Subgroups — C₅₃×#61601 #27269113

Order 13568.

2250 conjugacy classes of subgroups.

The subgroup lattice has 1406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3323	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3311	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3306	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3296	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3282	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3275	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3267	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3266	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3211	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3195	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3194	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3190	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
27	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
28	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
29	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
30	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#554	—	2	1	no	—
32	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
34	C₅₃×#551	—	2	1	no	—
35	C₅₃×#551	—	2	1	no	—
36	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#546	—	2	1	no	—
42	C₅₃×#546	—	2	1	no	—
43	C₅₃×#546	—	2	1	no	—
44	C₅₃×#546	—	2	1	no	—
45	C₅₃×#546	—	2	1	no	—
46	C₅₃×#546	C₂²	1	2	yes	—
47	C₅₃×#546	C₂²	1	2	yes	—
48	C₅₃×#546	C₂²	1	2	yes	—
49	C₅₃×#546	C₂²	1	2	yes	—
50	C₅₃×#542	—	2	1	no	—
51	C₅₃×#539	—	2	1	no	—
52	C₅₃×#539	—	2	1	no	—
53	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
55	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
56	C₅₃×#525	C₂²	1	1	yes	characteristic
57	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
58	C₂×#123×C₅₃	—	2	1	no	—
59	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
61	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×#121×C₅₃	—	2	1	no	—
63	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×#120×C₅₃	—	2	1	no	—
65	C₅₃×#520	—	2	1	no	—
66	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
67	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
68	C₂²×C₂²⋊C₄×C₅₃	—	2	1	no	—
69	C₅₃×#497	C₂²	1	2	yes	complemented
70	C₅₃×#495	C₂²	1	2	yes	complemented
71	C₅₃×#489	C₂²	1	2	yes	complemented
72	C₅₃×#488	C₂²	1	2	yes	complemented
73	C₅₃×#485	C₂²	1	2	yes	complemented
74	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#483	C₂²	1	2	yes	complemented
76	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#482	C₂²	1	2	yes	complemented
79	C₅₃×#481	C₂²	1	2	yes	complemented
80	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#478	C₂²	1	2	yes	complemented
82	C₅₃×#476	C₂²	1	2	yes	complemented
83	C₅₃×#470	C₂²	1	2	yes	complemented
84	C₅₃×#470	C₂²	1	2	yes	complemented
85	C₅₃×#469	C₂²	1	2	yes	complemented
86	C₅₃×#468	C₂²	1	2	yes	complemented
87	C₅₃×#467	C₂²	1	2	yes	complemented
88	C₅₃×#465	C₂²	1	2	yes	complemented
89	C₅₃×#465	C₂²	1	2	yes	complemented
90	C₅₃×#465	C₂²	1	2	yes	complemented
91	C₅₃×#464	C₂²	1	2	yes	complemented
92	C₅₃×#464	C₂²	1	2	yes	complemented
93	C₅₃×#464	C₂²	1	2	yes	complemented
94	C₅₃×#463	C₂²	1	2	yes	complemented
95	C₅₃×#463	C₂²	1	2	yes	complemented
96	C₅₃×#461	C₂²	1	2	yes	complemented
97	C₅₃×#452	C₂²	1	2	yes	complemented
98	C₅₃×#452	C₂²	1	2	yes	complemented
99	C₅₃×#452	C₂²	1	2	yes	complemented
100	C₅₃×#452	C₂²	1	2	yes	complemented
101	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#451	C₂²	1	2	yes	complemented
104	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#450	C₂²	1	1	yes	characteristic
106	C₅₃×#450	C₂²	1	1	yes	characteristic
107	C₅₃×#450	C₂²	1	1	yes	characteristic
108	C₅₃×#450	C₂²	1	1	yes	characteristic
109	C₅₃×#450	C₂²	1	1	yes	characteristic
110	C₅₃×#450	C₂²	1	1	yes	characteristic
111	C₅₃×#450	C₂²	1	2	yes	complemented
112	C₅₃×#450	C₂²	1	2	yes	complemented
113	C₅₃×#450	C₂²	1	2	yes	complemented
114	C₅₃×#449	C₂²	1	2	yes	complemented
115	C₅₃×#449	C₂²	1	2	yes	complemented
116	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#448	C₂²	1	2	yes	complemented
118	C₅₃×#447	C₂²	1	1	yes	characteristic
119	C₅₃×#447	C₂²	1	1	yes	characteristic
120	C₅₃×#447	C₂²	1	2	yes	complemented
121	C₅₃×#442	C₂²	1	2	yes	complemented
122	C₅₃×#440	C₂²	1	2	yes	complemented
123	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
124	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
125	C₅₃×#436	C₂²	1	2	yes	complemented
126	C₅₃×#435	C₂²	1	2	yes	complemented
127	C₅₃×#435	C₂²	1	2	yes	complemented
128	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
129	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#418	C₂²	1	2	yes	complemented
132	C₅₃×#417	C₂²	1	2	yes	complemented
133	C₅₃×#416	C₂²	1	2	yes	complemented
134	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
135	C₅₃×#407	C₂²	1	1	yes	characteristic
136	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
138	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₂⁵×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	1	no	—
141	C₂×#41×C₅₃	—	2	1	no	—
142	C₂×#41×C₅₃	—	2	1	no	—
143	C₂×#41×C₅₃	—	4	4	no	—
144	C₂×#41×C₅₃	C₂³	1	2	yes	—
145	C₂×#41×C₅₃	C₂³	1	2	yes	—
146	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic, complemented
148	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
151	C₂²×D₄×C₅₃	—	2	1	no	—
152	C₂²×D₄×C₅₃	—	2	1	no	—
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	—	4	4	no	—
157	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
158	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
159	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
160	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
161	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
162	C₂³×C₄×C₅₃	—	2	1	no	—
163	C₂³×C₄×C₅₃	—	2	1	no	—
164	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
165	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
166	#137×C₅₃	—	4	4	no	—
167	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
168	#135×C₅₃	—	4	4	no	—
169	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	complemented
170	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	complemented
171	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	complemented
172	C₂×SD₁₆×C₅₃	—	4	4	no	—
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	2	yes	—
177	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
178	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
179	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	complemented
180	C₂×D₈×C₅₃	C₂³	1	2	yes	—
181	C₂×D₈×C₅₃	C₂³	1	2	yes	—
182	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
183	C₂×M₁₆×C₅₃	C₂³	1	2	yes	complemented
184	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
185	C₂²×C₈×C₅₃	C₂³	1	2	yes	complemented
186	C₄⋊Q₈×C₅₃	—	2	1	no	—
187	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
188	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
189	#126×C₅₃	—	2	1	no	—
190	#126×C₅₃	—	2	1	no	—
191	#126×C₅₃	—	2	1	no	—
192	#126×C₅₃	—	2	1	no	—
193	#126×C₅₃	—	2	1	no	—
194	#125×C₅₃	—	2	1	no	—
195	#125×C₅₃	—	2	1	no	—
196	#125×C₅₃	—	2	1	no	—
197	#125×C₅₃	C₂³	1	1	yes	characteristic, complemented
198	#124×C₅₃	—	2	1	no	—
199	#124×C₅₃	—	2	1	no	—
200	#124×C₅₃	—	2	1	no	—
201	#124×C₅₃	—	2	1	no	—
202	#124×C₅₃	—	2	1	no	—
203	#124×C₅₃	C₂³	1	2	yes	—
204	#124×C₅₃	C₂³	1	2	yes	—
205	#124×C₅₃	C₂³	1	1	yes	characteristic, complemented
206	#123×C₅₃	—	2	2	no	—
207	#123×C₅₃	—	2	2	no	—
208	#123×C₅₃	—	2	2	no	—
209	#123×C₅₃	—	2	2	no	—
210	#123×C₅₃	—	2	1	no	—
211	#123×C₅₃	—	2	1	no	—
212	#123×C₅₃	—	2	1	no	—
213	#123×C₅₃	—	2	1	no	—
214	#123×C₅₃	—	2	1	no	—
215	#123×C₅₃	—	2	1	no	—
216	#123×C₅₃	—	2	1	no	—
217	#123×C₅₃	—	2	1	no	—
218	#123×C₅₃	—	2	1	no	—
219	C₂²⋊Q₈×C₅₃	—	2	1	no	—
220	C₂²⋊Q₈×C₅₃	—	2	1	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	1	no	—
226	C₂²⋊Q₈×C₅₃	—	2	1	no	—
227	C₂²⋊Q₈×C₅₃	—	2	1	no	—
228	C₂²⋊Q₈×C₅₃	—	2	1	no	—
229	C₂²⋊Q₈×C₅₃	—	2	1	no	—
230	C₂²⋊Q₈×C₅₃	—	2	1	no	—
231	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
232	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
233	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
234	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
235	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
236	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
237	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
238	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
239	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
240	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
241	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
242	#121×C₅₃	—	2	2	no	—
243	#121×C₅₃	—	2	2	no	—
244	#121×C₅₃	—	2	2	no	—
245	#121×C₅₃	—	2	2	no	—
246	#121×C₅₃	—	2	1	no	—
247	#121×C₅₃	—	2	1	no	—
248	#121×C₅₃	—	2	1	no	—
249	#121×C₅₃	—	2	1	no	—
250	#121×C₅₃	—	2	1	no	—
251	#121×C₅₃	C₂³	1	2	yes	—
252	#121×C₅₃	C₂³	1	2	yes	—
253	#121×C₅₃	C₂³	1	1	yes	characteristic
254	#121×C₅₃	C₂³	1	1	yes	characteristic
255	#121×C₅₃	C₂³	1	1	yes	characteristic, complemented
256	#120×C₅₃	—	2	1	no	—
257	#120×C₅₃	—	2	1	no	—
258	#120×C₅₃	—	2	2	no	—
259	#120×C₅₃	—	2	2	no	—
260	#120×C₅₃	—	2	2	no	—
261	#120×C₅₃	—	2	2	no	—
262	C₄×Q₈×C₅₃	—	2	1	no	—
263	C₄×Q₈×C₅₃	—	2	1	no	—
264	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
265	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
266	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
267	C₄×D₄×C₅₃	—	2	1	no	—
268	C₄×D₄×C₅₃	—	2	1	no	—
269	C₄×D₄×C₅₃	—	2	1	no	—
270	C₄×D₄×C₅₃	—	2	1	no	—
271	C₄×D₄×C₅₃	—	2	1	no	—
272	C₄×D₄×C₅₃	—	2	1	no	—
273	C₄×D₄×C₅₃	—	2	1	no	—
274	C₄×D₄×C₅₃	—	2	1	no	—
275	C₄×D₄×C₅₃	—	2	1	no	—
276	C₄×D₄×C₅₃	—	2	1	no	—
277	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
278	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
279	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
280	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
281	C₄×D₄×C₅₃	C₂³	1	2	yes	—
282	C₄×D₄×C₅₃	C₂³	1	2	yes	—
283	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
288	#117×C₅₃	—	2	1	no	—
289	#117×C₅₃	—	2	1	no	—
290	#117×C₅₃	—	2	1	no	—
291	#117×C₅₃	—	2	1	no	—
292	#117×C₅₃	C₂³	1	1	yes	characteristic
293	#117×C₅₃	C₂³	1	1	yes	characteristic, complemented
294	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
295	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
296	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
297	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
298	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
299	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
302	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
303	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
304	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
305	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
306	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
307	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
308	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
309	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
310	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
311	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
312	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
313	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
314	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
315	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
316	#107×C₅₃	C₂³	1	2	yes	complemented
317	#106×C₅₃	C₂³	1	2	yes	complemented
318	#106×C₅₃	C₂³	1	2	yes	complemented
319	#106×C₅₃	C₂³	1	2	yes	complemented
320	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
321	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
322	#103×C₅₃	C₂³	1	2	yes	complemented
323	#103×C₅₃	C₂³	1	2	yes	complemented
324	#103×C₅₃	C₂³	1	2	yes	complemented
325	#103×C₅₃	C₂³	1	2	yes	complemented
326	#103×C₅₃	C₂³	1	2	yes	complemented
327	#103×C₅₃	C₂³	1	2	yes	complemented
328	#103×C₅₃	C₂³	1	2	yes	complemented
329	#102×C₅₃	C₂³	1	2	yes	—
330	#102×C₅₃	C₂³	1	2	yes	—
331	#102×C₅₃	C₂³	1	2	yes	—
332	#102×C₅₃	C₂³	1	2	yes	—
333	#102×C₅₃	C₂³	1	2	yes	—
334	#102×C₅₃	C₂³	1	2	yes	—
335	#102×C₅₃	C₂³	1	2	yes	—
336	#102×C₅₃	C₂³	1	2	yes	—
337	#102×C₅₃	C₂³	1	2	yes	complemented
338	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
339	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
340	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
341	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
342	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
343	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
344	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	complemented
345	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	complemented
346	#97×C₅₃	C₂³	1	2	yes	complemented
347	C₄×C₈×C₅₃	C₂³	1	2	yes	complemented
348	C₂⁴×C₅₃	—	2	1	no	—
349	C₂⁴×C₅₃	—	2	1	no	—
350	C₂⁴×C₅₃	—	2	2	no	—
351	C₂⁴×C₅₃	—	2	2	no	—
352	C₂⁴×C₅₃	—	4	4	no	—
353	C₂⁴×C₅₃	—	4	4	no	—
354	C₂⁴×C₅₃	—	8	2	no	—
355	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
356	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
357	#41×C₅₃	—	2	4	no	—
358	#41×C₅₃	—	2	4	no	—
359	#41×C₅₃	—	4	2	no	—
360	#41×C₅₃	—	4	2	no	—
361	#41×C₅₃	—	4	2	no	—
362	#41×C₅₃	—	4	2	no	—
363	#41×C₅₃	—	4	4	no	—
364	#41×C₅₃	—	4	4	no	—
365	#41×C₅₃	—	4	4	no	—
366	C₂×Q₈×C₅₃	—	2	1	no	—
367	C₂×Q₈×C₅₃	—	2	1	no	—
368	C₂×Q₈×C₅₃	—	2	1	no	—
369	C₂×Q₈×C₅₃	—	2	1	no	—
370	C₂×Q₈×C₅₃	—	4	2	no	—
371	C₂×Q₈×C₅₃	—	4	2	no	—
372	C₂×Q₈×C₅₃	—	4	2	no	—
373	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
374	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂×D₄×C₅₃	—	2	4	no	—
378	C₂×D₄×C₅₃	—	2	4	no	—
379	C₂×D₄×C₅₃	—	2	4	no	—
380	C₂×D₄×C₅₃	—	2	1	no	—
381	C₂×D₄×C₅₃	—	2	1	no	—
382	C₂×D₄×C₅₃	—	2	1	no	—
383	C₂×D₄×C₅₃	—	2	2	no	—
384	C₂×D₄×C₅₃	—	2	2	no	—
385	C₂×D₄×C₅₃	—	2	2	no	—
386	C₂×D₄×C₅₃	—	2	2	no	—
387	C₂×D₄×C₅₃	—	2	1	no	—
388	C₂×D₄×C₅₃	—	2	1	no	—
389	C₂×D₄×C₅₃	—	2	1	no	—
390	C₂×D₄×C₅₃	—	2	2	no	—
391	C₂×D₄×C₅₃	—	2	2	no	—
392	C₂×D₄×C₅₃	—	2	1	no	—
393	C₂×D₄×C₅₃	—	4	2	no	—
394	C₂×D₄×C₅₃	—	4	2	no	—
395	C₂×D₄×C₅₃	—	4	2	no	—
396	C₂×D₄×C₅₃	—	4	2	no	—
397	C₂×D₄×C₅₃	—	4	4	no	—
398	C₂×D₄×C₅₃	—	4	4	no	—
399	C₂×D₄×C₅₃	—	4	4	no	—
400	C₂×D₄×C₅₃	—	4	4	no	—
401	C₂×D₄×C₅₃	—	8	2	no	—
402	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
403	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
404	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
405	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
406	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
407	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
409	C₂²×C₄×C₅₃	—	2	1	no	—
410	C₂²×C₄×C₅₃	—	2	1	no	—
411	C₂²×C₄×C₅₃	—	2	1	no	—
412	C₂²×C₄×C₅₃	—	2	1	no	—
413	C₂²×C₄×C₅₃	—	2	1	no	—
414	C₂²×C₄×C₅₃	—	2	1	no	—
415	C₂²×C₄×C₅₃	—	2	2	no	—
416	C₂²×C₄×C₅₃	—	2	2	no	—
417	C₂²×C₄×C₅₃	—	2	1	no	—
418	C₂²×C₄×C₅₃	—	2	2	no	—
419	C₂²×C₄×C₅₃	—	2	2	no	—
420	C₂²×C₄×C₅₃	—	2	1	no	—
421	C₂²×C₄×C₅₃	—	2	1	no	—
422	C₂²×C₄×C₅₃	—	4	2	no	—
423	C₂²×C₄×C₅₃	—	4	2	no	—
424	C₂²×C₄×C₅₃	—	4	4	no	—
425	C₂²×C₄×C₅₃	—	8	2	no	—
426	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
427	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
428	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
429	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
430	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
431	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
432	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
433	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
434	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
439	Q₁₆×C₅₃	—	4	2	no	—
440	Q₁₆×C₅₃	—	4	2	no	—
441	Q₁₆×C₅₃	—	4	2	no	—
442	SD₁₆×C₅₃	—	2	4	no	—
443	SD₁₆×C₅₃	—	2	4	no	—
444	SD₁₆×C₅₃	—	2	4	no	—
445	SD₁₆×C₅₃	—	4	2	no	—
446	SD₁₆×C₅₃	—	4	2	no	—
447	SD₁₆×C₅₃	—	4	2	no	—
448	SD₁₆×C₅₃	—	4	2	no	—
449	D₈×C₅₃	—	2	4	no	—
450	D₈×C₅₃	—	4	2	no	—
451	M₁₆×C₅₃	—	4	2	no	—
452	M₁₆×C₅₃	—	4	2	no	—
453	C₂×C₈×C₅₃	—	4	2	no	—
454	C₂×C₈×C₅₃	—	4	2	no	—
455	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
456	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
457	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
458	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
459	C₄⋊C₄×C₅₃	—	2	1	no	—
460	C₄⋊C₄×C₅₃	—	2	1	no	—
461	C₄⋊C₄×C₅₃	—	2	1	no	—
462	C₄⋊C₄×C₅₃	—	2	1	no	—
463	C₄⋊C₄×C₅₃	—	2	1	no	—
464	C₄⋊C₄×C₅₃	—	2	1	no	—
465	C₄⋊C₄×C₅₃	—	2	1	no	—
466	C₄⋊C₄×C₅₃	—	2	1	no	—
467	C₄⋊C₄×C₅₃	—	2	2	no	—
468	C₄⋊C₄×C₅₃	—	2	2	no	—
469	C₄⋊C₄×C₅₃	—	2	1	no	—
470	C₄⋊C₄×C₅₃	—	2	1	no	—
471	C₄⋊C₄×C₅₃	—	2	1	no	—
472	C₄⋊C₄×C₅₃	—	2	1	no	—
473	C₄⋊C₄×C₅₃	—	2	1	no	—
474	C₄⋊C₄×C₅₃	—	2	1	no	—
475	C₄⋊C₄×C₅₃	—	2	1	no	—
476	C₄⋊C₄×C₅₃	—	2	1	no	—
477	C₄⋊C₄×C₅₃	—	2	1	no	—
478	C₄⋊C₄×C₅₃	—	2	1	no	—
479	C₄⋊C₄×C₅₃	—	2	1	no	—
480	C₄⋊C₄×C₅₃	—	2	1	no	—
481	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
482	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
483	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
484	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
485	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
486	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
487	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
488	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
489	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
490	C₂²⋊C₄×C₅₃	—	2	2	no	—
491	C₂²⋊C₄×C₅₃	—	2	2	no	—
492	C₂²⋊C₄×C₅₃	—	2	1	no	—
493	C₂²⋊C₄×C₅₃	—	2	1	no	—
494	C₂²⋊C₄×C₅₃	—	2	1	no	—
495	C₂²⋊C₄×C₅₃	—	2	1	no	—
496	C₂²⋊C₄×C₅₃	—	2	1	no	—
497	C₂²⋊C₄×C₅₃	—	2	1	no	—
498	C₂²⋊C₄×C₅₃	—	2	1	no	—
499	C₂²⋊C₄×C₅₃	—	2	1	no	—
500	C₂²⋊C₄×C₅₃	—	2	1	no	—
501	C₂²⋊C₄×C₅₃	—	2	1	no	—
502	C₂²⋊C₄×C₅₃	—	2	1	no	—
503	C₂²⋊C₄×C₅₃	—	2	2	no	—
504	C₂²⋊C₄×C₅₃	—	2	2	no	—
505	C₂²⋊C₄×C₅₃	—	2	2	no	—
506	C₂²⋊C₄×C₅₃	—	2	2	no	—
507	C₂²⋊C₄×C₅₃	—	2	2	no	—
508	C₂²⋊C₄×C₅₃	—	2	2	no	—
509	C₂²⋊C₄×C₅₃	—	2	2	no	—
510	C₂²⋊C₄×C₅₃	—	2	2	no	—
511	C₂²⋊C₄×C₅₃	—	2	1	no	—
512	C₂²⋊C₄×C₅₃	—	2	1	no	—
513	C₂²⋊C₄×C₅₃	—	2	1	no	—
514	C₂²⋊C₄×C₅₃	—	2	1	no	—
515	C₂²⋊C₄×C₅₃	—	2	1	no	—
516	C₂²⋊C₄×C₅₃	—	2	1	no	—
517	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
518	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
519	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
520	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
521	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
522	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
523	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
524	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
525	C₄²×C₅₃	—	2	1	no	—
526	C₄²×C₅₃	—	2	1	no	—
527	C₄²×C₅₃	—	2	1	no	—
528	C₄²×C₅₃	—	2	1	no	—
529	C₄²×C₅₃	—	2	1	no	—
530	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
531	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
532	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
533	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
534	C₂³×C₅₃	—	2	4	no	—
535	C₂³×C₅₃	—	2	2	no	—
536	C₂³×C₅₃	—	2	2	no	—
537	C₂³×C₅₃	—	2	2	no	—
538	C₂³×C₅₃	—	2	2	no	—
539	C₂³×C₅₃	—	2	1	no	—
540	C₂³×C₅₃	—	2	2	no	—
541	C₂³×C₅₃	—	4	1	no	—
542	C₂³×C₅₃	—	4	1	no	—
543	C₂³×C₅₃	—	4	1	no	—
544	C₂³×C₅₃	—	4	4	no	—
545	C₂³×C₅₃	—	4	4	no	—
546	C₂³×C₅₃	—	4	2	no	—
547	C₂³×C₅₃	—	4	2	no	—
548	C₂³×C₅₃	—	4	2	no	—
549	C₂³×C₅₃	—	4	4	no	—
550	C₂³×C₅₃	—	4	2	no	—
551	C₂³×C₅₃	—	4	4	no	—
552	C₂³×C₅₃	—	4	2	no	—
553	C₂³×C₅₃	—	8	2	no	—
554	C₂³×C₅₃	—	8	2	no	—
555	C₂³×C₅₃	—	8	16	no	—
556	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
557	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
558	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
559	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
560	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
561	Q₈×C₅₃	—	2	2	no	—
562	Q₈×C₅₃	—	2	2	no	—
563	Q₈×C₅₃	—	2	2	no	—
564	Q₈×C₅₃	—	2	2	no	—
565	Q₈×C₅₃	—	2	2	no	—
566	Q₈×C₅₃	—	4	2	no	—
567	Q₈×C₅₃	—	4	2	no	—
568	Q₈×C₅₃	—	8	1	no	—
569	Q₈×C₅₃	—	8	1	no	—
570	D₄×C₅₃	—	2	4	no	—
571	D₄×C₅₃	—	2	2	no	—
572	D₄×C₅₃	—	2	2	no	—
573	D₄×C₅₃	—	2	2	no	—
574	D₄×C₅₃	—	2	2	no	—
575	D₄×C₅₃	—	2	2	no	—
576	D₄×C₅₃	—	2	2	no	—
577	D₄×C₅₃	—	4	1	no	—
578	D₄×C₅₃	—	4	1	no	—
579	D₄×C₅₃	—	4	4	no	—
580	D₄×C₅₃	—	4	4	no	—
581	D₄×C₅₃	—	4	2	no	—
582	D₄×C₅₃	—	4	4	no	—
583	D₄×C₅₃	—	4	4	no	—
584	D₄×C₅₃	—	4	2	no	—
585	D₄×C₅₃	—	4	2	no	—
586	D₄×C₅₃	—	4	2	no	—
587	D₄×C₅₃	—	8	2	no	—
588	D₄×C₅₃	—	8	2	no	—
589	D₄×C₅₃	—	8	1	no	—
590	D₄×C₅₃	—	8	1	no	—
591	D₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
592	C₂×C₄×C₅₃	—	2	2	no	—
593	C₂×C₄×C₅₃	—	2	2	no	—
594	C₂×C₄×C₅₃	—	2	2	no	—
595	C₂×C₄×C₅₃	—	2	2	no	—
596	C₂×C₄×C₅₃	—	2	2	no	—
597	C₂×C₄×C₅₃	—	2	2	no	—
598	C₂×C₄×C₅₃	—	2	2	no	—
599	C₂×C₄×C₅₃	—	2	2	no	—
600	C₂×C₄×C₅₃	—	2	1	no	—
601	C₂×C₄×C₅₃	—	2	1	no	—
602	C₂×C₄×C₅₃	—	2	1	no	—
603	C₂×C₄×C₅₃	—	2	1	no	—
604	C₂×C₄×C₅₃	—	2	1	no	—
605	C₂×C₄×C₅₃	—	2	1	no	—
606	C₂×C₄×C₅₃	—	2	1	no	—
607	C₂×C₄×C₅₃	—	4	1	no	—
608	C₂×C₄×C₅₃	—	4	1	no	—
609	C₂×C₄×C₅₃	—	4	1	no	—
610	C₂×C₄×C₅₃	—	4	1	no	—
611	C₂×C₄×C₅₃	—	4	1	no	—
612	C₂×C₄×C₅₃	—	4	1	no	—
613	C₂×C₄×C₅₃	—	4	1	no	—
614	C₂×C₄×C₅₃	—	4	4	no	—
615	C₂×C₄×C₅₃	—	4	4	no	—
616	C₂×C₄×C₅₃	—	4	2	no	—
617	C₂×C₄×C₅₃	—	4	2	no	—
618	C₂×C₄×C₅₃	—	4	2	no	—
619	C₂×C₄×C₅₃	—	4	2	no	—
620	C₂×C₄×C₅₃	—	4	2	no	—
621	C₂×C₄×C₅₃	—	8	2	no	—
622	C₂×C₄×C₅₃	—	8	2	no	—
623	C₂×C₄×C₅₃	—	8	1	no	—
624	C₂×C₄×C₅₃	—	8	1	no	—
625	C₂×C₄×C₅₃	—	8	1	no	—
626	C₂×C₄×C₅₃	—	8	1	no	—
627	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
628	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
629	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
630	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
631	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
632	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
633	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
634	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
635	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
636	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
637	C₈×C₅₃	—	2	2	no	—
638	C₈×C₅₃	—	2	2	no	—
639	C₈×C₅₃	—	2	2	no	—
640	C₈×C₅₃	—	2	2	no	—
641	#61601	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
642	C₂²×C₅₃	—	2	1	no	—
643	C₂²×C₅₃	—	2	1	no	—
644	C₂²×C₅₃	—	2	1	no	—
645	C₂²×C₅₃	—	2	1	no	—
646	C₂²×C₅₃	—	2	1	no	—
647	C₂²×C₅₃	—	2	1	no	—
648	C₂²×C₅₃	—	2	1	no	—
649	C₂²×C₅₃	—	2	4	no	—
650	C₂²×C₅₃	—	2	1	no	—
651	C₂²×C₅₃	—	2	1	no	—
652	C₂²×C₅₃	—	2	1	no	—
653	C₂²×C₅₃	—	2	1	no	—
654	C₂²×C₅₃	—	2	1	no	—
655	C₂²×C₅₃	—	2	1	no	—
656	C₂²×C₅₃	—	4	4	no	—
657	C₂²×C₅₃	—	4	8	no	—
658	C₂²×C₅₃	—	4	2	no	—
659	C₂²×C₅₃	—	4	2	no	—
660	C₂²×C₅₃	—	4	1	no	—
661	C₂²×C₅₃	—	4	2	no	—
662	C₂²×C₅₃	—	4	1	no	—
663	C₂²×C₅₃	—	4	2	no	—
664	C₂²×C₅₃	—	4	1	no	—
665	C₂²×C₅₃	—	4	2	no	—
666	C₂²×C₅₃	—	8	2	no	—
667	C₂²×C₅₃	—	8	8	no	—
668	C₂²×C₅₃	—	8	4	no	—
669	C₂²×C₅₃	—	8	8	no	—
670	C₂²×C₅₃	#575	1	2	yes	—
671	C₂²×C₅₃	#577	1	2	yes	—
672	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
673	C₄×C₅₃	—	2	1	no	—
674	C₄×C₅₃	—	2	1	no	—
675	C₄×C₅₃	—	2	1	no	—
676	C₄×C₅₃	—	2	1	no	—
677	C₄×C₅₃	—	2	1	no	—
678	C₄×C₅₃	—	2	1	no	—
679	C₄×C₅₃	—	2	1	no	—
680	C₄×C₅₃	—	2	1	no	—
681	C₄×C₅₃	—	2	1	no	—
682	C₄×C₅₃	—	4	2	no	—
683	C₄×C₅₃	—	4	1	no	—
684	C₄×C₅₃	—	4	1	no	—
685	C₄×C₅₃	—	4	1	no	—
686	C₄×C₅₃	—	4	1	no	—
687	C₄×C₅₃	—	4	1	no	—
688	C₄×C₅₃	—	4	1	no	—
689	C₄×C₅₃	—	4	2	no	—
690	C₄×C₅₃	—	4	1	no	—
691	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
692	#3520	C₂×C₅₃	1	1	yes	characteristic, complemented
693	C₂×#546	C₂×C₅₃	1	1	yes	characteristic, complemented
694	#3323	C₂×C₅₃	1	2	yes	complemented
695	#3311	C₂×C₅₃	1	2	yes	complemented
696	#3306	C₂×C₅₃	1	2	yes	complemented
697	#3296	C₂×C₅₃	1	2	yes	complemented
698	#3282	C₂×C₅₃	1	2	yes	complemented
699	#3275	C₂×C₅₃	1	2	yes	complemented
700	#3267	C₂×C₅₃	1	2	yes	complemented
701	#3266	C₂×C₅₃	1	2	yes	complemented
702	#3215	C₂×C₅₃	1	1	yes	characteristic, complemented
703	#3211	C₂×C₅₃	1	1	yes	characteristic, complemented
704	#3195	C₂×C₅₃	1	1	yes	characteristic, complemented
705	#3194	C₂×C₅₃	1	1	yes	characteristic, complemented
706	#3190	C₂×C₅₃	1	1	yes	characteristic, complemented
707	#3187	C₂×C₅₃	1	1	yes	characteristic, complemented
708	#3114	C₂×C₅₃	1	1	yes	characteristic, complemented
709	#3101	C₂×C₅₃	1	1	yes	characteristic, complemented
710	#3007	C₂×C₅₃	1	1	yes	characteristic, complemented
711	#3003	C₂×C₅₃	1	1	yes	characteristic, complemented
712	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
713	C₂×#450	C₂×C₅₃	1	1	yes	characteristic, complemented
714	#2974	C₂×C₅₃	1	1	yes	characteristic, complemented
715	C₂×C₅₃	—	2	2	no	—
716	C₂×C₅₃	—	2	2	no	—
717	C₂×C₅₃	—	4	1	no	—
718	C₂×C₅₃	—	4	1	no	—
719	C₂×C₅₃	—	4	1	no	—
720	C₂×C₅₃	—	4	4	no	—
721	C₂×C₅₃	—	8	1	no	—
722	C₂×C₅₃	—	8	2	no	—
723	C₂×C₅₃	#3484	1	1	yes	characteristic
724	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
725	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
726	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
727	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
728	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
729	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
730	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
731	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
732	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
733	#554	—	2	1	no	—
734	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
735	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
736	#551	—	2	1	no	—
737	#551	—	2	1	no	—
738	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
739	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
740	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
741	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
742	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
743	#546	—	2	1	no	—
744	#546	—	2	1	no	—
745	#546	—	2	1	no	—
746	#546	—	2	1	no	—
747	#546	—	2	1	no	—
748	#546	C₂²×C₅₃	1	2	yes	—
749	#546	C₂²×C₅₃	1	2	yes	—
750	#546	C₂²×C₅₃	1	2	yes	—
751	#546	C₂²×C₅₃	1	2	yes	—
752	#542	—	2	1	no	—
753	#539	—	2	1	no	—
754	#539	—	2	1	no	—
755	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
756	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
757	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
758	#525	C₂²×C₅₃	1	1	yes	characteristic
759	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
760	C₂×#123	—	2	1	no	—
761	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
762	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
763	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
764	C₂×#121	—	2	1	no	—
765	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
766	C₂×#120	—	2	1	no	—
767	#520	—	2	1	no	—
768	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
769	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
770	C₂²×C₂²⋊C₄	—	2	1	no	—
771	#497	C₂²×C₅₃	1	2	yes	complemented
772	#495	C₂²×C₅₃	1	2	yes	complemented
773	#489	C₂²×C₅₃	1	2	yes	complemented
774	#488	C₂²×C₅₃	1	2	yes	complemented
775	#485	C₂²×C₅₃	1	2	yes	complemented
776	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
777	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
778	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
779	#483	C₂²×C₅₃	1	2	yes	complemented
780	#482	C₂²×C₅₃	1	2	yes	complemented
781	#481	C₂²×C₅₃	1	2	yes	complemented
782	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
783	#478	C₂²×C₅₃	1	2	yes	complemented
784	#476	C₂²×C₅₃	1	2	yes	complemented
785	#470	C₂²×C₅₃	1	2	yes	complemented
786	#470	C₂²×C₅₃	1	2	yes	complemented
787	#469	C₂²×C₅₃	1	2	yes	complemented
788	#468	C₂²×C₅₃	1	2	yes	complemented
789	#467	C₂²×C₅₃	1	2	yes	complemented
790	#465	C₂²×C₅₃	1	2	yes	complemented
791	#465	C₂²×C₅₃	1	2	yes	complemented
792	#465	C₂²×C₅₃	1	2	yes	complemented
793	#464	C₂²×C₅₃	1	2	yes	complemented
794	#464	C₂²×C₅₃	1	2	yes	complemented
795	#464	C₂²×C₅₃	1	2	yes	complemented
796	#463	C₂²×C₅₃	1	2	yes	complemented
797	#463	C₂²×C₅₃	1	2	yes	complemented
798	#461	C₂²×C₅₃	1	2	yes	complemented
799	#452	C₂²×C₅₃	1	2	yes	complemented
800	#452	C₂²×C₅₃	1	2	yes	complemented
801	#452	C₂²×C₅₃	1	2	yes	complemented
802	#452	C₂²×C₅₃	1	2	yes	complemented
803	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
804	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
805	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
806	#451	C₂²×C₅₃	1	2	yes	complemented
807	#450	C₂²×C₅₃	1	1	yes	characteristic
808	#450	C₂²×C₅₃	1	1	yes	characteristic
809	#450	C₂²×C₅₃	1	1	yes	characteristic
810	#450	C₂²×C₅₃	1	1	yes	characteristic
811	#450	C₂²×C₅₃	1	1	yes	characteristic
812	#450	C₂²×C₅₃	1	1	yes	characteristic
813	#450	C₂²×C₅₃	1	2	yes	complemented
814	#450	C₂²×C₅₃	1	2	yes	complemented
815	#450	C₂²×C₅₃	1	2	yes	complemented
816	#449	C₂²×C₅₃	1	2	yes	complemented
817	#449	C₂²×C₅₃	1	2	yes	complemented
818	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
819	#448	C₂²×C₅₃	1	2	yes	complemented
820	#447	C₂²×C₅₃	1	1	yes	characteristic
821	#447	C₂²×C₅₃	1	1	yes	characteristic
822	#447	C₂²×C₅₃	1	2	yes	complemented
823	#442	C₂²×C₅₃	1	2	yes	complemented
824	#440	C₂²×C₅₃	1	2	yes	complemented
825	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
826	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
827	#436	C₂²×C₅₃	1	2	yes	complemented
828	#435	C₂²×C₅₃	1	2	yes	complemented
829	#435	C₂²×C₅₃	1	2	yes	complemented
830	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
831	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
832	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
833	#418	C₂²×C₅₃	1	2	yes	complemented
834	#417	C₂²×C₅₃	1	2	yes	complemented
835	#416	C₂²×C₅₃	1	2	yes	complemented
836	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
837	#407	C₂²×C₅₃	1	1	yes	characteristic
838	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
839	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
840	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
841	C₅₃	#61601	1	1	yes	characteristic, direct product factor, Sylow
842	C₂⁵	—	2	1	no	—
843	C₂×#41	—	2	1	no	—
844	C₂×#41	—	2	1	no	—
845	C₂×#41	—	2	1	no	—
846	C₂×#41	—	4	4	no	—
847	C₂×#41	C₂³×C₅₃	1	2	yes	—
848	C₂×#41	C₂³×C₅₃	1	2	yes	—
849	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
850	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic, complemented
851	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
852	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
853	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
854	C₂²×D₄	—	2	1	no	—
855	C₂²×D₄	—	2	1	no	—
856	C₂²×D₄	—	2	1	no	—
857	C₂²×D₄	—	2	1	no	—
858	C₂²×D₄	—	2	1	no	—
859	C₂²×D₄	—	4	4	no	—
860	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
861	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
862	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
863	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
864	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
865	C₂³×C₄	—	2	1	no	—
866	C₂³×C₄	—	2	1	no	—
867	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
868	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
869	#137	—	4	4	no	—
870	AGL(1,ℤ/8)	—	4	4	no	—
871	#135	—	4	4	no	—
872	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	complemented
873	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	complemented
874	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	complemented
875	C₂×SD₁₆	—	4	4	no	—
876	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
877	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
878	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
879	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
880	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
881	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
882	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	complemented
883	C₂×D₈	C₂³×C₅₃	1	2	yes	—
884	C₂×D₈	C₂³×C₅₃	1	2	yes	—
885	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
886	C₂×M₁₆	C₂³×C₅₃	1	2	yes	complemented
887	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
888	C₂²×C₈	C₂³×C₅₃	1	2	yes	complemented
889	C₄⋊Q₈	—	2	1	no	—
890	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
891	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
892	#126	—	2	1	no	—
893	#126	—	2	1	no	—
894	#126	—	2	1	no	—
895	#126	—	2	1	no	—
896	#126	—	2	1	no	—
897	#125	—	2	1	no	—
898	#125	—	2	1	no	—
899	#125	—	2	1	no	—
900	#125	C₂³×C₅₃	1	1	yes	characteristic, complemented
901	#124	—	2	1	no	—
902	#124	—	2	1	no	—
903	#124	—	2	1	no	—
904	#124	—	2	1	no	—
905	#124	—	2	1	no	—
906	#124	C₂³×C₅₃	1	2	yes	—
907	#124	C₂³×C₅₃	1	2	yes	—
908	#124	C₂³×C₅₃	1	1	yes	characteristic, complemented
909	#123	—	2	1	no	—
910	#123	—	2	1	no	—
911	#123	—	2	1	no	—
912	#123	—	2	1	no	—
913	#123	—	2	1	no	—
914	#123	—	2	2	no	—
915	#123	—	2	2	no	—
916	#123	—	2	2	no	—
917	#123	—	2	2	no	—
918	#123	—	2	1	no	—
919	#123	—	2	1	no	—
920	#123	—	2	1	no	—
921	#123	—	2	1	no	—
922	C₂²⋊Q₈	—	2	1	no	—
923	C₂²⋊Q₈	—	2	1	no	—
924	C₂²⋊Q₈	—	2	1	no	—
925	C₂²⋊Q₈	—	2	1	no	—
926	C₂²⋊Q₈	—	2	1	no	—
927	C₂²⋊Q₈	—	2	1	no	—
928	C₂²⋊Q₈	—	2	1	no	—
929	C₂²⋊Q₈	—	2	1	no	—
930	C₂²⋊Q₈	—	2	1	no	—
931	C₂²⋊Q₈	—	2	1	no	—
932	C₂²⋊Q₈	—	2	1	no	—
933	C₂²⋊Q₈	—	2	1	no	—
934	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
935	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
936	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
937	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
938	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
939	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
940	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
941	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
942	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
943	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
944	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
945	#121	—	2	1	no	—
946	#121	—	2	1	no	—
947	#121	—	2	1	no	—
948	#121	—	2	1	no	—
949	#121	—	2	1	no	—
950	#121	—	2	2	no	—
951	#121	—	2	2	no	—
952	#121	—	2	2	no	—
953	#121	—	2	2	no	—
954	#121	C₂³×C₅₃	1	2	yes	—
955	#121	C₂³×C₅₃	1	2	yes	—
956	#121	C₂³×C₅₃	1	1	yes	characteristic
957	#121	C₂³×C₅₃	1	1	yes	characteristic
958	#121	C₂³×C₅₃	1	1	yes	characteristic, complemented
959	#120	—	2	1	no	—
960	#120	—	2	1	no	—
961	#120	—	2	2	no	—
962	#120	—	2	2	no	—
963	#120	—	2	2	no	—
964	#120	—	2	2	no	—
965	C₄×Q₈	—	2	1	no	—
966	C₄×Q₈	—	2	1	no	—
967	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
968	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
969	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
970	C₄×D₄	—	2	1	no	—
971	C₄×D₄	—	2	1	no	—
972	C₄×D₄	—	2	1	no	—
973	C₄×D₄	—	2	1	no	—
974	C₄×D₄	—	2	1	no	—
975	C₄×D₄	—	2	1	no	—
976	C₄×D₄	—	2	1	no	—
977	C₄×D₄	—	2	1	no	—
978	C₄×D₄	—	2	1	no	—
979	C₄×D₄	—	2	1	no	—
980	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
981	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
982	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
983	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
984	C₄×D₄	C₂³×C₅₃	1	2	yes	—
985	C₄×D₄	C₂³×C₅₃	1	2	yes	—
986	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
987	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
988	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
989	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
990	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
991	#117	—	2	1	no	—
992	#117	—	2	1	no	—
993	#117	—	2	1	no	—
994	#117	—	2	1	no	—
995	#117	C₂³×C₅₃	1	1	yes	characteristic
996	#117	C₂³×C₅₃	1	1	yes	characteristic, complemented
997	C₂×C₄⋊C₄	—	2	1	no	—
998	C₂×C₄⋊C₄	—	2	1	no	—
999	C₂×C₄⋊C₄	—	2	1	no	—
1000	C₂×C₄⋊C₄	—	2	1	no	—
1001	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1002	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1003	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1004	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
1005	C₂×C₂²⋊C₄	—	2	1	no	—
1006	C₂×C₂²⋊C₄	—	2	1	no	—
1007	C₂×C₂²⋊C₄	—	2	1	no	—
1008	C₂×C₂²⋊C₄	—	2	1	no	—
1009	C₂×C₂²⋊C₄	—	2	1	no	—
1010	C₂×C₂²⋊C₄	—	2	1	no	—
1011	C₂×C₂²⋊C₄	—	2	1	no	—
1012	C₂×C₂²⋊C₄	—	2	2	no	—
1013	C₂×C₂²⋊C₄	—	2	2	no	—
1014	C₂×C₂²⋊C₄	—	2	2	no	—
1015	C₂×C₂²⋊C₄	—	2	2	no	—
1016	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1017	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1018	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1019	#107	C₂³×C₅₃	1	2	yes	complemented
1020	#106	C₂³×C₅₃	1	2	yes	complemented
1021	#106	C₂³×C₅₃	1	2	yes	complemented
1022	#106	C₂³×C₅₃	1	2	yes	complemented
1023	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
1024	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
1025	#103	C₂³×C₅₃	1	2	yes	complemented
1026	#103	C₂³×C₅₃	1	2	yes	complemented
1027	#103	C₂³×C₅₃	1	2	yes	complemented
1028	#103	C₂³×C₅₃	1	2	yes	complemented
1029	#103	C₂³×C₅₃	1	2	yes	complemented
1030	#103	C₂³×C₅₃	1	2	yes	complemented
1031	#103	C₂³×C₅₃	1	2	yes	complemented
1032	#102	C₂³×C₅₃	1	2	yes	—
1033	#102	C₂³×C₅₃	1	2	yes	—
1034	#102	C₂³×C₅₃	1	2	yes	—
1035	#102	C₂³×C₅₃	1	2	yes	—
1036	#102	C₂³×C₅₃	1	2	yes	—
1037	#102	C₂³×C₅₃	1	2	yes	—
1038	#102	C₂³×C₅₃	1	2	yes	—
1039	#102	C₂³×C₅₃	1	2	yes	—
1040	#102	C₂³×C₅₃	1	2	yes	complemented
1041	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1042	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1043	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1044	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1045	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1046	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1047	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	complemented
1048	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	complemented
1049	#97	C₂³×C₅₃	1	2	yes	complemented
1050	C₄×C₈	C₂³×C₅₃	1	2	yes	complemented
1051	C₂⁴	—	2	1	no	—
1052	C₂⁴	—	2	1	no	—
1053	C₂⁴	—	2	2	no	—
1054	C₂⁴	—	2	2	no	—
1055	C₂⁴	—	4	4	no	—
1056	C₂⁴	—	4	4	no	—
1057	C₂⁴	—	8	2	no	—
1058	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1059	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1060	#41	—	2	4	no	—
1061	#41	—	2	4	no	—
1062	#41	—	4	2	no	—
1063	#41	—	4	2	no	—
1064	#41	—	4	2	no	—
1065	#41	—	4	2	no	—
1066	#41	—	4	4	no	—
1067	#41	—	4	4	no	—
1068	#41	—	4	4	no	—
1069	C₂×Q₈	—	2	1	no	—
1070	C₂×Q₈	—	2	1	no	—
1071	C₂×Q₈	—	2	1	no	—
1072	C₂×Q₈	—	2	1	no	—
1073	C₂×Q₈	—	4	2	no	—
1074	C₂×Q₈	—	4	2	no	—
1075	C₂×Q₈	—	4	2	no	—
1076	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1077	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1078	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1079	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1080	C₂×D₄	—	2	4	no	—
1081	C₂×D₄	—	2	4	no	—
1082	C₂×D₄	—	2	4	no	—
1083	C₂×D₄	—	2	1	no	—
1084	C₂×D₄	—	2	1	no	—
1085	C₂×D₄	—	2	1	no	—
1086	C₂×D₄	—	2	2	no	—
1087	C₂×D₄	—	2	2	no	—
1088	C₂×D₄	—	2	2	no	—
1089	C₂×D₄	—	2	2	no	—
1090	C₂×D₄	—	2	1	no	—
1091	C₂×D₄	—	2	1	no	—
1092	C₂×D₄	—	2	1	no	—
1093	C₂×D₄	—	2	2	no	—
1094	C₂×D₄	—	2	2	no	—
1095	C₂×D₄	—	2	1	no	—
1096	C₂×D₄	—	4	2	no	—
1097	C₂×D₄	—	4	2	no	—
1098	C₂×D₄	—	4	2	no	—
1099	C₂×D₄	—	4	2	no	—
1100	C₂×D₄	—	4	4	no	—
1101	C₂×D₄	—	4	4	no	—
1102	C₂×D₄	—	4	4	no	—
1103	C₂×D₄	—	4	4	no	—
1104	C₂×D₄	—	8	2	no	—
1105	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1106	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1107	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1108	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1109	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1110	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1111	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1112	C₂²×C₄	—	2	1	no	—
1113	C₂²×C₄	—	2	1	no	—
1114	C₂²×C₄	—	2	1	no	—
1115	C₂²×C₄	—	2	1	no	—
1116	C₂²×C₄	—	2	1	no	—
1117	C₂²×C₄	—	2	1	no	—
1118	C₂²×C₄	—	2	2	no	—
1119	C₂²×C₄	—	2	2	no	—
1120	C₂²×C₄	—	2	1	no	—
1121	C₂²×C₄	—	2	2	no	—
1122	C₂²×C₄	—	2	2	no	—
1123	C₂²×C₄	—	2	1	no	—
1124	C₂²×C₄	—	2	1	no	—
1125	C₂²×C₄	—	4	2	no	—
1126	C₂²×C₄	—	4	2	no	—
1127	C₂²×C₄	—	4	4	no	—
1128	C₂²×C₄	—	8	2	no	—
1129	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1130	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1131	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1132	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1133	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1134	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1135	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1136	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1137	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1138	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1139	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1140	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1141	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1142	Q₁₆	—	4	2	no	—
1143	Q₁₆	—	4	2	no	—
1144	Q₁₆	—	4	2	no	—
1145	SD₁₆	—	2	4	no	—
1146	SD₁₆	—	2	4	no	—
1147	SD₁₆	—	2	4	no	—
1148	SD₁₆	—	4	2	no	—
1149	SD₁₆	—	4	2	no	—
1150	SD₁₆	—	4	2	no	—
1151	SD₁₆	—	4	2	no	—
1152	D₈	—	2	4	no	—
1153	D₈	—	4	2	no	—
1154	M₁₆	—	4	2	no	—
1155	M₁₆	—	4	2	no	—
1156	C₂×C₈	—	4	2	no	—
1157	C₂×C₈	—	4	2	no	—
1158	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1159	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1160	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1161	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1162	C₄⋊C₄	—	2	1	no	—
1163	C₄⋊C₄	—	2	1	no	—
1164	C₄⋊C₄	—	2	1	no	—
1165	C₄⋊C₄	—	2	1	no	—
1166	C₄⋊C₄	—	2	1	no	—
1167	C₄⋊C₄	—	2	1	no	—
1168	C₄⋊C₄	—	2	1	no	—
1169	C₄⋊C₄	—	2	1	no	—
1170	C₄⋊C₄	—	2	2	no	—
1171	C₄⋊C₄	—	2	2	no	—
1172	C₄⋊C₄	—	2	1	no	—
1173	C₄⋊C₄	—	2	1	no	—
1174	C₄⋊C₄	—	2	1	no	—
1175	C₄⋊C₄	—	2	1	no	—
1176	C₄⋊C₄	—	2	1	no	—
1177	C₄⋊C₄	—	2	1	no	—
1178	C₄⋊C₄	—	2	1	no	—
1179	C₄⋊C₄	—	2	1	no	—
1180	C₄⋊C₄	—	2	1	no	—
1181	C₄⋊C₄	—	2	1	no	—
1182	C₄⋊C₄	—	2	1	no	—
1183	C₄⋊C₄	—	2	1	no	—
1184	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1185	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1186	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1187	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1188	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1189	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1190	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1191	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1192	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1193	C₂²⋊C₄	—	2	2	no	—
1194	C₂²⋊C₄	—	2	2	no	—
1195	C₂²⋊C₄	—	2	1	no	—
1196	C₂²⋊C₄	—	2	1	no	—
1197	C₂²⋊C₄	—	2	1	no	—
1198	C₂²⋊C₄	—	2	1	no	—
1199	C₂²⋊C₄	—	2	1	no	—
1200	C₂²⋊C₄	—	2	1	no	—
1201	C₂²⋊C₄	—	2	1	no	—
1202	C₂²⋊C₄	—	2	1	no	—
1203	C₂²⋊C₄	—	2	1	no	—
1204	C₂²⋊C₄	—	2	1	no	—
1205	C₂²⋊C₄	—	2	1	no	—
1206	C₂²⋊C₄	—	2	2	no	—
1207	C₂²⋊C₄	—	2	2	no	—
1208	C₂²⋊C₄	—	2	2	no	—
1209	C₂²⋊C₄	—	2	2	no	—
1210	C₂²⋊C₄	—	2	2	no	—
1211	C₂²⋊C₄	—	2	2	no	—
1212	C₂²⋊C₄	—	2	2	no	—
1213	C₂²⋊C₄	—	2	2	no	—
1214	C₂²⋊C₄	—	2	1	no	—
1215	C₂²⋊C₄	—	2	1	no	—
1216	C₂²⋊C₄	—	2	1	no	—
1217	C₂²⋊C₄	—	2	1	no	—
1218	C₂²⋊C₄	—	2	1	no	—
1219	C₂²⋊C₄	—	2	1	no	—
1220	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1221	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1222	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1223	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1224	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1225	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1226	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1227	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1228	C₄²	—	2	1	no	—
1229	C₄²	—	2	1	no	—
1230	C₄²	—	2	1	no	—
1231	C₄²	—	2	1	no	—
1232	C₄²	—	2	1	no	—
1233	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1234	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1235	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1236	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1237	C₂³	—	2	4	no	—
1238	C₂³	—	2	2	no	—
1239	C₂³	—	2	2	no	—
1240	C₂³	—	2	2	no	—
1241	C₂³	—	2	2	no	—
1242	C₂³	—	2	1	no	—
1243	C₂³	—	2	2	no	—
1244	C₂³	—	4	1	no	—
1245	C₂³	—	4	1	no	—
1246	C₂³	—	4	1	no	—
1247	C₂³	—	4	4	no	—
1248	C₂³	—	4	4	no	—
1249	C₂³	—	4	2	no	—
1250	C₂³	—	4	2	no	—
1251	C₂³	—	4	2	no	—
1252	C₂³	—	4	4	no	—
1253	C₂³	—	4	2	no	—
1254	C₂³	—	4	4	no	—
1255	C₂³	—	4	2	no	—
1256	C₂³	—	8	2	no	—
1257	C₂³	—	8	2	no	—
1258	C₂³	—	8	16	no	—
1259	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1260	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1261	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1262	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1263	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1264	Q₈	—	2	2	no	—
1265	Q₈	—	2	2	no	—
1266	Q₈	—	2	2	no	—
1267	Q₈	—	2	2	no	—
1268	Q₈	—	2	2	no	—
1269	Q₈	—	4	2	no	—
1270	Q₈	—	4	2	no	—
1271	Q₈	—	8	1	no	—
1272	Q₈	—	8	1	no	—
1273	D₄	—	2	4	no	—
1274	D₄	—	2	2	no	—
1275	D₄	—	2	2	no	—
1276	D₄	—	2	2	no	—
1277	D₄	—	2	2	no	—
1278	D₄	—	2	2	no	—
1279	D₄	—	2	2	no	—
1280	D₄	—	4	1	no	—
1281	D₄	—	4	1	no	—
1282	D₄	—	4	4	no	—
1283	D₄	—	4	4	no	—
1284	D₄	—	4	2	no	—
1285	D₄	—	4	4	no	—
1286	D₄	—	4	4	no	—
1287	D₄	—	4	2	no	—
1288	D₄	—	4	2	no	—
1289	D₄	—	4	2	no	—
1290	D₄	—	8	2	no	—
1291	D₄	—	8	2	no	—
1292	D₄	—	8	1	no	—
1293	D₄	—	8	1	no	—
1294	D₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
1295	C₂×C₄	—	2	2	no	—
1296	C₂×C₄	—	2	2	no	—
1297	C₂×C₄	—	2	2	no	—
1298	C₂×C₄	—	2	2	no	—
1299	C₂×C₄	—	2	2	no	—
1300	C₂×C₄	—	2	2	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	2	no	—
1308	C₂×C₄	—	2	2	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	4	1	no	—
1311	C₂×C₄	—	4	1	no	—
1312	C₂×C₄	—	4	1	no	—
1313	C₂×C₄	—	4	1	no	—
1314	C₂×C₄	—	4	1	no	—
1315	C₂×C₄	—	4	1	no	—
1316	C₂×C₄	—	4	1	no	—
1317	C₂×C₄	—	4	4	no	—
1318	C₂×C₄	—	4	4	no	—
1319	C₂×C₄	—	4	2	no	—
1320	C₂×C₄	—	4	2	no	—
1321	C₂×C₄	—	4	2	no	—
1322	C₂×C₄	—	4	2	no	—
1323	C₂×C₄	—	4	2	no	—
1324	C₂×C₄	—	8	2	no	—
1325	C₂×C₄	—	8	2	no	—
1326	C₂×C₄	—	8	1	no	—
1327	C₂×C₄	—	8	1	no	—
1328	C₂×C₄	—	8	1	no	—
1329	C₂×C₄	—	8	1	no	—
1330	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1331	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1332	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1333	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1334	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1335	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1336	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1337	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1338	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1339	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1340	C₈	—	2	2	no	—
1341	C₈	—	2	2	no	—
1342	C₈	—	2	2	no	—
1343	C₈	—	2	2	no	—
1344	C₂²	—	2	1	no	—
1345	C₂²	—	2	1	no	—
1346	C₂²	—	2	1	no	—
1347	C₂²	—	2	1	no	—
1348	C₂²	—	2	1	no	—
1349	C₂²	—	2	1	no	—
1350	C₂²	—	2	1	no	—
1351	C₂²	—	2	4	no	—
1352	C₂²	—	2	1	no	—
1353	C₂²	—	2	1	no	—
1354	C₂²	—	2	1	no	—
1355	C₂²	—	2	1	no	—
1356	C₂²	—	2	1	no	—
1357	C₂²	—	2	1	no	—
1358	C₂²	—	4	4	no	—
1359	C₂²	—	4	8	no	—
1360	C₂²	—	4	2	no	—
1361	C₂²	—	4	2	no	—
1362	C₂²	—	4	1	no	—
1363	C₂²	—	4	2	no	—
1364	C₂²	—	4	1	no	—
1365	C₂²	—	4	2	no	—
1366	C₂²	—	4	1	no	—
1367	C₂²	—	4	2	no	—
1368	C₂²	—	8	2	no	—
1369	C₂²	—	8	8	no	—
1370	C₂²	—	8	4	no	—
1371	C₂²	—	8	8	no	—
1372	C₂²	C₅₃×#575	1	2	yes	—
1373	C₂²	C₅₃×#577	1	2	yes	—
1374	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1375	C₄	—	2	1	no	—
1376	C₄	—	2	1	no	—
1377	C₄	—	2	1	no	—
1378	C₄	—	2	1	no	—
1379	C₄	—	2	1	no	—
1380	C₄	—	2	1	no	—
1381	C₄	—	2	1	no	—
1382	C₄	—	2	1	no	—
1383	C₄	—	2	1	no	—
1384	C₄	—	4	2	no	—
1385	C₄	—	4	1	no	—
1386	C₄	—	4	1	no	—
1387	C₄	—	4	1	no	—
1388	C₄	—	4	1	no	—
1389	C₄	—	4	1	no	—
1390	C₄	—	4	1	no	—
1391	C₄	—	4	2	no	—
1392	C₄	—	4	1	no	—
1393	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1394	C₂	—	2	2	no	—
1395	C₂	—	2	2	no	—
1396	C₂	—	4	1	no	—
1397	C₂	—	4	1	no	—
1398	C₂	—	4	1	no	—
1399	C₂	—	4	4	no	—
1400	C₂	—	8	2	no	—
1401	C₂	—	8	1	no	—
1402	C₂	C₅₃×#3484	1	1	yes	characteristic
1403	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1404	C₂	C₂×C₅₃×#577	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3520	C₂	semidirect
2. C₂×C₅₃×#546	C₂	semidirect
3. C₅₃×#3323	C₂	semidirect
4. C₅₃×#3311	C₂	semidirect
5. C₅₃×#3306	C₂	semidirect
6. C₅₃×#3296	C₂	semidirect
7. C₅₃×#3282	C₂	semidirect
8. C₅₃×#3275	C₂	semidirect
9. C₅₃×#3267	C₂	semidirect
10. C₅₃×#3266	C₂	semidirect
11. C₅₃×#3215	C₂	semidirect
12. C₅₃×#3211	C₂	semidirect
13. C₅₃×#3195	C₂	semidirect
14. C₅₃×#3194	C₂	semidirect
15. C₅₃×#3190	C₂	semidirect
16. C₅₃×#3187	C₂	semidirect
17. C₅₃×#3114	C₂	semidirect
18. C₅₃×#3101	C₂	semidirect
19. C₅₃×#3007	C₂	semidirect
20. C₅₃×#3003	C₂	semidirect
21. C₅₃×#3002	C₂	semidirect
22. C₂×C₅₃×#450	C₂	semidirect
23. C₅₃×#2974	C₂	semidirect
26. C₂×#137×C₅₃	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
28. C₂×#135×C₅₃	C₂²	semidirect
29. C₂²×SD₁₆×C₅₃	C₂²	semidirect
30. C₅₃×#556	C₂²	semidirect
32. C₅₃×#552	C₂²	semidirect
33. C₅₃×#552	C₂²	semidirect
36. D₄×Q₈×C₅₃	C₂²	semidirect
37. C₅₃×#548	C₂²	semidirect
38. C₅₃×#548	C₂²	semidirect
39. C₅₃×#547	C₂²	semidirect
40. C₅₃×#547	C₂²	semidirect
53. C₅₃×#533	C₂²	semidirect
54. C₅₃×#529	C₂²	semidirect
57. C₅₃×#525	C₂²	semidirect
61. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
69. C₅₃×#497	C₂²	semidirect
70. C₅₃×#495	C₂²	semidirect
71. C₅₃×#489	C₂²	semidirect
72. C₅₃×#488	C₂²	semidirect
73. C₅₃×#485	C₂²	semidirect
74. C₅₃×#483	C₂²	semidirect
75. C₅₃×#483	C₂²	semidirect
76. C₅₃×#483	C₂²	semidirect
77. C₅₃×#483	C₂²	semidirect
78. C₅₃×#482	C₂²	semidirect
79. C₅₃×#481	C₂²	semidirect
80. C₅₃×#480	C₂²	semidirect
81. C₅₃×#478	C₂²	semidirect
82. C₅₃×#476	C₂²	semidirect
83. C₅₃×#470	C₂²	semidirect
84. C₅₃×#470	C₂²	semidirect
85. C₅₃×#469	C₂²	semidirect
86. C₅₃×#468	C₂²	semidirect
87. C₅₃×#467	C₂²	semidirect
88. C₅₃×#465	C₂²	semidirect
89. C₅₃×#465	C₂²	semidirect
90. C₅₃×#465	C₂²	semidirect
91. C₅₃×#464	C₂²	semidirect
92. C₅₃×#464	C₂²	semidirect
93. C₅₃×#464	C₂²	semidirect
94. C₅₃×#463	C₂²	semidirect
95. C₅₃×#463	C₂²	semidirect
96. C₅₃×#461	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×#451	C₂²	semidirect
103. C₅₃×#451	C₂²	semidirect
104. C₅₃×#451	C₂²	semidirect
111. C₅₃×#450	C₂²	semidirect
112. C₅₃×#450	C₂²	semidirect
113. C₅₃×#450	C₂²	semidirect
114. C₅₃×#449	C₂²	semidirect
115. C₅₃×#449	C₂²	semidirect
116. C₅₃×#448	C₂²	semidirect
117. C₅₃×#448	C₂²	semidirect
120. C₅₃×#447	C₂²	semidirect
121. C₅₃×#442	C₂²	semidirect
122. C₅₃×#440	C₂²	semidirect
123. C₄×SD₁₆×C₅₃	C₂²	semidirect
124. C₄×SD₁₆×C₅₃	C₂²	semidirect
125. C₅₃×#436	C₂²	semidirect
126. C₅₃×#435	C₂²	semidirect
127. C₅₃×#435	C₂²	semidirect
128. C₈×D₄×C₅₃	C₂²	semidirect
129. C₅₃×#432	C₂²	semidirect
130. C₅₃×#431	C₂²	semidirect
131. C₅₃×#418	C₂²	semidirect
132. C₅₃×#417	C₂²	semidirect
133. C₅₃×#416	C₂²	semidirect
134. C₂×#102×C₅₃	C₂²	semidirect
136. C₅₃×#407	C₂²	semidirect
138. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
147. C₂×#41×C₅₃	C₂³	semidirect
150. C₂²×Q₈×C₅₃	C₂³	semidirect
169. C₂×Q₁₆×C₅₃	C₂³	semidirect
170. C₂×Q₁₆×C₅₃	C₂³	semidirect
171. C₂×Q₁₆×C₅₃	C₂³	semidirect
179. C₂×SD₁₆×C₅₃	C₂³	semidirect
183. C₂×M₁₆×C₅₃	C₂³	semidirect
185. C₂²×C₈×C₅₃	C₂³	semidirect
187. C₄⋊Q₈×C₅₃	C₂³	semidirect
188. C₄⋊Q₈×C₅₃	C₂³	semidirect
197. #125×C₅₃	C₂³	semidirect
205. #124×C₅₃	C₂³	semidirect
239. C₂²⋊Q₈×C₅₃	C₂³	semidirect
240. C₂²⋊Q₈×C₅₃	C₂³	semidirect
241. C₂²⋊Q₈×C₅₃	C₂³	semidirect
255. #121×C₅₃	C₂³	semidirect
264. C₄×Q₈×C₅₃	C₂³	semidirect
265. C₄×Q₈×C₅₃	C₂³	semidirect
266. C₄×Q₈×C₅₃	C₂³	semidirect
287. C₄×D₄×C₅₃	C₂³	semidirect
293. #117×C₅₃	C₂³	semidirect
301. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
316. #107×C₅₃	C₂³	semidirect
317. #106×C₅₃	C₂³	semidirect
318. #106×C₅₃	C₂³	semidirect
319. #106×C₅₃	C₂³	semidirect
320. C₄⋊C₈×C₅₃	C₂³	semidirect
321. C₄⋊C₈×C₅₃	C₂³	semidirect
322. #103×C₅₃	C₂³	semidirect
323. #103×C₅₃	C₂³	semidirect
324. #103×C₅₃	C₂³	semidirect
325. #103×C₅₃	C₂³	semidirect
326. #103×C₅₃	C₂³	semidirect
327. #103×C₅₃	C₂³	semidirect
328. #103×C₅₃	C₂³	semidirect
337. #102×C₅₃	C₂³	semidirect
344. C₂²⋊C₈×C₅₃	C₂³	semidirect
345. C₂²⋊C₈×C₅₃	C₂³	semidirect
346. #97×C₅₃	C₂³	semidirect
347. C₄×C₈×C₅₃	C₂³	semidirect
641. #61601	C₅₃	direct (N × H)
692. #3520	C₂×C₅₃	semidirect
693. C₂×#546	C₂×C₅₃	semidirect
694. #3323	C₂×C₅₃	semidirect
695. #3311	C₂×C₅₃	semidirect
696. #3306	C₂×C₅₃	semidirect
697. #3296	C₂×C₅₃	semidirect
698. #3282	C₂×C₅₃	semidirect
699. #3275	C₂×C₅₃	semidirect
700. #3267	C₂×C₅₃	semidirect
701. #3266	C₂×C₅₃	semidirect
702. #3215	C₂×C₅₃	semidirect
703. #3211	C₂×C₅₃	semidirect
704. #3195	C₂×C₅₃	semidirect
705. #3194	C₂×C₅₃	semidirect
706. #3190	C₂×C₅₃	semidirect
707. #3187	C₂×C₅₃	semidirect
708. #3114	C₂×C₅₃	semidirect
709. #3101	C₂×C₅₃	semidirect
710. #3007	C₂×C₅₃	semidirect
711. #3003	C₂×C₅₃	semidirect
712. #3002	C₂×C₅₃	semidirect
713. C₂×#450	C₂×C₅₃	semidirect
714. #2974	C₂×C₅₃	semidirect
728. C₂×#137	C₂²×C₅₃	semidirect
729. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
730. C₂×#135	C₂²×C₅₃	semidirect
731. C₂²×SD₁₆	C₂²×C₅₃	semidirect
732. #556	C₂²×C₅₃	semidirect
734. #552	C₂²×C₅₃	semidirect
735. #552	C₂²×C₅₃	semidirect
738. D₄×Q₈	C₂²×C₅₃	semidirect
739. #548	C₂²×C₅₃	semidirect
740. #548	C₂²×C₅₃	semidirect
741. #547	C₂²×C₅₃	semidirect
742. #547	C₂²×C₅₃	semidirect
755. #533	C₂²×C₅₃	semidirect
756. #529	C₂²×C₅₃	semidirect
759. #525	C₂²×C₅₃	semidirect
763. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
771. #497	C₂²×C₅₃	semidirect
772. #495	C₂²×C₅₃	semidirect
773. #489	C₂²×C₅₃	semidirect
774. #488	C₂²×C₅₃	semidirect
775. #485	C₂²×C₅₃	semidirect
776. #483	C₂²×C₅₃	semidirect
777. #483	C₂²×C₅₃	semidirect
778. #483	C₂²×C₅₃	semidirect
779. #483	C₂²×C₅₃	semidirect
780. #482	C₂²×C₅₃	semidirect
781. #481	C₂²×C₅₃	semidirect
782. #480	C₂²×C₅₃	semidirect
783. #478	C₂²×C₅₃	semidirect
784. #476	C₂²×C₅₃	semidirect
785. #470	C₂²×C₅₃	semidirect
786. #470	C₂²×C₅₃	semidirect
787. #469	C₂²×C₅₃	semidirect
788. #468	C₂²×C₅₃	semidirect
789. #467	C₂²×C₅₃	semidirect
790. #465	C₂²×C₅₃	semidirect
791. #465	C₂²×C₅₃	semidirect
792. #465	C₂²×C₅₃	semidirect
793. #464	C₂²×C₅₃	semidirect
794. #464	C₂²×C₅₃	semidirect
795. #464	C₂²×C₅₃	semidirect
796. #463	C₂²×C₅₃	semidirect
797. #463	C₂²×C₅₃	semidirect
798. #461	C₂²×C₅₃	semidirect
799. #452	C₂²×C₅₃	semidirect
800. #452	C₂²×C₅₃	semidirect
801. #452	C₂²×C₅₃	semidirect
802. #452	C₂²×C₅₃	semidirect
803. #451	C₂²×C₅₃	semidirect
804. #451	C₂²×C₅₃	semidirect
805. #451	C₂²×C₅₃	semidirect
806. #451	C₂²×C₅₃	semidirect
813. #450	C₂²×C₅₃	semidirect
814. #450	C₂²×C₅₃	semidirect
815. #450	C₂²×C₅₃	semidirect
816. #449	C₂²×C₅₃	semidirect
817. #449	C₂²×C₅₃	semidirect
818. #448	C₂²×C₅₃	semidirect
819. #448	C₂²×C₅₃	semidirect
822. #447	C₂²×C₅₃	semidirect
823. #442	C₂²×C₅₃	semidirect
824. #440	C₂²×C₅₃	semidirect
825. C₄×SD₁₆	C₂²×C₅₃	semidirect
826. C₄×SD₁₆	C₂²×C₅₃	semidirect
827. #436	C₂²×C₅₃	semidirect
828. #435	C₂²×C₅₃	semidirect
829. #435	C₂²×C₅₃	semidirect
830. C₈×D₄	C₂²×C₅₃	semidirect
831. #432	C₂²×C₅₃	semidirect
832. #431	C₂²×C₅₃	semidirect
833. #418	C₂²×C₅₃	semidirect
834. #417	C₂²×C₅₃	semidirect
835. #416	C₂²×C₅₃	semidirect
836. C₂×#102	C₂²×C₅₃	semidirect
838. #407	C₂²×C₅₃	semidirect
840. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
841. C₅₃	#61601	direct (N × H)
850. C₂×#41	C₂³×C₅₃	semidirect
853. C₂²×Q₈	C₂³×C₅₃	semidirect
872. C₂×Q₁₆	C₂³×C₅₃	semidirect
873. C₂×Q₁₆	C₂³×C₅₃	semidirect
874. C₂×Q₁₆	C₂³×C₅₃	semidirect
882. C₂×SD₁₆	C₂³×C₅₃	semidirect
886. C₂×M₁₆	C₂³×C₅₃	semidirect
888. C₂²×C₈	C₂³×C₅₃	semidirect
890. C₄⋊Q₈	C₂³×C₅₃	semidirect
891. C₄⋊Q₈	C₂³×C₅₃	semidirect
900. #125	C₂³×C₅₃	semidirect
908. #124	C₂³×C₅₃	semidirect
942. C₂²⋊Q₈	C₂³×C₅₃	semidirect
943. C₂²⋊Q₈	C₂³×C₅₃	semidirect
944. C₂²⋊Q₈	C₂³×C₅₃	semidirect
958. #121	C₂³×C₅₃	semidirect
967. C₄×Q₈	C₂³×C₅₃	semidirect
968. C₄×Q₈	C₂³×C₅₃	semidirect
969. C₄×Q₈	C₂³×C₅₃	semidirect
990. C₄×D₄	C₂³×C₅₃	semidirect
996. #117	C₂³×C₅₃	semidirect
1004. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
1019. #107	C₂³×C₅₃	semidirect
1020. #106	C₂³×C₅₃	semidirect
1021. #106	C₂³×C₅₃	semidirect
1022. #106	C₂³×C₅₃	semidirect
1023. C₄⋊C₈	C₂³×C₅₃	semidirect
1024. C₄⋊C₈	C₂³×C₅₃	semidirect
1025. #103	C₂³×C₅₃	semidirect
1026. #103	C₂³×C₅₃	semidirect
1027. #103	C₂³×C₅₃	semidirect
1028. #103	C₂³×C₅₃	semidirect
1029. #103	C₂³×C₅₃	semidirect
1030. #103	C₂³×C₅₃	semidirect
1031. #103	C₂³×C₅₃	semidirect
1040. #102	C₂³×C₅₃	semidirect
1047. C₂²⋊C₈	C₂³×C₅₃	semidirect
1048. C₂²⋊C₈	C₂³×C₅₃	semidirect
1049. #97	C₂³×C₅₃	semidirect
1050. C₄×C₈	C₂³×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3520	2
C₂×C₅₃×#546	2
C₅₃×#3323	2
C₅₃×#3311	2
C₅₃×#3306	2
C₅₃×#3296	2
C₅₃×#3282	2
C₅₃×#3275	2
C₅₃×#3267	2
C₅₃×#3266	2
C₅₃×#3215	2
C₅₃×#3211	2
C₅₃×#3195	2
C₅₃×#3194	2
C₅₃×#3190	2
C₅₃×#3187	2
C₅₃×#3114	2
C₅₃×#3101	2
C₅₃×#3007	2
C₅₃×#3003	2
C₅₃×#3002	2
C₂×C₅₃×#450	2
C₅₃×#2974	2
#61601	53

Subgroups — C53×#61601 #27269113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61601 #27269113