Subgroups — #13114438

Order 1664.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	#11718749	C₂	1	2	yes	maximal
3	#11718742	C₂	1	2	yes	maximal, complemented
4	#11718354	C₂	1	1	yes	maximal, characteristic
5	C₈×#1055	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₂×#6095	—	2	2	no	—
8	#88128	C₂²	1	1	yes	characteristic
9	#88123	C₂²	1	1	yes	characteristic
10	C₁₃×#106	—	2	2	no	—
11	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	#88075	—	2	4	no	—
13	#88049	—	2	4	no	—
14	C₄×#1055	C₂²	1	2	yes	—
15	C₂×Q₈×C₁₃	—	2	2	no	—
16	C₂×D₅₂	—	2	1	no	—
17	C₂×D₅₂	—	2	2	no	—
18	C₂×Dic₂₆	—	2	1	no	—
19	C₂×C₈×C₁₃	D₄	1	2	yes	—
20	C₁₃×C₄⋊C₄	—	2	2	no	—
21	C₁₃×C₄⋊C₄	—	2	2	no	—
22	C₄²×C₁₃	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₁₃	—	2	2	no	—
24	C₂×#1055	D₄	1	4	yes	—
25	#6095	—	4	4	no	—
26	#1708	—	13	1	no	maximal, Sylow
27	C₂²×D₁₃	—	4	1	no	—
28	Q₈×C₁₃	—	4	4	no	—
29	C₂×C₄×C₁₃	—	4	2	no	—
30	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
32	C₂×Dic₁₃	—	4	1	no	—
33	D₅₂	—	4	2	no	—
34	D₅₂	—	4	4	no	—
35	Dic₂₆	—	4	2	no	—
36	C₈×C₁₃	SD₁₆	1	4	yes	—
37	#1055	—	2	4	no	—
38	#498	D₁₃	1	1	yes	characteristic, complemented
39	#492	—	13	1	no	—
40	#487	—	13	2	no	—
41	#486	—	13	2	no	—
42	C₈²	—	13	1	no	—
43	C₂²×C₁₃	#127	1	1	yes	characteristic
44	C₂×D₁₃	—	8	1	no	—
45	C₂×D₁₃	—	8	2	no	—
46	C₄×C₁₃	—	8	2	no	—
47	C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
48	C₄×C₁₃	#135	1	4	yes	—
49	Dic₁₃	—	8	1	no	—
50	C₂×SD₁₆	—	26	2	no	—
51	C₄⋊Q₈	—	13	1	no	—
52	C₄⋊Q₈	C₂×D₁₃	1	2	yes	—
53	#127	—	13	1	no	—
54	#106	—	2	2	no	—
55	#103	—	26	4	no	—
56	#102	—	26	4	no	—
57	C₄×C₈	—	13	2	no	—
58	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
59	C₂×C₁₃	#492	1	1	yes	characteristic
60	C₂×C₁₃	#495	1	2	yes	—
61	D₁₃	—	16	1	no	—
62	C₂×Q₈	—	2	2	no	—
63	C₂×Q₈	—	26	1	no	—
64	C₂×D₄	—	26	2	no	—
65	C₂×D₄	—	26	1	no	—
66	SD₁₆	—	52	4	no	—
67	C₂×C₈	—	13	4	no	—
68	C₂×C₈	C₂²⋊D₁₃	1	2	yes	—
69	C₄⋊C₄	—	2	2	no	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄⋊C₄	—	26	2	no	—
72	C₄²	C₂²×D₁₃	1	1	yes	characteristic
73	C₁₃	#1708	1	1	yes	characteristic, complemented, Sylow
74	C₂³	—	52	1	no	—
75	Q₈	—	4	4	no	—
76	Q₈	—	52	2	no	—
77	D₄	—	52	4	no	—
78	D₄	—	52	2	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	—	52	1	no	—
81	C₂×C₄	D₄×D₁₃	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
83	C₈	—	26	4	no	—
84	C₈	#6106	1	4	yes	—
85	C₂²	—	104	1	no	—
86	C₂²	—	104	2	no	—
87	C₂²	#88194	1	1	yes	characteristic
88	C₄	—	8	2	no	—
89	C₄	—	104	1	no	—
90	C₄	#88170	1	4	yes	—
91	C₄	C₂×#6106	1	2	yes	—
92	C₂	—	208	1	no	—
93	C₂	#11718746	1	1	yes	characteristic
94	C₂	#11718829	1	2	yes	—

	subgroup	G/H
center	C₂²	#88194
commutator, cosocle	C₄²×C₁₃	C₂³
Frattini	C₄²	C₂²×D₁₃
Fitting	C₁₃×#498	C₂
socle	C₂²×C₁₃	#127
prime radical	#88128	C₂²
hypercenter	#498	D₁₃
hypocenter	C₁₃	#1708
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

Complements

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

N	H ≅ G/N	type
1. C₁₃×#498	C₂	semidirect
3. #11718742	C₂	semidirect
5. C₈×#1055	C₂	semidirect
38. #498	D₁₃	semidirect
73. C₁₃	#1708	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#498	2
#11718749	2
#11718742	2
#11718354	2
C₈×#1055	2
#1708	13