Subgroups — C₃₁×#60806 #21517565

Order 7936.

2222 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3224	C₂	1	8	yes	maximal, complemented
4	C₃₁×#3222	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3220	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3153	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3040	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3038	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3005	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3003	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2921	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
18	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₃₁×#542	C₂²	1	4	yes	complemented
22	C₃₁×#541	C₂²	1	2	yes	complemented
23	C₃₁×#540	C₂²	1	2	yes	complemented
24	C₃₁×#539	—	2	2	no	—
25	C₃₁×#538	—	2	2	no	—
26	C₃₁×#535	—	2	4	no	—
27	C₃₁×#535	C₂²	1	4	yes	—
28	C₃₁×#535	C₂²	1	4	yes	—
29	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
33	C₃₁×#529	—	2	4	no	—
34	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
36	C₃₁×#525	C₂²	1	2	yes	—
37	C₂×C₃₁×#121	—	2	2	no	—
38	C₂×C₃₁×#120	—	2	2	no	—
39	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
40	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
41	C₃₁×#497	C₂²	1	2	yes	complemented
42	C₃₁×#496	C₂²	1	2	yes	complemented
43	C₃₁×#496	C₂²	1	4	yes	complemented
44	C₃₁×#495	C₂²	1	4	yes	complemented
45	C₃₁×#493	C₂²	1	2	yes	complemented
46	C₃₁×#492	C₂²	1	2	yes	complemented
47	C₃₁×#490	C₂²	1	4	yes	complemented
48	C₃₁×#489	C₂²	1	4	yes	complemented
49	C₃₁×#488	C₂²	1	4	yes	complemented
50	C₃₁×#486	C₂²	1	4	yes	complemented
51	C₃₁×#464	C₂²	1	8	yes	complemented
52	C₃₁×#463	C₂²	1	8	yes	complemented
53	C₃₁×#460	C₂²	1	8	yes	complemented
54	C₃₁×#459	C₂²	1	8	yes	complemented
55	C₃₁×#452	C₂²	1	8	yes	complemented
56	C₃₁×#450	C₂²	1	8	yes	complemented
57	C₃₁×#449	C₂²	1	8	yes	complemented
58	C₃₁×#447	C₂²	1	8	yes	complemented
59	C₃₁×#433	C₂²	1	4	yes	complemented
60	C₃₁×#433	C₂²	1	4	yes	complemented
61	C₃₁×#423	C₂²	1	2	yes	complemented
62	C₃₁×#419	C₂²	1	2	yes	complemented
63	C₃₁×#418	C₂²	1	2	yes	—
64	C₃₁×#418	C₂²	1	2	yes	—
65	C₃₁×#418	C₂²	1	2	yes	complemented
66	C₃₁×#407	C₂²	1	2	yes	—
67	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
68	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
69	C₂⁵×C₃₁	—	2	1	no	—
70	C₂×#41×C₃₁	—	2	2	no	—
71	C₂×#41×C₃₁	—	4	4	no	—
72	C₂×#41×C₃₁	C₂³	1	2	yes	—
73	C₂×#41×C₃₁	C₂³	1	4	yes	—
74	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₃₁	—	2	1	no	—
76	C₂²×D₄×C₃₁	—	2	1	no	—
77	C₂²×D₄×C₃₁	—	2	2	no	—
78	C₂²×D₄×C₃₁	—	2	2	no	—
79	C₂²×D₄×C₃₁	—	2	2	no	—
80	C₂²×D₄×C₃₁	—	4	4	no	—
81	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
85	C₂³×C₄×C₃₁	—	2	1	no	—
86	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₃₁×#137	—	4	4	no	—
88	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
89	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
90	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
91	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	complemented
92	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	complemented
95	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	complemented
96	C₂×D₈×C₃₁	C₂³	1	4	yes	—
97	C₂×D₈×C₃₁	C₂³	1	4	yes	—
98	C₂×D₈×C₃₁	C₂³	1	4	yes	complemented
99	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
100	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
101	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
102	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	complemented
103	C₃₁×#127	—	2	2	no	—
104	C₃₁×#127	—	2	2	no	—
105	C₃₁×#127	C₂³	1	4	yes	—
106	C₃₁×#127	C₂³	1	2	yes	—
107	C₃₁×#127	C₂³	1	2	yes	—
108	C₃₁×#127	C₂³	1	1	yes	characteristic, complemented
109	C₃₁×#126	—	2	4	no	—
110	C₃₁×#126	—	2	4	no	—
111	C₃₁×#125	—	2	4	no	—
112	C₃₁×#125	C₂³	1	2	yes	complemented
113	C₃₁×#124	—	2	4	no	—
114	C₃₁×#124	—	2	2	no	—
115	C₃₁×#124	—	2	2	no	—
116	C₃₁×#124	C₂³	1	4	yes	—
117	C₃₁×#124	C₂³	1	2	yes	—
118	C₃₁×#124	C₂³	1	2	yes	—
119	C₃₁×#124	C₂³	1	2	yes	complemented
120	C₃₁×#123	—	2	2	no	—
121	C₃₁×#123	—	2	4	no	—
122	C₃₁×#123	—	2	4	no	—
123	C₃₁×C₂²⋊Q₈	—	2	2	no	—
124	C₃₁×C₂²⋊Q₈	—	2	4	no	—
125	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₃₁×#121	—	2	2	no	—
127	C₃₁×#121	—	2	8	no	—
128	C₃₁×#121	—	2	8	no	—
129	C₃₁×#121	—	2	4	no	—
130	C₃₁×#121	C₂³	1	4	yes	—
131	C₃₁×#120	—	2	2	no	—
132	C₃₁×#120	—	2	8	no	—
133	C₃₁×#120	—	2	8	no	—
134	C₄×Q₈×C₃₁	—	2	2	no	—
135	C₄×Q₈×C₃₁	C₂³	1	4	yes	complemented
136	C₄×D₄×C₃₁	—	2	4	no	—
137	C₄×D₄×C₃₁	—	2	4	no	—
138	C₄×D₄×C₃₁	—	2	2	no	—
139	C₄×D₄×C₃₁	C₂³	1	4	yes	complemented
140	C₃₁×#117	—	2	2	no	—
141	C₃₁×#117	D₄	1	4	yes	—
142	C₃₁×#117	C₂³	1	2	yes	—
143	C₃₁×#117	C₂³	1	2	yes	—
144	C₃₁×#117	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
146	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
147	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
148	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
149	C₂×C₄²×C₃₁	—	2	2	no	—
150	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
152	C₃₁×C₄⋊C₈	C₂³	1	8	yes	complemented
153	C₃₁×#103	C₂³	1	8	yes	complemented
154	C₃₁×#102	C₂³	1	8	yes	—
155	C₃₁×#102	C₂³	1	8	yes	—
156	C₃₁×#102	C₂³	1	8	yes	complemented
157	C₃₁×C₂²⋊C₈	C₂³	1	8	yes	—
158	C₃₁×#97	C₂³	1	2	yes	complemented
159	C₃₁×#97	C₂³	1	2	yes	complemented
160	C₄×C₈×C₃₁	C₂³	1	2	yes	complemented
161	C₄×C₈×C₃₁	C₂³	1	2	yes	complemented
162	C₂⁴×C₃₁	—	2	1	no	—
163	C₂⁴×C₃₁	—	2	1	no	—
164	C₂⁴×C₃₁	—	2	1	no	—
165	C₂⁴×C₃₁	—	2	4	no	—
166	C₂⁴×C₃₁	—	4	4	no	—
167	C₂⁴×C₃₁	—	8	4	no	—
168	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
169	#41×C₃₁	—	2	4	no	—
170	#41×C₃₁	—	2	4	no	—
171	#41×C₃₁	—	4	8	no	—
172	#41×C₃₁	—	4	8	no	—
173	C₂×Q₈×C₃₁	—	2	1	no	—
174	C₂×Q₈×C₃₁	—	2	2	no	—
175	C₂×Q₈×C₃₁	—	2	4	no	—
176	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
177	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
178	C₂×D₄×C₃₁	—	2	2	no	—
179	C₂×D₄×C₃₁	—	2	4	no	—
180	C₂×D₄×C₃₁	—	2	4	no	—
181	C₂×D₄×C₃₁	—	2	4	no	—
182	C₂×D₄×C₃₁	—	2	1	no	—
183	C₂×D₄×C₃₁	—	2	1	no	—
184	C₂×D₄×C₃₁	—	2	1	no	—
185	C₂×D₄×C₃₁	—	2	2	no	—
186	C₂×D₄×C₃₁	—	2	8	no	—
187	C₂×D₄×C₃₁	—	2	4	no	—
188	C₂×D₄×C₃₁	—	2	4	no	—
189	C₂×D₄×C₃₁	—	2	4	no	—
190	C₂×D₄×C₃₁	—	2	4	no	—
191	C₂×D₄×C₃₁	—	2	4	no	—
192	C₂×D₄×C₃₁	—	4	8	no	—
193	C₂×D₄×C₃₁	—	4	4	no	—
194	C₂×D₄×C₃₁	—	4	8	no	—
195	C₂×D₄×C₃₁	—	4	4	no	—
196	C₂×D₄×C₃₁	—	8	4	no	—
197	C₂×D₄×C₃₁	—	8	4	no	—
198	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
199	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
200	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
201	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₃₁	—	2	4	no	—
203	C₂²×C₄×C₃₁	—	2	1	no	—
204	C₂²×C₄×C₃₁	—	2	2	no	—
205	C₂²×C₄×C₃₁	—	2	4	no	—
206	C₂²×C₄×C₃₁	—	2	4	no	—
207	C₂²×C₄×C₃₁	—	4	4	no	—
208	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
214	Q₁₆×C₃₁	—	4	4	no	—
215	SD₁₆×C₃₁	—	4	4	no	—
216	SD₁₆×C₃₁	—	4	4	no	—
217	SD₁₆×C₃₁	—	4	4	no	—
218	SD₁₆×C₃₁	—	4	4	no	—
219	D₈×C₃₁	—	4	4	no	—
220	D₈×C₃₁	—	4	4	no	—
221	D₈×C₃₁	—	4	4	no	—
222	M₁₆×C₃₁	—	2	4	no	—
223	M₁₆×C₃₁	—	2	4	no	—
224	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
225	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
226	C₄⋊C₄×C₃₁	—	2	4	no	—
227	C₄⋊C₄×C₃₁	—	2	2	no	—
228	C₄⋊C₄×C₃₁	—	2	4	no	—
229	C₄⋊C₄×C₃₁	—	2	4	no	—
230	C₄⋊C₄×C₃₁	—	2	2	no	—
231	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
232	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
233	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
234	C₂²⋊C₄×C₃₁	—	2	2	no	—
235	C₂²⋊C₄×C₃₁	—	2	4	no	—
236	C₂²⋊C₄×C₃₁	—	2	8	no	—
237	C₂²⋊C₄×C₃₁	—	2	4	no	—
238	C₂²⋊C₄×C₃₁	—	2	4	no	—
239	C₂²⋊C₄×C₃₁	—	2	4	no	—
240	C₂²⋊C₄×C₃₁	—	2	4	no	—
241	C₂²⋊C₄×C₃₁	—	2	4	no	—
242	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
243	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
244	C₄²×C₃₁	—	2	2	no	—
245	C₄²×C₃₁	—	2	4	no	—
246	C₄²×C₃₁	C₂×D₄	1	2	yes	—
247	C₄²×C₃₁	C₂×D₄	1	2	yes	—
248	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₄²×C₃₁	C₂⁴	1	2	yes	—
251	#60806	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂³×C₃₁	—	2	2	no	—
253	C₂³×C₃₁	—	2	2	no	—
254	C₂³×C₃₁	—	2	2	no	—
255	C₂³×C₃₁	—	2	2	no	—
256	C₂³×C₃₁	—	2	2	no	—
257	C₂³×C₃₁	—	4	2	no	—
258	C₂³×C₃₁	—	4	8	no	—
259	C₂³×C₃₁	—	4	4	no	—
260	C₂³×C₃₁	—	4	4	no	—
261	C₂³×C₃₁	—	4	4	no	—
262	C₂³×C₃₁	—	4	2	no	—
263	C₂³×C₃₁	—	4	2	no	—
264	C₂³×C₃₁	—	4	2	no	—
265	C₂³×C₃₁	—	8	8	no	—
266	C₂³×C₃₁	—	8	16	no	—
267	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
268	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
269	Q₈×C₃₁	—	2	2	no	—
270	Q₈×C₃₁	—	2	2	no	—
271	Q₈×C₃₁	—	2	4	no	—
272	Q₈×C₃₁	—	4	2	no	—
273	Q₈×C₃₁	—	8	2	no	—
274	D₄×C₃₁	—	2	2	no	—
275	D₄×C₃₁	—	2	2	no	—
276	D₄×C₃₁	—	2	4	no	—
277	D₄×C₃₁	—	2	4	no	—
278	D₄×C₃₁	—	2	4	no	—
279	D₄×C₃₁	—	4	8	no	—
280	D₄×C₃₁	—	4	8	no	—
281	D₄×C₃₁	—	4	4	no	—
282	D₄×C₃₁	—	4	2	no	—
283	D₄×C₃₁	—	4	2	no	—
284	D₄×C₃₁	—	4	2	no	—
285	D₄×C₃₁	—	8	2	no	—
286	D₄×C₃₁	—	8	8	no	—
287	D₄×C₃₁	—	8	4	no	—
288	D₄×C₃₁	—	8	4	no	—
289	D₄×C₃₁	—	8	4	no	—
290	C₂×C₄×C₃₁	—	2	2	no	—
291	C₂×C₄×C₃₁	—	2	4	no	—
292	C₂×C₄×C₃₁	—	2	4	no	—
293	C₂×C₄×C₃₁	—	2	2	no	—
294	C₂×C₄×C₃₁	—	2	4	no	—
295	C₂×C₄×C₃₁	—	2	2	no	—
296	C₂×C₄×C₃₁	—	4	2	no	—
297	C₂×C₄×C₃₁	—	4	2	no	—
298	C₂×C₄×C₃₁	—	4	8	no	—
299	C₂×C₄×C₃₁	—	4	2	no	—
300	C₂×C₄×C₃₁	—	4	4	no	—
301	C₂×C₄×C₃₁	—	8	4	no	—
302	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
303	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
306	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
308	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
309	C₈×C₃₁	—	2	4	no	—
310	C₈×C₃₁	—	2	4	no	—
311	#3455	C₂×C₃₁	1	1	yes	characteristic, complemented
312	C₂×#535	C₂×C₃₁	1	1	yes	characteristic, complemented
313	#3224	C₂×C₃₁	1	8	yes	complemented
314	#3222	C₂×C₃₁	1	4	yes	complemented
315	#3220	C₂×C₃₁	1	4	yes	complemented
316	#3153	C₂×C₃₁	1	1	yes	characteristic, complemented
317	#3151	C₂×C₃₁	1	1	yes	characteristic, complemented
318	#3140	C₂×C₃₁	1	1	yes	characteristic, complemented
319	#3138	C₂×C₃₁	1	1	yes	characteristic, complemented
320	#3040	C₂×C₃₁	1	2	yes	complemented
321	#3038	C₂×C₃₁	1	2	yes	complemented
322	#3005	C₂×C₃₁	1	2	yes	complemented
323	#3003	C₂×C₃₁	1	2	yes	complemented
324	#2921	C₂×C₃₁	1	1	yes	characteristic, complemented
325	C₂²×C₃₁	—	2	2	no	—
326	C₂²×C₃₁	—	2	4	no	—
327	C₂²×C₃₁	—	2	2	no	—
328	C₂²×C₃₁	—	4	4	no	—
329	C₂²×C₃₁	—	4	4	no	—
330	C₂²×C₃₁	—	4	4	no	—
331	C₂²×C₃₁	—	4	4	no	—
332	C₂²×C₃₁	—	4	4	no	—
333	C₂²×C₃₁	—	4	2	no	—
334	C₂²×C₃₁	—	4	2	no	—
335	C₂²×C₃₁	—	4	2	no	—
336	C₂²×C₃₁	—	4	2	no	—
337	C₂²×C₃₁	—	8	4	no	—
338	C₂²×C₃₁	—	8	4	no	—
339	C₂²×C₃₁	—	8	4	no	—
340	C₂²×C₃₁	—	8	16	no	—
341	C₂²×C₃₁	#535	1	2	yes	—
342	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
343	C₄×C₃₁	—	2	4	no	—
344	C₄×C₃₁	—	2	2	no	—
345	C₄×C₃₁	—	2	2	no	—
346	C₄×C₃₁	—	2	2	no	—
347	C₄×C₃₁	—	4	4	no	—
348	C₄×C₃₁	—	4	2	no	—
349	C₄×C₃₁	—	4	2	no	—
350	C₄×C₃₁	#535	1	2	yes	—
351	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
352	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
353	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
354	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
355	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
356	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
357	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
358	#542	C₂²×C₃₁	1	4	yes	complemented
359	#541	C₂²×C₃₁	1	2	yes	complemented
360	#540	C₂²×C₃₁	1	2	yes	complemented
361	#539	—	2	2	no	—
362	#538	—	2	2	no	—
363	#535	—	2	4	no	—
364	#535	C₂²×C₃₁	1	4	yes	—
365	#535	C₂²×C₃₁	1	4	yes	—
366	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
367	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
368	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
369	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
370	#529	—	2	4	no	—
371	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
372	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
373	#525	C₂²×C₃₁	1	2	yes	—
374	C₂×#121	—	2	2	no	—
375	C₂×#120	—	2	2	no	—
376	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
377	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
378	#497	C₂²×C₃₁	1	2	yes	complemented
379	#496	C₂²×C₃₁	1	2	yes	complemented
380	#496	C₂²×C₃₁	1	4	yes	complemented
381	#495	C₂²×C₃₁	1	4	yes	complemented
382	#493	C₂²×C₃₁	1	2	yes	complemented
383	#492	C₂²×C₃₁	1	2	yes	complemented
384	#490	C₂²×C₃₁	1	4	yes	complemented
385	#489	C₂²×C₃₁	1	4	yes	complemented
386	#488	C₂²×C₃₁	1	4	yes	complemented
387	#486	C₂²×C₃₁	1	4	yes	complemented
388	#464	C₂²×C₃₁	1	8	yes	complemented
389	#463	C₂²×C₃₁	1	8	yes	complemented
390	#460	C₂²×C₃₁	1	8	yes	complemented
391	#459	C₂²×C₃₁	1	8	yes	complemented
392	#452	C₂²×C₃₁	1	8	yes	complemented
393	#450	C₂²×C₃₁	1	8	yes	complemented
394	#449	C₂²×C₃₁	1	8	yes	complemented
395	#447	C₂²×C₃₁	1	8	yes	complemented
396	#433	C₂²×C₃₁	1	4	yes	complemented
397	#433	C₂²×C₃₁	1	4	yes	complemented
398	#423	C₂²×C₃₁	1	2	yes	complemented
399	#419	C₂²×C₃₁	1	2	yes	complemented
400	#418	C₂²×C₃₁	1	2	yes	—
401	#418	C₂²×C₃₁	1	2	yes	—
402	#418	C₂²×C₃₁	1	2	yes	complemented
403	#407	C₂²×C₃₁	1	2	yes	—
404	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
405	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
406	C₂×C₃₁	—	2	2	no	—
407	C₂×C₃₁	—	4	2	no	—
408	C₂×C₃₁	—	8	2	no	—
409	C₂×C₃₁	—	8	2	no	—
410	C₂×C₃₁	—	8	2	no	—
411	C₂×C₃₁	—	8	2	no	—
412	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
413	C₂×C₃₁	#3585	1	2	yes	—
414	C₂⁵	—	2	1	no	—
415	C₂×#41	—	2	2	no	—
416	C₂×#41	—	4	4	no	—
417	C₂×#41	C₂³×C₃₁	1	2	yes	—
418	C₂×#41	C₂³×C₃₁	1	4	yes	—
419	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
420	C₂²×D₄	—	2	1	no	—
421	C₂²×D₄	—	2	1	no	—
422	C₂²×D₄	—	2	2	no	—
423	C₂²×D₄	—	2	2	no	—
424	C₂²×D₄	—	2	2	no	—
425	C₂²×D₄	—	4	4	no	—
426	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
427	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
428	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
429	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
430	C₂³×C₄	—	2	1	no	—
431	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
432	#137	—	4	4	no	—
433	AGL(1,ℤ/8)	—	4	4	no	—
434	AGL(1,ℤ/8)	—	4	4	no	—
435	AGL(1,ℤ/8)	—	4	4	no	—
436	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	complemented
437	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
438	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
439	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	complemented
440	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	complemented
441	C₂×D₈	C₂³×C₃₁	1	4	yes	—
442	C₂×D₈	C₂³×C₃₁	1	4	yes	—
443	C₂×D₈	C₂³×C₃₁	1	4	yes	complemented
444	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
445	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
446	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic, complemented
447	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	complemented
448	#127	—	2	2	no	—
449	#127	—	2	2	no	—
450	#127	C₂³×C₃₁	1	4	yes	—
451	#127	C₂³×C₃₁	1	2	yes	—
452	#127	C₂³×C₃₁	1	2	yes	—
453	#127	C₂³×C₃₁	1	1	yes	characteristic, complemented
454	#126	—	2	4	no	—
455	#126	—	2	4	no	—
456	#125	—	2	4	no	—
457	#125	C₂³×C₃₁	1	2	yes	complemented
458	#124	—	2	4	no	—
459	#124	—	2	2	no	—
460	#124	—	2	2	no	—
461	#124	C₂³×C₃₁	1	4	yes	—
462	#124	C₂³×C₃₁	1	2	yes	—
463	#124	C₂³×C₃₁	1	2	yes	—
464	#124	C₂³×C₃₁	1	2	yes	complemented
465	#123	—	2	2	no	—
466	#123	—	2	4	no	—
467	#123	—	2	4	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	4	no	—
470	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
471	#121	—	2	2	no	—
472	#121	—	2	8	no	—
473	#121	—	2	8	no	—
474	#121	—	2	4	no	—
475	#121	C₂³×C₃₁	1	4	yes	—
476	#120	—	2	2	no	—
477	#120	—	2	8	no	—
478	#120	—	2	8	no	—
479	C₄×Q₈	—	2	2	no	—
480	C₄×Q₈	C₂³×C₃₁	1	4	yes	complemented
481	C₄×D₄	—	2	4	no	—
482	C₄×D₄	—	2	4	no	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	C₂³×C₃₁	1	4	yes	complemented
485	#117	—	2	2	no	—
486	#117	D₄×C₃₁	1	4	yes	—
487	#117	C₂³×C₃₁	1	2	yes	—
488	#117	C₂³×C₃₁	1	2	yes	—
489	#117	C₂³×C₃₁	1	2	yes	—
490	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
491	C₂×C₂²⋊C₄	—	2	2	no	—
492	C₂×C₂²⋊C₄	—	2	2	no	—
493	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
494	C₂×C₄²	—	2	2	no	—
495	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
497	C₄⋊C₈	C₂³×C₃₁	1	8	yes	complemented
498	#103	C₂³×C₃₁	1	8	yes	complemented
499	#102	C₂³×C₃₁	1	8	yes	—
500	#102	C₂³×C₃₁	1	8	yes	—
501	#102	C₂³×C₃₁	1	8	yes	complemented
502	C₂²⋊C₈	C₂³×C₃₁	1	8	yes	—
503	#97	C₂³×C₃₁	1	2	yes	complemented
504	#97	C₂³×C₃₁	1	2	yes	complemented
505	C₄×C₈	C₂³×C₃₁	1	2	yes	complemented
506	C₄×C₈	C₂³×C₃₁	1	2	yes	complemented
507	C₃₁	#60806	1	1	yes	characteristic, direct product factor, Sylow
508	C₂⁴	—	2	1	no	—
509	C₂⁴	—	2	1	no	—
510	C₂⁴	—	2	1	no	—
511	C₂⁴	—	2	4	no	—
512	C₂⁴	—	4	4	no	—
513	C₂⁴	—	8	4	no	—
514	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
515	#41	—	2	4	no	—
516	#41	—	2	4	no	—
517	#41	—	4	8	no	—
518	#41	—	4	8	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	4	no	—
522	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
523	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	4	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	4	8	no	—
539	C₂×D₄	—	4	4	no	—
540	C₂×D₄	—	4	8	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂×D₄	—	8	4	no	—
543	C₂×D₄	—	8	4	no	—
544	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
545	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
546	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
547	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	4	4	no	—
554	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
556	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
557	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
560	Q₁₆	—	4	4	no	—
561	SD₁₆	—	4	4	no	—
562	SD₁₆	—	4	4	no	—
563	SD₁₆	—	4	4	no	—
564	SD₁₆	—	4	4	no	—
565	D₈	—	4	4	no	—
566	D₈	—	4	4	no	—
567	D₈	—	4	4	no	—
568	M₁₆	—	2	4	no	—
569	M₁₆	—	2	4	no	—
570	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
571	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
578	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
579	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	8	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
589	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	4	no	—
592	C₄²	C₂×D₄×C₃₁	1	2	yes	—
593	C₄²	C₂×D₄×C₃₁	1	2	yes	—
594	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
595	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
596	C₄²	C₂⁴×C₃₁	1	2	yes	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	4	2	no	—
603	C₂³	—	4	8	no	—
604	C₂³	—	4	4	no	—
605	C₂³	—	4	4	no	—
606	C₂³	—	4	4	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	—	8	8	no	—
611	C₂³	—	8	16	no	—
612	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
613	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
614	Q₈	—	2	2	no	—
615	Q₈	—	2	2	no	—
616	Q₈	—	2	4	no	—
617	Q₈	—	4	2	no	—
618	Q₈	—	8	2	no	—
619	D₄	—	2	2	no	—
620	D₄	—	2	2	no	—
621	D₄	—	2	4	no	—
622	D₄	—	2	4	no	—
623	D₄	—	2	4	no	—
624	D₄	—	4	8	no	—
625	D₄	—	4	8	no	—
626	D₄	—	4	4	no	—
627	D₄	—	4	2	no	—
628	D₄	—	4	2	no	—
629	D₄	—	4	2	no	—
630	D₄	—	8	2	no	—
631	D₄	—	8	8	no	—
632	D₄	—	8	4	no	—
633	D₄	—	8	4	no	—
634	D₄	—	8	4	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	2	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	8	4	no	—
647	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
648	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
650	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
651	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
652	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
653	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
654	C₈	—	2	4	no	—
655	C₈	—	2	4	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	4	no	—
659	C₂²	—	4	4	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	4	no	—
665	C₂²	—	4	4	no	—
666	C₂²	—	4	4	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	8	4	no	—
669	C₂²	—	8	4	no	—
670	C₂²	—	8	4	no	—
671	C₂²	—	8	16	no	—
672	C₂²	C₃₁×#535	1	2	yes	—
673	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
674	C₄	—	2	2	no	—
675	C₄	—	2	4	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	4	2	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	4	no	—
681	C₄	C₃₁×#535	1	2	yes	—
682	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
683	C₂	—	2	2	no	—
684	C₂	—	4	2	no	—
685	C₂	—	8	2	no	—
686	C₂	—	8	2	no	—
687	C₂	—	8	2	no	—
688	C₂	—	8	2	no	—
689	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
690	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×#3455	C₂	semidirect
2. C₂×C₃₁×#535	C₂	semidirect
3. C₃₁×#3224	C₂	semidirect
4. C₃₁×#3222	C₂	semidirect
5. C₃₁×#3220	C₂	semidirect
6. C₃₁×#3153	C₂	semidirect
7. C₃₁×#3151	C₂	semidirect
8. C₃₁×#3140	C₂	semidirect
9. C₃₁×#3138	C₂	semidirect
10. C₃₁×#3040	C₂	semidirect
11. C₃₁×#3038	C₂	semidirect
12. C₃₁×#3005	C₂	semidirect
13. C₃₁×#3003	C₂	semidirect
14. C₃₁×#2921	C₂	semidirect
17. C₂×C₃₁×#137	C₂²	semidirect
20. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
21. C₃₁×#542	C₂²	semidirect
22. C₃₁×#541	C₂²	semidirect
23. C₃₁×#540	C₂²	semidirect
29. C₃₁×#533	C₂²	semidirect
30. C₃₁×#532	C₂²	semidirect
39. C₄×#41×C₃₁	C₂²	semidirect
41. C₃₁×#497	C₂²	semidirect
42. C₃₁×#496	C₂²	semidirect
43. C₃₁×#496	C₂²	semidirect
44. C₃₁×#495	C₂²	semidirect
45. C₃₁×#493	C₂²	semidirect
46. C₃₁×#492	C₂²	semidirect
47. C₃₁×#490	C₂²	semidirect
48. C₃₁×#489	C₂²	semidirect
49. C₃₁×#488	C₂²	semidirect
50. C₃₁×#486	C₂²	semidirect
51. C₃₁×#464	C₂²	semidirect
52. C₃₁×#463	C₂²	semidirect
53. C₃₁×#460	C₂²	semidirect
54. C₃₁×#459	C₂²	semidirect
55. C₃₁×#452	C₂²	semidirect
56. C₃₁×#450	C₂²	semidirect
57. C₃₁×#449	C₂²	semidirect
58. C₃₁×#447	C₂²	semidirect
59. C₃₁×#433	C₂²	semidirect
60. C₃₁×#433	C₂²	semidirect
61. C₃₁×#423	C₂²	semidirect
62. C₃₁×#419	C₂²	semidirect
65. C₃₁×#418	C₂²	semidirect
67. C₄×M₁₆×C₃₁	C₂²	semidirect
68. C₄×M₁₆×C₃₁	C₂²	semidirect
91. C₂×Q₁₆×C₃₁	C₂³	semidirect
94. C₂×SD₁₆×C₃₁	C₂³	semidirect
95. C₂×SD₁₆×C₃₁	C₂³	semidirect
98. C₂×D₈×C₃₁	C₂³	semidirect
101. C₃₁×C₄⋊Q₈	C₂³	semidirect
102. C₃₁×C₄⋊Q₈	C₂³	semidirect
108. C₃₁×#127	C₂³	semidirect
112. C₃₁×#125	C₂³	semidirect
119. C₃₁×#124	C₂³	semidirect
135. C₄×Q₈×C₃₁	C₂³	semidirect
139. C₄×D₄×C₃₁	C₂³	semidirect
152. C₃₁×C₄⋊C₈	C₂³	semidirect
153. C₃₁×#103	C₂³	semidirect
156. C₃₁×#102	C₂³	semidirect
158. C₃₁×#97	C₂³	semidirect
159. C₃₁×#97	C₂³	semidirect
160. C₄×C₈×C₃₁	C₂³	semidirect
161. C₄×C₈×C₃₁	C₂³	semidirect
251. #60806	C₃₁	direct (N × H)
311. #3455	C₂×C₃₁	semidirect
312. C₂×#535	C₂×C₃₁	semidirect
313. #3224	C₂×C₃₁	semidirect
314. #3222	C₂×C₃₁	semidirect
315. #3220	C₂×C₃₁	semidirect
316. #3153	C₂×C₃₁	semidirect
317. #3151	C₂×C₃₁	semidirect
318. #3140	C₂×C₃₁	semidirect
319. #3138	C₂×C₃₁	semidirect
320. #3040	C₂×C₃₁	semidirect
321. #3038	C₂×C₃₁	semidirect
322. #3005	C₂×C₃₁	semidirect
323. #3003	C₂×C₃₁	semidirect
324. #2921	C₂×C₃₁	semidirect
354. C₂×#137	C₂²×C₃₁	semidirect
357. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
358. #542	C₂²×C₃₁	semidirect
359. #541	C₂²×C₃₁	semidirect
360. #540	C₂²×C₃₁	semidirect
366. #533	C₂²×C₃₁	semidirect
367. #532	C₂²×C₃₁	semidirect
376. C₄×#41	C₂²×C₃₁	semidirect
378. #497	C₂²×C₃₁	semidirect
379. #496	C₂²×C₃₁	semidirect
380. #496	C₂²×C₃₁	semidirect
381. #495	C₂²×C₃₁	semidirect
382. #493	C₂²×C₃₁	semidirect
383. #492	C₂²×C₃₁	semidirect
384. #490	C₂²×C₃₁	semidirect
385. #489	C₂²×C₃₁	semidirect
386. #488	C₂²×C₃₁	semidirect
387. #486	C₂²×C₃₁	semidirect
388. #464	C₂²×C₃₁	semidirect
389. #463	C₂²×C₃₁	semidirect
390. #460	C₂²×C₃₁	semidirect
391. #459	C₂²×C₃₁	semidirect
392. #452	C₂²×C₃₁	semidirect
393. #450	C₂²×C₃₁	semidirect
394. #449	C₂²×C₃₁	semidirect
395. #447	C₂²×C₃₁	semidirect
396. #433	C₂²×C₃₁	semidirect
397. #433	C₂²×C₃₁	semidirect
398. #423	C₂²×C₃₁	semidirect
399. #419	C₂²×C₃₁	semidirect
402. #418	C₂²×C₃₁	semidirect
404. C₄×M₁₆	C₂²×C₃₁	semidirect
405. C₄×M₁₆	C₂²×C₃₁	semidirect
436. C₂×Q₁₆	C₂³×C₃₁	semidirect
439. C₂×SD₁₆	C₂³×C₃₁	semidirect
440. C₂×SD₁₆	C₂³×C₃₁	semidirect
443. C₂×D₈	C₂³×C₃₁	semidirect
446. C₄⋊Q₈	C₂³×C₃₁	semidirect
447. C₄⋊Q₈	C₂³×C₃₁	semidirect
453. #127	C₂³×C₃₁	semidirect
457. #125	C₂³×C₃₁	semidirect
464. #124	C₂³×C₃₁	semidirect
480. C₄×Q₈	C₂³×C₃₁	semidirect
484. C₄×D₄	C₂³×C₃₁	semidirect
497. C₄⋊C₈	C₂³×C₃₁	semidirect
498. #103	C₂³×C₃₁	semidirect
501. #102	C₂³×C₃₁	semidirect
503. #97	C₂³×C₃₁	semidirect
504. #97	C₂³×C₃₁	semidirect
505. C₄×C₈	C₂³×C₃₁	semidirect
506. C₄×C₈	C₂³×C₃₁	semidirect
507. C₃₁	#60806	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×#3455	2
C₂×C₃₁×#535	2
C₃₁×#3224	2
C₃₁×#3222	2
C₃₁×#3220	2
C₃₁×#3153	2
C₃₁×#3151	2
C₃₁×#3140	2
C₃₁×#3138	2
C₃₁×#3040	2
C₃₁×#3038	2
C₃₁×#3005	2
C₃₁×#3003	2
C₃₁×#2921	2
#60806	31

Subgroups — C31×#60806 #21517565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60806 #21517565