Subgroups — C₄×#88043 #13114521

Order 1664.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#88043	C₂	1	4	yes	maximal
3	C₂×C₄×#1055	C₂	1	2	yes	maximal
4	C₂×C₄²×C₁₃	C₄	1	4	yes	—
5	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#1055	C₂²	1	4	yes	—
8	#88043	C₄	1	16	yes	direct product factor
9	C₄×#1055	C₄	1	8	yes	complemented
10	C₂²×C₄×C₁₃	C₂×C₄	1	4	yes	—
11	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
13	C₄²×C₁₃	—	2	8	no	—
14	C₄²×C₁₃	C₂×C₄	1	4	yes	—
15	C₄²×C₁₃	C₂×C₄	1	8	yes	—
16	C₂×#1055	C₂×C₄	1	8	yes	—
17	C₂×#1055	C₂×C₄	1	16	yes	—
18	C₄×#97	—	13	1	no	maximal, Sylow
19	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₃	—	2	8	no	—
21	C₂×C₄×C₁₃	C₄²	1	8	yes	—
22	C₂×C₄×C₁₃	C₄²	1	4	yes	—
23	C₂×C₄×C₁₃	M₁₆	1	8	yes	—
24	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
25	C₂×C₄×C₁₃	C₂²×C₄	1	4	yes	—
26	#1055	C₄²	1	16	yes	complemented
27	C₂×#97	—	13	4	no	—
28	C₂×C₄×C₈	—	13	2	no	—
29	C₄³	D₁₃	1	1	yes	characteristic
30	C₂²×C₁₃	C₂×C₄²	1	1	yes	characteristic
31	C₂²×C₁₃	C₂×C₄²	1	2	yes	—
32	C₂²×C₁₃	C₂×M₁₆	1	4	yes	—
33	C₄×C₁₃	—	2	8	no	—
34	C₄×C₁₃	#97	1	8	yes	complemented
35	C₄×C₁₃	C₂×C₄²	1	4	yes	—
36	C₂²×C₈	—	13	4	no	—
37	C₂×C₄²	Dic₁₃	1	4	yes	—
38	C₂×C₄²	C₂×D₁₃	1	2	yes	—
39	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
40	#97	—	13	16	no	—
41	C₄×C₈	—	13	8	no	—
42	C₂×C₁₃	C₄³	1	1	yes	characteristic
43	C₂×C₁₃	C₂×#97	1	2	yes	—
44	C₂×C₁₃	C₄×M₁₆	1	4	yes	—
45	C₂²×C₄	C₂×Dic₁₃	1	4	yes	—
46	C₂²×C₄	C₂×Dic₁₃	1	2	yes	—
47	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
48	C₂×C₈	—	13	8	no	—
49	C₂×C₈	—	13	16	no	—
50	C₄²	—	2	8	no	—
51	C₄²	C₄×D₁₃	1	4	yes	—
52	C₄²	C₄×D₁₃	1	8	yes	—
53	C₁₃	C₄×#97	1	1	yes	characteristic, complemented, Sylow
54	C₂³	C₂²×Dic₁₃	1	1	yes	characteristic
55	C₂×C₄	—	2	8	no	—
56	C₂×C₄	#6099	1	8	yes	—
57	C₂×C₄	C₄×Dic₁₃	1	8	yes	—
58	C₂×C₄	C₄×Dic₁₃	1	4	yes	—
59	C₂×C₄	C₂×C₄×D₁₃	1	2	yes	—
60	C₂×C₄	C₂×C₄×D₁₃	1	4	yes	—
61	C₈	—	13	16	no	—
62	C₂²	C₂×#6099	1	4	yes	—
63	C₂²	C₂×C₄×Dic₁₃	1	1	yes	characteristic
64	C₂²	C₂×C₄×Dic₁₃	1	2	yes	—
65	C₄	—	2	8	no	—
66	C₄	#88043	1	8	yes	direct product factor
67	C₄	C₄²×D₁₃	1	4	yes	—
68	C₂	C₂×#88043	1	2	yes	—
69	C₂	C₄×#6099	1	4	yes	—
70	C₂	C₄²×Dic₁₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
8. #88043	C₄	direct (N × H)
9. C₄×#1055	C₄	semidirect
26. #1055	C₄²	semidirect
34. C₄×C₁₃	#97	semidirect
53. C₁₃	C₄×#97	semidirect
66. C₄	#88043	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄³×C₁₃	2
C₂×#88043	2
C₂×C₄×#1055	2
C₄×#97	13

Subgroups — C4×#88043 #13114521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#88043 #13114521