Subgroups — C₁₁×Dic₈₅₅ #49178308

Order 37620.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₁×Dic₂₈₅	—	3	1	no	maximal
3	C₅×C₉×C₁₁×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×Dic₁₇₁	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₁×C₁₉	D₃	1	1	yes	characteristic
6	C₁₁×Dic₉₅	—	9	1	no	Hall
7	C₂×C₉×C₁₁×C₁₉	D₅	1	1	yes	characteristic
8	Dic₈₅₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×C₁₁×C₁₉	Dic₃	1	1	yes	characteristic
10	C₁₁×Dic₅₇	—	15	1	no	—
11	C₂×C₅×C₁₁×C₁₉	D₉	1	1	yes	characteristic
12	C₁₁×Dic₄₅	—	19	1	no	maximal, Hall
13	C₉×C₁₁×C₁₉	Dic₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₉×C₁₉	C₂×C₁₁	1	1	yes	characteristic
15	C₂×C₃×C₁₁×C₁₉	D₁₅	1	1	yes	characteristic
16	Dic₂₈₅	—	3	1	no	—
17	C₅×C₁₁×C₁₉	Dic₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₉×C₁₁	D₁₉	1	1	yes	characteristic
19	C₅×C₉×C₁₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
20	C₁₁×Dic₁₉	—	45	1	no	Hall
21	Dic₁₇₁	—	5	1	no	Hall
22	C₁₁×Dic₁₅	—	57	1	no	—
23	C₃×C₁₁×C₁₉	Dic₁₅	1	1	yes	characteristic
24	C₂×C₃×C₅×C₁₉	D₃×C₁₁	1	1	yes	characteristic
25	C₅×C₉×C₁₁	Dic₁₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₁×C₁₉	D₄₅	1	1	yes	characteristic
27	C₁₁×Dic₉	—	95	1	no	Hall
28	Dic₉₅	—	9	1	no	Hall
29	C₂×C₉×C₁₉	D₅×C₁₁	1	1	yes	characteristic
30	C₂×C₃×C₅×C₁₁	D₅₇	1	1	yes	characteristic
31	C₃×C₅×C₁₉	C₁₁×Dic₃	1	1	yes	characteristic
32	Dic₅₇	—	15	1	no	—
33	C₁₁×Dic₅	—	171	1	no	Hall
34	C₁₁×C₁₉	Dic₄₅	1	1	yes	characteristic, complemented, Hall
35	C₂×C₉×C₁₁	D₉₅	1	1	yes	characteristic
36	C₂×C₅×C₁₉	C₁₁×D₉	1	1	yes	characteristic
37	Dic₄₅	—	19	1	no	Hall
38	C₉×C₁₉	C₁₁×Dic₅	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅×C₁₁	Dic₅₇	1	1	yes	characteristic
40	C₁₁×Dic₃	—	285	1	no	—
41	C₂×C₃×C₁₉	C₁₁×D₁₅	1	1	yes	characteristic
42	C₂×C₅×C₁₁	D₁₇₁	1	1	yes	characteristic
43	C₉×C₁₁	Dic₉₅	1	1	yes	characteristic, complemented, Hall
44	C₅×C₁₉	C₁₁×Dic₉	1	1	yes	characteristic, complemented, Hall
45	C₂×C₅×C₉	C₁₁×D₁₉	1	1	yes	characteristic
46	Dic₁₉	—	45	1	no	Hall
47	C₂×C₃×C₁₁	D₂₈₅	1	1	yes	characteristic
48	Dic₁₅	—	57	1	no	—
49	C₃×C₁₉	C₁₁×Dic₁₅	1	1	yes	characteristic
50	C₅×C₁₁	Dic₁₇₁	1	1	yes	characteristic, complemented, Hall
51	C₅×C₉	C₁₁×Dic₁₉	1	1	yes	characteristic, complemented, Hall
52	C₄×C₁₁	—	855	1	no	Hall
53	C₂×C₁₉	C₁₁×D₄₅	1	1	yes	characteristic
54	Dic₉	—	95	1	no	Hall
55	C₃×C₁₁	Dic₂₈₅	1	1	yes	characteristic
56	C₂×C₃×C₅	C₁₁×D₅₇	1	1	yes	characteristic
57	C₂×C₁₁	D₈₅₅	1	1	yes	characteristic
58	Dic₅	—	171	1	no	Hall
59	C₁₉	C₁₁×Dic₄₅	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₉	C₁₁×D₉₅	1	1	yes	characteristic
61	C₃×C₅	C₁₁×Dic₅₇	1	1	yes	characteristic
62	Dic₃	—	285	1	no	—
63	C₁₁	Dic₈₅₅	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₅	C₁₁×D₁₇₁	1	1	yes	characteristic
65	C₉	C₁₁×Dic₉₅	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	C₁₁×D₂₈₅	1	1	yes	characteristic
67	C₅	C₁₁×Dic₁₇₁	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	855	1	no	Sylow
69	C₃	C₁₁×Dic₂₈₅	1	1	yes	characteristic
70	C₂	C₁₁×D₈₅₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₈₅₅
commutator, hypocenter	C₅×C₉×C₁₉	C₄×C₁₁
Frattini	C₂×C₃	C₁₁×D₂₈₅
Fitting	C₂×C₅×C₉×C₁₁×C₁₉	C₂
socle, prime radical	C₂×C₃×C₅×C₁₁×C₁₉	D₃
cosocle	C₂×C₅×C₉×C₁₉	C₂×C₁₁
LCS	G ▷ C₅×C₉×C₁₉
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₁×C₁₉	C₄	semidirect
8. Dic₈₅₅	C₁₁	direct (N × H)
13. C₉×C₁₁×C₁₉	Dic₅	semidirect
17. C₅×C₁₁×C₁₉	Dic₉	semidirect
19. C₅×C₉×C₁₉	C₄×C₁₁	semidirect
25. C₅×C₉×C₁₁	Dic₁₉	semidirect
34. C₁₁×C₁₉	Dic₄₅	semidirect
38. C₉×C₁₉	C₁₁×Dic₅	semidirect
43. C₉×C₁₁	Dic₉₅	semidirect
44. C₅×C₁₉	C₁₁×Dic₉	semidirect
50. C₅×C₁₁	Dic₁₇₁	semidirect
51. C₅×C₉	C₁₁×Dic₁₉	semidirect
59. C₁₉	C₁₁×Dic₄₅	semidirect
63. C₁₁	Dic₈₅₅	direct (N × H)
65. C₉	C₁₁×Dic₉₅	semidirect
67. C₅	C₁₁×Dic₁₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₉×C₁₁×C₁₉	2
C₁₁×Dic₂₈₅	3
C₁₁×Dic₁₇₁	5
Dic₈₅₅	11
C₁₁×Dic₄₅	19

Subgroups — C11×Dic855 #49178308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×Dic₈₅₅ #49178308