Subgroups — C₉×Dic₁₀₂₅ #49146607

Order 36900.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₂₅×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₀₂₅	C₃	1	1	yes	maximal, characteristic
3	C₉×C₂₅×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉×Dic₂₀₅	—	5	1	no	maximal
5	C₂×C₃×C₂₅×C₄₁	C₂×C₃	1	1	yes	characteristic
6	Dic₁₀₂₅	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₉×C₄₁	D₅	1	1	yes	characteristic
8	C₃×C₂₅×C₄₁	C₃×C₄	1	1	yes	characteristic
9	C₃×Dic₂₀₅	—	5	1	no	—
10	C₂×C₂₅×C₄₁	C₂×C₉	1	1	yes	characteristic
11	C₅×C₉×C₄₁	Dic₅	1	1	yes	characteristic
12	C₉×Dic₄₁	—	25	1	no	Hall
13	C₂×C₃×C₅×C₄₁	C₃×D₅	1	1	yes	characteristic
14	C₂₅×C₄₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
15	C₉×Dic₂₅	—	41	1	no	maximal, Hall
16	Dic₂₀₅	—	5	1	no	—
17	C₂×C₉×C₄₁	D₂₅	1	1	yes	characteristic
18	C₃×C₅×C₄₁	C₃×Dic₅	1	1	yes	characteristic
19	C₃×Dic₄₁	—	25	1	no	—
20	C₂×C₉×C₂₅	D₄₁	1	1	yes	characteristic
21	C₂×C₅×C₄₁	C₉×D₅	1	1	yes	characteristic
22	C₉×C₄₁	Dic₂₅	1	1	yes	characteristic, complemented, Hall
23	C₃×Dic₂₅	—	41	1	no	—
24	C₂×C₃×C₄₁	C₃×D₂₅	1	1	yes	characteristic
25	C₉×C₂₅	Dic₄₁	1	1	yes	characteristic, complemented, Hall
26	C₅×C₄₁	C₉×Dic₅	1	1	yes	characteristic
27	C₉×Dic₅	—	205	1	no	—
28	Dic₄₁	—	25	1	no	Hall
29	C₂×C₃×C₂₅	C₃×D₄₁	1	1	yes	characteristic
30	C₃×C₄₁	C₃×Dic₂₅	1	1	yes	characteristic
31	Dic₂₅	—	41	1	no	Hall
32	C₂×C₅×C₉	D₂₀₅	1	1	yes	characteristic
33	C₂×C₄₁	C₉×D₂₅	1	1	yes	characteristic
34	C₃×C₂₅	C₃×Dic₄₁	1	1	yes	characteristic
35	C₃×Dic₅	—	205	1	no	—
36	C₂×C₂₅	C₉×D₄₁	1	1	yes	characteristic
37	C₅×C₉	Dic₂₀₅	1	1	yes	characteristic
38	C₄₁	C₉×Dic₂₅	1	1	yes	characteristic, complemented, Sylow
39	C₄×C₉	—	1025	1	no	Hall
40	C₂×C₃×C₅	C₃×D₂₀₅	1	1	yes	characteristic
41	C₂₅	C₉×Dic₄₁	1	1	yes	characteristic, complemented, Sylow
42	Dic₅	—	205	1	no	—
43	C₂×C₉	D₁₀₂₅	1	1	yes	characteristic
44	C₃×C₅	C₃×Dic₂₀₅	1	1	yes	characteristic
45	C₃×C₄	—	1025	1	no	—
46	C₂×C₅	C₉×D₂₀₅	1	1	yes	characteristic
47	C₉	Dic₁₀₂₅	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×C₃	C₃×D₁₀₂₅	1	1	yes	characteristic
49	C₅	C₉×Dic₂₀₅	1	1	yes	characteristic
50	C₄	—	1025	1	no	Sylow
51	C₃	C₃×Dic₁₀₂₅	1	1	yes	characteristic
52	C₂	C₉×D₁₀₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₉	D₁₀₂₅
commutator, hypocenter	C₂₅×C₄₁	C₄×C₉
Frattini	C₂×C₃×C₅	C₃×D₂₀₅
Fitting	C₂×C₉×C₂₅×C₄₁	C₂
socle, prime radical	C₂×C₃×C₅×C₄₁	C₃×D₅
cosocle	C₂×C₃×C₂₅×C₄₁	C₂×C₃
LCS	G ▷ C₂₅×C₄₁
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
3. C₉×C₂₅×C₄₁	C₄	semidirect
6. Dic₁₀₂₅	C₉	direct (N × H)
14. C₂₅×C₄₁	C₄×C₉	semidirect
22. C₉×C₄₁	Dic₂₅	semidirect
25. C₉×C₂₅	Dic₄₁	semidirect
38. C₄₁	C₉×Dic₂₅	semidirect
41. C₂₅	C₉×Dic₄₁	semidirect
47. C₉	Dic₁₀₂₅	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×C₉×C₂₅×C₄₁	2
C₃×Dic₁₀₂₅	3
C₉×Dic₂₀₅	5
C₉×Dic₂₅	41

Subgroups — C9×Dic1025 #49146607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×Dic₁₀₂₅ #49146607