Subgroups — C₁₁⋊(C₁₁⋊#64480) #49137567

Order 36300.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁⋊(C₁₁⋊#1044)	—	3	1	no	maximal, Hall
3	C₁₁²×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁²×C₅⋊D₅	D₃	1	1	yes	characteristic
5	C₁₁⋊#64480	—	11	4	no	maximal
6	C₁₁⋊#64480	—	11	4	no	maximal
7	C₁₁⋊#64480	—	11	4	no	maximal
8	C₅²×C₁₁²	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	—	15	1	no	—
10	C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	—	15	1	no	—
11	C₁₁×(C₅⋊D₅)⋊C₃	D₁₁	1	4	yes	—
12	C₁₁×(C₅⋊D₅)⋊C₃	D₁₁	1	4	yes	—
13	C₁₁×(C₅⋊D₅)⋊C₃	D₁₁	1	4	yes	—
14	C₃⋊(C₁₁⋊Dic₁₁)	—	25	1	no	maximal, Hall
15	D₅×C₁₁²	—	15	1	no	—
16	D₅×C₁₁²	—	30	1	no	—
17	C₁₁⋊#1044	—	33	4	no	—
18	C₁₁⋊#1044	—	33	4	no	—
19	C₁₁⋊#1044	—	33	4	no	—
20	C₁₁×C₅²⋊C₃	Dic₁₁	1	4	yes	complemented
21	C₁₁×C₅²⋊C₃	Dic₁₁	1	4	yes	complemented
22	C₁₁×C₅²⋊C₃	Dic₁₁	1	4	yes	complemented
23	C₂×C₃×C₁₁²	—	25	1	no	—
24	C₅×C₁₁²	—	3	1	no	—
25	C₅×C₁₁²	—	6	1	no	—
26	C₁₁×C₅⋊D₅	D₃₃	1	4	yes	—
27	C₁₁×C₅⋊D₅	D₃₃	1	4	yes	—
28	C₁₁×C₅⋊D₅	D₃₃	1	4	yes	—
29	C₁₁⋊Dic₁₁	—	75	1	no	Hall
30	C₃×C₁₁²	—	100	1	no	Hall
31	#64480	—	121	1	no	Hall
32	C₅²×C₁₁	Dic₃₃	1	4	yes	complemented
33	C₅²×C₁₁	Dic₃₃	1	4	yes	complemented
34	C₅²×C₁₁	Dic₃₃	1	4	yes	complemented
35	C₂×C₁₁²	—	25	1	no	—
36	C₁₁⋊AGL(1,𝔽₅)	—	165	4	no	—
37	C₁₁⋊AGL(1,𝔽₅)	—	165	4	no	—
38	C₁₁⋊AGL(1,𝔽₅)	—	165	4	no	—
39	C₁₁⋊AGL(1,𝔽₅)	—	165	4	no	—
40	C₁₁⋊AGL(1,𝔽₅)	—	165	4	no	—
41	C₁₁⋊AGL(1,𝔽₅)	—	165	4	no	—
42	(C₅⋊D₅)⋊C₃	C₁₁⋊D₁₁	1	1	yes	characteristic
43	Dic₃₃	—	275	4	no	—
44	Dic₃₃	—	275	4	no	—
45	Dic₃₃	—	275	4	no	—
46	C₁₁²	#64480	1	1	yes	characteristic, complemented, Sylow
47	D₅×C₁₁	—	15	4	no	—
48	D₅×C₁₁	—	15	4	no	—
49	D₅×C₁₁	—	30	4	no	—
50	D₅×C₁₁	—	30	4	no	—
51	D₅×C₁₁	—	30	4	no	—
52	D₅×C₁₁	—	30	4	no	—
53	#1044	—	363	1	no	Hall
54	C₅²⋊C₃	C₁₁⋊Dic₁₁	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₁₁	—	25	4	no	—
56	C₂×C₃×C₁₁	—	25	4	no	—
57	C₂×C₃×C₁₁	—	25	4	no	—
58	C₅×C₁₁	—	3	4	no	—
59	C₅×C₁₁	—	3	4	no	—
60	C₅×C₁₁	—	6	4	no	—
61	C₅×C₁₁	—	6	4	no	—
62	C₅×C₁₁	—	6	4	no	—
63	C₅×C₁₁	—	6	4	no	—
64	C₅⋊D₅	C₃⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic
65	Dic₁₁	—	825	4	no	—
66	Dic₁₁	—	825	4	no	—
67	Dic₁₁	—	825	4	no	—
68	C₃×C₁₁	—	100	4	no	—
69	C₃×C₁₁	—	100	4	no	—
70	C₃×C₁₁	—	100	4	no	—
71	C₅²	C₃⋊(C₁₁⋊Dic₁₁)	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₁₁	—	25	4	no	—
73	C₂×C₁₁	—	25	4	no	—
74	C₂×C₁₁	—	25	4	no	—
75	AGL(1,𝔽₅)	—	1815	1	no	—
76	AGL(1,𝔽₅)	—	1815	1	no	—
77	Dic₃	—	3025	1	no	Hall
78	C₁₁	C₁₁⋊#64480	1	4	yes	complemented
79	C₁₁	C₁₁⋊#64480	1	4	yes	complemented
80	C₁₁	C₁₁⋊#64480	1	4	yes	complemented
81	D₅	—	30	1	no	—
82	D₅	—	30	1	no	—
83	C₂×C₃	—	25	1	no	—
84	C₅	—	6	1	no	—
85	C₅	—	6	1	no	—
86	C₄	—	9075	1	no	Sylow
87	C₃	—	100	1	no	Sylow
88	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₁₁²×C₅²⋊C₃	C₄
Fitting, socle	C₅²×C₁₁²	Dic₃
prime radical, cosocle	C₁₁²×(C₅⋊D₅)⋊C₃	C₂
LCS	G ▷ C₁₁²×C₅²⋊C₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₁₁²×C₅²⋊C₃	C₄	semidirect
8. C₅²×C₁₁²	Dic₃	semidirect
20. C₁₁×C₅²⋊C₃	Dic₁₁	semidirect
21. C₁₁×C₅²⋊C₃	Dic₁₁	semidirect
22. C₁₁×C₅²⋊C₃	Dic₁₁	semidirect
32. C₅²×C₁₁	Dic₃₃	semidirect
33. C₅²×C₁₁	Dic₃₃	semidirect
34. C₅²×C₁₁	Dic₃₃	semidirect
46. C₁₁²	#64480	semidirect
54. C₅²⋊C₃	C₁₁⋊Dic₁₁	semidirect
71. C₅²	C₃⋊(C₁₁⋊Dic₁₁)	semidirect
78. C₁₁	C₁₁⋊#64480	semidirect
79. C₁₁	C₁₁⋊#64480	semidirect
80. C₁₁	C₁₁⋊#64480	semidirect

Maximal subgroups

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

subgroup	index
C₁₁²×(C₅⋊D₅)⋊C₃	2
C₁₁⋊(C₁₁⋊#1044)	3
C₁₁⋊#64480	11
C₃⋊(C₁₁⋊Dic₁₁)	25

Subgroups — C11⋊(C11⋊#64480) #49137567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊(C₁₁⋊#64480) #49137567