Subgroups — C₂×D₅×C₂₇₇⋊C₃ #30658952

Order 16620.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₂₇₇⋊C₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₂₇₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅×C₂₇₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₂₇₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₂₇₇⋊C₃	—	5	1	no	maximal, Hall
6	C₂×C₅×C₂₇₇	C₂×C₃	1	1	yes	characteristic, complemented
7	D₅×C₂₇₇	C₂×C₃	1	2	yes	complemented
8	C₂×C₂₇₇⋊C₃	—	5	2	no	—
9	C₂×C₂₇₇⋊C₃	D₅	1	1	yes	characteristic, direct product factor
10	C₅×C₂₇₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₂₇₇	—	5	1	no	Hall
12	C₂₇₇⋊C₃	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₂₇₇	—	5	2	no	—
14	C₂×C₂₇₇	C₃×D₅	1	1	yes	characteristic, complemented
15	C₂₇₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×D₅	—	277	1	no	maximal, Hall
17	C₂×C₃×C₅	—	277	1	no	—
18	C₃×D₅	—	277	2	no	—
19	C₂×D₅	C₂₇₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₅	—	277	1	no	Hall
21	C₂²×C₃	—	1385	1	no	Hall
22	C₂×C₅	C₂×C₂₇₇⋊C₃	1	1	yes	characteristic, complemented
23	D₅	C₂×C₂₇₇⋊C₃	1	2	yes	direct product factor
24	C₂×C₃	—	277	1	no	—
25	C₂×C₃	—	1385	2	no	—
26	C₅	C₂²×C₂₇₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	5	1	no	Sylow
28	C₃	—	277	1	no	Sylow
29	C₂	—	5	2	no	—
30	C₂	D₅×C₂₇₇⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅×C₂₇₇⋊C₃
commutator, cosocle, hypocenter	C₅×C₂₇₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₂₇₇	C₂×C₃
LCS	G ▷ C₅×C₂₇₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₅×C₂₇₇⋊C₃	C₂	direct (N × H)
2. C₂×C₅×C₂₇₇⋊C₃	C₂	semidirect
3. C₂×D₅×C₂₇₇	C₃	semidirect
4. C₅×C₂₇₇⋊C₃	C₂²	semidirect
6. C₂×C₅×C₂₇₇	C₂×C₃	semidirect
7. D₅×C₂₇₇	C₂×C₃	semidirect
9. C₂×C₂₇₇⋊C₃	D₅	direct (N × H)
10. C₅×C₂₇₇	C₂²×C₃	semidirect
12. C₂₇₇⋊C₃	C₂×D₅	direct (N × H)
14. C₂×C₂₇₇	C₃×D₅	semidirect
15. C₂₇₇	C₂×C₃×D₅	semidirect
19. C₂×D₅	C₂₇₇⋊C₃	direct (N × H)
22. C₂×C₅	C₂×C₂₇₇⋊C₃	semidirect
23. D₅	C₂×C₂₇₇⋊C₃	direct (N × H)
26. C₅	C₂²×C₂₇₇⋊C₃	semidirect
30. C₂	D₅×C₂₇₇⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
D₅×C₂₇₇⋊C₃	2
C₂×C₅×C₂₇₇⋊C₃	2
C₂×D₅×C₂₇₇	3
C₂²×C₂₇₇⋊C₃	5
C₂×C₃×D₅	277

Subgroups — C2×D5×C277⋊C3 #30658952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₂₇₇⋊C₃ #30658952