Subgroups — C₅²×A₄×C₈₃ #38735293

Order 24900.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₈₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅²×C₈₃	—	4	1	no	maximal, Hall
3	C₅×A₄×C₈₃	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₅²×C₈₃	—	3	1	no	—
5	C₅²×C₈₃	A₄	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₅×C₈₃	C₃×C₅	1	6	yes	complemented
7	C₃×C₅×C₈₃	—	4	6	no	—
8	A₄×C₈₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₈₃	—	3	6	no	—
10	C₅×C₈₃	C₅×A₄	1	6	yes	direct product factor
11	C₂²×C₈₃	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
12	C₅²×A₄	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₈₃	—	4	1	no	Hall
14	C₂×C₈₃	—	3	1	no	—
15	C₂²×C₅²	C₃×C₈₃	1	1	yes	characteristic, complemented, Hall
16	C₈₃	C₅²×A₄	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅²	—	4	1	no	Hall
18	C₅×A₄	C₅×C₈₃	1	6	yes	direct product factor
19	C₂×C₅²	—	3	1	no	—
20	C₅²	A₄×C₈₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₅	C₃×C₅×C₈₃	1	6	yes	complemented
22	C₃×C₅	—	4	6	no	—
23	A₄	C₅²×C₈₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₅	—	3	6	no	—
25	C₅	C₅×A₄×C₈₃	1	6	yes	direct product factor
26	C₂²	C₃×C₅²×C₈₃	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	4	1	no	Sylow
28	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅²×C₈₃	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₅²×C₈₃
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₈₃	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₅²×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.