Subgroups — C₅×(C₁₀₃⋊C₃)⋊Dic₅ #44525437

Order 30900.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₁₀₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₅₁₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₀₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	(C₁₀₃⋊C₃)⋊Dic₅	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×(C₁₀₃⋊C₃)⋊C₄	—	5	1	no	maximal
6	C₂×C₅²×C₁₀₃	C₂×C₃	1	1	yes	characteristic
7	C₂×C₅×C₁₀₃⋊C₃	—	2	2	no	—
8	C₂×C₅×C₁₀₃⋊C₃	D₅	1	1	yes	characteristic
9	C₂×C₅×C₁₀₃⋊C₃	C₂×C₅	1	1	yes	characteristic
10	C₅²×C₁₀₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
11	Dic₅₁₅	C₃×C₅	1	1	yes	characteristic, complemented
12	C₅×Dic₁₀₃	—	5	1	no	—
13	C₅×C₁₀₃⋊C₃	—	2	2	no	—
14	C₅×C₁₀₃⋊C₃	Dic₅	1	1	yes	characteristic, complemented
15	C₅×C₁₀₃⋊C₃	C₄×C₅	1	1	yes	characteristic, complemented
16	(C₁₀₃⋊C₃)⋊C₄	—	5	1	no	Hall
17	C₂×C₅×C₁₀₃	—	2	2	no	—
18	C₂×C₅×C₁₀₃	C₃×D₅	1	1	yes	characteristic
19	C₂×C₅×C₁₀₃	C₂×C₃×C₅	1	1	yes	characteristic
20	C₂×C₁₀₃⋊C₃	C₅×D₅	1	1	yes	characteristic
21	C₅×C₁₀₃	—	2	2	no	—
22	C₅×C₁₀₃	C₃×Dic₅	1	1	yes	characteristic, complemented
23	C₅×C₁₀₃	C₃×C₄×C₅	1	1	yes	characteristic, complemented
24	Dic₁₀₃	—	5	1	no	Hall
25	C₁₀₃⋊C₃	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
26	C₃×C₅×Dic₅	—	103	1	no	maximal, Hall
27	C₂×C₁₀₃	C₃×C₅×D₅	1	1	yes	characteristic
28	C₂×C₃×C₅²	—	103	1	no	—
29	C₁₀₃	C₃×C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
30	C₅×Dic₅	—	103	1	no	Hall
31	C₃×C₅²	—	103	1	no	Hall
32	C₃×C₄×C₅	—	515	1	no	—
33	C₃×Dic₅	—	103	1	no	—
34	C₂×C₅²	D₁₀₃⋊C₃	1	1	yes	characteristic
35	C₂×C₃×C₅	—	103	1	no	—
36	C₂×C₃×C₅	—	103	1	no	—
37	C₂×C₃×C₅	—	206	2	no	—
38	C₅²	(C₁₀₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
39	C₄×C₅	—	515	1	no	—
40	Dic₅	—	103	1	no	—
41	C₃×C₅	—	103	1	no	—
42	C₃×C₅	—	103	1	no	—
43	C₃×C₅	—	206	2	no	—
44	C₃×C₄	—	515	1	no	Hall
45	C₂×C₅	—	2	2	no	—
46	C₂×C₅	C₅×D₁₀₃⋊C₃	1	1	yes	characteristic
47	C₂×C₅	C₅⋊(D₁₀₃⋊C₃)	1	1	yes	characteristic
48	C₂×C₃	—	103	1	no	—
49	C₅	—	2	2	no	—
50	C₅	C₅×(C₁₀₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
51	C₅	(C₁₀₃⋊C₃)⋊Dic₅	1	1	yes	characteristic, direct product factor
52	C₄	—	515	1	no	Sylow
53	C₃	—	103	1	no	Sylow
54	C₂	C₅×C₅⋊(D₁₀₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₅⋊(D₁₀₃⋊C₃)
commutator, hypocenter	C₅×C₁₀₃	C₃×C₄×C₅
Frattini	C₂	C₅×C₅⋊(D₁₀₃⋊C₃)
Fitting, socle	C₂×C₅²×C₁₀₃	C₂×C₃
prime radical	C₂×C₅²×C₁₀₃⋊C₃	C₂
cosocle	C₂×C₅×C₁₀₃	C₂×C₃×C₅
LCS	G ▷ C₅×C₁₀₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×Dic₅₁₅	C₃	semidirect
3. C₅²×C₁₀₃⋊C₃	C₄	semidirect
4. (C₁₀₃⋊C₃)⋊Dic₅	C₅	direct (N × H)
10. C₅²×C₁₀₃	C₃×C₄	semidirect
11. Dic₅₁₅	C₃×C₅	semidirect
14. C₅×C₁₀₃⋊C₃	Dic₅	semidirect
15. C₅×C₁₀₃⋊C₃	C₄×C₅	semidirect
22. C₅×C₁₀₃	C₃×Dic₅	semidirect
23. C₅×C₁₀₃	C₃×C₄×C₅	semidirect
25. C₁₀₃⋊C₃	C₅×Dic₅	semidirect
29. C₁₀₃	C₃×C₅×Dic₅	semidirect
38. C₅²	(C₁₀₃⋊C₃)⋊C₄	semidirect
50. C₅	C₅×(C₁₀₃⋊C₃)⋊C₄	semidirect
51. C₅	(C₁₀₃⋊C₃)⋊Dic₅	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×C₅²×C₁₀₃⋊C₃	2
C₅×Dic₅₁₅	3
(C₁₀₃⋊C₃)⋊Dic₅	5
C₅×(C₁₀₃⋊C₃)⋊C₄	5
C₃×C₅×Dic₅	103

Subgroups — C5×(C103⋊C3)⋊Dic5 #44525437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×(C₁₀₃⋊C₃)⋊Dic₅ #44525437