Subgroups — #27382124

Order 13568.

1010 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#108×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#427×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#20283131	C₂	1	2	yes	maximal
4	C₂×#16810580	C₂	1	1	yes	maximal, characteristic
5	#20274602	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274601	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274599	C₂	1	1	yes	maximal, characteristic, complemented
8	#20274595	C₂	1	2	yes	maximal, complemented
9	#20274593	C₂	1	2	yes	maximal, complemented
10	#20274423	C₂	1	2	yes	maximal
11	C₅₃×#1773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11719912	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
14	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
15	C₂×#13133174	C₂²	1	1	yes	characteristic
16	#117×D₅₃	C₂²	1	2	yes	—
17	C₂×#13133153	C₂²	1	1	yes	characteristic
18	C₂×#13133152	C₂²	1	2	yes	—
19	#108×D₅₃	C₄	1	8	yes	complemented
20	#16810661	C₂²	1	1	yes	characteristic
21	#16810660	C₄	1	2	yes	complemented
22	#16810659	C₂²	1	2	yes	—
23	#16810658	C₄	1	2	yes	complemented
24	#107×D₅₃	C₄	1	2	yes	complemented
25	#106×D₅₃	C₄	1	2	yes	complemented
26	#16810581	C₂²	1	2	yes	—
27	#16810580	—	2	2	no	—
28	#16810580	C₄	1	8	yes	complemented
29	#16810579	C₂²	1	2	yes	—
30	#16810578	C₂²	1	2	yes	—
31	#16810577	—	2	2	no	—
32	#16810575	—	2	2	no	—
33	C₄×#11719912	—	2	2	no	—
34	C₂×#13133127	C₂²	1	1	yes	characteristic
35	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
37	#16810384	C₂²	1	2	yes	—
38	#16810383	C₂²	1	2	yes	—
39	#16810382	C₂²	1	2	yes	—
40	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#427	C₂²	1	1	yes	characteristic
42	C₅₃×#405	C₂²	1	2	yes	—
43	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
44	C₅₃×#339	C₂²	1	2	yes	—
45	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
46	C₂×#11719917	C₂³	1	2	yes	—
47	C₂×#11719912	—	2	2	no	—
48	C₂×#11719912	C₂×C₄	1	4	yes	—
49	C₂×#11719912	D₄	1	2	yes	—
50	C₂×#11719912	D₄	1	2	yes	—
51	C₂×#11719912	Q₈	1	4	yes	—
52	M₁₆×D₅₃	—	2	4	no	—
53	M₁₆×D₅₃	C₂×C₄	1	8	yes	—
54	C₂²×#88322	C₂³	1	1	yes	characteristic
55	C₂²×#88322	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₅₃	—	2	2	no	—
57	C₂×C₈×D₅₃	C₂×C₄	1	4	yes	—
58	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅₃	C₂×C₄	1	4	yes	—
63	#13133176	C₂³	1	2	yes	—
64	#13133175	C₂×C₄	1	4	yes	—
65	#13133174	—	2	2	no	—
66	#13133174	—	2	2	no	—
67	#13133174	C₂×C₄	1	4	yes	—
68	#13133173	—	2	2	no	—
69	C₂×#11719919	—	2	1	no	—
70	C₄⋊C₄×D₅₃	C₂×C₄	1	4	yes	—
71	C₂×#11719921	—	2	1	no	—
72	C₂²⋊C₄×D₅₃	—	2	2	no	—
73	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
74	C₄²×D₅₃	—	2	2	no	—
75	#13133153	C₂×C₄	1	4	yes	complemented
76	#13133152	C₂×C₄	1	8	yes	complemented
77	#13133151	C₂×C₄	1	2	yes	—
78	#13133150	C₂×C₄	1	4	yes	—
79	#13133149	C₂×C₄	1	2	yes	—
80	#13133148	C₂×C₄	1	4	yes	—
81	#13133128	—	2	2	no	—
82	#13133127	—	2	2	no	—
83	#13133127	—	2	2	no	—
84	#13133127	C₂×C₄	1	4	yes	complemented
85	C₄×#88322	—	2	2	no	—
86	C₄×#88322	C₂×C₄	1	4	yes	complemented
87	C₈×Dic₅₃	—	2	2	no	—
88	C₈×Dic₅₃	—	2	2	no	—
89	C₈×Dic₅₃	C₂×C₄	1	4	yes	complemented
90	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
91	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	#117×C₅₃	C₂³	1	2	yes	—
94	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
95	#108×C₅₃	C₂×C₄	1	4	yes	complemented
96	#107×C₅₃	C₂×C₄	1	2	yes	—
97	#106×C₅₃	C₂×C₄	1	2	yes	—
98	#97×C₅₃	—	2	2	no	—
99	#97×C₅₃	C₂×C₄	1	4	yes	complemented
100	C₄×C₈×C₅₃	—	2	2	no	—
101	C₂³×D₅₃	#41	1	1	yes	characteristic
102	C₂²×C₄×C₅₃	—	2	1	no	—
103	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
104	C₂²×Dic₅₃	—	2	1	no	—
105	C₂²×Dic₅₃	#41	1	1	yes	characteristic
106	C₂×C₄×D₅₃	—	2	4	no	—
107	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
108	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
109	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₄×D₅₃	C₂×Q₈	1	2	yes	—
114	C₂×C₄×D₅₃	#41	1	2	yes	—
115	M₁₆×C₅₃	—	2	2	no	—
116	M₁₆×C₅₃	C₂²×C₄	1	4	yes	—
117	C₂×C₈×C₅₃	—	2	2	no	—
118	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₅₃	C₂×Q₈	1	2	yes	—
125	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
126	C₂²⋊C₄×C₅₃	—	2	2	no	—
127	C₄²×C₅₃	—	2	2	no	—
128	C₄²×C₅₃	—	2	1	no	—
129	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
130	C₂²⋊Dic₅₃	—	2	2	no	—
131	#11719921	—	2	4	no	—
132	#11719921	—	2	4	no	—
133	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
134	#11719919	—	2	4	no	—
135	#11719919	—	2	4	no	—
136	C₄×Dic₅₃	—	2	2	no	—
137	C₄×Dic₅₃	—	2	1	no	—
138	C₄×Dic₅₃	—	2	4	no	—
139	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
140	#11719917	—	2	2	no	—
141	#11719917	C₂²×C₄	1	4	yes	—
142	C₂×#88322	—	2	2	no	—
143	C₂×#88322	C₂²×C₄	1	2	yes	—
144	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
145	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
146	C₂×#88322	C₂²×C₄	1	2	yes	—
147	C₂×#88322	C₂²×C₄	1	2	yes	—
148	C₂×#88322	C₂×D₄	1	2	yes	—
149	C₂×#88322	C₂×Q₈	1	2	yes	—
150	#11719912	—	2	8	no	—
151	#11719912	C₄⋊C₄	1	8	yes	—
152	#11719912	C₄⋊C₄	1	8	yes	—
153	C₈×D₅₃	—	2	8	no	—
154	C₈×D₅₃	C₄²	1	4	yes	—
155	C₈×D₅₃	C₄²	1	4	yes	—
156	C₈×D₅₃	C₄²	1	4	yes	—
157	C₈×D₅₃	C₄²	1	4	yes	—
158	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
159	C₂²×D₅₃	—	4	2	no	—
160	C₂²×D₅₃	#117	1	2	yes	—
161	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
162	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
163	C₂²×D₅₃	C₄×Q₈	1	2	yes	—
164	C₂×C₄×C₅₃	—	2	2	no	—
165	C₂×C₄×C₅₃	—	2	4	no	—
166	C₂×C₄×C₅₃	—	4	2	no	—
167	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
173	C₂×Dic₅₃	—	2	2	no	—
174	C₂×Dic₅₃	—	2	4	no	—
175	C₂×Dic₅₃	—	4	2	no	—
176	C₂×Dic₅₃	#117	1	2	yes	—
177	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
178	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
179	C₂×Dic₅₃	C₄×Q₈	1	2	yes	—
180	C₄×D₅₃	—	8	4	no	—
181	C₄×D₅₃	C₂×C₄²	1	2	yes	—
182	C₄×D₅₃	C₂×C₄²	1	2	yes	—
183	C₄×D₅₃	C₂×C₄⋊C₄	1	2	yes	—
184	C₄×D₅₃	C₂×C₄⋊C₄	1	2	yes	—
185	C₄×D₅₃	C₄×D₄	1	2	yes	—
186	C₄×D₅₃	C₄×D₄	1	2	yes	—
187	C₄×D₅₃	C₄×Q₈	1	2	yes	—
188	C₄×D₅₃	C₄×Q₈	1	2	yes	—
189	C₈×C₅₃	—	2	4	no	—
190	C₈×C₅₃	C₂×C₄²	1	2	yes	—
191	C₈×C₅₃	C₂×C₄²	1	2	yes	—
192	C₈×C₅₃	C₂×C₄⋊C₄	1	4	yes	—
193	#88322	—	2	4	no	—
194	#88322	C₂×C₄²	1	2	yes	—
195	#88322	C₂×C₄²	1	2	yes	—
196	#88322	C₂×C₄⋊C₄	1	4	yes	—
197	#20446	—	53	1	no	maximal, Sylow
198	C₂²×C₅₃	—	2	2	no	—
199	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
200	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂²×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
202	C₂×D₅₃	—	2	2	no	—
203	C₂×D₅₃	—	2	2	no	—
204	C₂×D₅₃	—	4	2	no	—
205	C₂×D₅₃	—	4	2	no	—
206	C₂×D₅₃	C₄×C₄⋊C₄	1	2	yes	—
207	C₂×D₅₃	C₄×C₄⋊C₄	1	2	yes	—
208	C₄×C₅₃	—	4	2	no	—
209	C₄×C₅₃	—	4	4	no	—
210	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
211	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
212	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₄×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
214	Dic₅₃	—	4	2	no	—
215	Dic₅₃	—	4	4	no	—
216	Dic₅₃	C₄×C₄⋊C₄	1	2	yes	—
217	Dic₅₃	C₄×C₄⋊C₄	1	2	yes	—
218	C₂²×#108	—	53	1	no	—
219	C₂×#427	—	53	1	no	—
220	#2873	—	53	2	no	—
221	C₂×#405	—	53	1	no	—
222	#1773	—	53	1	no	—
223	#1773	—	53	1	no	—
224	#1773	—	53	1	no	—
225	#1773	D₅₃	1	1	yes	characteristic, complemented
226	#1772	—	53	2	no	—
227	#1772	—	53	2	no	—
228	#1733	—	53	2	no	—
229	C₂×C₅₃	—	2	1	no	—
230	C₂×C₅₃	—	2	1	no	—
231	C₂×C₅₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
232	C₂×C₅₃	#2957	1	2	yes	—
233	D₅₃	—	2	2	no	—
234	D₅₃	—	2	2	no	—
235	C₂²×M₁₆	—	53	1	no	—
236	C₂²×M₁₆	—	53	2	no	—
237	C₂³×C₈	—	53	1	no	—
238	C₂×#117	—	53	1	no	—
239	C₂×#117	—	53	2	no	—
240	C₂×#108	—	53	2	no	—
241	C₂×#108	—	53	1	no	—
242	C₂×#108	—	53	8	no	—
243	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
244	#427	—	53	1	no	—
245	#427	—	53	2	no	—
246	#427	—	53	2	no	—
247	#427	—	53	2	no	—
248	#427	C₂×D₅₃	1	1	yes	characteristic
249	C₂×#107	—	53	2	no	—
250	C₂×#106	—	53	2	no	—
251	#405	—	53	8	no	—
252	#405	—	53	2	no	—
253	#405	—	53	2	no	—
254	#405	—	53	2	no	—
255	#405	—	106	2	no	—
256	#405	—	106	2	no	—
257	#405	C₂×D₅₃	1	2	yes	—
258	C₄×M₁₆	—	106	2	no	—
259	C₄×M₁₆	—	106	2	no	—
260	C₂×#97	—	53	1	no	—
261	C₂×#97	C₂×D₅₃	1	1	yes	characteristic
262	C₂×C₄×C₈	—	53	1	no	—
263	C₂×C₄×C₈	—	53	1	no	—
264	#339	—	53	2	no	—
265	#339	—	53	2	no	—
266	#339	—	53	2	no	—
267	#339	C₂×D₅₃	1	2	yes	—
268	C₅₃	#20446	1	1	yes	characteristic, complemented, Sylow
269	C₂³×C₄	—	53	1	no	—
270	C₂×M₁₆	—	53	4	no	—
271	C₂×M₁₆	—	53	2	no	—
272	C₂×M₁₆	—	53	2	no	—
273	C₂×M₁₆	—	53	4	no	—
274	C₂×M₁₆	—	53	2	no	—
275	C₂×M₁₆	—	53	8	no	—
276	C₂×M₁₆	—	106	2	no	—
277	C₂×M₁₆	—	106	4	no	—
278	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
279	C₂²×C₈	—	53	1	no	—
280	C₂²×C₈	—	53	1	no	—
281	C₂²×C₈	—	53	4	no	—
282	C₂²×C₈	—	53	1	no	—
283	C₂²×C₈	—	53	1	no	—
284	C₂²×C₈	—	53	1	no	—
285	C₂²×C₈	—	53	1	no	—
286	C₂²×C₈	—	53	4	no	—
287	C₂²×C₈	—	106	2	no	—
288	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
290	#117	—	53	4	no	—
291	#117	—	53	2	no	—
292	#117	—	53	4	no	—
293	#117	—	106	2	no	—
294	#117	—	106	2	no	—
295	#117	—	106	2	no	—
296	#117	C₂²×D₅₃	1	2	yes	—
297	C₂×C₄⋊C₄	—	53	4	no	—
298	C₂×C₄⋊C₄	—	106	1	no	—
299	C₂×C₂²⋊C₄	—	106	2	no	—
300	C₂×C₂²⋊C₄	—	106	1	no	—
301	C₂×C₄²	—	53	1	no	—
302	C₂×C₄²	—	106	2	no	—
303	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
304	#108	—	53	8	no	—
305	#108	—	53	4	no	—
306	#108	C₄×D₅₃	1	4	yes	complemented
307	#107	—	53	2	no	—
308	#107	—	53	4	no	—
309	#107	C₄×D₅₃	1	2	yes	—
310	#106	—	53	2	no	—
311	#106	—	53	4	no	—
312	#106	C₄×D₅₃	1	2	yes	—
313	#97	—	2	2	no	—
314	#97	—	53	4	no	—
315	#97	—	106	2	no	—
316	#97	—	106	2	no	—
317	#97	—	106	2	no	—
318	#97	C₄×D₅₃	1	4	yes	complemented
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	53	4	no	—
321	C₄×C₈	—	53	4	no	—
322	C₄×C₈	—	106	2	no	—
323	C₄×C₈	—	106	2	no	—
324	C₄×C₈	—	106	2	no	—
325	C₂⁴	—	53	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	53	1	no	—
328	C₂²×C₄	—	53	1	no	—
329	C₂²×C₄	—	53	1	no	—
330	C₂²×C₄	—	53	2	no	—
331	C₂²×C₄	—	53	2	no	—
332	C₂²×C₄	—	53	1	no	—
333	C₂²×C₄	—	53	1	no	—
334	C₂²×C₄	—	53	2	no	—
335	C₂²×C₄	—	53	2	no	—
336	C₂²×C₄	—	106	4	no	—
337	C₂²×C₄	—	106	1	no	—
338	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
339	M₁₆	—	2	2	no	—
340	M₁₆	—	53	8	no	—
341	M₁₆	—	53	8	no	—
342	M₁₆	—	53	4	no	—
343	M₁₆	—	106	8	no	—
344	M₁₆	—	106	2	no	—
345	M₁₆	C₂×C₄×D₅₃	1	4	yes	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	53	2	no	—
348	C₂×C₈	—	53	2	no	—
349	C₂×C₈	—	53	1	no	—
350	C₂×C₈	—	53	1	no	—
351	C₂×C₈	—	53	2	no	—
352	C₂×C₈	—	53	2	no	—
353	C₂×C₈	—	53	2	no	—
354	C₂×C₈	—	53	4	no	—
355	C₂×C₈	—	53	4	no	—
356	C₂×C₈	—	53	4	no	—
357	C₂×C₈	—	53	4	no	—
358	C₂×C₈	—	106	8	no	—
359	C₂×C₈	—	106	2	no	—
360	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
361	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
362	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
363	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
364	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
365	C₂×C₈	D₄×D₅₃	1	2	yes	—
366	C₂×C₈	Q₈×D₅₃	1	2	yes	—
367	C₄⋊C₄	—	53	4	no	—
368	C₄⋊C₄	—	106	4	no	—
369	C₄⋊C₄	—	106	4	no	—
370	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	106	4	no	—
373	C₂²⋊C₄	—	106	4	no	—
374	C₂²⋊C₄	—	106	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	53	2	no	—
378	C₄²	—	106	4	no	—
379	C₄²	—	106	2	no	—
380	C₄²	—	106	1	no	—
381	C₄²	C₂×C₄×D₅₃	1	2	yes	—
382	C₂³	—	53	1	no	—
383	C₂³	—	53	1	no	—
384	C₂³	—	53	2	no	—
385	C₂³	—	53	2	no	—
386	C₂³	—	212	2	no	—
387	C₂³	#41×D₅₃	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	53	2	no	—
392	C₂×C₄	—	53	1	no	—
393	C₂×C₄	—	53	1	no	—
394	C₂×C₄	—	53	2	no	—
395	C₂×C₄	—	53	2	no	—
396	C₂×C₄	—	53	2	no	—
397	C₂×C₄	—	53	2	no	—
398	C₂×C₄	—	53	2	no	—
399	C₂×C₄	—	53	2	no	—
400	C₂×C₄	—	53	2	no	—
401	C₂×C₄	—	53	2	no	—
402	C₂×C₄	—	53	2	no	—
403	C₂×C₄	—	106	2	no	—
404	C₂×C₄	—	106	4	no	—
405	C₂×C₄	—	424	4	no	—
406	C₂×C₄	—	212	2	no	—
407	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
408	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
410	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
411	C₂×C₄	C₂×Q₈×D₅₃	1	1	yes	characteristic
412	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
413	C₈	—	2	4	no	—
414	C₈	—	53	2	no	—
415	C₈	—	53	2	no	—
416	C₈	—	53	4	no	—
417	C₈	—	106	4	no	—
418	C₈	C₄²×D₅₃	1	2	yes	—
419	C₈	C₄²×D₅₃	1	2	yes	—
420	C₈	C₄⋊C₄×D₅₃	1	4	yes	—
421	C₂²	—	2	2	no	—
422	C₂²	—	53	2	no	—
423	C₂²	—	53	2	no	—
424	C₂²	—	106	2	no	—
425	C₂²	—	106	2	no	—
426	C₂²	—	212	2	no	—
427	C₂²	—	212	2	no	—
428	C₂²	#117×D₅₃	1	1	yes	characteristic
429	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
430	C₂²	C₄×Q₈×D₅₃	1	1	yes	characteristic
431	C₄	—	4	2	no	—
432	C₄	—	4	4	no	—
433	C₄	—	53	2	no	—
434	C₄	—	53	2	no	—
435	C₄	—	212	2	no	—
436	C₄	—	212	4	no	—
437	C₄	C₂×C₄²×D₅₃	1	1	yes	characteristic
438	C₄	C₂×C₄⋊C₄×D₅₃	1	1	yes	characteristic
439	C₄	C₄×D₄×D₅₃	1	1	yes	characteristic
440	C₄	C₄×Q₈×D₅₃	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	106	2	no	—
444	C₂	—	106	2	no	—
445	C₂	C₄×C₄⋊C₄×D₅₃	1	1	yes	characteristic
446	C₂	#20283629	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1773	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂³×D₅₃	#41
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1773	D₅₃
hypocenter	C₅₃	#20446
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1773

Complements

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

N	H ≅ G/N	type
5. #20274602	C₂	semidirect
6. #20274601	C₂	semidirect
7. #20274599	C₂	semidirect
8. #20274595	C₂	semidirect
9. #20274593	C₂	semidirect
11. C₅₃×#1773	C₂	semidirect
19. #108×D₅₃	C₄	semidirect
21. #16810660	C₄	semidirect
23. #16810658	C₄	semidirect
24. #107×D₅₃	C₄	semidirect
25. #106×D₅₃	C₄	semidirect
28. #16810580	C₄	semidirect
75. #13133153	C₂×C₄	semidirect
76. #13133152	C₂×C₄	semidirect
84. #13133127	C₂×C₄	semidirect
86. C₄×#88322	C₂×C₄	semidirect
89. C₈×Dic₅₃	C₂×C₄	semidirect
95. #108×C₅₃	C₂×C₄	semidirect
99. #97×C₅₃	C₂×C₄	semidirect
225. #1773	D₅₃	semidirect
268. C₅₃	#20446	semidirect
306. #108	C₄×D₅₃	semidirect
318. #97	C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#108×D₅₃	2
#427×D₅₃	2
#20283131	2
C₂×#16810580	2
#20274602	2
#20274601	2
#20274599	2
#20274595	2
#20274593	2
#20274423	2
C₅₃×#1773	2
#20446	53