Subgroups — C₃×C₅×D₆₈₇ #35207307

Order 20610.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₂₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₆₈₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅×D₂₂₉	—	3	1	no	maximal
4	C₃×D₆₈₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₂₂₉	—	2	1	no	—
6	C₃×C₅×C₂₂₉	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₂₂₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×D₂₂₉	—	3	1	no	Hall
9	C₃²×C₂₂₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	D₆₈₇	C₃×C₅	1	1	yes	characteristic, direct product factor
11	C₃×D₂₂₉	—	3	1	no	—
12	C₅×C₂₂₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₂₂₉	—	2	1	no	—
14	C₃×C₂₂₉	C₅×D₃	1	1	yes	characteristic, complemented
15	C₃×C₂₂₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
16	D₂₂₉	—	3	1	no	Hall
17	C₂₂₉	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₅×D₃	—	229	1	no	maximal, Hall
19	C₃²×C₅	D₂₂₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₅	—	687	1	no	—
21	C₅×D₃	—	229	1	no	—
22	C₃×D₃	—	229	1	no	Hall
23	C₃×C₅	—	2	1	no	—
24	C₃×C₅	C₃×D₂₂₉	1	1	yes	characteristic, complemented
25	C₃×C₅	D₆₈₇	1	1	yes	characteristic, direct product factor
26	C₂×C₅	—	687	1	no	Hall
27	C₃²	C₅×D₂₂₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	687	1	no	—
29	D₃	—	229	1	no	—
30	C₅	C₃×D₆₈₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₃	—	2	1	no	—
32	C₃	C₃×C₅×D₂₂₉	1	1	yes	characteristic, complemented
33	C₃	C₅×D₆₈₇	1	1	yes	characteristic, direct product factor
34	C₂	—	687	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	D₆₈₇
commutator, cosocle, hypocenter	C₃×C₂₂₉	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₂₂₉	C₂
LCS	G ▷ C₃×C₂₂₉
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₂₂₉	C₂	semidirect
2. C₅×D₆₈₇	C₃	direct (N × H)
4. C₃×D₆₈₇	C₅	direct (N × H)
6. C₃×C₅×C₂₂₉	D₃	semidirect
7. C₃×C₅×C₂₂₉	C₂×C₃	semidirect
9. C₃²×C₂₂₉	C₂×C₅	semidirect
10. D₆₈₇	C₃×C₅	direct (N × H)
12. C₅×C₂₂₉	C₃×D₃	semidirect
14. C₃×C₂₂₉	C₅×D₃	semidirect
15. C₃×C₂₂₉	C₂×C₃×C₅	semidirect
17. C₂₂₉	C₃×C₅×D₃	semidirect
19. C₃²×C₅	D₂₂₉	semidirect
24. C₃×C₅	C₃×D₂₂₉	semidirect
25. C₃×C₅	D₆₈₇	direct (N × H)
27. C₃²	C₅×D₂₂₉	semidirect
30. C₅	C₃×D₆₈₇	direct (N × H)
32. C₃	C₃×C₅×D₂₂₉	semidirect
33. C₃	C₅×D₆₈₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₂₂₉	2
C₅×D₆₈₇	3
C₃×C₅×D₂₂₉	3
C₃×D₆₈₇	5
C₃×C₅×D₃	229

Subgroups — C3×C5×D687 #35207307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₆₈₇ #35207307