Subgroups — C₃⋊#16812340 #23780680

Order 10380.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₁₇₃	C₂	1	1	yes	maximal, characteristic
2	#16812340	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#10621924	—	5	1	no	maximal, Hall
5	C₅×D₁₇₃	D₃	1	1	yes	characteristic
6	C₃×D₁₇₃	D₅	1	1	yes	characteristic
7	C₅×C₁₇₃	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#10621924	—	15	1	no	Hall
9	C₃×C₁₇₃	Dic₅	1	1	yes	characteristic, complemented, Hall
10	D₁₇₃	D₁₅	1	1	yes	characteristic
11	C₁₇₃	Dic₁₅	1	1	yes	characteristic, complemented, Sylow
12	Dic₁₅	—	173	1	no	maximal, Hall
13	C₂×C₃×C₅	—	173	1	no	—
14	Dic₅	—	519	1	no	Hall
15	C₃×C₅	#10621924	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	865	1	no	Hall
17	C₂×C₅	—	173	1	no	—
18	C₂×C₃	—	173	1	no	—
19	C₅	C₃⋊#10621924	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	2595	1	no	Sylow
21	C₃	#16812340	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	173	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₁₇₃	C₄
prime radical, cosocle	C₃×C₅×D₁₇₃	C₂
LCS	G ▷ C₃×C₅×C₁₇₃
UCS	C₁

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