Subgroups — C₂⁴×C₂²⋊D₃₁ #16860503

Order 3968.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊D₃₁	C₂	1	60	yes	maximal, direct product factor
3	C₂⁴×Dic₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁶×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁵×C₃₁	—	2	16	no	—
6	C₂⁵×C₃₁	C₂²	1	1	yes	characteristic
7	C₂⁵×C₃₁	C₂²	1	30	yes	complemented
8	C₂⁴×D₃₁	—	2	16	no	—
9	C₂⁴×D₃₁	C₂²	1	30	yes	complemented
10	C₂²×C₂²⋊D₃₁	C₂²	1	560	yes	direct product factor
11	C₂³×Dic₃₁	C₂²	1	30	yes	complemented
12	C₂⁴×C₃₁	—	2	240	no	—
13	C₂⁴×C₃₁	D₄	1	16	yes	complemented
14	C₂⁴×C₃₁	C₂³	1	15	yes	—
15	C₂⁴×C₃₁	C₂³	1	140	yes	complemented
16	C₂³×D₃₁	—	2	240	no	—
17	C₂³×D₃₁	C₂³	1	140	yes	complemented
18	C₂×C₂²⋊D₃₁	C₂³	1	960	yes	direct product factor
19	C₂²×Dic₃₁	C₂³	1	140	yes	complemented
20	C₂³×C₃₁	—	2	560	no	—
21	C₂³×C₃₁	C₂×D₄	1	120	yes	complemented
22	C₂³×C₃₁	C₂⁴	1	35	yes	—
23	C₂³×C₃₁	C₂⁴	1	120	yes	complemented
24	C₂²×D₃₁	—	2	560	no	—
25	C₂²×D₃₁	C₂⁴	1	120	yes	complemented
26	C₂²⋊D₃₁	C₂⁴	1	256	yes	direct product factor
27	C₂×Dic₃₁	C₂⁴	1	120	yes	complemented
28	C₂⁴×D₄	—	31	1	no	maximal, Sylow
29	C₂²×C₃₁	—	2	240	no	—
30	C₂²×C₃₁	C₂²×D₄	1	140	yes	complemented
31	C₂²×C₃₁	C₂⁵	1	15	yes	—
32	C₂²×C₃₁	C₂⁵	1	16	yes	complemented
33	C₂×D₃₁	—	2	240	no	—
34	C₂×D₃₁	C₂⁵	1	16	yes	complemented
35	Dic₃₁	C₂⁵	1	16	yes	complemented
36	C₂⁶	—	31	1	no	—
37	C₂⁶	D₃₁	1	1	yes	characteristic, complemented
38	C₂³×D₄	—	31	60	no	—
39	C₂⁴×C₄	—	31	1	no	—
40	C₂×C₃₁	—	2	16	no	—
41	C₂×C₃₁	C₂³×D₄	1	30	yes	complemented
42	C₂×C₃₁	C₂⁶	1	1	yes	characteristic
43	D₃₁	—	2	16	no	—
44	C₂⁵	—	2	16	no	—
45	C₂⁵	—	31	30	no	—
46	C₂⁵	—	62	16	no	—
47	C₂⁵	C₂×D₃₁	1	1	yes	characteristic
48	C₂⁵	C₂×D₃₁	1	30	yes	complemented
49	C₂²×D₄	—	31	560	no	—
50	C₂³×C₄	—	31	30	no	—
51	C₃₁	C₂⁴×D₄	1	1	yes	characteristic, complemented, Sylow
52	C₂⁴	—	2	240	no	—
53	C₂⁴	—	31	140	no	—
54	C₂⁴	—	62	240	no	—
55	C₂⁴	C₂²⋊D₃₁	1	16	yes	direct product factor
56	C₂⁴	C₂²×D₃₁	1	15	yes	—
57	C₂⁴	C₂²×D₃₁	1	140	yes	complemented
58	C₂×D₄	—	31	960	no	—
59	C₂²×C₄	—	31	140	no	—
60	C₂³	—	2	560	no	—
61	C₂³	—	31	120	no	—
62	C₂³	—	62	560	no	—
63	C₂³	C₂×C₂²⋊D₃₁	1	120	yes	direct product factor
64	C₂³	C₂³×D₃₁	1	35	yes	—
65	C₂³	C₂³×D₃₁	1	120	yes	complemented
66	D₄	—	31	256	no	—
67	C₂×C₄	—	31	120	no	—
68	C₂²	—	2	240	no	—
69	C₂²	—	31	16	no	—
70	C₂²	—	62	240	no	—
71	C₂²	C₂²×C₂²⋊D₃₁	1	140	yes	direct product factor
72	C₂²	C₂⁴×D₃₁	1	15	yes	—
73	C₂²	C₂⁴×D₃₁	1	16	yes	complemented
74	C₄	—	31	16	no	—
75	C₂	—	2	16	no	—
76	C₂	—	62	16	no	—
77	C₂	C₂³×C₂²⋊D₃₁	1	30	yes	direct product factor
78	C₂	C₂⁵×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂×D₃₁
commutator, cosocle	C₂×C₃₁	C₂⁶
Frattini	C₂	C₂⁵×D₃₁
Fitting	C₂⁶×C₃₁	C₂
socle	C₂⁵×C₃₁	C₂²
hypercenter	C₂⁶	D₃₁
hypocenter	C₃₁	C₂⁴×D₄
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂⁵ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁵×D₃₁	C₂	semidirect
2. C₂³×C₂²⋊D₃₁	C₂	direct (N × H)
3. C₂⁴×Dic₃₁	C₂	semidirect
4. C₂⁶×C₃₁	C₂	semidirect
7. C₂⁵×C₃₁	C₂²	semidirect
9. C₂⁴×D₃₁	C₂²	semidirect
10. C₂²×C₂²⋊D₃₁	C₂²	direct (N × H)
11. C₂³×Dic₃₁	C₂²	semidirect
13. C₂⁴×C₃₁	D₄	semidirect
15. C₂⁴×C₃₁	C₂³	semidirect
17. C₂³×D₃₁	C₂³	semidirect
18. C₂×C₂²⋊D₃₁	C₂³	direct (N × H)
19. C₂²×Dic₃₁	C₂³	semidirect
21. C₂³×C₃₁	C₂×D₄	semidirect
23. C₂³×C₃₁	C₂⁴	semidirect
25. C₂²×D₃₁	C₂⁴	semidirect
26. C₂²⋊D₃₁	C₂⁴	direct (N × H)
27. C₂×Dic₃₁	C₂⁴	semidirect
30. C₂²×C₃₁	C₂²×D₄	semidirect
32. C₂²×C₃₁	C₂⁵	semidirect
34. C₂×D₃₁	C₂⁵	semidirect
35. Dic₃₁	C₂⁵	semidirect
37. C₂⁶	D₃₁	semidirect
41. C₂×C₃₁	C₂³×D₄	semidirect
48. C₂⁵	C₂×D₃₁	semidirect
51. C₃₁	C₂⁴×D₄	semidirect
55. C₂⁴	C₂²⋊D₃₁	direct (N × H)
57. C₂⁴	C₂²×D₃₁	semidirect
63. C₂³	C₂×C₂²⋊D₃₁	direct (N × H)
65. C₂³	C₂³×D₃₁	semidirect
71. C₂²	C₂²×C₂²⋊D₃₁	direct (N × H)
73. C₂²	C₂⁴×D₃₁	semidirect
77. C₂	C₂³×C₂²⋊D₃₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁵×D₃₁	2
C₂³×C₂²⋊D₃₁	2
C₂⁴×Dic₃₁	2
C₂⁶×C₃₁	2
C₂⁴×D₄	31

Subgroups — C24×C22⋊D31 #16860503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₂²⋊D₃₁ #16860503