Subgroups — #28318462

Order 13568.

906 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₃⋊#433	C₂	1	1	yes	maximal, characteristic
2	#20291177	C₂	1	1	yes	maximal, characteristic
3	#20290513	C₂	1	2	yes	maximal, complemented
4	#20290509	C₂	1	2	yes	maximal, complemented
5	#20290455	C₂	1	2	yes	maximal
6	#20290451	C₂	1	2	yes	maximal
7	#20290435	C₂	1	1	yes	maximal, characteristic, complemented
8	#20290431	C₂	1	1	yes	maximal, characteristic, complemented
9	#20290371	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13133271	C₂	1	1	yes	maximal, characteristic, complemented
11	#405×D₅₃	C₂	1	1	yes	maximal, characteristic
12	#16811648	C₄	1	4	yes	complemented
13	#16811647	C₄	1	4	yes	complemented
14	D₅₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
15	D₅₃⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
16	#16811582	C₂²	1	1	yes	characteristic
17	C₂×#13133271	C₂²	1	2	yes	—
18	C₂×#13133271	C₂²	1	2	yes	—
19	C₂×#13133271	C₂²	1	2	yes	—
20	C₄×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₈×#6157	C₂²	1	2	yes	—
22	#16811573	C₄	1	4	yes	—
23	#16811572	C₄	1	4	yes	—
24	C₄×C₄⋊#6157	C₂²	1	2	yes	—
25	C₄×C₂²⋊#6157	C₂²	1	2	yes	—
26	#16811559	C₂²	1	1	yes	characteristic
27	C₄²×#6157	C₂²	1	1	yes	characteristic
28	(C₂×#6157)⋊C₈	C₂²	1	2	yes	—
29	(C₂×#6157)⋊C₈	C₂²	1	2	yes	—
30	(C₂×#6157)⋊C₈	C₂²	1	2	yes	—
31	(C₂×#6157)⋊C₈	C₂²	1	2	yes	—
32	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
33	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
34	#117×D₅₃	C₂²	1	1	yes	characteristic
35	#16810581	C₄	1	1	yes	characteristic, complemented
36	#16810580	C₄	1	1	yes	characteristic, complemented
37	#16810580	C₄	1	1	yes	characteristic, complemented
38	#16810579	C₄	1	1	yes	characteristic, complemented
39	#16810578	C₄	1	1	yes	characteristic, complemented
40	#16810577	C₄	1	1	yes	characteristic, complemented
41	#16810577	C₄	1	1	yes	characteristic, complemented
42	#97×D₅₃	C₂²	1	1	yes	characteristic
43	#97×D₅₃	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
46	C₅₃×#405	C₄	1	1	yes	characteristic, complemented
47	C₂×D₅₃⋊C₈	C₂³	1	2	yes	—
48	C₂×D₅₃⋊C₈	C₂³	1	2	yes	—
49	C₂×C₄⋊#6157	C₂×C₄	1	4	yes	—
50	C₂×C₂²⋊#6157	C₂×C₄	1	4	yes	—
51	C₂×C₄×#6157	C₂×C₄	1	4	yes	—
52	C₂×C₄×#6157	C₂³	1	2	yes	—
53	C₂×C₄×#6157	C₂³	1	2	yes	—
54	#13133284	C₂×C₄	1	4	yes	—
55	C₄⋊#88324	C₂×C₄	1	4	yes	—
56	#13133274	C₂×C₄	1	4	yes	—
57	C₂²⋊#88324	C₂×C₄	1	4	yes	—
58	#13133272	C₂×C₄	1	4	yes	—
59	#13133271	—	2	4	no	—
60	#13133271	—	2	4	no	—
61	#13133271	—	2	4	no	—
62	C₄×#88324	C₂×C₄	1	4	yes	—
63	C₈×#6157	—	2	4	no	—
64	(C₂×#6157)⋊C₄	C₂×C₄	1	4	yes	—
65	(C₂×#6157)⋊C₄	C₂×C₄	1	4	yes	—
66	(C₂×#6157)⋊C₄	C₂×C₄	1	4	yes	—
67	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
68	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
69	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
70	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
71	M₁₆×D₅₃	—	2	4	no	—
72	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₅₃	—	2	4	no	—
74	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
77	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
78	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
79	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
80	#13133176	C₂×C₄	1	1	yes	characteristic
81	#13133175	C₂×C₄	1	2	yes	—
82	#13133174	C₂×C₄	1	1	yes	characteristic
83	#13133174	C₂×C₄	1	1	yes	characteristic
84	#13133173	C₂×C₄	1	2	yes	—
85	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
86	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
87	C₄²×D₅₃	C₂³	1	1	yes	characteristic
88	C₄²×D₅₃	C₂³	1	1	yes	characteristic
89	#13133128	C₂×C₄	1	1	yes	characteristic
90	#13133128	C₂×C₄	1	1	yes	characteristic
91	#13133127	C₂×C₄	1	1	yes	characteristic
92	#13133127	C₂×C₄	1	1	yes	characteristic
93	#13133127	C₂×C₄	1	1	yes	characteristic
94	#13133127	C₂×C₄	1	1	yes	characteristic
95	C₄×#88322	C₂×C₄	1	1	yes	characteristic
96	C₄×#88322	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
101	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
102	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
103	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
104	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
105	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
106	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
107	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
108	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×#6157	C₂²×C₄	1	4	yes	—
110	C₂²×#6157	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₅₃	—	2	2	no	—
114	C₂×C₄×D₅₃	—	2	2	no	—
115	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
116	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
117	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
121	C₂²⋊#6157	—	4	4	no	—
122	C₂×#88324	C₂²×C₄	1	4	yes	—
123	C₂×#88324	C₂²×C₄	1	4	yes	—
124	C₄⋊#6157	—	4	4	no	—
125	C₄×#6157	—	2	2	no	—
126	C₄×#6157	—	2	2	no	—
127	C₄×#6157	—	2	2	no	—
128	C₄×#6157	—	2	2	no	—
129	C₄×#6157	—	4	4	no	—
130	D₅₃⋊C₈	—	2	2	no	—
131	D₅₃⋊C₈	—	2	2	no	—
132	D₅₃⋊C₈	—	2	2	no	—
133	D₅₃⋊C₈	—	2	2	no	—
134	M₁₆×C₅₃	—	2	2	no	—
135	C₂×C₈×C₅₃	—	2	2	no	—
136	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊C₄×C₅₃	C₄²	1	2	yes	—
141	C₂²⋊C₄×C₅₃	C₄²	1	2	yes	—
142	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²⋊Dic₅₃	C₄²	1	2	yes	—
145	#11719921	C₄²	1	2	yes	—
146	#11719921	C₄²	1	2	yes	—
147	C₄⋊Dic₅₃	C₄²	1	2	yes	—
148	#11719919	C₄²	1	2	yes	—
149	#11719919	C₄²	1	2	yes	—
150	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
153	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
154	#11719917	—	2	2	no	—
155	C₂×#88322	—	2	2	no	—
156	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
157	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
158	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
159	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
160	#11719912	—	2	2	no	—
161	#11719912	—	2	2	no	—
162	C₈×D₅₃	—	2	2	no	—
163	C₈×D₅₃	—	2	2	no	—
164	C₈×D₅₃	—	2	2	no	—
165	C₈×D₅₃	—	2	2	no	—
166	C₈×D₅₃	#41	1	4	yes	—
167	C₈×D₅₃	#41	1	4	yes	—
168	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
169	C₂²×D₅₃	—	2	2	no	—
170	C₂²×D₅₃	—	2	4	no	—
171	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
172	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×#6157	—	2	4	no	—
174	C₂×#6157	—	2	4	no	—
175	C₂×#6157	—	2	4	no	—
176	C₂×#6157	—	2	4	no	—
177	C₂×#6157	—	2	4	no	—
178	C₂×#6157	—	2	4	no	—
179	C₂×C₄×C₅₃	—	2	1	no	—
180	C₂×C₄×C₅₃	—	2	1	no	—
181	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
182	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
183	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
184	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
185	C₂×Dic₅₃	—	2	2	no	—
186	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
187	C₂×Dic₅₃	C₂×C₄²	1	2	yes	—
188	C₂×Dic₅₃	C₂×C₄²	1	2	yes	—
189	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
190	C₄×D₅₃	—	2	2	no	—
191	C₄×D₅₃	—	2	4	no	—
192	C₄×D₅₃	—	2	4	no	—
193	C₄×D₅₃	—	2	1	no	—
194	C₄×D₅₃	—	2	1	no	—
195	C₄×D₅₃	—	2	2	no	—
196	C₄×D₅₃	C₂×#41	1	2	yes	—
197	C₄×D₅₃	C₂×#41	1	2	yes	—
198	#88324	—	2	4	no	—
199	#88324	—	2	4	no	—
200	C₈×C₅₃	—	2	1	no	—
201	C₈×C₅₃	—	2	1	no	—
202	C₈×C₅₃	#117	1	2	yes	—
203	C₈×C₅₃	#117	1	2	yes	—
204	#88322	—	2	1	no	—
205	#88322	—	2	1	no	—
206	#88322	#117	1	2	yes	—
207	#88322	#117	1	2	yes	—
208	#20475	—	53	1	no	maximal, Sylow
209	C₂²×C₅₃	—	2	2	no	—
210	C₂²×C₅₃	—	2	1	no	—
211	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
212	C₂×D₅₃	—	2	2	no	—
213	C₂×D₅₃	—	2	1	no	—
214	C₂×D₅₃	—	4	4	no	—
215	C₂×D₅₃	C₄×#41	1	2	yes	—
216	C₂×D₅₃	#568	1	4	yes	—
217	#6157	—	4	4	no	—
218	#6157	—	4	4	no	—
219	C₄×C₅₃	—	2	2	no	—
220	C₄×C₅₃	—	2	2	no	—
221	C₄×C₅₃	—	2	1	no	—
222	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
223	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
224	Dic₅₃	—	2	2	no	—
225	Dic₅₃	—	2	2	no	—
226	Dic₅₃	—	2	1	no	—
227	Dic₅₃	C₄×#41	1	2	yes	—
228	C₂×#433	—	53	1	no	—
229	C₂×#405	—	53	1	no	—
230	#2298	—	53	1	no	—
231	#1771	—	53	2	no	—
232	#1770	—	53	2	no	—
233	#1753	—	53	2	no	—
234	#1752	—	53	2	no	—
235	#1746	—	53	1	no	—
236	#1745	—	53	1	no	—
237	#1726	—	53	1	no	—
238	C₄×#97	—	53	1	no	—
239	C₂×C₅₃	—	4	1	no	—
240	C₂×C₅₃	C₄×#117	1	1	yes	characteristic
241	C₂×C₅₃	#2875	1	2	yes	—
242	D₅₃	—	4	1	no	—
243	D₅₃	#2967	1	4	yes	—
244	C₂²×M₁₆	—	53	1	no	—
245	C₂³×C₈	—	53	1	no	—
246	C₂×#117	—	53	1	no	—
247	#433	—	53	4	no	—
248	#433	—	53	4	no	—
249	C₂×C₄⋊C₈	—	53	2	no	—
250	C₂×C₂²⋊C₈	—	53	2	no	—
251	#405	—	53	1	no	—
252	#405	—	53	1	no	—
253	#405	—	53	1	no	—
254	#405	—	53	1	no	—
255	#405	—	53	1	no	—
256	#405	—	53	1	no	—
257	#405	—	53	1	no	—
258	#405	#6157	1	1	yes	characteristic, complemented
259	C₂×#97	—	53	1	no	—
260	C₂×#97	—	53	1	no	—
261	C₂×#97	—	53	1	no	—
262	C₂×#97	—	53	2	no	—
263	C₂×#97	—	53	2	no	—
264	C₂×#97	—	53	2	no	—
265	C₂×C₄×C₈	—	53	1	no	—
266	C₂×C₄×C₈	—	53	1	no	—
267	C₂×C₄×C₈	—	53	1	no	—
268	C₂×C₄×C₈	—	53	2	no	—
269	#388	—	53	4	no	—
270	#387	—	53	4	no	—
271	C₄×C₄⋊C₄	—	53	2	no	—
272	C₄×C₂²⋊C₄	—	53	2	no	—
273	#376	—	53	1	no	—
274	C₄³	—	53	1	no	—
275	#336	—	53	2	no	—
276	#336	—	53	2	no	—
277	#336	—	53	2	no	—
278	#336	—	53	2	no	—
279	C₅₃	#20475	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	—	106	4	no	—
285	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
286	C₂²×C₈	—	53	1	no	—
287	C₂²×C₈	—	53	1	no	—
288	C₂²×C₈	—	53	2	no	—
289	C₂²×C₈	—	53	2	no	—
290	C₂²×C₈	—	53	1	no	—
291	C₂²×C₈	—	53	1	no	—
292	C₂²×C₈	—	53	1	no	—
293	C₂²×C₈	—	53	1	no	—
294	C₂²×C₈	—	53	1	no	—
295	C₂²×C₈	—	106	4	no	—
296	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
297	#117	—	53	1	no	—
298	#117	—	53	2	no	—
299	#117	—	53	2	no	—
300	#117	—	53	1	no	—
301	#117	—	53	1	no	—
302	#117	C₂×#6157	1	1	yes	characteristic
303	C₂×C₄⋊C₄	—	53	2	no	—
304	C₂×C₄⋊C₄	—	53	4	no	—
305	C₂×C₂²⋊C₄	—	53	2	no	—
306	C₂×C₂²⋊C₄	—	53	4	no	—
307	C₂×C₄²	—	53	1	no	—
308	C₂×C₄²	—	53	1	no	—
309	C₂×C₄²	—	53	2	no	—
310	C₂×C₄²	—	53	2	no	—
311	C₂×C₄²	—	53	4	no	—
312	C₄⋊C₈	—	53	4	no	—
313	C₄⋊C₈	—	53	4	no	—
314	C₂²⋊C₈	—	53	4	no	—
315	C₂²⋊C₈	—	53	4	no	—
316	#97	—	53	4	no	—
317	#97	—	53	1	no	—
318	#97	—	53	1	no	—
319	#97	—	53	1	no	—
320	#97	—	53	1	no	—
321	#97	—	53	1	no	—
322	#97	—	53	1	no	—
323	#97	—	106	4	no	—
324	#97	—	106	4	no	—
325	#97	—	106	4	no	—
326	#97	C₂×#6157	1	1	yes	characteristic
327	#97	C₂×#6157	1	1	yes	characteristic
328	C₄×C₈	—	53	4	no	—
329	C₄×C₈	—	53	1	no	—
330	C₄×C₈	—	53	1	no	—
331	C₄×C₈	—	53	1	no	—
332	C₄×C₈	—	53	1	no	—
333	C₄×C₈	—	53	1	no	—
334	C₄×C₈	—	53	1	no	—
335	C₄×C₈	—	106	4	no	—
336	C₄×C₈	C₂×#6157	1	1	yes	characteristic
337	C₄×C₈	C₂×#6157	1	1	yes	characteristic
338	#95	—	53	4	no	—
339	#95	—	53	4	no	—
340	#95	—	53	4	no	—
341	C₂⁴	—	53	1	no	—
342	C₂²×C₄	—	53	1	no	—
343	C₂²×C₄	—	53	1	no	—
344	C₂²×C₄	—	53	1	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	4	no	—
350	C₂²×C₄	—	53	4	no	—
351	C₂²×C₄	—	106	2	no	—
352	C₂²×C₄	—	106	2	no	—
353	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
354	M₁₆	—	2	2	no	—
355	M₁₆	—	106	2	no	—
356	M₁₆	—	106	2	no	—
357	M₁₆	—	106	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	53	1	no	—
360	C₂×C₈	—	53	1	no	—
361	C₂×C₈	—	53	4	no	—
362	C₂×C₈	—	53	4	no	—
363	C₂×C₈	—	53	4	no	—
364	C₂×C₈	—	53	4	no	—
365	C₂×C₈	—	53	1	no	—
366	C₂×C₈	—	53	1	no	—
367	C₂×C₈	—	106	2	no	—
368	C₂×C₈	—	106	2	no	—
369	C₂×C₈	—	106	2	no	—
370	C₂×C₈	—	106	2	no	—
371	C₂×C₈	—	106	2	no	—
372	C₂×C₈	—	106	2	no	—
373	C₂×C₈	—	106	2	no	—
374	C₂×C₈	—	106	2	no	—
375	C₂×C₈	—	106	2	no	—
376	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
377	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
378	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
379	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
380	C₄⋊C₄	—	53	2	no	—
381	C₄⋊C₄	—	53	2	no	—
382	C₄⋊C₄	—	53	2	no	—
383	C₄⋊C₄	—	212	4	no	—
384	C₄⋊C₄	C₄×#6157	1	2	yes	—
385	C₂²⋊C₄	—	53	2	no	—
386	C₂²⋊C₄	—	53	2	no	—
387	C₂²⋊C₄	—	53	2	no	—
388	C₂²⋊C₄	—	212	4	no	—
389	C₂²⋊C₄	C₄×#6157	1	2	yes	—
390	C₄²	—	53	2	no	—
391	C₄²	—	53	2	no	—
392	C₄²	—	53	1	no	—
393	C₄²	—	53	1	no	—
394	C₄²	—	106	2	no	—
395	C₄²	—	106	2	no	—
396	C₄²	—	106	2	no	—
397	C₄²	—	106	2	no	—
398	C₄²	—	212	4	no	—
399	C₄²	C₂²×#6157	1	1	yes	characteristic
400	C₄²	C₂²×#6157	1	1	yes	characteristic
401	C₂³	—	53	1	no	—
402	C₂³	—	53	1	no	—
403	C₂³	—	106	4	no	—
404	C₂³	—	106	2	no	—
405	C₂³	C₂×C₄×#6157	1	1	yes	characteristic
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	53	1	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	1	no	—
414	C₂×C₄	—	106	2	no	—
415	C₂×C₄	—	106	4	no	—
416	C₂×C₄	—	106	4	no	—
417	C₂×C₄	—	106	2	no	—
418	C₂×C₄	—	106	2	no	—
419	C₂×C₄	—	106	1	no	—
420	C₂×C₄	—	106	1	no	—
421	C₂×C₄	—	106	4	no	—
422	C₂×C₄	—	106	4	no	—
423	C₂×C₄	—	106	4	no	—
424	C₂×C₄	—	106	4	no	—
425	C₂×C₄	—	106	4	no	—
426	C₂×C₄	—	106	4	no	—
427	C₂×C₄	C₂×C₄×#6157	1	2	yes	—
428	C₂×C₄	C₂×C₄×#6157	1	2	yes	—
429	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
430	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	53	2	no	—
434	C₈	—	53	2	no	—
435	C₈	—	106	4	no	—
436	C₈	—	106	4	no	—
437	C₈	—	106	1	no	—
438	C₈	—	106	1	no	—
439	C₈	#13133296	1	2	yes	—
440	C₈	#13133296	1	2	yes	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	53	2	no	—
444	C₂²	—	53	4	no	—
445	C₂²	—	106	1	no	—
446	C₂²	—	106	2	no	—
447	C₂²	—	212	4	no	—
448	C₂²	C₂²×C₄×#6157	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	53	2	no	—
453	C₄	—	106	1	no	—
454	C₄	—	106	2	no	—
455	C₄	—	106	2	no	—
456	C₄	—	212	4	no	—
457	C₄	—	212	4	no	—
458	C₄	C₂×#13133296	1	1	yes	characteristic
459	C₄	C₂×#13133296	1	1	yes	characteristic
460	C₂	—	4	1	no	—
461	C₂	—	53	4	no	—
462	C₂	—	212	1	no	—
463	C₂	C₄×#13133296	1	1	yes	characteristic
464	C₂	#20291285	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂²×C₄²
Fitting	C₅₃×#405	C₄
prime radical	C₂³×D₅₃	C₂²×C₄
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	#405	#6157
hypocenter	C₅₃	#20475
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #20290513	C₂	semidirect
4. #20290509	C₂	semidirect
7. #20290435	C₂	semidirect
8. #20290431	C₂	semidirect
9. #20290371	C₂	semidirect
10. C₄×#13133271	C₂	semidirect
12. #16811648	C₄	semidirect
13. #16811647	C₄	semidirect
35. #16810581	C₄	semidirect
36. #16810580	C₄	semidirect
37. #16810580	C₄	semidirect
38. #16810579	C₄	semidirect
39. #16810578	C₄	semidirect
40. #16810577	C₄	semidirect
41. #16810577	C₄	semidirect
46. C₅₃×#405	C₄	semidirect
258. #405	#6157	semidirect
279. C₅₃	#20475	semidirect

Maximal subgroups

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

subgroup	index
D₅₃⋊#433	2
#20291177	2
#20290513	2
#20290509	2
#20290455	2
#20290451	2
#20290435	2
#20290431	2
#20290371	2
C₄×#13133271	2
#405×D₅₃	2
#20475	53