Subgroups — C₅₃×#61657 #27269169

Order 13568.

2174 conjugacy classes of subgroups.

The subgroup lattice has 1272 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×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3322	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3297	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3280	C₂	1	2	yes	maximal, complemented
11	D₄×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3273	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3203	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3198	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3100	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×#2979	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, complemented
34	C₅₃×#547	—	2	1	no	—
35	C₅₃×#547	C₂²	1	1	yes	characteristic
36	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#546	—	2	2	no	—
39	C₅₃×#546	—	2	1	no	—
40	C₅₃×#546	C₂²	1	2	yes	complemented
41	C₅₃×#546	C₂²	1	2	yes	complemented
42	C₅₃×#546	C₂²	1	2	yes	complemented
43	D₄²×C₅₃	—	2	1	no	—
44	D₄²×C₅₃	C₂²	1	1	yes	characteristic
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×#537	C₂²	1	2	yes	complemented
51	C₅₃×#535	—	2	1	no	—
52	C₅₃×#535	C₂²	1	2	yes	complemented
53	C₅₃×#534	—	2	2	no	—
54	C₅₃×#532	C₂²	1	1	yes	characteristic
55	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
58	C₂×#121×C₅₃	—	2	1	no	—
59	C₂×#121×C₅₃	—	2	1	no	—
60	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#495	C₂²	1	2	yes	complemented
62	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#488	C₂²	1	2	yes	complemented
65	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#485	C₂²	1	2	yes	complemented
68	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#484	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#480	C₂²	1	2	yes	complemented
73	C₅₃×#480	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#474	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×#468	C₂²	1	2	yes	complemented
80	C₅₃×#468	C₂²	1	2	yes	complemented
81	C₅₃×#468	C₂²	1	2	yes	complemented
82	C₅₃×#467	C₂²	1	2	yes	complemented
83	C₅₃×#466	C₂²	1	2	yes	complemented
84	C₅₃×#466	C₂²	1	2	yes	complemented
85	C₅₃×#465	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	1	yes	characteristic, complemented
89	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#452	C₂²	1	2	yes	complemented
97	C₅₃×#452	C₂²	1	2	yes	complemented
98	C₅₃×#452	C₂²	1	2	yes	complemented
99	C₅₃×#450	C₂²	1	2	yes	complemented
100	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#450	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×#449	C₂²	1	2	yes	complemented
108	C₅₃×#449	C₂²	1	2	yes	complemented
109	C₅₃×#447	C₂²	1	1	yes	characteristic
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	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
121	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#436	C₂²	1	2	yes	complemented
123	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
126	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#431	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	2	yes	—
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	1	no	—
151	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
152	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
153	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
154	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
155	C₂³×C₄×C₅₃	—	2	1	no	—
156	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
157	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
158	#135×C₅₃	—	4	4	no	—
159	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
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×D₈×C₅₃	—	4	4	no	—
167	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
168	C₂×D₈×C₅₃	C₂³	1	2	yes	—
169	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
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×M₁₆×C₅₃	C₂³	1	2	yes	—
175	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
176	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
177	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
178	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
179	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
180	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
181	#127×C₅₃	—	2	1	no	—
182	#127×C₅₃	—	2	2	no	—
183	#127×C₅₃	D₄	1	1	yes	characteristic
184	#127×C₅₃	C₂³	1	1	yes	characteristic
185	#127×C₅₃	C₂³	1	1	yes	characteristic
186	#126×C₅₃	—	2	2	no	—
187	#126×C₅₃	—	2	2	no	—
188	#126×C₅₃	—	2	1	no	—
189	#125×C₅₃	C₂³	1	1	yes	characteristic
190	#124×C₅₃	—	2	1	no	—
191	#124×C₅₃	—	2	2	no	—
192	#124×C₅₃	—	2	1	no	—
193	#124×C₅₃	D₄	1	2	yes	—
194	#124×C₅₃	C₂³	1	2	yes	—
195	#124×C₅₃	C₂³	1	1	yes	characteristic
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	2	no	—
201	#123×C₅₃	—	2	2	no	—
202	#123×C₅₃	—	2	2	no	—
203	#123×C₅₃	—	2	1	no	—
204	C₂²⋊Q₈×C₅₃	—	2	1	no	—
205	C₂²⋊Q₈×C₅₃	—	2	2	no	—
206	C₂²⋊Q₈×C₅₃	—	2	2	no	—
207	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
208	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
209	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	—	2	1	no	—
213	#121×C₅₃	—	2	1	no	—
214	#121×C₅₃	—	2	2	no	—
215	#121×C₅₃	—	2	2	no	—
216	#121×C₅₃	—	2	2	no	—
217	#121×C₅₃	—	2	2	no	—
218	#121×C₅₃	—	2	2	no	—
219	#121×C₅₃	—	2	2	no	—
220	#121×C₅₃	—	2	1	no	—
221	#121×C₅₃	—	2	1	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	—	2	1	no	—
229	#121×C₅₃	—	2	1	no	—
230	#121×C₅₃	D₄	1	1	yes	characteristic
231	#121×C₅₃	D₄	1	1	yes	characteristic
232	#121×C₅₃	D₄	1	2	yes	—
233	#121×C₅₃	C₂³	1	1	yes	characteristic
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	C₄×Q₈×C₅₃	—	2	1	no	—
249	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₅₃	—	2	1	no	—
251	C₄×D₄×C₅₃	—	2	2	no	—
252	C₄×D₄×C₅₃	—	2	1	no	—
253	C₄×D₄×C₅₃	—	2	1	no	—
254	C₄×D₄×C₅₃	—	2	1	no	—
255	C₄×D₄×C₅₃	—	2	1	no	—
256	C₄×D₄×C₅₃	—	2	1	no	—
257	C₄×D₄×C₅₃	—	2	1	no	—
258	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₅₃	C₂³	1	2	yes	—
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	#117×C₅₃	—	2	1	no	—
268	#117×C₅₃	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
270	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
271	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
273	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
276	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
277	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
278	#107×C₅₃	C₂³	1	2	yes	—
279	#107×C₅₃	C₂³	1	1	yes	characteristic
280	#107×C₅₃	C₂³	1	2	yes	—
281	#107×C₅₃	C₂³	1	1	yes	characteristic
282	#106×C₅₃	C₂³	1	1	yes	characteristic
283	#106×C₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	2	yes	—
306	#102×C₅₃	C₂³	1	2	yes	—
307	#102×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
315	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₅₃	C₂³	1	2	yes	—
318	C₂⁴×C₅₃	—	2	1	no	—
319	C₂⁴×C₅₃	—	2	2	no	—
320	C₂⁴×C₅₃	—	2	2	no	—
321	C₂⁴×C₅₃	—	2	2	no	—
322	#41×C₅₃	—	2	4	no	—
323	#41×C₅₃	—	2	4	no	—
324	#41×C₅₃	—	4	2	no	—
325	#41×C₅₃	—	4	2	no	—
326	#41×C₅₃	—	4	2	no	—
327	#41×C₅₃	—	4	2	no	—
328	#41×C₅₃	—	4	2	no	—
329	#41×C₅₃	—	4	2	no	—
330	#41×C₅₃	—	4	2	no	—
331	#41×C₅₃	—	4	2	no	—
332	#41×C₅₃	—	4	8	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	2	yes	—
338	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₅₃	—	2	2	no	—
340	C₂×D₄×C₅₃	—	2	2	no	—
341	C₂×D₄×C₅₃	—	2	4	no	—
342	C₂×D₄×C₅₃	—	2	4	no	—
343	C₂×D₄×C₅₃	—	2	2	no	—
344	C₂×D₄×C₅₃	—	2	2	no	—
345	C₂×D₄×C₅₃	—	2	2	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	—	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	1	no	—
356	C₂×D₄×C₅₃	—	2	1	no	—
357	C₂×D₄×C₅₃	—	2	2	no	—
358	C₂×D₄×C₅₃	—	2	2	no	—
359	C₂×D₄×C₅₃	—	2	1	no	—
360	C₂×D₄×C₅₃	—	2	1	no	—
361	C₂×D₄×C₅₃	—	2	2	no	—
362	C₂×D₄×C₅₃	—	4	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	8	no	—
367	C₂×D₄×C₅₃	—	4	8	no	—
368	C₂×D₄×C₅₃	—	4	8	no	—
369	C₂×D₄×C₅₃	—	8	2	no	—
370	C₂×D₄×C₅₃	—	8	2	no	—
371	C₂×D₄×C₅₃	—	8	2	no	—
372	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
375	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
376	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
377	C₂×D₄×C₅₃	C₂×D₄	1	2	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	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	—	2	1	no	—
384	C₂²×C₄×C₅₃	—	2	2	no	—
385	C₂²×C₄×C₅₃	—	2	2	no	—
386	C₂²×C₄×C₅₃	—	2	2	no	—
387	C₂²×C₄×C₅₃	—	2	1	no	—
388	C₂²×C₄×C₅₃	—	2	1	no	—
389	C₂²×C₄×C₅₃	—	2	1	no	—
390	C₂²×C₄×C₅₃	—	2	2	no	—
391	C₂²×C₄×C₅₃	—	2	1	no	—
392	C₂²×C₄×C₅₃	—	2	1	no	—
393	C₂²×C₄×C₅₃	—	2	2	no	—
394	C₂²×C₄×C₅₃	—	2	2	no	—
395	C₂²×C₄×C₅₃	—	8	2	no	—
396	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
400	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
401	Q₁₆×C₅₃	—	4	2	no	—
402	SD₁₆×C₅₃	—	2	2	no	—
403	SD₁₆×C₅₃	—	2	2	no	—
404	SD₁₆×C₅₃	—	4	2	no	—
405	SD₁₆×C₅₃	—	4	2	no	—
406	SD₁₆×C₅₃	—	4	2	no	—
407	SD₁₆×C₅₃	—	4	2	no	—
408	D₈×C₅₃	—	2	2	no	—
409	D₈×C₅₃	—	2	4	no	—
410	D₈×C₅₃	—	2	2	no	—
411	D₈×C₅₃	—	2	4	no	—
412	D₈×C₅₃	—	4	2	no	—
413	D₈×C₅₃	—	4	2	no	—
414	D₈×C₅₃	—	4	2	no	—
415	M₁₆×C₅₃	—	4	2	no	—
416	M₁₆×C₅₃	—	4	2	no	—
417	C₂×C₈×C₅₃	—	4	2	no	—
418	C₂×C₈×C₅₃	—	4	2	no	—
419	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
421	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
423	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₅₃	—	2	1	no	—
426	C₄⋊C₄×C₅₃	—	2	2	no	—
427	C₄⋊C₄×C₅₃	—	2	2	no	—
428	C₄⋊C₄×C₅₃	—	2	1	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	1	no	—
433	C₄⋊C₄×C₅₃	—	2	1	no	—
434	C₄⋊C₄×C₅₃	—	2	1	no	—
435	C₄⋊C₄×C₅₃	—	2	2	no	—
436	C₄⋊C₄×C₅₃	—	2	1	no	—
437	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₅₃	C₂×D₄	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	2	yes	—
443	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₂²⋊C₄×C₅₃	—	2	2	no	—
446	C₂²⋊C₄×C₅₃	—	2	2	no	—
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	—	2	2	no	—
449	C₂²⋊C₄×C₅₃	—	2	1	no	—
450	C₂²⋊C₄×C₅₃	—	2	2	no	—
451	C₂²⋊C₄×C₅₃	—	2	1	no	—
452	C₂²⋊C₄×C₅₃	—	2	1	no	—
453	C₂²⋊C₄×C₅₃	—	2	1	no	—
454	C₂²⋊C₄×C₅₃	—	2	1	no	—
455	C₂²⋊C₄×C₅₃	—	2	1	no	—
456	C₂²⋊C₄×C₅₃	—	2	2	no	—
457	C₂²⋊C₄×C₅₃	—	2	2	no	—
458	C₂²⋊C₄×C₅₃	—	2	2	no	—
459	C₂²⋊C₄×C₅₃	—	2	1	no	—
460	C₂²⋊C₄×C₅₃	—	2	1	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	2	no	—
465	C₂²⋊C₄×C₅₃	—	2	1	no	—
466	C₂²⋊C₄×C₅₃	—	2	2	no	—
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	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
471	C₄²×C₅₃	—	2	1	no	—
472	C₄²×C₅₃	—	2	2	no	—
473	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
474	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
475	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
476	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
477	C₂³×C₅₃	—	2	4	no	—
478	C₂³×C₅₃	—	2	1	no	—
479	C₂³×C₅₃	—	2	1	no	—
480	C₂³×C₅₃	—	2	2	no	—
481	C₂³×C₅₃	—	2	2	no	—
482	C₂³×C₅₃	—	2	1	no	—
483	C₂³×C₅₃	—	4	4	no	—
484	C₂³×C₅₃	—	4	4	no	—
485	C₂³×C₅₃	—	8	1	no	—
486	C₂³×C₅₃	—	8	1	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	C₂²×D₄	1	1	yes	characteristic
495	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
496	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
497	Q₈×C₅₃	—	2	2	no	—
498	Q₈×C₅₃	—	2	2	no	—
499	Q₈×C₅₃	—	2	1	no	—
500	Q₈×C₅₃	—	2	1	no	—
501	Q₈×C₅₃	—	4	2	no	—
502	Q₈×C₅₃	—	4	2	no	—
503	D₄×C₅₃	—	2	4	no	—
504	D₄×C₅₃	—	2	2	no	—
505	D₄×C₅₃	—	2	2	no	—
506	D₄×C₅₃	—	2	1	no	—
507	D₄×C₅₃	—	2	1	no	—
508	D₄×C₅₃	—	2	2	no	—
509	D₄×C₅₃	—	2	2	no	—
510	D₄×C₅₃	—	2	1	no	—
511	D₄×C₅₃	—	2	1	no	—
512	D₄×C₅₃	—	2	2	no	—
513	D₄×C₅₃	—	2	2	no	—
514	D₄×C₅₃	—	4	2	no	—
515	D₄×C₅₃	—	4	2	no	—
516	D₄×C₅₃	—	4	2	no	—
517	D₄×C₅₃	—	4	2	no	—
518	D₄×C₅₃	—	4	4	no	—
519	D₄×C₅₃	—	4	4	no	—
520	D₄×C₅₃	—	4	4	no	—
521	D₄×C₅₃	—	4	4	no	—
522	D₄×C₅₃	—	4	4	no	—
523	D₄×C₅₃	—	4	2	no	—
524	D₄×C₅₃	—	4	2	no	—
525	D₄×C₅₃	—	8	1	no	—
526	D₄×C₅₃	—	8	1	no	—
527	D₄×C₅₃	—	8	2	no	—
528	D₄×C₅₃	—	8	1	no	—
529	D₄×C₅₃	—	8	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	—	8	2	no	—
535	D₄×C₅₃	—	8	2	no	—
536	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
537	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
538	C₂×C₄×C₅₃	—	2	2	no	—
539	C₂×C₄×C₅₃	—	2	2	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	1	no	—
542	C₂×C₄×C₅₃	—	2	2	no	—
543	C₂×C₄×C₅₃	—	2	2	no	—
544	C₂×C₄×C₅₃	—	2	2	no	—
545	C₂×C₄×C₅₃	—	2	2	no	—
546	C₂×C₄×C₅₃	—	2	1	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	2	1	no	—
549	C₂×C₄×C₅₃	—	2	2	no	—
550	C₂×C₄×C₅₃	—	2	1	no	—
551	C₂×C₄×C₅₃	—	2	1	no	—
552	C₂×C₄×C₅₃	—	4	1	no	—
553	C₂×C₄×C₅₃	—	4	4	no	—
554	C₂×C₄×C₅₃	—	4	4	no	—
555	C₂×C₄×C₅₃	—	4	4	no	—
556	C₂×C₄×C₅₃	—	4	2	no	—
557	C₂×C₄×C₅₃	—	4	2	no	—
558	C₂×C₄×C₅₃	—	4	2	no	—
559	C₂×C₄×C₅₃	—	8	1	no	—
560	C₂×C₄×C₅₃	—	8	1	no	—
561	C₂×C₄×C₅₃	—	8	2	no	—
562	C₂×C₄×C₅₃	—	8	2	no	—
563	C₂×C₄×C₅₃	—	8	1	no	—
564	C₂×C₄×C₅₃	—	8	2	no	—
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	2	yes	—
568	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
569	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
573	C₈×C₅₃	—	2	1	no	—
574	C₈×C₅₃	—	2	2	no	—
575	C₈×C₅₃	—	2	1	no	—
576	C₈×C₅₃	—	2	1	no	—
577	C₈×C₅₃	—	2	2	no	—
578	C₈×C₅₃	—	2	1	no	—
579	#61657	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
580	C₂²×C₅₃	—	2	1	no	—
581	C₂²×C₅₃	—	2	2	no	—
582	C₂²×C₅₃	—	2	2	no	—
583	C₂²×C₅₃	—	2	1	no	—
584	C₂²×C₅₃	—	2	2	no	—
585	C₂²×C₅₃	—	2	2	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	—	4	1	no	—
592	C₂²×C₅₃	—	4	1	no	—
593	C₂²×C₅₃	—	4	1	no	—
594	C₂²×C₅₃	—	4	1	no	—
595	C₂²×C₅₃	—	4	2	no	—
596	C₂²×C₅₃	—	4	2	no	—
597	C₂²×C₅₃	—	4	1	no	—
598	C₂²×C₅₃	—	4	2	no	—
599	C₂²×C₅₃	—	4	2	no	—
600	C₂²×C₅₃	—	4	1	no	—
601	C₂²×C₅₃	—	4	1	no	—
602	C₂²×C₅₃	—	4	2	no	—
603	C₂²×C₅₃	—	4	2	no	—
604	C₂²×C₅₃	—	8	4	no	—
605	C₂²×C₅₃	—	16	4	no	—
606	C₂²×C₅₃	—	16	4	no	—
607	C₂²×C₅₃	—	16	4	no	—
608	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
609	C₄×C₅₃	—	2	1	no	—
610	C₄×C₅₃	—	2	1	no	—
611	C₄×C₅₃	—	2	1	no	—
612	C₄×C₅₃	—	2	2	no	—
613	C₄×C₅₃	—	2	2	no	—
614	C₄×C₅₃	—	2	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	—	4	1	no	—
621	C₄×C₅₃	—	4	2	no	—
622	C₄×C₅₃	#576	1	2	yes	—
623	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
624	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
625	#3546	C₂×C₅₃	1	1	yes	characteristic, complemented
626	#3496	C₂×C₅₃	1	1	yes	characteristic, complemented
627	#3330	C₂×C₅₃	1	1	yes	characteristic, complemented
628	#3324	C₂×C₅₃	1	1	yes	characteristic, complemented
629	#3322	C₂×C₅₃	1	2	yes	complemented
630	#3302	C₂×C₅₃	1	1	yes	characteristic, complemented
631	#3297	C₂×C₅₃	1	2	yes	complemented
632	#3294	C₂×C₅₃	1	1	yes	characteristic, complemented
633	#3284	C₂×C₅₃	1	1	yes	characteristic, complemented
634	#3280	C₂×C₅₃	1	2	yes	complemented
635	D₄×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
636	#3274	C₂×C₅₃	1	1	yes	characteristic, complemented
637	#3273	C₂×C₅₃	1	2	yes	complemented
638	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
639	#3212	C₂×C₅₃	1	1	yes	characteristic, complemented
640	#3207	C₂×C₅₃	1	1	yes	characteristic, complemented
641	#3203	C₂×C₅₃	1	2	yes	complemented
642	#3198	C₂×C₅₃	1	2	yes	complemented
643	#3105	C₂×C₅₃	1	1	yes	characteristic, complemented
644	#3100	C₂×C₅₃	1	1	yes	characteristic, complemented
645	#3012	C₂×C₅₃	1	2	yes	complemented
646	#3008	C₂×C₅₃	1	2	yes	complemented
647	#2979	C₂×C₅₃	1	1	yes	characteristic, complemented
648	C₂×C₅₃	—	4	1	no	—
649	C₂×C₅₃	—	4	2	no	—
650	C₂×C₅₃	—	4	2	no	—
651	C₂×C₅₃	—	4	2	no	—
652	C₂×C₅₃	—	4	2	no	—
653	C₂×C₅₃	—	8	2	no	—
654	C₂×C₅₃	—	8	2	no	—
655	C₂×C₅₃	—	8	1	no	—
656	C₂×C₅₃	#3484	1	1	yes	characteristic
657	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
658	C₂×C₅₃	#3584	1	1	yes	characteristic
659	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	2	yes	complemented
660	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
661	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
662	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
663	C₂²×D₈	C₂²×C₅₃	1	2	yes	complemented
664	#560	—	2	2	no	—
665	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
666	#553	C₂²×C₅₃	1	2	yes	complemented
667	#550	—	2	1	no	—
668	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
669	#547	—	2	1	no	—
670	#547	C₂²×C₅₃	1	1	yes	characteristic
671	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
672	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	#546	—	2	2	no	—
674	#546	—	2	1	no	—
675	#546	C₂²×C₅₃	1	2	yes	complemented
676	#546	C₂²×C₅₃	1	2	yes	complemented
677	#546	C₂²×C₅₃	1	2	yes	complemented
678	D₄²	—	2	1	no	—
679	D₄²	C₂²×C₅₃	1	1	yes	characteristic
680	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
682	#542	—	2	1	no	—
683	#538	—	2	2	no	—
684	#537	C₂²×C₅₃	1	2	yes	complemented
685	#537	C₂²×C₅₃	1	2	yes	complemented
686	#535	—	2	1	no	—
687	#535	C₂²×C₅₃	1	2	yes	complemented
688	#534	—	2	2	no	—
689	#532	C₂²×C₅₃	1	1	yes	characteristic
690	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
691	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	C₂×#121	—	2	1	no	—
694	C₂×#121	—	2	1	no	—
695	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	#495	C₂²×C₅₃	1	2	yes	complemented
697	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
698	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
699	#488	C₂²×C₅₃	1	2	yes	complemented
700	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
701	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
702	#485	C₂²×C₅₃	1	2	yes	complemented
703	#484	C₂²×C₅₃	1	2	yes	complemented
704	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
705	#482	C₂²×C₅₃	1	2	yes	complemented
706	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	#480	C₂²×C₅₃	1	2	yes	complemented
708	#480	C₂²×C₅₃	1	2	yes	complemented
709	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
710	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
711	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	#469	C₂²×C₅₃	1	2	yes	complemented
714	#468	C₂²×C₅₃	1	2	yes	complemented
715	#468	C₂²×C₅₃	1	2	yes	complemented
716	#468	C₂²×C₅₃	1	2	yes	complemented
717	#467	C₂²×C₅₃	1	2	yes	complemented
718	#466	C₂²×C₅₃	1	2	yes	complemented
719	#466	C₂²×C₅₃	1	2	yes	complemented
720	#465	C₂²×C₅₃	1	2	yes	complemented
721	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	#463	C₂²×C₅₃	1	2	yes	complemented
724	#463	C₂²×C₅₃	1	2	yes	complemented
725	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
726	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
727	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
728	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
729	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
730	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
731	#452	C₂²×C₅₃	1	2	yes	complemented
732	#452	C₂²×C₅₃	1	2	yes	complemented
733	#452	C₂²×C₅₃	1	2	yes	complemented
734	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
735	#450	C₂²×C₅₃	1	2	yes	complemented
736	#450	C₂²×C₅₃	1	2	yes	complemented
737	#449	C₂²×C₅₃	1	2	yes	complemented
738	#449	C₂²×C₅₃	1	2	yes	complemented
739	#449	C₂²×C₅₃	1	2	yes	complemented
740	#449	C₂²×C₅₃	1	2	yes	complemented
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	#447	C₂²×C₅₃	1	1	yes	characteristic
745	#447	C₂²×C₅₃	1	2	yes	complemented
746	#447	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	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
751	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
752	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
753	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
754	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
755	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
756	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
757	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
758	#436	C₂²×C₅₃	1	2	yes	complemented
759	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
760	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
761	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
762	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
763	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
764	#418	C₂²×C₅₃	1	2	yes	complemented
765	#417	C₂²×C₅₃	1	2	yes	complemented
766	#416	C₂²×C₅₃	1	2	yes	complemented
767	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
768	#408	C₂²×C₅₃	1	2	yes	complemented
769	#408	C₂²×C₅₃	1	2	yes	complemented
770	C₅₃	#61657	1	1	yes	characteristic, direct product factor, Sylow
771	H(5,𝔽₂)	—	4	4	no	—
772	H(5,𝔽₂)	—	4	4	no	—
773	C₂×#41	—	2	2	no	—
774	C₂×#41	—	2	1	no	—
775	C₂×#41	—	2	1	no	—
776	C₂×#41	C₂³×C₅₃	1	2	yes	—
777	C₂×#41	C₂³×C₅₃	1	2	yes	—
778	C₂×#41	C₂³×C₅₃	1	2	yes	—
779	C₂×#41	C₂³×C₅₃	1	2	yes	—
780	C₂×#41	C₂³×C₅₃	1	2	yes	—
781	C₂²×D₄	—	2	2	no	—
782	C₂²×D₄	—	2	2	no	—
783	C₂²×D₄	—	2	2	no	—
784	C₂²×D₄	—	2	1	no	—
785	C₂²×D₄	—	2	1	no	—
786	C₂²×D₄	—	2	1	no	—
787	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
788	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
789	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
790	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
791	C₂³×C₄	—	2	1	no	—
792	AGL(1,ℤ/8)	—	4	4	no	—
793	AGL(1,ℤ/8)	—	4	4	no	—
794	#135	—	4	4	no	—
795	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
796	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
797	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
798	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
799	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
800	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
801	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
802	C₂×D₈	—	4	4	no	—
803	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
804	C₂×D₈	C₂³×C₅₃	1	2	yes	—
805	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
806	C₂×D₈	C₂³×C₅₃	1	2	yes	—
807	C₂×D₈	C₂³×C₅₃	1	2	yes	—
808	C₂×D₈	C₂³×C₅₃	1	2	yes	—
809	C₂×D₈	C₂³×C₅₃	1	2	yes	—
810	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
811	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
812	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
813	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
814	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
815	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
816	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
817	#127	—	2	1	no	—
818	#127	—	2	2	no	—
819	#127	D₄×C₅₃	1	1	yes	characteristic
820	#127	C₂³×C₅₃	1	1	yes	characteristic
821	#127	C₂³×C₅₃	1	1	yes	characteristic
822	#126	—	2	2	no	—
823	#126	—	2	2	no	—
824	#126	—	2	1	no	—
825	#125	C₂³×C₅₃	1	1	yes	characteristic
826	#124	—	2	2	no	—
827	#124	—	2	1	no	—
828	#124	—	2	1	no	—
829	#124	D₄×C₅₃	1	2	yes	—
830	#124	C₂³×C₅₃	1	1	yes	characteristic
831	#124	C₂³×C₅₃	1	2	yes	—
832	#123	—	2	1	no	—
833	#123	—	2	2	no	—
834	#123	—	2	2	no	—
835	#123	—	2	2	no	—
836	#123	—	2	2	no	—
837	#123	—	2	2	no	—
838	#123	—	2	2	no	—
839	#123	—	2	2	no	—
840	C₂²⋊Q₈	—	2	2	no	—
841	C₂²⋊Q₈	—	2	2	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
844	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
845	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
846	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
847	#121	—	2	2	no	—
848	#121	—	2	2	no	—
849	#121	—	2	1	no	—
850	#121	—	2	1	no	—
851	#121	—	2	2	no	—
852	#121	—	2	2	no	—
853	#121	—	2	2	no	—
854	#121	—	2	2	no	—
855	#121	—	2	2	no	—
856	#121	—	2	1	no	—
857	#121	—	2	1	no	—
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	1	no	—
862	#121	—	2	2	no	—
863	#121	—	2	2	no	—
864	#121	—	2	2	no	—
865	#121	—	2	2	no	—
866	#121	D₄×C₅₃	1	1	yes	characteristic
867	#121	D₄×C₅₃	1	1	yes	characteristic
868	#121	D₄×C₅₃	1	2	yes	—
869	#121	C₂³×C₅₃	1	1	yes	characteristic
870	#121	C₂³×C₅₃	1	2	yes	—
871	#121	C₂³×C₅₃	1	2	yes	—
872	#121	C₂³×C₅₃	1	2	yes	—
873	#121	C₂³×C₅₃	1	2	yes	—
874	#121	C₂³×C₅₃	1	2	yes	—
875	#121	C₂³×C₅₃	1	2	yes	—
876	#120	—	2	2	no	—
877	#120	—	2	2	no	—
878	#120	—	2	2	no	—
879	#120	—	2	2	no	—
880	#120	—	2	2	no	—
881	#120	—	2	2	no	—
882	#120	—	2	2	no	—
883	#120	—	2	2	no	—
884	C₄×Q₈	—	2	1	no	—
885	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	2	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
895	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
896	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
897	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
898	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
899	C₄×D₄	C₂³×C₅₃	1	2	yes	—
900	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
901	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
902	C₄×D₄	C₂³×C₅₃	1	2	yes	—
903	#117	—	2	1	no	—
904	#117	C₂³×C₅₃	1	2	yes	—
905	C₂×C₄⋊C₄	—	2	1	no	—
906	C₂×C₄⋊C₄	—	2	1	no	—
907	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
908	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
909	C₂×C₂²⋊C₄	—	2	1	no	—
910	C₂×C₂²⋊C₄	—	2	2	no	—
911	C₂×C₂²⋊C₄	—	2	2	no	—
912	C₂×C₂²⋊C₄	—	2	2	no	—
913	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
914	#107	C₂³×C₅₃	1	1	yes	characteristic
915	#107	C₂³×C₅₃	1	2	yes	—
916	#107	C₂³×C₅₃	1	2	yes	—
917	#107	C₂³×C₅₃	1	1	yes	characteristic
918	#106	C₂³×C₅₃	1	1	yes	characteristic
919	#106	C₂³×C₅₃	1	1	yes	characteristic
920	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
921	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
922	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
923	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
924	#103	C₂³×C₅₃	1	2	yes	—
925	#103	C₂³×C₅₃	1	2	yes	—
926	#103	C₂³×C₅₃	1	2	yes	—
927	#103	C₂³×C₅₃	1	2	yes	—
928	#103	C₂³×C₅₃	1	1	yes	characteristic
929	#103	C₂³×C₅₃	1	1	yes	characteristic
930	#102	C₂³×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
935	#102	C₂³×C₅₃	1	1	yes	characteristic
936	#102	C₂³×C₅₃	1	2	yes	—
937	#102	C₂³×C₅₃	1	1	yes	characteristic
938	#102	C₂³×C₅₃	1	2	yes	—
939	#102	C₂³×C₅₃	1	2	yes	—
940	#102	C₂³×C₅₃	1	1	yes	characteristic
941	#102	C₂³×C₅₃	1	2	yes	—
942	#102	C₂³×C₅₃	1	2	yes	—
943	#102	C₂³×C₅₃	1	1	yes	characteristic
944	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
945	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
946	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
947	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
948	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
949	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
950	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
951	C₄×C₈	C₂³×C₅₃	1	2	yes	—
952	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
953	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
954	C₂⁴	—	2	1	no	—
955	C₂⁴	—	2	2	no	—
956	C₂⁴	—	2	2	no	—
957	C₂⁴	—	2	2	no	—
958	#41	—	2	4	no	—
959	#41	—	2	4	no	—
960	#41	—	4	2	no	—
961	#41	—	4	2	no	—
962	#41	—	4	2	no	—
963	#41	—	4	2	no	—
964	#41	—	4	2	no	—
965	#41	—	4	2	no	—
966	#41	—	4	2	no	—
967	#41	—	4	2	no	—
968	#41	—	4	8	no	—
969	#41	—	8	2	no	—
970	#41	—	8	2	no	—
971	C₂×Q₈	—	2	1	no	—
972	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
973	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
974	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	4	no	—
978	C₂×D₄	—	2	4	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	2	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	2	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	1	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	4	2	no	—
999	C₂×D₄	—	4	2	no	—
1000	C₂×D₄	—	4	2	no	—
1001	C₂×D₄	—	4	2	no	—
1002	C₂×D₄	—	4	8	no	—
1003	C₂×D₄	—	4	8	no	—
1004	C₂×D₄	—	4	8	no	—
1005	C₂×D₄	—	8	2	no	—
1006	C₂×D₄	—	8	2	no	—
1007	C₂×D₄	—	8	2	no	—
1008	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1009	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1010	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1011	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1012	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1013	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1014	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1015	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1016	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1017	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1018	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1019	C₂²×C₄	—	2	1	no	—
1020	C₂²×C₄	—	2	2	no	—
1021	C₂²×C₄	—	2	2	no	—
1022	C₂²×C₄	—	2	2	no	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	1	no	—
1026	C₂²×C₄	—	2	2	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	1	no	—
1029	C₂²×C₄	—	2	2	no	—
1030	C₂²×C₄	—	2	2	no	—
1031	C₂²×C₄	—	8	2	no	—
1032	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1033	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1034	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1035	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1036	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1037	Q₁₆	—	4	2	no	—
1038	SD₁₆	—	2	2	no	—
1039	SD₁₆	—	2	2	no	—
1040	SD₁₆	—	4	2	no	—
1041	SD₁₆	—	4	2	no	—
1042	SD₁₆	—	4	2	no	—
1043	SD₁₆	—	4	2	no	—
1044	D₈	—	2	2	no	—
1045	D₈	—	2	4	no	—
1046	D₈	—	2	4	no	—
1047	D₈	—	2	2	no	—
1048	D₈	—	4	2	no	—
1049	D₈	—	4	2	no	—
1050	D₈	—	4	2	no	—
1051	M₁₆	—	4	2	no	—
1052	M₁₆	—	4	2	no	—
1053	C₂×C₈	—	4	2	no	—
1054	C₂×C₈	—	4	2	no	—
1055	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1056	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1057	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1058	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1059	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1060	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1074	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1075	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1076	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1077	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1078	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1079	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1080	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1104	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1105	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1106	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1107	C₄²	—	2	1	no	—
1108	C₄²	—	2	2	no	—
1109	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1110	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1111	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1112	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1113	C₂³	—	2	4	no	—
1114	C₂³	—	2	1	no	—
1115	C₂³	—	2	1	no	—
1116	C₂³	—	2	1	no	—
1117	C₂³	—	2	2	no	—
1118	C₂³	—	2	2	no	—
1119	C₂³	—	4	4	no	—
1120	C₂³	—	4	4	no	—
1121	C₂³	—	8	1	no	—
1122	C₂³	—	8	1	no	—
1123	C₂³	—	8	2	no	—
1124	C₂³	—	8	2	no	—
1125	C₂³	—	8	2	no	—
1126	C₂³	—	8	2	no	—
1127	C₂³	—	8	2	no	—
1128	C₂³	—	8	2	no	—
1129	C₂³	—	8	2	no	—
1130	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1131	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1132	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1133	Q₈	—	2	1	no	—
1134	Q₈	—	2	1	no	—
1135	Q₈	—	2	2	no	—
1136	Q₈	—	2	2	no	—
1137	Q₈	—	4	2	no	—
1138	Q₈	—	4	2	no	—
1139	D₄	—	2	4	no	—
1140	D₄	—	2	2	no	—
1141	D₄	—	2	2	no	—
1142	D₄	—	2	1	no	—
1143	D₄	—	2	1	no	—
1144	D₄	—	2	1	no	—
1145	D₄	—	2	2	no	—
1146	D₄	—	2	2	no	—
1147	D₄	—	2	1	no	—
1148	D₄	—	2	2	no	—
1149	D₄	—	2	2	no	—
1150	D₄	—	4	2	no	—
1151	D₄	—	4	2	no	—
1152	D₄	—	4	2	no	—
1153	D₄	—	4	2	no	—
1154	D₄	—	4	4	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	—	8	1	no	—
1162	D₄	—	8	1	no	—
1163	D₄	—	8	2	no	—
1164	D₄	—	8	1	no	—
1165	D₄	—	8	2	no	—
1166	D₄	—	8	2	no	—
1167	D₄	—	8	2	no	—
1168	D₄	—	8	2	no	—
1169	D₄	—	8	2	no	—
1170	D₄	—	8	2	no	—
1171	D₄	—	8	2	no	—
1172	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1173	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	2	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	2	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	2	no	—
1188	C₂×C₄	—	4	1	no	—
1189	C₂×C₄	—	4	4	no	—
1190	C₂×C₄	—	4	4	no	—
1191	C₂×C₄	—	4	4	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	4	2	no	—
1194	C₂×C₄	—	4	2	no	—
1195	C₂×C₄	—	8	1	no	—
1196	C₂×C₄	—	8	1	no	—
1197	C₂×C₄	—	8	2	no	—
1198	C₂×C₄	—	8	2	no	—
1199	C₂×C₄	—	8	1	no	—
1200	C₂×C₄	—	8	2	no	—
1201	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1202	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1203	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1204	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1205	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1207	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1208	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1209	C₈	—	2	1	no	—
1210	C₈	—	2	2	no	—
1211	C₈	—	2	1	no	—
1212	C₈	—	2	2	no	—
1213	C₈	—	2	1	no	—
1214	C₈	—	2	1	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	2	no	—
1217	C₂²	—	2	2	no	—
1218	C₂²	—	2	2	no	—
1219	C₂²	—	2	2	no	—
1220	C₂²	—	2	1	no	—
1221	C₂²	—	2	2	no	—
1222	C₂²	—	2	2	no	—
1223	C₂²	—	2	1	no	—
1224	C₂²	—	2	2	no	—
1225	C₂²	—	2	2	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	1	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	2	no	—
1231	C₂²	—	4	2	no	—
1232	C₂²	—	4	1	no	—
1233	C₂²	—	4	1	no	—
1234	C₂²	—	4	2	no	—
1235	C₂²	—	4	2	no	—
1236	C₂²	—	4	2	no	—
1237	C₂²	—	4	2	no	—
1238	C₂²	—	4	1	no	—
1239	C₂²	—	8	4	no	—
1240	C₂²	—	16	4	no	—
1241	C₂²	—	16	4	no	—
1242	C₂²	—	16	4	no	—
1243	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1244	C₄	—	2	1	no	—
1245	C₄	—	2	2	no	—
1246	C₄	—	2	2	no	—
1247	C₄	—	2	1	no	—
1248	C₄	—	2	1	no	—
1249	C₄	—	2	1	no	—
1250	C₄	—	4	2	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	2	no	—
1256	C₄	—	4	1	no	—
1257	C₄	C₅₃×#576	1	2	yes	—
1258	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1259	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1260	C₂	—	4	1	no	—
1261	C₂	—	4	2	no	—
1262	C₂	—	4	2	no	—
1263	C₂	—	4	2	no	—
1264	C₂	—	4	2	no	—
1265	C₂	—	8	2	no	—
1266	C₂	—	8	1	no	—
1267	C₂	—	8	2	no	—
1268	C₂	C₅₃×#3484	1	1	yes	characteristic
1269	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1270	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ 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×#3496	C₂	semidirect
3. C₅₃×#3330	C₂	semidirect
4. C₅₃×#3324	C₂	semidirect
5. C₅₃×#3322	C₂	semidirect
6. C₅₃×#3302	C₂	semidirect
7. C₅₃×#3297	C₂	semidirect
8. C₅₃×#3294	C₂	semidirect
9. C₅₃×#3284	C₂	semidirect
10. C₅₃×#3280	C₂	semidirect
11. D₄×D₈×C₅₃	C₂	semidirect
12. C₅₃×#3274	C₂	semidirect
13. C₅₃×#3273	C₂	semidirect
14. C₅₃×#3272	C₂	semidirect
15. C₅₃×#3212	C₂	semidirect
16. C₅₃×#3207	C₂	semidirect
17. C₅₃×#3203	C₂	semidirect
18. C₅₃×#3198	C₂	semidirect
19. C₅₃×#3105	C₂	semidirect
20. C₅₃×#3100	C₂	semidirect
21. C₅₃×#3012	C₂	semidirect
22. C₅₃×#3008	C₂	semidirect
23. C₅₃×#2979	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
33. C₅₃×#550	C₂²	semidirect
36. C₅₃×#547	C₂²	semidirect
37. C₅₃×#547	C₂²	semidirect
40. C₅₃×#546	C₂²	semidirect
41. C₅₃×#546	C₂²	semidirect
42. C₅₃×#546	C₂²	semidirect
45. D₄²×C₅₃	C₂²	semidirect
46. D₄²×C₅₃	C₂²	semidirect
49. C₅₃×#537	C₂²	semidirect
50. C₅₃×#537	C₂²	semidirect
52. C₅₃×#535	C₂²	semidirect
55. C₅₃×#532	C₂²	semidirect
56. C₅₃×#532	C₂²	semidirect
57. C₅₃×#529	C₂²	semidirect
60. C₂×C₄×D₄×C₅₃	C₂²	semidirect
61. C₅₃×#495	C₂²	semidirect
62. C₅₃×#493	C₂²	semidirect
63. C₅₃×#492	C₂²	semidirect
64. C₅₃×#488	C₂²	semidirect
65. C₅₃×#487	C₂²	semidirect
66. C₅₃×#486	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#484	C₂²	semidirect
69. C₅₃×#484	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#481	C₂²	semidirect
72. C₅₃×#480	C₂²	semidirect
73. C₅₃×#480	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#474	C₂²	semidirect
77. C₅₃×#474	C₂²	semidirect
78. C₅₃×#469	C₂²	semidirect
79. C₅₃×#468	C₂²	semidirect
80. C₅₃×#468	C₂²	semidirect
81. C₅₃×#468	C₂²	semidirect
82. C₅₃×#467	C₂²	semidirect
83. C₅₃×#466	C₂²	semidirect
84. C₅₃×#466	C₂²	semidirect
85. C₅₃×#465	C₂²	semidirect
86. C₅₃×#463	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#463	C₂²	semidirect
90. C₅₃×#462	C₂²	semidirect
91. C₅₃×#461	C₂²	semidirect
92. C₅₃×#460	C₂²	semidirect
93. C₅₃×#459	C₂²	semidirect
94. C₅₃×#459	C₂²	semidirect
95. C₅₃×#459	C₂²	semidirect
96. C₅₃×#452	C₂²	semidirect
97. C₅₃×#452	C₂²	semidirect
98. C₅₃×#452	C₂²	semidirect
99. C₅₃×#450	C₂²	semidirect
100. C₅₃×#450	C₂²	semidirect
101. C₅₃×#450	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×#449	C₂²	semidirect
108. C₅₃×#449	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. C₄×SD₁₆×C₅₃	C₂²	semidirect
116. C₄×SD₁₆×C₅₃	C₂²	semidirect
117. C₄×D₈×C₅₃	C₂²	semidirect
118. C₄×D₈×C₅₃	C₂²	semidirect
119. C₄×D₈×C₅₃	C₂²	semidirect
120. C₄×D₈×C₅₃	C₂²	semidirect
121. C₅₃×#436	C₂²	semidirect
122. C₅₃×#436	C₂²	semidirect
123. C₅₃×#436	C₂²	semidirect
124. C₈×D₄×C₅₃	C₂²	semidirect
125. C₈×D₄×C₅₃	C₂²	semidirect
126. C₈×D₄×C₅₃	C₂²	semidirect
127. C₅₃×#431	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
579. #61657	C₅₃	direct (N × H)
625. #3546	C₂×C₅₃	semidirect
626. #3496	C₂×C₅₃	semidirect
627. #3330	C₂×C₅₃	semidirect
628. #3324	C₂×C₅₃	semidirect
629. #3322	C₂×C₅₃	semidirect
630. #3302	C₂×C₅₃	semidirect
631. #3297	C₂×C₅₃	semidirect
632. #3294	C₂×C₅₃	semidirect
633. #3284	C₂×C₅₃	semidirect
634. #3280	C₂×C₅₃	semidirect
635. D₄×D₈	C₂×C₅₃	semidirect
636. #3274	C₂×C₅₃	semidirect
637. #3273	C₂×C₅₃	semidirect
638. #3272	C₂×C₅₃	semidirect
639. #3212	C₂×C₅₃	semidirect
640. #3207	C₂×C₅₃	semidirect
641. #3203	C₂×C₅₃	semidirect
642. #3198	C₂×C₅₃	semidirect
643. #3105	C₂×C₅₃	semidirect
644. #3100	C₂×C₅₃	semidirect
645. #3012	C₂×C₅₃	semidirect
646. #3008	C₂×C₅₃	semidirect
647. #2979	C₂×C₅₃	semidirect
659. C₂×H(5,𝔽₂)	C₂²×C₅₃	semidirect
660. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
661. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
662. C₂×#135	C₂²×C₅₃	semidirect
663. C₂²×D₈	C₂²×C₅₃	semidirect
665. #556	C₂²×C₅₃	semidirect
666. #553	C₂²×C₅₃	semidirect
668. #550	C₂²×C₅₃	semidirect
671. #547	C₂²×C₅₃	semidirect
672. #547	C₂²×C₅₃	semidirect
675. #546	C₂²×C₅₃	semidirect
676. #546	C₂²×C₅₃	semidirect
677. #546	C₂²×C₅₃	semidirect
680. D₄²	C₂²×C₅₃	semidirect
681. D₄²	C₂²×C₅₃	semidirect
684. #537	C₂²×C₅₃	semidirect
685. #537	C₂²×C₅₃	semidirect
687. #535	C₂²×C₅₃	semidirect
690. #532	C₂²×C₅₃	semidirect
691. #532	C₂²×C₅₃	semidirect
692. #529	C₂²×C₅₃	semidirect
695. C₂×C₄×D₄	C₂²×C₅₃	semidirect
696. #495	C₂²×C₅₃	semidirect
697. #493	C₂²×C₅₃	semidirect
698. #492	C₂²×C₅₃	semidirect
699. #488	C₂²×C₅₃	semidirect
700. #487	C₂²×C₅₃	semidirect
701. #486	C₂²×C₅₃	semidirect
702. #485	C₂²×C₅₃	semidirect
703. #484	C₂²×C₅₃	semidirect
704. #484	C₂²×C₅₃	semidirect
705. #482	C₂²×C₅₃	semidirect
706. #481	C₂²×C₅₃	semidirect
707. #480	C₂²×C₅₃	semidirect
708. #480	C₂²×C₅₃	semidirect
709. #478	C₂²×C₅₃	semidirect
710. #478	C₂²×C₅₃	semidirect
711. #474	C₂²×C₅₃	semidirect
712. #474	C₂²×C₅₃	semidirect
713. #469	C₂²×C₅₃	semidirect
714. #468	C₂²×C₅₃	semidirect
715. #468	C₂²×C₅₃	semidirect
716. #468	C₂²×C₅₃	semidirect
717. #467	C₂²×C₅₃	semidirect
718. #466	C₂²×C₅₃	semidirect
719. #466	C₂²×C₅₃	semidirect
720. #465	C₂²×C₅₃	semidirect
721. #463	C₂²×C₅₃	semidirect
722. #463	C₂²×C₅₃	semidirect
723. #463	C₂²×C₅₃	semidirect
724. #463	C₂²×C₅₃	semidirect
725. #462	C₂²×C₅₃	semidirect
726. #461	C₂²×C₅₃	semidirect
727. #460	C₂²×C₅₃	semidirect
728. #459	C₂²×C₅₃	semidirect
729. #459	C₂²×C₅₃	semidirect
730. #459	C₂²×C₅₃	semidirect
731. #452	C₂²×C₅₃	semidirect
732. #452	C₂²×C₅₃	semidirect
733. #452	C₂²×C₅₃	semidirect
734. #450	C₂²×C₅₃	semidirect
735. #450	C₂²×C₅₃	semidirect
736. #450	C₂²×C₅₃	semidirect
737. #449	C₂²×C₅₃	semidirect
738. #449	C₂²×C₅₃	semidirect
739. #449	C₂²×C₅₃	semidirect
740. #449	C₂²×C₅₃	semidirect
741. #449	C₂²×C₅₃	semidirect
742. #449	C₂²×C₅₃	semidirect
743. #449	C₂²×C₅₃	semidirect
745. #447	C₂²×C₅₃	semidirect
746. #447	C₂²×C₅₃	semidirect
747. #447	C₂²×C₅₃	semidirect
748. #447	C₂²×C₅₃	semidirect
749. #447	C₂²×C₅₃	semidirect
750. C₄×SD₁₆	C₂²×C₅₃	semidirect
751. C₄×SD₁₆	C₂²×C₅₃	semidirect
752. C₄×D₈	C₂²×C₅₃	semidirect
753. C₄×D₈	C₂²×C₅₃	semidirect
754. C₄×D₈	C₂²×C₅₃	semidirect
755. C₄×D₈	C₂²×C₅₃	semidirect
756. #436	C₂²×C₅₃	semidirect
757. #436	C₂²×C₅₃	semidirect
758. #436	C₂²×C₅₃	semidirect
759. C₈×D₄	C₂²×C₅₃	semidirect
760. C₈×D₄	C₂²×C₅₃	semidirect
761. C₈×D₄	C₂²×C₅₃	semidirect
762. #431	C₂²×C₅₃	semidirect
763. #431	C₂²×C₅₃	semidirect
764. #418	C₂²×C₅₃	semidirect
765. #417	C₂²×C₅₃	semidirect
766. #416	C₂²×C₅₃	semidirect
767. C₂×#102	C₂²×C₅₃	semidirect
768. #408	C₂²×C₅₃	semidirect
769. #408	C₂²×C₅₃	semidirect
770. C₅₃	#61657	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×#3496	2
C₅₃×#3330	2
C₅₃×#3324	2
C₅₃×#3322	2
C₅₃×#3302	2
C₅₃×#3297	2
C₅₃×#3294	2
C₅₃×#3284	2
C₅₃×#3280	2
D₄×D₈×C₅₃	2
C₅₃×#3274	2
C₅₃×#3273	2
C₅₃×#3272	2
C₅₃×#3212	2
C₅₃×#3207	2
C₅₃×#3203	2
C₅₃×#3198	2
C₅₃×#3105	2
C₅₃×#3100	2
C₅₃×#3012	2
C₅₃×#3008	2
C₅₃×#2979	2
#61657	53

Subgroups — C53×#61657 #27269169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61657 #27269169