Subgroups — D₁₄₃⋊D₅₅ #44538270

Order 31460.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×D₁₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₇₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₅⋊(C₁₁⋊D₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₁²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	(C₁₁⋊D₁₁)⋊D₁₃	—	5	1	no	maximal, Hall
6	C₁₃×C₁₁⋊D₁₁	—	5	1	no	—
7	C₁₁×D₁₄₃	—	5	1	no	—
8	C₁₁×D₁₄₃	D₅	1	1	yes	characteristic, complemented
9	D₅₅⋊D₁₃	—	11	1	no	maximal
10	D₁₃×D₅₅	—	11	1	no	maximal
11	D₁₁×D₅₅	—	13	1	no	maximal, Hall
12	C₁₁²×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
13	D₇₁₅	D₁₁	1	1	yes	characteristic, complemented
14	C₁₃×D₅₅	—	11	1	no	—
15	C₁₃×D₅₅	—	11	1	no	—
16	C₁₃×D₅₅	—	22	5	no	—
17	C₁₁×D₆₅	—	11	1	no	—
18	C₅×D₁₄₃	D₁₁	1	1	yes	characteristic, complemented
19	C₅×C₁₁×D₁₃	—	11	1	no	—
20	C₅⋊(C₁₁⋊D₁₁)	D₁₃	1	1	yes	characteristic, complemented
21	C₁₁×D₅₅	—	13	1	no	—
22	C₅×C₁₁×D₁₁	—	13	1	no	—
23	C₅×C₁₁×C₁₃	—	2	5	no	—
24	C₅×C₁₁×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented
25	C₅×C₁₁×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented
26	C₅×C₁₁²	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
27	D₁₁×D₁₃	—	55	1	no	—
28	D₁₁×D₁₃	—	55	1	no	—
29	D₁₁²	—	65	1	no	Hall
30	D₁₄₃	—	5	1	no	—
31	D₁₄₃	D₅₅	1	1	yes	characteristic, complemented
32	C₁₁×D₁₃	—	11	1	no	—
33	C₁₁×D₁₃	—	55	1	no	—
34	C₁₃×D₁₁	—	55	1	no	—
35	C₁₃×D₁₁	—	55	1	no	—
36	C₁₃×D₁₁	—	110	5	no	—
37	D₅×D₁₃	—	121	1	no	Hall
38	C₁₁⋊D₁₁	—	5	1	no	—
39	C₁₁×D₁₁	—	13	1	no	—
40	C₁₁×D₁₁	—	65	1	no	—
41	C₂×D₅₅	—	143	1	no	—
42	D₅×D₁₁	—	143	1	no	—
43	C₁₁×C₁₃	—	2	5	no	—
44	C₁₁×C₁₃	D₅×D₁₁	1	1	yes	characteristic, complemented
45	C₁₁×C₁₃	C₂×D₅₅	1	1	yes	characteristic, complemented
46	D₆₅	—	11	1	no	—
47	C₅×D₁₃	—	11	1	no	—
48	D₅×C₁₃	—	121	1	no	—
49	C₁₁²	D₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₅×C₁₁	—	143	1	no	—
51	D₅₅	—	11	1	no	—
52	D₅₅	—	11	1	no	—
53	D₅₅	—	13	1	no	—
54	D₅₅	—	22	5	no	—
55	C₅×D₁₁	—	13	1	no	—
56	D₅×C₁₁	—	143	1	no	—
57	C₅×C₁₃	D₁₁²	1	1	yes	characteristic, complemented, Hall
58	C₅×C₁₁	—	2	5	no	—
59	C₅×C₁₁	D₁₁×D₁₃	1	1	yes	characteristic, complemented
60	C₅×C₁₁	D₁₁×D₁₃	1	1	yes	characteristic, complemented
61	C₂×D₁₃	—	605	1	no	Hall
62	C₂×D₁₁	—	715	1	no	—
63	C₂×D₁₁	—	715	1	no	—
64	C₂×C₁₃	—	605	1	no	—
65	D₁₃	—	11	1	no	—
66	D₁₃	—	55	1	no	—
67	C₂×C₁₁	—	143	1	no	—
68	C₂×C₁₁	—	715	1	no	—
69	D₁₁	—	13	1	no	—
70	D₁₁	—	55	1	no	—
71	D₁₁	—	55	1	no	—
72	D₁₁	—	65	1	no	—
73	D₁₁	—	110	5	no	—
74	C₂×D₅	—	1573	1	no	Hall
75	C₁₃	D₁₁×D₅₅	1	1	yes	characteristic, complemented, Sylow
76	C₁₁	—	2	5	no	—
77	C₁₁	D₁₃×D₅₅	1	1	yes	characteristic, complemented
78	C₁₁	D₅₅⋊D₁₃	1	1	yes	characteristic, complemented
79	C₂×C₅	—	143	1	no	—
80	D₅	—	121	1	no	—
81	D₅	—	143	1	no	—
82	C₅	(C₁₁⋊D₁₁)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	7865	1	no	Sylow
84	C₂	—	605	1	no	—
85	C₂	—	143	1	no	—
86	C₂	—	715	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁²×C₁₃	C₂²
LCS	G ▷ C₅×C₁₁²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×D₁₄₃	C₂	semidirect
2. C₁₁×D₇₁₅	C₂	semidirect
3. C₁₃×C₅⋊(C₁₁⋊D₁₁)	C₂	semidirect
4. C₅×C₁₁²×C₁₃	C₂²	semidirect
8. C₁₁×D₁₄₃	D₅	semidirect
12. C₁₁²×C₁₃	C₂×D₅	semidirect
13. D₇₁₅	D₁₁	semidirect
18. C₅×D₁₄₃	D₁₁	semidirect
20. C₅⋊(C₁₁⋊D₁₁)	D₁₃	semidirect
24. C₅×C₁₁×C₁₃	C₂×D₁₁	semidirect
25. C₅×C₁₁×C₁₃	C₂×D₁₁	semidirect
26. C₅×C₁₁²	C₂×D₁₃	semidirect
31. D₁₄₃	D₅₅	semidirect
44. C₁₁×C₁₃	D₅×D₁₁	semidirect
45. C₁₁×C₁₃	C₂×D₅₅	semidirect
49. C₁₁²	D₅×D₁₃	semidirect
57. C₅×C₁₃	D₁₁²	semidirect
59. C₅×C₁₁	D₁₁×D₁₃	semidirect
60. C₅×C₁₁	D₁₁×D₁₃	semidirect
75. C₁₃	D₁₁×D₅₅	semidirect
77. C₁₁	D₁₃×D₅₅	semidirect
78. C₁₁	D₅₅⋊D₁₃	semidirect
82. C₅	(C₁₁⋊D₁₁)⋊D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₁×D₁₄₃	2
C₁₁×D₇₁₅	2
C₁₃×C₅⋊(C₁₁⋊D₁₁)	2
(C₁₁⋊D₁₁)⋊D₁₃	5
D₅₅⋊D₁₃	11
D₁₃×D₅₅	11
D₁₁×D₅₅	13

Subgroups — D143⋊D55 #44538270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₄₃⋊D₅₅ #44538270