Subgroups — C₂⁵×Q₈×C₁₃ #15749435

Order 3328.

63326 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Q₈×C₁₃	C₂	1	124	yes	maximal, direct product factor
2	C₂⁵×C₄×C₁₃	C₂	1	3	yes	maximal
3	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
4	C₂³×Q₈×C₁₃	C₂²	1	2480	yes	direct product factor
5	C₂⁴×C₄×C₁₃	C₂²	1	186	yes	—
6	C₂⁵×C₁₃	Q₈	1	32	yes	direct product factor
7	C₂⁵×C₁₃	C₂³	1	31	yes	—
8	C₂²×Q₈×C₁₃	C₂³	1	9920	yes	direct product factor
9	C₂³×C₄×C₁₃	C₂³	1	1860	yes	—
10	C₂⁵×Q₈	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂⁴×C₁₃	C₂×Q₈	1	496	yes	direct product factor
12	C₂⁴×C₁₃	C₂⁴	1	155	yes	—
13	C₂×Q₈×C₁₃	C₂⁴	1	7936	yes	direct product factor
14	C₂²×C₄×C₁₃	C₂⁴	1	3720	yes	—
15	C₂⁴×Q₈	C₂×C₁₃	1	124	yes	direct product factor
16	C₂⁵×C₄	C₂×C₁₃	1	3	yes	—
17	C₂³×C₁₃	C₂²×Q₈	1	1240	yes	direct product factor
18	C₂³×C₁₃	C₂⁵	1	155	yes	—
19	Q₈×C₁₃	C₂⁵	1	1024	yes	direct product factor
20	C₂×C₄×C₁₃	C₂⁵	1	1488	yes	—
21	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
22	C₂³×Q₈	C₂²×C₁₃	1	2480	yes	direct product factor
23	C₂⁴×C₄	C₂²×C₁₃	1	186	yes	—
24	C₂²×C₁₃	C₂³×Q₈	1	620	yes	direct product factor
25	C₂²×C₁₃	C₂⁶	1	31	yes	—
26	C₄×C₁₃	C₂⁶	1	96	yes	—
27	C₂⁵	Q₈×C₁₃	1	32	yes	direct product factor
28	C₂⁵	C₂³×C₁₃	1	31	yes	—
29	C₂²×Q₈	C₂³×C₁₃	1	9920	yes	direct product factor
30	C₂³×C₄	C₂³×C₁₃	1	1860	yes	—
31	C₂×C₁₃	C₂⁴×Q₈	1	62	yes	direct product factor
32	C₂×C₁₃	C₂⁷	1	1	yes	characteristic
33	C₂⁴	C₂×Q₈×C₁₃	1	496	yes	direct product factor
34	C₂⁴	C₂⁴×C₁₃	1	155	yes	—
35	C₂×Q₈	C₂⁴×C₁₃	1	7936	yes	direct product factor
36	C₂²×C₄	C₂⁴×C₁₃	1	3720	yes	—
37	C₁₃	C₂⁵×Q₈	1	1	yes	characteristic, direct product factor, Sylow
38	C₂³	C₂²×Q₈×C₁₃	1	1240	yes	direct product factor
39	C₂³	C₂⁵×C₁₃	1	155	yes	—
40	Q₈	C₂⁵×C₁₃	1	1024	yes	direct product factor
41	C₂×C₄	C₂⁵×C₁₃	1	1488	yes	—
42	C₂²	C₂³×Q₈×C₁₃	1	620	yes	direct product factor
43	C₂²	C₂⁶×C₁₃	1	31	yes	—
44	C₄	C₂⁶×C₁₃	1	96	yes	—
45	C₂	C₂⁴×Q₈×C₁₃	1	62	yes	direct product factor
46	C₂	C₂⁷×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁶×C₁₃	C₂²
commutator, Frattini, cosocle	C₂	C₂⁷×C₁₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁶×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×Q₈×C₁₃	C₂	direct (N × H)
4. C₂³×Q₈×C₁₃	C₂²	direct (N × H)
6. C₂⁵×C₁₃	Q₈	direct (N × H)
8. C₂²×Q₈×C₁₃	C₂³	direct (N × H)
10. C₂⁵×Q₈	C₁₃	direct (N × H)
11. C₂⁴×C₁₃	C₂×Q₈	direct (N × H)
13. C₂×Q₈×C₁₃	C₂⁴	direct (N × H)
15. C₂⁴×Q₈	C₂×C₁₃	direct (N × H)
17. C₂³×C₁₃	C₂²×Q₈	direct (N × H)
19. Q₈×C₁₃	C₂⁵	direct (N × H)
22. C₂³×Q₈	C₂²×C₁₃	direct (N × H)
24. C₂²×C₁₃	C₂³×Q₈	direct (N × H)
27. C₂⁵	Q₈×C₁₃	direct (N × H)
29. C₂²×Q₈	C₂³×C₁₃	direct (N × H)
31. C₂×C₁₃	C₂⁴×Q₈	direct (N × H)
33. C₂⁴	C₂×Q₈×C₁₃	direct (N × H)
35. C₂×Q₈	C₂⁴×C₁₃	direct (N × H)
37. C₁₃	C₂⁵×Q₈	direct (N × H)
38. C₂³	C₂²×Q₈×C₁₃	direct (N × H)
40. Q₈	C₂⁵×C₁₃	direct (N × H)
42. C₂²	C₂³×Q₈×C₁₃	direct (N × H)
45. C₂	C₂⁴×Q₈×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
C₂⁴×Q₈×C₁₃	2
C₂⁵×C₄×C₁₃	2
C₂⁵×Q₈	13

Subgroups — C25×Q8×C13 #15749435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×Q₈×C₁₃ #15749435