Subgroups — #15753565

Order 3328.

562 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117297	C₂	1	1	yes	maximal, characteristic
2	#13114691	C₂	1	1	yes	maximal, characteristic, complemented
3	#13114581	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718051	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718075	C₂	1	1	yes	maximal, characteristic
6	#13112677	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
9	C₂×#88126	—	2	1	no	—
10	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×#88055	—	2	1	no	—
14	#11718649	C₄	1	2	yes	—
15	#11718634	C₄	1	2	yes	—
16	C₄×#6103	—	2	1	no	—
17	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
19	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
20	#11718330	—	2	2	no	—
21	#11718142	—	2	1	no	—
22	#11718142	—	2	2	no	—
23	#11718075	C₄	1	4	yes	complemented
24	#11718051	C₄	1	4	yes	complemented
25	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×D₁₃	—	2	1	no	—
27	C₂²×C₈×C₁₃	—	2	1	no	—
28	C₂²×C₈×C₁₃	—	2	1	no	—
29	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₃	—	2	1	no	—
31	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
32	C₂×#6103	—	2	1	no	—
33	C₂×#6103	—	2	2	no	—
34	C₂×#6103	—	2	2	no	—
35	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×#6101	—	2	2	no	—
37	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
38	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
39	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
40	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
41	C₂²×#1055	—	2	1	no	—
42	C₂²×#1055	—	2	1	no	—
43	C₄×D₅₂	—	2	1	no	—
44	C₄×D₅₂	—	2	1	no	—
45	C₄×D₅₂	C₂×C₄	1	2	yes	—
46	C₄×D₅₂	C₂×C₄	1	2	yes	—
47	#88126	—	4	2	no	—
48	#88126	—	4	2	no	—
49	C₁₃×C₄⋊C₈	—	2	1	no	—
50	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
51	C₄×C₈×C₁₃	—	2	1	no	—
52	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
53	C₁₃×#95	—	2	1	no	—
54	#88071	—	2	2	no	—
55	#88055	—	4	2	no	—
56	C₄⋊#1055	—	2	1	no	—
57	C₄⋊#1055	C₂×C₄	1	2	yes	—
58	C₄×#1055	—	2	1	no	—
59	C₄×#1055	C₂×C₄	1	2	yes	—
60	#8179	—	13	1	no	maximal, Sylow
61	C₂³×D₁₃	—	2	1	no	—
62	C₂²×C₄×C₁₃	—	2	2	no	—
63	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
66	C₂²×Dic₁₃	—	2	1	no	—
67	C₂²×Dic₁₃	C₂²⋊C₄	1	2	yes	—
68	C₂²×Dic₁₃	C₂²⋊C₄	1	2	yes	—
69	C₂×D₅₂	—	2	2	no	—
70	C₂×D₅₂	—	2	2	no	—
71	C₂×D₅₂	—	2	1	no	—
72	C₂×D₅₂	C₄²	1	2	yes	—
73	C₂×C₄×D₁₃	—	2	2	no	—
74	C₂×C₄×D₁₃	—	2	2	no	—
75	C₂×C₄×D₁₃	—	4	1	no	—
76	C₂×C₄×D₁₃	—	4	1	no	—
77	C₂×C₄×D₁₃	—	4	1	no	—
78	C₂×C₄×D₁₃	—	4	1	no	—
79	C₂×C₈×C₁₃	—	2	2	no	—
80	C₂×C₈×C₁₃	—	2	2	no	—
81	C₂×C₈×C₁₃	—	4	2	no	—
82	C₂×C₈×C₁₃	—	4	1	no	—
83	C₂×C₈×C₁₃	—	4	1	no	—
84	C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₁₃×C₄⋊C₄	—	2	2	no	—
86	C₄²×C₁₃	—	4	1	no	—
87	C₄²×C₁₃	—	4	1	no	—
88	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₄²×C₁₃	#41	1	1	yes	characteristic
91	C₄²×C₁₃	#41	1	1	yes	characteristic
92	#6103	—	2	2	no	—
93	#6103	—	2	2	no	—
94	#6103	—	4	4	no	—
95	#6103	—	4	4	no	—
96	C₄⋊Dic₁₃	—	2	1	no	—
97	C₄⋊Dic₁₃	C₄²	1	2	yes	—
98	#6101	—	4	4	no	—
99	C₄×Dic₁₃	—	2	2	no	—
100	C₄×Dic₁₃	—	2	2	no	—
101	C₄×Dic₁₃	—	2	1	no	—
102	C₄×Dic₁₃	—	2	1	no	—
103	C₄×Dic₁₃	—	2	1	no	—
104	C₄×Dic₁₃	—	2	1	no	—
105	C₄×Dic₁₃	—	4	2	no	—
106	C₂×#1055	—	2	2	no	—
107	C₂×#1055	—	2	2	no	—
108	C₂×#1055	—	4	2	no	—
109	C₂×#1055	—	4	1	no	—
110	C₂×#1055	—	4	1	no	—
111	#2293	—	13	1	no	—
112	#1767	—	13	1	no	—
113	#1744	—	13	1	no	—
114	C₂×D₄⋊C₈	—	13	1	no	—
115	C₂×D₄⋊C₈	—	13	1	no	—
116	#1279	—	13	1	no	—
117	#1279	D₁₃	1	1	yes	characteristic, complemented
118	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×D₁₃	—	2	2	no	—
120	C₂²×D₁₃	—	4	2	no	—
121	C₂²×D₁₃	—	4	1	no	—
122	C₂²×D₁₃	—	4	1	no	—
123	C₂²×D₁₃	—	4	2	no	—
124	C₂×C₄×C₁₃	—	2	2	no	—
125	C₂×C₄×C₁₃	—	4	2	no	—
126	C₂×C₄×C₁₃	—	4	2	no	—
127	C₂×C₄×C₁₃	—	4	2	no	—
128	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
129	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
130	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₁₃	#131	1	2	yes	—
135	C₂×C₄×C₁₃	#131	1	2	yes	—
136	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
137	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
138	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
139	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
140	C₂×Dic₁₃	—	2	2	no	—
141	C₂×Dic₁₃	—	2	2	no	—
142	C₂×Dic₁₃	—	2	2	no	—
143	C₂×Dic₁₃	—	2	2	no	—
144	C₂×Dic₁₃	—	2	2	no	—
145	C₂×Dic₁₃	—	2	2	no	—
146	C₂×Dic₁₃	—	2	2	no	—
147	C₂×Dic₁₃	—	4	1	no	—
148	C₂×Dic₁₃	—	4	1	no	—
149	D₅₂	—	2	2	no	—
150	D₅₂	—	2	2	no	—
151	D₅₂	—	4	2	no	—
152	C₄×D₁₃	—	4	2	no	—
153	C₄×D₁₃	—	4	2	no	—
154	C₄×D₁₃	—	4	2	no	—
155	C₄×D₁₃	—	4	2	no	—
156	C₈×C₁₃	—	4	2	no	—
157	C₈×C₁₃	—	4	2	no	—
158	#1055	—	4	2	no	—
159	#1055	—	4	2	no	—
160	C₂×C₄×D₄	—	13	1	no	—
161	C₂×#117	—	26	1	no	—
162	C₂×C₄⋊C₈	—	13	1	no	—
163	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
164	C₂×#97	—	26	1	no	—
165	C₂×C₄×C₈	—	13	1	no	—
166	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
167	#390	—	13	2	no	—
168	#389	—	13	2	no	—
169	#388	—	26	2	no	—
170	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
171	C₄×C₂²⋊C₄	—	26	1	no	—
172	C₄³	—	13	1	no	—
173	#336	—	26	2	no	—
174	#336	—	26	1	no	—
175	D₄⋊C₈	—	13	4	no	—
176	D₄⋊C₈	—	13	4	no	—
177	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
178	C₂²×C₁₃	#408	1	2	yes	—
179	C₂²×C₁₃	#417	1	1	yes	characteristic
180	C₂²×C₁₃	#418	1	1	yes	characteristic
181	C₂²×C₁₃	#421	1	2	yes	—
182	C₂×D₁₃	—	4	2	no	—
183	C₂×D₁₃	—	4	2	no	—
184	C₂×D₁₃	—	4	2	no	—
185	C₂×D₁₃	—	8	2	no	—
186	C₂×D₁₃	—	8	2	no	—
187	C₄×C₁₃	—	2	1	no	—
188	C₄×C₁₃	—	2	1	no	—
189	C₄×C₁₃	—	8	2	no	—
190	C₄×C₁₃	#405	1	1	yes	characteristic
191	C₄×C₁₃	#405	1	1	yes	characteristic
192	C₄×C₁₃	#433	1	2	yes	—
193	C₄×C₁₃	#440	1	1	yes	characteristic
194	C₄×C₁₃	#440	1	1	yes	characteristic
195	C₄×C₁₃	#442	1	1	yes	characteristic
196	C₄×C₁₃	#442	1	1	yes	characteristic
197	Dic₁₃	—	4	2	no	—
198	Dic₁₃	—	4	2	no	—
199	Dic₁₃	—	4	2	no	—
200	C₂²×D₄	—	13	1	no	—
201	C₂³×C₄	—	26	1	no	—
202	C₂²×C₈	—	2	1	no	—
203	C₂²×C₈	—	2	1	no	—
204	C₂²×C₈	—	26	1	no	—
205	C₂²×C₈	—	26	1	no	—
206	C₄×D₄	—	13	2	no	—
207	C₄×D₄	—	13	2	no	—
208	C₄×D₄	—	26	1	no	—
209	C₄×D₄	—	26	1	no	—
210	#117	—	52	2	no	—
211	#117	—	52	2	no	—
212	C₂×C₄⋊C₄	—	13	1	no	—
213	C₂×C₄⋊C₄	—	26	2	no	—
214	C₂×C₄⋊C₄	C₄×D₁₃	1	2	yes	—
215	C₂×C₂²⋊C₄	—	26	1	no	—
216	C₂×C₂²⋊C₄	—	26	2	no	—
217	C₂×C₂²⋊C₄	—	26	2	no	—
218	C₂×C₄²	—	2	1	no	—
219	C₂×C₄²	—	13	2	no	—
220	C₂×C₄²	—	13	1	no	—
221	C₂×C₄²	—	13	1	no	—
222	C₂×C₄²	—	13	2	no	—
223	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
224	C₄⋊C₈	—	2	1	no	—
225	C₄⋊C₈	—	13	2	no	—
226	C₄⋊C₈	—	26	1	no	—
227	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
228	#97	—	52	2	no	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	13	2	no	—
231	C₄×C₈	—	26	1	no	—
232	C₄×C₈	C₄×D₁₃	1	2	yes	—
233	#95	—	2	1	no	—
234	#95	—	26	2	no	—
235	C₂×C₁₃	#1495	1	2	yes	—
236	C₂×C₁₃	#1496	1	2	yes	—
237	C₂×C₁₃	#1750	1	1	yes	characteristic
238	C₂×C₁₃	#1759	1	1	yes	characteristic
239	C₂×C₁₃	#1762	1	1	yes	characteristic
240	D₁₃	—	8	2	no	—
241	C₂⁴	—	26	1	no	—
242	C₂×D₄	—	13	2	no	—
243	C₂×D₄	—	26	1	no	—
244	C₂×D₄	—	26	2	no	—
245	C₂×D₄	—	26	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	13	2	no	—
248	C₂²×C₄	—	13	2	no	—
249	C₂²×C₄	—	26	1	no	—
250	C₂²×C₄	—	26	2	no	—
251	C₂²×C₄	—	26	2	no	—
252	C₂²×C₄	—	52	1	no	—
253	C₂²×C₄	—	52	1	no	—
254	C₂²×C₄	—	52	1	no	—
255	C₂²×C₄	—	52	1	no	—
256	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
257	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
258	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	4	2	no	—
262	C₂×C₈	—	4	1	no	—
263	C₂×C₈	—	4	1	no	—
264	C₂×C₈	—	26	2	no	—
265	C₂×C₈	—	26	2	no	—
266	C₂×C₈	—	52	2	no	—
267	C₂×C₈	—	52	1	no	—
268	C₂×C₈	—	52	1	no	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	—	13	2	no	—
272	C₄⋊C₄	—	26	1	no	—
273	C₄⋊C₄	—	52	4	no	—
274	C₂²⋊C₄	—	26	2	no	—
275	C₂²⋊C₄	—	26	2	no	—
276	C₂²⋊C₄	—	52	4	no	—
277	C₂²⋊C₄	—	52	4	no	—
278	C₄²	—	4	1	no	—
279	C₄²	—	4	1	no	—
280	C₄²	—	26	2	no	—
281	C₄²	—	26	2	no	—
282	C₄²	—	26	1	no	—
283	C₄²	—	26	1	no	—
284	C₄²	—	26	1	no	—
285	C₄²	—	26	1	no	—
286	C₄²	—	52	2	no	—
287	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
288	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
289	C₄²	#6129	1	1	yes	characteristic
290	C₄²	#6131	1	1	yes	characteristic
291	C₁₃	#8179	1	1	yes	characteristic, complemented, Sylow
292	C₂³	—	26	2	no	—
293	C₂³	—	52	1	no	—
294	C₂³	—	52	1	no	—
295	C₂³	—	52	2	no	—
296	C₂³	—	52	2	no	—
297	C₂³	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
298	D₄	—	26	2	no	—
299	D₄	—	26	2	no	—
300	D₄	—	52	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	26	2	no	—
306	C₂×C₄	—	26	2	no	—
307	C₂×C₄	—	26	2	no	—
308	C₂×C₄	—	26	2	no	—
309	C₂×C₄	—	26	2	no	—
310	C₂×C₄	—	26	2	no	—
311	C₂×C₄	—	26	2	no	—
312	C₂×C₄	—	52	1	no	—
313	C₂×C₄	—	52	1	no	—
314	C₂×C₄	—	52	2	no	—
315	C₂×C₄	—	52	2	no	—
316	C₂×C₄	—	52	2	no	—
317	C₂×C₄	—	52	2	no	—
318	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
319	C₂×C₄	#88135	1	1	yes	characteristic
320	C₂×C₄	#88135	1	1	yes	characteristic
321	C₂×C₄	#88146	1	1	yes	characteristic
322	C₂×C₄	#88147	1	1	yes	characteristic
323	C₂×C₄	#88147	1	1	yes	characteristic
324	C₂×C₄	#88155	1	2	yes	—
325	C₂×C₄	#88161	1	2	yes	—
326	C₂×C₄	#88165	1	1	yes	characteristic
327	C₂×C₄	#88168	1	1	yes	characteristic
328	C₂×C₄	#88168	1	1	yes	characteristic
329	C₂×C₄	#88172	1	1	yes	characteristic
330	C₈	—	4	2	no	—
331	C₈	—	4	2	no	—
332	C₈	—	52	2	no	—
333	C₈	—	52	2	no	—
334	C₂²	—	52	2	no	—
335	C₂²	—	52	2	no	—
336	C₂²	—	52	2	no	—
337	C₂²	—	104	2	no	—
338	C₂²	—	104	2	no	—
339	C₂²	#11718327	1	1	yes	characteristic
340	C₂²	#11718388	1	2	yes	—
341	C₂²	#11718431	1	1	yes	characteristic
342	C₂²	#11718464	1	1	yes	characteristic
343	C₂²	#11718482	1	2	yes	—
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	8	2	no	—
347	C₄	—	52	2	no	—
348	C₄	—	52	2	no	—
349	C₄	—	52	2	no	—
350	C₄	#11718350	1	1	yes	characteristic
351	C₄	#11718369	1	1	yes	characteristic
352	C₄	#11718446	1	1	yes	characteristic
353	C₄	#11718478	1	1	yes	characteristic
354	C₄	#11718501	1	2	yes	—
355	C₄	#11718530	1	1	yes	characteristic
356	C₄	#11718550	1	1	yes	characteristic
357	C₂	—	104	2	no	—
358	C₂	#13113300	1	2	yes	—
359	C₂	#13113303	1	2	yes	—
360	C₂	#13114601	1	1	yes	characteristic
361	C₂	#13114645	1	1	yes	characteristic
362	C₂	#13114660	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1279	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₅₂	C₂×C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1279	D₁₃
hypocenter	C₁₃	#8179
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
2. #13114691	C₂	semidirect
3. #13114581	C₂	semidirect
6. #13112677	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
23. #11718075	C₄	semidirect
24. #11718051	C₄	semidirect
117. #1279	D₁₃	semidirect
291. C₁₃	#8179	semidirect

Maximal subgroups

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

subgroup	index
#13117297	2
#13114691	2
#13114581	2
C₂×#11718051	2
C₂×#11718075	2
#13112677	2
C₁₃×#1279	2
#8179	13