Subgroups — C₃₁×#33144 #21489903

Order 7936.

858 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#470	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2855	C₂	1	2	yes	maximal
4	C₃₁×#1971	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1935	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1933	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1894	C₂	1	2	yes	maximal
11	C₃₁×#1809	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#470	—	2	4	no	—
18	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#103	C₂²	1	2	yes	—
22	C₂×C₃₁×#103	C₂²	1	2	yes	—
23	C₂×C₃₁×#103	C₂²	1	2	yes	—
24	C₄×M₁₆×C₃₁	—	2	4	no	—
25	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#391	C₂²	1	2	yes	—
30	C₃₁×#391	C₂²	1	2	yes	—
31	C₃₁×#389	C₂²	1	2	yes	—
32	C₃₁×#389	C₂²	1	2	yes	—
33	C₃₁×#387	—	2	2	no	—
34	C₃₁×#387	—	2	2	no	—
35	C₃₁×#385	—	2	2	no	—
36	C₃₁×#381	—	2	2	no	—
37	C₃₁×#380	C₂²	1	2	yes	—
38	C₃₁×#340	C₂²	1	2	yes	—
39	C₃₁×#340	C₂²	1	2	yes	—
40	C₃₁×#340	C₂²	1	2	yes	—
41	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₃₁	D₄	1	2	yes	—
43	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₃₁	—	2	2	no	—
45	C₂×Q₁₆×C₃₁	—	2	2	no	—
46	C₂×Q₁₆×C₃₁	—	2	2	no	—
47	C₂×M₁₆×C₃₁	—	2	2	no	—
48	C₂×M₁₆×C₃₁	—	2	2	no	—
49	C₂×M₁₆×C₃₁	—	2	2	no	—
50	C₂×M₁₆×C₃₁	—	2	2	no	—
51	C₂×M₁₆×C₃₁	—	2	2	no	—
52	C₂×M₁₆×C₃₁	D₄	1	4	yes	—
53	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
57	C₃₁×C₂²⋊Q₈	—	2	4	no	—
58	C₃₁×C₂²⋊Q₈	—	2	4	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
67	C₂×C₄²×C₃₁	—	2	2	no	—
68	C₂×C₄²×C₃₁	—	2	2	no	—
69	C₂×C₄²×C₃₁	D₄	1	2	yes	—
70	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
72	C₃₁×#107	—	2	2	no	—
73	C₃₁×#106	—	2	2	no	—
74	C₃₁×#106	—	2	2	no	—
75	C₃₁×#103	—	2	4	no	—
76	C₃₁×#103	—	2	4	no	—
77	C₃₁×#103	—	2	4	no	—
78	C₃₁×#97	—	2	2	no	—
79	C₃₁×#97	—	2	2	no	—
80	C₄×C₈×C₃₁	—	2	2	no	—
81	C₄×C₈×C₃₁	—	2	2	no	—
82	C₃₁×#95	—	2	2	no	—
83	C₃₁×#95	—	2	2	no	—
84	C₃₁×#95	—	2	2	no	—
85	C₃₁×#95	—	2	2	no	—
86	C₃₁×#95	—	2	2	no	—
87	C₃₁×#95	—	2	2	no	—
88	C₃₁×#95	—	2	2	no	—
89	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₃₁	—	2	2	no	—
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	—	2	2	no	—
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	—	2	2	no	—
96	C₂²×C₄×C₃₁	—	2	1	no	—
97	C₂²×C₄×C₃₁	—	2	1	no	—
98	C₂²×C₄×C₃₁	—	2	1	no	—
99	C₂²×C₄×C₃₁	—	2	1	no	—
100	C₂²×C₄×C₃₁	—	2	4	no	—
101	C₂²×C₄×C₃₁	—	2	4	no	—
102	C₂²×C₄×C₃₁	—	2	2	no	—
103	C₂²×C₄×C₃₁	—	2	2	no	—
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	—	2	2	no	—
106	C₂²×C₄×C₃₁	—	4	2	no	—
107	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₃₁	#41	1	2	yes	—
112	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₃₁	—	4	4	no	—
114	M₁₆×C₃₁	—	2	8	no	—
115	M₁₆×C₃₁	—	2	8	no	—
116	C₂×C₈×C₃₁	—	2	1	no	—
117	C₂×C₈×C₃₁	—	2	1	no	—
118	C₂×C₈×C₃₁	—	2	1	no	—
119	C₂×C₈×C₃₁	—	2	1	no	—
120	C₂×C₈×C₃₁	—	2	1	no	—
121	C₂×C₈×C₃₁	—	2	1	no	—
122	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₃₁	#41	1	2	yes	—
125	C₂×C₈×C₃₁	#41	1	2	yes	—
126	C₂×C₈×C₃₁	#41	1	2	yes	—
127	C₂×C₈×C₃₁	#41	1	2	yes	—
128	C₄⋊C₄×C₃₁	—	2	2	no	—
129	C₄⋊C₄×C₃₁	—	2	2	no	—
130	C₄⋊C₄×C₃₁	—	2	2	no	—
131	C₄⋊C₄×C₃₁	—	2	2	no	—
132	C₄⋊C₄×C₃₁	—	2	2	no	—
133	C₄⋊C₄×C₃₁	—	2	2	no	—
134	C₄⋊C₄×C₃₁	—	4	4	no	—
135	C₄⋊C₄×C₃₁	—	4	4	no	—
136	C₄⋊C₄×C₃₁	—	4	4	no	—
137	C₂²⋊C₄×C₃₁	—	4	4	no	—
138	C₂²⋊C₄×C₃₁	—	4	4	no	—
139	C₄²×C₃₁	—	2	4	no	—
140	C₄²×C₃₁	—	2	1	no	—
141	C₄²×C₃₁	—	2	1	no	—
142	C₄²×C₃₁	—	2	1	no	—
143	C₄²×C₃₁	—	2	1	no	—
144	#33144	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	#121	1	2	yes	—
150	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₃₁	—	4	2	no	—
152	Q₈×C₃₁	—	4	2	no	—
153	Q₈×C₃₁	—	4	2	no	—
154	Q₈×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	2	1	no	—
157	C₂×C₄×C₃₁	—	2	1	no	—
158	C₂×C₄×C₃₁	—	2	2	no	—
159	C₂×C₄×C₃₁	—	2	2	no	—
160	C₂×C₄×C₃₁	—	2	2	no	—
161	C₂×C₄×C₃₁	—	2	2	no	—
162	C₂×C₄×C₃₁	—	2	2	no	—
163	C₂×C₄×C₃₁	—	2	2	no	—
164	C₂×C₄×C₃₁	—	2	2	no	—
165	C₂×C₄×C₃₁	—	2	2	no	—
166	C₂×C₄×C₃₁	—	4	8	no	—
167	C₂×C₄×C₃₁	—	4	2	no	—
168	C₂×C₄×C₃₁	—	4	2	no	—
169	C₂×C₄×C₃₁	—	4	2	no	—
170	C₂×C₄×C₃₁	—	4	2	no	—
171	C₂×C₄×C₃₁	—	4	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	2	no	—
177	C₂×C₄×C₃₁	—	4	2	no	—
178	C₂×C₄×C₃₁	—	4	2	no	—
179	C₂×C₄×C₃₁	#121	1	2	yes	—
180	C₂×C₄×C₃₁	#137	1	4	yes	—
181	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
187	C₈×C₃₁	—	2	2	no	—
188	C₈×C₃₁	—	2	2	no	—
189	C₈×C₃₁	—	2	2	no	—
190	C₈×C₃₁	#123	1	4	yes	—
191	C₂×#470	C₂×C₃₁	1	1	yes	characteristic
192	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic
193	#2855	C₂×C₃₁	1	2	yes	—
194	#1971	C₂×C₃₁	1	1	yes	characteristic, complemented
195	#1969	C₂×C₃₁	1	1	yes	characteristic, complemented
196	#1943	C₂×C₃₁	1	1	yes	characteristic, complemented
197	#1941	C₂×C₃₁	1	1	yes	characteristic, complemented
198	#1935	C₂×C₃₁	1	2	yes	complemented
199	#1933	C₂×C₃₁	1	2	yes	complemented
200	#1894	C₂×C₃₁	1	2	yes	—
201	#1809	C₂×C₃₁	1	1	yes	characteristic
202	C₂²×C₃₁	—	2	2	no	—
203	C₂²×C₃₁	—	2	4	no	—
204	C₂²×C₃₁	—	4	2	no	—
205	C₂²×C₃₁	—	4	1	no	—
206	C₂²×C₃₁	—	4	1	no	—
207	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
208	C₂²×C₃₁	#532	1	1	yes	characteristic
209	C₂²×C₃₁	#532	1	1	yes	characteristic
210	C₂²×C₃₁	C₂×#137	1	2	yes	—
211	C₂²×C₃₁	#575	1	2	yes	—
212	C₄×C₃₁	—	2	2	no	—
213	C₄×C₃₁	—	2	4	no	—
214	C₄×C₃₁	—	4	2	no	—
215	C₄×C₃₁	—	8	2	no	—
216	C₄×C₃₁	—	8	2	no	—
217	C₄×C₃₁	—	8	2	no	—
218	C₄×C₃₁	—	8	2	no	—
219	C₄×C₃₁	C₂×#123	1	1	yes	characteristic
220	C₄×C₃₁	#525	1	1	yes	characteristic
221	C₄×C₃₁	#529	1	1	yes	characteristic
222	C₄×C₃₁	#529	1	1	yes	characteristic
223	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
224	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
225	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
226	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
227	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
228	#470	—	2	4	no	—
229	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
230	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
231	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
232	C₂×#103	C₂²×C₃₁	1	2	yes	—
233	C₂×#103	C₂²×C₃₁	1	2	yes	—
234	C₂×#103	C₂²×C₃₁	1	2	yes	—
235	C₄×M₁₆	—	2	4	no	—
236	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
237	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
239	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
240	#391	C₂²×C₃₁	1	2	yes	—
241	#391	C₂²×C₃₁	1	2	yes	—
242	#389	C₂²×C₃₁	1	2	yes	—
243	#389	C₂²×C₃₁	1	2	yes	—
244	#387	—	2	2	no	—
245	#387	—	2	2	no	—
246	#385	—	2	2	no	—
247	#381	—	2	2	no	—
248	#380	C₂²×C₃₁	1	2	yes	—
249	#340	C₂²×C₃₁	1	2	yes	—
250	#340	C₂²×C₃₁	1	2	yes	—
251	#340	C₂²×C₃₁	1	2	yes	—
252	C₂×C₃₁	—	4	2	no	—
253	C₂×C₃₁	#2854	1	1	yes	characteristic
254	C₂×C₃₁	#3056	1	2	yes	—
255	C₂×C₃₁	#3172	1	2	yes	—
256	C₂×C₃₁	#3183	1	1	yes	characteristic
257	C₂×C₃₁	#3185	1	1	yes	characteristic
258	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
259	C₂³×C₄	D₄×C₃₁	1	2	yes	—
260	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
261	C₂×Q₁₆	—	2	2	no	—
262	C₂×Q₁₆	—	2	2	no	—
263	C₂×Q₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	2	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	D₄×C₃₁	1	4	yes	—
270	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
274	C₂²⋊Q₈	—	2	4	no	—
275	C₂²⋊Q₈	—	2	4	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	D₄×C₃₁	1	2	yes	—
287	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
289	#107	—	2	2	no	—
290	#106	—	2	2	no	—
291	#106	—	2	2	no	—
292	#103	—	2	4	no	—
293	#103	—	2	4	no	—
294	#103	—	2	4	no	—
295	#97	—	2	2	no	—
296	#97	—	2	2	no	—
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	C₃₁	#33144	1	1	yes	characteristic, direct product factor, Sylow
307	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
329	C₂²×C₄	#41×C₃₁	1	2	yes	—
330	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
331	Q₁₆	—	4	4	no	—
332	M₁₆	—	2	8	no	—
333	M₁₆	—	2	8	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
341	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
342	C₂×C₈	#41×C₃₁	1	2	yes	—
343	C₂×C₈	#41×C₃₁	1	2	yes	—
344	C₂×C₈	#41×C₃₁	1	2	yes	—
345	C₂×C₈	#41×C₃₁	1	2	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	4	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₄²	—	2	4	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	C₃₁×#121	1	2	yes	—
367	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	C₃₁×#121	1	2	yes	—
397	C₂×C₄	C₃₁×#137	1	4	yes	—
398	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
399	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
400	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
401	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
403	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
404	C₈	—	2	2	no	—
405	C₈	—	2	2	no	—
406	C₈	—	2	2	no	—
407	C₈	C₃₁×#123	1	4	yes	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
414	C₂²	C₃₁×#532	1	1	yes	characteristic
415	C₂²	C₃₁×#532	1	1	yes	characteristic
416	C₂²	C₂×C₃₁×#137	1	2	yes	—
417	C₂²	C₃₁×#575	1	2	yes	—
418	C₄	—	2	2	no	—
419	C₄	—	2	4	no	—
420	C₄	—	4	2	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	—	8	2	no	—
424	C₄	—	8	2	no	—
425	C₄	C₂×C₃₁×#123	1	1	yes	characteristic
426	C₄	C₃₁×#525	1	1	yes	characteristic
427	C₄	C₃₁×#529	1	1	yes	characteristic
428	C₄	C₃₁×#529	1	1	yes	characteristic
429	C₂	—	4	2	no	—
430	C₂	C₃₁×#2854	1	1	yes	characteristic
431	C₂	C₃₁×#3056	1	2	yes	—
432	C₂	C₃₁×#3172	1	2	yes	—
433	C₂	C₃₁×#3183	1	1	yes	characteristic
434	C₂	C₃₁×#3185	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1971	C₂	semidirect
5. C₃₁×#1969	C₂	semidirect
6. C₃₁×#1943	C₂	semidirect
7. C₃₁×#1941	C₂	semidirect
8. C₃₁×#1935	C₂	semidirect
9. C₃₁×#1933	C₂	semidirect
144. #33144	C₃₁	direct (N × H)
194. #1971	C₂×C₃₁	semidirect
195. #1969	C₂×C₃₁	semidirect
196. #1943	C₂×C₃₁	semidirect
197. #1941	C₂×C₃₁	semidirect
198. #1935	C₂×C₃₁	semidirect
199. #1933	C₂×C₃₁	semidirect
306. C₃₁	#33144	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×#470	2
C₂×C₄×M₁₆×C₃₁	2
C₃₁×#2855	2
C₃₁×#1971	2
C₃₁×#1969	2
C₃₁×#1943	2
C₃₁×#1941	2
C₃₁×#1935	2
C₃₁×#1933	2
C₃₁×#1894	2
C₃₁×#1809	2
#33144	31

Subgroups — C31×#33144 #21489903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33144 #21489903