Subgroups — C₅₃×#61468 #27268980

Order 13568.

1908 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3396	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3355	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3326	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	C₅₃×#3275	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3183	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3114	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3111	C₂	1	2	yes	maximal, complemented
21	C₅₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#137×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	2	yes	maximal, complemented
24	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
26	C₅₃×#559	—	2	1	no	—
27	C₅₃×#559	C₂²	1	1	yes	characteristic
28	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#556	—	2	1	no	—
31	C₅₃×#556	C₂²	1	1	yes	characteristic
32	C₅₃×#554	C₂²	1	1	yes	characteristic
33	C₅₃×#554	C₂²	1	1	yes	characteristic
34	C₅₃×#553	—	2	2	no	—
35	C₅₃×#553	—	2	1	no	—
36	C₅₃×#553	C₂²	1	2	yes	—
37	C₅₃×#553	C₂²	1	2	yes	complemented
38	C₅₃×#551	—	2	2	no	—
39	C₅₃×#550	C₂²	1	1	yes	characteristic
40	C₅₃×#548	C₂²	1	2	yes	complemented
41	C₅₃×#546	—	2	1	no	—
42	C₅₃×#546	C₂²	1	2	yes	—
43	D₄²×C₅₃	C₂²	1	1	yes	characteristic
44	C₅₃×#532	—	2	1	no	—
45	C₅₃×#532	C₂²	1	1	yes	characteristic
46	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#529	—	2	1	no	—
48	C₅₃×#529	—	2	2	no	—
49	C₅₃×#529	C₂²	1	2	yes	—
50	C₅₃×#529	C₂²	1	2	yes	complemented
51	C₅₃×#525	—	2	2	no	—
52	C₄×#41×C₅₃	—	2	1	no	—
53	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
54	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
55	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
56	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₅₃	—	2	1	no	—
58	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
59	C₅₃×#499	C₂²	1	2	yes	complemented
60	C₅₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#495	C₂²	1	2	yes	complemented
62	C₅₃×#493	C₂²	1	1	yes	characteristic
63	C₅₃×#488	C₂²	1	2	yes	complemented
64	C₅₃×#488	C₂²	1	2	yes	complemented
65	C₅₃×#486	C₂²	1	1	yes	characteristic
66	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#485	C₂²	1	2	yes	complemented
68	C₅₃×#483	C₂²	1	2	yes	complemented
69	C₅₃×#482	C₂²	1	2	yes	—
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#480	C₂²	1	2	yes	complemented
72	C₅₃×#480	C₂²	1	2	yes	complemented
73	C₅₃×#479	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	2	yes	—
75	C₅₃×#478	C₂²	1	2	yes	complemented
76	C₅₃×#478	C₂²	1	2	yes	complemented
77	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#474	C₂²	1	1	yes	characteristic
81	C₅₃×#470	C₂²	1	2	yes	complemented
82	C₅₃×#469	C₂²	1	2	yes	—
83	C₅₃×#469	C₂²	1	2	yes	complemented
84	C₅₃×#469	C₂²	1	2	yes	complemented
85	C₅₃×#468	C₂²	1	2	yes	—
86	C₅₃×#468	C₂²	1	2	yes	complemented
87	C₅₃×#464	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	2	yes	—
89	C₅₃×#463	C₂²	1	2	yes	complemented
90	C₅₃×#463	C₂²	1	2	yes	complemented
91	C₅₃×#460	C₂²	1	1	yes	characteristic
92	C₅₃×#460	C₂²	1	1	yes	characteristic
93	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#459	C₂²	1	1	yes	characteristic
95	C₅₃×#452	C₂²	1	2	yes	complemented
96	C₅₃×#450	C₂²	1	2	yes	—
97	C₅₃×#449	C₂²	1	2	yes	—
98	C₅₃×#449	C₂²	1	2	yes	—
99	C₅₃×#448	C₂²	1	2	yes	complemented
100	C₅₃×#447	C₂²	1	2	yes	—
101	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#442	C₂²	1	2	yes	—
104	C₅₃×#442	C₂²	1	2	yes	complemented
105	C₅₃×#442	C₂²	1	2	yes	complemented
106	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#440	C₂²	1	1	yes	characteristic
109	C₅₃×#440	C₂²	1	1	yes	characteristic
110	C₅₃×#440	C₂²	1	2	yes	complemented
111	C₅₃×#440	C₂²	1	2	yes	complemented
112	C₅₃×#440	C₂²	1	2	yes	complemented
113	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
119	C₄×D₈×C₅₃	C₂²	1	2	yes	—
120	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
121	C₅₃×#436	C₂²	1	1	yes	characteristic
122	C₅₃×#436	C₂²	1	1	yes	characteristic
123	C₅₃×#436	C₂²	1	2	yes	complemented
124	C₅₃×#436	C₂²	1	2	yes	complemented
125	C₅₃×#432	C₂²	1	2	yes	complemented
126	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#428	C₂²	1	2	yes	complemented
128	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#418	C₂²	1	2	yes	—
131	C₅₃×#417	C₂²	1	1	yes	characteristic
132	C₅₃×#417	C₂²	1	2	yes	complemented
133	C₄×M₁₆×C₅₃	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	D₄	1	1	yes	characteristic
138	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
139	C₂×#41×C₅₃	C₂³	1	2	yes	—
140	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₅₃	—	2	1	no	—
142	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₅₃	—	2	2	no	—
144	#137×C₅₃	—	2	4	no	—
145	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
146	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₅₃	C₂³	1	2	yes	—
154	C₂×D₈×C₅₃	C₂³	1	2	yes	—
155	C₂×D₈×C₅₃	C₂³	1	2	yes	—
156	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₅₃	—	2	1	no	—
161	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
163	#127×C₅₃	—	2	1	no	—
164	#127×C₅₃	C₂³	1	1	yes	characteristic
165	#127×C₅₃	C₂³	1	1	yes	characteristic
166	#126×C₅₃	—	2	2	no	—
167	#126×C₅₃	—	2	2	no	—
168	#126×C₅₃	—	2	2	no	—
169	#126×C₅₃	—	2	2	no	—
170	#126×C₅₃	—	2	2	no	—
171	#125×C₅₃	—	2	1	no	—
172	#125×C₅₃	—	2	2	no	—
173	#125×C₅₃	C₂³	1	2	yes	—
174	#125×C₅₃	C₂³	1	2	yes	—
175	#124×C₅₃	—	2	2	no	—
176	#124×C₅₃	—	2	1	no	—
177	#124×C₅₃	—	2	1	no	—
178	#124×C₅₃	—	2	1	no	—
179	#124×C₅₃	—	2	1	no	—
180	#124×C₅₃	—	2	1	no	—
181	#124×C₅₃	C₂³	1	2	yes	—
182	#124×C₅₃	C₂³	1	2	yes	—
183	#123×C₅₃	—	2	2	no	—
184	#123×C₅₃	—	2	2	no	—
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	C₂²⋊Q₈×C₅₃	—	2	2	no	—
191	C₂²⋊Q₈×C₅₃	—	2	2	no	—
192	C₂²⋊Q₈×C₅₃	—	2	2	no	—
193	C₂²⋊Q₈×C₅₃	—	2	1	no	—
194	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
196	#121×C₅₃	—	2	1	no	—
197	#121×C₅₃	—	2	2	no	—
198	#121×C₅₃	—	2	2	no	—
199	#121×C₅₃	—	2	2	no	—
200	#121×C₅₃	—	2	2	no	—
201	#121×C₅₃	—	2	2	no	—
202	#121×C₅₃	—	2	1	no	—
203	#121×C₅₃	—	2	1	no	—
204	#121×C₅₃	C₂³	1	2	yes	—
205	#121×C₅₃	C₂³	1	2	yes	—
206	#121×C₅₃	C₂³	1	2	yes	—
207	#121×C₅₃	C₂³	1	2	yes	—
208	#120×C₅₃	—	2	2	no	—
209	#120×C₅₃	—	2	2	no	—
210	C₄×Q₈×C₅₃	—	2	1	no	—
211	C₄×Q₈×C₅₃	—	2	1	no	—
212	C₄×Q₈×C₅₃	—	2	1	no	—
213	C₄×Q₈×C₅₃	—	2	1	no	—
214	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
215	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
223	C₄×D₄×C₅₃	—	2	1	no	—
224	C₄×D₄×C₅₃	—	2	1	no	—
225	C₄×D₄×C₅₃	—	2	1	no	—
226	C₄×D₄×C₅₃	—	2	2	no	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	—	2	2	no	—
229	C₄×D₄×C₅₃	—	2	1	no	—
230	C₄×D₄×C₅₃	—	2	2	no	—
231	C₄×D₄×C₅₃	—	2	2	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	2	no	—
235	C₄×D₄×C₅₃	—	2	1	no	—
236	C₄×D₄×C₅₃	—	2	1	no	—
237	C₄×D₄×C₅₃	—	2	2	no	—
238	C₄×D₄×C₅₃	—	2	2	no	—
239	C₄×D₄×C₅₃	—	2	2	no	—
240	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
241	C₄×D₄×C₅₃	D₄	1	2	yes	—
242	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₃	C₂³	1	2	yes	—
244	C₄×D₄×C₅₃	C₂³	1	2	yes	—
245	C₄×D₄×C₅₃	C₂³	1	2	yes	—
246	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₅₃	C₂³	1	2	yes	—
248	C₄×D₄×C₅₃	C₂³	1	2	yes	—
249	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₅₃	C₂³	1	2	yes	—
251	#117×C₅₃	—	2	2	no	—
252	#117×C₅₃	—	2	1	no	—
253	#117×C₅₃	—	2	2	no	—
254	#117×C₅₃	—	2	2	no	—
255	#117×C₅₃	D₄	1	1	yes	characteristic
256	#117×C₅₃	D₄	1	2	yes	—
257	#117×C₅₃	C₂³	1	2	yes	—
258	#117×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
260	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
265	C₂×C₄²×C₅₃	—	2	1	no	—
266	C₂×C₄²×C₅₃	—	2	2	no	—
267	C₂×C₄²×C₅₃	—	2	1	no	—
268	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
269	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
270	#107×C₅₃	C₂³	1	2	yes	—
271	#107×C₅₃	C₂³	1	2	yes	—
272	#107×C₅₃	C₂³	1	2	yes	—
273	#107×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
278	#106×C₅₃	C₂³	1	1	yes	characteristic
279	#106×C₅₃	C₂³	1	2	yes	—
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	#103×C₅₃	C₂³	1	1	yes	characteristic
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	1	yes	characteristic
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×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	1	yes	characteristic
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
308	#97×C₅₃	C₂³	1	1	yes	characteristic
309	#97×C₅₃	C₂³	1	2	yes	—
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	2	no	—
315	#41×C₅₃	—	2	4	no	—
316	#41×C₅₃	—	2	2	no	—
317	#41×C₅₃	—	4	2	no	—
318	#41×C₅₃	—	4	2	no	—
319	#41×C₅₃	—	4	1	no	—
320	#41×C₅₃	—	4	4	no	—
321	#41×C₅₃	—	8	2	no	—
322	C₂×Q₈×C₅₃	—	2	1	no	—
323	C₂×Q₈×C₅₃	—	2	1	no	—
324	C₂×Q₈×C₅₃	—	2	1	no	—
325	C₂×Q₈×C₅₃	—	2	2	no	—
326	C₂×Q₈×C₅₃	—	4	1	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×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₅₃	—	2	4	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	—	4	2	no	—
344	C₂×D₄×C₅₃	—	4	4	no	—
345	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
348	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
349	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₅₃	—	2	1	no	—
351	C₂²×C₄×C₅₃	—	2	1	no	—
352	C₂²×C₄×C₅₃	—	2	2	no	—
353	C₂²×C₄×C₅₃	—	2	1	no	—
354	C₂²×C₄×C₅₃	—	2	1	no	—
355	C₂²×C₄×C₅₃	—	2	2	no	—
356	C₂²×C₄×C₅₃	—	2	2	no	—
357	C₂²×C₄×C₅₃	—	2	1	no	—
358	C₂²×C₄×C₅₃	—	2	2	no	—
359	C₂²×C₄×C₅₃	—	2	2	no	—
360	C₂²×C₄×C₅₃	—	2	2	no	—
361	C₂²×C₄×C₅₃	—	2	2	no	—
362	C₂²×C₄×C₅₃	—	8	4	no	—
363	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
365	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
369	Q₁₆×C₅₃	—	2	2	no	—
370	Q₁₆×C₅₃	—	2	2	no	—
371	SD₁₆×C₅₃	—	2	4	no	—
372	SD₁₆×C₅₃	—	2	2	no	—
373	SD₁₆×C₅₃	—	4	2	no	—
374	SD₁₆×C₅₃	—	4	2	no	—
375	SD₁₆×C₅₃	#41	1	4	yes	complemented
376	D₈×C₅₃	—	2	4	no	—
377	D₈×C₅₃	—	2	4	no	—
378	D₈×C₅₃	—	4	2	no	—
379	M₁₆×C₅₃	—	2	4	no	—
380	M₁₆×C₅₃	—	2	2	no	—
381	M₁₆×C₅₃	—	4	1	no	—
382	M₁₆×C₅₃	—	4	2	no	—
383	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
386	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
387	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₅₃	—	2	1	no	—
390	C₄⋊C₄×C₅₃	—	2	1	no	—
391	C₄⋊C₄×C₅₃	—	2	2	no	—
392	C₄⋊C₄×C₅₃	—	2	1	no	—
393	C₄⋊C₄×C₅₃	—	2	1	no	—
394	C₄⋊C₄×C₅₃	—	2	1	no	—
395	C₄⋊C₄×C₅₃	—	2	2	no	—
396	C₄⋊C₄×C₅₃	—	2	1	no	—
397	C₄⋊C₄×C₅₃	—	2	2	no	—
398	C₄⋊C₄×C₅₃	—	2	2	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	2	no	—
403	C₄⋊C₄×C₅₃	—	2	2	no	—
404	C₄⋊C₄×C₅₃	—	2	1	no	—
405	C₄⋊C₄×C₅₃	—	2	2	no	—
406	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	C₂²⋊C₄×C₅₃	—	2	2	no	—
417	C₂²⋊C₄×C₅₃	—	2	1	no	—
418	C₂²⋊C₄×C₅₃	—	2	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	1	no	—
421	C₂²⋊C₄×C₅₃	—	2	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	2	no	—
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	2	no	—
426	C₂²⋊C₄×C₅₃	—	2	2	no	—
427	C₂²⋊C₄×C₅₃	—	2	2	no	—
428	C₂²⋊C₄×C₅₃	—	2	1	no	—
429	C₂²⋊C₄×C₅₃	—	2	2	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	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
438	C₄²×C₅₃	—	2	1	no	—
439	C₄²×C₅₃	—	2	1	no	—
440	C₄²×C₅₃	—	2	1	no	—
441	C₄²×C₅₃	—	2	1	no	—
442	C₄²×C₅₃	—	2	2	no	—
443	C₄²×C₅₃	—	2	1	no	—
444	C₄²×C₅₃	—	2	2	no	—
445	C₄²×C₅₃	—	2	1	no	—
446	C₄²×C₅₃	—	2	1	no	—
447	C₄²×C₅₃	C₂×D₄	1	2	yes	—
448	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₅₃	C₂×D₄	1	2	yes	—
450	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₅₃	C₂⁴	1	2	yes	—
452	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₂³×C₅₃	—	2	1	no	—
455	C₂³×C₅₃	—	2	2	no	—
456	C₂³×C₅₃	—	2	2	no	—
457	C₂³×C₅₃	—	4	4	no	—
458	C₂³×C₅₃	—	4	4	no	—
459	C₂³×C₅₃	—	8	2	no	—
460	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
461	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
462	Q₈×C₅₃	—	2	2	no	—
463	Q₈×C₅₃	—	2	1	no	—
464	Q₈×C₅₃	—	2	1	no	—
465	Q₈×C₅₃	—	2	1	no	—
466	Q₈×C₅₃	—	2	1	no	—
467	Q₈×C₅₃	—	2	1	no	—
468	Q₈×C₅₃	—	4	2	no	—
469	Q₈×C₅₃	—	4	2	no	—
470	Q₈×C₅₃	—	8	1	no	—
471	Q₈×C₅₃	C₂×#41	1	2	yes	—
472	D₄×C₅₃	—	2	2	no	—
473	D₄×C₅₃	—	2	2	no	—
474	D₄×C₅₃	—	2	2	no	—
475	D₄×C₅₃	—	2	1	no	—
476	D₄×C₅₃	—	2	2	no	—
477	D₄×C₅₃	—	2	2	no	—
478	D₄×C₅₃	—	4	2	no	—
479	D₄×C₅₃	—	4	4	no	—
480	D₄×C₅₃	—	4	4	no	—
481	D₄×C₅₃	—	4	2	no	—
482	D₄×C₅₃	—	4	4	no	—
483	D₄×C₅₃	—	4	4	no	—
484	D₄×C₅₃	—	4	2	no	—
485	D₄×C₅₃	—	4	2	no	—
486	D₄×C₅₃	—	8	1	no	—
487	D₄×C₅₃	—	8	1	no	—
488	D₄×C₅₃	—	8	2	no	—
489	D₄×C₅₃	—	8	2	no	—
490	D₄×C₅₃	C₂×#41	1	2	yes	—
491	C₂×C₄×C₅₃	—	2	1	no	—
492	C₂×C₄×C₅₃	—	2	2	no	—
493	C₂×C₄×C₅₃	—	2	2	no	—
494	C₂×C₄×C₅₃	—	2	1	no	—
495	C₂×C₄×C₅₃	—	2	2	no	—
496	C₂×C₄×C₅₃	—	2	1	no	—
497	C₂×C₄×C₅₃	—	2	1	no	—
498	C₂×C₄×C₅₃	—	2	2	no	—
499	C₂×C₄×C₅₃	—	2	1	no	—
500	C₂×C₄×C₅₃	—	2	1	no	—
501	C₂×C₄×C₅₃	—	2	1	no	—
502	C₂×C₄×C₅₃	—	2	2	no	—
503	C₂×C₄×C₅₃	—	2	1	no	—
504	C₂×C₄×C₅₃	—	2	1	no	—
505	C₂×C₄×C₅₃	—	4	2	no	—
506	C₂×C₄×C₅₃	—	4	2	no	—
507	C₂×C₄×C₅₃	—	4	1	no	—
508	C₂×C₄×C₅₃	—	4	4	no	—
509	C₂×C₄×C₅₃	—	4	2	no	—
510	C₂×C₄×C₅₃	—	4	2	no	—
511	C₂×C₄×C₅₃	—	4	2	no	—
512	C₂×C₄×C₅₃	—	4	4	no	—
513	C₂×C₄×C₅₃	—	4	4	no	—
514	C₂×C₄×C₅₃	—	4	2	no	—
515	C₂×C₄×C₅₃	—	8	2	no	—
516	C₂×C₄×C₅₃	—	8	2	no	—
517	C₂×C₄×C₅₃	—	8	2	no	—
518	C₂×C₄×C₅₃	—	8	1	no	—
519	C₂×C₄×C₅₃	—	8	2	no	—
520	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
529	C₈×C₅₃	—	2	2	no	—
530	C₈×C₅₃	—	2	1	no	—
531	C₈×C₅₃	—	2	1	no	—
532	C₈×C₅₃	—	2	1	no	—
533	C₈×C₅₃	—	2	2	no	—
534	C₈×C₅₃	C₂×#41	1	2	yes	—
535	#61468	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
536	C₂²×C₅₃	—	2	1	no	—
537	C₂²×C₅₃	—	2	2	no	—
538	C₂²×C₅₃	—	2	1	no	—
539	C₂²×C₅₃	—	2	2	no	—
540	C₂²×C₅₃	—	2	2	no	—
541	C₂²×C₅₃	—	2	1	no	—
542	C₂²×C₅₃	—	2	2	no	—
543	C₂²×C₅₃	—	4	1	no	—
544	C₂²×C₅₃	—	4	1	no	—
545	C₂²×C₅₃	—	4	2	no	—
546	C₂²×C₅₃	—	4	2	no	—
547	C₂²×C₅₃	—	4	2	no	—
548	C₂²×C₅₃	—	4	2	no	—
549	C₂²×C₅₃	—	4	2	no	—
550	C₂²×C₅₃	—	4	2	no	—
551	C₂²×C₅₃	—	8	8	no	—
552	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
553	C₄×C₅₃	—	2	1	no	—
554	C₄×C₅₃	—	2	2	no	—
555	C₄×C₅₃	—	2	1	no	—
556	C₄×C₅₃	—	2	2	no	—
557	C₄×C₅₃	—	2	1	no	—
558	C₄×C₅₃	—	2	2	no	—
559	C₄×C₅₃	—	2	1	no	—
560	C₄×C₅₃	—	2	2	no	—
561	C₄×C₅₃	—	4	1	no	—
562	C₄×C₅₃	—	4	2	no	—
563	C₄×C₅₃	—	4	1	no	—
564	C₄×C₅₃	—	4	1	no	—
565	C₄×C₅₃	—	4	1	no	—
566	C₄×C₅₃	—	4	1	no	—
567	C₄×C₅₃	—	4	1	no	—
568	C₄×C₅₃	—	4	2	no	—
569	C₄×C₅₃	#575	1	2	yes	—
570	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
571	C₄×C₅₃	#585	1	1	yes	characteristic
572	#3481	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#3480	C₂×C₅₃	1	1	yes	characteristic, complemented
574	#3396	C₂×C₅₃	1	1	yes	characteristic, complemented
575	#3381	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#3365	C₂×C₅₃	1	1	yes	characteristic, complemented
577	#3361	C₂×C₅₃	1	1	yes	characteristic, complemented
578	#3356	C₂×C₅₃	1	1	yes	characteristic, complemented
579	#3355	C₂×C₅₃	1	2	yes	complemented
580	#3333	C₂×C₅₃	1	1	yes	characteristic, complemented
581	#3326	C₂×C₅₃	1	2	yes	complemented
582	#3324	C₂×C₅₃	1	1	yes	characteristic, complemented
583	#3322	C₂×C₅₃	1	2	yes	complemented
584	#3275	C₂×C₅₃	1	2	yes	complemented
585	#3274	C₂×C₅₃	1	1	yes	characteristic, complemented
586	#3184	C₂×C₅₃	1	1	yes	characteristic, complemented
587	#3183	C₂×C₅₃	1	2	yes	complemented
588	#3115	C₂×C₅₃	1	1	yes	characteristic, complemented
589	#3114	C₂×C₅₃	1	2	yes	complemented
590	#3112	C₂×C₅₃	1	1	yes	characteristic, complemented
591	#3111	C₂×C₅₃	1	2	yes	complemented
592	#2971	C₂×C₅₃	1	1	yes	characteristic, complemented
593	C₄×#137	C₂×C₅₃	1	1	yes	characteristic, complemented
594	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	2	yes	complemented
595	C₂×C₅₃	—	4	1	no	—
596	C₂×C₅₃	—	4	2	no	—
597	C₂×C₅₃	—	4	2	no	—
598	C₂×C₅₃	—	8	2	no	—
599	C₂×C₅₃	—	8	2	no	—
600	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
601	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
602	C₂×C₅₃	#3585	1	1	yes	characteristic
603	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
604	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
605	#559	—	2	1	no	—
606	#559	C₂²×C₅₃	1	1	yes	characteristic
607	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
608	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
609	#556	—	2	1	no	—
610	#556	C₂²×C₅₃	1	1	yes	characteristic
611	#554	C₂²×C₅₃	1	1	yes	characteristic
612	#554	C₂²×C₅₃	1	1	yes	characteristic
613	#553	—	2	2	no	—
614	#553	—	2	1	no	—
615	#553	C₂²×C₅₃	1	2	yes	—
616	#553	C₂²×C₅₃	1	2	yes	complemented
617	#551	—	2	2	no	—
618	#550	C₂²×C₅₃	1	1	yes	characteristic
619	#548	C₂²×C₅₃	1	2	yes	complemented
620	#546	—	2	1	no	—
621	#546	C₂²×C₅₃	1	2	yes	—
622	D₄²	C₂²×C₅₃	1	1	yes	characteristic
623	#532	—	2	1	no	—
624	#532	C₂²×C₅₃	1	1	yes	characteristic
625	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
626	#529	—	2	1	no	—
627	#529	—	2	2	no	—
628	#529	C₂²×C₅₃	1	2	yes	—
629	#529	C₂²×C₅₃	1	2	yes	complemented
630	#525	—	2	2	no	—
631	C₄×#41	—	2	1	no	—
632	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
633	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
634	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
635	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
636	C₂×C₄×D₄	—	2	1	no	—
637	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
638	#499	C₂²×C₅₃	1	2	yes	complemented
639	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
640	#495	C₂²×C₅₃	1	2	yes	complemented
641	#493	C₂²×C₅₃	1	1	yes	characteristic
642	#488	C₂²×C₅₃	1	2	yes	complemented
643	#488	C₂²×C₅₃	1	2	yes	complemented
644	#486	C₂²×C₅₃	1	1	yes	characteristic
645	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
646	#485	C₂²×C₅₃	1	2	yes	complemented
647	#483	C₂²×C₅₃	1	2	yes	complemented
648	#482	C₂²×C₅₃	1	2	yes	—
649	#482	C₂²×C₅₃	1	2	yes	complemented
650	#480	C₂²×C₅₃	1	2	yes	complemented
651	#480	C₂²×C₅₃	1	2	yes	complemented
652	#479	C₂²×C₅₃	1	2	yes	complemented
653	#478	C₂²×C₅₃	1	2	yes	—
654	#478	C₂²×C₅₃	1	2	yes	complemented
655	#478	C₂²×C₅₃	1	2	yes	complemented
656	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
657	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
658	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	#474	C₂²×C₅₃	1	1	yes	characteristic
660	#470	C₂²×C₅₃	1	2	yes	complemented
661	#469	C₂²×C₅₃	1	2	yes	—
662	#469	C₂²×C₅₃	1	2	yes	complemented
663	#469	C₂²×C₅₃	1	2	yes	complemented
664	#468	C₂²×C₅₃	1	2	yes	—
665	#468	C₂²×C₅₃	1	2	yes	complemented
666	#464	C₂²×C₅₃	1	2	yes	complemented
667	#463	C₂²×C₅₃	1	2	yes	—
668	#463	C₂²×C₅₃	1	2	yes	complemented
669	#463	C₂²×C₅₃	1	2	yes	complemented
670	#460	C₂²×C₅₃	1	1	yes	characteristic
671	#460	C₂²×C₅₃	1	1	yes	characteristic
672	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	#459	C₂²×C₅₃	1	1	yes	characteristic
674	#452	C₂²×C₅₃	1	2	yes	complemented
675	#450	C₂²×C₅₃	1	2	yes	—
676	#449	C₂²×C₅₃	1	2	yes	—
677	#449	C₂²×C₅₃	1	2	yes	—
678	#448	C₂²×C₅₃	1	2	yes	complemented
679	#447	C₂²×C₅₃	1	2	yes	—
680	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
682	#442	C₂²×C₅₃	1	2	yes	—
683	#442	C₂²×C₅₃	1	2	yes	complemented
684	#442	C₂²×C₅₃	1	2	yes	complemented
685	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
686	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#440	C₂²×C₅₃	1	1	yes	characteristic
688	#440	C₂²×C₅₃	1	1	yes	characteristic
689	#440	C₂²×C₅₃	1	2	yes	complemented
690	#440	C₂²×C₅₃	1	2	yes	complemented
691	#440	C₂²×C₅₃	1	2	yes	complemented
692	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
694	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
695	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
696	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
697	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
698	C₄×D₈	C₂²×C₅₃	1	2	yes	—
699	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
700	#436	C₂²×C₅₃	1	1	yes	characteristic
701	#436	C₂²×C₅₃	1	1	yes	characteristic
702	#436	C₂²×C₅₃	1	2	yes	complemented
703	#436	C₂²×C₅₃	1	2	yes	complemented
704	#432	C₂²×C₅₃	1	2	yes	complemented
705	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
706	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	#428	C₂²×C₅₃	1	2	yes	complemented
708	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#418	C₂²×C₅₃	1	2	yes	—
710	#417	C₂²×C₅₃	1	1	yes	characteristic
711	#417	C₂²×C₅₃	1	2	yes	complemented
712	C₄×M₁₆	C₂²×C₅₃	1	2	yes	complemented
713	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
714	C₅₃	#61468	1	1	yes	characteristic, direct product factor, Sylow
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	2	1	no	—
717	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
718	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
719	C₂×#41	C₂³×C₅₃	1	2	yes	—
720	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
721	C₂²×D₄	—	2	1	no	—
722	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
723	C₂³×C₄	—	2	2	no	—
724	#137	—	2	4	no	—
725	AGL(1,ℤ/8)	—	2	8	no	—
726	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
727	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
728	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
733	C₂×D₈	C₂³×C₅₃	1	2	yes	—
734	C₂×D₈	C₂³×C₅₃	1	2	yes	—
735	C₂×D₈	C₂³×C₅₃	1	2	yes	—
736	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
737	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
739	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
740	C₄⋊Q₈	—	2	1	no	—
741	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
742	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
743	#127	—	2	1	no	—
744	#127	C₂³×C₅₃	1	1	yes	characteristic
745	#127	C₂³×C₅₃	1	1	yes	characteristic
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#126	—	2	2	no	—
751	#125	—	2	1	no	—
752	#125	—	2	2	no	—
753	#125	C₂³×C₅₃	1	2	yes	—
754	#125	C₂³×C₅₃	1	2	yes	—
755	#124	—	2	1	no	—
756	#124	—	2	1	no	—
757	#124	—	2	1	no	—
758	#124	—	2	2	no	—
759	#124	—	2	1	no	—
760	#124	—	2	1	no	—
761	#124	C₂³×C₅₃	1	2	yes	—
762	#124	C₂³×C₅₃	1	2	yes	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	—	2	1	no	—
780	#121	—	2	1	no	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	C₂³×C₅₃	1	2	yes	—
785	#121	C₂³×C₅₃	1	2	yes	—
786	#121	C₂³×C₅₃	1	2	yes	—
787	#121	C₂³×C₅₃	1	2	yes	—
788	#120	—	2	2	no	—
789	#120	—	2	2	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
802	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
821	C₄×D₄	D₄×C₅₃	1	2	yes	—
822	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₅₃	1	2	yes	—
824	C₄×D₄	C₂³×C₅₃	1	2	yes	—
825	C₄×D₄	C₂³×C₅₃	1	2	yes	—
826	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₅₃	1	2	yes	—
828	C₄×D₄	C₂³×C₅₃	1	2	yes	—
829	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₅₃	1	2	yes	—
831	#117	—	2	2	no	—
832	#117	—	2	1	no	—
833	#117	—	2	2	no	—
834	#117	—	2	2	no	—
835	#117	D₄×C₅₃	1	1	yes	characteristic
836	#117	D₄×C₅₃	1	2	yes	—
837	#117	C₂³×C₅₃	1	1	yes	characteristic
838	#117	C₂³×C₅₃	1	2	yes	—
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	—	2	1	no	—
841	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
842	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₄²	—	2	1	no	—
846	C₂×C₄²	—	2	1	no	—
847	C₂×C₄²	—	2	2	no	—
848	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
849	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
850	#107	C₂³×C₅₃	1	1	yes	characteristic
851	#107	C₂³×C₅₃	1	2	yes	—
852	#107	C₂³×C₅₃	1	1	yes	characteristic
853	#107	C₂³×C₅₃	1	2	yes	—
854	#107	C₂³×C₅₃	1	2	yes	—
855	#106	C₂³×C₅₃	1	1	yes	characteristic
856	#106	C₂³×C₅₃	1	1	yes	characteristic
857	#106	C₂³×C₅₃	1	2	yes	—
858	#106	C₂³×C₅₃	1	2	yes	—
859	#106	C₂³×C₅₃	1	2	yes	—
860	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
863	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
864	#103	C₂³×C₅₃	1	1	yes	characteristic
865	#103	C₂³×C₅₃	1	1	yes	characteristic
866	#103	C₂³×C₅₃	1	1	yes	characteristic
867	#103	C₂³×C₅₃	1	2	yes	—
868	#103	C₂³×C₅₃	1	1	yes	characteristic
869	#103	C₂³×C₅₃	1	1	yes	characteristic
870	#103	C₂³×C₅₃	1	1	yes	characteristic
871	#103	C₂³×C₅₃	1	2	yes	—
872	#103	C₂³×C₅₃	1	2	yes	—
873	#102	C₂³×C₅₃	1	1	yes	characteristic
874	#102	C₂³×C₅₃	1	1	yes	characteristic
875	#102	C₂³×C₅₃	1	2	yes	—
876	#102	C₂³×C₅₃	1	2	yes	—
877	#102	C₂³×C₅₃	1	2	yes	—
878	#102	C₂³×C₅₃	1	2	yes	—
879	#102	C₂³×C₅₃	1	2	yes	—
880	#102	C₂³×C₅₃	1	2	yes	—
881	#102	C₂³×C₅₃	1	2	yes	—
882	#102	C₂³×C₅₃	1	2	yes	—
883	#102	C₂³×C₅₃	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
887	#97	C₂³×C₅₃	1	1	yes	characteristic
888	#97	C₂³×C₅₃	1	1	yes	characteristic
889	#97	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	2	yes	—
893	C₄×C₈	C₂³×C₅₃	1	2	yes	—
894	C₂⁴	—	2	2	no	—
895	#41	—	2	4	no	—
896	#41	—	2	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	1	no	—
900	#41	—	4	4	no	—
901	#41	—	8	2	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	4	1	no	—
907	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
908	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
911	C₂×D₄	—	2	4	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	4	4	no	—
925	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
926	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
927	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
928	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
929	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	8	4	no	—
943	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
944	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
945	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
947	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
949	Q₁₆	—	2	2	no	—
950	Q₁₆	—	2	2	no	—
951	SD₁₆	—	2	4	no	—
952	SD₁₆	—	2	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	#41×C₅₃	1	4	yes	complemented
956	D₈	—	2	4	no	—
957	D₈	—	2	4	no	—
958	D₈	—	4	2	no	—
959	M₁₆	—	2	4	no	—
960	M₁₆	—	2	2	no	—
961	M₁₆	—	4	1	no	—
962	M₁₆	—	4	2	no	—
963	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
966	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
967	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
987	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
988	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
989	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1028	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1029	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1030	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₅₃	1	2	yes	—
1032	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	4	4	no	—
1038	C₂³	—	4	4	no	—
1039	C₂³	—	8	2	no	—
1040	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1041	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1042	Q₈	—	2	2	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	4	2	no	—
1049	Q₈	—	4	2	no	—
1050	Q₈	—	8	1	no	—
1051	Q₈	C₂×#41×C₅₃	1	2	yes	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	4	2	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	4	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	4	4	no	—
1063	D₄	—	4	4	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	8	1	no	—
1067	D₄	—	8	1	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	C₂×#41×C₅₃	1	2	yes	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	4	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	4	4	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	1	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1108	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	2	no	—
1114	C₈	C₂×#41×C₅₃	1	2	yes	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	8	8	no	—
1131	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1132	C₄	—	2	2	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	C₅₃×#575	1	2	yes	—
1149	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1150	C₄	C₅₃×#585	1	1	yes	characteristic
1151	C₂	—	4	2	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	2	no	—
1156	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1157	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1158	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 ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3481	C₂	semidirect
2. C₅₃×#3480	C₂	semidirect
3. C₅₃×#3396	C₂	semidirect
4. C₅₃×#3381	C₂	semidirect
5. C₅₃×#3365	C₂	semidirect
6. C₅₃×#3361	C₂	semidirect
7. C₅₃×#3356	C₂	semidirect
8. C₅₃×#3355	C₂	semidirect
9. C₅₃×#3333	C₂	semidirect
10. C₅₃×#3326	C₂	semidirect
11. C₅₃×#3324	C₂	semidirect
12. C₅₃×#3322	C₂	semidirect
13. C₅₃×#3275	C₂	semidirect
14. C₅₃×#3274	C₂	semidirect
15. C₅₃×#3184	C₂	semidirect
16. C₅₃×#3183	C₂	semidirect
17. C₅₃×#3115	C₂	semidirect
18. C₅₃×#3114	C₂	semidirect
19. C₅₃×#3112	C₂	semidirect
20. C₅₃×#3111	C₂	semidirect
21. C₅₃×#2971	C₂	semidirect
22. C₄×#137×C₅₃	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
28. C₅₃×#559	C₂²	semidirect
29. C₅₃×#557	C₂²	semidirect
37. C₅₃×#553	C₂²	semidirect
40. C₅₃×#548	C₂²	semidirect
46. C₅₃×#532	C₂²	semidirect
50. C₅₃×#529	C₂²	semidirect
55. C₄×#41×C₅₃	C₂²	semidirect
56. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
59. C₅₃×#499	C₂²	semidirect
60. C₅₃×#498	C₂²	semidirect
61. C₅₃×#495	C₂²	semidirect
63. C₅₃×#488	C₂²	semidirect
64. C₅₃×#488	C₂²	semidirect
66. C₅₃×#486	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#483	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#480	C₂²	semidirect
72. C₅₃×#480	C₂²	semidirect
73. C₅₃×#479	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#478	C₂²	semidirect
77. C₅₃×#477	C₂²	semidirect
78. C₅₃×#477	C₂²	semidirect
79. C₅₃×#475	C₂²	semidirect
81. C₅₃×#470	C₂²	semidirect
83. C₅₃×#469	C₂²	semidirect
84. C₅₃×#469	C₂²	semidirect
86. C₅₃×#468	C₂²	semidirect
87. C₅₃×#464	C₂²	semidirect
89. C₅₃×#463	C₂²	semidirect
90. C₅₃×#463	C₂²	semidirect
93. C₅₃×#460	C₂²	semidirect
95. C₅₃×#452	C₂²	semidirect
99. C₅₃×#448	C₂²	semidirect
101. C₈×Q₈×C₅₃	C₂²	semidirect
102. C₈×Q₈×C₅₃	C₂²	semidirect
104. C₅₃×#442	C₂²	semidirect
105. C₅₃×#442	C₂²	semidirect
106. C₅₃×#441	C₂²	semidirect
107. C₅₃×#441	C₂²	semidirect
110. C₅₃×#440	C₂²	semidirect
111. C₅₃×#440	C₂²	semidirect
112. C₅₃×#440	C₂²	semidirect
113. C₄×Q₁₆×C₅₃	C₂²	semidirect
114. C₄×Q₁₆×C₅₃	C₂²	semidirect
118. C₄×SD₁₆×C₅₃	C₂²	semidirect
120. C₄×D₈×C₅₃	C₂²	semidirect
123. C₅₃×#436	C₂²	semidirect
124. C₅₃×#436	C₂²	semidirect
125. C₅₃×#432	C₂²	semidirect
126. C₅₃×#432	C₂²	semidirect
127. C₅₃×#428	C₂²	semidirect
128. C₅₃×#428	C₂²	semidirect
129. C₅₃×#419	C₂²	semidirect
132. C₅₃×#417	C₂²	semidirect
133. C₄×M₁₆×C₅₃	C₂²	semidirect
134. C₄×M₁₆×C₅₃	C₂²	semidirect
375. SD₁₆×C₅₃	#41	semidirect
535. #61468	C₅₃	direct (N × H)
572. #3481	C₂×C₅₃	semidirect
573. #3480	C₂×C₅₃	semidirect
574. #3396	C₂×C₅₃	semidirect
575. #3381	C₂×C₅₃	semidirect
576. #3365	C₂×C₅₃	semidirect
577. #3361	C₂×C₅₃	semidirect
578. #3356	C₂×C₅₃	semidirect
579. #3355	C₂×C₅₃	semidirect
580. #3333	C₂×C₅₃	semidirect
581. #3326	C₂×C₅₃	semidirect
582. #3324	C₂×C₅₃	semidirect
583. #3322	C₂×C₅₃	semidirect
584. #3275	C₂×C₅₃	semidirect
585. #3274	C₂×C₅₃	semidirect
586. #3184	C₂×C₅₃	semidirect
587. #3183	C₂×C₅₃	semidirect
588. #3115	C₂×C₅₃	semidirect
589. #3114	C₂×C₅₃	semidirect
590. #3112	C₂×C₅₃	semidirect
591. #3111	C₂×C₅₃	semidirect
592. #2971	C₂×C₅₃	semidirect
593. C₄×#137	C₂×C₅₃	semidirect
594. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
607. #559	C₂²×C₅₃	semidirect
608. #557	C₂²×C₅₃	semidirect
616. #553	C₂²×C₅₃	semidirect
619. #548	C₂²×C₅₃	semidirect
625. #532	C₂²×C₅₃	semidirect
629. #529	C₂²×C₅₃	semidirect
634. C₄×#41	C₂²×C₅₃	semidirect
635. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
638. #499	C₂²×C₅₃	semidirect
639. #498	C₂²×C₅₃	semidirect
640. #495	C₂²×C₅₃	semidirect
642. #488	C₂²×C₅₃	semidirect
643. #488	C₂²×C₅₃	semidirect
645. #486	C₂²×C₅₃	semidirect
646. #485	C₂²×C₅₃	semidirect
647. #483	C₂²×C₅₃	semidirect
649. #482	C₂²×C₅₃	semidirect
650. #480	C₂²×C₅₃	semidirect
651. #480	C₂²×C₅₃	semidirect
652. #479	C₂²×C₅₃	semidirect
654. #478	C₂²×C₅₃	semidirect
655. #478	C₂²×C₅₃	semidirect
656. #477	C₂²×C₅₃	semidirect
657. #477	C₂²×C₅₃	semidirect
658. #475	C₂²×C₅₃	semidirect
660. #470	C₂²×C₅₃	semidirect
662. #469	C₂²×C₅₃	semidirect
663. #469	C₂²×C₅₃	semidirect
665. #468	C₂²×C₅₃	semidirect
666. #464	C₂²×C₅₃	semidirect
668. #463	C₂²×C₅₃	semidirect
669. #463	C₂²×C₅₃	semidirect
672. #460	C₂²×C₅₃	semidirect
674. #452	C₂²×C₅₃	semidirect
678. #448	C₂²×C₅₃	semidirect
680. C₈×Q₈	C₂²×C₅₃	semidirect
681. C₈×Q₈	C₂²×C₅₃	semidirect
683. #442	C₂²×C₅₃	semidirect
684. #442	C₂²×C₅₃	semidirect
685. #441	C₂²×C₅₃	semidirect
686. #441	C₂²×C₅₃	semidirect
689. #440	C₂²×C₅₃	semidirect
690. #440	C₂²×C₅₃	semidirect
691. #440	C₂²×C₅₃	semidirect
692. C₄×Q₁₆	C₂²×C₅₃	semidirect
693. C₄×Q₁₆	C₂²×C₅₃	semidirect
697. C₄×SD₁₆	C₂²×C₅₃	semidirect
699. C₄×D₈	C₂²×C₅₃	semidirect
702. #436	C₂²×C₅₃	semidirect
703. #436	C₂²×C₅₃	semidirect
704. #432	C₂²×C₅₃	semidirect
705. #432	C₂²×C₅₃	semidirect
706. #428	C₂²×C₅₃	semidirect
707. #428	C₂²×C₅₃	semidirect
708. #419	C₂²×C₅₃	semidirect
711. #417	C₂²×C₅₃	semidirect
712. C₄×M₁₆	C₂²×C₅₃	semidirect
713. C₄×M₁₆	C₂²×C₅₃	semidirect
714. C₅₃	#61468	direct (N × H)
955. SD₁₆	#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×#3481	2
C₅₃×#3480	2
C₅₃×#3396	2
C₅₃×#3381	2
C₅₃×#3365	2
C₅₃×#3361	2
C₅₃×#3356	2
C₅₃×#3355	2
C₅₃×#3333	2
C₅₃×#3326	2
C₅₃×#3324	2
C₅₃×#3322	2
C₅₃×#3275	2
C₅₃×#3274	2
C₅₃×#3184	2
C₅₃×#3183	2
C₅₃×#3115	2
C₅₃×#3114	2
C₅₃×#3112	2
C₅₃×#3111	2
C₅₃×#2971	2
C₄×#137×C₅₃	2
C₄×AGL(1,ℤ/8)×C₅₃	2
#61468	53

Subgroups — C53×#61468 #27268980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61468 #27268980