Subgroups — C₂³×#6016 #13099679

Order 1600.

507 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6016	C₂	1	14	yes	maximal, direct product factor
3	C₂⁴×C₂₅	C₄	1	1	yes	characteristic
4	C₂²×Dic₂₅	C₄	1	7	yes	—
5	C₂²×Dic₂₅	C₂²	1	7	yes	—
6	C₂×#6016	C₂²	1	28	yes	direct product factor
7	C₂³×#170	—	5	1	no	maximal
8	C₂³×C₂₅	C₈	1	8	yes	complemented
9	C₂³×C₂₅	C₂×C₄	1	7	yes	—
10	C₂×Dic₂₅	C₂×C₄	1	21	yes	—
11	C₂×Dic₂₅	C₂³	1	7	yes	—
12	#6016	C₂³	1	8	yes	direct product factor
13	C₂³×Dic₅	—	5	1	no	—
14	C₂²×#170	—	5	14	no	—
15	C₂²×C₂₅	C₂×C₈	1	28	yes	complemented
16	C₂²×C₂₅	C₂²×C₄	1	7	yes	—
17	Dic₂₅	C₂²×C₄	1	7	yes	—
18	Dic₂₅	C₂⁴	1	1	yes	characteristic
19	C₂⁴×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
20	C₂²×Dic₅	—	5	7	no	—
21	C₂²×Dic₅	—	5	7	no	—
22	C₂×#170	—	5	28	no	—
23	C₂³×C₈	—	25	1	no	Sylow
24	C₂×C₂₅	C₂²×C₈	1	14	yes	complemented
25	C₂×C₂₅	C₂³×C₄	1	1	yes	characteristic
26	C₂³×C₅	#170	1	8	yes	—
27	C₂³×C₅	C₂×AGL(1,𝔽₅)	1	7	yes	—
28	C₂×Dic₅	—	5	21	no	—
29	C₂×Dic₅	—	5	7	no	—
30	#170	—	5	8	no	—
31	C₂³×C₄	—	25	1	no	—
32	C₂²×C₈	—	25	14	no	—
33	C₂₅	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
34	C₂²×C₅	C₂×#170	1	28	yes	—
35	C₂²×C₅	C₂²×AGL(1,𝔽₅)	1	7	yes	—
36	Dic₅	—	5	7	no	—
37	Dic₅	—	5	1	no	—
38	C₂⁴	#1035	1	1	yes	characteristic
39	C₂²×C₄	—	25	7	no	—
40	C₂²×C₄	—	25	7	no	—
41	C₂×C₈	—	25	28	no	—
42	C₂×C₅	C₂²×#170	1	14	yes	—
43	C₂×C₅	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
44	C₂³	#6016	1	8	yes	direct product factor
45	C₂³	C₂×#1035	1	7	yes	—
46	C₂×C₄	—	25	7	no	—
47	C₂×C₄	—	25	21	no	—
48	C₈	—	25	8	no	—
49	C₅	C₂³×#170	1	1	yes	characteristic
50	C₂²	C₂×#6016	1	28	yes	direct product factor
51	C₂²	C₂²×#1035	1	7	yes	—
52	C₄	—	25	1	no	—
53	C₄	—	25	7	no	—
54	C₂	C₂²×#6016	1	14	yes	direct product factor
55	C₂	C₂³×#1035	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴	#1035
commutator, hypocenter	C₂₅	C₂³×C₈
Frattini	C₂×C₅	C₂³×AGL(1,𝔽₅)
Fitting	C₂⁴×C₂₅	C₄
socle, prime radical	C₂⁴×C₅	AGL(1,𝔽₅)
cosocle	Dic₂₅	C₂⁴
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
2. C₂²×#6016	C₂	direct (N × H)
6. C₂×#6016	C₂²	direct (N × H)
8. C₂³×C₂₅	C₈	semidirect
12. #6016	C₂³	direct (N × H)
15. C₂²×C₂₅	C₂×C₈	semidirect
24. C₂×C₂₅	C₂²×C₈	semidirect
33. C₂₅	C₂³×C₈	semidirect
44. C₂³	#6016	direct (N × H)
50. C₂²	C₂×#6016	direct (N × H)
54. C₂	C₂²×#6016	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×Dic₂₅	2
C₂²×#6016	2
C₂³×#170	5

Subgroups — C23×#6016 #13099679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#6016 #13099679