Subgroups — C₅×C₁₃×D₂₄₇ #44545771

Order 32110.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₂₄₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃²×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₂₄₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor
5	C₅×C₁₃×D₁₉	—	13	1	no	maximal
6	C₅×C₁₃×D₁₃	—	19	1	no	maximal, Hall
7	C₅×C₁₃×C₁₉	—	2	6	no	—
8	C₅×C₁₃×C₁₉	D₁₃	1	1	yes	characteristic, complemented
9	C₅×C₁₃×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
10	C₅×C₁₃²	D₁₉	1	1	yes	characteristic, complemented, Hall
11	D₂₄₇	C₅×C₁₃	1	1	yes	characteristic, direct product factor
12	C₁₃×D₁₉	—	13	1	no	—
13	C₁₃×D₁₃	—	19	1	no	Hall
14	C₁₃×C₁₉	—	2	6	no	—
15	C₁₃×C₁₉	C₅×D₁₃	1	1	yes	characteristic, complemented
16	C₁₃×C₁₉	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
17	C₅×D₁₉	—	13	1	no	Hall
18	C₁₃²	C₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅×C₁₃	—	247	1	no	—
20	C₅×D₁₃	—	19	1	no	—
21	C₅×C₁₉	C₁₃×D₁₃	1	1	yes	characteristic, complemented, Hall
22	C₅×C₁₃	—	2	6	no	—
23	C₅×C₁₃	C₁₃×D₁₉	1	1	yes	characteristic, complemented
24	C₅×C₁₃	D₂₄₇	1	1	yes	characteristic, direct product factor
25	D₁₉	—	13	1	no	Hall
26	C₂×C₁₃	—	247	1	no	—
27	D₁₃	—	19	1	no	—
28	C₁₉	C₅×C₁₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
29	C₁₃	—	2	6	no	—
30	C₁₃	C₅×C₁₃×D₁₉	1	1	yes	characteristic, complemented
31	C₁₃	C₅×D₂₄₇	1	1	yes	characteristic, direct product factor
32	C₂×C₅	—	247	1	no	Hall
33	C₅	C₁₃×D₂₄₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	247	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₂₄₇
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₃²×C₁₉	C₂
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃²×C₁₉	C₂	semidirect
2. C₁₃×D₂₄₇	C₅	direct (N × H)
3. C₁₃²×C₁₉	C₂×C₅	semidirect
4. C₅×D₂₄₇	C₁₃	direct (N × H)
8. C₅×C₁₃×C₁₉	D₁₃	semidirect
9. C₅×C₁₃×C₁₉	C₂×C₁₃	semidirect
10. C₅×C₁₃²	D₁₉	semidirect
11. D₂₄₇	C₅×C₁₃	direct (N × H)
15. C₁₃×C₁₉	C₅×D₁₃	semidirect
16. C₁₃×C₁₉	C₂×C₅×C₁₃	semidirect
18. C₁₃²	C₅×D₁₉	semidirect
21. C₅×C₁₉	C₁₃×D₁₃	semidirect
23. C₅×C₁₃	C₁₃×D₁₉	semidirect
24. C₅×C₁₃	D₂₄₇	direct (N × H)
28. C₁₉	C₅×C₁₃×D₁₃	semidirect
30. C₁₃	C₅×C₁₃×D₁₉	semidirect
31. C₁₃	C₅×D₂₄₇	direct (N × H)
33. C₅	C₁₃×D₂₄₇	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×C₁₃²×C₁₉	2
C₁₃×D₂₄₇	5
C₅×D₂₄₇	13
C₅×C₁₃×D₁₉	13
C₅×C₁₃×D₁₃	19

Subgroups — C5×C13×D247 #44545771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₃×D₂₄₇ #44545771