Subgroups — C₂×C₁₃×C₁₉×C₅⋊D₅ #37590871

Order 24700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉×C₅⋊D₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₅×C₁₃×C₁₉	—	5	6	no	maximal
5	D₅×C₁₃×C₁₉	—	5	12	no	—
6	C₂×C₅×C₁₃×C₁₉	D₅	1	6	yes	complemented
7	C₂×C₁₉×C₅⋊D₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₃×C₅⋊D₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₁₃×C₁₉	C₂×D₅	1	6	yes	complemented
10	C₂²×C₁₃×C₁₉	—	25	1	no	Hall
11	C₂×C₅²×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
12	C₁₉×C₅⋊D₅	C₂×C₁₃	1	2	yes	direct product factor
13	C₂×C₅²×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented
14	C₁₃×C₅⋊D₅	C₂×C₁₉	1	2	yes	direct product factor
15	C₂×C₁₃×C₁₉	—	25	2	no	—
16	C₂×C₁₃×C₁₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor
17	C₅²×C₁₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
18	C₂×D₅×C₁₉	—	5	6	no	—
19	C₅²×C₁₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
20	C₂×D₅×C₁₃	—	5	6	no	—
21	C₁₃×C₁₉	C₂×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₅×C₁₉	D₅×C₁₃	1	6	yes	complemented
23	D₅×C₁₉	—	5	12	no	—
24	C₂×C₅×C₁₃	D₅×C₁₉	1	6	yes	complemented
25	D₅×C₁₃	—	5	12	no	—
26	C₂×C₅⋊D₅	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
27	C₅×C₁₉	C₂×D₅×C₁₃	1	6	yes	complemented
28	C₂²×C₁₉	—	25	1	no	Hall
29	C₅×C₁₃	C₂×D₅×C₁₉	1	6	yes	complemented
30	C₂²×C₁₃	—	25	1	no	Hall
31	C₂×C₅²	C₂×C₁₃×C₁₉	1	1	yes	characteristic, complemented
32	C₅⋊D₅	C₂×C₁₃×C₁₉	1	2	yes	direct product factor
33	C₂×C₁₉	—	25	2	no	—
34	C₂×C₁₉	C₁₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor
35	C₂×C₁₃	—	25	2	no	—
36	C₂×C₁₃	C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor
37	C₅²	C₂²×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
38	C₂×D₅	—	5	6	no	—
39	C₁₉	C₂×C₁₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₁₃	C₂×C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	D₅×C₁₃×C₁₉	1	6	yes	complemented
42	D₅	—	5	12	no	—
43	C₅	C₂×D₅×C₁₃×C₁₉	1	6	yes	complemented
44	C₂²	—	25	1	no	Sylow
45	C₂	—	25	2	no	—
46	C₂	C₁₃×C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₁₉	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₃×C₁₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₁₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉×C₅⋊D₅	C₂	direct (N × H)
2. C₂×C₅²×C₁₃×C₁₉	C₂	semidirect
3. C₅²×C₁₃×C₁₉	C₂²	semidirect
6. C₂×C₅×C₁₃×C₁₉	D₅	semidirect
7. C₂×C₁₉×C₅⋊D₅	C₁₃	direct (N × H)
8. C₂×C₁₃×C₅⋊D₅	C₁₉	direct (N × H)
9. C₅×C₁₃×C₁₉	C₂×D₅	semidirect
11. C₂×C₅²×C₁₉	C₂×C₁₃	semidirect
12. C₁₉×C₅⋊D₅	C₂×C₁₃	direct (N × H)
13. C₂×C₅²×C₁₃	C₂×C₁₉	semidirect
14. C₁₃×C₅⋊D₅	C₂×C₁₉	direct (N × H)
16. C₂×C₁₃×C₁₉	C₅⋊D₅	direct (N × H)
17. C₅²×C₁₉	C₂²×C₁₃	semidirect
19. C₅²×C₁₃	C₂²×C₁₉	semidirect
21. C₁₃×C₁₉	C₂×C₅⋊D₅	direct (N × H)
22. C₂×C₅×C₁₉	D₅×C₁₃	semidirect
24. C₂×C₅×C₁₃	D₅×C₁₉	semidirect
26. C₂×C₅⋊D₅	C₁₃×C₁₉	direct (N × H)
27. C₅×C₁₉	C₂×D₅×C₁₃	semidirect
29. C₅×C₁₃	C₂×D₅×C₁₉	semidirect
31. C₂×C₅²	C₂×C₁₃×C₁₉	semidirect
32. C₅⋊D₅	C₂×C₁₃×C₁₉	direct (N × H)
34. C₂×C₁₉	C₁₃×C₅⋊D₅	direct (N × H)
36. C₂×C₁₃	C₁₉×C₅⋊D₅	direct (N × H)
37. C₅²	C₂²×C₁₃×C₁₉	semidirect
39. C₁₉	C₂×C₁₃×C₅⋊D₅	direct (N × H)
40. C₁₃	C₂×C₁₉×C₅⋊D₅	direct (N × H)
41. C₂×C₅	D₅×C₁₃×C₁₉	semidirect
43. C₅	C₂×D₅×C₁₃×C₁₉	semidirect
46. C₂	C₁₃×C₁₉×C₅⋊D₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₁₉×C₅⋊D₅	2
C₂×C₅²×C₁₃×C₁₉	2
C₂×D₅×C₁₃×C₁₉	5
C₂×C₁₉×C₅⋊D₅	13
C₂×C₁₃×C₅⋊D₅	19

Subgroups — C2×C13×C19×C5⋊D5 #37590871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₁₉×C₅⋊D₅ #37590871