Subgroups — #13117065

Order 1664.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#500	C₂	1	1	yes	maximal, characteristic
2	#11718360	C₂	1	1	yes	maximal, characteristic
3	#11718084	C₂	1	4	yes	maximal
4	C₄×#6090	C₂	1	1	yes	maximal, characteristic
5	C₁₃×C₄⋊Q₈	—	2	1	no	—
6	C₂×Dic₅₂	—	2	1	no	—
7	C₂×Dic₅₂	C₂²	1	2	yes	—
8	#88123	—	2	1	no	—
9	C₁₃×#107	—	2	1	no	—
10	C₁₃×#107	C₂²	1	2	yes	—
11	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×#6090	C₂²	1	2	yes	—
13	C₂×Q₈×C₁₃	—	4	1	no	—
14	C₂×Dic₂₆	—	2	2	no	—
15	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
17	C₁₃×C₄⋊C₄	—	2	2	no	—
18	C₁₃×C₄⋊C₄	—	4	1	no	—
19	C₄²×C₁₃	D₄	1	1	yes	characteristic
20	C₄⋊Dic₁₃	—	4	1	no	—
21	C₄⋊Dic₁₃	—	4	1	no	—
22	Dic₅₂	—	2	4	no	—
23	Dic₅₂	—	4	2	no	—
24	#6090	—	2	2	no	—
25	#2241	—	13	1	no	maximal, Sylow
26	Q₈×C₁₃	—	8	2	no	—
27	C₂×C₄×C₁₃	—	4	2	no	—
28	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
29	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
30	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₁₃	—	4	2	no	—
32	Dic₂₆	—	4	2	no	—
33	Dic₂₆	—	4	2	no	—
34	C₈×C₁₃	SD₁₆	1	2	yes	—
35	C₈×C₁₃	#41	1	2	yes	—
36	#500	D₁₃	1	1	yes	characteristic
37	#494	—	13	1	no	—
38	#358	—	13	4	no	—
39	C₄×C₁₆	—	13	1	no	—
40	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
41	C₄×C₁₃	—	8	2	no	—
42	C₄×C₁₃	SD₃₂	1	2	yes	—
43	C₄×C₁₃	Q₃₂	1	2	yes	—
44	C₄×C₁₃	#124	1	1	yes	characteristic
45	C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
46	Dic₁₃	—	8	2	no	—
47	C₂×Q₁₆	—	13	2	no	—
48	C₂×Q₁₆	—	26	1	no	—
49	C₄⋊Q₈	—	2	1	no	—
50	C₄⋊Q₈	—	26	1	no	—
51	C₂×C₁₆	—	13	2	no	—
52	#107	—	2	1	no	—
53	#107	C₂×D₁₃	1	2	yes	—
54	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
55	C₂×C₁₃	#486	1	1	yes	characteristic
56	C₂×C₁₃	C₂×SD₃₂	1	1	yes	characteristic
57	C₂×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
58	C₂×Q₈	—	4	1	no	—
59	C₂×Q₈	—	26	2	no	—
60	Q₁₆	—	26	4	no	—
61	Q₁₆	—	52	2	no	—
62	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
63	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
64	C₄⋊C₄	—	2	2	no	—
65	C₄⋊C₄	—	4	1	no	—
66	C₄⋊C₄	—	52	1	no	—
67	C₄⋊C₄	—	52	1	no	—
68	C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
69	C₁₆	—	26	2	no	—
70	C₁₃	#2241	1	1	yes	characteristic, complemented, Sylow
71	Q₈	—	8	2	no	—
72	Q₈	—	52	2	no	—
73	Q₈	—	52	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	52	2	no	—
76	C₂×C₄	#6104	1	1	yes	characteristic
77	C₂×C₄	#6104	1	1	yes	characteristic
78	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
79	C₈	#6106	1	2	yes	—
80	C₈	#6131	1	2	yes	—
81	C₂²	C₂×#6104	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	104	2	no	—
84	C₄	#88067	1	2	yes	—
85	C₄	#88069	1	2	yes	—
86	C₄	C₂×#6106	1	1	yes	characteristic
87	C₄	#88201	1	1	yes	characteristic
88	C₂	#11718749	1	1	yes	characteristic
89	C₂	C₂×#88067	1	1	yes	characteristic
90	C₂	C₂×#88069	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#500	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₈
hypercenter	#500	D₁₃
hypocenter	C₁₃	#2241
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
70. C₁₃	#2241	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#500	2
#11718360	2
#11718084	2
C₄×#6090	2
#2241	13