C₃₁×#3365	C₂	semidirect
7. C₃₁×#3364	C₂	semidirect
8. C₃₁×#3363	C₂	semidirect
9. C₃₁×#3137	C₂	semidirect
11. C₃₁×#3083	C₂	semidirect
12. C₃₁×#3078	C₂	semidirect
13. C₃₁×#3044	C₂	semidirect
15. C₃₁×#2960	C₂	semidirect
16. C₃₁×#2947	C₂	semidirect
17. C₂×C₄×Q₁₆×C₃₁	C₂	semidirect
304. #61328	C₃₁	direct (N × H)
356. #3502	C₂×C₃₁	semidirect
357. #3377	C₂×C₃₁	semidirect
358. #3375	C₂×C₃₁	semidirect
359. #3374	C₂×C₃₁	semidirect
360. #3365	C₂×C₃₁	semidirect
361. #3364	C₂×C₃₁	semidirect
362. #3363	C₂×C₃₁	semidirect
363. #3137	C₂×C₃₁	semidirect
365. #3083	C₂×C₃₁	semidirect
366. #3078	C₂×C₃₁	semidirect
367. #3044	C₂×C₃₁	semidirect
369. #2960	C₂×C₃₁	semidirect
370. #2947	C₂×C₃₁	semidirect
371. C₂×C₄×Q₁₆	C₂×C₃₁	semidirect
595. C₃₁	#61328	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×#3507	2
C₃₁×#3502	2
C₃₁×#3377	2
C₃₁×#3375	2
C₃₁×#3374	2
C₃₁×#3365	2
C₃₁×#3364	2
C₃₁×#3363	2
C₃₁×#3137	2
C₃₁×#3131	2
C₃₁×#3083	2
C₃₁×#3078	2
C₃₁×#3044	2
C₃₁×#3037	2
C₃₁×#2960	2
C₃₁×#2947	2
C₂×C₄×Q₁₆×C₃₁	2
#61328	31

Subgroups — C31×#61328 #21518087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61328 #21518087