Subgroups — #13116595

Order 1664.

160 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	1	yes	maximal, characteristic
3	C₂²×#6090	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#6090	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×M₁₆	C₄	1	1	yes	characteristic
6	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₁₃×#117	C₄	1	1	yes	characteristic
8	C₁₃×#97	C₄	1	2	yes	—
9	C₄×C₈×C₁₃	C₂²	1	2	yes	—
10	#88052	—	2	2	no	—
11	C₂×#6090	—	2	2	no	—
12	C₂×#6090	C₂²	1	2	yes	—
13	C₂×#6090	C₂²	1	2	yes	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₁₃×M₁₆	—	2	2	no	—
16	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₃	D₄	1	2	yes	—
19	C₂×C₈×C₁₃	Q₈	1	2	yes	—
20	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	C₁₃×C₄⋊C₄	C₈	1	2	yes	—
22	C₁₃×C₂²⋊C₄	C₈	1	2	yes	—
23	C₄²×C₁₃	C₂×C₄	1	2	yes	—
24	#6090	—	2	2	no	—
25	#6090	—	2	2	no	—
26	#2151	—	13	1	no	maximal, Sylow
27	C₂³×C₁₃	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₃	C₂×C₈	1	4	yes	—
30	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₁₃	M₁₆	1	2	yes	—
32	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₁₃	—	2	2	no	—
34	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
35	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
36	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
37	C₂×M₃₂	—	13	1	no	—
38	C₂²×C₁₆	—	13	1	no	—
39	#405	D₁₃	1	1	yes	characteristic
40	C₄⋊C₁₆	—	13	4	no	—
41	C₂²×C₁₃	—	2	2	no	—
42	C₂²×C₁₃	C₄⋊C₈	1	2	yes	—
43	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₁₃	—	2	4	no	—
45	C₄×C₁₃	C₄⋊C₈	1	2	yes	—
46	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
48	C₂×M₁₆	Dic₁₃	1	1	yes	characteristic
49	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
50	#117	Dic₁₃	1	1	yes	characteristic
51	M₃₂	—	26	2	no	—
52	C₂×C₁₆	—	13	2	no	—
53	C₂×C₁₆	—	13	2	no	—
54	C₂×C₁₆	—	26	2	no	—
55	#97	Dic₁₃	1	2	yes	—
56	C₄×C₈	C₂×D₁₃	1	2	yes	—
57	C₂×C₁₃	—	2	2	no	—
58	C₂×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
59	C₂×C₁₃	#504	1	2	yes	—
60	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
61	M₁₆	—	2	2	no	—
62	C₂×C₈	Dic₂₆	1	2	yes	—
63	C₂×C₈	D₅₂	1	2	yes	—
64	C₂×C₈	C₂×Dic₁₃	1	2	yes	—
65	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
66	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
67	C₄⋊C₄	#1055	1	2	yes	—
68	C₂²⋊C₄	#1055	1	2	yes	—
69	C₄²	C₂×Dic₁₃	1	2	yes	—
70	C₁₆	—	26	2	no	—
71	C₁₆	—	26	2	no	—
72	C₁₃	#2151	1	1	yes	characteristic, complemented, Sylow
73	C₂³	C₂×#1055	1	1	yes	characteristic
74	C₂×C₄	C₂×#1055	1	4	yes	—
75	C₂×C₄	C₂×#1055	1	1	yes	characteristic
76	C₂×C₄	#6099	1	2	yes	—
77	C₂×C₄	C₄⋊Dic₁₃	1	2	yes	—
78	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	C₄⋊Dic₁₃	1	2	yes	—
81	C₈	C₂×Dic₂₆	1	1	yes	characteristic
82	C₈	C₂×D₅₂	1	1	yes	characteristic
83	C₂²	—	2	2	no	—
84	C₂²	C₄⋊#1055	1	2	yes	—
85	C₂²	C₂²×#1055	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	C₄⋊#1055	1	2	yes	—
88	C₄	C₂×#6099	1	1	yes	characteristic
89	C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×C₄⋊#1055	1	1	yes	characteristic
92	C₂	#11718801	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₈
Fitting	C₁₃×#405	C₂
prime radical	C₂³×C₁₃	C₂×C₈
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	#405	D₁₃
hypocenter	C₁₃	#2151
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
4. C₄⋊#6090	C₂	semidirect
72. C₁₃	#2151	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
C₂²×#6090	2
C₄⋊#6090	2
#2151	13