Subgroups — D₅₃×#2155 #27537101

Order 13568.

658 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#108×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#427×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20276489	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276488	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276487	C₂	1	1	yes	maximal, characteristic, complemented
7	#20276486	C₂	1	4	yes	maximal, complemented
8	#365×D₅₃	C₂	1	4	yes	maximal, complemented
9	C₅₃×#2155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₅₃	—	2	1	no	—
11	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
12	#117×D₅₃	—	2	1	no	—
13	C₂×#13133157	C₂²	1	1	yes	characteristic
14	C₂×#13133156	C₄	1	2	yes	complemented
15	M₃₂×D₅₃	C₄	1	2	yes	complemented
16	M₃₂×D₅₃	C₄	1	2	yes	complemented
17	M₃₂×D₅₃	C₂²	1	2	yes	—
18	M₃₂×D₅₃	C₂²	1	2	yes	—
19	C₂×C₁₆×D₅₃	C₄	1	2	yes	complemented
20	C₂×#13133153	C₂²	1	1	yes	characteristic
21	C₂×#13133152	—	2	1	no	—
22	#108×D₅₃	—	2	1	no	—
23	#108×D₅₃	—	2	1	no	—
24	#108×D₅₃	C₂²	1	2	yes	—
25	#108×D₅₃	C₂²	1	2	yes	—
26	#16810661	C₂²	1	1	yes	characteristic
27	#16810660	—	2	1	no	—
28	#16810659	—	2	1	no	—
29	#16810658	C₂²	1	2	yes	—
30	#107×D₅₃	—	2	1	no	—
31	#106×D₅₃	C₂²	1	2	yes	—
32	#16810447	C₂²	1	4	yes	complemented
33	#16810446	C₂²	1	4	yes	complemented
34	#16810445	C₂²	1	4	yes	complemented
35	C₂×M₃₂×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
37	C₅₃×#427	C₂²	1	1	yes	characteristic
38	C₅₃×#365	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
40	C₂×#11719917	—	2	1	no	—
41	C₂×#11719912	—	4	1	no	—
42	M₁₆×D₅₃	—	2	2	no	—
43	M₁₆×D₅₃	—	2	2	no	—
44	M₁₆×D₅₃	—	4	1	no	—
45	M₁₆×D₅₃	—	4	1	no	—
46	C₂²×#88322	D₄	1	1	yes	characteristic
47	C₂×C₈×D₅₃	—	4	1	no	—
48	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
53	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
54	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
55	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
56	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
57	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
58	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
60	#13133176	—	2	1	no	—
61	#13133175	—	2	2	no	—
62	#13133174	—	4	1	no	—
63	#13133173	—	4	1	no	—
64	C₄⋊C₄×D₅₃	—	2	2	no	—
65	C₂²⋊C₄×D₅₃	—	4	1	no	—
66	C₄²×D₅₃	—	4	1	no	—
67	#13133157	C₂×C₄	1	2	yes	complemented
68	#13133157	C₂³	1	2	yes	—
69	#13133156	C₂×C₄	1	4	yes	—
70	#13133156	C₂×C₄	1	4	yes	complemented
71	C₂×#11719908	C₂×C₄	1	2	yes	complemented
72	C₁₆×D₅₃	C₂×C₄	1	4	yes	—
73	C₁₆×D₅₃	C₂×C₄	1	4	yes	complemented
74	#13133153	—	2	1	no	—
75	#13133153	C₂³	1	2	yes	—
76	#13133152	—	2	2	no	—
77	#13133152	—	2	2	no	—
78	#13133151	—	2	1	no	—
79	#13133150	—	2	2	no	—
80	#13133149	C₂³	1	2	yes	—
81	#13133148	—	2	2	no	—
82	C₂×M₁₆×C₅₃	—	2	1	no	—
83	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
84	#117×C₅₃	—	2	1	no	—
85	M₃₂×C₅₃	C₂×C₄	1	2	yes	complemented
86	M₃₂×C₅₃	C₂³	1	2	yes	—
87	C₂×C₁₆×C₅₃	C₂×C₄	1	2	yes	complemented
88	#108×C₅₃	—	2	1	no	—
89	#108×C₅₃	C₂³	1	2	yes	—
90	#107×C₅₃	—	2	1	no	—
91	#106×C₅₃	C₂³	1	2	yes	—
92	C₂³×D₅₃	SD₁₆	1	1	yes	characteristic
93	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×Dic₅₃	SD₁₆	1	1	yes	characteristic
95	C₂×C₄×D₅₃	—	4	2	no	—
96	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
101	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
102	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
103	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
104	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
105	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
108	M₁₆×C₅₃	—	2	2	no	—
109	M₁₆×C₅₃	—	4	1	no	—
110	C₂×C₈×C₅₃	—	4	1	no	—
111	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
115	C₂×C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
116	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
117	C₄⋊C₄×C₅₃	—	2	2	no	—
118	C₂²⋊C₄×C₅₃	—	4	1	no	—
119	C₄²×C₅₃	—	4	1	no	—
120	C₂²⋊Dic₅₃	—	4	1	no	—
121	#11719921	—	4	2	no	—
122	C₄⋊Dic₅₃	—	2	2	no	—
123	#11719919	—	4	2	no	—
124	C₄×Dic₅₃	—	4	1	no	—
125	C₄×Dic₅₃	—	4	2	no	—
126	#11719917	—	2	2	no	—
127	#11719917	—	4	1	no	—
128	C₂×#88322	—	4	1	no	—
129	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
130	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
131	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
132	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
133	C₂×#88322	C₂×D₄	1	1	yes	characteristic
134	C₂×#88322	C₂×D₄	1	1	yes	characteristic
135	#11719912	—	4	2	no	—
136	#11719912	—	4	2	no	—
137	C₈×D₅₃	—	4	2	no	—
138	C₈×D₅₃	—	4	2	no	—
139	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
140	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
141	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
142	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
143	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
144	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
145	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
146	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
147	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
148	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
149	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
150	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
151	C₈×D₅₃	C₂×Q₈	1	1	yes	characteristic
152	C₈×D₅₃	C₂×Q₈	1	1	yes	characteristic
153	C₈×D₅₃	C₂×Q₈	1	1	yes	characteristic
154	C₈×D₅₃	C₂×Q₈	1	1	yes	characteristic
155	C₁₆×C₅₃	C₂²×C₄	1	4	yes	—
156	#11719908	C₂²×C₄	1	4	yes	—
157	C₂³×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
158	C₂²×D₅₃	—	4	2	no	—
159	C₂²×D₅₃	#106	1	1	yes	characteristic
160	C₂²×D₅₃	#106	1	1	yes	characteristic
161	C₂²×D₅₃	#106	1	1	yes	characteristic
162	C₂²×D₅₃	#106	1	1	yes	characteristic
163	C₂²×D₅₃	C₂×SD₁₆	1	1	yes	characteristic
164	C₂²×D₅₃	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₅₃	—	4	2	no	—
166	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×Dic₅₃	—	4	2	no	—
173	C₂×Dic₅₃	#106	1	1	yes	characteristic
174	C₂×Dic₅₃	#106	1	1	yes	characteristic
175	C₂×Dic₅₃	#106	1	1	yes	characteristic
176	C₂×Dic₅₃	#106	1	1	yes	characteristic
177	C₂×Dic₅₃	C₂×SD₁₆	1	1	yes	characteristic
178	C₂×Dic₅₃	C₂×SD₁₆	1	1	yes	characteristic
179	C₄×D₅₃	—	8	4	no	—
180	C₄×D₅₃	#106	1	1	yes	characteristic
181	C₄×D₅₃	#106	1	1	yes	characteristic
182	C₄×D₅₃	#106	1	1	yes	characteristic
183	C₄×D₅₃	#106	1	1	yes	characteristic
184	C₄×D₅₃	#106	1	1	yes	characteristic
185	C₄×D₅₃	#106	1	1	yes	characteristic
186	C₄×D₅₃	#106	1	1	yes	characteristic
187	C₄×D₅₃	#106	1	1	yes	characteristic
188	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₄×D₅₃	C₂×SD₁₆	1	1	yes	characteristic
193	C₄×D₅₃	C₂×SD₁₆	1	1	yes	characteristic
194	C₄×D₅₃	C₂×SD₁₆	1	1	yes	characteristic
195	C₄×D₅₃	C₂×SD₁₆	1	1	yes	characteristic
196	C₈×C₅₃	—	4	2	no	—
197	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
200	C₈×C₅₃	C₂²×Q₈	1	1	yes	characteristic
201	#88322	—	4	2	no	—
202	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
203	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
204	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
205	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×#2155	—	53	1	no	maximal, Sylow
207	C₂²×C₅₃	—	4	1	no	—
208	C₂²×C₅₃	C₂×#106	1	1	yes	characteristic
209	C₂²×C₅₃	C₂×#106	1	1	yes	characteristic
210	C₂²×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
211	C₂×D₅₃	—	2	2	no	—
212	C₂×D₅₃	—	2	2	no	—
213	C₂×D₅₃	—	2	2	no	—
214	C₂×D₅₃	—	4	1	no	—
215	C₂×D₅₃	—	4	1	no	—
216	C₂×D₅₃	—	4	1	no	—
217	C₂×D₅₃	C₂×#106	1	1	yes	characteristic
218	C₂×D₅₃	C₂×#106	1	1	yes	characteristic
219	C₂×D₅₃	C₂×#106	1	1	yes	characteristic
220	C₂×D₅₃	C₂×#106	1	1	yes	characteristic
221	C₄×C₅₃	—	8	2	no	—
222	C₄×C₅₃	C₂×#106	1	1	yes	characteristic
223	C₄×C₅₃	C₂×#106	1	1	yes	characteristic
224	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
225	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
226	Dic₅₃	—	8	2	no	—
227	Dic₅₃	C₂×#106	1	1	yes	characteristic
228	Dic₅₃	C₂×#106	1	1	yes	characteristic
229	Dic₅₃	C₂×#106	1	1	yes	characteristic
230	Dic₅₃	C₂×#106	1	1	yes	characteristic
231	C₂²×M₃₂	—	53	1	no	—
232	C₂²×#108	—	53	1	no	—
233	C₂×#427	—	53	1	no	—
234	#2155	—	53	1	no	—
235	#2155	—	53	1	no	—
236	#2155	—	53	1	no	—
237	#2155	—	53	4	no	—
238	#2155	D₅₃	1	1	yes	characteristic, direct product factor
239	C₂×#365	—	53	4	no	—
240	C₂×C₅₃	—	2	1	no	—
241	C₂×C₅₃	—	2	1	no	—
242	C₂×C₅₃	—	2	1	no	—
243	C₂×C₅₃	C₂²×#106	1	1	yes	characteristic
244	D₅₃	—	2	1	no	—
245	D₅₃	—	2	1	no	—
246	D₅₃	—	2	1	no	—
247	D₅₃	#2155	1	2	yes	direct product factor
248	C₂²×M₁₆	—	106	1	no	—
249	C₂³×C₈	—	53	1	no	—
250	C₂×#117	—	106	1	no	—
251	C₂×M₃₂	—	53	1	no	—
252	C₂×M₃₂	—	53	2	no	—
253	C₂×M₃₂	—	53	2	no	—
254	C₂×M₃₂	—	53	2	no	—
255	C₂×M₃₂	—	53	2	no	—
256	C₂×M₃₂	—	53	2	no	—
257	C₂×M₃₂	C₂×D₅₃	1	1	yes	characteristic
258	C₂²×C₁₆	—	53	2	no	—
259	C₂×#108	—	53	1	no	—
260	C₂×#108	—	53	2	no	—
261	C₂×#108	—	53	2	no	—
262	C₂×#108	—	106	1	no	—
263	C₂×#108	—	106	1	no	—
264	C₂×#108	—	106	1	no	—
265	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
266	#427	—	53	1	no	—
267	#427	—	53	2	no	—
268	#427	—	106	1	no	—
269	#427	—	106	1	no	—
270	#427	C₂×D₅₃	1	1	yes	characteristic
271	C₂×#107	—	106	1	no	—
272	C₂×#106	—	53	2	no	—
273	#365	—	53	4	no	—
274	#365	—	53	4	no	—
275	#365	—	53	4	no	—
276	#365	C₂×D₅₃	1	4	yes	complemented
277	C₅₃	C₂×#2155	1	1	yes	characteristic, complemented, Sylow
278	C₂³×C₄	—	53	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	106	2	no	—
281	C₂×M₁₆	—	106	2	no	—
282	C₂×M₁₆	—	106	1	no	—
283	C₂×M₁₆	—	212	1	no	—
284	C₂×M₁₆	—	212	1	no	—
285	C₂×M₁₆	—	212	1	no	—
286	C₂²×C₈	—	53	1	no	—
287	C₂²×C₈	—	53	1	no	—
288	C₂²×C₈	—	53	1	no	—
289	C₂²×C₈	—	53	1	no	—
290	C₂²×C₈	—	53	1	no	—
291	C₂²×C₈	—	53	1	no	—
292	C₂²×C₈	—	53	1	no	—
293	C₂²×C₈	—	53	1	no	—
294	C₂²×C₈	—	53	1	no	—
295	C₂²×C₈	—	53	1	no	—
296	C₂²×C₈	—	53	1	no	—
297	C₂²×C₈	—	53	1	no	—
298	C₂²×C₈	—	53	1	no	—
299	C₂²×C₈	—	212	1	no	—
300	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
301	#117	—	2	1	no	—
302	#117	—	106	2	no	—
303	#117	—	106	1	no	—
304	#117	—	212	1	no	—
305	#117	—	212	1	no	—
306	C₂×C₄⋊C₄	—	106	2	no	—
307	C₂×C₂²⋊C₄	—	212	1	no	—
308	C₂×C₄²	—	212	1	no	—
309	M₃₂	—	53	2	no	—
310	M₃₂	—	53	2	no	—
311	M₃₂	—	53	4	no	—
312	M₃₂	—	53	4	no	—
313	M₃₂	C₄×D₅₃	1	2	yes	complemented
314	M₃₂	C₂²×D₅₃	1	2	yes	—
315	C₂×C₁₆	—	53	2	no	—
316	C₂×C₁₆	—	53	4	no	—
317	C₂×C₁₆	—	53	4	no	—
318	C₂×C₁₆	C₄×D₅₃	1	2	yes	complemented
319	#108	—	2	1	no	—
320	#108	—	53	2	no	—
321	#108	—	106	2	no	—
322	#108	—	106	2	no	—
323	#108	—	106	1	no	—
324	#108	C₂²×D₅₃	1	2	yes	—
325	#107	—	2	1	no	—
326	#107	—	106	2	no	—
327	#107	—	106	1	no	—
328	#106	—	53	2	no	—
329	#106	—	106	2	no	—
330	#106	C₂²×D₅₃	1	2	yes	—
331	C₂⁴	—	53	1	no	—
332	C₂²×C₄	—	53	1	no	—
333	C₂²×C₄	—	53	1	no	—
334	C₂²×C₄	—	53	1	no	—
335	C₂²×C₄	—	53	1	no	—
336	C₂²×C₄	—	53	1	no	—
337	C₂²×C₄	—	53	1	no	—
338	C₂²×C₄	—	53	1	no	—
339	C₂²×C₄	—	53	1	no	—
340	C₂²×C₄	—	53	1	no	—
341	C₂²×C₄	—	53	1	no	—
342	C₂²×C₄	—	53	1	no	—
343	C₂²×C₄	—	53	1	no	—
344	C₂²×C₄	—	53	1	no	—
345	C₂²×C₄	—	212	2	no	—
346	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
347	M₁₆	—	2	2	no	—
348	M₁₆	—	4	1	no	—
349	M₁₆	—	106	2	no	—
350	M₁₆	—	212	2	no	—
351	M₁₆	—	212	2	no	—
352	M₁₆	—	212	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	53	1	no	—
355	C₂×C₈	—	53	1	no	—
356	C₂×C₈	—	53	1	no	—
357	C₂×C₈	—	53	1	no	—
358	C₂×C₈	—	53	1	no	—
359	C₂×C₈	—	53	1	no	—
360	C₂×C₈	—	53	1	no	—
361	C₂×C₈	—	53	1	no	—
362	C₂×C₈	—	53	1	no	—
363	C₂×C₈	—	53	1	no	—
364	C₂×C₈	—	53	1	no	—
365	C₂×C₈	—	53	1	no	—
366	C₂×C₈	—	53	1	no	—
367	C₂×C₈	—	53	1	no	—
368	C₂×C₈	—	53	1	no	—
369	C₂×C₈	—	53	1	no	—
370	C₂×C₈	—	53	1	no	—
371	C₂×C₈	—	53	1	no	—
372	C₂×C₈	—	53	1	no	—
373	C₂×C₈	—	53	1	no	—
374	C₂×C₈	—	53	1	no	—
375	C₂×C₈	—	53	1	no	—
376	C₂×C₈	—	212	2	no	—
377	C₂×C₈	—	212	2	no	—
378	C₂×C₈	—	212	1	no	—
379	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
380	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
381	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
382	C₂×C₈	Q₈×D₅₃	1	1	yes	characteristic
383	C₂×C₈	Q₈×D₅₃	1	1	yes	characteristic
384	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	106	2	no	—
387	C₄⋊C₄	—	212	2	no	—
388	C₂²⋊C₄	—	4	1	no	—
389	C₂²⋊C₄	—	212	2	no	—
390	C₂²⋊C₄	—	212	1	no	—
391	C₄²	—	4	1	no	—
392	C₄²	—	212	2	no	—
393	C₄²	—	212	1	no	—
394	C₁₆	—	53	4	no	—
395	C₁₆	C₂×C₄×D₅₃	1	4	yes	—
396	C₂³	—	53	1	no	—
397	C₂³	—	53	1	no	—
398	C₂³	—	53	1	no	—
399	C₂³	—	53	1	no	—
400	C₂³	—	53	1	no	—
401	C₂³	—	53	1	no	—
402	C₂³	—	212	2	no	—
403	C₂³	SD₁₆×D₅₃	1	1	yes	characteristic
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	53	1	no	—
406	C₂×C₄	—	53	1	no	—
407	C₂×C₄	—	53	1	no	—
408	C₂×C₄	—	53	1	no	—
409	C₂×C₄	—	53	1	no	—
410	C₂×C₄	—	53	1	no	—
411	C₂×C₄	—	53	1	no	—
412	C₂×C₄	—	53	1	no	—
413	C₂×C₄	—	53	1	no	—
414	C₂×C₄	—	53	1	no	—
415	C₂×C₄	—	53	1	no	—
416	C₂×C₄	—	53	1	no	—
417	C₂×C₄	—	53	1	no	—
418	C₂×C₄	—	53	1	no	—
419	C₂×C₄	—	53	1	no	—
420	C₂×C₄	—	53	1	no	—
421	C₂×C₄	—	53	1	no	—
422	C₂×C₄	—	53	1	no	—
423	C₂×C₄	—	53	1	no	—
424	C₂×C₄	—	53	1	no	—
425	C₂×C₄	—	53	1	no	—
426	C₂×C₄	—	53	1	no	—
427	C₂×C₄	—	424	4	no	—
428	C₂×C₄	—	212	2	no	—
429	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
430	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
431	C₂×C₄	SD₁₆×D₅₃	1	1	yes	characteristic
432	C₂×C₄	SD₁₆×D₅₃	1	1	yes	characteristic
433	C₂×C₄	SD₁₆×D₅₃	1	1	yes	characteristic
434	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
435	C₈	—	4	2	no	—
436	C₈	—	53	1	no	—
437	C₈	—	53	1	no	—
438	C₈	—	53	1	no	—
439	C₈	—	53	1	no	—
440	C₈	—	212	2	no	—
441	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
442	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
443	C₈	C₂²×C₄×D₅₃	1	1	yes	characteristic
444	C₈	C₂×Q₈×D₅₃	1	1	yes	characteristic
445	C₂²	—	4	1	no	—
446	C₂²	—	53	1	no	—
447	C₂²	—	53	1	no	—
448	C₂²	—	53	1	no	—
449	C₂²	—	53	1	no	—
450	C₂²	—	106	2	no	—
451	C₂²	—	106	2	no	—
452	C₂²	—	106	2	no	—
453	C₂²	—	212	1	no	—
454	C₂²	—	212	1	no	—
455	C₂²	—	212	1	no	—
456	C₂²	#106×D₅₃	1	1	yes	characteristic
457	C₂²	#106×D₅₃	1	1	yes	characteristic
458	C₂²	C₂×SD₁₆×D₅₃	1	1	yes	characteristic
459	C₄	—	8	2	no	—
460	C₄	—	53	1	no	—
461	C₄	—	53	1	no	—
462	C₄	—	53	1	no	—
463	C₄	—	53	1	no	—
464	C₄	—	424	2	no	—
465	C₄	#106×D₅₃	1	1	yes	characteristic
466	C₄	#106×D₅₃	1	1	yes	characteristic
467	C₄	C₂×C₄⋊C₄×D₅₃	1	1	yes	characteristic
468	C₄	C₂×SD₁₆×D₅₃	1	1	yes	characteristic
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	—	2	1	no	—
472	C₂	—	53	2	no	—
473	C₂	—	106	1	no	—
474	C₂	—	106	1	no	—
475	C₂	—	106	1	no	—
476	C₂	C₂×#106×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#106×D₅₃
commutator	C₈×C₅₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₅₃×#2155	C₂
socle	C₂×C₅₃	C₂²×#106
prime radical	C₂³×D₅₃	SD₁₆
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	#2155	D₅₃
hypocenter	C₅₃	C₂×#2155
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2155

Complements

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

N	H ≅ G/N	type
4. #20276489	C₂	semidirect
5. #20276488	C₂	semidirect
6. #20276487	C₂	semidirect
7. #20276486	C₂	semidirect
8. #365×D₅₃	C₂	semidirect
9. C₅₃×#2155	C₂	semidirect
14. C₂×#13133156	C₄	semidirect
15. M₃₂×D₅₃	C₄	semidirect
16. M₃₂×D₅₃	C₄	semidirect
19. C₂×C₁₆×D₅₃	C₄	semidirect
32. #16810447	C₂²	semidirect
33. #16810446	C₂²	semidirect
34. #16810445	C₂²	semidirect
38. C₅₃×#365	C₂²	semidirect
67. #13133157	C₂×C₄	semidirect
70. #13133156	C₂×C₄	semidirect
71. C₂×#11719908	C₂×C₄	semidirect
73. C₁₆×D₅₃	C₂×C₄	semidirect
85. M₃₂×C₅₃	C₂×C₄	semidirect
87. C₂×C₁₆×C₅₃	C₂×C₄	semidirect
238. #2155	D₅₃	direct (N × H)
247. D₅₃	#2155	direct (N × H)
276. #365	C₂×D₅₃	semidirect
277. C₅₃	C₂×#2155	semidirect
313. M₃₂	C₄×D₅₃	semidirect
318. C₂×C₁₆	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×M₃₂×D₅₃	2
C₂×#108×D₅₃	2
#427×D₅₃	2
#20276489	2
#20276488	2
#20276487	2
#20276486	2
#365×D₅₃	2
C₅₃×#2155	2
C₂×#2155	53

Subgroups — D53×#2155 #27537101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2155 #27537101