Subgroups — C₂²×C₄×#1039 #13107310

Order 1600.

1992 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	C₄	1	16	yes	direct product factor
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	8	yes	—
12	C₂³×C₅²	C₂×C₄	1	4	yes	—
13	C₂³×C₅²	C₂³	1	3	yes	—
14	C₂×C₄×C₅²	C₂×C₄	1	24	yes	complemented
15	C₂×C₄×C₅²	C₂³	1	4	yes	—
16	C₂×#1039	C₂×C₄	1	48	yes	direct product factor
17	C₂×#1039	C₂³	1	8	yes	—
18	C₂³×C₄×C₅	D₅	1	6	yes	—
19	C₂³×Dic₅	—	5	12	no	—
20	C₂×C₄×Dic₅	—	5	72	no	—
21	C₂²×C₅²	C₄²	1	16	yes	complemented
22	C₂²×C₅²	C₂²×C₄	1	12	yes	—
23	C₂²×C₅²	C₂²×C₄	1	6	yes	—
24	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
25	C₄×C₅²	C₂²×C₄	1	8	yes	complemented
26	#1039	C₂²×C₄	1	16	yes	direct product factor
27	C₂⁴×C₅	C₂×D₅	1	6	yes	—
28	C₂²×C₄×C₅	Dic₅	1	48	yes	complemented
29	C₂²×C₄×C₅	C₂×D₅	1	36	yes	—
30	C₂²×Dic₅	—	5	96	no	—
31	C₂²×Dic₅	—	5	72	no	—
32	C₄×Dic₅	—	5	96	no	—
33	C₂²×C₄²	—	25	1	no	Sylow
34	C₂×C₅²	C₂×C₄²	1	12	yes	complemented
35	C₂×C₅²	C₂³×C₄	1	2	yes	—
36	C₂×C₅²	C₂³×C₄	1	1	yes	characteristic
37	C₂³×C₅	C₄×D₅	1	48	yes	—
38	C₂³×C₅	C₂×Dic₅	1	24	yes	—
39	C₂³×C₅	C₂²×D₅	1	18	yes	—
40	C₂×C₄×C₅	C₂×Dic₅	1	144	yes	complemented
41	C₂×C₄×C₅	C₂²×D₅	1	24	yes	—
42	C₂×Dic₅	—	5	288	no	—
43	C₂×Dic₅	—	5	48	no	—
44	C₂³×C₄	—	25	2	no	—
45	C₂³×C₄	C₅⋊D₅	1	1	yes	characteristic
46	C₂×C₄²	—	25	12	no	—
47	C₅²	C₂²×C₄²	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₅	C₄×Dic₅	1	96	yes	complemented
49	C₂²×C₅	C₂×C₄×D₅	1	72	yes	—
50	C₂²×C₅	C₂²×Dic₅	1	36	yes	—
51	C₂²×C₅	C₂³×D₅	1	6	yes	—
52	C₄×C₅	C₂²×Dic₅	1	48	yes	complemented
53	Dic₅	—	5	96	no	—
54	C₂⁴	C₂×C₅⋊D₅	1	1	yes	characteristic
55	C₂²×C₄	—	25	16	no	—
56	C₂²×C₄	—	25	12	no	—
57	C₂²×C₄	#1039	1	8	yes	direct product factor
58	C₂²×C₄	C₂×C₅⋊D₅	1	6	yes	—
59	C₄²	—	25	16	no	—
60	C₂×C₅	C₂×C₄×Dic₅	1	72	yes	complemented
61	C₂×C₅	C₂²×C₄×D₅	1	12	yes	—
62	C₂×C₅	C₂³×Dic₅	1	6	yes	—
63	C₂³	C₄×C₅⋊D₅	1	8	yes	—
64	C₂³	C₂×#1039	1	4	yes	—
65	C₂³	C₂²×C₅⋊D₅	1	3	yes	—
66	C₂×C₄	—	25	48	no	—
67	C₂×C₄	—	25	8	no	—
68	C₂×C₄	C₂×#1039	1	24	yes	direct product factor
69	C₂×C₄	C₂²×C₅⋊D₅	1	4	yes	—
70	C₅	C₂²×C₄×Dic₅	1	6	yes	complemented
71	C₂²	C₄×#1039	1	16	yes	direct product factor
72	C₂²	C₂×C₄×C₅⋊D₅	1	12	yes	—
73	C₂²	C₂²×#1039	1	6	yes	—
74	C₂²	C₂³×C₅⋊D₅	1	1	yes	characteristic
75	C₄	—	25	16	no	—
76	C₄	C₂²×#1039	1	8	yes	direct product factor
77	C₂	C₂×C₄×#1039	1	12	yes	direct product factor
78	C₂	C₂²×C₄×C₅⋊D₅	1	2	yes	—
79	C₂	C₂³×#1039	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	C₅⋊D₅
commutator, hypocenter	C₅²	C₂²×C₄²
Frattini	C₂²	C₂³×C₅⋊D₅
Fitting	C₂³×C₄×C₅²	C₂
socle, prime radical	C₂⁴×C₅²	C₂²
cosocle	C₂²×C₅²	C₂⁴
LCS	G ▷ C₅²
UCS	C₁ ◁ 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
7. C₂²×#1039	C₄	direct (N × H)
9. C₄×#1039	C₂²	direct (N × H)
14. C₂×C₄×C₅²	C₂×C₄	semidirect
16. C₂×#1039	C₂×C₄	direct (N × H)
21. C₂²×C₅²	C₄²	semidirect
25. C₄×C₅²	C₂²×C₄	semidirect
26. #1039	C₂²×C₄	direct (N × H)
28. C₂²×C₄×C₅	Dic₅	semidirect
34. C₂×C₅²	C₂×C₄²	semidirect
40. C₂×C₄×C₅	C₂×Dic₅	semidirect
47. C₅²	C₂²×C₄²	semidirect
48. C₂²×C₅	C₄×Dic₅	semidirect
52. C₄×C₅	C₂²×Dic₅	semidirect
57. C₂²×C₄	#1039	direct (N × H)
60. C₂×C₅	C₂×C₄×Dic₅	semidirect
68. C₂×C₄	C₂×#1039	direct (N × H)
70. C₅	C₂²×C₄×Dic₅	semidirect
71. C₂²	C₄×#1039	direct (N × H)
76. C₄	C₂²×#1039	direct (N × H)
77. 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 #13107310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×#1039 #13107310