Subgroups — C₅₃×#61599 #27269111

Order 13568.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3313	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3311	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3305	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3276	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3271	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3268	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3197	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3191	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3005	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3002	C₂	1	2	yes	maximal, complemented
23	C₅₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₃	C₂²	1	2	yes	—
25	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
27	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
28	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
29	C₅₃×#559	—	2	2	no	—
30	C₅₃×#556	C₂²	1	2	yes	complemented
31	C₅₃×#555	C₂²	1	1	yes	characteristic
32	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#553	—	2	1	no	—
34	C₅₃×#553	—	2	1	no	—
35	C₅₃×#550	C₂²	1	1	yes	characteristic
36	C₅₃×#550	C₂²	1	2	yes	complemented
37	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#548	C₂²	1	2	yes	—
39	C₅₃×#547	—	2	1	no	—
40	C₅₃×#547	C₂²	1	1	yes	characteristic
41	C₅₃×#547	C₂²	1	1	yes	characteristic
42	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#546	—	2	2	no	—
44	C₅₃×#546	C₂²	1	2	yes	—
45	D₄²×C₅₃	—	2	1	no	—
46	D₄²×C₅₃	C₂²	1	1	yes	characteristic
47	C₅₃×#538	—	2	2	no	—
48	C₅₃×#535	—	2	1	no	—
49	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#532	—	2	1	no	—
51	C₅₃×#532	C₂²	1	1	yes	characteristic
52	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#525	—	2	2	no	—
54	C₅₃×#525	C₂²	1	2	yes	—
55	C₅₃×#525	C₂²	1	2	yes	complemented
56	C₅₃×#525	C₂²	1	2	yes	complemented
57	C₅₃×#520	—	2	1	no	—
58	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₅₃	—	2	1	no	—
60	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
61	C₅₃×#496	C₂²	1	2	yes	complemented
62	C₅₃×#494	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#489	C₂²	1	2	yes	complemented
65	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#485	C₂²	1	2	yes	complemented
68	C₅₃×#485	C₂²	1	2	yes	complemented
69	C₅₃×#485	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#482	C₂²	1	2	yes	complemented
72	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#482	C₂²	1	2	yes	complemented
74	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#470	C₂²	1	2	yes	complemented
79	C₅₃×#469	C₂²	1	2	yes	complemented
80	C₅₃×#468	C₂²	1	2	yes	complemented
81	C₅₃×#468	C₂²	1	2	yes	complemented
82	C₅₃×#467	C₂²	1	2	yes	complemented
83	C₅₃×#466	C₂²	1	2	yes	complemented
84	C₅₃×#465	C₂²	1	2	yes	complemented
85	C₅₃×#465	C₂²	1	2	yes	complemented
86	C₅₃×#464	C₂²	1	2	yes	complemented
87	C₅₃×#464	C₂²	1	2	yes	complemented
88	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#452	C₂²	1	2	yes	—
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×#452	C₂²	1	2	yes	complemented
102	C₅₃×#452	C₂²	1	2	yes	complemented
103	C₅₃×#451	C₂²	1	2	yes	complemented
104	C₅₃×#450	C₂²	1	2	yes	complemented
105	C₅₃×#449	C₂²	1	1	yes	characteristic
106	C₅₃×#449	C₂²	1	1	yes	characteristic
107	C₅₃×#449	C₂²	1	2	yes	complemented
108	C₅₃×#449	C₂²	1	2	yes	complemented
109	C₅₃×#449	C₂²	1	2	yes	complemented
110	C₅₃×#449	C₂²	1	2	yes	complemented
111	C₅₃×#449	C₂²	1	2	yes	complemented
112	C₅₃×#449	C₂²	1	2	yes	complemented
113	C₅₃×#448	C₂²	1	2	yes	complemented
114	C₅₃×#447	C₂²	1	2	yes	complemented
115	C₅₃×#441	C₂²	1	2	yes	complemented
116	C₅₃×#440	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#436	C₂²	1	1	yes	characteristic
122	C₅₃×#436	C₂²	1	1	yes	characteristic
123	C₅₃×#435	C₂²	1	2	yes	complemented
124	C₅₃×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#419	C₂²	1	2	yes	complemented
130	C₅₃×#418	C₂²	1	2	yes	complemented
131	C₅₃×#416	C₂²	1	2	yes	complemented
132	C₅₃×#416	C₂²	1	2	yes	complemented
133	C₅₃×#407	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	complemented
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	2	no	—
137	C₂×#41×C₅₃	—	2	2	no	—
138	C₂×#41×C₅₃	—	4	4	no	—
139	C₂×#41×C₅₃	—	4	4	no	—
140	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₅₃	C₂³	1	2	yes	—
142	C₂×#41×C₅₃	C₂³	1	2	yes	—
143	C₂×#41×C₅₃	C₂³	1	2	yes	—
144	C₂×#41×C₅₃	C₂³	1	2	yes	—
145	C₂×#41×C₅₃	C₂³	1	2	yes	—
146	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
147	C₂²×D₄×C₅₃	—	2	2	no	—
148	C₂²×D₄×C₅₃	—	2	1	no	—
149	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
150	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
151	C₂³×C₄×C₅₃	—	2	2	no	—
152	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
153	#137×C₅₃	—	4	4	no	—
154	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
155	#135×C₅₃	—	4	4	no	—
156	#135×C₅₃	—	4	4	no	—
157	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
167	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
168	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×D₈×C₅₃	C₂³	1	2	yes	—
170	C₂×D₈×C₅₃	C₂³	1	2	yes	—
171	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
172	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
173	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
174	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
175	C₄⋊Q₈×C₅₃	—	2	1	no	—
176	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
177	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
178	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
180	#127×C₅₃	—	2	1	no	—
181	#127×C₅₃	—	2	2	no	—
182	#127×C₅₃	C₂³	1	1	yes	characteristic
183	#127×C₅₃	C₂³	1	1	yes	characteristic
184	#126×C₅₃	—	2	2	no	—
185	#126×C₅₃	—	2	2	no	—
186	#125×C₅₃	—	2	1	no	—
187	#124×C₅₃	—	2	2	no	—
188	#124×C₅₃	—	2	2	no	—
189	#124×C₅₃	—	2	2	no	—
190	#124×C₅₃	—	2	1	no	—
191	#124×C₅₃	—	2	2	no	—
192	#124×C₅₃	C₂³	1	2	yes	—
193	#123×C₅₃	—	2	2	no	—
194	#123×C₅₃	—	2	2	no	—
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	C₂²⋊Q₈×C₅₃	—	2	2	no	—
201	C₂²⋊Q₈×C₅₃	—	2	2	no	—
202	C₂²⋊Q₈×C₅₃	—	2	1	no	—
203	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
205	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
208	#121×C₅₃	—	2	1	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	2	no	—
211	#121×C₅₃	—	2	2	no	—
212	#121×C₅₃	—	2	2	no	—
213	#121×C₅₃	—	2	2	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	—	2	1	no	—
216	#121×C₅₃	—	2	1	no	—
217	#121×C₅₃	—	2	1	no	—
218	#121×C₅₃	—	2	1	no	—
219	#121×C₅₃	—	2	1	no	—
220	#121×C₅₃	—	2	1	no	—
221	#121×C₅₃	—	2	1	no	—
222	#121×C₅₃	C₂³	1	2	yes	—
223	#121×C₅₃	C₂³	1	2	yes	—
224	#121×C₅₃	C₂³	1	1	yes	characteristic
225	#121×C₅₃	C₂³	1	1	yes	characteristic
226	#121×C₅₃	C₂³	1	2	yes	—
227	#121×C₅₃	C₂³	1	2	yes	—
228	#120×C₅₃	—	2	2	no	—
229	#120×C₅₃	—	2	2	no	—
230	#120×C₅₃	—	2	2	no	—
231	#120×C₅₃	—	2	2	no	—
232	#120×C₅₃	—	2	2	no	—
233	C₄×Q₈×C₅₃	—	2	2	no	—
234	C₄×Q₈×C₅₃	—	2	1	no	—
235	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
238	C₄×D₄×C₅₃	—	2	1	no	—
239	C₄×D₄×C₅₃	—	2	2	no	—
240	C₄×D₄×C₅₃	—	2	2	no	—
241	C₄×D₄×C₅₃	—	2	1	no	—
242	C₄×D₄×C₅₃	—	2	1	no	—
243	C₄×D₄×C₅₃	—	2	1	no	—
244	C₄×D₄×C₅₃	—	2	1	no	—
245	C₄×D₄×C₅₃	—	2	2	no	—
246	C₄×D₄×C₅₃	—	2	1	no	—
247	C₄×D₄×C₅₃	—	2	1	no	—
248	C₄×D₄×C₅₃	—	2	2	no	—
249	C₄×D₄×C₅₃	—	2	2	no	—
250	C₄×D₄×C₅₃	—	2	2	no	—
251	C₄×D₄×C₅₃	—	2	2	no	—
252	C₄×D₄×C₅₃	—	2	2	no	—
253	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
254	C₄×D₄×C₅₃	D₄	1	2	yes	—
255	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
256	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₅₃	C₂³	1	2	yes	—
262	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
263	#117×C₅₃	—	2	1	no	—
264	#117×C₅₃	—	2	1	no	—
265	#117×C₅₃	—	2	1	no	—
266	#117×C₅₃	—	2	1	no	—
267	#117×C₅₃	C₂³	1	1	yes	characteristic
268	#117×C₅₃	C₂³	1	2	yes	—
269	#117×C₅₃	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
271	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
272	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
273	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
276	C₂×C₄²×C₅₃	—	2	1	no	—
277	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
278	#107×C₅₃	C₂³	1	1	yes	characteristic
279	#107×C₅₃	C₂³	1	2	yes	—
280	#107×C₅₃	C₂³	1	1	yes	characteristic
281	#106×C₅₃	C₂³	1	1	yes	characteristic
282	#106×C₅₃	C₂³	1	2	yes	—
283	#106×C₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	2	yes	—
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	1	yes	characteristic
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	2	yes	—
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	2	yes	—
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	1	yes	characteristic
307	#102×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
315	#97×C₅₃	C₂³	1	2	yes	—
316	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
318	C₂⁴×C₅₃	—	2	2	no	—
319	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
320	#41×C₅₃	—	2	2	no	—
321	#41×C₅₃	—	2	2	no	—
322	#41×C₅₃	—	2	4	no	—
323	#41×C₅₃	—	2	4	no	—
324	#41×C₅₃	—	4	2	no	—
325	#41×C₅₃	—	4	2	no	—
326	#41×C₅₃	—	4	2	no	—
327	#41×C₅₃	—	4	2	no	—
328	#41×C₅₃	—	4	4	no	—
329	#41×C₅₃	—	4	8	no	—
330	#41×C₅₃	—	4	2	no	—
331	#41×C₅₃	—	4	2	no	—
332	#41×C₅₃	—	4	2	no	—
333	#41×C₅₃	—	4	2	no	—
334	#41×C₅₃	—	4	8	no	—
335	C₂×Q₈×C₅₃	—	2	1	no	—
336	C₂×Q₈×C₅₃	—	2	2	no	—
337	C₂×Q₈×C₅₃	—	2	1	no	—
338	C₂×Q₈×C₅₃	—	2	4	no	—
339	C₂×Q₈×C₅₃	—	4	2	no	—
340	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
341	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
342	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₅₃	—	2	1	no	—
344	C₂×D₄×C₅₃	—	2	4	no	—
345	C₂×D₄×C₅₃	—	2	2	no	—
346	C₂×D₄×C₅₃	—	2	1	no	—
347	C₂×D₄×C₅₃	—	2	1	no	—
348	C₂×D₄×C₅₃	—	2	2	no	—
349	C₂×D₄×C₅₃	—	2	2	no	—
350	C₂×D₄×C₅₃	—	2	2	no	—
351	C₂×D₄×C₅₃	—	2	2	no	—
352	C₂×D₄×C₅₃	—	2	2	no	—
353	C₂×D₄×C₅₃	—	2	2	no	—
354	C₂×D₄×C₅₃	—	2	2	no	—
355	C₂×D₄×C₅₃	—	2	2	no	—
356	C₂×D₄×C₅₃	—	2	1	no	—
357	C₂×D₄×C₅₃	—	2	1	no	—
358	C₂×D₄×C₅₃	—	2	2	no	—
359	C₂×D₄×C₅₃	—	2	1	no	—
360	C₂×D₄×C₅₃	—	2	1	no	—
361	C₂×D₄×C₅₃	—	4	2	no	—
362	C₂×D₄×C₅₃	—	4	2	no	—
363	C₂×D₄×C₅₃	—	4	4	no	—
364	C₂×D₄×C₅₃	—	4	8	no	—
365	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
369	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	—	2	1	no	—
373	C₂²×C₄×C₅₃	—	2	2	no	—
374	C₂²×C₄×C₅₃	—	2	1	no	—
375	C₂²×C₄×C₅₃	—	2	2	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	1	no	—
381	C₂²×C₄×C₅₃	—	2	2	no	—
382	C₂²×C₄×C₅₃	—	2	2	no	—
383	C₂²×C₄×C₅₃	—	4	2	no	—
384	C₂²×C₄×C₅₃	—	4	2	no	—
385	C₂²×C₄×C₅₃	—	4	8	no	—
386	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
389	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
390	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
391	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
393	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
394	Q₁₆×C₅₃	—	2	4	no	—
395	Q₁₆×C₅₃	—	4	2	no	—
396	Q₁₆×C₅₃	—	4	2	no	—
397	SD₁₆×C₅₃	—	2	2	no	—
398	SD₁₆×C₅₃	—	2	2	no	—
399	SD₁₆×C₅₃	—	2	4	no	—
400	SD₁₆×C₅₃	—	4	2	no	—
401	SD₁₆×C₅₃	—	4	2	no	—
402	SD₁₆×C₅₃	—	4	2	no	—
403	SD₁₆×C₅₃	—	4	2	no	—
404	D₈×C₅₃	—	2	2	no	—
405	D₈×C₅₃	—	2	2	no	—
406	D₈×C₅₃	—	4	2	no	—
407	D₈×C₅₃	—	4	2	no	—
408	M₁₆×C₅₃	—	4	2	no	—
409	M₁₆×C₅₃	—	4	2	no	—
410	C₂×C₈×C₅₃	—	4	2	no	—
411	C₂×C₈×C₅₃	—	4	2	no	—
412	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
417	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
418	C₄⋊C₄×C₅₃	—	2	1	no	—
419	C₄⋊C₄×C₅₃	—	2	1	no	—
420	C₄⋊C₄×C₅₃	—	2	2	no	—
421	C₄⋊C₄×C₅₃	—	2	2	no	—
422	C₄⋊C₄×C₅₃	—	2	2	no	—
423	C₄⋊C₄×C₅₃	—	2	1	no	—
424	C₄⋊C₄×C₅₃	—	2	1	no	—
425	C₄⋊C₄×C₅₃	—	2	1	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	1	no	—
431	C₄⋊C₄×C₅₃	—	2	2	no	—
432	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
433	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
435	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄×C₅₃	—	2	2	no	—
441	C₂²⋊C₄×C₅₃	—	2	2	no	—
442	C₂²⋊C₄×C₅₃	—	2	1	no	—
443	C₂²⋊C₄×C₅₃	—	2	2	no	—
444	C₂²⋊C₄×C₅₃	—	2	2	no	—
445	C₂²⋊C₄×C₅₃	—	2	2	no	—
446	C₂²⋊C₄×C₅₃	—	2	2	no	—
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	—	2	2	no	—
449	C₂²⋊C₄×C₅₃	—	2	2	no	—
450	C₂²⋊C₄×C₅₃	—	2	2	no	—
451	C₂²⋊C₄×C₅₃	—	2	2	no	—
452	C₂²⋊C₄×C₅₃	—	2	1	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	2	no	—
457	C₂²⋊C₄×C₅₃	—	2	2	no	—
458	C₂²⋊C₄×C₅₃	—	2	1	no	—
459	C₂²⋊C₄×C₅₃	—	2	1	no	—
460	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
464	C₄²×C₅₃	—	2	1	no	—
465	C₄²×C₅₃	—	2	1	no	—
466	C₄²×C₅₃	—	2	1	no	—
467	C₄²×C₅₃	—	2	2	no	—
468	C₄²×C₅₃	—	2	2	no	—
469	C₄²×C₅₃	—	2	2	no	—
470	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
473	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
474	C₂³×C₅₃	—	2	1	no	—
475	C₂³×C₅₃	—	2	1	no	—
476	C₂³×C₅₃	—	2	1	no	—
477	C₂³×C₅₃	—	2	2	no	—
478	C₂³×C₅₃	—	4	2	no	—
479	C₂³×C₅₃	—	4	2	no	—
480	C₂³×C₅₃	—	4	2	no	—
481	C₂³×C₅₃	—	4	4	no	—
482	C₂³×C₅₃	—	4	4	no	—
483	C₂³×C₅₃	—	8	2	no	—
484	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
485	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
486	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
487	Q₈×C₅₃	—	2	1	no	—
488	Q₈×C₅₃	—	2	2	no	—
489	Q₈×C₅₃	—	2	2	no	—
490	Q₈×C₅₃	—	2	2	no	—
491	Q₈×C₅₃	—	2	2	no	—
492	Q₈×C₅₃	—	4	4	no	—
493	Q₈×C₅₃	—	4	2	no	—
494	Q₈×C₅₃	—	8	1	no	—
495	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
496	D₄×C₅₃	—	2	4	no	—
497	D₄×C₅₃	—	2	2	no	—
498	D₄×C₅₃	—	2	2	no	—
499	D₄×C₅₃	—	2	1	no	—
500	D₄×C₅₃	—	2	2	no	—
501	D₄×C₅₃	—	2	2	no	—
502	D₄×C₅₃	—	2	1	no	—
503	D₄×C₅₃	—	2	1	no	—
504	D₄×C₅₃	—	2	1	no	—
505	D₄×C₅₃	—	2	1	no	—
506	D₄×C₅₃	—	4	2	no	—
507	D₄×C₅₃	—	4	4	no	—
508	D₄×C₅₃	—	4	4	no	—
509	D₄×C₅₃	—	4	2	no	—
510	D₄×C₅₃	—	4	4	no	—
511	D₄×C₅₃	—	4	4	no	—
512	D₄×C₅₃	—	4	4	no	—
513	D₄×C₅₃	—	4	2	no	—
514	D₄×C₅₃	—	4	2	no	—
515	D₄×C₅₃	—	4	2	no	—
516	D₄×C₅₃	—	8	1	no	—
517	D₄×C₅₃	—	8	1	no	—
518	D₄×C₅₃	—	8	2	no	—
519	D₄×C₅₃	—	8	2	no	—
520	D₄×C₅₃	—	8	2	no	—
521	D₄×C₅₃	—	8	2	no	—
522	D₄×C₅₃	—	8	2	no	—
523	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
524	C₂×C₄×C₅₃	—	2	4	no	—
525	C₂×C₄×C₅₃	—	2	1	no	—
526	C₂×C₄×C₅₃	—	2	2	no	—
527	C₂×C₄×C₅₃	—	2	1	no	—
528	C₂×C₄×C₅₃	—	2	1	no	—
529	C₂×C₄×C₅₃	—	2	2	no	—
530	C₂×C₄×C₅₃	—	2	2	no	—
531	C₂×C₄×C₅₃	—	2	2	no	—
532	C₂×C₄×C₅₃	—	2	2	no	—
533	C₂×C₄×C₅₃	—	2	2	no	—
534	C₂×C₄×C₅₃	—	2	2	no	—
535	C₂×C₄×C₅₃	—	2	1	no	—
536	C₂×C₄×C₅₃	—	2	1	no	—
537	C₂×C₄×C₅₃	—	2	1	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	2	no	—
540	C₂×C₄×C₅₃	—	4	2	no	—
541	C₂×C₄×C₅₃	—	4	2	no	—
542	C₂×C₄×C₅₃	—	4	2	no	—
543	C₂×C₄×C₅₃	—	4	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	4	no	—
548	C₂×C₄×C₅₃	—	4	2	no	—
549	C₂×C₄×C₅₃	—	4	2	no	—
550	C₂×C₄×C₅₃	—	4	2	no	—
551	C₂×C₄×C₅₃	—	8	1	no	—
552	C₂×C₄×C₅₃	—	8	2	no	—
553	C₂×C₄×C₅₃	—	8	2	no	—
554	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
557	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
562	C₈×C₅₃	—	2	1	no	—
563	C₈×C₅₃	—	2	1	no	—
564	C₈×C₅₃	—	2	2	no	—
565	C₈×C₅₃	—	2	2	no	—
566	C₈×C₅₃	—	2	1	no	—
567	C₈×C₅₃	—	2	1	no	—
568	#61599	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
569	C₂²×C₅₃	—	2	1	no	—
570	C₂²×C₅₃	—	2	2	no	—
571	C₂²×C₅₃	—	2	2	no	—
572	C₂²×C₅₃	—	2	2	no	—
573	C₂²×C₅₃	—	2	1	no	—
574	C₂²×C₅₃	—	2	2	no	—
575	C₂²×C₅₃	—	2	2	no	—
576	C₂²×C₅₃	—	2	1	no	—
577	C₂²×C₅₃	—	2	2	no	—
578	C₂²×C₅₃	—	2	2	no	—
579	C₂²×C₅₃	—	4	1	no	—
580	C₂²×C₅₃	—	4	1	no	—
581	C₂²×C₅₃	—	4	1	no	—
582	C₂²×C₅₃	—	4	1	no	—
583	C₂²×C₅₃	—	4	2	no	—
584	C₂²×C₅₃	—	4	2	no	—
585	C₂²×C₅₃	—	4	1	no	—
586	C₂²×C₅₃	—	4	1	no	—
587	C₂²×C₅₃	—	4	1	no	—
588	C₂²×C₅₃	—	4	1	no	—
589	C₂²×C₅₃	—	4	2	no	—
590	C₂²×C₅₃	—	8	4	no	—
591	C₂²×C₅₃	—	8	8	no	—
592	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
593	C₄×C₅₃	—	2	1	no	—
594	C₄×C₅₃	—	2	1	no	—
595	C₄×C₅₃	—	2	1	no	—
596	C₄×C₅₃	—	2	2	no	—
597	C₄×C₅₃	—	2	2	no	—
598	C₄×C₅₃	—	2	2	no	—
599	C₄×C₅₃	—	2	1	no	—
600	C₄×C₅₃	—	4	1	no	—
601	C₄×C₅₃	—	4	2	no	—
602	C₄×C₅₃	—	4	2	no	—
603	C₄×C₅₃	—	4	2	no	—
604	C₄×C₅₃	—	4	1	no	—
605	C₄×C₅₃	—	4	1	no	—
606	C₄×C₅₃	—	4	1	no	—
607	C₄×C₅₃	#575	1	2	yes	—
608	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
609	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
610	#3506	C₂×C₅₃	1	1	yes	characteristic, complemented
611	D₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
612	#3329	C₂×C₅₃	1	1	yes	characteristic, complemented
613	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
614	#3313	C₂×C₅₃	1	2	yes	complemented
615	#3311	C₂×C₅₃	1	2	yes	complemented
616	#3305	C₂×C₅₃	1	1	yes	characteristic, complemented
617	#3303	C₂×C₅₃	1	1	yes	characteristic, complemented
618	#3284	C₂×C₅₃	1	1	yes	characteristic, complemented
619	#3283	C₂×C₅₃	1	1	yes	characteristic, complemented
620	#3276	C₂×C₅₃	1	1	yes	characteristic, complemented
621	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
622	#3271	C₂×C₅₃	1	2	yes	complemented
623	#3268	C₂×C₅₃	1	2	yes	complemented
624	#3214	C₂×C₅₃	1	1	yes	characteristic, complemented
625	#3210	C₂×C₅₃	1	1	yes	characteristic, complemented
626	#3197	C₂×C₅₃	1	2	yes	complemented
627	#3191	C₂×C₅₃	1	2	yes	complemented
628	#3116	C₂×C₅₃	1	1	yes	characteristic, complemented
629	#3106	C₂×C₅₃	1	1	yes	characteristic, complemented
630	#3005	C₂×C₅₃	1	2	yes	complemented
631	#3002	C₂×C₅₃	1	2	yes	complemented
632	#2974	C₂×C₅₃	1	1	yes	characteristic, complemented
633	C₂×C₅₃	—	4	2	no	—
634	C₂×C₅₃	—	4	1	no	—
635	C₂×C₅₃	—	4	2	no	—
636	C₂×C₅₃	—	4	2	no	—
637	C₂×C₅₃	—	8	1	no	—
638	C₂×C₅₃	—	8	1	no	—
639	C₂×C₅₃	—	8	2	no	—
640	C₂×C₅₃	#3484	1	1	yes	characteristic
641	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
642	C₂×C₅₃	#3584	1	1	yes	characteristic
643	C₂²×#41	C₂²×C₅₃	1	2	yes	—
644	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
645	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
646	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
647	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
648	#559	—	2	2	no	—
649	#556	C₂²×C₅₃	1	2	yes	complemented
650	#555	C₂²×C₅₃	1	1	yes	characteristic
651	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
652	#553	—	2	1	no	—
653	#553	—	2	1	no	—
654	#550	C₂²×C₅₃	1	1	yes	characteristic
655	#550	C₂²×C₅₃	1	2	yes	complemented
656	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
657	#548	C₂²×C₅₃	1	2	yes	—
658	#547	—	2	1	no	—
659	#547	C₂²×C₅₃	1	1	yes	characteristic
660	#547	C₂²×C₅₃	1	1	yes	characteristic
661	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
662	#546	—	2	2	no	—
663	#546	C₂²×C₅₃	1	2	yes	—
664	D₄²	—	2	1	no	—
665	D₄²	C₂²×C₅₃	1	1	yes	characteristic
666	#538	—	2	2	no	—
667	#535	—	2	1	no	—
668	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
669	#532	—	2	1	no	—
670	#532	C₂²×C₅₃	1	1	yes	characteristic
671	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
672	#525	—	2	2	no	—
673	#525	C₂²×C₅₃	1	2	yes	—
674	#525	C₂²×C₅₃	1	2	yes	complemented
675	#525	C₂²×C₅₃	1	2	yes	complemented
676	#520	—	2	1	no	—
677	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
678	C₂×C₄×D₄	—	2	1	no	—
679	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
680	#496	C₂²×C₅₃	1	2	yes	complemented
681	#494	C₂²×C₅₃	1	1	yes	characteristic, complemented
682	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	#489	C₂²×C₅₃	1	2	yes	complemented
684	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
685	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
686	#485	C₂²×C₅₃	1	2	yes	complemented
687	#485	C₂²×C₅₃	1	2	yes	complemented
688	#485	C₂²×C₅₃	1	2	yes	complemented
689	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
691	#482	C₂²×C₅₃	1	2	yes	complemented
692	#482	C₂²×C₅₃	1	2	yes	complemented
693	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
694	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
695	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
697	#470	C₂²×C₅₃	1	2	yes	complemented
698	#469	C₂²×C₅₃	1	2	yes	complemented
699	#468	C₂²×C₅₃	1	2	yes	complemented
700	#468	C₂²×C₅₃	1	2	yes	complemented
701	#467	C₂²×C₅₃	1	2	yes	complemented
702	#466	C₂²×C₅₃	1	2	yes	complemented
703	#465	C₂²×C₅₃	1	2	yes	complemented
704	#465	C₂²×C₅₃	1	2	yes	complemented
705	#464	C₂²×C₅₃	1	2	yes	complemented
706	#464	C₂²×C₅₃	1	2	yes	complemented
707	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
710	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
711	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
714	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
715	#452	C₂²×C₅₃	1	2	yes	—
716	#452	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	#452	C₂²×C₅₃	1	2	yes	complemented
721	#452	C₂²×C₅₃	1	2	yes	complemented
722	#451	C₂²×C₅₃	1	2	yes	complemented
723	#450	C₂²×C₅₃	1	2	yes	complemented
724	#449	C₂²×C₅₃	1	1	yes	characteristic
725	#449	C₂²×C₅₃	1	1	yes	characteristic
726	#449	C₂²×C₅₃	1	2	yes	complemented
727	#449	C₂²×C₅₃	1	2	yes	complemented
728	#449	C₂²×C₅₃	1	2	yes	complemented
729	#449	C₂²×C₅₃	1	2	yes	complemented
730	#449	C₂²×C₅₃	1	2	yes	complemented
731	#449	C₂²×C₅₃	1	2	yes	complemented
732	#448	C₂²×C₅₃	1	2	yes	complemented
733	#447	C₂²×C₅₃	1	2	yes	complemented
734	#441	C₂²×C₅₃	1	2	yes	complemented
735	#440	C₂²×C₅₃	1	2	yes	complemented
736	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
737	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
738	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
739	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
740	#436	C₂²×C₅₃	1	1	yes	characteristic
741	#436	C₂²×C₅₃	1	1	yes	characteristic
742	#435	C₂²×C₅₃	1	2	yes	complemented
743	#435	C₂²×C₅₃	1	2	yes	complemented
744	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
746	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
747	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
748	#419	C₂²×C₅₃	1	2	yes	complemented
749	#418	C₂²×C₅₃	1	2	yes	complemented
750	#416	C₂²×C₅₃	1	2	yes	complemented
751	#416	C₂²×C₅₃	1	2	yes	complemented
752	#407	C₂²×C₅₃	1	2	yes	complemented
753	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	complemented
754	C₅₃	#61599	1	1	yes	characteristic, direct product factor, Sylow
755	C₂×#41	—	2	1	no	—
756	C₂×#41	—	2	2	no	—
757	C₂×#41	—	2	2	no	—
758	C₂×#41	—	4	4	no	—
759	C₂×#41	—	4	4	no	—
760	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
761	C₂×#41	C₂³×C₅₃	1	2	yes	—
762	C₂×#41	C₂³×C₅₃	1	2	yes	—
763	C₂×#41	C₂³×C₅₃	1	2	yes	—
764	C₂×#41	C₂³×C₅₃	1	2	yes	—
765	C₂×#41	C₂³×C₅₃	1	2	yes	—
766	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
767	C₂²×D₄	—	2	2	no	—
768	C₂²×D₄	—	2	1	no	—
769	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
770	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
771	C₂³×C₄	—	2	2	no	—
772	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
773	#137	—	4	4	no	—
774	AGL(1,ℤ/8)	—	4	4	no	—
775	#135	—	4	4	no	—
776	#135	—	4	4	no	—
777	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
778	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
779	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
781	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
782	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
783	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
785	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
786	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
787	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
788	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
789	C₂×D₈	C₂³×C₅₃	1	2	yes	—
790	C₂×D₈	C₂³×C₅₃	1	2	yes	—
791	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
792	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
793	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
794	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
795	C₄⋊Q₈	—	2	1	no	—
796	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
797	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
798	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
799	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
800	#127	—	2	1	no	—
801	#127	—	2	2	no	—
802	#127	C₂³×C₅₃	1	1	yes	characteristic
803	#127	C₂³×C₅₃	1	1	yes	characteristic
804	#126	—	2	2	no	—
805	#126	—	2	2	no	—
806	#125	—	2	1	no	—
807	#124	—	2	2	no	—
808	#124	—	2	2	no	—
809	#124	—	2	2	no	—
810	#124	—	2	2	no	—
811	#124	—	2	1	no	—
812	#124	C₂³×C₅₃	1	2	yes	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	—	2	2	no	—
823	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
824	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
827	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
828	#121	—	2	2	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	1	no	—
833	#121	—	2	1	no	—
834	#121	—	2	1	no	—
835	#121	—	2	1	no	—
836	#121	—	2	1	no	—
837	#121	—	2	1	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	—	2	2	no	—
842	#121	C₂³×C₅₃	1	2	yes	—
843	#121	C₂³×C₅₃	1	2	yes	—
844	#121	C₂³×C₅₃	1	1	yes	characteristic
845	#121	C₂³×C₅₃	1	1	yes	characteristic
846	#121	C₂³×C₅₃	1	2	yes	—
847	#121	C₂³×C₅₃	1	2	yes	—
848	#120	—	2	2	no	—
849	#120	—	2	2	no	—
850	#120	—	2	2	no	—
851	#120	—	2	2	no	—
852	#120	—	2	2	no	—
853	C₄×Q₈	—	2	2	no	—
854	C₄×Q₈	—	2	1	no	—
855	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
856	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
857	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	2	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
874	C₄×D₄	D₄×C₅₃	1	2	yes	—
875	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
876	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
877	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
878	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
879	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
880	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
881	C₄×D₄	C₂³×C₅₃	1	2	yes	—
882	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
883	#117	—	2	1	no	—
884	#117	—	2	1	no	—
885	#117	—	2	1	no	—
886	#117	—	2	1	no	—
887	#117	C₂³×C₅₃	1	1	yes	characteristic
888	#117	C₂³×C₅₃	1	2	yes	—
889	#117	C₂³×C₅₃	1	2	yes	—
890	C₂×C₄⋊C₄	—	2	1	no	—
891	C₂×C₄⋊C₄	—	2	1	no	—
892	C₂×C₄⋊C₄	—	2	1	no	—
893	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
894	C₂×C₂²⋊C₄	—	2	2	no	—
895	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
896	C₂×C₄²	—	2	1	no	—
897	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
898	#107	C₂³×C₅₃	1	1	yes	characteristic
899	#107	C₂³×C₅₃	1	1	yes	characteristic
900	#107	C₂³×C₅₃	1	2	yes	—
901	#106	C₂³×C₅₃	1	1	yes	characteristic
902	#106	C₂³×C₅₃	1	1	yes	characteristic
903	#106	C₂³×C₅₃	1	2	yes	—
904	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
905	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
906	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
907	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
908	#103	C₂³×C₅₃	1	1	yes	characteristic
909	#103	C₂³×C₅₃	1	2	yes	—
910	#103	C₂³×C₅₃	1	2	yes	—
911	#103	C₂³×C₅₃	1	2	yes	—
912	#103	C₂³×C₅₃	1	1	yes	characteristic
913	#103	C₂³×C₅₃	1	2	yes	—
914	#103	C₂³×C₅₃	1	2	yes	—
915	#103	C₂³×C₅₃	1	2	yes	—
916	#103	C₂³×C₅₃	1	2	yes	—
917	#102	C₂³×C₅₃	1	1	yes	characteristic
918	#102	C₂³×C₅₃	1	2	yes	—
919	#102	C₂³×C₅₃	1	2	yes	—
920	#102	C₂³×C₅₃	1	2	yes	—
921	#102	C₂³×C₅₃	1	1	yes	characteristic
922	#102	C₂³×C₅₃	1	2	yes	—
923	#102	C₂³×C₅₃	1	2	yes	—
924	#102	C₂³×C₅₃	1	1	yes	characteristic
925	#102	C₂³×C₅₃	1	1	yes	characteristic
926	#102	C₂³×C₅₃	1	1	yes	characteristic
927	#102	C₂³×C₅₃	1	1	yes	characteristic
928	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
929	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
930	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
931	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
932	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
933	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
934	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
935	#97	C₂³×C₅₃	1	2	yes	—
936	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
937	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
938	C₂⁴	—	2	2	no	—
939	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
940	#41	—	2	2	no	—
941	#41	—	2	2	no	—
942	#41	—	2	4	no	—
943	#41	—	2	4	no	—
944	#41	—	4	2	no	—
945	#41	—	4	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	4	no	—
949	#41	—	4	8	no	—
950	#41	—	4	2	no	—
951	#41	—	4	2	no	—
952	#41	—	4	2	no	—
953	#41	—	4	2	no	—
954	#41	—	4	8	no	—
955	C₂×Q₈	—	2	1	no	—
956	C₂×Q₈	—	2	2	no	—
957	C₂×Q₈	—	2	1	no	—
958	C₂×Q₈	—	2	4	no	—
959	C₂×Q₈	—	4	2	no	—
960	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
961	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
962	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	4	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	2	1	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	4	2	no	—
982	C₂×D₄	—	4	2	no	—
983	C₂×D₄	—	4	4	no	—
984	C₂×D₄	—	4	8	no	—
985	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
986	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
987	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
988	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
989	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
990	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
991	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	4	2	no	—
1004	C₂²×C₄	—	4	2	no	—
1005	C₂²×C₄	—	4	8	no	—
1006	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1007	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1009	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1010	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1011	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1013	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1014	Q₁₆	—	2	4	no	—
1015	Q₁₆	—	4	2	no	—
1016	Q₁₆	—	4	2	no	—
1017	SD₁₆	—	2	2	no	—
1018	SD₁₆	—	2	2	no	—
1019	SD₁₆	—	2	4	no	—
1020	SD₁₆	—	4	2	no	—
1021	SD₁₆	—	4	2	no	—
1022	SD₁₆	—	4	2	no	—
1023	SD₁₆	—	4	2	no	—
1024	D₈	—	2	2	no	—
1025	D₈	—	2	2	no	—
1026	D₈	—	4	2	no	—
1027	D₈	—	4	2	no	—
1028	M₁₆	—	4	2	no	—
1029	M₁₆	—	4	2	no	—
1030	C₂×C₈	—	4	2	no	—
1031	C₂×C₈	—	4	2	no	—
1032	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1033	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1034	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1035	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1036	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1037	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
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	1	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1053	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1054	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1055	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1056	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1057	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1058	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1059	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1081	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1082	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1083	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1084	C₄²	—	2	1	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	—	2	1	no	—
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	2	no	—
1089	C₄²	—	2	2	no	—
1090	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1091	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1092	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1093	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1094	C₂³	—	2	1	no	—
1095	C₂³	—	2	1	no	—
1096	C₂³	—	2	1	no	—
1097	C₂³	—	2	2	no	—
1098	C₂³	—	4	2	no	—
1099	C₂³	—	4	2	no	—
1100	C₂³	—	4	2	no	—
1101	C₂³	—	4	4	no	—
1102	C₂³	—	4	4	no	—
1103	C₂³	—	8	2	no	—
1104	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1105	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1106	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1107	Q₈	—	2	1	no	—
1108	Q₈	—	2	2	no	—
1109	Q₈	—	2	2	no	—
1110	Q₈	—	2	2	no	—
1111	Q₈	—	2	2	no	—
1112	Q₈	—	4	4	no	—
1113	Q₈	—	4	2	no	—
1114	Q₈	—	8	1	no	—
1115	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1116	D₄	—	2	4	no	—
1117	D₄	—	2	2	no	—
1118	D₄	—	2	2	no	—
1119	D₄	—	2	1	no	—
1120	D₄	—	2	1	no	—
1121	D₄	—	2	1	no	—
1122	D₄	—	2	1	no	—
1123	D₄	—	2	2	no	—
1124	D₄	—	2	2	no	—
1125	D₄	—	2	1	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	4	no	—
1128	D₄	—	4	4	no	—
1129	D₄	—	4	2	no	—
1130	D₄	—	4	4	no	—
1131	D₄	—	4	4	no	—
1132	D₄	—	4	4	no	—
1133	D₄	—	4	2	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	8	1	no	—
1137	D₄	—	8	1	no	—
1138	D₄	—	8	2	no	—
1139	D₄	—	8	2	no	—
1140	D₄	—	8	2	no	—
1141	D₄	—	8	2	no	—
1142	D₄	—	8	2	no	—
1143	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1144	C₂×C₄	—	2	4	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	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	—	4	2	no	—
1161	C₂×C₄	—	4	2	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	4	no	—
1165	C₂×C₄	—	4	4	no	—
1166	C₂×C₄	—	4	4	no	—
1167	C₂×C₄	—	4	4	no	—
1168	C₂×C₄	—	4	2	no	—
1169	C₂×C₄	—	4	2	no	—
1170	C₂×C₄	—	4	2	no	—
1171	C₂×C₄	—	8	1	no	—
1172	C₂×C₄	—	8	2	no	—
1173	C₂×C₄	—	8	2	no	—
1174	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1175	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1176	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1177	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1178	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1179	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1180	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1181	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1182	C₈	—	2	1	no	—
1183	C₈	—	2	1	no	—
1184	C₈	—	2	2	no	—
1185	C₈	—	2	2	no	—
1186	C₈	—	2	1	no	—
1187	C₈	—	2	1	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	2	2	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	2	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	2	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	1	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	2	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	2	no	—
1209	C₂²	—	8	4	no	—
1210	C₂²	—	8	8	no	—
1211	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1212	C₄	—	2	1	no	—
1213	C₄	—	2	2	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	2	2	no	—
1216	C₄	—	2	1	no	—
1217	C₄	—	2	1	no	—
1218	C₄	—	2	1	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	2	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	2	no	—
1226	C₄	C₅₃×#575	1	2	yes	—
1227	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1228	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1229	C₂	—	4	2	no	—
1230	C₂	—	4	1	no	—
1231	C₂	—	4	2	no	—
1232	C₂	—	4	2	no	—
1233	C₂	—	8	2	no	—
1234	C₂	—	8	1	no	—
1235	C₂	—	8	1	no	—
1236	C₂	C₅₃×#3484	1	1	yes	characteristic
1237	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1238	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 ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3506	C₂	semidirect
2. D₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#3329	C₂	semidirect
4. C₅₃×#3325	C₂	semidirect
5. C₅₃×#3313	C₂	semidirect
6. C₅₃×#3311	C₂	semidirect
7. C₅₃×#3305	C₂	semidirect
8. C₅₃×#3303	C₂	semidirect
9. C₅₃×#3284	C₂	semidirect
10. C₅₃×#3283	C₂	semidirect
11. C₅₃×#3276	C₂	semidirect
12. C₅₃×#3272	C₂	semidirect
13. C₅₃×#3271	C₂	semidirect
14. C₅₃×#3268	C₂	semidirect
15. C₅₃×#3214	C₂	semidirect
16. C₅₃×#3210	C₂	semidirect
17. C₅₃×#3197	C₂	semidirect
18. C₅₃×#3191	C₂	semidirect
19. C₅₃×#3116	C₂	semidirect
20. C₅₃×#3106	C₂	semidirect
21. C₅₃×#3005	C₂	semidirect
22. C₅₃×#3002	C₂	semidirect
23. C₅₃×#2974	C₂	semidirect
25. C₂×#137×C₅₃	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
27. C₂×#135×C₅₃	C₂²	semidirect
28. C₂×#135×C₅₃	C₂²	semidirect
30. C₅₃×#556	C₂²	semidirect
32. C₅₃×#555	C₂²	semidirect
36. C₅₃×#550	C₂²	semidirect
42. C₅₃×#547	C₂²	semidirect
49. C₅₃×#533	C₂²	semidirect
52. C₅₃×#532	C₂²	semidirect
55. C₅₃×#525	C₂²	semidirect
56. C₅₃×#525	C₂²	semidirect
61. C₅₃×#496	C₂²	semidirect
62. C₅₃×#494	C₂²	semidirect
63. C₅₃×#492	C₂²	semidirect
64. C₅₃×#489	C₂²	semidirect
65. C₅₃×#487	C₂²	semidirect
66. C₅₃×#486	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
69. C₅₃×#485	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#482	C₂²	semidirect
73. C₅₃×#482	C₂²	semidirect
74. C₅₃×#477	C₂²	semidirect
75. C₅₃×#477	C₂²	semidirect
76. C₅₃×#476	C₂²	semidirect
77. C₅₃×#476	C₂²	semidirect
78. C₅₃×#470	C₂²	semidirect
79. C₅₃×#469	C₂²	semidirect
80. C₅₃×#468	C₂²	semidirect
81. C₅₃×#468	C₂²	semidirect
82. C₅₃×#467	C₂²	semidirect
83. C₅₃×#466	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
85. C₅₃×#465	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#464	C₂²	semidirect
88. C₅₃×#462	C₂²	semidirect
89. C₅₃×#461	C₂²	semidirect
90. C₅₃×#461	C₂²	semidirect
91. C₅₃×#461	C₂²	semidirect
92. C₅₃×#460	C₂²	semidirect
93. C₅₃×#459	C₂²	semidirect
94. C₅₃×#459	C₂²	semidirect
95. C₅₃×#459	C₂²	semidirect
97. C₅₃×#452	C₂²	semidirect
98. C₅₃×#452	C₂²	semidirect
99. C₅₃×#452	C₂²	semidirect
100. C₅₃×#452	C₂²	semidirect
101. C₅₃×#452	C₂²	semidirect
102. C₅₃×#452	C₂²	semidirect
103. C₅₃×#451	C₂²	semidirect
104. C₅₃×#450	C₂²	semidirect
107. C₅₃×#449	C₂²	semidirect
108. C₅₃×#449	C₂²	semidirect
109. C₅₃×#449	C₂²	semidirect
110. C₅₃×#449	C₂²	semidirect
111. C₅₃×#449	C₂²	semidirect
112. C₅₃×#449	C₂²	semidirect
113. C₅₃×#448	C₂²	semidirect
114. C₅₃×#447	C₂²	semidirect
115. C₅₃×#441	C₂²	semidirect
116. C₅₃×#440	C₂²	semidirect
117. C₄×SD₁₆×C₅₃	C₂²	semidirect
118. C₄×SD₁₆×C₅₃	C₂²	semidirect
119. C₄×D₈×C₅₃	C₂²	semidirect
120. C₄×D₈×C₅₃	C₂²	semidirect
123. C₅₃×#435	C₂²	semidirect
124. C₅₃×#435	C₂²	semidirect
125. C₈×D₄×C₅₃	C₂²	semidirect
126. C₈×D₄×C₅₃	C₂²	semidirect
127. C₅₃×#432	C₂²	semidirect
128. C₅₃×#431	C₂²	semidirect
129. C₅₃×#419	C₂²	semidirect
130. C₅₃×#418	C₂²	semidirect
131. C₅₃×#416	C₂²	semidirect
132. C₅₃×#416	C₂²	semidirect
133. C₅₃×#407	C₂²	semidirect
134. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
568. #61599	C₅₃	direct (N × H)
610. #3506	C₂×C₅₃	semidirect
611. D₄×#41	C₂×C₅₃	semidirect
612. #3329	C₂×C₅₃	semidirect
613. #3325	C₂×C₅₃	semidirect
614. #3313	C₂×C₅₃	semidirect
615. #3311	C₂×C₅₃	semidirect
616. #3305	C₂×C₅₃	semidirect
617. #3303	C₂×C₅₃	semidirect
618. #3284	C₂×C₅₃	semidirect
619. #3283	C₂×C₅₃	semidirect
620. #3276	C₂×C₅₃	semidirect
621. #3272	C₂×C₅₃	semidirect
622. #3271	C₂×C₅₃	semidirect
623. #3268	C₂×C₅₃	semidirect
624. #3214	C₂×C₅₃	semidirect
625. #3210	C₂×C₅₃	semidirect
626. #3197	C₂×C₅₃	semidirect
627. #3191	C₂×C₅₃	semidirect
628. #3116	C₂×C₅₃	semidirect
629. #3106	C₂×C₅₃	semidirect
630. #3005	C₂×C₅₃	semidirect
631. #3002	C₂×C₅₃	semidirect
632. #2974	C₂×C₅₃	semidirect
644. C₂×#137	C₂²×C₅₃	semidirect
645. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
646. C₂×#135	C₂²×C₅₃	semidirect
647. C₂×#135	C₂²×C₅₃	semidirect
649. #556	C₂²×C₅₃	semidirect
651. #555	C₂²×C₅₃	semidirect
655. #550	C₂²×C₅₃	semidirect
661. #547	C₂²×C₅₃	semidirect
668. #533	C₂²×C₅₃	semidirect
671. #532	C₂²×C₅₃	semidirect
674. #525	C₂²×C₅₃	semidirect
675. #525	C₂²×C₅₃	semidirect
680. #496	C₂²×C₅₃	semidirect
681. #494	C₂²×C₅₃	semidirect
682. #492	C₂²×C₅₃	semidirect
683. #489	C₂²×C₅₃	semidirect
684. #487	C₂²×C₅₃	semidirect
685. #486	C₂²×C₅₃	semidirect
686. #485	C₂²×C₅₃	semidirect
687. #485	C₂²×C₅₃	semidirect
688. #485	C₂²×C₅₃	semidirect
689. #482	C₂²×C₅₃	semidirect
690. #482	C₂²×C₅₃	semidirect
691. #482	C₂²×C₅₃	semidirect
692. #482	C₂²×C₅₃	semidirect
693. #477	C₂²×C₅₃	semidirect
694. #477	C₂²×C₅₃	semidirect
695. #476	C₂²×C₅₃	semidirect
696. #476	C₂²×C₅₃	semidirect
697. #470	C₂²×C₅₃	semidirect
698. #469	C₂²×C₅₃	semidirect
699. #468	C₂²×C₅₃	semidirect
700. #468	C₂²×C₅₃	semidirect
701. #467	C₂²×C₅₃	semidirect
702. #466	C₂²×C₅₃	semidirect
703. #465	C₂²×C₅₃	semidirect
704. #465	C₂²×C₅₃	semidirect
705. #464	C₂²×C₅₃	semidirect
706. #464	C₂²×C₅₃	semidirect
707. #462	C₂²×C₅₃	semidirect
708. #461	C₂²×C₅₃	semidirect
709. #461	C₂²×C₅₃	semidirect
710. #461	C₂²×C₅₃	semidirect
711. #460	C₂²×C₅₃	semidirect
712. #459	C₂²×C₅₃	semidirect
713. #459	C₂²×C₅₃	semidirect
714. #459	C₂²×C₅₃	semidirect
716. #452	C₂²×C₅₃	semidirect
717. #452	C₂²×C₅₃	semidirect
718. #452	C₂²×C₅₃	semidirect
719. #452	C₂²×C₅₃	semidirect
720. #452	C₂²×C₅₃	semidirect
721. #452	C₂²×C₅₃	semidirect
722. #451	C₂²×C₅₃	semidirect
723. #450	C₂²×C₅₃	semidirect
726. #449	C₂²×C₅₃	semidirect
727. #449	C₂²×C₅₃	semidirect
728. #449	C₂²×C₅₃	semidirect
729. #449	C₂²×C₅₃	semidirect
730. #449	C₂²×C₅₃	semidirect
731. #449	C₂²×C₅₃	semidirect
732. #448	C₂²×C₅₃	semidirect
733. #447	C₂²×C₅₃	semidirect
734. #441	C₂²×C₅₃	semidirect
735. #440	C₂²×C₅₃	semidirect
736. C₄×SD₁₆	C₂²×C₅₃	semidirect
737. C₄×SD₁₆	C₂²×C₅₃	semidirect
738. C₄×D₈	C₂²×C₅₃	semidirect
739. C₄×D₈	C₂²×C₅₃	semidirect
742. #435	C₂²×C₅₃	semidirect
743. #435	C₂²×C₅₃	semidirect
744. C₈×D₄	C₂²×C₅₃	semidirect
745. C₈×D₄	C₂²×C₅₃	semidirect
746. #432	C₂²×C₅₃	semidirect
747. #431	C₂²×C₅₃	semidirect
748. #419	C₂²×C₅₃	semidirect
749. #418	C₂²×C₅₃	semidirect
750. #416	C₂²×C₅₃	semidirect
751. #416	C₂²×C₅₃	semidirect
752. #407	C₂²×C₅₃	semidirect
753. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
754. C₅₃	#61599	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×#3506	2
D₄×#41×C₅₃	2
C₅₃×#3329	2
C₅₃×#3325	2
C₅₃×#3313	2
C₅₃×#3311	2
C₅₃×#3305	2
C₅₃×#3303	2
C₅₃×#3284	2
C₅₃×#3283	2
C₅₃×#3276	2
C₅₃×#3272	2
C₅₃×#3271	2
C₅₃×#3268	2
C₅₃×#3214	2
C₅₃×#3210	2
C₅₃×#3197	2
C₅₃×#3191	2
C₅₃×#3116	2
C₅₃×#3106	2
C₅₃×#3005	2
C₅₃×#3002	2
C₅₃×#2974	2
#61599	53

Subgroups — C53×#61599 #27269111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61599 #27269111