Subgroups — #13129904

Order 1664.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11719092	C₂	1	2	yes	maximal
2	C₂×#88038	C₂	1	1	yes	maximal, characteristic
3	#88237	—	2	2	no	—
4	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
5	#88102	—	2	2	no	—
6	#88101	C₄	1	4	yes	complemented
7	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic, complemented
8	C₂×#6090	C₄	1	1	yes	characteristic, complemented
9	#88038	—	2	2	no	—
10	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
11	C₂²⋊#261	—	4	2	no	—
12	C₄⋊#261	—	2	4	no	—
13	C₄×#261	—	4	2	no	—
14	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×#1055	Q₈	1	1	yes	characteristic
16	C₈×D₁₃	C₂×C₄	1	2	yes	—
17	C₈×D₁₃	D₄	1	2	yes	—
18	C₁₃×C₁₆	—	2	1	no	—
19	#6090	—	2	1	no	—
20	#1384	—	13	1	no	maximal, Sylow
21	C₂²×D₁₃	D₈	1	1	yes	characteristic
22	C₂×#261	—	4	4	no	—
23	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
24	C₂×Dic₁₃	Q₁₆	1	1	yes	characteristic
25	C₄×D₁₃	C₂²⋊C₄	1	2	yes	—
26	C₄×D₁₃	SD₁₆	1	2	yes	—
27	C₈×C₁₃	C₄²	1	1	yes	characteristic
28	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
29	#1055	C₄⋊C₄	1	2	yes	—
30	C₂×M₃₂	—	13	1	no	—
31	#427	—	13	2	no	—
32	C₂²×C₁₃	#107	1	1	yes	characteristic
33	C₂×D₁₃	—	4	1	no	—
34	C₂×D₁₃	#102	1	2	yes	—
35	#261	—	8	4	no	—
36	C₄×C₁₃	#95	1	1	yes	characteristic
37	C₄×C₁₃	#106	1	1	yes	characteristic
38	Dic₁₃	#103	1	2	yes	—
39	C₂²×C₈	—	13	1	no	—
40	#117	—	26	2	no	—
41	M₃₂	—	26	2	no	—
42	C₂×C₁₆	—	13	1	no	—
43	C₂×C₁₆	#261	1	1	yes	characteristic, complemented
44	#107	—	26	2	no	—
45	#106	—	13	4	no	—
46	C₂×C₁₃	—	2	1	no	—
47	C₂×C₁₃	#340	1	1	yes	characteristic
48	D₁₃	—	2	2	no	—
49	C₂²×C₄	—	13	1	no	—
50	C₂×C₈	—	13	1	no	—
51	C₂×C₈	—	13	2	no	—
52	C₂×C₈	—	13	2	no	—
53	C₂×C₈	C₂×#261	1	1	yes	characteristic
54	C₄⋊C₄	—	26	4	no	—
55	C₂²⋊C₄	—	52	2	no	—
56	C₄²	—	52	2	no	—
57	C₁₆	—	2	1	no	—
58	C₁₆	—	26	1	no	—
59	C₁₃	#1384	1	1	yes	characteristic, complemented, Sylow
60	C₂³	—	13	1	no	—
61	C₂×C₄	—	13	1	no	—
62	C₂×C₄	—	13	2	no	—
63	C₂×C₄	—	13	2	no	—
64	C₂×C₄	—	52	4	no	—
65	C₂×C₄	C₄⋊#261	1	1	yes	characteristic
66	C₈	—	13	2	no	—
67	C₈	C₄×#261	1	1	yes	characteristic
68	C₈	C₂²⋊#261	1	1	yes	characteristic
69	C₂²	—	13	2	no	—
70	C₂²	—	52	1	no	—
71	C₂²	#88102	1	1	yes	characteristic
72	C₄	—	13	2	no	—
73	C₄	—	104	4	no	—
74	C₄	#88101	1	1	yes	characteristic
75	C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	26	2	no	—
78	C₂	#11718265	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88101
commutator	C₈×C₁₃	C₄²
Frattini	C₂×C₈	C₂×#261
Fitting	C₂×C₁₃×C₁₆	C₄
socle	C₂×C₁₃	#340
prime radical	C₂²×D₁₃	D₈
cosocle	C₂×C₈×D₁₃	C₂²
hypercenter	C₂×C₁₆	#261
hypocenter	C₁₃	#1384
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
6. #88101	C₄	semidirect
7. C₂×C₁₃×C₁₆	C₄	semidirect
8. C₂×#6090	C₄	semidirect
43. C₂×C₁₆	#261	semidirect
59. C₁₃	#1384	semidirect

Maximal subgroups

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

subgroup	index
#11719092	2
C₂×#88038	2
#1384	13