Subgroups — C₅×C₁₁⋊#90865 #38788148

Order 25740.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₁₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊#90865	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×D₃×C₁₁×C₁₃	—	6	2	no	—
5	C₅×Dic₁₄₃	—	9	1	no	maximal, Hall
6	C₁₁×C₁₃×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic
7	C₅×#90865	—	11	1	no	maximal, Hall
8	C₃×C₅×C₁₁×C₁₃	—	2	2	no	—
9	C₅×C₁₁⋊#157	—	13	1	no	maximal, Hall
10	C₂×C₅×C₁₁×C₁₃	—	9	1	no	—
11	C₃²×C₁₁×C₁₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₅×C₁₃×C₃⋊D₃	D₁₁	1	1	yes	characteristic
13	C₅×C₁₁×C₃⋊D₃	D₁₃	1	1	yes	characteristic
14	D₃×C₁₁×C₁₃	—	6	2	no	—
15	C₅×C₁₁×C₁₃	#157	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₅×C₁₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
17	Dic₁₄₃	—	9	1	no	Hall
18	C₃²×C₅×C₁₁	Dic₁₃	1	1	yes	characteristic, complemented, Hall
19	#90865	—	11	1	no	Hall
20	C₃×C₁₁×C₁₃	—	2	2	no	—
21	C₁₁⋊#157	—	13	1	no	Hall
22	C₅×D₃×C₁₃	—	6	2	no	—
23	C₅×D₃×C₁₁	—	6	2	no	—
24	C₂×C₁₁×C₁₃	—	9	1	no	—
25	C₅×Dic₁₃	—	99	1	no	Hall
26	C₁₃×C₃⋊D₃	C₅×D₁₁	1	1	yes	characteristic
27	C₅×Dic₁₁	—	117	1	no	Hall
28	C₁₁×C₃⋊D₃	C₅×D₁₃	1	1	yes	characteristic
29	C₃×C₅×C₁₃	—	2	2	no	—
30	C₅×#157	—	143	1	no	Hall
31	C₃×C₅×C₁₁	—	2	2	no	—
32	C₁₁×C₁₃	C₅×#157	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×C₁₃	—	9	1	no	—
34	C₃²×C₁₃	C₅×Dic₁₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₅×C₁₁	—	9	1	no	—
36	C₃²×C₁₁	C₅×Dic₁₃	1	1	yes	characteristic, complemented, Hall
37	C₅×C₃⋊D₃	D₁₄₃	1	1	yes	characteristic
38	D₃×C₁₃	—	6	2	no	—
39	D₃×C₁₁	—	6	2	no	—
40	C₅×C₁₃	C₁₁⋊#157	1	1	yes	characteristic, complemented, Hall
41	C₅×C₁₁	#90865	1	1	yes	characteristic, complemented, Hall
42	Dic₁₃	—	99	1	no	Hall
43	C₃²×C₅	Dic₁₄₃	1	1	yes	characteristic, complemented, Hall
44	Dic₁₁	—	117	1	no	Hall
45	C₃×C₁₃	—	2	2	no	—
46	#157	—	143	1	no	Hall
47	C₃×C₁₁	—	2	2	no	—
48	C₅×D₃	—	6	2	no	—
49	C₂×C₁₃	—	9	1	no	—
50	C₂×C₁₁	—	9	1	no	—
51	C₄×C₅	—	1287	1	no	Hall
52	C₃⋊D₃	C₅×D₁₄₃	1	1	yes	characteristic
53	C₃×C₅	—	2	2	no	—
54	C₁₃	C₅×C₁₁⋊#157	1	1	yes	characteristic, complemented, Sylow
55	C₁₁	C₅×#90865	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₅	—	9	1	no	—
57	C₃²	C₅×Dic₁₄₃	1	1	yes	characteristic, complemented, Sylow
58	D₃	—	6	2	no	—
59	C₅	C₁₁⋊#90865	1	1	yes	characteristic, direct product factor, Sylow
60	C₄	—	1287	1	no	Sylow
61	C₃	—	2	2	no	—
62	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₁₁⋊#90865
commutator, hypocenter	C₃²×C₁₁×C₁₃	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁×C₁₃	C₄
prime radical	C₅×C₁₁×C₁₃×C₃⋊D₃	C₂
cosocle	C₁₁×C₁₃×C₃⋊D₃	C₂×C₅
LCS	G ▷ C₃²×C₁₁×C₁₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₁₁×C₁₃	C₄	semidirect
3. C₁₁⋊#90865	C₅	direct (N × H)
11. C₃²×C₁₁×C₁₃	C₄×C₅	semidirect
15. C₅×C₁₁×C₁₃	#157	semidirect
16. C₃²×C₅×C₁₃	Dic₁₁	semidirect
18. C₃²×C₅×C₁₁	Dic₁₃	semidirect
32. C₁₁×C₁₃	C₅×#157	semidirect
34. C₃²×C₁₃	C₅×Dic₁₁	semidirect
36. C₃²×C₁₁	C₅×Dic₁₃	semidirect
40. C₅×C₁₃	C₁₁⋊#157	semidirect
41. C₅×C₁₁	#90865	semidirect
43. C₃²×C₅	Dic₁₄₃	semidirect
54. C₁₃	C₅×C₁₁⋊#157	semidirect
55. C₁₁	C₅×#90865	semidirect
57. C₃²	C₅×Dic₁₄₃	semidirect
59. C₅	C₁₁⋊#90865	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×C₁₃×C₃⋊D₃	2
C₁₁⋊#90865	5
C₅×Dic₁₄₃	9
C₅×#90865	11
C₅×C₁₁⋊#157	13

Subgroups — C5×C11⋊#90865 #38788148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁⋊#90865 #38788148