Subgroups — C₃₁×#60710 #21517469

Order 7936.

1966 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3494	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3184	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3183	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3179	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3176	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3173	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3171	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3163	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3055	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3054	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#469	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2952	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2946	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2873	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
20	C₂²×D₈×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×#555	—	2	2	no	—
24	C₃₁×#553	—	2	2	no	—
25	C₃₁×#553	—	2	2	no	—
26	C₃₁×#551	—	2	4	no	—
27	C₃₁×#547	—	2	2	no	—
28	C₃₁×#546	—	2	4	no	—
29	C₃₁×#544	C₂²	1	2	yes	—
30	C₃₁×#542	C₂²	1	4	yes	complemented
31	C₃₁×#540	C₂²	1	4	yes	complemented
32	C₃₁×#535	C₂²	1	2	yes	—
33	C₃₁×#532	C₂²	1	4	yes	complemented
34	C₃₁×#529	C₂²	1	4	yes	complemented
35	C₃₁×#525	C₂²	1	2	yes	—
36	C₂×C₃₁×#121	C₂²	1	2	yes	—
37	C₃₁×#520	C₂²	1	2	yes	—
38	C₃₁×#518	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×#496	C₂²	1	4	yes	complemented
44	C₃₁×#495	C₂²	1	2	yes	complemented
45	C₃₁×#493	C₂²	1	2	yes	complemented
46	C₃₁×#490	C₂²	1	4	yes	complemented
47	C₃₁×#489	C₂²	1	4	yes	complemented
48	C₃₁×#488	C₂²	1	4	yes	complemented
49	C₃₁×#486	C₂²	1	4	yes	complemented
50	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#469	C₂²	1	2	yes	—
53	C₃₁×#469	C₂²	1	2	yes	—
54	C₃₁×#469	C₂²	1	2	yes	—
55	C₃₁×#469	C₂²	1	2	yes	—
56	C₃₁×#469	C₂²	1	4	yes	complemented
57	C₃₁×#469	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#469	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#468	C₂²	1	2	yes	complemented
60	C₃₁×#468	C₂²	1	4	yes	complemented
61	C₃₁×#468	C₂²	1	2	yes	complemented
62	C₃₁×#466	C₂²	1	4	yes	complemented
63	C₃₁×#465	C₂²	1	4	yes	complemented
64	C₃₁×#442	C₂²	1	2	yes	complemented
65	C₃₁×#442	C₂²	1	2	yes	complemented
66	C₃₁×#442	C₂²	1	2	yes	complemented
67	C₃₁×#442	C₂²	1	4	yes	complemented
68	C₃₁×#441	C₂²	1	2	yes	complemented
69	C₃₁×#440	C₂²	1	4	yes	complemented
70	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
71	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
72	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
73	C₄×D₈×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×#418	C₂²	1	2	yes	—
78	C₃₁×#417	C₂²	1	2	yes	—
79	C₃₁×#416	C₂²	1	2	yes	—
80	C₂×C₃₁×#102	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	1	yes	characteristic
84	C₃₁×#405	C₂²	1	1	yes	characteristic
85	C₃₁×#405	C₂²	1	2	yes	complemented
86	C₃₁×#405	C₂²	1	2	yes	complemented
87	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
88	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
89	C₂×#41×C₃₁	—	2	4	no	—
90	C₂×#41×C₃₁	C₂³	1	2	yes	—
91	C₂²×D₄×C₃₁	—	2	2	no	—
92	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
95	C₃₁×#135	—	2	4	no	—
96	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
98	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×D₈×C₃₁	—	2	4	no	—
100	C₂×D₈×C₃₁	C₂³	1	2	yes	—
101	C₂×D₈×C₃₁	C₂³	1	4	yes	—
102	C₂×D₈×C₃₁	C₂³	1	2	yes	—
103	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
104	C₂×M₁₆×C₃₁	—	2	4	no	—
105	C₂×M₁₆×C₃₁	—	2	4	no	—
106	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
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	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
112	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
115	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
116	C₃₁×C₄⋊Q₈	—	2	2	no	—
117	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
118	C₃₁×#127	C₂³	1	4	yes	—
119	C₃₁×#126	—	2	4	no	—
120	C₃₁×#126	—	2	4	no	—
121	C₃₁×#125	—	2	2	no	—
122	C₃₁×#125	C₂³	1	4	yes	—
123	C₃₁×#124	—	2	4	no	—
124	C₃₁×#124	—	2	4	no	—
125	C₃₁×#124	C₂³	1	4	yes	—
126	C₃₁×#123	—	2	2	no	—
127	C₃₁×#123	—	2	4	no	—
128	C₃₁×#123	—	2	4	no	—
129	C₃₁×#123	—	2	4	no	—
130	C₃₁×#123	—	2	4	no	—
131	C₃₁×C₂²⋊Q₈	—	2	4	no	—
132	C₃₁×C₂²⋊Q₈	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₃₁×#121	—	2	2	no	—
136	C₃₁×#121	—	2	2	no	—
137	C₃₁×#121	—	2	4	no	—
138	C₃₁×#121	—	2	2	no	—
139	C₃₁×#121	—	2	2	no	—
140	C₃₁×#121	—	2	4	no	—
141	C₃₁×#121	—	2	4	no	—
142	C₃₁×#121	C₂³	1	4	yes	—
143	C₃₁×#121	C₂³	1	2	yes	—
144	C₃₁×#121	C₂³	1	4	yes	—
145	C₃₁×#121	C₂³	1	2	yes	—
146	C₃₁×#120	—	2	2	no	—
147	C₃₁×#120	—	2	4	no	—
148	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
149	C₄×D₄×C₃₁	—	2	2	no	—
150	C₄×D₄×C₃₁	—	2	2	no	—
151	C₄×D₄×C₃₁	—	2	4	no	—
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	C₄×D₄×C₃₁	C₂³	1	4	yes	—
158	C₄×D₄×C₃₁	C₂³	1	4	yes	—
159	C₃₁×#117	—	2	2	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	D₄	1	2	yes	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
171	C₂×C₂²⋊C₄×C₃₁	—	2	4	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	2	yes	—
182	C₃₁×#103	C₂³	1	2	yes	—
183	C₃₁×#103	C₂³	1	4	yes	—
184	C₃₁×#102	C₂³	1	4	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	2	yes	—
187	C₃₁×#102	C₂³	1	2	yes	—
188	C₃₁×#102	C₂³	1	4	yes	—
189	C₃₁×#102	C₂³	1	4	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	—	2	2	no	—
200	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
201	#41×C₃₁	—	2	4	no	—
202	#41×C₃₁	—	2	4	no	—
203	#41×C₃₁	—	8	8	no	—
204	C₂×Q₈×C₃₁	—	2	4	no	—
205	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
206	C₂×D₄×C₃₁	—	2	2	no	—
207	C₂×D₄×C₃₁	—	2	2	no	—
208	C₂×D₄×C₃₁	—	2	4	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	2	no	—
212	C₂×D₄×C₃₁	—	2	4	no	—
213	C₂×D₄×C₃₁	—	2	4	no	—
214	C₂×D₄×C₃₁	—	2	4	no	—
215	C₂×D₄×C₃₁	—	2	4	no	—
216	C₂×D₄×C₃₁	—	8	4	no	—
217	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
218	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
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	—	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	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
230	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
233	Q₁₆×C₃₁	—	2	2	no	—
234	SD₁₆×C₃₁	—	2	4	no	—
235	SD₁₆×C₃₁	—	2	8	no	—
236	D₈×C₃₁	—	2	4	no	—
237	D₈×C₃₁	—	2	4	no	—
238	D₈×C₃₁	—	2	2	no	—
239	D₈×C₃₁	—	2	8	no	—
240	M₁₆×C₃₁	—	2	2	no	—
241	M₁₆×C₃₁	—	2	4	no	—
242	M₁₆×C₃₁	—	2	2	no	—
243	M₁₆×C₃₁	—	2	2	no	—
244	M₁₆×C₃₁	—	2	2	no	—
245	M₁₆×C₃₁	—	2	2	no	—
246	M₁₆×C₃₁	#41	1	4	yes	complemented
247	C₂×C₈×C₃₁	—	2	2	no	—
248	C₂×C₈×C₃₁	—	2	4	no	—
249	C₂×C₈×C₃₁	#41	1	4	yes	complemented
250	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
252	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
255	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
263	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
264	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
265	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
266	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
267	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	4	no	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	4	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	—	2	2	no	—
279	C₂²⋊C₄×C₃₁	—	2	4	no	—
280	C₂²⋊C₄×C₃₁	—	2	2	no	—
281	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
284	C₄²×C₃₁	—	2	4	no	—
285	C₄²×C₃₁	—	2	2	no	—
286	C₄²×C₃₁	C₂×D₄	1	4	yes	—
287	C₄²×C₃₁	C₂⁴	1	2	yes	—
288	C₄²×C₃₁	C₂⁴	1	2	yes	—
289	#60710	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₂³×C₃₁	—	2	2	no	—
291	C₂³×C₃₁	—	2	4	no	—
292	C₂³×C₃₁	—	2	2	no	—
293	C₂³×C₃₁	—	4	2	no	—
294	C₂³×C₃₁	—	4	4	no	—
295	C₂³×C₃₁	—	8	2	no	—
296	C₂³×C₃₁	—	8	2	no	—
297	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
298	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
299	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
300	Q₈×C₃₁	—	2	2	no	—
301	Q₈×C₃₁	—	2	2	no	—
302	Q₈×C₃₁	—	8	4	no	—
303	D₄×C₃₁	—	2	4	no	—
304	D₄×C₃₁	—	2	2	no	—
305	D₄×C₃₁	—	2	4	no	—
306	D₄×C₃₁	—	2	2	no	—
307	D₄×C₃₁	—	4	8	no	—
308	D₄×C₃₁	—	4	4	no	—
309	D₄×C₃₁	—	4	4	no	—
310	D₄×C₃₁	—	4	4	no	—
311	D₄×C₃₁	—	8	4	no	—
312	D₄×C₃₁	—	8	4	no	—
313	D₄×C₃₁	—	8	2	no	—
314	D₄×C₃₁	—	8	4	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	1	no	—
319	C₂×C₄×C₃₁	—	2	1	no	—
320	C₂×C₄×C₃₁	—	2	1	no	—
321	C₂×C₄×C₃₁	—	2	1	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	4	no	—
326	C₂×C₄×C₃₁	—	4	4	no	—
327	C₂×C₄×C₃₁	—	4	4	no	—
328	C₂×C₄×C₃₁	—	8	4	no	—
329	C₂×C₄×C₃₁	—	8	4	no	—
330	C₂×C₄×C₃₁	—	8	4	no	—
331	C₂×C₄×C₃₁	—	8	2	no	—
332	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
335	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
338	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
339	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
340	C₈×C₃₁	—	2	1	no	—
341	C₈×C₃₁	—	2	1	no	—
342	C₈×C₃₁	—	2	2	no	—
343	C₈×C₃₁	C₂×#41	1	4	yes	—
344	C₈×C₃₁	C₂×#41	1	2	yes	—
345	C₈×C₃₁	C₂×#41	1	2	yes	—
346	#3494	C₂×C₃₁	1	2	yes	complemented
347	#3184	C₂×C₃₁	1	2	yes	complemented
348	#3183	C₂×C₃₁	1	2	yes	complemented
349	#3179	C₂×C₃₁	1	4	yes	complemented
350	#3176	C₂×C₃₁	1	2	yes	complemented
351	#3173	C₂×C₃₁	1	2	yes	complemented
352	#3171	C₂×C₃₁	1	4	yes	complemented
353	#3163	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#3155	C₂×C₃₁	1	1	yes	characteristic, complemented
355	#3136	C₂×C₃₁	1	2	yes	complemented
356	#3055	C₂×C₃₁	1	2	yes	complemented
357	#3054	C₂×C₃₁	1	1	yes	characteristic, complemented
358	C₂×#469	C₂×C₃₁	1	1	yes	characteristic, complemented
359	#2952	C₂×C₃₁	1	1	yes	characteristic, complemented
360	#2948	C₂×C₃₁	1	1	yes	characteristic, complemented
361	#2946	C₂×C₃₁	1	2	yes	complemented
362	#2873	C₂×C₃₁	1	1	yes	characteristic, complemented
363	C₂²×C₃₁	—	2	2	no	—
364	C₂²×C₃₁	—	2	2	no	—
365	C₂²×C₃₁	—	2	2	no	—
366	C₂²×C₃₁	—	2	1	no	—
367	C₂²×C₃₁	—	2	1	no	—
368	C₂²×C₃₁	—	4	2	no	—
369	C₂²×C₃₁	—	4	4	no	—
370	C₂²×C₃₁	—	4	4	no	—
371	C₂²×C₃₁	—	4	2	no	—
372	C₂²×C₃₁	—	4	2	no	—
373	C₂²×C₃₁	—	4	4	no	—
374	C₂²×C₃₁	—	8	2	no	—
375	C₂²×C₃₁	—	16	4	no	—
376	C₂²×C₃₁	#532	1	2	yes	—
377	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
378	C₄×C₃₁	—	2	4	no	—
379	C₄×C₃₁	—	2	4	no	—
380	C₄×C₃₁	—	2	1	no	—
381	C₄×C₃₁	—	2	1	no	—
382	C₄×C₃₁	—	4	4	no	—
383	C₄×C₃₁	—	4	2	no	—
384	C₄×C₃₁	—	4	2	no	—
385	C₄×C₃₁	—	4	2	no	—
386	C₄×C₃₁	#532	1	2	yes	—
387	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
388	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
389	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
390	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
391	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
392	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
393	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
394	#555	—	2	2	no	—
395	#553	—	2	2	no	—
396	#553	—	2	2	no	—
397	#551	—	2	4	no	—
398	#547	—	2	2	no	—
399	#546	—	2	4	no	—
400	#544	C₂²×C₃₁	1	2	yes	—
401	#542	C₂²×C₃₁	1	4	yes	complemented
402	#540	C₂²×C₃₁	1	4	yes	complemented
403	#535	C₂²×C₃₁	1	2	yes	—
404	#532	C₂²×C₃₁	1	4	yes	complemented
405	#529	C₂²×C₃₁	1	4	yes	complemented
406	#525	C₂²×C₃₁	1	2	yes	—
407	C₂×#121	C₂²×C₃₁	1	2	yes	—
408	#520	C₂²×C₃₁	1	2	yes	—
409	#518	C₂²×C₃₁	1	2	yes	—
410	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
411	#501	C₂²×C₃₁	1	4	yes	complemented
412	#499	C₂²×C₃₁	1	2	yes	complemented
413	#498	C₂²×C₃₁	1	2	yes	complemented
414	#496	C₂²×C₃₁	1	4	yes	complemented
415	#495	C₂²×C₃₁	1	2	yes	complemented
416	#493	C₂²×C₃₁	1	2	yes	complemented
417	#490	C₂²×C₃₁	1	4	yes	complemented
418	#489	C₂²×C₃₁	1	4	yes	complemented
419	#488	C₂²×C₃₁	1	4	yes	complemented
420	#486	C₂²×C₃₁	1	4	yes	complemented
421	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
422	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
423	#469	C₂²×C₃₁	1	2	yes	—
424	#469	C₂²×C₃₁	1	2	yes	—
425	#469	C₂²×C₃₁	1	2	yes	—
426	#469	C₂²×C₃₁	1	2	yes	—
427	#469	C₂²×C₃₁	1	4	yes	complemented
428	#469	C₂²×C₃₁	1	1	yes	characteristic, complemented
429	#469	C₂²×C₃₁	1	1	yes	characteristic, complemented
430	#468	C₂²×C₃₁	1	2	yes	complemented
431	#468	C₂²×C₃₁	1	4	yes	complemented
432	#468	C₂²×C₃₁	1	2	yes	complemented
433	#466	C₂²×C₃₁	1	4	yes	complemented
434	#465	C₂²×C₃₁	1	4	yes	complemented
435	#442	C₂²×C₃₁	1	2	yes	complemented
436	#442	C₂²×C₃₁	1	2	yes	complemented
437	#442	C₂²×C₃₁	1	2	yes	complemented
438	#442	C₂²×C₃₁	1	4	yes	complemented
439	#441	C₂²×C₃₁	1	2	yes	complemented
440	#440	C₂²×C₃₁	1	4	yes	complemented
441	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
442	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
443	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
444	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
445	#428	C₂²×C₃₁	1	2	yes	—
446	#427	C₂²×C₃₁	1	1	yes	characteristic
447	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
448	#418	C₂²×C₃₁	1	2	yes	—
449	#417	C₂²×C₃₁	1	2	yes	—
450	#416	C₂²×C₃₁	1	2	yes	—
451	C₂×#102	C₂²×C₃₁	1	2	yes	—
452	#405	C₂²×C₃₁	1	1	yes	characteristic
453	#405	C₂²×C₃₁	1	1	yes	characteristic
454	#405	C₂²×C₃₁	1	1	yes	characteristic
455	#405	C₂²×C₃₁	1	1	yes	characteristic
456	#405	C₂²×C₃₁	1	2	yes	complemented
457	#405	C₂²×C₃₁	1	2	yes	complemented
458	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
459	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
460	C₂×C₃₁	—	2	2	no	—
461	C₂×C₃₁	—	4	1	no	—
462	C₂×C₃₁	—	4	1	no	—
463	C₂×C₃₁	—	8	2	no	—
464	C₂×C₃₁	—	8	4	no	—
465	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
466	C₂×C₃₁	#3585	1	2	yes	—
467	C₂×#41	—	2	4	no	—
468	C₂×#41	C₂³×C₃₁	1	2	yes	—
469	C₂²×D₄	—	2	2	no	—
470	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
471	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
472	AGL(1,ℤ/8)	—	2	8	no	—
473	#135	—	2	4	no	—
474	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
475	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
476	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
477	C₂×D₈	—	2	4	no	—
478	C₂×D₈	C₂³×C₃₁	1	2	yes	—
479	C₂×D₈	C₂³×C₃₁	1	2	yes	—
480	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
481	C₂×D₈	C₂³×C₃₁	1	4	yes	—
482	C₂×M₁₆	—	2	4	no	—
483	C₂×M₁₆	—	2	4	no	—
484	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
485	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
486	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
487	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
488	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
489	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
490	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
493	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
496	#127	C₂³×C₃₁	1	4	yes	—
497	#126	—	2	4	no	—
498	#126	—	2	4	no	—
499	#125	—	2	2	no	—
500	#125	C₂³×C₃₁	1	4	yes	—
501	#124	—	2	4	no	—
502	#124	—	2	4	no	—
503	#124	C₂³×C₃₁	1	4	yes	—
504	#123	—	2	2	no	—
505	#123	—	2	4	no	—
506	#123	—	2	4	no	—
507	#123	—	2	4	no	—
508	#123	—	2	4	no	—
509	C₂²⋊Q₈	—	2	4	no	—
510	C₂²⋊Q₈	—	2	4	no	—
511	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
512	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
513	#121	—	2	2	no	—
514	#121	—	2	2	no	—
515	#121	—	2	4	no	—
516	#121	—	2	2	no	—
517	#121	—	2	2	no	—
518	#121	—	2	4	no	—
519	#121	—	2	4	no	—
520	#121	C₂³×C₃₁	1	4	yes	—
521	#121	C₂³×C₃₁	1	4	yes	—
522	#121	C₂³×C₃₁	1	2	yes	—
523	#121	C₂³×C₃₁	1	2	yes	—
524	#120	—	2	2	no	—
525	#120	—	2	4	no	—
526	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	4	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	4	no	—
533	C₄×D₄	—	2	4	no	—
534	C₄×D₄	C₂³×C₃₁	1	4	yes	—
535	C₄×D₄	C₂³×C₃₁	1	4	yes	—
536	C₄×D₄	C₂³×C₃₁	1	4	yes	—
537	#117	—	2	2	no	—
538	#117	—	2	4	no	—
539	#117	D₄×C₃₁	1	2	yes	—
540	#117	D₄×C₃₁	1	2	yes	—
541	#117	C₂³×C₃₁	1	2	yes	—
542	#117	C₂³×C₃₁	1	1	yes	characteristic
543	#117	C₂³×C₃₁	1	1	yes	characteristic
544	#117	C₂³×C₃₁	1	2	yes	—
545	C₂×C₄⋊C₄	—	2	2	no	—
546	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
548	C₂×C₂²⋊C₄	—	2	2	no	—
549	C₂×C₂²⋊C₄	—	2	4	no	—
550	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
551	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
552	#107	C₂³×C₃₁	1	2	yes	—
553	#107	C₂³×C₃₁	1	4	yes	—
554	#106	C₂³×C₃₁	1	2	yes	—
555	#106	C₂³×C₃₁	1	2	yes	—
556	#106	C₂³×C₃₁	1	1	yes	characteristic
557	#106	C₂³×C₃₁	1	1	yes	characteristic
558	#106	C₂³×C₃₁	1	4	yes	—
559	#103	C₂³×C₃₁	1	2	yes	—
560	#103	C₂³×C₃₁	1	2	yes	—
561	#103	C₂³×C₃₁	1	4	yes	—
562	#102	C₂³×C₃₁	1	4	yes	—
563	#102	C₂³×C₃₁	1	4	yes	—
564	#102	C₂³×C₃₁	1	2	yes	—
565	#102	C₂³×C₃₁	1	2	yes	—
566	#102	C₂³×C₃₁	1	4	yes	—
567	#102	C₂³×C₃₁	1	4	yes	—
568	#102	C₂³×C₃₁	1	4	yes	—
569	#97	C₂³×C₃₁	1	2	yes	—
570	#97	C₂³×C₃₁	1	2	yes	—
571	#97	C₂³×C₃₁	1	2	yes	—
572	#97	C₂³×C₃₁	1	2	yes	—
573	C₄×C₈	C₂³×C₃₁	1	2	yes	—
574	C₄×C₈	C₂³×C₃₁	1	2	yes	—
575	C₄×C₈	C₂³×C₃₁	1	2	yes	—
576	C₄×C₈	C₂³×C₃₁	1	2	yes	—
577	C₃₁	#60710	1	1	yes	characteristic, direct product factor, Sylow
578	C₂⁴	—	2	2	no	—
579	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
580	#41	—	2	4	no	—
581	#41	—	2	4	no	—
582	#41	—	8	8	no	—
583	C₂×Q₈	—	2	4	no	—
584	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	8	4	no	—
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	2	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
609	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
612	Q₁₆	—	2	2	no	—
613	SD₁₆	—	2	4	no	—
614	SD₁₆	—	2	8	no	—
615	D₈	—	2	4	no	—
616	D₈	—	2	4	no	—
617	D₈	—	2	2	no	—
618	D₈	—	2	8	no	—
619	M₁₆	—	2	2	no	—
620	M₁₆	—	2	4	no	—
621	M₁₆	—	2	2	no	—
622	M₁₆	—	2	2	no	—
623	M₁₆	—	2	2	no	—
624	M₁₆	—	2	2	no	—
625	M₁₆	#41×C₃₁	1	4	yes	complemented
626	C₂×C₈	—	2	2	no	—
627	C₂×C₈	—	2	4	no	—
628	C₂×C₈	#41×C₃₁	1	4	yes	complemented
629	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
631	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
632	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
633	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
634	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
643	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
644	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
645	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
646	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
647	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
661	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
662	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
663	C₄²	—	2	4	no	—
664	C₄²	—	2	2	no	—
665	C₄²	C₂×D₄×C₃₁	1	4	yes	—
666	C₄²	C₂⁴×C₃₁	1	2	yes	—
667	C₄²	C₂⁴×C₃₁	1	2	yes	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	4	2	no	—
672	C₂³	—	4	4	no	—
673	C₂³	—	8	2	no	—
674	C₂³	—	8	2	no	—
675	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
676	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
677	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
678	Q₈	—	2	2	no	—
679	Q₈	—	2	2	no	—
680	Q₈	—	8	4	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	4	no	—
684	D₄	—	2	2	no	—
685	D₄	—	4	8	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	4	no	—
688	D₄	—	4	4	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	4	no	—
691	D₄	—	8	2	no	—
692	D₄	—	8	4	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	8	4	no	—
707	C₂×C₄	—	8	4	no	—
708	C₂×C₄	—	8	4	no	—
709	C₂×C₄	—	8	2	no	—
710	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
711	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
713	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
714	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
715	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
716	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
717	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
718	C₈	—	2	1	no	—
719	C₈	—	2	1	no	—
720	C₈	—	2	2	no	—
721	C₈	C₂×#41×C₃₁	1	4	yes	—
722	C₈	C₂×#41×C₃₁	1	2	yes	—
723	C₈	C₂×#41×C₃₁	1	2	yes	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	4	4	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	8	2	no	—
736	C₂²	—	16	4	no	—
737	C₂²	C₃₁×#532	1	2	yes	—
738	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
739	C₄	—	2	1	no	—
740	C₄	—	2	1	no	—
741	C₄	—	2	4	no	—
742	C₄	—	2	4	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	4	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	C₃₁×#532	1	2	yes	—
748	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
749	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
750	C₂	—	2	2	no	—
751	C₂	—	4	1	no	—
752	C₂	—	4	1	no	—
753	C₂	—	8	4	no	—
754	C₂	—	8	2	no	—
755	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
756	C₂	C₃₁×#3585	1	2	yes	—

	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 ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3494	C₂	semidirect
2. C₃₁×#3184	C₂	semidirect
3. C₃₁×#3183	C₂	semidirect
4. C₃₁×#3179	C₂	semidirect
5. C₃₁×#3176	C₂	semidirect
6. C₃₁×#3173	C₂	semidirect
7. C₃₁×#3171	C₂	semidirect
8. C₃₁×#3163	C₂	semidirect
9. C₃₁×#3155	C₂	semidirect
10. C₃₁×#3136	C₂	semidirect
11. C₃₁×#3055	C₂	semidirect
12. C₃₁×#3054	C₂	semidirect
13. C₂×C₃₁×#469	C₂	semidirect
14. C₃₁×#2952	C₂	semidirect
15. C₃₁×#2948	C₂	semidirect
16. C₃₁×#2946	C₂	semidirect
17. C₃₁×#2873	C₂	semidirect
30. C₃₁×#542	C₂²	semidirect
31. C₃₁×#540	C₂²	semidirect
33. C₃₁×#532	C₂²	semidirect
34. C₃₁×#529	C₂²	semidirect
40. C₃₁×#501	C₂²	semidirect
41. C₃₁×#499	C₂²	semidirect
42. C₃₁×#498	C₂²	semidirect
43. C₃₁×#496	C₂²	semidirect
44. C₃₁×#495	C₂²	semidirect
45. C₃₁×#493	C₂²	semidirect
46. C₃₁×#490	C₂²	semidirect
47. C₃₁×#489	C₂²	semidirect
48. C₃₁×#488	C₂²	semidirect
49. C₃₁×#486	C₂²	semidirect
50. C₃₁×#470	C₂²	semidirect
51. C₃₁×#470	C₂²	semidirect
56. C₃₁×#469	C₂²	semidirect
57. C₃₁×#469	C₂²	semidirect
58. C₃₁×#469	C₂²	semidirect
59. C₃₁×#468	C₂²	semidirect
60. C₃₁×#468	C₂²	semidirect
61. C₃₁×#468	C₂²	semidirect
62. C₃₁×#466	C₂²	semidirect
63. C₃₁×#465	C₂²	semidirect
64. C₃₁×#442	C₂²	semidirect
65. C₃₁×#442	C₂²	semidirect
66. C₃₁×#442	C₂²	semidirect
67. C₃₁×#442	C₂²	semidirect
68. C₃₁×#441	C₂²	semidirect
69. C₃₁×#440	C₂²	semidirect
70. C₄×SD₁₆×C₃₁	C₂²	semidirect
71. C₄×SD₁₆×C₃₁	C₂²	semidirect
72. C₄×D₈×C₃₁	C₂²	semidirect
73. C₄×D₈×C₃₁	C₂²	semidirect
85. C₃₁×#405	C₂²	semidirect
86. C₃₁×#405	C₂²	semidirect
87. C₄×M₁₆×C₃₁	C₂²	semidirect
88. C₄×M₁₆×C₃₁	C₂²	semidirect
246. M₁₆×C₃₁	#41	semidirect
249. C₂×C₈×C₃₁	#41	semidirect
289. #60710	C₃₁	direct (N × H)
346. #3494	C₂×C₃₁	semidirect
347. #3184	C₂×C₃₁	semidirect
348. #3183	C₂×C₃₁	semidirect
349. #3179	C₂×C₃₁	semidirect
350. #3176	C₂×C₃₁	semidirect
351. #3173	C₂×C₃₁	semidirect
352. #3171	C₂×C₃₁	semidirect
353. #3163	C₂×C₃₁	semidirect
354. #3155	C₂×C₃₁	semidirect
355. #3136	C₂×C₃₁	semidirect
356. #3055	C₂×C₃₁	semidirect
357. #3054	C₂×C₃₁	semidirect
358. C₂×#469	C₂×C₃₁	semidirect
359. #2952	C₂×C₃₁	semidirect
360. #2948	C₂×C₃₁	semidirect
361. #2946	C₂×C₃₁	semidirect
362. #2873	C₂×C₃₁	semidirect
401. #542	C₂²×C₃₁	semidirect
402. #540	C₂²×C₃₁	semidirect
404. #532	C₂²×C₃₁	semidirect
405. #529	C₂²×C₃₁	semidirect
411. #501	C₂²×C₃₁	semidirect
412. #499	C₂²×C₃₁	semidirect
413. #498	C₂²×C₃₁	semidirect
414. #496	C₂²×C₃₁	semidirect
415. #495	C₂²×C₃₁	semidirect
416. #493	C₂²×C₃₁	semidirect
417. #490	C₂²×C₃₁	semidirect
418. #489	C₂²×C₃₁	semidirect
419. #488	C₂²×C₃₁	semidirect
420. #486	C₂²×C₃₁	semidirect
421. #470	C₂²×C₃₁	semidirect
422. #470	C₂²×C₃₁	semidirect
427. #469	C₂²×C₃₁	semidirect
428. #469	C₂²×C₃₁	semidirect
429. #469	C₂²×C₃₁	semidirect
430. #468	C₂²×C₃₁	semidirect
431. #468	C₂²×C₃₁	semidirect
432. #468	C₂²×C₃₁	semidirect
433. #466	C₂²×C₃₁	semidirect
434. #465	C₂²×C₃₁	semidirect
435. #442	C₂²×C₃₁	semidirect
436. #442	C₂²×C₃₁	semidirect
437. #442	C₂²×C₃₁	semidirect
438. #442	C₂²×C₃₁	semidirect
439. #441	C₂²×C₃₁	semidirect
440. #440	C₂²×C₃₁	semidirect
441. C₄×SD₁₆	C₂²×C₃₁	semidirect
442. C₄×SD₁₆	C₂²×C₃₁	semidirect
443. C₄×D₈	C₂²×C₃₁	semidirect
444. C₄×D₈	C₂²×C₃₁	semidirect
456. #405	C₂²×C₃₁	semidirect
457. #405	C₂²×C₃₁	semidirect
458. C₄×M₁₆	C₂²×C₃₁	semidirect
459. C₄×M₁₆	C₂²×C₃₁	semidirect
577. C₃₁	#60710	direct (N × H)
625. M₁₆	#41×C₃₁	semidirect
628. C₂×C₈	#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×#3494	2
C₃₁×#3184	2
C₃₁×#3183	2
C₃₁×#3179	2
C₃₁×#3176	2
C₃₁×#3173	2
C₃₁×#3171	2
C₃₁×#3163	2
C₃₁×#3155	2
C₃₁×#3136	2
C₃₁×#3055	2
C₃₁×#3054	2
C₂×C₃₁×#469	2
C₃₁×#2952	2
C₃₁×#2948	2
C₃₁×#2946	2
C₃₁×#2873	2
#60710	31

Subgroups — C31×#60710 #21517469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60710 #21517469