Subgroups — C₅₃×#60592 #27268104

Order 13568.

2098 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×H(5,𝔽₂)×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3125	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3124	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3114	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3111	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3105	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3102	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3008	C₂	1	1	yes	maximal, characteristic
19	C₅₃×#2949	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₅₃×#559	—	2	1	no	—
30	C₅₃×#559	—	2	1	no	—
31	C₅₃×#556	—	2	1	no	—
32	C₅₃×#556	—	2	1	no	—
33	C₅₃×#551	—	2	2	no	—
34	C₅₃×#551	—	2	2	no	—
35	C₅₃×#542	C₂²	1	2	yes	complemented
36	C₅₃×#542	C₂²	1	2	yes	complemented
37	C₅₃×#536	C₂²	1	1	yes	characteristic
38	C₅₃×#535	C₂²	1	1	yes	characteristic
39	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#529	C₂²	1	2	yes	complemented
41	C₅₃×#529	C₂²	1	2	yes	complemented
42	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#520	—	2	1	no	—
44	C₅₃×#520	C₂²	1	1	yes	characteristic
45	C₅₃×#520	C₂²	1	1	yes	characteristic
46	C₅₃×#520	C₂²	1	2	yes	complemented
47	C₅₃×#519	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#518	—	2	2	no	—
49	C₅₃×#518	—	2	1	no	—
50	C₅₃×#518	C₂²	1	1	yes	characteristic
51	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#518	C₂²	1	2	yes	complemented
53	C₄×#41×C₅₃	—	2	1	no	—
54	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
55	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
56	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₅₃	—	2	1	no	—
58	C₂×C₄×D₄×C₅₃	—	2	2	no	—
59	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
61	C₅₃×#485	C₂²	1	2	yes	complemented
62	C₅₃×#485	C₂²	1	2	yes	complemented
63	C₅₃×#484	C₂²	1	2	yes	complemented
64	C₅₃×#483	C₂²	1	2	yes	complemented
65	C₅₃×#482	C₂²	1	2	yes	complemented
66	C₅₃×#482	C₂²	1	2	yes	complemented
67	C₅₃×#481	C₂²	1	2	yes	complemented
68	C₅₃×#480	C₂²	1	2	yes	complemented
69	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#478	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	2	yes	complemented
75	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#476	C₂²	1	2	yes	complemented
78	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#474	C₂²	1	2	yes	complemented
81	C₅₃×#464	C₂²	1	2	yes	complemented
82	C₅₃×#464	C₂²	1	2	yes	complemented
83	C₅₃×#463	C₂²	1	2	yes	complemented
84	C₅₃×#463	C₂²	1	2	yes	complemented
85	C₅₃×#463	C₂²	1	2	yes	complemented
86	C₅₃×#463	C₂²	1	2	yes	complemented
87	C₅₃×#463	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	2	yes	complemented
89	C₅₃×#452	C₂²	1	2	yes	complemented
90	C₅₃×#452	C₂²	1	2	yes	complemented
91	C₅₃×#450	C₂²	1	2	yes	complemented
92	C₅₃×#450	C₂²	1	2	yes	complemented
93	C₅₃×#449	C₂²	1	2	yes	—
94	C₅₃×#449	C₂²	1	2	yes	—
95	C₅₃×#447	C₂²	1	2	yes	—
96	C₅₃×#447	C₂²	1	2	yes	—
97	C₅₃×#442	C₂²	1	2	yes	complemented
98	C₅₃×#442	C₂²	1	2	yes	complemented
99	C₅₃×#442	C₂²	1	2	yes	complemented
100	C₅₃×#441	C₂²	1	2	yes	complemented
101	C₅₃×#440	C₂²	1	2	yes	complemented
102	C₅₃×#440	C₂²	1	2	yes	complemented
103	C₅₃×#440	C₂²	1	2	yes	complemented
104	C₅₃×#440	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
110	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
111	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
112	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
113	C₅₃×#433	C₂²	1	2	yes	complemented
114	C₅₃×#433	C₂²	1	2	yes	complemented
115	C₅₃×#432	C₂²	1	2	yes	complemented
116	C₅₃×#431	C₂²	1	2	yes	complemented
117	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#418	C₂²	1	1	yes	characteristic
125	C₅₃×#418	C₂²	1	1	yes	characteristic
126	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#416	C₂²	1	1	yes	characteristic
128	C₅₃×#416	C₂²	1	1	yes	characteristic
129	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#408	C₂²	1	1	yes	characteristic
132	C₅₃×#408	C₂²	1	1	yes	characteristic
133	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
135	H(5,𝔽₂)×C₅₃	—	2	4	no	—
136	H(5,𝔽₂)×C₅₃	—	2	4	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	C₂³	1	2	yes	—
139	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
140	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
141	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₅₃	—	2	2	no	—
143	C₂²×D₄×C₅₃	—	2	1	no	—
144	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
145	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₅₃	—	2	1	no	—
148	C₂³×C₄×C₅₃	—	2	2	no	—
149	#137×C₅₃	—	2	4	no	—
150	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
151	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₅₃	—	2	4	no	—
153	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂×D₈×C₅₃	—	2	4	no	—
158	C₂×D₈×C₅₃	C₂³	1	2	yes	—
159	C₂×D₈×C₅₃	C₂³	1	2	yes	—
160	C₂×D₈×C₅₃	C₂³	1	2	yes	—
161	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
162	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
164	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₅₃	—	2	1	no	—
166	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
168	#127×C₅₃	—	2	1	no	—
169	#126×C₅₃	—	2	2	no	—
170	#126×C₅₃	—	2	2	no	—
171	#126×C₅₃	—	2	2	no	—
172	#126×C₅₃	—	2	2	no	—
173	#125×C₅₃	C₂³	1	1	yes	characteristic
174	#125×C₅₃	C₂³	1	1	yes	characteristic
175	#124×C₅₃	—	2	2	no	—
176	#124×C₅₃	—	2	2	no	—
177	#124×C₅₃	—	2	1	no	—
178	#124×C₅₃	—	2	1	no	—
179	#124×C₅₃	—	2	1	no	—
180	#124×C₅₃	—	2	1	no	—
181	#124×C₅₃	C₂³	1	2	yes	—
182	#124×C₅₃	C₂³	1	2	yes	—
183	#123×C₅₃	—	2	2	no	—
184	#123×C₅₃	—	2	2	no	—
185	#123×C₅₃	—	2	2	no	—
186	#123×C₅₃	—	2	2	no	—
187	#123×C₅₃	—	2	2	no	—
188	C₂²⋊Q₈×C₅₃	—	2	2	no	—
189	C₂²⋊Q₈×C₅₃	—	2	2	no	—
190	C₂²⋊Q₈×C₅₃	—	2	1	no	—
191	C₂²⋊Q₈×C₅₃	—	2	1	no	—
192	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
193	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
194	#121×C₅₃	C₂³	1	2	yes	—
195	#121×C₅₃	C₂³	1	2	yes	—
196	#120×C₅₃	—	2	2	no	—
197	C₄×Q₈×C₅₃	—	2	1	no	—
198	C₄×Q₈×C₅₃	—	2	1	no	—
199	C₄×Q₈×C₅₃	—	2	1	no	—
200	C₄×Q₈×C₅₃	—	2	1	no	—
201	C₄×Q₈×C₅₃	—	2	1	no	—
202	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
203	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
204	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
205	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
207	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
208	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
209	C₄×D₄×C₅₃	—	2	1	no	—
210	C₄×D₄×C₅₃	—	2	2	no	—
211	C₄×D₄×C₅₃	—	2	1	no	—
212	C₄×D₄×C₅₃	—	2	2	no	—
213	C₄×D₄×C₅₃	—	2	1	no	—
214	C₄×D₄×C₅₃	—	2	1	no	—
215	C₄×D₄×C₅₃	—	2	2	no	—
216	C₄×D₄×C₅₃	—	2	2	no	—
217	C₄×D₄×C₅₃	—	2	2	no	—
218	C₄×D₄×C₅₃	—	2	1	no	—
219	C₄×D₄×C₅₃	—	2	2	no	—
220	C₄×D₄×C₅₃	—	2	1	no	—
221	C₄×D₄×C₅₃	—	2	2	no	—
222	C₄×D₄×C₅₃	—	2	2	no	—
223	C₄×D₄×C₅₃	—	2	1	no	—
224	C₄×D₄×C₅₃	—	2	1	no	—
225	C₄×D₄×C₅₃	—	2	2	no	—
226	C₄×D₄×C₅₃	—	2	1	no	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	—	2	2	no	—
229	C₄×D₄×C₅₃	—	2	2	no	—
230	C₄×D₄×C₅₃	D₄	1	2	yes	—
231	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
232	C₄×D₄×C₅₃	D₄	1	2	yes	—
233	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
234	C₄×D₄×C₅₃	C₂³	1	2	yes	—
235	C₄×D₄×C₅₃	C₂³	1	2	yes	—
236	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₅₃	C₂³	1	2	yes	—
238	C₄×D₄×C₅₃	C₂³	1	2	yes	—
239	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	C₂³	1	2	yes	—
242	C₄×D₄×C₅₃	C₂³	1	2	yes	—
243	#117×C₅₃	—	2	1	no	—
244	#117×C₅₃	—	2	2	no	—
245	#117×C₅₃	—	2	2	no	—
246	#117×C₅₃	—	2	1	no	—
247	#117×C₅₃	—	2	2	no	—
248	#117×C₅₃	—	2	2	no	—
249	#117×C₅₃	—	2	2	no	—
250	#117×C₅₃	C₂³	1	2	yes	—
251	#117×C₅₃	C₂³	1	1	yes	characteristic
252	#117×C₅₃	C₂³	1	1	yes	characteristic
253	#117×C₅₃	C₂³	1	1	yes	characteristic
254	#117×C₅₃	C₂³	1	1	yes	characteristic
255	#117×C₅₃	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
260	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
262	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
263	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
267	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
268	C₂×C₄²×C₅₃	—	2	1	no	—
269	C₂×C₄²×C₅₃	—	2	2	no	—
270	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
272	#107×C₅₃	C₂³	1	1	yes	characteristic
273	#107×C₅₃	C₂³	1	2	yes	—
274	#107×C₅₃	C₂³	1	1	yes	characteristic
275	#107×C₅₃	C₂³	1	1	yes	characteristic
276	#107×C₅₃	C₂³	1	1	yes	characteristic
277	#107×C₅₃	C₂³	1	2	yes	—
278	#106×C₅₃	C₂³	1	1	yes	characteristic
279	#106×C₅₃	C₂³	1	2	yes	—
280	#106×C₅₃	C₂³	1	1	yes	characteristic
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	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
289	C₄⋊C₈×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	1	yes	characteristic
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	1	yes	characteristic
296	#103×C₅₃	C₂³	1	1	yes	characteristic
297	#103×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	2	yes	—
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	2	yes	—
305	#102×C₅₃	C₂³	1	2	yes	—
306	#102×C₅₃	C₂³	1	2	yes	—
307	#102×C₅₃	C₂³	1	2	yes	—
308	#102×C₅₃	C₂³	1	2	yes	—
309	#102×C₅₃	C₂³	1	2	yes	—
310	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	#97×C₅₃	C₂³	1	2	yes	—
315	#97×C₅₃	C₂³	1	2	yes	—
316	C₄×C₈×C₅₃	C₂³	1	2	yes	—
317	C₄×C₈×C₅₃	C₂³	1	2	yes	—
318	C₂⁴×C₅₃	—	2	2	no	—
319	C₂⁴×C₅₃	—	2	1	no	—
320	C₂⁴×C₅₃	—	2	1	no	—
321	#41×C₅₃	—	2	8	no	—
322	#41×C₅₃	—	2	4	no	—
323	#41×C₅₃	—	2	4	no	—
324	#41×C₅₃	—	2	2	no	—
325	#41×C₅₃	—	2	2	no	—
326	#41×C₅₃	—	2	2	no	—
327	#41×C₅₃	#41	1	4	yes	—
328	C₂×Q₈×C₅₃	—	2	1	no	—
329	C₂×Q₈×C₅₃	—	2	1	no	—
330	C₂×Q₈×C₅₃	—	2	1	no	—
331	C₂×Q₈×C₅₃	—	2	2	no	—
332	C₂×Q₈×C₅₃	—	2	2	no	—
333	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
334	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₅₃	—	2	16	no	—
337	C₂×D₄×C₅₃	—	2	8	no	—
338	C₂×D₄×C₅₃	—	2	2	no	—
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	2	no	—
345	C₂×D₄×C₅₃	—	2	1	no	—
346	C₂×D₄×C₅₃	—	2	1	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	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
352	C₂×D₄×C₅₃	#41	1	4	yes	—
353	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
354	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₅₃	—	2	2	no	—
357	C₂²×C₄×C₅₃	—	2	1	no	—
358	C₂²×C₄×C₅₃	—	2	1	no	—
359	C₂²×C₄×C₅₃	—	2	2	no	—
360	C₂²×C₄×C₅₃	—	2	1	no	—
361	C₂²×C₄×C₅₃	—	2	1	no	—
362	C₂²×C₄×C₅₃	—	2	2	no	—
363	C₂²×C₄×C₅₃	—	2	2	no	—
364	C₂²×C₄×C₅₃	—	2	1	no	—
365	C₂²×C₄×C₅₃	—	2	2	no	—
366	C₂²×C₄×C₅₃	—	2	2	no	—
367	C₂²×C₄×C₅₃	—	2	2	no	—
368	C₂²×C₄×C₅₃	—	2	2	no	—
369	C₂²×C₄×C₅₃	—	2	2	no	—
370	C₂²×C₄×C₅₃	—	8	2	no	—
371	C₂²×C₄×C₅₃	—	8	4	no	—
372	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
374	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
376	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
377	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	Q₁₆×C₅₃	—	2	4	no	—
379	SD₁₆×C₅₃	—	2	4	no	—
380	SD₁₆×C₅₃	—	2	4	no	—
381	SD₁₆×C₅₃	—	2	4	no	—
382	SD₁₆×C₅₃	—	2	4	no	—
383	D₈×C₅₃	—	2	4	no	—
384	D₈×C₅₃	—	2	4	no	—
385	D₈×C₅₃	—	2	4	no	—
386	M₁₆×C₅₃	—	2	2	no	—
387	M₁₆×C₅₃	—	2	2	no	—
388	C₂×C₈×C₅₃	—	2	2	no	—
389	C₂×C₈×C₅₃	—	2	2	no	—
390	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
393	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
394	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₅₃	—	2	2	no	—
397	C₄⋊C₄×C₅₃	—	2	1	no	—
398	C₄⋊C₄×C₅₃	—	2	2	no	—
399	C₄⋊C₄×C₅₃	—	2	1	no	—
400	C₄⋊C₄×C₅₃	—	2	1	no	—
401	C₄⋊C₄×C₅₃	—	2	1	no	—
402	C₄⋊C₄×C₅₃	—	2	1	no	—
403	C₄⋊C₄×C₅₃	—	2	2	no	—
404	C₄⋊C₄×C₅₃	—	2	2	no	—
405	C₄⋊C₄×C₅₃	—	2	2	no	—
406	C₄⋊C₄×C₅₃	—	2	2	no	—
407	C₄⋊C₄×C₅₃	—	2	1	no	—
408	C₄⋊C₄×C₅₃	—	2	1	no	—
409	C₄⋊C₄×C₅₃	—	2	1	no	—
410	C₄⋊C₄×C₅₃	—	2	1	no	—
411	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²⋊C₄×C₅₃	—	2	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	1	no	—
424	C₂²⋊C₄×C₅₃	—	2	1	no	—
425	C₂²⋊C₄×C₅₃	—	2	1	no	—
426	C₂²⋊C₄×C₅₃	—	2	2	no	—
427	C₂²⋊C₄×C₅₃	—	2	2	no	—
428	C₂²⋊C₄×C₅₃	—	2	2	no	—
429	C₂²⋊C₄×C₅₃	—	2	2	no	—
430	C₂²⋊C₄×C₅₃	—	2	2	no	—
431	C₂²⋊C₄×C₅₃	—	2	2	no	—
432	C₂²⋊C₄×C₅₃	—	2	1	no	—
433	C₂²⋊C₄×C₅₃	—	2	2	no	—
434	C₂²⋊C₄×C₅₃	—	2	1	no	—
435	C₂²⋊C₄×C₅₃	—	2	2	no	—
436	C₂²⋊C₄×C₅₃	—	2	2	no	—
437	C₂²⋊C₄×C₅₃	—	2	2	no	—
438	C₂²⋊C₄×C₅₃	—	2	2	no	—
439	C₂²⋊C₄×C₅₃	—	2	2	no	—
440	C₂²⋊C₄×C₅₃	—	2	2	no	—
441	C₂²⋊C₄×C₅₃	—	2	2	no	—
442	C₂²⋊C₄×C₅₃	—	2	2	no	—
443	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
446	C₄²×C₅₃	—	2	1	no	—
447	C₄²×C₅₃	—	2	2	no	—
448	C₄²×C₅₃	—	2	1	no	—
449	C₄²×C₅₃	—	2	2	no	—
450	C₄²×C₅₃	—	2	1	no	—
451	C₄²×C₅₃	—	2	2	no	—
452	C₄²×C₅₃	—	2	2	no	—
453	C₄²×C₅₃	—	2	1	no	—
454	C₄²×C₅₃	—	2	1	no	—
455	C₄²×C₅₃	C₂×D₄	1	2	yes	—
456	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₅₃	C₂×D₄	1	2	yes	—
458	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₅₃	C₂⁴	1	2	yes	—
460	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
461	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
462	C₂³×C₅₃	—	2	8	no	—
463	C₂³×C₅₃	—	2	2	no	—
464	C₂³×C₅₃	—	2	1	no	—
465	C₂³×C₅₃	—	2	4	no	—
466	C₂³×C₅₃	—	2	2	no	—
467	C₂³×C₅₃	—	4	2	no	—
468	C₂³×C₅₃	—	8	1	no	—
469	C₂³×C₅₃	—	8	2	no	—
470	C₂³×C₅₃	—	8	1	no	—
471	C₂³×C₅₃	—	8	2	no	—
472	C₂³×C₅₃	—	8	1	no	—
473	C₂³×C₅₃	—	8	1	no	—
474	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
475	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
476	Q₈×C₅₃	—	2	2	no	—
477	Q₈×C₅₃	—	2	1	no	—
478	Q₈×C₅₃	—	2	2	no	—
479	Q₈×C₅₃	—	2	2	no	—
480	Q₈×C₅₃	—	4	2	no	—
481	Q₈×C₅₃	—	8	1	no	—
482	Q₈×C₅₃	—	8	1	no	—
483	Q₈×C₅₃	C₂×#41	1	2	yes	—
484	D₄×C₅₃	—	2	8	no	—
485	D₄×C₅₃	—	2	8	no	—
486	D₄×C₅₃	—	2	4	no	—
487	D₄×C₅₃	—	2	4	no	—
488	D₄×C₅₃	—	2	2	no	—
489	D₄×C₅₃	—	2	4	no	—
490	D₄×C₅₃	—	2	2	no	—
491	D₄×C₅₃	—	2	1	no	—
492	D₄×C₅₃	—	2	2	no	—
493	D₄×C₅₃	—	2	2	no	—
494	D₄×C₅₃	—	4	2	no	—
495	D₄×C₅₃	—	8	2	no	—
496	D₄×C₅₃	—	8	2	no	—
497	D₄×C₅₃	C₂×#41	1	2	yes	—
498	D₄×C₅₃	C₂×#41	1	4	yes	—
499	C₂×C₄×C₅₃	—	2	8	no	—
500	C₂×C₄×C₅₃	—	2	1	no	—
501	C₂×C₄×C₅₃	—	2	4	no	—
502	C₂×C₄×C₅₃	—	2	2	no	—
503	C₂×C₄×C₅₃	—	2	2	no	—
504	C₂×C₄×C₅₃	—	2	1	no	—
505	C₂×C₄×C₅₃	—	2	2	no	—
506	C₂×C₄×C₅₃	—	2	1	no	—
507	C₂×C₄×C₅₃	—	2	1	no	—
508	C₂×C₄×C₅₃	—	2	1	no	—
509	C₂×C₄×C₅₃	—	2	2	no	—
510	C₂×C₄×C₅₃	—	2	1	no	—
511	C₂×C₄×C₅₃	—	2	1	no	—
512	C₂×C₄×C₅₃	—	4	2	no	—
513	C₂×C₄×C₅₃	—	4	1	no	—
514	C₂×C₄×C₅₃	—	4	2	no	—
515	C₂×C₄×C₅₃	—	4	1	no	—
516	C₂×C₄×C₅₃	—	4	2	no	—
517	C₂×C₄×C₅₃	—	4	4	no	—
518	C₂×C₄×C₅₃	—	4	2	no	—
519	C₂×C₄×C₅₃	—	8	2	no	—
520	C₂×C₄×C₅₃	—	8	2	no	—
521	C₂×C₄×C₅₃	—	8	1	no	—
522	C₂×C₄×C₅₃	—	8	2	no	—
523	C₂×C₄×C₅₃	—	8	2	no	—
524	C₂×C₄×C₅₃	—	8	2	no	—
525	C₂×C₄×C₅₃	—	8	2	no	—
526	C₂×C₄×C₅₃	—	8	1	no	—
527	C₂×C₄×C₅₃	—	8	2	no	—
528	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
537	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
538	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
539	C₈×C₅₃	—	2	1	no	—
540	C₈×C₅₃	—	2	1	no	—
541	C₈×C₅₃	—	2	1	no	—
542	C₈×C₅₃	—	2	1	no	—
543	C₈×C₅₃	—	2	2	no	—
544	C₈×C₅₃	—	2	2	no	—
545	#60592	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
546	C₂²×C₅₃	—	2	1	no	—
547	C₂²×C₅₃	—	2	1	no	—
548	C₂²×C₅₃	—	2	2	no	—
549	C₂²×C₅₃	—	2	2	no	—
550	C₂²×C₅₃	—	2	2	no	—
551	C₂²×C₅₃	—	2	4	no	—
552	C₂²×C₅₃	—	2	2	no	—
553	C₂²×C₅₃	—	4	2	no	—
554	C₂²×C₅₃	—	4	1	no	—
555	C₂²×C₅₃	—	4	2	no	—
556	C₂²×C₅₃	—	4	1	no	—
557	C₂²×C₅₃	—	4	2	no	—
558	C₂²×C₅₃	—	4	2	no	—
559	C₂²×C₅₃	—	4	2	no	—
560	C₂²×C₅₃	—	8	4	no	—
561	C₂²×C₅₃	—	8	8	no	—
562	C₂²×C₅₃	—	16	2	no	—
563	C₂²×C₅₃	#525	1	2	yes	—
564	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
565	C₄×C₅₃	—	2	1	no	—
566	C₄×C₅₃	—	2	2	no	—
567	C₄×C₅₃	—	2	1	no	—
568	C₄×C₅₃	—	2	1	no	—
569	C₄×C₅₃	—	2	2	no	—
570	C₄×C₅₃	—	2	1	no	—
571	C₄×C₅₃	—	2	2	no	—
572	C₄×C₅₃	—	2	2	no	—
573	C₄×C₅₃	—	4	1	no	—
574	C₄×C₅₃	—	4	1	no	—
575	C₄×C₅₃	—	4	1	no	—
576	C₄×C₅₃	—	4	1	no	—
577	C₄×C₅₃	—	4	2	no	—
578	C₄×C₅₃	—	4	1	no	—
579	C₄×C₅₃	—	4	1	no	—
580	C₄×C₅₃	—	4	2	no	—
581	C₄×C₅₃	#525	1	2	yes	—
582	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
583	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
584	#3510	C₂×C₅₃	1	1	yes	characteristic, complemented
585	C₄×H(5,𝔽₂)	C₂×C₅₃	1	1	yes	characteristic, complemented
586	#3125	C₂×C₅₃	1	2	yes	complemented
587	#3124	C₂×C₅₃	1	2	yes	complemented
588	#3118	C₂×C₅₃	1	2	yes	complemented
589	#3118	C₂×C₅₃	1	2	yes	complemented
590	#3114	C₂×C₅₃	1	2	yes	complemented
591	#3111	C₂×C₅₃	1	2	yes	complemented
592	#3105	C₂×C₅₃	1	2	yes	complemented
593	#3102	C₂×C₅₃	1	2	yes	complemented
594	#3097	C₂×C₅₃	1	1	yes	characteristic, complemented
595	#3096	C₂×C₅₃	1	1	yes	characteristic, complemented
596	#3077	C₂×C₅₃	1	1	yes	characteristic, complemented
597	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
598	#3040	C₂×C₅₃	1	1	yes	characteristic, complemented
599	C₂×#463	C₂×C₅₃	1	1	yes	characteristic, complemented
600	#3009	C₂×C₅₃	1	1	yes	characteristic, complemented
601	#3008	C₂×C₅₃	1	1	yes	characteristic
602	#2949	C₂×C₅₃	1	1	yes	characteristic, complemented
603	#2948	C₂×C₅₃	1	1	yes	characteristic, complemented
604	#2947	C₂×C₅₃	1	1	yes	characteristic, complemented
605	#2946	C₂×C₅₃	1	1	yes	characteristic, complemented
606	#2925	C₂×C₅₃	1	1	yes	characteristic, complemented
607	C₂×C₅₃	—	2	2	no	—
608	C₂×C₅₃	—	4	2	no	—
609	C₂×C₅₃	—	4	4	no	—
610	C₂×C₅₃	—	4	2	no	—
611	C₂×C₅₃	—	8	2	no	—
612	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
613	C₂×C₅₃	#3584	1	1	yes	characteristic
614	C₂×C₅₃	#3585	1	1	yes	characteristic
615	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
616	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
617	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
618	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
619	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
620	#559	—	2	1	no	—
621	#559	—	2	1	no	—
622	#556	—	2	1	no	—
623	#556	—	2	1	no	—
624	#551	—	2	2	no	—
625	#551	—	2	2	no	—
626	#542	C₂²×C₅₃	1	2	yes	complemented
627	#542	C₂²×C₅₃	1	2	yes	complemented
628	#536	C₂²×C₅₃	1	1	yes	characteristic
629	#535	C₂²×C₅₃	1	1	yes	characteristic
630	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
631	#529	C₂²×C₅₃	1	2	yes	complemented
632	#529	C₂²×C₅₃	1	2	yes	complemented
633	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
634	#520	—	2	1	no	—
635	#520	C₂²×C₅₃	1	1	yes	characteristic
636	#520	C₂²×C₅₃	1	1	yes	characteristic
637	#520	C₂²×C₅₃	1	2	yes	complemented
638	#519	C₂²×C₅₃	1	1	yes	characteristic, complemented
639	#518	—	2	2	no	—
640	#518	—	2	1	no	—
641	#518	C₂²×C₅₃	1	1	yes	characteristic
642	#518	C₂²×C₅₃	1	2	yes	complemented
643	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
644	C₄×#41	—	2	1	no	—
645	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
646	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
647	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
648	C₂×C₄×D₄	—	2	1	no	—
649	C₂×C₄×D₄	—	2	2	no	—
650	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
651	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
652	#485	C₂²×C₅₃	1	2	yes	complemented
653	#485	C₂²×C₅₃	1	2	yes	complemented
654	#484	C₂²×C₅₃	1	2	yes	complemented
655	#483	C₂²×C₅₃	1	2	yes	complemented
656	#482	C₂²×C₅₃	1	2	yes	complemented
657	#482	C₂²×C₅₃	1	2	yes	complemented
658	#481	C₂²×C₅₃	1	2	yes	complemented
659	#480	C₂²×C₅₃	1	2	yes	complemented
660	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
661	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
662	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
664	#478	C₂²×C₅₃	1	2	yes	complemented
665	#478	C₂²×C₅₃	1	2	yes	complemented
666	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
667	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
668	#476	C₂²×C₅₃	1	2	yes	complemented
669	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
670	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
671	#474	C₂²×C₅₃	1	2	yes	complemented
672	#464	C₂²×C₅₃	1	2	yes	complemented
673	#464	C₂²×C₅₃	1	2	yes	complemented
674	#463	C₂²×C₅₃	1	2	yes	complemented
675	#463	C₂²×C₅₃	1	2	yes	complemented
676	#463	C₂²×C₅₃	1	2	yes	complemented
677	#463	C₂²×C₅₃	1	2	yes	complemented
678	#463	C₂²×C₅₃	1	2	yes	complemented
679	#463	C₂²×C₅₃	1	2	yes	complemented
680	#452	C₂²×C₅₃	1	2	yes	complemented
681	#452	C₂²×C₅₃	1	2	yes	complemented
682	#450	C₂²×C₅₃	1	2	yes	complemented
683	#450	C₂²×C₅₃	1	2	yes	complemented
684	#449	C₂²×C₅₃	1	2	yes	—
685	#449	C₂²×C₅₃	1	2	yes	—
686	#447	C₂²×C₅₃	1	2	yes	—
687	#447	C₂²×C₅₃	1	2	yes	—
688	#442	C₂²×C₅₃	1	2	yes	complemented
689	#442	C₂²×C₅₃	1	2	yes	complemented
690	#442	C₂²×C₅₃	1	2	yes	complemented
691	#441	C₂²×C₅₃	1	2	yes	complemented
692	#440	C₂²×C₅₃	1	2	yes	complemented
693	#440	C₂²×C₅₃	1	2	yes	complemented
694	#440	C₂²×C₅₃	1	2	yes	complemented
695	#440	C₂²×C₅₃	1	2	yes	complemented
696	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
697	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
698	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
699	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
700	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
701	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
702	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
703	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
704	#433	C₂²×C₅₃	1	2	yes	complemented
705	#433	C₂²×C₅₃	1	2	yes	complemented
706	#432	C₂²×C₅₃	1	2	yes	complemented
707	#431	C₂²×C₅₃	1	2	yes	complemented
708	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
710	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
711	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
714	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
715	#418	C₂²×C₅₃	1	1	yes	characteristic
716	#418	C₂²×C₅₃	1	1	yes	characteristic
717	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
718	#416	C₂²×C₅₃	1	1	yes	characteristic
719	#416	C₂²×C₅₃	1	1	yes	characteristic
720	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
721	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	#408	C₂²×C₅₃	1	1	yes	characteristic
723	#408	C₂²×C₅₃	1	1	yes	characteristic
724	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
725	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
726	C₅₃	#60592	1	1	yes	characteristic, direct product factor, Sylow
727	H(5,𝔽₂)	—	2	4	no	—
728	H(5,𝔽₂)	—	2	4	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	C₂³×C₅₃	1	2	yes	—
731	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
732	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
733	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
734	C₂²×D₄	—	2	2	no	—
735	C₂²×D₄	—	2	1	no	—
736	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
737	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
738	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
739	C₂³×C₄	—	2	1	no	—
740	C₂³×C₄	—	2	2	no	—
741	#137	—	2	4	no	—
742	AGL(1,ℤ/8)	—	2	4	no	—
743	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
744	C₂×SD₁₆	—	2	4	no	—
745	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
749	C₂×D₈	—	2	4	no	—
750	C₂×D₈	C₂³×C₅₃	1	2	yes	—
751	C₂×D₈	C₂³×C₅₃	1	2	yes	—
752	C₂×D₈	C₂³×C₅₃	1	2	yes	—
753	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
754	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
755	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
756	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
757	C₄⋊Q₈	—	2	1	no	—
758	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
759	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
760	#127	—	2	1	no	—
761	#126	—	2	2	no	—
762	#126	—	2	2	no	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#125	C₂³×C₅₃	1	1	yes	characteristic
766	#125	C₂³×C₅₃	1	1	yes	characteristic
767	#124	—	2	1	no	—
768	#124	—	2	1	no	—
769	#124	—	2	2	no	—
770	#124	—	2	2	no	—
771	#124	—	2	1	no	—
772	#124	—	2	1	no	—
773	#124	C₂³×C₅₃	1	2	yes	—
774	#124	C₂³×C₅₃	1	2	yes	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
785	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
786	#121	C₂³×C₅₃	1	2	yes	—
787	#121	C₂³×C₅₃	1	2	yes	—
788	#120	—	2	2	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
795	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
799	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
800	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	D₄×C₅₃	1	2	yes	—
823	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
824	C₄×D₄	D₄×C₅₃	1	2	yes	—
825	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₅₃	1	2	yes	—
827	C₄×D₄	C₂³×C₅₃	1	2	yes	—
828	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₅₃	1	2	yes	—
830	C₄×D₄	C₂³×C₅₃	1	2	yes	—
831	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₅₃	1	2	yes	—
833	C₄×D₄	C₂³×C₅₃	1	2	yes	—
834	C₄×D₄	C₂³×C₅₃	1	2	yes	—
835	#117	—	2	1	no	—
836	#117	—	2	2	no	—
837	#117	—	2	2	no	—
838	#117	—	2	1	no	—
839	#117	—	2	2	no	—
840	#117	—	2	2	no	—
841	#117	—	2	2	no	—
842	#117	C₂³×C₅₃	1	1	yes	characteristic
843	#117	C₂³×C₅₃	1	2	yes	—
844	#117	C₂³×C₅₃	1	1	yes	characteristic
845	#117	C₂³×C₅₃	1	1	yes	characteristic
846	#117	C₂³×C₅₃	1	1	yes	characteristic
847	#117	C₂³×C₅₃	1	2	yes	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	—	2	2	no	—
850	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
851	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
852	C₂×C₂²⋊C₄	—	2	1	no	—
853	C₂×C₂²⋊C₄	—	2	2	no	—
854	C₂×C₂²⋊C₄	—	2	1	no	—
855	C₂×C₂²⋊C₄	—	2	1	no	—
856	C₂×C₂²⋊C₄	—	2	2	no	—
857	C₂×C₂²⋊C₄	—	2	2	no	—
858	C₂×C₂²⋊C₄	—	2	2	no	—
859	C₂×C₂²⋊C₄	—	2	2	no	—
860	C₂×C₄²	—	2	1	no	—
861	C₂×C₄²	—	2	2	no	—
862	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
863	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
864	#107	C₂³×C₅₃	1	1	yes	characteristic
865	#107	C₂³×C₅₃	1	1	yes	characteristic
866	#107	C₂³×C₅₃	1	1	yes	characteristic
867	#107	C₂³×C₅₃	1	1	yes	characteristic
868	#107	C₂³×C₅₃	1	2	yes	—
869	#107	C₂³×C₅₃	1	2	yes	—
870	#106	C₂³×C₅₃	1	1	yes	characteristic
871	#106	C₂³×C₅₃	1	1	yes	characteristic
872	#106	C₂³×C₅₃	1	1	yes	characteristic
873	#106	C₂³×C₅₃	1	1	yes	characteristic
874	#106	C₂³×C₅₃	1	2	yes	—
875	#106	C₂³×C₅₃	1	2	yes	—
876	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
877	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
878	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
879	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
880	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
881	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
882	#103	C₂³×C₅₃	1	2	yes	—
883	#103	C₂³×C₅₃	1	2	yes	—
884	#103	C₂³×C₅₃	1	1	yes	characteristic
885	#103	C₂³×C₅₃	1	1	yes	characteristic
886	#103	C₂³×C₅₃	1	1	yes	characteristic
887	#103	C₂³×C₅₃	1	1	yes	characteristic
888	#103	C₂³×C₅₃	1	2	yes	—
889	#103	C₂³×C₅₃	1	2	yes	—
890	#102	C₂³×C₅₃	1	2	yes	—
891	#102	C₂³×C₅₃	1	2	yes	—
892	#102	C₂³×C₅₃	1	1	yes	characteristic
893	#102	C₂³×C₅₃	1	1	yes	characteristic
894	#102	C₂³×C₅₃	1	1	yes	characteristic
895	#102	C₂³×C₅₃	1	1	yes	characteristic
896	#102	C₂³×C₅₃	1	2	yes	—
897	#102	C₂³×C₅₃	1	2	yes	—
898	#102	C₂³×C₅₃	1	2	yes	—
899	#102	C₂³×C₅₃	1	2	yes	—
900	#102	C₂³×C₅₃	1	2	yes	—
901	#102	C₂³×C₅₃	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
904	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
905	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
906	#97	C₂³×C₅₃	1	2	yes	—
907	#97	C₂³×C₅₃	1	2	yes	—
908	C₄×C₈	C₂³×C₅₃	1	2	yes	—
909	C₄×C₈	C₂³×C₅₃	1	2	yes	—
910	C₂⁴	—	2	2	no	—
911	C₂⁴	—	2	1	no	—
912	C₂⁴	—	2	1	no	—
913	#41	—	2	8	no	—
914	#41	—	2	4	no	—
915	#41	—	2	4	no	—
916	#41	—	2	2	no	—
917	#41	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	#41×C₅₃	1	4	yes	—
920	C₂×Q₈	—	2	1	no	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	2	1	no	—
923	C₂×Q₈	—	2	2	no	—
924	C₂×Q₈	—	2	2	no	—
925	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
927	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
928	C₂×D₄	—	2	16	no	—
929	C₂×D₄	—	2	8	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	4	no	—
933	C₂×D₄	—	2	4	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
943	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
944	C₂×D₄	#41×C₅₃	1	4	yes	—
945	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
946	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
947	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	8	2	no	—
963	C₂²×C₄	—	8	4	no	—
964	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
965	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
966	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
967	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
968	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
969	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
970	Q₁₆	—	2	4	no	—
971	SD₁₆	—	2	4	no	—
972	SD₁₆	—	2	4	no	—
973	SD₁₆	—	2	4	no	—
974	SD₁₆	—	2	4	no	—
975	D₈	—	2	4	no	—
976	D₈	—	2	4	no	—
977	D₈	—	2	4	no	—
978	M₁₆	—	2	2	no	—
979	M₁₆	—	2	2	no	—
980	C₂×C₈	—	2	2	no	—
981	C₂×C₈	—	2	2	no	—
982	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
983	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
984	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
985	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
986	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1004	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1005	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1006	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1007	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1008	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1009	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1010	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1011	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1012	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1036	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1037	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	2	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	2	no	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1048	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1049	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1050	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₅₃	1	2	yes	—
1052	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1053	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1054	C₂³	—	2	8	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	2	4	no	—
1058	C₂³	—	2	2	no	—
1059	C₂³	—	4	2	no	—
1060	C₂³	—	8	1	no	—
1061	C₂³	—	8	2	no	—
1062	C₂³	—	8	1	no	—
1063	C₂³	—	8	2	no	—
1064	C₂³	—	8	1	no	—
1065	C₂³	—	8	1	no	—
1066	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1067	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	2	2	no	—
1071	Q₈	—	2	2	no	—
1072	Q₈	—	4	2	no	—
1073	Q₈	—	8	1	no	—
1074	Q₈	—	8	1	no	—
1075	Q₈	C₂×#41×C₅₃	1	2	yes	—
1076	D₄	—	2	8	no	—
1077	D₄	—	2	8	no	—
1078	D₄	—	2	4	no	—
1079	D₄	—	2	4	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	4	no	—
1082	D₄	—	2	2	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	2	2	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	C₂×#41×C₅₃	1	2	yes	—
1090	D₄	C₂×#41×C₅₃	1	4	yes	—
1091	C₂×C₄	—	2	8	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	4	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	4	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	—	8	1	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1121	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1123	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1125	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1126	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1128	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1129	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1130	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1131	C₈	—	2	1	no	—
1132	C₈	—	2	1	no	—
1133	C₈	—	2	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	2	no	—
1136	C₈	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	4	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	8	4	no	—
1152	C₂²	—	8	8	no	—
1153	C₂²	—	16	2	no	—
1154	C₂²	C₅₃×#525	1	2	yes	—
1155	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1156	C₄	—	2	1	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	C₅₃×#525	1	2	yes	—
1173	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1174	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1175	C₂	—	2	2	no	—
1176	C₂	—	4	2	no	—
1177	C₂	—	4	4	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	2	no	—
1180	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
1181	C₂	C₅₃×#3584	1	1	yes	characteristic
1182	C₂	C₅₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3008	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3510	C₂	semidirect
2. C₄×H(5,𝔽₂)×C₅₃	C₂	semidirect
3. C₅₃×#3125	C₂	semidirect
4. C₅₃×#3124	C₂	semidirect
5. C₅₃×#3118	C₂	semidirect
6. C₅₃×#3118	C₂	semidirect
7. C₅₃×#3114	C₂	semidirect
8. C₅₃×#3111	C₂	semidirect
9. C₅₃×#3105	C₂	semidirect
10. C₅₃×#3102	C₂	semidirect
11. C₅₃×#3097	C₂	semidirect
12. C₅₃×#3096	C₂	semidirect
13. C₅₃×#3077	C₂	semidirect
14. C₅₃×#3076	C₂	semidirect
15. C₅₃×#3040	C₂	semidirect
16. C₂×C₅₃×#463	C₂	semidirect
17. C₅₃×#3009	C₂	semidirect
19. C₅₃×#2949	C₂	semidirect
20. C₅₃×#2948	C₂	semidirect
21. C₅₃×#2947	C₂	semidirect
22. C₅₃×#2946	C₂	semidirect
23. C₅₃×#2925	C₂	semidirect
35. C₅₃×#542	C₂²	semidirect
36. C₅₃×#542	C₂²	semidirect
39. C₅₃×#533	C₂²	semidirect
40. C₅₃×#529	C₂²	semidirect
41. C₅₃×#529	C₂²	semidirect
42. C₂×#124×C₅₃	C₂²	semidirect
46. C₅₃×#520	C₂²	semidirect
47. C₅₃×#519	C₂²	semidirect
51. C₅₃×#518	C₂²	semidirect
52. C₅₃×#518	C₂²	semidirect
56. C₄×#41×C₅₃	C₂²	semidirect
60. C₂×C₄×D₄×C₅₃	C₂²	semidirect
61. C₅₃×#485	C₂²	semidirect
62. C₅₃×#485	C₂²	semidirect
63. C₅₃×#484	C₂²	semidirect
64. C₅₃×#483	C₂²	semidirect
65. C₅₃×#482	C₂²	semidirect
66. C₅₃×#482	C₂²	semidirect
67. C₅₃×#481	C₂²	semidirect
68. C₅₃×#480	C₂²	semidirect
69. C₅₃×#479	C₂²	semidirect
70. C₅₃×#479	C₂²	semidirect
71. C₅₃×#478	C₂²	semidirect
72. C₅₃×#478	C₂²	semidirect
73. C₅₃×#478	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#477	C₂²	semidirect
76. C₅₃×#476	C₂²	semidirect
77. C₅₃×#476	C₂²	semidirect
78. C₅₃×#475	C₂²	semidirect
79. C₅₃×#474	C₂²	semidirect
80. C₅₃×#474	C₂²	semidirect
81. C₅₃×#464	C₂²	semidirect
82. C₅₃×#464	C₂²	semidirect
83. C₅₃×#463	C₂²	semidirect
84. C₅₃×#463	C₂²	semidirect
85. C₅₃×#463	C₂²	semidirect
86. C₅₃×#463	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#452	C₂²	semidirect
90. C₅₃×#452	C₂²	semidirect
91. C₅₃×#450	C₂²	semidirect
92. C₅₃×#450	C₂²	semidirect
97. C₅₃×#442	C₂²	semidirect
98. C₅₃×#442	C₂²	semidirect
99. C₅₃×#442	C₂²	semidirect
100. C₅₃×#441	C₂²	semidirect
101. C₅₃×#440	C₂²	semidirect
102. C₅₃×#440	C₂²	semidirect
103. C₅₃×#440	C₂²	semidirect
104. C₅₃×#440	C₂²	semidirect
105. C₄×Q₁₆×C₅₃	C₂²	semidirect
106. C₄×SD₁₆×C₅₃	C₂²	semidirect
107. C₄×SD₁₆×C₅₃	C₂²	semidirect
108. C₄×SD₁₆×C₅₃	C₂²	semidirect
109. C₄×SD₁₆×C₅₃	C₂²	semidirect
110. C₄×D₈×C₅₃	C₂²	semidirect
111. C₄×D₈×C₅₃	C₂²	semidirect
112. C₄×D₈×C₅₃	C₂²	semidirect
113. C₅₃×#433	C₂²	semidirect
114. C₅₃×#433	C₂²	semidirect
115. C₅₃×#432	C₂²	semidirect
116. C₅₃×#431	C₂²	semidirect
117. C₅₃×#428	C₂²	semidirect
118. C₅₃×#428	C₂²	semidirect
119. C₅₃×#427	C₂²	semidirect
120. C₅₃×#427	C₂²	semidirect
121. C₅₃×#423	C₂²	semidirect
122. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
123. C₅₃×#419	C₂²	semidirect
126. C₅₃×#418	C₂²	semidirect
129. C₂×#103×C₅₃	C₂²	semidirect
130. C₂×#102×C₅₃	C₂²	semidirect
133. C₅₃×#405	C₂²	semidirect
134. C₅₃×#405	C₂²	semidirect
545. #60592	C₅₃	direct (N × H)
584. #3510	C₂×C₅₃	semidirect
585. C₄×H(5,𝔽₂)	C₂×C₅₃	semidirect
586. #3125	C₂×C₅₃	semidirect
587. #3124	C₂×C₅₃	semidirect
588. #3118	C₂×C₅₃	semidirect
589. #3118	C₂×C₅₃	semidirect
590. #3114	C₂×C₅₃	semidirect
591. #3111	C₂×C₅₃	semidirect
592. #3105	C₂×C₅₃	semidirect
593. #3102	C₂×C₅₃	semidirect
594. #3097	C₂×C₅₃	semidirect
595. #3096	C₂×C₅₃	semidirect
596. #3077	C₂×C₅₃	semidirect
597. #3076	C₂×C₅₃	semidirect
598. #3040	C₂×C₅₃	semidirect
599. C₂×#463	C₂×C₅₃	semidirect
600. #3009	C₂×C₅₃	semidirect
602. #2949	C₂×C₅₃	semidirect
603. #2948	C₂×C₅₃	semidirect
604. #2947	C₂×C₅₃	semidirect
605. #2946	C₂×C₅₃	semidirect
606. #2925	C₂×C₅₃	semidirect
626. #542	C₂²×C₅₃	semidirect
627. #542	C₂²×C₅₃	semidirect
630. #533	C₂²×C₅₃	semidirect
631. #529	C₂²×C₅₃	semidirect
632. #529	C₂²×C₅₃	semidirect
633. C₂×#124	C₂²×C₅₃	semidirect
637. #520	C₂²×C₅₃	semidirect
638. #519	C₂²×C₅₃	semidirect
642. #518	C₂²×C₅₃	semidirect
643. #518	C₂²×C₅₃	semidirect
647. C₄×#41	C₂²×C₅₃	semidirect
651. C₂×C₄×D₄	C₂²×C₅₃	semidirect
652. #485	C₂²×C₅₃	semidirect
653. #485	C₂²×C₅₃	semidirect
654. #484	C₂²×C₅₃	semidirect
655. #483	C₂²×C₅₃	semidirect
656. #482	C₂²×C₅₃	semidirect
657. #482	C₂²×C₅₃	semidirect
658. #481	C₂²×C₅₃	semidirect
659. #480	C₂²×C₅₃	semidirect
660. #479	C₂²×C₅₃	semidirect
661. #479	C₂²×C₅₃	semidirect
662. #478	C₂²×C₅₃	semidirect
663. #478	C₂²×C₅₃	semidirect
664. #478	C₂²×C₅₃	semidirect
665. #478	C₂²×C₅₃	semidirect
666. #477	C₂²×C₅₃	semidirect
667. #476	C₂²×C₅₃	semidirect
668. #476	C₂²×C₅₃	semidirect
669. #475	C₂²×C₅₃	semidirect
670. #474	C₂²×C₅₃	semidirect
671. #474	C₂²×C₅₃	semidirect
672. #464	C₂²×C₅₃	semidirect
673. #464	C₂²×C₅₃	semidirect
674. #463	C₂²×C₅₃	semidirect
675. #463	C₂²×C₅₃	semidirect
676. #463	C₂²×C₅₃	semidirect
677. #463	C₂²×C₅₃	semidirect
678. #463	C₂²×C₅₃	semidirect
679. #463	C₂²×C₅₃	semidirect
680. #452	C₂²×C₅₃	semidirect
681. #452	C₂²×C₅₃	semidirect
682. #450	C₂²×C₅₃	semidirect
683. #450	C₂²×C₅₃	semidirect
688. #442	C₂²×C₅₃	semidirect
689. #442	C₂²×C₅₃	semidirect
690. #442	C₂²×C₅₃	semidirect
691. #441	C₂²×C₅₃	semidirect
692. #440	C₂²×C₅₃	semidirect
693. #440	C₂²×C₅₃	semidirect
694. #440	C₂²×C₅₃	semidirect
695. #440	C₂²×C₅₃	semidirect
696. C₄×Q₁₆	C₂²×C₅₃	semidirect
697. C₄×SD₁₆	C₂²×C₅₃	semidirect
698. C₄×SD₁₆	C₂²×C₅₃	semidirect
699. C₄×SD₁₆	C₂²×C₅₃	semidirect
700. C₄×SD₁₆	C₂²×C₅₃	semidirect
701. C₄×D₈	C₂²×C₅₃	semidirect
702. C₄×D₈	C₂²×C₅₃	semidirect
703. C₄×D₈	C₂²×C₅₃	semidirect
704. #433	C₂²×C₅₃	semidirect
705. #433	C₂²×C₅₃	semidirect
706. #432	C₂²×C₅₃	semidirect
707. #431	C₂²×C₅₃	semidirect
708. #428	C₂²×C₅₃	semidirect
709. #428	C₂²×C₅₃	semidirect
710. #427	C₂²×C₅₃	semidirect
711. #427	C₂²×C₅₃	semidirect
712. #423	C₂²×C₅₃	semidirect
713. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
714. #419	C₂²×C₅₃	semidirect
717. #418	C₂²×C₅₃	semidirect
720. C₂×#103	C₂²×C₅₃	semidirect
721. C₂×#102	C₂²×C₅₃	semidirect
724. #405	C₂²×C₅₃	semidirect
725. #405	C₂²×C₅₃	semidirect
726. C₅₃	#60592	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×#3510	2
C₄×H(5,𝔽₂)×C₅₃	2
C₅₃×#3125	2
C₅₃×#3124	2
C₅₃×#3118	2
C₅₃×#3114	2
C₅₃×#3111	2
C₅₃×#3105	2
C₅₃×#3102	2
C₅₃×#3097	2
C₅₃×#3096	2
C₅₃×#3077	2
C₅₃×#3076	2
C₅₃×#3040	2
C₂×C₅₃×#463	2
C₅₃×#3009	2
C₅₃×#3008	2
C₅₃×#2949	2
C₅₃×#2948	2
C₅₃×#2947	2
C₅₃×#2946	2
C₅₃×#2925	2
#60592	53

Subgroups — C53×#60592 #27268104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60592 #27268104