Subgroups — C₃₁×#60804 #21517563

Order 7936.

2164 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3216	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3215	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3210	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3209	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3208	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3152	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3141	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3037	C₂	1	4	yes	maximal, complemented
11	C₃₁×#3007	C₂	1	4	yes	maximal, complemented
12	C₃₁×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₃₁	C₂²	1	2	yes	—
14	C₂×C₃₁×#137	C₂²	1	8	yes	complemented
15	C₃₁×#533	—	2	1	no	—
16	C₃₁×#533	—	2	1	no	—
17	C₃₁×#533	—	2	1	no	—
18	C₃₁×#533	—	2	1	no	—
19	C₃₁×#533	C₂²	1	2	yes	—
20	C₃₁×#533	C₂²	1	2	yes	—
21	C₃₁×#533	C₂²	1	2	yes	complemented
22	C₃₁×#533	C₂²	1	2	yes	complemented
23	C₃₁×#532	—	2	1	no	—
24	C₃₁×#532	—	2	1	no	—
25	C₃₁×#532	—	2	1	no	—
26	C₃₁×#532	—	2	1	no	—
27	C₃₁×#532	C₂²	1	2	yes	—
28	C₃₁×#532	C₂²	1	2	yes	—
29	C₃₁×#532	C₂²	1	2	yes	—
30	C₃₁×#532	C₂²	1	2	yes	—
31	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#125	—	2	1	no	—
36	C₂×C₃₁×#124	C₂²	1	2	yes	—
37	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
38	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
39	C₂×C₃₁×#121	—	2	1	no	—
40	C₂×C₃₁×#121	—	2	1	no	—
41	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
42	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
43	C₂×C₄×D₄×C₃₁	—	2	1	no	—
44	C₂×C₄×D₄×C₃₁	—	2	1	no	—
45	C₂×C₃₁×#117	—	2	1	no	—
46	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
47	C₃₁×#497	C₂²	1	8	yes	complemented
48	C₃₁×#494	C₂²	1	4	yes	complemented
49	C₃₁×#492	C₂²	1	4	yes	complemented
50	C₃₁×#489	C₂²	1	8	yes	complemented
51	C₃₁×#487	C₂²	1	4	yes	complemented
52	C₃₁×#486	C₂²	1	4	yes	complemented
53	C₃₁×#464	C₂²	1	16	yes	complemented
54	C₃₁×#462	C₂²	1	8	yes	complemented
55	C₃₁×#460	C₂²	1	8	yes	complemented
56	C₃₁×#452	C₂²	1	16	yes	complemented
57	C₃₁×#451	C₂²	1	8	yes	—
58	C₃₁×#450	C₂²	1	8	yes	—
59	C₃₁×#432	C₂²	1	2	yes	—
60	C₃₁×#432	C₂²	1	2	yes	complemented
61	C₃₁×#431	C₂²	1	2	yes	—
62	C₃₁×#431	C₂²	1	2	yes	complemented
63	C₃₁×#423	C₂²	1	2	yes	complemented
64	C₃₁×#417	C₂²	1	8	yes	complemented
65	C₃₁×#407	C₂²	1	2	yes	—
66	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
67	C₂×#41×C₃₁	—	2	2	no	—
68	C₂×#41×C₃₁	—	2	2	no	—
69	C₂×#41×C₃₁	—	4	8	no	—
70	C₂×#41×C₃₁	C₂³	1	4	yes	—
71	C₂×#41×C₃₁	C₂³	1	4	yes	—
72	C₂²×Q₈×C₃₁	—	2	1	no	—
73	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
74	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
75	C₂²×D₄×C₃₁	—	2	2	no	—
76	C₂²×D₄×C₃₁	—	2	1	no	—
77	C₂²×D₄×C₃₁	—	2	1	no	—
78	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
79	C₂³×C₄×C₃₁	—	2	2	no	—
80	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
83	C₃₁×#137	—	4	16	no	—
84	C₂×Q₁₆×C₃₁	C₂³	1	16	yes	—
85	C₂×SD₁₆×C₃₁	C₂³	1	16	yes	—
86	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
87	C₃₁×C₄⋊Q₈	—	2	1	no	—
88	C₃₁×C₄⋊Q₈	—	2	1	no	—
89	C₃₁×C₄⋊Q₈	—	2	1	no	—
90	C₃₁×C₄⋊Q₈	—	2	1	no	—
91	C₃₁×C₄⋊Q₈	—	2	1	no	—
92	C₃₁×C₄⋊Q₈	—	2	1	no	—
93	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
94	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
95	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₃₁×#127	—	2	1	no	—
100	C₃₁×#127	—	2	1	no	—
101	C₃₁×#127	C₂³	1	2	yes	—
102	C₃₁×#127	C₂³	1	2	yes	—
103	C₃₁×#125	—	2	2	no	—
104	C₃₁×#125	—	2	2	no	—
105	C₃₁×#125	—	2	2	no	—
106	C₃₁×#125	—	2	2	no	—
107	C₃₁×#124	—	2	2	no	—
108	C₃₁×#124	—	2	2	no	—
109	C₃₁×#124	C₂³	1	4	yes	—
110	C₃₁×#124	C₂³	1	4	yes	—
111	C₃₁×C₂²⋊Q₈	—	2	2	no	—
112	C₃₁×C₂²⋊Q₈	—	2	2	no	—
113	C₃₁×C₂²⋊Q₈	—	2	2	no	—
114	C₃₁×C₂²⋊Q₈	—	2	2	no	—
115	C₃₁×C₂²⋊Q₈	—	2	2	no	—
116	C₃₁×C₂²⋊Q₈	—	2	2	no	—
117	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
118	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
119	C₃₁×#121	—	2	2	no	—
120	C₃₁×#121	—	2	2	no	—
121	C₃₁×#121	—	2	2	no	—
122	C₃₁×#121	—	2	2	no	—
123	C₃₁×#121	—	2	2	no	—
124	C₃₁×#121	—	2	2	no	—
125	C₃₁×#121	—	2	2	no	—
126	C₃₁×#121	—	2	2	no	—
127	C₄×Q₈×C₃₁	—	2	2	no	—
128	C₄×Q₈×C₃₁	—	2	2	no	—
129	C₄×Q₈×C₃₁	—	2	2	no	—
130	C₄×Q₈×C₃₁	—	2	2	no	—
131	C₄×Q₈×C₃₁	—	2	2	no	—
132	C₄×Q₈×C₃₁	—	2	2	no	—
133	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
134	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
135	C₄×D₄×C₃₁	—	2	2	no	—
136	C₄×D₄×C₃₁	—	2	2	no	—
137	C₄×D₄×C₃₁	—	2	2	no	—
138	C₄×D₄×C₃₁	—	2	2	no	—
139	C₄×D₄×C₃₁	—	2	2	no	—
140	C₄×D₄×C₃₁	—	2	2	no	—
141	C₄×D₄×C₃₁	—	2	2	no	—
142	C₄×D₄×C₃₁	—	2	2	no	—
143	C₃₁×#117	—	2	2	no	—
144	C₃₁×#117	—	2	2	no	—
145	C₃₁×#117	—	2	2	no	—
146	C₃₁×#117	—	2	2	no	—
147	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
148	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
149	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
150	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
151	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
152	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
153	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
156	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
157	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
158	C₂×C₄²×C₃₁	—	2	2	no	—
159	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
162	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
171	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
172	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
173	C₃₁×#103	C₂³	1	16	yes	—
174	C₃₁×#102	C₂³	1	16	yes	—
175	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
176	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₃₁×#97	C₂³	1	4	yes	—
178	C₄×C₈×C₃₁	C₂³	1	4	yes	—
179	C₂⁴×C₃₁	—	2	2	no	—
180	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
181	#41×C₃₁	—	2	16	no	—
182	#41×C₃₁	—	4	8	no	—
183	#41×C₃₁	—	4	8	no	—
184	#41×C₃₁	—	4	8	no	—
185	C₂×Q₈×C₃₁	—	2	2	no	—
186	C₂×Q₈×C₃₁	—	2	2	no	—
187	C₂×Q₈×C₃₁	—	2	2	no	—
188	C₂×Q₈×C₃₁	—	2	2	no	—
189	C₂×Q₈×C₃₁	—	2	8	no	—
190	C₂×Q₈×C₃₁	—	4	4	no	—
191	C₂×Q₈×C₃₁	—	4	4	no	—
192	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
193	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
194	C₂×D₄×C₃₁	—	2	4	no	—
195	C₂×D₄×C₃₁	—	2	4	no	—
196	C₂×D₄×C₃₁	—	2	2	no	—
197	C₂×D₄×C₃₁	—	2	2	no	—
198	C₂×D₄×C₃₁	—	2	2	no	—
199	C₂×D₄×C₃₁	—	2	2	no	—
200	C₂×D₄×C₃₁	—	2	2	no	—
201	C₂×D₄×C₃₁	—	4	4	no	—
202	C₂×D₄×C₃₁	—	4	4	no	—
203	C₂×D₄×C₃₁	—	4	8	no	—
204	C₂×D₄×C₃₁	—	4	4	no	—
205	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₃₁	—	2	4	no	—
207	C₂²×C₄×C₃₁	—	2	4	no	—
208	C₂²×C₄×C₃₁	—	2	2	no	—
209	C₂²×C₄×C₃₁	—	2	2	no	—
210	C₂²×C₄×C₃₁	—	2	2	no	—
211	C₂²×C₄×C₃₁	—	2	4	no	—
212	C₂²×C₄×C₃₁	—	2	4	no	—
213	C₂²×C₄×C₃₁	—	4	2	no	—
214	C₂²×C₄×C₃₁	—	4	8	no	—
215	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
222	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
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	—	4	16	no	—
234	SD₁₆×C₃₁	—	4	16	no	—
235	M₁₆×C₃₁	—	2	8	no	—
236	C₂×C₈×C₃₁	C₂⁴	1	8	yes	—
237	C₄⋊C₄×C₃₁	—	2	2	no	—
238	C₄⋊C₄×C₃₁	—	2	2	no	—
239	C₄⋊C₄×C₃₁	—	2	2	no	—
240	C₄⋊C₄×C₃₁	—	2	2	no	—
241	C₄⋊C₄×C₃₁	—	2	2	no	—
242	C₄⋊C₄×C₃₁	—	2	2	no	—
243	C₄⋊C₄×C₃₁	—	2	2	no	—
244	C₄⋊C₄×C₃₁	—	2	2	no	—
245	C₄⋊C₄×C₃₁	—	2	2	no	—
246	C₄⋊C₄×C₃₁	—	2	2	no	—
247	C₄⋊C₄×C₃₁	—	2	4	no	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	4	no	—
251	C₄⋊C₄×C₃₁	—	2	2	no	—
252	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
253	C₂²⋊C₄×C₃₁	—	2	4	no	—
254	C₂²⋊C₄×C₃₁	—	2	4	no	—
255	C₂²⋊C₄×C₃₁	—	2	4	no	—
256	C₂²⋊C₄×C₃₁	—	2	4	no	—
257	C₂²⋊C₄×C₃₁	—	2	4	no	—
258	C₂²⋊C₄×C₃₁	—	2	4	no	—
259	C₄²×C₃₁	—	2	4	no	—
260	C₄²×C₃₁	—	2	4	no	—
261	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
277	#60804	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₃₁	—	2	2	no	—
279	C₂³×C₃₁	—	2	2	no	—
280	C₂³×C₃₁	—	2	4	no	—
281	C₂³×C₃₁	—	4	1	no	—
282	C₂³×C₃₁	—	4	4	no	—
283	C₂³×C₃₁	—	4	4	no	—
284	C₂³×C₃₁	—	4	4	no	—
285	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
286	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
287	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
288	Q₈×C₃₁	—	2	8	no	—
289	Q₈×C₃₁	—	2	8	no	—
290	Q₈×C₃₁	—	4	4	no	—
291	Q₈×C₃₁	—	4	4	no	—
292	Q₈×C₃₁	—	4	4	no	—
293	Q₈×C₃₁	—	4	4	no	—
294	D₄×C₃₁	—	2	8	no	—
295	D₄×C₃₁	—	4	4	no	—
296	D₄×C₃₁	—	4	4	no	—
297	D₄×C₃₁	—	4	8	no	—
298	D₄×C₃₁	—	4	8	no	—
299	D₄×C₃₁	—	4	4	no	—
300	D₄×C₃₁	—	4	4	no	—
301	D₄×C₃₁	—	4	4	no	—
302	C₂×C₄×C₃₁	—	2	2	no	—
303	C₂×C₄×C₃₁	—	2	2	no	—
304	C₂×C₄×C₃₁	—	2	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	2	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	4	no	—
316	C₂×C₄×C₃₁	—	2	4	no	—
317	C₂×C₄×C₃₁	—	2	4	no	—
318	C₂×C₄×C₃₁	—	4	1	no	—
319	C₂×C₄×C₃₁	—	4	1	no	—
320	C₂×C₄×C₃₁	—	4	1	no	—
321	C₂×C₄×C₃₁	—	4	8	no	—
322	C₂×C₄×C₃₁	—	4	4	no	—
323	C₂×C₄×C₃₁	—	4	4	no	—
324	C₂×C₄×C₃₁	—	4	4	no	—
325	C₂×C₄×C₃₁	—	4	8	no	—
326	C₂×C₄×C₃₁	#137	1	4	yes	complemented
327	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
339	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
340	C₈×C₃₁	—	2	8	no	—
341	C₂×#533	C₂×C₃₁	1	1	yes	characteristic, complemented
342	C₂×#532	C₂×C₃₁	1	1	yes	characteristic
343	#3216	C₂×C₃₁	1	4	yes	complemented
344	#3215	C₂×C₃₁	1	4	yes	complemented
345	#3210	C₂×C₃₁	1	4	yes	complemented
346	#3209	C₂×C₃₁	1	2	yes	complemented
347	#3208	C₂×C₃₁	1	2	yes	complemented
348	#3152	C₂×C₃₁	1	2	yes	complemented
349	#3141	C₂×C₃₁	1	2	yes	complemented
350	#3037	C₂×C₃₁	1	4	yes	complemented
351	#3007	C₂×C₃₁	1	4	yes	complemented
352	#2920	C₂×C₃₁	1	1	yes	characteristic, complemented
353	C₂²×C₃₁	—	2	1	no	—
354	C₂²×C₃₁	—	2	1	no	—
355	C₂²×C₃₁	—	2	1	no	—
356	C₂²×C₃₁	—	2	1	no	—
357	C₂²×C₃₁	—	2	1	no	—
358	C₂²×C₃₁	—	2	1	no	—
359	C₂²×C₃₁	—	2	1	no	—
360	C₂²×C₃₁	—	4	4	no	—
361	C₂²×C₃₁	—	4	4	no	—
362	C₂²×C₃₁	—	4	4	no	—
363	C₂²×C₃₁	—	4	4	no	—
364	C₂²×C₃₁	—	8	8	no	—
365	C₂²×C₃₁	#535	1	2	yes	—
366	C₂²×C₃₁	C₂×#137	1	2	yes	—
367	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
368	C₄×C₃₁	—	2	1	no	—
369	C₄×C₃₁	—	2	1	no	—
370	C₄×C₃₁	—	2	1	no	—
371	C₄×C₃₁	—	2	1	no	—
372	C₄×C₃₁	—	2	1	no	—
373	C₄×C₃₁	—	2	1	no	—
374	C₄×C₃₁	—	2	1	no	—
375	C₄×C₃₁	—	4	4	no	—
376	C₄×C₃₁	—	4	4	no	—
377	C₄×C₃₁	—	4	4	no	—
378	C₄×C₃₁	#535	1	2	yes	—
379	C₄×C₃₁	C₂×#137	1	2	yes	—
380	C₄×C₃₁	C₂×#137	1	2	yes	—
381	C₄×C₃₁	#575	1	2	yes	—
382	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
383	C₂²×#41	C₂²×C₃₁	1	2	yes	—
384	C₂×#137	C₂²×C₃₁	1	8	yes	complemented
385	#533	—	2	1	no	—
386	#533	—	2	1	no	—
387	#533	—	2	1	no	—
388	#533	—	2	1	no	—
389	#533	C₂²×C₃₁	1	2	yes	—
390	#533	C₂²×C₃₁	1	2	yes	—
391	#533	C₂²×C₃₁	1	2	yes	complemented
392	#533	C₂²×C₃₁	1	2	yes	complemented
393	#532	—	2	1	no	—
394	#532	—	2	1	no	—
395	#532	—	2	1	no	—
396	#532	—	2	1	no	—
397	#532	C₂²×C₃₁	1	2	yes	—
398	#532	C₂²×C₃₁	1	2	yes	—
399	#532	C₂²×C₃₁	1	2	yes	—
400	#532	C₂²×C₃₁	1	2	yes	—
401	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
402	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
403	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
404	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
405	C₂×#125	—	2	1	no	—
406	C₂×#124	C₂²×C₃₁	1	2	yes	—
407	C₂×C₂²⋊Q₈	—	2	1	no	—
408	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
409	C₂×#121	—	2	1	no	—
410	C₂×#121	—	2	1	no	—
411	C₂×C₄×Q₈	—	2	1	no	—
412	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
413	C₂×C₄×D₄	—	2	1	no	—
414	C₂×C₄×D₄	—	2	1	no	—
415	C₂×#117	—	2	1	no	—
416	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
417	#497	C₂²×C₃₁	1	8	yes	complemented
418	#494	C₂²×C₃₁	1	4	yes	complemented
419	#492	C₂²×C₃₁	1	4	yes	complemented
420	#489	C₂²×C₃₁	1	8	yes	complemented
421	#487	C₂²×C₃₁	1	4	yes	complemented
422	#486	C₂²×C₃₁	1	4	yes	complemented
423	#464	C₂²×C₃₁	1	16	yes	complemented
424	#462	C₂²×C₃₁	1	8	yes	complemented
425	#460	C₂²×C₃₁	1	8	yes	complemented
426	#452	C₂²×C₃₁	1	16	yes	complemented
427	#451	C₂²×C₃₁	1	8	yes	—
428	#450	C₂²×C₃₁	1	8	yes	—
429	#432	C₂²×C₃₁	1	2	yes	—
430	#432	C₂²×C₃₁	1	2	yes	complemented
431	#431	C₂²×C₃₁	1	2	yes	—
432	#431	C₂²×C₃₁	1	2	yes	complemented
433	#423	C₂²×C₃₁	1	2	yes	complemented
434	#417	C₂²×C₃₁	1	8	yes	complemented
435	#407	C₂²×C₃₁	1	2	yes	—
436	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
437	C₂×C₃₁	—	2	2	no	—
438	C₂×C₃₁	—	2	2	no	—
439	C₂×C₃₁	—	4	1	no	—
440	C₂×C₃₁	—	8	4	no	—
441	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
442	C₂×C₃₁	C₂²×#137	1	1	yes	characteristic
443	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
444	C₂×#41	—	2	2	no	—
445	C₂×#41	—	2	2	no	—
446	C₂×#41	—	4	8	no	—
447	C₂×#41	C₂³×C₃₁	1	4	yes	—
448	C₂×#41	C₂³×C₃₁	1	4	yes	—
449	C₂²×Q₈	—	2	1	no	—
450	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
451	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
452	C₂²×D₄	—	2	2	no	—
453	C₂²×D₄	—	2	1	no	—
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
456	C₂³×C₄	—	2	2	no	—
457	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
458	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
460	#137	—	4	16	no	—
461	C₂×Q₁₆	C₂³×C₃₁	1	16	yes	—
462	C₂×SD₁₆	C₂³×C₃₁	1	16	yes	—
463	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
464	C₄⋊Q₈	—	2	1	no	—
465	C₄⋊Q₈	—	2	1	no	—
466	C₄⋊Q₈	—	2	1	no	—
467	C₄⋊Q₈	—	2	1	no	—
468	C₄⋊Q₈	—	2	1	no	—
469	C₄⋊Q₈	—	2	1	no	—
470	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
471	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
472	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
473	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
474	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
475	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
476	#127	—	2	1	no	—
477	#127	—	2	1	no	—
478	#127	C₂³×C₃₁	1	2	yes	—
479	#127	C₂³×C₃₁	1	2	yes	—
480	#125	—	2	2	no	—
481	#125	—	2	2	no	—
482	#125	—	2	2	no	—
483	#125	—	2	2	no	—
484	#124	—	2	2	no	—
485	#124	—	2	2	no	—
486	#124	C₂³×C₃₁	1	4	yes	—
487	#124	C₂³×C₃₁	1	4	yes	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
495	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
496	#121	—	2	2	no	—
497	#121	—	2	2	no	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	2	no	—
502	#121	—	2	2	no	—
503	#121	—	2	2	no	—
504	C₄×Q₈	—	2	2	no	—
505	C₄×Q₈	—	2	2	no	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×Q₈	—	2	2	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
511	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	#117	—	2	2	no	—
521	#117	—	2	2	no	—
522	#117	—	2	2	no	—
523	#117	—	2	2	no	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	2	1	no	—
526	C₂×C₄⋊C₄	—	2	1	no	—
527	C₂×C₄⋊C₄	—	2	1	no	—
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	—	2	2	no	—
530	C₂×C₄⋊C₄	—	2	2	no	—
531	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
532	C₂×C₂²⋊C₄	—	2	2	no	—
533	C₂×C₂²⋊C₄	—	2	2	no	—
534	C₂×C₂²⋊C₄	—	2	2	no	—
535	C₂×C₄²	—	2	2	no	—
536	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
537	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
538	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
539	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
540	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
541	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
542	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
548	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
549	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
550	#103	C₂³×C₃₁	1	16	yes	—
551	#102	C₂³×C₃₁	1	16	yes	—
552	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
553	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
554	#97	C₂³×C₃₁	1	4	yes	—
555	C₄×C₈	C₂³×C₃₁	1	4	yes	—
556	C₃₁	#60804	1	1	yes	characteristic, direct product factor, Sylow
557	C₂⁴	—	2	2	no	—
558	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
559	#41	—	2	16	no	—
560	#41	—	4	8	no	—
561	#41	—	4	8	no	—
562	#41	—	4	8	no	—
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	—	2	8	no	—
568	C₂×Q₈	—	4	4	no	—
569	C₂×Q₈	—	4	4	no	—
570	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
571	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂×D₄	—	4	4	no	—
581	C₂×D₄	—	4	8	no	—
582	C₂×D₄	—	4	4	no	—
583	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	8	no	—
593	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	C₂⁴×C₃₁	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
611	Q₁₆	—	4	16	no	—
612	SD₁₆	—	4	16	no	—
613	M₁₆	—	2	8	no	—
614	C₂×C₈	C₂⁴×C₃₁	1	8	yes	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	4	no	—
639	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
641	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
642	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
643	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
644	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
645	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
646	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
647	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
648	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
649	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
650	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
651	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
652	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
653	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
654	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	4	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	4	no	—
660	C₂³	—	4	4	no	—
661	C₂³	—	4	4	no	—
662	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
663	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
664	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
665	Q₈	—	2	8	no	—
666	Q₈	—	2	8	no	—
667	Q₈	—	4	4	no	—
668	Q₈	—	4	4	no	—
669	Q₈	—	4	4	no	—
670	Q₈	—	4	4	no	—
671	D₄	—	2	8	no	—
672	D₄	—	4	4	no	—
673	D₄	—	4	4	no	—
674	D₄	—	4	8	no	—
675	D₄	—	4	8	no	—
676	D₄	—	4	4	no	—
677	D₄	—	4	4	no	—
678	D₄	—	4	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	8	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	4	8	no	—
703	C₂×C₄	C₃₁×#137	1	4	yes	complemented
704	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
714	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
715	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
716	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
717	C₈	—	2	8	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	4	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	4	no	—
729	C₂²	—	8	8	no	—
730	C₂²	C₃₁×#535	1	2	yes	—
731	C₂²	C₂×C₃₁×#137	1	2	yes	—
732	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	1	no	—
739	C₄	—	2	1	no	—
740	C₄	—	4	4	no	—
741	C₄	—	4	4	no	—
742	C₄	—	4	4	no	—
743	C₄	C₃₁×#535	1	2	yes	—
744	C₄	C₂×C₃₁×#137	1	2	yes	—
745	C₄	C₂×C₃₁×#137	1	2	yes	—
746	C₄	C₃₁×#575	1	2	yes	—
747	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
748	C₂	—	2	2	no	—
749	C₂	—	2	2	no	—
750	C₂	—	4	1	no	—
751	C₂	—	8	4	no	—
752	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
753	C₂	C₂²×C₃₁×#137	1	1	yes	characteristic
754	C₂	C₂×C₃₁×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#533	C₂	semidirect
3. C₃₁×#3216	C₂	semidirect
4. C₃₁×#3215	C₂	semidirect
5. C₃₁×#3210	C₂	semidirect
6. C₃₁×#3209	C₂	semidirect
7. C₃₁×#3208	C₂	semidirect
8. C₃₁×#3152	C₂	semidirect
9. C₃₁×#3141	C₂	semidirect
10. C₃₁×#3037	C₂	semidirect
11. C₃₁×#3007	C₂	semidirect
12. C₃₁×#2920	C₂	semidirect
14. C₂×C₃₁×#137	C₂²	semidirect
21. C₃₁×#533	C₂²	semidirect
22. C₃₁×#533	C₂²	semidirect
32. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
47. C₃₁×#497	C₂²	semidirect
48. C₃₁×#494	C₂²	semidirect
49. C₃₁×#492	C₂²	semidirect
50. C₃₁×#489	C₂²	semidirect
51. C₃₁×#487	C₂²	semidirect
52. C₃₁×#486	C₂²	semidirect
53. C₃₁×#464	C₂²	semidirect
54. C₃₁×#462	C₂²	semidirect
55. C₃₁×#460	C₂²	semidirect
56. C₃₁×#452	C₂²	semidirect
60. C₃₁×#432	C₂²	semidirect
62. C₃₁×#431	C₂²	semidirect
63. C₃₁×#423	C₂²	semidirect
64. C₃₁×#417	C₂²	semidirect
66. C₄×M₁₆×C₃₁	C₂²	semidirect
277. #60804	C₃₁	direct (N × H)
326. C₂×C₄×C₃₁	#137	semidirect
341. C₂×#533	C₂×C₃₁	semidirect
343. #3216	C₂×C₃₁	semidirect
344. #3215	C₂×C₃₁	semidirect
345. #3210	C₂×C₃₁	semidirect
346. #3209	C₂×C₃₁	semidirect
347. #3208	C₂×C₃₁	semidirect
348. #3152	C₂×C₃₁	semidirect
349. #3141	C₂×C₃₁	semidirect
350. #3037	C₂×C₃₁	semidirect
351. #3007	C₂×C₃₁	semidirect
352. #2920	C₂×C₃₁	semidirect
384. C₂×#137	C₂²×C₃₁	semidirect
391. #533	C₂²×C₃₁	semidirect
392. #533	C₂²×C₃₁	semidirect
402. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
403. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
412. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
417. #497	C₂²×C₃₁	semidirect
418. #494	C₂²×C₃₁	semidirect
419. #492	C₂²×C₃₁	semidirect
420. #489	C₂²×C₃₁	semidirect
421. #487	C₂²×C₃₁	semidirect
422. #486	C₂²×C₃₁	semidirect
423. #464	C₂²×C₃₁	semidirect
424. #462	C₂²×C₃₁	semidirect
425. #460	C₂²×C₃₁	semidirect
426. #452	C₂²×C₃₁	semidirect
430. #432	C₂²×C₃₁	semidirect
432. #431	C₂²×C₃₁	semidirect
433. #423	C₂²×C₃₁	semidirect
434. #417	C₂²×C₃₁	semidirect
436. C₄×M₁₆	C₂²×C₃₁	semidirect
556. C₃₁	#60804	direct (N × H)
703. C₂×C₄	C₃₁×#137	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#533	2
C₂×C₃₁×#532	2
C₃₁×#3216	2
C₃₁×#3215	2
C₃₁×#3210	2
C₃₁×#3209	2
C₃₁×#3208	2
C₃₁×#3152	2
C₃₁×#3141	2
C₃₁×#3037	2
C₃₁×#3007	2
C₃₁×#2920	2
#60804	31

Subgroups — C31×#60804 #21517563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60804 #21517563