Subgroups — C₄₃×#1039⋊C₃ #27166380

Order 12900.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#1039	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₃×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅²×C₄₃	C₂×C₃	1	1	yes	characteristic
5	C₅²×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	Dic₅×C₄₃	—	15	2	no	—
7	C₃×C₄×C₄₃	—	25	1	no	maximal, Hall
8	C₂×C₅×C₄₃	—	3	2	no	—
9	#1039⋊C₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₄₃	—	25	1	no	—
11	C₅×C₄₃	—	3	2	no	—
12	C₄×C₄₃	—	25	1	no	Hall
13	C₂×C₅²⋊C₃	C₂×C₄₃	1	1	yes	characteristic
14	C₃×C₄₃	—	25	1	no	Hall
15	#1039	C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₄₃	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
17	C₅²⋊C₃	C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅²	C₂×C₃×C₄₃	1	1	yes	characteristic
19	C₄₃	#1039⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₅²	C₃×C₄×C₄₃	1	1	yes	characteristic, complemented, Sylow
21	Dic₅	—	15	2	no	—
22	C₃×C₄	—	25	1	no	Hall
23	C₂×C₅	—	3	2	no	—
24	C₂×C₃	—	25	1	no	—
25	C₅	—	3	2	no	—
26	C₄	—	25	1	no	Sylow
27	C₃	—	25	1	no	Sylow
28	C₂	C₄₃×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic

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.