Subgroups — D₁₃×D₇₉⋊C₃ #27134530

Order 12324.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₇₉⋊C₃)⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₃×C₇₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×D₇₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₇₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₁₃×C₇₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₀₂₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₇₉	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₃×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₃×C₇₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₇₉⋊C₃	—	13	1	no	maximal, Hall
11	C₂×C₇₉⋊C₃	—	13	1	no	—
12	D₇₉⋊C₃	—	13	1	no	—
13	D₇₉⋊C₃	D₁₃	1	1	yes	characteristic, direct product factor
14	C₂×D₇₉	—	13	1	no	Hall
15	C₇₉⋊C₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇₉	—	13	1	no	—
17	D₇₉	—	13	1	no	—
18	D₇₉	C₃×D₁₃	1	1	yes	characteristic, complemented
19	C₂×C₃×D₁₃	—	79	1	no	maximal, Hall
20	C₇₉	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₁₃	—	79	1	no	—
22	C₃×D₁₃	—	79	1	no	—
23	C₃×D₁₃	—	79	1	no	—
24	C₂×D₁₃	—	79	1	no	Hall
25	C₃×C₁₃	—	79	1	no	Hall
26	C₂×C₁₃	—	79	1	no	—
27	D₁₃	—	79	1	no	—
28	D₁₃	D₇₉⋊C₃	1	1	yes	characteristic, direct product factor
29	C₁₃	C₂×D₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	1027	1	no	Hall
31	C₂×C₃	—	1027	1	no	—
32	C₂×C₃	—	1027	1	no	—
33	C₂×C₃	—	79	1	no	—
34	C₂²	—	1027	1	no	Sylow
35	C₃	—	79	1	no	Sylow
36	C₂	—	1027	1	no	—
37	C₂	—	13	1	no	—
38	C₂	—	79	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₇₉	C₂²×C₃
LCS	G ▷ C₁₃×C₇₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. (C₇₉⋊C₃)⋊D₁₃	C₂	semidirect
2. D₁₃×C₇₉⋊C₃	C₂	semidirect
3. C₁₃×D₇₉⋊C₃	C₂	semidirect
4. D₁₃×D₇₉	C₃	semidirect
5. C₁₃×C₇₉⋊C₃	C₂²	semidirect
6. D₁₀₂₇	C₂×C₃	semidirect
7. C₁₃×D₇₉	C₂×C₃	semidirect
8. D₁₃×C₇₉	C₂×C₃	semidirect
9. C₁₃×C₇₉	C₂²×C₃	semidirect
13. D₇₉⋊C₃	D₁₃	direct (N × H)
15. C₇₉⋊C₃	C₂×D₁₃	semidirect
18. D₇₉	C₃×D₁₃	semidirect
20. C₇₉	C₂×C₃×D₁₃	semidirect
28. D₁₃	D₇₉⋊C₃	direct (N × H)
29. C₁₃	C₂×D₇₉⋊C₃	semidirect

Maximal subgroups

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

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

Subgroups — D13×D79⋊C3 #27134530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×D₇₉⋊C₃ #27134530