Subgroups — C₅×C₁₁×Dic₃×C₄₉ #44568310

Order 32340.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₁×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₁₁×C₄₉	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₁×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×Dic₃×C₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₁×C₄₉	D₃	1	1	yes	characteristic
6	C₅×C₇×C₁₁×Dic₃	C₇	1	1	yes	maximal, characteristic
7	C₂×C₃×C₁₁×C₄₉	C₂×C₅	1	1	yes	characteristic
8	C₅×Dic₃×C₄₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₁₁×C₄₉	Dic₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₅×C₇×C₁₁	C₂×C₇	1	1	yes	characteristic
11	C₄×C₁₁×C₄₉	—	3	1	no	Hall
12	C₃×C₁₁×C₄₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
13	C₄×C₅×C₇×C₁₁	—	3	1	no	—
14	C₂×C₃×C₅×C₄₉	C₂×C₁₁	1	1	yes	characteristic
15	C₃×C₅×C₇×C₁₁	C₄×C₇	1	1	yes	characteristic
16	C₂×C₁₁×C₄₉	C₅×D₃	1	1	yes	characteristic
17	C₄×C₅×C₄₉	—	3	1	no	Hall
18	C₇×C₁₁×Dic₃	C₅×C₇	1	1	yes	characteristic
19	C₂×C₅×C₇×C₁₁	D₃×C₇	1	1	yes	characteristic
20	C₃×C₅×C₄₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₅×C₁₁×Dic₃	C₄₉	1	1	yes	characteristic, direct product factor, Hall
22	Dic₃×C₄₉	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
23	C₁₁×C₄₉	C₅×Dic₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₅×C₄₉	D₃×C₁₁	1	1	yes	characteristic
25	C₂×C₃×C₇×C₁₁	C₂×C₅×C₇	1	1	yes	characteristic
26	C₅×C₇×Dic₃	C₇×C₁₁	1	1	yes	characteristic
27	C₅×C₇×C₁₁	C₇×Dic₃	1	1	yes	characteristic
28	C₂×C₃×C₅×C₁₁	C₂×C₄₉	1	1	yes	characteristic
29	C₄×C₇×C₁₁	—	3	1	no	—
30	C₂×C₃×C₄₉	C₂×C₅×C₁₁	1	1	yes	characteristic
31	C₅×C₄₉	C₁₁×Dic₃	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₇×C₁₁	C₄×C₅×C₇	1	1	yes	characteristic
33	C₄×C₅×C₁₁	—	3	1	no	Hall
34	C₂×C₃×C₅×C₇	C₂×C₇×C₁₁	1	1	yes	characteristic
35	C₄×C₄₉	—	3	1	no	Hall
36	C₃×C₅×C₁₁	C₄×C₄₉	1	1	yes	characteristic, complemented, Hall
37	C₂×C₇×C₁₁	C₅×D₃×C₇	1	1	yes	characteristic
38	C₃×C₄₉	C₄×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
39	C₄×C₅×C₇	—	3	1	no	—
40	C₁₁×Dic₃	C₅×C₄₉	1	1	yes	characteristic, direct product factor, Hall
41	C₂×C₅×C₁₁	D₃×C₄₉	1	1	yes	characteristic
42	C₃×C₅×C₇	C₄×C₇×C₁₁	1	1	yes	characteristic
43	C₂×C₄₉	C₅×D₃×C₁₁	1	1	yes	characteristic
44	C₇×Dic₃	C₅×C₇×C₁₁	1	1	yes	characteristic
45	C₇×C₁₁	C₅×C₇×Dic₃	1	1	yes	characteristic
46	C₂×C₅×C₇	D₃×C₇×C₁₁	1	1	yes	characteristic
47	C₂×C₃×C₁₁	C₂×C₅×C₄₉	1	1	yes	characteristic
48	C₅×Dic₃	C₁₁×C₄₉	1	1	yes	characteristic, direct product factor, Hall
49	C₅×C₁₁	Dic₃×C₄₉	1	1	yes	characteristic, direct product factor, Hall
50	C₄₉	C₅×C₁₁×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
51	C₄×C₁₁	—	3	1	no	Hall
52	C₂×C₃×C₇	C₂×C₅×C₇×C₁₁	1	1	yes	characteristic
53	C₅×C₇	C₇×C₁₁×Dic₃	1	1	yes	characteristic
54	C₃×C₁₁	C₄×C₅×C₄₉	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₅	C₂×C₁₁×C₄₉	1	1	yes	characteristic
56	C₄×C₇	—	3	1	no	—
57	C₂×C₁₁	C₅×D₃×C₄₉	1	1	yes	characteristic
58	C₃×C₇	C₄×C₅×C₇×C₁₁	1	1	yes	characteristic
59	C₄×C₅	—	3	1	no	Hall
60	C₃×C₅	C₄×C₁₁×C₄₉	1	1	yes	characteristic, complemented, Hall
61	C₂×C₇	C₅×D₃×C₇×C₁₁	1	1	yes	characteristic
62	Dic₃	C₅×C₁₁×C₄₉	1	1	yes	characteristic, direct product factor, Hall
63	C₁₁	C₅×Dic₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₅	D₃×C₁₁×C₄₉	1	1	yes	characteristic
65	C₇	C₅×C₇×C₁₁×Dic₃	1	1	yes	characteristic
66	C₂×C₃	C₂×C₅×C₁₁×C₄₉	1	1	yes	characteristic
67	C₅	C₁₁×Dic₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
68	C₄	—	3	1	no	Sylow
69	C₃	C₄×C₅×C₁₁×C₄₉	1	1	yes	characteristic, complemented, Sylow
70	C₂	C₅×D₃×C₁₁×C₄₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₁×C₄₉	D₃
commutator, hypocenter	C₃	C₄×C₅×C₁₁×C₄₉
Frattini	C₂×C₇	C₅×D₃×C₇×C₁₁
Fitting	C₂×C₃×C₅×C₁₁×C₄₉	C₂
socle, prime radical	C₂×C₃×C₅×C₇×C₁₁	C₂×C₇
cosocle	C₂×C₃×C₇	C₂×C₅×C₇×C₁₁
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₁₁×C₄₉

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₁×C₄₉	C₄	semidirect
4. C₁₁×Dic₃×C₄₉	C₅	direct (N × H)
8. C₅×Dic₃×C₄₉	C₁₁	direct (N × H)
9. C₅×C₁₁×C₄₉	Dic₃	direct (N × H)
12. C₃×C₁₁×C₄₉	C₄×C₅	semidirect
20. C₃×C₅×C₄₉	C₄×C₁₁	semidirect
21. C₅×C₁₁×Dic₃	C₄₉	direct (N × H)
22. Dic₃×C₄₉	C₅×C₁₁	direct (N × H)
23. C₁₁×C₄₉	C₅×Dic₃	direct (N × H)
31. C₅×C₄₉	C₁₁×Dic₃	direct (N × H)
36. C₃×C₅×C₁₁	C₄×C₄₉	semidirect
38. C₃×C₄₉	C₄×C₅×C₁₁	semidirect
40. C₁₁×Dic₃	C₅×C₄₉	direct (N × H)
48. C₅×Dic₃	C₁₁×C₄₉	direct (N × H)
49. C₅×C₁₁	Dic₃×C₄₉	direct (N × H)
50. C₄₉	C₅×C₁₁×Dic₃	direct (N × H)
54. C₃×C₁₁	C₄×C₅×C₄₉	semidirect
60. C₃×C₅	C₄×C₁₁×C₄₉	semidirect
62. Dic₃	C₅×C₁₁×C₄₉	direct (N × H)
63. C₁₁	C₅×Dic₃×C₄₉	direct (N × H)
67. C₅	C₁₁×Dic₃×C₄₉	direct (N × H)
69. C₃	C₄×C₅×C₁₁×C₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₁₁×C₄₉	2
C₄×C₅×C₁₁×C₄₉	3
C₁₁×Dic₃×C₄₉	5
C₅×C₇×C₁₁×Dic₃	7
C₅×Dic₃×C₄₉	11

Subgroups — C5×C11×Dic3×C49 #44568310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×Dic₃×C₄₉ #44568310