Subgroups — C₃₁×#21993 #21478752

Order 7936.

724 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#423	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1950	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1855	C₂	1	4	yes	maximal
6	C₃₁×#1848	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1837	C₂	1	2	yes	maximal, complemented
8	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
9	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
10	C₃₁×#432	—	2	1	no	—
11	C₃₁×#432	—	2	1	no	—
12	C₃₁×#431	—	2	1	no	—
13	C₃₁×#431	—	2	1	no	—
14	C₃₁×#431	C₄	1	2	yes	—
15	C₃₁×#431	C₄	1	2	yes	—
16	C₃₁×#431	C₄	1	2	yes	—
17	C₃₁×#431	C₄	1	2	yes	—
18	C₂×C₃₁×#108	C₂²	1	8	yes	—
19	C₃₁×#423	—	2	1	no	—
20	C₃₁×#423	—	2	1	no	—
21	C₃₁×#423	C₂²	1	1	yes	characteristic
22	C₃₁×#423	C₂²	1	2	yes	—
23	C₃₁×#423	C₂²	1	1	yes	characteristic
24	C₃₁×#423	C₂²	1	2	yes	—
25	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
26	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
27	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
28	C₃₁×#407	C₂²	1	2	yes	—
29	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
32	C₃₁×#341	C₂²	1	8	yes	—
33	C₂³×C₄×C₃₁	Q₈	1	1	yes	characteristic
34	C₂³×C₄×C₃₁	Q₈	1	1	yes	characteristic
35	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₃₁	—	2	2	no	—
37	C₂×M₁₆×C₃₁	—	4	4	no	—
38	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
39	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
40	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
41	C₂²×C₈×C₃₁	—	2	2	no	—
42	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
43	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₃₁	Q₈	1	1	yes	characteristic
52	C₂×C₄²×C₃₁	Q₈	1	1	yes	characteristic
53	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
55	C₃₁×#108	—	4	8	no	—
56	C₃₁×C₄⋊C₈	—	2	2	no	—
57	C₃₁×C₄⋊C₈	—	2	2	no	—
58	C₃₁×C₄⋊C₈	—	2	2	no	—
59	C₃₁×C₄⋊C₈	—	2	2	no	—
60	C₃₁×C₄⋊C₈	—	2	1	no	—
61	C₃₁×C₄⋊C₈	—	2	1	no	—
62	C₃₁×C₄⋊C₈	—	2	1	no	—
63	C₃₁×C₄⋊C₈	—	2	1	no	—
64	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
65	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
66	C₃₁×C₂²⋊C₈	—	2	2	no	—
67	C₃₁×C₂²⋊C₈	—	2	2	no	—
68	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
69	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
70	C₃₁×#97	—	2	2	no	—
71	C₄×C₈×C₃₁	—	2	2	no	—
72	C₄×C₈×C₃₁	C₂×C₄	1	4	yes	—
73	C₄×C₈×C₃₁	C₂×C₄	1	4	yes	—
74	C₂⁴×C₃₁	C₂×Q₈	1	1	yes	characteristic
75	C₂²×C₄×C₃₁	—	2	4	no	—
76	C₂²×C₄×C₃₁	—	2	2	no	—
77	C₂²×C₄×C₃₁	—	2	2	no	—
78	C₂²×C₄×C₃₁	—	4	2	no	—
79	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
97	M₁₆×C₃₁	—	2	4	no	—
98	M₁₆×C₃₁	—	2	8	no	—
99	M₁₆×C₃₁	—	2	4	no	—
100	M₁₆×C₃₁	—	4	4	no	—
101	C₂×C₈×C₃₁	—	2	4	no	—
102	C₂×C₈×C₃₁	—	2	4	no	—
103	C₂×C₈×C₃₁	—	2	2	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	4	no	—
106	C₂×C₈×C₃₁	—	4	4	no	—
107	C₂×C₈×C₃₁	C₂²×C₄	1	8	yes	—
108	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
124	#21993	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₃₁	—	2	2	no	—
126	C₂³×C₃₁	—	2	2	no	—
127	C₂³×C₃₁	—	4	1	no	—
128	C₂³×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂³×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂³×C₃₁	C₂²×Q₈	1	1	yes	characteristic
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	2	2	no	—
133	C₂×C₄×C₃₁	—	2	2	no	—
134	C₂×C₄×C₃₁	—	2	2	no	—
135	C₂×C₄×C₃₁	—	2	1	no	—
136	C₂×C₄×C₃₁	—	2	1	no	—
137	C₂×C₄×C₃₁	—	2	1	no	—
138	C₂×C₄×C₃₁	—	2	1	no	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	4	1	no	—
147	C₂×C₄×C₃₁	—	4	1	no	—
148	C₂×C₄×C₃₁	—	4	1	no	—
149	C₂×C₄×C₃₁	#108	1	4	yes	complemented
150	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
163	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
164	C₈×C₃₁	—	2	8	no	—
165	C₈×C₃₁	—	4	4	no	—
166	C₈×C₃₁	—	4	2	no	—
167	C₈×C₃₁	—	4	2	no	—
168	#2920	C₂×C₃₁	1	1	yes	characteristic
169	C₂×#431	C₂×C₃₁	1	1	yes	characteristic
170	C₂×#423	C₂×C₃₁	1	1	yes	characteristic
171	#1950	C₂×C₃₁	1	4	yes	complemented
172	#1855	C₂×C₃₁	1	4	yes	—
173	#1848	C₂×C₃₁	1	2	yes	complemented
174	#1837	C₂×C₃₁	1	2	yes	complemented
175	C₂²×C₃₁	—	2	1	no	—
176	C₂²×C₃₁	—	2	1	no	—
177	C₂²×C₃₁	—	2	1	no	—
178	C₂²×C₃₁	—	2	1	no	—
179	C₂²×C₃₁	—	2	1	no	—
180	C₂²×C₃₁	—	2	1	no	—
181	C₂²×C₃₁	—	2	1	no	—
182	C₂²×C₃₁	—	4	4	no	—
183	C₂²×C₃₁	C₂×#108	1	2	yes	—
184	C₂²×C₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₂²×C₃₁	#544	1	2	yes	—
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	2	1	no	—
188	C₄×C₃₁	—	2	1	no	—
189	C₄×C₃₁	—	2	1	no	—
190	C₄×C₃₁	—	2	1	no	—
191	C₄×C₃₁	—	2	1	no	—
192	C₄×C₃₁	—	2	1	no	—
193	C₄×C₃₁	C₂×#108	1	2	yes	—
194	C₄×C₃₁	C₂×#108	1	2	yes	—
195	C₄×C₃₁	#430	1	2	yes	—
196	C₄×C₃₁	#520	1	2	yes	—
197	C₄×C₃₁	#535	1	1	yes	characteristic
198	C₄×C₃₁	#536	1	1	yes	characteristic
199	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
200	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
201	#432	—	2	1	no	—
202	#432	—	2	1	no	—
203	#431	—	2	1	no	—
204	#431	—	2	1	no	—
205	#431	C₄×C₃₁	1	2	yes	—
206	#431	C₄×C₃₁	1	2	yes	—
207	#431	C₄×C₃₁	1	2	yes	—
208	#431	C₄×C₃₁	1	2	yes	—
209	C₂×#108	C₂²×C₃₁	1	8	yes	—
210	#423	—	2	1	no	—
211	#423	—	2	1	no	—
212	#423	C₂²×C₃₁	1	1	yes	characteristic
213	#423	C₂²×C₃₁	1	2	yes	—
214	#423	C₂²×C₃₁	1	1	yes	characteristic
215	#423	C₂²×C₃₁	1	2	yes	—
216	C₂×C₄⋊C₈	—	2	1	no	—
217	C₂×C₄⋊C₈	—	2	1	no	—
218	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
219	#407	C₂²×C₃₁	1	2	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
221	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
222	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
223	#341	C₂²×C₃₁	1	8	yes	—
224	C₂×C₃₁	—	2	2	no	—
225	C₂×C₃₁	—	2	2	no	—
226	C₂×C₃₁	—	4	1	no	—
227	C₂×C₃₁	#2317	1	1	yes	characteristic
228	C₂×C₃₁	C₂²×#108	1	1	yes	characteristic
229	C₂×C₃₁	C₂×#430	1	1	yes	characteristic
230	C₂³×C₄	Q₈×C₃₁	1	1	yes	characteristic
231	C₂³×C₄	Q₈×C₃₁	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	4	4	no	—
235	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
236	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
237	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
240	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
242	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
243	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
244	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
245	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
246	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
247	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
248	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
249	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
252	#108	—	4	8	no	—
253	C₄⋊C₈	—	2	2	no	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
262	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
263	C₂²⋊C₈	—	2	2	no	—
264	C₂²⋊C₈	—	2	2	no	—
265	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
266	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
267	#97	—	2	2	no	—
268	C₄×C₈	—	2	2	no	—
269	C₄×C₈	C₂×C₄×C₃₁	1	4	yes	—
270	C₄×C₈	C₂×C₄×C₃₁	1	4	yes	—
271	C₃₁	#21993	1	1	yes	characteristic, direct product factor, Sylow
272	C₂⁴	C₂×Q₈×C₃₁	1	1	yes	characteristic
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
278	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
279	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
280	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
281	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
282	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
283	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
284	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
294	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
295	M₁₆	—	2	4	no	—
296	M₁₆	—	2	8	no	—
297	M₁₆	—	2	4	no	—
298	M₁₆	—	4	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	C₂²×C₄×C₃₁	1	8	yes	—
306	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
307	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
308	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
309	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
310	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
311	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
312	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
313	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
314	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
315	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
316	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
317	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
319	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
320	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
321	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	4	1	no	—
325	C₂³	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
326	C₂³	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
327	C₂³	C₂²×Q₈×C₃₁	1	1	yes	characteristic
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	C₃₁×#108	1	4	yes	complemented
347	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
355	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
357	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
359	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
360	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
361	C₈	—	2	8	no	—
362	C₈	—	4	4	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	4	4	no	—
373	C₂²	C₂×C₃₁×#108	1	2	yes	—
374	C₂²	C₂²×C₄⋊C₄×C₃₁	1	1	yes	characteristic
375	C₂²	C₃₁×#544	1	2	yes	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	C₂×C₃₁×#108	1	2	yes	—
384	C₄	C₂×C₃₁×#108	1	2	yes	—
385	C₄	C₃₁×#430	1	2	yes	—
386	C₄	C₃₁×#520	1	2	yes	—
387	C₄	C₃₁×#535	1	1	yes	characteristic
388	C₄	C₃₁×#536	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	2	2	no	—
391	C₂	—	4	1	no	—
392	C₂	C₃₁×#2317	1	1	yes	characteristic
393	C₂	C₂²×C₃₁×#108	1	1	yes	characteristic
394	C₂	C₂×C₃₁×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₃₁	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1950	C₂	semidirect
6. C₃₁×#1848	C₂	semidirect
7. C₃₁×#1837	C₂	semidirect
124. #21993	C₃₁	direct (N × H)
149. C₂×C₄×C₃₁	#108	semidirect
171. #1950	C₂×C₃₁	semidirect
173. #1848	C₂×C₃₁	semidirect
174. #1837	C₂×C₃₁	semidirect
271. C₃₁	#21993	direct (N × H)
346. C₂×C₄	C₃₁×#108	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#2920	2
C₂×C₃₁×#431	2
C₂×C₃₁×#423	2
C₃₁×#1950	2
C₃₁×#1855	2
C₃₁×#1848	2
C₃₁×#1837	2
#21993	31

Subgroups — C31×#21993 #21478752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#21993 #21478752