Subgroups — #15846366

Order 3328.

628 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13126162	C₂	1	2	yes	maximal, complemented
2	#13125415	C₂	1	1	yes	maximal, characteristic, complemented
3	#13114364	C₂	1	1	yes	maximal, characteristic, complemented
4	#13114359	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114320	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114315	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114252	C₂	1	2	yes	maximal, complemented
8	#13114245	C₂	1	2	yes	maximal, complemented
9	C₂×#11718049	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113532	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#529	C₂²	1	1	yes	characteristic
13	#11719182	C₂²	1	2	yes	—
14	C₁₃×#446	C₂²	1	1	yes	characteristic
15	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#436	C₂²	1	1	yes	characteristic
17	C₁₃×#435	—	2	1	no	—
18	C₈×D₄×C₁₃	—	2	1	no	—
19	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#433	—	2	1	no	—
21	C₁₃×#432	C₂²	1	1	yes	characteristic
22	C₁₃×#405	—	2	1	no	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	#11718776	—	2	1	no	—
25	#11718776	—	2	1	no	—
26	#11718727	—	2	2	no	—
27	#11718718	—	2	2	no	—
28	#11718709	—	2	2	no	—
29	#11718699	—	2	2	no	—
30	#11718688	C₂²	1	2	yes	—
31	#11718682	C₂²	1	2	yes	—
32	#11718676	C₂²	1	2	yes	—
33	#11718669	C₂²	1	2	yes	—
34	C₂×C₄⋊#1055	C₂²	1	2	yes	—
35	#11718356	C₂²	1	1	yes	characteristic
36	#11718355	C₂²	1	2	yes	—
37	C₄×D₁₀₄	—	2	1	no	—
38	C₄×D₁₀₄	—	2	1	no	—
39	#11718343	C₂²	1	1	yes	characteristic
40	#11718077	C₂²	1	2	yes	—
41	#11718077	C₂²	1	2	yes	—
42	#11718073	C₂²	1	2	yes	—
43	#11718073	C₂²	1	2	yes	—
44	#11718049	C₂²	1	2	yes	—
45	#11718049	C₂²	1	1	yes	characteristic
46	#11718049	C₂²	1	1	yes	characteristic
47	C₂×#6127	—	2	2	no	—
48	C₂×C₁₃×M₁₆	—	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	C₁₃×#126	—	2	1	no	—
53	C₁₃×#125	D₄	1	1	yes	characteristic
54	C₁₃×#124	D₄	1	1	yes	characteristic
55	C₁₃×#123	—	2	1	no	—
56	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₃×#121	D₄	1	1	yes	characteristic
58	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₄×D₄×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×#117	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×#6106	—	2	2	no	—
64	C₂×#6104	—	2	2	no	—
65	#88184	—	2	2	no	—
66	#88184	—	2	2	no	—
67	C₂²×#1055	—	2	2	no	—
68	C₂×D₁₀₄	—	2	1	no	—
69	C₂×D₁₀₄	—	2	1	no	—
70	#88129	—	2	2	no	—
71	#88128	C₂³	1	2	yes	—
72	C₄×D₅₂	—	2	2	no	—
73	C₄×D₅₂	—	2	2	no	—
74	#88123	C₂³	1	2	yes	—
75	C₁₃×C₄⋊C₈	—	2	1	no	—
76	C₁₃×C₄⋊C₈	—	2	1	no	—
77	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₁₃×C₂²⋊C₈	—	2	1	no	—
80	C₁₃×C₂²⋊C₈	—	2	1	no	—
81	C₁₃×C₂²⋊C₈	—	2	1	no	—
82	C₁₃×#97	—	2	1	no	—
83	C₁₃×#97	—	2	1	no	—
84	C₄×C₈×C₁₃	—	2	1	no	—
85	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
86	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	#88075	—	2	2	no	—
90	#88072	—	2	2	no	—
91	#88061	—	2	2	no	—
92	#88061	—	2	2	no	—
93	#88058	—	2	1	no	—
94	#88058	—	2	1	no	—
95	#88049	—	2	2	no	—
96	#88049	—	2	2	no	—
97	#88048	—	2	2	no	—
98	#88047	—	2	2	no	—
99	C₄⋊#1055	—	2	2	no	—
100	C₄⋊#1055	C₂³	1	2	yes	—
101	C₄⋊#1055	C₂³	1	2	yes	—
102	#19227	—	13	1	no	maximal, Sylow
103	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
110	C₂×C₂²⋊D₁₃	—	4	2	no	—
111	#6127	—	8	4	no	—
112	C₂×D₅₂	—	2	2	no	—
113	C₂×D₅₂	—	2	2	no	—
114	C₂×D₅₂	—	2	2	no	—
115	C₂×C₄×D₁₃	—	4	2	no	—
116	C₂×Dic₂₆	—	2	2	no	—
117	C₁₃×M₁₆	—	4	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	4	1	no	—
122	C₂×C₈×C₁₃	—	4	2	no	—
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	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
132	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
133	C₁₃×C₂²⋊C₄	—	2	1	no	—
134	C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₁₃×C₂²⋊C₄	—	2	1	no	—
136	C₁₃×C₂²⋊C₄	—	2	1	no	—
137	C₁₃×C₂²⋊C₄	—	2	1	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃	#41	1	1	yes	characteristic
142	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
143	#6106	—	8	2	no	—
144	#6104	—	8	2	no	—
145	#6103	—	4	2	no	—
146	#6103	—	4	2	no	—
147	C₄⋊Dic₁₃	—	2	2	no	—
148	C₄⋊Dic₁₃	—	2	2	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	—	2	2	no	—
151	C₂×#1055	—	8	2	no	—
152	D₁₀₄	—	4	2	no	—
153	D₁₀₄	—	4	2	no	—
154	#3247	—	13	2	no	—
155	#3169	—	13	1	no	—
156	#2966	D₁₃	1	1	yes	characteristic, complemented
157	#1696	—	13	1	no	—
158	#1695	—	13	1	no	—
159	#1688	—	13	1	no	—
160	#1687	—	13	1	no	—
161	#1678	—	13	2	no	—
162	#1677	—	13	2	no	—
163	C₂×#334	—	13	1	no	—
164	#1551	—	13	2	no	—
165	C₂³×C₁₃	—	2	1	no	—
166	C₂³×C₁₃	#121	1	1	yes	characteristic
167	C₂²×D₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	2	2	no	—
170	D₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	2	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	1	no	—
180	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
186	C₂²⋊D₁₃	—	8	4	no	—
187	C₂×Dic₁₃	—	4	2	no	—
188	D₅₂	—	4	2	no	—
189	D₅₂	—	4	2	no	—
190	D₅₂	—	4	2	no	—
191	D₅₂	—	4	2	no	—
192	D₅₂	—	8	2	no	—
193	C₄×D₁₃	—	8	4	no	—
194	Dic₂₆	—	8	2	no	—
195	C₈×C₁₃	—	2	1	no	—
196	C₈×C₁₃	—	2	1	no	—
197	C₈×C₁₃	—	2	1	no	—
198	C₈×C₁₃	—	4	1	no	—
199	C₈×C₁₃	—	4	1	no	—
200	C₈×C₁₃	#135	1	2	yes	—
201	#1055	—	4	2	no	—
202	#1055	—	4	2	no	—
203	#532	—	13	2	no	—
204	#529	C₂×D₁₃	1	1	yes	characteristic
205	#500	—	13	1	no	—
206	#493	—	13	1	no	—
207	#486	—	13	2	no	—
208	#478	—	26	2	no	—
209	#477	—	13	2	no	—
210	#476	—	13	2	no	—
211	#466	—	26	1	no	—
212	#466	—	26	1	no	—
213	#466	—	26	2	no	—
214	#465	—	26	2	no	—
215	#463	—	26	2	no	—
216	#460	—	13	2	no	—
217	#459	—	13	2	no	—
218	#446	C₂×D₁₃	1	1	yes	characteristic
219	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
220	C₄×D₈	—	26	1	no	—
221	C₄×D₈	—	26	1	no	—
222	#436	C₂×D₁₃	1	1	yes	characteristic
223	#435	—	2	1	no	—
224	C₈×D₄	—	2	1	no	—
225	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
226	#433	—	2	1	no	—
227	#432	C₂×D₁₃	1	1	yes	characteristic
228	C₂×C₄⋊C₈	—	13	2	no	—
229	#405	—	2	1	no	—
230	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
231	#334	—	13	2	no	—
232	#334	—	13	1	no	—
233	#334	—	13	1	no	—
234	#333	—	13	2	no	—
235	#333	—	13	2	no	—
236	#331	—	13	2	no	—
237	#331	—	13	2	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	—	4	1	no	—
242	C₂²×C₁₃	—	4	1	no	—
243	C₂²×C₁₃	#472	1	2	yes	—
244	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
245	C₂×D₁₃	—	8	2	no	—
246	C₂×D₁₃	—	8	2	no	—
247	C₂×D₁₃	—	8	2	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	2	1	no	—
252	C₄×C₁₃	—	4	1	no	—
253	C₄×C₁₃	—	4	1	no	—
254	C₄×C₁₃	—	4	1	no	—
255	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
256	C₄×C₁₃	#575	1	1	yes	characteristic
257	C₄×C₁₃	#577	1	2	yes	—
258	Dic₁₃	—	8	2	no	—
259	C₂×#41	—	26	2	no	—
260	C₂×SD₁₆	—	26	2	no	—
261	C₂×D₈	—	26	2	no	—
262	C₂×D₈	—	26	1	no	—
263	C₂×D₈	—	26	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	26	2	no	—
267	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
268	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
269	C₄⋊Q₈	—	13	2	no	—
270	#127	—	13	2	no	—
271	#126	—	2	1	no	—
272	#125	D₅₂	1	1	yes	characteristic
273	#124	—	26	2	no	—
274	#124	D₅₂	1	1	yes	characteristic
275	#123	—	2	1	no	—
276	C₂²⋊Q₈	D₅₂	1	1	yes	characteristic
277	#121	—	26	2	no	—
278	#121	—	26	2	no	—
279	#121	D₅₂	1	1	yes	characteristic
280	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	26	2	no	—
283	C₄×D₄	—	26	2	no	—
284	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
285	#117	—	2	1	no	—
286	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
287	#107	—	26	1	no	—
288	#107	—	26	1	no	—
289	#107	—	26	2	no	—
290	#106	—	26	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	13	2	no	—
294	C₄⋊C₈	—	13	2	no	—
295	C₄⋊C₈	—	26	2	no	—
296	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
298	#103	—	26	2	no	—
299	#102	—	26	2	no	—
300	#102	—	26	2	no	—
301	#102	—	26	2	no	—
302	#102	—	26	2	no	—
303	#102	—	26	2	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	1	no	—
307	#97	—	2	1	no	—
308	#97	—	2	1	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
311	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
314	C₂×C₁₃	—	2	2	no	—
315	C₂×C₁₃	—	8	1	no	—
316	C₂×C₁₃	#3035	1	1	yes	characteristic
317	C₂×C₁₃	#3060	1	1	yes	characteristic
318	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
319	D₁₃	—	16	2	no	—
320	#41	—	104	4	no	—
321	C₂×Q₈	—	26	2	no	—
322	C₂×Q₈	C₂×D₅₂	1	1	yes	characteristic
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	26	2	no	—
325	C₂×D₄	—	26	2	no	—
326	C₂×D₄	—	26	2	no	—
327	C₂×D₄	—	52	2	no	—
328	C₂×D₄	C₂×D₅₂	1	1	yes	characteristic
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	52	2	no	—
331	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
332	C₂²×C₄	#6127	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
334	SD₁₆	—	104	2	no	—
335	D₈	—	52	2	no	—
336	D₈	—	52	2	no	—
337	D₈	—	104	2	no	—
338	M₁₆	—	4	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	—	26	2	no	—
345	C₂×C₈	—	26	2	no	—
346	C₂×C₈	—	104	2	no	—
347	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
348	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
349	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
350	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	26	2	no	—
356	C₄⋊C₄	—	26	2	no	—
357	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
358	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
359	C₂²⋊C₄	—	2	1	no	—
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	52	2	no	—
365	C₂²⋊C₄	—	52	2	no	—
366	C₄²	—	2	1	no	—
367	C₄²	C₂×D₅₂	1	1	yes	characteristic
368	C₄²	#6127	1	1	yes	characteristic
369	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
370	C₄²	C₂³×D₁₃	1	1	yes	characteristic
371	C₁₃	#19227	1	1	yes	characteristic, complemented, Sylow
372	C₂³	—	2	1	no	—
373	C₂³	—	52	2	no	—
374	C₂³	#88184	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	104	2	no	—
377	D₄	—	2	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	52	2	no	—
380	D₄	—	52	2	no	—
381	D₄	—	52	2	no	—
382	D₄	—	52	2	no	—
383	D₄	—	104	2	no	—
384	D₄	—	104	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	52	2	no	—
395	C₂×C₄	—	104	4	no	—
396	C₂×C₄	#88184	1	1	yes	characteristic
397	C₂×C₄	#88184	1	1	yes	characteristic
398	C₂×C₄	#88184	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
400	C₂×C₄	C₂×#6127	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	4	1	no	—
407	C₈	—	52	2	no	—
408	C₈	—	52	2	no	—
409	C₈	#88204	1	2	yes	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	104	2	no	—
416	C₂²	—	104	2	no	—
417	C₂²	—	104	2	no	—
418	C₂²	#11718803	1	2	yes	—
419	C₂²	C₂×#88184	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	104	2	no	—
428	C₄	#11719456	1	2	yes	—
429	C₄	C₂×#88204	1	1	yes	characteristic
430	C₄	#11719527	1	1	yes	characteristic
431	C₂	—	2	2	no	—
432	C₂	—	8	1	no	—
433	C₂	—	208	2	no	—
434	C₂	#13124291	1	1	yes	characteristic
435	C₂	#13124498	1	1	yes	characteristic
436	C₂	C₂×#11718803	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#88184
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2966	C₂
socle	C₂²×C₁₃	C₂×#121
hypercenter	#2966	D₁₃
hypocenter	C₁₃	#19227
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2966

Complements

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

N	H ≅ G/N	type
1. #13126162	C₂	semidirect
2. #13125415	C₂	semidirect
3. #13114364	C₂	semidirect
4. #13114359	C₂	semidirect
5. #13114320	C₂	semidirect
6. #13114315	C₂	semidirect
7. #13114252	C₂	semidirect
8. #13114245	C₂	semidirect
9. C₂×#11718049	C₂	semidirect
10. #13113532	C₂	semidirect
11. C₁₃×#2966	C₂	semidirect
156. #2966	D₁₃	semidirect
371. C₁₃	#19227	semidirect

Maximal subgroups

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

subgroup	index
#13126162	2
#13125415	2
#13114364	2
#13114359	2
#13114320	2
#13114315	2
#13114252	2
#13114245	2
C₂×#11718049	2
#13113532	2
C₁₃×#2966	2
#19227	13