Subgroups — #27366566

Order 13568.

664 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20285294	C₂	1	1	yes	maximal, characteristic, complemented
2	#20284775	C₂	1	2	yes	maximal, complemented
3	#20274131	C₂	1	2	yes	maximal, complemented
4	#20274124	C₂	1	2	yes	maximal, complemented
5	#20274119	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274114	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274075	C₂	1	1	yes	maximal, characteristic, complemented
8	#20274070	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273463	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273375	C₂	1	2	yes	maximal, complemented
11	C₈×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811173	C₂²	1	2	yes	—
13	#16811028	C₂²	1	1	yes	characteristic
14	#16811000	C₂²	1	1	yes	characteristic
15	#16810970	C₂²	1	2	yes	—
16	#16810947	—	2	2	no	—
17	#16810918	C₂²	1	2	yes	—
18	#16810913	C₂²	1	2	yes	—
19	#16810859	—	2	1	no	—
20	#16810859	—	2	1	no	—
21	#16810823	C₂²	1	2	yes	—
22	#16810818	C₂²	1	2	yes	—
23	#16810768	—	2	2	no	—
24	C₄×#11719924	—	2	2	no	—
25	C₄×D₄₂₄	—	2	1	no	—
26	C₄×D₄₂₄	—	2	1	no	—
27	C₄×#11719922	—	2	2	no	—
28	#16810676	C₂²	1	2	yes	—
29	#16810376	C₂²	1	1	yes	characteristic
30	#16810376	C₂²	1	1	yes	characteristic
31	#16810374	C₂²	1	2	yes	—
32	#16810371	C₂²	1	2	yes	—
33	#16810371	C₂²	1	2	yes	—
34	#16810366	C₂²	1	2	yes	—
35	#16810366	C₂²	1	2	yes	—
36	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₅₃	—	2	1	no	—
40	C₈×D₄×C₅₃	—	2	1	no	—
41	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#431	—	2	1	no	—
44	C₅₃×#431	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₅₃	—	2	1	no	—
46	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×#11719945	—	2	2	no	—
48	C₂×#11719924	—	2	2	no	—
49	C₂×D₄₂₄	—	2	1	no	—
50	C₂×D₄₂₄	—	2	1	no	—
51	C₂×#11719922	—	2	2	no	—
52	#13133217	C₂³	1	2	yes	—
53	#13133214	C₂³	1	2	yes	—
54	#13133205	—	2	2	no	—
55	#13133191	—	2	2	no	—
56	#13133191	—	2	2	no	—
57	C₄×D₂₁₂	—	2	2	no	—
58	C₄×D₂₁₂	—	2	2	no	—
59	#13133151	—	2	1	no	—
60	#13133151	—	2	1	no	—
61	#13133150	—	2	2	no	—
62	#13133148	—	2	2	no	—
63	C₄⋊#88322	C₂³	1	2	yes	—
64	C₄⋊#88322	C₂³	1	2	yes	—
65	#13133141	—	2	2	no	—
66	#13133139	—	2	2	no	—
67	#13133139	—	2	2	no	—
68	#13133138	—	2	2	no	—
69	#13133137	—	2	2	no	—
70	#13133137	—	2	2	no	—
71	C₂²⋊#88322	—	2	2	no	—
72	C₄×#88322	—	2	2	no	—
73	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₅₃	—	2	1	no	—
75	C₂²×C₈×C₅₃	—	2	1	no	—
76	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₅₃	—	2	1	no	—
81	C₄×D₄×C₅₃	—	2	1	no	—
82	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
83	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
84	#117×C₅₃	—	2	1	no	—
85	#117×C₅₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₅₃	—	2	1	no	—
87	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₅₃	—	2	1	no	—
89	C₄⋊C₈×C₅₃	—	2	1	no	—
90	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₅₃	—	2	1	no	—
93	C₂²⋊C₈×C₅₃	—	2	1	no	—
94	C₂²⋊C₈×C₅₃	—	2	1	no	—
95	C₄×C₈×C₅₃	—	2	1	no	—
96	C₄×C₈×C₅₃	—	2	1	no	—
97	C₄×C₈×C₅₃	—	2	1	no	—
98	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
102	#41×C₅₃	—	2	2	no	—
103	#41×C₅₃	—	2	2	no	—
104	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₅₃	—	2	1	no	—
106	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₃	—	2	1	no	—
108	C₂²×C₄×C₅₃	—	2	1	no	—
109	C₂²×C₄×C₅₃	—	2	1	no	—
110	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₅₃	—	4	2	no	—
114	#11719945	—	8	4	no	—
115	C₂×D₂₁₂	—	2	2	no	—
116	C₂×D₂₁₂	—	2	2	no	—
117	C₂×D₂₁₂	—	2	2	no	—
118	C₂×C₄×D₅₃	—	4	2	no	—
119	C₂×Dic₁₀₆	—	2	2	no	—
120	C₂×C₈×C₅₃	—	2	2	no	—
121	C₂×C₈×C₅₃	—	2	1	no	—
122	C₂×C₈×C₅₃	—	2	1	no	—
123	C₂×C₈×C₅₃	—	4	1	no	—
124	C₂×C₈×C₅₃	—	4	2	no	—
125	C₂×C₈×C₅₃	—	4	2	no	—
126	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
130	C₄⋊C₄×C₅₃	—	2	1	no	—
131	C₄⋊C₄×C₅₃	—	2	1	no	—
132	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
133	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
134	C₂²⋊C₄×C₅₃	—	2	1	no	—
135	C₂²⋊C₄×C₅₃	—	2	1	no	—
136	C₂²⋊C₄×C₅₃	—	2	1	no	—
137	C₄²×C₅₃	—	2	1	no	—
138	C₄²×C₅₃	—	2	1	no	—
139	C₄²×C₅₃	—	2	1	no	—
140	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₅₃	#41	1	1	yes	characteristic
143	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
144	#11719924	—	4	4	no	—
145	#11719922	—	4	4	no	—
146	#11719921	—	4	2	no	—
147	#11719921	—	4	2	no	—
148	C₄⋊Dic₅₃	—	2	2	no	—
149	C₄⋊Dic₅₃	—	2	2	no	—
150	C₂×#88322	—	2	2	no	—
151	C₂×#88322	—	2	2	no	—
152	D₄₂₄	—	4	2	no	—
153	D₄₂₄	—	4	2	no	—
154	C₂³×C₅₃	—	2	1	no	—
155	C₂³×C₅₃	#121	1	1	yes	characteristic
156	C₂²×D₅₃	—	4	2	no	—
157	Q₈×C₅₃	—	2	1	no	—
158	Q₈×C₅₃	#135	1	2	yes	—
159	D₄×C₅₃	—	2	4	no	—
160	D₄×C₅₃	—	2	1	no	—
161	D₄×C₅₃	#135	1	2	yes	—
162	C₂×C₄×C₅₃	—	2	4	no	—
163	C₂×C₄×C₅₃	—	2	1	no	—
164	C₂×C₄×C₅₃	—	2	1	no	—
165	C₂×C₄×C₅₃	—	2	1	no	—
166	C₂×C₄×C₅₃	—	2	1	no	—
167	C₂×C₄×C₅₃	—	2	1	no	—
168	C₂×C₄×C₅₃	—	2	2	no	—
169	C₂×C₄×C₅₃	—	2	1	no	—
170	C₂×C₄×C₅₃	—	2	1	no	—
171	C₂×C₄×C₅₃	—	4	1	no	—
172	C₂×C₄×C₅₃	—	4	1	no	—
173	C₂×C₄×C₅₃	—	4	2	no	—
174	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
175	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
176	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
177	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₅₃	—	8	4	no	—
181	C₂×Dic₅₃	—	4	2	no	—
182	D₂₁₂	—	4	2	no	—
183	D₂₁₂	—	4	2	no	—
184	D₂₁₂	—	4	2	no	—
185	D₂₁₂	—	4	2	no	—
186	D₂₁₂	—	8	2	no	—
187	C₄×D₅₃	—	8	4	no	—
188	Dic₁₀₆	—	8	2	no	—
189	C₈×C₅₃	—	2	1	no	—
190	C₈×C₅₃	—	2	1	no	—
191	C₈×C₅₃	—	2	1	no	—
192	C₈×C₅₃	—	4	1	no	—
193	C₈×C₅₃	—	4	1	no	—
194	C₈×C₅₃	#135	1	2	yes	—
195	#88322	—	4	2	no	—
196	#88322	—	4	2	no	—
197	#19128	—	53	1	no	maximal, Sylow
198	C₂²×C₅₃	—	2	1	no	—
199	C₂²×C₅₃	—	2	1	no	—
200	C₂²×C₅₃	—	2	2	no	—
201	C₂²×C₅₃	—	2	1	no	—
202	C₂²×C₅₃	—	4	1	no	—
203	C₂²×C₅₃	—	4	1	no	—
204	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
205	C₂×D₅₃	—	8	2	no	—
206	C₂×D₅₃	—	8	2	no	—
207	C₂×D₅₃	—	8	2	no	—
208	C₄×C₅₃	—	2	1	no	—
209	C₄×C₅₃	—	2	1	no	—
210	C₄×C₅₃	—	2	2	no	—
211	C₄×C₅₃	—	2	1	no	—
212	C₄×C₅₃	—	4	1	no	—
213	C₄×C₅₃	—	4	1	no	—
214	C₄×C₅₃	#472	1	2	yes	—
215	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
216	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
217	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
218	C₄×C₅₃	#575	1	1	yes	characteristic
219	Dic₅₃	—	8	2	no	—
220	#3169	—	53	1	no	—
221	#3106	—	53	2	no	—
222	C₈×#41	D₅₃	1	1	yes	characteristic, complemented
223	#1678	—	53	2	no	—
224	#1677	—	53	2	no	—
225	#1676	—	53	1	no	—
226	#1675	—	53	1	no	—
227	#1668	—	53	1	no	—
228	#1667	—	53	1	no	—
229	#1564	—	53	1	no	—
230	#1543	—	53	2	no	—
231	C₂×C₅₃	—	4	1	no	—
232	C₂×C₅₃	—	4	2	no	—
233	C₂×C₅₃	#3035	1	1	yes	characteristic
234	C₂×C₅₃	#3050	1	1	yes	characteristic
235	C₂×C₅₃	C₂×#472	1	1	yes	characteristic
236	D₅₃	—	16	2	no	—
237	#532	—	53	2	no	—
238	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
239	#500	—	53	1	no	—
240	#493	—	53	1	no	—
241	#486	—	53	2	no	—
242	#482	—	106	2	no	—
243	#477	—	53	2	no	—
244	#476	—	53	2	no	—
245	#466	—	106	1	no	—
246	#466	—	106	1	no	—
247	#460	—	53	2	no	—
248	#459	—	53	2	no	—
249	#449	—	106	2	no	—
250	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic
251	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic
252	C₄×SD₁₆	—	106	2	no	—
253	C₄×D₈	—	106	2	no	—
254	C₄×D₈	—	106	1	no	—
255	C₄×D₈	—	106	1	no	—
256	C₈×D₄	—	2	1	no	—
257	C₈×D₄	—	2	1	no	—
258	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
259	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
260	#431	—	2	1	no	—
261	#431	—	53	2	no	—
262	#431	C₂×D₅₃	1	1	yes	characteristic
263	C₂×C₄×C₈	—	2	1	no	—
264	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
265	#335	—	53	1	no	—
266	#335	—	53	1	no	—
267	#334	—	53	2	no	—
268	#333	—	53	2	no	—
269	#333	—	53	2	no	—
270	#331	—	53	2	no	—
271	#331	—	53	2	no	—
272	C₅₃	#19128	1	1	yes	characteristic, complemented, Sylow
273	C₂×#41	—	106	2	no	—
274	C₂×#41	D₂₁₂	1	1	yes	characteristic
275	C₂×SD₁₆	—	106	2	no	—
276	C₂×D₈	—	106	2	no	—
277	C₂×D₈	—	106	1	no	—
278	C₂×D₈	—	106	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
282	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
283	C₄⋊Q₈	—	53	2	no	—
284	#127	—	53	2	no	—
285	#124	—	106	2	no	—
286	#121	—	106	2	no	—
287	#121	—	106	2	no	—
288	C₄×Q₈	D₂₁₂	1	1	yes	characteristic
289	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	106	2	no	—
293	C₄×D₄	—	106	2	no	—
294	C₄×D₄	D₂₁₂	1	1	yes	characteristic
295	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
296	#117	—	2	1	no	—
297	#117	D₂₁₂	1	1	yes	characteristic
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
300	#107	—	106	1	no	—
301	#107	—	106	1	no	—
302	#107	—	106	2	no	—
303	#106	—	106	2	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	53	2	no	—
307	C₄⋊C₈	—	53	2	no	—
308	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
309	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
310	#103	—	106	2	no	—
311	#102	—	106	2	no	—
312	#102	—	106	2	no	—
313	#102	—	106	2	no	—
314	#102	—	106	2	no	—
315	#102	—	106	2	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	106	2	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	106	2	no	—
324	C₄×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
325	C₄×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
327	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	424	4	no	—
331	C₂×Q₈	—	106	2	no	—
332	C₂×Q₈	C₂×D₂₁₂	1	1	yes	characteristic
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	106	2	no	—
335	C₂×D₄	—	106	2	no	—
336	C₂×D₄	—	106	2	no	—
337	C₂×D₄	—	212	2	no	—
338	C₂×D₄	C₂×D₂₁₂	1	1	yes	characteristic
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	212	2	no	—
343	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
344	C₂²×C₄	#11719945	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
346	SD₁₆	—	212	4	no	—
347	D₈	—	212	2	no	—
348	D₈	—	212	4	no	—
349	D₈	—	212	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	106	2	no	—
357	C₂×C₈	—	106	2	no	—
358	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
359	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
360	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
361	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	106	2	no	—
365	C₄⋊C₄	—	106	2	no	—
366	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
367	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	212	2	no	—
372	C₂²⋊C₄	—	212	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
377	C₄²	#11719945	1	1	yes	characteristic
378	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
379	C₄²	C₂³×D₅₃	1	1	yes	characteristic
380	C₂³	—	2	1	no	—
381	C₂³	—	212	2	no	—
382	C₂³	#13133191	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	—	424	2	no	—
385	Q₈	#13133239	1	2	yes	—
386	D₄	—	2	4	no	—
387	D₄	—	2	1	no	—
388	D₄	—	424	2	no	—
389	D₄	—	424	4	no	—
390	D₄	—	212	2	no	—
391	D₄	—	212	2	no	—
392	D₄	—	212	2	no	—
393	D₄	—	212	2	no	—
394	D₄	#13133239	1	2	yes	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	424	4	no	—
408	C₂×C₄	—	212	2	no	—
409	C₂×C₄	#13133191	1	1	yes	characteristic
410	C₂×C₄	#13133191	1	1	yes	characteristic
411	C₂×C₄	#13133191	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
414	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	2	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	212	2	no	—
421	C₈	—	212	2	no	—
422	C₈	#13133237	1	2	yes	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	424	2	no	—
430	C₂²	—	424	2	no	—
431	C₂²	—	424	2	no	—
432	C₂²	C₂×#13133191	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	2	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	424	2	no	—
440	C₄	#16810893	1	2	yes	—
441	C₄	C₂×#13133237	1	1	yes	characteristic
442	C₄	C₂×#13133239	1	1	yes	characteristic
443	C₄	C₂×#13133239	1	1	yes	characteristic
444	C₄	#16811421	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	4	2	no	—
447	C₂	—	848	2	no	—
448	C₂	#20284170	1	1	yes	characteristic
449	C₂	#20284296	1	1	yes	characteristic
450	C₂	C₂×#16810893	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13133191
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₈×#41×C₅₃	C₂
socle	C₂²×C₅₃	C₂×#121
hypercenter	C₈×#41	D₅₃
hypocenter	C₅₃	#19128
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #20285294	C₂	semidirect
2. #20284775	C₂	semidirect
3. #20274131	C₂	semidirect
4. #20274124	C₂	semidirect
5. #20274119	C₂	semidirect
6. #20274114	C₂	semidirect
7. #20274075	C₂	semidirect
8. #20274070	C₂	semidirect
9. #20273463	C₂	semidirect
10. #20273375	C₂	semidirect
11. C₈×#41×C₅₃	C₂	semidirect
222. C₈×#41	D₅₃	semidirect
272. C₅₃	#19128	semidirect

Maximal subgroups

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

subgroup	index
#20285294	2
#20284775	2
#20274131	2
#20274124	2
#20274119	2
#20274114	2
#20274075	2
#20274070	2
#20273463	2
#20273375	2
C₈×#41×C₅₃	2
#19128	53