Subgroups — C₅₃×#62031 #27269543

Order 13568.

1960 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3325	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3319	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3273	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3257	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3224	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3122	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3041	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
26	C₂²×D₈×C₅₃	C₂²	1	2	yes	complemented
27	C₅₃×#560	—	2	2	no	—
28	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#555	C₂²	1	2	yes	complemented
32	C₅₃×#551	—	2	2	no	—
33	C₅₃×#550	C₂²	1	1	yes	characteristic
34	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#548	—	2	1	no	—
37	C₅₃×#546	—	2	1	no	—
38	C₅₃×#546	—	2	1	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	C₂²	1	1	yes	characteristic
43	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
44	D₄²×C₅₃	C₂²	1	2	yes	complemented
45	C₅₃×#542	C₂²	1	2	yes	complemented
46	C₅₃×#540	—	2	1	no	—
47	C₅₃×#540	C₂²	1	2	yes	complemented
48	C₅₃×#538	—	2	2	no	—
49	C₅₃×#535	—	2	1	no	—
50	C₅₃×#535	C₂²	1	2	yes	complemented
51	C₅₃×#534	—	2	2	no	—
52	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
53	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#529	—	2	1	no	—
55	C₅₃×#529	C₂²	1	1	yes	characteristic
56	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
57	C₂×#124×C₅₃	—	2	1	no	—
58	C₅₃×#518	C₂²	1	2	yes	complemented
59	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#496	C₂²	1	2	yes	complemented
61	C₅₃×#495	C₂²	1	2	yes	complemented
62	C₅₃×#493	C₂²	1	1	yes	characteristic
63	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#489	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×#486	C₂²	1	2	yes	complemented
68	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#482	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#478	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#476	C₂²	1	2	yes	complemented
76	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#474	C₂²	1	2	yes	complemented
79	C₅₃×#469	C₂²	1	2	yes	complemented
80	C₅₃×#469	C₂²	1	2	yes	complemented
81	C₅₃×#468	C₂²	1	2	yes	complemented
82	C₅₃×#468	C₂²	1	2	yes	complemented
83	C₅₃×#466	C₂²	1	2	yes	complemented
84	C₅₃×#465	C₂²	1	2	yes	complemented
85	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#463	C₂²	1	2	yes	complemented
87	C₅₃×#463	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	2	yes	complemented
89	C₅₃×#463	C₂²	1	2	yes	complemented
90	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#463	C₂²	1	2	yes	complemented
92	C₅₃×#460	C₂²	1	2	yes	complemented
93	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#459	C₂²	1	1	yes	characteristic
97	C₅₃×#459	C₂²	1	2	yes	complemented
98	C₅₃×#459	C₂²	1	2	yes	complemented
99	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#459	C₂²	1	2	yes	complemented
101	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#459	C₂²	1	2	yes	complemented
103	C₅₃×#459	C₂²	1	2	yes	complemented
104	C₅₃×#452	C₂²	1	2	yes	complemented
105	C₅₃×#452	C₂²	1	1	yes	characteristic, 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×#447	C₂²	1	2	yes	complemented
110	C₅₃×#447	C₂²	1	2	yes	complemented
111	C₅₃×#447	C₂²	1	2	yes	complemented
112	C₅₃×#447	C₂²	1	2	yes	complemented
113	C₅₃×#447	C₂²	1	2	yes	complemented
114	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#442	C₂²	1	2	yes	complemented
117	C₅₃×#442	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
122	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
124	C₅₃×#436	C₂²	1	2	yes	complemented
125	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#435	C₂²	1	2	yes	complemented
127	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#433	C₂²	1	2	yes	complemented
129	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#424	C₂²	1	2	yes	complemented
131	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#418	C₂²	1	2	yes	complemented
133	C₅₃×#418	C₂²	1	2	yes	complemented
134	C₅₃×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	1	no	—
137	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
138	C₂×#41×C₅₃	C₂³	1	2	yes	—
139	C₂²×Q₈×C₅₃	—	2	1	no	—
140	C₂²×D₄×C₅₃	—	2	1	no	—
141	C₂²×D₄×C₅₃	—	2	2	no	—
142	C₂²×D₄×C₅₃	—	2	1	no	—
143	C₂²×D₄×C₅₃	—	2	1	no	—
144	C₂²×D₄×C₅₃	—	2	1	no	—
145	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
146	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
147	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
148	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
149	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
150	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×D₈×C₅₃	—	4	4	no	—
157	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₂×D₈×C₅₃	C₂³	1	2	yes	—
159	C₂×D₈×C₅₃	C₂³	1	2	yes	—
160	C₂×D₈×C₅₃	C₂³	1	2	yes	—
161	C₂×D₈×C₅₃	C₂³	1	2	yes	—
162	C₂×D₈×C₅₃	C₂³	1	2	yes	—
163	C₂×D₈×C₅₃	C₂³	1	2	yes	—
164	C₂×D₈×C₅₃	C₂³	1	2	yes	—
165	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
167	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
168	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
170	#127×C₅₃	—	2	1	no	—
171	#127×C₅₃	—	2	1	no	—
172	#127×C₅₃	—	2	1	no	—
173	#127×C₅₃	C₂³	1	1	yes	characteristic
174	#127×C₅₃	C₂³	1	1	yes	characteristic
175	#127×C₅₃	C₂³	1	2	yes	—
176	#127×C₅₃	C₂³	1	1	yes	characteristic
177	#127×C₅₃	C₂³	1	2	yes	—
178	#126×C₅₃	—	2	2	no	—
179	#126×C₅₃	—	2	2	no	—
180	#126×C₅₃	—	2	1	no	—
181	#126×C₅₃	D₄	1	2	yes	—
182	#125×C₅₃	D₄	1	1	yes	characteristic
183	#125×C₅₃	C₂³	1	1	yes	characteristic
184	#124×C₅₃	—	2	2	no	—
185	#124×C₅₃	—	2	2	no	—
186	#124×C₅₃	—	2	2	no	—
187	#124×C₅₃	—	2	1	no	—
188	#124×C₅₃	—	2	1	no	—
189	#124×C₅₃	—	2	1	no	—
190	#124×C₅₃	—	2	1	no	—
191	#124×C₅₃	D₄	1	1	yes	characteristic
192	#124×C₅₃	C₂³	1	2	yes	—
193	#124×C₅₃	C₂³	1	2	yes	—
194	#124×C₅₃	C₂³	1	1	yes	characteristic
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	2	no	—
200	#123×C₅₃	—	2	2	no	—
201	#123×C₅₃	—	2	2	no	—
202	#123×C₅₃	—	2	1	no	—
203	#123×C₅₃	D₄	1	2	yes	—
204	C₂²⋊Q₈×C₅₃	—	2	1	no	—
205	C₂²⋊Q₈×C₅₃	—	2	2	no	—
206	C₂²⋊Q₈×C₅₃	—	2	2	no	—
207	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
209	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
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	1	no	—
215	#121×C₅₃	—	2	1	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	2	no	—
221	#121×C₅₃	—	2	2	no	—
222	#121×C₅₃	—	2	2	no	—
223	#121×C₅₃	—	2	1	no	—
224	#121×C₅₃	D₄	1	1	yes	characteristic
225	#121×C₅₃	C₂³	1	1	yes	characteristic
226	#121×C₅₃	C₂³	1	2	yes	—
227	#121×C₅₃	C₂³	1	2	yes	—
228	#121×C₅₃	C₂³	1	2	yes	—
229	#121×C₅₃	C₂³	1	2	yes	—
230	#120×C₅₃	—	2	2	no	—
231	#120×C₅₃	—	2	2	no	—
232	#120×C₅₃	—	2	2	no	—
233	#120×C₅₃	—	2	2	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	C₄×Q₈×C₅₃	—	2	1	no	—
239	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₃	—	2	2	no	—
244	C₄×D₄×C₅₃	—	2	2	no	—
245	C₄×D₄×C₅₃	—	2	1	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	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₅₃	C₂³	1	2	yes	—
255	C₄×D₄×C₅₃	C₂³	1	2	yes	—
256	C₄×D₄×C₅₃	C₂³	1	2	yes	—
257	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₅₃	C₂³	1	2	yes	—
259	C₄×D₄×C₅₃	C₂³	1	2	yes	—
260	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₅₃	C₂³	1	2	yes	—
262	#117×C₅₃	—	2	2	no	—
263	#117×C₅₃	—	2	1	no	—
264	#117×C₅₃	—	2	1	no	—
265	#117×C₅₃	C₂³	1	1	yes	characteristic
266	#117×C₅₃	C₂³	1	2	yes	—
267	#117×C₅₃	C₂³	1	2	yes	—
268	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
272	C₂×C₄²×C₅₃	—	2	1	no	—
273	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
274	#107×C₅₃	C₂³	1	1	yes	characteristic
275	#107×C₅₃	C₂³	1	1	yes	characteristic
276	#107×C₅₃	C₂³	1	2	yes	—
277	#106×C₅₃	C₂³	1	1	yes	characteristic
278	#106×C₅₃	C₂³	1	1	yes	characteristic
279	#106×C₅₃	C₂³	1	2	yes	—
280	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
285	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	#103×C₅₃	C₂³	1	1	yes	characteristic
288	#103×C₅₃	C₂³	1	1	yes	characteristic
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	1	yes	characteristic
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#102×C₅₃	C₂³	1	1	yes	characteristic
293	#102×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
307	C₂²⋊C₈×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	2	yes	—
311	#97×C₅₃	C₂³	1	2	yes	—
312	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₅₃	C₂³	1	2	yes	—
315	C₂⁴×C₅₃	—	2	2	no	—
316	C₂⁴×C₅₃	—	2	2	no	—
317	C₂⁴×C₅₃	—	2	2	no	—
318	#41×C₅₃	—	2	2	no	—
319	#41×C₅₃	—	4	1	no	—
320	#41×C₅₃	—	4	2	no	—
321	#41×C₅₃	—	4	2	no	—
322	#41×C₅₃	—	8	2	no	—
323	#41×C₅₃	—	8	2	no	—
324	C₂×Q₈×C₅₃	—	2	1	no	—
325	C₂×Q₈×C₅₃	—	2	2	no	—
326	C₂×Q₈×C₅₃	—	8	2	no	—
327	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₅₃	—	2	4	no	—
331	C₂×D₄×C₅₃	—	2	1	no	—
332	C₂×D₄×C₅₃	—	2	1	no	—
333	C₂×D₄×C₅₃	—	2	2	no	—
334	C₂×D₄×C₅₃	—	2	2	no	—
335	C₂×D₄×C₅₃	—	2	2	no	—
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	—	2	2	no	—
338	C₂×D₄×C₅₃	—	2	2	no	—
339	C₂×D₄×C₅₃	—	2	1	no	—
340	C₂×D₄×C₅₃	—	2	1	no	—
341	C₂×D₄×C₅₃	—	2	1	no	—
342	C₂×D₄×C₅₃	—	2	1	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	1	no	—
351	C₂×D₄×C₅₃	—	4	2	no	—
352	C₂×D₄×C₅₃	—	4	2	no	—
353	C₂×D₄×C₅₃	—	4	2	no	—
354	C₂×D₄×C₅₃	—	4	2	no	—
355	C₂×D₄×C₅₃	—	4	2	no	—
356	C₂×D₄×C₅₃	—	8	2	no	—
357	C₂×D₄×C₅₃	—	8	2	no	—
358	C₂×D₄×C₅₃	—	8	2	no	—
359	C₂×D₄×C₅₃	—	8	2	no	—
360	C₂×D₄×C₅₃	—	8	4	no	—
361	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
362	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
363	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
365	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
366	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
367	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₅₃	—	2	1	no	—
369	C₂²×C₄×C₅₃	—	2	1	no	—
370	C₂²×C₄×C₅₃	—	2	1	no	—
371	C₂²×C₄×C₅₃	—	2	1	no	—
372	C₂²×C₄×C₅₃	—	2	2	no	—
373	C₂²×C₄×C₅₃	—	2	2	no	—
374	C₂²×C₄×C₅₃	—	2	2	no	—
375	C₂²×C₄×C₅₃	—	2	2	no	—
376	C₂²×C₄×C₅₃	—	2	2	no	—
377	C₂²×C₄×C₅₃	—	2	2	no	—
378	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
382	Q₁₆×C₅₃	—	4	1	no	—
383	SD₁₆×C₅₃	—	2	2	no	—
384	SD₁₆×C₅₃	—	4	1	no	—
385	SD₁₆×C₅₃	—	4	2	no	—
386	SD₁₆×C₅₃	—	4	2	no	—
387	SD₁₆×C₅₃	—	4	2	no	—
388	D₈×C₅₃	—	2	2	no	—
389	D₈×C₅₃	—	2	4	no	—
390	D₈×C₅₃	—	2	4	no	—
391	D₈×C₅₃	—	4	2	no	—
392	D₈×C₅₃	—	4	2	no	—
393	D₈×C₅₃	—	4	2	no	—
394	D₈×C₅₃	—	4	2	no	—
395	D₈×C₅₃	—	4	2	no	—
396	M₁₆×C₅₃	—	4	2	no	—
397	M₁₆×C₅₃	—	4	2	no	—
398	C₂×C₈×C₅₃	—	4	2	no	—
399	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
402	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₅₃	—	2	1	no	—
406	C₄⋊C₄×C₅₃	—	2	1	no	—
407	C₄⋊C₄×C₅₃	—	2	1	no	—
408	C₄⋊C₄×C₅₃	—	2	1	no	—
409	C₄⋊C₄×C₅₃	—	2	2	no	—
410	C₄⋊C₄×C₅₃	—	2	1	no	—
411	C₄⋊C₄×C₅₃	—	2	1	no	—
412	C₄⋊C₄×C₅₃	—	2	2	no	—
413	C₄⋊C₄×C₅₃	—	2	1	no	—
414	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₂²⋊C₄×C₅₃	—	2	2	no	—
426	C₂²⋊C₄×C₅₃	—	2	1	no	—
427	C₂²⋊C₄×C₅₃	—	2	2	no	—
428	C₂²⋊C₄×C₅₃	—	2	1	no	—
429	C₂²⋊C₄×C₅₃	—	2	1	no	—
430	C₂²⋊C₄×C₅₃	—	2	2	no	—
431	C₂²⋊C₄×C₅₃	—	2	2	no	—
432	C₂²⋊C₄×C₅₃	—	2	2	no	—
433	C₂²⋊C₄×C₅₃	—	2	2	no	—
434	C₂²⋊C₄×C₅₃	—	2	2	no	—
435	C₂²⋊C₄×C₅₃	—	2	2	no	—
436	C₂²⋊C₄×C₅₃	—	2	2	no	—
437	C₂²⋊C₄×C₅₃	—	2	1	no	—
438	C₂²⋊C₄×C₅₃	—	2	1	no	—
439	C₂²⋊C₄×C₅₃	—	2	1	no	—
440	C₂²⋊C₄×C₅₃	—	2	2	no	—
441	C₂²⋊C₄×C₅₃	—	2	1	no	—
442	C₂²⋊C₄×C₅₃	—	2	2	no	—
443	C₂²⋊C₄×C₅₃	—	2	2	no	—
444	C₂²⋊C₄×C₅₃	—	2	2	no	—
445	C₂²⋊C₄×C₅₃	—	2	1	no	—
446	C₂²⋊C₄×C₅₃	—	2	2	no	—
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
451	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
453	C₄²×C₅₃	—	2	1	no	—
454	C₄²×C₅₃	—	2	1	no	—
455	C₄²×C₅₃	—	2	1	no	—
456	C₄²×C₅₃	—	2	2	no	—
457	C₄²×C₅₃	—	2	1	no	—
458	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
460	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
461	C₄²×C₅₃	C₂⁴	1	2	yes	—
462	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
463	C₂³×C₅₃	—	2	1	no	—
464	C₂³×C₅₃	—	2	2	no	—
465	C₂³×C₅₃	—	2	2	no	—
466	C₂³×C₅₃	—	2	2	no	—
467	C₂³×C₅₃	—	2	1	no	—
468	C₂³×C₅₃	—	4	4	no	—
469	C₂³×C₅₃	—	4	4	no	—
470	C₂³×C₅₃	—	8	2	no	—
471	C₂³×C₅₃	—	8	2	no	—
472	C₂³×C₅₃	—	8	2	no	—
473	C₂³×C₅₃	—	8	2	no	—
474	C₂³×C₅₃	—	8	2	no	—
475	C₂³×C₅₃	—	8	2	no	—
476	C₂³×C₅₃	—	8	2	no	—
477	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
478	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
479	Q₈×C₅₃	—	2	2	no	—
480	Q₈×C₅₃	—	2	1	no	—
481	Q₈×C₅₃	—	2	1	no	—
482	Q₈×C₅₃	—	2	1	no	—
483	Q₈×C₅₃	—	2	1	no	—
484	Q₈×C₅₃	—	4	2	no	—
485	Q₈×C₅₃	—	8	2	no	—
486	D₄×C₅₃	—	2	2	no	—
487	D₄×C₅₃	—	2	2	no	—
488	D₄×C₅₃	—	2	1	no	—
489	D₄×C₅₃	—	2	2	no	—
490	D₄×C₅₃	—	2	2	no	—
491	D₄×C₅₃	—	2	1	no	—
492	D₄×C₅₃	—	2	2	no	—
493	D₄×C₅₃	—	2	1	no	—
494	D₄×C₅₃	—	2	2	no	—
495	D₄×C₅₃	—	2	2	no	—
496	D₄×C₅₃	—	4	2	no	—
497	D₄×C₅₃	—	4	4	no	—
498	D₄×C₅₃	—	4	2	no	—
499	D₄×C₅₃	—	4	2	no	—
500	D₄×C₅₃	—	4	2	no	—
501	D₄×C₅₃	—	4	2	no	—
502	D₄×C₅₃	—	4	2	no	—
503	D₄×C₅₃	—	8	1	no	—
504	D₄×C₅₃	—	8	2	no	—
505	D₄×C₅₃	—	8	2	no	—
506	D₄×C₅₃	—	8	2	no	—
507	D₄×C₅₃	—	8	1	no	—
508	D₄×C₅₃	—	8	1	no	—
509	D₄×C₅₃	—	8	2	no	—
510	D₄×C₅₃	—	8	2	no	—
511	D₄×C₅₃	—	8	2	no	—
512	D₄×C₅₃	—	8	2	no	—
513	D₄×C₅₃	—	8	2	no	—
514	D₄×C₅₃	—	8	2	no	—
515	D₄×C₅₃	—	8	2	no	—
516	D₄×C₅₃	—	8	2	no	—
517	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
518	C₂×C₄×C₅₃	—	2	2	no	—
519	C₂×C₄×C₅₃	—	2	2	no	—
520	C₂×C₄×C₅₃	—	2	1	no	—
521	C₂×C₄×C₅₃	—	2	1	no	—
522	C₂×C₄×C₅₃	—	2	2	no	—
523	C₂×C₄×C₅₃	—	2	1	no	—
524	C₂×C₄×C₅₃	—	2	1	no	—
525	C₂×C₄×C₅₃	—	2	1	no	—
526	C₂×C₄×C₅₃	—	2	1	no	—
527	C₂×C₄×C₅₃	—	2	2	no	—
528	C₂×C₄×C₅₃	—	2	1	no	—
529	C₂×C₄×C₅₃	—	2	1	no	—
530	C₂×C₄×C₅₃	—	4	1	no	—
531	C₂×C₄×C₅₃	—	4	2	no	—
532	C₂×C₄×C₅₃	—	4	2	no	—
533	C₂×C₄×C₅₃	—	4	2	no	—
534	C₂×C₄×C₅₃	—	8	1	no	—
535	C₂×C₄×C₅₃	—	8	2	no	—
536	C₂×C₄×C₅₃	—	8	2	no	—
537	C₂×C₄×C₅₃	—	8	2	no	—
538	C₂×C₄×C₅₃	—	8	2	no	—
539	C₂×C₄×C₅₃	—	8	2	no	—
540	C₂×C₄×C₅₃	—	8	2	no	—
541	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
547	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
550	C₈×C₅₃	—	2	1	no	—
551	C₈×C₅₃	—	2	2	no	—
552	C₈×C₅₃	—	2	2	no	—
553	C₈×C₅₃	—	2	1	no	—
554	C₈×C₅₃	—	2	1	no	—
555	C₈×C₅₃	—	2	1	no	—
556	#62031	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
557	C₂²×C₅₃	—	2	1	no	—
558	C₂²×C₅₃	—	2	2	no	—
559	C₂²×C₅₃	—	2	1	no	—
560	C₂²×C₅₃	—	2	2	no	—
561	C₂²×C₅₃	—	2	2	no	—
562	C₂²×C₅₃	—	2	1	no	—
563	C₂²×C₅₃	—	2	2	no	—
564	C₂²×C₅₃	—	4	1	no	—
565	C₂²×C₅₃	—	4	1	no	—
566	C₂²×C₅₃	—	4	2	no	—
567	C₂²×C₅₃	—	4	2	no	—
568	C₂²×C₅₃	—	4	1	no	—
569	C₂²×C₅₃	—	4	2	no	—
570	C₂²×C₅₃	—	4	2	no	—
571	C₂²×C₅₃	—	4	2	no	—
572	C₂²×C₅₃	—	4	1	no	—
573	C₂²×C₅₃	—	4	2	no	—
574	C₂²×C₅₃	—	4	1	no	—
575	C₂²×C₅₃	—	4	2	no	—
576	C₂²×C₅₃	—	4	2	no	—
577	C₂²×C₅₃	—	4	2	no	—
578	C₂²×C₅₃	—	16	4	no	—
579	C₂²×C₅₃	—	16	4	no	—
580	C₂²×C₅₃	—	16	4	no	—
581	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
582	C₄×C₅₃	—	2	1	no	—
583	C₄×C₅₃	—	2	1	no	—
584	C₄×C₅₃	—	2	2	no	—
585	C₄×C₅₃	—	2	1	no	—
586	C₄×C₅₃	—	2	2	no	—
587	C₄×C₅₃	—	2	1	no	—
588	C₄×C₅₃	—	2	2	no	—
589	C₄×C₅₃	—	4	1	no	—
590	C₄×C₅₃	—	4	1	no	—
591	C₄×C₅₃	—	4	1	no	—
592	C₄×C₅₃	—	4	1	no	—
593	C₄×C₅₃	—	4	1	no	—
594	C₄×C₅₃	—	4	1	no	—
595	C₄×C₅₃	—	4	2	no	—
596	C₄×C₅₃	#576	1	2	yes	—
597	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
598	C₄×C₅₃	#585	1	1	yes	characteristic
599	#3543	C₂×C₅₃	1	1	yes	characteristic, complemented
600	#3514	C₂×C₅₃	1	1	yes	characteristic, complemented
601	#3399	C₂×C₅₃	1	1	yes	characteristic, complemented
602	#3396	C₂×C₅₃	1	1	yes	characteristic, complemented
603	#3373	C₂×C₅₃	1	1	yes	characteristic, complemented
604	#3358	C₂×C₅₃	1	1	yes	characteristic, complemented
605	#3325	C₂×C₅₃	1	2	yes	complemented
606	#3324	C₂×C₅₃	1	1	yes	characteristic, complemented
607	#3319	C₂×C₅₃	1	2	yes	complemented
608	#3304	C₂×C₅₃	1	1	yes	characteristic, complemented
609	D₄×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
610	#3274	C₂×C₅₃	1	1	yes	characteristic, complemented
611	#3273	C₂×C₅₃	1	2	yes	complemented
612	#3264	C₂×C₅₃	1	2	yes	complemented
613	#3257	C₂×C₅₃	1	2	yes	complemented
614	#3251	C₂×C₅₃	1	1	yes	characteristic, complemented
615	#3224	C₂×C₅₃	1	2	yes	complemented
616	#3205	C₂×C₅₃	1	1	yes	characteristic, complemented
617	#3122	C₂×C₅₃	1	2	yes	complemented
618	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
619	#3041	C₂×C₅₃	1	2	yes	complemented
620	#3038	C₂×C₅₃	1	1	yes	characteristic, complemented
621	#2993	C₂×C₅₃	1	1	yes	characteristic, complemented
622	C₂×C₅₃	—	4	1	no	—
623	C₂×C₅₃	—	4	2	no	—
624	C₂×C₅₃	—	4	2	no	—
625	C₂×C₅₃	—	8	2	no	—
626	C₂×C₅₃	—	8	2	no	—
627	C₂×C₅₃	—	8	2	no	—
628	C₂×C₅₃	—	8	1	no	—
629	C₂×C₅₃	#3488	1	1	yes	characteristic
630	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
631	C₂×C₅₃	#3585	1	1	yes	characteristic
632	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
633	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
634	C₂²×D₈	C₂²×C₅₃	1	2	yes	complemented
635	#560	—	2	2	no	—
636	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
637	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
638	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
639	#555	C₂²×C₅₃	1	2	yes	complemented
640	#551	—	2	2	no	—
641	#550	C₂²×C₅₃	1	1	yes	characteristic
642	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
643	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
644	#548	—	2	1	no	—
645	#546	—	2	1	no	—
646	#546	—	2	1	no	—
647	#546	C₂²×C₅₃	1	2	yes	complemented
648	#546	C₂²×C₅₃	1	2	yes	complemented
649	D₄²	—	2	1	no	—
650	D₄²	C₂²×C₅₃	1	1	yes	characteristic
651	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
652	D₄²	C₂²×C₅₃	1	2	yes	complemented
653	#542	C₂²×C₅₃	1	2	yes	complemented
654	#540	—	2	1	no	—
655	#540	C₂²×C₅₃	1	2	yes	complemented
656	#538	—	2	2	no	—
657	#535	—	2	1	no	—
658	#535	C₂²×C₅₃	1	2	yes	complemented
659	#534	—	2	2	no	—
660	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
661	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic, complemented
662	#529	—	2	1	no	—
663	#529	C₂²×C₅₃	1	1	yes	characteristic
664	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
665	C₂×#124	—	2	1	no	—
666	#518	C₂²×C₅₃	1	2	yes	complemented
667	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
668	#496	C₂²×C₅₃	1	2	yes	complemented
669	#495	C₂²×C₅₃	1	2	yes	complemented
670	#493	C₂²×C₅₃	1	1	yes	characteristic
671	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
672	#489	C₂²×C₅₃	1	2	yes	complemented
673	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
674	#486	C₂²×C₅₃	1	2	yes	complemented
675	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
676	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
677	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	#482	C₂²×C₅₃	1	2	yes	complemented
679	#482	C₂²×C₅₃	1	2	yes	complemented
680	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
682	#478	C₂²×C₅₃	1	2	yes	complemented
683	#476	C₂²×C₅₃	1	2	yes	complemented
684	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
685	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
686	#474	C₂²×C₅₃	1	2	yes	complemented
687	#469	C₂²×C₅₃	1	2	yes	complemented
688	#469	C₂²×C₅₃	1	2	yes	complemented
689	#468	C₂²×C₅₃	1	2	yes	complemented
690	#468	C₂²×C₅₃	1	2	yes	complemented
691	#466	C₂²×C₅₃	1	2	yes	complemented
692	#465	C₂²×C₅₃	1	2	yes	complemented
693	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
694	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
695	#463	C₂²×C₅₃	1	2	yes	complemented
696	#463	C₂²×C₅₃	1	2	yes	complemented
697	#463	C₂²×C₅₃	1	2	yes	complemented
698	#463	C₂²×C₅₃	1	2	yes	complemented
699	#463	C₂²×C₅₃	1	2	yes	complemented
700	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
701	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
702	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	#460	C₂²×C₅₃	1	2	yes	complemented
704	#459	C₂²×C₅₃	1	1	yes	characteristic
705	#459	C₂²×C₅₃	1	2	yes	complemented
706	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	#459	C₂²×C₅₃	1	2	yes	complemented
708	#459	C₂²×C₅₃	1	2	yes	complemented
709	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
710	#459	C₂²×C₅₃	1	2	yes	complemented
711	#459	C₂²×C₅₃	1	2	yes	complemented
712	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	#452	C₂²×C₅₃	1	2	yes	complemented
714	#450	C₂²×C₅₃	1	2	yes	complemented
715	#449	C₂²×C₅₃	1	1	yes	characteristic
716	#449	C₂²×C₅₃	1	2	yes	complemented
717	#447	C₂²×C₅₃	1	2	yes	complemented
718	#447	C₂²×C₅₃	1	2	yes	complemented
719	#447	C₂²×C₅₃	1	2	yes	complemented
720	#447	C₂²×C₅₃	1	2	yes	complemented
721	#447	C₂²×C₅₃	1	2	yes	complemented
722	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
724	#442	C₂²×C₅₃	1	2	yes	complemented
725	#442	C₂²×C₅₃	1	2	yes	complemented
726	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
727	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
728	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
729	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
730	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
731	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
732	#436	C₂²×C₅₃	1	2	yes	complemented
733	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
734	#435	C₂²×C₅₃	1	2	yes	complemented
735	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
736	#433	C₂²×C₅₃	1	2	yes	complemented
737	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
738	#424	C₂²×C₅₃	1	2	yes	complemented
739	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
740	#418	C₂²×C₅₃	1	2	yes	complemented
741	#418	C₂²×C₅₃	1	2	yes	complemented
742	#416	C₂²×C₅₃	1	2	yes	complemented
743	C₅₃	#62031	1	1	yes	characteristic, direct product factor, Sylow
744	C₂×#41	—	2	1	no	—
745	C₂×#41	—	2	1	no	—
746	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
747	C₂×#41	C₂³×C₅₃	1	2	yes	—
748	C₂²×Q₈	—	2	1	no	—
749	C₂²×D₄	—	2	1	no	—
750	C₂²×D₄	—	2	2	no	—
751	C₂²×D₄	—	2	1	no	—
752	C₂²×D₄	—	2	1	no	—
753	C₂²×D₄	—	2	1	no	—
754	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
755	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
756	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
757	AGL(1,ℤ/8)	—	4	4	no	—
758	AGL(1,ℤ/8)	—	4	4	no	—
759	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
760	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
761	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
762	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
763	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
764	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
765	C₂×D₈	—	4	4	no	—
766	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
767	C₂×D₈	C₂³×C₅₃	1	2	yes	—
768	C₂×D₈	C₂³×C₅₃	1	2	yes	—
769	C₂×D₈	C₂³×C₅₃	1	2	yes	—
770	C₂×D₈	C₂³×C₅₃	1	2	yes	—
771	C₂×D₈	C₂³×C₅₃	1	2	yes	—
772	C₂×D₈	C₂³×C₅₃	1	2	yes	—
773	C₂×D₈	C₂³×C₅₃	1	2	yes	—
774	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
775	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
776	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
777	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
778	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
779	#127	—	2	1	no	—
780	#127	—	2	1	no	—
781	#127	—	2	1	no	—
782	#127	C₂³×C₅₃	1	2	yes	—
783	#127	C₂³×C₅₃	1	1	yes	characteristic
784	#127	C₂³×C₅₃	1	1	yes	characteristic
785	#127	C₂³×C₅₃	1	1	yes	characteristic
786	#127	C₂³×C₅₃	1	2	yes	—
787	#126	—	2	2	no	—
788	#126	—	2	2	no	—
789	#126	—	2	1	no	—
790	#126	D₄×C₅₃	1	2	yes	—
791	#125	D₄×C₅₃	1	1	yes	characteristic
792	#125	C₂³×C₅₃	1	1	yes	characteristic
793	#124	—	2	1	no	—
794	#124	—	2	1	no	—
795	#124	—	2	1	no	—
796	#124	—	2	2	no	—
797	#124	—	2	2	no	—
798	#124	—	2	2	no	—
799	#124	—	2	1	no	—
800	#124	D₄×C₅₃	1	1	yes	characteristic
801	#124	C₂³×C₅₃	1	1	yes	characteristic
802	#124	C₂³×C₅₃	1	2	yes	—
803	#124	C₂³×C₅₃	1	2	yes	—
804	#123	—	2	1	no	—
805	#123	—	2	2	no	—
806	#123	—	2	2	no	—
807	#123	—	2	2	no	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	D₄×C₅₃	1	2	yes	—
813	C₂²⋊Q₈	—	2	1	no	—
814	C₂²⋊Q₈	—	2	2	no	—
815	C₂²⋊Q₈	—	2	2	no	—
816	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
817	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
818	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
819	#121	—	2	2	no	—
820	#121	—	2	1	no	—
821	#121	—	2	1	no	—
822	#121	—	2	2	no	—
823	#121	—	2	2	no	—
824	#121	—	2	2	no	—
825	#121	—	2	1	no	—
826	#121	—	2	1	no	—
827	#121	—	2	2	no	—
828	#121	—	2	2	no	—
829	#121	—	2	2	no	—
830	#121	—	2	2	no	—
831	#121	—	2	2	no	—
832	#121	—	2	2	no	—
833	#121	D₄×C₅₃	1	1	yes	characteristic
834	#121	C₂³×C₅₃	1	1	yes	characteristic
835	#121	C₂³×C₅₃	1	2	yes	—
836	#121	C₂³×C₅₃	1	2	yes	—
837	#121	C₂³×C₅₃	1	2	yes	—
838	#121	C₂³×C₅₃	1	2	yes	—
839	#120	—	2	2	no	—
840	#120	—	2	2	no	—
841	#120	—	2	2	no	—
842	#120	—	2	2	no	—
843	#120	—	2	2	no	—
844	#120	—	2	2	no	—
845	#120	—	2	2	no	—
846	#120	—	2	2	no	—
847	C₄×Q₈	—	2	1	no	—
848	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
849	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
850	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
851	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	2	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
862	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
863	C₄×D₄	C₂³×C₅₃	1	2	yes	—
864	C₄×D₄	C₂³×C₅₃	1	2	yes	—
865	C₄×D₄	C₂³×C₅₃	1	2	yes	—
866	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
867	C₄×D₄	C₂³×C₅₃	1	2	yes	—
868	C₄×D₄	C₂³×C₅₃	1	2	yes	—
869	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
870	C₄×D₄	C₂³×C₅₃	1	2	yes	—
871	#117	—	2	2	no	—
872	#117	—	2	1	no	—
873	#117	—	2	1	no	—
874	#117	C₂³×C₅₃	1	1	yes	characteristic
875	#117	C₂³×C₅₃	1	2	yes	—
876	#117	C₂³×C₅₃	1	2	yes	—
877	C₂×C₂²⋊C₄	—	2	2	no	—
878	C₂×C₂²⋊C₄	—	2	2	no	—
879	C₂×C₂²⋊C₄	—	2	2	no	—
880	C₂×C₂²⋊C₄	—	2	2	no	—
881	C₂×C₄²	—	2	1	no	—
882	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
883	#107	C₂³×C₅₃	1	1	yes	characteristic
884	#107	C₂³×C₅₃	1	1	yes	characteristic
885	#107	C₂³×C₅₃	1	2	yes	—
886	#106	C₂³×C₅₃	1	1	yes	characteristic
887	#106	C₂³×C₅₃	1	1	yes	characteristic
888	#106	C₂³×C₅₃	1	2	yes	—
889	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
890	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
891	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
892	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
893	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
894	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
895	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
896	#103	C₂³×C₅₃	1	1	yes	characteristic
897	#103	C₂³×C₅₃	1	2	yes	—
898	#103	C₂³×C₅₃	1	1	yes	characteristic
899	#103	C₂³×C₅₃	1	1	yes	characteristic
900	#103	C₂³×C₅₃	1	1	yes	characteristic
901	#102	C₂³×C₅₃	1	2	yes	—
902	#102	C₂³×C₅₃	1	2	yes	—
903	#102	C₂³×C₅₃	1	2	yes	—
904	#102	C₂³×C₅₃	1	1	yes	characteristic
905	#102	C₂³×C₅₃	1	2	yes	—
906	#102	C₂³×C₅₃	1	2	yes	—
907	#102	C₂³×C₅₃	1	2	yes	—
908	#102	C₂³×C₅₃	1	2	yes	—
909	#102	C₂³×C₅₃	1	1	yes	characteristic
910	#102	C₂³×C₅₃	1	1	yes	characteristic
911	#102	C₂³×C₅₃	1	2	yes	—
912	#102	C₂³×C₅₃	1	2	yes	—
913	#102	C₂³×C₅₃	1	1	yes	characteristic
914	#102	C₂³×C₅₃	1	2	yes	—
915	#102	C₂³×C₅₃	1	2	yes	—
916	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
917	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
918	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
919	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
920	#97	C₂³×C₅₃	1	2	yes	—
921	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
922	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
923	C₄×C₈	C₂³×C₅₃	1	2	yes	—
924	C₂⁴	—	2	2	no	—
925	C₂⁴	—	2	2	no	—
926	C₂⁴	—	2	2	no	—
927	#41	—	2	2	no	—
928	#41	—	4	1	no	—
929	#41	—	4	2	no	—
930	#41	—	4	2	no	—
931	#41	—	8	2	no	—
932	#41	—	8	2	no	—
933	C₂×Q₈	—	2	1	no	—
934	C₂×Q₈	—	2	2	no	—
935	C₂×Q₈	—	8	2	no	—
936	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
937	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
938	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
939	C₂×D₄	—	2	4	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	1	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	1	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	4	2	no	—
961	C₂×D₄	—	4	2	no	—
962	C₂×D₄	—	4	2	no	—
963	C₂×D₄	—	4	2	no	—
964	C₂×D₄	—	4	2	no	—
965	C₂×D₄	—	8	2	no	—
966	C₂×D₄	—	8	2	no	—
967	C₂×D₄	—	8	2	no	—
968	C₂×D₄	—	8	2	no	—
969	C₂×D₄	—	8	4	no	—
970	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
971	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
972	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
973	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
974	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
975	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
976	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
977	C₂²×C₄	—	2	1	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	2	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
988	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
989	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
990	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
991	Q₁₆	—	4	1	no	—
992	SD₁₆	—	2	2	no	—
993	SD₁₆	—	4	2	no	—
994	SD₁₆	—	4	2	no	—
995	SD₁₆	—	4	2	no	—
996	SD₁₆	—	4	1	no	—
997	D₈	—	2	2	no	—
998	D₈	—	2	4	no	—
999	D₈	—	2	4	no	—
1000	D₈	—	4	2	no	—
1001	D₈	—	4	2	no	—
1002	D₈	—	4	2	no	—
1003	D₈	—	4	2	no	—
1004	D₈	—	4	2	no	—
1005	M₁₆	—	4	2	no	—
1006	M₁₆	—	4	2	no	—
1007	C₂×C₈	—	4	2	no	—
1008	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1009	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1010	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1011	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1012	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1013	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1024	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1025	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1026	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1027	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1028	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1029	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1030	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1031	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1032	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1033	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1058	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1059	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1060	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1061	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1062	C₄²	—	2	1	no	—
1063	C₄²	—	2	1	no	—
1064	C₄²	—	2	1	no	—
1065	C₄²	—	2	2	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1068	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1069	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1070	C₄²	C₂⁴×C₅₃	1	2	yes	—
1071	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1072	C₂³	—	2	1	no	—
1073	C₂³	—	2	2	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	2	2	no	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	4	4	no	—
1078	C₂³	—	4	4	no	—
1079	C₂³	—	8	2	no	—
1080	C₂³	—	8	2	no	—
1081	C₂³	—	8	2	no	—
1082	C₂³	—	8	2	no	—
1083	C₂³	—	8	2	no	—
1084	C₂³	—	8	2	no	—
1085	C₂³	—	8	2	no	—
1086	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1087	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1088	Q₈	—	2	2	no	—
1089	Q₈	—	2	1	no	—
1090	Q₈	—	2	1	no	—
1091	Q₈	—	2	1	no	—
1092	Q₈	—	2	1	no	—
1093	Q₈	—	4	2	no	—
1094	Q₈	—	8	2	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	2	2	no	—
1098	D₄	—	2	2	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	2	2	no	—
1103	D₄	—	2	2	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	4	2	no	—
1106	D₄	—	4	4	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	2	no	—
1109	D₄	—	4	2	no	—
1110	D₄	—	4	2	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	8	1	no	—
1113	D₄	—	8	2	no	—
1114	D₄	—	8	2	no	—
1115	D₄	—	8	2	no	—
1116	D₄	—	8	2	no	—
1117	D₄	—	8	1	no	—
1118	D₄	—	8	1	no	—
1119	D₄	—	8	2	no	—
1120	D₄	—	8	2	no	—
1121	D₄	—	8	2	no	—
1122	D₄	—	8	2	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	8	2	no	—
1125	D₄	—	8	2	no	—
1126	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	2	no	—
1143	C₂×C₄	—	8	1	no	—
1144	C₂×C₄	—	8	2	no	—
1145	C₂×C₄	—	8	2	no	—
1146	C₂×C₄	—	8	2	no	—
1147	C₂×C₄	—	8	2	no	—
1148	C₂×C₄	—	8	2	no	—
1149	C₂×C₄	—	8	2	no	—
1150	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1151	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1152	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1153	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1154	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1155	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1156	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1157	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1158	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1159	C₈	—	2	1	no	—
1160	C₈	—	2	2	no	—
1161	C₈	—	2	2	no	—
1162	C₈	—	2	1	no	—
1163	C₈	—	2	1	no	—
1164	C₈	—	2	1	no	—
1165	C₂²	—	2	1	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	1	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	1	no	—
1171	C₂²	—	2	2	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	4	2	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	16	4	no	—
1187	C₂²	—	16	4	no	—
1188	C₂²	—	16	4	no	—
1189	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1190	C₄	—	2	1	no	—
1191	C₄	—	2	2	no	—
1192	C₄	—	2	1	no	—
1193	C₄	—	2	2	no	—
1194	C₄	—	2	1	no	—
1195	C₄	—	2	1	no	—
1196	C₄	—	2	2	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	1	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	2	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	C₅₃×#576	1	2	yes	—
1205	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1206	C₄	C₅₃×#585	1	1	yes	characteristic
1207	C₂	—	4	1	no	—
1208	C₂	—	4	2	no	—
1209	C₂	—	4	2	no	—
1210	C₂	—	8	1	no	—
1211	C₂	—	8	2	no	—
1212	C₂	—	8	2	no	—
1213	C₂	—	8	2	no	—
1214	C₂	C₅₃×#3488	1	1	yes	characteristic
1215	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1216	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3543	C₂	semidirect
2. C₅₃×#3514	C₂	semidirect
3. C₅₃×#3399	C₂	semidirect
4. C₅₃×#3396	C₂	semidirect
5. C₅₃×#3373	C₂	semidirect
6. C₅₃×#3358	C₂	semidirect
7. C₅₃×#3325	C₂	semidirect
8. C₅₃×#3324	C₂	semidirect
9. C₅₃×#3319	C₂	semidirect
10. C₅₃×#3304	C₂	semidirect
11. D₄×D₈×C₅₃	C₂	semidirect
12. C₅₃×#3274	C₂	semidirect
13. C₅₃×#3273	C₂	semidirect
14. C₅₃×#3264	C₂	semidirect
15. C₅₃×#3257	C₂	semidirect
16. C₅₃×#3251	C₂	semidirect
17. C₅₃×#3224	C₂	semidirect
18. C₅₃×#3205	C₂	semidirect
19. C₅₃×#3122	C₂	semidirect
20. C₅₃×#3102	C₂	semidirect
21. C₅₃×#3041	C₂	semidirect
22. C₅₃×#3038	C₂	semidirect
23. C₅₃×#2993	C₂	semidirect
24. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
26. C₂²×D₈×C₅₃	C₂²	semidirect
28. C₅₃×#559	C₂²	semidirect
29. C₅₃×#559	C₂²	semidirect
30. C₅₃×#556	C₂²	semidirect
31. C₅₃×#555	C₂²	semidirect
34. C₅₃×#550	C₂²	semidirect
35. D₄×Q₈×C₅₃	C₂²	semidirect
39. C₅₃×#546	C₂²	semidirect
40. C₅₃×#546	C₂²	semidirect
43. D₄²×C₅₃	C₂²	semidirect
44. D₄²×C₅₃	C₂²	semidirect
45. C₅₃×#542	C₂²	semidirect
47. C₅₃×#540	C₂²	semidirect
50. C₅₃×#535	C₂²	semidirect
52. C₅₃×#532	C₂²	semidirect
53. C₂×#127×C₅₃	C₂²	semidirect
56. C₅₃×#529	C₂²	semidirect
58. C₅₃×#518	C₂²	semidirect
59. C₄×#41×C₅₃	C₂²	semidirect
60. C₅₃×#496	C₂²	semidirect
61. C₅₃×#495	C₂²	semidirect
63. C₅₃×#493	C₂²	semidirect
64. C₅₃×#489	C₂²	semidirect
65. C₅₃×#486	C₂²	semidirect
66. C₅₃×#486	C₂²	semidirect
67. C₅₃×#486	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#479	C₂²	semidirect
73. C₅₃×#478	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#476	C₂²	semidirect
76. C₅₃×#475	C₂²	semidirect
77. C₅₃×#474	C₂²	semidirect
78. C₅₃×#474	C₂²	semidirect
79. C₅₃×#469	C₂²	semidirect
80. C₅₃×#469	C₂²	semidirect
81. C₅₃×#468	C₂²	semidirect
82. C₅₃×#468	C₂²	semidirect
83. C₅₃×#466	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
85. C₅₃×#464	C₂²	semidirect
86. C₅₃×#463	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#463	C₂²	semidirect
90. C₅₃×#463	C₂²	semidirect
91. C₅₃×#463	C₂²	semidirect
92. C₅₃×#460	C₂²	semidirect
93. C₅₃×#460	C₂²	semidirect
94. C₅₃×#460	C₂²	semidirect
95. C₅₃×#460	C₂²	semidirect
97. C₅₃×#459	C₂²	semidirect
98. C₅₃×#459	C₂²	semidirect
99. C₅₃×#459	C₂²	semidirect
100. C₅₃×#459	C₂²	semidirect
101. C₅₃×#459	C₂²	semidirect
102. C₅₃×#459	C₂²	semidirect
103. C₅₃×#459	C₂²	semidirect
104. C₅₃×#452	C₂²	semidirect
105. C₅₃×#452	C₂²	semidirect
106. C₅₃×#450	C₂²	semidirect
108. C₅₃×#449	C₂²	semidirect
109. C₅₃×#447	C₂²	semidirect
110. C₅₃×#447	C₂²	semidirect
111. C₅₃×#447	C₂²	semidirect
112. C₅₃×#447	C₂²	semidirect
113. C₅₃×#447	C₂²	semidirect
114. C₅₃×#446	C₂²	semidirect
115. C₈×Q₈×C₅₃	C₂²	semidirect
116. C₅₃×#442	C₂²	semidirect
117. C₅₃×#442	C₂²	semidirect
118. C₄×Q₁₆×C₅₃	C₂²	semidirect
119. C₄×SD₁₆×C₅₃	C₂²	semidirect
120. C₄×SD₁₆×C₅₃	C₂²	semidirect
121. C₄×D₈×C₅₃	C₂²	semidirect
122. C₄×D₈×C₅₃	C₂²	semidirect
123. C₄×D₈×C₅₃	C₂²	semidirect
124. C₅₃×#436	C₂²	semidirect
125. C₅₃×#436	C₂²	semidirect
126. C₅₃×#435	C₂²	semidirect
127. C₈×D₄×C₅₃	C₂²	semidirect
128. C₅₃×#433	C₂²	semidirect
129. C₅₃×#431	C₂²	semidirect
130. C₅₃×#424	C₂²	semidirect
131. C₅₃×#423	C₂²	semidirect
132. C₅₃×#418	C₂²	semidirect
133. C₅₃×#418	C₂²	semidirect
134. C₅₃×#416	C₂²	semidirect
556. #62031	C₅₃	direct (N × H)
599. #3543	C₂×C₅₃	semidirect
600. #3514	C₂×C₅₃	semidirect
601. #3399	C₂×C₅₃	semidirect
602. #3396	C₂×C₅₃	semidirect
603. #3373	C₂×C₅₃	semidirect
604. #3358	C₂×C₅₃	semidirect
605. #3325	C₂×C₅₃	semidirect
606. #3324	C₂×C₅₃	semidirect
607. #3319	C₂×C₅₃	semidirect
608. #3304	C₂×C₅₃	semidirect
609. D₄×D₈	C₂×C₅₃	semidirect
610. #3274	C₂×C₅₃	semidirect
611. #3273	C₂×C₅₃	semidirect
612. #3264	C₂×C₅₃	semidirect
613. #3257	C₂×C₅₃	semidirect
614. #3251	C₂×C₅₃	semidirect
615. #3224	C₂×C₅₃	semidirect
616. #3205	C₂×C₅₃	semidirect
617. #3122	C₂×C₅₃	semidirect
618. #3102	C₂×C₅₃	semidirect
619. #3041	C₂×C₅₃	semidirect
620. #3038	C₂×C₅₃	semidirect
621. #2993	C₂×C₅₃	semidirect
632. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
633. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
634. C₂²×D₈	C₂²×C₅₃	semidirect
636. #559	C₂²×C₅₃	semidirect
637. #559	C₂²×C₅₃	semidirect
638. #556	C₂²×C₅₃	semidirect
639. #555	C₂²×C₅₃	semidirect
642. #550	C₂²×C₅₃	semidirect
643. D₄×Q₈	C₂²×C₅₃	semidirect
647. #546	C₂²×C₅₃	semidirect
648. #546	C₂²×C₅₃	semidirect
651. D₄²	C₂²×C₅₃	semidirect
652. D₄²	C₂²×C₅₃	semidirect
653. #542	C₂²×C₅₃	semidirect
655. #540	C₂²×C₅₃	semidirect
658. #535	C₂²×C₅₃	semidirect
660. #532	C₂²×C₅₃	semidirect
661. C₂×#127	C₂²×C₅₃	semidirect
664. #529	C₂²×C₅₃	semidirect
666. #518	C₂²×C₅₃	semidirect
667. C₄×#41	C₂²×C₅₃	semidirect
668. #496	C₂²×C₅₃	semidirect
669. #495	C₂²×C₅₃	semidirect
671. #493	C₂²×C₅₃	semidirect
672. #489	C₂²×C₅₃	semidirect
673. #486	C₂²×C₅₃	semidirect
674. #486	C₂²×C₅₃	semidirect
675. #486	C₂²×C₅₃	semidirect
676. #485	C₂²×C₅₃	semidirect
677. #482	C₂²×C₅₃	semidirect
678. #482	C₂²×C₅₃	semidirect
679. #482	C₂²×C₅₃	semidirect
680. #479	C₂²×C₅₃	semidirect
681. #478	C₂²×C₅₃	semidirect
682. #478	C₂²×C₅₃	semidirect
683. #476	C₂²×C₅₃	semidirect
684. #475	C₂²×C₅₃	semidirect
685. #474	C₂²×C₅₃	semidirect
686. #474	C₂²×C₅₃	semidirect
687. #469	C₂²×C₅₃	semidirect
688. #469	C₂²×C₅₃	semidirect
689. #468	C₂²×C₅₃	semidirect
690. #468	C₂²×C₅₃	semidirect
691. #466	C₂²×C₅₃	semidirect
692. #465	C₂²×C₅₃	semidirect
693. #464	C₂²×C₅₃	semidirect
694. #463	C₂²×C₅₃	semidirect
695. #463	C₂²×C₅₃	semidirect
696. #463	C₂²×C₅₃	semidirect
697. #463	C₂²×C₅₃	semidirect
698. #463	C₂²×C₅₃	semidirect
699. #463	C₂²×C₅₃	semidirect
700. #460	C₂²×C₅₃	semidirect
701. #460	C₂²×C₅₃	semidirect
702. #460	C₂²×C₅₃	semidirect
703. #460	C₂²×C₅₃	semidirect
705. #459	C₂²×C₅₃	semidirect
706. #459	C₂²×C₅₃	semidirect
707. #459	C₂²×C₅₃	semidirect
708. #459	C₂²×C₅₃	semidirect
709. #459	C₂²×C₅₃	semidirect
710. #459	C₂²×C₅₃	semidirect
711. #459	C₂²×C₅₃	semidirect
712. #452	C₂²×C₅₃	semidirect
713. #452	C₂²×C₅₃	semidirect
714. #450	C₂²×C₅₃	semidirect
716. #449	C₂²×C₅₃	semidirect
717. #447	C₂²×C₅₃	semidirect
718. #447	C₂²×C₅₃	semidirect
719. #447	C₂²×C₅₃	semidirect
720. #447	C₂²×C₅₃	semidirect
721. #447	C₂²×C₅₃	semidirect
722. #446	C₂²×C₅₃	semidirect
723. C₈×Q₈	C₂²×C₅₃	semidirect
724. #442	C₂²×C₅₃	semidirect
725. #442	C₂²×C₅₃	semidirect
726. C₄×Q₁₆	C₂²×C₅₃	semidirect
727. C₄×SD₁₆	C₂²×C₅₃	semidirect
728. C₄×SD₁₆	C₂²×C₅₃	semidirect
729. C₄×D₈	C₂²×C₅₃	semidirect
730. C₄×D₈	C₂²×C₅₃	semidirect
731. C₄×D₈	C₂²×C₅₃	semidirect
732. #436	C₂²×C₅₃	semidirect
733. #436	C₂²×C₅₃	semidirect
734. #435	C₂²×C₅₃	semidirect
735. C₈×D₄	C₂²×C₅₃	semidirect
736. #433	C₂²×C₅₃	semidirect
737. #431	C₂²×C₅₃	semidirect
738. #424	C₂²×C₅₃	semidirect
739. #423	C₂²×C₅₃	semidirect
740. #418	C₂²×C₅₃	semidirect
741. #418	C₂²×C₅₃	semidirect
742. #416	C₂²×C₅₃	semidirect
743. C₅₃	#62031	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×#3543	2
C₅₃×#3514	2
C₅₃×#3399	2
C₅₃×#3396	2
C₅₃×#3373	2
C₅₃×#3358	2
C₅₃×#3325	2
C₅₃×#3324	2
C₅₃×#3319	2
C₅₃×#3304	2
D₄×D₈×C₅₃	2
C₅₃×#3274	2
C₅₃×#3273	2
C₅₃×#3264	2
C₅₃×#3257	2
C₅₃×#3251	2
C₅₃×#3224	2
C₅₃×#3205	2
C₅₃×#3122	2
C₅₃×#3102	2
C₅₃×#3041	2
C₅₃×#3038	2
C₅₃×#2993	2
#62031	53

Subgroups — C53×#62031 #27269543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62031 #27269543