Subgroups — C₂³×#6032 #13107797

Order 1600.

743 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6032	C₂	1	14	yes	maximal, direct product factor
3	C₂⁴×C₅²	C₄	1	1	yes	characteristic
4	C₂²×C₅×Dic₅	C₄	1	7	yes	—
5	C₂²×C₅×Dic₅	C₂²	1	7	yes	—
6	C₂×#6032	C₂²	1	28	yes	direct product factor
7	C₂³×#170	—	5	1	no	maximal
8	C₂³×#168	—	5	1	no	maximal
9	C₂³×C₅²	C₈	1	8	yes	complemented
10	C₂³×C₅²	C₂×C₄	1	7	yes	—
11	C₂×C₅×Dic₅	C₂×C₄	1	21	yes	—
12	C₂×C₅×Dic₅	C₂³	1	7	yes	—
13	#6032	C₂³	1	8	yes	direct product factor
14	C₂³×C₄×C₅	—	5	1	no	—
15	C₂³×Dic₅	D₅	1	1	yes	characteristic
16	C₂²×#170	—	5	14	no	—
17	C₂²×#168	—	5	14	no	—
18	C₂²×C₅²	C₂×C₈	1	28	yes	complemented
19	C₂²×C₅²	C₂²×C₄	1	7	yes	—
20	C₅×Dic₅	C₂²×C₄	1	7	yes	—
21	C₅×Dic₅	C₂⁴	1	1	yes	characteristic
22	C₂⁴×C₅	—	4	1	no	—
23	C₂⁴×C₅	Dic₅	1	1	yes	characteristic
24	C₂⁴×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₂²×C₄×C₅	—	5	7	no	—
26	C₂²×C₄×C₅	—	5	7	no	—
27	C₂²×Dic₅	Dic₅	1	7	yes	—
28	C₂²×Dic₅	C₂×D₅	1	7	yes	—
29	C₂×#170	—	5	28	no	—
30	C₂×#168	—	5	28	no	—
31	C₂³×C₈	—	25	1	no	Sylow
32	C₂×C₅²	C₂²×C₈	1	14	yes	complemented
33	C₂×C₅²	C₂³×C₄	1	1	yes	characteristic
34	C₂³×C₅	—	4	8	no	—
35	C₂³×C₅	—	4	7	no	—
36	C₂³×C₅	#168	1	8	yes	complemented
37	C₂³×C₅	#170	1	8	yes	complemented
38	C₂³×C₅	C₂×Dic₅	1	7	yes	—
39	C₂³×C₅	C₂×AGL(1,𝔽₅)	1	7	yes	—
40	C₂×C₄×C₅	—	5	21	no	—
41	C₂×C₄×C₅	—	5	7	no	—
42	C₂×Dic₅	C₂×Dic₅	1	21	yes	—
43	C₂×Dic₅	C₂²×D₅	1	7	yes	—
44	#170	—	5	8	no	—
45	#168	—	5	8	no	—
46	C₂³×C₄	—	5	1	no	—
47	C₂²×C₈	—	25	14	no	—
48	C₅²	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₅	—	4	28	no	—
50	C₂²×C₅	—	4	7	no	—
51	C₂²×C₅	C₂×#168	1	28	yes	complemented
52	C₂²×C₅	C₂×#170	1	28	yes	complemented
53	C₂²×C₅	C₂²×Dic₅	1	7	yes	—
54	C₂²×C₅	C₂²×AGL(1,𝔽₅)	1	7	yes	—
55	C₄×C₅	—	5	7	no	—
56	C₄×C₅	—	5	1	no	—
57	Dic₅	C₂²×Dic₅	1	7	yes	—
58	Dic₅	C₂³×D₅	1	1	yes	characteristic
59	C₂⁴	#1042	1	1	yes	characteristic
60	C₂²×C₄	—	5	7	no	—
61	C₂²×C₄	—	5	7	no	—
62	C₂×C₈	—	25	28	no	—
63	C₂×C₅	—	4	14	no	—
64	C₂×C₅	—	4	1	no	—
65	C₂×C₅	C₂²×#168	1	14	yes	complemented
66	C₂×C₅	C₂²×#170	1	14	yes	complemented
67	C₂×C₅	C₂³×Dic₅	1	1	yes	characteristic
68	C₂×C₅	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
69	C₂³	#6032	1	8	yes	direct product factor
70	C₂³	C₂×#1042	1	7	yes	—
71	C₂×C₄	—	5	7	no	—
72	C₂×C₄	—	5	21	no	—
73	C₈	—	25	8	no	—
74	C₅	—	4	1	no	—
75	C₅	C₂³×#168	1	1	yes	characteristic, complemented
76	C₅	C₂³×#170	1	1	yes	characteristic, complemented
77	C₂²	C₂×#6032	1	28	yes	direct product factor
78	C₂²	C₂²×#1042	1	7	yes	—
79	C₄	—	5	1	no	—
80	C₄	—	5	7	no	—
81	C₂	C₂²×#6032	1	14	yes	direct product factor
82	C₂	C₂³×#1042	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴	#1042
commutator, hypocenter	C₅²	C₂³×C₈
Frattini	C₂	C₂³×#1042
Fitting, socle, prime radical	C₂⁴×C₅²	C₄
cosocle	C₅×Dic₅	C₂⁴
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
2. C₂²×#6032	C₂	direct (N × H)
6. C₂×#6032	C₂²	direct (N × H)
9. C₂³×C₅²	C₈	semidirect
13. #6032	C₂³	direct (N × H)
18. C₂²×C₅²	C₂×C₈	semidirect
32. C₂×C₅²	C₂²×C₈	semidirect
36. C₂³×C₅	#168	semidirect
37. C₂³×C₅	#170	semidirect
48. C₅²	C₂³×C₈	semidirect
51. C₂²×C₅	C₂×#168	semidirect
52. C₂²×C₅	C₂×#170	semidirect
65. C₂×C₅	C₂²×#168	semidirect
66. C₂×C₅	C₂²×#170	semidirect
69. C₂³	#6032	direct (N × H)
75. C₅	C₂³×#168	semidirect
76. C₅	C₂³×#170	semidirect
77. C₂²	C₂×#6032	direct (N × H)
81. C₂	C₂²×#6032	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×Dic₅	2
C₂²×#6032	2
C₂³×#170	5
C₂³×#168	5

Subgroups — C23×#6032 #13107797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#6032 #13107797