Subgroups — D₁₃×D₇₉⋊C₉ #49149404

Order 36972.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₇₉⋊C₉)⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₃×C₇₉⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×D₇₉⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₃×D₇₉	C₃	1	1	yes	maximal, characteristic
5	C₁₃×C₇₉⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₁₀₂₇	C₂×C₃	1	1	yes	characteristic
7	C₃×D₁₃×C₇₉	C₂×C₃	1	1	yes	characteristic
8	C₃×C₁₃×D₇₉	C₂×C₃	1	1	yes	characteristic
9	D₁₃×D₇₉	C₉	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₃×C₇₉	C₂²×C₃	1	1	yes	characteristic
11	C₂×D₇₉⋊C₉	—	13	1	no	maximal, Hall
12	D₁₀₂₇	C₂×C₉	1	1	yes	characteristic, complemented
13	C₁₃×D₇₉	C₂×C₉	1	1	yes	characteristic, complemented
14	D₁₃×C₇₉	C₂×C₉	1	1	yes	characteristic, complemented
15	C₂×C₇₉⋊C₉	—	13	1	no	—
16	D₇₉⋊C₉	—	13	1	no	—
17	D₇₉⋊C₉	D₁₃	1	1	yes	characteristic, direct product factor
18	C₁₃×C₇₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×D₇₉	—	13	1	no	—
20	C₇₉⋊C₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇₉	—	13	1	no	—
22	C₃×D₇₉	—	13	1	no	—
23	C₃×D₇₉	C₃×D₁₃	1	1	yes	characteristic
24	C₂×C₉×D₁₃	—	79	1	no	maximal, Hall
25	C₂×D₇₉	—	13	1	no	Hall
26	C₃×C₇₉	C₂×C₃×D₁₃	1	1	yes	characteristic
27	C₂×C₉×C₁₃	—	79	1	no	—
28	C₉×D₁₃	—	79	1	no	—
29	C₉×D₁₃	—	79	1	no	—
30	C₂×C₇₉	—	13	1	no	—
31	D₇₉	—	13	1	no	—
32	D₇₉	C₉×D₁₃	1	1	yes	characteristic, complemented
33	C₂×C₃×D₁₃	—	79	1	no	—
34	C₉×C₁₃	—	79	1	no	Hall
35	C₇₉	C₂×C₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₁₃	—	79	1	no	—
37	C₃×D₁₃	—	79	1	no	—
38	C₃×D₁₃	D₇₉⋊C₃	1	1	yes	characteristic
39	C₂×D₁₃	—	79	1	no	Hall
40	C₃×C₁₃	C₂×D₇₉⋊C₃	1	1	yes	characteristic
41	C₂²×C₉	—	1027	1	no	Hall
42	C₂×C₁₃	—	79	1	no	—
43	D₁₃	—	79	1	no	—
44	D₁₃	D₇₉⋊C₉	1	1	yes	characteristic, direct product factor
45	C₂×C₉	—	1027	1	no	—
46	C₂×C₉	—	1027	1	no	—
47	C₂×C₉	—	79	1	no	—
48	C₁₃	C₂×D₇₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₃	—	1027	1	no	—
50	C₉	—	79	1	no	Sylow
51	C₂×C₃	—	1027	1	no	—
52	C₂×C₃	—	13	1	no	—
53	C₂×C₃	—	79	1	no	—
54	C₂²	—	1027	1	no	Sylow
55	C₃	D₁₃×D₇₉⋊C₃	1	1	yes	characteristic
56	C₂	—	1027	1	no	—
57	C₂	—	13	1	no	—
58	C₂	—	79	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₁₃×D₇₉⋊C₃
commutator, hypocenter	C₁₃×C₇₉	C₂²×C₉
Fitting, socle, cosocle	C₃×C₁₃×C₇₉	C₂²×C₃
prime radical	C₃×D₁₃×D₇₉	C₃
LCS	G ▷ C₁₃×C₇₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. (C₇₉⋊C₉)⋊D₁₃	C₂	semidirect
2. D₁₃×C₇₉⋊C₉	C₂	semidirect
3. C₁₃×D₇₉⋊C₉	C₂	semidirect
5. C₁₃×C₇₉⋊C₉	C₂²	semidirect
9. D₁₃×D₇₉	C₉	semidirect
12. D₁₀₂₇	C₂×C₉	semidirect
13. C₁₃×D₇₉	C₂×C₉	semidirect
14. D₁₃×C₇₉	C₂×C₉	semidirect
17. D₇₉⋊C₉	D₁₃	direct (N × H)
18. C₁₃×C₇₉	C₂²×C₉	semidirect
20. C₇₉⋊C₉	C₂×D₁₃	semidirect
32. D₇₉	C₉×D₁₃	semidirect
35. C₇₉	C₂×C₉×D₁₃	semidirect
44. D₁₃	D₇₉⋊C₉	direct (N × H)
48. C₁₃	C₂×D₇₉⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
(C₇₉⋊C₉)⋊D₁₃	2
D₁₃×C₇₉⋊C₉	2
C₁₃×D₇₉⋊C₉	2
C₃×D₁₃×D₇₉	3
C₂×D₇₉⋊C₉	13
C₂×C₉×D₁₃	79

Subgroups — D13×D79⋊C9 #49149404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×D₇₉⋊C₉ #49149404