Subgroups — #15753452

Order 3328.

482 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718350	C₂	1	1	yes	maximal, characteristic
2	#13113148	C₂	1	2	yes	maximal
3	#13113128	C₂	1	1	yes	maximal, characteristic, complemented
4	#13112680	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1452	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#6094	C₄	1	1	yes	characteristic
7	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
8	C₂×#88126	C₂²	1	1	yes	characteristic
9	C₁₃×#431	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×#88055	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
13	#11718586	C₂²	1	2	yes	—
14	C₂×#88043	C₂²	1	1	yes	characteristic
15	#11718350	—	2	2	no	—
16	#11718350	—	2	2	no	—
17	C₁₃×#322	—	2	2	no	—
18	#11718061	C₄	1	4	yes	—
19	#11718060	C₄	1	4	yes	—
20	#11718046	—	2	2	no	—
21	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
25	C₂×#6103	C₂×C₄	1	2	yes	—
26	C₂×#6101	C₂×C₄	1	2	yes	—
27	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
29	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
30	C₂×#6094	—	2	2	no	—
31	C₂×#6094	—	2	2	no	—
32	C₂×#6094	—	2	2	no	—
33	C₂×C₈×D₁₃	—	2	2	no	—
34	C₂×C₈×D₁₃	—	2	2	no	—
35	C₂×C₈×D₁₃	—	2	2	no	—
36	#88126	—	2	1	no	—
37	#88126	—	2	1	no	—
38	#88126	—	2	2	no	—
39	C₁₃×C₄⋊C₈	—	2	2	no	—
40	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
41	C₄×C₈×C₁₃	—	2	2	no	—
42	C₄×C₈×C₁₃	D₄	1	2	yes	—
43	C₄×C₈×C₁₃	D₄	1	2	yes	—
44	C₂²⋊#1055	C₂×C₄	1	4	yes	—
45	#88055	—	2	2	no	—
46	C₈×Dic₁₃	—	2	2	no	—
47	C₄⋊#1055	—	2	2	no	—
48	#88043	—	2	1	no	—
49	#88043	—	2	1	no	—
50	C₄×#1055	—	2	2	no	—
51	#8157	—	13	1	no	maximal, Sylow
52	C₂³×D₁₃	C₄²	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
54	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
55	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
56	C₂²×Dic₁₃	C₄²	1	2	yes	—
57	C₂×C₄×D₁₃	—	2	1	no	—
58	C₂×C₄×D₁₃	—	2	1	no	—
59	C₂×C₄×D₁₃	—	2	1	no	—
60	C₂×C₄×D₁₃	—	2	1	no	—
61	C₂×C₄×D₁₃	M₁₆	1	2	yes	—
62	C₂×C₄×D₁₃	M₁₆	1	2	yes	—
63	C₂×C₈×C₁₃	—	2	1	no	—
64	C₂×C₈×C₁₃	—	2	1	no	—
65	C₂×C₈×C₁₃	—	2	1	no	—
66	C₂×C₈×C₁₃	—	2	1	no	—
67	C₂×C₈×C₁₃	—	2	4	no	—
68	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
69	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
70	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₃	#41	1	2	yes	—
73	#6103	—	2	2	no	—
74	#6103	—	2	2	no	—
75	#6101	—	2	2	no	—
76	#6101	—	2	2	no	—
77	C₄×Dic₁₃	—	2	1	no	—
78	C₄×Dic₁₃	—	2	1	no	—
79	C₂×#1055	—	2	1	no	—
80	C₂×#1055	—	2	1	no	—
81	C₂×#1055	—	2	1	no	—
82	C₂×#1055	—	2	1	no	—
83	C₂×#1055	—	2	4	no	—
84	C₂×#1055	M₁₆	1	2	yes	—
85	C₂×#1055	M₁₆	1	2	yes	—
86	#6094	—	2	8	no	—
87	C₈×D₁₃	—	2	8	no	—
88	C₂×#405	—	13	1	no	—
89	#1458	—	13	2	no	—
90	#1452	—	13	1	no	—
91	#1452	D₁₃	1	1	yes	characteristic, complemented
92	#1281	—	13	2	no	—
93	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
94	C₂²×D₁₃	—	2	1	no	—
95	C₂²×D₁₃	—	2	1	no	—
96	C₂²×D₁₃	—	4	2	no	—
97	C₂²×D₁₃	#97	1	2	yes	—
98	C₂×C₄×C₁₃	—	4	2	no	—
99	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
102	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
103	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
105	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
106	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
107	C₂×Dic₁₃	—	2	1	no	—
108	C₂×Dic₁₃	—	2	1	no	—
109	C₂×Dic₁₃	—	2	2	no	—
110	C₂×Dic₁₃	—	4	2	no	—
111	C₂×Dic₁₃	#97	1	2	yes	—
112	C₄×D₁₃	—	2	2	no	—
113	C₄×D₁₃	—	2	2	no	—
114	C₄×D₁₃	—	2	2	no	—
115	C₄×D₁₃	—	2	2	no	—
116	C₈×C₁₃	—	2	2	no	—
117	C₈×C₁₃	—	2	2	no	—
118	C₈×C₁₃	—	4	4	no	—
119	#1055	—	2	2	no	—
120	#1055	—	2	2	no	—
121	#1055	—	4	4	no	—
122	C₂²×M₁₆	—	13	1	no	—
123	C₂³×C₈	—	13	1	no	—
124	C₂×#117	—	13	1	no	—
125	#431	—	13	2	no	—
126	#431	C₂×D₁₃	1	2	yes	—
127	#405	—	26	2	no	—
128	#405	—	26	2	no	—
129	C₂×#97	—	13	1	no	—
130	C₂×#97	—	13	1	no	—
131	C₂×C₄×C₈	—	13	1	no	—
132	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
133	#324	—	13	4	no	—
134	#323	—	13	4	no	—
135	#322	—	2	2	no	—
136	#322	—	26	2	no	—
137	C₂²×C₁₃	—	2	2	no	—
138	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
140	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
141	C₂×D₁₃	—	2	2	no	—
142	C₂×D₁₃	—	4	2	no	—
143	C₂×D₁₃	—	4	2	no	—
144	C₂×D₁₃	—	4	2	no	—
145	C₄×C₁₃	—	2	2	no	—
146	C₄×C₁₃	—	2	2	no	—
147	C₄×C₁₃	#407	1	1	yes	characteristic
148	C₄×C₁₃	#407	1	1	yes	characteristic
149	C₄×C₁₃	#432	1	1	yes	characteristic
150	C₄×C₁₃	#432	1	1	yes	characteristic
151	Dic₁₃	—	2	2	no	—
152	Dic₁₃	—	4	2	no	—
153	C₂³×C₄	—	13	1	no	—
154	C₂×M₁₆	—	26	2	no	—
155	C₂×M₁₆	—	26	2	no	—
156	C₂×M₁₆	—	26	2	no	—
157	C₂²×C₈	—	13	1	no	—
158	C₂²×C₈	—	13	1	no	—
159	C₂²×C₈	—	26	2	no	—
160	C₂²×C₈	—	26	2	no	—
161	C₂²×C₈	—	26	2	no	—
162	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
163	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
164	#117	—	26	1	no	—
165	#117	—	26	2	no	—
166	#117	—	26	1	no	—
167	C₂×C₄⋊C₄	—	13	2	no	—
168	C₂×C₂²⋊C₄	—	13	2	no	—
169	C₂×C₄²	—	13	1	no	—
170	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
171	C₄⋊C₈	—	2	2	no	—
172	C₄⋊C₈	—	26	2	no	—
173	C₂²⋊C₈	—	13	4	no	—
174	C₂²⋊C₈	C₄×D₁₃	1	4	yes	—
175	#97	—	26	2	no	—
176	#97	—	26	1	no	—
177	#97	—	26	1	no	—
178	C₄×C₈	—	2	2	no	—
179	C₄×C₈	—	26	2	no	—
180	C₄×C₈	—	26	2	no	—
181	C₄×C₈	D₅₂	1	2	yes	—
182	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
183	C₂×C₁₃	—	2	1	no	—
184	C₂×C₁₃	—	2	1	no	—
185	C₂×C₁₃	#1749	1	1	yes	characteristic
186	C₂×C₁₃	#1757	1	2	yes	—
187	D₁₃	—	4	2	no	—
188	C₂⁴	—	13	1	no	—
189	C₂²×C₄	—	13	1	no	—
190	C₂²×C₄	—	13	2	no	—
191	C₂²×C₄	—	13	2	no	—
192	C₂²×C₄	—	13	2	no	—
193	C₂²×C₄	—	26	1	no	—
194	C₂²×C₄	—	26	1	no	—
195	C₂²×C₄	—	26	1	no	—
196	C₂²×C₄	—	26	1	no	—
197	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
198	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
199	M₁₆	—	26	8	no	—
200	C₂×C₈	—	2	1	no	—
201	C₂×C₈	—	2	1	no	—
202	C₂×C₈	—	2	1	no	—
203	C₂×C₈	—	2	1	no	—
204	C₂×C₈	—	2	4	no	—
205	C₂×C₈	—	13	2	no	—
206	C₂×C₈	—	13	2	no	—
207	C₂×C₈	—	26	8	no	—
208	C₂×C₈	—	26	1	no	—
209	C₂×C₈	—	26	1	no	—
210	C₂×C₈	—	26	1	no	—
211	C₂×C₈	—	26	1	no	—
212	C₂×C₈	—	26	4	no	—
213	C₂×C₈	#6103	1	2	yes	—
214	C₂×C₈	#6103	1	2	yes	—
215	C₄⋊C₄	—	26	2	no	—
216	C₄⋊C₄	—	26	2	no	—
217	C₂²⋊C₄	—	26	2	no	—
218	C₂²⋊C₄	—	26	2	no	—
219	C₄²	—	26	1	no	—
220	C₄²	—	26	1	no	—
221	C₄²	C₂×D₅₂	1	1	yes	characteristic
222	C₄²	#6127	1	2	yes	—
223	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
224	C₁₃	#8157	1	1	yes	characteristic, complemented, Sylow
225	C₂³	—	13	2	no	—
226	C₂³	—	26	1	no	—
227	C₂³	—	26	1	no	—
228	C₂³	—	52	2	no	—
229	C₂³	C₄²×D₁₃	1	1	yes	characteristic
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	13	2	no	—
232	C₂×C₄	—	26	1	no	—
233	C₂×C₄	—	26	1	no	—
234	C₂×C₄	—	26	2	no	—
235	C₂×C₄	—	26	2	no	—
236	C₂×C₄	—	26	2	no	—
237	C₂×C₄	—	26	2	no	—
238	C₂×C₄	—	26	2	no	—
239	C₂×C₄	—	52	2	no	—
240	C₂×C₄	#88126	1	1	yes	characteristic
241	C₂×C₄	C₄×D₅₂	1	2	yes	—
242	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
243	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
244	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
245	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
246	C₂×C₄	C₂×#6103	1	1	yes	characteristic
247	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
248	C₈	—	2	2	no	—
249	C₈	—	2	2	no	—
250	C₈	—	4	4	no	—
251	C₈	—	26	2	no	—
252	C₈	—	26	2	no	—
253	C₈	—	52	4	no	—
254	C₂²	—	2	2	no	—
255	C₂²	—	26	2	no	—
256	C₂²	—	52	2	no	—
257	C₂²	—	52	2	no	—
258	C₂²	—	52	2	no	—
259	C₂²	D₁₃×#97	1	1	yes	characteristic
260	C₂²	#11718368	1	1	yes	characteristic
261	C₂²	C₄×#6103	1	1	yes	characteristic
262	C₄	—	2	2	no	—
263	C₄	—	2	2	no	—
264	C₄	—	26	2	no	—
265	C₄	—	52	2	no	—
266	C₄	#11718366	1	1	yes	characteristic
267	C₄	#11718366	1	1	yes	characteristic
268	C₄	#11718787	1	1	yes	characteristic
269	C₄	#11718787	1	1	yes	characteristic
270	C₂	—	2	1	no	—
271	C₂	—	2	1	no	—
272	C₂	—	52	2	no	—
273	C₂	#13114599	1	1	yes	characteristic
274	C₂	#13114637	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#6103
commutator	C₂³×C₁₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1452	C₂
socle	C₂²×C₁₃	C₄×C₂²⋊C₄
prime radical	C₂³×D₁₃	C₄²
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1452	D₁₃
hypocenter	C₁₃	#8157
LCS	G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1452

Complements

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

N	H ≅ G/N	type
3. #13113128	C₂	semidirect
4. #13112680	C₂	semidirect
5. C₁₃×#1452	C₂	semidirect
91. #1452	D₁₃	semidirect
224. C₁₃	#8157	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718350	2
#13113148	2
#13113128	2
#13112680	2
C₁₃×#1452	2
#8157	13