Subgroups — C₃×C₁₁×C₁₇×A₅ #46778217

Order 33660.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇×A₅	C₃	1	1	yes	maximal, characteristic, direct product factor
2	C₃×C₁₁×A₄×C₁₇	—	5	1	no	maximal, Hall
3	C₃×D₅×C₁₁×C₁₇	—	6	1	no	maximal
4	C₃×D₃×C₁₁×C₁₇	—	10	1	no	maximal
5	C₃×C₁₇×A₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₁₁×C₁₇	—	6	1	no	—
7	C₁₁×A₄×C₁₇	—	5	1	no	—
8	C₁₁×A₄×C₁₇	—	5	2	no	—
9	C₂²×C₃×C₁₁×C₁₇	—	5	1	no	—
10	C₃×C₁₁×A₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	D₅×C₁₁×C₁₇	—	6	1	no	—
12	C₃²×C₁₁×C₁₇	—	10	1	no	Hall
13	C₂×C₃×C₁₁×C₁₇	—	15	1	no	—
14	D₃×C₁₁×C₁₇	—	10	1	no	—
15	C₁₇×A₅	C₃×C₁₁	1	1	yes	characteristic, direct product factor
16	C₅×C₁₁×C₁₇	—	6	1	no	Hall
17	C₂²×C₁₁×C₁₇	—	5	1	no	Hall
18	C₁₁×A₅	C₃×C₁₇	1	1	yes	characteristic, direct product factor
19	C₃×A₄×C₁₇	—	5	1	no	Hall
20	C₃×C₁₁×C₁₇	—	10	1	no	—
21	C₃×C₁₁×C₁₇	—	20	1	no	—
22	C₃×C₁₁×C₁₇	A₅	1	1	yes	maximal normal, characteristic, direct product factor
23	C₃×D₅×C₁₇	—	6	1	no	—
24	C₃×C₁₁×A₄	—	5	1	no	Hall
25	C₂×C₁₁×C₁₇	—	15	1	no	—
26	C₃×D₅×C₁₁	—	6	1	no	—
27	C₃×D₃×C₁₇	—	10	1	no	—
28	C₃×C₅×C₁₇	—	6	1	no	—
29	C₂²×C₃×C₁₇	—	5	1	no	—
30	A₄×C₁₇	—	5	1	no	—
31	A₄×C₁₇	—	5	2	no	—
32	C₃×D₃×C₁₁	—	10	1	no	—
33	C₁₁×C₁₇	C₃×A₅	1	1	yes	characteristic, direct product factor, Hall
34	C₃×A₅	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
35	D₅×C₁₇	—	6	1	no	—
36	C₃×C₅×C₁₁	—	6	1	no	—
37	C₃²×C₁₇	—	10	1	no	Hall
38	C₂²×C₃×C₁₁	—	5	1	no	—
39	C₁₁×A₄	—	5	1	no	—
40	C₁₁×A₄	—	5	2	no	—
41	D₅×C₁₁	—	6	1	no	—
42	C₂×C₃×C₁₇	—	15	1	no	—
43	D₃×C₁₇	—	10	1	no	—
44	C₃²×C₁₁	—	10	1	no	Hall
45	C₅×C₁₇	—	6	1	no	Hall
46	C₂²×C₁₇	—	5	1	no	Hall
47	C₂×C₃×C₁₁	—	15	1	no	—
48	D₃×C₁₁	—	10	1	no	—
49	A₅	C₃×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor
50	C₅×C₁₁	—	6	1	no	Hall
51	C₃×C₁₇	—	10	1	no	—
52	C₃×C₁₇	—	20	1	no	—
53	C₃×C₁₇	C₁₁×A₅	1	1	yes	characteristic, direct product factor
54	C₂²×C₁₁	—	5	1	no	Hall
55	C₃×A₄	—	5	1	no	Hall
56	C₂×C₁₇	—	15	1	no	—
57	C₃×C₁₁	—	10	1	no	—
58	C₃×C₁₁	—	20	1	no	—
59	C₃×C₁₁	C₁₇×A₅	1	1	yes	characteristic, direct product factor
60	C₃×D₅	—	6	1	no	—
61	C₂×C₁₁	—	15	1	no	—
62	C₃×D₃	—	10	1	no	—
63	C₁₇	C₃×C₁₁×A₅	1	1	yes	characteristic, direct product factor, Sylow
64	C₃×C₅	—	6	1	no	—
65	C₂²×C₃	—	5	1	no	—
66	A₄	—	5	1	no	—
67	A₄	—	5	2	no	—
68	C₁₁	C₃×C₁₇×A₅	1	1	yes	characteristic, direct product factor, Sylow
69	D₅	—	6	1	no	—
70	C₃²	—	10	1	no	Sylow
71	C₂×C₃	—	15	1	no	—
72	D₃	—	10	1	no	—
73	C₅	—	6	1	no	Sylow
74	C₂²	—	5	1	no	Sylow
75	C₃	—	10	1	no	—
76	C₃	—	20	1	no	—
77	C₃	C₁₁×C₁₇×A₅	1	1	yes	characteristic, direct product factor
78	C₂	—	15	1	no	—

	subgroup	G/H
center, Fitting, hypercenter	C₃×C₁₁×C₁₇	A₅
commutator, hypocenter	A₅	C₃×C₁₁×C₁₇
Frattini	C₁	G
LCS	G ▷ A₅
UCS	C₁ ◁ C₃×C₁₁×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₇×A₅	C₃	direct (N × H)
5. C₃×C₁₇×A₅	C₁₁	direct (N × H)
10. C₃×C₁₁×A₅	C₁₇	direct (N × H)
15. C₁₇×A₅	C₃×C₁₁	direct (N × H)
18. C₁₁×A₅	C₃×C₁₇	direct (N × H)
22. C₃×C₁₁×C₁₇	A₅	direct (N × H)
33. C₁₁×C₁₇	C₃×A₅	direct (N × H)
34. C₃×A₅	C₁₁×C₁₇	direct (N × H)
49. A₅	C₃×C₁₁×C₁₇	direct (N × H)
53. C₃×C₁₇	C₁₁×A₅	direct (N × H)
59. C₃×C₁₁	C₁₇×A₅	direct (N × H)
63. C₁₇	C₃×C₁₁×A₅	direct (N × H)
68. C₁₁	C₃×C₁₇×A₅	direct (N × H)
77. C₃	C₁₁×C₁₇×A₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₇×A₅	3
C₃×C₁₁×A₄×C₁₇	5
C₃×D₅×C₁₁×C₁₇	6
C₃×D₃×C₁₁×C₁₇	10
C₃×C₁₇×A₅	11
C₃×C₁₁×A₅	17

Subgroups — C3×C11×C17×A5 #46778217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×C₁₇×A₅ #46778217