Subgroups — #15779319

Order 3328.

342 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13112914	C₂	1	6	yes	maximal
2	C₄²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×C₁₃	C₄	1	3	yes	—
4	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
5	C₄³×C₁₃	C₄	1	1	yes	characteristic
6	C₂²×#6090	C₂²	1	4	yes	—
7	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
8	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
9	C₂×C₄²×C₁₃	C₈	1	3	yes	—
10	C₂×C₄²×C₁₃	C₈	1	1	yes	characteristic
11	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
12	C₄×C₈×C₁₃	—	2	6	no	—
13	C₄×C₈×C₁₃	—	2	6	no	—
14	C₂×#6090	—	2	12	no	—
15	#12894	—	13	1	no	maximal, Sylow
16	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
17	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
18	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₃	—	2	3	no	—
20	C₂×C₈×C₁₃	—	2	3	no	—
21	C₂×C₈×C₁₃	M₁₆	1	6	yes	—
22	C₂×C₈×C₁₃	#41	1	6	yes	—
23	C₄²×C₁₃	—	2	6	no	—
24	C₄²×C₁₃	—	2	3	no	—
25	C₄²×C₁₃	—	2	3	no	—
26	C₄²×C₁₃	C₁₆	1	4	yes	complemented
27	#6090	—	4	4	no	—
28	C₄²×C₈	D₁₃	1	1	yes	characteristic
29	#1374	—	13	6	no	—
30	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
31	C₂×C₄×C₁₃	—	2	3	no	—
32	C₂×C₄×C₁₃	—	2	3	no	—
33	C₂×C₄×C₁₃	—	2	3	no	—
34	C₂×C₄×C₁₃	—	2	3	no	—
35	C₂×C₄×C₁₃	C₂×C₁₆	1	6	yes	—
36	C₂×C₄×C₁₃	M₃₂	1	6	yes	—
37	C₂×C₄×C₁₃	#117	1	3	yes	—
38	C₂×C₄×C₁₃	C₂×M₁₆	1	3	yes	—
39	C₈×C₁₃	—	2	6	no	—
40	C₈×C₁₃	#126	1	4	yes	—
41	C₂²×C₁₆	—	13	4	no	—
42	C₂×C₄×C₈	Dic₁₃	1	3	yes	—
43	C₂×C₄×C₈	C₂×D₁₃	1	3	yes	—
44	C₄³	Dic₁₃	1	1	yes	characteristic
45	C₂²×C₁₃	#431	1	3	yes	—
46	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
47	C₂²×C₁₃	C₂×M₃₂	1	3	yes	—
48	C₄×C₁₃	—	2	6	no	—
49	C₄×C₁₃	—	2	6	no	—
50	C₄×C₁₃	#383	1	1	yes	characteristic
51	C₄×C₁₃	#432	1	3	yes	—
52	C₂²×C₈	C₂×Dic₁₃	1	3	yes	—
53	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
54	C₂×C₄²	#1055	1	3	yes	—
55	C₂×C₄²	#1055	1	1	yes	characteristic
56	C₂×C₄²	C₂×Dic₁₃	1	3	yes	—
57	C₂×C₁₆	—	26	12	no	—
58	C₄×C₈	—	2	6	no	—
59	C₄×C₈	—	2	6	no	—
60	C₂×C₁₃	#1839	1	1	yes	characteristic
61	C₂×C₁₃	#2162	1	3	yes	—
62	C₂×C₁₃	#2163	1	3	yes	—
63	C₂²×C₄	C₂×#1055	1	3	yes	—
64	C₂²×C₄	C₂×#1055	1	3	yes	—
65	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
66	C₂×C₈	—	2	3	no	—
67	C₂×C₈	—	2	3	no	—
68	C₂×C₈	#6099	1	6	yes	—
69	C₂×C₈	#6127	1	6	yes	—
70	C₄²	—	2	3	no	—
71	C₄²	—	2	3	no	—
72	C₄²	—	2	6	no	—
73	C₄²	#6090	1	4	yes	complemented
74	C₁₆	—	52	4	no	—
75	C₁₃	#12894	1	1	yes	characteristic, complemented, Sylow
76	C₂³	C₂²×#1055	1	1	yes	characteristic
77	C₂×C₄	—	2	3	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	C₂×#6090	1	6	yes	—
82	C₂×C₄	#88052	1	6	yes	—
83	C₂×C₄	C₂×#6099	1	3	yes	—
84	C₂×C₄	#88180	1	3	yes	—
85	C₈	—	2	6	no	—
86	C₈	#88130	1	4	yes	—
87	C₂²	#11718586	1	3	yes	—
88	C₂²	C₂²×#6090	1	1	yes	characteristic
89	C₂²	C₂×#88052	1	3	yes	—
90	C₄	—	2	6	no	—
91	C₄	—	2	6	no	—
92	C₄	#11718587	1	3	yes	—
93	C₄	#11718598	1	1	yes	characteristic
94	C₂	#13114979	1	1	yes	characteristic
95	C₂	#13116635	1	3	yes	—
96	C₂	#13116639	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂²×C₁₆
Fitting	C₄²×C₈×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₄²×C₈	D₁₃
hypocenter	C₁₃	#12894
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
26. C₄²×C₁₃	C₁₆	semidirect
73. C₄²	#6090	semidirect
75. C₁₃	#12894	semidirect

Maximal subgroups

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

subgroup	index
#13112914	2
C₄²×C₈×C₁₃	2
#12894	13