Subgroups — C₈₃×#3874⋊C₂ #38735239

Order 24900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3874	C₂	1	2	yes	maximal, complemented
3	D₅²×C₈₃	—	3	1	no	maximal, Hall
4	C₅²⋊C₃×C₈₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅⋊D₅×C₈₃	D₃	1	1	yes	characteristic, complemented
6	C₅×D₅×C₈₃	—	3	2	no	—
7	C₅²×C₈₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₅×C₈₃	—	15	2	no	—
9	C₂×D₃×C₈₃	—	25	1	no	maximal, Hall
10	C₂×C₅×C₈₃	—	15	2	no	—
11	D₅×C₈₃	—	3	2	no	—
12	D₅×C₈₃	—	15	2	no	—
13	C₂×C₃×C₈₃	—	25	1	no	—
14	D₃×C₈₃	—	25	2	no	—
15	C₅×C₈₃	—	3	2	no	—
16	C₂²×C₈₃	—	75	1	no	Hall
17	#3874⋊C₂	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₃×C₈₃	—	25	1	no	Hall
19	C₂×C₈₃	—	15	2	no	—
20	C₂×C₈₃	—	25	1	no	—
21	(C₅⋊D₅)⋊C₃	C₂×C₈₃	1	1	yes	characteristic, complemented
22	#3874	C₂×C₈₃	1	2	yes	complemented
23	D₅²	—	3	1	no	Hall
24	C₈₃	#3874⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
25	C₅²⋊C₃	C₂²×C₈₃	1	1	yes	characteristic, complemented, Hall
26	C₅⋊D₅	D₃×C₈₃	1	1	yes	characteristic, complemented
27	C₅×D₅	—	3	2	no	—
28	C₅²	C₂×D₃×C₈₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×D₅	—	15	2	no	—
30	C₂×D₃	—	25	1	no	Hall
31	C₂×C₅	—	15	2	no	—
32	D₅	—	3	2	no	—
33	D₅	—	15	2	no	—
34	C₂×C₃	—	25	1	no	—
35	D₃	—	25	2	no	—
36	C₅	—	3	2	no	—
37	C₂²	—	75	1	no	Sylow
38	C₃	—	25	1	no	Sylow
39	C₂	—	15	2	no	—
40	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₈₃	#3874⋊C₂
commutator, cosocle, hypocenter	C₅²⋊C₃	C₂²×C₈₃
Frattini	C₁	G
Fitting, socle	C₅²×C₈₃	C₂×D₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₈₃

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.