Subgroups — C₁₁⋊C₅×C₂²⋊#4294 #49178342

Order 37620.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₉×C₁₁⋊C₅	C₃	1	1	yes	maximal, characteristic
2	C₁₁⋊C₅×#4294	—	4	1	no	maximal, Hall
3	C₁₁×C₂²⋊#4294	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₃×C₁₉×C₁₁⋊C₅	—	3	1	no	—
5	C₂²×C₁₉×C₁₁⋊C₅	C₉	1	1	yes	characteristic, complemented, Hall
6	C₅×C₂²⋊#4294	—	11	1	no	maximal, Hall
7	C₃×C₁₉×C₁₁⋊C₅	A₄	1	1	yes	characteristic
8	C₂²×C₃×C₁₁×C₁₉	C₃×C₅	1	1	yes	characteristic
9	C₂×C₁₉×C₁₁⋊C₅	—	3	1	no	—
10	C₂²⋊C₉×C₁₁⋊C₅	—	19	1	no	maximal, Hall
11	C₁₁×#4294	—	4	1	no	Hall
12	C₂×C₃×C₁₁×C₁₉	—	3	1	no	—
13	C₂²×C₃×C₅×C₁₉	—	11	1	no	—
14	C₁₉×C₁₁⋊C₅	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
15	C₅×#4294	—	44	1	no	Hall
16	C₂²×C₁₁×C₁₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂²⋊#4294	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
18	C₂²×C₃×C₁₁⋊C₅	C₁₉⋊C₃	1	1	yes	characteristic
19	C₃×C₁₁×C₁₉	C₅×A₄	1	1	yes	characteristic
20	C₂×C₃×C₅×C₁₉	—	33	1	no	—
21	C₉×C₁₁⋊C₅	—	76	1	no	Hall
22	C₂×C₁₁×C₁₉	—	3	1	no	—
23	C₁₁×C₂²⋊C₉	—	19	1	no	Hall
24	C₂²×C₅×C₁₉	—	11	1	no	Hall
25	C₂×C₃×C₁₁⋊C₅	—	3	1	no	—
26	C₃×C₅×C₁₉	—	11	1	no	—
27	C₂²×C₃×C₁₉	C₃×C₁₁⋊C₅	1	1	yes	characteristic
28	C₂²×C₁₁⋊C₅	#4294	1	1	yes	characteristic, complemented, Hall
29	C₁₁×C₁₉	C₅×C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×C₁₉	—	33	1	no	—
31	C₅×C₂²⋊C₉	—	209	1	no	Hall
32	#4294	—	4	1	no	Hall
33	C₃×C₁₁⋊C₅	C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
34	C₂²×C₃×C₁₁	C₅×C₁₉⋊C₃	1	1	yes	characteristic
35	C₂×C₃×C₁₉	—	3	1	no	—
36	C₂×C₁₁⋊C₅	—	3	1	no	—
37	C₉×C₁₁	—	76	1	no	Hall
38	C₅×C₁₉	—	11	1	no	Hall
39	C₂²×C₁₉	C₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×C₁₁	—	3	1	no	—
41	C₂²×C₃×C₅	—	11	1	no	—
42	C₃×C₁₉	A₄×C₁₁⋊C₅	1	1	yes	characteristic
43	C₁₁⋊C₅	C₂²⋊#4294	1	1	yes	characteristic, direct product factor, Hall
44	C₅×C₉	—	836	1	no	Hall
45	C₂²×C₁₁	C₅×#4294	1	1	yes	characteristic, complemented, Hall
46	C₂×C₁₉	—	3	1	no	—
47	C₂²⋊C₉	—	19	1	no	Hall
48	C₃×C₁₁	C₅×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
49	C₂×C₃×C₅	—	33	1	no	—
50	C₂×C₁₁	—	3	1	no	—
51	C₂²×C₅	—	11	1	no	Hall
52	C₁₉	C₂²⋊C₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
53	C₃×C₅	—	11	1	no	—
54	C₂²×C₃	C₁₁⋊C₅×C₁₉⋊C₃	1	1	yes	characteristic
55	C₁₁	C₅×C₂²⋊#4294	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₅	—	33	1	no	—
57	C₉	—	76	1	no	Sylow
58	C₂×C₃	—	3	1	no	—
59	C₅	—	11	1	no	Sylow
60	C₂²	C₁₁⋊C₅×#4294	1	1	yes	characteristic, complemented, Sylow
61	C₃	C₁₁⋊C₅×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
62	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₁₁⋊C₅×C₂²⋊(C₁₉⋊C₃)
commutator, hypocenter	C₂²×C₁₁×C₁₉	C₅×C₉
Fitting, socle, cosocle	C₂²×C₃×C₁₁×C₁₉	C₃×C₅
prime radical	C₂²×C₃×C₁₉×C₁₁⋊C₅	C₃
LCS	G ▷ C₂²×C₁₁×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₁₁×C₂²⋊#4294	C₅	semidirect
5. C₂²×C₁₉×C₁₁⋊C₅	C₉	semidirect
14. C₁₉×C₁₁⋊C₅	C₂²⋊C₉	semidirect
16. C₂²×C₁₁×C₁₉	C₅×C₉	semidirect
17. C₂²⋊#4294	C₁₁⋊C₅	direct (N × H)
28. C₂²×C₁₁⋊C₅	#4294	semidirect
29. C₁₁×C₁₉	C₅×C₂²⋊C₉	semidirect
39. C₂²×C₁₉	C₉×C₁₁⋊C₅	semidirect
43. C₁₁⋊C₅	C₂²⋊#4294	direct (N × H)
45. C₂²×C₁₁	C₅×#4294	semidirect
52. C₁₉	C₂²⋊C₉×C₁₁⋊C₅	semidirect
55. C₁₁	C₅×C₂²⋊#4294	semidirect
60. C₂²	C₁₁⋊C₅×#4294	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₁₉×C₁₁⋊C₅	3
C₁₁⋊C₅×#4294	4
C₁₁×C₂²⋊#4294	5
C₅×C₂²⋊#4294	11
C₂²⋊C₉×C₁₁⋊C₅	19

Subgroups — C11⋊C5×C22⋊#4294 #49178342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊C₅×C₂²⋊#4294 #49178342