Subgroups — #27537180

Order 13568.

598 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13133223	C₂	1	1	yes	maximal, characteristic
2	#20276521	C₂	1	2	yes	maximal, complemented
3	#20276519	C₂	1	2	yes	maximal, complemented
4	#20276514	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276512	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276512	C₂	1	1	yes	maximal, characteristic, complemented
7	#20276472	C₂	1	2	yes	maximal, complemented
8	#20276327	C₂	1	2	yes	maximal
9	C₄×#13133156	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133223	C₄	1	1	yes	characteristic
13	C₂×#13133223	C₂²	1	1	yes	characteristic
14	C₄×#11719945	C₄	1	1	yes	characteristic
15	C₂×#13133156	C₂²	1	2	yes	—
16	C₂×C₁₆×D₅₃	C₂²	1	2	yes	—
17	#16810578	C₄	1	1	yes	characteristic
18	#16810578	C₂²	1	1	yes	characteristic
19	#16810577	C₄	1	1	yes	characteristic
20	#16810577	C₄	1	1	yes	characteristic
21	#16810577	C₂²	1	1	yes	characteristic
22	#16810577	C₂²	1	1	yes	characteristic
23	C₄×#11719917	C₄	1	1	yes	characteristic
24	C₄×#11719912	C₄	1	1	yes	characteristic
25	C₄×#11719912	C₄	1	1	yes	characteristic
26	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
28	C₄⋊#11719908	C₂²	1	2	yes	—
29	#16810441	C₂²	1	2	yes	—
30	#16810441	C₂²	1	2	yes	—
31	C₂²⋊#11719908	C₂²	1	2	yes	—
32	#16810402	C₂²	1	2	yes	—
33	#16810402	C₂²	1	2	yes	—
34	#16810398	C₂²	1	2	yes	—
35	C₄×#11719908	C₂²	1	1	yes	characteristic
36	C₄×#11719908	C₂²	1	1	yes	characteristic
37	C₁₆×Dic₅₃	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₅₃×C₄⋊C₁₆	C₂²	1	2	yes	—
40	C₅₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₄×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
44	#13133223	—	2	4	no	—
45	#13133223	—	2	4	no	—
46	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
47	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
48	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
49	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
50	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
51	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
56	C₄×Dic₁₀₆	C₈	1	1	yes	characteristic
57	C₄×Dic₁₀₆	C₈	1	1	yes	characteristic
58	C₄×D₂₁₂	C₈	1	1	yes	characteristic
59	C₄×D₂₁₂	C₈	1	1	yes	characteristic
60	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
61	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
62	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
63	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
64	#13133176	C₂×C₄	1	1	yes	characteristic
65	#13133174	C₂×C₄	1	1	yes	characteristic
66	#13133174	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
69	#13133156	—	2	4	no	—
70	C₂×#11719908	C₂³	1	2	yes	—
71	C₂×#11719908	C₂³	1	2	yes	—
72	C₁₆×D₅₃	—	2	4	no	—
73	#13133128	C₂×C₄	1	1	yes	characteristic
74	#13133128	C₂×C₄	1	1	yes	characteristic
75	#13133127	C₂×C₄	1	1	yes	characteristic
76	#13133127	C₂×C₄	1	1	yes	characteristic
77	#13133127	C₂×C₄	1	1	yes	characteristic
78	#13133127	C₂×C₄	1	1	yes	characteristic
79	C₄×#88322	C₂×C₄	1	1	yes	characteristic
80	C₄×#88322	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
84	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
89	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
90	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
98	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
99	#11719945	—	2	2	no	—
100	#11719945	—	2	2	no	—
101	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×Dic₁₀₆	C₂×C₈	1	1	yes	characteristic
109	C₂×C₈×C₅₃	—	2	2	no	—
110	C₂×C₈×C₅₃	—	2	2	no	—
111	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
115	C₄²×C₅₃	C₂×C₈	1	1	yes	characteristic
116	C₄²×C₅₃	C₂×C₈	1	1	yes	characteristic
117	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
120	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
121	#11719921	C₂×C₈	1	1	yes	characteristic
122	#11719921	C₂×C₈	1	1	yes	characteristic
123	#11719921	C₂×C₈	1	1	yes	characteristic
124	#11719921	C₂×C₈	1	1	yes	characteristic
125	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
126	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
127	#11719919	C₂×C₈	1	1	yes	characteristic
128	#11719919	C₂×C₈	1	1	yes	characteristic
129	#11719919	C₂×C₈	1	1	yes	characteristic
130	#11719919	C₂×C₈	1	1	yes	characteristic
131	C₄×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	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
137	#11719917	—	2	2	no	—
138	#11719917	—	2	2	no	—
139	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
140	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
141	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
142	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
143	#11719912	—	2	2	no	—
144	#11719912	—	2	2	no	—
145	#11719912	—	2	2	no	—
146	#11719912	—	2	2	no	—
147	C₈×D₅₃	—	2	2	no	—
148	C₈×D₅₃	—	2	2	no	—
149	C₈×D₅₃	M₁₆	1	4	yes	—
150	C₈×D₅₃	#41	1	4	yes	—
151	C₁₆×C₅₃	—	2	2	no	—
152	C₁₆×C₅₃	—	2	2	no	—
153	#11719908	—	2	2	no	—
154	#11719908	—	2	2	no	—
155	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
156	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
157	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₅₃	—	2	1	no	—
159	C₂×C₄×C₅₃	—	2	1	no	—
160	C₂×C₄×C₅₃	—	2	2	no	—
161	C₂×C₄×C₅₃	—	2	2	no	—
162	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
164	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
168	C₂²⋊D₅₃	—	2	2	no	—
169	C₂²⋊D₅₃	—	2	2	no	—
170	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
171	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
172	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
173	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
174	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
176	D₂₁₂	—	2	2	no	—
177	C₄×D₅₃	—	2	1	no	—
178	C₄×D₅₃	—	2	1	no	—
179	C₄×D₅₃	—	2	2	no	—
180	C₄×D₅₃	—	2	2	no	—
181	C₄×D₅₃	—	2	2	no	—
182	C₄×D₅₃	—	2	2	no	—
183	C₄×D₅₃	#117	1	2	yes	—
184	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
185	Dic₁₀₆	—	2	2	no	—
186	C₈×C₅₃	—	2	1	no	—
187	C₈×C₅₃	—	2	1	no	—
188	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
189	C₈×C₅₃	C₂×#41	1	2	yes	—
190	#88322	—	2	1	no	—
191	#88322	—	2	1	no	—
192	#88322	#117	1	2	yes	—
193	#88322	C₂×M₁₆	1	2	yes	—
194	#33420	—	53	1	no	maximal, Sylow
195	C₂²×C₅₃	—	2	1	no	—
196	C₂²×C₅₃	—	2	1	no	—
197	C₂²×C₅₃	—	2	1	no	—
198	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
199	C₂×D₅₃	—	2	1	no	—
200	C₂×D₅₃	—	2	1	no	—
201	C₂×D₅₃	—	2	1	no	—
202	C₂×D₅₃	—	2	1	no	—
203	C₂×D₅₃	—	2	1	no	—
204	C₂×D₅₃	#431	1	2	yes	—
205	C₄×C₅₃	—	2	1	no	—
206	C₄×C₅₃	—	2	1	no	—
207	C₄×C₅₃	—	2	1	no	—
208	C₄×C₅₃	#504	1	2	yes	—
209	C₄×C₅₃	#504	1	2	yes	—
210	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
211	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
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	#431	1	2	yes	—
218	C₄×#131	—	53	1	no	—
219	#2164	—	53	2	no	—
220	#2164	—	53	2	no	—
221	#2162	—	53	1	no	—
222	#2162	—	53	1	no	—
223	#2162	—	53	1	no	—
224	#2162	D₅₃	1	1	yes	characteristic, complemented
225	#2151	—	53	2	no	—
226	#2113	—	53	2	no	—
227	C₄×M₃₂	—	53	1	no	—
228	C₂×C₄×C₁₆	—	53	1	no	—
229	C₂×C₅₃	—	4	1	no	—
230	C₂×C₅₃	C₂×#431	1	1	yes	characteristic
231	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
232	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
233	D₅₃	—	2	2	no	—
234	D₅₃	—	4	1	no	—
235	C₂×#131	—	53	1	no	—
236	C₂×#131	—	53	1	no	—
237	C₄×#41	—	53	1	no	—
238	C₂×M₃₂	—	53	2	no	—
239	C₂²×C₁₆	—	53	2	no	—
240	#405	—	53	1	no	—
241	#405	—	53	1	no	—
242	#405	—	53	1	no	—
243	#405	—	53	1	no	—
244	#405	—	53	1	no	—
245	#405	—	53	1	no	—
246	C₄×M₁₆	—	53	1	no	—
247	C₄×M₁₆	—	53	1	no	—
248	C₄×M₁₆	—	53	1	no	—
249	C₂×C₄×C₈	—	53	1	no	—
250	C₂×C₄×C₈	—	53	1	no	—
251	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
252	C₄⋊C₁₆	—	53	2	no	—
253	C₄⋊C₁₆	—	53	2	no	—
254	C₄⋊C₁₆	—	53	2	no	—
255	C₄⋊C₁₆	C₂×D₅₃	1	2	yes	—
256	C₂²⋊C₁₆	—	53	2	no	—
257	C₂²⋊C₁₆	—	53	2	no	—
258	C₂²⋊C₁₆	—	53	2	no	—
259	C₂²⋊C₁₆	C₂×D₅₃	1	2	yes	—
260	#346	—	53	2	no	—
261	C₄×C₁₆	—	53	2	no	—
262	C₄×C₁₆	—	53	1	no	—
263	C₄×C₁₆	—	53	1	no	—
264	C₄×C₁₆	C₂×D₅₃	1	1	yes	characteristic
265	C₄×C₁₆	C₂×D₅₃	1	1	yes	characteristic
266	C₅₃	#33420	1	1	yes	characteristic, complemented, Sylow
267	C₂×#41	—	53	1	no	—
268	#131	—	106	4	no	—
269	#131	—	106	4	no	—
270	C₂×M₁₆	—	53	1	no	—
271	C₂×M₁₆	—	53	1	no	—
272	C₂×M₁₆	—	53	1	no	—
273	C₂×M₁₆	—	53	1	no	—
274	C₂×M₁₆	—	53	1	no	—
275	C₂×M₁₆	—	53	1	no	—
276	C₂²×C₈	—	53	1	no	—
277	C₂²×C₈	—	53	1	no	—
278	C₂²×C₈	—	53	1	no	—
279	C₂²×C₈	—	53	1	no	—
280	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
282	C₄×Q₈	—	53	1	no	—
283	C₄×Q₈	—	53	1	no	—
284	C₄×D₄	—	53	1	no	—
285	C₄×D₄	—	53	1	no	—
286	C₄×D₄	—	53	1	no	—
287	C₄×D₄	—	53	1	no	—
288	C₄×D₄	—	53	1	no	—
289	C₄×D₄	—	53	1	no	—
290	#117	—	53	1	no	—
291	#117	—	53	1	no	—
292	#117	—	53	1	no	—
293	C₂×C₄²	—	53	1	no	—
294	C₂×C₄²	—	53	1	no	—
295	C₂×C₄²	C₄×D₅₃	1	1	yes	characteristic
296	M₃₂	—	106	4	no	—
297	C₂×C₁₆	—	53	2	no	—
298	C₂×C₁₆	—	53	2	no	—
299	C₂×C₁₆	—	106	4	no	—
300	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
301	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
302	#97	—	53	1	no	—
303	#97	—	53	1	no	—
304	#97	—	53	1	no	—
305	#97	—	53	1	no	—
306	#97	—	53	1	no	—
307	#97	—	53	1	no	—
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	C₄×D₅₃	1	1	yes	characteristic
315	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
318	#41	—	106	2	no	—
319	#41	—	106	2	no	—
320	C₂×Q₈	—	53	1	no	—
321	C₂×D₄	—	53	1	no	—
322	C₂×D₄	—	53	1	no	—
323	C₂×D₄	—	53	1	no	—
324	C₂²×C₄	—	53	1	no	—
325	C₂²×C₄	—	53	1	no	—
326	C₂²×C₄	—	53	1	no	—
327	C₂²×C₄	—	53	1	no	—
328	C₂²×C₄	—	53	1	no	—
329	C₂²×C₄	—	53	1	no	—
330	C₂²×C₄	C₈×D₅₃	1	1	yes	characteristic
331	C₂²×C₄	C₈×D₅₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
333	M₁₆	—	106	2	no	—
334	M₁₆	—	106	2	no	—
335	M₁₆	—	106	2	no	—
336	M₁₆	—	106	2	no	—
337	M₁₆	—	106	2	no	—
338	M₁₆	—	106	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	53	1	no	—
342	C₂×C₈	—	53	1	no	—
343	C₂×C₈	—	53	4	no	—
344	C₂×C₈	—	53	4	no	—
345	C₂×C₈	—	53	1	no	—
346	C₂×C₈	—	53	1	no	—
347	C₂×C₈	—	106	2	no	—
348	C₂×C₈	—	106	2	no	—
349	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
350	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
351	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
352	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	53	1	no	—
360	C₂²⋊C₄	—	53	1	no	—
361	C₂²⋊C₄	—	53	1	no	—
362	C₂²⋊C₄	—	53	1	no	—
363	C₂²⋊C₄	—	53	1	no	—
364	C₂²⋊C₄	—	53	1	no	—
365	C₄²	—	53	1	no	—
366	C₄²	—	53	1	no	—
367	C₄²	—	53	1	no	—
368	C₄²	—	53	1	no	—
369	C₄²	—	53	1	no	—
370	C₄²	—	53	1	no	—
371	C₄²	C₈×D₅₃	1	1	yes	characteristic
372	C₄²	C₈×D₅₃	1	1	yes	characteristic
373	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
374	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
375	C₁₆	—	2	2	no	—
376	C₁₆	—	2	2	no	—
377	C₁₆	—	106	2	no	—
378	C₁₆	—	106	2	no	—
379	C₂³	—	53	1	no	—
380	C₂³	—	53	1	no	—
381	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
382	Q₈	—	106	2	no	—
383	D₄	—	106	2	no	—
384	D₄	—	106	2	no	—
385	D₄	—	106	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	53	1	no	—
391	C₂×C₄	—	53	2	no	—
392	C₂×C₄	—	53	2	no	—
393	C₂×C₄	—	53	1	no	—
394	C₂×C₄	—	53	1	no	—
395	C₂×C₄	—	53	1	no	—
396	C₂×C₄	—	53	1	no	—
397	C₂×C₄	—	53	1	no	—
398	C₂×C₄	—	106	2	no	—
399	C₂×C₄	—	106	2	no	—
400	C₂×C₄	—	106	2	no	—
401	C₂×C₄	—	106	2	no	—
402	C₂×C₄	—	106	1	no	—
403	C₂×C₄	—	106	1	no	—
404	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
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	C₂²×C₄×D₅₃	1	1	yes	characteristic
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	53	2	no	—
413	C₈	—	53	2	no	—
414	C₈	—	106	1	no	—
415	C₈	—	106	1	no	—
416	C₈	M₁₆×D₅₃	1	2	yes	—
417	C₈	#41×D₅₃	1	2	yes	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	53	2	no	—
422	C₂²	—	106	1	no	—
423	C₂²	—	106	1	no	—
424	C₂²	—	106	1	no	—
425	C₂²	—	106	1	no	—
426	C₂²	—	106	1	no	—
427	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	53	2	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	#16811039	1	2	yes	—
438	C₄	#16811041	1	2	yes	—
439	C₄	#117×D₅₃	1	1	yes	characteristic
440	C₄	C₂×M₁₆×D₅₃	1	1	yes	characteristic
441	C₂	—	4	1	no	—
442	C₂	—	106	2	no	—
443	C₂	—	212	1	no	—
444	C₂	#431×D₅₃	1	1	yes	characteristic
445	C₂	C₂×#16811039	1	1	yes	characteristic
446	C₂	C₂×#16811041	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₅₃
commutator, socle	C₂²×C₅₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₅₃×#2162	C₂
prime radical	C₂×#11719945	C₂×C₄
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	#2162	D₅₃
hypocenter	C₅₃	#33420
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄×C₈ ◁ #2162

Complements

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

N	H ≅ G/N	type
2. #20276521	C₂	semidirect
3. #20276519	C₂	semidirect
4. #20276514	C₂	semidirect
5. #20276512	C₂	semidirect
6. #20276512	C₂	semidirect
7. #20276472	C₂	semidirect
9. C₄×#13133156	C₂	semidirect
10. C₄×C₁₆×D₅₃	C₂	semidirect
11. C₅₃×#2162	C₂	semidirect
224. #2162	D₅₃	semidirect
266. C₅₃	#33420	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13133223	2
#20276521	2
#20276519	2
#20276514	2
#20276512	2
#20276472	2
#20276327	2
C₄×#13133156	2
C₄×C₁₆×D₅₃	2
C₅₃×#2162	2
#33420	53