Subgroups — C₂²⋊(#1039⋊C₅) #14522213

Order 2000.

183 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×H(3,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	C₂×#1039⋊C₅	C₂	1	2	yes	maximal, complemented
3	C₂²×H(3,𝔽₅)	—	2	2	no	—
4	C₂²×H(3,𝔽₅)	C₄	1	2	yes	complemented
5	C₂²×H(3,𝔽₅)	C₂²	1	1	yes	characteristic
6	#1039⋊C₅	—	2	2	no	—
7	C₂²⋊#1039	C₅	1	1	yes	maximal, characteristic, complemented
8	C₅×C₂²⋊Dic₅	—	5	1	no	maximal
9	C₂×H(3,𝔽₅)	—	2	2	no	—
10	C₂×H(3,𝔽₅)	C₂×C₄	1	1	yes	characteristic
11	C₂×H(3,𝔽₅)	D₄	1	2	yes	—
12	C₂³×C₅²	—	2	2	no	—
13	C₂³×C₅²	D₅	1	1	yes	characteristic
14	C₂³×C₅²	C₂×C₅	1	1	yes	characteristic
15	C₂×#1039	C₂×C₅	1	2	yes	complemented
16	C₂×C₅×Dic₅	—	5	2	no	—
17	H(3,𝔽₅)	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₅²	—	2	8	no	—
19	C₂²×C₅²	—	2	4	no	—
20	C₂²×C₅²	—	2	2	no	—
21	C₂²×C₅²	—	2	2	no	—
22	C₂²×C₅²	—	2	2	no	—
23	C₂²×C₅²	Dic₅	1	2	yes	complemented
24	C₂²×C₅²	C₄×C₅	1	2	yes	complemented
25	C₂²×C₅²	C₂×D₅	1	1	yes	characteristic
26	C₂²×C₅²	C₂²×C₅	1	1	yes	characteristic
27	#1039	—	2	2	no	—
28	C₅×Dic₅	—	10	2	no	—
29	C₅×C₂²⋊C₄	—	25	1	no	—
30	C₂²⋊Dic₅	—	5	1	no	—
31	C₂²⋊Dic₅	—	25	1	no	—
32	C₂×C₅²	—	2	8	no	—
33	C₂×C₅²	—	2	2	no	—
34	C₂×C₅²	—	2	2	no	—
35	C₂×C₅²	—	2	2	no	—
36	C₂×C₅²	—	2	4	no	—
37	C₂×C₅²	C₂×Dic₅	1	1	yes	characteristic
38	C₂×C₅²	C₂²⋊D₅	1	2	yes	—
39	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
40	C₂×C₅²	C₅×D₄	1	2	yes	—
41	C₂³×C₅	—	5	1	no	—
42	C₂³×C₅	—	5	1	no	—
43	C₂³×C₅	—	10	2	no	—
44	C₂³×C₅	C₅×D₅	1	1	yes	characteristic
45	C₂×C₄×C₅	—	25	2	no	—
46	C₂×Dic₅	—	5	2	no	—
47	C₂×Dic₅	—	25	2	no	—
48	C₅²	—	2	2	no	—
49	C₅²	C₂²⋊Dic₅	1	1	yes	characteristic, complemented
50	C₅²	C₅×C₂²⋊C₄	1	1	yes	characteristic, complemented
51	C₂²×C₅	—	2	2	no	—
52	C₂²×C₅	—	5	2	no	—
53	C₂²×C₅	—	5	2	no	—
54	C₂²×C₅	—	5	1	no	—
55	C₂²×C₅	—	5	1	no	—
56	C₂²×C₅	—	10	2	no	—
57	C₂²×C₅	—	10	2	no	—
58	C₂²×C₅	—	10	8	no	—
59	C₂²×C₅	—	10	4	no	—
60	C₂²×C₅	—	10	2	no	—
61	C₂²×C₅	C₅×Dic₅	1	2	yes	—
62	C₂²×C₅	C₂×C₅×D₅	1	1	yes	characteristic
63	C₄×C₅	—	50	2	no	—
64	Dic₅	—	10	2	no	—
65	Dic₅	—	50	2	no	—
66	C₂²⋊C₄	—	25	1	no	Sylow
67	C₂×C₅	—	2	2	no	—
68	C₂×C₅	—	5	1	no	—
69	C₂×C₅	—	5	1	no	—
70	C₂×C₅	—	5	2	no	—
71	C₂×C₅	—	5	2	no	—
72	C₂×C₅	—	10	2	no	—
73	C₂×C₅	—	10	2	no	—
74	C₂×C₅	—	10	8	no	—
75	C₂×C₅	—	10	2	no	—
76	C₂×C₅	—	10	4	no	—
77	C₂×C₅	C₂×C₅×Dic₅	1	1	yes	characteristic
78	C₂×C₅	C₅×C₂²⋊D₅	1	2	yes	—
79	C₂³	(C₅⋊D₅)⋊C₅	1	1	yes	characteristic
80	C₂×C₄	—	25	2	no	—
81	C₅	—	5	1	no	—
82	C₅	—	5	1	no	—
83	C₅	—	10	2	no	—
84	C₅	C₅×C₂²⋊Dic₅	1	1	yes	characteristic
85	C₂²	—	2	2	no	—
86	C₂²	#1039⋊C₅	1	2	yes	complemented
87	C₂²	C₂×(C₅⋊D₅)⋊C₅	1	1	yes	characteristic
88	C₄	—	50	2	no	—
89	C₂	—	2	2	no	—
90	C₂	C₂×#1039⋊C₅	1	1	yes	characteristic
91	C₂	C₂²⋊((C₅⋊D₅)⋊C₅)	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×(C₅⋊D₅)⋊C₅
commutator	C₂×C₅²	C₂×C₄×C₅
Frattini, socle	C₂²×C₅	C₂×C₅×D₅
Fitting, prime radical	C₂³×H(3,𝔽₅)	C₂
cosocle	C₂²×C₅²	C₂²×C₅
hypercenter	C₂³	(C₅⋊D₅)⋊C₅
hypocenter	C₅²	C₅×C₂²⋊C₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. C₂×#1039⋊C₅	C₂	semidirect
4. C₂²×H(3,𝔽₅)	C₄	semidirect
7. C₂²⋊#1039	C₅	semidirect
15. C₂×#1039	C₂×C₅	semidirect
17. H(3,𝔽₅)	C₂²⋊C₄	semidirect
23. C₂²×C₅²	Dic₅	semidirect
24. C₂²×C₅²	C₄×C₅	semidirect
49. C₅²	C₂²⋊Dic₅	semidirect
50. C₅²	C₅×C₂²⋊C₄	semidirect
86. C₂²	#1039⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₂³×H(3,𝔽₅)	2
C₂×#1039⋊C₅	2
C₂²⋊#1039	5
C₅×C₂²⋊Dic₅	5

Subgroups — C22⋊(#1039⋊C5) #14522213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊(#1039⋊C₅) #14522213