Subgroups — C₃₁×#29384 #21486143

Order 7936.

708 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2956	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2102	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2091	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2050	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2010	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1932	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1896	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1891	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1861	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1841	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#575	C₂²	1	1	yes	characteristic
13	C₃₁×#568	C₂²	1	2	yes	—
14	C₃₁×#525	C₂²	1	2	yes	—
15	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
16	C₃₁×#444	—	2	2	no	—
17	C₃₁×#443	—	2	2	no	—
18	C₃₁×#432	—	2	2	no	—
19	C₃₁×#431	—	2	2	no	—
20	C₃₁×#430	C₂²	1	1	yes	characteristic
21	C₃₁×#430	C₂²	1	2	yes	—
22	C₃₁×#423	C₂²	1	1	yes	characteristic
23	C₃₁×#423	C₂²	1	1	yes	characteristic
24	C₃₁×#421	C₂²	1	2	yes	—
25	C₂×C₃₁×#104	C₂²	1	2	yes	—
26	C₂×C₃₁×#104	C₂²	1	2	yes	—
27	C₃₁×#413	C₂²	1	2	yes	—
28	C₃₁×#407	C₂²	1	1	yes	characteristic
29	C₃₁×#407	C₂²	1	1	yes	characteristic
30	C₃₁×#407	C₂²	1	2	yes	—
31	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
32	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#344	C₂²	1	2	yes	—
34	C₃₁×#344	C₂²	1	2	yes	—
35	C₃₁×#339	C₂²	1	2	yes	—
36	C₃₁×#339	C₂²	1	2	yes	—
37	C₃₁×#338	C₂²	1	1	yes	characteristic
38	C₃₁×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
39	C₂×#41×C₃₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₃₁	—	2	1	no	—
41	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
42	C₃₁×#137	—	2	2	no	—
43	C₃₁×AGL(1,ℤ/8)	—	2	2	no	—
44	C₃₁×#135	—	2	2	no	—
45	C₃₁×#131	—	2	4	no	—
46	C₃₁×#131	—	4	2	no	—
47	C₂×M₁₆×C₃₁	—	4	2	no	—
48	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
51	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
52	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
53	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
54	C₃₁×#123	—	2	2	no	—
55	C₃₁×C₂²⋊Q₈	—	2	2	no	—
56	C₃₁×#121	—	2	2	no	—
57	C₃₁×#120	—	2	2	no	—
58	C₄×D₄×C₃₁	—	4	2	no	—
59	C₃₁×#117	C₂³	1	2	yes	—
60	C₂×C₄²×C₃₁	—	2	1	no	—
61	C₂×C₄²×C₃₁	—	2	1	no	—
62	C₂×C₄²×C₃₁	—	2	1	no	—
63	C₂×C₄²×C₃₁	—	2	1	no	—
64	C₂×C₄²×C₃₁	—	2	1	no	—
65	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
67	C₃₁×#108	—	2	2	no	—
68	C₃₁×#108	—	4	2	no	—
69	C₃₁×C₄⋊C₈	—	2	2	no	—
70	C₃₁×C₄⋊C₈	—	2	2	no	—
71	C₃₁×#104	—	2	2	no	—
72	C₃₁×#104	—	2	2	no	—
73	C₃₁×#104	—	2	2	no	—
74	C₃₁×#104	—	2	2	no	—
75	C₃₁×#104	—	4	2	no	—
76	C₃₁×#101	—	2	2	no	—
77	C₃₁×#100	—	2	2	no	—
78	C₃₁×C₂²⋊C₈	—	2	2	no	—
79	C₃₁×C₂²⋊C₈	—	2	2	no	—
80	C₃₁×C₂²⋊C₈	—	4	2	no	—
81	C₃₁×#97	—	2	1	no	—
82	C₃₁×#97	D₄	1	2	yes	complemented
83	C₄×C₈×C₃₁	—	2	1	no	—
84	C₄×C₈×C₃₁	D₄	1	2	yes	complemented
85	C₂⁴×C₃₁	#41	1	1	yes	characteristic
86	#41×C₃₁	—	2	2	no	—
87	#41×C₃₁	—	2	2	no	—
88	#41×C₃₁	—	2	2	no	—
89	#41×C₃₁	—	2	2	no	—
90	C₂×Q₈×C₃₁	#41	1	2	yes	—
91	C₂×D₄×C₃₁	—	2	2	no	—
92	C₂×D₄×C₃₁	—	4	2	no	—
93	C₂×D₄×C₃₁	#41	1	2	yes	—
94	C₂²×C₄×C₃₁	—	2	1	no	—
95	C₂²×C₄×C₃₁	—	2	1	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	1	no	—
101	C₂²×C₄×C₃₁	—	2	1	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	—	4	4	no	—
106	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
108	Q₁₆×C₃₁	—	2	2	no	—
109	SD₁₆×C₃₁	—	2	4	no	—
110	D₈×C₃₁	—	2	2	no	—
111	M₁₆×C₃₁	—	2	2	no	—
112	M₁₆×C₃₁	—	2	2	no	—
113	M₁₆×C₃₁	—	2	2	no	—
114	M₁₆×C₃₁	—	2	2	no	—
115	M₁₆×C₃₁	—	2	2	no	—
116	M₁₆×C₃₁	—	2	2	no	—
117	M₁₆×C₃₁	—	2	2	no	—
118	M₁₆×C₃₁	—	2	2	no	—
119	M₁₆×C₃₁	—	4	4	no	—
120	C₂×C₈×C₃₁	—	2	1	no	—
121	C₂×C₈×C₃₁	—	2	1	no	—
122	C₂×C₈×C₃₁	—	2	2	no	—
123	C₂×C₈×C₃₁	—	2	2	no	—
124	C₂×C₈×C₃₁	—	4	4	no	—
125	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
127	C₄⋊C₄×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	4	2	no	—
129	C₂²⋊C₄×C₃₁	—	2	2	no	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₄²×C₃₁	—	2	1	no	—
133	C₄²×C₃₁	—	2	1	no	—
134	C₄²×C₃₁	—	2	1	no	—
135	C₄²×C₃₁	—	2	1	no	—
136	C₄²×C₃₁	—	2	1	no	—
137	C₄²×C₃₁	—	2	1	no	—
138	C₄²×C₃₁	—	2	2	no	—
139	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₃₁	#41	1	1	yes	characteristic
142	C₄²×C₃₁	#41	1	1	yes	characteristic
143	#29384	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂³×C₃₁	—	2	1	no	—
145	C₂³×C₃₁	—	2	2	no	—
146	C₂³×C₃₁	—	2	2	no	—
147	C₂³×C₃₁	—	4	2	no	—
148	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
149	Q₈×C₃₁	—	2	2	no	—
150	Q₈×C₃₁	—	2	2	no	—
151	D₄×C₃₁	—	2	2	no	—
152	D₄×C₃₁	—	2	2	no	—
153	D₄×C₃₁	—	4	2	no	—
154	D₄×C₃₁	—	4	2	no	—
155	D₄×C₃₁	—	8	4	no	—
156	C₂×C₄×C₃₁	—	2	4	no	—
157	C₂×C₄×C₃₁	—	2	1	no	—
158	C₂×C₄×C₃₁	—	2	1	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	2	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	—	4	2	no	—
168	C₂×C₄×C₃₁	—	4	2	no	—
169	C₂×C₄×C₃₁	—	4	1	no	—
170	C₂×C₄×C₃₁	—	4	2	no	—
171	C₂×C₄×C₃₁	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
177	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
179	C₈×C₃₁	—	2	2	no	—
180	C₈×C₃₁	—	2	2	no	—
181	C₈×C₃₁	—	4	1	no	—
182	C₈×C₃₁	—	4	2	no	—
183	C₈×C₃₁	—	4	1	no	—
184	C₈×C₃₁	—	4	2	no	—
185	#2956	C₂×C₃₁	1	1	yes	characteristic, complemented
186	#2920	C₂×C₃₁	1	1	yes	characteristic, complemented
187	#2102	C₂×C₃₁	1	1	yes	characteristic, complemented
188	#2091	C₂×C₃₁	1	1	yes	characteristic, complemented
189	#2050	C₂×C₃₁	1	1	yes	characteristic, complemented
190	#2010	C₂×C₃₁	1	1	yes	characteristic
191	#1932	C₂×C₃₁	1	2	yes	complemented
192	#1896	C₂×C₃₁	1	2	yes	complemented
193	#1891	C₂×C₃₁	1	2	yes	complemented
194	#1861	C₂×C₃₁	1	2	yes	complemented
195	#1841	C₂×C₃₁	1	1	yes	characteristic, complemented
196	C₂²×C₃₁	—	2	2	no	—
197	C₂²×C₃₁	—	2	4	no	—
198	C₂²×C₃₁	—	4	1	no	—
199	C₂²×C₃₁	—	4	1	no	—
200	C₂²×C₃₁	—	4	2	no	—
201	C₂²×C₃₁	—	4	1	no	—
202	C₂²×C₃₁	—	4	2	no	—
203	C₂²×C₃₁	—	8	2	no	—
204	C₂²×C₃₁	#525	1	1	yes	characteristic
205	C₂²×C₃₁	#551	1	2	yes	—
206	C₄×C₃₁	—	2	2	no	—
207	C₄×C₃₁	—	2	2	no	—
208	C₄×C₃₁	—	4	1	no	—
209	C₄×C₃₁	—	4	1	no	—
210	C₄×C₃₁	—	4	1	no	—
211	C₄×C₃₁	—	4	2	no	—
212	C₄×C₃₁	—	8	2	no	—
213	C₄×C₃₁	#525	1	1	yes	characteristic
214	C₄×C₃₁	#535	1	1	yes	characteristic
215	C₄×C₃₁	#553	1	2	yes	—
216	#575	C₂²×C₃₁	1	1	yes	characteristic
217	#568	C₂²×C₃₁	1	2	yes	—
218	#525	C₂²×C₃₁	1	2	yes	—
219	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
220	#444	—	2	2	no	—
221	#443	—	2	2	no	—
222	#432	—	2	2	no	—
223	#431	—	2	2	no	—
224	#430	C₂²×C₃₁	1	1	yes	characteristic
225	#430	C₂²×C₃₁	1	2	yes	—
226	#423	C₂²×C₃₁	1	1	yes	characteristic
227	#423	C₂²×C₃₁	1	1	yes	characteristic
228	#421	C₂²×C₃₁	1	2	yes	—
229	C₂×#104	C₂²×C₃₁	1	2	yes	—
230	C₂×#104	C₂²×C₃₁	1	2	yes	—
231	#413	C₂²×C₃₁	1	2	yes	—
232	#407	C₂²×C₃₁	1	1	yes	characteristic
233	#407	C₂²×C₃₁	1	1	yes	characteristic
234	#407	C₂²×C₃₁	1	2	yes	—
235	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
236	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
237	#344	C₂²×C₃₁	1	2	yes	—
238	#344	C₂²×C₃₁	1	2	yes	—
239	#339	C₂²×C₃₁	1	2	yes	—
240	#339	C₂²×C₃₁	1	2	yes	—
241	#338	C₂²×C₃₁	1	1	yes	characteristic
242	H(3,ℤ/4)	C₂²×C₃₁	1	1	yes	characteristic
243	C₂×C₃₁	—	2	1	no	—
244	C₂×C₃₁	—	2	2	no	—
245	C₂×C₃₁	—	4	2	no	—
246	C₂×C₃₁	—	8	2	no	—
247	C₂×C₃₁	#2598	1	1	yes	characteristic
248	C₂×#41	C₂³×C₃₁	1	2	yes	—
249	C₂³×C₄	—	2	1	no	—
250	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
251	#137	—	2	2	no	—
252	AGL(1,ℤ/8)	—	2	2	no	—
253	#135	—	2	2	no	—
254	#131	—	2	4	no	—
255	#131	—	4	2	no	—
256	C₂×M₁₆	—	4	2	no	—
257	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
258	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
259	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
260	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
261	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
262	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
263	#123	—	2	2	no	—
264	C₂²⋊Q₈	—	2	2	no	—
265	#121	—	2	2	no	—
266	#120	—	2	2	no	—
267	C₄×D₄	—	4	2	no	—
268	#117	C₂³×C₃₁	1	2	yes	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
276	#108	—	2	2	no	—
277	#108	—	4	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	2	no	—
280	#104	—	2	2	no	—
281	#104	—	2	2	no	—
282	#104	—	2	2	no	—
283	#104	—	2	2	no	—
284	#104	—	4	2	no	—
285	#101	—	2	2	no	—
286	#100	—	2	2	no	—
287	C₂²⋊C₈	—	2	2	no	—
288	C₂²⋊C₈	—	2	2	no	—
289	C₂²⋊C₈	—	4	2	no	—
290	#97	—	2	1	no	—
291	#97	D₄×C₃₁	1	2	yes	complemented
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	D₄×C₃₁	1	2	yes	complemented
294	C₃₁	#29384	1	1	yes	characteristic, direct product factor, Sylow
295	C₂⁴	#41×C₃₁	1	1	yes	characteristic
296	#41	—	2	2	no	—
297	#41	—	2	2	no	—
298	#41	—	2	2	no	—
299	#41	—	2	2	no	—
300	C₂×Q₈	#41×C₃₁	1	2	yes	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	#41×C₃₁	1	2	yes	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	4	4	no	—
316	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
317	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
318	Q₁₆	—	2	2	no	—
319	SD₁₆	—	2	4	no	—
320	D₈	—	2	2	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	4	4	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	4	no	—
335	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
336	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	2	no	—
349	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
350	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
351	C₄²	#41×C₃₁	1	1	yes	characteristic
352	C₄²	#41×C₃₁	1	1	yes	characteristic
353	C₂³	—	2	1	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
358	Q₈	—	2	2	no	—
359	Q₈	—	2	2	no	—
360	D₄	—	2	2	no	—
361	D₄	—	2	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	8	4	no	—
365	C₂×C₄	—	2	4	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	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
385	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
386	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
387	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
388	C₈	—	2	2	no	—
389	C₈	—	2	2	no	—
390	C₈	—	4	1	no	—
391	C₈	—	4	2	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	C₃₁×#525	1	1	yes	characteristic
403	C₂²	C₃₁×#551	1	2	yes	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₃₁×#525	1	1	yes	characteristic
412	C₄	C₃₁×#535	1	1	yes	characteristic
413	C₄	C₃₁×#553	1	2	yes	—
414	C₂	—	2	1	no	—
415	C₂	—	2	2	no	—
416	C₂	—	4	2	no	—
417	C₂	—	8	2	no	—
418	C₂	C₃₁×#2598	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₃₁	#535
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂×C₃₁	#2598
prime radical	C₃₁×#2010	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2956	C₂	semidirect
2. C₃₁×#2920	C₂	semidirect
3. C₃₁×#2102	C₂	semidirect
4. C₃₁×#2091	C₂	semidirect
5. C₃₁×#2050	C₂	semidirect
7. C₃₁×#1932	C₂	semidirect
8. C₃₁×#1896	C₂	semidirect
9. C₃₁×#1891	C₂	semidirect
10. C₃₁×#1861	C₂	semidirect
11. C₃₁×#1841	C₂	semidirect
82. C₃₁×#97	D₄	semidirect
84. C₄×C₈×C₃₁	D₄	semidirect
143. #29384	C₃₁	direct (N × H)
185. #2956	C₂×C₃₁	semidirect
186. #2920	C₂×C₃₁	semidirect
187. #2102	C₂×C₃₁	semidirect
188. #2091	C₂×C₃₁	semidirect
189. #2050	C₂×C₃₁	semidirect
191. #1932	C₂×C₃₁	semidirect
192. #1896	C₂×C₃₁	semidirect
193. #1891	C₂×C₃₁	semidirect
194. #1861	C₂×C₃₁	semidirect
195. #1841	C₂×C₃₁	semidirect
291. #97	D₄×C₃₁	semidirect
293. C₄×C₈	D₄×C₃₁	semidirect
294. C₃₁	#29384	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×#2956	2
C₃₁×#2920	2
C₃₁×#2102	2
C₃₁×#2091	2
C₃₁×#2050	2
C₃₁×#2010	2
C₃₁×#1932	2
C₃₁×#1896	2
C₃₁×#1891	2
C₃₁×#1861	2
C₃₁×#1841	2
#29384	31

Subgroups — C31×#29384 #21486143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#29384 #21486143