Subgroups — #15755604

Order 3328.

588 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×Dic₂₆	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718076	C₂	1	2	yes	maximal
4	#13112675	C₂	1	2	yes	maximal
5	C₁₃×#1842	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₂₆	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₂₆	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
10	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
11	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
12	C₄³×C₁₃	C₂²	1	1	yes	characteristic
13	C₄×C₄⋊Dic₁₃	C₄	1	1	yes	characteristic
14	C₄×C₄⋊Dic₁₃	C₄	1	1	yes	characteristic
15	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
16	C₄×#6101	—	2	1	no	—
17	C₄×#6101	—	2	1	no	—
18	C₄×#6101	—	2	1	no	—
19	C₄²×Dic₁₃	—	2	1	no	—
20	C₂×C₄⋊#1055	—	2	1	no	—
21	C₂×C₄×#1055	C₂²	1	2	yes	—
22	#11718116	—	2	1	no	—
23	#11718076	—	2	4	no	—
24	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	—	2	2	no	—
26	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
33	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×#6101	—	2	1	no	—
37	C₂×#6101	—	2	1	no	—
38	C₂×#6101	—	2	1	no	—
39	C₂×C₄×Dic₁₃	—	2	1	no	—
40	C₂×C₄×Dic₁₃	—	2	1	no	—
41	C₂×C₄×Dic₁₃	—	2	1	no	—
42	C₂×C₄×Dic₁₃	—	2	1	no	—
43	C₂×C₄×Dic₁₃	—	2	1	no	—
44	C₂×C₄×Dic₁₃	—	2	1	no	—
45	C₂²×#1055	—	2	2	no	—
46	C₄×Dic₂₆	—	2	2	no	—
47	C₄×Dic₂₆	—	2	2	no	—
48	C₄×Dic₂₆	—	2	1	no	—
49	C₄×Dic₂₆	—	2	1	no	—
50	C₄×Dic₂₆	—	2	2	no	—
51	C₄×Dic₂₆	C₈	1	4	yes	complemented
52	C₄×Dic₂₆	D₄	1	2	yes	—
53	C₄×Dic₂₆	Q₈	1	2	yes	—
54	C₁₃×C₄⋊C₈	—	2	2	no	—
55	C₁₃×C₄⋊C₈	—	2	2	no	—
56	C₁₃×C₄⋊C₈	—	4	2	no	—
57	C₁₃×C₄⋊C₈	—	4	2	no	—
58	#88071	—	2	1	no	—
59	#88071	—	2	1	no	—
60	#88071	—	2	1	no	—
61	C₄⋊#1055	—	2	4	no	—
62	C₄×#1055	—	2	2	no	—
63	C₄×#1055	—	2	2	no	—
64	#8564	—	13	1	no	maximal, Sylow
65	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×Dic₁₃	—	2	1	no	—
73	C₂²×Dic₁₃	—	2	1	no	—
74	C₂²×Dic₁₃	—	2	1	no	—
75	C₂²×Dic₁₃	—	2	1	no	—
76	C₂×Dic₂₆	—	2	1	no	—
77	C₂×Dic₂₆	—	2	1	no	—
78	C₂×Dic₂₆	—	2	1	no	—
79	C₂×Dic₂₆	C₄⋊C₄	1	2	yes	—
80	C₂×Dic₂₆	C₂×C₈	1	2	yes	—
81	C₂×Dic₂₆	M₁₆	1	2	yes	—
82	C₂×C₈×C₁₃	—	4	2	no	—
83	C₂×C₈×C₁₃	—	4	2	no	—
84	C₂×C₈×C₁₃	—	4	2	no	—
85	C₄²×C₁₃	—	2	2	no	—
86	C₄²×C₁₃	—	2	1	no	—
87	C₄²×C₁₃	—	2	1	no	—
88	C₄²×C₁₃	—	2	1	no	—
89	C₄²×C₁₃	—	2	1	no	—
90	C₄²×C₁₃	—	4	1	no	—
91	C₄²×C₁₃	C₂×C₈	1	2	yes	—
92	C₄²×C₁₃	M₁₆	1	2	yes	—
93	C₄²×C₁₃	SD₁₆	1	2	yes	—
94	C₄²×C₁₃	Q₁₆	1	2	yes	—
95	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
97	C₄²×C₁₃	#41	1	1	yes	characteristic
98	C₄²×C₁₃	#41	1	1	yes	characteristic
99	C₄⋊Dic₁₃	—	2	1	no	—
100	C₄⋊Dic₁₃	—	2	1	no	—
101	C₄⋊Dic₁₃	—	2	1	no	—
102	C₄⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
103	C₄⋊Dic₁₃	C₂×C₈	1	2	yes	—
104	C₄⋊Dic₁₃	M₁₆	1	2	yes	—
105	#6101	—	2	4	no	—
106	#6101	—	2	4	no	—
107	#6101	—	2	2	no	—
108	#6101	—	2	2	no	—
109	C₄×Dic₁₃	—	2	4	no	—
110	C₄×Dic₁₃	—	2	4	no	—
111	C₄×Dic₁₃	—	2	2	no	—
112	C₄×Dic₁₃	—	2	2	no	—
113	C₄×Dic₁₃	—	4	2	no	—
114	C₄×Dic₁₃	—	4	2	no	—
115	C₄×Dic₁₃	—	4	1	no	—
116	C₄×Dic₁₃	—	4	1	no	—
117	C₂×#1055	—	2	4	no	—
118	C₂×#1055	—	4	2	no	—
119	C₂×#1055	—	4	2	no	—
120	C₄²×Q₈	—	13	1	no	—
121	#1842	D₁₃	1	1	yes	characteristic
122	C₄×C₄⋊C₈	—	13	1	no	—
123	C₂×Q₈⋊C₈	—	13	2	no	—
124	#1279	—	13	2	no	—
125	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₃	—	2	1	no	—
127	C₂×C₄×C₁₃	—	2	1	no	—
128	C₂×C₄×C₁₃	—	2	1	no	—
129	C₂×C₄×C₁₃	—	2	1	no	—
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	2	1	no	—
132	C₂×C₄×C₁₃	—	2	1	no	—
133	C₂×C₄×C₁₃	—	2	1	no	—
134	C₂×C₄×C₁₃	—	2	1	no	—
135	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
136	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
137	C₂×C₄×C₁₃	#103	1	2	yes	—
138	C₂×C₄×C₁₃	#103	1	2	yes	—
139	C₂×C₄×C₁₃	#104	1	2	yes	—
140	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
142	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
143	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
152	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
154	C₂×Dic₁₃	—	2	2	no	—
155	C₂×Dic₁₃	—	2	2	no	—
156	C₂×Dic₁₃	—	2	2	no	—
157	C₂×Dic₁₃	—	2	2	no	—
158	C₂×Dic₁₃	—	2	2	no	—
159	C₂×Dic₁₃	—	2	2	no	—
160	C₂×Dic₁₃	—	4	1	no	—
161	C₂×Dic₁₃	—	4	1	no	—
162	C₂×Dic₁₃	—	4	1	no	—
163	C₂×Dic₁₃	—	4	1	no	—
164	C₂×Dic₁₃	—	4	1	no	—
165	C₂×Dic₁₃	—	4	1	no	—
166	Dic₂₆	—	2	2	no	—
167	Dic₂₆	—	2	2	no	—
168	Dic₂₆	—	2	2	no	—
169	Dic₂₆	C₄⋊C₈	1	4	yes	complemented
170	C₈×C₁₃	—	8	2	no	—
171	#1055	—	4	4	no	—
172	C₂×C₄×Q₈	—	13	1	no	—
173	C₂×C₄×Q₈	—	13	1	no	—
174	C₂×C₄×Q₈	—	13	1	no	—
175	C₂×C₄⋊C₈	—	2	1	no	—
176	C₂×C₄⋊C₈	—	2	1	no	—
177	C₂×C₄⋊C₈	—	26	1	no	—
178	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
179	C₂×C₄×C₈	—	13	2	no	—
180	C₄×C₄⋊C₄	—	13	1	no	—
181	C₄×C₄⋊C₄	—	13	1	no	—
182	C₄×C₄⋊C₄	—	13	1	no	—
183	C₄×C₄⋊C₄	—	26	1	no	—
184	C₄×C₄⋊C₄	—	26	1	no	—
185	C₄×C₄⋊C₄	—	26	1	no	—
186	C₄³	—	26	1	no	—
187	C₄³	C₂×D₁₃	1	1	yes	characteristic
188	#336	—	26	1	no	—
189	Q₈⋊C₈	—	26	4	no	—
190	C₂²×C₁₃	#380	1	1	yes	characteristic
191	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
192	C₂²×C₁₃	#407	1	1	yes	characteristic
193	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
194	C₂²×C₁₃	#417	1	1	yes	characteristic
195	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
196	C₂²×C₁₃	#421	1	1	yes	characteristic
197	C₄×C₁₃	—	2	1	no	—
198	C₄×C₁₃	—	2	1	no	—
199	C₄×C₁₃	—	2	2	no	—
200	C₄×C₁₃	—	2	2	no	—
201	C₄×C₁₃	—	4	1	no	—
202	C₄×C₁₃	Q₈⋊C₈	1	4	yes	complemented
203	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
204	C₄×C₁₃	#423	1	1	yes	characteristic
205	C₄×C₁₃	#431	1	1	yes	characteristic
206	C₄×C₁₃	#432	1	1	yes	characteristic
207	C₄×C₁₃	#460	1	1	yes	characteristic
208	C₄×C₁₃	#462	1	1	yes	characteristic
209	C₄×C₁₃	#475	1	1	yes	characteristic
210	C₄×C₁₃	#477	1	1	yes	characteristic
211	Dic₁₃	—	2	4	no	—
212	Dic₁₃	—	4	2	no	—
213	Dic₁₃	—	4	2	no	—
214	Dic₁₃	—	4	2	no	—
215	C₂²×Q₈	—	13	1	no	—
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	—	26	2	no	—
218	C₄×Q₈	—	13	4	no	—
219	C₄×Q₈	—	13	2	no	—
220	C₄×Q₈	—	13	2	no	—
221	C₄×Q₈	—	26	2	no	—
222	C₄×Q₈	—	26	2	no	—
223	C₄×Q₈	—	26	2	no	—
224	C₄×Q₈	—	26	1	no	—
225	C₄×Q₈	—	26	1	no	—
226	C₂×C₄⋊C₄	—	13	1	no	—
227	C₂×C₄⋊C₄	—	13	1	no	—
228	C₂×C₄⋊C₄	—	13	1	no	—
229	C₂×C₄⋊C₄	—	26	1	no	—
230	C₂×C₄⋊C₄	—	26	1	no	—
231	C₂×C₄⋊C₄	—	26	1	no	—
232	C₂×C₄²	—	26	1	no	—
233	C₂×C₄²	—	26	1	no	—
234	C₂×C₄²	—	26	1	no	—
235	C₂×C₄²	—	26	1	no	—
236	C₂×C₄²	—	26	1	no	—
237	C₂×C₄²	—	26	1	no	—
238	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
239	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
240	C₂×C₄²	D₅₂	1	1	yes	characteristic
241	C₂×C₄²	D₅₂	1	1	yes	characteristic
242	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
243	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
244	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	—	4	2	no	—
248	C₄⋊C₈	—	4	2	no	—
249	C₄⋊C₈	—	26	4	no	—
250	C₄×C₈	—	26	2	no	—
251	C₄×C₈	—	26	2	no	—
252	#95	—	26	1	no	—
253	#95	—	26	1	no	—
254	#95	—	26	1	no	—
255	C₂×C₁₃	C₂×Q₈⋊C₈	1	1	yes	characteristic
256	C₂×C₁₃	#1477	1	1	yes	characteristic
257	C₂×C₁₃	#1487	1	1	yes	characteristic
258	C₂×C₁₃	#1489	1	1	yes	characteristic
259	C₂×C₁₃	#1797	1	1	yes	characteristic
260	C₂×C₁₃	#1803	1	1	yes	characteristic
261	C₂×C₁₃	#1806	1	1	yes	characteristic
262	C₂×Q₈	—	13	2	no	—
263	C₂×Q₈	—	13	2	no	—
264	C₂×Q₈	—	13	2	no	—
265	C₂×Q₈	—	26	1	no	—
266	C₂×Q₈	—	26	1	no	—
267	C₂×Q₈	—	26	1	no	—
268	C₂²×C₄	—	26	1	no	—
269	C₂²×C₄	—	26	1	no	—
270	C₂²×C₄	—	26	1	no	—
271	C₂²×C₄	—	26	1	no	—
272	C₂²×C₄	#6103	1	1	yes	characteristic
273	C₂²×C₄	#6103	1	1	yes	characteristic
274	C₂²×C₄	#6103	1	1	yes	characteristic
275	C₂²×C₄	#6103	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
279	C₂×C₈	—	4	2	no	—
280	C₂×C₈	—	4	2	no	—
281	C₂×C₈	—	4	2	no	—
282	C₂×C₈	—	26	4	no	—
283	C₂×C₈	—	52	2	no	—
284	C₂×C₈	—	52	2	no	—
285	C₄⋊C₄	—	13	2	no	—
286	C₄⋊C₄	—	13	2	no	—
287	C₄⋊C₄	—	13	2	no	—
288	C₄⋊C₄	—	26	4	no	—
289	C₄⋊C₄	—	26	1	no	—
290	C₄⋊C₄	—	26	2	no	—
291	C₄⋊C₄	—	26	2	no	—
292	C₄⋊C₄	—	26	1	no	—
293	C₄⋊C₄	—	26	1	no	—
294	C₄⋊C₄	—	26	4	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	4	1	no	—
301	C₄²	—	26	4	no	—
302	C₄²	—	26	2	no	—
303	C₄²	—	26	2	no	—
304	C₄²	—	26	4	no	—
305	C₄²	—	52	2	no	—
306	C₄²	—	52	2	no	—
307	C₄²	—	52	1	no	—
308	C₄²	—	52	1	no	—
309	C₄²	C₈×D₁₃	1	2	yes	—
310	C₄²	#6094	1	2	yes	—
311	C₄²	#6105	1	2	yes	—
312	C₄²	#6107	1	2	yes	—
313	C₄²	D₄×D₁₃	1	1	yes	characteristic
314	C₄²	#6129	1	1	yes	characteristic
315	C₄²	Q₈×D₁₃	1	1	yes	characteristic
316	C₄²	#6131	1	1	yes	characteristic
317	C₁₃	#8564	1	1	yes	characteristic, complemented, Sylow
318	C₂³	C₂×#6103	1	1	yes	characteristic
319	Q₈	—	13	4	no	—
320	Q₈	—	26	2	no	—
321	Q₈	—	26	2	no	—
322	Q₈	—	26	2	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	26	2	no	—
333	C₂×C₄	—	26	2	no	—
334	C₂×C₄	—	26	2	no	—
335	C₂×C₄	—	26	2	no	—
336	C₂×C₄	—	26	2	no	—
337	C₂×C₄	—	26	2	no	—
338	C₂×C₄	—	52	1	no	—
339	C₂×C₄	—	52	1	no	—
340	C₂×C₄	—	52	1	no	—
341	C₂×C₄	—	52	1	no	—
342	C₂×C₄	—	52	1	no	—
343	C₂×C₄	—	52	1	no	—
344	C₂×C₄	#88050	1	2	yes	—
345	C₂×C₄	#88050	1	2	yes	—
346	C₂×C₄	#88060	1	2	yes	—
347	C₂×C₄	#88060	1	2	yes	—
348	C₂×C₄	#88065	1	2	yes	—
349	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
350	C₂×C₄	#88146	1	1	yes	characteristic
351	C₂×C₄	#88149	1	1	yes	characteristic
352	C₂×C₄	#88151	1	1	yes	characteristic
353	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
354	C₂×C₄	C₂×#6094	1	1	yes	characteristic
355	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
356	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
357	C₂×C₄	#88186	1	1	yes	characteristic
358	C₂×C₄	C₂×#6105	1	1	yes	characteristic
359	C₂×C₄	#88192	1	1	yes	characteristic
360	C₂×C₄	#88196	1	1	yes	characteristic
361	C₂×C₄	C₂×#6107	1	1	yes	characteristic
362	C₂×C₄	#88200	1	1	yes	characteristic
363	C₈	—	8	2	no	—
364	C₈	—	52	4	no	—
365	C₂²	#11718627	1	1	yes	characteristic
366	C₂²	C₂×#88050	1	1	yes	characteristic
367	C₂²	#11718648	1	1	yes	characteristic
368	C₂²	C₂×#88060	1	1	yes	characteristic
369	C₂²	#11718787	1	1	yes	characteristic
370	C₂²	C₂×#88065	1	1	yes	characteristic
371	C₂²	#11718800	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	1	no	—
377	C₄	—	26	4	no	—
378	C₄	—	52	2	no	—
379	C₄	—	52	2	no	—
380	C₄	—	52	2	no	—
381	C₄	#11718076	1	4	yes	complemented
382	C₄	D₁₃×C₄⋊C₈	1	1	yes	characteristic
383	C₄	#11718494	1	1	yes	characteristic
384	C₄	#11718496	1	1	yes	characteristic
385	C₄	#11718498	1	1	yes	characteristic
386	C₄	#11718736	1	1	yes	characteristic
387	C₄	#11718751	1	1	yes	characteristic
388	C₄	#11718752	1	1	yes	characteristic
389	C₄	#11718755	1	1	yes	characteristic
390	C₂	C₂×#11718076	1	1	yes	characteristic
391	C₂	#13113221	1	1	yes	characteristic
392	C₂	#13113264	1	1	yes	characteristic
393	C₂	#13113273	1	1	yes	characteristic
394	C₂	#13114813	1	1	yes	characteristic
395	C₂	#13114838	1	1	yes	characteristic
396	C₂	#13114853	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1842	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1842	D₁₃
hypocenter	C₁₃	#8564
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

Complements

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

N	H ≅ G/N	type
51. C₄×Dic₂₆	C₈	semidirect
169. Dic₂₆	C₄⋊C₈	semidirect
202. C₄×C₁₃	Q₈⋊C₈	semidirect
317. C₁₃	#8564	semidirect
381. C₄	#11718076	semidirect

Maximal subgroups

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

subgroup	index
C₄²×Dic₂₆	2
C₄×C₄⋊#1055	2
C₂×#11718076	2
#13112675	2
C₁₃×#1842	2
#8564	13