Subgroups — #27384267

Order 13568.

772 conjugacy classes of subgroups.

The subgroup lattice has 474 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	#20283303	C₂	1	1	yes	maximal, characteristic
3	#20283131	C₂	1	1	yes	maximal, characteristic
4	#20274840	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274839	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274838	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274837	C₂	1	2	yes	maximal, complemented
8	#20274836	C₂	1	2	yes	maximal, complemented
9	#344×D₅₃	C₂	1	2	yes	maximal
10	H(3,ℤ/4)×D₅₃	C₂	1	2	yes	maximal
11	C₅₃×#1833	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	1	yes	characteristic
15	#117×D₅₃	C₂²	1	2	yes	—
16	#117×D₅₃	C₂²	1	1	yes	characteristic
17	#16810670	—	2	2	no	—
18	#16810670	—	2	2	no	—
19	C₂×#13133153	C₂²	1	1	yes	characteristic
20	C₂×#13133152	C₂²	1	2	yes	—
21	#16810664	—	2	2	no	—
22	#16810662	—	2	2	no	—
23	#16810661	C₂²	1	1	yes	characteristic
24	#16810659	C₂²	1	2	yes	—
25	#16810581	C₂²	1	1	yes	characteristic
26	#16810580	C₄	1	2	yes	complemented
27	#16810579	C₂²	1	1	yes	characteristic
28	#16810578	C₂²	1	1	yes	characteristic
29	#16810577	C₄	1	2	yes	complemented
30	#16810575	C₄	1	2	yes	complemented
31	C₄×#11719912	C₄	1	2	yes	complemented
32	#16810395	C₂²	1	2	yes	—
33	#16810394	C₂²	1	2	yes	—
34	#16810393	C₂²	1	2	yes	—
35	#16810380	C₂²	1	2	yes	—
36	#16810379	C₂²	1	2	yes	—
37	#16810379	C₂²	1	2	yes	—
38	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
39	C₅₃×#427	C₂²	1	1	yes	characteristic
40	C₅₃×#405	C₂²	1	1	yes	characteristic
41	C₅₃×#344	C₂²	1	2	yes	—
42	C₅₃×H(3,ℤ/4)	C₂²	1	2	yes	—
43	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
44	C₂×#11719917	C₂³	1	2	yes	—
45	C₂×#11719917	C₂³	1	1	yes	characteristic
46	C₂×#11719912	—	2	2	no	—
47	C₂×#11719912	C₂×C₄	1	2	yes	—
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×#11719912	D₄	1	2	yes	—
53	C₂×#11719912	D₄	1	2	yes	—
54	C₂×#11719912	Q₈	1	2	yes	—
55	C₂×#11719912	Q₈	1	2	yes	—
56	M₁₆×D₅₃	—	2	2	no	—
57	M₁₆×D₅₃	—	2	2	no	—
58	M₁₆×D₅₃	—	2	2	no	—
59	M₁₆×D₅₃	—	2	2	no	—
60	M₁₆×D₅₃	—	2	2	no	—
61	M₁₆×D₅₃	—	2	2	no	—
62	C₂²×#88322	C₂³	1	1	yes	characteristic
63	C₂×C₈×D₅₃	—	2	2	no	—
64	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
65	#13133176	C₂³	1	2	yes	—
66	#13133176	C₂³	1	1	yes	characteristic
67	#13133175	—	2	2	no	—
68	#13133175	—	2	1	no	—
69	#13133174	—	2	2	no	—
70	#13133174	C₂×C₄	1	2	yes	—
71	#13133173	—	2	1	no	—
72	#13133173	—	2	2	no	—
73	C₄⋊C₄×D₅₃	—	2	1	no	—
74	C₄⋊C₄×D₅₃	—	2	2	no	—
75	C₂²⋊C₄×D₅₃	—	2	1	no	—
76	C₂²⋊C₄×D₅₃	—	2	2	no	—
77	C₄²×D₅₃	—	2	2	no	—
78	C₄²×D₅₃	C₂×C₄	1	2	yes	—
79	#13133153	—	2	1	no	—
80	#13133153	—	2	1	no	—
81	#13133152	—	2	4	no	—
82	#13133151	—	2	1	no	—
83	#13133150	—	2	2	no	—
84	#13133149	—	2	1	no	—
85	#13133148	—	2	2	no	—
86	#13133128	C₂×C₄	1	2	yes	complemented
87	#13133127	C₂×C₄	1	2	yes	complemented
88	#13133127	C₂×C₄	1	2	yes	complemented
89	C₄×#88322	C₂×C₄	1	2	yes	complemented
90	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
91	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
92	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
93	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
95	#117×C₅₃	C₂³	1	2	yes	—
96	#117×C₅₃	C₂³	1	1	yes	characteristic
97	#108×C₅₃	—	2	1	no	—
98	#108×C₅₃	—	2	1	no	—
99	#107×C₅₃	—	2	1	no	—
100	#106×C₅₃	—	2	1	no	—
101	#97×C₅₃	C₂×C₄	1	2	yes	complemented
102	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	complemented
103	C₂³×D₅₃	#41	1	1	yes	characteristic
104	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₅₃	#41	1	1	yes	characteristic
106	C₂×C₄×D₅₃	—	2	2	no	—
107	C₂×C₄×D₅₃	—	4	2	no	—
108	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
111	C₂×C₄×D₅₃	C₂×Q₈	1	2	yes	—
112	C₂×C₄×D₅₃	#41	1	2	yes	—
113	C₂×C₄×D₅₃	#41	1	2	yes	—
114	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
115	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
116	M₁₆×C₅₃	—	2	1	no	—
117	M₁₆×C₅₃	—	2	1	no	—
118	M₁₆×C₅₃	—	2	2	no	—
119	M₁₆×C₅₃	—	2	2	no	—
120	C₂×C₈×C₅₃	—	2	2	no	—
121	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
127	C₂×C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
128	C₄⋊C₄×C₅₃	—	2	1	no	—
129	C₄⋊C₄×C₅₃	—	2	2	no	—
130	C₂²⋊C₄×C₅₃	—	2	1	no	—
131	C₂²⋊C₄×C₅₃	—	2	2	no	—
132	C₄²×C₅₃	—	2	2	no	—
133	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
134	C₂²⋊Dic₅₃	—	2	1	no	—
135	C₂²⋊Dic₅₃	—	2	2	no	—
136	#11719921	—	2	2	no	—
137	#11719921	—	4	2	no	—
138	C₄⋊Dic₅₃	—	2	1	no	—
139	C₄⋊Dic₅₃	—	2	2	no	—
140	#11719919	—	2	2	no	—
141	#11719919	—	4	2	no	—
142	C₄×Dic₅₃	—	2	2	no	—
143	C₄×Dic₅₃	—	2	2	no	—
144	C₄×Dic₅₃	—	4	2	no	—
145	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
146	#11719917	—	2	1	no	—
147	#11719917	—	2	1	no	—
148	#11719917	—	2	2	no	—
149	#11719917	—	2	2	no	—
150	C₂×#88322	—	2	2	no	—
151	C₂×#88322	C₂²×C₄	1	2	yes	—
152	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
153	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
154	C₂×#88322	C₂×D₄	1	2	yes	—
155	C₂×#88322	C₂×Q₈	1	2	yes	—
156	#11719912	—	2	4	no	—
157	#11719912	—	4	2	no	—
158	#11719912	—	4	2	no	—
159	#11719912	C₄⋊C₄	1	2	yes	—
160	#11719912	C₄⋊C₄	1	2	yes	—
161	#11719912	C₄⋊C₄	1	2	yes	—
162	#11719912	C₄⋊C₄	1	2	yes	—
163	#11719912	C₄⋊C₄	1	2	yes	—
164	#11719912	C₄⋊C₄	1	2	yes	—
165	#11719912	C₄⋊C₄	1	2	yes	—
166	#11719912	C₄⋊C₄	1	2	yes	—
167	C₈×D₅₃	—	2	4	no	—
168	C₈×D₅₃	—	4	2	no	—
169	C₈×D₅₃	—	4	2	no	—
170	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
171	C₂²×D₅₃	—	8	1	no	—
172	C₂²×D₅₃	#117	1	1	yes	characteristic
173	C₂²×D₅₃	#117	1	1	yes	characteristic
174	C₂²×D₅₃	#124	1	2	yes	—
175	C₂²×D₅₃	#125	1	2	yes	—
176	C₂×C₄×C₅₃	—	2	2	no	—
177	C₂×C₄×C₅₃	—	4	2	no	—
178	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
184	C₂×Dic₅₃	—	2	2	no	—
185	C₂×Dic₅₃	—	4	2	no	—
186	C₂×Dic₅₃	#117	1	1	yes	characteristic
187	C₂×Dic₅₃	#117	1	1	yes	characteristic
188	C₂×Dic₅₃	#124	1	2	yes	—
189	C₂×Dic₅₃	#125	1	2	yes	—
190	C₄×D₅₃	—	8	2	no	—
191	C₄×D₅₃	—	8	4	no	—
192	C₄×D₅₃	C₂×C₄⋊C₄	1	2	yes	—
193	C₄×D₅₃	C₂×C₄⋊C₄	1	2	yes	—
194	C₄×D₅₃	#117	1	2	yes	—
195	C₄×D₅₃	#117	1	2	yes	—
196	C₄×D₅₃	#124	1	2	yes	—
197	C₄×D₅₃	#124	1	2	yes	—
198	C₄×D₅₃	#125	1	2	yes	—
199	C₄×D₅₃	#125	1	2	yes	—
200	C₈×C₅₃	—	2	2	no	—
201	C₈×C₅₃	—	4	2	no	—
202	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
206	#88322	—	2	2	no	—
207	#88322	—	4	2	no	—
208	#88322	C₂×C₄⋊C₄	1	2	yes	—
209	#88322	C₂×C₄⋊C₄	1	2	yes	—
210	#20757	—	53	1	no	maximal, Sylow
211	C₂²×C₅₃	—	4	1	no	—
212	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
213	C₂²×C₅₃	C₂×#124	1	1	yes	characteristic
214	C₂²×C₅₃	C₂×#125	1	1	yes	characteristic
215	C₂×D₅₃	—	4	1	no	—
216	C₂×D₅₃	—	4	2	no	—
217	C₂×D₅₃	—	4	1	no	—
218	C₂×D₅₃	—	4	2	no	—
219	C₂×D₅₃	#382	1	2	yes	—
220	C₂×D₅₃	#382	1	2	yes	—
221	C₄×C₅₃	—	4	2	no	—
222	C₄×C₅₃	—	8	2	no	—
223	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
224	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
225	C₄×C₅₃	C₂×#124	1	1	yes	characteristic
226	C₄×C₅₃	C₂×#125	1	1	yes	characteristic
227	Dic₅₃	—	4	2	no	—
228	Dic₅₃	—	8	2	no	—
229	Dic₅₃	#382	1	2	yes	—
230	Dic₅₃	#382	1	2	yes	—
231	C₂×#430	—	53	1	no	—
232	#2911	—	53	1	no	—
233	#2873	—	53	1	no	—
234	#1833	—	53	1	no	—
235	#1833	—	53	1	no	—
236	#1833	—	53	1	no	—
237	#1833	—	53	2	no	—
238	#1833	—	53	2	no	—
239	#1833	D₅₃	1	1	yes	characteristic, complemented
240	C₂×#344	—	53	2	no	—
241	C₂×H(3,ℤ/4)	—	53	2	no	—
242	C₂×C₅₃	—	2	1	no	—
243	C₂×C₅₃	—	2	1	no	—
244	C₂×C₅₃	—	2	1	no	—
245	C₂×C₅₃	C₂×#382	1	1	yes	characteristic
246	D₅₃	—	2	2	no	—
247	D₅₃	—	2	2	no	—
248	C₂²×M₁₆	—	53	1	no	—
249	C₂²×M₁₆	—	53	1	no	—
250	C₂²×M₁₆	—	53	2	no	—
251	C₂×#117	—	53	1	no	—
252	C₂×#117	—	53	2	no	—
253	#430	—	106	2	no	—
254	#430	—	106	2	no	—
255	C₂×#108	—	53	2	no	—
256	C₂×#108	—	53	1	no	—
257	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
258	#428	—	106	2	no	—
259	#428	—	106	2	no	—
260	#427	—	53	1	no	—
261	#427	—	53	2	no	—
262	#427	C₂×D₅₃	1	1	yes	characteristic
263	#405	—	53	1	no	—
264	#405	—	53	1	no	—
265	#405	—	53	1	no	—
266	#405	—	53	2	no	—
267	#405	—	53	2	no	—
268	#405	C₂×D₅₃	1	1	yes	characteristic
269	C₄×M₁₆	—	53	2	no	—
270	C₄×M₁₆	—	53	2	no	—
271	#344	—	53	2	no	—
272	#344	—	53	2	no	—
273	#344	—	53	2	no	—
274	#344	C₂×D₅₃	1	2	yes	—
275	H(3,ℤ/4)	—	53	2	no	—
276	H(3,ℤ/4)	—	53	2	no	—
277	H(3,ℤ/4)	—	53	2	no	—
278	H(3,ℤ/4)	C₂×D₅₃	1	2	yes	—
279	C₅₃	#20757	1	1	yes	characteristic, complemented, Sylow
280	C₂³×C₄	—	53	1	no	—
281	C₂×M₁₆	—	53	1	no	—
282	C₂×M₁₆	—	53	1	no	—
283	C₂×M₁₆	—	53	1	no	—
284	C₂×M₁₆	—	53	1	no	—
285	C₂×M₁₆	—	53	1	no	—
286	C₂×M₁₆	—	53	2	no	—
287	C₂×M₁₆	—	53	2	no	—
288	C₂×M₁₆	—	53	2	no	—
289	C₂×M₁₆	—	53	2	no	—
290	C₂×M₁₆	—	53	2	no	—
291	C₂×M₁₆	—	53	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	—	106	2	no	—
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	—	53	2	no	—
303	C₂²×C₈	—	106	2	no	—
304	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
305	#117	—	53	1	no	—
306	#117	—	53	2	no	—
307	#117	—	53	2	no	—
308	#117	—	106	2	no	—
309	#117	—	106	1	no	—
310	#117	—	106	1	no	—
311	#117	—	106	2	no	—
312	#117	—	106	2	no	—
313	#117	C₂²×D₅₃	1	2	yes	—
314	#117	C₂²×D₅₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	—	106	1	no	—
316	C₂×C₄⋊C₄	—	106	2	no	—
317	C₂×C₂²⋊C₄	—	106	1	no	—
318	C₂×C₂²⋊C₄	—	106	2	no	—
319	C₂×C₄²	—	53	2	no	—
320	C₂×C₄²	—	106	2	no	—
321	#108	—	2	1	no	—
322	#108	—	2	1	no	—
323	#108	—	106	4	no	—
324	#108	—	106	1	no	—
325	#108	—	106	1	no	—
326	#107	—	2	1	no	—
327	#107	—	106	2	no	—
328	#107	—	106	1	no	—
329	#106	—	2	1	no	—
330	#106	—	106	2	no	—
331	#106	—	106	1	no	—
332	#97	—	53	2	no	—
333	#97	—	53	2	no	—
334	#97	—	53	2	no	—
335	#97	C₄×D₅₃	1	2	yes	complemented
336	C₄×C₈	—	53	2	no	—
337	C₄×C₈	—	53	2	no	—
338	C₄×C₈	—	53	2	no	—
339	C₄×C₈	C₄×D₅₃	1	2	yes	complemented
340	C₂⁴	—	53	1	no	—
341	C₂²×C₄	—	53	1	no	—
342	C₂²×C₄	—	53	1	no	—
343	C₂²×C₄	—	53	1	no	—
344	C₂²×C₄	—	53	2	no	—
345	C₂²×C₄	—	53	2	no	—
346	C₂²×C₄	—	53	2	no	—
347	C₂²×C₄	—	53	1	no	—
348	C₂²×C₄	—	53	1	no	—
349	C₂²×C₄	—	53	2	no	—
350	C₂²×C₄	—	106	2	no	—
351	C₂²×C₄	—	212	2	no	—
352	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	53	2	no	—
358	M₁₆	—	53	2	no	—
359	M₁₆	—	53	2	no	—
360	M₁₆	—	53	2	no	—
361	M₁₆	—	53	2	no	—
362	M₁₆	—	53	2	no	—
363	M₁₆	—	53	2	no	—
364	M₁₆	—	53	2	no	—
365	M₁₆	—	106	4	no	—
366	M₁₆	—	106	1	no	—
367	M₁₆	—	106	1	no	—
368	M₁₆	—	106	2	no	—
369	M₁₆	—	106	2	no	—
370	M₁₆	—	212	2	no	—
371	M₁₆	—	212	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	53	1	no	—
374	C₂×C₈	—	53	1	no	—
375	C₂×C₈	—	53	2	no	—
376	C₂×C₈	—	53	2	no	—
377	C₂×C₈	—	53	2	no	—
378	C₂×C₈	—	106	4	no	—
379	C₂×C₈	—	106	2	no	—
380	C₂×C₈	—	212	2	no	—
381	C₂×C₈	—	212	2	no	—
382	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
383	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
384	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
385	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
386	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
387	C₂×C₈	Q₈×D₅₃	1	1	yes	characteristic
388	C₂×C₈	Q₈×D₅₃	1	1	yes	characteristic
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	106	2	no	—
392	C₄⋊C₄	—	106	1	no	—
393	C₄⋊C₄	—	106	2	no	—
394	C₄⋊C₄	—	212	2	no	—
395	C₂²⋊C₄	—	2	1	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	106	2	no	—
398	C₂²⋊C₄	—	106	1	no	—
399	C₂²⋊C₄	—	106	2	no	—
400	C₂²⋊C₄	—	212	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	53	2	no	—
403	C₄²	—	106	2	no	—
404	C₄²	—	106	2	no	—
405	C₄²	—	212	2	no	—
406	C₄²	C₂×C₄×D₅₃	1	2	yes	—
407	C₂³	—	53	1	no	—
408	C₂³	—	53	1	no	—
409	C₂³	—	53	2	no	—
410	C₂³	—	53	2	no	—
411	C₂³	—	424	1	no	—
412	C₂³	#41×D₅₃	1	1	yes	characteristic
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	53	1	no	—
416	C₂×C₄	—	53	1	no	—
417	C₂×C₄	—	53	2	no	—
418	C₂×C₄	—	53	2	no	—
419	C₂×C₄	—	53	2	no	—
420	C₂×C₄	—	53	2	no	—
421	C₂×C₄	—	53	2	no	—
422	C₂×C₄	—	53	2	no	—
423	C₂×C₄	—	53	2	no	—
424	C₂×C₄	—	53	2	no	—
425	C₂×C₄	—	53	2	no	—
426	C₂×C₄	—	53	2	no	—
427	C₂×C₄	—	106	2	no	—
428	C₂×C₄	—	424	2	no	—
429	C₂×C₄	—	424	4	no	—
430	C₂×C₄	—	212	2	no	—
431	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
432	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
433	C₂×C₄	C₂×Q₈×D₅₃	1	1	yes	characteristic
434	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
435	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
436	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	4	2	no	—
439	C₈	—	53	2	no	—
440	C₈	—	53	2	no	—
441	C₈	—	106	2	no	—
442	C₈	—	212	2	no	—
443	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
444	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
445	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
446	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
447	C₂²	—	4	1	no	—
448	C₂²	—	53	2	no	—
449	C₂²	—	53	2	no	—
450	C₂²	—	212	1	no	—
451	C₂²	—	212	2	no	—
452	C₂²	—	212	1	no	—
453	C₂²	—	212	2	no	—
454	C₂²	#117×D₅₃	1	1	yes	characteristic
455	C₂²	#124×D₅₃	1	1	yes	characteristic
456	C₂²	#125×D₅₃	1	1	yes	characteristic
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	53	2	no	—
460	C₄	—	53	2	no	—
461	C₄	—	424	2	no	—
462	C₄	—	212	2	no	—
463	C₄	C₂×C₄⋊C₄×D₅₃	1	1	yes	characteristic
464	C₄	#117×D₅₃	1	1	yes	characteristic
465	C₄	#124×D₅₃	1	1	yes	characteristic
466	C₄	#125×D₅₃	1	1	yes	characteristic
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	106	2	no	—
471	C₂	—	106	2	no	—
472	C₂	#382×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#117×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1833	C₂
socle	C₂×C₅₃	C₂×#382
prime radical	C₂³×D₅₃	#41
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1833	D₅₃
hypocenter	C₅₃	#20757
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ #117 ◁ #1833

Complements

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

N	H ≅ G/N	type
4. #20274840	C₂	semidirect
5. #20274839	C₂	semidirect
6. #20274838	C₂	semidirect
7. #20274837	C₂	semidirect
8. #20274836	C₂	semidirect
11. C₅₃×#1833	C₂	semidirect
26. #16810580	C₄	semidirect
29. #16810577	C₄	semidirect
30. #16810575	C₄	semidirect
31. C₄×#11719912	C₄	semidirect
86. #13133128	C₂×C₄	semidirect
87. #13133127	C₂×C₄	semidirect
88. #13133127	C₂×C₄	semidirect
89. C₄×#88322	C₂×C₄	semidirect
90. C₈×Dic₅₃	C₂×C₄	semidirect
91. C₈×Dic₅₃	C₂×C₄	semidirect
101. #97×C₅₃	C₂×C₄	semidirect
102. C₄×C₈×C₅₃	C₂×C₄	semidirect
239. #1833	D₅₃	semidirect
279. C₅₃	#20757	semidirect
335. #97	C₄×D₅₃	semidirect
339. C₄×C₈	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
#20283303	2
#20283131	2
#20274840	2
#20274839	2
#20274838	2
#20274837	2
#20274836	2
#344×D₅₃	2
H(3,ℤ/4)×D₅₃	2
C₅₃×#1833	2
#20757	53