Subgroups — C₂×#41×C₁₃⋊C₃ #11929249

Order 1248.

328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₁₃⋊C₃	C₂	1	8	yes	maximal, direct product factor
2	C₂×Q₈×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄×C₁₃⋊C₃	C₂	1	3	yes	maximal, complemented
4	C₂²×C₄×C₁₃⋊C₃	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₃×#41	C₃	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂³×C₁₃⋊C₃	C₂²	1	3	yes	—
7	Q₈×C₁₃⋊C₃	C₂²	1	4	yes	complemented
8	D₄×C₁₃⋊C₃	C₂²	1	12	yes	complemented
9	C₂×C₄×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₃⋊C₃	C₂²	1	3	yes	—
11	C₂×C₄×C₁₃⋊C₃	C₂²	1	12	yes	complemented
12	C₁₃×#41	C₂×C₃	1	8	yes	complemented
13	C₂×Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×D₄×C₁₃	C₂×C₃	1	3	yes	complemented
15	C₂²×C₄×C₁₃	C₂×C₃	1	3	yes	complemented
16	C₂²×C₁₃⋊C₃	—	2	6	no	—
17	C₂²×C₁₃⋊C₃	C₂³	1	6	yes	—
18	C₂²×C₁₃⋊C₃	C₂³	1	1	yes	characteristic
19	C₄×C₁₃⋊C₃	C₂³	1	2	yes	—
20	C₄×C₁₃⋊C₃	C₂³	1	6	yes	—
21	C₂³×C₁₃	C₂²×C₃	1	3	yes	—
22	Q₈×C₁₃	C₂²×C₃	1	4	yes	complemented
23	D₄×C₁₃	C₂²×C₃	1	12	yes	complemented
24	C₂×C₄×C₁₃	C₂²×C₃	1	3	yes	—
25	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₂²×C₃	1	12	yes	complemented
27	C₂×C₃×#41	—	13	1	no	maximal, Hall
28	C₂×C₁₃⋊C₃	—	2	6	no	—
29	C₂×C₁₃⋊C₃	#41	1	2	yes	direct product factor
30	C₂×C₁₃⋊C₃	C₂⁴	1	1	yes	characteristic
31	C₂²×C₁₃	—	2	6	no	—
32	C₂²×C₁₃	C₂³×C₃	1	6	yes	—
33	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
34	C₄×C₁₃	C₂³×C₃	1	2	yes	—
35	C₄×C₁₃	C₂³×C₃	1	6	yes	—
36	C₃×#41	—	13	8	no	—
37	C₂×C₃×Q₈	—	13	1	no	—
38	C₂×C₃×D₄	—	13	3	no	—
39	C₂²×C₃×C₄	—	13	3	no	—
40	C₁₃⋊C₃	C₂×#41	1	1	yes	characteristic, direct product factor, Hall
41	C₂×#41	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₁₃	—	2	6	no	—
43	C₂×C₁₃	C₃×#41	1	2	yes	complemented
44	C₂×C₁₃	C₂⁴×C₃	1	1	yes	characteristic
45	C₂³×C₃	—	13	3	no	—
46	C₃×Q₈	—	13	4	no	—
47	C₃×D₄	—	13	12	no	—
48	C₂×C₃×C₄	—	13	3	no	—
49	C₂×C₃×C₄	—	13	1	no	—
50	C₂×C₃×C₄	—	13	12	no	—
51	#41	C₂×C₁₃⋊C₃	1	8	yes	direct product factor
52	C₂×Q₈	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
53	C₂×D₄	C₂×C₁₃⋊C₃	1	3	yes	complemented
54	C₂²×C₄	C₂×C₁₃⋊C₃	1	3	yes	complemented
55	C₁₃	C₂×C₃×#41	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₃	—	13	1	no	—
57	C₂²×C₃	—	13	6	no	—
58	C₂²×C₃	—	26	6	no	—
59	C₃×C₄	—	13	2	no	—
60	C₃×C₄	—	13	6	no	—
61	C₂³	C₂²×C₁₃⋊C₃	1	3	yes	—
62	Q₈	C₂²×C₁₃⋊C₃	1	4	yes	complemented
63	D₄	C₂²×C₁₃⋊C₃	1	12	yes	complemented
64	C₂×C₄	C₂²×C₁₃⋊C₃	1	3	yes	—
65	C₂×C₄	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
66	C₂×C₄	C₂²×C₁₃⋊C₃	1	12	yes	complemented
67	C₂×C₃	—	13	2	no	—
68	C₂×C₃	—	13	1	no	—
69	C₂×C₃	—	26	6	no	—
70	C₂²	—	2	6	no	—
71	C₂²	C₂³×C₁₃⋊C₃	1	6	yes	—
72	C₂²	C₂³×C₁₃⋊C₃	1	1	yes	characteristic
73	C₄	C₂³×C₁₃⋊C₃	1	6	yes	—
74	C₄	C₂³×C₁₃⋊C₃	1	2	yes	—
75	C₃	—	13	1	no	Sylow
76	C₂	—	2	6	no	—
77	C₂	#41×C₁₃⋊C₃	1	2	yes	direct product factor
78	C₂	C₂⁴×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₁₃⋊C₃
commutator, cosocle	C₂×C₁₃	C₂⁴×C₃
Frattini	C₂	C₂⁴×C₁₃⋊C₃
Fitting	C₂×C₁₃×#41	C₃
socle	C₂²×C₁₃	C₂³×C₃
hypercenter	C₂×#41	C₁₃⋊C₃
hypocenter	C₁₃	C₂×C₃×#41
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. #41×C₁₃⋊C₃	C₂	direct (N × H)
2. C₂×Q₈×C₁₃⋊C₃	C₂	semidirect
3. C₂×D₄×C₁₃⋊C₃	C₂	semidirect
4. C₂²×C₄×C₁₃⋊C₃	C₂	semidirect
5. C₂×C₁₃×#41	C₃	semidirect
7. Q₈×C₁₃⋊C₃	C₂²	semidirect
8. D₄×C₁₃⋊C₃	C₂²	semidirect
11. C₂×C₄×C₁₃⋊C₃	C₂²	semidirect
12. C₁₃×#41	C₂×C₃	semidirect
13. C₂×Q₈×C₁₃	C₂×C₃	semidirect
14. C₂×D₄×C₁₃	C₂×C₃	semidirect
15. C₂²×C₄×C₁₃	C₂×C₃	semidirect
22. Q₈×C₁₃	C₂²×C₃	semidirect
23. D₄×C₁₃	C₂²×C₃	semidirect
26. C₂×C₄×C₁₃	C₂²×C₃	semidirect
29. C₂×C₁₃⋊C₃	#41	direct (N × H)
40. C₁₃⋊C₃	C₂×#41	direct (N × H)
41. C₂×#41	C₁₃⋊C₃	direct (N × H)
43. C₂×C₁₃	C₃×#41	semidirect
51. #41	C₂×C₁₃⋊C₃	direct (N × H)
52. C₂×Q₈	C₂×C₁₃⋊C₃	semidirect
53. C₂×D₄	C₂×C₁₃⋊C₃	semidirect
54. C₂²×C₄	C₂×C₁₃⋊C₃	semidirect
55. C₁₃	C₂×C₃×#41	semidirect
62. Q₈	C₂²×C₁₃⋊C₃	semidirect
63. D₄	C₂²×C₁₃⋊C₃	semidirect
66. C₂×C₄	C₂²×C₁₃⋊C₃	semidirect
77. C₂	#41×C₁₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
#41×C₁₃⋊C₃	2
C₂×Q₈×C₁₃⋊C₃	2
C₂×D₄×C₁₃⋊C₃	2
C₂²×C₄×C₁₃⋊C₃	2
C₂×C₁₃×#41	3
C₂×C₃×#41	13

Subgroups — C2×#41×C13⋊C3 #11929249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#41×C₁₃⋊C₃ #11929249