Subgroups — C₃₁×#19995 #21476754

Order 7936.

638 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3391	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3304	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1709	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1681	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1670	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1668	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1642	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1628	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#556	C₂²	1	2	yes	—
13	C₃₁×#550	C₂²	1	2	yes	—
14	C₃₁×#495	—	2	1	no	—
15	C₃₁×#494	C₂²	1	1	yes	characteristic
16	C₃₁×#493	—	2	1	no	—
17	C₃₁×#493	C₂²	1	1	yes	characteristic
18	C₃₁×#486	C₂²	1	2	yes	—
19	C₃₁×#486	C₂²	1	2	yes	—
20	C₃₁×#482	—	2	2	no	—
21	C₃₁×#475	C₂²	1	2	yes	—
22	C₃₁×#465	—	2	2	no	—
23	C₃₁×#464	—	2	2	no	—
24	C₃₁×#461	C₂²	1	2	yes	—
25	C₃₁×#460	C₂²	1	2	yes	—
26	C₃₁×#459	—	2	2	no	—
27	C₃₁×#459	C₂²	1	2	yes	—
28	C₃₁×#452	—	2	2	no	—
29	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₄×Q₁₆×C₃₁	—	2	1	no	—
32	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
33	C₄×D₈×C₃₁	—	2	1	no	—
34	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₈×D₄×C₃₁	C₂²	1	2	yes	—
36	C₃₁×#416	—	2	2	no	—
37	C₃₁×#335	C₂²	1	1	yes	characteristic
38	C₃₁×#335	C₂²	1	1	yes	characteristic
39	C₃₁×#332	C₂²	1	2	yes	—
40	C₃₁×#331	C₂²	1	2	yes	—
41	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₃₁×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×#41×C₃₁	—	2	2	no	—
46	C₂×Q₁₆×C₃₁	—	2	1	no	—
47	C₂×Q₁₆×C₃₁	—	2	1	no	—
48	C₂×Q₁₆×C₃₁	D₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₃₁	—	2	2	no	—
50	C₂×SD₁₆×C₃₁	—	2	2	no	—
51	C₂×D₈×C₃₁	—	2	2	no	—
52	C₂×D₈×C₃₁	—	2	1	no	—
53	C₂×D₈×C₃₁	—	2	1	no	—
54	C₂×D₈×C₃₁	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₃₁	—	2	2	no	—
56	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₃₁×#127	—	2	2	no	—
58	C₃₁×#127	C₂³	1	2	yes	—
59	C₃₁×#126	—	4	2	no	—
60	C₃₁×#124	—	2	2	no	—
61	C₃₁×C₂²⋊Q₈	—	2	2	no	—
62	C₃₁×#121	—	2	2	no	—
63	C₃₁×#121	—	4	2	no	—
64	C₄×Q₈×C₃₁	—	2	2	no	—
65	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
66	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₃₁	—	2	2	no	—
68	C₄×D₄×C₃₁	C₂³	1	2	yes	—
69	C₃₁×#117	—	2	2	no	—
70	C₃₁×#107	D₄	1	1	yes	characteristic
71	C₃₁×#107	D₄	1	1	yes	characteristic
72	C₃₁×#106	—	2	2	no	—
73	C₃₁×C₄⋊C₈	—	2	1	no	—
74	C₃₁×C₄⋊C₈	—	2	1	no	—
75	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
76	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₃₁×#103	—	2	2	no	—
79	C₃₁×#103	—	2	2	no	—
80	C₃₁×#103	D₄	1	1	yes	characteristic
81	C₃₁×#103	D₄	1	1	yes	characteristic
82	C₃₁×#102	—	2	2	no	—
83	C₃₁×#102	—	2	2	no	—
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×#102	—	2	2	no	—
86	C₃₁×#102	—	4	2	no	—
87	C₃₁×#102	D₄	1	2	yes	—
88	C₃₁×C₂²⋊C₈	—	2	2	no	—
89	C₄×C₈×C₃₁	—	2	1	no	—
90	C₄×C₈×C₃₁	—	2	1	no	—
91	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
94	#41×C₃₁	—	4	4	no	—
95	#41×C₃₁	—	8	2	no	—
96	C₂×Q₈×C₃₁	—	2	2	no	—
97	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
99	C₂×D₄×C₃₁	—	2	2	no	—
100	C₂×D₄×C₃₁	—	2	2	no	—
101	C₂×D₄×C₃₁	—	2	2	no	—
102	C₂×D₄×C₃₁	—	4	2	no	—
103	C₂×D₄×C₃₁	—	4	2	no	—
104	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₃₁	—	2	2	no	—
106	C₂²×C₄×C₃₁	—	4	2	no	—
107	Q₁₆×C₃₁	—	2	2	no	—
108	Q₁₆×C₃₁	—	4	2	no	—
109	Q₁₆×C₃₁	—	8	1	no	—
110	SD₁₆×C₃₁	—	8	2	no	—
111	SD₁₆×C₃₁	—	8	2	no	—
112	D₈×C₃₁	—	2	2	no	—
113	D₈×C₃₁	—	4	2	no	—
114	D₈×C₃₁	—	8	1	no	—
115	D₈×C₃₁	—	8	2	no	—
116	C₂×C₈×C₃₁	—	2	1	no	—
117	C₂×C₈×C₃₁	—	2	1	no	—
118	C₂×C₈×C₃₁	—	2	2	no	—
119	C₂×C₈×C₃₁	—	2	1	no	—
120	C₂×C₈×C₃₁	—	8	2	no	—
121	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₃₁	—	2	1	no	—
126	C₄⋊C₄×C₃₁	—	2	1	no	—
127	C₄⋊C₄×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	2	2	no	—
129	C₄⋊C₄×C₃₁	—	4	2	no	—
130	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
131	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₃₁	—	2	2	no	—
134	C₂²⋊C₄×C₃₁	—	4	2	no	—
135	C₂²⋊C₄×C₃₁	—	4	2	no	—
136	C₂²⋊C₄×C₃₁	—	4	2	no	—
137	C₄²×C₃₁	—	2	1	no	—
138	C₄²×C₃₁	—	2	1	no	—
139	C₄²×C₃₁	—	4	2	no	—
140	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
141	#19995	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₃₁	—	2	2	no	—
143	C₂³×C₃₁	—	4	2	no	—
144	Q₈×C₃₁	—	2	1	no	—
145	Q₈×C₃₁	—	2	1	no	—
146	Q₈×C₃₁	—	2	1	no	—
147	Q₈×C₃₁	—	4	2	no	—
148	Q₈×C₃₁	—	4	2	no	—
149	Q₈×C₃₁	#135	1	2	yes	—
150	D₄×C₃₁	—	2	2	no	—
151	D₄×C₃₁	—	2	2	no	—
152	D₄×C₃₁	—	4	2	no	—
153	D₄×C₃₁	—	4	2	no	—
154	D₄×C₃₁	—	4	2	no	—
155	D₄×C₃₁	—	4	2	no	—
156	D₄×C₃₁	—	8	4	no	—
157	D₄×C₃₁	—	8	2	no	—
158	D₄×C₃₁	—	16	2	no	—
159	C₂×C₄×C₃₁	—	2	1	no	—
160	C₂×C₄×C₃₁	—	2	1	no	—
161	C₂×C₄×C₃₁	—	2	1	no	—
162	C₂×C₄×C₃₁	—	2	1	no	—
163	C₂×C₄×C₃₁	—	2	2	no	—
164	C₂×C₄×C₃₁	—	4	2	no	—
165	C₂×C₄×C₃₁	—	4	2	no	—
166	C₂×C₄×C₃₁	—	4	2	no	—
167	C₂×C₄×C₃₁	—	8	4	no	—
168	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
171	C₈×C₃₁	—	2	1	no	—
172	C₈×C₃₁	—	2	1	no	—
173	C₈×C₃₁	—	2	1	no	—
174	C₈×C₃₁	—	4	1	no	—
175	C₈×C₃₁	—	4	2	no	—
176	C₈×C₃₁	—	4	1	no	—
177	C₈×C₃₁	—	4	1	no	—
178	C₈×C₃₁	#135	1	2	yes	—
179	#3393	C₂×C₃₁	1	1	yes	characteristic, complemented
180	#3391	C₂×C₃₁	1	1	yes	characteristic
181	#3304	C₂×C₃₁	1	2	yes	complemented
182	#1709	C₂×C₃₁	1	1	yes	characteristic, complemented
183	#1681	C₂×C₃₁	1	2	yes	complemented
184	#1670	C₂×C₃₁	1	1	yes	characteristic, complemented
185	#1668	C₂×C₃₁	1	1	yes	characteristic, complemented
186	#1642	C₂×C₃₁	1	2	yes	complemented
187	#1628	C₂×C₃₁	1	2	yes	complemented
188	C₈×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
189	C₈×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
190	C₂²×C₃₁	—	4	2	no	—
191	C₂²×C₃₁	—	4	2	no	—
192	C₂²×C₃₁	—	4	2	no	—
193	C₂²×C₃₁	—	8	2	no	—
194	C₂²×C₃₁	—	8	2	no	—
195	C₂²×C₃₁	—	8	2	no	—
196	C₂²×C₃₁	D₄²	1	1	yes	characteristic
197	C₄×C₃₁	—	2	2	no	—
198	C₄×C₃₁	—	2	1	no	—
199	C₄×C₃₁	—	4	2	no	—
200	C₄×C₃₁	—	4	1	no	—
201	C₄×C₃₁	—	4	1	no	—
202	C₄×C₃₁	—	4	1	no	—
203	C₄×C₃₁	—	8	2	no	—
204	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
205	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
206	C₄×C₃₁	#576	1	1	yes	characteristic
207	C₄×C₃₁	#576	1	1	yes	characteristic
208	#556	C₂²×C₃₁	1	2	yes	—
209	#550	C₂²×C₃₁	1	2	yes	—
210	#495	—	2	1	no	—
211	#494	C₂²×C₃₁	1	1	yes	characteristic
212	#493	—	2	1	no	—
213	#493	C₂²×C₃₁	1	1	yes	characteristic
214	#486	C₂²×C₃₁	1	2	yes	—
215	#486	C₂²×C₃₁	1	2	yes	—
216	#482	—	2	2	no	—
217	#475	C₂²×C₃₁	1	2	yes	—
218	#465	—	2	2	no	—
219	#464	—	2	2	no	—
220	#461	C₂²×C₃₁	1	2	yes	—
221	#460	C₂²×C₃₁	1	2	yes	—
222	#459	—	2	2	no	—
223	#459	C₂²×C₃₁	1	2	yes	—
224	#452	—	2	2	no	—
225	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
226	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
227	C₄×Q₁₆	—	2	1	no	—
228	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
229	C₄×D₈	—	2	1	no	—
230	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
231	C₈×D₄	C₂²×C₃₁	1	2	yes	—
232	#416	—	2	2	no	—
233	#335	C₂²×C₃₁	1	1	yes	characteristic
234	#335	C₂²×C₃₁	1	1	yes	characteristic
235	#332	C₂²×C₃₁	1	2	yes	—
236	#331	C₂²×C₃₁	1	2	yes	—
237	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
238	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
239	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
240	C₈²	C₂²×C₃₁	1	1	yes	characteristic
241	C₂×C₃₁	—	8	2	no	—
242	C₂×C₃₁	—	16	2	no	—
243	C₂×C₃₁	#3280	1	1	yes	characteristic
244	C₂×C₃₁	#3287	1	1	yes	characteristic
245	C₂×C₃₁	#3290	1	1	yes	characteristic
246	C₂×#41	—	2	2	no	—
247	C₂×Q₁₆	—	2	1	no	—
248	C₂×Q₁₆	—	2	1	no	—
249	C₂×Q₁₆	D₄×C₃₁	1	1	yes	characteristic
250	C₂×SD₁₆	—	2	2	no	—
251	C₂×SD₁₆	—	2	2	no	—
252	C₂×D₈	—	2	2	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂×D₈	—	2	1	no	—
255	C₂×D₈	D₄×C₃₁	1	1	yes	characteristic
256	C₂²×C₈	—	2	2	no	—
257	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
258	#127	—	2	2	no	—
259	#127	C₂³×C₃₁	1	2	yes	—
260	#126	—	4	2	no	—
261	#124	—	2	2	no	—
262	C₂²⋊Q₈	—	2	2	no	—
263	#121	—	2	2	no	—
264	#121	—	4	2	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
267	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	C₂³×C₃₁	1	2	yes	—
270	#117	—	2	2	no	—
271	#107	D₄×C₃₁	1	1	yes	characteristic
272	#107	D₄×C₃₁	1	1	yes	characteristic
273	#106	—	2	2	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
277	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
278	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
279	#103	—	2	2	no	—
280	#103	—	2	2	no	—
281	#103	D₄×C₃₁	1	1	yes	characteristic
282	#103	D₄×C₃₁	1	1	yes	characteristic
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	—	4	2	no	—
288	#102	D₄×C₃₁	1	2	yes	—
289	C₂²⋊C₈	—	2	2	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
293	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
294	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
295	C₃₁	#19995	1	1	yes	characteristic, direct product factor, Sylow
296	#41	—	4	4	no	—
297	#41	—	8	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
300	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	Q₁₆	—	2	2	no	—
310	Q₁₆	—	4	2	no	—
311	Q₁₆	—	8	1	no	—
312	SD₁₆	—	8	2	no	—
313	SD₁₆	—	8	2	no	—
314	D₈	—	2	2	no	—
315	D₈	—	4	2	no	—
316	D₈	—	8	1	no	—
317	D₈	—	8	2	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	8	2	no	—
323	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
324	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
325	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
333	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
334	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	4	2	no	—
342	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
343	C₂³	—	2	2	no	—
344	C₂³	—	4	2	no	—
345	Q₈	—	2	1	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	2	1	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	Q₈	C₃₁×#135	1	2	yes	—
351	D₄	—	2	2	no	—
352	D₄	—	2	2	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	8	4	no	—
358	D₄	—	8	2	no	—
359	D₄	—	16	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	4	no	—
369	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
371	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
372	C₈	—	2	1	no	—
373	C₈	—	2	1	no	—
374	C₈	—	2	1	no	—
375	C₈	—	4	1	no	—
376	C₈	—	4	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	1	no	—
379	C₈	C₃₁×#135	1	2	yes	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	D₄²×C₃₁	1	1	yes	characteristic
387	C₄	—	2	2	no	—
388	C₄	—	2	1	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	8	2	no	—
394	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
395	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
396	C₄	C₃₁×#576	1	1	yes	characteristic
397	C₄	C₃₁×#576	1	1	yes	characteristic
398	C₂	—	8	2	no	—
399	C₂	—	16	2	no	—
400	C₂	C₃₁×#3280	1	1	yes	characteristic
401	C₂	C₃₁×#3287	1	1	yes	characteristic
402	C₂	C₃₁×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₃₁×#3391	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3393	C₂	semidirect
3. C₃₁×#3304	C₂	semidirect
4. C₃₁×#1709	C₂	semidirect
5. C₃₁×#1681	C₂	semidirect
6. C₃₁×#1670	C₂	semidirect
7. C₃₁×#1668	C₂	semidirect
8. C₃₁×#1642	C₂	semidirect
9. C₃₁×#1628	C₂	semidirect
10. C₈×Q₁₆×C₃₁	C₂	semidirect
11. C₈×D₈×C₃₁	C₂	semidirect
141. #19995	C₃₁	direct (N × H)
179. #3393	C₂×C₃₁	semidirect
181. #3304	C₂×C₃₁	semidirect
182. #1709	C₂×C₃₁	semidirect
183. #1681	C₂×C₃₁	semidirect
184. #1670	C₂×C₃₁	semidirect
185. #1668	C₂×C₃₁	semidirect
186. #1642	C₂×C₃₁	semidirect
187. #1628	C₂×C₃₁	semidirect
188. C₈×Q₁₆	C₂×C₃₁	semidirect
189. C₈×D₈	C₂×C₃₁	semidirect
295. C₃₁	#19995	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×#3393	2
C₃₁×#3391	2
C₃₁×#3304	2
C₃₁×#1709	2
C₃₁×#1681	2
C₃₁×#1670	2
C₃₁×#1668	2
C₃₁×#1642	2
C₃₁×#1628	2
C₈×Q₁₆×C₃₁	2
C₈×D₈×C₃₁	2
#19995	31

Subgroups — C31×#19995 #21476754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19995 #21476754