Subgroups — D₅₃×#1946 #27387503

Order 13568.

934 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	C₂×#108×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#427×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#424×D₅₃	C₂	1	2	yes	maximal
4	C₂×#97×D₅₃	C₂	1	1	yes	maximal, characteristic
5	#20275469	C₂	1	1	yes	maximal, characteristic, complemented
6	#20275468	C₂	1	1	yes	maximal, characteristic, complemented
7	#20275467	C₂	1	2	yes	maximal, complemented
8	#20275466	C₂	1	1	yes	maximal, characteristic, complemented
9	#20275465	C₂	1	2	yes	maximal, complemented
10	#339×D₅₃	C₂	1	2	yes	maximal
11	C₅₃×#1946	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
13	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
15	#117×D₅₃	C₂²	1	2	yes	—
16	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
17	C₂×#13133153	C₂²	1	1	yes	characteristic
18	C₂×#13133152	C₂²	1	2	yes	—
19	#108×D₅₃	—	2	4	no	—
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	#16810651	C₂²	1	2	yes	—
27	#16810650	C₂²	1	2	yes	—
28	#16810649	C₂²	1	2	yes	—
29	#16810648	—	2	4	no	—
30	C₄⋊C₈×D₅₃	—	2	4	no	—
31	C₂×#13133128	C₂²	1	1	yes	characteristic
32	C₂×#13133127	C₂²	1	1	yes	characteristic
33	C₂×#13133127	C₂²	1	1	yes	characteristic
34	#97×D₅₃	—	2	4	no	—
35	#16810384	C₂²	1	2	yes	—
36	#16810383	C₂²	1	2	yes	—
37	#16810382	C₂²	1	2	yes	—
38	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
39	C₅₃×#427	C₂²	1	1	yes	characteristic
40	C₅₃×#424	C₂²	1	2	yes	—
41	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
42	C₅₃×#339	C₂²	1	2	yes	—
43	C₂²×C₄×D₅₃	—	2	1	no	—
44	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
45	C₂×#11719917	C₂³	1	2	yes	—
46	C₂×#11719912	—	2	2	no	—
47	M₁₆×D₅₃	—	2	4	no	—
48	M₁₆×D₅₃	—	2	4	no	—
49	C₂²×#88322	C₂³	1	1	yes	characteristic
50	C₂²×#88322	C₂³	1	1	yes	characteristic
51	C₂×C₈×D₅₃	—	2	2	no	—
52	C₂×C₈×D₅₃	—	2	2	no	—
53	C₂×C₈×D₅₃	—	2	2	no	—
54	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₅₃	D₄	1	2	yes	—
59	C₂×C₈×D₅₃	D₄	1	2	yes	—
60	C₂×C₈×D₅₃	D₄	1	4	yes	—
61	C₂×C₈×D₅₃	Q₈	1	4	yes	—
62	#13133176	C₂³	1	2	yes	—
63	#13133175	C₂×C₄	1	4	yes	—
64	#13133174	—	2	2	no	—
65	#13133173	—	2	2	no	—
66	C₄⋊C₄×D₅₃	C₂×C₄	1	4	yes	—
67	C₂²⋊C₄×D₅₃	—	2	2	no	—
68	C₂×C₄×Dic₅₃	—	2	1	no	—
69	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
70	C₄²×D₅₃	—	2	2	no	—
71	C₄²×D₅₃	—	2	2	no	—
72	C₄²×D₅₃	Q₈	1	4	yes	—
73	#13133153	—	2	2	no	—
74	#13133152	—	2	4	no	—
75	#13133151	C₂×C₄	1	2	yes	complemented
76	#13133150	C₂×C₄	1	4	yes	complemented
77	#13133149	C₂×C₄	1	2	yes	complemented
78	#13133148	C₂×C₄	1	4	yes	complemented
79	C₄⋊#88322	—	2	4	no	—
80	#13133146	—	2	4	no	—
81	#13133146	—	2	4	no	—
82	#13133128	—	2	2	no	—
83	#13133127	—	2	2	no	—
84	#13133127	—	2	2	no	—
85	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
86	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
88	#117×C₅₃	C₂³	1	2	yes	—
89	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
90	#108×C₅₃	—	2	2	no	—
91	#107×C₅₃	C₂×C₄	1	2	yes	complemented
92	#106×C₅₃	C₂×C₄	1	2	yes	complemented
93	C₄⋊C₈×C₅₃	—	2	4	no	—
94	#97×C₅₃	—	2	2	no	—
95	C₂³×D₅₃	#41	1	1	yes	characteristic
96	C₂²×C₄×C₅₃	—	2	1	no	—
97	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
98	C₂²×Dic₅₃	—	2	1	no	—
99	C₂²×Dic₅₃	#41	1	1	yes	characteristic
100	C₂×C₄×D₅₃	—	2	4	no	—
101	C₂×C₄×D₅₃	—	2	4	no	—
102	C₂×C₄×D₅₃	—	4	4	no	—
103	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
106	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×D₅₃	C₂×Q₈	1	2	yes	—
109	C₂×C₄×D₅₃	C₂×Q₈	1	2	yes	—
110	C₂×C₄×D₅₃	#41	1	2	yes	—
111	M₁₆×C₅₃	—	2	2	no	—
112	M₁₆×C₅₃	—	2	2	no	—
113	C₂×C₈×C₅₃	—	2	1	no	—
114	C₂×C₈×C₅₃	—	2	1	no	—
115	C₂×C₈×C₅₃	—	2	2	no	—
116	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₅₃	C₂×Q₈	1	2	yes	—
121	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
122	C₂²⋊C₄×C₅₃	—	2	2	no	—
123	C₄²×C₅₃	—	2	1	no	—
124	C₄²×C₅₃	—	2	2	no	—
125	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
126	C₂²⋊Dic₅₃	—	2	2	no	—
127	#11719921	—	2	4	no	—
128	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
129	#11719919	—	2	4	no	—
130	C₄×Dic₅₃	—	2	1	no	—
131	C₄×Dic₅₃	—	2	2	no	—
132	C₄×Dic₅₃	—	2	4	no	—
133	C₄×Dic₅₃	—	2	4	no	—
134	C₄×Dic₅₃	C₂×Q₈	1	2	yes	—
135	#11719917	—	2	2	no	—
136	#11719917	—	2	2	no	—
137	C₂×#88322	—	2	1	no	—
138	C₂×#88322	—	2	1	no	—
139	C₂×#88322	—	2	2	no	—
140	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
141	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
142	C₂×#88322	C₂×D₄	1	2	yes	—
143	C₂×#88322	C₂×D₄	1	2	yes	—
144	C₂×#88322	C₂×Q₈	1	2	yes	—
145	#11719912	—	4	4	no	—
146	C₈×D₅₃	—	2	4	no	—
147	C₈×D₅₃	—	2	4	no	—
148	C₈×D₅₃	—	4	4	no	—
149	C₈×D₅₃	C₄⋊C₄	1	4	yes	—
150	C₈×D₅₃	C₄⋊C₄	1	4	yes	—
151	C₈×D₅₃	C₄⋊C₄	1	4	yes	—
152	C₈×D₅₃	C₄⋊C₄	1	4	yes	—
153	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
154	C₂²×D₅₃	—	2	4	no	—
155	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
156	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
157	C₂²×D₅₃	C₂²⋊Q₈	1	2	yes	—
158	C₂²×D₅₃	#125	1	2	yes	—
159	C₂×C₄×C₅₃	—	2	4	no	—
160	C₂×C₄×C₅₃	—	2	2	no	—
161	C₂×C₄×C₅₃	—	4	2	no	—
162	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
168	C₂×Dic₅₃	—	2	4	no	—
169	C₂×Dic₅₃	—	2	2	no	—
170	C₂×Dic₅₃	—	4	2	no	—
171	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
172	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
173	C₂×Dic₅₃	C₂²⋊Q₈	1	2	yes	—
174	C₂×Dic₅₃	#125	1	2	yes	—
175	C₄×D₅₃	—	4	8	no	—
176	C₄×D₅₃	—	4	8	no	—
177	C₄×D₅₃	C₂×C₄⋊C₄	1	2	yes	—
178	C₄×D₅₃	C₂×C₄⋊C₄	1	2	yes	—
179	C₄×D₅₃	C₄×Q₈	1	2	yes	—
180	C₄×D₅₃	C₄×Q₈	1	2	yes	—
181	C₄×D₅₃	#121	1	2	yes	—
182	C₄×D₅₃	#121	1	2	yes	—
183	C₄×D₅₃	C₄⋊Q₈	1	2	yes	—
184	C₄×D₅₃	C₄⋊Q₈	1	2	yes	—
185	C₈×C₅₃	—	2	2	no	—
186	C₈×C₅₃	—	4	2	no	—
187	C₈×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
188	C₈×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
189	#88322	—	2	2	no	—
190	#88322	—	4	2	no	—
191	#88322	C₂×C₄⋊C₄	1	2	yes	—
192	#88322	C₂×C₄⋊C₄	1	2	yes	—
193	C₂×#1946	—	53	1	no	maximal, Sylow
194	C₂²×C₅₃	—	2	2	no	—
195	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂²×C₅₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
197	C₂²×C₅₃	C₂×#125	1	1	yes	characteristic
198	C₂×D₅₃	—	2	2	no	—
199	C₂×D₅₃	—	2	4	no	—
200	C₂×D₅₃	—	2	4	no	—
201	C₂×D₅₃	#389	1	2	yes	—
202	C₂×D₅₃	#389	1	2	yes	—
203	C₂×D₅₃	#444	1	4	yes	—
204	C₄×C₅₃	—	4	2	no	—
205	C₄×C₅₃	—	4	4	no	—
206	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
207	C₄×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
208	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
209	C₄×C₅₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
210	Dic₅₃	—	4	2	no	—
211	Dic₅₃	—	4	4	no	—
212	Dic₅₃	#389	1	2	yes	—
213	Dic₅₃	#389	1	2	yes	—
214	C₂²×#108	—	53	1	no	—
215	C₂×#427	—	53	1	no	—
216	C₂×#424	—	53	2	no	—
217	C₂²×#97	—	53	1	no	—
218	#1946	—	53	1	no	—
219	#1946	—	53	1	no	—
220	#1946	—	53	2	no	—
221	#1946	—	53	1	no	—
222	#1946	—	53	2	no	—
223	#1946	D₅₃	1	1	yes	characteristic, direct product factor
224	C₂×#339	—	53	2	no	—
225	C₂×C₅₃	—	2	1	no	—
226	C₂×C₅₃	—	2	1	no	—
227	C₂×C₅₃	C₂×#389	1	1	yes	characteristic
228	C₂×C₅₃	C₂×#444	1	2	yes	—
229	D₅₃	—	2	2	no	—
230	D₅₃	#1946	1	4	yes	direct product factor
231	C₂²×M₁₆	—	53	2	no	—
232	C₂³×C₈	—	53	1	no	—
233	C₂³×C₈	—	53	1	no	—
234	C₂×#117	—	53	2	no	—
235	C₂²×C₄²	—	53	1	no	—
236	C₂×#108	—	53	2	no	—
237	C₂×#108	—	53	1	no	—
238	C₂×#108	—	106	4	no	—
239	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
240	#427	—	53	1	no	—
241	#427	—	53	2	no	—
242	#427	—	53	2	no	—
243	#427	—	53	2	no	—
244	#427	C₂×D₅₃	1	1	yes	characteristic
245	C₂×#107	—	53	2	no	—
246	C₂×#106	—	53	2	no	—
247	#424	—	53	2	no	—
248	#424	—	53	2	no	—
249	#424	—	53	2	no	—
250	#424	—	106	4	no	—
251	#424	C₂×D₅₃	1	2	yes	—
252	C₂×C₄⋊C₈	—	106	4	no	—
253	C₂×#97	—	53	1	no	—
254	C₂×#97	—	53	1	no	—
255	C₂×#97	—	53	1	no	—
256	C₂×#97	—	106	4	no	—
257	C₂×#97	C₂×D₅₃	1	1	yes	characteristic
258	#339	—	53	2	no	—
259	#339	—	53	2	no	—
260	#339	—	53	2	no	—
261	#339	C₂×D₅₃	1	2	yes	—
262	C₅₃	C₂×#1946	1	1	yes	characteristic, complemented, Sylow
263	C₂³×C₄	—	53	1	no	—
264	C₂³×C₄	—	106	1	no	—
265	C₂×M₁₆	—	53	2	no	—
266	C₂×M₁₆	—	106	2	no	—
267	C₂×M₁₆	—	106	4	no	—
268	C₂×M₁₆	—	106	4	no	—
269	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
270	C₂²×C₈	—	53	1	no	—
271	C₂²×C₈	—	53	1	no	—
272	C₂²×C₈	—	53	1	no	—
273	C₂²×C₈	—	53	1	no	—
274	C₂²×C₈	—	53	1	no	—
275	C₂²×C₈	—	53	4	no	—
276	C₂²×C₈	—	53	4	no	—
277	C₂²×C₈	—	53	1	no	—
278	C₂²×C₈	—	53	2	no	—
279	C₂²×C₈	—	53	2	no	—
280	C₂²×C₈	—	106	2	no	—
281	C₂²×C₈	—	106	2	no	—
282	C₂²×C₈	—	106	2	no	—
283	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
284	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
285	#117	—	53	2	no	—
286	#117	—	53	4	no	—
287	#117	—	106	2	no	—
288	#117	—	106	2	no	—
289	#117	C₂²×D₅₃	1	2	yes	—
290	C₂×C₄⋊C₄	—	53	4	no	—
291	C₂×C₂²⋊C₄	—	106	2	no	—
292	C₂×C₄²	—	53	1	no	—
293	C₂×C₄²	—	53	4	no	—
294	C₂×C₄²	—	106	2	no	—
295	C₂×C₄²	—	106	2	no	—
296	C₂×C₄²	—	106	1	no	—
297	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
298	#108	—	2	2	no	—
299	#108	—	106	4	no	—
300	#108	—	106	2	no	—
301	#107	—	53	2	no	—
302	#107	—	53	4	no	—
303	#107	C₄×D₅₃	1	2	yes	complemented
304	#106	—	53	2	no	—
305	#106	—	53	4	no	—
306	#106	C₄×D₅₃	1	2	yes	complemented
307	C₄⋊C₈	—	2	4	no	—
308	C₄⋊C₈	—	106	4	no	—
309	C₄⋊C₈	—	106	4	no	—
310	C₄⋊C₈	—	106	4	no	—
311	#97	—	2	2	no	—
312	#97	—	106	2	no	—
313	#97	—	106	2	no	—
314	#97	—	106	2	no	—
315	C₂⁴	—	53	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	53	1	no	—
318	C₂²×C₄	—	53	1	no	—
319	C₂²×C₄	—	53	1	no	—
320	C₂²×C₄	—	53	2	no	—
321	C₂²×C₄	—	53	1	no	—
322	C₂²×C₄	—	53	1	no	—
323	C₂²×C₄	—	53	2	no	—
324	C₂²×C₄	—	53	2	no	—
325	C₂²×C₄	—	53	2	no	—
326	C₂²×C₄	—	106	4	no	—
327	C₂²×C₄	—	106	4	no	—
328	C₂²×C₄	—	106	1	no	—
329	C₂²×C₄	—	212	4	no	—
330	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	106	2	no	—
334	M₁₆	—	106	2	no	—
335	M₁₆	—	212	4	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	53	1	no	—
340	C₂×C₈	—	53	1	no	—
341	C₂×C₈	—	53	2	no	—
342	C₂×C₈	—	53	2	no	—
343	C₂×C₈	—	53	4	no	—
344	C₂×C₈	—	53	4	no	—
345	C₂×C₈	—	53	4	no	—
346	C₂×C₈	—	53	4	no	—
347	C₂×C₈	—	53	2	no	—
348	C₂×C₈	—	106	4	no	—
349	C₂×C₈	—	106	4	no	—
350	C₂×C₈	—	106	1	no	—
351	C₂×C₈	—	106	1	no	—
352	C₂×C₈	—	106	2	no	—
353	C₂×C₈	—	212	4	no	—
354	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
355	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
356	C₂×C₈	D₄×D₅₃	1	2	yes	—
357	C₂×C₈	D₄×D₅₃	1	2	yes	—
358	C₂×C₈	Q₈×D₅₃	1	2	yes	—
359	C₄⋊C₄	—	53	4	no	—
360	C₄⋊C₄	—	106	4	no	—
361	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	—	106	4	no	—
364	C₂²⋊C₄	—	106	2	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	53	2	no	—
368	C₄²	—	106	4	no	—
369	C₄²	—	106	4	no	—
370	C₄²	—	106	1	no	—
371	C₄²	—	106	2	no	—
372	C₄²	Q₈×D₅₃	1	2	yes	—
373	C₂³	—	53	1	no	—
374	C₂³	—	53	1	no	—
375	C₂³	—	53	2	no	—
376	C₂³	—	53	2	no	—
377	C₂³	—	106	4	no	—
378	C₂³	#41×D₅₃	1	1	yes	characteristic
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	53	1	no	—
383	C₂×C₄	—	53	1	no	—
384	C₂×C₄	—	53	2	no	—
385	C₂×C₄	—	53	2	no	—
386	C₂×C₄	—	53	2	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	—	53	2	no	—
393	C₂×C₄	—	53	2	no	—
394	C₂×C₄	—	106	4	no	—
395	C₂×C₄	—	106	2	no	—
396	C₂×C₄	—	212	8	no	—
397	C₂×C₄	—	212	8	no	—
398	C₂×C₄	—	212	2	no	—
399	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
400	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
401	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
402	C₂×C₄	C₂×Q₈×D₅₃	1	1	yes	characteristic
403	C₂×C₄	C₂×Q₈×D₅₃	1	1	yes	characteristic
404	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	—	4	2	no	—
407	C₈	—	53	2	no	—
408	C₈	—	53	2	no	—
409	C₈	—	106	2	no	—
410	C₈	—	212	2	no	—
411	C₈	C₄⋊C₄×D₅₃	1	2	yes	—
412	C₈	C₄⋊C₄×D₅₃	1	2	yes	—
413	C₂²	—	2	2	no	—
414	C₂²	—	53	2	no	—
415	C₂²	—	53	4	no	—
416	C₂²	—	53	2	no	—
417	C₂²	—	106	4	no	—
418	C₂²	—	106	4	no	—
419	C₂²	—	106	2	no	—
420	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
421	C₂²	C₂²⋊Q₈×D₅₃	1	1	yes	characteristic
422	C₂²	#125×D₅₃	1	1	yes	characteristic
423	C₄	—	4	2	no	—
424	C₄	—	4	4	no	—
425	C₄	—	53	2	no	—
426	C₄	—	53	2	no	—
427	C₄	—	212	2	no	—
428	C₄	—	212	4	no	—
429	C₄	C₂×C₄⋊C₄×D₅₃	1	1	yes	characteristic
430	C₄	C₄×Q₈×D₅₃	1	1	yes	characteristic
431	C₄	#121×D₅₃	1	1	yes	characteristic
432	C₄	C₄⋊Q₈×D₅₃	1	1	yes	characteristic
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	53	4	no	—
436	C₂	—	106	2	no	—
437	C₂	#389×D₅₃	1	1	yes	characteristic
438	C₂	#444×D₅₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1946	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂³×D₅₃	#41
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1946	D₅₃
hypocenter	C₅₃	C₂×#1946
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1946

Complements

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

N	H ≅ G/N	type
5. #20275469	C₂	semidirect
6. #20275468	C₂	semidirect
7. #20275467	C₂	semidirect
8. #20275466	C₂	semidirect
9. #20275465	C₂	semidirect
11. C₅₃×#1946	C₂	semidirect
21. #16810660	C₄	semidirect
23. #16810658	C₄	semidirect
24. #107×D₅₃	C₄	semidirect
25. #106×D₅₃	C₄	semidirect
75. #13133151	C₂×C₄	semidirect
76. #13133150	C₂×C₄	semidirect
77. #13133149	C₂×C₄	semidirect
78. #13133148	C₂×C₄	semidirect
91. #107×C₅₃	C₂×C₄	semidirect
92. #106×C₅₃	C₂×C₄	semidirect
223. #1946	D₅₃	direct (N × H)
230. D₅₃	#1946	direct (N × H)
262. C₅₃	C₂×#1946	semidirect
303. #107	C₄×D₅₃	semidirect
306. #106	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
#424×D₅₃	2
C₂×#97×D₅₃	2
#20275469	2
#20275468	2
#20275467	2
#20275466	2
#20275465	2
#339×D₅₃	2
C₅₃×#1946	2
C₂×#1946	53

Subgroups — D53×#1946 #27387503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1946 #27387503