Subgroups — C₁₀₃×Dic₇₅ #44525402

Order 30900.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₅×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	Dic₂₅×C₁₀₃	—	3	1	no	maximal, Hall
3	C₃×C₂₅×C₁₀₃	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₅×C₁₀₃	—	5	1	no	maximal
5	C₂×C₂₅×C₁₀₃	D₃	1	1	yes	characteristic
6	C₂×C₃×C₅×C₁₀₃	D₅	1	1	yes	characteristic
7	C₂₅×C₁₀₃	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₅×C₁₀₃	—	15	1	no	—
9	C₃×C₅×C₁₀₃	Dic₅	1	1	yes	characteristic
10	Dic₃×C₁₀₃	—	25	1	no	Hall
11	C₂×C₅×C₁₀₃	D₁₅	1	1	yes	characteristic
12	C₂×C₃×C₁₀₃	D₂₅	1	1	yes	characteristic
13	C₅×C₁₀₃	Dic₁₅	1	1	yes	characteristic
14	C₄×C₁₀₃	—	75	1	no	Hall
15	C₃×C₁₀₃	Dic₂₅	1	1	yes	characteristic, complemented, Hall
16	Dic₇₅	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₁₀₃	D₇₅	1	1	yes	characteristic
18	C₂×C₃×C₂₅	C₂×C₁₀₃	1	1	yes	characteristic
19	C₁₀₃	Dic₇₅	1	1	yes	characteristic, direct product factor, Sylow
20	Dic₂₅	—	3	1	no	Hall
21	C₃×C₂₅	C₄×C₁₀₃	1	1	yes	characteristic, complemented, Hall
22	Dic₁₅	—	5	1	no	—
23	C₂×C₂₅	D₃×C₁₀₃	1	1	yes	characteristic
24	C₂×C₃×C₅	D₅×C₁₀₃	1	1	yes	characteristic
25	C₂₅	Dic₃×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
26	Dic₅	—	15	1	no	—
27	C₃×C₅	Dic₅×C₁₀₃	1	1	yes	characteristic
28	Dic₃	—	25	1	no	Hall
29	C₂×C₅	D₁₅×C₁₀₃	1	1	yes	characteristic
30	C₂×C₃	D₂₅×C₁₀₃	1	1	yes	characteristic
31	C₅	Dic₁₅×C₁₀₃	1	1	yes	characteristic
32	C₄	—	75	1	no	Sylow
33	C₃	Dic₂₅×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
34	C₂	C₁₀₃×D₇₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₀₃	D₇₅
commutator, hypocenter	C₃×C₂₅	C₄×C₁₀₃
Frattini	C₂×C₅	D₁₅×C₁₀₃
Fitting	C₂×C₃×C₂₅×C₁₀₃	C₂
socle, prime radical	C₂×C₃×C₅×C₁₀₃	D₅
cosocle	C₂×C₃×C₂₅	C₂×C₁₀₃
LCS	G ▷ C₃×C₂₅
UCS	C₁ ◁ C₂×C₁₀₃

Complements

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

N	H ≅ G/N	type
3. C₃×C₂₅×C₁₀₃	C₄	semidirect
7. C₂₅×C₁₀₃	Dic₃	semidirect
15. C₃×C₁₀₃	Dic₂₅	semidirect
16. Dic₇₅	C₁₀₃	direct (N × H)
19. C₁₀₃	Dic₇₅	direct (N × H)
21. C₃×C₂₅	C₄×C₁₀₃	semidirect
25. C₂₅	Dic₃×C₁₀₃	semidirect
33. C₃	Dic₂₅×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₂₅×C₁₀₃	2
Dic₂₅×C₁₀₃	3
Dic₁₅×C₁₀₃	5
Dic₇₅	103

Subgroups — C103×Dic75 #44525402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×Dic₇₅ #44525402