Subgroups — C₂³×#6037 #13107849

Order 1600.

2960 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×D₅	C₂	1	2	yes	maximal, complemented
2	C₂³×#1039	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#6037	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₅²	C₂²	1	1	yes	characteristic
5	C₂³×C₅×D₅	—	2	16	no	—
6	C₂³×C₅×D₅	C₂²	1	28	yes	complemented
7	C₂²×#1039	C₂²	1	14	yes	complemented
8	C₂×#6037	C₂²	1	112	yes	direct product factor
9	C₂³×C₂²⋊D₅	—	5	2	no	maximal
10	C₂³×C₅²	D₄	1	8	yes	complemented
11	C₂³×C₅²	C₂³	1	7	yes	—
12	C₂²×C₅×D₅	—	2	112	no	—
13	C₂²×C₅×D₅	C₂³	1	56	yes	complemented
14	C₂×#1039	C₂³	1	28	yes	complemented
15	#6037	C₂³	1	64	yes	direct product factor
16	C₂⁵×C₅	—	5	2	no	—
17	C₂⁴×D₅	D₅	1	2	yes	complemented
18	C₂²×C₂²⋊D₅	—	5	56	no	—
19	C₂³×Dic₅	—	5	2	no	—
20	C₂³×Dic₅	—	10	2	no	—
21	C₂²×C₅²	C₂×D₄	1	28	yes	complemented
22	C₂²×C₅²	C₂⁴	1	7	yes	—
23	C₂×C₅×D₅	—	2	112	no	—
24	C₂×C₅×D₅	C₂⁴	1	16	yes	complemented
25	#1039	C₂⁴	1	8	yes	complemented
26	C₂⁴×C₅	—	2	2	no	—
27	C₂⁴×C₅	—	5	28	no	—
28	C₂⁴×C₅	—	10	16	no	—
29	C₂⁴×C₅	C₂×D₅	1	2	yes	—
30	C₂³×D₅	—	2	16	no	—
31	C₂³×D₅	C₂×D₅	1	28	yes	complemented
32	C₂×C₂²⋊D₅	—	5	224	no	—
33	C₂²×Dic₅	—	5	28	no	—
34	C₂²×Dic₅	—	10	28	no	—
35	C₂³×D₄	—	25	1	no	Sylow
36	C₂×C₅²	C₂²×D₄	1	14	yes	complemented
37	C₂×C₅²	C₂⁵	1	1	yes	characteristic
38	C₅×D₅	—	2	16	no	—
39	C₂³×C₅	—	2	16	no	—
40	C₂³×C₅	—	2	14	no	—
41	C₂³×C₅	—	5	56	no	—
42	C₂³×C₅	—	10	112	no	—
43	C₂³×C₅	C₂²⋊D₅	1	16	yes	complemented
44	C₂³×C₅	C₂²×D₅	1	14	yes	—
45	C₂²×D₅	—	2	112	no	—
46	C₂²×D₅	C₂²×D₅	1	56	yes	complemented
47	C₂²⋊D₅	—	5	128	no	—
48	C₂×Dic₅	—	5	56	no	—
49	C₂×Dic₅	—	10	56	no	—
50	C₂⁵	—	5	2	no	—
51	C₂²×D₄	—	25	28	no	—
52	C₂³×C₄	—	25	1	no	—
53	C₅²	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₅	—	2	56	no	—
55	C₂²×C₅	—	2	14	no	—
56	C₂²×C₅	—	5	16	no	—
57	C₂²×C₅	—	10	112	no	—
58	C₂²×C₅	C₂×C₂²⋊D₅	1	56	yes	complemented
59	C₂²×C₅	C₂³×D₅	1	14	yes	—
60	C₂×D₅	—	2	112	no	—
61	C₂×D₅	C₂³×D₅	1	16	yes	complemented
62	Dic₅	—	5	16	no	—
63	Dic₅	—	10	16	no	—
64	C₂⁴	—	5	28	no	—
65	C₂⁴	—	10	16	no	—
66	C₂⁴	D₅²	1	1	yes	characteristic
67	C₂×D₄	—	25	112	no	—
68	C₂²×C₄	—	25	14	no	—
69	C₂×C₅	—	2	28	no	—
70	C₂×C₅	—	2	2	no	—
71	C₂×C₅	—	10	16	no	—
72	C₂×C₅	C₂²×C₂²⋊D₅	1	28	yes	complemented
73	C₂×C₅	C₂⁴×D₅	1	2	yes	—
74	D₅	—	2	16	no	—
75	C₂³	—	5	56	no	—
76	C₂³	—	10	112	no	—
77	C₂³	#6037	1	8	yes	direct product factor
78	C₂³	C₂×D₅²	1	7	yes	—
79	D₄	—	25	64	no	—
80	C₂×C₄	—	25	28	no	—
81	C₅	—	2	2	no	—
82	C₅	C₂³×C₂²⋊D₅	1	2	yes	complemented
83	C₂²	—	5	16	no	—
84	C₂²	—	10	112	no	—
85	C₂²	C₂×#6037	1	28	yes	direct product factor
86	C₂²	C₂²×D₅²	1	7	yes	—
87	C₄	—	25	8	no	—
88	C₂	—	10	16	no	—
89	C₂	C₂²×#6037	1	14	yes	direct product factor
90	C₂	C₂³×D₅²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴	D₅²
commutator, cosocle	C₂×C₅²	C₂⁵
Frattini	C₂	C₂³×D₅²
Fitting, socle	C₂⁴×C₅²	C₂²
hypocenter	C₅²	C₂³×D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₅×D₅	C₂	semidirect
2. C₂³×#1039	C₂	semidirect
3. C₂²×#6037	C₂	direct (N × H)
6. C₂³×C₅×D₅	C₂²	semidirect
7. C₂²×#1039	C₂²	semidirect
8. C₂×#6037	C₂²	direct (N × H)
10. C₂³×C₅²	D₄	semidirect
13. C₂²×C₅×D₅	C₂³	semidirect
14. C₂×#1039	C₂³	semidirect
15. #6037	C₂³	direct (N × H)
17. C₂⁴×D₅	D₅	semidirect
21. C₂²×C₅²	C₂×D₄	semidirect
24. C₂×C₅×D₅	C₂⁴	semidirect
25. #1039	C₂⁴	semidirect
31. C₂³×D₅	C₂×D₅	semidirect
36. C₂×C₅²	C₂²×D₄	semidirect
43. C₂³×C₅	C₂²⋊D₅	semidirect
46. C₂²×D₅	C₂²×D₅	semidirect
53. C₅²	C₂³×D₄	semidirect
58. C₂²×C₅	C₂×C₂²⋊D₅	semidirect
61. C₂×D₅	C₂³×D₅	semidirect
72. C₂×C₅	C₂²×C₂²⋊D₅	semidirect
77. C₂³	#6037	direct (N × H)
82. C₅	C₂³×C₂²⋊D₅	semidirect
85. C₂²	C₂×#6037	direct (N × H)
89. C₂	C₂²×#6037	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₅×D₅	2
C₂³×#1039	2
C₂²×#6037	2
C₂³×C₂²⋊D₅	5

Subgroups — C23×#6037 #13107849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#6037 #13107849