Subgroups — C₁₃×#904 #11928880

Order 1248.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#235	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#204	C₂	1	2	yes	maximal, complemented
6	C₁₃×#135	—	3	1	no	maximal, Hall
7	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×#67	—	2	2	no	—
9	C₁₃×D₁₂	C₂²	1	2	yes	—
10	C₄×D₃×C₁₃	—	2	2	no	—
11	C₁₃×Dic₆	C₂²	1	2	yes	—
12	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#41	—	3	2	no	—
15	C₁₃×Q₁₆	—	3	1	no	—
16	C₁₃×SD₁₆	—	3	2	no	—
17	C₁₃×D₈	—	3	1	no	—
18	C₂×C₈×C₁₃	D₃	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
20	C₂×D₃×C₁₃	—	2	2	no	—
21	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
22	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
23	Dic₃×C₁₃	—	2	2	no	—
24	Q₈×C₁₃	—	3	2	no	—
25	D₄×C₁₃	—	3	2	no	—
26	D₄×C₁₃	—	6	2	no	—
27	C₂×C₄×C₁₃	—	6	2	no	—
28	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
29	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic
30	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic
31	#904	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₃×C₁₃	—	2	1	no	—
33	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
34	D₃×C₁₃	—	4	2	no	—
35	C₂²×C₁₃	—	6	2	no	—
36	C₂²×C₁₃	D₁₂	1	1	yes	characteristic
37	C₄×C₁₃	—	6	2	no	—
38	C₄×C₁₃	D₁₂	1	1	yes	characteristic
39	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
40	#235	C₂×C₁₃	1	2	yes	complemented
41	C₂×C₃×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
42	Dic₁₂	C₂×C₁₃	1	1	yes	characteristic, complemented
43	D₂₄	C₂×C₁₃	1	1	yes	characteristic, complemented
44	#204	C₂×C₁₃	1	2	yes	complemented
45	C₃×C₁₃	#135	1	1	yes	characteristic, complemented, Hall
46	#135	—	3	1	no	Sylow
47	C₂×C₁₃	—	2	1	no	—
48	C₂×C₁₃	—	12	2	no	—
49	C₂×C₁₃	C₂×D₁₂	1	1	yes	characteristic
50	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
51	#67	—	2	2	no	—
52	D₁₂	C₂²×C₁₃	1	2	yes	—
53	C₄×D₃	—	2	2	no	—
54	Dic₆	C₂²×C₁₃	1	2	yes	—
55	C₃×C₈	C₂²×C₁₃	1	1	yes	characteristic
56	C₃×C₈	C₂²×C₁₃	1	1	yes	characteristic
57	#41	—	3	2	no	—
58	Q₁₆	—	3	1	no	—
59	SD₁₆	—	3	2	no	—
60	D₈	—	3	1	no	—
61	C₂×C₈	D₃×C₁₃	1	1	yes	characteristic, complemented
62	C₁₃	#904	1	1	yes	characteristic, direct product factor, Sylow
63	C₂²×C₃	D₄×C₁₃	1	1	yes	characteristic
64	C₂×D₃	—	2	2	no	—
65	C₃×C₄	D₄×C₁₃	1	1	yes	characteristic
66	C₃×C₄	C₂³×C₁₃	1	1	yes	characteristic
67	Dic₃	—	2	2	no	—
68	Q₈	—	3	2	no	—
69	D₄	—	3	2	no	—
70	D₄	—	6	2	no	—
71	C₂×C₄	—	6	2	no	—
72	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
73	C₈	C₂×D₃×C₁₃	1	1	yes	characteristic
74	C₈	C₂×D₃×C₁₃	1	1	yes	characteristic
75	C₂×C₃	—	2	1	no	—
76	C₂×C₃	C₂×D₄×C₁₃	1	1	yes	characteristic
77	D₃	—	4	2	no	—
78	C₂²	—	6	2	no	—
79	C₂²	C₁₃×D₁₂	1	1	yes	characteristic
80	C₄	—	6	2	no	—
81	C₄	C₁₃×D₁₂	1	1	yes	characteristic
82	C₄	C₂²×D₃×C₁₃	1	1	yes	characteristic
83	C₃	C₁₃×#135	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	2	1	no	—
85	C₂	—	12	2	no	—
86	C₂	C₂×C₁₃×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	D₁₂
commutator, cosocle	C₃×C₄	C₂³×C₁₃
Frattini	C₄	C₂²×D₃×C₁₃
Fitting	C₂×C₃×C₈×C₁₃	C₂
socle	C₂×C₃×C₁₃	C₂×D₄
hypercenter	C₂×C₈×C₁₃	D₃
hypocenter	C₃	C₁₃×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₈×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×#235	C₂	semidirect
2. C₂×C₃×C₈×C₁₃	C₂	semidirect
3. C₁₃×Dic₁₂	C₂	semidirect
4. C₁₃×D₂₄	C₂	semidirect
5. C₁₃×#204	C₂	semidirect
18. C₂×C₈×C₁₃	D₃	semidirect
31. #904	C₁₃	direct (N × H)
40. #235	C₂×C₁₃	semidirect
41. C₂×C₃×C₈	C₂×C₁₃	semidirect
42. Dic₁₂	C₂×C₁₃	semidirect
43. D₂₄	C₂×C₁₃	semidirect
44. #204	C₂×C₁₃	semidirect
45. C₃×C₁₃	#135	semidirect
61. C₂×C₈	D₃×C₁₃	semidirect
62. C₁₃	#904	direct (N × H)
83. C₃	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#235	2
C₂×C₃×C₈×C₁₃	2
C₁₃×Dic₁₂	2
C₁₃×D₂₄	2
C₁₃×#204	2
C₁₃×#135	3
#904	13

Subgroups — C13×#904 #11928880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#904 #11928880