Subgroups — C₃₁×#60825 #21517584

Order 7936.

2146 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3221	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3220	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3214	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3213	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#496	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3135	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3042	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3041	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3010	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3008	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
20	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
21	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
22	C₃₁×#559	—	2	2	no	—
23	C₃₁×#550	—	2	2	no	—
24	C₃₁×#548	—	2	2	no	—
25	C₃₁×#546	—	2	4	no	—
26	C₃₁×#546	—	2	2	no	—
27	C₃₁×#546	—	2	4	no	—
28	C₃₁×#540	C₂²	1	4	yes	complemented
29	C₃₁×#536	C₂²	1	1	yes	characteristic
30	C₃₁×#536	C₂²	1	2	yes	complemented
31	C₃₁×#535	C₂²	1	1	yes	characteristic
32	C₃₁×#535	C₂²	1	2	yes	—
33	C₃₁×#535	C₂²	1	2	yes	complemented
34	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#532	C₂²	1	1	yes	characteristic
36	C₃₁×#532	C₂²	1	2	yes	complemented
37	C₃₁×#532	C₂²	1	4	yes	complemented
38	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
41	C₃₁×#518	C₂²	1	2	yes	complemented
42	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
43	C₃₁×#496	C₂²	1	4	yes	complemented
44	C₃₁×#496	C₂²	1	4	yes	complemented
45	C₃₁×#496	C₂²	1	2	yes	complemented
46	C₃₁×#496	C₂²	1	2	yes	complemented
47	C₃₁×#493	C₂²	1	2	yes	complemented
48	C₃₁×#492	C₂²	1	2	yes	complemented
49	C₃₁×#491	C₂²	1	2	yes	complemented
50	C₃₁×#490	C₂²	1	2	yes	complemented
51	C₃₁×#489	C₂²	1	2	yes	complemented
52	C₃₁×#489	C₂²	1	2	yes	complemented
53	C₃₁×#489	C₂²	1	4	yes	complemented
54	C₃₁×#488	C₂²	1	4	yes	complemented
55	C₃₁×#463	C₂²	1	8	yes	complemented
56	C₃₁×#463	C₂²	1	8	yes	complemented
57	C₃₁×#461	C₂²	1	8	yes	complemented
58	C₃₁×#459	C₂²	1	8	yes	complemented
59	C₃₁×#449	C₂²	1	8	yes	complemented
60	C₃₁×#449	C₂²	1	8	yes	complemented
61	C₃₁×#448	C₂²	1	8	yes	complemented
62	C₃₁×#447	C₂²	1	8	yes	complemented
63	C₃₁×#433	C₂²	1	4	yes	complemented
64	C₃₁×#432	C₂²	1	4	yes	complemented
65	C₃₁×#424	C₂²	1	2	yes	complemented
66	C₃₁×#419	C₂²	1	2	yes	complemented
67	C₃₁×#418	C₂²	1	2	yes	—
68	C₃₁×#416	C₂²	1	2	yes	—
69	C₃₁×#416	C₂²	1	2	yes	complemented
70	C₃₁×#408	C₂²	1	2	yes	—
71	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×2₋¹⁺⁴	—	4	4	no	—
74	C₃₁×H(5,𝔽₂)	—	4	4	no	—
75	C₂×#41×C₃₁	—	2	1	no	—
76	C₂×#41×C₃₁	—	2	2	no	—
77	C₂×#41×C₃₁	—	2	1	no	—
78	C₂×#41×C₃₁	—	2	4	no	—
79	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
80	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
81	C₂×#41×C₃₁	C₂³	1	2	yes	—
82	C₂×#41×C₃₁	C₂³	1	2	yes	—
83	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₃₁	—	2	1	no	—
85	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
87	C₂²×D₄×C₃₁	—	2	2	no	—
88	C₂²×D₄×C₃₁	—	2	1	no	—
89	C₂²×D₄×C₃₁	—	2	2	no	—
90	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
92	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
93	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
94	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
95	C₂×SD₁₆×C₃₁	—	4	4	no	—
96	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
98	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×D₈×C₃₁	—	4	4	no	—
100	C₂×D₈×C₃₁	C₂³	1	4	yes	—
101	C₂×D₈×C₃₁	C₂³	1	8	yes	—
102	C₂×D₈×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	C₂³	1	2	yes	—
106	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
107	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₃₁×#127	—	2	2	no	—
109	C₃₁×#127	—	2	2	no	—
110	C₃₁×#127	C₂³	1	2	yes	—
111	C₃₁×#127	C₂³	1	1	yes	characteristic
112	C₃₁×#127	C₂³	1	2	yes	—
113	C₃₁×#127	C₂³	1	2	yes	—
114	C₃₁×#125	C₂³	1	2	yes	—
115	C₃₁×#124	—	2	2	no	—
116	C₃₁×#124	—	2	2	no	—
117	C₃₁×#124	—	2	4	no	—
118	C₃₁×#124	—	2	4	no	—
119	C₃₁×#124	C₂³	1	2	yes	—
120	C₃₁×#124	C₂³	1	2	yes	—
121	C₃₁×#124	C₂³	1	2	yes	—
122	C₃₁×#124	C₂³	1	2	yes	—
123	C₃₁×#124	C₂³	1	1	yes	characteristic
124	C₃₁×#124	C₂³	1	1	yes	characteristic
125	C₃₁×#123	—	2	8	no	—
126	C₃₁×#123	—	2	2	no	—
127	C₃₁×#123	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	—	2	2	no	—
129	C₃₁×C₂²⋊Q₈	—	2	2	no	—
130	C₃₁×C₂²⋊Q₈	—	2	4	no	—
131	C₃₁×#121	—	2	2	no	—
132	C₃₁×#121	—	2	4	no	—
133	C₃₁×#121	—	2	4	no	—
134	C₃₁×#121	—	2	2	no	—
135	C₃₁×#121	—	2	4	no	—
136	C₃₁×#121	—	2	8	no	—
137	C₃₁×#121	C₂³	1	8	yes	—
138	C₃₁×#120	—	2	4	no	—
139	C₃₁×#120	—	2	2	no	—
140	C₃₁×#120	—	2	4	no	—
141	C₄×Q₈×C₃₁	—	2	2	no	—
142	C₄×Q₈×C₃₁	D₄	1	2	yes	—
143	C₄×D₄×C₃₁	—	2	4	no	—
144	C₄×D₄×C₃₁	—	2	2	no	—
145	C₄×D₄×C₃₁	—	2	4	no	—
146	C₄×D₄×C₃₁	—	2	4	no	—
147	C₄×D₄×C₃₁	D₄	1	4	yes	—
148	C₄×D₄×C₃₁	D₄	1	2	yes	—
149	C₄×D₄×C₃₁	C₂³	1	8	yes	—
150	C₃₁×#117	C₂³	1	2	yes	—
151	C₃₁×#117	C₂³	1	1	yes	characteristic
152	C₃₁×#117	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
154	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
155	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
156	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
158	C₃₁×C₄⋊C₈	C₂³	1	8	yes	—
159	C₃₁×#103	C₂³	1	4	yes	—
160	C₃₁×#103	C₂³	1	4	yes	—
161	C₃₁×#103	C₂³	1	8	yes	—
162	C₃₁×#102	C₂³	1	4	yes	—
163	C₃₁×#102	C₂³	1	4	yes	—
164	C₃₁×#102	C₂³	1	8	yes	—
165	C₃₁×C₂²⋊C₈	C₂³	1	8	yes	—
166	C₃₁×#97	C₂³	1	2	yes	—
167	C₃₁×#97	C₂³	1	2	yes	—
168	C₃₁×#97	C₂³	1	2	yes	—
169	C₄×C₈×C₃₁	C₂³	1	2	yes	—
170	C₂⁴×C₃₁	—	2	2	no	—
171	C₂⁴×C₃₁	—	2	1	no	—
172	C₂⁴×C₃₁	—	2	2	no	—
173	#41×C₃₁	—	2	4	no	—
174	#41×C₃₁	—	2	4	no	—
175	#41×C₃₁	—	2	4	no	—
176	#41×C₃₁	—	4	4	no	—
177	#41×C₃₁	—	4	4	no	—
178	#41×C₃₁	—	4	8	no	—
179	#41×C₃₁	—	4	4	no	—
180	#41×C₃₁	—	4	4	no	—
181	#41×C₃₁	—	8	8	no	—
182	C₂×Q₈×C₃₁	—	2	2	no	—
183	C₂×Q₈×C₃₁	—	2	2	no	—
184	C₂×Q₈×C₃₁	—	2	1	no	—
185	C₂×Q₈×C₃₁	—	2	4	no	—
186	C₂×Q₈×C₃₁	—	4	4	no	—
187	C₂×Q₈×C₃₁	—	4	4	no	—
188	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
189	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
190	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
191	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
192	C₂×D₄×C₃₁	—	2	2	no	—
193	C₂×D₄×C₃₁	—	2	1	no	—
194	C₂×D₄×C₃₁	—	2	2	no	—
195	C₂×D₄×C₃₁	—	2	1	no	—
196	C₂×D₄×C₃₁	—	2	8	no	—
197	C₂×D₄×C₃₁	—	2	2	no	—
198	C₂×D₄×C₃₁	—	2	4	no	—
199	C₂×D₄×C₃₁	—	2	2	no	—
200	C₂×D₄×C₃₁	—	2	1	no	—
201	C₂×D₄×C₃₁	—	2	4	no	—
202	C₂×D₄×C₃₁	—	2	2	no	—
203	C₂×D₄×C₃₁	—	2	4	no	—
204	C₂×D₄×C₃₁	—	2	4	no	—
205	C₂×D₄×C₃₁	—	2	4	no	—
206	C₂×D₄×C₃₁	—	2	4	no	—
207	C₂×D₄×C₃₁	—	4	4	no	—
208	C₂×D₄×C₃₁	—	4	8	no	—
209	C₂×D₄×C₃₁	—	4	4	no	—
210	C₂×D₄×C₃₁	—	8	4	no	—
211	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
212	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
213	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
214	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
215	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
216	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₃₁	—	2	2	no	—
218	C₂²×C₄×C₃₁	—	2	1	no	—
219	C₂²×C₄×C₃₁	—	2	2	no	—
220	C₂²×C₄×C₃₁	—	2	1	no	—
221	C₂²×C₄×C₃₁	—	2	2	no	—
222	C₂²×C₄×C₃₁	—	2	1	no	—
223	C₂²×C₄×C₃₁	—	2	8	no	—
224	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
225	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
228	SD₁₆×C₃₁	—	4	8	no	—
229	SD₁₆×C₃₁	—	4	4	no	—
230	SD₁₆×C₃₁	—	4	4	no	—
231	D₈×C₃₁	—	4	8	no	—
232	D₈×C₃₁	—	4	4	no	—
233	D₈×C₃₁	—	4	4	no	—
234	M₁₆×C₃₁	—	2	4	no	—
235	C₂×C₈×C₃₁	—	2	4	no	—
236	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
237	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
238	C₄⋊C₄×C₃₁	—	2	2	no	—
239	C₄⋊C₄×C₃₁	—	2	4	no	—
240	C₄⋊C₄×C₃₁	—	2	2	no	—
241	C₄⋊C₄×C₃₁	—	2	4	no	—
242	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
243	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
244	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
245	C₂²⋊C₄×C₃₁	—	2	2	no	—
246	C₂²⋊C₄×C₃₁	—	2	4	no	—
247	C₂²⋊C₄×C₃₁	—	2	2	no	—
248	C₂²⋊C₄×C₃₁	—	2	8	no	—
249	C₂²⋊C₄×C₃₁	—	2	4	no	—
250	C₂²⋊C₄×C₃₁	—	2	4	no	—
251	C₂²⋊C₄×C₃₁	—	2	4	no	—
252	C₂²⋊C₄×C₃₁	—	2	2	no	—
253	C₂²⋊C₄×C₃₁	—	2	8	no	—
254	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
255	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
256	C₄²×C₃₁	—	2	2	no	—
257	C₄²×C₃₁	C₂×D₄	1	4	yes	—
258	C₄²×C₃₁	C₂×D₄	1	2	yes	—
259	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
261	C₄²×C₃₁	C₂⁴	1	2	yes	—
262	#60825	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂³×C₃₁	—	2	2	no	—
264	C₂³×C₃₁	—	2	1	no	—
265	C₂³×C₃₁	—	2	4	no	—
266	C₂³×C₃₁	—	2	1	no	—
267	C₂³×C₃₁	—	4	4	no	—
268	C₂³×C₃₁	—	4	2	no	—
269	C₂³×C₃₁	—	4	4	no	—
270	C₂³×C₃₁	—	8	4	no	—
271	C₂³×C₃₁	—	8	2	no	—
272	C₂³×C₃₁	—	8	4	no	—
273	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
274	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
275	Q₈×C₃₁	—	2	2	no	—
276	Q₈×C₃₁	—	2	4	no	—
277	Q₈×C₃₁	—	2	2	no	—
278	Q₈×C₃₁	—	2	2	no	—
279	Q₈×C₃₁	—	4	4	no	—
280	Q₈×C₃₁	—	4	4	no	—
281	Q₈×C₃₁	—	4	2	no	—
282	D₄×C₃₁	—	2	4	no	—
283	D₄×C₃₁	—	2	2	no	—
284	D₄×C₃₁	—	2	4	no	—
285	D₄×C₃₁	—	2	4	no	—
286	D₄×C₃₁	—	2	2	no	—
287	D₄×C₃₁	—	2	2	no	—
288	D₄×C₃₁	—	2	4	no	—
289	D₄×C₃₁	—	4	4	no	—
290	D₄×C₃₁	—	4	8	no	—
291	D₄×C₃₁	—	4	4	no	—
292	D₄×C₃₁	—	4	4	no	—
293	D₄×C₃₁	—	4	2	no	—
294	D₄×C₃₁	—	4	2	no	—
295	D₄×C₃₁	—	4	4	no	—
296	D₄×C₃₁	—	4	2	no	—
297	D₄×C₃₁	—	8	4	no	—
298	D₄×C₃₁	—	8	2	no	—
299	D₄×C₃₁	—	8	4	no	—
300	D₄×C₃₁	—	8	8	no	—
301	C₂×C₄×C₃₁	—	2	4	no	—
302	C₂×C₄×C₃₁	—	2	4	no	—
303	C₂×C₄×C₃₁	—	2	2	no	—
304	C₂×C₄×C₃₁	—	2	1	no	—
305	C₂×C₄×C₃₁	—	2	1	no	—
306	C₂×C₄×C₃₁	—	4	2	no	—
307	C₂×C₄×C₃₁	—	4	4	no	—
308	C₂×C₄×C₃₁	—	4	4	no	—
309	C₂×C₄×C₃₁	—	4	4	no	—
310	C₂×C₄×C₃₁	—	4	4	no	—
311	C₂×C₄×C₃₁	—	4	2	no	—
312	C₂×C₄×C₃₁	—	4	2	no	—
313	C₂×C₄×C₃₁	—	4	2	no	—
314	C₂×C₄×C₃₁	—	8	8	no	—
315	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
318	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
321	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
322	C₈×C₃₁	—	2	4	no	—
323	C₈×C₃₁	—	2	4	no	—
324	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
325	#3500	C₂×C₃₁	1	1	yes	characteristic, complemented
326	#3221	C₂×C₃₁	1	4	yes	complemented
327	#3220	C₂×C₃₁	1	4	yes	complemented
328	#3214	C₂×C₃₁	1	4	yes	complemented
329	#3213	C₂×C₃₁	1	4	yes	complemented
330	#3151	C₂×C₃₁	1	1	yes	characteristic, complemented
331	C₂×#496	C₂×C₃₁	1	1	yes	characteristic, complemented
332	#3140	C₂×C₃₁	1	1	yes	characteristic, complemented
333	#3135	C₂×C₃₁	1	1	yes	characteristic, complemented
334	#3042	C₂×C₃₁	1	2	yes	complemented
335	#3041	C₂×C₃₁	1	2	yes	complemented
336	#3010	C₂×C₃₁	1	2	yes	complemented
337	#3008	C₂×C₃₁	1	2	yes	complemented
338	#2923	C₂×C₃₁	1	1	yes	characteristic, complemented
339	C₂²×C₃₁	—	2	2	no	—
340	C₂²×C₃₁	—	2	4	no	—
341	C₂²×C₃₁	—	2	2	no	—
342	C₂²×C₃₁	—	4	8	no	—
343	C₂²×C₃₁	—	4	2	no	—
344	C₂²×C₃₁	—	4	4	no	—
345	C₂²×C₃₁	—	4	2	no	—
346	C₂²×C₃₁	—	4	1	no	—
347	C₂²×C₃₁	—	4	2	no	—
348	C₂²×C₃₁	—	4	1	no	—
349	C₂²×C₃₁	—	4	4	no	—
350	C₂²×C₃₁	—	16	4	no	—
351	C₂²×C₃₁	—	16	2	no	—
352	C₂²×C₃₁	—	16	4	no	—
353	C₂²×C₃₁	#535	1	2	yes	—
354	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
355	C₄×C₃₁	—	2	2	no	—
356	C₄×C₃₁	—	2	4	no	—
357	C₄×C₃₁	—	2	2	no	—
358	C₄×C₃₁	—	2	2	no	—
359	C₄×C₃₁	—	4	4	no	—
360	C₄×C₃₁	—	4	1	no	—
361	C₄×C₃₁	—	4	2	no	—
362	C₄×C₃₁	—	4	1	no	—
363	C₄×C₃₁	#535	1	2	yes	—
364	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
365	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
366	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
367	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
368	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
369	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
370	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
371	#559	—	2	2	no	—
372	#550	—	2	2	no	—
373	#548	—	2	2	no	—
374	#546	—	2	4	no	—
375	#546	—	2	2	no	—
376	#546	—	2	4	no	—
377	#540	C₂²×C₃₁	1	4	yes	complemented
378	#536	C₂²×C₃₁	1	1	yes	characteristic
379	#536	C₂²×C₃₁	1	2	yes	complemented
380	#535	C₂²×C₃₁	1	1	yes	characteristic
381	#535	C₂²×C₃₁	1	2	yes	—
382	#535	C₂²×C₃₁	1	2	yes	complemented
383	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
384	#532	C₂²×C₃₁	1	1	yes	characteristic
385	#532	C₂²×C₃₁	1	2	yes	complemented
386	#532	C₂²×C₃₁	1	4	yes	complemented
387	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
388	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
389	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
390	#518	C₂²×C₃₁	1	2	yes	complemented
391	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
392	#496	C₂²×C₃₁	1	4	yes	complemented
393	#496	C₂²×C₃₁	1	4	yes	complemented
394	#496	C₂²×C₃₁	1	2	yes	complemented
395	#496	C₂²×C₃₁	1	2	yes	complemented
396	#493	C₂²×C₃₁	1	2	yes	complemented
397	#492	C₂²×C₃₁	1	2	yes	complemented
398	#491	C₂²×C₃₁	1	2	yes	complemented
399	#490	C₂²×C₃₁	1	2	yes	complemented
400	#489	C₂²×C₃₁	1	2	yes	complemented
401	#489	C₂²×C₃₁	1	2	yes	complemented
402	#489	C₂²×C₃₁	1	4	yes	complemented
403	#488	C₂²×C₃₁	1	4	yes	complemented
404	#463	C₂²×C₃₁	1	8	yes	complemented
405	#463	C₂²×C₃₁	1	8	yes	complemented
406	#461	C₂²×C₃₁	1	8	yes	complemented
407	#459	C₂²×C₃₁	1	8	yes	complemented
408	#449	C₂²×C₃₁	1	8	yes	complemented
409	#449	C₂²×C₃₁	1	8	yes	complemented
410	#448	C₂²×C₃₁	1	8	yes	complemented
411	#447	C₂²×C₃₁	1	8	yes	complemented
412	#433	C₂²×C₃₁	1	4	yes	complemented
413	#432	C₂²×C₃₁	1	4	yes	complemented
414	#424	C₂²×C₃₁	1	2	yes	complemented
415	#419	C₂²×C₃₁	1	2	yes	complemented
416	#418	C₂²×C₃₁	1	2	yes	—
417	#416	C₂²×C₃₁	1	2	yes	—
418	#416	C₂²×C₃₁	1	2	yes	complemented
419	#408	C₂²×C₃₁	1	2	yes	—
420	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
421	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
422	C₂×C₃₁	—	2	2	no	—
423	C₂×C₃₁	—	4	2	no	—
424	C₂×C₃₁	—	8	1	no	—
425	C₂×C₃₁	—	8	4	no	—
426	C₂×C₃₁	—	8	2	no	—
427	C₂×C₃₁	—	8	1	no	—
428	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
429	C₂×C₃₁	#3585	1	2	yes	—
430	2₋¹⁺⁴	—	4	4	no	—
431	H(5,𝔽₂)	—	4	4	no	—
432	C₂×#41	—	2	1	no	—
433	C₂×#41	—	2	2	no	—
434	C₂×#41	—	2	1	no	—
435	C₂×#41	—	2	4	no	—
436	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
437	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
438	C₂×#41	C₂³×C₃₁	1	2	yes	—
439	C₂×#41	C₂³×C₃₁	1	2	yes	—
440	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
441	C₂²×Q₈	—	2	1	no	—
442	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
443	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
444	C₂²×D₄	—	2	2	no	—
445	C₂²×D₄	—	2	1	no	—
446	C₂²×D₄	—	2	2	no	—
447	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
448	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
449	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
450	AGL(1,ℤ/8)	—	4	4	no	—
451	AGL(1,ℤ/8)	—	4	4	no	—
452	C₂×SD₁₆	—	4	4	no	—
453	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
454	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
455	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
456	C₂×D₈	—	4	4	no	—
457	C₂×D₈	C₂³×C₃₁	1	8	yes	—
458	C₂×D₈	C₂³×C₃₁	1	4	yes	—
459	C₂×D₈	C₂³×C₃₁	1	4	yes	—
460	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
461	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
462	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
463	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
464	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
465	#127	—	2	2	no	—
466	#127	—	2	2	no	—
467	#127	C₂³×C₃₁	1	2	yes	—
468	#127	C₂³×C₃₁	1	2	yes	—
469	#127	C₂³×C₃₁	1	1	yes	characteristic
470	#127	C₂³×C₃₁	1	2	yes	—
471	#125	C₂³×C₃₁	1	2	yes	—
472	#124	—	2	2	no	—
473	#124	—	2	2	no	—
474	#124	—	2	4	no	—
475	#124	—	2	4	no	—
476	#124	C₂³×C₃₁	1	2	yes	—
477	#124	C₂³×C₃₁	1	2	yes	—
478	#124	C₂³×C₃₁	1	1	yes	characteristic
479	#124	C₂³×C₃₁	1	2	yes	—
480	#124	C₂³×C₃₁	1	2	yes	—
481	#124	C₂³×C₃₁	1	1	yes	characteristic
482	#123	—	2	8	no	—
483	#123	—	2	2	no	—
484	#123	—	2	4	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	4	no	—
488	#121	—	2	2	no	—
489	#121	—	2	4	no	—
490	#121	—	2	4	no	—
491	#121	—	2	2	no	—
492	#121	—	2	4	no	—
493	#121	—	2	8	no	—
494	#121	C₂³×C₃₁	1	8	yes	—
495	#120	—	2	4	no	—
496	#120	—	2	2	no	—
497	#120	—	2	4	no	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	D₄×C₃₁	1	2	yes	—
500	C₄×D₄	—	2	4	no	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	—	2	4	no	—
503	C₄×D₄	—	2	4	no	—
504	C₄×D₄	D₄×C₃₁	1	4	yes	—
505	C₄×D₄	D₄×C₃₁	1	2	yes	—
506	C₄×D₄	C₂³×C₃₁	1	8	yes	—
507	#117	C₂³×C₃₁	1	2	yes	—
508	#117	C₂³×C₃₁	1	1	yes	characteristic
509	#117	C₂³×C₃₁	1	2	yes	—
510	C₂×C₂²⋊C₄	—	2	2	no	—
511	C₂×C₂²⋊C₄	—	2	4	no	—
512	C₂×C₂²⋊C₄	—	2	4	no	—
513	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
515	C₄⋊C₈	C₂³×C₃₁	1	8	yes	—
516	#103	C₂³×C₃₁	1	4	yes	—
517	#103	C₂³×C₃₁	1	4	yes	—
518	#103	C₂³×C₃₁	1	8	yes	—
519	#102	C₂³×C₃₁	1	4	yes	—
520	#102	C₂³×C₃₁	1	4	yes	—
521	#102	C₂³×C₃₁	1	8	yes	—
522	C₂²⋊C₈	C₂³×C₃₁	1	8	yes	—
523	#97	C₂³×C₃₁	1	2	yes	—
524	#97	C₂³×C₃₁	1	2	yes	—
525	#97	C₂³×C₃₁	1	2	yes	—
526	C₄×C₈	C₂³×C₃₁	1	2	yes	—
527	C₃₁	#60825	1	1	yes	characteristic, direct product factor, Sylow
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	1	no	—
530	C₂⁴	—	2	2	no	—
531	#41	—	2	4	no	—
532	#41	—	2	4	no	—
533	#41	—	2	4	no	—
534	#41	—	4	4	no	—
535	#41	—	4	4	no	—
536	#41	—	4	8	no	—
537	#41	—	4	4	no	—
538	#41	—	4	4	no	—
539	#41	—	8	8	no	—
540	C₂×Q₈	—	2	2	no	—
541	C₂×Q₈	—	2	2	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	4	no	—
544	C₂×Q₈	—	4	4	no	—
545	C₂×Q₈	—	4	4	no	—
546	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
547	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
548	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
549	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	8	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	4	4	no	—
566	C₂×D₄	—	4	8	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	—	8	4	no	—
569	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
570	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
571	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
572	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
573	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
574	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	8	no	—
582	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
583	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
586	SD₁₆	—	4	8	no	—
587	SD₁₆	—	4	4	no	—
588	SD₁₆	—	4	4	no	—
589	D₈	—	4	8	no	—
590	D₈	—	4	4	no	—
591	D₈	—	4	4	no	—
592	M₁₆	—	2	4	no	—
593	C₂×C₈	—	2	4	no	—
594	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
595	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
601	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
602	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	8	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
613	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
614	C₄²	—	2	2	no	—
615	C₄²	C₂×D₄×C₃₁	1	4	yes	—
616	C₄²	C₂×D₄×C₃₁	1	2	yes	—
617	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
618	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
619	C₄²	C₂⁴×C₃₁	1	2	yes	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	4	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	4	4	no	—
625	C₂³	—	4	2	no	—
626	C₂³	—	4	4	no	—
627	C₂³	—	8	4	no	—
628	C₂³	—	8	2	no	—
629	C₂³	—	8	4	no	—
630	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
631	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
632	Q₈	—	2	2	no	—
633	Q₈	—	2	4	no	—
634	Q₈	—	2	2	no	—
635	Q₈	—	2	2	no	—
636	Q₈	—	4	4	no	—
637	Q₈	—	4	4	no	—
638	Q₈	—	4	2	no	—
639	D₄	—	2	4	no	—
640	D₄	—	2	2	no	—
641	D₄	—	2	4	no	—
642	D₄	—	2	4	no	—
643	D₄	—	2	2	no	—
644	D₄	—	2	2	no	—
645	D₄	—	2	4	no	—
646	D₄	—	4	4	no	—
647	D₄	—	4	8	no	—
648	D₄	—	4	4	no	—
649	D₄	—	4	4	no	—
650	D₄	—	4	2	no	—
651	D₄	—	4	2	no	—
652	D₄	—	4	4	no	—
653	D₄	—	4	2	no	—
654	D₄	—	8	4	no	—
655	D₄	—	8	2	no	—
656	D₄	—	8	4	no	—
657	D₄	—	8	8	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	4	2	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	8	8	no	—
672	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
674	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
675	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
676	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
677	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
678	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
679	C₈	—	2	4	no	—
680	C₈	—	2	4	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	4	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	4	no	—
688	C₂²	—	4	8	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	16	2	no	—
693	C₂²	—	16	4	no	—
694	C₂²	—	16	4	no	—
695	C₂²	C₃₁×#535	1	2	yes	—
696	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
697	C₄	—	2	2	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	4	no	—
700	C₄	—	2	2	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	4	no	—
705	C₄	C₃₁×#535	1	2	yes	—
706	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
707	C₂	—	2	2	no	—
708	C₂	—	4	2	no	—
709	C₂	—	8	2	no	—
710	C₂	—	8	1	no	—
711	C₂	—	8	4	no	—
712	C₂	—	8	1	no	—
713	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
714	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3508	C₂	semidirect
2. C₃₁×#3500	C₂	semidirect
3. C₃₁×#3221	C₂	semidirect
4. C₃₁×#3220	C₂	semidirect
5. C₃₁×#3214	C₂	semidirect
6. C₃₁×#3213	C₂	semidirect
7. C₃₁×#3151	C₂	semidirect
8. C₂×C₃₁×#496	C₂	semidirect
9. C₃₁×#3140	C₂	semidirect
10. C₃₁×#3135	C₂	semidirect
11. C₃₁×#3042	C₂	semidirect
12. C₃₁×#3041	C₂	semidirect
13. C₃₁×#3010	C₂	semidirect
14. C₃₁×#3008	C₂	semidirect
15. C₃₁×#2923	C₂	semidirect
19. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂²×SD₁₆×C₃₁	C₂²	semidirect
28. C₃₁×#540	C₂²	semidirect
30. C₃₁×#536	C₂²	semidirect
33. C₃₁×#535	C₂²	semidirect
34. C₃₁×#533	C₂²	semidirect
36. C₃₁×#532	C₂²	semidirect
37. C₃₁×#532	C₂²	semidirect
38. C₂×C₃₁×#127	C₂²	semidirect
40. C₂×C₃₁×#124	C₂²	semidirect
41. C₃₁×#518	C₂²	semidirect
43. C₃₁×#496	C₂²	semidirect
44. C₃₁×#496	C₂²	semidirect
45. C₃₁×#496	C₂²	semidirect
46. C₃₁×#496	C₂²	semidirect
47. C₃₁×#493	C₂²	semidirect
48. C₃₁×#492	C₂²	semidirect
49. C₃₁×#491	C₂²	semidirect
50. C₃₁×#490	C₂²	semidirect
51. C₃₁×#489	C₂²	semidirect
52. C₃₁×#489	C₂²	semidirect
53. C₃₁×#489	C₂²	semidirect
54. C₃₁×#488	C₂²	semidirect
55. C₃₁×#463	C₂²	semidirect
56. C₃₁×#463	C₂²	semidirect
57. C₃₁×#461	C₂²	semidirect
58. C₃₁×#459	C₂²	semidirect
59. C₃₁×#449	C₂²	semidirect
60. C₃₁×#449	C₂²	semidirect
61. C₃₁×#448	C₂²	semidirect
62. C₃₁×#447	C₂²	semidirect
63. C₃₁×#433	C₂²	semidirect
64. C₃₁×#432	C₂²	semidirect
65. C₃₁×#424	C₂²	semidirect
66. C₃₁×#419	C₂²	semidirect
69. C₃₁×#416	C₂²	semidirect
71. C₄×M₁₆×C₃₁	C₂²	semidirect
72. C₂×C₃₁×#97	C₂²	semidirect
262. #60825	C₃₁	direct (N × H)
324. #3508	C₂×C₃₁	semidirect
325. #3500	C₂×C₃₁	semidirect
326. #3221	C₂×C₃₁	semidirect
327. #3220	C₂×C₃₁	semidirect
328. #3214	C₂×C₃₁	semidirect
329. #3213	C₂×C₃₁	semidirect
330. #3151	C₂×C₃₁	semidirect
331. C₂×#496	C₂×C₃₁	semidirect
332. #3140	C₂×C₃₁	semidirect
333. #3135	C₂×C₃₁	semidirect
334. #3042	C₂×C₃₁	semidirect
335. #3041	C₂×C₃₁	semidirect
336. #3010	C₂×C₃₁	semidirect
337. #3008	C₂×C₃₁	semidirect
338. #2923	C₂×C₃₁	semidirect
368. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
369. C₂²×SD₁₆	C₂²×C₃₁	semidirect
377. #540	C₂²×C₃₁	semidirect
379. #536	C₂²×C₃₁	semidirect
382. #535	C₂²×C₃₁	semidirect
383. #533	C₂²×C₃₁	semidirect
385. #532	C₂²×C₃₁	semidirect
386. #532	C₂²×C₃₁	semidirect
387. C₂×#127	C₂²×C₃₁	semidirect
389. C₂×#124	C₂²×C₃₁	semidirect
390. #518	C₂²×C₃₁	semidirect
392. #496	C₂²×C₃₁	semidirect
393. #496	C₂²×C₃₁	semidirect
394. #496	C₂²×C₃₁	semidirect
395. #496	C₂²×C₃₁	semidirect
396. #493	C₂²×C₃₁	semidirect
397. #492	C₂²×C₃₁	semidirect
398. #491	C₂²×C₃₁	semidirect
399. #490	C₂²×C₃₁	semidirect
400. #489	C₂²×C₃₁	semidirect
401. #489	C₂²×C₃₁	semidirect
402. #489	C₂²×C₃₁	semidirect
403. #488	C₂²×C₃₁	semidirect
404. #463	C₂²×C₃₁	semidirect
405. #463	C₂²×C₃₁	semidirect
406. #461	C₂²×C₃₁	semidirect
407. #459	C₂²×C₃₁	semidirect
408. #449	C₂²×C₃₁	semidirect
409. #449	C₂²×C₃₁	semidirect
410. #448	C₂²×C₃₁	semidirect
411. #447	C₂²×C₃₁	semidirect
412. #433	C₂²×C₃₁	semidirect
413. #432	C₂²×C₃₁	semidirect
414. #424	C₂²×C₃₁	semidirect
415. #419	C₂²×C₃₁	semidirect
418. #416	C₂²×C₃₁	semidirect
420. C₄×M₁₆	C₂²×C₃₁	semidirect
421. C₂×#97	C₂²×C₃₁	semidirect
527. C₃₁	#60825	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×#3508	2
C₃₁×#3500	2
C₃₁×#3221	2
C₃₁×#3220	2
C₃₁×#3214	2
C₃₁×#3213	2
C₃₁×#3151	2
C₂×C₃₁×#496	2
C₃₁×#3140	2
C₃₁×#3135	2
C₃₁×#3042	2
C₃₁×#3041	2
C₃₁×#3010	2
C₃₁×#3008	2
C₃₁×#2923	2
#60825	31

Subgroups — C31×#60825 #21517584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60825 #21517584