Subgroups — C₂×C₁₉²×C₃₂ #72200450

Order 23104.

374 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×C₁₉²	C₂	1	1	yes	maximal, characteristic
2	C₁₉²×C₃₂	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₈×C₁₉²	C₄	1	1	yes	characteristic
4	C₁₆×C₁₉²	C₄	1	1	yes	characteristic
5	C₁₆×C₁₉²	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₁₉²	C₈	1	1	yes	characteristic
7	C₈×C₁₉²	C₈	1	1	yes	characteristic
8	C₈×C₁₉²	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₁₉²	C₁₆	1	1	yes	characteristic
10	C₄×C₁₉²	C₁₆	1	1	yes	characteristic
11	C₄×C₁₉²	C₂×C₈	1	1	yes	characteristic
12	C₂×C₁₉×C₃₂	C₁₉	1	20	yes	maximal, direct product factor
13	C₂×C₁₉²	C₃₂	1	2	yes	direct product factor
14	C₂×C₁₉²	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₁₆×C₁₉	C₂×C₁₉	1	20	yes	—
16	C₁₉×C₃₂	C₂×C₁₉	1	40	yes	direct product factor
17	C₁₉²	C₂×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₈×C₁₉	C₄×C₁₉	1	20	yes	—
19	C₁₆×C₁₉	C₄×C₁₉	1	20	yes	—
20	C₁₆×C₁₉	C₂²×C₁₉	1	20	yes	—
21	C₂×C₄×C₁₉	C₈×C₁₉	1	20	yes	—
22	C₈×C₁₉	C₈×C₁₉	1	20	yes	—
23	C₈×C₁₉	C₂×C₄×C₁₉	1	20	yes	—
24	C₂²×C₁₉	C₁₆×C₁₉	1	20	yes	—
25	C₄×C₁₉	C₁₆×C₁₉	1	20	yes	—
26	C₄×C₁₉	C₂×C₈×C₁₉	1	20	yes	—
27	C₂×C₃₂	C₁₉²	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₁₉	C₁₉×C₃₂	1	40	yes	direct product factor
29	C₂×C₁₉	C₂×C₁₆×C₁₉	1	20	yes	—
30	C₂×C₁₆	C₂×C₁₉²	1	1	yes	characteristic
31	C₃₂	C₂×C₁₉²	1	2	yes	direct product factor
32	C₁₉	C₂×C₁₉×C₃₂	1	20	yes	direct product factor
33	C₂×C₈	C₄×C₁₉²	1	1	yes	characteristic
34	C₁₆	C₄×C₁₉²	1	1	yes	characteristic
35	C₁₆	C₂²×C₁₉²	1	1	yes	characteristic
36	C₂×C₄	C₈×C₁₉²	1	1	yes	characteristic
37	C₈	C₈×C₁₉²	1	1	yes	characteristic
38	C₈	C₂×C₄×C₁₉²	1	1	yes	characteristic
39	C₂²	C₁₆×C₁₉²	1	1	yes	characteristic
40	C₄	C₁₆×C₁₉²	1	1	yes	characteristic
41	C₄	C₂×C₈×C₁₉²	1	1	yes	characteristic
42	C₂	C₁₉²×C₃₂	1	2	yes	direct product factor
43	C₂	C₂×C₁₆×C₁₉²	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂²×C₁₉²
socle, prime radical	C₂²×C₁₉²	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉²×C₃₂	C₂	direct (N × H)
12. C₂×C₁₉×C₃₂	C₁₉	direct (N × H)
13. C₂×C₁₉²	C₃₂	direct (N × H)
16. C₁₉×C₃₂	C₂×C₁₉	direct (N × H)
17. C₁₉²	C₂×C₃₂	direct (N × H)
27. C₂×C₃₂	C₁₉²	direct (N × H)
28. C₂×C₁₉	C₁₉×C₃₂	direct (N × H)
31. C₃₂	C₂×C₁₉²	direct (N × H)
32. C₁₉	C₂×C₁₉×C₃₂	direct (N × H)
42. C₂	C₁₉²×C₃₂	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×C₁₆×C₁₉²	2
C₁₉²×C₃₂	2
C₂×C₁₉×C₃₂	19

Subgroups — C2×C192×C32 #72200450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉²×C₃₂ #72200450