Subgroups — (C₂₃⋊Dic₁₁₅)⋊C₃ #44540695

Order 31740.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₃²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃⋊Dic₁₁₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₂₃²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	(C₂₃⋊Dic₂₃)⋊C₃	—	5	1	no	maximal, Hall
5	C₂×C₅×C₂₃²	C₂×C₃	1	1	yes	characteristic
6	C₂×C₂₃²⋊C₃	D₅	1	1	yes	characteristic
7	C₅×C₂₃²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂₃⋊Dic₂₃	—	5	1	no	Hall
9	C₂₃²⋊C₃	Dic₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₂₃²	C₃×D₅	1	1	yes	characteristic
11	C₂₃²	C₃×Dic₅	1	1	yes	characteristic, complemented, Sylow
12	Dic₁₁₅	—	69	8	no	—
13	C₂×C₅×C₂₃	—	3	8	no	—
14	C₅×C₂₃	—	3	8	no	—
15	Dic₂₃	—	345	8	no	—
16	C₃×Dic₅	—	529	1	no	maximal, Hall
17	C₂×C₂₃	—	3	8	no	—
18	C₂×C₃×C₅	—	529	1	no	—
19	C₂₃	—	3	8	no	—
20	Dic₅	—	529	1	no	Hall
21	C₃×C₅	—	529	1	no	Hall
22	C₃×C₄	—	2645	1	no	Hall
23	C₂×C₅	(C₂₃⋊D₂₃)⋊C₃	1	1	yes	characteristic
24	C₂×C₃	—	529	1	no	—
25	C₅	(C₂₃⋊Dic₂₃)⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₄	—	2645	1	no	Sylow
27	C₃	—	529	1	no	Sylow
28	C₂	C₅⋊((C₂₃⋊D₂₃)⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊((C₂₃⋊D₂₃)⋊C₃)
commutator, hypocenter	C₅×C₂₃²	C₃×C₄
Fitting, socle, cosocle	C₂×C₅×C₂₃²	C₂×C₃
prime radical	C₂×C₅×C₂₃²⋊C₃	C₂
LCS	G ▷ C₅×C₂₃²
UCS	C₁ ◁ C₂

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.