Subgroups — C₅₃×#61172 #27268684

Order 13568.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3488	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3317	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3316	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3311	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3310	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3304	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3300	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3296	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3295	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₅₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#556	C₂²	1	2	yes	complemented
32	C₅₃×#554	C₂²	1	2	yes	complemented
33	C₅₃×#552	—	2	2	no	—
34	C₅₃×#552	C₂²	1	2	yes	complemented
35	C₅₃×#552	C₂²	1	2	yes	complemented
36	C₅₃×#551	—	2	2	no	—
37	C₅₃×#550	C₂²	1	2	yes	—
38	C₅₃×#548	C₂²	1	2	yes	—
39	C₅₃×#546	—	2	2	no	—
40	C₅₃×#546	C₂²	1	2	yes	—
41	D₄²×C₅₃	—	2	2	no	—
42	D₄²×C₅₃	C₂²	1	2	yes	—
43	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#542	—	2	1	no	—
45	C₅₃×#541	—	2	1	no	—
46	C₅₃×#537	—	2	1	no	—
47	C₅₃×#537	C₂²	1	1	yes	characteristic
48	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#535	—	2	1	no	—
50	C₅₃×#535	C₂²	1	1	yes	characteristic
51	C₅₃×#533	—	2	1	no	—
52	C₅₃×#529	—	2	1	no	—
53	C₅₃×#525	—	2	1	no	—
54	C₅₃×#525	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×#121×C₅₃	—	2	1	no	—
57	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
58	C₅₃×#520	C₂²	1	1	yes	characteristic
59	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#519	C₂²	1	1	yes	characteristic, complemented
61	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#490	C₂²	1	2	yes	complemented
63	C₅₃×#489	C₂²	1	2	yes	complemented
64	C₅₃×#488	C₂²	1	2	yes	complemented
65	C₅₃×#486	C₂²	1	2	yes	complemented
66	C₅₃×#485	C₂²	1	2	yes	complemented
67	C₅₃×#483	C₂²	1	2	yes	complemented
68	C₅₃×#482	C₂²	1	2	yes	complemented
69	C₅₃×#482	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#481	C₂²	1	2	yes	complemented
72	C₅₃×#481	C₂²	1	2	yes	complemented
73	C₅₃×#480	C₂²	1	2	yes	complemented
74	C₅₃×#479	C₂²	1	2	yes	complemented
75	C₅₃×#478	C₂²	1	2	yes	complemented
76	C₅₃×#476	C₂²	1	2	yes	complemented
77	C₅₃×#475	C₂²	1	2	yes	complemented
78	C₅₃×#470	C₂²	1	2	yes	complemented
79	C₅₃×#468	C₂²	1	2	yes	complemented
80	C₅₃×#467	C₂²	1	2	yes	complemented
81	C₅₃×#465	C₂²	1	2	yes	complemented
82	C₅₃×#465	C₂²	1	2	yes	complemented
83	C₅₃×#465	C₂²	1	2	yes	complemented
84	C₅₃×#465	C₂²	1	2	yes	complemented
85	C₅₃×#465	C₂²	1	2	yes	complemented
86	C₅₃×#464	C₂²	1	2	yes	complemented
87	C₅₃×#464	C₂²	1	2	yes	complemented
88	C₅₃×#460	C₂²	1	2	yes	complemented
89	C₅₃×#460	C₂²	1	2	yes	complemented
90	C₅₃×#452	C₂²	1	2	yes	complemented
91	C₅₃×#452	C₂²	1	2	yes	complemented
92	C₅₃×#452	C₂²	1	2	yes	complemented
93	C₅₃×#452	C₂²	1	2	yes	complemented
94	C₅₃×#451	C₂²	1	2	yes	complemented
95	C₅₃×#450	C₂²	1	2	yes	complemented
96	C₅₃×#450	C₂²	1	2	yes	complemented
97	C₅₃×#450	C₂²	1	2	yes	complemented
98	C₅₃×#441	C₂²	1	2	yes	complemented
99	C₅₃×#440	C₂²	1	2	yes	complemented
100	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
102	C₅₃×#435	C₂²	1	2	yes	complemented
103	C₅₃×#435	C₂²	1	2	yes	complemented
104	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
105	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
106	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
108	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#418	C₂²	1	2	yes	complemented
113	C₅₃×#417	C₂²	1	1	yes	characteristic
114	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#417	C₂²	1	2	yes	complemented
116	C₅₃×#416	C₂²	1	1	yes	characteristic
117	C₅₃×#416	C₂²	1	1	yes	characteristic
118	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#416	C₂²	1	2	yes	complemented
121	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
126	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
128	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
129	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
130	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
135	H(5,𝔽₂)×C₅₃	—	2	4	no	—
136	H(5,𝔽₂)×C₅₃	—	4	2	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	4	no	—
141	C₂×#41×C₅₃	—	4	2	no	—
142	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×#41×C₅₃	C₂³	1	2	yes	—
145	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₅₃	—	2	1	no	—
151	C₂²×D₄×C₅₃	—	2	1	no	—
152	C₂²×D₄×C₅₃	—	2	1	no	—
153	C₂²×D₄×C₅₃	—	2	2	no	—
154	C₂²×D₄×C₅₃	—	2	2	no	—
155	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
156	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
158	C₂³×C₄×C₅₃	—	2	1	no	—
159	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
160	#137×C₅₃	—	2	4	no	—
161	#137×C₅₃	—	4	2	no	—
162	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
163	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₅₃	—	4	2	no	—
165	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
169	#131×C₅₃	—	4	2	no	—
170	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
173	C₂²×C₈×C₅₃	—	4	2	no	—
174	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
179	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
181	C₄⋊Q₈×C₅₃	—	2	1	no	—
182	C₄⋊Q₈×C₅₃	—	2	1	no	—
183	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
184	#127×C₅₃	—	2	2	no	—
185	#127×C₅₃	C₂³	1	2	yes	—
186	#126×C₅₃	—	2	2	no	—
187	#126×C₅₃	—	2	2	no	—
188	#126×C₅₃	—	2	2	no	—
189	#126×C₅₃	—	2	2	no	—
190	#125×C₅₃	—	2	1	no	—
191	#125×C₅₃	—	2	2	no	—
192	#125×C₅₃	—	2	2	no	—
193	#125×C₅₃	—	2	2	no	—
194	#125×C₅₃	C₂³	1	2	yes	—
195	#124×C₅₃	—	2	2	no	—
196	#124×C₅₃	—	2	1	no	—
197	#124×C₅₃	—	2	2	no	—
198	#124×C₅₃	C₂³	1	2	yes	—
199	#123×C₅₃	—	2	2	no	—
200	#123×C₅₃	—	2	2	no	—
201	#123×C₅₃	—	2	2	no	—
202	#123×C₅₃	—	2	2	no	—
203	#123×C₅₃	D₄	1	2	yes	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	2	no	—
206	C₂²⋊Q₈×C₅₃	—	2	2	no	—
207	C₂²⋊Q₈×C₅₃	—	2	2	no	—
208	C₂²⋊Q₈×C₅₃	—	2	1	no	—
209	C₂²⋊Q₈×C₅₃	—	2	1	no	—
210	C₂²⋊Q₈×C₅₃	—	2	1	no	—
211	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
212	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
213	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
215	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
218	#121×C₅₃	—	2	1	no	—
219	#121×C₅₃	—	2	1	no	—
220	#121×C₅₃	—	2	2	no	—
221	#121×C₅₃	—	2	2	no	—
222	#121×C₅₃	—	2	2	no	—
223	#121×C₅₃	—	2	2	no	—
224	#121×C₅₃	—	2	1	no	—
225	#121×C₅₃	—	2	2	no	—
226	#121×C₅₃	—	2	2	no	—
227	#121×C₅₃	—	2	1	no	—
228	#121×C₅₃	—	2	1	no	—
229	#121×C₅₃	D₄	1	1	yes	characteristic
230	#121×C₅₃	D₄	1	1	yes	characteristic
231	#121×C₅₃	C₂³	1	2	yes	—
232	#121×C₅₃	C₂³	1	2	yes	—
233	#121×C₅₃	C₂³	1	2	yes	—
234	#120×C₅₃	—	2	2	no	—
235	#120×C₅₃	—	2	2	no	—
236	#120×C₅₃	—	2	2	no	—
237	#120×C₅₃	—	2	2	no	—
238	#120×C₅₃	D₄	1	2	yes	—
239	C₄×Q₈×C₅₃	—	2	1	no	—
240	C₄×Q₈×C₅₃	—	2	1	no	—
241	C₄×Q₈×C₅₃	—	2	2	no	—
242	C₄×Q₈×C₅₃	—	2	1	no	—
243	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
244	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
245	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
246	C₄×D₄×C₅₃	—	2	2	no	—
247	C₄×D₄×C₅₃	—	2	2	no	—
248	C₄×D₄×C₅₃	—	2	2	no	—
249	C₄×D₄×C₅₃	—	2	1	no	—
250	C₄×D₄×C₅₃	—	2	2	no	—
251	C₄×D₄×C₅₃	—	2	2	no	—
252	C₄×D₄×C₅₃	C₂³	1	2	yes	—
253	C₄×D₄×C₅₃	C₂³	1	2	yes	—
254	C₄×D₄×C₅₃	C₂³	1	2	yes	—
255	#117×C₅₃	—	2	1	no	—
256	#117×C₅₃	—	2	2	no	—
257	#117×C₅₃	—	2	2	no	—
258	#117×C₅₃	—	2	2	no	—
259	#117×C₅₃	—	2	1	no	—
260	#117×C₅₃	—	2	1	no	—
261	#117×C₅₃	C₂³	1	2	yes	—
262	#117×C₅₃	C₂³	1	1	yes	characteristic
263	#117×C₅₃	C₂³	1	1	yes	characteristic
264	#117×C₅₃	C₂³	1	1	yes	characteristic
265	#117×C₅₃	C₂³	1	1	yes	characteristic
266	#117×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
268	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
269	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
274	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
276	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
277	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
278	C₂×C₄²×C₅₃	—	2	1	no	—
279	#107×C₅₃	C₂³	1	2	yes	—
280	#107×C₅₃	C₂³	1	2	yes	—
281	#106×C₅₃	C₂³	1	2	yes	—
282	#106×C₅₃	C₂³	1	2	yes	—
283	#106×C₅₃	C₂³	1	2	yes	—
284	#106×C₅₃	C₂³	1	2	yes	—
285	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
287	#103×C₅₃	C₂³	1	1	yes	characteristic
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	1	yes	characteristic
290	#103×C₅₃	C₂³	1	1	yes	characteristic
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	1	yes	characteristic
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	1	yes	characteristic
296	#103×C₅₃	C₂³	1	2	yes	—
297	#103×C₅₃	C₂³	1	2	yes	—
298	#103×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
303	#102×C₅₃	C₂³	1	2	yes	—
304	#102×C₅₃	C₂³	1	2	yes	—
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	1	yes	characteristic
307	#102×C₅₃	C₂³	1	1	yes	characteristic
308	#102×C₅₃	C₂³	1	1	yes	characteristic
309	#102×C₅₃	C₂³	1	1	yes	characteristic
310	#102×C₅₃	C₂³	1	1	yes	characteristic
311	#102×C₅₃	C₂³	1	1	yes	characteristic
312	#102×C₅₃	C₂³	1	2	yes	—
313	#102×C₅₃	C₂³	1	2	yes	—
314	#102×C₅₃	C₂³	1	2	yes	—
315	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
316	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
319	#97×C₅₃	C₂³	1	2	yes	—
320	C₄×C₈×C₅₃	C₂³	1	2	yes	—
321	C₂⁴×C₅₃	—	2	1	no	—
322	C₂⁴×C₅₃	—	2	2	no	—
323	C₂⁴×C₅₃	—	2	1	no	—
324	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
325	#41×C₅₃	—	2	2	no	—
326	#41×C₅₃	—	2	2	no	—
327	#41×C₅₃	—	2	2	no	—
328	#41×C₅₃	—	2	2	no	—
329	#41×C₅₃	—	2	4	no	—
330	#41×C₅₃	—	2	2	no	—
331	#41×C₅₃	—	2	2	no	—
332	#41×C₅₃	—	2	2	no	—
333	#41×C₅₃	—	4	4	no	—
334	#41×C₅₃	—	4	1	no	—
335	#41×C₅₃	—	4	1	no	—
336	#41×C₅₃	—	4	2	no	—
337	#41×C₅₃	—	4	4	no	—
338	#41×C₅₃	—	4	4	no	—
339	#41×C₅₃	#41	1	4	yes	—
340	C₂×Q₈×C₅₃	—	2	1	no	—
341	C₂×Q₈×C₅₃	—	2	1	no	—
342	C₂×Q₈×C₅₃	—	2	2	no	—
343	C₂×Q₈×C₅₃	—	2	2	no	—
344	C₂×Q₈×C₅₃	—	2	2	no	—
345	C₂×Q₈×C₅₃	—	2	2	no	—
346	C₂×Q₈×C₅₃	—	4	1	no	—
347	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
348	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
350	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₅₃	—	2	1	no	—
352	C₂×D₄×C₅₃	—	2	2	no	—
353	C₂×D₄×C₅₃	—	2	4	no	—
354	C₂×D₄×C₅₃	—	2	2	no	—
355	C₂×D₄×C₅₃	—	2	1	no	—
356	C₂×D₄×C₅₃	—	2	1	no	—
357	C₂×D₄×C₅₃	—	2	2	no	—
358	C₂×D₄×C₅₃	—	2	1	no	—
359	C₂×D₄×C₅₃	—	2	2	no	—
360	C₂×D₄×C₅₃	—	2	2	no	—
361	C₂×D₄×C₅₃	—	2	1	no	—
362	C₂×D₄×C₅₃	—	2	2	no	—
363	C₂×D₄×C₅₃	—	2	1	no	—
364	C₂×D₄×C₅₃	—	2	2	no	—
365	C₂×D₄×C₅₃	—	2	2	no	—
366	C₂×D₄×C₅₃	—	2	2	no	—
367	C₂×D₄×C₅₃	—	2	2	no	—
368	C₂×D₄×C₅₃	—	4	1	no	—
369	C₂×D₄×C₅₃	—	4	2	no	—
370	C₂×D₄×C₅₃	—	4	4	no	—
371	C₂×D₄×C₅₃	—	4	8	no	—
372	C₂×D₄×C₅₃	—	4	4	no	—
373	C₂×D₄×C₅₃	—	8	4	no	—
374	C₂×D₄×C₅₃	—	8	2	no	—
375	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
376	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
377	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
378	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
379	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
380	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	—	2	1	no	—
383	C₂²×C₄×C₅₃	—	2	2	no	—
384	C₂²×C₄×C₅₃	—	2	2	no	—
385	C₂²×C₄×C₅₃	—	2	1	no	—
386	C₂²×C₄×C₅₃	—	2	1	no	—
387	C₂²×C₄×C₅₃	—	2	1	no	—
388	C₂²×C₄×C₅₃	—	2	1	no	—
389	C₂²×C₄×C₅₃	—	2	1	no	—
390	C₂²×C₄×C₅₃	—	2	1	no	—
391	C₂²×C₄×C₅₃	—	2	2	no	—
392	C₂²×C₄×C₅₃	—	2	1	no	—
393	C₂²×C₄×C₅₃	—	2	1	no	—
394	C₂²×C₄×C₅₃	—	2	2	no	—
395	C₂²×C₄×C₅₃	—	2	1	no	—
396	C₂²×C₄×C₅₃	—	2	2	no	—
397	C₂²×C₄×C₅₃	—	4	4	no	—
398	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
403	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	Q₁₆×C₅₃	—	2	4	no	—
406	Q₁₆×C₅₃	—	4	2	no	—
407	SD₁₆×C₅₃	—	2	4	no	—
408	SD₁₆×C₅₃	—	4	2	no	—
409	SD₁₆×C₅₃	—	4	2	no	—
410	SD₁₆×C₅₃	—	4	2	no	—
411	M₁₆×C₅₃	—	2	2	no	—
412	M₁₆×C₅₃	—	2	2	no	—
413	M₁₆×C₅₃	—	4	2	no	—
414	C₂×C₈×C₅₃	—	2	2	no	—
415	C₂×C₈×C₅₃	—	2	2	no	—
416	C₂×C₈×C₅₃	—	4	1	no	—
417	C₂×C₈×C₅₃	—	4	1	no	—
418	C₂×C₈×C₅₃	—	4	1	no	—
419	C₂×C₈×C₅₃	—	4	1	no	—
420	C₂×C₈×C₅₃	—	4	2	no	—
421	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
423	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
425	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₅₃	—	2	1	no	—
428	C₄⋊C₄×C₅₃	—	2	2	no	—
429	C₄⋊C₄×C₅₃	—	2	2	no	—
430	C₄⋊C₄×C₅₃	—	2	2	no	—
431	C₄⋊C₄×C₅₃	—	2	1	no	—
432	C₄⋊C₄×C₅₃	—	2	1	no	—
433	C₄⋊C₄×C₅₃	—	2	1	no	—
434	C₄⋊C₄×C₅₃	—	2	2	no	—
435	C₄⋊C₄×C₅₃	—	2	2	no	—
436	C₄⋊C₄×C₅₃	—	2	2	no	—
437	C₄⋊C₄×C₅₃	—	2	2	no	—
438	C₄⋊C₄×C₅₃	—	2	2	no	—
439	C₄⋊C₄×C₅₃	—	2	2	no	—
440	C₄⋊C₄×C₅₃	—	2	2	no	—
441	C₄⋊C₄×C₅₃	—	2	2	no	—
442	C₄⋊C₄×C₅₃	—	2	2	no	—
443	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
446	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
447	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
449	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
453	C₂²⋊C₄×C₅₃	—	2	1	no	—
454	C₂²⋊C₄×C₅₃	—	2	1	no	—
455	C₂²⋊C₄×C₅₃	—	2	1	no	—
456	C₂²⋊C₄×C₅₃	—	2	1	no	—
457	C₂²⋊C₄×C₅₃	—	2	2	no	—
458	C₂²⋊C₄×C₅₃	—	2	2	no	—
459	C₂²⋊C₄×C₅₃	—	2	2	no	—
460	C₂²⋊C₄×C₅₃	—	2	2	no	—
461	C₂²⋊C₄×C₅₃	—	2	2	no	—
462	C₂²⋊C₄×C₅₃	—	2	2	no	—
463	C₂²⋊C₄×C₅₃	—	2	2	no	—
464	C₂²⋊C₄×C₅₃	—	2	2	no	—
465	C₂²⋊C₄×C₅₃	—	2	2	no	—
466	C₂²⋊C₄×C₅₃	—	2	2	no	—
467	C₂²⋊C₄×C₅₃	—	2	2	no	—
468	C₂²⋊C₄×C₅₃	—	2	2	no	—
469	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
470	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
471	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
472	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
473	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
474	C₄²×C₅₃	—	2	1	no	—
475	C₄²×C₅₃	—	2	1	no	—
476	C₄²×C₅₃	—	2	1	no	—
477	C₄²×C₅₃	—	2	1	no	—
478	C₄²×C₅₃	—	2	2	no	—
479	C₄²×C₅₃	—	2	2	no	—
480	C₄²×C₅₃	—	2	2	no	—
481	C₄²×C₅₃	—	2	2	no	—
482	C₄²×C₅₃	C₂⁴	1	2	yes	—
483	C₂³×C₅₃	—	2	2	no	—
484	C₂³×C₅₃	—	2	2	no	—
485	C₂³×C₅₃	—	2	1	no	—
486	C₂³×C₅₃	—	2	1	no	—
487	C₂³×C₅₃	—	2	2	no	—
488	C₂³×C₅₃	—	4	1	no	—
489	C₂³×C₅₃	—	4	2	no	—
490	C₂³×C₅₃	—	4	4	no	—
491	C₂³×C₅₃	—	4	2	no	—
492	C₂³×C₅₃	—	4	2	no	—
493	C₂³×C₅₃	—	8	1	no	—
494	C₂³×C₅₃	—	8	1	no	—
495	C₂³×C₅₃	—	8	2	no	—
496	C₂³×C₅₃	—	8	1	no	—
497	C₂³×C₅₃	—	8	2	no	—
498	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
499	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
500	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
501	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
502	Q₈×C₅₃	—	2	2	no	—
503	Q₈×C₅₃	—	2	1	no	—
504	Q₈×C₅₃	—	2	1	no	—
505	Q₈×C₅₃	—	2	2	no	—
506	Q₈×C₅₃	—	2	2	no	—
507	Q₈×C₅₃	—	2	1	no	—
508	Q₈×C₅₃	—	4	2	no	—
509	Q₈×C₅₃	—	4	2	no	—
510	Q₈×C₅₃	—	8	2	no	—
511	Q₈×C₅₃	C₂×#41	1	2	yes	—
512	D₄×C₅₃	—	2	4	no	—
513	D₄×C₅₃	—	2	4	no	—
514	D₄×C₅₃	—	2	4	no	—
515	D₄×C₅₃	—	2	2	no	—
516	D₄×C₅₃	—	2	2	no	—
517	D₄×C₅₃	—	2	1	no	—
518	D₄×C₅₃	—	2	1	no	—
519	D₄×C₅₃	—	2	2	no	—
520	D₄×C₅₃	—	2	1	no	—
521	D₄×C₅₃	—	4	2	no	—
522	D₄×C₅₃	—	4	4	no	—
523	D₄×C₅₃	—	4	2	no	—
524	D₄×C₅₃	—	4	4	no	—
525	D₄×C₅₃	—	4	2	no	—
526	D₄×C₅₃	—	4	2	no	—
527	D₄×C₅₃	—	4	2	no	—
528	D₄×C₅₃	—	4	4	no	—
529	D₄×C₅₃	—	4	2	no	—
530	D₄×C₅₃	—	8	2	no	—
531	D₄×C₅₃	—	8	2	no	—
532	D₄×C₅₃	—	8	2	no	—
533	D₄×C₅₃	—	8	2	no	—
534	D₄×C₅₃	C₂×#41	1	2	yes	—
535	C₂×C₄×C₅₃	—	2	2	no	—
536	C₂×C₄×C₅₃	—	2	1	no	—
537	C₂×C₄×C₅₃	—	2	2	no	—
538	C₂×C₄×C₅₃	—	2	2	no	—
539	C₂×C₄×C₅₃	—	2	4	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	1	no	—
542	C₂×C₄×C₅₃	—	2	2	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	2	no	—
546	C₂×C₄×C₅₃	—	2	1	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	2	2	no	—
549	C₂×C₄×C₅₃	—	2	2	no	—
550	C₂×C₄×C₅₃	—	2	1	no	—
551	C₂×C₄×C₅₃	—	2	2	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	1	no	—
554	C₂×C₄×C₅₃	—	4	2	no	—
555	C₂×C₄×C₅₃	—	4	4	no	—
556	C₂×C₄×C₅₃	—	4	2	no	—
557	C₂×C₄×C₅₃	—	4	2	no	—
558	C₂×C₄×C₅₃	—	4	2	no	—
559	C₂×C₄×C₅₃	—	4	2	no	—
560	C₂×C₄×C₅₃	—	4	2	no	—
561	C₂×C₄×C₅₃	—	8	2	no	—
562	C₂×C₄×C₅₃	—	8	2	no	—
563	C₂×C₄×C₅₃	—	8	1	no	—
564	C₂×C₄×C₅₃	—	8	1	no	—
565	C₂×C₄×C₅₃	—	8	1	no	—
566	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
568	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
569	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
571	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
573	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
574	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
575	C₈×C₅₃	—	2	2	no	—
576	C₈×C₅₃	—	2	1	no	—
577	C₈×C₅₃	—	2	1	no	—
578	C₈×C₅₃	—	2	1	no	—
579	C₈×C₅₃	—	2	1	no	—
580	C₈×C₅₃	—	2	2	no	—
581	#61172	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
582	C₂²×C₅₃	—	2	1	no	—
583	C₂²×C₅₃	—	2	1	no	—
584	C₂²×C₅₃	—	2	1	no	—
585	C₂²×C₅₃	—	2	1	no	—
586	C₂²×C₅₃	—	2	2	no	—
587	C₂²×C₅₃	—	2	1	no	—
588	C₂²×C₅₃	—	2	1	no	—
589	C₂²×C₅₃	—	2	2	no	—
590	C₂²×C₅₃	—	2	2	no	—
591	C₂²×C₅₃	—	2	2	no	—
592	C₂²×C₅₃	—	2	1	no	—
593	C₂²×C₅₃	—	4	4	no	—
594	C₂²×C₅₃	—	4	1	no	—
595	C₂²×C₅₃	—	4	1	no	—
596	C₂²×C₅₃	—	4	1	no	—
597	C₂²×C₅₃	—	4	2	no	—
598	C₂²×C₅₃	—	4	1	no	—
599	C₂²×C₅₃	—	4	2	no	—
600	C₂²×C₅₃	—	4	2	no	—
601	C₂²×C₅₃	—	4	1	no	—
602	C₂²×C₅₃	—	8	4	no	—
603	C₂²×C₅₃	—	16	2	no	—
604	C₂²×C₅₃	—	16	4	no	—
605	C₂²×C₅₃	#546	1	2	yes	—
606	C₂²×C₅₃	#577	1	2	yes	—
607	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
608	C₄×C₅₃	—	2	2	no	—
609	C₄×C₅₃	—	2	1	no	—
610	C₄×C₅₃	—	2	1	no	—
611	C₄×C₅₃	—	2	2	no	—
612	C₄×C₅₃	—	2	2	no	—
613	C₄×C₅₃	—	2	2	no	—
614	C₄×C₅₃	—	4	1	no	—
615	C₄×C₅₃	—	4	2	no	—
616	C₄×C₅₃	—	4	1	no	—
617	C₄×C₅₃	—	4	1	no	—
618	C₄×C₅₃	—	4	2	no	—
619	C₄×C₅₃	—	4	1	no	—
620	C₄×C₅₃	—	4	1	no	—
621	C₄×C₅₃	—	4	2	no	—
622	C₄×C₅₃	#546	1	2	yes	—
623	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
624	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
625	#3495	C₂×C₅₃	1	1	yes	characteristic, complemented
626	#3488	C₂×C₅₃	1	1	yes	characteristic
627	#3317	C₂×C₅₃	1	2	yes	complemented
628	#3316	C₂×C₅₃	1	2	yes	complemented
629	#3311	C₂×C₅₃	1	2	yes	complemented
630	#3310	C₂×C₅₃	1	2	yes	complemented
631	#3304	C₂×C₅₃	1	2	yes	complemented
632	#3300	C₂×C₅₃	1	2	yes	complemented
633	#3296	C₂×C₅₃	1	2	yes	complemented
634	#3295	C₂×C₅₃	1	2	yes	complemented
635	#3136	C₂×C₅₃	1	1	yes	characteristic, complemented
636	#3099	C₂×C₅₃	1	1	yes	characteristic, complemented
637	#3094	C₂×C₅₃	1	1	yes	characteristic, complemented
638	#3084	C₂×C₅₃	1	1	yes	characteristic, complemented
639	#3063	C₂×C₅₃	1	1	yes	characteristic, complemented
640	C₂×#465	C₂×C₅₃	1	1	yes	characteristic, complemented
641	#3043	C₂×C₅₃	1	1	yes	characteristic, complemented
642	#3009	C₂×C₅₃	1	1	yes	characteristic, complemented
643	#3007	C₂×C₅₃	1	1	yes	characteristic, complemented
644	#2947	C₂×C₅₃	1	1	yes	characteristic, complemented
645	#2929	C₂×C₅₃	1	1	yes	characteristic, complemented
646	#2897	C₂×C₅₃	1	1	yes	characteristic, complemented
647	C₂×#416	C₂×C₅₃	1	1	yes	characteristic, complemented
648	C₂×C₅₃	—	2	2	no	—
649	C₂×C₅₃	—	2	2	no	—
650	C₂×C₅₃	—	4	1	no	—
651	C₂×C₅₃	—	4	2	no	—
652	C₂×C₅₃	—	4	2	no	—
653	C₂×C₅₃	—	8	1	no	—
654	C₂×C₅₃	—	8	2	no	—
655	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
656	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
657	C₂×C₅₃	#3584	1	1	yes	characteristic
658	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
659	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
660	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
661	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
662	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic, complemented
664	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
665	#556	C₂²×C₅₃	1	2	yes	complemented
666	#554	C₂²×C₅₃	1	2	yes	complemented
667	#552	—	2	2	no	—
668	#552	C₂²×C₅₃	1	2	yes	complemented
669	#552	C₂²×C₅₃	1	2	yes	complemented
670	#551	—	2	2	no	—
671	#550	C₂²×C₅₃	1	2	yes	—
672	#548	C₂²×C₅₃	1	2	yes	—
673	#546	—	2	2	no	—
674	#546	C₂²×C₅₃	1	2	yes	—
675	D₄²	—	2	2	no	—
676	D₄²	C₂²×C₅₃	1	2	yes	—
677	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	#542	—	2	1	no	—
679	#541	—	2	1	no	—
680	#537	—	2	1	no	—
681	#537	C₂²×C₅₃	1	1	yes	characteristic
682	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	#535	—	2	1	no	—
684	#535	C₂²×C₅₃	1	1	yes	characteristic
685	#533	—	2	1	no	—
686	#529	—	2	1	no	—
687	#525	—	2	1	no	—
688	#525	C₂²×C₅₃	1	1	yes	characteristic
689	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	C₂×#121	—	2	1	no	—
691	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
692	#520	C₂²×C₅₃	1	1	yes	characteristic
693	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
694	#519	C₂²×C₅₃	1	1	yes	characteristic, complemented
695	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	#490	C₂²×C₅₃	1	2	yes	complemented
697	#489	C₂²×C₅₃	1	2	yes	complemented
698	#488	C₂²×C₅₃	1	2	yes	complemented
699	#486	C₂²×C₅₃	1	2	yes	complemented
700	#485	C₂²×C₅₃	1	2	yes	complemented
701	#483	C₂²×C₅₃	1	2	yes	complemented
702	#482	C₂²×C₅₃	1	2	yes	complemented
703	#482	C₂²×C₅₃	1	2	yes	complemented
704	#482	C₂²×C₅₃	1	2	yes	complemented
705	#481	C₂²×C₅₃	1	2	yes	complemented
706	#481	C₂²×C₅₃	1	2	yes	complemented
707	#480	C₂²×C₅₃	1	2	yes	complemented
708	#479	C₂²×C₅₃	1	2	yes	complemented
709	#478	C₂²×C₅₃	1	2	yes	complemented
710	#476	C₂²×C₅₃	1	2	yes	complemented
711	#475	C₂²×C₅₃	1	2	yes	complemented
712	#470	C₂²×C₅₃	1	2	yes	complemented
713	#468	C₂²×C₅₃	1	2	yes	complemented
714	#467	C₂²×C₅₃	1	2	yes	complemented
715	#465	C₂²×C₅₃	1	2	yes	complemented
716	#465	C₂²×C₅₃	1	2	yes	complemented
717	#465	C₂²×C₅₃	1	2	yes	complemented
718	#465	C₂²×C₅₃	1	2	yes	complemented
719	#465	C₂²×C₅₃	1	2	yes	complemented
720	#464	C₂²×C₅₃	1	2	yes	complemented
721	#464	C₂²×C₅₃	1	2	yes	complemented
722	#460	C₂²×C₅₃	1	2	yes	complemented
723	#460	C₂²×C₅₃	1	2	yes	complemented
724	#452	C₂²×C₅₃	1	2	yes	complemented
725	#452	C₂²×C₅₃	1	2	yes	complemented
726	#452	C₂²×C₅₃	1	2	yes	complemented
727	#452	C₂²×C₅₃	1	2	yes	complemented
728	#451	C₂²×C₅₃	1	2	yes	complemented
729	#450	C₂²×C₅₃	1	2	yes	complemented
730	#450	C₂²×C₅₃	1	2	yes	complemented
731	#450	C₂²×C₅₃	1	2	yes	complemented
732	#441	C₂²×C₅₃	1	2	yes	complemented
733	#440	C₂²×C₅₃	1	2	yes	complemented
734	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
735	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
736	#435	C₂²×C₅₃	1	2	yes	complemented
737	#435	C₂²×C₅₃	1	2	yes	complemented
738	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
739	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
740	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
741	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
742	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
743	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
744	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
746	#418	C₂²×C₅₃	1	2	yes	complemented
747	#417	C₂²×C₅₃	1	1	yes	characteristic
748	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
749	#417	C₂²×C₅₃	1	2	yes	complemented
750	#416	C₂²×C₅₃	1	1	yes	characteristic
751	#416	C₂²×C₅₃	1	1	yes	characteristic
752	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
753	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
754	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
755	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
756	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
757	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
758	#416	C₂²×C₅₃	1	2	yes	complemented
759	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
760	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
761	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
762	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
763	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
764	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
765	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
766	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
767	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
768	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
769	C₅₃	#61172	1	1	yes	characteristic, direct product factor, Sylow
770	H(5,𝔽₂)	—	2	4	no	—
771	H(5,𝔽₂)	—	4	2	no	—
772	C₂×#41	—	2	1	no	—
773	C₂×#41	—	2	1	no	—
774	C₂×#41	—	2	1	no	—
775	C₂×#41	—	2	4	no	—
776	C₂×#41	—	4	2	no	—
777	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
778	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
779	C₂×#41	C₂³×C₅₃	1	2	yes	—
780	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
781	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
782	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
783	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
784	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
785	C₂²×D₄	—	2	1	no	—
786	C₂²×D₄	—	2	1	no	—
787	C₂²×D₄	—	2	1	no	—
788	C₂²×D₄	—	2	2	no	—
789	C₂²×D₄	—	2	2	no	—
790	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
791	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
792	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
793	C₂³×C₄	—	2	1	no	—
794	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
795	#137	—	2	4	no	—
796	#137	—	4	2	no	—
797	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
798	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
799	C₂×SD₁₆	—	4	2	no	—
800	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
801	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
802	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
803	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
804	#131	—	4	2	no	—
805	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
806	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
807	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
808	C₂²×C₈	—	4	2	no	—
809	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
810	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
811	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
812	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
813	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
814	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
815	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
816	C₄⋊Q₈	—	2	1	no	—
817	C₄⋊Q₈	—	2	1	no	—
818	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
819	#127	—	2	2	no	—
820	#127	C₂³×C₅₃	1	2	yes	—
821	#126	—	2	2	no	—
822	#126	—	2	2	no	—
823	#126	—	2	2	no	—
824	#126	—	2	2	no	—
825	#125	—	2	1	no	—
826	#125	—	2	2	no	—
827	#125	—	2	2	no	—
828	#125	—	2	2	no	—
829	#125	C₂³×C₅₃	1	2	yes	—
830	#124	—	2	1	no	—
831	#124	—	2	2	no	—
832	#124	—	2	2	no	—
833	#124	C₂³×C₅₃	1	2	yes	—
834	#123	—	2	2	no	—
835	#123	—	2	2	no	—
836	#123	—	2	2	no	—
837	#123	—	2	2	no	—
838	#123	D₄×C₅₃	1	2	yes	—
839	C₂²⋊Q₈	—	2	1	no	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	—	2	1	no	—
842	C₂²⋊Q₈	—	2	2	no	—
843	C₂²⋊Q₈	—	2	2	no	—
844	C₂²⋊Q₈	—	2	2	no	—
845	C₂²⋊Q₈	—	2	2	no	—
846	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
847	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
848	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
849	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
850	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
851	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
852	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
853	#121	—	2	1	no	—
854	#121	—	2	2	no	—
855	#121	—	2	2	no	—
856	#121	—	2	1	no	—
857	#121	—	2	1	no	—
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	—	2	2	no	—
861	#121	—	2	2	no	—
862	#121	—	2	2	no	—
863	#121	—	2	2	no	—
864	#121	D₄×C₅₃	1	1	yes	characteristic
865	#121	D₄×C₅₃	1	1	yes	characteristic
866	#121	C₂³×C₅₃	1	2	yes	—
867	#121	C₂³×C₅₃	1	2	yes	—
868	#121	C₂³×C₅₃	1	2	yes	—
869	#120	—	2	2	no	—
870	#120	—	2	2	no	—
871	#120	—	2	2	no	—
872	#120	—	2	2	no	—
873	#120	D₄×C₅₃	1	2	yes	—
874	C₄×Q₈	—	2	1	no	—
875	C₄×Q₈	—	2	1	no	—
876	C₄×Q₈	—	2	1	no	—
877	C₄×Q₈	—	2	2	no	—
878	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
879	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
880	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	2	no	—
883	C₄×D₄	—	2	2	no	—
884	C₄×D₄	—	2	2	no	—
885	C₄×D₄	—	2	2	no	—
886	C₄×D₄	—	2	2	no	—
887	C₄×D₄	C₂³×C₅₃	1	2	yes	—
888	C₄×D₄	C₂³×C₅₃	1	2	yes	—
889	C₄×D₄	C₂³×C₅₃	1	2	yes	—
890	#117	—	2	1	no	—
891	#117	—	2	1	no	—
892	#117	—	2	1	no	—
893	#117	—	2	2	no	—
894	#117	—	2	2	no	—
895	#117	—	2	2	no	—
896	#117	C₂³×C₅₃	1	1	yes	characteristic
897	#117	C₂³×C₅₃	1	1	yes	characteristic
898	#117	C₂³×C₅₃	1	1	yes	characteristic
899	#117	C₂³×C₅₃	1	1	yes	characteristic
900	#117	C₂³×C₅₃	1	2	yes	—
901	#117	C₂³×C₅₃	1	1	yes	characteristic
902	C₂×C₄⋊C₄	—	2	1	no	—
903	C₂×C₄⋊C₄	—	2	1	no	—
904	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
905	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
906	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
907	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
908	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
909	C₂×C₂²⋊C₄	—	2	1	no	—
910	C₂×C₂²⋊C₄	—	2	1	no	—
911	C₂×C₂²⋊C₄	—	2	1	no	—
912	C₂×C₂²⋊C₄	—	2	2	no	—
913	C₂×C₄²	—	2	1	no	—
914	#107	C₂³×C₅₃	1	2	yes	—
915	#107	C₂³×C₅₃	1	2	yes	—
916	#106	C₂³×C₅₃	1	2	yes	—
917	#106	C₂³×C₅₃	1	2	yes	—
918	#106	C₂³×C₅₃	1	2	yes	—
919	#106	C₂³×C₅₃	1	2	yes	—
920	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
921	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
922	#103	C₂³×C₅₃	1	1	yes	characteristic
923	#103	C₂³×C₅₃	1	1	yes	characteristic
924	#103	C₂³×C₅₃	1	1	yes	characteristic
925	#103	C₂³×C₅₃	1	1	yes	characteristic
926	#103	C₂³×C₅₃	1	1	yes	characteristic
927	#103	C₂³×C₅₃	1	1	yes	characteristic
928	#103	C₂³×C₅₃	1	1	yes	characteristic
929	#103	C₂³×C₅₃	1	1	yes	characteristic
930	#103	C₂³×C₅₃	1	2	yes	—
931	#103	C₂³×C₅₃	1	2	yes	—
932	#103	C₂³×C₅₃	1	2	yes	—
933	#103	C₂³×C₅₃	1	2	yes	—
934	#102	C₂³×C₅₃	1	1	yes	characteristic
935	#102	C₂³×C₅₃	1	2	yes	—
936	#102	C₂³×C₅₃	1	1	yes	characteristic
937	#102	C₂³×C₅₃	1	1	yes	characteristic
938	#102	C₂³×C₅₃	1	1	yes	characteristic
939	#102	C₂³×C₅₃	1	1	yes	characteristic
940	#102	C₂³×C₅₃	1	1	yes	characteristic
941	#102	C₂³×C₅₃	1	1	yes	characteristic
942	#102	C₂³×C₅₃	1	1	yes	characteristic
943	#102	C₂³×C₅₃	1	2	yes	—
944	#102	C₂³×C₅₃	1	2	yes	—
945	#102	C₂³×C₅₃	1	2	yes	—
946	#102	C₂³×C₅₃	1	2	yes	—
947	#102	C₂³×C₅₃	1	2	yes	—
948	#102	C₂³×C₅₃	1	2	yes	—
949	#102	C₂³×C₅₃	1	2	yes	—
950	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
951	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
952	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
953	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
954	#97	C₂³×C₅₃	1	2	yes	—
955	C₄×C₈	C₂³×C₅₃	1	2	yes	—
956	C₂⁴	—	2	1	no	—
957	C₂⁴	—	2	2	no	—
958	C₂⁴	—	2	1	no	—
959	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
960	#41	—	2	2	no	—
961	#41	—	2	2	no	—
962	#41	—	2	2	no	—
963	#41	—	2	2	no	—
964	#41	—	2	4	no	—
965	#41	—	2	2	no	—
966	#41	—	2	2	no	—
967	#41	—	2	2	no	—
968	#41	—	4	4	no	—
969	#41	—	4	1	no	—
970	#41	—	4	1	no	—
971	#41	—	4	2	no	—
972	#41	—	4	4	no	—
973	#41	—	4	4	no	—
974	#41	#41×C₅₃	1	4	yes	—
975	C₂×Q₈	—	2	1	no	—
976	C₂×Q₈	—	2	1	no	—
977	C₂×Q₈	—	2	2	no	—
978	C₂×Q₈	—	2	2	no	—
979	C₂×Q₈	—	2	2	no	—
980	C₂×Q₈	—	2	2	no	—
981	C₂×Q₈	—	4	1	no	—
982	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
983	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
984	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
985	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	4	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	2	no	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	2	2	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	4	1	no	—
1004	C₂×D₄	—	4	2	no	—
1005	C₂×D₄	—	4	4	no	—
1006	C₂×D₄	—	4	8	no	—
1007	C₂×D₄	—	4	4	no	—
1008	C₂×D₄	—	8	4	no	—
1009	C₂×D₄	—	8	2	no	—
1010	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1011	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1012	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1013	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1014	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1015	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1016	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1017	C₂²×C₄	—	2	1	no	—
1018	C₂²×C₄	—	2	2	no	—
1019	C₂²×C₄	—	2	2	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	1	no	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	1	no	—
1026	C₂²×C₄	—	2	2	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	1	no	—
1029	C₂²×C₄	—	2	2	no	—
1030	C₂²×C₄	—	2	1	no	—
1031	C₂²×C₄	—	2	2	no	—
1032	C₂²×C₄	—	4	4	no	—
1033	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1034	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1035	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1036	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1037	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1038	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1039	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1040	Q₁₆	—	2	4	no	—
1041	Q₁₆	—	4	2	no	—
1042	SD₁₆	—	2	4	no	—
1043	SD₁₆	—	4	2	no	—
1044	SD₁₆	—	4	2	no	—
1045	SD₁₆	—	4	2	no	—
1046	M₁₆	—	2	2	no	—
1047	M₁₆	—	2	2	no	—
1048	M₁₆	—	4	2	no	—
1049	C₂×C₈	—	2	2	no	—
1050	C₂×C₈	—	2	2	no	—
1051	C₂×C₈	—	4	1	no	—
1052	C₂×C₈	—	4	1	no	—
1053	C₂×C₈	—	4	1	no	—
1054	C₂×C₈	—	4	1	no	—
1055	C₂×C₈	—	4	2	no	—
1056	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1057	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1058	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1059	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1060	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1061	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	2	no	—
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1079	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1080	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1081	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1082	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1083	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1084	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1085	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1086	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1087	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	2	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1105	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1106	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1107	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1108	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1109	C₄²	—	2	1	no	—
1110	C₄²	—	2	1	no	—
1111	C₄²	—	2	1	no	—
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	2	no	—
1114	C₄²	—	2	2	no	—
1115	C₄²	—	2	2	no	—
1116	C₄²	—	2	2	no	—
1117	C₄²	C₂⁴×C₅₃	1	2	yes	—
1118	C₂³	—	2	2	no	—
1119	C₂³	—	2	2	no	—
1120	C₂³	—	2	1	no	—
1121	C₂³	—	2	2	no	—
1122	C₂³	—	2	1	no	—
1123	C₂³	—	4	1	no	—
1124	C₂³	—	4	2	no	—
1125	C₂³	—	4	4	no	—
1126	C₂³	—	4	2	no	—
1127	C₂³	—	4	2	no	—
1128	C₂³	—	8	1	no	—
1129	C₂³	—	8	1	no	—
1130	C₂³	—	8	2	no	—
1131	C₂³	—	8	1	no	—
1132	C₂³	—	8	2	no	—
1133	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1134	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1135	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1136	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1137	Q₈	—	2	2	no	—
1138	Q₈	—	2	1	no	—
1139	Q₈	—	2	2	no	—
1140	Q₈	—	2	1	no	—
1141	Q₈	—	2	2	no	—
1142	Q₈	—	2	1	no	—
1143	Q₈	—	4	2	no	—
1144	Q₈	—	4	2	no	—
1145	Q₈	—	8	2	no	—
1146	Q₈	C₂×#41×C₅₃	1	2	yes	—
1147	D₄	—	2	4	no	—
1148	D₄	—	2	4	no	—
1149	D₄	—	2	4	no	—
1150	D₄	—	2	2	no	—
1151	D₄	—	2	2	no	—
1152	D₄	—	2	1	no	—
1153	D₄	—	2	1	no	—
1154	D₄	—	2	2	no	—
1155	D₄	—	2	1	no	—
1156	D₄	—	4	2	no	—
1157	D₄	—	4	4	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	4	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	4	2	no	—
1163	D₄	—	4	4	no	—
1164	D₄	—	4	2	no	—
1165	D₄	—	8	2	no	—
1166	D₄	—	8	2	no	—
1167	D₄	—	8	2	no	—
1168	D₄	—	8	2	no	—
1169	D₄	C₂×#41×C₅₃	1	2	yes	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	4	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	2	no	—
1187	C₂×C₄	—	2	2	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	4	4	no	—
1191	C₂×C₄	—	4	2	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	4	2	no	—
1194	C₂×C₄	—	4	2	no	—
1195	C₂×C₄	—	4	2	no	—
1196	C₂×C₄	—	8	2	no	—
1197	C₂×C₄	—	8	2	no	—
1198	C₂×C₄	—	8	1	no	—
1199	C₂×C₄	—	8	1	no	—
1200	C₂×C₄	—	8	1	no	—
1201	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1202	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1203	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1204	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1205	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1207	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1208	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1209	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1210	C₈	—	2	2	no	—
1211	C₈	—	2	1	no	—
1212	C₈	—	2	1	no	—
1213	C₈	—	2	1	no	—
1214	C₈	—	2	1	no	—
1215	C₈	—	2	2	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	1	no	—
1221	C₂²	—	2	2	no	—
1222	C₂²	—	2	2	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	1	no	—
1225	C₂²	—	2	2	no	—
1226	C₂²	—	2	1	no	—
1227	C₂²	—	4	4	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	2	no	—
1232	C₂²	—	4	2	no	—
1233	C₂²	—	4	1	no	—
1234	C₂²	—	4	1	no	—
1235	C₂²	—	4	2	no	—
1236	C₂²	—	8	4	no	—
1237	C₂²	—	16	2	no	—
1238	C₂²	—	16	4	no	—
1239	C₂²	C₅₃×#546	1	2	yes	—
1240	C₂²	C₅₃×#577	1	2	yes	—
1241	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1242	C₄	—	2	1	no	—
1243	C₄	—	2	1	no	—
1244	C₄	—	2	2	no	—
1245	C₄	—	2	2	no	—
1246	C₄	—	2	2	no	—
1247	C₄	—	2	2	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	2	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	2	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	2	no	—
1255	C₄	—	4	1	no	—
1256	C₄	C₅₃×#546	1	2	yes	—
1257	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1258	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1259	C₂	—	2	2	no	—
1260	C₂	—	2	2	no	—
1261	C₂	—	4	1	no	—
1262	C₂	—	4	2	no	—
1263	C₂	—	4	2	no	—
1264	C₂	—	8	1	no	—
1265	C₂	—	8	2	no	—
1266	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
1267	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1268	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×#3488	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3495	C₂	semidirect
3. C₅₃×#3317	C₂	semidirect
4. C₅₃×#3316	C₂	semidirect
5. C₅₃×#3311	C₂	semidirect
6. C₅₃×#3310	C₂	semidirect
7. C₅₃×#3304	C₂	semidirect
8. C₅₃×#3300	C₂	semidirect
9. C₅₃×#3296	C₂	semidirect
10. C₅₃×#3295	C₂	semidirect
11. C₅₃×#3136	C₂	semidirect
12. C₅₃×#3099	C₂	semidirect
13. C₅₃×#3094	C₂	semidirect
14. C₅₃×#3084	C₂	semidirect
15. C₅₃×#3063	C₂	semidirect
16. C₂×C₅₃×#465	C₂	semidirect
17. C₅₃×#3043	C₂	semidirect
18. C₅₃×#3009	C₂	semidirect
19. C₅₃×#3007	C₂	semidirect
20. C₅₃×#2947	C₂	semidirect
21. C₅₃×#2929	C₂	semidirect
22. C₅₃×#2897	C₂	semidirect
23. C₂×C₅₃×#416	C₂	semidirect
27. C₂×#137×C₅₃	C₂²	semidirect
28. C₂²×SD₁₆×C₅₃	C₂²	semidirect
29. C₂×#131×C₅₃	C₂²	semidirect
30. C₂³×C₈×C₅₃	C₂²	semidirect
31. C₅₃×#556	C₂²	semidirect
32. C₅₃×#554	C₂²	semidirect
34. C₅₃×#552	C₂²	semidirect
35. C₅₃×#552	C₂²	semidirect
43. C₅₃×#544	C₂²	semidirect
48. C₅₃×#536	C₂²	semidirect
55. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
59. C₅₃×#520	C₂²	semidirect
60. C₅₃×#519	C₂²	semidirect
61. C₂×#117×C₅₃	C₂²	semidirect
62. C₅₃×#490	C₂²	semidirect
63. C₅₃×#489	C₂²	semidirect
64. C₅₃×#488	C₂²	semidirect
65. C₅₃×#486	C₂²	semidirect
66. C₅₃×#485	C₂²	semidirect
67. C₅₃×#483	C₂²	semidirect
68. C₅₃×#482	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#481	C₂²	semidirect
72. C₅₃×#481	C₂²	semidirect
73. C₅₃×#480	C₂²	semidirect
74. C₅₃×#479	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#476	C₂²	semidirect
77. C₅₃×#475	C₂²	semidirect
78. C₅₃×#470	C₂²	semidirect
79. C₅₃×#468	C₂²	semidirect
80. C₅₃×#467	C₂²	semidirect
81. C₅₃×#465	C₂²	semidirect
82. C₅₃×#465	C₂²	semidirect
83. C₅₃×#465	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
85. C₅₃×#465	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#464	C₂²	semidirect
88. C₅₃×#460	C₂²	semidirect
89. C₅₃×#460	C₂²	semidirect
90. C₅₃×#452	C₂²	semidirect
91. C₅₃×#452	C₂²	semidirect
92. C₅₃×#452	C₂²	semidirect
93. C₅₃×#452	C₂²	semidirect
94. C₅₃×#451	C₂²	semidirect
95. C₅₃×#450	C₂²	semidirect
96. C₅₃×#450	C₂²	semidirect
97. C₅₃×#450	C₂²	semidirect
98. C₅₃×#441	C₂²	semidirect
99. C₅₃×#440	C₂²	semidirect
100. C₄×Q₁₆×C₅₃	C₂²	semidirect
101. C₄×SD₁₆×C₅₃	C₂²	semidirect
102. C₅₃×#435	C₂²	semidirect
103. C₅₃×#435	C₂²	semidirect
104. C₈×D₄×C₅₃	C₂²	semidirect
105. C₈×D₄×C₅₃	C₂²	semidirect
106. C₅₃×#428	C₂²	semidirect
107. C₅₃×#428	C₂²	semidirect
108. C₂×#106×C₅₃	C₂²	semidirect
109. C₅₃×#424	C₂²	semidirect
110. C₅₃×#418	C₂²	semidirect
111. C₅₃×#418	C₂²	semidirect
112. C₅₃×#418	C₂²	semidirect
114. C₅₃×#417	C₂²	semidirect
115. C₅₃×#417	C₂²	semidirect
118. C₅₃×#416	C₂²	semidirect
119. C₅₃×#416	C₂²	semidirect
120. C₅₃×#416	C₂²	semidirect
121. C₅₃×#416	C₂²	semidirect
122. C₅₃×#416	C₂²	semidirect
123. C₅₃×#416	C₂²	semidirect
124. C₅₃×#416	C₂²	semidirect
125. C₂×#103×C₅₃	C₂²	semidirect
126. C₂×#103×C₅₃	C₂²	semidirect
127. C₂×#103×C₅₃	C₂²	semidirect
128. C₂×#102×C₅₃	C₂²	semidirect
129. C₂×#102×C₅₃	C₂²	semidirect
130. C₂×#102×C₅₃	C₂²	semidirect
131. C₂×#102×C₅₃	C₂²	semidirect
132. C₅₃×#408	C₂²	semidirect
133. C₅₃×#407	C₂²	semidirect
134. C₅₃×#405	C₂²	semidirect
581. #61172	C₅₃	direct (N × H)
625. #3495	C₂×C₅₃	semidirect
627. #3317	C₂×C₅₃	semidirect
628. #3316	C₂×C₅₃	semidirect
629. #3311	C₂×C₅₃	semidirect
630. #3310	C₂×C₅₃	semidirect
631. #3304	C₂×C₅₃	semidirect
632. #3300	C₂×C₅₃	semidirect
633. #3296	C₂×C₅₃	semidirect
634. #3295	C₂×C₅₃	semidirect
635. #3136	C₂×C₅₃	semidirect
636. #3099	C₂×C₅₃	semidirect
637. #3094	C₂×C₅₃	semidirect
638. #3084	C₂×C₅₃	semidirect
639. #3063	C₂×C₅₃	semidirect
640. C₂×#465	C₂×C₅₃	semidirect
641. #3043	C₂×C₅₃	semidirect
642. #3009	C₂×C₅₃	semidirect
643. #3007	C₂×C₅₃	semidirect
644. #2947	C₂×C₅₃	semidirect
645. #2929	C₂×C₅₃	semidirect
646. #2897	C₂×C₅₃	semidirect
647. C₂×#416	C₂×C₅₃	semidirect
661. C₂×#137	C₂²×C₅₃	semidirect
662. C₂²×SD₁₆	C₂²×C₅₃	semidirect
663. C₂×#131	C₂²×C₅₃	semidirect
664. C₂³×C₈	C₂²×C₅₃	semidirect
665. #556	C₂²×C₅₃	semidirect
666. #554	C₂²×C₅₃	semidirect
668. #552	C₂²×C₅₃	semidirect
669. #552	C₂²×C₅₃	semidirect
677. #544	C₂²×C₅₃	semidirect
682. #536	C₂²×C₅₃	semidirect
689. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
693. #520	C₂²×C₅₃	semidirect
694. #519	C₂²×C₅₃	semidirect
695. C₂×#117	C₂²×C₅₃	semidirect
696. #490	C₂²×C₅₃	semidirect
697. #489	C₂²×C₅₃	semidirect
698. #488	C₂²×C₅₃	semidirect
699. #486	C₂²×C₅₃	semidirect
700. #485	C₂²×C₅₃	semidirect
701. #483	C₂²×C₅₃	semidirect
702. #482	C₂²×C₅₃	semidirect
703. #482	C₂²×C₅₃	semidirect
704. #482	C₂²×C₅₃	semidirect
705. #481	C₂²×C₅₃	semidirect
706. #481	C₂²×C₅₃	semidirect
707. #480	C₂²×C₅₃	semidirect
708. #479	C₂²×C₅₃	semidirect
709. #478	C₂²×C₅₃	semidirect
710. #476	C₂²×C₅₃	semidirect
711. #475	C₂²×C₅₃	semidirect
712. #470	C₂²×C₅₃	semidirect
713. #468	C₂²×C₅₃	semidirect
714. #467	C₂²×C₅₃	semidirect
715. #465	C₂²×C₅₃	semidirect
716. #465	C₂²×C₅₃	semidirect
717. #465	C₂²×C₅₃	semidirect
718. #465	C₂²×C₅₃	semidirect
719. #465	C₂²×C₅₃	semidirect
720. #464	C₂²×C₅₃	semidirect
721. #464	C₂²×C₅₃	semidirect
722. #460	C₂²×C₅₃	semidirect
723. #460	C₂²×C₅₃	semidirect
724. #452	C₂²×C₅₃	semidirect
725. #452	C₂²×C₅₃	semidirect
726. #452	C₂²×C₅₃	semidirect
727. #452	C₂²×C₅₃	semidirect
728. #451	C₂²×C₅₃	semidirect
729. #450	C₂²×C₅₃	semidirect
730. #450	C₂²×C₅₃	semidirect
731. #450	C₂²×C₅₃	semidirect
732. #441	C₂²×C₅₃	semidirect
733. #440	C₂²×C₅₃	semidirect
734. C₄×Q₁₆	C₂²×C₅₃	semidirect
735. C₄×SD₁₆	C₂²×C₅₃	semidirect
736. #435	C₂²×C₅₃	semidirect
737. #435	C₂²×C₅₃	semidirect
738. C₈×D₄	C₂²×C₅₃	semidirect
739. C₈×D₄	C₂²×C₅₃	semidirect
740. #428	C₂²×C₅₃	semidirect
741. #428	C₂²×C₅₃	semidirect
742. C₂×#106	C₂²×C₅₃	semidirect
743. #424	C₂²×C₅₃	semidirect
744. #418	C₂²×C₅₃	semidirect
745. #418	C₂²×C₅₃	semidirect
746. #418	C₂²×C₅₃	semidirect
748. #417	C₂²×C₅₃	semidirect
749. #417	C₂²×C₅₃	semidirect
752. #416	C₂²×C₅₃	semidirect
753. #416	C₂²×C₅₃	semidirect
754. #416	C₂²×C₅₃	semidirect
755. #416	C₂²×C₅₃	semidirect
756. #416	C₂²×C₅₃	semidirect
757. #416	C₂²×C₅₃	semidirect
758. #416	C₂²×C₅₃	semidirect
759. C₂×#103	C₂²×C₅₃	semidirect
760. C₂×#103	C₂²×C₅₃	semidirect
761. C₂×#103	C₂²×C₅₃	semidirect
762. C₂×#102	C₂²×C₅₃	semidirect
763. C₂×#102	C₂²×C₅₃	semidirect
764. C₂×#102	C₂²×C₅₃	semidirect
765. C₂×#102	C₂²×C₅₃	semidirect
766. #408	C₂²×C₅₃	semidirect
767. #407	C₂²×C₅₃	semidirect
768. #405	C₂²×C₅₃	semidirect
769. C₅₃	#61172	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×#3495	2
C₅₃×#3488	2
C₅₃×#3317	2
C₅₃×#3316	2
C₅₃×#3311	2
C₅₃×#3310	2
C₅₃×#3304	2
C₅₃×#3300	2
C₅₃×#3296	2
C₅₃×#3295	2
C₅₃×#3136	2
C₅₃×#3099	2
C₅₃×#3094	2
C₅₃×#3084	2
C₅₃×#3063	2
C₂×C₅₃×#465	2
C₅₃×#3043	2
C₅₃×#3009	2
C₅₃×#3007	2
C₅₃×#2947	2
C₅₃×#2929	2
C₅₃×#2897	2
C₂×C₅₃×#416	2
#61172	53

Subgroups — C53×#61172 #27268684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61172 #27268684