Subgroups — C₄₃×#64470 #27166378

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	C₅×Dic₅×C₄₃	—	3	1	no	maximal, Hall
3	C₄₃×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅²×C₄₃	D₃	1	1	yes	characteristic
5	C₅²×C₄₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₄×C₅×C₄₃	—	15	1	no	—
7	Dic₅×C₄₃	—	3	1	no	—
8	Dic₃×C₄₃	—	25	1	no	maximal, Hall
9	C₂×C₅×C₄₃	—	3	1	no	—
10	C₂×C₅×C₄₃	—	3	1	no	—
11	#64470	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₄₃	—	25	1	no	—
13	C₅×C₄₃	—	3	1	no	—
14	C₅×C₄₃	—	3	1	no	—
15	C₄×C₄₃	—	15	1	no	Hall
16	C₂×C₅²⋊C₃	C₂×C₄₃	1	1	yes	characteristic
17	C₃×C₄₃	—	25	1	no	Hall
18	C₅×Dic₅	—	3	1	no	Hall
19	C₂×C₄₃	#3874	1	1	yes	characteristic
20	C₅²⋊C₃	C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅²	D₃×C₄₃	1	1	yes	characteristic
22	C₄₃	#64470	1	1	yes	characteristic, direct product factor, Sylow
23	C₅²	Dic₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
24	C₄×C₅	—	15	1	no	—
25	Dic₅	—	3	1	no	—
26	Dic₃	—	25	1	no	Hall
27	C₂×C₅	—	3	1	no	—
28	C₂×C₅	—	3	1	no	—
29	C₂×C₃	—	25	1	no	—
30	C₅	—	3	1	no	—
31	C₅	—	3	1	no	—
32	C₄	—	15	1	no	Sylow
33	C₃	—	25	1	no	Sylow
34	C₂	C₄₃×#3874	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.