Subgroups — #15779267

Order 3328.

322 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718093	C₂	1	2	yes	maximal
2	#13114522	C₂	1	1	yes	maximal, characteristic
3	#13112914	C₂	1	1	yes	maximal, characteristic
4	#13112913	C₂	1	2	yes	maximal
5	C₁₃×#1374	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88055	C₄	1	1	yes	characteristic
9	C₂×#88055	C₄	1	1	yes	characteristic
10	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂²×#6090	C₂²	1	2	yes	—
13	#11718593	C₄	1	1	yes	characteristic
14	C₂×#88043	C₄	1	1	yes	characteristic
15	#11718093	—	2	4	no	—
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
22	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₃×C₁₆	—	2	2	no	—
24	C₂×C₁₃×C₁₆	—	2	2	no	—
25	C₂×C₁₃×C₁₆	—	2	2	no	—
26	C₄×C₈×C₁₃	—	2	2	no	—
27	#88071	C₈	1	2	yes	—
28	#88071	C₈	1	2	yes	—
29	#88055	—	2	2	no	—
30	#88055	—	2	2	no	—
31	C₈×Dic₁₃	—	2	2	no	—
32	C₈×Dic₁₃	D₄	1	2	yes	—
33	C₈×Dic₁₃	Q₈	1	2	yes	—
34	C₂×#6090	—	2	2	no	—
35	C₂×#6090	—	2	2	no	—
36	C₂×#6090	—	2	2	no	—
37	#88043	—	2	2	no	—
38	#12880	—	13	1	no	maximal, Sylow
39	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
40	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
42	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
43	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
44	C₂×C₈×C₁₃	—	2	1	no	—
45	C₂×C₈×C₁₃	—	2	1	no	—
46	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
47	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
49	C₂×C₈×C₁₃	#41	1	2	yes	—
50	C₂×C₈×C₁₃	#41	1	2	yes	—
51	C₄²×C₁₃	—	2	1	no	—
52	C₄²×C₁₃	—	2	1	no	—
53	C₄×Dic₁₃	—	2	1	no	—
54	C₄×Dic₁₃	—	2	1	no	—
55	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
56	C₄×Dic₁₃	M₁₆	1	2	yes	—
57	C₂×#1055	—	2	1	no	—
58	C₂×#1055	—	2	1	no	—
59	C₂×#1055	—	2	1	no	—
60	C₂×#1055	—	2	1	no	—
61	C₂×#1055	C₄⋊C₄	1	2	yes	—
62	C₂×#1055	M₁₆	1	2	yes	—
63	C₁₃×C₁₆	—	4	2	no	—
64	#6090	—	4	2	no	—
65	C₂×C₄⋊C₁₆	—	13	2	no	—
66	#1726	—	13	1	no	—
67	#1374	—	13	2	no	—
68	#1374	—	13	1	no	—
69	#1374	D₁₃	1	1	yes	characteristic
70	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
71	C₂×C₄×C₁₃	—	2	2	no	—
72	C₂×C₄×C₁₃	—	2	2	no	—
73	C₂×C₄×C₁₃	—	2	2	no	—
74	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
76	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
80	C₂×Dic₁₃	—	2	2	no	—
81	C₂×Dic₁₃	—	2	2	no	—
82	C₂×Dic₁₃	—	2	1	no	—
83	C₂×Dic₁₃	—	2	1	no	—
84	C₂×Dic₁₃	—	2	2	no	—
85	C₂×Dic₁₃	—	2	2	no	—
86	C₂×Dic₁₃	C₄⋊C₈	1	4	yes	—
87	C₈×C₁₃	—	2	2	no	—
88	C₈×C₁₃	#124	1	2	yes	—
89	C₈×C₁₃	#125	1	2	yes	—
90	#1055	—	2	2	no	—
91	#1055	—	2	2	no	—
92	C₂²×C₁₆	—	13	2	no	—
93	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
94	C₂×#97	—	13	1	no	—
95	C₂×#97	—	13	1	no	—
96	C₂×#97	—	13	1	no	—
97	C₂×C₄×C₈	—	13	1	no	—
98	C₂×C₄×C₈	—	13	1	no	—
99	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
100	#376	—	13	1	no	—
101	C₄⋊C₁₆	—	26	4	no	—
102	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
103	C₂²×C₁₃	#431	1	1	yes	characteristic
104	C₂²×C₁₃	#431	1	1	yes	characteristic
105	C₂²×C₁₃	#504	1	2	yes	—
106	C₂²×C₁₃	#504	1	2	yes	—
107	C₄×C₁₃	—	4	2	no	—
108	C₄×C₁₃	#382	1	1	yes	characteristic
109	C₄×C₁₃	#423	1	1	yes	characteristic
110	C₄×C₁₃	#432	1	1	yes	characteristic
111	C₄×C₁₃	#432	1	1	yes	characteristic
112	Dic₁₃	—	2	4	no	—
113	Dic₁₃	—	4	1	no	—
114	Dic₁₃	—	4	1	no	—
115	C₂²×C₈	—	13	1	no	—
116	C₂²×C₈	—	13	1	no	—
117	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
118	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
119	C₂×C₄²	—	13	1	no	—
120	C₂×C₄²	—	13	1	no	—
121	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
122	C₂×C₁₆	—	2	2	no	—
123	C₂×C₁₆	—	2	2	no	—
124	C₂×C₁₆	—	2	2	no	—
125	C₂×C₁₆	—	26	2	no	—
126	C₂×C₁₆	—	26	2	no	—
127	C₂×C₁₆	—	26	2	no	—
128	#97	—	26	2	no	—
129	#97	—	26	2	no	—
130	#97	—	26	2	no	—
131	C₄×C₈	—	2	2	no	—
132	C₄×C₈	—	13	2	no	—
133	C₄×C₈	—	13	2	no	—
134	C₄×C₈	—	26	2	no	—
135	#95	—	13	2	no	—
136	#95	—	13	2	no	—
137	C₂×C₁₃	#1831	1	1	yes	characteristic
138	C₂×C₁₃	#2151	1	2	yes	—
139	C₂×C₁₃	#2164	1	2	yes	—
140	C₂×C₁₃	#2164	1	1	yes	characteristic
141	C₂×C₁₃	#2164	1	1	yes	characteristic
142	C₂²×C₄	—	13	2	no	—
143	C₂²×C₄	—	13	1	no	—
144	C₂²×C₄	—	13	1	no	—
145	C₂²×C₄	C₈×D₁₃	1	2	yes	—
146	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
147	C₂×C₈	—	2	1	no	—
148	C₂×C₈	—	2	1	no	—
149	C₂×C₈	—	13	2	no	—
150	C₂×C₈	—	13	2	no	—
151	C₂×C₈	—	26	1	no	—
152	C₂×C₈	—	26	1	no	—
153	C₂×C₈	—	26	1	no	—
154	C₂×C₈	—	26	1	no	—
155	C₂×C₈	#6094	1	2	yes	—
156	C₂×C₈	#6127	1	2	yes	—
157	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
158	C₂×C₈	#6129	1	2	yes	—
159	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
160	C₄²	—	2	1	no	—
161	C₄²	—	2	1	no	—
162	C₄²	—	13	2	no	—
163	C₄²	—	13	2	no	—
164	C₄²	—	26	1	no	—
165	C₄²	—	26	1	no	—
166	C₁₆	—	4	2	no	—
167	C₁₆	—	52	2	no	—
168	C₁₃	#12880	1	1	yes	characteristic, complemented, Sylow
169	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	13	4	no	—
174	C₂×C₄	—	26	2	no	—
175	C₂×C₄	—	26	2	no	—
176	C₂×C₄	—	26	2	no	—
177	C₂×C₄	—	26	2	no	—
178	C₂×C₄	—	26	1	no	—
179	C₂×C₄	—	26	1	no	—
180	C₂×C₄	#88126	1	1	yes	characteristic
181	C₂×C₄	#88131	1	1	yes	characteristic
182	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
183	C₂×C₄	C₂×#6094	1	1	yes	characteristic
184	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
185	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
186	C₈	—	2	2	no	—
187	C₈	—	26	2	no	—
188	C₈	—	26	2	no	—
189	C₈	#88139	1	2	yes	—
190	C₈	#88143	1	2	yes	—
191	C₂²	#11718346	1	1	yes	characteristic
192	C₂²	#11718379	1	1	yes	characteristic
193	C₂²	D₁₃×C₄⋊C₈	1	1	yes	characteristic
194	C₂²	#11718562	1	2	yes	—
195	C₂²	#11718568	1	2	yes	—
196	C₄	—	4	2	no	—
197	C₄	—	26	4	no	—
198	C₄	—	52	1	no	—
199	C₄	—	52	1	no	—
200	C₄	#11718311	1	1	yes	characteristic
201	C₄	#11718366	1	1	yes	characteristic
202	C₄	#11718380	1	1	yes	characteristic
203	C₄	#11718498	1	1	yes	characteristic
204	C₂	#13114951	1	1	yes	characteristic
205	C₂	#13116593	1	2	yes	—
206	C₂	#13116640	1	2	yes	—
207	C₂	#13116641	1	1	yes	characteristic
208	C₂	#13116644	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂²×C₈
Fitting	C₁₃×#1374	C₂
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1374	D₁₃
hypocenter	C₁₃	#12880
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ #1374

Complements

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

N	H ≅ G/N	type
168. C₁₃	#12880	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718093	2
#13114522	2
#13112914	2
#13112913	2
C₁₃×#1374	2
#12880	13