Subgroups — #16792598

Order 3328.

966 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13130044	C₂	1	4	yes	maximal, complemented
4	#13130043	C₂	1	4	yes	maximal, complemented
5	#13130032	C₂	1	2	yes	maximal, complemented
6	#13130032	C₂	1	2	yes	maximal, complemented
7	C₄×M₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×D₁₃⋊C₈	C₄	1	2	yes	—
9	C₂×M₁₆×D₁₃	C₄	1	2	yes	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	#11719125	C₄	1	2	yes	—
12	D₁₃⋊(C₂²⋊C₈)	C₄	1	2	yes	—
13	#11719119	C₂²	1	2	yes	—
14	C₂×C₄×#1057	C₄	1	2	yes	—
15	C₂×C₄×#1057	C₂²	1	2	yes	—
16	#11719051	C₄	1	2	yes	—
17	D₁₃⋊(C₄⋊C₈)	C₄	1	2	yes	—
18	#11719049	C₂²	1	2	yes	—
19	C₄×D₁₃⋊C₈	C₄	1	2	yes	—
20	C₄×D₁₃⋊C₈	C₄	1	2	yes	—
21	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
24	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
25	C₄×C₁₃×M₁₆	C₄	1	1	yes	characteristic
26	M₁₆×Dic₁₃	C₂²	1	2	yes	—
27	C₄×#6099	C₄	1	1	yes	characteristic
28	#11718368	C₂²	1	2	yes	—
29	D₁₃×#97	C₄	1	2	yes	—
30	C₄×#6094	C₄	1	2	yes	—
31	C₄×C₈×D₁₃	C₂²	1	2	yes	—
32	#1057⋊C₈	C₂²	1	8	yes	complemented
33	#1057⋊C₈	C₂²	1	8	yes	complemented
34	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×#1057	C₂×C₄	1	4	yes	—
38	C₂×D₁₃⋊C₈	—	2	8	no	—
39	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
40	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
41	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
42	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
48	C₂×#6099	C₂×C₄	1	2	yes	—
49	M₁₆×D₁₃	—	2	8	no	—
50	C₂×#6094	C₂×C₄	1	4	yes	—
51	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
52	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂³	1	1	yes	characteristic
59	C₄²×D₁₃	C₂³	1	1	yes	characteristic
60	C₂²⋊#1057	C₂×C₄	1	4	yes	—
61	#88112	C₂×C₄	1	4	yes	—
62	#88111	C₂×C₄	1	4	yes	—
63	C₄⋊#1057	C₂×C₄	1	4	yes	—
64	C₄×#1057	C₂×C₄	1	4	yes	—
65	C₄×#1057	C₂×C₄	1	2	yes	—
66	C₄×#1057	C₂×C₄	1	4	yes	—
67	C₄×#1057	C₂×C₄	1	2	yes	—
68	C₄×#1057	C₂×C₄	1	4	yes	—
69	C₄×#1057	C₂³	1	2	yes	—
70	C₄×#1057	C₂³	1	2	yes	—
71	C₄×#1057	C₂³	1	4	yes	—
72	C₁₃×#97	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
74	#88055	C₂×C₄	1	4	yes	—
75	C₈×Dic₁₃	C₂³	1	4	yes	—
76	#88043	C₂×C₄	1	2	yes	—
77	C₄×#1055	C₂×C₄	1	2	yes	—
78	C₂×#1451	—	13	1	no	maximal, Sylow
79	C₂³×D₁₃	C₄²	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
84	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₃	—	2	4	no	—
87	C₂×C₄×D₁₃	—	2	4	no	—
88	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
94	C₂×C₄×D₁₃	M₁₆	1	8	yes	—
95	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×#1057	—	2	8	no	—
102	C₂×#1057	C₂²×C₄	1	4	yes	—
103	C₂×#1057	C₂²×C₄	1	8	yes	—
104	C₂×#1057	C₂²×C₄	1	4	yes	—
105	D₁₃⋊C₈	—	2	4	no	—
106	D₁₃⋊C₈	—	2	8	no	—
107	D₁₃⋊C₈	—	2	8	no	—
108	D₁₃⋊C₈	M₁₆	1	8	yes	complemented
109	C₁₃×M₁₆	—	2	4	no	—
110	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
111	C₄²×C₁₃	C₄²	1	1	yes	characteristic
112	C₄²×C₁₃	C₄²	1	1	yes	characteristic
113	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
116	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
117	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
118	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
119	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
127	#6099	—	2	4	no	—
128	C₂×#1055	C₂²×C₄	1	4	yes	—
129	#6094	—	2	8	no	—
130	C₈×D₁₃	—	2	8	no	—
131	C₂×#431	—	13	1	no	—
132	C₂×C₄×M₁₆	—	13	1	no	—
133	C₂²×C₄×C₈	—	13	1	no	—
134	#1451	—	13	4	no	—
135	#1451	—	13	4	no	—
136	C₂×#322	—	13	2	no	—
137	C₂×#322	—	13	2	no	—
138	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
139	C₂²×D₁₃	—	2	2	no	—
140	C₂²×D₁₃	—	2	2	no	—
141	C₂²×D₁₃	#97	1	4	yes	—
142	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
143	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
152	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
153	C₂×Dic₁₃	—	2	2	no	—
154	C₂×Dic₁₃	—	2	2	no	—
155	C₂×Dic₁₃	#97	1	4	yes	—
156	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
157	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
160	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
162	C₄×D₁₃	—	2	2	no	—
163	C₄×D₁₃	—	2	2	no	—
164	C₄×D₁₃	—	2	2	no	—
165	C₄×D₁₃	—	2	2	no	—
166	C₄×D₁₃	—	2	2	no	—
167	C₄×D₁₃	—	2	2	no	—
168	C₄×D₁₃	#97	1	4	yes	—
169	C₄×D₁₃	#97	1	4	yes	—
170	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
171	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
172	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
173	C₄×D₁₃	#131	1	4	yes	—
174	#1057	—	2	4	no	—
175	#1057	—	2	8	no	—
176	#1057	C₂×M₁₆	1	8	yes	complemented
177	C₈×C₁₃	—	2	4	no	—
178	#1055	—	2	4	no	—
179	C₂²×M₁₆	—	13	2	no	—
180	C₂³×C₈	—	13	2	no	—
181	C₂²×C₄²	—	13	1	no	—
182	#431	—	13	2	no	—
183	#431	—	13	2	no	—
184	#431	—	13	2	no	—
185	#431	—	13	2	no	—
186	C₂×C₄⋊C₈	—	13	2	no	—
187	C₂×C₂²⋊C₈	—	13	2	no	—
188	C₄×M₁₆	—	13	2	no	—
189	C₄×M₁₆	—	13	1	no	—
190	C₄×M₁₆	—	13	2	no	—
191	C₄×M₁₆	—	13	2	no	—
192	C₄×M₁₆	#261	1	1	yes	characteristic
193	C₂×#97	—	13	2	no	—
194	C₂×C₄×C₈	—	13	2	no	—
195	C₂×C₄×C₈	—	13	2	no	—
196	C₂×C₄×C₈	—	13	1	no	—
197	C₂×C₄×C₈	—	13	1	no	—
198	C₂×C₄×C₈	—	13	2	no	—
199	C₂×C₄×C₈	—	13	2	no	—
200	C₂×C₄×C₈	—	13	2	no	—
201	C₂×C₄×C₈	—	13	2	no	—
202	C₂×C₄×C₈	—	13	2	no	—
203	#322	—	13	8	no	—
204	#322	—	13	8	no	—
205	C₂²×C₁₃	—	2	1	no	—
206	C₂²×C₁₃	—	2	1	no	—
207	C₂²×C₁₃	C₂×#97	1	2	yes	—
208	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
209	C₂×D₁₃	—	2	1	no	—
210	C₂×D₁₃	—	2	1	no	—
211	C₂×D₁₃	—	2	8	no	—
212	C₂×D₁₃	C₂×#97	1	2	yes	—
213	C₂×D₁₃	C₂×#97	1	2	yes	—
214	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
215	C₂×D₁₃	#405	1	2	yes	—
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	—	2	1	no	—
218	C₄×C₁₃	C₂×#97	1	2	yes	—
219	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
220	C₄×C₁₃	#405	1	2	yes	—
221	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
222	Dic₁₃	—	2	1	no	—
223	Dic₁₃	—	2	1	no	—
224	Dic₁₃	C₂×#97	1	2	yes	—
225	Dic₁₃	C₂×#97	1	2	yes	—
226	Dic₁₃	C₂²×M₁₆	1	2	yes	—
227	Dic₁₃	C₂×#131	1	2	yes	—
228	C₂³×C₄	—	13	1	no	—
229	C₂³×C₄	—	13	1	no	—
230	C₂³×C₄	—	13	1	no	—
231	C₂×M₁₆	—	13	2	no	—
232	C₂×M₁₆	—	13	4	no	—
233	C₂×M₁₆	—	26	8	no	—
234	C₂×M₁₆	C₂×#261	1	2	yes	—
235	C₂²×C₈	—	13	2	no	—
236	C₂²×C₈	—	13	4	no	—
237	C₂²×C₈	—	13	2	no	—
238	C₂²×C₈	—	13	4	no	—
239	C₂²×C₈	—	13	4	no	—
240	C₂²×C₈	—	13	4	no	—
241	C₂²×C₈	—	26	8	no	—
242	C₂×C₄²	—	13	1	no	—
243	C₂×C₄²	—	13	1	no	—
244	C₂×C₄²	—	13	1	no	—
245	C₂×C₄²	—	13	1	no	—
246	C₂×C₄²	—	13	1	no	—
247	C₂×C₄²	—	13	1	no	—
248	C₂×C₄²	—	13	1	no	—
249	C₂×C₄²	—	13	1	no	—
250	C₂×C₄²	—	13	1	no	—
251	C₂×C₄²	—	13	1	no	—
252	C₂×C₄²	—	13	1	no	—
253	C₂×C₄²	C₂×#261	1	1	yes	characteristic
254	C₄⋊C₈	—	13	4	no	—
255	C₄⋊C₈	—	13	4	no	—
256	C₂²⋊C₈	—	13	4	no	—
257	C₂²⋊C₈	—	13	4	no	—
258	#97	—	13	4	no	—
259	#97	—	13	2	no	—
260	#97	C₂×#261	1	2	yes	—
261	C₄×C₈	—	13	2	no	—
262	C₄×C₈	—	13	4	no	—
263	C₄×C₈	—	13	4	no	—
264	C₄×C₈	—	13	2	no	—
265	C₄×C₈	—	13	4	no	—
266	C₄×C₈	—	13	2	no	—
267	C₄×C₈	—	13	2	no	—
268	C₄×C₈	—	13	4	no	—
269	C₄×C₈	—	13	4	no	—
270	C₄×C₈	—	13	2	no	—
271	C₄×C₈	C₂×#261	1	2	yes	—
272	C₂×C₁₃	—	2	2	no	—
273	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
274	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
275	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
276	D₁₃	—	2	2	no	—
277	D₁₃	#1451	1	4	yes	complemented
278	C₂⁴	—	13	1	no	—
279	C₂²×C₄	—	13	1	no	—
280	C₂²×C₄	—	13	8	no	—
281	C₂²×C₄	—	13	1	no	—
282	C₂²×C₄	—	13	1	no	—
283	C₂²×C₄	—	13	1	no	—
284	C₂²×C₄	—	13	1	no	—
285	C₂²×C₄	—	13	1	no	—
286	C₂²×C₄	—	13	1	no	—
287	C₂²×C₄	—	13	1	no	—
288	C₂²×C₄	—	13	1	no	—
289	C₂²×C₄	—	13	1	no	—
290	C₂²×C₄	—	13	1	no	—
291	C₂²×C₄	—	13	1	no	—
292	C₂²×C₄	—	13	1	no	—
293	C₂²×C₄	—	13	1	no	—
294	C₂²×C₄	—	13	1	no	—
295	C₂²×C₄	—	26	4	no	—
296	C₂²×C₄	—	26	4	no	—
297	C₂²×C₄	C₄×#261	1	1	yes	characteristic
298	C₂²×C₄	C₄×#261	1	1	yes	characteristic
299	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
300	M₁₆	—	2	4	no	—
301	M₁₆	—	26	8	no	—
302	M₁₆	—	26	4	no	—
303	C₂×C₈	—	13	4	no	—
304	C₂×C₈	—	13	8	no	—
305	C₂×C₈	—	13	4	no	—
306	C₂×C₈	—	13	8	no	—
307	C₂×C₈	—	13	4	no	—
308	C₂×C₈	—	26	8	no	—
309	C₂×C₈	—	26	8	no	—
310	C₂×C₈	—	26	8	no	—
311	C₂×C₈	—	26	4	no	—
312	C₂×C₈	—	26	8	no	—
313	C₂×C₈	C₂²×#261	1	4	yes	—
314	C₄²	—	13	1	no	—
315	C₄²	—	13	1	no	—
316	C₄²	—	13	1	no	—
317	C₄²	—	13	1	no	—
318	C₄²	—	13	1	no	—
319	C₄²	—	13	1	no	—
320	C₄²	—	13	1	no	—
321	C₄²	—	13	1	no	—
322	C₄²	—	13	1	no	—
323	C₄²	—	13	1	no	—
324	C₄²	—	13	1	no	—
325	C₄²	—	13	1	no	—
326	C₄²	C₄×#261	1	1	yes	characteristic
327	C₄²	C₄×#261	1	1	yes	characteristic
328	C₄²	C₂²×#261	1	1	yes	characteristic
329	C₄²	C₂²×#261	1	1	yes	characteristic
330	C₁₃	C₂×#1451	1	1	yes	characteristic, complemented, Sylow
331	C₂³	—	13	1	no	—
332	C₂³	—	13	4	no	—
333	C₂³	—	13	1	no	—
334	C₂³	—	26	2	no	—
335	C₂³	—	26	2	no	—
336	C₂³	C₂×C₄×#261	1	1	yes	characteristic
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	13	4	no	—
340	C₂×C₄	—	13	1	no	—
341	C₂×C₄	—	13	1	no	—
342	C₂×C₄	—	13	1	no	—
343	C₂×C₄	—	13	1	no	—
344	C₂×C₄	—	13	4	no	—
345	C₂×C₄	—	13	4	no	—
346	C₂×C₄	—	13	4	no	—
347	C₂×C₄	—	13	4	no	—
348	C₂×C₄	—	13	4	no	—
349	C₂×C₄	—	13	4	no	—
350	C₂×C₄	—	13	1	no	—
351	C₂×C₄	—	13	1	no	—
352	C₂×C₄	—	26	2	no	—
353	C₂×C₄	—	26	2	no	—
354	C₂×C₄	—	26	2	no	—
355	C₂×C₄	—	26	2	no	—
356	C₂×C₄	—	26	2	no	—
357	C₂×C₄	—	26	2	no	—
358	C₂×C₄	—	26	2	no	—
359	C₂×C₄	—	26	2	no	—
360	C₂×C₄	D₁₃⋊M₁₆	1	4	yes	—
361	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
364	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
365	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
366	C₂×C₄	C₂³×#261	1	1	yes	characteristic
367	C₈	—	2	4	no	—
368	C₈	—	13	8	no	—
369	C₈	—	26	4	no	—
370	C₈	—	26	8	no	—
371	C₈	—	26	4	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	13	2	no	—
375	C₂²	—	13	2	no	—
376	C₂²	—	13	2	no	—
377	C₂²	—	13	2	no	—
378	C₂²	—	26	8	no	—
379	C₂²	—	26	1	no	—
380	C₂²	—	26	1	no	—
381	C₂²	#11719047	1	2	yes	—
382	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	13	2	no	—
386	C₄	—	13	2	no	—
387	C₄	—	13	2	no	—
388	C₄	—	13	2	no	—
389	C₄	—	26	1	no	—
390	C₄	—	26	1	no	—
391	C₄	#11719047	1	2	yes	—
392	C₄	M₁₆×#261	1	2	yes	—
393	C₄	#11719099	1	2	yes	—
394	C₄	C₂×D₁₃⋊M₁₆	1	2	yes	—
395	C₂	—	2	2	no	—
396	C₂	—	13	4	no	—
397	C₂	—	26	2	no	—
398	C₂	C₂×#11719047	1	1	yes	characteristic
399	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
400	C₂	C₂×#11719099	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₄×C₁₃×M₁₆	C₄
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₄×M₁₆	#261
hypocenter	C₁₃	C₂×#1451
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13130044	C₂	semidirect
4. #13130043	C₂	semidirect
5. #13130032	C₂	semidirect
6. #13130032	C₂	semidirect
32. #1057⋊C₈	C₂²	semidirect
33. #1057⋊C₈	C₂²	semidirect
108. D₁₃⋊C₈	M₁₆	semidirect
176. #1057	C₂×M₁₆	semidirect
277. D₁₃	#1451	semidirect
330. C₁₃	C₂×#1451	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#431	2
C₂×C₄×D₁₃⋊C₈	2
#13130044	2
#13130043	2
#13130032	2
C₄×M₁₆×D₁₃	2
C₂×#1451	13