Subgroups — C₂²×C₃×D₅₂ #11929272

Order 1248.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×D₁₃	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₅₂	C₂	1	12	yes	maximal, direct product factor
4	C₂²×D₅₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₃×D₁₃	—	2	8	no	—
7	C₂²×C₃×D₁₃	C₂²	1	12	yes	complemented
8	C₂×C₃×C₄×C₁₃	C₂²	1	6	yes	complemented
9	C₃×D₅₂	C₂²	1	16	yes	direct product factor
10	C₂³×D₁₃	C₂×C₃	1	2	yes	complemented
11	C₂²×C₄×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×D₅₂	C₂×C₃	1	12	yes	direct product factor
13	C₂²×C₃×C₁₃	D₄	1	4	yes	complemented
14	C₂²×C₃×C₁₃	C₂³	1	3	yes	—
15	C₂×C₃×D₁₃	—	2	24	no	—
16	C₂×C₃×D₁₃	C₂³	1	8	yes	complemented
17	C₃×C₄×C₁₃	C₂³	1	4	yes	complemented
18	C₂³×C₁₃	C₂²×C₃	1	1	yes	characteristic
19	C₂²×D₁₃	—	2	8	no	—
20	C₂²×D₁₃	C₂²×C₃	1	12	yes	complemented
21	C₂×C₄×C₁₃	C₂²×C₃	1	6	yes	complemented
22	D₅₂	C₂²×C₃	1	16	yes	direct product factor
23	C₂²×C₃×D₄	—	13	1	no	maximal, Hall
24	C₂×C₃×C₁₃	C₂×D₄	1	6	yes	complemented
25	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
26	C₃×D₁₃	—	2	8	no	—
27	C₂²×C₁₃	C₃×D₄	1	4	yes	complemented
28	C₂²×C₁₃	C₂³×C₃	1	3	yes	—
29	C₂×D₁₃	—	2	24	no	—
30	C₂×D₁₃	C₂³×C₃	1	8	yes	complemented
31	C₄×C₁₃	C₂³×C₃	1	4	yes	complemented
32	C₂⁴×C₃	—	13	2	no	—
33	C₂×C₃×D₄	—	13	12	no	—
34	C₂²×C₃×C₄	D₁₃	1	1	yes	characteristic, complemented
35	C₃×C₁₃	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
36	C₂²×D₄	—	13	1	no	Sylow
37	C₂×C₁₃	C₂×C₃×D₄	1	6	yes	complemented
38	C₂×C₁₃	C₂⁴×C₃	1	1	yes	characteristic
39	D₁₃	—	2	8	no	—
40	C₂³×C₃	—	13	12	no	—
41	C₂³×C₃	—	26	8	no	—
42	C₂³×C₃	C₂×D₁₃	1	1	yes	characteristic
43	C₃×D₄	—	13	16	no	—
44	C₂×C₃×C₄	C₂×D₁₃	1	6	yes	complemented
45	C₂⁴	—	13	2	no	—
46	C₂×D₄	—	13	12	no	—
47	C₂²×C₄	C₃×D₁₃	1	1	yes	characteristic, complemented
48	C₁₃	C₂²×C₃×D₄	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₃	—	13	8	no	—
50	C₂²×C₃	—	26	24	no	—
51	C₂²×C₃	D₅₂	1	4	yes	direct product factor
52	C₂²×C₃	C₂²×D₁₃	1	3	yes	—
53	C₃×C₄	C₂²×D₁₃	1	4	yes	complemented
54	C₂³	—	13	12	no	—
55	C₂³	—	26	8	no	—
56	C₂³	C₂×C₃×D₁₃	1	1	yes	characteristic
57	D₄	—	13	16	no	—
58	C₂×C₄	C₂×C₃×D₁₃	1	6	yes	complemented
59	C₂×C₃	—	26	8	no	—
60	C₂×C₃	C₂×D₅₂	1	6	yes	direct product factor
61	C₂×C₃	C₂³×D₁₃	1	1	yes	characteristic
62	C₂²	—	13	8	no	—
63	C₂²	—	26	24	no	—
64	C₂²	C₃×D₅₂	1	4	yes	direct product factor
65	C₂²	C₂²×C₃×D₁₃	1	3	yes	—
66	C₄	C₂²×C₃×D₁₃	1	4	yes	complemented
67	C₃	C₂²×D₅₂	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	—	26	8	no	—
69	C₂	C₂×C₃×D₅₂	1	6	yes	direct product factor
70	C₂	C₂³×C₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₁₃
commutator, cosocle	C₂×C₁₃	C₂⁴×C₃
Frattini	C₂	C₂³×C₃×D₁₃
Fitting	C₂²×C₃×C₄×C₁₃	C₂
socle	C₂³×C₃×C₁₃	C₂²
hypercenter	C₂²×C₃×C₄	D₁₃
hypocenter	C₁₃	C₂²×C₃×D₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×D₁₃	C₂	semidirect
2. C₂²×C₃×C₄×C₁₃	C₂	semidirect
3. C₂×C₃×D₅₂	C₂	direct (N × H)
4. C₂²×D₅₂	C₃	direct (N × H)
7. C₂²×C₃×D₁₃	C₂²	semidirect
8. C₂×C₃×C₄×C₁₃	C₂²	semidirect
9. C₃×D₅₂	C₂²	direct (N × H)
10. C₂³×D₁₃	C₂×C₃	semidirect
11. C₂²×C₄×C₁₃	C₂×C₃	semidirect
12. C₂×D₅₂	C₂×C₃	direct (N × H)
13. C₂²×C₃×C₁₃	D₄	semidirect
16. C₂×C₃×D₁₃	C₂³	semidirect
17. C₃×C₄×C₁₃	C₂³	semidirect
20. C₂²×D₁₃	C₂²×C₃	semidirect
21. C₂×C₄×C₁₃	C₂²×C₃	semidirect
22. D₅₂	C₂²×C₃	direct (N × H)
24. C₂×C₃×C₁₃	C₂×D₄	semidirect
27. C₂²×C₁₃	C₃×D₄	semidirect
30. C₂×D₁₃	C₂³×C₃	semidirect
31. C₄×C₁₃	C₂³×C₃	semidirect
34. C₂²×C₃×C₄	D₁₃	semidirect
35. C₃×C₁₃	C₂²×D₄	semidirect
37. C₂×C₁₃	C₂×C₃×D₄	semidirect
44. C₂×C₃×C₄	C₂×D₁₃	semidirect
47. C₂²×C₄	C₃×D₁₃	semidirect
48. C₁₃	C₂²×C₃×D₄	semidirect
51. C₂²×C₃	D₅₂	direct (N × H)
53. C₃×C₄	C₂²×D₁₃	semidirect
58. C₂×C₄	C₂×C₃×D₁₃	semidirect
60. C₂×C₃	C₂×D₅₂	direct (N × H)
64. C₂²	C₃×D₅₂	direct (N × H)
66. C₄	C₂²×C₃×D₁₃	semidirect
67. C₃	C₂²×D₅₂	direct (N × H)
69. C₂	C₂×C₃×D₅₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×D₁₃	2
C₂²×C₃×C₄×C₁₃	2
C₂×C₃×D₅₂	2
C₂²×D₅₂	3
C₂²×C₃×D₄	13

Subgroups — C22×C3×D52 #11929272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×D₅₂ #11929272