Subgroups — C₅×C₁₇×C₁₁⋊#157 #46778041

Order 33660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₁₇×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₁×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₇×C₁₁⋊#157	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×D₃×C₁₁×C₁₇	—	6	2	no	—
5	C₅×C₁₇×Dic₁₁	—	9	1	no	maximal, Hall
6	C₁₁×C₁₇×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₇×#157	—	11	1	no	maximal, Hall
8	C₃×C₅×C₁₁×C₁₇	—	2	2	no	—
9	C₅×C₁₁⋊#157	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅×C₁₁×C₁₇	—	9	1	no	—
11	C₃²×C₁₁×C₁₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₅×C₁₇×C₃⋊D₃	D₁₁	1	1	yes	characteristic
13	D₃×C₁₁×C₁₇	—	6	2	no	—
14	C₅×C₁₁×C₃⋊D₃	C₂×C₁₇	1	1	yes	characteristic
15	C₅×C₁₁×C₁₇	#157	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₅×C₁₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
17	C₁₇×Dic₁₁	—	9	1	no	Hall
18	C₁₇×#157	—	11	1	no	Hall
19	C₃×C₁₁×C₁₇	—	2	2	no	—
20	C₅×D₃×C₁₇	—	6	2	no	—
21	C₃²×C₅×C₁₁	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
22	C₁₁⋊#157	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₁×C₁₇	—	9	1	no	—
24	C₄×C₅×C₁₇	—	99	1	no	Hall
25	C₅×D₃×C₁₁	—	6	2	no	—
26	C₁₇×C₃⋊D₃	C₅×D₁₁	1	1	yes	characteristic
27	C₃×C₅×C₁₇	—	2	2	no	—
28	C₅×Dic₁₁	—	9	1	no	Hall
29	C₁₁×C₃⋊D₃	C₂×C₅×C₁₇	1	1	yes	characteristic
30	C₁₁×C₁₇	C₅×#157	1	1	yes	characteristic, complemented, Hall
31	C₅×#157	—	11	1	no	Hall
32	C₂×C₅×C₁₇	—	9	1	no	—
33	C₃×C₅×C₁₁	—	2	2	no	—
34	C₃²×C₁₇	C₅×Dic₁₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₅×C₁₁	—	9	1	no	—
36	D₃×C₁₇	—	6	2	no	—
37	C₃²×C₁₁	C₄×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
38	C₅×C₃⋊D₃	C₁₇×D₁₁	1	1	yes	characteristic
39	C₅×C₁₇	C₁₁⋊#157	1	1	yes	characteristic, direct product factor, Hall
40	C₄×C₁₇	—	99	1	no	Hall
41	D₃×C₁₁	—	6	2	no	—
42	C₅×C₁₁	C₁₇×#157	1	1	yes	characteristic, complemented, Hall
43	C₃×C₁₇	—	2	2	no	—
44	C₃²×C₅	C₁₇×Dic₁₁	1	1	yes	characteristic, complemented, Hall
45	Dic₁₁	—	9	1	no	Hall
46	#157	—	11	1	no	Hall
47	C₂×C₁₇	—	9	1	no	—
48	C₃×C₁₁	—	2	2	no	—
49	C₅×D₃	—	6	2	no	—
50	C₂×C₁₁	—	9	1	no	—
51	C₄×C₅	—	99	1	no	Hall
52	C₃⋊D₃	C₅×C₁₇×D₁₁	1	1	yes	characteristic
53	C₁₇	C₅×C₁₁⋊#157	1	1	yes	characteristic, direct product factor, Sylow
54	C₃×C₅	—	2	2	no	—
55	C₁₁	C₅×C₁₇×#157	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₅	—	9	1	no	—
57	C₃²	C₅×C₁₇×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
58	D₃	—	6	2	no	—
59	C₅	C₁₇×C₁₁⋊#157	1	1	yes	characteristic, direct product factor, Sylow
60	C₄	—	99	1	no	Sylow
61	C₃	—	2	2	no	—
62	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₇	C₁₁⋊#157
commutator, hypocenter	C₃²×C₁₁	C₄×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁×C₁₇	C₄
prime radical	C₅×C₁₁×C₁₇×C₃⋊D₃	C₂
cosocle	C₁₁×C₃⋊D₃	C₂×C₅×C₁₇
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₅×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₁₁×C₁₇	C₄	semidirect
3. C₁₇×C₁₁⋊#157	C₅	direct (N × H)
9. C₅×C₁₁⋊#157	C₁₇	direct (N × H)
11. C₃²×C₁₁×C₁₇	C₄×C₅	semidirect
15. C₅×C₁₁×C₁₇	#157	semidirect
16. C₃²×C₅×C₁₇	Dic₁₁	semidirect
21. C₃²×C₅×C₁₁	C₄×C₁₇	semidirect
22. C₁₁⋊#157	C₅×C₁₇	direct (N × H)
30. C₁₁×C₁₇	C₅×#157	semidirect
34. C₃²×C₁₇	C₅×Dic₁₁	semidirect
37. C₃²×C₁₁	C₄×C₅×C₁₇	semidirect
39. C₅×C₁₇	C₁₁⋊#157	direct (N × H)
42. C₅×C₁₁	C₁₇×#157	semidirect
44. C₃²×C₅	C₁₇×Dic₁₁	semidirect
53. C₁₇	C₅×C₁₁⋊#157	direct (N × H)
55. C₁₁	C₅×C₁₇×#157	semidirect
57. C₃²	C₅×C₁₇×Dic₁₁	semidirect
59. C₅	C₁₇×C₁₁⋊#157	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×C₁₇×C₃⋊D₃	2
C₁₇×C₁₁⋊#157	5
C₅×C₁₇×Dic₁₁	9
C₅×C₁₇×#157	11
C₅×C₁₁⋊#157	17

Subgroups — C5×C17×C11⋊#157 #46778041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₇×C₁₁⋊#157 #46778041