Subgroups — C₅₃×#62052 #27269564

Order 13568.

1892 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3320	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3301	C₂	1	2	yes	maximal, complemented
11	D₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×SD₁₆×C₅₃	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3265	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3260	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3221	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3123	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3042	C₂	1	2	yes	maximal, complemented
22	C₂×C₅₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
25	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
26	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
27	C₅₃×#563	—	2	2	no	—
28	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#555	C₂²	1	1	yes	characteristic
31	C₅₃×#554	—	2	1	no	—
32	C₅₃×#554	C₂²	1	1	yes	characteristic
33	C₅₃×#553	—	2	1	no	—
34	C₅₃×#553	—	2	1	no	—
35	C₅₃×#553	C₂²	1	2	yes	—
36	C₅₃×#550	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
38	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#548	C₂²	1	2	yes	complemented
40	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#546	—	2	1	no	—
42	C₅₃×#546	—	2	2	no	—
43	D₄²×C₅₃	C₂²	1	2	yes	—
44	D₄²×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#544	—	2	1	no	—
46	C₅₃×#542	—	2	1	no	—
47	C₅₃×#541	C₂²	1	2	yes	complemented
48	C₅₃×#540	C₂²	1	2	yes	—
49	C₅₃×#539	—	2	2	no	—
50	C₅₃×#538	—	2	2	no	—
51	C₅₃×#536	C₂²	1	2	yes	complemented
52	C₅₃×#532	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#529	C₂²	1	1	yes	characteristic
55	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#525	—	2	1	no	—
57	C₂×#121×C₅₃	—	2	1	no	—
58	C₅₃×#518	C₂²	1	2	yes	—
59	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
60	C₅₃×#496	C₂²	1	2	yes	complemented
61	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#492	C₂²	1	2	yes	complemented
64	C₅₃×#491	C₂²	1	2	yes	complemented
65	C₅₃×#488	C₂²	1	2	yes	complemented
66	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#487	C₂²	1	1	yes	characteristic, 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, complemented
71	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#479	C₂²	1	2	yes	complemented
73	C₅₃×#479	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	1	yes	characteristic
75	C₅₃×#478	C₂²	1	2	yes	complemented
76	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#468	C₂²	1	2	yes	complemented
80	C₅₃×#468	C₂²	1	2	yes	complemented
81	C₅₃×#466	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×#463	C₂²	1	2	yes	—
86	C₅₃×#463	C₂²	1	1	yes	characteristic
87	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#463	C₂²	1	2	yes	complemented
89	C₅₃×#463	C₂²	1	2	yes	complemented
90	C₅₃×#461	C₂²	1	1	yes	characteristic
91	C₅₃×#461	C₂²	1	1	yes	characteristic
92	C₅₃×#461	C₂²	1	2	yes	—
93	C₅₃×#461	C₂²	1	2	yes	—
94	C₅₃×#461	C₂²	1	2	yes	complemented
95	C₅₃×#461	C₂²	1	2	yes	complemented
96	C₅₃×#461	C₂²	1	2	yes	complemented
97	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#461	C₂²	1	2	yes	complemented
100	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#460	C₂²	1	2	yes	complemented
102	C₅₃×#460	C₂²	1	2	yes	complemented
103	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#450	C₂²	1	2	yes	—
105	C₅₃×#450	C₂²	1	2	yes	—
106	C₅₃×#450	C₂²	1	1	yes	characteristic
107	C₅₃×#449	C₂²	1	2	yes	complemented
108	C₅₃×#449	C₂²	1	2	yes	complemented
109	C₅₃×#448	C₂²	1	2	yes	complemented
110	C₅₃×#448	C₂²	1	2	yes	complemented
111	C₅₃×#448	C₂²	1	2	yes	complemented
112	C₅₃×#448	C₂²	1	2	yes	complemented
113	C₅₃×#447	C₂²	1	1	yes	characteristic
114	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#440	C₂²	1	2	yes	—
117	C₅₃×#440	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
127	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#433	C₂²	1	2	yes	complemented
129	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#419	C₂²	1	2	yes	complemented
133	C₅₃×#416	C₂²	1	2	yes	complemented
134	C₂×#103×C₅₃	C₂²	1	2	yes	complemented
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	1	no	—
137	C₂×#41×C₅₃	C₂³	1	2	yes	—
138	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
139	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
140	C₂²×D₄×C₅₃	—	2	1	no	—
141	C₂²×D₄×C₅₃	—	2	2	no	—
142	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₅₃	—	2	1	no	—
145	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
146	C₂×SD₁₆×C₅₃	—	4	4	no	—
147	C₂×SD₁₆×C₅₃	—	4	4	no	—
148	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
159	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₅₃	C₂³	1	2	yes	—
162	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
163	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
164	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₅₃	—	2	1	no	—
166	C₄⋊Q₈×C₅₃	—	2	2	no	—
167	C₄⋊Q₈×C₅₃	—	2	1	no	—
168	C₄⋊Q₈×C₅₃	—	2	1	no	—
169	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
173	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
174	#127×C₅₃	C₂³	1	1	yes	characteristic
175	#127×C₅₃	C₂³	1	2	yes	—
176	#126×C₅₃	—	2	2	no	—
177	#126×C₅₃	—	2	2	no	—
178	#126×C₅₃	—	2	2	no	—
179	#126×C₅₃	—	2	2	no	—
180	#126×C₅₃	—	2	1	no	—
181	#126×C₅₃	D₄	1	2	yes	—
182	#125×C₅₃	—	2	2	no	—
183	#125×C₅₃	—	2	2	no	—
184	#125×C₅₃	—	2	2	no	—
185	#125×C₅₃	—	2	1	no	—
186	#125×C₅₃	D₄	1	1	yes	characteristic
187	#125×C₅₃	C₂³	1	2	yes	—
188	#125×C₅₃	C₂³	1	1	yes	characteristic
189	#124×C₅₃	—	2	2	no	—
190	#124×C₅₃	—	2	2	no	—
191	#124×C₅₃	—	2	1	no	—
192	#124×C₅₃	D₄	1	1	yes	characteristic
193	#124×C₅₃	C₂³	1	2	yes	—
194	#124×C₅₃	C₂³	1	1	yes	characteristic
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	2	no	—
200	#123×C₅₃	—	2	2	no	—
201	#123×C₅₃	—	2	1	no	—
202	#123×C₅₃	D₄	1	2	yes	—
203	C₂²⋊Q₈×C₅₃	—	2	2	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	2	no	—
206	C₂²⋊Q₈×C₅₃	—	2	2	no	—
207	C₂²⋊Q₈×C₅₃	—	2	2	no	—
208	C₂²⋊Q₈×C₅₃	—	2	2	no	—
209	C₂²⋊Q₈×C₅₃	—	2	2	no	—
210	C₂²⋊Q₈×C₅₃	—	2	1	no	—
211	C₂²⋊Q₈×C₅₃	—	2	1	no	—
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	1	yes	characteristic
216	#121×C₅₃	—	2	1	no	—
217	#121×C₅₃	—	2	1	no	—
218	#121×C₅₃	—	2	2	no	—
219	#121×C₅₃	—	2	2	no	—
220	#121×C₅₃	—	2	2	no	—
221	#121×C₅₃	—	2	2	no	—
222	#121×C₅₃	—	2	2	no	—
223	#121×C₅₃	—	2	1	no	—
224	#121×C₅₃	—	2	2	no	—
225	#121×C₅₃	—	2	1	no	—
226	#121×C₅₃	—	2	1	no	—
227	#121×C₅₃	D₄	1	1	yes	characteristic
228	#121×C₅₃	C₂³	1	1	yes	characteristic
229	#121×C₅₃	C₂³	1	2	yes	—
230	#121×C₅₃	C₂³	1	2	yes	—
231	#121×C₅₃	C₂³	1	2	yes	—
232	#120×C₅₃	—	2	2	no	—
233	#120×C₅₃	—	2	2	no	—
234	#120×C₅₃	—	2	2	no	—
235	C₄×Q₈×C₅₃	—	2	1	no	—
236	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
239	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
240	C₄×D₄×C₅₃	—	2	2	no	—
241	C₄×D₄×C₅₃	—	2	2	no	—
242	C₄×D₄×C₅₃	—	2	2	no	—
243	C₄×D₄×C₅₃	—	2	2	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	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₅₃	C₂³	1	2	yes	—
255	C₄×D₄×C₅₃	C₂³	1	2	yes	—
256	C₄×D₄×C₅₃	C₂³	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	2	yes	—
260	#117×C₅₃	—	2	1	no	—
261	#117×C₅₃	—	2	1	no	—
262	#117×C₅₃	—	2	1	no	—
263	#117×C₅₃	C₂³	1	2	yes	—
264	#117×C₅₃	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
266	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
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×C₂²⋊C₄×C₅₃	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
273	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
274	#107×C₅₃	C₂³	1	1	yes	characteristic
275	#107×C₅₃	C₂³	1	2	yes	—
276	#107×C₅₃	C₂³	1	1	yes	characteristic
277	#106×C₅₃	C₂³	1	1	yes	characteristic
278	#106×C₅₃	C₂³	1	2	yes	—
279	#106×C₅₃	C₂³	1	1	yes	characteristic
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	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
285	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	2	yes	—
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	2	yes	—
297	#103×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	1	yes	characteristic
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	2	yes	—
306	#102×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
311	#97×C₅₃	C₂³	1	2	yes	—
312	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₅₃	C₂³	1	2	yes	—
315	C₂⁴×C₅₃	—	2	1	no	—
316	C₂⁴×C₅₃	—	2	2	no	—
317	#41×C₅₃	—	4	2	no	—
318	#41×C₅₃	—	4	2	no	—
319	#41×C₅₃	—	8	2	no	—
320	#41×C₅₃	—	8	2	no	—
321	C₂×Q₈×C₅₃	—	2	2	no	—
322	C₂×Q₈×C₅₃	—	2	1	no	—
323	C₂×Q₈×C₅₃	—	2	2	no	—
324	C₂×Q₈×C₅₃	—	4	2	no	—
325	C₂×Q₈×C₅₃	—	4	2	no	—
326	C₂×Q₈×C₅₃	—	4	2	no	—
327	C₂×Q₈×C₅₃	—	4	2	no	—
328	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
332	C₂×D₄×C₅₃	—	2	2	no	—
333	C₂×D₄×C₅₃	—	2	4	no	—
334	C₂×D₄×C₅₃	—	2	1	no	—
335	C₂×D₄×C₅₃	—	2	2	no	—
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	—	2	2	no	—
338	C₂×D₄×C₅₃	—	2	2	no	—
339	C₂×D₄×C₅₃	—	2	2	no	—
340	C₂×D₄×C₅₃	—	2	1	no	—
341	C₂×D₄×C₅₃	—	2	1	no	—
342	C₂×D₄×C₅₃	—	2	2	no	—
343	C₂×D₄×C₅₃	—	2	1	no	—
344	C₂×D₄×C₅₃	—	2	2	no	—
345	C₂×D₄×C₅₃	—	4	1	no	—
346	C₂×D₄×C₅₃	—	4	2	no	—
347	C₂×D₄×C₅₃	—	8	2	no	—
348	C₂×D₄×C₅₃	—	8	4	no	—
349	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
353	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₅₃	—	2	1	no	—
356	C₂²×C₄×C₅₃	—	2	2	no	—
357	C₂²×C₄×C₅₃	—	2	2	no	—
358	C₂²×C₄×C₅₃	—	2	1	no	—
359	C₂²×C₄×C₅₃	—	2	1	no	—
360	C₂²×C₄×C₅₃	—	2	1	no	—
361	C₂²×C₄×C₅₃	—	2	1	no	—
362	C₂²×C₄×C₅₃	—	2	2	no	—
363	C₂²×C₄×C₅₃	—	2	2	no	—
364	C₂²×C₄×C₅₃	—	2	2	no	—
365	C₂²×C₄×C₅₃	—	2	2	no	—
366	C₂²×C₄×C₅₃	—	2	1	no	—
367	C₂²×C₄×C₅₃	—	8	2	no	—
368	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
372	SD₁₆×C₅₃	—	2	4	no	—
373	SD₁₆×C₅₃	—	2	2	no	—
374	SD₁₆×C₅₃	—	2	4	no	—
375	SD₁₆×C₅₃	—	4	2	no	—
376	SD₁₆×C₅₃	—	4	2	no	—
377	SD₁₆×C₅₃	—	4	2	no	—
378	SD₁₆×C₅₃	—	4	2	no	—
379	SD₁₆×C₅₃	—	4	2	no	—
380	SD₁₆×C₅₃	—	4	1	no	—
381	SD₁₆×C₅₃	—	4	2	no	—
382	SD₁₆×C₅₃	—	4	2	no	—
383	D₈×C₅₃	—	2	2	no	—
384	D₈×C₅₃	—	4	1	no	—
385	D₈×C₅₃	—	4	2	no	—
386	M₁₆×C₅₃	—	4	2	no	—
387	C₂×C₈×C₅₃	—	4	2	no	—
388	C₂×C₈×C₅₃	—	4	2	no	—
389	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
393	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
395	C₄⋊C₄×C₅₃	—	2	1	no	—
396	C₄⋊C₄×C₅₃	—	2	1	no	—
397	C₄⋊C₄×C₅₃	—	2	1	no	—
398	C₄⋊C₄×C₅₃	—	2	2	no	—
399	C₄⋊C₄×C₅₃	—	2	1	no	—
400	C₄⋊C₄×C₅₃	—	2	2	no	—
401	C₄⋊C₄×C₅₃	—	2	2	no	—
402	C₄⋊C₄×C₅₃	—	2	2	no	—
403	C₄⋊C₄×C₅₃	—	2	1	no	—
404	C₄⋊C₄×C₅₃	—	2	1	no	—
405	C₄⋊C₄×C₅₃	—	2	1	no	—
406	C₄⋊C₄×C₅₃	—	2	1	no	—
407	C₄⋊C₄×C₅₃	—	2	2	no	—
408	C₄⋊C₄×C₅₃	—	2	2	no	—
409	C₄⋊C₄×C₅₃	—	2	2	no	—
410	C₄⋊C₄×C₅₃	—	2	1	no	—
411	C₄⋊C₄×C₅₃	—	2	2	no	—
412	C₄⋊C₄×C₅₃	—	2	2	no	—
413	C₄⋊C₄×C₅₃	—	2	2	no	—
414	C₄⋊C₄×C₅₃	—	2	1	no	—
415	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
426	C₂²⋊C₄×C₅₃	—	2	2	no	—
427	C₂²⋊C₄×C₅₃	—	2	1	no	—
428	C₂²⋊C₄×C₅₃	—	2	2	no	—
429	C₂²⋊C₄×C₅₃	—	2	2	no	—
430	C₂²⋊C₄×C₅₃	—	2	1	no	—
431	C₂²⋊C₄×C₅₃	—	2	1	no	—
432	C₂²⋊C₄×C₅₃	—	2	2	no	—
433	C₂²⋊C₄×C₅₃	—	2	2	no	—
434	C₂²⋊C₄×C₅₃	—	2	1	no	—
435	C₂²⋊C₄×C₅₃	—	2	2	no	—
436	C₂²⋊C₄×C₅₃	—	2	1	no	—
437	C₂²⋊C₄×C₅₃	—	2	2	no	—
438	C₂²⋊C₄×C₅₃	—	2	2	no	—
439	C₂²⋊C₄×C₅₃	—	2	1	no	—
440	C₂²⋊C₄×C₅₃	—	2	1	no	—
441	C₂²⋊C₄×C₅₃	—	2	2	no	—
442	C₂²⋊C₄×C₅₃	—	2	2	no	—
443	C₂²⋊C₄×C₅₃	—	2	1	no	—
444	C₂²⋊C₄×C₅₃	—	2	2	no	—
445	C₂²⋊C₄×C₅₃	—	2	1	no	—
446	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
451	C₄²×C₅₃	—	2	2	no	—
452	C₄²×C₅₃	—	2	1	no	—
453	C₄²×C₅₃	—	2	2	no	—
454	C₄²×C₅₃	—	2	2	no	—
455	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
458	C₄²×C₅₃	C₂⁴	1	2	yes	—
459	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
460	C₂³×C₅₃	—	2	1	no	—
461	C₂³×C₅₃	—	2	1	no	—
462	C₂³×C₅₃	—	2	1	no	—
463	C₂³×C₅₃	—	2	2	no	—
464	C₂³×C₅₃	—	4	2	no	—
465	C₂³×C₅₃	—	4	4	no	—
466	C₂³×C₅₃	—	4	2	no	—
467	C₂³×C₅₃	—	8	1	no	—
468	C₂³×C₅₃	—	8	2	no	—
469	C₂³×C₅₃	—	8	2	no	—
470	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
471	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
472	Q₈×C₅₃	—	2	2	no	—
473	Q₈×C₅₃	—	2	2	no	—
474	Q₈×C₅₃	—	2	1	no	—
475	Q₈×C₅₃	—	2	2	no	—
476	Q₈×C₅₃	—	2	2	no	—
477	Q₈×C₅₃	—	2	1	no	—
478	Q₈×C₅₃	—	2	2	no	—
479	Q₈×C₅₃	—	8	2	no	—
480	Q₈×C₅₃	—	8	2	no	—
481	Q₈×C₅₃	—	8	1	no	—
482	D₄×C₅₃	—	2	4	no	—
483	D₄×C₅₃	—	2	2	no	—
484	D₄×C₅₃	—	2	2	no	—
485	D₄×C₅₃	—	2	1	no	—
486	D₄×C₅₃	—	2	1	no	—
487	D₄×C₅₃	—	2	1	no	—
488	D₄×C₅₃	—	2	1	no	—
489	D₄×C₅₃	—	2	2	no	—
490	D₄×C₅₃	—	2	1	no	—
491	D₄×C₅₃	—	4	4	no	—
492	D₄×C₅₃	—	4	2	no	—
493	D₄×C₅₃	—	4	2	no	—
494	D₄×C₅₃	—	4	4	no	—
495	D₄×C₅₃	—	4	2	no	—
496	D₄×C₅₃	—	8	2	no	—
497	D₄×C₅₃	—	8	1	no	—
498	D₄×C₅₃	—	8	2	no	—
499	D₄×C₅₃	—	8	2	no	—
500	D₄×C₅₃	—	8	2	no	—
501	D₄×C₅₃	—	8	2	no	—
502	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
503	C₂×C₄×C₅₃	—	2	2	no	—
504	C₂×C₄×C₅₃	—	2	2	no	—
505	C₂×C₄×C₅₃	—	2	1	no	—
506	C₂×C₄×C₅₃	—	2	2	no	—
507	C₂×C₄×C₅₃	—	2	1	no	—
508	C₂×C₄×C₅₃	—	2	2	no	—
509	C₂×C₄×C₅₃	—	2	1	no	—
510	C₂×C₄×C₅₃	—	2	1	no	—
511	C₂×C₄×C₅₃	—	2	2	no	—
512	C₂×C₄×C₅₃	—	2	2	no	—
513	C₂×C₄×C₅₃	—	2	2	no	—
514	C₂×C₄×C₅₃	—	2	1	no	—
515	C₂×C₄×C₅₃	—	2	1	no	—
516	C₂×C₄×C₅₃	—	2	1	no	—
517	C₂×C₄×C₅₃	—	4	2	no	—
518	C₂×C₄×C₅₃	—	4	2	no	—
519	C₂×C₄×C₅₃	—	4	2	no	—
520	C₂×C₄×C₅₃	—	8	1	no	—
521	C₂×C₄×C₅₃	—	8	1	no	—
522	C₂×C₄×C₅₃	—	8	2	no	—
523	C₂×C₄×C₅₃	—	8	2	no	—
524	C₂×C₄×C₅₃	—	8	2	no	—
525	C₂×C₄×C₅₃	—	8	2	no	—
526	C₂×C₄×C₅₃	—	8	1	no	—
527	C₂×C₄×C₅₃	—	8	2	no	—
528	C₂×C₄×C₅₃	—	8	2	no	—
529	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
538	C₈×C₅₃	—	2	1	no	—
539	C₈×C₅₃	—	2	2	no	—
540	C₈×C₅₃	—	2	2	no	—
541	C₈×C₅₃	—	2	1	no	—
542	C₈×C₅₃	—	2	1	no	—
543	C₈×C₅₃	—	2	1	no	—
544	#62052	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
545	C₂²×C₅₃	—	2	1	no	—
546	C₂²×C₅₃	—	2	1	no	—
547	C₂²×C₅₃	—	2	2	no	—
548	C₂²×C₅₃	—	2	2	no	—
549	C₂²×C₅₃	—	2	2	no	—
550	C₂²×C₅₃	—	2	2	no	—
551	C₂²×C₅₃	—	4	1	no	—
552	C₂²×C₅₃	—	4	1	no	—
553	C₂²×C₅₃	—	4	1	no	—
554	C₂²×C₅₃	—	4	1	no	—
555	C₂²×C₅₃	—	4	2	no	—
556	C₂²×C₅₃	—	4	1	no	—
557	C₂²×C₅₃	—	4	1	no	—
558	C₂²×C₅₃	—	4	2	no	—
559	C₂²×C₅₃	—	4	2	no	—
560	C₂²×C₅₃	—	4	1	no	—
561	C₂²×C₅₃	—	4	1	no	—
562	C₂²×C₅₃	—	8	4	no	—
563	C₂²×C₅₃	—	16	4	no	—
564	C₂²×C₅₃	#577	1	2	yes	—
565	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
566	C₄×C₅₃	—	2	2	no	—
567	C₄×C₅₃	—	2	1	no	—
568	C₄×C₅₃	—	2	1	no	—
569	C₄×C₅₃	—	2	1	no	—
570	C₄×C₅₃	—	2	1	no	—
571	C₄×C₅₃	—	2	2	no	—
572	C₄×C₅₃	—	2	2	no	—
573	C₄×C₅₃	—	4	2	no	—
574	C₄×C₅₃	—	4	2	no	—
575	C₄×C₅₃	—	4	1	no	—
576	C₄×C₅₃	—	4	1	no	—
577	C₄×C₅₃	—	4	1	no	—
578	C₄×C₅₃	—	4	1	no	—
579	C₄×C₅₃	—	4	2	no	—
580	C₄×C₅₃	—	4	1	no	—
581	C₄×C₅₃	#577	1	2	yes	—
582	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
583	C₄×C₅₃	#585	1	1	yes	characteristic
584	#3552	C₂×C₅₃	1	1	yes	characteristic, complemented
585	#3519	C₂×C₅₃	1	1	yes	characteristic, complemented
586	#3397	C₂×C₅₃	1	1	yes	characteristic, complemented
587	#3392	C₂×C₅₃	1	1	yes	characteristic, complemented
588	#3372	C₂×C₅₃	1	1	yes	characteristic, complemented
589	#3360	C₂×C₅₃	1	1	yes	characteristic, complemented
590	#3329	C₂×C₅₃	1	1	yes	characteristic, complemented
591	#3320	C₂×C₅₃	1	2	yes	complemented
592	#3303	C₂×C₅₃	1	1	yes	characteristic, complemented
593	#3301	C₂×C₅₃	1	2	yes	complemented
594	D₄×SD₁₆	C₂×C₅₃	1	2	yes	complemented
595	D₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
596	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
597	#3265	C₂×C₅₃	1	2	yes	complemented
598	#3260	C₂×C₅₃	1	2	yes	complemented
599	#3247	C₂×C₅₃	1	1	yes	characteristic, complemented
600	#3221	C₂×C₅₃	1	2	yes	complemented
601	#3206	C₂×C₅₃	1	1	yes	characteristic, complemented
602	#3123	C₂×C₅₃	1	2	yes	complemented
603	#3105	C₂×C₅₃	1	1	yes	characteristic, complemented
604	#3042	C₂×C₅₃	1	2	yes	complemented
605	C₂×#461	C₂×C₅₃	1	1	yes	characteristic, complemented
606	#2994	C₂×C₅₃	1	1	yes	characteristic, complemented
607	C₂×C₅₃	—	2	2	no	—
608	C₂×C₅₃	—	4	2	no	—
609	C₂×C₅₃	—	4	2	no	—
610	C₂×C₅₃	—	8	1	no	—
611	C₂×C₅₃	—	8	1	no	—
612	C₂×C₅₃	—	8	2	no	—
613	C₂×C₅₃	#3488	1	1	yes	characteristic
614	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
615	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
616	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
617	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
618	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
619	#563	—	2	2	no	—
620	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
621	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
622	#555	C₂²×C₅₃	1	1	yes	characteristic
623	#554	—	2	1	no	—
624	#554	C₂²×C₅₃	1	1	yes	characteristic
625	#553	—	2	1	no	—
626	#553	—	2	1	no	—
627	#553	C₂²×C₅₃	1	2	yes	—
628	#550	C₂²×C₅₃	1	1	yes	characteristic
629	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
630	D₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
631	#548	C₂²×C₅₃	1	2	yes	complemented
632	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
633	#546	—	2	1	no	—
634	#546	—	2	2	no	—
635	D₄²	C₂²×C₅₃	1	2	yes	—
636	D₄²	C₂²×C₅₃	1	1	yes	characteristic
637	#544	—	2	1	no	—
638	#542	—	2	1	no	—
639	#541	C₂²×C₅₃	1	2	yes	complemented
640	#540	C₂²×C₅₃	1	2	yes	—
641	#539	—	2	2	no	—
642	#538	—	2	2	no	—
643	#536	C₂²×C₅₃	1	2	yes	complemented
644	#532	C₂²×C₅₃	1	1	yes	characteristic
645	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
646	#529	C₂²×C₅₃	1	1	yes	characteristic
647	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
648	#525	—	2	1	no	—
649	C₂×#121	—	2	1	no	—
650	#518	C₂²×C₅₃	1	2	yes	—
651	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
652	#496	C₂²×C₅₃	1	2	yes	complemented
653	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
654	#492	C₂²×C₅₃	1	2	yes	complemented
655	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	#491	C₂²×C₅₃	1	2	yes	complemented
657	#488	C₂²×C₅₃	1	2	yes	complemented
658	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
660	#485	C₂²×C₅₃	1	2	yes	complemented
661	#485	C₂²×C₅₃	1	2	yes	complemented
662	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
664	#479	C₂²×C₅₃	1	2	yes	complemented
665	#479	C₂²×C₅₃	1	2	yes	complemented
666	#478	C₂²×C₅₃	1	1	yes	characteristic
667	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
668	#478	C₂²×C₅₃	1	2	yes	complemented
669	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
670	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
671	#468	C₂²×C₅₃	1	2	yes	complemented
672	#468	C₂²×C₅₃	1	2	yes	complemented
673	#466	C₂²×C₅₃	1	2	yes	complemented
674	#465	C₂²×C₅₃	1	2	yes	complemented
675	#465	C₂²×C₅₃	1	2	yes	complemented
676	#465	C₂²×C₅₃	1	2	yes	complemented
677	#463	C₂²×C₅₃	1	2	yes	—
678	#463	C₂²×C₅₃	1	1	yes	characteristic
679	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
680	#463	C₂²×C₅₃	1	2	yes	complemented
681	#463	C₂²×C₅₃	1	2	yes	complemented
682	#461	C₂²×C₅₃	1	1	yes	characteristic
683	#461	C₂²×C₅₃	1	1	yes	characteristic
684	#461	C₂²×C₅₃	1	2	yes	—
685	#461	C₂²×C₅₃	1	2	yes	—
686	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#461	C₂²×C₅₃	1	2	yes	complemented
688	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	#461	C₂²×C₅₃	1	2	yes	complemented
690	#461	C₂²×C₅₃	1	2	yes	complemented
691	#461	C₂²×C₅₃	1	2	yes	complemented
692	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#460	C₂²×C₅₃	1	2	yes	complemented
694	#460	C₂²×C₅₃	1	2	yes	complemented
695	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	#450	C₂²×C₅₃	1	1	yes	characteristic
697	#450	C₂²×C₅₃	1	2	yes	—
698	#450	C₂²×C₅₃	1	2	yes	—
699	#449	C₂²×C₅₃	1	2	yes	complemented
700	#449	C₂²×C₅₃	1	2	yes	complemented
701	#448	C₂²×C₅₃	1	2	yes	complemented
702	#448	C₂²×C₅₃	1	2	yes	complemented
703	#448	C₂²×C₅₃	1	2	yes	complemented
704	#448	C₂²×C₅₃	1	2	yes	complemented
705	#447	C₂²×C₅₃	1	1	yes	characteristic
706	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	#440	C₂²×C₅₃	1	2	yes	—
709	#440	C₂²×C₅₃	1	2	yes	complemented
710	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
711	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
712	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
714	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
715	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
716	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
717	#435	C₂²×C₅₃	1	2	yes	complemented
718	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
719	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
720	#433	C₂²×C₅₃	1	2	yes	complemented
721	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	#424	C₂²×C₅₃	1	2	yes	complemented
723	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
724	#419	C₂²×C₅₃	1	2	yes	complemented
725	#416	C₂²×C₅₃	1	2	yes	complemented
726	C₂×#103	C₂²×C₅₃	1	2	yes	complemented
727	C₅₃	#62052	1	1	yes	characteristic, direct product factor, Sylow
728	C₂×#41	—	2	1	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	C₂³×C₅₃	1	2	yes	—
731	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
732	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
733	C₂²×D₄	—	2	1	no	—
734	C₂²×D₄	—	2	2	no	—
735	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
736	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
737	C₂³×C₄	—	2	1	no	—
738	AGL(1,ℤ/8)	—	4	4	no	—
739	C₂×SD₁₆	—	4	4	no	—
740	C₂×SD₁₆	—	4	4	no	—
741	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
749	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
750	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
751	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
752	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
753	C₂×D₈	C₂³×C₅₃	1	2	yes	—
754	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
755	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
756	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
757	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
758	C₄⋊Q₈	—	2	1	no	—
759	C₄⋊Q₈	—	2	2	no	—
760	C₄⋊Q₈	—	2	1	no	—
761	C₄⋊Q₈	—	2	1	no	—
762	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
763	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
764	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
765	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
766	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
767	#127	C₂³×C₅₃	1	1	yes	characteristic
768	#127	C₂³×C₅₃	1	2	yes	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#126	—	2	2	no	—
772	#126	—	2	2	no	—
773	#126	—	2	1	no	—
774	#126	D₄×C₅₃	1	2	yes	—
775	#125	—	2	2	no	—
776	#125	—	2	2	no	—
777	#125	—	2	2	no	—
778	#125	—	2	1	no	—
779	#125	D₄×C₅₃	1	1	yes	characteristic
780	#125	C₂³×C₅₃	1	1	yes	characteristic
781	#125	C₂³×C₅₃	1	2	yes	—
782	#124	—	2	2	no	—
783	#124	—	2	2	no	—
784	#124	—	2	1	no	—
785	#124	D₄×C₅₃	1	1	yes	characteristic
786	#124	C₂³×C₅₃	1	1	yes	characteristic
787	#124	C₂³×C₅₃	1	2	yes	—
788	#123	—	2	1	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	D₄×C₅₃	1	2	yes	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	—	2	2	no	—
805	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
806	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
807	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
808	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
809	#121	—	2	2	no	—
810	#121	—	2	1	no	—
811	#121	—	2	2	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	—	2	2	no	—
819	#121	—	2	2	no	—
820	#121	D₄×C₅₃	1	1	yes	characteristic
821	#121	C₂³×C₅₃	1	1	yes	characteristic
822	#121	C₂³×C₅₃	1	2	yes	—
823	#121	C₂³×C₅₃	1	2	yes	—
824	#121	C₂³×C₅₃	1	2	yes	—
825	#120	—	2	2	no	—
826	#120	—	2	2	no	—
827	#120	—	2	2	no	—
828	C₄×Q₈	—	2	1	no	—
829	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
830	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
831	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
832	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	2	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
847	C₄×D₄	C₂³×C₅₃	1	2	yes	—
848	C₄×D₄	C₂³×C₅₃	1	2	yes	—
849	C₄×D₄	C₂³×C₅₃	1	2	yes	—
850	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
851	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
852	C₄×D₄	C₂³×C₅₃	1	2	yes	—
853	#117	—	2	1	no	—
854	#117	—	2	1	no	—
855	#117	—	2	1	no	—
856	#117	C₂³×C₅₃	1	2	yes	—
857	#117	C₂³×C₅₃	1	2	yes	—
858	C₂×C₄⋊C₄	—	2	1	no	—
859	C₂×C₄⋊C₄	—	2	1	no	—
860	C₂×C₄⋊C₄	—	2	1	no	—
861	C₂×C₄⋊C₄	—	2	1	no	—
862	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
863	C₂×C₂²⋊C₄	—	2	1	no	—
864	C₂×C₂²⋊C₄	—	2	2	no	—
865	C₂×C₂²⋊C₄	—	2	2	no	—
866	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
867	#107	C₂³×C₅₃	1	1	yes	characteristic
868	#107	C₂³×C₅₃	1	1	yes	characteristic
869	#107	C₂³×C₅₃	1	2	yes	—
870	#106	C₂³×C₅₃	1	2	yes	—
871	#106	C₂³×C₅₃	1	1	yes	characteristic
872	#106	C₂³×C₅₃	1	1	yes	characteristic
873	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
874	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
875	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
877	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
878	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
879	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
880	#103	C₂³×C₅₃	1	2	yes	—
881	#103	C₂³×C₅₃	1	2	yes	—
882	#103	C₂³×C₅₃	1	2	yes	—
883	#103	C₂³×C₅₃	1	2	yes	—
884	#103	C₂³×C₅₃	1	2	yes	—
885	#103	C₂³×C₅₃	1	1	yes	characteristic
886	#103	C₂³×C₅₃	1	2	yes	—
887	#103	C₂³×C₅₃	1	2	yes	—
888	#103	C₂³×C₅₃	1	2	yes	—
889	#103	C₂³×C₅₃	1	1	yes	characteristic
890	#103	C₂³×C₅₃	1	2	yes	—
891	#102	C₂³×C₅₃	1	1	yes	characteristic
892	#102	C₂³×C₅₃	1	2	yes	—
893	#102	C₂³×C₅₃	1	1	yes	characteristic
894	#102	C₂³×C₅₃	1	1	yes	characteristic
895	#102	C₂³×C₅₃	1	1	yes	characteristic
896	#102	C₂³×C₅₃	1	1	yes	characteristic
897	#102	C₂³×C₅₃	1	1	yes	characteristic
898	#102	C₂³×C₅₃	1	2	yes	—
899	#102	C₂³×C₅₃	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
901	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
902	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
904	#97	C₂³×C₅₃	1	2	yes	—
905	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
906	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
907	C₄×C₈	C₂³×C₅₃	1	2	yes	—
908	C₂⁴	—	2	1	no	—
909	C₂⁴	—	2	2	no	—
910	#41	—	4	2	no	—
911	#41	—	4	2	no	—
912	#41	—	8	2	no	—
913	#41	—	8	2	no	—
914	C₂×Q₈	—	2	2	no	—
915	C₂×Q₈	—	2	1	no	—
916	C₂×Q₈	—	2	2	no	—
917	C₂×Q₈	—	4	2	no	—
918	C₂×Q₈	—	4	2	no	—
919	C₂×Q₈	—	4	2	no	—
920	C₂×Q₈	—	4	2	no	—
921	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
923	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
924	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	4	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	1	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	4	1	no	—
939	C₂×D₄	—	4	2	no	—
940	C₂×D₄	—	8	2	no	—
941	C₂×D₄	—	8	4	no	—
942	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
943	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
946	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
947	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	8	2	no	—
961	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
962	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
965	SD₁₆	—	2	2	no	—
966	SD₁₆	—	2	4	no	—
967	SD₁₆	—	2	4	no	—
968	SD₁₆	—	4	2	no	—
969	SD₁₆	—	4	2	no	—
970	SD₁₆	—	4	2	no	—
971	SD₁₆	—	4	2	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	1	no	—
975	SD₁₆	—	4	2	no	—
976	D₈	—	2	2	no	—
977	D₈	—	4	2	no	—
978	D₈	—	4	1	no	—
979	M₁₆	—	4	2	no	—
980	C₂×C₈	—	4	2	no	—
981	C₂×C₈	—	4	2	no	—
982	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
983	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
984	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
985	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
986	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1011	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1012	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1013	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1016	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1018	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1040	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1041	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1042	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1043	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	2	no	—
1047	C₄²	—	2	2	no	—
1048	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1049	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1050	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₅₃	1	2	yes	—
1052	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	4	2	no	—
1058	C₂³	—	4	4	no	—
1059	C₂³	—	4	2	no	—
1060	C₂³	—	8	1	no	—
1061	C₂³	—	8	2	no	—
1062	C₂³	—	8	2	no	—
1063	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1064	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1065	Q₈	—	2	2	no	—
1066	Q₈	—	2	1	no	—
1067	Q₈	—	2	2	no	—
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	2	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	2	2	no	—
1072	Q₈	—	8	2	no	—
1073	Q₈	—	8	2	no	—
1074	Q₈	—	8	1	no	—
1075	D₄	—	2	4	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	2	1	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	4	4	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	4	no	—
1088	D₄	—	4	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	1	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	—	8	2	no	—
1095	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	8	1	no	—
1114	C₂×C₄	—	8	1	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	—	8	1	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1123	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1124	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1125	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1126	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1128	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1129	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1130	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1131	C₈	—	2	1	no	—
1132	C₈	—	2	2	no	—
1133	C₈	—	2	2	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	1	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	2	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	8	4	no	—
1155	C₂²	—	16	4	no	—
1156	C₂²	C₅₃×#577	1	2	yes	—
1157	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1158	C₄	—	2	2	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	4	2	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	1	no	—
1173	C₄	C₅₃×#577	1	2	yes	—
1174	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1175	C₄	C₅₃×#585	1	1	yes	characteristic
1176	C₂	—	2	2	no	—
1177	C₂	—	4	2	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	1	no	—
1180	C₂	—	8	2	no	—
1181	C₂	—	8	1	no	—
1182	C₂	C₅₃×#3488	1	1	yes	characteristic
1183	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1184	C₂	C₂×C₅₃×#577	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 ◁ C₅₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3552	C₂	semidirect
2. C₅₃×#3519	C₂	semidirect
3. C₅₃×#3397	C₂	semidirect
4. C₅₃×#3392	C₂	semidirect
5. C₅₃×#3372	C₂	semidirect
6. C₅₃×#3360	C₂	semidirect
7. C₅₃×#3329	C₂	semidirect
8. C₅₃×#3320	C₂	semidirect
9. C₅₃×#3303	C₂	semidirect
10. C₅₃×#3301	C₂	semidirect
11. D₄×SD₁₆×C₅₃	C₂	semidirect
12. D₄×SD₁₆×C₅₃	C₂	semidirect
13. C₅₃×#3272	C₂	semidirect
14. C₅₃×#3265	C₂	semidirect
15. C₅₃×#3260	C₂	semidirect
16. C₅₃×#3247	C₂	semidirect
17. C₅₃×#3221	C₂	semidirect
18. C₅₃×#3206	C₂	semidirect
19. C₅₃×#3123	C₂	semidirect
20. C₅₃×#3105	C₂	semidirect
21. C₅₃×#3042	C₂	semidirect
22. C₂×C₅₃×#461	C₂	semidirect
23. C₅₃×#2994	C₂	semidirect
28. C₅₃×#557	C₂²	semidirect
29. C₅₃×#556	C₂²	semidirect
37. D₄×Q₈×C₅₃	C₂²	semidirect
38. D₄×Q₈×C₅₃	C₂²	semidirect
39. C₅₃×#548	C₂²	semidirect
40. C₅₃×#547	C₂²	semidirect
47. C₅₃×#541	C₂²	semidirect
51. C₅₃×#536	C₂²	semidirect
53. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
55. C₅₃×#529	C₂²	semidirect
60. C₅₃×#496	C₂²	semidirect
61. C₅₃×#492	C₂²	semidirect
62. C₅₃×#492	C₂²	semidirect
63. C₅₃×#492	C₂²	semidirect
64. C₅₃×#491	C₂²	semidirect
65. C₅₃×#488	C₂²	semidirect
66. C₅₃×#487	C₂²	semidirect
67. C₅₃×#487	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
69. C₅₃×#485	C₂²	semidirect
70. C₅₃×#484	C₂²	semidirect
71. C₅₃×#481	C₂²	semidirect
72. C₅₃×#479	C₂²	semidirect
73. C₅₃×#479	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#478	C₂²	semidirect
77. C₅₃×#477	C₂²	semidirect
78. C₅₃×#476	C₂²	semidirect
79. C₅₃×#468	C₂²	semidirect
80. C₅₃×#468	C₂²	semidirect
81. C₅₃×#466	C₂²	semidirect
82. C₅₃×#465	C₂²	semidirect
83. C₅₃×#465	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#463	C₂²	semidirect
94. C₅₃×#461	C₂²	semidirect
95. C₅₃×#461	C₂²	semidirect
96. C₅₃×#461	C₂²	semidirect
97. C₅₃×#461	C₂²	semidirect
98. C₅₃×#461	C₂²	semidirect
99. C₅₃×#461	C₂²	semidirect
100. C₅₃×#460	C₂²	semidirect
101. C₅₃×#460	C₂²	semidirect
102. C₅₃×#460	C₂²	semidirect
103. C₅₃×#459	C₂²	semidirect
107. C₅₃×#449	C₂²	semidirect
108. C₅₃×#449	C₂²	semidirect
109. C₅₃×#448	C₂²	semidirect
110. C₅₃×#448	C₂²	semidirect
111. C₅₃×#448	C₂²	semidirect
112. C₅₃×#448	C₂²	semidirect
114. C₅₃×#446	C₂²	semidirect
115. C₈×Q₈×C₅₃	C₂²	semidirect
117. C₅₃×#440	C₂²	semidirect
120. C₄×SD₁₆×C₅₃	C₂²	semidirect
121. C₄×SD₁₆×C₅₃	C₂²	semidirect
123. C₄×D₈×C₅₃	C₂²	semidirect
124. C₅₃×#436	C₂²	semidirect
125. C₅₃×#435	C₂²	semidirect
126. C₈×D₄×C₅₃	C₂²	semidirect
127. C₈×D₄×C₅₃	C₂²	semidirect
128. C₅₃×#433	C₂²	semidirect
129. C₅₃×#431	C₂²	semidirect
130. C₅₃×#424	C₂²	semidirect
131. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
132. C₅₃×#419	C₂²	semidirect
133. C₅₃×#416	C₂²	semidirect
134. C₂×#103×C₅₃	C₂²	semidirect
544. #62052	C₅₃	direct (N × H)
584. #3552	C₂×C₅₃	semidirect
585. #3519	C₂×C₅₃	semidirect
586. #3397	C₂×C₅₃	semidirect
587. #3392	C₂×C₅₃	semidirect
588. #3372	C₂×C₅₃	semidirect
589. #3360	C₂×C₅₃	semidirect
590. #3329	C₂×C₅₃	semidirect
591. #3320	C₂×C₅₃	semidirect
592. #3303	C₂×C₅₃	semidirect
593. #3301	C₂×C₅₃	semidirect
594. D₄×SD₁₆	C₂×C₅₃	semidirect
595. D₄×SD₁₆	C₂×C₅₃	semidirect
596. #3272	C₂×C₅₃	semidirect
597. #3265	C₂×C₅₃	semidirect
598. #3260	C₂×C₅₃	semidirect
599. #3247	C₂×C₅₃	semidirect
600. #3221	C₂×C₅₃	semidirect
601. #3206	C₂×C₅₃	semidirect
602. #3123	C₂×C₅₃	semidirect
603. #3105	C₂×C₅₃	semidirect
604. #3042	C₂×C₅₃	semidirect
605. C₂×#461	C₂×C₅₃	semidirect
606. #2994	C₂×C₅₃	semidirect
620. #557	C₂²×C₅₃	semidirect
621. #556	C₂²×C₅₃	semidirect
629. D₄×Q₈	C₂²×C₅₃	semidirect
630. D₄×Q₈	C₂²×C₅₃	semidirect
631. #548	C₂²×C₅₃	semidirect
632. #547	C₂²×C₅₃	semidirect
639. #541	C₂²×C₅₃	semidirect
643. #536	C₂²×C₅₃	semidirect
645. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
647. #529	C₂²×C₅₃	semidirect
652. #496	C₂²×C₅₃	semidirect
653. #492	C₂²×C₅₃	semidirect
654. #492	C₂²×C₅₃	semidirect
655. #492	C₂²×C₅₃	semidirect
656. #491	C₂²×C₅₃	semidirect
657. #488	C₂²×C₅₃	semidirect
658. #487	C₂²×C₅₃	semidirect
659. #487	C₂²×C₅₃	semidirect
660. #485	C₂²×C₅₃	semidirect
661. #485	C₂²×C₅₃	semidirect
662. #484	C₂²×C₅₃	semidirect
663. #481	C₂²×C₅₃	semidirect
664. #479	C₂²×C₅₃	semidirect
665. #479	C₂²×C₅₃	semidirect
667. #478	C₂²×C₅₃	semidirect
668. #478	C₂²×C₅₃	semidirect
669. #477	C₂²×C₅₃	semidirect
670. #476	C₂²×C₅₃	semidirect
671. #468	C₂²×C₅₃	semidirect
672. #468	C₂²×C₅₃	semidirect
673. #466	C₂²×C₅₃	semidirect
674. #465	C₂²×C₅₃	semidirect
675. #465	C₂²×C₅₃	semidirect
676. #465	C₂²×C₅₃	semidirect
679. #463	C₂²×C₅₃	semidirect
680. #463	C₂²×C₅₃	semidirect
681. #463	C₂²×C₅₃	semidirect
686. #461	C₂²×C₅₃	semidirect
687. #461	C₂²×C₅₃	semidirect
688. #461	C₂²×C₅₃	semidirect
689. #461	C₂²×C₅₃	semidirect
690. #461	C₂²×C₅₃	semidirect
691. #461	C₂²×C₅₃	semidirect
692. #460	C₂²×C₅₃	semidirect
693. #460	C₂²×C₅₃	semidirect
694. #460	C₂²×C₅₃	semidirect
695. #459	C₂²×C₅₃	semidirect
699. #449	C₂²×C₅₃	semidirect
700. #449	C₂²×C₅₃	semidirect
701. #448	C₂²×C₅₃	semidirect
702. #448	C₂²×C₅₃	semidirect
703. #448	C₂²×C₅₃	semidirect
704. #448	C₂²×C₅₃	semidirect
706. #446	C₂²×C₅₃	semidirect
707. C₈×Q₈	C₂²×C₅₃	semidirect
709. #440	C₂²×C₅₃	semidirect
712. C₄×SD₁₆	C₂²×C₅₃	semidirect
713. C₄×SD₁₆	C₂²×C₅₃	semidirect
715. C₄×D₈	C₂²×C₅₃	semidirect
716. #436	C₂²×C₅₃	semidirect
717. #435	C₂²×C₅₃	semidirect
718. C₈×D₄	C₂²×C₅₃	semidirect
719. C₈×D₄	C₂²×C₅₃	semidirect
720. #433	C₂²×C₅₃	semidirect
721. #431	C₂²×C₅₃	semidirect
722. #424	C₂²×C₅₃	semidirect
723. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
724. #419	C₂²×C₅₃	semidirect
725. #416	C₂²×C₅₃	semidirect
726. C₂×#103	C₂²×C₅₃	semidirect
727. C₅₃	#62052	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×#3552	2
C₅₃×#3519	2
C₅₃×#3397	2
C₅₃×#3392	2
C₅₃×#3372	2
C₅₃×#3360	2
C₅₃×#3329	2
C₅₃×#3320	2
C₅₃×#3303	2
C₅₃×#3301	2
D₄×SD₁₆×C₅₃	2
C₅₃×#3272	2
C₅₃×#3265	2
C₅₃×#3260	2
C₅₃×#3247	2
C₅₃×#3221	2
C₅₃×#3206	2
C₅₃×#3123	2
C₅₃×#3105	2
C₅₃×#3042	2
C₂×C₅₃×#461	2
C₅₃×#2994	2
#62052	53

Subgroups — C53×#62052 #27269564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62052 #27269564