Subgroups — C₃×C₅²×D₇₉⋊C₃ #48001237

Order 35550.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₇₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅²×D₇₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅²×D₇₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₅×D₇₉⋊C₃	C₅	1	6	yes	maximal, direct product factor
5	C₅²×C₇₉⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₃×C₅²×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅²×D₇₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅×C₇₉⋊C₃	C₂×C₅	1	6	yes	complemented
9	C₅×D₇₉⋊C₃	C₃×C₅	1	18	yes	direct product factor
10	C₃×C₅×D₇₉	C₃×C₅	1	6	yes	complemented
11	C₅²×C₇₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×D₇₉⋊C₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₇₉	C₂×C₃×C₅	1	6	yes	complemented
14	C₅×C₇₉⋊C₃	C₂×C₃×C₅	1	18	yes	complemented
15	C₅×D₇₉	C₃²×C₅	1	6	yes	complemented
16	C₃×C₇₉⋊C₃	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
17	C₃×D₇₉	C₃×C₅²	1	1	yes	characteristic, complemented
18	D₇₉⋊C₃	C₃×C₅²	1	3	yes	direct product factor
19	C₂×C₃²×C₅²	—	79	1	no	maximal, Hall
20	C₅×C₇₉	C₂×C₃²×C₅	1	6	yes	complemented
21	C₃×C₇₉	C₂×C₃×C₅²	1	1	yes	characteristic, complemented
22	C₇₉⋊C₃	C₂×C₃×C₅²	1	3	yes	complemented
23	C₃²×C₅²	—	79	1	no	Hall
24	D₇₉	C₃²×C₅²	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₅²	—	79	3	no	—
26	C₂×C₃×C₅²	—	79	1	no	—
27	C₂×C₃²×C₅	—	79	6	no	—
28	C₇₉	C₂×C₃²×C₅²	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₅²	—	79	3	no	—
30	C₃×C₅²	D₇₉⋊C₃	1	1	yes	characteristic, direct product factor
31	C₂×C₅²	—	79	1	no	Hall
32	C₃²×C₅	—	79	6	no	—
33	C₂×C₃×C₅	—	79	18	no	—
34	C₂×C₃×C₅	—	79	6	no	—
35	C₅²	C₃×D₇₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃²	—	79	1	no	Hall
37	C₃×C₅	—	79	18	no	—
38	C₃×C₅	C₅×D₇₉⋊C₃	1	6	yes	direct product factor
39	C₂×C₅	—	79	6	no	—
40	C₃²	—	79	1	no	Sylow
41	C₂×C₃	—	79	3	no	—
42	C₂×C₃	—	79	1	no	—
43	C₅	C₃×C₅×D₇₉⋊C₃	1	6	yes	direct product factor
44	C₃	—	79	3	no	—
45	C₃	C₅²×D₇₉⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂	—	79	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅²	D₇₉⋊C₃
commutator, cosocle, hypocenter	C₇₉	C₂×C₃²×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇₉	C₂×C₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₃×C₅²

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₇₉⋊C₃	C₂	semidirect
2. C₃×C₅²×D₇₉	C₃	semidirect
3. C₅²×D₇₉⋊C₃	C₃	direct (N × H)
4. C₃×C₅×D₇₉⋊C₃	C₅	direct (N × H)
5. C₅²×C₇₉⋊C₃	C₂×C₃	semidirect
6. C₃×C₅²×C₇₉	C₂×C₃	semidirect
7. C₅²×D₇₉	C₃²	semidirect
8. C₃×C₅×C₇₉⋊C₃	C₂×C₅	semidirect
9. C₅×D₇₉⋊C₃	C₃×C₅	direct (N × H)
10. C₃×C₅×D₇₉	C₃×C₅	semidirect
11. C₅²×C₇₉	C₂×C₃²	semidirect
12. C₃×D₇₉⋊C₃	C₅²	direct (N × H)
13. C₃×C₅×C₇₉	C₂×C₃×C₅	semidirect
14. C₅×C₇₉⋊C₃	C₂×C₃×C₅	semidirect
15. C₅×D₇₉	C₃²×C₅	semidirect
16. C₃×C₇₉⋊C₃	C₂×C₅²	semidirect
17. C₃×D₇₉	C₃×C₅²	semidirect
18. D₇₉⋊C₃	C₃×C₅²	direct (N × H)
20. C₅×C₇₉	C₂×C₃²×C₅	semidirect
21. C₃×C₇₉	C₂×C₃×C₅²	semidirect
22. C₇₉⋊C₃	C₂×C₃×C₅²	semidirect
24. D₇₉	C₃²×C₅²	semidirect
28. C₇₉	C₂×C₃²×C₅²	semidirect
30. C₃×C₅²	D₇₉⋊C₃	direct (N × H)
35. C₅²	C₃×D₇₉⋊C₃	direct (N × H)
38. C₃×C₅	C₅×D₇₉⋊C₃	direct (N × H)
43. C₅	C₃×C₅×D₇₉⋊C₃	direct (N × H)
45. C₃	C₅²×D₇₉⋊C₃	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×C₅²×C₇₉⋊C₃	2
C₃×C₅²×D₇₉	3
C₅²×D₇₉⋊C₃	3
C₃×C₅×D₇₉⋊C₃	5
C₂×C₃²×C₅²	79

Subgroups — C3×C52×D79⋊C3 #48001237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅²×D₇₉⋊C₃ #48001237