Subgroups — C₁₃×#1010 #11929297

Order 1248.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×Q₈×C₁₃	C₂	1	2	yes	maximal, complemented
3	C₁₃×#237	C₂	1	6	yes	maximal, complemented
4	C₁₃×#235	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₃×Dic₆	C₂	1	3	yes	maximal, complemented
6	C₁₃×2₋¹⁺⁴	—	3	1	no	maximal, Hall
7	C₃×Q₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₃×D₄×C₁₃	C₂²	1	3	yes	—
9	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
10	C₁₃×#67	C₂²	1	6	yes	—
11	C₂×Dic₃×C₁₃	C₂²	1	6	yes	—
12	C₁₃×D₁₂	C₂²	1	1	yes	characteristic
13	C₄×D₃×C₁₃	C₂²	1	6	yes	—
14	C₁₃×Dic₆	C₂²	1	3	yes	—
15	C₁₃×Dic₆	C₂²	1	6	yes	—
16	C₁₃×#41	—	3	6	no	—
17	C₁₃×#41	—	3	3	no	—
18	C₁₃×#41	D₃	1	1	yes	characteristic, complemented
19	C₂×Q₈×C₁₃	—	3	2	no	—
20	C₂×Q₈×C₁₃	—	3	3	no	—
21	C₂²×C₃×C₁₃	C₂³	1	3	yes	—
22	C₂×D₃×C₁₃	C₂³	1	2	yes	—
23	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₃×C₄×C₁₃	C₂³	1	3	yes	—
25	Dic₃×C₁₃	C₂³	1	6	yes	—
26	Q₈×C₁₃	—	3	6	no	—
27	Q₈×C₁₃	—	3	3	no	—
28	Q₈×C₁₃	C₂×D₃	1	1	yes	characteristic
29	D₄×C₁₃	—	3	6	no	—
30	D₄×C₁₃	—	3	1	no	—
31	D₄×C₁₃	C₂×D₃	1	3	yes	—
32	C₂×C₄×C₁₃	—	3	6	no	—
33	C₂×C₄×C₁₃	—	3	6	no	—
34	C₂×C₄×C₁₃	C₂×D₃	1	3	yes	—
35	#1010	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₂×C₃×C₁₃	—	2	3	no	—
37	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
38	D₃×C₁₃	—	2	2	no	—
39	C₂²×C₁₃	—	3	2	no	—
40	C₂²×C₁₃	C₂²×D₃	1	3	yes	—
41	C₄×C₁₃	—	3	6	no	—
42	C₄×C₁₃	C₂²×D₃	1	3	yes	—
43	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
44	C₃×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
45	D₃×Q₈	C₂×C₁₃	1	2	yes	complemented
46	#237	C₂×C₁₃	1	6	yes	complemented
47	#235	C₂×C₁₃	1	3	yes	complemented
48	C₂×Dic₆	C₂×C₁₃	1	3	yes	complemented
49	C₃×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Hall
50	2₋¹⁺⁴	—	3	1	no	Sylow
51	C₂×C₁₃	—	2	3	no	—
52	C₂×C₁₃	—	6	2	no	—
53	C₂×C₁₃	C₂³×D₃	1	1	yes	characteristic
54	C₃×Q₈	C₂²×C₁₃	1	1	yes	characteristic
55	C₃×D₄	C₂²×C₁₃	1	3	yes	—
56	C₂×C₃×C₄	C₂²×C₁₃	1	3	yes	—
57	#67	C₂²×C₁₃	1	6	yes	—
58	C₂×Dic₃	C₂²×C₁₃	1	6	yes	—
59	D₁₂	C₂²×C₁₃	1	1	yes	characteristic
60	C₄×D₃	C₂²×C₁₃	1	6	yes	—
61	Dic₆	C₂²×C₁₃	1	3	yes	—
62	Dic₆	C₂²×C₁₃	1	6	yes	—
63	#41	—	3	6	no	—
64	#41	—	3	3	no	—
65	#41	D₃×C₁₃	1	1	yes	characteristic, complemented
66	C₂×Q₈	—	3	2	no	—
67	C₂×Q₈	—	3	3	no	—
68	C₁₃	#1010	1	1	yes	characteristic, direct product factor, Sylow
69	C₂²×C₃	C₂³×C₁₃	1	3	yes	—
70	C₂×D₃	C₂³×C₁₃	1	2	yes	—
71	C₃×C₄	C₂³×C₁₃	1	1	yes	characteristic
72	C₃×C₄	C₂³×C₁₃	1	3	yes	—
73	Dic₃	C₂³×C₁₃	1	6	yes	—
74	Q₈	—	3	6	no	—
75	Q₈	—	3	3	no	—
76	Q₈	C₂×D₃×C₁₃	1	1	yes	characteristic
77	D₄	—	3	6	no	—
78	D₄	—	3	1	no	—
79	D₄	C₂×D₃×C₁₃	1	3	yes	—
80	C₂×C₄	—	3	6	no	—
81	C₂×C₄	—	3	6	no	—
82	C₂×C₄	C₂×D₃×C₁₃	1	3	yes	—
83	C₂×C₃	—	2	3	no	—
84	C₂×C₃	C₂⁴×C₁₃	1	1	yes	characteristic
85	D₃	—	2	2	no	—
86	C₂²	—	3	2	no	—
87	C₂²	C₂²×D₃×C₁₃	1	3	yes	—
88	C₄	—	3	6	no	—
89	C₄	C₂²×D₃×C₁₃	1	3	yes	—
90	C₄	C₂²×D₃×C₁₃	1	1	yes	characteristic
91	C₃	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
92	C₂	—	2	3	no	—
93	C₂	—	6	2	no	—
94	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	C₃×C₁₃×#41	C₂
socle	C₂×C₃×C₁₃	C₂⁴
hypercenter	C₁₃×#41	D₃
hypocenter	C₃	C₁₃×2₋¹⁺⁴
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₃ ◁ C₁₃×#41

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×#41	C₂	semidirect
2. D₃×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#237	C₂	semidirect
4. C₁₃×#235	C₂	semidirect
5. C₂×C₁₃×Dic₆	C₂	semidirect
18. C₁₃×#41	D₃	semidirect
35. #1010	C₁₃	direct (N × H)
44. C₃×#41	C₂×C₁₃	semidirect
45. D₃×Q₈	C₂×C₁₃	semidirect
46. #237	C₂×C₁₃	semidirect
47. #235	C₂×C₁₃	semidirect
48. C₂×Dic₆	C₂×C₁₃	semidirect
49. C₃×C₁₃	2₋¹⁺⁴	semidirect
65. #41	D₃×C₁₃	semidirect
68. C₁₃	#1010	direct (N × H)
91. 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
C₃×C₁₃×#41	2
D₃×Q₈×C₁₃	2
C₁₃×#237	2
C₁₃×#235	2
C₂×C₁₃×Dic₆	2
C₁₃×2₋¹⁺⁴	3
#1010	13

Subgroups — C13×#1010 #11929297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1010 #11929297