Subgroups — C₁₃×#912 #11928888

Order 1248.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#237	C₂	1	2	yes	maximal, complemented
2	C₃×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#214	C₂	1	2	yes	maximal, complemented
4	C₁₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#135	—	3	1	no	maximal, Hall
7	C₃×D₄×C₁₃	C₂²	1	2	yes	—
8	C₁₃×#67	—	2	2	no	—
9	C₂×Dic₃×C₁₃	—	2	2	no	—
10	C₄×D₃×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×Dic₆	C₂²	1	2	yes	—
12	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×C₃⋊C₈	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	D₃	1	1	yes	characteristic, complemented
18	C₂×C₈×C₁₃	—	3	1	no	—
19	C₂²×C₃×C₁₃	—	2	2	no	—
20	C₂×D₃×C₁₃	D₄	1	1	yes	characteristic
21	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	Dic₃×C₁₃	—	2	2	no	—
23	Dic₃×C₁₃	D₄	1	1	yes	characteristic
24	Q₈×C₁₃	—	3	2	no	—
25	D₄×C₁₃	—	6	2	no	—
26	D₄×C₁₃	C₂×D₃	1	2	yes	—
27	C₂×C₄×C₁₃	—	3	1	no	—
28	C₂×C₄×C₁₃	—	6	2	no	—
29	C₈×C₁₃	—	3	1	no	—
30	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic
31	#912	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₃×C₁₃	—	4	2	no	—
33	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
34	D₃×C₁₃	—	2	1	no	—
35	C₂²×C₁₃	—	2	2	no	—
36	C₂²×C₁₃	—	3	1	no	—
37	C₄×C₁₃	—	3	1	no	—
38	C₄×C₁₃	—	6	2	no	—
39	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
40	#237	C₂×C₁₃	1	2	yes	complemented
41	C₃×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
42	#214	C₂×C₁₃	1	2	yes	complemented
43	Dic₁₂	C₂×C₁₃	1	1	yes	characteristic, complemented
44	D₃×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
45	C₃×C₁₃	#135	1	1	yes	characteristic, complemented, Hall
46	#135	—	3	1	no	Sylow
47	C₂×C₁₃	—	4	2	no	—
48	C₂×C₁₃	—	6	1	no	—
49	C₂×C₁₃	D₃×D₄	1	1	yes	characteristic
50	C₃×D₄	C₂²×C₁₃	1	2	yes	—
51	#67	—	2	2	no	—
52	C₂×Dic₃	—	2	2	no	—
53	C₄×D₃	C₂²×C₁₃	1	1	yes	characteristic
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	D₃×C₁₃	1	1	yes	characteristic, complemented
61	C₂×C₈	—	3	1	no	—
62	C₁₃	#912	1	1	yes	characteristic, direct product factor, Sylow
63	C₂²×C₃	—	2	2	no	—
64	C₂×D₃	D₄×C₁₃	1	1	yes	characteristic
65	C₃×C₄	C₂³×C₁₃	1	1	yes	characteristic
66	Dic₃	—	2	2	no	—
67	Dic₃	D₄×C₁₃	1	1	yes	characteristic
68	Q₈	—	3	2	no	—
69	D₄	—	6	2	no	—
70	D₄	C₂×D₃×C₁₃	1	2	yes	—
71	C₂×C₄	—	3	1	no	—
72	C₂×C₄	—	6	2	no	—
73	C₈	—	3	1	no	—
74	C₈	C₂×D₃×C₁₃	1	1	yes	characteristic
75	C₂×C₃	—	4	2	no	—
76	C₂×C₃	C₂×D₄×C₁₃	1	1	yes	characteristic
77	D₃	—	2	1	no	—
78	C₂²	—	2	2	no	—
79	C₂²	—	3	1	no	—
80	C₄	—	3	1	no	—
81	C₄	—	6	2	no	—
82	C₄	C₂²×D₃×C₁₃	1	1	yes	characteristic
83	C₃	C₁₃×#135	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	4	2	no	—
85	C₂	—	6	1	no	—
86	C₂	D₃×D₄×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₃	D₃×D₄
commutator, cosocle	C₃×C₄	C₂³×C₁₃
Frattini	C₄	C₂²×D₃×C₁₃
Fitting	C₃×C₁₃×D₈	C₂
socle	C₂×C₃×C₁₃	C₂×D₄
hypercenter	C₁₃×D₈	D₃
hypocenter	C₃	C₁₃×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃ ◁ C₁₃×D₈

Complements

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

N	H ≅ G/N	type
1. C₁₃×#237	C₂	semidirect
2. C₃×C₁₃×D₈	C₂	semidirect
3. C₁₃×#214	C₂	semidirect
4. C₁₃×Dic₁₂	C₂	semidirect
5. D₃×C₈×C₁₃	C₂	semidirect
17. C₁₃×D₈	D₃	semidirect
31. #912	C₁₃	direct (N × H)
40. #237	C₂×C₁₃	semidirect
41. C₃×D₈	C₂×C₁₃	semidirect
42. #214	C₂×C₁₃	semidirect
43. Dic₁₂	C₂×C₁₃	semidirect
44. D₃×C₈	C₂×C₁₃	semidirect
45. C₃×C₁₃	#135	semidirect
60. D₈	D₃×C₁₃	semidirect
62. C₁₃	#912	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×#237	2
C₃×C₁₃×D₈	2
C₁₃×#214	2
C₁₃×Dic₁₂	2
D₃×C₈×C₁₃	2
C₁₃×#135	3
#912	13

Subgroups — C13×#912 #11928888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#912 #11928888