Subgroups — D₁₃×#1953 #15866483

Order 3328.

858 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#430	C₂	1	2	yes	maximal
2	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic
3	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic
4	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
5	#13115627	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115626	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115625	C₂	1	2	yes	maximal, complemented
8	#13115624	C₂	1	1	yes	maximal, characteristic, complemented
9	#13115623	C₂	1	2	yes	maximal, complemented
10	D₁₃×#344	C₂	1	2	yes	maximal
11	C₁₃×#1953	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
13	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
14	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
16	D₁₃×#117	C₂²	1	1	yes	characteristic
17	C₁₃×#430	C₂²	1	2	yes	—
18	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
20	C₁₃×#405	C₂²	1	1	yes	characteristic
21	#11718786	C₂²	1	2	yes	—
22	#11718785	C₂²	1	2	yes	—
23	#11718785	C₂²	1	2	yes	—
24	C₂×#88062	C₂²	1	2	yes	—
25	C₂×#88062	C₂²	1	2	yes	—
26	#11718783	C₂²	1	1	yes	characteristic
27	C₂×#88059	C₂²	1	1	yes	characteristic
28	C₂×#88059	C₂²	1	1	yes	characteristic
29	#11718762	C₂²	1	1	yes	characteristic
30	#11718658	C₂²	1	1	yes	characteristic
31	#11718554	—	2	4	no	—
32	D₁₃×#108	—	2	4	no	—
33	D₁₃×#108	—	2	1	no	—
34	D₁₃×#108	—	2	1	no	—
35	D₁₃×#108	—	2	1	no	—
36	D₁₃×#108	—	2	1	no	—
37	D₁₃×#108	C₄	1	4	yes	complemented
38	D₁₃×#108	C₄	1	4	yes	complemented
39	#11718369	—	2	1	no	—
40	D₁₃×#97	—	2	1	no	—
41	#11718350	—	2	1	no	—
42	C₄×C₈×D₁₃	—	2	1	no	—
43	C₁₃×#344	C₂²	1	2	yes	—
44	#11718151	C₂²	1	2	yes	—
45	#11718148	C₂²	1	2	yes	—
46	#11718125	C₂²	1	2	yes	—
47	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
49	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
50	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₁₃×#117	C₂³	1	1	yes	characteristic
53	#88180	C₂³	1	1	yes	characteristic
54	C₂×#6099	C₂³	1	2	yes	—
55	C₂×#6099	C₂³	1	2	yes	—
56	C₂×#6099	C₂³	1	1	yes	characteristic
57	C₂²×#1055	C₂³	1	1	yes	characteristic
58	M₁₆×D₁₃	—	2	2	no	—
59	M₁₆×D₁₃	—	2	2	no	—
60	M₁₆×D₁₃	—	2	1	no	—
61	M₁₆×D₁₃	—	2	1	no	—
62	M₁₆×D₁₃	—	2	2	no	—
63	M₁₆×D₁₃	—	2	2	no	—
64	M₁₆×D₁₃	—	2	2	no	—
65	M₁₆×D₁₃	—	2	2	no	—
66	M₁₆×D₁₃	C₂×C₄	1	4	yes	—
67	M₁₆×D₁₃	C₂×C₄	1	4	yes	—
68	M₁₆×D₁₃	D₄	1	2	yes	—
69	M₁₆×D₁₃	D₄	1	2	yes	—
70	C₂×#6094	—	2	2	no	—
71	C₂×#6094	—	2	1	no	—
72	C₂×#6094	—	2	2	no	—
73	C₂×C₈×D₁₃	—	2	2	no	—
74	C₂×C₈×D₁₃	—	2	1	no	—
75	C₂×C₈×D₁₃	—	2	2	no	—
76	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
77	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
78	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
79	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
80	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
81	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
82	C₂×C₈×D₁₃	Q₈	1	2	yes	—
83	C₂×C₈×D₁₃	Q₈	1	2	yes	—
84	#88146	—	2	1	no	—
85	C₄⋊C₄×D₁₃	—	2	1	no	—
86	C₂²⋊C₄×D₁₃	Q₈	1	2	yes	—
87	#88131	Q₈	1	2	yes	—
88	#88126	—	2	1	no	—
89	C₄²×D₁₃	—	2	1	no	—
90	C₁₃×#108	—	2	4	no	—
91	C₁₃×#108	—	2	1	no	—
92	C₁₃×#108	—	2	1	no	—
93	C₁₃×#108	C₂×C₄	1	4	yes	complemented
94	C₁₃×#97	—	2	1	no	—
95	C₄×C₈×C₁₃	—	2	1	no	—
96	#88062	—	2	4	no	—
97	#88062	—	2	4	no	—
98	#88062	—	2	2	no	—
99	#88062	—	2	2	no	—
100	#88062	C₂×C₄	1	8	yes	complemented
101	#88059	—	2	1	no	—
102	#88059	—	2	1	no	—
103	#88059	—	2	4	no	—
104	#88059	C₂×C₄	1	4	yes	complemented
105	#88055	—	2	1	no	—
106	#88055	—	2	1	no	—
107	C₈×Dic₁₃	—	2	1	no	—
108	C₈×Dic₁₃	—	2	1	no	—
109	#88043	—	2	1	no	—
110	C₄×#1055	—	2	1	no	—
111	C₂×#1953	—	13	1	no	maximal, Sylow
112	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
115	C₂×C₄×D₁₃	—	2	2	no	—
116	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
123	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
124	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
125	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
126	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
127	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
128	C₁₃×M₁₆	—	2	2	no	—
129	C₁₃×M₁₆	—	2	1	no	—
130	C₁₃×M₁₆	—	2	2	no	—
131	C₁₃×M₁₆	—	2	2	no	—
132	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
133	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₂²⋊C₄	C₂×Q₈	1	2	yes	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₂²⋊Dic₁₃	C₂×Q₈	1	2	yes	—
145	#6103	—	2	2	no	—
146	C₄⋊Dic₁₃	—	2	1	no	—
147	#6101	—	2	2	no	—
148	C₄×Dic₁₃	—	2	1	no	—
149	C₄×Dic₁₃	—	2	2	no	—
150	#6099	—	2	2	no	—
151	#6099	—	2	1	no	—
152	#6099	—	2	2	no	—
153	#6099	—	2	2	no	—
154	#6099	C₂²×C₄	1	4	yes	—
155	#6099	C₂×D₄	1	2	yes	—
156	C₂×#1055	—	2	1	no	—
157	C₂×#1055	—	2	2	no	—
158	C₂×#1055	—	2	2	no	—
159	C₂×#1055	C₂²×C₄	1	2	yes	—
160	C₂×#1055	C₂×D₄	1	1	yes	characteristic
161	C₂×#1055	C₂×D₄	1	1	yes	characteristic
162	C₂×#1055	C₂×Q₈	1	2	yes	—
163	#6094	—	2	4	no	—
164	#6094	—	2	4	no	—
165	#6094	—	2	2	no	—
166	#6094	—	2	2	no	—
167	#6094	—	4	2	no	—
168	#6094	—	4	2	no	—
169	C₈×D₁₃	—	2	4	no	—
170	C₈×D₁₃	—	2	4	no	—
171	C₈×D₁₃	—	2	2	no	—
172	C₈×D₁₃	—	2	2	no	—
173	C₈×D₁₃	—	4	2	no	—
174	C₈×D₁₃	—	4	2	no	—
175	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
176	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
177	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
178	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
179	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
180	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
181	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
182	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
183	C₂×#430	—	13	2	no	—
184	C₂²×#108	—	13	1	no	—
185	C₂²×#108	—	13	1	no	—
186	C₂×#405	—	13	1	no	—
187	#1953	—	13	2	no	—
188	#1953	—	13	1	no	—
189	#1953	—	13	1	no	—
190	#1953	—	13	1	no	—
191	#1953	—	13	2	no	—
192	#1953	D₁₃	1	1	yes	characteristic, direct product factor
193	C₂×#344	—	13	2	no	—
194	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
195	C₂²×D₁₃	—	4	2	no	—
196	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
197	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
198	C₂²×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂²×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
200	C₂²×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
201	C₂²×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₂×Dic₁₃	—	2	2	no	—
210	C₂×Dic₁₃	C₄×Q₈	1	1	yes	characteristic
211	C₂×Dic₁₃	C₄×Q₈	1	1	yes	characteristic
212	C₂×Dic₁₃	C₂²⋊Q₈	1	1	yes	characteristic
213	C₂×Dic₁₃	C₂²⋊Q₈	1	1	yes	characteristic
214	C₂×Dic₁₃	C₄⋊Q₈	1	1	yes	characteristic
215	C₂×Dic₁₃	C₄⋊Q₈	1	1	yes	characteristic
216	C₄×D₁₃	—	4	4	no	—
217	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
222	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
223	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
224	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
225	C₄×D₁₃	#121	1	1	yes	characteristic
226	C₄×D₁₃	#121	1	1	yes	characteristic
227	C₄×D₁₃	#121	1	1	yes	characteristic
228	C₄×D₁₃	#121	1	1	yes	characteristic
229	C₄×D₁₃	#125	1	1	yes	characteristic
230	C₄×D₁₃	#125	1	1	yes	characteristic
231	C₄×D₁₃	#125	1	1	yes	characteristic
232	C₄×D₁₃	#125	1	1	yes	characteristic
233	C₈×C₁₃	—	2	4	no	—
234	C₈×C₁₃	—	2	2	no	—
235	C₈×C₁₃	—	4	2	no	—
236	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
237	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
238	#1055	—	2	4	no	—
239	#1055	—	2	2	no	—
240	#1055	—	4	2	no	—
241	#1055	C₂×C₄⋊C₄	1	2	yes	—
242	#1055	C₂×C₄⋊C₄	1	2	yes	—
243	C₂²×M₁₆	—	13	1	no	—
244	C₂²×M₁₆	—	13	2	no	—
245	C₂²×M₁₆	—	13	2	no	—
246	C₂³×C₈	—	13	1	no	—
247	C₂×#117	—	13	1	no	—
248	#430	—	13	2	no	—
249	#430	—	13	2	no	—
250	#430	—	13	2	no	—
251	#430	—	26	4	no	—
252	#430	C₂×D₁₃	1	2	yes	—
253	C₂×#108	—	13	2	no	—
254	C₂×#108	—	13	1	no	—
255	C₂×#108	—	13	4	no	—
256	C₂×#108	—	13	4	no	—
257	C₂×#108	—	13	2	no	—
258	C₂×#108	—	13	1	no	—
259	C₂×#108	—	26	1	no	—
260	C₂×#108	—	26	1	no	—
261	C₂×#108	—	26	1	no	—
262	C₂×#108	—	26	1	no	—
263	C₂×#108	—	26	4	no	—
264	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
265	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
266	#405	—	13	1	no	—
267	#405	—	13	1	no	—
268	#405	—	13	1	no	—
269	#405	—	26	1	no	—
270	#405	—	26	1	no	—
271	#405	C₂×D₁₃	1	1	yes	characteristic
272	C₂×#97	—	26	1	no	—
273	C₂×C₄×C₈	—	26	1	no	—
274	#344	—	13	2	no	—
275	#344	—	13	2	no	—
276	#344	—	13	2	no	—
277	#344	C₂×D₁₃	1	2	yes	—
278	C₂²×C₁₃	—	4	1	no	—
279	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
280	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
281	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
282	C₂×D₁₃	—	2	2	no	—
283	C₂×D₁₃	—	2	2	no	—
284	C₂×D₁₃	—	2	2	no	—
285	C₂×D₁₃	—	4	1	no	—
286	C₂×D₁₃	—	4	1	no	—
287	C₂×D₁₃	—	4	1	no	—
288	C₂×D₁₃	#389	1	1	yes	characteristic
289	C₂×D₁₃	#389	1	1	yes	characteristic
290	C₂×D₁₃	#389	1	1	yes	characteristic
291	C₂×D₁₃	#389	1	1	yes	characteristic
292	C₄×C₁₃	—	4	2	no	—
293	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
294	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
295	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
296	C₄×C₁₃	C₂×#125	1	1	yes	characteristic
297	Dic₁₃	—	4	2	no	—
298	Dic₁₃	#389	1	1	yes	characteristic
299	Dic₁₃	#389	1	1	yes	characteristic
300	Dic₁₃	#389	1	1	yes	characteristic
301	Dic₁₃	#389	1	1	yes	characteristic
302	C₂³×C₄	—	13	1	no	—
303	C₂×M₁₆	—	13	2	no	—
304	C₂×M₁₆	—	13	1	no	—
305	C₂×M₁₆	—	13	4	no	—
306	C₂×M₁₆	—	13	4	no	—
307	C₂×M₁₆	—	13	2	no	—
308	C₂×M₁₆	—	13	2	no	—
309	C₂×M₁₆	—	13	2	no	—
310	C₂×M₁₆	—	26	1	no	—
311	C₂×M₁₆	—	26	2	no	—
312	C₂×M₁₆	—	26	2	no	—
313	C₂×M₁₆	—	26	2	no	—
314	C₂×M₁₆	—	26	2	no	—
315	C₂×M₁₆	—	26	1	no	—
316	C₂×M₁₆	—	26	1	no	—
317	C₂×M₁₆	—	26	2	no	—
318	C₂×M₁₆	—	26	2	no	—
319	C₂×M₁₆	—	26	2	no	—
320	C₂×M₁₆	—	26	2	no	—
321	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
322	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
323	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
324	C₂²×C₈	—	13	1	no	—
325	C₂²×C₈	—	13	2	no	—
326	C₂²×C₈	—	13	2	no	—
327	C₂²×C₈	—	13	1	no	—
328	C₂²×C₈	—	13	1	no	—
329	C₂²×C₈	—	13	1	no	—
330	C₂²×C₈	—	13	1	no	—
331	C₂²×C₈	—	13	2	no	—
332	C₂²×C₈	—	13	2	no	—
333	C₂²×C₈	—	26	1	no	—
334	C₂²×C₈	—	26	2	no	—
335	C₂²×C₈	—	26	2	no	—
336	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
337	#117	—	13	1	no	—
338	#117	—	13	2	no	—
339	#117	—	26	1	no	—
340	#117	—	26	1	no	—
341	#117	C₂²×D₁₃	1	1	yes	characteristic
342	C₂×C₄⋊C₄	—	26	1	no	—
343	C₂×C₂²⋊C₄	—	13	2	no	—
344	C₂×C₄²	—	26	1	no	—
345	#108	—	2	4	no	—
346	#108	—	2	1	no	—
347	#108	—	2	1	no	—
348	#108	—	13	8	no	—
349	#108	—	13	4	no	—
350	#108	—	26	4	no	—
351	#108	—	26	2	no	—
352	#108	—	26	2	no	—
353	#108	—	26	4	no	—
354	#108	—	26	4	no	—
355	#108	—	26	1	no	—
356	#108	—	26	1	no	—
357	#108	C₄×D₁₃	1	4	yes	complemented
358	#97	—	2	1	no	—
359	#97	—	26	1	no	—
360	#97	—	26	1	no	—
361	#97	—	26	1	no	—
362	C₄×C₈	—	2	1	no	—
363	C₄×C₈	—	26	1	no	—
364	C₄×C₈	—	26	1	no	—
365	C₄×C₈	—	26	1	no	—
366	C₂×C₁₃	—	2	1	no	—
367	C₂×C₁₃	—	2	1	no	—
368	C₂×C₁₃	—	2	1	no	—
369	C₂×C₁₃	C₂×#389	1	1	yes	characteristic
370	D₁₃	—	2	1	no	—
371	D₁₃	—	2	1	no	—
372	D₁₃	—	2	1	no	—
373	D₁₃	#1953	1	2	yes	direct product factor
374	C₂⁴	—	13	1	no	—
375	C₂²×C₄	—	13	1	no	—
376	C₂²×C₄	—	13	1	no	—
377	C₂²×C₄	—	13	1	no	—
378	C₂²×C₄	—	13	1	no	—
379	C₂²×C₄	—	13	1	no	—
380	C₂²×C₄	—	13	1	no	—
381	C₂²×C₄	—	13	1	no	—
382	C₂²×C₄	—	13	1	no	—
383	C₂²×C₄	—	13	1	no	—
384	C₂²×C₄	—	13	1	no	—
385	C₂²×C₄	—	13	1	no	—
386	C₂²×C₄	—	13	1	no	—
387	C₂²×C₄	—	13	1	no	—
388	C₂²×C₄	—	26	2	no	—
389	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
390	M₁₆	—	2	2	no	—
391	M₁₆	—	2	1	no	—
392	M₁₆	—	2	2	no	—
393	M₁₆	—	2	2	no	—
394	M₁₆	—	13	4	no	—
395	M₁₆	—	13	2	no	—
396	M₁₆	—	26	4	no	—
397	M₁₆	—	26	4	no	—
398	M₁₆	—	26	2	no	—
399	M₁₆	—	26	2	no	—
400	M₁₆	—	26	2	no	—
401	M₁₆	—	26	1	no	—
402	M₁₆	—	26	2	no	—
403	M₁₆	—	26	2	no	—
404	M₁₆	—	52	2	no	—
405	M₁₆	—	52	2	no	—
406	M₁₆	C₂×C₄×D₁₃	1	4	yes	—
407	M₁₆	D₄×D₁₃	1	2	yes	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	13	2	no	—
412	C₂×C₈	—	13	1	no	—
413	C₂×C₈	—	13	1	no	—
414	C₂×C₈	—	13	2	no	—
415	C₂×C₈	—	13	2	no	—
416	C₂×C₈	—	13	2	no	—
417	C₂×C₈	—	13	2	no	—
418	C₂×C₈	—	13	2	no	—
419	C₂×C₈	—	13	2	no	—
420	C₂×C₈	—	13	2	no	—
421	C₂×C₈	—	13	2	no	—
422	C₂×C₈	—	13	2	no	—
423	C₂×C₈	—	26	4	no	—
424	C₂×C₈	—	26	4	no	—
425	C₂×C₈	—	26	2	no	—
426	C₂×C₈	—	26	2	no	—
427	C₂×C₈	—	26	1	no	—
428	C₂×C₈	—	26	2	no	—
429	C₂×C₈	—	26	2	no	—
430	C₂×C₈	—	52	2	no	—
431	C₂×C₈	—	52	2	no	—
432	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
433	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
434	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
435	C₂×C₈	Q₈×D₁₃	1	2	yes	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	26	2	no	—
438	C₄⋊C₄	—	26	1	no	—
439	C₂²⋊C₄	—	13	2	no	—
440	C₂²⋊C₄	—	26	2	no	—
441	C₂²⋊C₄	Q₈×D₁₃	1	2	yes	—
442	C₄²	—	2	1	no	—
443	C₄²	—	26	2	no	—
444	C₄²	—	26	1	no	—
445	C₁₃	C₂×#1953	1	1	yes	characteristic, complemented, Sylow
446	C₂³	—	13	1	no	—
447	C₂³	—	13	1	no	—
448	C₂³	—	13	1	no	—
449	C₂³	—	13	1	no	—
450	C₂³	—	13	1	no	—
451	C₂³	—	13	1	no	—
452	C₂³	—	52	2	no	—
453	C₂³	C₂×Q₈×D₁₃	1	1	yes	characteristic
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	13	1	no	—
456	C₂×C₄	—	13	1	no	—
457	C₂×C₄	—	13	1	no	—
458	C₂×C₄	—	13	1	no	—
459	C₂×C₄	—	13	1	no	—
460	C₂×C₄	—	13	1	no	—
461	C₂×C₄	—	13	1	no	—
462	C₂×C₄	—	13	1	no	—
463	C₂×C₄	—	13	1	no	—
464	C₂×C₄	—	13	1	no	—
465	C₂×C₄	—	13	1	no	—
466	C₂×C₄	—	13	1	no	—
467	C₂×C₄	—	13	1	no	—
468	C₂×C₄	—	13	1	no	—
469	C₂×C₄	—	13	1	no	—
470	C₂×C₄	—	13	1	no	—
471	C₂×C₄	—	13	1	no	—
472	C₂×C₄	—	13	1	no	—
473	C₂×C₄	—	13	1	no	—
474	C₂×C₄	—	13	1	no	—
475	C₂×C₄	—	13	1	no	—
476	C₂×C₄	—	13	1	no	—
477	C₂×C₄	—	26	2	no	—
478	C₂×C₄	—	52	4	no	—
479	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
480	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
481	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
482	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
483	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
484	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
485	C₈	—	2	4	no	—
486	C₈	—	2	2	no	—
487	C₈	—	4	2	no	—
488	C₈	—	13	2	no	—
489	C₈	—	13	2	no	—
490	C₈	—	26	4	no	—
491	C₈	—	26	2	no	—
492	C₈	—	52	2	no	—
493	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
494	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
495	C₂²	—	4	1	no	—
496	C₂²	—	13	1	no	—
497	C₂²	—	13	1	no	—
498	C₂²	—	13	1	no	—
499	C₂²	—	13	1	no	—
500	C₂²	—	26	2	no	—
501	C₂²	—	26	2	no	—
502	C₂²	—	26	2	no	—
503	C₂²	—	52	1	no	—
504	C₂²	—	52	1	no	—
505	C₂²	—	52	1	no	—
506	C₂²	C₄×Q₈×D₁₃	1	1	yes	characteristic
507	C₂²	D₁₃×C₂²⋊Q₈	1	1	yes	characteristic
508	C₂²	D₁₃×C₄⋊Q₈	1	1	yes	characteristic
509	C₄	—	4	2	no	—
510	C₄	—	13	1	no	—
511	C₄	—	13	1	no	—
512	C₄	—	13	1	no	—
513	C₄	—	13	1	no	—
514	C₄	—	52	2	no	—
515	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
516	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
517	C₄	D₁₃×#121	1	1	yes	characteristic
518	C₄	D₁₃×#125	1	1	yes	characteristic
519	C₂	—	2	1	no	—
520	C₂	—	2	1	no	—
521	C₂	—	2	1	no	—
522	C₂	—	13	2	no	—
523	C₂	—	26	1	no	—
524	C₂	—	26	1	no	—
525	C₂	—	26	1	no	—
526	C₂	D₁₃×#389	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₃×#121
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1953	C₂
socle	C₂×C₁₃	C₂×#389
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1953	D₁₃
hypocenter	C₁₃	C₂×#1953
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1953

Complements

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

N	H ≅ G/N	type
5. #13115627	C₂	semidirect
6. #13115626	C₂	semidirect
7. #13115625	C₂	semidirect
8. #13115624	C₂	semidirect
9. #13115623	C₂	semidirect
11. C₁₃×#1953	C₂	semidirect
37. D₁₃×#108	C₄	semidirect
38. D₁₃×#108	C₄	semidirect
93. C₁₃×#108	C₂×C₄	semidirect
100. #88062	C₂×C₄	semidirect
104. #88059	C₂×C₄	semidirect
192. #1953	D₁₃	direct (N × H)
357. #108	C₄×D₁₃	semidirect
373. D₁₃	#1953	direct (N × H)
445. C₁₃	C₂×#1953	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#430	2
C₂×D₁₃×#108	2
D₁₃×#405	2
#13115627	2
#13115626	2
#13115625	2
#13115624	2
#13115623	2
D₁₃×#344	2
C₁₃×#1953	2
C₂×#1953	13

Subgroups — D13×#1953 #15866483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#1953 #15866483