Subgroups — C₅₃×#62141 #27269653

Order 13568.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3349	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3348	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3341	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3319	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3311	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3252	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3250	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3240	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3111	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3076	C₂	1	2	yes	maximal, complemented
23	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	Q₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₅₃×#556	—	2	2	no	—
26	C₅₃×#556	—	2	1	no	—
27	C₅₃×#556	C₂²	1	1	yes	characteristic
28	C₅₃×#556	C₂²	1	2	yes	—
29	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#555	C₂²	1	1	yes	characteristic
31	C₅₃×#555	C₂²	1	2	yes	—
32	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#554	C₂²	1	1	yes	characteristic
34	C₅₃×#553	—	2	1	no	—
35	C₅₃×#552	—	2	1	no	—
36	C₅₃×#552	C₂²	1	2	yes	—
37	C₅₃×#551	—	2	2	no	—
38	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#548	—	2	1	no	—
40	C₅₃×#547	C₂²	1	1	yes	characteristic
41	C₅₃×#546	C₂²	1	2	yes	—
42	C₅₃×#542	—	2	1	no	—
43	C₅₃×#542	—	2	2	no	—
44	C₅₃×#533	C₂²	1	1	yes	characteristic
45	C₅₃×#533	C₂²	1	1	yes	characteristic
46	C₅₃×#533	C₂²	1	2	yes	complemented
47	C₅₃×#529	—	2	2	no	—
48	C₅₃×#529	C₂²	1	2	yes	—
49	C₅₃×#529	C₂²	1	1	yes	characteristic
50	C₅₃×#529	C₂²	1	2	yes	complemented
51	C₅₃×#525	—	2	1	no	—
52	C₅₃×#519	—	2	1	no	—
53	C₄×#41×C₅₃	C₂²	1	2	yes	—
54	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
56	C₂×#117×C₅₃	—	2	1	no	—
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×#498	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#489	C₂²	1	2	yes	—
62	C₅₃×#489	C₂²	1	2	yes	—
63	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#485	C₂²	1	2	yes	—
66	C₅₃×#485	C₂²	1	2	yes	—
67	C₅₃×#485	C₂²	1	2	yes	complemented
68	C₅₃×#485	C₂²	1	2	yes	complemented
69	C₅₃×#485	C₂²	1	2	yes	complemented
70	C₅₃×#484	C₂²	1	1	yes	characteristic
71	C₅₃×#482	C₂²	1	2	yes	—
72	C₅₃×#482	C₂²	1	2	yes	—
73	C₅₃×#482	C₂²	1	2	yes	complemented
74	C₅₃×#481	C₂²	1	1	yes	characteristic
75	C₅₃×#479	C₂²	1	2	yes	complemented
76	C₅₃×#479	C₂²	1	2	yes	complemented
77	C₅₃×#479	C₂²	1	2	yes	complemented
78	C₅₃×#479	C₂²	1	2	yes	complemented
79	C₅₃×#478	C₂²	1	1	yes	characteristic
80	C₅₃×#478	C₂²	1	2	yes	—
81	C₅₃×#478	C₂²	1	1	yes	characteristic
82	C₅₃×#478	C₂²	1	2	yes	—
83	C₅₃×#478	C₂²	1	2	yes	complemented
84	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#477	C₂²	1	2	yes	complemented
86	C₅₃×#476	C₂²	1	1	yes	characteristic
87	C₅₃×#476	C₂²	1	2	yes	—
88	C₅₃×#476	C₂²	1	1	yes	characteristic
89	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#475	C₂²	1	2	yes	complemented
91	C₅₃×#474	C₂²	1	1	yes	characteristic
92	C₅₃×#474	C₂²	1	2	yes	—
93	C₅₃×#474	C₂²	1	1	yes	characteristic
94	C₅₃×#470	C₂²	1	2	yes	—
95	C₅₃×#468	C₂²	1	2	yes	—
96	C₅₃×#467	C₂²	1	2	yes	complemented
97	C₅₃×#466	C₂²	1	2	yes	—
98	C₅₃×#465	C₂²	1	2	yes	—
99	C₅₃×#465	C₂²	1	2	yes	complemented
100	C₅₃×#464	C₂²	1	2	yes	—
101	C₅₃×#464	C₂²	1	2	yes	complemented
102	C₅₃×#463	C₂²	1	1	yes	characteristic
103	C₅₃×#463	C₂²	1	2	yes	—
104	C₅₃×#463	C₂²	1	1	yes	characteristic
105	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#452	C₂²	1	2	yes	—
108	C₅₃×#450	C₂²	1	1	yes	characteristic
109	C₅₃×#449	C₂²	1	2	yes	—
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×#442	C₂²	1	2	yes	—
114	C₅₃×#441	C₂²	1	2	yes	complemented
115	C₅₃×#440	C₂²	1	2	yes	—
116	C₅₃×#440	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
121	C₅₃×#435	C₂²	1	2	yes	—
122	C₅₃×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#432	C₂²	1	2	yes	complemented
126	C₅₃×#431	C₂²	1	1	yes	characteristic
127	C₅₃×#428	C₂²	1	2	yes	—
128	C₅₃×#427	C₂²	1	2	yes	complemented
129	C₅₃×#427	C₂²	1	2	yes	complemented
130	C₅₃×#423	C₂²	1	1	yes	characteristic
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	complemented
132	C₅₃×#418	C₂²	1	2	yes	—
133	C₅₃×#416	C₂²	1	2	yes	—
134	C₅₃×#416	C₂²	1	2	yes	—
135	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
136	C₂×#41×C₅₃	C₂³	1	2	yes	—
137	C₂²×Q₈×C₅₃	—	2	1	no	—
138	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅₃	—	2	1	no	—
140	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
144	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
148	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₅₃	—	2	1	no	—
150	C₄⋊Q₈×C₅₃	—	2	2	no	—
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	1	yes	characteristic
157	#126×C₅₃	—	2	2	no	—
158	#126×C₅₃	—	2	2	no	—
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	1	no	—
164	#126×C₅₃	—	2	2	no	—
165	#125×C₅₃	—	2	2	no	—
166	#125×C₅₃	—	2	1	no	—
167	#125×C₅₃	C₂³	1	2	yes	—
168	#125×C₅₃	C₂³	1	1	yes	characteristic
169	#125×C₅₃	C₂³	1	2	yes	—
170	#124×C₅₃	—	2	2	no	—
171	#124×C₅₃	—	2	2	no	—
172	#124×C₅₃	—	2	2	no	—
173	#124×C₅₃	—	2	2	no	—
174	#124×C₅₃	—	2	2	no	—
175	#124×C₅₃	—	2	1	no	—
176	#124×C₅₃	C₂³	1	2	yes	—
177	#124×C₅₃	C₂³	1	1	yes	characteristic
178	#123×C₅₃	—	2	2	no	—
179	#123×C₅₃	—	2	2	no	—
180	#123×C₅₃	—	2	2	no	—
181	#123×C₅₃	—	2	1	no	—
182	#123×C₅₃	—	2	2	no	—
183	#123×C₅₃	—	2	2	no	—
184	C₂²⋊Q₈×C₅₃	—	2	2	no	—
185	C₂²⋊Q₈×C₅₃	—	2	1	no	—
186	C₂²⋊Q₈×C₅₃	—	2	2	no	—
187	C₂²⋊Q₈×C₅₃	—	2	1	no	—
188	C₂²⋊Q₈×C₅₃	—	2	1	no	—
189	C₂²⋊Q₈×C₅₃	—	2	1	no	—
190	C₂²⋊Q₈×C₅₃	—	2	1	no	—
191	C₂²⋊Q₈×C₅₃	—	2	1	no	—
192	C₂²⋊Q₈×C₅₃	—	2	2	no	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
198	#121×C₅₃	—	2	2	no	—
199	#121×C₅₃	—	2	1	no	—
200	#121×C₅₃	—	2	1	no	—
201	#121×C₅₃	—	2	2	no	—
202	#121×C₅₃	—	2	1	no	—
203	#121×C₅₃	C₂³	1	2	yes	—
204	#121×C₅₃	C₂³	1	1	yes	characteristic
205	#121×C₅₃	C₂³	1	2	yes	—
206	#120×C₅₃	—	2	2	no	—
207	C₄×Q₈×C₅₃	—	2	2	no	—
208	C₄×Q₈×C₅₃	—	2	1	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	1	no	—
213	C₄×Q₈×C₅₃	—	2	2	no	—
214	C₄×Q₈×C₅₃	—	2	1	no	—
215	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₅₃	C₂³	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	2	yes	—
221	C₄×D₄×C₅₃	—	2	1	no	—
222	C₄×D₄×C₅₃	—	2	1	no	—
223	C₄×D₄×C₅₃	—	2	2	no	—
224	C₄×D₄×C₅₃	—	2	2	no	—
225	C₄×D₄×C₅₃	—	2	2	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	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₅₃	C₂³	1	2	yes	—
235	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₅₃	C₂³	1	2	yes	—
237	C₄×D₄×C₅₃	C₂³	1	2	yes	—
238	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
239	#117×C₅₃	—	2	1	no	—
240	#117×C₅₃	—	2	1	no	—
241	#117×C₅₃	—	2	2	no	—
242	#117×C₅₃	—	2	1	no	—
243	#117×C₅₃	—	2	2	no	—
244	#117×C₅₃	—	2	2	no	—
245	#117×C₅₃	—	2	2	no	—
246	#117×C₅₃	—	2	1	no	—
247	#117×C₅₃	—	2	2	no	—
248	#117×C₅₃	—	2	1	no	—
249	#117×C₅₃	D₄	1	1	yes	characteristic
250	#117×C₅₃	D₄	1	2	yes	—
251	#117×C₅₃	C₂³	1	2	yes	—
252	#117×C₅₃	C₂³	1	2	yes	—
253	#117×C₅₃	C₂³	1	2	yes	—
254	#117×C₅₃	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
260	C₂×C₄²×C₅₃	—	2	2	no	—
261	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
263	#107×C₅₃	C₂³	1	2	yes	—
264	#107×C₅₃	C₂³	1	2	yes	—
265	#107×C₅₃	C₂³	1	1	yes	characteristic
266	#107×C₅₃	C₂³	1	2	yes	—
267	#107×C₅₃	C₂³	1	2	yes	—
268	#107×C₅₃	C₂³	1	2	yes	—
269	#107×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	#106×C₅₃	C₂³	1	2	yes	—
275	#106×C₅₃	C₂³	1	1	yes	characteristic
276	#106×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
282	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#102×C₅₃	C₂³	1	1	yes	characteristic
294	#102×C₅₃	C₂³	1	1	yes	characteristic
295	#102×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
300	#102×C₅₃	C₂³	1	2	yes	—
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
311	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₂⁴×C₅₃	—	2	1	no	—
313	#41×C₅₃	—	2	4	no	—
314	#41×C₅₃	—	4	2	no	—
315	#41×C₅₃	—	4	2	no	—
316	C₂×Q₈×C₅₃	—	2	2	no	—
317	C₂×Q₈×C₅₃	—	2	1	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	—	4	4	no	—
322	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₅₃	—	2	2	no	—
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	2	no	—
330	C₂×D₄×C₅₃	—	2	1	no	—
331	C₂×D₄×C₅₃	—	4	1	no	—
332	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
333	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₅₃	—	2	1	no	—
338	C₂²×C₄×C₅₃	—	2	1	no	—
339	C₂²×C₄×C₅₃	—	2	2	no	—
340	C₂²×C₄×C₅₃	—	2	1	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	—	2	1	no	—
345	C₂²×C₄×C₅₃	—	2	2	no	—
346	C₂²×C₄×C₅₃	—	4	4	no	—
347	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
350	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
351	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
353	Q₁₆×C₅₃	—	4	2	no	—
354	SD₁₆×C₅₃	—	2	2	no	—
355	SD₁₆×C₅₃	—	4	1	no	—
356	SD₁₆×C₅₃	—	4	2	no	—
357	D₈×C₅₃	—	2	2	no	—
358	D₈×C₅₃	—	4	1	no	—
359	M₁₆×C₅₃	—	4	2	no	—
360	C₂×C₈×C₅₃	—	4	2	no	—
361	C₂×C₈×C₅₃	—	4	2	no	—
362	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
367	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₅₃	—	2	1	no	—
369	C₄⋊C₄×C₅₃	—	2	1	no	—
370	C₄⋊C₄×C₅₃	—	2	2	no	—
371	C₄⋊C₄×C₅₃	—	2	2	no	—
372	C₄⋊C₄×C₅₃	—	2	1	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	2	no	—
376	C₄⋊C₄×C₅₃	—	2	1	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	1	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	1	no	—
387	C₄⋊C₄×C₅₃	—	2	1	no	—
388	C₄⋊C₄×C₅₃	—	2	2	no	—
389	C₄⋊C₄×C₅₃	—	2	1	no	—
390	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
391	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	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	2	yes	—
401	C₂²⋊C₄×C₅₃	—	2	2	no	—
402	C₂²⋊C₄×C₅₃	—	2	2	no	—
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	2	no	—
409	C₂²⋊C₄×C₅₃	—	2	1	no	—
410	C₂²⋊C₄×C₅₃	—	2	2	no	—
411	C₂²⋊C₄×C₅₃	—	2	2	no	—
412	C₂²⋊C₄×C₅₃	—	2	1	no	—
413	C₂²⋊C₄×C₅₃	—	2	1	no	—
414	C₂²⋊C₄×C₅₃	—	2	1	no	—
415	C₂²⋊C₄×C₅₃	—	2	2	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	1	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	1	no	—
423	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
431	C₄²×C₅₃	—	2	2	no	—
432	C₄²×C₅₃	—	2	2	no	—
433	C₄²×C₅₃	—	2	1	no	—
434	C₄²×C₅₃	C₂×D₄	1	2	yes	—
435	C₄²×C₅₃	C₂×D₄	1	2	yes	—
436	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
439	C₄²×C₅₃	C₂⁴	1	2	yes	—
440	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₂³×C₅₃	—	2	1	no	—
442	C₂³×C₅₃	—	2	1	no	—
443	C₂³×C₅₃	—	2	1	no	—
444	C₂³×C₅₃	—	4	2	no	—
445	C₂³×C₅₃	—	4	2	no	—
446	C₂³×C₅₃	—	8	1	no	—
447	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
448	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
449	Q₈×C₅₃	—	2	2	no	—
450	Q₈×C₅₃	—	2	2	no	—
451	Q₈×C₅₃	—	2	1	no	—
452	Q₈×C₅₃	—	2	2	no	—
453	Q₈×C₅₃	—	2	1	no	—
454	Q₈×C₅₃	—	4	4	no	—
455	Q₈×C₅₃	—	4	2	no	—
456	Q₈×C₅₃	—	8	2	no	—
457	Q₈×C₅₃	—	8	1	no	—
458	Q₈×C₅₃	—	8	1	no	—
459	D₄×C₅₃	—	2	2	no	—
460	D₄×C₅₃	—	2	1	no	—
461	D₄×C₅₃	—	2	1	no	—
462	D₄×C₅₃	—	2	1	no	—
463	D₄×C₅₃	—	2	1	no	—
464	D₄×C₅₃	—	2	1	no	—
465	D₄×C₅₃	—	4	2	no	—
466	D₄×C₅₃	—	4	2	no	—
467	D₄×C₅₃	—	4	4	no	—
468	D₄×C₅₃	—	8	2	no	—
469	D₄×C₅₃	—	8	2	no	—
470	D₄×C₅₃	—	8	1	no	—
471	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
472	C₂×C₄×C₅₃	—	2	2	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	—	2	2	no	—
477	C₂×C₄×C₅₃	—	2	1	no	—
478	C₂×C₄×C₅₃	—	2	1	no	—
479	C₂×C₄×C₅₃	—	2	2	no	—
480	C₂×C₄×C₅₃	—	2	2	no	—
481	C₂×C₄×C₅₃	—	2	2	no	—
482	C₂×C₄×C₅₃	—	2	1	no	—
483	C₂×C₄×C₅₃	—	2	1	no	—
484	C₂×C₄×C₅₃	—	2	2	no	—
485	C₂×C₄×C₅₃	—	2	1	no	—
486	C₂×C₄×C₅₃	—	4	2	no	—
487	C₂×C₄×C₅₃	—	4	1	no	—
488	C₂×C₄×C₅₃	—	4	2	no	—
489	C₂×C₄×C₅₃	—	4	4	no	—
490	C₂×C₄×C₅₃	—	4	2	no	—
491	C₂×C₄×C₅₃	—	4	2	no	—
492	C₂×C₄×C₅₃	—	4	4	no	—
493	C₂×C₄×C₅₃	—	4	2	no	—
494	C₂×C₄×C₅₃	—	4	2	no	—
495	C₂×C₄×C₅₃	—	4	2	no	—
496	C₂×C₄×C₅₃	—	4	2	no	—
497	C₂×C₄×C₅₃	—	8	2	no	—
498	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
507	C₈×C₅₃	—	2	1	no	—
508	C₈×C₅₃	—	2	1	no	—
509	C₈×C₅₃	—	2	1	no	—
510	C₈×C₅₃	—	2	1	no	—
511	C₈×C₅₃	—	2	2	no	—
512	C₈×C₅₃	—	2	2	no	—
513	#62141	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
514	C₂²×C₅₃	—	2	2	no	—
515	C₂²×C₅₃	—	2	1	no	—
516	C₂²×C₅₃	—	2	2	no	—
517	C₂²×C₅₃	—	2	1	no	—
518	C₂²×C₅₃	—	2	2	no	—
519	C₂²×C₅₃	—	2	1	no	—
520	C₂²×C₅₃	—	2	2	no	—
521	C₂²×C₅₃	—	4	1	no	—
522	C₂²×C₅₃	—	4	1	no	—
523	C₂²×C₅₃	—	4	1	no	—
524	C₂²×C₅₃	—	4	1	no	—
525	C₂²×C₅₃	—	4	1	no	—
526	C₂²×C₅₃	—	4	1	no	—
527	C₂²×C₅₃	—	4	1	no	—
528	C₂²×C₅₃	—	4	1	no	—
529	C₂²×C₅₃	—	8	4	no	—
530	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
531	C₄×C₅₃	—	2	1	no	—
532	C₄×C₅₃	—	2	2	no	—
533	C₄×C₅₃	—	2	1	no	—
534	C₄×C₅₃	—	2	2	no	—
535	C₄×C₅₃	—	2	1	no	—
536	C₄×C₅₃	—	2	1	no	—
537	C₄×C₅₃	—	2	2	no	—
538	C₄×C₅₃	—	4	2	no	—
539	C₄×C₅₃	—	4	2	no	—
540	C₄×C₅₃	—	4	1	no	—
541	C₄×C₅₃	—	4	2	no	—
542	C₄×C₅₃	—	4	1	no	—
543	C₄×C₅₃	—	4	1	no	—
544	C₄×C₅₃	—	4	1	no	—
545	C₄×C₅₃	—	4	2	no	—
546	C₄×C₅₃	—	4	1	no	—
547	C₄×C₅₃	#575	1	2	yes	—
548	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
549	C₄×C₅₃	#585	1	1	yes	characteristic
550	#3518	C₂×C₅₃	1	1	yes	characteristic, complemented
551	#3475	C₂×C₅₃	1	1	yes	characteristic, complemented
552	#3385	C₂×C₅₃	1	1	yes	characteristic, complemented
553	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
554	#3369	C₂×C₅₃	1	1	yes	characteristic, complemented
555	#3367	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#3349	C₂×C₅₃	1	2	yes	complemented
557	#3348	C₂×C₅₃	1	2	yes	complemented
558	#3341	C₂×C₅₃	1	1	yes	characteristic, complemented
559	#3340	C₂×C₅₃	1	1	yes	characteristic, complemented
560	#3319	C₂×C₅₃	1	2	yes	complemented
561	#3311	C₂×C₅₃	1	2	yes	complemented
562	#3303	C₂×C₅₃	1	1	yes	characteristic, complemented
563	#3302	C₂×C₅₃	1	1	yes	characteristic, complemented
564	#3252	C₂×C₅₃	1	1	yes	characteristic, complemented
565	#3250	C₂×C₅₃	1	2	yes	complemented
566	#3240	C₂×C₅₃	1	2	yes	complemented
567	#3231	C₂×C₅₃	1	1	yes	characteristic, complemented
568	#3111	C₂×C₅₃	1	2	yes	complemented
569	#3105	C₂×C₅₃	1	1	yes	characteristic, complemented
570	#3077	C₂×C₅₃	1	1	yes	characteristic, complemented
571	#3076	C₂×C₅₃	1	2	yes	complemented
572	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
573	C₂×C₅₃	—	4	2	no	—
574	C₂×C₅₃	—	4	1	no	—
575	C₂×C₅₃	—	4	2	no	—
576	C₂×C₅₃	—	8	1	no	—
577	C₂×C₅₃	—	8	1	no	—
578	C₂×C₅₃	#3489	1	1	yes	characteristic
579	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
580	C₂×C₅₃	#3584	1	1	yes	characteristic
581	Q₈²	C₂²×C₅₃	1	1	yes	characteristic, complemented
582	#556	—	2	2	no	—
583	#556	—	2	1	no	—
584	#556	C₂²×C₅₃	1	1	yes	characteristic
585	#556	C₂²×C₅₃	1	2	yes	—
586	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
587	#555	C₂²×C₅₃	1	1	yes	characteristic
588	#555	C₂²×C₅₃	1	2	yes	—
589	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
590	#554	C₂²×C₅₃	1	1	yes	characteristic
591	#553	—	2	1	no	—
592	#552	—	2	1	no	—
593	#552	C₂²×C₅₃	1	2	yes	—
594	#551	—	2	2	no	—
595	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
596	#548	—	2	1	no	—
597	#547	C₂²×C₅₃	1	1	yes	characteristic
598	#546	C₂²×C₅₃	1	2	yes	—
599	#542	—	2	1	no	—
600	#542	—	2	2	no	—
601	#533	C₂²×C₅₃	1	1	yes	characteristic
602	#533	C₂²×C₅₃	1	1	yes	characteristic
603	#533	C₂²×C₅₃	1	2	yes	complemented
604	#529	—	2	2	no	—
605	#529	C₂²×C₅₃	1	1	yes	characteristic
606	#529	C₂²×C₅₃	1	2	yes	—
607	#529	C₂²×C₅₃	1	2	yes	complemented
608	#525	—	2	1	no	—
609	#519	—	2	1	no	—
610	C₄×#41	C₂²×C₅₃	1	2	yes	—
611	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
612	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
613	C₂×#117	—	2	1	no	—
614	#501	C₂²×C₅₃	1	2	yes	complemented
615	#501	C₂²×C₅₃	1	2	yes	complemented
616	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
617	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
618	#489	C₂²×C₅₃	1	2	yes	—
619	#489	C₂²×C₅₃	1	2	yes	—
620	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
621	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
622	#485	C₂²×C₅₃	1	2	yes	—
623	#485	C₂²×C₅₃	1	2	yes	—
624	#485	C₂²×C₅₃	1	2	yes	complemented
625	#485	C₂²×C₅₃	1	2	yes	complemented
626	#485	C₂²×C₅₃	1	2	yes	complemented
627	#484	C₂²×C₅₃	1	1	yes	characteristic
628	#482	C₂²×C₅₃	1	2	yes	—
629	#482	C₂²×C₅₃	1	2	yes	—
630	#482	C₂²×C₅₃	1	2	yes	complemented
631	#481	C₂²×C₅₃	1	1	yes	characteristic
632	#479	C₂²×C₅₃	1	2	yes	complemented
633	#479	C₂²×C₅₃	1	2	yes	complemented
634	#479	C₂²×C₅₃	1	2	yes	complemented
635	#479	C₂²×C₅₃	1	2	yes	complemented
636	#478	C₂²×C₅₃	1	1	yes	characteristic
637	#478	C₂²×C₅₃	1	2	yes	—
638	#478	C₂²×C₅₃	1	2	yes	—
639	#478	C₂²×C₅₃	1	1	yes	characteristic
640	#478	C₂²×C₅₃	1	2	yes	complemented
641	#477	C₂²×C₅₃	1	2	yes	complemented
642	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
643	#476	C₂²×C₅₃	1	2	yes	—
644	#476	C₂²×C₅₃	1	1	yes	characteristic
645	#476	C₂²×C₅₃	1	1	yes	characteristic
646	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
647	#475	C₂²×C₅₃	1	2	yes	complemented
648	#474	C₂²×C₅₃	1	2	yes	—
649	#474	C₂²×C₅₃	1	1	yes	characteristic
650	#474	C₂²×C₅₃	1	1	yes	characteristic
651	#470	C₂²×C₅₃	1	2	yes	—
652	#468	C₂²×C₅₃	1	2	yes	—
653	#467	C₂²×C₅₃	1	2	yes	complemented
654	#466	C₂²×C₅₃	1	2	yes	—
655	#465	C₂²×C₅₃	1	2	yes	—
656	#465	C₂²×C₅₃	1	2	yes	complemented
657	#464	C₂²×C₅₃	1	2	yes	—
658	#464	C₂²×C₅₃	1	2	yes	complemented
659	#463	C₂²×C₅₃	1	1	yes	characteristic
660	#463	C₂²×C₅₃	1	1	yes	characteristic
661	#463	C₂²×C₅₃	1	2	yes	—
662	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
664	#452	C₂²×C₅₃	1	2	yes	—
665	#450	C₂²×C₅₃	1	1	yes	characteristic
666	#449	C₂²×C₅₃	1	2	yes	—
667	#447	C₂²×C₅₃	1	1	yes	characteristic
668	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
669	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
670	#442	C₂²×C₅₃	1	2	yes	—
671	#441	C₂²×C₅₃	1	2	yes	complemented
672	#440	C₂²×C₅₃	1	2	yes	—
673	#440	C₂²×C₅₃	1	2	yes	complemented
674	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
675	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
676	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
677	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
678	#435	C₂²×C₅₃	1	2	yes	—
679	#435	C₂²×C₅₃	1	2	yes	—
680	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
682	#432	C₂²×C₅₃	1	2	yes	complemented
683	#431	C₂²×C₅₃	1	1	yes	characteristic
684	#428	C₂²×C₅₃	1	2	yes	—
685	#427	C₂²×C₅₃	1	2	yes	complemented
686	#427	C₂²×C₅₃	1	2	yes	complemented
687	#423	C₂²×C₅₃	1	1	yes	characteristic
688	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	complemented
689	#418	C₂²×C₅₃	1	2	yes	—
690	#416	C₂²×C₅₃	1	2	yes	—
691	#416	C₂²×C₅₃	1	2	yes	—
692	C₅₃	#62141	1	1	yes	characteristic, direct product factor, Sylow
693	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
694	C₂×#41	C₂³×C₅₃	1	2	yes	—
695	C₂²×Q₈	—	2	1	no	—
696	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
697	C₂³×C₄	—	2	1	no	—
698	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
699	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
700	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
701	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
702	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
703	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
704	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
705	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
706	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	—	2	2	no	—
709	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
712	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
713	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
714	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	1	no	—
722	#126	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	1	no	—
725	#125	C₂³×C₅₃	1	1	yes	characteristic
726	#125	C₂³×C₅₃	1	2	yes	—
727	#125	C₂³×C₅₃	1	2	yes	—
728	#124	—	2	2	no	—
729	#124	—	2	1	no	—
730	#124	—	2	2	no	—
731	#124	—	2	2	no	—
732	#124	—	2	2	no	—
733	#124	—	2	2	no	—
734	#124	C₂³×C₅₃	1	1	yes	characteristic
735	#124	C₂³×C₅₃	1	2	yes	—
736	#123	—	2	2	no	—
737	#123	—	2	1	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
753	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
754	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
755	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
756	#121	—	2	1	no	—
757	#121	—	2	1	no	—
758	#121	—	2	2	no	—
759	#121	—	2	1	no	—
760	#121	—	2	2	no	—
761	#121	C₂³×C₅₃	1	2	yes	—
762	#121	C₂³×C₅₃	1	1	yes	characteristic
763	#121	C₂³×C₅₃	1	2	yes	—
764	#120	—	2	2	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	2	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	2	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	2	no	—
773	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
775	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
776	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
778	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	2	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	D₄×C₅₃	1	2	yes	—
787	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
788	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
789	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
791	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
792	C₄×D₄	C₂³×C₅₃	1	2	yes	—
793	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₅₃	1	2	yes	—
795	C₄×D₄	C₂³×C₅₃	1	2	yes	—
796	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
797	#117	—	2	1	no	—
798	#117	—	2	1	no	—
799	#117	—	2	1	no	—
800	#117	—	2	2	no	—
801	#117	—	2	1	no	—
802	#117	—	2	2	no	—
803	#117	—	2	2	no	—
804	#117	—	2	2	no	—
805	#117	—	2	1	no	—
806	#117	—	2	2	no	—
807	#117	D₄×C₅₃	1	1	yes	characteristic
808	#117	D₄×C₅₃	1	2	yes	—
809	#117	C₂³×C₅₃	1	2	yes	—
810	#117	C₂³×C₅₃	1	2	yes	—
811	#117	C₂³×C₅₃	1	2	yes	—
812	#117	C₂³×C₅₃	1	2	yes	—
813	C₂×C₄⋊C₄	—	2	1	no	—
814	C₂×C₄⋊C₄	—	2	1	no	—
815	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	—	2	1	no	—
817	C₂×C₂²⋊C₄	—	2	2	no	—
818	C₂×C₄²	—	2	2	no	—
819	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
820	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
821	#107	C₂³×C₅₃	1	1	yes	characteristic
822	#107	C₂³×C₅₃	1	2	yes	—
823	#107	C₂³×C₅₃	1	2	yes	—
824	#107	C₂³×C₅₃	1	2	yes	—
825	#107	C₂³×C₅₃	1	2	yes	—
826	#107	C₂³×C₅₃	1	1	yes	characteristic
827	#107	C₂³×C₅₃	1	2	yes	—
828	#106	C₂³×C₅₃	1	1	yes	characteristic
829	#106	C₂³×C₅₃	1	2	yes	—
830	#106	C₂³×C₅₃	1	2	yes	—
831	#106	C₂³×C₅₃	1	2	yes	—
832	#106	C₂³×C₅₃	1	2	yes	—
833	#106	C₂³×C₅₃	1	1	yes	characteristic
834	#106	C₂³×C₅₃	1	2	yes	—
835	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
836	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
837	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
838	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
839	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
842	#103	C₂³×C₅₃	1	2	yes	—
843	#103	C₂³×C₅₃	1	2	yes	—
844	#103	C₂³×C₅₃	1	2	yes	—
845	#103	C₂³×C₅₃	1	2	yes	—
846	#103	C₂³×C₅₃	1	1	yes	characteristic
847	#103	C₂³×C₅₃	1	1	yes	characteristic
848	#103	C₂³×C₅₃	1	2	yes	—
849	#103	C₂³×C₅₃	1	2	yes	—
850	#103	C₂³×C₅₃	1	2	yes	—
851	#102	C₂³×C₅₃	1	1	yes	characteristic
852	#102	C₂³×C₅₃	1	1	yes	characteristic
853	#102	C₂³×C₅₃	1	2	yes	—
854	#102	C₂³×C₅₃	1	2	yes	—
855	#102	C₂³×C₅₃	1	2	yes	—
856	#102	C₂³×C₅₃	1	2	yes	—
857	#102	C₂³×C₅₃	1	1	yes	characteristic
858	#102	C₂³×C₅₃	1	1	yes	characteristic
859	#102	C₂³×C₅₃	1	1	yes	characteristic
860	#102	C₂³×C₅₃	1	1	yes	characteristic
861	#102	C₂³×C₅₃	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
863	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
864	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
866	#97	C₂³×C₅₃	1	2	yes	—
867	#97	C₂³×C₅₃	1	2	yes	—
868	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
869	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
870	C₂⁴	—	2	1	no	—
871	#41	—	2	4	no	—
872	#41	—	4	2	no	—
873	#41	—	4	2	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	—	2	1	no	—
879	C₂×Q₈	—	4	4	no	—
880	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
881	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
882	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	4	1	no	—
890	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
891	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
892	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
893	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
894	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	4	4	no	—
905	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
906	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
907	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
908	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
911	Q₁₆	—	4	2	no	—
912	SD₁₆	—	2	2	no	—
913	SD₁₆	—	4	1	no	—
914	SD₁₆	—	4	2	no	—
915	D₈	—	2	2	no	—
916	D₈	—	4	1	no	—
917	M₁₆	—	4	2	no	—
918	C₂×C₈	—	4	2	no	—
919	C₂×C₈	—	4	2	no	—
920	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
921	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
925	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
949	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
950	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
951	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
952	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
953	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
955	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
956	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
982	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
983	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	1	no	—
992	C₄²	C₂×D₄×C₅₃	1	2	yes	—
993	C₄²	C₂×D₄×C₅₃	1	2	yes	—
994	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
995	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
996	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
997	C₄²	C₂⁴×C₅₃	1	2	yes	—
998	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	4	2	no	—
1003	C₂³	—	4	2	no	—
1004	C₂³	—	8	1	no	—
1005	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1006	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	2	1	no	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	4	4	no	—
1013	Q₈	—	4	2	no	—
1014	Q₈	—	8	2	no	—
1015	Q₈	—	8	1	no	—
1016	Q₈	—	8	1	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	1	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	1	no	—
1023	D₄	—	4	2	no	—
1024	D₄	—	4	2	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	8	2	no	—
1027	D₄	—	8	2	no	—
1028	D₄	—	8	1	no	—
1029	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	4	2	no	—
1045	C₂×C₄	—	4	1	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	4	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	4	4	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	8	2	no	—
1056	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1057	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1058	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1059	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1060	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1061	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1064	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1065	C₈	—	2	1	no	—
1066	C₈	—	2	1	no	—
1067	C₈	—	2	1	no	—
1068	C₈	—	2	1	no	—
1069	C₈	—	2	2	no	—
1070	C₈	—	2	2	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	1	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	2	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	8	4	no	—
1087	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1088	C₄	—	2	2	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	C₅₃×#575	1	2	yes	—
1105	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1106	C₄	C₅₃×#585	1	1	yes	characteristic
1107	C₂	—	4	1	no	—
1108	C₂	—	4	2	no	—
1109	C₂	—	4	2	no	—
1110	C₂	—	8	1	no	—
1111	C₂	—	8	1	no	—
1112	C₂	C₅₃×#3489	1	1	yes	characteristic
1113	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1114	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
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×#3518	C₂	semidirect
2. C₅₃×#3475	C₂	semidirect
3. C₅₃×#3385	C₂	semidirect
4. C₅₃×#3384	C₂	semidirect
5. C₅₃×#3369	C₂	semidirect
6. C₅₃×#3367	C₂	semidirect
7. C₅₃×#3349	C₂	semidirect
8. C₅₃×#3348	C₂	semidirect
9. C₅₃×#3341	C₂	semidirect
10. C₅₃×#3340	C₂	semidirect
11. C₅₃×#3319	C₂	semidirect
12. C₅₃×#3311	C₂	semidirect
13. C₅₃×#3303	C₂	semidirect
14. C₅₃×#3302	C₂	semidirect
15. C₅₃×#3252	C₂	semidirect
16. C₅₃×#3250	C₂	semidirect
17. C₅₃×#3240	C₂	semidirect
18. C₅₃×#3231	C₂	semidirect
19. C₅₃×#3111	C₂	semidirect
20. C₅₃×#3105	C₂	semidirect
21. C₅₃×#3077	C₂	semidirect
22. C₅₃×#3076	C₂	semidirect
23. C₅₃×#2990	C₂	semidirect
24. Q₈²×C₅₃	C₂²	semidirect
29. C₅₃×#556	C₂²	semidirect
32. C₅₃×#555	C₂²	semidirect
38. D₄×Q₈×C₅₃	C₂²	semidirect
46. C₅₃×#533	C₂²	semidirect
50. C₅₃×#529	C₂²	semidirect
57. C₅₃×#501	C₂²	semidirect
58. C₅₃×#501	C₂²	semidirect
59. C₅₃×#500	C₂²	semidirect
60. C₅₃×#498	C₂²	semidirect
63. C₅₃×#487	C₂²	semidirect
64. C₅₃×#487	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
69. C₅₃×#485	C₂²	semidirect
73. C₅₃×#482	C₂²	semidirect
75. C₅₃×#479	C₂²	semidirect
76. C₅₃×#479	C₂²	semidirect
77. C₅₃×#479	C₂²	semidirect
78. C₅₃×#479	C₂²	semidirect
83. C₅₃×#478	C₂²	semidirect
84. C₅₃×#477	C₂²	semidirect
85. C₅₃×#477	C₂²	semidirect
89. C₅₃×#476	C₂²	semidirect
90. C₅₃×#475	C₂²	semidirect
96. C₅₃×#467	C₂²	semidirect
99. C₅₃×#465	C₂²	semidirect
101. C₅₃×#464	C₂²	semidirect
105. C₅₃×#462	C₂²	semidirect
106. C₅₃×#461	C₂²	semidirect
111. C₅₃×#446	C₂²	semidirect
112. C₅₃×#446	C₂²	semidirect
114. C₅₃×#441	C₂²	semidirect
116. C₅₃×#440	C₂²	semidirect
123. C₈×D₄×C₅₃	C₂²	semidirect
124. C₈×D₄×C₅₃	C₂²	semidirect
125. C₅₃×#432	C₂²	semidirect
128. C₅₃×#427	C₂²	semidirect
129. C₅₃×#427	C₂²	semidirect
131. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
513. #62141	C₅₃	direct (N × H)
550. #3518	C₂×C₅₃	semidirect
551. #3475	C₂×C₅₃	semidirect
552. #3385	C₂×C₅₃	semidirect
553. #3384	C₂×C₅₃	semidirect
554. #3369	C₂×C₅₃	semidirect
555. #3367	C₂×C₅₃	semidirect
556. #3349	C₂×C₅₃	semidirect
557. #3348	C₂×C₅₃	semidirect
558. #3341	C₂×C₅₃	semidirect
559. #3340	C₂×C₅₃	semidirect
560. #3319	C₂×C₅₃	semidirect
561. #3311	C₂×C₅₃	semidirect
562. #3303	C₂×C₅₃	semidirect
563. #3302	C₂×C₅₃	semidirect
564. #3252	C₂×C₅₃	semidirect
565. #3250	C₂×C₅₃	semidirect
566. #3240	C₂×C₅₃	semidirect
567. #3231	C₂×C₅₃	semidirect
568. #3111	C₂×C₅₃	semidirect
569. #3105	C₂×C₅₃	semidirect
570. #3077	C₂×C₅₃	semidirect
571. #3076	C₂×C₅₃	semidirect
572. #2990	C₂×C₅₃	semidirect
581. Q₈²	C₂²×C₅₃	semidirect
586. #556	C₂²×C₅₃	semidirect
589. #555	C₂²×C₅₃	semidirect
595. D₄×Q₈	C₂²×C₅₃	semidirect
603. #533	C₂²×C₅₃	semidirect
607. #529	C₂²×C₅₃	semidirect
614. #501	C₂²×C₅₃	semidirect
615. #501	C₂²×C₅₃	semidirect
616. #500	C₂²×C₅₃	semidirect
617. #498	C₂²×C₅₃	semidirect
620. #487	C₂²×C₅₃	semidirect
621. #487	C₂²×C₅₃	semidirect
624. #485	C₂²×C₅₃	semidirect
625. #485	C₂²×C₅₃	semidirect
626. #485	C₂²×C₅₃	semidirect
630. #482	C₂²×C₅₃	semidirect
632. #479	C₂²×C₅₃	semidirect
633. #479	C₂²×C₅₃	semidirect
634. #479	C₂²×C₅₃	semidirect
635. #479	C₂²×C₅₃	semidirect
640. #478	C₂²×C₅₃	semidirect
641. #477	C₂²×C₅₃	semidirect
642. #477	C₂²×C₅₃	semidirect
646. #476	C₂²×C₅₃	semidirect
647. #475	C₂²×C₅₃	semidirect
653. #467	C₂²×C₅₃	semidirect
656. #465	C₂²×C₅₃	semidirect
658. #464	C₂²×C₅₃	semidirect
662. #462	C₂²×C₅₃	semidirect
663. #461	C₂²×C₅₃	semidirect
668. #446	C₂²×C₅₃	semidirect
669. #446	C₂²×C₅₃	semidirect
671. #441	C₂²×C₅₃	semidirect
673. #440	C₂²×C₅₃	semidirect
680. C₈×D₄	C₂²×C₅₃	semidirect
681. C₈×D₄	C₂²×C₅₃	semidirect
682. #432	C₂²×C₅₃	semidirect
685. #427	C₂²×C₅₃	semidirect
686. #427	C₂²×C₅₃	semidirect
688. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
692. C₅₃	#62141	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×#3518	2
C₅₃×#3475	2
C₅₃×#3385	2
C₅₃×#3384	2
C₅₃×#3369	2
C₅₃×#3367	2
C₅₃×#3349	2
C₅₃×#3348	2
C₅₃×#3341	2
C₅₃×#3340	2
C₅₃×#3319	2
C₅₃×#3311	2
C₅₃×#3303	2
C₅₃×#3302	2
C₅₃×#3252	2
C₅₃×#3250	2
C₅₃×#3240	2
C₅₃×#3231	2
C₅₃×#3111	2
C₅₃×#3105	2
C₅₃×#3077	2
C₅₃×#3076	2
C₅₃×#2990	2
#62141	53

Subgroups — C53×#62141 #27269653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62141 #27269653