Subgroups — C₃⋊#24902426 #44540749

Order 31740.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₃⋊D₂₃	C₂	1	1	yes	maximal, characteristic
2	#24902426	—	3	1	no	maximal, Hall
3	C₃×C₅×C₂₃²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#14523747	—	5	1	no	maximal, Hall
5	C₅×C₂₃⋊D₂₃	D₃	1	1	yes	characteristic
6	C₃×C₂₃⋊D₂₃	D₅	1	1	yes	characteristic
7	C₅×C₂₃²	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#14523747	—	15	1	no	Hall
9	C₃×C₂₃²	Dic₅	1	1	yes	characteristic, complemented, Hall
10	C₂₃⋊D₂₃	D₁₅	1	1	yes	characteristic
11	C₃×C₅×D₂₃	—	46	12	no	—
12	C₂₃²	Dic₁₅	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₅×C₂₃	—	2	12	no	—
14	C₅×D₂₃	—	46	12	no	—
15	C₃×D₂₃	—	46	12	no	—
16	C₅×C₂₃	—	2	12	no	—
17	C₃×C₂₃	—	2	12	no	—
18	Dic₁₅	—	529	1	no	maximal, Hall
19	D₂₃	—	46	12	no	—
20	C₂×C₃×C₅	—	529	1	no	—
21	C₂₃	—	2	12	no	—
22	Dic₅	—	1587	1	no	Hall
23	C₃×C₅	#14523747	1	1	yes	characteristic, complemented, Hall
24	Dic₃	—	2645	1	no	Hall
25	C₂×C₅	—	529	1	no	—
26	C₂×C₃	—	529	1	no	—
27	C₅	C₃⋊#14523747	1	1	yes	characteristic, complemented, Sylow
28	C₄	—	7935	1	no	Sylow
29	C₃	#24902426	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	529	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₂₃²	C₄
prime radical, cosocle	C₃×C₅×C₂₃⋊D₂₃	C₂
LCS	G ▷ C₃×C₅×C₂₃²
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.