Subgroups — C₅⋊D₅×D₈₃ #22552154

Order 8300.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₄₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊D₅×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₈₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₈₃	—	5	6	no	maximal
6	D₄₁₅	—	5	6	no	—
7	C₅×D₈₃	D₅	1	6	yes	complemented
8	D₅×C₈₃	—	5	6	no	—
9	C₅×C₈₃	C₂×D₅	1	6	yes	complemented
10	C₂×D₈₃	—	25	1	no	Hall
11	C₂×C₈₃	—	25	1	no	—
12	D₈₃	—	25	1	no	—
13	D₈₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor
14	C₂×C₅⋊D₅	—	83	1	no	maximal, Hall
15	C₈₃	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₅²	—	83	1	no	—
17	C₅⋊D₅	—	83	1	no	—
18	C₅⋊D₅	D₈₃	1	1	yes	characteristic, direct product factor
19	C₅²	C₂×D₈₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₅	—	415	6	no	—
21	C₂×C₅	—	83	6	no	—
22	D₅	—	5	6	no	—
23	D₅	—	415	6	no	—
24	C₅	D₅×D₈₃	1	6	yes	complemented
25	C₂²	—	2075	1	no	Sylow
26	C₂	—	25	1	no	—
27	C₂	—	2075	1	no	—
28	C₂	—	83	1	no	—

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

Splittings G = N ⋊ H with N normal; H ≅ G/N.