Subgroups — C₅₃×#61864 #27269376

Order 13568.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3388	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3381	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3376	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3360	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3244	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3242	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3123	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3118	C₂	1	2	yes	maximal
21	C₅₃×#3105	C₂	1	1	yes	maximal, characteristic
22	C₅₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#563	—	2	2	no	—
25	Q₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
27	C₅₃×#557	C₂²	1	2	yes	complemented
28	C₅₃×#556	—	2	1	no	—
29	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#556	C₂²	1	2	yes	complemented
31	C₅₃×#554	—	2	1	no	—
32	C₅₃×#554	—	2	2	no	—
33	C₅₃×#554	C₂²	1	1	yes	characteristic
34	C₅₃×#554	C₂²	1	2	yes	—
35	C₅₃×#554	C₂²	1	1	yes	characteristic
36	C₅₃×#554	C₂²	1	2	yes	—
37	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#552	—	2	1	no	—
39	D₄×Q₈×C₅₃	—	2	1	no	—
40	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
42	C₅₃×#544	—	2	1	no	—
43	C₅₃×#544	C₂²	1	2	yes	—
44	C₅₃×#543	—	2	2	no	—
45	C₅₃×#542	C₂²	1	2	yes	—
46	C₅₃×#541	—	2	1	no	—
47	C₅₃×#541	—	2	2	no	—
48	C₅₃×#541	C₂²	1	2	yes	—
49	C₅₃×#533	C₂²	1	1	yes	characteristic
50	C₅₃×#533	C₂²	1	1	yes	characteristic
51	C₅₃×#533	C₂²	1	1	yes	characteristic
52	C₅₃×#529	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
54	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
55	C₅₃×#518	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#501	C₂²	1	2	yes	complemented
58	C₅₃×#501	C₂²	1	2	yes	complemented
59	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#499	C₂²	1	2	yes	complemented
61	C₅₃×#499	C₂²	1	2	yes	complemented
62	C₅₃×#498	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#498	C₂²	1	2	yes	complemented
64	C₅₃×#491	C₂²	1	2	yes	complemented
65	C₅₃×#489	C₂²	1	2	yes	complemented
66	C₅₃×#488	C₂²	1	2	yes	complemented
67	C₅₃×#488	C₂²	1	2	yes	complemented
68	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#487	C₂²	1	2	yes	complemented
71	C₅₃×#485	C₂²	1	2	yes	—
72	C₅₃×#485	C₂²	1	2	yes	—
73	C₅₃×#485	C₂²	1	2	yes	—
74	C₅₃×#484	C₂²	1	1	yes	characteristic
75	C₅₃×#483	C₂²	1	2	yes	—
76	C₅₃×#482	C₂²	1	2	yes	—
77	C₅₃×#481	C₂²	1	1	yes	characteristic
78	C₅₃×#479	C₂²	1	2	yes	complemented
79	C₅₃×#479	C₂²	1	2	yes	complemented
80	C₅₃×#479	C₂²	1	2	yes	complemented
81	C₅₃×#479	C₂²	1	2	yes	complemented
82	C₅₃×#479	C₂²	1	2	yes	complemented
83	C₅₃×#478	C₂²	1	1	yes	characteristic
84	C₅₃×#478	C₂²	1	1	yes	characteristic
85	C₅₃×#478	C₂²	1	2	yes	—
86	C₅₃×#478	C₂²	1	2	yes	—
87	C₅₃×#478	C₂²	1	2	yes	complemented
88	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#477	C₂²	1	2	yes	complemented
90	C₅₃×#476	C₂²	1	1	yes	characteristic
91	C₅₃×#476	C₂²	1	1	yes	characteristic
92	C₅₃×#476	C₂²	1	2	yes	—
93	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#476	C₂²	1	2	yes	complemented
95	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#475	C₂²	1	2	yes	complemented
97	C₅₃×#475	C₂²	1	2	yes	complemented
98	C₅₃×#474	C₂²	1	2	yes	—
99	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#463	C₂²	1	1	yes	characteristic
101	C₅₃×#463	C₂²	1	2	yes	—
102	C₅₃×#463	C₂²	1	2	yes	—
103	C₅₃×#463	C₂²	1	1	yes	characteristic
104	C₅₃×#461	C₂²	1	1	yes	characteristic
105	C₅₃×#461	C₂²	1	1	yes	characteristic
106	C₅₃×#461	C₂²	1	2	yes	—
107	C₅₃×#461	C₂²	1	2	yes	—
108	C₅₃×#450	C₂²	1	2	yes	—
109	C₅₃×#450	C₂²	1	1	yes	characteristic
110	C₅₃×#447	C₂²	1	1	yes	characteristic
111	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#446	C₂²	1	2	yes	complemented
114	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
117	C₅₃×#442	C₂²	1	2	yes	—
118	C₅₃×#440	C₂²	1	2	yes	—
119	C₅₃×#440	C₂²	1	2	yes	—
120	C₅₃×#440	C₂²	1	2	yes	—
121	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
122	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
123	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
124	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
125	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
126	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
128	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₅₃	C₂²	1	2	yes	—
130	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
131	C₅₃×#433	C₂²	1	2	yes	—
132	C₅₃×#433	C₂²	1	2	yes	—
133	C₅₃×#431	C₂²	1	1	yes	characteristic
134	C₅₃×#431	C₂²	1	1	yes	characteristic
135	C₂²×Q₈×C₅₃	—	2	1	no	—
136	C₂²×Q₈×C₅₃	—	2	1	no	—
137	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅₃	—	2	1	no	—
139	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
145	C₄⋊Q₈×C₅₃	—	2	2	no	—
146	C₄⋊Q₈×C₅₃	—	2	1	no	—
147	C₄⋊Q₈×C₅₃	—	2	2	no	—
148	C₄⋊Q₈×C₅₃	—	2	2	no	—
149	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
150	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
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	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
159	#126×C₅₃	—	2	2	no	—
160	#126×C₅₃	—	2	2	no	—
161	#126×C₅₃	—	2	2	no	—
162	#126×C₅₃	—	2	2	no	—
163	#126×C₅₃	—	2	2	no	—
164	#126×C₅₃	—	2	2	no	—
165	#126×C₅₃	—	2	1	no	—
166	#125×C₅₃	—	2	2	no	—
167	#125×C₅₃	—	2	2	no	—
168	#125×C₅₃	—	2	2	no	—
169	#125×C₅₃	—	2	2	no	—
170	#125×C₅₃	—	2	2	no	—
171	#125×C₅₃	—	2	1	no	—
172	#125×C₅₃	—	2	2	no	—
173	#125×C₅₃	—	2	1	no	—
174	#125×C₅₃	D₄	1	2	yes	—
175	#125×C₅₃	C₂³	1	2	yes	—
176	#125×C₅₃	C₂³	1	2	yes	—
177	#125×C₅₃	C₂³	1	2	yes	—
178	#125×C₅₃	C₂³	1	1	yes	characteristic
179	#125×C₅₃	C₂³	1	2	yes	—
180	#124×C₅₃	—	2	2	no	—
181	#124×C₅₃	C₂³	1	1	yes	characteristic
182	#124×C₅₃	C₂³	1	2	yes	—
183	#123×C₅₃	—	2	2	no	—
184	#123×C₅₃	—	2	1	no	—
185	C₂²⋊Q₈×C₅₃	—	2	1	no	—
186	C₂²⋊Q₈×C₅₃	—	2	1	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	2	no	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	—	2	2	no	—
198	C₂²⋊Q₈×C₅₃	—	2	2	no	—
199	C₂²⋊Q₈×C₅₃	—	2	1	no	—
200	C₂²⋊Q₈×C₅₃	—	2	1	no	—
201	C₂²⋊Q₈×C₅₃	—	2	1	no	—
202	C₂²⋊Q₈×C₅₃	—	2	1	no	—
203	C₂²⋊Q₈×C₅₃	—	2	2	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	2	no	—
206	C₂²⋊Q₈×C₅₃	—	2	1	no	—
207	C₂²⋊Q₈×C₅₃	—	2	1	no	—
208	C₂²⋊Q₈×C₅₃	—	2	1	no	—
209	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
211	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
212	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
214	#121×C₅₃	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₅₃	—	2	2	no	—
216	C₄×Q₈×C₅₃	—	2	1	no	—
217	C₄×Q₈×C₅₃	—	2	1	no	—
218	C₄×Q₈×C₅₃	—	2	1	no	—
219	C₄×Q₈×C₅₃	—	2	1	no	—
220	C₄×Q₈×C₅₃	—	2	1	no	—
221	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
227	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
228	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
229	C₄×D₄×C₅₃	—	2	2	no	—
230	C₄×D₄×C₅₃	—	2	2	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₅₃	C₂³	1	2	yes	—
239	C₄×D₄×C₅₃	C₂³	1	2	yes	—
240	C₄×D₄×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	C₂³	1	2	yes	—
242	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₃	C₂³	1	2	yes	—
244	#117×C₅₃	—	2	2	no	—
245	#117×C₅₃	—	2	1	no	—
246	#117×C₅₃	—	2	1	no	—
247	#117×C₅₃	—	2	1	no	—
248	#117×C₅₃	C₂³	1	2	yes	—
249	#117×C₅₃	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
251	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
252	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
253	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
254	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
257	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
258	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
259	C₂×C₄²×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	1	yes	characteristic
264	#107×C₅₃	C₂³	1	2	yes	—
265	#107×C₅₃	C₂³	1	1	yes	characteristic
266	#106×C₅₃	C₂³	1	2	yes	—
267	#106×C₅₃	C₂³	1	2	yes	—
268	#106×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
273	#106×C₅₃	C₂³	1	2	yes	—
274	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
279	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
280	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	#103×C₅₃	C₂³	1	2	yes	—
283	#103×C₅₃	C₂³	1	2	yes	—
284	#103×C₅₃	C₂³	1	2	yes	—
285	#103×C₅₃	C₂³	1	2	yes	—
286	#103×C₅₃	C₂³	1	2	yes	—
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	1	yes	characteristic
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#102×C₅₃	C₂³	1	1	yes	characteristic
293	#102×C₅₃	C₂³	1	2	yes	—
294	#102×C₅₃	C₂³	1	2	yes	—
295	#102×C₅₃	C₂³	1	1	yes	characteristic
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×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	1	yes	characteristic
301	#102×C₅₃	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
305	#97×C₅₃	C₂³	1	2	yes	—
306	#97×C₅₃	C₂³	1	2	yes	—
307	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₃	C₂³	1	2	yes	—
311	C₄×C₈×C₅₃	C₂³	1	2	yes	—
312	C₂⁴×C₅₃	—	2	1	no	—
313	C₂×Q₈×C₅₃	—	2	1	no	—
314	C₂×Q₈×C₅₃	—	2	1	no	—
315	C₂×Q₈×C₅₃	—	2	1	no	—
316	C₂×Q₈×C₅₃	—	2	2	no	—
317	C₂×Q₈×C₅₃	—	2	2	no	—
318	C₂×Q₈×C₅₃	—	2	2	no	—
319	C₂×Q₈×C₅₃	—	8	2	no	—
320	C₂×Q₈×C₅₃	—	8	2	no	—
321	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
324	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₅₃	—	2	2	no	—
327	C₂×D₄×C₅₃	—	2	2	no	—
328	C₂×D₄×C₅₃	—	2	1	no	—
329	C₂×D₄×C₅₃	—	2	1	no	—
330	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₅₃	—	2	1	no	—
334	C₂²×C₄×C₅₃	—	2	1	no	—
335	C₂²×C₄×C₅₃	—	2	1	no	—
336	C₂²×C₄×C₅₃	—	2	1	no	—
337	C₂²×C₄×C₅₃	—	2	2	no	—
338	C₂²×C₄×C₅₃	—	2	2	no	—
339	C₂²×C₄×C₅₃	—	2	2	no	—
340	C₂²×C₄×C₅₃	—	2	2	no	—
341	C₂²×C₄×C₅₃	—	2	1	no	—
342	C₂²×C₄×C₅₃	—	2	1	no	—
343	C₂²×C₄×C₅₃	—	2	2	no	—
344	C₂²×C₄×C₅₃	—	8	2	no	—
345	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
348	SD₁₆×C₅₃	—	2	4	no	—
349	SD₁₆×C₅₃	—	2	2	no	—
350	SD₁₆×C₅₃	—	2	4	no	—
351	SD₁₆×C₅₃	—	2	2	no	—
352	D₈×C₅₃	—	2	2	no	—
353	D₈×C₅₃	—	2	2	no	—
354	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
356	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
359	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₄⋊C₄×C₅₃	—	2	2	no	—
361	C₄⋊C₄×C₅₃	—	2	1	no	—
362	C₄⋊C₄×C₅₃	—	2	1	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	1	no	—
371	C₄⋊C₄×C₅₃	—	2	1	no	—
372	C₄⋊C₄×C₅₃	—	2	2	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	1	no	—
378	C₄⋊C₄×C₅₃	—	2	2	no	—
379	C₄⋊C₄×C₅₃	—	2	2	no	—
380	C₄⋊C₄×C₅₃	—	2	1	no	—
381	C₄⋊C₄×C₅₃	—	2	2	no	—
382	C₄⋊C₄×C₅₃	—	2	2	no	—
383	C₄⋊C₄×C₅₃	—	2	2	no	—
384	C₄⋊C₄×C₅₃	—	2	2	no	—
385	C₄⋊C₄×C₅₃	—	2	2	no	—
386	C₄⋊C₄×C₅₃	—	2	2	no	—
387	C₄⋊C₄×C₅₃	—	2	1	no	—
388	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
389	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
390	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
391	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
404	C₂²⋊C₄×C₅₃	—	2	2	no	—
405	C₂²⋊C₄×C₅₃	—	2	2	no	—
406	C₂²⋊C₄×C₅₃	—	2	1	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	1	no	—
411	C₂²⋊C₄×C₅₃	—	2	2	no	—
412	C₂²⋊C₄×C₅₃	—	2	2	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
414	C₂²⋊C₄×C₅₃	—	2	2	no	—
415	C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂²⋊C₄×C₅₃	—	2	1	no	—
417	C₂²⋊C₄×C₅₃	—	2	1	no	—
418	C₂²⋊C₄×C₅₃	—	2	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	1	no	—
421	C₂²⋊C₄×C₅₃	—	2	2	no	—
422	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
424	C₄²×C₅₃	—	2	2	no	—
425	C₄²×C₅₃	—	2	1	no	—
426	C₄²×C₅₃	—	2	2	no	—
427	C₄²×C₅₃	—	2	2	no	—
428	C₄²×C₅₃	—	2	2	no	—
429	C₄²×C₅₃	—	2	2	no	—
430	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
432	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
433	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
434	C₄²×C₅₃	C₂⁴	1	2	yes	—
435	C₄²×C₅₃	C₂⁴	1	2	yes	—
436	C₂³×C₅₃	—	2	4	no	—
437	C₂³×C₅₃	—	2	1	no	—
438	C₂³×C₅₃	—	2	1	no	—
439	C₂³×C₅₃	—	2	1	no	—
440	C₂³×C₅₃	—	8	1	no	—
441	C₂³×C₅₃	—	8	1	no	—
442	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
443	Q₈×C₅₃	—	2	2	no	—
444	Q₈×C₅₃	—	2	2	no	—
445	Q₈×C₅₃	—	2	2	no	—
446	Q₈×C₅₃	—	2	2	no	—
447	Q₈×C₅₃	—	2	1	no	—
448	Q₈×C₅₃	—	2	1	no	—
449	Q₈×C₅₃	—	4	2	no	—
450	Q₈×C₅₃	—	4	2	no	—
451	Q₈×C₅₃	—	8	1	no	—
452	Q₈×C₅₃	—	8	1	no	—
453	Q₈×C₅₃	—	8	2	no	—
454	Q₈×C₅₃	—	8	2	no	—
455	Q₈×C₅₃	—	8	2	no	—
456	D₄×C₅₃	—	2	4	no	—
457	D₄×C₅₃	—	2	1	no	—
458	D₄×C₅₃	—	2	1	no	—
459	D₄×C₅₃	—	2	1	no	—
460	D₄×C₅₃	—	2	1	no	—
461	D₄×C₅₃	—	8	1	no	—
462	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
463	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
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	—	2	1	no	—
469	C₂×C₄×C₅₃	—	2	2	no	—
470	C₂×C₄×C₅₃	—	2	2	no	—
471	C₂×C₄×C₅₃	—	2	2	no	—
472	C₂×C₄×C₅₃	—	2	1	no	—
473	C₂×C₄×C₅₃	—	2	1	no	—
474	C₂×C₄×C₅₃	—	2	2	no	—
475	C₂×C₄×C₅₃	—	2	1	no	—
476	C₂×C₄×C₅₃	—	4	1	no	—
477	C₂×C₄×C₅₃	—	4	2	no	—
478	C₂×C₄×C₅₃	—	4	2	no	—
479	C₂×C₄×C₅₃	—	4	2	no	—
480	C₂×C₄×C₅₃	—	8	2	no	—
481	C₂×C₄×C₅₃	—	8	2	no	—
482	C₂×C₄×C₅₃	—	8	2	no	—
483	C₂×C₄×C₅₃	—	8	1	no	—
484	C₂×C₄×C₅₃	—	8	1	no	—
485	C₂×C₄×C₅₃	—	8	2	no	—
486	C₂×C₄×C₅₃	—	8	2	no	—
487	C₂×C₄×C₅₃	—	8	1	no	—
488	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
498	C₈×C₅₃	—	2	1	no	—
499	C₈×C₅₃	—	2	1	no	—
500	C₈×C₅₃	—	2	1	no	—
501	C₈×C₅₃	—	2	2	no	—
502	C₈×C₅₃	—	2	1	no	—
503	C₈×C₅₃	—	2	2	no	—
504	#61864	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
505	C₂²×C₅₃	—	2	1	no	—
506	C₂²×C₅₃	—	2	1	no	—
507	C₂²×C₅₃	—	2	2	no	—
508	C₂²×C₅₃	—	2	2	no	—
509	C₂²×C₅₃	—	2	1	no	—
510	C₂²×C₅₃	—	4	1	no	—
511	C₂²×C₅₃	—	4	1	no	—
512	C₂²×C₅₃	—	4	1	no	—
513	C₂²×C₅₃	—	4	1	no	—
514	C₂²×C₅₃	—	4	1	no	—
515	C₂²×C₅₃	—	4	1	no	—
516	C₂²×C₅₃	—	4	1	no	—
517	C₂²×C₅₃	—	8	4	no	—
518	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
519	C₄×C₅₃	—	2	1	no	—
520	C₄×C₅₃	—	2	1	no	—
521	C₄×C₅₃	—	2	2	no	—
522	C₄×C₅₃	—	2	2	no	—
523	C₄×C₅₃	—	2	1	no	—
524	C₄×C₅₃	—	2	1	no	—
525	C₄×C₅₃	—	2	2	no	—
526	C₄×C₅₃	—	2	2	no	—
527	C₄×C₅₃	—	4	2	no	—
528	C₄×C₅₃	—	4	2	no	—
529	C₄×C₅₃	—	4	1	no	—
530	C₄×C₅₃	—	4	2	no	—
531	C₄×C₅₃	—	4	1	no	—
532	C₄×C₅₃	—	4	1	no	—
533	C₄×C₅₃	—	4	1	no	—
534	C₄×C₅₃	—	4	1	no	—
535	C₄×C₅₃	—	4	2	no	—
536	C₄×C₅₃	#577	1	2	yes	—
537	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
538	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
539	#3555	C₂×C₅₃	1	1	yes	characteristic, complemented
540	#3501	C₂×C₅₃	1	1	yes	characteristic, complemented
541	#3388	C₂×C₅₃	1	2	yes	complemented
542	#3385	C₂×C₅₃	1	1	yes	characteristic, complemented
543	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
544	#3381	C₂×C₅₃	1	2	yes	complemented
545	#3380	C₂×C₅₃	1	1	yes	characteristic, complemented
546	Q₈×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
547	#3376	C₂×C₅₃	1	2	yes	complemented
548	#3372	C₂×C₅₃	1	1	yes	characteristic, complemented
549	#3367	C₂×C₅₃	1	1	yes	characteristic, complemented
550	#3360	C₂×C₅₃	1	1	yes	characteristic, complemented
551	#3360	C₂×C₅₃	1	2	yes	complemented
552	#3359	C₂×C₅₃	1	1	yes	characteristic, complemented
553	#3244	C₂×C₅₃	1	2	yes	complemented
554	#3242	C₂×C₅₃	1	2	yes	complemented
555	#3233	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#3231	C₂×C₅₃	1	1	yes	characteristic, complemented
557	#3123	C₂×C₅₃	1	2	yes	complemented
558	#3118	C₂×C₅₃	1	2	yes	—
559	#3105	C₂×C₅₃	1	1	yes	characteristic
560	#3101	C₂×C₅₃	1	1	yes	characteristic, complemented
561	#2986	C₂×C₅₃	1	1	yes	characteristic, complemented
562	C₂×C₅₃	—	4	1	no	—
563	C₂×C₅₃	—	4	2	no	—
564	C₂×C₅₃	—	4	2	no	—
565	C₂×C₅₃	—	8	1	no	—
566	C₂×C₅₃	#3486	1	1	yes	characteristic
567	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
568	C₂×C₅₃	#3584	1	1	yes	characteristic
569	#563	—	2	2	no	—
570	Q₈²	C₂²×C₅₃	1	1	yes	characteristic, complemented
571	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
572	#557	C₂²×C₅₃	1	2	yes	complemented
573	#556	—	2	1	no	—
574	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
575	#556	C₂²×C₅₃	1	2	yes	complemented
576	#554	—	2	1	no	—
577	#554	—	2	2	no	—
578	#554	C₂²×C₅₃	1	1	yes	characteristic
579	#554	C₂²×C₅₃	1	2	yes	—
580	#554	C₂²×C₅₃	1	1	yes	characteristic
581	#554	C₂²×C₅₃	1	2	yes	—
582	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
583	#552	—	2	1	no	—
584	D₄×Q₈	—	2	1	no	—
585	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
586	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
587	#544	—	2	1	no	—
588	#544	C₂²×C₅₃	1	2	yes	—
589	#543	—	2	2	no	—
590	#542	C₂²×C₅₃	1	2	yes	—
591	#541	—	2	1	no	—
592	#541	—	2	2	no	—
593	#541	C₂²×C₅₃	1	2	yes	—
594	#533	C₂²×C₅₃	1	1	yes	characteristic
595	#533	C₂²×C₅₃	1	1	yes	characteristic
596	#533	C₂²×C₅₃	1	1	yes	characteristic
597	#529	C₂²×C₅₃	1	1	yes	characteristic
598	C₂×C₂²⋊Q₈	—	2	1	no	—
599	C₂×C₂²⋊Q₈	—	2	1	no	—
600	#518	C₂²×C₅₃	1	2	yes	—
601	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
602	#501	C₂²×C₅₃	1	2	yes	complemented
603	#501	C₂²×C₅₃	1	2	yes	complemented
604	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
605	#499	C₂²×C₅₃	1	2	yes	complemented
606	#499	C₂²×C₅₃	1	2	yes	complemented
607	#498	C₂²×C₅₃	1	2	yes	complemented
608	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
609	#491	C₂²×C₅₃	1	2	yes	complemented
610	#489	C₂²×C₅₃	1	2	yes	complemented
611	#488	C₂²×C₅₃	1	2	yes	complemented
612	#488	C₂²×C₅₃	1	2	yes	complemented
613	#487	C₂²×C₅₃	1	2	yes	complemented
614	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
615	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
616	#485	C₂²×C₅₃	1	2	yes	—
617	#485	C₂²×C₅₃	1	2	yes	—
618	#485	C₂²×C₅₃	1	2	yes	—
619	#484	C₂²×C₅₃	1	1	yes	characteristic
620	#483	C₂²×C₅₃	1	2	yes	—
621	#482	C₂²×C₅₃	1	2	yes	—
622	#481	C₂²×C₅₃	1	1	yes	characteristic
623	#479	C₂²×C₅₃	1	2	yes	complemented
624	#479	C₂²×C₅₃	1	2	yes	complemented
625	#479	C₂²×C₅₃	1	2	yes	complemented
626	#479	C₂²×C₅₃	1	2	yes	complemented
627	#479	C₂²×C₅₃	1	2	yes	complemented
628	#478	C₂²×C₅₃	1	1	yes	characteristic
629	#478	C₂²×C₅₃	1	1	yes	characteristic
630	#478	C₂²×C₅₃	1	2	yes	—
631	#478	C₂²×C₅₃	1	2	yes	—
632	#478	C₂²×C₅₃	1	2	yes	complemented
633	#477	C₂²×C₅₃	1	2	yes	complemented
634	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
635	#476	C₂²×C₅₃	1	1	yes	characteristic
636	#476	C₂²×C₅₃	1	1	yes	characteristic
637	#476	C₂²×C₅₃	1	2	yes	—
638	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
639	#476	C₂²×C₅₃	1	2	yes	complemented
640	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
641	#475	C₂²×C₅₃	1	2	yes	complemented
642	#475	C₂²×C₅₃	1	2	yes	complemented
643	#474	C₂²×C₅₃	1	2	yes	—
644	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
645	#463	C₂²×C₅₃	1	1	yes	characteristic
646	#463	C₂²×C₅₃	1	2	yes	—
647	#463	C₂²×C₅₃	1	2	yes	—
648	#463	C₂²×C₅₃	1	1	yes	characteristic
649	#461	C₂²×C₅₃	1	1	yes	characteristic
650	#461	C₂²×C₅₃	1	1	yes	characteristic
651	#461	C₂²×C₅₃	1	2	yes	—
652	#461	C₂²×C₅₃	1	2	yes	—
653	#450	C₂²×C₅₃	1	2	yes	—
654	#450	C₂²×C₅₃	1	1	yes	characteristic
655	#447	C₂²×C₅₃	1	1	yes	characteristic
656	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
657	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
658	#446	C₂²×C₅₃	1	2	yes	complemented
659	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
660	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
661	C₈×Q₈	C₂²×C₅₃	1	2	yes	complemented
662	#442	C₂²×C₅₃	1	2	yes	—
663	#440	C₂²×C₅₃	1	2	yes	—
664	#440	C₂²×C₅₃	1	2	yes	—
665	#440	C₂²×C₅₃	1	2	yes	—
666	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
667	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
668	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
669	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
670	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
671	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
672	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
673	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
674	C₄×D₈	C₂²×C₅₃	1	2	yes	—
675	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
676	#433	C₂²×C₅₃	1	2	yes	—
677	#433	C₂²×C₅₃	1	2	yes	—
678	#431	C₂²×C₅₃	1	1	yes	characteristic
679	#431	C₂²×C₅₃	1	1	yes	characteristic
680	C₅₃	#61864	1	1	yes	characteristic, direct product factor, Sylow
681	C₂²×Q₈	—	2	1	no	—
682	C₂²×Q₈	—	2	1	no	—
683	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
684	C₂³×C₄	—	2	1	no	—
685	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
686	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
687	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
689	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
690	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
691	C₄⋊Q₈	—	2	2	no	—
692	C₄⋊Q₈	—	2	2	no	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	2	no	—
695	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
696	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
699	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
703	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
704	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	1	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	—	2	1	no	—
718	#125	—	2	2	no	—
719	#125	—	2	1	no	—
720	#125	D₄×C₅₃	1	2	yes	—
721	#125	C₂³×C₅₃	1	1	yes	characteristic
722	#125	C₂³×C₅₃	1	2	yes	—
723	#125	C₂³×C₅₃	1	2	yes	—
724	#125	C₂³×C₅₃	1	2	yes	—
725	#125	C₂³×C₅₃	1	2	yes	—
726	#124	—	2	2	no	—
727	#124	C₂³×C₅₃	1	1	yes	characteristic
728	#124	C₂³×C₅₃	1	2	yes	—
729	#123	—	2	1	no	—
730	#123	—	2	2	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	1	no	—
734	C₂²⋊Q₈	—	2	1	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	1	no	—
739	C₂²⋊Q₈	—	2	1	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
756	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
757	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
758	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
760	#121	C₂³×C₅₃	1	1	yes	characteristic
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	2	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
769	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
770	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
771	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
772	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
781	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
782	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
783	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
784	C₄×D₄	C₂³×C₅₃	1	2	yes	—
785	C₄×D₄	C₂³×C₅₃	1	2	yes	—
786	C₄×D₄	C₂³×C₅₃	1	2	yes	—
787	C₄×D₄	C₂³×C₅₃	1	2	yes	—
788	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
789	C₄×D₄	C₂³×C₅₃	1	2	yes	—
790	#117	—	2	1	no	—
791	#117	—	2	2	no	—
792	#117	—	2	1	no	—
793	#117	—	2	1	no	—
794	#117	C₂³×C₅₃	1	2	yes	—
795	#117	C₂³×C₅₃	1	2	yes	—
796	C₂×C₄⋊C₄	—	2	2	no	—
797	C₂×C₄⋊C₄	—	2	2	no	—
798	C₂×C₄⋊C₄	—	2	1	no	—
799	C₂×C₄⋊C₄	—	2	1	no	—
800	C₂×C₄⋊C₄	—	2	1	no	—
801	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
802	C₂×C₂²⋊C₄	—	2	1	no	—
803	C₂×C₂²⋊C₄	—	2	2	no	—
804	C₂×C₂²⋊C₄	—	2	2	no	—
805	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
806	#107	C₂³×C₅₃	1	2	yes	—
807	#107	C₂³×C₅₃	1	1	yes	characteristic
808	#107	C₂³×C₅₃	1	1	yes	characteristic
809	#107	C₂³×C₅₃	1	2	yes	—
810	#107	C₂³×C₅₃	1	2	yes	—
811	#107	C₂³×C₅₃	1	2	yes	—
812	#106	C₂³×C₅₃	1	2	yes	—
813	#106	C₂³×C₅₃	1	1	yes	characteristic
814	#106	C₂³×C₅₃	1	2	yes	—
815	#106	C₂³×C₅₃	1	2	yes	—
816	#106	C₂³×C₅₃	1	2	yes	—
817	#106	C₂³×C₅₃	1	2	yes	—
818	#106	C₂³×C₅₃	1	1	yes	characteristic
819	#106	C₂³×C₅₃	1	2	yes	—
820	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
821	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
823	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
825	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
826	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
827	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
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	1	yes	characteristic
833	#103	C₂³×C₅₃	1	2	yes	—
834	#103	C₂³×C₅₃	1	1	yes	characteristic
835	#103	C₂³×C₅₃	1	2	yes	—
836	#103	C₂³×C₅₃	1	2	yes	—
837	#103	C₂³×C₅₃	1	2	yes	—
838	#102	C₂³×C₅₃	1	2	yes	—
839	#102	C₂³×C₅₃	1	1	yes	characteristic
840	#102	C₂³×C₅₃	1	1	yes	characteristic
841	#102	C₂³×C₅₃	1	1	yes	characteristic
842	#102	C₂³×C₅₃	1	2	yes	—
843	#102	C₂³×C₅₃	1	1	yes	characteristic
844	#102	C₂³×C₅₃	1	1	yes	characteristic
845	#102	C₂³×C₅₃	1	1	yes	characteristic
846	#102	C₂³×C₅₃	1	2	yes	—
847	#102	C₂³×C₅₃	1	2	yes	—
848	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
849	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
850	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
851	#97	C₂³×C₅₃	1	2	yes	—
852	#97	C₂³×C₅₃	1	2	yes	—
853	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
854	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
855	C₄×C₈	C₂³×C₅₃	1	2	yes	—
856	C₄×C₈	C₂³×C₅₃	1	2	yes	—
857	C₄×C₈	C₂³×C₅₃	1	2	yes	—
858	C₂⁴	—	2	1	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	1	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	8	2	no	—
866	C₂×Q₈	—	8	2	no	—
867	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
868	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
869	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
870	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
871	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
877	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
878	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	1	no	—
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	8	2	no	—
891	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
892	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
894	SD₁₆	—	2	4	no	—
895	SD₁₆	—	2	2	no	—
896	SD₁₆	—	2	4	no	—
897	SD₁₆	—	2	2	no	—
898	D₈	—	2	2	no	—
899	D₈	—	2	2	no	—
900	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
901	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
902	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
904	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
905	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	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	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
935	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
936	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
938	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
939	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
940	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
941	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
942	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
943	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
945	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
947	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
969	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
970	C₄²	—	2	2	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
977	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
978	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
979	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
980	C₄²	C₂⁴×C₅₃	1	2	yes	—
981	C₄²	C₂⁴×C₅₃	1	2	yes	—
982	C₂³	—	2	4	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	8	1	no	—
987	C₂³	—	8	1	no	—
988	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
989	Q₈	—	2	2	no	—
990	Q₈	—	2	2	no	—
991	Q₈	—	2	1	no	—
992	Q₈	—	2	2	no	—
993	Q₈	—	2	1	no	—
994	Q₈	—	2	2	no	—
995	Q₈	—	4	2	no	—
996	Q₈	—	4	2	no	—
997	Q₈	—	8	1	no	—
998	Q₈	—	8	1	no	—
999	Q₈	—	8	2	no	—
1000	Q₈	—	8	2	no	—
1001	Q₈	—	8	2	no	—
1002	D₄	—	2	4	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	2	1	no	—
1005	D₄	—	2	1	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	8	1	no	—
1008	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1009	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	4	1	no	—
1023	C₂×C₄	—	4	2	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	—	4	2	no	—
1026	C₂×C₄	—	8	2	no	—
1027	C₂×C₄	—	8	2	no	—
1028	C₂×C₄	—	8	2	no	—
1029	C₂×C₄	—	8	1	no	—
1030	C₂×C₄	—	8	1	no	—
1031	C₂×C₄	—	8	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	1	no	—
1034	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1035	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1037	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1039	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1040	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1042	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1043	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1044	C₈	—	2	1	no	—
1045	C₈	—	2	1	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	2	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	2	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	—	4	1	no	—
1062	C₂²	—	8	4	no	—
1063	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	2	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	2	no	—
1080	C₄	—	4	1	no	—
1081	C₄	C₅₃×#577	1	2	yes	—
1082	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1083	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1084	C₂	—	4	1	no	—
1085	C₂	—	4	2	no	—
1086	C₂	—	4	2	no	—
1087	C₂	—	8	1	no	—
1088	C₂	C₅₃×#3486	1	1	yes	characteristic
1089	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1090	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#447	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3555	C₂	semidirect
2. C₅₃×#3501	C₂	semidirect
3. C₅₃×#3388	C₂	semidirect
4. C₅₃×#3385	C₂	semidirect
5. C₅₃×#3384	C₂	semidirect
6. C₅₃×#3381	C₂	semidirect
7. C₅₃×#3380	C₂	semidirect
8. Q₈×SD₁₆×C₅₃	C₂	semidirect
9. C₅₃×#3376	C₂	semidirect
10. C₅₃×#3372	C₂	semidirect
11. C₅₃×#3367	C₂	semidirect
12. C₅₃×#3360	C₂	semidirect
13. C₅₃×#3360	C₂	semidirect
14. C₅₃×#3359	C₂	semidirect
15. C₅₃×#3244	C₂	semidirect
16. C₅₃×#3242	C₂	semidirect
17. C₅₃×#3233	C₂	semidirect
18. C₅₃×#3231	C₂	semidirect
19. C₅₃×#3123	C₂	semidirect
22. C₅₃×#3101	C₂	semidirect
23. C₅₃×#2986	C₂	semidirect
25. Q₈²×C₅₃	C₂²	semidirect
26. C₅₃×#557	C₂²	semidirect
27. C₅₃×#557	C₂²	semidirect
29. C₅₃×#556	C₂²	semidirect
30. C₅₃×#556	C₂²	semidirect
37. C₅₃×#554	C₂²	semidirect
57. C₅₃×#501	C₂²	semidirect
58. C₅₃×#501	C₂²	semidirect
59. C₅₃×#500	C₂²	semidirect
60. C₅₃×#499	C₂²	semidirect
61. C₅₃×#499	C₂²	semidirect
62. C₅₃×#498	C₂²	semidirect
63. C₅₃×#498	C₂²	semidirect
64. C₅₃×#491	C₂²	semidirect
65. C₅₃×#489	C₂²	semidirect
66. C₅₃×#488	C₂²	semidirect
67. C₅₃×#488	C₂²	semidirect
68. C₅₃×#487	C₂²	semidirect
69. C₅₃×#487	C₂²	semidirect
70. C₅₃×#487	C₂²	semidirect
78. C₅₃×#479	C₂²	semidirect
79. C₅₃×#479	C₂²	semidirect
80. C₅₃×#479	C₂²	semidirect
81. C₅₃×#479	C₂²	semidirect
82. C₅₃×#479	C₂²	semidirect
87. C₅₃×#478	C₂²	semidirect
88. C₅₃×#477	C₂²	semidirect
89. C₅₃×#477	C₂²	semidirect
93. C₅₃×#476	C₂²	semidirect
94. C₅₃×#476	C₂²	semidirect
95. C₅₃×#475	C₂²	semidirect
96. C₅₃×#475	C₂²	semidirect
97. C₅₃×#475	C₂²	semidirect
99. C₅₃×#474	C₂²	semidirect
111. C₅₃×#446	C₂²	semidirect
112. C₅₃×#446	C₂²	semidirect
113. C₅₃×#446	C₂²	semidirect
114. C₈×Q₈×C₅₃	C₂²	semidirect
115. C₈×Q₈×C₅₃	C₂²	semidirect
116. C₈×Q₈×C₅₃	C₂²	semidirect
504. #61864	C₅₃	direct (N × H)
539. #3555	C₂×C₅₃	semidirect
540. #3501	C₂×C₅₃	semidirect
541. #3388	C₂×C₅₃	semidirect
542. #3385	C₂×C₅₃	semidirect
543. #3384	C₂×C₅₃	semidirect
544. #3381	C₂×C₅₃	semidirect
545. #3380	C₂×C₅₃	semidirect
546. Q₈×SD₁₆	C₂×C₅₃	semidirect
547. #3376	C₂×C₅₃	semidirect
548. #3372	C₂×C₅₃	semidirect
549. #3367	C₂×C₅₃	semidirect
550. #3360	C₂×C₅₃	semidirect
551. #3360	C₂×C₅₃	semidirect
552. #3359	C₂×C₅₃	semidirect
553. #3244	C₂×C₅₃	semidirect
554. #3242	C₂×C₅₃	semidirect
555. #3233	C₂×C₅₃	semidirect
556. #3231	C₂×C₅₃	semidirect
557. #3123	C₂×C₅₃	semidirect
560. #3101	C₂×C₅₃	semidirect
561. #2986	C₂×C₅₃	semidirect
570. Q₈²	C₂²×C₅₃	semidirect
571. #557	C₂²×C₅₃	semidirect
572. #557	C₂²×C₅₃	semidirect
574. #556	C₂²×C₅₃	semidirect
575. #556	C₂²×C₅₃	semidirect
582. #554	C₂²×C₅₃	semidirect
602. #501	C₂²×C₅₃	semidirect
603. #501	C₂²×C₅₃	semidirect
604. #500	C₂²×C₅₃	semidirect
605. #499	C₂²×C₅₃	semidirect
606. #499	C₂²×C₅₃	semidirect
607. #498	C₂²×C₅₃	semidirect
608. #498	C₂²×C₅₃	semidirect
609. #491	C₂²×C₅₃	semidirect
610. #489	C₂²×C₅₃	semidirect
611. #488	C₂²×C₅₃	semidirect
612. #488	C₂²×C₅₃	semidirect
613. #487	C₂²×C₅₃	semidirect
614. #487	C₂²×C₅₃	semidirect
615. #487	C₂²×C₅₃	semidirect
623. #479	C₂²×C₅₃	semidirect
624. #479	C₂²×C₅₃	semidirect
625. #479	C₂²×C₅₃	semidirect
626. #479	C₂²×C₅₃	semidirect
627. #479	C₂²×C₅₃	semidirect
632. #478	C₂²×C₅₃	semidirect
633. #477	C₂²×C₅₃	semidirect
634. #477	C₂²×C₅₃	semidirect
638. #476	C₂²×C₅₃	semidirect
639. #476	C₂²×C₅₃	semidirect
640. #475	C₂²×C₅₃	semidirect
641. #475	C₂²×C₅₃	semidirect
642. #475	C₂²×C₅₃	semidirect
644. #474	C₂²×C₅₃	semidirect
656. #446	C₂²×C₅₃	semidirect
657. #446	C₂²×C₅₃	semidirect
658. #446	C₂²×C₅₃	semidirect
659. C₈×Q₈	C₂²×C₅₃	semidirect
660. C₈×Q₈	C₂²×C₅₃	semidirect
661. C₈×Q₈	C₂²×C₅₃	semidirect
680. C₅₃	#61864	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×#3555	2
C₅₃×#3501	2
C₅₃×#3388	2
C₅₃×#3385	2
C₅₃×#3384	2
C₅₃×#3381	2
C₅₃×#3380	2
Q₈×SD₁₆×C₅₃	2
C₅₃×#3376	2
C₅₃×#3372	2
C₅₃×#3367	2
C₅₃×#3360	2
C₅₃×#3359	2
C₅₃×#3244	2
C₅₃×#3242	2
C₅₃×#3233	2
C₅₃×#3231	2
C₅₃×#3123	2
C₅₃×#3118	2
C₅₃×#3105	2
C₅₃×#3101	2
C₅₃×#2986	2
#61864	53

Subgroups — C53×#61864 #27269376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61864 #27269376