Subgroups — #15845395

Order 3328.

664 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125415	C₂	1	1	yes	maximal, characteristic, complemented
2	#13124897	C₂	1	2	yes	maximal, complemented
3	C₈×#6127	C₂	1	1	yes	maximal, characteristic, complemented
4	#13114253	C₂	1	2	yes	maximal, complemented
5	#13114246	C₂	1	2	yes	maximal, complemented
6	#13114241	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114236	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114197	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114192	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113496	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719182	C₂²	1	2	yes	—
13	C₄×#6127	C₂²	1	1	yes	characteristic
14	C₁₃×#431	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	#11718776	—	2	1	no	—
17	#11718776	—	2	1	no	—
18	C₈×C₂²⋊D₁₃	—	2	1	no	—
19	C₈×C₂²⋊D₁₃	—	2	1	no	—
20	#11718586	C₂²	1	1	yes	characteristic
21	#11718511	C₂²	1	2	yes	—
22	#11718509	C₂²	1	2	yes	—
23	#11718504	C₂²	1	2	yes	—
24	#11718503	C₂²	1	2	yes	—
25	#11718398	—	2	2	no	—
26	#11718395	—	2	2	no	—
27	#11718356	C₂²	1	1	yes	characteristic
28	#11718355	C₂²	1	2	yes	—
29	C₄×D₁₀₄	—	2	2	no	—
30	C₄×D₁₀₄	—	2	1	no	—
31	C₄×D₁₀₄	—	2	1	no	—
32	C₄×#6095	—	2	2	no	—
33	C₈×D₅₂	C₂²	1	1	yes	characteristic
34	C₈×D₅₂	C₂²	1	1	yes	characteristic
35	#11718346	—	2	1	no	—
36	C₄×C₈×D₁₃	—	2	1	no	—
37	#11718343	C₂²	1	1	yes	characteristic
38	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
39	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
40	C₁₃×#335	C₂²	1	1	yes	characteristic
41	C₁₃×#335	C₂²	1	1	yes	characteristic
42	C₁₃×#334	C₂²	1	2	yes	—
43	#11718077	C₂²	1	2	yes	—
44	#11718077	C₂²	1	2	yes	—
45	#11718073	C₂²	1	2	yes	—
46	#11718073	C₂²	1	2	yes	—
47	C₂×#6127	—	2	2	no	—
48	C₂×#6127	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	#88184	—	2	2	no	—
53	#88184	—	2	2	no	—
54	C₄×C₂²⋊D₁₃	—	2	1	no	—
55	C₄×C₂²⋊D₁₃	—	2	1	no	—
56	#88180	D₄	1	1	yes	characteristic
57	C₂×D₁₀₄	—	2	2	no	—
58	C₂×D₁₀₄	—	2	1	no	—
59	C₂×D₁₀₄	—	2	1	no	—
60	C₂×#6095	—	2	2	no	—
61	C₂×C₈×D₁₃	—	2	1	no	—
62	C₂×C₈×D₁₃	—	2	1	no	—
63	#88129	—	2	2	no	—
64	#88128	C₂³	1	2	yes	—
65	C₄×D₅₂	—	2	2	no	—
66	C₄×D₅₂	—	2	2	no	—
67	C₄×D₅₂	D₄	1	1	yes	characteristic
68	C₄×D₅₂	C₂³	1	1	yes	characteristic
69	#88126	—	2	1	no	—
70	C₄²×D₁₃	—	2	1	no	—
71	#88123	C₂³	1	2	yes	—
72	C₄×Dic₂₆	D₄	1	1	yes	characteristic
73	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
74	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
75	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
76	C₁₃×C₂²⋊C₈	—	2	2	no	—
77	C₄×C₈×C₁₃	—	2	2	no	—
78	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²⋊#1055	—	2	1	no	—
83	#88061	—	2	2	no	—
84	#88061	—	2	2	no	—
85	#88061	—	2	2	no	—
86	#88061	—	2	2	no	—
87	#88061	—	2	2	no	—
88	#88060	—	2	1	no	—
89	#88060	—	2	1	no	—
90	#88058	—	2	1	no	—
91	#88058	—	2	1	no	—
92	#88058	—	2	2	no	—
93	#88057	—	2	2	no	—
94	#88056	—	2	2	no	—
95	#88054	—	2	1	no	—
96	#88054	—	2	1	no	—
97	C₈×Dic₁₃	—	2	1	no	—
98	C₈×Dic₁₃	—	2	1	no	—
99	C₄⋊#1055	C₂³	1	1	yes	characteristic
100	C₄⋊#1055	C₂³	1	1	yes	characteristic
101	C₄×#1055	—	2	1	no	—
102	#19128	—	13	1	no	maximal, Sylow
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
106	C₂×C₂²⋊D₁₃	—	2	1	no	—
107	C₂×C₂²⋊D₁₃	—	4	2	no	—
108	#6127	—	2	2	no	—
109	#6127	—	2	2	no	—
110	#6127	—	8	4	no	—
111	C₂×D₅₂	—	2	2	no	—
112	C₂×D₅₂	—	2	2	no	—
113	C₂×D₅₂	—	2	2	no	—
114	C₂×D₅₂	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	—	2	1	no	—
116	C₂×C₄×D₁₃	—	2	1	no	—
117	C₂×C₄×D₁₃	—	2	1	no	—
118	C₂×C₄×D₁₃	—	4	2	no	—
119	C₂×Dic₂₆	—	2	2	no	—
120	C₂×Dic₂₆	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	4	1	no	—
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃	#41	1	1	yes	characteristic
132	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₂²⋊Dic₁₃	—	2	1	no	—
134	#6103	—	2	1	no	—
135	#6103	—	2	1	no	—
136	#6103	—	4	2	no	—
137	#6103	—	4	2	no	—
138	C₄⋊Dic₁₃	—	2	2	no	—
139	C₄⋊Dic₁₃	—	2	2	no	—
140	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
142	#6101	—	2	1	no	—
143	#6101	—	2	1	no	—
144	C₄×Dic₁₃	—	2	1	no	—
145	C₄×Dic₁₃	—	2	1	no	—
146	C₄×Dic₁₃	—	2	1	no	—
147	C₂×#1055	—	2	1	no	—
148	C₂×#1055	—	2	1	no	—
149	D₁₀₄	—	4	2	no	—
150	D₁₀₄	—	4	4	no	—
151	D₁₀₄	—	4	2	no	—
152	#6095	—	4	4	no	—
153	C₈×D₁₃	—	4	2	no	—
154	C₈×D₁₃	—	4	2	no	—
155	#3169	—	13	1	no	—
156	#3106	—	13	2	no	—
157	C₈×#41	—	13	1	no	—
158	#1678	—	13	2	no	—
159	#1677	—	13	2	no	—
160	#1676	—	13	1	no	—
161	#1675	—	13	1	no	—
162	#1668	—	13	1	no	—
163	#1667	—	13	1	no	—
164	#1564	D₁₃	1	1	yes	characteristic, complemented
165	#1543	—	13	2	no	—
166	C₂³×C₁₃	#121	1	1	yes	characteristic
167	C₂²×D₁₃	—	2	1	no	—
168	C₂²×D₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₁₃	—	2	4	no	—
181	C₂²⋊D₁₃	—	8	4	no	—
182	C₂×Dic₁₃	—	2	1	no	—
183	C₂×Dic₁₃	—	2	1	no	—
184	C₂×Dic₁₃	—	2	1	no	—
185	C₂×Dic₁₃	—	4	2	no	—
186	D₅₂	—	2	1	no	—
187	D₅₂	—	4	2	no	—
188	D₅₂	—	4	2	no	—
189	D₅₂	—	4	2	no	—
190	D₅₂	—	4	2	no	—
191	D₅₂	—	8	2	no	—
192	D₅₂	#135	1	2	yes	—
193	C₄×D₁₃	—	2	4	no	—
194	C₄×D₁₃	—	4	1	no	—
195	C₄×D₁₃	—	4	1	no	—
196	C₄×D₁₃	—	4	2	no	—
197	C₄×D₁₃	—	8	4	no	—
198	Dic₂₆	—	2	1	no	—
199	Dic₂₆	—	8	2	no	—
200	Dic₂₆	#135	1	2	yes	—
201	C₈×C₁₃	—	2	1	no	—
202	C₈×C₁₃	—	2	1	no	—
203	C₈×C₁₃	—	2	1	no	—
204	C₈×C₁₃	—	4	2	no	—
205	C₈×C₁₃	—	4	2	no	—
206	C₈×C₁₃	#135	1	2	yes	—
207	#1055	—	4	1	no	—
208	#1055	—	4	1	no	—
209	#532	—	13	2	no	—
210	C₄×#41	—	13	1	no	—
211	#500	—	13	1	no	—
212	#493	—	13	1	no	—
213	#486	—	13	2	no	—
214	#482	—	26	2	no	—
215	#477	—	13	2	no	—
216	#476	—	13	2	no	—
217	#466	—	26	1	no	—
218	#466	—	26	1	no	—
219	#460	—	13	2	no	—
220	#459	—	13	2	no	—
221	#449	—	26	2	no	—
222	C₈×Q₈	—	13	1	no	—
223	C₈×Q₈	—	13	1	no	—
224	C₄×SD₁₆	—	26	2	no	—
225	C₄×D₈	—	26	2	no	—
226	C₄×D₈	—	26	1	no	—
227	C₄×D₈	—	26	1	no	—
228	C₈×D₄	—	13	1	no	—
229	C₈×D₄	—	13	1	no	—
230	C₈×D₄	—	26	1	no	—
231	C₈×D₄	—	26	1	no	—
232	#431	—	13	1	no	—
233	#431	—	26	1	no	—
234	#431	C₂×D₁₃	1	2	yes	—
235	C₂×C₄×C₈	—	26	1	no	—
236	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
237	#335	C₂×D₁₃	1	1	yes	characteristic
238	#335	C₂×D₁₃	1	1	yes	characteristic
239	#334	C₂×D₁₃	1	2	yes	—
240	#333	—	13	2	no	—
241	#333	—	13	2	no	—
242	#331	—	13	2	no	—
243	#331	—	13	2	no	—
244	C₂²×C₁₃	—	2	1	no	—
245	C₂²×C₁₃	—	2	1	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
248	C₂×D₁₃	—	2	2	no	—
249	C₂×D₁₃	—	4	1	no	—
250	C₂×D₁₃	—	4	1	no	—
251	C₂×D₁₃	—	8	2	no	—
252	C₂×D₁₃	—	8	2	no	—
253	C₂×D₁₃	—	8	2	no	—
254	C₄×C₁₃	—	2	1	no	—
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	#472	1	2	yes	—
258	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
259	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
260	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
261	C₄×C₁₃	#575	1	1	yes	characteristic
262	Dic₁₃	—	2	2	no	—
263	Dic₁₃	—	4	1	no	—
264	Dic₁₃	—	4	1	no	—
265	Dic₁₃	—	8	2	no	—
266	C₂×#41	—	13	1	no	—
267	C₂×#41	—	26	2	no	—
268	C₂×SD₁₆	—	26	2	no	—
269	C₂×D₈	—	26	2	no	—
270	C₂×D₈	—	26	1	no	—
271	C₂×D₈	—	26	1	no	—
272	C₂²×C₈	—	26	1	no	—
273	C₂²×C₈	—	26	1	no	—
274	C₂²×C₈	D₅₂	1	1	yes	characteristic
275	C₂²×C₈	D₅₂	1	1	yes	characteristic
276	C₄⋊Q₈	—	13	2	no	—
277	#127	—	13	2	no	—
278	#124	—	26	2	no	—
279	#121	—	26	2	no	—
280	#121	—	26	2	no	—
281	C₄×Q₈	—	13	1	no	—
282	C₄×Q₈	—	13	1	no	—
283	C₄×D₄	—	13	1	no	—
284	C₄×D₄	—	13	1	no	—
285	C₄×D₄	—	26	1	no	—
286	C₄×D₄	—	26	1	no	—
287	C₄×D₄	—	26	2	no	—
288	C₄×D₄	—	26	2	no	—
289	#117	—	13	1	no	—
290	#117	—	26	1	no	—
291	C₂×C₄²	—	26	1	no	—
292	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
293	#107	—	26	2	no	—
294	#107	—	26	1	no	—
295	#107	—	26	1	no	—
296	#106	—	26	2	no	—
297	C₄⋊C₈	—	13	1	no	—
298	C₄⋊C₈	—	13	1	no	—
299	C₄⋊C₈	—	26	1	no	—
300	C₄⋊C₈	—	26	1	no	—
301	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
302	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
303	#103	—	26	2	no	—
304	#102	—	26	2	no	—
305	#102	—	26	2	no	—
306	#102	—	26	2	no	—
307	#102	—	26	2	no	—
308	#102	—	26	2	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₂²⋊C₈	—	26	1	no	—
311	C₂²⋊C₈	—	26	1	no	—
312	C₂²⋊C₈	—	26	1	no	—
313	C₄×C₈	—	2	2	no	—
314	C₄×C₈	—	26	1	no	—
315	C₄×C₈	—	26	1	no	—
316	C₄×C₈	—	26	1	no	—
317	C₄×C₈	D₅₂	1	1	yes	characteristic
318	C₄×C₈	D₅₂	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
321	C₂×C₁₃	—	4	1	no	—
322	C₂×C₁₃	#3035	1	1	yes	characteristic
323	C₂×C₁₃	#3050	1	1	yes	characteristic
324	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
325	D₁₃	—	4	2	no	—
326	D₁₃	—	16	2	no	—
327	#41	—	26	2	no	—
328	#41	—	26	2	no	—
329	#41	—	104	4	no	—
330	C₂×Q₈	—	13	1	no	—
331	C₂×Q₈	—	26	2	no	—
332	C₂×D₄	—	13	1	no	—
333	C₂×D₄	—	26	1	no	—
334	C₂×D₄	—	26	2	no	—
335	C₂×D₄	—	26	2	no	—
336	C₂×D₄	—	26	2	no	—
337	C₂×D₄	—	52	2	no	—
338	C₂²×C₄	—	26	1	no	—
339	C₂²×C₄	—	26	1	no	—
340	C₂²×C₄	—	26	1	no	—
341	C₂²×C₄	—	52	2	no	—
342	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
343	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
344	C₂²×C₄	#6131	1	1	yes	characteristic
345	SD₁₆	—	52	4	no	—
346	D₈	—	52	2	no	—
347	D₈	—	52	4	no	—
348	D₈	—	52	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	26	1	no	—
354	C₂×C₈	—	26	1	no	—
355	C₂×C₈	—	52	2	no	—
356	C₂×C₈	—	52	2	no	—
357	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
358	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
359	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
360	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
361	C₄⋊C₄	—	13	1	no	—
362	C₄⋊C₄	—	13	1	no	—
363	C₄⋊C₄	—	26	1	no	—
364	C₄⋊C₄	—	26	1	no	—
365	C₄⋊C₄	—	26	2	no	—
366	C₄⋊C₄	—	26	2	no	—
367	C₂²⋊C₄	—	26	1	no	—
368	C₂²⋊C₄	—	26	1	no	—
369	C₂²⋊C₄	—	26	1	no	—
370	C₂²⋊C₄	—	52	2	no	—
371	C₂²⋊C₄	—	52	2	no	—
372	C₄²	—	26	1	no	—
373	C₄²	—	26	1	no	—
374	C₄²	—	26	1	no	—
375	C₄²	C₂×D₅₂	1	1	yes	characteristic
376	C₄²	D₄×D₁₃	1	1	yes	characteristic
377	C₄²	#6131	1	1	yes	characteristic
378	C₄²	C₂³×D₁₃	1	1	yes	characteristic
379	C₁₃	#19128	1	1	yes	characteristic, complemented, Sylow
380	C₂³	—	26	1	no	—
381	C₂³	—	52	2	no	—
382	C₂³	#88149	1	1	yes	characteristic
383	Q₈	—	13	2	no	—
384	Q₈	—	26	1	no	—
385	Q₈	—	104	2	no	—
386	D₄	—	13	2	no	—
387	D₄	—	26	4	no	—
388	D₄	—	26	1	no	—
389	D₄	—	52	2	no	—
390	D₄	—	52	2	no	—
391	D₄	—	52	2	no	—
392	D₄	—	52	2	no	—
393	D₄	—	104	2	no	—
394	D₄	—	104	4	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	26	4	no	—
401	C₂×C₄	—	26	1	no	—
402	C₂×C₄	—	26	1	no	—
403	C₂×C₄	—	26	1	no	—
404	C₂×C₄	—	52	1	no	—
405	C₂×C₄	—	52	1	no	—
406	C₂×C₄	—	52	2	no	—
407	C₂×C₄	—	52	2	no	—
408	C₂×C₄	—	104	4	no	—
409	C₂×C₄	#88149	1	1	yes	characteristic
410	C₂×C₄	#88149	1	1	yes	characteristic
411	C₂×C₄	#88149	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂×#6131	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	2	1	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	52	1	no	—
421	C₈	—	52	1	no	—
422	C₈	#88158	1	2	yes	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	26	2	no	—
427	C₂²	—	52	1	no	—
428	C₂²	—	52	1	no	—
429	C₂²	—	104	2	no	—
430	C₂²	—	104	2	no	—
431	C₂²	—	104	2	no	—
432	C₂²	C₂×#88149	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	26	2	no	—
437	C₄	—	52	1	no	—
438	C₄	—	52	1	no	—
439	C₄	—	104	2	no	—
440	C₄	#11718558	1	2	yes	—
441	C₄	C₂×#88158	1	1	yes	characteristic
442	C₄	#11719453	1	1	yes	characteristic
443	C₄	D₁₃×#135	1	1	yes	characteristic
444	C₄	D₁₃×#135	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	52	2	no	—
447	C₂	—	208	2	no	—
448	C₂	#13124293	1	1	yes	characteristic
449	C₂	#13124418	1	1	yes	characteristic
450	C₂	C₂×#11718558	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88149
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1564	C₂
socle	C₂²×C₁₃	C₂×#121
hypercenter	#1564	D₁₃
hypocenter	C₁₃	#19128
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
1. #13125415	C₂	semidirect
2. #13124897	C₂	semidirect
3. C₈×#6127	C₂	semidirect
4. #13114253	C₂	semidirect
5. #13114246	C₂	semidirect
6. #13114241	C₂	semidirect
7. #13114236	C₂	semidirect
8. #13114197	C₂	semidirect
9. #13114192	C₂	semidirect
10. #13113496	C₂	semidirect
11. C₁₃×#1564	C₂	semidirect
164. #1564	D₁₃	semidirect
379. C₁₃	#19128	semidirect

Maximal subgroups

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

subgroup	index
#13125415	2
#13124897	2
C₈×#6127	2
#13114253	2
#13114246	2
#13114241	2
#13114236	2
#13114197	2
#13114192	2
#13113496	2
C₁₃×#1564	2
#19128	13