Subgroups — C₃₁×#33250 #21490009

Order 7936.

912 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#497	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#491	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#489	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2862	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2861	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1973	C₂	1	2	yes	maximal
8	C₃₁×#1971	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1969	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1968	C₂	1	2	yes	maximal
11	C₄×C₃₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
14	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
18	C₃₁×#501	—	2	4	no	—
19	C₃₁×#497	—	2	4	no	—
20	C₃₁×#491	—	2	4	no	—
21	C₃₁×#489	—	2	4	no	—
22	C₂×C₃₁×#107	C₂²	1	2	yes	—
23	C₂×C₃₁×#106	C₂²	1	2	yes	—
24	C₂×C₃₁×#103	C₂²	1	2	yes	—
25	C₂×C₃₁×#103	C₂²	1	2	yes	—
26	C₂×C₃₁×#103	C₂²	1	2	yes	—
27	C₂×C₃₁×#102	C₂²	1	2	yes	—
28	C₂×C₃₁×#97	C₂²	1	2	yes	—
29	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
32	C₃₁×#391	—	2	2	no	—
33	C₃₁×#391	C₂²	1	1	yes	characteristic
34	C₃₁×#391	C₂²	1	1	yes	characteristic
35	C₃₁×#391	C₂²	1	2	yes	—
36	C₃₁×#391	C₂²	1	2	yes	—
37	C₃₁×#390	C₂²	1	1	yes	characteristic
38	C₃₁×#390	C₂²	1	1	yes	characteristic
39	C₃₁×#388	—	2	2	no	—
40	C₃₁×#388	—	2	2	no	—
41	C₃₁×#382	—	2	2	no	—
42	C₄³×C₃₁	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₃₁	—	2	1	no	—
44	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
46	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₃₁	—	2	4	no	—
48	C₂×Q₁₆×C₃₁	—	2	4	no	—
49	C₂×Q₁₆×C₃₁	—	2	4	no	—
50	C₂×SD₁₆×C₃₁	—	2	4	no	—
51	C₂×SD₁₆×C₃₁	—	2	4	no	—
52	C₂×SD₁₆×C₃₁	—	2	4	no	—
53	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
55	C₃₁×C₄⋊Q₈	—	2	2	no	—
56	C₃₁×C₄⋊Q₈	—	2	2	no	—
57	C₃₁×C₄⋊Q₈	—	2	2	no	—
58	C₃₁×C₄⋊Q₈	—	2	2	no	—
59	C₃₁×#125	—	2	2	no	—
60	C₃₁×#125	—	2	2	no	—
61	C₃₁×#124	—	2	2	no	—
62	C₃₁×#124	—	2	2	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
75	C₂×C₄²×C₃₁	D₄	1	2	yes	—
76	C₂×C₄²×C₃₁	D₄	1	2	yes	—
77	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
80	C₃₁×#107	—	2	4	no	—
81	C₃₁×#106	—	2	4	no	—
82	C₃₁×#103	—	2	4	no	—
83	C₃₁×#103	—	2	4	no	—
84	C₃₁×#103	—	2	4	no	—
85	C₃₁×#102	—	2	4	no	—
86	C₃₁×#97	—	2	4	no	—
87	C₃₁×#97	D₄	1	4	yes	—
88	C₃₁×#97	D₄	1	4	yes	—
89	C₄×C₈×C₃₁	—	2	4	no	—
90	C₃₁×#95	—	2	4	no	—
91	C₃₁×#95	—	2	4	no	—
92	C₃₁×#95	—	2	2	no	—
93	C₃₁×#95	—	2	2	no	—
94	C₂⁴×C₃₁	—	2	1	no	—
95	C₂×Q₈×C₃₁	—	2	1	no	—
96	C₂×Q₈×C₃₁	—	2	2	no	—
97	C₂×Q₈×C₃₁	—	2	1	no	—
98	C₂×Q₈×C₃₁	—	2	2	no	—
99	C₂×Q₈×C₃₁	—	2	2	no	—
100	C₂×Q₈×C₃₁	—	2	2	no	—
101	C₂×Q₈×C₃₁	—	2	2	no	—
102	C₂×Q₈×C₃₁	—	2	2	no	—
103	C₂×Q₈×C₃₁	—	2	2	no	—
104	C₂×Q₈×C₃₁	—	2	2	no	—
105	C₂×Q₈×C₃₁	—	4	4	no	—
106	C₂×Q₈×C₃₁	—	4	2	no	—
107	C₂×D₄×C₃₁	—	2	1	no	—
108	C₂×D₄×C₃₁	—	2	1	no	—
109	C₂×D₄×C₃₁	—	2	2	no	—
110	C₂×D₄×C₃₁	—	2	2	no	—
111	C₂²×C₄×C₃₁	—	2	1	no	—
112	C₂²×C₄×C₃₁	—	2	2	no	—
113	C₂²×C₄×C₃₁	—	2	2	no	—
114	C₂²×C₄×C₃₁	—	2	1	no	—
115	C₂²×C₄×C₃₁	—	2	1	no	—
116	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
121	Q₁₆×C₃₁	—	4	8	no	—
122	SD₁₆×C₃₁	—	4	8	no	—
123	C₂×C₈×C₃₁	—	2	2	no	—
124	C₂×C₈×C₃₁	—	2	2	no	—
125	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
126	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
127	C₂×C₈×C₃₁	#41	1	4	yes	—
128	C₂×C₈×C₃₁	#41	1	4	yes	—
129	C₄⋊C₄×C₃₁	—	2	2	no	—
130	C₄⋊C₄×C₃₁	—	2	1	no	—
131	C₄⋊C₄×C₃₁	—	2	1	no	—
132	C₄⋊C₄×C₃₁	—	2	1	no	—
133	C₄⋊C₄×C₃₁	—	2	2	no	—
134	C₄⋊C₄×C₃₁	—	2	1	no	—
135	C₄⋊C₄×C₃₁	—	4	2	no	—
136	C₄⋊C₄×C₃₁	—	4	2	no	—
137	C₄⋊C₄×C₃₁	—	4	2	no	—
138	C₄⋊C₄×C₃₁	—	4	2	no	—
139	C₄⋊C₄×C₃₁	—	4	2	no	—
140	C₂²⋊C₄×C₃₁	—	4	4	no	—
141	C₂²⋊C₄×C₃₁	—	4	2	no	—
142	C₂²⋊C₄×C₃₁	—	4	2	no	—
143	C₂²⋊C₄×C₃₁	—	4	4	no	—
144	C₄²×C₃₁	—	2	4	no	—
145	C₄²×C₃₁	—	2	2	no	—
146	C₄²×C₃₁	—	2	2	no	—
147	C₄²×C₃₁	—	4	2	no	—
148	C₄²×C₃₁	C₂×D₄	1	2	yes	—
149	C₄²×C₃₁	C₂×D₄	1	2	yes	—
150	#33250	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₃₁	—	4	1	no	—
152	C₂³×C₃₁	—	4	1	no	—
153	C₂³×C₃₁	—	4	1	no	—
154	C₂³×C₃₁	—	4	2	no	—
155	C₂³×C₃₁	—	4	2	no	—
156	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₃₁	—	4	2	no	—
158	Q₈×C₃₁	—	4	2	no	—
159	Q₈×C₃₁	—	4	2	no	—
160	Q₈×C₃₁	—	4	2	no	—
161	Q₈×C₃₁	—	4	2	no	—
162	Q₈×C₃₁	—	4	2	no	—
163	Q₈×C₃₁	—	8	4	no	—
164	D₄×C₃₁	—	4	2	no	—
165	D₄×C₃₁	—	4	2	no	—
166	C₂×C₄×C₃₁	—	2	2	no	—
167	C₂×C₄×C₃₁	—	2	2	no	—
168	C₂×C₄×C₃₁	—	2	2	no	—
169	C₂×C₄×C₃₁	—	2	2	no	—
170	C₂×C₄×C₃₁	—	2	2	no	—
171	C₂×C₄×C₃₁	—	2	2	no	—
172	C₂×C₄×C₃₁	—	2	2	no	—
173	C₂×C₄×C₃₁	—	4	1	no	—
174	C₂×C₄×C₃₁	—	4	1	no	—
175	C₂×C₄×C₃₁	—	4	1	no	—
176	C₂×C₄×C₃₁	—	4	2	no	—
177	C₂×C₄×C₃₁	—	4	2	no	—
178	C₂×C₄×C₃₁	—	4	1	no	—
179	C₂×C₄×C₃₁	—	4	2	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	—	4	2	no	—
184	C₂×C₄×C₃₁	—	4	4	no	—
185	C₂×C₄×C₃₁	#127	1	2	yes	—
186	C₂×C₄×C₃₁	#127	1	2	yes	—
187	C₂×C₄×C₃₁	#137	1	4	yes	—
188	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
191	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
192	C₈×C₃₁	—	2	4	no	—
193	C₈×C₃₁	#124	1	8	yes	—
194	C₂×#501	C₂×C₃₁	1	1	yes	characteristic, complemented
195	C₂×#497	C₂×C₃₁	1	1	yes	characteristic
196	C₂×#491	C₂×C₃₁	1	1	yes	characteristic, complemented
197	C₂×#489	C₂×C₃₁	1	1	yes	characteristic
198	#2862	C₂×C₃₁	1	1	yes	characteristic, complemented
199	#2861	C₂×C₃₁	1	1	yes	characteristic
200	#1973	C₂×C₃₁	1	2	yes	—
201	#1971	C₂×C₃₁	1	2	yes	complemented
202	#1969	C₂×C₃₁	1	2	yes	complemented
203	#1968	C₂×C₃₁	1	2	yes	—
204	C₄×#97	C₂×C₃₁	1	1	yes	characteristic, complemented
205	C₂²×C₃₁	—	8	1	no	—
206	C₂²×C₃₁	—	8	1	no	—
207	C₂²×C₃₁	—	8	1	no	—
208	C₂²×C₃₁	—	8	2	no	—
209	C₂²×C₃₁	—	8	2	no	—
210	C₂²×C₃₁	C₂×#127	1	1	yes	characteristic
211	C₂²×C₃₁	#532	1	1	yes	characteristic
212	C₂²×C₃₁	#532	1	1	yes	characteristic
213	C₂²×C₃₁	C₂×#137	1	2	yes	—
214	C₂²×C₃₁	#575	1	2	yes	—
215	C₄×C₃₁	—	2	2	no	—
216	C₄×C₃₁	—	2	2	no	—
217	C₄×C₃₁	—	2	4	no	—
218	C₄×C₃₁	—	4	2	no	—
219	C₄×C₃₁	—	8	1	no	—
220	C₄×C₃₁	—	8	2	no	—
221	C₄×C₃₁	—	8	1	no	—
222	C₄×C₃₁	—	8	1	no	—
223	C₄×C₃₁	—	8	2	no	—
224	C₄×C₃₁	C₂×#124	1	2	yes	—
225	C₄×C₃₁	#532	1	2	yes	—
226	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
227	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
228	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
229	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
230	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
231	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
232	#501	—	2	4	no	—
233	#497	—	2	4	no	—
234	#491	—	2	4	no	—
235	#489	—	2	4	no	—
236	C₂×#107	C₂²×C₃₁	1	2	yes	—
237	C₂×#106	C₂²×C₃₁	1	2	yes	—
238	C₂×#103	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×#97	C₂²×C₃₁	1	2	yes	—
243	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
244	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
246	#391	—	2	2	no	—
247	#391	C₂²×C₃₁	1	1	yes	characteristic
248	#391	C₂²×C₃₁	1	1	yes	characteristic
249	#391	C₂²×C₃₁	1	2	yes	—
250	#391	C₂²×C₃₁	1	2	yes	—
251	#390	C₂²×C₃₁	1	1	yes	characteristic
252	#390	C₂²×C₃₁	1	1	yes	characteristic
253	#388	—	2	2	no	—
254	#388	—	2	2	no	—
255	#382	—	2	2	no	—
256	C₄³	C₂²×C₃₁	1	1	yes	characteristic
257	C₂×C₃₁	—	16	1	no	—
258	C₂×C₃₁	#2858	1	1	yes	characteristic
259	C₂×C₃₁	#3152	1	1	yes	characteristic
260	C₂×C₃₁	#3153	1	1	yes	characteristic
261	C₂×C₃₁	#3172	1	2	yes	—
262	C₂×C₃₁	#3181	1	2	yes	—
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
265	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
266	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
267	C₂×Q₁₆	—	2	4	no	—
268	C₂×Q₁₆	—	2	4	no	—
269	C₂×Q₁₆	—	2	4	no	—
270	C₂×SD₁₆	—	2	4	no	—
271	C₂×SD₁₆	—	2	4	no	—
272	C₂×SD₁₆	—	2	4	no	—
273	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
274	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	#125	—	2	2	no	—
280	#125	—	2	2	no	—
281	#124	—	2	2	no	—
282	#124	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₄²	D₄×C₃₁	1	2	yes	—
296	C₂×C₄²	D₄×C₃₁	1	2	yes	—
297	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
300	#107	—	2	4	no	—
301	#106	—	2	4	no	—
302	#103	—	2	4	no	—
303	#103	—	2	4	no	—
304	#103	—	2	4	no	—
305	#102	—	2	4	no	—
306	#97	—	2	4	no	—
307	#97	D₄×C₃₁	1	4	yes	—
308	#97	D₄×C₃₁	1	4	yes	—
309	C₄×C₈	—	2	4	no	—
310	#95	—	2	4	no	—
311	#95	—	2	4	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	C₃₁	#33250	1	1	yes	characteristic, direct product factor, Sylow
315	C₂⁴	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	4	4	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
342	Q₁₆	—	4	8	no	—
343	SD₁₆	—	4	8	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
347	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
348	C₂×C₈	#41×C₃₁	1	4	yes	—
349	C₂×C₈	#41×C₃₁	1	4	yes	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	4	4	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	4	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	2	no	—
369	C₄²	C₂×D₄×C₃₁	1	2	yes	—
370	C₄²	C₂×D₄×C₃₁	1	2	yes	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	8	4	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	C₃₁×#127	1	2	yes	—
406	C₂×C₄	C₃₁×#127	1	2	yes	—
407	C₂×C₄	C₃₁×#137	1	4	yes	—
408	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
411	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
412	C₈	—	2	4	no	—
413	C₈	C₃₁×#124	1	8	yes	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	C₂×C₃₁×#127	1	1	yes	characteristic
420	C₂²	C₃₁×#532	1	1	yes	characteristic
421	C₂²	C₃₁×#532	1	1	yes	characteristic
422	C₂²	C₂×C₃₁×#137	1	2	yes	—
423	C₂²	C₃₁×#575	1	2	yes	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	4	no	—
427	C₄	—	4	2	no	—
428	C₄	—	8	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	1	no	—
433	C₄	C₂×C₃₁×#124	1	2	yes	—
434	C₄	C₃₁×#532	1	2	yes	—
435	C₂	—	16	1	no	—
436	C₂	C₃₁×#2858	1	1	yes	characteristic
437	C₂	C₃₁×#3152	1	1	yes	characteristic
438	C₂	C₃₁×#3153	1	1	yes	characteristic
439	C₂	C₃₁×#3172	1	2	yes	—
440	C₂	C₃₁×#3181	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₄³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#501	C₂	semidirect
3. C₂×C₃₁×#491	C₂	semidirect
5. C₃₁×#2862	C₂	semidirect
8. C₃₁×#1971	C₂	semidirect
9. C₃₁×#1969	C₂	semidirect
11. C₄×C₃₁×#97	C₂	semidirect
150. #33250	C₃₁	direct (N × H)
194. C₂×#501	C₂×C₃₁	semidirect
196. C₂×#491	C₂×C₃₁	semidirect
198. #2862	C₂×C₃₁	semidirect
201. #1971	C₂×C₃₁	semidirect
202. #1969	C₂×C₃₁	semidirect
204. C₄×#97	C₂×C₃₁	semidirect
314. C₃₁	#33250	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×#501	2
C₂×C₃₁×#497	2
C₂×C₃₁×#491	2
C₂×C₃₁×#489	2
C₃₁×#2862	2
C₃₁×#2861	2
C₃₁×#1973	2
C₃₁×#1971	2
C₃₁×#1969	2
C₃₁×#1968	2
C₄×C₃₁×#97	2
#33250	31

Subgroups — C31×#33250 #21490009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33250 #21490009