Subgroups — C₃₁×#61803 #21518562

Order 7936.

1732 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3353	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3350	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3340	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3329	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3320	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3298	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3200	C₂	1	4	yes	maximal, complemented
12	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3097	C₂	1	4	yes	maximal, complemented
15	C₃₁×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#563	—	2	2	no	—
17	C₃₁×#559	—	2	1	no	—
18	C₃₁×#559	—	2	2	no	—
19	Q₈²×C₃₁	—	2	1	no	—
20	C₃₁×#556	—	2	1	no	—
21	C₃₁×#556	C₂²	1	2	yes	complemented
22	C₃₁×#556	C₂²	1	2	yes	complemented
23	C₃₁×#555	C₂²	1	2	yes	—
24	C₃₁×#553	C₂²	1	4	yes	—
25	C₃₁×#550	—	2	1	no	—
26	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
27	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
28	C₃₁×#547	C₂²	1	2	yes	—
29	C₃₁×#542	—	2	2	no	—
30	C₃₁×#542	—	2	2	no	—
31	C₃₁×#538	—	2	2	no	—
32	C₃₁×#536	C₂²	1	4	yes	—
33	C₃₁×#535	C₂²	1	2	yes	—
34	C₃₁×#533	C₂²	1	1	yes	characteristic
35	C₃₁×#533	C₂²	1	1	yes	characteristic
36	C₃₁×#533	C₂²	1	1	yes	characteristic
37	C₃₁×#532	C₂²	1	1	yes	characteristic
38	C₃₁×#525	—	2	2	no	—
39	C₃₁×#520	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#501	C₂²	1	2	yes	complemented
42	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#491	C₂²	1	2	yes	complemented
45	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#485	C₂²	1	4	yes	—
48	C₃₁×#485	C₂²	1	4	yes	—
49	C₃₁×#485	C₂²	1	4	yes	complemented
50	C₃₁×#485	C₂²	1	4	yes	complemented
51	C₃₁×#484	C₂²	1	2	yes	—
52	C₃₁×#484	C₂²	1	4	yes	complemented
53	C₃₁×#483	C₂²	1	2	yes	—
54	C₃₁×#483	C₂²	1	4	yes	complemented
55	C₃₁×#482	C₂²	1	4	yes	—
56	C₃₁×#482	C₂²	1	4	yes	—
57	C₃₁×#479	C₂²	1	4	yes	complemented
58	C₃₁×#477	C₂²	1	2	yes	complemented
59	C₃₁×#476	C₂²	1	2	yes	—
60	C₃₁×#475	C₂²	1	2	yes	complemented
61	C₃₁×#474	C₂²	1	2	yes	—
62	C₃₁×#468	C₂²	1	4	yes	—
63	C₃₁×#468	C₂²	1	4	yes	—
64	C₃₁×#465	C₂²	1	4	yes	—
65	C₃₁×#465	C₂²	1	4	yes	—
66	C₃₁×#461	C₂²	1	2	yes	—
67	C₃₁×#461	C₂²	1	2	yes	—
68	C₃₁×#450	C₂²	1	2	yes	—
69	C₃₁×#450	C₂²	1	2	yes	—
70	C₃₁×#448	C₂²	1	4	yes	—
71	C₃₁×#448	C₂²	1	4	yes	—
72	C₃₁×#440	C₂²	1	4	yes	—
73	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
74	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
75	C₃₁×#436	C₂²	1	2	yes	complemented
76	C₃₁×#435	C₂²	1	4	yes	complemented
77	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
78	C₃₁×#432	C₂²	1	1	yes	characteristic
79	C₃₁×#431	C₂²	1	1	yes	characteristic
80	C₃₁×#428	C₂²	1	4	yes	complemented
81	C₃₁×#427	C₂²	1	4	yes	complemented
82	C₃₁×#419	C₂²	1	4	yes	complemented
83	C₂×C₃₁×#103	C₂²	1	4	yes	complemented
84	C₃₁×#408	C₂²	1	4	yes	—
85	C₂×#41×C₃₁	—	2	2	no	—
86	C₂×#41×C₃₁	C₂³	1	2	yes	—
87	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
88	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₃₁	—	2	1	no	—
90	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
91	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
92	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
93	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
94	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
95	C₃₁×C₄⋊Q₈	—	2	4	no	—
96	C₃₁×C₄⋊Q₈	—	2	2	no	—
97	C₃₁×C₄⋊Q₈	—	2	2	no	—
98	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
99	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
102	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₃₁×#127	—	2	2	no	—
106	C₃₁×#127	D₄	1	1	yes	characteristic
107	C₃₁×#126	—	2	4	no	—
108	C₃₁×#126	—	2	4	no	—
109	C₃₁×#126	—	2	4	no	—
110	C₃₁×#125	—	2	1	no	—
111	C₃₁×#125	—	2	1	no	—
112	C₃₁×#125	C₂³	1	2	yes	—
113	C₃₁×#124	—	2	2	no	—
114	C₃₁×#124	—	2	4	no	—
115	C₃₁×#124	—	2	2	no	—
116	C₃₁×#124	—	2	2	no	—
117	C₃₁×#124	—	2	4	no	—
118	C₃₁×#124	D₄	1	2	yes	—
119	C₃₁×#123	—	2	4	no	—
120	C₃₁×#123	—	2	4	no	—
121	C₃₁×#123	—	2	4	no	—
122	C₃₁×#123	—	2	4	no	—
123	C₃₁×C₂²⋊Q₈	—	2	1	no	—
124	C₃₁×C₂²⋊Q₈	—	2	1	no	—
125	C₃₁×C₂²⋊Q₈	—	2	1	no	—
126	C₃₁×C₂²⋊Q₈	—	2	1	no	—
127	C₃₁×C₂²⋊Q₈	—	2	2	no	—
128	C₃₁×C₂²⋊Q₈	—	2	4	no	—
129	C₃₁×C₂²⋊Q₈	—	2	4	no	—
130	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
131	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₃₁×#121	—	2	2	no	—
135	C₃₁×#121	—	2	4	no	—
136	C₃₁×#121	D₄	1	2	yes	—
137	C₃₁×#121	D₄	1	2	yes	—
138	C₃₁×#121	C₂³	1	4	yes	—
139	C₃₁×#121	C₂³	1	4	yes	—
140	C₃₁×#120	—	2	4	no	—
141	C₄×Q₈×C₃₁	—	2	2	no	—
142	C₄×Q₈×C₃₁	—	2	2	no	—
143	C₄×Q₈×C₃₁	—	2	2	no	—
144	C₄×Q₈×C₃₁	—	2	1	no	—
145	C₄×Q₈×C₃₁	—	2	1	no	—
146	C₄×Q₈×C₃₁	—	2	1	no	—
147	C₄×Q₈×C₃₁	—	2	1	no	—
148	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
149	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
150	C₄×D₄×C₃₁	—	2	4	no	—
151	C₄×D₄×C₃₁	—	2	2	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	1	no	—
156	C₄×D₄×C₃₁	—	2	1	no	—
157	C₄×D₄×C₃₁	C₂³	1	2	yes	—
158	C₄×D₄×C₃₁	C₂³	1	2	yes	—
159	C₄×D₄×C₃₁	C₂³	1	2	yes	—
160	C₄×D₄×C₃₁	C₂³	1	2	yes	—
161	C₃₁×#117	—	2	1	no	—
162	C₃₁×#117	—	2	1	no	—
163	C₃₁×#117	—	2	2	no	—
164	C₃₁×#117	C₂³	1	4	yes	—
165	C₃₁×#117	C₂³	1	4	yes	—
166	C₃₁×#117	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
170	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
171	C₃₁×#107	C₂³	1	4	yes	—
172	C₃₁×#107	C₂³	1	4	yes	—
173	C₃₁×#107	C₂³	1	4	yes	—
174	C₃₁×#106	C₂³	1	2	yes	—
175	C₃₁×#106	C₂³	1	4	yes	—
176	C₃₁×#106	C₂³	1	2	yes	—
177	C₃₁×#106	C₂³	1	4	yes	—
178	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
179	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
180	C₃₁×#103	C₂³	1	2	yes	—
181	C₃₁×#103	C₂³	1	4	yes	—
182	C₃₁×#103	C₂³	1	4	yes	—
183	C₃₁×#103	C₂³	1	4	yes	—
184	C₃₁×#103	C₂³	1	2	yes	—
185	C₃₁×#103	C₂³	1	4	yes	—
186	C₃₁×#103	C₂³	1	4	yes	—
187	C₃₁×#102	C₂³	1	2	yes	—
188	C₃₁×#102	C₂³	1	2	yes	—
189	C₃₁×#102	C₂³	1	4	yes	—
190	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
193	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
194	C₃₁×#97	C₂³	1	2	yes	—
195	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
197	C₂⁴×C₃₁	—	2	1	no	—
198	#41×C₃₁	—	4	4	no	—
199	#41×C₃₁	—	8	4	no	—
200	C₂×Q₈×C₃₁	—	2	1	no	—
201	C₂×Q₈×C₃₁	—	2	1	no	—
202	C₂×Q₈×C₃₁	—	2	1	no	—
203	C₂×Q₈×C₃₁	—	2	1	no	—
204	C₂×Q₈×C₃₁	—	2	4	no	—
205	C₂×Q₈×C₃₁	—	4	4	no	—
206	C₂×Q₈×C₃₁	—	4	4	no	—
207	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	4	no	—
212	C₂×D₄×C₃₁	—	2	1	no	—
213	C₂×D₄×C₃₁	—	4	2	no	—
214	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
216	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
217	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₃₁	—	2	1	no	—
220	C₂²×C₄×C₃₁	—	2	4	no	—
221	C₂²×C₄×C₃₁	—	2	4	no	—
222	C₂²×C₄×C₃₁	—	2	2	no	—
223	C₂²×C₄×C₃₁	—	2	2	no	—
224	C₂²×C₄×C₃₁	—	8	2	no	—
225	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
229	SD₁₆×C₃₁	—	4	2	no	—
230	SD₁₆×C₃₁	—	4	4	no	—
231	SD₁₆×C₃₁	—	4	2	no	—
232	M₁₆×C₃₁	—	4	4	no	—
233	C₂×C₈×C₃₁	—	4	4	no	—
234	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
235	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
236	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
237	C₄⋊C₄×C₃₁	—	2	1	no	—
238	C₄⋊C₄×C₃₁	—	2	4	no	—
239	C₄⋊C₄×C₃₁	—	2	1	no	—
240	C₄⋊C₄×C₃₁	—	2	1	no	—
241	C₄⋊C₄×C₃₁	—	2	1	no	—
242	C₄⋊C₄×C₃₁	—	2	1	no	—
243	C₄⋊C₄×C₃₁	—	2	1	no	—
244	C₄⋊C₄×C₃₁	—	2	2	no	—
245	C₄⋊C₄×C₃₁	—	2	1	no	—
246	C₄⋊C₄×C₃₁	—	2	1	no	—
247	C₄⋊C₄×C₃₁	—	2	2	no	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	1	no	—
251	C₄⋊C₄×C₃₁	—	2	2	no	—
252	C₄⋊C₄×C₃₁	—	2	2	no	—
253	C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
262	C₂²⋊C₄×C₃₁	—	2	2	no	—
263	C₂²⋊C₄×C₃₁	—	2	2	no	—
264	C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂²⋊C₄×C₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	—	2	4	no	—
273	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
274	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
275	C₄²×C₃₁	—	2	4	no	—
276	C₄²×C₃₁	—	2	2	no	—
277	C₄²×C₃₁	—	2	2	no	—
278	C₄²×C₃₁	—	2	2	no	—
279	C₄²×C₃₁	—	2	4	no	—
280	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
284	#61803	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂³×C₃₁	—	2	2	no	—
286	C₂³×C₃₁	—	4	2	no	—
287	C₂³×C₃₁	—	8	1	no	—
288	C₂³×C₃₁	—	8	1	no	—
289	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
290	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
291	Q₈×C₃₁	—	2	2	no	—
292	Q₈×C₃₁	—	2	4	no	—
293	Q₈×C₃₁	—	2	2	no	—
294	Q₈×C₃₁	—	4	2	no	—
295	Q₈×C₃₁	—	4	2	no	—
296	Q₈×C₃₁	—	4	2	no	—
297	Q₈×C₃₁	—	4	2	no	—
298	Q₈×C₃₁	—	8	1	no	—
299	Q₈×C₃₁	—	8	4	no	—
300	D₄×C₃₁	—	2	4	no	—
301	D₄×C₃₁	—	2	2	no	—
302	D₄×C₃₁	—	2	2	no	—
303	D₄×C₃₁	—	4	2	no	—
304	D₄×C₃₁	—	4	2	no	—
305	D₄×C₃₁	—	4	4	no	—
306	D₄×C₃₁	—	4	2	no	—
307	D₄×C₃₁	—	8	4	no	—
308	D₄×C₃₁	—	8	4	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	4	no	—
311	C₂×C₄×C₃₁	—	2	4	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	2	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	2	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	4	1	no	—
321	C₂×C₄×C₃₁	—	4	4	no	—
322	C₂×C₄×C₃₁	—	8	2	no	—
323	C₂×C₄×C₃₁	—	8	1	no	—
324	C₂×C₄×C₃₁	—	8	4	no	—
325	C₂×C₄×C₃₁	—	8	4	no	—
326	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
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	C₂⁵	1	1	yes	characteristic
333	C₈×C₃₁	—	2	2	no	—
334	C₈×C₃₁	—	2	4	no	—
335	C₈×C₃₁	—	2	2	no	—
336	#3550	C₂×C₃₁	1	1	yes	characteristic, complemented
337	#3506	C₂×C₃₁	1	1	yes	characteristic
338	#3353	C₂×C₃₁	1	2	yes	complemented
339	#3350	C₂×C₃₁	1	4	yes	complemented
340	#3340	C₂×C₃₁	1	2	yes	complemented
341	#3329	C₂×C₃₁	1	2	yes	complemented
342	#3320	C₂×C₃₁	1	4	yes	complemented
343	#3298	C₂×C₃₁	1	2	yes	complemented
344	#3237	C₂×C₃₁	1	1	yes	characteristic, complemented
345	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
346	#3200	C₂×C₃₁	1	4	yes	complemented
347	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
348	#3101	C₂×C₃₁	1	1	yes	characteristic, complemented
349	#3097	C₂×C₃₁	1	4	yes	complemented
350	#2981	C₂×C₃₁	1	1	yes	characteristic, complemented
351	C₂²×C₃₁	—	2	1	no	—
352	C₂²×C₃₁	—	2	4	no	—
353	C₂²×C₃₁	—	2	4	no	—
354	C₂²×C₃₁	—	2	1	no	—
355	C₂²×C₃₁	—	2	1	no	—
356	C₂²×C₃₁	—	2	4	no	—
357	C₂²×C₃₁	—	4	2	no	—
358	C₂²×C₃₁	—	4	2	no	—
359	C₂²×C₃₁	—	4	2	no	—
360	C₂²×C₃₁	—	8	4	no	—
361	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
362	C₄×C₃₁	—	2	1	no	—
363	C₄×C₃₁	—	2	1	no	—
364	C₄×C₃₁	—	2	1	no	—
365	C₄×C₃₁	—	2	4	no	—
366	C₄×C₃₁	—	2	1	no	—
367	C₄×C₃₁	—	4	2	no	—
368	C₄×C₃₁	—	4	2	no	—
369	C₄×C₃₁	—	4	2	no	—
370	C₄×C₃₁	—	4	2	no	—
371	C₄×C₃₁	—	4	2	no	—
372	C₄×C₃₁	—	4	2	no	—
373	C₄×C₃₁	—	4	2	no	—
374	C₄×C₃₁	#577	1	2	yes	—
375	C₄×C₃₁	#585	1	2	yes	—
376	#563	—	2	2	no	—
377	#559	—	2	1	no	—
378	#559	—	2	2	no	—
379	Q₈²	—	2	1	no	—
380	#556	—	2	1	no	—
381	#556	C₂²×C₃₁	1	2	yes	complemented
382	#556	C₂²×C₃₁	1	2	yes	complemented
383	#555	C₂²×C₃₁	1	2	yes	—
384	#553	C₂²×C₃₁	1	4	yes	—
385	#550	—	2	1	no	—
386	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
387	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
388	#547	C₂²×C₃₁	1	2	yes	—
389	#542	—	2	2	no	—
390	#542	—	2	2	no	—
391	#538	—	2	2	no	—
392	#536	C₂²×C₃₁	1	4	yes	—
393	#535	C₂²×C₃₁	1	2	yes	—
394	#533	C₂²×C₃₁	1	1	yes	characteristic
395	#533	C₂²×C₃₁	1	1	yes	characteristic
396	#533	C₂²×C₃₁	1	1	yes	characteristic
397	#532	C₂²×C₃₁	1	1	yes	characteristic
398	#525	—	2	2	no	—
399	#520	C₂²×C₃₁	1	2	yes	—
400	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
401	#501	C₂²×C₃₁	1	2	yes	complemented
402	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
403	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
404	#491	C₂²×C₃₁	1	2	yes	complemented
405	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
406	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
407	#485	C₂²×C₃₁	1	4	yes	—
408	#485	C₂²×C₃₁	1	4	yes	—
409	#485	C₂²×C₃₁	1	4	yes	complemented
410	#485	C₂²×C₃₁	1	4	yes	complemented
411	#484	C₂²×C₃₁	1	2	yes	—
412	#484	C₂²×C₃₁	1	4	yes	complemented
413	#483	C₂²×C₃₁	1	2	yes	—
414	#483	C₂²×C₃₁	1	4	yes	complemented
415	#482	C₂²×C₃₁	1	4	yes	—
416	#482	C₂²×C₃₁	1	4	yes	—
417	#479	C₂²×C₃₁	1	4	yes	complemented
418	#477	C₂²×C₃₁	1	2	yes	complemented
419	#476	C₂²×C₃₁	1	2	yes	—
420	#475	C₂²×C₃₁	1	2	yes	complemented
421	#474	C₂²×C₃₁	1	2	yes	—
422	#468	C₂²×C₃₁	1	4	yes	—
423	#468	C₂²×C₃₁	1	4	yes	—
424	#465	C₂²×C₃₁	1	4	yes	—
425	#465	C₂²×C₃₁	1	4	yes	—
426	#461	C₂²×C₃₁	1	2	yes	—
427	#461	C₂²×C₃₁	1	2	yes	—
428	#450	C₂²×C₃₁	1	2	yes	—
429	#450	C₂²×C₃₁	1	2	yes	—
430	#448	C₂²×C₃₁	1	4	yes	—
431	#448	C₂²×C₃₁	1	4	yes	—
432	#440	C₂²×C₃₁	1	4	yes	—
433	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
434	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
435	#436	C₂²×C₃₁	1	2	yes	complemented
436	#435	C₂²×C₃₁	1	4	yes	complemented
437	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
438	#432	C₂²×C₃₁	1	1	yes	characteristic
439	#431	C₂²×C₃₁	1	1	yes	characteristic
440	#428	C₂²×C₃₁	1	4	yes	complemented
441	#427	C₂²×C₃₁	1	4	yes	complemented
442	#419	C₂²×C₃₁	1	4	yes	complemented
443	C₂×#103	C₂²×C₃₁	1	4	yes	complemented
444	#408	C₂²×C₃₁	1	4	yes	—
445	C₂×C₃₁	—	4	4	no	—
446	C₂×C₃₁	—	4	1	no	—
447	C₂×C₃₁	—	8	2	no	—
448	C₂×C₃₁	#3485	1	1	yes	characteristic
449	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
450	C₂×C₃₁	#3586	1	1	yes	characteristic
451	C₂×#41	—	2	2	no	—
452	C₂×#41	C₂³×C₃₁	1	2	yes	—
453	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
454	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
455	C₂³×C₄	—	2	1	no	—
456	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
457	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
458	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
459	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
460	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
461	C₄⋊Q₈	—	2	4	no	—
462	C₄⋊Q₈	—	2	2	no	—
463	C₄⋊Q₈	—	2	2	no	—
464	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
468	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
469	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
470	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
471	#127	—	2	2	no	—
472	#127	D₄×C₃₁	1	1	yes	characteristic
473	#126	—	2	4	no	—
474	#126	—	2	4	no	—
475	#126	—	2	4	no	—
476	#125	—	2	1	no	—
477	#125	—	2	1	no	—
478	#125	C₂³×C₃₁	1	2	yes	—
479	#124	—	2	2	no	—
480	#124	—	2	4	no	—
481	#124	—	2	2	no	—
482	#124	—	2	2	no	—
483	#124	—	2	4	no	—
484	#124	D₄×C₃₁	1	2	yes	—
485	#123	—	2	4	no	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	#123	—	2	4	no	—
489	C₂²⋊Q₈	—	2	1	no	—
490	C₂²⋊Q₈	—	2	1	no	—
491	C₂²⋊Q₈	—	2	1	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	4	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
497	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
498	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
499	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
500	#121	—	2	2	no	—
501	#121	—	2	4	no	—
502	#121	D₄×C₃₁	1	2	yes	—
503	#121	D₄×C₃₁	1	2	yes	—
504	#121	C₂³×C₃₁	1	4	yes	—
505	#121	C₂³×C₃₁	1	4	yes	—
506	#120	—	2	4	no	—
507	C₄×Q₈	—	2	2	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	—	2	1	no	—
511	C₄×Q₈	—	2	1	no	—
512	C₄×Q₈	—	2	1	no	—
513	C₄×Q₈	—	2	1	no	—
514	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
515	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
516	C₄×D₄	—	2	4	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	4	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	C₂³×C₃₁	1	2	yes	—
524	C₄×D₄	C₂³×C₃₁	1	2	yes	—
525	C₄×D₄	C₂³×C₃₁	1	2	yes	—
526	C₄×D₄	C₂³×C₃₁	1	2	yes	—
527	#117	—	2	1	no	—
528	#117	—	2	1	no	—
529	#117	—	2	2	no	—
530	#117	C₂³×C₃₁	1	2	yes	—
531	#117	C₂³×C₃₁	1	4	yes	—
532	#117	C₂³×C₃₁	1	4	yes	—
533	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
537	#107	C₂³×C₃₁	1	4	yes	—
538	#107	C₂³×C₃₁	1	4	yes	—
539	#107	C₂³×C₃₁	1	4	yes	—
540	#106	C₂³×C₃₁	1	2	yes	—
541	#106	C₂³×C₃₁	1	4	yes	—
542	#106	C₂³×C₃₁	1	2	yes	—
543	#106	C₂³×C₃₁	1	4	yes	—
544	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
545	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
546	#103	C₂³×C₃₁	1	2	yes	—
547	#103	C₂³×C₃₁	1	4	yes	—
548	#103	C₂³×C₃₁	1	4	yes	—
549	#103	C₂³×C₃₁	1	4	yes	—
550	#103	C₂³×C₃₁	1	2	yes	—
551	#103	C₂³×C₃₁	1	4	yes	—
552	#103	C₂³×C₃₁	1	4	yes	—
553	#102	C₂³×C₃₁	1	2	yes	—
554	#102	C₂³×C₃₁	1	2	yes	—
555	#102	C₂³×C₃₁	1	4	yes	—
556	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
557	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
558	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
559	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
560	#97	C₂³×C₃₁	1	2	yes	—
561	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
562	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
563	C₃₁	#61803	1	1	yes	characteristic, direct product factor, Sylow
564	C₂⁴	—	2	1	no	—
565	#41	—	4	4	no	—
566	#41	—	8	4	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	—	4	4	no	—
573	C₂×Q₈	—	4	4	no	—
574	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
575	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
576	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
582	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
583	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
584	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
585	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	8	2	no	—
592	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
596	SD₁₆	—	4	2	no	—
597	SD₁₆	—	4	4	no	—
598	SD₁₆	—	4	2	no	—
599	M₁₆	—	4	4	no	—
600	C₂×C₈	—	4	4	no	—
601	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
602	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
603	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	1	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	C₂×D₄×C₃₁	1	2	yes	—
623	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
624	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
625	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	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	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
641	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	2	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	2	no	—
646	C₄²	—	2	4	no	—
647	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
648	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
649	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
650	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
651	C₂³	—	2	2	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	8	1	no	—
654	C₂³	—	8	1	no	—
655	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
656	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
657	Q₈	—	2	2	no	—
658	Q₈	—	2	4	no	—
659	Q₈	—	2	2	no	—
660	Q₈	—	4	2	no	—
661	Q₈	—	4	2	no	—
662	Q₈	—	4	2	no	—
663	Q₈	—	4	2	no	—
664	Q₈	—	8	1	no	—
665	Q₈	—	8	4	no	—
666	D₄	—	2	4	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	2	no	—
669	D₄	—	4	2	no	—
670	D₄	—	4	2	no	—
671	D₄	—	4	4	no	—
672	D₄	—	4	2	no	—
673	D₄	—	8	4	no	—
674	D₄	—	8	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	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	—	4	1	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	8	2	no	—
689	C₂×C₄	—	8	1	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	—	8	4	no	—
692	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
695	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
697	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
698	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
699	C₈	—	2	2	no	—
700	C₈	—	2	4	no	—
701	C₈	—	2	2	no	—
702	C₂²	—	2	4	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	8	4	no	—
712	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	4	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	1	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	C₃₁×#577	1	2	yes	—
726	C₄	C₃₁×#585	1	2	yes	—
727	C₂	—	4	1	no	—
728	C₂	—	4	4	no	—
729	C₂	—	8	2	no	—
730	C₂	C₃₁×#3485	1	1	yes	characteristic
731	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
732	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3550	C₂	semidirect
3. C₃₁×#3353	C₂	semidirect
4. C₃₁×#3350	C₂	semidirect
5. C₃₁×#3340	C₂	semidirect
6. C₃₁×#3329	C₂	semidirect
7. C₃₁×#3320	C₂	semidirect
8. C₃₁×#3298	C₂	semidirect
9. C₃₁×#3237	C₂	semidirect
10. C₃₁×#3231	C₂	semidirect
11. C₃₁×#3200	C₂	semidirect
12. C₃₁×#3110	C₂	semidirect
13. C₃₁×#3101	C₂	semidirect
14. C₃₁×#3097	C₂	semidirect
15. C₃₁×#2981	C₂	semidirect
21. C₃₁×#556	C₂²	semidirect
22. C₃₁×#556	C₂²	semidirect
26. D₄×Q₈×C₃₁	C₂²	semidirect
27. D₄×Q₈×C₃₁	C₂²	semidirect
41. C₃₁×#501	C₂²	semidirect
42. C₃₁×#500	C₂²	semidirect
43. C₃₁×#498	C₂²	semidirect
44. C₃₁×#491	C₂²	semidirect
45. C₃₁×#487	C₂²	semidirect
46. C₃₁×#487	C₂²	semidirect
49. C₃₁×#485	C₂²	semidirect
50. C₃₁×#485	C₂²	semidirect
52. C₃₁×#484	C₂²	semidirect
54. C₃₁×#483	C₂²	semidirect
57. C₃₁×#479	C₂²	semidirect
58. C₃₁×#477	C₂²	semidirect
60. C₃₁×#475	C₂²	semidirect
75. C₃₁×#436	C₂²	semidirect
76. C₃₁×#435	C₂²	semidirect
77. C₈×D₄×C₃₁	C₂²	semidirect
80. C₃₁×#428	C₂²	semidirect
81. C₃₁×#427	C₂²	semidirect
82. C₃₁×#419	C₂²	semidirect
83. C₂×C₃₁×#103	C₂²	semidirect
284. #61803	C₃₁	direct (N × H)
336. #3550	C₂×C₃₁	semidirect
338. #3353	C₂×C₃₁	semidirect
339. #3350	C₂×C₃₁	semidirect
340. #3340	C₂×C₃₁	semidirect
341. #3329	C₂×C₃₁	semidirect
342. #3320	C₂×C₃₁	semidirect
343. #3298	C₂×C₃₁	semidirect
344. #3237	C₂×C₃₁	semidirect
345. #3231	C₂×C₃₁	semidirect
346. #3200	C₂×C₃₁	semidirect
347. #3110	C₂×C₃₁	semidirect
348. #3101	C₂×C₃₁	semidirect
349. #3097	C₂×C₃₁	semidirect
350. #2981	C₂×C₃₁	semidirect
381. #556	C₂²×C₃₁	semidirect
382. #556	C₂²×C₃₁	semidirect
386. D₄×Q₈	C₂²×C₃₁	semidirect
387. D₄×Q₈	C₂²×C₃₁	semidirect
401. #501	C₂²×C₃₁	semidirect
402. #500	C₂²×C₃₁	semidirect
403. #498	C₂²×C₃₁	semidirect
404. #491	C₂²×C₃₁	semidirect
405. #487	C₂²×C₃₁	semidirect
406. #487	C₂²×C₃₁	semidirect
409. #485	C₂²×C₃₁	semidirect
410. #485	C₂²×C₃₁	semidirect
412. #484	C₂²×C₃₁	semidirect
414. #483	C₂²×C₃₁	semidirect
417. #479	C₂²×C₃₁	semidirect
418. #477	C₂²×C₃₁	semidirect
420. #475	C₂²×C₃₁	semidirect
435. #436	C₂²×C₃₁	semidirect
436. #435	C₂²×C₃₁	semidirect
437. C₈×D₄	C₂²×C₃₁	semidirect
440. #428	C₂²×C₃₁	semidirect
441. #427	C₂²×C₃₁	semidirect
442. #419	C₂²×C₃₁	semidirect
443. C₂×#103	C₂²×C₃₁	semidirect
563. C₃₁	#61803	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×#3550	2
C₃₁×#3506	2
C₃₁×#3353	2
C₃₁×#3350	2
C₃₁×#3340	2
C₃₁×#3329	2
C₃₁×#3320	2
C₃₁×#3298	2
C₃₁×#3237	2
C₃₁×#3231	2
C₃₁×#3200	2
C₃₁×#3110	2
C₃₁×#3101	2
C₃₁×#3097	2
C₃₁×#2981	2
#61803	31

Subgroups — C31×#61803 #21518562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61803 #21518562