Subgroups — C₃×C₁₃×D₂₇₅ #36339686

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	C₁₃×D₂₇₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×D₅₅	—	5	1	no	maximal
4	C₁₁×C₁₃×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₁×C₁₃	D₅	1	1	yes	characteristic
6	C₃×C₁₃×D₂₅	—	11	1	no	maximal, Hall
7	C₃×D₂₇₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₃×D₅₅	—	5	1	no	—
9	C₃×C₁₃×C₂₅	D₁₁	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₃×D₁₁	—	25	1	no	Hall
11	C₃×C₁₁×C₂₅	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₅×C₁₁×C₁₃	C₃×D₅	1	1	yes	characteristic
13	C₁₃×D₂₅	—	11	1	no	Hall
14	D₂₇₅	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₁×C₁₃	D₂₅	1	1	yes	characteristic, complemented, Hall
16	C₃×D₅×C₁₃	—	55	1	no	—
17	C₃×D₅₅	—	5	1	no	—
18	C₁₃×C₂₅	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
19	C₁₃×D₁₁	—	25	1	no	Hall
20	C₁₁×C₂₅	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₃	D₅₅	1	1	yes	characteristic
22	C₃×C₅×C₁₁	D₅×C₁₃	1	1	yes	characteristic
23	C₃×D₂₅	—	11	1	no	Hall
24	C₁₁×C₁₃	C₃×D₂₅	1	1	yes	characteristic, complemented, Hall
25	D₅×C₁₃	—	55	1	no	—
26	D₅₅	—	5	1	no	—
27	C₂×C₃×C₁₃	—	275	1	no	Hall
28	C₃×C₂₅	C₁₃×D₁₁	1	1	yes	characteristic, complemented, Hall
29	C₃×D₁₁	—	25	1	no	Hall
30	C₅×C₁₃	C₃×D₅₅	1	1	yes	characteristic
31	C₅×C₁₁	C₃×D₅×C₁₃	1	1	yes	characteristic
32	D₂₅	—	11	1	no	Hall
33	C₃×C₁₃	D₂₇₅	1	1	yes	characteristic, direct product factor, Hall
34	C₃×C₁₁	C₁₃×D₂₅	1	1	yes	characteristic, complemented, Hall
35	C₃×D₅	—	55	1	no	—
36	C₂×C₁₃	—	275	1	no	Hall
37	C₂₅	C₃×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
38	D₁₁	—	25	1	no	Hall
39	C₃×C₅	C₁₃×D₅₅	1	1	yes	characteristic
40	C₁₃	C₃×D₂₇₅	1	1	yes	characteristic, direct product factor, Sylow
41	C₁₁	C₃×C₁₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
42	D₅	—	55	1	no	—
43	C₂×C₃	—	275	1	no	Hall
44	C₅	C₃×C₁₃×D₅₅	1	1	yes	characteristic
45	C₃	C₁₃×D₂₇₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	275	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₂₇₅
commutator, cosocle, hypocenter	C₁₁×C₂₅	C₂×C₃×C₁₃
Frattini	C₅	C₃×C₁₃×D₅₅
Fitting	C₃×C₁₁×C₁₃×C₂₅	C₂
socle	C₃×C₅×C₁₁×C₁₃	D₅
LCS	G ▷ C₁₁×C₂₅
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₁₃×C₂₅	C₂	semidirect
2. C₁₃×D₂₇₅	C₃	direct (N × H)
4. C₁₁×C₁₃×C₂₅	C₂×C₃	semidirect
7. C₃×D₂₇₅	C₁₃	direct (N × H)
9. C₃×C₁₃×C₂₅	D₁₁	semidirect
11. C₃×C₁₁×C₂₅	C₂×C₁₃	semidirect
14. D₂₇₅	C₃×C₁₃	direct (N × H)
15. C₃×C₁₁×C₁₃	D₂₅	semidirect
18. C₁₃×C₂₅	C₃×D₁₁	semidirect
20. C₁₁×C₂₅	C₂×C₃×C₁₃	semidirect
24. C₁₁×C₁₃	C₃×D₂₅	semidirect
28. C₃×C₂₅	C₁₃×D₁₁	semidirect
33. C₃×C₁₃	D₂₇₅	direct (N × H)
34. C₃×C₁₁	C₁₃×D₂₅	semidirect
37. C₂₅	C₃×C₁₃×D₁₁	semidirect
40. C₁₃	C₃×D₂₇₅	direct (N × H)
41. C₁₁	C₃×C₁₃×D₂₅	semidirect
45. C₃	C₁₃×D₂₇₅	direct (N × H)

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
C₁₃×D₂₇₅	3
C₃×C₁₃×D₅₅	5
C₃×C₁₃×D₂₅	11
C₃×D₂₇₅	13

Subgroups — C3×C13×D275 #36339686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×D₂₇₅ #36339686