Subgroups — C₂²×C₁₃×C₁₆×C₂₃ #72196839

Order 19136.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₁₆×C₂₃	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₄×C₁₃×C₂₃	C₄	1	1	yes	characteristic
4	C₂×C₈×C₁₃×C₂₃	C₄	1	3	yes	—
5	C₂×C₈×C₁₃×C₂₃	C₂²	1	3	yes	—
6	C₁₃×C₁₆×C₂₃	C₂²	1	4	yes	direct product factor
7	C₂³×C₁₃×C₂₃	C₈	1	1	yes	characteristic
8	C₂×C₄×C₁₃×C₂₃	C₈	1	3	yes	—
9	C₂×C₄×C₁₃×C₂₃	C₂×C₄	1	3	yes	—
10	C₈×C₁₃×C₂₃	C₂×C₄	1	3	yes	—
11	C₈×C₁₃×C₂₃	C₂³	1	1	yes	characteristic
12	C₂²×C₁₆×C₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₁₃×C₂₃	C₁₆	1	4	yes	direct product factor
14	C₂²×C₁₃×C₂₃	C₂×C₈	1	3	yes	—
15	C₄×C₁₃×C₂₃	C₂×C₈	1	3	yes	—
16	C₄×C₁₃×C₂₃	C₂²×C₄	1	1	yes	characteristic
17	C₂²×C₁₃×C₁₆	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂²×C₈×C₂₃	C₂×C₁₃	1	1	yes	characteristic
19	C₂×C₁₆×C₂₃	C₂×C₁₃	1	6	yes	direct product factor
20	C₂×C₁₃×C₂₃	C₂×C₁₆	1	6	yes	direct product factor
21	C₂×C₁₃×C₂₃	C₂²×C₈	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂×C₂₃	1	1	yes	characteristic
23	C₂×C₁₃×C₁₆	C₂×C₂₃	1	6	yes	direct product factor
24	C₂²×C₄×C₂₃	C₄×C₁₃	1	1	yes	characteristic
25	C₂×C₈×C₂₃	C₄×C₁₃	1	3	yes	—
26	C₂×C₈×C₂₃	C₂²×C₁₃	1	3	yes	—
27	C₁₆×C₂₃	C₂²×C₁₃	1	4	yes	direct product factor
28	C₁₃×C₂₃	C₂²×C₁₆	1	1	yes	characteristic, direct product factor, Hall
29	C₂²×C₄×C₁₃	C₄×C₂₃	1	1	yes	characteristic
30	C₂×C₈×C₁₃	C₄×C₂₃	1	3	yes	—
31	C₂×C₈×C₁₃	C₂²×C₂₃	1	3	yes	—
32	C₁₃×C₁₆	C₂²×C₂₃	1	4	yes	direct product factor
33	C₂³×C₂₃	C₈×C₁₃	1	1	yes	characteristic
34	C₂×C₄×C₂₃	C₈×C₁₃	1	3	yes	—
35	C₂×C₄×C₂₃	C₂×C₄×C₁₃	1	3	yes	—
36	C₈×C₂₃	C₂×C₄×C₁₃	1	3	yes	—
37	C₈×C₂₃	C₂³×C₁₃	1	1	yes	characteristic
38	C₂³×C₁₃	C₈×C₂₃	1	1	yes	characteristic
39	C₂×C₄×C₁₃	C₈×C₂₃	1	3	yes	—
40	C₂×C₄×C₁₃	C₂×C₄×C₂₃	1	3	yes	—
41	C₈×C₁₃	C₂×C₄×C₂₃	1	3	yes	—
42	C₈×C₁₃	C₂³×C₂₃	1	1	yes	characteristic
43	C₂²×C₂₃	C₁₃×C₁₆	1	4	yes	direct product factor
44	C₂²×C₂₃	C₂×C₈×C₁₃	1	3	yes	—
45	C₄×C₂₃	C₂×C₈×C₁₃	1	3	yes	—
46	C₄×C₂₃	C₂²×C₄×C₁₃	1	1	yes	characteristic
47	C₂²×C₁₆	C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
48	C₂²×C₁₃	C₁₆×C₂₃	1	4	yes	direct product factor
49	C₂²×C₁₃	C₂×C₈×C₂₃	1	3	yes	—
50	C₄×C₁₃	C₂×C₈×C₂₃	1	3	yes	—
51	C₄×C₁₃	C₂²×C₄×C₂₃	1	1	yes	characteristic
52	C₂×C₂₃	C₂×C₁₃×C₁₆	1	6	yes	direct product factor
53	C₂×C₂₃	C₂²×C₈×C₁₃	1	1	yes	characteristic
54	C₂²×C₈	C₂×C₁₃×C₂₃	1	1	yes	characteristic
55	C₂×C₁₆	C₂×C₁₃×C₂₃	1	6	yes	direct product factor
56	C₂×C₁₃	C₂×C₁₆×C₂₃	1	6	yes	direct product factor
57	C₂×C₁₃	C₂²×C₈×C₂₃	1	1	yes	characteristic
58	C₂₃	C₂²×C₁₃×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²×C₄	C₄×C₁₃×C₂₃	1	1	yes	characteristic
60	C₂×C₈	C₄×C₁₃×C₂₃	1	3	yes	—
61	C₂×C₈	C₂²×C₁₃×C₂₃	1	3	yes	—
62	C₁₆	C₂²×C₁₃×C₂₃	1	4	yes	direct product factor
63	C₁₃	C₂²×C₁₆×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
64	C₂³	C₈×C₁₃×C₂₃	1	1	yes	characteristic
65	C₂×C₄	C₈×C₁₃×C₂₃	1	3	yes	—
66	C₂×C₄	C₂×C₄×C₁₃×C₂₃	1	3	yes	—
67	C₈	C₂×C₄×C₁₃×C₂₃	1	3	yes	—
68	C₈	C₂³×C₁₃×C₂₃	1	1	yes	characteristic
69	C₂²	C₁₃×C₁₆×C₂₃	1	4	yes	direct product factor
70	C₂²	C₂×C₈×C₁₃×C₂₃	1	3	yes	—
71	C₄	C₂×C₈×C₁₃×C₂₃	1	3	yes	—
72	C₄	C₂²×C₄×C₁₃×C₂₃	1	1	yes	characteristic
73	C₂	C₂×C₁₃×C₁₆×C₂₃	1	6	yes	direct product factor
74	C₂	C₂²×C₈×C₁₃×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂³×C₁₃×C₂₃
socle, prime radical	C₂³×C₁₃×C₂₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×C₁₆×C₂₃	C₂	direct (N × H)
6. C₁₃×C₁₆×C₂₃	C₂²	direct (N × H)
12. C₂²×C₁₆×C₂₃	C₁₃	direct (N × H)
13. C₂²×C₁₃×C₂₃	C₁₆	direct (N × H)
17. C₂²×C₁₃×C₁₆	C₂₃	direct (N × H)
19. C₂×C₁₆×C₂₃	C₂×C₁₃	direct (N × H)
20. C₂×C₁₃×C₂₃	C₂×C₁₆	direct (N × H)
23. C₂×C₁₃×C₁₆	C₂×C₂₃	direct (N × H)
27. C₁₆×C₂₃	C₂²×C₁₃	direct (N × H)
28. C₁₃×C₂₃	C₂²×C₁₆	direct (N × H)
32. C₁₃×C₁₆	C₂²×C₂₃	direct (N × H)
43. C₂²×C₂₃	C₁₃×C₁₆	direct (N × H)
47. C₂²×C₁₆	C₁₃×C₂₃	direct (N × H)
48. C₂²×C₁₃	C₁₆×C₂₃	direct (N × H)
52. C₂×C₂₃	C₂×C₁₃×C₁₆	direct (N × H)
55. C₂×C₁₆	C₂×C₁₃×C₂₃	direct (N × H)
56. C₂×C₁₃	C₂×C₁₆×C₂₃	direct (N × H)
58. C₂₃	C₂²×C₁₃×C₁₆	direct (N × H)
62. C₁₆	C₂²×C₁₃×C₂₃	direct (N × H)
63. C₁₃	C₂²×C₁₆×C₂₃	direct (N × H)
69. C₂²	C₁₃×C₁₆×C₂₃	direct (N × H)
73. C₂	C₂×C₁₃×C₁₆×C₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₁₃×C₂₃	2
C₂×C₁₃×C₁₆×C₂₃	2
C₂²×C₁₆×C₂₃	13
C₂²×C₁₃×C₁₆	23

Subgroups — C22×C13×C16×C23 #72196839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×C₁₆×C₂₃ #72196839