Subgroups — C₃₁×#21271 #21478030

Order 7936.

962 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#432	C₂	1	2	yes	maximal, complemented
2	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1955	C₂	1	2	yes	maximal
4	C₃₁×#1940	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1923	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1749	C₂	1	2	yes	maximal, complemented
8	C₄×C₃₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₄×C₃₁	C₄	1	2	yes	—
10	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
12	C₃₁×#432	—	2	8	no	—
13	C₂×C₃₁×C₄⋊C₈	C₂²	1	4	yes	—
14	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₃₁×C₂²⋊C₈	C₂²	1	4	yes	—
16	C₂×C₃₁×C₂²⋊C₈	C₂²	1	4	yes	—
17	C₂×C₃₁×#97	C₂²	1	2	yes	—
18	C₂×C₃₁×#97	C₂²	1	2	yes	—
19	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
22	C₄×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
23	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₃₁	C₄	1	2	yes	—
25	C₄×C₂²⋊C₄×C₃₁	C₄	1	2	yes	—
26	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
27	C₄³×C₃₁	C₂²	1	1	yes	characteristic
28	C₃₁×#336	C₂²	1	2	yes	—
29	C₃₁×#336	C₂²	1	4	yes	—
30	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₃₁	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₃₁	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
34	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
35	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
36	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
37	C₄×D₄×C₃₁	—	2	8	no	—
38	C₄×D₄×C₃₁	—	2	4	no	—
39	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
42	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
43	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₃₁	—	2	4	no	—
45	C₂×C₄²×C₃₁	—	2	4	no	—
46	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
52	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
54	C₃₁×C₄⋊C₈	—	2	8	no	—
55	C₃₁×C₄⋊C₈	—	2	4	no	—
56	C₃₁×C₂²⋊C₈	—	2	8	no	—
57	C₃₁×C₂²⋊C₈	—	2	8	no	—
58	C₃₁×#97	—	2	4	no	—
59	C₃₁×#97	—	2	4	no	—
60	C₃₁×#97	—	2	2	no	—
61	C₃₁×#97	D₄	1	4	yes	complemented
62	C₄×C₈×C₃₁	—	2	4	no	—
63	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
64	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
65	C₃₁×#95	C₂×C₄	1	2	yes	—
66	C₃₁×#95	C₂×C₄	1	2	yes	—
67	C₂⁴×C₃₁	C₂²×C₄	1	2	yes	—
68	C₂×D₄×C₃₁	—	2	4	no	—
69	C₂×D₄×C₃₁	—	2	2	no	—
70	C₂²×C₄×C₃₁	—	2	4	no	—
71	C₂²×C₄×C₃₁	—	2	4	no	—
72	C₂²×C₄×C₃₁	—	2	4	no	—
73	C₂²×C₄×C₃₁	—	2	4	no	—
74	C₂²×C₄×C₃₁	—	2	2	no	—
75	C₂²×C₄×C₃₁	—	2	4	no	—
76	C₂²×C₄×C₃₁	—	2	2	no	—
77	C₂²×C₄×C₃₁	—	2	4	no	—
78	C₂²×C₄×C₃₁	—	4	2	no	—
79	C₂²×C₄×C₃₁	—	4	2	no	—
80	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
88	C₂×C₈×C₃₁	—	2	2	no	—
89	C₂×C₈×C₃₁	—	2	2	no	—
90	C₂×C₈×C₃₁	—	2	2	no	—
91	C₂×C₈×C₃₁	—	2	2	no	—
92	C₂×C₈×C₃₁	—	2	4	no	—
93	C₂×C₈×C₃₁	—	2	4	no	—
94	C₂×C₈×C₃₁	—	2	4	no	—
95	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
96	C₂×C₈×C₃₁	#41	1	4	yes	—
97	C₄⋊C₄×C₃₁	—	2	2	no	—
98	C₄⋊C₄×C₃₁	—	2	4	no	—
99	C₂²⋊C₄×C₃₁	—	2	4	no	—
100	C₂²⋊C₄×C₃₁	—	2	4	no	—
101	C₂²⋊C₄×C₃₁	M₁₆	1	8	yes	—
102	C₄²×C₃₁	—	2	4	no	—
103	C₄²×C₃₁	—	2	4	no	—
104	C₄²×C₃₁	—	2	4	no	—
105	C₄²×C₃₁	—	2	2	no	—
106	C₄²×C₃₁	—	2	2	no	—
107	C₄²×C₃₁	—	2	2	no	—
108	C₄²×C₃₁	—	4	2	no	—
109	C₄²×C₃₁	C₂×D₄	1	2	yes	—
110	C₄²×C₃₁	#41	1	4	yes	—
111	C₄²×C₃₁	#41	1	2	yes	—
112	#21271	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₃₁	—	2	2	no	—
114	C₂³×C₃₁	—	2	2	no	—
115	C₂³×C₃₁	—	2	2	no	—
116	C₂³×C₃₁	—	2	2	no	—
117	C₂³×C₃₁	—	2	2	no	—
118	C₂³×C₃₁	—	2	2	no	—
119	C₂³×C₃₁	C₂×M₁₆	1	4	yes	—
120	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
121	D₄×C₃₁	—	2	8	no	—
122	C₂×C₄×C₃₁	—	2	2	no	—
123	C₂×C₄×C₃₁	—	2	2	no	—
124	C₂×C₄×C₃₁	—	2	2	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	2	no	—
127	C₂×C₄×C₃₁	—	2	2	no	—
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	2	no	—
130	C₂×C₄×C₃₁	—	2	2	no	—
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	2	no	—
136	C₂×C₄×C₃₁	—	4	8	no	—
137	C₂×C₄×C₃₁	—	4	8	no	—
138	C₂×C₄×C₃₁	—	4	4	no	—
139	C₂×C₄×C₃₁	—	4	4	no	—
140	C₂×C₄×C₃₁	#117	1	2	yes	—
141	C₂×C₄×C₃₁	#117	1	2	yes	—
142	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
143	C₂×C₄×C₃₁	C₂×M₁₆	1	4	yes	—
144	C₂×C₄×C₃₁	C₂×M₁₆	1	4	yes	—
145	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
147	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
148	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
149	C₈×C₃₁	—	2	4	no	—
150	C₈×C₃₁	—	2	4	no	—
151	C₈×C₃₁	—	4	4	no	—
152	C₂×#432	C₂×C₃₁	1	2	yes	complemented
153	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic
154	#1955	C₂×C₃₁	1	2	yes	—
155	#1940	C₂×C₃₁	1	2	yes	complemented
156	#1923	C₂×C₃₁	1	4	yes	complemented
157	#1767	C₂×C₃₁	1	1	yes	characteristic, complemented
158	#1749	C₂×C₃₁	1	2	yes	complemented
159	C₄×#97	C₂×C₃₁	1	1	yes	characteristic, complemented
160	C₂²×C₃₁	—	2	4	no	—
161	C₂²×C₃₁	—	2	4	no	—
162	C₂²×C₃₁	—	2	4	no	—
163	C₂²×C₃₁	—	4	2	no	—
164	C₂²×C₃₁	—	4	2	no	—
165	C₂²×C₃₁	—	4	2	no	—
166	C₂²×C₃₁	—	4	2	no	—
167	C₂²×C₃₁	C₂×#117	1	1	yes	characteristic
168	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
169	C₂²×C₃₁	C₄×#41	1	1	yes	characteristic
170	C₂²×C₃₁	C₂²×M₁₆	1	2	yes	—
171	C₂²×C₃₁	#568	1	2	yes	—
172	C₄×C₃₁	—	2	2	no	—
173	C₄×C₃₁	—	2	2	no	—
174	C₄×C₃₁	—	2	4	no	—
175	C₄×C₃₁	—	2	4	no	—
176	C₄×C₃₁	—	2	4	no	—
177	C₄×C₃₁	—	4	2	no	—
178	C₄×C₃₁	—	4	2	no	—
179	C₄×C₃₁	#529	1	2	yes	—
180	C₄×C₃₁	#532	1	2	yes	—
181	C₂×C₄×D₄	C₄×C₃₁	1	2	yes	—
182	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
183	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
184	#432	—	2	8	no	—
185	C₂×C₄⋊C₈	C₂²×C₃₁	1	4	yes	—
186	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
187	C₂×C₂²⋊C₈	C₂²×C₃₁	1	4	yes	—
188	C₂×C₂²⋊C₈	C₂²×C₃₁	1	4	yes	—
189	C₂×#97	C₂²×C₃₁	1	2	yes	—
190	C₂×#97	C₂²×C₃₁	1	2	yes	—
191	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
192	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
193	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
194	C₄×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
195	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
196	C₄×C₂²⋊C₄	C₄×C₃₁	1	2	yes	—
197	C₄×C₂²⋊C₄	C₄×C₃₁	1	2	yes	—
198	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
199	C₄³	C₂²×C₃₁	1	1	yes	characteristic
200	#336	C₂²×C₃₁	1	2	yes	—
201	#336	C₂²×C₃₁	1	4	yes	—
202	C₂×C₃₁	—	4	4	no	—
203	C₂×C₃₁	#2293	1	1	yes	characteristic
204	C₂×C₃₁	#2920	1	1	yes	characteristic
205	C₂×C₃₁	#2923	1	1	yes	characteristic
206	C₂×C₃₁	D₄×M₁₆	1	2	yes	—
207	C₂×C₃₁	#2970	1	2	yes	—
208	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
209	C₂³×C₄	C₂×C₄×C₃₁	1	2	yes	—
210	C₂³×C₄	C₂×C₄×C₃₁	1	2	yes	—
211	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
212	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
213	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
214	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
215	C₄×D₄	—	2	8	no	—
216	C₄×D₄	—	2	4	no	—
217	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
219	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
220	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
221	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
222	C₂×C₄²	—	2	4	no	—
223	C₂×C₄²	—	2	4	no	—
224	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
225	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
226	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
227	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
228	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
230	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
232	C₄⋊C₈	—	2	8	no	—
233	C₄⋊C₈	—	2	4	no	—
234	C₂²⋊C₈	—	2	8	no	—
235	C₂²⋊C₈	—	2	8	no	—
236	#97	—	2	4	no	—
237	#97	—	2	4	no	—
238	#97	—	2	2	no	—
239	#97	D₄×C₃₁	1	4	yes	complemented
240	C₄×C₈	—	2	4	no	—
241	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
242	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
243	#95	C₂×C₄×C₃₁	1	2	yes	—
244	#95	C₂×C₄×C₃₁	1	2	yes	—
245	C₃₁	#21271	1	1	yes	characteristic, direct product factor, Sylow
246	C₂⁴	C₂²×C₄×C₃₁	1	2	yes	—
247	C₂×D₄	—	2	4	no	—
248	C₂×D₄	—	2	2	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
260	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
263	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
265	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
266	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
275	C₂×C₈	#41×C₃₁	1	4	yes	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₂²⋊C₄	—	2	4	no	—
279	C₂²⋊C₄	—	2	4	no	—
280	C₂²⋊C₄	M₁₆×C₃₁	1	8	yes	—
281	C₄²	—	2	4	no	—
282	C₄²	—	2	4	no	—
283	C₄²	—	2	4	no	—
284	C₄²	—	2	2	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	4	2	no	—
288	C₄²	C₂×D₄×C₃₁	1	2	yes	—
289	C₄²	#41×C₃₁	1	4	yes	—
290	C₄²	#41×C₃₁	1	2	yes	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	2	no	—
297	C₂³	C₂×M₁₆×C₃₁	1	4	yes	—
298	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
299	D₄	—	2	8	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	4	8	no	—
315	C₂×C₄	—	4	8	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	C₃₁×#117	1	2	yes	—
319	C₂×C₄	C₃₁×#117	1	2	yes	—
320	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
321	C₂×C₄	C₂×M₁₆×C₃₁	1	4	yes	—
322	C₂×C₄	C₂×M₁₆×C₃₁	1	4	yes	—
323	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
324	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
325	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
326	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
327	C₈	—	2	4	no	—
328	C₈	—	2	4	no	—
329	C₈	—	4	4	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	C₂×C₃₁×#117	1	1	yes	characteristic
338	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
339	C₂²	C₄×#41×C₃₁	1	1	yes	characteristic
340	C₂²	C₂²×M₁₆×C₃₁	1	2	yes	—
341	C₂²	C₃₁×#568	1	2	yes	—
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	2	4	no	—
345	C₄	—	2	4	no	—
346	C₄	—	2	4	no	—
347	C₄	—	4	2	no	—
348	C₄	—	4	2	no	—
349	C₄	C₃₁×#529	1	2	yes	—
350	C₄	C₃₁×#532	1	2	yes	—
351	C₂	—	4	4	no	—
352	C₂	C₃₁×#2293	1	1	yes	characteristic
353	C₂	C₃₁×#2920	1	1	yes	characteristic
354	C₂	C₃₁×#2923	1	1	yes	characteristic
355	C₂	D₄×M₁₆×C₃₁	1	2	yes	—
356	C₂	C₃₁×#2970	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#432	C₂	semidirect
4. C₃₁×#1940	C₂	semidirect
5. C₃₁×#1923	C₂	semidirect
6. C₃₁×#1767	C₂	semidirect
7. C₃₁×#1749	C₂	semidirect
8. C₄×C₃₁×#97	C₂	semidirect
61. C₃₁×#97	D₄	semidirect
112. #21271	C₃₁	direct (N × H)
152. C₂×#432	C₂×C₃₁	semidirect
155. #1940	C₂×C₃₁	semidirect
156. #1923	C₂×C₃₁	semidirect
157. #1767	C₂×C₃₁	semidirect
158. #1749	C₂×C₃₁	semidirect
159. C₄×#97	C₂×C₃₁	semidirect
239. #97	D₄×C₃₁	semidirect
245. C₃₁	#21271	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×#432	2
C₄²×D₄×C₃₁	2
C₃₁×#1955	2
C₃₁×#1940	2
C₃₁×#1923	2
C₃₁×#1767	2
C₃₁×#1749	2
C₄×C₃₁×#97	2
#21271	31

Subgroups — C31×#21271 #21478030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#21271 #21478030