Subgroups — ((C₂₃⋊D₂₃)⋊C₃)⋊D₅ #44540723

Order 31740.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊#15691772	C₂	1	2	yes	maximal, complemented
2	C₅×(C₂₃⋊D₂₃)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₁₅⋊D₂₃	—	3	1	no	maximal, Hall
4	C₅×C₂₃²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	#15691772⋊C₂	—	5	1	no	maximal, Hall
6	C₂₃×D₁₁₅	—	3	2	no	—
7	C₅×C₂₃⋊D₂₃	D₃	1	1	yes	characteristic, complemented
8	(C₂₃⋊D₂₃)⋊C₃	D₅	1	1	yes	characteristic, complemented
9	#15691772	—	5	2	no	—
10	C₅×C₂₃²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₂₃²	—	15	1	no	Hall
12	C₂₃²⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
13	C₂₃⋊D₂₃	D₁₅	1	1	yes	characteristic, complemented
14	C₂₃×D₂₃	—	15	2	no	—
15	C₂₃²	C₂×D₁₅	1	1	yes	characteristic, complemented, Sylow
16	D₅×D₂₃	—	69	2	no	—
17	D₁₁₅	—	3	2	no	—
18	C₅×D₂₃	—	69	2	no	—
19	C₅×D₂₃	—	138	3	no	—
20	D₅×C₂₃	—	69	2	no	—
21	C₅×C₂₃	—	3	2	no	—
22	C₅×C₂₃	—	6	3	no	—
23	C₂×D₂₃	—	345	2	no	—
24	C₂×D₁₅	—	529	1	no	maximal, Hall
25	C₂×C₂₃	—	345	2	no	—
26	D₂₃	—	15	2	no	—
27	D₂₃	—	69	2	no	—
28	D₂₃	—	138	3	no	—
29	C₂×C₃×C₅	—	529	1	no	—
30	D₁₅	—	529	2	no	—
31	C₂₃	—	3	2	no	—
32	C₂₃	—	6	3	no	—
33	C₂×D₅	—	1587	1	no	Hall
34	C₃×C₅	—	529	1	no	Hall
35	C₂×D₃	—	2645	1	no	Hall
36	C₂×C₅	—	529	1	no	—
37	D₅	—	69	2	no	—
38	C₂×C₃	—	529	1	no	—
39	D₃	—	2645	2	no	—
40	C₅	#15691772⋊C₂	1	1	yes	characteristic, complemented, Sylow
41	C₂²	—	7935	1	no	Sylow
42	C₃	—	529	1	no	Sylow
43	C₂	—	529	1	no	—
44	C₂	—	345	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅×C₂₃²⋊C₃	C₂²
Fitting, socle	C₅×C₂₃²	C₂×D₃
LCS	G ▷ C₅×C₂₃²⋊C₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅⋊#15691772	C₂	semidirect
2. C₅×(C₂₃⋊D₂₃)⋊C₃	C₂	semidirect
4. C₅×C₂₃²⋊C₃	C₂²	semidirect
7. C₅×C₂₃⋊D₂₃	D₃	semidirect
8. (C₂₃⋊D₂₃)⋊C₃	D₅	semidirect
10. C₅×C₂₃²	C₂×D₃	semidirect
12. C₂₃²⋊C₃	C₂×D₅	semidirect
13. C₂₃⋊D₂₃	D₁₅	semidirect
15. C₂₃²	C₂×D₁₅	semidirect
40. C₅	#15691772⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊#15691772	2
C₅×(C₂₃⋊D₂₃)⋊C₃	2
D₁₁₅⋊D₂₃	3
#15691772⋊C₂	5
C₂×D₁₅	529

Subgroups — ((C23⋊D23)⋊C3)⋊D5 #44540723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ((C₂₃⋊D₂₃)⋊C₃)⋊D₅ #44540723