Subgroups — C₂×C₅×D₁₅₃₃ #44501469

Order 30660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₅₃₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₅₁₁	—	3	1	no	maximal, Hall
4	C₃×C₅×C₇×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₅₃₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₅₁₁	—	3	2	no	—
7	C₂×C₅×C₇×C₇₃	D₃	1	1	yes	characteristic, complemented
8	C₂×C₅×D₂₁₉	—	7	1	no	maximal, Hall
9	D₁₅₃₃	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₃×C₇×C₇₃	C₂×C₅	1	1	yes	characteristic, complemented
11	C₅×C₇×C₇₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₅×D₂₁₉	—	7	2	no	—
13	C₂×C₃×C₅×C₇₃	D₇	1	1	yes	characteristic, complemented
14	C₂×D₅₁₁	—	3	1	no	Hall
15	C₃×C₇×C₇₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×D₇₃	—	21	1	no	Hall
17	C₃×C₅×C₇₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇×C₇₃	C₅×D₃	1	1	yes	characteristic, complemented
19	D₅₁₁	—	3	2	no	—
20	C₂×D₂₁₉	—	7	1	no	Hall
21	C₂×C₅×C₇₃	D₂₁	1	1	yes	characteristic, complemented
22	C₅×D₇₃	—	21	2	no	—
23	C₇×C₇₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₇₃	C₅×D₇	1	1	yes	characteristic, complemented
25	D₂₁₉	—	7	2	no	—
26	C₂×C₅×D₂₁	—	73	1	no	maximal, Hall
27	C₅×C₇₃	C₂×D₂₁	1	1	yes	characteristic, complemented, Hall
28	C₂×D₇₃	—	21	1	no	Hall
29	C₃×C₇₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₅×C₇	D₇₃	1	1	yes	characteristic, complemented
31	C₅×D₂₁	—	73	2	no	—
32	C₂×C₇₃	C₅×D₂₁	1	1	yes	characteristic, complemented
33	D₇₃	—	21	2	no	—
34	C₂×C₅×D₇	—	219	1	no	Hall
35	C₃×C₅×C₇	C₂×D₇₃	1	1	yes	characteristic, complemented, Hall
36	C₂×D₂₁	—	73	1	no	Hall
37	C₇₃	C₂×C₅×D₂₁	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₅×C₇	D₂₁₉	1	1	yes	characteristic, complemented
39	C₅×D₇	—	219	2	no	—
40	C₂×C₅×D₃	—	511	1	no	Hall
41	C₂×C₃×C₇	C₅×D₇₃	1	1	yes	characteristic, complemented
42	D₂₁	—	73	2	no	—
43	C₅×C₇	C₂×D₂₁₉	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₅	D₅₁₁	1	1	yes	characteristic, complemented
45	C₅×D₃	—	511	2	no	—
46	C₂×D₇	—	219	1	no	Hall
47	C₃×C₇	C₂×C₅×D₇₃	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₅	—	1533	1	no	Hall
49	C₃×C₅	C₂×D₅₁₁	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇	C₅×D₂₁₉	1	1	yes	characteristic, complemented
51	D₇	—	219	2	no	—
52	C₂×D₃	—	511	1	no	Hall
53	C₂×C₅	—	1533	2	no	—
54	C₂×C₅	D₁₅₃₃	1	1	yes	characteristic, direct product factor
55	C₇	C₂×C₅×D₂₁₉	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	C₅×D₅₁₁	1	1	yes	characteristic, complemented
57	D₃	—	511	2	no	—
58	C₅	C₂×D₁₅₃₃	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	1533	1	no	Sylow
60	C₃	C₂×C₅×D₅₁₁	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	1533	2	no	—
62	C₂	C₅×D₁₅₃₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₅₃₃
commutator, cosocle, hypocenter	C₃×C₇×C₇₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₇₃	C₂
LCS	G ▷ C₃×C₇×C₇₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₅₃₃	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₇₃	C₂	semidirect
4. C₃×C₅×C₇×C₇₃	C₂²	semidirect
5. C₂×D₁₅₃₃	C₅	direct (N × H)
7. C₂×C₅×C₇×C₇₃	D₃	semidirect
9. D₁₅₃₃	C₂×C₅	direct (N × H)
10. C₂×C₃×C₇×C₇₃	C₂×C₅	semidirect
11. C₅×C₇×C₇₃	C₂×D₃	semidirect
13. C₂×C₃×C₅×C₇₃	D₇	semidirect
15. C₃×C₇×C₇₃	C₂²×C₅	semidirect
17. C₃×C₅×C₇₃	C₂×D₇	semidirect
18. C₂×C₇×C₇₃	C₅×D₃	semidirect
21. C₂×C₅×C₇₃	D₂₁	semidirect
23. C₇×C₇₃	C₂×C₅×D₃	semidirect
24. C₂×C₃×C₇₃	C₅×D₇	semidirect
27. C₅×C₇₃	C₂×D₂₁	semidirect
29. C₃×C₇₃	C₂×C₅×D₇	semidirect
30. C₂×C₃×C₅×C₇	D₇₃	semidirect
32. C₂×C₇₃	C₅×D₂₁	semidirect
35. C₃×C₅×C₇	C₂×D₇₃	semidirect
37. C₇₃	C₂×C₅×D₂₁	semidirect
38. C₂×C₅×C₇	D₂₁₉	semidirect
41. C₂×C₃×C₇	C₅×D₇₃	semidirect
43. C₅×C₇	C₂×D₂₁₉	semidirect
44. C₂×C₃×C₅	D₅₁₁	semidirect
47. C₃×C₇	C₂×C₅×D₇₃	semidirect
49. C₃×C₅	C₂×D₅₁₁	semidirect
50. C₂×C₇	C₅×D₂₁₉	semidirect
54. C₂×C₅	D₁₅₃₃	direct (N × H)
55. C₇	C₂×C₅×D₂₁₉	semidirect
56. C₂×C₃	C₅×D₅₁₁	semidirect
58. C₅	C₂×D₁₅₃₃	direct (N × H)
60. C₃	C₂×C₅×D₅₁₁	semidirect
62. C₂	C₅×D₁₅₃₃	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×D₁₅₃₃	2
C₂×C₃×C₅×C₇×C₇₃	2
C₂×C₅×D₅₁₁	3
C₂×D₁₅₃₃	5
C₂×C₅×D₂₁₉	7
C₂×C₅×D₂₁	73

Subgroups — C2×C5×D1533 #44501469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₁₅₃₃ #44501469