Subgroups — #13123447

Order 1664.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#131	C₂	1	1	yes	maximal, characteristic
2	#11719524	C₂	1	2	yes	maximal
3	#11718786	C₂	1	6	yes	maximal, complemented
4	C₂×#88059	C₂	1	6	yes	maximal, complemented
5	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
6	C₁₃×#131	C₄	1	8	yes	—
7	C₂×C₁₃×M₁₆	C₂²	1	3	yes	—
8	C₂²×C₈×C₁₃	C₂²	1	3	yes	—
9	#88202	—	2	8	no	—
10	C₂×#6099	C₂²	1	12	yes	—
11	#88059	C₂²	1	4	yes	—
12	#88059	C₂²	1	12	yes	—
13	C₁₃×#41	C₂×C₄	1	4	yes	—
14	C₁₃×#41	D₄	1	4	yes	—
15	C₂×Q₈×C₁₃	Q₈	1	1	yes	characteristic
16	C₂×D₄×C₁₃	Q₈	1	3	yes	—
17	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
18	C₁₃×M₁₆	C₂×C₄	1	12	yes	—
19	C₂×C₈×C₁₃	C₂×C₄	1	12	yes	—
20	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	C₂×C₈×C₁₃	C₂³	1	3	yes	—
22	#6099	—	2	12	no	—
23	#6099	C₂³	1	8	yes	—
24	C₂×#1055	—	2	12	no	—
25	#2916	—	13	1	no	maximal, Sylow
26	C₂³×C₁₃	C₂×Q₈	1	3	yes	—
27	Q₈×C₁₃	C₄⋊C₄	1	4	yes	—
28	D₄×C₁₃	C₄⋊C₄	1	12	yes	—
29	C₂×C₄×C₁₃	C₂²×C₄	1	6	yes	—
30	C₂×C₄×C₁₃	C₂×D₄	1	6	yes	—
31	C₂×C₄×C₁₃	C₂×Q₈	1	3	yes	—
32	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
33	C₈×C₁₃	C₂²×C₄	1	2	yes	—
34	C₈×C₁₃	C₂²×C₄	1	6	yes	—
35	#1055	—	2	8	no	—
36	#568	—	13	2	no	—
37	C₂×#131	D₁₃	1	1	yes	characteristic
38	#430	—	13	6	no	—
39	C₂×#108	—	13	6	no	—
40	C₂²×C₁₃	—	4	3	no	—
41	C₂²×C₁₃	C₂×C₄⋊C₄	1	6	yes	—
42	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
43	C₄×C₁₃	C₂×C₄⋊C₄	1	6	yes	—
44	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
45	C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
46	C₂×#41	C₂×D₁₃	1	1	yes	characteristic
47	#131	—	26	8	no	—
48	#131	Dic₁₃	1	8	yes	—
49	C₂×M₁₆	—	13	12	no	—
50	C₂×M₁₆	C₂×D₁₃	1	3	yes	—
51	C₂²×C₈	C₂×D₁₃	1	3	yes	—
52	#108	—	13	4	no	—
53	#108	—	13	12	no	—
54	C₂×C₁₃	—	2	1	no	—
55	C₂×C₁₃	—	2	6	no	—
56	C₂×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
57	#41	D₅₂	1	4	yes	—
58	#41	C₂×Dic₁₃	1	4	yes	—
59	C₂×Q₈	Dic₂₆	1	1	yes	characteristic
60	C₂×D₄	Dic₂₆	1	3	yes	—
61	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
62	M₁₆	—	13	8	no	—
63	M₁₆	—	26	12	no	—
64	M₁₆	C₂×Dic₁₃	1	12	yes	—
65	C₂×C₈	—	26	12	no	—
66	C₂×C₈	C₂×Dic₁₃	1	12	yes	—
67	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
68	C₂×C₈	C₂²×D₁₃	1	3	yes	—
69	C₁₃	#2916	1	1	yes	characteristic, complemented, Sylow
70	C₂³	C₂×Dic₂₆	1	3	yes	—
71	Q₈	C₄⋊Dic₁₃	1	4	yes	—
72	D₄	C₄⋊Dic₁₃	1	12	yes	—
73	C₂×C₄	C₂×Dic₂₆	1	3	yes	—
74	C₂×C₄	C₂×D₅₂	1	6	yes	—
75	C₂×C₄	C₂²×Dic₁₃	1	6	yes	—
76	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
77	C₈	—	26	8	no	—
78	C₈	C₂²×Dic₁₃	1	2	yes	—
79	C₈	C₂²×Dic₁₃	1	6	yes	—
80	C₂²	—	4	3	no	—
81	C₂²	C₂×C₄⋊Dic₁₃	1	6	yes	—
82	C₂²	C₂²×Dic₂₆	1	1	yes	characteristic
83	C₄	C₂×C₄⋊Dic₁₃	1	6	yes	—
84	C₄	C₂²×D₅₂	1	1	yes	characteristic
85	C₄	C₂³×Dic₁₃	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	2	6	no	—
88	C₂	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₅₂
commutator	C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#131	C₂
socle	C₂×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×C₁₃×#41	C₂²
cosocle	C₂×C₄×C₁₃	C₂⁴
hypercenter	C₂×#131	D₁₃
hypocenter	C₁₃	#2916
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×#41 ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
3. #11718786	C₂	semidirect
4. C₂×#88059	C₂	semidirect
69. C₁₃	#2916	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#131	2
#11719524	2
#11718786	2
C₂×#88059	2
#2916	13