Subgroups — C₅₃×#61689 #27269201

Order 13568.

2150 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3317	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3310	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3305	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3271	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3265	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3200	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3198	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3012	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3009	C₂	1	2	yes	maximal, complemented
23	C₅₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	—
25	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
27	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
29	C₅₃×#562	—	2	2	no	—
30	C₅₃×#555	—	2	1	no	—
31	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
32	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#553	—	2	1	no	—
34	C₅₃×#552	C₂²	1	2	yes	complemented
35	C₅₃×#550	C₂²	1	2	yes	—
36	C₅₃×#550	C₂²	1	1	yes	characteristic
37	C₅₃×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#548	C₂²	1	2	yes	complemented
40	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
41	D₄²×C₅₃	—	2	1	no	—
42	D₄²×C₅₃	—	2	1	no	—
43	D₄²×C₅₃	—	2	2	no	—
44	D₄²×C₅₃	C₂²	1	2	yes	—
45	D₄²×C₅₃	C₂²	1	1	yes	characteristic
46	D₄²×C₅₃	C₂²	1	1	yes	characteristic
47	C₅₃×#544	—	2	1	no	—
48	C₅₃×#542	—	2	2	no	—
49	C₅₃×#540	—	2	1	no	—
50	C₅₃×#537	C₂²	1	2	yes	complemented
51	C₅₃×#536	C₂²	1	2	yes	complemented
52	C₅₃×#535	—	2	2	no	—
53	C₅₃×#535	C₂²	1	2	yes	—
54	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#532	—	2	1	no	—
56	C₅₃×#532	C₂²	1	1	yes	characteristic
57	C₂×#127×C₅₃	—	2	1	no	—
58	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
59	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
60	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
61	C₅₃×#496	C₂²	1	2	yes	complemented
62	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#490	C₂²	1	2	yes	complemented
65	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#485	C₂²	1	2	yes	complemented
68	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#482	C₂²	1	1	yes	characteristic, 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×#479	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#469	C₂²	1	2	yes	complemented
79	C₅₃×#468	C₂²	1	2	yes	complemented
80	C₅₃×#468	C₂²	1	2	yes	complemented
81	C₅₃×#468	C₂²	1	2	yes	complemented
82	C₅₃×#466	C₂²	1	2	yes	complemented
83	C₅₃×#465	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×#463	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#460	C₂²	1	2	yes	complemented
91	C₅₃×#460	C₂²	1	2	yes	complemented
92	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#452	C₂²	1	1	yes	characteristic
97	C₅₃×#452	C₂²	1	2	yes	—
98	C₅₃×#452	C₂²	1	2	yes	complemented
99	C₅₃×#452	C₂²	1	2	yes	complemented
100	C₅₃×#452	C₂²	1	2	yes	complemented
101	C₅₃×#450	C₂²	1	2	yes	complemented
102	C₅₃×#450	C₂²	1	2	yes	complemented
103	C₅₃×#450	C₂²	1	2	yes	complemented
104	C₅₃×#450	C₂²	1	2	yes	complemented
105	C₅₃×#450	C₂²	1	2	yes	complemented
106	C₅₃×#450	C₂²	1	2	yes	complemented
107	C₅₃×#449	C₂²	1	1	yes	characteristic
108	C₅₃×#449	C₂²	1	2	yes	complemented
109	C₅₃×#449	C₂²	1	2	yes	complemented
110	C₅₃×#449	C₂²	1	2	yes	complemented
111	C₅₃×#448	C₂²	1	2	yes	complemented
112	C₅₃×#448	C₂²	1	2	yes	complemented
113	C₅₃×#447	C₂²	1	2	yes	complemented
114	C₅₃×#447	C₂²	1	2	yes	complemented
115	C₅₃×#441	C₂²	1	2	yes	complemented
116	C₅₃×#440	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#435	C₂²	1	2	yes	complemented
124	C₅₃×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#418	C₂²	1	2	yes	complemented
130	C₅₃×#417	C₂²	1	2	yes	complemented
131	C₅₃×#416	C₂²	1	2	yes	complemented
132	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
133	C₅₃×#408	C₂²	1	2	yes	complemented
134	C₅₃×#408	C₂²	1	2	yes	complemented
135	H(5,𝔽₂)×C₅₃	—	4	4	no	—
136	H(5,𝔽₂)×C₅₃	—	4	4	no	—
137	C₂×#41×C₅₃	—	2	2	no	—
138	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
139	C₂×#41×C₅₃	C₂³	1	2	yes	—
140	C₂×#41×C₅₃	C₂³	1	2	yes	—
141	C₂×#41×C₅₃	C₂³	1	2	yes	—
142	C₂×#41×C₅₃	C₂³	1	2	yes	—
143	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
144	C₂²×D₄×C₅₃	—	2	2	no	—
145	C₂²×D₄×C₅₃	—	2	2	no	—
146	C₂²×D₄×C₅₃	—	2	2	no	—
147	C₂²×D₄×C₅₃	—	2	1	no	—
148	C₂²×D₄×C₅₃	—	2	1	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	C₂³	1	2	yes	—
153	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
154	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
155	#137×C₅₃	—	4	4	no	—
156	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
157	#135×C₅₃	—	4	4	no	—
158	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×SD₁₆×C₅₃	—	4	4	no	—
161	C₂×SD₁₆×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	2	yes	—
165	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
169	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
170	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
171	C₂×D₈×C₅₃	C₂³	1	2	yes	—
172	C₂×D₈×C₅₃	C₂³	1	2	yes	—
173	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
174	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
175	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
176	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
177	C₄⋊Q₈×C₅₃	—	2	1	no	—
178	C₄⋊Q₈×C₅₃	—	2	2	no	—
179	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
180	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
181	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
182	#127×C₅₃	—	2	1	no	—
183	#127×C₅₃	—	2	1	no	—
184	#127×C₅₃	—	2	2	no	—
185	#127×C₅₃	—	2	1	no	—
186	#127×C₅₃	—	2	1	no	—
187	#127×C₅₃	—	2	2	no	—
188	#127×C₅₃	D₄	1	1	yes	characteristic
189	#127×C₅₃	C₂³	1	1	yes	characteristic
190	#127×C₅₃	C₂³	1	1	yes	characteristic
191	#127×C₅₃	C₂³	1	2	yes	—
192	#126×C₅₃	—	2	2	no	—
193	#126×C₅₃	—	2	1	no	—
194	#125×C₅₃	—	2	2	no	—
195	#125×C₅₃	—	2	1	no	—
196	#125×C₅₃	—	2	1	no	—
197	#125×C₅₃	C₂³	1	1	yes	characteristic
198	#124×C₅₃	—	2	2	no	—
199	#124×C₅₃	—	2	2	no	—
200	#124×C₅₃	—	2	2	no	—
201	#124×C₅₃	—	2	2	no	—
202	#124×C₅₃	D₄	1	2	yes	—
203	#124×C₅₃	C₂³	1	1	yes	characteristic
204	#123×C₅₃	—	2	2	no	—
205	#123×C₅₃	—	2	2	no	—
206	#123×C₅₃	—	2	2	no	—
207	#123×C₅₃	—	2	2	no	—
208	#123×C₅₃	—	2	1	no	—
209	C₂²⋊Q₈×C₅₃	—	2	2	no	—
210	C₂²⋊Q₈×C₅₃	—	2	2	no	—
211	C₂²⋊Q₈×C₅₃	—	2	2	no	—
212	C₂²⋊Q₈×C₅₃	—	2	2	no	—
213	C₂²⋊Q₈×C₅₃	—	2	1	no	—
214	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
215	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
219	#121×C₅₃	—	2	1	no	—
220	#121×C₅₃	—	2	1	no	—
221	#121×C₅₃	—	2	2	no	—
222	#121×C₅₃	—	2	2	no	—
223	#121×C₅₃	—	2	2	no	—
224	#121×C₅₃	—	2	2	no	—
225	#121×C₅₃	—	2	2	no	—
226	#121×C₅₃	—	2	2	no	—
227	#121×C₅₃	—	2	2	no	—
228	#121×C₅₃	—	2	2	no	—
229	#121×C₅₃	—	2	1	no	—
230	#121×C₅₃	—	2	2	no	—
231	#121×C₅₃	—	2	1	no	—
232	#121×C₅₃	D₄	1	1	yes	characteristic
233	#121×C₅₃	D₄	1	1	yes	characteristic
234	#121×C₅₃	D₄	1	2	yes	—
235	#121×C₅₃	C₂³	1	1	yes	characteristic
236	#121×C₅₃	C₂³	1	2	yes	—
237	#121×C₅₃	C₂³	1	2	yes	—
238	#121×C₅₃	C₂³	1	2	yes	—
239	#121×C₅₃	C₂³	1	2	yes	—
240	#121×C₅₃	C₂³	1	2	yes	—
241	#120×C₅₃	—	2	2	no	—
242	#120×C₅₃	—	2	2	no	—
243	#120×C₅₃	—	2	2	no	—
244	#120×C₅₃	—	2	2	no	—
245	#120×C₅₃	—	2	2	no	—
246	#120×C₅₃	—	2	2	no	—
247	C₄×Q₈×C₅₃	—	2	1	no	—
248	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
252	C₄×D₄×C₅₃	—	2	1	no	—
253	C₄×D₄×C₅₃	—	2	1	no	—
254	C₄×D₄×C₅₃	—	2	2	no	—
255	C₄×D₄×C₅₃	—	2	2	no	—
256	C₄×D₄×C₅₃	—	2	1	no	—
257	C₄×D₄×C₅₃	—	2	1	no	—
258	C₄×D₄×C₅₃	—	2	1	no	—
259	C₄×D₄×C₅₃	—	2	1	no	—
260	C₄×D₄×C₅₃	—	2	1	no	—
261	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₅₃	C₂³	1	2	yes	—
266	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
267	#117×C₅₃	—	2	1	no	—
268	#117×C₅₃	—	2	2	no	—
269	#117×C₅₃	—	2	1	no	—
270	#117×C₅₃	—	2	1	no	—
271	#117×C₅₃	—	2	1	no	—
272	#117×C₅₃	C₂³	1	1	yes	characteristic
273	#117×C₅₃	C₂³	1	2	yes	—
274	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
275	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
276	C₂×C₄²×C₅₃	—	2	1	no	—
277	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
278	#107×C₅₃	C₂³	1	1	yes	characteristic
279	#107×C₅₃	C₂³	1	2	yes	—
280	#107×C₅₃	C₂³	1	1	yes	characteristic
281	#106×C₅₃	C₂³	1	1	yes	characteristic
282	#106×C₅₃	C₂³	1	2	yes	—
283	#106×C₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
288	#103×C₅₃	C₂³	1	1	yes	characteristic
289	#103×C₅₃	C₂³	1	1	yes	characteristic
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
304	#102×C₅₃	C₂³	1	2	yes	—
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	1	yes	characteristic
307	#102×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
315	#97×C₅₃	C₂³	1	2	yes	—
316	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
318	C₂⁴×C₅₃	—	2	2	no	—
319	C₂⁴×C₅₃	—	2	2	no	—
320	C₂⁴×C₅₃	—	2	2	no	—
321	#41×C₅₃	—	2	2	no	—
322	#41×C₅₃	—	2	2	no	—
323	#41×C₅₃	—	2	4	no	—
324	#41×C₅₃	—	2	4	no	—
325	#41×C₅₃	—	4	2	no	—
326	#41×C₅₃	—	4	2	no	—
327	#41×C₅₃	—	4	2	no	—
328	#41×C₅₃	—	4	2	no	—
329	#41×C₅₃	—	4	8	no	—
330	#41×C₅₃	—	4	2	no	—
331	#41×C₅₃	—	4	2	no	—
332	C₂×Q₈×C₅₃	—	2	1	no	—
333	C₂×Q₈×C₅₃	—	2	2	no	—
334	C₂×Q₈×C₅₃	—	4	2	no	—
335	C₂×Q₈×C₅₃	—	4	2	no	—
336	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
337	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
339	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₅₃	—	2	1	no	—
341	C₂×D₄×C₅₃	—	2	4	no	—
342	C₂×D₄×C₅₃	—	2	4	no	—
343	C₂×D₄×C₅₃	—	2	2	no	—
344	C₂×D₄×C₅₃	—	2	2	no	—
345	C₂×D₄×C₅₃	—	2	1	no	—
346	C₂×D₄×C₅₃	—	2	2	no	—
347	C₂×D₄×C₅₃	—	2	2	no	—
348	C₂×D₄×C₅₃	—	2	2	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	1	no	—
354	C₂×D₄×C₅₃	—	2	1	no	—
355	C₂×D₄×C₅₃	—	2	2	no	—
356	C₂×D₄×C₅₃	—	2	2	no	—
357	C₂×D₄×C₅₃	—	2	2	no	—
358	C₂×D₄×C₅₃	—	2	1	no	—
359	C₂×D₄×C₅₃	—	2	1	no	—
360	C₂×D₄×C₅₃	—	2	2	no	—
361	C₂×D₄×C₅₃	—	4	2	no	—
362	C₂×D₄×C₅₃	—	4	2	no	—
363	C₂×D₄×C₅₃	—	4	2	no	—
364	C₂×D₄×C₅₃	—	4	2	no	—
365	C₂×D₄×C₅₃	—	4	8	no	—
366	C₂×D₄×C₅₃	—	4	8	no	—
367	C₂×D₄×C₅₃	—	4	8	no	—
368	C₂×D₄×C₅₃	—	8	2	no	—
369	C₂×D₄×C₅₃	—	8	2	no	—
370	C₂×D₄×C₅₃	—	8	2	no	—
371	C₂×D₄×C₅₃	—	8	2	no	—
372	C₂×D₄×C₅₃	—	8	4	no	—
373	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
376	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
377	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
378	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
379	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
380	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
381	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	—	2	1	no	—
384	C₂²×C₄×C₅₃	—	2	2	no	—
385	C₂²×C₄×C₅₃	—	2	2	no	—
386	C₂²×C₄×C₅₃	—	2	1	no	—
387	C₂²×C₄×C₅₃	—	2	1	no	—
388	C₂²×C₄×C₅₃	—	2	1	no	—
389	C₂²×C₄×C₅₃	—	2	2	no	—
390	C₂²×C₄×C₅₃	—	2	2	no	—
391	C₂²×C₄×C₅₃	—	2	2	no	—
392	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
396	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
397	Q₁₆×C₅₃	—	2	4	no	—
398	Q₁₆×C₅₃	—	2	2	no	—
399	SD₁₆×C₅₃	—	2	2	no	—
400	SD₁₆×C₅₃	—	2	2	no	—
401	SD₁₆×C₅₃	—	2	4	no	—
402	SD₁₆×C₅₃	—	4	2	no	—
403	SD₁₆×C₅₃	—	4	2	no	—
404	SD₁₆×C₅₃	—	4	2	no	—
405	SD₁₆×C₅₃	—	4	2	no	—
406	SD₁₆×C₅₃	—	4	2	no	—
407	SD₁₆×C₅₃	—	4	2	no	—
408	D₈×C₅₃	—	2	2	no	—
409	D₈×C₅₃	—	4	2	no	—
410	D₈×C₅₃	—	4	2	no	—
411	M₁₆×C₅₃	—	4	2	no	—
412	M₁₆×C₅₃	—	4	2	no	—
413	C₂×C₈×C₅₃	—	4	2	no	—
414	C₂×C₈×C₅₃	—	4	2	no	—
415	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
420	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₅₃	—	2	1	no	—
422	C₄⋊C₄×C₅₃	—	2	2	no	—
423	C₄⋊C₄×C₅₃	—	2	2	no	—
424	C₄⋊C₄×C₅₃	—	2	1	no	—
425	C₄⋊C₄×C₅₃	—	2	1	no	—
426	C₄⋊C₄×C₅₃	—	2	1	no	—
427	C₄⋊C₄×C₅₃	—	2	1	no	—
428	C₄⋊C₄×C₅₃	—	2	2	no	—
429	C₄⋊C₄×C₅₃	—	2	1	no	—
430	C₄⋊C₄×C₅₃	—	2	1	no	—
431	C₄⋊C₄×C₅₃	—	2	2	no	—
432	C₄⋊C₄×C₅₃	—	2	2	no	—
433	C₄⋊C₄×C₅₃	—	2	1	no	—
434	C₄⋊C₄×C₅₃	—	2	2	no	—
435	C₄⋊C₄×C₅₃	—	2	1	no	—
436	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
439	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
441	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₂²⋊C₄×C₅₃	—	2	2	no	—
445	C₂²⋊C₄×C₅₃	—	2	2	no	—
446	C₂²⋊C₄×C₅₃	—	2	1	no	—
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	—	2	2	no	—
449	C₂²⋊C₄×C₅₃	—	2	2	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	1	no	—
455	C₂²⋊C₄×C₅₃	—	2	2	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	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
466	C₄²×C₅₃	—	2	1	no	—
467	C₄²×C₅₃	—	2	1	no	—
468	C₄²×C₅₃	—	2	1	no	—
469	C₄²×C₅₃	—	2	2	no	—
470	C₄²×C₅₃	—	2	2	no	—
471	C₄²×C₅₃	—	2	1	no	—
472	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
473	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
474	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
475	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
476	C₂³×C₅₃	—	2	1	no	—
477	C₂³×C₅₃	—	2	1	no	—
478	C₂³×C₅₃	—	2	2	no	—
479	C₂³×C₅₃	—	2	2	no	—
480	C₂³×C₅₃	—	4	4	no	—
481	C₂³×C₅₃	—	4	4	no	—
482	C₂³×C₅₃	—	4	4	no	—
483	C₂³×C₅₃	—	8	2	no	—
484	C₂³×C₅₃	—	8	2	no	—
485	C₂³×C₅₃	—	8	2	no	—
486	C₂³×C₅₃	—	8	2	no	—
487	C₂³×C₅₃	—	8	2	no	—
488	C₂³×C₅₃	—	8	2	no	—
489	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
490	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
491	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
492	Q₈×C₅₃	—	2	1	no	—
493	Q₈×C₅₃	—	2	1	no	—
494	Q₈×C₅₃	—	2	1	no	—
495	Q₈×C₅₃	—	2	2	no	—
496	Q₈×C₅₃	—	2	2	no	—
497	Q₈×C₅₃	—	4	2	no	—
498	Q₈×C₅₃	—	8	1	no	—
499	Q₈×C₅₃	—	8	2	no	—
500	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
501	D₄×C₅₃	—	2	4	no	—
502	D₄×C₅₃	—	2	2	no	—
503	D₄×C₅₃	—	2	2	no	—
504	D₄×C₅₃	—	2	1	no	—
505	D₄×C₅₃	—	2	2	no	—
506	D₄×C₅₃	—	2	2	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	—	4	2	no	—
512	D₄×C₅₃	—	4	2	no	—
513	D₄×C₅₃	—	4	2	no	—
514	D₄×C₅₃	—	4	2	no	—
515	D₄×C₅₃	—	4	4	no	—
516	D₄×C₅₃	—	4	4	no	—
517	D₄×C₅₃	—	4	4	no	—
518	D₄×C₅₃	—	4	4	no	—
519	D₄×C₅₃	—	4	4	no	—
520	D₄×C₅₃	—	4	4	no	—
521	D₄×C₅₃	—	4	2	no	—
522	D₄×C₅₃	—	4	2	no	—
523	D₄×C₅₃	—	8	1	no	—
524	D₄×C₅₃	—	8	1	no	—
525	D₄×C₅₃	—	8	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	—	8	2	no	—
532	D₄×C₅₃	—	8	2	no	—
533	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
534	C₂×C₄×C₅₃	—	2	4	no	—
535	C₂×C₄×C₅₃	—	2	1	no	—
536	C₂×C₄×C₅₃	—	2	2	no	—
537	C₂×C₄×C₅₃	—	2	2	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	2	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	1	no	—
546	C₂×C₄×C₅₃	—	2	1	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	2	2	no	—
549	C₂×C₄×C₅₃	—	2	1	no	—
550	C₂×C₄×C₅₃	—	4	1	no	—
551	C₂×C₄×C₅₃	—	4	4	no	—
552	C₂×C₄×C₅₃	—	4	4	no	—
553	C₂×C₄×C₅₃	—	4	2	no	—
554	C₂×C₄×C₅₃	—	4	2	no	—
555	C₂×C₄×C₅₃	—	4	2	no	—
556	C₂×C₄×C₅₃	—	8	2	no	—
557	C₂×C₄×C₅₃	—	8	2	no	—
558	C₂×C₄×C₅₃	—	8	2	no	—
559	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
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	2	yes	—
563	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
567	C₈×C₅₃	—	2	1	no	—
568	C₈×C₅₃	—	2	1	no	—
569	C₈×C₅₃	—	2	2	no	—
570	C₈×C₅₃	—	2	2	no	—
571	C₈×C₅₃	—	2	1	no	—
572	C₈×C₅₃	—	2	1	no	—
573	#61689	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
574	C₂²×C₅₃	—	2	1	no	—
575	C₂²×C₅₃	—	2	2	no	—
576	C₂²×C₅₃	—	2	2	no	—
577	C₂²×C₅₃	—	2	2	no	—
578	C₂²×C₅₃	—	2	1	no	—
579	C₂²×C₅₃	—	2	2	no	—
580	C₂²×C₅₃	—	2	2	no	—
581	C₂²×C₅₃	—	2	1	no	—
582	C₂²×C₅₃	—	2	2	no	—
583	C₂²×C₅₃	—	2	2	no	—
584	C₂²×C₅₃	—	4	1	no	—
585	C₂²×C₅₃	—	4	1	no	—
586	C₂²×C₅₃	—	4	2	no	—
587	C₂²×C₅₃	—	4	2	no	—
588	C₂²×C₅₃	—	4	1	no	—
589	C₂²×C₅₃	—	4	2	no	—
590	C₂²×C₅₃	—	4	2	no	—
591	C₂²×C₅₃	—	4	1	no	—
592	C₂²×C₅₃	—	4	1	no	—
593	C₂²×C₅₃	—	4	2	no	—
594	C₂²×C₅₃	—	4	2	no	—
595	C₂²×C₅₃	—	16	4	no	—
596	C₂²×C₅₃	—	16	4	no	—
597	C₂²×C₅₃	—	16	4	no	—
598	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
599	C₄×C₅₃	—	2	1	no	—
600	C₄×C₅₃	—	2	1	no	—
601	C₄×C₅₃	—	2	1	no	—
602	C₄×C₅₃	—	2	2	no	—
603	C₄×C₅₃	—	2	2	no	—
604	C₄×C₅₃	—	2	2	no	—
605	C₄×C₅₃	—	2	1	no	—
606	C₄×C₅₃	—	4	1	no	—
607	C₄×C₅₃	—	4	1	no	—
608	C₄×C₅₃	—	4	2	no	—
609	C₄×C₅₃	—	4	2	no	—
610	C₄×C₅₃	—	4	1	no	—
611	C₄×C₅₃	—	4	1	no	—
612	C₄×C₅₃	—	4	1	no	—
613	C₄×C₅₃	#577	1	2	yes	—
614	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
615	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
616	#3547	C₂×C₅₃	1	1	yes	characteristic, complemented
617	#3498	C₂×C₅₃	1	1	yes	characteristic, complemented
618	#3333	C₂×C₅₃	1	1	yes	characteristic, complemented
619	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
620	#3317	C₂×C₅₃	1	2	yes	complemented
621	#3310	C₂×C₅₃	1	2	yes	complemented
622	#3305	C₂×C₅₃	1	1	yes	characteristic, complemented
623	#3295	C₂×C₅₃	1	1	yes	characteristic, complemented
624	#3284	C₂×C₅₃	1	1	yes	characteristic, complemented
625	D₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
626	#3278	C₂×C₅₃	1	1	yes	characteristic, complemented
627	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
628	#3271	C₂×C₅₃	1	2	yes	complemented
629	#3265	C₂×C₅₃	1	2	yes	complemented
630	#3217	C₂×C₅₃	1	1	yes	characteristic, complemented
631	#3208	C₂×C₅₃	1	1	yes	characteristic, complemented
632	#3200	C₂×C₅₃	1	2	yes	complemented
633	#3198	C₂×C₅₃	1	2	yes	complemented
634	#3116	C₂×C₅₃	1	1	yes	characteristic, complemented
635	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
636	#3012	C₂×C₅₃	1	2	yes	complemented
637	#3009	C₂×C₅₃	1	2	yes	complemented
638	#2981	C₂×C₅₃	1	1	yes	characteristic, complemented
639	C₂×C₅₃	—	4	2	no	—
640	C₂×C₅₃	—	4	2	no	—
641	C₂×C₅₃	—	4	1	no	—
642	C₂×C₅₃	—	4	2	no	—
643	C₂×C₅₃	—	8	1	no	—
644	C₂×C₅₃	—	8	2	no	—
645	C₂×C₅₃	—	8	2	no	—
646	C₂×C₅₃	#3484	1	1	yes	characteristic
647	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
648	C₂×C₅₃	#3585	1	1	yes	characteristic
649	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	2	yes	—
650	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
651	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
652	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
653	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
654	#562	—	2	2	no	—
655	#555	—	2	1	no	—
656	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
657	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
658	#553	—	2	1	no	—
659	#552	C₂²×C₅₃	1	2	yes	complemented
660	#550	C₂²×C₅₃	1	1	yes	characteristic
661	#550	C₂²×C₅₃	1	2	yes	—
662	#550	C₂²×C₅₃	1	1	yes	characteristic
663	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
664	#548	C₂²×C₅₃	1	2	yes	complemented
665	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
666	D₄²	—	2	1	no	—
667	D₄²	—	2	1	no	—
668	D₄²	—	2	2	no	—
669	D₄²	C₂²×C₅₃	1	2	yes	—
670	D₄²	C₂²×C₅₃	1	1	yes	characteristic
671	D₄²	C₂²×C₅₃	1	1	yes	characteristic
672	#544	—	2	1	no	—
673	#542	—	2	2	no	—
674	#540	—	2	1	no	—
675	#537	C₂²×C₅₃	1	2	yes	complemented
676	#536	C₂²×C₅₃	1	2	yes	complemented
677	#535	—	2	2	no	—
678	#535	C₂²×C₅₃	1	2	yes	—
679	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
680	#532	—	2	1	no	—
681	#532	C₂²×C₅₃	1	1	yes	characteristic
682	C₂×#127	—	2	1	no	—
683	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
684	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
685	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
686	#496	C₂²×C₅₃	1	2	yes	complemented
687	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
688	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	#490	C₂²×C₅₃	1	2	yes	complemented
690	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
691	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#485	C₂²×C₅₃	1	2	yes	complemented
694	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
695	#482	C₂²×C₅₃	1	2	yes	complemented
696	#482	C₂²×C₅₃	1	2	yes	complemented
697	#481	C₂²×C₅₃	1	2	yes	complemented
698	#480	C₂²×C₅₃	1	2	yes	complemented
699	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
700	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
701	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
702	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	#469	C₂²×C₅₃	1	2	yes	complemented
704	#468	C₂²×C₅₃	1	2	yes	complemented
705	#468	C₂²×C₅₃	1	2	yes	complemented
706	#468	C₂²×C₅₃	1	2	yes	complemented
707	#466	C₂²×C₅₃	1	2	yes	complemented
708	#465	C₂²×C₅₃	1	2	yes	complemented
709	#465	C₂²×C₅₃	1	2	yes	complemented
710	#465	C₂²×C₅₃	1	2	yes	complemented
711	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
714	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
715	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
716	#460	C₂²×C₅₃	1	2	yes	complemented
717	#460	C₂²×C₅₃	1	2	yes	complemented
718	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
719	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
720	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
721	#452	C₂²×C₅₃	1	1	yes	characteristic
722	#452	C₂²×C₅₃	1	2	yes	—
723	#452	C₂²×C₅₃	1	2	yes	complemented
724	#452	C₂²×C₅₃	1	2	yes	complemented
725	#452	C₂²×C₅₃	1	2	yes	complemented
726	#450	C₂²×C₅₃	1	2	yes	complemented
727	#450	C₂²×C₅₃	1	2	yes	complemented
728	#450	C₂²×C₅₃	1	2	yes	complemented
729	#450	C₂²×C₅₃	1	2	yes	complemented
730	#450	C₂²×C₅₃	1	2	yes	complemented
731	#450	C₂²×C₅₃	1	2	yes	complemented
732	#449	C₂²×C₅₃	1	1	yes	characteristic
733	#449	C₂²×C₅₃	1	2	yes	complemented
734	#449	C₂²×C₅₃	1	2	yes	complemented
735	#449	C₂²×C₅₃	1	2	yes	complemented
736	#448	C₂²×C₅₃	1	2	yes	complemented
737	#448	C₂²×C₅₃	1	2	yes	complemented
738	#447	C₂²×C₅₃	1	2	yes	complemented
739	#447	C₂²×C₅₃	1	2	yes	complemented
740	#441	C₂²×C₅₃	1	2	yes	complemented
741	#440	C₂²×C₅₃	1	2	yes	complemented
742	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
743	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
744	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
746	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
747	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
748	#435	C₂²×C₅₃	1	2	yes	complemented
749	#435	C₂²×C₅₃	1	2	yes	complemented
750	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
751	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
752	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
753	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
754	#418	C₂²×C₅₃	1	2	yes	complemented
755	#417	C₂²×C₅₃	1	2	yes	complemented
756	#416	C₂²×C₅₃	1	2	yes	complemented
757	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
758	#408	C₂²×C₅₃	1	2	yes	complemented
759	#408	C₂²×C₅₃	1	2	yes	complemented
760	C₅₃	#61689	1	1	yes	characteristic, direct product factor, Sylow
761	H(5,𝔽₂)	—	4	4	no	—
762	H(5,𝔽₂)	—	4	4	no	—
763	C₂×#41	—	2	2	no	—
764	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
765	C₂×#41	C₂³×C₅₃	1	2	yes	—
766	C₂×#41	C₂³×C₅₃	1	2	yes	—
767	C₂×#41	C₂³×C₅₃	1	2	yes	—
768	C₂×#41	C₂³×C₅₃	1	2	yes	—
769	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
770	C₂²×D₄	—	2	2	no	—
771	C₂²×D₄	—	2	2	no	—
772	C₂²×D₄	—	2	2	no	—
773	C₂²×D₄	—	2	1	no	—
774	C₂²×D₄	—	2	1	no	—
775	C₂²×D₄	—	2	2	no	—
776	C₂²×D₄	—	2	1	no	—
777	C₂²×D₄	—	2	1	no	—
778	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
779	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
780	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
781	#137	—	4	4	no	—
782	AGL(1,ℤ/8)	—	4	4	no	—
783	#135	—	4	4	no	—
784	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
785	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
786	C₂×SD₁₆	—	4	4	no	—
787	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
788	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
789	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
790	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
791	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
792	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
793	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
794	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
795	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
796	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
797	C₂×D₈	C₂³×C₅₃	1	2	yes	—
798	C₂×D₈	C₂³×C₅₃	1	2	yes	—
799	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
800	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
801	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
802	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
803	C₄⋊Q₈	—	2	2	no	—
804	C₄⋊Q₈	—	2	1	no	—
805	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
806	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
807	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
808	#127	—	2	2	no	—
809	#127	—	2	1	no	—
810	#127	—	2	1	no	—
811	#127	—	2	2	no	—
812	#127	—	2	1	no	—
813	#127	—	2	1	no	—
814	#127	D₄×C₅₃	1	1	yes	characteristic
815	#127	C₂³×C₅₃	1	1	yes	characteristic
816	#127	C₂³×C₅₃	1	1	yes	characteristic
817	#127	C₂³×C₅₃	1	2	yes	—
818	#126	—	2	2	no	—
819	#126	—	2	1	no	—
820	#125	—	2	2	no	—
821	#125	—	2	1	no	—
822	#125	—	2	1	no	—
823	#125	C₂³×C₅₃	1	1	yes	characteristic
824	#124	—	2	2	no	—
825	#124	—	2	2	no	—
826	#124	—	2	2	no	—
827	#124	—	2	2	no	—
828	#124	D₄×C₅₃	1	2	yes	—
829	#124	C₂³×C₅₃	1	1	yes	characteristic
830	#123	—	2	2	no	—
831	#123	—	2	2	no	—
832	#123	—	2	2	no	—
833	#123	—	2	1	no	—
834	#123	—	2	2	no	—
835	C₂²⋊Q₈	—	2	2	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	2	no	—
838	C₂²⋊Q₈	—	2	2	no	—
839	C₂²⋊Q₈	—	2	2	no	—
840	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
841	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
842	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
843	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
844	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
845	#121	—	2	2	no	—
846	#121	—	2	2	no	—
847	#121	—	2	2	no	—
848	#121	—	2	1	no	—
849	#121	—	2	2	no	—
850	#121	—	2	1	no	—
851	#121	—	2	1	no	—
852	#121	—	2	1	no	—
853	#121	—	2	2	no	—
854	#121	—	2	2	no	—
855	#121	—	2	2	no	—
856	#121	—	2	2	no	—
857	#121	—	2	2	no	—
858	#121	D₄×C₅₃	1	1	yes	characteristic
859	#121	D₄×C₅₃	1	1	yes	characteristic
860	#121	D₄×C₅₃	1	2	yes	—
861	#121	C₂³×C₅₃	1	1	yes	characteristic
862	#121	C₂³×C₅₃	1	2	yes	—
863	#121	C₂³×C₅₃	1	2	yes	—
864	#121	C₂³×C₅₃	1	2	yes	—
865	#121	C₂³×C₅₃	1	2	yes	—
866	#121	C₂³×C₅₃	1	2	yes	—
867	#120	—	2	2	no	—
868	#120	—	2	2	no	—
869	#120	—	2	2	no	—
870	#120	—	2	2	no	—
871	#120	—	2	2	no	—
872	#120	—	2	2	no	—
873	C₄×Q₈	—	2	1	no	—
874	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
875	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
876	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
877	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	—	2	1	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	—	2	2	no	—
886	C₄×D₄	—	2	2	no	—
887	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
888	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
889	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
890	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
891	C₄×D₄	C₂³×C₅₃	1	2	yes	—
892	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
893	#117	—	2	1	no	—
894	#117	—	2	1	no	—
895	#117	—	2	2	no	—
896	#117	—	2	1	no	—
897	#117	—	2	1	no	—
898	#117	C₂³×C₅₃	1	1	yes	characteristic
899	#117	C₂³×C₅₃	1	2	yes	—
900	C₂×C₄⋊C₄	—	2	1	no	—
901	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
902	C₂×C₄²	—	2	1	no	—
903	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
904	#107	C₂³×C₅₃	1	1	yes	characteristic
905	#107	C₂³×C₅₃	1	1	yes	characteristic
906	#107	C₂³×C₅₃	1	2	yes	—
907	#106	C₂³×C₅₃	1	1	yes	characteristic
908	#106	C₂³×C₅₃	1	1	yes	characteristic
909	#106	C₂³×C₅₃	1	2	yes	—
910	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
911	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
912	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
913	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
914	#103	C₂³×C₅₃	1	1	yes	characteristic
915	#103	C₂³×C₅₃	1	2	yes	—
916	#103	C₂³×C₅₃	1	1	yes	characteristic
917	#103	C₂³×C₅₃	1	1	yes	characteristic
918	#103	C₂³×C₅₃	1	1	yes	characteristic
919	#103	C₂³×C₅₃	1	2	yes	—
920	#103	C₂³×C₅₃	1	2	yes	—
921	#102	C₂³×C₅₃	1	1	yes	characteristic
922	#102	C₂³×C₅₃	1	2	yes	—
923	#102	C₂³×C₅₃	1	2	yes	—
924	#102	C₂³×C₅₃	1	2	yes	—
925	#102	C₂³×C₅₃	1	2	yes	—
926	#102	C₂³×C₅₃	1	2	yes	—
927	#102	C₂³×C₅₃	1	2	yes	—
928	#102	C₂³×C₅₃	1	2	yes	—
929	#102	C₂³×C₅₃	1	1	yes	characteristic
930	#102	C₂³×C₅₃	1	2	yes	—
931	#102	C₂³×C₅₃	1	2	yes	—
932	#102	C₂³×C₅₃	1	1	yes	characteristic
933	#102	C₂³×C₅₃	1	1	yes	characteristic
934	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
935	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
936	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
937	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
938	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
939	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
940	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
941	#97	C₂³×C₅₃	1	2	yes	—
942	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
943	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
944	C₂⁴	—	2	2	no	—
945	C₂⁴	—	2	2	no	—
946	C₂⁴	—	2	2	no	—
947	#41	—	2	2	no	—
948	#41	—	2	2	no	—
949	#41	—	2	4	no	—
950	#41	—	2	4	no	—
951	#41	—	4	2	no	—
952	#41	—	4	2	no	—
953	#41	—	4	2	no	—
954	#41	—	4	2	no	—
955	#41	—	4	8	no	—
956	#41	—	4	2	no	—
957	#41	—	4	2	no	—
958	C₂×Q₈	—	2	1	no	—
959	C₂×Q₈	—	2	2	no	—
960	C₂×Q₈	—	4	2	no	—
961	C₂×Q₈	—	4	2	no	—
962	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
963	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
964	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
965	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	4	no	—
968	C₂×D₄	—	2	4	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	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	—	4	2	no	—
988	C₂×D₄	—	4	2	no	—
989	C₂×D₄	—	4	2	no	—
990	C₂×D₄	—	4	2	no	—
991	C₂×D₄	—	4	8	no	—
992	C₂×D₄	—	4	8	no	—
993	C₂×D₄	—	4	8	no	—
994	C₂×D₄	—	8	2	no	—
995	C₂×D₄	—	8	2	no	—
996	C₂×D₄	—	8	2	no	—
997	C₂×D₄	—	8	2	no	—
998	C₂×D₄	—	8	4	no	—
999	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1000	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1001	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1002	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1003	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1004	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1005	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1006	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1007	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1008	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	1	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	C₂×D₄×C₅₃	1	1	yes	characteristic
1019	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1022	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1023	Q₁₆	—	2	4	no	—
1024	Q₁₆	—	2	2	no	—
1025	SD₁₆	—	2	2	no	—
1026	SD₁₆	—	2	2	no	—
1027	SD₁₆	—	2	4	no	—
1028	SD₁₆	—	4	2	no	—
1029	SD₁₆	—	4	2	no	—
1030	SD₁₆	—	4	2	no	—
1031	SD₁₆	—	4	2	no	—
1032	SD₁₆	—	4	2	no	—
1033	SD₁₆	—	4	2	no	—
1034	D₈	—	2	2	no	—
1035	D₈	—	4	2	no	—
1036	D₈	—	4	2	no	—
1037	M₁₆	—	4	2	no	—
1038	M₁₆	—	4	2	no	—
1039	C₂×C₈	—	4	2	no	—
1040	C₂×C₈	—	4	2	no	—
1041	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1042	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1043	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1044	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1045	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1046	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1063	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1065	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1067	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1068	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1069	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1089	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1090	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1091	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1092	C₄²	—	2	1	no	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	2	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	1	no	—
1098	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1099	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1100	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1101	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1102	C₂³	—	2	1	no	—
1103	C₂³	—	2	1	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	4	4	no	—
1107	C₂³	—	4	4	no	—
1108	C₂³	—	4	4	no	—
1109	C₂³	—	8	2	no	—
1110	C₂³	—	8	2	no	—
1111	C₂³	—	8	2	no	—
1112	C₂³	—	8	2	no	—
1113	C₂³	—	8	2	no	—
1114	C₂³	—	8	2	no	—
1115	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1116	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1117	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1118	Q₈	—	2	1	no	—
1119	Q₈	—	2	1	no	—
1120	Q₈	—	2	2	no	—
1121	Q₈	—	2	1	no	—
1122	Q₈	—	2	2	no	—
1123	Q₈	—	4	2	no	—
1124	Q₈	—	8	1	no	—
1125	Q₈	—	8	2	no	—
1126	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1127	D₄	—	2	4	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	2	2	no	—
1130	D₄	—	2	1	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	2	2	no	—
1134	D₄	—	2	2	no	—
1135	D₄	—	2	2	no	—
1136	D₄	—	2	2	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	4	2	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	4	4	no	—
1143	D₄	—	4	4	no	—
1144	D₄	—	4	4	no	—
1145	D₄	—	4	4	no	—
1146	D₄	—	4	4	no	—
1147	D₄	—	4	2	no	—
1148	D₄	—	4	2	no	—
1149	D₄	—	8	2	no	—
1150	D₄	—	8	1	no	—
1151	D₄	—	8	1	no	—
1152	D₄	—	8	1	no	—
1153	D₄	—	8	2	no	—
1154	D₄	—	8	2	no	—
1155	D₄	—	8	2	no	—
1156	D₄	—	8	2	no	—
1157	D₄	—	8	2	no	—
1158	D₄	—	8	2	no	—
1159	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1160	C₂×C₄	—	2	4	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	4	no	—
1178	C₂×C₄	—	4	4	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	4	2	no	—
1182	C₂×C₄	—	8	2	no	—
1183	C₂×C₄	—	8	2	no	—
1184	C₂×C₄	—	8	2	no	—
1185	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1186	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1187	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1188	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1189	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1190	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1191	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1192	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1193	C₈	—	2	1	no	—
1194	C₈	—	2	1	no	—
1195	C₈	—	2	2	no	—
1196	C₈	—	2	2	no	—
1197	C₈	—	2	1	no	—
1198	C₈	—	2	1	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	2	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	2	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	2	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	16	4	no	—
1221	C₂²	—	16	4	no	—
1222	C₂²	—	16	4	no	—
1223	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1224	C₄	—	2	1	no	—
1225	C₄	—	2	2	no	—
1226	C₄	—	2	2	no	—
1227	C₄	—	2	2	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	2	1	no	—
1231	C₄	—	4	2	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	2	no	—
1238	C₄	C₅₃×#577	1	2	yes	—
1239	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1240	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1241	C₂	—	4	1	no	—
1242	C₂	—	4	2	no	—
1243	C₂	—	4	2	no	—
1244	C₂	—	4	2	no	—
1245	C₂	—	8	2	no	—
1246	C₂	—	8	2	no	—
1247	C₂	—	8	1	no	—
1248	C₂	C₅₃×#3484	1	1	yes	characteristic
1249	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1250	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×#3547	C₂	semidirect
2. C₅₃×#3498	C₂	semidirect
3. C₅₃×#3333	C₂	semidirect
4. C₅₃×#3325	C₂	semidirect
5. C₅₃×#3317	C₂	semidirect
6. C₅₃×#3310	C₂	semidirect
7. C₅₃×#3305	C₂	semidirect
8. C₅₃×#3295	C₂	semidirect
9. C₅₃×#3284	C₂	semidirect
10. D₄×SD₁₆×C₅₃	C₂	semidirect
11. C₅₃×#3278	C₂	semidirect
12. C₅₃×#3272	C₂	semidirect
13. C₅₃×#3271	C₂	semidirect
14. C₅₃×#3265	C₂	semidirect
15. C₅₃×#3217	C₂	semidirect
16. C₅₃×#3208	C₂	semidirect
17. C₅₃×#3200	C₂	semidirect
18. C₅₃×#3198	C₂	semidirect
19. C₅₃×#3116	C₂	semidirect
20. C₅₃×#3102	C₂	semidirect
21. C₅₃×#3012	C₂	semidirect
22. C₅₃×#3009	C₂	semidirect
23. C₅₃×#2981	C₂	semidirect
25. C₂×#137×C₅₃	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
27. C₂×#135×C₅₃	C₂²	semidirect
28. C₂²×SD₁₆×C₅₃	C₂²	semidirect
31. C₅₃×#555	C₂²	semidirect
32. C₅₃×#554	C₂²	semidirect
34. C₅₃×#552	C₂²	semidirect
38. D₄×Q₈×C₅₃	C₂²	semidirect
39. C₅₃×#548	C₂²	semidirect
40. C₅₃×#547	C₂²	semidirect
50. C₅₃×#537	C₂²	semidirect
51. C₅₃×#536	C₂²	semidirect
54. C₅₃×#533	C₂²	semidirect
59. C₅₃×#529	C₂²	semidirect
61. C₅₃×#496	C₂²	semidirect
62. C₅₃×#492	C₂²	semidirect
63. C₅₃×#492	C₂²	semidirect
64. C₅₃×#490	C₂²	semidirect
65. C₅₃×#486	C₂²	semidirect
66. C₅₃×#486	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#481	C₂²	semidirect
73. C₅₃×#480	C₂²	semidirect
74. C₅₃×#479	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#477	C₂²	semidirect
77. C₅₃×#476	C₂²	semidirect
78. C₅₃×#469	C₂²	semidirect
79. C₅₃×#468	C₂²	semidirect
80. C₅₃×#468	C₂²	semidirect
81. C₅₃×#468	C₂²	semidirect
82. C₅₃×#466	C₂²	semidirect
83. C₅₃×#465	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
85. C₅₃×#465	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#462	C₂²	semidirect
89. C₅₃×#461	C₂²	semidirect
90. C₅₃×#460	C₂²	semidirect
91. C₅₃×#460	C₂²	semidirect
92. C₅₃×#460	C₂²	semidirect
93. C₅₃×#460	C₂²	semidirect
94. C₅₃×#459	C₂²	semidirect
95. C₅₃×#459	C₂²	semidirect
98. C₅₃×#452	C₂²	semidirect
99. C₅₃×#452	C₂²	semidirect
100. C₅₃×#452	C₂²	semidirect
101. C₅₃×#450	C₂²	semidirect
102. C₅₃×#450	C₂²	semidirect
103. C₅₃×#450	C₂²	semidirect
104. C₅₃×#450	C₂²	semidirect
105. C₅₃×#450	C₂²	semidirect
106. C₅₃×#450	C₂²	semidirect
108. C₅₃×#449	C₂²	semidirect
109. C₅₃×#449	C₂²	semidirect
110. C₅₃×#449	C₂²	semidirect
111. C₅₃×#448	C₂²	semidirect
112. C₅₃×#448	C₂²	semidirect
113. C₅₃×#447	C₂²	semidirect
114. C₅₃×#447	C₂²	semidirect
115. C₅₃×#441	C₂²	semidirect
116. C₅₃×#440	C₂²	semidirect
117. C₄×Q₁₆×C₅₃	C₂²	semidirect
118. C₄×SD₁₆×C₅₃	C₂²	semidirect
119. C₄×SD₁₆×C₅₃	C₂²	semidirect
120. C₄×D₈×C₅₃	C₂²	semidirect
121. C₅₃×#436	C₂²	semidirect
122. C₅₃×#436	C₂²	semidirect
123. C₅₃×#435	C₂²	semidirect
124. C₅₃×#435	C₂²	semidirect
125. C₈×D₄×C₅₃	C₂²	semidirect
126. C₈×D₄×C₅₃	C₂²	semidirect
127. C₅₃×#432	C₂²	semidirect
128. C₅₃×#431	C₂²	semidirect
129. C₅₃×#418	C₂²	semidirect
130. C₅₃×#417	C₂²	semidirect
131. C₅₃×#416	C₂²	semidirect
132. C₂×#102×C₅₃	C₂²	semidirect
133. C₅₃×#408	C₂²	semidirect
134. C₅₃×#408	C₂²	semidirect
573. #61689	C₅₃	direct (N × H)
616. #3547	C₂×C₅₃	semidirect
617. #3498	C₂×C₅₃	semidirect
618. #3333	C₂×C₅₃	semidirect
619. #3325	C₂×C₅₃	semidirect
620. #3317	C₂×C₅₃	semidirect
621. #3310	C₂×C₅₃	semidirect
622. #3305	C₂×C₅₃	semidirect
623. #3295	C₂×C₅₃	semidirect
624. #3284	C₂×C₅₃	semidirect
625. D₄×SD₁₆	C₂×C₅₃	semidirect
626. #3278	C₂×C₅₃	semidirect
627. #3272	C₂×C₅₃	semidirect
628. #3271	C₂×C₅₃	semidirect
629. #3265	C₂×C₅₃	semidirect
630. #3217	C₂×C₅₃	semidirect
631. #3208	C₂×C₅₃	semidirect
632. #3200	C₂×C₅₃	semidirect
633. #3198	C₂×C₅₃	semidirect
634. #3116	C₂×C₅₃	semidirect
635. #3102	C₂×C₅₃	semidirect
636. #3012	C₂×C₅₃	semidirect
637. #3009	C₂×C₅₃	semidirect
638. #2981	C₂×C₅₃	semidirect
650. C₂×#137	C₂²×C₅₃	semidirect
651. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
652. C₂×#135	C₂²×C₅₃	semidirect
653. C₂²×SD₁₆	C₂²×C₅₃	semidirect
656. #555	C₂²×C₅₃	semidirect
657. #554	C₂²×C₅₃	semidirect
659. #552	C₂²×C₅₃	semidirect
663. D₄×Q₈	C₂²×C₅₃	semidirect
664. #548	C₂²×C₅₃	semidirect
665. #547	C₂²×C₅₃	semidirect
675. #537	C₂²×C₅₃	semidirect
676. #536	C₂²×C₅₃	semidirect
679. #533	C₂²×C₅₃	semidirect
684. #529	C₂²×C₅₃	semidirect
686. #496	C₂²×C₅₃	semidirect
687. #492	C₂²×C₅₃	semidirect
688. #492	C₂²×C₅₃	semidirect
689. #490	C₂²×C₅₃	semidirect
690. #486	C₂²×C₅₃	semidirect
691. #486	C₂²×C₅₃	semidirect
692. #485	C₂²×C₅₃	semidirect
693. #485	C₂²×C₅₃	semidirect
694. #482	C₂²×C₅₃	semidirect
695. #482	C₂²×C₅₃	semidirect
696. #482	C₂²×C₅₃	semidirect
697. #481	C₂²×C₅₃	semidirect
698. #480	C₂²×C₅₃	semidirect
699. #479	C₂²×C₅₃	semidirect
700. #478	C₂²×C₅₃	semidirect
701. #477	C₂²×C₅₃	semidirect
702. #476	C₂²×C₅₃	semidirect
703. #469	C₂²×C₅₃	semidirect
704. #468	C₂²×C₅₃	semidirect
705. #468	C₂²×C₅₃	semidirect
706. #468	C₂²×C₅₃	semidirect
707. #466	C₂²×C₅₃	semidirect
708. #465	C₂²×C₅₃	semidirect
709. #465	C₂²×C₅₃	semidirect
710. #465	C₂²×C₅₃	semidirect
711. #464	C₂²×C₅₃	semidirect
712. #463	C₂²×C₅₃	semidirect
713. #462	C₂²×C₅₃	semidirect
714. #461	C₂²×C₅₃	semidirect
715. #460	C₂²×C₅₃	semidirect
716. #460	C₂²×C₅₃	semidirect
717. #460	C₂²×C₅₃	semidirect
718. #460	C₂²×C₅₃	semidirect
719. #459	C₂²×C₅₃	semidirect
720. #459	C₂²×C₅₃	semidirect
723. #452	C₂²×C₅₃	semidirect
724. #452	C₂²×C₅₃	semidirect
725. #452	C₂²×C₅₃	semidirect
726. #450	C₂²×C₅₃	semidirect
727. #450	C₂²×C₅₃	semidirect
728. #450	C₂²×C₅₃	semidirect
729. #450	C₂²×C₅₃	semidirect
730. #450	C₂²×C₅₃	semidirect
731. #450	C₂²×C₅₃	semidirect
733. #449	C₂²×C₅₃	semidirect
734. #449	C₂²×C₅₃	semidirect
735. #449	C₂²×C₅₃	semidirect
736. #448	C₂²×C₅₃	semidirect
737. #448	C₂²×C₅₃	semidirect
738. #447	C₂²×C₅₃	semidirect
739. #447	C₂²×C₅₃	semidirect
740. #441	C₂²×C₅₃	semidirect
741. #440	C₂²×C₅₃	semidirect
742. C₄×Q₁₆	C₂²×C₅₃	semidirect
743. C₄×SD₁₆	C₂²×C₅₃	semidirect
744. C₄×SD₁₆	C₂²×C₅₃	semidirect
745. C₄×D₈	C₂²×C₅₃	semidirect
746. #436	C₂²×C₅₃	semidirect
747. #436	C₂²×C₅₃	semidirect
748. #435	C₂²×C₅₃	semidirect
749. #435	C₂²×C₅₃	semidirect
750. C₈×D₄	C₂²×C₅₃	semidirect
751. C₈×D₄	C₂²×C₅₃	semidirect
752. #432	C₂²×C₅₃	semidirect
753. #431	C₂²×C₅₃	semidirect
754. #418	C₂²×C₅₃	semidirect
755. #417	C₂²×C₅₃	semidirect
756. #416	C₂²×C₅₃	semidirect
757. C₂×#102	C₂²×C₅₃	semidirect
758. #408	C₂²×C₅₃	semidirect
759. #408	C₂²×C₅₃	semidirect
760. C₅₃	#61689	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×#3547	2
C₅₃×#3498	2
C₅₃×#3333	2
C₅₃×#3325	2
C₅₃×#3317	2
C₅₃×#3310	2
C₅₃×#3305	2
C₅₃×#3295	2
C₅₃×#3284	2
D₄×SD₁₆×C₅₃	2
C₅₃×#3278	2
C₅₃×#3272	2
C₅₃×#3271	2
C₅₃×#3265	2
C₅₃×#3217	2
C₅₃×#3208	2
C₅₃×#3200	2
C₅₃×#3198	2
C₅₃×#3116	2
C₅₃×#3102	2
C₅₃×#3012	2
C₅₃×#3009	2
C₅₃×#2981	2
#61689	53

Subgroups — C53×#61689 #27269201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61689 #27269201