Subgroups — C₂³×#6118 #13131823

Order 1664.

1720 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×#1057	C₂	1	2	yes	maximal, complemented
3	C₂²×#6118	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×D₁₃	C₄	1	1	yes	characteristic
5	C₂³×C₄×C₁₃	C₄	1	1	yes	characteristic
6	C₂³×Dic₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₄×D₁₃	C₄	1	14	yes	—
8	C₂²×C₄×D₁₃	C₂²	1	14	yes	—
9	C₂²×#1057	C₂²	1	28	yes	complemented
10	C₂×#6118	C₂²	1	112	yes	direct product factor
11	C₂⁴×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂³×D₁₃	—	2	8	no	—
13	C₂³×D₁₃	C₂×C₄	1	14	yes	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	14	yes	—
15	C₂²×Dic₁₃	C₂×C₄	1	7	yes	—
16	C₂²×Dic₁₃	C₂³	1	7	yes	—
17	C₂×C₄×D₁₃	C₂×C₄	1	84	yes	—
18	C₂×C₄×D₁₃	C₂³	1	28	yes	—
19	C₂×#1057	C₂³	1	56	yes	complemented
20	#6118	C₂³	1	64	yes	direct product factor
21	C₂³×M₁₆	—	13	1	no	maximal, Sylow
22	C₂³×C₁₃	M₁₆	1	8	yes	complemented
23	C₂³×C₁₃	C₂²×C₄	1	7	yes	—
24	C₂²×D₁₃	—	2	56	no	—
25	C₂²×D₁₃	C₂²×C₄	1	28	yes	—
26	C₂×C₄×C₁₃	C₂²×C₄	1	28	yes	—
27	C₂×Dic₁₃	C₂²×C₄	1	21	yes	—
28	C₂×Dic₁₃	C₂⁴	1	7	yes	—
29	C₄×D₁₃	C₂²×C₄	1	56	yes	—
30	C₄×D₁₃	C₂⁴	1	8	yes	—
31	#1057	C₂⁴	1	16	yes	complemented
32	C₂⁴×C₄	—	13	1	no	—
33	C₂²×M₁₆	—	13	28	no	—
34	C₂³×C₈	—	13	2	no	—
35	C₂²×C₁₃	C₂×M₁₆	1	28	yes	complemented
36	C₂²×C₁₃	C₂³×C₄	1	7	yes	—
37	C₂×D₁₃	—	2	56	no	—
38	C₂×D₁₃	C₂³×C₄	1	8	yes	—
39	C₄×C₁₃	C₂³×C₄	1	8	yes	—
40	Dic₁₃	C₂³×C₄	1	7	yes	—
41	Dic₁₃	C₂⁵	1	1	yes	characteristic
42	C₂⁵	—	13	1	no	—
43	C₂³×C₄	—	13	1	no	—
44	C₂³×C₄	—	13	14	no	—
45	C₂³×C₄	—	13	14	no	—
46	C₂³×C₄	#261	1	1	yes	characteristic
47	C₂×M₁₆	—	13	112	no	—
48	C₂²×C₈	—	13	28	no	—
49	C₂×C₁₃	C₂²×M₁₆	1	14	yes	complemented
50	C₂×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
51	D₁₃	—	2	8	no	—
52	C₂⁴	—	13	14	no	—
53	C₂⁴	—	26	8	no	—
54	C₂⁴	C₂×#261	1	1	yes	characteristic
55	C₂²×C₄	—	13	7	no	—
56	C₂²×C₄	—	13	7	no	—
57	C₂²×C₄	—	13	28	no	—
58	C₂²×C₄	—	13	84	no	—
59	C₂²×C₄	C₂×#261	1	14	yes	—
60	M₁₆	—	13	64	no	—
61	C₂×C₈	—	13	56	no	—
62	C₁₃	C₂³×M₁₆	1	1	yes	characteristic, complemented, Sylow
63	C₂³	—	13	28	no	—
64	C₂³	—	26	56	no	—
65	C₂³	#6118	1	8	yes	direct product factor
66	C₂³	C₂²×#261	1	7	yes	—
67	C₂×C₄	—	13	7	no	—
68	C₂×C₄	—	13	21	no	—
69	C₂×C₄	—	13	8	no	—
70	C₂×C₄	—	13	56	no	—
71	C₂×C₄	C₂²×#261	1	28	yes	—
72	C₈	—	13	16	no	—
73	C₂²	—	13	8	no	—
74	C₂²	—	26	56	no	—
75	C₂²	C₂×#6118	1	28	yes	direct product factor
76	C₂²	C₂³×#261	1	7	yes	—
77	C₄	—	13	7	no	—
78	C₄	—	13	1	no	—
79	C₄	C₂³×#261	1	8	yes	—
80	C₂	—	26	8	no	—
81	C₂	C₂²×#6118	1	14	yes	direct product factor
82	C₂	C₂⁴×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×#261
commutator	C₂×C₁₃	C₂⁴×C₄
Frattini	C₂	C₂⁴×#261
Fitting	C₂³×C₄×C₁₃	C₄
socle	C₂⁴×C₁₃	C₂×C₄
prime radical	C₂⁴×D₁₃	C₄
cosocle	Dic₁₃	C₂⁵
hypercenter	C₂³×C₄	#261
hypocenter	C₁₃	C₂³×M₁₆
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×#1057	C₂	semidirect
3. C₂²×#6118	C₂	direct (N × H)
9. C₂²×#1057	C₂²	semidirect
10. C₂×#6118	C₂²	direct (N × H)
19. C₂×#1057	C₂³	semidirect
20. #6118	C₂³	direct (N × H)
22. C₂³×C₁₃	M₁₆	semidirect
31. #1057	C₂⁴	semidirect
35. C₂²×C₁₃	C₂×M₁₆	semidirect
49. C₂×C₁₃	C₂²×M₁₆	semidirect
62. C₁₃	C₂³×M₁₆	semidirect
65. C₂³	#6118	direct (N × H)
75. C₂²	C₂×#6118	direct (N × H)
81. C₂	C₂²×#6118	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×D₁₃	2
C₂³×#1057	2
C₂²×#6118	2
C₂³×M₁₆	13

Subgroups — C23×#6118 #13131823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#6118 #13131823