Subgroups — C₅₃×#60761 #27268273

Order 13568.

2140 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3204	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3203	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3201	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3201	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3197	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3196	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3191	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3190	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3005	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
33	D₄×Q₈×C₅₃	—	2	1	no	—
34	C₅₃×#548	—	2	1	no	—
35	C₅₃×#547	—	2	2	no	—
36	C₅₃×#547	—	2	1	no	—
37	C₅₃×#546	—	2	2	no	—
38	C₅₃×#546	—	2	1	no	—
39	C₅₃×#537	C₂²	1	2	yes	—
40	C₅₃×#537	C₂²	1	2	yes	—
41	C₅₃×#537	C₂²	1	1	yes	characteristic
42	C₅₃×#537	C₂²	1	2	yes	complemented
43	C₅₃×#536	—	2	1	no	—
44	C₅₃×#536	C₂²	1	1	yes	characteristic
45	C₅₃×#536	C₂²	1	1	yes	characteristic
46	C₅₃×#536	C₂²	1	1	yes	characteristic
47	C₅₃×#536	C₂²	1	2	yes	complemented
48	C₅₃×#535	—	2	1	no	—
49	C₅₃×#535	C₂²	1	1	yes	characteristic
50	C₅₃×#535	C₂²	1	1	yes	characteristic
51	C₅₃×#534	—	2	2	no	—
52	C₅₃×#532	—	2	1	no	—
53	C₅₃×#532	—	2	1	no	—
54	C₅₃×#525	—	2	2	no	—
55	C₅₃×#525	C₂²	1	2	yes	—
56	C₅₃×#525	C₂²	1	2	yes	—
57	C₅₃×#525	C₂²	1	1	yes	characteristic
58	C₅₃×#525	C₂²	1	2	yes	complemented
59	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
61	C₅₃×#520	C₂²	1	1	yes	characteristic
62	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
63	C₅₃×#485	C₂²	1	2	yes	complemented
64	C₅₃×#485	C₂²	1	2	yes	complemented
65	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#485	C₂²	1	2	yes	complemented
67	C₅₃×#485	C₂²	1	2	yes	complemented
68	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#484	C₂²	1	2	yes	complemented
70	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#484	C₂²	1	2	yes	complemented
72	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#483	C₂²	1	2	yes	complemented
74	C₅₃×#483	C₂²	1	2	yes	complemented
75	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#482	C₂²	1	2	yes	complemented
77	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#482	C₂²	1	2	yes	complemented
79	C₅₃×#481	C₂²	1	2	yes	complemented
80	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#480	C₂²	1	2	yes	complemented
83	C₅₃×#470	C₂²	1	2	yes	complemented
84	C₅₃×#470	C₂²	1	2	yes	complemented
85	C₅₃×#470	C₂²	1	2	yes	complemented
86	C₅₃×#469	C₂²	1	2	yes	complemented
87	C₅₃×#468	C₂²	1	2	yes	complemented
88	C₅₃×#468	C₂²	1	2	yes	complemented
89	C₅₃×#468	C₂²	1	2	yes	complemented
90	C₅₃×#468	C₂²	1	2	yes	complemented
91	C₅₃×#467	C₂²	1	2	yes	complemented
92	C₅₃×#467	C₂²	1	2	yes	complemented
93	C₅₃×#467	C₂²	1	2	yes	complemented
94	C₅₃×#466	C₂²	1	2	yes	complemented
95	C₅₃×#465	C₂²	1	2	yes	complemented
96	C₅₃×#465	C₂²	1	2	yes	complemented
97	C₅₃×#465	C₂²	1	2	yes	complemented
98	C₅₃×#465	C₂²	1	2	yes	complemented
99	C₅₃×#452	C₂²	1	2	yes	—
100	C₅₃×#452	C₂²	1	2	yes	—
101	C₅₃×#452	C₂²	1	2	yes	—
102	C₅₃×#452	C₂²	1	2	yes	complemented
103	C₅₃×#452	C₂²	1	2	yes	complemented
104	C₅₃×#452	C₂²	1	2	yes	complemented
105	C₅₃×#452	C₂²	1	2	yes	complemented
106	C₅₃×#452	C₂²	1	2	yes	complemented
107	C₅₃×#451	C₂²	1	2	yes	complemented
108	C₅₃×#451	C₂²	1	2	yes	complemented
109	C₅₃×#449	C₂²	1	2	yes	—
110	C₅₃×#449	C₂²	1	2	yes	complemented
111	C₅₃×#449	C₂²	1	2	yes	complemented
112	C₅₃×#449	C₂²	1	2	yes	complemented
113	C₅₃×#448	C₂²	1	2	yes	complemented
114	C₅₃×#448	C₂²	1	2	yes	complemented
115	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
126	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#408	C₂²	1	1	yes	characteristic
128	C₅₃×#408	C₂²	1	1	yes	characteristic
129	C₅₃×#408	C₂²	1	2	yes	complemented
130	C₅₃×#408	C₂²	1	2	yes	complemented
131	C₅₃×#407	C₂²	1	1	yes	characteristic
132	C₅₃×#407	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
134	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	complemented
135	2₋¹⁺⁴×C₅₃	—	4	2	no	—
136	2₋¹⁺⁴×C₅₃	—	4	2	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	—	2	1	no	—
141	C₂×#41×C₅₃	—	4	2	no	—
142	C₂×#41×C₅₃	—	4	2	no	—
143	C₂×#41×C₅₃	—	4	2	no	—
144	C₂×#41×C₅₃	—	4	2	no	—
145	C₂×#41×C₅₃	D₄	1	2	yes	—
146	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
147	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
148	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×#41×C₅₃	C₂³	1	2	yes	—
150	C₂×#41×C₅₃	C₂³	1	2	yes	—
151	C₂×#41×C₅₃	C₂³	1	2	yes	—
152	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
153	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
154	C₂×#41×C₅₃	C₂³	1	2	yes	—
155	C₂²×Q₈×C₅₃	—	2	1	no	—
156	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
157	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
160	C₂²×D₄×C₅₃	—	2	1	no	—
161	C₂²×D₄×C₅₃	D₄	1	2	yes	—
162	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
163	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
164	C₂³×C₄×C₅₃	—	2	1	no	—
165	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
166	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
167	#137×C₅₃	—	4	2	no	—
168	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
169	C₂×Q₁₆×C₅₃	—	4	2	no	—
170	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
171	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
172	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
173	C₂×SD₁₆×C₅₃	—	4	2	no	—
174	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
175	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
176	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
177	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
178	C₂×D₈×C₅₃	C₂³	1	2	yes	—
179	#131×C₅₃	—	4	2	no	—
180	#131×C₅₃	—	4	2	no	—
181	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
182	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
183	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
184	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
185	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
186	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
187	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
188	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
189	C₄⋊Q₈×C₅₃	—	2	1	no	—
190	C₄⋊Q₈×C₅₃	—	2	1	no	—
191	C₄⋊Q₈×C₅₃	—	2	1	no	—
192	C₄⋊Q₈×C₅₃	—	2	2	no	—
193	#127×C₅₃	—	2	1	no	—
194	#127×C₅₃	—	2	1	no	—
195	#124×C₅₃	—	2	1	no	—
196	#124×C₅₃	—	2	1	no	—
197	#124×C₅₃	—	2	1	no	—
198	#124×C₅₃	—	2	1	no	—
199	#124×C₅₃	—	2	1	no	—
200	#124×C₅₃	—	2	2	no	—
201	#123×C₅₃	—	2	2	no	—
202	#123×C₅₃	—	2	2	no	—
203	#123×C₅₃	—	2	2	no	—
204	#123×C₅₃	—	2	2	no	—
205	#123×C₅₃	—	2	2	no	—
206	#123×C₅₃	—	2	2	no	—
207	#123×C₅₃	—	2	2	no	—
208	#123×C₅₃	—	2	1	no	—
209	#123×C₅₃	—	2	2	no	—
210	C₂²⋊Q₈×C₅₃	—	2	2	no	—
211	C₂²⋊Q₈×C₅₃	—	2	2	no	—
212	C₂²⋊Q₈×C₅₃	—	2	1	no	—
213	C₂²⋊Q₈×C₅₃	—	2	2	no	—
214	C₂²⋊Q₈×C₅₃	—	2	1	no	—
215	C₂²⋊Q₈×C₅₃	—	2	1	no	—
216	C₂²⋊Q₈×C₅₃	—	2	2	no	—
217	C₂²⋊Q₈×C₅₃	—	2	2	no	—
218	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
223	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
225	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
226	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
227	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
229	#121×C₅₃	—	2	2	no	—
230	#121×C₅₃	—	2	2	no	—
231	#121×C₅₃	—	2	2	no	—
232	#121×C₅₃	—	2	2	no	—
233	#121×C₅₃	—	2	2	no	—
234	#121×C₅₃	—	2	2	no	—
235	#121×C₅₃	—	2	2	no	—
236	#121×C₅₃	—	2	1	no	—
237	#121×C₅₃	—	2	2	no	—
238	#121×C₅₃	—	2	2	no	—
239	#121×C₅₃	—	2	2	no	—
240	#121×C₅₃	C₂³	1	1	yes	characteristic
241	#121×C₅₃	C₂³	1	2	yes	—
242	#121×C₅₃	C₂³	1	2	yes	—
243	#121×C₅₃	C₂³	1	2	yes	—
244	#121×C₅₃	C₂³	1	2	yes	—
245	#121×C₅₃	C₂³	1	1	yes	characteristic
246	#121×C₅₃	C₂³	1	2	yes	—
247	#120×C₅₃	—	2	2	no	—
248	#120×C₅₃	—	2	2	no	—
249	#120×C₅₃	—	2	1	no	—
250	#120×C₅₃	—	2	2	no	—
251	#120×C₅₃	—	2	2	no	—
252	#120×C₅₃	—	2	2	no	—
253	C₄×Q₈×C₅₃	—	2	1	no	—
254	C₄×D₄×C₅₃	—	2	2	no	—
255	C₄×D₄×C₅₃	—	2	1	no	—
256	C₄×D₄×C₅₃	—	2	2	no	—
257	C₄×D₄×C₅₃	—	2	2	no	—
258	C₄×D₄×C₅₃	—	2	2	no	—
259	C₄×D₄×C₅₃	—	2	2	no	—
260	C₄×D₄×C₅₃	—	2	1	no	—
261	C₄×D₄×C₅₃	—	2	1	no	—
262	C₄×D₄×C₅₃	—	2	2	no	—
263	C₄×D₄×C₅₃	—	2	2	no	—
264	#117×C₅₃	—	2	1	no	—
265	#117×C₅₃	—	2	1	no	—
266	#117×C₅₃	C₂³	1	1	yes	characteristic
267	#117×C₅₃	C₂³	1	1	yes	characteristic
268	#117×C₅₃	C₂³	1	2	yes	—
269	#117×C₅₃	C₂³	1	1	yes	characteristic
270	#117×C₅₃	C₂³	1	1	yes	characteristic
271	#117×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
273	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
274	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
278	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
279	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
280	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
281	C₂×C₄²×C₅₃	—	2	1	no	—
282	#107×C₅₃	C₂³	1	1	yes	characteristic
283	#107×C₅₃	C₂³	1	2	yes	—
284	#107×C₅₃	C₂³	1	1	yes	characteristic
285	#107×C₅₃	C₂³	1	1	yes	characteristic
286	#107×C₅₃	C₂³	1	2	yes	—
287	#107×C₅₃	C₂³	1	1	yes	characteristic
288	#106×C₅₃	C₂³	1	1	yes	characteristic
289	#106×C₅₃	C₂³	1	2	yes	—
290	#106×C₅₃	C₂³	1	1	yes	characteristic
291	#106×C₅₃	C₂³	1	1	yes	characteristic
292	#106×C₅₃	C₂³	1	2	yes	—
293	#106×C₅₃	C₂³	1	1	yes	characteristic
294	#103×C₅₃	C₂³	1	2	yes	—
295	#103×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	2	yes	—
297	#103×C₅₃	C₂³	1	1	yes	characteristic
298	#103×C₅₃	C₂³	1	1	yes	characteristic
299	#103×C₅₃	C₂³	1	1	yes	characteristic
300	#103×C₅₃	C₂³	1	1	yes	characteristic
301	#103×C₅₃	C₂³	1	2	yes	—
302	#103×C₅₃	C₂³	1	2	yes	—
303	#103×C₅₃	C₂³	1	2	yes	—
304	#103×C₅₃	C₂³	1	2	yes	—
305	#103×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
309	#102×C₅₃	C₂³	1	1	yes	characteristic
310	#102×C₅₃	C₂³	1	1	yes	characteristic
311	#102×C₅₃	C₂³	1	1	yes	characteristic
312	#102×C₅₃	C₂³	1	2	yes	—
313	#102×C₅₃	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
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	—
318	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
319	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
320	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
321	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
322	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
323	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
324	C₂⁴×C₅₃	—	2	1	no	—
325	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
326	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
327	#41×C₅₃	—	2	2	no	—
328	#41×C₅₃	—	2	2	no	—
329	#41×C₅₃	—	2	2	no	—
330	#41×C₅₃	—	2	2	no	—
331	#41×C₅₃	—	2	2	no	—
332	#41×C₅₃	—	2	2	no	—
333	#41×C₅₃	—	4	2	no	—
334	#41×C₅₃	—	4	2	no	—
335	#41×C₅₃	—	4	4	no	—
336	#41×C₅₃	—	4	2	no	—
337	#41×C₅₃	—	4	2	no	—
338	#41×C₅₃	—	4	2	no	—
339	#41×C₅₃	—	4	2	no	—
340	#41×C₅₃	—	4	2	no	—
341	#41×C₅₃	—	4	2	no	—
342	#41×C₅₃	—	4	2	no	—
343	#41×C₅₃	—	4	2	no	—
344	#41×C₅₃	—	4	4	no	—
345	#41×C₅₃	—	4	4	no	—
346	#41×C₅₃	—	4	8	no	—
347	#41×C₅₃	—	4	4	no	—
348	C₂×Q₈×C₅₃	—	2	2	no	—
349	C₂×Q₈×C₅₃	—	2	1	no	—
350	C₂×Q₈×C₅₃	—	2	1	no	—
351	C₂×Q₈×C₅₃	—	2	2	no	—
352	C₂×Q₈×C₅₃	—	2	2	no	—
353	C₂×Q₈×C₅₃	—	2	2	no	—
354	C₂×Q₈×C₅₃	—	2	2	no	—
355	C₂×Q₈×C₅₃	—	4	2	no	—
356	C₂×Q₈×C₅₃	—	4	2	no	—
357	C₂×Q₈×C₅₃	—	4	2	no	—
358	C₂×Q₈×C₅₃	—	4	4	no	—
359	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
360	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
361	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
362	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
363	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
365	C₂×D₄×C₅₃	—	2	1	no	—
366	C₂×D₄×C₅₃	—	2	2	no	—
367	C₂×D₄×C₅₃	—	2	2	no	—
368	C₂×D₄×C₅₃	—	2	1	no	—
369	C₂×D₄×C₅₃	—	2	2	no	—
370	C₂×D₄×C₅₃	—	2	2	no	—
371	C₂×D₄×C₅₃	—	2	2	no	—
372	C₂×D₄×C₅₃	—	2	2	no	—
373	C₂×D₄×C₅₃	—	2	2	no	—
374	C₂×D₄×C₅₃	—	2	1	no	—
375	C₂×D₄×C₅₃	—	2	2	no	—
376	C₂×D₄×C₅₃	—	2	1	no	—
377	C₂×D₄×C₅₃	—	2	2	no	—
378	C₂×D₄×C₅₃	—	2	2	no	—
379	C₂×D₄×C₅₃	—	4	2	no	—
380	C₂×D₄×C₅₃	—	4	4	no	—
381	C₂×D₄×C₅₃	—	4	4	no	—
382	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
383	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
384	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
385	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
386	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
387	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
388	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
389	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₅₃	—	2	2	no	—
392	C₂²×C₄×C₅₃	—	2	2	no	—
393	C₂²×C₄×C₅₃	—	2	2	no	—
394	C₂²×C₄×C₅₃	—	2	1	no	—
395	C₂²×C₄×C₅₃	—	2	1	no	—
396	C₂²×C₄×C₅₃	—	2	1	no	—
397	C₂²×C₄×C₅₃	—	2	1	no	—
398	C₂²×C₄×C₅₃	—	2	2	no	—
399	C₂²×C₄×C₅₃	—	2	1	no	—
400	C₂²×C₄×C₅₃	—	2	2	no	—
401	C₂²×C₄×C₅₃	—	2	2	no	—
402	C₂²×C₄×C₅₃	—	2	1	no	—
403	C₂²×C₄×C₅₃	—	2	2	no	—
404	C₂²×C₄×C₅₃	—	4	2	no	—
405	C₂²×C₄×C₅₃	—	4	2	no	—
406	C₂²×C₄×C₅₃	—	4	4	no	—
407	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
411	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
412	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
413	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
415	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
417	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	Q₁₆×C₅₃	—	4	2	no	—
419	Q₁₆×C₅₃	—	4	2	no	—
420	Q₁₆×C₅₃	—	4	2	no	—
421	SD₁₆×C₅₃	—	4	2	no	—
422	SD₁₆×C₅₃	—	4	2	no	—
423	SD₁₆×C₅₃	—	4	2	no	—
424	SD₁₆×C₅₃	—	4	2	no	—
425	D₈×C₅₃	—	4	2	no	—
426	M₁₆×C₅₃	—	2	2	no	—
427	M₁₆×C₅₃	—	2	2	no	—
428	M₁₆×C₅₃	—	4	2	no	—
429	M₁₆×C₅₃	—	4	2	no	—
430	C₂×C₈×C₅₃	—	2	2	no	—
431	C₂×C₈×C₅₃	—	2	2	no	—
432	C₂×C₈×C₅₃	—	4	2	no	—
433	C₂×C₈×C₅₃	—	4	2	no	—
434	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
435	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
436	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
437	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
438	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
439	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
440	C₄⋊C₄×C₅₃	—	2	2	no	—
441	C₄⋊C₄×C₅₃	—	2	1	no	—
442	C₄⋊C₄×C₅₃	—	2	2	no	—
443	C₄⋊C₄×C₅₃	—	2	2	no	—
444	C₄⋊C₄×C₅₃	—	2	2	no	—
445	C₄⋊C₄×C₅₃	—	2	1	no	—
446	C₄⋊C₄×C₅₃	—	2	1	no	—
447	C₄⋊C₄×C₅₃	—	2	2	no	—
448	C₄⋊C₄×C₅₃	—	2	1	no	—
449	C₄⋊C₄×C₅₃	—	2	2	no	—
450	C₄⋊C₄×C₅₃	—	2	2	no	—
451	C₄⋊C₄×C₅₃	—	2	2	no	—
452	C₄⋊C₄×C₅₃	—	2	2	no	—
453	C₄⋊C₄×C₅₃	—	2	1	no	—
454	C₄⋊C₄×C₅₃	—	2	2	no	—
455	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
456	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
458	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
459	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
460	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
461	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
466	C₂²⋊C₄×C₅₃	—	2	1	no	—
467	C₂²⋊C₄×C₅₃	—	2	1	no	—
468	C₂²⋊C₄×C₅₃	—	2	2	no	—
469	C₂²⋊C₄×C₅₃	—	2	2	no	—
470	C₂²⋊C₄×C₅₃	—	2	2	no	—
471	C₂²⋊C₄×C₅₃	—	2	2	no	—
472	C₂²⋊C₄×C₅₃	—	2	1	no	—
473	C₂²⋊C₄×C₅₃	—	2	2	no	—
474	C₂²⋊C₄×C₅₃	—	2	2	no	—
475	C₂²⋊C₄×C₅₃	—	2	2	no	—
476	C₂²⋊C₄×C₅₃	—	2	2	no	—
477	C₂²⋊C₄×C₅₃	—	2	1	no	—
478	C₂²⋊C₄×C₅₃	—	2	2	no	—
479	C₂²⋊C₄×C₅₃	—	2	1	no	—
480	C₂²⋊C₄×C₅₃	—	2	2	no	—
481	C₂²⋊C₄×C₅₃	—	2	2	no	—
482	C₂²⋊C₄×C₅₃	—	2	2	no	—
483	C₂²⋊C₄×C₅₃	—	2	2	no	—
484	C₂²⋊C₄×C₅₃	—	2	1	no	—
485	C₂²⋊C₄×C₅₃	—	2	2	no	—
486	C₄²×C₅₃	—	2	1	no	—
487	C₄²×C₅₃	—	2	1	no	—
488	C₄²×C₅₃	—	2	1	no	—
489	C₄²×C₅₃	—	2	1	no	—
490	C₄²×C₅₃	—	2	2	no	—
491	C₄²×C₅₃	—	2	1	no	—
492	C₂³×C₅₃	—	2	2	no	—
493	C₂³×C₅₃	—	2	1	no	—
494	C₂³×C₅₃	—	2	2	no	—
495	C₂³×C₅₃	—	4	2	no	—
496	C₂³×C₅₃	—	4	1	no	—
497	C₂³×C₅₃	—	4	1	no	—
498	C₂³×C₅₃	—	4	2	no	—
499	C₂³×C₅₃	—	4	2	no	—
500	C₂³×C₅₃	—	4	2	no	—
501	C₂³×C₅₃	—	8	1	no	—
502	C₂³×C₅₃	—	8	1	no	—
503	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
504	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
505	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
506	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
507	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
508	Q₈×C₅₃	—	2	2	no	—
509	Q₈×C₅₃	—	2	2	no	—
510	Q₈×C₅₃	—	2	2	no	—
511	Q₈×C₅₃	—	2	2	no	—
512	Q₈×C₅₃	—	2	2	no	—
513	Q₈×C₅₃	—	2	2	no	—
514	Q₈×C₅₃	—	2	1	no	—
515	Q₈×C₅₃	—	2	1	no	—
516	Q₈×C₅₃	—	4	2	no	—
517	Q₈×C₅₃	—	4	4	no	—
518	Q₈×C₅₃	—	4	2	no	—
519	Q₈×C₅₃	—	4	2	no	—
520	D₄×C₅₃	—	2	4	no	—
521	D₄×C₅₃	—	2	4	no	—
522	D₄×C₅₃	—	2	2	no	—
523	D₄×C₅₃	—	2	2	no	—
524	D₄×C₅₃	—	2	2	no	—
525	D₄×C₅₃	—	2	2	no	—
526	D₄×C₅₃	—	2	1	no	—
527	D₄×C₅₃	—	2	1	no	—
528	D₄×C₅₃	—	4	2	no	—
529	D₄×C₅₃	—	4	2	no	—
530	D₄×C₅₃	—	4	2	no	—
531	D₄×C₅₃	—	4	2	no	—
532	D₄×C₅₃	—	4	4	no	—
533	D₄×C₅₃	—	4	4	no	—
534	D₄×C₅₃	—	4	4	no	—
535	D₄×C₅₃	—	4	2	no	—
536	D₄×C₅₃	—	4	2	no	—
537	D₄×C₅₃	—	8	1	no	—
538	D₄×C₅₃	—	8	2	no	—
539	D₄×C₅₃	—	8	2	no	—
540	D₄×C₅₃	—	8	2	no	—
541	D₄×C₅₃	—	8	2	no	—
542	D₄×C₅₃	—	8	2	no	—
543	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	1	no	—
550	C₂×C₄×C₅₃	—	2	2	no	—
551	C₂×C₄×C₅₃	—	2	2	no	—
552	C₂×C₄×C₅₃	—	2	2	no	—
553	C₂×C₄×C₅₃	—	2	2	no	—
554	C₂×C₄×C₅₃	—	2	2	no	—
555	C₂×C₄×C₅₃	—	2	2	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	2	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	1	no	—
563	C₂×C₄×C₅₃	—	2	1	no	—
564	C₂×C₄×C₅₃	—	4	2	no	—
565	C₂×C₄×C₅₃	—	4	2	no	—
566	C₂×C₄×C₅₃	—	4	2	no	—
567	C₂×C₄×C₅₃	—	4	4	no	—
568	C₂×C₄×C₅₃	—	4	4	no	—
569	C₂×C₄×C₅₃	—	4	4	no	—
570	C₂×C₄×C₅₃	—	4	4	no	—
571	C₂×C₄×C₅₃	—	4	2	no	—
572	C₂×C₄×C₅₃	—	4	2	no	—
573	C₂×C₄×C₅₃	—	4	2	no	—
574	C₂×C₄×C₅₃	—	8	1	no	—
575	C₂×C₄×C₅₃	—	8	2	no	—
576	C₂×C₄×C₅₃	—	8	1	no	—
577	C₂×C₄×C₅₃	—	8	1	no	—
578	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
581	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
582	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
584	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
585	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
586	C₈×C₅₃	—	2	1	no	—
587	C₈×C₅₃	—	2	1	no	—
588	C₈×C₅₃	—	2	1	no	—
589	C₈×C₅₃	—	2	1	no	—
590	C₈×C₅₃	—	2	2	no	—
591	C₈×C₅₃	—	2	2	no	—
592	#60761	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
593	C₂²×C₅₃	—	2	1	no	—
594	C₂²×C₅₃	—	2	1	no	—
595	C₂²×C₅₃	—	2	1	no	—
596	C₂²×C₅₃	—	2	2	no	—
597	C₂²×C₅₃	—	2	2	no	—
598	C₂²×C₅₃	—	2	1	no	—
599	C₂²×C₅₃	—	2	1	no	—
600	C₂²×C₅₃	—	2	1	no	—
601	C₂²×C₅₃	—	2	2	no	—
602	C₂²×C₅₃	—	2	2	no	—
603	C₂²×C₅₃	—	2	1	no	—
604	C₂²×C₅₃	—	2	1	no	—
605	C₂²×C₅₃	—	2	2	no	—
606	C₂²×C₅₃	—	2	2	no	—
607	C₂²×C₅₃	—	4	1	no	—
608	C₂²×C₅₃	—	4	2	no	—
609	C₂²×C₅₃	—	4	1	no	—
610	C₂²×C₅₃	—	4	2	no	—
611	C₂²×C₅₃	—	4	1	no	—
612	C₂²×C₅₃	—	4	2	no	—
613	C₂²×C₅₃	—	8	2	no	—
614	C₂²×C₅₃	—	8	4	no	—
615	C₂²×C₅₃	—	8	4	no	—
616	C₂²×C₅₃	#534	1	2	yes	—
617	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
618	C₄×C₅₃	—	2	1	no	—
619	C₄×C₅₃	—	2	1	no	—
620	C₄×C₅₃	—	2	2	no	—
621	C₄×C₅₃	—	2	2	no	—
622	C₄×C₅₃	—	4	2	no	—
623	C₄×C₅₃	—	4	1	no	—
624	C₄×C₅₃	—	4	1	no	—
625	C₄×C₅₃	—	4	1	no	—
626	C₄×C₅₃	—	4	1	no	—
627	C₄×C₅₃	—	4	1	no	—
628	C₄×C₅₃	—	4	1	no	—
629	C₄×C₅₃	—	4	2	no	—
630	C₄×C₅₃	—	4	2	no	—
631	C₄×C₅₃	—	4	1	no	—
632	C₄×C₅₃	#534	1	2	yes	—
633	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
634	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
635	#3489	C₂×C₅₃	1	1	yes	characteristic, complemented
636	#3449	C₂×C₅₃	1	1	yes	characteristic, complemented
637	#3204	C₂×C₅₃	1	2	yes	complemented
638	#3203	C₂×C₅₃	1	2	yes	complemented
639	#3201	C₂×C₅₃	1	2	yes	complemented
640	#3201	C₂×C₅₃	1	2	yes	complemented
641	#3197	C₂×C₅₃	1	2	yes	complemented
642	#3196	C₂×C₅₃	1	2	yes	complemented
643	#3191	C₂×C₅₃	1	2	yes	complemented
644	#3190	C₂×C₅₃	1	2	yes	complemented
645	#3097	C₂×C₅₃	1	1	yes	characteristic, complemented
646	#3096	C₂×C₅₃	1	1	yes	characteristic, complemented
647	#3095	C₂×C₅₃	1	1	yes	characteristic, complemented
648	#3091	C₂×C₅₃	1	1	yes	characteristic, complemented
649	#3063	C₂×C₅₃	1	1	yes	characteristic, complemented
650	#3062	C₂×C₅₃	1	1	yes	characteristic, complemented
651	#3059	C₂×C₅₃	1	1	yes	characteristic, complemented
652	#3057	C₂×C₅₃	1	1	yes	characteristic, complemented
653	#3011	C₂×C₅₃	1	1	yes	characteristic, complemented
654	#3010	C₂×C₅₃	1	1	yes	characteristic, complemented
655	#3005	C₂×C₅₃	1	1	yes	characteristic, complemented
656	C₂×#452	C₂×C₅₃	1	1	yes	characteristic, complemented
657	#2880	C₂×C₅₃	1	1	yes	characteristic, complemented
658	C₂×C₅₃	—	2	2	no	—
659	C₂×C₅₃	—	4	1	no	—
660	C₂×C₅₃	—	4	2	no	—
661	C₂×C₅₃	—	4	2	no	—
662	C₂×C₅₃	—	4	1	no	—
663	C₂×C₅₃	—	8	1	no	—
664	C₂×C₅₃	—	8	2	no	—
665	C₂×C₅₃	C₂×#534	1	1	yes	characteristic
666	C₂×C₅₃	#3584	1	1	yes	characteristic
667	C₂×C₅₃	#3586	1	1	yes	characteristic
668	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic
669	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
670	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
671	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
672	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
674	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
675	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
676	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
677	D₄×Q₈	—	2	1	no	—
678	#548	—	2	1	no	—
679	#547	—	2	2	no	—
680	#547	—	2	1	no	—
681	#546	—	2	2	no	—
682	#546	—	2	1	no	—
683	#537	C₂²×C₅₃	1	2	yes	—
684	#537	C₂²×C₅₃	1	2	yes	—
685	#537	C₂²×C₅₃	1	1	yes	characteristic
686	#537	C₂²×C₅₃	1	2	yes	complemented
687	#536	—	2	1	no	—
688	#536	C₂²×C₅₃	1	1	yes	characteristic
689	#536	C₂²×C₅₃	1	1	yes	characteristic
690	#536	C₂²×C₅₃	1	1	yes	characteristic
691	#536	C₂²×C₅₃	1	2	yes	complemented
692	#535	—	2	1	no	—
693	#535	C₂²×C₅₃	1	1	yes	characteristic
694	#535	C₂²×C₅₃	1	1	yes	characteristic
695	#534	—	2	2	no	—
696	#532	—	2	1	no	—
697	#532	—	2	1	no	—
698	#525	—	2	2	no	—
699	#525	C₂²×C₅₃	1	1	yes	characteristic
700	#525	C₂²×C₅₃	1	2	yes	—
701	#525	C₂²×C₅₃	1	2	yes	—
702	#525	C₂²×C₅₃	1	2	yes	complemented
703	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
704	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
705	#520	C₂²×C₅₃	1	1	yes	characteristic
706	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
707	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#485	C₂²×C₅₃	1	2	yes	complemented
710	#485	C₂²×C₅₃	1	2	yes	complemented
711	#485	C₂²×C₅₃	1	2	yes	complemented
712	#485	C₂²×C₅₃	1	2	yes	complemented
713	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
714	#484	C₂²×C₅₃	1	2	yes	complemented
715	#484	C₂²×C₅₃	1	2	yes	complemented
716	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
717	#483	C₂²×C₅₃	1	2	yes	complemented
718	#483	C₂²×C₅₃	1	2	yes	complemented
719	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
720	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
721	#482	C₂²×C₅₃	1	2	yes	complemented
722	#482	C₂²×C₅₃	1	2	yes	complemented
723	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
724	#481	C₂²×C₅₃	1	2	yes	complemented
725	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
726	#480	C₂²×C₅₃	1	2	yes	complemented
727	#470	C₂²×C₅₃	1	2	yes	complemented
728	#470	C₂²×C₅₃	1	2	yes	complemented
729	#470	C₂²×C₅₃	1	2	yes	complemented
730	#469	C₂²×C₅₃	1	2	yes	complemented
731	#468	C₂²×C₅₃	1	2	yes	complemented
732	#468	C₂²×C₅₃	1	2	yes	complemented
733	#468	C₂²×C₅₃	1	2	yes	complemented
734	#468	C₂²×C₅₃	1	2	yes	complemented
735	#467	C₂²×C₅₃	1	2	yes	complemented
736	#467	C₂²×C₅₃	1	2	yes	complemented
737	#467	C₂²×C₅₃	1	2	yes	complemented
738	#466	C₂²×C₅₃	1	2	yes	complemented
739	#465	C₂²×C₅₃	1	2	yes	complemented
740	#465	C₂²×C₅₃	1	2	yes	complemented
741	#465	C₂²×C₅₃	1	2	yes	complemented
742	#465	C₂²×C₅₃	1	2	yes	complemented
743	#452	C₂²×C₅₃	1	2	yes	—
744	#452	C₂²×C₅₃	1	2	yes	—
745	#452	C₂²×C₅₃	1	2	yes	—
746	#452	C₂²×C₅₃	1	2	yes	complemented
747	#452	C₂²×C₅₃	1	2	yes	complemented
748	#452	C₂²×C₅₃	1	2	yes	complemented
749	#452	C₂²×C₅₃	1	2	yes	complemented
750	#452	C₂²×C₅₃	1	2	yes	complemented
751	#451	C₂²×C₅₃	1	2	yes	complemented
752	#451	C₂²×C₅₃	1	2	yes	complemented
753	#449	C₂²×C₅₃	1	2	yes	—
754	#449	C₂²×C₅₃	1	2	yes	complemented
755	#449	C₂²×C₅₃	1	2	yes	complemented
756	#449	C₂²×C₅₃	1	2	yes	complemented
757	#448	C₂²×C₅₃	1	2	yes	complemented
758	#448	C₂²×C₅₃	1	2	yes	complemented
759	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
760	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
761	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
762	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
763	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
764	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
765	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
766	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
767	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
768	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
769	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
770	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
771	#408	C₂²×C₅₃	1	1	yes	characteristic
772	#408	C₂²×C₅₃	1	1	yes	characteristic
773	#408	C₂²×C₅₃	1	2	yes	complemented
774	#408	C₂²×C₅₃	1	2	yes	complemented
775	#407	C₂²×C₅₃	1	1	yes	characteristic
776	#407	C₂²×C₅₃	1	2	yes	complemented
777	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
778	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	complemented
779	C₅₃	#60761	1	1	yes	characteristic, direct product factor, Sylow
780	2₋¹⁺⁴	—	4	2	no	—
781	2₋¹⁺⁴	—	4	2	no	—
782	C₂×#41	—	2	2	no	—
783	C₂×#41	—	2	1	no	—
784	C₂×#41	—	2	1	no	—
785	C₂×#41	—	2	1	no	—
786	C₂×#41	—	4	2	no	—
787	C₂×#41	—	4	2	no	—
788	C₂×#41	—	4	2	no	—
789	C₂×#41	—	4	2	no	—
790	C₂×#41	D₄×C₅₃	1	2	yes	—
791	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
792	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
793	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
794	C₂×#41	C₂³×C₅₃	1	2	yes	—
795	C₂×#41	C₂³×C₅₃	1	2	yes	—
796	C₂×#41	C₂³×C₅₃	1	2	yes	—
797	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
798	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
799	C₂×#41	C₂³×C₅₃	1	2	yes	—
800	C₂²×Q₈	—	2	1	no	—
801	C₂²×Q₈	D₄×C₅₃	1	1	yes	characteristic
802	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
803	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
804	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
805	C₂²×D₄	—	2	1	no	—
806	C₂²×D₄	D₄×C₅₃	1	2	yes	—
807	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
808	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
809	C₂³×C₄	—	2	1	no	—
810	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
811	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
812	#137	—	4	2	no	—
813	AGL(1,ℤ/8)	—	4	2	no	—
814	C₂×Q₁₆	—	4	2	no	—
815	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
816	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
817	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
818	C₂×SD₁₆	—	4	2	no	—
819	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
820	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
821	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
822	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
823	C₂×D₈	C₂³×C₅₃	1	2	yes	—
824	#131	—	4	2	no	—
825	#131	—	4	2	no	—
826	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
827	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
828	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
829	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
830	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
831	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
832	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
833	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
834	C₄⋊Q₈	—	2	1	no	—
835	C₄⋊Q₈	—	2	1	no	—
836	C₄⋊Q₈	—	2	1	no	—
837	C₄⋊Q₈	—	2	2	no	—
838	#127	—	2	1	no	—
839	#127	—	2	1	no	—
840	#124	—	2	1	no	—
841	#124	—	2	1	no	—
842	#124	—	2	1	no	—
843	#124	—	2	1	no	—
844	#124	—	2	1	no	—
845	#124	—	2	2	no	—
846	#123	—	2	2	no	—
847	#123	—	2	2	no	—
848	#123	—	2	2	no	—
849	#123	—	2	2	no	—
850	#123	—	2	2	no	—
851	#123	—	2	2	no	—
852	#123	—	2	2	no	—
853	#123	—	2	1	no	—
854	#123	—	2	2	no	—
855	C₂²⋊Q₈	—	2	2	no	—
856	C₂²⋊Q₈	—	2	2	no	—
857	C₂²⋊Q₈	—	2	1	no	—
858	C₂²⋊Q₈	—	2	2	no	—
859	C₂²⋊Q₈	—	2	1	no	—
860	C₂²⋊Q₈	—	2	1	no	—
861	C₂²⋊Q₈	—	2	2	no	—
862	C₂²⋊Q₈	—	2	2	no	—
863	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
864	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
865	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
866	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
867	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
868	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
869	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
870	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
871	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
872	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
873	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
874	#121	—	2	2	no	—
875	#121	—	2	2	no	—
876	#121	—	2	2	no	—
877	#121	—	2	2	no	—
878	#121	—	2	2	no	—
879	#121	—	2	2	no	—
880	#121	—	2	2	no	—
881	#121	—	2	1	no	—
882	#121	—	2	2	no	—
883	#121	—	2	2	no	—
884	#121	—	2	2	no	—
885	#121	C₂³×C₅₃	1	1	yes	characteristic
886	#121	C₂³×C₅₃	1	2	yes	—
887	#121	C₂³×C₅₃	1	2	yes	—
888	#121	C₂³×C₅₃	1	2	yes	—
889	#121	C₂³×C₅₃	1	2	yes	—
890	#121	C₂³×C₅₃	1	1	yes	characteristic
891	#121	C₂³×C₅₃	1	2	yes	—
892	#120	—	2	2	no	—
893	#120	—	2	2	no	—
894	#120	—	2	1	no	—
895	#120	—	2	2	no	—
896	#120	—	2	2	no	—
897	#120	—	2	2	no	—
898	C₄×Q₈	—	2	1	no	—
899	C₄×D₄	—	2	2	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	2	no	—
902	C₄×D₄	—	2	2	no	—
903	C₄×D₄	—	2	2	no	—
904	C₄×D₄	—	2	2	no	—
905	C₄×D₄	—	2	1	no	—
906	C₄×D₄	—	2	1	no	—
907	C₄×D₄	—	2	2	no	—
908	C₄×D₄	—	2	2	no	—
909	#117	—	2	1	no	—
910	#117	—	2	1	no	—
911	#117	C₂³×C₅₃	1	1	yes	characteristic
912	#117	C₂³×C₅₃	1	1	yes	characteristic
913	#117	C₂³×C₅₃	1	1	yes	characteristic
914	#117	C₂³×C₅₃	1	1	yes	characteristic
915	#117	C₂³×C₅₃	1	1	yes	characteristic
916	#117	C₂³×C₅₃	1	2	yes	—
917	C₂×C₄⋊C₄	—	2	1	no	—
918	C₂×C₄⋊C₄	—	2	2	no	—
919	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
920	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
921	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
922	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
923	C₂×C₂²⋊C₄	—	2	1	no	—
924	C₂×C₂²⋊C₄	—	2	1	no	—
925	C₂×C₂²⋊C₄	—	2	2	no	—
926	C₂×C₄²	—	2	1	no	—
927	#107	C₂³×C₅₃	1	1	yes	characteristic
928	#107	C₂³×C₅₃	1	1	yes	characteristic
929	#107	C₂³×C₅₃	1	1	yes	characteristic
930	#107	C₂³×C₅₃	1	1	yes	characteristic
931	#107	C₂³×C₅₃	1	2	yes	—
932	#107	C₂³×C₅₃	1	2	yes	—
933	#106	C₂³×C₅₃	1	1	yes	characteristic
934	#106	C₂³×C₅₃	1	1	yes	characteristic
935	#106	C₂³×C₅₃	1	1	yes	characteristic
936	#106	C₂³×C₅₃	1	1	yes	characteristic
937	#106	C₂³×C₅₃	1	2	yes	—
938	#106	C₂³×C₅₃	1	2	yes	—
939	#103	C₂³×C₅₃	1	2	yes	—
940	#103	C₂³×C₅₃	1	2	yes	—
941	#103	C₂³×C₅₃	1	1	yes	characteristic
942	#103	C₂³×C₅₃	1	1	yes	characteristic
943	#103	C₂³×C₅₃	1	1	yes	characteristic
944	#103	C₂³×C₅₃	1	1	yes	characteristic
945	#103	C₂³×C₅₃	1	2	yes	—
946	#103	C₂³×C₅₃	1	2	yes	—
947	#103	C₂³×C₅₃	1	2	yes	—
948	#103	C₂³×C₅₃	1	2	yes	—
949	#103	C₂³×C₅₃	1	2	yes	—
950	#103	C₂³×C₅₃	1	2	yes	—
951	#102	C₂³×C₅₃	1	2	yes	—
952	#102	C₂³×C₅₃	1	2	yes	—
953	#102	C₂³×C₅₃	1	1	yes	characteristic
954	#102	C₂³×C₅₃	1	1	yes	characteristic
955	#102	C₂³×C₅₃	1	1	yes	characteristic
956	#102	C₂³×C₅₃	1	1	yes	characteristic
957	#102	C₂³×C₅₃	1	2	yes	—
958	#102	C₂³×C₅₃	1	2	yes	—
959	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
960	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
961	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
962	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
963	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
964	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
965	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
966	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
967	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
968	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
969	C₂⁴	—	2	1	no	—
970	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
971	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
972	#41	—	2	2	no	—
973	#41	—	2	2	no	—
974	#41	—	2	2	no	—
975	#41	—	2	2	no	—
976	#41	—	2	2	no	—
977	#41	—	2	2	no	—
978	#41	—	4	2	no	—
979	#41	—	4	2	no	—
980	#41	—	4	4	no	—
981	#41	—	4	2	no	—
982	#41	—	4	2	no	—
983	#41	—	4	2	no	—
984	#41	—	4	2	no	—
985	#41	—	4	2	no	—
986	#41	—	4	2	no	—
987	#41	—	4	2	no	—
988	#41	—	4	2	no	—
989	#41	—	4	4	no	—
990	#41	—	4	4	no	—
991	#41	—	4	8	no	—
992	#41	—	4	4	no	—
993	C₂×Q₈	—	2	2	no	—
994	C₂×Q₈	—	2	1	no	—
995	C₂×Q₈	—	2	1	no	—
996	C₂×Q₈	—	2	2	no	—
997	C₂×Q₈	—	2	2	no	—
998	C₂×Q₈	—	2	2	no	—
999	C₂×Q₈	—	2	2	no	—
1000	C₂×Q₈	—	4	2	no	—
1001	C₂×Q₈	—	4	2	no	—
1002	C₂×Q₈	—	4	2	no	—
1003	C₂×Q₈	—	4	4	no	—
1004	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1005	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1006	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
1007	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1008	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1009	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	2	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	2	no	—
1018	C₂×D₄	—	2	2	no	—
1019	C₂×D₄	—	2	2	no	—
1020	C₂×D₄	—	2	1	no	—
1021	C₂×D₄	—	2	1	no	—
1022	C₂×D₄	—	2	2	no	—
1023	C₂×D₄	—	2	2	no	—
1024	C₂×D₄	—	4	2	no	—
1025	C₂×D₄	—	4	4	no	—
1026	C₂×D₄	—	4	4	no	—
1027	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1028	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1029	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1030	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1031	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1032	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1033	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1034	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1035	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	2	2	no	—
1039	C₂²×C₄	—	2	1	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	1	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	2	no	—
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	2	2	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	2	2	no	—
1049	C₂²×C₄	—	4	2	no	—
1050	C₂²×C₄	—	4	2	no	—
1051	C₂²×C₄	—	4	4	no	—
1052	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1053	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1054	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1055	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1056	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1057	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1058	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1059	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1060	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1061	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1062	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1063	Q₁₆	—	4	2	no	—
1064	Q₁₆	—	4	2	no	—
1065	Q₁₆	—	4	2	no	—
1066	SD₁₆	—	4	2	no	—
1067	SD₁₆	—	4	2	no	—
1068	SD₁₆	—	4	2	no	—
1069	SD₁₆	—	4	2	no	—
1070	D₈	—	4	2	no	—
1071	M₁₆	—	2	2	no	—
1072	M₁₆	—	2	2	no	—
1073	M₁₆	—	4	2	no	—
1074	M₁₆	—	4	2	no	—
1075	C₂×C₈	—	2	2	no	—
1076	C₂×C₈	—	2	2	no	—
1077	C₂×C₈	—	4	2	no	—
1078	C₂×C₈	—	4	2	no	—
1079	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1080	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1081	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1082	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1083	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1084	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	2	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	2	no	—
1095	C₄⋊C₄	—	2	2	no	—
1096	C₄⋊C₄	—	2	2	no	—
1097	C₄⋊C₄	—	2	2	no	—
1098	C₄⋊C₄	—	2	2	no	—
1099	C₄⋊C₄	—	2	1	no	—
1100	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1101	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1102	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1103	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1104	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1105	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1106	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	2	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	1	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	2	no	—
1126	C₂²⋊C₄	—	2	2	no	—
1127	C₂²⋊C₄	—	2	2	no	—
1128	C₂²⋊C₄	—	2	2	no	—
1129	C₂²⋊C₄	—	2	2	no	—
1130	C₂²⋊C₄	—	2	1	no	—
1131	C₄²	—	2	1	no	—
1132	C₄²	—	2	1	no	—
1133	C₄²	—	2	1	no	—
1134	C₄²	—	2	1	no	—
1135	C₄²	—	2	2	no	—
1136	C₄²	—	2	1	no	—
1137	C₂³	—	2	2	no	—
1138	C₂³	—	2	1	no	—
1139	C₂³	—	2	2	no	—
1140	C₂³	—	4	2	no	—
1141	C₂³	—	4	1	no	—
1142	C₂³	—	4	1	no	—
1143	C₂³	—	4	2	no	—
1144	C₂³	—	4	2	no	—
1145	C₂³	—	4	2	no	—
1146	C₂³	—	8	1	no	—
1147	C₂³	—	8	1	no	—
1148	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1149	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1150	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1151	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1152	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1153	Q₈	—	2	2	no	—
1154	Q₈	—	2	2	no	—
1155	Q₈	—	2	2	no	—
1156	Q₈	—	2	1	no	—
1157	Q₈	—	2	2	no	—
1158	Q₈	—	2	2	no	—
1159	Q₈	—	2	2	no	—
1160	Q₈	—	2	1	no	—
1161	Q₈	—	4	2	no	—
1162	Q₈	—	4	4	no	—
1163	Q₈	—	4	2	no	—
1164	Q₈	—	4	2	no	—
1165	D₄	—	2	4	no	—
1166	D₄	—	2	4	no	—
1167	D₄	—	2	2	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	2	no	—
1171	D₄	—	2	2	no	—
1172	D₄	—	2	1	no	—
1173	D₄	—	4	2	no	—
1174	D₄	—	4	2	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	4	4	no	—
1178	D₄	—	4	4	no	—
1179	D₄	—	4	4	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	8	1	no	—
1183	D₄	—	8	2	no	—
1184	D₄	—	8	2	no	—
1185	D₄	—	8	2	no	—
1186	D₄	—	8	2	no	—
1187	D₄	—	8	2	no	—
1188	C₂×C₄	—	2	2	no	—
1189	C₂×C₄	—	2	2	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	4	4	no	—
1213	C₂×C₄	—	4	4	no	—
1214	C₂×C₄	—	4	4	no	—
1215	C₂×C₄	—	4	4	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	8	1	no	—
1220	C₂×C₄	—	8	2	no	—
1221	C₂×C₄	—	8	1	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1224	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1225	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1226	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1227	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1228	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1229	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1230	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1231	C₈	—	2	1	no	—
1232	C₈	—	2	1	no	—
1233	C₈	—	2	1	no	—
1234	C₈	—	2	1	no	—
1235	C₈	—	2	2	no	—
1236	C₈	—	2	2	no	—
1237	C₂²	—	2	1	no	—
1238	C₂²	—	2	1	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	2	no	—
1241	C₂²	—	2	2	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	2	no	—
1246	C₂²	—	2	2	no	—
1247	C₂²	—	2	1	no	—
1248	C₂²	—	2	1	no	—
1249	C₂²	—	2	2	no	—
1250	C₂²	—	2	2	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	8	2	no	—
1258	C₂²	—	8	4	no	—
1259	C₂²	—	8	4	no	—
1260	C₂²	C₅₃×#534	1	2	yes	—
1261	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1262	C₄	—	2	1	no	—
1263	C₄	—	2	1	no	—
1264	C₄	—	2	2	no	—
1265	C₄	—	2	2	no	—
1266	C₄	—	4	2	no	—
1267	C₄	—	4	1	no	—
1268	C₄	—	4	1	no	—
1269	C₄	—	4	1	no	—
1270	C₄	—	4	1	no	—
1271	C₄	—	4	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	2	no	—
1274	C₄	—	4	2	no	—
1275	C₄	—	4	1	no	—
1276	C₄	C₅₃×#534	1	2	yes	—
1277	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1278	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1279	C₂	—	2	2	no	—
1280	C₂	—	4	1	no	—
1281	C₂	—	4	1	no	—
1282	C₂	—	4	2	no	—
1283	C₂	—	4	2	no	—
1284	C₂	—	8	2	no	—
1285	C₂	—	8	1	no	—
1286	C₂	C₂×C₅₃×#534	1	1	yes	characteristic
1287	C₂	C₅₃×#3584	1	1	yes	characteristic
1288	C₂	C₅₃×#3586	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 ◁ C₂²×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3489	C₂	semidirect
2. C₅₃×#3449	C₂	semidirect
3. C₅₃×#3204	C₂	semidirect
4. C₅₃×#3203	C₂	semidirect
5. C₅₃×#3201	C₂	semidirect
6. C₅₃×#3201	C₂	semidirect
7. C₅₃×#3197	C₂	semidirect
8. C₅₃×#3196	C₂	semidirect
9. C₅₃×#3191	C₂	semidirect
10. C₅₃×#3190	C₂	semidirect
11. C₅₃×#3097	C₂	semidirect
12. C₅₃×#3096	C₂	semidirect
13. C₅₃×#3095	C₂	semidirect
14. C₅₃×#3091	C₂	semidirect
15. C₅₃×#3063	C₂	semidirect
16. C₅₃×#3062	C₂	semidirect
17. C₅₃×#3059	C₂	semidirect
18. C₅₃×#3057	C₂	semidirect
19. C₅₃×#3011	C₂	semidirect
20. C₅₃×#3010	C₂	semidirect
21. C₅₃×#3005	C₂	semidirect
22. C₂×C₅₃×#452	C₂	semidirect
23. C₅₃×#2880	C₂	semidirect
27. C₂×#137×C₅₃	C₂²	semidirect
28. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
29. C₂²×Q₁₆×C₅₃	C₂²	semidirect
30. C₂²×SD₁₆×C₅₃	C₂²	semidirect
42. C₅₃×#537	C₂²	semidirect
47. C₅₃×#536	C₂²	semidirect
58. C₅₃×#525	C₂²	semidirect
60. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
63. C₅₃×#485	C₂²	semidirect
64. C₅₃×#485	C₂²	semidirect
65. C₅₃×#485	C₂²	semidirect
66. C₅₃×#485	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
69. C₅₃×#484	C₂²	semidirect
70. C₅₃×#484	C₂²	semidirect
71. C₅₃×#484	C₂²	semidirect
72. C₅₃×#483	C₂²	semidirect
73. C₅₃×#483	C₂²	semidirect
74. C₅₃×#483	C₂²	semidirect
75. C₅₃×#482	C₂²	semidirect
76. C₅₃×#482	C₂²	semidirect
77. C₅₃×#482	C₂²	semidirect
78. C₅₃×#482	C₂²	semidirect
79. C₅₃×#481	C₂²	semidirect
80. C₅₃×#481	C₂²	semidirect
81. C₅₃×#480	C₂²	semidirect
82. C₅₃×#480	C₂²	semidirect
83. C₅₃×#470	C₂²	semidirect
84. C₅₃×#470	C₂²	semidirect
85. C₅₃×#470	C₂²	semidirect
86. C₅₃×#469	C₂²	semidirect
87. C₅₃×#468	C₂²	semidirect
88. C₅₃×#468	C₂²	semidirect
89. C₅₃×#468	C₂²	semidirect
90. C₅₃×#468	C₂²	semidirect
91. C₅₃×#467	C₂²	semidirect
92. C₅₃×#467	C₂²	semidirect
93. C₅₃×#467	C₂²	semidirect
94. C₅₃×#466	C₂²	semidirect
95. C₅₃×#465	C₂²	semidirect
96. C₅₃×#465	C₂²	semidirect
97. C₅₃×#465	C₂²	semidirect
98. C₅₃×#465	C₂²	semidirect
102. C₅₃×#452	C₂²	semidirect
103. C₅₃×#452	C₂²	semidirect
104. C₅₃×#452	C₂²	semidirect
105. C₅₃×#452	C₂²	semidirect
106. C₅₃×#452	C₂²	semidirect
107. C₅₃×#451	C₂²	semidirect
108. C₅₃×#451	C₂²	semidirect
110. C₅₃×#449	C₂²	semidirect
111. C₅₃×#449	C₂²	semidirect
112. C₅₃×#449	C₂²	semidirect
113. C₅₃×#448	C₂²	semidirect
114. C₅₃×#448	C₂²	semidirect
115. C₅₃×#428	C₂²	semidirect
116. C₅₃×#428	C₂²	semidirect
117. C₅₃×#427	C₂²	semidirect
118. C₅₃×#427	C₂²	semidirect
119. C₅₃×#419	C₂²	semidirect
120. C₅₃×#419	C₂²	semidirect
121. C₅₃×#419	C₂²	semidirect
122. C₅₃×#418	C₂²	semidirect
123. C₅₃×#416	C₂²	semidirect
124. C₅₃×#416	C₂²	semidirect
125. C₂×#103×C₅₃	C₂²	semidirect
126. C₂×#102×C₅₃	C₂²	semidirect
129. C₅₃×#408	C₂²	semidirect
130. C₅₃×#408	C₂²	semidirect
132. C₅₃×#407	C₂²	semidirect
134. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
592. #60761	C₅₃	direct (N × H)
635. #3489	C₂×C₅₃	semidirect
636. #3449	C₂×C₅₃	semidirect
637. #3204	C₂×C₅₃	semidirect
638. #3203	C₂×C₅₃	semidirect
639. #3201	C₂×C₅₃	semidirect
640. #3201	C₂×C₅₃	semidirect
641. #3197	C₂×C₅₃	semidirect
642. #3196	C₂×C₅₃	semidirect
643. #3191	C₂×C₅₃	semidirect
644. #3190	C₂×C₅₃	semidirect
645. #3097	C₂×C₅₃	semidirect
646. #3096	C₂×C₅₃	semidirect
647. #3095	C₂×C₅₃	semidirect
648. #3091	C₂×C₅₃	semidirect
649. #3063	C₂×C₅₃	semidirect
650. #3062	C₂×C₅₃	semidirect
651. #3059	C₂×C₅₃	semidirect
652. #3057	C₂×C₅₃	semidirect
653. #3011	C₂×C₅₃	semidirect
654. #3010	C₂×C₅₃	semidirect
655. #3005	C₂×C₅₃	semidirect
656. C₂×#452	C₂×C₅₃	semidirect
657. #2880	C₂×C₅₃	semidirect
671. C₂×#137	C₂²×C₅₃	semidirect
672. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
673. C₂²×Q₁₆	C₂²×C₅₃	semidirect
674. C₂²×SD₁₆	C₂²×C₅₃	semidirect
686. #537	C₂²×C₅₃	semidirect
691. #536	C₂²×C₅₃	semidirect
702. #525	C₂²×C₅₃	semidirect
704. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
707. #485	C₂²×C₅₃	semidirect
708. #485	C₂²×C₅₃	semidirect
709. #485	C₂²×C₅₃	semidirect
710. #485	C₂²×C₅₃	semidirect
711. #485	C₂²×C₅₃	semidirect
712. #485	C₂²×C₅₃	semidirect
713. #484	C₂²×C₅₃	semidirect
714. #484	C₂²×C₅₃	semidirect
715. #484	C₂²×C₅₃	semidirect
716. #483	C₂²×C₅₃	semidirect
717. #483	C₂²×C₅₃	semidirect
718. #483	C₂²×C₅₃	semidirect
719. #482	C₂²×C₅₃	semidirect
720. #482	C₂²×C₅₃	semidirect
721. #482	C₂²×C₅₃	semidirect
722. #482	C₂²×C₅₃	semidirect
723. #481	C₂²×C₅₃	semidirect
724. #481	C₂²×C₅₃	semidirect
725. #480	C₂²×C₅₃	semidirect
726. #480	C₂²×C₅₃	semidirect
727. #470	C₂²×C₅₃	semidirect
728. #470	C₂²×C₅₃	semidirect
729. #470	C₂²×C₅₃	semidirect
730. #469	C₂²×C₅₃	semidirect
731. #468	C₂²×C₅₃	semidirect
732. #468	C₂²×C₅₃	semidirect
733. #468	C₂²×C₅₃	semidirect
734. #468	C₂²×C₅₃	semidirect
735. #467	C₂²×C₅₃	semidirect
736. #467	C₂²×C₅₃	semidirect
737. #467	C₂²×C₅₃	semidirect
738. #466	C₂²×C₅₃	semidirect
739. #465	C₂²×C₅₃	semidirect
740. #465	C₂²×C₅₃	semidirect
741. #465	C₂²×C₅₃	semidirect
742. #465	C₂²×C₅₃	semidirect
746. #452	C₂²×C₅₃	semidirect
747. #452	C₂²×C₅₃	semidirect
748. #452	C₂²×C₅₃	semidirect
749. #452	C₂²×C₅₃	semidirect
750. #452	C₂²×C₅₃	semidirect
751. #451	C₂²×C₅₃	semidirect
752. #451	C₂²×C₅₃	semidirect
754. #449	C₂²×C₅₃	semidirect
755. #449	C₂²×C₅₃	semidirect
756. #449	C₂²×C₅₃	semidirect
757. #448	C₂²×C₅₃	semidirect
758. #448	C₂²×C₅₃	semidirect
759. #428	C₂²×C₅₃	semidirect
760. #428	C₂²×C₅₃	semidirect
761. #427	C₂²×C₅₃	semidirect
762. #427	C₂²×C₅₃	semidirect
763. #419	C₂²×C₅₃	semidirect
764. #419	C₂²×C₅₃	semidirect
765. #419	C₂²×C₅₃	semidirect
766. #418	C₂²×C₅₃	semidirect
767. #416	C₂²×C₅₃	semidirect
768. #416	C₂²×C₅₃	semidirect
769. C₂×#103	C₂²×C₅₃	semidirect
770. C₂×#102	C₂²×C₅₃	semidirect
773. #408	C₂²×C₅₃	semidirect
774. #408	C₂²×C₅₃	semidirect
776. #407	C₂²×C₅₃	semidirect
778. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
779. C₅₃	#60761	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×#3489	2
C₅₃×#3449	2
C₅₃×#3204	2
C₅₃×#3203	2
C₅₃×#3201	2
C₅₃×#3197	2
C₅₃×#3196	2
C₅₃×#3191	2
C₅₃×#3190	2
C₅₃×#3097	2
C₅₃×#3096	2
C₅₃×#3095	2
C₅₃×#3091	2
C₅₃×#3063	2
C₅₃×#3062	2
C₅₃×#3059	2
C₅₃×#3057	2
C₅₃×#3011	2
C₅₃×#3010	2
C₅₃×#3005	2
C₂×C₅₃×#452	2
C₅₃×#2880	2
#60761	53

Subgroups — C53×#60761 #27268273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60761 #27268273