Subgroups — #27391032

Order 13568.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283618	C₂	1	2	yes	maximal, complemented
2	C₂×#16810740	C₂	1	1	yes	maximal, characteristic, complemented
3	#131×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#20275614	C₂	1	1	yes	maximal, characteristic, complemented
5	#20275506	C₂	1	1	yes	maximal, characteristic, complemented
6	#20275386	C₂	1	2	yes	maximal, complemented
7	#20275218	C₂	1	2	yes	maximal, complemented
8	#20274769	C₂	1	1	yes	maximal, characteristic, complemented
9	#20274597	C₂	1	1	yes	maximal, characteristic, complemented
10	#20274518	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3067	C₂	1	1	yes	maximal, characteristic
12	C₂×#13133224	C₂²	1	2	yes	—
13	C₂×#13133224	C₂²	1	1	yes	characteristic
14	#41×Dic₅₃	C₂²	1	1	yes	characteristic
15	#16810745	—	2	4	no	—
16	#16810740	—	2	4	no	—
17	#16810740	—	2	1	no	—
18	#16810740	—	2	1	no	—
19	#16810740	—	2	1	no	—
20	#16810740	—	2	1	no	—
21	#16810672	C₂²	1	2	yes	—
22	C₂×#13133153	C₂²	1	1	yes	characteristic
23	#16810661	C₂²	1	1	yes	characteristic
24	#16810640	C₂²	1	2	yes	—
25	#16810640	C₂²	1	2	yes	—
26	C₂×#13133144	C₂²	1	2	yes	—
27	#16810597	C₂²	1	2	yes	—
28	#16810581	—	2	1	no	—
29	#16810581	C₂²	1	1	yes	characteristic
30	#16810581	C₂²	1	2	yes	—
31	#16810578	—	2	1	no	—
32	#16810578	C₂²	1	1	yes	characteristic
33	M₁₆×Dic₅₃	—	2	1	no	—
34	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₅₃	—	2	1	no	—
36	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
37	#16810395	C₂²	1	2	yes	—
38	#16810395	C₂²	1	2	yes	—
39	#16810384	C₂²	1	2	yes	—
40	C₅₃×#575	C₂²	1	2	yes	—
41	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#473	C₄	1	2	yes	complemented
44	C₅₃×#472	C₄	1	2	yes	complemented
45	C₅₃×#471	C₄	1	4	yes	complemented
46	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
47	C₅₃×#413	C₂²	1	2	yes	—
48	#13133224	—	2	1	no	—
49	#13133224	—	2	1	no	—
50	#13133224	—	2	2	no	—
51	#13133224	—	2	2	no	—
52	#13133224	—	2	2	no	—
53	#13133224	—	2	2	no	—
54	#13133224	D₄	1	2	yes	—
55	#13133224	D₄	1	2	yes	—
56	C₂×#11719917	—	2	1	no	—
57	C₂×#11719917	—	2	2	no	—
58	C₂×#11719917	C₂³	1	2	yes	—
59	C₂×#11719917	C₂³	1	1	yes	characteristic
60	C₂²×#88322	—	2	1	no	—
61	C₂²×#88322	—	2	2	no	—
62	C₂²×#88322	C₂³	1	1	yes	characteristic
63	Q₈×Dic₅₃	—	2	1	no	—
64	D₄×Dic₅₃	—	2	2	no	—
65	D₄×Dic₅₃	—	2	1	no	—
66	#13133176	—	2	1	no	—
67	#13133176	C₂³	1	2	yes	—
68	#13133176	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₅₃	—	2	1	no	—
70	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
71	#13133153	—	2	1	no	—
72	#13133153	—	2	1	no	—
73	#13133153	—	2	4	no	—
74	#13133151	—	2	1	no	—
75	#13133149	—	2	1	no	—
76	#13133144	—	2	2	no	—
77	#13133144	—	2	2	no	—
78	#13133144	—	2	4	no	—
79	#13133144	—	2	4	no	—
80	#13133132	—	2	4	no	—
81	#13133127	—	2	1	no	—
82	#13133127	—	2	1	no	—
83	#13133127	—	2	1	no	—
84	#13133127	—	2	2	no	—
85	C₈×Dic₅₃	—	2	1	no	—
86	C₈×Dic₅₃	—	2	1	no	—
87	C₈×Dic₅₃	—	2	1	no	—
88	C₈×Dic₅₃	—	2	2	no	—
89	C₈×Dic₅₃	D₄	1	1	yes	characteristic
90	C₈×Dic₅₃	D₄	1	1	yes	characteristic
91	C₈×Dic₅₃	D₄	1	1	yes	characteristic
92	C₈×Dic₅₃	D₄	1	1	yes	characteristic
93	C₂×#41×C₅₃	C₂³	1	2	yes	—
94	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
95	#137×C₅₃	—	2	2	no	—
96	#137×C₅₃	C₂×C₄	1	4	yes	—
97	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
98	AGL(1,ℤ/8)×C₅₃	C₂×C₄	1	4	yes	—
99	#135×C₅₃	—	2	1	no	—
100	#135×C₅₃	—	2	1	no	—
101	#135×C₅₃	—	2	1	no	—
102	#135×C₅₃	—	2	1	no	—
103	#135×C₅₃	—	2	4	no	—
104	C₂×Q₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
105	C₂×SD₁₆×C₅₃	C₂×C₄	1	2	yes	complemented
106	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
107	#131×C₅₃	—	2	1	no	—
108	#131×C₅₃	—	2	1	no	—
109	#131×C₅₃	C₂×C₄	1	2	yes	—
110	#131×C₅₃	C₂×C₄	1	2	yes	—
111	C₂×M₁₆×C₅₃	—	2	1	no	—
112	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
113	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
114	C₂²×C₈×C₅₃	—	2	1	no	—
115	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
116	#108×C₅₃	C₂×C₄	1	2	yes	complemented
117	#108×C₅₃	C₂×C₄	1	2	yes	complemented
118	#101×C₅₃	C₂×C₄	1	4	yes	complemented
119	#100×C₅₃	C₂×C₄	1	4	yes	complemented
120	#41×C₅₃	—	2	1	no	—
121	#41×C₅₃	—	2	1	no	—
122	#41×C₅₃	—	2	2	no	—
123	#41×C₅₃	—	2	2	no	—
124	#41×C₅₃	—	2	2	no	—
125	#41×C₅₃	—	2	2	no	—
126	#41×C₅₃	C₂²×C₄	1	2	yes	—
127	#41×C₅₃	C₂×D₄	1	2	yes	—
128	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
129	C₂×Q₈×C₅₃	#41	1	1	yes	characteristic
130	C₂×D₄×C₅₃	—	2	1	no	—
131	C₂×D₄×C₅₃	—	2	2	no	—
132	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
133	C₂×D₄×C₅₃	#41	1	1	yes	characteristic
134	C₂²×C₄×C₅₃	—	2	1	no	—
135	C₂²×C₄×C₅₃	—	2	2	no	—
136	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
137	C₂²×Dic₅₃	—	2	2	no	—
138	C₂²×Dic₅₃	—	2	1	no	—
139	Q₁₆×C₅₃	—	2	4	no	—
140	Q₁₆×C₅₃	—	2	1	no	—
141	Q₁₆×C₅₃	—	2	1	no	—
142	SD₁₆×C₅₃	—	2	4	no	—
143	SD₁₆×C₅₃	—	2	4	no	—
144	SD₁₆×C₅₃	—	2	2	no	—
145	SD₁₆×C₅₃	—	2	2	no	—
146	D₈×C₅₃	—	2	4	no	—
147	D₈×C₅₃	—	2	1	no	—
148	D₈×C₅₃	—	2	1	no	—
149	M₁₆×C₅₃	—	2	1	no	—
150	M₁₆×C₅₃	—	2	2	no	—
151	M₁₆×C₅₃	—	2	2	no	—
152	M₁₆×C₅₃	—	2	2	no	—
153	M₁₆×C₅₃	C₂²×C₄	1	2	yes	—
154	M₁₆×C₅₃	C₂²×C₄	1	4	yes	—
155	C₂×C₈×C₅₃	—	2	1	no	—
156	C₂×C₈×C₅₃	—	2	2	no	—
157	C₂×C₈×C₅₃	—	2	2	no	—
158	C₂×C₈×C₅₃	—	2	2	no	—
159	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
164	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
165	C₂²⋊Dic₅₃	—	2	2	no	—
166	C₂²⋊Dic₅₃	—	2	2	no	—
167	C₂²⋊Dic₅₃	#41	1	2	yes	—
168	C₄⋊Dic₅₃	—	2	2	no	—
169	C₄⋊Dic₅₃	—	2	1	no	—
170	C₄⋊Dic₅₃	—	2	2	no	—
171	C₄×Dic₅₃	—	2	2	no	—
172	C₄×Dic₅₃	—	2	1	no	—
173	C₄×Dic₅₃	—	2	1	no	—
174	C₄×Dic₅₃	—	2	2	no	—
175	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
176	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
177	#11719917	—	2	1	no	—
178	#11719917	—	2	2	no	—
179	#11719917	—	2	2	no	—
180	#11719917	—	2	2	no	—
181	#11719917	—	2	2	no	—
182	#11719917	—	4	2	no	—
183	#11719917	—	4	2	no	—
184	#11719917	C₂×D₄	1	2	yes	—
185	C₂×#88322	—	2	1	no	—
186	C₂×#88322	—	2	2	no	—
187	C₂×#88322	—	2	2	no	—
188	C₂×#88322	—	2	2	no	—
189	C₂×#88322	—	4	2	no	—
190	C₂×#88322	—	4	2	no	—
191	C₂×#88322	C₂×D₄	1	1	yes	characteristic
192	C₂×#88322	C₂×D₄	1	1	yes	characteristic
193	C₂×#88322	C₂×D₄	1	1	yes	characteristic
194	C₂×#88322	C₂×D₄	1	1	yes	characteristic
195	C₂×#88322	#41	1	1	yes	characteristic
196	C₂×#88322	#41	1	1	yes	characteristic
197	C₂³×C₅₃	—	2	1	no	—
198	C₂³×C₅₃	—	2	2	no	—
199	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
200	Q₈×C₅₃	—	2	1	no	—
201	Q₈×C₅₃	—	2	2	no	—
202	Q₈×C₅₃	—	2	2	no	—
203	Q₈×C₅₃	C₄×D₄	1	2	yes	—
204	D₄×C₅₃	—	2	2	no	—
205	D₄×C₅₃	—	2	2	no	—
206	D₄×C₅₃	—	2	2	no	—
207	D₄×C₅₃	—	2	2	no	—
208	D₄×C₅₃	—	2	1	no	—
209	D₄×C₅₃	—	4	2	no	—
210	D₄×C₅₃	—	4	2	no	—
211	D₄×C₅₃	C₄×D₄	1	2	yes	—
212	C₂×C₄×C₅₃	—	2	1	no	—
213	C₂×C₄×C₅₃	—	2	2	no	—
214	C₂×C₄×C₅₃	—	2	2	no	—
215	C₂×C₄×C₅₃	—	2	2	no	—
216	C₂×C₄×C₅₃	—	4	2	no	—
217	C₂×C₄×C₅₃	—	4	2	no	—
218	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
224	C₂×Dic₅₃	—	2	1	no	—
225	C₂×Dic₅₃	—	2	2	no	—
226	C₂×Dic₅₃	—	2	1	no	—
227	C₂×Dic₅₃	—	4	2	no	—
228	C₂×Dic₅₃	—	4	4	no	—
229	C₂×Dic₅₃	—	4	2	no	—
230	C₈×C₅₃	—	2	2	no	—
231	C₈×C₅₃	—	2	4	no	—
232	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
233	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
234	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
235	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
236	#88322	—	2	2	no	—
237	#88322	—	4	2	no	—
238	#88322	#121	1	1	yes	characteristic
239	#88322	#121	1	1	yes	characteristic
240	#88322	#121	1	1	yes	characteristic
241	#88322	#121	1	1	yes	characteristic
242	#21558	—	53	1	no	maximal, Sylow
243	C₂²×C₅₃	—	2	2	no	—
244	C₂²×C₅₃	—	4	1	no	—
245	C₂²×C₅₃	—	4	2	no	—
246	C₂²×C₅₃	—	4	2	no	—
247	C₂²×C₅₃	—	8	2	no	—
248	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
249	C₂²×C₅₃	#525	1	1	yes	characteristic
250	C₂²×C₅₃	#532	1	1	yes	characteristic
251	C₄×C₅₃	—	2	2	no	—
252	C₄×C₅₃	—	4	2	no	—
253	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
254	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
256	C₄×C₅₃	#529	1	1	yes	characteristic
257	Dic₅₃	—	2	2	no	—
258	Dic₅₃	—	4	2	no	—
259	Dic₅₃	—	4	1	no	—
260	Dic₅₃	—	8	2	no	—
261	#3067	D₅₃	1	1	yes	characteristic
262	#2955	—	53	2	no	—
263	C₂×#443	—	53	1	no	—
264	C₄×#131	—	53	1	no	—
265	#1976	—	53	1	no	—
266	#1953	—	53	1	no	—
267	#1932	—	53	2	no	—
268	#1906	—	53	2	no	—
269	#1814	—	53	1	no	—
270	#1772	—	53	1	no	—
271	#1757	—	53	2	no	—
272	C₂×C₅₃	—	2	1	no	—
273	C₂×C₅₃	—	2	1	no	—
274	C₂×C₅₃	—	2	1	no	—
275	C₂×C₅₃	—	4	2	no	—
276	C₂×C₅₃	—	8	2	no	—
277	C₂×C₅₃	C₄×#121	1	1	yes	characteristic
278	#575	C₂×D₅₃	1	2	yes	—
279	C₂×#135	C₂×D₅₃	1	1	yes	characteristic
280	C₂×#131	—	53	1	no	—
281	C₂×#131	—	53	2	no	—
282	C₂×#131	C₂×D₅₃	1	1	yes	characteristic
283	C₄×#41	—	53	1	no	—
284	#473	Dic₅₃	1	2	yes	complemented
285	#472	Dic₅₃	1	2	yes	complemented
286	#471	Dic₅₃	1	4	yes	complemented
287	#444	—	106	4	no	—
288	#443	—	106	1	no	—
289	#443	—	106	1	no	—
290	#443	—	106	1	no	—
291	#443	—	106	1	no	—
292	#443	—	106	4	no	—
293	#430	—	53	2	no	—
294	C₂×#108	—	53	1	no	—
295	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
296	#427	—	53	1	no	—
297	#421	—	53	2	no	—
298	#421	—	53	2	no	—
299	C₂×#104	—	53	2	no	—
300	#413	C₂×D₅₃	1	2	yes	—
301	#410	—	53	2	no	—
302	#405	—	53	1	no	—
303	#405	—	53	2	no	—
304	#405	—	53	1	no	—
305	#405	—	106	1	no	—
306	#405	—	106	1	no	—
307	C₄×M₁₆	—	53	1	no	—
308	C₄×M₁₆	—	106	1	no	—
309	C₂×C₄×C₈	—	53	1	no	—
310	C₂×C₄×C₈	—	106	1	no	—
311	#344	—	53	2	no	—
312	#344	—	53	2	no	—
313	#339	—	53	2	no	—
314	C₅₃	#21558	1	1	yes	characteristic, complemented, Sylow
315	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
316	C₂×#41	C₂²×D₅₃	1	2	yes	—
317	#137	—	2	2	no	—
318	#137	C₂×Dic₅₃	1	4	yes	—
319	AGL(1,ℤ/8)	—	2	2	no	—
320	AGL(1,ℤ/8)	C₂×Dic₅₃	1	4	yes	—
321	#135	—	2	4	no	—
322	#135	—	2	1	no	—
323	#135	—	2	1	no	—
324	#135	—	2	1	no	—
325	#135	—	2	1	no	—
326	C₂×Q₁₆	C₂×Dic₅₃	1	1	yes	characteristic, complemented
327	C₂×SD₁₆	C₂×Dic₅₃	1	2	yes	complemented
328	C₂×D₈	C₂×Dic₅₃	1	1	yes	characteristic, complemented
329	#131	—	2	1	no	—
330	#131	—	2	1	no	—
331	#131	—	53	2	no	—
332	#131	—	53	2	no	—
333	#131	—	106	1	no	—
334	#131	—	106	1	no	—
335	#131	—	106	2	no	—
336	#131	—	106	2	no	—
337	#131	—	106	2	no	—
338	#131	—	106	2	no	—
339	#131	C₂×Dic₅₃	1	2	yes	—
340	#131	C₂×Dic₅₃	1	2	yes	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	53	1	no	—
343	C₂×M₁₆	—	53	2	no	—
344	C₂×M₁₆	—	106	1	no	—
345	C₂×M₁₆	—	106	2	no	—
346	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
347	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	53	1	no	—
350	C₂²×C₈	—	106	1	no	—
351	C₂²×C₈	—	106	2	no	—
352	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
353	C₄×Q₈	—	106	1	no	—
354	C₄×D₄	—	106	2	no	—
355	C₄×D₄	—	106	1	no	—
356	#117	—	53	1	no	—
357	#117	—	53	2	no	—
358	#117	—	106	1	no	—
359	C₂×C₄²	—	53	1	no	—
360	C₂×C₄²	—	106	1	no	—
361	#108	—	106	4	no	—
362	#108	—	106	1	no	—
363	#108	—	106	1	no	—
364	#108	C₂×Dic₅₃	1	2	yes	complemented
365	#108	C₂×Dic₅₃	1	2	yes	complemented
366	#107	—	106	1	no	—
367	#106	—	106	1	no	—
368	#104	—	106	2	no	—
369	#104	—	106	2	no	—
370	#104	—	106	4	no	—
371	#104	—	106	4	no	—
372	#101	C₂×Dic₅₃	1	4	yes	complemented
373	#100	C₂×Dic₅₃	1	4	yes	complemented
374	#99	—	106	4	no	—
375	#97	—	106	1	no	—
376	#97	—	106	1	no	—
377	#97	—	106	2	no	—
378	#97	—	106	1	no	—
379	C₄×C₈	—	53	1	no	—
380	C₄×C₈	—	53	1	no	—
381	C₄×C₈	—	53	1	no	—
382	C₄×C₈	—	53	1	no	—
383	C₄×C₈	—	106	1	no	—
384	C₄×C₈	—	106	1	no	—
385	C₄×C₈	—	106	2	no	—
386	C₄×C₈	—	106	1	no	—
387	#41	—	2	1	no	—
388	#41	—	2	1	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	2	no	—
392	#41	—	2	2	no	—
393	#41	D₄×D₅₃	1	2	yes	—
394	#41	C₂²×Dic₅₃	1	2	yes	—
395	C₂×Q₈	#11719947	1	1	yes	characteristic
396	C₂×Q₈	C₂²×Dic₅₃	1	2	yes	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	#11719947	1	1	yes	characteristic
400	C₂×D₄	C₂²×Dic₅₃	1	2	yes	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	106	2	no	—
404	C₂²×C₄	—	106	1	no	—
405	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
406	Q₁₆	—	2	4	no	—
407	Q₁₆	—	2	1	no	—
408	Q₁₆	—	2	1	no	—
409	SD₁₆	—	2	4	no	—
410	SD₁₆	—	2	4	no	—
411	SD₁₆	—	2	2	no	—
412	SD₁₆	—	2	2	no	—
413	D₈	—	2	4	no	—
414	D₈	—	2	1	no	—
415	D₈	—	2	1	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	53	2	no	—
421	M₁₆	—	106	2	no	—
422	M₁₆	—	106	2	no	—
423	M₁₆	—	106	1	no	—
424	M₁₆	—	106	2	no	—
425	M₁₆	—	106	2	no	—
426	M₁₆	—	212	2	no	—
427	M₁₆	—	212	2	no	—
428	M₁₆	C₂²×Dic₅₃	1	2	yes	—
429	M₁₆	C₂²×Dic₅₃	1	4	yes	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	53	1	no	—
435	C₂×C₈	—	53	1	no	—
436	C₂×C₈	—	53	1	no	—
437	C₂×C₈	—	53	1	no	—
438	C₂×C₈	—	53	1	no	—
439	C₂×C₈	—	53	1	no	—
440	C₂×C₈	—	106	2	no	—
441	C₂×C₈	—	106	2	no	—
442	C₂×C₈	—	106	1	no	—
443	C₂×C₈	—	106	2	no	—
444	C₂×C₈	—	212	2	no	—
445	C₂×C₈	—	212	2	no	—
446	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
447	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
448	C₂×C₈	#11719947	1	1	yes	characteristic
449	C₂×C₈	#11719947	1	1	yes	characteristic
450	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
451	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
452	C₄⋊C₄	—	106	2	no	—
453	C₄⋊C₄	—	106	1	no	—
454	C₄⋊C₄	—	106	2	no	—
455	C₂²⋊C₄	—	53	2	no	—
456	C₂²⋊C₄	—	106	2	no	—
457	C₂²⋊C₄	—	106	2	no	—
458	C₄²	—	53	1	no	—
459	C₄²	—	53	1	no	—
460	C₄²	—	106	2	no	—
461	C₄²	—	106	1	no	—
462	C₄²	—	106	1	no	—
463	C₄²	—	106	2	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	#41×D₅₃	1	1	yes	characteristic
467	Q₈	—	2	1	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	2	2	no	—
470	Q₈	D₄×Dic₅₃	1	2	yes	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	1	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	D₄×Dic₅₃	1	2	yes	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	106	1	no	—
486	C₂×C₄	—	106	1	no	—
487	C₂×C₄	—	106	2	no	—
488	C₂×C₄	—	212	2	no	—
489	C₂×C₄	—	212	4	no	—
490	C₂×C₄	—	212	2	no	—
491	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
493	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
494	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
495	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
496	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	2	4	no	—
499	C₈	—	53	1	no	—
500	C₈	—	53	1	no	—
501	C₈	—	53	1	no	—
502	C₈	—	53	1	no	—
503	C₈	—	106	2	no	—
504	C₈	—	212	2	no	—
505	C₈	D₄×Dic₅₃	1	1	yes	characteristic
506	C₈	D₄×Dic₅₃	1	1	yes	characteristic
507	C₈	D₄×Dic₅₃	1	1	yes	characteristic
508	C₈	D₄×Dic₅₃	1	1	yes	characteristic
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	#41×Dic₅₃	1	1	yes	characteristic
515	C₂²	#16811133	1	1	yes	characteristic
516	C₂²	#16811168	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	106	2	no	—
520	C₄	—	424	2	no	—
521	C₄	—	212	1	no	—
522	C₄	—	212	2	no	—
523	C₄	C₂×D₄×Dic₅₃	1	1	yes	characteristic
524	C₄	C₂×D₄×Dic₅₃	1	1	yes	characteristic
525	C₄	#121×D₅₃	1	1	yes	characteristic
526	C₄	#16811154	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	4	2	no	—
531	C₂	—	8	2	no	—
532	C₂	#121×Dic₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting, prime radical	C₅₃×#3067	C₂
socle	C₂×C₅₃	C₄×#121
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#3067	D₅₃
hypocenter	C₅₃	#21558
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #3067

Complements

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

N	H ≅ G/N	type
1. #20283618	C₂	semidirect
2. C₂×#16810740	C₂	semidirect
3. #131×Dic₅₃	C₂	semidirect
4. #20275614	C₂	semidirect
5. #20275506	C₂	semidirect
6. #20275386	C₂	semidirect
7. #20275218	C₂	semidirect
8. #20274769	C₂	semidirect
9. #20274597	C₂	semidirect
10. #20274518	C₂	semidirect
43. C₅₃×#473	C₄	semidirect
44. C₅₃×#472	C₄	semidirect
45. C₅₃×#471	C₄	semidirect
104. C₂×Q₁₆×C₅₃	C₂×C₄	semidirect
105. C₂×SD₁₆×C₅₃	C₂×C₄	semidirect
106. C₂×D₈×C₅₃	C₂×C₄	semidirect
116. #108×C₅₃	C₂×C₄	semidirect
117. #108×C₅₃	C₂×C₄	semidirect
118. #101×C₅₃	C₂×C₄	semidirect
119. #100×C₅₃	C₂×C₄	semidirect
284. #473	Dic₅₃	semidirect
285. #472	Dic₅₃	semidirect
286. #471	Dic₅₃	semidirect
314. C₅₃	#21558	semidirect
326. C₂×Q₁₆	C₂×Dic₅₃	semidirect
327. C₂×SD₁₆	C₂×Dic₅₃	semidirect
328. C₂×D₈	C₂×Dic₅₃	semidirect
364. #108	C₂×Dic₅₃	semidirect
365. #108	C₂×Dic₅₃	semidirect
372. #101	C₂×Dic₅₃	semidirect
373. #100	C₂×Dic₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20283618	2
C₂×#16810740	2
#131×Dic₅₃	2
#20275614	2
#20275506	2
#20275386	2
#20275218	2
#20274769	2
#20274597	2
#20274518	2
C₅₃×#3067	2
#21558	53