Subgroups — C₂×C₁₃⋊C₃×C₄₁⋊C₅ #30630516

Order 15990.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₃×C₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃×C₄₁⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₁₃⋊C₃×C₄₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃×C₄₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃⋊C₃×C₄₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₄₁⋊C₅	—	13	1	no	maximal, Hall
7	C₂×C₁₃×C₄₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄₁⋊C₅	—	13	1	no	Hall
9	C₁₃×C₄₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₄₁⋊C₅	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₁₃⋊C₃	—	41	1	no	maximal, Hall
12	C₂×C₃×C₄₁	—	13	1	no	Hall
13	C₄₁⋊C₅	C₂×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
14	C₅×C₁₃⋊C₃	—	41	1	no	Hall
15	C₂×C₅×C₁₃	—	41	1	no	Hall
16	C₃×C₄₁	—	13	1	no	Hall
17	C₂×C₄₁	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃⋊C₃	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₁₃	—	41	1	no	Hall
20	C₄₁	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₁₃⋊C₃	C₂×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₅	—	533	1	no	Hall
23	C₂×C₁₃	C₃×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅	—	533	1	no	Hall
25	C₁₃	C₂×C₃×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	41	1	no	Hall
27	C₂×C₃	—	13	1	no	Hall
28	C₅	—	41	1	no	Sylow
29	C₃	—	13	1	no	Sylow
30	C₂	C₁₃⋊C₃×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊C₃×C₄₁⋊C₅	C₂	direct (N × H)
2. C₂×C₁₃×C₄₁⋊C₅	C₃	semidirect
3. C₂×C₁₃⋊C₃×C₄₁	C₅	semidirect
4. C₁₃×C₄₁⋊C₅	C₂×C₃	semidirect
5. C₁₃⋊C₃×C₄₁	C₂×C₅	semidirect
7. C₂×C₁₃×C₄₁	C₃×C₅	semidirect
9. C₁₃×C₄₁	C₂×C₃×C₅	semidirect
10. C₂×C₄₁⋊C₅	C₁₃⋊C₃	direct (N × H)
13. C₄₁⋊C₅	C₂×C₁₃⋊C₃	direct (N × H)
17. C₂×C₄₁	C₅×C₁₃⋊C₃	semidirect
18. C₂×C₁₃⋊C₃	C₄₁⋊C₅	direct (N × H)
20. C₄₁	C₂×C₅×C₁₃⋊C₃	semidirect
21. C₁₃⋊C₃	C₂×C₄₁⋊C₅	direct (N × H)
23. C₂×C₁₃	C₃×C₄₁⋊C₅	semidirect
25. C₁₃	C₂×C₃×C₄₁⋊C₅	semidirect
30. C₂	C₁₃⋊C₃×C₄₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃⋊C₃×C₄₁⋊C₅	2
C₂×C₁₃×C₄₁⋊C₅	3
C₂×C₁₃⋊C₃×C₄₁	5
C₂×C₃×C₄₁⋊C₅	13
C₂×C₅×C₁₃⋊C₃	41

Subgroups — C2×C13⋊C3×C41⋊C5 #30630516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃⋊C₃×C₄₁⋊C₅ #30630516