Subgroups — Dic₁₃×#344 #15768126

Order 3328.

906 conjugacy classes of subgroups.

The subgroup lattice has 520 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×M₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#117×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718151	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718148	C₂	1	1	yes	maximal, characteristic
6	C₂×#11718125	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#344	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
9	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
11	C₂×#88180	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂²×#6099	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	M₁₆×Dic₁₃	—	2	1	no	—
16	M₁₆×Dic₁₃	—	2	1	no	—
17	M₁₆×Dic₁₃	—	2	1	no	—
18	M₁₆×Dic₁₃	—	2	1	no	—
19	M₁₆×Dic₁₃	—	2	2	no	—
20	M₁₆×Dic₁₃	C₄	1	4	yes	complemented
21	C₂×#88055	—	2	1	no	—
22	C₂×#88055	C₄	1	2	yes	complemented
23	C₂×C₈×Dic₁₃	—	2	1	no	—
24	C₂×C₈×Dic₁₃	C₄	1	2	yes	complemented
25	C₄⋊C₄×Dic₁₃	—	2	2	no	—
26	C₂²⋊C₄×Dic₁₃	C₄	1	4	yes	—
27	#11718593	—	2	1	no	—
28	C₄²×Dic₁₃	—	2	1	no	—
29	C₁₃×#344	C₄	1	4	yes	complemented
30	#11718151	C₄	1	4	yes	complemented
31	#11718148	C₄	1	4	yes	complemented
32	#11718125	C₄	1	4	yes	complemented
33	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
34	C₂³×Dic₁₃	C₂×C₄	1	2	yes	—
35	C₂×C₁₃×M₁₆	—	2	1	no	—
36	C₂×C₁₃×M₁₆	—	2	1	no	—
37	C₂×C₁₃×M₁₆	—	2	1	no	—
38	C₂×C₁₃×M₁₆	—	2	1	no	—
39	C₂×C₁₃×M₁₆	—	2	1	no	—
40	C₂×C₁₃×M₁₆	—	2	1	no	—
41	C₂×C₁₃×M₁₆	—	2	1	no	—
42	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
44	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
45	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
46	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
47	C₂²×C₈×C₁₃	—	2	1	no	—
48	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
49	C₁₃×#117	—	2	1	no	—
50	C₁₃×#117	—	2	1	no	—
51	C₁₃×#117	C₂×C₄	1	2	yes	—
52	C₁₃×#117	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₃	—	2	1	no	—
56	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	2	yes	—
57	#88180	—	2	1	no	—
58	#88180	—	2	1	no	—
59	#88180	C₂×C₄	1	2	yes	—
60	#88180	C₂×C₄	1	2	yes	—
61	C₂×C₄⋊Dic₁₃	—	2	1	no	—
62	C₂×C₄×Dic₁₃	—	2	1	no	—
63	C₂×C₄×Dic₁₃	—	2	4	no	—
64	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
67	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
68	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
69	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
70	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
71	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
72	C₂×C₄×Dic₁₃	Q₈	1	2	yes	—
73	C₂×#6099	—	2	1	no	—
74	C₂×#6099	—	2	1	no	—
75	C₂×#6099	—	2	1	no	—
76	C₂×#6099	—	2	1	no	—
77	C₂×#6099	—	2	1	no	—
78	C₂×#6099	—	2	1	no	—
79	C₂×#6099	—	2	1	no	—
80	C₂×#6099	C₂×C₄	1	2	yes	—
81	C₂×#6099	C₂×C₄	1	2	yes	—
82	C₂×#6099	C₂×C₄	1	2	yes	—
83	C₂×#6099	C₂×C₄	1	2	yes	—
84	C₂×#6099	C₂×C₄	1	2	yes	—
85	C₂²×#1055	—	2	1	no	—
86	C₂²×#1055	C₂×C₄	1	2	yes	—
87	#88071	—	2	4	no	—
88	#88055	—	2	4	no	—
89	#88055	—	2	2	no	—
90	#88055	—	2	2	no	—
91	C₈×Dic₁₃	—	2	4	no	—
92	C₈×Dic₁₃	—	2	2	no	—
93	C₈×Dic₁₃	—	2	2	no	—
94	C₄×#344	—	13	1	no	maximal, Sylow
95	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
111	C₂²×Dic₁₃	—	2	2	no	—
112	C₂²×Dic₁₃	—	4	4	no	—
113	C₂²×Dic₁₃	C₄²	1	2	yes	—
114	C₂²×Dic₁₃	C₄²	1	2	yes	—
115	C₂²×Dic₁₃	C₂²⋊C₄	1	2	yes	—
116	C₂²×Dic₁₃	C₂²⋊C₄	1	2	yes	—
117	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
118	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
119	C₁₃×M₁₆	—	2	2	no	—
120	C₁₃×M₁₆	—	2	2	no	—
121	C₁₃×M₁₆	—	2	2	no	—
122	C₁₃×M₁₆	—	2	2	no	—
123	C₁₃×M₁₆	—	2	2	no	—
124	C₁₃×M₁₆	—	2	2	no	—
125	C₁₃×M₁₆	—	2	2	no	—
126	C₁₃×M₁₆	C₄²	1	4	yes	complemented
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	C₄²	1	4	yes	complemented
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₂²⋊C₄	—	2	2	no	—
136	C₁₃×C₂²⋊C₄	C₄²	1	4	yes	—
137	C₄²×C₁₃	—	2	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₂²⋊Dic₁₃	—	2	2	no	—
140	C₂²⋊Dic₁₃	C₄²	1	4	yes	—
141	C₄⋊Dic₁₃	—	2	2	no	—
142	C₄⋊Dic₁₃	—	2	2	no	—
143	C₄×Dic₁₃	—	2	2	no	—
144	C₄×Dic₁₃	—	2	2	no	—
145	C₄×Dic₁₃	—	4	8	no	—
146	C₄×Dic₁₃	C₂²⋊C₄	1	2	yes	—
147	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
148	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
149	C₄×Dic₁₃	C₂²⋊C₄	1	2	yes	—
150	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
152	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
153	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
154	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
155	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
156	#6099	—	2	2	no	—
157	#6099	—	2	2	no	—
158	#6099	—	2	2	no	—
159	#6099	—	2	2	no	—
160	#6099	—	2	2	no	—
161	#6099	—	2	2	no	—
162	#6099	—	2	2	no	—
163	#6099	C₄²	1	4	yes	complemented
164	C₂×#1055	—	2	2	no	—
165	C₂×#1055	—	2	2	no	—
166	C₂×#1055	—	2	2	no	—
167	C₂×#1055	—	2	2	no	—
168	C₂×#1055	—	2	2	no	—
169	C₂×#1055	C₄²	1	4	yes	complemented
170	C₂×C₄×M₁₆	—	13	1	no	—
171	C₂×C₄×M₁₆	—	13	1	no	—
172	C₄×#117	—	13	1	no	—
173	C₂×#344	—	13	1	no	—
174	C₂×#344	—	13	1	no	—
175	C₂×#344	—	13	1	no	—
176	C₂×#344	D₁₃	1	1	yes	characteristic
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
179	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
180	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
181	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂³×C₁₃	#117	1	1	yes	characteristic
184	C₂³×C₁₃	#117	1	1	yes	characteristic
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	4	4	no	—
187	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
196	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
197	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
198	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
215	C₂×Dic₁₃	—	2	4	no	—
216	C₂×Dic₁₃	—	2	4	no	—
217	C₂×Dic₁₃	—	2	4	no	—
218	C₂×Dic₁₃	—	2	4	no	—
219	C₂×Dic₁₃	—	4	2	no	—
220	C₂×Dic₁₃	—	4	2	no	—
221	C₂×Dic₁₃	—	4	2	no	—
222	C₂×Dic₁₃	—	4	4	no	—
223	C₂×Dic₁₃	#95	1	2	yes	—
224	C₂×Dic₁₃	#95	1	2	yes	—
225	C₂×Dic₁₃	#95	1	2	yes	—
226	C₂×Dic₁₃	#95	1	2	yes	—
227	C₈×C₁₃	—	2	4	no	—
228	C₈×C₁₃	—	2	4	no	—
229	#1055	—	2	4	no	—
230	#1055	—	2	4	no	—
231	C₂²×M₁₆	—	13	1	no	—
232	C₂²×M₁₆	—	13	1	no	—
233	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
234	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
235	C₂×#117	—	13	1	no	—
236	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
237	C₂²×C₄²	—	13	1	no	—
238	C₄×M₁₆	—	13	4	no	—
239	C₄×M₁₆	—	26	1	no	—
240	C₄×M₁₆	—	26	1	no	—
241	C₄×M₁₆	—	26	1	no	—
242	C₄×M₁₆	—	26	1	no	—
243	C₄×M₁₆	—	26	2	no	—
244	C₂×#97	—	13	2	no	—
245	C₂×#97	—	26	1	no	—
246	C₂×C₄×C₈	—	13	2	no	—
247	C₂×C₄×C₈	—	26	1	no	—
248	C₄×C₄⋊C₄	—	26	2	no	—
249	C₄×C₂²⋊C₄	—	13	4	no	—
250	#376	—	26	1	no	—
251	C₄³	—	26	1	no	—
252	#344	—	13	4	no	—
253	#344	—	13	4	no	—
254	#344	—	13	4	no	—
255	#344	Dic₁₃	1	4	yes	direct product factor
256	C₂²×C₁₃	—	2	2	no	—
257	C₂²×C₁₃	—	2	2	no	—
258	C₂²×C₁₃	—	2	2	no	—
259	C₂²×C₁₃	—	4	1	no	—
260	C₂²×C₁₃	—	4	1	no	—
261	C₂²×C₁₃	—	4	1	no	—
262	C₂²×C₁₃	—	4	1	no	—
263	C₂²×C₁₃	C₄³	1	1	yes	characteristic
264	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
265	C₂²×C₁₃	#376	1	1	yes	characteristic
266	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
267	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
269	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
270	C₄×C₁₃	—	4	4	no	—
271	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
272	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
273	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
274	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
275	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
276	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
277	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
278	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
279	Dic₁₃	—	2	2	no	—
280	Dic₁₃	—	2	2	no	—
281	Dic₁₃	—	2	2	no	—
282	Dic₁₃	—	4	4	no	—
283	Dic₁₃	#344	1	4	yes	direct product factor
284	C₂³×C₄	—	13	2	no	—
285	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	2	1	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	—	2	1	no	—
293	C₂×M₁₆	—	13	2	no	—
294	C₂×M₁₆	—	13	2	no	—
295	C₂×M₁₆	—	13	2	no	—
296	C₂×M₁₆	—	13	2	no	—
297	C₂×M₁₆	—	13	2	no	—
298	C₂×M₁₆	—	26	1	no	—
299	C₂×M₁₆	—	26	1	no	—
300	C₂×M₁₆	—	26	1	no	—
301	C₂×M₁₆	—	26	1	no	—
302	C₂×M₁₆	—	26	1	no	—
303	C₂×M₁₆	—	26	1	no	—
304	C₂×M₁₆	—	26	1	no	—
305	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
306	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
307	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
308	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
309	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	—	13	2	no	—
312	C₂²×C₈	—	26	1	no	—
313	C₂²×C₈	C₄×D₁₃	1	2	yes	—
314	#117	—	2	1	no	—
315	#117	—	2	1	no	—
316	#117	—	13	2	no	—
317	#117	—	13	2	no	—
318	#117	—	26	1	no	—
319	#117	—	26	1	no	—
320	#117	C₄×D₁₃	1	2	yes	—
321	#117	C₂×Dic₁₃	1	2	yes	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	26	1	no	—
324	C₂×C₂²⋊C₄	—	13	2	no	—
325	C₂×C₂²⋊C₄	C₄×D₁₃	1	2	yes	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	13	1	no	—
328	C₂×C₄²	—	13	1	no	—
329	C₂×C₄²	—	13	2	no	—
330	C₂×C₄²	—	13	1	no	—
331	C₂×C₄²	—	13	1	no	—
332	C₂×C₄²	—	13	2	no	—
333	C₂×C₄²	—	13	1	no	—
334	C₂×C₄²	—	13	1	no	—
335	C₂×C₄²	—	13	2	no	—
336	C₂×C₄²	—	26	1	no	—
337	C₂×C₄²	—	26	4	no	—
338	#97	—	26	2	no	—
339	#97	—	26	2	no	—
340	#97	—	26	4	no	—
341	C₄×C₈	—	26	2	no	—
342	C₄×C₈	—	26	2	no	—
343	C₄×C₈	—	26	4	no	—
344	#95	—	26	4	no	—
345	C₂×C₁₃	—	2	1	no	—
346	C₂×C₁₃	—	2	1	no	—
347	C₂×C₁₃	—	2	1	no	—
348	C₂×C₁₃	—	2	1	no	—
349	C₂×C₁₃	—	2	1	no	—
350	C₂×C₁₃	—	2	1	no	—
351	C₂×C₁₃	C₄×#95	1	1	yes	characteristic
352	C₂×C₁₃	C₂×#344	1	2	yes	—
353	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	13	2	no	—
356	C₂²×C₄	—	13	2	no	—
357	C₂²×C₄	—	13	2	no	—
358	C₂²×C₄	—	13	2	no	—
359	C₂²×C₄	—	13	2	no	—
360	C₂²×C₄	—	13	2	no	—
361	C₂²×C₄	—	26	2	no	—
362	C₂²×C₄	—	52	4	no	—
363	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
368	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
369	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
370	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
371	C₂²×C₄	#6129	1	1	yes	characteristic
372	C₂²×C₄	#6129	1	1	yes	characteristic
373	C₂²×C₄	#6129	1	1	yes	characteristic
374	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
375	C₂²×C₄	#6131	1	1	yes	characteristic
376	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
377	M₁₆	—	2	2	no	—
378	M₁₆	—	2	2	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	—	2	2	no	—
383	M₁₆	—	2	2	no	—
384	M₁₆	—	13	4	no	—
385	M₁₆	—	26	2	no	—
386	M₁₆	—	26	2	no	—
387	M₁₆	—	26	2	no	—
388	M₁₆	—	26	2	no	—
389	M₁₆	—	26	2	no	—
390	M₁₆	—	26	2	no	—
391	M₁₆	—	26	2	no	—
392	M₁₆	C₄×Dic₁₃	1	4	yes	complemented
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	13	4	no	—
399	C₂×C₈	—	26	2	no	—
400	C₂×C₈	—	26	2	no	—
401	C₂×C₈	—	26	2	no	—
402	C₂×C₈	—	26	2	no	—
403	C₂×C₈	—	26	2	no	—
404	C₂×C₈	C₄×Dic₁₃	1	4	yes	complemented
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	26	2	no	—
408	C₄⋊C₄	—	26	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	13	4	no	—
411	C₂²⋊C₄	—	26	2	no	—
412	C₂²⋊C₄	C₄×Dic₁₃	1	4	yes	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	13	2	no	—
416	C₄²	—	13	2	no	—
417	C₄²	—	13	1	no	—
418	C₄²	—	13	1	no	—
419	C₄²	—	13	1	no	—
420	C₄²	—	13	1	no	—
421	C₄²	—	13	2	no	—
422	C₄²	—	13	2	no	—
423	C₄²	—	13	2	no	—
424	C₄²	—	13	2	no	—
425	C₄²	—	26	2	no	—
426	C₄²	—	26	2	no	—
427	C₄²	—	52	8	no	—
428	C₁₃	C₄×#344	1	1	yes	characteristic, complemented, Sylow
429	C₂³	—	4	2	no	—
430	C₂³	C₄²×D₁₃	1	1	yes	characteristic
431	C₂³	C₄²×D₁₃	1	1	yes	characteristic
432	C₂³	#88131	1	1	yes	characteristic
433	C₂³	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
434	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
435	C₂³	#88146	1	1	yes	characteristic
436	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	13	2	no	—
440	C₂×C₄	—	13	2	no	—
441	C₂×C₄	—	13	2	no	—
442	C₂×C₄	—	13	2	no	—
443	C₂×C₄	—	26	4	no	—
444	C₂×C₄	—	26	4	no	—
445	C₂×C₄	—	26	4	no	—
446	C₂×C₄	—	26	4	no	—
447	C₂×C₄	—	52	2	no	—
448	C₂×C₄	—	52	2	no	—
449	C₂×C₄	—	52	2	no	—
450	C₂×C₄	—	52	4	no	—
451	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
452	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
453	C₂×C₄	#88131	1	1	yes	characteristic
454	C₂×C₄	#88131	1	1	yes	characteristic
455	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
456	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
457	C₂×C₄	#88135	1	1	yes	characteristic
458	C₂×C₄	#88135	1	1	yes	characteristic
459	C₂×C₄	#88135	1	1	yes	characteristic
460	C₂×C₄	#88135	1	1	yes	characteristic
461	C₂×C₄	#88135	1	1	yes	characteristic
462	C₂×C₄	#88135	1	1	yes	characteristic
463	C₂×C₄	#88141	1	1	yes	characteristic
464	C₂×C₄	#88141	1	1	yes	characteristic
465	C₂×C₄	#88141	1	1	yes	characteristic
466	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
467	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
468	C₂×C₄	#88146	1	1	yes	characteristic
469	C₂×C₄	#88146	1	1	yes	characteristic
470	C₂×C₄	#88147	1	1	yes	characteristic
471	C₂×C₄	#88147	1	1	yes	characteristic
472	C₂×C₄	#88147	1	1	yes	characteristic
473	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
474	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
475	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
476	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
477	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
478	C₂×C₄	Q₈×Dic₁₃	1	1	yes	characteristic
479	C₈	—	2	4	no	—
480	C₈	—	2	4	no	—
481	C₈	—	26	4	no	—
482	C₈	—	26	4	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	1	no	—
490	C₂²	#11718309	1	1	yes	characteristic
491	C₂²	#11718310	1	1	yes	characteristic
492	C₂²	D₁₃×#95	1	1	yes	characteristic
493	C₂²	#11718327	1	1	yes	characteristic
494	C₂²	C₄²×Dic₁₃	1	1	yes	characteristic
495	C₂²	C₂²⋊C₄×Dic₁₃	1	1	yes	characteristic
496	C₂²	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
497	C₄	—	4	4	no	—
498	C₄	—	13	4	no	—
499	C₄	—	26	2	no	—
500	C₄	—	26	2	no	—
501	C₄	—	26	2	no	—
502	C₄	—	52	4	no	—
503	C₄	#11718310	1	1	yes	characteristic
504	C₄	#11718310	1	1	yes	characteristic
505	C₄	#11718327	1	1	yes	characteristic
506	C₄	#11718327	1	1	yes	characteristic
507	C₄	C₂²⋊C₄×Dic₁₃	1	1	yes	characteristic
508	C₄	C₂²⋊C₄×Dic₁₃	1	1	yes	characteristic
509	C₄	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
510	C₄	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	2	1	no	—
515	C₂	—	2	1	no	—
516	C₂	—	2	1	no	—
517	C₂	#95×Dic₁₃	1	1	yes	characteristic
518	C₂	D₁₃×#344	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₃
commutator	C₂²×C₁₃	C₄³
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#344	C₂
socle	C₂²×C₁₃	C₂×#95
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#344	D₁₃
hypocenter	C₁₃	C₄×#344
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
20. M₁₆×Dic₁₃	C₄	semidirect
22. C₂×#88055	C₄	semidirect
24. C₂×C₈×Dic₁₃	C₄	semidirect
29. C₁₃×#344	C₄	semidirect
30. #11718151	C₄	semidirect
31. #11718148	C₄	semidirect
32. #11718125	C₄	semidirect
126. C₁₃×M₁₆	C₄²	semidirect
132. C₂×C₈×C₁₃	C₄²	semidirect
163. #6099	C₄²	semidirect
169. C₂×#1055	C₄²	semidirect
255. #344	Dic₁₃	direct (N × H)
283. Dic₁₃	#344	direct (N × H)
392. M₁₆	C₄×Dic₁₃	semidirect
404. C₂×C₈	C₄×Dic₁₃	semidirect
428. C₁₃	C₄×#344	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
#117×Dic₁₃	2
C₂×#11718151	2
C₂×#11718148	2
C₂×#11718125	2
C₂×C₁₃×#344	2
C₄×#344	13

Subgroups — Dic13×#344 #15768126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₃×#344 #15768126