Subgroups — C₂⁸×C₄×C₁₉ #72197151

Order 19456.

32299434 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁹×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂⁷×C₄×C₁₉	C₂	1	510	yes	maximal, direct product factor
3	C₂⁸×C₄	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂⁸×C₁₉	C₄	1	256	yes	direct product factor
5	C₂⁸×C₁₉	C₂²	1	255	yes	—
6	C₂⁶×C₄×C₁₉	C₂²	1	43180	yes	direct product factor
7	C₂⁷×C₁₉	C₂×C₄	1	32640	yes	direct product factor
8	C₂⁷×C₁₉	C₂³	1	10795	yes	—
9	C₂⁵×C₄×C₁₉	C₂³	1	777240	yes	direct product factor
10	C₂⁶×C₁₉	C₂²×C₄	1	690880	yes	direct product factor
11	C₂⁶×C₁₉	C₂⁴	1	97155	yes	—
12	C₂⁴×C₄×C₁₉	C₂⁴	1	3212592	yes	direct product factor
13	C₂⁵×C₁₉	C₂³×C₄	1	3108960	yes	direct product factor
14	C₂⁵×C₁₉	C₂⁵	1	200787	yes	—
15	C₂³×C₄×C₁₉	C₂⁵	1	3108960	yes	direct product factor
16	C₂⁹	C₂×C₁₉	1	1	yes	characteristic
17	C₂⁷×C₄	C₂×C₁₉	1	510	yes	direct product factor
18	C₂⁴×C₁₉	C₂⁴×C₄	1	3212592	yes	direct product factor
19	C₂⁴×C₁₉	C₂⁶	1	97155	yes	—
20	C₂²×C₄×C₁₉	C₂⁶	1	690880	yes	direct product factor
21	C₂⁸	C₄×C₁₉	1	256	yes	direct product factor
22	C₂⁸	C₂²×C₁₉	1	255	yes	—
23	C₂⁶×C₄	C₂²×C₁₉	1	43180	yes	direct product factor
24	C₂³×C₁₉	C₂⁵×C₄	1	777240	yes	direct product factor
25	C₂³×C₁₉	C₂⁷	1	10795	yes	—
26	C₂×C₄×C₁₉	C₂⁷	1	32640	yes	direct product factor
27	C₂⁷	C₂×C₄×C₁₉	1	32640	yes	direct product factor
28	C₂⁷	C₂³×C₁₉	1	10795	yes	—
29	C₂⁵×C₄	C₂³×C₁₉	1	777240	yes	direct product factor
30	C₂²×C₁₉	C₂⁶×C₄	1	43180	yes	direct product factor
31	C₂²×C₁₉	C₂⁸	1	255	yes	—
32	C₄×C₁₉	C₂⁸	1	256	yes	direct product factor
33	C₂⁶	C₂²×C₄×C₁₉	1	690880	yes	direct product factor
34	C₂⁶	C₂⁴×C₁₉	1	97155	yes	—
35	C₂⁴×C₄	C₂⁴×C₁₉	1	3212592	yes	direct product factor
36	C₂×C₁₉	C₂⁷×C₄	1	510	yes	direct product factor
37	C₂×C₁₉	C₂⁹	1	1	yes	characteristic
38	C₂⁵	C₂³×C₄×C₁₉	1	3108960	yes	direct product factor
39	C₂⁵	C₂⁵×C₁₉	1	200787	yes	—
40	C₂³×C₄	C₂⁵×C₁₉	1	3108960	yes	direct product factor
41	C₁₉	C₂⁸×C₄	1	1	yes	characteristic, direct product factor, Sylow
42	C₂⁴	C₂⁴×C₄×C₁₉	1	3212592	yes	direct product factor
43	C₂⁴	C₂⁶×C₁₉	1	97155	yes	—
44	C₂²×C₄	C₂⁶×C₁₉	1	690880	yes	direct product factor
45	C₂³	C₂⁵×C₄×C₁₉	1	777240	yes	direct product factor
46	C₂³	C₂⁷×C₁₉	1	10795	yes	—
47	C₂×C₄	C₂⁷×C₁₉	1	32640	yes	direct product factor
48	C₂²	C₂⁶×C₄×C₁₉	1	43180	yes	direct product factor
49	C₂²	C₂⁸×C₁₉	1	255	yes	—
50	C₄	C₂⁸×C₁₉	1	256	yes	direct product factor
51	C₂	C₂⁷×C₄×C₁₉	1	510	yes	direct product factor
52	C₂	C₂⁹×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁹×C₁₉
socle, prime radical	C₂⁹×C₁₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁷×C₄×C₁₉	C₂	direct (N × H)
3. C₂⁸×C₄	C₁₉	direct (N × H)
4. C₂⁸×C₁₉	C₄	direct (N × H)
6. C₂⁶×C₄×C₁₉	C₂²	direct (N × H)
7. C₂⁷×C₁₉	C₂×C₄	direct (N × H)
9. C₂⁵×C₄×C₁₉	C₂³	direct (N × H)
10. C₂⁶×C₁₉	C₂²×C₄	direct (N × H)
12. C₂⁴×C₄×C₁₉	C₂⁴	direct (N × H)
13. C₂⁵×C₁₉	C₂³×C₄	direct (N × H)
15. C₂³×C₄×C₁₉	C₂⁵	direct (N × H)
17. C₂⁷×C₄	C₂×C₁₉	direct (N × H)
18. C₂⁴×C₁₉	C₂⁴×C₄	direct (N × H)
20. C₂²×C₄×C₁₉	C₂⁶	direct (N × H)
21. C₂⁸	C₄×C₁₉	direct (N × H)
23. C₂⁶×C₄	C₂²×C₁₉	direct (N × H)
24. C₂³×C₁₉	C₂⁵×C₄	direct (N × H)
26. C₂×C₄×C₁₉	C₂⁷	direct (N × H)
27. C₂⁷	C₂×C₄×C₁₉	direct (N × H)
29. C₂⁵×C₄	C₂³×C₁₉	direct (N × H)
30. C₂²×C₁₉	C₂⁶×C₄	direct (N × H)
32. C₄×C₁₉	C₂⁸	direct (N × H)
33. C₂⁶	C₂²×C₄×C₁₉	direct (N × H)
35. C₂⁴×C₄	C₂⁴×C₁₉	direct (N × H)
36. C₂×C₁₉	C₂⁷×C₄	direct (N × H)
38. C₂⁵	C₂³×C₄×C₁₉	direct (N × H)
40. C₂³×C₄	C₂⁵×C₁₉	direct (N × H)
41. C₁₉	C₂⁸×C₄	direct (N × H)
42. C₂⁴	C₂⁴×C₄×C₁₉	direct (N × H)
44. C₂²×C₄	C₂⁶×C₁₉	direct (N × H)
45. C₂³	C₂⁵×C₄×C₁₉	direct (N × H)
47. C₂×C₄	C₂⁷×C₁₉	direct (N × H)
48. C₂²	C₂⁶×C₄×C₁₉	direct (N × H)
50. C₄	C₂⁸×C₁₉	direct (N × H)
51. C₂	C₂⁷×C₄×C₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁹×C₁₉	2
C₂⁷×C₄×C₁₉	2
C₂⁸×C₄	19

Subgroups — C28×C4×C19 #72197151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁸×C₄×C₁₉ #72197151