Subgroups — C₃⋊#6034 #10597098

Order 600.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#1039	C₂	1	1	yes	maximal, characteristic
2	#6034	—	3	1	no	maximal, Hall
3	C₂×C₃×C₅²	C₄	1	1	yes	characteristic
4	C₃⋊#170	—	5	2	no	maximal
5	#1039	D₃	1	1	yes	characteristic
6	C₃×C₅²	C₈	1	1	yes	characteristic, complemented, Hall
7	C₃×Dic₅	—	5	2	no	—
8	C₃×Dic₅	—	10	2	no	—
9	C₂×C₅²	Dic₃	1	1	yes	characteristic
10	#170	—	15	2	no	—
11	C₂×C₃×C₅	—	2	2	no	—
12	C₂×C₃×C₅	AGL(1,𝔽₅)	1	2	yes	—
13	C₅²	C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
14	C₃⋊C₈	—	25	1	no	Hall
15	Dic₅	—	5	2	no	—
16	Dic₅	—	10	2	no	—
17	C₃×C₅	—	2	2	no	—
18	C₃×C₅	#170	1	2	yes	complemented
19	C₃×C₄	—	25	1	no	—
20	C₂×C₅	—	2	2	no	—
21	C₂×C₅	ΓL(1,𝔽₁₆)	1	2	yes	—
22	C₈	—	75	1	no	Sylow
23	C₂×C₃	#1044	1	1	yes	characteristic
24	C₅	—	2	2	no	—
25	C₅	C₃⋊#170	1	2	yes	complemented
26	C₄	—	25	1	no	—
27	C₃	#6034	1	1	yes	characteristic, complemented, Sylow
28	C₂	C₃⋊#1044	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊#1044
commutator, hypocenter	C₃×C₅²	C₈
Fitting, socle, prime radical	C₂×C₃×C₅²	C₄
cosocle	C₃×#1039	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.