Subgroups — C₃₁×#24282 #21481041

Order 7936.

1308 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#473	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3004	C₂	1	2	yes	maximal
4	C₃₁×#2929	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2047	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2020	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1979	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1784	C₂	1	2	yes	maximal, complemented
10	C₂³×Q₈×C₃₁	C₂²	1	2	yes	—
11	C₂×C₃₁×#137	C₂²	1	4	yes	—
12	C₂²×Q₁₆×C₃₁	—	2	8	no	—
13	C₂²×Q₁₆×C₃₁	—	2	2	no	—
14	C₂²×Q₁₆×C₃₁	—	2	2	no	—
15	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
16	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
17	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#525	C₂²	1	1	yes	characteristic
20	C₃₁×#473	—	2	8	no	—
21	C₃₁×#451	—	2	4	no	—
22	C₃₁×#448	—	2	4	no	—
23	C₃₁×#435	—	2	2	no	—
24	C₈×D₄×C₃₁	—	2	2	no	—
25	C₂×C₃₁×#108	C₂²	1	2	yes	—
26	C₃₁×#424	C₂²	1	1	yes	characteristic
27	C₃₁×#419	C₂²	1	4	yes	—
28	C₂×C₃₁×#101	C₂²	1	4	yes	—
29	C₂×C₃₁×#101	C₂²	1	4	yes	—
30	C₃₁×#408	C₂²	1	1	yes	characteristic
31	C₃₁×#407	C₂²	1	2	yes	—
32	C₃₁×#407	C₂²	1	1	yes	characteristic
33	C₃₁×#405	C₂²	1	1	yes	characteristic
34	C₃₁×#341	C₂²	1	2	yes	—
35	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
36	C₂²×Q₈×C₃₁	—	2	2	no	—
37	C₂²×Q₈×C₃₁	—	2	8	no	—
38	C₂²×Q₈×C₃₁	—	2	4	no	—
39	C₂²×Q₈×C₃₁	—	2	4	no	—
40	C₂²×Q₈×C₃₁	—	4	4	no	—
41	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
42	C₂³×C₄×C₃₁	—	2	2	no	—
43	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
44	C₃₁×#137	—	2	8	no	—
45	C₃₁×#137	—	4	4	no	—
46	C₂×Q₁₆×C₃₁	—	2	16	no	—
47	C₂×Q₁₆×C₃₁	—	2	16	no	—
48	C₂×Q₁₆×C₃₁	—	2	8	no	—
49	C₂×Q₁₆×C₃₁	—	2	4	no	—
50	C₂×Q₁₆×C₃₁	—	2	4	no	—
51	C₂×Q₁₆×C₃₁	—	2	2	no	—
52	C₂×Q₁₆×C₃₁	—	2	2	no	—
53	C₂×Q₁₆×C₃₁	—	2	4	no	—
54	C₂×Q₁₆×C₃₁	D₄	1	8	yes	complemented
55	C₂×SD₁₆×C₃₁	—	2	4	no	—
56	C₃₁×#131	—	2	4	no	—
57	C₂×M₁₆×C₃₁	—	2	1	no	—
58	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
61	C₂²×C₈×C₃₁	—	2	4	no	—
62	C₂²×C₈×C₃₁	—	2	1	no	—
63	C₂²×C₈×C₃₁	D₄	1	2	yes	—
64	C₂²×C₈×C₃₁	D₄	1	2	yes	—
65	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
67	C₃₁×#123	—	2	1	no	—
68	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
69	C₃₁×#121	D₄	1	2	yes	—
70	C₃₁×#120	—	2	1	no	—
71	C₄×D₄×C₃₁	—	2	2	no	—
72	C₃₁×#117	C₂³	1	1	yes	characteristic
73	C₃₁×#108	—	2	4	no	—
74	C₃₁×C₄⋊C₈	—	2	2	no	—
75	C₃₁×#103	—	2	8	no	—
76	C₃₁×#101	—	2	8	no	—
77	C₃₁×#101	—	4	4	no	—
78	C₃₁×C₂²⋊C₈	—	2	2	no	—
79	C₃₁×C₂²⋊C₈	—	2	4	no	—
80	C₃₁×C₂²⋊C₈	—	2	2	no	—
81	C₃₁×#97	—	2	1	no	—
82	C₄×C₈×C₃₁	—	2	1	no	—
83	C₂⁴×C₃₁	#41	1	1	yes	characteristic
84	#41×C₃₁	—	2	2	no	—
85	#41×C₃₁	—	2	2	no	—
86	C₂×Q₈×C₃₁	—	2	4	no	—
87	C₂×Q₈×C₃₁	—	2	16	no	—
88	C₂×Q₈×C₃₁	—	2	4	no	—
89	C₂×Q₈×C₃₁	—	2	4	no	—
90	C₂×Q₈×C₃₁	—	2	4	no	—
91	C₂×Q₈×C₃₁	—	2	4	no	—
92	C₂×Q₈×C₃₁	—	4	8	no	—
93	C₂×Q₈×C₃₁	—	4	16	no	—
94	C₂×Q₈×C₃₁	—	4	8	no	—
95	C₂×Q₈×C₃₁	—	4	4	no	—
96	C₂×Q₈×C₃₁	C₂×D₄	1	8	yes	—
97	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₃₁	—	2	2	no	—
99	C₂×D₄×C₃₁	—	2	1	no	—
100	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	—	2	2	no	—
102	C₂²×C₄×C₃₁	—	2	2	no	—
103	C₂²×C₄×C₃₁	—	2	4	no	—
104	C₂²×C₄×C₃₁	—	2	1	no	—
105	C₂²×C₄×C₃₁	—	4	8	no	—
106	C₂²×C₄×C₃₁	—	4	4	no	—
107	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
110	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
111	Q₁₆×C₃₁	—	2	16	no	—
112	Q₁₆×C₃₁	—	2	8	no	—
113	Q₁₆×C₃₁	—	2	8	no	—
114	Q₁₆×C₃₁	—	4	8	no	—
115	SD₁₆×C₃₁	—	4	8	no	—
116	M₁₆×C₃₁	—	2	2	no	—
117	M₁₆×C₃₁	—	2	4	no	—
118	M₁₆×C₃₁	—	2	2	no	—
119	M₁₆×C₃₁	—	2	4	no	—
120	M₁₆×C₃₁	—	4	2	no	—
121	C₂×C₈×C₃₁	—	2	2	no	—
122	C₂×C₈×C₃₁	—	2	4	no	—
123	C₂×C₈×C₃₁	—	2	4	no	—
124	C₂×C₈×C₃₁	—	2	1	no	—
125	C₂×C₈×C₃₁	—	2	4	no	—
126	C₂×C₈×C₃₁	—	2	1	no	—
127	C₂×C₈×C₃₁	—	4	2	no	—
128	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
132	C₄⋊C₄×C₃₁	—	2	2	no	—
133	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
134	C₂²⋊C₄×C₃₁	—	2	2	no	—
135	C₂²⋊C₄×C₃₁	—	2	1	no	—
136	C₂²⋊C₄×C₃₁	—	2	2	no	—
137	C₄²×C₃₁	—	2	1	no	—
138	#24282	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₃₁	—	2	2	no	—
140	C₂³×C₃₁	—	2	4	no	—
141	C₂³×C₃₁	—	2	1	no	—
142	C₂³×C₃₁	#121	1	2	yes	—
143	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
144	Q₈×C₃₁	—	2	8	no	—
145	Q₈×C₃₁	—	2	8	no	—
146	Q₈×C₃₁	—	2	2	no	—
147	Q₈×C₃₁	—	4	16	no	—
148	Q₈×C₃₁	—	4	4	no	—
149	Q₈×C₃₁	—	4	4	no	—
150	D₄×C₃₁	—	2	2	no	—
151	D₄×C₃₁	—	4	2	no	—
152	D₄×C₃₁	—	4	4	no	—
153	C₂×C₄×C₃₁	—	2	2	no	—
154	C₂×C₄×C₃₁	—	2	2	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	2	4	no	—
157	C₂×C₄×C₃₁	—	2	2	no	—
158	C₂×C₄×C₃₁	—	2	1	no	—
159	C₂×C₄×C₃₁	—	2	8	no	—
160	C₂×C₄×C₃₁	—	4	16	no	—
161	C₂×C₄×C₃₁	—	4	4	no	—
162	C₂×C₄×C₃₁	—	4	4	no	—
163	C₂×C₄×C₃₁	—	4	1	no	—
164	C₂×C₄×C₃₁	—	4	1	no	—
165	C₂×C₄×C₃₁	#121	1	2	yes	—
166	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
170	C₈×C₃₁	—	2	2	no	—
171	C₈×C₃₁	—	4	1	no	—
172	C₈×C₃₁	—	4	1	no	—
173	C₈×C₃₁	—	4	4	no	—
174	C₈×C₃₁	#120	1	2	yes	—
175	C₈×C₃₁	#120	1	2	yes	—
176	C₂³×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
177	C₂×#473	C₂×C₃₁	1	2	yes	complemented
178	#3004	C₂×C₃₁	1	2	yes	—
179	#2929	C₂×C₃₁	1	1	yes	characteristic
180	#2047	C₂×C₃₁	1	2	yes	complemented
181	#2020	C₂×C₃₁	1	2	yes	complemented
182	#1979	C₂×C₃₁	1	2	yes	complemented
183	#1810	C₂×C₃₁	1	1	yes	characteristic, complemented
184	#1784	C₂×C₃₁	1	2	yes	complemented
185	C₂²×C₃₁	—	2	8	no	—
186	C₂²×C₃₁	—	2	2	no	—
187	C₂²×C₃₁	—	2	2	no	—
188	C₂²×C₃₁	—	2	2	no	—
189	C₂²×C₃₁	—	4	1	no	—
190	C₂²×C₃₁	—	4	2	no	—
191	C₂²×C₃₁	#473	1	4	yes	complemented
192	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
193	C₂²×C₃₁	#546	1	2	yes	—
194	C₄×C₃₁	—	2	2	no	—
195	C₄×C₃₁	—	4	8	no	—
196	C₄×C₃₁	—	4	1	no	—
197	C₄×C₃₁	—	4	2	no	—
198	C₄×C₃₁	C₂×#120	1	1	yes	characteristic
199	C₄×C₃₁	#535	1	1	yes	characteristic
200	C₄×C₃₁	D₄²	1	2	yes	—
201	C₂³×Q₈	C₂²×C₃₁	1	2	yes	—
202	C₂×#137	C₂²×C₃₁	1	4	yes	—
203	C₂²×Q₁₆	—	2	8	no	—
204	C₂²×Q₁₆	—	2	2	no	—
205	C₂²×Q₁₆	—	2	2	no	—
206	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
207	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
208	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
209	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
210	#525	C₂²×C₃₁	1	1	yes	characteristic
211	#473	—	2	8	no	—
212	#451	—	2	4	no	—
213	#448	—	2	4	no	—
214	#435	—	2	2	no	—
215	C₈×D₄	—	2	2	no	—
216	C₂×#108	C₂²×C₃₁	1	2	yes	—
217	#424	C₂²×C₃₁	1	1	yes	characteristic
218	#419	C₂²×C₃₁	1	4	yes	—
219	C₂×#101	C₂²×C₃₁	1	4	yes	—
220	C₂×#101	C₂²×C₃₁	1	4	yes	—
221	#408	C₂²×C₃₁	1	1	yes	characteristic
222	#407	C₂²×C₃₁	1	2	yes	—
223	#407	C₂²×C₃₁	1	1	yes	characteristic
224	#405	C₂²×C₃₁	1	1	yes	characteristic
225	#341	C₂²×C₃₁	1	2	yes	—
226	C₂×C₃₁	—	2	2	no	—
227	C₂×C₃₁	—	2	4	no	—
228	C₂×C₃₁	—	8	1	no	—
229	C₂×C₃₁	#2408	1	1	yes	characteristic
230	C₂×C₃₁	C₂×#473	1	2	yes	—
231	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
232	C₂²×Q₈	—	2	2	no	—
233	C₂²×Q₈	—	2	8	no	—
234	C₂²×Q₈	—	2	4	no	—
235	C₂²×Q₈	—	2	4	no	—
236	C₂²×Q₈	—	4	4	no	—
237	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
238	C₂³×C₄	—	2	2	no	—
239	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
240	#137	—	2	8	no	—
241	#137	—	4	4	no	—
242	C₂×Q₁₆	—	2	16	no	—
243	C₂×Q₁₆	—	2	16	no	—
244	C₂×Q₁₆	—	2	8	no	—
245	C₂×Q₁₆	—	2	4	no	—
246	C₂×Q₁₆	—	2	4	no	—
247	C₂×Q₁₆	—	2	2	no	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×Q₁₆	—	2	4	no	—
250	C₂×Q₁₆	D₄×C₃₁	1	8	yes	complemented
251	C₂×SD₁₆	—	2	4	no	—
252	#131	—	2	4	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
255	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
256	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
257	C₂²×C₈	—	2	4	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	D₄×C₃₁	1	2	yes	—
260	C₂²×C₈	D₄×C₃₁	1	2	yes	—
261	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
263	#123	—	2	1	no	—
264	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
265	#121	D₄×C₃₁	1	2	yes	—
266	#120	—	2	1	no	—
267	C₄×D₄	—	2	2	no	—
268	#117	C₂³×C₃₁	1	1	yes	characteristic
269	#108	—	2	4	no	—
270	C₄⋊C₈	—	2	2	no	—
271	#103	—	2	8	no	—
272	#101	—	2	8	no	—
273	#101	—	4	4	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	—	2	4	no	—
276	C₂²⋊C₈	—	2	2	no	—
277	#97	—	2	1	no	—
278	C₄×C₈	—	2	1	no	—
279	C₃₁	#24282	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	#41×C₃₁	1	1	yes	characteristic
281	#41	—	2	2	no	—
282	#41	—	2	2	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	16	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	4	8	no	—
290	C₂×Q₈	—	4	16	no	—
291	C₂×Q₈	—	4	8	no	—
292	C₂×Q₈	—	4	4	no	—
293	C₂×Q₈	C₂×D₄×C₃₁	1	8	yes	—
294	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	4	8	no	—
303	C₂²×C₄	—	4	4	no	—
304	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
306	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
308	Q₁₆	—	2	16	no	—
309	Q₁₆	—	2	8	no	—
310	Q₁₆	—	2	8	no	—
311	Q₁₆	—	4	8	no	—
312	SD₁₆	—	4	8	no	—
313	M₁₆	—	2	2	no	—
314	M₁₆	—	2	4	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	4	no	—
317	M₁₆	—	4	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
326	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₄²	—	2	1	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	1	no	—
338	C₂³	C₃₁×#121	1	2	yes	—
339	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
340	Q₈	—	2	8	no	—
341	Q₈	—	2	8	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	4	16	no	—
344	Q₈	—	4	4	no	—
345	Q₈	—	4	4	no	—
346	D₄	—	2	2	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	4	16	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	C₃₁×#121	1	2	yes	—
362	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
363	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
364	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
365	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
366	C₈	—	2	2	no	—
367	C₈	—	4	1	no	—
368	C₈	—	4	1	no	—
369	C₈	—	4	4	no	—
370	C₈	C₃₁×#120	1	2	yes	—
371	C₈	C₃₁×#120	1	2	yes	—
372	C₂²	—	2	8	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	C₃₁×#473	1	4	yes	complemented
379	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
380	C₂²	C₃₁×#546	1	2	yes	—
381	C₄	—	2	2	no	—
382	C₄	—	4	8	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	2	no	—
385	C₄	C₂×C₃₁×#120	1	1	yes	characteristic
386	C₄	C₃₁×#535	1	1	yes	characteristic
387	C₄	D₄²×C₃₁	1	2	yes	—
388	C₂	—	2	4	no	—
389	C₂	—	2	2	no	—
390	C₂	—	8	1	no	—
391	C₂	C₃₁×#2408	1	1	yes	characteristic
392	C₂	C₂×C₃₁×#473	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₃₁×#525	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₁₆×C₃₁	C₂	semidirect
2. C₂×C₃₁×#473	C₂	semidirect
5. C₃₁×#2047	C₂	semidirect
6. C₃₁×#2020	C₂	semidirect
7. C₃₁×#1979	C₂	semidirect
8. C₃₁×#1810	C₂	semidirect
9. C₃₁×#1784	C₂	semidirect
54. C₂×Q₁₆×C₃₁	D₄	semidirect
138. #24282	C₃₁	direct (N × H)
176. C₂³×Q₁₆	C₂×C₃₁	semidirect
177. C₂×#473	C₂×C₃₁	semidirect
180. #2047	C₂×C₃₁	semidirect
181. #2020	C₂×C₃₁	semidirect
182. #1979	C₂×C₃₁	semidirect
183. #1810	C₂×C₃₁	semidirect
184. #1784	C₂×C₃₁	semidirect
191. C₂²×C₃₁	#473	semidirect
250. C₂×Q₁₆	D₄×C₃₁	semidirect
279. C₃₁	#24282	direct (N × H)
378. C₂²	C₃₁×#473	semidirect

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₃₁	2
C₂×C₃₁×#473	2
C₃₁×#3004	2
C₃₁×#2929	2
C₃₁×#2047	2
C₃₁×#2020	2
C₃₁×#1979	2
C₃₁×#1810	2
C₃₁×#1784	2
#24282	31

Subgroups — C31×#24282 #21481041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#24282 #21481041