Subgroups — C₅×D₁₃×D₄₇ #27132016

Order 12220.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₆₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₃×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₃×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₃×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₃×D₄₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	D₆₁₁	C₂×C₅	1	1	yes	characteristic, complemented
7	C₁₃×D₄₇	C₂×C₅	1	1	yes	characteristic, complemented
8	D₁₃×C₄₇	C₂×C₅	1	1	yes	characteristic, complemented
9	C₂×C₅×D₄₇	—	13	1	no	maximal, Hall
10	C₁₃×C₄₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₄₇	—	13	1	no	—
12	C₅×D₄₇	—	13	1	no	—
13	C₅×D₄₇	D₁₃	1	1	yes	characteristic, direct product factor
14	C₂×C₅×D₁₃	—	47	1	no	maximal, Hall
15	C₅×C₄₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×D₄₇	—	13	1	no	Hall
17	C₂×C₅×C₁₃	—	47	1	no	—
18	C₅×D₁₃	—	47	1	no	—
19	C₅×D₁₃	D₄₇	1	1	yes	characteristic, direct product factor
20	C₂×C₄₇	—	13	1	no	—
21	D₄₇	—	13	1	no	—
22	D₄₇	C₅×D₁₃	1	1	yes	characteristic, direct product factor
23	C₅×C₁₃	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₃	—	47	1	no	Hall
25	C₄₇	C₂×C₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₃	—	47	1	no	—
27	D₁₃	—	47	1	no	—
28	D₁₃	C₅×D₄₇	1	1	yes	characteristic, direct product factor
29	C₂²×C₅	—	611	1	no	Hall
30	C₁₃	C₂×C₅×D₄₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	13	1	no	—
32	C₂×C₅	—	47	1	no	—
33	C₂×C₅	—	611	1	no	—
34	C₅	D₁₃×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	—	611	1	no	Sylow
36	C₂	—	13	1	no	—
37	C₂	—	47	1	no	—
38	C₂	—	611	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₁₃×D₄₇
commutator, cosocle, hypocenter	C₁₃×C₄₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₄₇	C₂²
LCS	G ▷ C₁₃×C₄₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₆₁₁	C₂	semidirect
2. C₅×D₁₃×C₄₇	C₂	semidirect
3. C₅×C₁₃×D₄₇	C₂	semidirect
4. C₅×C₁₃×C₄₇	C₂²	semidirect
5. D₁₃×D₄₇	C₅	direct (N × H)
6. D₆₁₁	C₂×C₅	semidirect
7. C₁₃×D₄₇	C₂×C₅	semidirect
8. D₁₃×C₄₇	C₂×C₅	semidirect
10. C₁₃×C₄₇	C₂²×C₅	semidirect
13. C₅×D₄₇	D₁₃	direct (N × H)
15. C₅×C₄₇	C₂×D₁₃	semidirect
19. C₅×D₁₃	D₄₇	direct (N × H)
22. D₄₇	C₅×D₁₃	direct (N × H)
23. C₅×C₁₃	C₂×D₄₇	semidirect
25. C₄₇	C₂×C₅×D₁₃	semidirect
28. D₁₃	C₅×D₄₇	direct (N × H)
30. C₁₃	C₂×C₅×D₄₇	semidirect
34. C₅	D₁₃×D₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₆₁₁	2
C₅×D₁₃×C₄₇	2
C₅×C₁₃×D₄₇	2
D₁₃×D₄₇	5
C₂×C₅×D₄₇	13
C₂×C₅×D₁₃	47

Subgroups — C5×D13×D47 #27132016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₃×D₄₇ #27132016