Subgroups — C₅×C₇×D₄₄₅ #44528274

Order 31150.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₄₄₅	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×C₇×D₈₉	—	5	1	no	maximal
4	C₅×D₄₄₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇×C₈₉	—	2	2	no	—
6	C₅×C₇×C₈₉	D₅	1	1	yes	characteristic, complemented
7	C₅×C₇×C₈₉	C₂×C₅	1	1	yes	characteristic, complemented
8	C₅²×C₈₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×D₈₉	—	5	1	no	Hall
10	D₄₄₅	C₅×C₇	1	1	yes	characteristic, direct product factor
11	C₅×D₈₉	—	5	1	no	—
12	C₇×C₈₉	C₅×D₅	1	1	yes	characteristic, complemented, Hall
13	C₅×C₈₉	—	2	2	no	—
14	C₅×C₈₉	C₇×D₅	1	1	yes	characteristic, complemented
15	C₅×C₈₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
16	C₅×C₇×D₅	—	89	1	no	maximal, Hall
17	D₈₉	—	5	1	no	Hall
18	C₅²×C₇	D₈₉	1	1	yes	characteristic, complemented, Hall
19	C₈₉	C₅×C₇×D₅	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅×C₇	—	445	1	no	—
21	C₇×D₅	—	89	1	no	—
22	C₅×D₅	—	89	1	no	Hall
23	C₅×C₇	—	2	2	no	—
24	C₅×C₇	C₅×D₈₉	1	1	yes	characteristic, complemented
25	C₅×C₇	D₄₄₅	1	1	yes	characteristic, direct product factor
26	C₅²	C₇×D₈₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₇	—	445	1	no	Hall
28	C₂×C₅	—	445	1	no	—
29	D₅	—	89	1	no	—
30	C₇	C₅×D₄₄₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₅	—	2	2	no	—
32	C₅	C₅×C₇×D₈₉	1	1	yes	characteristic, complemented
33	C₅	C₇×D₄₄₅	1	1	yes	characteristic, direct product factor
34	C₂	—	445	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇	D₄₄₅
commutator, cosocle, hypocenter	C₅×C₈₉	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₈₉	C₂
LCS	G ▷ C₅×C₈₉
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₅²×C₇×C₈₉	C₂	semidirect
2. C₇×D₄₄₅	C₅	direct (N × H)
4. C₅×D₄₄₅	C₇	direct (N × H)
6. C₅×C₇×C₈₉	D₅	semidirect
7. C₅×C₇×C₈₉	C₂×C₅	semidirect
8. C₅²×C₈₉	C₂×C₇	semidirect
10. D₄₄₅	C₅×C₇	direct (N × H)
12. C₇×C₈₉	C₅×D₅	semidirect
14. C₅×C₈₉	C₇×D₅	semidirect
15. C₅×C₈₉	C₂×C₅×C₇	semidirect
18. C₅²×C₇	D₈₉	semidirect
19. C₈₉	C₅×C₇×D₅	semidirect
24. C₅×C₇	C₅×D₈₉	semidirect
25. C₅×C₇	D₄₄₅	direct (N × H)
26. C₅²	C₇×D₈₉	semidirect
30. C₇	C₅×D₄₄₅	direct (N × H)
32. C₅	C₅×C₇×D₈₉	semidirect
33. C₅	C₇×D₄₄₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₇×C₈₉	2
C₇×D₄₄₅	5
C₅×C₇×D₈₉	5
C₅×D₄₄₅	7
C₅×C₇×D₅	89

Subgroups — C5×C7×D445 #44528274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×D₄₄₅ #44528274