Subgroups — C₃⋊#6032 #10597096

Order 600.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×Dic₅	C₂	1	1	yes	maximal, characteristic
2	#6032	—	3	1	no	maximal, Hall
3	C₂×C₃×C₅²	C₄	1	1	yes	characteristic
4	C₃⋊#170	—	5	1	no	maximal
5	C₃⋊#168	—	5	1	no	maximal
6	C₅×Dic₅	D₃	1	1	yes	characteristic
7	C₃×C₅²	C₈	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄×C₅	—	5	1	no	—
9	C₃×Dic₅	D₅	1	1	yes	characteristic
10	C₂×C₅²	Dic₃	1	1	yes	characteristic
11	#170	—	15	1	no	—
12	#168	—	15	1	no	—
13	C₂×C₃×C₅	—	4	1	no	—
14	C₂×C₃×C₅	Dic₅	1	1	yes	characteristic
15	C₂×C₃×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
16	C₅²	C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
17	C₃⋊C₈	—	25	1	no	Hall
18	C₄×C₅	—	5	1	no	—
19	Dic₅	D₁₅	1	1	yes	characteristic
20	C₃×C₅	—	4	1	no	—
21	C₃×C₅	#168	1	1	yes	characteristic, complemented
22	C₃×C₅	#170	1	1	yes	characteristic, complemented
23	C₃×C₄	—	5	1	no	—
24	C₂×C₅	—	4	1	no	—
25	C₂×C₅	Dic₁₅	1	1	yes	characteristic
26	C₂×C₅	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
27	C₈	—	75	1	no	Sylow
28	C₂×C₃	#1042	1	1	yes	characteristic
29	C₅	—	4	1	no	—
30	C₅	C₃⋊#168	1	1	yes	characteristic, complemented
31	C₅	C₃⋊#170	1	1	yes	characteristic, complemented
32	C₄	—	5	1	no	—
33	C₃	#6032	1	1	yes	characteristic, complemented, Sylow
34	C₂	C₃⋊#1042	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊#1042
commutator, hypocenter	C₃×C₅²	C₈
Fitting, socle, prime radical	C₂×C₃×C₅²	C₄
cosocle	C₃×C₅×Dic₅	C₂
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂

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.