Subgroups — #13112975

Order 1664.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88038	C₂	1	1	yes	maximal, characteristic
2	C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718091	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₁₃	C₄	1	1	yes	characteristic
5	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×#6090	C₄	1	1	yes	characteristic
7	#88038	—	2	1	no	—
8	#88038	—	2	1	no	—
9	C₁₃×C₃₂	—	2	1	no	—
10	#88034	—	2	1	no	—
11	C₂×C₄×D₁₃	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂×#1055	C₈	1	1	yes	characteristic
14	C₈×D₁₃	—	2	1	no	—
15	C₈×D₁₃	—	2	1	no	—
16	C₁₃×C₁₆	D₄	1	1	yes	characteristic
17	C₁₃×C₁₆	D₄	1	1	yes	characteristic
18	#6090	—	2	1	no	—
19	#1400	—	13	1	no	maximal, Sylow
20	C₂²×D₁₃	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
22	C₂×Dic₁₃	C₁₆	1	1	yes	characteristic
23	C₄×D₁₃	—	2	1	no	—
24	C₄×D₁₃	—	2	1	no	—
25	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₃	M₁₆	1	1	yes	characteristic
27	#1055	—	2	1	no	—
28	C₂×M₃₂	—	13	1	no	—
29	M₆₄	—	13	1	no	—
30	M₆₄	D₁₃	1	1	yes	characteristic, complemented
31	C₂²×C₁₃	C₂×C₁₆	1	1	yes	characteristic
32	C₂×D₁₃	—	2	1	no	—
33	C₂×D₁₃	—	4	1	no	—
34	C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
35	C₄×C₁₃	M₃₂	1	1	yes	characteristic
36	Dic₁₃	—	2	1	no	—
37	C₂²×C₈	—	13	1	no	—
38	M₃₂	—	26	1	no	—
39	M₃₂	—	26	1	no	—
40	C₂×C₁₆	—	13	1	no	—
41	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
42	C₃₂	—	2	1	no	—
43	C₃₂	—	26	1	no	—
44	C₂×C₁₃	—	2	1	no	—
45	C₂×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
46	D₁₃	—	4	1	no	—
47	C₂²×C₄	—	13	1	no	—
48	C₂×C₈	—	13	1	no	—
49	C₂×C₈	—	26	1	no	—
50	C₂×C₈	—	26	1	no	—
51	C₂×C₈	C₄×D₁₃	1	1	yes	characteristic
52	C₁₆	—	26	1	no	—
53	C₁₆	D₅₂	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
55	C₁₃	#1400	1	1	yes	characteristic, complemented, Sylow
56	C₂³	—	13	1	no	—
57	C₂×C₄	—	13	1	no	—
58	C₂×C₄	—	26	1	no	—
59	C₂×C₄	—	26	1	no	—
60	C₂×C₄	C₈×D₁₃	1	1	yes	characteristic
61	C₈	—	26	1	no	—
62	C₈	#6094	1	1	yes	characteristic
63	C₈	#6103	1	1	yes	characteristic
64	C₂²	—	26	1	no	—
65	C₂²	—	52	1	no	—
66	C₂²	C₁₆×D₁₃	1	1	yes	characteristic
67	C₄	—	26	1	no	—
68	C₄	#88038	1	1	yes	characteristic
69	C₄	#88060	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	52	1	no	—
72	C₂	#11718099	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#6103
commutator	C₂²×C₁₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₁₃
Fitting	C₁₃×M₆₄	C₂
socle	C₂×C₁₃	C₂²⋊C₁₆
prime radical	C₂²×D₁₃	C₁₆
cosocle	C₂×C₁₃×C₁₆	C₂²
hypercenter	M₆₄	D₁₃
hypocenter	C₁₃	#1400
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. C₁₃×M₆₄	C₂	semidirect
3. #11718091	C₂	semidirect
30. M₆₄	D₁₃	semidirect
55. C₁₃	#1400	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88038	2
C₁₃×M₆₄	2
#11718091	2
#1400	13