Subgroups — #13117088

Order 1664.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×#88069	C₂	1	4	yes	maximal
3	#11718360	C₂	1	1	yes	maximal, characteristic
4	C₄×#6090	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×Q₁₆	—	2	1	no	—
6	C₂×C₁₃×Q₁₆	C₂²	1	2	yes	—
7	C₁₃×C₄⋊Q₈	—	2	1	no	—
8	C₂×Dic₅₂	—	2	1	no	—
9	C₂×Dic₅₂	C₂²	1	2	yes	—
10	#88123	—	2	1	no	—
11	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	#88069	—	2	8	no	—
13	C₂×#6090	C₂²	1	2	yes	—
14	C₂×Q₈×C₁₃	—	2	2	no	—
15	C₂×Dic₂₆	—	2	2	no	—
16	C₁₃×Q₁₆	—	2	4	no	—
17	C₁₃×Q₁₆	—	4	2	no	—
18	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
20	C₁₃×C₄⋊C₄	—	4	2	no	—
21	C₄²×C₁₃	D₄	1	1	yes	characteristic
22	C₄⋊Dic₁₃	—	4	2	no	—
23	Dic₅₂	—	2	4	no	—
24	Dic₅₂	—	4	2	no	—
25	#6090	D₄	1	4	yes	—
26	#2247	—	13	1	no	maximal, Sylow
27	Q₈×C₁₃	—	4	2	no	—
28	Q₈×C₁₃	—	4	2	no	—
29	C₂×C₄×C₁₃	—	4	2	no	—
30	C₂×C₄×C₁₃	D₈	1	2	yes	—
31	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₁₃	—	4	2	no	—
33	Dic₂₆	—	4	2	no	—
34	Dic₂₆	—	4	2	no	—
35	C₈×C₁₃	D₈	1	2	yes	—
36	C₈×C₁₃	C₂×D₄	1	2	yes	—
37	C₂×Q₃₂	—	13	4	no	—
38	#494	—	13	1	no	—
39	#494	D₁₃	1	1	yes	characteristic
40	C₄×C₁₆	—	13	1	no	—
41	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
42	C₄×C₁₃	—	8	2	no	—
43	C₄×C₁₃	Q₃₂	1	4	yes	complemented
44	C₄×C₁₃	#127	1	1	yes	characteristic
45	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
46	Dic₁₃	—	8	2	no	—
47	C₂×Q₁₆	—	2	1	no	—
48	C₂×Q₁₆	—	13	2	no	—
49	C₂×Q₁₆	—	26	1	no	—
50	C₂×Q₁₆	C₂×D₁₃	1	2	yes	—
51	C₄⋊Q₈	—	2	1	no	—
52	C₄⋊Q₈	—	26	1	no	—
53	Q₃₂	—	26	8	no	—
54	C₂×C₁₆	—	13	2	no	—
55	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
56	C₂×C₁₃	#493	1	1	yes	characteristic
57	C₂×C₁₃	C₂×Q₃₂	1	2	yes	—
58	C₂×Q₈	—	2	2	no	—
59	C₂×Q₈	—	26	2	no	—
60	Q₁₆	—	2	4	no	—
61	Q₁₆	—	4	2	no	—
62	Q₁₆	—	26	4	no	—
63	Q₁₆	—	52	2	no	—
64	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
65	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
66	C₄⋊C₄	—	4	2	no	—
67	C₄⋊C₄	—	52	2	no	—
68	C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
69	C₁₆	—	13	4	no	—
70	C₁₃	#2247	1	1	yes	characteristic, complemented, Sylow
71	Q₈	—	4	2	no	—
72	Q₈	—	4	2	no	—
73	Q₈	—	52	2	no	—
74	Q₈	—	52	2	no	—
75	C₂×C₄	—	4	2	no	—
76	C₂×C₄	—	52	2	no	—
77	C₂×C₄	#6104	1	2	yes	—
78	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
79	C₈	#6104	1	2	yes	—
80	C₈	D₄×D₁₃	1	2	yes	—
81	C₂²	C₂×#6104	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	104	2	no	—
84	C₄	#88069	1	4	yes	complemented
85	C₄	C₂×#6104	1	1	yes	characteristic
86	C₄	#88194	1	1	yes	characteristic
87	C₂	#11718734	1	1	yes	characteristic
88	C₂	C₂×#88069	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#494	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₈
hypercenter	#494	D₁₃
hypocenter	C₁₃	#2247
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
43. C₄×C₁₃	Q₃₂	semidirect
70. C₁₃	#2247	semidirect
84. C₄	#88069	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#494	2
C₂×#88069	2
#11718360	2
C₄×#6090	2
#2247	13