Subgroups — #27355294

Order 13568.

638 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20284775	C₂	1	1	yes	maximal, characteristic
2	#20283847	C₂	1	1	yes	maximal, characteristic, complemented
3	#20283781	C₂	1	1	yes	maximal, characteristic, complemented
4	#20273597	C₂	1	2	yes	maximal, complemented
5	#20273590	C₂	1	2	yes	maximal, complemented
6	#20273582	C₂	1	2	yes	maximal, complemented
7	#20273512	C₂	1	2	yes	maximal, complemented
8	#20273503	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273167	C₂	1	1	yes	maximal, characteristic, complemented
10	#20272998	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811173	C₂²	1	1	yes	characteristic
13	#16810947	C₄	1	2	yes	—
14	#16810918	C₄	1	1	yes	characteristic
15	#16810913	C₄	1	1	yes	characteristic
16	#16810823	C₄	1	1	yes	characteristic
17	#16810818	C₄	1	1	yes	characteristic
18	#16810768	C₄	1	2	yes	—
19	Q₈×#88322	C₂²	1	2	yes	—
20	C₄×#11719924	C₂²	1	2	yes	—
21	C₄×#11719922	C₂²	1	2	yes	—
22	#16810702	—	2	1	no	—
23	#16810701	—	2	2	no	—
24	#16810701	C₂²	1	2	yes	—
25	#16810700	C₂²	1	2	yes	—
26	C₈×D₂₁₂	—	2	1	no	—
27	#16810688	C₂²	1	2	yes	—
28	#16810676	—	2	1	no	—
29	#16810676	C₂²	1	1	yes	characteristic
30	#16810676	C₂²	1	1	yes	characteristic
31	#16810647	—	2	1	no	—
32	#16810647	C₂²	1	1	yes	characteristic
33	#16810588	—	2	2	no	—
34	#16810375	C₂²	1	2	yes	—
35	#16810373	C₂²	1	2	yes	—
36	#16810352	C₂²	1	2	yes	—
37	#16810352	C₂²	1	2	yes	—
38	#16810344	C₂²	1	2	yes	—
39	C₈×#88322	C₂²	1	2	yes	—
40	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#431	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
44	C₅₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
45	C₅₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₅₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×#11719945	—	2	1	no	—
48	C₂×#11719924	C₂×C₄	1	2	yes	—
49	C₂×#11719922	C₂×C₄	1	2	yes	—
50	C₂×#11719917	—	2	2	no	—
51	C₂×#11719917	—	2	1	no	—
52	C₂×#11719912	—	2	2	no	—
53	C₂×C₈×D₅₃	—	2	2	no	—
54	#13133217	C₂×C₄	1	1	yes	characteristic
55	#13133214	C₂×C₄	1	1	yes	characteristic
56	#13133205	—	2	1	no	—
57	#13133191	—	2	1	no	—
58	#13133191	C₂×C₄	1	2	yes	—
59	C₄×D₂₁₂	—	2	1	no	—
60	C₄×D₂₁₂	C₂³	1	2	yes	—
61	#13133150	C₂×C₄	1	2	yes	—
62	#13133148	C₂×C₄	1	2	yes	—
63	C₄⋊#88322	—	2	1	no	—
64	C₄⋊#88322	—	2	2	no	—
65	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
66	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
67	C₄⋊#88322	D₄	1	1	yes	characteristic
68	C₄⋊#88322	D₄	1	1	yes	characteristic
69	C₄⋊#88322	C₂³	1	2	yes	—
70	#13133141	C₂×C₄	1	2	yes	—
71	#13133138	C₂×C₄	1	2	yes	—
72	#13133137	C₂×C₄	1	2	yes	—
73	#13133137	C₂×C₄	1	2	yes	—
74	C₂²⋊#88322	—	2	2	no	—
75	C₂²⋊#88322	C₂×C₄	1	2	yes	—
76	C₂²⋊#88322	D₄	1	2	yes	—
77	#13133129	—	2	2	no	—
78	#13133129	—	2	2	no	—
79	C₄×#88322	—	2	2	no	—
80	C₄×#88322	C₂³	1	2	yes	—
81	C₄×#88322	C₂³	1	2	yes	—
82	C₂×#41×C₅₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₅₃	—	2	1	no	—
84	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₄×D₄×C₅₃	—	2	1	no	—
87	C₄×D₄×C₅₃	—	2	1	no	—
88	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
89	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
90	#117×C₅₃	—	2	1	no	—
91	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₅₃	—	2	1	no	—
93	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
96	C₂²⋊C₈×C₅₃	—	2	1	no	—
97	C₄×C₈×C₅₃	—	2	1	no	—
98	C₄×C₈×C₅₃	—	2	1	no	—
99	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
101	#41×C₅₃	—	2	2	no	—
102	#41×C₅₃	—	4	1	no	—
103	C₂×Q₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×D₄×C₅₃	—	2	1	no	—
105	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅₃	—	2	1	no	—
107	C₂²×C₄×C₅₃	—	2	1	no	—
108	C₂²×C₄×C₅₃	—	2	1	no	—
109	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₅₃	—	2	2	no	—
113	#11719945	—	8	1	no	—
114	#11719945	—	8	1	no	—
115	C₂×D₂₁₂	—	2	1	no	—
116	C₂×D₂₁₂	—	2	1	no	—
117	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
118	C₂×C₄×D₅₃	—	2	2	no	—
119	C₂×Dic₁₀₆	—	2	1	no	—
120	C₂×C₈×C₅₃	—	2	4	no	—
121	C₂×C₈×C₅₃	—	2	1	no	—
122	C₂×C₈×C₅₃	—	2	1	no	—
123	C₂×C₈×C₅₃	—	2	1	no	—
124	C₂×C₈×C₅₃	—	2	1	no	—
125	C₄⋊C₄×C₅₃	—	2	1	no	—
126	C₄⋊C₄×C₅₃	—	2	1	no	—
127	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
128	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₅₃	—	2	1	no	—
130	C₂²⋊C₄×C₅₃	—	2	1	no	—
131	C₂²⋊C₄×C₅₃	—	2	1	no	—
132	C₄²×C₅₃	—	2	1	no	—
133	C₄²×C₅₃	—	2	1	no	—
134	C₄²×C₅₃	—	2	1	no	—
135	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₅₃	#41	1	1	yes	characteristic
138	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
139	#11719924	—	2	4	no	—
140	#11719922	—	4	2	no	—
141	#11719921	—	2	2	no	—
142	#11719921	—	2	2	no	—
143	C₄⋊Dic₅₃	—	2	1	no	—
144	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
145	#11719917	—	8	2	no	—
146	#11719917	—	8	1	no	—
147	C₂×#88322	—	2	2	no	—
148	C₂×#88322	C₂²×C₄	1	2	yes	—
149	C₂×#88322	C₂²×C₄	1	2	yes	—
150	C₂×#88322	C₂×D₄	1	2	yes	—
151	C₂×#88322	C₂×D₄	1	2	yes	—
152	#11719912	—	8	2	no	—
153	C₈×D₅₃	—	8	2	no	—
154	C₂³×C₅₃	—	2	1	no	—
155	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
156	C₂²×D₅₃	—	2	2	no	—
157	Q₈×C₅₃	—	2	1	no	—
158	Q₈×C₅₃	#131	1	2	yes	—
159	D₄×C₅₃	—	2	1	no	—
160	D₄×C₅₃	—	2	1	no	—
161	D₄×C₅₃	—	4	2	no	—
162	C₂×C₄×C₅₃	—	2	1	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	2	no	—
168	C₂×C₄×C₅₃	—	2	1	no	—
169	C₂×C₄×C₅₃	—	2	1	no	—
170	C₂×C₄×C₅₃	—	4	2	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	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₅₃	C₂³×C₄	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	2	no	—
181	C₂×Dic₅₃	—	2	2	no	—
182	D₂₁₂	—	2	2	no	—
183	D₂₁₂	—	2	2	no	—
184	D₂₁₂	—	4	2	no	—
185	D₂₁₂	—	8	1	no	—
186	C₄×D₅₃	—	4	2	no	—
187	C₄×D₅₃	—	4	2	no	—
188	Dic₁₀₆	—	8	1	no	—
189	C₈×C₅₃	—	2	2	no	—
190	C₈×C₅₃	—	2	2	no	—
191	C₈×C₅₃	—	4	1	no	—
192	C₈×C₅₃	—	4	1	no	—
193	#88322	—	2	2	no	—
194	#88322	—	2	2	no	—
195	#88322	—	2	2	no	—
196	#88322	—	2	2	no	—
197	#88322	—	4	2	no	—
198	#18018	—	53	1	no	maximal, Sylow
199	C₂²×C₅₃	—	2	1	no	—
200	C₂²×C₅₃	—	2	1	no	—
201	C₂²×C₅₃	—	2	1	no	—
202	C₂²×C₅₃	—	4	1	no	—
203	C₂²×C₅₃	—	4	1	no	—
204	C₂²×C₅₃	—	4	1	no	—
205	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
206	C₂×D₅₃	—	4	2	no	—
207	C₂×D₅₃	—	4	2	no	—
208	C₂×D₅₃	—	4	2	no	—
209	C₄×C₅₃	—	2	1	no	—
210	C₄×C₅₃	—	2	2	no	—
211	C₄×C₅₃	—	2	1	no	—
212	C₄×C₅₃	—	2	1	no	—
213	C₄×C₅₃	—	4	1	no	—
214	C₄×C₅₃	—	4	1	no	—
215	C₄×C₅₃	#443	1	2	yes	—
216	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
217	C₄×C₅₃	#568	1	1	yes	characteristic
218	C₄×C₅₃	#576	1	1	yes	characteristic
219	C₄×C₅₃	#577	1	1	yes	characteristic
220	Dic₅₃	—	4	2	no	—
221	#3106	—	53	1	no	—
222	#2991	—	53	1	no	—
223	#2979	—	53	1	no	—
224	#1589	—	53	2	no	—
225	#1588	—	53	2	no	—
226	#1586	—	53	2	no	—
227	C₈×SD₁₆	—	53	2	no	—
228	#1574	—	53	1	no	—
229	#1492	—	53	1	no	—
230	#1476	D₅₃	1	1	yes	characteristic, complemented
231	#1450	—	53	1	no	—
232	C₂×C₅₃	—	4	1	no	—
233	C₂×C₅₃	—	8	1	no	—
234	C₂×C₅₃	#2933	1	1	yes	characteristic
235	C₂×C₅₃	#2946	1	1	yes	characteristic
236	C₂×C₅₃	C₂×#443	1	1	yes	characteristic
237	D₅₃	—	8	2	no	—
238	#532	—	53	1	no	—
239	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
240	#482	—	53	2	no	—
241	#477	—	53	1	no	—
242	#476	—	53	1	no	—
243	#460	—	53	1	no	—
244	#459	—	53	1	no	—
245	#449	—	53	2	no	—
246	C₈×Q₈	—	53	2	no	—
247	C₄×SD₁₆	—	53	2	no	—
248	C₄×D₈	—	53	2	no	—
249	#436	—	53	2	no	—
250	#436	—	53	2	no	—
251	#436	—	106	1	no	—
252	#436	—	106	2	no	—
253	C₈×D₄	—	53	2	no	—
254	C₈×D₄	—	106	1	no	—
255	#431	—	53	1	no	—
256	#431	—	53	1	no	—
257	#431	—	106	1	no	—
258	#431	C₂×D₅₃	1	1	yes	characteristic
259	#423	—	53	1	no	—
260	#423	—	106	1	no	—
261	#408	—	106	2	no	—
262	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
263	#335	—	53	2	no	—
264	#334	—	53	2	no	—
265	Q₈⋊C₈	C₂×D₅₃	1	1	yes	characteristic
266	Q₈⋊C₈	C₂×D₅₃	1	1	yes	characteristic
267	D₄⋊C₈	—	53	2	no	—
268	D₄⋊C₈	—	53	2	no	—
269	D₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
270	D₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
271	#322	—	53	2	no	—
272	C₈²	—	53	2	no	—
273	C₅₃	#18018	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	106	1	no	—
275	C₂×#41	C₄×D₅₃	1	1	yes	characteristic
276	C₂×SD₁₆	—	53	2	no	—
277	C₂×D₈	—	53	2	no	—
278	C₂×M₁₆	—	106	2	no	—
279	C₂×M₁₆	—	106	2	no	—
280	C₂×M₁₆	—	106	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	106	2	no	—
283	C₄⋊Q₈	—	53	1	no	—
284	#127	—	53	1	no	—
285	#124	—	106	1	no	—
286	#121	—	53	2	no	—
287	#121	—	106	1	no	—
288	C₄×Q₈	C₄×D₅₃	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	—	53	2	no	—
293	C₄×D₄	—	106	1	no	—
294	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
295	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
296	#117	—	2	1	no	—
297	#117	C₄×D₅₃	1	1	yes	characteristic
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
300	#107	—	53	2	no	—
301	#106	—	53	2	no	—
302	C₄⋊C₈	—	53	1	no	—
303	C₄⋊C₈	—	53	1	no	—
304	C₄⋊C₈	—	53	1	no	—
305	C₄⋊C₈	—	53	1	no	—
306	C₄⋊C₈	—	53	2	no	—
307	C₄⋊C₈	—	106	2	no	—
308	C₄⋊C₈	—	106	1	no	—
309	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
310	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
311	#103	—	53	2	no	—
312	#102	—	53	2	no	—
313	#102	—	53	2	no	—
314	#102	—	53	2	no	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	53	2	no	—
317	C₂²⋊C₈	—	53	2	no	—
318	C₂²⋊C₈	—	106	2	no	—
319	C₂²⋊C₈	—	106	2	no	—
320	C₂²⋊C₈	—	106	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	53	2	no	—
324	C₄×C₈	—	53	2	no	—
325	C₄×C₈	—	106	2	no	—
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	—	4	1	no	—
330	#41	—	424	1	no	—
331	#41	—	424	1	no	—
332	C₂×Q₈	—	106	1	no	—
333	C₂×Q₈	C₂×C₄×D₅₃	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	53	2	no	—
336	C₂×D₄	—	106	2	no	—
337	C₂×D₄	—	106	1	no	—
338	C₂×D₄	—	106	1	no	—
339	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	106	2	no	—
344	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
346	C₂²×C₄	#11719947	1	1	yes	characteristic
347	SD₁₆	—	106	4	no	—
348	D₈	—	212	2	no	—
349	M₁₆	—	424	2	no	—
350	M₁₆	—	424	2	no	—
351	M₁₆	—	424	1	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	53	2	no	—
358	C₂×C₈	—	53	2	no	—
359	C₂×C₈	—	53	2	no	—
360	C₂×C₈	—	53	2	no	—
361	C₂×C₈	—	106	2	no	—
362	C₂×C₈	—	424	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	53	2	no	—
366	C₄⋊C₄	—	106	1	no	—
367	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
368	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	106	2	no	—
373	C₂²⋊C₄	—	106	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
378	C₄²	D₄×D₅₃	1	1	yes	characteristic
379	C₄²	#11719947	1	1	yes	characteristic
380	C₄²	C₂³×D₅₃	1	1	yes	characteristic
381	C₂³	—	2	1	no	—
382	C₂³	—	106	2	no	—
383	C₂³	#13133177	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	424	1	no	—
386	Q₈	#13133223	1	2	yes	—
387	D₄	—	2	1	no	—
388	D₄	—	2	1	no	—
389	D₄	—	4	2	no	—
390	D₄	—	106	2	no	—
391	D₄	—	106	2	no	—
392	D₄	—	424	1	no	—
393	D₄	—	424	2	no	—
394	D₄	—	212	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	106	2	no	—
408	C₂×C₄	—	212	2	no	—
409	C₂×C₄	—	212	2	no	—
410	C₂×C₄	#13133177	1	1	yes	characteristic
411	C₂×C₄	#13133177	1	1	yes	characteristic
412	C₂×C₄	#13133177	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
414	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
415	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	106	2	no	—
421	C₈	—	106	2	no	—
422	C₈	—	106	2	no	—
423	C₈	—	106	2	no	—
424	C₈	—	212	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	212	2	no	—
432	C₂²	—	212	2	no	—
433	C₂²	—	212	2	no	—
434	C₂²	C₂×#13133177	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	212	2	no	—
442	C₄	#16810737	1	2	yes	—
443	C₄	C₂×#13133223	1	1	yes	characteristic
444	C₄	#16811389	1	1	yes	characteristic
445	C₄	#16811425	1	1	yes	characteristic
446	C₄	#16811430	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	8	1	no	—
449	C₂	—	424	2	no	—
450	C₂	#20283436	1	1	yes	characteristic
451	C₂	#20283550	1	1	yes	characteristic
452	C₂	C₂×#16810737	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1476	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	#20284775	C₂
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#1476	D₅₃
hypocenter	C₅₃	#18018
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1476

Complements

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

N	H ≅ G/N	type
2. #20283847	C₂	semidirect
3. #20283781	C₂	semidirect
4. #20273597	C₂	semidirect
5. #20273590	C₂	semidirect
6. #20273582	C₂	semidirect
7. #20273512	C₂	semidirect
8. #20273503	C₂	semidirect
9. #20273167	C₂	semidirect
10. #20272998	C₂	semidirect
11. C₅₃×#1476	C₂	semidirect
230. #1476	D₅₃	semidirect
273. C₅₃	#18018	semidirect

Maximal subgroups

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

subgroup	index
#20284775	2
#20283847	2
#20283781	2
#20273597	2
#20273590	2
#20273582	2
#20273512	2
#20273503	2
#20273167	2
#20272998	2
C₅₃×#1476	2
#18018	53