Subgroups — C₂×C₅⋊(#13091812⋊C₂) #44440002

Order 29340.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(#13091812⋊C₂)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×#13091812	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₈₁₅	C₃	1	1	yes	maximal, characteristic
4	C₅×#13091812	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#13091812⋊C₂	—	5	1	no	maximal, Hall
6	C₃×D₈₁₅	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₁₆₃	C₂×C₃	1	1	yes	characteristic
8	C₂×D₈₁₅	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×#13091812	D₅	1	1	yes	characteristic, complemented
10	#13091812⋊C₂	—	5	2	no	—
11	C₃×C₅×C₁₆₃	C₂²×C₃	1	1	yes	characteristic
12	C₂×C₃×D₁₆₃	—	5	1	no	—
13	C₂×C₅×C₁₆₃	C₂×C₉	1	1	yes	characteristic, complemented
14	D₈₁₅	C₂×C₉	1	2	yes	complemented
15	#13091812	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₆₃	C₃×D₅	1	1	yes	characteristic
17	C₃×D₁₆₃	—	5	2	no	—
18	C₅×C₁₆₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×D₁₆₃	—	5	1	no	Hall
20	C₃×C₁₆₃	C₂×C₃×D₅	1	1	yes	characteristic
21	C₂×C₁₆₃	C₉×D₅	1	1	yes	characteristic, complemented
22	D₁₆₃	—	5	2	no	—
23	C₂×C₉×D₅	—	163	1	no	maximal, Hall
24	C₁₆₃	C₂×C₉×D₅	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅×C₉	—	163	1	no	—
26	C₉×D₅	—	163	2	no	—
27	C₂×C₃×D₅	—	489	1	no	—
28	C₅×C₉	—	163	1	no	Hall
29	C₂²×C₉	—	815	1	no	Hall
30	C₂×C₃×C₅	D₁₆₃⋊C₃	1	1	yes	characteristic
31	C₃×D₅	—	489	2	no	—
32	C₂×D₅	—	489	1	no	Hall
33	C₂×C₉	—	815	2	no	—
34	C₂×C₉	—	163	1	no	—
35	C₃×C₅	C₂×D₁₆₃⋊C₃	1	1	yes	characteristic
36	C₂²×C₃	—	2445	1	no	—
37	C₂×C₅	#13091812⋊C₂	1	1	yes	characteristic, complemented
38	D₅	—	489	2	no	—
39	C₉	—	163	1	no	Sylow
40	C₂×C₃	—	2445	2	no	—
41	C₂×C₃	C₅⋊(D₁₆₃⋊C₃)	1	1	yes	characteristic
42	C₅	C₂×#13091812⋊C₂	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	2445	1	no	Sylow
44	C₃	C₂×C₅⋊(D₁₆₃⋊C₃)	1	1	yes	characteristic
45	C₂	—	2445	2	no	—
46	C₂	C₅⋊(#13091812⋊C₂)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₅⋊(D₁₆₃⋊C₃)
commutator, hypocenter	C₅×C₁₆₃	C₂²×C₉
Frattini	C₃	C₂×C₅⋊(D₁₆₃⋊C₃)
Fitting, socle	C₂×C₃×C₅×C₁₆₃	C₂×C₃
prime radical	C₂×C₃×D₈₁₅	C₃
cosocle	C₃×C₅×C₁₆₃	C₂²×C₃
LCS	G ▷ C₅×C₁₆₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₅⋊(#13091812⋊C₂)	C₂	direct (N × H)
2. C₂×C₅×#13091812	C₂	semidirect
4. C₅×#13091812	C₂²	semidirect
8. C₂×D₈₁₅	C₉	semidirect
9. C₂×#13091812	D₅	semidirect
13. C₂×C₅×C₁₆₃	C₂×C₉	semidirect
14. D₈₁₅	C₂×C₉	semidirect
15. #13091812	C₂×D₅	semidirect
18. C₅×C₁₆₃	C₂²×C₉	semidirect
21. C₂×C₁₆₃	C₉×D₅	semidirect
24. C₁₆₃	C₂×C₉×D₅	semidirect
37. C₂×C₅	#13091812⋊C₂	semidirect
42. C₅	C₂×#13091812⋊C₂	semidirect
46. C₂	C₅⋊(#13091812⋊C₂)	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⋊(#13091812⋊C₂)	2
C₂×C₅×#13091812	2
C₂×C₃×D₈₁₅	3
C₂×#13091812⋊C₂	5
C₂×C₉×D₅	163

Subgroups — C2×C5⋊(#13091812⋊C2) #44440002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊(#13091812⋊C₂) #44440002