Subgroups — #27274334

Order 13568.

544 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283347	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810679	C₂	1	1	yes	maximal, characteristic
3	#431×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20272612	C₂	1	1	yes	maximal, characteristic, complemented
5	#20272611	C₂	1	1	yes	maximal, characteristic, complemented
6	#20272610	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1301	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
9	#16810679	—	2	1	no	—
10	#16810679	—	2	1	no	—
11	#16810679	—	2	1	no	—
12	#16810679	C₄	1	2	yes	—
13	#16810679	C₄	1	2	yes	—
14	#16810679	C₄	1	2	yes	—
15	#16810676	C₂²	1	1	yes	characteristic
16	#16810675	—	2	1	no	—
17	#16810675	—	2	1	no	—
18	#16810675	C₄	1	2	yes	—
19	#16810674	—	2	1	no	—
20	#16810673	C₄	1	2	yes	—
21	#16810647	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
23	C₄⋊C₈×D₅₃	—	2	1	no	—
24	#16810586	—	2	1	no	—
25	C₂×#13133129	—	2	1	no	—
26	C₂²⋊C₈×D₅₃	C₄	1	2	yes	—
27	M₁₆×Dic₅₃	—	2	1	no	—
28	C₂×#13133127	—	2	1	no	—
29	C₄×C₈×D₅₃	—	2	1	no	—
30	C₅₃×#431	C₂²	1	1	yes	characteristic
31	C₅₃×#423	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₅₃	Q₈	1	1	yes	characteristic
36	C₂×#11719917	—	2	1	no	—
37	C₂²×#88322	—	2	1	no	—
38	C₂×C₈×D₅₃	—	2	2	no	—
39	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
41	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
42	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
43	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
44	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
45	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
46	C₄²×D₅₃	D₄	1	1	yes	characteristic
47	C₄²×D₅₃	D₄	1	1	yes	characteristic
48	C₄²×D₅₃	D₄	1	1	yes	characteristic
49	C₄²×D₅₃	D₄	1	1	yes	characteristic
50	C₄⋊#88322	—	2	1	no	—
51	C₄⋊#88322	—	2	1	no	—
52	C₄⋊#88322	—	2	1	no	—
53	C₄⋊#88322	C₂×C₄	1	2	yes	—
54	C₄⋊#88322	C₂×C₄	1	2	yes	—
55	#13133146	—	2	2	no	—
56	C₂²⋊#88322	C₂×C₄	1	2	yes	—
57	#13133129	—	2	2	no	—
58	#13133129	—	2	2	no	—
59	#13133129	—	2	2	no	—
60	#13133129	—	2	2	no	—
61	#13133129	—	2	2	no	—
62	#13133127	—	2	2	no	—
63	#13133127	—	2	2	no	—
64	#13133127	—	2	2	no	—
65	C₄×#88322	—	2	1	no	—
66	C₈×Dic₅₃	—	2	2	no	—
67	C₈×Dic₅₃	—	2	2	no	—
68	C₂×M₁₆×C₅₃	—	2	1	no	—
69	C₂²×C₈×C₅₃	—	2	1	no	—
70	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₅₃	—	2	1	no	—
72	C₄⋊C₈×C₅₃	—	2	1	no	—
73	C₄⋊C₈×C₅₃	—	2	1	no	—
74	C₄⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
75	C₄⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
76	C₂²⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
77	C₄×C₈×C₅₃	—	2	1	no	—
78	C₂³×D₅₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
82	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₅₃	—	2	1	no	—
86	C₂×C₄×D₅₃	—	2	1	no	—
87	C₂×C₄×D₅₃	—	2	1	no	—
88	C₂×C₄×D₅₃	—	2	1	no	—
89	C₂×C₄×D₅₃	—	4	2	no	—
90	C₂×C₄×D₅₃	—	4	2	no	—
91	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
92	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
103	M₁₆×C₅₃	—	4	1	no	—
104	M₁₆×C₅₃	—	4	1	no	—
105	C₂×C₈×C₅₃	—	2	2	no	—
106	C₂×C₈×C₅₃	—	2	2	no	—
107	C₂×C₈×C₅₃	—	2	2	no	—
108	C₂×C₈×C₅₃	—	4	1	no	—
109	C₂×C₈×C₅₃	—	4	1	no	—
110	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
114	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
115	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
116	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
126	#11719917	—	4	1	no	—
127	#11719917	—	4	1	no	—
128	C₂×#88322	—	2	2	no	—
129	C₂×#88322	—	2	2	no	—
130	C₂×#88322	—	2	2	no	—
131	C₂×#88322	—	4	1	no	—
132	C₂×#88322	—	4	1	no	—
133	C₈×D₅₃	—	4	4	no	—
134	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂²×D₅₃	—	2	1	no	—
136	C₂²×D₅₃	—	2	1	no	—
137	C₂²×D₅₃	—	2	2	no	—
138	C₂²×D₅₃	—	4	1	no	—
139	C₂²×D₅₃	#95	1	1	yes	characteristic
140	C₂²×D₅₃	#95	1	1	yes	characteristic
141	C₂×C₄×C₅₃	—	2	2	no	—
142	C₂×C₄×C₅₃	—	4	1	no	—
143	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₅₃	#135	1	1	yes	characteristic
150	C₂×C₄×C₅₃	#135	1	1	yes	characteristic
151	C₂×C₄×C₅₃	#135	1	1	yes	characteristic
152	C₂×C₄×C₅₃	#135	1	1	yes	characteristic
153	C₂×Dic₅₃	—	2	1	no	—
154	C₂×Dic₅₃	—	2	1	no	—
155	C₂×Dic₅₃	—	4	1	no	—
156	C₂×Dic₅₃	—	4	1	no	—
157	C₂×Dic₅₃	#95	1	1	yes	characteristic
158	C₂×Dic₅₃	#95	1	1	yes	characteristic
159	C₂×Dic₅₃	#95	1	1	yes	characteristic
160	C₂×Dic₅₃	#95	1	1	yes	characteristic
161	C₂×Dic₅₃	#95	1	1	yes	characteristic
162	C₂×Dic₅₃	#95	1	1	yes	characteristic
163	C₄×D₅₃	—	2	2	no	—
164	C₄×D₅₃	—	2	2	no	—
165	C₄×D₅₃	—	2	1	no	—
166	C₄×D₅₃	—	2	1	no	—
167	C₄×D₅₃	—	2	1	no	—
168	C₄×D₅₃	—	2	1	no	—
169	C₄×D₅₃	—	2	1	no	—
170	C₄×D₅₃	—	2	1	no	—
171	C₄×D₅₃	—	2	1	no	—
172	C₄×D₅₃	—	2	1	no	—
173	C₄×D₅₃	—	2	2	no	—
174	C₄×D₅₃	—	2	2	no	—
175	C₄×D₅₃	—	4	1	no	—
176	C₄×D₅₃	—	4	1	no	—
177	C₄×D₅₃	—	4	1	no	—
178	C₄×D₅₃	—	4	1	no	—
179	C₈×C₅₃	—	4	2	no	—
180	C₈×C₅₃	—	4	2	no	—
181	C₈×C₅₃	—	4	2	no	—
182	#88322	—	4	2	no	—
183	#88322	—	4	2	no	—
184	#88322	—	4	2	no	—
185	#8080	—	53	1	no	maximal, Sylow
186	C₂²×C₅₃	—	2	1	no	—
187	C₂²×C₅₃	—	2	1	no	—
188	C₂²×C₅₃	C₂×#95	1	1	yes	characteristic
189	C₂²×C₅₃	#427	1	1	yes	characteristic
190	C₂²×C₅₃	#427	1	1	yes	characteristic
191	C₂×D₅₃	—	2	1	no	—
192	C₂×D₅₃	—	2	1	no	—
193	C₂×D₅₃	—	2	1	no	—
194	C₂×D₅₃	—	2	1	no	—
195	C₂×D₅₃	—	2	1	no	—
196	C₂×D₅₃	—	4	2	no	—
197	C₂×D₅₃	—	4	2	no	—
198	C₂×D₅₃	#344	1	2	yes	—
199	C₄×C₅₃	—	2	1	no	—
200	C₄×C₅₃	—	2	1	no	—
201	C₄×C₅₃	—	2	1	no	—
202	C₄×C₅₃	#416	1	1	yes	characteristic
203	C₄×C₅₃	#416	1	1	yes	characteristic
204	C₄×C₅₃	#416	1	1	yes	characteristic
205	C₄×C₅₃	#416	1	1	yes	characteristic
206	C₄×C₅₃	#430	1	2	yes	—
207	Dic₅₃	—	2	1	no	—
208	Dic₅₃	—	2	1	no	—
209	Dic₅₃	—	2	1	no	—
210	Dic₅₃	—	2	1	no	—
211	Dic₅₃	—	2	1	no	—
212	Dic₅₃	—	2	1	no	—
213	#2920	—	53	1	no	—
214	C₂×#432	—	53	1	no	—
215	C₂×#431	—	53	1	no	—
216	#1301	—	53	1	no	—
217	#1301	—	53	1	no	—
218	#1301	—	53	1	no	—
219	#1301	D₅₃	1	1	yes	characteristic, complemented
220	C₂×C₅₃	—	2	1	no	—
221	C₂×C₅₃	—	2	1	no	—
222	C₂×C₅₃	#1735	1	1	yes	characteristic
223	C₂×C₅₃	#1738	1	1	yes	characteristic
224	C₂×C₅₃	C₂×#344	1	1	yes	characteristic
225	D₅₃	—	2	2	no	—
226	D₅₃	—	4	1	no	—
227	C₂²×C₄²	—	53	1	no	—
228	#432	—	53	2	no	—
229	#432	—	53	2	no	—
230	#432	—	53	2	no	—
231	#432	—	106	1	no	—
232	#432	—	106	1	no	—
233	#432	—	106	1	no	—
234	#431	—	53	1	no	—
235	#431	—	53	2	no	—
236	#431	—	53	2	no	—
237	#431	—	106	1	no	—
238	#431	—	106	1	no	—
239	#431	—	106	1	no	—
240	#431	C₂×D₅₃	1	1	yes	characteristic
241	#423	—	53	1	no	—
242	#423	C₂×D₅₃	1	1	yes	characteristic
243	C₂×C₄⋊C₈	—	53	1	no	—
244	C₂×C₄⋊C₈	—	106	1	no	—
245	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
246	#407	—	106	1	no	—
247	C₂×C₂²⋊C₈	—	53	2	no	—
248	C₂×C₂²⋊C₈	—	106	1	no	—
249	C₄×M₁₆	—	106	1	no	—
250	C₂×#97	—	106	1	no	—
251	C₂×C₄×C₈	—	106	1	no	—
252	C₅₃	#8080	1	1	yes	characteristic, complemented, Sylow
253	C₂³×C₄	—	53	1	no	—
254	C₂³×C₄	—	53	1	no	—
255	C₂³×C₄	—	53	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	106	1	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	106	2	no	—
260	C₂²×C₈	—	106	1	no	—
261	C₂×C₄²	—	53	1	no	—
262	C₂×C₄²	—	53	1	no	—
263	C₂×C₄²	—	53	1	no	—
264	C₂×C₄²	—	53	1	no	—
265	C₂×C₄²	—	53	1	no	—
266	C₂×C₄²	—	53	1	no	—
267	C₂×C₄²	—	53	1	no	—
268	C₂×C₄²	—	53	1	no	—
269	C₂×C₄²	—	53	1	no	—
270	C₂×C₄²	—	53	1	no	—
271	C₂×C₄²	—	53	1	no	—
272	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	53	2	no	—
277	C₄⋊C₈	—	53	2	no	—
278	C₄⋊C₈	—	106	2	no	—
279	C₄⋊C₈	—	106	1	no	—
280	C₄⋊C₈	—	106	1	no	—
281	C₄⋊C₈	—	106	1	no	—
282	C₄⋊C₈	C₄×D₅₃	1	2	yes	—
283	C₄⋊C₈	C₄×D₅₃	1	2	yes	—
284	C₂²⋊C₈	—	53	2	no	—
285	C₂²⋊C₈	—	106	2	no	—
286	C₂²⋊C₈	—	106	2	no	—
287	C₂²⋊C₈	—	106	2	no	—
288	C₂²⋊C₈	—	106	2	no	—
289	C₂²⋊C₈	—	106	2	no	—
290	C₂²⋊C₈	C₄×D₅₃	1	2	yes	—
291	#97	—	106	2	no	—
292	#97	—	106	2	no	—
293	#97	—	106	2	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	106	2	no	—
296	C₄×C₈	—	106	2	no	—
297	C₄×C₈	—	106	1	no	—
298	C₂⁴	—	53	1	no	—
299	C₂²×C₄	—	53	1	no	—
300	C₂²×C₄	—	53	1	no	—
301	C₂²×C₄	—	53	1	no	—
302	C₂²×C₄	—	53	1	no	—
303	C₂²×C₄	—	53	1	no	—
304	C₂²×C₄	—	53	1	no	—
305	C₂²×C₄	—	53	1	no	—
306	C₂²×C₄	—	53	1	no	—
307	C₂²×C₄	—	53	1	no	—
308	C₂²×C₄	—	53	1	no	—
309	C₂²×C₄	—	53	1	no	—
310	C₂²×C₄	—	53	1	no	—
311	C₂²×C₄	—	53	1	no	—
312	C₂²×C₄	—	53	1	no	—
313	C₂²×C₄	—	53	1	no	—
314	C₂²×C₄	—	106	1	no	—
315	C₂²×C₄	—	106	1	no	—
316	C₂²×C₄	—	106	1	no	—
317	C₂²×C₄	—	106	1	no	—
318	C₂²×C₄	—	212	2	no	—
319	C₂²×C₄	—	212	2	no	—
320	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
321	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
322	C₂²×C₄	Q₈×D₅₃	1	1	yes	characteristic
323	M₁₆	—	4	1	no	—
324	M₁₆	—	4	1	no	—
325	M₁₆	—	212	1	no	—
326	M₁₆	—	212	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	106	2	no	—
333	C₂×C₈	—	106	2	no	—
334	C₂×C₈	—	106	2	no	—
335	C₂×C₈	—	212	4	no	—
336	C₂×C₈	—	212	1	no	—
337	C₂×C₈	—	212	1	no	—
338	C₄²	—	53	1	no	—
339	C₄²	—	53	1	no	—
340	C₄²	—	53	1	no	—
341	C₄²	—	53	1	no	—
342	C₄²	—	53	1	no	—
343	C₄²	—	53	1	no	—
344	C₄²	—	53	1	no	—
345	C₄²	—	53	1	no	—
346	C₄²	—	53	1	no	—
347	C₄²	—	53	1	no	—
348	C₄²	—	53	1	no	—
349	C₄²	—	53	1	no	—
350	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
351	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
352	C₄²	D₄×D₅₃	1	1	yes	characteristic
353	C₄²	D₄×D₅₃	1	1	yes	characteristic
354	C₂³	—	53	1	no	—
355	C₂³	—	53	1	no	—
356	C₂³	—	106	2	no	—
357	C₂³	—	106	1	no	—
358	C₂³	—	106	1	no	—
359	C₂³	—	212	1	no	—
360	C₂³	C₄⋊C₄×D₅₃	1	1	yes	characteristic
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	53	1	no	—
364	C₂×C₄	—	53	1	no	—
365	C₂×C₄	—	53	1	no	—
366	C₂×C₄	—	53	1	no	—
367	C₂×C₄	—	53	1	no	—
368	C₂×C₄	—	53	1	no	—
369	C₂×C₄	—	106	2	no	—
370	C₂×C₄	—	106	2	no	—
371	C₂×C₄	—	106	1	no	—
372	C₂×C₄	—	106	1	no	—
373	C₂×C₄	—	106	1	no	—
374	C₂×C₄	—	106	1	no	—
375	C₂×C₄	—	106	1	no	—
376	C₂×C₄	—	106	1	no	—
377	C₂×C₄	—	106	1	no	—
378	C₂×C₄	—	106	1	no	—
379	C₂×C₄	—	106	1	no	—
380	C₂×C₄	—	106	1	no	—
381	C₂×C₄	—	106	2	no	—
382	C₂×C₄	—	106	2	no	—
383	C₂×C₄	—	212	1	no	—
384	C₂×C₄	—	212	1	no	—
385	C₂×C₄	—	212	1	no	—
386	C₂×C₄	—	212	1	no	—
387	C₂×C₄	—	212	1	no	—
388	C₂×C₄	—	212	1	no	—
389	C₂×C₄	C₄²×D₅₃	1	1	yes	characteristic
390	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
391	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
392	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
393	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
394	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
395	C₂×C₄	#13133236	1	1	yes	characteristic
396	C₂×C₄	#13133238	1	1	yes	characteristic
397	C₂×C₄	#13133238	1	1	yes	characteristic
398	C₂×C₄	#13133240	1	1	yes	characteristic
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₈	—	212	2	no	—
403	C₈	—	212	2	no	—
404	C₈	—	212	2	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	53	2	no	—
408	C₂²	—	106	1	no	—
409	C₂²	—	106	1	no	—
410	C₂²	—	106	1	no	—
411	C₂²	—	106	1	no	—
412	C₂²	—	106	1	no	—
413	C₂²	—	212	2	no	—
414	C₂²	—	212	2	no	—
415	C₂²	#95×D₅₃	1	1	yes	characteristic
416	C₂²	#16810658	1	1	yes	characteristic
417	C₂²	#16810660	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	106	1	no	—
422	C₄	—	106	1	no	—
423	C₄	—	106	1	no	—
424	C₄	—	106	1	no	—
425	C₄	—	106	1	no	—
426	C₄	—	106	1	no	—
427	C₄	#16810616	1	1	yes	characteristic
428	C₄	#16810616	1	1	yes	characteristic
429	C₄	#16810618	1	1	yes	characteristic
430	C₄	#16810618	1	1	yes	characteristic
431	C₄	#16810670	1	2	yes	—
432	C₂	—	2	1	no	—
433	C₂	—	2	1	no	—
434	C₂	—	106	2	no	—
435	C₂	—	212	1	no	—
436	C₂	#20274430	1	1	yes	characteristic
437	C₂	#20274440	1	1	yes	characteristic
438	C₂	#344×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₅₃×#1301	C₂
socle	C₂²×C₅₃	C₂×#95
prime radical	C₂³×D₅₃	C₄⋊C₄
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	#1301	D₅₃
hypocenter	C₅₃	#8080
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

Complements

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

N	H ≅ G/N	type
4. #20272612	C₂	semidirect
5. #20272611	C₂	semidirect
6. #20272610	C₂	semidirect
7. C₅₃×#1301	C₂	semidirect
219. #1301	D₅₃	semidirect
252. C₅₃	#8080	semidirect

Maximal subgroups

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

subgroup	index
#20283347	2
C₂×#16810679	2
#431×D₅₃	2
#20272612	2
#20272611	2
#20272610	2
C₅₃×#1301	2
#8080	53