Subgroups — C₂×C₃₁×#1678 #21475878

Order 7936.

722 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#486	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1678	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#331	C₂	1	1	yes	maximal, characteristic
9	C₂²×SD₁₆×C₃₁	—	2	1	no	—
10	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₃₁×#486	—	2	2	no	—
14	C₃₁×#486	C₂²	1	4	yes	—
15	C₃₁×#477	—	2	2	no	—
16	C₃₁×#477	C₂²	1	4	yes	complemented
17	C₃₁×#460	—	2	2	no	—
18	C₃₁×#460	C₂²	1	4	yes	—
19	C₈×Q₈×C₃₁	—	2	2	no	—
20	C₈×Q₈×C₃₁	C₂²	1	4	yes	complemented
21	C₂×C₃₁×#107	—	2	1	no	—
22	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
23	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#103	—	2	1	no	—
27	C₂×C₃₁×#102	—	2	1	no	—
28	C₂×C₃₁×#102	—	2	1	no	—
29	C₂×C₃₁×#102	—	2	1	no	—
30	C₂×C₄×C₈×C₃₁	—	2	1	no	—
31	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#334	C₂²	1	4	yes	complemented
33	C₃₁×#333	C₂²	1	4	yes	complemented
34	C₃₁×#331	C₂²	1	4	yes	—
35	C₂²×Q₈×C₃₁	—	2	1	no	—
36	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
37	C₂²×D₄×C₃₁	—	2	1	no	—
38	C₂²×D₄×C₃₁	—	2	1	no	—
39	C₂²×D₄×C₃₁	—	2	1	no	—
40	C₂×SD₁₆×C₃₁	—	2	4	no	—
41	C₂×SD₁₆×C₃₁	—	4	4	no	—
42	C₂²×C₈×C₃₁	—	2	1	no	—
43	C₂²×C₈×C₃₁	—	2	1	no	—
44	C₂²×C₈×C₃₁	—	2	1	no	—
45	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
47	C₃₁×C₄⋊Q₈	—	2	1	no	—
48	C₃₁×C₄⋊Q₈	—	2	1	no	—
49	C₃₁×C₄⋊Q₈	—	2	1	no	—
50	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
51	C₃₁×#127	—	2	1	no	—
52	C₃₁×#127	—	2	1	no	—
53	C₃₁×#127	—	2	1	no	—
54	C₃₁×#127	C₂³	1	2	yes	—
55	C₄×Q₈×C₃₁	—	2	1	no	—
56	C₄×Q₈×C₃₁	—	2	1	no	—
57	C₄×Q₈×C₃₁	D₄	1	2	yes	—
58	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₃₁	—	2	1	no	—
64	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
65	C₃₁×#107	—	2	4	no	—
66	C₃₁×C₄⋊C₈	—	2	4	no	—
67	C₃₁×C₄⋊C₈	—	2	1	no	—
68	C₃₁×C₄⋊C₈	—	2	1	no	—
69	C₃₁×C₄⋊C₈	—	2	1	no	—
70	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
71	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
72	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
73	C₃₁×#103	—	2	4	no	—
74	C₃₁×#102	—	2	4	no	—
75	C₃₁×#102	—	2	4	no	—
76	C₃₁×#102	—	2	4	no	—
77	C₄×C₈×C₃₁	—	2	4	no	—
78	C₄×C₈×C₃₁	D₄	1	2	yes	—
79	C₄×C₈×C₃₁	C₂³	1	2	yes	—
80	C₂⁴×C₃₁	—	4	1	no	—
81	C₂×Q₈×C₃₁	—	2	1	no	—
82	C₂×Q₈×C₃₁	—	2	2	no	—
83	C₂×Q₈×C₃₁	—	2	2	no	—
84	C₂×Q₈×C₃₁	—	4	1	no	—
85	C₂×Q₈×C₃₁	—	8	2	no	—
86	C₂×Q₈×C₃₁	SD₁₆	1	4	yes	—
87	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
88	C₂×D₄×C₃₁	—	2	2	no	—
89	C₂×D₄×C₃₁	—	2	2	no	—
90	C₂×D₄×C₃₁	—	2	2	no	—
91	C₂×D₄×C₃₁	—	4	1	no	—
92	C₂×D₄×C₃₁	—	4	1	no	—
93	C₂×D₄×C₃₁	—	4	1	no	—
94	C₂×D₄×C₃₁	—	4	2	no	—
95	C₂×D₄×C₃₁	—	4	2	no	—
96	C₂×D₄×C₃₁	—	4	2	no	—
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	—	8	2	no	—
99	C₂²×C₄×C₃₁	—	2	1	no	—
100	C₂²×C₄×C₃₁	—	2	1	no	—
101	C₂²×C₄×C₃₁	—	4	1	no	—
102	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
105	SD₁₆×C₃₁	—	4	8	no	—
106	C₂×C₈×C₃₁	—	2	2	no	—
107	C₂×C₈×C₃₁	—	2	2	no	—
108	C₂×C₈×C₃₁	—	2	2	no	—
109	C₂×C₈×C₃₁	—	2	2	no	—
110	C₂×C₈×C₃₁	—	2	2	no	—
111	C₂×C₈×C₃₁	—	4	2	no	—
112	C₂×C₈×C₃₁	—	4	2	no	—
113	C₂×C₈×C₃₁	—	4	2	no	—
114	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
116	C₄⋊C₄×C₃₁	—	2	2	no	—
117	C₄⋊C₄×C₃₁	—	2	1	no	—
118	C₄⋊C₄×C₃₁	—	2	2	no	—
119	C₄⋊C₄×C₃₁	—	2	2	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	4	1	no	—
122	C₄⋊C₄×C₃₁	—	4	1	no	—
123	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
124	C₄²×C₃₁	—	2	2	no	—
125	C₄²×C₃₁	—	2	2	no	—
126	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₃₁	#41	1	1	yes	characteristic
129	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
130	C₂×#1678	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₃₁	—	4	2	no	—
132	C₂³×C₃₁	—	8	2	no	—
133	C₂³×C₃₁	—	8	2	no	—
134	C₂³×C₃₁	—	8	2	no	—
135	C₂³×C₃₁	#121	1	1	yes	characteristic
136	Q₈×C₃₁	—	2	2	no	—
137	Q₈×C₃₁	—	2	4	no	—
138	Q₈×C₃₁	—	8	2	no	—
139	Q₈×C₃₁	—	8	2	no	—
140	Q₈×C₃₁	C₂×SD₁₆	1	4	yes	—
141	D₄×C₃₁	—	4	2	no	—
142	D₄×C₃₁	—	4	2	no	—
143	D₄×C₃₁	—	4	2	no	—
144	D₄×C₃₁	—	4	2	no	—
145	D₄×C₃₁	—	8	2	no	—
146	D₄×C₃₁	—	8	2	no	—
147	D₄×C₃₁	—	8	2	no	—
148	D₄×C₃₁	—	8	2	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	2	4	no	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	—	8	2	no	—
156	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
157	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
158	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₃₁	#135	1	2	yes	—
161	C₂×C₄×C₃₁	#135	1	2	yes	—
162	C₂×C₄×C₃₁	#137	1	2	yes	—
163	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
166	C₈×C₃₁	—	2	2	no	—
167	C₈×C₃₁	—	2	2	no	—
168	C₈×C₃₁	—	4	2	no	—
169	C₈×C₃₁	—	4	2	no	—
170	C₈×C₃₁	—	4	2	no	—
171	C₂×#486	C₂×C₃₁	1	1	yes	characteristic
172	C₂×#477	C₂×C₃₁	1	1	yes	characteristic, complemented
173	C₂×#460	C₂×C₃₁	1	1	yes	characteristic
174	C₂×C₈×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#1678	C₂×C₃₁	1	8	yes	direct product factor
176	C₂×#334	C₂×C₃₁	1	1	yes	characteristic, complemented
177	C₂×#333	C₂×C₃₁	1	1	yes	characteristic, complemented
178	C₂×#331	C₂×C₃₁	1	1	yes	characteristic
179	C₂²×C₃₁	—	8	2	no	—
180	C₂²×C₃₁	—	8	2	no	—
181	C₂²×C₃₁	—	8	2	no	—
182	C₂²×C₃₁	—	16	4	no	—
183	C₂²×C₃₁	#464	1	2	yes	—
184	C₂²×C₃₁	#465	1	2	yes	—
185	C₂²×C₃₁	#472	1	2	yes	—
186	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
187	C₄×C₃₁	—	2	4	no	—
188	C₄×C₃₁	—	2	1	no	—
189	C₄×C₃₁	—	2	1	no	—
190	C₄×C₃₁	—	4	2	no	—
191	C₄×C₃₁	—	8	2	no	—
192	C₄×C₃₁	#464	1	2	yes	—
193	C₄×C₃₁	#465	1	2	yes	—
194	C₄×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
195	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
196	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
197	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
198	C₂²×SD₁₆	—	2	1	no	—
199	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
200	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
201	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
202	#486	—	2	2	no	—
203	#486	C₂²×C₃₁	1	4	yes	—
204	#477	—	2	2	no	—
205	#477	C₂²×C₃₁	1	4	yes	complemented
206	#460	—	2	2	no	—
207	#460	C₂²×C₃₁	1	4	yes	—
208	C₈×Q₈	—	2	2	no	—
209	C₈×Q₈	C₂²×C₃₁	1	4	yes	complemented
210	C₂×#107	—	2	1	no	—
211	C₂×C₄⋊C₈	—	2	1	no	—
212	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
215	C₂×#103	—	2	1	no	—
216	C₂×#102	—	2	1	no	—
217	C₂×#102	—	2	1	no	—
218	C₂×#102	—	2	1	no	—
219	C₂×C₄×C₈	—	2	1	no	—
220	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
221	#334	C₂²×C₃₁	1	4	yes	complemented
222	#333	C₂²×C₃₁	1	4	yes	complemented
223	#331	C₂²×C₃₁	1	4	yes	—
224	C₂×C₃₁	—	16	2	no	—
225	C₂×C₃₁	#1678	1	4	yes	direct product factor
226	C₂×C₃₁	C₂×#464	1	1	yes	characteristic
227	C₂×C₃₁	C₂×#465	1	1	yes	characteristic
228	C₂×C₃₁	C₂×#472	1	1	yes	characteristic
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	—	2	1	no	—
234	C₂×SD₁₆	—	2	4	no	—
235	C₂×SD₁₆	—	4	4	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
240	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
245	#127	—	2	1	no	—
246	#127	—	2	1	no	—
247	#127	—	2	1	no	—
248	#127	C₂³×C₃₁	1	2	yes	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×Q₈	D₄×C₃₁	1	2	yes	—
252	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
259	#107	—	2	4	no	—
260	C₄⋊C₈	—	2	4	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
265	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
266	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
267	#103	—	2	4	no	—
268	#102	—	2	4	no	—
269	#102	—	2	4	no	—
270	#102	—	2	4	no	—
271	C₄×C₈	—	2	4	no	—
272	C₄×C₈	D₄×C₃₁	1	2	yes	—
273	C₄×C₈	C₂³×C₃₁	1	2	yes	—
274	C₃₁	C₂×#1678	1	1	yes	characteristic, direct product factor, Sylow
275	C₂⁴	—	4	1	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	8	2	no	—
281	C₂×Q₈	SD₁₆×C₃₁	1	4	yes	—
282	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	8	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
299	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
300	SD₁₆	—	4	8	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
310	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
322	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
323	C₄²	#41×C₃₁	1	1	yes	characteristic
324	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
325	C₂³	—	4	2	no	—
326	C₂³	—	8	2	no	—
327	C₂³	—	8	2	no	—
328	C₂³	—	8	2	no	—
329	C₂³	C₃₁×#121	1	1	yes	characteristic
330	Q₈	—	2	4	no	—
331	Q₈	—	2	2	no	—
332	Q₈	—	8	2	no	—
333	Q₈	—	8	2	no	—
334	Q₈	C₂×SD₁₆×C₃₁	1	4	yes	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	8	2	no	—
340	D₄	—	8	2	no	—
341	D₄	—	8	2	no	—
342	D₄	—	8	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
351	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
352	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
353	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
354	C₂×C₄	C₃₁×#135	1	2	yes	—
355	C₂×C₄	C₃₁×#135	1	2	yes	—
356	C₂×C₄	C₃₁×#137	1	2	yes	—
357	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
359	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
360	C₈	—	2	2	no	—
361	C₈	—	2	2	no	—
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	16	4	no	—
369	C₂²	C₃₁×#464	1	2	yes	—
370	C₂²	C₃₁×#465	1	2	yes	—
371	C₂²	C₃₁×#472	1	2	yes	—
372	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
373	C₄	—	2	4	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	8	2	no	—
378	C₄	C₃₁×#464	1	2	yes	—
379	C₄	C₃₁×#465	1	2	yes	—
380	C₄	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
381	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
382	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
383	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
384	C₂	—	16	2	no	—
385	C₂	C₃₁×#1678	1	4	yes	direct product factor
386	C₂	C₂×C₃₁×#464	1	1	yes	characteristic
387	C₂	C₂×C₃₁×#465	1	1	yes	characteristic
388	C₂	C₂×C₃₁×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#477	C₂	semidirect
4. C₂×C₈×Q₈×C₃₁	C₂	semidirect
5. C₃₁×#1678	C₂	direct (N × H)
6. C₂×C₃₁×#334	C₂	semidirect
7. C₂×C₃₁×#333	C₂	semidirect
16. C₃₁×#477	C₂²	semidirect
20. C₈×Q₈×C₃₁	C₂²	semidirect
32. C₃₁×#334	C₂²	semidirect
33. C₃₁×#333	C₂²	semidirect
130. C₂×#1678	C₃₁	direct (N × H)
172. C₂×#477	C₂×C₃₁	semidirect
174. C₂×C₈×Q₈	C₂×C₃₁	semidirect
175. #1678	C₂×C₃₁	direct (N × H)
176. C₂×#334	C₂×C₃₁	semidirect
177. C₂×#333	C₂×C₃₁	semidirect
205. #477	C₂²×C₃₁	semidirect
209. C₈×Q₈	C₂²×C₃₁	semidirect
221. #334	C₂²×C₃₁	semidirect
222. #333	C₂²×C₃₁	semidirect
225. C₂×C₃₁	#1678	direct (N × H)
274. C₃₁	C₂×#1678	direct (N × H)
385. C₂	C₃₁×#1678	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×#486	2
C₂×C₃₁×#477	2
C₂×C₃₁×#460	2
C₂×C₈×Q₈×C₃₁	2
C₃₁×#1678	2
C₂×C₃₁×#334	2
C₂×C₃₁×#333	2
C₂×C₃₁×#331	2
C₂×#1678	31

Subgroups — C2×C31×#1678 #21475878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1678 #21475878