Subgroups — #27355514

Order 13568.

794 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#20283451	C₂	1	2	yes	maximal, complemented
3	#20273600	C₂	1	1	yes	maximal, characteristic, complemented
4	#20273547	C₂	1	2	yes	maximal, complemented
5	#20273542	C₂	1	2	yes	maximal, complemented
6	C₈×D₄₂₄	C₂	1	1	yes	maximal, characteristic, complemented
7	#20273509	C₂	1	1	yes	maximal, characteristic, complemented
8	#20273472	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273138	C₂	1	2	yes	maximal, complemented
10	C₈×#11719912	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₅₃	C₄	1	1	yes	characteristic
13	C₂×M₁₆×D₅₃	—	2	2	no	—
14	C₄×D₄×D₅₃	C₂²	1	2	yes	—
15	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
16	D₈×Dic₅₃	C₄	1	1	yes	characteristic
17	#16810705	C₄	1	1	yes	characteristic
18	C₄×#11719922	C₂²	1	2	yes	—
19	#16810703	C₄	1	2	yes	—
20	#16810701	C₂²	1	2	yes	complemented
21	#16810697	—	2	2	no	—
22	#16810692	—	2	2	no	—
23	C₈×D₂₁₂	C₂²	1	2	yes	complemented
24	#16810688	C₂²	1	2	yes	complemented
25	#16810674	C₂²	1	1	yes	characteristic
26	#107×D₅₃	C₄	1	1	yes	characteristic
27	#16810645	C₂²	1	2	yes	—
28	#102×D₅₃	C₄	1	2	yes	—
29	#16810585	—	2	2	no	—
30	C₄×#11719912	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
32	#16810376	C₂²	1	1	yes	characteristic, complemented
33	#16810375	C₂²	1	2	yes	complemented
34	#16810352	C₂²	1	2	yes	complemented
35	D₄⋊#88322	C₂²	1	2	yes	complemented
36	#16810350	C₂²	1	2	yes	complemented
37	#16810345	C₂²	1	1	yes	characteristic, complemented
38	#16810344	C₂²	1	1	yes	characteristic, complemented
39	C₈×#88322	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#436	C₂²	1	2	yes	complemented
42	C₅₃×#335	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×D₄⋊C₈	C₂²	1	2	yes	complemented
44	C₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₅₃	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₅₃	—	2	2	no	—
47	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
48	C₂×#11719922	C₂×C₄	1	2	yes	—
49	D₈×D₅₃	—	2	4	no	—
50	C₂×#11719917	—	2	2	no	—
51	C₂×#11719912	—	2	2	no	—
52	C₂×#11719912	D₄	1	1	yes	characteristic
53	C₂×#11719912	D₄	1	1	yes	characteristic
54	M₁₆×D₅₃	—	4	8	no	—
55	C₂×C₈×D₅₃	—	2	2	no	—
56	C₂×C₈×D₅₃	—	2	2	no	—
57	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
59	C₄×D₂₁₂	C₂³	1	2	yes	—
60	D₄×Dic₅₃	C₂×C₄	1	2	yes	—
61	#13133179	C₂×C₄	1	2	yes	—
62	C₄×C₂²⋊D₅₃	—	2	2	no	—
63	#13133177	—	2	2	no	—
64	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
65	C₂²⋊C₄×D₅₃	—	2	2	no	—
66	C₄²×D₅₃	C₂³	1	1	yes	characteristic
67	#13133151	C₂×C₄	1	1	yes	characteristic
68	#13133150	C₂×C₄	1	2	yes	—
69	C₄⋊#88322	C₂³	1	2	yes	—
70	#13133146	—	2	2	no	—
71	#13133146	—	2	1	no	—
72	#13133139	C₂×C₄	1	2	yes	—
73	#13133138	C₂×C₄	1	2	yes	—
74	#13133137	C₂×C₄	1	2	yes	—
75	C₂²⋊#88322	—	2	2	no	—
76	#13133129	—	2	2	no	—
77	#13133129	—	2	2	no	—
78	#13133129	—	2	1	no	—
79	#13133127	D₄	1	1	yes	characteristic
80	#13133127	D₄	1	1	yes	characteristic
81	C₄×#88322	C₂³	1	1	yes	characteristic
82	C₄×#88322	C₂³	1	1	yes	characteristic
83	C₄×#88322	C₂³	1	1	yes	characteristic
84	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
86	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
87	C₂×M₁₆×C₅₃	—	2	2	no	—
88	C₄×D₄×C₅₃	C₂³	1	2	yes	—
89	#107×C₅₃	C₂×C₄	1	1	yes	characteristic
90	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
91	#102×C₅₃	C₂×C₄	1	2	yes	—
92	C₂²⋊C₈×C₅₃	—	2	2	no	—
93	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
96	C₂³×D₅₃	—	2	2	no	—
97	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₅₃	—	2	2	no	—
99	C₂×C₂²⋊D₅₃	—	2	2	no	—
100	C₂²×Dic₅₃	—	2	2	no	—
101	D₄×D₅₃	—	2	4	no	—
102	D₄×D₅₃	—	4	2	no	—
103	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₅₃	—	2	2	no	—
105	C₂×C₄×D₅₃	—	2	2	no	—
106	C₂×C₄×D₅₃	—	2	2	no	—
107	C₂×C₄×D₅₃	—	4	4	no	—
108	C₂×C₄×D₅₃	—	4	4	no	—
109	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
112	D₈×C₅₃	—	2	2	no	—
113	M₁₆×C₅₃	—	4	4	no	—
114	C₂×C₈×C₅₃	—	2	2	no	—
115	C₂×C₈×C₅₃	—	2	1	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	1	yes	characteristic
119	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
121	C₂²⋊C₄×C₅₃	—	2	2	no	—
122	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
123	C₂²⋊Dic₅₃	—	2	2	no	—
124	#11719922	—	2	4	no	—
125	#11719921	—	2	2	no	—
126	#11719921	—	2	2	no	—
127	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
128	#11719919	—	2	2	no	—
129	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
131	C₄×Dic₅₃	#41	1	1	yes	characteristic
132	#11719917	—	4	4	no	—
133	C₂×#88322	—	2	2	no	—
134	C₂×#88322	—	2	1	no	—
135	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
136	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
137	C₂×#88322	C₂×D₄	1	1	yes	characteristic
138	C₂×#88322	C₂×D₄	1	1	yes	characteristic
139	D₄₂₄	M₁₆	1	4	yes	complemented
140	#11719912	—	2	2	no	—
141	#11719912	—	4	4	no	—
142	#11719912	D₈	1	4	yes	complemented
143	C₈×D₅₃	—	2	2	no	—
144	C₈×D₅₃	—	4	1	no	—
145	C₈×D₅₃	—	4	4	no	—
146	C₈×D₅₃	—	4	4	no	—
147	C₂³×C₅₃	—	2	2	no	—
148	C₂²×D₅₃	—	2	2	no	—
149	C₂²×D₅₃	—	4	4	no	—
150	C₂²×D₅₃	—	4	4	no	—
151	C₂²×D₅₃	—	8	2	no	—
152	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
153	D₄×C₅₃	—	2	2	no	—
154	D₄×C₅₃	—	2	2	no	—
155	C₂×C₄×C₅₃	—	2	2	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	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
161	C₂²⋊D₅₃	—	4	4	no	—
162	C₂×Dic₅₃	—	2	2	no	—
163	C₂×Dic₅₃	—	4	4	no	—
164	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
165	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
166	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
167	D₂₁₂	—	2	2	no	—
168	D₂₁₂	C₂×M₁₆	1	4	yes	complemented
169	C₄×D₅₃	—	2	1	no	—
170	C₄×D₅₃	—	2	1	no	—
171	C₄×D₅₃	—	4	1	no	—
172	C₄×D₅₃	—	4	4	no	—
173	C₄×D₅₃	—	4	2	no	—
174	C₄×D₅₃	—	4	2	no	—
175	C₄×D₅₃	—	4	4	no	—
176	C₄×D₅₃	C₂×D₈	1	2	yes	—
177	C₄×D₅₃	#135	1	2	yes	—
178	C₈×C₅₃	—	2	1	no	—
179	C₈×C₅₃	—	2	1	no	—
180	C₈×C₅₃	—	4	1	no	—
181	C₈×C₅₃	—	4	2	no	—
182	C₈×C₅₃	C₂×M₁₆	1	2	yes	complemented
183	C₈×C₅₃	C₂×D₈	1	2	yes	complemented
184	#88322	—	2	1	no	—
185	#88322	—	2	1	no	—
186	#88322	—	2	1	no	—
187	#88322	—	4	1	no	—
188	#88322	—	4	2	no	—
189	#88322	C₂×D₈	1	2	yes	complemented
190	M₁₆×D₈	—	53	1	no	maximal, Sylow
191	C₂²×C₅₃	—	4	2	no	—
192	C₂²×C₅₃	—	4	2	no	—
193	C₂²×C₅₃	—	4	2	no	—
194	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂×D₅₃	—	2	1	no	—
196	C₂×D₅₃	—	2	1	no	—
197	C₂×D₅₃	—	2	4	no	—
198	C₂×D₅₃	—	4	2	no	—
199	C₂×D₅₃	—	4	2	no	—
200	C₂×D₅₃	—	8	8	no	—
201	C₂×D₅₃	C₄×D₈	1	2	yes	—
202	C₄×C₅₃	—	2	1	no	—
203	C₄×C₅₃	—	4	2	no	—
204	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
205	C₄×C₅₃	#568	1	1	yes	characteristic
206	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
207	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
208	Dic₅₃	—	2	1	no	—
209	Dic₅₃	—	2	1	no	—
210	Dic₅₃	—	4	2	no	—
211	Dic₅₃	C₄×D₈	1	2	yes	—
212	C₂×C₄×D₈	—	53	1	no	—
213	D₄×M₁₆	—	53	2	no	—
214	#1589	—	53	1	no	—
215	#1589	D₅₃	1	1	yes	characteristic, complemented
216	#1581	—	53	2	no	—
217	#1581	—	53	2	no	—
218	C₈×D₈	—	53	1	no	—
219	C₈×D₈	—	53	1	no	—
220	#1567	—	53	1	no	—
221	#1486	—	53	2	no	—
222	C₈×M₁₆	—	53	1	no	—
223	C₂×C₅₃	—	8	2	no	—
224	C₂×C₅₃	D₄×M₁₆	1	1	yes	characteristic
225	C₂×C₅₃	C₂×C₄×D₈	1	1	yes	characteristic
226	C₂×C₅₃	#2957	1	1	yes	characteristic
227	D₅₃	—	2	2	no	—
228	D₅₃	—	4	4	no	—
229	C₂²×D₈	—	53	1	no	—
230	C₂²×M₁₆	—	106	2	no	—
231	C₂×C₄×D₄	—	53	2	no	—
232	C₄×D₈	—	53	1	no	—
233	C₄×D₈	—	53	2	no	—
234	C₄×D₈	—	53	1	no	—
235	C₄×D₈	—	53	2	no	—
236	C₄×D₈	—	53	1	no	—
237	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic
238	#436	—	53	2	no	—
239	#436	C₂×D₅₃	1	2	yes	complemented
240	#435	—	106	2	no	—
241	#435	—	106	2	no	—
242	C₈×D₄	—	53	2	no	—
243	C₈×D₄	—	53	2	no	—
244	#431	—	53	1	no	—
245	C₂×#107	—	53	1	no	—
246	#423	—	53	2	no	—
247	C₂×#102	—	53	2	no	—
248	#407	—	106	2	no	—
249	C₄×M₁₆	—	53	1	no	—
250	C₂×C₄×C₈	—	53	1	no	—
251	#335	—	53	2	no	—
252	#335	—	53	1	no	—
253	#335	C₂×D₅₃	1	1	yes	characteristic, complemented
254	D₄⋊C₈	—	53	2	no	—
255	D₄⋊C₈	—	53	2	no	—
256	D₄⋊C₈	—	53	2	no	—
257	D₄⋊C₈	C₂×D₅₃	1	2	yes	complemented
258	#322	—	53	1	no	—
259	#322	—	53	1	no	—
260	C₈²	—	53	1	no	—
261	C₈²	C₂×D₅₃	1	1	yes	characteristic, complemented
262	C₅₃	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
263	C₂²×D₄	—	53	2	no	—
264	C₂³×C₄	—	106	2	no	—
265	C₂×D₈	—	53	2	no	—
266	C₂×D₈	—	53	1	no	—
267	C₂×D₈	—	106	4	no	—
268	C₂×D₈	C₄×D₅₃	1	1	yes	characteristic
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	53	1	no	—
271	C₂×M₁₆	—	53	1	no	—
272	C₂×M₁₆	—	106	2	no	—
273	C₂×M₁₆	—	106	2	no	—
274	C₂×M₁₆	—	212	8	no	—
275	C₂²×C₈	—	53	1	no	—
276	C₂²×C₈	—	53	1	no	—
277	C₂²×C₈	—	106	2	no	—
278	C₂²×C₈	—	106	2	no	—
279	C₄×D₄	—	53	2	no	—
280	C₄×D₄	—	53	2	no	—
281	C₄×D₄	—	53	2	no	—
282	C₄×D₄	—	106	2	no	—
283	C₄×D₄	—	106	2	no	—
284	C₄×D₄	C₂²×D₅₃	1	2	yes	—
285	C₂×C₄⋊C₄	—	53	2	no	—
286	C₂×C₂²⋊C₄	—	106	2	no	—
287	C₂×C₄²	—	53	1	no	—
288	#107	—	53	1	no	—
289	#107	—	53	2	no	—
290	#107	C₄×D₅₃	1	1	yes	characteristic
291	C₄⋊C₈	—	53	2	no	—
292	C₄⋊C₈	—	106	2	no	—
293	C₄⋊C₈	—	106	1	no	—
294	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
295	#102	—	53	2	no	—
296	#102	—	53	2	no	—
297	#102	—	53	2	no	—
298	#102	C₄×D₅₃	1	2	yes	—
299	C₂²⋊C₈	—	2	2	no	—
300	C₂²⋊C₈	—	106	2	no	—
301	C₂²⋊C₈	—	106	1	no	—
302	C₂²⋊C₈	—	106	2	no	—
303	C₂²⋊C₈	—	106	2	no	—
304	#97	—	53	1	no	—
305	#97	—	53	1	no	—
306	C₄×C₈	—	53	1	no	—
307	C₄×C₈	—	53	1	no	—
308	C₄×C₈	—	53	1	no	—
309	C₄×C₈	—	53	1	no	—
310	C₄×C₈	—	53	1	no	—
311	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
314	C₂⁴	—	106	2	no	—
315	C₂×D₄	—	53	2	no	—
316	C₂×D₄	—	106	2	no	—
317	C₂×D₄	—	106	4	no	—
318	C₂×D₄	—	212	2	no	—
319	C₂×D₄	C₂×C₄×D₅₃	1	2	yes	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	53	1	no	—
322	C₂²×C₄	—	53	1	no	—
323	C₂²×C₄	—	53	1	no	—
324	C₂²×C₄	—	106	2	no	—
325	C₂²×C₄	—	106	2	no	—
326	C₂²×C₄	—	106	2	no	—
327	C₂²×C₄	—	106	2	no	—
328	C₂²×C₄	—	212	4	no	—
329	C₂²×C₄	—	212	4	no	—
330	D₈	—	2	2	no	—
331	D₈	—	53	4	no	—
332	D₈	—	106	4	no	—
333	M₁₆	—	4	4	no	—
334	M₁₆	—	53	4	no	—
335	M₁₆	—	106	2	no	—
336	M₁₆	—	212	4	no	—
337	M₁₆	—	212	4	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	53	1	no	—
341	C₂×C₈	—	53	1	no	—
342	C₂×C₈	—	53	1	no	—
343	C₂×C₈	—	53	1	no	—
344	C₂×C₈	—	106	2	no	—
345	C₂×C₈	—	106	2	no	—
346	C₂×C₈	—	106	1	no	—
347	C₂×C₈	—	212	1	no	—
348	C₂×C₈	—	212	4	no	—
349	C₂×C₈	—	212	4	no	—
350	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
351	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
352	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
353	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
354	C₄⋊C₄	—	53	2	no	—
355	C₄⋊C₄	—	106	2	no	—
356	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	106	2	no	—
359	C₂²⋊C₄	—	106	2	no	—
360	C₂²⋊C₄	—	106	2	no	—
361	C₄²	—	53	1	no	—
362	C₄²	—	53	1	no	—
363	C₄²	—	53	1	no	—
364	C₄²	C₂³×D₅₃	1	1	yes	characteristic
365	C₂³	—	2	2	no	—
366	C₂³	—	53	1	no	—
367	C₂³	—	106	2	no	—
368	C₂³	—	424	2	no	—
369	C₂³	—	212	4	no	—
370	C₂³	—	212	4	no	—
371	D₄	—	2	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	53	4	no	—
374	D₄	—	106	2	no	—
375	D₄	—	212	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	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	—	106	1	no	—
385	C₂×C₄	—	106	1	no	—
386	C₂×C₄	—	106	2	no	—
387	C₂×C₄	—	212	1	no	—
388	C₂×C₄	—	212	4	no	—
389	C₂×C₄	—	212	4	no	—
390	C₂×C₄	—	212	4	no	—
391	C₂×C₄	—	212	2	no	—
392	C₂×C₄	—	212	2	no	—
393	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
394	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
395	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	2	no	—
400	C₈	—	53	2	no	—
401	C₈	—	106	1	no	—
402	C₈	—	106	1	no	—
403	C₈	—	106	1	no	—
404	C₈	—	212	1	no	—
405	C₈	—	212	2	no	—
406	C₈	M₁₆×D₅₃	1	2	yes	complemented
407	C₈	D₈×D₅₃	1	2	yes	complemented
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	53	2	no	—
412	C₂²	—	106	1	no	—
413	C₂²	—	106	1	no	—
414	C₂²	—	106	4	no	—
415	C₂²	—	424	8	no	—
416	C₂²	—	212	2	no	—
417	C₂²	—	212	2	no	—
418	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
419	C₄	—	2	1	no	—
420	C₄	—	4	2	no	—
421	C₄	—	53	2	no	—
422	C₄	—	106	1	no	—
423	C₄	—	106	1	no	—
424	C₄	—	212	2	no	—
425	C₄	C₂×M₁₆×D₅₃	1	1	yes	characteristic
426	C₄	#16811388	1	1	yes	characteristic
427	C₄	C₂×D₈×D₅₃	1	1	yes	characteristic
428	C₄	#135×D₅₃	1	1	yes	characteristic
429	C₂	—	8	2	no	—
430	C₂	—	106	2	no	—
431	C₂	—	212	4	no	—
432	C₂	#20283451	1	1	yes	characteristic
433	C₂	C₄×D₈×D₅₃	1	1	yes	characteristic
434	C₂	#20283627	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1589	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₅₃	C₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#1589	D₅₃
hypocenter	C₅₃	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1589

Complements

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

N	H ≅ G/N	type
2. #20283451	C₂	semidirect
3. #20273600	C₂	semidirect
4. #20273547	C₂	semidirect
5. #20273542	C₂	semidirect
6. C₈×D₄₂₄	C₂	semidirect
7. #20273509	C₂	semidirect
8. #20273472	C₂	semidirect
9. #20273138	C₂	semidirect
10. C₈×#11719912	C₂	semidirect
11. C₅₃×#1589	C₂	semidirect
20. #16810701	C₂²	semidirect
23. C₈×D₂₁₂	C₂²	semidirect
24. #16810688	C₂²	semidirect
32. #16810376	C₂²	semidirect
33. #16810375	C₂²	semidirect
34. #16810352	C₂²	semidirect
35. D₄⋊#88322	C₂²	semidirect
36. #16810350	C₂²	semidirect
37. #16810345	C₂²	semidirect
38. #16810344	C₂²	semidirect
39. C₈×#88322	C₂²	semidirect
41. C₅₃×#436	C₂²	semidirect
42. C₅₃×#335	C₂²	semidirect
43. C₅₃×D₄⋊C₈	C₂²	semidirect
44. C₈²×C₅₃	C₂²	semidirect
139. D₄₂₄	M₁₆	semidirect
142. #11719912	D₈	semidirect
168. D₂₁₂	C₂×M₁₆	semidirect
182. C₈×C₅₃	C₂×M₁₆	semidirect
183. C₈×C₅₃	C₂×D₈	semidirect
189. #88322	C₂×D₈	semidirect
215. #1589	D₅₃	semidirect
239. #436	C₂×D₅₃	semidirect
253. #335	C₂×D₅₃	semidirect
257. D₄⋊C₈	C₂×D₅₃	semidirect
261. C₈²	C₂×D₅₃	semidirect
262. C₅₃	M₁₆×D₈	semidirect
406. C₈	M₁₆×D₅₃	semidirect
407. C₈	D₈×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₈×D₅₃	2
#20283451	2
#20273600	2
#20273547	2
#20273542	2
C₈×D₄₂₄	2
#20273509	2
#20273472	2
#20273138	2
C₈×#11719912	2
C₅₃×#1589	2
M₁₆×D₈	53