Subgroups — C₃⋊#21418654 #36375488

Order 22380.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₃₇₃	C₂	1	1	yes	maximal, characteristic
2	#21418654	—	3	1	no	maximal, Hall
3	C₃×C₅×C₃₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#13093637	—	5	1	no	maximal, Hall
5	C₅×D₃₇₃	D₃	1	1	yes	characteristic
6	C₃×D₃₇₃	D₅	1	1	yes	characteristic
7	C₅×C₃₇₃	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#13093637	—	15	1	no	Hall
9	C₃×C₃₇₃	Dic₅	1	1	yes	characteristic, complemented, Hall
10	D₃₇₃	D₁₅	1	1	yes	characteristic
11	C₃₇₃	Dic₁₅	1	1	yes	characteristic, complemented, Sylow
12	Dic₁₅	—	373	1	no	maximal, Hall
13	C₂×C₃×C₅	—	373	1	no	—
14	Dic₅	—	1119	1	no	Hall
15	C₃×C₅	#13093637	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	1865	1	no	Hall
17	C₂×C₅	—	373	1	no	—
18	C₂×C₃	—	373	1	no	—
19	C₅	C₃⋊#13093637	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	5595	1	no	Sylow
21	C₃	#21418654	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	373	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₃₇₃	C₄
prime radical, cosocle	C₃×C₅×D₃₇₃	C₂
LCS	G ▷ C₃×C₅×C₃₇₃
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.