Subgroups — C₂×C₃×D₂₅₅₅ #44501465

Order 30660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₅₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₅₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₅₁₁	—	5	1	no	maximal, Hall
6	D₂₅₅₅	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₅×C₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₃×D₃₆₅	—	7	1	no	maximal, Hall
9	C₃×D₅₁₁	—	5	2	no	—
10	C₂×C₃×C₇×C₇₃	D₅	1	1	yes	characteristic, complemented
11	C₅×C₇×C₇₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₃×D₃₆₅	—	7	2	no	—
13	C₂×C₃×C₅×C₇₃	D₇	1	1	yes	characteristic, complemented
14	C₂×D₅₁₁	—	5	1	no	Hall
15	C₃×C₇×C₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×D₃₆₅	—	7	1	no	Hall
17	C₃×C₅×C₇₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇×C₇₃	C₃×D₅	1	1	yes	characteristic, complemented
19	D₅₁₁	—	5	2	no	—
20	C₂×C₃×D₇₃	—	35	1	no	Hall
21	C₂×C₅×C₇₃	C₃×D₇	1	1	yes	characteristic, complemented
22	D₃₆₅	—	7	2	no	—
23	C₇×C₇₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₇₃	D₃₅	1	1	yes	characteristic, complemented
25	C₃×D₇₃	—	35	2	no	—
26	C₂×C₃×D₃₅	—	73	1	no	maximal, Hall
27	C₅×C₇₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
28	C₂×D₇₃	—	35	1	no	Hall
29	C₃×C₇₃	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₅×C₇	D₇₃	1	1	yes	characteristic, complemented
31	C₃×D₃₅	—	73	2	no	—
32	C₂×C₇₃	C₃×D₃₅	1	1	yes	characteristic, complemented
33	D₇₃	—	35	2	no	—
34	C₂×D₃₅	—	73	1	no	Hall
35	C₃×C₅×C₇	C₂×D₇₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×D₇	—	365	1	no	Hall
37	C₇₃	C₂×C₃×D₃₅	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₅×C₇	C₃×D₇₃	1	1	yes	characteristic, complemented
39	D₃₅	—	73	2	no	—
40	C₂×C₃×D₅	—	511	1	no	Hall
41	C₂×C₃×C₇	D₃₆₅	1	1	yes	characteristic, complemented
42	C₃×D₇	—	365	2	no	—
43	C₅×C₇	C₂×C₃×D₇₃	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₅	D₅₁₁	1	1	yes	characteristic, complemented
45	C₃×D₅	—	511	2	no	—
46	C₂×D₇	—	365	1	no	Hall
47	C₃×C₇	C₂×D₃₆₅	1	1	yes	characteristic, complemented, Hall
48	C₂×D₅	—	511	1	no	Hall
49	C₃×C₅	C₂×D₅₁₁	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇	C₃×D₃₆₅	1	1	yes	characteristic, complemented
51	D₇	—	365	2	no	—
52	C₂²×C₃	—	2555	1	no	Hall
53	C₂×C₅	C₃×D₅₁₁	1	1	yes	characteristic, complemented
54	D₅	—	511	2	no	—
55	C₇	C₂×C₃×D₃₆₅	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	2555	2	no	—
57	C₂×C₃	D₂₅₅₅	1	1	yes	characteristic, direct product factor
58	C₅	C₂×C₃×D₅₁₁	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	2555	1	no	Sylow
60	C₃	C₂×D₂₅₅₅	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	2555	2	no	—
62	C₂	C₃×D₂₅₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₅₅₅
commutator, cosocle, hypocenter	C₅×C₇×C₇₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₇₃	C₂
LCS	G ▷ C₅×C₇×C₇₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₅₅₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₇₃	C₂	semidirect
3. C₂×D₂₅₅₅	C₃	direct (N × H)
4. C₃×C₅×C₇×C₇₃	C₂²	semidirect
6. D₂₅₅₅	C₂×C₃	direct (N × H)
7. C₂×C₅×C₇×C₇₃	C₂×C₃	semidirect
10. C₂×C₃×C₇×C₇₃	D₅	semidirect
11. C₅×C₇×C₇₃	C₂²×C₃	semidirect
13. C₂×C₃×C₅×C₇₃	D₇	semidirect
15. C₃×C₇×C₇₃	C₂×D₅	semidirect
17. C₃×C₅×C₇₃	C₂×D₇	semidirect
18. C₂×C₇×C₇₃	C₃×D₅	semidirect
21. C₂×C₅×C₇₃	C₃×D₇	semidirect
23. C₇×C₇₃	C₂×C₃×D₅	semidirect
24. C₂×C₃×C₇₃	D₃₅	semidirect
27. C₅×C₇₃	C₂×C₃×D₇	semidirect
29. C₃×C₇₃	C₂×D₃₅	semidirect
30. C₂×C₃×C₅×C₇	D₇₃	semidirect
32. C₂×C₇₃	C₃×D₃₅	semidirect
35. C₃×C₅×C₇	C₂×D₇₃	semidirect
37. C₇₃	C₂×C₃×D₃₅	semidirect
38. C₂×C₅×C₇	C₃×D₇₃	semidirect
41. C₂×C₃×C₇	D₃₆₅	semidirect
43. C₅×C₇	C₂×C₃×D₇₃	semidirect
44. C₂×C₃×C₅	D₅₁₁	semidirect
47. C₃×C₇	C₂×D₃₆₅	semidirect
49. C₃×C₅	C₂×D₅₁₁	semidirect
50. C₂×C₇	C₃×D₃₆₅	semidirect
53. C₂×C₅	C₃×D₅₁₁	semidirect
55. C₇	C₂×C₃×D₃₆₅	semidirect
57. C₂×C₃	D₂₅₅₅	direct (N × H)
58. C₅	C₂×C₃×D₅₁₁	semidirect
60. C₃	C₂×D₂₅₅₅	direct (N × H)
62. C₂	C₃×D₂₅₅₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₂₅₅₅	2
C₂×C₃×C₅×C₇×C₇₃	2
C₂×D₂₅₅₅	3
C₂×C₃×D₅₁₁	5
C₂×C₃×D₃₆₅	7
C₂×C₃×D₃₅	73

Subgroups — C2×C3×D2555 #44501465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₂₅₅₅ #44501465