Subgroups — C₇×C₁₉×Dic₁₁⋊C₅ #44417954

Order 29260.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₉×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×C₁₉×Dic₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₉×Dic₁₁⋊C₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₁₁×C₁₉	C₂×C₅	1	1	yes	characteristic
6	C₄×C₅×C₇×C₁₉	—	11	1	no	maximal, Hall
7	C₂×C₁₉×C₁₁⋊C₅	C₂×C₇	1	1	yes	characteristic
8	C₇×Dic₁₁⋊C₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₁×C₁₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₇×C₁₉	—	11	1	no	—
11	C₁₉×C₁₁⋊C₅	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₁₉×Dic₁₁	C₅×C₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₁₁⋊C₅	C₂×C₁₉	1	1	yes	characteristic
14	C₅×C₇×C₁₉	—	11	1	no	Hall
15	C₄×C₇×C₁₉	—	11	1	no	Hall
16	C₂×C₁₁×C₁₉	C₂×C₅×C₇	1	1	yes	characteristic
17	C₇×C₁₁⋊C₅	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
18	C₄×C₅×C₁₉	—	11	1	no	Hall
19	C₇×Dic₁₁	C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₇×C₁₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic
21	Dic₁₁⋊C₅	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
22	C₁₁×C₁₉	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×C₁₉	—	11	1	no	—
24	C₂×C₇×C₁₁	C₂×C₅×C₁₉	1	1	yes	characteristic
25	C₄×C₅×C₇	—	11	1	no	Hall
26	C₇×C₁₉	Dic₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₁₁⋊C₅	C₂×C₇×C₁₉	1	1	yes	characteristic
28	C₅×C₁₉	—	11	1	no	Hall
29	C₇×C₁₁	C₄×C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
30	C₄×C₁₉	—	11	1	no	Hall
31	C₂×C₅×C₇	—	11	1	no	—
32	C₁₁⋊C₅	C₄×C₇×C₁₉	1	1	yes	characteristic, complemented, Hall
33	Dic₁₁	C₅×C₇×C₁₉	1	1	yes	characteristic, complemented, Hall
34	C₂×C₁₉	C₇×AGL(1,𝔽₁₁)	1	1	yes	characteristic
35	C₅×C₇	—	11	1	no	Hall
36	C₄×C₇	—	11	1	no	Hall
37	C₂×C₁₁	C₂×C₅×C₇×C₁₉	1	1	yes	characteristic
38	C₄×C₅	—	11	1	no	Hall
39	C₁₉	C₇×Dic₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₇	C₁₉×AGL(1,𝔽₁₁)	1	1	yes	characteristic
41	C₁₁	C₄×C₅×C₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₅	—	11	1	no	—
43	C₇	C₁₉×Dic₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
44	C₅	—	11	1	no	Sylow
45	C₄	—	11	1	no	Sylow
46	C₂	C₇×C₁₉×AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₉	AGL(1,𝔽₁₁)
commutator, hypocenter	C₁₁	C₄×C₅×C₇×C₁₉
Frattini	C₂	C₇×C₁₉×AGL(1,𝔽₁₁)
Fitting, socle	C₂×C₇×C₁₁×C₁₉	C₂×C₅
prime radical	C₂×C₇×C₁₉×C₁₁⋊C₅	C₂
cosocle	C₂×C₁₁	C₂×C₅×C₇×C₁₉
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₇×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₇×C₁₉×C₁₁⋊C₅	C₄	semidirect
3. C₇×C₁₉×Dic₁₁	C₅	semidirect
4. C₁₉×Dic₁₁⋊C₅	C₇	direct (N × H)
8. C₇×Dic₁₁⋊C₅	C₁₉	direct (N × H)
9. C₇×C₁₁×C₁₉	C₄×C₅	semidirect
11. C₁₉×C₁₁⋊C₅	C₄×C₇	semidirect
12. C₁₉×Dic₁₁	C₅×C₇	semidirect
17. C₇×C₁₁⋊C₅	C₄×C₁₉	semidirect
19. C₇×Dic₁₁	C₅×C₁₉	semidirect
21. Dic₁₁⋊C₅	C₇×C₁₉	direct (N × H)
22. C₁₁×C₁₉	C₄×C₅×C₇	semidirect
26. C₇×C₁₉	Dic₁₁⋊C₅	direct (N × H)
29. C₇×C₁₁	C₄×C₅×C₁₉	semidirect
32. C₁₁⋊C₅	C₄×C₇×C₁₉	semidirect
33. Dic₁₁	C₅×C₇×C₁₉	semidirect
39. C₁₉	C₇×Dic₁₁⋊C₅	direct (N × H)
41. C₁₁	C₄×C₅×C₇×C₁₉	semidirect
43. C₇	C₁₉×Dic₁₁⋊C₅	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×C₇×C₁₉×C₁₁⋊C₅	2
C₇×C₁₉×Dic₁₁	5
C₁₉×Dic₁₁⋊C₅	7
C₄×C₅×C₇×C₁₉	11
C₇×Dic₁₁⋊C₅	19

Subgroups — C7×C19×Dic11⋊C5 #44417954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₉×Dic₁₁⋊C₅ #44417954