Subgroups — C₂×C₅×D₅₄₇⋊C₃ #45659113

Order 32820.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅₄₇⋊C₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₅₄₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₅₄₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₅₄₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₅₄₇⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₅₄₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×D₅₄₇	C₂×C₃	1	2	yes	complemented
8	C₂×C₅₄₇⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
9	D₅₄₇⋊C₃	C₂×C₅	1	2	yes	direct product factor
10	C₅×C₅₄₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅₄₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
12	C₅₄₇⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅₄₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
14	D₅₄₇	C₂×C₃×C₅	1	2	yes	complemented
15	C₅₄₇	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₃×C₅	—	547	1	no	maximal, Hall
17	C₂×C₃×C₅	—	547	2	no	—
18	C₂×C₃×C₅	—	547	1	no	—
19	C₂²×C₅	—	547	1	no	Hall
20	C₃×C₅	—	547	1	no	Hall
21	C₂²×C₃	—	547	1	no	Hall
22	C₂×C₅	—	547	2	no	—
23	C₂×C₅	D₅₄₇⋊C₃	1	1	yes	characteristic, direct product factor
24	C₂×C₃	—	547	2	no	—
25	C₂×C₃	—	547	1	no	—
26	C₅	C₂×D₅₄₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²	—	547	1	no	Sylow
28	C₃	—	547	1	no	Sylow
29	C₂	—	547	2	no	—
30	C₂	C₅×D₅₄₇⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₅₄₇⋊C₃
commutator, cosocle, hypocenter	C₅₄₇	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₅₄₇	C₂×C₃
LCS	G ▷ C₅₄₇
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₅₄₇⋊C₃	C₂	direct (N × H)
2. C₂×C₅×C₅₄₇⋊C₃	C₂	semidirect
3. C₂×C₅×D₅₄₇	C₃	semidirect
4. C₅×C₅₄₇⋊C₃	C₂²	semidirect
5. C₂×D₅₄₇⋊C₃	C₅	direct (N × H)
6. C₂×C₅×C₅₄₇	C₂×C₃	semidirect
7. C₅×D₅₄₇	C₂×C₃	semidirect
8. C₂×C₅₄₇⋊C₃	C₂×C₅	semidirect
9. D₅₄₇⋊C₃	C₂×C₅	direct (N × H)
10. C₅×C₅₄₇	C₂²×C₃	semidirect
11. C₂×D₅₄₇	C₃×C₅	semidirect
12. C₅₄₇⋊C₃	C₂²×C₅	semidirect
13. C₂×C₅₄₇	C₂×C₃×C₅	semidirect
14. D₅₄₇	C₂×C₃×C₅	semidirect
15. C₅₄₇	C₂²×C₃×C₅	semidirect
23. C₂×C₅	D₅₄₇⋊C₃	direct (N × H)
26. C₅	C₂×D₅₄₇⋊C₃	direct (N × H)
30. C₂	C₅×D₅₄₇⋊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
C₅×D₅₄₇⋊C₃	2
C₂×C₅×C₅₄₇⋊C₃	2
C₂×C₅×D₅₄₇	3
C₂×D₅₄₇⋊C₃	5
C₂²×C₃×C₅	547

Subgroups — C2×C5×D547⋊C3 #45659113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₅₄₇⋊C₃ #45659113