Subgroups — C₄×(C₇₉⋊C₉)⋊C₁₃ #49149359

Order 36972.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×(C₇₉⋊C₉)⋊C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₇₉⋊C₁₃	C₃	1	1	yes	maximal, characteristic
3	(C₇₉⋊C₉)⋊C₁₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇₉⋊C₁₃	C₂×C₃	1	1	yes	characteristic
5	C₄×C₇₉⋊C₁₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇₉⋊C₁₃	C₃×C₄	1	1	yes	characteristic
7	C₄×C₇₉⋊C₉	C₁₃	1	1	yes	maximal, characteristic, complemented, Hall
8	C₂×C₇₉⋊C₁₃	C₂×C₉	1	1	yes	characteristic
9	C₂×C₇₉⋊C₉	C₂×C₁₃	1	1	yes	characteristic
10	C₇₉⋊C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₄×C₇₉	C₃×C₁₃	1	1	yes	characteristic
12	C₇₉⋊C₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₇₉	C₂×C₃×C₁₃	1	1	yes	characteristic
14	C₄×C₉×C₁₃	—	79	1	no	maximal, Hall
15	C₄×C₇₉	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇₉	C₃×C₄×C₁₃	1	1	yes	characteristic
17	C₂×C₉×C₁₃	—	79	1	no	—
18	C₂×C₇₉	C₂×C₉×C₁₃	1	1	yes	characteristic
19	C₃×C₄×C₁₃	—	79	1	no	—
20	C₉×C₁₃	—	79	1	no	Hall
21	C₇₉	C₄×C₉×C₁₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×C₁₃	—	79	1	no	—
23	C₄×C₁₃	—	79	1	no	Hall
24	C₃×C₁₃	—	79	1	no	—
25	C₄×C₉	—	79	1	no	Hall
26	C₂×C₁₃	—	79	1	no	—
27	C₂×C₉	—	79	1	no	—
28	C₁₃	—	79	1	no	Sylow
29	C₃×C₄	(C₇₉⋊C₃)⋊C₁₃	1	1	yes	characteristic
30	C₉	—	79	1	no	Sylow
31	C₂×C₃	C₂×(C₇₉⋊C₃)⋊C₁₃	1	1	yes	characteristic
32	C₄	(C₇₉⋊C₉)⋊C₁₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₄×(C₇₉⋊C₃)⋊C₁₃	1	1	yes	characteristic
34	C₂	C₂×(C₇₉⋊C₉)⋊C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	(C₇₉⋊C₃)⋊C₁₃
commutator, hypocenter	C₇₉	C₄×C₉×C₁₃
Frattini	C₂×C₃	C₂×(C₇₉⋊C₃)⋊C₁₃
Fitting	C₃×C₄×C₇₉	C₃×C₁₃
socle, cosocle	C₂×C₃×C₇₉	C₂×C₃×C₁₃
prime radical	C₂×C₃×C₇₉⋊C₁₃	C₂×C₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
3. (C₇₉⋊C₉)⋊C₁₃	C₄	direct (N × H)
5. C₄×C₇₉⋊C₁₃	C₉	semidirect
7. C₄×C₇₉⋊C₉	C₁₃	semidirect
10. C₇₉⋊C₁₃	C₄×C₉	semidirect
12. C₇₉⋊C₉	C₄×C₁₃	semidirect
15. C₄×C₇₉	C₉×C₁₃	semidirect
21. C₇₉	C₄×C₉×C₁₃	semidirect
32. C₄	(C₇₉⋊C₉)⋊C₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×(C₇₉⋊C₉)⋊C₁₃	2
C₃×C₄×C₇₉⋊C₁₃	3
C₄×C₇₉⋊C₉	13
C₄×C₉×C₁₃	79

Subgroups — C4×(C79⋊C9)⋊C13 #49149359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×(C₇₉⋊C₉)⋊C₁₃ #49149359