Subgroups — C₃₁×#60711 #21517470

Order 7936.

1846 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3495	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3185	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3183	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3178	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3177	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3173	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3172	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3163	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×#3056	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3054	C₂	1	1	yes	maximal, characteristic
13	C₂×C₃₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2952	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2947	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2873	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	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×#556	—	2	2	no	—
24	C₃₁×#554	—	2	2	no	—
25	C₃₁×#552	—	2	4	no	—
26	C₃₁×#552	—	2	2	no	—
27	C₃₁×#552	—	2	2	no	—
28	C₃₁×#551	—	2	4	no	—
29	C₃₁×#544	C₂²	1	2	yes	—
30	C₃₁×#542	C₂²	1	4	yes	—
31	C₃₁×#541	C₂²	1	4	yes	—
32	C₃₁×#536	C₂²	1	2	yes	—
33	C₃₁×#533	C₂²	1	4	yes	—
34	C₃₁×#529	C₂²	1	4	yes	—
35	C₃₁×#525	C₂²	1	2	yes	—
36	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₃₁×#520	C₂²	1	2	yes	—
38	C₃₁×#519	C₂²	1	2	yes	—
39	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
40	C₃₁×#501	C₂²	1	4	yes	complemented
41	C₃₁×#499	C₂²	1	2	yes	complemented
42	C₃₁×#498	C₂²	1	2	yes	complemented
43	C₃₁×#497	C₂²	1	4	yes	complemented
44	C₃₁×#495	C₂²	1	2	yes	complemented
45	C₃₁×#494	C₂²	1	2	yes	complemented
46	C₃₁×#491	C₂²	1	4	yes	complemented
47	C₃₁×#489	C₂²	1	4	yes	complemented
48	C₃₁×#488	C₂²	1	4	yes	complemented
49	C₃₁×#487	C₂²	1	4	yes	complemented
50	C₃₁×#470	C₂²	1	2	yes	—
51	C₃₁×#470	C₂²	1	4	yes	—
52	C₃₁×#470	C₂²	1	2	yes	—
53	C₃₁×#470	C₂²	1	1	yes	characteristic
54	C₃₁×#470	C₂²	1	2	yes	—
55	C₃₁×#470	C₂²	1	2	yes	—
56	C₃₁×#470	C₂²	1	1	yes	characteristic
57	C₃₁×#469	C₂²	1	1	yes	characteristic
58	C₃₁×#469	C₂²	1	1	yes	characteristic
59	C₃₁×#468	C₂²	1	2	yes	—
60	C₃₁×#468	C₂²	1	4	yes	—
61	C₃₁×#468	C₂²	1	2	yes	—
62	C₃₁×#467	C₂²	1	4	yes	—
63	C₃₁×#465	C₂²	1	4	yes	—
64	C₃₁×#442	C₂²	1	2	yes	complemented
65	C₃₁×#441	C₂²	1	2	yes	complemented
66	C₃₁×#441	C₂²	1	2	yes	complemented
67	C₃₁×#441	C₂²	1	2	yes	complemented
68	C₃₁×#441	C₂²	1	4	yes	complemented
69	C₃₁×#440	C₂²	1	4	yes	complemented
70	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
71	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
72	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
73	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
74	C₃₁×#428	C₂²	1	2	yes	—
75	C₃₁×#427	C₂²	1	1	yes	characteristic
76	C₂×C₃₁×#106	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	C₃₁×#405	C₂²	1	1	yes	characteristic
86	C₃₁×#405	C₂²	1	1	yes	characteristic
87	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
88	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
89	C₂×#41×C₃₁	C₂³	1	2	yes	—
90	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
91	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
96	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
97	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
98	C₂×Q₁₆×C₃₁	C₂³	1	2	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	C₂×M₁₆×C₃₁	—	2	4	no	—
103	C₂×M₁₆×C₃₁	—	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	1	yes	characteristic
107	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
110	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
113	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
114	C₃₁×C₄⋊Q₈	—	2	2	no	—
115	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₃₁×#126	—	2	4	no	—
118	C₃₁×#126	—	2	4	no	—
119	C₃₁×#126	—	2	4	no	—
120	C₃₁×#126	—	2	4	no	—
121	C₃₁×#125	—	2	4	no	—
122	C₃₁×#125	—	2	4	no	—
123	C₃₁×#125	—	2	2	no	—
124	C₃₁×#125	—	2	4	no	—
125	C₃₁×#125	C₂³	1	4	yes	—
126	C₃₁×#124	—	2	4	no	—
127	C₃₁×#124	C₂³	1	4	yes	—
128	C₃₁×#123	—	2	2	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	2	no	—
134	C₃₁×C₂²⋊Q₈	—	2	4	no	—
135	C₃₁×C₂²⋊Q₈	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	2	no	—
137	C₃₁×C₂²⋊Q₈	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	4	no	—
139	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
142	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₃₁×#121	C₂³	1	2	yes	—
144	C₃₁×#121	C₂³	1	2	yes	—
145	C₃₁×#120	—	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	C₂³	1	4	yes	—
150	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
151	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
152	C₄×D₄×C₃₁	—	2	2	no	—
153	C₄×D₄×C₃₁	—	2	2	no	—
154	C₄×D₄×C₃₁	—	2	4	no	—
155	C₄×D₄×C₃₁	—	2	4	no	—
156	C₄×D₄×C₃₁	C₂³	1	4	yes	—
157	C₃₁×#117	—	2	4	no	—
158	C₃₁×#117	—	2	2	no	—
159	C₃₁×#117	—	2	4	no	—
160	C₃₁×#117	—	2	4	no	—
161	C₃₁×#117	D₄	1	2	yes	—
162	C₃₁×#117	D₄	1	2	yes	—
163	C₃₁×#117	C₂³	1	2	yes	—
164	C₃₁×#117	C₂³	1	1	yes	characteristic
165	C₃₁×#117	C₂³	1	1	yes	characteristic
166	C₃₁×#117	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
168	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
169	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
172	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
173	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
174	C₃₁×#107	C₂³	1	2	yes	—
175	C₃₁×#107	C₂³	1	4	yes	—
176	C₃₁×#106	C₂³	1	2	yes	—
177	C₃₁×#106	C₂³	1	2	yes	—
178	C₃₁×#106	C₂³	1	1	yes	characteristic
179	C₃₁×#106	C₂³	1	1	yes	characteristic
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	C₃₁×#97	C₂³	1	2	yes	—
195	C₄×C₈×C₃₁	C₂³	1	2	yes	—
196	C₄×C₈×C₃₁	C₂³	1	2	yes	—
197	C₄×C₈×C₃₁	C₂³	1	2	yes	—
198	C₄×C₈×C₃₁	C₂³	1	2	yes	—
199	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
200	#41×C₃₁	—	2	4	no	—
201	#41×C₃₁	—	2	4	no	—
202	C₂×Q₈×C₃₁	—	2	2	no	—
203	C₂×Q₈×C₃₁	—	2	4	no	—
204	C₂×Q₈×C₃₁	—	2	4	no	—
205	C₂×Q₈×C₃₁	—	2	4	no	—
206	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
207	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
208	C₂×D₄×C₃₁	—	2	2	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	2	no	—
211	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₃₁	—	2	2	no	—
213	C₂²×C₄×C₃₁	—	2	2	no	—
214	C₂²×C₄×C₃₁	—	2	2	no	—
215	C₂²×C₄×C₃₁	—	2	2	no	—
216	C₂²×C₄×C₃₁	—	2	2	no	—
217	C₂²×C₄×C₃₁	—	2	4	no	—
218	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
222	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
225	Q₁₆×C₃₁	—	2	4	no	—
226	Q₁₆×C₃₁	—	2	4	no	—
227	Q₁₆×C₃₁	—	2	2	no	—
228	Q₁₆×C₃₁	—	2	8	no	—
229	SD₁₆×C₃₁	—	2	4	no	—
230	SD₁₆×C₃₁	—	2	8	no	—
231	D₈×C₃₁	—	2	2	no	—
232	M₁₆×C₃₁	—	2	2	no	—
233	M₁₆×C₃₁	—	2	4	no	—
234	M₁₆×C₃₁	—	2	2	no	—
235	M₁₆×C₃₁	—	2	2	no	—
236	M₁₆×C₃₁	—	2	2	no	—
237	M₁₆×C₃₁	—	2	2	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	#41	1	4	yes	—
242	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
244	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
247	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₄⋊C₄×C₃₁	—	2	2	no	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	4	no	—
251	C₄⋊C₄×C₃₁	—	2	4	no	—
252	C₄⋊C₄×C₃₁	—	2	4	no	—
253	C₄⋊C₄×C₃₁	—	2	4	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	2	no	—
258	C₄⋊C₄×C₃₁	—	2	4	no	—
259	C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₄⋊C₄×C₃₁	—	2	4	no	—
261	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
264	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
265	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂²⋊C₄×C₃₁	—	2	2	no	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	4	no	—
275	C₂²⋊C₄×C₃₁	—	2	2	no	—
276	C₂²⋊C₄×C₃₁	—	2	4	no	—
277	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
279	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
280	C₄²×C₃₁	—	2	4	no	—
281	C₄²×C₃₁	—	2	4	no	—
282	C₄²×C₃₁	—	2	4	no	—
283	C₄²×C₃₁	—	2	2	no	—
284	C₄²×C₃₁	C₂×D₄	1	4	yes	—
285	C₄²×C₃₁	C₂⁴	1	2	yes	—
286	C₄²×C₃₁	C₂⁴	1	2	yes	—
287	#60711	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	2	2	no	—
290	C₂³×C₃₁	—	4	2	no	—
291	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
292	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
293	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
294	Q₈×C₃₁	—	2	4	no	—
295	Q₈×C₃₁	—	2	2	no	—
296	Q₈×C₃₁	—	2	4	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	2	no	—
302	D₄×C₃₁	—	4	4	no	—
303	D₄×C₃₁	—	4	4	no	—
304	D₄×C₃₁	—	8	2	no	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	2	2	no	—
307	C₂×C₄×C₃₁	—	2	2	no	—
308	C₂×C₄×C₃₁	—	2	1	no	—
309	C₂×C₄×C₃₁	—	2	1	no	—
310	C₂×C₄×C₃₁	—	2	1	no	—
311	C₂×C₄×C₃₁	—	2	1	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	4	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	4	no	—
317	C₂×C₄×C₃₁	—	4	4	no	—
318	C₂×C₄×C₃₁	—	4	4	no	—
319	C₂×C₄×C₃₁	—	4	4	no	—
320	C₂×C₄×C₃₁	—	8	4	no	—
321	C₂×C₄×C₃₁	—	8	2	no	—
322	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
325	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
328	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
329	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
330	C₈×C₃₁	—	2	1	no	—
331	C₈×C₃₁	—	2	1	no	—
332	C₈×C₃₁	—	2	2	no	—
333	C₈×C₃₁	C₂×#41	1	4	yes	—
334	C₈×C₃₁	C₂×#41	1	2	yes	—
335	C₈×C₃₁	C₂×#41	1	2	yes	—
336	#3495	C₂×C₃₁	1	2	yes	complemented
337	#3185	C₂×C₃₁	1	2	yes	complemented
338	#3183	C₂×C₃₁	1	2	yes	complemented
339	#3178	C₂×C₃₁	1	4	yes	complemented
340	#3177	C₂×C₃₁	1	2	yes	complemented
341	#3173	C₂×C₃₁	1	2	yes	complemented
342	#3172	C₂×C₃₁	1	4	yes	complemented
343	#3163	C₂×C₃₁	1	1	yes	characteristic, complemented
344	#3156	C₂×C₃₁	1	1	yes	characteristic, complemented
345	#3137	C₂×C₃₁	1	2	yes	complemented
346	#3056	C₂×C₃₁	1	2	yes	complemented
347	#3054	C₂×C₃₁	1	1	yes	characteristic
348	C₂×#470	C₂×C₃₁	1	1	yes	characteristic, complemented
349	#2952	C₂×C₃₁	1	1	yes	characteristic, complemented
350	#2950	C₂×C₃₁	1	1	yes	characteristic, complemented
351	#2947	C₂×C₃₁	1	2	yes	complemented
352	#2873	C₂×C₃₁	1	1	yes	characteristic, complemented
353	C₂²×C₃₁	—	2	2	no	—
354	C₂²×C₃₁	—	2	2	no	—
355	C₂²×C₃₁	—	2	2	no	—
356	C₂²×C₃₁	—	2	1	no	—
357	C₂²×C₃₁	—	2	1	no	—
358	C₂²×C₃₁	—	4	2	no	—
359	C₂²×C₃₁	—	4	2	no	—
360	C₂²×C₃₁	—	4	2	no	—
361	C₂²×C₃₁	—	8	2	no	—
362	C₂²×C₃₁	#532	1	2	yes	—
363	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
364	C₄×C₃₁	—	2	4	no	—
365	C₄×C₃₁	—	2	4	no	—
366	C₄×C₃₁	—	2	1	no	—
367	C₄×C₃₁	—	2	1	no	—
368	C₄×C₃₁	—	4	4	no	—
369	C₄×C₃₁	—	4	2	no	—
370	C₄×C₃₁	—	4	2	no	—
371	C₄×C₃₁	—	4	2	no	—
372	C₄×C₃₁	—	4	4	no	—
373	C₄×C₃₁	#532	1	2	yes	—
374	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
375	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
376	C₂×#137	C₂²×C₃₁	1	2	yes	—
377	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
378	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
379	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
380	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
381	#556	—	2	2	no	—
382	#554	—	2	2	no	—
383	#552	—	2	4	no	—
384	#552	—	2	2	no	—
385	#552	—	2	2	no	—
386	#551	—	2	4	no	—
387	#544	C₂²×C₃₁	1	2	yes	—
388	#542	C₂²×C₃₁	1	4	yes	—
389	#541	C₂²×C₃₁	1	4	yes	—
390	#536	C₂²×C₃₁	1	2	yes	—
391	#533	C₂²×C₃₁	1	4	yes	—
392	#529	C₂²×C₃₁	1	4	yes	—
393	#525	C₂²×C₃₁	1	2	yes	—
394	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
395	#520	C₂²×C₃₁	1	2	yes	—
396	#519	C₂²×C₃₁	1	2	yes	—
397	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
398	#501	C₂²×C₃₁	1	4	yes	complemented
399	#499	C₂²×C₃₁	1	2	yes	complemented
400	#498	C₂²×C₃₁	1	2	yes	complemented
401	#497	C₂²×C₃₁	1	4	yes	complemented
402	#495	C₂²×C₃₁	1	2	yes	complemented
403	#494	C₂²×C₃₁	1	2	yes	complemented
404	#491	C₂²×C₃₁	1	4	yes	complemented
405	#489	C₂²×C₃₁	1	4	yes	complemented
406	#488	C₂²×C₃₁	1	4	yes	complemented
407	#487	C₂²×C₃₁	1	4	yes	complemented
408	#470	C₂²×C₃₁	1	2	yes	—
409	#470	C₂²×C₃₁	1	4	yes	—
410	#470	C₂²×C₃₁	1	2	yes	—
411	#470	C₂²×C₃₁	1	1	yes	characteristic
412	#470	C₂²×C₃₁	1	2	yes	—
413	#470	C₂²×C₃₁	1	2	yes	—
414	#470	C₂²×C₃₁	1	1	yes	characteristic
415	#469	C₂²×C₃₁	1	1	yes	characteristic
416	#469	C₂²×C₃₁	1	1	yes	characteristic
417	#468	C₂²×C₃₁	1	2	yes	—
418	#468	C₂²×C₃₁	1	4	yes	—
419	#468	C₂²×C₃₁	1	2	yes	—
420	#467	C₂²×C₃₁	1	4	yes	—
421	#465	C₂²×C₃₁	1	4	yes	—
422	#442	C₂²×C₃₁	1	2	yes	complemented
423	#441	C₂²×C₃₁	1	2	yes	complemented
424	#441	C₂²×C₃₁	1	2	yes	complemented
425	#441	C₂²×C₃₁	1	2	yes	complemented
426	#441	C₂²×C₃₁	1	4	yes	complemented
427	#440	C₂²×C₃₁	1	4	yes	complemented
428	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
429	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
430	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
431	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
432	#428	C₂²×C₃₁	1	2	yes	—
433	#427	C₂²×C₃₁	1	1	yes	characteristic
434	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
435	#419	C₂²×C₃₁	1	2	yes	—
436	#417	C₂²×C₃₁	1	2	yes	—
437	#416	C₂²×C₃₁	1	2	yes	—
438	C₂×#103	C₂²×C₃₁	1	2	yes	—
439	#405	C₂²×C₃₁	1	1	yes	characteristic
440	#405	C₂²×C₃₁	1	1	yes	characteristic
441	#405	C₂²×C₃₁	1	2	yes	—
442	#405	C₂²×C₃₁	1	2	yes	—
443	#405	C₂²×C₃₁	1	1	yes	characteristic
444	#405	C₂²×C₃₁	1	1	yes	characteristic
445	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
446	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
447	C₂×C₃₁	—	2	2	no	—
448	C₂×C₃₁	—	4	1	no	—
449	C₂×C₃₁	—	4	1	no	—
450	C₂×C₃₁	—	8	2	no	—
451	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
452	C₂×C₃₁	#3586	1	2	yes	—
453	C₂×#41	C₂³×C₃₁	1	2	yes	—
454	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
455	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
456	#137	—	2	8	no	—
457	#135	—	2	4	no	—
458	C₂×Q₁₆	—	2	4	no	—
459	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
460	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
461	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
462	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
463	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
464	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
465	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
466	C₂×M₁₆	—	2	4	no	—
467	C₂×M₁₆	—	2	4	no	—
468	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
469	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
470	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
471	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
472	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
473	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
474	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
477	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
478	C₄⋊Q₈	—	2	2	no	—
479	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
480	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
481	#126	—	2	4	no	—
482	#126	—	2	4	no	—
483	#126	—	2	4	no	—
484	#126	—	2	4	no	—
485	#125	—	2	4	no	—
486	#125	—	2	4	no	—
487	#125	—	2	2	no	—
488	#125	—	2	4	no	—
489	#125	C₂³×C₃₁	1	4	yes	—
490	#124	—	2	4	no	—
491	#124	C₂³×C₃₁	1	4	yes	—
492	#123	—	2	2	no	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	#123	—	2	4	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	2	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	4	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
504	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
505	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
506	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
507	#121	C₂³×C₃₁	1	2	yes	—
508	#121	C₂³×C₃₁	1	2	yes	—
509	#120	—	2	2	no	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	—	2	2	no	—
512	C₄×Q₈	—	2	4	no	—
513	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
514	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
515	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	4	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	C₂³×C₃₁	1	4	yes	—
521	#117	—	2	4	no	—
522	#117	—	2	2	no	—
523	#117	—	2	4	no	—
524	#117	—	2	4	no	—
525	#117	D₄×C₃₁	1	2	yes	—
526	#117	D₄×C₃₁	1	2	yes	—
527	#117	C₂³×C₃₁	1	2	yes	—
528	#117	C₂³×C₃₁	1	1	yes	characteristic
529	#117	C₂³×C₃₁	1	1	yes	characteristic
530	#117	C₂³×C₃₁	1	2	yes	—
531	C₂×C₄⋊C₄	—	2	2	no	—
532	C₂×C₄⋊C₄	—	2	2	no	—
533	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
535	C₂×C₂²⋊C₄	—	2	2	no	—
536	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
537	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
538	#107	C₂³×C₃₁	1	2	yes	—
539	#107	C₂³×C₃₁	1	4	yes	—
540	#106	C₂³×C₃₁	1	2	yes	—
541	#106	C₂³×C₃₁	1	2	yes	—
542	#106	C₂³×C₃₁	1	1	yes	characteristic
543	#106	C₂³×C₃₁	1	1	yes	characteristic
544	#106	C₂³×C₃₁	1	4	yes	—
545	#103	C₂³×C₃₁	1	4	yes	—
546	#103	C₂³×C₃₁	1	4	yes	—
547	#103	C₂³×C₃₁	1	2	yes	—
548	#103	C₂³×C₃₁	1	2	yes	—
549	#103	C₂³×C₃₁	1	4	yes	—
550	#103	C₂³×C₃₁	1	4	yes	—
551	#103	C₂³×C₃₁	1	4	yes	—
552	#102	C₂³×C₃₁	1	2	yes	—
553	#102	C₂³×C₃₁	1	2	yes	—
554	#102	C₂³×C₃₁	1	4	yes	—
555	#97	C₂³×C₃₁	1	2	yes	—
556	#97	C₂³×C₃₁	1	2	yes	—
557	#97	C₂³×C₃₁	1	2	yes	—
558	#97	C₂³×C₃₁	1	2	yes	—
559	C₄×C₈	C₂³×C₃₁	1	2	yes	—
560	C₄×C₈	C₂³×C₃₁	1	2	yes	—
561	C₄×C₈	C₂³×C₃₁	1	2	yes	—
562	C₄×C₈	C₂³×C₃₁	1	2	yes	—
563	C₃₁	#60711	1	1	yes	characteristic, direct product factor, Sylow
564	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
565	#41	—	2	4	no	—
566	#41	—	2	4	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	4	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
572	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
587	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
590	Q₁₆	—	2	4	no	—
591	Q₁₆	—	2	4	no	—
592	Q₁₆	—	2	2	no	—
593	Q₁₆	—	2	8	no	—
594	SD₁₆	—	2	4	no	—
595	SD₁₆	—	2	8	no	—
596	D₈	—	2	2	no	—
597	M₁₆	—	2	2	no	—
598	M₁₆	—	2	4	no	—
599	M₁₆	—	2	2	no	—
600	M₁₆	—	2	2	no	—
601	M₁₆	—	2	2	no	—
602	M₁₆	—	2	2	no	—
603	M₁₆	#41×C₃₁	1	4	yes	—
604	C₂×C₈	—	2	2	no	—
605	C₂×C₈	—	2	4	no	—
606	C₂×C₈	#41×C₃₁	1	4	yes	—
607	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
608	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
609	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
610	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
611	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
612	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
627	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
628	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
629	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
630	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
631	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
643	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
644	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
645	C₄²	—	2	4	no	—
646	C₄²	—	2	4	no	—
647	C₄²	—	2	4	no	—
648	C₄²	—	2	2	no	—
649	C₄²	C₂×D₄×C₃₁	1	4	yes	—
650	C₄²	C₂⁴×C₃₁	1	2	yes	—
651	C₄²	C₂⁴×C₃₁	1	2	yes	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	4	2	no	—
655	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
656	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
657	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
658	Q₈	—	2	4	no	—
659	Q₈	—	2	2	no	—
660	Q₈	—	2	4	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	4	4	no	—
663	Q₈	—	8	4	no	—
664	D₄	—	2	2	no	—
665	D₄	—	2	2	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	4	no	—
668	D₄	—	8	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	4	4	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	8	4	no	—
685	C₂×C₄	—	8	2	no	—
686	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
687	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
688	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
689	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
691	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
692	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
693	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
694	C₈	—	2	1	no	—
695	C₈	—	2	1	no	—
696	C₈	—	2	2	no	—
697	C₈	C₂×#41×C₃₁	1	4	yes	—
698	C₈	C₂×#41×C₃₁	1	2	yes	—
699	C₈	C₂×#41×C₃₁	1	2	yes	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	8	2	no	—
709	C₂²	C₃₁×#532	1	2	yes	—
710	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
711	C₄	—	2	1	no	—
712	C₄	—	2	1	no	—
713	C₄	—	2	4	no	—
714	C₄	—	2	4	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	4	no	—
717	C₄	—	4	4	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	C₃₁×#532	1	2	yes	—
721	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
722	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
723	C₂	—	2	2	no	—
724	C₂	—	4	1	no	—
725	C₂	—	4	1	no	—
726	C₂	—	8	2	no	—
727	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
728	C₂	C₃₁×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3495	C₂	semidirect
2. C₃₁×#3185	C₂	semidirect
3. C₃₁×#3183	C₂	semidirect
4. C₃₁×#3178	C₂	semidirect
5. C₃₁×#3177	C₂	semidirect
6. C₃₁×#3173	C₂	semidirect
7. C₃₁×#3172	C₂	semidirect
8. C₃₁×#3163	C₂	semidirect
9. C₃₁×#3156	C₂	semidirect
10. C₃₁×#3137	C₂	semidirect
11. C₃₁×#3056	C₂	semidirect
13. C₂×C₃₁×#470	C₂	semidirect
14. C₃₁×#2952	C₂	semidirect
15. C₃₁×#2950	C₂	semidirect
16. C₃₁×#2947	C₂	semidirect
17. C₃₁×#2873	C₂	semidirect
40. C₃₁×#501	C₂²	semidirect
41. C₃₁×#499	C₂²	semidirect
42. C₃₁×#498	C₂²	semidirect
43. C₃₁×#497	C₂²	semidirect
44. C₃₁×#495	C₂²	semidirect
45. C₃₁×#494	C₂²	semidirect
46. C₃₁×#491	C₂²	semidirect
47. C₃₁×#489	C₂²	semidirect
48. C₃₁×#488	C₂²	semidirect
49. C₃₁×#487	C₂²	semidirect
64. C₃₁×#442	C₂²	semidirect
65. C₃₁×#441	C₂²	semidirect
66. C₃₁×#441	C₂²	semidirect
67. C₃₁×#441	C₂²	semidirect
68. C₃₁×#441	C₂²	semidirect
69. C₃₁×#440	C₂²	semidirect
70. C₄×Q₁₆×C₃₁	C₂²	semidirect
71. C₄×Q₁₆×C₃₁	C₂²	semidirect
72. C₄×SD₁₆×C₃₁	C₂²	semidirect
73. C₄×SD₁₆×C₃₁	C₂²	semidirect
287. #60711	C₃₁	direct (N × H)
336. #3495	C₂×C₃₁	semidirect
337. #3185	C₂×C₃₁	semidirect
338. #3183	C₂×C₃₁	semidirect
339. #3178	C₂×C₃₁	semidirect
340. #3177	C₂×C₃₁	semidirect
341. #3173	C₂×C₃₁	semidirect
342. #3172	C₂×C₃₁	semidirect
343. #3163	C₂×C₃₁	semidirect
344. #3156	C₂×C₃₁	semidirect
345. #3137	C₂×C₃₁	semidirect
346. #3056	C₂×C₃₁	semidirect
348. C₂×#470	C₂×C₃₁	semidirect
349. #2952	C₂×C₃₁	semidirect
350. #2950	C₂×C₃₁	semidirect
351. #2947	C₂×C₃₁	semidirect
352. #2873	C₂×C₃₁	semidirect
398. #501	C₂²×C₃₁	semidirect
399. #499	C₂²×C₃₁	semidirect
400. #498	C₂²×C₃₁	semidirect
401. #497	C₂²×C₃₁	semidirect
402. #495	C₂²×C₃₁	semidirect
403. #494	C₂²×C₃₁	semidirect
404. #491	C₂²×C₃₁	semidirect
405. #489	C₂²×C₃₁	semidirect
406. #488	C₂²×C₃₁	semidirect
407. #487	C₂²×C₃₁	semidirect
422. #442	C₂²×C₃₁	semidirect
423. #441	C₂²×C₃₁	semidirect
424. #441	C₂²×C₃₁	semidirect
425. #441	C₂²×C₃₁	semidirect
426. #441	C₂²×C₃₁	semidirect
427. #440	C₂²×C₃₁	semidirect
428. C₄×Q₁₆	C₂²×C₃₁	semidirect
429. C₄×Q₁₆	C₂²×C₃₁	semidirect
430. C₄×SD₁₆	C₂²×C₃₁	semidirect
431. C₄×SD₁₆	C₂²×C₃₁	semidirect
563. C₃₁	#60711	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×#3495	2
C₃₁×#3185	2
C₃₁×#3183	2
C₃₁×#3178	2
C₃₁×#3177	2
C₃₁×#3173	2
C₃₁×#3172	2
C₃₁×#3163	2
C₃₁×#3156	2
C₃₁×#3137	2
C₃₁×#3056	2
C₃₁×#3054	2
C₂×C₃₁×#470	2
C₃₁×#2952	2
C₃₁×#2950	2
C₃₁×#2947	2
C₃₁×#2873	2
#60711	31

Subgroups — C31×#60711 #21517470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60711 #21517470