Subgroups — #15752401

Order 3328.

630 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718496	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718346	C₂	1	1	yes	maximal, characteristic
3	C₂×D₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#13112671	C₂	1	1	yes	maximal, characteristic, complemented
5	#13112670	C₂	1	1	yes	maximal, characteristic, complemented
6	#13112670	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₁₃	—	2	1	no	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×#88060	—	2	1	no	—
14	C₂×#88060	C₄	1	2	yes	—
15	C₂×#88055	—	2	1	no	—
16	C₂×#88054	—	2	1	no	—
17	C₂×#88054	C₄	1	2	yes	—
18	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
20	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
21	#11718496	—	2	2	no	—
22	#11718496	C₄	1	4	yes	—
23	D₁₃×C₄⋊C₈	—	2	2	no	—
24	D₁₃×C₄⋊C₈	C₄	1	4	yes	—
25	#11718346	—	2	2	no	—
26	#11718346	—	2	2	no	—
27	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	—	2	1	no	—
31	C₂²×C₈×C₁₃	—	2	1	no	—
32	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
34	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
36	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
37	C₂²×#1055	—	2	1	no	—
38	C₂²×#1055	—	2	1	no	—
39	C₂²×#1055	C₂×C₄	1	2	yes	—
40	C₂×C₈×D₁₃	—	2	4	no	—
41	C₂×C₈×D₁₃	—	4	2	no	—
42	C₂×C₈×D₁₃	—	4	2	no	—
43	C₄²×D₁₃	C₂×C₄	1	2	yes	—
44	C₄²×D₁₃	C₂×C₄	1	2	yes	—
45	C₄²×D₁₃	D₄	1	2	yes	—
46	C₄²×D₁₃	D₄	1	2	yes	—
47	C₁₃×C₄⋊C₈	—	2	1	no	—
48	C₁₃×C₄⋊C₈	—	2	1	no	—
49	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
50	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
51	C₄×C₈×C₁₃	—	2	1	no	—
52	C₄×C₈×C₁₃	—	2	1	no	—
53	#88060	—	2	4	no	—
54	#88060	—	2	4	no	—
55	#88055	—	2	4	no	—
56	#88054	—	2	4	no	—
57	#88054	—	2	4	no	—
58	C₄⋊#1055	—	2	1	no	—
59	C₄⋊#1055	—	2	1	no	—
60	C₄⋊#1055	C₂×C₄	1	2	yes	—
61	C₄⋊#1055	C₂×C₄	1	2	yes	—
62	C₄×#1055	—	2	1	no	—
63	C₄×#1055	—	2	1	no	—
64	#7879	—	13	1	no	maximal, Sylow
65	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
69	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×D₁₃	—	2	4	no	—
73	C₂×C₄×D₁₃	—	2	2	no	—
74	C₂×C₄×D₁₃	—	2	2	no	—
75	C₂×C₄×D₁₃	—	2	1	no	—
76	C₂×C₄×D₁₃	—	2	1	no	—
77	C₂×C₄×D₁₃	—	2	1	no	—
78	C₂×C₄×D₁₃	—	2	1	no	—
79	C₂×C₄×D₁₃	C₄²	1	2	yes	—
80	C₂×C₄×D₁₃	C₂²⋊C₄	1	2	yes	—
81	C₂×C₄×D₁₃	C₂²⋊C₄	1	2	yes	—
82	C₂×C₄×D₁₃	C₂²⋊C₄	1	2	yes	—
83	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
84	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
85	C₂×C₈×C₁₃	—	2	2	no	—
86	C₂×C₈×C₁₃	—	2	2	no	—
87	C₂×C₈×C₁₃	—	2	2	no	—
88	C₂×C₈×C₁₃	—	2	2	no	—
89	C₂×C₈×C₁₃	—	2	2	no	—
90	C₂×C₈×C₁₃	—	4	1	no	—
91	C₂×C₈×C₁₃	—	4	1	no	—
92	C₂×C₈×C₁₃	—	4	1	no	—
93	C₂×C₈×C₁₃	—	4	1	no	—
94	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₄×Dic₁₃	C₄²	1	2	yes	—
99	C₄×Dic₁₃	C₂²⋊C₄	1	2	yes	—
100	C₄×Dic₁₃	C₂²⋊C₄	1	2	yes	—
101	C₄×Dic₁₃	C₂²⋊C₄	1	2	yes	—
102	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
103	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
104	C₂×#1055	—	2	2	no	—
105	C₂×#1055	—	2	2	no	—
106	C₂×#1055	—	2	2	no	—
107	C₂×#1055	—	2	2	no	—
108	C₂×#1055	—	2	2	no	—
109	C₂×#1055	—	4	1	no	—
110	C₂×#1055	—	4	1	no	—
111	C₂×#1055	—	4	1	no	—
112	C₂×#1055	—	4	1	no	—
113	C₈×D₁₃	—	4	8	no	—
114	C₂×#432	—	13	1	no	—
115	C₂×#431	—	13	1	no	—
116	C₂²×C₄⋊C₈	—	13	1	no	—
117	#1277	—	13	1	no	—
118	#1277	—	13	1	no	—
119	#1277	—	13	1	no	—
120	#1277	D₁₃	1	1	yes	characteristic, complemented
121	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂²×D₁₃	—	2	2	no	—
123	C₂²×D₁₃	—	2	1	no	—
124	C₂²×D₁₃	—	2	1	no	—
125	C₂²×D₁₃	#95	1	2	yes	—
126	C₂²×D₁₃	#108	1	4	yes	—
127	C₂×C₄×C₁₃	—	2	2	no	—
128	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
129	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃	C₂×C₄⋊C₄	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	#137	1	1	yes	characteristic
139	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
140	C₂×Dic₁₃	—	2	2	no	—
141	C₂×Dic₁₃	—	2	1	no	—
142	C₂×Dic₁₃	—	2	1	no	—
143	C₂×Dic₁₃	—	2	2	no	—
144	C₂×Dic₁₃	#95	1	2	yes	—
145	C₂×Dic₁₃	#95	1	2	yes	—
146	C₂×Dic₁₃	#95	1	2	yes	—
147	C₄×D₁₃	—	2	4	no	—
148	C₄×D₁₃	—	2	4	no	—
149	C₄×D₁₃	—	2	2	no	—
150	C₄×D₁₃	—	2	2	no	—
151	C₄×D₁₃	—	2	4	no	—
152	C₄×D₁₃	—	2	2	no	—
153	C₄×D₁₃	—	2	2	no	—
154	C₄×D₁₃	—	2	2	no	—
155	C₄×D₁₃	—	2	2	no	—
156	C₈×C₁₃	—	4	2	no	—
157	C₈×C₁₃	—	4	2	no	—
158	C₈×C₁₃	—	4	2	no	—
159	#1055	—	4	2	no	—
160	#1055	—	4	2	no	—
161	#1055	—	4	2	no	—
162	C₂³×C₈	—	26	1	no	—
163	C₂²×C₄²	—	13	1	no	—
164	#432	—	13	4	no	—
165	#432	—	26	2	no	—
166	#431	—	26	2	no	—
167	#431	—	26	2	no	—
168	C₂×C₄⋊C₈	—	13	1	no	—
169	C₂×C₄⋊C₈	—	13	1	no	—
170	C₂×C₄⋊C₈	—	13	4	no	—
171	C₂×C₄⋊C₈	—	13	2	no	—
172	C₂×C₄⋊C₈	—	26	2	no	—
173	C₂×C₄⋊C₈	—	26	1	no	—
174	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
175	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
176	C₂×C₂²⋊C₈	—	13	2	no	—
177	C₂×C₂²⋊C₈	—	26	1	no	—
178	C₂×#97	—	26	1	no	—
179	C₂×C₄×C₈	—	13	1	no	—
180	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
181	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
182	C₂²×C₁₃	#424	1	2	yes	—
183	C₂²×C₁₃	#428	1	1	yes	characteristic
184	C₂²×C₁₃	#428	1	1	yes	characteristic
185	C₂²×C₁₃	C₂×#108	1	2	yes	—
186	C₂×D₁₃	—	2	4	no	—
187	C₂×D₁₃	—	2	4	no	—
188	C₂×D₁₃	—	2	2	no	—
189	C₂×D₁₃	—	2	2	no	—
190	C₂×D₁₃	#341	1	4	yes	—
191	C₄×C₁₃	—	2	1	no	—
192	C₄×C₁₃	—	2	1	no	—
193	C₄×C₁₃	#405	1	1	yes	characteristic
194	C₄×C₁₃	#405	1	1	yes	characteristic
195	C₄×C₁₃	#408	1	2	yes	—
196	C₄×C₁₃	#417	1	1	yes	characteristic
197	C₄×C₁₃	#417	1	1	yes	characteristic
198	C₄×C₁₃	#418	1	1	yes	characteristic
199	C₄×C₁₃	#419	1	1	yes	characteristic
200	Dic₁₃	—	2	2	no	—
201	Dic₁₃	—	2	2	no	—
202	Dic₁₃	—	2	2	no	—
203	C₂³×C₄	—	13	1	no	—
204	C₂³×C₄	—	13	1	no	—
205	C₂³×C₄	—	13	1	no	—
206	C₂²×C₈	—	2	1	no	—
207	C₂²×C₈	—	2	1	no	—
208	C₂²×C₈	—	13	2	no	—
209	C₂²×C₈	—	26	4	no	—
210	C₂²×C₈	—	26	1	no	—
211	C₂²×C₈	—	26	1	no	—
212	C₂²×C₈	—	52	2	no	—
213	C₂²×C₈	—	52	2	no	—
214	C₂²×C₈	C₄×D₁₃	1	2	yes	—
215	C₂×C₄²	—	13	1	no	—
216	C₂×C₄²	—	13	1	no	—
217	C₂×C₄²	—	13	1	no	—
218	C₂×C₄²	—	13	2	no	—
219	C₂×C₄²	—	13	2	no	—
220	C₂×C₄²	—	13	2	no	—
221	C₂×C₄²	—	13	2	no	—
222	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
223	C₄⋊C₈	—	2	1	no	—
224	C₄⋊C₈	—	2	1	no	—
225	C₄⋊C₈	—	13	2	no	—
226	C₄⋊C₈	—	13	2	no	—
227	C₄⋊C₈	—	26	4	no	—
228	C₄⋊C₈	—	26	4	no	—
229	C₄⋊C₈	—	26	1	no	—
230	C₄⋊C₈	—	26	1	no	—
231	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
232	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
233	C₂²⋊C₈	—	26	4	no	—
234	C₂²⋊C₈	—	26	4	no	—
235	#97	—	26	4	no	—
236	C₄×C₈	—	2	1	no	—
237	C₄×C₈	—	2	1	no	—
238	C₄×C₈	—	26	1	no	—
239	C₄×C₈	—	26	1	no	—
240	C₂×C₁₃	#1573	1	2	yes	—
241	C₂×C₁₃	#1573	1	2	yes	—
242	C₂×C₁₃	#1729	1	1	yes	characteristic
243	C₂×C₁₃	#1736	1	1	yes	characteristic
244	C₂×C₁₃	C₂×#341	1	1	yes	characteristic
245	D₁₃	—	2	4	no	—
246	C₂⁴	—	13	1	no	—
247	C₂²×C₄	—	13	1	no	—
248	C₂²×C₄	—	13	1	no	—
249	C₂²×C₄	—	13	1	no	—
250	C₂²×C₄	—	13	2	no	—
251	C₂²×C₄	—	13	2	no	—
252	C₂²×C₄	—	13	2	no	—
253	C₂²×C₄	—	13	2	no	—
254	C₂²×C₄	—	13	2	no	—
255	C₂²×C₄	—	13	2	no	—
256	C₂²×C₄	—	26	4	no	—
257	C₂²×C₄	—	26	2	no	—
258	C₂²×C₄	—	26	2	no	—
259	C₂²×C₄	—	26	1	no	—
260	C₂²×C₄	—	26	1	no	—
261	C₂²×C₄	—	26	1	no	—
262	C₂²×C₄	—	26	1	no	—
263	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
264	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
265	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	4	1	no	—
272	C₂×C₈	—	4	1	no	—
273	C₂×C₈	—	4	1	no	—
274	C₂×C₈	—	4	1	no	—
275	C₂×C₈	—	26	2	no	—
276	C₂×C₈	—	26	2	no	—
277	C₂×C₈	—	26	2	no	—
278	C₂×C₈	—	26	2	no	—
279	C₂×C₈	—	26	2	no	—
280	C₂×C₈	—	52	8	no	—
281	C₂×C₈	—	52	1	no	—
282	C₂×C₈	—	52	1	no	—
283	C₂×C₈	—	52	1	no	—
284	C₂×C₈	—	52	1	no	—
285	C₄²	—	13	2	no	—
286	C₄²	—	13	2	no	—
287	C₄²	—	13	2	no	—
288	C₄²	—	13	2	no	—
289	C₄²	—	13	2	no	—
290	C₄²	—	13	2	no	—
291	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
292	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
293	C₄²	D₄×D₁₃	1	1	yes	characteristic
294	C₄²	D₄×D₁₃	1	1	yes	characteristic
295	C₁₃	#7879	1	1	yes	characteristic, complemented, Sylow
296	C₂³	—	13	4	no	—
297	C₂³	—	13	2	no	—
298	C₂³	—	26	2	no	—
299	C₂³	—	26	1	no	—
300	C₂³	—	26	1	no	—
301	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	13	2	no	—
304	C₂×C₄	—	13	2	no	—
305	C₂×C₄	—	13	2	no	—
306	C₂×C₄	—	26	4	no	—
307	C₂×C₄	—	26	4	no	—
308	C₂×C₄	—	26	2	no	—
309	C₂×C₄	—	26	1	no	—
310	C₂×C₄	—	26	1	no	—
311	C₂×C₄	—	26	2	no	—
312	C₂×C₄	—	26	2	no	—
313	C₂×C₄	—	26	2	no	—
314	C₂×C₄	—	26	2	no	—
315	C₂×C₄	—	26	2	no	—
316	C₂×C₄	—	26	2	no	—
317	C₂×C₄	—	26	2	no	—
318	C₂×C₄	—	26	4	no	—
319	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
320	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
321	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
322	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
323	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
324	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
325	C₂×C₄	#88155	1	2	yes	—
326	C₂×C₄	#88161	1	2	yes	—
327	C₂×C₄	#88165	1	1	yes	characteristic
328	C₂×C₄	#88168	1	1	yes	characteristic
329	C₂×C₄	#88169	1	1	yes	characteristic
330	C₂×C₄	#88172	1	1	yes	characteristic
331	C₈	—	4	2	no	—
332	C₈	—	4	2	no	—
333	C₈	—	4	2	no	—
334	C₈	—	52	2	no	—
335	C₈	—	52	2	no	—
336	C₈	—	52	2	no	—
337	C₂²	—	13	4	no	—
338	C₂²	—	26	4	no	—
339	C₂²	—	26	4	no	—
340	C₂²	—	26	2	no	—
341	C₂²	—	26	2	no	—
342	C₂²	D₁₃×#95	1	1	yes	characteristic
343	C₂²	#11718500	1	2	yes	—
344	C₂²	#11718522	1	1	yes	characteristic
345	C₂²	#11718542	1	1	yes	characteristic
346	C₂²	D₁₃×#108	1	2	yes	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	26	2	no	—
350	C₄	—	26	2	no	—
351	C₄	—	26	2	no	—
352	C₄	#11718350	1	1	yes	characteristic
353	C₄	#11718369	1	1	yes	characteristic
354	C₄	#11718388	1	2	yes	—
355	C₄	#11718431	1	1	yes	characteristic
356	C₄	#11718432	1	1	yes	characteristic
357	C₄	#11718463	1	1	yes	characteristic
358	C₄	#11718464	1	1	yes	characteristic
359	C₂	—	26	4	no	—
360	C₂	#13113618	1	2	yes	—
361	C₂	#13113620	1	2	yes	—
362	C₂	#13114531	1	1	yes	characteristic
363	C₂	#13114554	1	1	yes	characteristic
364	C₂	D₁₃×#341	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×#1277	C₂
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1277	D₁₃
hypocenter	C₁₃	#7879
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
4. #13112671	C₂	semidirect
5. #13112670	C₂	semidirect
6. #13112670	C₂	semidirect
7. C₁₃×#1277	C₂	semidirect
120. #1277	D₁₃	semidirect
295. C₁₃	#7879	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718496	2
C₂×#11718346	2
C₂×D₁₃×C₄⋊C₈	2
#13112671	2
#13112670	2
C₁₃×#1277	2
#7879	13