Subgroups — C₂×C₃×C₁₁×D₂₅ #15693113

Order 3300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₁×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₁×D₂₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₁×D₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₁×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₅×C₁₁	—	5	1	no	maximal
6	C₂×C₁₁×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₁×D₂₅	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₅×C₁₁	D₅	1	1	yes	characteristic
9	C₃×D₅×C₁₁	—	5	2	no	—
10	C₂×C₃×D₂₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₁×C₂₅	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×D₅×C₁₁	—	5	1	no	—
13	C₃×C₅×C₁₁	C₂×D₅	1	1	yes	characteristic
14	C₂×C₃×C₂₅	C₂×C₁₁	1	1	yes	characteristic, complemented
15	C₃×D₂₅	C₂×C₁₁	1	2	yes	direct product factor
16	C₂²×C₃×C₁₁	—	25	1	no	Hall
17	C₂×C₅×C₁₁	C₃×D₅	1	1	yes	characteristic
18	D₅×C₁₁	—	5	2	no	—
19	C₂×D₂₅	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₂₅	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₁	—	25	2	no	—
22	C₂×C₃×C₁₁	D₂₅	1	1	yes	characteristic, direct product factor
23	C₂×C₃×D₅	—	5	1	no	—
24	C₅×C₁₁	C₂×C₃×D₅	1	1	yes	characteristic
25	C₂×C₂₅	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
26	D₂₅	C₂×C₃×C₁₁	1	2	yes	direct product factor
27	C₂²×C₁₁	—	25	1	no	Hall
28	C₃×C₁₁	C₂×D₂₅	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₃×C₅	D₅×C₁₁	1	1	yes	characteristic
30	C₃×D₅	—	5	2	no	—
31	C₂₅	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₁₁	—	25	2	no	—
33	C₂×C₁₁	C₃×D₂₅	1	1	yes	characteristic, direct product factor
34	C₂×D₅	—	5	1	no	—
35	C₃×C₅	C₂×D₅×C₁₁	1	1	yes	characteristic
36	C₂²×C₃	—	25	1	no	Hall
37	C₁₁	C₂×C₃×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₅	C₃×D₅×C₁₁	1	1	yes	characteristic
39	D₅	—	5	2	no	—
40	C₂×C₃	—	25	2	no	—
41	C₂×C₃	C₁₁×D₂₅	1	1	yes	characteristic, direct product factor
42	C₅	C₂×C₃×D₅×C₁₁	1	1	yes	characteristic
43	C₂²	—	25	1	no	Sylow
44	C₃	C₂×C₁₁×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	25	2	no	—
46	C₂	C₃×C₁₁×D₂₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂²×C₃×C₁₁
Frattini	C₅	C₂×C₃×D₅×C₁₁
Fitting	C₂×C₃×C₁₁×C₂₅	C₂
socle	C₂×C₃×C₅×C₁₁	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₃×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₁×C₂₅	C₂	semidirect
2. C₃×C₁₁×D₂₅	C₂	direct (N × H)
3. C₂×C₁₁×D₂₅	C₃	direct (N × H)
4. C₃×C₁₁×C₂₅	C₂²	semidirect
6. C₂×C₁₁×C₂₅	C₂×C₃	semidirect
7. C₁₁×D₂₅	C₂×C₃	direct (N × H)
10. C₂×C₃×D₂₅	C₁₁	direct (N × H)
11. C₁₁×C₂₅	C₂²×C₃	semidirect
14. C₂×C₃×C₂₅	C₂×C₁₁	semidirect
15. C₃×D₂₅	C₂×C₁₁	direct (N × H)
19. C₂×D₂₅	C₃×C₁₁	direct (N × H)
20. C₃×C₂₅	C₂²×C₁₁	semidirect
22. C₂×C₃×C₁₁	D₂₅	direct (N × H)
25. C₂×C₂₅	C₂×C₃×C₁₁	semidirect
26. D₂₅	C₂×C₃×C₁₁	direct (N × H)
28. C₃×C₁₁	C₂×D₂₅	direct (N × H)
31. C₂₅	C₂²×C₃×C₁₁	semidirect
33. C₂×C₁₁	C₃×D₂₅	direct (N × H)
37. C₁₁	C₂×C₃×D₂₅	direct (N × H)
41. C₂×C₃	C₁₁×D₂₅	direct (N × H)
44. C₃	C₂×C₁₁×D₂₅	direct (N × H)
46. C₂	C₃×C₁₁×D₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₁×C₂₅	2
C₃×C₁₁×D₂₅	2
C₂×C₁₁×D₂₅	3
C₂×C₃×D₅×C₁₁	5
C₂×C₃×D₂₅	11

Subgroups — C2×C3×C11×D25 #15693113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₁×D₂₅ #15693113