Subgroups — #13117129

Order 1664.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718562	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718091	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718039	C₂	1	2	yes	maximal, complemented
5	D₁₃×C₃₂	C₂	1	2	yes	maximal, complemented
6	#88155	C₄	1	1	yes	characteristic
7	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	#88052	C₄	1	1	yes	characteristic
9	#88038	C₄	1	2	yes	—
10	C₁₆×D₁₃	C₂²	1	2	yes	—
11	C₁₃×C₃₂	C₂²	1	1	yes	characteristic
12	C₁₃×C₃₂	C₂²	1	1	yes	characteristic
13	#88034	C₂²	1	2	yes	—
14	#6127	C₈	1	1	yes	characteristic
15	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	#6099	C₈	1	1	yes	characteristic
17	#6094	C₈	1	2	yes	—
18	C₈×D₁₃	C₂×C₄	1	2	yes	—
19	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
21	#6090	C₂×C₄	1	2	yes	—
22	#2258	—	13	1	no	maximal, Sylow
23	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
24	C₂²⋊D₁₃	C₁₆	1	2	yes	—
25	D₅₂	C₁₆	1	1	yes	characteristic
26	C₄×D₁₃	C₂×C₈	1	2	yes	—
27	Dic₂₆	C₁₆	1	1	yes	characteristic
28	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
29	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	#1055	C₂×C₈	1	2	yes	—
31	#504	—	13	1	no	—
32	M₆₄	—	13	1	no	—
33	M₆₄	—	13	2	no	—
34	C₂×C₃₂	—	13	2	no	—
35	C₂×C₃₂	D₁₃	1	1	yes	characteristic, complemented
36	C₂²×C₁₃	C₂×C₁₆	1	1	yes	characteristic
37	C₂×D₁₃	C₂×C₁₆	1	2	yes	—
38	C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
39	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
40	Dic₁₃	C₂×C₁₆	1	2	yes	—
41	#131	—	13	1	no	—
42	M₃₂	—	13	1	no	—
43	M₃₂	—	13	2	no	—
44	C₂×C₁₆	—	13	2	no	—
45	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
46	C₃₂	—	13	2	no	—
47	C₃₂	C₂×D₁₃	1	1	yes	characteristic
48	C₃₂	C₂×D₁₃	1	1	yes	characteristic
49	C₂×C₁₃	—	2	1	no	—
50	C₂×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
51	D₁₃	—	2	2	no	—
52	#41	—	13	1	no	—
53	M₁₆	—	13	1	no	—
54	M₁₆	—	13	2	no	—
55	C₂×C₈	—	13	2	no	—
56	C₂×C₈	C₄×D₁₃	1	1	yes	characteristic
57	C₁₆	—	13	2	no	—
58	C₁₆	C₄×D₁₃	1	1	yes	characteristic
59	C₁₆	C₂²×D₁₃	1	1	yes	characteristic
60	C₁₃	#2258	1	1	yes	characteristic, complemented, Sylow
61	Q₈	—	13	1	no	—
62	D₄	—	13	2	no	—
63	D₄	—	13	1	no	—
64	C₂×C₄	—	13	2	no	—
65	C₂×C₄	C₈×D₁₃	1	1	yes	characteristic
66	C₈	—	13	2	no	—
67	C₈	C₈×D₁₃	1	1	yes	characteristic
68	C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
69	C₂²	—	13	2	no	—
70	C₂²	C₁₆×D₁₃	1	1	yes	characteristic
71	C₄	—	13	2	no	—
72	C₄	C₁₆×D₁₃	1	1	yes	characteristic
73	C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	26	2	no	—
76	C₂	C₂×C₁₆×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	C₂×D₁₃
commutator, socle	C₂×C₁₃	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₁₃
Fitting	C₂×C₁₃×C₃₂	C₂
prime radical	#6127	C₈
cosocle	C₁₃×C₁₆	C₂³
hypercenter	C₂×C₃₂	D₁₃
hypocenter	C₁₃	#2258
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×C₃₂	C₂	semidirect
3. #11718091	C₂	semidirect
4. #11718039	C₂	semidirect
5. D₁₃×C₃₂	C₂	semidirect
35. C₂×C₃₂	D₁₃	semidirect
60. C₁₃	#2258	semidirect

Maximal subgroups

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

subgroup	index
#11718562	2
C₂×C₁₃×C₃₂	2
#11718091	2
#11718039	2
D₁₃×C₃₂	2
#2258	13