Subgroups — D₇₉×C₃⋊D₃₉ #49149641

Order 36972.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₃₀₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₉×D₇₉	—	3	4	no	maximal
5	C₃²×C₁₃×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃₀₈₁	—	3	4	no	—
7	D₃₉×C₇₉	—	3	4	no	—
8	C₃×C₁₃×D₇₉	D₃	1	4	yes	complemented
9	D₁₃×D₇₉	—	9	1	no	Hall
10	C₃×C₁₃×C₇₉	C₂×D₃	1	4	yes	complemented
11	C₃⋊D₃×D₇₉	—	13	1	no	maximal, Hall
12	D₁₀₂₇	—	9	1	no	—
13	C₁₃×D₇₉	C₃⋊D₃	1	1	yes	characteristic, complemented
14	D₁₃×C₇₉	—	9	1	no	—
15	C₃⋊D₂₃₇	—	13	1	no	—
16	C₃⋊D₃×C₇₉	—	13	1	no	—
17	C₃²×D₇₉	D₁₃	1	1	yes	characteristic, complemented
18	C₁₃×C₇₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
19	D₃×D₇₉	—	39	4	no	—
20	C₃²×C₇₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
21	D₂₃₇	—	39	4	no	—
22	C₃×D₇₉	D₃₉	1	4	yes	complemented
23	D₃×C₇₉	—	39	4	no	—
24	C₂×C₃⋊D₃₉	—	79	1	no	maximal, Hall
25	C₂×D₇₉	—	117	1	no	Hall
26	C₃×C₇₉	C₂×D₃₉	1	4	yes	complemented
27	C₂×C₃²×C₁₃	—	79	1	no	—
28	C₃⋊D₃₉	—	79	1	no	—
29	C₃⋊D₃₉	D₇₉	1	1	yes	characteristic, direct product factor
30	C₂×C₇₉	—	117	1	no	—
31	D₇₉	—	117	1	no	—
32	D₇₉	C₃⋊D₃₉	1	1	yes	characteristic, direct product factor
33	C₂×D₃₉	—	237	4	no	—
34	C₃²×C₁₃	C₂×D₇₉	1	1	yes	characteristic, complemented, Hall
35	C₇₉	C₂×C₃⋊D₃₉	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₁₃	—	79	4	no	—
37	D₃₉	—	3	4	no	—
38	D₃₉	—	237	4	no	—
39	C₂×D₁₃	—	711	1	no	Hall
40	C₃×C₁₃	D₃×D₇₉	1	4	yes	complemented
41	C₂×C₃⋊D₃	—	1027	1	no	Hall
42	C₂×C₁₃	—	79	1	no	—
43	D₁₃	—	9	1	no	—
44	D₁₃	—	711	1	no	—
45	C₂×C₃²	—	79	1	no	—
46	C₃⋊D₃	—	1027	1	no	—
47	C₃⋊D₃	—	13	1	no	—
48	C₁₃	C₃⋊D₃×D₇₉	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₃	—	3081	4	no	—
50	C₃²	D₁₃×D₇₉	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	79	4	no	—
52	D₃	—	3081	4	no	—
53	D₃	—	39	4	no	—
54	C₂²	—	9243	1	no	Sylow
55	C₃	D₃₉×D₇₉	1	4	yes	complemented
56	C₂	—	9243	1	no	—
57	C₂	—	79	1	no	—
58	C₂	—	117	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×D₇₉	C₂	semidirect
2. C₇₉×C₃⋊D₃₉	C₂	semidirect
3. C₃⋊D₃₀₈₁	C₂	semidirect
5. C₃²×C₁₃×C₇₉	C₂²	semidirect
8. C₃×C₁₃×D₇₉	D₃	semidirect
10. C₃×C₁₃×C₇₉	C₂×D₃	semidirect
13. C₁₃×D₇₉	C₃⋊D₃	semidirect
17. C₃²×D₇₉	D₁₃	semidirect
18. C₁₃×C₇₉	C₂×C₃⋊D₃	semidirect
20. C₃²×C₇₉	C₂×D₁₃	semidirect
22. C₃×D₇₉	D₃₉	semidirect
26. C₃×C₇₉	C₂×D₃₉	semidirect
29. C₃⋊D₃₉	D₇₉	direct (N × H)
32. D₇₉	C₃⋊D₃₉	direct (N × H)
34. C₃²×C₁₃	C₂×D₇₉	semidirect
35. C₇₉	C₂×C₃⋊D₃₉	semidirect
40. C₃×C₁₃	D₃×D₇₉	semidirect
48. C₁₃	C₃⋊D₃×D₇₉	semidirect
50. C₃²	D₁₃×D₇₉	semidirect
55. C₃	D₃₉×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×D₇₉	2
C₇₉×C₃⋊D₃₉	2
C₃⋊D₃₀₈₁	2
D₃₉×D₇₉	3
C₃⋊D₃×D₇₉	13
C₂×C₃⋊D₃₉	79

Subgroups — D79×C3⋊D39 #49149641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₉×C₃⋊D₃₉ #49149641