Subgroups — C₂×C₃₁⋊C₃×D₇₉ #44440511

Order 29388.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁⋊C₃×D₇₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇₉×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×D₇₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇₉×C₃₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₁×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃₁×D₇₉	C₂×C₃	1	2	yes	complemented
7	C₃₁×C₇₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₇₉	—	31	1	no	maximal, Hall
9	C₂×C₃×C₇₉	—	31	1	no	—
10	C₃×D₇₉	—	31	2	no	—
11	C₂²×C₃₁⋊C₃	—	79	1	no	maximal, Hall
12	C₂×D₇₉	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₇₉	—	31	1	no	Hall
14	C₂×C₃₁⋊C₃	—	79	2	no	—
15	C₂×C₃₁⋊C₃	D₇₉	1	1	yes	characteristic, direct product factor
16	C₂×C₇₉	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
17	D₇₉	C₂×C₃₁⋊C₃	1	2	yes	direct product factor
18	C₂²×C₃₁	—	79	1	no	Hall
19	C₃₁⋊C₃	C₂×D₇₉	1	1	yes	characteristic, direct product factor, Hall
20	C₇₉	C₂²×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃₁	—	79	2	no	—
22	C₂×C₃₁	C₃×D₇₉	1	1	yes	characteristic, complemented
23	C₃₁	C₂×C₃×D₇₉	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	2449	1	no	Hall
25	C₂×C₃	—	31	1	no	—
26	C₂×C₃	—	2449	2	no	—
27	C₂²	—	79	1	no	Sylow
28	C₃	—	31	1	no	Sylow
29	C₂	—	79	2	no	—
30	C₂	C₃₁⋊C₃×D₇₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃₁⋊C₃×D₇₉
commutator, cosocle, hypocenter	C₃₁×C₇₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃₁×C₇₉	C₂×C₃
LCS	G ▷ C₃₁×C₇₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃₁⋊C₃×D₇₉	C₂	direct (N × H)
2. C₂×C₇₉×C₃₁⋊C₃	C₂	semidirect
3. C₂×C₃₁×D₇₉	C₃	semidirect
4. C₇₉×C₃₁⋊C₃	C₂²	semidirect
5. C₂×C₃₁×C₇₉	C₂×C₃	semidirect
6. C₃₁×D₇₉	C₂×C₃	semidirect
7. C₃₁×C₇₉	C₂²×C₃	semidirect
12. C₂×D₇₉	C₃₁⋊C₃	direct (N × H)
15. C₂×C₃₁⋊C₃	D₇₉	direct (N × H)
16. C₂×C₇₉	C₂×C₃₁⋊C₃	semidirect
17. D₇₉	C₂×C₃₁⋊C₃	direct (N × H)
19. C₃₁⋊C₃	C₂×D₇₉	direct (N × H)
20. C₇₉	C₂²×C₃₁⋊C₃	semidirect
22. C₂×C₃₁	C₃×D₇₉	semidirect
23. C₃₁	C₂×C₃×D₇₉	semidirect
30. C₂	C₃₁⋊C₃×D₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁⋊C₃×D₇₉	2
C₂×C₇₉×C₃₁⋊C₃	2
C₂×C₃₁×D₇₉	3
C₂×C₃×D₇₉	31
C₂²×C₃₁⋊C₃	79

Subgroups — C2×C31⋊C3×D79 #44440511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁⋊C₃×D₇₉ #44440511