Subgroups — C₁₁×C₁₃×D₇₅ #36339692

Order 21450.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₁₃×D₂₅	—	3	1	no	maximal, Hall
3	C₁₁×C₁₃×D₁₅	—	5	1	no	maximal
4	C₁₁×C₁₃×C₂₅	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₁×C₁₃	D₅	1	1	yes	characteristic
6	C₁₃×D₇₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×D₇₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	D₅×C₁₁×C₁₃	—	15	1	no	—
9	C₃×C₁₃×C₂₅	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
10	D₃×C₁₁×C₁₃	—	25	1	no	Hall
11	C₃×C₁₁×C₂₅	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₅×C₁₁×C₁₃	D₁₅	1	1	yes	characteristic
13	C₁₃×D₂₅	—	3	1	no	Hall
14	C₁₁×D₂₅	—	3	1	no	Hall
15	C₃×C₁₁×C₁₃	D₂₅	1	1	yes	characteristic, complemented, Hall
16	C₁₃×D₁₅	—	5	1	no	—
17	C₁₁×D₁₅	—	5	1	no	—
18	C₁₃×C₂₅	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
19	C₂×C₁₁×C₁₃	—	75	1	no	Hall
20	C₁₁×C₂₅	D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₃	D₅×C₁₁	1	1	yes	characteristic
22	C₃×C₅×C₁₁	D₅×C₁₃	1	1	yes	characteristic
23	D₇₅	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
24	C₁₁×C₁₃	D₇₅	1	1	yes	characteristic, direct product factor, Hall
25	D₅×C₁₃	—	15	1	no	—
26	D₅×C₁₁	—	15	1	no	—
27	D₃×C₁₃	—	25	1	no	Hall
28	C₃×C₂₅	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
29	D₃×C₁₁	—	25	1	no	Hall
30	C₅×C₁₃	C₁₁×D₁₅	1	1	yes	characteristic
31	C₅×C₁₁	C₁₃×D₁₅	1	1	yes	characteristic
32	D₂₅	—	3	1	no	Hall
33	C₃×C₁₃	C₁₁×D₂₅	1	1	yes	characteristic, complemented, Hall
34	C₃×C₁₁	C₁₃×D₂₅	1	1	yes	characteristic, complemented, Hall
35	D₁₅	—	5	1	no	—
36	C₂×C₁₃	—	75	1	no	Hall
37	C₂₅	D₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₁₁	—	75	1	no	Hall
39	C₃×C₅	D₅×C₁₁×C₁₃	1	1	yes	characteristic
40	C₁₃	C₁₁×D₇₅	1	1	yes	characteristic, direct product factor, Sylow
41	C₁₁	C₁₃×D₇₅	1	1	yes	characteristic, direct product factor, Sylow
42	D₅	—	15	1	no	—
43	D₃	—	25	1	no	Hall
44	C₅	C₁₁×C₁₃×D₁₅	1	1	yes	characteristic
45	C₃	C₁₁×C₁₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	75	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	D₇₅
commutator, cosocle, hypocenter	C₃×C₂₅	C₂×C₁₁×C₁₃
Frattini	C₅	C₁₁×C₁₃×D₁₅
Fitting	C₃×C₁₁×C₁₃×C₂₅	C₂
socle	C₃×C₅×C₁₁×C₁₃	D₅
LCS	G ▷ C₃×C₂₅
UCS	C₁ ◁ C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₁₃×C₂₅	C₂	semidirect
4. C₁₁×C₁₃×C₂₅	D₃	semidirect
6. C₁₃×D₇₅	C₁₁	direct (N × H)
7. C₁₁×D₇₅	C₁₃	direct (N × H)
9. C₃×C₁₃×C₂₅	C₂×C₁₁	semidirect
11. C₃×C₁₁×C₂₅	C₂×C₁₃	semidirect
15. C₃×C₁₁×C₁₃	D₂₅	semidirect
18. C₁₃×C₂₅	D₃×C₁₁	semidirect
20. C₁₁×C₂₅	D₃×C₁₃	semidirect
23. D₇₅	C₁₁×C₁₃	direct (N × H)
24. C₁₁×C₁₃	D₇₅	direct (N × H)
28. C₃×C₂₅	C₂×C₁₁×C₁₃	semidirect
33. C₃×C₁₃	C₁₁×D₂₅	semidirect
34. C₃×C₁₁	C₁₃×D₂₅	semidirect
37. C₂₅	D₃×C₁₁×C₁₃	semidirect
40. C₁₃	C₁₁×D₇₅	direct (N × H)
41. C₁₁	C₁₃×D₇₅	direct (N × H)
45. C₃	C₁₁×C₁₃×D₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₁×C₁₃×C₂₅	2
C₁₁×C₁₃×D₂₅	3
C₁₁×C₁₃×D₁₅	5
C₁₃×D₇₅	11
C₁₁×D₇₅	13

Subgroups — C11×C13×D75 #36339692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₃×D₇₅ #36339692