Subgroups — C₃×#20259076 #32912921

Order 18300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₅₂₅	C₂	1	1	yes	maximal, characteristic
2	#20259076	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₂₅×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#11927412	—	5	1	no	maximal
5	D₁₅₂₅	C₂×C₃	1	1	yes	characteristic
6	C₃×D₃₀₅	—	5	1	no	—
7	C₂₅×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#11927412	—	5	1	no	—
9	C₃×C₅×C₆₁	AGL(1,𝔽₅)	1	1	yes	characteristic
10	C₃×#6923	—	25	1	no	Hall
11	D₃₀₅	—	5	1	no	—
12	C₃×D₆₁	—	25	1	no	—
13	C₅×C₆₁	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
14	C₃×#1035	—	61	1	no	maximal, Hall
15	#6923	—	25	1	no	Hall
16	C₃×C₆₁	#1035	1	1	yes	characteristic, complemented, Hall
17	C₃×D₂₅	—	61	1	no	—
18	D₆₁	—	25	1	no	—
19	#1035	—	61	1	no	Hall
20	C₃×C₂₅	#6923	1	1	yes	characteristic, complemented, Hall
21	C₆₁	C₃×#1035	1	1	yes	characteristic, complemented, Sylow
22	C₃×AGL(1,𝔽₅)	—	305	1	no	—
23	D₂₅	—	61	1	no	—
24	C₃×D₅	—	305	1	no	—
25	C₂₅	C₃×#6923	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	305	1	no	—
27	C₃×C₅	#11927412	1	1	yes	characteristic
28	C₃×C₄	—	1525	1	no	Hall
29	D₅	—	305	1	no	—
30	C₂×C₃	—	1525	1	no	—
31	C₅	C₃×#11927412	1	1	yes	characteristic
32	C₄	—	1525	1	no	Sylow
33	C₃	#20259076	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	1525	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.