Subgroups — C₅₃×#61539 #27269051

Order 13568.

1950 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3519	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×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3347	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3325	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3322	C₂	1	2	yes	maximal, complemented
13	D₄×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3179	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3122	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2948	C₂	1	2	yes	maximal, complemented
23	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₅₃	C₂²	1	2	yes	—
26	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
27	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×#555	C₂²	1	1	yes	characteristic
29	C₅₃×#555	C₂²	1	2	yes	complemented
30	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#553	—	2	1	no	—
32	C₅₃×#553	C₂²	1	2	yes	complemented
33	C₅₃×#551	—	2	2	no	—
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	2	no	—
39	C₅₃×#546	—	2	1	no	—
40	C₅₃×#546	C₂²	1	2	yes	complemented
41	D₄²×C₅₃	C₂²	1	1	yes	characteristic
42	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	D₄²×C₅₃	C₂²	1	2	yes	complemented
44	C₅₃×#542	C₂²	1	2	yes	complemented
45	C₅₃×#540	C₂²	1	2	yes	complemented
46	C₅₃×#538	—	2	2	no	—
47	C₅₃×#538	—	2	2	no	—
48	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#529	—	2	1	no	—
51	C₅₃×#529	C₂²	1	1	yes	characteristic
52	C₂×#124×C₅₃	—	2	1	no	—
53	C₅₃×#525	—	2	1	no	—
54	C₂×#121×C₅₃	—	2	1	no	—
55	C₅₃×#518	C₂²	1	2	yes	complemented
56	C₅₃×#518	C₂²	1	2	yes	complemented
57	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#501	C₂²	1	2	yes	complemented
60	C₅₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#496	C₂²	1	2	yes	complemented
62	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#488	C₂²	1	2	yes	complemented
64	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#486	C₂²	1	2	yes	complemented
66	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#485	C₂²	1	2	yes	complemented
68	C₅₃×#482	C₂²	1	2	yes	complemented
69	C₅₃×#482	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#482	C₂²	1	2	yes	complemented
72	C₅₃×#480	C₂²	1	2	yes	complemented
73	C₅₃×#478	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	2	yes	complemented
75	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#476	C₂²	1	2	yes	complemented
78	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#474	C₂²	1	2	yes	complemented
81	C₅₃×#469	C₂²	1	2	yes	complemented
82	C₅₃×#469	C₂²	1	2	yes	complemented
83	C₅₃×#469	C₂²	1	2	yes	complemented
84	C₅₃×#468	C₂²	1	2	yes	complemented
85	C₅₃×#466	C₂²	1	2	yes	complemented
86	C₅₃×#465	C₂²	1	2	yes	complemented
87	C₅₃×#463	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	2	yes	complemented
89	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#459	C₂²	1	1	yes	characteristic
91	C₅₃×#459	C₂²	1	2	yes	complemented
92	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#459	C₂²	1	2	yes	complemented
95	C₅₃×#450	C₂²	1	2	yes	complemented
96	C₅₃×#449	C₂²	1	2	yes	complemented
97	C₅₃×#447	C₂²	1	2	yes	—
98	C₅₃×#447	C₂²	1	2	yes	complemented
99	C₅₃×#447	C₂²	1	2	yes	complemented
100	C₅₃×#447	C₂²	1	2	yes	complemented
101	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#442	C₂²	1	1	yes	characteristic
104	C₅₃×#442	C₂²	1	2	yes	—
105	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#442	C₂²	1	2	yes	complemented
107	C₅₃×#442	C₂²	1	2	yes	complemented
108	C₅₃×#442	C₂²	1	2	yes	complemented
109	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
114	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
115	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
117	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
118	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
119	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
120	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
121	C₅₃×#436	C₂²	1	2	yes	complemented
122	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#433	C₂²	1	2	yes	complemented
126	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#427	C₂²	1	2	yes	complemented
129	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#418	C₂²	1	2	yes	complemented
131	C₅₃×#418	C₂²	1	2	yes	complemented
132	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#405	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	1	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
145	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
146	C₂³×C₄×C₅₃	—	2	1	no	—
147	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
148	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂×D₈×C₅₃	—	2	8	no	—
152	C₂×D₈×C₅₃	C₂³	1	2	yes	—
153	C₂×D₈×C₅₃	C₂³	1	2	yes	—
154	C₂×D₈×C₅₃	C₂³	1	2	yes	—
155	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
156	C₂×D₈×C₅₃	C₂³	1	2	yes	—
157	C₂×D₈×C₅₃	C₂³	1	2	yes	—
158	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
162	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
166	#127×C₅₃	C₂³	1	1	yes	characteristic
167	#127×C₅₃	C₂³	1	1	yes	characteristic
168	#127×C₅₃	C₂³	1	2	yes	—
169	#126×C₅₃	—	2	2	no	—
170	#126×C₅₃	—	2	2	no	—
171	#126×C₅₃	—	2	2	no	—
172	#126×C₅₃	D₄	1	2	yes	—
173	#125×C₅₃	D₄	1	1	yes	characteristic
174	#125×C₅₃	C₂³	1	2	yes	—
175	#124×C₅₃	—	2	2	no	—
176	#124×C₅₃	—	2	2	no	—
177	#124×C₅₃	—	2	2	no	—
178	#124×C₅₃	—	2	2	no	—
179	#124×C₅₃	—	2	1	no	—
180	#124×C₅₃	—	2	1	no	—
181	#124×C₅₃	—	2	1	no	—
182	#124×C₅₃	—	2	1	no	—
183	#124×C₅₃	D₄	1	1	yes	characteristic
184	#124×C₅₃	C₂³	1	2	yes	—
185	#123×C₅₃	—	2	2	no	—
186	#123×C₅₃	—	2	2	no	—
187	#123×C₅₃	—	2	2	no	—
188	#123×C₅₃	—	2	2	no	—
189	#123×C₅₃	—	2	2	no	—
190	#123×C₅₃	—	2	2	no	—
191	#123×C₅₃	D₄	1	2	yes	—
192	C₂²⋊Q₈×C₅₃	—	2	1	no	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	2	no	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	1	no	—
197	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
198	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
199	#121×C₅₃	—	2	1	no	—
200	#121×C₅₃	—	2	1	no	—
201	#121×C₅₃	—	2	1	no	—
202	#121×C₅₃	—	2	2	no	—
203	#121×C₅₃	—	2	2	no	—
204	#121×C₅₃	—	2	2	no	—
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	2	no	—
207	#121×C₅₃	—	2	2	no	—
208	#121×C₅₃	—	2	1	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	1	no	—
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	D₄	1	1	yes	characteristic
213	#121×C₅₃	C₂³	1	2	yes	—
214	#121×C₅₃	C₂³	1	2	yes	—
215	#121×C₅₃	C₂³	1	2	yes	—
216	#121×C₅₃	C₂³	1	2	yes	—
217	#121×C₅₃	C₂³	1	2	yes	—
218	#120×C₅₃	—	2	2	no	—
219	#120×C₅₃	—	2	2	no	—
220	#120×C₅₃	—	2	2	no	—
221	#120×C₅₃	—	2	2	no	—
222	#120×C₅₃	—	2	2	no	—
223	C₄×Q₈×C₅₃	—	2	1	no	—
224	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	—	2	2	no	—
229	C₄×D₄×C₅₃	—	2	2	no	—
230	C₄×D₄×C₅₃	—	2	2	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	2	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	1	no	—
235	C₄×D₄×C₅₃	—	2	1	no	—
236	C₄×D₄×C₅₃	—	2	1	no	—
237	C₄×D₄×C₅₃	—	2	1	no	—
238	C₄×D₄×C₅₃	—	2	1	no	—
239	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₅₃	C₂³	1	2	yes	—
246	C₄×D₄×C₅₃	C₂³	1	2	yes	—
247	C₄×D₄×C₅₃	C₂³	1	2	yes	—
248	C₄×D₄×C₅₃	C₂³	1	2	yes	—
249	C₄×D₄×C₅₃	C₂³	1	2	yes	—
250	C₄×D₄×C₅₃	C₂³	1	2	yes	—
251	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₅₃	C₂³	1	2	yes	—
253	#117×C₅₃	—	2	1	no	—
254	#117×C₅₃	—	2	2	no	—
255	#117×C₅₃	—	2	1	no	—
256	#117×C₅₃	C₂³	1	2	yes	—
257	#117×C₅₃	C₂³	1	1	yes	characteristic
258	#117×C₅₃	C₂³	1	2	yes	—
259	#117×C₅₃	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
263	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
268	C₂×C₄²×C₅₃	—	2	1	no	—
269	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
270	#107×C₅₃	C₂³	1	2	yes	—
271	#107×C₅₃	C₂³	1	1	yes	characteristic
272	#107×C₅₃	C₂³	1	2	yes	—
273	#107×C₅₃	C₂³	1	2	yes	—
274	#107×C₅₃	C₂³	1	1	yes	characteristic
275	#106×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	2	yes	—
277	#106×C₅₃	C₂³	1	2	yes	—
278	#106×C₅₃	C₂³	1	1	yes	characteristic
279	#106×C₅₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
284	#103×C₅₃	C₂³	1	1	yes	characteristic
285	#103×C₅₃	C₂³	1	2	yes	—
286	#103×C₅₃	C₂³	1	1	yes	characteristic
287	#102×C₅₃	C₂³	1	1	yes	characteristic
288	#102×C₅₃	C₂³	1	2	yes	—
289	#102×C₅₃	C₂³	1	2	yes	—
290	#102×C₅₃	C₂³	1	2	yes	—
291	#102×C₅₃	C₂³	1	2	yes	—
292	#102×C₅₃	C₂³	1	2	yes	—
293	#102×C₅₃	C₂³	1	2	yes	—
294	#102×C₅₃	C₂³	1	2	yes	—
295	#102×C₅₃	C₂³	1	1	yes	characteristic
296	#102×C₅₃	C₂³	1	1	yes	characteristic
297	#102×C₅₃	C₂³	1	1	yes	characteristic
298	#102×C₅₃	C₂³	1	1	yes	characteristic
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	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
307	#97×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	1	yes	characteristic
309	#97×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₃	C₂³	1	2	yes	—
312	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₅₃	C₂³	1	2	yes	—
314	C₂⁴×C₅₃	—	2	1	no	—
315	C₂⁴×C₅₃	—	2	2	no	—
316	C₂⁴×C₅₃	—	2	2	no	—
317	#41×C₅₃	—	2	2	no	—
318	#41×C₅₃	—	4	1	no	—
319	#41×C₅₃	—	8	2	no	—
320	#41×C₅₃	—	8	2	no	—
321	#41×C₅₃	—	8	2	no	—
322	C₂×Q₈×C₅₃	—	2	1	no	—
323	C₂×Q₈×C₅₃	—	2	2	no	—
324	C₂×Q₈×C₅₃	—	2	1	no	—
325	C₂×Q₈×C₅₃	—	8	2	no	—
326	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₅₃	—	2	4	no	—
329	C₂×D₄×C₅₃	—	2	4	no	—
330	C₂×D₄×C₅₃	—	2	2	no	—
331	C₂×D₄×C₅₃	—	2	1	no	—
332	C₂×D₄×C₅₃	—	2	2	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	1	no	—
338	C₂×D₄×C₅₃	—	2	2	no	—
339	C₂×D₄×C₅₃	—	2	2	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	1	no	—
345	C₂×D₄×C₅₃	—	2	2	no	—
346	C₂×D₄×C₅₃	—	4	2	no	—
347	C₂×D₄×C₅₃	—	4	2	no	—
348	C₂×D₄×C₅₃	—	4	1	no	—
349	C₂×D₄×C₅₃	—	8	2	no	—
350	C₂×D₄×C₅₃	—	8	2	no	—
351	C₂×D₄×C₅₃	—	8	4	no	—
352	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
353	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
354	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
355	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
356	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₅₃	—	2	1	no	—
360	C₂²×C₄×C₅₃	—	2	1	no	—
361	C₂²×C₄×C₅₃	—	2	1	no	—
362	C₂²×C₄×C₅₃	—	2	1	no	—
363	C₂²×C₄×C₅₃	—	2	1	no	—
364	C₂²×C₄×C₅₃	—	2	1	no	—
365	C₂²×C₄×C₅₃	—	2	1	no	—
366	C₂²×C₄×C₅₃	—	2	2	no	—
367	C₂²×C₄×C₅₃	—	2	2	no	—
368	C₂²×C₄×C₅₃	—	2	2	no	—
369	C₂²×C₄×C₅₃	—	2	2	no	—
370	C₂²×C₄×C₅₃	—	2	2	no	—
371	C₂²×C₄×C₅₃	—	2	2	no	—
372	C₂²×C₄×C₅₃	—	2	1	no	—
373	C₂²×C₄×C₅₃	—	8	2	no	—
374	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
378	SD₁₆×C₅₃	—	2	2	no	—
379	SD₁₆×C₅₃	—	2	2	no	—
380	SD₁₆×C₅₃	—	4	2	no	—
381	D₈×C₅₃	—	2	4	no	—
382	D₈×C₅₃	—	2	4	no	—
383	D₈×C₅₃	—	2	2	no	—
384	D₈×C₅₃	—	2	4	no	—
385	D₈×C₅₃	—	4	2	no	—
386	D₈×C₅₃	—	4	2	no	—
387	D₈×C₅₃	#41	1	4	yes	complemented
388	M₁₆×C₅₃	—	2	2	no	—
389	M₁₆×C₅₃	—	4	1	no	—
390	M₁₆×C₅₃	—	4	2	no	—
391	C₂×C₈×C₅₃	—	2	4	no	—
392	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
394	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
396	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₅₃	—	2	1	no	—
399	C₄⋊C₄×C₅₃	—	2	2	no	—
400	C₄⋊C₄×C₅₃	—	2	1	no	—
401	C₄⋊C₄×C₅₃	—	2	1	no	—
402	C₄⋊C₄×C₅₃	—	2	1	no	—
403	C₄⋊C₄×C₅₃	—	2	2	no	—
404	C₄⋊C₄×C₅₃	—	2	2	no	—
405	C₄⋊C₄×C₅₃	—	2	1	no	—
406	C₄⋊C₄×C₅₃	—	2	2	no	—
407	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	1	no	—
423	C₂²⋊C₄×C₅₃	—	2	1	no	—
424	C₂²⋊C₄×C₅₃	—	2	1	no	—
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	2	no	—
429	C₂²⋊C₄×C₅₃	—	2	2	no	—
430	C₂²⋊C₄×C₅₃	—	2	1	no	—
431	C₂²⋊C₄×C₅₃	—	2	2	no	—
432	C₂²⋊C₄×C₅₃	—	2	1	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	1	no	—
437	C₂²⋊C₄×C₅₃	—	2	2	no	—
438	C₂²⋊C₄×C₅₃	—	2	2	no	—
439	C₂²⋊C₄×C₅₃	—	2	2	no	—
440	C₂²⋊C₄×C₅₃	—	2	2	no	—
441	C₂²⋊C₄×C₅₃	—	2	2	no	—
442	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
447	C₄²×C₅₃	—	2	1	no	—
448	C₄²×C₅₃	—	2	1	no	—
449	C₄²×C₅₃	—	2	1	no	—
450	C₄²×C₅₃	—	2	2	no	—
451	C₄²×C₅₃	—	2	2	no	—
452	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
455	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
456	C₄²×C₅₃	C₂⁴	1	2	yes	—
457	C₂³×C₅₃	—	2	1	no	—
458	C₂³×C₅₃	—	2	1	no	—
459	C₂³×C₅₃	—	2	2	no	—
460	C₂³×C₅₃	—	2	1	no	—
461	C₂³×C₅₃	—	2	2	no	—
462	C₂³×C₅₃	—	4	2	no	—
463	C₂³×C₅₃	—	4	4	no	—
464	C₂³×C₅₃	—	4	4	no	—
465	C₂³×C₅₃	—	4	2	no	—
466	C₂³×C₅₃	—	8	1	no	—
467	C₂³×C₅₃	—	8	2	no	—
468	C₂³×C₅₃	—	8	2	no	—
469	C₂³×C₅₃	—	8	2	no	—
470	C₂³×C₅₃	—	8	2	no	—
471	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
472	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
473	Q₈×C₅₃	—	2	2	no	—
474	Q₈×C₅₃	—	2	1	no	—
475	Q₈×C₅₃	—	2	1	no	—
476	Q₈×C₅₃	—	4	2	no	—
477	Q₈×C₅₃	—	8	2	no	—
478	Q₈×C₅₃	—	8	1	no	—
479	D₄×C₅₃	—	2	2	no	—
480	D₄×C₅₃	—	2	2	no	—
481	D₄×C₅₃	—	2	2	no	—
482	D₄×C₅₃	—	2	1	no	—
483	D₄×C₅₃	—	2	1	no	—
484	D₄×C₅₃	—	2	1	no	—
485	D₄×C₅₃	—	2	2	no	—
486	D₄×C₅₃	—	2	1	no	—
487	D₄×C₅₃	—	2	2	no	—
488	D₄×C₅₃	—	4	2	no	—
489	D₄×C₅₃	—	4	2	no	—
490	D₄×C₅₃	—	4	4	no	—
491	D₄×C₅₃	—	4	4	no	—
492	D₄×C₅₃	—	4	2	no	—
493	D₄×C₅₃	—	4	4	no	—
494	D₄×C₅₃	—	4	2	no	—
495	D₄×C₅₃	—	4	2	no	—
496	D₄×C₅₃	—	8	1	no	—
497	D₄×C₅₃	—	8	2	no	—
498	D₄×C₅₃	—	8	1	no	—
499	D₄×C₅₃	—	8	2	no	—
500	D₄×C₅₃	—	8	2	no	—
501	D₄×C₅₃	—	8	2	no	—
502	D₄×C₅₃	—	8	2	no	—
503	D₄×C₅₃	—	8	2	no	—
504	D₄×C₅₃	C₂×#41	1	2	yes	—
505	D₄×C₅₃	C₂×#41	1	2	yes	—
506	C₂×C₄×C₅₃	—	2	2	no	—
507	C₂×C₄×C₅₃	—	2	2	no	—
508	C₂×C₄×C₅₃	—	2	1	no	—
509	C₂×C₄×C₅₃	—	2	2	no	—
510	C₂×C₄×C₅₃	—	2	1	no	—
511	C₂×C₄×C₅₃	—	2	1	no	—
512	C₂×C₄×C₅₃	—	2	1	no	—
513	C₂×C₄×C₅₃	—	2	1	no	—
514	C₂×C₄×C₅₃	—	2	2	no	—
515	C₂×C₄×C₅₃	—	2	2	no	—
516	C₂×C₄×C₅₃	—	2	1	no	—
517	C₂×C₄×C₅₃	—	2	1	no	—
518	C₂×C₄×C₅₃	—	4	1	no	—
519	C₂×C₄×C₅₃	—	4	2	no	—
520	C₂×C₄×C₅₃	—	4	2	no	—
521	C₂×C₄×C₅₃	—	4	2	no	—
522	C₂×C₄×C₅₃	—	4	2	no	—
523	C₂×C₄×C₅₃	—	8	1	no	—
524	C₂×C₄×C₅₃	—	8	2	no	—
525	C₂×C₄×C₅₃	—	8	1	no	—
526	C₂×C₄×C₅₃	—	8	1	no	—
527	C₂×C₄×C₅₃	—	8	2	no	—
528	C₂×C₄×C₅₃	—	8	2	no	—
529	C₂×C₄×C₅₃	—	8	2	no	—
530	C₂×C₄×C₅₃	—	8	2	no	—
531	C₂×C₄×C₅₃	—	8	2	no	—
532	C₂×C₄×C₅₃	—	8	1	no	—
533	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
542	C₈×C₅₃	—	2	2	no	—
543	C₈×C₅₃	—	2	1	no	—
544	C₈×C₅₃	—	2	1	no	—
545	C₈×C₅₃	—	2	1	no	—
546	C₈×C₅₃	—	2	2	no	—
547	C₈×C₅₃	C₂×#41	1	2	yes	—
548	#61539	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
549	C₂²×C₅₃	—	2	1	no	—
550	C₂²×C₅₃	—	2	2	no	—
551	C₂²×C₅₃	—	2	1	no	—
552	C₂²×C₅₃	—	2	2	no	—
553	C₂²×C₅₃	—	2	2	no	—
554	C₂²×C₅₃	—	2	2	no	—
555	C₂²×C₅₃	—	2	1	no	—
556	C₂²×C₅₃	—	2	2	no	—
557	C₂²×C₅₃	—	4	1	no	—
558	C₂²×C₅₃	—	4	1	no	—
559	C₂²×C₅₃	—	4	1	no	—
560	C₂²×C₅₃	—	4	1	no	—
561	C₂²×C₅₃	—	4	2	no	—
562	C₂²×C₅₃	—	4	2	no	—
563	C₂²×C₅₃	—	4	1	no	—
564	C₂²×C₅₃	—	4	1	no	—
565	C₂²×C₅₃	—	4	2	no	—
566	C₂²×C₅₃	—	4	2	no	—
567	C₂²×C₅₃	—	4	1	no	—
568	C₂²×C₅₃	—	4	2	no	—
569	C₂²×C₅₃	—	4	2	no	—
570	C₂²×C₅₃	—	8	4	no	—
571	C₂²×C₅₃	—	16	4	no	—
572	C₂²×C₅₃	—	16	4	no	—
573	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
574	C₄×C₅₃	—	2	1	no	—
575	C₄×C₅₃	—	2	1	no	—
576	C₄×C₅₃	—	2	2	no	—
577	C₄×C₅₃	—	2	1	no	—
578	C₄×C₅₃	—	2	2	no	—
579	C₄×C₅₃	—	2	1	no	—
580	C₄×C₅₃	—	2	2	no	—
581	C₄×C₅₃	—	4	1	no	—
582	C₄×C₅₃	—	4	2	no	—
583	C₄×C₅₃	—	4	1	no	—
584	C₄×C₅₃	—	4	1	no	—
585	C₄×C₅₃	—	4	1	no	—
586	C₄×C₅₃	—	4	1	no	—
587	C₄×C₅₃	—	4	2	no	—
588	C₄×C₅₃	#576	1	2	yes	—
589	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
590	C₄×C₅₃	#585	1	1	yes	characteristic
591	#3519	C₂×C₅₃	1	1	yes	characteristic, complemented
592	#3514	C₂×C₅₃	1	1	yes	characteristic, complemented
593	#3399	C₂×C₅₃	1	1	yes	characteristic, complemented
594	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
595	#3361	C₂×C₅₃	1	1	yes	characteristic, complemented
596	#3358	C₂×C₅₃	1	1	yes	characteristic, complemented
597	#3347	C₂×C₅₃	1	2	yes	complemented
598	#3340	C₂×C₅₃	1	1	yes	characteristic, complemented
599	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
600	#3325	C₂×C₅₃	1	2	yes	complemented
601	#3324	C₂×C₅₃	1	1	yes	characteristic, complemented
602	#3322	C₂×C₅₃	1	2	yes	complemented
603	D₄×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
604	#3264	C₂×C₅₃	1	2	yes	complemented
605	#3184	C₂×C₅₃	1	1	yes	characteristic, complemented
606	#3179	C₂×C₅₃	1	2	yes	complemented
607	#3122	C₂×C₅₃	1	2	yes	complemented
608	#3118	C₂×C₅₃	1	2	yes	complemented
609	#3106	C₂×C₅₃	1	1	yes	characteristic, complemented
610	#3100	C₂×C₅₃	1	1	yes	characteristic, complemented
611	#2969	C₂×C₅₃	1	1	yes	characteristic, complemented
612	#2948	C₂×C₅₃	1	2	yes	complemented
613	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	1	yes	characteristic, complemented
614	C₂×C₅₃	—	4	1	no	—
615	C₂×C₅₃	—	4	2	no	—
616	C₂×C₅₃	—	4	2	no	—
617	C₂×C₅₃	—	4	2	no	—
618	C₂×C₅₃	—	8	1	no	—
619	C₂×C₅₃	—	8	2	no	—
620	C₂×C₅₃	—	8	2	no	—
621	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
622	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
623	C₂×C₅₃	#3585	1	1	yes	characteristic
624	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
625	C₂²×D₈	C₂²×C₅₃	1	2	yes	—
626	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
627	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
628	#555	C₂²×C₅₃	1	1	yes	characteristic
629	#555	C₂²×C₅₃	1	2	yes	complemented
630	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
631	#553	—	2	1	no	—
632	#553	C₂²×C₅₃	1	2	yes	complemented
633	#551	—	2	2	no	—
634	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
635	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
636	#548	—	2	1	no	—
637	#546	—	2	1	no	—
638	#546	—	2	2	no	—
639	#546	—	2	1	no	—
640	#546	C₂²×C₅₃	1	2	yes	complemented
641	D₄²	C₂²×C₅₃	1	1	yes	characteristic
642	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
643	D₄²	C₂²×C₅₃	1	2	yes	complemented
644	#542	C₂²×C₅₃	1	2	yes	complemented
645	#540	C₂²×C₅₃	1	2	yes	complemented
646	#538	—	2	2	no	—
647	#538	—	2	2	no	—
648	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
649	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
650	#529	—	2	1	no	—
651	#529	C₂²×C₅₃	1	1	yes	characteristic
652	C₂×#124	—	2	1	no	—
653	#525	—	2	1	no	—
654	C₂×#121	—	2	1	no	—
655	#518	C₂²×C₅₃	1	2	yes	complemented
656	#518	C₂²×C₅₃	1	2	yes	complemented
657	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
658	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	#501	C₂²×C₅₃	1	2	yes	complemented
660	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
661	#496	C₂²×C₅₃	1	2	yes	complemented
662	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	#488	C₂²×C₅₃	1	2	yes	complemented
664	#486	C₂²×C₅₃	1	2	yes	complemented
665	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
666	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
667	#485	C₂²×C₅₃	1	2	yes	complemented
668	#482	C₂²×C₅₃	1	2	yes	complemented
669	#482	C₂²×C₅₃	1	2	yes	complemented
670	#482	C₂²×C₅₃	1	2	yes	complemented
671	#482	C₂²×C₅₃	1	2	yes	complemented
672	#480	C₂²×C₅₃	1	2	yes	complemented
673	#478	C₂²×C₅₃	1	2	yes	complemented
674	#478	C₂²×C₅₃	1	2	yes	complemented
675	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
676	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
677	#476	C₂²×C₅₃	1	2	yes	complemented
678	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
679	#474	C₂²×C₅₃	1	2	yes	complemented
680	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	#469	C₂²×C₅₃	1	2	yes	complemented
682	#469	C₂²×C₅₃	1	2	yes	complemented
683	#469	C₂²×C₅₃	1	2	yes	complemented
684	#468	C₂²×C₅₃	1	2	yes	complemented
685	#466	C₂²×C₅₃	1	2	yes	complemented
686	#465	C₂²×C₅₃	1	2	yes	complemented
687	#463	C₂²×C₅₃	1	2	yes	complemented
688	#463	C₂²×C₅₃	1	2	yes	complemented
689	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	#459	C₂²×C₅₃	1	1	yes	characteristic
691	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#459	C₂²×C₅₃	1	2	yes	complemented
694	#459	C₂²×C₅₃	1	2	yes	complemented
695	#450	C₂²×C₅₃	1	2	yes	complemented
696	#449	C₂²×C₅₃	1	2	yes	complemented
697	#447	C₂²×C₅₃	1	2	yes	—
698	#447	C₂²×C₅₃	1	2	yes	complemented
699	#447	C₂²×C₅₃	1	2	yes	complemented
700	#447	C₂²×C₅₃	1	2	yes	complemented
701	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
702	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	#442	C₂²×C₅₃	1	2	yes	—
704	#442	C₂²×C₅₃	1	1	yes	characteristic
705	#442	C₂²×C₅₃	1	2	yes	complemented
706	#442	C₂²×C₅₃	1	2	yes	complemented
707	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	#442	C₂²×C₅₃	1	2	yes	complemented
709	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
710	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
711	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
714	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
715	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
716	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
717	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
718	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
719	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
720	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
721	#436	C₂²×C₅₃	1	2	yes	complemented
722	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	#435	C₂²×C₅₃	1	2	yes	complemented
724	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
725	#433	C₂²×C₅₃	1	2	yes	complemented
726	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
727	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
728	#427	C₂²×C₅₃	1	2	yes	complemented
729	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
730	#418	C₂²×C₅₃	1	2	yes	complemented
731	#418	C₂²×C₅₃	1	2	yes	complemented
732	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
733	#405	C₂²×C₅₃	1	2	yes	complemented
734	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
735	C₅₃	#61539	1	1	yes	characteristic, direct product factor, Sylow
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
740	C₂²×Q₈	—	2	1	no	—
741	C₂²×D₄	—	2	1	no	—
742	C₂²×D₄	—	2	2	no	—
743	C₂²×D₄	—	2	1	no	—
744	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
745	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
746	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
747	C₂³×C₄	—	2	1	no	—
748	AGL(1,ℤ/8)	—	2	4	no	—
749	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
750	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
751	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
752	C₂×D₈	—	2	8	no	—
753	C₂×D₈	C₂³×C₅₃	1	2	yes	—
754	C₂×D₈	C₂³×C₅₃	1	2	yes	—
755	C₂×D₈	C₂³×C₅₃	1	2	yes	—
756	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
757	C₂×D₈	C₂³×C₅₃	1	2	yes	—
758	C₂×D₈	C₂³×C₅₃	1	2	yes	—
759	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
760	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
761	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
762	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
763	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
764	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
765	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
766	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
767	#127	C₂³×C₅₃	1	1	yes	characteristic
768	#127	C₂³×C₅₃	1	1	yes	characteristic
769	#127	C₂³×C₅₃	1	2	yes	—
770	#126	—	2	2	no	—
771	#126	—	2	2	no	—
772	#126	—	2	2	no	—
773	#126	D₄×C₅₃	1	2	yes	—
774	#125	D₄×C₅₃	1	1	yes	characteristic
775	#125	C₂³×C₅₃	1	2	yes	—
776	#124	—	2	1	no	—
777	#124	—	2	1	no	—
778	#124	—	2	2	no	—
779	#124	—	2	2	no	—
780	#124	—	2	2	no	—
781	#124	—	2	2	no	—
782	#124	—	2	1	no	—
783	#124	—	2	1	no	—
784	#124	D₄×C₅₃	1	1	yes	characteristic
785	#124	C₂³×C₅₃	1	2	yes	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	D₄×C₅₃	1	2	yes	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	1	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
799	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
800	#121	—	2	2	no	—
801	#121	—	2	1	no	—
802	#121	—	2	2	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	1	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	D₄×C₅₃	1	1	yes	characteristic
814	#121	C₂³×C₅₃	1	2	yes	—
815	#121	C₂³×C₅₃	1	2	yes	—
816	#121	C₂³×C₅₃	1	2	yes	—
817	#121	C₂³×C₅₃	1	2	yes	—
818	#121	C₂³×C₅₃	1	2	yes	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	C₄×Q₈	—	2	1	no	—
825	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
826	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
827	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₅₃	1	2	yes	—
847	C₄×D₄	C₂³×C₅₃	1	2	yes	—
848	C₄×D₄	C₂³×C₅₃	1	2	yes	—
849	C₄×D₄	C₂³×C₅₃	1	2	yes	—
850	C₄×D₄	C₂³×C₅₃	1	2	yes	—
851	C₄×D₄	C₂³×C₅₃	1	2	yes	—
852	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
853	C₄×D₄	C₂³×C₅₃	1	2	yes	—
854	#117	—	2	1	no	—
855	#117	—	2	2	no	—
856	#117	—	2	1	no	—
857	#117	C₂³×C₅₃	1	1	yes	characteristic
858	#117	C₂³×C₅₃	1	2	yes	—
859	#117	C₂³×C₅₃	1	2	yes	—
860	#117	C₂³×C₅₃	1	2	yes	—
861	C₂×C₄⋊C₄	—	2	1	no	—
862	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
863	C₂×C₂²⋊C₄	—	2	1	no	—
864	C₂×C₂²⋊C₄	—	2	2	no	—
865	C₂×C₂²⋊C₄	—	2	2	no	—
866	C₂×C₂²⋊C₄	—	2	2	no	—
867	C₂×C₂²⋊C₄	—	2	2	no	—
868	C₂×C₂²⋊C₄	—	2	2	no	—
869	C₂×C₄²	—	2	1	no	—
870	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
871	#107	C₂³×C₅₃	1	2	yes	—
872	#107	C₂³×C₅₃	1	2	yes	—
873	#107	C₂³×C₅₃	1	1	yes	characteristic
874	#107	C₂³×C₅₃	1	1	yes	characteristic
875	#107	C₂³×C₅₃	1	2	yes	—
876	#106	C₂³×C₅₃	1	1	yes	characteristic
877	#106	C₂³×C₅₃	1	2	yes	—
878	#106	C₂³×C₅₃	1	1	yes	characteristic
879	#106	C₂³×C₅₃	1	2	yes	—
880	#106	C₂³×C₅₃	1	2	yes	—
881	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
884	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
885	#103	C₂³×C₅₃	1	1	yes	characteristic
886	#103	C₂³×C₅₃	1	1	yes	characteristic
887	#103	C₂³×C₅₃	1	2	yes	—
888	#102	C₂³×C₅₃	1	1	yes	characteristic
889	#102	C₂³×C₅₃	1	1	yes	characteristic
890	#102	C₂³×C₅₃	1	1	yes	characteristic
891	#102	C₂³×C₅₃	1	1	yes	characteristic
892	#102	C₂³×C₅₃	1	1	yes	characteristic
893	#102	C₂³×C₅₃	1	2	yes	—
894	#102	C₂³×C₅₃	1	2	yes	—
895	#102	C₂³×C₅₃	1	2	yes	—
896	#102	C₂³×C₅₃	1	2	yes	—
897	#102	C₂³×C₅₃	1	2	yes	—
898	#102	C₂³×C₅₃	1	2	yes	—
899	#102	C₂³×C₅₃	1	1	yes	characteristic
900	#102	C₂³×C₅₃	1	2	yes	—
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	2	yes	—
905	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
906	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
907	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
908	#97	C₂³×C₅₃	1	1	yes	characteristic
909	#97	C₂³×C₅₃	1	1	yes	characteristic
910	#97	C₂³×C₅₃	1	2	yes	—
911	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
912	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
913	C₄×C₈	C₂³×C₅₃	1	2	yes	—
914	C₄×C₈	C₂³×C₅₃	1	2	yes	—
915	C₂⁴	—	2	1	no	—
916	C₂⁴	—	2	2	no	—
917	C₂⁴	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	4	1	no	—
920	#41	—	8	2	no	—
921	#41	—	8	2	no	—
922	#41	—	8	2	no	—
923	C₂×Q₈	—	2	1	no	—
924	C₂×Q₈	—	2	2	no	—
925	C₂×Q₈	—	2	1	no	—
926	C₂×Q₈	—	8	2	no	—
927	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
928	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
929	C₂×D₄	—	2	4	no	—
930	C₂×D₄	—	2	4	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	4	2	no	—
948	C₂×D₄	—	4	2	no	—
949	C₂×D₄	—	4	1	no	—
950	C₂×D₄	—	8	2	no	—
951	C₂×D₄	—	8	2	no	—
952	C₂×D₄	—	8	4	no	—
953	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
954	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
955	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
956	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
957	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
958	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
959	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	8	2	no	—
975	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
976	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
977	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
979	SD₁₆	—	2	2	no	—
980	SD₁₆	—	2	2	no	—
981	SD₁₆	—	4	2	no	—
982	D₈	—	2	4	no	—
983	D₈	—	2	4	no	—
984	D₈	—	2	2	no	—
985	D₈	—	2	4	no	—
986	D₈	—	4	2	no	—
987	D₈	—	4	2	no	—
988	D₈	#41×C₅₃	1	4	yes	complemented
989	M₁₆	—	2	2	no	—
990	M₁₆	—	4	1	no	—
991	M₁₆	—	4	2	no	—
992	C₂×C₈	—	2	4	no	—
993	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
994	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
995	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
996	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
997	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
998	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1011	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1012	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1013	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1018	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	2	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	C₂×D₄×C₅₃	1	2	yes	—
1044	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1047	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	2	1	no	—
1051	C₄²	—	2	2	no	—
1052	C₄²	—	2	2	no	—
1053	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1054	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1056	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1057	C₄²	C₂⁴×C₅₃	1	2	yes	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	2	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	2	no	—
1063	C₂³	—	4	2	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	4	no	—
1066	C₂³	—	4	2	no	—
1067	C₂³	—	8	1	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	—	8	2	no	—
1071	C₂³	—	8	2	no	—
1072	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1073	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1074	Q₈	—	2	2	no	—
1075	Q₈	—	2	1	no	—
1076	Q₈	—	2	1	no	—
1077	Q₈	—	4	2	no	—
1078	Q₈	—	8	2	no	—
1079	Q₈	—	8	1	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	2	2	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	2	no	—
1087	D₄	—	2	1	no	—
1088	D₄	—	2	2	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	4	no	—
1092	D₄	—	4	4	no	—
1093	D₄	—	4	2	no	—
1094	D₄	—	4	4	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	8	1	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	2	no	—
1100	D₄	—	8	1	no	—
1101	D₄	—	8	2	no	—
1102	D₄	—	8	2	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	2	no	—
1105	D₄	C₂×#41×C₅₃	1	2	yes	—
1106	D₄	C₂×#41×C₅₃	1	2	yes	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	4	2	no	—
1123	C₂×C₄	—	4	2	no	—
1124	C₂×C₄	—	8	1	no	—
1125	C₂×C₄	—	8	2	no	—
1126	C₂×C₄	—	8	1	no	—
1127	C₂×C₄	—	8	1	no	—
1128	C₂×C₄	—	8	2	no	—
1129	C₂×C₄	—	8	2	no	—
1130	C₂×C₄	—	8	2	no	—
1131	C₂×C₄	—	8	2	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	1	no	—
1134	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1135	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1136	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1137	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1139	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1140	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1141	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1142	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1143	C₈	—	2	2	no	—
1144	C₈	—	2	1	no	—
1145	C₈	—	2	1	no	—
1146	C₈	—	2	1	no	—
1147	C₈	—	2	2	no	—
1148	C₈	C₂×#41×C₅₃	1	2	yes	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	8	4	no	—
1171	C₂²	—	16	4	no	—
1172	C₂²	—	16	4	no	—
1173	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1174	C₄	—	2	1	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	2	1	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	2	1	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	2	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	C₅₃×#576	1	2	yes	—
1189	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1190	C₄	C₅₃×#585	1	1	yes	characteristic
1191	C₂	—	4	1	no	—
1192	C₂	—	4	2	no	—
1193	C₂	—	4	2	no	—
1194	C₂	—	4	2	no	—
1195	C₂	—	8	1	no	—
1196	C₂	—	8	2	no	—
1197	C₂	—	8	2	no	—
1198	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1199	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1200	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×#3519	C₂	semidirect
2. C₅₃×#3514	C₂	semidirect
3. C₅₃×#3399	C₂	semidirect
4. C₅₃×#3384	C₂	semidirect
5. C₅₃×#3361	C₂	semidirect
6. C₅₃×#3358	C₂	semidirect
7. C₅₃×#3347	C₂	semidirect
8. C₅₃×#3340	C₂	semidirect
9. C₅₃×#3325	C₂	semidirect
10. C₅₃×#3325	C₂	semidirect
11. C₅₃×#3324	C₂	semidirect
12. C₅₃×#3322	C₂	semidirect
13. D₄×D₈×C₅₃	C₂	semidirect
14. C₅₃×#3264	C₂	semidirect
15. C₅₃×#3184	C₂	semidirect
16. C₅₃×#3179	C₂	semidirect
17. C₅₃×#3122	C₂	semidirect
18. C₅₃×#3118	C₂	semidirect
19. C₅₃×#3106	C₂	semidirect
20. C₅₃×#3100	C₂	semidirect
21. C₅₃×#2969	C₂	semidirect
22. C₅₃×#2948	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
26. C₅₃×#559	C₂²	semidirect
27. C₅₃×#556	C₂²	semidirect
29. C₅₃×#555	C₂²	semidirect
30. C₅₃×#554	C₂²	semidirect
32. C₅₃×#553	C₂²	semidirect
34. C₅₃×#550	C₂²	semidirect
35. D₄×Q₈×C₅₃	C₂²	semidirect
40. C₅₃×#546	C₂²	semidirect
42. D₄²×C₅₃	C₂²	semidirect
43. D₄²×C₅₃	C₂²	semidirect
44. C₅₃×#542	C₂²	semidirect
45. C₅₃×#540	C₂²	semidirect
48. C₅₃×#532	C₂²	semidirect
49. C₅₃×#532	C₂²	semidirect
55. C₅₃×#518	C₂²	semidirect
56. C₅₃×#518	C₂²	semidirect
57. C₄×#41×C₅₃	C₂²	semidirect
58. C₂×C₄×D₄×C₅₃	C₂²	semidirect
59. C₅₃×#501	C₂²	semidirect
60. C₅₃×#498	C₂²	semidirect
61. C₅₃×#496	C₂²	semidirect
62. C₅₃×#493	C₂²	semidirect
63. C₅₃×#488	C₂²	semidirect
64. C₅₃×#486	C₂²	semidirect
65. C₅₃×#486	C₂²	semidirect
66. C₅₃×#486	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#482	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#480	C₂²	semidirect
73. C₅₃×#478	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#477	C₂²	semidirect
76. C₅₃×#476	C₂²	semidirect
77. C₅₃×#476	C₂²	semidirect
78. C₅₃×#474	C₂²	semidirect
79. C₅₃×#474	C₂²	semidirect
80. C₅₃×#474	C₂²	semidirect
81. C₅₃×#469	C₂²	semidirect
82. C₅₃×#469	C₂²	semidirect
83. C₅₃×#469	C₂²	semidirect
84. C₅₃×#468	C₂²	semidirect
85. C₅₃×#466	C₂²	semidirect
86. C₅₃×#465	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#460	C₂²	semidirect
91. C₅₃×#459	C₂²	semidirect
92. C₅₃×#459	C₂²	semidirect
93. C₅₃×#459	C₂²	semidirect
94. C₅₃×#459	C₂²	semidirect
95. C₅₃×#450	C₂²	semidirect
96. C₅₃×#449	C₂²	semidirect
98. C₅₃×#447	C₂²	semidirect
99. C₅₃×#447	C₂²	semidirect
100. C₅₃×#447	C₂²	semidirect
101. C₅₃×#446	C₂²	semidirect
102. C₈×Q₈×C₅₃	C₂²	semidirect
105. C₅₃×#442	C₂²	semidirect
106. C₅₃×#442	C₂²	semidirect
107. C₅₃×#442	C₂²	semidirect
108. C₅₃×#442	C₂²	semidirect
109. C₅₃×#440	C₂²	semidirect
110. C₅₃×#440	C₂²	semidirect
111. C₄×SD₁₆×C₅₃	C₂²	semidirect
112. C₄×SD₁₆×C₅₃	C₂²	semidirect
113. C₄×SD₁₆×C₅₃	C₂²	semidirect
115. C₄×D₈×C₅₃	C₂²	semidirect
116. C₄×D₈×C₅₃	C₂²	semidirect
117. C₄×D₈×C₅₃	C₂²	semidirect
118. C₄×D₈×C₅₃	C₂²	semidirect
119. C₄×D₈×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. C₈×D₄×C₅₃	C₂²	semidirect
125. C₅₃×#433	C₂²	semidirect
126. C₅₃×#431	C₂²	semidirect
127. C₅₃×#428	C₂²	semidirect
128. C₅₃×#427	C₂²	semidirect
129. C₅₃×#418	C₂²	semidirect
130. C₅₃×#418	C₂²	semidirect
131. C₅₃×#418	C₂²	semidirect
132. C₅₃×#417	C₂²	semidirect
133. C₅₃×#405	C₂²	semidirect
134. C₄×M₁₆×C₅₃	C₂²	semidirect
387. D₈×C₅₃	#41	semidirect
548. #61539	C₅₃	direct (N × H)
591. #3519	C₂×C₅₃	semidirect
592. #3514	C₂×C₅₃	semidirect
593. #3399	C₂×C₅₃	semidirect
594. #3384	C₂×C₅₃	semidirect
595. #3361	C₂×C₅₃	semidirect
596. #3358	C₂×C₅₃	semidirect
597. #3347	C₂×C₅₃	semidirect
598. #3340	C₂×C₅₃	semidirect
599. #3325	C₂×C₅₃	semidirect
600. #3325	C₂×C₅₃	semidirect
601. #3324	C₂×C₅₃	semidirect
602. #3322	C₂×C₅₃	semidirect
603. D₄×D₈	C₂×C₅₃	semidirect
604. #3264	C₂×C₅₃	semidirect
605. #3184	C₂×C₅₃	semidirect
606. #3179	C₂×C₅₃	semidirect
607. #3122	C₂×C₅₃	semidirect
608. #3118	C₂×C₅₃	semidirect
609. #3106	C₂×C₅₃	semidirect
610. #3100	C₂×C₅₃	semidirect
611. #2969	C₂×C₅₃	semidirect
612. #2948	C₂×C₅₃	semidirect
613. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
626. #559	C₂²×C₅₃	semidirect
627. #556	C₂²×C₅₃	semidirect
629. #555	C₂²×C₅₃	semidirect
630. #554	C₂²×C₅₃	semidirect
632. #553	C₂²×C₅₃	semidirect
634. #550	C₂²×C₅₃	semidirect
635. D₄×Q₈	C₂²×C₅₃	semidirect
640. #546	C₂²×C₅₃	semidirect
642. D₄²	C₂²×C₅₃	semidirect
643. D₄²	C₂²×C₅₃	semidirect
644. #542	C₂²×C₅₃	semidirect
645. #540	C₂²×C₅₃	semidirect
648. #532	C₂²×C₅₃	semidirect
649. #532	C₂²×C₅₃	semidirect
655. #518	C₂²×C₅₃	semidirect
656. #518	C₂²×C₅₃	semidirect
657. C₄×#41	C₂²×C₅₃	semidirect
658. C₂×C₄×D₄	C₂²×C₅₃	semidirect
659. #501	C₂²×C₅₃	semidirect
660. #498	C₂²×C₅₃	semidirect
661. #496	C₂²×C₅₃	semidirect
662. #493	C₂²×C₅₃	semidirect
663. #488	C₂²×C₅₃	semidirect
664. #486	C₂²×C₅₃	semidirect
665. #486	C₂²×C₅₃	semidirect
666. #486	C₂²×C₅₃	semidirect
667. #485	C₂²×C₅₃	semidirect
668. #482	C₂²×C₅₃	semidirect
669. #482	C₂²×C₅₃	semidirect
670. #482	C₂²×C₅₃	semidirect
671. #482	C₂²×C₅₃	semidirect
672. #480	C₂²×C₅₃	semidirect
673. #478	C₂²×C₅₃	semidirect
674. #478	C₂²×C₅₃	semidirect
675. #477	C₂²×C₅₃	semidirect
676. #476	C₂²×C₅₃	semidirect
677. #476	C₂²×C₅₃	semidirect
678. #474	C₂²×C₅₃	semidirect
679. #474	C₂²×C₅₃	semidirect
680. #474	C₂²×C₅₃	semidirect
681. #469	C₂²×C₅₃	semidirect
682. #469	C₂²×C₅₃	semidirect
683. #469	C₂²×C₅₃	semidirect
684. #468	C₂²×C₅₃	semidirect
685. #466	C₂²×C₅₃	semidirect
686. #465	C₂²×C₅₃	semidirect
687. #463	C₂²×C₅₃	semidirect
688. #463	C₂²×C₅₃	semidirect
689. #460	C₂²×C₅₃	semidirect
691. #459	C₂²×C₅₃	semidirect
692. #459	C₂²×C₅₃	semidirect
693. #459	C₂²×C₅₃	semidirect
694. #459	C₂²×C₅₃	semidirect
695. #450	C₂²×C₅₃	semidirect
696. #449	C₂²×C₅₃	semidirect
698. #447	C₂²×C₅₃	semidirect
699. #447	C₂²×C₅₃	semidirect
700. #447	C₂²×C₅₃	semidirect
701. #446	C₂²×C₅₃	semidirect
702. C₈×Q₈	C₂²×C₅₃	semidirect
705. #442	C₂²×C₅₃	semidirect
706. #442	C₂²×C₅₃	semidirect
707. #442	C₂²×C₅₃	semidirect
708. #442	C₂²×C₅₃	semidirect
709. #440	C₂²×C₅₃	semidirect
710. #440	C₂²×C₅₃	semidirect
711. C₄×SD₁₆	C₂²×C₅₃	semidirect
712. C₄×SD₁₆	C₂²×C₅₃	semidirect
713. C₄×SD₁₆	C₂²×C₅₃	semidirect
715. C₄×D₈	C₂²×C₅₃	semidirect
716. C₄×D₈	C₂²×C₅₃	semidirect
717. C₄×D₈	C₂²×C₅₃	semidirect
718. C₄×D₈	C₂²×C₅₃	semidirect
719. C₄×D₈	C₂²×C₅₃	semidirect
720. C₄×D₈	C₂²×C₅₃	semidirect
721. #436	C₂²×C₅₃	semidirect
722. #436	C₂²×C₅₃	semidirect
723. #435	C₂²×C₅₃	semidirect
724. C₈×D₄	C₂²×C₅₃	semidirect
725. #433	C₂²×C₅₃	semidirect
726. #431	C₂²×C₅₃	semidirect
727. #428	C₂²×C₅₃	semidirect
728. #427	C₂²×C₅₃	semidirect
729. #418	C₂²×C₅₃	semidirect
730. #418	C₂²×C₅₃	semidirect
731. #418	C₂²×C₅₃	semidirect
732. #417	C₂²×C₅₃	semidirect
733. #405	C₂²×C₅₃	semidirect
734. C₄×M₁₆	C₂²×C₅₃	semidirect
735. C₅₃	#61539	direct (N × H)
988. D₈	#41×C₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#3519	2
C₅₃×#3514	2
C₅₃×#3399	2
C₅₃×#3384	2
C₅₃×#3361	2
C₅₃×#3358	2
C₅₃×#3347	2
C₅₃×#3340	2
C₅₃×#3325	2
C₅₃×#3324	2
C₅₃×#3322	2
D₄×D₈×C₅₃	2
C₅₃×#3264	2
C₅₃×#3184	2
C₅₃×#3179	2
C₅₃×#3122	2
C₅₃×#3118	2
C₅₃×#3106	2
C₅₃×#3100	2
C₅₃×#2969	2
C₅₃×#2948	2
C₄×AGL(1,ℤ/8)×C₅₃	2
#61539	53

Subgroups — C53×#61539 #27269051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61539 #27269051