Subgroups — #13130758

Order 1664.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11719060	C₂	1	2	yes	maximal
2	C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#11718265	C₂	1	4	yes	maximal
4	C₂×C₄⋊#261	C₂²	1	4	yes	—
5	C₂×C₈×D₁₃	C₂²	1	2	yes	—
6	C₄²×D₁₃	C₂²	1	1	yes	characteristic
7	(C₂×#261)⋊C₄	—	2	4	no	—
8	C₄×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
9	C₈×Dic₁₃	C₄	1	2	yes	complemented
10	C₄×#1055	C₄	1	1	yes	characteristic, complemented
11	C₂²×#261	—	2	4	no	—
12	C₂×C₄×D₁₃	D₄	1	2	yes	—
13	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
14	C₄⋊#261	—	2	8	no	—
15	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
16	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₁₃	Q₈	1	2	yes	—
19	C₂×#1055	C₂×C₄	1	2	yes	—
20	C₈×D₁₃	—	2	4	no	—
21	#1835	—	13	1	no	maximal, Sylow
22	C₂²×D₁₃	C₂×D₄	1	1	yes	characteristic
23	C₂×#261	—	4	4	no	—
24	C₂×#261	—	4	8	no	—
25	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
28	C₂×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
29	C₄×D₁₃	—	2	4	no	—
30	C₄×D₁₃	#41	1	4	yes	—
31	C₈×C₁₃	—	2	2	no	—
32	#1055	—	2	2	no	—
33	C₂×C₄×C₈	—	13	1	no	—
34	#382	—	13	2	no	—
35	#340	—	13	4	no	—
36	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₂×D₁₃	#124	1	2	yes	—
38	C₂×D₁₃	#135	1	4	yes	—
39	#261	—	8	4	no	—
40	C₄×C₁₃	—	2	2	no	—
41	C₄×C₁₃	#117	1	2	yes	—
42	Dic₁₃	—	2	2	no	—
43	Dic₁₃	#125	1	2	yes	—
44	C₂²×C₈	—	13	2	no	—
45	C₂×C₄⋊C₄	—	13	4	no	—
46	C₂×C₄²	—	13	1	no	—
47	C₄×C₈	—	13	2	no	—
48	C₄×C₈	—	13	1	no	—
49	C₄×C₈	#261	1	1	yes	characteristic, complemented
50	#95	—	26	4	no	—
51	C₂×C₁₃	#382	1	1	yes	characteristic
52	C₂×C₁₃	#427	1	2	yes	—
53	D₁₃	#488	1	4	yes	—
54	C₂²×C₄	—	13	1	no	—
55	C₂²×C₄	—	13	2	no	—
56	C₂²×C₄	—	26	4	no	—
57	C₂×C₈	—	13	2	no	—
58	C₂×C₈	—	26	4	no	—
59	C₂×C₈	C₂×#261	1	2	yes	—
60	C₄⋊C₄	—	26	8	no	—
61	C₄²	—	13	2	no	—
62	C₄²	—	13	1	no	—
63	C₄²	C₂×#261	1	1	yes	characteristic
64	C₁₃	#1835	1	1	yes	characteristic, complemented, Sylow
65	C₂³	—	13	1	no	—
66	C₂×C₄	—	13	1	no	—
67	C₂×C₄	—	13	4	no	—
68	C₂×C₄	—	13	2	no	—
69	C₂×C₄	—	26	4	no	—
70	C₂×C₄	—	52	4	no	—
71	C₂×C₄	—	52	8	no	—
72	C₂×C₄	C₄⋊#261	1	2	yes	—
73	C₂×C₄	C₂²×#261	1	1	yes	characteristic
74	C₈	—	2	2	no	—
75	C₈	—	26	2	no	—
76	C₂²	—	13	2	no	—
77	C₂²	—	13	4	no	—
78	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	13	2	no	—
81	C₄	—	26	2	no	—
82	C₄	—	104	4	no	—
83	C₄	#88237	1	2	yes	—
84	C₂	—	13	4	no	—
85	C₂	#11719060	1	1	yes	characteristic
86	C₂	#11719092	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂²×D₁₃	C₂×D₄
cosocle	C₂×C₄×D₁₃	C₂³
hypercenter	C₄×C₈	#261
hypocenter	C₁₃	#1835
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
8. C₄×C₈×C₁₃	C₄	semidirect
9. C₈×Dic₁₃	C₄	semidirect
10. C₄×#1055	C₄	semidirect
49. C₄×C₈	#261	semidirect
64. C₁₃	#1835	semidirect

Maximal subgroups

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

subgroup	index
#11719060	2
C₄×C₈×D₁₃	2
#11718265	2
#1835	13