Subgroups — C₄₃×C₃⋊#1035 #27166355

Order 12900.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#1035	—	3	1	no	maximal, Hall
3	C₃×C₂₅×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄₃×ΓL(1,𝔽₁₆)	—	5	1	no	maximal
5	C₄₃×D₂₅	D₃	1	1	yes	characteristic
6	C₃×D₅×C₄₃	—	5	1	no	—
7	C₂₅×C₄₃	Dic₃	1	1	yes	characteristic, complemented, Hall
8	AGL(1,𝔽₅)×C₄₃	—	15	1	no	—
9	C₃×C₅×C₄₃	AGL(1,𝔽₅)	1	1	yes	characteristic
10	Dic₃×C₄₃	—	25	1	no	Hall
11	D₅×C₄₃	—	5	1	no	—
12	C₃⋊#1035	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₄₃	—	25	1	no	—
14	C₅×C₄₃	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
15	C₄×C₄₃	—	75	1	no	Hall
16	C₃×D₂₅	C₂×C₄₃	1	1	yes	characteristic
17	C₃×C₄₃	#1035	1	1	yes	characteristic, complemented, Hall
18	#1035	—	3	1	no	Hall
19	C₂×C₄₃	—	25	1	no	—
20	C₃×C₂₅	C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
21	ΓL(1,𝔽₁₆)	—	5	1	no	—
22	D₂₅	D₃×C₄₃	1	1	yes	characteristic
23	C₄₃	C₃⋊#1035	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×D₅	—	5	1	no	—
25	C₂₅	Dic₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	15	1	no	—
27	C₃×C₅	AGL(1,𝔽₅)×C₄₃	1	1	yes	characteristic
28	Dic₃	—	25	1	no	Hall
29	D₅	—	5	1	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	C₄₃×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
32	C₄	—	75	1	no	Sylow
33	C₃	C₄₃×#1035	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	25	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.