Subgroups — C₃×#24926248 #45658191

Order 32700.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₇₂₅	C₂	1	1	yes	maximal, characteristic
2	#24926248	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₂₅×C₁₀₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#14546127	—	5	1	no	maximal
5	D₂₇₂₅	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅₄₅	—	5	1	no	—
7	C₂₅×C₁₀₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#14546127	—	5	1	no	—
9	C₃×C₅×C₁₀₉	AGL(1,𝔽₅)	1	1	yes	characteristic
10	C₃×#89137	—	25	1	no	Hall
11	D₅₄₅	—	5	1	no	—
12	C₃×D₁₀₉	—	25	1	no	—
13	C₅×C₁₀₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
14	#89137	—	25	1	no	Hall
15	C₃×C₁₀₉	#1035	1	1	yes	characteristic, complemented, Hall
16	C₃×#1035	—	109	1	no	maximal, Hall
17	D₁₀₉	—	25	1	no	—
18	C₃×D₂₅	—	109	1	no	—
19	C₁₀₉	C₃×#1035	1	1	yes	characteristic, complemented, Sylow
20	#1035	—	109	1	no	Hall
21	C₃×C₂₅	#89137	1	1	yes	characteristic, complemented, Hall
22	C₃×AGL(1,𝔽₅)	—	545	1	no	—
23	D₂₅	—	109	1	no	—
24	C₃×D₅	—	545	1	no	—
25	C₂₅	C₃×#89137	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	545	1	no	—
27	C₃×C₅	#14546127	1	1	yes	characteristic
28	C₃×C₄	—	2725	1	no	Hall
29	D₅	—	545	1	no	—
30	C₂×C₃	—	2725	1	no	—
31	C₅	C₃×#14546127	1	1	yes	characteristic
32	C₄	—	2725	1	no	Sylow
33	C₃	#24926248	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	2725	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.