Subgroups — C₅×C₁₁⋊#10587723 #44473299

Order 30030.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×#63271	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₀₀₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁⋊#10587723	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₁⋊(D₁₃⋊C₃)	—	7	1	no	maximal, Hall
6	C₁₁×#63271	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×#10587723	—	11	1	no	maximal, Hall
8	C₅×C₁₁⋊AGL(1,𝔽₇)	—	13	1	no	maximal, Hall
9	C₅×C₁₁×C₁₃⋊C₃	—	7	1	no	Hall
10	D₁₀₀₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	C₅×D₁₄₃	—	7	1	no	Hall
12	C₅×#63271	D₁₁	1	1	yes	characteristic, complemented, Hall
13	C₅×C₁₁×ΓL(1,𝔽₈)	—	13	1	no	Hall
14	C₇×C₁₁×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
15	C₅×D₉₁	—	11	1	no	Hall
16	C₁₁⋊(D₁₃⋊C₃)	—	7	1	no	Hall
17	C₅×D₇₇	—	13	1	no	Hall
18	C₅×C₁₁×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
19	#10587723	—	11	1	no	Hall
20	C₁₁⋊AGL(1,𝔽₇)	—	13	1	no	Hall
21	C₅×C₇×C₁₃	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
22	C₁₁×C₁₃⋊C₃	—	7	1	no	Hall
23	C₅×D₁₃⋊C₃	—	77	1	no	Hall
24	C₅×C₇×C₁₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅×D₁₁	—	91	1	no	Hall
26	D₁₄₃	—	7	1	no	Hall
27	#63271	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
28	C₁₁×ΓL(1,𝔽₈)	—	13	1	no	Hall
29	C₅×AGL(1,𝔽₇)	—	143	1	no	Hall
30	C₅×C₁₃⋊C₃	—	7	1	no	Hall
31	D₉₁	—	11	1	no	Hall
32	C₃×C₅×C₁₁	—	91	1	no	Hall
33	D₇₇	—	13	1	no	Hall
34	C₁₁×C₁₃	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
35	C₅×D₁₃	—	77	1	no	Hall
36	C₅×D₁₁	—	91	1	no	Hall
37	C₅×ΓL(1,𝔽₈)	—	13	1	no	Hall
38	C₇×C₁₃	C₃×C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
39	D₁₃⋊C₃	—	77	1	no	Hall
40	C₇×C₁₁	C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
41	C₅×D₇	—	143	1	no	Hall
42	C₃×D₁₁	—	91	1	no	Hall
43	C₅×C₁₃	C₁₁⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
44	C₅×C₁₁	#10587723	1	1	yes	characteristic, complemented, Hall
45	AGL(1,𝔽₇)	—	143	1	no	Hall
46	C₁₃⋊C₃	—	7	1	no	Hall
47	C₅×C₇	C₁₁⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Hall
48	C₃×C₁₁	—	91	1	no	Hall
49	C₂×C₃×C₅	—	1001	1	no	Hall
50	D₁₃	—	77	1	no	Hall
51	D₁₁	—	91	1	no	Hall
52	ΓL(1,𝔽₈)	—	13	1	no	Hall
53	C₃×C₅	—	91	1	no	Hall
54	D₇	—	143	1	no	Hall
55	C₁₃	C₅×C₁₁⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
56	C₁₁	C₅×#10587723	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₅	—	1001	1	no	Hall
58	C₇	C₅×C₁₁⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	1001	1	no	Hall
60	C₅	C₁₁⋊#10587723	1	1	yes	characteristic, direct product factor, Sylow
61	C₃	—	91	1	no	Sylow
62	C₂	—	1001	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₁₁⋊#10587723
commutator, cosocle, hypocenter	C₇×C₁₁×C₁₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₁×C₁₃	C₂×C₃
LCS	G ▷ C₇×C₁₁×C₁₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×#63271	C₂	semidirect
2. C₅×D₁₀₀₁	C₃	semidirect
3. C₁₁⋊#10587723	C₅	direct (N × H)
4. C₅×C₇×C₁₁×C₁₃	C₂×C₃	semidirect
6. C₁₁×#63271	C₂×C₅	semidirect
10. D₁₀₀₁	C₃×C₅	semidirect
12. C₅×#63271	D₁₁	semidirect
14. C₇×C₁₁×C₁₃	C₂×C₃×C₅	semidirect
18. C₅×C₁₁×C₁₃	AGL(1,𝔽₇)	semidirect
21. C₅×C₇×C₁₃	C₃×D₁₁	semidirect
24. C₅×C₇×C₁₁	D₁₃⋊C₃	semidirect
27. #63271	C₅×D₁₁	semidirect
34. C₁₁×C₁₃	C₅×AGL(1,𝔽₇)	semidirect
38. C₇×C₁₃	C₃×C₅×D₁₁	semidirect
40. C₇×C₁₁	C₅×D₁₃⋊C₃	semidirect
43. C₅×C₁₃	C₁₁⋊AGL(1,𝔽₇)	semidirect
44. C₅×C₁₁	#10587723	semidirect
47. C₅×C₇	C₁₁⋊(D₁₃⋊C₃)	semidirect
55. C₁₃	C₅×C₁₁⋊AGL(1,𝔽₇)	semidirect
56. C₁₁	C₅×#10587723	semidirect
58. C₇	C₅×C₁₁⋊(D₁₃⋊C₃)	semidirect
60. C₅	C₁₁⋊#10587723	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×C₁₁×#63271	2
C₅×D₁₀₀₁	3
C₁₁⋊#10587723	5
C₅×C₁₁⋊(D₁₃⋊C₃)	7
C₅×#10587723	11
C₅×C₁₁⋊AGL(1,𝔽₇)	13

Subgroups — C5×C11⋊#10587723 #44473299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁⋊#10587723 #44473299