Subgroups — #13113121

Order 1664.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718346	C₂	1	2	yes	maximal
2	C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718047	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×#1055	C₂	1	2	yes	maximal, complemented
6	C₂×C₈×D₁₃	C₄	1	2	yes	—
7	C₄²×D₁₃	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₁₃	C₂²	1	2	yes	—
9	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	#88060	C₄	1	4	yes	—
11	#88054	C₄	1	4	yes	—
12	C₈×Dic₁₃	C₄	1	2	yes	—
13	C₄×#1055	C₂²	1	1	yes	characteristic
14	C₄×#1055	C₂²	1	2	yes	—
15	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
19	C₄²×C₁₃	C₂³	1	1	yes	characteristic
20	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₁₃	C₂×C₄	1	2	yes	—
22	C₂×#1055	C₂×C₄	1	4	yes	—
23	C₂×#1055	C₂×C₄	1	2	yes	—
24	C₈×D₁₃	C₈	1	8	yes	complemented
25	#1450	—	13	1	no	maximal, Sylow
26	C₂²×D₁₃	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
29	C₂×Dic₁₃	C₄²	1	2	yes	—
30	C₂×Dic₁₃	C₄²	1	1	yes	characteristic
31	C₄×D₁₃	—	2	4	no	—
32	C₄×D₁₃	C₂×C₈	1	4	yes	—
33	C₈×C₁₃	—	2	4	no	—
34	C₈×C₁₃	C₂×C₈	1	4	yes	—
35	#1055	—	2	4	no	—
36	#1055	C₂×C₈	1	4	yes	—
37	#431	—	13	2	no	—
38	C₂×C₄×C₈	—	13	1	no	—
39	#322	—	13	1	no	—
40	#322	D₁₃	1	1	yes	characteristic, complemented
41	C₈²	—	13	2	no	—
42	C₂²×C₁₃	C₂×C₄²	1	1	yes	characteristic
43	C₂×D₁₃	—	2	2	no	—
44	C₂×D₁₃	C₄×C₈	1	2	yes	—
45	C₄×C₁₃	C₂²×C₈	1	2	yes	—
46	C₄×C₁₃	#131	1	4	yes	—
47	Dic₁₃	—	2	2	no	—
48	Dic₁₃	C₄×C₈	1	2	yes	—
49	C₂²×C₈	—	13	2	no	—
50	C₂×C₄²	—	13	1	no	—
51	C₄⋊C₈	—	13	4	no	—
52	C₂²⋊C₈	—	13	4	no	—
53	C₄×C₈	—	13	2	no	—
54	C₄×C₈	—	13	1	no	—
55	C₄×C₈	—	13	2	no	—
56	C₄×C₈	C₂×D₁₃	1	2	yes	—
57	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
58	C₂×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
59	C₂×C₁₃	#405	1	2	yes	—
60	D₁₃	—	2	2	no	—
61	C₂²×C₄	—	13	1	no	—
62	C₂²×C₄	—	13	2	no	—
63	C₂×C₈	—	13	2	no	—
64	C₂×C₈	—	13	8	no	—
65	C₂×C₈	—	13	4	no	—
66	C₂×C₈	C₄×D₁₃	1	4	yes	—
67	C₂×C₈	C₄×D₁₃	1	2	yes	—
68	C₄²	—	13	1	no	—
69	C₄²	—	13	2	no	—
70	C₄²	C₂²×D₁₃	1	1	yes	characteristic
71	C₁₃	#1450	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	13	1	no	—
73	C₂×C₄	—	13	1	no	—
74	C₂×C₄	—	13	4	no	—
75	C₂×C₄	—	13	2	no	—
76	C₂×C₄	—	26	4	no	—
77	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
78	C₂×C₄	C₂×C₄×D₁₃	1	2	yes	—
79	C₈	—	2	4	no	—
80	C₈	—	13	4	no	—
81	C₈	—	26	4	no	—
82	C₈	C₈×D₁₃	1	4	yes	—
83	C₂²	—	13	2	no	—
84	C₂²	—	26	2	no	—
85	C₂²	C₄²×D₁₃	1	1	yes	characteristic
86	C₄	—	13	2	no	—
87	C₄	—	26	2	no	—
88	C₄	C₂×C₈×D₁₃	1	2	yes	—
89	C₄	#88161	1	4	yes	—
90	C₂	—	26	2	no	—
91	C₂	C₄×C₈×D₁₃	1	1	yes	characteristic
92	C₂	#11718369	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₁₃
commutator	C₂×C₁₃	C₂×C₄×C₈
Fitting	C₁₃×#322	C₂
socle	C₂²×C₁₃	C₂×C₄²
prime radical	C₂²×D₁₃	C₄²
cosocle	C₄²×C₁₃	C₂³
hypercenter	#322	D₁₃
hypocenter	C₁₃	#1450
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
3. C₁₃×#322	C₂	semidirect
4. #11718047	C₂	semidirect
5. C₈×#1055	C₂	semidirect
24. C₈×D₁₃	C₈	semidirect
40. #322	D₁₃	semidirect
71. C₁₃	#1450	semidirect

Maximal subgroups

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

subgroup	index
#11718346	2
C₄×C₈×D₁₃	2
C₁₃×#322	2
#11718047	2
C₈×#1055	2
#1450	13