Subgroups — C₂⁴×C₄×C₁₃² #72189384

Order 10816.

10896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₁₃²	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×C₁₃²	C₂	1	30	yes	maximal, direct product factor
3	C₂⁴×C₁₃²	C₄	1	16	yes	direct product factor
4	C₂⁴×C₁₃²	C₂²	1	15	yes	—
5	C₂²×C₄×C₁₃²	C₂²	1	140	yes	direct product factor
6	C₂³×C₁₃²	C₂×C₄	1	120	yes	direct product factor
7	C₂³×C₁₃²	C₂³	1	35	yes	—
8	C₂×C₄×C₁₃²	C₂³	1	120	yes	direct product factor
9	C₂⁴×C₄×C₁₃	C₁₃	1	14	yes	maximal, direct product factor
10	C₂²×C₁₃²	C₂²×C₄	1	140	yes	direct product factor
11	C₂²×C₁₃²	C₂⁴	1	15	yes	—
12	C₄×C₁₃²	C₂⁴	1	16	yes	direct product factor
13	C₂⁵×C₁₃	C₂×C₁₃	1	14	yes	—
14	C₂³×C₄×C₁₃	C₂×C₁₃	1	420	yes	direct product factor
15	C₂×C₁₃²	C₂³×C₄	1	30	yes	direct product factor
16	C₂×C₁₃²	C₂⁵	1	1	yes	characteristic
17	C₂⁴×C₁₃	C₄×C₁₃	1	224	yes	direct product factor
18	C₂⁴×C₁₃	C₂²×C₁₃	1	210	yes	—
19	C₂²×C₄×C₁₃	C₂²×C₁₃	1	1960	yes	direct product factor
20	C₁₃²	C₂⁴×C₄	1	1	yes	characteristic, direct product factor, Sylow
21	C₂³×C₁₃	C₂×C₄×C₁₃	1	1680	yes	direct product factor
22	C₂³×C₁₃	C₂³×C₁₃	1	490	yes	—
23	C₂×C₄×C₁₃	C₂³×C₁₃	1	1680	yes	direct product factor
24	C₂⁴×C₄	C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₁₃	C₂²×C₄×C₁₃	1	1960	yes	direct product factor
26	C₂²×C₁₃	C₂⁴×C₁₃	1	210	yes	—
27	C₄×C₁₃	C₂⁴×C₁₃	1	224	yes	direct product factor
28	C₂⁵	C₂×C₁₃²	1	1	yes	characteristic
29	C₂³×C₄	C₂×C₁₃²	1	30	yes	direct product factor
30	C₂×C₁₃	C₂³×C₄×C₁₃	1	420	yes	direct product factor
31	C₂×C₁₃	C₂⁵×C₁₃	1	14	yes	—
32	C₂⁴	C₄×C₁₃²	1	16	yes	direct product factor
33	C₂⁴	C₂²×C₁₃²	1	15	yes	—
34	C₂²×C₄	C₂²×C₁₃²	1	140	yes	direct product factor
35	C₁₃	C₂⁴×C₄×C₁₃	1	14	yes	direct product factor
36	C₂³	C₂×C₄×C₁₃²	1	120	yes	direct product factor
37	C₂³	C₂³×C₁₃²	1	35	yes	—
38	C₂×C₄	C₂³×C₁₃²	1	120	yes	direct product factor
39	C₂²	C₂²×C₄×C₁₃²	1	140	yes	direct product factor
40	C₂²	C₂⁴×C₁₃²	1	15	yes	—
41	C₄	C₂⁴×C₁₃²	1	16	yes	direct product factor
42	C₂	C₂³×C₄×C₁₃²	1	30	yes	direct product factor
43	C₂	C₂⁵×C₁₃²	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁵×C₁₃²
socle, prime radical	C₂⁵×C₁₃²	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄×C₁₃²	C₂	direct (N × H)
3. C₂⁴×C₁₃²	C₄	direct (N × H)
5. C₂²×C₄×C₁₃²	C₂²	direct (N × H)
6. C₂³×C₁₃²	C₂×C₄	direct (N × H)
8. C₂×C₄×C₁₃²	C₂³	direct (N × H)
9. C₂⁴×C₄×C₁₃	C₁₃	direct (N × H)
10. C₂²×C₁₃²	C₂²×C₄	direct (N × H)
12. C₄×C₁₃²	C₂⁴	direct (N × H)
14. C₂³×C₄×C₁₃	C₂×C₁₃	direct (N × H)
15. C₂×C₁₃²	C₂³×C₄	direct (N × H)
17. C₂⁴×C₁₃	C₄×C₁₃	direct (N × H)
19. C₂²×C₄×C₁₃	C₂²×C₁₃	direct (N × H)
20. C₁₃²	C₂⁴×C₄	direct (N × H)
21. C₂³×C₁₃	C₂×C₄×C₁₃	direct (N × H)
23. C₂×C₄×C₁₃	C₂³×C₁₃	direct (N × H)
24. C₂⁴×C₄	C₁₃²	direct (N × H)
25. C₂²×C₁₃	C₂²×C₄×C₁₃	direct (N × H)
27. C₄×C₁₃	C₂⁴×C₁₃	direct (N × H)
29. C₂³×C₄	C₂×C₁₃²	direct (N × H)
30. C₂×C₁₃	C₂³×C₄×C₁₃	direct (N × H)
32. C₂⁴	C₄×C₁₃²	direct (N × H)
34. C₂²×C₄	C₂²×C₁₃²	direct (N × H)
35. C₁₃	C₂⁴×C₄×C₁₃	direct (N × H)
36. C₂³	C₂×C₄×C₁₃²	direct (N × H)
38. C₂×C₄	C₂³×C₁₃²	direct (N × H)
39. C₂²	C₂²×C₄×C₁₃²	direct (N × H)
41. C₄	C₂⁴×C₁₃²	direct (N × H)
42. C₂	C₂³×C₄×C₁₃²	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×C₁₃²	2
C₂³×C₄×C₁₃²	2
C₂⁴×C₄×C₁₃	13

Subgroups — C24×C4×C132 #72189384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₄×C₁₃² #72189384