Subgroups — C₃×Dic₂₅₅₅ #44501249

Order 30660.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₇×C₇₃	C₂	1	1	yes	maximal, characteristic
2	Dic₂₅₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₇×C₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×Dic₅₁₁	—	5	1	no	maximal, Hall
5	C₂×C₅×C₇×C₇₃	C₂×C₃	1	1	yes	characteristic
6	C₃×Dic₃₆₅	—	7	1	no	maximal, Hall
7	C₂×C₃×C₇×C₇₃	D₅	1	1	yes	characteristic
8	C₅×C₇×C₇₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₅×C₇₃	D₇	1	1	yes	characteristic
10	Dic₅₁₁	—	5	1	no	Hall
11	C₃×C₇×C₇₃	Dic₅	1	1	yes	characteristic, complemented, Hall
12	Dic₃₆₅	—	7	1	no	Hall
13	C₃×C₅×C₇₃	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×C₇₃	C₃×D₅	1	1	yes	characteristic
15	C₃×Dic₇₃	—	35	1	no	Hall
16	C₂×C₅×C₇₃	C₃×D₇	1	1	yes	characteristic
17	C₇×C₇₃	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₇₃	D₃₅	1	1	yes	characteristic
19	C₃×Dic₃₅	—	73	1	no	maximal, Hall
20	C₅×C₇₃	C₃×Dic₇	1	1	yes	characteristic, complemented, Hall
21	Dic₇₃	—	35	1	no	Hall
22	C₃×C₇₃	Dic₃₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₅×C₇	D₇₃	1	1	yes	characteristic
24	C₂×C₇₃	C₃×D₃₅	1	1	yes	characteristic
25	Dic₃₅	—	73	1	no	Hall
26	C₃×C₅×C₇	Dic₇₃	1	1	yes	characteristic, complemented, Hall
27	C₃×Dic₇	—	365	1	no	Hall
28	C₇₃	C₃×Dic₃₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅×C₇	C₃×D₇₃	1	1	yes	characteristic
30	C₃×Dic₅	—	511	1	no	Hall
31	C₂×C₃×C₇	D₃₆₅	1	1	yes	characteristic
32	C₅×C₇	C₃×Dic₇₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₅	D₅₁₁	1	1	yes	characteristic
34	Dic₇	—	365	1	no	Hall
35	C₃×C₇	Dic₃₆₅	1	1	yes	characteristic, complemented, Hall
36	Dic₅	—	511	1	no	Hall
37	C₃×C₅	Dic₅₁₁	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇	C₃×D₃₆₅	1	1	yes	characteristic
39	C₃×C₄	—	2555	1	no	Hall
40	C₂×C₅	C₃×D₅₁₁	1	1	yes	characteristic
41	C₇	C₃×Dic₃₆₅	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	D₂₅₅₅	1	1	yes	characteristic
43	C₅	C₃×Dic₅₁₁	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	2555	1	no	Sylow
45	C₃	Dic₂₅₅₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×D₂₅₅₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₅₅₅
commutator, hypocenter	C₅×C₇×C₇₃	C₃×C₄
Frattini	C₂	C₃×D₂₅₅₅
Fitting, socle, prime radical	C₂×C₃×C₅×C₇×C₇₃	C₂
cosocle	C₂×C₅×C₇×C₇₃	C₂×C₃
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
2. Dic₂₅₅₅	C₃	direct (N × H)
3. C₃×C₅×C₇×C₇₃	C₄	semidirect
8. C₅×C₇×C₇₃	C₃×C₄	semidirect
11. C₃×C₇×C₇₃	Dic₅	semidirect
13. C₃×C₅×C₇₃	Dic₇	semidirect
17. C₇×C₇₃	C₃×Dic₅	semidirect
20. C₅×C₇₃	C₃×Dic₇	semidirect
22. C₃×C₇₃	Dic₃₅	semidirect
26. C₃×C₅×C₇	Dic₇₃	semidirect
28. C₇₃	C₃×Dic₃₅	semidirect
32. C₅×C₇	C₃×Dic₇₃	semidirect
35. C₃×C₇	Dic₃₆₅	semidirect
37. C₃×C₅	Dic₅₁₁	semidirect
41. C₇	C₃×Dic₃₆₅	semidirect
43. C₅	C₃×Dic₅₁₁	semidirect
45. C₃	Dic₂₅₅₅	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×C₃×C₅×C₇×C₇₃	2
Dic₂₅₅₅	3
C₃×Dic₅₁₁	5
C₃×Dic₃₆₅	7
C₃×Dic₃₅	73

Subgroups — C3×Dic2555 #44501249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₂₅₅₅ #44501249