Subgroups — D₂₃×D₃₄₅ #44540751

Order 31740.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₃×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×D₃₄₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₅⋊(C₂₃⋊D₂₃))	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₃×D₁₁₅	—	3	1	no	maximal, Hall
5	C₃×C₅×C₂₃²	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₃×D₆₉	—	5	1	no	maximal, Hall
7	C₅⋊(C₂₃⋊D₂₃)	—	3	1	no	—
8	C₂₃×D₁₁₅	—	3	1	no	—
9	C₅×C₂₃×D₂₃	D₃	1	1	yes	characteristic, complemented
10	C₃⋊(C₂₃⋊D₂₃)	—	5	1	no	—
11	C₂₃×D₆₉	—	5	1	no	—
12	C₃×C₂₃×D₂₃	D₅	1	1	yes	characteristic, complemented
13	C₅×C₂₃²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₂₃²	—	15	1	no	Hall
15	C₃×C₂₃²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×D₃₄₅	—	23	1	no	maximal
17	D₁₅×D₂₃	—	23	1	no	maximal
18	C₂₃⋊D₂₃	—	15	1	no	—
19	C₂₃×D₂₃	—	15	1	no	—
20	C₂₃×D₂₃	D₁₅	1	1	yes	characteristic, complemented
21	C₂×C₃×C₅×C₂₃	—	23	1	no	—
22	D₃₄₅	—	23	1	no	—
23	D₃₄₅	—	23	1	no	—
24	D₃₄₅	—	46	11	no	—
25	D₃₄₅	D₂₃	1	1	yes	characteristic, direct product factor
26	C₂₃×D₁₅	—	23	1	no	—
27	C₃×C₅×D₂₃	D₂₃	1	1	yes	characteristic, complemented
28	C₂₃²	C₂×D₁₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×D₁₁₅	—	69	1	no	—
30	D₅×D₂₃	—	69	1	no	—
31	C₃×C₅×C₂₃	—	2	11	no	—
32	C₃×C₅×C₂₃	C₂×D₂₃	1	1	yes	characteristic, complemented
33	C₃×C₅×C₂₃	C₂×D₂₃	1	1	yes	characteristic, complemented
34	C₂×D₆₉	—	115	1	no	—
35	D₃×D₂₃	—	115	1	no	—
36	C₂×C₅×C₂₃	—	23	1	no	—
37	D₁₁₅	—	3	1	no	—
38	D₁₁₅	—	69	1	no	—
39	D₁₁₅	—	69	1	no	—
40	D₁₁₅	—	138	11	no	—
41	C₅×D₂₃	D₆₉	1	1	yes	characteristic, complemented
42	D₅×C₂₃	—	69	1	no	—
43	C₂×C₃×C₂₃	—	23	1	no	—
44	D₆₉	—	5	1	no	—
45	D₆₉	—	115	1	no	—
46	D₆₉	—	115	1	no	—
47	D₆₉	—	230	11	no	—
48	C₃×D₂₃	D₁₁₅	1	1	yes	characteristic, complemented
49	D₃×C₂₃	—	115	1	no	—
50	C₅×C₂₃	—	2	11	no	—
51	C₅×C₂₃	D₃×D₂₃	1	1	yes	characteristic, complemented
52	C₅×C₂₃	C₂×D₆₉	1	1	yes	characteristic, complemented
53	C₂×D₂₃	—	345	1	no	—
54	C₂×D₂₃	—	345	1	no	—
55	C₃×C₂₃	—	2	11	no	—
56	C₃×C₂₃	D₅×D₂₃	1	1	yes	characteristic, complemented
57	C₃×C₂₃	C₂×D₁₁₅	1	1	yes	characteristic, complemented
58	C₂×D₁₅	—	529	1	no	Hall
59	C₂×C₂₃	—	23	1	no	—
60	C₂×C₂₃	—	345	1	no	—
61	D₂₃	—	15	1	no	—
62	D₂₃	—	345	1	no	—
63	D₂₃	—	345	1	no	—
64	D₂₃	—	690	11	no	—
65	D₂₃	D₃₄₅	1	1	yes	characteristic, direct product factor
66	C₂×C₃×C₅	—	23	1	no	—
67	D₁₅	—	529	1	no	—
68	D₁₅	—	23	1	no	—
69	C₂₃	—	2	11	no	—
70	C₂₃	D₁₅×D₂₃	1	1	yes	characteristic, complemented
71	C₂₃	C₂×D₃₄₅	1	1	yes	characteristic, complemented
72	C₂×D₅	—	1587	1	no	Hall
73	C₃×C₅	D₂₃²	1	1	yes	characteristic, complemented, Hall
74	C₂×D₃	—	2645	1	no	Hall
75	C₂×C₅	—	23	1	no	—
76	D₅	—	1587	1	no	—
77	D₅	—	69	1	no	—
78	C₂×C₃	—	23	1	no	—
79	D₃	—	2645	1	no	—
80	D₃	—	115	1	no	—
81	C₅	D₂₃×D₆₉	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	7935	1	no	Sylow
83	C₃	D₂₃×D₁₁₅	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	23	1	no	—
85	C₂	—	345	1	no	—
86	C₂	—	7935	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₂₃²	C₂²
LCS	G ▷ C₃×C₅×C₂₃²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂₃×D₂₃	C₂	semidirect
2. C₂₃×D₃₄₅	C₂	semidirect
3. C₃⋊(C₅⋊(C₂₃⋊D₂₃))	C₂	semidirect
5. C₃×C₅×C₂₃²	C₂²	semidirect
9. C₅×C₂₃×D₂₃	D₃	semidirect
12. C₃×C₂₃×D₂₃	D₅	semidirect
13. C₅×C₂₃²	C₂×D₃	semidirect
15. C₃×C₂₃²	C₂×D₅	semidirect
20. C₂₃×D₂₃	D₁₅	semidirect
25. D₃₄₅	D₂₃	direct (N × H)
27. C₃×C₅×D₂₃	D₂₃	semidirect
28. C₂₃²	C₂×D₁₅	semidirect
32. C₃×C₅×C₂₃	C₂×D₂₃	semidirect
33. C₃×C₅×C₂₃	C₂×D₂₃	semidirect
41. C₅×D₂₃	D₆₉	semidirect
48. C₃×D₂₃	D₁₁₅	semidirect
51. C₅×C₂₃	D₃×D₂₃	semidirect
52. C₅×C₂₃	C₂×D₆₉	semidirect
56. C₃×C₂₃	D₅×D₂₃	semidirect
57. C₃×C₂₃	C₂×D₁₁₅	semidirect
65. D₂₃	D₃₄₅	direct (N × H)
70. C₂₃	D₁₅×D₂₃	semidirect
71. C₂₃	C₂×D₃₄₅	semidirect
73. C₃×C₅	D₂₃²	semidirect
81. C₅	D₂₃×D₆₉	semidirect
83. C₃	D₂₃×D₁₁₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₂₃×D₂₃	2
C₂₃×D₃₄₅	2
C₃⋊(C₅⋊(C₂₃⋊D₂₃))	2
D₂₃×D₁₁₅	3
D₂₃×D₆₉	5
C₂×D₃₄₅	23
D₁₅×D₂₃	23

Subgroups — D23×D345 #44540751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×D₃₄₅ #44540751