Subgroups — C₂⁵×#170 #13046022

Order 1280.

15454 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×#170	C₂	1	62	yes	maximal, direct product factor
3	C₂⁶×C₅	C₄	1	1	yes	characteristic
4	C₂⁴×Dic₅	C₄	1	31	yes	—
5	C₂⁴×Dic₅	C₂²	1	31	yes	—
6	C₂³×#170	C₂²	1	620	yes	direct product factor
7	C₂⁵×C₈	—	5	1	no	maximal, Sylow
8	C₂⁵×C₅	C₈	1	32	yes	complemented
9	C₂⁵×C₅	C₂×C₄	1	31	yes	—
10	C₂³×Dic₅	C₂×C₄	1	465	yes	—
11	C₂³×Dic₅	C₂³	1	155	yes	—
12	C₂²×#170	C₂³	1	1240	yes	direct product factor
13	C₂⁵×C₄	—	5	1	no	—
14	C₂⁴×C₈	—	5	62	no	—
15	C₂⁴×C₅	C₂×C₈	1	496	yes	complemented
16	C₂⁴×C₅	C₂²×C₄	1	155	yes	—
17	C₂²×Dic₅	C₂²×C₄	1	1085	yes	—
18	C₂²×Dic₅	C₂⁴	1	155	yes	—
19	C₂×#170	C₂⁴	1	496	yes	direct product factor
20	C₂⁶	AGL(1,𝔽₅)	1	1	yes	characteristic
21	C₂⁴×C₄	—	5	31	no	—
22	C₂⁴×C₄	—	5	31	no	—
23	C₂³×C₈	—	5	620	no	—
24	C₂³×C₅	C₂²×C₈	1	1240	yes	complemented
25	C₂³×C₅	C₂³×C₄	1	155	yes	—
26	C₂×Dic₅	C₂³×C₄	1	465	yes	—
27	C₂×Dic₅	C₂⁵	1	31	yes	—
28	#170	C₂⁵	1	32	yes	direct product factor
29	C₂⁵	#170	1	32	yes	direct product factor
30	C₂⁵	C₂×AGL(1,𝔽₅)	1	31	yes	—
31	C₂³×C₄	—	5	155	no	—
32	C₂³×C₄	—	5	465	no	—
33	C₂²×C₈	—	5	1240	no	—
34	C₂²×C₅	C₂³×C₈	1	620	yes	complemented
35	C₂²×C₅	C₂⁴×C₄	1	31	yes	—
36	Dic₅	C₂⁴×C₄	1	31	yes	—
37	Dic₅	C₂⁶	1	1	yes	characteristic
38	C₂⁴	C₂×#170	1	496	yes	direct product factor
39	C₂⁴	C₂²×AGL(1,𝔽₅)	1	155	yes	—
40	C₂²×C₄	—	5	155	no	—
41	C₂²×C₄	—	5	1085	no	—
42	C₂×C₈	—	5	496	no	—
43	C₂×C₅	C₂⁴×C₈	1	62	yes	complemented
44	C₂×C₅	C₂⁵×C₄	1	1	yes	characteristic
45	C₂³	C₂²×#170	1	1240	yes	direct product factor
46	C₂³	C₂³×AGL(1,𝔽₅)	1	155	yes	—
47	C₂×C₄	—	5	31	no	—
48	C₂×C₄	—	5	465	no	—
49	C₈	—	5	32	no	—
50	C₅	C₂⁵×C₈	1	1	yes	characteristic, complemented, Sylow
51	C₂²	C₂³×#170	1	620	yes	direct product factor
52	C₂²	C₂⁴×AGL(1,𝔽₅)	1	31	yes	—
53	C₄	—	5	1	no	—
54	C₄	—	5	31	no	—
55	C₂	C₂⁴×#170	1	62	yes	direct product factor
56	C₂	C₂⁵×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁶	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₂⁵×C₈
Frattini	C₂	C₂⁵×AGL(1,𝔽₅)
Fitting, socle, prime radical	C₂⁶×C₅	C₄
cosocle	Dic₅	C₂⁶
LCS	G ▷ C₅
UCS	C₁ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
2. C₂⁴×#170	C₂	direct (N × H)
6. C₂³×#170	C₂²	direct (N × H)
8. C₂⁵×C₅	C₈	semidirect
12. C₂²×#170	C₂³	direct (N × H)
15. C₂⁴×C₅	C₂×C₈	semidirect
19. C₂×#170	C₂⁴	direct (N × H)
24. C₂³×C₅	C₂²×C₈	semidirect
28. #170	C₂⁵	direct (N × H)
29. C₂⁵	#170	direct (N × H)
34. C₂²×C₅	C₂³×C₈	semidirect
38. C₂⁴	C₂×#170	direct (N × H)
43. C₂×C₅	C₂⁴×C₈	semidirect
45. C₂³	C₂²×#170	direct (N × H)
50. C₅	C₂⁵×C₈	semidirect
51. C₂²	C₂³×#170	direct (N × H)
55. C₂	C₂⁴×#170	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×Dic₅	2
C₂⁴×#170	2
C₂⁵×C₈	5

Subgroups — C25×#170 #13046022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×#170 #13046022