Subgroups — C₃₁×#33691 #21490450

Order 7936.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3173	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2955	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2239	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2238	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2230	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2212	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2191	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2190	C₂	1	1	yes	maximal, characteristic
9	C₃₁×AGL(1,ℤ/16)	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2180	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#575	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#131	—	2	1	no	—
14	C₃₁×#542	—	2	1	no	—
15	C₃₁×#510	C₂²	1	2	yes	—
16	C₃₁×#509	C₂²	1	2	yes	—
17	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
18	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
19	C₃₁×#489	—	2	1	no	—
20	C₃₁×#470	C₂²	1	1	yes	characteristic
21	C₃₁×#469	C₂²	1	1	yes	characteristic
22	C₃₁×#465	—	2	1	no	—
23	C₃₁×#444	—	2	1	no	—
24	C₃₁×#444	C₂²	1	2	yes	—
25	C₃₁×#443	—	2	1	no	—
26	C₃₁×#443	C₂²	1	2	yes	—
27	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
29	C₄×SD₁₆×C₃₁	—	2	1	no	—
30	C₃₁×#430	C₂²	1	1	yes	characteristic
31	C₃₁×#421	—	2	1	no	—
32	C₃₁×#405	C₂²	1	1	yes	characteristic
33	C₃₁×#365	C₂²	1	2	yes	complemented
34	C₃₁×#365	C₂²	1	2	yes	complemented
35	C₃₁×#364	C₂²	1	2	yes	complemented
36	C₃₁×#362	C₂²	1	2	yes	complemented
37	C₃₁×#361	C₂²	1	2	yes	complemented
38	C₃₁×#360	C₂²	1	2	yes	—
39	C₃₁×#360	C₂²	1	2	yes	—
40	C₃₁×#349	C₂²	1	1	yes	characteristic
41	C₃₁×#349	C₂²	1	1	yes	characteristic
42	C₃₁×#347	C₂²	1	2	yes	complemented
43	C₂×#41×C₃₁	—	2	1	no	—
44	C₃₁×#137	—	2	2	no	—
45	C₃₁×AGL(1,ℤ/8)	—	2	2	no	—
46	C₃₁×#135	—	2	1	no	—
47	C₃₁×#135	C₂³	1	2	yes	—
48	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
49	C₂×SD₁₆×C₃₁	—	2	1	no	—
50	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
51	C₃₁×#131	—	2	2	no	—
52	C₃₁×#131	—	2	2	no	—
53	C₃₁×#131	—	4	1	no	—
54	C₃₁×#131	—	4	1	no	—
55	C₂×M₁₆×C₃₁	—	2	1	no	—
56	C₂×M₁₆×C₃₁	—	4	1	no	—
57	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₃₁	—	4	1	no	—
59	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
60	C₃₁×C₄⋊Q₈	—	2	1	no	—
61	C₃₁×#126	—	4	1	no	—
62	C₃₁×#124	—	2	1	no	—
63	C₃₁×#124	—	4	1	no	—
64	C₃₁×#123	—	4	1	no	—
65	C₃₁×C₂²⋊Q₈	—	2	1	no	—
66	C₃₁×C₂²⋊Q₈	—	4	1	no	—
67	C₃₁×#121	—	2	1	no	—
68	C₄×Q₈×C₃₁	—	2	1	no	—
69	C₄×D₄×C₃₁	—	2	1	no	—
70	C₃₁×#117	D₄	1	1	yes	characteristic
71	C₃₁×Q₃₂	—	2	2	no	—
72	C₃₁×SD₃₂	—	2	2	no	—
73	C₃₁×SD₃₂	—	2	2	no	—
74	C₃₁×D₁₆	—	2	2	no	—
75	C₃₁×M₃₂	C₂³	1	2	yes	—
76	C₃₁×M₃₂	C₂³	1	2	yes	—
77	C₃₁×#108	—	2	1	no	—
78	C₃₁×#108	C₂³	1	2	yes	—
79	C₃₁×#106	—	2	1	no	—
80	C₃₁×#106	C₂³	1	1	yes	characteristic
81	C₃₁×#106	C₂³	1	1	yes	characteristic
82	C₃₁×#104	—	2	2	no	—
83	C₃₁×#104	—	2	2	no	—
84	C₃₁×#103	—	2	1	no	—
85	C₃₁×#103	—	2	1	no	—
86	C₃₁×#102	—	2	1	no	—
87	C₃₁×#102	—	2	1	no	—
88	C₃₁×#97	D₄	1	1	yes	characteristic
89	C₃₁×#97	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
91	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
92	#41×C₃₁	—	2	2	no	—
93	#41×C₃₁	—	2	2	no	—
94	#41×C₃₁	—	4	1	no	—
95	#41×C₃₁	—	4	1	no	—
96	C₂×Q₈×C₃₁	—	2	1	no	—
97	C₂×Q₈×C₃₁	—	2	1	no	—
98	C₂×Q₈×C₃₁	—	4	1	no	—
99	C₂×D₄×C₃₁	—	2	1	no	—
100	C₂×D₄×C₃₁	—	2	1	no	—
101	C₂×D₄×C₃₁	—	4	1	no	—
102	C₂×D₄×C₃₁	—	4	1	no	—
103	C₂²×C₄×C₃₁	—	4	1	no	—
104	C₂²×C₄×C₃₁	—	4	1	no	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
106	Q₁₆×C₃₁	—	2	1	no	—
107	Q₁₆×C₃₁	—	2	2	no	—
108	Q₁₆×C₃₁	#41	1	2	yes	—
109	SD₁₆×C₃₁	—	2	2	no	—
110	SD₁₆×C₃₁	—	2	2	no	—
111	SD₁₆×C₃₁	—	4	1	no	—
112	SD₁₆×C₃₁	—	4	1	no	—
113	D₈×C₃₁	—	2	1	no	—
114	D₈×C₃₁	—	2	2	no	—
115	D₈×C₃₁	#41	1	2	yes	—
116	M₁₆×C₃₁	—	2	2	no	—
117	M₁₆×C₃₁	—	2	2	no	—
118	M₁₆×C₃₁	—	4	2	no	—
119	M₁₆×C₃₁	—	4	1	no	—
120	M₁₆×C₃₁	—	4	2	no	—
121	C₂×C₈×C₃₁	—	2	1	no	—
122	C₂×C₈×C₃₁	—	2	1	no	—
123	C₂×C₈×C₃₁	—	4	2	no	—
124	C₂×C₈×C₃₁	—	4	1	no	—
125	C₂×C₈×C₃₁	—	4	2	no	—
126	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	4	1	no	—
134	C₄⋊C₄×C₃₁	—	4	1	no	—
135	C₄⋊C₄×C₃₁	—	4	1	no	—
136	C₂²⋊C₄×C₃₁	—	2	1	no	—
137	C₂²⋊C₄×C₃₁	—	4	1	no	—
138	C₂²⋊C₄×C₃₁	—	4	1	no	—
139	C₂²⋊C₄×C₃₁	—	4	1	no	—
140	C₂²⋊C₄×C₃₁	—	4	1	no	—
141	C₂²⋊C₄×C₃₁	—	4	1	no	—
142	C₄²×C₃₁	—	4	1	no	—
143	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
145	C₁₆×C₃₁	—	2	2	no	—
146	C₁₆×C₃₁	—	2	2	no	—
147	#33691	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₃₁	—	4	1	no	—
149	C₂³×C₃₁	—	4	1	no	—
150	C₂³×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
151	Q₈×C₃₁	—	2	2	no	—
152	Q₈×C₃₁	—	4	1	no	—
153	Q₈×C₃₁	—	4	1	no	—
154	Q₈×C₃₁	—	4	1	no	—
155	Q₈×C₃₁	—	16	1	no	—
156	D₄×C₃₁	—	2	2	no	—
157	D₄×C₃₁	—	4	1	no	—
158	D₄×C₃₁	—	4	2	no	—
159	D₄×C₃₁	—	4	2	no	—
160	D₄×C₃₁	—	4	1	no	—
161	D₄×C₃₁	—	4	1	no	—
162	D₄×C₃₁	—	16	1	no	—
163	C₂×C₄×C₃₁	—	2	1	no	—
164	C₂×C₄×C₃₁	—	2	1	no	—
165	C₂×C₄×C₃₁	—	2	1	no	—
166	C₂×C₄×C₃₁	—	2	1	no	—
167	C₂×C₄×C₃₁	—	4	2	no	—
168	C₂×C₄×C₃₁	—	4	1	no	—
169	C₂×C₄×C₃₁	—	4	2	no	—
170	C₂×C₄×C₃₁	—	4	1	no	—
171	C₂×C₄×C₃₁	—	4	1	no	—
172	C₂×C₄×C₃₁	—	4	1	no	—
173	C₂×C₄×C₃₁	—	16	1	no	—
174	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
176	C₈×C₃₁	—	2	1	no	—
177	C₈×C₃₁	—	2	1	no	—
178	C₈×C₃₁	—	4	2	no	—
179	C₈×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₈×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₈×C₃₁	C₂×#41	1	2	yes	—
182	#3173	C₂×C₃₁	1	1	yes	characteristic, complemented
183	#2955	C₂×C₃₁	1	1	yes	characteristic, complemented
184	#2239	C₂×C₃₁	1	1	yes	characteristic, complemented
185	#2238	C₂×C₃₁	1	1	yes	characteristic, complemented
186	#2230	C₂×C₃₁	1	2	yes	complemented
187	#2212	C₂×C₃₁	1	2	yes	complemented
188	#2191	C₂×C₃₁	1	1	yes	characteristic, complemented
189	#2190	C₂×C₃₁	1	1	yes	characteristic
190	AGL(1,ℤ/16)	C₂×C₃₁	1	2	yes	complemented
191	#2180	C₂×C₃₁	1	2	yes	complemented
192	#2166	C₂×C₃₁	1	1	yes	characteristic, complemented
193	C₂²×C₃₁	—	2	1	no	—
194	C₂²×C₃₁	—	4	1	no	—
195	C₂²×C₃₁	—	4	2	no	—
196	C₂²×C₃₁	—	8	1	no	—
197	C₂²×C₃₁	—	8	1	no	—
198	C₂²×C₃₁	—	8	2	no	—
199	C₂²×C₃₁	—	8	1	no	—
200	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₄×C₃₁	—	2	1	no	—
202	C₄×C₃₁	—	4	1	no	—
203	C₄×C₃₁	—	4	1	no	—
204	C₄×C₃₁	—	4	2	no	—
205	C₄×C₃₁	—	8	1	no	—
206	C₄×C₃₁	—	8	1	no	—
207	C₄×C₃₁	—	8	1	no	—
208	C₄×C₃₁	#525	1	1	yes	characteristic
209	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
210	#575	C₂²×C₃₁	1	1	yes	characteristic
211	C₂×#131	—	2	1	no	—
212	#542	—	2	1	no	—
213	#510	C₂²×C₃₁	1	2	yes	—
214	#509	C₂²×C₃₁	1	2	yes	—
215	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
216	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
217	#489	—	2	1	no	—
218	#470	C₂²×C₃₁	1	1	yes	characteristic
219	#469	C₂²×C₃₁	1	1	yes	characteristic
220	#465	—	2	1	no	—
221	#444	—	2	1	no	—
222	#444	C₂²×C₃₁	1	2	yes	—
223	#443	—	2	1	no	—
224	#443	C₂²×C₃₁	1	2	yes	—
225	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
226	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
227	C₄×SD₁₆	—	2	1	no	—
228	#430	C₂²×C₃₁	1	1	yes	characteristic
229	#421	—	2	1	no	—
230	#405	C₂²×C₃₁	1	1	yes	characteristic
231	#365	C₂²×C₃₁	1	2	yes	complemented
232	#365	C₂²×C₃₁	1	2	yes	complemented
233	#364	C₂²×C₃₁	1	2	yes	complemented
234	#362	C₂²×C₃₁	1	2	yes	complemented
235	#361	C₂²×C₃₁	1	2	yes	complemented
236	#360	C₂²×C₃₁	1	2	yes	—
237	#360	C₂²×C₃₁	1	2	yes	—
238	#349	C₂²×C₃₁	1	1	yes	characteristic
239	#349	C₂²×C₃₁	1	1	yes	characteristic
240	#347	C₂²×C₃₁	1	2	yes	complemented
241	C₂×C₃₁	—	2	1	no	—
242	C₂×C₃₁	—	4	1	no	—
243	C₂×C₃₁	—	8	2	no	—
244	C₂×C₃₁	—	16	1	no	—
245	C₂×C₃₁	#3109	1	1	yes	characteristic
246	C₂×#41	—	2	1	no	—
247	#137	—	2	2	no	—
248	AGL(1,ℤ/8)	—	2	2	no	—
249	#135	—	2	1	no	—
250	#135	C₂³×C₃₁	1	2	yes	—
251	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
252	C₂×SD₁₆	—	2	1	no	—
253	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
254	#131	—	2	2	no	—
255	#131	—	2	2	no	—
256	#131	—	4	1	no	—
257	#131	—	4	1	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	4	1	no	—
260	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
261	C₂²×C₈	—	4	1	no	—
262	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
263	C₄⋊Q₈	—	2	1	no	—
264	#126	—	4	1	no	—
265	#124	—	2	1	no	—
266	#124	—	4	1	no	—
267	#123	—	4	1	no	—
268	C₂²⋊Q₈	—	2	1	no	—
269	C₂²⋊Q₈	—	4	1	no	—
270	#121	—	2	1	no	—
271	C₄×Q₈	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	#117	D₄×C₃₁	1	1	yes	characteristic
274	Q₃₂	—	2	2	no	—
275	SD₃₂	—	2	2	no	—
276	SD₃₂	—	2	2	no	—
277	D₁₆	—	2	2	no	—
278	M₃₂	C₂³×C₃₁	1	2	yes	—
279	M₃₂	C₂³×C₃₁	1	2	yes	—
280	#108	—	2	1	no	—
281	#108	C₂³×C₃₁	1	2	yes	—
282	#106	—	2	1	no	—
283	#106	C₂³×C₃₁	1	1	yes	characteristic
284	#106	C₂³×C₃₁	1	1	yes	characteristic
285	#104	—	2	2	no	—
286	#104	—	2	2	no	—
287	#103	—	2	1	no	—
288	#103	—	2	1	no	—
289	#102	—	2	1	no	—
290	#102	—	2	1	no	—
291	#97	D₄×C₃₁	1	1	yes	characteristic
292	#97	C₂³×C₃₁	1	1	yes	characteristic
293	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
294	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
295	C₃₁	#33691	1	1	yes	characteristic, direct product factor, Sylow
296	#41	—	2	2	no	—
297	#41	—	2	2	no	—
298	#41	—	4	1	no	—
299	#41	—	4	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
310	Q₁₆	—	2	1	no	—
311	Q₁₆	—	2	2	no	—
312	Q₁₆	#41×C₃₁	1	2	yes	—
313	SD₁₆	—	2	2	no	—
314	SD₁₆	—	2	2	no	—
315	SD₁₆	—	4	1	no	—
316	SD₁₆	—	4	1	no	—
317	D₈	—	2	1	no	—
318	D₈	—	2	2	no	—
319	D₈	#41×C₃₁	1	2	yes	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	4	2	no	—
323	M₁₆	—	4	1	no	—
324	M₁₆	—	4	2	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	2	no	—
330	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
331	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
332	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
333	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₄²	—	4	1	no	—
347	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
348	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
349	C₁₆	—	2	2	no	—
350	C₁₆	—	2	2	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	4	1	no	—
358	Q₈	—	16	1	no	—
359	D₄	—	2	2	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	1	no	—
364	D₄	—	4	1	no	—
365	D₄	—	16	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	16	1	no	—
377	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
379	C₈	—	2	1	no	—
380	C₈	—	2	1	no	—
381	C₈	—	4	2	no	—
382	C₈	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
383	C₈	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
384	C₈	C₂×#41×C₃₁	1	2	yes	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	1	no	—
392	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	2	no	—
397	C₄	—	8	1	no	—
398	C₄	—	8	1	no	—
399	C₄	—	8	1	no	—
400	C₄	C₃₁×#525	1	1	yes	characteristic
401	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
402	C₂	—	2	1	no	—
403	C₂	—	4	1	no	—
404	C₂	—	8	2	no	—
405	C₂	—	16	1	no	—
406	C₂	C₃₁×#3109	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₁	#3109
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	C₃₁×#2190	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₁ ◁ C₂×C₄×C₃₁ ◁ C₃₁×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3173	C₂	semidirect
2. C₃₁×#2955	C₂	semidirect
3. C₃₁×#2239	C₂	semidirect
4. C₃₁×#2238	C₂	semidirect
5. C₃₁×#2230	C₂	semidirect
6. C₃₁×#2212	C₂	semidirect
7. C₃₁×#2191	C₂	semidirect
9. C₃₁×AGL(1,ℤ/16)	C₂	semidirect
10. C₃₁×#2180	C₂	semidirect
11. C₃₁×#2166	C₂	semidirect
17. C₃₁×#498	C₂²	semidirect
18. C₃₁×#495	C₂²	semidirect
27. C₃₁×#442	C₂²	semidirect
28. C₃₁×#441	C₂²	semidirect
33. C₃₁×#365	C₂²	semidirect
34. C₃₁×#365	C₂²	semidirect
35. C₃₁×#364	C₂²	semidirect
36. C₃₁×#362	C₂²	semidirect
37. C₃₁×#361	C₂²	semidirect
42. C₃₁×#347	C₂²	semidirect
147. #33691	C₃₁	direct (N × H)
182. #3173	C₂×C₃₁	semidirect
183. #2955	C₂×C₃₁	semidirect
184. #2239	C₂×C₃₁	semidirect
185. #2238	C₂×C₃₁	semidirect
186. #2230	C₂×C₃₁	semidirect
187. #2212	C₂×C₃₁	semidirect
188. #2191	C₂×C₃₁	semidirect
190. AGL(1,ℤ/16)	C₂×C₃₁	semidirect
191. #2180	C₂×C₃₁	semidirect
192. #2166	C₂×C₃₁	semidirect
215. #498	C₂²×C₃₁	semidirect
216. #495	C₂²×C₃₁	semidirect
225. #442	C₂²×C₃₁	semidirect
226. #441	C₂²×C₃₁	semidirect
231. #365	C₂²×C₃₁	semidirect
232. #365	C₂²×C₃₁	semidirect
233. #364	C₂²×C₃₁	semidirect
234. #362	C₂²×C₃₁	semidirect
235. #361	C₂²×C₃₁	semidirect
240. #347	C₂²×C₃₁	semidirect
295. C₃₁	#33691	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3173	2
C₃₁×#2955	2
C₃₁×#2239	2
C₃₁×#2238	2
C₃₁×#2230	2
C₃₁×#2212	2
C₃₁×#2191	2
C₃₁×#2190	2
C₃₁×AGL(1,ℤ/16)	2
C₃₁×#2180	2
C₃₁×#2166	2
#33691	31

Subgroups — C31×#33691 #21490450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33691 #21490450