Subgroups — C₅₃×#61183 #27268695

Order 13568.

2286 conjugacy classes of subgroups.

The subgroup lattice has 1294 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×#3484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3325	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3322	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3319	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3318	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3318	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3306	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3297	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3294	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×#3081	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×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₅₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₅₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
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×#547	C₂²	1	2	yes	complemented
36	C₅₃×#546	—	2	1	no	—
37	C₅₃×#546	—	2	1	no	—
38	C₅₃×#546	—	2	2	no	—
39	C₅₃×#546	C₂²	1	2	yes	complemented
40	C₅₃×#546	C₂²	1	2	yes	complemented
41	D₄²×C₅₃	—	2	1	no	—
42	D₄²×C₅₃	—	2	1	no	—
43	D₄²×C₅₃	C₂²	1	2	yes	complemented
44	D₄²×C₅₃	C₂²	1	2	yes	complemented
45	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#542	—	2	1	no	—
47	C₅₃×#540	—	2	1	no	—
48	C₅₃×#535	C₂²	1	1	yes	characteristic
49	C₅₃×#535	C₂²	1	1	yes	characteristic
50	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#534	—	2	2	no	—
52	C₅₃×#532	—	2	1	no	—
53	C₅₃×#529	—	2	1	no	—
54	C₅₃×#525	C₂²	1	1	yes	characteristic
55	C₅₃×#525	C₂²	1	1	yes	characteristic
56	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×#120×C₅₃	—	2	2	no	—
58	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#518	C₂²	1	1	yes	characteristic
60	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
61	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
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	1	yes	characteristic, complemented
72	C₅₃×#482	C₂²	1	2	yes	complemented
73	C₅₃×#482	C₂²	1	2	yes	complemented
74	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#481	C₂²	1	2	yes	complemented
76	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#480	C₂²	1	2	yes	complemented
78	C₅₃×#478	C₂²	1	2	yes	complemented
79	C₅₃×#478	C₂²	1	2	yes	complemented
80	C₅₃×#476	C₂²	1	2	yes	complemented
81	C₅₃×#474	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	complemented
95	C₅₃×#449	C₂²	1	2	yes	complemented
96	C₅₃×#447	C₂²	1	2	yes	complemented
97	C₅₃×#447	C₂²	1	2	yes	complemented
98	C₅₃×#447	C₂²	1	2	yes	complemented
99	C₅₃×#447	C₂²	1	2	yes	complemented
100	C₅₃×#447	C₂²	1	2	yes	complemented
101	C₅₃×#447	C₂²	1	2	yes	complemented
102	C₅₃×#442	C₂²	1	2	yes	complemented
103	C₅₃×#442	C₂²	1	2	yes	complemented
104	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
105	C₄×D₈×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, complemented
111	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#418	C₂²	1	1	yes	characteristic
115	C₅₃×#418	C₂²	1	1	yes	characteristic
116	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#418	C₂²	1	2	yes	complemented
119	C₅₃×#418	C₂²	1	2	yes	complemented
120	C₅₃×#418	C₂²	1	2	yes	complemented
121	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#417	C₂²	1	2	yes	complemented
123	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#416	C₂²	1	2	yes	complemented
125	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
127	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
128	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
129	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
130	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
131	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
132	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂⁵×C₅₃	—	2	1	no	—
136	H(5,𝔽₂)×C₅₃	—	2	4	no	—
137	H(5,𝔽₂)×C₅₃	—	4	2	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	—	2	2	no	—
140	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₅₃	C₂³	1	2	yes	—
142	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₅₃	—	2	4	no	—
144	C₂²×D₄×C₅₃	—	2	1	no	—
145	C₂²×D₄×C₅₃	—	2	2	no	—
146	C₂²×D₄×C₅₃	—	2	1	no	—
147	C₂²×D₄×C₅₃	—	2	2	no	—
148	C₂²×D₄×C₅₃	—	2	2	no	—
149	C₂²×D₄×C₅₃	—	2	1	no	—
150	C₂²×D₄×C₅₃	—	2	1	no	—
151	C₂²×D₄×C₅₃	—	2	1	no	—
152	C₂²×D₄×C₅₃	—	4	2	no	—
153	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
155	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
156	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
157	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
158	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
159	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
160	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
161	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	complemented
162	C₂×D₈×C₅₃	—	2	4	no	—
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	C₂×D₈×C₅₃	C₂³	1	2	yes	—
168	C₂×D₈×C₅₃	C₂³	1	2	yes	complemented
169	#131×C₅₃	—	4	2	no	—
170	C₂×M₁₆×C₅₃	—	4	2	no	—
171	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
174	C₂×M₁₆×C₅₃	C₂³	1	2	yes	complemented
175	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
178	C₂²×C₈×C₅₃	C₂³	1	2	yes	complemented
179	C₄⋊Q₈×C₅₃	—	2	1	no	—
180	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
181	#127×C₅₃	—	2	1	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	complemented
188	#124×C₅₃	—	2	2	no	—
189	#124×C₅₃	—	2	2	no	—
190	#124×C₅₃	—	2	1	no	—
191	#124×C₅₃	—	2	1	no	—
192	#124×C₅₃	C₂³	1	2	yes	—
193	#123×C₅₃	—	2	2	no	—
194	#123×C₅₃	—	2	2	no	—
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	D₄	1	1	yes	characteristic
204	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
205	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
206	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
207	#121×C₅₃	—	2	2	no	—
208	#121×C₅₃	—	2	2	no	—
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	1	no	—
217	#121×C₅₃	—	2	1	no	—
218	#121×C₅₃	D₄	1	1	yes	characteristic
219	#121×C₅₃	D₄	1	1	yes	characteristic
220	#121×C₅₃	C₂³	1	2	yes	—
221	#121×C₅₃	C₂³	1	2	yes	—
222	#121×C₅₃	C₂³	1	1	yes	characteristic
223	#121×C₅₃	C₂³	1	1	yes	characteristic
224	#121×C₅₃	C₂³	1	2	yes	—
225	#121×C₅₃	C₂³	1	2	yes	—
226	#121×C₅₃	C₂³	1	2	yes	complemented
227	#121×C₅₃	C₂³	1	2	yes	complemented
228	#120×C₅₃	—	2	2	no	—
229	#120×C₅₃	—	2	2	no	—
230	#120×C₅₃	—	2	2	no	—
231	#120×C₅₃	—	2	2	no	—
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	—	2	2	no	—
237	#120×C₅₃	—	2	2	no	—
238	#120×C₅₃	D₄	1	2	yes	—
239	C₄×Q₈×C₅₃	—	2	1	no	—
240	C₄×D₄×C₅₃	—	2	1	no	—
241	C₄×D₄×C₅₃	—	2	1	no	—
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	1	no	—
247	C₄×D₄×C₅₃	—	2	2	no	—
248	C₄×D₄×C₅₃	—	2	1	no	—
249	C₄×D₄×C₅₃	—	2	1	no	—
250	C₄×D₄×C₅₃	C₂³	1	2	yes	—
251	C₄×D₄×C₅₃	C₂³	1	2	yes	—
252	C₄×D₄×C₅₃	C₂³	1	2	yes	—
253	C₄×D₄×C₅₃	C₂³	1	2	yes	—
254	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
255	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
256	#117×C₅₃	—	2	2	no	—
257	#117×C₅₃	—	2	1	no	—
258	#117×C₅₃	—	2	1	no	—
259	#117×C₅₃	C₂³	1	1	yes	characteristic
260	#117×C₅₃	C₂³	1	1	yes	characteristic
261	#117×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	complemented
266	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
270	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
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, complemented
278	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
279	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
280	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
281	#107×C₅₃	C₂³	1	2	yes	complemented
282	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
283	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
284	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
285	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
286	#106×C₅₃	C₂³	1	2	yes	complemented
287	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
288	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
289	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
290	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
291	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
292	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
293	#103×C₅₃	C₂³	1	2	yes	complemented
294	#102×C₅₃	C₂³	1	2	yes	—
295	#102×C₅₃	C₂³	1	2	yes	—
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	2	yes	—
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	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, complemented
307	#102×C₅₃	C₂³	1	2	yes	complemented
308	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
309	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
310	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
311	#102×C₅₃	C₂³	1	2	yes	complemented
312	#102×C₅₃	C₂³	1	2	yes	complemented
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	complemented
318	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	complemented
319	#97×C₅₃	C₂³	1	2	yes	complemented
320	C₄×C₈×C₅₃	C₂³	1	2	yes	complemented
321	C₂⁴×C₅₃	—	2	1	no	—
322	C₂⁴×C₅₃	—	2	2	no	—
323	C₂⁴×C₅₃	—	2	2	no	—
324	C₂⁴×C₅₃	—	2	1	no	—
325	C₂⁴×C₅₃	—	2	1	no	—
326	C₂⁴×C₅₃	—	2	2	no	—
327	C₂⁴×C₅₃	—	4	4	no	—
328	C₂⁴×C₅₃	—	8	2	no	—
329	C₂⁴×C₅₃	—	8	2	no	—
330	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
331	#41×C₅₃	—	2	2	no	—
332	#41×C₅₃	—	2	2	no	—
333	#41×C₅₃	—	2	4	no	—
334	#41×C₅₃	—	2	2	no	—
335	#41×C₅₃	—	2	2	no	—
336	#41×C₅₃	—	4	2	no	—
337	#41×C₅₃	—	4	4	no	—
338	#41×C₅₃	—	8	4	no	—
339	C₂×Q₈×C₅₃	—	2	2	no	—
340	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
341	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₅₃	—	2	4	no	—
343	C₂×D₄×C₅₃	—	2	4	no	—
344	C₂×D₄×C₅₃	—	2	4	no	—
345	C₂×D₄×C₅₃	—	2	1	no	—
346	C₂×D₄×C₅₃	—	2	1	no	—
347	C₂×D₄×C₅₃	—	2	2	no	—
348	C₂×D₄×C₅₃	—	2	1	no	—
349	C₂×D₄×C₅₃	—	2	2	no	—
350	C₂×D₄×C₅₃	—	2	2	no	—
351	C₂×D₄×C₅₃	—	2	2	no	—
352	C₂×D₄×C₅₃	—	2	2	no	—
353	C₂×D₄×C₅₃	—	2	2	no	—
354	C₂×D₄×C₅₃	—	2	2	no	—
355	C₂×D₄×C₅₃	—	2	1	no	—
356	C₂×D₄×C₅₃	—	2	1	no	—
357	C₂×D₄×C₅₃	—	2	2	no	—
358	C₂×D₄×C₅₃	—	2	2	no	—
359	C₂×D₄×C₅₃	—	2	2	no	—
360	C₂×D₄×C₅₃	—	2	1	no	—
361	C₂×D₄×C₅₃	—	2	2	no	—
362	C₂×D₄×C₅₃	—	2	2	no	—
363	C₂×D₄×C₅₃	—	2	2	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	—	4	2	no	—
369	C₂×D₄×C₅₃	—	4	2	no	—
370	C₂×D₄×C₅₃	—	4	2	no	—
371	C₂×D₄×C₅₃	—	4	4	no	—
372	C₂×D₄×C₅₃	—	4	4	no	—
373	C₂×D₄×C₅₃	—	4	4	no	—
374	C₂×D₄×C₅₃	—	4	4	no	—
375	C₂×D₄×C₅₃	—	4	8	no	—
376	C₂×D₄×C₅₃	—	8	4	no	—
377	C₂×D₄×C₅₃	—	8	2	no	—
378	C₂×D₄×C₅₃	—	8	4	no	—
379	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
380	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
381	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
382	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
383	C₂×D₄×C₅₃	#41	1	4	yes	complemented
384	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
385	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
387	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
388	C₂²×C₄×C₅₃	—	2	2	no	—
389	C₂²×C₄×C₅₃	—	2	2	no	—
390	C₂²×C₄×C₅₃	—	2	1	no	—
391	C₂²×C₄×C₅₃	—	2	1	no	—
392	C₂²×C₄×C₅₃	—	2	1	no	—
393	C₂²×C₄×C₅₃	—	2	2	no	—
394	C₂²×C₄×C₅₃	—	2	2	no	—
395	C₂²×C₄×C₅₃	—	2	1	no	—
396	C₂²×C₄×C₅₃	—	2	2	no	—
397	C₂²×C₄×C₅₃	—	2	2	no	—
398	C₂²×C₄×C₅₃	—	2	2	no	—
399	C₂²×C₄×C₅₃	—	2	2	no	—
400	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	SD₁₆×C₅₃	—	4	2	no	—
408	D₈×C₅₃	—	2	4	no	—
409	D₈×C₅₃	—	2	4	no	—
410	D₈×C₅₃	—	4	2	no	—
411	D₈×C₅₃	—	4	2	no	—
412	D₈×C₅₃	—	4	2	no	—
413	M₁₆×C₅₃	—	2	2	no	—
414	M₁₆×C₅₃	—	2	2	no	—
415	M₁₆×C₅₃	—	4	2	no	—
416	M₁₆×C₅₃	—	4	2	no	—
417	C₂×C₈×C₅₃	—	2	2	no	—
418	C₂×C₈×C₅₃	—	2	2	no	—
419	C₂×C₈×C₅₃	—	4	2	no	—
420	C₂×C₈×C₅₃	—	4	2	no	—
421	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
423	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
427	C₄⋊C₄×C₅₃	—	2	1	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	—	2	1	no	—
433	C₄⋊C₄×C₅₃	—	2	1	no	—
434	C₄⋊C₄×C₅₃	—	2	2	no	—
435	C₄⋊C₄×C₅₃	—	2	2	no	—
436	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
437	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
440	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
442	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
447	C₂²⋊C₄×C₅₃	—	2	1	no	—
448	C₂²⋊C₄×C₅₃	—	2	1	no	—
449	C₂²⋊C₄×C₅₃	—	2	1	no	—
450	C₂²⋊C₄×C₅₃	—	2	1	no	—
451	C₂²⋊C₄×C₅₃	—	2	1	no	—
452	C₂²⋊C₄×C₅₃	—	2	1	no	—
453	C₂²⋊C₄×C₅₃	—	2	1	no	—
454	C₂²⋊C₄×C₅₃	—	2	2	no	—
455	C₂²⋊C₄×C₅₃	—	2	2	no	—
456	C₂²⋊C₄×C₅₃	—	2	2	no	—
457	C₂²⋊C₄×C₅₃	—	2	2	no	—
458	C₂²⋊C₄×C₅₃	—	2	2	no	—
459	C₂²⋊C₄×C₅₃	—	2	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	—	2	2	no	—
464	C₂²⋊C₄×C₅₃	—	2	2	no	—
465	C₂²⋊C₄×C₅₃	—	2	2	no	—
466	C₂²⋊C₄×C₅₃	—	2	1	no	—
467	C₂²⋊C₄×C₅₃	—	2	1	no	—
468	C₂²⋊C₄×C₅₃	—	2	2	no	—
469	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
470	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
471	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
472	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
473	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
474	C₄²×C₅₃	—	2	1	no	—
475	C₄²×C₅₃	—	2	1	no	—
476	C₄²×C₅₃	—	2	1	no	—
477	C₄²×C₅₃	—	2	1	no	—
478	C₄²×C₅₃	—	2	2	no	—
479	C₄²×C₅₃	—	2	1	no	—
480	C₄²×C₅₃	C₂⁴	1	2	yes	—
481	C₂³×C₅₃	—	2	2	no	—
482	C₂³×C₅₃	—	2	2	no	—
483	C₂³×C₅₃	—	2	2	no	—
484	C₂³×C₅₃	—	2	4	no	—
485	C₂³×C₅₃	—	2	2	no	—
486	C₂³×C₅₃	—	2	1	no	—
487	C₂³×C₅₃	—	2	2	no	—
488	C₂³×C₅₃	—	4	1	no	—
489	C₂³×C₅₃	—	4	4	no	—
490	C₂³×C₅₃	—	4	4	no	—
491	C₂³×C₅₃	—	4	4	no	—
492	C₂³×C₅₃	—	4	4	no	—
493	C₂³×C₅₃	—	4	2	no	—
494	C₂³×C₅₃	—	4	4	no	—
495	C₂³×C₅₃	—	4	2	no	—
496	C₂³×C₅₃	—	8	2	no	—
497	C₂³×C₅₃	—	8	1	no	—
498	C₂³×C₅₃	—	8	1	no	—
499	C₂³×C₅₃	—	8	1	no	—
500	C₂³×C₅₃	—	8	1	no	—
501	C₂³×C₅₃	—	8	2	no	—
502	C₂³×C₅₃	—	8	1	no	—
503	C₂³×C₅₃	—	8	2	no	—
504	C₂³×C₅₃	—	8	2	no	—
505	C₂³×C₅₃	—	8	1	no	—
506	C₂³×C₅₃	—	8	16	no	—
507	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
508	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
509	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
511	Q₈×C₅₃	—	2	2	no	—
512	Q₈×C₅₃	—	2	1	no	—
513	Q₈×C₅₃	—	2	1	no	—
514	Q₈×C₅₃	—	8	2	no	—
515	D₄×C₅₃	—	2	4	no	—
516	D₄×C₅₃	—	2	4	no	—
517	D₄×C₅₃	—	2	4	no	—
518	D₄×C₅₃	—	2	2	no	—
519	D₄×C₅₃	—	2	2	no	—
520	D₄×C₅₃	—	2	1	no	—
521	D₄×C₅₃	—	2	2	no	—
522	D₄×C₅₃	—	2	2	no	—
523	D₄×C₅₃	—	2	2	no	—
524	D₄×C₅₃	—	2	2	no	—
525	D₄×C₅₃	—	2	1	no	—
526	D₄×C₅₃	—	4	2	no	—
527	D₄×C₅₃	—	4	4	no	—
528	D₄×C₅₃	—	4	4	no	—
529	D₄×C₅₃	—	4	4	no	—
530	D₄×C₅₃	—	4	4	no	—
531	D₄×C₅₃	—	4	2	no	—
532	D₄×C₅₃	—	4	2	no	—
533	D₄×C₅₃	—	4	2	no	—
534	D₄×C₅₃	—	4	4	no	—
535	D₄×C₅₃	—	4	2	no	—
536	D₄×C₅₃	—	4	2	no	—
537	D₄×C₅₃	—	8	2	no	—
538	D₄×C₅₃	—	8	2	no	—
539	D₄×C₅₃	—	8	2	no	—
540	D₄×C₅₃	—	8	2	no	—
541	D₄×C₅₃	—	8	2	no	—
542	D₄×C₅₃	—	8	2	no	—
543	D₄×C₅₃	—	8	2	no	—
544	D₄×C₅₃	C₂×#41	1	4	yes	—
545	C₂×C₄×C₅₃	—	2	2	no	—
546	C₂×C₄×C₅₃	—	2	2	no	—
547	C₂×C₄×C₅₃	—	2	2	no	—
548	C₂×C₄×C₅₃	—	2	1	no	—
549	C₂×C₄×C₅₃	—	2	1	no	—
550	C₂×C₄×C₅₃	—	2	2	no	—
551	C₂×C₄×C₅₃	—	2	1	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	2	no	—
554	C₂×C₄×C₅₃	—	2	1	no	—
555	C₂×C₄×C₅₃	—	2	1	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	1	no	—
559	C₂×C₄×C₅₃	—	2	2	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	4	4	no	—
563	C₂×C₄×C₅₃	—	4	2	no	—
564	C₂×C₄×C₅₃	—	4	2	no	—
565	C₂×C₄×C₅₃	—	8	2	no	—
566	C₂×C₄×C₅₃	—	8	2	no	—
567	C₂×C₄×C₅₃	—	8	2	no	—
568	C₂×C₄×C₅₃	—	8	2	no	—
569	C₂×C₄×C₅₃	—	8	1	no	—
570	C₂×C₄×C₅₃	—	8	1	no	—
571	C₂×C₄×C₅₃	—	8	2	no	—
572	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
573	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
574	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
575	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
579	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
580	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
581	C₈×C₅₃	—	2	1	no	—
582	C₈×C₅₃	—	2	1	no	—
583	C₈×C₅₃	—	2	1	no	—
584	C₈×C₅₃	—	2	1	no	—
585	C₈×C₅₃	—	2	2	no	—
586	C₈×C₅₃	—	2	2	no	—
587	#61183	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
588	C₂²×C₅₃	—	2	1	no	—
589	C₂²×C₅₃	—	2	1	no	—
590	C₂²×C₅₃	—	2	1	no	—
591	C₂²×C₅₃	—	2	1	no	—
592	C₂²×C₅₃	—	2	1	no	—
593	C₂²×C₅₃	—	2	2	no	—
594	C₂²×C₅₃	—	2	1	no	—
595	C₂²×C₅₃	—	2	2	no	—
596	C₂²×C₅₃	—	2	4	no	—
597	C₂²×C₅₃	—	2	2	no	—
598	C₂²×C₅₃	—	2	1	no	—
599	C₂²×C₅₃	—	4	4	no	—
600	C₂²×C₅₃	—	4	2	no	—
601	C₂²×C₅₃	—	4	2	no	—
602	C₂²×C₅₃	—	4	2	no	—
603	C₂²×C₅₃	—	4	1	no	—
604	C₂²×C₅₃	—	4	2	no	—
605	C₂²×C₅₃	—	4	1	no	—
606	C₂²×C₅₃	—	4	2	no	—
607	C₂²×C₅₃	—	4	2	no	—
608	C₂²×C₅₃	—	4	2	no	—
609	C₂²×C₅₃	—	4	1	no	—
610	C₂²×C₅₃	—	4	2	no	—
611	C₂²×C₅₃	—	8	4	no	—
612	C₂²×C₅₃	—	8	8	no	—
613	C₂²×C₅₃	—	8	4	no	—
614	C₂²×C₅₃	—	8	8	no	—
615	C₂²×C₅₃	—	16	2	no	—
616	C₂²×C₅₃	—	16	4	no	—
617	C₂²×C₅₃	#546	1	2	yes	—
618	C₂²×C₅₃	#576	1	2	yes	—
619	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
620	C₄×C₅₃	—	2	2	no	—
621	C₄×C₅₃	—	2	1	no	—
622	C₄×C₅₃	—	2	1	no	—
623	C₄×C₅₃	—	2	2	no	—
624	C₄×C₅₃	—	2	2	no	—
625	C₄×C₅₃	—	4	1	no	—
626	C₄×C₅₃	—	4	1	no	—
627	C₄×C₅₃	—	4	1	no	—
628	C₄×C₅₃	—	4	1	no	—
629	C₄×C₅₃	—	4	1	no	—
630	C₄×C₅₃	—	4	1	no	—
631	C₄×C₅₃	—	4	1	no	—
632	C₄×C₅₃	—	4	2	no	—
633	C₄×C₅₃	#546	1	2	yes	—
634	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
635	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
636	#3494	C₂×C₅₃	1	1	yes	characteristic, complemented
637	#3484	C₂×C₅₃	1	1	yes	characteristic, complemented
638	#3325	C₂×C₅₃	1	2	yes	complemented
639	#3322	C₂×C₅₃	1	2	yes	complemented
640	#3319	C₂×C₅₃	1	2	yes	complemented
641	#3318	C₂×C₅₃	1	2	yes	complemented
642	#3318	C₂×C₅₃	1	2	yes	complemented
643	#3306	C₂×C₅₃	1	2	yes	complemented
644	#3297	C₂×C₅₃	1	2	yes	complemented
645	#3294	C₂×C₅₃	1	2	yes	complemented
646	#3136	C₂×C₅₃	1	1	yes	characteristic, complemented
647	#3096	C₂×C₅₃	1	1	yes	characteristic, complemented
648	#3091	C₂×C₅₃	1	1	yes	characteristic, complemented
649	#3081	C₂×C₅₃	1	1	yes	characteristic, complemented
650	#3058	C₂×C₅₃	1	1	yes	characteristic, complemented
651	#3055	C₂×C₅₃	1	1	yes	characteristic, complemented
652	#3041	C₂×C₅₃	1	1	yes	characteristic, complemented
653	#3008	C₂×C₅₃	1	1	yes	characteristic, complemented
654	C₂×#447	C₂×C₅₃	1	1	yes	characteristic, complemented
655	#2948	C₂×C₅₃	1	1	yes	characteristic, complemented
656	#2933	C₂×C₅₃	1	1	yes	characteristic, complemented
657	#2897	C₂×C₅₃	1	1	yes	characteristic, complemented
658	C₂×#418	C₂×C₅₃	1	1	yes	characteristic, complemented
659	C₂×C₅₃	—	2	2	no	—
660	C₂×C₅₃	—	2	2	no	—
661	C₂×C₅₃	—	4	1	no	—
662	C₂×C₅₃	—	4	2	no	—
663	C₂×C₅₃	—	4	4	no	—
664	C₂×C₅₃	—	8	2	no	—
665	C₂×C₅₃	—	8	2	no	—
666	C₂×C₅₃	—	8	1	no	—
667	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
668	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
669	C₂×C₅₃	#3585	1	1	yes	characteristic
670	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
671	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
672	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
674	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
675	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic, complemented
676	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
677	#555	C₂²×C₅₃	1	2	yes	complemented
678	#553	C₂²×C₅₃	1	2	yes	complemented
679	#553	C₂²×C₅₃	1	2	yes	complemented
680	#551	—	2	2	no	—
681	#547	C₂²×C₅₃	1	2	yes	complemented
682	#546	—	2	1	no	—
683	#546	—	2	1	no	—
684	#546	—	2	2	no	—
685	#546	C₂²×C₅₃	1	2	yes	complemented
686	#546	C₂²×C₅₃	1	2	yes	complemented
687	D₄²	—	2	1	no	—
688	D₄²	—	2	1	no	—
689	D₄²	C₂²×C₅₃	1	2	yes	complemented
690	D₄²	C₂²×C₅₃	1	2	yes	complemented
691	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	#542	—	2	1	no	—
693	#540	—	2	1	no	—
694	#535	C₂²×C₅₃	1	1	yes	characteristic
695	#535	C₂²×C₅₃	1	1	yes	characteristic
696	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
697	#534	—	2	2	no	—
698	#532	—	2	1	no	—
699	#529	—	2	1	no	—
700	#525	C₂²×C₅₃	1	1	yes	characteristic
701	#525	C₂²×C₅₃	1	1	yes	characteristic
702	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	C₂×#120	—	2	2	no	—
704	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
705	#518	C₂²×C₅₃	1	1	yes	characteristic
706	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	#490	C₂²×C₅₃	1	2	yes	complemented
709	#489	C₂²×C₅₃	1	2	yes	complemented
710	#488	C₂²×C₅₃	1	2	yes	complemented
711	#486	C₂²×C₅₃	1	2	yes	complemented
712	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
714	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
715	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
716	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
717	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
718	#482	C₂²×C₅₃	1	2	yes	complemented
719	#482	C₂²×C₅₃	1	2	yes	complemented
720	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
721	#481	C₂²×C₅₃	1	2	yes	complemented
722	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	#480	C₂²×C₅₃	1	2	yes	complemented
724	#478	C₂²×C₅₃	1	2	yes	complemented
725	#478	C₂²×C₅₃	1	2	yes	complemented
726	#476	C₂²×C₅₃	1	2	yes	complemented
727	#474	C₂²×C₅₃	1	2	yes	complemented
728	#469	C₂²×C₅₃	1	2	yes	complemented
729	#469	C₂²×C₅₃	1	2	yes	complemented
730	#469	C₂²×C₅₃	1	2	yes	complemented
731	#468	C₂²×C₅₃	1	2	yes	complemented
732	#466	C₂²×C₅₃	1	2	yes	complemented
733	#466	C₂²×C₅₃	1	2	yes	complemented
734	#466	C₂²×C₅₃	1	2	yes	complemented
735	#465	C₂²×C₅₃	1	2	yes	complemented
736	#463	C₂²×C₅₃	1	2	yes	complemented
737	#463	C₂²×C₅₃	1	2	yes	complemented
738	#459	C₂²×C₅₃	1	2	yes	complemented
739	#459	C₂²×C₅₃	1	2	yes	complemented
740	#449	C₂²×C₅₃	1	2	yes	complemented
741	#449	C₂²×C₅₃	1	2	yes	complemented
742	#447	C₂²×C₅₃	1	2	yes	complemented
743	#447	C₂²×C₅₃	1	2	yes	complemented
744	#447	C₂²×C₅₃	1	2	yes	complemented
745	#447	C₂²×C₅₃	1	2	yes	complemented
746	#447	C₂²×C₅₃	1	2	yes	complemented
747	#447	C₂²×C₅₃	1	2	yes	complemented
748	#442	C₂²×C₅₃	1	2	yes	complemented
749	#442	C₂²×C₅₃	1	2	yes	complemented
750	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
751	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
752	#436	C₂²×C₅₃	1	2	yes	complemented
753	#435	C₂²×C₅₃	1	2	yes	complemented
754	#435	C₂²×C₅₃	1	2	yes	complemented
755	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
756	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
757	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
758	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
759	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
760	#418	C₂²×C₅₃	1	1	yes	characteristic
761	#418	C₂²×C₅₃	1	1	yes	characteristic
762	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
763	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
764	#418	C₂²×C₅₃	1	2	yes	complemented
765	#418	C₂²×C₅₃	1	2	yes	complemented
766	#418	C₂²×C₅₃	1	2	yes	complemented
767	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
768	#417	C₂²×C₅₃	1	2	yes	complemented
769	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
770	#416	C₂²×C₅₃	1	2	yes	complemented
771	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
772	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
773	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
774	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
775	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
776	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
777	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
778	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
779	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
780	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
781	C₅₃	#61183	1	1	yes	characteristic, direct product factor, Sylow
782	C₂⁵	—	2	1	no	—
783	H(5,𝔽₂)	—	2	4	no	—
784	H(5,𝔽₂)	—	4	2	no	—
785	C₂×#41	—	2	1	no	—
786	C₂×#41	—	2	2	no	—
787	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
788	C₂×#41	C₂³×C₅₃	1	2	yes	—
789	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
790	C₂²×D₄	—	2	4	no	—
791	C₂²×D₄	—	2	1	no	—
792	C₂²×D₄	—	2	2	no	—
793	C₂²×D₄	—	2	1	no	—
794	C₂²×D₄	—	2	2	no	—
795	C₂²×D₄	—	2	2	no	—
796	C₂²×D₄	—	2	1	no	—
797	C₂²×D₄	—	2	1	no	—
798	C₂²×D₄	—	2	1	no	—
799	C₂²×D₄	—	4	2	no	—
800	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
801	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
802	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
803	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
804	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
805	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
806	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
807	AGL(1,ℤ/8)	—	4	2	no	—
808	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	complemented
809	C₂×D₈	—	2	4	no	—
810	C₂×D₈	—	4	2	no	—
811	C₂×D₈	C₂³×C₅₃	1	2	yes	—
812	C₂×D₈	C₂³×C₅₃	1	2	yes	—
813	C₂×D₈	C₂³×C₅₃	1	2	yes	—
814	C₂×D₈	C₂³×C₅₃	1	2	yes	—
815	C₂×D₈	C₂³×C₅₃	1	2	yes	complemented
816	#131	—	4	2	no	—
817	C₂×M₁₆	—	4	2	no	—
818	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
819	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
820	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
821	C₂×M₁₆	C₂³×C₅₃	1	2	yes	complemented
822	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
823	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
824	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
825	C₂²×C₈	C₂³×C₅₃	1	2	yes	complemented
826	C₄⋊Q₈	—	2	1	no	—
827	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
828	#127	—	2	1	no	—
829	#127	—	2	1	no	—
830	#127	C₂³×C₅₃	1	2	yes	—
831	#126	—	2	2	no	—
832	#126	—	2	2	no	—
833	#125	—	2	1	no	—
834	#125	C₂³×C₅₃	1	2	yes	complemented
835	#124	—	2	1	no	—
836	#124	—	2	1	no	—
837	#124	—	2	2	no	—
838	#124	—	2	2	no	—
839	#124	C₂³×C₅₃	1	2	yes	—
840	#123	—	2	1	no	—
841	#123	—	2	2	no	—
842	#123	—	2	2	no	—
843	#123	—	2	2	no	—
844	#123	—	2	2	no	—
845	#123	—	2	2	no	—
846	#123	—	2	2	no	—
847	#123	D₄×C₅₃	1	2	yes	—
848	C₂²⋊Q₈	—	2	2	no	—
849	C₂²⋊Q₈	—	2	2	no	—
850	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
851	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
852	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
853	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
854	#121	—	2	2	no	—
855	#121	—	2	2	no	—
856	#121	—	2	2	no	—
857	#121	—	2	1	no	—
858	#121	—	2	1	no	—
859	#121	—	2	2	no	—
860	#121	—	2	2	no	—
861	#121	—	2	1	no	—
862	#121	—	2	1	no	—
863	#121	—	2	2	no	—
864	#121	—	2	2	no	—
865	#121	D₄×C₅₃	1	1	yes	characteristic
866	#121	D₄×C₅₃	1	1	yes	characteristic
867	#121	C₂³×C₅₃	1	2	yes	—
868	#121	C₂³×C₅₃	1	2	yes	—
869	#121	C₂³×C₅₃	1	1	yes	characteristic
870	#121	C₂³×C₅₃	1	1	yes	characteristic
871	#121	C₂³×C₅₃	1	2	yes	—
872	#121	C₂³×C₅₃	1	2	yes	—
873	#121	C₂³×C₅₃	1	2	yes	complemented
874	#121	C₂³×C₅₃	1	2	yes	complemented
875	#120	—	2	1	no	—
876	#120	—	2	2	no	—
877	#120	—	2	2	no	—
878	#120	—	2	2	no	—
879	#120	—	2	2	no	—
880	#120	—	2	2	no	—
881	#120	—	2	2	no	—
882	#120	—	2	2	no	—
883	#120	—	2	2	no	—
884	#120	—	2	2	no	—
885	#120	D₄×C₅₃	1	2	yes	—
886	C₄×Q₈	—	2	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	2	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	2	no	—
896	C₄×D₄	—	2	2	no	—
897	C₄×D₄	C₂³×C₅₃	1	2	yes	—
898	C₄×D₄	C₂³×C₅₃	1	2	yes	—
899	C₄×D₄	C₂³×C₅₃	1	2	yes	—
900	C₄×D₄	C₂³×C₅₃	1	2	yes	—
901	C₄×D₄	C₂³×C₅₃	1	2	yes	complemented
902	C₄×D₄	C₂³×C₅₃	1	2	yes	complemented
903	#117	—	2	1	no	—
904	#117	—	2	1	no	—
905	#117	—	2	2	no	—
906	#117	C₂³×C₅₃	1	1	yes	characteristic
907	#117	C₂³×C₅₃	1	1	yes	characteristic
908	#117	C₂³×C₅₃	1	1	yes	characteristic
909	#117	C₂³×C₅₃	1	1	yes	characteristic
910	#117	C₂³×C₅₃	1	1	yes	characteristic
911	#117	C₂³×C₅₃	1	1	yes	characteristic
912	#117	C₂³×C₅₃	1	2	yes	complemented
913	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
914	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
915	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
916	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
917	C₂×C₂²⋊C₄	—	2	1	no	—
918	C₂×C₂²⋊C₄	—	2	1	no	—
919	C₂×C₂²⋊C₄	—	2	2	no	—
920	C₂×C₂²⋊C₄	—	2	2	no	—
921	C₂×C₂²⋊C₄	—	2	2	no	—
922	C₂×C₂²⋊C₄	—	2	2	no	—
923	C₂×C₄²	—	2	1	no	—
924	#107	C₂³×C₅₃	1	1	yes	characteristic, complemented
925	#107	C₂³×C₅₃	1	1	yes	characteristic, complemented
926	#107	C₂³×C₅₃	1	1	yes	characteristic, complemented
927	#107	C₂³×C₅₃	1	1	yes	characteristic, complemented
928	#107	C₂³×C₅₃	1	2	yes	complemented
929	#106	C₂³×C₅₃	1	1	yes	characteristic, complemented
930	#106	C₂³×C₅₃	1	1	yes	characteristic, complemented
931	#106	C₂³×C₅₃	1	1	yes	characteristic, complemented
932	#106	C₂³×C₅₃	1	1	yes	characteristic, complemented
933	#106	C₂³×C₅₃	1	2	yes	complemented
934	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
935	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
936	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
937	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
938	#103	C₂³×C₅₃	1	2	yes	complemented
939	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
940	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
941	#102	C₂³×C₅₃	1	2	yes	—
942	#102	C₂³×C₅₃	1	2	yes	—
943	#102	C₂³×C₅₃	1	2	yes	—
944	#102	C₂³×C₅₃	1	2	yes	—
945	#102	C₂³×C₅₃	1	2	yes	—
946	#102	C₂³×C₅₃	1	2	yes	—
947	#102	C₂³×C₅₃	1	2	yes	—
948	#102	C₂³×C₅₃	1	2	yes	—
949	#102	C₂³×C₅₃	1	2	yes	—
950	#102	C₂³×C₅₃	1	2	yes	—
951	#102	C₂³×C₅₃	1	2	yes	—
952	#102	C₂³×C₅₃	1	2	yes	—
953	#102	C₂³×C₅₃	1	1	yes	characteristic, complemented
954	#102	C₂³×C₅₃	1	2	yes	complemented
955	#102	C₂³×C₅₃	1	1	yes	characteristic, complemented
956	#102	C₂³×C₅₃	1	1	yes	characteristic, complemented
957	#102	C₂³×C₅₃	1	1	yes	characteristic, complemented
958	#102	C₂³×C₅₃	1	2	yes	complemented
959	#102	C₂³×C₅₃	1	2	yes	complemented
960	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
961	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
962	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
963	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
964	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	complemented
965	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	complemented
966	#97	C₂³×C₅₃	1	2	yes	complemented
967	C₄×C₈	C₂³×C₅₃	1	2	yes	complemented
968	C₂⁴	—	2	1	no	—
969	C₂⁴	—	2	2	no	—
970	C₂⁴	—	2	2	no	—
971	C₂⁴	—	2	1	no	—
972	C₂⁴	—	2	1	no	—
973	C₂⁴	—	2	2	no	—
974	C₂⁴	—	4	4	no	—
975	C₂⁴	—	8	2	no	—
976	C₂⁴	—	8	2	no	—
977	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
978	#41	—	2	2	no	—
979	#41	—	2	2	no	—
980	#41	—	2	4	no	—
981	#41	—	2	2	no	—
982	#41	—	2	2	no	—
983	#41	—	4	2	no	—
984	#41	—	4	4	no	—
985	#41	—	8	4	no	—
986	C₂×Q₈	—	2	2	no	—
987	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
988	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
989	C₂×D₄	—	2	4	no	—
990	C₂×D₄	—	2	4	no	—
991	C₂×D₄	—	2	4	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	2	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	2	no	—
1010	C₂×D₄	—	2	2	no	—
1011	C₂×D₄	—	2	2	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	4	2	no	—
1016	C₂×D₄	—	4	2	no	—
1017	C₂×D₄	—	4	2	no	—
1018	C₂×D₄	—	4	4	no	—
1019	C₂×D₄	—	4	4	no	—
1020	C₂×D₄	—	4	4	no	—
1021	C₂×D₄	—	4	4	no	—
1022	C₂×D₄	—	4	8	no	—
1023	C₂×D₄	—	8	4	no	—
1024	C₂×D₄	—	8	2	no	—
1025	C₂×D₄	—	8	4	no	—
1026	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1027	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1028	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1029	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1030	C₂×D₄	#41×C₅₃	1	4	yes	complemented
1031	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1032	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1033	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1034	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	1	no	—
1040	C₂²×C₄	—	2	2	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	2	no	—
1044	C₂²×C₄	—	2	2	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	2	2	no	—
1047	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1048	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1049	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1050	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1051	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1052	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1053	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1054	SD₁₆	—	4	2	no	—
1055	D₈	—	2	4	no	—
1056	D₈	—	2	4	no	—
1057	D₈	—	4	2	no	—
1058	D₈	—	4	2	no	—
1059	D₈	—	4	2	no	—
1060	M₁₆	—	2	2	no	—
1061	M₁₆	—	2	2	no	—
1062	M₁₆	—	4	2	no	—
1063	M₁₆	—	4	2	no	—
1064	C₂×C₈	—	2	2	no	—
1065	C₂×C₈	—	2	2	no	—
1066	C₂×C₈	—	4	2	no	—
1067	C₂×C₈	—	4	2	no	—
1068	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1069	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1070	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1071	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1072	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1073	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	2	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	2	no	—
1082	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1084	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1085	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1086	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1087	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1088	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1089	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1090	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1091	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1092	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1093	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1117	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1118	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1119	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1120	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1121	C₄²	—	2	1	no	—
1122	C₄²	—	2	1	no	—
1123	C₄²	—	2	1	no	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	2	no	—
1126	C₄²	—	2	1	no	—
1127	C₄²	C₂⁴×C₅₃	1	2	yes	—
1128	C₂³	—	2	2	no	—
1129	C₂³	—	2	2	no	—
1130	C₂³	—	2	2	no	—
1131	C₂³	—	2	4	no	—
1132	C₂³	—	2	2	no	—
1133	C₂³	—	2	2	no	—
1134	C₂³	—	2	1	no	—
1135	C₂³	—	4	1	no	—
1136	C₂³	—	4	4	no	—
1137	C₂³	—	4	4	no	—
1138	C₂³	—	4	4	no	—
1139	C₂³	—	4	4	no	—
1140	C₂³	—	4	2	no	—
1141	C₂³	—	4	4	no	—
1142	C₂³	—	4	2	no	—
1143	C₂³	—	8	1	no	—
1144	C₂³	—	8	1	no	—
1145	C₂³	—	8	2	no	—
1146	C₂³	—	8	1	no	—
1147	C₂³	—	8	1	no	—
1148	C₂³	—	8	2	no	—
1149	C₂³	—	8	1	no	—
1150	C₂³	—	8	2	no	—
1151	C₂³	—	8	2	no	—
1152	C₂³	—	8	1	no	—
1153	C₂³	—	8	16	no	—
1154	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1155	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1156	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1157	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1158	Q₈	—	2	2	no	—
1159	Q₈	—	2	1	no	—
1160	Q₈	—	2	1	no	—
1161	Q₈	—	8	2	no	—
1162	D₄	—	2	4	no	—
1163	D₄	—	2	4	no	—
1164	D₄	—	2	4	no	—
1165	D₄	—	2	2	no	—
1166	D₄	—	2	2	no	—
1167	D₄	—	2	2	no	—
1168	D₄	—	2	1	no	—
1169	D₄	—	2	2	no	—
1170	D₄	—	2	2	no	—
1171	D₄	—	2	2	no	—
1172	D₄	—	2	1	no	—
1173	D₄	—	4	2	no	—
1174	D₄	—	4	4	no	—
1175	D₄	—	4	4	no	—
1176	D₄	—	4	4	no	—
1177	D₄	—	4	4	no	—
1178	D₄	—	4	2	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	4	no	—
1182	D₄	—	4	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	8	2	no	—
1185	D₄	—	8	2	no	—
1186	D₄	—	8	2	no	—
1187	D₄	—	8	2	no	—
1188	D₄	—	8	2	no	—
1189	D₄	—	8	2	no	—
1190	D₄	—	8	2	no	—
1191	D₄	C₂×#41×C₅₃	1	4	yes	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	4	4	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	8	2	no	—
1213	C₂×C₄	—	8	2	no	—
1214	C₂×C₄	—	8	2	no	—
1215	C₂×C₄	—	8	2	no	—
1216	C₂×C₄	—	8	1	no	—
1217	C₂×C₄	—	8	1	no	—
1218	C₂×C₄	—	8	2	no	—
1219	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1220	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1221	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1222	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1223	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1224	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1225	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1226	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1227	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1228	C₈	—	2	1	no	—
1229	C₈	—	2	1	no	—
1230	C₈	—	2	1	no	—
1231	C₈	—	2	1	no	—
1232	C₈	—	2	2	no	—
1233	C₈	—	2	2	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	1	no	—
1236	C₂²	—	2	1	no	—
1237	C₂²	—	2	1	no	—
1238	C₂²	—	2	1	no	—
1239	C₂²	—	2	2	no	—
1240	C₂²	—	2	4	no	—
1241	C₂²	—	2	2	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	2	no	—
1245	C₂²	—	4	4	no	—
1246	C₂²	—	4	2	no	—
1247	C₂²	—	4	2	no	—
1248	C₂²	—	4	1	no	—
1249	C₂²	—	4	2	no	—
1250	C₂²	—	4	2	no	—
1251	C₂²	—	4	2	no	—
1252	C₂²	—	4	1	no	—
1253	C₂²	—	4	2	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	8	4	no	—
1258	C₂²	—	8	8	no	—
1259	C₂²	—	8	4	no	—
1260	C₂²	—	8	8	no	—
1261	C₂²	—	16	2	no	—
1262	C₂²	—	16	4	no	—
1263	C₂²	C₅₃×#546	1	2	yes	—
1264	C₂²	C₅₃×#576	1	2	yes	—
1265	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1266	C₄	—	2	1	no	—
1267	C₄	—	2	1	no	—
1268	C₄	—	2	2	no	—
1269	C₄	—	2	2	no	—
1270	C₄	—	2	2	no	—
1271	C₄	—	4	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	1	no	—
1275	C₄	—	4	2	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	1	no	—
1279	C₄	C₅₃×#546	1	2	yes	—
1280	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1281	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1282	C₂	—	2	2	no	—
1283	C₂	—	2	2	no	—
1284	C₂	—	4	1	no	—
1285	C₂	—	4	2	no	—
1286	C₂	—	4	4	no	—
1287	C₂	—	8	2	no	—
1288	C₂	—	8	1	no	—
1289	C₂	—	8	2	no	—
1290	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
1291	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1292	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×#3484	C₂	semidirect
3. C₅₃×#3325	C₂	semidirect
4. C₅₃×#3322	C₂	semidirect
5. C₅₃×#3319	C₂	semidirect
6. C₅₃×#3318	C₂	semidirect
7. C₅₃×#3318	C₂	semidirect
8. C₅₃×#3306	C₂	semidirect
9. C₅₃×#3297	C₂	semidirect
10. C₅₃×#3294	C₂	semidirect
11. C₅₃×#3136	C₂	semidirect
12. C₅₃×#3096	C₂	semidirect
13. C₅₃×#3091	C₂	semidirect
14. C₅₃×#3081	C₂	semidirect
15. C₅₃×#3058	C₂	semidirect
16. C₅₃×#3055	C₂	semidirect
17. C₅₃×#3041	C₂	semidirect
18. C₅₃×#3008	C₂	semidirect
19. C₂×C₅₃×#447	C₂	semidirect
20. C₅₃×#2948	C₂	semidirect
21. C₅₃×#2933	C₂	semidirect
22. C₅₃×#2897	C₂	semidirect
23. C₂×C₅₃×#418	C₂	semidirect
26. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
28. C₂²×D₈×C₅₃	C₂²	semidirect
29. C₂×#131×C₅₃	C₂²	semidirect
30. C₂²×M₁₆×C₅₃	C₂²	semidirect
31. C₅₃×#555	C₂²	semidirect
32. C₅₃×#553	C₂²	semidirect
33. C₅₃×#553	C₂²	semidirect
35. C₅₃×#547	C₂²	semidirect
39. C₅₃×#546	C₂²	semidirect
40. C₅₃×#546	C₂²	semidirect
43. D₄²×C₅₃	C₂²	semidirect
44. D₄²×C₅₃	C₂²	semidirect
45. C₅₃×#544	C₂²	semidirect
50. C₅₃×#535	C₂²	semidirect
56. C₂×#121×C₅₃	C₂²	semidirect
58. C₅₃×#520	C₂²	semidirect
60. C₅₃×#518	C₂²	semidirect
61. C₂×#117×C₅₃	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×#478	C₂²	semidirect
79. C₅₃×#478	C₂²	semidirect
80. C₅₃×#476	C₂²	semidirect
81. C₅₃×#474	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
94. C₅₃×#449	C₂²	semidirect
95. C₅₃×#449	C₂²	semidirect
96. C₅₃×#447	C₂²	semidirect
97. C₅₃×#447	C₂²	semidirect
98. C₅₃×#447	C₂²	semidirect
99. C₅₃×#447	C₂²	semidirect
100. C₅₃×#447	C₂²	semidirect
101. C₅₃×#447	C₂²	semidirect
102. C₅₃×#442	C₂²	semidirect
103. C₅₃×#442	C₂²	semidirect
104. C₄×D₈×C₅₃	C₂²	semidirect
105. C₄×D₈×C₅₃	C₂²	semidirect
106. C₅₃×#436	C₂²	semidirect
107. C₅₃×#435	C₂²	semidirect
108. C₅₃×#435	C₂²	semidirect
109. C₈×D₄×C₅₃	C₂²	semidirect
110. C₅₃×#428	C₂²	semidirect
111. C₅₃×#427	C₂²	semidirect
112. C₅₃×#427	C₂²	semidirect
113. C₅₃×#424	C₂²	semidirect
116. C₅₃×#418	C₂²	semidirect
117. C₅₃×#418	C₂²	semidirect
118. C₅₃×#418	C₂²	semidirect
119. C₅₃×#418	C₂²	semidirect
120. C₅₃×#418	C₂²	semidirect
121. C₅₃×#418	C₂²	semidirect
122. C₅₃×#417	C₂²	semidirect
123. C₅₃×#417	C₂²	semidirect
124. C₅₃×#416	C₂²	semidirect
125. C₅₃×#416	C₂²	semidirect
126. C₅₃×#416	C₂²	semidirect
128. C₂×#102×C₅₃	C₂²	semidirect
129. C₂×#102×C₅₃	C₂²	semidirect
130. C₂×#102×C₅₃	C₂²	semidirect
131. C₂×#102×C₅₃	C₂²	semidirect
132. C₅₃×#408	C₂²	semidirect
133. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
134. C₅₃×#405	C₂²	semidirect
161. C₂×SD₁₆×C₅₃	C₂³	semidirect
168. C₂×D₈×C₅₃	C₂³	semidirect
174. C₂×M₁₆×C₅₃	C₂³	semidirect
178. C₂²×C₈×C₅₃	C₂³	semidirect
180. C₄⋊Q₈×C₅₃	C₂³	semidirect
187. #125×C₅₃	C₂³	semidirect
226. #121×C₅₃	C₂³	semidirect
227. #121×C₅₃	C₂³	semidirect
254. C₄×D₄×C₅₃	C₂³	semidirect
255. C₄×D₄×C₅₃	C₂³	semidirect
265. #117×C₅₃	C₂³	semidirect
269. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
277. #107×C₅₃	C₂³	semidirect
278. #107×C₅₃	C₂³	semidirect
279. #107×C₅₃	C₂³	semidirect
280. #107×C₅₃	C₂³	semidirect
281. #107×C₅₃	C₂³	semidirect
282. #106×C₅₃	C₂³	semidirect
283. #106×C₅₃	C₂³	semidirect
284. #106×C₅₃	C₂³	semidirect
285. #106×C₅₃	C₂³	semidirect
286. #106×C₅₃	C₂³	semidirect
287. C₄⋊C₈×C₅₃	C₂³	semidirect
288. C₄⋊C₈×C₅₃	C₂³	semidirect
289. #103×C₅₃	C₂³	semidirect
290. #103×C₅₃	C₂³	semidirect
291. #103×C₅₃	C₂³	semidirect
292. #103×C₅₃	C₂³	semidirect
293. #103×C₅₃	C₂³	semidirect
306. #102×C₅₃	C₂³	semidirect
307. #102×C₅₃	C₂³	semidirect
308. #102×C₅₃	C₂³	semidirect
309. #102×C₅₃	C₂³	semidirect
310. #102×C₅₃	C₂³	semidirect
311. #102×C₅₃	C₂³	semidirect
312. #102×C₅₃	C₂³	semidirect
317. C₂²⋊C₈×C₅₃	C₂³	semidirect
318. C₂²⋊C₈×C₅₃	C₂³	semidirect
319. #97×C₅₃	C₂³	semidirect
320. C₄×C₈×C₅₃	C₂³	semidirect
383. C₂×D₄×C₅₃	#41	semidirect
587. #61183	C₅₃	direct (N × H)
636. #3494	C₂×C₅₃	semidirect
637. #3484	C₂×C₅₃	semidirect
638. #3325	C₂×C₅₃	semidirect
639. #3322	C₂×C₅₃	semidirect
640. #3319	C₂×C₅₃	semidirect
641. #3318	C₂×C₅₃	semidirect
642. #3318	C₂×C₅₃	semidirect
643. #3306	C₂×C₅₃	semidirect
644. #3297	C₂×C₅₃	semidirect
645. #3294	C₂×C₅₃	semidirect
646. #3136	C₂×C₅₃	semidirect
647. #3096	C₂×C₅₃	semidirect
648. #3091	C₂×C₅₃	semidirect
649. #3081	C₂×C₅₃	semidirect
650. #3058	C₂×C₅₃	semidirect
651. #3055	C₂×C₅₃	semidirect
652. #3041	C₂×C₅₃	semidirect
653. #3008	C₂×C₅₃	semidirect
654. C₂×#447	C₂×C₅₃	semidirect
655. #2948	C₂×C₅₃	semidirect
656. #2933	C₂×C₅₃	semidirect
657. #2897	C₂×C₅₃	semidirect
658. C₂×#418	C₂×C₅₃	semidirect
672. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
674. C₂²×D₈	C₂²×C₅₃	semidirect
675. C₂×#131	C₂²×C₅₃	semidirect
676. C₂²×M₁₆	C₂²×C₅₃	semidirect
677. #555	C₂²×C₅₃	semidirect
678. #553	C₂²×C₅₃	semidirect
679. #553	C₂²×C₅₃	semidirect
681. #547	C₂²×C₅₃	semidirect
685. #546	C₂²×C₅₃	semidirect
686. #546	C₂²×C₅₃	semidirect
689. D₄²	C₂²×C₅₃	semidirect
690. D₄²	C₂²×C₅₃	semidirect
691. #544	C₂²×C₅₃	semidirect
696. #535	C₂²×C₅₃	semidirect
702. C₂×#121	C₂²×C₅₃	semidirect
704. #520	C₂²×C₅₃	semidirect
706. #518	C₂²×C₅₃	semidirect
707. C₂×#117	C₂²×C₅₃	semidirect
708. #490	C₂²×C₅₃	semidirect
709. #489	C₂²×C₅₃	semidirect
710. #488	C₂²×C₅₃	semidirect
711. #486	C₂²×C₅₃	semidirect
712. #485	C₂²×C₅₃	semidirect
713. #485	C₂²×C₅₃	semidirect
714. #484	C₂²×C₅₃	semidirect
715. #483	C₂²×C₅₃	semidirect
716. #482	C₂²×C₅₃	semidirect
717. #482	C₂²×C₅₃	semidirect
718. #482	C₂²×C₅₃	semidirect
719. #482	C₂²×C₅₃	semidirect
720. #481	C₂²×C₅₃	semidirect
721. #481	C₂²×C₅₃	semidirect
722. #480	C₂²×C₅₃	semidirect
723. #480	C₂²×C₅₃	semidirect
724. #478	C₂²×C₅₃	semidirect
725. #478	C₂²×C₅₃	semidirect
726. #476	C₂²×C₅₃	semidirect
727. #474	C₂²×C₅₃	semidirect
728. #469	C₂²×C₅₃	semidirect
729. #469	C₂²×C₅₃	semidirect
730. #469	C₂²×C₅₃	semidirect
731. #468	C₂²×C₅₃	semidirect
732. #466	C₂²×C₅₃	semidirect
733. #466	C₂²×C₅₃	semidirect
734. #466	C₂²×C₅₃	semidirect
735. #465	C₂²×C₅₃	semidirect
736. #463	C₂²×C₅₃	semidirect
737. #463	C₂²×C₅₃	semidirect
738. #459	C₂²×C₅₃	semidirect
739. #459	C₂²×C₅₃	semidirect
740. #449	C₂²×C₅₃	semidirect
741. #449	C₂²×C₅₃	semidirect
742. #447	C₂²×C₅₃	semidirect
743. #447	C₂²×C₅₃	semidirect
744. #447	C₂²×C₅₃	semidirect
745. #447	C₂²×C₅₃	semidirect
746. #447	C₂²×C₅₃	semidirect
747. #447	C₂²×C₅₃	semidirect
748. #442	C₂²×C₅₃	semidirect
749. #442	C₂²×C₅₃	semidirect
750. C₄×D₈	C₂²×C₅₃	semidirect
751. C₄×D₈	C₂²×C₅₃	semidirect
752. #436	C₂²×C₅₃	semidirect
753. #435	C₂²×C₅₃	semidirect
754. #435	C₂²×C₅₃	semidirect
755. C₈×D₄	C₂²×C₅₃	semidirect
756. #428	C₂²×C₅₃	semidirect
757. #427	C₂²×C₅₃	semidirect
758. #427	C₂²×C₅₃	semidirect
759. #424	C₂²×C₅₃	semidirect
762. #418	C₂²×C₅₃	semidirect
763. #418	C₂²×C₅₃	semidirect
764. #418	C₂²×C₅₃	semidirect
765. #418	C₂²×C₅₃	semidirect
766. #418	C₂²×C₅₃	semidirect
767. #418	C₂²×C₅₃	semidirect
768. #417	C₂²×C₅₃	semidirect
769. #417	C₂²×C₅₃	semidirect
770. #416	C₂²×C₅₃	semidirect
771. #416	C₂²×C₅₃	semidirect
772. #416	C₂²×C₅₃	semidirect
774. C₂×#102	C₂²×C₅₃	semidirect
775. C₂×#102	C₂²×C₅₃	semidirect
776. C₂×#102	C₂²×C₅₃	semidirect
777. C₂×#102	C₂²×C₅₃	semidirect
778. #408	C₂²×C₅₃	semidirect
779. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
780. #405	C₂²×C₅₃	semidirect
781. C₅₃	#61183	direct (N × H)
808. C₂×SD₁₆	C₂³×C₅₃	semidirect
815. C₂×D₈	C₂³×C₅₃	semidirect
821. C₂×M₁₆	C₂³×C₅₃	semidirect
825. C₂²×C₈	C₂³×C₅₃	semidirect
827. C₄⋊Q₈	C₂³×C₅₃	semidirect
834. #125	C₂³×C₅₃	semidirect
873. #121	C₂³×C₅₃	semidirect
874. #121	C₂³×C₅₃	semidirect
901. C₄×D₄	C₂³×C₅₃	semidirect
902. C₄×D₄	C₂³×C₅₃	semidirect
912. #117	C₂³×C₅₃	semidirect
916. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
924. #107	C₂³×C₅₃	semidirect
925. #107	C₂³×C₅₃	semidirect
926. #107	C₂³×C₅₃	semidirect
927. #107	C₂³×C₅₃	semidirect
928. #107	C₂³×C₅₃	semidirect
929. #106	C₂³×C₅₃	semidirect
930. #106	C₂³×C₅₃	semidirect
931. #106	C₂³×C₅₃	semidirect
932. #106	C₂³×C₅₃	semidirect
933. #106	C₂³×C₅₃	semidirect
934. C₄⋊C₈	C₂³×C₅₃	semidirect
935. C₄⋊C₈	C₂³×C₅₃	semidirect
936. #103	C₂³×C₅₃	semidirect
937. #103	C₂³×C₅₃	semidirect
938. #103	C₂³×C₅₃	semidirect
939. #103	C₂³×C₅₃	semidirect
940. #103	C₂³×C₅₃	semidirect
953. #102	C₂³×C₅₃	semidirect
954. #102	C₂³×C₅₃	semidirect
955. #102	C₂³×C₅₃	semidirect
956. #102	C₂³×C₅₃	semidirect
957. #102	C₂³×C₅₃	semidirect
958. #102	C₂³×C₅₃	semidirect
959. #102	C₂³×C₅₃	semidirect
964. C₂²⋊C₈	C₂³×C₅₃	semidirect
965. C₂²⋊C₈	C₂³×C₅₃	semidirect
966. #97	C₂³×C₅₃	semidirect
967. C₄×C₈	C₂³×C₅₃	semidirect
1030. C₂×D₄	#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×#3484	2
C₅₃×#3325	2
C₅₃×#3322	2
C₅₃×#3319	2
C₅₃×#3318	2
C₅₃×#3306	2
C₅₃×#3297	2
C₅₃×#3294	2
C₅₃×#3136	2
C₅₃×#3096	2
C₅₃×#3091	2
C₅₃×#3081	2
C₅₃×#3058	2
C₅₃×#3055	2
C₅₃×#3041	2
C₅₃×#3008	2
C₂×C₅₃×#447	2
C₅₃×#2948	2
C₅₃×#2933	2
C₅₃×#2897	2
C₂×C₅₃×#418	2
#61183	53

Subgroups — C53×#61183 #27268695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61183 #27268695