Subgroups — C₂×C₁₆×C₁₉×C₂₉ #72195508

Order 17632.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₁₉×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₁₆×C₁₉×C₂₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄×C₁₉×C₂₉	C₄	1	1	yes	characteristic
4	C₈×C₁₉×C₂₉	C₄	1	1	yes	characteristic
5	C₈×C₁₉×C₂₉	C₂²	1	1	yes	characteristic
6	C₂²×C₁₉×C₂₉	C₈	1	1	yes	characteristic
7	C₄×C₁₉×C₂₉	C₈	1	1	yes	characteristic
8	C₄×C₁₉×C₂₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₉×C₂₉	C₁₆	1	2	yes	direct product factor
10	C₂×C₁₉×C₂₉	C₂×C₈	1	1	yes	characteristic
11	C₂×C₁₆×C₂₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₁₆×C₁₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₁₉×C₂₉	C₂×C₁₆	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₈×C₂₉	C₂×C₁₉	1	1	yes	characteristic
15	C₁₆×C₂₉	C₂×C₁₉	1	2	yes	direct product factor
16	C₂×C₈×C₁₉	C₂×C₂₉	1	1	yes	characteristic
17	C₁₆×C₁₉	C₂×C₂₉	1	2	yes	direct product factor
18	C₂×C₄×C₂₉	C₄×C₁₉	1	1	yes	characteristic
19	C₈×C₂₉	C₄×C₁₉	1	1	yes	characteristic
20	C₈×C₂₉	C₂²×C₁₉	1	1	yes	characteristic
21	C₂×C₄×C₁₉	C₄×C₂₉	1	1	yes	characteristic
22	C₈×C₁₉	C₄×C₂₉	1	1	yes	characteristic
23	C₈×C₁₉	C₂²×C₂₉	1	1	yes	characteristic
24	C₂²×C₂₉	C₈×C₁₉	1	1	yes	characteristic
25	C₄×C₂₉	C₈×C₁₉	1	1	yes	characteristic
26	C₄×C₂₉	C₂×C₄×C₁₉	1	1	yes	characteristic
27	C₂²×C₁₉	C₈×C₂₉	1	1	yes	characteristic
28	C₄×C₁₉	C₈×C₂₉	1	1	yes	characteristic
29	C₄×C₁₉	C₂×C₄×C₂₉	1	1	yes	characteristic
30	C₂×C₂₉	C₁₆×C₁₉	1	2	yes	direct product factor
31	C₂×C₂₉	C₂×C₈×C₁₉	1	1	yes	characteristic
32	C₂×C₁₉	C₁₆×C₂₉	1	2	yes	direct product factor
33	C₂×C₁₉	C₂×C₈×C₂₉	1	1	yes	characteristic
34	C₂×C₁₆	C₁₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
35	C₂₉	C₂×C₁₆×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₁₉	C₂×C₁₆×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₈	C₂×C₁₉×C₂₉	1	1	yes	characteristic
38	C₁₆	C₂×C₁₉×C₂₉	1	2	yes	direct product factor
39	C₂×C₄	C₄×C₁₉×C₂₉	1	1	yes	characteristic
40	C₈	C₄×C₁₉×C₂₉	1	1	yes	characteristic
41	C₈	C₂²×C₁₉×C₂₉	1	1	yes	characteristic
42	C₂²	C₈×C₁₉×C₂₉	1	1	yes	characteristic
43	C₄	C₈×C₁₉×C₂₉	1	1	yes	characteristic
44	C₄	C₂×C₄×C₁₉×C₂₉	1	1	yes	characteristic
45	C₂	C₁₆×C₁₉×C₂₉	1	2	yes	direct product factor
46	C₂	C₂×C₈×C₁₉×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂²×C₁₉×C₂₉
socle, prime radical	C₂²×C₁₉×C₂₉	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₆×C₁₉×C₂₉	C₂	direct (N × H)
9. C₂×C₁₉×C₂₉	C₁₆	direct (N × H)
11. C₂×C₁₆×C₂₉	C₁₉	direct (N × H)
12. C₂×C₁₆×C₁₉	C₂₉	direct (N × H)
13. C₁₉×C₂₉	C₂×C₁₆	direct (N × H)
15. C₁₆×C₂₉	C₂×C₁₉	direct (N × H)
17. C₁₆×C₁₉	C₂×C₂₉	direct (N × H)
30. C₂×C₂₉	C₁₆×C₁₉	direct (N × H)
32. C₂×C₁₉	C₁₆×C₂₉	direct (N × H)
34. C₂×C₁₆	C₁₉×C₂₉	direct (N × H)
35. C₂₉	C₂×C₁₆×C₁₉	direct (N × H)
36. C₁₉	C₂×C₁₆×C₂₉	direct (N × H)
38. C₁₆	C₂×C₁₉×C₂₉	direct (N × H)
45. C₂	C₁₆×C₁₉×C₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₈×C₁₉×C₂₉	2
C₁₆×C₁₉×C₂₉	2
C₂×C₁₆×C₂₉	19
C₂×C₁₆×C₁₉	29

Subgroups — C2×C16×C19×C29 #72195508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₆×C₁₉×C₂₉ #72195508