Subgroups — C₂×C₃²×D₁₃×C₇₉ #49149656

Order 36972.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₃×C₇₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₁₃×C₇₉	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₁₃×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₁₃×C₇₉	C₂×C₃	1	8	yes	direct product factor
6	C₂×C₃×C₁₃×C₇₉	C₂×C₃	1	4	yes	complemented
7	C₂×D₁₃×C₇₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₁₃×C₇₉	C₂²×C₃	1	4	yes	complemented
9	C₂²×C₃²×C₇₉	—	13	1	no	maximal, Hall
10	C₂×C₁₃×C₇₉	C₂×C₃²	1	1	yes	characteristic, complemented
11	D₁₃×C₇₉	C₂×C₃²	1	2	yes	direct product factor
12	C₂×C₃²×C₇₉	—	13	2	no	—
13	C₂×C₃²×C₇₉	D₁₃	1	1	yes	characteristic, direct product factor
14	C₁₃×C₇₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₃×C₇₉	—	13	4	no	—
16	C₃²×C₇₉	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₇₉	—	13	8	no	—
18	C₂×C₃×C₇₉	C₃×D₁₃	1	4	yes	direct product factor
19	C₂×C₃²×D₁₃	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₇₉	—	13	1	no	Hall
21	C₃×C₇₉	C₂×C₃×D₁₃	1	4	yes	direct product factor
22	C₂×C₃²×C₁₃	C₂×C₇₉	1	1	yes	characteristic, complemented
23	C₃²×D₁₃	C₂×C₇₉	1	2	yes	direct product factor
24	C₂×C₇₉	—	13	2	no	—
25	C₂×C₇₉	C₃²×D₁₃	1	1	yes	characteristic, direct product factor
26	C₂×C₃×D₁₃	C₃×C₇₉	1	4	yes	direct product factor
27	C₃²×C₁₃	C₂²×C₇₉	1	1	yes	characteristic, complemented, Hall
28	C₇₉	C₂×C₃²×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃×C₁₃	C₂×C₃×C₇₉	1	4	yes	complemented
30	C₃×D₁₃	C₂×C₃×C₇₉	1	8	yes	direct product factor
31	C₂×D₁₃	C₃²×C₇₉	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₃	C₂²×C₃×C₇₉	1	4	yes	complemented
33	C₂²×C₃²	—	13	1	no	Hall
34	C₂×C₁₃	C₂×C₃²×C₇₉	1	1	yes	characteristic, complemented
35	D₁₃	C₂×C₃²×C₇₉	1	2	yes	direct product factor
36	C₂×C₃²	—	13	2	no	—
37	C₂×C₃²	D₁₃×C₇₉	1	1	yes	characteristic, direct product factor
38	C₁₃	C₂²×C₃²×C₇₉	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	13	4	no	—
40	C₃²	C₂×D₁₃×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	13	8	no	—
42	C₂×C₃	C₃×D₁₃×C₇₉	1	4	yes	direct product factor
43	C₂²	—	13	1	no	Sylow
44	C₃	C₂×C₃×D₁₃×C₇₉	1	4	yes	direct product factor
45	C₂	—	13	2	no	—
46	C₂	C₃²×D₁₃×C₇₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₇₉	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₃²×C₇₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₇₉	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃²×C₇₉

Complements

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

N	H ≅ G/N	type
1. C₃²×D₁₃×C₇₉	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₇₉	C₂	semidirect
3. C₂×C₃×D₁₃×C₇₉	C₃	direct (N × H)
4. C₃²×C₁₃×C₇₉	C₂²	semidirect
5. C₃×D₁₃×C₇₉	C₂×C₃	direct (N × H)
6. C₂×C₃×C₁₃×C₇₉	C₂×C₃	semidirect
7. C₂×D₁₃×C₇₉	C₃²	direct (N × H)
8. C₃×C₁₃×C₇₉	C₂²×C₃	semidirect
10. C₂×C₁₃×C₇₉	C₂×C₃²	semidirect
11. D₁₃×C₇₉	C₂×C₃²	direct (N × H)
13. C₂×C₃²×C₇₉	D₁₃	direct (N × H)
14. C₁₃×C₇₉	C₂²×C₃²	semidirect
16. C₃²×C₇₉	C₂×D₁₃	direct (N × H)
18. C₂×C₃×C₇₉	C₃×D₁₃	direct (N × H)
19. C₂×C₃²×D₁₃	C₇₉	direct (N × H)
21. C₃×C₇₉	C₂×C₃×D₁₃	direct (N × H)
22. C₂×C₃²×C₁₃	C₂×C₇₉	semidirect
23. C₃²×D₁₃	C₂×C₇₉	direct (N × H)
25. C₂×C₇₉	C₃²×D₁₃	direct (N × H)
26. C₂×C₃×D₁₃	C₃×C₇₉	direct (N × H)
27. C₃²×C₁₃	C₂²×C₇₉	semidirect
28. C₇₉	C₂×C₃²×D₁₃	direct (N × H)
29. C₂×C₃×C₁₃	C₂×C₃×C₇₉	semidirect
30. C₃×D₁₃	C₂×C₃×C₇₉	direct (N × H)
31. C₂×D₁₃	C₃²×C₇₉	direct (N × H)
32. C₃×C₁₃	C₂²×C₃×C₇₉	semidirect
34. C₂×C₁₃	C₂×C₃²×C₇₉	semidirect
35. D₁₃	C₂×C₃²×C₇₉	direct (N × H)
37. C₂×C₃²	D₁₃×C₇₉	direct (N × H)
38. C₁₃	C₂²×C₃²×C₇₉	semidirect
40. C₃²	C₂×D₁₃×C₇₉	direct (N × H)
42. C₂×C₃	C₃×D₁₃×C₇₉	direct (N × H)
44. C₃	C₂×C₃×D₁₃×C₇₉	direct (N × H)
46. C₂	C₃²×D₁₃×C₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×D₁₃×C₇₉	2
C₂×C₃²×C₁₃×C₇₉	2
C₂×C₃×D₁₃×C₇₉	3
C₂²×C₃²×C₇₉	13
C₂×C₃²×D₁₃	79

Subgroups — C2×C32×D13×C79 #49149656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×D₁₃×C₇₉ #49149656