Subgroups — C₂×C₃₁×#1701 #21475899

Order 7936.

810 conjugacy classes of subgroups.

The subgroup lattice has 424 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, complemented
2	C₂×C₃₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#459	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1701	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₃₁	—	2	1	no	—
10	C₂²×D₈×C₃₁	—	2	1	no	—
11	C₂²×M₁₆×C₃₁	—	2	1	no	—
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
15	C₃₁×#486	—	2	2	no	—
16	C₃₁×#486	C₂²	1	4	yes	complemented
17	C₃₁×#461	—	2	2	no	—
18	C₃₁×#461	C₂²	1	4	yes	complemented
19	C₃₁×#459	—	2	2	no	—
20	C₃₁×#459	C₂²	1	4	yes	—
21	C₃₁×#436	—	2	2	no	—
22	C₃₁×#436	C₂²	1	4	yes	complemented
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×C₃₁×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#334	C₂²	1	4	yes	complemented
33	C₃₁×#332	C₂²	1	4	yes	complemented
34	C₃₁×#331	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₃₁	—	2	1	no	—
36	C₂²×D₄×C₃₁	—	2	1	no	—
37	C₂²×D₄×C₃₁	—	2	1	no	—
38	C₂²×D₄×C₃₁	—	2	1	no	—
39	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₃₁	—	2	1	no	—
41	C₂×SD₁₆×C₃₁	—	2	4	no	—
42	C₂×SD₁₆×C₃₁	—	4	4	no	—
43	C₂×D₈×C₃₁	—	2	4	no	—
44	C₂×D₈×C₃₁	—	4	4	no	—
45	C₂×M₁₆×C₃₁	—	2	4	no	—
46	C₂×M₁₆×C₃₁	—	4	4	no	—
47	C₂²×C₈×C₃₁	—	2	1	no	—
48	C₂²×C₈×C₃₁	—	2	1	no	—
49	C₂²×C₈×C₃₁	—	2	1	no	—
50	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
52	C₃₁×C₄⋊Q₈	—	2	1	no	—
53	C₃₁×C₄⋊Q₈	—	2	1	no	—
54	C₃₁×C₄⋊Q₈	—	2	1	no	—
55	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₃₁×#127	—	2	1	no	—
57	C₃₁×#127	—	2	1	no	—
58	C₃₁×#127	—	2	1	no	—
59	C₃₁×#127	C₂³	1	2	yes	—
60	C₄×D₄×C₃₁	—	2	1	no	—
61	C₄×D₄×C₃₁	—	2	1	no	—
62	C₄×D₄×C₃₁	D₄	1	2	yes	—
63	C₄×D₄×C₃₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
68	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
69	C₃₁×C₄⋊C₈	—	2	1	no	—
70	C₃₁×C₄⋊C₈	—	2	1	no	—
71	C₃₁×C₄⋊C₈	—	2	1	no	—
72	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
73	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
74	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
75	C₃₁×#103	—	2	4	no	—
76	C₃₁×#102	—	2	4	no	—
77	C₃₁×#102	—	2	4	no	—
78	C₃₁×#102	—	2	4	no	—
79	C₃₁×C₂²⋊C₈	—	2	4	no	—
80	C₄×C₈×C₃₁	D₄	1	2	yes	—
81	C₄×C₈×C₃₁	C₂³	1	2	yes	—
82	C₂⁴×C₃₁	—	2	1	no	—
83	C₂⁴×C₃₁	—	4	1	no	—
84	C₂×Q₈×C₃₁	—	2	2	no	—
85	C₂×Q₈×C₃₁	—	4	1	no	—
86	C₂×Q₈×C₃₁	—	4	2	no	—
87	C₂×Q₈×C₃₁	—	4	2	no	—
88	C₂×D₄×C₃₁	—	2	1	no	—
89	C₂×D₄×C₃₁	—	2	2	no	—
90	C₂×D₄×C₃₁	—	2	2	no	—
91	C₂×D₄×C₃₁	—	2	2	no	—
92	C₂×D₄×C₃₁	—	2	2	no	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	—	4	1	no	—
95	C₂×D₄×C₃₁	—	4	1	no	—
96	C₂×D₄×C₃₁	—	4	1	no	—
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	—	4	2	no	—
99	C₂×D₄×C₃₁	—	4	2	no	—
100	C₂×D₄×C₃₁	—	4	2	no	—
101	C₂×D₄×C₃₁	—	8	2	no	—
102	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₃₁	—	2	1	no	—
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	—	2	2	no	—
106	C₂²×C₄×C₃₁	—	4	2	no	—
107	C₂²×C₄×C₃₁	—	4	2	no	—
108	C₂²×C₄×C₃₁	—	4	1	no	—
109	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
112	SD₁₆×C₃₁	—	4	8	no	—
113	D₈×C₃₁	—	4	8	no	—
114	M₁₆×C₃₁	—	4	8	no	—
115	C₂×C₈×C₃₁	—	2	2	no	—
116	C₂×C₈×C₃₁	—	2	2	no	—
117	C₂×C₈×C₃₁	—	2	2	no	—
118	C₂×C₈×C₃₁	—	2	2	no	—
119	C₂×C₈×C₃₁	—	2	2	no	—
120	C₂×C₈×C₃₁	—	4	2	no	—
121	C₂×C₈×C₃₁	—	4	2	no	—
122	C₂×C₈×C₃₁	—	4	2	no	—
123	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₃₁	—	2	1	no	—
126	C₄⋊C₄×C₃₁	—	2	2	no	—
127	C₄⋊C₄×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	4	1	no	—
129	C₄⋊C₄×C₃₁	—	4	1	no	—
130	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
131	C₂²⋊C₄×C₃₁	—	2	2	no	—
132	C₂²⋊C₄×C₃₁	—	2	2	no	—
133	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₃₁	#41	1	1	yes	characteristic
136	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
137	C₂×#1701	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₃₁	—	2	2	no	—
139	C₂³×C₃₁	—	4	2	no	—
140	C₂³×C₃₁	—	4	2	no	—
141	C₂³×C₃₁	—	4	2	no	—
142	C₂³×C₃₁	—	4	2	no	—
143	C₂³×C₃₁	—	8	2	no	—
144	C₂³×C₃₁	—	8	2	no	—
145	C₂³×C₃₁	—	8	2	no	—
146	C₂³×C₃₁	#121	1	1	yes	characteristic
147	Q₈×C₃₁	—	4	2	no	—
148	Q₈×C₃₁	—	4	2	no	—
149	Q₈×C₃₁	—	8	2	no	—
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	—	4	2	no	—
157	D₄×C₃₁	—	8	2	no	—
158	D₄×C₃₁	—	8	2	no	—
159	D₄×C₃₁	—	8	2	no	—
160	D₄×C₃₁	—	8	2	no	—
161	C₂×C₄×C₃₁	—	2	2	no	—
162	C₂×C₄×C₃₁	—	2	2	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	—	4	2	no	—
165	C₂×C₄×C₃₁	—	4	2	no	—
166	C₂×C₄×C₃₁	—	4	4	no	—
167	C₂×C₄×C₃₁	—	4	2	no	—
168	C₂×C₄×C₃₁	—	8	2	no	—
169	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
170	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
171	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
172	C₂×C₄×C₃₁	#135	1	2	yes	—
173	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
174	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
176	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
179	C₈×C₃₁	—	2	2	no	—
180	C₈×C₃₁	—	2	2	no	—
181	C₈×C₃₁	—	4	2	no	—
182	C₈×C₃₁	—	4	2	no	—
183	C₈×C₃₁	—	4	2	no	—
184	C₂×#486	C₂×C₃₁	1	1	yes	characteristic, complemented
185	C₂×#461	C₂×C₃₁	1	1	yes	characteristic, complemented
186	C₂×#459	C₂×C₃₁	1	1	yes	characteristic
187	C₂×#436	C₂×C₃₁	1	1	yes	characteristic, complemented
188	#1701	C₂×C₃₁	1	8	yes	direct product factor
189	C₂×#334	C₂×C₃₁	1	1	yes	characteristic, complemented
190	C₂×#332	C₂×C₃₁	1	1	yes	characteristic, complemented
191	C₂×#331	C₂×C₃₁	1	1	yes	characteristic, complemented
192	C₂²×C₃₁	—	4	2	no	—
193	C₂²×C₃₁	—	4	2	no	—
194	C₂²×C₃₁	—	4	2	no	—
195	C₂²×C₃₁	—	8	4	no	—
196	C₂²×C₃₁	—	8	2	no	—
197	C₂²×C₃₁	—	8	2	no	—
198	C₂²×C₃₁	—	8	2	no	—
199	C₂²×C₃₁	—	16	4	no	—
200	C₂²×C₃₁	#463	1	2	yes	—
201	C₂²×C₃₁	#469	1	2	yes	—
202	C₂²×C₃₁	#471	1	2	yes	—
203	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
204	C₄×C₃₁	—	2	1	no	—
205	C₄×C₃₁	—	2	1	no	—
206	C₄×C₃₁	—	4	2	no	—
207	C₄×C₃₁	—	8	2	no	—
208	C₄×C₃₁	#463	1	2	yes	—
209	C₄×C₃₁	#469	1	2	yes	—
210	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
211	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂²×SD₁₆	—	2	1	no	—
215	C₂²×D₈	—	2	1	no	—
216	C₂²×M₁₆	—	2	1	no	—
217	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
218	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
219	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
220	#486	—	2	2	no	—
221	#486	C₂²×C₃₁	1	4	yes	complemented
222	#461	—	2	2	no	—
223	#461	C₂²×C₃₁	1	4	yes	complemented
224	#459	—	2	2	no	—
225	#459	C₂²×C₃₁	1	4	yes	—
226	#436	—	2	2	no	—
227	#436	C₂²×C₃₁	1	4	yes	complemented
228	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
231	C₂×#103	—	2	1	no	—
232	C₂×#102	—	2	1	no	—
233	C₂×#102	—	2	1	no	—
234	C₂×#102	—	2	1	no	—
235	C₂×C₂²⋊C₈	—	2	1	no	—
236	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
237	#334	C₂²×C₃₁	1	4	yes	complemented
238	#332	C₂²×C₃₁	1	4	yes	complemented
239	#331	C₂²×C₃₁	1	4	yes	complemented
240	C₂×C₃₁	—	8	2	no	—
241	C₂×C₃₁	—	16	2	no	—
242	C₂×C₃₁	#1701	1	4	yes	direct product factor
243	C₂×C₃₁	C₂×#463	1	1	yes	characteristic
244	C₂×C₃₁	C₂×#469	1	1	yes	characteristic
245	C₂×C₃₁	C₂×#471	1	1	yes	characteristic
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
251	C₂³×C₄	—	2	1	no	—
252	C₂×SD₁₆	—	2	4	no	—
253	C₂×SD₁₆	—	4	4	no	—
254	C₂×D₈	—	2	4	no	—
255	C₂×D₈	—	4	4	no	—
256	C₂×M₁₆	—	2	4	no	—
257	C₂×M₁₆	—	4	4	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
262	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
267	#127	—	2	1	no	—
268	#127	—	2	1	no	—
269	#127	—	2	1	no	—
270	#127	C₂³×C₃₁	1	2	yes	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	D₄×C₃₁	1	2	yes	—
274	C₄×D₄	C₂³×C₃₁	1	2	yes	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
284	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
285	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
286	#103	—	2	4	no	—
287	#102	—	2	4	no	—
288	#102	—	2	4	no	—
289	#102	—	2	4	no	—
290	C₂²⋊C₈	—	2	4	no	—
291	C₄×C₈	D₄×C₃₁	1	2	yes	—
292	C₄×C₈	C₂³×C₃₁	1	2	yes	—
293	C₃₁	C₂×#1701	1	1	yes	characteristic, direct product factor, Sylow
294	C₂⁴	—	2	1	no	—
295	C₂⁴	—	4	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
323	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
324	SD₁₆	—	4	8	no	—
325	D₈	—	4	8	no	—
326	M₁₆	—	4	8	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	2	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
336	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
346	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
347	C₄²	#41×C₃₁	1	1	yes	characteristic
348	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
349	C₂³	—	2	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	8	2	no	—
355	C₂³	—	8	2	no	—
356	C₂³	—	8	2	no	—
357	C₂³	C₃₁×#121	1	1	yes	characteristic
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	8	2	no	—
361	D₄	—	2	2	no	—
362	D₄	—	2	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	8	2	no	—
369	D₄	—	8	2	no	—
370	D₄	—	8	2	no	—
371	D₄	—	8	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
381	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
382	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
383	C₂×C₄	C₃₁×#135	1	2	yes	—
384	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
385	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
386	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
387	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
388	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	—	2	2	no	—
392	C₈	—	4	2	no	—
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	8	4	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	16	4	no	—
403	C₂²	C₃₁×#463	1	2	yes	—
404	C₂²	C₃₁×#469	1	2	yes	—
405	C₂²	C₃₁×#471	1	2	yes	—
406	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₃₁×#463	1	2	yes	—
412	C₄	C₃₁×#469	1	2	yes	—
413	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
414	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
415	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
416	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
417	C₂	—	8	2	no	—
418	C₂	—	16	2	no	—
419	C₂	C₃₁×#1701	1	4	yes	direct product factor
420	C₂	C₂×C₃₁×#463	1	1	yes	characteristic
421	C₂	C₂×C₃₁×#469	1	1	yes	characteristic
422	C₂	C₂×C₃₁×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#459	C₂
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
1. C₂×C₃₁×#486	C₂	semidirect
2. C₂×C₃₁×#461	C₂	semidirect
4. C₂×C₃₁×#436	C₂	semidirect
5. C₃₁×#1701	C₂	direct (N × H)
6. C₂×C₃₁×#334	C₂	semidirect
7. C₂×C₃₁×#332	C₂	semidirect
8. C₂×C₃₁×#331	C₂	semidirect
16. C₃₁×#486	C₂²	semidirect
18. C₃₁×#461	C₂²	semidirect
22. C₃₁×#436	C₂²	semidirect
32. C₃₁×#334	C₂²	semidirect
33. C₃₁×#332	C₂²	semidirect
34. C₃₁×#331	C₂²	semidirect
137. C₂×#1701	C₃₁	direct (N × H)
184. C₂×#486	C₂×C₃₁	semidirect
185. C₂×#461	C₂×C₃₁	semidirect
187. C₂×#436	C₂×C₃₁	semidirect
188. #1701	C₂×C₃₁	direct (N × H)
189. C₂×#334	C₂×C₃₁	semidirect
190. C₂×#332	C₂×C₃₁	semidirect
191. C₂×#331	C₂×C₃₁	semidirect
221. #486	C₂²×C₃₁	semidirect
223. #461	C₂²×C₃₁	semidirect
227. #436	C₂²×C₃₁	semidirect
237. #334	C₂²×C₃₁	semidirect
238. #332	C₂²×C₃₁	semidirect
239. #331	C₂²×C₃₁	semidirect
242. C₂×C₃₁	#1701	direct (N × H)
293. C₃₁	C₂×#1701	direct (N × H)
419. C₂	C₃₁×#1701	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×#461	2
C₂×C₃₁×#459	2
C₂×C₃₁×#436	2
C₃₁×#1701	2
C₂×C₃₁×#334	2
C₂×C₃₁×#332	2
C₂×C₃₁×#331	2
C₂×#1701	31

Subgroups — C2×C31×#1701 #21475899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1701 #21475899