Subgroups — C₃×Dic₁₃×C₄₁⋊C₅ #44544293

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	Dic₁₃×C₄₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×C₄₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₄₁×Dic₁₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₃×C₄₁⋊C₅	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₃×C₄₁	C₂×C₅	1	1	yes	characteristic
7	C₁₃×C₄₁⋊C₅	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄×C₄₁⋊C₅	—	13	1	no	maximal, Hall
9	C₄₁×Dic₁₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₃×C₄₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₄₁⋊C₅	D₁₃	1	1	yes	characteristic
12	C₂×C₁₃×C₄₁	C₂×C₃×C₅	1	1	yes	characteristic
13	C₄×C₄₁⋊C₅	—	13	1	no	Hall
14	C₃×C₅×Dic₁₃	—	41	1	no	maximal, Hall
15	C₃×C₄₁⋊C₅	Dic₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₁₃×C₄₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
17	C₃×C₄×C₄₁	—	13	1	no	Hall
18	C₂×C₄₁⋊C₅	C₃×D₁₃	1	1	yes	characteristic
19	C₂×C₃×C₅×C₁₃	—	41	1	no	—
20	C₅×Dic₁₃	—	41	1	no	Hall
21	C₂×C₃×C₄₁	C₅×D₁₃	1	1	yes	characteristic
22	C₄₁⋊C₅	C₃×Dic₁₃	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅×C₁₃	—	41	1	no	Hall
24	C₄×C₄₁	—	13	1	no	Hall
25	C₃×Dic₁₃	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅×C₁₃	—	41	1	no	—
27	C₃×C₄₁	C₅×Dic₁₃	1	1	yes	characteristic, complemented, Hall
28	C₂×C₄₁	C₃×C₅×D₁₃	1	1	yes	characteristic
29	C₂×C₃×C₁₃	C₂×C₄₁⋊C₅	1	1	yes	characteristic
30	C₅×C₁₃	—	41	1	no	Hall
31	C₃×C₄×C₅	—	533	1	no	Hall
32	Dic₁₃	C₃×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
33	C₄₁	C₃×C₅×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₁₃	C₄×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	—	41	1	no	—
36	C₂×C₁₃	C₂×C₃×C₄₁⋊C₅	1	1	yes	characteristic
37	C₄×C₅	—	533	1	no	Hall
38	C₃×C₅	—	41	1	no	Hall
39	C₁₃	C₃×C₄×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	13	1	no	Hall
41	C₂×C₅	—	41	1	no	—
42	C₂×C₃	D₁₃×C₄₁⋊C₅	1	1	yes	characteristic
43	C₅	—	41	1	no	Sylow
44	C₄	—	13	1	no	Sylow
45	C₃	Dic₁₃×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×D₁₃×C₄₁⋊C₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. Dic₁₃×C₄₁⋊C₅	C₃	direct (N × H)
3. C₃×C₁₃×C₄₁⋊C₅	C₄	semidirect
4. C₃×C₄₁×Dic₁₃	C₅	semidirect
7. C₁₃×C₄₁⋊C₅	C₃×C₄	semidirect
9. C₄₁×Dic₁₃	C₃×C₅	semidirect
10. C₃×C₁₃×C₄₁	C₄×C₅	semidirect
15. C₃×C₄₁⋊C₅	Dic₁₃	direct (N × H)
16. C₁₃×C₄₁	C₃×C₄×C₅	semidirect
22. C₄₁⋊C₅	C₃×Dic₁₃	direct (N × H)
25. C₃×Dic₁₃	C₄₁⋊C₅	direct (N × H)
27. C₃×C₄₁	C₅×Dic₁₃	semidirect
32. Dic₁₃	C₃×C₄₁⋊C₅	direct (N × H)
33. C₄₁	C₃×C₅×Dic₁₃	semidirect
34. C₃×C₁₃	C₄×C₄₁⋊C₅	semidirect
39. C₁₃	C₃×C₄×C₄₁⋊C₅	semidirect
45. C₃	Dic₁₃×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×C₃×C₁₃×C₄₁⋊C₅	2
Dic₁₃×C₄₁⋊C₅	3
C₃×C₄₁×Dic₁₃	5
C₃×C₄×C₄₁⋊C₅	13
C₃×C₅×Dic₁₃	41

Subgroups — C3×Dic13×C41⋊C5 #44544293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₁₃×C₄₁⋊C₅ #44544293