Subgroups — #27537744

Order 13568.

452 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283647	C₂	1	1	yes	maximal, characteristic
2	#20276623	C₂	1	1	yes	maximal, characteristic, complemented
3	#20276622	C₂	1	1	yes	maximal, characteristic, complemented
4	#20276622	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276621	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276621	C₂	1	1	yes	maximal, characteristic, complemented
7	#20276620	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₆×Dic₁₀₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#20276617	C₂	1	1	yes	maximal, characteristic, complemented
10	#20276522	C₂	1	1	yes	maximal, characteristic
11	#20276519	C₂	1	1	yes	maximal, characteristic
12	#20276519	C₂	1	1	yes	maximal, characteristic
13	#20276515	C₂	1	1	yes	maximal, characteristic
14	#20276511	C₂	1	1	yes	maximal, characteristic
15	C₅₃×#2164	C₂	1	1	yes	maximal, characteristic
16	#16811176	C₄	1	1	yes	characteristic
17	#16810751	C₄	1	1	yes	characteristic
18	#16810751	C₄	1	1	yes	characteristic
19	#16810751	C₄	1	1	yes	characteristic
20	#16810751	C₄	1	1	yes	characteristic
21	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
22	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
23	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
24	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
25	#16810651	C₄	1	1	yes	characteristic
26	#16810650	C₄	1	1	yes	characteristic
27	#16810646	C₄	1	1	yes	characteristic
28	#16810578	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
30	C₄⋊#11719908	C₂²	1	1	yes	characteristic
31	C₄⋊#11719908	C₂²	1	1	yes	characteristic
32	#16810441	C₂²	1	1	yes	characteristic
33	#16810441	C₂²	1	1	yes	characteristic
34	#16810441	C₂²	1	1	yes	characteristic
35	#16810441	C₂²	1	1	yes	characteristic
36	#16810441	C₂²	1	1	yes	characteristic
37	#16810441	C₂²	1	1	yes	characteristic
38	#16810441	C₂²	1	1	yes	characteristic
39	#16810441	C₂²	1	1	yes	characteristic
40	C₂²⋊#11719908	C₂²	1	1	yes	characteristic
41	C₂²⋊#11719908	C₂²	1	1	yes	characteristic
42	#16810399	C₂²	1	1	yes	characteristic
43	#16810398	C₂²	1	1	yes	characteristic
44	#16810398	C₂²	1	1	yes	characteristic
45	#16810398	C₂²	1	1	yes	characteristic
46	#16810398	C₂²	1	1	yes	characteristic
47	C₄×#11719908	C₂²	1	1	yes	characteristic
48	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
49	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
50	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
52	C₅₃×#405	C₂²	1	1	yes	characteristic
53	C₅₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
54	C₅₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
55	C₅₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
56	C₅₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₅₃×#346	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
60	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
61	#13133216	C₈	1	1	yes	characteristic
62	#13133216	C₈	1	1	yes	characteristic
63	#13133208	C₈	1	1	yes	characteristic
64	#13133208	C₈	1	1	yes	characteristic
65	#13133194	C₈	1	1	yes	characteristic
66	#13133194	C₈	1	1	yes	characteristic
67	#13133194	C₈	1	1	yes	characteristic
68	#13133194	C₈	1	1	yes	characteristic
69	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
71	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
72	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
73	#13133176	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
75	C₂×#11719908	C₂³	1	1	yes	characteristic
76	C₂×#11719908	C₂³	1	1	yes	characteristic
77	C₂×#11719908	C₂³	1	1	yes	characteristic
78	C₂×#11719908	C₂³	1	1	yes	characteristic
79	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
80	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
81	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
82	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
83	#13133146	C₂×C₄	1	1	yes	characteristic
84	#13133146	C₂×C₄	1	1	yes	characteristic
85	#13133146	C₂×C₄	1	1	yes	characteristic
86	#13133146	C₂×C₄	1	1	yes	characteristic
87	#13133146	C₂×C₄	1	1	yes	characteristic
88	#13133146	C₂×C₄	1	1	yes	characteristic
89	#13133146	C₂×C₄	1	1	yes	characteristic
90	#13133146	C₂×C₄	1	1	yes	characteristic
91	#13133127	C₂×C₄	1	1	yes	characteristic
92	#13133127	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
96	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
97	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
98	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
100	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
101	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
102	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
103	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
104	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
105	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
106	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
107	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
108	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
112	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
113	C₂×Dic₁₀₆	C₂×C₈	1	1	yes	characteristic
114	C₂×Dic₁₀₆	C₂×C₈	1	1	yes	characteristic
115	C₂×Dic₁₀₆	C₂×C₈	1	1	yes	characteristic
116	C₂×Dic₁₀₆	C₂×C₈	1	1	yes	characteristic
117	M₁₆×C₅₃	—	4	1	no	—
118	C₂×C₈×C₅₃	—	2	1	no	—
119	C₂×C₈×C₅₃	—	2	1	no	—
120	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
124	C₄⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
125	C₄⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
126	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
127	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
128	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
131	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
132	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
133	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
134	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
135	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
136	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
137	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
138	#11719919	C₂×C₈	1	1	yes	characteristic
139	#11719919	C₂×C₈	1	1	yes	characteristic
140	#11719919	C₂×C₈	1	1	yes	characteristic
141	#11719919	C₂×C₈	1	1	yes	characteristic
142	#11719919	C₂×C₈	1	1	yes	characteristic
143	#11719919	C₂×C₈	1	1	yes	characteristic
144	#11719919	C₂×C₈	1	1	yes	characteristic
145	#11719919	C₂×C₈	1	1	yes	characteristic
146	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
147	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
148	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
152	#11719917	—	4	1	no	—
153	C₂×#88322	—	4	1	no	—
154	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
155	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
156	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
157	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
158	C₁₆×C₅₃	—	2	1	no	—
159	C₁₆×C₅₃	—	2	1	no	—
160	C₁₆×C₅₃	—	2	1	no	—
161	C₁₆×C₅₃	—	2	1	no	—
162	#11719908	—	2	1	no	—
163	#11719908	—	2	1	no	—
164	#11719908	—	2	1	no	—
165	#11719908	—	2	1	no	—
166	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₅₃	—	2	1	no	—
168	C₂×C₄×C₅₃	—	2	1	no	—
169	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
172	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
174	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×Dic₅₃	—	2	2	no	—
176	C₂×Dic₅₃	—	4	1	no	—
177	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
181	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
182	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
183	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
184	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
185	Dic₁₀₆	—	2	2	no	—
186	Dic₁₀₆	—	2	2	no	—
187	Dic₁₀₆	—	4	1	no	—
188	Dic₁₀₆	—	4	1	no	—
189	C₈×C₅₃	—	2	1	no	—
190	C₈×C₅₃	—	2	1	no	—
191	C₈×C₅₃	—	2	1	no	—
192	C₈×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
193	C₈×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
194	#88322	—	2	1	no	—
195	#88322	—	2	1	no	—
196	#88322	—	2	1	no	—
197	#88322	—	2	1	no	—
198	#33499	—	53	1	no	maximal, Sylow
199	C₂²×C₅₃	—	2	1	no	—
200	C₂²×C₅₃	—	2	1	no	—
201	C₂²×C₅₃	—	2	1	no	—
202	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
203	C₄×C₅₃	—	2	1	no	—
204	C₄×C₅₃	—	2	1	no	—
205	C₄×C₅₃	—	2	1	no	—
206	C₄×C₅₃	—	2	1	no	—
207	C₄×C₅₃	—	2	1	no	—
208	C₄×C₅₃	#519	1	1	yes	characteristic
209	C₄×C₅₃	#568	1	1	yes	characteristic
210	Dic₅₃	—	2	1	no	—
211	Dic₅₃	—	2	1	no	—
212	Dic₅₃	—	2	1	no	—
213	Dic₅₃	—	2	1	no	—
214	Dic₅₃	—	2	1	no	—
215	Dic₅₃	—	2	1	no	—
216	Dic₅₃	—	2	1	no	—
217	Dic₅₃	#504	1	2	yes	—
218	#2960	—	53	1	no	—
219	#2183	—	53	1	no	—
220	#2183	—	53	1	no	—
221	#2183	—	53	1	no	—
222	#2183	—	53	1	no	—
223	#2183	—	53	1	no	—
224	#2183	—	53	1	no	—
225	Q₈×C₁₆	—	53	1	no	—
226	Q₈×C₁₆	—	53	1	no	—
227	#2164	—	53	1	no	—
228	#2164	—	53	1	no	—
229	#2164	—	53	1	no	—
230	#2164	D₅₃	1	1	yes	characteristic
231	#2163	—	53	1	no	—
232	#2162	—	53	1	no	—
233	C₂×C₅₃	—	4	1	no	—
234	C₂×C₅₃	#2982	1	1	yes	characteristic
235	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
236	C₂×C₅₃	#3407	1	1	yes	characteristic
237	#533	—	53	1	no	—
238	#446	—	53	1	no	—
239	#446	—	53	1	no	—
240	#446	—	53	1	no	—
241	#446	—	53	1	no	—
242	C₈×Q₈	—	53	1	no	—
243	C₈×Q₈	—	53	1	no	—
244	C₈×Q₈	—	53	1	no	—
245	C₈×Q₈	—	53	1	no	—
246	#424	—	53	1	no	—
247	#424	—	53	1	no	—
248	#423	—	53	1	no	—
249	#405	—	53	1	no	—
250	#405	C₂×D₅₃	1	1	yes	characteristic
251	C₂×C₄×C₈	—	53	1	no	—
252	C₄⋊C₁₆	—	53	1	no	—
253	C₄⋊C₁₆	—	53	1	no	—
254	C₄⋊C₁₆	—	53	1	no	—
255	C₄⋊C₁₆	—	53	1	no	—
256	C₄⋊C₁₆	—	53	1	no	—
257	C₄⋊C₁₆	—	53	1	no	—
258	C₄⋊C₁₆	—	53	1	no	—
259	C₄⋊C₁₆	—	53	1	no	—
260	C₄⋊C₁₆	—	53	1	no	—
261	C₄⋊C₁₆	—	53	1	no	—
262	C₄⋊C₁₆	C₂×D₅₃	1	1	yes	characteristic
263	C₄⋊C₁₆	C₂×D₅₃	1	1	yes	characteristic
264	C₂²⋊C₁₆	—	53	1	no	—
265	C₂²⋊C₁₆	—	53	1	no	—
266	C₂²⋊C₁₆	C₂×D₅₃	1	1	yes	characteristic
267	C₂²⋊C₁₆	C₂×D₅₃	1	1	yes	characteristic
268	#346	—	53	1	no	—
269	#346	—	53	1	no	—
270	#346	—	53	1	no	—
271	#346	—	53	1	no	—
272	#346	—	53	1	no	—
273	#346	C₂×D₅₃	1	1	yes	characteristic
274	C₄×C₁₆	—	53	1	no	—
275	C₄×C₁₆	—	53	1	no	—
276	C₄×C₁₆	—	53	1	no	—
277	C₄×C₁₆	—	53	1	no	—
278	C₄×C₁₆	—	53	1	no	—
279	C₄×C₁₆	C₂×D₅₃	1	1	yes	characteristic
280	C₅₃	#33499	1	1	yes	characteristic, complemented, Sylow
281	C₂×M₁₆	—	53	1	no	—
282	C₂×M₁₆	C₄×D₅₃	1	1	yes	characteristic
283	C₂²×C₈	—	53	1	no	—
284	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
285	C₄⋊Q₈	—	53	1	no	—
286	C₄⋊Q₈	—	53	1	no	—
287	#125	—	53	1	no	—
288	#125	—	53	1	no	—
289	C₂²⋊Q₈	—	53	1	no	—
290	C₂²⋊Q₈	—	53	1	no	—
291	C₂²⋊Q₈	—	53	1	no	—
292	C₂²⋊Q₈	—	53	1	no	—
293	C₄×Q₈	—	53	1	no	—
294	C₄×Q₈	—	53	1	no	—
295	C₄×Q₈	—	53	1	no	—
296	C₄×Q₈	—	53	1	no	—
297	#117	—	53	1	no	—
298	#117	C₄×D₅₃	1	1	yes	characteristic
299	C₂×C₄²	—	53	1	no	—
300	C₂×C₁₆	—	53	1	no	—
301	C₂×C₁₆	—	53	1	no	—
302	C₂×C₁₆	—	53	1	no	—
303	C₂×C₁₆	—	53	1	no	—
304	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
305	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
306	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
307	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
308	C₄⋊C₈	—	53	1	no	—
309	C₄⋊C₈	—	53	1	no	—
310	C₄⋊C₈	—	53	1	no	—
311	C₄⋊C₈	—	53	1	no	—
312	C₄⋊C₈	—	53	1	no	—
313	C₄⋊C₈	—	53	1	no	—
314	C₄⋊C₈	—	53	1	no	—
315	C₄⋊C₈	—	53	1	no	—
316	C₄⋊C₈	—	53	1	no	—
317	C₄⋊C₈	—	53	1	no	—
318	C₄⋊C₈	—	53	1	no	—
319	C₄⋊C₈	—	53	1	no	—
320	#97	—	53	1	no	—
321	#97	—	53	1	no	—
322	#97	C₄×D₅₃	1	1	yes	characteristic
323	#97	C₄×D₅₃	1	1	yes	characteristic
324	C₄×C₈	—	53	1	no	—
325	C₄×C₈	—	53	1	no	—
326	C₄×C₈	—	53	1	no	—
327	C₄×C₈	—	53	1	no	—
328	C₄×C₈	—	53	1	no	—
329	C₄×C₈	—	53	1	no	—
330	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
331	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
332	C₂×Q₈	—	53	1	no	—
333	C₂×Q₈	—	53	1	no	—
334	C₂×Q₈	—	53	1	no	—
335	C₂×Q₈	—	53	1	no	—
336	C₂²×C₄	—	53	1	no	—
337	C₂²×C₄	—	53	1	no	—
338	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
339	M₁₆	—	4	1	no	—
340	M₁₆	—	212	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	53	1	no	—
344	C₂×C₈	—	53	1	no	—
345	C₂×C₈	—	53	1	no	—
346	C₂×C₈	—	53	1	no	—
347	C₂×C₈	—	212	1	no	—
348	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
350	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
351	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
352	C₄⋊C₄	—	53	1	no	—
353	C₄⋊C₄	—	53	1	no	—
354	C₄⋊C₄	—	53	1	no	—
355	C₄⋊C₄	—	53	1	no	—
356	C₄⋊C₄	—	53	1	no	—
357	C₄⋊C₄	—	53	1	no	—
358	C₄⋊C₄	—	53	1	no	—
359	C₄⋊C₄	—	53	1	no	—
360	C₄⋊C₄	—	53	1	no	—
361	C₄⋊C₄	—	53	1	no	—
362	C₄⋊C₄	—	53	1	no	—
363	C₄⋊C₄	—	53	1	no	—
364	C₄⋊C₄	—	53	1	no	—
365	C₄⋊C₄	—	53	1	no	—
366	C₄⋊C₄	C₈×D₅₃	1	1	yes	characteristic
367	C₄⋊C₄	C₈×D₅₃	1	1	yes	characteristic
368	C₂²⋊C₄	—	53	1	no	—
369	C₂²⋊C₄	—	53	1	no	—
370	C₂²⋊C₄	C₈×D₅₃	1	1	yes	characteristic
371	C₂²⋊C₄	C₈×D₅₃	1	1	yes	characteristic
372	C₄²	—	53	1	no	—
373	C₄²	—	53	1	no	—
374	C₄²	—	53	1	no	—
375	C₄²	—	53	1	no	—
376	C₄²	—	53	1	no	—
377	C₄²	—	53	1	no	—
378	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
379	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
380	C₁₆	—	2	1	no	—
381	C₁₆	—	2	1	no	—
382	C₁₆	—	2	1	no	—
383	C₁₆	—	2	1	no	—
384	C₁₆	—	106	1	no	—
385	C₁₆	—	106	1	no	—
386	C₁₆	—	106	1	no	—
387	C₁₆	—	106	1	no	—
388	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
389	Q₈	—	106	2	no	—
390	Q₈	—	106	2	no	—
391	Q₈	—	212	1	no	—
392	Q₈	—	212	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	53	1	no	—
396	C₂×C₄	—	53	1	no	—
397	C₂×C₄	—	53	1	no	—
398	C₂×C₄	—	53	1	no	—
399	C₂×C₄	—	53	1	no	—
400	C₂×C₄	—	53	1	no	—
401	C₂×C₄	—	53	1	no	—
402	C₂×C₄	—	53	1	no	—
403	C₂×C₄	—	106	2	no	—
404	C₂×C₄	—	212	1	no	—
405	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
406	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
407	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
408	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
409	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	2	1	no	—
414	C₈	—	106	1	no	—
415	C₈	—	106	1	no	—
416	C₈	—	106	1	no	—
417	C₈	—	106	1	no	—
418	C₈	#13133264	1	1	yes	characteristic
419	C₈	#13133264	1	1	yes	characteristic
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	53	2	no	—
430	C₄	—	106	1	no	—
431	C₄	—	106	1	no	—
432	C₄	—	106	1	no	—
433	C₄	—	106	1	no	—
434	C₄	—	106	1	no	—
435	C₄	—	106	1	no	—
436	C₄	—	106	1	no	—
437	C₄	#16811100	1	1	yes	characteristic
438	C₄	#16811389	1	1	yes	characteristic
439	C₂	—	4	1	no	—
440	C₂	#20283795	1	1	yes	characteristic
441	C₂	#504×D₅₃	1	1	yes	characteristic
442	C₂	#20287816	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅₃
commutator, socle	C₂²×C₅₃	C₂³×C₈
Fitting	C₅₃×#2164	C₂
prime radical	C₂³×C₅₃	C₂²×C₈
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	#2164	D₅₃
hypocenter	C₅₃	#33499
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ #2164

Complements

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

N	H ≅ G/N	type
2. #20276623	C₂	semidirect
3. #20276622	C₂	semidirect
4. #20276622	C₂	semidirect
5. #20276621	C₂	semidirect
6. #20276621	C₂	semidirect
7. #20276620	C₂	semidirect
8. C₁₆×Dic₁₀₆	C₂	semidirect
9. #20276617	C₂	semidirect
280. C₅₃	#33499	semidirect

Maximal subgroups

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

subgroup	index
#20283647	2
#20276623	2
#20276622	2
#20276621	2
#20276620	2
C₁₆×Dic₁₀₆	2
#20276617	2
#20276522	2
#20276519	2
#20276515	2
#20276511	2
C₅₃×#2164	2
#33499	53