Subgroups — C₁₃×#1007 #11929294

Order 1248.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#239	C₂	1	4	yes	maximal, complemented
3	D₃×Q₈×C₁₃	C₂	1	4	yes	maximal, complemented
4	C₁₃×#235	C₂	1	6	yes	maximal, complemented
5	C₁₃×2₋¹⁺⁴	—	3	1	no	maximal, Hall
6	C₃×Q₈×C₁₃	C₂²	1	4	yes	—
7	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
8	C₁₃×#67	C₂²	1	4	yes	—
9	C₁₃×D₁₂	C₂²	1	6	yes	—
10	C₄×D₃×C₁₃	C₂²	1	12	yes	—
11	C₁₃×Dic₆	C₂²	1	6	yes	—
12	C₁₃×#41	—	3	4	no	—
13	C₁₃×#41	—	3	6	no	—
14	C₂×Q₈×C₁₃	—	3	4	no	—
15	C₂×Q₈×C₁₃	D₃	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×D₃×C₁₃	C₂³	1	4	yes	—
18	C₃×C₄×C₁₃	C₂³	1	6	yes	—
19	Dic₃×C₁₃	C₂³	1	4	yes	—
20	Q₈×C₁₃	—	3	6	no	—
21	Q₈×C₁₃	C₂×D₃	1	4	yes	—
22	D₄×C₁₃	—	3	4	no	—
23	D₄×C₁₃	—	3	6	no	—
24	C₂×C₄×C₁₃	—	3	12	no	—
25	C₂×C₄×C₁₃	C₂×D₃	1	3	yes	—
26	#1007	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₃×C₁₃	—	2	1	no	—
28	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
29	D₃×C₁₃	—	2	4	no	—
30	C₂²×C₁₃	—	3	4	no	—
31	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
32	C₄×C₁₃	—	3	4	no	—
33	C₄×C₁₃	C₂²×D₃	1	6	yes	—
34	C₂×C₃×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
35	#239	C₂×C₁₃	1	4	yes	complemented
36	D₃×Q₈	C₂×C₁₃	1	4	yes	complemented
37	#235	C₂×C₁₃	1	6	yes	complemented
38	C₃×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Hall
39	2₋¹⁺⁴	—	3	1	no	Sylow
40	C₂×C₁₃	—	2	1	no	—
41	C₂×C₁₃	—	6	4	no	—
42	C₂×C₁₃	C₂³×D₃	1	1	yes	characteristic
43	C₃×Q₈	C₂²×C₁₃	1	4	yes	—
44	C₂×C₃×C₄	C₂²×C₁₃	1	3	yes	—
45	#67	C₂²×C₁₃	1	4	yes	—
46	D₁₂	C₂²×C₁₃	1	6	yes	—
47	C₄×D₃	C₂²×C₁₃	1	12	yes	—
48	Dic₆	C₂²×C₁₃	1	6	yes	—
49	#41	—	3	4	no	—
50	#41	—	3	6	no	—
51	C₂×Q₈	—	3	4	no	—
52	C₂×Q₈	D₃×C₁₃	1	1	yes	characteristic, complemented
53	C₁₃	#1007	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
55	C₂×D₃	C₂³×C₁₃	1	4	yes	—
56	C₃×C₄	C₂³×C₁₃	1	6	yes	—
57	Dic₃	C₂³×C₁₃	1	4	yes	—
58	Q₈	—	3	6	no	—
59	Q₈	C₂×D₃×C₁₃	1	4	yes	—
60	D₄	—	3	4	no	—
61	D₄	—	3	6	no	—
62	C₂×C₄	—	3	12	no	—
63	C₂×C₄	C₂×D₃×C₁₃	1	3	yes	—
64	C₂×C₃	—	2	1	no	—
65	C₂×C₃	C₂⁴×C₁₃	1	1	yes	characteristic
66	D₃	—	2	4	no	—
67	C₂²	—	3	4	no	—
68	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
69	C₄	—	3	4	no	—
70	C₄	C₂²×D₃×C₁₃	1	6	yes	—
71	C₃	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
72	C₂	—	2	1	no	—
73	C₂	—	6	4	no	—
74	C₂	C₂³×D₃×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₃	C₂³×D₃
commutator, cosocle	C₂×C₃	C₂⁴×C₁₃
Frattini	C₂	C₂³×D₃×C₁₃
Fitting	C₂×C₃×Q₈×C₁₃	C₂
socle	C₂×C₃×C₁₃	C₂⁴
hypercenter	C₂×Q₈×C₁₃	D₃
hypocenter	C₃	C₁₃×2₋¹⁺⁴
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×Q₈×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₈×C₁₃	C₂	semidirect
2. C₁₃×#239	C₂	semidirect
3. D₃×Q₈×C₁₃	C₂	semidirect
4. C₁₃×#235	C₂	semidirect
15. C₂×Q₈×C₁₃	D₃	semidirect
26. #1007	C₁₃	direct (N × H)
34. C₂×C₃×Q₈	C₂×C₁₃	semidirect
35. #239	C₂×C₁₃	semidirect
36. D₃×Q₈	C₂×C₁₃	semidirect
37. #235	C₂×C₁₃	semidirect
38. C₃×C₁₃	2₋¹⁺⁴	semidirect
52. C₂×Q₈	D₃×C₁₃	semidirect
53. C₁₃	#1007	direct (N × H)
71. C₃	C₁₃×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×Q₈×C₁₃	2
C₁₃×#239	2
D₃×Q₈×C₁₃	2
C₁₃×#235	2
C₁₃×2₋¹⁺⁴	3
#1007	13

Subgroups — C13×#1007 #11929294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1007 #11929294