Subgroups — #13114975

Order 1664.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718779	C₂	1	2	yes	maximal
2	C₂×#88055	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#341	C₂	1	1	yes	maximal, characteristic
4	#11718150	C₂	1	2	yes	maximal
5	#11718144	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
9	C₂×#6099	C₂²	1	2	yes	—
10	C₂²×#1055	C₂²	1	1	yes	characteristic
11	#88055	C₄	1	4	yes	—
12	#88054	—	2	4	no	—
13	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
14	C₂²×Dic₁₃	Q₈	1	2	yes	—
15	C₁₃×M₁₆	—	2	2	no	—
16	C₁₃×M₁₆	—	2	2	no	—
17	C₂×C₈×C₁₃	—	2	2	no	—
18	C₂×C₈×C₁₃	—	2	2	no	—
19	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
20	C₄×Dic₁₃	C₂×C₄	1	2	yes	—
21	C₄×Dic₁₃	D₄	1	2	yes	—
22	#6099	—	2	2	no	—
23	#6099	—	2	2	no	—
24	C₂×#1055	—	2	2	no	—
25	C₂×#1055	—	2	2	no	—
26	C₂×#1055	C₂×C₄	1	2	yes	—
27	#1838	—	13	1	no	maximal, Sylow
28	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₁₃	#41	1	2	yes	—
32	C₂×C₄×C₁₃	#41	1	2	yes	—
33	C₂×Dic₁₃	—	4	2	no	—
34	C₂×Dic₁₃	C₄⋊C₄	1	4	yes	—
35	C₈×C₁₃	—	2	2	no	—
36	C₈×C₁₃	—	4	2	no	—
37	#1055	—	2	2	no	—
38	#1055	—	4	2	no	—
39	#423	—	13	2	no	—
40	C₂×#97	—	13	1	no	—
41	#341	—	13	2	no	—
42	#341	—	13	1	no	—
43	#341	D₁₃	1	1	yes	characteristic
44	C₂²×C₁₃	—	2	2	no	—
45	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₁₃	#125	1	2	yes	—
47	C₄×C₁₃	#117	1	1	yes	characteristic
48	C₄×C₁₃	#117	1	1	yes	characteristic
49	C₄×C₁₃	#124	1	2	yes	—
50	Dic₁₃	—	2	4	no	—
51	C₂×M₁₆	—	13	2	no	—
52	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
53	C₂²×C₈	—	13	1	no	—
54	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
55	C₂×C₄²	—	13	1	no	—
56	C₄⋊C₈	—	26	4	no	—
57	#97	—	13	4	no	—
58	C₂×C₁₃	—	2	2	no	—
59	C₂×C₁₃	#382	1	1	yes	characteristic
60	C₂×C₁₃	#430	1	2	yes	—
61	C₂²×C₄	—	13	2	no	—
62	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
63	M₁₆	—	2	2	no	—
64	M₁₆	—	2	2	no	—
65	M₁₆	—	26	2	no	—
66	M₁₆	—	26	2	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	13	2	no	—
70	C₂×C₈	—	26	2	no	—
71	C₂×C₈	—	26	2	no	—
72	C₂×C₈	C₄×D₁₃	1	2	yes	—
73	C₄²	—	13	2	no	—
74	C₄²	—	13	2	no	—
75	C₁₃	#1838	1	1	yes	characteristic, complemented, Sylow
76	C₂³	Q₈×D₁₃	1	1	yes	characteristic
77	C₂×C₄	—	13	4	no	—
78	C₂×C₄	—	52	2	no	—
79	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
80	C₂×C₄	#6127	1	2	yes	—
81	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
82	C₂×C₄	#6129	1	2	yes	—
83	C₈	—	2	2	no	—
84	C₈	—	4	2	no	—
85	C₈	—	26	2	no	—
86	C₈	—	52	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	#88143	1	2	yes	—
89	C₂²	C₄⋊C₄×D₁₃	1	1	yes	characteristic
90	C₄	—	26	4	no	—
91	C₄	#88126	1	1	yes	characteristic
92	C₄	#88131	1	1	yes	characteristic
93	C₄	#88139	1	2	yes	—
94	C₂	—	2	2	no	—
95	C₂	#11718311	1	1	yes	characteristic
96	C₂	#11718554	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#341	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#341	D₁₃
hypocenter	C₁₃	#1838
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

Complements

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

N	H ≅ G/N	type
75. C₁₃	#1838	semidirect

Maximal subgroups

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

subgroup	index
#11718779	2
C₂×#88055	2
C₁₃×#341	2
#11718150	2
#11718144	2
#1838	13