Subgroups — C₅₃×#61184 #27268696

Order 13568.

2226 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3484	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3324	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3323	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3314	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3311	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3310	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3310	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3296	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3295	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3057	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₅₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₅₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#556	C₂²	1	2	yes	complemented
32	C₅₃×#554	C₂²	1	2	yes	complemented
33	C₅₃×#552	—	2	2	no	—
34	C₅₃×#552	C₂²	1	2	yes	complemented
35	C₅₃×#552	C₂²	1	2	yes	complemented
36	C₅₃×#551	—	2	2	no	—
37	C₅₃×#546	—	2	1	no	—
38	C₅₃×#546	—	2	1	no	—
39	C₅₃×#546	C₂²	1	2	yes	—
40	C₅₃×#546	C₂²	1	2	yes	—
41	D₄²×C₅₃	—	2	1	no	—
42	D₄²×C₅₃	—	2	1	no	—
43	D₄²×C₅₃	C₂²	1	2	yes	—
44	D₄²×C₅₃	C₂²	1	2	yes	—
45	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#542	—	2	1	no	—
47	C₅₃×#541	—	2	1	no	—
48	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#535	C₂²	1	1	yes	characteristic
50	C₅₃×#535	C₂²	1	1	yes	characteristic
51	C₅₃×#534	—	2	2	no	—
52	C₅₃×#533	—	2	1	no	—
53	C₅₃×#529	—	2	1	no	—
54	C₅₃×#525	C₂²	1	1	yes	characteristic
55	C₅₃×#525	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×#120×C₅₃	—	2	2	no	—
58	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#519	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#518	C₂²	1	1	yes	characteristic
61	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#490	C₂²	1	2	yes	complemented
63	C₅₃×#489	C₂²	1	2	yes	complemented
64	C₅₃×#488	C₂²	1	2	yes	complemented
65	C₅₃×#486	C₂²	1	2	yes	complemented
66	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#482	C₂²	1	2	yes	complemented
73	C₅₃×#482	C₂²	1	2	yes	complemented
74	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#481	C₂²	1	2	yes	complemented
76	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#480	C₂²	1	2	yes	complemented
78	C₅₃×#478	C₂²	1	2	yes	complemented
79	C₅₃×#478	C₂²	1	2	yes	complemented
80	C₅₃×#476	C₂²	1	2	yes	complemented
81	C₅₃×#474	C₂²	1	2	yes	complemented
82	C₅₃×#470	C₂²	1	2	yes	complemented
83	C₅₃×#468	C₂²	1	2	yes	complemented
84	C₅₃×#468	C₂²	1	2	yes	complemented
85	C₅₃×#468	C₂²	1	2	yes	complemented
86	C₅₃×#467	C₂²	1	2	yes	complemented
87	C₅₃×#465	C₂²	1	2	yes	complemented
88	C₅₃×#465	C₂²	1	2	yes	complemented
89	C₅₃×#465	C₂²	1	2	yes	complemented
90	C₅₃×#464	C₂²	1	2	yes	complemented
91	C₅₃×#464	C₂²	1	2	yes	complemented
92	C₅₃×#460	C₂²	1	2	yes	complemented
93	C₅₃×#460	C₂²	1	2	yes	complemented
94	C₅₃×#452	C₂²	1	2	yes	complemented
95	C₅₃×#452	C₂²	1	2	yes	complemented
96	C₅₃×#450	C₂²	1	2	yes	complemented
97	C₅₃×#450	C₂²	1	2	yes	complemented
98	C₅₃×#450	C₂²	1	2	yes	complemented
99	C₅₃×#450	C₂²	1	2	yes	complemented
100	C₅₃×#450	C₂²	1	2	yes	complemented
101	C₅₃×#450	C₂²	1	2	yes	complemented
102	C₅₃×#440	C₂²	1	2	yes	complemented
103	C₅₃×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
106	C₅₃×#436	C₂²	1	2	yes	complemented
107	C₅₃×#435	C₂²	1	2	yes	complemented
108	C₅₃×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
110	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#418	C₂²	1	1	yes	characteristic
116	C₅₃×#418	C₂²	1	1	yes	characteristic
117	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#418	C₂²	1	2	yes	complemented
119	C₅₃×#418	C₂²	1	2	yes	complemented
120	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#418	C₂²	1	2	yes	complemented
122	C₅₃×#417	C₂²	1	2	yes	complemented
123	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#416	C₂²	1	2	yes	complemented
125	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
127	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
128	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
129	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
130	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
131	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
132	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂⁵×C₅₃	—	2	1	no	—
136	H(5,𝔽₂)×C₅₃	—	2	4	no	—
137	H(5,𝔽₂)×C₅₃	—	4	2	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
140	C₂×#41×C₅₃	C₂³	1	2	yes	—
141	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₅₃	—	2	4	no	—
144	C₂²×D₄×C₅₃	—	2	2	no	—
145	C₂²×D₄×C₅₃	—	2	1	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	1	no	—
151	C₂²×D₄×C₅₃	—	4	2	no	—
152	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
153	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
154	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
155	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
156	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
158	#137×C₅₃	—	4	2	no	—
159	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	complemented
160	C₂×SD₁₆×C₅₃	—	2	4	no	—
161	C₂×SD₁₆×C₅₃	—	4	2	no	—
162	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
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	complemented
167	#131×C₅₃	—	4	2	no	—
168	C₂×M₁₆×C₅₃	—	4	2	no	—
169	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
172	C₂×M₁₆×C₅₃	C₂³	1	2	yes	complemented
173	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
176	C₂²×C₈×C₅₃	C₂³	1	2	yes	complemented
177	C₄⋊Q₈×C₅₃	—	2	1	no	—
178	C₄⋊Q₈×C₅₃	—	2	1	no	—
179	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
180	#127×C₅₃	—	2	1	no	—
181	#127×C₅₃	C₂³	1	2	yes	—
182	#126×C₅₃	—	2	2	no	—
183	#126×C₅₃	—	2	2	no	—
184	#126×C₅₃	—	2	2	no	—
185	#126×C₅₃	—	2	2	no	—
186	#125×C₅₃	—	2	1	no	—
187	#125×C₅₃	—	2	2	no	—
188	#125×C₅₃	—	2	2	no	—
189	#125×C₅₃	—	2	2	no	—
190	#125×C₅₃	C₂³	1	2	yes	complemented
191	#124×C₅₃	—	2	1	no	—
192	#124×C₅₃	—	2	1	no	—
193	#124×C₅₃	—	2	2	no	—
194	#124×C₅₃	C₂³	1	2	yes	—
195	#123×C₅₃	—	2	2	no	—
196	#123×C₅₃	—	2	2	no	—
197	#123×C₅₃	—	2	2	no	—
198	#123×C₅₃	—	2	2	no	—
199	#123×C₅₃	—	2	2	no	—
200	#123×C₅₃	—	2	1	no	—
201	#123×C₅₃	D₄	1	2	yes	—
202	C₂²⋊Q₈×C₅₃	—	2	2	no	—
203	C₂²⋊Q₈×C₅₃	—	2	2	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	1	no	—
206	C₂²⋊Q₈×C₅₃	—	2	1	no	—
207	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
210	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
214	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
215	#121×C₅₃	—	2	2	no	—
216	#121×C₅₃	—	2	2	no	—
217	#121×C₅₃	—	2	1	no	—
218	#121×C₅₃	—	2	1	no	—
219	#121×C₅₃	—	2	2	no	—
220	#121×C₅₃	—	2	2	no	—
221	#121×C₅₃	D₄	1	1	yes	characteristic
222	#121×C₅₃	D₄	1	1	yes	characteristic
223	#121×C₅₃	C₂³	1	1	yes	characteristic
224	#121×C₅₃	C₂³	1	1	yes	characteristic
225	#121×C₅₃	C₂³	1	2	yes	—
226	#121×C₅₃	C₂³	1	2	yes	—
227	#120×C₅₃	—	2	2	no	—
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	1	no	—
233	#120×C₅₃	—	2	2	no	—
234	#120×C₅₃	—	2	2	no	—
235	#120×C₅₃	—	2	2	no	—
236	#120×C₅₃	D₄	1	2	yes	—
237	C₄×Q₈×C₅₃	—	2	1	no	—
238	C₄×Q₈×C₅₃	—	2	1	no	—
239	C₄×Q₈×C₅₃	—	2	2	no	—
240	C₄×Q₈×C₅₃	—	2	1	no	—
241	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
242	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
243	C₄×D₄×C₅₃	—	2	1	no	—
244	C₄×D₄×C₅₃	—	2	1	no	—
245	C₄×D₄×C₅₃	—	2	1	no	—
246	C₄×D₄×C₅₃	—	2	2	no	—
247	C₄×D₄×C₅₃	—	2	2	no	—
248	C₄×D₄×C₅₃	—	2	1	no	—
249	C₄×D₄×C₅₃	—	2	1	no	—
250	C₄×D₄×C₅₃	C₂³	1	2	yes	—
251	C₄×D₄×C₅₃	C₂³	1	2	yes	—
252	C₄×D₄×C₅₃	C₂³	1	2	yes	—
253	C₄×D₄×C₅₃	C₂³	1	2	yes	—
254	#117×C₅₃	—	2	2	no	—
255	#117×C₅₃	—	2	2	no	—
256	#117×C₅₃	—	2	2	no	—
257	#117×C₅₃	—	2	1	no	—
258	#117×C₅₃	—	2	1	no	—
259	#117×C₅₃	C₂³	1	1	yes	characteristic
260	#117×C₅₃	C₂³	1	1	yes	characteristic
261	#117×C₅₃	C₂³	1	1	yes	characteristic
262	#117×C₅₃	C₂³	1	1	yes	characteristic
263	#117×C₅₃	C₂³	1	1	yes	characteristic
264	#117×C₅₃	C₂³	1	1	yes	characteristic
265	#117×C₅₃	C₂³	1	2	yes	complemented
266	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
267	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
271	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
273	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
275	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
276	C₂×C₄²×C₅₃	—	2	1	no	—
277	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
278	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
279	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
280	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
281	#107×C₅₃	C₂³	1	2	yes	complemented
282	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
283	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
284	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
285	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
286	#106×C₅₃	C₂³	1	2	yes	complemented
287	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
288	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
289	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
290	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
291	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
292	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
293	#103×C₅₃	C₂³	1	2	yes	complemented
294	#103×C₅₃	C₂³	1	2	yes	complemented
295	#103×C₅₃	C₂³	1	2	yes	complemented
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	2	yes	—
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic, complemented
309	#102×C₅₃	C₂³	1	2	yes	complemented
310	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
311	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
312	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
313	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	complemented
318	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	complemented
319	#97×C₅₃	C₂³	1	2	yes	complemented
320	C₄×C₈×C₅₃	C₂³	1	2	yes	complemented
321	C₂⁴×C₅₃	—	2	1	no	—
322	C₂⁴×C₅₃	—	2	2	no	—
323	C₂⁴×C₅₃	—	2	2	no	—
324	C₂⁴×C₅₃	—	2	1	no	—
325	C₂⁴×C₅₃	—	2	2	no	—
326	C₂⁴×C₅₃	—	4	4	no	—
327	C₂⁴×C₅₃	—	8	2	no	—
328	C₂⁴×C₅₃	—	8	2	no	—
329	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
330	#41×C₅₃	—	2	2	no	—
331	#41×C₅₃	—	2	2	no	—
332	#41×C₅₃	—	2	4	no	—
333	#41×C₅₃	—	2	2	no	—
334	#41×C₅₃	—	2	2	no	—
335	#41×C₅₃	—	4	2	no	—
336	#41×C₅₃	—	4	4	no	—
337	C₂×Q₈×C₅₃	—	2	1	no	—
338	C₂×Q₈×C₅₃	—	2	2	no	—
339	C₂×Q₈×C₅₃	—	2	2	no	—
340	C₂×Q₈×C₅₃	—	2	2	no	—
341	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
342	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
343	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
344	C₂×D₄×C₅₃	—	2	4	no	—
345	C₂×D₄×C₅₃	—	2	4	no	—
346	C₂×D₄×C₅₃	—	2	4	no	—
347	C₂×D₄×C₅₃	—	2	1	no	—
348	C₂×D₄×C₅₃	—	2	1	no	—
349	C₂×D₄×C₅₃	—	2	1	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	1	no	—
354	C₂×D₄×C₅₃	—	2	2	no	—
355	C₂×D₄×C₅₃	—	2	2	no	—
356	C₂×D₄×C₅₃	—	2	2	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	2	no	—
362	C₂×D₄×C₅₃	—	2	2	no	—
363	C₂×D₄×C₅₃	—	4	2	no	—
364	C₂×D₄×C₅₃	—	4	2	no	—
365	C₂×D₄×C₅₃	—	4	2	no	—
366	C₂×D₄×C₅₃	—	4	4	no	—
367	C₂×D₄×C₅₃	—	4	4	no	—
368	C₂×D₄×C₅₃	—	4	4	no	—
369	C₂×D₄×C₅₃	—	4	4	no	—
370	C₂×D₄×C₅₃	—	4	8	no	—
371	C₂×D₄×C₅₃	—	8	4	no	—
372	C₂×D₄×C₅₃	—	8	4	no	—
373	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
374	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
375	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
376	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
377	C₂×D₄×C₅₃	#41	1	4	yes	—
378	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
379	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₅₃	—	2	2	no	—
382	C₂²×C₄×C₅₃	—	2	2	no	—
383	C₂²×C₄×C₅₃	—	2	1	no	—
384	C₂²×C₄×C₅₃	—	2	1	no	—
385	C₂²×C₄×C₅₃	—	2	1	no	—
386	C₂²×C₄×C₅₃	—	2	1	no	—
387	C₂²×C₄×C₅₃	—	2	2	no	—
388	C₂²×C₄×C₅₃	—	2	2	no	—
389	C₂²×C₄×C₅₃	—	2	1	no	—
390	C₂²×C₄×C₅₃	—	2	2	no	—
391	C₂²×C₄×C₅₃	—	2	2	no	—
392	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
398	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	Q₁₆×C₅₃	—	4	2	no	—
400	SD₁₆×C₅₃	—	2	4	no	—
401	SD₁₆×C₅₃	—	2	4	no	—
402	SD₁₆×C₅₃	—	4	2	no	—
403	SD₁₆×C₅₃	—	4	2	no	—
404	SD₁₆×C₅₃	—	4	2	no	—
405	M₁₆×C₅₃	—	2	2	no	—
406	M₁₆×C₅₃	—	2	2	no	—
407	M₁₆×C₅₃	—	4	2	no	—
408	M₁₆×C₅₃	—	4	2	no	—
409	C₂×C₈×C₅₃	—	2	2	no	—
410	C₂×C₈×C₅₃	—	2	2	no	—
411	C₂×C₈×C₅₃	—	4	2	no	—
412	C₂×C₈×C₅₃	—	4	2	no	—
413	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
415	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
419	C₄⋊C₄×C₅₃	—	2	2	no	—
420	C₄⋊C₄×C₅₃	—	2	2	no	—
421	C₄⋊C₄×C₅₃	—	2	1	no	—
422	C₄⋊C₄×C₅₃	—	2	1	no	—
423	C₄⋊C₄×C₅₃	—	2	1	no	—
424	C₄⋊C₄×C₅₃	—	2	2	no	—
425	C₄⋊C₄×C₅₃	—	2	2	no	—
426	C₄⋊C₄×C₅₃	—	2	2	no	—
427	C₄⋊C₄×C₅₃	—	2	2	no	—
428	C₄⋊C₄×C₅₃	—	2	2	no	—
429	C₄⋊C₄×C₅₃	—	2	2	no	—
430	C₄⋊C₄×C₅₃	—	2	1	no	—
431	C₄⋊C₄×C₅₃	—	2	1	no	—
432	C₄⋊C₄×C₅₃	—	2	2	no	—
433	C₄⋊C₄×C₅₃	—	2	2	no	—
434	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
437	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
438	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
440	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₂²⋊C₄×C₅₃	—	2	1	no	—
446	C₂²⋊C₄×C₅₃	—	2	1	no	—
447	C₂²⋊C₄×C₅₃	—	2	1	no	—
448	C₂²⋊C₄×C₅₃	—	2	1	no	—
449	C₂²⋊C₄×C₅₃	—	2	1	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	2	no	—
454	C₂²⋊C₄×C₅₃	—	2	2	no	—
455	C₂²⋊C₄×C₅₃	—	2	2	no	—
456	C₂²⋊C₄×C₅₃	—	2	2	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	1	no	—
464	C₂²⋊C₄×C₅₃	—	2	1	no	—
465	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
476	C₄²×C₅₃	—	2	2	no	—
477	C₄²×C₅₃	—	2	1	no	—
478	C₄²×C₅₃	C₂⁴	1	2	yes	—
479	C₂³×C₅₃	—	2	2	no	—
480	C₂³×C₅₃	—	2	2	no	—
481	C₂³×C₅₃	—	2	2	no	—
482	C₂³×C₅₃	—	2	4	no	—
483	C₂³×C₅₃	—	2	1	no	—
484	C₂³×C₅₃	—	2	2	no	—
485	C₂³×C₅₃	—	4	1	no	—
486	C₂³×C₅₃	—	4	4	no	—
487	C₂³×C₅₃	—	4	4	no	—
488	C₂³×C₅₃	—	4	4	no	—
489	C₂³×C₅₃	—	4	4	no	—
490	C₂³×C₅₃	—	4	2	no	—
491	C₂³×C₅₃	—	4	4	no	—
492	C₂³×C₅₃	—	8	1	no	—
493	C₂³×C₅₃	—	8	2	no	—
494	C₂³×C₅₃	—	8	1	no	—
495	C₂³×C₅₃	—	8	1	no	—
496	C₂³×C₅₃	—	8	1	no	—
497	C₂³×C₅₃	—	8	2	no	—
498	C₂³×C₅₃	—	8	2	no	—
499	C₂³×C₅₃	—	8	2	no	—
500	C₂³×C₅₃	—	8	16	no	—
501	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
502	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
503	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
504	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
505	Q₈×C₅₃	—	2	2	no	—
506	Q₈×C₅₃	—	2	2	no	—
507	Q₈×C₅₃	—	2	1	no	—
508	Q₈×C₅₃	—	2	2	no	—
509	Q₈×C₅₃	—	2	1	no	—
510	Q₈×C₅₃	—	4	2	no	—
511	Q₈×C₅₃	—	8	2	no	—
512	D₄×C₅₃	—	2	4	no	—
513	D₄×C₅₃	—	2	4	no	—
514	D₄×C₅₃	—	2	4	no	—
515	D₄×C₅₃	—	2	2	no	—
516	D₄×C₅₃	—	2	2	no	—
517	D₄×C₅₃	—	2	1	no	—
518	D₄×C₅₃	—	2	2	no	—
519	D₄×C₅₃	—	2	2	no	—
520	D₄×C₅₃	—	2	1	no	—
521	D₄×C₅₃	—	4	2	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	2	no	—
527	D₄×C₅₃	—	4	2	no	—
528	D₄×C₅₃	—	4	2	no	—
529	D₄×C₅₃	—	4	2	no	—
530	D₄×C₅₃	—	8	2	no	—
531	D₄×C₅₃	—	8	2	no	—
532	D₄×C₅₃	—	8	2	no	—
533	D₄×C₅₃	—	8	2	no	—
534	D₄×C₅₃	C₂×#41	1	4	yes	—
535	C₂×C₄×C₅₃	—	2	2	no	—
536	C₂×C₄×C₅₃	—	2	2	no	—
537	C₂×C₄×C₅₃	—	2	2	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	2	no	—
541	C₂×C₄×C₅₃	—	2	1	no	—
542	C₂×C₄×C₅₃	—	2	1	no	—
543	C₂×C₄×C₅₃	—	2	2	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	1	no	—
546	C₂×C₄×C₅₃	—	2	1	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	2	2	no	—
549	C₂×C₄×C₅₃	—	2	1	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	—	4	4	no	—
554	C₂×C₄×C₅₃	—	4	2	no	—
555	C₂×C₄×C₅₃	—	4	2	no	—
556	C₂×C₄×C₅₃	—	4	2	no	—
557	C₂×C₄×C₅₃	—	8	2	no	—
558	C₂×C₄×C₅₃	—	8	2	no	—
559	C₂×C₄×C₅₃	—	8	2	no	—
560	C₂×C₄×C₅₃	—	8	1	no	—
561	C₂×C₄×C₅₃	—	8	1	no	—
562	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
563	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
564	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
565	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
569	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
570	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
571	C₈×C₅₃	—	2	1	no	—
572	C₈×C₅₃	—	2	1	no	—
573	C₈×C₅₃	—	2	1	no	—
574	C₈×C₅₃	—	2	1	no	—
575	C₈×C₅₃	—	2	2	no	—
576	C₈×C₅₃	—	2	2	no	—
577	#61184	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
578	C₂²×C₅₃	—	2	1	no	—
579	C₂²×C₅₃	—	2	1	no	—
580	C₂²×C₅₃	—	2	1	no	—
581	C₂²×C₅₃	—	2	1	no	—
582	C₂²×C₅₃	—	2	2	no	—
583	C₂²×C₅₃	—	2	1	no	—
584	C₂²×C₅₃	—	2	1	no	—
585	C₂²×C₅₃	—	2	2	no	—
586	C₂²×C₅₃	—	2	4	no	—
587	C₂²×C₅₃	—	2	2	no	—
588	C₂²×C₅₃	—	2	1	no	—
589	C₂²×C₅₃	—	4	4	no	—
590	C₂²×C₅₃	—	4	2	no	—
591	C₂²×C₅₃	—	4	2	no	—
592	C₂²×C₅₃	—	4	1	no	—
593	C₂²×C₅₃	—	4	2	no	—
594	C₂²×C₅₃	—	4	1	no	—
595	C₂²×C₅₃	—	4	2	no	—
596	C₂²×C₅₃	—	4	1	no	—
597	C₂²×C₅₃	—	4	2	no	—
598	C₂²×C₅₃	—	8	4	no	—
599	C₂²×C₅₃	—	8	8	no	—
600	C₂²×C₅₃	—	8	4	no	—
601	C₂²×C₅₃	—	8	8	no	—
602	C₂²×C₅₃	—	16	4	no	—
603	C₂²×C₅₃	#546	1	2	yes	—
604	C₂²×C₅₃	#577	1	2	yes	—
605	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
606	C₄×C₅₃	—	2	2	no	—
607	C₄×C₅₃	—	2	1	no	—
608	C₄×C₅₃	—	2	1	no	—
609	C₄×C₅₃	—	2	2	no	—
610	C₄×C₅₃	—	2	2	no	—
611	C₄×C₅₃	—	4	1	no	—
612	C₄×C₅₃	—	4	1	no	—
613	C₄×C₅₃	—	4	2	no	—
614	C₄×C₅₃	—	4	1	no	—
615	C₄×C₅₃	—	4	1	no	—
616	C₄×C₅₃	—	4	2	no	—
617	C₄×C₅₃	—	4	1	no	—
618	C₄×C₅₃	—	4	1	no	—
619	C₄×C₅₃	—	4	1	no	—
620	C₄×C₅₃	#546	1	2	yes	—
621	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
622	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
623	#3495	C₂×C₅₃	1	1	yes	characteristic, complemented
624	#3484	C₂×C₅₃	1	1	yes	characteristic
625	#3324	C₂×C₅₃	1	2	yes	complemented
626	#3323	C₂×C₅₃	1	2	yes	complemented
627	#3314	C₂×C₅₃	1	2	yes	complemented
628	#3311	C₂×C₅₃	1	2	yes	complemented
629	#3310	C₂×C₅₃	1	2	yes	complemented
630	#3310	C₂×C₅₃	1	2	yes	complemented
631	#3296	C₂×C₅₃	1	2	yes	complemented
632	#3295	C₂×C₅₃	1	2	yes	complemented
633	#3136	C₂×C₅₃	1	1	yes	characteristic, complemented
634	#3096	C₂×C₅₃	1	1	yes	characteristic, complemented
635	#3091	C₂×C₅₃	1	1	yes	characteristic, complemented
636	#3081	C₂×C₅₃	1	1	yes	characteristic, complemented
637	#3057	C₂×C₅₃	1	1	yes	characteristic, complemented
638	#3056	C₂×C₅₃	1	1	yes	characteristic, complemented
639	#3043	C₂×C₅₃	1	1	yes	characteristic, complemented
640	#3009	C₂×C₅₃	1	1	yes	characteristic, complemented
641	C₂×#450	C₂×C₅₃	1	1	yes	characteristic, complemented
642	#2949	C₂×C₅₃	1	1	yes	characteristic, complemented
643	#2933	C₂×C₅₃	1	1	yes	characteristic, complemented
644	#2897	C₂×C₅₃	1	1	yes	characteristic, complemented
645	C₂×#418	C₂×C₅₃	1	1	yes	characteristic, complemented
646	C₂×C₅₃	—	2	2	no	—
647	C₂×C₅₃	—	2	2	no	—
648	C₂×C₅₃	—	4	1	no	—
649	C₂×C₅₃	—	4	2	no	—
650	C₂×C₅₃	—	4	4	no	—
651	C₂×C₅₃	—	8	2	no	—
652	C₂×C₅₃	—	8	1	no	—
653	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
654	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
655	C₂×C₅₃	#3585	1	1	yes	characteristic
656	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
657	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
658	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
660	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
661	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic, complemented
662	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	#556	C₂²×C₅₃	1	2	yes	complemented
664	#554	C₂²×C₅₃	1	2	yes	complemented
665	#552	—	2	2	no	—
666	#552	C₂²×C₅₃	1	2	yes	complemented
667	#552	C₂²×C₅₃	1	2	yes	complemented
668	#551	—	2	2	no	—
669	#546	—	2	1	no	—
670	#546	—	2	1	no	—
671	#546	C₂²×C₅₃	1	2	yes	—
672	#546	C₂²×C₅₃	1	2	yes	—
673	D₄²	—	2	1	no	—
674	D₄²	—	2	1	no	—
675	D₄²	C₂²×C₅₃	1	2	yes	—
676	D₄²	C₂²×C₅₃	1	2	yes	—
677	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	#542	—	2	1	no	—
679	#541	—	2	1	no	—
680	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	#535	C₂²×C₅₃	1	1	yes	characteristic
682	#535	C₂²×C₅₃	1	1	yes	characteristic
683	#534	—	2	2	no	—
684	#533	—	2	1	no	—
685	#529	—	2	1	no	—
686	#525	C₂²×C₅₃	1	1	yes	characteristic
687	#525	C₂²×C₅₃	1	1	yes	characteristic
688	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	C₂×#120	—	2	2	no	—
690	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
691	#519	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	#518	C₂²×C₅₃	1	1	yes	characteristic
693	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
694	#490	C₂²×C₅₃	1	2	yes	complemented
695	#489	C₂²×C₅₃	1	2	yes	complemented
696	#488	C₂²×C₅₃	1	2	yes	complemented
697	#486	C₂²×C₅₃	1	2	yes	complemented
698	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
699	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
700	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
701	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
702	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
704	#482	C₂²×C₅₃	1	2	yes	complemented
705	#482	C₂²×C₅₃	1	2	yes	complemented
706	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	#481	C₂²×C₅₃	1	2	yes	complemented
708	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#480	C₂²×C₅₃	1	2	yes	complemented
710	#478	C₂²×C₅₃	1	2	yes	complemented
711	#478	C₂²×C₅₃	1	2	yes	complemented
712	#476	C₂²×C₅₃	1	2	yes	complemented
713	#474	C₂²×C₅₃	1	2	yes	complemented
714	#470	C₂²×C₅₃	1	2	yes	complemented
715	#468	C₂²×C₅₃	1	2	yes	complemented
716	#468	C₂²×C₅₃	1	2	yes	complemented
717	#468	C₂²×C₅₃	1	2	yes	complemented
718	#467	C₂²×C₅₃	1	2	yes	complemented
719	#465	C₂²×C₅₃	1	2	yes	complemented
720	#465	C₂²×C₅₃	1	2	yes	complemented
721	#465	C₂²×C₅₃	1	2	yes	complemented
722	#464	C₂²×C₅₃	1	2	yes	complemented
723	#464	C₂²×C₅₃	1	2	yes	complemented
724	#460	C₂²×C₅₃	1	2	yes	complemented
725	#460	C₂²×C₅₃	1	2	yes	complemented
726	#452	C₂²×C₅₃	1	2	yes	complemented
727	#452	C₂²×C₅₃	1	2	yes	complemented
728	#450	C₂²×C₅₃	1	2	yes	complemented
729	#450	C₂²×C₅₃	1	2	yes	complemented
730	#450	C₂²×C₅₃	1	2	yes	complemented
731	#450	C₂²×C₅₃	1	2	yes	complemented
732	#450	C₂²×C₅₃	1	2	yes	complemented
733	#450	C₂²×C₅₃	1	2	yes	complemented
734	#440	C₂²×C₅₃	1	2	yes	complemented
735	#440	C₂²×C₅₃	1	2	yes	complemented
736	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
737	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
738	#436	C₂²×C₅₃	1	2	yes	complemented
739	#435	C₂²×C₅₃	1	2	yes	complemented
740	#435	C₂²×C₅₃	1	2	yes	complemented
741	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
742	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
743	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
744	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
746	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
747	#418	C₂²×C₅₃	1	1	yes	characteristic
748	#418	C₂²×C₅₃	1	1	yes	characteristic
749	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
750	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
751	#418	C₂²×C₅₃	1	2	yes	complemented
752	#418	C₂²×C₅₃	1	2	yes	complemented
753	#418	C₂²×C₅₃	1	2	yes	complemented
754	#417	C₂²×C₅₃	1	2	yes	complemented
755	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
756	#416	C₂²×C₅₃	1	2	yes	complemented
757	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
758	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
759	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
760	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
761	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
762	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
763	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
764	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
765	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
766	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
767	C₅₃	#61184	1	1	yes	characteristic, direct product factor, Sylow
768	C₂⁵	—	2	1	no	—
769	H(5,𝔽₂)	—	2	4	no	—
770	H(5,𝔽₂)	—	4	2	no	—
771	C₂×#41	—	2	1	no	—
772	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
773	C₂×#41	C₂³×C₅₃	1	2	yes	—
774	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
775	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
776	C₂²×D₄	—	2	4	no	—
777	C₂²×D₄	—	2	2	no	—
778	C₂²×D₄	—	2	1	no	—
779	C₂²×D₄	—	2	2	no	—
780	C₂²×D₄	—	2	2	no	—
781	C₂²×D₄	—	2	1	no	—
782	C₂²×D₄	—	2	1	no	—
783	C₂²×D₄	—	2	1	no	—
784	C₂²×D₄	—	4	2	no	—
785	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
786	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
787	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
788	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
789	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
790	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
791	#137	—	4	2	no	—
792	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	complemented
793	C₂×SD₁₆	—	2	4	no	—
794	C₂×SD₁₆	—	4	2	no	—
795	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
796	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
797	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
798	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
799	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	complemented
800	#131	—	4	2	no	—
801	C₂×M₁₆	—	4	2	no	—
802	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
803	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
804	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
805	C₂×M₁₆	C₂³×C₅₃	1	2	yes	complemented
806	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
807	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
808	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
809	C₂²×C₈	C₂³×C₅₃	1	2	yes	complemented
810	C₄⋊Q₈	—	2	1	no	—
811	C₄⋊Q₈	—	2	1	no	—
812	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
813	#127	—	2	1	no	—
814	#127	C₂³×C₅₃	1	2	yes	—
815	#126	—	2	2	no	—
816	#126	—	2	2	no	—
817	#126	—	2	2	no	—
818	#126	—	2	2	no	—
819	#125	—	2	1	no	—
820	#125	—	2	2	no	—
821	#125	—	2	2	no	—
822	#125	—	2	2	no	—
823	#125	C₂³×C₅₃	1	2	yes	complemented
824	#124	—	2	1	no	—
825	#124	—	2	1	no	—
826	#124	—	2	2	no	—
827	#124	C₂³×C₅₃	1	2	yes	—
828	#123	—	2	2	no	—
829	#123	—	2	2	no	—
830	#123	—	2	2	no	—
831	#123	—	2	1	no	—
832	#123	—	2	2	no	—
833	#123	—	2	2	no	—
834	#123	D₄×C₅₃	1	2	yes	—
835	C₂²⋊Q₈	—	2	1	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	2	no	—
838	C₂²⋊Q₈	—	2	2	no	—
839	C₂²⋊Q₈	—	2	2	no	—
840	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
841	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
842	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
843	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
844	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
845	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
846	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
847	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
848	#121	—	2	2	no	—
849	#121	—	2	2	no	—
850	#121	—	2	1	no	—
851	#121	—	2	1	no	—
852	#121	—	2	2	no	—
853	#121	—	2	2	no	—
854	#121	D₄×C₅₃	1	1	yes	characteristic
855	#121	D₄×C₅₃	1	1	yes	characteristic
856	#121	C₂³×C₅₃	1	1	yes	characteristic
857	#121	C₂³×C₅₃	1	1	yes	characteristic
858	#121	C₂³×C₅₃	1	2	yes	—
859	#121	C₂³×C₅₃	1	2	yes	—
860	#120	—	2	1	no	—
861	#120	—	2	2	no	—
862	#120	—	2	2	no	—
863	#120	—	2	2	no	—
864	#120	—	2	2	no	—
865	#120	—	2	2	no	—
866	#120	—	2	2	no	—
867	#120	—	2	2	no	—
868	#120	—	2	2	no	—
869	#120	D₄×C₅₃	1	2	yes	—
870	C₄×Q₈	—	2	1	no	—
871	C₄×Q₈	—	2	1	no	—
872	C₄×Q₈	—	2	1	no	—
873	C₄×Q₈	—	2	2	no	—
874	C₄×Q₈	C₂³×C₅₃	1	2	yes	complemented
875	C₄×Q₈	C₂³×C₅₃	1	2	yes	complemented
876	C₄×D₄	—	2	1	no	—
877	C₄×D₄	—	2	2	no	—
878	C₄×D₄	—	2	2	no	—
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	C₂³×C₅₃	1	2	yes	—
884	C₄×D₄	C₂³×C₅₃	1	2	yes	—
885	C₄×D₄	C₂³×C₅₃	1	2	yes	—
886	C₄×D₄	C₂³×C₅₃	1	2	yes	—
887	#117	—	2	1	no	—
888	#117	—	2	1	no	—
889	#117	—	2	2	no	—
890	#117	—	2	2	no	—
891	#117	—	2	2	no	—
892	#117	C₂³×C₅₃	1	1	yes	characteristic
893	#117	C₂³×C₅₃	1	1	yes	characteristic
894	#117	C₂³×C₅₃	1	1	yes	characteristic
895	#117	C₂³×C₅₃	1	1	yes	characteristic
896	#117	C₂³×C₅₃	1	1	yes	characteristic
897	#117	C₂³×C₅₃	1	1	yes	characteristic
898	#117	C₂³×C₅₃	1	2	yes	complemented
899	C₂×C₄⋊C₄	—	2	1	no	—
900	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
901	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
902	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
903	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
904	C₂×C₂²⋊C₄	—	2	1	no	—
905	C₂×C₂²⋊C₄	—	2	1	no	—
906	C₂×C₂²⋊C₄	—	2	2	no	—
907	C₂×C₂²⋊C₄	—	2	2	no	—
908	C₂×C₂²⋊C₄	—	2	2	no	—
909	C₂×C₄²	—	2	1	no	—
910	#107	C₂³×C₅₃	1	1	yes	characteristic, complemented
911	#107	C₂³×C₅₃	1	1	yes	characteristic, complemented
912	#107	C₂³×C₅₃	1	1	yes	characteristic, complemented
913	#107	C₂³×C₅₃	1	1	yes	characteristic, complemented
914	#107	C₂³×C₅₃	1	2	yes	complemented
915	#106	C₂³×C₅₃	1	1	yes	characteristic, complemented
916	#106	C₂³×C₅₃	1	1	yes	characteristic, complemented
917	#106	C₂³×C₅₃	1	1	yes	characteristic, complemented
918	#106	C₂³×C₅₃	1	1	yes	characteristic, complemented
919	#106	C₂³×C₅₃	1	2	yes	complemented
920	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
921	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
922	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
923	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
924	#103	C₂³×C₅₃	1	2	yes	complemented
925	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
926	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
927	#103	C₂³×C₅₃	1	2	yes	complemented
928	#103	C₂³×C₅₃	1	2	yes	complemented
929	#102	C₂³×C₅₃	1	2	yes	—
930	#102	C₂³×C₅₃	1	2	yes	—
931	#102	C₂³×C₅₃	1	2	yes	—
932	#102	C₂³×C₅₃	1	2	yes	—
933	#102	C₂³×C₅₃	1	2	yes	—
934	#102	C₂³×C₅₃	1	2	yes	—
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	1	yes	characteristic, complemented
942	#102	C₂³×C₅₃	1	2	yes	complemented
943	#102	C₂³×C₅₃	1	1	yes	characteristic, complemented
944	#102	C₂³×C₅₃	1	1	yes	characteristic, complemented
945	#102	C₂³×C₅₃	1	1	yes	characteristic, complemented
946	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
947	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
948	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
949	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
950	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	complemented
951	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	complemented
952	#97	C₂³×C₅₃	1	2	yes	complemented
953	C₄×C₈	C₂³×C₅₃	1	2	yes	complemented
954	C₂⁴	—	2	1	no	—
955	C₂⁴	—	2	2	no	—
956	C₂⁴	—	2	2	no	—
957	C₂⁴	—	2	1	no	—
958	C₂⁴	—	2	2	no	—
959	C₂⁴	—	4	4	no	—
960	C₂⁴	—	8	2	no	—
961	C₂⁴	—	8	2	no	—
962	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
963	#41	—	2	2	no	—
964	#41	—	2	2	no	—
965	#41	—	2	4	no	—
966	#41	—	2	2	no	—
967	#41	—	2	2	no	—
968	#41	—	4	2	no	—
969	#41	—	4	4	no	—
970	C₂×Q₈	—	2	1	no	—
971	C₂×Q₈	—	2	2	no	—
972	C₂×Q₈	—	2	2	no	—
973	C₂×Q₈	—	2	2	no	—
974	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
975	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
976	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
977	C₂×D₄	—	2	4	no	—
978	C₂×D₄	—	2	4	no	—
979	C₂×D₄	—	2	4	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	2	2	no	—
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	2	1	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	2	no	—
996	C₂×D₄	—	4	2	no	—
997	C₂×D₄	—	4	2	no	—
998	C₂×D₄	—	4	2	no	—
999	C₂×D₄	—	4	4	no	—
1000	C₂×D₄	—	4	4	no	—
1001	C₂×D₄	—	4	4	no	—
1002	C₂×D₄	—	4	4	no	—
1003	C₂×D₄	—	4	8	no	—
1004	C₂×D₄	—	8	4	no	—
1005	C₂×D₄	—	8	4	no	—
1006	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1007	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1008	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1009	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1010	C₂×D₄	#41×C₅₃	1	4	yes	—
1011	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1012	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1013	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1014	C₂²×C₄	—	2	2	no	—
1015	C₂²×C₄	—	2	2	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	1	no	—
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	2	1	no	—
1020	C₂²×C₄	—	2	2	no	—
1021	C₂²×C₄	—	2	2	no	—
1022	C₂²×C₄	—	2	1	no	—
1023	C₂²×C₄	—	2	2	no	—
1024	C₂²×C₄	—	2	2	no	—
1025	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1026	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1027	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1028	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1029	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1030	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1031	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1032	Q₁₆	—	4	2	no	—
1033	SD₁₆	—	2	4	no	—
1034	SD₁₆	—	2	4	no	—
1035	SD₁₆	—	4	2	no	—
1036	SD₁₆	—	4	2	no	—
1037	SD₁₆	—	4	2	no	—
1038	M₁₆	—	2	2	no	—
1039	M₁₆	—	2	2	no	—
1040	M₁₆	—	4	2	no	—
1041	M₁₆	—	4	2	no	—
1042	C₂×C₈	—	2	2	no	—
1043	C₂×C₈	—	2	2	no	—
1044	C₂×C₈	—	4	2	no	—
1045	C₂×C₈	—	4	2	no	—
1046	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1047	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1048	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1049	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1050	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1051	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	2	no	—
1067	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1068	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1069	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1070	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1071	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1072	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1073	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1074	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1075	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1076	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1077	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1099	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1100	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1101	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1102	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1103	C₄²	—	2	1	no	—
1104	C₄²	—	2	1	no	—
1105	C₄²	—	2	1	no	—
1106	C₄²	—	2	1	no	—
1107	C₄²	—	2	2	no	—
1108	C₄²	—	2	2	no	—
1109	C₄²	—	2	2	no	—
1110	C₄²	—	2	1	no	—
1111	C₄²	C₂⁴×C₅₃	1	2	yes	—
1112	C₂³	—	2	2	no	—
1113	C₂³	—	2	2	no	—
1114	C₂³	—	2	2	no	—
1115	C₂³	—	2	4	no	—
1116	C₂³	—	2	2	no	—
1117	C₂³	—	2	1	no	—
1118	C₂³	—	4	1	no	—
1119	C₂³	—	4	4	no	—
1120	C₂³	—	4	4	no	—
1121	C₂³	—	4	4	no	—
1122	C₂³	—	4	4	no	—
1123	C₂³	—	4	2	no	—
1124	C₂³	—	4	4	no	—
1125	C₂³	—	8	1	no	—
1126	C₂³	—	8	1	no	—
1127	C₂³	—	8	1	no	—
1128	C₂³	—	8	2	no	—
1129	C₂³	—	8	1	no	—
1130	C₂³	—	8	2	no	—
1131	C₂³	—	8	2	no	—
1132	C₂³	—	8	2	no	—
1133	C₂³	—	8	16	no	—
1134	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1135	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1136	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1137	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1138	Q₈	—	2	2	no	—
1139	Q₈	—	2	2	no	—
1140	Q₈	—	2	1	no	—
1141	Q₈	—	2	2	no	—
1142	Q₈	—	2	1	no	—
1143	Q₈	—	4	2	no	—
1144	Q₈	—	8	2	no	—
1145	D₄	—	2	4	no	—
1146	D₄	—	2	4	no	—
1147	D₄	—	2	4	no	—
1148	D₄	—	2	2	no	—
1149	D₄	—	2	2	no	—
1150	D₄	—	2	1	no	—
1151	D₄	—	2	2	no	—
1152	D₄	—	2	2	no	—
1153	D₄	—	2	1	no	—
1154	D₄	—	4	2	no	—
1155	D₄	—	4	4	no	—
1156	D₄	—	4	4	no	—
1157	D₄	—	4	4	no	—
1158	D₄	—	4	4	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	4	2	no	—
1163	D₄	—	8	2	no	—
1164	D₄	—	8	2	no	—
1165	D₄	—	8	2	no	—
1166	D₄	—	8	2	no	—
1167	D₄	C₂×#41×C₅₃	1	4	yes	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	4	4	no	—
1187	C₂×C₄	—	4	2	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	8	2	no	—
1191	C₂×C₄	—	8	2	no	—
1192	C₂×C₄	—	8	2	no	—
1193	C₂×C₄	—	8	1	no	—
1194	C₂×C₄	—	8	1	no	—
1195	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1196	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1197	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1198	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1199	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1200	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1201	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1202	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1203	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1204	C₈	—	2	1	no	—
1205	C₈	—	2	1	no	—
1206	C₈	—	2	1	no	—
1207	C₈	—	2	1	no	—
1208	C₈	—	2	2	no	—
1209	C₈	—	2	2	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	1	no	—
1212	C₂²	—	2	1	no	—
1213	C₂²	—	2	1	no	—
1214	C₂²	—	2	1	no	—
1215	C₂²	—	2	2	no	—
1216	C₂²	—	2	4	no	—
1217	C₂²	—	2	2	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	2	no	—
1220	C₂²	—	2	1	no	—
1221	C₂²	—	4	4	no	—
1222	C₂²	—	4	2	no	—
1223	C₂²	—	4	2	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	2	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	2	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	2	no	—
1230	C₂²	—	8	4	no	—
1231	C₂²	—	8	8	no	—
1232	C₂²	—	8	4	no	—
1233	C₂²	—	8	8	no	—
1234	C₂²	—	16	4	no	—
1235	C₂²	C₅₃×#546	1	2	yes	—
1236	C₂²	C₅₃×#577	1	2	yes	—
1237	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1238	C₄	—	2	1	no	—
1239	C₄	—	2	1	no	—
1240	C₄	—	2	2	no	—
1241	C₄	—	2	2	no	—
1242	C₄	—	2	2	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	2	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	2	no	—
1251	C₄	—	4	1	no	—
1252	C₄	C₅₃×#546	1	2	yes	—
1253	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1254	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1255	C₂	—	2	2	no	—
1256	C₂	—	2	2	no	—
1257	C₂	—	4	1	no	—
1258	C₂	—	4	2	no	—
1259	C₂	—	4	4	no	—
1260	C₂	—	8	2	no	—
1261	C₂	—	8	1	no	—
1262	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
1263	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1264	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×#3484	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3495	C₂	semidirect
3. C₅₃×#3324	C₂	semidirect
4. C₅₃×#3323	C₂	semidirect
5. C₅₃×#3314	C₂	semidirect
6. C₅₃×#3311	C₂	semidirect
7. C₅₃×#3310	C₂	semidirect
8. C₅₃×#3310	C₂	semidirect
9. C₅₃×#3296	C₂	semidirect
10. C₅₃×#3295	C₂	semidirect
11. C₅₃×#3136	C₂	semidirect
12. C₅₃×#3096	C₂	semidirect
13. C₅₃×#3091	C₂	semidirect
14. C₅₃×#3081	C₂	semidirect
15. C₅₃×#3057	C₂	semidirect
16. C₅₃×#3056	C₂	semidirect
17. C₅₃×#3043	C₂	semidirect
18. C₅₃×#3009	C₂	semidirect
19. C₂×C₅₃×#450	C₂	semidirect
20. C₅₃×#2949	C₂	semidirect
21. C₅₃×#2933	C₂	semidirect
22. C₅₃×#2897	C₂	semidirect
23. C₂×C₅₃×#418	C₂	semidirect
26. C₂×#137×C₅₃	C₂²	semidirect
28. C₂²×SD₁₆×C₅₃	C₂²	semidirect
29. C₂×#131×C₅₃	C₂²	semidirect
30. C₂²×M₁₆×C₅₃	C₂²	semidirect
31. C₅₃×#556	C₂²	semidirect
32. C₅₃×#554	C₂²	semidirect
34. C₅₃×#552	C₂²	semidirect
35. C₅₃×#552	C₂²	semidirect
45. C₅₃×#544	C₂²	semidirect
48. C₅₃×#536	C₂²	semidirect
56. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
58. C₅₃×#520	C₂²	semidirect
59. C₅₃×#519	C₂²	semidirect
61. C₂×#117×C₅₃	C₂²	semidirect
62. C₅₃×#490	C₂²	semidirect
63. C₅₃×#489	C₂²	semidirect
64. C₅₃×#488	C₂²	semidirect
65. C₅₃×#486	C₂²	semidirect
66. C₅₃×#485	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#484	C₂²	semidirect
69. C₅₃×#483	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#482	C₂²	semidirect
73. C₅₃×#482	C₂²	semidirect
74. C₅₃×#481	C₂²	semidirect
75. C₅₃×#481	C₂²	semidirect
76. C₅₃×#480	C₂²	semidirect
77. C₅₃×#480	C₂²	semidirect
78. C₅₃×#478	C₂²	semidirect
79. C₅₃×#478	C₂²	semidirect
80. C₅₃×#476	C₂²	semidirect
81. C₅₃×#474	C₂²	semidirect
82. C₅₃×#470	C₂²	semidirect
83. C₅₃×#468	C₂²	semidirect
84. C₅₃×#468	C₂²	semidirect
85. C₅₃×#468	C₂²	semidirect
86. C₅₃×#467	C₂²	semidirect
87. C₅₃×#465	C₂²	semidirect
88. C₅₃×#465	C₂²	semidirect
89. C₅₃×#465	C₂²	semidirect
90. C₅₃×#464	C₂²	semidirect
91. C₅₃×#464	C₂²	semidirect
92. C₅₃×#460	C₂²	semidirect
93. C₅₃×#460	C₂²	semidirect
94. C₅₃×#452	C₂²	semidirect
95. C₅₃×#452	C₂²	semidirect
96. C₅₃×#450	C₂²	semidirect
97. C₅₃×#450	C₂²	semidirect
98. C₅₃×#450	C₂²	semidirect
99. C₅₃×#450	C₂²	semidirect
100. C₅₃×#450	C₂²	semidirect
101. C₅₃×#450	C₂²	semidirect
102. C₅₃×#440	C₂²	semidirect
103. C₅₃×#440	C₂²	semidirect
104. C₄×SD₁₆×C₅₃	C₂²	semidirect
105. C₄×SD₁₆×C₅₃	C₂²	semidirect
106. C₅₃×#436	C₂²	semidirect
107. C₅₃×#435	C₂²	semidirect
108. C₅₃×#435	C₂²	semidirect
109. C₈×D₄×C₅₃	C₂²	semidirect
110. C₅₃×#428	C₂²	semidirect
111. C₅₃×#427	C₂²	semidirect
112. C₅₃×#427	C₂²	semidirect
113. C₅₃×#424	C₂²	semidirect
114. C₅₃×#419	C₂²	semidirect
117. C₅₃×#418	C₂²	semidirect
118. C₅₃×#418	C₂²	semidirect
119. C₅₃×#418	C₂²	semidirect
120. C₅₃×#418	C₂²	semidirect
121. C₅₃×#418	C₂²	semidirect
122. C₅₃×#417	C₂²	semidirect
123. C₅₃×#417	C₂²	semidirect
124. C₅₃×#416	C₂²	semidirect
125. C₅₃×#416	C₂²	semidirect
126. C₅₃×#416	C₂²	semidirect
128. C₂×#102×C₅₃	C₂²	semidirect
129. C₂×#102×C₅₃	C₂²	semidirect
130. C₂×#102×C₅₃	C₂²	semidirect
131. C₂×#102×C₅₃	C₂²	semidirect
132. C₅₃×#408	C₂²	semidirect
133. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
134. C₅₃×#405	C₂²	semidirect
159. C₂×Q₁₆×C₅₃	C₂³	semidirect
166. C₂×SD₁₆×C₅₃	C₂³	semidirect
172. C₂×M₁₆×C₅₃	C₂³	semidirect
176. C₂²×C₈×C₅₃	C₂³	semidirect
179. C₄⋊Q₈×C₅₃	C₂³	semidirect
190. #125×C₅₃	C₂³	semidirect
213. C₂²⋊Q₈×C₅₃	C₂³	semidirect
214. C₂²⋊Q₈×C₅₃	C₂³	semidirect
241. C₄×Q₈×C₅₃	C₂³	semidirect
242. C₄×Q₈×C₅₃	C₂³	semidirect
265. #117×C₅₃	C₂³	semidirect
270. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
277. #107×C₅₃	C₂³	semidirect
278. #107×C₅₃	C₂³	semidirect
279. #107×C₅₃	C₂³	semidirect
280. #107×C₅₃	C₂³	semidirect
281. #107×C₅₃	C₂³	semidirect
282. #106×C₅₃	C₂³	semidirect
283. #106×C₅₃	C₂³	semidirect
284. #106×C₅₃	C₂³	semidirect
285. #106×C₅₃	C₂³	semidirect
286. #106×C₅₃	C₂³	semidirect
287. C₄⋊C₈×C₅₃	C₂³	semidirect
288. C₄⋊C₈×C₅₃	C₂³	semidirect
289. #103×C₅₃	C₂³	semidirect
290. #103×C₅₃	C₂³	semidirect
291. #103×C₅₃	C₂³	semidirect
292. #103×C₅₃	C₂³	semidirect
293. #103×C₅₃	C₂³	semidirect
294. #103×C₅₃	C₂³	semidirect
295. #103×C₅₃	C₂³	semidirect
308. #102×C₅₃	C₂³	semidirect
309. #102×C₅₃	C₂³	semidirect
310. #102×C₅₃	C₂³	semidirect
311. #102×C₅₃	C₂³	semidirect
312. #102×C₅₃	C₂³	semidirect
317. C₂²⋊C₈×C₅₃	C₂³	semidirect
318. C₂²⋊C₈×C₅₃	C₂³	semidirect
319. #97×C₅₃	C₂³	semidirect
320. C₄×C₈×C₅₃	C₂³	semidirect
577. #61184	C₅₃	direct (N × H)
623. #3495	C₂×C₅₃	semidirect
625. #3324	C₂×C₅₃	semidirect
626. #3323	C₂×C₅₃	semidirect
627. #3314	C₂×C₅₃	semidirect
628. #3311	C₂×C₅₃	semidirect
629. #3310	C₂×C₅₃	semidirect
630. #3310	C₂×C₅₃	semidirect
631. #3296	C₂×C₅₃	semidirect
632. #3295	C₂×C₅₃	semidirect
633. #3136	C₂×C₅₃	semidirect
634. #3096	C₂×C₅₃	semidirect
635. #3091	C₂×C₅₃	semidirect
636. #3081	C₂×C₅₃	semidirect
637. #3057	C₂×C₅₃	semidirect
638. #3056	C₂×C₅₃	semidirect
639. #3043	C₂×C₅₃	semidirect
640. #3009	C₂×C₅₃	semidirect
641. C₂×#450	C₂×C₅₃	semidirect
642. #2949	C₂×C₅₃	semidirect
643. #2933	C₂×C₅₃	semidirect
644. #2897	C₂×C₅₃	semidirect
645. C₂×#418	C₂×C₅₃	semidirect
658. C₂×#137	C₂²×C₅₃	semidirect
660. C₂²×SD₁₆	C₂²×C₅₃	semidirect
661. C₂×#131	C₂²×C₅₃	semidirect
662. C₂²×M₁₆	C₂²×C₅₃	semidirect
663. #556	C₂²×C₅₃	semidirect
664. #554	C₂²×C₅₃	semidirect
666. #552	C₂²×C₅₃	semidirect
667. #552	C₂²×C₅₃	semidirect
677. #544	C₂²×C₅₃	semidirect
680. #536	C₂²×C₅₃	semidirect
688. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
690. #520	C₂²×C₅₃	semidirect
691. #519	C₂²×C₅₃	semidirect
693. C₂×#117	C₂²×C₅₃	semidirect
694. #490	C₂²×C₅₃	semidirect
695. #489	C₂²×C₅₃	semidirect
696. #488	C₂²×C₅₃	semidirect
697. #486	C₂²×C₅₃	semidirect
698. #485	C₂²×C₅₃	semidirect
699. #485	C₂²×C₅₃	semidirect
700. #484	C₂²×C₅₃	semidirect
701. #483	C₂²×C₅₃	semidirect
702. #482	C₂²×C₅₃	semidirect
703. #482	C₂²×C₅₃	semidirect
704. #482	C₂²×C₅₃	semidirect
705. #482	C₂²×C₅₃	semidirect
706. #481	C₂²×C₅₃	semidirect
707. #481	C₂²×C₅₃	semidirect
708. #480	C₂²×C₅₃	semidirect
709. #480	C₂²×C₅₃	semidirect
710. #478	C₂²×C₅₃	semidirect
711. #478	C₂²×C₅₃	semidirect
712. #476	C₂²×C₅₃	semidirect
713. #474	C₂²×C₅₃	semidirect
714. #470	C₂²×C₅₃	semidirect
715. #468	C₂²×C₅₃	semidirect
716. #468	C₂²×C₅₃	semidirect
717. #468	C₂²×C₅₃	semidirect
718. #467	C₂²×C₅₃	semidirect
719. #465	C₂²×C₅₃	semidirect
720. #465	C₂²×C₅₃	semidirect
721. #465	C₂²×C₅₃	semidirect
722. #464	C₂²×C₅₃	semidirect
723. #464	C₂²×C₅₃	semidirect
724. #460	C₂²×C₅₃	semidirect
725. #460	C₂²×C₅₃	semidirect
726. #452	C₂²×C₅₃	semidirect
727. #452	C₂²×C₅₃	semidirect
728. #450	C₂²×C₅₃	semidirect
729. #450	C₂²×C₅₃	semidirect
730. #450	C₂²×C₅₃	semidirect
731. #450	C₂²×C₅₃	semidirect
732. #450	C₂²×C₅₃	semidirect
733. #450	C₂²×C₅₃	semidirect
734. #440	C₂²×C₅₃	semidirect
735. #440	C₂²×C₅₃	semidirect
736. C₄×SD₁₆	C₂²×C₅₃	semidirect
737. C₄×SD₁₆	C₂²×C₅₃	semidirect
738. #436	C₂²×C₅₃	semidirect
739. #435	C₂²×C₅₃	semidirect
740. #435	C₂²×C₅₃	semidirect
741. C₈×D₄	C₂²×C₅₃	semidirect
742. #428	C₂²×C₅₃	semidirect
743. #427	C₂²×C₅₃	semidirect
744. #427	C₂²×C₅₃	semidirect
745. #424	C₂²×C₅₃	semidirect
746. #419	C₂²×C₅₃	semidirect
749. #418	C₂²×C₅₃	semidirect
750. #418	C₂²×C₅₃	semidirect
751. #418	C₂²×C₅₃	semidirect
752. #418	C₂²×C₅₃	semidirect
753. #418	C₂²×C₅₃	semidirect
754. #417	C₂²×C₅₃	semidirect
755. #417	C₂²×C₅₃	semidirect
756. #416	C₂²×C₅₃	semidirect
757. #416	C₂²×C₅₃	semidirect
758. #416	C₂²×C₅₃	semidirect
760. C₂×#102	C₂²×C₅₃	semidirect
761. C₂×#102	C₂²×C₅₃	semidirect
762. C₂×#102	C₂²×C₅₃	semidirect
763. C₂×#102	C₂²×C₅₃	semidirect
764. #408	C₂²×C₅₃	semidirect
765. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
766. #405	C₂²×C₅₃	semidirect
767. C₅₃	#61184	direct (N × H)
792. C₂×Q₁₆	C₂³×C₅₃	semidirect
799. C₂×SD₁₆	C₂³×C₅₃	semidirect
805. C₂×M₁₆	C₂³×C₅₃	semidirect
809. C₂²×C₈	C₂³×C₅₃	semidirect
812. C₄⋊Q₈	C₂³×C₅₃	semidirect
823. #125	C₂³×C₅₃	semidirect
846. C₂²⋊Q₈	C₂³×C₅₃	semidirect
847. C₂²⋊Q₈	C₂³×C₅₃	semidirect
874. C₄×Q₈	C₂³×C₅₃	semidirect
875. C₄×Q₈	C₂³×C₅₃	semidirect
898. #117	C₂³×C₅₃	semidirect
903. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
910. #107	C₂³×C₅₃	semidirect
911. #107	C₂³×C₅₃	semidirect
912. #107	C₂³×C₅₃	semidirect
913. #107	C₂³×C₅₃	semidirect
914. #107	C₂³×C₅₃	semidirect
915. #106	C₂³×C₅₃	semidirect
916. #106	C₂³×C₅₃	semidirect
917. #106	C₂³×C₅₃	semidirect
918. #106	C₂³×C₅₃	semidirect
919. #106	C₂³×C₅₃	semidirect
920. C₄⋊C₈	C₂³×C₅₃	semidirect
921. C₄⋊C₈	C₂³×C₅₃	semidirect
922. #103	C₂³×C₅₃	semidirect
923. #103	C₂³×C₅₃	semidirect
924. #103	C₂³×C₅₃	semidirect
925. #103	C₂³×C₅₃	semidirect
926. #103	C₂³×C₅₃	semidirect
927. #103	C₂³×C₅₃	semidirect
928. #103	C₂³×C₅₃	semidirect
941. #102	C₂³×C₅₃	semidirect
942. #102	C₂³×C₅₃	semidirect
943. #102	C₂³×C₅₃	semidirect
944. #102	C₂³×C₅₃	semidirect
945. #102	C₂³×C₅₃	semidirect
950. C₂²⋊C₈	C₂³×C₅₃	semidirect
951. C₂²⋊C₈	C₂³×C₅₃	semidirect
952. #97	C₂³×C₅₃	semidirect
953. C₄×C₈	C₂³×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3495	2
C₅₃×#3484	2
C₅₃×#3324	2
C₅₃×#3323	2
C₅₃×#3314	2
C₅₃×#3311	2
C₅₃×#3310	2
C₅₃×#3296	2
C₅₃×#3295	2
C₅₃×#3136	2
C₅₃×#3096	2
C₅₃×#3091	2
C₅₃×#3081	2
C₅₃×#3057	2
C₅₃×#3056	2
C₅₃×#3043	2
C₅₃×#3009	2
C₂×C₅₃×#450	2
C₅₃×#2949	2
C₅₃×#2933	2
C₅₃×#2897	2
C₂×C₅₃×#418	2
#61184	53

Subgroups — C53×#61184 #27268696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61184 #27268696