Subgroups — C₅₃×#61169 #27268681

Order 13568.

2074 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3319	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3315	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3311	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3307	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3303	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3302	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3297	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3296	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3005	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₅₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
30	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#556	—	2	1	no	—
32	C₅₃×#556	C₂²	1	2	yes	complemented
33	C₅₃×#555	—	2	1	no	—
34	C₅₃×#555	C₂²	1	2	yes	complemented
35	C₅₃×#553	—	2	1	no	—
36	C₅₃×#553	C₂²	1	2	yes	complemented
37	C₅₃×#552	—	2	1	no	—
38	C₅₃×#552	C₂²	1	2	yes	complemented
39	C₅₃×#547	—	2	1	no	—
40	C₅₃×#547	—	2	1	no	—
41	C₅₃×#547	C₂²	1	2	yes	—
42	C₅₃×#547	C₂²	1	2	yes	—
43	C₅₃×#546	—	2	1	no	—
44	C₅₃×#546	—	2	1	no	—
45	C₅₃×#546	C₂²	1	2	yes	—
46	C₅₃×#546	C₂²	1	2	yes	—
47	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#538	—	2	2	no	—
49	C₅₃×#537	C₂²	1	1	yes	characteristic
50	C₅₃×#536	C₂²	1	1	yes	characteristic
51	C₅₃×#536	C₂²	1	1	yes	characteristic
52	C₅₃×#534	—	2	2	no	—
53	C₅₃×#529	—	2	2	no	—
54	C₅₃×#525	C₂²	1	1	yes	characteristic
55	C₅₃×#525	C₂²	1	1	yes	characteristic
56	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
57	C₂×#123×C₅₃	—	2	2	no	—
58	C₅₃×#520	C₂²	1	1	yes	characteristic
59	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#518	C₂²	1	1	yes	characteristic
61	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#491	C₂²	1	2	yes	complemented
63	C₅₃×#489	C₂²	1	2	yes	complemented
64	C₅₃×#488	C₂²	1	2	yes	complemented
65	C₅₃×#487	C₂²	1	2	yes	complemented
66	C₅₃×#485	C₂²	1	2	yes	complemented
67	C₅₃×#485	C₂²	1	2	yes	complemented
68	C₅₃×#485	C₂²	1	2	yes	complemented
69	C₅₃×#485	C₂²	1	2	yes	complemented
70	C₅₃×#484	C₂²	1	2	yes	complemented
71	C₅₃×#483	C₂²	1	2	yes	complemented
72	C₅₃×#482	C₂²	1	2	yes	complemented
73	C₅₃×#482	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	2	yes	complemented
75	C₅₃×#478	C₂²	1	2	yes	complemented
76	C₅₃×#476	C₂²	1	2	yes	complemented
77	C₅₃×#474	C₂²	1	2	yes	complemented
78	C₅₃×#470	C₂²	1	2	yes	complemented
79	C₅₃×#468	C₂²	1	2	yes	complemented
80	C₅₃×#467	C₂²	1	2	yes	complemented
81	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#465	C₂²	1	2	yes	complemented
87	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#464	C₂²	1	2	yes	complemented
91	C₅₃×#463	C₂²	1	2	yes	complemented
92	C₅₃×#462	C₂²	1	2	yes	complemented
93	C₅₃×#461	C₂²	1	2	yes	complemented
94	C₅₃×#452	C₂²	1	2	yes	complemented
95	C₅₃×#452	C₂²	1	2	yes	complemented
96	C₅₃×#452	C₂²	1	2	yes	complemented
97	C₅₃×#450	C₂²	1	2	yes	complemented
98	C₅₃×#449	C₂²	1	2	yes	complemented
99	C₅₃×#449	C₂²	1	2	yes	complemented
100	C₅₃×#449	C₂²	1	2	yes	complemented
101	C₅₃×#447	C₂²	1	2	yes	complemented
102	C₅₃×#442	C₂²	1	2	yes	complemented
103	C₅₃×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
105	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
106	C₅₃×#435	C₂²	1	2	yes	complemented
107	C₅₃×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
109	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
110	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#418	C₂²	1	1	yes	characteristic
116	C₅₃×#418	C₂²	1	2	yes	complemented
117	C₅₃×#417	C₂²	1	1	yes	characteristic
118	C₅₃×#417	C₂²	1	1	yes	characteristic
119	C₅₃×#417	C₂²	1	2	yes	complemented
120	C₅₃×#416	C₂²	1	1	yes	characteristic
121	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#416	C₂²	1	2	yes	complemented
123	C₅₃×#416	C₂²	1	2	yes	complemented
124	C₅₃×#416	C₂²	1	2	yes	complemented
125	C₅₃×#416	C₂²	1	2	yes	complemented
126	C₅₃×#416	C₂²	1	2	yes	complemented
127	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
128	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
129	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
130	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
131	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
132	C₅₃×#408	C₂²	1	1	yes	characteristic
133	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
135	H(5,𝔽₂)×C₅₃	—	2	4	no	—
136	H(5,𝔽₂)×C₅₃	—	4	2	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	4	no	—
141	C₂×#41×C₅₃	—	4	2	no	—
142	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×#41×C₅₃	C₂³	1	2	yes	—
145	C₂×#41×C₅₃	C₂³	1	2	yes	—
146	C₂×#41×C₅₃	C₂³	1	2	yes	—
147	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₅₃	—	2	1	no	—
150	C₂²×D₄×C₅₃	—	2	2	no	—
151	C₂²×D₄×C₅₃	—	2	1	no	—
152	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
153	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₅₃	—	2	1	no	—
155	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
156	#137×C₅₃	—	4	2	no	—
157	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
158	#135×C₅₃	—	4	2	no	—
159	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
165	C₂×D₈×C₅₃	C₂³	1	2	yes	—
166	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
167	#131×C₅₃	—	4	2	no	—
168	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
171	C₂²×C₈×C₅₃	—	4	2	no	—
172	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
179	C₄⋊Q₈×C₅₃	—	2	1	no	—
180	C₄⋊Q₈×C₅₃	—	2	1	no	—
181	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
182	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
183	#126×C₅₃	—	2	2	no	—
184	#126×C₅₃	—	2	2	no	—
185	#126×C₅₃	—	2	2	no	—
186	#126×C₅₃	—	2	2	no	—
187	#125×C₅₃	—	2	2	no	—
188	#125×C₅₃	—	2	1	no	—
189	#125×C₅₃	C₂³	1	2	yes	—
190	#124×C₅₃	—	2	2	no	—
191	#124×C₅₃	—	2	2	no	—
192	#124×C₅₃	—	2	1	no	—
193	#124×C₅₃	—	2	2	no	—
194	#124×C₅₃	C₂³	1	2	yes	—
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	2	no	—
202	#123×C₅₃	—	2	2	no	—
203	#123×C₅₃	—	2	2	no	—
204	#123×C₅₃	—	2	2	no	—
205	#123×C₅₃	—	2	1	no	—
206	#123×C₅₃	—	2	1	no	—
207	#123×C₅₃	D₄	1	2	yes	—
208	C₂²⋊Q₈×C₅₃	—	2	1	no	—
209	C₂²⋊Q₈×C₅₃	—	2	1	no	—
210	C₂²⋊Q₈×C₅₃	—	2	2	no	—
211	C₂²⋊Q₈×C₅₃	—	2	1	no	—
212	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
213	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
214	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
215	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
216	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
219	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
221	#121×C₅₃	—	2	2	no	—
222	#121×C₅₃	—	2	2	no	—
223	#121×C₅₃	—	2	2	no	—
224	#121×C₅₃	—	2	2	no	—
225	#121×C₅₃	—	2	2	no	—
226	#121×C₅₃	—	2	1	no	—
227	#121×C₅₃	—	2	2	no	—
228	#121×C₅₃	—	2	2	no	—
229	#121×C₅₃	D₄	1	1	yes	characteristic
230	#121×C₅₃	D₄	1	1	yes	characteristic
231	#121×C₅₃	C₂³	1	1	yes	characteristic
232	#121×C₅₃	C₂³	1	1	yes	characteristic
233	#121×C₅₃	C₂³	1	1	yes	characteristic
234	#121×C₅₃	C₂³	1	1	yes	characteristic
235	#121×C₅₃	C₂³	1	2	yes	—
236	#120×C₅₃	—	2	1	no	—
237	#120×C₅₃	—	2	1	no	—
238	#120×C₅₃	—	2	2	no	—
239	#120×C₅₃	—	2	2	no	—
240	#120×C₅₃	D₄	1	2	yes	—
241	C₄×Q₈×C₅₃	—	2	2	no	—
242	C₄×Q₈×C₅₃	—	2	1	no	—
243	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
244	C₄×D₄×C₅₃	—	2	1	no	—
245	C₄×D₄×C₅₃	—	2	1	no	—
246	C₄×D₄×C₅₃	—	2	2	no	—
247	C₄×D₄×C₅₃	—	2	2	no	—
248	C₄×D₄×C₅₃	—	2	2	no	—
249	C₄×D₄×C₅₃	—	2	1	no	—
250	C₄×D₄×C₅₃	—	2	1	no	—
251	C₄×D₄×C₅₃	—	2	1	no	—
252	C₄×D₄×C₅₃	—	2	1	no	—
253	C₄×D₄×C₅₃	—	2	1	no	—
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	2	yes	—
258	C₄×D₄×C₅₃	C₂³	1	2	yes	—
259	#117×C₅₃	—	2	1	no	—
260	#117×C₅₃	—	2	2	no	—
261	#117×C₅₃	—	2	2	no	—
262	#117×C₅₃	—	2	1	no	—
263	#117×C₅₃	—	2	1	no	—
264	#117×C₅₃	C₂³	1	2	yes	—
265	#117×C₅₃	C₂³	1	2	yes	—
266	#117×C₅₃	C₂³	1	2	yes	—
267	#117×C₅₃	C₂³	1	1	yes	characteristic
268	#117×C₅₃	C₂³	1	1	yes	characteristic
269	#117×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
271	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
272	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
273	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
276	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
277	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
278	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
279	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
280	C₂×C₄²×C₅₃	—	2	1	no	—
281	#107×C₅₃	C₂³	1	1	yes	characteristic
282	#107×C₅₃	C₂³	1	2	yes	—
283	#107×C₅₃	C₂³	1	2	yes	—
284	#107×C₅₃	C₂³	1	1	yes	characteristic
285	#106×C₅₃	C₂³	1	1	yes	characteristic
286	#106×C₅₃	C₂³	1	2	yes	—
287	#106×C₅₃	C₂³	1	2	yes	—
288	#106×C₅₃	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
290	C₄⋊C₈×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	2	yes	—
295	#103×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	1	yes	characteristic
297	#103×C₅₃	C₂³	1	2	yes	—
298	#103×C₅₃	C₂³	1	2	yes	—
299	#103×C₅₃	C₂³	1	2	yes	—
300	#103×C₅₃	C₂³	1	1	yes	characteristic
301	#103×C₅₃	C₂³	1	1	yes	characteristic
302	#103×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	2	yes	—
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	2	yes	—
307	#102×C₅₃	C₂³	1	2	yes	—
308	#102×C₅₃	C₂³	1	2	yes	—
309	#102×C₅₃	C₂³	1	2	yes	—
310	#102×C₅₃	C₂³	1	2	yes	—
311	#102×C₅₃	C₂³	1	2	yes	—
312	#102×C₅₃	C₂³	1	2	yes	—
313	#102×C₅₃	C₂³	1	1	yes	characteristic
314	#102×C₅₃	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
316	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
319	#97×C₅₃	C₂³	1	2	yes	—
320	C₄×C₈×C₅₃	C₂³	1	2	yes	—
321	C₂⁴×C₅₃	—	2	1	no	—
322	C₂⁴×C₅₃	—	2	2	no	—
323	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
324	#41×C₅₃	—	2	2	no	—
325	#41×C₅₃	—	2	2	no	—
326	#41×C₅₃	—	2	4	no	—
327	#41×C₅₃	—	2	4	no	—
328	#41×C₅₃	—	2	4	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	—	4	2	no	—
334	#41×C₅₃	—	4	2	no	—
335	#41×C₅₃	—	4	2	no	—
336	#41×C₅₃	—	4	4	no	—
337	#41×C₅₃	—	4	4	no	—
338	#41×C₅₃	—	4	4	no	—
339	C₂×Q₈×C₅₃	—	2	1	no	—
340	C₂×Q₈×C₅₃	—	2	2	no	—
341	C₂×Q₈×C₅₃	—	2	2	no	—
342	C₂×Q₈×C₅₃	—	2	2	no	—
343	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
344	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
345	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
346	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₅₃	—	2	4	no	—
348	C₂×D₄×C₅₃	—	2	1	no	—
349	C₂×D₄×C₅₃	—	2	2	no	—
350	C₂×D₄×C₅₃	—	2	2	no	—
351	C₂×D₄×C₅₃	—	2	1	no	—
352	C₂×D₄×C₅₃	—	2	2	no	—
353	C₂×D₄×C₅₃	—	2	1	no	—
354	C₂×D₄×C₅₃	—	2	1	no	—
355	C₂×D₄×C₅₃	—	2	1	no	—
356	C₂×D₄×C₅₃	—	2	1	no	—
357	C₂×D₄×C₅₃	—	2	2	no	—
358	C₂×D₄×C₅₃	—	2	1	no	—
359	C₂×D₄×C₅₃	—	2	2	no	—
360	C₂×D₄×C₅₃	—	2	2	no	—
361	C₂×D₄×C₅₃	—	4	2	no	—
362	C₂×D₄×C₅₃	—	4	4	no	—
363	C₂×D₄×C₅₃	—	4	8	no	—
364	C₂×D₄×C₅₃	—	4	4	no	—
365	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
366	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₅₃	#41	1	4	yes	—
370	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
373	C₂²×C₄×C₅₃	—	2	2	no	—
374	C₂²×C₄×C₅₃	—	2	2	no	—
375	C₂²×C₄×C₅₃	—	2	1	no	—
376	C₂²×C₄×C₅₃	—	2	1	no	—
377	C₂²×C₄×C₅₃	—	2	1	no	—
378	C₂²×C₄×C₅₃	—	2	2	no	—
379	C₂²×C₄×C₅₃	—	2	2	no	—
380	C₂²×C₄×C₅₃	—	2	2	no	—
381	C₂²×C₄×C₅₃	—	2	2	no	—
382	C₂²×C₄×C₅₃	—	2	1	no	—
383	C₂²×C₄×C₅₃	—	2	1	no	—
384	C₂²×C₄×C₅₃	—	2	2	no	—
385	C₂²×C₄×C₅₃	—	2	2	no	—
386	C₂²×C₄×C₅₃	—	2	2	no	—
387	C₂²×C₄×C₅₃	—	4	4	no	—
388	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
392	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	Q₁₆×C₅₃	—	4	1	no	—
396	Q₁₆×C₅₃	—	4	2	no	—
397	SD₁₆×C₅₃	—	2	4	no	—
398	SD₁₆×C₅₃	—	4	1	no	—
399	SD₁₆×C₅₃	—	4	1	no	—
400	SD₁₆×C₅₃	—	4	2	no	—
401	D₈×C₅₃	—	2	4	no	—
402	D₈×C₅₃	—	4	1	no	—
403	M₁₆×C₅₃	—	2	2	no	—
404	M₁₆×C₅₃	—	2	2	no	—
405	M₁₆×C₅₃	—	4	2	no	—
406	C₂×C₈×C₅₃	—	2	2	no	—
407	C₂×C₈×C₅₃	—	2	2	no	—
408	C₂×C₈×C₅₃	—	4	1	no	—
409	C₂×C₈×C₅₃	—	4	1	no	—
410	C₂×C₈×C₅₃	—	4	1	no	—
411	C₂×C₈×C₅₃	—	4	1	no	—
412	C₂×C₈×C₅₃	—	4	2	no	—
413	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
415	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
417	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₅₃	—	2	1	no	—
420	C₄⋊C₄×C₅₃	—	2	1	no	—
421	C₄⋊C₄×C₅₃	—	2	1	no	—
422	C₄⋊C₄×C₅₃	—	2	2	no	—
423	C₄⋊C₄×C₅₃	—	2	2	no	—
424	C₄⋊C₄×C₅₃	—	2	2	no	—
425	C₄⋊C₄×C₅₃	—	2	2	no	—
426	C₄⋊C₄×C₅₃	—	2	2	no	—
427	C₄⋊C₄×C₅₃	—	2	1	no	—
428	C₄⋊C₄×C₅₃	—	2	2	no	—
429	C₄⋊C₄×C₅₃	—	2	1	no	—
430	C₄⋊C₄×C₅₃	—	2	2	no	—
431	C₄⋊C₄×C₅₃	—	2	2	no	—
432	C₄⋊C₄×C₅₃	—	2	1	no	—
433	C₄⋊C₄×C₅₃	—	2	2	no	—
434	C₄⋊C₄×C₅₃	—	2	2	no	—
435	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
436	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
438	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
440	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
442	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₂²⋊C₄×C₅₃	—	2	1	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	—	2	2	no	—
450	C₂²⋊C₄×C₅₃	—	2	2	no	—
451	C₂²⋊C₄×C₅₃	—	2	1	no	—
452	C₂²⋊C₄×C₅₃	—	2	2	no	—
453	C₂²⋊C₄×C₅₃	—	2	1	no	—
454	C₂²⋊C₄×C₅₃	—	2	1	no	—
455	C₂²⋊C₄×C₅₃	—	2	1	no	—
456	C₂²⋊C₄×C₅₃	—	2	1	no	—
457	C₂²⋊C₄×C₅₃	—	2	1	no	—
458	C₂²⋊C₄×C₅₃	—	2	1	no	—
459	C₂²⋊C₄×C₅₃	—	2	2	no	—
460	C₂²⋊C₄×C₅₃	—	2	2	no	—
461	C₂²⋊C₄×C₅₃	—	2	2	no	—
462	C₂²⋊C₄×C₅₃	—	2	2	no	—
463	C₂²⋊C₄×C₅₃	—	2	1	no	—
464	C₂²⋊C₄×C₅₃	—	2	2	no	—
465	C₂²⋊C₄×C₅₃	—	2	2	no	—
466	C₂²⋊C₄×C₅₃	—	2	1	no	—
467	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
468	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
469	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
470	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
471	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
472	C₄²×C₅₃	—	2	2	no	—
473	C₄²×C₅₃	—	2	2	no	—
474	C₄²×C₅₃	—	2	2	no	—
475	C₄²×C₅₃	—	2	2	no	—
476	C₄²×C₅₃	—	2	1	no	—
477	C₄²×C₅₃	—	2	1	no	—
478	C₄²×C₅₃	C₂⁴	1	2	yes	—
479	C₂³×C₅₃	—	2	2	no	—
480	C₂³×C₅₃	—	2	2	no	—
481	C₂³×C₅₃	—	2	4	no	—
482	C₂³×C₅₃	—	2	1	no	—
483	C₂³×C₅₃	—	2	1	no	—
484	C₂³×C₅₃	—	4	1	no	—
485	C₂³×C₅₃	—	4	1	no	—
486	C₂³×C₅₃	—	4	4	no	—
487	C₂³×C₅₃	—	8	1	no	—
488	C₂³×C₅₃	—	8	1	no	—
489	C₂³×C₅₃	—	8	2	no	—
490	C₂³×C₅₃	—	8	2	no	—
491	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
492	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
493	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
494	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
495	Q₈×C₅₃	—	2	2	no	—
496	Q₈×C₅₃	—	2	2	no	—
497	Q₈×C₅₃	—	2	1	no	—
498	Q₈×C₅₃	—	2	1	no	—
499	Q₈×C₅₃	—	2	2	no	—
500	Q₈×C₅₃	—	2	1	no	—
501	Q₈×C₅₃	—	2	1	no	—
502	Q₈×C₅₃	—	4	2	no	—
503	Q₈×C₅₃	—	8	2	no	—
504	D₄×C₅₃	—	2	4	no	—
505	D₄×C₅₃	—	2	4	no	—
506	D₄×C₅₃	—	2	2	no	—
507	D₄×C₅₃	—	2	1	no	—
508	D₄×C₅₃	—	2	1	no	—
509	D₄×C₅₃	—	2	2	no	—
510	D₄×C₅₃	—	2	1	no	—
511	D₄×C₅₃	—	2	1	no	—
512	D₄×C₅₃	—	4	2	no	—
513	D₄×C₅₃	—	4	2	no	—
514	D₄×C₅₃	—	4	4	no	—
515	D₄×C₅₃	—	4	4	no	—
516	D₄×C₅₃	—	4	4	no	—
517	D₄×C₅₃	—	4	4	no	—
518	D₄×C₅₃	—	4	2	no	—
519	D₄×C₅₃	—	4	2	no	—
520	D₄×C₅₃	—	8	1	no	—
521	D₄×C₅₃	—	8	1	no	—
522	D₄×C₅₃	—	8	1	no	—
523	D₄×C₅₃	—	8	2	no	—
524	D₄×C₅₃	—	8	1	no	—
525	D₄×C₅₃	C₂×#41	1	4	yes	—
526	C₂×C₄×C₅₃	—	2	2	no	—
527	C₂×C₄×C₅₃	—	2	2	no	—
528	C₂×C₄×C₅₃	—	2	2	no	—
529	C₂×C₄×C₅₃	—	2	1	no	—
530	C₂×C₄×C₅₃	—	2	1	no	—
531	C₂×C₄×C₅₃	—	2	2	no	—
532	C₂×C₄×C₅₃	—	2	1	no	—
533	C₂×C₄×C₅₃	—	2	1	no	—
534	C₂×C₄×C₅₃	—	2	2	no	—
535	C₂×C₄×C₅₃	—	2	1	no	—
536	C₂×C₄×C₅₃	—	2	2	no	—
537	C₂×C₄×C₅₃	—	2	2	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	2	no	—
542	C₂×C₄×C₅₃	—	2	1	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	4	4	no	—
545	C₂×C₄×C₅₃	—	4	4	no	—
546	C₂×C₄×C₅₃	—	4	4	no	—
547	C₂×C₄×C₅₃	—	4	2	no	—
548	C₂×C₄×C₅₃	—	4	2	no	—
549	C₂×C₄×C₅₃	—	4	2	no	—
550	C₂×C₄×C₅₃	—	8	2	no	—
551	C₂×C₄×C₅₃	—	8	2	no	—
552	C₂×C₄×C₅₃	—	8	2	no	—
553	C₂×C₄×C₅₃	—	8	1	no	—
554	C₂×C₄×C₅₃	—	8	2	no	—
555	C₂×C₄×C₅₃	—	8	1	no	—
556	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
559	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
561	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
563	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
564	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
565	C₈×C₅₃	—	2	2	no	—
566	C₈×C₅₃	—	2	1	no	—
567	C₈×C₅₃	—	2	1	no	—
568	C₈×C₅₃	—	2	1	no	—
569	C₈×C₅₃	—	2	1	no	—
570	C₈×C₅₃	—	2	2	no	—
571	#61169	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
572	C₂²×C₅₃	—	2	1	no	—
573	C₂²×C₅₃	—	2	1	no	—
574	C₂²×C₅₃	—	2	2	no	—
575	C₂²×C₅₃	—	2	1	no	—
576	C₂²×C₅₃	—	2	1	no	—
577	C₂²×C₅₃	—	2	2	no	—
578	C₂²×C₅₃	—	2	1	no	—
579	C₂²×C₅₃	—	2	1	no	—
580	C₂²×C₅₃	—	2	1	no	—
581	C₂²×C₅₃	—	2	1	no	—
582	C₂²×C₅₃	—	2	2	no	—
583	C₂²×C₅₃	—	2	4	no	—
584	C₂²×C₅₃	—	4	4	no	—
585	C₂²×C₅₃	—	4	2	no	—
586	C₂²×C₅₃	—	4	2	no	—
587	C₂²×C₅₃	—	4	1	no	—
588	C₂²×C₅₃	—	4	1	no	—
589	C₂²×C₅₃	—	4	1	no	—
590	C₂²×C₅₃	—	4	1	no	—
591	C₂²×C₅₃	—	4	1	no	—
592	C₂²×C₅₃	—	4	1	no	—
593	C₂²×C₅₃	—	8	4	no	—
594	C₂²×C₅₃	—	16	4	no	—
595	C₂²×C₅₃	#546	1	2	yes	—
596	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
597	C₄×C₅₃	—	2	2	no	—
598	C₄×C₅₃	—	2	2	no	—
599	C₄×C₅₃	—	2	1	no	—
600	C₄×C₅₃	—	2	1	no	—
601	C₄×C₅₃	—	2	2	no	—
602	C₄×C₅₃	—	4	2	no	—
603	C₄×C₅₃	—	4	1	no	—
604	C₄×C₅₃	—	4	1	no	—
605	C₄×C₅₃	—	4	1	no	—
606	C₄×C₅₃	—	4	2	no	—
607	C₄×C₅₃	—	4	1	no	—
608	C₄×C₅₃	—	4	1	no	—
609	C₄×C₅₃	—	4	2	no	—
610	C₄×C₅₃	—	4	1	no	—
611	C₄×C₅₃	#546	1	2	yes	—
612	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
613	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
614	#3493	C₂×C₅₃	1	1	yes	characteristic, complemented
615	#3485	C₂×C₅₃	1	1	yes	characteristic, complemented
616	#3319	C₂×C₅₃	1	2	yes	complemented
617	#3315	C₂×C₅₃	1	2	yes	complemented
618	#3311	C₂×C₅₃	1	2	yes	complemented
619	#3307	C₂×C₅₃	1	2	yes	complemented
620	#3303	C₂×C₅₃	1	2	yes	complemented
621	#3302	C₂×C₅₃	1	2	yes	complemented
622	#3297	C₂×C₅₃	1	2	yes	complemented
623	#3296	C₂×C₅₃	1	2	yes	complemented
624	#3137	C₂×C₅₃	1	1	yes	characteristic, complemented
625	#3097	C₂×C₅₃	1	1	yes	characteristic, complemented
626	#3093	C₂×C₅₃	1	1	yes	characteristic, complemented
627	#3081	C₂×C₅₃	1	1	yes	characteristic, complemented
628	#3063	C₂×C₅₃	1	1	yes	characteristic, complemented
629	#3050	C₂×C₅₃	1	1	yes	characteristic, complemented
630	#3046	C₂×C₅₃	1	1	yes	characteristic, complemented
631	#3012	C₂×C₅₃	1	1	yes	characteristic, complemented
632	#3005	C₂×C₅₃	1	1	yes	characteristic, complemented
633	#2946	C₂×C₅₃	1	1	yes	characteristic, complemented
634	#2929	C₂×C₅₃	1	1	yes	characteristic, complemented
635	#2897	C₂×C₅₃	1	1	yes	characteristic, complemented
636	C₂×#416	C₂×C₅₃	1	1	yes	characteristic, complemented
637	C₂×C₅₃	—	2	2	no	—
638	C₂×C₅₃	—	4	1	no	—
639	C₂×C₅₃	—	4	1	no	—
640	C₂×C₅₃	—	4	2	no	—
641	C₂×C₅₃	—	4	4	no	—
642	C₂×C₅₃	—	8	1	no	—
643	C₂×C₅₃	—	8	1	no	—
644	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
645	C₂×C₅₃	#3584	1	1	yes	characteristic
646	C₂×C₅₃	#3584	1	1	yes	characteristic
647	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
648	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
649	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
650	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
651	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
652	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
653	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
654	#556	—	2	1	no	—
655	#556	C₂²×C₅₃	1	2	yes	complemented
656	#555	—	2	1	no	—
657	#555	C₂²×C₅₃	1	2	yes	complemented
658	#553	—	2	1	no	—
659	#553	C₂²×C₅₃	1	2	yes	complemented
660	#552	—	2	1	no	—
661	#552	C₂²×C₅₃	1	2	yes	complemented
662	#547	—	2	1	no	—
663	#547	—	2	1	no	—
664	#547	C₂²×C₅₃	1	2	yes	—
665	#547	C₂²×C₅₃	1	2	yes	—
666	#546	—	2	1	no	—
667	#546	—	2	1	no	—
668	#546	C₂²×C₅₃	1	2	yes	—
669	#546	C₂²×C₅₃	1	2	yes	—
670	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
671	#538	—	2	2	no	—
672	#537	C₂²×C₅₃	1	1	yes	characteristic
673	#536	C₂²×C₅₃	1	1	yes	characteristic
674	#536	C₂²×C₅₃	1	1	yes	characteristic
675	#534	—	2	2	no	—
676	#529	—	2	2	no	—
677	#525	C₂²×C₅₃	1	1	yes	characteristic
678	#525	C₂²×C₅₃	1	1	yes	characteristic
679	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
680	C₂×#123	—	2	2	no	—
681	#520	C₂²×C₅₃	1	1	yes	characteristic
682	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	#518	C₂²×C₅₃	1	1	yes	characteristic
684	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
685	#491	C₂²×C₅₃	1	2	yes	complemented
686	#489	C₂²×C₅₃	1	2	yes	complemented
687	#488	C₂²×C₅₃	1	2	yes	complemented
688	#487	C₂²×C₅₃	1	2	yes	complemented
689	#485	C₂²×C₅₃	1	2	yes	complemented
690	#485	C₂²×C₅₃	1	2	yes	complemented
691	#485	C₂²×C₅₃	1	2	yes	complemented
692	#485	C₂²×C₅₃	1	2	yes	complemented
693	#484	C₂²×C₅₃	1	2	yes	complemented
694	#483	C₂²×C₅₃	1	2	yes	complemented
695	#482	C₂²×C₅₃	1	2	yes	complemented
696	#482	C₂²×C₅₃	1	2	yes	complemented
697	#478	C₂²×C₅₃	1	2	yes	complemented
698	#478	C₂²×C₅₃	1	2	yes	complemented
699	#476	C₂²×C₅₃	1	2	yes	complemented
700	#474	C₂²×C₅₃	1	2	yes	complemented
701	#470	C₂²×C₅₃	1	2	yes	complemented
702	#468	C₂²×C₅₃	1	2	yes	complemented
703	#467	C₂²×C₅₃	1	2	yes	complemented
704	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
705	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
706	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#465	C₂²×C₅₃	1	2	yes	complemented
710	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
711	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	#464	C₂²×C₅₃	1	2	yes	complemented
714	#463	C₂²×C₅₃	1	2	yes	complemented
715	#462	C₂²×C₅₃	1	2	yes	complemented
716	#461	C₂²×C₅₃	1	2	yes	complemented
717	#452	C₂²×C₅₃	1	2	yes	complemented
718	#452	C₂²×C₅₃	1	2	yes	complemented
719	#452	C₂²×C₅₃	1	2	yes	complemented
720	#450	C₂²×C₅₃	1	2	yes	complemented
721	#449	C₂²×C₅₃	1	2	yes	complemented
722	#449	C₂²×C₅₃	1	2	yes	complemented
723	#449	C₂²×C₅₃	1	2	yes	complemented
724	#447	C₂²×C₅₃	1	2	yes	complemented
725	#442	C₂²×C₅₃	1	2	yes	complemented
726	#440	C₂²×C₅₃	1	2	yes	complemented
727	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
728	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
729	#435	C₂²×C₅₃	1	2	yes	complemented
730	#435	C₂²×C₅₃	1	2	yes	complemented
731	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
732	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
733	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
734	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
735	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
736	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
737	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
738	#418	C₂²×C₅₃	1	1	yes	characteristic
739	#418	C₂²×C₅₃	1	2	yes	complemented
740	#417	C₂²×C₅₃	1	1	yes	characteristic
741	#417	C₂²×C₅₃	1	1	yes	characteristic
742	#417	C₂²×C₅₃	1	2	yes	complemented
743	#416	C₂²×C₅₃	1	1	yes	characteristic
744	#416	C₂²×C₅₃	1	2	yes	complemented
745	#416	C₂²×C₅₃	1	2	yes	complemented
746	#416	C₂²×C₅₃	1	2	yes	complemented
747	#416	C₂²×C₅₃	1	2	yes	complemented
748	#416	C₂²×C₅₃	1	2	yes	complemented
749	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
750	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
751	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
752	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
753	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
754	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
755	#408	C₂²×C₅₃	1	1	yes	characteristic
756	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
757	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
758	C₅₃	#61169	1	1	yes	characteristic, direct product factor, Sylow
759	H(5,𝔽₂)	—	2	4	no	—
760	H(5,𝔽₂)	—	4	2	no	—
761	C₂×#41	—	2	1	no	—
762	C₂×#41	—	2	1	no	—
763	C₂×#41	—	2	1	no	—
764	C₂×#41	—	2	4	no	—
765	C₂×#41	—	4	2	no	—
766	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
767	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
768	C₂×#41	C₂³×C₅₃	1	2	yes	—
769	C₂×#41	C₂³×C₅₃	1	2	yes	—
770	C₂×#41	C₂³×C₅₃	1	2	yes	—
771	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
772	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
773	C₂²×D₄	—	2	1	no	—
774	C₂²×D₄	—	2	2	no	—
775	C₂²×D₄	—	2	1	no	—
776	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
777	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
778	C₂³×C₄	—	2	1	no	—
779	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
780	#137	—	4	2	no	—
781	AGL(1,ℤ/8)	—	2	4	no	—
782	#135	—	4	2	no	—
783	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
784	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
785	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
786	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
787	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
788	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
789	C₂×D₈	C₂³×C₅₃	1	2	yes	—
790	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
791	#131	—	4	2	no	—
792	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
793	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
794	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
795	C₂²×C₈	—	4	2	no	—
796	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
797	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
798	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
799	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
800	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
801	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
802	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
803	C₄⋊Q₈	—	2	1	no	—
804	C₄⋊Q₈	—	2	1	no	—
805	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
806	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
807	#126	—	2	2	no	—
808	#126	—	2	2	no	—
809	#126	—	2	2	no	—
810	#126	—	2	2	no	—
811	#125	—	2	2	no	—
812	#125	—	2	1	no	—
813	#125	C₂³×C₅₃	1	2	yes	—
814	#124	—	2	1	no	—
815	#124	—	2	2	no	—
816	#124	—	2	2	no	—
817	#124	—	2	2	no	—
818	#124	C₂³×C₅₃	1	2	yes	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	1	no	—
822	#123	—	2	1	no	—
823	#123	—	2	2	no	—
824	#123	—	2	2	no	—
825	#123	—	2	2	no	—
826	#123	—	2	2	no	—
827	#123	—	2	2	no	—
828	#123	—	2	2	no	—
829	#123	—	2	2	no	—
830	#123	—	2	2	no	—
831	#123	D₄×C₅₃	1	2	yes	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	—	2	1	no	—
834	C₂²⋊Q₈	—	2	1	no	—
835	C₂²⋊Q₈	—	2	2	no	—
836	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
837	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
838	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
839	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
840	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
841	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
842	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
843	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
844	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
845	#121	—	2	2	no	—
846	#121	—	2	2	no	—
847	#121	—	2	2	no	—
848	#121	—	2	1	no	—
849	#121	—	2	2	no	—
850	#121	—	2	2	no	—
851	#121	—	2	2	no	—
852	#121	—	2	2	no	—
853	#121	D₄×C₅₃	1	1	yes	characteristic
854	#121	D₄×C₅₃	1	1	yes	characteristic
855	#121	C₂³×C₅₃	1	1	yes	characteristic
856	#121	C₂³×C₅₃	1	1	yes	characteristic
857	#121	C₂³×C₅₃	1	1	yes	characteristic
858	#121	C₂³×C₅₃	1	1	yes	characteristic
859	#121	C₂³×C₅₃	1	2	yes	—
860	#120	—	2	1	no	—
861	#120	—	2	1	no	—
862	#120	—	2	2	no	—
863	#120	—	2	2	no	—
864	#120	D₄×C₅₃	1	2	yes	—
865	C₄×Q₈	—	2	1	no	—
866	C₄×Q₈	—	2	2	no	—
867	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	1	no	—
876	C₄×D₄	—	2	2	no	—
877	C₄×D₄	—	2	2	no	—
878	C₄×D₄	C₂³×C₅₃	1	2	yes	—
879	C₄×D₄	C₂³×C₅₃	1	2	yes	—
880	C₄×D₄	C₂³×C₅₃	1	2	yes	—
881	C₄×D₄	C₂³×C₅₃	1	2	yes	—
882	C₄×D₄	C₂³×C₅₃	1	2	yes	—
883	#117	—	2	1	no	—
884	#117	—	2	1	no	—
885	#117	—	2	1	no	—
886	#117	—	2	2	no	—
887	#117	—	2	2	no	—
888	#117	C₂³×C₅₃	1	2	yes	—
889	#117	C₂³×C₅₃	1	2	yes	—
890	#117	C₂³×C₅₃	1	1	yes	characteristic
891	#117	C₂³×C₅₃	1	1	yes	characteristic
892	#117	C₂³×C₅₃	1	2	yes	—
893	#117	C₂³×C₅₃	1	1	yes	characteristic
894	C₂×C₄⋊C₄	—	2	1	no	—
895	C₂×C₄⋊C₄	—	2	2	no	—
896	C₂×C₄⋊C₄	—	2	2	no	—
897	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
898	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
899	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
900	C₂×C₂²⋊C₄	—	2	1	no	—
901	C₂×C₂²⋊C₄	—	2	2	no	—
902	C₂×C₂²⋊C₄	—	2	2	no	—
903	C₂×C₂²⋊C₄	—	2	2	no	—
904	C₂×C₄²	—	2	1	no	—
905	#107	C₂³×C₅₃	1	1	yes	characteristic
906	#107	C₂³×C₅₃	1	1	yes	characteristic
907	#107	C₂³×C₅₃	1	2	yes	—
908	#107	C₂³×C₅₃	1	2	yes	—
909	#106	C₂³×C₅₃	1	1	yes	characteristic
910	#106	C₂³×C₅₃	1	1	yes	characteristic
911	#106	C₂³×C₅₃	1	2	yes	—
912	#106	C₂³×C₅₃	1	2	yes	—
913	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
914	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
915	#103	C₂³×C₅₃	1	2	yes	—
916	#103	C₂³×C₅₃	1	2	yes	—
917	#103	C₂³×C₅₃	1	2	yes	—
918	#103	C₂³×C₅₃	1	2	yes	—
919	#103	C₂³×C₅₃	1	1	yes	characteristic
920	#103	C₂³×C₅₃	1	1	yes	characteristic
921	#103	C₂³×C₅₃	1	2	yes	—
922	#103	C₂³×C₅₃	1	1	yes	characteristic
923	#103	C₂³×C₅₃	1	1	yes	characteristic
924	#103	C₂³×C₅₃	1	2	yes	—
925	#103	C₂³×C₅₃	1	2	yes	—
926	#103	C₂³×C₅₃	1	2	yes	—
927	#102	C₂³×C₅₃	1	2	yes	—
928	#102	C₂³×C₅₃	1	2	yes	—
929	#102	C₂³×C₅₃	1	2	yes	—
930	#102	C₂³×C₅₃	1	2	yes	—
931	#102	C₂³×C₅₃	1	1	yes	characteristic
932	#102	C₂³×C₅₃	1	2	yes	—
933	#102	C₂³×C₅₃	1	2	yes	—
934	#102	C₂³×C₅₃	1	1	yes	characteristic
935	#102	C₂³×C₅₃	1	2	yes	—
936	#102	C₂³×C₅₃	1	1	yes	characteristic
937	#102	C₂³×C₅₃	1	1	yes	characteristic
938	#102	C₂³×C₅₃	1	2	yes	—
939	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
940	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
941	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
942	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
943	#97	C₂³×C₅₃	1	2	yes	—
944	C₄×C₈	C₂³×C₅₃	1	2	yes	—
945	C₂⁴	—	2	1	no	—
946	C₂⁴	—	2	2	no	—
947	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
948	#41	—	2	2	no	—
949	#41	—	2	2	no	—
950	#41	—	2	4	no	—
951	#41	—	2	4	no	—
952	#41	—	2	4	no	—
953	#41	—	2	2	no	—
954	#41	—	2	2	no	—
955	#41	—	2	2	no	—
956	#41	—	2	2	no	—
957	#41	—	4	2	no	—
958	#41	—	4	2	no	—
959	#41	—	4	2	no	—
960	#41	—	4	4	no	—
961	#41	—	4	4	no	—
962	#41	—	4	4	no	—
963	C₂×Q₈	—	2	1	no	—
964	C₂×Q₈	—	2	2	no	—
965	C₂×Q₈	—	2	2	no	—
966	C₂×Q₈	—	2	2	no	—
967	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
968	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
969	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
970	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
971	C₂×D₄	—	2	4	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	1	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	1	no	—
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	2	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	4	2	no	—
986	C₂×D₄	—	4	4	no	—
987	C₂×D₄	—	4	8	no	—
988	C₂×D₄	—	4	4	no	—
989	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
990	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
991	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
992	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
993	C₂×D₄	#41×C₅₃	1	4	yes	—
994	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
995	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
996	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	2	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	4	4	no	—
1012	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1013	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1014	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1016	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1017	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1019	Q₁₆	—	4	1	no	—
1020	Q₁₆	—	4	2	no	—
1021	SD₁₆	—	2	4	no	—
1022	SD₁₆	—	4	1	no	—
1023	SD₁₆	—	4	1	no	—
1024	SD₁₆	—	4	2	no	—
1025	D₈	—	2	4	no	—
1026	D₈	—	4	1	no	—
1027	M₁₆	—	2	2	no	—
1028	M₁₆	—	2	2	no	—
1029	M₁₆	—	4	2	no	—
1030	C₂×C₈	—	2	2	no	—
1031	C₂×C₈	—	2	2	no	—
1032	C₂×C₈	—	4	1	no	—
1033	C₂×C₈	—	4	1	no	—
1034	C₂×C₈	—	4	1	no	—
1035	C₂×C₈	—	4	1	no	—
1036	C₂×C₈	—	4	2	no	—
1037	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1038	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1039	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1040	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1041	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1042	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1060	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1062	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1063	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1064	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1065	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1066	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1068	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1092	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1093	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1094	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1095	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	2	no	—
1098	C₄²	—	2	2	no	—
1099	C₄²	—	2	2	no	—
1100	C₄²	—	2	1	no	—
1101	C₄²	—	2	1	no	—
1102	C₄²	C₂⁴×C₅₃	1	2	yes	—
1103	C₂³	—	2	2	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	4	no	—
1106	C₂³	—	2	1	no	—
1107	C₂³	—	2	1	no	—
1108	C₂³	—	4	1	no	—
1109	C₂³	—	4	1	no	—
1110	C₂³	—	4	4	no	—
1111	C₂³	—	8	1	no	—
1112	C₂³	—	8	1	no	—
1113	C₂³	—	8	2	no	—
1114	C₂³	—	8	2	no	—
1115	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1116	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1117	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1118	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1119	Q₈	—	2	2	no	—
1120	Q₈	—	2	1	no	—
1121	Q₈	—	2	2	no	—
1122	Q₈	—	2	1	no	—
1123	Q₈	—	2	1	no	—
1124	Q₈	—	2	2	no	—
1125	Q₈	—	2	1	no	—
1126	Q₈	—	4	2	no	—
1127	Q₈	—	8	2	no	—
1128	D₄	—	2	4	no	—
1129	D₄	—	2	4	no	—
1130	D₄	—	2	2	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	2	2	no	—
1134	D₄	—	2	1	no	—
1135	D₄	—	2	1	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	4	no	—
1139	D₄	—	4	4	no	—
1140	D₄	—	4	4	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	4	2	no	—
1143	D₄	—	4	2	no	—
1144	D₄	—	8	1	no	—
1145	D₄	—	8	1	no	—
1146	D₄	—	8	1	no	—
1147	D₄	—	8	2	no	—
1148	D₄	—	8	1	no	—
1149	D₄	C₂×#41×C₅₃	1	4	yes	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	4	4	no	—
1169	C₂×C₄	—	4	4	no	—
1170	C₂×C₄	—	4	4	no	—
1171	C₂×C₄	—	4	2	no	—
1172	C₂×C₄	—	4	2	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	8	2	no	—
1175	C₂×C₄	—	8	2	no	—
1176	C₂×C₄	—	8	2	no	—
1177	C₂×C₄	—	8	1	no	—
1178	C₂×C₄	—	8	2	no	—
1179	C₂×C₄	—	8	1	no	—
1180	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1181	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1182	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1183	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1184	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1185	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1186	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1187	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1188	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1189	C₈	—	2	2	no	—
1190	C₈	—	2	1	no	—
1191	C₈	—	2	1	no	—
1192	C₈	—	2	1	no	—
1193	C₈	—	2	1	no	—
1194	C₈	—	2	2	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	1	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	2	4	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	4	4	no	—
1208	C₂²	—	4	2	no	—
1209	C₂²	—	4	2	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	1	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	8	4	no	—
1217	C₂²	—	16	4	no	—
1218	C₂²	C₅₃×#546	1	2	yes	—
1219	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1220	C₄	—	2	1	no	—
1221	C₄	—	2	1	no	—
1222	C₄	—	2	2	no	—
1223	C₄	—	2	2	no	—
1224	C₄	—	2	2	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	2	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	2	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	2	no	—
1233	C₄	—	4	1	no	—
1234	C₄	C₅₃×#546	1	2	yes	—
1235	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1236	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1237	C₂	—	2	2	no	—
1238	C₂	—	4	1	no	—
1239	C₂	—	4	1	no	—
1240	C₂	—	4	2	no	—
1241	C₂	—	4	4	no	—
1242	C₂	—	8	1	no	—
1243	C₂	—	8	1	no	—
1244	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
1245	C₂	C₅₃×#3584	1	1	yes	characteristic
1246	C₂	C₅₃×#3584	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3493	C₂	semidirect
2. C₅₃×#3485	C₂	semidirect
3. C₅₃×#3319	C₂	semidirect
4. C₅₃×#3315	C₂	semidirect
5. C₅₃×#3311	C₂	semidirect
6. C₅₃×#3307	C₂	semidirect
7. C₅₃×#3303	C₂	semidirect
8. C₅₃×#3302	C₂	semidirect
9. C₅₃×#3297	C₂	semidirect
10. C₅₃×#3296	C₂	semidirect
11. C₅₃×#3137	C₂	semidirect
12. C₅₃×#3097	C₂	semidirect
13. C₅₃×#3093	C₂	semidirect
14. C₅₃×#3081	C₂	semidirect
15. C₅₃×#3063	C₂	semidirect
16. C₅₃×#3050	C₂	semidirect
17. C₅₃×#3046	C₂	semidirect
18. C₅₃×#3012	C₂	semidirect
19. C₅₃×#3005	C₂	semidirect
20. C₅₃×#2946	C₂	semidirect
21. C₅₃×#2929	C₂	semidirect
22. C₅₃×#2897	C₂	semidirect
23. C₂×C₅₃×#416	C₂	semidirect
26. C₂×#137×C₅₃	C₂²	semidirect
30. C₂³×C₈×C₅₃	C₂²	semidirect
32. C₅₃×#556	C₂²	semidirect
34. C₅₃×#555	C₂²	semidirect
36. C₅₃×#553	C₂²	semidirect
38. C₅₃×#552	C₂²	semidirect
47. C₅₃×#544	C₂²	semidirect
56. C₅₃×#525	C₂²	semidirect
59. C₅₃×#520	C₂²	semidirect
61. C₂×#117×C₅₃	C₂²	semidirect
62. C₅₃×#491	C₂²	semidirect
63. C₅₃×#489	C₂²	semidirect
64. C₅₃×#488	C₂²	semidirect
65. C₅₃×#487	C₂²	semidirect
66. C₅₃×#485	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
69. C₅₃×#485	C₂²	semidirect
70. C₅₃×#484	C₂²	semidirect
71. C₅₃×#483	C₂²	semidirect
72. C₅₃×#482	C₂²	semidirect
73. C₅₃×#482	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#476	C₂²	semidirect
77. C₅₃×#474	C₂²	semidirect
78. C₅₃×#470	C₂²	semidirect
79. C₅₃×#468	C₂²	semidirect
80. C₅₃×#467	C₂²	semidirect
81. C₅₃×#467	C₂²	semidirect
82. C₅₃×#467	C₂²	semidirect
83. C₅₃×#466	C₂²	semidirect
84. C₅₃×#466	C₂²	semidirect
85. C₅₃×#465	C₂²	semidirect
86. C₅₃×#465	C₂²	semidirect
87. C₅₃×#465	C₂²	semidirect
88. C₅₃×#465	C₂²	semidirect
89. C₅₃×#465	C₂²	semidirect
90. C₅₃×#464	C₂²	semidirect
91. C₅₃×#463	C₂²	semidirect
92. C₅₃×#462	C₂²	semidirect
93. C₅₃×#461	C₂²	semidirect
94. C₅₃×#452	C₂²	semidirect
95. C₅₃×#452	C₂²	semidirect
96. C₅₃×#452	C₂²	semidirect
97. C₅₃×#450	C₂²	semidirect
98. C₅₃×#449	C₂²	semidirect
99. C₅₃×#449	C₂²	semidirect
100. C₅₃×#449	C₂²	semidirect
101. C₅₃×#447	C₂²	semidirect
102. C₅₃×#442	C₂²	semidirect
103. C₅₃×#440	C₂²	semidirect
104. C₄×SD₁₆×C₅₃	C₂²	semidirect
105. C₄×D₈×C₅₃	C₂²	semidirect
106. C₅₃×#435	C₂²	semidirect
107. C₅₃×#435	C₂²	semidirect
108. C₈×D₄×C₅₃	C₂²	semidirect
109. C₈×D₄×C₅₃	C₂²	semidirect
110. C₅₃×#428	C₂²	semidirect
111. C₅₃×#428	C₂²	semidirect
112. C₅₃×#427	C₂²	semidirect
113. C₅₃×#424	C₂²	semidirect
114. C₅₃×#419	C₂²	semidirect
116. C₅₃×#418	C₂²	semidirect
119. C₅₃×#417	C₂²	semidirect
121. C₅₃×#416	C₂²	semidirect
122. C₅₃×#416	C₂²	semidirect
123. C₅₃×#416	C₂²	semidirect
124. C₅₃×#416	C₂²	semidirect
125. C₅₃×#416	C₂²	semidirect
126. C₅₃×#416	C₂²	semidirect
127. C₂×#103×C₅₃	C₂²	semidirect
128. C₂×#103×C₅₃	C₂²	semidirect
131. C₂×#102×C₅₃	C₂²	semidirect
133. C₅₃×#407	C₂²	semidirect
134. C₅₃×#405	C₂²	semidirect
571. #61169	C₅₃	direct (N × H)
614. #3493	C₂×C₅₃	semidirect
615. #3485	C₂×C₅₃	semidirect
616. #3319	C₂×C₅₃	semidirect
617. #3315	C₂×C₅₃	semidirect
618. #3311	C₂×C₅₃	semidirect
619. #3307	C₂×C₅₃	semidirect
620. #3303	C₂×C₅₃	semidirect
621. #3302	C₂×C₅₃	semidirect
622. #3297	C₂×C₅₃	semidirect
623. #3296	C₂×C₅₃	semidirect
624. #3137	C₂×C₅₃	semidirect
625. #3097	C₂×C₅₃	semidirect
626. #3093	C₂×C₅₃	semidirect
627. #3081	C₂×C₅₃	semidirect
628. #3063	C₂×C₅₃	semidirect
629. #3050	C₂×C₅₃	semidirect
630. #3046	C₂×C₅₃	semidirect
631. #3012	C₂×C₅₃	semidirect
632. #3005	C₂×C₅₃	semidirect
633. #2946	C₂×C₅₃	semidirect
634. #2929	C₂×C₅₃	semidirect
635. #2897	C₂×C₅₃	semidirect
636. C₂×#416	C₂×C₅₃	semidirect
649. C₂×#137	C₂²×C₅₃	semidirect
653. C₂³×C₈	C₂²×C₅₃	semidirect
655. #556	C₂²×C₅₃	semidirect
657. #555	C₂²×C₅₃	semidirect
659. #553	C₂²×C₅₃	semidirect
661. #552	C₂²×C₅₃	semidirect
670. #544	C₂²×C₅₃	semidirect
679. #525	C₂²×C₅₃	semidirect
682. #520	C₂²×C₅₃	semidirect
684. C₂×#117	C₂²×C₅₃	semidirect
685. #491	C₂²×C₅₃	semidirect
686. #489	C₂²×C₅₃	semidirect
687. #488	C₂²×C₅₃	semidirect
688. #487	C₂²×C₅₃	semidirect
689. #485	C₂²×C₅₃	semidirect
690. #485	C₂²×C₅₃	semidirect
691. #485	C₂²×C₅₃	semidirect
692. #485	C₂²×C₅₃	semidirect
693. #484	C₂²×C₅₃	semidirect
694. #483	C₂²×C₅₃	semidirect
695. #482	C₂²×C₅₃	semidirect
696. #482	C₂²×C₅₃	semidirect
697. #478	C₂²×C₅₃	semidirect
698. #478	C₂²×C₅₃	semidirect
699. #476	C₂²×C₅₃	semidirect
700. #474	C₂²×C₅₃	semidirect
701. #470	C₂²×C₅₃	semidirect
702. #468	C₂²×C₅₃	semidirect
703. #467	C₂²×C₅₃	semidirect
704. #467	C₂²×C₅₃	semidirect
705. #467	C₂²×C₅₃	semidirect
706. #466	C₂²×C₅₃	semidirect
707. #466	C₂²×C₅₃	semidirect
708. #465	C₂²×C₅₃	semidirect
709. #465	C₂²×C₅₃	semidirect
710. #465	C₂²×C₅₃	semidirect
711. #465	C₂²×C₅₃	semidirect
712. #465	C₂²×C₅₃	semidirect
713. #464	C₂²×C₅₃	semidirect
714. #463	C₂²×C₅₃	semidirect
715. #462	C₂²×C₅₃	semidirect
716. #461	C₂²×C₅₃	semidirect
717. #452	C₂²×C₅₃	semidirect
718. #452	C₂²×C₅₃	semidirect
719. #452	C₂²×C₅₃	semidirect
720. #450	C₂²×C₅₃	semidirect
721. #449	C₂²×C₅₃	semidirect
722. #449	C₂²×C₅₃	semidirect
723. #449	C₂²×C₅₃	semidirect
724. #447	C₂²×C₅₃	semidirect
725. #442	C₂²×C₅₃	semidirect
726. #440	C₂²×C₅₃	semidirect
727. C₄×SD₁₆	C₂²×C₅₃	semidirect
728. C₄×D₈	C₂²×C₅₃	semidirect
729. #435	C₂²×C₅₃	semidirect
730. #435	C₂²×C₅₃	semidirect
731. C₈×D₄	C₂²×C₅₃	semidirect
732. C₈×D₄	C₂²×C₅₃	semidirect
733. #428	C₂²×C₅₃	semidirect
734. #428	C₂²×C₅₃	semidirect
735. #427	C₂²×C₅₃	semidirect
736. #424	C₂²×C₅₃	semidirect
737. #419	C₂²×C₅₃	semidirect
739. #418	C₂²×C₅₃	semidirect
742. #417	C₂²×C₅₃	semidirect
744. #416	C₂²×C₅₃	semidirect
745. #416	C₂²×C₅₃	semidirect
746. #416	C₂²×C₅₃	semidirect
747. #416	C₂²×C₅₃	semidirect
748. #416	C₂²×C₅₃	semidirect
749. #416	C₂²×C₅₃	semidirect
750. C₂×#103	C₂²×C₅₃	semidirect
751. C₂×#103	C₂²×C₅₃	semidirect
754. C₂×#102	C₂²×C₅₃	semidirect
756. #407	C₂²×C₅₃	semidirect
757. #405	C₂²×C₅₃	semidirect
758. C₅₃	#61169	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×#3493	2
C₅₃×#3485	2
C₅₃×#3319	2
C₅₃×#3315	2
C₅₃×#3311	2
C₅₃×#3307	2
C₅₃×#3303	2
C₅₃×#3302	2
C₅₃×#3297	2
C₅₃×#3296	2
C₅₃×#3137	2
C₅₃×#3097	2
C₅₃×#3093	2
C₅₃×#3081	2
C₅₃×#3063	2
C₅₃×#3050	2
C₅₃×#3046	2
C₅₃×#3012	2
C₅₃×#3005	2
C₅₃×#2946	2
C₅₃×#2929	2
C₅₃×#2897	2
C₂×C₅₃×#416	2
#61169	53

Subgroups — C53×#61169 #27268681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61169 #27268681