Subgroups — #13114974

Order 1664.

188 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	#11718585	C₂	1	2	yes	maximal
3	#11718144	C₂	1	4	yes	maximal
4	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
5	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×#6099	C₂²	1	4	yes	—
7	C₄×C₈×C₁₃	C₄	1	2	yes	—
8	C₄×C₈×C₁₃	C₄	1	2	yes	—
9	C₄⋊#1055	—	2	4	no	—
10	C₂²×C₄×C₁₃	Q₈	1	2	yes	—
11	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
12	C₂×C₈×C₁₃	—	2	4	no	—
13	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
14	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₄²×C₁₃	D₄	1	2	yes	—
17	#6099	—	2	8	no	—
18	C₂×#1055	—	2	4	no	—
19	#1837	—	13	1	no	maximal, Sylow
20	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
21	C₂×C₄×C₁₃	—	2	4	no	—
22	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
26	C₂×C₄×C₁₃	#41	1	4	yes	—
27	C₈×C₁₃	—	2	4	no	—
28	#1055	—	4	4	no	—
29	#423	—	13	2	no	—
30	C₂×C₄×C₈	D₁₃	1	1	yes	characteristic
31	#341	—	13	4	no	—
32	C₂²×C₁₃	—	2	2	no	—
33	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂²×C₁₃	#125	1	2	yes	—
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	#108	1	4	yes	—
37	C₄×C₁₃	#117	1	2	yes	—
38	C₄×C₁₃	#124	1	2	yes	—
39	C₂×M₁₆	—	13	4	no	—
40	C₂²×C₈	C₂×D₁₃	1	2	yes	—
41	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
42	C₄⋊C₈	—	26	4	no	—
43	C₄×C₈	Dic₁₃	1	2	yes	—
44	C₄×C₈	Dic₁₃	1	2	yes	—
45	C₂×C₁₃	—	2	2	no	—
46	C₂×C₁₃	#382	1	1	yes	characteristic
47	C₂×C₁₃	C₂×#108	1	2	yes	—
48	C₂²×C₄	Dic₂₆	1	2	yes	—
49	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
50	M₁₆	—	26	8	no	—
51	C₂×C₈	—	2	4	no	—
52	C₂×C₈	—	26	4	no	—
53	C₂×C₈	C₂×Dic₁₃	1	4	yes	—
54	C₄²	D₅₂	1	2	yes	—
55	C₄²	C₂×Dic₁₃	1	1	yes	characteristic
56	C₄²	C₂×Dic₁₃	1	1	yes	characteristic
57	C₁₃	#1837	1	1	yes	characteristic, complemented, Sylow
58	C₂³	C₂×Dic₂₆	1	1	yes	characteristic
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	C₄⋊Dic₁₃	1	2	yes	—
61	C₂×C₄	C₄⋊Dic₁₃	1	2	yes	—
62	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
63	C₂×C₄	#6127	1	4	yes	—
64	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
65	C₈	—	2	4	no	—
66	C₈	—	52	4	no	—
67	C₂²	—	2	2	no	—
68	C₂²	#88124	1	2	yes	—
69	C₂²	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	#88059	1	4	yes	—
72	C₄	#88129	1	2	yes	—
73	C₄	#88180	1	2	yes	—
74	C₂	—	2	2	no	—
75	C₂	#11718597	1	1	yes	characteristic
76	C₂	C₂×#88059	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂×C₄×C₈×C₁₃	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×C₄×C₈	D₁₃
hypocenter	C₁₃	#1837
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

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

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
#11718585	2
#11718144	2
#1837	13