Subgroups — C₃₁×#33120 #21489879

Order 7936.

872 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#484	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#480	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2620	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2274	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1983	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1947	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1928	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1925	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1875	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#484	—	2	4	no	—
19	C₃₁×#480	—	2	4	no	—
20	C₂×C₃₁×#107	C₂²	1	2	yes	—
21	C₂×C₃₁×#107	C₂²	1	2	yes	—
22	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₃₁×#103	C₂²	1	2	yes	—
24	C₂×C₃₁×#103	C₂²	1	2	yes	—
25	C₂×C₃₁×#102	C₂²	1	2	yes	—
26	C₂×C₃₁×#102	C₂²	1	2	yes	—
27	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₃₁×#396	—	2	2	no	—
30	C₃₁×#394	—	2	2	no	—
31	C₃₁×#391	C₂²	1	1	yes	characteristic
32	C₃₁×#390	C₂²	1	1	yes	characteristic
33	C₃₁×#384	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
35	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₃₁	—	2	2	no	—
38	C₃₁×#340	C₂²	1	2	yes	—
39	C₃₁×#340	C₂²	1	2	yes	—
40	C₃₁×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₃₁	—	2	1	no	—
43	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₃₁	—	2	1	no	—
45	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
48	C₃₁×#124	—	2	4	no	—
49	C₃₁×C₂²⋊Q₈	—	2	2	no	—
50	C₃₁×C₂²⋊Q₈	—	2	2	no	—
51	C₃₁×#121	—	2	2	no	—
52	C₃₁×#121	—	2	2	no	—
53	C₃₁×#117	—	2	4	no	—
54	C₃₁×#117	—	2	4	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₃₁	D₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
71	C₂×C₄²×C₃₁	—	2	1	no	—
72	C₂×C₄²×C₃₁	—	2	2	no	—
73	C₂×C₄²×C₃₁	—	2	2	no	—
74	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
76	C₃₁×#107	—	2	4	no	—
77	C₃₁×#107	—	2	4	no	—
78	C₃₁×C₄⋊C₈	—	2	4	no	—
79	C₃₁×#103	—	2	4	no	—
80	C₃₁×#103	—	2	4	no	—
81	C₃₁×#102	—	2	4	no	—
82	C₃₁×#102	—	2	4	no	—
83	C₃₁×C₂²⋊C₈	—	2	2	no	—
84	C₃₁×C₂²⋊C₈	—	2	2	no	—
85	C₃₁×#95	—	2	2	no	—
86	C₃₁×#95	—	2	2	no	—
87	C₃₁×#95	—	2	2	no	—
88	C₂⁴×C₃₁	—	2	1	no	—
89	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₃₁	—	2	1	no	—
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	1	no	—
93	C₂×Q₈×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	—	2	1	no	—
95	C₂×D₄×C₃₁	—	2	2	no	—
96	C₂×D₄×C₃₁	—	2	1	no	—
97	C₂×D₄×C₃₁	—	2	2	no	—
98	C₂×D₄×C₃₁	—	4	2	no	—
99	C₂×D₄×C₃₁	—	8	2	no	—
100	C₂²×C₄×C₃₁	—	2	2	no	—
101	C₂²×C₄×C₃₁	—	2	2	no	—
102	C₂²×C₄×C₃₁	—	2	2	no	—
103	C₂²×C₄×C₃₁	—	2	2	no	—
104	C₂²×C₄×C₃₁	—	2	4	no	—
105	C₂²×C₄×C₃₁	—	2	1	no	—
106	C₂²×C₄×C₃₁	—	2	1	no	—
107	C₂²×C₄×C₃₁	—	2	1	no	—
108	C₂²×C₄×C₃₁	—	8	2	no	—
109	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₃₁	#41	1	2	yes	—
114	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₃₁	—	2	2	no	—
116	C₂×C₈×C₃₁	—	2	2	no	—
117	C₂×C₈×C₃₁	—	2	2	no	—
118	C₂×C₈×C₃₁	—	2	2	no	—
119	C₂×C₈×C₃₁	—	2	2	no	—
120	C₂×C₈×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	4	no	—
122	C₄⋊C₄×C₃₁	—	2	4	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	2	1	no	—
126	C₄⋊C₄×C₃₁	—	2	1	no	—
127	C₄⋊C₄×C₃₁	—	2	1	no	—
128	C₄⋊C₄×C₃₁	—	2	1	no	—
129	C₄⋊C₄×C₃₁	—	4	2	no	—
130	C₄⋊C₄×C₃₁	—	8	2	no	—
131	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
132	C₄⋊C₄×C₃₁	#41	1	4	yes	—
133	C₂²⋊C₄×C₃₁	—	2	4	no	—
134	C₂²⋊C₄×C₃₁	—	2	4	no	—
135	C₂²⋊C₄×C₃₁	—	4	2	no	—
136	C₂²⋊C₄×C₃₁	—	4	2	no	—
137	C₂²⋊C₄×C₃₁	—	4	4	no	—
138	C₂²⋊C₄×C₃₁	—	8	2	no	—
139	C₄²×C₃₁	—	2	4	no	—
140	C₄²×C₃₁	—	2	2	no	—
141	C₄²×C₃₁	—	8	2	no	—
142	C₄²×C₃₁	—	8	2	no	—
143	C₄²×C₃₁	#41	1	4	yes	—
144	#33120	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₃₁	—	2	1	no	—
146	C₂³×C₃₁	—	2	1	no	—
147	C₂³×C₃₁	—	2	2	no	—
148	C₂³×C₃₁	—	2	2	no	—
149	C₂³×C₃₁	—	4	1	no	—
150	C₂³×C₃₁	—	4	1	no	—
151	C₂³×C₃₁	—	4	1	no	—
152	C₂³×C₃₁	—	4	2	no	—
153	C₂³×C₃₁	—	4	2	no	—
154	C₂³×C₃₁	#121	1	2	yes	—
155	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₃₁	—	4	2	no	—
157	Q₈×C₃₁	—	4	2	no	—
158	D₄×C₃₁	—	4	2	no	—
159	D₄×C₃₁	—	4	2	no	—
160	D₄×C₃₁	—	8	4	no	—
161	C₂×C₄×C₃₁	—	2	1	no	—
162	C₂×C₄×C₃₁	—	2	1	no	—
163	C₂×C₄×C₃₁	—	2	2	no	—
164	C₂×C₄×C₃₁	—	2	2	no	—
165	C₂×C₄×C₃₁	—	2	4	no	—
166	C₂×C₄×C₃₁	—	2	4	no	—
167	C₂×C₄×C₃₁	—	2	4	no	—
168	C₂×C₄×C₃₁	—	2	2	no	—
169	C₂×C₄×C₃₁	—	2	4	no	—
170	C₂×C₄×C₃₁	—	2	2	no	—
171	C₂×C₄×C₃₁	—	2	2	no	—
172	C₂×C₄×C₃₁	—	4	2	no	—
173	C₂×C₄×C₃₁	—	4	2	no	—
174	C₂×C₄×C₃₁	—	4	2	no	—
175	C₂×C₄×C₃₁	—	4	2	no	—
176	C₂×C₄×C₃₁	—	4	1	no	—
177	C₂×C₄×C₃₁	—	4	1	no	—
178	C₂×C₄×C₃₁	—	4	1	no	—
179	C₂×C₄×C₃₁	—	4	1	no	—
180	C₂×C₄×C₃₁	—	4	1	no	—
181	C₂×C₄×C₃₁	—	4	2	no	—
182	C₂×C₄×C₃₁	—	4	2	no	—
183	C₂×C₄×C₃₁	—	8	4	no	—
184	C₂×C₄×C₃₁	#121	1	2	yes	—
185	C₂×C₄×C₃₁	#123	1	4	yes	—
186	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
189	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
190	C₈×C₃₁	—	4	2	no	—
191	C₈×C₃₁	—	4	2	no	—
192	C₂×#484	C₂×C₃₁	1	1	yes	characteristic, complemented
193	C₂×#480	C₂×C₃₁	1	1	yes	characteristic
194	#2620	C₂×C₃₁	1	1	yes	characteristic
195	#2274	C₂×C₃₁	1	1	yes	characteristic, complemented
196	#1983	C₂×C₃₁	1	2	yes	complemented
197	#1947	C₂×C₃₁	1	2	yes	complemented
198	#1928	C₂×C₃₁	1	2	yes	complemented
199	#1925	C₂×C₃₁	1	2	yes	complemented
200	#1875	C₂×C₃₁	1	1	yes	characteristic
201	#1873	C₂×C₃₁	1	1	yes	characteristic, complemented
202	#1798	C₂×C₃₁	1	1	yes	characteristic, complemented
203	C₂²×C₃₁	—	2	2	no	—
204	C₂²×C₃₁	—	2	2	no	—
205	C₂²×C₃₁	—	2	2	no	—
206	C₂²×C₃₁	—	4	2	no	—
207	C₂²×C₃₁	—	4	2	no	—
208	C₂²×C₃₁	—	8	2	no	—
209	C₂²×C₃₁	—	8	1	no	—
210	C₂²×C₃₁	—	8	2	no	—
211	C₂²×C₃₁	—	8	1	no	—
212	C₂²×C₃₁	—	8	1	no	—
213	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
214	C₂²×C₃₁	C₂×#123	1	1	yes	characteristic
215	C₂²×C₃₁	#525	1	1	yes	characteristic
216	C₂²×C₃₁	#576	1	2	yes	—
217	C₂²×C₃₁	#578	1	2	yes	—
218	C₄×C₃₁	—	2	4	no	—
219	C₄×C₃₁	—	2	2	no	—
220	C₄×C₃₁	—	4	2	no	—
221	C₄×C₃₁	—	4	4	no	—
222	C₄×C₃₁	—	4	4	no	—
223	C₄×C₃₁	—	8	1	no	—
224	C₄×C₃₁	—	8	1	no	—
225	C₄×C₃₁	—	8	1	no	—
226	C₄×C₃₁	#529	1	2	yes	—
227	C₄×C₃₁	#532	1	2	yes	—
228	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
229	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
230	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
231	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
232	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
233	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
234	#484	—	2	4	no	—
235	#480	—	2	4	no	—
236	C₂×#107	C₂²×C₃₁	1	2	yes	—
237	C₂×#107	C₂²×C₃₁	1	2	yes	—
238	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
239	C₂×#103	C₂²×C₃₁	1	2	yes	—
240	C₂×#103	C₂²×C₃₁	1	2	yes	—
241	C₂×#102	C₂²×C₃₁	1	2	yes	—
242	C₂×#102	C₂²×C₃₁	1	2	yes	—
243	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
244	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
245	#396	—	2	2	no	—
246	#394	—	2	2	no	—
247	#391	C₂²×C₃₁	1	1	yes	characteristic
248	#390	C₂²×C₃₁	1	1	yes	characteristic
249	#384	C₂²×C₃₁	1	1	yes	characteristic
250	C₄×C₄⋊C₄	—	2	2	no	—
251	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
252	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
253	C₄×C₂²⋊C₄	—	2	2	no	—
254	#340	C₂²×C₃₁	1	2	yes	—
255	#340	C₂²×C₃₁	1	2	yes	—
256	#336	C₂²×C₃₁	1	2	yes	—
257	C₂×C₃₁	—	4	2	no	—
258	C₂×C₃₁	—	16	1	no	—
259	C₂×C₃₁	#2854	1	1	yes	characteristic
260	C₂×C₃₁	#3041	1	1	yes	characteristic
261	C₂×C₃₁	#3044	1	1	yes	characteristic
262	C₂×C₃₁	#3098	1	2	yes	—
263	C₂×C₃₁	#3124	1	2	yes	—
264	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
270	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
271	#124	—	2	4	no	—
272	C₂²⋊Q₈	—	2	2	no	—
273	C₂²⋊Q₈	—	2	2	no	—
274	#121	—	2	2	no	—
275	#121	—	2	2	no	—
276	#117	—	2	4	no	—
277	#117	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
283	C₂×C₄⋊C₄	D₄×C₃₁	1	4	yes	—
284	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
299	#107	—	2	4	no	—
300	#107	—	2	4	no	—
301	C₄⋊C₈	—	2	4	no	—
302	#103	—	2	4	no	—
303	#103	—	2	4	no	—
304	#102	—	2	4	no	—
305	#102	—	2	4	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	C₂²⋊C₈	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	C₃₁	#33120	1	1	yes	characteristic, direct product factor, Sylow
312	C₂⁴	—	2	1	no	—
313	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	8	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	8	2	no	—
333	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
337	C₂²×C₄	#41×C₃₁	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	8	2	no	—
355	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
356	C₄⋊C₄	#41×C₃₁	1	4	yes	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	4	4	no	—
362	C₂²⋊C₄	—	8	2	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	8	2	no	—
366	C₄²	—	8	2	no	—
367	C₄²	#41×C₃₁	1	4	yes	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	C₃₁×#121	1	2	yes	—
378	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	4	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	4	no	—
407	C₂×C₄	C₃₁×#121	1	2	yes	—
408	C₂×C₄	C₃₁×#123	1	4	yes	—
409	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
412	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
413	C₈	—	4	2	no	—
414	C₈	—	4	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
426	C₂²	C₂×C₃₁×#123	1	1	yes	characteristic
427	C₂²	C₃₁×#525	1	1	yes	characteristic
428	C₂²	C₃₁×#576	1	2	yes	—
429	C₂²	C₃₁×#578	1	2	yes	—
430	C₄	—	2	4	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	4	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	1	no	—
437	C₄	—	8	1	no	—
438	C₄	C₃₁×#529	1	2	yes	—
439	C₄	C₃₁×#532	1	2	yes	—
440	C₂	—	4	2	no	—
441	C₂	—	16	1	no	—
442	C₂	C₃₁×#2854	1	1	yes	characteristic
443	C₂	C₃₁×#3041	1	1	yes	characteristic
444	C₂	C₃₁×#3044	1	1	yes	characteristic
445	C₂	C₃₁×#3098	1	2	yes	—
446	C₂	C₃₁×#3124	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#484	C₂	semidirect
4. C₃₁×#2274	C₂	semidirect
5. C₃₁×#1983	C₂	semidirect
6. C₃₁×#1947	C₂	semidirect
7. C₃₁×#1928	C₂	semidirect
8. C₃₁×#1925	C₂	semidirect
10. C₃₁×#1873	C₂	semidirect
11. C₃₁×#1798	C₂	semidirect
144. #33120	C₃₁	direct (N × H)
192. C₂×#484	C₂×C₃₁	semidirect
195. #2274	C₂×C₃₁	semidirect
196. #1983	C₂×C₃₁	semidirect
197. #1947	C₂×C₃₁	semidirect
198. #1928	C₂×C₃₁	semidirect
199. #1925	C₂×C₃₁	semidirect
201. #1873	C₂×C₃₁	semidirect
202. #1798	C₂×C₃₁	semidirect
311. C₃₁	#33120	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#484	2
C₂×C₃₁×#480	2
C₃₁×#2620	2
C₃₁×#2274	2
C₃₁×#1983	2
C₃₁×#1947	2
C₃₁×#1928	2
C₃₁×#1925	2
C₃₁×#1875	2
C₃₁×#1873	2
C₃₁×#1798	2
#33120	31

Subgroups — C31×#33120 #21489879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33120 #21489879