Subgroups — #13130761

Order 1664.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11719053	C₂	1	2	yes	maximal
2	C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#11718268	C₂	1	4	yes	maximal
4	C₂×#6118	C₂²	1	4	yes	—
5	C₂×C₈×D₁₃	C₂²	1	2	yes	—
6	C₄²×D₁₃	C₂²	1	1	yes	characteristic
7	#88112	—	2	4	no	—
8	C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
9	C₈×Dic₁₃	C₄	1	2	yes	—
10	C₄×#1055	C₄	1	1	yes	characteristic
11	C₂×C₄×D₁₃	Q₈	1	2	yes	—
12	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
13	C₂×#1057	—	2	4	no	—
14	#6118	—	2	8	no	—
15	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
16	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₁₃	D₄	1	2	yes	—
19	C₂×#1055	C₂×C₄	1	2	yes	—
20	C₈×D₁₃	—	2	4	no	—
21	#1837	—	13	1	no	maximal, Sylow
22	C₂²×D₁₃	C₂×Q₈	1	1	yes	characteristic
23	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
25	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
26	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
27	C₄×D₁₃	—	2	4	no	—
28	C₄×D₁₃	#41	1	4	yes	—
29	#1057	—	4	4	no	—
30	C₈×C₁₃	—	2	2	no	—
31	#1055	—	2	2	no	—
32	#423	—	13	2	no	—
33	C₂×C₄×C₈	—	13	1	no	—
34	#341	—	13	4	no	—
35	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×D₁₃	—	2	2	no	—
37	C₂×D₁₃	#125	1	2	yes	—
38	C₄×C₁₃	—	2	2	no	—
39	C₄×C₁₃	#117	1	2	yes	—
40	Dic₁₃	#108	1	4	yes	—
41	Dic₁₃	#124	1	2	yes	—
42	C₂×M₁₆	—	13	4	no	—
43	C₂²×C₈	—	13	2	no	—
44	C₂×C₄²	—	13	1	no	—
45	C₄⋊C₈	—	26	4	no	—
46	C₄×C₈	—	13	2	no	—
47	C₄×C₈	—	13	1	no	—
48	C₄×C₈	#261	1	1	yes	characteristic
49	C₂×C₁₃	#382	1	1	yes	characteristic
50	C₂×C₁₃	C₂×#108	1	2	yes	—
51	D₁₃	—	2	2	no	—
52	C₂²×C₄	—	13	1	no	—
53	C₂²×C₄	—	13	2	no	—
54	M₁₆	—	26	8	no	—
55	C₂×C₈	—	13	2	no	—
56	C₂×C₈	—	26	4	no	—
57	C₂×C₈	—	26	4	no	—
58	C₂×C₈	C₂×#261	1	2	yes	—
59	C₄²	—	13	2	no	—
60	C₄²	—	13	1	no	—
61	C₄²	C₂×#261	1	1	yes	characteristic
62	C₁₃	#1837	1	1	yes	characteristic, complemented, Sylow
63	C₂³	—	13	1	no	—
64	C₂×C₄	—	13	1	no	—
65	C₂×C₄	—	13	2	no	—
66	C₂×C₄	—	13	4	no	—
67	C₂×C₄	—	26	4	no	—
68	C₂×C₄	C₄⋊#261	1	2	yes	—
69	C₂×C₄	C₂²×#261	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₈	—	26	2	no	—
72	C₈	—	52	4	no	—
73	C₂²	—	13	2	no	—
74	C₂²	—	26	2	no	—
75	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	13	2	no	—
78	C₄	—	13	4	no	—
79	C₄	#88237	1	2	yes	—
80	C₂	—	26	2	no	—
81	C₂	#11719060	1	1	yes	characteristic
82	C₂	D₁₃⋊#108	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂²×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂³
hypercenter	C₄×C₈	#261
hypocenter	C₁₃	#1837
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
62. C₁₃	#1837	semidirect

Maximal subgroups

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

subgroup	index
#11719053	2
C₄×C₈×D₁₃	2
#11718268	2
#1837	13