Subgroups — C₅×C₇×Dic₃×C₇₉ #45684382

Order 33180.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₇×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₇×C₇₉	—	3	1	no	maximal, Hall
3	C₃×C₅×C₇×C₇₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×Dic₃×C₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₇×C₇₉	D₃	1	1	yes	characteristic
6	C₅×Dic₃×C₇₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₇×C₇₉	C₂×C₅	1	1	yes	characteristic
8	C₅×C₇×C₇₉	Dic₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₅×C₇₉	C₂×C₇	1	1	yes	characteristic
10	C₄×C₇×C₇₉	—	3	1	no	Hall
11	C₃×C₇×C₇₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₄×C₅×C₇₉	—	3	1	no	Hall
13	C₃×C₅×C₇₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×C₇₉	C₅×D₃	1	1	yes	characteristic
15	Dic₃×C₇₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₅×C₇₉	D₃×C₇	1	1	yes	characteristic
17	C₇×C₇₉	C₅×Dic₃	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₇₉	C₂×C₅×C₇	1	1	yes	characteristic
19	C₅×C₇×Dic₃	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₅×C₇₉	C₇×Dic₃	1	1	yes	characteristic, direct product factor, Hall
21	C₄×C₇₉	—	3	1	no	Hall
22	C₃×C₇₉	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₅×C₇	C₂×C₇₉	1	1	yes	characteristic
24	C₂×C₇₉	C₅×D₃×C₇	1	1	yes	characteristic
25	C₄×C₅×C₇	—	3	1	no	Hall
26	C₃×C₅×C₇	C₄×C₇₉	1	1	yes	characteristic, complemented, Hall
27	C₇×Dic₃	C₅×C₇₉	1	1	yes	characteristic, direct product factor, Hall
28	C₇₉	C₅×C₇×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₅×C₇	D₃×C₇₉	1	1	yes	characteristic
30	C₅×Dic₃	C₇×C₇₉	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃×C₇	C₂×C₅×C₇₉	1	1	yes	characteristic
32	C₅×C₇	Dic₃×C₇₉	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×C₅	C₂×C₇×C₇₉	1	1	yes	characteristic
34	C₄×C₇	—	3	1	no	Hall
35	C₃×C₇	C₄×C₅×C₇₉	1	1	yes	characteristic, complemented, Hall
36	C₄×C₅	—	3	1	no	Hall
37	C₃×C₅	C₄×C₇×C₇₉	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇	C₅×D₃×C₇₉	1	1	yes	characteristic
39	Dic₃	C₅×C₇×C₇₉	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₅	D₃×C₇×C₇₉	1	1	yes	characteristic
41	C₇	C₅×Dic₃×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃	C₂×C₅×C₇×C₇₉	1	1	yes	characteristic
43	C₅	C₇×Dic₃×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	3	1	no	Sylow
45	C₃	C₄×C₅×C₇×C₇₉	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₅×D₃×C₇×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₇₉	D₃
commutator, hypocenter	C₃	C₄×C₅×C₇×C₇₉
Frattini	C₂	C₅×D₃×C₇×C₇₉
Fitting, socle, prime radical	C₂×C₃×C₅×C₇×C₇₉	C₂
cosocle	C₂×C₃	C₂×C₅×C₇×C₇₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₇×C₇₉

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₇×C₇₉	C₄	semidirect
4. C₇×Dic₃×C₇₉	C₅	direct (N × H)
6. C₅×Dic₃×C₇₉	C₇	direct (N × H)
8. C₅×C₇×C₇₉	Dic₃	direct (N × H)
11. C₃×C₇×C₇₉	C₄×C₅	semidirect
13. C₃×C₅×C₇₉	C₄×C₇	semidirect
15. Dic₃×C₇₉	C₅×C₇	direct (N × H)
17. C₇×C₇₉	C₅×Dic₃	direct (N × H)
19. C₅×C₇×Dic₃	C₇₉	direct (N × H)
20. C₅×C₇₉	C₇×Dic₃	direct (N × H)
22. C₃×C₇₉	C₄×C₅×C₇	semidirect
26. C₃×C₅×C₇	C₄×C₇₉	semidirect
27. C₇×Dic₃	C₅×C₇₉	direct (N × H)
28. C₇₉	C₅×C₇×Dic₃	direct (N × H)
30. C₅×Dic₃	C₇×C₇₉	direct (N × H)
32. C₅×C₇	Dic₃×C₇₉	direct (N × H)
35. C₃×C₇	C₄×C₅×C₇₉	semidirect
37. C₃×C₅	C₄×C₇×C₇₉	semidirect
39. Dic₃	C₅×C₇×C₇₉	direct (N × H)
41. C₇	C₅×Dic₃×C₇₉	direct (N × H)
43. C₅	C₇×Dic₃×C₇₉	direct (N × H)
45. C₃	C₄×C₅×C₇×C₇₉	semidirect

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×C₇₉	2
C₄×C₅×C₇×C₇₉	3
C₇×Dic₃×C₇₉	5
C₅×Dic₃×C₇₉	7
C₅×C₇×Dic₃	79

Subgroups — C5×C7×Dic3×C79 #45684382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×Dic₃×C₇₉ #45684382