Subgroups — C₁₃×#953 #11928929

Order 1248.

260 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#67	C₂	1	3	yes	maximal, complemented
3	C₁₃×#217	C₂	1	3	yes	maximal, complemented
4	C₁₃×#120	—	3	1	no	maximal, Hall
5	C₂³×C₃×C₁₃	—	2	6	no	—
6	C₂³×C₃×C₁₃	C₂²	1	3	yes	—
7	C₂²×D₃×C₁₃	C₂²	1	1	yes	characteristic, complemented
8	C₁₃×#67	—	2	6	no	—
9	C₂×Dic₃×C₁₃	C₂²	1	3	yes	complemented
10	C₂⁴×C₁₃	D₃	1	1	yes	characteristic, complemented
11	C₂×D₄×C₁₃	—	3	3	no	—
12	C₁₃×C₂²⋊C₄	—	3	3	no	—
13	C₂²×C₃×C₁₃	—	2	8	no	—
14	C₂²×C₃×C₁₃	—	2	6	no	—
15	C₂²×C₃×C₁₃	D₄	1	6	yes	complemented
16	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×D₃×C₁₃	—	2	3	no	—
18	Dic₃×C₁₃	—	2	3	no	—
19	C₂³×C₁₃	—	2	6	no	—
20	C₂³×C₁₃	—	3	1	no	—
21	C₂³×C₁₃	C₂×D₃	1	3	yes	—
22	D₄×C₁₃	—	6	6	no	—
23	C₂×C₄×C₁₃	—	3	3	no	—
24	#953	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₃×C₁₃	—	2	6	no	—
26	C₂×C₃×C₁₃	C₂×D₄	1	3	yes	—
27	D₃×C₁₃	—	4	1	no	—
28	C₂²×C₁₃	—	2	8	no	—
29	C₂²×C₁₃	—	2	6	no	—
30	C₂²×C₁₃	—	6	3	no	—
31	C₂²×C₁₃	#67	1	6	yes	complemented
32	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
33	C₄×C₁₃	—	6	3	no	—
34	C₂⁴×C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
35	C₂×#67	C₂×C₁₃	1	3	yes	complemented
36	#217	C₂×C₁₃	1	3	yes	complemented
37	C₃×C₁₃	#120	1	1	yes	characteristic, complemented, Hall
38	#120	—	3	1	no	Sylow
39	C₂×C₁₃	—	2	6	no	—
40	C₂×C₁₃	—	12	1	no	—
41	C₂×C₁₃	C₂×#67	1	3	yes	—
42	C₂³×C₃	—	2	6	no	—
43	C₂³×C₃	C₂²×C₁₃	1	3	yes	—
44	C₂²×D₃	C₂²×C₁₃	1	1	yes	characteristic, complemented
45	#67	—	2	6	no	—
46	C₂×Dic₃	C₂²×C₁₃	1	3	yes	complemented
47	C₂⁴	D₃×C₁₃	1	1	yes	characteristic, complemented
48	C₂×D₄	—	3	3	no	—
49	C₂²⋊C₄	—	3	3	no	—
50	C₁₃	#953	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²×C₃	—	2	8	no	—
52	C₂²×C₃	—	2	6	no	—
53	C₂²×C₃	D₄×C₁₃	1	6	yes	complemented
54	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
55	C₂×D₃	—	2	3	no	—
56	Dic₃	—	2	3	no	—
57	C₂³	—	2	6	no	—
58	C₂³	—	3	1	no	—
59	C₂³	C₂×D₃×C₁₃	1	3	yes	—
60	D₄	—	6	6	no	—
61	C₂×C₄	—	3	3	no	—
62	C₂×C₃	—	2	6	no	—
63	C₂×C₃	C₂×D₄×C₁₃	1	3	yes	—
64	D₃	—	4	1	no	—
65	C₂²	—	2	8	no	—
66	C₂²	—	2	6	no	—
67	C₂²	—	6	3	no	—
68	C₂²	C₁₃×#67	1	6	yes	complemented
69	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
70	C₄	—	6	3	no	—
71	C₃	C₁₃×#120	1	1	yes	characteristic, complemented, Sylow
72	C₂	—	2	6	no	—
73	C₂	—	12	1	no	—
74	C₂	C₂×C₁₃×#67	1	3	yes	—

	subgroup	G/H
center	C₂²×C₁₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₃
Frattini	C₂²	C₂²×D₃×C₁₃
Fitting	C₂⁴×C₃×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
hypercenter	C₂⁴×C₁₃	D₃
hypocenter	C₃	C₁₃×#120
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂⁴×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₁₃	C₂	semidirect
2. C₂×C₁₃×#67	C₂	semidirect
3. C₁₃×#217	C₂	semidirect
7. C₂²×D₃×C₁₃	C₂²	semidirect
9. C₂×Dic₃×C₁₃	C₂²	semidirect
10. C₂⁴×C₁₃	D₃	semidirect
15. C₂²×C₃×C₁₃	D₄	semidirect
24. #953	C₁₃	direct (N × H)
31. C₂²×C₁₃	#67	semidirect
34. C₂⁴×C₃	C₂×C₁₃	semidirect
35. C₂×#67	C₂×C₁₃	semidirect
36. #217	C₂×C₁₃	semidirect
37. C₃×C₁₃	#120	semidirect
44. C₂²×D₃	C₂²×C₁₃	semidirect
46. C₂×Dic₃	C₂²×C₁₃	semidirect
47. C₂⁴	D₃×C₁₃	semidirect
50. C₁₃	#953	direct (N × H)
53. C₂²×C₃	D₄×C₁₃	semidirect
68. C₂²	C₁₃×#67	semidirect
71. C₃	C₁₃×#120	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₁₃	2
C₂×C₁₃×#67	2
C₁₃×#217	2
C₁₃×#120	3
#953	13

Subgroups — C13×#953 #11928929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#953 #11928929