Subgroups — C₃⋊(C₂₃⋊Dic₁₁₅) #44540698

Order 31740.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂₃²	C₂	1	1	yes	maximal, characteristic
2	C₂₃⋊Dic₁₁₅	—	3	1	no	maximal, Hall
3	C₃×C₅×C₂₃²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₂₃⋊Dic₂₃)	—	5	1	no	maximal, Hall
5	C₂×C₅×C₂₃²	D₃	1	1	yes	characteristic
6	C₂×C₃×C₂₃²	D₅	1	1	yes	characteristic
7	C₅×C₂₃²	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₂₃⋊Dic₂₃	—	15	1	no	Hall
9	C₃×C₂₃²	Dic₅	1	1	yes	characteristic, complemented, Hall
10	Dic₃₄₅	—	23	24	no	maximal
11	C₂×C₂₃²	D₁₅	1	1	yes	characteristic
12	C₂×C₃×C₅×C₂₃	D₂₃	1	24	yes	—
13	C₂₃²	Dic₁₅	1	1	yes	characteristic, complemented, Sylow
14	Dic₁₁₅	—	69	24	no	—
15	C₃×C₅×C₂₃	Dic₂₃	1	24	yes	complemented
16	Dic₆₉	—	115	24	no	—
17	C₂×C₅×C₂₃	D₆₉	1	24	yes	—
18	C₂×C₃×C₂₃	D₁₁₅	1	24	yes	—
19	C₅×C₂₃	Dic₆₉	1	24	yes	complemented
20	Dic₂₃	—	345	24	no	—
21	C₃×C₂₃	Dic₁₁₅	1	24	yes	complemented
22	Dic₁₅	—	529	1	no	Hall
23	C₂×C₂₃	D₃₄₅	1	24	yes	—
24	C₂×C₃×C₅	C₂₃⋊D₂₃	1	1	yes	characteristic
25	C₂₃	Dic₃₄₅	1	24	yes	complemented
26	Dic₅	—	1587	1	no	Hall
27	C₃×C₅	C₂₃⋊Dic₂₃	1	1	yes	characteristic, complemented, Hall
28	Dic₃	—	2645	1	no	Hall
29	C₂×C₅	C₃⋊(C₂₃⋊D₂₃)	1	1	yes	characteristic
30	C₂×C₃	C₅⋊(C₂₃⋊D₂₃)	1	1	yes	characteristic
31	C₅	C₃⋊(C₂₃⋊Dic₂₃)	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	7935	1	no	Sylow
33	C₃	C₂₃⋊Dic₁₁₅	1	1	yes	characteristic, complemented, Sylow
34	C₂	C₃⋊(C₅⋊(C₂₃⋊D₂₃))	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₂₃²	C₄	semidirect
7. C₅×C₂₃²	Dic₃	semidirect
9. C₃×C₂₃²	Dic₅	semidirect
13. C₂₃²	Dic₁₅	semidirect
15. C₃×C₅×C₂₃	Dic₂₃	semidirect
19. C₅×C₂₃	Dic₆₉	semidirect
21. C₃×C₂₃	Dic₁₁₅	semidirect
25. C₂₃	Dic₃₄₅	semidirect
27. C₃×C₅	C₂₃⋊Dic₂₃	semidirect
31. C₅	C₃⋊(C₂₃⋊Dic₂₃)	semidirect
33. C₃	C₂₃⋊Dic₁₁₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×C₂₃²	2
C₂₃⋊Dic₁₁₅	3
C₃⋊(C₂₃⋊Dic₂₃)	5
Dic₃₄₅	23

Subgroups — C3⋊(C23⋊Dic115) #44540698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₂₃⋊Dic₁₁₅) #44540698