Subgroups — #16797176

Order 3328.

1018 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#430	C₂	1	1	yes	maximal, characteristic
2	#13131489	C₂	1	1	yes	maximal, characteristic
3	C₂×#11719089	C₂	1	2	yes	maximal
4	#13130642	C₂	1	4	yes	maximal, complemented
5	#13130638	C₂	1	4	yes	maximal, complemented
6	#13130517	C₂	1	2	yes	maximal
7	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
8	C₂×#88237	C₂²	1	2	yes	—
9	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
10	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	D₁₃×#117	C₂²	1	1	yes	characteristic
13	#11719100	C₄	1	8	yes	complemented
14	#11719098	C₄	1	8	yes	complemented
15	D₁₃⋊#108	C₂²	1	4	yes	—
16	#11719092	C₂²	1	4	yes	—
17	#11719089	—	2	2	no	—
18	#11719089	—	2	2	no	—
19	#11719089	C₂²	1	4	yes	—
20	#11719089	C₂²	1	4	yes	—
21	C₂×#88100	—	2	2	no	—
22	C₂×C₈×#261	—	2	2	no	—
23	C₁₃×#405	C₄	1	1	yes	characteristic, complemented
24	#11718783	C₄	1	1	yes	characteristic, complemented
25	#11718762	C₄	1	1	yes	characteristic, complemented
26	#11718658	C₄	1	1	yes	characteristic, complemented
27	#11718369	C₄	1	2	yes	complemented
28	D₁₃×#97	C₂²	1	2	yes	—
29	#11718350	C₄	1	2	yes	complemented
30	C₄×C₈×D₁₃	C₂²	1	2	yes	—
31	#11718234	C₂²	1	8	yes	—
32	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
33	C₂×C₂²⋊#261	—	2	2	no	—
34	C₂×#6122	—	2	2	no	—
35	#88237	—	2	2	no	—
36	#88237	—	2	2	no	—
37	#88237	C₂×C₄	1	4	yes	—
38	#88237	C₂³	1	4	yes	—
39	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
40	C₂×C₄×#261	—	2	2	no	—
41	D₁₃⋊M₁₆	—	2	2	no	—
42	D₁₃⋊M₁₆	—	2	2	no	—
43	D₁₃⋊M₁₆	C₂×C₄	1	4	yes	—
44	D₁₃⋊M₁₆	C₂³	1	4	yes	—
45	C₂×#6118	C₂×C₄	1	4	yes	—
46	C₂×D₁₃⋊C₈	—	2	2	no	—
47	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
50	#88180	C₂×C₄	1	1	yes	characteristic
51	C₂×#6099	C₂×C₄	1	1	yes	characteristic
52	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
53	M₁₆×D₁₃	C₂×C₄	1	4	yes	—
54	M₁₆×D₁₃	C₂×C₄	1	4	yes	—
55	C₂×#6094	C₂×C₄	1	2	yes	—
56	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₁₃	D₄	1	2	yes	—
59	C₂×C₈×D₁₃	D₄	1	2	yes	—
60	C₂×C₈×D₁₃	Q₈	1	2	yes	—
61	C₂×C₈×D₁₃	Q₈	1	2	yes	—
62	C₂×C₈×D₁₃	C₂³	1	2	yes	—
63	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
65	#88146	—	2	1	no	—
66	C₄⋊C₄×D₁₃	—	2	1	no	—
67	C₂²⋊C₄×D₁₃	—	2	1	no	—
68	#88131	—	2	1	no	—
69	#88126	C₂×C₄	1	2	yes	—
70	C₄²×D₁₃	C₂³	1	2	yes	—
71	#88104	C₂×C₄	1	8	yes	complemented
72	#88103	C₂×C₄	1	8	yes	complemented
73	#88102	C₂×C₄	1	8	yes	—
74	#88101	C₂×C₄	1	8	yes	—
75	#88100	—	2	4	no	—
76	#88100	—	2	4	no	—
77	C₈×#261	—	2	4	no	—
78	C₈×#261	—	2	4	no	—
79	C₁₃×#97	C₂×C₄	1	2	yes	complemented
80	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
81	#88055	C₂×C₄	1	2	yes	complemented
82	#88055	C₂×C₄	1	2	yes	complemented
83	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
84	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
85	#88043	C₂×C₄	1	2	yes	complemented
86	C₄×#1055	C₂×C₄	1	2	yes	complemented
87	#20444	—	13	1	no	maximal, Sylow
88	C₂³×D₁₃	#41	1	1	yes	characteristic
89	C₂²×#261	—	2	4	no	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×Dic₁₃	#41	1	1	yes	characteristic
92	C₂×C₄×D₁₃	—	2	2	no	—
93	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
95	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
96	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
97	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
98	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
99	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
101	C₂²⋊#261	—	2	4	no	—
102	C₂²⋊#261	—	2	4	no	—
103	#6122	—	2	4	no	—
104	#6122	—	2	4	no	—
105	C₂×#1057	—	2	4	no	—
106	C₄⋊#261	—	2	4	no	—
107	C₄⋊#261	C₂²×C₄	1	8	yes	—
108	C₄×#261	—	2	4	no	—
109	C₄×#261	—	2	4	no	—
110	#6118	—	2	4	no	—
111	#6118	C₂²×C₄	1	8	yes	—
112	D₁₃⋊C₈	—	2	4	no	—
113	D₁₃⋊C₈	—	2	4	no	—
114	C₁₃×M₁₆	C₄²	1	4	yes	—
115	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
116	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂²⋊Dic₁₃	—	2	1	no	—
124	#6103	—	2	2	no	—
125	C₄⋊Dic₁₃	—	2	1	no	—
126	#6101	—	2	2	no	—
127	C₄×Dic₁₃	—	2	2	no	—
128	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
129	#6099	C₄²	1	4	yes	—
130	C₂×#1055	C₄⋊C₄	1	2	yes	—
131	C₂×#1055	C₄⋊C₄	1	2	yes	—
132	C₂×#1055	C₂²×C₄	1	2	yes	—
133	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
134	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
135	#6094	C₄²	1	8	yes	—
136	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
137	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
138	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
139	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
140	C₈×D₁₃	C₂²×C₄	1	4	yes	—
141	C₈×D₁₃	C₂²×C₄	1	4	yes	—
142	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
143	C₈×D₁₃	C₂×D₄	1	2	yes	—
144	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
145	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
146	C₈×D₁₃	C₂×Q₈	1	2	yes	—
147	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
148	C₂×#430	—	13	1	no	—
149	#2911	—	13	1	no	—
150	C₂×#405	—	13	1	no	—
151	C₂×#405	—	13	2	no	—
152	#1773	—	13	4	no	—
153	#1772	—	13	4	no	—
154	#1733	—	13	2	no	—
155	C₂³×C₁₃	#117	1	1	yes	characteristic
156	C₂²×D₁₃	—	4	2	no	—
157	C₂²×D₁₃	#117	1	1	yes	characteristic
158	C₂²×D₁₃	C₄×D₄	1	2	yes	—
159	C₂²×D₁₃	C₄×Q₈	1	2	yes	—
160	C₂²×D₁₃	C₂×#41	1	1	yes	characteristic
161	C₂×#261	—	2	8	no	—
162	C₂×#261	—	4	8	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×Dic₁₃	—	2	2	no	—
169	C₂×Dic₁₃	#117	1	1	yes	characteristic
170	C₂×Dic₁₃	C₄×D₄	1	2	yes	—
171	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
172	C₂×Dic₁₃	C₂×#41	1	1	yes	characteristic
173	C₄×D₁₃	—	4	4	no	—
174	C₄×D₁₃	C₂×C₄²	1	2	yes	—
175	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
176	C₄×D₁₃	C₄×D₄	1	2	yes	—
177	C₄×D₁₃	C₄×D₄	1	2	yes	—
178	C₄×D₁₃	C₄×Q₈	1	2	yes	—
179	C₄×D₁₃	C₄×Q₈	1	2	yes	—
180	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
181	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
182	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
183	C₄×D₁₃	C₂²×Q₈	1	1	yes	characteristic
184	#1057	—	2	8	no	—
185	C₈×C₁₃	C₂×C₄²	1	4	yes	—
186	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
187	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	#1055	C₂×C₄²	1	4	yes	—
190	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
191	#1055	C₂×C₄⋊C₄	1	2	yes	—
192	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×M₁₆	—	13	1	no	—
194	C₂²×M₁₆	—	13	2	no	—
195	C₂³×C₈	—	13	1	no	—
196	C₂×#117	—	13	1	no	—
197	C₂×#117	—	13	2	no	—
198	#430	—	13	8	no	—
199	C₂×#108	—	13	4	no	—
200	#428	—	13	8	no	—
201	#427	—	13	4	no	—
202	#405	—	13	1	no	—
203	#405	—	13	1	no	—
204	#405	—	13	1	no	—
205	#405	—	13	2	no	—
206	#405	—	13	2	no	—
207	#405	—	13	4	no	—
208	#405	—	13	4	no	—
209	#405	—	26	2	no	—
210	#405	—	26	2	no	—
211	#405	#261	1	1	yes	characteristic, complemented
212	C₂×#97	—	13	2	no	—
213	C₂×#97	—	26	2	no	—
214	C₂×C₄×C₈	—	13	2	no	—
215	C₂×C₄×C₈	—	26	2	no	—
216	#339	—	13	8	no	—
217	C₂²×C₁₃	—	4	1	no	—
218	C₂²×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
219	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
220	C₂×D₁₃	—	2	2	no	—
221	C₂×D₁₃	—	2	4	no	—
222	C₂×D₁₃	—	4	1	no	—
223	C₂×D₁₃	—	4	2	no	—
224	C₂×D₁₃	C₄×C₄⋊C₄	1	2	yes	—
225	C₂×D₁₃	C₂×C₄×D₄	1	1	yes	characteristic
226	C₂×D₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
227	#261	—	4	8	no	—
228	C₄×C₁₃	—	4	2	no	—
229	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
230	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
231	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
232	Dic₁₃	—	4	2	no	—
233	Dic₁₃	C₄×C₄⋊C₄	1	2	yes	—
234	Dic₁₃	C₂×C₄×D₄	1	1	yes	characteristic
235	Dic₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
236	C₂³×C₄	—	13	1	no	—
237	C₂×M₁₆	—	13	1	no	—
238	C₂×M₁₆	—	13	4	no	—
239	C₂×M₁₆	—	13	4	no	—
240	C₂×M₁₆	—	13	2	no	—
241	C₂×M₁₆	—	13	4	no	—
242	C₂×M₁₆	—	13	4	no	—
243	C₂×M₁₆	—	13	4	no	—
244	C₂×M₁₆	—	26	2	no	—
245	C₂×M₁₆	—	26	2	no	—
246	C₂×M₁₆	—	26	2	no	—
247	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
248	C₂²×C₈	—	13	1	no	—
249	C₂²×C₈	—	13	2	no	—
250	C₂²×C₈	—	13	2	no	—
251	C₂²×C₈	—	13	2	no	—
252	C₂²×C₈	—	13	2	no	—
253	C₂²×C₈	—	13	1	no	—
254	C₂²×C₈	—	13	1	no	—
255	C₂²×C₈	—	13	1	no	—
256	C₂²×C₈	—	13	1	no	—
257	C₂²×C₈	—	13	2	no	—
258	C₂²×C₈	—	26	2	no	—
259	C₂²×C₈	C₂×#261	1	1	yes	characteristic
260	#117	—	13	1	no	—
261	#117	—	13	2	no	—
262	#117	—	13	4	no	—
263	#117	—	13	4	no	—
264	#117	—	26	1	no	—
265	#117	—	26	1	no	—
266	#117	—	26	2	no	—
267	#117	—	26	2	no	—
268	#117	C₂×#261	1	1	yes	characteristic
269	C₂×C₄⋊C₄	—	13	4	no	—
270	C₂×C₄⋊C₄	—	26	1	no	—
271	C₂×C₂²⋊C₄	—	26	1	no	—
272	C₂×C₂²⋊C₄	—	26	2	no	—
273	C₂×C₄²	—	13	2	no	—
274	C₂×C₄²	—	26	2	no	—
275	#108	—	13	8	no	—
276	#108	—	13	8	no	—
277	#107	—	13	8	no	—
278	#106	—	13	8	no	—
279	#97	—	13	2	no	—
280	#97	—	13	2	no	—
281	#97	—	13	2	no	—
282	#97	—	26	4	no	—
283	#97	—	26	4	no	—
284	#97	C₂×#261	1	2	yes	complemented
285	C₄×C₈	—	13	2	no	—
286	C₄×C₈	—	13	2	no	—
287	C₄×C₈	—	13	2	no	—
288	C₄×C₈	—	26	4	no	—
289	C₄×C₈	—	26	4	no	—
290	C₄×C₈	C₂×#261	1	2	yes	complemented
291	C₂×C₁₃	—	2	1	no	—
292	C₂×C₁₃	—	2	2	no	—
293	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
294	D₁₃	—	2	1	no	—
295	D₁₃	—	2	2	no	—
296	D₁₃	#2955	1	2	yes	—
297	C₂⁴	—	13	1	no	—
298	C₂²×C₄	—	13	1	no	—
299	C₂²×C₄	—	13	2	no	—
300	C₂²×C₄	—	13	2	no	—
301	C₂²×C₄	—	13	2	no	—
302	C₂²×C₄	—	13	2	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	—	26	2	no	—
308	C₂²×C₄	—	26	4	no	—
309	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
310	M₁₆	—	13	4	no	—
311	M₁₆	—	13	8	no	—
312	M₁₆	—	13	8	no	—
313	M₁₆	—	26	4	no	—
314	M₁₆	—	26	4	no	—
315	M₁₆	—	26	4	no	—
316	M₁₆	C₄×#261	1	4	yes	—
317	C₂×C₈	—	13	2	no	—
318	C₂×C₈	—	13	2	no	—
319	C₂×C₈	—	13	1	no	—
320	C₂×C₈	—	13	2	no	—
321	C₂×C₈	—	13	1	no	—
322	C₂×C₈	—	13	4	no	—
323	C₂×C₈	—	13	4	no	—
324	C₂×C₈	—	13	2	no	—
325	C₂×C₈	—	13	1	no	—
326	C₂×C₈	—	13	2	no	—
327	C₂×C₈	—	13	2	no	—
328	C₂×C₈	—	13	2	no	—
329	C₂×C₈	—	13	1	no	—
330	C₂×C₈	—	13	2	no	—
331	C₂×C₈	—	13	1	no	—
332	C₂×C₈	—	13	2	no	—
333	C₂×C₈	—	13	1	no	—
334	C₂×C₈	—	26	4	no	—
335	C₂×C₈	—	26	4	no	—
336	C₂×C₈	—	26	4	no	—
337	C₂×C₈	C₄⋊#261	1	2	yes	—
338	C₂×C₈	C₄⋊#261	1	2	yes	—
339	C₂×C₈	C₂²×#261	1	2	yes	—
340	C₂×C₈	C₂²×#261	1	1	yes	characteristic
341	C₂×C₈	C₂²×#261	1	1	yes	characteristic
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	13	8	no	—
344	C₄⋊C₄	—	26	2	no	—
345	C₄⋊C₄	—	26	4	no	—
346	C₄⋊C₄	—	26	1	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₂²⋊C₄	—	26	2	no	—
349	C₂²⋊C₄	—	26	4	no	—
350	C₂²⋊C₄	—	26	4	no	—
351	C₂²⋊C₄	—	26	1	no	—
352	C₄²	—	13	2	no	—
353	C₄²	—	26	2	no	—
354	C₄²	—	26	4	no	—
355	C₄²	—	26	4	no	—
356	C₄²	C₂²×#261	1	2	yes	—
357	C₁₃	#20444	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	13	2	no	—
359	C₂³	—	13	1	no	—
360	C₂³	—	13	2	no	—
361	C₂³	—	13	1	no	—
362	C₂³	—	52	2	no	—
363	C₂³	#88237	1	1	yes	characteristic
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	13	2	no	—
366	C₂×C₄	—	13	2	no	—
367	C₂×C₄	—	13	1	no	—
368	C₂×C₄	—	13	1	no	—
369	C₂×C₄	—	13	2	no	—
370	C₂×C₄	—	13	2	no	—
371	C₂×C₄	—	13	2	no	—
372	C₂×C₄	—	13	2	no	—
373	C₂×C₄	—	13	1	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	13	2	no	—
376	C₂×C₄	—	13	1	no	—
377	C₂×C₄	—	13	2	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	26	8	no	—
380	C₂×C₄	—	26	2	no	—
381	C₂×C₄	—	52	4	no	—
382	C₂×C₄	—	52	8	no	—
383	C₂×C₄	C₂×C₄×#261	1	2	yes	—
384	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
385	C₂×C₄	#88237	1	1	yes	characteristic
386	C₂×C₄	C₂³×#261	1	1	yes	characteristic
387	C₈	—	13	4	no	—
388	C₈	—	13	1	no	—
389	C₈	—	13	1	no	—
390	C₈	—	13	2	no	—
391	C₈	—	26	8	no	—
392	C₈	C₂×C₄×#261	1	4	yes	—
393	C₈	C₂×C₄⋊#261	1	2	yes	—
394	C₈	C₂×C₄⋊#261	1	1	yes	characteristic
395	C₈	C₂×C₄⋊#261	1	1	yes	characteristic
396	C₂²	—	4	1	no	—
397	C₂²	—	13	1	no	—
398	C₂²	—	13	1	no	—
399	C₂²	—	13	2	no	—
400	C₂²	—	26	2	no	—
401	C₂²	—	26	4	no	—
402	C₂²	—	52	1	no	—
403	C₂²	—	52	2	no	—
404	C₂²	C₄×C₄⋊#261	1	2	yes	—
405	C₂²	C₂×#88237	1	1	yes	characteristic
406	C₄	—	4	2	no	—
407	C₄	—	13	1	no	—
408	C₄	—	13	1	no	—
409	C₄	—	13	2	no	—
410	C₄	—	52	2	no	—
411	C₄	—	52	8	no	—
412	C₄	C₄×C₄⋊#261	1	2	yes	—
413	C₄	C₂²×C₄×#261	1	1	yes	characteristic
414	C₄	C₂²×C₄⋊#261	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	2	2	no	—
417	C₂	—	13	2	no	—
418	C₂	—	26	1	no	—
419	C₂	—	26	2	no	—
420	C₂	C₂×C₄×C₄⋊#261	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×C₄⋊#261
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#405	C₄
socle	C₂×C₁₃	C₂×C₄×C₄⋊C₄
prime radical	C₂³×D₁₃	#41
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	#20444
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
4. #13130642	C₂	semidirect
5. #13130638	C₂	semidirect
13. #11719100	C₄	semidirect
14. #11719098	C₄	semidirect
23. C₁₃×#405	C₄	semidirect
24. #11718783	C₄	semidirect
25. #11718762	C₄	semidirect
26. #11718658	C₄	semidirect
27. #11718369	C₄	semidirect
29. #11718350	C₄	semidirect
71. #88104	C₂×C₄	semidirect
72. #88103	C₂×C₄	semidirect
79. C₁₃×#97	C₂×C₄	semidirect
80. C₄×C₈×C₁₃	C₂×C₄	semidirect
81. #88055	C₂×C₄	semidirect
82. #88055	C₂×C₄	semidirect
83. C₈×Dic₁₃	C₂×C₄	semidirect
84. C₈×Dic₁₃	C₂×C₄	semidirect
85. #88043	C₂×C₄	semidirect
86. C₄×#1055	C₂×C₄	semidirect
211. #405	#261	semidirect
284. #97	C₂×#261	semidirect
290. C₄×C₈	C₂×#261	semidirect
357. C₁₃	#20444	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#430	2
#13131489	2
C₂×#11719089	2
#13130642	2
#13130638	2
#13130517	2
D₁₃×#405	2
#20444	13