Subgroups — C₄×C₁₃×C₁₆×C₂₃ #72196838

Order 19136.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₁₆×C₂₃	C₂	1	2	yes	maximal
3	C₂×C₈×C₁₃×C₂₃	C₄	1	1	yes	characteristic
4	C₂×C₈×C₁₃×C₂₃	C₂²	1	1	yes	characteristic
5	C₄²×C₁₃×C₂₃	C₄	1	1	yes	characteristic
6	C₁₃×C₁₆×C₂₃	C₄	1	4	yes	direct product factor
7	C₂×C₄×C₁₃×C₂₃	C₈	1	2	yes	—
8	C₂×C₄×C₁₃×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₃×C₂₃	C₈	1	2	yes	—
10	C₈×C₁₃×C₂₃	C₂×C₄	1	2	yes	—
11	C₄×C₁₆×C₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₁₃×C₂₃	C₂×C₈	1	1	yes	characteristic
13	C₄×C₁₃×C₂₃	C₁₆	1	4	yes	direct product factor
14	C₄×C₁₃×C₂₃	C₄²	1	1	yes	characteristic
15	C₄×C₁₃×C₂₃	C₂×C₈	1	1	yes	characteristic
16	C₄×C₁₃×C₁₆	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₁₆×C₂₃	C₂×C₁₃	1	2	yes	—
18	C₄×C₈×C₂₃	C₂×C₁₃	1	1	yes	characteristic
19	C₂×C₁₃×C₂₃	C₄×C₈	1	1	yes	characteristic
20	C₂×C₁₃×C₂₃	C₂×C₁₆	1	2	yes	—
21	C₂×C₁₃×C₁₆	C₂×C₂₃	1	2	yes	—
22	C₄×C₈×C₁₃	C₂×C₂₃	1	1	yes	characteristic
23	C₂×C₈×C₂₃	C₄×C₁₃	1	1	yes	characteristic
24	C₂×C₈×C₂₃	C₂²×C₁₃	1	1	yes	characteristic
25	C₄²×C₂₃	C₄×C₁₃	1	1	yes	characteristic
26	C₁₆×C₂₃	C₄×C₁₃	1	4	yes	direct product factor
27	C₁₃×C₂₃	C₄×C₁₆	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₈×C₁₃	C₄×C₂₃	1	1	yes	characteristic
29	C₂×C₈×C₁₃	C₂²×C₂₃	1	1	yes	characteristic
30	C₄²×C₁₃	C₄×C₂₃	1	1	yes	characteristic
31	C₁₃×C₁₆	C₄×C₂₃	1	4	yes	direct product factor
32	C₂×C₄×C₂₃	C₈×C₁₃	1	2	yes	—
33	C₂×C₄×C₂₃	C₂×C₄×C₁₃	1	1	yes	characteristic
34	C₈×C₂₃	C₈×C₁₃	1	2	yes	—
35	C₈×C₂₃	C₂×C₄×C₁₃	1	2	yes	—
36	C₂×C₄×C₁₃	C₈×C₂₃	1	2	yes	—
37	C₂×C₄×C₁₃	C₂×C₄×C₂₃	1	1	yes	characteristic
38	C₈×C₁₃	C₈×C₂₃	1	2	yes	—
39	C₈×C₁₃	C₂×C₄×C₂₃	1	2	yes	—
40	C₂²×C₂₃	C₂×C₈×C₁₃	1	1	yes	characteristic
41	C₄×C₂₃	C₁₃×C₁₆	1	4	yes	direct product factor
42	C₄×C₂₃	C₄²×C₁₃	1	1	yes	characteristic
43	C₄×C₂₃	C₂×C₈×C₁₃	1	1	yes	characteristic
44	C₄×C₁₆	C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₂²×C₁₃	C₂×C₈×C₂₃	1	1	yes	characteristic
46	C₄×C₁₃	C₁₆×C₂₃	1	4	yes	direct product factor
47	C₄×C₁₃	C₄²×C₂₃	1	1	yes	characteristic
48	C₄×C₁₃	C₂×C₈×C₂₃	1	1	yes	characteristic
49	C₂×C₂₃	C₄×C₈×C₁₃	1	1	yes	characteristic
50	C₂×C₂₃	C₂×C₁₃×C₁₆	1	2	yes	—
51	C₂×C₁₆	C₂×C₁₃×C₂₃	1	2	yes	—
52	C₄×C₈	C₂×C₁₃×C₂₃	1	1	yes	characteristic
53	C₂×C₁₃	C₄×C₈×C₂₃	1	1	yes	characteristic
54	C₂×C₁₃	C₂×C₁₆×C₂₃	1	2	yes	—
55	C₂₃	C₄×C₁₃×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₈	C₄×C₁₃×C₂₃	1	1	yes	characteristic
57	C₂×C₈	C₂²×C₁₃×C₂₃	1	1	yes	characteristic
58	C₄²	C₄×C₁₃×C₂₃	1	1	yes	characteristic
59	C₁₆	C₄×C₁₃×C₂₃	1	4	yes	direct product factor
60	C₁₃	C₄×C₁₆×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
61	C₂×C₄	C₈×C₁₃×C₂₃	1	2	yes	—
62	C₂×C₄	C₂×C₄×C₁₃×C₂₃	1	1	yes	characteristic
63	C₈	C₈×C₁₃×C₂₃	1	2	yes	—
64	C₈	C₂×C₄×C₁₃×C₂₃	1	2	yes	—
65	C₂²	C₂×C₈×C₁₃×C₂₃	1	1	yes	characteristic
66	C₄	C₁₃×C₁₆×C₂₃	1	4	yes	direct product factor
67	C₄	C₄²×C₁₃×C₂₃	1	1	yes	characteristic
68	C₄	C₂×C₈×C₁₃×C₂₃	1	1	yes	characteristic
69	C₂	C₂×C₁₃×C₁₆×C₂₃	1	2	yes	—
70	C₂	C₄×C₈×C₁₃×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂²×C₁₃×C₂₃
socle, prime radical	C₂²×C₁₃×C₂₃	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₁₃×C₁₆×C₂₃	C₄	direct (N × H)
11. C₄×C₁₆×C₂₃	C₁₃	direct (N × H)
13. C₄×C₁₃×C₂₃	C₁₆	direct (N × H)
16. C₄×C₁₃×C₁₆	C₂₃	direct (N × H)
26. C₁₆×C₂₃	C₄×C₁₃	direct (N × H)
27. C₁₃×C₂₃	C₄×C₁₆	direct (N × H)
31. C₁₃×C₁₆	C₄×C₂₃	direct (N × H)
41. C₄×C₂₃	C₁₃×C₁₆	direct (N × H)
44. C₄×C₁₆	C₁₃×C₂₃	direct (N × H)
46. C₄×C₁₃	C₁₆×C₂₃	direct (N × H)
55. C₂₃	C₄×C₁₃×C₁₆	direct (N × H)
59. C₁₆	C₄×C₁₃×C₂₃	direct (N × H)
60. C₁₃	C₄×C₁₆×C₂₃	direct (N × H)
66. C₄	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
C₄×C₈×C₁₃×C₂₃	2
C₂×C₁₃×C₁₆×C₂₃	2
C₄×C₁₆×C₂₃	13
C₄×C₁₃×C₁₆	23

Subgroups — C4×C13×C16×C23 #72196838

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×C₁₆×C₂₃ #72196838