Subgroups — #13116602

Order 1664.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#405	C₂	1	1	yes	maximal, characteristic
2	C₂×#88052	C₂	1	2	yes	maximal
3	#11718055	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×M₁₆	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₁₃×#117	C₄	1	1	yes	characteristic
7	C₁₃×#97	C₄	1	2	yes	—
8	C₄×C₈×C₁₃	C₂²	1	2	yes	—
9	#88052	—	2	2	no	—
10	#88052	C₂²	1	4	yes	—
11	C₂×#6090	—	2	2	no	—
12	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₁₃×M₁₆	C₈	1	4	yes	—
14	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₁₃	D₄	1	2	yes	—
17	C₂×C₈×C₁₃	Q₈	1	2	yes	—
18	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₁₃×C₄⋊C₄	—	2	1	no	—
20	C₁₃×C₂²⋊C₄	—	2	1	no	—
21	C₄²×C₁₃	C₂×C₄	1	2	yes	—
22	#6090	—	2	4	no	—
23	#2153	—	13	1	no	maximal, Sylow
24	C₂³×C₁₃	M₁₆	1	1	yes	characteristic
25	C₂×C₄×C₁₃	—	2	2	no	—
26	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
28	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
31	C₈×C₁₃	C₂×C₈	1	4	yes	—
32	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
33	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
34	C₂×M₃₂	—	13	2	no	—
35	#405	D₁₃	1	1	yes	characteristic
36	#364	—	13	4	no	—
37	C₂²×C₁₃	—	4	1	no	—
38	C₂²×C₁₃	C₄⋊C₈	1	2	yes	—
39	C₂²×C₁₃	C₂×M₁₆	1	1	yes	characteristic
40	C₄×C₁₃	—	4	2	no	—
41	C₄×C₁₃	C₄⋊C₈	1	2	yes	—
42	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
44	C₂×M₁₆	Dic₁₃	1	1	yes	characteristic
45	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
46	#117	Dic₁₃	1	1	yes	characteristic
47	M₃₂	—	13	4	no	—
48	M₃₂	—	26	2	no	—
49	C₂×C₁₆	—	26	2	no	—
50	#97	Dic₁₃	1	2	yes	—
51	C₄×C₈	C₂×D₁₃	1	2	yes	—
52	C₂×C₁₃	—	2	1	no	—
53	C₂×C₁₃	—	2	2	no	—
54	C₂×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
55	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
56	M₁₆	#1055	1	4	yes	—
57	C₂×C₈	Dic₂₆	1	2	yes	—
58	C₂×C₈	D₅₂	1	2	yes	—
59	C₂×C₈	C₂×Dic₁₃	1	2	yes	—
60	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
62	C₄⋊C₄	—	2	1	no	—
63	C₂²⋊C₄	—	2	1	no	—
64	C₄²	C₂×Dic₁₃	1	2	yes	—
65	C₁₆	—	26	4	no	—
66	C₁₃	#2153	1	1	yes	characteristic, complemented, Sylow
67	C₂³	#6099	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	C₂×#1055	1	2	yes	—
70	C₂×C₄	#6099	1	1	yes	characteristic
71	C₂×C₄	C₄⋊Dic₁₃	1	2	yes	—
72	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
73	C₈	C₂×#1055	1	4	yes	—
74	C₈	C₄⋊Dic₁₃	1	2	yes	—
75	C₈	C₂×Dic₂₆	1	1	yes	characteristic
76	C₈	C₂×D₅₂	1	1	yes	characteristic
77	C₂²	—	4	1	no	—
78	C₂²	C₄⋊#1055	1	2	yes	—
79	C₂²	C₂×#6099	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	C₄⋊#1055	1	2	yes	—
82	C₄	C₂²×#1055	1	1	yes	characteristic
83	C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×C₄⋊#1055	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₅₂
commutator	C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#405	C₂
socle	C₂×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₃	M₁₆
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	#405	D₁₃
hypocenter	C₁₃	#2153
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #11718055	C₂	semidirect
66. C₁₃	#2153	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#405	2
C₂×#88052	2
#11718055	2
#2153	13