Subgroups — #15845562

Order 3328.

586 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125347	C₂	1	1	yes	maximal, characteristic
2	#13124877	C₂	1	2	yes	maximal
3	D₁₃×#446	C₂	1	1	yes	maximal, characteristic
4	#13114361	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114355	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114354	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114345	C₂	1	2	yes	maximal, complemented
8	#13114344	C₂	1	2	yes	maximal, complemented
9	#13113581	C₂	1	1	yes	maximal, characteristic
10	#13113490	C₂	1	2	yes	maximal
11	C₁₃×#1696	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719433	C₂²	1	2	yes	—
13	C₄×Q₈×D₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#500	C₂²	1	1	yes	characteristic
15	C₁₃×#477	C₂²	1	2	yes	—
16	C₁₃×#446	C₂²	1	1	yes	characteristic
17	#11718752	C₂²	1	2	yes	—
18	#11718740	C₂²	1	2	yes	—
19	#11718692	C₂²	1	2	yes	—
20	#11718685	C₂²	1	1	yes	characteristic
21	#11718545	—	2	2	no	—
22	#11718541	—	2	1	no	—
23	#11718541	—	2	1	no	—
24	#11718539	—	2	1	no	—
25	#11718539	—	2	1	no	—
26	#11718534	—	2	2	no	—
27	#11718510	C₂²	1	2	yes	—
28	#11718494	C₂²	1	2	yes	—
29	D₁₃×C₄⋊C₈	—	2	1	no	—
30	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	#11718492	C₂²	1	1	yes	characteristic
32	#11718489	—	2	1	no	—
33	#11718469	—	2	2	no	—
34	#11718451	—	2	2	no	—
35	D₁₃×#97	—	2	1	no	—
36	#11718362	—	2	1	no	—
37	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
38	#11718343	C₂²	1	1	yes	characteristic
39	#11718340	C₂²	1	1	yes	characteristic
40	C₁₃×#334	C₂²	1	1	yes	characteristic
41	C₁₃×#333	C₂²	1	2	yes	—
42	#11718138	C₂²	1	2	yes	—
43	#11718078	C₂²	1	2	yes	—
44	#11718074	C₂²	1	2	yes	—
45	#11718071	C₂²	1	2	yes	—
46	#11718049	C₂²	1	1	yes	characteristic
47	C₂×Q₈×D₁₃	D₄	1	1	yes	characteristic
48	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
49	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
50	#88200	—	2	2	no	—
51	Q₈×Dic₁₃	—	2	2	no	—
52	Q₈×Dic₁₃	D₄	1	1	yes	characteristic
53	C₂×#6107	—	2	2	no	—
54	C₂×Dic₅₂	—	2	2	no	—
55	C₂×C₈×D₁₃	—	2	1	no	—
56	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
57	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
58	#88151	—	2	2	no	—
59	#88146	—	2	2	no	—
60	C₄⋊C₄×D₁₃	—	2	1	no	—
61	C₄⋊C₄×D₁₃	D₄	1	1	yes	characteristic
62	#88144	—	2	2	no	—
63	#88141	—	2	1	no	—
64	#88141	—	2	2	no	—
65	#88141	D₄	1	1	yes	characteristic
66	C₄²×D₁₃	—	2	1	no	—
67	C₄²×D₁₃	C₂³	1	1	yes	characteristic
68	#88123	C₂³	1	2	yes	—
69	C₄×Dic₂₆	—	2	1	no	—
70	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
71	C₁₃×#107	—	2	1	no	—
72	C₁₃×#107	—	2	1	no	—
73	C₁₃×#107	—	2	2	no	—
74	C₁₃×C₄⋊C₈	—	2	1	no	—
75	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
77	C₁₃×#103	—	2	2	no	—
78	C₁₃×#97	—	2	1	no	—
79	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	#88060	—	2	2	no	—
81	#88058	—	2	1	no	—
82	#88058	—	2	1	no	—
83	#88056	—	2	2	no	—
84	#88055	—	2	1	no	—
85	#88055	—	2	1	no	—
86	#88054	—	2	1	no	—
87	#88054	—	2	1	no	—
88	#88054	—	2	1	no	—
89	C₈×Dic₁₃	—	2	2	no	—
90	C₈×Dic₁₃	D₄	1	1	yes	characteristic
91	C₈×Dic₁₃	D₄	1	1	yes	characteristic
92	#88050	—	2	2	no	—
93	#88050	—	2	2	no	—
94	#88048	—	2	2	no	—
95	#88048	—	2	2	no	—
96	#88047	—	2	2	no	—
97	C₄⋊#1055	—	2	1	no	—
98	C₄⋊#1055	C₂³	1	1	yes	characteristic
99	C₄⋊#1055	C₂³	1	2	yes	—
100	#88043	—	2	1	no	—
101	C₄×#1055	C₂³	1	1	yes	characteristic
102	#19150	—	13	1	no	maximal, Sylow
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
105	Q₈×D₁₃	—	4	2	no	—
106	C₂×C₄×D₁₃	—	2	1	no	—
107	C₂×C₄×D₁₃	—	2	1	no	—
108	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
111	C₂×Dic₂₆	—	2	1	no	—
112	C₂×Dic₂₆	—	2	2	no	—
113	C₂×Dic₂₆	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₃	—	2	1	no	—
123	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
124	#6107	—	4	4	no	—
125	#6103	—	4	2	no	—
126	C₄⋊Dic₁₃	—	2	1	no	—
127	C₄⋊Dic₁₃	—	2	2	no	—
128	C₄⋊Dic₁₃	—	2	2	no	—
129	C₄⋊Dic₁₃	—	4	2	no	—
130	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
131	#6101	—	2	1	no	—
132	#6101	—	2	1	no	—
133	#6101	—	2	1	no	—
134	#6101	—	4	2	no	—
135	C₄×Dic₁₃	—	2	1	no	—
136	C₄×Dic₁₃	—	2	1	no	—
137	C₄×Dic₁₃	—	2	1	no	—
138	C₄×Dic₁₃	—	4	2	no	—
139	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄×Dic₁₃	#41	1	1	yes	characteristic
142	C₂×#1055	—	2	1	no	—
143	C₂×#1055	—	2	2	no	—
144	C₂×#1055	C₂×D₄	1	1	yes	characteristic
145	C₂×#1055	C₂×D₄	1	1	yes	characteristic
146	Dic₅₂	—	4	4	no	—
147	C₈×D₁₃	—	2	2	no	—
148	C₈×D₁₃	—	4	2	no	—
149	C₈×D₁₃	Q₁₆	1	4	yes	complemented
150	#3160	—	13	1	no	—
151	#3104	—	13	2	no	—
152	C₂×#446	—	13	1	no	—
153	#1696	—	13	1	no	—
154	#1696	D₁₃	1	1	yes	characteristic, complemented
155	#1694	—	13	1	no	—
156	#1694	—	13	1	no	—
157	#1692	—	13	2	no	—
158	#1692	—	13	2	no	—
159	#1564	—	13	1	no	—
160	#1542	—	13	2	no	—
161	C₂²×D₁₃	#121	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	2	no	—
163	Q₈×C₁₃	—	8	2	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
170	C₂×Dic₁₃	—	2	1	no	—
171	C₂×Dic₁₃	—	2	1	no	—
172	C₂×Dic₁₃	—	4	2	no	—
173	C₂×Dic₁₃	#121	1	1	yes	characteristic
174	C₂×Dic₁₃	#121	1	1	yes	characteristic
175	C₂×Dic₁₃	#121	1	1	yes	characteristic
176	C₄×D₁₃	—	2	2	no	—
177	C₄×D₁₃	—	4	1	no	—
178	C₄×D₁₃	—	4	2	no	—
179	C₄×D₁₃	—	4	2	no	—
180	C₄×D₁₃	C₂×Q₁₆	1	2	yes	—
181	C₄×D₁₃	#137	1	2	yes	—
182	Dic₂₆	—	2	2	no	—
183	Dic₂₆	—	4	2	no	—
184	Dic₂₆	—	4	2	no	—
185	Dic₂₆	—	4	2	no	—
186	C₈×C₁₃	—	2	1	no	—
187	C₈×C₁₃	—	4	1	no	—
188	C₈×C₁₃	—	4	2	no	—
189	C₈×C₁₃	C₂×Q₁₆	1	2	yes	—
190	#1055	—	2	1	no	—
191	#1055	—	4	1	no	—
192	#1055	—	4	2	no	—
193	#1055	C₂×Q₁₆	1	2	yes	—
194	#533	—	13	2	no	—
195	C₂×C₄×Q₈	—	13	1	no	—
196	#500	—	13	1	no	—
197	#500	C₂×D₁₃	1	1	yes	characteristic
198	#499	—	26	1	no	—
199	#499	—	26	1	no	—
200	#498	—	13	2	no	—
201	#484	—	26	2	no	—
202	#477	—	13	2	no	—
203	#477	C₂×D₁₃	1	2	yes	—
204	#462	—	13	2	no	—
205	#462	—	13	2	no	—
206	#451	—	26	2	no	—
207	#446	—	13	1	no	—
208	#446	—	13	1	no	—
209	#446	—	13	1	no	—
210	#446	—	26	1	no	—
211	#446	—	26	1	no	—
212	#446	C₂×D₁₃	1	1	yes	characteristic
213	C₄×Q₁₆	—	26	2	no	—
214	C₄×Q₁₆	—	26	2	no	—
215	#431	—	13	2	no	—
216	#427	—	26	1	no	—
217	#427	—	26	1	no	—
218	C₂×C₄⋊C₈	—	13	1	no	—
219	C₂×C₄⋊C₈	—	26	1	no	—
220	C₂×#97	—	26	1	no	—
221	C₂×C₄×C₈	—	13	1	no	—
222	#335	—	13	2	no	—
223	#334	—	13	1	no	—
224	#334	C₂×D₁₃	1	1	yes	characteristic
225	#333	—	13	2	no	—
226	#333	C₂×D₁₃	1	2	yes	—
227	#332	—	13	2	no	—
228	#332	—	13	2	no	—
229	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
230	C₂×D₁₃	—	2	1	no	—
231	C₂×D₁₃	—	2	1	no	—
232	C₂×D₁₃	#462	1	2	yes	—
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	4	1	no	—
235	C₄×C₁₃	—	4	1	no	—
236	C₄×C₁₃	—	8	2	no	—
237	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
238	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
239	C₄×C₁₃	#575	1	2	yes	—
240	Dic₁₃	—	2	1	no	—
241	Dic₁₃	—	2	1	no	—
242	Dic₁₃	—	4	1	no	—
243	Dic₁₃	—	4	1	no	—
244	Dic₁₃	—	8	2	no	—
245	Dic₁₃	#462	1	2	yes	—
246	C₂²×Q₈	—	13	1	no	—
247	C₂×Q₁₆	—	26	2	no	—
248	C₂×Q₁₆	—	26	2	no	—
249	C₂²×C₈	—	13	1	no	—
250	C₂²×C₈	—	13	1	no	—
251	C₂²×C₈	—	26	1	no	—
252	C₄⋊Q₈	—	13	2	no	—
253	C₄⋊Q₈	C₂²×D₁₃	1	2	yes	—
254	#125	—	26	2	no	—
255	C₂²⋊Q₈	—	26	2	no	—
256	C₂²⋊Q₈	—	26	2	no	—
257	C₄×Q₈	—	13	1	no	—
258	C₄×Q₈	—	13	1	no	—
259	C₄×Q₈	—	13	1	no	—
260	C₄×Q₈	—	26	1	no	—
261	C₄×Q₈	—	26	1	no	—
262	C₄×Q₈	—	26	2	no	—
263	C₄×Q₈	—	26	2	no	—
264	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
265	#117	—	26	2	no	—
266	C₂×C₄⋊C₄	—	13	1	no	—
267	C₂×C₄⋊C₄	—	26	1	no	—
268	C₂×C₄²	—	13	1	no	—
269	C₂×C₄²	—	26	1	no	—
270	#107	—	2	1	no	—
271	#107	—	2	1	no	—
272	#107	—	2	2	no	—
273	#107	—	26	2	no	—
274	#107	—	26	1	no	—
275	#107	—	26	1	no	—
276	#106	—	26	2	no	—
277	#106	—	26	2	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	13	1	no	—
280	C₄⋊C₈	—	13	2	no	—
281	C₄⋊C₈	—	26	1	no	—
282	C₄⋊C₈	—	26	1	no	—
283	C₄⋊C₈	—	26	1	no	—
284	C₄⋊C₈	—	26	1	no	—
285	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
286	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
287	#103	—	2	2	no	—
288	#103	—	26	2	no	—
289	#103	—	26	2	no	—
290	#103	—	26	2	no	—
291	C₂²⋊C₈	—	26	2	no	—
292	#97	—	2	1	no	—
293	#97	—	26	1	no	—
294	#97	—	26	1	no	—
295	#97	—	26	1	no	—
296	C₄×C₈	—	13	1	no	—
297	C₄×C₈	—	13	1	no	—
298	C₄×C₈	—	13	1	no	—
299	C₄×C₈	—	26	2	no	—
300	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
301	C₂×C₁₃	C₂×#462	1	1	yes	characteristic
302	C₂×C₁₃	#3054	1	1	yes	characteristic
303	C₂×C₁₃	#3067	1	1	yes	characteristic
304	D₁₃	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	13	1	no	—
307	C₂×Q₈	—	26	1	no	—
308	C₂×Q₈	—	26	2	no	—
309	C₂×Q₈	—	52	2	no	—
310	C₂×Q₈	D₄×D₁₃	1	1	yes	characteristic
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	13	1	no	—
314	C₂²×C₄	—	26	1	no	—
315	C₂²×C₄	—	26	1	no	—
316	Q₁₆	—	52	4	no	—
317	Q₁₆	—	52	4	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	13	1	no	—
321	C₂×C₈	—	13	4	no	—
322	C₂×C₈	—	13	1	no	—
323	C₂×C₈	—	26	2	no	—
324	C₂×C₈	—	26	2	no	—
325	C₂×C₈	—	26	1	no	—
326	C₂×C₈	—	52	2	no	—
327	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
328	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	13	1	no	—
333	C₄⋊C₄	—	26	1	no	—
334	C₄⋊C₄	—	26	1	no	—
335	C₄⋊C₄	—	26	1	no	—
336	C₄⋊C₄	—	26	1	no	—
337	C₄⋊C₄	—	26	2	no	—
338	C₄⋊C₄	—	26	2	no	—
339	C₄⋊C₄	—	52	2	no	—
340	C₄⋊C₄	—	52	2	no	—
341	C₄⋊C₄	D₄×D₁₃	1	1	yes	characteristic
342	C₂²⋊C₄	—	52	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	13	1	no	—
345	C₄²	—	13	1	no	—
346	C₄²	—	13	1	no	—
347	C₄²	—	26	1	no	—
348	C₄²	—	26	1	no	—
349	C₄²	—	26	1	no	—
350	C₄²	—	52	2	no	—
351	C₄²	C₂³×D₁₃	1	1	yes	characteristic
352	C₁₃	#19150	1	1	yes	characteristic, complemented, Sylow
353	C₂³	—	13	1	no	—
354	Q₈	—	2	2	no	—
355	Q₈	—	8	2	no	—
356	Q₈	—	26	2	no	—
357	Q₈	—	52	2	no	—
358	Q₈	—	52	2	no	—
359	Q₈	—	52	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	13	1	no	—
364	C₂×C₄	—	13	2	no	—
365	C₂×C₄	—	13	2	no	—
366	C₂×C₄	—	13	1	no	—
367	C₂×C₄	—	13	1	no	—
368	C₂×C₄	—	26	2	no	—
369	C₂×C₄	—	26	1	no	—
370	C₂×C₄	—	26	1	no	—
371	C₂×C₄	—	52	1	no	—
372	C₂×C₄	—	52	2	no	—
373	C₂×C₄	—	52	2	no	—
374	C₂×C₄	—	52	2	no	—
375	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
376	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
377	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
378	C₈	—	2	1	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	2	no	—
381	C₈	—	13	2	no	—
382	C₈	—	26	1	no	—
383	C₈	—	52	1	no	—
384	C₈	—	52	2	no	—
385	C₈	Q₁₆×D₁₃	1	2	yes	—
386	C₂²	—	13	2	no	—
387	C₂²	—	26	1	no	—
388	C₂²	—	26	1	no	—
389	C₂²	D₁₃×#121	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	8	2	no	—
394	C₄	—	13	2	no	—
395	C₄	—	26	1	no	—
396	C₄	—	26	1	no	—
397	C₄	—	52	1	no	—
398	C₄	—	52	1	no	—
399	C₄	—	104	2	no	—
400	C₄	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
401	C₄	D₁₃×#137	1	1	yes	characteristic
402	C₄	#11719482	1	2	yes	—
403	C₂	—	26	2	no	—
404	C₂	D₁₃×#462	1	1	yes	characteristic
405	C₂	#13124447	1	1	yes	characteristic
406	C₂	#13124554	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₃×#121
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1696	C₂
socle	C₂²×C₁₃	C₂×#121
prime radical	C₂²×D₁₃	#121
hypercenter	#1696	D₁₃
hypocenter	C₁₃	#19150
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1696

Complements

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

N	H ≅ G/N	type
4. #13114361	C₂	semidirect
5. #13114355	C₂	semidirect
6. #13114354	C₂	semidirect
7. #13114345	C₂	semidirect
8. #13114344	C₂	semidirect
11. C₁₃×#1696	C₂	semidirect
149. C₈×D₁₃	Q₁₆	semidirect
154. #1696	D₁₃	semidirect
352. C₁₃	#19150	semidirect

Maximal subgroups

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

subgroup	index
#13125347	2
#13124877	2
D₁₃×#446	2
#13114361	2
#13114355	2
#13114354	2
#13114345	2
#13114344	2
#13113581	2
#13113490	2
C₁₃×#1696	2
#19150	13