Subgroups — C₅₃×#61189 #27268701

Order 13568.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3332	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3326	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3321	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3309	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3309	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3308	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3305	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3301	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₅₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2896	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	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
31	C₅₃×#555	C₂²	1	2	yes	complemented
32	C₅₃×#553	C₂²	1	2	yes	complemented
33	C₅₃×#553	C₂²	1	2	yes	complemented
34	C₅₃×#551	—	2	2	no	—
35	C₅₃×#550	—	2	1	no	—
36	C₅₃×#550	—	2	1	no	—
37	C₅₃×#550	C₂²	1	2	yes	complemented
38	C₅₃×#550	C₂²	1	2	yes	complemented
39	C₅₃×#548	—	2	1	no	—
40	C₅₃×#548	—	2	1	no	—
41	C₅₃×#548	C₂²	1	2	yes	complemented
42	C₅₃×#548	C₂²	1	2	yes	complemented
43	C₅₃×#547	C₂²	1	2	yes	complemented
44	C₅₃×#546	—	2	2	no	—
45	C₅₃×#544	C₂²	1	1	yes	characteristic
46	C₅₃×#542	—	2	1	no	—
47	C₅₃×#540	—	2	1	no	—
48	C₅₃×#535	—	2	2	no	—
49	C₅₃×#535	C₂²	1	1	yes	characteristic
50	C₅₃×#535	C₂²	1	1	yes	characteristic
51	C₅₃×#535	C₂²	1	1	yes	characteristic
52	C₅₃×#532	—	2	1	no	—
53	C₅₃×#529	—	2	1	no	—
54	C₅₃×#525	—	2	2	no	—
55	C₅₃×#525	C₂²	1	1	yes	characteristic
56	C₅₃×#525	C₂²	1	1	yes	characteristic
57	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
58	C₅₃×#520	C₂²	1	1	yes	characteristic
59	C₅₃×#519	C₂²	1	1	yes	characteristic
60	C₅₃×#518	C₂²	1	1	yes	characteristic
61	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
62	C₅₃×#490	C₂²	1	2	yes	complemented
63	C₅₃×#489	C₂²	1	2	yes	complemented
64	C₅₃×#488	C₂²	1	2	yes	complemented
65	C₅₃×#486	C₂²	1	2	yes	complemented
66	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#482	C₂²	1	2	yes	complemented
72	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#482	C₂²	1	2	yes	complemented
74	C₅₃×#481	C₂²	1	2	yes	complemented
75	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#480	C₂²	1	2	yes	complemented
77	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#479	C₂²	1	2	yes	complemented
79	C₅₃×#479	C₂²	1	2	yes	complemented
80	C₅₃×#477	C₂²	1	2	yes	complemented
81	C₅₃×#475	C₂²	1	2	yes	complemented
82	C₅₃×#469	C₂²	1	2	yes	complemented
83	C₅₃×#469	C₂²	1	2	yes	complemented
84	C₅₃×#469	C₂²	1	2	yes	complemented
85	C₅₃×#468	C₂²	1	2	yes	complemented
86	C₅₃×#466	C₂²	1	2	yes	complemented
87	C₅₃×#466	C₂²	1	2	yes	complemented
88	C₅₃×#466	C₂²	1	2	yes	complemented
89	C₅₃×#465	C₂²	1	2	yes	complemented
90	C₅₃×#463	C₂²	1	2	yes	complemented
91	C₅₃×#463	C₂²	1	2	yes	complemented
92	C₅₃×#459	C₂²	1	2	yes	complemented
93	C₅₃×#459	C₂²	1	2	yes	complemented
94	C₅₃×#449	C₂²	1	2	yes	—
95	C₅₃×#449	C₂²	1	2	yes	—
96	C₅₃×#449	C₂²	1	2	yes	—
97	C₅₃×#449	C₂²	1	2	yes	—
98	C₅₃×#449	C₂²	1	2	yes	complemented
99	C₅₃×#449	C₂²	1	2	yes	complemented
100	C₅₃×#448	C₂²	1	2	yes	complemented
101	C₅₃×#448	C₂²	1	2	yes	complemented
102	C₅₃×#440	C₂²	1	2	yes	complemented
103	C₅₃×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
106	C₅₃×#436	C₂²	1	2	yes	complemented
107	C₅₃×#435	C₂²	1	2	yes	complemented
108	C₅₃×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
110	C₅₃×#428	C₂²	1	1	yes	characteristic
111	C₅₃×#427	C₂²	1	1	yes	characteristic
112	C₅₃×#427	C₂²	1	1	yes	characteristic
113	C₅₃×#424	C₂²	1	1	yes	characteristic
114	C₅₃×#419	C₂²	1	1	yes	characteristic
115	C₅₃×#419	C₂²	1	1	yes	characteristic
116	C₅₃×#419	C₂²	1	2	yes	complemented
117	C₅₃×#418	C₂²	1	1	yes	characteristic
118	C₅₃×#418	C₂²	1	1	yes	characteristic
119	C₅₃×#418	C₂²	1	1	yes	characteristic
120	C₅₃×#417	C₂²	1	1	yes	characteristic
121	C₅₃×#417	C₂²	1	2	yes	complemented
122	C₅₃×#417	C₂²	1	2	yes	complemented
123	C₅₃×#417	C₂²	1	2	yes	complemented
124	C₅₃×#416	C₂²	1	1	yes	characteristic
125	C₅₃×#416	C₂²	1	1	yes	characteristic
126	C₅₃×#416	C₂²	1	2	yes	complemented
127	C₅₃×#416	C₂²	1	2	yes	complemented
128	C₅₃×#416	C₂²	1	2	yes	complemented
129	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
130	C₂×#103×C₅₃	C₂²	1	2	yes	complemented
131	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
132	C₅₃×#408	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
134	C₅₃×#405	C₂²	1	1	yes	characteristic
135	2₋¹⁺⁴×C₅₃	—	2	4	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	2	no	—
140	C₂×#41×C₅₃	—	2	1	no	—
141	C₂×#41×C₅₃	—	2	1	no	—
142	C₂×#41×C₅₃	—	2	4	no	—
143	C₂×#41×C₅₃	—	4	2	no	—
144	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×#41×C₅₃	C₂³	1	2	yes	—
146	C₂×#41×C₅₃	C₂³	1	2	yes	—
147	C₂×#41×C₅₃	C₂³	1	2	yes	—
148	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₅₃	—	2	1	no	—
150	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
151	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
152	C₂²×D₄×C₅₃	—	2	1	no	—
153	C₂²×D₄×C₅₃	—	2	1	no	—
154	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
155	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₅₃	—	2	1	no	—
157	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
158	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
159	C₂×SD₁₆×C₅₃	—	2	4	no	—
160	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
163	C₂×D₈×C₅₃	—	4	2	no	—
164	C₂×D₈×C₅₃	C₂³	1	2	yes	—
165	C₂×D₈×C₅₃	C₂³	1	2	yes	—
166	C₂×D₈×C₅₃	C₂³	1	2	yes	—
167	#131×C₅₃	—	4	2	no	—
168	C₂×M₁₆×C₅₃	—	4	2	no	—
169	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
172	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
173	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
176	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
177	C₄⋊Q₈×C₅₃	—	2	1	no	—
178	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
179	#127×C₅₃	—	2	1	no	—
180	#127×C₅₃	—	2	2	no	—
181	#127×C₅₃	—	2	2	no	—
182	#127×C₅₃	—	2	1	no	—
183	#127×C₅₃	C₂³	1	2	yes	—
184	#126×C₅₃	—	2	2	no	—
185	#126×C₅₃	—	2	2	no	—
186	#125×C₅₃	—	2	1	no	—
187	#125×C₅₃	C₂³	1	2	yes	—
188	#124×C₅₃	—	2	2	no	—
189	#124×C₅₃	—	2	2	no	—
190	#124×C₅₃	—	2	2	no	—
191	#124×C₅₃	—	2	2	no	—
192	#124×C₅₃	—	2	1	no	—
193	#124×C₅₃	—	2	1	no	—
194	#124×C₅₃	C₂³	1	2	yes	—
195	#123×C₅₃	—	2	2	no	—
196	#123×C₅₃	—	2	2	no	—
197	#123×C₅₃	—	2	2	no	—
198	#123×C₅₃	—	2	2	no	—
199	#123×C₅₃	—	2	1	no	—
200	#123×C₅₃	D₄	1	2	yes	—
201	C₂²⋊Q₈×C₅₃	—	2	2	no	—
202	C₂²⋊Q₈×C₅₃	—	2	2	no	—
203	C₂²⋊Q₈×C₅₃	—	2	2	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
206	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
207	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
209	#121×C₅₃	—	2	1	no	—
210	#121×C₅₃	—	2	1	no	—
211	#121×C₅₃	—	2	2	no	—
212	#121×C₅₃	—	2	2	no	—
213	#121×C₅₃	—	2	2	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	D₄	1	1	yes	characteristic
223	#121×C₅₃	D₄	1	1	yes	characteristic
224	#121×C₅₃	C₂³	1	2	yes	—
225	#121×C₅₃	C₂³	1	2	yes	—
226	#121×C₅₃	C₂³	1	1	yes	characteristic
227	#121×C₅₃	C₂³	1	1	yes	characteristic
228	#121×C₅₃	C₂³	1	2	yes	—
229	#121×C₅₃	C₂³	1	2	yes	—
230	#121×C₅₃	C₂³	1	2	yes	—
231	#121×C₅₃	C₂³	1	2	yes	—
232	#120×C₅₃	—	2	2	no	—
233	#120×C₅₃	—	2	1	no	—
234	#120×C₅₃	—	2	2	no	—
235	#120×C₅₃	—	2	2	no	—
236	#120×C₅₃	D₄	1	2	yes	—
237	C₄×Q₈×C₅₃	—	2	1	no	—
238	C₄×Q₈×C₅₃	—	2	1	no	—
239	C₄×Q₈×C₅₃	—	2	1	no	—
240	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
241	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
242	C₄×D₄×C₅₃	—	2	1	no	—
243	C₄×D₄×C₅₃	—	2	1	no	—
244	C₄×D₄×C₅₃	—	2	2	no	—
245	C₄×D₄×C₅₃	—	2	2	no	—
246	C₄×D₄×C₅₃	—	2	2	no	—
247	C₄×D₄×C₅₃	—	2	2	no	—
248	C₄×D₄×C₅₃	—	2	2	no	—
249	C₄×D₄×C₅₃	—	2	2	no	—
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	C₂³	1	2	yes	—
255	C₄×D₄×C₅₃	C₂³	1	2	yes	—
256	C₄×D₄×C₅₃	C₂³	1	2	yes	—
257	C₄×D₄×C₅₃	C₂³	1	2	yes	—
258	#117×C₅₃	—	2	2	no	—
259	#117×C₅₃	—	2	2	no	—
260	#117×C₅₃	—	2	1	no	—
261	#117×C₅₃	—	2	1	no	—
262	#117×C₅₃	C₂³	1	1	yes	characteristic
263	#117×C₅₃	C₂³	1	1	yes	characteristic
264	#117×C₅₃	C₂³	1	1	yes	characteristic
265	#117×C₅₃	C₂³	1	1	yes	characteristic
266	#117×C₅₃	C₂³	1	1	yes	characteristic
267	#117×C₅₃	C₂³	1	2	yes	—
268	#117×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	1	no	—
275	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
276	C₂×C₄²×C₅₃	—	2	1	no	—
277	#107×C₅₃	C₂³	1	1	yes	characteristic
278	#107×C₅₃	C₂³	1	1	yes	characteristic
279	#107×C₅₃	C₂³	1	1	yes	characteristic
280	#107×C₅₃	C₂³	1	1	yes	characteristic
281	#107×C₅₃	C₂³	1	2	yes	—
282	#106×C₅₃	C₂³	1	1	yes	characteristic
283	#106×C₅₃	C₂³	1	1	yes	characteristic
284	#106×C₅₃	C₂³	1	1	yes	characteristic
285	#106×C₅₃	C₂³	1	1	yes	characteristic
286	#106×C₅₃	C₂³	1	2	yes	—
287	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
288	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	1	yes	characteristic
290	#103×C₅₃	C₂³	1	1	yes	characteristic
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
298	#103×C₅₃	C₂³	1	2	yes	—
299	#103×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	2	yes	—
304	#102×C₅₃	C₂³	1	2	yes	—
305	#102×C₅₃	C₂³	1	2	yes	—
306	#102×C₅₃	C₂³	1	1	yes	characteristic
307	#102×C₅₃	C₂³	1	1	yes	characteristic
308	#102×C₅₃	C₂³	1	1	yes	characteristic
309	#102×C₅₃	C₂³	1	2	yes	—
310	#102×C₅₃	C₂³	1	2	yes	—
311	#102×C₅₃	C₂³	1	2	yes	—
312	#102×C₅₃	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
319	#97×C₅₃	C₂³	1	2	yes	—
320	C₄×C₈×C₅₃	C₂³	1	2	yes	—
321	C₂⁴×C₅₃	—	2	1	no	—
322	C₂⁴×C₅₃	—	2	1	no	—
323	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
324	#41×C₅₃	—	2	2	no	—
325	#41×C₅₃	—	2	2	no	—
326	#41×C₅₃	—	2	4	no	—
327	#41×C₅₃	—	2	4	no	—
328	#41×C₅₃	—	2	4	no	—
329	#41×C₅₃	—	2	2	no	—
330	#41×C₅₃	—	2	2	no	—
331	#41×C₅₃	—	4	2	no	—
332	#41×C₅₃	—	4	2	no	—
333	#41×C₅₃	—	4	2	no	—
334	#41×C₅₃	—	4	8	no	—
335	#41×C₅₃	—	4	4	no	—
336	#41×C₅₃	—	4	4	no	—
337	#41×C₅₃	—	4	4	no	—
338	#41×C₅₃	—	8	4	no	—
339	C₂×Q₈×C₅₃	—	2	1	no	—
340	C₂×Q₈×C₅₃	—	2	2	no	—
341	C₂×Q₈×C₅₃	—	2	2	no	—
342	C₂×Q₈×C₅₃	—	2	2	no	—
343	C₂×Q₈×C₅₃	—	2	4	no	—
344	C₂×Q₈×C₅₃	—	4	2	no	—
345	C₂×Q₈×C₅₃	—	4	4	no	—
346	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
347	C₂×Q₈×C₅₃	#41	1	4	yes	complemented
348	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
350	C₂×D₄×C₅₃	—	2	2	no	—
351	C₂×D₄×C₅₃	—	2	1	no	—
352	C₂×D₄×C₅₃	—	2	2	no	—
353	C₂×D₄×C₅₃	—	2	2	no	—
354	C₂×D₄×C₅₃	—	2	2	no	—
355	C₂×D₄×C₅₃	—	2	2	no	—
356	C₂×D₄×C₅₃	—	2	1	no	—
357	C₂×D₄×C₅₃	—	2	1	no	—
358	C₂×D₄×C₅₃	—	2	2	no	—
359	C₂×D₄×C₅₃	—	2	2	no	—
360	C₂×D₄×C₅₃	—	2	2	no	—
361	C₂×D₄×C₅₃	—	2	2	no	—
362	C₂×D₄×C₅₃	—	2	1	no	—
363	C₂×D₄×C₅₃	—	2	1	no	—
364	C₂×D₄×C₅₃	—	2	2	no	—
365	C₂×D₄×C₅₃	—	2	2	no	—
366	C₂×D₄×C₅₃	—	2	2	no	—
367	C₂×D₄×C₅₃	—	2	2	no	—
368	C₂×D₄×C₅₃	—	2	2	no	—
369	C₂×D₄×C₅₃	—	2	2	no	—
370	C₂×D₄×C₅₃	—	4	4	no	—
371	C₂×D₄×C₅₃	—	8	2	no	—
372	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
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	C₂⁴	1	2	yes	—
377	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
379	C₂²×C₄×C₅₃	—	2	1	no	—
380	C₂²×C₄×C₅₃	—	2	2	no	—
381	C₂²×C₄×C₅₃	—	2	2	no	—
382	C₂²×C₄×C₅₃	—	2	1	no	—
383	C₂²×C₄×C₅₃	—	2	2	no	—
384	C₂²×C₄×C₅₃	—	2	1	no	—
385	C₂²×C₄×C₅₃	—	2	1	no	—
386	C₂²×C₄×C₅₃	—	2	2	no	—
387	C₂²×C₄×C₅₃	—	2	2	no	—
388	C₂²×C₄×C₅₃	—	2	1	no	—
389	C₂²×C₄×C₅₃	—	2	2	no	—
390	C₂²×C₄×C₅₃	—	2	2	no	—
391	C₂²×C₄×C₅₃	—	2	2	no	—
392	C₂²×C₄×C₅₃	—	2	2	no	—
393	C₂²×C₄×C₅₃	—	4	4	no	—
394	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
399	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	SD₁₆×C₅₃	—	2	4	no	—
402	SD₁₆×C₅₃	—	2	4	no	—
403	SD₁₆×C₅₃	—	4	2	no	—
404	D₈×C₅₃	—	4	2	no	—
405	D₈×C₅₃	—	4	2	no	—
406	D₈×C₅₃	—	4	2	no	—
407	M₁₆×C₅₃	—	2	2	no	—
408	M₁₆×C₅₃	—	2	2	no	—
409	M₁₆×C₅₃	—	4	2	no	—
410	M₁₆×C₅₃	—	4	2	no	—
411	C₂×C₈×C₅₃	—	2	2	no	—
412	C₂×C₈×C₅₃	—	2	2	no	—
413	C₂×C₈×C₅₃	—	4	2	no	—
414	C₂×C₈×C₅₃	—	4	2	no	—
415	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
417	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
419	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₅₃	—	2	1	no	—
422	C₄⋊C₄×C₅₃	—	2	1	no	—
423	C₄⋊C₄×C₅₃	—	2	1	no	—
424	C₄⋊C₄×C₅₃	—	2	2	no	—
425	C₄⋊C₄×C₅₃	—	2	2	no	—
426	C₄⋊C₄×C₅₃	—	2	2	no	—
427	C₄⋊C₄×C₅₃	—	2	2	no	—
428	C₄⋊C₄×C₅₃	—	2	1	no	—
429	C₄⋊C₄×C₅₃	—	2	1	no	—
430	C₄⋊C₄×C₅₃	—	2	2	no	—
431	C₄⋊C₄×C₅₃	—	2	2	no	—
432	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
436	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₂²⋊C₄×C₅₃	—	2	1	no	—
444	C₂²⋊C₄×C₅₃	—	2	1	no	—
445	C₂²⋊C₄×C₅₃	—	2	1	no	—
446	C₂²⋊C₄×C₅₃	—	2	1	no	—
447	C₂²⋊C₄×C₅₃	—	2	1	no	—
448	C₂²⋊C₄×C₅₃	—	2	2	no	—
449	C₂²⋊C₄×C₅₃	—	2	1	no	—
450	C₂²⋊C₄×C₅₃	—	2	1	no	—
451	C₂²⋊C₄×C₅₃	—	2	2	no	—
452	C₂²⋊C₄×C₅₃	—	2	2	no	—
453	C₂²⋊C₄×C₅₃	—	2	2	no	—
454	C₂²⋊C₄×C₅₃	—	2	2	no	—
455	C₂²⋊C₄×C₅₃	—	2	2	no	—
456	C₂²⋊C₄×C₅₃	—	2	1	no	—
457	C₂²⋊C₄×C₅₃	—	2	1	no	—
458	C₂²⋊C₄×C₅₃	—	2	2	no	—
459	C₂²⋊C₄×C₅₃	—	2	2	no	—
460	C₂²⋊C₄×C₅₃	—	2	2	no	—
461	C₂²⋊C₄×C₅₃	—	2	2	no	—
462	C₂²⋊C₄×C₅₃	—	2	2	no	—
463	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
467	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
468	C₄²×C₅₃	—	2	1	no	—
469	C₄²×C₅₃	—	2	1	no	—
470	C₄²×C₅₃	—	2	1	no	—
471	C₄²×C₅₃	—	2	1	no	—
472	C₄²×C₅₃	—	2	2	no	—
473	C₄²×C₅₃	—	2	2	no	—
474	C₄²×C₅₃	—	2	2	no	—
475	C₄²×C₅₃	—	2	1	no	—
476	C₄²×C₅₃	C₂⁴	1	2	yes	—
477	C₂³×C₅₃	—	2	2	no	—
478	C₂³×C₅₃	—	2	1	no	—
479	C₂³×C₅₃	—	2	2	no	—
480	C₂³×C₅₃	—	2	2	no	—
481	C₂³×C₅₃	—	4	1	no	—
482	C₂³×C₅₃	—	4	1	no	—
483	C₂³×C₅₃	—	4	2	no	—
484	C₂³×C₅₃	—	4	2	no	—
485	C₂³×C₅₃	—	8	1	no	—
486	C₂³×C₅₃	—	8	1	no	—
487	C₂³×C₅₃	—	8	1	no	—
488	C₂³×C₅₃	—	8	1	no	—
489	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
490	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
491	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
492	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
493	Q₈×C₅₃	—	2	4	no	—
494	Q₈×C₅₃	—	2	2	no	—
495	Q₈×C₅₃	—	2	2	no	—
496	Q₈×C₅₃	—	2	1	no	—
497	Q₈×C₅₃	—	2	1	no	—
498	Q₈×C₅₃	—	4	4	no	—
499	Q₈×C₅₃	—	8	2	no	—
500	Q₈×C₅₃	C₂×#41	1	4	yes	—
501	D₄×C₅₃	—	2	4	no	—
502	D₄×C₅₃	—	2	2	no	—
503	D₄×C₅₃	—	2	2	no	—
504	D₄×C₅₃	—	2	2	no	—
505	D₄×C₅₃	—	2	1	no	—
506	D₄×C₅₃	—	2	2	no	—
507	D₄×C₅₃	—	2	2	no	—
508	D₄×C₅₃	—	2	1	no	—
509	D₄×C₅₃	—	4	2	no	—
510	D₄×C₅₃	—	4	2	no	—
511	D₄×C₅₃	—	4	4	no	—
512	D₄×C₅₃	—	4	4	no	—
513	D₄×C₅₃	—	4	4	no	—
514	D₄×C₅₃	—	4	4	no	—
515	D₄×C₅₃	—	4	2	no	—
516	D₄×C₅₃	—	4	2	no	—
517	D₄×C₅₃	—	4	2	no	—
518	D₄×C₅₃	—	8	2	no	—
519	D₄×C₅₃	—	8	2	no	—
520	D₄×C₅₃	—	8	2	no	—
521	D₄×C₅₃	—	8	1	no	—
522	D₄×C₅₃	—	8	2	no	—
523	D₄×C₅₃	—	8	2	no	—
524	D₄×C₅₃	—	8	1	no	—
525	D₄×C₅₃	—	8	2	no	—
526	D₄×C₅₃	—	8	2	no	—
527	C₂×C₄×C₅₃	—	2	2	no	—
528	C₂×C₄×C₅₃	—	2	4	no	—
529	C₂×C₄×C₅₃	—	2	2	no	—
530	C₂×C₄×C₅₃	—	2	2	no	—
531	C₂×C₄×C₅₃	—	2	2	no	—
532	C₂×C₄×C₅₃	—	2	1	no	—
533	C₂×C₄×C₅₃	—	2	1	no	—
534	C₂×C₄×C₅₃	—	2	2	no	—
535	C₂×C₄×C₅₃	—	2	1	no	—
536	C₂×C₄×C₅₃	—	2	1	no	—
537	C₂×C₄×C₅₃	—	2	2	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	2	no	—
542	C₂×C₄×C₅₃	—	2	1	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	1	no	—
546	C₂×C₄×C₅₃	—	4	4	no	—
547	C₂×C₄×C₅₃	—	4	4	no	—
548	C₂×C₄×C₅₃	—	4	4	no	—
549	C₂×C₄×C₅₃	—	4	4	no	—
550	C₂×C₄×C₅₃	—	4	2	no	—
551	C₂×C₄×C₅₃	—	4	2	no	—
552	C₂×C₄×C₅₃	—	8	2	no	—
553	C₂×C₄×C₅₃	—	8	2	no	—
554	C₂×C₄×C₅₃	—	8	1	no	—
555	C₂×C₄×C₅₃	—	8	1	no	—
556	C₂×C₄×C₅₃	—	8	2	no	—
557	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
561	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
562	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
564	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
565	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
566	C₈×C₅₃	—	2	1	no	—
567	C₈×C₅₃	—	2	1	no	—
568	C₈×C₅₃	—	2	1	no	—
569	C₈×C₅₃	—	2	1	no	—
570	C₈×C₅₃	—	2	2	no	—
571	C₈×C₅₃	—	2	2	no	—
572	#61189	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
573	C₂²×C₅₃	—	2	1	no	—
574	C₂²×C₅₃	—	2	1	no	—
575	C₂²×C₅₃	—	2	1	no	—
576	C₂²×C₅₃	—	2	1	no	—
577	C₂²×C₅₃	—	2	2	no	—
578	C₂²×C₅₃	—	2	1	no	—
579	C₂²×C₅₃	—	2	2	no	—
580	C₂²×C₅₃	—	2	1	no	—
581	C₂²×C₅₃	—	2	1	no	—
582	C₂²×C₅₃	—	2	1	no	—
583	C₂²×C₅₃	—	2	2	no	—
584	C₂²×C₅₃	—	4	2	no	—
585	C₂²×C₅₃	—	4	1	no	—
586	C₂²×C₅₃	—	4	2	no	—
587	C₂²×C₅₃	—	4	2	no	—
588	C₂²×C₅₃	—	4	1	no	—
589	C₂²×C₅₃	—	4	2	no	—
590	C₂²×C₅₃	—	4	1	no	—
591	C₂²×C₅₃	—	4	2	no	—
592	C₂²×C₅₃	—	4	2	no	—
593	C₂²×C₅₃	—	8	2	no	—
594	C₂²×C₅₃	—	8	4	no	—
595	C₂²×C₅₃	—	16	2	no	—
596	C₂²×C₅₃	#546	1	2	yes	—
597	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
598	C₄×C₅₃	—	2	2	no	—
599	C₄×C₅₃	—	2	2	no	—
600	C₄×C₅₃	—	2	1	no	—
601	C₄×C₅₃	—	2	1	no	—
602	C₄×C₅₃	—	2	4	no	—
603	C₄×C₅₃	—	2	2	no	—
604	C₄×C₅₃	—	4	1	no	—
605	C₄×C₅₃	—	4	1	no	—
606	C₄×C₅₃	—	4	1	no	—
607	C₄×C₅₃	—	4	1	no	—
608	C₄×C₅₃	—	4	1	no	—
609	C₄×C₅₃	—	4	2	no	—
610	C₄×C₅₃	—	4	1	no	—
611	C₄×C₅₃	—	4	1	no	—
612	C₄×C₅₃	#546	1	2	yes	—
613	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
614	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
615	#3494	C₂×C₅₃	1	1	yes	characteristic, complemented
616	#3487	C₂×C₅₃	1	1	yes	characteristic, complemented
617	#3332	C₂×C₅₃	1	2	yes	complemented
618	#3326	C₂×C₅₃	1	2	yes	complemented
619	#3321	C₂×C₅₃	1	2	yes	complemented
620	#3309	C₂×C₅₃	1	2	yes	complemented
621	#3309	C₂×C₅₃	1	2	yes	complemented
622	#3308	C₂×C₅₃	1	2	yes	complemented
623	#3305	C₂×C₅₃	1	2	yes	complemented
624	#3301	C₂×C₅₃	1	2	yes	complemented
625	#3136	C₂×C₅₃	1	1	yes	characteristic, complemented
626	#3096	C₂×C₅₃	1	1	yes	characteristic, complemented
627	#3091	C₂×C₅₃	1	1	yes	characteristic, complemented
628	#3082	C₂×C₅₃	1	1	yes	characteristic, complemented
629	#3058	C₂×C₅₃	1	1	yes	characteristic, complemented
630	#3055	C₂×C₅₃	1	1	yes	characteristic, complemented
631	#3041	C₂×C₅₃	1	1	yes	characteristic, complemented
632	#3010	C₂×C₅₃	1	1	yes	characteristic, complemented
633	C₂×#449	C₂×C₅₃	1	1	yes	characteristic, complemented
634	#2949	C₂×C₅₃	1	1	yes	characteristic, complemented
635	#2933	C₂×C₅₃	1	1	yes	characteristic, complemented
636	#2898	C₂×C₅₃	1	1	yes	characteristic, complemented
637	#2896	C₂×C₅₃	1	1	yes	characteristic, complemented
638	C₂×C₅₃	—	2	2	no	—
639	C₂×C₅₃	—	4	2	no	—
640	C₂×C₅₃	—	4	1	no	—
641	C₂×C₅₃	—	4	1	no	—
642	C₂×C₅₃	—	8	1	no	—
643	C₂×C₅₃	—	8	2	no	—
644	C₂×C₅₃	—	8	2	no	—
645	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
646	C₂×C₅₃	#3584	1	1	yes	characteristic
647	C₂×C₅₃	#3585	1	1	yes	characteristic
648	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic
649	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
650	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
651	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
652	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
653	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
654	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
655	#555	C₂²×C₅₃	1	2	yes	complemented
656	#553	C₂²×C₅₃	1	2	yes	complemented
657	#553	C₂²×C₅₃	1	2	yes	complemented
658	#551	—	2	2	no	—
659	#550	—	2	1	no	—
660	#550	—	2	1	no	—
661	#550	C₂²×C₅₃	1	2	yes	complemented
662	#550	C₂²×C₅₃	1	2	yes	complemented
663	#548	—	2	1	no	—
664	#548	—	2	1	no	—
665	#548	C₂²×C₅₃	1	2	yes	complemented
666	#548	C₂²×C₅₃	1	2	yes	complemented
667	#547	C₂²×C₅₃	1	2	yes	complemented
668	#546	—	2	2	no	—
669	#544	C₂²×C₅₃	1	1	yes	characteristic
670	#542	—	2	1	no	—
671	#540	—	2	1	no	—
672	#535	—	2	2	no	—
673	#535	C₂²×C₅₃	1	1	yes	characteristic
674	#535	C₂²×C₅₃	1	1	yes	characteristic
675	#535	C₂²×C₅₃	1	1	yes	characteristic
676	#532	—	2	1	no	—
677	#529	—	2	1	no	—
678	#525	—	2	2	no	—
679	#525	C₂²×C₅₃	1	1	yes	characteristic
680	#525	C₂²×C₅₃	1	1	yes	characteristic
681	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
682	#520	C₂²×C₅₃	1	1	yes	characteristic
683	#519	C₂²×C₅₃	1	1	yes	characteristic
684	#518	C₂²×C₅₃	1	1	yes	characteristic
685	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
686	#490	C₂²×C₅₃	1	2	yes	complemented
687	#489	C₂²×C₅₃	1	2	yes	complemented
688	#488	C₂²×C₅₃	1	2	yes	complemented
689	#486	C₂²×C₅₃	1	2	yes	complemented
690	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
691	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
694	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
695	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	#482	C₂²×C₅₃	1	2	yes	complemented
697	#482	C₂²×C₅₃	1	2	yes	complemented
698	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
699	#481	C₂²×C₅₃	1	2	yes	complemented
700	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
701	#480	C₂²×C₅₃	1	2	yes	complemented
702	#479	C₂²×C₅₃	1	2	yes	complemented
703	#479	C₂²×C₅₃	1	2	yes	complemented
704	#477	C₂²×C₅₃	1	2	yes	complemented
705	#475	C₂²×C₅₃	1	2	yes	complemented
706	#469	C₂²×C₅₃	1	2	yes	complemented
707	#469	C₂²×C₅₃	1	2	yes	complemented
708	#469	C₂²×C₅₃	1	2	yes	complemented
709	#468	C₂²×C₅₃	1	2	yes	complemented
710	#466	C₂²×C₅₃	1	2	yes	complemented
711	#466	C₂²×C₅₃	1	2	yes	complemented
712	#466	C₂²×C₅₃	1	2	yes	complemented
713	#465	C₂²×C₅₃	1	2	yes	complemented
714	#463	C₂²×C₅₃	1	2	yes	complemented
715	#463	C₂²×C₅₃	1	2	yes	complemented
716	#459	C₂²×C₅₃	1	2	yes	complemented
717	#459	C₂²×C₅₃	1	2	yes	complemented
718	#449	C₂²×C₅₃	1	2	yes	—
719	#449	C₂²×C₅₃	1	2	yes	—
720	#449	C₂²×C₅₃	1	2	yes	—
721	#449	C₂²×C₅₃	1	2	yes	—
722	#449	C₂²×C₅₃	1	2	yes	complemented
723	#449	C₂²×C₅₃	1	2	yes	complemented
724	#448	C₂²×C₅₃	1	2	yes	complemented
725	#448	C₂²×C₅₃	1	2	yes	complemented
726	#440	C₂²×C₅₃	1	2	yes	complemented
727	#440	C₂²×C₅₃	1	2	yes	complemented
728	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
729	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
730	#436	C₂²×C₅₃	1	2	yes	complemented
731	#435	C₂²×C₅₃	1	2	yes	complemented
732	#435	C₂²×C₅₃	1	2	yes	complemented
733	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
734	#428	C₂²×C₅₃	1	1	yes	characteristic
735	#427	C₂²×C₅₃	1	1	yes	characteristic
736	#427	C₂²×C₅₃	1	1	yes	characteristic
737	#424	C₂²×C₅₃	1	1	yes	characteristic
738	#419	C₂²×C₅₃	1	1	yes	characteristic
739	#419	C₂²×C₅₃	1	1	yes	characteristic
740	#419	C₂²×C₅₃	1	2	yes	complemented
741	#418	C₂²×C₅₃	1	1	yes	characteristic
742	#418	C₂²×C₅₃	1	1	yes	characteristic
743	#418	C₂²×C₅₃	1	1	yes	characteristic
744	#417	C₂²×C₅₃	1	1	yes	characteristic
745	#417	C₂²×C₅₃	1	2	yes	complemented
746	#417	C₂²×C₅₃	1	2	yes	complemented
747	#417	C₂²×C₅₃	1	2	yes	complemented
748	#416	C₂²×C₅₃	1	1	yes	characteristic
749	#416	C₂²×C₅₃	1	1	yes	characteristic
750	#416	C₂²×C₅₃	1	2	yes	complemented
751	#416	C₂²×C₅₃	1	2	yes	complemented
752	#416	C₂²×C₅₃	1	2	yes	complemented
753	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
754	C₂×#103	C₂²×C₅₃	1	2	yes	complemented
755	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
756	#408	C₂²×C₅₃	1	1	yes	characteristic
757	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
758	#405	C₂²×C₅₃	1	1	yes	characteristic
759	C₅₃	#61189	1	1	yes	characteristic, direct product factor, Sylow
760	2₋¹⁺⁴	—	2	4	no	—
761	2₋¹⁺⁴	—	4	2	no	—
762	C₂×#41	—	2	2	no	—
763	C₂×#41	—	2	1	no	—
764	C₂×#41	—	2	2	no	—
765	C₂×#41	—	2	1	no	—
766	C₂×#41	—	2	1	no	—
767	C₂×#41	—	2	4	no	—
768	C₂×#41	—	4	2	no	—
769	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
770	C₂×#41	C₂³×C₅₃	1	2	yes	—
771	C₂×#41	C₂³×C₅₃	1	2	yes	—
772	C₂×#41	C₂³×C₅₃	1	2	yes	—
773	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
774	C₂²×Q₈	—	2	1	no	—
775	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
776	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
777	C₂²×D₄	—	2	1	no	—
778	C₂²×D₄	—	2	1	no	—
779	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
780	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
781	C₂³×C₄	—	2	1	no	—
782	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
783	AGL(1,ℤ/8)	—	4	2	no	—
784	C₂×SD₁₆	—	2	4	no	—
785	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
786	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
787	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
788	C₂×D₈	—	4	2	no	—
789	C₂×D₈	C₂³×C₅₃	1	2	yes	—
790	C₂×D₈	C₂³×C₅₃	1	2	yes	—
791	C₂×D₈	C₂³×C₅₃	1	2	yes	—
792	#131	—	4	2	no	—
793	C₂×M₁₆	—	4	2	no	—
794	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
795	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
796	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
797	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
798	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
799	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
800	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
801	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
802	C₄⋊Q₈	—	2	1	no	—
803	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
804	#127	—	2	1	no	—
805	#127	—	2	2	no	—
806	#127	—	2	2	no	—
807	#127	—	2	1	no	—
808	#127	C₂³×C₅₃	1	2	yes	—
809	#126	—	2	2	no	—
810	#126	—	2	2	no	—
811	#125	—	2	1	no	—
812	#125	C₂³×C₅₃	1	2	yes	—
813	#124	—	2	1	no	—
814	#124	—	2	1	no	—
815	#124	—	2	2	no	—
816	#124	—	2	2	no	—
817	#124	—	2	2	no	—
818	#124	—	2	2	no	—
819	#124	C₂³×C₅₃	1	2	yes	—
820	#123	—	2	1	no	—
821	#123	—	2	2	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	#123	—	2	2	no	—
825	#123	D₄×C₅₃	1	2	yes	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	—	2	2	no	—
828	C₂²⋊Q₈	—	2	2	no	—
829	C₂²⋊Q₈	—	2	2	no	—
830	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
831	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
832	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
833	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	1	no	—
840	#121	—	2	1	no	—
841	#121	—	2	1	no	—
842	#121	—	2	1	no	—
843	#121	—	2	2	no	—
844	#121	—	2	2	no	—
845	#121	—	2	2	no	—
846	#121	—	2	2	no	—
847	#121	D₄×C₅₃	1	1	yes	characteristic
848	#121	D₄×C₅₃	1	1	yes	characteristic
849	#121	C₂³×C₅₃	1	2	yes	—
850	#121	C₂³×C₅₃	1	2	yes	—
851	#121	C₂³×C₅₃	1	1	yes	characteristic
852	#121	C₂³×C₅₃	1	1	yes	characteristic
853	#121	C₂³×C₅₃	1	2	yes	—
854	#121	C₂³×C₅₃	1	2	yes	—
855	#121	C₂³×C₅₃	1	2	yes	—
856	#121	C₂³×C₅₃	1	2	yes	—
857	#120	—	2	1	no	—
858	#120	—	2	2	no	—
859	#120	—	2	2	no	—
860	#120	—	2	2	no	—
861	#120	D₄×C₅₃	1	2	yes	—
862	C₄×Q₈	—	2	1	no	—
863	C₄×Q₈	—	2	1	no	—
864	C₄×Q₈	—	2	1	no	—
865	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
866	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	—	2	2	no	—
874	C₄×D₄	—	2	2	no	—
875	C₄×D₄	—	2	2	no	—
876	C₄×D₄	—	2	2	no	—
877	C₄×D₄	—	2	2	no	—
878	C₄×D₄	—	2	2	no	—
879	C₄×D₄	C₂³×C₅₃	1	2	yes	—
880	C₄×D₄	C₂³×C₅₃	1	2	yes	—
881	C₄×D₄	C₂³×C₅₃	1	2	yes	—
882	C₄×D₄	C₂³×C₅₃	1	2	yes	—
883	#117	—	2	1	no	—
884	#117	—	2	1	no	—
885	#117	—	2	2	no	—
886	#117	—	2	2	no	—
887	#117	C₂³×C₅₃	1	1	yes	characteristic
888	#117	C₂³×C₅₃	1	1	yes	characteristic
889	#117	C₂³×C₅₃	1	1	yes	characteristic
890	#117	C₂³×C₅₃	1	1	yes	characteristic
891	#117	C₂³×C₅₃	1	1	yes	characteristic
892	#117	C₂³×C₅₃	1	2	yes	—
893	#117	C₂³×C₅₃	1	1	yes	characteristic
894	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
895	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
896	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
897	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
898	C₂×C₂²⋊C₄	—	2	1	no	—
899	C₂×C₂²⋊C₄	—	2	1	no	—
900	C₂×C₂²⋊C₄	—	2	2	no	—
901	C₂×C₄²	—	2	1	no	—
902	#107	C₂³×C₅₃	1	1	yes	characteristic
903	#107	C₂³×C₅₃	1	1	yes	characteristic
904	#107	C₂³×C₅₃	1	1	yes	characteristic
905	#107	C₂³×C₅₃	1	1	yes	characteristic
906	#107	C₂³×C₅₃	1	2	yes	—
907	#106	C₂³×C₅₃	1	1	yes	characteristic
908	#106	C₂³×C₅₃	1	1	yes	characteristic
909	#106	C₂³×C₅₃	1	1	yes	characteristic
910	#106	C₂³×C₅₃	1	1	yes	characteristic
911	#106	C₂³×C₅₃	1	2	yes	—
912	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
913	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
914	#103	C₂³×C₅₃	1	2	yes	—
915	#103	C₂³×C₅₃	1	2	yes	—
916	#103	C₂³×C₅₃	1	1	yes	characteristic
917	#103	C₂³×C₅₃	1	2	yes	—
918	#103	C₂³×C₅₃	1	2	yes	—
919	#103	C₂³×C₅₃	1	1	yes	characteristic
920	#103	C₂³×C₅₃	1	1	yes	characteristic
921	#103	C₂³×C₅₃	1	1	yes	characteristic
922	#103	C₂³×C₅₃	1	2	yes	—
923	#103	C₂³×C₅₃	1	2	yes	—
924	#103	C₂³×C₅₃	1	2	yes	—
925	#102	C₂³×C₅₃	1	2	yes	—
926	#102	C₂³×C₅₃	1	2	yes	—
927	#102	C₂³×C₅₃	1	1	yes	characteristic
928	#102	C₂³×C₅₃	1	1	yes	characteristic
929	#102	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	2	yes	—
935	#102	C₂³×C₅₃	1	2	yes	—
936	#102	C₂³×C₅₃	1	2	yes	—
937	#102	C₂³×C₅₃	1	2	yes	—
938	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
939	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
940	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
941	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
942	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
943	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
944	#97	C₂³×C₅₃	1	2	yes	—
945	C₄×C₈	C₂³×C₅₃	1	2	yes	—
946	C₂⁴	—	2	1	no	—
947	C₂⁴	—	2	1	no	—
948	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
949	#41	—	2	2	no	—
950	#41	—	2	2	no	—
951	#41	—	2	4	no	—
952	#41	—	2	4	no	—
953	#41	—	2	4	no	—
954	#41	—	2	2	no	—
955	#41	—	2	2	no	—
956	#41	—	4	2	no	—
957	#41	—	4	2	no	—
958	#41	—	4	2	no	—
959	#41	—	4	8	no	—
960	#41	—	4	4	no	—
961	#41	—	4	4	no	—
962	#41	—	4	4	no	—
963	#41	—	8	4	no	—
964	C₂×Q₈	—	2	1	no	—
965	C₂×Q₈	—	2	2	no	—
966	C₂×Q₈	—	2	2	no	—
967	C₂×Q₈	—	2	2	no	—
968	C₂×Q₈	—	2	4	no	—
969	C₂×Q₈	—	4	2	no	—
970	C₂×Q₈	—	4	4	no	—
971	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
972	C₂×Q₈	#41×C₅₃	1	4	yes	complemented
973	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
974	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	2	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	2	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	2	2	no	—
991	C₂×D₄	—	2	2	no	—
992	C₂×D₄	—	2	2	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	4	4	no	—
996	C₂×D₄	—	8	2	no	—
997	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
998	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
999	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1000	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1001	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1002	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1003	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	2	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	1	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	2	no	—
1015	C₂²×C₄	—	2	2	no	—
1016	C₂²×C₄	—	2	2	no	—
1017	C₂²×C₄	—	2	2	no	—
1018	C₂²×C₄	—	4	4	no	—
1019	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1022	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1023	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1024	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1025	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1026	SD₁₆	—	2	4	no	—
1027	SD₁₆	—	2	4	no	—
1028	SD₁₆	—	4	2	no	—
1029	D₈	—	4	2	no	—
1030	D₈	—	4	2	no	—
1031	D₈	—	4	2	no	—
1032	M₁₆	—	2	2	no	—
1033	M₁₆	—	2	2	no	—
1034	M₁₆	—	4	2	no	—
1035	M₁₆	—	4	2	no	—
1036	C₂×C₈	—	2	2	no	—
1037	C₂×C₈	—	2	2	no	—
1038	C₂×C₈	—	4	2	no	—
1039	C₂×C₈	—	4	2	no	—
1040	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1041	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1042	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1043	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1044	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1045	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1058	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1059	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1060	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1061	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1062	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1063	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1064	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1065	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1089	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1090	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1091	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1092	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	1	no	—
1096	C₄²	—	2	1	no	—
1097	C₄²	—	2	2	no	—
1098	C₄²	—	2	2	no	—
1099	C₄²	—	2	2	no	—
1100	C₄²	—	2	1	no	—
1101	C₄²	C₂⁴×C₅₃	1	2	yes	—
1102	C₂³	—	2	2	no	—
1103	C₂³	—	2	2	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	1	no	—
1106	C₂³	—	4	1	no	—
1107	C₂³	—	4	1	no	—
1108	C₂³	—	4	2	no	—
1109	C₂³	—	4	2	no	—
1110	C₂³	—	8	1	no	—
1111	C₂³	—	8	1	no	—
1112	C₂³	—	8	1	no	—
1113	C₂³	—	8	1	no	—
1114	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1115	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1116	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1117	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1118	Q₈	—	2	4	no	—
1119	Q₈	—	2	2	no	—
1120	Q₈	—	2	2	no	—
1121	Q₈	—	2	1	no	—
1122	Q₈	—	2	1	no	—
1123	Q₈	—	4	4	no	—
1124	Q₈	—	8	2	no	—
1125	Q₈	C₂×#41×C₅₃	1	4	yes	—
1126	D₄	—	2	4	no	—
1127	D₄	—	2	2	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	2	2	no	—
1130	D₄	—	2	1	no	—
1131	D₄	—	2	2	no	—
1132	D₄	—	2	2	no	—
1133	D₄	—	2	1	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	4	4	no	—
1137	D₄	—	4	4	no	—
1138	D₄	—	4	4	no	—
1139	D₄	—	4	4	no	—
1140	D₄	—	4	2	no	—
1141	D₄	—	4	2	no	—
1142	D₄	—	4	2	no	—
1143	D₄	—	8	2	no	—
1144	D₄	—	8	2	no	—
1145	D₄	—	8	2	no	—
1146	D₄	—	8	1	no	—
1147	D₄	—	8	2	no	—
1148	D₄	—	8	2	no	—
1149	D₄	—	8	1	no	—
1150	D₄	—	8	2	no	—
1151	D₄	—	8	2	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	4	no	—
1154	C₂×C₄	—	2	2	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	4	4	no	—
1172	C₂×C₄	—	4	4	no	—
1173	C₂×C₄	—	4	4	no	—
1174	C₂×C₄	—	4	4	no	—
1175	C₂×C₄	—	4	2	no	—
1176	C₂×C₄	—	4	2	no	—
1177	C₂×C₄	—	8	2	no	—
1178	C₂×C₄	—	8	2	no	—
1179	C₂×C₄	—	8	1	no	—
1180	C₂×C₄	—	8	1	no	—
1181	C₂×C₄	—	8	2	no	—
1182	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1183	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1184	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1185	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1186	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1187	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1188	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1189	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1190	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1191	C₈	—	2	1	no	—
1192	C₈	—	2	1	no	—
1193	C₈	—	2	1	no	—
1194	C₈	—	2	1	no	—
1195	C₈	—	2	2	no	—
1196	C₈	—	2	2	no	—
1197	C₂²	—	2	1	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	2	no	—
1207	C₂²	—	2	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	2	no	—
1210	C₂²	—	4	2	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	2	no	—
1214	C₂²	—	4	2	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	8	2	no	—
1218	C₂²	—	8	4	no	—
1219	C₂²	—	16	2	no	—
1220	C₂²	C₅₃×#546	1	2	yes	—
1221	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1222	C₄	—	2	1	no	—
1223	C₄	—	2	1	no	—
1224	C₄	—	2	4	no	—
1225	C₄	—	2	2	no	—
1226	C₄	—	2	2	no	—
1227	C₄	—	2	2	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	2	no	—
1235	C₄	—	4	1	no	—
1236	C₄	C₅₃×#546	1	2	yes	—
1237	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1238	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1239	C₂	—	2	2	no	—
1240	C₂	—	4	1	no	—
1241	C₂	—	4	1	no	—
1242	C₂	—	4	2	no	—
1243	C₂	—	8	2	no	—
1244	C₂	—	8	2	no	—
1245	C₂	—	8	1	no	—
1246	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
1247	C₂	C₅₃×#3584	1	1	yes	characteristic
1248	C₂	C₅₃×#3585	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3494	C₂	semidirect
2. C₅₃×#3487	C₂	semidirect
3. C₅₃×#3332	C₂	semidirect
4. C₅₃×#3326	C₂	semidirect
5. C₅₃×#3321	C₂	semidirect
6. C₅₃×#3309	C₂	semidirect
7. C₅₃×#3309	C₂	semidirect
8. C₅₃×#3308	C₂	semidirect
9. C₅₃×#3305	C₂	semidirect
10. C₅₃×#3301	C₂	semidirect
11. C₅₃×#3136	C₂	semidirect
12. C₅₃×#3096	C₂	semidirect
13. C₅₃×#3091	C₂	semidirect
14. C₅₃×#3082	C₂	semidirect
15. C₅₃×#3058	C₂	semidirect
16. C₅₃×#3055	C₂	semidirect
17. C₅₃×#3041	C₂	semidirect
18. C₅₃×#3010	C₂	semidirect
19. C₂×C₅₃×#449	C₂	semidirect
20. C₅₃×#2949	C₂	semidirect
21. C₅₃×#2933	C₂	semidirect
22. C₅₃×#2898	C₂	semidirect
23. C₅₃×#2896	C₂	semidirect
31. C₅₃×#555	C₂²	semidirect
32. C₅₃×#553	C₂²	semidirect
33. C₅₃×#553	C₂²	semidirect
37. C₅₃×#550	C₂²	semidirect
38. C₅₃×#550	C₂²	semidirect
41. C₅₃×#548	C₂²	semidirect
42. C₅₃×#548	C₂²	semidirect
43. C₅₃×#547	C₂²	semidirect
62. C₅₃×#490	C₂²	semidirect
63. C₅₃×#489	C₂²	semidirect
64. C₅₃×#488	C₂²	semidirect
65. C₅₃×#486	C₂²	semidirect
66. C₅₃×#485	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#484	C₂²	semidirect
69. C₅₃×#483	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#482	C₂²	semidirect
73. C₅₃×#482	C₂²	semidirect
74. C₅₃×#481	C₂²	semidirect
75. C₅₃×#481	C₂²	semidirect
76. C₅₃×#480	C₂²	semidirect
77. C₅₃×#480	C₂²	semidirect
78. C₅₃×#479	C₂²	semidirect
79. C₅₃×#479	C₂²	semidirect
80. C₅₃×#477	C₂²	semidirect
81. C₅₃×#475	C₂²	semidirect
82. C₅₃×#469	C₂²	semidirect
83. C₅₃×#469	C₂²	semidirect
84. C₅₃×#469	C₂²	semidirect
85. C₅₃×#468	C₂²	semidirect
86. C₅₃×#466	C₂²	semidirect
87. C₅₃×#466	C₂²	semidirect
88. C₅₃×#466	C₂²	semidirect
89. C₅₃×#465	C₂²	semidirect
90. C₅₃×#463	C₂²	semidirect
91. C₅₃×#463	C₂²	semidirect
92. C₅₃×#459	C₂²	semidirect
93. C₅₃×#459	C₂²	semidirect
98. C₅₃×#449	C₂²	semidirect
99. C₅₃×#449	C₂²	semidirect
100. C₅₃×#448	C₂²	semidirect
101. C₅₃×#448	C₂²	semidirect
102. C₅₃×#440	C₂²	semidirect
103. C₅₃×#440	C₂²	semidirect
104. C₄×SD₁₆×C₅₃	C₂²	semidirect
105. C₄×SD₁₆×C₅₃	C₂²	semidirect
106. C₅₃×#436	C₂²	semidirect
107. C₅₃×#435	C₂²	semidirect
108. C₅₃×#435	C₂²	semidirect
109. C₈×D₄×C₅₃	C₂²	semidirect
116. C₅₃×#419	C₂²	semidirect
121. C₅₃×#417	C₂²	semidirect
122. C₅₃×#417	C₂²	semidirect
123. C₅₃×#417	C₂²	semidirect
126. C₅₃×#416	C₂²	semidirect
127. C₅₃×#416	C₂²	semidirect
128. C₅₃×#416	C₂²	semidirect
130. C₂×#103×C₅₃	C₂²	semidirect
347. C₂×Q₈×C₅₃	#41	semidirect
572. #61189	C₅₃	direct (N × H)
615. #3494	C₂×C₅₃	semidirect
616. #3487	C₂×C₅₃	semidirect
617. #3332	C₂×C₅₃	semidirect
618. #3326	C₂×C₅₃	semidirect
619. #3321	C₂×C₅₃	semidirect
620. #3309	C₂×C₅₃	semidirect
621. #3309	C₂×C₅₃	semidirect
622. #3308	C₂×C₅₃	semidirect
623. #3305	C₂×C₅₃	semidirect
624. #3301	C₂×C₅₃	semidirect
625. #3136	C₂×C₅₃	semidirect
626. #3096	C₂×C₅₃	semidirect
627. #3091	C₂×C₅₃	semidirect
628. #3082	C₂×C₅₃	semidirect
629. #3058	C₂×C₅₃	semidirect
630. #3055	C₂×C₅₃	semidirect
631. #3041	C₂×C₅₃	semidirect
632. #3010	C₂×C₅₃	semidirect
633. C₂×#449	C₂×C₅₃	semidirect
634. #2949	C₂×C₅₃	semidirect
635. #2933	C₂×C₅₃	semidirect
636. #2898	C₂×C₅₃	semidirect
637. #2896	C₂×C₅₃	semidirect
655. #555	C₂²×C₅₃	semidirect
656. #553	C₂²×C₅₃	semidirect
657. #553	C₂²×C₅₃	semidirect
661. #550	C₂²×C₅₃	semidirect
662. #550	C₂²×C₅₃	semidirect
665. #548	C₂²×C₅₃	semidirect
666. #548	C₂²×C₅₃	semidirect
667. #547	C₂²×C₅₃	semidirect
686. #490	C₂²×C₅₃	semidirect
687. #489	C₂²×C₅₃	semidirect
688. #488	C₂²×C₅₃	semidirect
689. #486	C₂²×C₅₃	semidirect
690. #485	C₂²×C₅₃	semidirect
691. #485	C₂²×C₅₃	semidirect
692. #484	C₂²×C₅₃	semidirect
693. #483	C₂²×C₅₃	semidirect
694. #482	C₂²×C₅₃	semidirect
695. #482	C₂²×C₅₃	semidirect
696. #482	C₂²×C₅₃	semidirect
697. #482	C₂²×C₅₃	semidirect
698. #481	C₂²×C₅₃	semidirect
699. #481	C₂²×C₅₃	semidirect
700. #480	C₂²×C₅₃	semidirect
701. #480	C₂²×C₅₃	semidirect
702. #479	C₂²×C₅₃	semidirect
703. #479	C₂²×C₅₃	semidirect
704. #477	C₂²×C₅₃	semidirect
705. #475	C₂²×C₅₃	semidirect
706. #469	C₂²×C₅₃	semidirect
707. #469	C₂²×C₅₃	semidirect
708. #469	C₂²×C₅₃	semidirect
709. #468	C₂²×C₅₃	semidirect
710. #466	C₂²×C₅₃	semidirect
711. #466	C₂²×C₅₃	semidirect
712. #466	C₂²×C₅₃	semidirect
713. #465	C₂²×C₅₃	semidirect
714. #463	C₂²×C₅₃	semidirect
715. #463	C₂²×C₅₃	semidirect
716. #459	C₂²×C₅₃	semidirect
717. #459	C₂²×C₅₃	semidirect
722. #449	C₂²×C₅₃	semidirect
723. #449	C₂²×C₅₃	semidirect
724. #448	C₂²×C₅₃	semidirect
725. #448	C₂²×C₅₃	semidirect
726. #440	C₂²×C₅₃	semidirect
727. #440	C₂²×C₅₃	semidirect
728. C₄×SD₁₆	C₂²×C₅₃	semidirect
729. C₄×SD₁₆	C₂²×C₅₃	semidirect
730. #436	C₂²×C₅₃	semidirect
731. #435	C₂²×C₅₃	semidirect
732. #435	C₂²×C₅₃	semidirect
733. C₈×D₄	C₂²×C₅₃	semidirect
740. #419	C₂²×C₅₃	semidirect
745. #417	C₂²×C₅₃	semidirect
746. #417	C₂²×C₅₃	semidirect
747. #417	C₂²×C₅₃	semidirect
750. #416	C₂²×C₅₃	semidirect
751. #416	C₂²×C₅₃	semidirect
752. #416	C₂²×C₅₃	semidirect
754. C₂×#103	C₂²×C₅₃	semidirect
759. C₅₃	#61189	direct (N × H)
972. C₂×Q₈	#41×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3494	2
C₅₃×#3487	2
C₅₃×#3332	2
C₅₃×#3326	2
C₅₃×#3321	2
C₅₃×#3309	2
C₅₃×#3308	2
C₅₃×#3305	2
C₅₃×#3301	2
C₅₃×#3136	2
C₅₃×#3096	2
C₅₃×#3091	2
C₅₃×#3082	2
C₅₃×#3058	2
C₅₃×#3055	2
C₅₃×#3041	2
C₅₃×#3010	2
C₂×C₅₃×#449	2
C₅₃×#2949	2
C₅₃×#2933	2
C₅₃×#2898	2
C₅₃×#2896	2
#61189	53

Subgroups — C53×#61189 #27268701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61189 #27268701