Subgroups — C₅₃×#61977 #27269489

Order 13568.

1980 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3403	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3370	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3314	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3309	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3297	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3280	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3268	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3264	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
25	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
26	C₂²×D₈×C₅₃	C₂²	1	2	yes	—
27	C₅₃×#559	—	2	1	no	—
28	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#559	C₂²	1	2	yes	complemented
30	C₅₃×#554	C₂²	1	1	yes	characteristic
31	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
32	C₅₃×#553	—	2	1	no	—
33	C₅₃×#553	C₂²	1	1	yes	characteristic
34	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
35	C₅₃×#551	—	2	1	no	—
36	C₅₃×#551	—	2	1	no	—
37	C₅₃×#550	—	2	1	no	—
38	C₅₃×#550	C₂²	1	2	yes	complemented
39	C₅₃×#546	—	2	1	no	—
40	C₅₃×#546	—	2	1	no	—
41	C₅₃×#546	—	2	1	no	—
42	C₅₃×#546	C₂²	1	1	yes	characteristic
43	C₅₃×#546	C₂²	1	2	yes	—
44	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#546	C₂²	1	2	yes	complemented
46	D₄²×C₅₃	C₂²	1	1	yes	characteristic
47	C₅₃×#540	—	2	1	no	—
48	C₅₃×#540	—	2	1	no	—
49	C₅₃×#535	—	2	1	no	—
50	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
56	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#529	—	2	1	no	—
58	C₅₃×#529	C₂²	1	1	yes	characteristic
59	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#525	—	2	1	no	—
61	C₅₃×#525	—	2	1	no	—
62	C₅₃×#518	—	2	1	no	—
63	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
64	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×D₄×C₅₃	—	2	1	no	—
66	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
67	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#496	C₂²	1	2	yes	complemented
69	C₅₃×#496	C₂²	1	2	yes	complemented
70	C₅₃×#495	C₂²	1	2	yes	complemented
71	C₅₃×#490	C₂²	1	2	yes	complemented
72	C₅₃×#489	C₂²	1	2	yes	complemented
73	C₅₃×#488	C₂²	1	2	yes	complemented
74	C₅₃×#484	C₂²	1	2	yes	complemented
75	C₅₃×#482	C₂²	1	2	yes	complemented
76	C₅₃×#480	C₂²	1	2	yes	complemented
77	C₅₃×#479	C₂²	1	2	yes	complemented
78	C₅₃×#478	C₂²	1	2	yes	complemented
79	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#474	C₂²	1	2	yes	complemented
83	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#469	C₂²	1	2	yes	complemented
85	C₅₃×#468	C₂²	1	2	yes	complemented
86	C₅₃×#467	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	—
90	C₅₃×#464	C₂²	1	2	yes	complemented
91	C₅₃×#464	C₂²	1	2	yes	complemented
92	C₅₃×#463	C₂²	1	2	yes	complemented
93	C₅₃×#463	C₂²	1	2	yes	complemented
94	C₅₃×#463	C₂²	1	2	yes	complemented
95	C₅₃×#463	C₂²	1	2	yes	complemented
96	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#459	C₂²	1	2	yes	—
103	C₅₃×#459	C₂²	1	1	yes	characteristic
104	C₅₃×#459	C₂²	1	1	yes	characteristic
105	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#459	C₂²	1	2	yes	complemented
110	C₅₃×#459	C₂²	1	2	yes	complemented
111	C₅₃×#452	C₂²	1	2	yes	complemented
112	C₅₃×#450	C₂²	1	2	yes	—
113	C₅₃×#450	C₂²	1	2	yes	complemented
114	C₅₃×#449	C₂²	1	2	yes	complemented
115	C₅₃×#449	C₂²	1	2	yes	complemented
116	C₅₃×#449	C₂²	1	2	yes	complemented
117	C₅₃×#449	C₂²	1	2	yes	complemented
118	C₅₃×#447	C₂²	1	2	yes	—
119	C₅₃×#447	C₂²	1	2	yes	complemented
120	C₅₃×#446	C₂²	1	2	yes	complemented
121	C₅₃×#442	C₂²	1	2	yes	complemented
122	C₅₃×#440	C₂²	1	2	yes	complemented
123	C₅₃×#440	C₂²	1	2	yes	complemented
124	C₅₃×#440	C₂²	1	2	yes	complemented
125	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
126	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
127	C₅₃×#435	C₂²	1	2	yes	—
128	C₅₃×#435	C₂²	1	2	yes	complemented
129	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
130	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#417	C₂²	1	2	yes	complemented
137	C₅₃×#416	C₂²	1	2	yes	complemented
138	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	1	no	—
141	C₂×#41×C₅₃	—	2	1	no	—
142	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
143	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×#41×C₅₃	C₂³	1	2	yes	—
145	C₂×#41×C₅₃	C₂³	1	2	yes	—
146	C₂²×D₄×C₅₃	—	2	1	no	—
147	C₂²×D₄×C₅₃	—	2	1	no	—
148	C₂²×D₄×C₅₃	—	2	1	no	—
149	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
151	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
152	C₂³×C₄×C₅₃	—	2	1	no	—
153	C₂³×C₄×C₅₃	—	2	1	no	—
154	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
155	#135×C₅₃	—	4	4	no	—
156	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
162	C₂×D₈×C₅₃	—	4	4	no	—
163	C₂×D₈×C₅₃	C₂³	1	2	yes	—
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	C₂×D₈×C₅₃	C₂³	1	2	yes	—
168	C₂×D₈×C₅₃	C₂³	1	2	yes	—
169	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
170	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
171	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
172	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
173	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
174	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
175	#127×C₅₃	—	2	1	no	—
176	#127×C₅₃	—	2	1	no	—
177	#127×C₅₃	—	2	2	no	—
178	#127×C₅₃	C₂³	1	2	yes	—
179	#127×C₅₃	C₂³	1	1	yes	characteristic
180	#127×C₅₃	C₂³	1	1	yes	characteristic
181	#127×C₅₃	C₂³	1	1	yes	characteristic
182	#126×C₅₃	—	2	1	no	—
183	#126×C₅₃	—	2	1	no	—
184	#126×C₅₃	—	2	1	no	—
185	#126×C₅₃	—	2	1	no	—
186	#125×C₅₃	—	2	1	no	—
187	#125×C₅₃	—	2	1	no	—
188	#125×C₅₃	C₂³	1	1	yes	characteristic
189	#125×C₅₃	C₂³	1	1	yes	characteristic
190	#124×C₅₃	—	2	1	no	—
191	#124×C₅₃	—	2	1	no	—
192	#124×C₅₃	—	2	1	no	—
193	#124×C₅₃	—	2	1	no	—
194	#124×C₅₃	—	2	2	no	—
195	#124×C₅₃	C₂³	1	2	yes	—
196	#124×C₅₃	C₂³	1	2	yes	—
197	#124×C₅₃	C₂³	1	1	yes	characteristic
198	#124×C₅₃	C₂³	1	1	yes	characteristic
199	#123×C₅₃	—	2	1	no	—
200	#123×C₅₃	—	2	1	no	—
201	#123×C₅₃	—	2	1	no	—
202	#123×C₅₃	—	2	1	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	1	no	—
208	#123×C₅₃	—	2	1	no	—
209	#123×C₅₃	—	2	1	no	—
210	#123×C₅₃	—	2	1	no	—
211	C₂²⋊Q₈×C₅₃	—	2	1	no	—
212	C₂²⋊Q₈×C₅₃	—	2	1	no	—
213	C₂²⋊Q₈×C₅₃	—	2	1	no	—
214	C₂²⋊Q₈×C₅₃	—	2	1	no	—
215	C₂²⋊Q₈×C₅₃	—	2	1	no	—
216	C₂²⋊Q₈×C₅₃	—	2	1	no	—
217	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
218	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
219	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
220	#121×C₅₃	—	2	1	no	—
221	#121×C₅₃	—	2	1	no	—
222	#121×C₅₃	—	2	1	no	—
223	#121×C₅₃	—	2	2	no	—
224	#121×C₅₃	—	2	2	no	—
225	#121×C₅₃	—	2	2	no	—
226	#121×C₅₃	—	2	2	no	—
227	#121×C₅₃	—	2	1	no	—
228	#121×C₅₃	—	2	1	no	—
229	#121×C₅₃	—	2	1	no	—
230	#121×C₅₃	—	2	1	no	—
231	#121×C₅₃	—	2	1	no	—
232	#121×C₅₃	—	2	1	no	—
233	#121×C₅₃	—	2	1	no	—
234	#121×C₅₃	—	2	1	no	—
235	#121×C₅₃	—	2	1	no	—
236	#121×C₅₃	C₂³	1	1	yes	characteristic
237	#121×C₅₃	C₂³	1	1	yes	characteristic
238	#121×C₅₃	C₂³	1	2	yes	—
239	#121×C₅₃	C₂³	1	1	yes	characteristic
240	#121×C₅₃	C₂³	1	2	yes	—
241	#121×C₅₃	C₂³	1	1	yes	characteristic
242	#120×C₅₃	—	2	1	no	—
243	#120×C₅₃	—	2	1	no	—
244	#120×C₅₃	—	2	1	no	—
245	#120×C₅₃	—	2	1	no	—
246	#120×C₅₃	—	2	2	no	—
247	#120×C₅₃	—	2	2	no	—
248	C₄×Q₈×C₅₃	—	2	1	no	—
249	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
250	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
252	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
253	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
254	C₄×D₄×C₅₃	—	2	1	no	—
255	C₄×D₄×C₅₃	—	2	2	no	—
256	C₄×D₄×C₅₃	—	2	2	no	—
257	C₄×D₄×C₅₃	—	2	1	no	—
258	C₄×D₄×C₅₃	—	2	1	no	—
259	C₄×D₄×C₅₃	—	2	1	no	—
260	C₄×D₄×C₅₃	—	2	1	no	—
261	C₄×D₄×C₅₃	—	2	1	no	—
262	C₄×D₄×C₅₃	—	2	1	no	—
263	C₄×D₄×C₅₃	—	2	1	no	—
264	C₄×D₄×C₅₃	—	2	1	no	—
265	C₄×D₄×C₅₃	—	2	1	no	—
266	C₄×D₄×C₅₃	—	2	1	no	—
267	C₄×D₄×C₅₃	—	2	1	no	—
268	C₄×D₄×C₅₃	—	2	1	no	—
269	C₄×D₄×C₅₃	—	2	1	no	—
270	C₄×D₄×C₅₃	—	2	1	no	—
271	C₄×D₄×C₅₃	—	2	1	no	—
272	C₄×D₄×C₅₃	—	2	1	no	—
273	C₄×D₄×C₅₃	—	2	1	no	—
274	C₄×D₄×C₅₃	—	2	1	no	—
275	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
276	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
277	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
278	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₅₃	C₂³	1	2	yes	—
287	C₄×D₄×C₅₃	C₂³	1	2	yes	—
288	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
291	#117×C₅₃	—	2	1	no	—
292	#117×C₅₃	—	2	1	no	—
293	#117×C₅₃	—	2	1	no	—
294	#117×C₅₃	—	2	1	no	—
295	#117×C₅₃	D₄	1	1	yes	characteristic
296	#117×C₅₃	D₄	1	1	yes	characteristic
297	#117×C₅₃	D₄	1	1	yes	characteristic
298	#117×C₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
300	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
303	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
304	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
305	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
306	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
307	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
308	C₂×C₄²×C₅₃	—	2	1	no	—
309	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
312	#107×C₅₃	C₂³	1	2	yes	—
313	#107×C₅₃	C₂³	1	2	yes	—
314	#107×C₅₃	C₂³	1	2	yes	—
315	#106×C₅₃	C₂³	1	2	yes	—
316	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
318	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
319	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
320	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
321	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
322	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
323	#103×C₅₃	C₂³	1	2	yes	—
324	#103×C₅₃	C₂³	1	2	yes	—
325	#103×C₅₃	C₂³	1	2	yes	—
326	#103×C₅₃	C₂³	1	2	yes	—
327	#103×C₅₃	C₂³	1	2	yes	—
328	#102×C₅₃	C₂³	1	2	yes	—
329	#102×C₅₃	C₂³	1	2	yes	—
330	#102×C₅₃	C₂³	1	2	yes	—
331	#102×C₅₃	C₂³	1	2	yes	—
332	#102×C₅₃	C₂³	1	2	yes	—
333	#102×C₅₃	C₂³	1	2	yes	—
334	#102×C₅₃	C₂³	1	2	yes	—
335	#102×C₅₃	C₂³	1	2	yes	—
336	#102×C₅₃	C₂³	1	2	yes	—
337	#102×C₅₃	C₂³	1	2	yes	—
338	#102×C₅₃	C₂³	1	2	yes	—
339	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
340	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
341	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
342	#97×C₅₃	C₂³	1	2	yes	—
343	#97×C₅₃	C₂³	1	2	yes	—
344	C₄×C₈×C₅₃	C₂³	1	2	yes	—
345	C₂⁴×C₅₃	—	2	1	no	—
346	C₂⁴×C₅₃	—	2	1	no	—
347	C₂⁴×C₅₃	—	2	2	no	—
348	#41×C₅₃	—	2	2	no	—
349	#41×C₅₃	—	4	2	no	—
350	#41×C₅₃	—	4	1	no	—
351	#41×C₅₃	—	4	2	no	—
352	#41×C₅₃	—	4	2	no	—
353	#41×C₅₃	—	4	2	no	—
354	#41×C₅₃	—	4	2	no	—
355	#41×C₅₃	—	8	2	no	—
356	#41×C₅₃	—	8	2	no	—
357	#41×C₅₃	—	8	2	no	—
358	C₂×Q₈×C₅₃	—	2	1	no	—
359	C₂×Q₈×C₅₃	—	2	1	no	—
360	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
361	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
362	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₅₃	—	2	2	no	—
364	C₂×D₄×C₅₃	—	2	2	no	—
365	C₂×D₄×C₅₃	—	2	1	no	—
366	C₂×D₄×C₅₃	—	2	1	no	—
367	C₂×D₄×C₅₃	—	2	1	no	—
368	C₂×D₄×C₅₃	—	2	2	no	—
369	C₂×D₄×C₅₃	—	2	2	no	—
370	C₂×D₄×C₅₃	—	2	1	no	—
371	C₂×D₄×C₅₃	—	2	1	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	1	no	—
376	C₂×D₄×C₅₃	—	2	1	no	—
377	C₂×D₄×C₅₃	—	2	1	no	—
378	C₂×D₄×C₅₃	—	2	1	no	—
379	C₂×D₄×C₅₃	—	2	2	no	—
380	C₂×D₄×C₅₃	—	2	1	no	—
381	C₂×D₄×C₅₃	—	2	1	no	—
382	C₂×D₄×C₅₃	—	2	1	no	—
383	C₂×D₄×C₅₃	—	2	2	no	—
384	C₂×D₄×C₅₃	—	2	2	no	—
385	C₂×D₄×C₅₃	—	4	1	no	—
386	C₂×D₄×C₅₃	—	4	1	no	—
387	C₂×D₄×C₅₃	—	4	2	no	—
388	C₂×D₄×C₅₃	—	4	2	no	—
389	C₂×D₄×C₅₃	—	4	4	no	—
390	C₂×D₄×C₅₃	—	4	4	no	—
391	C₂×D₄×C₅₃	—	8	2	no	—
392	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
393	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
394	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
395	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
396	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
397	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₅₃	—	2	1	no	—
401	C₂²×C₄×C₅₃	—	2	1	no	—
402	C₂²×C₄×C₅₃	—	2	1	no	—
403	C₂²×C₄×C₅₃	—	2	1	no	—
404	C₂²×C₄×C₅₃	—	2	1	no	—
405	C₂²×C₄×C₅₃	—	2	1	no	—
406	C₂²×C₄×C₅₃	—	2	1	no	—
407	C₂²×C₄×C₅₃	—	2	1	no	—
408	C₂²×C₄×C₅₃	—	2	1	no	—
409	C₂²×C₄×C₅₃	—	2	2	no	—
410	C₂²×C₄×C₅₃	—	2	2	no	—
411	C₂²×C₄×C₅₃	—	2	2	no	—
412	C₂²×C₄×C₅₃	—	2	2	no	—
413	C₂²×C₄×C₅₃	—	2	1	no	—
414	C₂²×C₄×C₅₃	—	2	1	no	—
415	C₂²×C₄×C₅₃	—	8	2	no	—
416	C₂²×C₄×C₅₃	—	8	2	no	—
417	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
418	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
419	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
420	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
421	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
422	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
423	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
426	Q₁₆×C₅₃	—	4	2	no	—
427	SD₁₆×C₅₃	—	2	4	no	—
428	SD₁₆×C₅₃	—	4	2	no	—
429	SD₁₆×C₅₃	—	4	2	no	—
430	SD₁₆×C₅₃	—	4	2	no	—
431	SD₁₆×C₅₃	—	4	2	no	—
432	D₈×C₅₃	—	2	4	no	—
433	D₈×C₅₃	—	2	4	no	—
434	D₈×C₅₃	—	4	2	no	—
435	D₈×C₅₃	—	4	2	no	—
436	D₈×C₅₃	—	4	2	no	—
437	D₈×C₅₃	—	4	2	no	—
438	M₁₆×C₅₃	—	4	2	no	—
439	C₂×C₈×C₅₃	—	4	2	no	—
440	C₂×C₈×C₅₃	—	4	2	no	—
441	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
442	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
443	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
444	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
445	C₄⋊C₄×C₅₃	—	2	1	no	—
446	C₄⋊C₄×C₅₃	—	2	1	no	—
447	C₄⋊C₄×C₅₃	—	2	1	no	—
448	C₄⋊C₄×C₅₃	—	2	1	no	—
449	C₄⋊C₄×C₅₃	—	2	1	no	—
450	C₄⋊C₄×C₅₃	—	2	1	no	—
451	C₄⋊C₄×C₅₃	—	2	1	no	—
452	C₄⋊C₄×C₅₃	—	2	1	no	—
453	C₄⋊C₄×C₅₃	—	2	1	no	—
454	C₄⋊C₄×C₅₃	—	2	1	no	—
455	C₄⋊C₄×C₅₃	—	2	1	no	—
456	C₄⋊C₄×C₅₃	—	2	1	no	—
457	C₄⋊C₄×C₅₃	—	2	1	no	—
458	C₄⋊C₄×C₅₃	—	2	1	no	—
459	C₄⋊C₄×C₅₃	—	2	2	no	—
460	C₄⋊C₄×C₅₃	—	2	2	no	—
461	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
462	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
463	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
464	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
465	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
466	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
467	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
468	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
469	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
470	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
471	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
472	C₂²⋊C₄×C₅₃	—	2	2	no	—
473	C₂²⋊C₄×C₅₃	—	2	1	no	—
474	C₂²⋊C₄×C₅₃	—	2	1	no	—
475	C₂²⋊C₄×C₅₃	—	2	1	no	—
476	C₂²⋊C₄×C₅₃	—	2	1	no	—
477	C₂²⋊C₄×C₅₃	—	2	2	no	—
478	C₂²⋊C₄×C₅₃	—	2	2	no	—
479	C₂²⋊C₄×C₅₃	—	2	2	no	—
480	C₂²⋊C₄×C₅₃	—	2	2	no	—
481	C₂²⋊C₄×C₅₃	—	2	1	no	—
482	C₂²⋊C₄×C₅₃	—	2	1	no	—
483	C₂²⋊C₄×C₅₃	—	2	1	no	—
484	C₂²⋊C₄×C₅₃	—	2	1	no	—
485	C₂²⋊C₄×C₅₃	—	2	1	no	—
486	C₂²⋊C₄×C₅₃	—	2	1	no	—
487	C₂²⋊C₄×C₅₃	—	2	1	no	—
488	C₂²⋊C₄×C₅₃	—	2	1	no	—
489	C₂²⋊C₄×C₅₃	—	2	1	no	—
490	C₂²⋊C₄×C₅₃	—	2	1	no	—
491	C₂²⋊C₄×C₅₃	—	2	1	no	—
492	C₂²⋊C₄×C₅₃	—	2	1	no	—
493	C₂²⋊C₄×C₅₃	—	2	1	no	—
494	C₂²⋊C₄×C₅₃	—	2	1	no	—
495	C₂²⋊C₄×C₅₃	—	2	1	no	—
496	C₂²⋊C₄×C₅₃	—	2	2	no	—
497	C₂²⋊C₄×C₅₃	—	2	2	no	—
498	C₂²⋊C₄×C₅₃	—	2	2	no	—
499	C₂²⋊C₄×C₅₃	—	2	2	no	—
500	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
501	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
502	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
503	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
504	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
505	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
506	C₄²×C₅₃	—	2	1	no	—
507	C₄²×C₅₃	—	2	1	no	—
508	C₄²×C₅₃	—	2	1	no	—
509	C₄²×C₅₃	—	2	2	no	—
510	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
511	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
512	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
513	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
514	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
515	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
516	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
517	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
518	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
519	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
520	C₂³×C₅₃	—	2	1	no	—
521	C₂³×C₅₃	—	2	2	no	—
522	C₂³×C₅₃	—	2	2	no	—
523	C₂³×C₅₃	—	2	1	no	—
524	C₂³×C₅₃	—	2	1	no	—
525	C₂³×C₅₃	—	4	2	no	—
526	C₂³×C₅₃	—	4	2	no	—
527	C₂³×C₅₃	—	4	2	no	—
528	C₂³×C₅₃	—	4	2	no	—
529	C₂³×C₅₃	—	4	4	no	—
530	C₂³×C₅₃	—	8	1	no	—
531	C₂³×C₅₃	—	8	1	no	—
532	C₂³×C₅₃	—	8	2	no	—
533	C₂³×C₅₃	—	8	2	no	—
534	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
535	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
536	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
537	Q₈×C₅₃	—	2	1	no	—
538	Q₈×C₅₃	—	2	2	no	—
539	Q₈×C₅₃	—	2	2	no	—
540	Q₈×C₅₃	—	2	1	no	—
541	Q₈×C₅₃	—	4	1	no	—
542	Q₈×C₅₃	—	4	2	no	—
543	Q₈×C₅₃	—	8	1	no	—
544	D₄×C₅₃	—	2	2	no	—
545	D₄×C₅₃	—	2	2	no	—
546	D₄×C₅₃	—	2	1	no	—
547	D₄×C₅₃	—	2	1	no	—
548	D₄×C₅₃	—	2	2	no	—
549	D₄×C₅₃	—	2	2	no	—
550	D₄×C₅₃	—	2	1	no	—
551	D₄×C₅₃	—	2	2	no	—
552	D₄×C₅₃	—	2	2	no	—
553	D₄×C₅₃	—	2	1	no	—
554	D₄×C₅₃	—	2	1	no	—
555	D₄×C₅₃	—	4	1	no	—
556	D₄×C₅₃	—	4	2	no	—
557	D₄×C₅₃	—	4	2	no	—
558	D₄×C₅₃	—	4	2	no	—
559	D₄×C₅₃	—	4	2	no	—
560	D₄×C₅₃	—	4	4	no	—
561	D₄×C₅₃	—	4	2	no	—
562	D₄×C₅₃	—	4	2	no	—
563	D₄×C₅₃	—	4	2	no	—
564	D₄×C₅₃	—	4	2	no	—
565	D₄×C₅₃	—	4	2	no	—
566	D₄×C₅₃	—	4	2	no	—
567	D₄×C₅₃	—	8	2	no	—
568	D₄×C₅₃	—	8	2	no	—
569	D₄×C₅₃	—	8	1	no	—
570	D₄×C₅₃	—	8	2	no	—
571	D₄×C₅₃	—	8	2	no	—
572	D₄×C₅₃	—	8	1	no	—
573	D₄×C₅₃	—	8	1	no	—
574	D₄×C₅₃	—	8	2	no	—
575	D₄×C₅₃	—	8	2	no	—
576	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
577	C₂×C₄×C₅₃	—	2	2	no	—
578	C₂×C₄×C₅₃	—	2	2	no	—
579	C₂×C₄×C₅₃	—	2	2	no	—
580	C₂×C₄×C₅₃	—	2	2	no	—
581	C₂×C₄×C₅₃	—	2	1	no	—
582	C₂×C₄×C₅₃	—	2	1	no	—
583	C₂×C₄×C₅₃	—	2	1	no	—
584	C₂×C₄×C₅₃	—	2	1	no	—
585	C₂×C₄×C₅₃	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	2	2	no	—
591	C₂×C₄×C₅₃	—	2	2	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	—	2	1	no	—
594	C₂×C₄×C₅₃	—	4	1	no	—
595	C₂×C₄×C₅₃	—	4	1	no	—
596	C₂×C₄×C₅₃	—	4	2	no	—
597	C₂×C₄×C₅₃	—	4	2	no	—
598	C₂×C₄×C₅₃	—	4	2	no	—
599	C₂×C₄×C₅₃	—	4	2	no	—
600	C₂×C₄×C₅₃	—	4	2	no	—
601	C₂×C₄×C₅₃	—	8	1	no	—
602	C₂×C₄×C₅₃	—	8	1	no	—
603	C₂×C₄×C₅₃	—	8	1	no	—
604	C₂×C₄×C₅₃	—	8	1	no	—
605	C₂×C₄×C₅₃	—	8	2	no	—
606	C₂×C₄×C₅₃	—	8	2	no	—
607	C₂×C₄×C₅₃	—	8	2	no	—
608	C₂×C₄×C₅₃	—	8	2	no	—
609	C₂×C₄×C₅₃	—	8	1	no	—
610	C₂×C₄×C₅₃	—	8	1	no	—
611	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
612	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
613	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
614	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
615	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
616	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
617	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
618	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
619	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
620	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
621	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
622	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
623	C₈×C₅₃	—	2	2	no	—
624	C₈×C₅₃	—	2	2	no	—
625	C₈×C₅₃	—	2	2	no	—
626	C₈×C₅₃	—	2	2	no	—
627	#61977	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
628	C₂²×C₅₃	—	2	1	no	—
629	C₂²×C₅₃	—	2	1	no	—
630	C₂²×C₅₃	—	2	1	no	—
631	C₂²×C₅₃	—	2	1	no	—
632	C₂²×C₅₃	—	2	2	no	—
633	C₂²×C₅₃	—	2	1	no	—
634	C₂²×C₅₃	—	2	1	no	—
635	C₂²×C₅₃	—	2	1	no	—
636	C₂²×C₅₃	—	2	1	no	—
637	C₂²×C₅₃	—	4	1	no	—
638	C₂²×C₅₃	—	4	1	no	—
639	C₂²×C₅₃	—	4	2	no	—
640	C₂²×C₅₃	—	4	2	no	—
641	C₂²×C₅₃	—	4	1	no	—
642	C₂²×C₅₃	—	4	1	no	—
643	C₂²×C₅₃	—	4	1	no	—
644	C₂²×C₅₃	—	4	1	no	—
645	C₂²×C₅₃	—	4	2	no	—
646	C₂²×C₅₃	—	4	2	no	—
647	C₂²×C₅₃	—	4	1	no	—
648	C₂²×C₅₃	—	4	1	no	—
649	C₂²×C₅₃	—	4	2	no	—
650	C₂²×C₅₃	—	4	2	no	—
651	C₂²×C₅₃	—	8	4	no	—
652	C₂²×C₅₃	—	8	4	no	—
653	C₂²×C₅₃	—	16	4	no	—
654	C₂²×C₅₃	#575	1	2	yes	—
655	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
656	C₄×C₅₃	—	2	1	no	—
657	C₄×C₅₃	—	2	1	no	—
658	C₄×C₅₃	—	2	1	no	—
659	C₄×C₅₃	—	2	1	no	—
660	C₄×C₅₃	—	2	1	no	—
661	C₄×C₅₃	—	2	1	no	—
662	C₄×C₅₃	—	2	1	no	—
663	C₄×C₅₃	—	2	1	no	—
664	C₄×C₅₃	—	2	1	no	—
665	C₄×C₅₃	—	2	1	no	—
666	C₄×C₅₃	—	4	1	no	—
667	C₄×C₅₃	—	4	2	no	—
668	C₄×C₅₃	—	4	1	no	—
669	C₄×C₅₃	—	4	1	no	—
670	C₄×C₅₃	—	4	1	no	—
671	C₄×C₅₃	—	4	1	no	—
672	C₄×C₅₃	—	4	2	no	—
673	C₄×C₅₃	#576	1	2	yes	—
674	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
675	C₄×C₅₃	#585	1	1	yes	characteristic
676	#3508	C₂×C₅₃	1	1	yes	characteristic, complemented
677	#3481	C₂×C₅₃	1	1	yes	characteristic, complemented
678	#3403	C₂×C₅₃	1	2	yes	complemented
679	#3370	C₂×C₅₃	1	2	yes	complemented
680	#3314	C₂×C₅₃	1	2	yes	complemented
681	#3309	C₂×C₅₃	1	2	yes	complemented
682	#3297	C₂×C₅₃	1	2	yes	complemented
683	#3280	C₂×C₅₃	1	2	yes	complemented
684	#3268	C₂×C₅₃	1	2	yes	complemented
685	#3264	C₂×C₅₃	1	2	yes	complemented
686	#3251	C₂×C₅₃	1	1	yes	characteristic, complemented
687	#3248	C₂×C₅₃	1	1	yes	characteristic, complemented
688	#3245	C₂×C₅₃	1	1	yes	characteristic, complemented
689	#3217	C₂×C₅₃	1	1	yes	characteristic, complemented
690	#3214	C₂×C₅₃	1	1	yes	characteristic, complemented
691	#3212	C₂×C₅₃	1	1	yes	characteristic, complemented
692	#3115	C₂×C₅₃	1	1	yes	characteristic, complemented
693	#3110	C₂×C₅₃	1	1	yes	characteristic, complemented
694	#3100	C₂×C₅₃	1	1	yes	characteristic, complemented
695	#3036	C₂×C₅₃	1	1	yes	characteristic, complemented
696	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
697	C₂×#459	C₂×C₅₃	1	1	yes	characteristic, complemented
698	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
699	C₂×C₅₃	—	2	2	no	—
700	C₂×C₅₃	—	4	1	no	—
701	C₂×C₅₃	—	4	1	no	—
702	C₂×C₅₃	—	4	2	no	—
703	C₂×C₅₃	—	8	1	no	—
704	C₂×C₅₃	—	8	1	no	—
705	C₂×C₅₃	—	8	2	no	—
706	C₂×C₅₃	—	8	2	no	—
707	C₂×C₅₃	#3488	1	1	yes	characteristic
708	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
709	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
710	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
711	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
712	C₂²×D₈	C₂²×C₅₃	1	2	yes	—
713	#559	—	2	1	no	—
714	#559	C₂²×C₅₃	1	2	yes	complemented
715	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
716	#554	C₂²×C₅₃	1	1	yes	characteristic
717	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
718	#553	—	2	1	no	—
719	#553	C₂²×C₅₃	1	1	yes	characteristic
720	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
721	#551	—	2	1	no	—
722	#551	—	2	1	no	—
723	#550	—	2	1	no	—
724	#550	C₂²×C₅₃	1	2	yes	complemented
725	#546	—	2	1	no	—
726	#546	—	2	1	no	—
727	#546	—	2	1	no	—
728	#546	C₂²×C₅₃	1	1	yes	characteristic
729	#546	C₂²×C₅₃	1	2	yes	—
730	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
731	#546	C₂²×C₅₃	1	2	yes	complemented
732	D₄²	C₂²×C₅₃	1	1	yes	characteristic
733	#540	—	2	1	no	—
734	#540	—	2	1	no	—
735	#535	—	2	1	no	—
736	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
737	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
738	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
739	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
740	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
741	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
742	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic, complemented
743	#529	—	2	1	no	—
744	#529	C₂²×C₅₃	1	1	yes	characteristic
745	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
746	#525	—	2	1	no	—
747	#525	—	2	1	no	—
748	#518	—	2	1	no	—
749	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
750	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
751	C₂×C₄×D₄	—	2	1	no	—
752	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
753	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
754	#496	C₂²×C₅₃	1	2	yes	complemented
755	#496	C₂²×C₅₃	1	2	yes	complemented
756	#495	C₂²×C₅₃	1	2	yes	complemented
757	#490	C₂²×C₅₃	1	2	yes	complemented
758	#489	C₂²×C₅₃	1	2	yes	complemented
759	#488	C₂²×C₅₃	1	2	yes	complemented
760	#484	C₂²×C₅₃	1	2	yes	complemented
761	#482	C₂²×C₅₃	1	2	yes	complemented
762	#480	C₂²×C₅₃	1	2	yes	complemented
763	#479	C₂²×C₅₃	1	2	yes	complemented
764	#478	C₂²×C₅₃	1	2	yes	complemented
765	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
766	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
767	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
768	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
769	#474	C₂²×C₅₃	1	2	yes	complemented
770	#469	C₂²×C₅₃	1	2	yes	complemented
771	#468	C₂²×C₅₃	1	2	yes	complemented
772	#467	C₂²×C₅₃	1	2	yes	complemented
773	#466	C₂²×C₅₃	1	2	yes	complemented
774	#466	C₂²×C₅₃	1	2	yes	complemented
775	#465	C₂²×C₅₃	1	2	yes	—
776	#464	C₂²×C₅₃	1	2	yes	complemented
777	#464	C₂²×C₅₃	1	2	yes	complemented
778	#463	C₂²×C₅₃	1	2	yes	complemented
779	#463	C₂²×C₅₃	1	2	yes	complemented
780	#463	C₂²×C₅₃	1	2	yes	complemented
781	#463	C₂²×C₅₃	1	2	yes	complemented
782	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
783	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
784	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
785	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
786	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
787	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
788	#459	C₂²×C₅₃	1	1	yes	characteristic
789	#459	C₂²×C₅₃	1	2	yes	—
790	#459	C₂²×C₅₃	1	1	yes	characteristic
791	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
792	#459	C₂²×C₅₃	1	2	yes	complemented
793	#459	C₂²×C₅₃	1	2	yes	complemented
794	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
795	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
796	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
797	#452	C₂²×C₅₃	1	2	yes	complemented
798	#450	C₂²×C₅₃	1	2	yes	—
799	#450	C₂²×C₅₃	1	2	yes	complemented
800	#449	C₂²×C₅₃	1	2	yes	complemented
801	#449	C₂²×C₅₃	1	2	yes	complemented
802	#449	C₂²×C₅₃	1	2	yes	complemented
803	#449	C₂²×C₅₃	1	2	yes	complemented
804	#447	C₂²×C₅₃	1	2	yes	—
805	#447	C₂²×C₅₃	1	2	yes	complemented
806	#446	C₂²×C₅₃	1	2	yes	complemented
807	#442	C₂²×C₅₃	1	2	yes	complemented
808	#440	C₂²×C₅₃	1	2	yes	complemented
809	#440	C₂²×C₅₃	1	2	yes	complemented
810	#440	C₂²×C₅₃	1	2	yes	complemented
811	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
812	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
813	#435	C₂²×C₅₃	1	2	yes	—
814	#435	C₂²×C₅₃	1	2	yes	complemented
815	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
816	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
817	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
818	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
819	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
820	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
821	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
822	#417	C₂²×C₅₃	1	2	yes	complemented
823	#416	C₂²×C₅₃	1	2	yes	complemented
824	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
825	C₅₃	#61977	1	1	yes	characteristic, direct product factor, Sylow
826	C₂×#41	—	2	1	no	—
827	C₂×#41	—	2	1	no	—
828	C₂×#41	—	2	1	no	—
829	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
830	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
831	C₂×#41	C₂³×C₅₃	1	2	yes	—
832	C₂×#41	C₂³×C₅₃	1	2	yes	—
833	C₂²×D₄	—	2	1	no	—
834	C₂²×D₄	—	2	1	no	—
835	C₂²×D₄	—	2	1	no	—
836	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
837	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
838	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
839	C₂³×C₄	—	2	1	no	—
840	C₂³×C₄	—	2	1	no	—
841	AGL(1,ℤ/8)	—	4	4	no	—
842	#135	—	4	4	no	—
843	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
844	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
845	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
846	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
847	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
848	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
849	C₂×D₈	—	4	4	no	—
850	C₂×D₈	C₂³×C₅₃	1	2	yes	—
851	C₂×D₈	C₂³×C₅₃	1	2	yes	—
852	C₂×D₈	C₂³×C₅₃	1	2	yes	—
853	C₂×D₈	C₂³×C₅₃	1	2	yes	—
854	C₂×D₈	C₂³×C₅₃	1	2	yes	—
855	C₂×D₈	C₂³×C₅₃	1	2	yes	—
856	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
857	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
858	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
859	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
860	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
861	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
862	#127	—	2	2	no	—
863	#127	—	2	1	no	—
864	#127	—	2	1	no	—
865	#127	C₂³×C₅₃	1	1	yes	characteristic
866	#127	C₂³×C₅₃	1	1	yes	characteristic
867	#127	C₂³×C₅₃	1	2	yes	—
868	#127	C₂³×C₅₃	1	1	yes	characteristic
869	#126	—	2	1	no	—
870	#126	—	2	1	no	—
871	#126	—	2	1	no	—
872	#126	—	2	1	no	—
873	#125	—	2	1	no	—
874	#125	—	2	1	no	—
875	#125	C₂³×C₅₃	1	1	yes	characteristic
876	#125	C₂³×C₅₃	1	1	yes	characteristic
877	#124	—	2	1	no	—
878	#124	—	2	2	no	—
879	#124	—	2	1	no	—
880	#124	—	2	1	no	—
881	#124	—	2	1	no	—
882	#124	C₂³×C₅₃	1	1	yes	characteristic
883	#124	C₂³×C₅₃	1	1	yes	characteristic
884	#124	C₂³×C₅₃	1	2	yes	—
885	#124	C₂³×C₅₃	1	2	yes	—
886	#123	—	2	1	no	—
887	#123	—	2	1	no	—
888	#123	—	2	1	no	—
889	#123	—	2	1	no	—
890	#123	—	2	1	no	—
891	#123	—	2	1	no	—
892	#123	—	2	2	no	—
893	#123	—	2	2	no	—
894	#123	—	2	2	no	—
895	#123	—	2	2	no	—
896	#123	—	2	1	no	—
897	#123	—	2	1	no	—
898	C₂²⋊Q₈	—	2	1	no	—
899	C₂²⋊Q₈	—	2	1	no	—
900	C₂²⋊Q₈	—	2	1	no	—
901	C₂²⋊Q₈	—	2	1	no	—
902	C₂²⋊Q₈	—	2	1	no	—
903	C₂²⋊Q₈	—	2	1	no	—
904	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
905	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
906	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
907	#121	—	2	1	no	—
908	#121	—	2	1	no	—
909	#121	—	2	1	no	—
910	#121	—	2	1	no	—
911	#121	—	2	1	no	—
912	#121	—	2	1	no	—
913	#121	—	2	1	no	—
914	#121	—	2	1	no	—
915	#121	—	2	1	no	—
916	#121	—	2	1	no	—
917	#121	—	2	1	no	—
918	#121	—	2	1	no	—
919	#121	—	2	2	no	—
920	#121	—	2	2	no	—
921	#121	—	2	2	no	—
922	#121	—	2	2	no	—
923	#121	C₂³×C₅₃	1	1	yes	characteristic
924	#121	C₂³×C₅₃	1	1	yes	characteristic
925	#121	C₂³×C₅₃	1	2	yes	—
926	#121	C₂³×C₅₃	1	1	yes	characteristic
927	#121	C₂³×C₅₃	1	2	yes	—
928	#121	C₂³×C₅₃	1	1	yes	characteristic
929	#120	—	2	1	no	—
930	#120	—	2	1	no	—
931	#120	—	2	2	no	—
932	#120	—	2	2	no	—
933	#120	—	2	1	no	—
934	#120	—	2	1	no	—
935	C₄×Q₈	—	2	1	no	—
936	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
937	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
938	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
939	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
940	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
941	C₄×D₄	—	2	1	no	—
942	C₄×D₄	—	2	1	no	—
943	C₄×D₄	—	2	1	no	—
944	C₄×D₄	—	2	1	no	—
945	C₄×D₄	—	2	1	no	—
946	C₄×D₄	—	2	1	no	—
947	C₄×D₄	—	2	2	no	—
948	C₄×D₄	—	2	2	no	—
949	C₄×D₄	—	2	1	no	—
950	C₄×D₄	—	2	1	no	—
951	C₄×D₄	—	2	1	no	—
952	C₄×D₄	—	2	1	no	—
953	C₄×D₄	—	2	1	no	—
954	C₄×D₄	—	2	1	no	—
955	C₄×D₄	—	2	1	no	—
956	C₄×D₄	—	2	1	no	—
957	C₄×D₄	—	2	1	no	—
958	C₄×D₄	—	2	1	no	—
959	C₄×D₄	—	2	1	no	—
960	C₄×D₄	—	2	1	no	—
961	C₄×D₄	—	2	1	no	—
962	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
963	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
964	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
965	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
966	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
967	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
968	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
969	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
970	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
971	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
972	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
973	C₄×D₄	C₂³×C₅₃	1	2	yes	—
974	C₄×D₄	C₂³×C₅₃	1	2	yes	—
975	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
976	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
977	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
978	#117	—	2	1	no	—
979	#117	—	2	1	no	—
980	#117	—	2	1	no	—
981	#117	—	2	1	no	—
982	#117	D₄×C₅₃	1	1	yes	characteristic
983	#117	D₄×C₅₃	1	1	yes	characteristic
984	#117	D₄×C₅₃	1	1	yes	characteristic
985	#117	C₂³×C₅₃	1	1	yes	characteristic
986	C₂×C₄⋊C₄	—	2	1	no	—
987	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
988	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
989	C₂×C₂²⋊C₄	—	2	1	no	—
990	C₂×C₂²⋊C₄	—	2	1	no	—
991	C₂×C₂²⋊C₄	—	2	1	no	—
992	C₂×C₂²⋊C₄	—	2	1	no	—
993	C₂×C₂²⋊C₄	—	2	2	no	—
994	C₂×C₂²⋊C₄	—	2	2	no	—
995	C₂×C₄²	—	2	1	no	—
996	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
997	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
998	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
999	#107	C₂³×C₅₃	1	2	yes	—
1000	#107	C₂³×C₅₃	1	2	yes	—
1001	#107	C₂³×C₅₃	1	2	yes	—
1002	#106	C₂³×C₅₃	1	2	yes	—
1003	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1004	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1005	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1006	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
1007	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
1008	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
1009	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1010	#103	C₂³×C₅₃	1	2	yes	—
1011	#103	C₂³×C₅₃	1	2	yes	—
1012	#103	C₂³×C₅₃	1	2	yes	—
1013	#103	C₂³×C₅₃	1	2	yes	—
1014	#103	C₂³×C₅₃	1	2	yes	—
1015	#102	C₂³×C₅₃	1	2	yes	—
1016	#102	C₂³×C₅₃	1	2	yes	—
1017	#102	C₂³×C₅₃	1	2	yes	—
1018	#102	C₂³×C₅₃	1	2	yes	—
1019	#102	C₂³×C₅₃	1	2	yes	—
1020	#102	C₂³×C₅₃	1	2	yes	—
1021	#102	C₂³×C₅₃	1	2	yes	—
1022	#102	C₂³×C₅₃	1	2	yes	—
1023	#102	C₂³×C₅₃	1	2	yes	—
1024	#102	C₂³×C₅₃	1	2	yes	—
1025	#102	C₂³×C₅₃	1	2	yes	—
1026	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1027	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1028	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1029	#97	C₂³×C₅₃	1	2	yes	—
1030	#97	C₂³×C₅₃	1	2	yes	—
1031	C₄×C₈	C₂³×C₅₃	1	2	yes	—
1032	C₂⁴	—	2	1	no	—
1033	C₂⁴	—	2	1	no	—
1034	C₂⁴	—	2	2	no	—
1035	#41	—	2	2	no	—
1036	#41	—	4	2	no	—
1037	#41	—	4	1	no	—
1038	#41	—	4	2	no	—
1039	#41	—	4	2	no	—
1040	#41	—	4	2	no	—
1041	#41	—	4	2	no	—
1042	#41	—	8	2	no	—
1043	#41	—	8	2	no	—
1044	#41	—	8	2	no	—
1045	C₂×Q₈	—	2	1	no	—
1046	C₂×Q₈	—	2	1	no	—
1047	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1048	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1049	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1050	C₂×D₄	—	2	2	no	—
1051	C₂×D₄	—	2	2	no	—
1052	C₂×D₄	—	2	1	no	—
1053	C₂×D₄	—	2	1	no	—
1054	C₂×D₄	—	2	1	no	—
1055	C₂×D₄	—	2	2	no	—
1056	C₂×D₄	—	2	2	no	—
1057	C₂×D₄	—	2	1	no	—
1058	C₂×D₄	—	2	1	no	—
1059	C₂×D₄	—	2	2	no	—
1060	C₂×D₄	—	2	2	no	—
1061	C₂×D₄	—	2	1	no	—
1062	C₂×D₄	—	2	1	no	—
1063	C₂×D₄	—	2	1	no	—
1064	C₂×D₄	—	2	1	no	—
1065	C₂×D₄	—	2	1	no	—
1066	C₂×D₄	—	2	2	no	—
1067	C₂×D₄	—	2	1	no	—
1068	C₂×D₄	—	2	1	no	—
1069	C₂×D₄	—	2	1	no	—
1070	C₂×D₄	—	2	2	no	—
1071	C₂×D₄	—	2	2	no	—
1072	C₂×D₄	—	4	1	no	—
1073	C₂×D₄	—	4	1	no	—
1074	C₂×D₄	—	4	2	no	—
1075	C₂×D₄	—	4	2	no	—
1076	C₂×D₄	—	4	4	no	—
1077	C₂×D₄	—	4	4	no	—
1078	C₂×D₄	—	8	2	no	—
1079	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1080	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1081	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1082	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1083	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1084	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1085	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1086	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1087	C₂²×C₄	—	2	1	no	—
1088	C₂²×C₄	—	2	1	no	—
1089	C₂²×C₄	—	2	1	no	—
1090	C₂²×C₄	—	2	1	no	—
1091	C₂²×C₄	—	2	1	no	—
1092	C₂²×C₄	—	2	1	no	—
1093	C₂²×C₄	—	2	1	no	—
1094	C₂²×C₄	—	2	1	no	—
1095	C₂²×C₄	—	2	1	no	—
1096	C₂²×C₄	—	2	2	no	—
1097	C₂²×C₄	—	2	2	no	—
1098	C₂²×C₄	—	2	2	no	—
1099	C₂²×C₄	—	2	2	no	—
1100	C₂²×C₄	—	2	1	no	—
1101	C₂²×C₄	—	2	1	no	—
1102	C₂²×C₄	—	8	2	no	—
1103	C₂²×C₄	—	8	2	no	—
1104	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1105	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1106	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1107	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1108	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1109	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1110	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1111	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1112	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1113	Q₁₆	—	4	2	no	—
1114	SD₁₆	—	2	4	no	—
1115	SD₁₆	—	4	2	no	—
1116	SD₁₆	—	4	2	no	—
1117	SD₁₆	—	4	2	no	—
1118	SD₁₆	—	4	2	no	—
1119	D₈	—	2	4	no	—
1120	D₈	—	2	4	no	—
1121	D₈	—	4	2	no	—
1122	D₈	—	4	2	no	—
1123	D₈	—	4	2	no	—
1124	D₈	—	4	2	no	—
1125	M₁₆	—	4	2	no	—
1126	C₂×C₈	—	4	2	no	—
1127	C₂×C₈	—	4	2	no	—
1128	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1129	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1130	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1131	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1132	C₄⋊C₄	—	2	1	no	—
1133	C₄⋊C₄	—	2	1	no	—
1134	C₄⋊C₄	—	2	1	no	—
1135	C₄⋊C₄	—	2	1	no	—
1136	C₄⋊C₄	—	2	1	no	—
1137	C₄⋊C₄	—	2	1	no	—
1138	C₄⋊C₄	—	2	1	no	—
1139	C₄⋊C₄	—	2	1	no	—
1140	C₄⋊C₄	—	2	1	no	—
1141	C₄⋊C₄	—	2	1	no	—
1142	C₄⋊C₄	—	2	1	no	—
1143	C₄⋊C₄	—	2	1	no	—
1144	C₄⋊C₄	—	2	1	no	—
1145	C₄⋊C₄	—	2	1	no	—
1146	C₄⋊C₄	—	2	2	no	—
1147	C₄⋊C₄	—	2	2	no	—
1148	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1149	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1150	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1151	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1152	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1153	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1154	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1155	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1156	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1157	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1158	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1159	C₂²⋊C₄	—	2	2	no	—
1160	C₂²⋊C₄	—	2	1	no	—
1161	C₂²⋊C₄	—	2	1	no	—
1162	C₂²⋊C₄	—	2	1	no	—
1163	C₂²⋊C₄	—	2	1	no	—
1164	C₂²⋊C₄	—	2	2	no	—
1165	C₂²⋊C₄	—	2	2	no	—
1166	C₂²⋊C₄	—	2	2	no	—
1167	C₂²⋊C₄	—	2	2	no	—
1168	C₂²⋊C₄	—	2	1	no	—
1169	C₂²⋊C₄	—	2	1	no	—
1170	C₂²⋊C₄	—	2	1	no	—
1171	C₂²⋊C₄	—	2	1	no	—
1172	C₂²⋊C₄	—	2	1	no	—
1173	C₂²⋊C₄	—	2	1	no	—
1174	C₂²⋊C₄	—	2	1	no	—
1175	C₂²⋊C₄	—	2	1	no	—
1176	C₂²⋊C₄	—	2	1	no	—
1177	C₂²⋊C₄	—	2	1	no	—
1178	C₂²⋊C₄	—	2	1	no	—
1179	C₂²⋊C₄	—	2	1	no	—
1180	C₂²⋊C₄	—	2	1	no	—
1181	C₂²⋊C₄	—	2	1	no	—
1182	C₂²⋊C₄	—	2	1	no	—
1183	C₂²⋊C₄	—	2	2	no	—
1184	C₂²⋊C₄	—	2	2	no	—
1185	C₂²⋊C₄	—	2	2	no	—
1186	C₂²⋊C₄	—	2	2	no	—
1187	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1188	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1189	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1190	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1191	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1192	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1193	C₄²	—	2	1	no	—
1194	C₄²	—	2	1	no	—
1195	C₄²	—	2	1	no	—
1196	C₄²	—	2	2	no	—
1197	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1198	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1199	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1200	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1201	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1202	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1203	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1204	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1205	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1206	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1207	C₂³	—	2	1	no	—
1208	C₂³	—	2	1	no	—
1209	C₂³	—	2	1	no	—
1210	C₂³	—	2	2	no	—
1211	C₂³	—	2	2	no	—
1212	C₂³	—	4	2	no	—
1213	C₂³	—	4	2	no	—
1214	C₂³	—	4	2	no	—
1215	C₂³	—	4	2	no	—
1216	C₂³	—	4	4	no	—
1217	C₂³	—	8	1	no	—
1218	C₂³	—	8	1	no	—
1219	C₂³	—	8	2	no	—
1220	C₂³	—	8	2	no	—
1221	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1222	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1223	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1224	Q₈	—	2	2	no	—
1225	Q₈	—	2	1	no	—
1226	Q₈	—	2	1	no	—
1227	Q₈	—	2	2	no	—
1228	Q₈	—	4	1	no	—
1229	Q₈	—	4	2	no	—
1230	Q₈	—	8	1	no	—
1231	D₄	—	2	2	no	—
1232	D₄	—	2	2	no	—
1233	D₄	—	2	2	no	—
1234	D₄	—	2	2	no	—
1235	D₄	—	2	1	no	—
1236	D₄	—	2	1	no	—
1237	D₄	—	2	1	no	—
1238	D₄	—	2	1	no	—
1239	D₄	—	2	2	no	—
1240	D₄	—	2	1	no	—
1241	D₄	—	2	2	no	—
1242	D₄	—	4	1	no	—
1243	D₄	—	4	2	no	—
1244	D₄	—	4	2	no	—
1245	D₄	—	4	2	no	—
1246	D₄	—	4	2	no	—
1247	D₄	—	4	4	no	—
1248	D₄	—	4	2	no	—
1249	D₄	—	4	2	no	—
1250	D₄	—	4	2	no	—
1251	D₄	—	4	2	no	—
1252	D₄	—	4	2	no	—
1253	D₄	—	4	2	no	—
1254	D₄	—	8	2	no	—
1255	D₄	—	8	2	no	—
1256	D₄	—	8	1	no	—
1257	D₄	—	8	2	no	—
1258	D₄	—	8	2	no	—
1259	D₄	—	8	1	no	—
1260	D₄	—	8	1	no	—
1261	D₄	—	8	2	no	—
1262	D₄	—	8	2	no	—
1263	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1264	C₂×C₄	—	2	2	no	—
1265	C₂×C₄	—	2	2	no	—
1266	C₂×C₄	—	2	2	no	—
1267	C₂×C₄	—	2	2	no	—
1268	C₂×C₄	—	2	1	no	—
1269	C₂×C₄	—	2	1	no	—
1270	C₂×C₄	—	2	1	no	—
1271	C₂×C₄	—	2	1	no	—
1272	C₂×C₄	—	2	1	no	—
1273	C₂×C₄	—	2	1	no	—
1274	C₂×C₄	—	2	1	no	—
1275	C₂×C₄	—	2	1	no	—
1276	C₂×C₄	—	2	1	no	—
1277	C₂×C₄	—	2	2	no	—
1278	C₂×C₄	—	2	2	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	4	1	no	—
1282	C₂×C₄	—	4	1	no	—
1283	C₂×C₄	—	4	2	no	—
1284	C₂×C₄	—	4	2	no	—
1285	C₂×C₄	—	4	2	no	—
1286	C₂×C₄	—	4	2	no	—
1287	C₂×C₄	—	4	2	no	—
1288	C₂×C₄	—	8	1	no	—
1289	C₂×C₄	—	8	1	no	—
1290	C₂×C₄	—	8	1	no	—
1291	C₂×C₄	—	8	1	no	—
1292	C₂×C₄	—	8	2	no	—
1293	C₂×C₄	—	8	2	no	—
1294	C₂×C₄	—	8	2	no	—
1295	C₂×C₄	—	8	2	no	—
1296	C₂×C₄	—	8	1	no	—
1297	C₂×C₄	—	8	1	no	—
1298	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1299	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1300	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1301	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1302	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1303	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1304	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1305	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1306	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1307	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1308	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1309	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1310	C₈	—	2	2	no	—
1311	C₈	—	2	2	no	—
1312	C₈	—	2	2	no	—
1313	C₈	—	2	2	no	—
1314	C₂²	—	2	1	no	—
1315	C₂²	—	2	1	no	—
1316	C₂²	—	2	1	no	—
1317	C₂²	—	2	1	no	—
1318	C₂²	—	2	2	no	—
1319	C₂²	—	2	1	no	—
1320	C₂²	—	2	1	no	—
1321	C₂²	—	2	1	no	—
1322	C₂²	—	2	1	no	—
1323	C₂²	—	4	1	no	—
1324	C₂²	—	4	1	no	—
1325	C₂²	—	4	2	no	—
1326	C₂²	—	4	2	no	—
1327	C₂²	—	4	1	no	—
1328	C₂²	—	4	1	no	—
1329	C₂²	—	4	1	no	—
1330	C₂²	—	4	1	no	—
1331	C₂²	—	4	2	no	—
1332	C₂²	—	4	2	no	—
1333	C₂²	—	4	1	no	—
1334	C₂²	—	4	1	no	—
1335	C₂²	—	4	2	no	—
1336	C₂²	—	4	2	no	—
1337	C₂²	—	8	4	no	—
1338	C₂²	—	8	4	no	—
1339	C₂²	—	16	4	no	—
1340	C₂²	C₅₃×#575	1	2	yes	—
1341	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1342	C₄	—	2	1	no	—
1343	C₄	—	2	1	no	—
1344	C₄	—	2	1	no	—
1345	C₄	—	2	1	no	—
1346	C₄	—	2	1	no	—
1347	C₄	—	2	1	no	—
1348	C₄	—	2	1	no	—
1349	C₄	—	2	1	no	—
1350	C₄	—	2	1	no	—
1351	C₄	—	2	1	no	—
1352	C₄	—	4	1	no	—
1353	C₄	—	4	2	no	—
1354	C₄	—	4	1	no	—
1355	C₄	—	4	1	no	—
1356	C₄	—	4	1	no	—
1357	C₄	—	4	1	no	—
1358	C₄	—	4	2	no	—
1359	C₄	C₅₃×#576	1	2	yes	—
1360	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1361	C₄	C₅₃×#585	1	1	yes	characteristic
1362	C₂	—	2	2	no	—
1363	C₂	—	4	1	no	—
1364	C₂	—	4	1	no	—
1365	C₂	—	4	2	no	—
1366	C₂	—	8	1	no	—
1367	C₂	—	8	1	no	—
1368	C₂	—	8	2	no	—
1369	C₂	—	8	2	no	—
1370	C₂	C₅₃×#3488	1	1	yes	characteristic
1371	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1372	C₂	C₂×C₅₃×#576	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×#3508	C₂	semidirect
2. C₅₃×#3481	C₂	semidirect
3. C₅₃×#3403	C₂	semidirect
4. C₅₃×#3370	C₂	semidirect
5. C₅₃×#3314	C₂	semidirect
6. C₅₃×#3309	C₂	semidirect
7. C₅₃×#3297	C₂	semidirect
8. C₅₃×#3280	C₂	semidirect
9. C₅₃×#3268	C₂	semidirect
10. C₅₃×#3264	C₂	semidirect
11. C₅₃×#3251	C₂	semidirect
12. C₅₃×#3248	C₂	semidirect
13. C₅₃×#3245	C₂	semidirect
14. C₅₃×#3217	C₂	semidirect
15. C₅₃×#3214	C₂	semidirect
16. C₅₃×#3212	C₂	semidirect
17. C₅₃×#3115	C₂	semidirect
18. C₅₃×#3110	C₂	semidirect
19. C₅₃×#3100	C₂	semidirect
20. C₅₃×#3036	C₂	semidirect
21. C₅₃×#3035	C₂	semidirect
22. C₂×C₅₃×#459	C₂	semidirect
23. C₅₃×#2990	C₂	semidirect
24. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
25. C₂×#135×C₅₃	C₂²	semidirect
28. C₅₃×#559	C₂²	semidirect
29. C₅₃×#559	C₂²	semidirect
31. C₅₃×#554	C₂²	semidirect
34. C₅₃×#553	C₂²	semidirect
38. C₅₃×#550	C₂²	semidirect
44. C₅₃×#546	C₂²	semidirect
45. C₅₃×#546	C₂²	semidirect
50. C₅₃×#533	C₂²	semidirect
51. C₅₃×#532	C₂²	semidirect
52. C₅₃×#532	C₂²	semidirect
53. C₅₃×#532	C₂²	semidirect
54. C₅₃×#532	C₂²	semidirect
55. C₅₃×#532	C₂²	semidirect
56. C₂×#127×C₅₃	C₂²	semidirect
59. C₅₃×#529	C₂²	semidirect
64. C₄×#41×C₅₃	C₂²	semidirect
67. C₂×C₄×D₄×C₅₃	C₂²	semidirect
68. C₅₃×#496	C₂²	semidirect
69. C₅₃×#496	C₂²	semidirect
70. C₅₃×#495	C₂²	semidirect
71. C₅₃×#490	C₂²	semidirect
72. C₅₃×#489	C₂²	semidirect
73. C₅₃×#488	C₂²	semidirect
74. C₅₃×#484	C₂²	semidirect
75. C₅₃×#482	C₂²	semidirect
76. C₅₃×#480	C₂²	semidirect
77. C₅₃×#479	C₂²	semidirect
78. C₅₃×#478	C₂²	semidirect
79. C₅₃×#475	C₂²	semidirect
80. C₅₃×#474	C₂²	semidirect
81. C₅₃×#474	C₂²	semidirect
82. C₅₃×#474	C₂²	semidirect
83. C₅₃×#474	C₂²	semidirect
84. C₅₃×#469	C₂²	semidirect
85. C₅₃×#468	C₂²	semidirect
86. C₅₃×#467	C₂²	semidirect
87. C₅₃×#466	C₂²	semidirect
88. C₅₃×#466	C₂²	semidirect
90. C₅₃×#464	C₂²	semidirect
91. C₅₃×#464	C₂²	semidirect
92. C₅₃×#463	C₂²	semidirect
93. C₅₃×#463	C₂²	semidirect
94. C₅₃×#463	C₂²	semidirect
95. C₅₃×#463	C₂²	semidirect
96. C₅₃×#462	C₂²	semidirect
97. C₅₃×#461	C₂²	semidirect
98. C₅₃×#461	C₂²	semidirect
99. C₅₃×#461	C₂²	semidirect
100. C₅₃×#460	C₂²	semidirect
101. C₅₃×#460	C₂²	semidirect
105. C₅₃×#459	C₂²	semidirect
106. C₅₃×#459	C₂²	semidirect
107. C₅₃×#459	C₂²	semidirect
108. C₅₃×#459	C₂²	semidirect
109. C₅₃×#459	C₂²	semidirect
110. C₅₃×#459	C₂²	semidirect
111. C₅₃×#452	C₂²	semidirect
113. C₅₃×#450	C₂²	semidirect
114. C₅₃×#449	C₂²	semidirect
115. C₅₃×#449	C₂²	semidirect
116. C₅₃×#449	C₂²	semidirect
117. C₅₃×#449	C₂²	semidirect
119. C₅₃×#447	C₂²	semidirect
120. C₅₃×#446	C₂²	semidirect
121. C₅₃×#442	C₂²	semidirect
122. C₅₃×#440	C₂²	semidirect
123. C₅₃×#440	C₂²	semidirect
124. C₅₃×#440	C₂²	semidirect
125. C₄×D₈×C₅₃	C₂²	semidirect
126. C₄×D₈×C₅₃	C₂²	semidirect
128. C₅₃×#435	C₂²	semidirect
129. C₈×D₄×C₅₃	C₂²	semidirect
130. C₅₃×#432	C₂²	semidirect
131. C₅₃×#432	C₂²	semidirect
132. C₅₃×#431	C₂²	semidirect
133. C₅₃×#423	C₂²	semidirect
134. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
135. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
136. C₅₃×#417	C₂²	semidirect
137. C₅₃×#416	C₂²	semidirect
138. C₂×#102×C₅₃	C₂²	semidirect
627. #61977	C₅₃	direct (N × H)
676. #3508	C₂×C₅₃	semidirect
677. #3481	C₂×C₅₃	semidirect
678. #3403	C₂×C₅₃	semidirect
679. #3370	C₂×C₅₃	semidirect
680. #3314	C₂×C₅₃	semidirect
681. #3309	C₂×C₅₃	semidirect
682. #3297	C₂×C₅₃	semidirect
683. #3280	C₂×C₅₃	semidirect
684. #3268	C₂×C₅₃	semidirect
685. #3264	C₂×C₅₃	semidirect
686. #3251	C₂×C₅₃	semidirect
687. #3248	C₂×C₅₃	semidirect
688. #3245	C₂×C₅₃	semidirect
689. #3217	C₂×C₅₃	semidirect
690. #3214	C₂×C₅₃	semidirect
691. #3212	C₂×C₅₃	semidirect
692. #3115	C₂×C₅₃	semidirect
693. #3110	C₂×C₅₃	semidirect
694. #3100	C₂×C₅₃	semidirect
695. #3036	C₂×C₅₃	semidirect
696. #3035	C₂×C₅₃	semidirect
697. C₂×#459	C₂×C₅₃	semidirect
698. #2990	C₂×C₅₃	semidirect
710. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
711. C₂×#135	C₂²×C₅₃	semidirect
714. #559	C₂²×C₅₃	semidirect
715. #559	C₂²×C₅₃	semidirect
717. #554	C₂²×C₅₃	semidirect
720. #553	C₂²×C₅₃	semidirect
724. #550	C₂²×C₅₃	semidirect
730. #546	C₂²×C₅₃	semidirect
731. #546	C₂²×C₅₃	semidirect
736. #533	C₂²×C₅₃	semidirect
737. #532	C₂²×C₅₃	semidirect
738. #532	C₂²×C₅₃	semidirect
739. #532	C₂²×C₅₃	semidirect
740. #532	C₂²×C₅₃	semidirect
741. #532	C₂²×C₅₃	semidirect
742. C₂×#127	C₂²×C₅₃	semidirect
745. #529	C₂²×C₅₃	semidirect
750. C₄×#41	C₂²×C₅₃	semidirect
753. C₂×C₄×D₄	C₂²×C₅₃	semidirect
754. #496	C₂²×C₅₃	semidirect
755. #496	C₂²×C₅₃	semidirect
756. #495	C₂²×C₅₃	semidirect
757. #490	C₂²×C₅₃	semidirect
758. #489	C₂²×C₅₃	semidirect
759. #488	C₂²×C₅₃	semidirect
760. #484	C₂²×C₅₃	semidirect
761. #482	C₂²×C₅₃	semidirect
762. #480	C₂²×C₅₃	semidirect
763. #479	C₂²×C₅₃	semidirect
764. #478	C₂²×C₅₃	semidirect
765. #475	C₂²×C₅₃	semidirect
766. #474	C₂²×C₅₃	semidirect
767. #474	C₂²×C₅₃	semidirect
768. #474	C₂²×C₅₃	semidirect
769. #474	C₂²×C₅₃	semidirect
770. #469	C₂²×C₅₃	semidirect
771. #468	C₂²×C₅₃	semidirect
772. #467	C₂²×C₅₃	semidirect
773. #466	C₂²×C₅₃	semidirect
774. #466	C₂²×C₅₃	semidirect
776. #464	C₂²×C₅₃	semidirect
777. #464	C₂²×C₅₃	semidirect
778. #463	C₂²×C₅₃	semidirect
779. #463	C₂²×C₅₃	semidirect
780. #463	C₂²×C₅₃	semidirect
781. #463	C₂²×C₅₃	semidirect
782. #462	C₂²×C₅₃	semidirect
783. #461	C₂²×C₅₃	semidirect
784. #461	C₂²×C₅₃	semidirect
785. #461	C₂²×C₅₃	semidirect
786. #460	C₂²×C₅₃	semidirect
787. #460	C₂²×C₅₃	semidirect
791. #459	C₂²×C₅₃	semidirect
792. #459	C₂²×C₅₃	semidirect
793. #459	C₂²×C₅₃	semidirect
794. #459	C₂²×C₅₃	semidirect
795. #459	C₂²×C₅₃	semidirect
796. #459	C₂²×C₅₃	semidirect
797. #452	C₂²×C₅₃	semidirect
799. #450	C₂²×C₅₃	semidirect
800. #449	C₂²×C₅₃	semidirect
801. #449	C₂²×C₅₃	semidirect
802. #449	C₂²×C₅₃	semidirect
803. #449	C₂²×C₅₃	semidirect
805. #447	C₂²×C₅₃	semidirect
806. #446	C₂²×C₅₃	semidirect
807. #442	C₂²×C₅₃	semidirect
808. #440	C₂²×C₅₃	semidirect
809. #440	C₂²×C₅₃	semidirect
810. #440	C₂²×C₅₃	semidirect
811. C₄×D₈	C₂²×C₅₃	semidirect
812. C₄×D₈	C₂²×C₅₃	semidirect
814. #435	C₂²×C₅₃	semidirect
815. C₈×D₄	C₂²×C₅₃	semidirect
816. #432	C₂²×C₅₃	semidirect
817. #432	C₂²×C₅₃	semidirect
818. #431	C₂²×C₅₃	semidirect
819. #423	C₂²×C₅₃	semidirect
820. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
821. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
822. #417	C₂²×C₅₃	semidirect
823. #416	C₂²×C₅₃	semidirect
824. C₂×#102	C₂²×C₅₃	semidirect
825. C₅₃	#61977	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×#3508	2
C₅₃×#3481	2
C₅₃×#3403	2
C₅₃×#3370	2
C₅₃×#3314	2
C₅₃×#3309	2
C₅₃×#3297	2
C₅₃×#3280	2
C₅₃×#3268	2
C₅₃×#3264	2
C₅₃×#3251	2
C₅₃×#3248	2
C₅₃×#3245	2
C₅₃×#3217	2
C₅₃×#3214	2
C₅₃×#3212	2
C₅₃×#3115	2
C₅₃×#3110	2
C₅₃×#3100	2
C₅₃×#3036	2
C₅₃×#3035	2
C₂×C₅₃×#459	2
C₅₃×#2990	2
#61977	53

Subgroups — C53×#61977 #27269489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61977 #27269489