Subgroups — C₂³×#6029 #13107308

Order 1600.

1352 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	C₂²×#6029	C₂	1	14	yes	maximal, direct product factor
3	C₂⁴×C₅²	C₄	1	1	yes	characteristic
4	C₂²×C₄×C₅²	C₄	1	7	yes	—
5	C₂²×C₄×C₅²	C₂²	1	7	yes	—
6	C₂×#6029	C₂²	1	28	yes	direct product factor
7	C₂³×#168	—	5	6	no	maximal
8	C₂³×C₅²	C₈	1	8	yes	complemented
9	C₂³×C₅²	C₂×C₄	1	7	yes	—
10	C₂×C₄×C₅²	C₂×C₄	1	21	yes	—
11	C₂×C₄×C₅²	C₂³	1	7	yes	—
12	#6029	C₂³	1	8	yes	direct product factor
13	C₂³×C₄×C₅	D₅	1	6	yes	—
14	C₂²×#168	—	5	84	no	—
15	C₂²×C₅²	C₂×C₈	1	28	yes	complemented
16	C₂²×C₅²	C₂²×C₄	1	7	yes	—
17	C₄×C₅²	C₂²×C₄	1	7	yes	—
18	C₄×C₅²	C₂⁴	1	1	yes	characteristic
19	C₂⁴×C₅	Dic₅	1	6	yes	—
20	C₂²×C₄×C₅	Dic₅	1	42	yes	—
21	C₂²×C₄×C₅	C₂×D₅	1	42	yes	—
22	C₂×#168	—	5	168	no	—
23	C₂³×C₈	—	25	1	no	Sylow
24	C₂×C₅²	C₂²×C₈	1	14	yes	complemented
25	C₂×C₅²	C₂³×C₄	1	1	yes	characteristic
26	C₂³×C₅	#168	1	48	yes	complemented
27	C₂³×C₅	C₂×Dic₅	1	42	yes	—
28	C₂×C₄×C₅	C₂×Dic₅	1	126	yes	—
29	C₂×C₄×C₅	C₂²×D₅	1	42	yes	—
30	#168	—	5	48	no	—
31	C₂³×C₄	C₅⋊D₅	1	1	yes	characteristic
32	C₂²×C₈	—	25	14	no	—
33	C₅²	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
34	C₂²×C₅	C₂×#168	1	168	yes	complemented
35	C₂²×C₅	C₂²×Dic₅	1	42	yes	—
36	C₄×C₅	C₂²×Dic₅	1	42	yes	—
37	C₄×C₅	C₂³×D₅	1	6	yes	—
38	C₂⁴	#1039	1	1	yes	characteristic
39	C₂²×C₄	#1039	1	7	yes	—
40	C₂²×C₄	C₂×C₅⋊D₅	1	7	yes	—
41	C₂×C₈	—	25	28	no	—
42	C₂×C₅	C₂²×#168	1	84	yes	complemented
43	C₂×C₅	C₂³×Dic₅	1	6	yes	—
44	C₂³	#6029	1	8	yes	direct product factor
45	C₂³	C₂×#1039	1	7	yes	—
46	C₂×C₄	C₂×#1039	1	21	yes	—
47	C₂×C₄	C₂²×C₅⋊D₅	1	7	yes	—
48	C₈	—	25	8	no	—
49	C₅	C₂³×#168	1	6	yes	complemented
50	C₂²	C₂×#6029	1	28	yes	direct product factor
51	C₂²	C₂²×#1039	1	7	yes	—
52	C₄	C₂²×#1039	1	7	yes	—
53	C₄	C₂³×C₅⋊D₅	1	1	yes	characteristic
54	C₂	C₂²×#6029	1	14	yes	direct product factor
55	C₂	C₂³×#1039	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	C₅⋊D₅
commutator, hypocenter	C₅²	C₂³×C₈
Frattini	C₄	C₂³×C₅⋊D₅
Fitting	C₂³×C₄×C₅²	C₂
socle, prime radical	C₂⁴×C₅²	C₄
cosocle	C₄×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
2. C₂²×#6029	C₂	direct (N × H)
6. C₂×#6029	C₂²	direct (N × H)
8. C₂³×C₅²	C₈	semidirect
12. #6029	C₂³	direct (N × H)
15. C₂²×C₅²	C₂×C₈	semidirect
24. C₂×C₅²	C₂²×C₈	semidirect
26. C₂³×C₅	#168	semidirect
33. C₅²	C₂³×C₈	semidirect
34. C₂²×C₅	C₂×#168	semidirect
42. C₂×C₅	C₂²×#168	semidirect
44. C₂³	#6029	direct (N × H)
49. C₅	C₂³×#168	semidirect
50. C₂²	C₂×#6029	direct (N × H)
54. C₂	C₂²×#6029	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
C₂²×#6029	2
C₂³×#168	5

Subgroups — C23×#6029 #13107308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#6029 #13107308