Subgroups — C₃×#23781029 #44530461

Order 31260.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅₂₁	C₂	1	1	yes	maximal, characteristic
2	#23781029	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₅₂₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#14523438	—	5	1	no	maximal, Hall
5	C₅×D₅₂₁	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅₂₁	D₅	1	1	yes	characteristic
7	C₅×C₅₂₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#14523438	—	5	1	no	Hall
9	C₃×C₅₂₁	Dic₅	1	1	yes	characteristic, complemented, Hall
10	D₅₂₁	C₃×D₅	1	1	yes	characteristic
11	C₅₂₁	C₃×Dic₅	1	1	yes	characteristic, complemented, Sylow
12	C₃×Dic₅	—	521	1	no	maximal, Hall
13	C₂×C₃×C₅	—	521	1	no	—
14	Dic₅	—	521	1	no	Hall
15	C₃×C₅	#14523438	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄	—	2605	1	no	Hall
17	C₂×C₅	—	521	1	no	—
18	C₂×C₃	—	521	1	no	—
19	C₅	C₃×#14523438	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	2605	1	no	Sylow
21	C₃	#23781029	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	521	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.