Subgroups — D₅₃×#1841 #27384353

Order 13568.

730 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	C₄×M₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#20274865	C₂	1	1	yes	maximal, characteristic, complemented
3	#20274864	C₂	1	1	yes	maximal, characteristic, complemented
4	#20274863	C₂	1	2	yes	maximal, complemented
5	#20274862	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274861	C₂	1	2	yes	maximal, complemented
7	#344×D₅₃	C₂	1	2	yes	maximal
8	#339×D₅₃	C₂	1	2	yes	maximal
9	#338×D₅₃	C₂	1	1	yes	maximal, characteristic
10	H(3,ℤ/4)×D₅₃	C₂	1	1	yes	maximal, characteristic
11	C₅₃×#1841	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
13	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
15	#117×D₅₃	C₂²	1	2	yes	—
16	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
17	C₄×#11719917	C₂²	1	1	yes	characteristic
18	#16810575	C₄	1	2	yes	complemented
19	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
20	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
21	C₄×#11719912	C₄	1	2	yes	complemented
22	#97×D₅₃	C₄	1	2	yes	complemented
23	C₄×C₈×D₅₃	C₄	1	2	yes	complemented
24	#16810395	C₂²	1	2	yes	—
25	#16810394	C₂²	1	2	yes	—
26	#16810393	C₂²	1	2	yes	—
27	#16810384	C₂²	1	2	yes	—
28	#16810383	C₂²	1	2	yes	—
29	#16810382	C₂²	1	2	yes	—
30	#16810381	C₂²	1	2	yes	—
31	#16810381	C₂²	1	1	yes	characteristic
32	#16810380	C₂²	1	1	yes	characteristic
33	#16810379	C₂²	1	2	yes	—
34	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#344	C₂²	1	2	yes	—
36	C₅₃×#339	C₂²	1	2	yes	—
37	C₅₃×#338	C₂²	1	1	yes	characteristic
38	C₅₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
39	C₂²×C₄×D₅₃	—	2	1	no	—
40	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
41	C₂×#11719917	C₂³	1	2	yes	—
42	C₂×#11719917	C₂³	1	1	yes	characteristic
43	C₂×#11719917	C₂³	1	1	yes	characteristic
44	C₂×#11719912	—	2	2	no	—
45	C₂×#11719912	C₂×C₄	1	2	yes	—
46	C₂×#11719912	C₂×C₄	1	2	yes	—
47	M₁₆×D₅₃	—	2	2	no	—
48	M₁₆×D₅₃	—	2	2	no	—
49	M₁₆×D₅₃	—	2	2	no	—
50	M₁₆×D₅₃	—	2	2	no	—
51	M₁₆×D₅₃	—	2	2	no	—
52	M₁₆×D₅₃	—	2	2	no	—
53	M₁₆×D₅₃	—	2	2	no	—
54	M₁₆×D₅₃	—	2	2	no	—
55	C₂×C₈×D₅₃	—	2	2	no	—
56	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
57	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
58	#13133176	C₂³	1	2	yes	—
59	#13133175	—	2	2	no	—
60	#13133174	—	2	2	no	—
61	#13133173	—	2	2	no	—
62	C₄⋊C₄×D₅₃	—	2	2	no	—
63	C₂²⋊C₄×D₅₃	—	2	2	no	—
64	C₂×C₄×Dic₅₃	—	2	1	no	—
65	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
66	C₄²×D₅₃	—	2	1	no	—
67	C₄²×D₅₃	—	2	1	no	—
68	C₄²×D₅₃	—	2	2	no	—
69	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
73	#13133128	C₂×C₄	1	2	yes	complemented
74	#13133127	C₂×C₄	1	2	yes	complemented
75	#13133127	C₂×C₄	1	2	yes	complemented
76	C₄×#88322	C₂×C₄	1	2	yes	complemented
77	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
78	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
79	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
80	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
82	#117×C₅₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
84	#97×C₅₃	C₂×C₄	1	2	yes	complemented
85	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	complemented
86	C₂³×D₅₃	#41	1	1	yes	characteristic
87	C₂²×C₄×C₅₃	—	2	1	no	—
88	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
89	C₂²×Dic₅₃	—	2	1	no	—
90	C₂²×Dic₅₃	#41	1	1	yes	characteristic
91	C₂×C₄×D₅₃	—	2	1	no	—
92	C₂×C₄×D₅₃	—	2	1	no	—
93	C₂×C₄×D₅₃	—	2	1	no	—
94	C₂×C₄×D₅₃	—	2	1	no	—
95	C₂×C₄×D₅₃	—	4	4	no	—
96	C₂×C₄×D₅₃	—	4	2	no	—
97	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₅₃	#41	1	2	yes	—
100	C₂×C₄×D₅₃	#41	1	2	yes	—
101	C₂×C₄×D₅₃	#41	1	2	yes	—
102	C₂×C₄×D₅₃	#41	1	2	yes	—
103	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
104	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
105	M₁₆×C₅₃	—	2	2	no	—
106	M₁₆×C₅₃	—	2	2	no	—
107	M₁₆×C₅₃	—	2	2	no	—
108	M₁₆×C₅₃	—	2	2	no	—
109	C₂×C₈×C₅₃	—	2	2	no	—
110	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
111	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
112	C₄⋊C₄×C₅₃	—	2	2	no	—
113	C₂²⋊C₄×C₅₃	—	2	2	no	—
114	C₄²×C₅₃	—	2	1	no	—
115	C₄²×C₅₃	—	2	2	no	—
116	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²⋊Dic₅₃	—	2	2	no	—
119	#11719921	—	4	2	no	—
120	C₄⋊Dic₅₃	—	2	2	no	—
121	#11719919	—	4	2	no	—
122	C₄×Dic₅₃	—	2	1	no	—
123	C₄×Dic₅₃	—	2	1	no	—
124	C₄×Dic₅₃	—	2	1	no	—
125	C₄×Dic₅₃	—	2	1	no	—
126	C₄×Dic₅₃	—	2	1	no	—
127	C₄×Dic₅₃	—	2	2	no	—
128	C₄×Dic₅₃	—	4	2	no	—
129	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
131	#11719917	—	2	2	no	—
132	#11719917	—	2	2	no	—
133	#11719917	—	2	2	no	—
134	#11719917	—	2	2	no	—
135	C₂×#88322	—	2	2	no	—
136	C₂×#88322	C₂²×C₄	1	2	yes	—
137	C₂×#88322	C₂²×C₄	1	2	yes	—
138	#11719912	—	2	4	no	—
139	#11719912	—	2	4	no	—
140	#11719912	—	4	2	no	—
141	#11719912	—	4	2	no	—
142	C₈×D₅₃	—	2	2	no	—
143	C₈×D₅₃	—	2	2	no	—
144	C₈×D₅₃	—	2	2	no	—
145	C₈×D₅₃	—	2	2	no	—
146	C₈×D₅₃	—	4	2	no	—
147	C₈×D₅₃	—	4	2	no	—
148	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
149	C₂²×D₅₃	—	4	2	no	—
150	C₂²×D₅₃	#117	1	1	yes	characteristic
151	C₂²×D₅₃	#117	1	1	yes	characteristic
152	C₂²×D₅₃	#126	1	2	yes	—
153	C₂²×D₅₃	#126	1	2	yes	—
154	C₂×C₄×C₅₃	—	2	1	no	—
155	C₂×C₄×C₅₃	—	2	1	no	—
156	C₂×C₄×C₅₃	—	4	2	no	—
157	C₂×C₄×C₅₃	—	4	2	no	—
158	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
160	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
161	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
162	C₂×Dic₅₃	—	2	1	no	—
163	C₂×Dic₅₃	—	2	1	no	—
164	C₂×Dic₅₃	—	4	2	no	—
165	C₂×Dic₅₃	—	4	2	no	—
166	C₂×Dic₅₃	#117	1	1	yes	characteristic
167	C₂×Dic₅₃	#117	1	1	yes	characteristic
168	C₂×Dic₅₃	#126	1	2	yes	—
169	C₂×Dic₅₃	#126	1	2	yes	—
170	C₄×D₅₃	—	2	4	no	—
171	C₄×D₅₃	—	4	2	no	—
172	C₄×D₅₃	—	4	2	no	—
173	C₄×D₅₃	—	4	2	no	—
174	C₄×D₅₃	—	8	4	no	—
175	C₄×D₅₃	#117	1	1	yes	characteristic
176	C₄×D₅₃	#117	1	1	yes	characteristic
177	C₄×D₅₃	#117	1	1	yes	characteristic
178	C₄×D₅₃	#117	1	1	yes	characteristic
179	C₄×D₅₃	#117	1	2	yes	—
180	C₄×D₅₃	#117	1	2	yes	—
181	C₄×D₅₃	#126	1	2	yes	—
182	C₄×D₅₃	#126	1	2	yes	—
183	C₄×D₅₃	#126	1	2	yes	—
184	C₄×D₅₃	#126	1	2	yes	—
185	C₈×C₅₃	—	2	2	no	—
186	C₈×C₅₃	—	2	2	no	—
187	C₈×C₅₃	—	4	2	no	—
188	#88322	—	2	2	no	—
189	#88322	—	2	2	no	—
190	#88322	—	4	2	no	—
191	C₂×#1841	—	53	1	no	maximal, Sylow
192	C₂²×C₅₃	—	4	1	no	—
193	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
194	C₂²×C₅₃	C₂×#126	1	2	yes	—
195	C₂×D₅₃	—	2	2	no	—
196	C₂×D₅₃	—	2	4	no	—
197	C₂×D₅₃	—	4	1	no	—
198	C₂×D₅₃	—	4	2	no	—
199	C₂×D₅₃	#383	1	1	yes	characteristic
200	C₂×D₅₃	#383	1	2	yes	—
201	C₂×D₅₃	#383	1	1	yes	characteristic
202	C₄×C₅₃	—	2	2	no	—
203	C₄×C₅₃	—	4	1	no	—
204	C₄×C₅₃	—	8	2	no	—
205	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
206	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
207	C₄×C₅₃	C₂×#126	1	2	yes	—
208	Dic₅₃	—	2	2	no	—
209	Dic₅₃	—	4	1	no	—
210	Dic₅₃	—	8	2	no	—
211	Dic₅₃	#383	1	1	yes	characteristic
212	Dic₅₃	#383	1	1	yes	characteristic
213	Dic₅₃	#383	1	2	yes	—
214	C₂×C₄×M₁₆	—	53	1	no	—
215	#1841	—	53	1	no	—
216	#1841	—	53	2	no	—
217	#1841	—	53	2	no	—
218	#1841	—	53	1	no	—
219	#1841	—	53	1	no	—
220	#1841	D₅₃	1	1	yes	characteristic, direct product factor
221	C₂×#344	—	53	2	no	—
222	C₂×#339	—	53	2	no	—
223	C₂×#338	—	53	1	no	—
224	C₂×H(3,ℤ/4)	—	53	1	no	—
225	C₂×C₅₃	—	2	1	no	—
226	C₂×C₅₃	—	2	2	no	—
227	C₂×C₅₃	C₂×#383	1	1	yes	characteristic
228	D₅₃	—	2	1	no	—
229	D₅₃	—	2	2	no	—
230	D₅₃	#1841	1	2	yes	direct product factor
231	C₂²×M₁₆	—	53	1	no	—
232	C₂²×M₁₆	—	53	1	no	—
233	C₂²×M₁₆	—	53	2	no	—
234	C₂×#117	—	53	2	no	—
235	C₂²×C₄²	—	53	1	no	—
236	C₄×M₁₆	—	53	1	no	—
237	C₄×M₁₆	—	53	1	no	—
238	C₄×M₁₆	—	53	1	no	—
239	C₄×M₁₆	—	53	2	no	—
240	C₄×M₁₆	—	53	2	no	—
241	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic
242	C₂×#97	—	53	2	no	—
243	C₂×C₄×C₈	—	53	2	no	—
244	#344	—	53	2	no	—
245	#344	—	53	2	no	—
246	#344	—	53	2	no	—
247	#344	C₂×D₅₃	1	2	yes	—
248	#339	—	53	2	no	—
249	#339	—	53	2	no	—
250	#339	—	53	2	no	—
251	#339	C₂×D₅₃	1	2	yes	—
252	#338	—	53	2	no	—
253	#338	—	53	1	no	—
254	#338	C₂×D₅₃	1	1	yes	characteristic
255	H(3,ℤ/4)	—	53	1	no	—
256	H(3,ℤ/4)	—	53	2	no	—
257	H(3,ℤ/4)	C₂×D₅₃	1	1	yes	characteristic
258	C₅₃	C₂×#1841	1	1	yes	characteristic, complemented, Sylow
259	C₂³×C₄	—	53	1	no	—
260	C₂³×C₄	—	106	1	no	—
261	C₂×M₁₆	—	53	1	no	—
262	C₂×M₁₆	—	53	1	no	—
263	C₂×M₁₆	—	53	2	no	—
264	C₂×M₁₆	—	53	2	no	—
265	C₂×M₁₆	—	53	2	no	—
266	C₂×M₁₆	—	106	2	no	—
267	C₂×M₁₆	—	106	2	no	—
268	C₂×M₁₆	—	106	2	no	—
269	C₂×M₁₆	—	106	2	no	—
270	C₂×M₁₆	—	106	2	no	—
271	C₂×M₁₆	—	106	2	no	—
272	C₂×M₁₆	—	106	2	no	—
273	C₂×M₁₆	—	106	2	no	—
274	C₂×M₁₆	—	106	2	no	—
275	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
276	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
277	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
278	C₂²×C₈	—	53	2	no	—
279	C₂²×C₈	—	53	2	no	—
280	C₂²×C₈	—	106	2	no	—
281	#117	—	53	2	no	—
282	#117	—	106	2	no	—
283	#117	—	106	2	no	—
284	#117	—	106	2	no	—
285	#117	C₂²×D₅₃	1	2	yes	—
286	C₂×C₄⋊C₄	—	106	2	no	—
287	C₂×C₂²⋊C₄	—	106	2	no	—
288	C₂×C₄²	—	53	1	no	—
289	C₂×C₄²	—	53	1	no	—
290	C₂×C₄²	—	53	1	no	—
291	C₂×C₄²	—	53	1	no	—
292	C₂×C₄²	—	53	1	no	—
293	C₂×C₄²	—	106	1	no	—
294	C₂×C₄²	—	106	1	no	—
295	C₂×C₄²	—	106	2	no	—
296	C₂×C₄²	—	106	1	no	—
297	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
298	#97	—	53	2	no	—
299	#97	—	53	2	no	—
300	#97	—	53	2	no	—
301	#97	C₄×D₅₃	1	2	yes	complemented
302	C₄×C₈	—	53	2	no	—
303	C₄×C₈	—	53	2	no	—
304	C₄×C₈	—	53	2	no	—
305	C₄×C₈	C₄×D₅₃	1	2	yes	complemented
306	C₂⁴	—	53	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	53	1	no	—
309	C₂²×C₄	—	53	1	no	—
310	C₂²×C₄	—	53	1	no	—
311	C₂²×C₄	—	53	2	no	—
312	C₂²×C₄	—	53	1	no	—
313	C₂²×C₄	—	53	1	no	—
314	C₂²×C₄	—	53	2	no	—
315	C₂²×C₄	—	53	2	no	—
316	C₂²×C₄	—	53	2	no	—
317	C₂²×C₄	—	106	1	no	—
318	C₂²×C₄	—	106	1	no	—
319	C₂²×C₄	—	106	1	no	—
320	C₂²×C₄	—	106	1	no	—
321	C₂²×C₄	—	106	1	no	—
322	C₂²×C₄	—	212	4	no	—
323	C₂²×C₄	—	212	2	no	—
324	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	106	4	no	—
330	M₁₆	—	106	4	no	—
331	M₁₆	—	106	2	no	—
332	M₁₆	—	106	2	no	—
333	M₁₆	—	106	2	no	—
334	M₁₆	—	106	2	no	—
335	M₁₆	—	212	2	no	—
336	M₁₆	—	212	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	53	2	no	—
339	C₂×C₈	—	53	2	no	—
340	C₂×C₈	—	106	2	no	—
341	C₂×C₈	—	106	2	no	—
342	C₂×C₈	—	106	2	no	—
343	C₂×C₈	—	106	2	no	—
344	C₂×C₈	—	106	2	no	—
345	C₂×C₈	—	212	2	no	—
346	C₂×C₈	—	212	2	no	—
347	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
348	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	106	2	no	—
351	C₄⋊C₄	—	212	2	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	106	2	no	—
354	C₂²⋊C₄	—	212	2	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	53	1	no	—
358	C₄²	—	53	1	no	—
359	C₄²	—	106	1	no	—
360	C₄²	—	106	1	no	—
361	C₄²	—	106	1	no	—
362	C₄²	—	106	1	no	—
363	C₄²	—	106	1	no	—
364	C₄²	—	106	2	no	—
365	C₄²	—	212	2	no	—
366	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
367	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
368	C₂³	—	53	1	no	—
369	C₂³	—	53	2	no	—
370	C₂³	—	53	1	no	—
371	C₂³	—	53	2	no	—
372	C₂³	—	212	2	no	—
373	C₂³	#41×D₅₃	1	1	yes	characteristic
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	53	1	no	—
379	C₂×C₄	—	53	1	no	—
380	C₂×C₄	—	53	2	no	—
381	C₂×C₄	—	53	2	no	—
382	C₂×C₄	—	53	1	no	—
383	C₂×C₄	—	53	1	no	—
384	C₂×C₄	—	53	2	no	—
385	C₂×C₄	—	53	1	no	—
386	C₂×C₄	—	53	1	no	—
387	C₂×C₄	—	53	2	no	—
388	C₂×C₄	—	53	2	no	—
389	C₂×C₄	—	53	2	no	—
390	C₂×C₄	—	53	2	no	—
391	C₂×C₄	—	53	2	no	—
392	C₂×C₄	—	106	4	no	—
393	C₂×C₄	—	106	1	no	—
394	C₂×C₄	—	106	1	no	—
395	C₂×C₄	—	424	4	no	—
396	C₂×C₄	—	212	2	no	—
397	C₂×C₄	—	212	2	no	—
398	C₂×C₄	—	212	2	no	—
399	C₂×C₄	—	212	2	no	—
400	C₂×C₄	—	212	2	no	—
401	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
402	C₂×C₄	#41×D₅₃	1	2	yes	—
403	C₂×C₄	#41×D₅₃	1	2	yes	—
404	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	—	2	2	no	—
407	C₈	—	4	2	no	—
408	C₈	—	106	2	no	—
409	C₈	—	106	2	no	—
410	C₈	—	212	2	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	53	1	no	—
413	C₂²	—	53	1	no	—
414	C₂²	—	53	2	no	—
415	C₂²	—	106	2	no	—
416	C₂²	—	106	4	no	—
417	C₂²	—	212	1	no	—
418	C₂²	—	212	2	no	—
419	C₂²	#117×D₅₃	1	1	yes	characteristic
420	C₂²	#126×D₅₃	1	2	yes	—
421	C₄	—	2	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	8	2	no	—
424	C₄	—	53	1	no	—
425	C₄	—	53	2	no	—
426	C₄	—	53	1	no	—
427	C₄	—	106	2	no	—
428	C₄	—	424	2	no	—
429	C₄	—	212	1	no	—
430	C₄	#117×D₅₃	1	1	yes	characteristic
431	C₄	#117×D₅₃	1	1	yes	characteristic
432	C₄	#126×D₅₃	1	2	yes	—
433	C₂	—	2	1	no	—
434	C₂	—	2	2	no	—
435	C₂	—	53	2	no	—
436	C₂	—	106	1	no	—
437	C₂	—	106	2	no	—
438	C₂	#383×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#117×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1841	C₂
socle	C₂×C₅₃	C₂×#383
prime radical	C₂³×D₅₃	#41
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1841	D₅₃
hypocenter	C₅₃	C₂×#1841
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #1841

Complements

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

N	H ≅ G/N	type
2. #20274865	C₂	semidirect
3. #20274864	C₂	semidirect
4. #20274863	C₂	semidirect
5. #20274862	C₂	semidirect
6. #20274861	C₂	semidirect
11. C₅₃×#1841	C₂	semidirect
18. #16810575	C₄	semidirect
21. C₄×#11719912	C₄	semidirect
22. #97×D₅₃	C₄	semidirect
23. C₄×C₈×D₅₃	C₄	semidirect
73. #13133128	C₂×C₄	semidirect
74. #13133127	C₂×C₄	semidirect
75. #13133127	C₂×C₄	semidirect
76. C₄×#88322	C₂×C₄	semidirect
77. C₈×Dic₅₃	C₂×C₄	semidirect
78. C₈×Dic₅₃	C₂×C₄	semidirect
84. #97×C₅₃	C₂×C₄	semidirect
85. C₄×C₈×C₅₃	C₂×C₄	semidirect
220. #1841	D₅₃	direct (N × H)
230. D₅₃	#1841	direct (N × H)
258. C₅₃	C₂×#1841	semidirect
301. #97	C₄×D₅₃	semidirect
305. C₄×C₈	C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×M₁₆×D₅₃	2
#20274865	2
#20274864	2
#20274863	2
#20274862	2
#20274861	2
#344×D₅₃	2
#339×D₅₃	2
#338×D₅₃	2
H(3,ℤ/4)×D₅₃	2
C₅₃×#1841	2
C₂×#1841	53

Subgroups — D53×#1841 #27384353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1841 #27384353