Subgroups — C₅⋊#63419 #13083941

Order 1440.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#91089	—	3	1	no	maximal
3	C₅⋊((C₂²⋊C₉)⋊C₂)	—	4	1	no	maximal
4	#63419	—	5	1	no	maximal, Hall
5	#6817	—	3	1	no	—
6	C₃×C₄²×C₅	D₃	1	1	yes	characteristic
7	#6710	—	3	1	no	—
8	C₅×C₂²⋊C₉	—	4	1	no	—
9	#3937	—	9	1	no	Hall
10	C₄²⋊C₉	D₅	1	1	yes	characteristic, complemented
11	C₂×C₃×C₄×C₅	—	3	1	no	—
12	#1220	—	6	1	no	—
13	D₆₀	—	3	1	no	—
14	C₄×D₁₅	—	6	1	no	—
15	Dic₃₀	—	3	1	no	—
16	C₃⋊#168	—	6	1	no	—
17	#805	—	15	1	no	—
18	D₄₅	—	16	1	no	—
19	#709	—	9	1	no	—
20	C₄²×C₅	D₉	1	1	yes	characteristic, complemented
21	#681	—	9	1	no	—
22	(C₂²⋊C₉)⋊C₂	—	20	1	no	—
23	C₂²×C₃×C₅	S₄	1	1	yes	characteristic
24	C₂×D₁₅	—	6	1	no	—
25	C₃×C₄×C₅	—	3	1	no	—
26	C₃×C₄×C₅	—	3	1	no	—
27	Dic₁₅	—	6	1	no	—
28	#235	—	15	1	no	—
29	C₃×C₄²	D₁₅	1	1	yes	characteristic
30	#208	—	15	1	no	—
31	C₅×C₉	—	16	1	no	Hall
32	C₂×C₄×C₅	—	3	1	no	—
33	C₂²⋊D₅	—	18	1	no	—
34	D₂₀	—	9	1	no	—
35	C₄×D₅	—	18	1	no	—
36	Dic₁₀	—	9	1	no	—
37	#168	—	18	1	no	—
38	C₂²⋊C₉	—	4	1	no	—
39	#104	—	45	1	no	Sylow
40	C₂×C₃×C₅	—	3	1	no	—
41	D₁₅	—	12	1	no	—
42	C₂×C₃×C₄	—	3	1	no	—
43	#67	—	30	1	no	—
44	D₁₂	—	15	1	no	—
45	C₄×D₃	—	30	1	no	—
46	Dic₆	—	15	1	no	—
47	C₃⋊C₈	—	30	1	no	—
48	C₂²×C₅	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic
49	C₂×D₅	—	18	1	no	—
50	C₄×C₅	—	3	1	no	—
51	C₄×C₅	—	3	1	no	—
52	Dic₅	—	18	1	no	—
53	D₉	—	80	1	no	—
54	#41	—	45	1	no	—
55	M₁₆	—	45	1	no	—
56	C₄²	D₄₅	1	1	yes	characteristic, complemented
57	C₃×C₅	#857	1	1	yes	characteristic
58	C₂²×C₃	C₅⋊S₄	1	1	yes	characteristic
59	C₂×D₃	—	30	1	no	—
60	C₃×C₄	—	3	1	no	—
61	C₃×C₄	—	3	1	no	—
62	Dic₃	—	30	1	no	—
63	C₂×C₅	—	3	1	no	—
64	D₅	—	36	1	no	—
65	C₉	—	16	1	no	Sylow
66	Q₈	—	45	1	no	—
67	D₄	—	45	1	no	—
68	D₄	—	90	1	no	—
69	C₂×C₄	—	3	1	no	—
70	C₂×C₄	—	90	1	no	—
71	C₈	—	90	1	no	—
72	C₂×C₃	—	3	1	no	—
73	D₃	—	60	1	no	—
74	C₅	#63419	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	90	1	no	—
76	C₂²	C₅⋊((C₂²⋊C₉)⋊C₂)	1	1	yes	characteristic
77	C₄	—	3	1	no	—
78	C₄	—	3	1	no	—
79	C₄	—	90	1	no	—
80	C₃	C₅⋊#857	1	1	yes	characteristic
81	C₂	—	3	1	no	—
82	C₂	—	180	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅×C₄²⋊C₉	C₂
Frattini	C₂²×C₃	C₅⋊S₄
Fitting	C₃×C₄²×C₅	D₃
socle	C₂²×C₃×C₅	S₄
LCS	G ▷ C₅×C₄²⋊C₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₄²⋊C₉	C₂	semidirect
10. C₄²⋊C₉	D₅	semidirect
20. C₄²×C₅	D₉	semidirect
56. C₄²	D₄₅	semidirect
74. C₅	#63419	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₄²⋊C₉	2
#91089	3
C₅⋊((C₂²⋊C₉)⋊C₂)	4
#63419	5

Subgroups — C5⋊#63419 #13083941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊#63419 #13083941