Subgroups — C₃₁×#61649 #21518408

Order 7936.

2042 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×#3538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3485	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3323	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3315	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3276	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3266	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3223	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3202	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3196	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3009	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3007	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2978	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
15	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#137	C₂²	1	4	yes	complemented
17	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
18	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
19	C₃₁×#563	—	2	2	no	—
20	C₃₁×#552	C₂²	1	4	yes	complemented
21	C₃₁×#551	—	2	2	no	—
22	D₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
23	C₃₁×#547	—	2	2	no	—
24	C₃₁×#547	C₂²	1	4	yes	—
25	C₃₁×#546	—	2	2	no	—
26	C₃₁×#546	C₂²	1	4	yes	—
27	C₃₁×#544	—	2	2	no	—
28	C₃₁×#541	C₂²	1	2	yes	complemented
29	C₃₁×#539	—	2	2	no	—
30	C₃₁×#536	C₂²	1	1	yes	characteristic
31	C₃₁×#536	C₂²	1	1	yes	characteristic
32	C₃₁×#536	C₂²	1	2	yes	—
33	C₃₁×#534	—	2	2	no	—
34	C₃₁×#525	C₂²	1	1	yes	characteristic
35	C₃₁×#525	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#123	—	2	2	no	—
37	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
38	C₃₁×#518	C₂²	1	1	yes	characteristic
39	C₃₁×#497	C₂²	1	2	yes	complemented
40	C₃₁×#494	C₂²	1	2	yes	complemented
41	C₃₁×#491	C₂²	1	2	yes	complemented
42	C₃₁×#488	C₂²	1	2	yes	complemented
43	C₃₁×#485	C₂²	1	4	yes	complemented
44	C₃₁×#485	C₂²	1	4	yes	complemented
45	C₃₁×#484	C₂²	1	2	yes	complemented
46	C₃₁×#481	C₂²	1	2	yes	complemented
47	C₃₁×#478	C₂²	1	4	yes	complemented
48	C₃₁×#470	C₂²	1	4	yes	complemented
49	C₃₁×#470	C₂²	1	4	yes	complemented
50	C₃₁×#468	C₂²	1	4	yes	complemented
51	C₃₁×#467	C₂²	1	4	yes	complemented
52	C₃₁×#464	C₂²	1	4	yes	complemented
53	C₃₁×#462	C₂²	1	4	yes	complemented
54	C₃₁×#461	C₂²	1	4	yes	complemented
55	C₃₁×#452	C₂²	1	4	yes	—
56	C₃₁×#452	C₂²	1	4	yes	complemented
57	C₃₁×#452	C₂²	1	4	yes	complemented
58	C₃₁×#452	C₂²	1	4	yes	complemented
59	C₃₁×#451	C₂²	1	2	yes	complemented
60	C₃₁×#451	C₂²	1	4	yes	complemented
61	C₃₁×#451	C₂²	1	4	yes	complemented
62	C₃₁×#450	C₂²	1	4	yes	—
63	C₃₁×#450	C₂²	1	4	yes	complemented
64	C₃₁×#448	C₂²	1	2	yes	complemented
65	C₃₁×#440	C₂²	1	4	yes	complemented
66	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
67	C₃₁×#436	C₂²	1	4	yes	complemented
68	C₃₁×#435	C₂²	1	4	yes	complemented
69	C₃₁×#433	C₂²	1	2	yes	complemented
70	C₃₁×#418	C₂²	1	2	yes	complemented
71	C₃₁×#417	C₂²	1	4	yes	complemented
72	C₃₁×#416	C₂²	1	2	yes	complemented
73	C₃₁×#408	C₂²	1	2	yes	—
74	C₃₁×#407	C₂²	1	2	yes	complemented
75	C₃₁×H(5,𝔽₂)	—	4	4	no	—
76	C₂×#41×C₃₁	—	2	1	no	—
77	C₂×#41×C₃₁	—	2	2	no	—
78	C₂×#41×C₃₁	—	4	4	no	—
79	C₂×#41×C₃₁	C₂³	1	2	yes	—
80	C₂×#41×C₃₁	C₂³	1	4	yes	—
81	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
82	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
84	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
86	C₂²×D₄×C₃₁	—	2	1	no	—
87	C₂²×D₄×C₃₁	—	2	2	no	—
88	C₂²×D₄×C₃₁	—	2	1	no	—
89	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
91	C₂³×C₄×C₃₁	—	2	1	no	—
92	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₃₁×#137	—	4	8	no	—
94	C₃₁×#137	—	4	4	no	—
95	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
96	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
97	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₃₁	—	4	4	no	—
99	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
102	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
103	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
105	C₃₁×C₄⋊Q₈	—	2	2	no	—
106	C₃₁×C₄⋊Q₈	—	2	1	no	—
107	C₃₁×C₄⋊Q₈	—	2	4	no	—
108	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₃₁×#126	—	2	4	no	—
111	C₃₁×#126	—	2	4	no	—
112	C₃₁×#125	—	2	4	no	—
113	C₃₁×#125	—	2	4	no	—
114	C₃₁×#125	C₂³	1	2	yes	—
115	C₃₁×#124	—	2	1	no	—
116	C₃₁×#124	—	2	2	no	—
117	C₃₁×#124	C₂³	1	2	yes	—
118	C₃₁×#123	—	2	2	no	—
119	C₃₁×#123	—	2	2	no	—
120	C₃₁×#123	—	2	2	no	—
121	C₃₁×#123	—	2	4	no	—
122	C₃₁×#123	—	2	1	no	—
123	C₃₁×#123	—	2	4	no	—
124	C₃₁×#123	—	2	2	no	—
125	C₃₁×#123	—	2	4	no	—
126	C₃₁×#123	—	2	4	no	—
127	C₃₁×#123	D₄	1	2	yes	—
128	C₃₁×C₂²⋊Q₈	—	2	2	no	—
129	C₃₁×C₂²⋊Q₈	—	2	2	no	—
130	C₃₁×C₂²⋊Q₈	—	2	2	no	—
131	C₃₁×C₂²⋊Q₈	—	2	4	no	—
132	C₃₁×C₂²⋊Q₈	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₃₁×#121	—	2	4	no	—
140	C₃₁×#121	—	2	4	no	—
141	C₃₁×#121	D₄	1	2	yes	—
142	C₃₁×#121	C₂³	1	2	yes	—
143	C₃₁×#120	—	2	1	no	—
144	C₃₁×#120	—	2	4	no	—
145	C₃₁×#120	D₄	1	2	yes	—
146	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
147	C₄×D₄×C₃₁	—	2	4	no	—
148	C₄×D₄×C₃₁	—	2	2	no	—
149	C₄×D₄×C₃₁	—	2	2	no	—
150	C₄×D₄×C₃₁	C₂³	1	4	yes	—
151	C₄×D₄×C₃₁	C₂³	1	4	yes	—
152	C₃₁×#117	—	2	4	no	—
153	C₃₁×#117	C₂³	1	2	yes	—
154	C₃₁×#117	C₂³	1	1	yes	characteristic
155	C₃₁×#117	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
157	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
160	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
161	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
162	C₃₁×#107	C₂³	1	4	yes	—
163	C₃₁×#106	C₂³	1	4	yes	—
164	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
165	C₃₁×#103	C₂³	1	4	yes	—
166	C₃₁×#103	C₂³	1	4	yes	—
167	C₃₁×#103	C₂³	1	4	yes	—
168	C₃₁×#103	C₂³	1	4	yes	—
169	C₃₁×#103	C₂³	1	4	yes	—
170	C₃₁×#102	C₂³	1	4	yes	—
171	C₃₁×#102	C₂³	1	4	yes	—
172	C₃₁×#102	C₂³	1	4	yes	—
173	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
174	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
175	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
176	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₃₁×#97	C₂³	1	2	yes	—
178	C₄×C₈×C₃₁	C₂³	1	2	yes	—
179	C₂⁴×C₃₁	—	2	1	no	—
180	C₂⁴×C₃₁	—	2	2	no	—
181	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
182	#41×C₃₁	—	2	8	no	—
183	#41×C₃₁	—	2	4	no	—
184	#41×C₃₁	—	4	2	no	—
185	#41×C₃₁	—	4	4	no	—
186	#41×C₃₁	—	4	2	no	—
187	#41×C₃₁	—	4	2	no	—
188	#41×C₃₁	—	4	8	no	—
189	#41×C₃₁	—	4	4	no	—
190	C₂×Q₈×C₃₁	—	2	1	no	—
191	C₂×Q₈×C₃₁	—	2	2	no	—
192	C₂×Q₈×C₃₁	—	2	2	no	—
193	C₂×Q₈×C₃₁	—	4	2	no	—
194	C₂×Q₈×C₃₁	—	4	2	no	—
195	C₂×Q₈×C₃₁	—	4	4	no	—
196	C₂×Q₈×C₃₁	—	4	2	no	—
197	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
198	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
199	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
200	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
201	C₂×D₄×C₃₁	—	2	4	no	—
202	C₂×D₄×C₃₁	—	2	4	no	—
203	C₂×D₄×C₃₁	—	2	4	no	—
204	C₂×D₄×C₃₁	—	2	1	no	—
205	C₂×D₄×C₃₁	—	2	2	no	—
206	C₂×D₄×C₃₁	—	2	2	no	—
207	C₂×D₄×C₃₁	—	2	1	no	—
208	C₂×D₄×C₃₁	—	2	2	no	—
209	C₂×D₄×C₃₁	—	4	2	no	—
210	C₂×D₄×C₃₁	—	4	4	no	—
211	C₂×D₄×C₃₁	—	4	4	no	—
212	C₂×D₄×C₃₁	—	4	8	no	—
213	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
214	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
217	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₃₁	—	2	2	no	—
219	C₂²×C₄×C₃₁	—	2	1	no	—
220	C₂²×C₄×C₃₁	—	2	2	no	—
221	C₂²×C₄×C₃₁	—	2	2	no	—
222	C₂²×C₄×C₃₁	—	2	4	no	—
223	C₂²×C₄×C₃₁	—	2	2	no	—
224	C₂²×C₄×C₃₁	—	2	1	no	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	4	2	no	—
227	C₂²×C₄×C₃₁	—	4	4	no	—
228	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
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	2	yes	—
232	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
233	Q₁₆×C₃₁	—	4	4	no	—
234	Q₁₆×C₃₁	—	4	4	no	—
235	Q₁₆×C₃₁	—	4	4	no	—
236	SD₁₆×C₃₁	—	2	8	no	—
237	SD₁₆×C₃₁	—	2	8	no	—
238	SD₁₆×C₃₁	—	4	4	no	—
239	M₁₆×C₃₁	—	4	4	no	—
240	M₁₆×C₃₁	—	4	2	no	—
241	C₂×C₈×C₃₁	—	4	2	no	—
242	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
243	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
244	C₄⋊C₄×C₃₁	—	2	2	no	—
245	C₄⋊C₄×C₃₁	—	2	4	no	—
246	C₄⋊C₄×C₃₁	—	2	4	no	—
247	C₄⋊C₄×C₃₁	—	2	4	no	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	4	yes	—
255	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
257	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
258	C₂²⋊C₄×C₃₁	—	2	1	no	—
259	C₂²⋊C₄×C₃₁	—	2	4	no	—
260	C₂²⋊C₄×C₃₁	—	2	4	no	—
261	C₂²⋊C₄×C₃₁	—	2	4	no	—
262	C₂²⋊C₄×C₃₁	—	2	2	no	—
263	C₂²⋊C₄×C₃₁	—	2	2	no	—
264	C₂²⋊C₄×C₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
269	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
270	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
271	C₄²×C₃₁	—	2	2	no	—
272	C₄²×C₃₁	—	2	4	no	—
273	C₄²×C₃₁	—	2	1	no	—
274	C₄²×C₃₁	C₂⁴	1	2	yes	—
275	#61649	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂³×C₃₁	—	2	4	no	—
277	C₂³×C₃₁	—	2	2	no	—
278	C₂³×C₃₁	—	2	1	no	—
279	C₂³×C₃₁	—	4	1	no	—
280	C₂³×C₃₁	—	4	2	no	—
281	C₂³×C₃₁	—	4	4	no	—
282	C₂³×C₃₁	—	8	2	no	—
283	C₂³×C₃₁	—	8	4	no	—
284	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
285	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
286	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
287	Q₈×C₃₁	—	2	4	no	—
288	Q₈×C₃₁	—	2	4	no	—
289	Q₈×C₃₁	—	2	4	no	—
290	Q₈×C₃₁	—	2	2	no	—
291	Q₈×C₃₁	—	4	1	no	—
292	Q₈×C₃₁	—	4	2	no	—
293	Q₈×C₃₁	—	8	2	no	—
294	Q₈×C₃₁	—	8	2	no	—
295	D₄×C₃₁	—	2	4	no	—
296	D₄×C₃₁	—	2	2	no	—
297	D₄×C₃₁	—	2	2	no	—
298	D₄×C₃₁	—	4	1	no	—
299	D₄×C₃₁	—	4	2	no	—
300	D₄×C₃₁	—	4	4	no	—
301	D₄×C₃₁	—	4	4	no	—
302	D₄×C₃₁	—	4	4	no	—
303	D₄×C₃₁	—	4	8	no	—
304	D₄×C₃₁	—	4	2	no	—
305	D₄×C₃₁	—	8	2	no	—
306	D₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
307	C₂×C₄×C₃₁	—	2	2	no	—
308	C₂×C₄×C₃₁	—	2	4	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	4	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	4	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	1	no	—
316	C₂×C₄×C₃₁	—	4	1	no	—
317	C₂×C₄×C₃₁	—	4	2	no	—
318	C₂×C₄×C₃₁	—	4	8	no	—
319	C₂×C₄×C₃₁	—	4	4	no	—
320	C₂×C₄×C₃₁	—	4	2	no	—
321	C₂×C₄×C₃₁	—	4	4	no	—
322	C₂×C₄×C₃₁	—	4	2	no	—
323	C₂×C₄×C₃₁	—	8	4	no	—
324	C₂×C₄×C₃₁	—	8	2	no	—
325	C₂×C₄×C₃₁	—	8	2	no	—
326	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
327	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
331	C₈×C₃₁	—	2	4	no	—
332	C₈×C₃₁	—	2	4	no	—
333	#3538	C₂×C₃₁	1	1	yes	characteristic, complemented
334	#3485	C₂×C₃₁	1	1	yes	characteristic
335	#3323	C₂×C₃₁	1	4	yes	complemented
336	#3315	C₂×C₃₁	1	4	yes	complemented
337	#3276	C₂×C₃₁	1	4	yes	complemented
338	#3266	C₂×C₃₁	1	4	yes	complemented
339	#3223	C₂×C₃₁	1	2	yes	complemented
340	#3202	C₂×C₃₁	1	2	yes	complemented
341	#3196	C₂×C₃₁	1	2	yes	complemented
342	#3123	C₂×C₃₁	1	2	yes	complemented
343	#3009	C₂×C₃₁	1	2	yes	complemented
344	#3007	C₂×C₃₁	1	2	yes	complemented
345	#2978	C₂×C₃₁	1	1	yes	characteristic, complemented
346	C₂²×C₃₁	—	2	2	no	—
347	C₂²×C₃₁	—	2	4	no	—
348	C₂²×C₃₁	—	2	2	no	—
349	C₂²×C₃₁	—	2	2	no	—
350	C₂²×C₃₁	—	2	1	no	—
351	C₂²×C₃₁	—	2	2	no	—
352	C₂²×C₃₁	—	2	2	no	—
353	C₂²×C₃₁	—	2	4	no	—
354	C₂²×C₃₁	—	4	4	no	—
355	C₂²×C₃₁	—	4	2	no	—
356	C₂²×C₃₁	—	4	1	no	—
357	C₂²×C₃₁	—	8	4	no	—
358	C₂²×C₃₁	—	8	2	no	—
359	C₂²×C₃₁	—	16	4	no	—
360	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
361	C₄×C₃₁	—	2	4	no	—
362	C₄×C₃₁	—	2	2	no	—
363	C₄×C₃₁	—	2	1	no	—
364	C₄×C₃₁	—	2	2	no	—
365	C₄×C₃₁	—	4	4	no	—
366	C₄×C₃₁	—	4	2	no	—
367	C₄×C₃₁	—	4	1	no	—
368	C₄×C₃₁	—	4	2	no	—
369	C₄×C₃₁	—	4	4	no	—
370	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
371	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
372	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
373	C₂×#137	C₂²×C₃₁	1	4	yes	complemented
374	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
375	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
376	#563	—	2	2	no	—
377	#552	C₂²×C₃₁	1	4	yes	complemented
378	#551	—	2	2	no	—
379	D₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
380	#547	—	2	2	no	—
381	#547	C₂²×C₃₁	1	4	yes	—
382	#546	—	2	2	no	—
383	#546	C₂²×C₃₁	1	4	yes	—
384	#544	—	2	2	no	—
385	#541	C₂²×C₃₁	1	2	yes	complemented
386	#539	—	2	2	no	—
387	#536	C₂²×C₃₁	1	1	yes	characteristic
388	#536	C₂²×C₃₁	1	1	yes	characteristic
389	#536	C₂²×C₃₁	1	2	yes	—
390	#534	—	2	2	no	—
391	#525	C₂²×C₃₁	1	1	yes	characteristic
392	#525	C₂²×C₃₁	1	1	yes	characteristic
393	C₂×#123	—	2	2	no	—
394	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
395	#518	C₂²×C₃₁	1	1	yes	characteristic
396	#497	C₂²×C₃₁	1	2	yes	complemented
397	#494	C₂²×C₃₁	1	2	yes	complemented
398	#491	C₂²×C₃₁	1	2	yes	complemented
399	#488	C₂²×C₃₁	1	2	yes	complemented
400	#485	C₂²×C₃₁	1	4	yes	complemented
401	#485	C₂²×C₃₁	1	4	yes	complemented
402	#484	C₂²×C₃₁	1	2	yes	complemented
403	#481	C₂²×C₃₁	1	2	yes	complemented
404	#478	C₂²×C₃₁	1	4	yes	complemented
405	#470	C₂²×C₃₁	1	4	yes	complemented
406	#470	C₂²×C₃₁	1	4	yes	complemented
407	#468	C₂²×C₃₁	1	4	yes	complemented
408	#467	C₂²×C₃₁	1	4	yes	complemented
409	#464	C₂²×C₃₁	1	4	yes	complemented
410	#462	C₂²×C₃₁	1	4	yes	complemented
411	#461	C₂²×C₃₁	1	4	yes	complemented
412	#452	C₂²×C₃₁	1	4	yes	—
413	#452	C₂²×C₃₁	1	4	yes	complemented
414	#452	C₂²×C₃₁	1	4	yes	complemented
415	#452	C₂²×C₃₁	1	4	yes	complemented
416	#451	C₂²×C₃₁	1	2	yes	complemented
417	#451	C₂²×C₃₁	1	4	yes	complemented
418	#451	C₂²×C₃₁	1	4	yes	complemented
419	#450	C₂²×C₃₁	1	4	yes	—
420	#450	C₂²×C₃₁	1	4	yes	complemented
421	#448	C₂²×C₃₁	1	2	yes	complemented
422	#440	C₂²×C₃₁	1	4	yes	complemented
423	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
424	#436	C₂²×C₃₁	1	4	yes	complemented
425	#435	C₂²×C₃₁	1	4	yes	complemented
426	#433	C₂²×C₃₁	1	2	yes	complemented
427	#418	C₂²×C₃₁	1	2	yes	complemented
428	#417	C₂²×C₃₁	1	4	yes	complemented
429	#416	C₂²×C₃₁	1	2	yes	complemented
430	#408	C₂²×C₃₁	1	2	yes	—
431	#407	C₂²×C₃₁	1	2	yes	complemented
432	C₂×C₃₁	—	4	2	no	—
433	C₂×C₃₁	—	4	1	no	—
434	C₂×C₃₁	—	4	2	no	—
435	C₂×C₃₁	—	4	4	no	—
436	C₂×C₃₁	—	8	1	no	—
437	C₂×C₃₁	#3484	1	1	yes	characteristic
438	C₂×C₃₁	#3586	1	2	yes	—
439	H(5,𝔽₂)	—	4	4	no	—
440	C₂×#41	—	2	1	no	—
441	C₂×#41	—	2	2	no	—
442	C₂×#41	—	4	4	no	—
443	C₂×#41	C₂³×C₃₁	1	4	yes	—
444	C₂×#41	C₂³×C₃₁	1	2	yes	—
445	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
446	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
447	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
448	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
449	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
450	C₂²×D₄	—	2	1	no	—
451	C₂²×D₄	—	2	2	no	—
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
454	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
455	C₂³×C₄	—	2	1	no	—
456	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
457	#137	—	4	8	no	—
458	#137	—	4	4	no	—
459	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
460	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
461	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
462	C₂×SD₁₆	—	4	4	no	—
463	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
464	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
465	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
466	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
467	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
468	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
469	C₄⋊Q₈	—	2	2	no	—
470	C₄⋊Q₈	—	2	1	no	—
471	C₄⋊Q₈	—	2	4	no	—
472	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
473	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
474	#126	—	2	4	no	—
475	#126	—	2	4	no	—
476	#125	—	2	4	no	—
477	#125	—	2	4	no	—
478	#125	C₂³×C₃₁	1	2	yes	—
479	#124	—	2	1	no	—
480	#124	—	2	2	no	—
481	#124	C₂³×C₃₁	1	2	yes	—
482	#123	—	2	2	no	—
483	#123	—	2	2	no	—
484	#123	—	2	2	no	—
485	#123	—	2	4	no	—
486	#123	—	2	1	no	—
487	#123	—	2	4	no	—
488	#123	—	2	2	no	—
489	#123	—	2	4	no	—
490	#123	—	2	4	no	—
491	#123	D₄×C₃₁	1	2	yes	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
498	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
499	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
500	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
501	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
502	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
503	#121	—	2	4	no	—
504	#121	—	2	4	no	—
505	#121	D₄×C₃₁	1	2	yes	—
506	#121	C₂³×C₃₁	1	2	yes	—
507	#120	—	2	1	no	—
508	#120	—	2	4	no	—
509	#120	D₄×C₃₁	1	2	yes	—
510	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	C₂³×C₃₁	1	4	yes	—
515	C₄×D₄	C₂³×C₃₁	1	4	yes	—
516	#117	—	2	4	no	—
517	#117	C₂³×C₃₁	1	1	yes	characteristic
518	#117	C₂³×C₃₁	1	2	yes	—
519	#117	C₂³×C₃₁	1	1	yes	characteristic
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	—	2	4	no	—
522	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
523	C₂×C₂²⋊C₄	—	2	2	no	—
524	C₂×C₂²⋊C₄	—	2	2	no	—
525	C₂×C₂²⋊C₄	—	2	4	no	—
526	#107	C₂³×C₃₁	1	4	yes	—
527	#106	C₂³×C₃₁	1	4	yes	—
528	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
529	#103	C₂³×C₃₁	1	4	yes	—
530	#103	C₂³×C₃₁	1	4	yes	—
531	#103	C₂³×C₃₁	1	4	yes	—
532	#103	C₂³×C₃₁	1	4	yes	—
533	#103	C₂³×C₃₁	1	4	yes	—
534	#102	C₂³×C₃₁	1	4	yes	—
535	#102	C₂³×C₃₁	1	4	yes	—
536	#102	C₂³×C₃₁	1	4	yes	—
537	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
538	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
539	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
540	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
541	#97	C₂³×C₃₁	1	2	yes	—
542	C₄×C₈	C₂³×C₃₁	1	2	yes	—
543	C₃₁	#61649	1	1	yes	characteristic, direct product factor, Sylow
544	C₂⁴	—	2	1	no	—
545	C₂⁴	—	2	2	no	—
546	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
547	#41	—	2	8	no	—
548	#41	—	2	4	no	—
549	#41	—	4	2	no	—
550	#41	—	4	4	no	—
551	#41	—	4	2	no	—
552	#41	—	4	2	no	—
553	#41	—	4	8	no	—
554	#41	—	4	4	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	4	2	no	—
559	C₂×Q₈	—	4	2	no	—
560	C₂×Q₈	—	4	4	no	—
561	C₂×Q₈	—	4	2	no	—
562	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
563	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
564	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
565	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	4	2	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	—	4	4	no	—
577	C₂×D₄	—	4	8	no	—
578	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
579	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
580	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
581	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
582	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	4	no	—
593	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
594	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
598	Q₁₆	—	4	4	no	—
599	Q₁₆	—	4	4	no	—
600	Q₁₆	—	4	4	no	—
601	SD₁₆	—	2	8	no	—
602	SD₁₆	—	2	8	no	—
603	SD₁₆	—	4	4	no	—
604	M₁₆	—	4	4	no	—
605	M₁₆	—	4	2	no	—
606	C₂×C₈	—	4	2	no	—
607	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
608	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	2	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	C₂×D₄×C₃₁	1	4	yes	—
620	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
621	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
622	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
634	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
635	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	1	no	—
639	C₄²	C₂⁴×C₃₁	1	2	yes	—
640	C₂³	—	2	4	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	8	2	no	—
647	C₂³	—	8	4	no	—
648	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
649	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
650	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
651	Q₈	—	2	4	no	—
652	Q₈	—	2	4	no	—
653	Q₈	—	2	4	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	8	2	no	—
658	Q₈	—	8	2	no	—
659	D₄	—	2	4	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	4	1	no	—
663	D₄	—	4	2	no	—
664	D₄	—	4	4	no	—
665	D₄	—	4	4	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	8	no	—
668	D₄	—	4	2	no	—
669	D₄	—	8	2	no	—
670	D₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	8	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	4	2	no	—
687	C₂×C₄	—	8	4	no	—
688	C₂×C₄	—	8	2	no	—
689	C₂×C₄	—	8	2	no	—
690	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
691	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
692	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
694	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
695	C₈	—	2	4	no	—
696	C₈	—	2	4	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	4	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	4	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	2	no	—
705	C₂²	—	4	4	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	8	4	no	—
709	C₂²	—	8	2	no	—
710	C₂²	—	16	4	no	—
711	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
712	C₄	—	2	2	no	—
713	C₄	—	2	1	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	4	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	4	no	—
719	C₄	—	4	4	no	—
720	C₄	—	4	2	no	—
721	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
722	C₂	—	4	1	no	—
723	C₂	—	4	2	no	—
724	C₂	—	4	2	no	—
725	C₂	—	4	4	no	—
726	C₂	—	8	1	no	—
727	C₂	C₃₁×#3484	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×#3485	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3538	C₂	semidirect
3. C₃₁×#3323	C₂	semidirect
4. C₃₁×#3315	C₂	semidirect
5. C₃₁×#3276	C₂	semidirect
6. C₃₁×#3266	C₂	semidirect
7. C₃₁×#3223	C₂	semidirect
8. C₃₁×#3202	C₂	semidirect
9. C₃₁×#3196	C₂	semidirect
10. C₃₁×#3123	C₂	semidirect
11. C₃₁×#3009	C₂	semidirect
12. C₃₁×#3007	C₂	semidirect
13. C₃₁×#2978	C₂	semidirect
16. C₂×C₃₁×#137	C₂²	semidirect
17. C₂×C₃₁×#137	C₂²	semidirect
18. C₂²×SD₁₆×C₃₁	C₂²	semidirect
20. C₃₁×#552	C₂²	semidirect
22. D₄×Q₈×C₃₁	C₂²	semidirect
28. C₃₁×#541	C₂²	semidirect
37. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
39. C₃₁×#497	C₂²	semidirect
40. C₃₁×#494	C₂²	semidirect
41. C₃₁×#491	C₂²	semidirect
42. C₃₁×#488	C₂²	semidirect
43. C₃₁×#485	C₂²	semidirect
44. C₃₁×#485	C₂²	semidirect
45. C₃₁×#484	C₂²	semidirect
46. C₃₁×#481	C₂²	semidirect
47. C₃₁×#478	C₂²	semidirect
48. C₃₁×#470	C₂²	semidirect
49. C₃₁×#470	C₂²	semidirect
50. C₃₁×#468	C₂²	semidirect
51. C₃₁×#467	C₂²	semidirect
52. C₃₁×#464	C₂²	semidirect
53. C₃₁×#462	C₂²	semidirect
54. C₃₁×#461	C₂²	semidirect
56. C₃₁×#452	C₂²	semidirect
57. C₃₁×#452	C₂²	semidirect
58. C₃₁×#452	C₂²	semidirect
59. C₃₁×#451	C₂²	semidirect
60. C₃₁×#451	C₂²	semidirect
61. C₃₁×#451	C₂²	semidirect
63. C₃₁×#450	C₂²	semidirect
64. C₃₁×#448	C₂²	semidirect
65. C₃₁×#440	C₂²	semidirect
66. C₄×SD₁₆×C₃₁	C₂²	semidirect
67. C₃₁×#436	C₂²	semidirect
68. C₃₁×#435	C₂²	semidirect
69. C₃₁×#433	C₂²	semidirect
70. C₃₁×#418	C₂²	semidirect
71. C₃₁×#417	C₂²	semidirect
72. C₃₁×#416	C₂²	semidirect
74. C₃₁×#407	C₂²	semidirect
275. #61649	C₃₁	direct (N × H)
333. #3538	C₂×C₃₁	semidirect
335. #3323	C₂×C₃₁	semidirect
336. #3315	C₂×C₃₁	semidirect
337. #3276	C₂×C₃₁	semidirect
338. #3266	C₂×C₃₁	semidirect
339. #3223	C₂×C₃₁	semidirect
340. #3202	C₂×C₃₁	semidirect
341. #3196	C₂×C₃₁	semidirect
342. #3123	C₂×C₃₁	semidirect
343. #3009	C₂×C₃₁	semidirect
344. #3007	C₂×C₃₁	semidirect
345. #2978	C₂×C₃₁	semidirect
373. C₂×#137	C₂²×C₃₁	semidirect
374. C₂×#137	C₂²×C₃₁	semidirect
375. C₂²×SD₁₆	C₂²×C₃₁	semidirect
377. #552	C₂²×C₃₁	semidirect
379. D₄×Q₈	C₂²×C₃₁	semidirect
385. #541	C₂²×C₃₁	semidirect
394. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
396. #497	C₂²×C₃₁	semidirect
397. #494	C₂²×C₃₁	semidirect
398. #491	C₂²×C₃₁	semidirect
399. #488	C₂²×C₃₁	semidirect
400. #485	C₂²×C₃₁	semidirect
401. #485	C₂²×C₃₁	semidirect
402. #484	C₂²×C₃₁	semidirect
403. #481	C₂²×C₃₁	semidirect
404. #478	C₂²×C₃₁	semidirect
405. #470	C₂²×C₃₁	semidirect
406. #470	C₂²×C₃₁	semidirect
407. #468	C₂²×C₃₁	semidirect
408. #467	C₂²×C₃₁	semidirect
409. #464	C₂²×C₃₁	semidirect
410. #462	C₂²×C₃₁	semidirect
411. #461	C₂²×C₃₁	semidirect
413. #452	C₂²×C₃₁	semidirect
414. #452	C₂²×C₃₁	semidirect
415. #452	C₂²×C₃₁	semidirect
416. #451	C₂²×C₃₁	semidirect
417. #451	C₂²×C₃₁	semidirect
418. #451	C₂²×C₃₁	semidirect
420. #450	C₂²×C₃₁	semidirect
421. #448	C₂²×C₃₁	semidirect
422. #440	C₂²×C₃₁	semidirect
423. C₄×SD₁₆	C₂²×C₃₁	semidirect
424. #436	C₂²×C₃₁	semidirect
425. #435	C₂²×C₃₁	semidirect
426. #433	C₂²×C₃₁	semidirect
427. #418	C₂²×C₃₁	semidirect
428. #417	C₂²×C₃₁	semidirect
429. #416	C₂²×C₃₁	semidirect
431. #407	C₂²×C₃₁	semidirect
543. C₃₁	#61649	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×#3538	2
C₃₁×#3485	2
C₃₁×#3323	2
C₃₁×#3315	2
C₃₁×#3276	2
C₃₁×#3266	2
C₃₁×#3223	2
C₃₁×#3202	2
C₃₁×#3196	2
C₃₁×#3123	2
C₃₁×#3009	2
C₃₁×#3007	2
C₃₁×#2978	2
#61649	31

Subgroups — C31×#61649 #21518408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61649 #21518408