Subgroups — C₂²×C₁₃⋊C₃×C₄₁⋊C₅ #44544341

Order 31980.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃⋊C₃×C₄₁⋊C₅	C₂	direct (N × H)
2. C₂²×C₁₃×C₄₁⋊C₅	C₃	semidirect
3. C₁₃⋊C₃×C₄₁⋊C₅	C₂²	direct (N × H)
4. C₂²×C₁₃⋊C₃×C₄₁	C₅	semidirect
5. C₂×C₁₃×C₄₁⋊C₅	C₂×C₃	semidirect
6. C₂×C₁₃⋊C₃×C₄₁	C₂×C₅	semidirect
7. C₁₃×C₄₁⋊C₅	C₂²×C₃	semidirect
9. C₂²×C₁₃×C₄₁	C₃×C₅	semidirect
10. C₁₃⋊C₃×C₄₁	C₂²×C₅	semidirect
12. C₂×C₁₃×C₄₁	C₂×C₃×C₅	semidirect
13. C₂²×C₄₁⋊C₅	C₁₃⋊C₃	direct (N × H)
16. C₁₃×C₄₁	C₂²×C₃×C₅	semidirect
18. C₂×C₄₁⋊C₅	C₂×C₁₃⋊C₃	direct (N × H)
22. C₄₁⋊C₅	C₂²×C₁₃⋊C₃	direct (N × H)
24. C₂²×C₄₁	C₅×C₁₃⋊C₃	semidirect
25. C₂²×C₁₃⋊C₃	C₄₁⋊C₅	direct (N × H)
28. C₂×C₄₁	C₂×C₅×C₁₃⋊C₃	semidirect
29. C₂×C₁₃⋊C₃	C₂×C₄₁⋊C₅	direct (N × H)
32. C₂²×C₁₃	C₃×C₄₁⋊C₅	semidirect
33. C₄₁	C₂²×C₅×C₁₃⋊C₃	semidirect
34. C₁₃⋊C₃	C₂²×C₄₁⋊C₅	direct (N × H)
36. C₂×C₁₃	C₂×C₃×C₄₁⋊C₅	semidirect
39. C₁₃	C₂²×C₃×C₄₁⋊C₅	semidirect
44. C₂²	C₁₃⋊C₃×C₄₁⋊C₅	direct (N × H)
46. C₂	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
C₂×C₁₃⋊C₃×C₄₁⋊C₅	2
C₂²×C₁₃×C₄₁⋊C₅	3
C₂²×C₁₃⋊C₃×C₄₁	5
C₂²×C₃×C₄₁⋊C₅	13
C₂²×C₅×C₁₃⋊C₃	41

Subgroups — C22×C13⋊C3×C41⋊C5 #44544341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃⋊C₃×C₄₁⋊C₅ #44544341