Subgroups — #15846864

Order 3328.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125350	C₂	1	1	yes	maximal, characteristic, complemented
2	#13124998	C₂	1	2	yes	maximal
3	#13114240	C₂	1	1	yes	maximal, characteristic, complemented
4	#13114235	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114230	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114225	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114218	C₂	1	2	yes	maximal, complemented
8	#13114211	C₂	1	2	yes	maximal, complemented
9	#13113599	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113544	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	#11719175	C₂²	1	2	yes	—
14	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₈×D₄×C₁₃	—	2	1	no	—
17	C₈×D₄×C₁₃	—	2	1	no	—
18	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#431	—	2	1	no	—
21	C₁₃×#431	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	—	2	1	no	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	#11718900	—	2	2	no	—
25	#11718767	—	2	1	no	—
26	#11718767	—	2	1	no	—
27	#11718692	C₂²	1	2	yes	—
28	#11718691	—	2	2	no	—
29	#11718682	C₂²	1	2	yes	—
30	#11718680	C₂²	1	2	yes	—
31	#11718679	—	2	2	no	—
32	#11718669	C₂²	1	2	yes	—
33	#11718657	—	2	2	no	—
34	#11718587	C₂²	1	2	yes	—
35	#11718344	—	2	1	no	—
36	#11718344	—	2	1	no	—
37	#11718343	C₂²	1	1	yes	characteristic
38	#11718343	C₂²	1	1	yes	characteristic
39	#11718341	C₂²	1	2	yes	—
40	#11718078	C₂²	1	2	yes	—
41	#11718078	C₂²	1	2	yes	—
42	#11718073	C₂²	1	2	yes	—
43	#11718073	C₂²	1	2	yes	—
44	#11718050	C₂²	1	1	yes	characteristic
45	#11718050	C₂²	1	1	yes	characteristic
46	#11718049	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	—	2	1	no	—
49	C₂²×C₈×C₁₃	—	2	1	no	—
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
53	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₄×D₄×C₁₃	—	2	1	no	—
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
57	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×#117	—	2	1	no	—
59	C₁₃×#117	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×#6107	—	2	2	no	—
63	C₂×#6105	—	2	2	no	—
64	#88180	—	2	2	no	—
65	#88178	—	2	2	no	—
66	#88178	—	2	2	no	—
67	#88124	—	2	2	no	—
68	#88123	C₂³	1	2	yes	—
69	#88123	C₂³	1	2	yes	—
70	C₄×Dic₂₆	—	2	2	no	—
71	C₄×Dic₂₆	—	2	2	no	—
72	C₁₃×C₄⋊C₈	—	2	1	no	—
73	C₁₃×C₄⋊C₈	—	2	1	no	—
74	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
75	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₁₃×C₂²⋊C₈	—	2	1	no	—
77	C₁₃×C₂²⋊C₈	—	2	1	no	—
78	C₁₃×C₂²⋊C₈	—	2	1	no	—
79	C₄×C₈×C₁₃	—	2	1	no	—
80	C₄×C₈×C₁₃	—	2	1	no	—
81	C₄×C₈×C₁₃	—	2	1	no	—
82	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	#88075	—	2	2	no	—
87	#88072	—	2	2	no	—
88	C₂²⋊#1055	—	2	2	no	—
89	#88058	—	2	1	no	—
90	#88058	—	2	1	no	—
91	#88058	—	2	1	no	—
92	#88058	—	2	1	no	—
93	#88057	—	2	2	no	—
94	#88057	—	2	2	no	—
95	#88050	—	2	2	no	—
96	#88050	—	2	2	no	—
97	#88048	—	2	2	no	—
98	#88047	—	2	2	no	—
99	C₄⋊#1055	C₂³	1	2	yes	—
100	C₄⋊#1055	C₂³	1	2	yes	—
101	#88043	—	2	2	no	—
102	#19273	—	13	1	no	maximal, Sylow
103	C₁₃×#41	—	2	2	no	—
104	C₁₃×#41	—	2	2	no	—
105	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
114	C₂×Dic₂₆	—	2	2	no	—
115	C₂×Dic₂₆	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	4	2	no	—
121	C₂×C₈×C₁₃	—	4	2	no	—
122	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
129	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
130	C₁₃×C₂²⋊C₄	—	2	1	no	—
131	C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₄²×C₁₃	—	2	1	no	—
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₃	#41	1	1	yes	characteristic
139	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₂²⋊Dic₁₃	—	4	2	no	—
141	#6107	—	4	4	no	—
142	#6105	—	4	4	no	—
143	C₄⋊Dic₁₃	—	2	2	no	—
144	C₄⋊Dic₁₃	—	2	2	no	—
145	C₄⋊Dic₁₃	—	2	2	no	—
146	C₄⋊Dic₁₃	—	2	2	no	—
147	#6101	—	4	2	no	—
148	#6101	—	4	2	no	—
149	C₄×Dic₁₃	—	4	2	no	—
150	C₂×#1055	—	2	2	no	—
151	C₂×#1055	—	2	2	no	—
152	#3160	—	13	1	no	—
153	#3116	—	13	2	no	—
154	C₈×#41	D₁₃	1	1	yes	characteristic
155	#1676	—	13	1	no	—
156	#1675	—	13	1	no	—
157	#1674	—	13	1	no	—
158	#1673	—	13	1	no	—
159	#1672	—	13	2	no	—
160	#1671	—	13	2	no	—
161	#1568	—	13	1	no	—
162	#1554	—	13	2	no	—
163	C₂³×C₁₃	—	2	1	no	—
164	C₂³×C₁₃	#121	1	1	yes	characteristic
165	Q₈×C₁₃	—	2	1	no	—
166	Q₈×C₁₃	#135	1	2	yes	—
167	D₄×C₁₃	—	2	4	no	—
168	D₄×C₁₃	—	2	1	no	—
169	D₄×C₁₃	#135	1	2	yes	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
188	C₂×Dic₁₃	—	4	2	no	—
189	C₂×Dic₁₃	—	4	2	no	—
190	Dic₂₆	—	4	2	no	—
191	Dic₂₆	—	4	2	no	—
192	Dic₂₆	—	8	2	no	—
193	C₈×C₁₃	—	2	1	no	—
194	C₈×C₁₃	—	2	1	no	—
195	C₈×C₁₃	—	4	1	no	—
196	C₈×C₁₃	—	4	1	no	—
197	C₈×C₁₃	#137	1	2	yes	—
198	C₈×C₁₃	#137	1	2	yes	—
199	#1055	—	4	2	no	—
200	#1055	—	4	2	no	—
201	#533	—	13	2	no	—
202	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
203	#500	—	13	1	no	—
204	#500	—	13	1	no	—
205	#499	—	26	1	no	—
206	#499	—	26	1	no	—
207	#498	—	13	2	no	—
208	#485	—	26	2	no	—
209	#477	—	13	2	no	—
210	#476	—	13	2	no	—
211	#462	—	13	2	no	—
212	#461	—	13	2	no	—
213	#452	—	26	2	no	—
214	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
215	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
216	#441	—	26	2	no	—
217	#440	—	26	2	no	—
218	C₈×D₄	—	2	1	no	—
219	C₈×D₄	—	2	1	no	—
220	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
221	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
222	#432	—	13	2	no	—
223	#431	—	2	1	no	—
224	#431	C₂×D₁₃	1	1	yes	characteristic
225	#427	—	26	1	no	—
226	#427	—	26	1	no	—
227	C₂×C₄×C₈	—	2	1	no	—
228	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
229	#335	—	13	1	no	—
230	#335	—	13	1	no	—
231	#334	—	13	2	no	—
232	#333	—	13	2	no	—
233	#333	—	13	2	no	—
234	#332	—	13	2	no	—
235	#332	—	13	2	no	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	—	4	1	no	—
242	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
243	C₄×C₁₃	—	2	1	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	4	1	no	—
249	C₄×C₁₃	—	4	1	no	—
250	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
251	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
252	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
253	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
254	Dic₁₃	—	8	2	no	—
255	Dic₁₃	—	8	2	no	—
256	C₂×#41	D₅₂	1	1	yes	characteristic
257	C₂×Q₁₆	—	26	2	no	—
258	C₂×SD₁₆	—	26	2	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
262	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
263	C₄⋊Q₈	—	13	2	no	—
264	C₄⋊Q₈	—	13	2	no	—
265	#125	—	26	2	no	—
266	C₂²⋊Q₈	—	26	2	no	—
267	C₂²⋊Q₈	—	26	2	no	—
268	C₄×Q₈	—	26	2	no	—
269	C₄×Q₈	—	26	2	no	—
270	C₄×Q₈	D₅₂	1	1	yes	characteristic
271	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	D₅₂	1	1	yes	characteristic
275	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
276	#117	—	2	1	no	—
277	#117	—	26	2	no	—
278	#117	D₅₂	1	1	yes	characteristic
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
281	#107	—	26	1	no	—
282	#107	—	26	1	no	—
283	#107	—	26	1	no	—
284	#107	—	26	1	no	—
285	#107	—	26	2	no	—
286	#106	—	26	2	no	—
287	#106	—	26	2	no	—
288	#106	—	26	2	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	13	2	no	—
292	C₄⋊C₈	—	13	2	no	—
293	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
294	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
295	#103	—	26	2	no	—
296	#103	—	26	2	no	—
297	#103	—	26	2	no	—
298	#102	—	26	2	no	—
299	C₂²⋊C₈	—	2	1	no	—
300	C₂²⋊C₈	—	2	1	no	—
301	C₂²⋊C₈	—	2	1	no	—
302	C₂²⋊C₈	—	26	2	no	—
303	#97	—	26	2	no	—
304	C₄×C₈	—	2	1	no	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	—	2	1	no	—
307	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
308	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
309	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
311	C₂×C₁₃	—	4	1	no	—
312	C₂×C₁₃	—	4	2	no	—
313	C₂×C₁₃	#3039	1	1	yes	characteristic
314	C₂×C₁₃	#3050	1	1	yes	characteristic
315	C₂×C₁₃	#3067	1	1	yes	characteristic
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	C₂×Q₈	—	26	2	no	—
319	C₂×Q₈	—	26	2	no	—
320	C₂×Q₈	C₂×D₅₂	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	C₂×D₅₂	1	1	yes	characteristic
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
327	C₂²×C₄	#6127	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
329	Q₁₆	—	52	4	no	—
330	SD₁₆	—	52	4	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	4	2	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	26	2	no	—
338	C₂×C₈	—	26	2	no	—
339	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
340	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
342	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	26	2	no	—
346	C₄⋊C₄	—	26	2	no	—
347	C₄⋊C₄	—	26	2	no	—
348	C₄⋊C₄	—	26	2	no	—
349	C₄⋊C₄	—	52	2	no	—
350	C₄⋊C₄	—	52	2	no	—
351	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
352	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	52	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	52	2	no	—
361	C₄²	C₂×D₅₂	1	1	yes	characteristic
362	C₄²	#6127	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
364	C₄²	C₂³×D₁₃	1	1	yes	characteristic
365	C₁₃	#19273	1	1	yes	characteristic, complemented, Sylow
366	C₂³	—	2	1	no	—
367	C₂³	#88184	1	1	yes	characteristic
368	Q₈	—	2	1	no	—
369	Q₈	—	52	2	no	—
370	Q₈	—	52	2	no	—
371	Q₈	—	104	2	no	—
372	Q₈	#88158	1	2	yes	—
373	D₄	—	2	4	no	—
374	D₄	—	2	1	no	—
375	D₄	#88158	1	2	yes	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	52	2	no	—
389	C₂×C₄	—	52	2	no	—
390	C₂×C₄	#88184	1	1	yes	characteristic
391	C₂×C₄	#88184	1	1	yes	characteristic
392	C₂×C₄	#88184	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
394	C₂×C₄	C₂×#6127	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	52	2	no	—
401	C₈	—	52	2	no	—
402	C₈	#88205	1	2	yes	—
403	C₈	#88205	1	2	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂×#88184	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	104	2	no	—
419	C₄	—	104	2	no	—
420	C₄	C₂×#88158	1	1	yes	characteristic
421	C₄	C₂×#88158	1	1	yes	characteristic
422	C₄	C₂×#88205	1	1	yes	characteristic
423	C₄	C₂×#88205	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	4	2	no	—
426	C₂	#13124323	1	1	yes	characteristic
427	C₂	#13124417	1	1	yes	characteristic
428	C₂	#13124556	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#88184
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₈×C₁₃×#41	C₂
socle	C₂²×C₁₃	C₂×#121
prime radical	C₂×C₁₃×#41	D₄
hypercenter	C₈×#41	D₁₃
hypocenter	C₁₃	#19273
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #13125350	C₂	semidirect
3. #13114240	C₂	semidirect
4. #13114235	C₂	semidirect
5. #13114230	C₂	semidirect
6. #13114225	C₂	semidirect
7. #13114218	C₂	semidirect
8. #13114211	C₂	semidirect
9. #13113599	C₂	semidirect
10. #13113544	C₂	semidirect
365. C₁₃	#19273	semidirect

Maximal subgroups

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

subgroup	index
#13125350	2
#13124998	2
#13114240	2
#13114235	2
#13114230	2
#13114225	2
#13114218	2
#13114211	2
#13113599	2
#13113544	2
C₈×C₁₃×#41	2
#19273	13