Subgroups — C₂×C₅×D₁₅×C₁₀₃ #44525555

Order 30900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₅×C₁₀₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₅×C₁₀₃	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₅×C₁₀₃	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅×D₃×C₁₀₃	—	5	1	no	maximal
7	C₅×D₅×C₁₀₃	—	3	2	no	—
8	C₂×C₅²×C₁₀₃	D₃	1	1	yes	characteristic, complemented
9	D₁₅×C₁₀₃	C₂×C₅	1	2	yes	direct product factor
10	C₅×D₃×C₁₀₃	—	5	2	no	—
11	C₂×C₃×C₅×C₁₀₃	—	2	2	no	—
12	C₂×C₃×C₅×C₁₀₃	D₅	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅×C₁₀₃	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅²×C₁₀₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₅×C₁₀₃	—	3	1	no	—
16	C₂²×C₅×C₁₀₃	—	15	1	no	—
17	C₃×C₅×C₁₀₃	—	2	2	no	—
18	C₃×C₅×C₁₀₃	C₂×D₅	1	1	yes	characteristic, complemented
19	C₃×C₅×C₁₀₃	C₂²×C₅	1	1	yes	characteristic, complemented
20	C₂×D₃×C₁₀₃	—	5	1	no	Hall
21	C₂×C₅×C₁₀₃	—	2	2	no	—
22	C₂×C₅×C₁₀₃	—	15	2	no	—
23	C₂×C₅×C₁₀₃	C₅×D₃	1	1	yes	characteristic, complemented
24	C₂×C₅×C₁₀₃	D₁₅	1	1	yes	characteristic, direct product factor
25	D₅×C₁₀₃	—	3	2	no	—
26	C₂×C₃×C₁₀₃	C₅×D₅	1	1	yes	characteristic, complemented
27	D₃×C₁₀₃	—	5	2	no	—
28	C₅×C₁₀₃	—	2	2	no	—
29	C₅×C₁₀₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
30	C₅×C₁₀₃	C₂×D₁₅	1	1	yes	characteristic, direct product factor
31	C₂²×C₁₀₃	—	15	1	no	Hall
32	C₃×C₁₀₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×D₁₅	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₁₀₃	—	15	2	no	—
35	C₂×C₁₀₃	C₅×D₁₅	1	1	yes	characteristic, direct product factor
36	C₂×C₃×C₅²	C₂×C₁₀₃	1	1	yes	characteristic, complemented
37	C₅×D₁₅	C₂×C₁₀₃	1	2	yes	direct product factor
38	C₁₀₃	C₂×C₅×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₅×D₅	—	3	1	no	Hall
40	C₃×C₅²	C₂²×C₁₀₃	1	1	yes	characteristic, complemented, Hall
41	C₂×D₁₅	C₅×C₁₀₃	1	1	yes	characteristic, direct product factor
42	C₂×C₅×D₃	—	5	1	no	—
43	C₂×C₅²	D₃×C₁₀₃	1	1	yes	characteristic, complemented
44	C₅×D₅	—	3	2	no	—
45	C₂×C₃×C₅	—	2	2	no	—
46	C₂×C₃×C₅	D₅×C₁₀₃	1	1	yes	characteristic, complemented
47	C₂×C₃×C₅	C₂×C₅×C₁₀₃	1	1	yes	characteristic, complemented
48	D₁₅	C₂×C₅×C₁₀₃	1	2	yes	direct product factor
49	C₅×D₃	—	5	2	no	—
50	C₅²	C₂×D₃×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₅	—	15	1	no	—
52	C₂×D₅	—	3	1	no	—
53	C₃×C₅	—	2	2	no	—
54	C₃×C₅	C₂²×C₅×C₁₀₃	1	1	yes	characteristic, complemented
55	C₃×C₅	C₂×D₅×C₁₀₃	1	1	yes	characteristic, complemented
56	C₂×D₃	—	5	1	no	Hall
57	C₂×C₅	—	2	2	no	—
58	C₂×C₅	—	15	2	no	—
59	C₂×C₅	C₅×D₃×C₁₀₃	1	1	yes	characteristic, complemented
60	C₂×C₅	D₁₅×C₁₀₃	1	1	yes	characteristic, direct product factor
61	D₅	—	3	2	no	—
62	C₂×C₃	C₅×D₅×C₁₀₃	1	1	yes	characteristic, complemented
63	D₃	—	5	2	no	—
64	C₅	—	2	2	no	—
65	C₅	C₂×C₅×D₃×C₁₀₃	1	1	yes	characteristic, complemented
66	C₅	C₂×D₁₅×C₁₀₃	1	1	yes	characteristic, direct product factor
67	C₂²	—	15	1	no	Sylow
68	C₃	C₂×C₅×D₅×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
69	C₂	—	15	2	no	—
70	C₂	C₅×D₁₅×C₁₀₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₀₃	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₅×C₁₀₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₀₃	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₅×C₁₀₃

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₅×C₁₀₃	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₁₀₃	C₂	semidirect
4. C₃×C₅²×C₁₀₃	C₂²	semidirect
5. C₂×D₁₅×C₁₀₃	C₅	direct (N × H)
8. C₂×C₅²×C₁₀₃	D₃	semidirect
9. D₁₅×C₁₀₃	C₂×C₅	direct (N × H)
12. C₂×C₃×C₅×C₁₀₃	D₅	semidirect
13. C₂×C₃×C₅×C₁₀₃	C₂×C₅	semidirect
14. C₅²×C₁₀₃	C₂×D₃	semidirect
18. C₃×C₅×C₁₀₃	C₂×D₅	semidirect
19. C₃×C₅×C₁₀₃	C₂²×C₅	semidirect
23. C₂×C₅×C₁₀₃	C₅×D₃	semidirect
24. C₂×C₅×C₁₀₃	D₁₅	direct (N × H)
26. C₂×C₃×C₁₀₃	C₅×D₅	semidirect
29. C₅×C₁₀₃	C₂×C₅×D₃	semidirect
30. C₅×C₁₀₃	C₂×D₁₅	direct (N × H)
32. C₃×C₁₀₃	C₂×C₅×D₅	semidirect
33. C₂×C₅×D₁₅	C₁₀₃	direct (N × H)
35. C₂×C₁₀₃	C₅×D₁₅	direct (N × H)
36. C₂×C₃×C₅²	C₂×C₁₀₃	semidirect
37. C₅×D₁₅	C₂×C₁₀₃	direct (N × H)
38. C₁₀₃	C₂×C₅×D₁₅	direct (N × H)
40. C₃×C₅²	C₂²×C₁₀₃	semidirect
41. C₂×D₁₅	C₅×C₁₀₃	direct (N × H)
43. C₂×C₅²	D₃×C₁₀₃	semidirect
46. C₂×C₃×C₅	D₅×C₁₀₃	semidirect
47. C₂×C₃×C₅	C₂×C₅×C₁₀₃	semidirect
48. D₁₅	C₂×C₅×C₁₀₃	direct (N × H)
50. C₅²	C₂×D₃×C₁₀₃	semidirect
54. C₃×C₅	C₂²×C₅×C₁₀₃	semidirect
55. C₃×C₅	C₂×D₅×C₁₀₃	semidirect
59. C₂×C₅	C₅×D₃×C₁₀₃	semidirect
60. C₂×C₅	D₁₅×C₁₀₃	direct (N × H)
62. C₂×C₃	C₅×D₅×C₁₀₃	semidirect
65. C₅	C₂×C₅×D₃×C₁₀₃	semidirect
66. C₅	C₂×D₁₅×C₁₀₃	direct (N × H)
68. C₃	C₂×C₅×D₅×C₁₀₃	semidirect
70. C₂	C₅×D₁₅×C₁₀₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₁₅×C₁₀₃	2
C₂×C₃×C₅²×C₁₀₃	2
C₂×C₅×D₅×C₁₀₃	3
C₂×D₁₅×C₁₀₃	5
C₂×C₅×D₃×C₁₀₃	5
C₂×C₅×D₁₅	103

Subgroups — C2×C5×D15×C103 #44525555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₁₅×C₁₀₃ #44525555