Subgroups — C₃×#24902421 #44540731

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	#24902421	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₂₃²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#14523747	—	5	1	no	maximal, Hall
5	C₅⋊(C₂₃⋊D₂₃)	C₂×C₃	1	1	yes	characteristic
6	C₃×C₂₃⋊D₂₃	—	5	1	no	—
7	C₅×C₂₃²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#14523747	—	5	1	no	Hall
9	C₃×C₂₃²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	C₂₃⋊D₂₃	—	5	1	no	—
11	C₃×D₁₁₅	—	46	12	no	—
12	C₂₃²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₅×C₂₃	—	2	12	no	—
14	D₁₁₅	—	46	12	no	—
15	C₃×D₂₃	—	230	12	no	—
16	C₅×C₂₃	—	2	12	no	—
17	C₃×C₂₃	—	2	12	no	—
18	C₃×AGL(1,𝔽₅)	—	529	1	no	maximal, Hall
19	D₂₃	—	230	12	no	—
20	C₃×D₅	—	529	1	no	—
21	C₂₃	—	2	12	no	—
22	AGL(1,𝔽₅)	—	529	1	no	Hall
23	C₃×C₅	#14523747	1	1	yes	characteristic, complemented, Hall
24	C₃×C₄	—	2645	1	no	Hall
25	D₅	—	529	1	no	—
26	C₂×C₃	—	2645	1	no	—
27	C₅	C₃×#14523747	1	1	yes	characteristic, complemented, Sylow
28	C₄	—	2645	1	no	Sylow
29	C₃	#24902421	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	2645	1	no	—

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.