Subgroups — #27387662

Order 13568.

844 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810670	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810670	C₂	1	1	yes	maximal, characteristic
3	#430×D₅₃	C₂	1	2	yes	maximal
4	#20283131	C₂	1	1	yes	maximal, characteristic
5	#20275506	C₂	1	1	yes	maximal, characteristic, complemented
6	#20275505	C₂	1	1	yes	maximal, characteristic, complemented
7	#20275504	C₂	1	2	yes	maximal, complemented
8	#20275503	C₂	1	1	yes	maximal, characteristic, complemented
9	#20275502	C₂	1	2	yes	maximal, complemented
10	#344×D₅₃	C₂	1	2	yes	maximal
11	C₅₃×#1953	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11719912	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
14	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
15	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
16	#117×D₅₃	C₂²	1	1	yes	characteristic
17	#16810672	C₂²	1	2	yes	—
18	#16810671	C₂²	1	2	yes	—
19	#16810671	C₂²	1	2	yes	—
20	#16810670	—	2	1	no	—
21	#16810670	—	2	1	no	—
22	#16810670	—	2	1	no	—
23	#16810670	—	2	1	no	—
24	#16810670	—	2	4	no	—
25	#16810670	C₄	1	8	yes	complemented
26	C₂×#13133153	C₂²	1	1	yes	characteristic
27	C₂×#13133153	C₂²	1	1	yes	characteristic
28	C₂×#13133152	C₂²	1	2	yes	—
29	C₂×#13133152	C₂²	1	2	yes	—
30	#108×D₅₃	—	2	4	no	—
31	#16810581	C₂²	1	1	yes	characteristic
32	#16810580	—	2	1	no	—
33	#16810579	C₂²	1	1	yes	characteristic
34	#16810578	C₂²	1	1	yes	characteristic
35	#16810577	—	2	1	no	—
36	#16810575	—	2	1	no	—
37	C₄×#11719912	—	2	1	no	—
38	#16810395	C₂²	1	2	yes	—
39	#16810394	C₂²	1	2	yes	—
40	#16810393	C₂²	1	2	yes	—
41	C₅₃×#430	C₂²	1	2	yes	—
42	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
44	C₅₃×#405	C₂²	1	1	yes	characteristic
45	C₅₃×#344	C₂²	1	2	yes	—
46	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
47	C₂×#11719917	C₂³	1	2	yes	—
48	C₂×#11719917	C₂³	1	2	yes	—
49	C₂×#11719917	C₂³	1	1	yes	characteristic
50	C₂×#11719912	—	2	1	no	—
51	C₂×#11719912	—	2	2	no	—
52	C₂×#11719912	—	2	2	no	—
53	C₂×#11719912	C₂×C₄	1	4	yes	—
54	C₂×#11719912	D₄	1	1	yes	characteristic
55	C₂×#11719912	D₄	1	1	yes	characteristic
56	C₂×#11719912	D₄	1	1	yes	characteristic
57	C₂×#11719912	D₄	1	1	yes	characteristic
58	C₂×#11719912	Q₈	1	4	yes	—
59	M₁₆×D₅₃	—	2	2	no	—
60	M₁₆×D₅₃	—	2	2	no	—
61	M₁₆×D₅₃	—	2	2	no	—
62	M₁₆×D₅₃	—	2	2	no	—
63	M₁₆×D₅₃	—	2	2	no	—
64	M₁₆×D₅₃	—	2	2	no	—
65	M₁₆×D₅₃	—	2	2	no	—
66	M₁₆×D₅₃	C₂×C₄	1	4	yes	—
67	M₁₆×D₅₃	C₂×C₄	1	4	yes	—
68	M₁₆×D₅₃	D₄	1	4	yes	—
69	C₂²×#88322	C₂³	1	1	yes	characteristic
70	C₂×C₈×D₅₃	—	2	1	no	—
71	C₂×C₈×D₅₃	—	2	2	no	—
72	C₂×C₈×D₅₃	—	2	2	no	—
73	#13133176	C₂³	1	1	yes	characteristic
74	#13133175	—	2	1	no	—
75	#13133174	—	2	1	no	—
76	#13133173	Q₈	1	2	yes	—
77	C₄⋊C₄×D₅₃	—	2	1	no	—
78	C₂²⋊C₄×D₅₃	Q₈	1	2	yes	—
79	C₄²×D₅₃	—	2	1	no	—
80	#13133153	—	2	1	no	—
81	#13133153	—	2	1	no	—
82	#13133153	—	2	4	no	—
83	#13133153	C₂×C₄	1	4	yes	complemented
84	#13133152	—	2	4	no	—
85	#13133152	—	2	4	no	—
86	#13133152	—	2	2	no	—
87	#13133152	—	2	2	no	—
88	#13133152	C₂×C₄	1	8	yes	complemented
89	#13133128	—	2	1	no	—
90	#13133127	—	2	1	no	—
91	#13133127	—	2	1	no	—
92	C₄×#88322	—	2	1	no	—
93	C₈×Dic₅₃	—	2	1	no	—
94	C₈×Dic₅₃	—	2	1	no	—
95	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
96	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
97	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
99	#117×C₅₃	C₂³	1	1	yes	characteristic
100	#108×C₅₃	—	2	4	no	—
101	#108×C₅₃	—	2	1	no	—
102	#108×C₅₃	—	2	1	no	—
103	#108×C₅₃	C₂×C₄	1	4	yes	complemented
104	#97×C₅₃	—	2	1	no	—
105	C₄×C₈×C₅₃	—	2	1	no	—
106	C₂³×D₅₃	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
108	C₂²×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₄×D₅₃	—	2	2	no	—
110	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
111	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
114	C₂×C₄×D₅₃	C₂×Q₈	1	2	yes	—
115	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
116	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
117	C₂×C₄×D₅₃	#41	1	2	yes	—
118	M₁₆×C₅₃	—	2	2	no	—
119	M₁₆×C₅₃	—	2	1	no	—
120	M₁₆×C₅₃	—	2	2	no	—
121	M₁₆×C₅₃	—	2	2	no	—
122	M₁₆×C₅₃	C₂²×C₄	1	4	yes	—
123	M₁₆×C₅₃	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₅₃	—	2	1	no	—
125	C₂×C₈×C₅₃	—	2	2	no	—
126	C₂×C₈×C₅₃	—	2	2	no	—
127	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₅₃	C₂×Q₈	1	2	yes	—
131	C₄⋊C₄×C₅₃	—	2	1	no	—
132	C₂²⋊C₄×C₅₃	C₂×Q₈	1	2	yes	—
133	C₄²×C₅₃	—	2	1	no	—
134	C₂²⋊Dic₅₃	C₂×Q₈	1	2	yes	—
135	#11719921	—	2	2	no	—
136	C₄⋊Dic₅₃	—	2	1	no	—
137	#11719919	—	2	2	no	—
138	C₄×Dic₅₃	—	2	1	no	—
139	C₄×Dic₅₃	—	2	2	no	—
140	#11719917	—	2	2	no	—
141	#11719917	—	2	1	no	—
142	#11719917	—	2	2	no	—
143	#11719917	—	2	2	no	—
144	#11719917	C₂²×C₄	1	4	yes	—
145	#11719917	C₂×D₄	1	2	yes	—
146	C₂×#88322	—	2	1	no	—
147	C₂×#88322	—	2	2	no	—
148	C₂×#88322	—	2	2	no	—
149	C₂×#88322	C₂²×C₄	1	2	yes	—
150	C₂×#88322	C₂×D₄	1	1	yes	characteristic
151	C₂×#88322	C₂×D₄	1	1	yes	characteristic
152	C₂×#88322	C₂×Q₈	1	2	yes	—
153	#11719912	—	2	4	no	—
154	#11719912	—	2	4	no	—
155	#11719912	—	2	4	no	—
156	#11719912	—	4	2	no	—
157	#11719912	—	4	2	no	—
158	#11719912	C₄⋊C₄	1	4	yes	—
159	#11719912	C₄⋊C₄	1	4	yes	—
160	#11719912	C₄⋊C₄	1	4	yes	—
161	#11719912	C₄⋊C₄	1	4	yes	—
162	C₈×D₅₃	—	2	4	no	—
163	C₈×D₅₃	—	2	4	no	—
164	C₈×D₅₃	—	2	4	no	—
165	C₈×D₅₃	—	4	2	no	—
166	C₈×D₅₃	—	4	2	no	—
167	C₂³×C₅₃	C₂²×Q₈	1	1	yes	characteristic
168	C₂²×D₅₃	—	8	1	no	—
169	C₂²×D₅₃	C₄×Q₈	1	2	yes	—
170	C₂²×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
171	C₂²×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
172	C₂²×D₅₃	C₄⋊Q₈	1	2	yes	—
173	C₂×C₄×C₅₃	—	2	2	no	—
174	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
180	C₂×Dic₅₃	—	2	2	no	—
181	C₂×Dic₅₃	C₄×Q₈	1	2	yes	—
182	C₂×Dic₅₃	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂×Dic₅₃	C₂²⋊Q₈	1	1	yes	characteristic
184	C₂×Dic₅₃	C₄⋊Q₈	1	2	yes	—
185	C₄×D₅₃	—	8	2	no	—
186	C₄×D₅₃	C₂×C₄⋊C₄	1	2	yes	—
187	C₄×D₅₃	C₂×C₄⋊C₄	1	2	yes	—
188	C₄×D₅₃	C₄×D₄	1	2	yes	—
189	C₄×D₅₃	C₄×D₄	1	2	yes	—
190	C₄×D₅₃	#121	1	2	yes	—
191	C₄×D₅₃	#121	1	2	yes	—
192	C₄×D₅₃	#125	1	2	yes	—
193	C₄×D₅₃	#125	1	2	yes	—
194	C₈×C₅₃	—	2	4	no	—
195	C₈×C₅₃	—	2	2	no	—
196	C₈×C₅₃	—	4	2	no	—
197	C₈×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
198	C₈×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
199	#88322	—	2	4	no	—
200	#88322	—	2	2	no	—
201	#88322	—	4	2	no	—
202	#88322	C₂×C₄⋊C₄	1	2	yes	—
203	#88322	C₂×C₄⋊C₄	1	2	yes	—
204	#21184	—	53	1	no	maximal, Sylow
205	C₂²×C₅₃	—	4	1	no	—
206	C₂²×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
207	C₂²×C₅₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
208	C₂²×C₅₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
209	C₂×D₅₃	—	4	1	no	—
210	C₂×D₅₃	—	4	2	no	—
211	C₂×D₅₃	—	4	1	no	—
212	C₂×D₅₃	—	4	2	no	—
213	C₂×D₅₃	#389	1	2	yes	—
214	C₂×D₅₃	#389	1	2	yes	—
215	C₄×C₅₃	—	4	2	no	—
216	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
217	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
218	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
219	C₄×C₅₃	C₂×#125	1	1	yes	characteristic
220	Dic₅₃	—	4	2	no	—
221	Dic₅₃	#389	1	2	yes	—
222	Dic₅₃	#389	1	2	yes	—
223	C₂×#430	—	53	1	no	—
224	C₂×#430	—	53	1	no	—
225	C₂×#430	—	53	2	no	—
226	#2873	—	53	1	no	—
227	#1953	—	53	2	no	—
228	#1953	—	53	1	no	—
229	#1953	—	53	1	no	—
230	#1953	—	53	1	no	—
231	#1953	—	53	2	no	—
232	#1953	D₅₃	1	1	yes	characteristic, complemented
233	C₂×#344	—	53	2	no	—
234	C₂×C₅₃	—	2	1	no	—
235	C₂×C₅₃	—	2	1	no	—
236	C₂×C₅₃	—	2	1	no	—
237	C₂×C₅₃	C₂×#389	1	1	yes	characteristic
238	D₅₃	—	2	2	no	—
239	D₅₃	—	2	2	no	—
240	C₂²×M₁₆	—	53	1	no	—
241	C₂²×M₁₆	—	53	1	no	—
242	C₂²×M₁₆	—	53	2	no	—
243	C₂²×M₁₆	—	53	2	no	—
244	C₂×#117	—	53	1	no	—
245	#430	—	53	8	no	—
246	#430	—	53	2	no	—
247	#430	—	53	2	no	—
248	#430	—	53	2	no	—
249	#430	—	106	4	no	—
250	#430	—	106	1	no	—
251	#430	—	106	1	no	—
252	#430	—	106	1	no	—
253	#430	—	106	1	no	—
254	#430	C₂×D₅₃	1	2	yes	—
255	C₂×#108	—	53	2	no	—
256	C₂×#108	—	53	1	no	—
257	C₂×#108	—	53	2	no	—
258	C₂×#108	—	53	1	no	—
259	C₂×#108	—	106	4	no	—
260	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
261	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
262	#405	—	53	1	no	—
263	#405	—	53	1	no	—
264	#405	—	53	1	no	—
265	#405	—	106	1	no	—
266	#405	—	106	1	no	—
267	#405	C₂×D₅₃	1	1	yes	characteristic
268	C₄×M₁₆	—	106	1	no	—
269	C₄×M₁₆	—	106	1	no	—
270	#344	—	53	2	no	—
271	#344	—	53	2	no	—
272	#344	—	53	2	no	—
273	#344	C₂×D₅₃	1	2	yes	—
274	C₅₃	#21184	1	1	yes	characteristic, complemented, Sylow
275	C₂³×C₄	—	53	1	no	—
276	C₂×M₁₆	—	53	4	no	—
277	C₂×M₁₆	—	53	1	no	—
278	C₂×M₁₆	—	53	1	no	—
279	C₂×M₁₆	—	53	1	no	—
280	C₂×M₁₆	—	53	1	no	—
281	C₂×M₁₆	—	53	4	no	—
282	C₂×M₁₆	—	53	2	no	—
283	C₂×M₁₆	—	53	1	no	—
284	C₂×M₁₆	—	53	4	no	—
285	C₂×M₁₆	—	53	4	no	—
286	C₂×M₁₆	—	53	4	no	—
287	C₂×M₁₆	—	53	2	no	—
288	C₂×M₁₆	—	106	1	no	—
289	C₂×M₁₆	—	106	2	no	—
290	C₂×M₁₆	—	106	2	no	—
291	C₂×M₁₆	—	106	2	no	—
292	C₂×M₁₆	—	106	2	no	—
293	C₂×M₁₆	—	106	2	no	—
294	C₂×M₁₆	—	106	2	no	—
295	C₂×M₁₆	—	106	2	no	—
296	C₂×M₁₆	—	106	2	no	—
297	C₂×M₁₆	—	106	2	no	—
298	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
299	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
300	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
301	C₂²×C₈	—	53	1	no	—
302	C₂²×C₈	—	106	1	no	—
303	C₂²×C₈	—	106	2	no	—
304	C₂²×C₈	—	106	2	no	—
305	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
306	#117	—	53	1	no	—
307	#117	—	53	2	no	—
308	#117	—	106	1	no	—
309	#117	—	106	1	no	—
310	#117	C₂²×D₅₃	1	1	yes	characteristic
311	C₂×C₄⋊C₄	—	106	1	no	—
312	C₂×C₂²⋊C₄	—	53	2	no	—
313	C₂×C₄²	—	106	1	no	—
314	#108	—	2	4	no	—
315	#108	—	2	1	no	—
316	#108	—	2	1	no	—
317	#108	—	53	8	no	—
318	#108	—	53	4	no	—
319	#108	—	106	4	no	—
320	#108	—	106	2	no	—
321	#108	—	106	2	no	—
322	#108	—	106	4	no	—
323	#108	—	106	4	no	—
324	#108	—	106	1	no	—
325	#108	—	106	1	no	—
326	#108	C₄×D₅₃	1	4	yes	complemented
327	#97	—	2	1	no	—
328	#97	—	106	1	no	—
329	#97	—	106	1	no	—
330	#97	—	106	1	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	106	1	no	—
333	C₄×C₈	—	106	1	no	—
334	C₄×C₈	—	106	1	no	—
335	C₂⁴	—	53	1	no	—
336	C₂²×C₄	—	53	1	no	—
337	C₂²×C₄	—	53	2	no	—
338	C₂²×C₄	—	53	1	no	—
339	C₂²×C₄	—	53	1	no	—
340	C₂²×C₄	—	53	2	no	—
341	C₂²×C₄	—	53	2	no	—
342	C₂²×C₄	—	53	1	no	—
343	C₂²×C₄	—	53	1	no	—
344	C₂²×C₄	—	53	2	no	—
345	C₂²×C₄	—	106	2	no	—
346	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	1	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	53	4	no	—
352	M₁₆	—	53	4	no	—
353	M₁₆	—	53	4	no	—
354	M₁₆	—	53	4	no	—
355	M₁₆	—	53	4	no	—
356	M₁₆	—	53	2	no	—
357	M₁₆	—	106	4	no	—
358	M₁₆	—	106	4	no	—
359	M₁₆	—	106	4	no	—
360	M₁₆	—	106	2	no	—
361	M₁₆	—	106	1	no	—
362	M₁₆	—	106	2	no	—
363	M₁₆	—	106	2	no	—
364	M₁₆	—	212	2	no	—
365	M₁₆	—	212	2	no	—
366	M₁₆	C₂×C₄×D₅₃	1	4	yes	—
367	M₁₆	D₄×D₅₃	1	2	yes	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	53	2	no	—
372	C₂×C₈	—	53	1	no	—
373	C₂×C₈	—	53	1	no	—
374	C₂×C₈	—	53	2	no	—
375	C₂×C₈	—	106	4	no	—
376	C₂×C₈	—	106	4	no	—
377	C₂×C₈	—	106	4	no	—
378	C₂×C₈	—	106	1	no	—
379	C₂×C₈	—	106	2	no	—
380	C₂×C₈	—	106	2	no	—
381	C₂×C₈	—	212	2	no	—
382	C₂×C₈	—	212	2	no	—
383	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
384	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
385	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
386	C₂×C₈	Q₈×D₅₃	1	2	yes	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	106	2	no	—
389	C₄⋊C₄	—	106	1	no	—
390	C₂²⋊C₄	—	53	2	no	—
391	C₂²⋊C₄	—	106	2	no	—
392	C₂²⋊C₄	Q₈×D₅₃	1	2	yes	—
393	C₄²	—	2	1	no	—
394	C₄²	—	106	2	no	—
395	C₄²	—	106	1	no	—
396	C₂³	—	53	2	no	—
397	C₂³	—	53	1	no	—
398	C₂³	—	53	1	no	—
399	C₂³	—	53	2	no	—
400	C₂³	—	424	1	no	—
401	C₂³	C₂×Q₈×D₅₃	1	1	yes	characteristic
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	53	2	no	—
404	C₂×C₄	—	53	1	no	—
405	C₂×C₄	—	53	1	no	—
406	C₂×C₄	—	53	2	no	—
407	C₂×C₄	—	53	2	no	—
408	C₂×C₄	—	53	2	no	—
409	C₂×C₄	—	53	2	no	—
410	C₂×C₄	—	53	2	no	—
411	C₂×C₄	—	53	2	no	—
412	C₂×C₄	—	53	2	no	—
413	C₂×C₄	—	53	2	no	—
414	C₂×C₄	—	53	2	no	—
415	C₂×C₄	—	106	2	no	—
416	C₂×C₄	—	424	2	no	—
417	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
418	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
419	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
420	C₂×C₄	C₂×Q₈×D₅₃	1	1	yes	characteristic
421	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
422	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	2	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	53	2	no	—
427	C₈	—	53	2	no	—
428	C₈	—	106	4	no	—
429	C₈	—	106	2	no	—
430	C₈	—	212	2	no	—
431	C₈	C₄⋊C₄×D₅₃	1	2	yes	—
432	C₈	C₄⋊C₄×D₅₃	1	2	yes	—
433	C₂²	—	4	1	no	—
434	C₂²	—	53	2	no	—
435	C₂²	—	53	2	no	—
436	C₂²	—	212	1	no	—
437	C₂²	—	212	1	no	—
438	C₂²	—	212	2	no	—
439	C₂²	—	212	2	no	—
440	C₂²	C₄×Q₈×D₅₃	1	1	yes	characteristic
441	C₂²	C₂²⋊Q₈×D₅₃	1	1	yes	characteristic
442	C₂²	C₄⋊Q₈×D₅₃	1	1	yes	characteristic
443	C₄	—	4	2	no	—
444	C₄	—	53	2	no	—
445	C₄	—	53	2	no	—
446	C₄	—	212	2	no	—
447	C₄	C₂×C₄⋊C₄×D₅₃	1	1	yes	characteristic
448	C₄	C₄×D₄×D₅₃	1	1	yes	characteristic
449	C₄	#121×D₅₃	1	1	yes	characteristic
450	C₄	#125×D₅₃	1	1	yes	characteristic
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	106	2	no	—
455	C₂	—	106	2	no	—
456	C₂	#389×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1953	C₂
socle	C₂×C₅₃	C₂×#389
prime radical	C₂³×D₅₃	C₂×Q₈
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1953	D₅₃
hypocenter	C₅₃	#21184
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1953

Complements

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

N	H ≅ G/N	type
5. #20275506	C₂	semidirect
6. #20275505	C₂	semidirect
7. #20275504	C₂	semidirect
8. #20275503	C₂	semidirect
9. #20275502	C₂	semidirect
11. C₅₃×#1953	C₂	semidirect
25. #16810670	C₄	semidirect
83. #13133153	C₂×C₄	semidirect
88. #13133152	C₂×C₄	semidirect
103. #108×C₅₃	C₂×C₄	semidirect
232. #1953	D₅₃	semidirect
274. C₅₃	#21184	semidirect
326. #108	C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16810670	2
#430×D₅₃	2
#20283131	2
#20275506	2
#20275505	2
#20275504	2
#20275503	2
#20275502	2
#344×D₅₃	2
C₅₃×#1953	2
#21184	53