Subgroups — #15777924

Order 3328.

358 conjugacy classes of subgroups.

The subgroup lattice has 142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718053	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6090	C₂	1	1	yes	maximal, characteristic
3	#13112914	C₂	1	4	yes	maximal
4	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#97	C₄	1	2	yes	—
6	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#376	C₄	1	1	yes	characteristic
10	C₂²×#6090	C₂²	1	2	yes	—
11	C₂²×#6090	C₂²	1	2	yes	—
12	#11718053	C₄	1	4	yes	complemented
13	C₄×#6090	C₄	1	4	yes	complemented
14	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₁₃×#97	—	2	4	no	—
20	C₁₃×#97	C₈	1	4	yes	—
21	C₄×C₈×C₁₃	—	2	4	no	—
22	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
24	C₁₃×#95	C₈	1	4	yes	—
25	C₂×#6090	—	2	4	no	—
26	C₂×#6090	—	2	4	no	—
27	C₂×#6090	C₂×C₄	1	4	yes	—
28	C₂×#6090	C₂×C₄	1	4	yes	—
29	#12592	—	13	1	no	maximal, Sylow
30	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
31	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
32	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₃	—	2	2	no	—
34	C₂×C₈×C₁₃	—	2	2	no	—
35	C₂×C₈×C₁₃	C₄²	1	2	yes	—
36	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
37	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
38	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₃	#41	1	4	yes	—
41	C₄²×C₁₃	—	2	2	no	—
42	C₄²×C₁₃	—	2	2	no	—
43	C₄²×C₁₃	C₄²	1	2	yes	—
44	C₄²×C₁₃	C₂×C₈	1	2	yes	—
45	#6090	—	2	4	no	—
46	#6090	—	2	4	no	—
47	C₂×#346	—	13	1	no	—
48	C₂×C₄×C₁₆	—	13	1	no	—
49	#1726	D₁₃	1	1	yes	characteristic
50	#1374	—	13	4	no	—
51	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₃	—	2	4	no	—
53	C₂×C₄×C₁₃	—	2	4	no	—
54	C₂×C₄×C₁₃	—	2	8	no	—
55	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	—
56	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
57	C₂×C₄×C₁₃	#117	1	2	yes	—
58	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
60	C₈×C₁₃	—	2	4	no	—
61	C₈×C₁₃	#97	1	4	yes	—
62	C₈×C₁₃	#117	1	2	yes	—
63	C₈×C₁₃	#117	1	2	yes	—
64	C₂²×C₁₆	—	13	2	no	—
65	C₂²×C₁₆	—	13	2	no	—
66	C₂×#97	Dic₁₃	1	2	yes	—
67	C₂×#97	Dic₁₃	1	1	yes	characteristic
68	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
69	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
70	#376	Dic₁₃	1	1	yes	characteristic
71	#346	—	13	4	no	—
72	C₄×C₁₆	—	13	4	no	—
73	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
74	C₂²×C₁₃	#431	1	2	yes	—
75	C₂²×C₁₃	#504	1	4	yes	—
76	C₄×C₁₃	—	2	4	no	—
77	C₄×C₁₃	—	4	4	no	—
78	C₄×C₁₃	#376	1	1	yes	characteristic
79	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
80	C₄×C₁₃	#431	1	2	yes	—
81	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
82	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
83	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
84	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
85	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
86	C₂×C₁₆	—	13	4	no	—
87	C₂×C₁₆	—	13	4	no	—
88	C₂×C₁₆	—	26	4	no	—
89	C₂×C₁₆	—	26	4	no	—
90	#97	—	2	4	no	—
91	#97	#1055	1	4	yes	—
92	C₄×C₈	—	2	4	no	—
93	C₄×C₈	C₄×D₁₃	1	2	yes	—
94	C₄×C₈	C₄×D₁₃	1	2	yes	—
95	#95	#1055	1	4	yes	—
96	C₂×C₁₃	#1744	1	1	yes	characteristic
97	C₂×C₁₃	#2108	1	2	yes	—
98	C₂×C₁₃	#2164	1	4	yes	—
99	C₂²×C₄	C₂×#1055	1	4	yes	—
100	C₂²×C₄	C₂×#1055	1	2	yes	—
101	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
102	C₂×C₈	—	2	2	no	—
103	C₂×C₈	—	2	2	no	—
104	C₂×C₈	C₂×#1055	1	4	yes	—
105	C₂×C₈	#6099	1	4	yes	—
106	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
107	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
108	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
109	C₂×C₈	#6127	1	4	yes	—
110	C₄²	—	2	2	no	—
111	C₄²	—	2	2	no	—
112	C₄²	C₂×#1055	1	2	yes	—
113	C₄²	C₄×Dic₁₃	1	2	yes	—
114	C₁₆	—	26	4	no	—
115	C₁₆	—	26	4	no	—
116	C₁₃	#12592	1	1	yes	characteristic, complemented, Sylow
117	C₂³	C₂²×#1055	1	1	yes	characteristic
118	C₂×C₄	—	2	4	no	—
119	C₂×C₄	—	2	8	no	—
120	C₂×C₄	—	2	4	no	—
121	C₂×C₄	C₄×#1055	1	4	yes	—
122	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
123	C₂×C₄	C₂×#6099	1	2	yes	—
124	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
125	C₂×C₄	#88180	1	2	yes	—
126	C₈	—	2	4	no	—
127	C₈	#88043	1	4	yes	—
128	C₈	#88126	1	2	yes	—
129	C₈	#88126	1	2	yes	—
130	C₂²	C₂×C₄×#1055	1	1	yes	characteristic
131	C₂²	#11718586	1	2	yes	—
132	C₂²	#11718801	1	4	yes	—
133	C₄	—	2	4	no	—
134	C₄	—	4	4	no	—
135	C₄	C₂×#88043	1	1	yes	characteristic
136	C₄	#11718586	1	2	yes	—
137	C₄	#11718593	1	1	yes	characteristic
138	C₂	#13114582	1	1	yes	characteristic
139	C₂	#13116433	1	2	yes	—
140	C₂	#13116643	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂×C₄×C₈
Fitting	C₁₃×#1726	C₂
socle, prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1726	D₁₃
hypocenter	C₁₃	#12592
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ #1726

Complements

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

N	H ≅ G/N	type
12. #11718053	C₄	semidirect
13. C₄×#6090	C₄	semidirect
116. C₁₃	#12592	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718053	2
C₂×C₄×#6090	2
#13112914	2
C₁₃×#1726	2
#12592	13