Subgroups — C₁₃×#875 #11928851

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×(C₂×D₃)⋊C₄	C₂	1	4	yes	maximal, complemented
5	C₁₃×#124	—	3	1	no	maximal, Hall
6	C₂²×D₃×C₁₃	C₂²	1	2	yes	—
7	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₃×C₁₃	C₂²	1	2	yes	—
10	C₁₃×D₁₂	—	2	2	no	—
11	C₁₃×Dic₆	—	2	2	no	—
12	C₂×Q₈×C₁₃	—	3	1	no	—
13	C₂×D₄×C₁₃	—	3	1	no	—
14	C₁₃×C₂²⋊C₄	—	3	4	no	—
15	C₄²×C₁₃	D₃	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×D₃×C₁₃	—	2	2	no	—
18	C₂×D₃×C₁₃	—	2	4	no	—
19	C₃×C₄×C₁₃	—	2	2	no	—
20	C₃×C₄×C₁₃	D₄	1	2	yes	—
21	Dic₃×C₁₃	—	2	2	no	—
22	C₂³×C₁₃	—	3	2	no	—
23	Q₈×C₁₃	—	6	2	no	—
24	D₄×C₁₃	—	6	2	no	—
25	C₂×C₄×C₁₃	—	3	2	no	—
26	C₂×C₄×C₁₃	C₂×D₃	1	2	yes	—
27	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
28	#875	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₃×C₁₃	#41	1	2	yes	—
31	D₃×C₁₃	—	4	2	no	—
32	C₂²×C₁₃	—	6	2	no	—
33	C₂²×C₁₃	—	6	4	no	—
34	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	—	6	2	no	—
37	C₄×C₁₃	D₁₂	1	2	yes	—
38	C₂×D₁₂	C₂×C₁₃	1	1	yes	characteristic
39	C₂×Dic₆	C₂×C₁₃	1	1	yes	characteristic, complemented
40	C₃×C₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
41	(C₂×D₃)⋊C₄	C₂×C₁₃	1	4	yes	complemented
42	C₃×C₁₃	#124	1	1	yes	characteristic, complemented, Hall
43	#124	—	3	1	no	Sylow
44	C₂×C₁₃	—	12	2	no	—
45	C₂×C₁₃	C₂×D₁₂	1	1	yes	characteristic
46	C₂×C₁₃	#235	1	2	yes	—
47	C₂²×D₃	C₂²×C₁₃	1	2	yes	—
48	C₂×C₃×C₄	C₂²×C₁₃	1	2	yes	—
49	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
50	C₂×Dic₃	C₂²×C₁₃	1	2	yes	—
51	D₁₂	—	2	2	no	—
52	Dic₆	—	2	2	no	—
53	C₂×Q₈	—	3	1	no	—
54	C₂×D₄	—	3	1	no	—
55	C₂²⋊C₄	—	3	4	no	—
56	C₄²	D₃×C₁₃	1	1	yes	characteristic, complemented
57	C₁₃	#875	1	1	yes	characteristic, direct product factor, Sylow
58	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
59	C₂×D₃	—	2	2	no	—
60	C₂×D₃	—	2	4	no	—
61	C₃×C₄	—	2	2	no	—
62	C₃×C₄	D₄×C₁₃	1	2	yes	—
63	Dic₃	—	2	2	no	—
64	C₂³	—	3	2	no	—
65	Q₈	—	6	2	no	—
66	D₄	—	6	2	no	—
67	C₂×C₄	—	3	2	no	—
68	C₂×C₄	C₂×D₃×C₁₃	1	2	yes	—
69	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
70	C₂×C₃	C₂×D₄×C₁₃	1	1	yes	characteristic
71	C₂×C₃	C₁₃×#41	1	2	yes	—
72	D₃	—	4	2	no	—
73	C₂²	—	6	2	no	—
74	C₂²	—	6	4	no	—
75	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	6	2	no	—
78	C₄	C₁₃×D₁₂	1	2	yes	—
79	C₃	C₁₃×#124	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	12	2	no	—
81	C₂	C₂×C₁₃×D₁₂	1	1	yes	characteristic
82	C₂	C₁₃×#235	1	2	yes	—

	subgroup	G/H
center	C₂²×C₁₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₃
Frattini	C₂²	C₂²×D₃×C₁₃
Fitting	C₃×C₄²×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
prime radical	C₂×C₁₃×D₁₂	C₂
hypercenter	C₄²×C₁₃	D₃
hypocenter	C₃	C₁₃×#124
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×Dic₆	C₂	semidirect
3. C₃×C₄²×C₁₃	C₂	semidirect
4. C₁₃×(C₂×D₃)⋊C₄	C₂	semidirect
15. C₄²×C₁₃	D₃	semidirect
28. #875	C₁₃	direct (N × H)
39. C₂×Dic₆	C₂×C₁₃	semidirect
40. C₃×C₄²	C₂×C₁₃	semidirect
41. (C₂×D₃)⋊C₄	C₂×C₁₃	semidirect
42. C₃×C₁₃	#124	semidirect
56. C₄²	D₃×C₁₃	semidirect
57. C₁₃	#875	direct (N × H)
79. C₃	C₁₃×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×D₁₂	2
C₂×C₁₃×Dic₆	2
C₃×C₄²×C₁₃	2
C₁₃×(C₂×D₃)⋊C₄	2
C₁₃×#124	3
#875	13

Subgroups — C13×#875 #11928851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#875 #11928851