Subgroups — #15777752

Order 3328.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13116441	C₂	1	3	yes	maximal
2	#13116433	C₂	1	3	yes	maximal
3	C₁₃×#1747	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#405	C₂²	1	3	yes	—
5	C₂×#88052	C₂²	1	3	yes	—
6	C₂²×#6090	C₂²	1	1	yes	characteristic
7	C₁₃×#338	C₄	1	1	yes	characteristic
8	C₁₃×H(3,ℤ/4)	C₄	1	3	yes	—
9	#11718058	C₄	1	12	yes	complemented
10	#11718053	C₄	1	6	yes	complemented
11	C₄×#6090	C₄	1	6	yes	complemented
12	C₂×C₁₃×M₁₆	C₂×C₄	1	3	yes	—
13	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
14	C₁₃×#117	C₂×C₄	1	3	yes	—
15	C₁₃×#97	C₂×C₄	1	6	yes	—
16	C₄×C₈×C₁₃	C₂×C₄	1	6	yes	—
17	#88052	C₂×C₄	1	12	yes	—
18	C₂×#6090	C₂×C₄	1	3	yes	—
19	C₂×#6090	C₂×C₄	1	3	yes	—
20	C₂×#6090	C₂×C₄	1	6	yes	—
21	#12542	—	13	1	no	maximal, Sylow
22	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
23	C₁₃×M₁₆	—	2	6	no	—
24	C₂×C₈×C₁₃	C₄²	1	6	yes	—
25	C₂×C₈×C₁₃	C₂²×C₄	1	3	yes	—
26	C₂×C₈×C₁₃	C₂²×C₄	1	3	yes	—
27	C₁₃×C₄⋊C₄	—	2	3	no	—
28	C₁₃×C₂²⋊C₄	—	2	3	no	—
29	C₄²×C₁₃	C₄²	1	6	yes	—
30	#6090	C₄²	1	1	yes	characteristic
31	#6090	C₄²	1	3	yes	—
32	#6090	C₄²	1	12	yes	—
33	#2110	—	13	3	no	—
34	#2108	—	13	3	no	—
35	#1747	D₁₃	1	1	yes	characteristic
36	C₂³×C₁₃	#131	1	1	yes	characteristic
37	C₂×C₄×C₁₃	—	2	6	no	—
38	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
39	C₂×C₄×C₁₃	#131	1	3	yes	—
40	C₈×C₁₃	—	2	6	no	—
41	C₈×C₁₃	C₂×C₄²	1	3	yes	—
42	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
43	C₂×M₃₂	—	13	3	no	—
44	C₂²×C₁₆	—	13	1	no	—
45	#405	C₂×D₁₃	1	3	yes	—
46	#347	—	13	12	no	—
47	#346	—	13	6	no	—
48	C₄×C₁₆	—	13	6	no	—
49	#338	Dic₁₃	1	1	yes	characteristic
50	H(3,ℤ/4)	Dic₁₃	1	3	yes	—
51	C₂²×C₁₃	—	4	1	no	—
52	C₂²×C₁₃	#405	1	3	yes	—
53	C₄×C₁₃	—	4	6	no	—
54	C₄×C₁₃	C₄³	1	1	yes	characteristic
55	C₄×C₁₃	#405	1	3	yes	—
56	C₂×M₁₆	C₂×Dic₁₃	1	3	yes	—
57	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
58	#117	C₂×Dic₁₃	1	3	yes	—
59	M₃₂	—	13	12	no	—
60	C₂×C₁₆	—	13	3	no	—
61	C₂×C₁₆	—	13	6	no	—
62	C₂×C₁₆	—	13	3	no	—
63	#97	C₄×D₁₃	1	6	yes	—
64	C₄×C₈	C₄×D₁₃	1	6	yes	—
65	C₂×C₁₃	—	2	3	no	—
66	C₂×C₁₃	#1726	1	1	yes	characteristic
67	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
68	M₁₆	—	2	6	no	—
69	C₂×C₈	C₄×Dic₁₃	1	6	yes	—
70	C₂×C₈	C₂×C₄×D₁₃	1	3	yes	—
71	C₂×C₈	C₂×C₄×D₁₃	1	3	yes	—
72	C₄⋊C₄	—	2	3	no	—
73	C₂²⋊C₄	—	2	3	no	—
74	C₄²	C₄×Dic₁₃	1	6	yes	—
75	C₁₆	—	13	12	no	—
76	C₁₆	—	13	1	no	—
77	C₁₆	—	13	3	no	—
78	C₁₃	#12542	1	1	yes	characteristic, complemented, Sylow
79	C₂³	#88202	1	1	yes	characteristic
80	C₂×C₄	—	2	6	no	—
81	C₂×C₄	C₂×C₄×Dic₁₃	1	3	yes	—
82	C₂×C₄	#88202	1	3	yes	—
83	C₈	—	2	6	no	—
84	C₈	C₄²×D₁₃	1	3	yes	—
85	C₈	C₄²×D₁₃	1	1	yes	characteristic
86	C₂²	—	4	1	no	—
87	C₂²	#11718658	1	3	yes	—
88	C₄	—	4	6	no	—
89	C₄	C₄²×Dic₁₃	1	1	yes	characteristic
90	C₄	#11718658	1	3	yes	—
91	C₂	—	2	3	no	—
92	C₂	#13114523	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄²×D₁₃
commutator	C₄×C₁₃	C₄³
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1747	C₂
socle	C₂×C₁₃	#1726
prime radical	C₂³×C₁₃	#131
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1747	D₁₃
hypocenter	C₁₃	#12542
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ #1747

Complements

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

N	H ≅ G/N	type
9. #11718058	C₄	semidirect
10. #11718053	C₄	semidirect
11. C₄×#6090	C₄	semidirect
78. C₁₃	#12542	semidirect

Maximal subgroups

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

subgroup	index
#13116441	2
#13116433	2
C₁₃×#1747	2
#12542	13