Subgroups — C₅×#64085 #13088059

Order 1440.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3752	C₂	1	3	yes	maximal
3	C₅×#3750	C₂	1	3	yes	maximal, complemented
4	C₅×#876	—	3	4	no	maximal
5	C₂²×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
6	C₂×C₃²×C₄×C₅	C₂²	1	3	yes	—
7	C₂×C₅×C₃⋊Dic₃	C₂²	1	3	yes	—
8	#64085	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₄²×C₅	D₃	1	4	yes	complemented
10	C₅×(C₂×D₃)⋊C₄	—	3	12	no	—
11	C₅×Dic₃⋊C₄	—	3	12	no	—
12	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
13	C₂×C₅×C₃⋊D₃	—	2	3	no	—
14	C₃²×C₄×C₅	—	2	3	no	—
15	C₅×C₃⋊Dic₃	—	2	3	no	—
16	C₅×#126	—	9	1	no	Hall
17	C₃²×C₄²	C₂×C₅	1	1	yes	characteristic, complemented
18	#3752	C₂×C₅	1	3	yes	—
19	#3750	C₂×C₅	1	3	yes	complemented
20	C₂²×C₅×D₃	—	3	4	no	—
21	C₂×C₃×C₄×C₅	C₂×D₃	1	12	yes	—
22	C₂×C₅×Dic₃	—	3	12	no	—
23	#876	—	3	4	no	—
24	C₂×C₃²×C₅	#41	1	3	yes	—
25	C₅×C₃⋊D₃	—	4	1	no	—
26	C₅×C₄⋊C₄	—	9	3	no	—
27	C₅×C₂²⋊C₄	—	9	3	no	—
28	C₄²×C₅	C₃⋊D₃	1	1	yes	characteristic, complemented
29	C₂²×C₃⋊D₃	C₂²×C₅	1	1	yes	characteristic
30	C₂×C₃²×C₄	C₂²×C₅	1	3	yes	—
31	C₂×C₃⋊Dic₃	C₂²×C₅	1	3	yes	—
32	C₂²×C₃×C₅	C₂²×D₃	1	4	yes	—
33	C₂×C₅×D₃	—	6	12	no	—
34	C₃×C₄×C₅	—	2	12	no	—
35	C₅×Dic₃	—	6	12	no	—
36	C₃×C₄²	C₅×D₃	1	4	yes	complemented
37	(C₂×D₃)⋊C₄	—	3	12	no	—
38	Dic₃⋊C₄	—	3	12	no	—
39	C₃²×C₅	#126	1	1	yes	characteristic, complemented, Hall
40	C₂³×C₅	—	9	1	no	—
41	C₂×C₄×C₅	—	9	3	no	—
42	C₂×C₄×C₅	C₂×C₃⋊D₃	1	3	yes	—
43	C₂²×C₃²	C₂³×C₅	1	1	yes	characteristic
44	C₂×C₃⋊D₃	—	2	3	no	—
45	C₃²×C₄	—	2	3	no	—
46	C₃⋊Dic₃	—	2	3	no	—
47	#126	—	9	1	no	Sylow
48	C₂×C₃×C₅	#235	1	12	yes	—
49	C₅×D₃	—	12	4	no	—
50	C₂²×D₃	—	3	4	no	—
51	C₂×C₃×C₄	C₂×C₅×D₃	1	12	yes	—
52	C₂×Dic₃	—	3	12	no	—
53	C₂²×C₅	—	18	3	no	—
54	C₂²×C₅	C₂²×C₃⋊D₃	1	1	yes	characteristic
55	C₄×C₅	—	2	3	no	—
56	C₄×C₅	—	18	3	no	—
57	C₂×C₃²	C₅×#41	1	3	yes	—
58	C₃⋊D₃	—	4	1	no	—
59	C₄⋊C₄	—	9	3	no	—
60	C₂²⋊C₄	—	9	3	no	—
61	C₄²	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
62	C₃×C₅	#876	1	4	yes	complemented
63	C₂²×C₃	C₂²×C₅×D₃	1	4	yes	—
64	C₂×D₃	—	6	12	no	—
65	C₃×C₄	—	2	12	no	—
66	Dic₃	—	6	12	no	—
67	C₂×C₅	—	36	1	no	—
68	C₂×C₅	#3828	1	3	yes	—
69	C₃²	C₅×#126	1	1	yes	characteristic, complemented, Sylow
70	C₂³	—	9	1	no	—
71	C₂×C₄	—	9	3	no	—
72	C₂×C₄	C₂×C₅×C₃⋊D₃	1	3	yes	—
73	C₂×C₃	C₅×#235	1	12	yes	—
74	D₃	—	12	4	no	—
75	C₅	#64085	1	1	yes	characteristic, direct product factor, Sylow
76	C₂²	—	18	3	no	—
77	C₂²	C₂²×C₅×C₃⋊D₃	1	1	yes	characteristic
78	C₄	—	2	3	no	—
79	C₄	—	18	3	no	—
80	C₃	C₅×#876	1	4	yes	complemented
81	C₂	—	36	1	no	—
82	C₂	C₅×#3828	1	3	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂²×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂³×C₅
Frattini	C₂²	C₂²×C₅×C₃⋊D₃
Fitting	C₃²×C₄²×C₅	C₂
socle	C₂²×C₃²×C₅	C₂³
prime radical	C₂²×C₅×C₃⋊D₃	C₂²
hypercenter	C₄²×C₅	C₃⋊D₃
hypocenter	C₃²	C₅×#126
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₄²×C₅	C₂	semidirect
3. C₅×#3750	C₂	semidirect
8. #64085	C₅	direct (N × H)
9. C₃×C₄²×C₅	D₃	semidirect
17. C₃²×C₄²	C₂×C₅	semidirect
19. #3750	C₂×C₅	semidirect
28. C₄²×C₅	C₃⋊D₃	semidirect
36. C₃×C₄²	C₅×D₃	semidirect
39. C₃²×C₅	#126	semidirect
61. C₄²	C₅×C₃⋊D₃	semidirect
62. C₃×C₅	#876	semidirect
69. C₃²	C₅×#126	semidirect
75. C₅	#64085	direct (N × H)
80. C₃	C₅×#876	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄²×C₅	2
C₅×#3752	2
C₅×#3750	2
C₅×#876	3
#64085	5

Subgroups — C5×#64085 #13088059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#64085 #13088059