Subgroups — #15780668

Order 3328.

312 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13116602	C₂	1	1	yes	maximal, characteristic, complemented
2	#13116463	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718100	C₂	1	1	yes	maximal, characteristic
4	#13116432	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114637	C₂	1	1	yes	maximal, characteristic
6	#13112923	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1379	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#88155	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
11	C₁₃×#405	C₂²	1	1	yes	characteristic
12	#11718793	C₄	1	1	yes	characteristic
13	#11718762	C₂²	1	1	yes	characteristic
14	C₂×#88052	C₂²	1	1	yes	characteristic
15	C₂×#88052	C₂²	1	1	yes	characteristic
16	#11718667	C₄	1	1	yes	characteristic
17	#11718151	C₄	1	1	yes	characteristic
18	#11718125	C₄	1	1	yes	characteristic
19	#11718100	—	2	2	no	—
20	#11718100	—	2	1	no	—
21	#11718100	—	2	1	no	—
22	#11718094	—	2	1	no	—
23	C₁₆×Dic₁₃	—	2	1	no	—
24	#11718055	—	2	2	no	—
25	C₂×#6127	C₂×C₄	1	1	yes	characteristic
26	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
29	#88180	C₂×C₄	1	1	yes	characteristic
30	C₂×#6099	C₂×C₄	1	1	yes	characteristic
31	C₂×#6099	C₂×C₄	1	1	yes	characteristic
32	#88155	—	2	1	no	—
33	#88155	—	2	1	no	—
34	#88155	—	2	1	no	—
35	#88155	—	2	1	no	—
36	C₂×#6094	—	2	1	no	—
37	C₂×C₈×D₁₃	—	2	1	no	—
38	C₁₃×M₃₂	—	2	1	no	—
39	C₁₃×M₃₂	—	2	1	no	—
40	C₂×C₁₃×C₁₆	—	2	1	no	—
41	C₂×C₁₃×C₁₆	—	2	1	no	—
42	C₂×C₁₃×C₁₆	—	2	1	no	—
43	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
44	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
45	C₁₃×#97	—	2	1	no	—
46	C₄×C₈×C₁₃	—	2	1	no	—
47	#88064	C₈	1	2	yes	—
48	#88063	C₈	1	2	yes	—
49	#88055	—	2	1	no	—
50	C₈×Dic₁₃	—	2	1	no	—
51	#88052	—	2	1	no	—
52	#88052	—	2	1	no	—
53	#88052	—	2	1	no	—
54	#88052	D₄	1	2	yes	—
55	C₂×#6090	—	2	1	no	—
56	C₂×#6090	—	2	1	no	—
57	#88046	—	2	2	no	—
58	#13123	—	13	1	no	maximal, Sylow
59	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₂²⋊D₁₃	—	2	1	no	—
61	#6127	—	2	1	no	—
62	#6127	—	2	1	no	—
63	#6127	—	2	1	no	—
64	#6127	—	2	1	no	—
65	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
66	C₂×C₄×D₁₃	—	2	1	no	—
67	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
68	C₁₃×M₁₆	—	2	1	no	—
69	C₁₃×M₁₆	C₂×C₈	1	2	yes	—
70	C₂×C₈×C₁₃	—	2	1	no	—
71	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
74	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
75	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
76	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
77	C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₁₃×C₂²⋊C₄	—	2	1	no	—
79	C₄²×C₁₃	—	2	1	no	—
80	C₂²⋊Dic₁₃	M₁₆	1	2	yes	—
81	C₄⋊Dic₁₃	—	2	1	no	—
82	C₄×Dic₁₃	—	2	1	no	—
83	#6099	—	2	1	no	—
84	#6099	—	2	1	no	—
85	#6099	—	2	1	no	—
86	#6099	C₂×C₈	1	2	yes	—
87	C₂×#1055	—	2	1	no	—
88	C₂×#1055	—	2	1	no	—
89	#6094	—	4	1	no	—
90	#6094	—	4	1	no	—
91	C₈×D₁₃	—	4	1	no	—
92	C₈×D₁₃	—	4	1	no	—
93	C₁₃×C₁₆	—	2	1	no	—
94	C₁₃×C₁₆	—	2	1	no	—
95	C₁₃×C₁₆	—	4	1	no	—
96	#6090	—	2	2	no	—
97	#6090	—	4	1	no	—
98	#2153	—	13	1	no	—
99	#2117	—	13	1	no	—
100	C₂×#350	—	13	1	no	—
101	#2108	—	13	1	no	—
102	#1757	—	13	1	no	—
103	#1379	D₁₃	1	1	yes	characteristic, complemented
104	#1378	—	13	1	no	—
105	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
106	C₂²×D₁₃	—	2	1	no	—
107	C₂×C₄×C₁₃	—	4	1	no	—
108	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
109	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
110	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
111	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
112	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
113	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
114	C₂²⋊D₁₃	—	4	1	no	—
115	C₂²⋊D₁₃	—	4	1	no	—
116	C₂×Dic₁₃	—	2	1	no	—
117	C₂×Dic₁₃	—	2	2	no	—
118	D₅₂	—	2	1	no	—
119	D₅₂	—	2	1	no	—
120	C₄×D₁₃	—	4	1	no	—
121	C₄×D₁₃	—	4	1	no	—
122	Dic₂₆	—	2	1	no	—
123	Dic₂₆	—	2	1	no	—
124	C₈×C₁₃	—	2	2	no	—
125	C₈×C₁₃	#121	1	1	yes	characteristic
126	C₈×C₁₃	#123	1	1	yes	characteristic
127	C₈×C₁₃	#124	1	1	yes	characteristic
128	C₈×C₁₃	#126	1	1	yes	characteristic
129	#1055	—	2	2	no	—
130	#1055	—	4	1	no	—
131	C₂×#131	—	13	1	no	—
132	C₂×M₃₂	—	13	1	no	—
133	C₂×M₃₂	—	13	1	no	—
134	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
135	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
136	#413	—	13	1	no	—
137	#410	—	13	1	no	—
138	#405	—	13	1	no	—
139	#405	C₂×D₁₃	1	1	yes	characteristic
140	#364	—	26	2	no	—
141	#350	—	26	2	no	—
142	#350	—	26	1	no	—
143	#350	—	26	1	no	—
144	#346	—	26	1	no	—
145	C₄×C₁₆	—	26	1	no	—
146	#344	—	13	1	no	—
147	#344	—	13	1	no	—
148	C₂²×C₁₃	—	4	1	no	—
149	C₂²×C₁₃	#431	1	1	yes	characteristic
150	C₂²×C₁₃	#435	1	1	yes	characteristic
151	C₂²×C₁₃	#436	1	1	yes	characteristic
152	C₂×D₁₃	—	4	1	no	—
153	C₂×D₁₃	—	8	1	no	—
154	C₄×C₁₃	—	8	1	no	—
155	C₄×C₁₃	#388	1	1	yes	characteristic
156	C₄×C₁₃	#433	1	1	yes	characteristic
157	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
158	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
159	Dic₁₃	—	4	2	no	—
160	Dic₁₃	—	4	1	no	—
161	C₂×#41	—	13	1	no	—
162	#131	—	26	1	no	—
163	#131	—	26	1	no	—
164	#131	—	26	1	no	—
165	#131	—	26	1	no	—
166	C₂×M₁₆	—	13	1	no	—
167	C₂×M₁₆	—	13	1	no	—
168	C₂×M₁₆	—	26	1	no	—
169	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
170	C₂²×C₈	—	26	1	no	—
171	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
172	#117	—	13	1	no	—
173	#117	C₄×D₁₃	1	1	yes	characteristic
174	M₃₂	—	2	1	no	—
175	M₃₂	—	2	1	no	—
176	M₃₂	—	13	2	no	—
177	M₃₂	—	26	1	no	—
178	M₃₂	—	26	1	no	—
179	M₃₂	—	26	1	no	—
180	C₂×C₁₆	—	2	1	no	—
181	C₂×C₁₆	—	2	1	no	—
182	C₂×C₁₆	—	2	1	no	—
183	C₂×C₁₆	—	26	1	no	—
184	C₂×C₁₆	—	26	1	no	—
185	C₂×C₁₆	D₅₂	1	1	yes	characteristic
186	C₂×C₁₆	D₅₂	1	1	yes	characteristic
187	#101	—	13	2	no	—
188	#100	—	13	2	no	—
189	#99	—	26	2	no	—
190	#97	—	2	1	no	—
191	#97	—	26	1	no	—
192	C₄×C₈	—	2	1	no	—
193	C₄×C₈	—	26	1	no	—
194	C₂×C₁₃	—	2	1	no	—
195	C₂×C₁₃	—	2	1	no	—
196	C₂×C₁₃	—	2	1	no	—
197	C₂×C₁₃	#1923	1	1	yes	characteristic
198	D₁₃	—	8	1	no	—
199	#41	—	26	1	no	—
200	#41	—	26	1	no	—
201	#41	—	26	1	no	—
202	#41	—	26	1	no	—
203	C₂×Q₈	—	13	1	no	—
204	C₂×D₄	—	13	1	no	—
205	C₂×D₄	—	26	1	no	—
206	C₂²×C₄	—	26	1	no	—
207	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
208	M₁₆	—	2	1	no	—
209	M₁₆	—	13	2	no	—
210	M₁₆	—	26	1	no	—
211	M₁₆	—	26	1	no	—
212	M₁₆	—	26	1	no	—
213	M₁₆	—	52	1	no	—
214	M₁₆	—	52	1	no	—
215	M₁₆	C₈×D₁₃	1	2	yes	—
216	C₂×C₈	—	2	1	no	—
217	C₂×C₈	—	26	1	no	—
218	C₂×C₈	—	26	1	no	—
219	C₂×C₈	—	52	1	no	—
220	C₂×C₈	—	52	1	no	—
221	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
222	C₂×C₈	#6127	1	1	yes	characteristic
223	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
224	C₂×C₈	#6129	1	1	yes	characteristic
225	C₂×C₈	#6129	1	1	yes	characteristic
226	C₂×C₈	#6131	1	1	yes	characteristic
227	C₄⋊C₄	—	2	1	no	—
228	C₄⋊C₄	—	26	1	no	—
229	C₂²⋊C₄	—	2	1	no	—
230	C₂²⋊C₄	—	13	2	no	—
231	C₄²	—	2	1	no	—
232	C₄²	—	26	1	no	—
233	C₁₆	—	2	1	no	—
234	C₁₆	—	2	1	no	—
235	C₁₆	—	4	1	no	—
236	C₁₆	—	26	2	no	—
237	C₁₆	—	52	1	no	—
238	C₁₃	#13123	1	1	yes	characteristic, complemented, Sylow
239	C₂³	—	26	1	no	—
240	C₂³	M₁₆×D₁₃	1	1	yes	characteristic
241	Q₈	—	26	1	no	—
242	Q₈	—	26	1	no	—
243	D₄	—	26	1	no	—
244	D₄	—	26	1	no	—
245	D₄	—	52	1	no	—
246	D₄	—	52	1	no	—
247	C₂×C₄	—	4	1	no	—
248	C₂×C₄	—	26	1	no	—
249	C₂×C₄	—	26	2	no	—
250	C₂×C₄	—	52	1	no	—
251	C₂×C₄	—	52	1	no	—
252	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
253	C₂×C₄	#88135	1	1	yes	characteristic
254	C₂×C₄	#88146	1	1	yes	characteristic
255	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
256	C₂×C₄	#88155	1	1	yes	characteristic
257	C₂×C₄	#88161	1	1	yes	characteristic
258	C₈	—	2	2	no	—
259	C₈	—	26	2	no	—
260	C₈	—	52	1	no	—
261	C₈	#88139	1	1	yes	characteristic
262	C₈	#88140	1	1	yes	characteristic
263	C₈	#88149	1	1	yes	characteristic
264	C₈	#88152	1	1	yes	characteristic
265	C₂²	—	4	1	no	—
266	C₂²	—	52	1	no	—
267	C₂²	—	104	1	no	—
268	C₂²	#11718367	1	1	yes	characteristic
269	C₂²	#11718390	1	1	yes	characteristic
270	C₂²	#11718494	1	1	yes	characteristic
271	C₄	—	8	1	no	—
272	C₄	—	52	2	no	—
273	C₄	—	52	1	no	—
274	C₄	#11718331	1	1	yes	characteristic
275	C₄	C₈×D₅₂	1	1	yes	characteristic
276	C₄	#11718386	1	1	yes	characteristic
277	C₄	#11718501	1	1	yes	characteristic
278	C₂	—	2	1	no	—
279	C₂	—	2	1	no	—
280	C₂	—	2	1	no	—
281	C₂	—	104	1	no	—
282	C₂	#13115443	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#88149
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1379	C₂
socle	C₂×C₁₃	#1923
prime radical	C₂×#6127	C₂×C₄
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1379	D₁₃
hypocenter	C₁₃	#13123
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #1379

Complements

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

N	H ≅ G/N	type
1. #13116602	C₂	semidirect
4. #13116432	C₂	semidirect
6. #13112923	C₂	semidirect
7. C₁₃×#1379	C₂	semidirect
103. #1379	D₁₃	semidirect
238. C₁₃	#13123	semidirect

Maximal subgroups

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

subgroup	index
#13116602	2
#13116463	2
C₂×#11718100	2
#13116432	2
#13114637	2
#13112923	2
C₁₃×#1379	2
#13123	13