Subgroups — C₅₃×#60891 #27268403

Order 13568.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3461	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3244	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3243	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3242	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3242	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3240	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3236	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3232	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3231	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3099	C₂	1	1	yes	maximal, characteristic
16	C₅₃×#3098	C₂	1	1	yes	maximal, characteristic
17	C₅₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#557	—	2	1	no	—
25	C₅₃×#557	—	2	1	no	—
26	C₅₃×#554	—	2	2	no	—
27	C₅₃×#554	—	2	1	no	—
28	C₅₃×#554	—	2	2	no	—
29	C₅₃×#554	—	2	1	no	—
30	C₅₃×#544	C₂²	1	1	yes	characteristic
31	C₅₃×#544	C₂²	1	2	yes	—
32	C₅₃×#544	C₂²	1	2	yes	—
33	C₅₃×#544	C₂²	1	1	yes	characteristic
34	C₅₃×#544	C₂²	1	1	yes	characteristic
35	C₅₃×#542	—	2	1	no	—
36	C₅₃×#542	C₂²	1	2	yes	—
37	C₅₃×#541	—	2	1	no	—
38	C₅₃×#541	C₂²	1	2	yes	—
39	C₅₃×#539	—	2	2	no	—
40	C₅₃×#537	C₂²	1	1	yes	characteristic
41	C₅₃×#536	C₂²	1	1	yes	characteristic
42	C₅₃×#536	C₂²	1	1	yes	characteristic
43	C₅₃×#533	—	2	1	no	—
44	C₅₃×#533	C₂²	1	2	yes	—
45	C₅₃×#533	C₂²	1	2	yes	—
46	C₅₃×#533	C₂²	1	1	yes	characteristic
47	C₅₃×#529	—	2	1	no	—
48	C₅₃×#529	—	2	2	no	—
49	C₅₃×#529	C₂²	1	2	yes	—
50	C₂×#125×C₅₃	C₂²	1	2	yes	—
51	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
52	C₅₃×#520	C₂²	1	1	yes	characteristic
53	C₅₃×#520	C₂²	1	1	yes	characteristic
54	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
55	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#501	C₂²	1	2	yes	—
58	C₅₃×#501	C₂²	1	2	yes	—
59	C₅₃×#501	C₂²	1	2	yes	—
60	C₅₃×#501	C₂²	1	2	yes	—
61	C₅₃×#500	C₂²	1	2	yes	—
62	C₅₃×#499	C₂²	1	2	yes	—
63	C₅₃×#499	C₂²	1	2	yes	—
64	C₅₃×#498	C₂²	1	2	yes	—
65	C₅₃×#491	C₂²	1	2	yes	—
66	C₅₃×#491	C₂²	1	2	yes	—
67	C₅₃×#489	C₂²	1	2	yes	—
68	C₅₃×#489	C₂²	1	2	yes	—
69	C₅₃×#488	C₂²	1	2	yes	—
70	C₅₃×#488	C₂²	1	2	yes	—
71	C₅₃×#487	C₂²	1	2	yes	—
72	C₅₃×#487	C₂²	1	2	yes	—
73	C₅₃×#485	C₂²	1	2	yes	—
74	C₅₃×#485	C₂²	1	2	yes	—
75	C₅₃×#485	C₂²	1	2	yes	—
76	C₅₃×#485	C₂²	1	2	yes	—
77	C₅₃×#485	C₂²	1	2	yes	—
78	C₅₃×#485	C₂²	1	2	yes	—
79	C₅₃×#484	C₂²	1	2	yes	—
80	C₅₃×#484	C₂²	1	2	yes	—
81	C₅₃×#484	C₂²	1	2	yes	—
82	C₅₃×#483	C₂²	1	2	yes	—
83	C₅₃×#483	C₂²	1	2	yes	—
84	C₅₃×#483	C₂²	1	2	yes	—
85	C₅₃×#482	C₂²	1	2	yes	—
86	C₅₃×#482	C₂²	1	2	yes	—
87	C₅₃×#481	C₂²	1	2	yes	—
88	C₅₃×#480	C₂²	1	2	yes	—
89	C₅₃×#479	C₂²	1	1	yes	characteristic
90	C₅₃×#479	C₂²	1	2	yes	—
91	C₅₃×#479	C₂²	1	2	yes	—
92	C₅₃×#479	C₂²	1	2	yes	—
93	C₅₃×#479	C₂²	1	2	yes	—
94	C₅₃×#479	C₂²	1	1	yes	characteristic
95	C₅₃×#479	C₂²	1	2	yes	—
96	C₅₃×#479	C₂²	1	2	yes	—
97	C₅₃×#479	C₂²	1	2	yes	—
98	C₅₃×#479	C₂²	1	2	yes	—
99	C₅₃×#478	C₂²	1	1	yes	characteristic
100	C₅₃×#478	C₂²	1	2	yes	—
101	C₅₃×#478	C₂²	1	1	yes	characteristic
102	C₅₃×#478	C₂²	1	2	yes	—
103	C₅₃×#477	C₂²	1	1	yes	characteristic
104	C₅₃×#477	C₂²	1	2	yes	—
105	C₅₃×#476	C₂²	1	1	yes	characteristic
106	C₅₃×#475	C₂²	1	1	yes	characteristic
107	C₅₃×#475	C₂²	1	2	yes	—
108	C₅₃×#474	C₂²	1	1	yes	characteristic
109	C₅₃×#433	C₂²	1	2	yes	—
110	C₅₃×#433	C₂²	1	2	yes	—
111	C₅₃×#432	C₂²	1	2	yes	—
112	C₅₃×#431	C₂²	1	2	yes	—
113	C₅₃×#428	C₂²	1	1	yes	characteristic
114	C₅₃×#428	C₂²	1	1	yes	characteristic
115	C₅₃×#428	C₂²	1	1	yes	characteristic
116	C₅₃×#428	C₂²	1	1	yes	characteristic
117	C₅₃×#427	C₂²	1	1	yes	characteristic
118	C₅₃×#427	C₂²	1	1	yes	characteristic
119	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
120	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
121	C₅₃×#423	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
123	C₅₃×#419	C₂²	1	1	yes	characteristic
124	C₅₃×#419	C₂²	1	1	yes	characteristic
125	C₅₃×#417	C₂²	1	1	yes	characteristic
126	C₅₃×#417	C₂²	1	1	yes	characteristic
127	C₅₃×#416	C₂²	1	1	yes	characteristic
128	C₅₃×#416	C₂²	1	1	yes	characteristic
129	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
130	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
131	C₅₃×#408	C₂²	1	1	yes	characteristic
132	C₅₃×#408	C₂²	1	1	yes	characteristic
133	C₅₃×#405	C₂²	1	1	yes	characteristic
134	C₅₃×#405	C₂²	1	1	yes	characteristic
135	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
136	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₅₃	—	2	1	no	—
143	C₄⋊Q₈×C₅₃	—	2	2	no	—
144	C₄⋊Q₈×C₅₃	—	2	1	no	—
145	C₄⋊Q₈×C₅₃	—	2	1	no	—
146	C₄⋊Q₈×C₅₃	—	2	2	no	—
147	C₄⋊Q₈×C₅₃	—	2	1	no	—
148	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
150	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
151	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
154	#126×C₅₃	—	2	2	no	—
155	#126×C₅₃	—	2	2	no	—
156	#126×C₅₃	—	2	2	no	—
157	#126×C₅₃	—	2	2	no	—
158	#125×C₅₃	—	2	2	no	—
159	#125×C₅₃	—	2	1	no	—
160	#125×C₅₃	—	2	2	no	—
161	#125×C₅₃	—	2	2	no	—
162	#125×C₅₃	—	2	1	no	—
163	#125×C₅₃	—	2	1	no	—
164	#125×C₅₃	—	2	2	no	—
165	#125×C₅₃	—	2	1	no	—
166	#125×C₅₃	—	2	2	no	—
167	#125×C₅₃	—	2	1	no	—
168	#125×C₅₃	—	2	2	no	—
169	#125×C₅₃	—	2	2	no	—
170	#125×C₅₃	C₂³	1	2	yes	—
171	#125×C₅₃	C₂³	1	2	yes	—
172	#125×C₅₃	C₂³	1	2	yes	—
173	#125×C₅₃	C₂³	1	1	yes	characteristic
174	#125×C₅₃	C₂³	1	2	yes	—
175	#125×C₅₃	C₂³	1	2	yes	—
176	#125×C₅₃	C₂³	1	1	yes	characteristic
177	#124×C₅₃	—	2	2	no	—
178	#124×C₅₃	—	2	1	no	—
179	#124×C₅₃	C₂³	1	2	yes	—
180	#123×C₅₃	—	2	2	no	—
181	#123×C₅₃	—	2	2	no	—
182	#123×C₅₃	—	2	2	no	—
183	#123×C₅₃	—	2	2	no	—
184	C₂²⋊Q₈×C₅₃	—	2	1	no	—
185	C₂²⋊Q₈×C₅₃	—	2	1	no	—
186	C₂²⋊Q₈×C₅₃	—	2	2	no	—
187	C₂²⋊Q₈×C₅₃	—	2	2	no	—
188	C₂²⋊Q₈×C₅₃	—	2	2	no	—
189	C₂²⋊Q₈×C₅₃	—	2	2	no	—
190	C₂²⋊Q₈×C₅₃	—	2	2	no	—
191	C₂²⋊Q₈×C₅₃	—	2	2	no	—
192	C₂²⋊Q₈×C₅₃	—	2	2	no	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	1	no	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	1	no	—
197	C₂²⋊Q₈×C₅₃	—	2	1	no	—
198	C₂²⋊Q₈×C₅₃	—	2	2	no	—
199	C₂²⋊Q₈×C₅₃	—	2	2	no	—
200	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
203	#121×C₅₃	—	2	2	no	—
204	#121×C₅₃	—	2	1	no	—
205	#121×C₅₃	C₂³	1	2	yes	—
206	C₄×Q₈×C₅₃	—	2	1	no	—
207	C₄×Q₈×C₅₃	—	2	1	no	—
208	C₄×Q₈×C₅₃	—	2	2	no	—
209	C₄×Q₈×C₅₃	—	2	1	no	—
210	C₄×Q₈×C₅₃	—	2	2	no	—
211	C₄×Q₈×C₅₃	—	2	1	no	—
212	C₄×Q₈×C₅₃	—	2	2	no	—
213	C₄×Q₈×C₅₃	—	2	1	no	—
214	C₄×Q₈×C₅₃	—	2	1	no	—
215	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
217	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
218	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
221	C₄×D₄×C₅₃	—	2	2	no	—
222	C₄×D₄×C₅₃	—	2	2	no	—
223	C₄×D₄×C₅₃	—	2	1	no	—
224	C₄×D₄×C₅₃	—	2	1	no	—
225	C₄×D₄×C₅₃	—	2	1	no	—
226	C₄×D₄×C₅₃	—	2	1	no	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	D₄	1	2	yes	—
229	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
230	C₄×D₄×C₅₃	D₄	1	2	yes	—
231	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
232	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
234	#117×C₅₃	—	2	1	no	—
235	#117×C₅₃	—	2	2	no	—
236	#117×C₅₃	—	2	2	no	—
237	#117×C₅₃	C₂³	1	2	yes	—
238	#117×C₅₃	C₂³	1	2	yes	—
239	#117×C₅₃	C₂³	1	1	yes	characteristic
240	#117×C₅₃	C₂³	1	1	yes	characteristic
241	#117×C₅₃	C₂³	1	1	yes	characteristic
242	#117×C₅₃	C₂³	1	1	yes	characteristic
243	#117×C₅₃	C₂³	1	2	yes	—
244	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
245	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
246	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
247	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
248	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
249	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
254	C₂×C₄²×C₅₃	—	2	1	no	—
255	C₂×C₄²×C₅₃	—	2	1	no	—
256	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
258	#107×C₅₃	C₂³	1	1	yes	characteristic
259	#107×C₅₃	C₂³	1	1	yes	characteristic
260	#107×C₅₃	C₂³	1	2	yes	—
261	#107×C₅₃	C₂³	1	2	yes	—
262	#107×C₅₃	C₂³	1	2	yes	—
263	#107×C₅₃	C₂³	1	2	yes	—
264	#107×C₅₃	C₂³	1	1	yes	characteristic
265	#107×C₅₃	C₂³	1	2	yes	—
266	#107×C₅₃	C₂³	1	2	yes	—
267	#107×C₅₃	C₂³	1	1	yes	characteristic
268	#106×C₅₃	C₂³	1	1	yes	characteristic
269	#106×C₅₃	C₂³	1	1	yes	characteristic
270	#106×C₅₃	C₂³	1	2	yes	—
271	#106×C₅₃	C₂³	1	2	yes	—
272	#106×C₅₃	C₂³	1	2	yes	—
273	#106×C₅₃	C₂³	1	2	yes	—
274	#106×C₅₃	C₂³	1	1	yes	characteristic
275	#106×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	2	yes	—
277	#106×C₅₃	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
284	#103×C₅₃	C₂³	1	1	yes	characteristic
285	#103×C₅₃	C₂³	1	1	yes	characteristic
286	#103×C₅₃	C₂³	1	2	yes	—
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	2	yes	—
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	2	yes	—
295	#103×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	1	yes	characteristic
297	#103×C₅₃	C₂³	1	1	yes	characteristic
298	#102×C₅₃	C₂³	1	1	yes	characteristic
299	#102×C₅₃	C₂³	1	1	yes	characteristic
300	#102×C₅₃	C₂³	1	2	yes	—
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	#97×C₅₃	C₂³	1	2	yes	—
310	C₄×C₈×C₅₃	C₂³	1	2	yes	—
311	C₄×C₈×C₅₃	C₂³	1	2	yes	—
312	#41×C₅₃	—	2	2	no	—
313	#41×C₅₃	—	2	2	no	—
314	#41×C₅₃	—	2	2	no	—
315	#41×C₅₃	—	2	2	no	—
316	C₂×Q₈×C₅₃	—	2	1	no	—
317	C₂×Q₈×C₅₃	—	2	2	no	—
318	C₂×Q₈×C₅₃	—	2	1	no	—
319	C₂×Q₈×C₅₃	—	2	2	no	—
320	C₂×Q₈×C₅₃	—	2	1	no	—
321	C₂×Q₈×C₅₃	—	2	2	no	—
322	C₂×Q₈×C₅₃	—	2	2	no	—
323	C₂×Q₈×C₅₃	—	2	2	no	—
324	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₅₃	—	2	1	no	—
328	C₂×D₄×C₅₃	—	2	2	no	—
329	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
330	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
331	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₅₃	—	2	1	no	—
333	C₂²×C₄×C₅₃	—	2	1	no	—
334	C₂²×C₄×C₅₃	—	2	2	no	—
335	C₂²×C₄×C₅₃	—	2	2	no	—
336	C₂²×C₄×C₅₃	—	2	1	no	—
337	C₂²×C₄×C₅₃	—	2	1	no	—
338	C₂²×C₄×C₅₃	—	2	1	no	—
339	C₂²×C₄×C₅₃	—	2	1	no	—
340	C₂²×C₄×C₅₃	—	2	1	no	—
341	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
344	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
345	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
347	M₁₆×C₅₃	—	2	2	no	—
348	M₁₆×C₅₃	—	2	2	no	—
349	C₂×C₈×C₅₃	—	2	2	no	—
350	C₂×C₈×C₅₃	—	2	2	no	—
351	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
354	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
355	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₅₃	—	2	2	no	—
358	C₄⋊C₄×C₅₃	—	2	1	no	—
359	C₄⋊C₄×C₅₃	—	2	2	no	—
360	C₄⋊C₄×C₅₃	—	2	1	no	—
361	C₄⋊C₄×C₅₃	—	2	2	no	—
362	C₄⋊C₄×C₅₃	—	2	2	no	—
363	C₄⋊C₄×C₅₃	—	2	2	no	—
364	C₄⋊C₄×C₅₃	—	2	2	no	—
365	C₄⋊C₄×C₅₃	—	2	2	no	—
366	C₄⋊C₄×C₅₃	—	2	2	no	—
367	C₄⋊C₄×C₅₃	—	2	2	no	—
368	C₄⋊C₄×C₅₃	—	2	2	no	—
369	C₄⋊C₄×C₅₃	—	2	2	no	—
370	C₄⋊C₄×C₅₃	—	2	2	no	—
371	C₄⋊C₄×C₅₃	—	2	1	no	—
372	C₄⋊C₄×C₅₃	—	2	1	no	—
373	C₄⋊C₄×C₅₃	—	2	1	no	—
374	C₄⋊C₄×C₅₃	—	2	1	no	—
375	C₄⋊C₄×C₅₃	—	2	1	no	—
376	C₄⋊C₄×C₅₃	—	2	2	no	—
377	C₄⋊C₄×C₅₃	—	2	2	no	—
378	C₄⋊C₄×C₅₃	—	2	2	no	—
379	C₄⋊C₄×C₅₃	—	2	2	no	—
380	C₄⋊C₄×C₅₃	—	2	2	no	—
381	C₄⋊C₄×C₅₃	—	2	1	no	—
382	C₄⋊C₄×C₅₃	—	2	1	no	—
383	C₄⋊C₄×C₅₃	—	2	2	no	—
384	C₄⋊C₄×C₅₃	—	2	1	no	—
385	C₄⋊C₄×C₅₃	—	2	2	no	—
386	C₄⋊C₄×C₅₃	—	2	1	no	—
387	C₄⋊C₄×C₅₃	—	2	2	no	—
388	C₄⋊C₄×C₅₃	—	2	2	no	—
389	C₄⋊C₄×C₅₃	—	2	2	no	—
390	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
396	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²⋊C₄×C₅₃	—	2	2	no	—
404	C₂²⋊C₄×C₅₃	—	2	2	no	—
405	C₂²⋊C₄×C₅₃	—	2	2	no	—
406	C₂²⋊C₄×C₅₃	—	2	2	no	—
407	C₂²⋊C₄×C₅₃	—	2	1	no	—
408	C₂²⋊C₄×C₅₃	—	2	1	no	—
409	C₂²⋊C₄×C₅₃	—	2	1	no	—
410	C₂²⋊C₄×C₅₃	—	2	2	no	—
411	C₂²⋊C₄×C₅₃	—	2	1	no	—
412	C₂²⋊C₄×C₅₃	—	2	1	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
414	C₂²⋊C₄×C₅₃	—	2	2	no	—
415	C₂²⋊C₄×C₅₃	—	2	2	no	—
416	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
417	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
418	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
419	C₄²×C₅₃	—	2	2	no	—
420	C₄²×C₅₃	—	2	1	no	—
421	C₄²×C₅₃	—	2	1	no	—
422	C₄²×C₅₃	—	2	1	no	—
423	C₄²×C₅₃	—	2	2	no	—
424	C₄²×C₅₃	—	2	2	no	—
425	C₄²×C₅₃	—	2	2	no	—
426	C₄²×C₅₃	—	2	1	no	—
427	C₄²×C₅₃	—	2	1	no	—
428	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
429	C₄²×C₅₃	C₂×D₄	1	2	yes	—
430	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₅₃	C₂×D₄	1	2	yes	—
432	C₄²×C₅₃	C₂⁴	1	2	yes	—
433	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
434	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
435	C₂³×C₅₃	—	2	1	no	—
436	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
437	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
438	Q₈×C₅₃	—	2	2	no	—
439	Q₈×C₅₃	—	2	2	no	—
440	Q₈×C₅₃	—	2	2	no	—
441	Q₈×C₅₃	—	2	1	no	—
442	Q₈×C₅₃	—	2	1	no	—
443	Q₈×C₅₃	—	4	2	no	—
444	Q₈×C₅₃	—	8	1	no	—
445	Q₈×C₅₃	—	8	2	no	—
446	Q₈×C₅₃	—	8	2	no	—
447	Q₈×C₅₃	—	8	1	no	—
448	Q₈×C₅₃	—	8	2	no	—
449	D₄×C₅₃	—	2	4	no	—
450	D₄×C₅₃	—	2	2	no	—
451	D₄×C₅₃	—	2	1	no	—
452	D₄×C₅₃	—	2	1	no	—
453	D₄×C₅₃	—	4	2	no	—
454	D₄×C₅₃	—	8	2	no	—
455	C₂×C₄×C₅₃	—	2	2	no	—
456	C₂×C₄×C₅₃	—	2	2	no	—
457	C₂×C₄×C₅₃	—	2	1	no	—
458	C₂×C₄×C₅₃	—	2	2	no	—
459	C₂×C₄×C₅₃	—	2	1	no	—
460	C₂×C₄×C₅₃	—	2	2	no	—
461	C₂×C₄×C₅₃	—	2	2	no	—
462	C₂×C₄×C₅₃	—	2	1	no	—
463	C₂×C₄×C₅₃	—	2	1	no	—
464	C₂×C₄×C₅₃	—	2	2	no	—
465	C₂×C₄×C₅₃	—	2	1	no	—
466	C₂×C₄×C₅₃	—	2	1	no	—
467	C₂×C₄×C₅₃	—	2	1	no	—
468	C₂×C₄×C₅₃	—	4	1	no	—
469	C₂×C₄×C₅₃	—	4	2	no	—
470	C₂×C₄×C₅₃	—	4	1	no	—
471	C₂×C₄×C₅₃	—	4	2	no	—
472	C₂×C₄×C₅₃	—	4	2	no	—
473	C₂×C₄×C₅₃	—	4	2	no	—
474	C₂×C₄×C₅₃	—	4	2	no	—
475	C₂×C₄×C₅₃	—	8	1	no	—
476	C₂×C₄×C₅₃	—	8	1	no	—
477	C₂×C₄×C₅₃	—	8	2	no	—
478	C₂×C₄×C₅₃	—	8	1	no	—
479	C₂×C₄×C₅₃	—	8	1	no	—
480	C₂×C₄×C₅₃	—	8	2	no	—
481	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
490	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
491	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
492	C₈×C₅₃	—	2	1	no	—
493	C₈×C₅₃	—	2	1	no	—
494	C₈×C₅₃	—	2	1	no	—
495	C₈×C₅₃	—	2	1	no	—
496	C₈×C₅₃	—	2	2	no	—
497	C₈×C₅₃	—	2	2	no	—
498	#60891	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
499	C₂²×C₅₃	—	2	1	no	—
500	C₂²×C₅₃	—	2	1	no	—
501	C₂²×C₅₃	—	2	2	no	—
502	C₂²×C₅₃	—	2	2	no	—
503	C₂²×C₅₃	—	2	2	no	—
504	C₂²×C₅₃	—	4	1	no	—
505	C₂²×C₅₃	—	4	1	no	—
506	C₂²×C₅₃	—	4	1	no	—
507	C₂²×C₅₃	#536	1	2	yes	—
508	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
509	C₄×C₅₃	—	2	1	no	—
510	C₄×C₅₃	—	2	1	no	—
511	C₄×C₅₃	—	2	2	no	—
512	C₄×C₅₃	—	2	1	no	—
513	C₄×C₅₃	—	2	1	no	—
514	C₄×C₅₃	—	2	2	no	—
515	C₄×C₅₃	—	2	2	no	—
516	C₄×C₅₃	—	4	2	no	—
517	C₄×C₅₃	—	4	1	no	—
518	C₄×C₅₃	—	4	2	no	—
519	C₄×C₅₃	—	4	1	no	—
520	C₄×C₅₃	—	4	1	no	—
521	C₄×C₅₃	—	4	1	no	—
522	C₄×C₅₃	—	4	2	no	—
523	C₄×C₅₃	—	4	1	no	—
524	C₄×C₅₃	—	4	1	no	—
525	C₄×C₅₃	—	4	1	no	—
526	C₄×C₅₃	—	4	2	no	—
527	C₄×C₅₃	#536	1	2	yes	—
528	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
529	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	#3504	C₂×C₅₃	1	1	yes	characteristic, complemented
531	#3461	C₂×C₅₃	1	1	yes	characteristic
532	#3244	C₂×C₅₃	1	2	yes	complemented
533	#3243	C₂×C₅₃	1	2	yes	complemented
534	#3242	C₂×C₅₃	1	2	yes	complemented
535	#3242	C₂×C₅₃	1	2	yes	complemented
536	#3240	C₂×C₅₃	1	2	yes	complemented
537	#3236	C₂×C₅₃	1	2	yes	complemented
538	#3232	C₂×C₅₃	1	2	yes	complemented
539	#3231	C₂×C₅₃	1	2	yes	complemented
540	#3164	C₂×C₅₃	1	1	yes	characteristic, complemented
541	#3163	C₂×C₅₃	1	1	yes	characteristic, complemented
542	#3137	C₂×C₅₃	1	1	yes	characteristic, complemented
543	#3137	C₂×C₅₃	1	1	yes	characteristic, complemented
544	#3099	C₂×C₅₃	1	1	yes	characteristic
545	#3098	C₂×C₅₃	1	1	yes	characteristic
546	#3097	C₂×C₅₃	1	1	yes	characteristic, complemented
547	#3097	C₂×C₅₃	1	1	yes	characteristic, complemented
548	#3080	C₂×C₅₃	1	1	yes	characteristic, complemented
549	#3078	C₂×C₅₃	1	1	yes	characteristic, complemented
550	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
551	C₂×#479	C₂×C₅₃	1	1	yes	characteristic, complemented
552	#2925	C₂×C₅₃	1	1	yes	characteristic, complemented
553	C₂×C₅₃	—	2	2	no	—
554	C₂×C₅₃	—	4	2	no	—
555	C₂×C₅₃	—	8	1	no	—
556	C₂×C₅₃	C₂×#536	1	1	yes	characteristic
557	C₂×C₅₃	#3584	1	1	yes	characteristic
558	C₂×C₅₃	#3586	1	1	yes	characteristic
559	#557	—	2	1	no	—
560	#557	—	2	1	no	—
561	#554	—	2	2	no	—
562	#554	—	2	1	no	—
563	#554	—	2	2	no	—
564	#554	—	2	1	no	—
565	#544	C₂²×C₅₃	1	1	yes	characteristic
566	#544	C₂²×C₅₃	1	1	yes	characteristic
567	#544	C₂²×C₅₃	1	1	yes	characteristic
568	#544	C₂²×C₅₃	1	2	yes	—
569	#544	C₂²×C₅₃	1	2	yes	—
570	#542	—	2	1	no	—
571	#542	C₂²×C₅₃	1	2	yes	—
572	#541	—	2	1	no	—
573	#541	C₂²×C₅₃	1	2	yes	—
574	#539	—	2	2	no	—
575	#537	C₂²×C₅₃	1	1	yes	characteristic
576	#536	C₂²×C₅₃	1	1	yes	characteristic
577	#536	C₂²×C₅₃	1	1	yes	characteristic
578	#533	—	2	1	no	—
579	#533	C₂²×C₅₃	1	2	yes	—
580	#533	C₂²×C₅₃	1	1	yes	characteristic
581	#533	C₂²×C₅₃	1	2	yes	—
582	#529	—	2	2	no	—
583	#529	—	2	1	no	—
584	#529	C₂²×C₅₃	1	2	yes	—
585	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
586	C₂×#125	C₂²×C₅₃	1	2	yes	—
587	#520	C₂²×C₅₃	1	1	yes	characteristic
588	#520	C₂²×C₅₃	1	1	yes	characteristic
589	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
590	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
591	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
592	#501	C₂²×C₅₃	1	2	yes	—
593	#501	C₂²×C₅₃	1	2	yes	—
594	#501	C₂²×C₅₃	1	2	yes	—
595	#501	C₂²×C₅₃	1	2	yes	—
596	#500	C₂²×C₅₃	1	2	yes	—
597	#499	C₂²×C₅₃	1	2	yes	—
598	#499	C₂²×C₅₃	1	2	yes	—
599	#498	C₂²×C₅₃	1	2	yes	—
600	#491	C₂²×C₅₃	1	2	yes	—
601	#491	C₂²×C₅₃	1	2	yes	—
602	#489	C₂²×C₅₃	1	2	yes	—
603	#489	C₂²×C₅₃	1	2	yes	—
604	#488	C₂²×C₅₃	1	2	yes	—
605	#488	C₂²×C₅₃	1	2	yes	—
606	#487	C₂²×C₅₃	1	2	yes	—
607	#487	C₂²×C₅₃	1	2	yes	—
608	#485	C₂²×C₅₃	1	2	yes	—
609	#485	C₂²×C₅₃	1	2	yes	—
610	#485	C₂²×C₅₃	1	2	yes	—
611	#485	C₂²×C₅₃	1	2	yes	—
612	#485	C₂²×C₅₃	1	2	yes	—
613	#485	C₂²×C₅₃	1	2	yes	—
614	#484	C₂²×C₅₃	1	2	yes	—
615	#484	C₂²×C₅₃	1	2	yes	—
616	#484	C₂²×C₅₃	1	2	yes	—
617	#483	C₂²×C₅₃	1	2	yes	—
618	#483	C₂²×C₅₃	1	2	yes	—
619	#483	C₂²×C₅₃	1	2	yes	—
620	#482	C₂²×C₅₃	1	2	yes	—
621	#482	C₂²×C₅₃	1	2	yes	—
622	#481	C₂²×C₅₃	1	2	yes	—
623	#480	C₂²×C₅₃	1	2	yes	—
624	#479	C₂²×C₅₃	1	2	yes	—
625	#479	C₂²×C₅₃	1	2	yes	—
626	#479	C₂²×C₅₃	1	2	yes	—
627	#479	C₂²×C₅₃	1	2	yes	—
628	#479	C₂²×C₅₃	1	1	yes	characteristic
629	#479	C₂²×C₅₃	1	1	yes	characteristic
630	#479	C₂²×C₅₃	1	2	yes	—
631	#479	C₂²×C₅₃	1	2	yes	—
632	#479	C₂²×C₅₃	1	2	yes	—
633	#479	C₂²×C₅₃	1	2	yes	—
634	#478	C₂²×C₅₃	1	1	yes	characteristic
635	#478	C₂²×C₅₃	1	1	yes	characteristic
636	#478	C₂²×C₅₃	1	2	yes	—
637	#478	C₂²×C₅₃	1	2	yes	—
638	#477	C₂²×C₅₃	1	1	yes	characteristic
639	#477	C₂²×C₅₃	1	2	yes	—
640	#476	C₂²×C₅₃	1	1	yes	characteristic
641	#475	C₂²×C₅₃	1	1	yes	characteristic
642	#475	C₂²×C₅₃	1	2	yes	—
643	#474	C₂²×C₅₃	1	1	yes	characteristic
644	#433	C₂²×C₅₃	1	2	yes	—
645	#433	C₂²×C₅₃	1	2	yes	—
646	#432	C₂²×C₅₃	1	2	yes	—
647	#431	C₂²×C₅₃	1	2	yes	—
648	#428	C₂²×C₅₃	1	1	yes	characteristic
649	#428	C₂²×C₅₃	1	1	yes	characteristic
650	#428	C₂²×C₅₃	1	1	yes	characteristic
651	#428	C₂²×C₅₃	1	1	yes	characteristic
652	#427	C₂²×C₅₃	1	1	yes	characteristic
653	#427	C₂²×C₅₃	1	1	yes	characteristic
654	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
655	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
656	#423	C₂²×C₅₃	1	1	yes	characteristic
657	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
658	#419	C₂²×C₅₃	1	1	yes	characteristic
659	#419	C₂²×C₅₃	1	1	yes	characteristic
660	#417	C₂²×C₅₃	1	1	yes	characteristic
661	#417	C₂²×C₅₃	1	1	yes	characteristic
662	#416	C₂²×C₅₃	1	1	yes	characteristic
663	#416	C₂²×C₅₃	1	1	yes	characteristic
664	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
665	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
666	#408	C₂²×C₅₃	1	1	yes	characteristic
667	#408	C₂²×C₅₃	1	1	yes	characteristic
668	#405	C₂²×C₅₃	1	1	yes	characteristic
669	#405	C₂²×C₅₃	1	1	yes	characteristic
670	C₅₃	#60891	1	1	yes	characteristic, direct product factor, Sylow
671	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
672	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
673	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
674	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
675	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
676	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
677	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	—	2	1	no	—
680	C₄⋊Q₈	—	2	1	no	—
681	C₄⋊Q₈	—	2	2	no	—
682	C₄⋊Q₈	—	2	1	no	—
683	C₄⋊Q₈	—	2	2	no	—
684	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
685	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
686	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
687	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
688	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
689	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
690	#126	—	2	2	no	—
691	#126	—	2	2	no	—
692	#126	—	2	2	no	—
693	#126	—	2	2	no	—
694	#125	—	2	2	no	—
695	#125	—	2	1	no	—
696	#125	—	2	2	no	—
697	#125	—	2	1	no	—
698	#125	—	2	2	no	—
699	#125	—	2	1	no	—
700	#125	—	2	2	no	—
701	#125	—	2	1	no	—
702	#125	—	2	1	no	—
703	#125	—	2	2	no	—
704	#125	—	2	2	no	—
705	#125	—	2	2	no	—
706	#125	C₂³×C₅₃	1	2	yes	—
707	#125	C₂³×C₅₃	1	1	yes	characteristic
708	#125	C₂³×C₅₃	1	2	yes	—
709	#125	C₂³×C₅₃	1	2	yes	—
710	#125	C₂³×C₅₃	1	2	yes	—
711	#125	C₂³×C₅₃	1	2	yes	—
712	#125	C₂³×C₅₃	1	1	yes	characteristic
713	#124	—	2	1	no	—
714	#124	—	2	2	no	—
715	#124	C₂³×C₅₃	1	2	yes	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	1	no	—
727	C₂²⋊Q₈	—	2	1	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
737	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
738	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
739	#121	—	2	2	no	—
740	#121	—	2	1	no	—
741	#121	C₂³×C₅₃	1	2	yes	—
742	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	2	no	—
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	2	no	—
750	C₄×Q₈	—	2	2	no	—
751	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
752	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
753	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
754	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
755	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
757	C₄×D₄	—	2	2	no	—
758	C₄×D₄	—	2	2	no	—
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	1	no	—
762	C₄×D₄	—	2	1	no	—
763	C₄×D₄	—	2	2	no	—
764	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
765	C₄×D₄	D₄×C₅₃	1	2	yes	—
766	C₄×D₄	D₄×C₅₃	1	2	yes	—
767	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
768	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
769	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
770	#117	—	2	2	no	—
771	#117	—	2	1	no	—
772	#117	—	2	2	no	—
773	#117	C₂³×C₅₃	1	1	yes	characteristic
774	#117	C₂³×C₅₃	1	1	yes	characteristic
775	#117	C₂³×C₅₃	1	1	yes	characteristic
776	#117	C₂³×C₅₃	1	2	yes	—
777	#117	C₂³×C₅₃	1	2	yes	—
778	#117	C₂³×C₅₃	1	1	yes	characteristic
779	#117	C₂³×C₅₃	1	2	yes	—
780	C₂×C₄⋊C₄	—	2	1	no	—
781	C₂×C₄⋊C₄	—	2	1	no	—
782	C₂×C₄⋊C₄	—	2	1	no	—
783	C₂×C₄⋊C₄	—	2	2	no	—
784	C₂×C₄⋊C₄	—	2	2	no	—
785	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
787	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
788	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
789	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
790	C₂×C₄²	—	2	1	no	—
791	C₂×C₄²	—	2	1	no	—
792	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
794	#107	C₂³×C₅₃	1	2	yes	—
795	#107	C₂³×C₅₃	1	2	yes	—
796	#107	C₂³×C₅₃	1	1	yes	characteristic
797	#107	C₂³×C₅₃	1	1	yes	characteristic
798	#107	C₂³×C₅₃	1	1	yes	characteristic
799	#107	C₂³×C₅₃	1	1	yes	characteristic
800	#107	C₂³×C₅₃	1	2	yes	—
801	#107	C₂³×C₅₃	1	2	yes	—
802	#107	C₂³×C₅₃	1	2	yes	—
803	#107	C₂³×C₅₃	1	2	yes	—
804	#106	C₂³×C₅₃	1	2	yes	—
805	#106	C₂³×C₅₃	1	2	yes	—
806	#106	C₂³×C₅₃	1	1	yes	characteristic
807	#106	C₂³×C₅₃	1	1	yes	characteristic
808	#106	C₂³×C₅₃	1	1	yes	characteristic
809	#106	C₂³×C₅₃	1	1	yes	characteristic
810	#106	C₂³×C₅₃	1	2	yes	—
811	#106	C₂³×C₅₃	1	2	yes	—
812	#106	C₂³×C₅₃	1	2	yes	—
813	#106	C₂³×C₅₃	1	2	yes	—
814	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
819	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
820	#103	C₂³×C₅₃	1	2	yes	—
821	#103	C₂³×C₅₃	1	2	yes	—
822	#103	C₂³×C₅₃	1	2	yes	—
823	#103	C₂³×C₅₃	1	2	yes	—
824	#103	C₂³×C₅₃	1	1	yes	characteristic
825	#103	C₂³×C₅₃	1	1	yes	characteristic
826	#103	C₂³×C₅₃	1	1	yes	characteristic
827	#103	C₂³×C₅₃	1	1	yes	characteristic
828	#103	C₂³×C₅₃	1	2	yes	—
829	#103	C₂³×C₅₃	1	2	yes	—
830	#103	C₂³×C₅₃	1	2	yes	—
831	#103	C₂³×C₅₃	1	2	yes	—
832	#103	C₂³×C₅₃	1	2	yes	—
833	#103	C₂³×C₅₃	1	2	yes	—
834	#102	C₂³×C₅₃	1	1	yes	characteristic
835	#102	C₂³×C₅₃	1	1	yes	characteristic
836	#102	C₂³×C₅₃	1	1	yes	characteristic
837	#102	C₂³×C₅₃	1	1	yes	characteristic
838	#102	C₂³×C₅₃	1	2	yes	—
839	#102	C₂³×C₅₃	1	2	yes	—
840	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
841	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
842	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
843	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
844	#97	C₂³×C₅₃	1	2	yes	—
845	#97	C₂³×C₅₃	1	2	yes	—
846	C₄×C₈	C₂³×C₅₃	1	2	yes	—
847	C₄×C₈	C₂³×C₅₃	1	2	yes	—
848	#41	—	2	2	no	—
849	#41	—	2	2	no	—
850	#41	—	2	2	no	—
851	#41	—	2	2	no	—
852	C₂×Q₈	—	2	1	no	—
853	C₂×Q₈	—	2	2	no	—
854	C₂×Q₈	—	2	1	no	—
855	C₂×Q₈	—	2	1	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	2	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
861	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
862	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
863	C₂×D₄	—	2	1	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
866	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
867	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
878	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
879	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
880	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
882	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
883	M₁₆	—	2	2	no	—
884	M₁₆	—	2	2	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	—	2	2	no	—
887	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
888	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
889	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
890	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
891	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
892	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
927	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
928	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
929	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
930	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
931	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
932	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
934	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
936	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
937	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
938	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	1	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	1	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
953	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
954	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	1	no	—
957	C₄²	—	2	1	no	—
958	C₄²	—	2	1	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	1	no	—
963	C₄²	—	2	1	no	—
964	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
965	C₄²	C₂×D₄×C₅₃	1	2	yes	—
966	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
967	C₄²	C₂×D₄×C₅₃	1	2	yes	—
968	C₄²	C₂⁴×C₅₃	1	2	yes	—
969	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
970	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
971	C₂³	—	2	1	no	—
972	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
973	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	2	2	no	—
977	Q₈	—	2	1	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	4	2	no	—
980	Q₈	—	8	1	no	—
981	Q₈	—	8	2	no	—
982	Q₈	—	8	2	no	—
983	Q₈	—	8	1	no	—
984	Q₈	—	8	2	no	—
985	D₄	—	2	4	no	—
986	D₄	—	2	2	no	—
987	D₄	—	2	1	no	—
988	D₄	—	2	1	no	—
989	D₄	—	4	2	no	—
990	D₄	—	8	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	4	2	no	—
1006	C₂×C₄	—	4	1	no	—
1007	C₂×C₄	—	4	2	no	—
1008	C₂×C₄	—	4	2	no	—
1009	C₂×C₄	—	4	2	no	—
1010	C₂×C₄	—	4	2	no	—
1011	C₂×C₄	—	8	1	no	—
1012	C₂×C₄	—	8	1	no	—
1013	C₂×C₄	—	8	2	no	—
1014	C₂×C₄	—	8	1	no	—
1015	C₂×C₄	—	8	1	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1019	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1020	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1023	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1024	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1025	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1026	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1027	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	2	no	—
1033	C₈	—	2	2	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	C₅₃×#536	1	2	yes	—
1043	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1044	C₄	—	2	2	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	2	1	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	2	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	1	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	1	no	—
1062	C₄	C₅₃×#536	1	2	yes	—
1063	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1064	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1065	C₂	—	2	2	no	—
1066	C₂	—	4	2	no	—
1067	C₂	—	8	1	no	—
1068	C₂	C₂×C₅₃×#536	1	1	yes	characteristic
1069	C₂	C₅₃×#3584	1	1	yes	characteristic
1070	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#537	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3504	C₂	semidirect
3. C₅₃×#3244	C₂	semidirect
4. C₅₃×#3243	C₂	semidirect
5. C₅₃×#3242	C₂	semidirect
6. C₅₃×#3242	C₂	semidirect
7. C₅₃×#3240	C₂	semidirect
8. C₅₃×#3236	C₂	semidirect
9. C₅₃×#3232	C₂	semidirect
10. C₅₃×#3231	C₂	semidirect
11. C₅₃×#3164	C₂	semidirect
12. C₅₃×#3163	C₂	semidirect
13. C₅₃×#3137	C₂	semidirect
14. C₅₃×#3137	C₂	semidirect
17. C₅₃×#3097	C₂	semidirect
18. C₅₃×#3097	C₂	semidirect
19. C₅₃×#3080	C₂	semidirect
20. C₅₃×#3078	C₂	semidirect
21. C₅₃×#3076	C₂	semidirect
22. C₂×C₅₃×#479	C₂	semidirect
23. C₅₃×#2925	C₂	semidirect
498. #60891	C₅₃	direct (N × H)
530. #3504	C₂×C₅₃	semidirect
532. #3244	C₂×C₅₃	semidirect
533. #3243	C₂×C₅₃	semidirect
534. #3242	C₂×C₅₃	semidirect
535. #3242	C₂×C₅₃	semidirect
536. #3240	C₂×C₅₃	semidirect
537. #3236	C₂×C₅₃	semidirect
538. #3232	C₂×C₅₃	semidirect
539. #3231	C₂×C₅₃	semidirect
540. #3164	C₂×C₅₃	semidirect
541. #3163	C₂×C₅₃	semidirect
542. #3137	C₂×C₅₃	semidirect
543. #3137	C₂×C₅₃	semidirect
546. #3097	C₂×C₅₃	semidirect
547. #3097	C₂×C₅₃	semidirect
548. #3080	C₂×C₅₃	semidirect
549. #3078	C₂×C₅₃	semidirect
550. #3076	C₂×C₅₃	semidirect
551. C₂×#479	C₂×C₅₃	semidirect
552. #2925	C₂×C₅₃	semidirect
670. C₅₃	#60891	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3504	2
C₅₃×#3461	2
C₅₃×#3244	2
C₅₃×#3243	2
C₅₃×#3242	2
C₅₃×#3240	2
C₅₃×#3236	2
C₅₃×#3232	2
C₅₃×#3231	2
C₅₃×#3164	2
C₅₃×#3163	2
C₅₃×#3137	2
C₅₃×#3099	2
C₅₃×#3098	2
C₅₃×#3097	2
C₅₃×#3080	2
C₅₃×#3078	2
C₅₃×#3076	2
C₂×C₅₃×#479	2
C₅₃×#2925	2
#60891	53

Subgroups — C53×#60891 #27268403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60891 #27268403