Subgroups — #27133904⋊C₃ #49145402

Order 36780.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₆₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#27133904	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₆₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	#14578580⋊C₃	—	5	1	no	maximal, Hall
5	C₅×D₆₁₃	C₂×C₃	1	1	yes	characteristic
6	D₆₁₃⋊C₃	D₅	1	1	yes	characteristic
7	C₅×C₆₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#14578580	—	5	1	no	Hall
9	C₆₁₃⋊C₃	Dic₅	1	1	yes	characteristic, complemented, Hall
10	D₆₁₃	C₃×D₅	1	1	yes	characteristic
11	C₆₁₃	C₃×Dic₅	1	1	yes	characteristic, complemented, Sylow
12	C₃×Dic₅	—	613	1	no	maximal, Hall
13	C₂×C₃×C₅	—	613	1	no	—
14	Dic₅	—	613	1	no	Hall
15	C₃×C₅	—	613	1	no	Hall
16	C₃×C₄	—	3065	1	no	Hall
17	C₂×C₅	—	613	1	no	—
18	C₂×C₃	—	613	1	no	—
19	C₅	#14578580⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	3065	1	no	Sylow
21	C₃	—	613	1	no	Sylow
22	C₂	—	613	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₆₁₃	C₃×C₄
prime radical	C₅×D₆₁₃⋊C₃	C₂
cosocle	C₅×D₆₁₃	C₂×C₃
LCS	G ▷ C₅×C₆₁₃
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.