Subgroups — C₃×D₁₅₈₇ #23749005

Order 9522.

27 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₅₈₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₅₂₉	—	3	1	no	maximal
4	C₃×C₅₂₉	—	2	1	no	—
5	C₃×C₅₂₉	D₃	1	1	yes	characteristic, complemented
6	C₃×C₅₂₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₅₂₉	—	3	1	no	Hall
8	C₅₂₉	C₃×D₃	1	1	yes	characteristic, complemented, Sylow
9	C₃×D₆₉	—	23	1	no	maximal
10	C₃²×C₂₃	D₂₃	1	1	yes	characteristic
11	D₆₉	—	23	1	no	—
12	C₃×D₂₃	—	69	1	no	—
13	C₃×C₂₃	—	2	1	no	—
14	C₃×C₂₃	C₃×D₂₃	1	1	yes	characteristic
15	C₃×C₂₃	D₆₉	1	1	yes	characteristic
16	D₂₃	—	69	1	no	—
17	C₂₃	C₃×D₆₉	1	1	yes	characteristic
18	C₃×D₃	—	529	1	no	Hall
19	C₃²	D₅₂₉	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	1587	1	no	—
21	D₃	—	529	1	no	—
22	C₃	—	2	1	no	—
23	C₃	C₃×D₅₂₉	1	1	yes	characteristic, complemented
24	C₃	D₁₅₈₇	1	1	yes	characteristic, direct product factor
25	C₂	—	1587	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₁₅₈₇
commutator, cosocle, hypocenter	C₃×C₅₂₉	C₂×C₃
Frattini	C₂₃	C₃×D₆₉
Fitting	C₃²×C₅₂₉	C₂
socle	C₃²×C₂₃	D₂₃
LCS	G ▷ C₃×C₅₂₉
UCS	C₁ ◁ C₃

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