Subgroups — C₂²×C₄⋊#1039 #13107313

Order 1600.

1672 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₂³×#1039	C₂	1	2	yes	maximal
3	C₂×C₄⋊#1039	C₂	1	12	yes	maximal, direct product factor
4	C₂⁴×C₅²	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₅²	C₄	1	8	yes	complemented
6	C₂²×C₄×C₅²	C₂²	1	6	yes	—
7	C₂²×#1039	—	2	8	no	—
8	C₂²×#1039	C₂²	1	12	yes	—
9	C₄⋊#1039	C₂²	1	16	yes	direct product factor
10	C₂²×C₄⋊Dic₅	—	5	6	no	maximal
11	C₂³×C₅²	C₂×C₄	1	4	yes	—
12	C₂³×C₅²	D₄	1	4	yes	—
13	C₂³×C₅²	Q₈	1	4	yes	—
14	C₂³×C₅²	C₂³	1	3	yes	—
15	C₂×C₄×C₅²	C₂×C₄	1	24	yes	complemented
16	C₂×C₄×C₅²	C₂³	1	4	yes	—
17	C₂×#1039	—	2	24	no	—
18	C₂×#1039	C₂³	1	8	yes	—
19	C₂³×C₄×C₅	D₅	1	6	yes	—
20	C₂³×Dic₅	—	5	12	no	—
21	C₂×C₄⋊Dic₅	—	5	72	no	—
22	C₂²×C₅²	C₄⋊C₄	1	16	yes	complemented
23	C₂²×C₅²	C₂²×C₄	1	6	yes	—
24	C₂²×C₅²	C₂×D₄	1	6	yes	—
25	C₂²×C₅²	C₂×Q₈	1	6	yes	—
26	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
27	C₄×C₅²	C₂²×C₄	1	8	yes	complemented
28	#1039	—	2	8	no	—
29	C₂⁴×C₅	C₂×D₅	1	6	yes	—
30	C₂²×C₄×C₅	Dic₅	1	48	yes	complemented
31	C₂²×C₄×C₅	C₂×D₅	1	36	yes	—
32	C₂²×Dic₅	—	5	72	no	—
33	C₂²×Dic₅	—	10	48	no	—
34	C₄⋊Dic₅	—	5	96	no	—
35	C₂²×C₄⋊C₄	—	25	1	no	Sylow
36	C₂×C₅²	C₂×C₄⋊C₄	1	12	yes	complemented
37	C₂×C₅²	C₂³×C₄	1	1	yes	characteristic
38	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
39	C₂×C₅²	C₂²×Q₈	1	1	yes	characteristic
40	C₂³×C₅	Dic₁₀	1	24	yes	—
41	C₂³×C₅	D₂₀	1	24	yes	—
42	C₂³×C₅	C₂×Dic₅	1	24	yes	—
43	C₂³×C₅	C₂²×D₅	1	18	yes	—
44	C₂×C₄×C₅	C₂×Dic₅	1	144	yes	complemented
45	C₂×C₄×C₅	C₂²×D₅	1	24	yes	—
46	C₂×Dic₅	—	5	48	no	—
47	C₂×Dic₅	—	10	144	no	—
48	C₂³×C₄	—	25	2	no	—
49	C₂³×C₄	C₅⋊D₅	1	1	yes	characteristic
50	C₂×C₄⋊C₄	—	25	12	no	—
51	C₅²	C₂²×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₅	C₄⋊Dic₅	1	96	yes	complemented
53	C₂²×C₅	C₂×Dic₁₀	1	36	yes	—
54	C₂²×C₅	C₂×D₂₀	1	36	yes	—
55	C₂²×C₅	C₂²×Dic₅	1	36	yes	—
56	C₂²×C₅	C₂³×D₅	1	6	yes	—
57	C₄×C₅	C₂²×Dic₅	1	48	yes	complemented
58	Dic₅	—	10	48	no	—
59	C₂⁴	C₂×C₅⋊D₅	1	1	yes	characteristic
60	C₂²×C₄	—	25	12	no	—
61	C₂²×C₄	—	50	8	no	—
62	C₂²×C₄	#1039	1	8	yes	complemented
63	C₂²×C₄	C₂×C₅⋊D₅	1	6	yes	—
64	C₄⋊C₄	—	25	16	no	—
65	C₂×C₅	C₂×C₄⋊Dic₅	1	72	yes	complemented
66	C₂×C₅	C₂²×Dic₁₀	1	6	yes	—
67	C₂×C₅	C₂²×D₂₀	1	6	yes	—
68	C₂×C₅	C₂³×Dic₅	1	6	yes	—
69	C₂³	#6045	1	4	yes	—
70	C₂³	C₄⋊(C₅⋊D₅)	1	4	yes	—
71	C₂³	C₂×#1039	1	4	yes	—
72	C₂³	C₂²×C₅⋊D₅	1	3	yes	—
73	C₂×C₄	—	25	8	no	—
74	C₂×C₄	—	50	24	no	—
75	C₂×C₄	C₂×#1039	1	24	yes	complemented
76	C₂×C₄	C₂²×C₅⋊D₅	1	4	yes	—
77	C₅	C₂²×C₄⋊Dic₅	1	6	yes	complemented
78	C₂²	C₄⋊#1039	1	16	yes	direct product factor
79	C₂²	C₂×#6045	1	6	yes	—
80	C₂²	C₂×C₄⋊(C₅⋊D₅)	1	6	yes	—
81	C₂²	C₂²×#1039	1	6	yes	—
82	C₂²	C₂³×C₅⋊D₅	1	1	yes	characteristic
83	C₄	—	50	8	no	—
84	C₄	C₂²×#1039	1	8	yes	complemented
85	C₂	C₂×C₄⋊#1039	1	12	yes	direct product factor
86	C₂	C₂²×#6045	1	1	yes	characteristic
87	C₂	C₂²×C₄⋊(C₅⋊D₅)	1	1	yes	characteristic
88	C₂	C₂³×#1039	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₅⋊D₅
commutator	C₂×C₅²	C₂³×C₄
Frattini	C₂²	C₂³×C₅⋊D₅
Fitting	C₂³×C₄×C₅²	C₂
socle, prime radical	C₂⁴×C₅²	C₂²
cosocle	C₂²×C₅²	C₂⁴
hypercenter	C₂³×C₄	C₅⋊D₅
hypocenter	C₅²	C₂²×C₄⋊C₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₄⋊#1039	C₂	direct (N × H)
5. C₂²×C₄×C₅²	C₄	semidirect
9. C₄⋊#1039	C₂²	direct (N × H)
15. C₂×C₄×C₅²	C₂×C₄	semidirect
22. C₂²×C₅²	C₄⋊C₄	semidirect
27. C₄×C₅²	C₂²×C₄	semidirect
30. C₂²×C₄×C₅	Dic₅	semidirect
36. C₂×C₅²	C₂×C₄⋊C₄	semidirect
44. C₂×C₄×C₅	C₂×Dic₅	semidirect
51. C₅²	C₂²×C₄⋊C₄	semidirect
52. C₂²×C₅	C₄⋊Dic₅	semidirect
57. C₄×C₅	C₂²×Dic₅	semidirect
62. C₂²×C₄	#1039	semidirect
65. C₂×C₅	C₂×C₄⋊Dic₅	semidirect
75. C₂×C₄	C₂×#1039	semidirect
77. C₅	C₂²×C₄⋊Dic₅	semidirect
78. C₂²	C₄⋊#1039	direct (N × H)
84. C₄	C₂²×#1039	semidirect
85. C₂	C₂×C₄⋊#1039	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₅²	2
C₂³×#1039	2
C₂×C₄⋊#1039	2
C₂²×C₄⋊Dic₅	5

Subgroups — C22×C4⋊#1039 #13107313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄⋊#1039 #13107313