Subgroups — C₂×C₅×D₁₁₃⋊C₇ #30629099

Order 15820.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₁₃⋊C₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₁₃⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₁₃⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁₃⋊C₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×D₁₁₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×C₁₁₃⋊C₇	C₂×C₅	1	1	yes	characteristic, complemented
7	D₁₁₃⋊C₇	C₂×C₅	1	2	yes	direct product factor
8	C₂×C₅×C₁₁₃	C₂×C₇	1	1	yes	characteristic, complemented
9	C₅×D₁₁₃	C₂×C₇	1	2	yes	complemented
10	C₁₁₃⋊C₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₁₁₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
12	C₂×D₁₁₃	C₅×C₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₁₃	C₂×C₅×C₇	1	1	yes	characteristic, complemented
14	D₁₁₃	C₂×C₅×C₇	1	2	yes	complemented
15	C₂²×C₅×C₇	—	113	1	no	maximal, Hall
16	C₁₁₃	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₅×C₇	—	113	2	no	—
18	C₂×C₅×C₇	—	113	1	no	—
19	C₅×C₇	—	113	1	no	Hall
20	C₂²×C₇	—	113	1	no	Hall
21	C₂²×C₅	—	791	1	no	Hall
22	C₂×C₇	—	113	2	no	—
23	C₂×C₇	—	113	1	no	—
24	C₂×C₅	—	791	2	no	—
25	C₂×C₅	D₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor
26	C₇	—	113	1	no	Sylow
27	C₅	C₂×D₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	791	1	no	Sylow
29	C₂	—	791	2	no	—
30	C₂	C₅×D₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₁₃⋊C₇
commutator, cosocle, hypocenter	C₁₁₃	C₂²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁₃	C₂×C₇
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₁₃⋊C₇	C₂	direct (N × H)
2. C₂×C₅×C₁₁₃⋊C₇	C₂	semidirect
3. C₅×C₁₁₃⋊C₇	C₂²	semidirect
4. C₂×D₁₁₃⋊C₇	C₅	direct (N × H)
5. C₂×C₅×D₁₁₃	C₇	semidirect
6. C₂×C₁₁₃⋊C₇	C₂×C₅	semidirect
7. D₁₁₃⋊C₇	C₂×C₅	direct (N × H)
8. C₂×C₅×C₁₁₃	C₂×C₇	semidirect
9. C₅×D₁₁₃	C₂×C₇	semidirect
10. C₁₁₃⋊C₇	C₂²×C₅	semidirect
11. C₅×C₁₁₃	C₂²×C₇	semidirect
12. C₂×D₁₁₃	C₅×C₇	semidirect
13. C₂×C₁₁₃	C₂×C₅×C₇	semidirect
14. D₁₁₃	C₂×C₅×C₇	semidirect
16. C₁₁₃	C₂²×C₅×C₇	semidirect
25. C₂×C₅	D₁₁₃⋊C₇	direct (N × H)
27. C₅	C₂×D₁₁₃⋊C₇	direct (N × H)
30. C₂	C₅×D₁₁₃⋊C₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₁₁₃⋊C₇	2
C₂×C₅×C₁₁₃⋊C₇	2
C₂×D₁₁₃⋊C₇	5
C₂×C₅×D₁₁₃	7
C₂²×C₅×C₇	113

Subgroups — C2×C5×D113⋊C7 #30629099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₁₁₃⋊C₇ #30629099