Subgroups — D₅₅×#4294 #34037839

Order 18810.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×#4294	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₉×D₅₅	C₃	1	1	yes	maximal, characteristic
3	D₁₁×#4294	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₁₉×D₅₅	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₁×#4294	D₅	1	1	yes	characteristic, complemented, Hall
7	D₅×#4294	—	11	1	no	maximal, Hall
8	C₃×C₁₉×D₁₁	—	5	1	no	—
9	C₅×C₁₁×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₉×D₅₅	—	19	1	no	maximal, Hall
11	C₅×#4294	D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁×C₁₉	C₃×D₅	1	1	yes	characteristic
13	C₃×D₅×C₁₉	—	11	1	no	—
14	C₅×C₉×C₁₁	—	19	1	no	Hall
15	C₁₉×D₁₁	—	5	1	no	Hall
16	C₂×#4294	—	55	1	no	Hall
17	C₃×D₅₅	C₁₉⋊C₃	1	1	yes	characteristic
18	C₃×C₅×C₁₉	C₃×D₁₁	1	1	yes	characteristic
19	C₁₁×C₁₉	C₉×D₅	1	1	yes	characteristic, complemented, Hall
20	C₉×D₁₁	—	95	1	no	Hall
21	D₅×C₁₉	—	11	1	no	Hall
22	#4294	D₅₅	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅×C₁₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic
24	C₂×C₃×C₁₉	—	55	1	no	—
25	D₅₅	#4294	1	1	yes	characteristic, direct product factor, Hall
26	C₉×C₁₁	—	19	1	no	Hall
27	C₅×C₁₉	C₉×D₁₁	1	1	yes	characteristic, complemented, Hall
28	C₉×D₅	—	209	1	no	Hall
29	C₃×D₁₁	—	5	1	no	—
30	C₃×C₁₉	C₃×D₅₅	1	1	yes	characteristic
31	C₅×C₁₁	C₂×#4294	1	1	yes	characteristic, complemented, Hall
32	C₅×C₉	—	19	1	no	Hall
33	C₂×C₁₉	—	55	1	no	Hall
34	C₃×C₁₁	D₅×C₁₉⋊C₃	1	1	yes	characteristic
35	C₃×D₅	—	11	1	no	—
36	D₁₁	—	5	1	no	Hall
37	C₁₉	C₉×D₅₅	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₉	—	1045	1	no	Hall
39	C₃×C₅	D₁₁×C₁₉⋊C₃	1	1	yes	characteristic
40	C₁₁	D₅×#4294	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	11	1	no	Hall
42	C₉	—	19	1	no	Sylow
43	C₂×C₃	—	55	1	no	—
44	C₅	D₁₁×#4294	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₁₉⋊C₃×D₅₅	1	1	yes	characteristic
46	C₂	—	55	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₁₉⋊C₃×D₅₅
commutator, hypocenter	C₅×C₁₁×C₁₉	C₂×C₉
Fitting, socle, cosocle	C₃×C₅×C₁₁×C₁₉	C₂×C₃
prime radical	C₃×C₁₉×D₅₅	C₃
LCS	G ▷ C₅×C₁₁×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×#4294	C₂	semidirect
5. C₁₉×D₅₅	C₉	semidirect
6. C₁₁×#4294	D₅	semidirect
9. C₅×C₁₁×C₁₉	C₂×C₉	semidirect
11. C₅×#4294	D₁₁	semidirect
19. C₁₁×C₁₉	C₉×D₅	semidirect
22. #4294	D₅₅	direct (N × H)
25. D₅₅	#4294	direct (N × H)
27. C₅×C₁₉	C₉×D₁₁	semidirect
31. C₅×C₁₁	C₂×#4294	semidirect
37. C₁₉	C₉×D₅₅	semidirect
40. C₁₁	D₅×#4294	semidirect
44. C₅	D₁₁×#4294	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₁×#4294	2
C₃×C₁₉×D₅₅	3
D₁₁×#4294	5
D₅×#4294	11
C₉×D₅₅	19

Subgroups — D55×#4294 #34037839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₅×#4294 #34037839