Subgroups — #27366431

Order 13568.

714 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20285142	C₂	1	1	yes	maximal, characteristic
2	#20284745	C₂	1	2	yes	maximal, complemented
3	C₈×Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#20274086	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274085	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274072	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274062	C₂	1	2	yes	maximal, complemented
8	#20274061	C₂	1	2	yes	maximal, complemented
9	#20273462	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273361	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1668	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133236	—	2	1	no	—
13	C₂×#13133236	—	2	1	no	—
14	#16811171	C₂²	1	2	yes	—
15	C₄×Q₈×D₅₃	C₂²	1	1	yes	characteristic
16	#16811006	—	2	1	no	—
17	#16811006	—	2	1	no	—
18	#16811003	C₂²	1	1	yes	characteristic
19	#16810995	C₂²	1	2	yes	—
20	#16810940	—	2	2	no	—
21	#16810909	C₂²	1	2	yes	—
22	#16810908	C₂²	1	2	yes	—
23	#16810820	C₂²	1	2	yes	—
24	#16810760	—	2	2	no	—
25	Q₈×#88322	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₀₆	—	2	1	no	—
27	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
28	#16810747	—	2	1	no	—
29	#16810747	C₂²	1	1	yes	characteristic
30	#16810714	—	2	2	no	—
31	SD₁₆×Dic₅₃	—	2	2	no	—
32	#16810675	C₂²	1	2	yes	—
33	C₄⋊C₈×D₅₃	—	2	1	no	—
34	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₅₃	—	2	1	no	—
36	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
37	#16810376	C₂²	1	1	yes	characteristic
38	#16810373	C₂²	1	2	yes	—
39	#16810370	C₂²	1	2	yes	—
40	#16810368	C₂²	1	2	yes	—
41	#16810367	C₂²	1	2	yes	—
42	C₅₃×#493	C₂²	1	1	yes	characteristic
43	C₅₃×#460	C₂²	1	2	yes	—
44	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#335	C₂²	1	1	yes	characteristic
46	C₅₃×#331	C₂²	1	2	yes	—
47	C₂×#11719947	—	2	2	no	—
48	C₂×Q₈×D₅₃	D₄	1	1	yes	characteristic
49	#13133236	—	4	4	no	—
50	#13133236	—	4	4	no	—
51	C₂×Dic₂₁₂	—	2	1	no	—
52	C₂×Dic₂₁₂	—	2	1	no	—
53	C₂×#11719923	—	2	2	no	—
54	C₂×#11719923	—	2	2	no	—
55	C₂×#11719923	—	2	2	no	—
56	C₂×C₈×D₅₃	—	2	1	no	—
57	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
58	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
59	#13133217	C₂³	1	2	yes	—
60	#13133204	—	2	2	no	—
61	#13133188	—	2	2	no	—
62	#13133188	—	2	2	no	—
63	Q₈×Dic₅₃	D₄	1	1	yes	characteristic
64	C₄×Dic₁₀₆	—	2	1	no	—
65	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
66	#13133182	—	2	1	no	—
67	#13133182	D₄	1	1	yes	characteristic
68	D₄×Dic₅₃	—	2	2	no	—
69	D₄×Dic₅₃	—	2	2	no	—
70	C₄⋊C₄×D₅₃	—	2	1	no	—
71	C₄⋊C₄×D₅₃	D₄	1	1	yes	characteristic
72	C₄²×D₅₃	—	2	1	no	—
73	C₄²×D₅₃	C₂³	1	1	yes	characteristic
74	#13133149	—	2	2	no	—
75	#13133148	—	2	2	no	—
76	C₄⋊#88322	—	2	1	no	—
77	C₄⋊#88322	C₂³	1	2	yes	—
78	C₄⋊#88322	C₂³	1	1	yes	characteristic
79	#13133146	—	2	1	no	—
80	#13133146	—	2	1	no	—
81	#13133146	—	2	1	no	—
82	#13133142	—	2	2	no	—
83	#13133141	—	2	2	no	—
84	#13133138	—	2	2	no	—
85	#13133129	—	2	2	no	—
86	C₄×#88322	—	2	1	no	—
87	C₄×#88322	C₂³	1	1	yes	characteristic
88	C₈×Dic₅₃	—	2	1	no	—
89	C₈×Dic₅₃	—	2	2	no	—
90	C₈×Dic₅₃	—	2	1	no	—
91	C₈×Dic₅₃	D₄	1	1	yes	characteristic
92	C₈×Dic₅₃	D₄	1	1	yes	characteristic
93	C₂×SD₁₆×C₅₃	—	2	2	no	—
94	C₂×D₈×C₅₃	—	2	1	no	—
95	C₂×D₈×C₅₃	—	2	1	no	—
96	#127×C₅₃	C₂³	1	2	yes	—
97	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₅₃	—	2	1	no	—
99	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
101	#102×C₅₃	—	2	2	no	—
102	C₄×C₈×C₅₃	—	2	1	no	—
103	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₅₃	—	2	2	no	—
106	C₂×D₄×C₅₃	—	2	2	no	—
107	C₂×D₄×C₅₃	—	2	2	no	—
108	C₂×C₂²⋊D₅₃	—	4	2	no	—
109	C₂²×Dic₅₃	—	4	2	no	—
110	Q₈×D₅₃	—	2	2	no	—
111	Q₈×D₅₃	—	2	2	no	—
112	#11719947	—	4	4	no	—
113	#11719947	—	4	4	no	—
114	C₂×C₄×D₅₃	—	2	1	no	—
115	C₂×C₄×D₅₃	—	2	1	no	—
116	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
119	C₂×Dic₁₀₆	—	2	1	no	—
120	C₂×Dic₁₀₆	—	2	2	no	—
121	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
122	SD₁₆×C₅₃	—	4	4	no	—
123	D₈×C₅₃	—	4	2	no	—
124	D₈×C₅₃	—	4	2	no	—
125	C₂×C₈×C₅₃	—	2	1	no	—
126	C₂×C₈×C₅₃	—	2	2	no	—
127	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
129	C₄⋊C₄×C₅₃	—	2	1	no	—
130	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₅₃	—	2	1	no	—
132	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
133	C₂²⋊Dic₅₃	—	4	2	no	—
134	C₂²⋊Dic₅₃	—	4	2	no	—
135	#11719923	—	4	4	no	—
136	#11719923	—	4	4	no	—
137	#11719923	—	4	4	no	—
138	C₄⋊Dic₅₃	—	2	1	no	—
139	C₄⋊Dic₅₃	—	2	2	no	—
140	C₄⋊Dic₅₃	—	2	2	no	—
141	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
142	#11719919	—	2	1	no	—
143	#11719919	—	2	1	no	—
144	#11719919	—	2	1	no	—
145	C₄×Dic₅₃	—	2	1	no	—
146	C₄×Dic₅₃	—	2	1	no	—
147	C₄×Dic₅₃	—	2	1	no	—
148	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₅₃	#41	1	1	yes	characteristic
151	C₂×#88322	—	2	1	no	—
152	C₂×#88322	—	2	2	no	—
153	C₂×#88322	C₂×D₄	1	1	yes	characteristic
154	C₂×#88322	C₂×D₄	1	1	yes	characteristic
155	Dic₂₁₂	—	4	2	no	—
156	Dic₂₁₂	—	4	2	no	—
157	C₈×D₅₃	—	2	2	no	—
158	C₈×D₅₃	—	4	2	no	—
159	C₈×D₅₃	SD₁₆	1	4	yes	complemented
160	C₂³×C₅₃	—	4	2	no	—
161	C₂²×D₅₃	#121	1	1	yes	characteristic
162	Q₈×C₅₃	—	2	1	no	—
163	Q₈×C₅₃	#135	1	2	yes	complemented
164	D₄×C₅₃	—	4	2	no	—
165	D₄×C₅₃	—	4	2	no	—
166	D₄×C₅₃	—	4	2	no	—
167	D₄×C₅₃	—	4	2	no	—
168	D₄×C₅₃	—	8	2	no	—
169	C₂×C₄×C₅₃	—	2	1	no	—
170	C₂×C₄×C₅₃	—	2	1	no	—
171	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
174	C₂²⋊D₅₃	—	8	4	no	—
175	C₂×Dic₅₃	—	2	1	no	—
176	C₂×Dic₅₃	—	2	1	no	—
177	C₂×Dic₅₃	—	4	2	no	—
178	C₂×Dic₅₃	—	8	4	no	—
179	C₂×Dic₅₃	#121	1	1	yes	characteristic
180	C₂×Dic₅₃	#121	1	1	yes	characteristic
181	C₂×Dic₅₃	#121	1	1	yes	characteristic
182	C₄×D₅₃	—	2	4	no	—
183	C₄×D₅₃	—	2	1	no	—
184	C₄×D₅₃	—	2	1	no	—
185	C₄×D₅₃	—	4	1	no	—
186	C₄×D₅₃	—	4	2	no	—
187	C₄×D₅₃	C₂×SD₁₆	1	2	yes	—
188	C₄×D₅₃	AGL(1,ℤ/8)	1	2	yes	—
189	Dic₁₀₆	—	2	4	no	—
190	Dic₁₀₆	—	2	1	no	—
191	Dic₁₀₆	—	4	2	no	—
192	Dic₁₀₆	—	4	2	no	—
193	Dic₁₀₆	#135	1	2	yes	complemented
194	C₈×C₅₃	—	2	1	no	—
195	C₈×C₅₃	—	4	2	no	—
196	C₈×C₅₃	—	4	1	no	—
197	C₈×C₅₃	C₂×SD₁₆	1	2	yes	—
198	#88322	—	2	1	no	—
199	#88322	—	4	2	no	—
200	#88322	—	4	1	no	—
201	#88322	C₂×SD₁₆	1	2	yes	—
202	#19114	—	53	1	no	maximal, Sylow
203	C₂²×C₅₃	—	8	2	no	—
204	C₂²×C₅₃	—	8	2	no	—
205	C₂²×C₅₃	—	8	2	no	—
206	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
207	C₂×D₅₃	—	2	1	no	—
208	C₂×D₅₃	—	2	1	no	—
209	C₂×D₅₃	#460	1	2	yes	—
210	C₄×C₅₃	—	2	2	no	—
211	C₄×C₅₃	—	2	1	no	—
212	C₄×C₅₃	—	4	1	no	—
213	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
214	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
215	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
216	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	Dic₅₃	—	2	1	no	—
218	Dic₅₃	—	2	2	no	—
219	Dic₅₃	—	2	1	no	—
220	Dic₅₃	—	4	1	no	—
221	Dic₅₃	—	8	2	no	—
222	Dic₅₃	#460	1	2	yes	—
223	#3147	—	53	1	no	—
224	#3103	—	53	2	no	—
225	C₂×C₈×Q₈	—	53	1	no	—
226	#1670	—	53	1	no	—
227	#1670	—	53	1	no	—
228	#1668	—	53	1	no	—
229	#1668	D₅₃	1	1	yes	characteristic, complemented
230	#1666	—	53	2	no	—
231	#1666	—	53	2	no	—
232	#1564	—	53	1	no	—
233	#1540	—	53	2	no	—
234	C₂×C₅₃	—	16	2	no	—
235	C₂×C₅₃	C₂×#460	1	1	yes	characteristic
236	C₂×C₅₃	#3050	1	1	yes	characteristic
237	C₂×C₅₃	#3067	1	1	yes	characteristic
238	D₅₃	—	2	2	no	—
239	C₂×#135	—	106	1	no	—
240	C₂×#135	—	106	1	no	—
241	#532	—	53	2	no	—
242	C₂×C₄×Q₈	—	53	1	no	—
243	#495	—	106	1	no	—
244	#495	—	106	1	no	—
245	#494	—	53	1	no	—
246	#493	C₂×D₅₃	1	1	yes	characteristic
247	#492	—	53	2	no	—
248	#481	—	106	2	no	—
249	#475	—	53	2	no	—
250	#475	—	53	2	no	—
251	#460	—	53	2	no	—
252	#460	C₂×D₅₃	1	2	yes	—
253	#448	—	106	2	no	—
254	C₈×Q₈	—	53	1	no	—
255	C₈×Q₈	—	53	1	no	—
256	C₈×Q₈	—	53	1	no	—
257	C₈×Q₈	—	106	1	no	—
258	C₈×Q₈	—	106	1	no	—
259	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic
260	C₄×SD₁₆	—	106	2	no	—
261	C₄×SD₁₆	—	106	2	no	—
262	#431	—	53	2	no	—
263	C₂×C₄⋊C₈	—	53	1	no	—
264	C₂×C₄⋊C₈	—	106	1	no	—
265	C₂×C₄×C₈	—	53	1	no	—
266	C₂×C₄×C₈	—	106	1	no	—
267	#335	—	53	1	no	—
268	#335	C₂×D₅₃	1	1	yes	characteristic
269	#334	—	53	2	no	—
270	#332	—	53	2	no	—
271	#332	—	53	2	no	—
272	#331	—	53	2	no	—
273	#331	C₂×D₅₃	1	2	yes	—
274	C₅₃	#19114	1	1	yes	characteristic, complemented, Sylow
275	C₂×#41	—	106	2	no	—
276	C₂²×Q₈	—	53	1	no	—
277	#135	—	212	4	no	—
278	#135	—	212	4	no	—
279	C₂×Q₁₆	—	106	1	no	—
280	C₂×Q₁₆	—	106	1	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×SD₁₆	—	106	2	no	—
283	C₂×SD₁₆	—	106	2	no	—
284	C₂×SD₁₆	—	106	2	no	—
285	C₂×D₈	—	2	1	no	—
286	C₂×D₈	—	2	1	no	—
287	C₂²×C₈	—	53	1	no	—
288	C₂²×C₈	—	53	1	no	—
289	C₂²×C₈	—	106	1	no	—
290	C₄⋊Q₈	—	53	2	no	—
291	#127	C₂²×D₅₃	1	2	yes	—
292	#124	—	106	2	no	—
293	#121	—	106	2	no	—
294	#121	—	106	2	no	—
295	C₄×Q₈	—	53	1	no	—
296	C₄×Q₈	—	53	1	no	—
297	C₄×Q₈	—	53	1	no	—
298	C₄×Q₈	—	106	1	no	—
299	C₄×Q₈	—	106	1	no	—
300	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
301	C₄×D₄	—	106	2	no	—
302	C₄×D₄	—	106	2	no	—
303	C₂×C₄⋊C₄	—	53	1	no	—
304	C₂×C₄⋊C₄	—	106	1	no	—
305	C₂×C₄²	—	53	1	no	—
306	C₂×C₄²	—	106	1	no	—
307	#106	—	106	2	no	—
308	#106	—	106	2	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	53	1	no	—
311	C₄⋊C₈	—	53	2	no	—
312	C₄⋊C₈	—	106	1	no	—
313	C₄⋊C₈	—	106	1	no	—
314	C₄⋊C₈	—	106	1	no	—
315	C₄⋊C₈	—	106	1	no	—
316	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
317	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
318	#103	—	106	2	no	—
319	#103	—	106	2	no	—
320	#102	—	2	2	no	—
321	#102	—	106	2	no	—
322	C₂²⋊C₈	—	106	2	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	—	53	1	no	—
325	C₄×C₈	—	53	1	no	—
326	C₄×C₈	—	53	1	no	—
327	C₄×C₈	—	106	1	no	—
328	C₄×C₈	—	106	2	no	—
329	C₄×C₈	—	106	1	no	—
330	C₄×C₈	—	106	1	no	—
331	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
332	#41	—	212	4	no	—
333	#41	—	212	4	no	—
334	C₂×Q₈	—	53	1	no	—
335	C₂×Q₈	—	106	1	no	—
336	C₂×Q₈	—	106	2	no	—
337	C₂×Q₈	—	106	2	no	—
338	C₂×Q₈	—	106	2	no	—
339	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	212	2	no	—
344	C₂²×C₄	—	53	1	no	—
345	C₂²×C₄	—	53	1	no	—
346	C₂²×C₄	—	53	1	no	—
347	C₂²×C₄	—	106	1	no	—
348	C₂²×C₄	—	106	1	no	—
349	C₂²×C₄	—	212	2	no	—
350	Q₁₆	—	212	2	no	—
351	Q₁₆	—	212	2	no	—
352	SD₁₆	—	4	4	no	—
353	SD₁₆	—	212	4	no	—
354	SD₁₆	—	212	4	no	—
355	SD₁₆	—	212	4	no	—
356	D₈	—	4	2	no	—
357	D₈	—	4	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	53	1	no	—
361	C₂×C₈	—	53	4	no	—
362	C₂×C₈	—	53	1	no	—
363	C₂×C₈	—	106	2	no	—
364	C₂×C₈	—	106	1	no	—
365	C₂×C₈	—	106	2	no	—
366	C₂×C₈	—	212	2	no	—
367	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
368	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	53	1	no	—
371	C₄⋊C₄	—	106	1	no	—
372	C₄⋊C₄	—	106	1	no	—
373	C₄⋊C₄	—	106	1	no	—
374	C₄⋊C₄	—	106	1	no	—
375	C₄⋊C₄	—	106	2	no	—
376	C₄⋊C₄	—	106	2	no	—
377	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
378	C₂²⋊C₄	—	212	2	no	—
379	C₂²⋊C₄	—	212	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	53	1	no	—
382	C₄²	—	53	1	no	—
383	C₄²	—	53	1	no	—
384	C₄²	—	106	1	no	—
385	C₄²	—	106	1	no	—
386	C₄²	—	106	1	no	—
387	C₄²	C₂³×D₅₃	1	1	yes	characteristic
388	C₂³	—	4	2	no	—
389	C₂³	—	53	1	no	—
390	Q₈	—	2	1	no	—
391	Q₈	—	53	2	no	—
392	Q₈	—	106	4	no	—
393	Q₈	—	106	1	no	—
394	Q₈	—	212	2	no	—
395	Q₈	—	212	2	no	—
396	Q₈	#13133236	1	2	yes	complemented
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	8	2	no	—
402	D₄	—	424	4	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	53	1	no	—
406	C₂×C₄	—	53	2	no	—
407	C₂×C₄	—	53	2	no	—
408	C₂×C₄	—	53	1	no	—
409	C₂×C₄	—	53	1	no	—
410	C₂×C₄	—	106	4	no	—
411	C₂×C₄	—	106	1	no	—
412	C₂×C₄	—	106	1	no	—
413	C₂×C₄	—	106	1	no	—
414	C₂×C₄	—	106	1	no	—
415	C₂×C₄	—	424	4	no	—
416	C₂×C₄	—	212	1	no	—
417	C₂×C₄	—	212	2	no	—
418	C₂×C₄	—	212	2	no	—
419	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
420	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
421	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
422	C₈	—	2	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	1	no	—
425	C₈	—	53	2	no	—
426	C₈	—	106	1	no	—
427	C₈	—	212	2	no	—
428	C₈	—	212	1	no	—
429	C₈	SD₁₆×D₅₃	1	2	yes	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	53	2	no	—
434	C₂²	—	106	1	no	—
435	C₂²	—	106	1	no	—
436	C₂²	#121×D₅₃	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	53	2	no	—
441	C₄	—	106	1	no	—
442	C₄	—	106	1	no	—
443	C₄	—	106	2	no	—
444	C₄	—	424	2	no	—
445	C₄	—	212	1	no	—
446	C₄	C₂×SD₁₆×D₅₃	1	1	yes	characteristic
447	C₄	#135×D₅₃	1	1	yes	characteristic
448	C₄	C₂×#13133236	1	1	yes	characteristic
449	C₄	AGL(1,ℤ/8)×D₅₃	1	1	yes	characteristic
450	C₂	—	16	2	no	—
451	C₂	—	106	2	no	—
452	C₂	#460×D₅₃	1	1	yes	characteristic
453	C₂	#20284294	1	1	yes	characteristic
454	C₂	#20284433	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₅₃
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1668	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	#20285142	C₂
hypercenter	#1668	D₅₃
hypocenter	C₅₃	#19114
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1668

Complements

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

N	H ≅ G/N	type
2. #20284745	C₂	semidirect
3. C₈×Q₈×D₅₃	C₂	semidirect
4. #20274086	C₂	semidirect
5. #20274085	C₂	semidirect
6. #20274072	C₂	semidirect
7. #20274062	C₂	semidirect
8. #20274061	C₂	semidirect
9. #20273462	C₂	semidirect
10. #20273361	C₂	semidirect
11. C₅₃×#1668	C₂	semidirect
159. C₈×D₅₃	SD₁₆	semidirect
163. Q₈×C₅₃	#135	semidirect
193. Dic₁₀₆	#135	semidirect
229. #1668	D₅₃	semidirect
274. C₅₃	#19114	semidirect
396. Q₈	#13133236	semidirect

Maximal subgroups

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

subgroup	index
#20285142	2
#20284745	2
C₈×Q₈×D₅₃	2
#20274086	2
#20274085	2
#20274072	2
#20274062	2
#20274061	2
#20273462	2
#20273361	2
C₅₃×#1668	2
#19114	53