Subgroups — C₃₁×#10873 #21467632

Order 7936.

714 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#108	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×#108	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#405	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₁×#344	C₂	1	2	yes	maximal
5	C₃₁×#1738	C₂	1	2	yes	maximal
6	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
7	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
10	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×#108	—	2	1	no	—
12	C₂×C₃₁×#108	—	2	1	no	—
13	C₂×C₃₁×#108	—	2	2	no	—
14	C₂×C₃₁×#108	—	2	2	no	—
15	C₂×C₃₁×#108	—	2	2	no	—
16	C₂×C₃₁×#108	C₄	1	4	yes	complemented
17	C₂×C₃₁×#108	C₄	1	4	yes	complemented
18	C₃₁×#405	—	2	2	no	—
19	C₃₁×#405	C₄	1	4	yes	—
20	C₂×C₃₁×#97	—	2	1	no	—
21	C₂×C₄×C₈×C₃₁	—	2	1	no	—
22	C₃₁×#344	—	2	4	no	—
23	C₃₁×#341	—	2	4	no	—
24	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
25	C₂×M₁₆×C₃₁	—	2	1	no	—
26	C₂×M₁₆×C₃₁	—	2	1	no	—
27	C₂×M₁₆×C₃₁	—	2	1	no	—
28	C₂×M₁₆×C₃₁	—	2	2	no	—
29	C₂×M₁₆×C₃₁	—	2	2	no	—
30	C₂×M₁₆×C₃₁	—	2	2	no	—
31	C₂×M₁₆×C₃₁	—	2	2	no	—
32	C₂×M₁₆×C₃₁	—	2	2	no	—
33	C₂×M₁₆×C₃₁	—	2	2	no	—
34	C₂×M₁₆×C₃₁	—	2	2	no	—
35	C₂×M₁₆×C₃₁	—	2	2	no	—
36	C₂×M₁₆×C₃₁	—	2	2	no	—
37	C₂×M₁₆×C₃₁	—	2	2	no	—
38	C₂×M₁₆×C₃₁	C₂×C₄	1	4	yes	—
39	C₂×M₁₆×C₃₁	C₂×C₄	1	4	yes	—
40	C₂×M₁₆×C₃₁	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₃₁	D₄	1	2	yes	—
42	C₂×M₁₆×C₃₁	Q₈	1	2	yes	—
43	C₂²×C₈×C₃₁	—	2	1	no	—
44	C₂²×C₈×C₃₁	—	2	2	no	—
45	C₂²×C₈×C₃₁	—	2	2	no	—
46	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
47	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
48	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₃₁	D₄	1	2	yes	—
52	C₂²×C₈×C₃₁	D₄	1	2	yes	—
53	C₂²×C₈×C₃₁	Q₈	1	2	yes	—
54	C₃₁×#117	—	2	1	no	—
55	C₃₁×#117	—	2	1	no	—
56	C₃₁×#117	C₂×C₄	1	2	yes	—
57	C₃₁×#117	D₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₃₁	Q₈	1	2	yes	—
60	C₂×C₄²×C₃₁	—	2	1	no	—
61	C₃₁×#108	—	2	4	no	—
62	C₃₁×#108	—	2	4	no	—
63	C₃₁×#108	—	2	8	no	—
64	C₃₁×#97	—	2	4	no	—
65	C₄×C₈×C₃₁	—	2	4	no	—
66	C₂⁴×C₃₁	C₂×Q₈	1	1	yes	characteristic
67	C₂²×C₄×C₃₁	—	2	2	no	—
68	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
79	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
80	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
82	M₁₆×C₃₁	—	2	2	no	—
83	M₁₆×C₃₁	—	2	2	no	—
84	M₁₆×C₃₁	—	2	2	no	—
85	M₁₆×C₃₁	—	2	4	no	—
86	M₁₆×C₃₁	—	2	4	no	—
87	M₁₆×C₃₁	—	2	4	no	—
88	M₁₆×C₃₁	—	2	4	no	—
89	M₁₆×C₃₁	—	4	2	no	—
90	M₁₆×C₃₁	—	4	2	no	—
91	M₁₆×C₃₁	—	4	2	no	—
92	M₁₆×C₃₁	—	4	2	no	—
93	M₁₆×C₃₁	C₄⋊C₄	1	4	yes	—
94	C₂×C₈×C₃₁	—	2	2	no	—
95	C₂×C₈×C₃₁	—	2	2	no	—
96	C₂×C₈×C₃₁	—	2	2	no	—
97	C₂×C₈×C₃₁	—	2	4	no	—
98	C₂×C₈×C₃₁	—	2	4	no	—
99	C₂×C₈×C₃₁	—	4	2	no	—
100	C₂×C₈×C₃₁	—	4	2	no	—
101	C₂×C₈×C₃₁	—	4	2	no	—
102	C₂×C₈×C₃₁	—	4	2	no	—
103	C₂×C₈×C₃₁	C₄²	1	4	yes	—
104	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
105	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
106	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
107	C₂×C₈×C₃₁	C₂²⋊C₄	1	2	yes	—
108	C₂×C₈×C₃₁	C₂²⋊C₄	1	4	yes	—
109	C₂×C₈×C₃₁	C₄⋊C₄	1	4	yes	—
110	C₂×C₈×C₃₁	C₄⋊C₄	1	2	yes	—
111	C₂×C₈×C₃₁	C₄⋊C₄	1	2	yes	—
112	C₂×C₈×C₃₁	C₄⋊C₄	1	4	yes	—
113	C₄⋊C₄×C₃₁	—	2	2	no	—
114	C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₂²⋊C₄×C₃₁	—	2	2	no	—
116	C₂²⋊C₄×C₃₁	C₄⋊C₄	1	4	yes	—
117	C₄²×C₃₁	—	2	2	no	—
118	C₄²×C₃₁	—	2	2	no	—
119	#10873	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₃₁	—	4	2	no	—
121	C₂³×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₃₁	C₄×Q₈	1	1	yes	characteristic
123	C₂³×C₃₁	C₄×Q₈	1	1	yes	characteristic
124	C₂³×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
125	C₂³×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
126	C₂³×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
127	C₂³×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
128	C₂×C₄×C₃₁	—	2	4	no	—
129	C₂×C₄×C₃₁	—	4	4	no	—
130	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
131	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
139	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
140	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₃₁	C₄×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₃₁	C₄×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
147	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
148	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
149	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂×C₄×C₃₁	#124	1	1	yes	characteristic
153	C₂×C₄×C₃₁	#124	1	1	yes	characteristic
154	C₂×C₄×C₃₁	#125	1	1	yes	characteristic
155	C₂×C₄×C₃₁	#125	1	1	yes	characteristic
156	C₂×C₄×C₃₁	#127	1	1	yes	characteristic
157	C₂×C₄×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
158	C₈×C₃₁	—	2	4	no	—
159	C₈×C₃₁	—	4	4	no	—
160	C₈×C₃₁	—	4	4	no	—
161	C₈×C₃₁	#95	1	4	yes	—
162	C₈×C₃₁	#95	1	4	yes	—
163	C₂²×#108	C₂×C₃₁	1	1	yes	characteristic
164	C₂²×#108	C₂×C₃₁	1	1	yes	characteristic
165	C₂×#405	C₂×C₃₁	1	1	yes	characteristic
166	C₂×#344	C₂×C₃₁	1	2	yes	—
167	#1738	C₂×C₃₁	1	2	yes	—
168	C₂²×C₃₁	—	2	2	no	—
169	C₂²×C₃₁	—	2	2	no	—
170	C₂²×C₃₁	—	2	2	no	—
171	C₂²×C₃₁	—	4	1	no	—
172	C₂²×C₃₁	—	4	1	no	—
173	C₂²×C₃₁	—	4	1	no	—
174	C₂²×C₃₁	—	4	1	no	—
175	C₂²×C₃₁	C₄×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₃₁	#380	1	1	yes	characteristic
177	C₂²×C₃₁	#384	1	1	yes	characteristic
178	C₂²×C₃₁	#389	1	1	yes	characteristic
179	C₂²×C₃₁	#389	1	1	yes	characteristic
180	C₂²×C₃₁	#391	1	1	yes	characteristic
181	C₂²×C₃₁	#391	1	1	yes	characteristic
182	C₄×C₃₁	—	4	4	no	—
183	C₄×C₃₁	C₂×#95	1	1	yes	characteristic
184	C₄×C₃₁	C₄×C₄⋊C₄	1	1	yes	characteristic
185	C₄×C₃₁	#380	1	1	yes	characteristic
186	C₄×C₃₁	#382	1	1	yes	characteristic
187	C₄×C₃₁	#389	1	1	yes	characteristic
188	C₄×C₃₁	#389	1	1	yes	characteristic
189	C₄×C₃₁	#390	1	1	yes	characteristic
190	C₄×C₃₁	#390	1	1	yes	characteristic
191	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
192	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
193	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
194	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
195	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
196	C₂×#108	—	2	1	no	—
197	C₂×#108	—	2	1	no	—
198	C₂×#108	—	2	2	no	—
199	C₂×#108	—	2	2	no	—
200	C₂×#108	—	2	2	no	—
201	C₂×#108	C₄×C₃₁	1	4	yes	complemented
202	C₂×#108	C₄×C₃₁	1	4	yes	complemented
203	#405	—	2	2	no	—
204	#405	C₄×C₃₁	1	4	yes	—
205	C₂×#97	—	2	1	no	—
206	C₂×C₄×C₈	—	2	1	no	—
207	#344	—	2	4	no	—
208	#341	—	2	4	no	—
209	C₂×C₃₁	—	2	1	no	—
210	C₂×C₃₁	—	2	1	no	—
211	C₂×C₃₁	—	2	1	no	—
212	C₂×C₃₁	—	2	1	no	—
213	C₂×C₃₁	—	2	1	no	—
214	C₂×C₃₁	—	2	1	no	—
215	C₂×C₃₁	C₄⋊#95	1	1	yes	characteristic
216	C₂×C₃₁	#1953	1	2	yes	—
217	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
218	C₂×M₁₆	—	2	1	no	—
219	C₂×M₁₆	—	2	1	no	—
220	C₂×M₁₆	—	2	1	no	—
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	—	2	2	no	—
227	C₂×M₁₆	—	2	2	no	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	C₂×C₄×C₃₁	1	4	yes	—
232	C₂×M₁₆	C₂×C₄×C₃₁	1	4	yes	—
233	C₂×M₁₆	C₂×C₄×C₃₁	1	2	yes	—
234	C₂×M₁₆	D₄×C₃₁	1	2	yes	—
235	C₂×M₁₆	Q₈×C₃₁	1	2	yes	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
240	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
241	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
242	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
243	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
244	C₂²×C₈	D₄×C₃₁	1	2	yes	—
245	C₂²×C₈	D₄×C₃₁	1	2	yes	—
246	C₂²×C₈	Q₈×C₃₁	1	2	yes	—
247	#117	—	2	1	no	—
248	#117	—	2	1	no	—
249	#117	C₂×C₄×C₃₁	1	2	yes	—
250	#117	D₄×C₃₁	1	2	yes	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	Q₈×C₃₁	1	2	yes	—
253	C₂×C₄²	—	2	1	no	—
254	#108	—	2	4	no	—
255	#108	—	2	4	no	—
256	#108	—	2	8	no	—
257	#97	—	2	4	no	—
258	C₄×C₈	—	2	4	no	—
259	C₃₁	#10873	1	1	yes	characteristic, direct product factor, Sylow
260	C₂⁴	C₂×Q₈×C₃₁	1	1	yes	characteristic
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
263	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
271	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
272	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
273	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
274	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
275	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
276	M₁₆	—	2	2	no	—
277	M₁₆	—	2	2	no	—
278	M₁₆	—	2	2	no	—
279	M₁₆	—	2	4	no	—
280	M₁₆	—	2	4	no	—
281	M₁₆	—	2	4	no	—
282	M₁₆	—	2	4	no	—
283	M₁₆	—	4	2	no	—
284	M₁₆	—	4	2	no	—
285	M₁₆	—	4	2	no	—
286	M₁₆	—	4	2	no	—
287	M₁₆	C₄⋊C₄×C₃₁	1	4	yes	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₂×C₈	—	4	2	no	—
296	C₂×C₈	—	4	2	no	—
297	C₂×C₈	C₄²×C₃₁	1	4	yes	—
298	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
299	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
300	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
301	C₂×C₈	C₂²⋊C₄×C₃₁	1	2	yes	—
302	C₂×C₈	C₂²⋊C₄×C₃₁	1	4	yes	—
303	C₂×C₈	C₄⋊C₄×C₃₁	1	4	yes	—
304	C₂×C₈	C₄⋊C₄×C₃₁	1	2	yes	—
305	C₂×C₈	C₄⋊C₄×C₃₁	1	2	yes	—
306	C₂×C₈	C₄⋊C₄×C₃₁	1	4	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	C₄⋊C₄×C₃₁	1	4	yes	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
315	C₂³	C₄×Q₈×C₃₁	1	1	yes	characteristic
316	C₂³	C₄×Q₈×C₃₁	1	1	yes	characteristic
317	C₂³	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
318	C₂³	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
319	C₂³	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
320	C₂³	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
324	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
325	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
326	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
327	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
331	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
332	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
333	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
334	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
335	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
336	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
337	C₂×C₄	C₄×Q₈×C₃₁	1	1	yes	characteristic
338	C₂×C₄	C₄×Q₈×C₃₁	1	1	yes	characteristic
339	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
340	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
341	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
342	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
343	C₂×C₄	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
344	C₂×C₄	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
345	C₂×C₄	C₃₁×#124	1	1	yes	characteristic
346	C₂×C₄	C₃₁×#124	1	1	yes	characteristic
347	C₂×C₄	C₃₁×#125	1	1	yes	characteristic
348	C₂×C₄	C₃₁×#125	1	1	yes	characteristic
349	C₂×C₄	C₃₁×#127	1	1	yes	characteristic
350	C₂×C₄	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
351	C₈	—	2	4	no	—
352	C₈	—	4	4	no	—
353	C₈	—	4	4	no	—
354	C₈	C₃₁×#95	1	4	yes	—
355	C₈	C₃₁×#95	1	4	yes	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	C₄×C₄⋊C₄×C₃₁	1	1	yes	characteristic
364	C₂²	C₃₁×#380	1	1	yes	characteristic
365	C₂²	C₃₁×#384	1	1	yes	characteristic
366	C₂²	C₃₁×#389	1	1	yes	characteristic
367	C₂²	C₃₁×#389	1	1	yes	characteristic
368	C₂²	C₃₁×#391	1	1	yes	characteristic
369	C₂²	C₃₁×#391	1	1	yes	characteristic
370	C₄	—	4	4	no	—
371	C₄	C₂×C₃₁×#95	1	1	yes	characteristic
372	C₄	C₄×C₄⋊C₄×C₃₁	1	1	yes	characteristic
373	C₄	C₃₁×#380	1	1	yes	characteristic
374	C₄	C₃₁×#382	1	1	yes	characteristic
375	C₄	C₃₁×#389	1	1	yes	characteristic
376	C₄	C₃₁×#389	1	1	yes	characteristic
377	C₄	C₃₁×#390	1	1	yes	characteristic
378	C₄	C₃₁×#390	1	1	yes	characteristic
379	C₂	—	2	1	no	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	C₃₁×C₄⋊#95	1	1	yes	characteristic
386	C₂	C₃₁×#1953	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₃₁	#121
commutator	C₂×C₄	C₂×C₄²×C₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₃₁
socle	C₂²×C₃₁	#389
prime radical	C₂⁴×C₃₁	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₂×C₃₁×#108	C₄	semidirect
17. C₂×C₃₁×#108	C₄	semidirect
119. #10873	C₃₁	direct (N × H)
201. C₂×#108	C₄×C₃₁	semidirect
202. C₂×#108	C₄×C₃₁	semidirect
259. C₃₁	#10873	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#108	2
C₂×C₃₁×#405	2
C₂×C₃₁×#344	2
C₃₁×#1738	2
#10873	31

Subgroups — C31×#10873 #21467632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10873 #21467632