Subgroups — C₄×#88055 #13114520

Order 1664.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#88055	C₂	1	4	yes	maximal
3	C₄²×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#1055	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₁₃	C₄	1	4	yes	—
8	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
9	C₂²×#1055	C₂²	1	2	yes	—
10	C₄×C₈×C₁₃	C₄	1	4	yes	complemented
11	#88055	C₄	1	16	yes	direct product factor
12	C₄×#1055	C₄	1	4	yes	complemented
13	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
15	C₂²×Dic₁₃	C₂×C₄	1	4	yes	—
16	C₂×C₈×C₁₃	C₂×C₄	1	8	yes	—
17	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
18	C₄²×C₁₃	C₂×C₄	1	2	yes	—
19	C₄²×C₁₃	C₂×C₄	1	2	yes	—
20	C₄×Dic₁₃	—	2	8	no	—
21	C₄×Dic₁₃	C₂×C₄	1	8	yes	—
22	C₂×#1055	C₂×C₄	1	4	yes	—
23	C₂×#1055	C₂×C₄	1	8	yes	—
24	C₄×#97	—	13	1	no	maximal, Sylow
25	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₄²	1	4	yes	—
27	C₂×C₄×C₁₃	M₁₆	1	8	yes	—
28	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₃	C₂²×C₄	1	4	yes	—
30	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₁₃	—	2	8	no	—
32	C₂×Dic₁₃	C₄²	1	8	yes	—
33	C₈×C₁₃	C₄²	1	8	yes	complemented
34	#1055	C₄²	1	8	yes	complemented
35	C₂×#97	—	13	4	no	—
36	C₂×C₄×C₈	—	13	1	no	—
37	C₂×C₄×C₈	D₁₃	1	1	yes	characteristic
38	C₄³	—	13	1	no	—
39	C₂²×C₁₃	C₂×C₄²	1	2	yes	—
40	C₂²×C₁₃	C₂×C₄²	1	1	yes	characteristic
41	C₂²×C₁₃	C₂×M₁₆	1	4	yes	—
42	C₄×C₁₃	#97	1	8	yes	complemented
43	C₄×C₁₃	C₂×C₄²	1	2	yes	—
44	C₄×C₁₃	C₂×C₄²	1	2	yes	—
45	Dic₁₃	—	2	8	no	—
46	C₂²×C₈	—	13	2	no	—
47	C₂²×C₈	C₂×D₁₃	1	2	yes	—
48	C₂×C₄²	—	13	2	no	—
49	C₂×C₄²	—	13	4	no	—
50	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
51	#97	—	13	16	no	—
52	C₄×C₈	—	13	4	no	—
53	C₄×C₈	Dic₁₃	1	4	yes	complemented
54	C₂×C₁₃	C₄³	1	1	yes	characteristic
55	C₂×C₁₃	C₂×#97	1	2	yes	—
56	C₂×C₁₃	C₄×M₁₆	1	4	yes	—
57	C₂²×C₄	—	13	4	no	—
58	C₂²×C₄	C₄×D₁₃	1	2	yes	—
59	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
60	C₂×C₈	—	13	4	no	—
61	C₂×C₈	—	13	8	no	—
62	C₂×C₈	C₄×D₁₃	1	8	yes	—
63	C₂×C₈	C₂×Dic₁₃	1	4	yes	—
64	C₄²	—	13	8	no	—
65	C₄²	—	26	8	no	—
66	C₄²	C₄×D₁₃	1	2	yes	—
67	C₄²	C₂×Dic₁₃	1	2	yes	—
68	C₁₃	C₄×#97	1	1	yes	characteristic, complemented, Sylow
69	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
70	C₂×C₄	—	13	8	no	—
71	C₂×C₄	—	26	8	no	—
72	C₂×C₄	#6094	1	8	yes	—
73	C₂×C₄	C₄×Dic₁₃	1	4	yes	—
74	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
75	C₂×C₄	C₂×C₄×D₁₃	1	4	yes	—
76	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
77	C₈	—	13	8	no	—
78	C₈	C₄×Dic₁₃	1	8	yes	complemented
79	C₂²	C₄²×D₁₃	1	2	yes	—
80	C₂²	C₂×#6094	1	4	yes	—
81	C₂²	C₂×C₄×Dic₁₃	1	1	yes	characteristic
82	C₄	—	26	8	no	—
83	C₄	#88055	1	8	yes	direct product factor
84	C₄	C₄²×D₁₃	1	2	yes	—
85	C₄	C₂×C₄×Dic₁₃	1	2	yes	—
86	C₂	C₄×#6094	1	4	yes	—
87	C₂	C₄²×Dic₁₃	1	1	yes	characteristic
88	C₂	C₂×#88055	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂×D₁₃
commutator	C₂×C₁₃	C₄³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂×C₄×C₈×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×C₄×C₈	D₁₃
hypocenter	C₁₃	C₄×#97
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
10. C₄×C₈×C₁₃	C₄	semidirect
11. #88055	C₄	direct (N × H)
12. C₄×#1055	C₄	semidirect
33. C₈×C₁₃	C₄²	semidirect
34. #1055	C₄²	semidirect
42. C₄×C₁₃	#97	semidirect
53. C₄×C₈	Dic₁₃	semidirect
68. C₁₃	C₄×#97	semidirect
78. C₈	C₄×Dic₁₃	semidirect
83. C₄	#88055	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×C₁₃	2
C₂×#88055	2
C₄²×Dic₁₃	2
C₂×C₄×#1055	2
C₄×#97	13

Subgroups — C4×#88055 #13114520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#88055 #13114520