Subgroups — C₁₃⋊C₃×D₃₄₅ #41002113

Order 26910.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃⋊C₃×D₁₁₅	—	3	1	no	maximal
3	C₁₃×D₃₄₅	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃⋊C₃×D₆₉	—	5	1	no	maximal, Hall
5	C₅×C₂₃×C₁₃⋊C₃	—	2	1	no	—
6	C₅×C₂₃×C₁₃⋊C₃	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₃×D₁₁₅	—	3	1	no	Hall
9	C₃×C₂₃×C₁₃⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
10	C₃×D₃₄₅	—	13	1	no	maximal, Hall
11	C₁₃×D₆₉	—	5	1	no	—
12	C₁₃⋊C₃×D₂₃	—	15	1	no	—
13	C₅×C₁₃×C₂₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
14	D₁₅×C₁₃⋊C₃	—	23	1	no	maximal, Hall
15	C₃²×C₅×C₂₃	—	13	1	no	Hall
16	C₃×C₁₃×C₂₃	C₃×D₅	1	1	yes	characteristic, complemented
17	C₂₃×C₁₃⋊C₃	—	2	1	no	—
18	C₂₃×C₁₃⋊C₃	D₁₅	1	1	yes	characteristic, complemented
19	D₃₄₅	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
20	C₃×D₁₁₅	—	39	1	no	—
21	C₁₃×D₂₃	—	15	1	no	Hall
22	C₃×C₅×C₁₃⋊C₃	D₂₃	1	1	yes	characteristic, complemented, Hall
23	C₃×D₆₉	—	65	1	no	Hall
24	C₁₃×D₁₅	—	23	1	no	—
25	D₅×C₁₃⋊C₃	—	69	1	no	—
26	C₃×C₅×C₂₃	—	13	1	no	—
27	C₃×C₅×C₂₃	—	26	1	no	—
28	C₃×C₅×C₂₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
29	C₁₃×C₂₃	C₃×D₁₅	1	1	yes	characteristic, complemented, Hall
30	D₃×C₁₃⋊C₃	—	115	1	no	Hall
31	D₁₁₅	—	3	1	no	Hall
32	C₃²×C₂₃	—	13	1	no	Hall
33	C₃×C₅×C₁₃	C₃×D₂₃	1	1	yes	characteristic, complemented
34	C₅×C₁₃⋊C₃	—	2	1	no	—
35	C₅×C₁₃⋊C₃	D₆₉	1	1	yes	characteristic, complemented
36	D₆₉	—	5	1	no	—
37	C₃×D₂₃	—	195	1	no	—
38	D₅×C₁₃	—	69	1	no	Hall
39	C₃×C₁₃⋊C₃	D₁₁₅	1	1	yes	characteristic, complemented, Hall
40	C₅×C₂₃	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
41	C₃×D₁₅	—	299	1	no	Hall
42	D₃×C₁₃	—	115	1	no	—
43	C₂×C₁₃⋊C₃	—	345	1	no	—
44	C₃×C₂₃	—	13	1	no	—
45	C₃×C₂₃	—	26	1	no	—
46	C₃×C₂₃	D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
47	C₅×C₁₃	C₃×D₆₉	1	1	yes	characteristic, complemented, Hall
48	D₂₃	—	15	1	no	Hall
49	C₃²×C₅	—	13	1	no	Hall
50	C₃×C₁₃	C₃×D₁₁₅	1	1	yes	characteristic, complemented
51	C₁₃⋊C₃	—	2	1	no	—
52	C₁₃⋊C₃	D₃₄₅	1	1	yes	characteristic, direct product factor
53	D₁₅	—	23	1	no	—
54	C₃×D₅	—	897	1	no	—
55	C₂×C₁₃	—	345	1	no	Hall
56	C₂₃	D₁₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
57	C₃×D₃	—	1495	1	no	Hall
58	C₃×C₅	—	13	1	no	—
59	C₃×C₅	—	26	1	no	—
60	C₃×C₅	C₁₃⋊C₃×D₂₃	1	1	yes	characteristic, complemented
61	C₁₃	C₃×D₃₄₅	1	1	yes	characteristic, complemented, Sylow
62	D₅	—	69	1	no	Hall
63	C₃²	—	13	1	no	Sylow
64	C₂×C₃	—	4485	1	no	—
65	D₃	—	115	1	no	—
66	C₅	C₁₃⋊C₃×D₆₉	1	1	yes	characteristic, complemented, Sylow
67	C₃	—	13	1	no	—
68	C₃	—	26	1	no	—
69	C₃	C₁₃⋊C₃×D₁₁₅	1	1	yes	characteristic, complemented
70	C₂	—	345	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₃×C₂₃	C₂×C₃
LCS	G ▷ C₃×C₅×C₁₃×C₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂₃×C₁₃⋊C₃	C₂	semidirect
3. C₁₃×D₃₄₅	C₃	semidirect
6. C₅×C₂₃×C₁₃⋊C₃	D₃	semidirect
7. C₃×C₅×C₁₃×C₂₃	C₂×C₃	semidirect
9. C₃×C₂₃×C₁₃⋊C₃	D₅	semidirect
13. C₅×C₁₃×C₂₃	C₃×D₃	semidirect
16. C₃×C₁₃×C₂₃	C₃×D₅	semidirect
18. C₂₃×C₁₃⋊C₃	D₁₅	semidirect
19. D₃₄₅	C₁₃⋊C₃	direct (N × H)
22. C₃×C₅×C₁₃⋊C₃	D₂₃	semidirect
28. C₃×C₅×C₂₃	C₂×C₁₃⋊C₃	semidirect
29. C₁₃×C₂₃	C₃×D₁₅	semidirect
33. C₃×C₅×C₁₃	C₃×D₂₃	semidirect
35. C₅×C₁₃⋊C₃	D₆₉	semidirect
39. C₃×C₁₃⋊C₃	D₁₁₅	semidirect
40. C₅×C₂₃	D₃×C₁₃⋊C₃	semidirect
46. C₃×C₂₃	D₅×C₁₃⋊C₃	semidirect
47. C₅×C₁₃	C₃×D₆₉	semidirect
50. C₃×C₁₃	C₃×D₁₁₅	semidirect
52. C₁₃⋊C₃	D₃₄₅	direct (N × H)
56. C₂₃	D₁₅×C₁₃⋊C₃	semidirect
60. C₃×C₅	C₁₃⋊C₃×D₂₃	semidirect
61. C₁₃	C₃×D₃₄₅	semidirect
66. C₅	C₁₃⋊C₃×D₆₉	semidirect
69. C₃	C₁₃⋊C₃×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×C₁₃⋊C₃	2
C₁₃⋊C₃×D₁₁₅	3
C₁₃×D₃₄₅	3
C₁₃⋊C₃×D₆₉	5
C₃×D₃₄₅	13
D₁₅×C₁₃⋊C₃	23

Subgroups — C13⋊C3×D345 #41002113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₃×D₃₄₅ #41002113