Subgroups — C₅₃×#60815 #27268327

Order 13568.

2108 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3225	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3224	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3221	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3220	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3219	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3214	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3212	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3207	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3005	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
32	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₅₃×#555	—	2	1	no	—
35	C₅₃×#553	—	2	1	no	—
36	C₅₃×#553	—	2	1	no	—
37	C₅₃×#551	—	2	2	no	—
38	C₅₃×#547	—	2	1	no	—
39	C₅₃×#546	—	2	2	no	—
40	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#542	C₂²	1	2	yes	complemented
42	C₅₃×#540	C₂²	1	2	yes	complemented
43	C₅₃×#537	—	2	1	no	—
44	C₅₃×#537	—	2	1	no	—
45	C₅₃×#536	C₂²	1	1	yes	characteristic
46	C₅₃×#536	C₂²	1	1	yes	characteristic
47	C₅₃×#536	C₂²	1	2	yes	complemented
48	C₅₃×#535	C₂²	1	1	yes	characteristic
49	C₅₃×#535	C₂²	1	1	yes	characteristic
50	C₅₃×#535	C₂²	1	2	yes	complemented
51	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#534	—	2	2	no	—
53	C₅₃×#532	C₂²	1	2	yes	complemented
54	C₅₃×#532	C₂²	1	2	yes	complemented
55	C₅₃×#532	C₂²	1	2	yes	complemented
56	C₅₃×#529	C₂²	1	2	yes	complemented
57	C₅₃×#525	—	2	2	no	—
58	C₅₃×#525	—	2	1	no	—
59	C₅₃×#525	—	2	1	no	—
60	C₅₃×#525	C₂²	1	1	yes	characteristic
61	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
62	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
64	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
65	C₅₃×#497	C₂²	1	2	yes	complemented
66	C₅₃×#496	C₂²	1	2	yes	complemented
67	C₅₃×#496	C₂²	1	2	yes	complemented
68	C₅₃×#496	C₂²	1	2	yes	complemented
69	C₅₃×#495	C₂²	1	2	yes	complemented
70	C₅₃×#495	C₂²	1	2	yes	complemented
71	C₅₃×#493	C₂²	1	2	yes	complemented
72	C₅₃×#492	C₂²	1	2	yes	complemented
73	C₅₃×#491	C₂²	1	2	yes	complemented
74	C₅₃×#490	C₂²	1	2	yes	complemented
75	C₅₃×#489	C₂²	1	2	yes	complemented
76	C₅₃×#489	C₂²	1	2	yes	complemented
77	C₅₃×#488	C₂²	1	2	yes	complemented
78	C₅₃×#488	C₂²	1	2	yes	complemented
79	C₅₃×#487	C₂²	1	2	yes	complemented
80	C₅₃×#486	C₂²	1	2	yes	complemented
81	C₅₃×#464	C₂²	1	2	yes	complemented
82	C₅₃×#464	C₂²	1	2	yes	complemented
83	C₅₃×#463	C₂²	1	2	yes	complemented
84	C₅₃×#463	C₂²	1	2	yes	complemented
85	C₅₃×#463	C₂²	1	2	yes	complemented
86	C₅₃×#463	C₂²	1	2	yes	complemented
87	C₅₃×#463	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	2	yes	complemented
89	C₅₃×#462	C₂²	1	2	yes	complemented
90	C₅₃×#461	C₂²	1	2	yes	complemented
91	C₅₃×#461	C₂²	1	2	yes	complemented
92	C₅₃×#461	C₂²	1	2	yes	complemented
93	C₅₃×#460	C₂²	1	2	yes	complemented
94	C₅₃×#459	C₂²	1	2	yes	complemented
95	C₅₃×#459	C₂²	1	2	yes	complemented
96	C₅₃×#459	C₂²	1	2	yes	complemented
97	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#452	C₂²	1	2	yes	complemented
99	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#452	C₂²	1	2	yes	complemented
101	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#449	C₂²	1	2	yes	—
104	C₅₃×#449	C₂²	1	2	yes	—
105	C₅₃×#449	C₂²	1	1	yes	characteristic, 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×#449	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#449	C₂²	1	2	yes	complemented
112	C₅₃×#449	C₂²	1	2	yes	complemented
113	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#448	C₂²	1	2	yes	complemented
115	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#447	C₂²	1	2	yes	complemented
117	C₅₃×#433	C₂²	1	2	yes	complemented
118	C₅₃×#433	C₂²	1	2	yes	complemented
119	C₅₃×#432	C₂²	1	2	yes	complemented
120	C₅₃×#431	C₂²	1	2	yes	complemented
121	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#417	C₂²	1	1	yes	characteristic
126	C₅₃×#417	C₂²	1	1	yes	characteristic
127	C₅₃×#416	C₂²	1	1	yes	characteristic
128	C₅₃×#416	C₂²	1	1	yes	characteristic
129	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#407	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
133	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	1	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	2	no	—
141	C₂×#41×C₅₃	—	4	2	no	—
142	C₂×#41×C₅₃	—	4	2	no	—
143	C₂×#41×C₅₃	—	4	2	no	—
144	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×#41×C₅₃	C₂³	1	2	yes	—
149	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×#41×C₅₃	C₂³	1	2	yes	—
151	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
152	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
153	C₂²×D₄×C₅₃	—	2	1	no	—
154	C₂²×D₄×C₅₃	—	2	1	no	—
155	C₂²×D₄×C₅₃	—	2	1	no	—
156	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
158	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
159	C₂³×C₄×C₅₃	—	2	1	no	—
160	C₂³×C₄×C₅₃	—	2	1	no	—
161	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
162	#137×C₅₃	—	4	2	no	—
163	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
164	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
165	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
166	#135×C₅₃	—	4	2	no	—
167	#135×C₅₃	—	4	2	no	—
168	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
170	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
171	C₂×SD₁₆×C₅₃	—	4	2	no	—
172	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
173	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
174	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
175	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
176	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
177	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
178	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
179	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
180	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
181	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
182	C₂×D₈×C₅₃	—	4	2	no	—
183	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
184	C₂×D₈×C₅₃	C₂³	1	2	yes	—
185	C₂×D₈×C₅₃	C₂³	1	2	yes	—
186	C₂×D₈×C₅₃	C₂³	1	2	yes	—
187	C₂×D₈×C₅₃	C₂³	1	2	yes	—
188	C₂×D₈×C₅₃	C₂³	1	2	yes	—
189	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
192	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
193	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
194	C₄⋊Q₈×C₅₃	—	2	1	no	—
195	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
196	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
197	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
198	#127×C₅₃	C₂³	1	2	yes	—
199	#127×C₅₃	C₂³	1	2	yes	—
200	#127×C₅₃	C₂³	1	2	yes	—
201	#126×C₅₃	—	2	2	no	—
202	#126×C₅₃	—	2	2	no	—
203	#125×C₅₃	—	2	1	no	—
204	#125×C₅₃	C₂³	1	2	yes	—
205	#124×C₅₃	—	2	2	no	—
206	#124×C₅₃	—	2	2	no	—
207	#124×C₅₃	C₂³	1	2	yes	—
208	#124×C₅₃	C₂³	1	2	yes	—
209	#124×C₅₃	C₂³	1	2	yes	—
210	#124×C₅₃	C₂³	1	2	yes	—
211	#124×C₅₃	C₂³	1	2	yes	—
212	#123×C₅₃	—	2	2	no	—
213	#123×C₅₃	—	2	2	no	—
214	#123×C₅₃	—	2	2	no	—
215	#123×C₅₃	—	2	2	no	—
216	#123×C₅₃	—	2	2	no	—
217	#123×C₅₃	—	2	2	no	—
218	#123×C₅₃	—	2	2	no	—
219	#123×C₅₃	—	2	1	no	—
220	#123×C₅₃	—	2	2	no	—
221	C₂²⋊Q₈×C₅₃	—	2	1	no	—
222	C₂²⋊Q₈×C₅₃	—	2	1	no	—
223	C₂²⋊Q₈×C₅₃	—	2	1	no	—
224	C₂²⋊Q₈×C₅₃	—	2	1	no	—
225	C₂²⋊Q₈×C₅₃	—	2	2	no	—
226	C₂²⋊Q₈×C₅₃	—	2	2	no	—
227	C₂²⋊Q₈×C₅₃	—	2	2	no	—
228	C₂²⋊Q₈×C₅₃	—	2	2	no	—
229	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
230	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
231	#121×C₅₃	—	2	1	no	—
232	#121×C₅₃	—	2	1	no	—
233	#121×C₅₃	—	2	1	no	—
234	#121×C₅₃	—	2	1	no	—
235	#121×C₅₃	—	2	2	no	—
236	#121×C₅₃	—	2	2	no	—
237	#121×C₅₃	—	2	1	no	—
238	#121×C₅₃	—	2	1	no	—
239	#121×C₅₃	—	2	2	no	—
240	#121×C₅₃	—	2	2	no	—
241	#121×C₅₃	—	2	1	no	—
242	#121×C₅₃	—	2	1	no	—
243	#121×C₅₃	—	2	2	no	—
244	#121×C₅₃	—	2	2	no	—
245	#121×C₅₃	—	2	2	no	—
246	#121×C₅₃	—	2	2	no	—
247	#121×C₅₃	—	2	2	no	—
248	#121×C₅₃	C₂³	1	2	yes	—
249	#121×C₅₃	C₂³	1	2	yes	—
250	#121×C₅₃	C₂³	1	1	yes	characteristic
251	#121×C₅₃	C₂³	1	1	yes	characteristic
252	#120×C₅₃	—	2	2	no	—
253	#120×C₅₃	—	2	2	no	—
254	#120×C₅₃	—	2	2	no	—
255	#120×C₅₃	—	2	2	no	—
256	#120×C₅₃	—	2	2	no	—
257	#120×C₅₃	—	2	1	no	—
258	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
259	C₄×D₄×C₅₃	—	2	1	no	—
260	C₄×D₄×C₅₃	—	2	1	no	—
261	C₄×D₄×C₅₃	—	2	2	no	—
262	C₄×D₄×C₅₃	—	2	2	no	—
263	C₄×D₄×C₅₃	—	2	2	no	—
264	C₄×D₄×C₅₃	—	2	2	no	—
265	C₄×D₄×C₅₃	—	2	2	no	—
266	C₄×D₄×C₅₃	—	2	2	no	—
267	C₄×D₄×C₅₃	—	2	1	no	—
268	C₄×D₄×C₅₃	—	2	1	no	—
269	C₄×D₄×C₅₃	—	2	2	no	—
270	C₄×D₄×C₅₃	C₂³	1	2	yes	—
271	C₄×D₄×C₅₃	C₂³	1	2	yes	—
272	C₄×D₄×C₅₃	C₂³	1	2	yes	—
273	#117×C₅₃	—	2	1	no	—
274	#117×C₅₃	—	2	2	no	—
275	#117×C₅₃	D₄	1	2	yes	—
276	#117×C₅₃	D₄	1	1	yes	characteristic
277	#117×C₅₃	D₄	1	1	yes	characteristic
278	#117×C₅₃	C₂³	1	1	yes	characteristic
279	#117×C₅₃	C₂³	1	1	yes	characteristic
280	#117×C₅₃	C₂³	1	1	yes	characteristic
281	#117×C₅₃	C₂³	1	2	yes	—
282	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
283	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
284	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
287	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
288	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
289	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
290	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
291	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
292	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
293	C₄⋊C₈×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	2	yes	—
298	#103×C₅₃	C₂³	1	1	yes	characteristic
299	#103×C₅₃	C₂³	1	2	yes	—
300	#103×C₅₃	C₂³	1	2	yes	—
301	#103×C₅₃	C₂³	1	1	yes	characteristic
302	#103×C₅₃	C₂³	1	2	yes	—
303	#103×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	#102×C₅₃	C₂³	1	2	yes	—
308	#102×C₅₃	C₂³	1	1	yes	characteristic
309	#102×C₅₃	C₂³	1	2	yes	—
310	#102×C₅₃	C₂³	1	2	yes	—
311	#102×C₅₃	C₂³	1	1	yes	characteristic
312	#102×C₅₃	C₂³	1	2	yes	—
313	#102×C₅₃	C₂³	1	1	yes	characteristic
314	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
318	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
319	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
320	#97×C₅₃	C₂³	1	2	yes	—
321	#97×C₅₃	C₂³	1	2	yes	—
322	C₄×C₈×C₅₃	C₂³	1	2	yes	—
323	C₄×C₈×C₅₃	C₂³	1	2	yes	—
324	C₂⁴×C₅₃	—	2	1	no	—
325	C₂⁴×C₅₃	—	2	1	no	—
326	C₂⁴×C₅₃	—	2	1	no	—
327	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
328	#41×C₅₃	—	2	2	no	—
329	#41×C₅₃	—	2	2	no	—
330	#41×C₅₃	—	2	2	no	—
331	#41×C₅₃	—	2	2	no	—
332	#41×C₅₃	—	2	2	no	—
333	#41×C₅₃	—	2	2	no	—
334	#41×C₅₃	—	4	2	no	—
335	#41×C₅₃	—	4	2	no	—
336	#41×C₅₃	—	4	2	no	—
337	#41×C₅₃	—	4	2	no	—
338	#41×C₅₃	—	4	1	no	—
339	#41×C₅₃	—	4	1	no	—
340	#41×C₅₃	—	4	1	no	—
341	#41×C₅₃	—	4	1	no	—
342	#41×C₅₃	—	4	4	no	—
343	#41×C₅₃	—	4	4	no	—
344	#41×C₅₃	—	4	4	no	—
345	#41×C₅₃	—	4	4	no	—
346	#41×C₅₃	—	8	4	no	—
347	C₂×Q₈×C₅₃	—	2	1	no	—
348	C₂×Q₈×C₅₃	—	2	1	no	—
349	C₂×Q₈×C₅₃	—	2	2	no	—
350	C₂×Q₈×C₅₃	—	2	2	no	—
351	C₂×Q₈×C₅₃	—	2	2	no	—
352	C₂×Q₈×C₅₃	—	4	1	no	—
353	C₂×Q₈×C₅₃	—	4	1	no	—
354	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₅₃	—	2	1	no	—
359	C₂×D₄×C₅₃	—	2	1	no	—
360	C₂×D₄×C₅₃	—	2	2	no	—
361	C₂×D₄×C₅₃	—	2	2	no	—
362	C₂×D₄×C₅₃	—	2	1	no	—
363	C₂×D₄×C₅₃	—	2	1	no	—
364	C₂×D₄×C₅₃	—	2	1	no	—
365	C₂×D₄×C₅₃	—	2	2	no	—
366	C₂×D₄×C₅₃	—	2	1	no	—
367	C₂×D₄×C₅₃	—	2	1	no	—
368	C₂×D₄×C₅₃	—	2	2	no	—
369	C₂×D₄×C₅₃	—	2	1	no	—
370	C₂×D₄×C₅₃	—	2	1	no	—
371	C₂×D₄×C₅₃	—	2	1	no	—
372	C₂×D₄×C₅₃	—	2	2	no	—
373	C₂×D₄×C₅₃	—	2	2	no	—
374	C₂×D₄×C₅₃	—	2	2	no	—
375	C₂×D₄×C₅₃	—	2	2	no	—
376	C₂×D₄×C₅₃	—	2	2	no	—
377	C₂×D₄×C₅₃	—	2	2	no	—
378	C₂×D₄×C₅₃	—	2	2	no	—
379	C₂×D₄×C₅₃	—	2	2	no	—
380	C₂×D₄×C₅₃	—	2	2	no	—
381	C₂×D₄×C₅₃	—	2	2	no	—
382	C₂×D₄×C₅₃	—	4	1	no	—
383	C₂×D₄×C₅₃	—	4	1	no	—
384	C₂×D₄×C₅₃	—	4	4	no	—
385	C₂×D₄×C₅₃	—	4	4	no	—
386	C₂×D₄×C₅₃	—	8	2	no	—
387	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
388	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
391	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₅₃	—	2	2	no	—
393	C₂²×C₄×C₅₃	—	2	2	no	—
394	C₂²×C₄×C₅₃	—	2	1	no	—
395	C₂²×C₄×C₅₃	—	2	1	no	—
396	C₂²×C₄×C₅₃	—	2	1	no	—
397	C₂²×C₄×C₅₃	—	2	1	no	—
398	C₂²×C₄×C₅₃	—	2	1	no	—
399	C₂²×C₄×C₅₃	—	2	2	no	—
400	C₂²×C₄×C₅₃	—	2	1	no	—
401	C₂²×C₄×C₅₃	—	2	2	no	—
402	C₂²×C₄×C₅₃	—	2	1	no	—
403	C₂²×C₄×C₅₃	—	2	1	no	—
404	C₂²×C₄×C₅₃	—	2	2	no	—
405	C₂²×C₄×C₅₃	—	2	2	no	—
406	C₂²×C₄×C₅₃	—	2	2	no	—
407	C₂²×C₄×C₅₃	—	4	4	no	—
408	C₂²×C₄×C₅₃	—	4	4	no	—
409	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
412	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
413	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
414	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	Q₁₆×C₅₃	—	4	1	no	—
418	Q₁₆×C₅₃	—	4	1	no	—
419	Q₁₆×C₅₃	—	4	2	no	—
420	SD₁₆×C₅₃	—	4	2	no	—
421	SD₁₆×C₅₃	—	4	2	no	—
422	SD₁₆×C₅₃	—	4	1	no	—
423	SD₁₆×C₅₃	—	4	1	no	—
424	SD₁₆×C₅₃	—	4	1	no	—
425	SD₁₆×C₅₃	—	4	1	no	—
426	SD₁₆×C₅₃	—	4	2	no	—
427	SD₁₆×C₅₃	—	4	2	no	—
428	SD₁₆×C₅₃	—	4	2	no	—
429	SD₁₆×C₅₃	—	4	2	no	—
430	D₈×C₅₃	—	4	2	no	—
431	D₈×C₅₃	—	4	2	no	—
432	D₈×C₅₃	—	4	1	no	—
433	D₈×C₅₃	—	4	1	no	—
434	D₈×C₅₃	—	4	2	no	—
435	D₈×C₅₃	—	4	2	no	—
436	D₈×C₅₃	—	4	2	no	—
437	M₁₆×C₅₃	—	2	2	no	—
438	M₁₆×C₅₃	—	2	2	no	—
439	C₂×C₈×C₅₃	—	2	2	no	—
440	C₂×C₈×C₅₃	—	2	2	no	—
441	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
444	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
445	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄×C₅₃	—	2	1	no	—
448	C₄⋊C₄×C₅₃	—	2	2	no	—
449	C₄⋊C₄×C₅₃	—	2	1	no	—
450	C₄⋊C₄×C₅₃	—	2	2	no	—
451	C₄⋊C₄×C₅₃	—	2	2	no	—
452	C₄⋊C₄×C₅₃	—	2	2	no	—
453	C₄⋊C₄×C₅₃	—	2	2	no	—
454	C₄⋊C₄×C₅₃	—	2	2	no	—
455	C₄⋊C₄×C₅₃	—	2	2	no	—
456	C₄⋊C₄×C₅₃	—	2	2	no	—
457	C₄⋊C₄×C₅₃	—	2	1	no	—
458	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
459	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
460	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
461	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
462	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
463	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
464	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
465	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
466	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
467	C₂²⋊C₄×C₅₃	—	2	1	no	—
468	C₂²⋊C₄×C₅₃	—	2	1	no	—
469	C₂²⋊C₄×C₅₃	—	2	1	no	—
470	C₂²⋊C₄×C₅₃	—	2	2	no	—
471	C₂²⋊C₄×C₅₃	—	2	2	no	—
472	C₂²⋊C₄×C₅₃	—	2	2	no	—
473	C₂²⋊C₄×C₅₃	—	2	2	no	—
474	C₂²⋊C₄×C₅₃	—	2	2	no	—
475	C₂²⋊C₄×C₅₃	—	2	2	no	—
476	C₂²⋊C₄×C₅₃	—	2	1	no	—
477	C₂²⋊C₄×C₅₃	—	2	2	no	—
478	C₂²⋊C₄×C₅₃	—	2	2	no	—
479	C₂²⋊C₄×C₅₃	—	2	2	no	—
480	C₂²⋊C₄×C₅₃	—	2	2	no	—
481	C₂²⋊C₄×C₅₃	—	2	2	no	—
482	C₂²⋊C₄×C₅₃	—	2	2	no	—
483	C₂²⋊C₄×C₅₃	—	2	2	no	—
484	C₂²⋊C₄×C₅₃	—	2	2	no	—
485	C₂²⋊C₄×C₅₃	—	2	2	no	—
486	C₂²⋊C₄×C₅₃	—	2	1	no	—
487	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
488	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
489	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
490	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
491	C₄²×C₅₃	—	2	2	no	—
492	C₄²×C₅₃	—	2	1	no	—
493	C₄²×C₅₃	C₂×D₄	1	2	yes	—
494	C₄²×C₅₃	C₂×D₄	1	2	yes	—
495	C₄²×C₅₃	C₂⁴	1	2	yes	—
496	C₄²×C₅₃	C₂⁴	1	2	yes	—
497	C₂³×C₅₃	—	2	2	no	—
498	C₂³×C₅₃	—	2	1	no	—
499	C₂³×C₅₃	—	2	2	no	—
500	C₂³×C₅₃	—	2	1	no	—
501	C₂³×C₅₃	—	2	1	no	—
502	C₂³×C₅₃	—	2	2	no	—
503	C₂³×C₅₃	—	4	1	no	—
504	C₂³×C₅₃	—	4	1	no	—
505	C₂³×C₅₃	—	4	2	no	—
506	C₂³×C₅₃	—	4	2	no	—
507	C₂³×C₅₃	—	4	2	no	—
508	C₂³×C₅₃	—	8	1	no	—
509	C₂³×C₅₃	—	8	1	no	—
510	C₂³×C₅₃	—	8	1	no	—
511	C₂³×C₅₃	—	8	1	no	—
512	C₂³×C₅₃	—	8	1	no	—
513	C₂³×C₅₃	—	8	1	no	—
514	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
515	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
516	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
517	Q₈×C₅₃	—	2	2	no	—
518	Q₈×C₅₃	—	2	2	no	—
519	Q₈×C₅₃	—	2	1	no	—
520	Q₈×C₅₃	—	2	1	no	—
521	Q₈×C₅₃	—	2	1	no	—
522	Q₈×C₅₃	—	2	1	no	—
523	Q₈×C₅₃	—	2	1	no	—
524	Q₈×C₅₃	—	2	1	no	—
525	Q₈×C₅₃	—	4	2	no	—
526	Q₈×C₅₃	—	4	2	no	—
527	Q₈×C₅₃	—	8	2	no	—
528	D₄×C₅₃	—	2	2	no	—
529	D₄×C₅₃	—	2	2	no	—
530	D₄×C₅₃	—	2	2	no	—
531	D₄×C₅₃	—	2	2	no	—
532	D₄×C₅₃	—	2	1	no	—
533	D₄×C₅₃	—	2	1	no	—
534	D₄×C₅₃	—	2	1	no	—
535	D₄×C₅₃	—	2	1	no	—
536	D₄×C₅₃	—	2	1	no	—
537	D₄×C₅₃	—	2	1	no	—
538	D₄×C₅₃	—	4	2	no	—
539	D₄×C₅₃	—	4	4	no	—
540	D₄×C₅₃	—	4	4	no	—
541	D₄×C₅₃	—	4	2	no	—
542	D₄×C₅₃	—	4	2	no	—
543	D₄×C₅₃	—	4	4	no	—
544	D₄×C₅₃	—	4	2	no	—
545	D₄×C₅₃	—	4	2	no	—
546	D₄×C₅₃	—	4	2	no	—
547	D₄×C₅₃	—	4	2	no	—
548	D₄×C₅₃	—	4	2	no	—
549	D₄×C₅₃	—	4	2	no	—
550	D₄×C₅₃	—	8	2	no	—
551	D₄×C₅₃	—	8	2	no	—
552	D₄×C₅₃	—	8	2	no	—
553	D₄×C₅₃	—	8	2	no	—
554	D₄×C₅₃	—	8	2	no	—
555	D₄×C₅₃	—	8	2	no	—
556	D₄×C₅₃	—	8	1	no	—
557	D₄×C₅₃	—	8	2	no	—
558	C₂×C₄×C₅₃	—	2	2	no	—
559	C₂×C₄×C₅₃	—	2	2	no	—
560	C₂×C₄×C₅₃	—	2	2	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	1	no	—
563	C₂×C₄×C₅₃	—	2	1	no	—
564	C₂×C₄×C₅₃	—	2	1	no	—
565	C₂×C₄×C₅₃	—	2	2	no	—
566	C₂×C₄×C₅₃	—	2	1	no	—
567	C₂×C₄×C₅₃	—	2	1	no	—
568	C₂×C₄×C₅₃	—	2	2	no	—
569	C₂×C₄×C₅₃	—	2	1	no	—
570	C₂×C₄×C₅₃	—	2	1	no	—
571	C₂×C₄×C₅₃	—	2	1	no	—
572	C₂×C₄×C₅₃	—	4	2	no	—
573	C₂×C₄×C₅₃	—	4	2	no	—
574	C₂×C₄×C₅₃	—	4	4	no	—
575	C₂×C₄×C₅₃	—	4	2	no	—
576	C₂×C₄×C₅₃	—	4	2	no	—
577	C₂×C₄×C₅₃	—	4	4	no	—
578	C₂×C₄×C₅₃	—	4	2	no	—
579	C₂×C₄×C₅₃	—	4	2	no	—
580	C₂×C₄×C₅₃	—	4	2	no	—
581	C₂×C₄×C₅₃	—	4	2	no	—
582	C₂×C₄×C₅₃	—	4	2	no	—
583	C₂×C₄×C₅₃	—	8	2	no	—
584	C₂×C₄×C₅₃	—	8	2	no	—
585	C₂×C₄×C₅₃	—	8	2	no	—
586	C₂×C₄×C₅₃	—	8	1	no	—
587	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
590	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
591	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
592	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
593	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
595	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
596	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
597	C₈×C₅₃	—	2	1	no	—
598	C₈×C₅₃	—	2	1	no	—
599	C₈×C₅₃	—	2	1	no	—
600	C₈×C₅₃	—	2	1	no	—
601	C₈×C₅₃	—	2	2	no	—
602	C₈×C₅₃	—	2	2	no	—
603	#60815	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
604	C₂²×C₅₃	—	2	1	no	—
605	C₂²×C₅₃	—	2	1	no	—
606	C₂²×C₅₃	—	2	1	no	—
607	C₂²×C₅₃	—	2	1	no	—
608	C₂²×C₅₃	—	2	1	no	—
609	C₂²×C₅₃	—	2	1	no	—
610	C₂²×C₅₃	—	2	1	no	—
611	C₂²×C₅₃	—	2	1	no	—
612	C₂²×C₅₃	—	4	2	no	—
613	C₂²×C₅₃	—	4	1	no	—
614	C₂²×C₅₃	—	4	2	no	—
615	C₂²×C₅₃	—	4	1	no	—
616	C₂²×C₅₃	—	4	1	no	—
617	C₂²×C₅₃	—	4	1	no	—
618	C₂²×C₅₃	—	4	2	no	—
619	C₂²×C₅₃	—	4	2	no	—
620	C₂²×C₅₃	—	4	1	no	—
621	C₂²×C₅₃	—	4	1	no	—
622	C₂²×C₅₃	—	4	2	no	—
623	C₂²×C₅₃	—	4	1	no	—
624	C₂²×C₅₃	—	4	1	no	—
625	C₂²×C₅₃	—	4	1	no	—
626	C₂²×C₅₃	—	4	2	no	—
627	C₂²×C₅₃	—	8	2	no	—
628	C₂²×C₅₃	—	8	4	no	—
629	C₂²×C₅₃	—	8	4	no	—
630	C₂²×C₅₃	—	16	2	no	—
631	C₂²×C₅₃	#535	1	2	yes	—
632	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
633	C₄×C₅₃	—	2	2	no	—
634	C₄×C₅₃	—	2	2	no	—
635	C₄×C₅₃	—	2	2	no	—
636	C₄×C₅₃	—	2	2	no	—
637	C₄×C₅₃	—	2	1	no	—
638	C₄×C₅₃	—	2	1	no	—
639	C₄×C₅₃	—	4	1	no	—
640	C₄×C₅₃	—	4	2	no	—
641	C₄×C₅₃	—	4	1	no	—
642	C₄×C₅₃	—	4	2	no	—
643	C₄×C₅₃	—	4	1	no	—
644	C₄×C₅₃	—	4	1	no	—
645	C₄×C₅₃	—	4	1	no	—
646	C₄×C₅₃	#535	1	2	yes	—
647	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
648	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
649	#3494	C₂×C₅₃	1	1	yes	characteristic, complemented
650	#3449	C₂×C₅₃	1	1	yes	characteristic, complemented
651	#3225	C₂×C₅₃	1	2	yes	complemented
652	#3224	C₂×C₅₃	1	2	yes	complemented
653	#3221	C₂×C₅₃	1	2	yes	complemented
654	#3220	C₂×C₅₃	1	2	yes	complemented
655	#3219	C₂×C₅₃	1	2	yes	complemented
656	#3214	C₂×C₅₃	1	2	yes	complemented
657	#3212	C₂×C₅₃	1	2	yes	complemented
658	#3207	C₂×C₅₃	1	2	yes	complemented
659	#3155	C₂×C₅₃	1	1	yes	characteristic, complemented
660	#3154	C₂×C₅₃	1	1	yes	characteristic, complemented
661	#3137	C₂×C₅₃	1	1	yes	characteristic, complemented
662	#3136	C₂×C₅₃	1	1	yes	characteristic, complemented
663	#3046	C₂×C₅₃	1	1	yes	characteristic, complemented
664	#3045	C₂×C₅₃	1	1	yes	characteristic, complemented
665	#3042	C₂×C₅₃	1	1	yes	characteristic, complemented
666	#3041	C₂×C₅₃	1	1	yes	characteristic, complemented
667	#3006	C₂×C₅₃	1	1	yes	characteristic, complemented
668	#3005	C₂×C₅₃	1	1	yes	characteristic, complemented
669	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
670	C₂×#449	C₂×C₅₃	1	1	yes	characteristic, complemented
671	#2924	C₂×C₅₃	1	1	yes	characteristic, complemented
672	C₂×C₅₃	—	2	2	no	—
673	C₂×C₅₃	—	4	1	no	—
674	C₂×C₅₃	—	4	1	no	—
675	C₂×C₅₃	—	8	1	no	—
676	C₂×C₅₃	—	8	2	no	—
677	C₂×C₅₃	—	8	1	no	—
678	C₂×C₅₃	—	8	1	no	—
679	C₂×C₅₃	—	8	2	no	—
680	C₂×C₅₃	C₂×#535	1	1	yes	characteristic
681	C₂×C₅₃	#3584	1	1	yes	characteristic
682	C₂×C₅₃	#3585	1	1	yes	characteristic
683	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
684	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
685	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
686	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
687	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
688	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
690	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
691	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#555	—	2	1	no	—
694	#553	—	2	1	no	—
695	#553	—	2	1	no	—
696	#551	—	2	2	no	—
697	#547	—	2	1	no	—
698	#546	—	2	2	no	—
699	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
700	#542	C₂²×C₅₃	1	2	yes	complemented
701	#540	C₂²×C₅₃	1	2	yes	complemented
702	#537	—	2	1	no	—
703	#537	—	2	1	no	—
704	#536	C₂²×C₅₃	1	1	yes	characteristic
705	#536	C₂²×C₅₃	1	1	yes	characteristic
706	#536	C₂²×C₅₃	1	2	yes	complemented
707	#535	C₂²×C₅₃	1	1	yes	characteristic
708	#535	C₂²×C₅₃	1	1	yes	characteristic
709	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
710	#535	C₂²×C₅₃	1	2	yes	complemented
711	#534	—	2	2	no	—
712	#532	C₂²×C₅₃	1	2	yes	complemented
713	#532	C₂²×C₅₃	1	2	yes	complemented
714	#532	C₂²×C₅₃	1	2	yes	complemented
715	#529	C₂²×C₅₃	1	2	yes	complemented
716	#525	—	2	2	no	—
717	#525	—	2	1	no	—
718	#525	—	2	1	no	—
719	#525	C₂²×C₅₃	1	1	yes	characteristic
720	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
721	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
724	#497	C₂²×C₅₃	1	2	yes	complemented
725	#496	C₂²×C₅₃	1	2	yes	complemented
726	#496	C₂²×C₅₃	1	2	yes	complemented
727	#496	C₂²×C₅₃	1	2	yes	complemented
728	#495	C₂²×C₅₃	1	2	yes	complemented
729	#495	C₂²×C₅₃	1	2	yes	complemented
730	#493	C₂²×C₅₃	1	2	yes	complemented
731	#492	C₂²×C₅₃	1	2	yes	complemented
732	#491	C₂²×C₅₃	1	2	yes	complemented
733	#490	C₂²×C₅₃	1	2	yes	complemented
734	#489	C₂²×C₅₃	1	2	yes	complemented
735	#489	C₂²×C₅₃	1	2	yes	complemented
736	#488	C₂²×C₅₃	1	2	yes	complemented
737	#488	C₂²×C₅₃	1	2	yes	complemented
738	#487	C₂²×C₅₃	1	2	yes	complemented
739	#486	C₂²×C₅₃	1	2	yes	complemented
740	#464	C₂²×C₅₃	1	2	yes	complemented
741	#464	C₂²×C₅₃	1	2	yes	complemented
742	#463	C₂²×C₅₃	1	2	yes	complemented
743	#463	C₂²×C₅₃	1	2	yes	complemented
744	#463	C₂²×C₅₃	1	2	yes	complemented
745	#463	C₂²×C₅₃	1	2	yes	complemented
746	#463	C₂²×C₅₃	1	2	yes	complemented
747	#463	C₂²×C₅₃	1	2	yes	complemented
748	#462	C₂²×C₅₃	1	2	yes	complemented
749	#461	C₂²×C₅₃	1	2	yes	complemented
750	#461	C₂²×C₅₃	1	2	yes	complemented
751	#461	C₂²×C₅₃	1	2	yes	complemented
752	#460	C₂²×C₅₃	1	2	yes	complemented
753	#459	C₂²×C₅₃	1	2	yes	complemented
754	#459	C₂²×C₅₃	1	2	yes	complemented
755	#459	C₂²×C₅₃	1	2	yes	complemented
756	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
757	#452	C₂²×C₅₃	1	2	yes	complemented
758	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
759	#452	C₂²×C₅₃	1	2	yes	complemented
760	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
761	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
762	#449	C₂²×C₅₃	1	2	yes	—
763	#449	C₂²×C₅₃	1	2	yes	—
764	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
765	#449	C₂²×C₅₃	1	2	yes	complemented
766	#449	C₂²×C₅₃	1	2	yes	complemented
767	#449	C₂²×C₅₃	1	2	yes	complemented
768	#449	C₂²×C₅₃	1	2	yes	complemented
769	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
770	#449	C₂²×C₅₃	1	2	yes	complemented
771	#449	C₂²×C₅₃	1	2	yes	complemented
772	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
773	#448	C₂²×C₅₃	1	2	yes	complemented
774	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
775	#447	C₂²×C₅₃	1	2	yes	complemented
776	#433	C₂²×C₅₃	1	2	yes	complemented
777	#433	C₂²×C₅₃	1	2	yes	complemented
778	#432	C₂²×C₅₃	1	2	yes	complemented
779	#431	C₂²×C₅₃	1	2	yes	complemented
780	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
781	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
782	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
783	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
784	#417	C₂²×C₅₃	1	1	yes	characteristic
785	#417	C₂²×C₅₃	1	1	yes	characteristic
786	#416	C₂²×C₅₃	1	1	yes	characteristic
787	#416	C₂²×C₅₃	1	1	yes	characteristic
788	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
789	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
790	#407	C₂²×C₅₃	1	1	yes	characteristic
791	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
792	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
793	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
794	C₅₃	#60815	1	1	yes	characteristic, direct product factor, Sylow
795	C₂×#41	—	2	1	no	—
796	C₂×#41	—	2	1	no	—
797	C₂×#41	—	2	1	no	—
798	C₂×#41	—	2	1	no	—
799	C₂×#41	—	2	2	no	—
800	C₂×#41	—	4	2	no	—
801	C₂×#41	—	4	2	no	—
802	C₂×#41	—	4	2	no	—
803	C₂×#41	—	4	2	no	—
804	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
805	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
806	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
807	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
808	C₂×#41	C₂³×C₅₃	1	2	yes	—
809	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
810	C₂×#41	C₂³×C₅₃	1	2	yes	—
811	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
812	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
813	C₂²×D₄	—	2	1	no	—
814	C₂²×D₄	—	2	1	no	—
815	C₂²×D₄	—	2	1	no	—
816	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
817	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
818	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
819	C₂³×C₄	—	2	1	no	—
820	C₂³×C₄	—	2	1	no	—
821	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
822	#137	—	4	2	no	—
823	AGL(1,ℤ/8)	—	4	2	no	—
824	AGL(1,ℤ/8)	—	4	2	no	—
825	AGL(1,ℤ/8)	—	4	2	no	—
826	#135	—	4	2	no	—
827	#135	—	4	2	no	—
828	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
829	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
830	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
831	C₂×SD₁₆	—	4	2	no	—
832	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
833	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
834	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
835	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
836	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
837	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
838	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
839	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
840	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
841	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
842	C₂×D₈	—	4	2	no	—
843	C₂×D₈	C₂³×C₅₃	1	2	yes	—
844	C₂×D₈	C₂³×C₅₃	1	2	yes	—
845	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
846	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
847	C₂×D₈	C₂³×C₅₃	1	2	yes	—
848	C₂×D₈	C₂³×C₅₃	1	2	yes	—
849	C₂×D₈	C₂³×C₅₃	1	2	yes	—
850	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
851	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
852	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
853	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
854	C₄⋊Q₈	—	2	1	no	—
855	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
856	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
857	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
858	#127	C₂³×C₅₃	1	2	yes	—
859	#127	C₂³×C₅₃	1	2	yes	—
860	#127	C₂³×C₅₃	1	2	yes	—
861	#126	—	2	2	no	—
862	#126	—	2	2	no	—
863	#125	—	2	1	no	—
864	#125	C₂³×C₅₃	1	2	yes	—
865	#124	—	2	2	no	—
866	#124	—	2	2	no	—
867	#124	C₂³×C₅₃	1	2	yes	—
868	#124	C₂³×C₅₃	1	2	yes	—
869	#124	C₂³×C₅₃	1	2	yes	—
870	#124	C₂³×C₅₃	1	2	yes	—
871	#124	C₂³×C₅₃	1	2	yes	—
872	#123	—	2	1	no	—
873	#123	—	2	2	no	—
874	#123	—	2	2	no	—
875	#123	—	2	2	no	—
876	#123	—	2	2	no	—
877	#123	—	2	2	no	—
878	#123	—	2	2	no	—
879	#123	—	2	2	no	—
880	#123	—	2	2	no	—
881	C₂²⋊Q₈	—	2	1	no	—
882	C₂²⋊Q₈	—	2	1	no	—
883	C₂²⋊Q₈	—	2	1	no	—
884	C₂²⋊Q₈	—	2	1	no	—
885	C₂²⋊Q₈	—	2	2	no	—
886	C₂²⋊Q₈	—	2	2	no	—
887	C₂²⋊Q₈	—	2	2	no	—
888	C₂²⋊Q₈	—	2	2	no	—
889	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
890	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
891	#121	—	2	1	no	—
892	#121	—	2	1	no	—
893	#121	—	2	2	no	—
894	#121	—	2	2	no	—
895	#121	—	2	2	no	—
896	#121	—	2	2	no	—
897	#121	—	2	2	no	—
898	#121	—	2	1	no	—
899	#121	—	2	1	no	—
900	#121	—	2	1	no	—
901	#121	—	2	1	no	—
902	#121	—	2	2	no	—
903	#121	—	2	2	no	—
904	#121	—	2	1	no	—
905	#121	—	2	1	no	—
906	#121	—	2	2	no	—
907	#121	—	2	2	no	—
908	#121	C₂³×C₅₃	1	2	yes	—
909	#121	C₂³×C₅₃	1	2	yes	—
910	#121	C₂³×C₅₃	1	1	yes	characteristic
911	#121	C₂³×C₅₃	1	1	yes	characteristic
912	#120	—	2	1	no	—
913	#120	—	2	2	no	—
914	#120	—	2	2	no	—
915	#120	—	2	2	no	—
916	#120	—	2	2	no	—
917	#120	—	2	2	no	—
918	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
919	C₄×D₄	—	2	1	no	—
920	C₄×D₄	—	2	1	no	—
921	C₄×D₄	—	2	2	no	—
922	C₄×D₄	—	2	1	no	—
923	C₄×D₄	—	2	1	no	—
924	C₄×D₄	—	2	2	no	—
925	C₄×D₄	—	2	2	no	—
926	C₄×D₄	—	2	2	no	—
927	C₄×D₄	—	2	2	no	—
928	C₄×D₄	—	2	2	no	—
929	C₄×D₄	—	2	2	no	—
930	C₄×D₄	C₂³×C₅₃	1	2	yes	—
931	C₄×D₄	C₂³×C₅₃	1	2	yes	—
932	C₄×D₄	C₂³×C₅₃	1	2	yes	—
933	#117	—	2	1	no	—
934	#117	—	2	2	no	—
935	#117	D₄×C₅₃	1	2	yes	—
936	#117	D₄×C₅₃	1	1	yes	characteristic
937	#117	D₄×C₅₃	1	1	yes	characteristic
938	#117	C₂³×C₅₃	1	1	yes	characteristic
939	#117	C₂³×C₅₃	1	1	yes	characteristic
940	#117	C₂³×C₅₃	1	1	yes	characteristic
941	#117	C₂³×C₅₃	1	2	yes	—
942	C₂×C₄⋊C₄	—	2	1	no	—
943	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
944	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
946	C₂×C₂²⋊C₄	—	2	1	no	—
947	C₂×C₂²⋊C₄	—	2	2	no	—
948	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
949	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
950	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
951	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
952	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
953	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
954	#103	C₂³×C₅₃	1	2	yes	—
955	#103	C₂³×C₅₃	1	2	yes	—
956	#103	C₂³×C₅₃	1	1	yes	characteristic
957	#103	C₂³×C₅₃	1	1	yes	characteristic
958	#103	C₂³×C₅₃	1	1	yes	characteristic
959	#103	C₂³×C₅₃	1	1	yes	characteristic
960	#103	C₂³×C₅₃	1	2	yes	—
961	#103	C₂³×C₅₃	1	2	yes	—
962	#103	C₂³×C₅₃	1	2	yes	—
963	#103	C₂³×C₅₃	1	2	yes	—
964	#102	C₂³×C₅₃	1	2	yes	—
965	#102	C₂³×C₅₃	1	2	yes	—
966	#102	C₂³×C₅₃	1	1	yes	characteristic
967	#102	C₂³×C₅₃	1	1	yes	characteristic
968	#102	C₂³×C₅₃	1	1	yes	characteristic
969	#102	C₂³×C₅₃	1	1	yes	characteristic
970	#102	C₂³×C₅₃	1	2	yes	—
971	#102	C₂³×C₅₃	1	2	yes	—
972	#102	C₂³×C₅₃	1	2	yes	—
973	#102	C₂³×C₅₃	1	2	yes	—
974	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
975	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
976	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
977	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
978	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
979	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
980	#97	C₂³×C₅₃	1	2	yes	—
981	#97	C₂³×C₅₃	1	2	yes	—
982	C₄×C₈	C₂³×C₅₃	1	2	yes	—
983	C₄×C₈	C₂³×C₅₃	1	2	yes	—
984	C₂⁴	—	2	1	no	—
985	C₂⁴	—	2	1	no	—
986	C₂⁴	—	2	1	no	—
987	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
988	#41	—	2	2	no	—
989	#41	—	2	2	no	—
990	#41	—	2	2	no	—
991	#41	—	2	2	no	—
992	#41	—	2	2	no	—
993	#41	—	2	2	no	—
994	#41	—	4	2	no	—
995	#41	—	4	2	no	—
996	#41	—	4	2	no	—
997	#41	—	4	1	no	—
998	#41	—	4	1	no	—
999	#41	—	4	2	no	—
1000	#41	—	4	1	no	—
1001	#41	—	4	1	no	—
1002	#41	—	4	4	no	—
1003	#41	—	4	4	no	—
1004	#41	—	4	4	no	—
1005	#41	—	4	4	no	—
1006	#41	—	8	4	no	—
1007	C₂×Q₈	—	2	1	no	—
1008	C₂×Q₈	—	2	1	no	—
1009	C₂×Q₈	—	2	2	no	—
1010	C₂×Q₈	—	2	2	no	—
1011	C₂×Q₈	—	2	2	no	—
1012	C₂×Q₈	—	4	1	no	—
1013	C₂×Q₈	—	4	1	no	—
1014	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1015	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1016	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1017	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1018	C₂×D₄	—	2	1	no	—
1019	C₂×D₄	—	2	1	no	—
1020	C₂×D₄	—	2	2	no	—
1021	C₂×D₄	—	2	2	no	—
1022	C₂×D₄	—	2	1	no	—
1023	C₂×D₄	—	2	1	no	—
1024	C₂×D₄	—	2	1	no	—
1025	C₂×D₄	—	2	2	no	—
1026	C₂×D₄	—	2	1	no	—
1027	C₂×D₄	—	2	1	no	—
1028	C₂×D₄	—	2	2	no	—
1029	C₂×D₄	—	2	1	no	—
1030	C₂×D₄	—	2	1	no	—
1031	C₂×D₄	—	2	1	no	—
1032	C₂×D₄	—	2	2	no	—
1033	C₂×D₄	—	2	2	no	—
1034	C₂×D₄	—	2	2	no	—
1035	C₂×D₄	—	2	2	no	—
1036	C₂×D₄	—	2	2	no	—
1037	C₂×D₄	—	2	2	no	—
1038	C₂×D₄	—	2	2	no	—
1039	C₂×D₄	—	2	2	no	—
1040	C₂×D₄	—	2	2	no	—
1041	C₂×D₄	—	2	2	no	—
1042	C₂×D₄	—	4	1	no	—
1043	C₂×D₄	—	4	1	no	—
1044	C₂×D₄	—	4	4	no	—
1045	C₂×D₄	—	4	4	no	—
1046	C₂×D₄	—	8	2	no	—
1047	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1048	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1049	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1050	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1051	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1052	C₂²×C₄	—	2	2	no	—
1053	C₂²×C₄	—	2	2	no	—
1054	C₂²×C₄	—	2	1	no	—
1055	C₂²×C₄	—	2	1	no	—
1056	C₂²×C₄	—	2	1	no	—
1057	C₂²×C₄	—	2	1	no	—
1058	C₂²×C₄	—	2	1	no	—
1059	C₂²×C₄	—	2	2	no	—
1060	C₂²×C₄	—	2	1	no	—
1061	C₂²×C₄	—	2	2	no	—
1062	C₂²×C₄	—	2	1	no	—
1063	C₂²×C₄	—	2	1	no	—
1064	C₂²×C₄	—	2	2	no	—
1065	C₂²×C₄	—	2	2	no	—
1066	C₂²×C₄	—	2	2	no	—
1067	C₂²×C₄	—	4	4	no	—
1068	C₂²×C₄	—	4	4	no	—
1069	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1070	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1071	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1072	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1073	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1074	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1075	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1076	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1077	Q₁₆	—	4	1	no	—
1078	Q₁₆	—	4	1	no	—
1079	Q₁₆	—	4	2	no	—
1080	SD₁₆	—	4	2	no	—
1081	SD₁₆	—	4	2	no	—
1082	SD₁₆	—	4	1	no	—
1083	SD₁₆	—	4	1	no	—
1084	SD₁₆	—	4	1	no	—
1085	SD₁₆	—	4	1	no	—
1086	SD₁₆	—	4	2	no	—
1087	SD₁₆	—	4	2	no	—
1088	SD₁₆	—	4	2	no	—
1089	SD₁₆	—	4	2	no	—
1090	D₈	—	4	2	no	—
1091	D₈	—	4	2	no	—
1092	D₈	—	4	1	no	—
1093	D₈	—	4	1	no	—
1094	D₈	—	4	2	no	—
1095	D₈	—	4	2	no	—
1096	D₈	—	4	2	no	—
1097	M₁₆	—	2	2	no	—
1098	M₁₆	—	2	2	no	—
1099	C₂×C₈	—	2	2	no	—
1100	C₂×C₈	—	2	2	no	—
1101	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1102	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1103	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1104	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1105	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1106	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1107	C₄⋊C₄	—	2	1	no	—
1108	C₄⋊C₄	—	2	2	no	—
1109	C₄⋊C₄	—	2	1	no	—
1110	C₄⋊C₄	—	2	2	no	—
1111	C₄⋊C₄	—	2	2	no	—
1112	C₄⋊C₄	—	2	2	no	—
1113	C₄⋊C₄	—	2	2	no	—
1114	C₄⋊C₄	—	2	2	no	—
1115	C₄⋊C₄	—	2	2	no	—
1116	C₄⋊C₄	—	2	2	no	—
1117	C₄⋊C₄	—	2	1	no	—
1118	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1119	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1120	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1121	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1122	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1123	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1124	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1125	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1126	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	1	no	—
1129	C₂²⋊C₄	—	2	1	no	—
1130	C₂²⋊C₄	—	2	2	no	—
1131	C₂²⋊C₄	—	2	2	no	—
1132	C₂²⋊C₄	—	2	2	no	—
1133	C₂²⋊C₄	—	2	2	no	—
1134	C₂²⋊C₄	—	2	2	no	—
1135	C₂²⋊C₄	—	2	2	no	—
1136	C₂²⋊C₄	—	2	1	no	—
1137	C₂²⋊C₄	—	2	2	no	—
1138	C₂²⋊C₄	—	2	2	no	—
1139	C₂²⋊C₄	—	2	2	no	—
1140	C₂²⋊C₄	—	2	2	no	—
1141	C₂²⋊C₄	—	2	2	no	—
1142	C₂²⋊C₄	—	2	2	no	—
1143	C₂²⋊C₄	—	2	2	no	—
1144	C₂²⋊C₄	—	2	2	no	—
1145	C₂²⋊C₄	—	2	2	no	—
1146	C₂²⋊C₄	—	2	1	no	—
1147	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1148	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1149	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1150	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1151	C₄²	—	2	2	no	—
1152	C₄²	—	2	1	no	—
1153	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1154	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1155	C₄²	C₂⁴×C₅₃	1	2	yes	—
1156	C₄²	C₂⁴×C₅₃	1	2	yes	—
1157	C₂³	—	2	2	no	—
1158	C₂³	—	2	2	no	—
1159	C₂³	—	2	1	no	—
1160	C₂³	—	2	2	no	—
1161	C₂³	—	2	1	no	—
1162	C₂³	—	2	1	no	—
1163	C₂³	—	4	1	no	—
1164	C₂³	—	4	1	no	—
1165	C₂³	—	4	2	no	—
1166	C₂³	—	4	2	no	—
1167	C₂³	—	4	2	no	—
1168	C₂³	—	8	1	no	—
1169	C₂³	—	8	1	no	—
1170	C₂³	—	8	1	no	—
1171	C₂³	—	8	1	no	—
1172	C₂³	—	8	1	no	—
1173	C₂³	—	8	1	no	—
1174	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1175	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1176	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1177	Q₈	—	2	1	no	—
1178	Q₈	—	2	2	no	—
1179	Q₈	—	2	1	no	—
1180	Q₈	—	2	1	no	—
1181	Q₈	—	2	1	no	—
1182	Q₈	—	2	2	no	—
1183	Q₈	—	2	1	no	—
1184	Q₈	—	2	1	no	—
1185	Q₈	—	4	2	no	—
1186	Q₈	—	4	2	no	—
1187	Q₈	—	8	2	no	—
1188	D₄	—	2	2	no	—
1189	D₄	—	2	1	no	—
1190	D₄	—	2	2	no	—
1191	D₄	—	2	1	no	—
1192	D₄	—	2	1	no	—
1193	D₄	—	2	2	no	—
1194	D₄	—	2	1	no	—
1195	D₄	—	2	2	no	—
1196	D₄	—	2	1	no	—
1197	D₄	—	2	1	no	—
1198	D₄	—	4	2	no	—
1199	D₄	—	4	4	no	—
1200	D₄	—	4	4	no	—
1201	D₄	—	4	2	no	—
1202	D₄	—	4	2	no	—
1203	D₄	—	4	4	no	—
1204	D₄	—	4	2	no	—
1205	D₄	—	4	2	no	—
1206	D₄	—	4	2	no	—
1207	D₄	—	4	2	no	—
1208	D₄	—	4	2	no	—
1209	D₄	—	4	2	no	—
1210	D₄	—	8	2	no	—
1211	D₄	—	8	2	no	—
1212	D₄	—	8	2	no	—
1213	D₄	—	8	2	no	—
1214	D₄	—	8	2	no	—
1215	D₄	—	8	2	no	—
1216	D₄	—	8	1	no	—
1217	D₄	—	8	2	no	—
1218	C₂×C₄	—	2	2	no	—
1219	C₂×C₄	—	2	2	no	—
1220	C₂×C₄	—	2	2	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	1	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	2	1	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	2	no	—
1229	C₂×C₄	—	2	2	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	4	2	no	—
1233	C₂×C₄	—	4	2	no	—
1234	C₂×C₄	—	4	4	no	—
1235	C₂×C₄	—	4	2	no	—
1236	C₂×C₄	—	4	2	no	—
1237	C₂×C₄	—	4	4	no	—
1238	C₂×C₄	—	4	2	no	—
1239	C₂×C₄	—	4	2	no	—
1240	C₂×C₄	—	4	2	no	—
1241	C₂×C₄	—	4	2	no	—
1242	C₂×C₄	—	4	2	no	—
1243	C₂×C₄	—	8	2	no	—
1244	C₂×C₄	—	8	2	no	—
1245	C₂×C₄	—	8	2	no	—
1246	C₂×C₄	—	8	1	no	—
1247	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1248	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1249	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1250	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1251	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1252	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1253	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1254	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1255	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1256	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1257	C₈	—	2	1	no	—
1258	C₈	—	2	1	no	—
1259	C₈	—	2	1	no	—
1260	C₈	—	2	1	no	—
1261	C₈	—	2	2	no	—
1262	C₈	—	2	2	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	1	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	1	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	4	2	no	—
1272	C₂²	—	4	1	no	—
1273	C₂²	—	4	2	no	—
1274	C₂²	—	4	1	no	—
1275	C₂²	—	4	1	no	—
1276	C₂²	—	4	1	no	—
1277	C₂²	—	4	2	no	—
1278	C₂²	—	4	2	no	—
1279	C₂²	—	4	1	no	—
1280	C₂²	—	4	1	no	—
1281	C₂²	—	4	2	no	—
1282	C₂²	—	4	1	no	—
1283	C₂²	—	4	1	no	—
1284	C₂²	—	4	1	no	—
1285	C₂²	—	4	2	no	—
1286	C₂²	—	8	2	no	—
1287	C₂²	—	8	4	no	—
1288	C₂²	—	8	4	no	—
1289	C₂²	—	16	2	no	—
1290	C₂²	C₅₃×#535	1	2	yes	—
1291	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1292	C₄	—	2	2	no	—
1293	C₄	—	2	2	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	2	no	—
1296	C₄	—	2	1	no	—
1297	C₄	—	2	1	no	—
1298	C₄	—	4	1	no	—
1299	C₄	—	4	2	no	—
1300	C₄	—	4	1	no	—
1301	C₄	—	4	2	no	—
1302	C₄	—	4	1	no	—
1303	C₄	—	4	1	no	—
1304	C₄	—	4	1	no	—
1305	C₄	C₅₃×#535	1	2	yes	—
1306	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1307	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1308	C₂	—	2	2	no	—
1309	C₂	—	4	1	no	—
1310	C₂	—	4	1	no	—
1311	C₂	—	8	2	no	—
1312	C₂	—	8	1	no	—
1313	C₂	—	8	1	no	—
1314	C₂	—	8	2	no	—
1315	C₂	—	8	1	no	—
1316	C₂	C₂×C₅₃×#535	1	1	yes	characteristic
1317	C₂	C₅₃×#3584	1	1	yes	characteristic
1318	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×#117×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3494	C₂	semidirect
2. C₅₃×#3449	C₂	semidirect
3. C₅₃×#3225	C₂	semidirect
4. C₅₃×#3224	C₂	semidirect
5. C₅₃×#3221	C₂	semidirect
6. C₅₃×#3220	C₂	semidirect
7. C₅₃×#3219	C₂	semidirect
8. C₅₃×#3214	C₂	semidirect
9. C₅₃×#3212	C₂	semidirect
10. C₅₃×#3207	C₂	semidirect
11. C₅₃×#3155	C₂	semidirect
12. C₅₃×#3154	C₂	semidirect
13. C₅₃×#3137	C₂	semidirect
14. C₅₃×#3136	C₂	semidirect
15. C₅₃×#3046	C₂	semidirect
16. C₅₃×#3045	C₂	semidirect
17. C₅₃×#3042	C₂	semidirect
18. C₅₃×#3041	C₂	semidirect
19. C₅₃×#3006	C₂	semidirect
20. C₅₃×#3005	C₂	semidirect
21. C₅₃×#3002	C₂	semidirect
22. C₂×C₅₃×#449	C₂	semidirect
23. C₅₃×#2924	C₂	semidirect
26. C₂×#137×C₅₃	C₂²	semidirect
29. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
32. C₂²×SD₁₆×C₅₃	C₂²	semidirect
33. C₂²×D₈×C₅₃	C₂²	semidirect
40. C₅₃×#544	C₂²	semidirect
41. C₅₃×#542	C₂²	semidirect
42. C₅₃×#540	C₂²	semidirect
47. C₅₃×#536	C₂²	semidirect
50. C₅₃×#535	C₂²	semidirect
51. C₅₃×#535	C₂²	semidirect
53. C₅₃×#532	C₂²	semidirect
54. C₅₃×#532	C₂²	semidirect
55. C₅₃×#532	C₂²	semidirect
56. C₅₃×#529	C₂²	semidirect
62. C₅₃×#520	C₂²	semidirect
63. C₅₃×#518	C₂²	semidirect
65. C₅₃×#497	C₂²	semidirect
66. C₅₃×#496	C₂²	semidirect
67. C₅₃×#496	C₂²	semidirect
68. C₅₃×#496	C₂²	semidirect
69. C₅₃×#495	C₂²	semidirect
70. C₅₃×#495	C₂²	semidirect
71. C₅₃×#493	C₂²	semidirect
72. C₅₃×#492	C₂²	semidirect
73. C₅₃×#491	C₂²	semidirect
74. C₅₃×#490	C₂²	semidirect
75. C₅₃×#489	C₂²	semidirect
76. C₅₃×#489	C₂²	semidirect
77. C₅₃×#488	C₂²	semidirect
78. C₅₃×#488	C₂²	semidirect
79. C₅₃×#487	C₂²	semidirect
80. C₅₃×#486	C₂²	semidirect
81. C₅₃×#464	C₂²	semidirect
82. C₅₃×#464	C₂²	semidirect
83. C₅₃×#463	C₂²	semidirect
84. C₅₃×#463	C₂²	semidirect
85. C₅₃×#463	C₂²	semidirect
86. C₅₃×#463	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#462	C₂²	semidirect
90. C₅₃×#461	C₂²	semidirect
91. C₅₃×#461	C₂²	semidirect
92. C₅₃×#461	C₂²	semidirect
93. C₅₃×#460	C₂²	semidirect
94. C₅₃×#459	C₂²	semidirect
95. C₅₃×#459	C₂²	semidirect
96. C₅₃×#459	C₂²	semidirect
97. C₅₃×#452	C₂²	semidirect
98. C₅₃×#452	C₂²	semidirect
99. C₅₃×#452	C₂²	semidirect
100. C₅₃×#452	C₂²	semidirect
101. C₅₃×#451	C₂²	semidirect
102. C₅₃×#450	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×#449	C₂²	semidirect
111. C₅₃×#449	C₂²	semidirect
112. C₅₃×#449	C₂²	semidirect
113. C₅₃×#448	C₂²	semidirect
114. C₅₃×#448	C₂²	semidirect
115. C₅₃×#447	C₂²	semidirect
116. C₅₃×#447	C₂²	semidirect
117. C₅₃×#433	C₂²	semidirect
118. C₅₃×#433	C₂²	semidirect
119. C₅₃×#432	C₂²	semidirect
120. C₅₃×#431	C₂²	semidirect
121. C₅₃×#424	C₂²	semidirect
122. C₅₃×#424	C₂²	semidirect
123. C₅₃×#419	C₂²	semidirect
124. C₅₃×#418	C₂²	semidirect
129. C₂×#103×C₅₃	C₂²	semidirect
130. C₂×#102×C₅₃	C₂²	semidirect
133. C₅₃×#405	C₂²	semidirect
134. C₅₃×#405	C₂²	semidirect
603. #60815	C₅₃	direct (N × H)
649. #3494	C₂×C₅₃	semidirect
650. #3449	C₂×C₅₃	semidirect
651. #3225	C₂×C₅₃	semidirect
652. #3224	C₂×C₅₃	semidirect
653. #3221	C₂×C₅₃	semidirect
654. #3220	C₂×C₅₃	semidirect
655. #3219	C₂×C₅₃	semidirect
656. #3214	C₂×C₅₃	semidirect
657. #3212	C₂×C₅₃	semidirect
658. #3207	C₂×C₅₃	semidirect
659. #3155	C₂×C₅₃	semidirect
660. #3154	C₂×C₅₃	semidirect
661. #3137	C₂×C₅₃	semidirect
662. #3136	C₂×C₅₃	semidirect
663. #3046	C₂×C₅₃	semidirect
664. #3045	C₂×C₅₃	semidirect
665. #3042	C₂×C₅₃	semidirect
666. #3041	C₂×C₅₃	semidirect
667. #3006	C₂×C₅₃	semidirect
668. #3005	C₂×C₅₃	semidirect
669. #3002	C₂×C₅₃	semidirect
670. C₂×#449	C₂×C₅₃	semidirect
671. #2924	C₂×C₅₃	semidirect
685. C₂×#137	C₂²×C₅₃	semidirect
688. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
691. C₂²×SD₁₆	C₂²×C₅₃	semidirect
692. C₂²×D₈	C₂²×C₅₃	semidirect
699. #544	C₂²×C₅₃	semidirect
700. #542	C₂²×C₅₃	semidirect
701. #540	C₂²×C₅₃	semidirect
706. #536	C₂²×C₅₃	semidirect
709. #535	C₂²×C₅₃	semidirect
710. #535	C₂²×C₅₃	semidirect
712. #532	C₂²×C₅₃	semidirect
713. #532	C₂²×C₅₃	semidirect
714. #532	C₂²×C₅₃	semidirect
715. #529	C₂²×C₅₃	semidirect
721. #520	C₂²×C₅₃	semidirect
722. #518	C₂²×C₅₃	semidirect
724. #497	C₂²×C₅₃	semidirect
725. #496	C₂²×C₅₃	semidirect
726. #496	C₂²×C₅₃	semidirect
727. #496	C₂²×C₅₃	semidirect
728. #495	C₂²×C₅₃	semidirect
729. #495	C₂²×C₅₃	semidirect
730. #493	C₂²×C₅₃	semidirect
731. #492	C₂²×C₅₃	semidirect
732. #491	C₂²×C₅₃	semidirect
733. #490	C₂²×C₅₃	semidirect
734. #489	C₂²×C₅₃	semidirect
735. #489	C₂²×C₅₃	semidirect
736. #488	C₂²×C₅₃	semidirect
737. #488	C₂²×C₅₃	semidirect
738. #487	C₂²×C₅₃	semidirect
739. #486	C₂²×C₅₃	semidirect
740. #464	C₂²×C₅₃	semidirect
741. #464	C₂²×C₅₃	semidirect
742. #463	C₂²×C₅₃	semidirect
743. #463	C₂²×C₅₃	semidirect
744. #463	C₂²×C₅₃	semidirect
745. #463	C₂²×C₅₃	semidirect
746. #463	C₂²×C₅₃	semidirect
747. #463	C₂²×C₅₃	semidirect
748. #462	C₂²×C₅₃	semidirect
749. #461	C₂²×C₅₃	semidirect
750. #461	C₂²×C₅₃	semidirect
751. #461	C₂²×C₅₃	semidirect
752. #460	C₂²×C₅₃	semidirect
753. #459	C₂²×C₅₃	semidirect
754. #459	C₂²×C₅₃	semidirect
755. #459	C₂²×C₅₃	semidirect
756. #452	C₂²×C₅₃	semidirect
757. #452	C₂²×C₅₃	semidirect
758. #452	C₂²×C₅₃	semidirect
759. #452	C₂²×C₅₃	semidirect
760. #451	C₂²×C₅₃	semidirect
761. #450	C₂²×C₅₃	semidirect
764. #449	C₂²×C₅₃	semidirect
765. #449	C₂²×C₅₃	semidirect
766. #449	C₂²×C₅₃	semidirect
767. #449	C₂²×C₅₃	semidirect
768. #449	C₂²×C₅₃	semidirect
769. #449	C₂²×C₅₃	semidirect
770. #449	C₂²×C₅₃	semidirect
771. #449	C₂²×C₅₃	semidirect
772. #448	C₂²×C₅₃	semidirect
773. #448	C₂²×C₅₃	semidirect
774. #447	C₂²×C₅₃	semidirect
775. #447	C₂²×C₅₃	semidirect
776. #433	C₂²×C₅₃	semidirect
777. #433	C₂²×C₅₃	semidirect
778. #432	C₂²×C₅₃	semidirect
779. #431	C₂²×C₅₃	semidirect
780. #424	C₂²×C₅₃	semidirect
781. #424	C₂²×C₅₃	semidirect
782. #419	C₂²×C₅₃	semidirect
783. #418	C₂²×C₅₃	semidirect
788. C₂×#103	C₂²×C₅₃	semidirect
789. C₂×#102	C₂²×C₅₃	semidirect
792. #405	C₂²×C₅₃	semidirect
793. #405	C₂²×C₅₃	semidirect
794. C₅₃	#60815	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×#3494	2
C₅₃×#3449	2
C₅₃×#3225	2
C₅₃×#3224	2
C₅₃×#3221	2
C₅₃×#3220	2
C₅₃×#3219	2
C₅₃×#3214	2
C₅₃×#3212	2
C₅₃×#3207	2
C₅₃×#3155	2
C₅₃×#3154	2
C₅₃×#3137	2
C₅₃×#3136	2
C₅₃×#3046	2
C₅₃×#3045	2
C₅₃×#3042	2
C₅₃×#3041	2
C₅₃×#3006	2
C₅₃×#3005	2
C₅₃×#3002	2
C₂×C₅₃×#449	2
C₅₃×#2924	2
#60815	53

Subgroups — C53×#60815 #27268327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60815 #27268327