Subgroups — C₂²⋊(C₁₃⋊C₃)×C₄₁⋊C₅ #44544340

Order 31980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄₁⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃⋊C₃×C₄₁⋊C₅	—	4	1	no	maximal, Hall
3	C₄₁×C₂²⋊(C₁₃⋊C₃)	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₃×C₄₁⋊C₅	—	3	1	no	—
5	C₁₃×C₄₁⋊C₅	A₄	1	1	yes	characteristic, complemented, Hall
6	A₄×C₄₁⋊C₅	—	13	1	no	maximal, Hall
7	C₂²×C₁₃×C₄₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₁₃⋊C₃×C₄₁	—	4	1	no	Hall
9	C₂×C₁₃×C₄₁	—	3	1	no	—
10	C₂²×C₄₁⋊C₅	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
11	C₅×C₂²⋊(C₁₃⋊C₃)	—	41	1	no	maximal, Hall
12	C₃×C₄₁⋊C₅	—	52	1	no	Hall
13	C₁₃×C₄₁	C₅×A₄	1	1	yes	characteristic, complemented, Hall
14	A₄×C₄₁	—	13	1	no	Hall
15	C₂×C₄₁⋊C₅	—	3	1	no	—
16	C₂²×C₅×C₁₃	—	41	1	no	Hall
17	C₄₁⋊C₅	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₁₃⋊C₃	—	164	1	no	Hall
19	C₂²×C₄₁	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₂²⋊(C₁₃⋊C₃)	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₅×C₁₃	—	123	1	no	—
22	C₃×C₄₁	—	52	1	no	Hall
23	C₂×C₄₁	—	3	1	no	—
24	C₅×C₁₃	—	41	1	no	Hall
25	C₅×A₄	—	533	1	no	Hall
26	C₂²×C₁₃	C₃×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Hall
27	C₄₁	C₅×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
28	C₁₃⋊C₃	—	4	1	no	Hall
29	C₂×C₁₃	—	3	1	no	—
30	C₂²×C₅	—	41	1	no	Hall
31	C₃×C₅	—	2132	1	no	Hall
32	C₁₃	A₄×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
33	A₄	—	13	1	no	Hall
34	C₂×C₅	—	123	1	no	—
35	C₅	—	41	1	no	Sylow
36	C₂²	C₁₃⋊C₃×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
37	C₃	—	52	1	no	Sylow
38	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₁₃×C₄₁	C₃×C₅
LCS	G ▷ C₂²×C₁₃×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×C₄₁⋊C₅	C₃	semidirect
3. C₄₁×C₂²⋊(C₁₃⋊C₃)	C₅	semidirect
5. C₁₃×C₄₁⋊C₅	A₄	semidirect
7. C₂²×C₁₃×C₄₁	C₃×C₅	semidirect
10. C₂²×C₄₁⋊C₅	C₁₃⋊C₃	semidirect
13. C₁₃×C₄₁	C₅×A₄	semidirect
17. C₄₁⋊C₅	C₂²⋊(C₁₃⋊C₃)	direct (N × H)
19. C₂²×C₄₁	C₅×C₁₃⋊C₃	semidirect
20. C₂²⋊(C₁₃⋊C₃)	C₄₁⋊C₅	direct (N × H)
26. C₂²×C₁₃	C₃×C₄₁⋊C₅	semidirect
27. C₄₁	C₅×C₂²⋊(C₁₃⋊C₃)	semidirect
32. C₁₃	A₄×C₄₁⋊C₅	semidirect
36. C₂²	C₁₃⋊C₃×C₄₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₄₁⋊C₅	3
C₁₃⋊C₃×C₄₁⋊C₅	4
C₄₁×C₂²⋊(C₁₃⋊C₃)	5
A₄×C₄₁⋊C₅	13
C₅×C₂²⋊(C₁₃⋊C₃)	41

Subgroups — C22⋊(C13⋊C3)×C41⋊C5 #44544340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊(C₁₃⋊C₃)×C₄₁⋊C₅ #44544340