Subgroups — C₁₃×C₃⋊(Dic₄₁⋊C₅) #44544296

Order 31980.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₃⋊(D₄₁⋊C₅)
commutator, hypocenter	C₃×C₄₁	C₄×C₅×C₁₃
Frattini	C₂	C₁₃×C₃⋊(D₄₁⋊C₅)
Fitting, socle	C₂×C₃×C₁₃×C₄₁	C₂×C₅
prime radical	C₂×C₃×C₁₃×C₄₁⋊C₅	C₂
cosocle	C₂×C₃×C₄₁	C₂×C₅×C₁₃
LCS	G ▷ C₃×C₄₁
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₃×C₁₃×C₄₁⋊C₅	C₄	semidirect
4. C₁₃×Dic₁₂₃	C₅	semidirect
7. C₁₃×C₄₁⋊C₅	Dic₃	semidirect
8. C₃⋊(Dic₄₁⋊C₅)	C₁₃	direct (N × H)
10. C₃×C₁₃×C₄₁	C₄×C₅	semidirect
15. C₃×C₄₁⋊C₅	C₄×C₁₃	semidirect
16. C₁₃×C₄₁	C₅×Dic₃	semidirect
17. Dic₁₂₃	C₅×C₁₃	semidirect
22. C₄₁⋊C₅	Dic₃×C₁₃	semidirect
27. C₃×C₄₁	C₄×C₅×C₁₃	semidirect
33. C₄₁	C₅×Dic₃×C₁₃	semidirect
34. C₃×C₁₃	Dic₄₁⋊C₅	semidirect
39. C₁₃	C₃⋊(Dic₄₁⋊C₅)	direct (N × H)
45. C₃	C₁₃×Dic₄₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₃×C₄₁⋊C₅	2
C₁₃×Dic₄₁⋊C₅	3
C₁₃×Dic₁₂₃	5
C₃⋊(Dic₄₁⋊C₅)	13
C₅×Dic₃×C₁₃	41

Subgroups — C13×C3⋊(Dic41⋊C5) #44544296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₃⋊(Dic₄₁⋊C₅) #44544296