Subgroups — C₅⋊((C₂²⋊C₉)⋊C₂) #67111

Order 360.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#1220	—	3	1	no	maximal
3	D₄₅	—	4	1	no	maximal
4	(C₂²⋊C₉)⋊C₂	—	5	1	no	maximal, Hall
5	C₂²×C₃×C₅	D₃	1	1	yes	characteristic
6	C₂×D₁₅	—	3	1	no	—
7	Dic₁₅	—	3	1	no	—
8	C₅×C₉	—	4	1	no	Hall
9	C₂²⋊D₅	—	9	1	no	Hall
10	C₂²⋊C₉	D₅	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅	—	3	1	no	—
12	D₁₅	—	6	1	no	—
13	#67	—	15	1	no	—
14	C₂²×C₅	D₉	1	1	yes	characteristic, complemented
15	C₂×D₅	—	9	1	no	—
16	Dic₅	—	9	1	no	—
17	D₉	—	20	1	no	—
18	C₃×C₅	S₄	1	1	yes	characteristic
19	C₂²×C₃	D₁₅	1	1	yes	characteristic
20	C₂×D₃	—	15	1	no	—
21	Dic₃	—	15	1	no	—
22	C₂×C₅	—	3	1	no	—
23	D₅	—	18	1	no	—
24	C₉	—	4	1	no	Sylow
25	D₄	—	45	1	no	Sylow
26	C₂×C₃	—	3	1	no	—
27	D₃	—	30	1	no	—
28	C₅	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic, complemented, Sylow
29	C₂²	—	45	1	no	—
30	C₂²	D₄₅	1	1	yes	characteristic, complemented
31	C₄	—	45	1	no	—
32	C₃	C₅⋊S₄	1	1	yes	characteristic
33	C₂	—	3	1	no	—
34	C₂	—	90	1	no	—

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

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

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