Subgroups — #16792739

Order 3328.

814 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131647	C₂	1	2	yes	maximal
2	#13130060	C₂	1	1	yes	maximal, characteristic, complemented
3	#13130059	C₂	1	1	yes	maximal, characteristic, complemented
4	#13130056	C₂	1	1	yes	maximal, characteristic, complemented
5	#13130055	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130044	C₂	1	2	yes	maximal, complemented
7	#13130040	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#6118	C₂	1	2	yes	maximal, complemented
9	C₈×#6122	C₂	1	2	yes	maximal, complemented
10	C₈×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#13123258	C₂	1	1	yes	maximal, characteristic
12	C₂×#88161	C₄	1	1	yes	characteristic
13	C₂×#88155	C₄	1	1	yes	characteristic
14	#11719227	C₂²	1	1	yes	characteristic
15	#11719125	C₂²	1	2	yes	—
16	C₄×#6122	C₂²	1	2	yes	—
17	#11719078	C₄	1	4	yes	—
18	#11719075	C₄	1	4	yes	—
19	#11719066	C₄	1	4	yes	—
20	#11719065	C₄	1	4	yes	—
21	#11719051	C₂²	1	2	yes	—
22	#11719049	C₂²	1	2	yes	—
23	C₄×#6118	C₂²	1	2	yes	—
24	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
25	C₁₃×#405	C₄	1	1	yes	characteristic
26	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
28	#11718658	C₄	1	1	yes	characteristic
29	#11718369	C₄	1	1	yes	characteristic
30	#11718369	C₄	1	1	yes	characteristic
31	#11718368	C₂²	1	1	yes	characteristic
32	#11718368	C₂²	1	1	yes	characteristic
33	#11718350	C₄	1	1	yes	characteristic
34	#11718350	C₄	1	1	yes	characteristic
35	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
36	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
37	#1057⋊C₈	C₂²	1	2	yes	—
38	#1057⋊C₈	C₂²	1	2	yes	—
39	#1057⋊C₈	C₂²	1	2	yes	—
40	#1057⋊C₈	C₂²	1	2	yes	—
41	#11718251	C₂²	1	1	yes	characteristic
42	#11718251	C₂²	1	1	yes	characteristic
43	C₈×#1057	C₂²	1	2	yes	—
44	C₈×#1057	C₂²	1	1	yes	characteristic
45	C₈×#1057	C₂²	1	1	yes	characteristic
46	C₈×#1057	C₂²	1	2	yes	—
47	C₂×#6127	C₂×C₄	1	1	yes	characteristic
48	C₂×#6122	C₂×C₄	1	4	yes	—
49	C₂×#6118	C₂×C₄	1	4	yes	—
50	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
51	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
55	C₂×#6099	C₂×C₄	1	1	yes	characteristic
56	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
57	#88161	—	2	4	no	—
58	#88155	—	2	4	no	—
59	C₂×#6094	C₂×C₄	1	1	yes	characteristic
60	C₂×#6094	C₂×C₄	1	1	yes	characteristic
61	C₂×#6094	C₂×C₄	1	1	yes	characteristic
62	C₂×#6094	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
67	#88147	C₂×C₄	1	2	yes	—
68	#88141	C₂×C₄	1	2	yes	—
69	#88135	C₂×C₄	1	2	yes	—
70	#88135	C₂×C₄	1	2	yes	—
71	#88126	C₂×C₄	1	1	yes	characteristic
72	#88126	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₁₃	C₂³	1	1	yes	characteristic
74	C₄²×D₁₃	C₂³	1	1	yes	characteristic
75	C₂²⋊#1057	C₂×C₄	1	4	yes	—
76	#88112	C₂×C₄	1	4	yes	—
77	#88112	C₂×C₄	1	4	yes	—
78	#88111	C₂×C₄	1	4	yes	—
79	#88111	C₂×C₄	1	4	yes	—
80	#88110	C₂×C₄	1	4	yes	—
81	#88110	C₂×C₄	1	4	yes	—
82	C₄⋊#1057	C₂×C₄	1	4	yes	—
83	C₄×#1057	C₂×C₄	1	4	yes	—
84	C₄×#1057	C₂³	1	2	yes	—
85	C₄×#1057	C₂³	1	2	yes	—
86	C₄×#1057	C₂³	1	2	yes	—
87	C₄×#1057	C₂³	1	2	yes	—
88	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
89	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
92	#88055	C₂×C₄	1	1	yes	characteristic
93	#88055	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
97	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
98	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
99	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
100	#88043	C₂×C₄	1	1	yes	characteristic
101	#88043	C₂×C₄	1	1	yes	characteristic
102	C₄×#1055	C₂×C₄	1	1	yes	characteristic
103	C₄×#1055	C₂×C₄	1	1	yes	characteristic
104	#17335	—	13	1	no	maximal, Sylow
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₁₃	C₄²	1	1	yes	characteristic
107	C₂×C₂²⋊D₁₃	C₄²	1	1	yes	characteristic
108	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
109	#6127	—	2	2	no	—
110	#6127	—	2	2	no	—
111	C₂×D₅₂	C₄²	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
115	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
117	#6122	—	2	8	no	—
118	C₂×#1057	C₂²×C₄	1	4	yes	—
119	C₂×#1057	C₂²×C₄	1	4	yes	—
120	C₂×#1057	C₂²×C₄	1	4	yes	—
121	C₂×#1057	C₂²×C₄	1	4	yes	—
122	#6118	—	2	8	no	—
123	D₁₃⋊C₈	—	2	8	no	—
124	C₁₃×M₁₆	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₁₃×C₄⋊C₄	C₄²	1	2	yes	—
131	C₁₃×C₂²⋊C₄	C₄²	1	2	yes	—
132	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	#6103	C₄²	1	2	yes	—
135	#6103	C₄²	1	2	yes	—
136	#6101	C₄²	1	2	yes	—
137	#6101	C₄²	1	2	yes	—
138	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
140	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
141	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
142	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
143	#6099	—	2	2	no	—
144	C₂×#1055	—	2	2	no	—
145	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
146	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
147	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
148	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
149	#6094	—	2	2	no	—
150	#6094	—	2	2	no	—
151	#6094	—	2	2	no	—
152	#6094	—	2	2	no	—
153	C₈×D₁₃	—	2	2	no	—
154	C₈×D₁₃	—	2	2	no	—
155	C₈×D₁₃	M₁₆	1	4	yes	complemented
156	C₈×D₁₃	M₁₆	1	4	yes	complemented
157	#2965	—	13	2	no	—
158	C₄×#131	—	13	1	no	—
159	#1455	—	13	1	no	—
160	#1455	—	13	1	no	—
161	#1453	—	13	1	no	—
162	#1453	—	13	1	no	—
163	#1451	—	13	2	no	—
164	#1450	—	13	1	no	—
165	C₈×M₁₆	—	13	2	no	—
166	C₈×M₁₆	—	13	2	no	—
167	C₂×C₈²	—	13	1	no	—
168	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
169	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
170	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
175	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
176	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
177	C₂²⋊D₁₃	—	2	2	no	—
178	C₂²⋊D₁₃	—	2	2	no	—
179	C₂×Dic₁₃	—	2	4	no	—
180	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
181	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
182	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
183	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
184	D₅₂	—	2	2	no	—
185	C₄×D₁₃	—	2	1	no	—
186	C₄×D₁₃	—	2	1	no	—
187	C₄×D₁₃	—	2	4	no	—
188	C₄×D₁₃	—	2	4	no	—
189	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
190	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
191	Dic₂₆	—	2	2	no	—
192	#1057	—	2	4	no	—
193	#1057	—	2	4	no	—
194	#1057	—	2	4	no	—
195	#1057	#131	1	8	yes	complemented
196	C₈×C₁₃	—	2	1	no	—
197	C₈×C₁₃	—	2	1	no	—
198	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
199	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
200	#1055	—	2	1	no	—
201	#1055	—	2	1	no	—
202	#1055	C₂×M₁₆	1	2	yes	—
203	#1055	C₂×M₁₆	1	2	yes	—
204	C₂×#131	—	13	1	no	—
205	C₂×#131	—	13	1	no	—
206	C₄×#41	—	13	1	no	—
207	#446	—	13	4	no	—
208	#436	—	13	4	no	—
209	#435	—	13	4	no	—
210	#435	—	13	4	no	—
211	#431	—	13	2	no	—
212	#431	—	13	2	no	—
213	#431	—	13	2	no	—
214	#405	—	13	1	no	—
215	#405	—	13	1	no	—
216	#405	—	13	1	no	—
217	#405	—	13	1	no	—
218	#405	—	13	1	no	—
219	#405	#261	1	1	yes	characteristic
220	C₄×M₁₆	—	13	2	no	—
221	C₄×M₁₆	—	13	2	no	—
222	C₄×M₁₆	—	13	1	no	—
223	C₄×M₁₆	—	13	1	no	—
224	C₄×M₁₆	—	13	1	no	—
225	C₂×C₄×C₈	—	13	2	no	—
226	C₂×C₄×C₈	—	13	1	no	—
227	C₂×C₄×C₈	—	13	1	no	—
228	C₂×C₄×C₈	—	13	1	no	—
229	#322	—	13	1	no	—
230	#322	—	13	1	no	—
231	#322	—	13	2	no	—
232	#322	—	13	2	no	—
233	#322	—	13	2	no	—
234	#322	—	13	2	no	—
235	C₈²	—	13	2	no	—
236	C₈²	—	13	1	no	—
237	C₈²	—	13	1	no	—
238	C₈²	—	13	2	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
242	C₂×D₁₃	—	2	2	no	—
243	C₂×D₁₃	—	2	1	no	—
244	C₂×D₁₃	—	2	2	no	—
245	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	2	2	no	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
250	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
251	Dic₁₃	—	2	1	no	—
252	Dic₁₃	—	2	2	no	—
253	Dic₁₃	C₄×M₁₆	1	2	yes	—
254	Dic₁₃	C₂×#131	1	4	yes	—
255	C₂×#41	—	13	1	no	—
256	#131	—	26	4	no	—
257	#131	—	26	4	no	—
258	C₂×M₁₆	—	13	4	no	—
259	C₂×M₁₆	—	13	4	no	—
260	C₂×M₁₆	—	13	1	no	—
261	C₂×M₁₆	—	13	1	no	—
262	C₂×M₁₆	—	13	1	no	—
263	C₂×M₁₆	—	13	1	no	—
264	C₂×M₁₆	—	13	1	no	—
265	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
266	C₂²×C₈	—	13	1	no	—
267	C₂²×C₈	—	13	1	no	—
268	C₂²×C₈	—	13	4	no	—
269	C₂²×C₈	—	13	1	no	—
270	C₂²×C₈	—	13	1	no	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	C₂×#261	1	1	yes	characteristic
273	C₄×Q₈	—	13	2	no	—
274	C₄×D₄	—	13	2	no	—
275	C₄×D₄	—	13	2	no	—
276	C₄×D₄	—	13	2	no	—
277	#117	—	13	1	no	—
278	#117	—	13	1	no	—
279	#117	C₂×#261	1	1	yes	characteristic
280	C₂×C₄²	—	13	1	no	—
281	C₂×C₄²	—	13	1	no	—
282	C₂×C₄²	—	13	1	no	—
283	C₄⋊C₈	—	13	4	no	—
284	C₄⋊C₈	—	13	4	no	—
285	C₄⋊C₈	—	13	4	no	—
286	C₂²⋊C₈	—	13	4	no	—
287	C₂²⋊C₈	—	13	4	no	—
288	C₂²⋊C₈	—	13	4	no	—
289	#97	—	13	4	no	—
290	#97	—	13	4	no	—
291	#97	—	13	1	no	—
292	#97	—	13	1	no	—
293	#97	—	13	1	no	—
294	#97	—	13	1	no	—
295	#97	C₂×#261	1	1	yes	characteristic
296	#97	C₂×#261	1	1	yes	characteristic
297	C₄×C₈	—	13	4	no	—
298	C₄×C₈	—	13	2	no	—
299	C₄×C₈	—	13	2	no	—
300	C₄×C₈	—	13	2	no	—
301	C₄×C₈	—	13	2	no	—
302	C₄×C₈	—	13	1	no	—
303	C₄×C₈	—	13	1	no	—
304	C₄×C₈	—	13	1	no	—
305	C₄×C₈	—	13	1	no	—
306	C₄×C₈	—	13	1	no	—
307	C₄×C₈	—	13	1	no	—
308	C₄×C₈	—	13	1	no	—
309	C₄×C₈	—	13	1	no	—
310	C₄×C₈	C₂×#261	1	1	yes	characteristic
311	C₄×C₈	C₂×#261	1	1	yes	characteristic
312	C₂×C₁₃	—	4	1	no	—
313	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
314	C₂×C₁₃	C₄×#131	1	2	yes	—
315	D₁₃	—	2	2	no	—
316	D₁₃	—	4	1	no	—
317	#41	—	26	2	no	—
318	#41	—	26	2	no	—
319	C₂×Q₈	—	13	1	no	—
320	C₂×D₄	—	13	1	no	—
321	C₂×D₄	—	13	1	no	—
322	C₂×D₄	—	13	1	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	13	2	no	—
325	C₂²×C₄	—	13	2	no	—
326	C₂²×C₄	—	13	2	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
329	M₁₆	—	2	2	no	—
330	M₁₆	—	26	2	no	—
331	M₁₆	—	26	2	no	—
332	M₁₆	—	26	2	no	—
333	M₁₆	—	26	2	no	—
334	M₁₆	—	26	8	no	—
335	M₁₆	—	26	8	no	—
336	M₁₆	—	26	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	13	4	no	—
339	C₂×C₈	—	13	1	no	—
340	C₂×C₈	—	13	1	no	—
341	C₂×C₈	—	13	4	no	—
342	C₂×C₈	—	13	4	no	—
343	C₂×C₈	—	13	4	no	—
344	C₂×C₈	—	13	4	no	—
345	C₂×C₈	—	13	4	no	—
346	C₂×C₈	—	13	1	no	—
347	C₂×C₈	—	13	1	no	—
348	C₂×C₈	—	26	2	no	—
349	C₂×C₈	—	26	2	no	—
350	C₂×C₈	—	26	8	no	—
351	C₂×C₈	—	26	2	no	—
352	C₂×C₈	C₂²×#261	1	1	yes	characteristic
353	C₂×C₈	C₂²×#261	1	1	yes	characteristic
354	C₂×C₈	C₂²×#261	1	1	yes	characteristic
355	C₂×C₈	C₂²×#261	1	1	yes	characteristic
356	C₄⋊C₄	—	13	2	no	—
357	C₄⋊C₄	—	13	2	no	—
358	C₄⋊C₄	C₄×#261	1	2	yes	—
359	C₂²⋊C₄	—	13	2	no	—
360	C₂²⋊C₄	—	13	2	no	—
361	C₂²⋊C₄	C₄×#261	1	2	yes	—
362	C₄²	—	13	2	no	—
363	C₄²	—	13	2	no	—
364	C₄²	—	13	2	no	—
365	C₄²	—	13	1	no	—
366	C₄²	—	13	1	no	—
367	C₄²	C₂²×#261	1	1	yes	characteristic
368	C₄²	C₂²×#261	1	1	yes	characteristic
369	C₁₃	#17335	1	1	yes	characteristic, complemented, Sylow
370	C₂³	—	13	1	no	—
371	C₂³	—	13	1	no	—
372	C₂³	C₂×C₄×#261	1	1	yes	characteristic
373	Q₈	—	26	2	no	—
374	D₄	—	26	2	no	—
375	D₄	—	26	2	no	—
376	D₄	—	26	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	13	2	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	13	2	no	—
382	C₂×C₄	—	13	2	no	—
383	C₂×C₄	—	13	2	no	—
384	C₂×C₄	—	13	1	no	—
385	C₂×C₄	—	26	4	no	—
386	C₂×C₄	—	26	4	no	—
387	C₂×C₄	—	26	4	no	—
388	C₂×C₄	—	26	1	no	—
389	C₂×C₄	—	26	1	no	—
390	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄×#261	1	2	yes	—
392	C₂×C₄	C₂×C₄×#261	1	2	yes	—
393	C₂×C₄	C₂³×#261	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	13	8	no	—
397	C₈	—	13	2	no	—
398	C₈	—	13	2	no	—
399	C₈	—	26	4	no	—
400	C₈	—	26	4	no	—
401	C₈	—	26	4	no	—
402	C₈	—	26	1	no	—
403	C₈	—	26	1	no	—
404	C₈	D₁₃⋊M₁₆	1	2	yes	—
405	C₈	D₁₃⋊M₁₆	1	2	yes	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	13	2	no	—
409	C₂²	—	26	2	no	—
410	C₂²	—	26	1	no	—
411	C₂²	—	26	2	no	—
412	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	13	2	no	—
417	C₄	—	13	4	no	—
418	C₄	—	26	1	no	—
419	C₄	—	26	2	no	—
420	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
421	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
422	C₂	—	4	1	no	—
423	C₂	—	26	2	no	—
424	C₂	—	52	1	no	—
425	C₂	C₄×D₁₃⋊M₁₆	1	1	yes	characteristic
426	C₂	#131×#261	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#405	C₄
prime radical	C₂×#6127	C₂×C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	#17335
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
2. #13130060	C₂	semidirect
3. #13130059	C₂	semidirect
4. #13130056	C₂	semidirect
5. #13130055	C₂	semidirect
6. #13130044	C₂	semidirect
7. #13130040	C₂	semidirect
8. C₈×#6118	C₂	semidirect
9. C₈×#6122	C₂	semidirect
10. C₈×D₁₃⋊C₈	C₂	semidirect
155. C₈×D₁₃	M₁₆	semidirect
156. C₈×D₁₃	M₁₆	semidirect
195. #1057	#131	semidirect
369. C₁₃	#17335	semidirect

Maximal subgroups

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

subgroup	index
#13131647	2
#13130060	2
#13130059	2
#13130056	2
#13130055	2
#13130044	2
#13130040	2
C₈×#6118	2
C₈×#6122	2
C₈×D₁₃⋊C₈	2
#13123258	2
#17335	13