Subgroups — C₅₃×#61201 #27268713

Order 13568.

2116 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3323	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3322	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3318	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3315	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3310	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3307	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3297	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3296	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#553	—	2	2	no	—
32	C₅₃×#553	—	2	2	no	—
33	C₅₃×#553	C₂²	1	2	yes	complemented
34	C₅₃×#553	C₂²	1	2	yes	complemented
35	C₅₃×#552	C₂²	1	2	yes	complemented
36	C₅₃×#552	C₂²	1	2	yes	complemented
37	C₅₃×#547	—	2	1	no	—
38	C₅₃×#547	C₂²	1	2	yes	—
39	C₅₃×#546	—	2	1	no	—
40	C₅₃×#546	—	2	1	no	—
41	C₅₃×#546	C₂²	1	2	yes	—
42	C₅₃×#546	C₂²	1	2	yes	—
43	D₄²×C₅₃	—	2	1	no	—
44	D₄²×C₅₃	C₂²	1	2	yes	—
45	C₅₃×#541	—	2	1	no	—
46	C₅₃×#540	—	2	1	no	—
47	C₅₃×#537	C₂²	1	1	yes	characteristic
48	C₅₃×#537	C₂²	1	1	yes	characteristic
49	C₅₃×#537	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#537	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#534	—	2	2	no	—
52	C₅₃×#532	C₂²	1	1	yes	characteristic
53	C₅₃×#532	C₂²	1	1	yes	characteristic
54	C₅₃×#529	—	2	1	no	—
55	C₅₃×#529	—	2	1	no	—
56	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×#121×C₅₃	—	2	2	no	—
58	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
60	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
62	C₅₃×#491	C₂²	1	2	yes	complemented
63	C₅₃×#490	C₂²	1	2	yes	complemented
64	C₅₃×#488	C₂²	1	2	yes	complemented
65	C₅₃×#488	C₂²	1	2	yes	complemented
66	C₅₃×#485	C₂²	1	2	yes	complemented
67	C₅₃×#485	C₂²	1	2	yes	complemented
68	C₅₃×#484	C₂²	1	2	yes	complemented
69	C₅₃×#483	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#482	C₂²	1	2	yes	complemented
72	C₅₃×#481	C₂²	1	2	yes	complemented
73	C₅₃×#480	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	2	yes	complemented
75	C₅₃×#478	C₂²	1	2	yes	complemented
76	C₅₃×#478	C₂²	1	2	yes	complemented
77	C₅₃×#478	C₂²	1	2	yes	complemented
78	C₅₃×#470	C₂²	1	2	yes	complemented
79	C₅₃×#469	C₂²	1	2	yes	complemented
80	C₅₃×#468	C₂²	1	2	yes	complemented
81	C₅₃×#468	C₂²	1	2	yes	complemented
82	C₅₃×#467	C₂²	1	2	yes	complemented
83	C₅₃×#466	C₂²	1	2	yes	complemented
84	C₅₃×#465	C₂²	1	2	yes	complemented
85	C₅₃×#465	C₂²	1	2	yes	complemented
86	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#452	C₂²	1	2	yes	complemented
95	C₅₃×#452	C₂²	1	2	yes	complemented
96	C₅₃×#450	C₂²	1	2	yes	complemented
97	C₅₃×#450	C₂²	1	2	yes	complemented
98	C₅₃×#449	C₂²	1	2	yes	complemented
99	C₅₃×#449	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×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×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	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#418	C₂²	1	1	yes	characteristic
115	C₅₃×#418	C₂²	1	2	yes	complemented
116	C₅₃×#418	C₂²	1	2	yes	complemented
117	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#417	C₂²	1	2	yes	complemented
121	C₅₃×#417	C₂²	1	2	yes	complemented
122	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#416	C₂²	1	2	yes	complemented
127	C₅₃×#416	C₂²	1	2	yes	complemented
128	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
129	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
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	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
134	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
135	H(5,𝔽₂)×C₅₃	—	2	4	no	—
136	H(5,𝔽₂)×C₅₃	—	2	4	no	—
137	H(5,𝔽₂)×C₅₃	—	4	2	no	—
138	H(5,𝔽₂)×C₅₃	—	4	2	no	—
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	1	no	—
141	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×#41×C₅₃	C₂³	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	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
148	C₂²×D₄×C₅₃	—	2	2	no	—
149	C₂²×D₄×C₅₃	—	2	2	no	—
150	C₂²×D₄×C₅₃	—	2	1	no	—
151	C₂²×D₄×C₅₃	—	2	1	no	—
152	C₂²×D₄×C₅₃	—	2	2	no	—
153	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
154	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
155	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₅₃	—	2	1	no	—
157	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
158	#135×C₅₃	—	4	2	no	—
159	#135×C₅₃	—	4	2	no	—
160	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
166	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
167	C₂×D₈×C₅₃	C₂³	1	2	yes	—
168	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
170	#131×C₅₃	—	4	2	no	—
171	#131×C₅₃	—	4	2	no	—
172	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
175	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
176	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
179	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
180	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
181	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
182	#127×C₅₃	D₄	1	1	yes	characteristic
183	#127×C₅₃	C₂³	1	1	yes	characteristic
184	#126×C₅₃	—	2	2	no	—
185	#126×C₅₃	—	2	2	no	—
186	#126×C₅₃	—	2	2	no	—
187	#126×C₅₃	—	2	2	no	—
188	#125×C₅₃	—	2	2	no	—
189	#125×C₅₃	—	2	2	no	—
190	#125×C₅₃	—	2	1	no	—
191	#125×C₅₃	—	2	1	no	—
192	#125×C₅₃	C₂³	1	2	yes	—
193	#125×C₅₃	C₂³	1	2	yes	—
194	#124×C₅₃	D₄	1	1	yes	characteristic
195	#124×C₅₃	D₄	1	1	yes	characteristic
196	#124×C₅₃	C₂³	1	1	yes	characteristic
197	#124×C₅₃	C₂³	1	1	yes	characteristic
198	#123×C₅₃	—	2	2	no	—
199	#123×C₅₃	—	2	2	no	—
200	#123×C₅₃	—	2	2	no	—
201	#123×C₅₃	—	2	2	no	—
202	#123×C₅₃	—	2	2	no	—
203	#123×C₅₃	—	2	2	no	—
204	#123×C₅₃	—	2	2	no	—
205	#123×C₅₃	—	2	2	no	—
206	C₂²⋊Q₈×C₅₃	—	2	1	no	—
207	C₂²⋊Q₈×C₅₃	—	2	1	no	—
208	C₂²⋊Q₈×C₅₃	—	2	1	no	—
209	C₂²⋊Q₈×C₅₃	—	2	1	no	—
210	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
214	#121×C₅₃	—	2	2	no	—
215	#121×C₅₃	—	2	2	no	—
216	#121×C₅₃	—	2	2	no	—
217	#121×C₅₃	—	2	2	no	—
218	#121×C₅₃	—	2	2	no	—
219	#121×C₅₃	—	2	2	no	—
220	#121×C₅₃	—	2	1	no	—
221	#121×C₅₃	—	2	1	no	—
222	#121×C₅₃	—	2	1	no	—
223	#121×C₅₃	—	2	1	no	—
224	#121×C₅₃	—	2	2	no	—
225	#121×C₅₃	—	2	2	no	—
226	#121×C₅₃	—	2	2	no	—
227	#121×C₅₃	—	2	2	no	—
228	#121×C₅₃	—	2	1	no	—
229	#121×C₅₃	—	2	1	no	—
230	#121×C₅₃	D₄	1	2	yes	—
231	#121×C₅₃	D₄	1	2	yes	—
232	#121×C₅₃	C₂³	1	2	yes	—
233	#121×C₅₃	C₂³	1	2	yes	—
234	#121×C₅₃	C₂³	1	2	yes	—
235	#121×C₅₃	C₂³	1	2	yes	—
236	#120×C₅₃	—	2	2	no	—
237	#120×C₅₃	—	2	2	no	—
238	#120×C₅₃	—	2	2	no	—
239	#120×C₅₃	—	2	2	no	—
240	C₄×Q₈×C₅₃	—	2	1	no	—
241	C₄×Q₈×C₅₃	—	2	1	no	—
242	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	1	no	—
248	C₄×D₄×C₅₃	—	2	1	no	—
249	C₄×D₄×C₅₃	—	2	1	no	—
250	C₄×D₄×C₅₃	—	2	1	no	—
251	C₄×D₄×C₅₃	—	2	1	no	—
252	C₄×D₄×C₅₃	—	2	2	no	—
253	C₄×D₄×C₅₃	—	2	2	no	—
254	C₄×D₄×C₅₃	—	2	1	no	—
255	C₄×D₄×C₅₃	—	2	1	no	—
256	C₄×D₄×C₅₃	C₂³	1	2	yes	—
257	C₄×D₄×C₅₃	C₂³	1	2	yes	—
258	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₅₃	C₂³	1	2	yes	—
261	C₄×D₄×C₅₃	C₂³	1	2	yes	—
262	#117×C₅₃	—	2	2	no	—
263	#117×C₅₃	—	2	2	no	—
264	#117×C₅₃	—	2	1	no	—
265	#117×C₅₃	C₂³	1	2	yes	—
266	#117×C₅₃	C₂³	1	2	yes	—
267	#117×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
269	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
270	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
271	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
275	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
276	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
277	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
278	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
279	C₂×C₄²×C₅₃	—	2	1	no	—
280	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
281	#107×C₅₃	C₂³	1	2	yes	—
282	#107×C₅₃	C₂³	1	2	yes	—
283	#107×C₅₃	C₂³	1	2	yes	—
284	#106×C₅₃	C₂³	1	2	yes	—
285	#106×C₅₃	C₂³	1	2	yes	—
286	#106×C₅₃	C₂³	1	2	yes	—
287	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	2	yes	—
295	#103×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	2	yes	—
297	#103×C₅₃	C₂³	1	1	yes	characteristic
298	#103×C₅₃	C₂³	1	1	yes	characteristic
299	#103×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	2	yes	—
307	#102×C₅₃	C₂³	1	2	yes	—
308	#102×C₅₃	C₂³	1	1	yes	characteristic
309	#102×C₅₃	C₂³	1	1	yes	characteristic
310	#102×C₅₃	C₂³	1	2	yes	—
311	#102×C₅₃	C₂³	1	2	yes	—
312	#102×C₅₃	C₂³	1	1	yes	characteristic
313	#102×C₅₃	C₂³	1	1	yes	characteristic
314	#102×C₅₃	C₂³	1	2	yes	—
315	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
316	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
319	#97×C₅₃	C₂³	1	2	yes	—
320	C₄×C₈×C₅₃	C₂³	1	2	yes	—
321	C₂⁴×C₅₃	—	2	1	no	—
322	C₂⁴×C₅₃	—	2	2	no	—
323	C₂⁴×C₅₃	—	2	2	no	—
324	#41×C₅₃	—	2	2	no	—
325	#41×C₅₃	—	2	2	no	—
326	#41×C₅₃	—	2	2	no	—
327	#41×C₅₃	—	2	2	no	—
328	#41×C₅₃	—	2	4	no	—
329	#41×C₅₃	—	2	4	no	—
330	#41×C₅₃	—	2	2	no	—
331	#41×C₅₃	—	2	2	no	—
332	#41×C₅₃	—	2	2	no	—
333	#41×C₅₃	—	2	2	no	—
334	#41×C₅₃	—	2	2	no	—
335	#41×C₅₃	—	2	2	no	—
336	#41×C₅₃	—	4	2	no	—
337	#41×C₅₃	—	4	2	no	—
338	#41×C₅₃	—	4	4	no	—
339	#41×C₅₃	—	4	4	no	—
340	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
341	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
342	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
343	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
344	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₅₃	—	2	4	no	—
346	C₂×D₄×C₅₃	—	2	4	no	—
347	C₂×D₄×C₅₃	—	2	1	no	—
348	C₂×D₄×C₅₃	—	2	2	no	—
349	C₂×D₄×C₅₃	—	2	2	no	—
350	C₂×D₄×C₅₃	—	2	1	no	—
351	C₂×D₄×C₅₃	—	2	1	no	—
352	C₂×D₄×C₅₃	—	2	2	no	—
353	C₂×D₄×C₅₃	—	2	2	no	—
354	C₂×D₄×C₅₃	—	2	2	no	—
355	C₂×D₄×C₅₃	—	2	2	no	—
356	C₂×D₄×C₅₃	—	2	1	no	—
357	C₂×D₄×C₅₃	—	2	1	no	—
358	C₂×D₄×C₅₃	—	2	2	no	—
359	C₂×D₄×C₅₃	—	2	2	no	—
360	C₂×D₄×C₅₃	—	2	1	no	—
361	C₂×D₄×C₅₃	—	2	2	no	—
362	C₂×D₄×C₅₃	—	4	2	no	—
363	C₂×D₄×C₅₃	—	4	2	no	—
364	C₂×D₄×C₅₃	—	4	4	no	—
365	C₂×D₄×C₅₃	—	4	4	no	—
366	C₂×D₄×C₅₃	—	4	8	no	—
367	C₂×D₄×C₅₃	—	4	8	no	—
368	C₂×D₄×C₅₃	—	8	4	no	—
369	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
372	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
374	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
375	C₂×D₄×C₅₃	#41	1	4	yes	—
376	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
380	C₂²×C₄×C₅₃	—	2	1	no	—
381	C₂²×C₄×C₅₃	—	2	1	no	—
382	C₂²×C₄×C₅₃	—	2	1	no	—
383	C₂²×C₄×C₅₃	—	2	2	no	—
384	C₂²×C₄×C₅₃	—	2	2	no	—
385	C₂²×C₄×C₅₃	—	2	1	no	—
386	C₂²×C₄×C₅₃	—	2	2	no	—
387	C₂²×C₄×C₅₃	—	2	2	no	—
388	C₂²×C₄×C₅₃	—	2	2	no	—
389	C₂²×C₄×C₅₃	—	2	1	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	—	8	2	no	—
395	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
398	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
399	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	Q₁₆×C₅₃	—	4	1	no	—
401	Q₁₆×C₅₃	—	4	1	no	—
402	SD₁₆×C₅₃	—	2	4	no	—
403	SD₁₆×C₅₃	—	4	1	no	—
404	SD₁₆×C₅₃	—	4	1	no	—
405	SD₁₆×C₅₃	—	4	1	no	—
406	SD₁₆×C₅₃	—	4	1	no	—
407	D₈×C₅₃	—	2	4	no	—
408	D₈×C₅₃	—	4	1	no	—
409	D₈×C₅₃	—	4	1	no	—
410	M₁₆×C₅₃	—	2	2	no	—
411	M₁₆×C₅₃	—	2	2	no	—
412	M₁₆×C₅₃	—	4	2	no	—
413	M₁₆×C₅₃	—	4	2	no	—
414	C₂×C₈×C₅₃	—	2	2	no	—
415	C₂×C₈×C₅₃	—	2	2	no	—
416	C₂×C₈×C₅₃	—	4	2	no	—
417	C₂×C₈×C₅₃	—	4	2	no	—
418	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
419	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
420	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₅₃	—	2	1	no	—
425	C₄⋊C₄×C₅₃	—	2	2	no	—
426	C₄⋊C₄×C₅₃	—	2	2	no	—
427	C₄⋊C₄×C₅₃	—	2	2	no	—
428	C₄⋊C₄×C₅₃	—	2	2	no	—
429	C₄⋊C₄×C₅₃	—	2	2	no	—
430	C₄⋊C₄×C₅₃	—	2	2	no	—
431	C₄⋊C₄×C₅₃	—	2	1	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	—	2	1	no	—
437	C₄⋊C₄×C₅₃	—	2	1	no	—
438	C₄⋊C₄×C₅₃	—	2	2	no	—
439	C₄⋊C₄×C₅₃	—	2	2	no	—
440	C₄⋊C₄×C₅₃	—	2	1	no	—
441	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
442	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
443	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
445	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
447	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
448	C₂²⋊C₄×C₅₃	—	2	2	no	—
449	C₂²⋊C₄×C₅₃	—	2	2	no	—
450	C₂²⋊C₄×C₅₃	—	2	2	no	—
451	C₂²⋊C₄×C₅₃	—	2	2	no	—
452	C₂²⋊C₄×C₅₃	—	2	1	no	—
453	C₂²⋊C₄×C₅₃	—	2	2	no	—
454	C₂²⋊C₄×C₅₃	—	2	2	no	—
455	C₂²⋊C₄×C₅₃	—	2	1	no	—
456	C₂²⋊C₄×C₅₃	—	2	1	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	1	no	—
462	C₂²⋊C₄×C₅₃	—	2	1	no	—
463	C₂²⋊C₄×C₅₃	—	2	1	no	—
464	C₂²⋊C₄×C₅₃	—	2	1	no	—
465	C₂²⋊C₄×C₅₃	—	2	2	no	—
466	C₂²⋊C₄×C₅₃	—	2	2	no	—
467	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
468	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
469	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
470	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
471	C₄²×C₅₃	—	2	1	no	—
472	C₄²×C₅₃	—	2	1	no	—
473	C₄²×C₅₃	—	2	1	no	—
474	C₄²×C₅₃	—	2	2	no	—
475	C₄²×C₅₃	—	2	2	no	—
476	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
477	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
478	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
479	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
480	C₂³×C₅₃	—	2	2	no	—
481	C₂³×C₅₃	—	2	4	no	—
482	C₂³×C₅₃	—	2	1	no	—
483	C₂³×C₅₃	—	2	1	no	—
484	C₂³×C₅₃	—	2	1	no	—
485	C₂³×C₅₃	—	4	4	no	—
486	C₂³×C₅₃	—	4	4	no	—
487	C₂³×C₅₃	—	8	1	no	—
488	C₂³×C₅₃	—	8	1	no	—
489	C₂³×C₅₃	—	8	2	no	—
490	C₂³×C₅₃	—	8	2	no	—
491	C₂³×C₅₃	—	8	2	no	—
492	C₂³×C₅₃	—	8	2	no	—
493	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
494	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
495	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
496	Q₈×C₅₃	—	2	2	no	—
497	Q₈×C₅₃	—	2	2	no	—
498	Q₈×C₅₃	—	2	1	no	—
499	Q₈×C₅₃	—	2	1	no	—
500	Q₈×C₅₃	—	2	1	no	—
501	Q₈×C₅₃	—	2	1	no	—
502	Q₈×C₅₃	—	2	1	no	—
503	Q₈×C₅₃	—	2	1	no	—
504	D₄×C₅₃	—	2	4	no	—
505	D₄×C₅₃	—	2	4	no	—
506	D₄×C₅₃	—	2	4	no	—
507	D₄×C₅₃	—	2	2	no	—
508	D₄×C₅₃	—	2	2	no	—
509	D₄×C₅₃	—	2	1	no	—
510	D₄×C₅₃	—	2	1	no	—
511	D₄×C₅₃	—	2	1	no	—
512	D₄×C₅₃	—	2	2	no	—
513	D₄×C₅₃	—	2	1	no	—
514	D₄×C₅₃	—	2	1	no	—
515	D₄×C₅₃	—	2	1	no	—
516	D₄×C₅₃	—	4	2	no	—
517	D₄×C₅₃	—	4	2	no	—
518	D₄×C₅₃	—	4	4	no	—
519	D₄×C₅₃	—	4	4	no	—
520	D₄×C₅₃	—	4	2	no	—
521	D₄×C₅₃	—	4	4	no	—
522	D₄×C₅₃	—	4	4	no	—
523	D₄×C₅₃	—	4	2	no	—
524	D₄×C₅₃	—	4	2	no	—
525	D₄×C₅₃	—	4	2	no	—
526	D₄×C₅₃	—	8	1	no	—
527	D₄×C₅₃	—	8	2	no	—
528	D₄×C₅₃	—	8	2	no	—
529	D₄×C₅₃	—	8	2	no	—
530	D₄×C₅₃	—	8	2	no	—
531	D₄×C₅₃	C₂×#41	1	4	yes	—
532	C₂×C₄×C₅₃	—	2	2	no	—
533	C₂×C₄×C₅₃	—	2	2	no	—
534	C₂×C₄×C₅₃	—	2	2	no	—
535	C₂×C₄×C₅₃	—	2	2	no	—
536	C₂×C₄×C₅₃	—	2	1	no	—
537	C₂×C₄×C₅₃	—	2	1	no	—
538	C₂×C₄×C₅₃	—	2	2	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	2	no	—
542	C₂×C₄×C₅₃	—	2	2	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	4	1	no	—
545	C₂×C₄×C₅₃	—	4	1	no	—
546	C₂×C₄×C₅₃	—	4	4	no	—
547	C₂×C₄×C₅₃	—	4	4	no	—
548	C₂×C₄×C₅₃	—	4	4	no	—
549	C₂×C₄×C₅₃	—	4	2	no	—
550	C₂×C₄×C₅₃	—	4	2	no	—
551	C₂×C₄×C₅₃	—	4	2	no	—
552	C₂×C₄×C₅₃	—	8	1	no	—
553	C₂×C₄×C₅₃	—	8	1	no	—
554	C₂×C₄×C₅₃	—	8	2	no	—
555	C₂×C₄×C₅₃	—	8	2	no	—
556	C₂×C₄×C₅₃	—	8	1	no	—
557	C₂×C₄×C₅₃	—	8	2	no	—
558	C₂×C₄×C₅₃	—	8	1	no	—
559	C₂×C₄×C₅₃	—	8	1	no	—
560	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
564	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
565	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
568	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
569	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
570	C₈×C₅₃	—	2	2	no	—
571	C₈×C₅₃	—	2	1	no	—
572	C₈×C₅₃	—	2	1	no	—
573	C₈×C₅₃	—	2	1	no	—
574	C₈×C₅₃	—	2	1	no	—
575	C₈×C₅₃	—	2	2	no	—
576	#61201	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
577	C₂²×C₅₃	—	2	1	no	—
578	C₂²×C₅₃	—	2	1	no	—
579	C₂²×C₅₃	—	2	2	no	—
580	C₂²×C₅₃	—	2	2	no	—
581	C₂²×C₅₃	—	2	2	no	—
582	C₂²×C₅₃	—	2	2	no	—
583	C₂²×C₅₃	—	2	2	no	—
584	C₂²×C₅₃	—	2	2	no	—
585	C₂²×C₅₃	—	2	4	no	—
586	C₂²×C₅₃	—	4	2	no	—
587	C₂²×C₅₃	—	4	2	no	—
588	C₂²×C₅₃	—	4	1	no	—
589	C₂²×C₅₃	—	4	1	no	—
590	C₂²×C₅₃	—	4	1	no	—
591	C₂²×C₅₃	—	4	1	no	—
592	C₂²×C₅₃	—	4	1	no	—
593	C₂²×C₅₃	—	4	1	no	—
594	C₂²×C₅₃	—	4	1	no	—
595	C₂²×C₅₃	—	4	1	no	—
596	C₂²×C₅₃	—	4	1	no	—
597	C₂²×C₅₃	—	8	4	no	—
598	C₂²×C₅₃	—	16	4	no	—
599	C₂²×C₅₃	—	16	4	no	—
600	C₂²×C₅₃	#546	1	2	yes	—
601	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
602	C₄×C₅₃	—	2	1	no	—
603	C₄×C₅₃	—	2	1	no	—
604	C₄×C₅₃	—	2	1	no	—
605	C₄×C₅₃	—	2	1	no	—
606	C₄×C₅₃	—	2	2	no	—
607	C₄×C₅₃	—	2	2	no	—
608	C₄×C₅₃	—	4	1	no	—
609	C₄×C₅₃	—	4	2	no	—
610	C₄×C₅₃	—	4	2	no	—
611	C₄×C₅₃	—	4	1	no	—
612	C₄×C₅₃	—	4	2	no	—
613	C₄×C₅₃	—	4	1	no	—
614	C₄×C₅₃	—	4	1	no	—
615	C₄×C₅₃	—	4	1	no	—
616	C₄×C₅₃	#546	1	2	yes	—
617	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
618	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
619	#3512	C₂×C₅₃	1	1	yes	characteristic, complemented
620	#3496	C₂×C₅₃	1	1	yes	characteristic, complemented
621	#3323	C₂×C₅₃	1	2	yes	complemented
622	#3322	C₂×C₅₃	1	2	yes	complemented
623	#3318	C₂×C₅₃	1	2	yes	complemented
624	#3315	C₂×C₅₃	1	2	yes	complemented
625	#3310	C₂×C₅₃	1	2	yes	complemented
626	#3307	C₂×C₅₃	1	2	yes	complemented
627	#3297	C₂×C₅₃	1	2	yes	complemented
628	#3296	C₂×C₅₃	1	2	yes	complemented
629	#3142	C₂×C₅₃	1	1	yes	characteristic, complemented
630	#3099	C₂×C₅₃	1	1	yes	characteristic, complemented
631	#3098	C₂×C₅₃	1	1	yes	characteristic, complemented
632	C₂×#478	C₂×C₅₃	1	1	yes	characteristic, complemented
633	#3061	C₂×C₅₃	1	1	yes	characteristic, complemented
634	#3060	C₂×C₅₃	1	1	yes	characteristic, complemented
635	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
636	#3012	C₂×C₅₃	1	1	yes	characteristic, complemented
637	#3012	C₂×C₅₃	1	1	yes	characteristic, complemented
638	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	1	yes	characteristic, complemented
639	#2935	C₂×C₅₃	1	1	yes	characteristic, complemented
640	#2897	C₂×C₅₃	1	1	yes	characteristic, complemented
641	#2897	C₂×C₅₃	1	1	yes	characteristic, complemented
642	C₂×C₅₃	—	2	2	no	—
643	C₂×C₅₃	—	4	2	no	—
644	C₂×C₅₃	—	4	2	no	—
645	C₂×C₅₃	—	4	4	no	—
646	C₂×C₅₃	—	8	1	no	—
647	C₂×C₅₃	—	8	1	no	—
648	C₂×C₅₃	—	8	1	no	—
649	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
650	C₂×C₅₃	#3584	1	1	yes	characteristic
651	C₂×C₅₃	#3585	1	1	yes	characteristic
652	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
653	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
654	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
655	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
657	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic, complemented
658	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	#553	—	2	2	no	—
660	#553	—	2	2	no	—
661	#553	C₂²×C₅₃	1	2	yes	complemented
662	#553	C₂²×C₅₃	1	2	yes	complemented
663	#552	C₂²×C₅₃	1	2	yes	complemented
664	#552	C₂²×C₅₃	1	2	yes	complemented
665	#547	—	2	1	no	—
666	#547	C₂²×C₅₃	1	2	yes	—
667	#546	—	2	1	no	—
668	#546	—	2	1	no	—
669	#546	C₂²×C₅₃	1	2	yes	—
670	#546	C₂²×C₅₃	1	2	yes	—
671	D₄²	—	2	1	no	—
672	D₄²	C₂²×C₅₃	1	2	yes	—
673	#541	—	2	1	no	—
674	#540	—	2	1	no	—
675	#537	C₂²×C₅₃	1	1	yes	characteristic
676	#537	C₂²×C₅₃	1	1	yes	characteristic
677	#537	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	#537	C₂²×C₅₃	1	1	yes	characteristic, complemented
679	#534	—	2	2	no	—
680	#532	C₂²×C₅₃	1	1	yes	characteristic
681	#532	C₂²×C₅₃	1	1	yes	characteristic
682	#529	—	2	1	no	—
683	#529	—	2	1	no	—
684	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
685	C₂×#121	—	2	2	no	—
686	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
688	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
690	#491	C₂²×C₅₃	1	2	yes	complemented
691	#490	C₂²×C₅₃	1	2	yes	complemented
692	#488	C₂²×C₅₃	1	2	yes	complemented
693	#488	C₂²×C₅₃	1	2	yes	complemented
694	#485	C₂²×C₅₃	1	2	yes	complemented
695	#485	C₂²×C₅₃	1	2	yes	complemented
696	#484	C₂²×C₅₃	1	2	yes	complemented
697	#483	C₂²×C₅₃	1	2	yes	complemented
698	#482	C₂²×C₅₃	1	2	yes	complemented
699	#482	C₂²×C₅₃	1	2	yes	complemented
700	#481	C₂²×C₅₃	1	2	yes	complemented
701	#480	C₂²×C₅₃	1	2	yes	complemented
702	#478	C₂²×C₅₃	1	2	yes	complemented
703	#478	C₂²×C₅₃	1	2	yes	complemented
704	#478	C₂²×C₅₃	1	2	yes	complemented
705	#478	C₂²×C₅₃	1	2	yes	complemented
706	#470	C₂²×C₅₃	1	2	yes	complemented
707	#469	C₂²×C₅₃	1	2	yes	complemented
708	#468	C₂²×C₅₃	1	2	yes	complemented
709	#468	C₂²×C₅₃	1	2	yes	complemented
710	#467	C₂²×C₅₃	1	2	yes	complemented
711	#466	C₂²×C₅₃	1	2	yes	complemented
712	#465	C₂²×C₅₃	1	2	yes	complemented
713	#465	C₂²×C₅₃	1	2	yes	complemented
714	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
715	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
716	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
717	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
718	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
719	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
720	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
721	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	#452	C₂²×C₅₃	1	2	yes	complemented
723	#452	C₂²×C₅₃	1	2	yes	complemented
724	#450	C₂²×C₅₃	1	2	yes	complemented
725	#450	C₂²×C₅₃	1	2	yes	complemented
726	#449	C₂²×C₅₃	1	2	yes	complemented
727	#449	C₂²×C₅₃	1	2	yes	complemented
728	#447	C₂²×C₅₃	1	2	yes	complemented
729	#447	C₂²×C₅₃	1	2	yes	complemented
730	#442	C₂²×C₅₃	1	2	yes	complemented
731	#440	C₂²×C₅₃	1	2	yes	complemented
732	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
733	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
734	#436	C₂²×C₅₃	1	2	yes	complemented
735	#435	C₂²×C₅₃	1	2	yes	complemented
736	#435	C₂²×C₅₃	1	2	yes	complemented
737	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
738	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
739	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
740	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
741	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
742	#418	C₂²×C₅₃	1	1	yes	characteristic
743	#418	C₂²×C₅₃	1	2	yes	complemented
744	#418	C₂²×C₅₃	1	2	yes	complemented
745	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
746	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
747	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
748	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
749	#417	C₂²×C₅₃	1	2	yes	complemented
750	#417	C₂²×C₅₃	1	2	yes	complemented
751	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
752	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
753	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
754	#416	C₂²×C₅₃	1	2	yes	complemented
755	#416	C₂²×C₅₃	1	2	yes	complemented
756	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
757	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
758	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
759	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
760	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
761	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
762	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
763	C₅₃	#61201	1	1	yes	characteristic, direct product factor, Sylow
764	H(5,𝔽₂)	—	2	4	no	—
765	H(5,𝔽₂)	—	2	4	no	—
766	H(5,𝔽₂)	—	4	2	no	—
767	H(5,𝔽₂)	—	4	2	no	—
768	C₂×#41	—	2	1	no	—
769	C₂×#41	—	2	1	no	—
770	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
771	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
772	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
773	C₂×#41	C₂³×C₅₃	1	2	yes	—
774	C₂×#41	C₂³×C₅₃	1	2	yes	—
775	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
776	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
777	C₂²×D₄	—	2	2	no	—
778	C₂²×D₄	—	2	2	no	—
779	C₂²×D₄	—	2	1	no	—
780	C₂²×D₄	—	2	1	no	—
781	C₂²×D₄	—	2	2	no	—
782	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
783	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
784	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
785	C₂³×C₄	—	2	1	no	—
786	AGL(1,ℤ/8)	—	2	4	no	—
787	#135	—	4	2	no	—
788	#135	—	4	2	no	—
789	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
790	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
791	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
792	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
793	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
794	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
795	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
796	C₂×D₈	C₂³×C₅₃	1	2	yes	—
797	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
798	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
799	#131	—	4	2	no	—
800	#131	—	4	2	no	—
801	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
802	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
803	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
804	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
805	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
806	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
807	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
808	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
809	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
810	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
811	#127	D₄×C₅₃	1	1	yes	characteristic
812	#127	C₂³×C₅₃	1	1	yes	characteristic
813	#126	—	2	2	no	—
814	#126	—	2	2	no	—
815	#126	—	2	2	no	—
816	#126	—	2	2	no	—
817	#125	—	2	2	no	—
818	#125	—	2	2	no	—
819	#125	—	2	1	no	—
820	#125	—	2	1	no	—
821	#125	C₂³×C₅₃	1	2	yes	—
822	#125	C₂³×C₅₃	1	2	yes	—
823	#124	D₄×C₅₃	1	1	yes	characteristic
824	#124	D₄×C₅₃	1	1	yes	characteristic
825	#124	C₂³×C₅₃	1	1	yes	characteristic
826	#124	C₂³×C₅₃	1	1	yes	characteristic
827	#123	—	2	2	no	—
828	#123	—	2	2	no	—
829	#123	—	2	2	no	—
830	#123	—	2	2	no	—
831	#123	—	2	2	no	—
832	#123	—	2	2	no	—
833	#123	—	2	2	no	—
834	#123	—	2	2	no	—
835	C₂²⋊Q₈	—	2	1	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	—	2	1	no	—
839	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
840	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
841	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
842	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
843	#121	—	2	2	no	—
844	#121	—	2	2	no	—
845	#121	—	2	2	no	—
846	#121	—	2	1	no	—
847	#121	—	2	1	no	—
848	#121	—	2	1	no	—
849	#121	—	2	1	no	—
850	#121	—	2	2	no	—
851	#121	—	2	2	no	—
852	#121	—	2	2	no	—
853	#121	—	2	2	no	—
854	#121	—	2	1	no	—
855	#121	—	2	1	no	—
856	#121	—	2	2	no	—
857	#121	—	2	2	no	—
858	#121	—	2	2	no	—
859	#121	D₄×C₅₃	1	2	yes	—
860	#121	D₄×C₅₃	1	2	yes	—
861	#121	C₂³×C₅₃	1	2	yes	—
862	#121	C₂³×C₅₃	1	2	yes	—
863	#121	C₂³×C₅₃	1	2	yes	—
864	#121	C₂³×C₅₃	1	2	yes	—
865	#120	—	2	2	no	—
866	#120	—	2	2	no	—
867	#120	—	2	2	no	—
868	#120	—	2	2	no	—
869	C₄×Q₈	—	2	1	no	—
870	C₄×Q₈	—	2	1	no	—
871	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
872	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	2	no	—
876	C₄×D₄	—	2	2	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	—	2	2	no	—
880	C₄×D₄	—	2	2	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	C₂³×C₅₃	1	2	yes	—
886	C₄×D₄	C₂³×C₅₃	1	2	yes	—
887	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
888	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
889	C₄×D₄	C₂³×C₅₃	1	2	yes	—
890	C₄×D₄	C₂³×C₅₃	1	2	yes	—
891	#117	—	2	2	no	—
892	#117	—	2	2	no	—
893	#117	—	2	1	no	—
894	#117	C₂³×C₅₃	1	1	yes	characteristic
895	#117	C₂³×C₅₃	1	2	yes	—
896	#117	C₂³×C₅₃	1	2	yes	—
897	C₂×C₄⋊C₄	—	2	1	no	—
898	C₂×C₄⋊C₄	—	2	1	no	—
899	C₂×C₄⋊C₄	—	2	2	no	—
900	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
901	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
902	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
903	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
904	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
905	C₂×C₂²⋊C₄	—	2	1	no	—
906	C₂×C₂²⋊C₄	—	2	2	no	—
907	C₂×C₂²⋊C₄	—	2	2	no	—
908	C₂×C₄²	—	2	1	no	—
909	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
910	#107	C₂³×C₅₃	1	2	yes	—
911	#107	C₂³×C₅₃	1	2	yes	—
912	#107	C₂³×C₅₃	1	2	yes	—
913	#106	C₂³×C₅₃	1	2	yes	—
914	#106	C₂³×C₅₃	1	2	yes	—
915	#106	C₂³×C₅₃	1	2	yes	—
916	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
917	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
918	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
919	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
920	#103	C₂³×C₅₃	1	1	yes	characteristic
921	#103	C₂³×C₅₃	1	1	yes	characteristic
922	#103	C₂³×C₅₃	1	1	yes	characteristic
923	#103	C₂³×C₅₃	1	1	yes	characteristic
924	#103	C₂³×C₅₃	1	2	yes	—
925	#103	C₂³×C₅₃	1	2	yes	—
926	#103	C₂³×C₅₃	1	2	yes	—
927	#103	C₂³×C₅₃	1	2	yes	—
928	#103	C₂³×C₅₃	1	2	yes	—
929	#102	C₂³×C₅₃	1	2	yes	—
930	#102	C₂³×C₅₃	1	2	yes	—
931	#102	C₂³×C₅₃	1	2	yes	—
932	#102	C₂³×C₅₃	1	2	yes	—
933	#102	C₂³×C₅₃	1	1	yes	characteristic
934	#102	C₂³×C₅₃	1	1	yes	characteristic
935	#102	C₂³×C₅₃	1	2	yes	—
936	#102	C₂³×C₅₃	1	2	yes	—
937	#102	C₂³×C₅₃	1	2	yes	—
938	#102	C₂³×C₅₃	1	2	yes	—
939	#102	C₂³×C₅₃	1	1	yes	characteristic
940	#102	C₂³×C₅₃	1	1	yes	characteristic
941	#102	C₂³×C₅₃	1	2	yes	—
942	#102	C₂³×C₅₃	1	2	yes	—
943	#102	C₂³×C₅₃	1	2	yes	—
944	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
945	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
946	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
947	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
948	#97	C₂³×C₅₃	1	2	yes	—
949	C₄×C₈	C₂³×C₅₃	1	2	yes	—
950	C₂⁴	—	2	1	no	—
951	C₂⁴	—	2	2	no	—
952	C₂⁴	—	2	2	no	—
953	#41	—	2	2	no	—
954	#41	—	2	2	no	—
955	#41	—	2	2	no	—
956	#41	—	2	2	no	—
957	#41	—	2	4	no	—
958	#41	—	2	4	no	—
959	#41	—	2	2	no	—
960	#41	—	2	2	no	—
961	#41	—	2	2	no	—
962	#41	—	2	2	no	—
963	#41	—	2	2	no	—
964	#41	—	2	2	no	—
965	#41	—	4	2	no	—
966	#41	—	4	2	no	—
967	#41	—	4	4	no	—
968	#41	—	4	4	no	—
969	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
970	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
971	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
972	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
973	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
974	C₂×D₄	—	2	4	no	—
975	C₂×D₄	—	2	4	no	—
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	2	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	2	2	no	—
991	C₂×D₄	—	4	2	no	—
992	C₂×D₄	—	4	2	no	—
993	C₂×D₄	—	4	4	no	—
994	C₂×D₄	—	4	4	no	—
995	C₂×D₄	—	4	8	no	—
996	C₂×D₄	—	4	8	no	—
997	C₂×D₄	—	8	4	no	—
998	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
999	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1000	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1001	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1002	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1003	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1004	C₂×D₄	#41×C₅₃	1	4	yes	—
1005	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1006	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1007	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1008	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	2	no	—
1013	C₂²×C₄	—	2	2	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	2	2	no	—
1016	C₂²×C₄	—	2	2	no	—
1017	C₂²×C₄	—	2	2	no	—
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	2	1	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	2	no	—
1023	C₂²×C₄	—	8	2	no	—
1024	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1025	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1026	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1027	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1028	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1029	Q₁₆	—	4	1	no	—
1030	Q₁₆	—	4	1	no	—
1031	SD₁₆	—	2	4	no	—
1032	SD₁₆	—	4	1	no	—
1033	SD₁₆	—	4	1	no	—
1034	SD₁₆	—	4	1	no	—
1035	SD₁₆	—	4	1	no	—
1036	D₈	—	2	4	no	—
1037	D₈	—	4	1	no	—
1038	D₈	—	4	1	no	—
1039	M₁₆	—	2	2	no	—
1040	M₁₆	—	2	2	no	—
1041	M₁₆	—	4	2	no	—
1042	M₁₆	—	4	2	no	—
1043	C₂×C₈	—	2	2	no	—
1044	C₂×C₈	—	2	2	no	—
1045	C₂×C₈	—	4	2	no	—
1046	C₂×C₈	—	4	2	no	—
1047	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1048	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1049	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1050	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1051	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1052	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	2	no	—
1068	C₄⋊C₄	—	2	2	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1071	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1072	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1073	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1074	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1075	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1076	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	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	2	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1097	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1098	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1099	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1100	C₄²	—	2	1	no	—
1101	C₄²	—	2	1	no	—
1102	C₄²	—	2	1	no	—
1103	C₄²	—	2	2	no	—
1104	C₄²	—	2	2	no	—
1105	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1106	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1107	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1108	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1109	C₂³	—	2	2	no	—
1110	C₂³	—	2	4	no	—
1111	C₂³	—	2	1	no	—
1112	C₂³	—	2	1	no	—
1113	C₂³	—	2	1	no	—
1114	C₂³	—	4	4	no	—
1115	C₂³	—	4	4	no	—
1116	C₂³	—	8	1	no	—
1117	C₂³	—	8	1	no	—
1118	C₂³	—	8	2	no	—
1119	C₂³	—	8	2	no	—
1120	C₂³	—	8	2	no	—
1121	C₂³	—	8	2	no	—
1122	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1123	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1124	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1125	Q₈	—	2	2	no	—
1126	Q₈	—	2	2	no	—
1127	Q₈	—	2	1	no	—
1128	Q₈	—	2	1	no	—
1129	Q₈	—	2	1	no	—
1130	Q₈	—	2	1	no	—
1131	Q₈	—	2	1	no	—
1132	Q₈	—	2	1	no	—
1133	D₄	—	2	4	no	—
1134	D₄	—	2	4	no	—
1135	D₄	—	2	4	no	—
1136	D₄	—	2	2	no	—
1137	D₄	—	2	2	no	—
1138	D₄	—	2	1	no	—
1139	D₄	—	2	1	no	—
1140	D₄	—	2	1	no	—
1141	D₄	—	2	2	no	—
1142	D₄	—	2	1	no	—
1143	D₄	—	2	1	no	—
1144	D₄	—	2	1	no	—
1145	D₄	—	4	2	no	—
1146	D₄	—	4	2	no	—
1147	D₄	—	4	4	no	—
1148	D₄	—	4	4	no	—
1149	D₄	—	4	2	no	—
1150	D₄	—	4	4	no	—
1151	D₄	—	4	4	no	—
1152	D₄	—	4	2	no	—
1153	D₄	—	4	2	no	—
1154	D₄	—	4	2	no	—
1155	D₄	—	8	1	no	—
1156	D₄	—	8	2	no	—
1157	D₄	—	8	2	no	—
1158	D₄	—	8	2	no	—
1159	D₄	—	8	2	no	—
1160	D₄	C₂×#41×C₅₃	1	4	yes	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	4	no	—
1176	C₂×C₄	—	4	4	no	—
1177	C₂×C₄	—	4	4	no	—
1178	C₂×C₄	—	4	2	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	8	1	no	—
1182	C₂×C₄	—	8	1	no	—
1183	C₂×C₄	—	8	2	no	—
1184	C₂×C₄	—	8	2	no	—
1185	C₂×C₄	—	8	1	no	—
1186	C₂×C₄	—	8	2	no	—
1187	C₂×C₄	—	8	1	no	—
1188	C₂×C₄	—	8	1	no	—
1189	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1190	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1191	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1192	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1193	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1194	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1195	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1196	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1197	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1198	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1199	C₈	—	2	2	no	—
1200	C₈	—	2	1	no	—
1201	C₈	—	2	1	no	—
1202	C₈	—	2	1	no	—
1203	C₈	—	2	1	no	—
1204	C₈	—	2	2	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	4	no	—
1210	C₂²	—	2	2	no	—
1211	C₂²	—	2	2	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	2	2	no	—
1214	C₂²	—	4	2	no	—
1215	C₂²	—	4	2	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	1	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	8	4	no	—
1226	C₂²	—	16	4	no	—
1227	C₂²	—	16	4	no	—
1228	C₂²	C₅₃×#546	1	2	yes	—
1229	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1230	C₄	—	2	2	no	—
1231	C₄	—	2	2	no	—
1232	C₄	—	2	1	no	—
1233	C₄	—	2	1	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	2	no	—
1241	C₄	—	4	2	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	2	no	—
1244	C₄	C₅₃×#546	1	2	yes	—
1245	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1246	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1247	C₂	—	2	2	no	—
1248	C₂	—	4	2	no	—
1249	C₂	—	4	2	no	—
1250	C₂	—	4	4	no	—
1251	C₂	—	8	1	no	—
1252	C₂	—	8	1	no	—
1253	C₂	—	8	1	no	—
1254	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
1255	C₂	C₅₃×#3584	1	1	yes	characteristic
1256	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3512	C₂	semidirect
2. C₅₃×#3496	C₂	semidirect
3. C₅₃×#3323	C₂	semidirect
4. C₅₃×#3322	C₂	semidirect
5. C₅₃×#3318	C₂	semidirect
6. C₅₃×#3315	C₂	semidirect
7. C₅₃×#3310	C₂	semidirect
8. C₅₃×#3307	C₂	semidirect
9. C₅₃×#3297	C₂	semidirect
10. C₅₃×#3296	C₂	semidirect
11. C₅₃×#3142	C₂	semidirect
12. C₅₃×#3099	C₂	semidirect
13. C₅₃×#3098	C₂	semidirect
14. C₂×C₅₃×#478	C₂	semidirect
15. C₅₃×#3061	C₂	semidirect
16. C₅₃×#3060	C₂	semidirect
17. C₅₃×#3035	C₂	semidirect
18. C₅₃×#3012	C₂	semidirect
19. C₅₃×#3012	C₂	semidirect
20. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
21. C₅₃×#2935	C₂	semidirect
22. C₅₃×#2897	C₂	semidirect
23. C₅₃×#2897	C₂	semidirect
27. C₂×#135×C₅₃	C₂²	semidirect
28. C₂×#135×C₅₃	C₂²	semidirect
29. C₂×#131×C₅₃	C₂²	semidirect
30. C₂×#131×C₅₃	C₂²	semidirect
33. C₅₃×#553	C₂²	semidirect
34. C₅₃×#553	C₂²	semidirect
35. C₅₃×#552	C₂²	semidirect
36. C₅₃×#552	C₂²	semidirect
49. C₅₃×#537	C₂²	semidirect
50. C₅₃×#537	C₂²	semidirect
56. C₂×#125×C₅₃	C₂²	semidirect
58. C₅₃×#520	C₂²	semidirect
59. C₅₃×#520	C₂²	semidirect
60. C₄×#41×C₅₃	C₂²	semidirect
62. C₅₃×#491	C₂²	semidirect
63. C₅₃×#490	C₂²	semidirect
64. C₅₃×#488	C₂²	semidirect
65. C₅₃×#488	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×#481	C₂²	semidirect
73. C₅₃×#480	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#478	C₂²	semidirect
77. C₅₃×#478	C₂²	semidirect
78. C₅₃×#470	C₂²	semidirect
79. C₅₃×#469	C₂²	semidirect
80. C₅₃×#468	C₂²	semidirect
81. C₅₃×#468	C₂²	semidirect
82. C₅₃×#467	C₂²	semidirect
83. C₅₃×#466	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
85. C₅₃×#465	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#464	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#463	C₂²	semidirect
90. C₅₃×#462	C₂²	semidirect
91. C₅₃×#461	C₂²	semidirect
92. C₅₃×#460	C₂²	semidirect
93. C₅₃×#459	C₂²	semidirect
94. C₅₃×#452	C₂²	semidirect
95. C₅₃×#452	C₂²	semidirect
96. C₅₃×#450	C₂²	semidirect
97. C₅₃×#450	C₂²	semidirect
98. C₅₃×#449	C₂²	semidirect
99. C₅₃×#449	C₂²	semidirect
100. C₅₃×#447	C₂²	semidirect
101. C₅₃×#447	C₂²	semidirect
102. C₅₃×#442	C₂²	semidirect
103. C₅₃×#440	C₂²	semidirect
104. C₄×SD₁₆×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. C₂×#107×C₅₃	C₂²	semidirect
112. C₂×#106×C₅₃	C₂²	semidirect
113. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
115. C₅₃×#418	C₂²	semidirect
116. C₅₃×#418	C₂²	semidirect
117. C₅₃×#417	C₂²	semidirect
118. C₅₃×#417	C₂²	semidirect
119. C₅₃×#417	C₂²	semidirect
120. C₅₃×#417	C₂²	semidirect
121. C₅₃×#417	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
127. C₅₃×#416	C₂²	semidirect
130. C₂×#102×C₅₃	C₂²	semidirect
131. C₂×#102×C₅₃	C₂²	semidirect
132. C₅₃×#408	C₂²	semidirect
133. C₅₃×#408	C₂²	semidirect
134. C₄×M₁₆×C₅₃	C₂²	semidirect
576. #61201	C₅₃	direct (N × H)
619. #3512	C₂×C₅₃	semidirect
620. #3496	C₂×C₅₃	semidirect
621. #3323	C₂×C₅₃	semidirect
622. #3322	C₂×C₅₃	semidirect
623. #3318	C₂×C₅₃	semidirect
624. #3315	C₂×C₅₃	semidirect
625. #3310	C₂×C₅₃	semidirect
626. #3307	C₂×C₅₃	semidirect
627. #3297	C₂×C₅₃	semidirect
628. #3296	C₂×C₅₃	semidirect
629. #3142	C₂×C₅₃	semidirect
630. #3099	C₂×C₅₃	semidirect
631. #3098	C₂×C₅₃	semidirect
632. C₂×#478	C₂×C₅₃	semidirect
633. #3061	C₂×C₅₃	semidirect
634. #3060	C₂×C₅₃	semidirect
635. #3035	C₂×C₅₃	semidirect
636. #3012	C₂×C₅₃	semidirect
637. #3012	C₂×C₅₃	semidirect
638. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
639. #2935	C₂×C₅₃	semidirect
640. #2897	C₂×C₅₃	semidirect
641. #2897	C₂×C₅₃	semidirect
655. C₂×#135	C₂²×C₅₃	semidirect
656. C₂×#135	C₂²×C₅₃	semidirect
657. C₂×#131	C₂²×C₅₃	semidirect
658. C₂×#131	C₂²×C₅₃	semidirect
661. #553	C₂²×C₅₃	semidirect
662. #553	C₂²×C₅₃	semidirect
663. #552	C₂²×C₅₃	semidirect
664. #552	C₂²×C₅₃	semidirect
677. #537	C₂²×C₅₃	semidirect
678. #537	C₂²×C₅₃	semidirect
684. C₂×#125	C₂²×C₅₃	semidirect
686. #520	C₂²×C₅₃	semidirect
687. #520	C₂²×C₅₃	semidirect
688. C₄×#41	C₂²×C₅₃	semidirect
690. #491	C₂²×C₅₃	semidirect
691. #490	C₂²×C₅₃	semidirect
692. #488	C₂²×C₅₃	semidirect
693. #488	C₂²×C₅₃	semidirect
694. #485	C₂²×C₅₃	semidirect
695. #485	C₂²×C₅₃	semidirect
696. #484	C₂²×C₅₃	semidirect
697. #483	C₂²×C₅₃	semidirect
698. #482	C₂²×C₅₃	semidirect
699. #482	C₂²×C₅₃	semidirect
700. #481	C₂²×C₅₃	semidirect
701. #480	C₂²×C₅₃	semidirect
702. #478	C₂²×C₅₃	semidirect
703. #478	C₂²×C₅₃	semidirect
704. #478	C₂²×C₅₃	semidirect
705. #478	C₂²×C₅₃	semidirect
706. #470	C₂²×C₅₃	semidirect
707. #469	C₂²×C₅₃	semidirect
708. #468	C₂²×C₅₃	semidirect
709. #468	C₂²×C₅₃	semidirect
710. #467	C₂²×C₅₃	semidirect
711. #466	C₂²×C₅₃	semidirect
712. #465	C₂²×C₅₃	semidirect
713. #465	C₂²×C₅₃	semidirect
714. #464	C₂²×C₅₃	semidirect
715. #464	C₂²×C₅₃	semidirect
716. #463	C₂²×C₅₃	semidirect
717. #463	C₂²×C₅₃	semidirect
718. #462	C₂²×C₅₃	semidirect
719. #461	C₂²×C₅₃	semidirect
720. #460	C₂²×C₅₃	semidirect
721. #459	C₂²×C₅₃	semidirect
722. #452	C₂²×C₅₃	semidirect
723. #452	C₂²×C₅₃	semidirect
724. #450	C₂²×C₅₃	semidirect
725. #450	C₂²×C₅₃	semidirect
726. #449	C₂²×C₅₃	semidirect
727. #449	C₂²×C₅₃	semidirect
728. #447	C₂²×C₅₃	semidirect
729. #447	C₂²×C₅₃	semidirect
730. #442	C₂²×C₅₃	semidirect
731. #440	C₂²×C₅₃	semidirect
732. C₄×SD₁₆	C₂²×C₅₃	semidirect
733. C₄×D₈	C₂²×C₅₃	semidirect
734. #436	C₂²×C₅₃	semidirect
735. #435	C₂²×C₅₃	semidirect
736. #435	C₂²×C₅₃	semidirect
737. C₈×D₄	C₂²×C₅₃	semidirect
738. #428	C₂²×C₅₃	semidirect
739. C₂×#107	C₂²×C₅₃	semidirect
740. C₂×#106	C₂²×C₅₃	semidirect
741. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
743. #418	C₂²×C₅₃	semidirect
744. #418	C₂²×C₅₃	semidirect
745. #417	C₂²×C₅₃	semidirect
746. #417	C₂²×C₅₃	semidirect
747. #417	C₂²×C₅₃	semidirect
748. #417	C₂²×C₅₃	semidirect
749. #417	C₂²×C₅₃	semidirect
750. #417	C₂²×C₅₃	semidirect
751. #417	C₂²×C₅₃	semidirect
752. #416	C₂²×C₅₃	semidirect
753. #416	C₂²×C₅₃	semidirect
754. #416	C₂²×C₅₃	semidirect
755. #416	C₂²×C₅₃	semidirect
758. C₂×#102	C₂²×C₅₃	semidirect
759. C₂×#102	C₂²×C₅₃	semidirect
760. #408	C₂²×C₅₃	semidirect
761. #408	C₂²×C₅₃	semidirect
762. C₄×M₁₆	C₂²×C₅₃	semidirect
763. C₅₃	#61201	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×#3512	2
C₅₃×#3496	2
C₅₃×#3323	2
C₅₃×#3322	2
C₅₃×#3318	2
C₅₃×#3315	2
C₅₃×#3310	2
C₅₃×#3307	2
C₅₃×#3297	2
C₅₃×#3296	2
C₅₃×#3142	2
C₅₃×#3099	2
C₅₃×#3098	2
C₂×C₅₃×#478	2
C₅₃×#3061	2
C₅₃×#3060	2
C₅₃×#3035	2
C₅₃×#3012	2
C₄×AGL(1,ℤ/8)×C₅₃	2
C₅₃×#2935	2
C₅₃×#2897	2
#61201	53

Subgroups — C53×#61201 #27268713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61201 #27268713