Subgroups — Dic₁₃×#349 #15777961

Order 3328.

522 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718145	C₂	1	1	yes	maximal, characteristic
3	M₃₂×Dic₁₃	C₂	1	2	yes	maximal, complemented
4	#13112919	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#349	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₄×Dic₁₃	C₄	1	1	yes	characteristic
8	C₂²×#6099	C₄	1	1	yes	characteristic
9	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
10	M₁₆×Dic₁₃	—	2	2	no	—
11	M₁₆×Dic₁₃	—	2	2	no	—
12	C₂×#88055	C₄	1	1	yes	characteristic
13	C₂×#88055	C₂²	1	1	yes	characteristic
14	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
15	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
16	C₂×#88052	C₂²	1	2	yes	—
17	C₁₃×#349	C₄	1	4	yes	complemented
18	#11718145	C₄	1	4	yes	complemented
19	#11718094	—	2	2	no	—
20	C₁₆×Dic₁₃	—	2	2	no	—
21	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×Dic₁₃	C₈	1	2	yes	—
23	C₂×C₁₃×M₁₆	—	2	2	no	—
24	C₂×C₁₃×M₁₆	—	2	2	no	—
25	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
26	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₄×Dic₁₃	—	2	1	no	—
30	C₂×C₄×Dic₁₃	—	2	1	no	—
31	C₂×C₄×Dic₁₃	—	2	2	no	—
32	C₂×C₄×Dic₁₃	C₈	1	2	yes	—
33	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×#6099	—	2	2	no	—
36	C₂×#6099	—	2	2	no	—
37	C₂×#6099	C₈	1	4	yes	—
38	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
39	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
40	C₁₃×M₃₂	—	2	2	no	—
41	C₁₃×M₃₂	C₂×C₄	1	4	yes	complemented
42	C₂×C₁₃×C₁₆	—	2	2	no	—
43	#88055	—	2	2	no	—
44	#88055	—	2	2	no	—
45	C₈×Dic₁₃	—	2	1	no	—
46	C₈×Dic₁₃	—	2	1	no	—
47	C₈×Dic₁₃	D₄	1	2	yes	—
48	C₈×Dic₁₃	D₄	1	2	yes	—
49	#88052	—	2	2	no	—
50	#88052	C₂×C₄	1	4	yes	complemented
51	C₂×#6090	—	2	2	no	—
52	C₄×#349	—	13	1	no	maximal, Sylow
53	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	—	2	1	no	—
55	C₂²×C₄×C₁₃	—	2	1	no	—
56	C₂²×C₄×C₁₃	—	2	1	no	—
57	C₂²×C₄×C₁₃	—	2	1	no	—
58	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
59	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
61	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×Dic₁₃	—	2	2	no	—
63	C₂²×Dic₁₃	—	2	2	no	—
64	C₂²×Dic₁₃	—	4	4	no	—
65	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
66	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
67	C₁₃×M₁₆	—	2	4	no	—
68	C₁₃×M₁₆	—	2	4	no	—
69	C₂×C₈×C₁₃	—	2	1	no	—
70	C₂×C₈×C₁₃	—	2	1	no	—
71	C₂×C₈×C₁₃	C₄²	1	2	yes	—
72	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₁₃	#41	1	2	yes	—
76	C₄×Dic₁₃	—	2	1	no	—
77	C₄×Dic₁₃	—	2	1	no	—
78	C₄×Dic₁₃	—	2	2	no	—
79	C₄×Dic₁₃	—	2	2	no	—
80	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₄×Dic₁₃	M₁₆	1	2	yes	—
83	#6099	—	2	8	no	—
84	C₂×#1055	—	2	1	no	—
85	C₂×#1055	—	2	1	no	—
86	C₂×#1055	C₂²⋊C₄	1	2	yes	—
87	C₂×#1055	C₂×C₈	1	2	yes	—
88	C₂×#1055	C₂×C₈	1	2	yes	—
89	C₂×#1055	M₁₆	1	2	yes	—
90	C₁₃×C₁₆	—	2	4	no	—
91	#6090	—	2	4	no	—
92	C₂×C₄×M₁₆	—	13	1	no	—
93	C₂×#349	—	13	1	no	—
94	C₂×#349	D₁₃	1	1	yes	characteristic
95	C₄×M₃₂	—	13	2	no	—
96	#1377	—	13	2	no	—
97	C₂³×C₁₃	—	2	1	no	—
98	C₂³×C₁₃	—	2	1	no	—
99	C₂³×C₁₃	—	4	2	no	—
100	C₂³×C₁₃	C₄×C₈	1	2	yes	—
101	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
102	C₂×C₄×C₁₃	—	2	1	no	—
103	C₂×C₄×C₁₃	—	2	1	no	—
104	C₂×C₄×C₁₃	—	2	2	no	—
105	C₂×C₄×C₁₃	—	2	2	no	—
106	C₂×C₄×C₁₃	—	2	2	no	—
107	C₂×C₄×C₁₃	—	2	2	no	—
108	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
109	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
110	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
112	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
113	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
114	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
115	C₂×Dic₁₃	—	2	4	no	—
116	C₂×Dic₁₃	—	2	2	no	—
117	C₂×Dic₁₃	—	4	4	no	—
118	C₂×Dic₁₃	—	4	4	no	—
119	C₂×Dic₁₃	—	4	2	no	—
120	C₂×Dic₁₃	C₂²⋊C₈	1	2	yes	—
121	C₂×Dic₁₃	C₂²⋊C₈	1	2	yes	—
122	C₈×C₁₃	—	2	2	no	—
123	C₈×C₁₃	C₄×D₄	1	2	yes	—
124	C₈×C₁₃	C₄×D₄	1	2	yes	—
125	#1055	—	2	2	no	—
126	#1055	C₂²⋊C₈	1	4	yes	—
127	C₂²×M₁₆	—	13	1	no	—
128	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
129	C₂²×C₄²	—	13	1	no	—
130	C₂×M₃₂	—	13	2	no	—
131	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
132	C₄×M₁₆	—	26	2	no	—
133	C₄×M₁₆	—	26	2	no	—
134	C₂×#97	—	13	1	no	—
135	C₂×#97	—	13	1	no	—
136	C₂×C₄×C₈	—	13	1	no	—
137	C₂×C₄×C₈	—	13	1	no	—
138	#349	—	13	4	no	—
139	#349	Dic₁₃	1	4	yes	direct product factor
140	#346	—	26	2	no	—
141	C₄×C₁₆	—	26	2	no	—
142	C₂²×C₁₃	—	2	2	no	—
143	C₂²×C₁₃	—	2	2	no	—
144	C₂²×C₁₃	—	4	2	no	—
145	C₂²×C₁₃	—	4	2	no	—
146	C₂²×C₁₃	—	4	2	no	—
147	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
148	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
149	C₂²×C₁₃	#431	1	1	yes	characteristic
150	C₄×C₁₃	—	2	2	no	—
151	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
152	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
153	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
154	C₄×C₁₃	#431	1	1	yes	characteristic
155	Dic₁₃	—	2	2	no	—
156	Dic₁₃	—	4	2	no	—
157	Dic₁₃	#349	1	4	yes	direct product factor
158	C₂³×C₄	—	13	2	no	—
159	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
160	C₂×M₁₆	—	2	2	no	—
161	C₂×M₁₆	—	2	2	no	—
162	C₂×M₁₆	—	13	4	no	—
163	C₂×M₁₆	—	26	2	no	—
164	C₂×M₁₆	—	26	2	no	—
165	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
166	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
167	C₂²×C₈	—	13	1	no	—
168	C₂²×C₈	—	13	1	no	—
169	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
170	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
171	C₂×C₄²	—	13	1	no	—
172	C₂×C₄²	—	13	2	no	—
173	C₂×C₄²	—	13	1	no	—
174	C₂×C₄²	—	26	1	no	—
175	C₂×C₄²	—	26	1	no	—
176	C₂×C₄²	—	26	2	no	—
177	M₃₂	—	2	2	no	—
178	M₃₂	—	13	4	no	—
179	M₃₂	—	26	2	no	—
180	M₃₂	C₂×Dic₁₃	1	4	yes	complemented
181	C₂×C₁₆	—	2	2	no	—
182	C₂×C₁₆	—	26	2	no	—
183	#97	—	26	2	no	—
184	#97	—	26	2	no	—
185	C₄×C₈	—	13	2	no	—
186	C₄×C₈	—	13	2	no	—
187	C₄×C₈	—	26	1	no	—
188	C₄×C₈	—	26	1	no	—
189	C₂×C₁₃	—	2	1	no	—
190	C₂×C₁₃	—	2	1	no	—
191	C₂×C₁₃	—	4	2	no	—
192	C₂×C₁₃	C₄×C₂²⋊C₈	1	1	yes	characteristic
193	C₂×C₁₃	C₂×#349	1	2	yes	—
194	C₂⁴	C₈×D₁₃	1	1	yes	characteristic
195	C₂²×C₄	—	2	1	no	—
196	C₂²×C₄	—	2	1	no	—
197	C₂²×C₄	—	2	1	no	—
198	C₂²×C₄	—	2	1	no	—
199	C₂²×C₄	—	13	2	no	—
200	C₂²×C₄	—	13	2	no	—
201	C₂²×C₄	—	26	2	no	—
202	C₂²×C₄	—	26	2	no	—
203	C₂²×C₄	—	52	4	no	—
204	C₂²×C₄	C₈×D₁₃	1	2	yes	—
205	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
206	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
207	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
208	M₁₆	—	2	4	no	—
209	M₁₆	—	2	4	no	—
210	M₁₆	—	26	8	no	—
211	C₂×C₈	—	2	1	no	—
212	C₂×C₈	—	2	1	no	—
213	C₂×C₈	—	13	2	no	—
214	C₂×C₈	—	13	2	no	—
215	C₂×C₈	—	13	2	no	—
216	C₂×C₈	—	13	2	no	—
217	C₂×C₈	—	26	1	no	—
218	C₂×C₈	—	26	1	no	—
219	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
220	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
221	C₂×C₈	D₄×D₁₃	1	2	yes	—
222	C₂×C₈	#6129	1	2	yes	—
223	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
224	C₄²	—	13	1	no	—
225	C₄²	—	13	1	no	—
226	C₄²	—	13	2	no	—
227	C₄²	—	26	2	no	—
228	C₄²	—	26	2	no	—
229	C₄²	—	26	1	no	—
230	C₄²	—	26	1	no	—
231	C₁₆	—	2	4	no	—
232	C₁₆	—	26	4	no	—
233	C₁₃	C₄×#349	1	1	yes	characteristic, complemented, Sylow
234	C₂³	—	2	1	no	—
235	C₂³	—	2	1	no	—
236	C₂³	—	4	2	no	—
237	C₂³	C₈×Dic₁₃	1	2	yes	—
238	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	13	2	no	—
246	C₂×C₄	—	13	2	no	—
247	C₂×C₄	—	26	4	no	—
248	C₂×C₄	—	26	2	no	—
249	C₂×C₄	—	52	4	no	—
250	C₂×C₄	—	52	4	no	—
251	C₂×C₄	—	52	2	no	—
252	C₂×C₄	C₈×Dic₁₃	1	2	yes	—
253	C₂×C₄	#88131	1	1	yes	characteristic
254	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
255	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
256	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
257	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
258	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
259	C₈	—	2	2	no	—
260	C₈	—	13	4	no	—
261	C₈	—	26	2	no	—
262	C₈	#88135	1	2	yes	—
263	C₈	D₄×Dic₁₃	1	2	yes	—
264	C₂²	—	2	2	no	—
265	C₂²	—	2	2	no	—
266	C₂²	—	4	2	no	—
267	C₂²	—	4	2	no	—
268	C₂²	—	4	2	no	—
269	C₂²	#11718379	1	1	yes	characteristic
270	C₂²	D₁₃×C₂²⋊C₈	1	1	yes	characteristic
271	C₂²	C₂×C₈×Dic₁₃	1	1	yes	characteristic
272	C₄	—	2	2	no	—
273	C₄	—	13	4	no	—
274	C₄	—	26	2	no	—
275	C₄	—	52	2	no	—
276	C₄	#11718379	1	1	yes	characteristic
277	C₄	D₁₃×C₂²⋊C₈	1	1	yes	characteristic
278	C₄	C₂²⋊C₄×Dic₁₃	1	1	yes	characteristic
279	C₄	M₁₆×Dic₁₃	1	1	yes	characteristic
280	C₂	—	2	1	no	—
281	C₂	—	2	1	no	—
282	C₂	—	4	2	no	—
283	C₂	C₂²⋊C₈×Dic₁₃	1	1	yes	characteristic
284	C₂	D₁₃×#349	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₃
commutator	C₂²×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#349	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₂⁴×C₁₃	C₂×C₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×#349	D₁₃
hypocenter	C₁₃	C₄×#349
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#349

Complements

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

N	H ≅ G/N	type
3. M₃₂×Dic₁₃	C₂	semidirect
4. #13112919	C₂	semidirect
17. C₁₃×#349	C₄	semidirect
18. #11718145	C₄	semidirect
41. C₁₃×M₃₂	C₂×C₄	semidirect
50. #88052	C₂×C₄	semidirect
139. #349	Dic₁₃	direct (N × H)
157. Dic₁₃	#349	direct (N × H)
180. M₃₂	C₂×Dic₁₃	semidirect
233. C₁₃	C₄×#349	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×Dic₁₃	2
C₂×#11718145	2
M₃₂×Dic₁₃	2
#13112919	2
C₂×C₁₃×#349	2
C₄×#349	13

Subgroups — Dic13×#349 #15777961

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₃×#349 #15777961