Subgroups — C₂⁵×C₈×C₁₃ #15749410

Order 3328.

15454 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₈×C₁₃	C₂	1	62	yes	maximal, direct product factor
3	C₂⁶×C₁₃	C₄	1	1	yes	characteristic
4	C₂⁴×C₄×C₁₃	C₄	1	31	yes	—
5	C₂⁴×C₄×C₁₃	C₂²	1	31	yes	—
6	C₂³×C₈×C₁₃	C₂²	1	620	yes	direct product factor
7	C₂⁵×C₁₃	C₈	1	32	yes	direct product factor
8	C₂⁵×C₁₃	C₂×C₄	1	31	yes	—
9	C₂³×C₄×C₁₃	C₂×C₄	1	465	yes	—
10	C₂³×C₄×C₁₃	C₂³	1	155	yes	—
11	C₂²×C₈×C₁₃	C₂³	1	1240	yes	direct product factor
12	C₂⁵×C₈	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂⁴×C₁₃	C₂×C₈	1	496	yes	direct product factor
14	C₂⁴×C₁₃	C₂²×C₄	1	155	yes	—
15	C₂²×C₄×C₁₃	C₂²×C₄	1	1085	yes	—
16	C₂²×C₄×C₁₃	C₂⁴	1	155	yes	—
17	C₂×C₈×C₁₃	C₂⁴	1	496	yes	direct product factor
18	C₂⁵×C₄	C₂×C₁₃	1	1	yes	characteristic
19	C₂⁴×C₈	C₂×C₁₃	1	62	yes	direct product factor
20	C₂³×C₁₃	C₂²×C₈	1	1240	yes	direct product factor
21	C₂³×C₁₃	C₂³×C₄	1	155	yes	—
22	C₂×C₄×C₁₃	C₂³×C₄	1	465	yes	—
23	C₂×C₄×C₁₃	C₂⁵	1	31	yes	—
24	C₈×C₁₃	C₂⁵	1	32	yes	direct product factor
25	C₂⁶	C₄×C₁₃	1	1	yes	characteristic
26	C₂⁴×C₄	C₄×C₁₃	1	31	yes	—
27	C₂⁴×C₄	C₂²×C₁₃	1	31	yes	—
28	C₂³×C₈	C₂²×C₁₃	1	620	yes	direct product factor
29	C₂²×C₁₃	C₂³×C₈	1	620	yes	direct product factor
30	C₂²×C₁₃	C₂⁴×C₄	1	31	yes	—
31	C₄×C₁₃	C₂⁴×C₄	1	31	yes	—
32	C₄×C₁₃	C₂⁶	1	1	yes	characteristic
33	C₂⁵	C₈×C₁₃	1	32	yes	direct product factor
34	C₂⁵	C₂×C₄×C₁₃	1	31	yes	—
35	C₂³×C₄	C₂×C₄×C₁₃	1	465	yes	—
36	C₂³×C₄	C₂³×C₁₃	1	155	yes	—
37	C₂²×C₈	C₂³×C₁₃	1	1240	yes	direct product factor
38	C₂×C₁₃	C₂⁴×C₈	1	62	yes	direct product factor
39	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
40	C₂⁴	C₂×C₈×C₁₃	1	496	yes	direct product factor
41	C₂⁴	C₂²×C₄×C₁₃	1	155	yes	—
42	C₂²×C₄	C₂²×C₄×C₁₃	1	1085	yes	—
43	C₂²×C₄	C₂⁴×C₁₃	1	155	yes	—
44	C₂×C₈	C₂⁴×C₁₃	1	496	yes	direct product factor
45	C₁₃	C₂⁵×C₈	1	1	yes	characteristic, direct product factor, Sylow
46	C₂³	C₂²×C₈×C₁₃	1	1240	yes	direct product factor
47	C₂³	C₂³×C₄×C₁₃	1	155	yes	—
48	C₂×C₄	C₂³×C₄×C₁₃	1	465	yes	—
49	C₂×C₄	C₂⁵×C₁₃	1	31	yes	—
50	C₈	C₂⁵×C₁₃	1	32	yes	direct product factor
51	C₂²	C₂³×C₈×C₁₃	1	620	yes	direct product factor
52	C₂²	C₂⁴×C₄×C₁₃	1	31	yes	—
53	C₄	C₂⁴×C₄×C₁₃	1	31	yes	—
54	C₄	C₂⁶×C₁₃	1	1	yes	characteristic
55	C₂	C₂⁴×C₈×C₁₃	1	62	yes	direct product factor
56	C₂	C₂⁵×C₄×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁶×C₁₃
socle, prime radical	C₂⁶×C₁₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₈×C₁₃	C₂	direct (N × H)
6. C₂³×C₈×C₁₃	C₂²	direct (N × H)
7. C₂⁵×C₁₃	C₈	direct (N × H)
11. C₂²×C₈×C₁₃	C₂³	direct (N × H)
12. C₂⁵×C₈	C₁₃	direct (N × H)
13. C₂⁴×C₁₃	C₂×C₈	direct (N × H)
17. C₂×C₈×C₁₃	C₂⁴	direct (N × H)
19. C₂⁴×C₈	C₂×C₁₃	direct (N × H)
20. C₂³×C₁₃	C₂²×C₈	direct (N × H)
24. C₈×C₁₃	C₂⁵	direct (N × H)
28. C₂³×C₈	C₂²×C₁₃	direct (N × H)
29. C₂²×C₁₃	C₂³×C₈	direct (N × H)
33. C₂⁵	C₈×C₁₃	direct (N × H)
37. C₂²×C₈	C₂³×C₁₃	direct (N × H)
38. C₂×C₁₃	C₂⁴×C₈	direct (N × H)
40. C₂⁴	C₂×C₈×C₁₃	direct (N × H)
44. C₂×C₈	C₂⁴×C₁₃	direct (N × H)
45. C₁₃	C₂⁵×C₈	direct (N × H)
46. C₂³	C₂²×C₈×C₁₃	direct (N × H)
50. C₈	C₂⁵×C₁₃	direct (N × H)
51. C₂²	C₂³×C₈×C₁₃	direct (N × H)
55. C₂	C₂⁴×C₈×C₁₃	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×C₄×C₁₃	2
C₂⁴×C₈×C₁₃	2
C₂⁵×C₈	13

Subgroups — C25×C8×C13 #15749410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₈×C₁₃ #15749410