Subgroups — C₃⋊(#14523823⋊C₅) #44544331

Order 31980.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃×C₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	#14523823⋊C₅	—	3	1	no	maximal, Hall
3	C₃×C₁₃×C₄₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#14523823	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	D₁₃×C₄₁⋊C₅	D₃	1	1	yes	characteristic
6	C₃×D₁₃×C₄₁	C₂×C₅	1	1	yes	characteristic
7	C₁₃×C₄₁⋊C₅	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₃⋊(Dic₄₁⋊C₅)	—	13	1	no	maximal, Hall
9	#14523823	—	3	1	no	Hall
10	C₃×C₁₃×C₄₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₄₁⋊C₅	—	13	1	no	—
12	D₁₃×C₄₁	C₅×D₃	1	1	yes	characteristic
13	Dic₄₁⋊C₅	—	39	1	no	Hall
14	C₅×C₃⋊#261	—	41	1	no	maximal, Hall
15	C₃×C₄₁⋊C₅	#261	1	1	yes	characteristic, complemented, Hall
16	C₁₃×C₄₁	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
17	Dic₁₂₃	—	13	1	no	Hall
18	C₂×C₄₁⋊C₅	—	13	1	no	—
19	C₃×C₅×D₁₃	—	41	1	no	—
20	C₅×#261	—	123	1	no	Hall
21	C₂×C₃×C₄₁	—	13	1	no	—
22	C₄₁⋊C₅	C₃⋊#261	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	—	41	1	no	Hall
24	Dic₄₁	—	39	1	no	Hall
25	C₃⋊#261	—	41	1	no	Hall
26	C₅×D₁₃	—	41	1	no	—
27	C₃×C₄₁	C₅×#261	1	1	yes	characteristic, complemented, Hall
28	C₂×C₄₁	—	13	1	no	—
29	C₃×D₁₃	D₄₁⋊C₅	1	1	yes	characteristic
30	C₅×C₁₃	—	41	1	no	Hall
31	C₅×Dic₃	—	533	1	no	Hall
32	#261	—	123	1	no	Hall
33	C₄₁	C₅×C₃⋊#261	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₁₃	Dic₄₁⋊C₅	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	—	533	1	no	—
36	D₁₃	C₃⋊(D₄₁⋊C₅)	1	1	yes	characteristic
37	C₄×C₅	—	1599	1	no	Hall
38	C₃×C₅	—	41	1	no	Hall
39	C₁₃	C₃⋊(Dic₄₁⋊C₅)	1	1	yes	characteristic, complemented, Sylow
40	Dic₃	—	533	1	no	Hall
41	C₂×C₅	—	533	1	no	—
42	C₂×C₃	—	13	1	no	—
43	C₅	—	41	1	no	Sylow
44	C₄	—	1599	1	no	Sylow
45	C₃	#14523823⋊C₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₃×C₄₁	C₄×C₅
prime radical	C₃×D₁₃×C₄₁⋊C₅	C₂
cosocle	C₃×D₁₃×C₄₁	C₂×C₅
LCS	G ▷ C₃×C₁₃×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₁₃×C₄₁⋊C₅	C₄	semidirect
4. C₃⋊#14523823	C₅	semidirect
7. C₁₃×C₄₁⋊C₅	Dic₃	semidirect
10. C₃×C₁₃×C₄₁	C₄×C₅	semidirect
15. C₃×C₄₁⋊C₅	#261	semidirect
16. C₁₃×C₄₁	C₅×Dic₃	semidirect
22. C₄₁⋊C₅	C₃⋊#261	semidirect
27. C₃×C₄₁	C₅×#261	semidirect
33. C₄₁	C₅×C₃⋊#261	semidirect
34. C₃×C₁₃	Dic₄₁⋊C₅	semidirect
39. C₁₃	C₃⋊(Dic₄₁⋊C₅)	semidirect
45. C₃	#14523823⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₁₃×C₄₁⋊C₅	2
#14523823⋊C₅	3
C₃⋊#14523823	5
C₃⋊(Dic₄₁⋊C₅)	13
C₅×C₃⋊#261	41

Subgroups — C3⋊(#14523823⋊C5) #44544331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(#14523823⋊C₅) #44544331