Subgroups — #28310331

Order 13568.

570 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₃⋊M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×D₅₃⋊#108	C₂	1	1	yes	maximal, characteristic
3	#20289797	C₂	1	4	yes	maximal, complemented
4	#427×D₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂×D₅₃⋊M₁₆	—	2	1	no	—
6	C₂×#13133292	C₄	1	2	yes	complemented
7	D₅₃⋊M₃₂	—	2	1	no	—
8	D₅₃⋊M₃₂	—	2	1	no	—
9	D₅₃⋊M₃₂	C₄	1	2	yes	complemented
10	D₅₃⋊M₃₂	C₂²	1	2	yes	—
11	C₂×#13133291	—	2	1	no	—
12	C₂×D₅₃⋊C₁₆	—	2	1	no	—
13	C₂×#13133288	C₄	1	2	yes	complemented
14	D₅₃⋊#108	—	2	1	no	—
15	D₅₃⋊#108	—	2	1	no	—
16	D₅₃⋊#108	C₄	1	2	yes	complemented
17	D₅₃⋊#108	C₂²	1	2	yes	—
18	C₂×#13133287	—	2	1	no	—
19	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
20	#117×D₅₃	—	2	1	no	—
21	#16810661	C₄	1	1	yes	characteristic
22	#16810660	—	2	1	no	—
23	#16810659	—	2	1	no	—
24	#16810658	C₂²	1	2	yes	—
25	#107×D₅₃	—	2	1	no	—
26	#106×D₅₃	C₄	1	2	yes	—
27	C₅₃×#427	C₄	1	1	yes	characteristic
28	C₂×#11719936	—	2	2	no	—
29	D₅₃⋊M₁₆	—	2	2	no	—
30	D₅₃⋊M₁₆	—	2	2	no	—
31	D₅₃⋊M₁₆	—	4	1	no	—
32	D₅₃⋊M₁₆	—	4	1	no	—
33	C₂×#11719940	—	4	1	no	—
34	C₂×D₅₃⋊C₈	—	4	1	no	—
35	#13133292	—	2	2	no	—
36	#13133292	C₂×C₄	1	4	yes	complemented
37	#13133291	—	2	2	no	—
38	#13133291	—	2	2	no	—
39	D₅₃⋊C₁₆	—	2	2	no	—
40	D₅₃⋊C₁₆	—	2	2	no	—
41	C₂×#11719910	—	2	2	no	—
42	#13133288	—	2	2	no	—
43	#13133288	C₂×C₄	1	4	yes	complemented
44	#13133287	—	2	2	no	—
45	#13133287	—	2	2	no	—
46	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
47	C₂²×#88322	D₄	1	1	yes	characteristic
48	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
54	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
55	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
56	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
58	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
59	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
60	#13133176	—	2	1	no	—
61	#13133175	—	2	2	no	—
62	#13133174	—	4	1	no	—
63	#13133173	—	4	1	no	—
64	C₄⋊C₄×D₅₃	—	2	2	no	—
65	C₂²⋊C₄×D₅₃	—	4	1	no	—
66	C₄²×D₅₃	—	4	1	no	—
67	#13133151	—	2	1	no	—
68	#13133150	—	2	2	no	—
69	#13133149	C₂×C₄	1	2	yes	—
70	#13133148	—	2	2	no	—
71	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
72	#117×C₅₃	—	2	1	no	—
73	#107×C₅₃	—	2	1	no	—
74	#106×C₅₃	C₂×C₄	1	2	yes	—
75	C₂³×D₅₃	SD₁₆	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₅₃	D₈	1	1	yes	characteristic
78	C₂×C₄×D₅₃	—	4	2	no	—
79	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₅₃	D₈	1	1	yes	characteristic
85	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
86	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
87	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
88	C₂×C₄×D₅₃	Q₁₆	1	1	yes	characteristic
89	C₂×C₄×D₅₃	Q₁₆	1	1	yes	characteristic
90	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
91	#11719940	—	4	2	no	—
92	#11719940	—	4	2	no	—
93	C₂×#88324	—	4	2	no	—
94	#11719936	—	2	4	no	—
95	#11719936	—	4	2	no	—
96	D₅₃⋊C₈	—	4	2	no	—
97	D₅₃⋊C₈	—	4	2	no	—
98	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
99	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
100	C₂×C₈×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
104	C₄⋊C₄×C₅₃	—	2	2	no	—
105	C₂²⋊C₄×C₅₃	—	4	1	no	—
106	C₄²×C₅₃	—	4	1	no	—
107	C₂²⋊Dic₅₃	—	4	1	no	—
108	#11719921	—	4	2	no	—
109	C₄⋊Dic₅₃	—	2	2	no	—
110	#11719919	—	4	2	no	—
111	C₄×Dic₅₃	—	4	1	no	—
112	C₄×Dic₅₃	—	4	2	no	—
113	C₂×#88322	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×#88322	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×#88322	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
117	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
118	C₂×#88322	C₂×D₄	1	1	yes	characteristic
119	C₈×D₅₃	C₄²	1	1	yes	characteristic
120	C₈×D₅₃	C₄²	1	1	yes	characteristic
121	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
126	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
127	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
128	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
129	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
130	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
131	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
132	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
134	C₈×D₅₃	C₂×Q₈	1	1	yes	characteristic
135	#11719910	—	2	4	no	—
136	C₂³×C₅₃	#102	1	1	yes	characteristic
137	C₂²×D₅₃	—	4	2	no	—
138	C₂²×D₅₃	#102	1	1	yes	characteristic
139	C₂²×D₅₃	#103	1	1	yes	characteristic
140	C₂²×D₅₃	#103	1	1	yes	characteristic
141	C₂²×D₅₃	#106	1	1	yes	characteristic
142	C₂²×D₅₃	#106	1	1	yes	characteristic
143	C₂²×D₅₃	C₂×SD₁₆	1	1	yes	characteristic
144	C₂×C₄×C₅₃	—	4	2	no	—
145	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
146	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
147	C₂×C₄×C₅₃	#102	1	1	yes	characteristic
148	C₂×C₄×C₅₃	#103	1	1	yes	characteristic
149	C₂×C₄×C₅₃	#103	1	1	yes	characteristic
150	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×Dic₅₃	—	4	2	no	—
152	C₂×Dic₅₃	#102	1	1	yes	characteristic
153	C₂×Dic₅₃	#102	1	1	yes	characteristic
154	C₂×Dic₅₃	#102	1	1	yes	characteristic
155	C₂×Dic₅₃	#107	1	1	yes	characteristic
156	C₂×Dic₅₃	#107	1	1	yes	characteristic
157	C₂×Dic₅₃	C₂×D₈	1	1	yes	characteristic
158	C₄×D₅₃	—	8	4	no	—
159	C₄×D₅₃	#95	1	1	yes	characteristic
160	C₄×D₅₃	#95	1	1	yes	characteristic
161	C₄×D₅₃	#102	1	1	yes	characteristic
162	C₄×D₅₃	#102	1	1	yes	characteristic
163	C₄×D₅₃	#103	1	1	yes	characteristic
164	C₄×D₅₃	#103	1	1	yes	characteristic
165	C₄×D₅₃	#103	1	1	yes	characteristic
166	C₄×D₅₃	#103	1	1	yes	characteristic
167	C₄×D₅₃	#106	1	1	yes	characteristic
168	C₄×D₅₃	#106	1	1	yes	characteristic
169	C₄×D₅₃	#107	1	1	yes	characteristic
170	C₄×D₅₃	#107	1	1	yes	characteristic
171	C₄×D₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₄×D₅₃	C₂×SD₁₆	1	1	yes	characteristic
174	C₄×D₅₃	C₂×Q₁₆	1	1	yes	characteristic
175	#88324	—	4	4	no	—
176	C₈×C₅₃	#95	1	1	yes	characteristic
177	C₈×C₅₃	#95	1	1	yes	characteristic
178	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
179	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	#88322	#95	1	1	yes	characteristic
181	#88322	#95	1	1	yes	characteristic
182	#88322	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×#1389	—	53	1	no	maximal, Sylow
185	C₂²×C₅₃	—	4	1	no	—
186	C₂²×C₅₃	#340	1	1	yes	characteristic
187	C₂²×C₅₃	#340	1	1	yes	characteristic
188	C₂²×C₅₃	C₂×#102	1	1	yes	characteristic
189	C₂×D₅₃	—	2	2	no	—
190	C₂×D₅₃	—	2	2	no	—
191	C₂×D₅₃	—	2	2	no	—
192	C₂×D₅₃	—	4	1	no	—
193	C₂×D₅₃	—	4	1	no	—
194	C₂×D₅₃	—	4	1	no	—
195	C₂×D₅₃	#340	1	1	yes	characteristic
196	C₂×D₅₃	#340	1	1	yes	characteristic
197	C₂×D₅₃	C₂×#103	1	1	yes	characteristic
198	C₂×D₅₃	C₂×#106	1	1	yes	characteristic
199	C₄×C₅₃	—	8	2	no	—
200	C₄×C₅₃	#340	1	1	yes	characteristic
201	C₄×C₅₃	#340	1	1	yes	characteristic
202	C₄×C₅₃	C₂×#95	1	1	yes	characteristic
203	C₄×C₅₃	C₂×#103	1	1	yes	characteristic
204	Dic₅₃	—	8	2	no	—
205	Dic₅₃	#340	1	1	yes	characteristic
206	Dic₅₃	#340	1	1	yes	characteristic
207	Dic₅₃	C₂×#102	1	1	yes	characteristic
208	Dic₅₃	C₂×#107	1	1	yes	characteristic
209	C₂²×M₃₂	—	53	1	no	—
210	C₂²×#108	—	53	1	no	—
211	C₂×#427	—	53	1	no	—
212	#1389	—	53	4	no	—
213	C₂×C₅₃	—	2	1	no	—
214	C₂×C₅₃	—	2	1	no	—
215	C₂×C₅₃	—	2	1	no	—
216	C₂×C₅₃	C₂×#340	1	1	yes	characteristic
217	D₅₃	—	2	1	no	—
218	D₅₃	—	2	1	no	—
219	D₅₃	—	2	1	no	—
220	D₅₃	#1389	1	2	yes	complemented
221	C₂²×M₁₆	—	106	1	no	—
222	C₂³×C₈	—	53	1	no	—
223	C₂×#117	—	106	1	no	—
224	C₂×M₃₂	—	53	2	no	—
225	C₂×M₃₂	—	53	2	no	—
226	C₂×M₃₂	—	53	2	no	—
227	C₂×M₃₂	—	106	1	no	—
228	C₂×M₃₂	—	106	1	no	—
229	C₂×M₃₂	—	106	1	no	—
230	C₂²×C₁₆	—	106	1	no	—
231	C₂×#108	—	53	2	no	—
232	C₂×#108	—	53	2	no	—
233	C₂×#108	—	53	2	no	—
234	C₂×#108	—	106	1	no	—
235	C₂×#108	—	106	1	no	—
236	C₂×#108	—	106	1	no	—
237	#427	—	53	1	no	—
238	#427	—	53	2	no	—
239	#427	—	106	1	no	—
240	#427	—	106	1	no	—
241	#427	#6157	1	1	yes	characteristic
242	C₂×#107	—	106	1	no	—
243	C₂×#106	—	53	2	no	—
244	C₅₃	C₂×#1389	1	1	yes	characteristic, complemented, Sylow
245	C₂³×C₄	—	53	1	no	—
246	C₂×M₁₆	—	106	2	no	—
247	C₂×M₁₆	—	106	2	no	—
248	C₂×M₁₆	—	106	2	no	—
249	C₂×M₁₆	—	212	1	no	—
250	C₂×M₁₆	—	212	1	no	—
251	C₂×M₁₆	—	212	1	no	—
252	C₂²×C₈	—	53	1	no	—
253	C₂²×C₈	—	53	1	no	—
254	C₂²×C₈	—	53	1	no	—
255	C₂²×C₈	—	53	1	no	—
256	C₂²×C₈	—	53	1	no	—
257	C₂²×C₈	—	53	1	no	—
258	C₂²×C₈	—	53	1	no	—
259	C₂²×C₈	—	53	1	no	—
260	C₂²×C₈	—	53	1	no	—
261	C₂²×C₈	—	53	1	no	—
262	C₂²×C₈	—	53	1	no	—
263	C₂²×C₈	—	53	1	no	—
264	C₂²×C₈	—	53	1	no	—
265	C₂²×C₈	—	212	1	no	—
266	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
267	#117	—	2	1	no	—
268	#117	—	106	2	no	—
269	#117	—	106	1	no	—
270	#117	—	212	1	no	—
271	#117	—	212	1	no	—
272	C₂×C₄⋊C₄	—	106	2	no	—
273	C₂×C₂²⋊C₄	—	212	1	no	—
274	C₂×C₄²	—	212	1	no	—
275	M₃₂	—	53	4	no	—
276	M₃₂	—	106	2	no	—
277	M₃₂	—	106	2	no	—
278	M₃₂	—	106	2	no	—
279	C₂×C₁₆	—	106	2	no	—
280	C₂×C₁₆	—	106	2	no	—
281	C₂×C₁₆	—	106	2	no	—
282	#108	—	53	4	no	—
283	#108	—	106	2	no	—
284	#108	—	106	2	no	—
285	#108	—	106	2	no	—
286	#107	—	2	1	no	—
287	#107	—	106	2	no	—
288	#107	—	106	1	no	—
289	#106	—	53	2	no	—
290	#106	—	106	2	no	—
291	#106	C₂×#6157	1	2	yes	—
292	C₂⁴	—	53	1	no	—
293	C₂²×C₄	—	53	1	no	—
294	C₂²×C₄	—	53	1	no	—
295	C₂²×C₄	—	53	1	no	—
296	C₂²×C₄	—	53	1	no	—
297	C₂²×C₄	—	53	1	no	—
298	C₂²×C₄	—	53	1	no	—
299	C₂²×C₄	—	53	1	no	—
300	C₂²×C₄	—	53	1	no	—
301	C₂²×C₄	—	53	1	no	—
302	C₂²×C₄	—	53	1	no	—
303	C₂²×C₄	—	53	1	no	—
304	C₂²×C₄	—	53	1	no	—
305	C₂²×C₄	—	53	1	no	—
306	C₂²×C₄	—	212	2	no	—
307	C₂²×C₄	C₂²⋊#6157	1	1	yes	characteristic
308	M₁₆	—	106	4	no	—
309	M₁₆	—	212	2	no	—
310	M₁₆	—	212	2	no	—
311	M₁₆	—	212	2	no	—
312	C₂×C₈	—	53	1	no	—
313	C₂×C₈	—	53	1	no	—
314	C₂×C₈	—	53	1	no	—
315	C₂×C₈	—	53	1	no	—
316	C₂×C₈	—	53	1	no	—
317	C₂×C₈	—	53	1	no	—
318	C₂×C₈	—	53	1	no	—
319	C₂×C₈	—	53	1	no	—
320	C₂×C₈	—	53	1	no	—
321	C₂×C₈	—	53	1	no	—
322	C₂×C₈	—	53	1	no	—
323	C₂×C₈	—	53	1	no	—
324	C₂×C₈	—	53	1	no	—
325	C₂×C₈	—	53	1	no	—
326	C₂×C₈	—	53	1	no	—
327	C₂×C₈	—	53	1	no	—
328	C₂×C₈	—	53	1	no	—
329	C₂×C₈	—	53	1	no	—
330	C₂×C₈	—	53	1	no	—
331	C₂×C₈	—	53	1	no	—
332	C₂×C₈	—	53	1	no	—
333	C₂×C₈	—	53	1	no	—
334	C₂×C₈	—	212	2	no	—
335	C₂×C₈	—	212	2	no	—
336	C₂×C₈	—	212	2	no	—
337	C₂×C₈	C₄×#6157	1	1	yes	characteristic
338	C₂×C₈	C₄×#6157	1	1	yes	characteristic
339	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
340	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
341	C₂×C₈	C₂²⋊#6157	1	1	yes	characteristic
342	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	106	2	no	—
345	C₄⋊C₄	—	212	2	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	212	2	no	—
348	C₂²⋊C₄	—	212	1	no	—
349	C₄²	—	4	1	no	—
350	C₄²	—	212	2	no	—
351	C₄²	—	212	1	no	—
352	C₁₆	—	106	4	no	—
353	C₂³	—	53	1	no	—
354	C₂³	—	53	1	no	—
355	C₂³	—	53	1	no	—
356	C₂³	—	53	1	no	—
357	C₂³	—	53	1	no	—
358	C₂³	—	53	1	no	—
359	C₂³	—	212	2	no	—
360	C₂³	#13133279	1	1	yes	characteristic
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	53	1	no	—
363	C₂×C₄	—	53	1	no	—
364	C₂×C₄	—	53	1	no	—
365	C₂×C₄	—	53	1	no	—
366	C₂×C₄	—	53	1	no	—
367	C₂×C₄	—	53	1	no	—
368	C₂×C₄	—	53	1	no	—
369	C₂×C₄	—	53	1	no	—
370	C₂×C₄	—	53	1	no	—
371	C₂×C₄	—	53	1	no	—
372	C₂×C₄	—	53	1	no	—
373	C₂×C₄	—	53	1	no	—
374	C₂×C₄	—	53	1	no	—
375	C₂×C₄	—	53	1	no	—
376	C₂×C₄	—	53	1	no	—
377	C₂×C₄	—	53	1	no	—
378	C₂×C₄	—	53	1	no	—
379	C₂×C₄	—	53	1	no	—
380	C₂×C₄	—	53	1	no	—
381	C₂×C₄	—	53	1	no	—
382	C₂×C₄	—	53	1	no	—
383	C₂×C₄	—	53	1	no	—
384	C₂×C₄	—	424	4	no	—
385	C₂×C₄	—	212	2	no	—
386	C₂×C₄	(C₂×#6157)⋊C₄	1	1	yes	characteristic
387	C₂×C₄	(C₂×#6157)⋊C₄	1	1	yes	characteristic
388	C₂×C₄	#13133279	1	1	yes	characteristic
389	C₂×C₄	#13133280	1	1	yes	characteristic
390	C₂×C₄	#13133280	1	1	yes	characteristic
391	C₂×C₄	C₂×C₂²⋊#6157	1	1	yes	characteristic
392	C₈	—	53	1	no	—
393	C₈	—	53	1	no	—
394	C₈	—	53	1	no	—
395	C₈	—	53	1	no	—
396	C₈	—	212	4	no	—
397	C₈	(C₂×#6157)⋊C₄	1	1	yes	characteristic
398	C₈	(C₂×#6157)⋊C₄	1	1	yes	characteristic
399	C₈	C₂×C₄×#6157	1	1	yes	characteristic
400	C₈	C₂×C₄⋊#6157	1	1	yes	characteristic
401	C₂²	—	4	1	no	—
402	C₂²	—	53	1	no	—
403	C₂²	—	53	1	no	—
404	C₂²	—	53	1	no	—
405	C₂²	—	53	1	no	—
406	C₂²	—	106	2	no	—
407	C₂²	—	106	2	no	—
408	C₂²	—	106	2	no	—
409	C₂²	—	212	1	no	—
410	C₂²	—	212	1	no	—
411	C₂²	—	212	1	no	—
412	C₂²	#16811496	1	1	yes	characteristic
413	C₂²	#16811496	1	1	yes	characteristic
414	C₂²	C₂×#13133279	1	1	yes	characteristic
415	C₄	—	8	2	no	—
416	C₄	—	53	1	no	—
417	C₄	—	53	1	no	—
418	C₄	—	53	1	no	—
419	C₄	—	53	1	no	—
420	C₄	—	424	2	no	—
421	C₄	#16811496	1	1	yes	characteristic
422	C₄	#16811496	1	1	yes	characteristic
423	C₄	C₂×(C₂×#6157)⋊C₄	1	1	yes	characteristic
424	C₄	C₂×#13133280	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	53	2	no	—
429	C₂	—	106	1	no	—
430	C₂	—	106	1	no	—
431	C₂	—	106	1	no	—
432	C₂	C₂×#16811496	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16811496
commutator	C₈×C₅₃	C₂×C₄²
Frattini	C₂×C₈	C₂²×#6157
Fitting	C₅₃×#427	C₄
socle	C₂×C₅₃	C₂×#340
prime radical	C₂³×D₅₃	SD₁₆
cosocle	C₂×C₈×D₅₃	C₂³
hypercenter	#427	#6157
hypocenter	C₅₃	C₂×#1389
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

Complements

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

N	H ≅ G/N	type
3. #20289797	C₂	semidirect
6. C₂×#13133292	C₄	semidirect
9. D₅₃⋊M₃₂	C₄	semidirect
13. C₂×#13133288	C₄	semidirect
16. D₅₃⋊#108	C₄	semidirect
36. #13133292	C₂×C₄	semidirect
43. #13133288	C₂×C₄	semidirect
220. D₅₃	#1389	semidirect
244. C₅₃	C₂×#1389	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅₃⋊M₃₂	2
C₂×D₅₃⋊#108	2
#20289797	2
#427×D₅₃	2
C₂×#1389	53