Subgroups — C₅₃×#62004 #27269516

Order 13568.

1878 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3327	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3323	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3276	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3275	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3273	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3256	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3211	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3102	C₂	1	2	yes	maximal, complemented
21	C₅₃×#3040	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
26	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
27	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#555	—	2	1	no	—
31	C₅₃×#555	C₂²	1	1	yes	characteristic
32	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#553	—	2	1	no	—
34	C₅₃×#552	—	2	1	no	—
35	C₅₃×#552	C₂²	1	2	yes	complemented
36	C₅₃×#551	—	2	2	no	—
37	C₅₃×#551	—	2	2	no	—
38	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#548	C₂²	1	2	yes	—
40	C₅₃×#547	C₂²	1	1	yes	characteristic
41	C₅₃×#546	—	2	1	no	—
42	C₅₃×#546	C₂²	1	2	yes	—
43	C₅₃×#546	C₂²	1	2	yes	complemented
44	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#542	—	2	1	no	—
46	C₅₃×#538	—	2	2	no	—
47	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#532	C₂²	1	1	yes	characteristic
49	C₅₃×#529	—	2	2	no	—
50	C₅₃×#529	C₂²	1	1	yes	characteristic
51	C₅₃×#529	C₂²	1	2	yes	complemented
52	C₅₃×#529	C₂²	1	2	yes	complemented
53	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
54	C₅₃×#525	—	2	1	no	—
55	C₅₃×#518	—	2	1	no	—
56	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
57	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
58	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×#117×C₅₃	—	2	1	no	—
60	C₅₃×#495	C₂²	1	2	yes	—
61	C₅₃×#495	C₂²	1	2	yes	complemented
62	C₅₃×#494	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×#488	C₂²	1	2	yes	complemented
66	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#485	C₂²	1	2	yes	complemented
69	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#481	C₂²	1	1	yes	characteristic
72	C₅₃×#479	C₂²	1	2	yes	complemented
73	C₅₃×#479	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#478	C₂²	1	2	yes	complemented
76	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#470	C₂²	1	2	yes	complemented
80	C₅₃×#470	C₂²	1	2	yes	complemented
81	C₅₃×#469	C₂²	1	2	yes	—
82	C₅₃×#468	C₂²	1	2	yes	—
83	C₅₃×#468	C₂²	1	2	yes	complemented
84	C₅₃×#468	C₂²	1	2	yes	complemented
85	C₅₃×#464	C₂²	1	2	yes	complemented
86	C₅₃×#464	C₂²	1	2	yes	complemented
87	C₅₃×#464	C₂²	1	2	yes	complemented
88	C₅₃×#464	C₂²	1	2	yes	complemented
89	C₅₃×#464	C₂²	1	2	yes	complemented
90	C₅₃×#464	C₂²	1	2	yes	complemented
91	C₅₃×#463	C₂²	1	1	yes	characteristic
92	C₅₃×#463	C₂²	1	2	yes	—
93	C₅₃×#463	C₂²	1	1	yes	characteristic
94	C₅₃×#463	C₂²	1	2	yes	complemented
95	C₅₃×#463	C₂²	1	2	yes	complemented
96	C₅₃×#463	C₂²	1	2	yes	complemented
97	C₅₃×#463	C₂²	1	2	yes	complemented
98	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#459	C₂²	1	1	yes	characteristic
103	C₅₃×#459	C₂²	1	1	yes	characteristic
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×#450	C₂²	1	2	yes	complemented
109	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#449	C₂²	1	2	yes	—
111	C₅₃×#448	C₂²	1	2	yes	complemented
112	C₅₃×#447	C₂²	1	2	yes	—
113	C₅₃×#447	C₂²	1	1	yes	characteristic
114	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
122	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
124	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#436	C₂²	1	2	yes	complemented
126	C₅₃×#436	C₂²	1	2	yes	complemented
127	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#431	C₂²	1	2	yes	complemented
130	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#423	C₂²	1	2	yes	complemented
132	C₅₃×#419	C₂²	1	2	yes	complemented
133	C₅₃×#418	C₂²	1	2	yes	complemented
134	C₅₃×#417	C₂²	1	2	yes	complemented
135	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
136	C₂×#41×C₅₃	C₂³	1	2	yes	—
137	C₂×#41×C₅₃	C₂³	1	2	yes	—
138	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₅₃	—	2	1	no	—
140	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₅₃	—	2	1	no	—
143	#137×C₅₃	—	4	4	no	—
144	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
145	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
146	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
156	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×D₈×C₅₃	C₂³	1	2	yes	—
158	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₅₃	C₂³	1	2	yes	—
160	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
161	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
162	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₅₃	—	2	1	no	—
164	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
167	#127×C₅₃	C₂³	1	1	yes	characteristic
168	#126×C₅₃	—	2	2	no	—
169	#126×C₅₃	—	2	2	no	—
170	#126×C₅₃	—	2	2	no	—
171	#126×C₅₃	—	2	1	no	—
172	#126×C₅₃	—	2	2	no	—
173	#126×C₅₃	—	2	2	no	—
174	#125×C₅₃	—	2	2	no	—
175	#125×C₅₃	—	2	1	no	—
176	#125×C₅₃	C₂³	1	2	yes	—
177	#125×C₅₃	C₂³	1	1	yes	characteristic
178	#124×C₅₃	—	2	2	no	—
179	#124×C₅₃	—	2	2	no	—
180	#124×C₅₃	—	2	2	no	—
181	#124×C₅₃	—	2	2	no	—
182	#124×C₅₃	—	2	1	no	—
183	#124×C₅₃	C₂³	1	2	yes	—
184	#124×C₅₃	C₂³	1	2	yes	—
185	#124×C₅₃	C₂³	1	2	yes	—
186	#124×C₅₃	C₂³	1	1	yes	characteristic
187	#124×C₅₃	C₂³	1	2	yes	—
188	#123×C₅₃	—	2	2	no	—
189	#123×C₅₃	—	2	2	no	—
190	#123×C₅₃	—	2	2	no	—
191	#123×C₅₃	—	2	2	no	—
192	#123×C₅₃	—	2	2	no	—
193	#123×C₅₃	—	2	1	no	—
194	#123×C₅₃	—	2	2	no	—
195	#123×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	—	2	2	no	—
198	C₂²⋊Q₈×C₅₃	—	2	2	no	—
199	C₂²⋊Q₈×C₅₃	—	2	1	no	—
200	C₂²⋊Q₈×C₅₃	—	2	1	no	—
201	C₂²⋊Q₈×C₅₃	—	2	1	no	—
202	C₂²⋊Q₈×C₅₃	—	2	1	no	—
203	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
205	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
207	#121×C₅₃	—	2	1	no	—
208	#121×C₅₃	—	2	2	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	1	no	—
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	—	2	2	no	—
213	#121×C₅₃	—	2	1	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	C₂³	1	1	yes	characteristic
216	#121×C₅₃	C₂³	1	2	yes	—
217	#121×C₅₃	C₂³	1	2	yes	—
218	#120×C₅₃	—	2	2	no	—
219	#120×C₅₃	—	2	2	no	—
220	#120×C₅₃	—	2	2	no	—
221	C₄×Q₈×C₅₃	—	2	1	no	—
222	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
223	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
225	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
228	C₄×D₄×C₅₃	—	2	1	no	—
229	C₄×D₄×C₅₃	—	2	2	no	—
230	C₄×D₄×C₅₃	—	2	1	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	1	no	—
235	C₄×D₄×C₅₃	—	2	2	no	—
236	C₄×D₄×C₅₃	—	2	2	no	—
237	C₄×D₄×C₅₃	—	2	2	no	—
238	C₄×D₄×C₅₃	—	2	2	no	—
239	C₄×D₄×C₅₃	—	2	1	no	—
240	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
241	C₄×D₄×C₅₃	D₄	1	2	yes	—
242	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₅₃	C₂³	1	2	yes	—
247	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₅₃	C₂³	1	2	yes	—
249	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₅₃	C₂³	1	2	yes	—
251	#117×C₅₃	—	2	1	no	—
252	#117×C₅₃	—	2	1	no	—
253	#117×C₅₃	—	2	1	no	—
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	2	no	—
259	#117×C₅₃	—	2	1	no	—
260	#117×C₅₃	D₄	1	1	yes	characteristic
261	#117×C₅₃	D₄	1	2	yes	—
262	#117×C₅₃	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
264	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
265	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
269	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
271	C₂×C₄²×C₅₃	—	2	2	no	—
272	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
274	#107×C₅₃	C₂³	1	2	yes	—
275	#107×C₅₃	C₂³	1	1	yes	characteristic
276	#107×C₅₃	C₂³	1	1	yes	characteristic
277	#106×C₅₃	C₂³	1	1	yes	characteristic
278	#106×C₅₃	C₂³	1	2	yes	—
279	#106×C₅₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
285	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	1	yes	characteristic
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	2	yes	—
293	#103×C₅₃	C₂³	1	1	yes	characteristic
294	#103×C₅₃	C₂³	1	2	yes	—
295	#103×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	2	yes	—
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₅₃	C₂³	1	2	yes	—
314	C₄×C₈×C₅₃	C₂³	1	2	yes	—
315	C₂⁴×C₅₃	—	2	1	no	—
316	C₂⁴×C₅₃	—	2	2	no	—
317	#41×C₅₃	—	2	4	no	—
318	#41×C₅₃	—	4	2	no	—
319	#41×C₅₃	—	4	2	no	—
320	#41×C₅₃	—	4	2	no	—
321	#41×C₅₃	—	4	2	no	—
322	C₂×Q₈×C₅₃	—	2	1	no	—
323	C₂×Q₈×C₅₃	—	2	2	no	—
324	C₂×Q₈×C₅₃	—	4	2	no	—
325	C₂×Q₈×C₅₃	—	4	2	no	—
326	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
330	C₂×D₄×C₅₃	—	2	2	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	2	no	—
333	C₂×D₄×C₅₃	—	2	1	no	—
334	C₂×D₄×C₅₃	—	2	2	no	—
335	C₂×D₄×C₅₃	—	2	2	no	—
336	C₂×D₄×C₅₃	—	2	1	no	—
337	C₂×D₄×C₅₃	—	2	1	no	—
338	C₂×D₄×C₅₃	—	2	1	no	—
339	C₂×D₄×C₅₃	—	2	2	no	—
340	C₂×D₄×C₅₃	—	4	1	no	—
341	C₂×D₄×C₅₃	—	4	2	no	—
342	C₂×D₄×C₅₃	—	4	2	no	—
343	C₂×D₄×C₅₃	—	4	4	no	—
344	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
345	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
348	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₅₃	—	2	1	no	—
351	C₂²×C₄×C₅₃	—	2	2	no	—
352	C₂²×C₄×C₅₃	—	2	1	no	—
353	C₂²×C₄×C₅₃	—	2	2	no	—
354	C₂²×C₄×C₅₃	—	2	1	no	—
355	C₂²×C₄×C₅₃	—	2	1	no	—
356	C₂²×C₄×C₅₃	—	2	1	no	—
357	C₂²×C₄×C₅₃	—	2	1	no	—
358	C₂²×C₄×C₅₃	—	2	2	no	—
359	C₂²×C₄×C₅₃	—	2	2	no	—
360	C₂²×C₄×C₅₃	—	2	2	no	—
361	C₂²×C₄×C₅₃	—	4	4	no	—
362	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
364	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
365	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
368	Q₁₆×C₅₃	—	4	2	no	—
369	Q₁₆×C₅₃	—	4	2	no	—
370	Q₁₆×C₅₃	—	4	2	no	—
371	SD₁₆×C₅₃	—	2	4	no	—
372	SD₁₆×C₅₃	—	2	2	no	—
373	SD₁₆×C₅₃	—	4	2	no	—
374	SD₁₆×C₅₃	—	4	1	no	—
375	SD₁₆×C₅₃	—	4	2	no	—
376	SD₁₆×C₅₃	—	4	2	no	—
377	SD₁₆×C₅₃	—	4	2	no	—
378	D₈×C₅₃	—	2	2	no	—
379	D₈×C₅₃	—	2	4	no	—
380	D₈×C₅₃	—	4	1	no	—
381	D₈×C₅₃	—	4	2	no	—
382	M₁₆×C₅₃	—	4	2	no	—
383	M₁₆×C₅₃	—	4	2	no	—
384	M₁₆×C₅₃	—	4	2	no	—
385	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
389	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
391	C₄⋊C₄×C₅₃	—	2	1	no	—
392	C₄⋊C₄×C₅₃	—	2	1	no	—
393	C₄⋊C₄×C₅₃	—	2	2	no	—
394	C₄⋊C₄×C₅₃	—	2	2	no	—
395	C₄⋊C₄×C₅₃	—	2	1	no	—
396	C₄⋊C₄×C₅₃	—	2	1	no	—
397	C₄⋊C₄×C₅₃	—	2	1	no	—
398	C₄⋊C₄×C₅₃	—	2	1	no	—
399	C₄⋊C₄×C₅₃	—	2	1	no	—
400	C₄⋊C₄×C₅₃	—	2	2	no	—
401	C₄⋊C₄×C₅₃	—	2	2	no	—
402	C₄⋊C₄×C₅₃	—	2	2	no	—
403	C₄⋊C₄×C₅₃	—	2	1	no	—
404	C₄⋊C₄×C₅₃	—	2	2	no	—
405	C₄⋊C₄×C₅₃	—	2	2	no	—
406	C₄⋊C₄×C₅₃	—	2	1	no	—
407	C₄⋊C₄×C₅₃	—	2	2	no	—
408	C₄⋊C₄×C₅₃	—	2	1	no	—
409	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²⋊C₄×C₅₃	—	2	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	1	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	2	no	—
424	C₂²⋊C₄×C₅₃	—	2	1	no	—
425	C₂²⋊C₄×C₅₃	—	2	1	no	—
426	C₂²⋊C₄×C₅₃	—	2	1	no	—
427	C₂²⋊C₄×C₅₃	—	2	1	no	—
428	C₂²⋊C₄×C₅₃	—	2	2	no	—
429	C₂²⋊C₄×C₅₃	—	2	2	no	—
430	C₂²⋊C₄×C₅₃	—	2	2	no	—
431	C₂²⋊C₄×C₅₃	—	2	2	no	—
432	C₂²⋊C₄×C₅₃	—	2	2	no	—
433	C₂²⋊C₄×C₅₃	—	2	1	no	—
434	C₂²⋊C₄×C₅₃	—	2	1	no	—
435	C₂²⋊C₄×C₅₃	—	2	1	no	—
436	C₂²⋊C₄×C₅₃	—	2	2	no	—
437	C₂²⋊C₄×C₅₃	—	2	2	no	—
438	C₂²⋊C₄×C₅₃	—	2	2	no	—
439	C₂²⋊C₄×C₅₃	—	2	2	no	—
440	C₂²⋊C₄×C₅₃	—	2	2	no	—
441	C₂²⋊C₄×C₅₃	—	2	1	no	—
442	C₂²⋊C₄×C₅₃	—	2	2	no	—
443	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
446	C₄²×C₅₃	—	2	2	no	—
447	C₄²×C₅₃	—	2	2	no	—
448	C₄²×C₅₃	—	2	2	no	—
449	C₄²×C₅₃	—	2	2	no	—
450	C₄²×C₅₃	—	2	1	no	—
451	C₄²×C₅₃	C₂×D₄	1	2	yes	—
452	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₅₃	C₂×D₄	1	2	yes	—
454	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
456	C₄²×C₅₃	C₂⁴	1	2	yes	—
457	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
458	C₂³×C₅₃	—	2	1	no	—
459	C₂³×C₅₃	—	2	2	no	—
460	C₂³×C₅₃	—	2	1	no	—
461	C₂³×C₅₃	—	2	1	no	—
462	C₂³×C₅₃	—	4	2	no	—
463	C₂³×C₅₃	—	4	2	no	—
464	C₂³×C₅₃	—	4	4	no	—
465	C₂³×C₅₃	—	8	1	no	—
466	C₂³×C₅₃	—	8	2	no	—
467	C₂³×C₅₃	—	8	2	no	—
468	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
469	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
470	Q₈×C₅₃	—	2	2	no	—
471	Q₈×C₅₃	—	2	1	no	—
472	Q₈×C₅₃	—	2	2	no	—
473	Q₈×C₅₃	—	2	2	no	—
474	Q₈×C₅₃	—	2	1	no	—
475	Q₈×C₅₃	—	2	2	no	—
476	Q₈×C₅₃	—	2	2	no	—
477	Q₈×C₅₃	—	8	1	no	—
478	Q₈×C₅₃	—	8	2	no	—
479	D₄×C₅₃	—	2	2	no	—
480	D₄×C₅₃	—	2	1	no	—
481	D₄×C₅₃	—	2	1	no	—
482	D₄×C₅₃	—	2	2	no	—
483	D₄×C₅₃	—	2	1	no	—
484	D₄×C₅₃	—	2	1	no	—
485	D₄×C₅₃	—	2	2	no	—
486	D₄×C₅₃	—	2	1	no	—
487	D₄×C₅₃	—	4	2	no	—
488	D₄×C₅₃	—	4	2	no	—
489	D₄×C₅₃	—	4	4	no	—
490	D₄×C₅₃	—	4	4	no	—
491	D₄×C₅₃	—	4	2	no	—
492	D₄×C₅₃	—	8	1	no	—
493	D₄×C₅₃	—	8	2	no	—
494	D₄×C₅₃	—	8	1	no	—
495	D₄×C₅₃	—	8	2	no	—
496	D₄×C₅₃	—	8	2	no	—
497	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
498	C₂×C₄×C₅₃	—	2	2	no	—
499	C₂×C₄×C₅₃	—	2	1	no	—
500	C₂×C₄×C₅₃	—	2	2	no	—
501	C₂×C₄×C₅₃	—	2	2	no	—
502	C₂×C₄×C₅₃	—	2	1	no	—
503	C₂×C₄×C₅₃	—	2	1	no	—
504	C₂×C₄×C₅₃	—	2	1	no	—
505	C₂×C₄×C₅₃	—	2	2	no	—
506	C₂×C₄×C₅₃	—	2	1	no	—
507	C₂×C₄×C₅₃	—	2	1	no	—
508	C₂×C₄×C₅₃	—	2	1	no	—
509	C₂×C₄×C₅₃	—	2	2	no	—
510	C₂×C₄×C₅₃	—	2	2	no	—
511	C₂×C₄×C₅₃	—	4	2	no	—
512	C₂×C₄×C₅₃	—	4	1	no	—
513	C₂×C₄×C₅₃	—	4	2	no	—
514	C₂×C₄×C₅₃	—	4	4	no	—
515	C₂×C₄×C₅₃	—	4	2	no	—
516	C₂×C₄×C₅₃	—	4	2	no	—
517	C₂×C₄×C₅₃	—	4	2	no	—
518	C₂×C₄×C₅₃	—	4	2	no	—
519	C₂×C₄×C₅₃	—	4	2	no	—
520	C₂×C₄×C₅₃	—	4	2	no	—
521	C₂×C₄×C₅₃	—	8	2	no	—
522	C₂×C₄×C₅₃	—	8	2	no	—
523	C₂×C₄×C₅₃	—	8	2	no	—
524	C₂×C₄×C₅₃	—	8	2	no	—
525	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
534	C₈×C₅₃	—	2	1	no	—
535	C₈×C₅₃	—	2	2	no	—
536	C₈×C₅₃	—	2	2	no	—
537	C₈×C₅₃	—	2	1	no	—
538	C₈×C₅₃	—	2	1	no	—
539	C₈×C₅₃	—	2	1	no	—
540	#62004	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
541	C₂²×C₅₃	—	2	1	no	—
542	C₂²×C₅₃	—	2	2	no	—
543	C₂²×C₅₃	—	2	2	no	—
544	C₂²×C₅₃	—	2	1	no	—
545	C₂²×C₅₃	—	2	2	no	—
546	C₂²×C₅₃	—	2	1	no	—
547	C₂²×C₅₃	—	2	2	no	—
548	C₂²×C₅₃	—	4	1	no	—
549	C₂²×C₅₃	—	4	1	no	—
550	C₂²×C₅₃	—	4	2	no	—
551	C₂²×C₅₃	—	4	1	no	—
552	C₂²×C₅₃	—	4	1	no	—
553	C₂²×C₅₃	—	4	2	no	—
554	C₂²×C₅₃	—	4	1	no	—
555	C₂²×C₅₃	—	4	1	no	—
556	C₂²×C₅₃	—	4	1	no	—
557	C₂²×C₅₃	—	4	1	no	—
558	C₂²×C₅₃	—	4	2	no	—
559	C₂²×C₅₃	—	8	4	no	—
560	C₂²×C₅₃	—	16	4	no	—
561	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
562	C₄×C₅₃	—	2	1	no	—
563	C₄×C₅₃	—	2	2	no	—
564	C₄×C₅₃	—	2	1	no	—
565	C₄×C₅₃	—	2	2	no	—
566	C₄×C₅₃	—	2	1	no	—
567	C₄×C₅₃	—	2	1	no	—
568	C₄×C₅₃	—	2	2	no	—
569	C₄×C₅₃	—	4	1	no	—
570	C₄×C₅₃	—	4	2	no	—
571	C₄×C₅₃	—	4	2	no	—
572	C₄×C₅₃	—	4	2	no	—
573	C₄×C₅₃	—	4	1	no	—
574	C₄×C₅₃	—	4	1	no	—
575	C₄×C₅₃	—	4	1	no	—
576	C₄×C₅₃	—	4	1	no	—
577	C₄×C₅₃	#575	1	2	yes	—
578	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₄×C₅₃	#585	1	1	yes	characteristic
580	#3514	C₂×C₅₃	1	1	yes	characteristic, complemented
581	#3475	C₂×C₅₃	1	1	yes	characteristic, complemented
582	#3394	C₂×C₅₃	1	1	yes	characteristic, complemented
583	#3393	C₂×C₅₃	1	1	yes	characteristic, complemented
584	#3361	C₂×C₅₃	1	1	yes	characteristic, complemented
585	#3360	C₂×C₅₃	1	1	yes	characteristic, complemented
586	#3329	C₂×C₅₃	1	1	yes	characteristic, complemented
587	#3327	C₂×C₅₃	1	2	yes	complemented
588	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
589	#3323	C₂×C₅₃	1	2	yes	complemented
590	#3276	C₂×C₅₃	1	1	yes	characteristic, complemented
591	#3275	C₂×C₅₃	1	2	yes	complemented
592	#3273	C₂×C₅₃	1	2	yes	complemented
593	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
594	#3256	C₂×C₅₃	1	2	yes	complemented
595	#3252	C₂×C₅₃	1	1	yes	characteristic, complemented
596	#3211	C₂×C₅₃	1	2	yes	complemented
597	#3210	C₂×C₅₃	1	1	yes	characteristic, complemented
598	#3105	C₂×C₅₃	1	1	yes	characteristic, complemented
599	#3102	C₂×C₅₃	1	2	yes	complemented
600	#3040	C₂×C₅₃	1	2	yes	complemented
601	#3036	C₂×C₅₃	1	1	yes	characteristic, complemented
602	#2991	C₂×C₅₃	1	1	yes	characteristic, complemented
603	C₂×C₅₃	—	4	1	no	—
604	C₂×C₅₃	—	4	2	no	—
605	C₂×C₅₃	—	4	2	no	—
606	C₂×C₅₃	—	8	1	no	—
607	C₂×C₅₃	—	8	2	no	—
608	C₂×C₅₃	—	8	1	no	—
609	C₂×C₅₃	#3488	1	1	yes	characteristic
610	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
611	C₂×C₅₃	#3584	1	1	yes	characteristic
612	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
613	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
614	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
615	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
616	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
617	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
618	#555	—	2	1	no	—
619	#555	C₂²×C₅₃	1	1	yes	characteristic
620	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
621	#553	—	2	1	no	—
622	#552	—	2	1	no	—
623	#552	C₂²×C₅₃	1	2	yes	complemented
624	#551	—	2	2	no	—
625	#551	—	2	2	no	—
626	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
627	#548	C₂²×C₅₃	1	2	yes	—
628	#547	C₂²×C₅₃	1	1	yes	characteristic
629	#546	—	2	1	no	—
630	#546	C₂²×C₅₃	1	2	yes	—
631	#546	C₂²×C₅₃	1	2	yes	complemented
632	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
633	#542	—	2	1	no	—
634	#538	—	2	2	no	—
635	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
636	#532	C₂²×C₅₃	1	1	yes	characteristic
637	#529	—	2	2	no	—
638	#529	C₂²×C₅₃	1	1	yes	characteristic
639	#529	C₂²×C₅₃	1	2	yes	complemented
640	#529	C₂²×C₅₃	1	2	yes	complemented
641	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
642	#525	—	2	1	no	—
643	#518	—	2	1	no	—
644	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
645	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
646	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
647	C₂×#117	—	2	1	no	—
648	#495	C₂²×C₅₃	1	2	yes	—
649	#495	C₂²×C₅₃	1	2	yes	complemented
650	#494	C₂²×C₅₃	1	1	yes	characteristic, complemented
651	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
652	#488	C₂²×C₅₃	1	2	yes	complemented
653	#488	C₂²×C₅₃	1	2	yes	complemented
654	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
655	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	#485	C₂²×C₅₃	1	2	yes	complemented
657	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
658	#482	C₂²×C₅₃	1	2	yes	complemented
659	#481	C₂²×C₅₃	1	1	yes	characteristic
660	#479	C₂²×C₅₃	1	2	yes	complemented
661	#479	C₂²×C₅₃	1	2	yes	complemented
662	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
664	#478	C₂²×C₅₃	1	2	yes	complemented
665	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
666	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
667	#470	C₂²×C₅₃	1	2	yes	complemented
668	#470	C₂²×C₅₃	1	2	yes	complemented
669	#469	C₂²×C₅₃	1	2	yes	—
670	#468	C₂²×C₅₃	1	2	yes	—
671	#468	C₂²×C₅₃	1	2	yes	complemented
672	#468	C₂²×C₅₃	1	2	yes	complemented
673	#464	C₂²×C₅₃	1	2	yes	complemented
674	#464	C₂²×C₅₃	1	2	yes	complemented
675	#464	C₂²×C₅₃	1	2	yes	complemented
676	#464	C₂²×C₅₃	1	2	yes	complemented
677	#464	C₂²×C₅₃	1	2	yes	complemented
678	#464	C₂²×C₅₃	1	2	yes	complemented
679	#463	C₂²×C₅₃	1	2	yes	—
680	#463	C₂²×C₅₃	1	1	yes	characteristic
681	#463	C₂²×C₅₃	1	1	yes	characteristic
682	#463	C₂²×C₅₃	1	2	yes	complemented
683	#463	C₂²×C₅₃	1	2	yes	complemented
684	#463	C₂²×C₅₃	1	2	yes	complemented
685	#463	C₂²×C₅₃	1	2	yes	complemented
686	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
688	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	#459	C₂²×C₅₃	1	1	yes	characteristic
691	#459	C₂²×C₅₃	1	1	yes	characteristic
692	#452	C₂²×C₅₃	1	2	yes	complemented
693	#452	C₂²×C₅₃	1	2	yes	complemented
694	#452	C₂²×C₅₃	1	2	yes	complemented
695	#451	C₂²×C₅₃	1	2	yes	complemented
696	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
697	#450	C₂²×C₅₃	1	2	yes	complemented
698	#449	C₂²×C₅₃	1	2	yes	—
699	#448	C₂²×C₅₃	1	2	yes	complemented
700	#447	C₂²×C₅₃	1	1	yes	characteristic
701	#447	C₂²×C₅₃	1	2	yes	—
702	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
704	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
705	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
706	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
707	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
708	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
710	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
711	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
712	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	#436	C₂²×C₅₃	1	2	yes	complemented
714	#436	C₂²×C₅₃	1	2	yes	complemented
715	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
716	#431	C₂²×C₅₃	1	2	yes	complemented
717	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
718	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
719	#423	C₂²×C₅₃	1	2	yes	complemented
720	#419	C₂²×C₅₃	1	2	yes	complemented
721	#418	C₂²×C₅₃	1	2	yes	complemented
722	#417	C₂²×C₅₃	1	2	yes	complemented
723	C₅₃	#62004	1	1	yes	characteristic, direct product factor, Sylow
724	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
725	C₂×#41	C₂³×C₅₃	1	2	yes	—
726	C₂×#41	C₂³×C₅₃	1	2	yes	—
727	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
728	C₂²×D₄	—	2	1	no	—
729	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
730	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
731	C₂³×C₄	—	2	1	no	—
732	#137	—	4	4	no	—
733	AGL(1,ℤ/8)	—	4	4	no	—
734	AGL(1,ℤ/8)	—	4	4	no	—
735	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
736	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
737	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
739	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
740	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
744	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
745	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
746	C₂×D₈	C₂³×C₅₃	1	2	yes	—
747	C₂×D₈	C₂³×C₅₃	1	2	yes	—
748	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
749	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
750	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
751	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
752	C₄⋊Q₈	—	2	1	no	—
753	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
754	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
755	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
756	#127	C₂³×C₅₃	1	1	yes	characteristic
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	2	1	no	—
761	#126	—	2	2	no	—
762	#126	—	2	2	no	—
763	#125	—	2	2	no	—
764	#125	—	2	1	no	—
765	#125	C₂³×C₅₃	1	1	yes	characteristic
766	#125	C₂³×C₅₃	1	2	yes	—
767	#124	—	2	1	no	—
768	#124	—	2	2	no	—
769	#124	—	2	2	no	—
770	#124	—	2	2	no	—
771	#124	—	2	2	no	—
772	#124	C₂³×C₅₃	1	1	yes	characteristic
773	#124	C₂³×C₅₃	1	2	yes	—
774	#124	C₂³×C₅₃	1	2	yes	—
775	#124	C₂³×C₅₃	1	2	yes	—
776	#124	C₂³×C₅₃	1	2	yes	—
777	#123	—	2	2	no	—
778	#123	—	2	1	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
793	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
795	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
796	#121	—	2	1	no	—
797	#121	—	2	1	no	—
798	#121	—	2	2	no	—
799	#121	—	2	1	no	—
800	#121	—	2	1	no	—
801	#121	—	2	1	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	C₂³×C₅₃	1	1	yes	characteristic
805	#121	C₂³×C₅₃	1	2	yes	—
806	#121	C₂³×C₅₃	1	2	yes	—
807	#120	—	2	2	no	—
808	#120	—	2	2	no	—
809	#120	—	2	2	no	—
810	C₄×Q₈	—	2	1	no	—
811	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
813	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
814	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
815	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
816	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
830	C₄×D₄	D₄×C₅₃	1	2	yes	—
831	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₅₃	1	2	yes	—
836	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₅₃	1	2	yes	—
838	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₅₃	1	2	yes	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	—	2	1	no	—
844	#117	—	2	2	no	—
845	#117	—	2	2	no	—
846	#117	—	2	2	no	—
847	#117	—	2	1	no	—
848	#117	—	2	2	no	—
849	#117	D₄×C₅₃	1	1	yes	characteristic
850	#117	D₄×C₅₃	1	2	yes	—
851	#117	C₂³×C₅₃	1	2	yes	—
852	C₂×C₄⋊C₄	—	2	1	no	—
853	C₂×C₄⋊C₄	—	2	1	no	—
854	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
855	C₂×C₂²⋊C₄	—	2	1	no	—
856	C₂×C₂²⋊C₄	—	2	2	no	—
857	C₂×C₂²⋊C₄	—	2	2	no	—
858	C₂×C₂²⋊C₄	—	2	2	no	—
859	C₂×C₂²⋊C₄	—	2	2	no	—
860	C₂×C₄²	—	2	2	no	—
861	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
862	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
863	#107	C₂³×C₅₃	1	1	yes	characteristic
864	#107	C₂³×C₅₃	1	1	yes	characteristic
865	#107	C₂³×C₅₃	1	2	yes	—
866	#106	C₂³×C₅₃	1	1	yes	characteristic
867	#106	C₂³×C₅₃	1	2	yes	—
868	#106	C₂³×C₅₃	1	1	yes	characteristic
869	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
870	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
871	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
873	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
874	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
875	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
876	#103	C₂³×C₅₃	1	2	yes	—
877	#103	C₂³×C₅₃	1	2	yes	—
878	#103	C₂³×C₅₃	1	1	yes	characteristic
879	#103	C₂³×C₅₃	1	2	yes	—
880	#103	C₂³×C₅₃	1	2	yes	—
881	#103	C₂³×C₅₃	1	2	yes	—
882	#103	C₂³×C₅₃	1	1	yes	characteristic
883	#103	C₂³×C₅₃	1	2	yes	—
884	#103	C₂³×C₅₃	1	2	yes	—
885	#102	C₂³×C₅₃	1	2	yes	—
886	#102	C₂³×C₅₃	1	2	yes	—
887	#102	C₂³×C₅₃	1	1	yes	characteristic
888	#102	C₂³×C₅₃	1	2	yes	—
889	#102	C₂³×C₅₃	1	2	yes	—
890	#102	C₂³×C₅₃	1	1	yes	characteristic
891	#102	C₂³×C₅₃	1	1	yes	characteristic
892	#102	C₂³×C₅₃	1	1	yes	characteristic
893	#102	C₂³×C₅₃	1	1	yes	characteristic
894	#102	C₂³×C₅₃	1	2	yes	—
895	#102	C₂³×C₅₃	1	1	yes	characteristic
896	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
898	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
899	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
900	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
902	C₄×C₈	C₂³×C₅₃	1	2	yes	—
903	C₄×C₈	C₂³×C₅₃	1	2	yes	—
904	C₂⁴	—	2	1	no	—
905	C₂⁴	—	2	2	no	—
906	#41	—	2	4	no	—
907	#41	—	4	2	no	—
908	#41	—	4	2	no	—
909	#41	—	4	2	no	—
910	#41	—	4	2	no	—
911	C₂×Q₈	—	2	1	no	—
912	C₂×Q₈	—	2	2	no	—
913	C₂×Q₈	—	4	2	no	—
914	C₂×Q₈	—	4	2	no	—
915	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
918	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	4	1	no	—
930	C₂×D₄	—	4	2	no	—
931	C₂×D₄	—	4	2	no	—
932	C₂×D₄	—	4	4	no	—
933	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
934	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
935	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
936	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
937	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
938	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	4	4	no	—
951	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
953	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
954	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
957	Q₁₆	—	4	2	no	—
958	Q₁₆	—	4	2	no	—
959	Q₁₆	—	4	2	no	—
960	SD₁₆	—	2	4	no	—
961	SD₁₆	—	2	2	no	—
962	SD₁₆	—	4	2	no	—
963	SD₁₆	—	4	2	no	—
964	SD₁₆	—	4	2	no	—
965	SD₁₆	—	4	1	no	—
966	SD₁₆	—	4	2	no	—
967	D₈	—	2	4	no	—
968	D₈	—	2	2	no	—
969	D₈	—	4	2	no	—
970	D₈	—	4	1	no	—
971	M₁₆	—	4	2	no	—
972	M₁₆	—	4	2	no	—
973	M₁₆	—	4	2	no	—
974	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
978	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
979	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
999	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1000	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1001	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1005	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1006	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1033	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1034	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	—	2	2	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1041	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1042	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1043	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1044	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1045	C₄²	C₂⁴×C₅₃	1	2	yes	—
1046	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	2	no	—
1051	C₂³	—	4	2	no	—
1052	C₂³	—	4	2	no	—
1053	C₂³	—	4	4	no	—
1054	C₂³	—	8	1	no	—
1055	C₂³	—	8	2	no	—
1056	C₂³	—	8	2	no	—
1057	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1058	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	2	no	—
1061	Q₈	—	2	1	no	—
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	2	no	—
1064	Q₈	—	2	1	no	—
1065	Q₈	—	2	2	no	—
1066	Q₈	—	8	1	no	—
1067	Q₈	—	8	2	no	—
1068	D₄	—	2	2	no	—
1069	D₄	—	2	2	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	1	no	—
1073	D₄	—	2	1	no	—
1074	D₄	—	2	1	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	4	4	no	—
1079	D₄	—	4	4	no	—
1080	D₄	—	4	2	no	—
1081	D₄	—	8	1	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	1	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	2	no	—
1086	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	4	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	2	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1115	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1116	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1117	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1118	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1119	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1120	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1121	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1122	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1123	C₈	—	2	1	no	—
1124	C₈	—	2	2	no	—
1125	C₈	—	2	2	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	2	1	no	—
1128	C₈	—	2	1	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	8	4	no	—
1148	C₂²	—	16	4	no	—
1149	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1150	C₄	—	2	2	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	2	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	1	no	—
1164	C₄	—	4	2	no	—
1165	C₄	C₅₃×#575	1	2	yes	—
1166	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1167	C₄	C₅₃×#585	1	1	yes	characteristic
1168	C₂	—	4	1	no	—
1169	C₂	—	4	2	no	—
1170	C₂	—	4	2	no	—
1171	C₂	—	8	1	no	—
1172	C₂	—	8	1	no	—
1173	C₂	—	8	2	no	—
1174	C₂	C₅₃×#3488	1	1	yes	characteristic
1175	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1176	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 ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3514	C₂	semidirect
2. C₅₃×#3475	C₂	semidirect
3. C₅₃×#3394	C₂	semidirect
4. C₅₃×#3393	C₂	semidirect
5. C₅₃×#3361	C₂	semidirect
6. C₅₃×#3360	C₂	semidirect
7. C₅₃×#3329	C₂	semidirect
8. C₅₃×#3327	C₂	semidirect
9. C₅₃×#3325	C₂	semidirect
10. C₅₃×#3323	C₂	semidirect
11. C₅₃×#3276	C₂	semidirect
12. C₅₃×#3275	C₂	semidirect
13. C₅₃×#3273	C₂	semidirect
14. C₅₃×#3272	C₂	semidirect
15. C₅₃×#3256	C₂	semidirect
16. C₅₃×#3252	C₂	semidirect
17. C₅₃×#3211	C₂	semidirect
18. C₅₃×#3210	C₂	semidirect
19. C₅₃×#3105	C₂	semidirect
20. C₅₃×#3102	C₂	semidirect
21. C₅₃×#3040	C₂	semidirect
22. C₅₃×#3036	C₂	semidirect
23. C₅₃×#2991	C₂	semidirect
24. C₂×#137×C₅₃	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
27. C₅₃×#559	C₂²	semidirect
28. C₅₃×#556	C₂²	semidirect
29. C₅₃×#556	C₂²	semidirect
32. C₅₃×#554	C₂²	semidirect
35. C₅₃×#552	C₂²	semidirect
38. D₄×Q₈×C₅₃	C₂²	semidirect
43. C₅₃×#546	C₂²	semidirect
44. D₄²×C₅₃	C₂²	semidirect
47. C₅₃×#533	C₂²	semidirect
51. C₅₃×#529	C₂²	semidirect
52. C₅₃×#529	C₂²	semidirect
53. C₂×#124×C₅₃	C₂²	semidirect
57. C₄×#41×C₅₃	C₂²	semidirect
58. C₂×C₄×D₄×C₅₃	C₂²	semidirect
61. C₅₃×#495	C₂²	semidirect
62. C₅₃×#494	C₂²	semidirect
63. C₅₃×#492	C₂²	semidirect
64. C₅₃×#488	C₂²	semidirect
65. C₅₃×#488	C₂²	semidirect
66. C₅₃×#487	C₂²	semidirect
67. C₅₃×#486	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
69. C₅₃×#484	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
72. C₅₃×#479	C₂²	semidirect
73. C₅₃×#479	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#478	C₂²	semidirect
77. C₅₃×#477	C₂²	semidirect
78. C₅₃×#476	C₂²	semidirect
79. C₅₃×#470	C₂²	semidirect
80. C₅₃×#470	C₂²	semidirect
83. C₅₃×#468	C₂²	semidirect
84. C₅₃×#468	C₂²	semidirect
85. C₅₃×#464	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#464	C₂²	semidirect
88. C₅₃×#464	C₂²	semidirect
89. C₅₃×#464	C₂²	semidirect
90. C₅₃×#464	C₂²	semidirect
94. C₅₃×#463	C₂²	semidirect
95. C₅₃×#463	C₂²	semidirect
96. C₅₃×#463	C₂²	semidirect
97. C₅₃×#463	C₂²	semidirect
98. C₅₃×#462	C₂²	semidirect
99. C₅₃×#461	C₂²	semidirect
100. C₅₃×#461	C₂²	semidirect
101. C₅₃×#461	C₂²	semidirect
104. C₅₃×#452	C₂²	semidirect
105. C₅₃×#452	C₂²	semidirect
106. C₅₃×#452	C₂²	semidirect
107. C₅₃×#451	C₂²	semidirect
108. C₅₃×#450	C₂²	semidirect
109. C₅₃×#450	C₂²	semidirect
111. C₅₃×#448	C₂²	semidirect
114. C₈×Q₈×C₅₃	C₂²	semidirect
115. C₈×Q₈×C₅₃	C₂²	semidirect
116. C₄×Q₁₆×C₅₃	C₂²	semidirect
117. C₄×SD₁₆×C₅₃	C₂²	semidirect
118. C₄×SD₁₆×C₅₃	C₂²	semidirect
119. C₄×SD₁₆×C₅₃	C₂²	semidirect
120. C₄×SD₁₆×C₅₃	C₂²	semidirect
123. C₄×D₈×C₅₃	C₂²	semidirect
124. C₅₃×#436	C₂²	semidirect
125. C₅₃×#436	C₂²	semidirect
126. C₅₃×#436	C₂²	semidirect
127. C₅₃×#436	C₂²	semidirect
128. C₅₃×#431	C₂²	semidirect
129. C₅₃×#431	C₂²	semidirect
130. C₅₃×#423	C₂²	semidirect
131. C₅₃×#423	C₂²	semidirect
132. C₅₃×#419	C₂²	semidirect
133. C₅₃×#418	C₂²	semidirect
134. C₅₃×#417	C₂²	semidirect
540. #62004	C₅₃	direct (N × H)
580. #3514	C₂×C₅₃	semidirect
581. #3475	C₂×C₅₃	semidirect
582. #3394	C₂×C₅₃	semidirect
583. #3393	C₂×C₅₃	semidirect
584. #3361	C₂×C₅₃	semidirect
585. #3360	C₂×C₅₃	semidirect
586. #3329	C₂×C₅₃	semidirect
587. #3327	C₂×C₅₃	semidirect
588. #3325	C₂×C₅₃	semidirect
589. #3323	C₂×C₅₃	semidirect
590. #3276	C₂×C₅₃	semidirect
591. #3275	C₂×C₅₃	semidirect
592. #3273	C₂×C₅₃	semidirect
593. #3272	C₂×C₅₃	semidirect
594. #3256	C₂×C₅₃	semidirect
595. #3252	C₂×C₅₃	semidirect
596. #3211	C₂×C₅₃	semidirect
597. #3210	C₂×C₅₃	semidirect
598. #3105	C₂×C₅₃	semidirect
599. #3102	C₂×C₅₃	semidirect
600. #3040	C₂×C₅₃	semidirect
601. #3036	C₂×C₅₃	semidirect
602. #2991	C₂×C₅₃	semidirect
612. C₂×#137	C₂²×C₅₃	semidirect
614. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
615. #559	C₂²×C₅₃	semidirect
616. #556	C₂²×C₅₃	semidirect
617. #556	C₂²×C₅₃	semidirect
620. #554	C₂²×C₅₃	semidirect
623. #552	C₂²×C₅₃	semidirect
626. D₄×Q₈	C₂²×C₅₃	semidirect
631. #546	C₂²×C₅₃	semidirect
632. D₄²	C₂²×C₅₃	semidirect
635. #533	C₂²×C₅₃	semidirect
639. #529	C₂²×C₅₃	semidirect
640. #529	C₂²×C₅₃	semidirect
641. C₂×#124	C₂²×C₅₃	semidirect
645. C₄×#41	C₂²×C₅₃	semidirect
646. C₂×C₄×D₄	C₂²×C₅₃	semidirect
649. #495	C₂²×C₅₃	semidirect
650. #494	C₂²×C₅₃	semidirect
651. #492	C₂²×C₅₃	semidirect
652. #488	C₂²×C₅₃	semidirect
653. #488	C₂²×C₅₃	semidirect
654. #487	C₂²×C₅₃	semidirect
655. #486	C₂²×C₅₃	semidirect
656. #485	C₂²×C₅₃	semidirect
657. #484	C₂²×C₅₃	semidirect
658. #482	C₂²×C₅₃	semidirect
660. #479	C₂²×C₅₃	semidirect
661. #479	C₂²×C₅₃	semidirect
662. #478	C₂²×C₅₃	semidirect
663. #478	C₂²×C₅₃	semidirect
664. #478	C₂²×C₅₃	semidirect
665. #477	C₂²×C₅₃	semidirect
666. #476	C₂²×C₅₃	semidirect
667. #470	C₂²×C₅₃	semidirect
668. #470	C₂²×C₅₃	semidirect
671. #468	C₂²×C₅₃	semidirect
672. #468	C₂²×C₅₃	semidirect
673. #464	C₂²×C₅₃	semidirect
674. #464	C₂²×C₅₃	semidirect
675. #464	C₂²×C₅₃	semidirect
676. #464	C₂²×C₅₃	semidirect
677. #464	C₂²×C₅₃	semidirect
678. #464	C₂²×C₅₃	semidirect
682. #463	C₂²×C₅₃	semidirect
683. #463	C₂²×C₅₃	semidirect
684. #463	C₂²×C₅₃	semidirect
685. #463	C₂²×C₅₃	semidirect
686. #462	C₂²×C₅₃	semidirect
687. #461	C₂²×C₅₃	semidirect
688. #461	C₂²×C₅₃	semidirect
689. #461	C₂²×C₅₃	semidirect
692. #452	C₂²×C₅₃	semidirect
693. #452	C₂²×C₅₃	semidirect
694. #452	C₂²×C₅₃	semidirect
695. #451	C₂²×C₅₃	semidirect
696. #450	C₂²×C₅₃	semidirect
697. #450	C₂²×C₅₃	semidirect
699. #448	C₂²×C₅₃	semidirect
702. C₈×Q₈	C₂²×C₅₃	semidirect
703. C₈×Q₈	C₂²×C₅₃	semidirect
704. C₄×Q₁₆	C₂²×C₅₃	semidirect
705. C₄×SD₁₆	C₂²×C₅₃	semidirect
706. C₄×SD₁₆	C₂²×C₅₃	semidirect
707. C₄×SD₁₆	C₂²×C₅₃	semidirect
708. C₄×SD₁₆	C₂²×C₅₃	semidirect
711. C₄×D₈	C₂²×C₅₃	semidirect
712. #436	C₂²×C₅₃	semidirect
713. #436	C₂²×C₅₃	semidirect
714. #436	C₂²×C₅₃	semidirect
715. #436	C₂²×C₅₃	semidirect
716. #431	C₂²×C₅₃	semidirect
717. #431	C₂²×C₅₃	semidirect
718. #423	C₂²×C₅₃	semidirect
719. #423	C₂²×C₅₃	semidirect
720. #419	C₂²×C₅₃	semidirect
721. #418	C₂²×C₅₃	semidirect
722. #417	C₂²×C₅₃	semidirect
723. C₅₃	#62004	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×#3514	2
C₅₃×#3475	2
C₅₃×#3394	2
C₅₃×#3393	2
C₅₃×#3361	2
C₅₃×#3360	2
C₅₃×#3329	2
C₅₃×#3327	2
C₅₃×#3325	2
C₅₃×#3323	2
C₅₃×#3276	2
C₅₃×#3275	2
C₅₃×#3273	2
C₅₃×#3272	2
C₅₃×#3256	2
C₅₃×#3252	2
C₅₃×#3211	2
C₅₃×#3210	2
C₅₃×#3105	2
C₅₃×#3102	2
C₅₃×#3040	2
C₅₃×#3036	2
C₅₃×#2991	2
#62004	53

Subgroups — C53×#62004 #27269516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62004 #27269516