Subgroups — C₅₃×#61590 #27269102

Order 13568.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3326	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3322	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3275	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3273	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3197	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3194	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3006	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3005	C₂	1	2	yes	maximal, complemented
23	C₅₃×#2975	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
25	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
27	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
28	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
29	C₅₃×#555	C₂²	1	1	yes	characteristic
30	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#553	—	2	1	no	—
32	C₅₃×#553	C₂²	1	2	yes	complemented
33	C₅₃×#550	C₂²	1	1	yes	characteristic
34	C₅₃×#550	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#548	C₂²	1	2	yes	complemented
37	C₅₃×#547	—	2	1	no	—
38	C₅₃×#547	C₂²	1	1	yes	characteristic
39	C₅₃×#546	—	2	2	no	—
40	C₅₃×#546	—	2	2	no	—
41	C₅₃×#546	C₂²	1	2	yes	complemented
42	C₅₃×#546	C₂²	1	2	yes	complemented
43	D₄²×C₅₃	—	2	1	no	—
44	D₄²×C₅₃	—	2	1	no	—
45	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
46	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#540	—	2	1	no	—
48	C₅₃×#538	—	2	2	no	—
49	C₅₃×#532	—	2	1	no	—
50	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#525	—	2	2	no	—
54	C₅₃×#525	C₂²	1	2	yes	complemented
55	C₅₃×#525	C₂²	1	2	yes	complemented
56	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
57	C₅₃×#518	—	2	1	no	—
58	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×D₄×C₅₃	—	2	1	no	—
60	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
61	C₅₃×#495	C₂²	1	2	yes	complemented
62	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#488	C₂²	1	2	yes	complemented
65	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#485	C₂²	1	2	yes	complemented
69	C₅₃×#483	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#482	C₂²	1	2	yes	complemented
72	C₅₃×#482	C₂²	1	2	yes	complemented
73	C₅₃×#480	C₂²	1	2	yes	complemented
74	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#470	C₂²	1	2	yes	complemented
79	C₅₃×#469	C₂²	1	2	yes	complemented
80	C₅₃×#469	C₂²	1	2	yes	complemented
81	C₅₃×#469	C₂²	1	2	yes	complemented
82	C₅₃×#468	C₂²	1	2	yes	complemented
83	C₅₃×#468	C₂²	1	2	yes	complemented
84	C₅₃×#468	C₂²	1	2	yes	complemented
85	C₅₃×#468	C₂²	1	2	yes	complemented
86	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#463	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	2	yes	complemented
89	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#452	C₂²	1	2	yes	complemented
97	C₅₃×#452	C₂²	1	2	yes	complemented
98	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#452	C₂²	1	2	yes	complemented
100	C₅₃×#452	C₂²	1	2	yes	complemented
101	C₅₃×#450	C₂²	1	2	yes	complemented
102	C₅₃×#449	C₂²	1	1	yes	characteristic
103	C₅₃×#449	C₂²	1	2	yes	complemented
104	C₅₃×#449	C₂²	1	2	yes	complemented
105	C₅₃×#449	C₂²	1	2	yes	complemented
106	C₅₃×#449	C₂²	1	2	yes	complemented
107	C₅₃×#449	C₂²	1	2	yes	complemented
108	C₅₃×#449	C₂²	1	2	yes	complemented
109	C₅₃×#449	C₂²	1	2	yes	complemented
110	C₅₃×#448	C₂²	1	2	yes	complemented
111	C₅₃×#448	C₂²	1	2	yes	complemented
112	C₅₃×#447	C₂²	1	2	yes	complemented
113	C₅₃×#447	C₂²	1	2	yes	complemented
114	C₅₃×#447	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
121	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#436	C₂²	1	2	yes	complemented
123	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#436	C₂²	1	2	yes	complemented
126	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#419	C₂²	1	2	yes	complemented
130	C₅₃×#418	C₂²	1	2	yes	complemented
131	C₅₃×#417	C₂²	1	2	yes	complemented
132	C₅₃×#417	C₂²	1	2	yes	complemented
133	C₅₃×#407	C₂²	1	2	yes	complemented
134	C₅₃×#407	C₂²	1	2	yes	complemented
135	C₂×#41×C₅₃	—	2	2	no	—
136	C₂×#41×C₅₃	—	2	2	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	—	4	4	no	—
139	C₂×#41×C₅₃	—	4	4	no	—
140	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₅₃	C₂³	1	2	yes	—
142	C₂×#41×C₅₃	C₂³	1	2	yes	—
143	C₂×#41×C₅₃	C₂³	1	2	yes	—
144	C₂×#41×C₅₃	C₂³	1	2	yes	—
145	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
146	C₂²×D₄×C₅₃	—	2	2	no	—
147	C₂²×D₄×C₅₃	—	2	2	no	—
148	C₂²×D₄×C₅₃	—	2	1	no	—
149	C₂²×D₄×C₅₃	—	2	1	no	—
150	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
151	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
152	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
153	C₂³×C₄×C₅₃	—	2	2	no	—
154	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
155	#137×C₅₃	—	4	4	no	—
156	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
157	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
158	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
159	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
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×D₈×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×D₈×C₅₃	C₂³	1	2	yes	—
170	C₂×D₈×C₅₃	C₂³	1	2	yes	—
171	C₂×D₈×C₅₃	C₂³	1	2	yes	—
172	C₂×D₈×C₅₃	C₂³	1	2	yes	—
173	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
174	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
175	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
176	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
177	C₄⋊Q₈×C₅₃	—	2	1	no	—
178	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
180	#127×C₅₃	—	2	1	no	—
181	#127×C₅₃	—	2	1	no	—
182	#127×C₅₃	C₂³	1	1	yes	characteristic
183	#127×C₅₃	C₂³	1	1	yes	characteristic
184	#126×C₅₃	—	2	2	no	—
185	#126×C₅₃	—	2	1	no	—
186	#125×C₅₃	—	2	1	no	—
187	#125×C₅₃	C₂³	1	1	yes	characteristic
188	#124×C₅₃	—	2	2	no	—
189	#124×C₅₃	—	2	2	no	—
190	#124×C₅₃	—	2	1	no	—
191	#124×C₅₃	C₂³	1	2	yes	—
192	#124×C₅₃	C₂³	1	1	yes	characteristic
193	#123×C₅₃	—	2	2	no	—
194	#123×C₅₃	—	2	2	no	—
195	#123×C₅₃	—	2	2	no	—
196	#123×C₅₃	—	2	2	no	—
197	#123×C₅₃	—	2	2	no	—
198	#123×C₅₃	—	2	2	no	—
199	#123×C₅₃	—	2	1	no	—
200	C₂²⋊Q₈×C₅₃	—	2	2	no	—
201	C₂²⋊Q₈×C₅₃	—	2	2	no	—
202	C₂²⋊Q₈×C₅₃	—	2	2	no	—
203	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
204	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
205	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
207	#121×C₅₃	—	2	1	no	—
208	#121×C₅₃	—	2	1	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	2	no	—
211	#121×C₅₃	—	2	2	no	—
212	#121×C₅₃	—	2	2	no	—
213	#121×C₅₃	—	2	2	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	—	2	2	no	—
216	#121×C₅₃	—	2	1	no	—
217	#121×C₅₃	—	2	2	no	—
218	#121×C₅₃	—	2	2	no	—
219	#121×C₅₃	—	2	1	no	—
220	#121×C₅₃	—	2	1	no	—
221	#121×C₅₃	—	2	1	no	—
222	#121×C₅₃	C₂³	1	1	yes	characteristic
223	#121×C₅₃	C₂³	1	2	yes	—
224	#121×C₅₃	C₂³	1	2	yes	—
225	#121×C₅₃	C₂³	1	2	yes	—
226	#121×C₅₃	C₂³	1	2	yes	—
227	#121×C₅₃	C₂³	1	2	yes	—
228	#121×C₅₃	C₂³	1	2	yes	—
229	#120×C₅₃	—	2	2	no	—
230	#120×C₅₃	—	2	2	no	—
231	#120×C₅₃	—	2	2	no	—
232	#120×C₅₃	—	2	2	no	—
233	#120×C₅₃	—	2	2	no	—
234	#120×C₅₃	—	2	2	no	—
235	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₅₃	—	2	1	no	—
239	C₄×D₄×C₅₃	—	2	1	no	—
240	C₄×D₄×C₅₃	—	2	2	no	—
241	C₄×D₄×C₅₃	—	2	2	no	—
242	C₄×D₄×C₅₃	—	2	1	no	—
243	C₄×D₄×C₅₃	—	2	1	no	—
244	C₄×D₄×C₅₃	—	2	1	no	—
245	C₄×D₄×C₅₃	—	2	1	no	—
246	C₄×D₄×C₅₃	—	2	1	no	—
247	C₄×D₄×C₅₃	—	2	2	no	—
248	C₄×D₄×C₅₃	—	2	1	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	—	2	2	no	—
253	C₄×D₄×C₅₃	—	2	1	no	—
254	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
255	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
256	C₄×D₄×C₅₃	D₄	1	2	yes	—
257	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₅₃	C₂³	1	2	yes	—
261	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₅₃	C₂³	1	2	yes	—
264	#117×C₅₃	—	2	1	no	—
265	#117×C₅₃	—	2	1	no	—
266	#117×C₅₃	—	2	1	no	—
267	#117×C₅₃	C₂³	1	1	yes	characteristic
268	#117×C₅₃	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
270	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
273	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
276	C₂×C₄²×C₅₃	—	2	1	no	—
277	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
278	#107×C₅₃	C₂³	1	2	yes	—
279	#107×C₅₃	C₂³	1	1	yes	characteristic
280	#107×C₅₃	C₂³	1	1	yes	characteristic
281	#106×C₅₃	C₂³	1	1	yes	characteristic
282	#106×C₅₃	C₂³	1	1	yes	characteristic
283	#106×C₅₃	C₂³	1	2	yes	—
284	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	1	yes	characteristic
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×C₅₃	C₂³	1	2	yes	—
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	1	yes	characteristic
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
303	#102×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
308	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
315	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₅₃	C₂³	1	2	yes	—
318	C₂⁴×C₅₃	—	2	2	no	—
319	C₂⁴×C₅₃	—	2	2	no	—
320	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
321	#41×C₅₃	—	2	2	no	—
322	#41×C₅₃	—	2	2	no	—
323	#41×C₅₃	—	2	4	no	—
324	#41×C₅₃	—	2	4	no	—
325	#41×C₅₃	—	4	2	no	—
326	#41×C₅₃	—	4	2	no	—
327	#41×C₅₃	—	4	2	no	—
328	#41×C₅₃	—	4	2	no	—
329	#41×C₅₃	—	4	8	no	—
330	#41×C₅₃	—	4	2	no	—
331	#41×C₅₃	—	4	2	no	—
332	#41×C₅₃	—	4	8	no	—
333	#41×C₅₃	—	8	2	no	—
334	C₂×Q₈×C₅₃	—	2	2	no	—
335	C₂×Q₈×C₅₃	—	2	1	no	—
336	C₂×Q₈×C₅₃	—	2	4	no	—
337	C₂×Q₈×C₅₃	—	4	2	no	—
338	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
339	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₅₃	—	2	1	no	—
342	C₂×D₄×C₅₃	—	2	4	no	—
343	C₂×D₄×C₅₃	—	2	2	no	—
344	C₂×D₄×C₅₃	—	2	2	no	—
345	C₂×D₄×C₅₃	—	2	2	no	—
346	C₂×D₄×C₅₃	—	2	1	no	—
347	C₂×D₄×C₅₃	—	2	2	no	—
348	C₂×D₄×C₅₃	—	2	2	no	—
349	C₂×D₄×C₅₃	—	2	2	no	—
350	C₂×D₄×C₅₃	—	2	2	no	—
351	C₂×D₄×C₅₃	—	2	2	no	—
352	C₂×D₄×C₅₃	—	2	2	no	—
353	C₂×D₄×C₅₃	—	2	2	no	—
354	C₂×D₄×C₅₃	—	2	1	no	—
355	C₂×D₄×C₅₃	—	2	1	no	—
356	C₂×D₄×C₅₃	—	2	2	no	—
357	C₂×D₄×C₅₃	—	2	1	no	—
358	C₂×D₄×C₅₃	—	2	1	no	—
359	C₂×D₄×C₅₃	—	2	2	no	—
360	C₂×D₄×C₅₃	—	4	2	no	—
361	C₂×D₄×C₅₃	—	4	2	no	—
362	C₂×D₄×C₅₃	—	4	2	no	—
363	C₂×D₄×C₅₃	—	4	2	no	—
364	C₂×D₄×C₅₃	—	4	4	no	—
365	C₂×D₄×C₅₃	—	4	4	no	—
366	C₂×D₄×C₅₃	—	4	8	no	—
367	C₂×D₄×C₅₃	—	8	4	no	—
368	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
369	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
372	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
374	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	—	2	1	no	—
376	C₂²×C₄×C₅₃	—	2	2	no	—
377	C₂²×C₄×C₅₃	—	2	2	no	—
378	C₂²×C₄×C₅₃	—	2	1	no	—
379	C₂²×C₄×C₅₃	—	2	2	no	—
380	C₂²×C₄×C₅₃	—	2	1	no	—
381	C₂²×C₄×C₅₃	—	2	2	no	—
382	C₂²×C₄×C₅₃	—	2	2	no	—
383	C₂²×C₄×C₅₃	—	2	1	no	—
384	C₂²×C₄×C₅₃	—	2	2	no	—
385	C₂²×C₄×C₅₃	—	2	2	no	—
386	C₂²×C₄×C₅₃	—	4	2	no	—
387	C₂²×C₄×C₅₃	—	4	2	no	—
388	C₂²×C₄×C₅₃	—	4	8	no	—
389	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
392	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
393	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
394	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
396	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
397	Q₁₆×C₅₃	—	2	2	no	—
398	Q₁₆×C₅₃	—	4	2	no	—
399	SD₁₆×C₅₃	—	2	2	no	—
400	SD₁₆×C₅₃	—	2	4	no	—
401	SD₁₆×C₅₃	—	2	2	no	—
402	SD₁₆×C₅₃	—	4	2	no	—
403	SD₁₆×C₅₃	—	4	2	no	—
404	SD₁₆×C₅₃	—	4	2	no	—
405	SD₁₆×C₅₃	—	4	2	no	—
406	D₈×C₅₃	—	2	2	no	—
407	D₈×C₅₃	—	2	4	no	—
408	D₈×C₅₃	—	4	2	no	—
409	D₈×C₅₃	—	4	2	no	—
410	D₈×C₅₃	—	4	2	no	—
411	M₁₆×C₅₃	—	4	2	no	—
412	M₁₆×C₅₃	—	4	2	no	—
413	M₁₆×C₅₃	—	4	2	no	—
414	M₁₆×C₅₃	—	4	2	no	—
415	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
417	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
419	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₅₃	—	2	1	no	—
422	C₄⋊C₄×C₅₃	—	2	2	no	—
423	C₄⋊C₄×C₅₃	—	2	2	no	—
424	C₄⋊C₄×C₅₃	—	2	1	no	—
425	C₄⋊C₄×C₅₃	—	2	1	no	—
426	C₄⋊C₄×C₅₃	—	2	1	no	—
427	C₄⋊C₄×C₅₃	—	2	1	no	—
428	C₄⋊C₄×C₅₃	—	2	1	no	—
429	C₄⋊C₄×C₅₃	—	2	1	no	—
430	C₄⋊C₄×C₅₃	—	2	1	no	—
431	C₄⋊C₄×C₅₃	—	2	2	no	—
432	C₄⋊C₄×C₅₃	—	2	2	no	—
433	C₄⋊C₄×C₅₃	—	2	1	no	—
434	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
437	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
439	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₂²⋊C₄×C₅₃	—	2	2	no	—
443	C₂²⋊C₄×C₅₃	—	2	2	no	—
444	C₂²⋊C₄×C₅₃	—	2	1	no	—
445	C₂²⋊C₄×C₅₃	—	2	2	no	—
446	C₂²⋊C₄×C₅₃	—	2	1	no	—
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	—	2	1	no	—
449	C₂²⋊C₄×C₅₃	—	2	1	no	—
450	C₂²⋊C₄×C₅₃	—	2	2	no	—
451	C₂²⋊C₄×C₅₃	—	2	2	no	—
452	C₂²⋊C₄×C₅₃	—	2	2	no	—
453	C₂²⋊C₄×C₅₃	—	2	2	no	—
454	C₂²⋊C₄×C₅₃	—	2	2	no	—
455	C₂²⋊C₄×C₅₃	—	2	1	no	—
456	C₂²⋊C₄×C₅₃	—	2	1	no	—
457	C₂²⋊C₄×C₅₃	—	2	1	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	1	no	—
462	C₂²⋊C₄×C₅₃	—	2	2	no	—
463	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
467	C₄²×C₅₃	—	2	1	no	—
468	C₄²×C₅₃	—	2	1	no	—
469	C₄²×C₅₃	—	2	1	no	—
470	C₄²×C₅₃	—	2	2	no	—
471	C₄²×C₅₃	—	2	1	no	—
472	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
473	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
474	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
475	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
476	C₂³×C₅₃	—	2	1	no	—
477	C₂³×C₅₃	—	2	2	no	—
478	C₂³×C₅₃	—	2	2	no	—
479	C₂³×C₅₃	—	2	1	no	—
480	C₂³×C₅₃	—	4	2	no	—
481	C₂³×C₅₃	—	4	2	no	—
482	C₂³×C₅₃	—	4	2	no	—
483	C₂³×C₅₃	—	4	4	no	—
484	C₂³×C₅₃	—	4	4	no	—
485	C₂³×C₅₃	—	4	4	no	—
486	C₂³×C₅₃	—	8	2	no	—
487	C₂³×C₅₃	—	8	2	no	—
488	C₂³×C₅₃	—	8	2	no	—
489	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
490	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
491	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
492	Q₈×C₅₃	—	2	1	no	—
493	Q₈×C₅₃	—	2	2	no	—
494	Q₈×C₅₃	—	2	2	no	—
495	Q₈×C₅₃	—	2	1	no	—
496	Q₈×C₅₃	—	2	1	no	—
497	Q₈×C₅₃	—	4	4	no	—
498	Q₈×C₅₃	—	8	1	no	—
499	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
500	D₄×C₅₃	—	2	4	no	—
501	D₄×C₅₃	—	2	2	no	—
502	D₄×C₅₃	—	2	2	no	—
503	D₄×C₅₃	—	2	1	no	—
504	D₄×C₅₃	—	2	2	no	—
505	D₄×C₅₃	—	2	1	no	—
506	D₄×C₅₃	—	2	1	no	—
507	D₄×C₅₃	—	2	2	no	—
508	D₄×C₅₃	—	2	2	no	—
509	D₄×C₅₃	—	2	2	no	—
510	D₄×C₅₃	—	4	2	no	—
511	D₄×C₅₃	—	4	4	no	—
512	D₄×C₅₃	—	4	4	no	—
513	D₄×C₅₃	—	4	4	no	—
514	D₄×C₅₃	—	4	4	no	—
515	D₄×C₅₃	—	4	4	no	—
516	D₄×C₅₃	—	4	4	no	—
517	D₄×C₅₃	—	4	2	no	—
518	D₄×C₅₃	—	4	4	no	—
519	D₄×C₅₃	—	4	2	no	—
520	D₄×C₅₃	—	4	2	no	—
521	D₄×C₅₃	—	8	1	no	—
522	D₄×C₅₃	—	8	2	no	—
523	D₄×C₅₃	—	8	1	no	—
524	D₄×C₅₃	—	8	2	no	—
525	D₄×C₅₃	—	8	2	no	—
526	D₄×C₅₃	—	8	2	no	—
527	D₄×C₅₃	—	8	2	no	—
528	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
529	C₂×C₄×C₅₃	—	2	4	no	—
530	C₂×C₄×C₅₃	—	2	1	no	—
531	C₂×C₄×C₅₃	—	2	2	no	—
532	C₂×C₄×C₅₃	—	2	1	no	—
533	C₂×C₄×C₅₃	—	2	1	no	—
534	C₂×C₄×C₅₃	—	2	2	no	—
535	C₂×C₄×C₅₃	—	2	2	no	—
536	C₂×C₄×C₅₃	—	2	2	no	—
537	C₂×C₄×C₅₃	—	2	2	no	—
538	C₂×C₄×C₅₃	—	2	2	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	2	no	—
541	C₂×C₄×C₅₃	—	2	1	no	—
542	C₂×C₄×C₅₃	—	2	1	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	4	2	no	—
546	C₂×C₄×C₅₃	—	4	2	no	—
547	C₂×C₄×C₅₃	—	4	2	no	—
548	C₂×C₄×C₅₃	—	4	1	no	—
549	C₂×C₄×C₅₃	—	4	4	no	—
550	C₂×C₄×C₅₃	—	4	4	no	—
551	C₂×C₄×C₅₃	—	4	4	no	—
552	C₂×C₄×C₅₃	—	4	4	no	—
553	C₂×C₄×C₅₃	—	4	2	no	—
554	C₂×C₄×C₅₃	—	4	2	no	—
555	C₂×C₄×C₅₃	—	8	1	no	—
556	C₂×C₄×C₅₃	—	8	2	no	—
557	C₂×C₄×C₅₃	—	8	2	no	—
558	C₂×C₄×C₅₃	—	8	2	no	—
559	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
562	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
563	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
567	C₈×C₅₃	—	2	1	no	—
568	C₈×C₅₃	—	2	2	no	—
569	C₈×C₅₃	—	2	1	no	—
570	C₈×C₅₃	—	2	1	no	—
571	C₈×C₅₃	—	2	2	no	—
572	C₈×C₅₃	—	2	1	no	—
573	#61590	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
574	C₂²×C₅₃	—	2	1	no	—
575	C₂²×C₅₃	—	2	2	no	—
576	C₂²×C₅₃	—	2	2	no	—
577	C₂²×C₅₃	—	2	2	no	—
578	C₂²×C₅₃	—	2	1	no	—
579	C₂²×C₅₃	—	2	2	no	—
580	C₂²×C₅₃	—	2	2	no	—
581	C₂²×C₅₃	—	2	1	no	—
582	C₂²×C₅₃	—	2	2	no	—
583	C₂²×C₅₃	—	2	2	no	—
584	C₂²×C₅₃	—	4	1	no	—
585	C₂²×C₅₃	—	4	1	no	—
586	C₂²×C₅₃	—	4	2	no	—
587	C₂²×C₅₃	—	4	1	no	—
588	C₂²×C₅₃	—	4	2	no	—
589	C₂²×C₅₃	—	4	2	no	—
590	C₂²×C₅₃	—	4	2	no	—
591	C₂²×C₅₃	—	4	1	no	—
592	C₂²×C₅₃	—	4	1	no	—
593	C₂²×C₅₃	—	4	2	no	—
594	C₂²×C₅₃	—	4	2	no	—
595	C₂²×C₅₃	—	8	4	no	—
596	C₂²×C₅₃	—	8	8	no	—
597	C₂²×C₅₃	—	16	4	no	—
598	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
599	C₄×C₅₃	—	2	1	no	—
600	C₄×C₅₃	—	2	1	no	—
601	C₄×C₅₃	—	2	1	no	—
602	C₄×C₅₃	—	2	2	no	—
603	C₄×C₅₃	—	2	2	no	—
604	C₄×C₅₃	—	2	2	no	—
605	C₄×C₅₃	—	2	1	no	—
606	C₄×C₅₃	—	4	1	no	—
607	C₄×C₅₃	—	4	2	no	—
608	C₄×C₅₃	—	4	1	no	—
609	C₄×C₅₃	—	4	2	no	—
610	C₄×C₅₃	—	4	1	no	—
611	C₄×C₅₃	—	4	1	no	—
612	C₄×C₅₃	—	4	1	no	—
613	C₄×C₅₃	#575	1	2	yes	—
614	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
615	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
616	#3519	C₂×C₅₃	1	1	yes	characteristic, complemented
617	D₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
618	#3333	C₂×C₅₃	1	1	yes	characteristic, complemented
619	#3331	C₂×C₅₃	1	1	yes	characteristic, complemented
620	#3329	C₂×C₅₃	1	1	yes	characteristic, complemented
621	#3326	C₂×C₅₃	1	2	yes	complemented
622	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
623	#3322	C₂×C₅₃	1	2	yes	complemented
624	#3278	C₂×C₅₃	1	1	yes	characteristic, complemented
625	#3275	C₂×C₅₃	1	2	yes	complemented
626	#3274	C₂×C₅₃	1	1	yes	characteristic, complemented
627	#3274	C₂×C₅₃	1	1	yes	characteristic, complemented
628	#3273	C₂×C₅₃	1	2	yes	complemented
629	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
630	#3212	C₂×C₅₃	1	1	yes	characteristic, complemented
631	#3207	C₂×C₅₃	1	1	yes	characteristic, complemented
632	#3197	C₂×C₅₃	1	2	yes	complemented
633	#3194	C₂×C₅₃	1	2	yes	complemented
634	#3106	C₂×C₅₃	1	1	yes	characteristic, complemented
635	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
636	#3006	C₂×C₅₃	1	2	yes	complemented
637	#3005	C₂×C₅₃	1	2	yes	complemented
638	#2975	C₂×C₅₃	1	1	yes	characteristic, complemented
639	C₂×C₅₃	—	4	1	no	—
640	C₂×C₅₃	—	4	2	no	—
641	C₂×C₅₃	—	4	2	no	—
642	C₂×C₅₃	—	4	2	no	—
643	C₂×C₅₃	—	8	2	no	—
644	C₂×C₅₃	—	8	2	no	—
645	C₂×C₅₃	—	8	1	no	—
646	C₂×C₅₃	#3484	1	1	yes	characteristic
647	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
648	C₂×C₅₃	#3585	1	1	yes	characteristic
649	C₂²×#41	C₂²×C₅₃	1	2	yes	complemented
650	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
651	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
652	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
653	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
654	#555	C₂²×C₅₃	1	1	yes	characteristic
655	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	#553	—	2	1	no	—
657	#553	C₂²×C₅₃	1	2	yes	complemented
658	#550	C₂²×C₅₃	1	1	yes	characteristic
659	#550	C₂²×C₅₃	1	1	yes	characteristic
660	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
661	#548	C₂²×C₅₃	1	2	yes	complemented
662	#547	—	2	1	no	—
663	#547	C₂²×C₅₃	1	1	yes	characteristic
664	#546	—	2	2	no	—
665	#546	—	2	2	no	—
666	#546	C₂²×C₅₃	1	2	yes	complemented
667	#546	C₂²×C₅₃	1	2	yes	complemented
668	D₄²	—	2	1	no	—
669	D₄²	—	2	1	no	—
670	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
671	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
672	#540	—	2	1	no	—
673	#538	—	2	2	no	—
674	#532	—	2	1	no	—
675	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
676	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
677	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	#525	—	2	2	no	—
679	#525	C₂²×C₅₃	1	2	yes	complemented
680	#525	C₂²×C₅₃	1	2	yes	complemented
681	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
682	#518	—	2	1	no	—
683	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
684	C₂×C₄×D₄	—	2	1	no	—
685	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
686	#495	C₂²×C₅₃	1	2	yes	complemented
687	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
688	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	#488	C₂²×C₅₃	1	2	yes	complemented
690	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
691	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	#485	C₂²×C₅₃	1	2	yes	complemented
693	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
694	#483	C₂²×C₅₃	1	2	yes	complemented
695	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	#482	C₂²×C₅₃	1	2	yes	complemented
697	#482	C₂²×C₅₃	1	2	yes	complemented
698	#480	C₂²×C₅₃	1	2	yes	complemented
699	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
700	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
701	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
702	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	#470	C₂²×C₅₃	1	2	yes	complemented
704	#469	C₂²×C₅₃	1	2	yes	complemented
705	#469	C₂²×C₅₃	1	2	yes	complemented
706	#469	C₂²×C₅₃	1	2	yes	complemented
707	#468	C₂²×C₅₃	1	2	yes	complemented
708	#468	C₂²×C₅₃	1	2	yes	complemented
709	#468	C₂²×C₅₃	1	2	yes	complemented
710	#468	C₂²×C₅₃	1	2	yes	complemented
711	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	#463	C₂²×C₅₃	1	2	yes	complemented
714	#463	C₂²×C₅₃	1	2	yes	complemented
715	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
716	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
717	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
718	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
719	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
720	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
721	#452	C₂²×C₅₃	1	2	yes	complemented
722	#452	C₂²×C₅₃	1	2	yes	complemented
723	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
724	#452	C₂²×C₅₃	1	2	yes	complemented
725	#452	C₂²×C₅₃	1	2	yes	complemented
726	#450	C₂²×C₅₃	1	2	yes	complemented
727	#449	C₂²×C₅₃	1	1	yes	characteristic
728	#449	C₂²×C₅₃	1	2	yes	complemented
729	#449	C₂²×C₅₃	1	2	yes	complemented
730	#449	C₂²×C₅₃	1	2	yes	complemented
731	#449	C₂²×C₅₃	1	2	yes	complemented
732	#449	C₂²×C₅₃	1	2	yes	complemented
733	#449	C₂²×C₅₃	1	2	yes	complemented
734	#449	C₂²×C₅₃	1	2	yes	complemented
735	#448	C₂²×C₅₃	1	2	yes	complemented
736	#448	C₂²×C₅₃	1	2	yes	complemented
737	#447	C₂²×C₅₃	1	2	yes	complemented
738	#447	C₂²×C₅₃	1	2	yes	complemented
739	#447	C₂²×C₅₃	1	2	yes	complemented
740	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
741	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
742	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
743	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
744	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
746	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
747	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
748	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
749	#436	C₂²×C₅₃	1	2	yes	complemented
750	#436	C₂²×C₅₃	1	2	yes	complemented
751	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
752	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
753	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
754	#419	C₂²×C₅₃	1	2	yes	complemented
755	#418	C₂²×C₅₃	1	2	yes	complemented
756	#417	C₂²×C₅₃	1	2	yes	complemented
757	#417	C₂²×C₅₃	1	2	yes	complemented
758	#407	C₂²×C₅₃	1	2	yes	complemented
759	#407	C₂²×C₅₃	1	2	yes	complemented
760	C₅₃	#61590	1	1	yes	characteristic, direct product factor, Sylow
761	C₂×#41	—	2	2	no	—
762	C₂×#41	—	2	2	no	—
763	C₂×#41	—	2	1	no	—
764	C₂×#41	—	4	4	no	—
765	C₂×#41	—	4	4	no	—
766	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
767	C₂×#41	C₂³×C₅₃	1	2	yes	—
768	C₂×#41	C₂³×C₅₃	1	2	yes	—
769	C₂×#41	C₂³×C₅₃	1	2	yes	—
770	C₂×#41	C₂³×C₅₃	1	2	yes	—
771	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
772	C₂²×D₄	—	2	2	no	—
773	C₂²×D₄	—	2	2	no	—
774	C₂²×D₄	—	2	1	no	—
775	C₂²×D₄	—	2	1	no	—
776	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
777	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
778	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
779	C₂³×C₄	—	2	2	no	—
780	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
781	#137	—	4	4	no	—
782	AGL(1,ℤ/8)	—	4	4	no	—
783	AGL(1,ℤ/8)	—	4	4	no	—
784	AGL(1,ℤ/8)	—	4	4	no	—
785	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
786	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
787	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
788	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
789	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
790	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
791	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
792	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
793	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
794	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
795	C₂×D₈	C₂³×C₅₃	1	2	yes	—
796	C₂×D₈	C₂³×C₅₃	1	2	yes	—
797	C₂×D₈	C₂³×C₅₃	1	2	yes	—
798	C₂×D₈	C₂³×C₅₃	1	2	yes	—
799	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
800	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
801	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
802	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
803	C₄⋊Q₈	—	2	1	no	—
804	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
805	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
806	#127	—	2	1	no	—
807	#127	—	2	1	no	—
808	#127	C₂³×C₅₃	1	1	yes	characteristic
809	#127	C₂³×C₅₃	1	1	yes	characteristic
810	#126	—	2	2	no	—
811	#126	—	2	1	no	—
812	#125	—	2	1	no	—
813	#125	C₂³×C₅₃	1	1	yes	characteristic
814	#124	—	2	2	no	—
815	#124	—	2	2	no	—
816	#124	—	2	1	no	—
817	#124	C₂³×C₅₃	1	1	yes	characteristic
818	#124	C₂³×C₅₃	1	2	yes	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	1	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	#123	—	2	2	no	—
825	#123	—	2	2	no	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	—	2	2	no	—
828	C₂²⋊Q₈	—	2	2	no	—
829	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
830	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
831	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
832	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
833	#121	—	2	2	no	—
834	#121	—	2	1	no	—
835	#121	—	2	2	no	—
836	#121	—	2	1	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	1	no	—
840	#121	—	2	1	no	—
841	#121	—	2	1	no	—
842	#121	—	2	1	no	—
843	#121	—	2	1	no	—
844	#121	—	2	2	no	—
845	#121	—	2	2	no	—
846	#121	—	2	2	no	—
847	#121	—	2	2	no	—
848	#121	C₂³×C₅₃	1	1	yes	characteristic
849	#121	C₂³×C₅₃	1	2	yes	—
850	#121	C₂³×C₅₃	1	2	yes	—
851	#121	C₂³×C₅₃	1	2	yes	—
852	#121	C₂³×C₅₃	1	2	yes	—
853	#121	C₂³×C₅₃	1	2	yes	—
854	#121	C₂³×C₅₃	1	2	yes	—
855	#120	—	2	2	no	—
856	#120	—	2	2	no	—
857	#120	—	2	2	no	—
858	#120	—	2	2	no	—
859	#120	—	2	2	no	—
860	#120	—	2	2	no	—
861	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
862	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
863	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	2	no	—
871	C₄×D₄	—	2	2	no	—
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	2	no	—
876	C₄×D₄	—	2	2	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
881	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
882	C₄×D₄	D₄×C₅₃	1	2	yes	—
883	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
884	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
885	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
886	C₄×D₄	C₂³×C₅₃	1	2	yes	—
887	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
888	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
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	C₂³×C₅₃	1	1	yes	characteristic
894	#117	C₂³×C₅₃	1	2	yes	—
895	C₂×C₄⋊C₄	—	2	1	no	—
896	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
897	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
898	C₂×C₂²⋊C₄	—	2	2	no	—
899	C₂×C₂²⋊C₄	—	2	2	no	—
900	C₂×C₂²⋊C₄	—	2	2	no	—
901	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
902	C₂×C₄²	—	2	1	no	—
903	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
904	#107	C₂³×C₅₃	1	2	yes	—
905	#107	C₂³×C₅₃	1	1	yes	characteristic
906	#107	C₂³×C₅₃	1	1	yes	characteristic
907	#106	C₂³×C₅₃	1	1	yes	characteristic
908	#106	C₂³×C₅₃	1	1	yes	characteristic
909	#106	C₂³×C₅₃	1	2	yes	—
910	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
911	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
912	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
913	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
914	#103	C₂³×C₅₃	1	1	yes	characteristic
915	#103	C₂³×C₅₃	1	2	yes	—
916	#103	C₂³×C₅₃	1	2	yes	—
917	#103	C₂³×C₅₃	1	2	yes	—
918	#103	C₂³×C₅₃	1	1	yes	characteristic
919	#103	C₂³×C₅₃	1	2	yes	—
920	#103	C₂³×C₅₃	1	2	yes	—
921	#103	C₂³×C₅₃	1	1	yes	characteristic
922	#103	C₂³×C₅₃	1	1	yes	characteristic
923	#102	C₂³×C₅₃	1	1	yes	characteristic
924	#102	C₂³×C₅₃	1	2	yes	—
925	#102	C₂³×C₅₃	1	2	yes	—
926	#102	C₂³×C₅₃	1	2	yes	—
927	#102	C₂³×C₅₃	1	1	yes	characteristic
928	#102	C₂³×C₅₃	1	2	yes	—
929	#102	C₂³×C₅₃	1	2	yes	—
930	#102	C₂³×C₅₃	1	2	yes	—
931	#102	C₂³×C₅₃	1	1	yes	characteristic
932	#102	C₂³×C₅₃	1	1	yes	characteristic
933	#102	C₂³×C₅₃	1	2	yes	—
934	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
935	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
936	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
937	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
938	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
939	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
940	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
941	C₄×C₈	C₂³×C₅₃	1	2	yes	—
942	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
943	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
944	C₂⁴	—	2	2	no	—
945	C₂⁴	—	2	2	no	—
946	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
947	#41	—	2	2	no	—
948	#41	—	2	2	no	—
949	#41	—	2	4	no	—
950	#41	—	2	4	no	—
951	#41	—	4	2	no	—
952	#41	—	4	2	no	—
953	#41	—	4	2	no	—
954	#41	—	4	2	no	—
955	#41	—	4	8	no	—
956	#41	—	4	2	no	—
957	#41	—	4	2	no	—
958	#41	—	4	8	no	—
959	#41	—	8	2	no	—
960	C₂×Q₈	—	2	2	no	—
961	C₂×Q₈	—	2	1	no	—
962	C₂×Q₈	—	2	4	no	—
963	C₂×Q₈	—	4	2	no	—
964	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
965	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
966	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	4	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	2	no	—
986	C₂×D₄	—	4	2	no	—
987	C₂×D₄	—	4	2	no	—
988	C₂×D₄	—	4	2	no	—
989	C₂×D₄	—	4	2	no	—
990	C₂×D₄	—	4	4	no	—
991	C₂×D₄	—	4	4	no	—
992	C₂×D₄	—	4	8	no	—
993	C₂×D₄	—	8	4	no	—
994	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
995	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
996	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
997	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
998	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
999	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1000	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	4	2	no	—
1013	C₂²×C₄	—	4	2	no	—
1014	C₂²×C₄	—	4	8	no	—
1015	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1016	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1017	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1018	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1019	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1020	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1022	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1023	Q₁₆	—	2	2	no	—
1024	Q₁₆	—	4	2	no	—
1025	SD₁₆	—	2	2	no	—
1026	SD₁₆	—	2	4	no	—
1027	SD₁₆	—	2	2	no	—
1028	SD₁₆	—	4	2	no	—
1029	SD₁₆	—	4	2	no	—
1030	SD₁₆	—	4	2	no	—
1031	SD₁₆	—	4	2	no	—
1032	D₈	—	2	4	no	—
1033	D₈	—	2	2	no	—
1034	D₈	—	4	2	no	—
1035	D₈	—	4	2	no	—
1036	D₈	—	4	2	no	—
1037	M₁₆	—	4	2	no	—
1038	M₁₆	—	4	2	no	—
1039	M₁₆	—	4	2	no	—
1040	M₁₆	—	4	2	no	—
1041	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1042	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1043	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1044	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1045	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1046	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1063	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1064	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1065	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1090	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1091	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1092	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	1	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	1	no	—
1098	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1099	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1100	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1101	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1102	C₂³	—	2	1	no	—
1103	C₂³	—	2	1	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	4	2	no	—
1107	C₂³	—	4	2	no	—
1108	C₂³	—	4	2	no	—
1109	C₂³	—	4	4	no	—
1110	C₂³	—	4	4	no	—
1111	C₂³	—	4	4	no	—
1112	C₂³	—	8	2	no	—
1113	C₂³	—	8	2	no	—
1114	C₂³	—	8	2	no	—
1115	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1116	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1117	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1118	Q₈	—	2	1	no	—
1119	Q₈	—	2	1	no	—
1120	Q₈	—	2	2	no	—
1121	Q₈	—	2	2	no	—
1122	Q₈	—	2	1	no	—
1123	Q₈	—	4	4	no	—
1124	Q₈	—	8	1	no	—
1125	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1126	D₄	—	2	4	no	—
1127	D₄	—	2	2	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	2	1	no	—
1130	D₄	—	2	2	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	2	2	no	—
1134	D₄	—	2	2	no	—
1135	D₄	—	2	2	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	4	4	no	—
1138	D₄	—	4	4	no	—
1139	D₄	—	4	4	no	—
1140	D₄	—	4	4	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	4	4	no	—
1143	D₄	—	4	2	no	—
1144	D₄	—	4	4	no	—
1145	D₄	—	4	2	no	—
1146	D₄	—	4	2	no	—
1147	D₄	—	8	1	no	—
1148	D₄	—	8	2	no	—
1149	D₄	—	8	1	no	—
1150	D₄	—	8	2	no	—
1151	D₄	—	8	2	no	—
1152	D₄	—	8	2	no	—
1153	D₄	—	8	2	no	—
1154	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1155	C₂×C₄	—	2	4	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	4	2	no	—
1172	C₂×C₄	—	4	2	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	4	no	—
1176	C₂×C₄	—	4	4	no	—
1177	C₂×C₄	—	4	4	no	—
1178	C₂×C₄	—	4	4	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	8	1	no	—
1182	C₂×C₄	—	8	2	no	—
1183	C₂×C₄	—	8	2	no	—
1184	C₂×C₄	—	8	2	no	—
1185	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1186	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1187	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1188	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1189	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1190	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1191	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1192	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1193	C₈	—	2	2	no	—
1194	C₈	—	2	1	no	—
1195	C₈	—	2	1	no	—
1196	C₈	—	2	1	no	—
1197	C₈	—	2	2	no	—
1198	C₈	—	2	1	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	2	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	2	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	2	no	—
1220	C₂²	—	8	4	no	—
1221	C₂²	—	8	8	no	—
1222	C₂²	—	16	4	no	—
1223	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1224	C₄	—	2	1	no	—
1225	C₄	—	2	2	no	—
1226	C₄	—	2	2	no	—
1227	C₄	—	2	2	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	2	1	no	—
1231	C₄	—	4	2	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	C₅₃×#575	1	2	yes	—
1239	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1240	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1241	C₂	—	4	2	no	—
1242	C₂	—	4	1	no	—
1243	C₂	—	4	2	no	—
1244	C₂	—	4	2	no	—
1245	C₂	—	8	2	no	—
1246	C₂	—	8	1	no	—
1247	C₂	—	8	2	no	—
1248	C₂	C₅₃×#3484	1	1	yes	characteristic
1249	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1250	C₂	C₅₃×#3585	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 ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3519	C₂	semidirect
2. D₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#3333	C₂	semidirect
4. C₅₃×#3331	C₂	semidirect
5. C₅₃×#3329	C₂	semidirect
6. C₅₃×#3326	C₂	semidirect
7. C₅₃×#3325	C₂	semidirect
8. C₅₃×#3322	C₂	semidirect
9. C₅₃×#3278	C₂	semidirect
10. C₅₃×#3275	C₂	semidirect
11. C₅₃×#3274	C₂	semidirect
12. C₅₃×#3274	C₂	semidirect
13. C₅₃×#3273	C₂	semidirect
14. C₅₃×#3272	C₂	semidirect
15. C₅₃×#3212	C₂	semidirect
16. C₅₃×#3207	C₂	semidirect
17. C₅₃×#3197	C₂	semidirect
18. C₅₃×#3194	C₂	semidirect
19. C₅₃×#3106	C₂	semidirect
20. C₅₃×#3102	C₂	semidirect
21. C₅₃×#3006	C₂	semidirect
22. C₅₃×#3005	C₂	semidirect
23. C₅₃×#2975	C₂	semidirect
24. C₂²×#41×C₅₃	C₂²	semidirect
25. C₂×#137×C₅₃	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
28. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
30. C₅₃×#554	C₂²	semidirect
32. C₅₃×#553	C₂²	semidirect
35. D₄×Q₈×C₅₃	C₂²	semidirect
36. C₅₃×#548	C₂²	semidirect
41. C₅₃×#546	C₂²	semidirect
42. C₅₃×#546	C₂²	semidirect
45. D₄²×C₅₃	C₂²	semidirect
46. D₄²×C₅₃	C₂²	semidirect
50. C₅₃×#532	C₂²	semidirect
51. C₅₃×#532	C₂²	semidirect
52. C₅₃×#529	C₂²	semidirect
54. C₅₃×#525	C₂²	semidirect
55. C₅₃×#525	C₂²	semidirect
56. C₂×#121×C₅₃	C₂²	semidirect
58. C₄×#41×C₅₃	C₂²	semidirect
61. C₅₃×#495	C₂²	semidirect
62. C₅₃×#493	C₂²	semidirect
63. C₅₃×#492	C₂²	semidirect
64. C₅₃×#488	C₂²	semidirect
65. C₅₃×#487	C₂²	semidirect
66. C₅₃×#486	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
69. C₅₃×#483	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#482	C₂²	semidirect
73. C₅₃×#480	C₂²	semidirect
74. C₅₃×#479	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#477	C₂²	semidirect
77. C₅₃×#476	C₂²	semidirect
78. C₅₃×#470	C₂²	semidirect
79. C₅₃×#469	C₂²	semidirect
80. C₅₃×#469	C₂²	semidirect
81. C₅₃×#469	C₂²	semidirect
82. C₅₃×#468	C₂²	semidirect
83. C₅₃×#468	C₂²	semidirect
84. C₅₃×#468	C₂²	semidirect
85. C₅₃×#468	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#463	C₂²	semidirect
90. C₅₃×#462	C₂²	semidirect
91. C₅₃×#461	C₂²	semidirect
92. C₅₃×#460	C₂²	semidirect
93. C₅₃×#460	C₂²	semidirect
94. C₅₃×#459	C₂²	semidirect
95. C₅₃×#459	C₂²	semidirect
96. C₅₃×#452	C₂²	semidirect
97. C₅₃×#452	C₂²	semidirect
98. C₅₃×#452	C₂²	semidirect
99. C₅₃×#452	C₂²	semidirect
100. C₅₃×#452	C₂²	semidirect
101. C₅₃×#450	C₂²	semidirect
103. C₅₃×#449	C₂²	semidirect
104. C₅₃×#449	C₂²	semidirect
105. C₅₃×#449	C₂²	semidirect
106. C₅₃×#449	C₂²	semidirect
107. C₅₃×#449	C₂²	semidirect
108. C₅₃×#449	C₂²	semidirect
109. C₅₃×#449	C₂²	semidirect
110. C₅₃×#448	C₂²	semidirect
111. C₅₃×#448	C₂²	semidirect
112. C₅₃×#447	C₂²	semidirect
113. C₅₃×#447	C₂²	semidirect
114. C₅₃×#447	C₂²	semidirect
115. C₄×Q₁₆×C₅₃	C₂²	semidirect
116. C₄×SD₁₆×C₅₃	C₂²	semidirect
117. C₄×SD₁₆×C₅₃	C₂²	semidirect
118. C₄×SD₁₆×C₅₃	C₂²	semidirect
119. C₄×D₈×C₅₃	C₂²	semidirect
120. C₄×D₈×C₅₃	C₂²	semidirect
121. C₅₃×#436	C₂²	semidirect
122. C₅₃×#436	C₂²	semidirect
123. C₅₃×#436	C₂²	semidirect
124. C₅₃×#436	C₂²	semidirect
125. C₅₃×#436	C₂²	semidirect
126. C₅₃×#436	C₂²	semidirect
127. C₅₃×#431	C₂²	semidirect
128. C₅₃×#431	C₂²	semidirect
129. C₅₃×#419	C₂²	semidirect
130. C₅₃×#418	C₂²	semidirect
131. C₅₃×#417	C₂²	semidirect
132. C₅₃×#417	C₂²	semidirect
133. C₅₃×#407	C₂²	semidirect
134. C₅₃×#407	C₂²	semidirect
573. #61590	C₅₃	direct (N × H)
616. #3519	C₂×C₅₃	semidirect
617. D₄×#41	C₂×C₅₃	semidirect
618. #3333	C₂×C₅₃	semidirect
619. #3331	C₂×C₅₃	semidirect
620. #3329	C₂×C₅₃	semidirect
621. #3326	C₂×C₅₃	semidirect
622. #3325	C₂×C₅₃	semidirect
623. #3322	C₂×C₅₃	semidirect
624. #3278	C₂×C₅₃	semidirect
625. #3275	C₂×C₅₃	semidirect
626. #3274	C₂×C₅₃	semidirect
627. #3274	C₂×C₅₃	semidirect
628. #3273	C₂×C₅₃	semidirect
629. #3272	C₂×C₅₃	semidirect
630. #3212	C₂×C₅₃	semidirect
631. #3207	C₂×C₅₃	semidirect
632. #3197	C₂×C₅₃	semidirect
633. #3194	C₂×C₅₃	semidirect
634. #3106	C₂×C₅₃	semidirect
635. #3102	C₂×C₅₃	semidirect
636. #3006	C₂×C₅₃	semidirect
637. #3005	C₂×C₅₃	semidirect
638. #2975	C₂×C₅₃	semidirect
649. C₂²×#41	C₂²×C₅₃	semidirect
650. C₂×#137	C₂²×C₅₃	semidirect
651. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
652. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
653. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
655. #554	C₂²×C₅₃	semidirect
657. #553	C₂²×C₅₃	semidirect
660. D₄×Q₈	C₂²×C₅₃	semidirect
661. #548	C₂²×C₅₃	semidirect
666. #546	C₂²×C₅₃	semidirect
667. #546	C₂²×C₅₃	semidirect
670. D₄²	C₂²×C₅₃	semidirect
671. D₄²	C₂²×C₅₃	semidirect
675. #532	C₂²×C₅₃	semidirect
676. #532	C₂²×C₅₃	semidirect
677. #529	C₂²×C₅₃	semidirect
679. #525	C₂²×C₅₃	semidirect
680. #525	C₂²×C₅₃	semidirect
681. C₂×#121	C₂²×C₅₃	semidirect
683. C₄×#41	C₂²×C₅₃	semidirect
686. #495	C₂²×C₅₃	semidirect
687. #493	C₂²×C₅₃	semidirect
688. #492	C₂²×C₅₃	semidirect
689. #488	C₂²×C₅₃	semidirect
690. #487	C₂²×C₅₃	semidirect
691. #486	C₂²×C₅₃	semidirect
692. #485	C₂²×C₅₃	semidirect
693. #485	C₂²×C₅₃	semidirect
694. #483	C₂²×C₅₃	semidirect
695. #482	C₂²×C₅₃	semidirect
696. #482	C₂²×C₅₃	semidirect
697. #482	C₂²×C₅₃	semidirect
698. #480	C₂²×C₅₃	semidirect
699. #479	C₂²×C₅₃	semidirect
700. #478	C₂²×C₅₃	semidirect
701. #477	C₂²×C₅₃	semidirect
702. #476	C₂²×C₅₃	semidirect
703. #470	C₂²×C₅₃	semidirect
704. #469	C₂²×C₅₃	semidirect
705. #469	C₂²×C₅₃	semidirect
706. #469	C₂²×C₅₃	semidirect
707. #468	C₂²×C₅₃	semidirect
708. #468	C₂²×C₅₃	semidirect
709. #468	C₂²×C₅₃	semidirect
710. #468	C₂²×C₅₃	semidirect
711. #464	C₂²×C₅₃	semidirect
712. #463	C₂²×C₅₃	semidirect
713. #463	C₂²×C₅₃	semidirect
714. #463	C₂²×C₅₃	semidirect
715. #462	C₂²×C₅₃	semidirect
716. #461	C₂²×C₅₃	semidirect
717. #460	C₂²×C₅₃	semidirect
718. #460	C₂²×C₅₃	semidirect
719. #459	C₂²×C₅₃	semidirect
720. #459	C₂²×C₅₃	semidirect
721. #452	C₂²×C₅₃	semidirect
722. #452	C₂²×C₅₃	semidirect
723. #452	C₂²×C₅₃	semidirect
724. #452	C₂²×C₅₃	semidirect
725. #452	C₂²×C₅₃	semidirect
726. #450	C₂²×C₅₃	semidirect
728. #449	C₂²×C₅₃	semidirect
729. #449	C₂²×C₅₃	semidirect
730. #449	C₂²×C₅₃	semidirect
731. #449	C₂²×C₅₃	semidirect
732. #449	C₂²×C₅₃	semidirect
733. #449	C₂²×C₅₃	semidirect
734. #449	C₂²×C₅₃	semidirect
735. #448	C₂²×C₅₃	semidirect
736. #448	C₂²×C₅₃	semidirect
737. #447	C₂²×C₅₃	semidirect
738. #447	C₂²×C₅₃	semidirect
739. #447	C₂²×C₅₃	semidirect
740. C₄×Q₁₆	C₂²×C₅₃	semidirect
741. C₄×SD₁₆	C₂²×C₅₃	semidirect
742. C₄×SD₁₆	C₂²×C₅₃	semidirect
743. C₄×SD₁₆	C₂²×C₅₃	semidirect
744. C₄×D₈	C₂²×C₅₃	semidirect
745. C₄×D₈	C₂²×C₅₃	semidirect
746. #436	C₂²×C₅₃	semidirect
747. #436	C₂²×C₅₃	semidirect
748. #436	C₂²×C₅₃	semidirect
749. #436	C₂²×C₅₃	semidirect
750. #436	C₂²×C₅₃	semidirect
751. #436	C₂²×C₅₃	semidirect
752. #431	C₂²×C₅₃	semidirect
753. #431	C₂²×C₅₃	semidirect
754. #419	C₂²×C₅₃	semidirect
755. #418	C₂²×C₅₃	semidirect
756. #417	C₂²×C₅₃	semidirect
757. #417	C₂²×C₅₃	semidirect
758. #407	C₂²×C₅₃	semidirect
759. #407	C₂²×C₅₃	semidirect
760. C₅₃	#61590	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×#3519	2
D₄×#41×C₅₃	2
C₅₃×#3333	2
C₅₃×#3331	2
C₅₃×#3329	2
C₅₃×#3326	2
C₅₃×#3325	2
C₅₃×#3322	2
C₅₃×#3278	2
C₅₃×#3275	2
C₅₃×#3274	2
C₅₃×#3273	2
C₅₃×#3272	2
C₅₃×#3212	2
C₅₃×#3207	2
C₅₃×#3197	2
C₅₃×#3194	2
C₅₃×#3106	2
C₅₃×#3102	2
C₅₃×#3006	2
C₅₃×#3005	2
C₅₃×#2975	2
#61590	53

Subgroups — C53×#61590 #27269102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61590 #27269102