Subgroups — C₂×C₃₁×#1677 #21475865

Order 7936.

810 conjugacy classes of subgroups.

The subgroup lattice has 416 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×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#459	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1677	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, complemented
9	C₂²×D₈×C₃₁	—	2	1	no	—
10	C₂³×C₈×C₃₁	—	2	1	no	—
11	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
14	C₃₁×#486	—	2	2	no	—
15	C₃₁×#486	C₂²	1	4	yes	complemented
16	C₃₁×#476	—	2	2	no	—
17	C₃₁×#476	C₂²	1	4	yes	complemented
18	C₃₁×#459	—	2	2	no	—
19	C₃₁×#459	C₂²	1	4	yes	—
20	C₈×D₄×C₃₁	—	2	2	no	—
21	C₈×D₄×C₃₁	C₂²	1	4	yes	complemented
22	C₂×C₃₁×#106	—	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×#102	—	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×#333	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×D₈×C₃₁	—	2	4	no	—
42	C₂×D₈×C₃₁	—	4	4	no	—
43	C₂²×C₈×C₃₁	—	2	1	no	—
44	C₂²×C₈×C₃₁	—	2	1	no	—
45	C₂²×C₈×C₃₁	—	2	1	no	—
46	C₂²×C₈×C₃₁	—	2	4	no	—
47	C₂²×C₈×C₃₁	—	4	4	no	—
48	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
50	C₃₁×C₄⋊Q₈	—	2	1	no	—
51	C₃₁×C₄⋊Q₈	—	2	1	no	—
52	C₃₁×C₄⋊Q₈	—	2	1	no	—
53	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₃₁×#127	—	2	1	no	—
55	C₃₁×#127	—	2	1	no	—
56	C₃₁×#127	—	2	1	no	—
57	C₃₁×#127	C₂³	1	2	yes	—
58	C₄×D₄×C₃₁	—	2	1	no	—
59	C₄×D₄×C₃₁	—	2	1	no	—
60	C₄×D₄×C₃₁	D₄	1	2	yes	—
61	C₄×D₄×C₃₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
66	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
67	C₃₁×#106	—	2	4	no	—
68	C₃₁×C₄⋊C₈	—	2	1	no	—
69	C₃₁×C₄⋊C₈	—	2	1	no	—
70	C₃₁×C₄⋊C₈	—	2	1	no	—
71	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
72	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
73	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
74	C₃₁×#102	—	2	4	no	—
75	C₃₁×#102	—	2	4	no	—
76	C₃₁×#102	—	2	4	no	—
77	C₃₁×#102	—	2	4	no	—
78	C₃₁×C₂²⋊C₈	—	2	4	no	—
79	C₄×C₈×C₃₁	D₄	1	2	yes	—
80	C₄×C₈×C₃₁	C₂³	1	2	yes	—
81	C₂⁴×C₃₁	—	2	1	no	—
82	C₂⁴×C₃₁	—	4	1	no	—
83	C₂×Q₈×C₃₁	—	2	2	no	—
84	C₂×Q₈×C₃₁	—	4	1	no	—
85	C₂×Q₈×C₃₁	—	8	2	no	—
86	C₂×D₄×C₃₁	—	2	1	no	—
87	C₂×D₄×C₃₁	—	2	2	no	—
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	C₂×D₄×C₃₁	SD₁₆	1	4	yes	—
100	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
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	—	4	2	no	—
105	C₂²×C₄×C₃₁	—	4	2	no	—
106	C₂²×C₄×C₃₁	—	4	1	no	—
107	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
110	D₈×C₃₁	—	4	8	no	—
111	C₂×C₈×C₃₁	—	2	2	no	—
112	C₂×C₈×C₃₁	—	2	2	no	—
113	C₂×C₈×C₃₁	—	2	2	no	—
114	C₂×C₈×C₃₁	—	2	2	no	—
115	C₂×C₈×C₃₁	—	2	2	no	—
116	C₂×C₈×C₃₁	—	4	8	no	—
117	C₂×C₈×C₃₁	—	4	2	no	—
118	C₂×C₈×C₃₁	—	4	2	no	—
119	C₂×C₈×C₃₁	—	4	2	no	—
120	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
122	C₄⋊C₄×C₃₁	—	2	1	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	4	1	no	—
126	C₄⋊C₄×C₃₁	—	4	1	no	—
127	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
128	C₂²⋊C₄×C₃₁	—	2	2	no	—
129	C₂²⋊C₄×C₃₁	—	2	2	no	—
130	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₃₁	#41	1	1	yes	characteristic
133	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
134	C₂×#1677	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₃₁	—	2	2	no	—
136	C₂³×C₃₁	—	2	4	no	—
137	C₂³×C₃₁	—	4	2	no	—
138	C₂³×C₃₁	—	4	2	no	—
139	C₂³×C₃₁	—	4	2	no	—
140	C₂³×C₃₁	—	8	2	no	—
141	C₂³×C₃₁	—	8	2	no	—
142	C₂³×C₃₁	—	8	2	no	—
143	C₂³×C₃₁	#121	1	1	yes	characteristic
144	Q₈×C₃₁	—	8	2	no	—
145	Q₈×C₃₁	—	8	2	no	—
146	D₄×C₃₁	—	2	2	no	—
147	D₄×C₃₁	—	2	4	no	—
148	D₄×C₃₁	—	4	2	no	—
149	D₄×C₃₁	—	4	2	no	—
150	D₄×C₃₁	—	4	2	no	—
151	D₄×C₃₁	—	4	2	no	—
152	D₄×C₃₁	—	8	2	no	—
153	D₄×C₃₁	—	8	2	no	—
154	D₄×C₃₁	—	8	2	no	—
155	D₄×C₃₁	—	8	2	no	—
156	D₄×C₃₁	C₂×SD₁₆	1	4	yes	—
157	C₂×C₄×C₃₁	—	2	2	no	—
158	C₂×C₄×C₃₁	—	2	2	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	4	2	no	—
161	C₂×C₄×C₃₁	—	4	2	no	—
162	C₂×C₄×C₃₁	—	4	4	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	—	8	2	no	—
165	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
166	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
167	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
168	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
169	C₂×C₄×C₃₁	#135	1	2	yes	—
170	C₂×C₄×C₃₁	#135	1	2	yes	—
171	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
172	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
175	C₈×C₃₁	—	2	2	no	—
176	C₈×C₃₁	—	2	2	no	—
177	C₈×C₃₁	—	4	2	no	—
178	C₈×C₃₁	—	4	2	no	—
179	C₈×C₃₁	—	4	2	no	—
180	C₂×#486	C₂×C₃₁	1	1	yes	characteristic, complemented
181	C₂×#476	C₂×C₃₁	1	1	yes	characteristic, complemented
182	C₂×#459	C₂×C₃₁	1	1	yes	characteristic
183	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
184	#1677	C₂×C₃₁	1	8	yes	direct product factor
185	C₂×#334	C₂×C₃₁	1	1	yes	characteristic, complemented
186	C₂×#333	C₂×C₃₁	1	1	yes	characteristic, complemented
187	C₂×#331	C₂×C₃₁	1	1	yes	characteristic, complemented
188	C₂²×C₃₁	—	2	4	no	—
189	C₂²×C₃₁	—	4	8	no	—
190	C₂²×C₃₁	—	4	2	no	—
191	C₂²×C₃₁	—	4	2	no	—
192	C₂²×C₃₁	—	8	2	no	—
193	C₂²×C₃₁	—	8	2	no	—
194	C₂²×C₃₁	—	8	2	no	—
195	C₂²×C₃₁	—	16	4	no	—
196	C₂²×C₃₁	#463	1	2	yes	—
197	C₂²×C₃₁	#465	1	2	yes	—
198	C₂²×C₃₁	#472	1	2	yes	—
199	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
200	C₄×C₃₁	—	2	1	no	—
201	C₄×C₃₁	—	2	1	no	—
202	C₄×C₃₁	—	4	2	no	—
203	C₄×C₃₁	—	8	2	no	—
204	C₄×C₃₁	#463	1	2	yes	—
205	C₄×C₃₁	#465	1	2	yes	—
206	C₄×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
207	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
208	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
209	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
210	C₂²×D₈	—	2	1	no	—
211	C₂³×C₈	—	2	1	no	—
212	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
214	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
215	#486	—	2	2	no	—
216	#486	C₂²×C₃₁	1	4	yes	complemented
217	#476	—	2	2	no	—
218	#476	C₂²×C₃₁	1	4	yes	complemented
219	#459	—	2	2	no	—
220	#459	C₂²×C₃₁	1	4	yes	—
221	C₈×D₄	—	2	2	no	—
222	C₈×D₄	C₂²×C₃₁	1	4	yes	complemented
223	C₂×#106	—	2	1	no	—
224	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
227	C₂×#102	—	2	1	no	—
228	C₂×#102	—	2	1	no	—
229	C₂×#102	—	2	1	no	—
230	C₂×#102	—	2	1	no	—
231	C₂×C₂²⋊C₈	—	2	1	no	—
232	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
233	#334	C₂²×C₃₁	1	4	yes	complemented
234	#333	C₂²×C₃₁	1	4	yes	complemented
235	#331	C₂²×C₃₁	1	4	yes	complemented
236	C₂×C₃₁	—	4	4	no	—
237	C₂×C₃₁	—	16	2	no	—
238	C₂×C₃₁	#1677	1	4	yes	direct product factor
239	C₂×C₃₁	C₂×#463	1	1	yes	characteristic
240	C₂×C₃₁	C₂×#465	1	1	yes	characteristic
241	C₂×C₃₁	C₂×#472	1	1	yes	characteristic
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
247	C₂³×C₄	—	2	1	no	—
248	C₂×D₈	—	2	4	no	—
249	C₂×D₈	—	4	4	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	4	no	—
254	C₂²×C₈	—	4	4	no	—
255	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
256	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
261	#127	—	2	1	no	—
262	#127	—	2	1	no	—
263	#127	—	2	1	no	—
264	#127	C₂³×C₃₁	1	2	yes	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	D₄×C₃₁	1	2	yes	—
268	C₄×D₄	C₂³×C₃₁	1	2	yes	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
274	#106	—	2	4	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
279	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
280	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
281	#102	—	2	4	no	—
282	#102	—	2	4	no	—
283	#102	—	2	4	no	—
284	#102	—	2	4	no	—
285	C₂²⋊C₈	—	2	4	no	—
286	C₄×C₈	D₄×C₃₁	1	2	yes	—
287	C₄×C₈	C₂³×C₃₁	1	2	yes	—
288	C₃₁	C₂×#1677	1	1	yes	characteristic, direct product factor, Sylow
289	C₂⁴	—	2	1	no	—
290	C₂⁴	—	4	1	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×Q₈	—	8	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	8	2	no	—
307	C₂×D₄	SD₁₆×C₃₁	1	4	yes	—
308	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
317	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
318	D₈	—	4	8	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	4	8	no	—
325	C₂×C₈	—	4	2	no	—
326	C₂×C₈	—	4	2	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
329	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
340	C₄²	#41×C₃₁	1	1	yes	characteristic
341	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
342	C₂³	—	2	4	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	8	2	no	—
348	C₂³	—	8	2	no	—
349	C₂³	—	8	2	no	—
350	C₂³	C₃₁×#121	1	1	yes	characteristic
351	Q₈	—	8	2	no	—
352	Q₈	—	8	2	no	—
353	D₄	—	2	4	no	—
354	D₄	—	2	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	8	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	2	no	—
362	D₄	—	8	2	no	—
363	D₄	C₂×SD₁₆×C₃₁	1	4	yes	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	8	2	no	—
372	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
373	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
374	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
375	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
376	C₂×C₄	C₃₁×#135	1	2	yes	—
377	C₂×C₄	C₃₁×#135	1	2	yes	—
378	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
379	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
380	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	4	8	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	16	4	no	—
395	C₂²	C₃₁×#463	1	2	yes	—
396	C₂²	C₃₁×#465	1	2	yes	—
397	C₂²	C₃₁×#472	1	2	yes	—
398	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	4	2	no	—
402	C₄	—	8	2	no	—
403	C₄	C₃₁×#463	1	2	yes	—
404	C₄	C₃₁×#465	1	2	yes	—
405	C₄	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
406	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
407	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
408	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
409	C₂	—	4	4	no	—
410	C₂	—	16	2	no	—
411	C₂	C₃₁×#1677	1	4	yes	direct product factor
412	C₂	C₂×C₃₁×#463	1	1	yes	characteristic
413	C₂	C₂×C₃₁×#465	1	1	yes	characteristic
414	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×#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×#476	C₂	semidirect
4. C₂×C₈×D₄×C₃₁	C₂	semidirect
5. C₃₁×#1677	C₂	direct (N × H)
6. C₂×C₃₁×#334	C₂	semidirect
7. C₂×C₃₁×#333	C₂	semidirect
8. C₂×C₃₁×#331	C₂	semidirect
15. C₃₁×#486	C₂²	semidirect
17. C₃₁×#476	C₂²	semidirect
21. C₈×D₄×C₃₁	C₂²	semidirect
32. C₃₁×#334	C₂²	semidirect
33. C₃₁×#333	C₂²	semidirect
34. C₃₁×#331	C₂²	semidirect
134. C₂×#1677	C₃₁	direct (N × H)
180. C₂×#486	C₂×C₃₁	semidirect
181. C₂×#476	C₂×C₃₁	semidirect
183. C₂×C₈×D₄	C₂×C₃₁	semidirect
184. #1677	C₂×C₃₁	direct (N × H)
185. C₂×#334	C₂×C₃₁	semidirect
186. C₂×#333	C₂×C₃₁	semidirect
187. C₂×#331	C₂×C₃₁	semidirect
216. #486	C₂²×C₃₁	semidirect
218. #476	C₂²×C₃₁	semidirect
222. C₈×D₄	C₂²×C₃₁	semidirect
233. #334	C₂²×C₃₁	semidirect
234. #333	C₂²×C₃₁	semidirect
235. #331	C₂²×C₃₁	semidirect
238. C₂×C₃₁	#1677	direct (N × H)
288. C₃₁	C₂×#1677	direct (N × H)
411. C₂	C₃₁×#1677	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×#476	2
C₂×C₃₁×#459	2
C₂×C₈×D₄×C₃₁	2
C₃₁×#1677	2
C₂×C₃₁×#334	2
C₂×C₃₁×#333	2
C₂×C₃₁×#331	2
C₂×#1677	31

Subgroups — C2×C31×#1677 #21475865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1677 #21475865