Subgroups — C₁₃×D₉×C₁₅₁ #47977458

Order 35334.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₃×C₁₅₁	—	3	1	no	maximal
3	C₃×C₁₃×C₁₅₁	D₃	1	1	yes	characteristic
4	C₂×C₁₃×C₁₅₁	—	9	1	no	Hall
5	D₉×C₁₅₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₁₅₁	D₉	1	1	yes	characteristic, direct product factor, Hall
7	C₉×C₁₅₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
8	D₃×C₁₅₁	—	3	1	no	—
9	C₃×C₁₅₁	D₃×C₁₃	1	1	yes	characteristic
10	C₂×C₁₅₁	—	9	1	no	Hall
11	C₁₃×D₉	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₅₁	C₁₃×D₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₉×C₁₃	C₂×C₁₅₁	1	1	yes	characteristic, complemented, Hall
14	D₃×C₁₃	—	3	1	no	—
15	C₃×C₁₃	D₃×C₁₅₁	1	1	yes	characteristic
16	C₂×C₁₃	—	9	1	no	Hall
17	D₉	C₁₃×C₁₅₁	1	1	yes	characteristic, direct product factor, Hall
18	C₁₃	D₉×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₉	C₂×C₁₃×C₁₅₁	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	3	1	no	—
21	C₃	D₃×C₁₃×C₁₅₁	1	1	yes	characteristic
22	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₁₅₁	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₁₃×C₁₅₁
Frattini	C₃	D₃×C₁₃×C₁₅₁
Fitting	C₉×C₁₃×C₁₅₁	C₂
socle	C₃×C₁₃×C₁₅₁	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₃×C₁₅₁

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.