Subgroups — C₅₃×#61688 #27269200

Order 13568.

2214 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3318	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3309	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3268	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3199	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3198	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3012	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3008	C₂	1	2	yes	maximal, complemented
23	C₅₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×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	C₂²×D₈×C₅₃	C₂²	1	2	yes	complemented
29	C₅₃×#560	—	2	2	no	—
30	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#553	C₂²	1	2	yes	complemented
32	C₅₃×#550	—	2	1	no	—
33	C₅₃×#550	C₂²	1	1	yes	characteristic
34	C₅₃×#550	C₂²	1	2	yes	complemented
35	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#546	—	2	1	no	—
39	C₅₃×#546	C₂²	1	2	yes	complemented
40	D₄²×C₅₃	—	2	1	no	—
41	D₄²×C₅₃	—	2	2	no	—
42	D₄²×C₅₃	—	2	1	no	—
43	D₄²×C₅₃	C₂²	1	1	yes	characteristic
44	D₄²×C₅₃	C₂²	1	2	yes	complemented
45	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
46	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#542	—	2	1	no	—
48	C₅₃×#538	—	2	2	no	—
49	C₅₃×#537	C₂²	1	2	yes	complemented
50	C₅₃×#535	—	2	1	no	—
51	C₅₃×#535	—	2	2	no	—
52	C₅₃×#535	C₂²	1	2	yes	complemented
53	C₅₃×#535	C₂²	1	2	yes	complemented
54	C₅₃×#532	—	2	1	no	—
55	C₅₃×#532	C₂²	1	1	yes	characteristic
56	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
57	C₂×#127×C₅₃	—	2	1	no	—
58	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
60	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#496	C₂²	1	2	yes	complemented
62	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#490	C₂²	1	2	yes	complemented
65	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#482	C₂²	1	2	yes	complemented
69	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#482	C₂²	1	2	yes	complemented
72	C₅₃×#481	C₂²	1	2	yes	complemented
73	C₅₃×#480	C₂²	1	2	yes	complemented
74	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#469	C₂²	1	2	yes	complemented
79	C₅₃×#469	C₂²	1	2	yes	complemented
80	C₅₃×#469	C₂²	1	2	yes	complemented
81	C₅₃×#468	C₂²	1	2	yes	complemented
82	C₅₃×#466	C₂²	1	2	yes	complemented
83	C₅₃×#466	C₂²	1	2	yes	complemented
84	C₅₃×#466	C₂²	1	2	yes	complemented
85	C₅₃×#465	C₂²	1	2	yes	complemented
86	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#459	C₂²	1	2	yes	complemented
92	C₅₃×#459	C₂²	1	2	yes	complemented
93	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#452	C₂²	1	2	yes	complemented
98	C₅₃×#450	C₂²	1	2	yes	complemented
99	C₅₃×#450	C₂²	1	2	yes	complemented
100	C₅₃×#449	C₂²	1	1	yes	characteristic
101	C₅₃×#449	C₂²	1	2	yes	complemented
102	C₅₃×#449	C₂²	1	2	yes	complemented
103	C₅₃×#449	C₂²	1	2	yes	complemented
104	C₅₃×#449	C₂²	1	2	yes	complemented
105	C₅₃×#449	C₂²	1	2	yes	complemented
106	C₅₃×#449	C₂²	1	2	yes	complemented
107	C₅₃×#447	C₂²	1	2	yes	complemented
108	C₅₃×#447	C₂²	1	2	yes	complemented
109	C₅₃×#447	C₂²	1	2	yes	complemented
110	C₅₃×#447	C₂²	1	2	yes	complemented
111	C₅₃×#447	C₂²	1	2	yes	complemented
112	C₅₃×#447	C₂²	1	2	yes	complemented
113	C₅₃×#447	C₂²	1	2	yes	complemented
114	C₅₃×#447	C₂²	1	2	yes	complemented
115	C₅₃×#442	C₂²	1	2	yes	complemented
116	C₅₃×#440	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×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, complemented
122	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#435	C₂²	1	2	yes	complemented
124	C₅₃×#435	C₂²	1	2	yes	complemented
125	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×#418	C₂²	1	2	yes	complemented
130	C₅₃×#417	C₂²	1	2	yes	complemented
131	C₅₃×#416	C₂²	1	2	yes	complemented
132	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
133	C₅₃×#408	C₂²	1	2	yes	complemented
134	C₅₃×#408	C₂²	1	2	yes	complemented
135	H(5,𝔽₂)×C₅₃	—	4	4	no	—
136	H(5,𝔽₂)×C₅₃	—	4	4	no	—
137	C₂×#41×C₅₃	—	2	2	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	—	2	1	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	C₂²×D₄×C₅₃	—	2	2	no	—
146	C₂²×D₄×C₅₃	—	2	2	no	—
147	C₂²×D₄×C₅₃	—	2	2	no	—
148	C₂²×D₄×C₅₃	—	2	1	no	—
149	C₂²×D₄×C₅₃	—	2	1	no	—
150	C₂²×D₄×C₅₃	—	2	2	no	—
151	C₂²×D₄×C₅₃	—	2	1	no	—
152	C₂²×D₄×C₅₃	—	2	1	no	—
153	C₂²×D₄×C₅₃	—	2	1	no	—
154	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
155	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
156	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
157	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
158	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
159	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
160	#135×C₅₃	—	4	4	no	—
161	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
167	C₂×D₈×C₅₃	—	4	4	no	—
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×D₈×C₅₃	C₂³	1	2	yes	—
172	C₂×D₈×C₅₃	C₂³	1	2	yes	—
173	C₂×D₈×C₅₃	C₂³	1	2	yes	—
174	C₂×D₈×C₅₃	C₂³	1	2	yes	—
175	C₂×D₈×C₅₃	C₂³	1	2	yes	—
176	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
177	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
178	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
179	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
180	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
181	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
182	#127×C₅₃	—	2	1	no	—
183	#127×C₅₃	—	2	1	no	—
184	#127×C₅₃	—	2	2	no	—
185	#127×C₅₃	—	2	1	no	—
186	#127×C₅₃	—	2	1	no	—
187	#127×C₅₃	—	2	2	no	—
188	#127×C₅₃	—	2	1	no	—
189	#127×C₅₃	—	2	2	no	—
190	#127×C₅₃	D₄	1	1	yes	characteristic
191	#127×C₅₃	C₂³	1	1	yes	characteristic
192	#127×C₅₃	C₂³	1	1	yes	characteristic
193	#127×C₅₃	C₂³	1	2	yes	—
194	#127×C₅₃	C₂³	1	1	yes	characteristic
195	#126×C₅₃	—	2	2	no	—
196	#126×C₅₃	—	2	2	no	—
197	#126×C₅₃	—	2	1	no	—
198	#125×C₅₃	C₂³	1	1	yes	characteristic
199	#124×C₅₃	—	2	1	no	—
200	#124×C₅₃	—	2	2	no	—
201	#124×C₅₃	—	2	2	no	—
202	#124×C₅₃	—	2	1	no	—
203	#124×C₅₃	D₄	1	2	yes	—
204	#124×C₅₃	C₂³	1	1	yes	characteristic
205	#123×C₅₃	—	2	2	no	—
206	#123×C₅₃	—	2	2	no	—
207	#123×C₅₃	—	2	2	no	—
208	#123×C₅₃	—	2	1	no	—
209	C₂²⋊Q₈×C₅₃	—	2	1	no	—
210	C₂²⋊Q₈×C₅₃	—	2	2	no	—
211	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
213	#121×C₅₃	—	2	1	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	—	2	2	no	—
216	#121×C₅₃	—	2	1	no	—
217	#121×C₅₃	—	2	2	no	—
218	#121×C₅₃	—	2	2	no	—
219	#121×C₅₃	—	2	2	no	—
220	#121×C₅₃	—	2	2	no	—
221	#121×C₅₃	—	2	2	no	—
222	#121×C₅₃	—	2	2	no	—
223	#121×C₅₃	—	2	2	no	—
224	#121×C₅₃	—	2	2	no	—
225	#121×C₅₃	—	2	2	no	—
226	#121×C₅₃	—	2	2	no	—
227	#121×C₅₃	—	2	1	no	—
228	#121×C₅₃	D₄	1	1	yes	characteristic
229	#121×C₅₃	D₄	1	1	yes	characteristic
230	#121×C₅₃	D₄	1	2	yes	—
231	#121×C₅₃	C₂³	1	1	yes	characteristic
232	#121×C₅₃	C₂³	1	2	yes	—
233	#121×C₅₃	C₂³	1	2	yes	—
234	#121×C₅₃	C₂³	1	2	yes	—
235	#121×C₅₃	C₂³	1	2	yes	—
236	#121×C₅₃	C₂³	1	2	yes	—
237	#121×C₅₃	C₂³	1	2	yes	—
238	#121×C₅₃	C₂³	1	2	yes	—
239	#121×C₅₃	C₂³	1	2	yes	—
240	#120×C₅₃	—	2	2	no	—
241	#120×C₅₃	—	2	2	no	—
242	#120×C₅₃	—	2	2	no	—
243	#120×C₅₃	—	2	2	no	—
244	#120×C₅₃	—	2	2	no	—
245	#120×C₅₃	—	2	2	no	—
246	#120×C₅₃	—	2	2	no	—
247	#120×C₅₃	—	2	2	no	—
248	#120×C₅₃	—	2	2	no	—
249	#120×C₅₃	—	2	2	no	—
250	C₄×Q₈×C₅₃	—	2	1	no	—
251	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
252	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
253	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₅₃	—	2	1	no	—
255	C₄×D₄×C₅₃	—	2	1	no	—
256	C₄×D₄×C₅₃	—	2	2	no	—
257	C₄×D₄×C₅₃	—	2	1	no	—
258	C₄×D₄×C₅₃	—	2	2	no	—
259	C₄×D₄×C₅₃	—	2	1	no	—
260	C₄×D₄×C₅₃	—	2	1	no	—
261	C₄×D₄×C₅₃	—	2	1	no	—
262	C₄×D₄×C₅₃	—	2	1	no	—
263	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₄×D₄×C₅₃	C₂³	1	2	yes	—
267	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₄×D₄×C₅₃	C₂³	1	2	yes	—
269	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
270	#117×C₅₃	—	2	1	no	—
271	#117×C₅₃	—	2	1	no	—
272	#117×C₅₃	C₂³	1	1	yes	characteristic
273	#117×C₅₃	C₂³	1	2	yes	—
274	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
275	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
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	1	yes	characteristic
280	#107×C₅₃	C₂³	1	2	yes	—
281	#106×C₅₃	C₂³	1	1	yes	characteristic
282	#106×C₅₃	C₂³	1	1	yes	characteristic
283	#106×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
289	#103×C₅₃	C₂³	1	1	yes	characteristic
290	#103×C₅₃	C₂³	1	1	yes	characteristic
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#102×C₅₃	C₂³	1	2	yes	—
294	#102×C₅₃	C₂³	1	2	yes	—
295	#102×C₅₃	C₂³	1	2	yes	—
296	#102×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
307	#102×C₅₃	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
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	—	2	2	no	—
320	C₂⁴×C₅₃	—	2	2	no	—
321	C₂⁴×C₅₃	—	2	2	no	—
322	#41×C₅₃	—	2	2	no	—
323	#41×C₅₃	—	2	2	no	—
324	#41×C₅₃	—	2	4	no	—
325	#41×C₅₃	—	2	4	no	—
326	#41×C₅₃	—	4	2	no	—
327	#41×C₅₃	—	4	2	no	—
328	#41×C₅₃	—	4	2	no	—
329	#41×C₅₃	—	4	2	no	—
330	#41×C₅₃	—	4	8	no	—
331	#41×C₅₃	—	4	2	no	—
332	#41×C₅₃	—	4	2	no	—
333	#41×C₅₃	—	8	2	no	—
334	#41×C₅₃	—	8	2	no	—
335	C₂×Q₈×C₅₃	—	2	1	no	—
336	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
337	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₅₃	—	2	1	no	—
340	C₂×D₄×C₅₃	—	2	4	no	—
341	C₂×D₄×C₅₃	—	2	4	no	—
342	C₂×D₄×C₅₃	—	2	2	no	—
343	C₂×D₄×C₅₃	—	2	2	no	—
344	C₂×D₄×C₅₃	—	2	1	no	—
345	C₂×D₄×C₅₃	—	2	2	no	—
346	C₂×D₄×C₅₃	—	2	2	no	—
347	C₂×D₄×C₅₃	—	2	2	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	1	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	2	no	—
360	C₂×D₄×C₅₃	—	2	2	no	—
361	C₂×D₄×C₅₃	—	2	1	no	—
362	C₂×D₄×C₅₃	—	2	2	no	—
363	C₂×D₄×C₅₃	—	2	1	no	—
364	C₂×D₄×C₅₃	—	2	1	no	—
365	C₂×D₄×C₅₃	—	2	2	no	—
366	C₂×D₄×C₅₃	—	4	2	no	—
367	C₂×D₄×C₅₃	—	4	2	no	—
368	C₂×D₄×C₅₃	—	4	2	no	—
369	C₂×D₄×C₅₃	—	4	2	no	—
370	C₂×D₄×C₅₃	—	4	2	no	—
371	C₂×D₄×C₅₃	—	4	2	no	—
372	C₂×D₄×C₅₃	—	4	8	no	—
373	C₂×D₄×C₅₃	—	4	8	no	—
374	C₂×D₄×C₅₃	—	4	8	no	—
375	C₂×D₄×C₅₃	—	8	2	no	—
376	C₂×D₄×C₅₃	—	8	2	no	—
377	C₂×D₄×C₅₃	—	8	2	no	—
378	C₂×D₄×C₅₃	—	8	2	no	—
379	C₂×D₄×C₅₃	—	8	2	no	—
380	C₂×D₄×C₅₃	—	8	4	no	—
381	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
382	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
384	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
385	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
386	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
387	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
388	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
389	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
391	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₅₃	—	2	1	no	—
393	C₂²×C₄×C₅₃	—	2	2	no	—
394	C₂²×C₄×C₅₃	—	2	1	no	—
395	C₂²×C₄×C₅₃	—	2	1	no	—
396	C₂²×C₄×C₅₃	—	2	1	no	—
397	C₂²×C₄×C₅₃	—	2	2	no	—
398	C₂²×C₄×C₅₃	—	2	2	no	—
399	C₂²×C₄×C₅₃	—	2	2	no	—
400	C₂²×C₄×C₅₃	—	2	2	no	—
401	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
405	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
406	Q₁₆×C₅₃	—	2	2	no	—
407	SD₁₆×C₅₃	—	2	4	no	—
408	SD₁₆×C₅₃	—	2	2	no	—
409	SD₁₆×C₅₃	—	2	2	no	—
410	SD₁₆×C₅₃	—	4	2	no	—
411	SD₁₆×C₅₃	—	4	2	no	—
412	D₈×C₅₃	—	2	2	no	—
413	D₈×C₅₃	—	2	4	no	—
414	D₈×C₅₃	—	4	2	no	—
415	D₈×C₅₃	—	4	2	no	—
416	D₈×C₅₃	—	4	2	no	—
417	D₈×C₅₃	—	4	2	no	—
418	D₈×C₅₃	—	4	2	no	—
419	D₈×C₅₃	—	4	2	no	—
420	M₁₆×C₅₃	—	4	2	no	—
421	M₁₆×C₅₃	—	4	2	no	—
422	C₂×C₈×C₅₃	—	4	2	no	—
423	C₂×C₈×C₅₃	—	4	2	no	—
424	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
427	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
428	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
429	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
430	C₄⋊C₄×C₅₃	—	2	2	no	—
431	C₄⋊C₄×C₅₃	—	2	1	no	—
432	C₄⋊C₄×C₅₃	—	2	1	no	—
433	C₄⋊C₄×C₅₃	—	2	1	no	—
434	C₄⋊C₄×C₅₃	—	2	1	no	—
435	C₄⋊C₄×C₅₃	—	2	1	no	—
436	C₄⋊C₄×C₅₃	—	2	1	no	—
437	C₄⋊C₄×C₅₃	—	2	2	no	—
438	C₄⋊C₄×C₅₃	—	2	1	no	—
439	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
442	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
444	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	—	2	1	no	—
449	C₂²⋊C₄×C₅₃	—	2	2	no	—
450	C₂²⋊C₄×C₅₃	—	2	1	no	—
451	C₂²⋊C₄×C₅₃	—	2	1	no	—
452	C₂²⋊C₄×C₅₃	—	2	2	no	—
453	C₂²⋊C₄×C₅₃	—	2	1	no	—
454	C₂²⋊C₄×C₅₃	—	2	1	no	—
455	C₂²⋊C₄×C₅₃	—	2	1	no	—
456	C₂²⋊C₄×C₅₃	—	2	1	no	—
457	C₂²⋊C₄×C₅₃	—	2	2	no	—
458	C₂²⋊C₄×C₅₃	—	2	2	no	—
459	C₂²⋊C₄×C₅₃	—	2	2	no	—
460	C₂²⋊C₄×C₅₃	—	2	2	no	—
461	C₂²⋊C₄×C₅₃	—	2	2	no	—
462	C₂²⋊C₄×C₅₃	—	2	2	no	—
463	C₂²⋊C₄×C₅₃	—	2	2	no	—
464	C₂²⋊C₄×C₅₃	—	2	1	no	—
465	C₂²⋊C₄×C₅₃	—	2	2	no	—
466	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
467	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
468	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
469	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
470	C₄²×C₅₃	—	2	1	no	—
471	C₄²×C₅₃	—	2	1	no	—
472	C₄²×C₅₃	—	2	1	no	—
473	C₄²×C₅₃	—	2	1	no	—
474	C₄²×C₅₃	—	2	2	no	—
475	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
476	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
477	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
478	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
479	C₂³×C₅₃	—	2	1	no	—
480	C₂³×C₅₃	—	2	2	no	—
481	C₂³×C₅₃	—	2	2	no	—
482	C₂³×C₅₃	—	2	2	no	—
483	C₂³×C₅₃	—	2	1	no	—
484	C₂³×C₅₃	—	4	4	no	—
485	C₂³×C₅₃	—	4	4	no	—
486	C₂³×C₅₃	—	4	4	no	—
487	C₂³×C₅₃	—	8	2	no	—
488	C₂³×C₅₃	—	8	2	no	—
489	C₂³×C₅₃	—	8	2	no	—
490	C₂³×C₅₃	—	8	2	no	—
491	C₂³×C₅₃	—	8	2	no	—
492	C₂³×C₅₃	—	8	2	no	—
493	C₂³×C₅₃	—	8	2	no	—
494	C₂³×C₅₃	—	8	2	no	—
495	C₂³×C₅₃	—	8	2	no	—
496	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
497	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
498	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
499	Q₈×C₅₃	—	2	1	no	—
500	Q₈×C₅₃	—	2	1	no	—
501	Q₈×C₅₃	—	2	1	no	—
502	Q₈×C₅₃	—	4	2	no	—
503	Q₈×C₅₃	—	4	2	no	—
504	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
505	D₄×C₅₃	—	2	4	no	—
506	D₄×C₅₃	—	2	2	no	—
507	D₄×C₅₃	—	2	2	no	—
508	D₄×C₅₃	—	2	1	no	—
509	D₄×C₅₃	—	2	2	no	—
510	D₄×C₅₃	—	2	2	no	—
511	D₄×C₅₃	—	2	2	no	—
512	D₄×C₅₃	—	2	2	no	—
513	D₄×C₅₃	—	2	1	no	—
514	D₄×C₅₃	—	2	1	no	—
515	D₄×C₅₃	—	2	2	no	—
516	D₄×C₅₃	—	2	2	no	—
517	D₄×C₅₃	—	4	2	no	—
518	D₄×C₅₃	—	4	2	no	—
519	D₄×C₅₃	—	4	2	no	—
520	D₄×C₅₃	—	4	2	no	—
521	D₄×C₅₃	—	4	4	no	—
522	D₄×C₅₃	—	4	4	no	—
523	D₄×C₅₃	—	4	4	no	—
524	D₄×C₅₃	—	4	4	no	—
525	D₄×C₅₃	—	4	4	no	—
526	D₄×C₅₃	—	4	4	no	—
527	D₄×C₅₃	—	4	2	no	—
528	D₄×C₅₃	—	4	2	no	—
529	D₄×C₅₃	—	4	2	no	—
530	D₄×C₅₃	—	8	1	no	—
531	D₄×C₅₃	—	8	2	no	—
532	D₄×C₅₃	—	8	1	no	—
533	D₄×C₅₃	—	8	1	no	—
534	D₄×C₅₃	—	8	2	no	—
535	D₄×C₅₃	—	8	1	no	—
536	D₄×C₅₃	—	8	2	no	—
537	D₄×C₅₃	—	8	2	no	—
538	D₄×C₅₃	—	8	2	no	—
539	D₄×C₅₃	—	8	2	no	—
540	D₄×C₅₃	—	8	2	no	—
541	D₄×C₅₃	—	8	2	no	—
542	D₄×C₅₃	—	8	2	no	—
543	D₄×C₅₃	—	8	2	no	—
544	D₄×C₅₃	—	8	2	no	—
545	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
546	C₂×C₄×C₅₃	—	2	4	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	2	2	no	—
549	C₂×C₄×C₅₃	—	2	2	no	—
550	C₂×C₄×C₅₃	—	2	2	no	—
551	C₂×C₄×C₅₃	—	2	1	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	2	no	—
554	C₂×C₄×C₅₃	—	2	2	no	—
555	C₂×C₄×C₅₃	—	2	1	no	—
556	C₂×C₄×C₅₃	—	2	2	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	1	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	4	1	no	—
562	C₂×C₄×C₅₃	—	4	4	no	—
563	C₂×C₄×C₅₃	—	4	4	no	—
564	C₂×C₄×C₅₃	—	4	2	no	—
565	C₂×C₄×C₅₃	—	4	2	no	—
566	C₂×C₄×C₅₃	—	4	2	no	—
567	C₂×C₄×C₅₃	—	8	2	no	—
568	C₂×C₄×C₅₃	—	8	2	no	—
569	C₂×C₄×C₅₃	—	8	2	no	—
570	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
572	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
575	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
578	C₈×C₅₃	—	2	1	no	—
579	C₈×C₅₃	—	2	1	no	—
580	C₈×C₅₃	—	2	2	no	—
581	C₈×C₅₃	—	2	2	no	—
582	C₈×C₅₃	—	2	1	no	—
583	C₈×C₅₃	—	2	1	no	—
584	#61688	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
585	C₂²×C₅₃	—	2	1	no	—
586	C₂²×C₅₃	—	2	2	no	—
587	C₂²×C₅₃	—	2	2	no	—
588	C₂²×C₅₃	—	2	1	no	—
589	C₂²×C₅₃	—	2	2	no	—
590	C₂²×C₅₃	—	2	2	no	—
591	C₂²×C₅₃	—	2	2	no	—
592	C₂²×C₅₃	—	2	1	no	—
593	C₂²×C₅₃	—	2	2	no	—
594	C₂²×C₅₃	—	2	2	no	—
595	C₂²×C₅₃	—	4	1	no	—
596	C₂²×C₅₃	—	4	1	no	—
597	C₂²×C₅₃	—	4	2	no	—
598	C₂²×C₅₃	—	4	2	no	—
599	C₂²×C₅₃	—	4	2	no	—
600	C₂²×C₅₃	—	4	1	no	—
601	C₂²×C₅₃	—	4	2	no	—
602	C₂²×C₅₃	—	4	2	no	—
603	C₂²×C₅₃	—	4	2	no	—
604	C₂²×C₅₃	—	4	1	no	—
605	C₂²×C₅₃	—	4	1	no	—
606	C₂²×C₅₃	—	4	2	no	—
607	C₂²×C₅₃	—	4	2	no	—
608	C₂²×C₅₃	—	4	2	no	—
609	C₂²×C₅₃	—	16	4	no	—
610	C₂²×C₅₃	—	16	4	no	—
611	C₂²×C₅₃	—	16	4	no	—
612	C₂²×C₅₃	—	16	4	no	—
613	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
614	C₄×C₅₃	—	2	1	no	—
615	C₄×C₅₃	—	2	1	no	—
616	C₄×C₅₃	—	2	1	no	—
617	C₄×C₅₃	—	2	2	no	—
618	C₄×C₅₃	—	2	2	no	—
619	C₄×C₅₃	—	2	2	no	—
620	C₄×C₅₃	—	2	1	no	—
621	C₄×C₅₃	—	4	1	no	—
622	C₄×C₅₃	—	4	1	no	—
623	C₄×C₅₃	—	4	1	no	—
624	C₄×C₅₃	—	4	1	no	—
625	C₄×C₅₃	—	4	1	no	—
626	C₄×C₅₃	—	4	2	no	—
627	C₄×C₅₃	#576	1	2	yes	—
628	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
629	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
630	#3546	C₂×C₅₃	1	1	yes	characteristic, complemented
631	#3498	C₂×C₅₃	1	1	yes	characteristic, complemented
632	#3332	C₂×C₅₃	1	1	yes	characteristic, complemented
633	#3324	C₂×C₅₃	1	1	yes	characteristic, complemented
634	#3318	C₂×C₅₃	1	2	yes	complemented
635	#3309	C₂×C₅₃	1	2	yes	complemented
636	#3304	C₂×C₅₃	1	1	yes	characteristic, complemented
637	#3294	C₂×C₅₃	1	1	yes	characteristic, complemented
638	#3287	C₂×C₅₃	1	1	yes	characteristic, complemented
639	D₄×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
640	#3274	C₂×C₅₃	1	1	yes	characteristic, complemented
641	#3274	C₂×C₅₃	1	1	yes	characteristic, complemented
642	#3268	C₂×C₅₃	1	2	yes	complemented
643	#3264	C₂×C₅₃	1	2	yes	complemented
644	#3217	C₂×C₅₃	1	1	yes	characteristic, complemented
645	#3205	C₂×C₅₃	1	1	yes	characteristic, complemented
646	#3199	C₂×C₅₃	1	2	yes	complemented
647	#3198	C₂×C₅₃	1	2	yes	complemented
648	#3115	C₂×C₅₃	1	1	yes	characteristic, complemented
649	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
650	#3012	C₂×C₅₃	1	2	yes	complemented
651	#3008	C₂×C₅₃	1	2	yes	complemented
652	#2981	C₂×C₅₃	1	1	yes	characteristic, complemented
653	C₂×C₅₃	—	4	2	no	—
654	C₂×C₅₃	—	4	1	no	—
655	C₂×C₅₃	—	4	2	no	—
656	C₂×C₅₃	—	4	2	no	—
657	C₂×C₅₃	—	8	2	no	—
658	C₂×C₅₃	—	8	2	no	—
659	C₂×C₅₃	—	8	2	no	—
660	C₂×C₅₃	—	8	1	no	—
661	C₂×C₅₃	#3484	1	1	yes	characteristic
662	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
663	C₂×C₅₃	#3585	1	1	yes	characteristic
664	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	2	yes	complemented
665	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
666	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
667	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
668	C₂²×D₈	C₂²×C₅₃	1	2	yes	complemented
669	#560	—	2	2	no	—
670	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
671	#553	C₂²×C₅₃	1	2	yes	complemented
672	#550	—	2	1	no	—
673	#550	C₂²×C₅₃	1	1	yes	characteristic
674	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
675	#550	C₂²×C₅₃	1	2	yes	complemented
676	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
677	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	#546	—	2	1	no	—
679	#546	C₂²×C₅₃	1	2	yes	complemented
680	D₄²	—	2	1	no	—
681	D₄²	—	2	2	no	—
682	D₄²	—	2	1	no	—
683	D₄²	C₂²×C₅₃	1	1	yes	characteristic
684	D₄²	C₂²×C₅₃	1	2	yes	complemented
685	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
686	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#542	—	2	1	no	—
688	#538	—	2	2	no	—
689	#537	C₂²×C₅₃	1	2	yes	complemented
690	#535	—	2	1	no	—
691	#535	—	2	2	no	—
692	#535	C₂²×C₅₃	1	2	yes	complemented
693	#535	C₂²×C₅₃	1	2	yes	complemented
694	#532	—	2	1	no	—
695	#532	C₂²×C₅₃	1	1	yes	characteristic
696	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
697	C₂×#127	—	2	1	no	—
698	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic, complemented
699	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
700	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
701	#496	C₂²×C₅₃	1	2	yes	complemented
702	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
704	#490	C₂²×C₅₃	1	2	yes	complemented
705	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
706	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#482	C₂²×C₅₃	1	2	yes	complemented
710	#482	C₂²×C₅₃	1	2	yes	complemented
711	#482	C₂²×C₅₃	1	2	yes	complemented
712	#481	C₂²×C₅₃	1	2	yes	complemented
713	#480	C₂²×C₅₃	1	2	yes	complemented
714	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
715	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
716	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
717	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
718	#469	C₂²×C₅₃	1	2	yes	complemented
719	#469	C₂²×C₅₃	1	2	yes	complemented
720	#469	C₂²×C₅₃	1	2	yes	complemented
721	#468	C₂²×C₅₃	1	2	yes	complemented
722	#466	C₂²×C₅₃	1	2	yes	complemented
723	#466	C₂²×C₅₃	1	2	yes	complemented
724	#466	C₂²×C₅₃	1	2	yes	complemented
725	#465	C₂²×C₅₃	1	2	yes	complemented
726	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
727	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
728	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
729	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
730	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
731	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
732	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
733	#459	C₂²×C₅₃	1	2	yes	complemented
734	#459	C₂²×C₅₃	1	2	yes	complemented
735	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
736	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
737	#452	C₂²×C₅₃	1	2	yes	complemented
738	#450	C₂²×C₅₃	1	2	yes	complemented
739	#450	C₂²×C₅₃	1	2	yes	complemented
740	#449	C₂²×C₅₃	1	1	yes	characteristic
741	#449	C₂²×C₅₃	1	2	yes	complemented
742	#449	C₂²×C₅₃	1	2	yes	complemented
743	#449	C₂²×C₅₃	1	2	yes	complemented
744	#449	C₂²×C₅₃	1	2	yes	complemented
745	#449	C₂²×C₅₃	1	2	yes	complemented
746	#449	C₂²×C₅₃	1	2	yes	complemented
747	#447	C₂²×C₅₃	1	2	yes	complemented
748	#447	C₂²×C₅₃	1	2	yes	complemented
749	#447	C₂²×C₅₃	1	2	yes	complemented
750	#447	C₂²×C₅₃	1	2	yes	complemented
751	#447	C₂²×C₅₃	1	2	yes	complemented
752	#447	C₂²×C₅₃	1	2	yes	complemented
753	#447	C₂²×C₅₃	1	2	yes	complemented
754	#447	C₂²×C₅₃	1	2	yes	complemented
755	#442	C₂²×C₅₃	1	2	yes	complemented
756	#440	C₂²×C₅₃	1	2	yes	complemented
757	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
758	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
759	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
760	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
761	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
762	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
763	#435	C₂²×C₅₃	1	2	yes	complemented
764	#435	C₂²×C₅₃	1	2	yes	complemented
765	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
766	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
767	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
768	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
769	#418	C₂²×C₅₃	1	2	yes	complemented
770	#417	C₂²×C₅₃	1	2	yes	complemented
771	#416	C₂²×C₅₃	1	2	yes	complemented
772	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
773	#408	C₂²×C₅₃	1	2	yes	complemented
774	#408	C₂²×C₅₃	1	2	yes	complemented
775	C₅₃	#61688	1	1	yes	characteristic, direct product factor, Sylow
776	H(5,𝔽₂)	—	4	4	no	—
777	H(5,𝔽₂)	—	4	4	no	—
778	C₂×#41	—	2	2	no	—
779	C₂×#41	—	2	1	no	—
780	C₂×#41	—	2	1	no	—
781	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
782	C₂×#41	C₂³×C₅₃	1	2	yes	—
783	C₂×#41	C₂³×C₅₃	1	2	yes	—
784	C₂×#41	C₂³×C₅₃	1	2	yes	—
785	C₂×#41	C₂³×C₅₃	1	2	yes	—
786	C₂²×D₄	—	2	2	no	—
787	C₂²×D₄	—	2	2	no	—
788	C₂²×D₄	—	2	2	no	—
789	C₂²×D₄	—	2	1	no	—
790	C₂²×D₄	—	2	1	no	—
791	C₂²×D₄	—	2	2	no	—
792	C₂²×D₄	—	2	1	no	—
793	C₂²×D₄	—	2	1	no	—
794	C₂²×D₄	—	2	1	no	—
795	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
796	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
797	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
798	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
799	AGL(1,ℤ/8)	—	4	4	no	—
800	AGL(1,ℤ/8)	—	4	4	no	—
801	#135	—	4	4	no	—
802	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
803	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
804	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
805	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
806	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
807	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
808	C₂×D₈	—	4	4	no	—
809	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
810	C₂×D₈	C₂³×C₅₃	1	2	yes	—
811	C₂×D₈	C₂³×C₅₃	1	2	yes	—
812	C₂×D₈	C₂³×C₅₃	1	2	yes	—
813	C₂×D₈	C₂³×C₅₃	1	2	yes	—
814	C₂×D₈	C₂³×C₅₃	1	2	yes	—
815	C₂×D₈	C₂³×C₅₃	1	2	yes	—
816	C₂×D₈	C₂³×C₅₃	1	2	yes	—
817	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
818	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
819	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
820	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
821	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
822	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
823	#127	—	2	2	no	—
824	#127	—	2	1	no	—
825	#127	—	2	1	no	—
826	#127	—	2	2	no	—
827	#127	—	2	1	no	—
828	#127	—	2	2	no	—
829	#127	—	2	1	no	—
830	#127	—	2	1	no	—
831	#127	D₄×C₅₃	1	1	yes	characteristic
832	#127	C₂³×C₅₃	1	1	yes	characteristic
833	#127	C₂³×C₅₃	1	1	yes	characteristic
834	#127	C₂³×C₅₃	1	2	yes	—
835	#127	C₂³×C₅₃	1	1	yes	characteristic
836	#126	—	2	2	no	—
837	#126	—	2	2	no	—
838	#126	—	2	1	no	—
839	#125	C₂³×C₅₃	1	1	yes	characteristic
840	#124	—	2	2	no	—
841	#124	—	2	2	no	—
842	#124	—	2	1	no	—
843	#124	—	2	1	no	—
844	#124	D₄×C₅₃	1	2	yes	—
845	#124	C₂³×C₅₃	1	1	yes	characteristic
846	#123	—	2	1	no	—
847	#123	—	2	2	no	—
848	#123	—	2	2	no	—
849	#123	—	2	2	no	—
850	C₂²⋊Q₈	—	2	2	no	—
851	C₂²⋊Q₈	—	2	1	no	—
852	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
853	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
854	#121	—	2	2	no	—
855	#121	—	2	2	no	—
856	#121	—	2	2	no	—
857	#121	—	2	2	no	—
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	2	no	—
862	#121	—	2	1	no	—
863	#121	—	2	2	no	—
864	#121	—	2	2	no	—
865	#121	—	2	2	no	—
866	#121	—	2	2	no	—
867	#121	—	2	2	no	—
868	#121	—	2	2	no	—
869	#121	D₄×C₅₃	1	1	yes	characteristic
870	#121	D₄×C₅₃	1	1	yes	characteristic
871	#121	D₄×C₅₃	1	2	yes	—
872	#121	C₂³×C₅₃	1	1	yes	characteristic
873	#121	C₂³×C₅₃	1	2	yes	—
874	#121	C₂³×C₅₃	1	2	yes	—
875	#121	C₂³×C₅₃	1	2	yes	—
876	#121	C₂³×C₅₃	1	2	yes	—
877	#121	C₂³×C₅₃	1	2	yes	—
878	#121	C₂³×C₅₃	1	2	yes	—
879	#121	C₂³×C₅₃	1	2	yes	—
880	#121	C₂³×C₅₃	1	2	yes	—
881	#120	—	2	2	no	—
882	#120	—	2	2	no	—
883	#120	—	2	2	no	—
884	#120	—	2	2	no	—
885	#120	—	2	2	no	—
886	#120	—	2	2	no	—
887	#120	—	2	2	no	—
888	#120	—	2	2	no	—
889	#120	—	2	2	no	—
890	#120	—	2	2	no	—
891	C₄×Q₈	—	2	1	no	—
892	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
893	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
894	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	1	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	2	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	2	no	—
903	C₄×D₄	—	2	1	no	—
904	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
905	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
906	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
907	C₄×D₄	C₂³×C₅₃	1	2	yes	—
908	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
909	C₄×D₄	C₂³×C₅₃	1	2	yes	—
910	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
911	#117	—	2	1	no	—
912	#117	—	2	1	no	—
913	#117	C₂³×C₅₃	1	1	yes	characteristic
914	#117	C₂³×C₅₃	1	2	yes	—
915	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
916	C₂×C₂²⋊C₄	—	2	2	no	—
917	C₂×C₄²	—	2	1	no	—
918	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
919	#107	C₂³×C₅₃	1	1	yes	characteristic
920	#107	C₂³×C₅₃	1	1	yes	characteristic
921	#107	C₂³×C₅₃	1	2	yes	—
922	#106	C₂³×C₅₃	1	1	yes	characteristic
923	#106	C₂³×C₅₃	1	1	yes	characteristic
924	#106	C₂³×C₅₃	1	2	yes	—
925	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
926	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
927	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
928	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
929	#103	C₂³×C₅₃	1	1	yes	characteristic
930	#103	C₂³×C₅₃	1	2	yes	—
931	#103	C₂³×C₅₃	1	1	yes	characteristic
932	#103	C₂³×C₅₃	1	1	yes	characteristic
933	#103	C₂³×C₅₃	1	1	yes	characteristic
934	#102	C₂³×C₅₃	1	1	yes	characteristic
935	#102	C₂³×C₅₃	1	2	yes	—
936	#102	C₂³×C₅₃	1	2	yes	—
937	#102	C₂³×C₅₃	1	2	yes	—
938	#102	C₂³×C₅₃	1	2	yes	—
939	#102	C₂³×C₅₃	1	2	yes	—
940	#102	C₂³×C₅₃	1	2	yes	—
941	#102	C₂³×C₅₃	1	2	yes	—
942	#102	C₂³×C₅₃	1	1	yes	characteristic
943	#102	C₂³×C₅₃	1	2	yes	—
944	#102	C₂³×C₅₃	1	2	yes	—
945	#102	C₂³×C₅₃	1	1	yes	characteristic
946	#102	C₂³×C₅₃	1	1	yes	characteristic
947	#102	C₂³×C₅₃	1	2	yes	—
948	#102	C₂³×C₅₃	1	2	yes	—
949	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
950	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
951	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
952	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
953	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
954	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
955	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
956	#97	C₂³×C₅₃	1	2	yes	—
957	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
958	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
959	C₂⁴	—	2	2	no	—
960	C₂⁴	—	2	2	no	—
961	C₂⁴	—	2	2	no	—
962	C₂⁴	—	2	2	no	—
963	#41	—	2	2	no	—
964	#41	—	2	2	no	—
965	#41	—	2	4	no	—
966	#41	—	2	4	no	—
967	#41	—	4	2	no	—
968	#41	—	4	2	no	—
969	#41	—	4	2	no	—
970	#41	—	4	2	no	—
971	#41	—	4	8	no	—
972	#41	—	4	2	no	—
973	#41	—	4	2	no	—
974	#41	—	8	2	no	—
975	#41	—	8	2	no	—
976	C₂×Q₈	—	2	1	no	—
977	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
978	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
979	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	4	no	—
982	C₂×D₄	—	2	4	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	2	2	no	—
991	C₂×D₄	—	2	2	no	—
992	C₂×D₄	—	2	2	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	4	2	no	—
1008	C₂×D₄	—	4	2	no	—
1009	C₂×D₄	—	4	2	no	—
1010	C₂×D₄	—	4	2	no	—
1011	C₂×D₄	—	4	2	no	—
1012	C₂×D₄	—	4	2	no	—
1013	C₂×D₄	—	4	8	no	—
1014	C₂×D₄	—	4	8	no	—
1015	C₂×D₄	—	4	8	no	—
1016	C₂×D₄	—	8	2	no	—
1017	C₂×D₄	—	8	2	no	—
1018	C₂×D₄	—	8	2	no	—
1019	C₂×D₄	—	8	2	no	—
1020	C₂×D₄	—	8	2	no	—
1021	C₂×D₄	—	8	4	no	—
1022	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1023	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1024	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1025	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1026	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1027	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1028	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1029	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1030	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1031	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1032	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1033	C₂²×C₄	—	2	1	no	—
1034	C₂²×C₄	—	2	2	no	—
1035	C₂²×C₄	—	2	1	no	—
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	2	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	2	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1043	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1044	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1045	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1046	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1047	Q₁₆	—	2	2	no	—
1048	SD₁₆	—	2	4	no	—
1049	SD₁₆	—	2	2	no	—
1050	SD₁₆	—	2	2	no	—
1051	SD₁₆	—	4	2	no	—
1052	SD₁₆	—	4	2	no	—
1053	D₈	—	2	2	no	—
1054	D₈	—	2	4	no	—
1055	D₈	—	4	2	no	—
1056	D₈	—	4	2	no	—
1057	D₈	—	4	2	no	—
1058	D₈	—	4	2	no	—
1059	D₈	—	4	2	no	—
1060	D₈	—	4	2	no	—
1061	M₁₆	—	4	2	no	—
1062	M₁₆	—	4	2	no	—
1063	C₂×C₈	—	4	2	no	—
1064	C₂×C₈	—	4	2	no	—
1065	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1066	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1067	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1068	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1069	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1070	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	1	no	—
1078	C₄⋊C₄	—	2	2	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1081	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1082	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1083	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1084	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1085	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1086	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1087	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1108	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1109	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1110	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1111	C₄²	—	2	1	no	—
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	—	2	2	no	—
1116	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1117	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1118	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1119	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1120	C₂³	—	2	1	no	—
1121	C₂³	—	2	1	no	—
1122	C₂³	—	2	2	no	—
1123	C₂³	—	2	2	no	—
1124	C₂³	—	2	2	no	—
1125	C₂³	—	4	4	no	—
1126	C₂³	—	4	4	no	—
1127	C₂³	—	4	4	no	—
1128	C₂³	—	8	2	no	—
1129	C₂³	—	8	2	no	—
1130	C₂³	—	8	2	no	—
1131	C₂³	—	8	2	no	—
1132	C₂³	—	8	2	no	—
1133	C₂³	—	8	2	no	—
1134	C₂³	—	8	2	no	—
1135	C₂³	—	8	2	no	—
1136	C₂³	—	8	2	no	—
1137	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1138	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1139	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1140	Q₈	—	2	1	no	—
1141	Q₈	—	2	1	no	—
1142	Q₈	—	2	1	no	—
1143	Q₈	—	4	2	no	—
1144	Q₈	—	4	2	no	—
1145	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1146	D₄	—	2	4	no	—
1147	D₄	—	2	2	no	—
1148	D₄	—	2	2	no	—
1149	D₄	—	2	1	no	—
1150	D₄	—	2	1	no	—
1151	D₄	—	2	2	no	—
1152	D₄	—	2	1	no	—
1153	D₄	—	2	2	no	—
1154	D₄	—	2	2	no	—
1155	D₄	—	2	2	no	—
1156	D₄	—	2	2	no	—
1157	D₄	—	2	2	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	4	4	no	—
1163	D₄	—	4	4	no	—
1164	D₄	—	4	4	no	—
1165	D₄	—	4	4	no	—
1166	D₄	—	4	4	no	—
1167	D₄	—	4	4	no	—
1168	D₄	—	4	2	no	—
1169	D₄	—	4	2	no	—
1170	D₄	—	4	2	no	—
1171	D₄	—	8	1	no	—
1172	D₄	—	8	2	no	—
1173	D₄	—	8	2	no	—
1174	D₄	—	8	1	no	—
1175	D₄	—	8	1	no	—
1176	D₄	—	8	1	no	—
1177	D₄	—	8	2	no	—
1178	D₄	—	8	2	no	—
1179	D₄	—	8	2	no	—
1180	D₄	—	8	2	no	—
1181	D₄	—	8	2	no	—
1182	D₄	—	8	2	no	—
1183	D₄	—	8	2	no	—
1184	D₄	—	8	2	no	—
1185	D₄	—	8	2	no	—
1186	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1187	C₂×C₄	—	2	4	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	2	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	2	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	4	1	no	—
1203	C₂×C₄	—	4	4	no	—
1204	C₂×C₄	—	4	4	no	—
1205	C₂×C₄	—	4	2	no	—
1206	C₂×C₄	—	4	2	no	—
1207	C₂×C₄	—	4	2	no	—
1208	C₂×C₄	—	8	2	no	—
1209	C₂×C₄	—	8	2	no	—
1210	C₂×C₄	—	8	2	no	—
1211	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1212	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1213	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1214	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1215	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1216	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1217	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1218	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1219	C₈	—	2	1	no	—
1220	C₈	—	2	1	no	—
1221	C₈	—	2	2	no	—
1222	C₈	—	2	2	no	—
1223	C₈	—	2	1	no	—
1224	C₈	—	2	1	no	—
1225	C₂²	—	2	1	no	—
1226	C₂²	—	2	2	no	—
1227	C₂²	—	2	2	no	—
1228	C₂²	—	2	2	no	—
1229	C₂²	—	2	1	no	—
1230	C₂²	—	2	2	no	—
1231	C₂²	—	2	2	no	—
1232	C₂²	—	2	1	no	—
1233	C₂²	—	2	2	no	—
1234	C₂²	—	2	2	no	—
1235	C₂²	—	4	1	no	—
1236	C₂²	—	4	1	no	—
1237	C₂²	—	4	2	no	—
1238	C₂²	—	4	2	no	—
1239	C₂²	—	4	2	no	—
1240	C₂²	—	4	1	no	—
1241	C₂²	—	4	1	no	—
1242	C₂²	—	4	2	no	—
1243	C₂²	—	4	2	no	—
1244	C₂²	—	4	2	no	—
1245	C₂²	—	4	2	no	—
1246	C₂²	—	4	2	no	—
1247	C₂²	—	4	2	no	—
1248	C₂²	—	4	1	no	—
1249	C₂²	—	16	4	no	—
1250	C₂²	—	16	4	no	—
1251	C₂²	—	16	4	no	—
1252	C₂²	—	16	4	no	—
1253	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1254	C₄	—	2	1	no	—
1255	C₄	—	2	2	no	—
1256	C₄	—	2	2	no	—
1257	C₄	—	2	2	no	—
1258	C₄	—	2	1	no	—
1259	C₄	—	2	1	no	—
1260	C₄	—	2	1	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	4	1	no	—
1263	C₄	—	4	1	no	—
1264	C₄	—	4	2	no	—
1265	C₄	—	4	1	no	—
1266	C₄	—	4	1	no	—
1267	C₄	C₅₃×#576	1	2	yes	—
1268	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1269	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1270	C₂	—	4	1	no	—
1271	C₂	—	4	2	no	—
1272	C₂	—	4	2	no	—
1273	C₂	—	4	2	no	—
1274	C₂	—	8	2	no	—
1275	C₂	—	8	2	no	—
1276	C₂	—	8	1	no	—
1277	C₂	—	8	2	no	—
1278	C₂	C₅₃×#3484	1	1	yes	characteristic
1279	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1280	C₂	C₅₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3546	C₂	semidirect
2. C₅₃×#3498	C₂	semidirect
3. C₅₃×#3332	C₂	semidirect
4. C₅₃×#3324	C₂	semidirect
5. C₅₃×#3318	C₂	semidirect
6. C₅₃×#3309	C₂	semidirect
7. C₅₃×#3304	C₂	semidirect
8. C₅₃×#3294	C₂	semidirect
9. C₅₃×#3287	C₂	semidirect
10. D₄×D₈×C₅₃	C₂	semidirect
11. C₅₃×#3274	C₂	semidirect
12. C₅₃×#3274	C₂	semidirect
13. C₅₃×#3268	C₂	semidirect
14. C₅₃×#3264	C₂	semidirect
15. C₅₃×#3217	C₂	semidirect
16. C₅₃×#3205	C₂	semidirect
17. C₅₃×#3199	C₂	semidirect
18. C₅₃×#3198	C₂	semidirect
19. C₅₃×#3115	C₂	semidirect
20. C₅₃×#3102	C₂	semidirect
21. C₅₃×#3012	C₂	semidirect
22. C₅₃×#3008	C₂	semidirect
23. C₅₃×#2981	C₂	semidirect
24. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
27. C₂×#135×C₅₃	C₂²	semidirect
28. C₂²×D₈×C₅₃	C₂²	semidirect
30. C₅₃×#556	C₂²	semidirect
31. C₅₃×#553	C₂²	semidirect
34. C₅₃×#550	C₂²	semidirect
35. C₅₃×#550	C₂²	semidirect
36. C₅₃×#550	C₂²	semidirect
37. C₅₃×#547	C₂²	semidirect
39. C₅₃×#546	C₂²	semidirect
44. D₄²×C₅₃	C₂²	semidirect
45. D₄²×C₅₃	C₂²	semidirect
46. D₄²×C₅₃	C₂²	semidirect
49. C₅₃×#537	C₂²	semidirect
52. C₅₃×#535	C₂²	semidirect
53. C₅₃×#535	C₂²	semidirect
56. C₅₃×#532	C₂²	semidirect
58. C₂×#127×C₅₃	C₂²	semidirect
59. C₅₃×#529	C₂²	semidirect
60. C₄×#41×C₅₃	C₂²	semidirect
61. C₅₃×#496	C₂²	semidirect
62. C₅₃×#493	C₂²	semidirect
63. C₅₃×#493	C₂²	semidirect
64. C₅₃×#490	C₂²	semidirect
65. C₅₃×#486	C₂²	semidirect
66. C₅₃×#486	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#482	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#481	C₂²	semidirect
73. C₅₃×#480	C₂²	semidirect
74. C₅₃×#479	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#475	C₂²	semidirect
77. C₅₃×#474	C₂²	semidirect
78. C₅₃×#469	C₂²	semidirect
79. C₅₃×#469	C₂²	semidirect
80. C₅₃×#469	C₂²	semidirect
81. C₅₃×#468	C₂²	semidirect
82. C₅₃×#466	C₂²	semidirect
83. C₅₃×#466	C₂²	semidirect
84. C₅₃×#466	C₂²	semidirect
85. C₅₃×#465	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#460	C₂²	semidirect
89. C₅₃×#460	C₂²	semidirect
90. C₅₃×#460	C₂²	semidirect
91. C₅₃×#459	C₂²	semidirect
92. C₅₃×#459	C₂²	semidirect
93. C₅₃×#459	C₂²	semidirect
94. C₅₃×#459	C₂²	semidirect
95. C₅₃×#459	C₂²	semidirect
96. C₅₃×#452	C₂²	semidirect
97. C₅₃×#452	C₂²	semidirect
98. C₅₃×#450	C₂²	semidirect
99. C₅₃×#450	C₂²	semidirect
101. C₅₃×#449	C₂²	semidirect
102. C₅₃×#449	C₂²	semidirect
103. C₅₃×#449	C₂²	semidirect
104. C₅₃×#449	C₂²	semidirect
105. C₅₃×#449	C₂²	semidirect
106. C₅₃×#449	C₂²	semidirect
107. C₅₃×#447	C₂²	semidirect
108. C₅₃×#447	C₂²	semidirect
109. C₅₃×#447	C₂²	semidirect
110. C₅₃×#447	C₂²	semidirect
111. C₅₃×#447	C₂²	semidirect
112. C₅₃×#447	C₂²	semidirect
113. C₅₃×#447	C₂²	semidirect
114. C₅₃×#447	C₂²	semidirect
115. C₅₃×#442	C₂²	semidirect
116. C₅₃×#440	C₂²	semidirect
117. C₄×Q₁₆×C₅₃	C₂²	semidirect
118. C₄×SD₁₆×C₅₃	C₂²	semidirect
119. C₄×SD₁₆×C₅₃	C₂²	semidirect
120. C₄×D₈×C₅₃	C₂²	semidirect
121. C₅₃×#436	C₂²	semidirect
122. C₅₃×#436	C₂²	semidirect
123. C₅₃×#435	C₂²	semidirect
124. C₅₃×#435	C₂²	semidirect
125. C₈×D₄×C₅₃	C₂²	semidirect
126. C₈×D₄×C₅₃	C₂²	semidirect
127. C₅₃×#432	C₂²	semidirect
128. C₅₃×#431	C₂²	semidirect
129. C₅₃×#418	C₂²	semidirect
130. C₅₃×#417	C₂²	semidirect
131. C₅₃×#416	C₂²	semidirect
132. C₂×#102×C₅₃	C₂²	semidirect
133. C₅₃×#408	C₂²	semidirect
134. C₅₃×#408	C₂²	semidirect
584. #61688	C₅₃	direct (N × H)
630. #3546	C₂×C₅₃	semidirect
631. #3498	C₂×C₅₃	semidirect
632. #3332	C₂×C₅₃	semidirect
633. #3324	C₂×C₅₃	semidirect
634. #3318	C₂×C₅₃	semidirect
635. #3309	C₂×C₅₃	semidirect
636. #3304	C₂×C₅₃	semidirect
637. #3294	C₂×C₅₃	semidirect
638. #3287	C₂×C₅₃	semidirect
639. D₄×D₈	C₂×C₅₃	semidirect
640. #3274	C₂×C₅₃	semidirect
641. #3274	C₂×C₅₃	semidirect
642. #3268	C₂×C₅₃	semidirect
643. #3264	C₂×C₅₃	semidirect
644. #3217	C₂×C₅₃	semidirect
645. #3205	C₂×C₅₃	semidirect
646. #3199	C₂×C₅₃	semidirect
647. #3198	C₂×C₅₃	semidirect
648. #3115	C₂×C₅₃	semidirect
649. #3102	C₂×C₅₃	semidirect
650. #3012	C₂×C₅₃	semidirect
651. #3008	C₂×C₅₃	semidirect
652. #2981	C₂×C₅₃	semidirect
664. C₂×H(5,𝔽₂)	C₂²×C₅₃	semidirect
665. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
666. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
667. C₂×#135	C₂²×C₅₃	semidirect
668. C₂²×D₈	C₂²×C₅₃	semidirect
670. #556	C₂²×C₅₃	semidirect
671. #553	C₂²×C₅₃	semidirect
674. #550	C₂²×C₅₃	semidirect
675. #550	C₂²×C₅₃	semidirect
676. #550	C₂²×C₅₃	semidirect
677. #547	C₂²×C₅₃	semidirect
679. #546	C₂²×C₅₃	semidirect
684. D₄²	C₂²×C₅₃	semidirect
685. D₄²	C₂²×C₅₃	semidirect
686. D₄²	C₂²×C₅₃	semidirect
689. #537	C₂²×C₅₃	semidirect
692. #535	C₂²×C₅₃	semidirect
693. #535	C₂²×C₅₃	semidirect
696. #532	C₂²×C₅₃	semidirect
698. C₂×#127	C₂²×C₅₃	semidirect
699. #529	C₂²×C₅₃	semidirect
700. C₄×#41	C₂²×C₅₃	semidirect
701. #496	C₂²×C₅₃	semidirect
702. #493	C₂²×C₅₃	semidirect
703. #493	C₂²×C₅₃	semidirect
704. #490	C₂²×C₅₃	semidirect
705. #486	C₂²×C₅₃	semidirect
706. #486	C₂²×C₅₃	semidirect
707. #485	C₂²×C₅₃	semidirect
708. #482	C₂²×C₅₃	semidirect
709. #482	C₂²×C₅₃	semidirect
710. #482	C₂²×C₅₃	semidirect
711. #482	C₂²×C₅₃	semidirect
712. #481	C₂²×C₅₃	semidirect
713. #480	C₂²×C₅₃	semidirect
714. #479	C₂²×C₅₃	semidirect
715. #478	C₂²×C₅₃	semidirect
716. #475	C₂²×C₅₃	semidirect
717. #474	C₂²×C₅₃	semidirect
718. #469	C₂²×C₅₃	semidirect
719. #469	C₂²×C₅₃	semidirect
720. #469	C₂²×C₅₃	semidirect
721. #468	C₂²×C₅₃	semidirect
722. #466	C₂²×C₅₃	semidirect
723. #466	C₂²×C₅₃	semidirect
724. #466	C₂²×C₅₃	semidirect
725. #465	C₂²×C₅₃	semidirect
726. #464	C₂²×C₅₃	semidirect
727. #463	C₂²×C₅₃	semidirect
728. #460	C₂²×C₅₃	semidirect
729. #460	C₂²×C₅₃	semidirect
730. #460	C₂²×C₅₃	semidirect
731. #459	C₂²×C₅₃	semidirect
732. #459	C₂²×C₅₃	semidirect
733. #459	C₂²×C₅₃	semidirect
734. #459	C₂²×C₅₃	semidirect
735. #459	C₂²×C₅₃	semidirect
736. #452	C₂²×C₅₃	semidirect
737. #452	C₂²×C₅₃	semidirect
738. #450	C₂²×C₅₃	semidirect
739. #450	C₂²×C₅₃	semidirect
741. #449	C₂²×C₅₃	semidirect
742. #449	C₂²×C₅₃	semidirect
743. #449	C₂²×C₅₃	semidirect
744. #449	C₂²×C₅₃	semidirect
745. #449	C₂²×C₅₃	semidirect
746. #449	C₂²×C₅₃	semidirect
747. #447	C₂²×C₅₃	semidirect
748. #447	C₂²×C₅₃	semidirect
749. #447	C₂²×C₅₃	semidirect
750. #447	C₂²×C₅₃	semidirect
751. #447	C₂²×C₅₃	semidirect
752. #447	C₂²×C₅₃	semidirect
753. #447	C₂²×C₅₃	semidirect
754. #447	C₂²×C₅₃	semidirect
755. #442	C₂²×C₅₃	semidirect
756. #440	C₂²×C₅₃	semidirect
757. C₄×Q₁₆	C₂²×C₅₃	semidirect
758. C₄×SD₁₆	C₂²×C₅₃	semidirect
759. C₄×SD₁₆	C₂²×C₅₃	semidirect
760. C₄×D₈	C₂²×C₅₃	semidirect
761. #436	C₂²×C₅₃	semidirect
762. #436	C₂²×C₅₃	semidirect
763. #435	C₂²×C₅₃	semidirect
764. #435	C₂²×C₅₃	semidirect
765. C₈×D₄	C₂²×C₅₃	semidirect
766. C₈×D₄	C₂²×C₅₃	semidirect
767. #432	C₂²×C₅₃	semidirect
768. #431	C₂²×C₅₃	semidirect
769. #418	C₂²×C₅₃	semidirect
770. #417	C₂²×C₅₃	semidirect
771. #416	C₂²×C₅₃	semidirect
772. C₂×#102	C₂²×C₅₃	semidirect
773. #408	C₂²×C₅₃	semidirect
774. #408	C₂²×C₅₃	semidirect
775. C₅₃	#61688	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×#3546	2
C₅₃×#3498	2
C₅₃×#3332	2
C₅₃×#3324	2
C₅₃×#3318	2
C₅₃×#3309	2
C₅₃×#3304	2
C₅₃×#3294	2
C₅₃×#3287	2
D₄×D₈×C₅₃	2
C₅₃×#3274	2
C₅₃×#3268	2
C₅₃×#3264	2
C₅₃×#3217	2
C₅₃×#3205	2
C₅₃×#3199	2
C₅₃×#3198	2
C₅₃×#3115	2
C₅₃×#3102	2
C₅₃×#3012	2
C₅₃×#3008	2
C₅₃×#2981	2
#61688	53

Subgroups — C53×#61688 #27269200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61688 #27269200