Subgroups — C₂×C₃₁×#1637 #21475248

Order 7936.

1174 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#476	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1637	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₃₁	—	2	1	no	—
10	D₄×Q₈×C₃₁	—	2	2	no	—
11	D₄×Q₈×C₃₁	—	2	2	no	—
12	D₄×Q₈×C₃₁	—	2	2	no	—
13	D₄×Q₈×C₃₁	C₂²	1	4	yes	—
14	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₃₁	—	2	1	no	—
21	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#487	—	2	2	no	—
23	C₃₁×#487	C₂²	1	4	yes	complemented
24	C₃₁×#477	—	2	2	no	—
25	C₃₁×#477	C₂²	1	4	yes	complemented
26	C₃₁×#476	—	2	2	no	—
27	C₃₁×#476	C₂²	1	4	yes	—
28	C₂×C₃₁×#107	—	2	1	no	—
29	C₂×C₃₁×#106	—	2	1	no	—
30	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#103	—	2	1	no	—
33	C₂×C₃₁×#103	—	2	2	no	—
34	C₂×C₃₁×#102	—	2	1	no	—
35	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₃₁×#332	C₂²	1	4	yes	complemented
37	C₃₁×Q₈⋊C₈	C₂²	1	4	yes	complemented
38	C₃₁×D₄⋊C₈	C₂²	1	4	yes	—
39	C₂²×Q₈×C₃₁	—	2	2	no	—
40	C₂²×Q₈×C₃₁	—	2	4	no	—
41	C₂²×Q₈×C₃₁	—	2	4	no	—
42	C₂²×Q₈×C₃₁	—	2	1	no	—
43	C₂²×Q₈×C₃₁	—	2	1	no	—
44	C₂²×Q₈×C₃₁	—	4	4	no	—
45	C₂²×Q₈×C₃₁	—	4	4	no	—
46	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₃₁	—	2	2	no	—
49	C₂³×C₄×C₃₁	—	2	1	no	—
50	C₂²×C₈×C₃₁	—	2	1	no	—
51	C₂²×C₈×C₃₁	—	2	1	no	—
52	C₂²×C₈×C₃₁	—	2	1	no	—
53	C₃₁×C₄⋊Q₈	—	2	4	no	—
54	C₃₁×C₄⋊Q₈	—	2	4	no	—
55	C₃₁×C₄⋊Q₈	—	2	1	no	—
56	C₃₁×C₄⋊Q₈	—	2	1	no	—
57	C₃₁×C₄⋊Q₈	—	2	1	no	—
58	C₃₁×C₄⋊Q₈	—	2	1	no	—
59	C₃₁×C₄⋊Q₈	—	2	1	no	—
60	C₃₁×C₄⋊Q₈	D₄	1	2	yes	—
61	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₃₁×C₂²⋊Q₈	—	2	4	no	—
64	C₃₁×C₂²⋊Q₈	—	2	8	no	—
65	C₃₁×C₂²⋊Q₈	—	2	4	no	—
66	C₃₁×C₂²⋊Q₈	—	2	8	no	—
67	C₄×Q₈×C₃₁	—	2	1	no	—
68	C₄×Q₈×C₃₁	—	2	1	no	—
69	C₄×Q₈×C₃₁	D₄	1	2	yes	—
70	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
71	C₄×D₄×C₃₁	—	2	4	no	—
72	C₄×D₄×C₃₁	—	2	4	no	—
73	C₄×D₄×C₃₁	—	2	1	no	—
74	C₄×D₄×C₃₁	—	2	1	no	—
75	C₄×D₄×C₃₁	D₄	1	2	yes	—
76	C₄×D₄×C₃₁	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
82	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
87	C₂×C₄²×C₃₁	—	2	1	no	—
88	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
89	C₃₁×#107	—	2	4	no	—
90	C₃₁×#106	—	2	4	no	—
91	C₃₁×C₄⋊C₈	—	2	1	no	—
92	C₃₁×C₄⋊C₈	—	2	1	no	—
93	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
94	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
95	C₃₁×#103	—	2	4	no	—
96	C₃₁×#103	—	2	8	no	—
97	C₃₁×#102	—	2	4	no	—
98	C₄×C₈×C₃₁	—	2	1	no	—
99	C₄×C₈×C₃₁	C₂³	1	2	yes	—
100	C₂⁴×C₃₁	—	2	1	no	—
101	C₂×Q₈×C₃₁	—	2	8	no	—
102	C₂×Q₈×C₃₁	—	2	1	no	—
103	C₂×Q₈×C₃₁	—	2	2	no	—
104	C₂×Q₈×C₃₁	—	2	2	no	—
105	C₂×Q₈×C₃₁	—	2	2	no	—
106	C₂×Q₈×C₃₁	—	2	2	no	—
107	C₂×Q₈×C₃₁	—	4	8	no	—
108	C₂×Q₈×C₃₁	—	4	4	no	—
109	C₂×Q₈×C₃₁	—	4	8	no	—
110	C₂×Q₈×C₃₁	—	4	16	no	—
111	C₂×Q₈×C₃₁	—	4	8	no	—
112	C₂×Q₈×C₃₁	—	4	1	no	—
113	C₂×Q₈×C₃₁	—	4	2	no	—
114	C₂×Q₈×C₃₁	—	4	2	no	—
115	C₂×Q₈×C₃₁	SD₁₆	1	4	yes	—
116	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₃₁	—	2	1	no	—
118	C₂×D₄×C₃₁	—	2	2	no	—
119	C₂×D₄×C₃₁	Q₁₆	1	4	yes	—
120	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₃₁	—	2	1	no	—
122	C₂²×C₄×C₃₁	—	2	8	no	—
123	C₂²×C₄×C₃₁	—	2	1	no	—
124	C₂²×C₄×C₃₁	—	2	2	no	—
125	C₂²×C₄×C₃₁	—	2	1	no	—
126	C₂²×C₄×C₃₁	—	2	2	no	—
127	C₂²×C₄×C₃₁	—	2	2	no	—
128	C₂²×C₄×C₃₁	—	4	8	no	—
129	C₂²×C₄×C₃₁	—	4	2	no	—
130	C₂²×C₄×C₃₁	—	4	2	no	—
131	C₂²×C₄×C₃₁	—	4	1	no	—
132	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₃₁	—	2	2	no	—
136	C₂×C₈×C₃₁	—	2	2	no	—
137	C₂×C₈×C₃₁	—	2	2	no	—
138	C₂×C₈×C₃₁	—	4	2	no	—
139	C₂×C₈×C₃₁	—	4	2	no	—
140	C₂×C₈×C₃₁	—	4	2	no	—
141	C₄⋊C₄×C₃₁	—	2	8	no	—
142	C₄⋊C₄×C₃₁	—	2	2	no	—
143	C₄⋊C₄×C₃₁	—	2	2	no	—
144	C₄⋊C₄×C₃₁	—	2	1	no	—
145	C₄⋊C₄×C₃₁	—	2	1	no	—
146	C₄⋊C₄×C₃₁	—	2	2	no	—
147	C₄⋊C₄×C₃₁	—	2	2	no	—
148	C₄⋊C₄×C₃₁	—	2	2	no	—
149	C₄⋊C₄×C₃₁	—	2	2	no	—
150	C₄⋊C₄×C₃₁	—	2	2	no	—
151	C₄⋊C₄×C₃₁	—	4	1	no	—
152	C₄⋊C₄×C₃₁	—	4	1	no	—
153	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
154	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
155	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
156	C₂²⋊C₄×C₃₁	—	2	8	no	—
157	C₂²⋊C₄×C₃₁	—	2	2	no	—
158	C₂²⋊C₄×C₃₁	—	2	2	no	—
159	C₄²×C₃₁	—	2	2	no	—
160	C₄²×C₃₁	—	2	2	no	—
161	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
165	C₂×#1637	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₃₁	—	2	2	no	—
167	C₂³×C₃₁	—	2	4	no	—
168	C₂³×C₃₁	—	4	2	no	—
169	C₂³×C₃₁	—	4	2	no	—
170	C₂³×C₃₁	#120	1	1	yes	characteristic
171	Q₈×C₃₁	—	2	2	no	—
172	Q₈×C₃₁	—	2	4	no	—
173	Q₈×C₃₁	—	4	16	no	—
174	Q₈×C₃₁	—	4	4	no	—
175	Q₈×C₃₁	—	4	2	no	—
176	Q₈×C₃₁	—	4	2	no	—
177	Q₈×C₃₁	—	4	4	no	—
178	Q₈×C₃₁	—	8	2	no	—
179	Q₈×C₃₁	C₂×SD₁₆	1	4	yes	—
180	D₄×C₃₁	—	2	2	no	—
181	D₄×C₃₁	—	2	4	no	—
182	D₄×C₃₁	C₂×Q₁₆	1	4	yes	—
183	C₂×C₄×C₃₁	—	2	2	no	—
184	C₂×C₄×C₃₁	—	2	4	no	—
185	C₂×C₄×C₃₁	—	2	2	no	—
186	C₂×C₄×C₃₁	—	2	2	no	—
187	C₂×C₄×C₃₁	—	2	4	no	—
188	C₂×C₄×C₃₁	—	2	2	no	—
189	C₂×C₄×C₃₁	—	4	16	no	—
190	C₂×C₄×C₃₁	—	4	4	no	—
191	C₂×C₄×C₃₁	—	4	2	no	—
192	C₂×C₄×C₃₁	—	4	2	no	—
193	C₂×C₄×C₃₁	—	4	2	no	—
194	C₂×C₄×C₃₁	—	4	2	no	—
195	C₂×C₄×C₃₁	—	4	4	no	—
196	C₂×C₄×C₃₁	—	4	2	no	—
197	C₂×C₄×C₃₁	—	8	2	no	—
198	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
199	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
200	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
201	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
202	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
203	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₃₁	#137	1	2	yes	—
205	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
208	C₈×C₃₁	—	4	2	no	—
209	C₈×C₃₁	—	4	2	no	—
210	C₈×C₃₁	—	4	2	no	—
211	C₂×D₄×Q₈	C₂×C₃₁	1	1	yes	characteristic
212	C₂×#487	C₂×C₃₁	1	1	yes	characteristic, complemented
213	C₂×#477	C₂×C₃₁	1	1	yes	characteristic, complemented
214	C₂×#476	C₂×C₃₁	1	1	yes	characteristic
215	#1637	C₂×C₃₁	1	8	yes	direct product factor
216	C₂×#332	C₂×C₃₁	1	1	yes	characteristic, complemented
217	C₂×Q₈⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
218	C₂×D₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic
219	C₂²×C₃₁	—	2	4	no	—
220	C₂²×C₃₁	—	4	8	no	—
221	C₂²×C₃₁	—	4	2	no	—
222	C₂²×C₃₁	—	4	2	no	—
223	C₂²×C₃₁	#450	1	2	yes	—
224	C₂²×C₃₁	#451	1	2	yes	—
225	C₂²×C₃₁	#454	1	2	yes	—
226	C₂²×C₃₁	C₂×#120	1	1	yes	characteristic
227	C₄×C₃₁	—	2	4	no	—
228	C₄×C₃₁	—	2	1	no	—
229	C₄×C₃₁	—	2	1	no	—
230	C₄×C₃₁	—	4	4	no	—
231	C₄×C₃₁	—	4	2	no	—
232	C₄×C₃₁	—	4	2	no	—
233	C₄×C₃₁	—	8	2	no	—
234	C₄×C₃₁	#450	1	2	yes	—
235	C₄×C₃₁	#451	1	2	yes	—
236	C₄×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
237	C₄×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
238	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
239	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
240	C₂³×Q₈	—	2	1	no	—
241	D₄×Q₈	—	2	2	no	—
242	D₄×Q₈	—	2	2	no	—
243	D₄×Q₈	—	2	2	no	—
244	D₄×Q₈	C₂²×C₃₁	1	4	yes	—
245	C₂×C₄⋊Q₈	—	2	1	no	—
246	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
248	C₂×C₂²⋊Q₈	—	2	1	no	—
249	C₂×C₂²⋊Q₈	—	2	2	no	—
250	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
251	C₂×C₄×D₄	—	2	1	no	—
252	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
253	#487	—	2	2	no	—
254	#487	C₂²×C₃₁	1	4	yes	complemented
255	#477	—	2	2	no	—
256	#477	C₂²×C₃₁	1	4	yes	complemented
257	#476	—	2	2	no	—
258	#476	C₂²×C₃₁	1	4	yes	—
259	C₂×#107	—	2	1	no	—
260	C₂×#106	—	2	1	no	—
261	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
263	C₂×#103	—	2	1	no	—
264	C₂×#103	—	2	2	no	—
265	C₂×#102	—	2	1	no	—
266	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
267	#332	C₂²×C₃₁	1	4	yes	complemented
268	Q₈⋊C₈	C₂²×C₃₁	1	4	yes	complemented
269	D₄⋊C₈	C₂²×C₃₁	1	4	yes	—
270	C₂×C₃₁	—	4	4	no	—
271	C₂×C₃₁	#1637	1	4	yes	direct product factor
272	C₂×C₃₁	C₂×#450	1	1	yes	characteristic
273	C₂×C₃₁	C₂×#451	1	1	yes	characteristic
274	C₂×C₃₁	C₂×#454	1	1	yes	characteristic
275	C₂²×Q₈	—	2	2	no	—
276	C₂²×Q₈	—	2	4	no	—
277	C₂²×Q₈	—	2	4	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×Q₈	—	2	1	no	—
280	C₂²×Q₈	—	4	4	no	—
281	C₂²×Q₈	—	4	4	no	—
282	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
283	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
284	C₂³×C₄	—	2	2	no	—
285	C₂³×C₄	—	2	1	no	—
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	—	2	1	no	—
289	C₄⋊Q₈	—	2	4	no	—
290	C₄⋊Q₈	—	2	4	no	—
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	—	2	1	no	—
295	C₄⋊Q₈	—	2	1	no	—
296	C₄⋊Q₈	D₄×C₃₁	1	2	yes	—
297	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
298	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	—	2	8	no	—
301	C₂²⋊Q₈	—	2	4	no	—
302	C₂²⋊Q₈	—	2	8	no	—
303	C₄×Q₈	—	2	1	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	D₄×C₃₁	1	2	yes	—
306	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	D₄×C₃₁	1	2	yes	—
312	C₄×D₄	C₂³×C₃₁	1	2	yes	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
319	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
320	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
325	#107	—	2	4	no	—
326	#106	—	2	4	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	—	2	1	no	—
329	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
330	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
331	#103	—	2	4	no	—
332	#103	—	2	8	no	—
333	#102	—	2	4	no	—
334	C₄×C₈	—	2	1	no	—
335	C₄×C₈	C₂³×C₃₁	1	2	yes	—
336	C₃₁	C₂×#1637	1	1	yes	characteristic, direct product factor, Sylow
337	C₂⁴	—	2	1	no	—
338	C₂×Q₈	—	2	8	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	4	8	no	—
345	C₂×Q₈	—	4	4	no	—
346	C₂×Q₈	—	4	16	no	—
347	C₂×Q₈	—	4	8	no	—
348	C₂×Q₈	—	4	8	no	—
349	C₂×Q₈	—	4	1	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	SD₁₆×C₃₁	1	4	yes	—
353	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	Q₁₆×C₃₁	1	4	yes	—
357	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	8	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	—	4	2	no	—
377	C₂×C₈	—	4	2	no	—
378	C₄⋊C₄	—	2	8	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
391	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
392	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
399	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
400	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
401	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
402	C₂³	—	2	4	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	C₃₁×#120	1	1	yes	characteristic
407	Q₈	—	2	4	no	—
408	Q₈	—	2	2	no	—
409	Q₈	—	4	16	no	—
410	Q₈	—	4	4	no	—
411	Q₈	—	4	4	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	8	2	no	—
415	Q₈	C₂×SD₁₆×C₃₁	1	4	yes	—
416	D₄	—	2	4	no	—
417	D₄	—	2	2	no	—
418	D₄	C₂×Q₁₆×C₃₁	1	4	yes	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	16	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	8	2	no	—
434	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
435	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
436	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
437	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
438	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
439	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
440	C₂×C₄	C₃₁×#137	1	2	yes	—
441	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
444	C₈	—	4	2	no	—
445	C₈	—	4	2	no	—
446	C₈	—	4	2	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	4	8	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	C₃₁×#450	1	2	yes	—
452	C₂²	C₃₁×#451	1	2	yes	—
453	C₂²	C₃₁×#454	1	2	yes	—
454	C₂²	C₂×C₃₁×#120	1	1	yes	characteristic
455	C₄	—	2	4	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	4	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	8	2	no	—
462	C₄	C₃₁×#450	1	2	yes	—
463	C₄	C₃₁×#451	1	2	yes	—
464	C₄	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
465	C₄	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
466	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
467	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
468	C₂	—	4	4	no	—
469	C₂	C₃₁×#1637	1	4	yes	direct product factor
470	C₂	C₂×C₃₁×#450	1	1	yes	characteristic
471	C₂	C₂×C₃₁×#451	1	1	yes	characteristic
472	C₂	C₂×C₃₁×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	D₄
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×#487	C₂	semidirect
3. C₂×C₃₁×#477	C₂	semidirect
5. C₃₁×#1637	C₂	direct (N × H)
6. C₂×C₃₁×#332	C₂	semidirect
7. C₂×C₃₁×Q₈⋊C₈	C₂	semidirect
23. C₃₁×#487	C₂²	semidirect
25. C₃₁×#477	C₂²	semidirect
36. C₃₁×#332	C₂²	semidirect
37. C₃₁×Q₈⋊C₈	C₂²	semidirect
165. C₂×#1637	C₃₁	direct (N × H)
212. C₂×#487	C₂×C₃₁	semidirect
213. C₂×#477	C₂×C₃₁	semidirect
215. #1637	C₂×C₃₁	direct (N × H)
216. C₂×#332	C₂×C₃₁	semidirect
217. C₂×Q₈⋊C₈	C₂×C₃₁	semidirect
254. #487	C₂²×C₃₁	semidirect
256. #477	C₂²×C₃₁	semidirect
267. #332	C₂²×C₃₁	semidirect
268. Q₈⋊C₈	C₂²×C₃₁	semidirect
271. C₂×C₃₁	#1637	direct (N × H)
336. C₃₁	C₂×#1637	direct (N × H)
469. C₂	C₃₁×#1637	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×D₄×Q₈×C₃₁	2
C₂×C₃₁×#487	2
C₂×C₃₁×#477	2
C₂×C₃₁×#476	2
C₃₁×#1637	2
C₂×C₃₁×#332	2
C₂×C₃₁×Q₈⋊C₈	2
C₂×C₃₁×D₄⋊C₈	2
C₂×#1637	31

Subgroups — C2×C31×#1637 #21475248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1637 #21475248