Subgroups — C₂×C₁₁×C₂₅×C₁₉⋊C₃ #44535430

Order 31350.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₅×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₁×C₁₉×C₂₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₅×C₁₁×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic
4	C₁₁×C₁₉×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₁×C₁₉⋊C₃	C₂×C₅	1	1	yes	characteristic
6	C₂×C₂₅×C₁₉⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₁₁×C₁₉	C₃×C₅	1	1	yes	characteristic
8	C₂×C₃×C₁₁×C₂₅	—	19	1	no	maximal, Hall
9	C₂₅×C₁₉⋊C₃	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₁×C₁₉⋊C₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
11	C₅×C₁₁×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
12	C₂×C₁₉×C₂₅	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₁×C₂₅	—	19	1	no	Hall
14	C₁₁×C₁₉⋊C₃	C₂×C₂₅	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₅×C₁₉⋊C₃	C₅×C₁₁	1	1	yes	characteristic
16	C₂×C₁₁×C₂₅	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
17	C₁₉×C₂₅	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₁×C₁₉	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₅×C₁₁	—	19	1	no	—
20	C₅×C₁₉⋊C₃	C₂×C₅×C₁₁	1	1	yes	characteristic
21	C₁₁×C₂₅	C₂×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
22	C₁₁×C₁₉	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×C₁₉	C₃×C₅×C₁₁	1	1	yes	characteristic
24	C₃×C₅×C₁₁	—	19	1	no	—
25	C₂×C₃×C₂₅	—	19	1	no	Hall
26	C₂×C₁₉⋊C₃	C₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₅×C₁₁	C₅×C₁₉⋊C₃	1	1	yes	characteristic
28	C₅×C₁₉	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic
29	C₃×C₂₅	—	19	1	no	Hall
30	C₂×C₃×C₁₁	—	19	1	no	Hall
31	C₁₉⋊C₃	C₂×C₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Hall
32	C₅×C₁₁	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic
33	C₂×C₂₅	C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₁₉	C₃×C₁₁×C₂₅	1	1	yes	characteristic, complemented, Hall
35	C₃×C₁₁	—	19	1	no	Hall
36	C₂×C₃×C₅	—	19	1	no	—
37	C₂₅	C₂×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₁₁	C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
39	C₁₉	C₂×C₃×C₁₁×C₂₅	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₅	—	19	1	no	—
41	C₁₁	C₂×C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₅	C₅×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic
43	C₂×C₃	—	19	1	no	Hall
44	C₅	C₂×C₅×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic
45	C₃	—	19	1	no	Sylow
46	C₂	C₁₁×C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₂₅	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₂×C₃×C₁₁×C₂₅
Frattini	C₅	C₂×C₅×C₁₁×C₁₉⋊C₃
Fitting	C₂×C₁₁×C₁₉×C₂₅	C₃
socle	C₂×C₅×C₁₁×C₁₉	C₃×C₅
prime radical	C₂×C₅×C₁₁×C₁₉⋊C₃	C₅
cosocle	C₅×C₁₉	C₂×C₃×C₅×C₁₁
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₁₁×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₂₅×C₁₉⋊C₃	C₂	direct (N × H)
2. C₂×C₁₁×C₁₉×C₂₅	C₃	semidirect
4. C₁₁×C₁₉×C₂₅	C₂×C₃	semidirect
6. C₂×C₂₅×C₁₉⋊C₃	C₁₁	direct (N × H)
9. C₂₅×C₁₉⋊C₃	C₂×C₁₁	direct (N × H)
10. C₂×C₁₁×C₁₉⋊C₃	C₂₅	direct (N × H)
12. C₂×C₁₉×C₂₅	C₃×C₁₁	semidirect
14. C₁₁×C₁₉⋊C₃	C₂×C₂₅	direct (N × H)
16. C₂×C₁₁×C₂₅	C₁₉⋊C₃	direct (N × H)
17. C₁₉×C₂₅	C₂×C₃×C₁₁	semidirect
18. C₂×C₁₁×C₁₉	C₃×C₂₅	semidirect
21. C₁₁×C₂₅	C₂×C₁₉⋊C₃	direct (N × H)
22. C₁₁×C₁₉	C₂×C₃×C₂₅	semidirect
26. C₂×C₁₉⋊C₃	C₁₁×C₂₅	direct (N × H)
31. C₁₉⋊C₃	C₂×C₁₁×C₂₅	direct (N × H)
33. C₂×C₂₅	C₁₁×C₁₉⋊C₃	direct (N × H)
34. C₂×C₁₉	C₃×C₁₁×C₂₅	semidirect
37. C₂₅	C₂×C₁₁×C₁₉⋊C₃	direct (N × H)
38. C₂×C₁₁	C₂₅×C₁₉⋊C₃	direct (N × H)
39. C₁₉	C₂×C₃×C₁₁×C₂₅	semidirect
41. C₁₁	C₂×C₂₅×C₁₉⋊C₃	direct (N × H)
46. C₂	C₁₁×C₂₅×C₁₉⋊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
C₁₁×C₂₅×C₁₉⋊C₃	2
C₂×C₁₁×C₁₉×C₂₅	3
C₂×C₅×C₁₁×C₁₉⋊C₃	5
C₂×C₂₅×C₁₉⋊C₃	11
C₂×C₃×C₁₁×C₂₅	19

Subgroups — C2×C11×C25×C19⋊C3 #44535430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₂₅×C₁₉⋊C₃ #44535430