Subgroups — C₅₃×#61437 #27268949

Order 13568.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3343	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3310	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3306	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3171	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3106	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3105	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₃	—	2	1	no	—
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
26	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#553	—	2	1	no	—
31	C₅₃×#552	—	2	1	no	—
32	C₅₃×#552	C₂²	1	2	yes	complemented
33	C₅₃×#551	—	2	2	no	—
34	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#548	—	2	1	no	—
37	C₅₃×#547	C₂²	1	2	yes	—
38	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#546	—	2	2	no	—
41	C₅₃×#546	—	2	1	no	—
42	C₅₃×#546	C₂²	1	2	yes	complemented
43	D₄²×C₅₃	C₂²	1	2	yes	—
44	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#532	C₂²	1	1	yes	characteristic
47	C₅₃×#532	C₂²	1	2	yes	complemented
48	C₅₃×#529	—	2	2	no	—
49	C₅₃×#529	C₂²	1	2	yes	complemented
50	C₅₃×#525	—	2	1	no	—
51	C₅₃×#525	—	2	1	no	—
52	C₅₃×#525	—	2	2	no	—
53	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
54	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
55	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
58	C₂×#117×C₅₃	—	2	1	no	—
59	C₅₃×#501	C₂²	1	2	yes	complemented
60	C₅₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#496	C₂²	1	2	yes	complemented
62	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#490	C₂²	1	2	yes	complemented
64	C₅₃×#489	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×#484	C₂²	1	2	yes	complemented
68	C₅₃×#483	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×#480	C₂²	1	2	yes	complemented
73	C₅₃×#478	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	2	yes	complemented
75	C₅₃×#477	C₂²	1	2	yes	complemented
76	C₅₃×#476	C₂²	1	2	yes	complemented
77	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#469	C₂²	1	2	yes	complemented
82	C₅₃×#469	C₂²	1	2	yes	complemented
83	C₅₃×#468	C₂²	1	2	yes	complemented
84	C₅₃×#468	C₂²	1	2	yes	complemented
85	C₅₃×#465	C₂²	1	2	yes	complemented
86	C₅₃×#465	C₂²	1	2	yes	complemented
87	C₅₃×#463	C₂²	1	2	yes	—
88	C₅₃×#463	C₂²	1	2	yes	complemented
89	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#460	C₂²	1	2	yes	complemented
92	C₅₃×#459	C₂²	1	2	yes	complemented
93	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#450	C₂²	1	2	yes	—
96	C₅₃×#450	C₂²	1	2	yes	complemented
97	C₅₃×#449	C₂²	1	2	yes	complemented
98	C₅₃×#449	C₂²	1	2	yes	complemented
99	C₅₃×#447	C₂²	1	2	yes	—
100	C₅₃×#447	C₂²	1	2	yes	complemented
101	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#442	C₂²	1	2	yes	—
104	C₅₃×#442	C₂²	1	2	yes	complemented
105	C₅₃×#440	C₂²	1	2	yes	complemented
106	C₅₃×#440	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
110	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
111	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
112	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
113	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
114	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
115	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
120	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
121	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#435	C₂²	1	2	yes	complemented
124	C₅₃×#435	C₂²	1	2	yes	complemented
125	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#431	C₂²	1	2	yes	complemented
127	C₅₃×#428	C₂²	1	2	yes	complemented
128	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#418	C₂²	1	2	yes	complemented
130	C₅₃×#417	C₂²	1	2	yes	complemented
131	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
132	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
133	C₄×M₁₆×C₅₃	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	2	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	—	2	2	no	—
140	C₂×#41×C₅₃	—	4	8	no	—
141	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
142	C₂×#41×C₅₃	C₂³	1	2	yes	—
143	C₂²×Q₈×C₅₃	—	2	1	no	—
144	C₂²×D₄×C₅₃	—	2	2	no	—
145	C₂²×D₄×C₅₃	—	2	1	no	—
146	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
148	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₅₃	—	2	1	no	—
150	C₂³×C₄×C₅₃	—	2	1	no	—
151	C₂³×C₄×C₅₃	—	2	2	no	—
152	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
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×D₈×C₅₃	—	2	4	no	—
158	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
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×D₈×C₅₃	C₂³	1	2	yes	—
163	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
164	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
165	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
171	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
172	#127×C₅₃	C₂³	1	1	yes	characteristic
173	#127×C₅₃	C₂³	1	2	yes	—
174	#126×C₅₃	—	2	2	no	—
175	#126×C₅₃	—	2	2	no	—
176	#126×C₅₃	—	2	2	no	—
177	#125×C₅₃	—	2	2	no	—
178	#125×C₅₃	—	2	1	no	—
179	#125×C₅₃	C₂³	1	2	yes	—
180	#124×C₅₃	—	2	2	no	—
181	#124×C₅₃	—	2	1	no	—
182	#124×C₅₃	—	2	2	no	—
183	#124×C₅₃	C₂³	1	2	yes	—
184	#123×C₅₃	—	2	2	no	—
185	#123×C₅₃	—	2	2	no	—
186	#123×C₅₃	—	2	2	no	—
187	#123×C₅₃	—	2	2	no	—
188	#123×C₅₃	—	2	2	no	—
189	#123×C₅₃	—	2	2	no	—
190	#123×C₅₃	—	2	2	no	—
191	C₂²⋊Q₈×C₅₃	—	2	1	no	—
192	C₂²⋊Q₈×C₅₃	—	2	2	no	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	1	no	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	1	no	—
197	C₂²⋊Q₈×C₅₃	—	2	1	no	—
198	C₂²⋊Q₈×C₅₃	—	2	1	no	—
199	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
201	#121×C₅₃	—	2	2	no	—
202	#121×C₅₃	—	2	1	no	—
203	#121×C₅₃	—	2	1	no	—
204	#121×C₅₃	—	2	2	no	—
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	1	no	—
207	#121×C₅₃	—	2	1	no	—
208	#121×C₅₃	—	2	1	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	C₂³	1	2	yes	—
211	#121×C₅₃	C₂³	1	2	yes	—
212	#121×C₅₃	C₂³	1	2	yes	—
213	#121×C₅₃	C₂³	1	2	yes	—
214	#120×C₅₃	—	2	2	no	—
215	#120×C₅₃	—	2	2	no	—
216	#120×C₅₃	—	2	2	no	—
217	#120×C₅₃	—	2	2	no	—
218	C₄×Q₈×C₅₃	—	2	1	no	—
219	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
220	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
223	C₄×D₄×C₅₃	—	2	1	no	—
224	C₄×D₄×C₅₃	—	2	1	no	—
225	C₄×D₄×C₅₃	—	2	2	no	—
226	C₄×D₄×C₅₃	—	2	1	no	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	—	2	1	no	—
229	C₄×D₄×C₅₃	—	2	1	no	—
230	C₄×D₄×C₅₃	—	2	2	no	—
231	C₄×D₄×C₅₃	—	2	2	no	—
232	C₄×D₄×C₅₃	—	2	2	no	—
233	C₄×D₄×C₅₃	—	2	2	no	—
234	C₄×D₄×C₅₃	D₄	1	2	yes	—
235	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
236	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₃	C₂³	1	2	yes	—
243	C₄×D₄×C₅₃	C₂³	1	2	yes	—
244	C₄×D₄×C₅₃	C₂³	1	2	yes	—
245	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₅₃	C₂³	1	2	yes	—
248	C₄×D₄×C₅₃	C₂³	1	2	yes	—
249	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
250	#117×C₅₃	—	2	1	no	—
251	#117×C₅₃	—	2	1	no	—
252	#117×C₅₃	—	2	2	no	—
253	#117×C₅₃	—	2	2	no	—
254	#117×C₅₃	—	2	2	no	—
255	#117×C₅₃	—	2	1	no	—
256	#117×C₅₃	D₄	1	1	yes	characteristic
257	#117×C₅₃	D₄	1	2	yes	—
258	#117×C₅₃	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
260	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
268	C₂×C₄²×C₅₃	—	2	2	no	—
269	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
271	#107×C₅₃	C₂³	1	1	yes	characteristic
272	#107×C₅₃	C₂³	1	2	yes	—
273	#107×C₅₃	C₂³	1	1	yes	characteristic
274	#107×C₅₃	C₂³	1	1	yes	characteristic
275	#107×C₅₃	C₂³	1	1	yes	characteristic
276	#107×C₅₃	C₂³	1	2	yes	—
277	#106×C₅₃	C₂³	1	2	yes	—
278	#106×C₅₃	C₂³	1	2	yes	—
279	#106×C₅₃	C₂³	1	2	yes	—
280	#106×C₅₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
285	#103×C₅₃	C₂³	1	2	yes	—
286	#103×C₅₃	C₂³	1	2	yes	—
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	2	yes	—
289	#102×C₅₃	C₂³	1	2	yes	—
290	#102×C₅₃	C₂³	1	2	yes	—
291	#102×C₅₃	C₂³	1	1	yes	characteristic
292	#102×C₅₃	C₂³	1	2	yes	—
293	#102×C₅₃	C₂³	1	1	yes	characteristic
294	#102×C₅₃	C₂³	1	2	yes	—
295	#102×C₅₃	C₂³	1	2	yes	—
296	#102×C₅₃	C₂³	1	1	yes	characteristic
297	#102×C₅₃	C₂³	1	1	yes	characteristic
298	#102×C₅₃	C₂³	1	1	yes	characteristic
299	#102×C₅₃	C₂³	1	1	yes	characteristic
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	2	yes	—
304	#102×C₅₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	#97×C₅₃	C₂³	1	2	yes	—
310	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
312	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	C₂⁴×C₅₃	—	2	1	no	—
318	#41×C₅₃	—	2	4	no	—
319	#41×C₅₃	—	2	4	no	—
320	#41×C₅₃	—	4	2	no	—
321	#41×C₅₃	—	4	8	no	—
322	#41×C₅₃	—	4	8	no	—
323	#41×C₅₃	—	4	4	no	—
324	#41×C₅₃	—	4	4	no	—
325	#41×C₅₃	—	4	4	no	—
326	C₂×Q₈×C₅₃	—	2	2	no	—
327	C₂×Q₈×C₅₃	—	2	1	no	—
328	C₂×Q₈×C₅₃	—	2	1	no	—
329	C₂×Q₈×C₅₃	—	4	4	no	—
330	C₂×Q₈×C₅₃	C₂×D₄	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	2	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	2	no	—
341	C₂×D₄×C₅₃	—	2	1	no	—
342	C₂×D₄×C₅₃	—	2	1	no	—
343	C₂×D₄×C₅₃	—	2	2	no	—
344	C₂×D₄×C₅₃	—	2	1	no	—
345	C₂×D₄×C₅₃	—	2	2	no	—
346	C₂×D₄×C₅₃	—	2	1	no	—
347	C₂×D₄×C₅₃	—	4	1	no	—
348	C₂×D₄×C₅₃	—	4	1	no	—
349	C₂×D₄×C₅₃	—	4	2	no	—
350	C₂×D₄×C₅₃	—	4	8	no	—
351	C₂×D₄×C₅₃	—	4	4	no	—
352	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
353	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
354	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
357	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₅₃	—	2	1	no	—
360	C₂²×C₄×C₅₃	—	2	2	no	—
361	C₂²×C₄×C₅₃	—	2	1	no	—
362	C₂²×C₄×C₅₃	—	2	2	no	—
363	C₂²×C₄×C₅₃	—	2	1	no	—
364	C₂²×C₄×C₅₃	—	2	1	no	—
365	C₂²×C₄×C₅₃	—	2	2	no	—
366	C₂²×C₄×C₅₃	—	2	1	no	—
367	C₂²×C₄×C₅₃	—	2	2	no	—
368	C₂²×C₄×C₅₃	—	2	1	no	—
369	C₂²×C₄×C₅₃	—	2	1	no	—
370	C₂²×C₄×C₅₃	—	2	1	no	—
371	C₂²×C₄×C₅₃	—	2	1	no	—
372	C₂²×C₄×C₅₃	—	2	1	no	—
373	C₂²×C₄×C₅₃	—	2	2	no	—
374	C₂²×C₄×C₅₃	—	2	2	no	—
375	C₂²×C₄×C₅₃	—	4	8	no	—
376	C₂²×C₄×C₅₃	—	4	4	no	—
377	C₂²×C₄×C₅₃	—	4	4	no	—
378	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
379	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
381	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
384	SD₁₆×C₅₃	—	2	4	no	—
385	SD₁₆×C₅₃	—	2	4	no	—
386	SD₁₆×C₅₃	—	4	2	no	—
387	SD₁₆×C₅₃	—	4	2	no	—
388	D₈×C₅₃	—	2	2	no	—
389	D₈×C₅₃	—	2	2	no	—
390	D₈×C₅₃	—	2	4	no	—
391	D₈×C₅₃	—	2	2	no	—
392	D₈×C₅₃	—	4	2	no	—
393	D₈×C₅₃	#41	1	4	yes	complemented
394	M₁₆×C₅₃	—	2	4	no	—
395	M₁₆×C₅₃	—	4	2	no	—
396	C₂×C₈×C₅₃	—	2	2	no	—
397	C₂×C₈×C₅₃	—	4	1	no	—
398	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
402	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
403	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₅₃	—	2	1	no	—
405	C₄⋊C₄×C₅₃	—	2	1	no	—
406	C₄⋊C₄×C₅₃	—	2	2	no	—
407	C₄⋊C₄×C₅₃	—	2	2	no	—
408	C₄⋊C₄×C₅₃	—	2	2	no	—
409	C₄⋊C₄×C₅₃	—	2	1	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	—	2	2	no	—
416	C₄⋊C₄×C₅₃	—	2	2	no	—
417	C₄⋊C₄×C₅₃	—	2	1	no	—
418	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
428	C₂²⋊C₄×C₅₃	—	2	2	no	—
429	C₂²⋊C₄×C₅₃	—	2	2	no	—
430	C₂²⋊C₄×C₅₃	—	2	2	no	—
431	C₂²⋊C₄×C₅₃	—	2	1	no	—
432	C₂²⋊C₄×C₅₃	—	2	1	no	—
433	C₂²⋊C₄×C₅₃	—	2	2	no	—
434	C₂²⋊C₄×C₅₃	—	2	2	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	1	no	—
439	C₂²⋊C₄×C₅₃	—	2	1	no	—
440	C₂²⋊C₄×C₅₃	—	2	2	no	—
441	C₂²⋊C₄×C₅₃	—	2	1	no	—
442	C₂²⋊C₄×C₅₃	—	2	1	no	—
443	C₂²⋊C₄×C₅₃	—	2	1	no	—
444	C₂²⋊C₄×C₅₃	—	2	2	no	—
445	C₂²⋊C₄×C₅₃	—	2	2	no	—
446	C₂²⋊C₄×C₅₃	—	2	2	no	—
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	—	2	2	no	—
449	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
451	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
452	C₄²×C₅₃	—	2	2	no	—
453	C₄²×C₅₃	—	2	2	no	—
454	C₄²×C₅₃	—	2	2	no	—
455	C₄²×C₅₃	C₂×D₄	1	2	yes	—
456	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₅₃	C₂×D₄	1	2	yes	—
458	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
460	C₄²×C₅₃	C₂⁴	1	2	yes	—
461	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
462	C₂³×C₅₃	—	2	1	no	—
463	C₂³×C₅₃	—	2	1	no	—
464	C₂³×C₅₃	—	2	1	no	—
465	C₂³×C₅₃	—	2	2	no	—
466	C₂³×C₅₃	—	2	1	no	—
467	C₂³×C₅₃	—	4	2	no	—
468	C₂³×C₅₃	—	4	2	no	—
469	C₂³×C₅₃	—	4	4	no	—
470	C₂³×C₅₃	—	4	4	no	—
471	C₂³×C₅₃	—	4	2	no	—
472	C₂³×C₅₃	—	4	2	no	—
473	C₂³×C₅₃	—	8	1	no	—
474	C₂³×C₅₃	—	8	1	no	—
475	C₂³×C₅₃	—	8	2	no	—
476	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
477	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
478	Q₈×C₅₃	—	2	2	no	—
479	Q₈×C₅₃	—	2	2	no	—
480	Q₈×C₅₃	—	2	2	no	—
481	Q₈×C₅₃	—	4	4	no	—
482	Q₈×C₅₃	—	4	2	no	—
483	Q₈×C₅₃	—	8	1	no	—
484	D₄×C₅₃	—	2	4	no	—
485	D₄×C₅₃	—	2	2	no	—
486	D₄×C₅₃	—	2	1	no	—
487	D₄×C₅₃	—	2	1	no	—
488	D₄×C₅₃	—	2	2	no	—
489	D₄×C₅₃	—	2	1	no	—
490	D₄×C₅₃	—	2	1	no	—
491	D₄×C₅₃	—	2	1	no	—
492	D₄×C₅₃	—	2	2	no	—
493	D₄×C₅₃	—	2	1	no	—
494	D₄×C₅₃	—	4	4	no	—
495	D₄×C₅₃	—	4	2	no	—
496	D₄×C₅₃	—	4	2	no	—
497	D₄×C₅₃	—	4	4	no	—
498	D₄×C₅₃	—	4	4	no	—
499	D₄×C₅₃	—	4	4	no	—
500	D₄×C₅₃	—	4	4	no	—
501	D₄×C₅₃	—	4	4	no	—
502	D₄×C₅₃	—	4	2	no	—
503	D₄×C₅₃	—	8	2	no	—
504	D₄×C₅₃	—	8	1	no	—
505	D₄×C₅₃	—	8	2	no	—
506	D₄×C₅₃	C₂×#41	1	2	yes	—
507	D₄×C₅₃	C₂×#41	1	2	yes	complemented
508	C₂×C₄×C₅₃	—	2	4	no	—
509	C₂×C₄×C₅₃	—	2	1	no	—
510	C₂×C₄×C₅₃	—	2	2	no	—
511	C₂×C₄×C₅₃	—	2	1	no	—
512	C₂×C₄×C₅₃	—	2	2	no	—
513	C₂×C₄×C₅₃	—	2	1	no	—
514	C₂×C₄×C₅₃	—	2	2	no	—
515	C₂×C₄×C₅₃	—	2	1	no	—
516	C₂×C₄×C₅₃	—	2	1	no	—
517	C₂×C₄×C₅₃	—	2	1	no	—
518	C₂×C₄×C₅₃	—	2	2	no	—
519	C₂×C₄×C₅₃	—	2	2	no	—
520	C₂×C₄×C₅₃	—	4	2	no	—
521	C₂×C₄×C₅₃	—	4	1	no	—
522	C₂×C₄×C₅₃	—	4	4	no	—
523	C₂×C₄×C₅₃	—	4	4	no	—
524	C₂×C₄×C₅₃	—	4	4	no	—
525	C₂×C₄×C₅₃	—	4	4	no	—
526	C₂×C₄×C₅₃	—	4	2	no	—
527	C₂×C₄×C₅₃	—	4	2	no	—
528	C₂×C₄×C₅₃	—	4	2	no	—
529	C₂×C₄×C₅₃	—	4	2	no	—
530	C₂×C₄×C₅₃	—	4	2	no	—
531	C₂×C₄×C₅₃	—	4	2	no	—
532	C₂×C₄×C₅₃	—	4	2	no	—
533	C₂×C₄×C₅₃	—	4	2	no	—
534	C₂×C₄×C₅₃	—	4	2	no	—
535	C₂×C₄×C₅₃	—	4	4	no	—
536	C₂×C₄×C₅₃	—	4	2	no	—
537	C₂×C₄×C₅₃	—	8	2	no	—
538	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	4	yes	complemented
539	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
542	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
548	C₈×C₅₃	—	2	1	no	—
549	C₈×C₅₃	—	2	2	no	—
550	C₈×C₅₃	—	2	1	no	—
551	C₈×C₅₃	—	2	1	no	—
552	C₈×C₅₃	—	2	2	no	—
553	C₈×C₅₃	C₂×#41	1	2	yes	complemented
554	#61437	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
555	C₂²×C₅₃	—	2	1	no	—
556	C₂²×C₅₃	—	2	1	no	—
557	C₂²×C₅₃	—	2	2	no	—
558	C₂²×C₅₃	—	2	2	no	—
559	C₂²×C₅₃	—	2	2	no	—
560	C₂²×C₅₃	—	2	2	no	—
561	C₂²×C₅₃	—	2	2	no	—
562	C₂²×C₅₃	—	4	1	no	—
563	C₂²×C₅₃	—	4	1	no	—
564	C₂²×C₅₃	—	4	1	no	—
565	C₂²×C₅₃	—	4	1	no	—
566	C₂²×C₅₃	—	4	1	no	—
567	C₂²×C₅₃	—	4	2	no	—
568	C₂²×C₅₃	—	4	1	no	—
569	C₂²×C₅₃	—	4	1	no	—
570	C₂²×C₅₃	—	4	1	no	—
571	C₂²×C₅₃	—	4	2	no	—
572	C₂²×C₅₃	—	4	2	no	—
573	C₂²×C₅₃	—	4	1	no	—
574	C₂²×C₅₃	—	4	1	no	—
575	C₂²×C₅₃	—	8	4	no	—
576	C₂²×C₅₃	—	8	4	no	—
577	C₂²×C₅₃	—	8	8	no	—
578	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
579	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
580	C₄×C₅₃	—	2	1	no	—
581	C₄×C₅₃	—	2	2	no	—
582	C₄×C₅₃	—	2	1	no	—
583	C₄×C₅₃	—	2	2	no	—
584	C₄×C₅₃	—	2	1	no	—
585	C₄×C₅₃	—	2	2	no	—
586	C₄×C₅₃	—	4	2	no	—
587	C₄×C₅₃	—	4	2	no	—
588	C₄×C₅₃	—	4	1	no	—
589	C₄×C₅₃	—	4	1	no	—
590	C₄×C₅₃	—	4	1	no	—
591	C₄×C₅₃	—	4	2	no	—
592	C₄×C₅₃	—	4	1	no	—
593	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
594	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
595	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
596	C₄×C₅₃	#585	1	1	yes	characteristic
597	#3475	C₂×C₅₃	1	1	yes	characteristic, complemented
598	D₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
599	#3397	C₂×C₅₃	1	1	yes	characteristic, complemented
600	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
601	#3367	C₂×C₅₃	1	1	yes	characteristic, complemented
602	#3366	C₂×C₅₃	1	1	yes	characteristic, complemented
603	#3354	C₂×C₅₃	1	1	yes	characteristic, complemented
604	#3343	C₂×C₅₃	1	2	yes	complemented
605	#3330	C₂×C₅₃	1	1	yes	characteristic, complemented
606	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
607	#3310	C₂×C₅₃	1	2	yes	complemented
608	#3306	C₂×C₅₃	1	2	yes	complemented
609	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
610	#3264	C₂×C₅₃	1	2	yes	complemented
611	#3171	C₂×C₅₃	1	2	yes	complemented
612	#3167	C₂×C₅₃	1	1	yes	characteristic, complemented
613	#3106	C₂×C₅₃	1	2	yes	complemented
614	#3105	C₂×C₅₃	1	2	yes	complemented
615	#3101	C₂×C₅₃	1	1	yes	characteristic, complemented
616	#3100	C₂×C₅₃	1	1	yes	characteristic, complemented
617	#2965	C₂×C₅₃	1	1	yes	characteristic, complemented
618	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	2	yes	complemented
619	C₂×C₄×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
620	C₂×C₅₃	—	2	2	no	—
621	C₂×C₅₃	—	4	2	no	—
622	C₂×C₅₃	—	4	2	no	—
623	C₂×C₅₃	—	4	2	no	—
624	C₂×C₅₃	—	8	1	no	—
625	C₂×C₅₃	—	8	2	no	—
626	C₂×C₅₃	—	8	1	no	—
627	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
628	C₂×C₅₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
629	C₂×C₅₃	#3584	1	1	yes	characteristic
630	C₂²×#41	—	2	1	no	—
631	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
632	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
633	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
634	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
635	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
636	#553	—	2	1	no	—
637	#552	—	2	1	no	—
638	#552	C₂²×C₅₃	1	2	yes	complemented
639	#551	—	2	2	no	—
640	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
641	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
642	#548	—	2	1	no	—
643	#547	C₂²×C₅₃	1	2	yes	—
644	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
645	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
646	#546	—	2	2	no	—
647	#546	—	2	1	no	—
648	#546	C₂²×C₅₃	1	2	yes	complemented
649	D₄²	C₂²×C₅₃	1	2	yes	—
650	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
651	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
652	#532	C₂²×C₅₃	1	1	yes	characteristic
653	#532	C₂²×C₅₃	1	2	yes	complemented
654	#529	—	2	2	no	—
655	#529	C₂²×C₅₃	1	2	yes	complemented
656	#525	—	2	1	no	—
657	#525	—	2	1	no	—
658	#525	—	2	2	no	—
659	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
660	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
661	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
662	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
664	C₂×#117	—	2	1	no	—
665	#501	C₂²×C₅₃	1	2	yes	complemented
666	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
667	#496	C₂²×C₅₃	1	2	yes	complemented
668	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
669	#490	C₂²×C₅₃	1	2	yes	complemented
670	#489	C₂²×C₅₃	1	2	yes	complemented
671	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
672	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	#484	C₂²×C₅₃	1	2	yes	complemented
674	#483	C₂²×C₅₃	1	2	yes	complemented
675	#482	C₂²×C₅₃	1	2	yes	complemented
676	#482	C₂²×C₅₃	1	2	yes	complemented
677	#481	C₂²×C₅₃	1	2	yes	complemented
678	#480	C₂²×C₅₃	1	2	yes	complemented
679	#478	C₂²×C₅₃	1	2	yes	complemented
680	#478	C₂²×C₅₃	1	2	yes	complemented
681	#477	C₂²×C₅₃	1	2	yes	complemented
682	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
684	#476	C₂²×C₅₃	1	2	yes	complemented
685	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
686	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#469	C₂²×C₅₃	1	2	yes	complemented
688	#469	C₂²×C₅₃	1	2	yes	complemented
689	#468	C₂²×C₅₃	1	2	yes	complemented
690	#468	C₂²×C₅₃	1	2	yes	complemented
691	#465	C₂²×C₅₃	1	2	yes	complemented
692	#465	C₂²×C₅₃	1	2	yes	complemented
693	#463	C₂²×C₅₃	1	2	yes	—
694	#463	C₂²×C₅₃	1	2	yes	complemented
695	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
697	#460	C₂²×C₅₃	1	2	yes	complemented
698	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
699	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
700	#459	C₂²×C₅₃	1	2	yes	complemented
701	#450	C₂²×C₅₃	1	2	yes	—
702	#450	C₂²×C₅₃	1	2	yes	complemented
703	#449	C₂²×C₅₃	1	2	yes	complemented
704	#449	C₂²×C₅₃	1	2	yes	complemented
705	#447	C₂²×C₅₃	1	2	yes	—
706	#447	C₂²×C₅₃	1	2	yes	complemented
707	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#442	C₂²×C₅₃	1	2	yes	—
710	#442	C₂²×C₅₃	1	2	yes	complemented
711	#440	C₂²×C₅₃	1	2	yes	complemented
712	#440	C₂²×C₅₃	1	2	yes	complemented
713	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
714	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
715	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
716	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
717	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
718	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
719	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
720	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
721	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
724	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
725	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
726	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
727	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
728	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
729	#435	C₂²×C₅₃	1	2	yes	complemented
730	#435	C₂²×C₅₃	1	2	yes	complemented
731	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
732	#431	C₂²×C₅₃	1	2	yes	complemented
733	#428	C₂²×C₅₃	1	2	yes	complemented
734	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
735	#418	C₂²×C₅₃	1	2	yes	complemented
736	#417	C₂²×C₅₃	1	2	yes	complemented
737	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
738	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
739	C₄×M₁₆	C₂²×C₅₃	1	2	yes	complemented
740	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
741	C₅₃	#61437	1	1	yes	characteristic, direct product factor, Sylow
742	C₂×#41	—	2	1	no	—
743	C₂×#41	—	2	2	no	—
744	C₂×#41	—	2	1	no	—
745	C₂×#41	—	2	1	no	—
746	C₂×#41	—	2	2	no	—
747	C₂×#41	—	4	8	no	—
748	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
749	C₂×#41	C₂³×C₅₃	1	2	yes	—
750	C₂²×Q₈	—	2	1	no	—
751	C₂²×D₄	—	2	2	no	—
752	C₂²×D₄	—	2	1	no	—
753	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
754	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
755	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
756	C₂³×C₄	—	2	1	no	—
757	C₂³×C₄	—	2	1	no	—
758	C₂³×C₄	—	2	2	no	—
759	AGL(1,ℤ/8)	—	2	8	no	—
760	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
761	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
762	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
763	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
764	C₂×D₈	—	2	4	no	—
765	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
766	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
767	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
768	C₂×D₈	C₂³×C₅₃	1	2	yes	—
769	C₂×D₈	C₂³×C₅₃	1	2	yes	—
770	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
771	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
772	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
773	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
774	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
775	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
776	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
777	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
778	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
779	#127	C₂³×C₅₃	1	1	yes	characteristic
780	#127	C₂³×C₅₃	1	2	yes	—
781	#126	—	2	2	no	—
782	#126	—	2	2	no	—
783	#126	—	2	2	no	—
784	#125	—	2	2	no	—
785	#125	—	2	1	no	—
786	#125	C₂³×C₅₃	1	2	yes	—
787	#124	—	2	2	no	—
788	#124	—	2	1	no	—
789	#124	—	2	2	no	—
790	#124	C₂³×C₅₃	1	2	yes	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	C₂²⋊Q₈	—	2	1	no	—
799	C₂²⋊Q₈	—	2	1	no	—
800	C₂²⋊Q₈	—	2	1	no	—
801	C₂²⋊Q₈	—	2	1	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	—	2	1	no	—
805	C₂²⋊Q₈	—	2	2	no	—
806	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
807	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
808	#121	—	2	1	no	—
809	#121	—	2	1	no	—
810	#121	—	2	1	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	1	no	—
814	#121	—	2	1	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	C₂³×C₅₃	1	2	yes	—
818	#121	C₂³×C₅₃	1	2	yes	—
819	#121	C₂³×C₅₃	1	2	yes	—
820	#121	C₂³×C₅₃	1	2	yes	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	#120	—	2	2	no	—
825	C₄×Q₈	—	2	1	no	—
826	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
827	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
828	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
829	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	D₄×C₅₃	1	2	yes	—
842	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
848	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
849	C₄×D₄	C₂³×C₅₃	1	2	yes	—
850	C₄×D₄	C₂³×C₅₃	1	2	yes	—
851	C₄×D₄	C₂³×C₅₃	1	2	yes	—
852	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
853	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₅₃	1	2	yes	—
855	C₄×D₄	C₂³×C₅₃	1	2	yes	—
856	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
857	#117	—	2	1	no	—
858	#117	—	2	1	no	—
859	#117	—	2	1	no	—
860	#117	—	2	2	no	—
861	#117	—	2	2	no	—
862	#117	—	2	2	no	—
863	#117	D₄×C₅₃	1	1	yes	characteristic
864	#117	D₄×C₅₃	1	2	yes	—
865	#117	C₂³×C₅₃	1	2	yes	—
866	C₂×C₄⋊C₄	—	2	1	no	—
867	C₂×C₄⋊C₄	—	2	1	no	—
868	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
869	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
870	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
871	C₂×C₂²⋊C₄	—	2	1	no	—
872	C₂×C₂²⋊C₄	—	2	2	no	—
873	C₂×C₂²⋊C₄	—	2	1	no	—
874	C₂×C₂²⋊C₄	—	2	2	no	—
875	C₂×C₄²	—	2	2	no	—
876	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
877	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
878	#107	C₂³×C₅₃	1	1	yes	characteristic
879	#107	C₂³×C₅₃	1	1	yes	characteristic
880	#107	C₂³×C₅₃	1	1	yes	characteristic
881	#107	C₂³×C₅₃	1	1	yes	characteristic
882	#107	C₂³×C₅₃	1	2	yes	—
883	#107	C₂³×C₅₃	1	2	yes	—
884	#106	C₂³×C₅₃	1	2	yes	—
885	#106	C₂³×C₅₃	1	2	yes	—
886	#106	C₂³×C₅₃	1	2	yes	—
887	#106	C₂³×C₅₃	1	2	yes	—
888	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
889	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
890	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
891	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
892	#103	C₂³×C₅₃	1	2	yes	—
893	#103	C₂³×C₅₃	1	2	yes	—
894	#103	C₂³×C₅₃	1	2	yes	—
895	#103	C₂³×C₅₃	1	2	yes	—
896	#102	C₂³×C₅₃	1	1	yes	characteristic
897	#102	C₂³×C₅₃	1	1	yes	characteristic
898	#102	C₂³×C₅₃	1	1	yes	characteristic
899	#102	C₂³×C₅₃	1	1	yes	characteristic
900	#102	C₂³×C₅₃	1	1	yes	characteristic
901	#102	C₂³×C₅₃	1	1	yes	characteristic
902	#102	C₂³×C₅₃	1	1	yes	characteristic
903	#102	C₂³×C₅₃	1	1	yes	characteristic
904	#102	C₂³×C₅₃	1	2	yes	—
905	#102	C₂³×C₅₃	1	2	yes	—
906	#102	C₂³×C₅₃	1	2	yes	—
907	#102	C₂³×C₅₃	1	2	yes	—
908	#102	C₂³×C₅₃	1	2	yes	—
909	#102	C₂³×C₅₃	1	2	yes	—
910	#102	C₂³×C₅₃	1	2	yes	—
911	#102	C₂³×C₅₃	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
913	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
915	#97	C₂³×C₅₃	1	2	yes	—
916	#97	C₂³×C₅₃	1	2	yes	—
917	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
918	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
919	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
920	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
921	C₄×C₈	C₂³×C₅₃	1	2	yes	—
922	C₂⁴	—	2	1	no	—
923	C₂⁴	—	2	2	no	—
924	C₂⁴	—	2	1	no	—
925	#41	—	2	4	no	—
926	#41	—	2	4	no	—
927	#41	—	4	2	no	—
928	#41	—	4	8	no	—
929	#41	—	4	8	no	—
930	#41	—	4	4	no	—
931	#41	—	4	4	no	—
932	#41	—	4	4	no	—
933	C₂×Q₈	—	2	2	no	—
934	C₂×Q₈	—	2	1	no	—
935	C₂×Q₈	—	2	1	no	—
936	C₂×Q₈	—	4	4	no	—
937	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
938	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	4	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	4	1	no	—
955	C₂×D₄	—	4	1	no	—
956	C₂×D₄	—	4	2	no	—
957	C₂×D₄	—	4	8	no	—
958	C₂×D₄	—	4	4	no	—
959	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
960	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
961	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
962	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
963	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
964	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
965	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	2	1	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	4	8	no	—
983	C₂²×C₄	—	4	4	no	—
984	C₂²×C₄	—	4	4	no	—
985	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
986	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
987	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
988	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
989	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
990	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
991	SD₁₆	—	2	4	no	—
992	SD₁₆	—	2	4	no	—
993	SD₁₆	—	4	2	no	—
994	SD₁₆	—	4	2	no	—
995	D₈	—	2	2	no	—
996	D₈	—	2	2	no	—
997	D₈	—	2	4	no	—
998	D₈	—	2	2	no	—
999	D₈	—	4	2	no	—
1000	D₈	#41×C₅₃	1	4	yes	complemented
1001	M₁₆	—	2	4	no	—
1002	M₁₆	—	4	2	no	—
1003	C₂×C₈	—	2	2	no	—
1004	C₂×C₈	—	4	1	no	—
1005	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1006	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1007	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1008	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1009	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1010	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1026	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1027	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1028	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1029	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1030	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1031	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1032	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1033	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1034	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1057	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1058	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1059	C₄²	—	2	2	no	—
1060	C₄²	—	2	2	no	—
1061	C₄²	—	2	2	no	—
1062	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1063	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1064	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1065	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1066	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1067	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1068	C₄²	C₂⁴×C₅₃	1	2	yes	—
1069	C₂³	—	2	1	no	—
1070	C₂³	—	2	1	no	—
1071	C₂³	—	2	1	no	—
1072	C₂³	—	2	1	no	—
1073	C₂³	—	2	2	no	—
1074	C₂³	—	4	2	no	—
1075	C₂³	—	4	2	no	—
1076	C₂³	—	4	4	no	—
1077	C₂³	—	4	4	no	—
1078	C₂³	—	4	2	no	—
1079	C₂³	—	4	2	no	—
1080	C₂³	—	8	1	no	—
1081	C₂³	—	8	1	no	—
1082	C₂³	—	8	2	no	—
1083	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1084	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1085	Q₈	—	2	2	no	—
1086	Q₈	—	2	2	no	—
1087	Q₈	—	2	2	no	—
1088	Q₈	—	4	4	no	—
1089	Q₈	—	4	2	no	—
1090	Q₈	—	8	1	no	—
1091	D₄	—	2	4	no	—
1092	D₄	—	2	2	no	—
1093	D₄	—	2	1	no	—
1094	D₄	—	2	1	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	2	1	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	4	4	no	—
1102	D₄	—	4	2	no	—
1103	D₄	—	4	2	no	—
1104	D₄	—	4	4	no	—
1105	D₄	—	4	4	no	—
1106	D₄	—	4	4	no	—
1107	D₄	—	4	4	no	—
1108	D₄	—	4	4	no	—
1109	D₄	—	4	2	no	—
1110	D₄	—	8	2	no	—
1111	D₄	—	8	1	no	—
1112	D₄	—	8	2	no	—
1113	D₄	C₂×#41×C₅₃	1	2	yes	—
1114	D₄	C₂×#41×C₅₃	1	2	yes	complemented
1115	C₂×C₄	—	2	4	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	4	2	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	4	no	—
1130	C₂×C₄	—	4	4	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	2	no	—
1134	C₂×C₄	—	4	2	no	—
1135	C₂×C₄	—	4	2	no	—
1136	C₂×C₄	—	4	2	no	—
1137	C₂×C₄	—	4	2	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	4	no	—
1143	C₂×C₄	—	4	2	no	—
1144	C₂×C₄	—	8	2	no	—
1145	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	4	yes	complemented
1146	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1147	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1148	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1149	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1150	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1151	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1152	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1153	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1154	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1155	C₈	—	2	1	no	—
1156	C₈	—	2	2	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	2	2	no	—
1160	C₈	C₂×#41×C₅₃	1	2	yes	complemented
1161	C₂²	—	2	1	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	1	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	1	no	—
1181	C₂²	—	8	4	no	—
1182	C₂²	—	8	4	no	—
1183	C₂²	—	8	8	no	—
1184	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
1185	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1186	C₄	—	2	2	no	—
1187	C₄	—	2	1	no	—
1188	C₄	—	2	2	no	—
1189	C₄	—	2	1	no	—
1190	C₄	—	2	2	no	—
1191	C₄	—	2	1	no	—
1192	C₄	—	4	2	no	—
1193	C₄	—	4	1	no	—
1194	C₄	—	4	2	no	—
1195	C₄	—	4	1	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	2	no	—
1199	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
1200	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
1201	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1202	C₄	C₅₃×#585	1	1	yes	characteristic
1203	C₂	—	2	2	no	—
1204	C₂	—	4	2	no	—
1205	C₂	—	4	2	no	—
1206	C₂	—	4	2	no	—
1207	C₂	—	8	1	no	—
1208	C₂	—	8	2	no	—
1209	C₂	—	8	1	no	—
1210	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1211	C₂	C₂²×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
1212	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
socle	C₂²×C₅₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3475	C₂	semidirect
2. D₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#3397	C₂	semidirect
4. C₅₃×#3384	C₂	semidirect
5. C₅₃×#3367	C₂	semidirect
6. C₅₃×#3366	C₂	semidirect
7. C₅₃×#3354	C₂	semidirect
8. C₅₃×#3343	C₂	semidirect
9. C₅₃×#3330	C₂	semidirect
10. C₅₃×#3325	C₂	semidirect
11. C₅₃×#3310	C₂	semidirect
12. C₅₃×#3306	C₂	semidirect
13. C₅₃×#3272	C₂	semidirect
14. C₅₃×#3264	C₂	semidirect
15. C₅₃×#3171	C₂	semidirect
16. C₅₃×#3167	C₂	semidirect
17. C₅₃×#3106	C₂	semidirect
18. C₅₃×#3105	C₂	semidirect
19. C₅₃×#3101	C₂	semidirect
20. C₅₃×#3100	C₂	semidirect
21. C₅₃×#2965	C₂	semidirect
22. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
23. C₂×C₄×D₈×C₅₃	C₂	semidirect
27. C₅₃×#556	C₂²	semidirect
28. C₅₃×#555	C₂²	semidirect
29. C₅₃×#554	C₂²	semidirect
32. C₅₃×#552	C₂²	semidirect
34. C₅₃×#550	C₂²	semidirect
35. D₄×Q₈×C₅₃	C₂²	semidirect
38. C₅₃×#547	C₂²	semidirect
39. C₅₃×#547	C₂²	semidirect
42. C₅₃×#546	C₂²	semidirect
44. D₄²×C₅₃	C₂²	semidirect
45. C₅₃×#533	C₂²	semidirect
47. C₅₃×#532	C₂²	semidirect
49. C₅₃×#529	C₂²	semidirect
54. C₄×#41×C₅₃	C₂²	semidirect
56. C₂×C₄×D₄×C₅₃	C₂²	semidirect
57. C₂×C₄×D₄×C₅₃	C₂²	semidirect
59. C₅₃×#501	C₂²	semidirect
60. C₅₃×#498	C₂²	semidirect
61. C₅₃×#496	C₂²	semidirect
62. C₅₃×#492	C₂²	semidirect
63. C₅₃×#490	C₂²	semidirect
64. C₅₃×#489	C₂²	semidirect
65. C₅₃×#487	C₂²	semidirect
66. C₅₃×#486	C₂²	semidirect
67. C₅₃×#484	C₂²	semidirect
68. C₅₃×#483	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#481	C₂²	semidirect
72. C₅₃×#480	C₂²	semidirect
73. C₅₃×#478	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#477	C₂²	semidirect
76. C₅₃×#476	C₂²	semidirect
77. C₅₃×#476	C₂²	semidirect
78. C₅₃×#476	C₂²	semidirect
79. C₅₃×#474	C₂²	semidirect
80. C₅₃×#474	C₂²	semidirect
81. C₅₃×#469	C₂²	semidirect
82. C₅₃×#469	C₂²	semidirect
83. C₅₃×#468	C₂²	semidirect
84. C₅₃×#468	C₂²	semidirect
85. C₅₃×#465	C₂²	semidirect
86. C₅₃×#465	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#461	C₂²	semidirect
90. C₅₃×#461	C₂²	semidirect
91. C₅₃×#460	C₂²	semidirect
92. C₅₃×#459	C₂²	semidirect
93. C₅₃×#459	C₂²	semidirect
94. C₅₃×#459	C₂²	semidirect
96. C₅₃×#450	C₂²	semidirect
97. C₅₃×#449	C₂²	semidirect
98. C₅₃×#449	C₂²	semidirect
100. C₅₃×#447	C₂²	semidirect
101. C₅₃×#446	C₂²	semidirect
102. C₅₃×#446	C₂²	semidirect
104. C₅₃×#442	C₂²	semidirect
105. C₅₃×#440	C₂²	semidirect
106. C₅₃×#440	C₂²	semidirect
107. C₄×SD₁₆×C₅₃	C₂²	semidirect
108. C₄×SD₁₆×C₅₃	C₂²	semidirect
109. C₄×SD₁₆×C₅₃	C₂²	semidirect
110. C₄×SD₁₆×C₅₃	C₂²	semidirect
115. C₄×D₈×C₅₃	C₂²	semidirect
116. C₄×D₈×C₅₃	C₂²	semidirect
117. C₄×D₈×C₅₃	C₂²	semidirect
118. C₄×D₈×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×#435	C₂²	semidirect
124. C₅₃×#435	C₂²	semidirect
125. C₅₃×#431	C₂²	semidirect
126. C₅₃×#431	C₂²	semidirect
127. C₅₃×#428	C₂²	semidirect
128. C₂×#107×C₅₃	C₂²	semidirect
129. C₅₃×#418	C₂²	semidirect
130. C₅₃×#417	C₂²	semidirect
132. C₂×#102×C₅₃	C₂²	semidirect
133. C₄×M₁₆×C₅₃	C₂²	semidirect
134. C₂×C₄×C₈×C₅₃	C₂²	semidirect
393. D₈×C₅₃	#41	semidirect
507. D₄×C₅₃	C₂×#41	semidirect
538. C₂×C₄×C₅₃	AGL(1,ℤ/8)	semidirect
553. C₈×C₅₃	C₂×#41	semidirect
554. #61437	C₅₃	direct (N × H)
597. #3475	C₂×C₅₃	semidirect
598. D₄×#41	C₂×C₅₃	semidirect
599. #3397	C₂×C₅₃	semidirect
600. #3384	C₂×C₅₃	semidirect
601. #3367	C₂×C₅₃	semidirect
602. #3366	C₂×C₅₃	semidirect
603. #3354	C₂×C₅₃	semidirect
604. #3343	C₂×C₅₃	semidirect
605. #3330	C₂×C₅₃	semidirect
606. #3325	C₂×C₅₃	semidirect
607. #3310	C₂×C₅₃	semidirect
608. #3306	C₂×C₅₃	semidirect
609. #3272	C₂×C₅₃	semidirect
610. #3264	C₂×C₅₃	semidirect
611. #3171	C₂×C₅₃	semidirect
612. #3167	C₂×C₅₃	semidirect
613. #3106	C₂×C₅₃	semidirect
614. #3105	C₂×C₅₃	semidirect
615. #3101	C₂×C₅₃	semidirect
616. #3100	C₂×C₅₃	semidirect
617. #2965	C₂×C₅₃	semidirect
618. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
619. C₂×C₄×D₈	C₂×C₅₃	semidirect
633. #556	C₂²×C₅₃	semidirect
634. #555	C₂²×C₅₃	semidirect
635. #554	C₂²×C₅₃	semidirect
638. #552	C₂²×C₅₃	semidirect
640. #550	C₂²×C₅₃	semidirect
641. D₄×Q₈	C₂²×C₅₃	semidirect
644. #547	C₂²×C₅₃	semidirect
645. #547	C₂²×C₅₃	semidirect
648. #546	C₂²×C₅₃	semidirect
650. D₄²	C₂²×C₅₃	semidirect
651. #533	C₂²×C₅₃	semidirect
653. #532	C₂²×C₅₃	semidirect
655. #529	C₂²×C₅₃	semidirect
660. C₄×#41	C₂²×C₅₃	semidirect
662. C₂×C₄×D₄	C₂²×C₅₃	semidirect
663. C₂×C₄×D₄	C₂²×C₅₃	semidirect
665. #501	C₂²×C₅₃	semidirect
666. #498	C₂²×C₅₃	semidirect
667. #496	C₂²×C₅₃	semidirect
668. #492	C₂²×C₅₃	semidirect
669. #490	C₂²×C₅₃	semidirect
670. #489	C₂²×C₅₃	semidirect
671. #487	C₂²×C₅₃	semidirect
672. #486	C₂²×C₅₃	semidirect
673. #484	C₂²×C₅₃	semidirect
674. #483	C₂²×C₅₃	semidirect
675. #482	C₂²×C₅₃	semidirect
676. #482	C₂²×C₅₃	semidirect
677. #481	C₂²×C₅₃	semidirect
678. #480	C₂²×C₅₃	semidirect
679. #478	C₂²×C₅₃	semidirect
680. #478	C₂²×C₅₃	semidirect
681. #477	C₂²×C₅₃	semidirect
682. #476	C₂²×C₅₃	semidirect
683. #476	C₂²×C₅₃	semidirect
684. #476	C₂²×C₅₃	semidirect
685. #474	C₂²×C₅₃	semidirect
686. #474	C₂²×C₅₃	semidirect
687. #469	C₂²×C₅₃	semidirect
688. #469	C₂²×C₅₃	semidirect
689. #468	C₂²×C₅₃	semidirect
690. #468	C₂²×C₅₃	semidirect
691. #465	C₂²×C₅₃	semidirect
692. #465	C₂²×C₅₃	semidirect
694. #463	C₂²×C₅₃	semidirect
695. #461	C₂²×C₅₃	semidirect
696. #461	C₂²×C₅₃	semidirect
697. #460	C₂²×C₅₃	semidirect
698. #459	C₂²×C₅₃	semidirect
699. #459	C₂²×C₅₃	semidirect
700. #459	C₂²×C₅₃	semidirect
702. #450	C₂²×C₅₃	semidirect
703. #449	C₂²×C₅₃	semidirect
704. #449	C₂²×C₅₃	semidirect
706. #447	C₂²×C₅₃	semidirect
707. #446	C₂²×C₅₃	semidirect
708. #446	C₂²×C₅₃	semidirect
710. #442	C₂²×C₅₃	semidirect
711. #440	C₂²×C₅₃	semidirect
712. #440	C₂²×C₅₃	semidirect
713. C₄×SD₁₆	C₂²×C₅₃	semidirect
714. C₄×SD₁₆	C₂²×C₅₃	semidirect
715. C₄×SD₁₆	C₂²×C₅₃	semidirect
716. C₄×SD₁₆	C₂²×C₅₃	semidirect
721. C₄×D₈	C₂²×C₅₃	semidirect
722. C₄×D₈	C₂²×C₅₃	semidirect
723. C₄×D₈	C₂²×C₅₃	semidirect
724. C₄×D₈	C₂²×C₅₃	semidirect
725. C₄×D₈	C₂²×C₅₃	semidirect
726. C₄×D₈	C₂²×C₅₃	semidirect
727. #436	C₂²×C₅₃	semidirect
728. #436	C₂²×C₅₃	semidirect
729. #435	C₂²×C₅₃	semidirect
730. #435	C₂²×C₅₃	semidirect
731. #431	C₂²×C₅₃	semidirect
732. #431	C₂²×C₅₃	semidirect
733. #428	C₂²×C₅₃	semidirect
734. C₂×#107	C₂²×C₅₃	semidirect
735. #418	C₂²×C₅₃	semidirect
736. #417	C₂²×C₅₃	semidirect
738. C₂×#102	C₂²×C₅₃	semidirect
739. C₄×M₁₆	C₂²×C₅₃	semidirect
740. C₂×C₄×C₈	C₂²×C₅₃	semidirect
741. C₅₃	#61437	direct (N × H)
1000. D₈	#41×C₅₃	semidirect
1114. D₄	C₂×#41×C₅₃	semidirect
1145. C₂×C₄	AGL(1,ℤ/8)×C₅₃	semidirect
1160. C₈	C₂×#41×C₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#3475	2
D₄×#41×C₅₃	2
C₅₃×#3397	2
C₅₃×#3384	2
C₅₃×#3367	2
C₅₃×#3366	2
C₅₃×#3354	2
C₅₃×#3343	2
C₅₃×#3330	2
C₅₃×#3325	2
C₅₃×#3310	2
C₅₃×#3306	2
C₅₃×#3272	2
C₅₃×#3264	2
C₅₃×#3171	2
C₅₃×#3167	2
C₅₃×#3106	2
C₅₃×#3105	2
C₅₃×#3101	2
C₅₃×#3100	2
C₅₃×#2965	2
C₄×AGL(1,ℤ/8)×C₅₃	2
C₂×C₄×D₈×C₅₃	2
#61437	53

Subgroups — C53×#61437 #27268949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61437 #27268949