Subgroups — C₅₃×#61473 #27268985

Order 13568.

1770 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3516	C₂	1	2	yes	maximal, complemented
2	C₅₃×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3377	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3339	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3327	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3320	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3316	C₂	1	2	yes	maximal, complemented
11	D₄×Q₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3285	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3177	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3175	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3121	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3120	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3117	C₂	1	2	yes	maximal, complemented
20	C₅₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×Q₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
25	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#557	C₂²	1	2	yes	—
28	C₅₃×#556	—	2	2	no	—
29	C₅₃×#556	C₂²	1	2	yes	—
30	C₅₃×#554	—	2	2	no	—
31	C₅₃×#554	C₂²	1	2	yes	—
32	C₅₃×#553	—	2	2	no	—
33	C₅₃×#553	C₂²	1	2	yes	—
34	C₅₃×#552	—	2	2	no	—
35	C₅₃×#552	C₂²	1	2	yes	—
36	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
37	C₅₃×#548	C₂²	1	2	yes	—
38	C₅₃×#548	C₂²	1	2	yes	—
39	C₅₃×#542	—	2	2	no	—
40	C₅₃×#542	C₂²	1	2	yes	—
41	C₅₃×#541	—	2	2	no	—
42	C₅₃×#541	C₂²	1	2	yes	—
43	C₅₃×#529	—	2	2	no	—
44	C₅₃×#529	—	2	2	no	—
45	C₅₃×#529	C₂²	1	2	yes	—
46	C₅₃×#529	C₂²	1	1	yes	characteristic
47	C₅₃×#520	C₂²	1	2	yes	—
48	C₅₃×#519	C₂²	1	2	yes	—
49	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
50	C₅₃×#500	C₂²	1	1	yes	characteristic
51	C₅₃×#499	C₂²	1	1	yes	characteristic
52	C₅₃×#499	C₂²	1	1	yes	characteristic
53	C₅₃×#495	C₂²	1	1	yes	characteristic
54	C₅₃×#495	C₂²	1	1	yes	characteristic
55	C₅₃×#494	C₂²	1	1	yes	characteristic
56	C₅₃×#491	C₂²	1	2	yes	—
57	C₅₃×#489	C₂²	1	2	yes	—
58	C₅₃×#488	C₂²	1	2	yes	—
59	C₅₃×#485	C₂²	1	2	yes	—
60	C₅₃×#484	C₂²	1	2	yes	—
61	C₅₃×#484	C₂²	1	2	yes	—
62	C₅₃×#483	C₂²	1	2	yes	—
63	C₅₃×#482	C₂²	1	2	yes	—
64	C₅₃×#481	C₂²	1	2	yes	—
65	C₅₃×#479	C₂²	1	2	yes	—
66	C₅₃×#479	C₂²	1	2	yes	—
67	C₅₃×#479	C₂²	1	2	yes	—
68	C₅₃×#478	C₂²	1	2	yes	—
69	C₅₃×#477	C₂²	1	2	yes	—
70	C₅₃×#475	C₂²	1	2	yes	—
71	C₅₃×#470	C₂²	1	2	yes	—
72	C₅₃×#468	C₂²	1	2	yes	—
73	C₅₃×#467	C₂²	1	1	yes	characteristic
74	C₅₃×#467	C₂²	1	1	yes	characteristic
75	C₅₃×#467	C₂²	1	1	yes	characteristic
76	C₅₃×#467	C₂²	1	1	yes	characteristic
77	C₅₃×#466	C₂²	1	1	yes	characteristic
78	C₅₃×#466	C₂²	1	1	yes	characteristic
79	C₅₃×#465	C₂²	1	2	yes	—
80	C₅₃×#464	C₂²	1	2	yes	—
81	C₅₃×#464	C₂²	1	2	yes	—
82	C₅₃×#464	C₂²	1	2	yes	—
83	C₅₃×#464	C₂²	1	2	yes	—
84	C₅₃×#462	C₂²	1	2	yes	—
85	C₅₃×#461	C₂²	1	2	yes	—
86	C₅₃×#452	C₂²	1	2	yes	—
87	C₅₃×#452	C₂²	1	2	yes	—
88	C₅₃×#451	C₂²	1	2	yes	—
89	C₅₃×#451	C₂²	1	2	yes	—
90	C₅₃×#448	C₂²	1	2	yes	—
91	C₅₃×#448	C₂²	1	2	yes	—
92	C₅₃×#446	C₂²	1	1	yes	characteristic
93	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
94	C₅₃×#441	C₂²	1	2	yes	—
95	C₅₃×#441	C₂²	1	2	yes	—
96	C₅₃×#441	C₂²	1	2	yes	—
97	C₅₃×#440	C₂²	1	2	yes	—
98	C₅₃×#440	C₂²	1	2	yes	—
99	C₅₃×#440	C₂²	1	2	yes	—
100	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
101	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
102	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
103	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
104	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
105	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
106	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
107	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
108	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
109	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
110	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
111	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
112	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
113	C₅₃×#436	C₂²	1	1	yes	characteristic
114	C₅₃×#435	C₂²	1	1	yes	characteristic
115	C₅₃×#435	C₂²	1	1	yes	characteristic
116	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
117	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
118	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
119	C₅₃×#433	C₂²	1	1	yes	characteristic
120	C₅₃×#433	C₂²	1	1	yes	characteristic
121	C₅₃×#432	C₂²	1	1	yes	characteristic
122	C₅₃×#427	C₂²	1	1	yes	characteristic
123	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
124	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
125	C₅₃×#419	C₂²	1	2	yes	—
126	C₅₃×#417	C₂²	1	2	yes	—
127	C₂×#103×C₅₃	C₂²	1	2	yes	—
128	C₅₃×#405	C₂²	1	1	yes	characteristic
129	C₅₃×#405	C₂²	1	1	yes	characteristic
130	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
131	C₂×#41×C₅₃	C₂³	1	2	yes	—
132	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
133	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
134	#135×C₅₃	—	2	4	no	—
135	C₂×Q₁₆×C₅₃	—	2	4	no	—
136	C₂×Q₁₆×C₅₃	—	2	4	no	—
137	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
146	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₅₃	—	2	2	no	—
154	C₄⋊Q₈×C₅₃	—	2	2	no	—
155	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
157	#126×C₅₃	—	2	2	no	—
158	#126×C₅₃	—	2	2	no	—
159	#126×C₅₃	—	2	2	no	—
160	#126×C₅₃	—	2	2	no	—
161	#126×C₅₃	—	2	2	no	—
162	#126×C₅₃	—	2	2	no	—
163	#126×C₅₃	—	2	2	no	—
164	#126×C₅₃	—	2	2	no	—
165	#126×C₅₃	D₄	1	1	yes	characteristic
166	#126×C₅₃	D₄	1	1	yes	characteristic
167	#125×C₅₃	—	2	2	no	—
168	#125×C₅₃	—	2	2	no	—
169	#125×C₅₃	—	2	2	no	—
170	#125×C₅₃	—	2	2	no	—
171	#125×C₅₃	—	2	2	no	—
172	#125×C₅₃	—	2	2	no	—
173	#125×C₅₃	D₄	1	1	yes	characteristic
174	#125×C₅₃	C₂³	1	2	yes	—
175	#125×C₅₃	C₂³	1	2	yes	—
176	#124×C₅₃	—	2	2	no	—
177	#124×C₅₃	—	2	2	no	—
178	#124×C₅₃	—	2	2	no	—
179	#124×C₅₃	D₄	1	1	yes	characteristic
180	#124×C₅₃	C₂³	1	2	yes	—
181	#124×C₅₃	C₂³	1	2	yes	—
182	#123×C₅₃	—	2	2	no	—
183	#123×C₅₃	—	2	2	no	—
184	#123×C₅₃	—	2	2	no	—
185	#123×C₅₃	—	2	2	no	—
186	#123×C₅₃	D₄	1	1	yes	characteristic
187	#123×C₅₃	D₄	1	1	yes	characteristic
188	C₂²⋊Q₈×C₅₃	—	2	2	no	—
189	C₂²⋊Q₈×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	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	2	no	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
197	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
201	#121×C₅₃	—	2	2	no	—
202	#121×C₅₃	—	2	2	no	—
203	#121×C₅₃	—	2	2	no	—
204	#121×C₅₃	D₄	1	1	yes	characteristic
205	#121×C₅₃	C₂³	1	2	yes	—
206	#121×C₅₃	C₂³	1	2	yes	—
207	C₄×Q₈×C₅₃	—	2	2	no	—
208	C₄×Q₈×C₅₃	—	2	2	no	—
209	C₄×Q₈×C₅₃	—	2	2	no	—
210	C₄×Q₈×C₅₃	—	2	2	no	—
211	C₄×Q₈×C₅₃	—	2	2	no	—
212	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
214	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
218	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
221	C₄×D₄×C₅₃	—	2	2	no	—
222	C₄×D₄×C₅₃	—	2	2	no	—
223	C₄×D₄×C₅₃	—	2	2	no	—
224	C₄×D₄×C₅₃	—	2	2	no	—
225	C₄×D₄×C₅₃	—	2	2	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	C₂³	1	2	yes	—
230	C₄×D₄×C₅₃	C₂³	1	2	yes	—
231	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
234	#117×C₅₃	—	2	2	no	—
235	#117×C₅₃	—	2	2	no	—
236	#117×C₅₃	—	2	2	no	—
237	#117×C₅₃	—	2	2	no	—
238	#117×C₅₃	—	2	2	no	—
239	#117×C₅₃	—	2	2	no	—
240	#117×C₅₃	C₂³	1	2	yes	—
241	#117×C₅₃	C₂³	1	1	yes	characteristic
242	#117×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
244	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
245	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
246	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
247	C₂×C₄²×C₅₃	—	2	2	no	—
248	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
249	#107×C₅₃	C₂³	1	2	yes	—
250	#107×C₅₃	C₂³	1	1	yes	characteristic
251	#107×C₅₃	C₂³	1	1	yes	characteristic
252	#107×C₅₃	C₂³	1	1	yes	characteristic
253	#107×C₅₃	C₂³	1	2	yes	—
254	#107×C₅₃	C₂³	1	1	yes	characteristic
255	#107×C₅₃	C₂³	1	2	yes	—
256	#106×C₅₃	C₂³	1	2	yes	—
257	#106×C₅₃	C₂³	1	2	yes	—
258	#106×C₅₃	C₂³	1	2	yes	—
259	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
260	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
261	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
262	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
263	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
264	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
265	#103×C₅₃	C₂³	1	2	yes	—
266	#103×C₅₃	C₂³	1	2	yes	—
267	#103×C₅₃	C₂³	1	2	yes	—
268	#103×C₅₃	C₂³	1	2	yes	—
269	#103×C₅₃	C₂³	1	2	yes	—
270	#103×C₅₃	C₂³	1	2	yes	—
271	#103×C₅₃	C₂³	1	2	yes	—
272	#103×C₅₃	C₂³	1	2	yes	—
273	#103×C₅₃	C₂³	1	2	yes	—
274	#103×C₅₃	C₂³	1	2	yes	—
275	#103×C₅₃	C₂³	1	2	yes	—
276	#103×C₅₃	C₂³	1	2	yes	—
277	#102×C₅₃	C₂³	1	2	yes	—
278	#102×C₅₃	C₂³	1	2	yes	—
279	#102×C₅₃	C₂³	1	2	yes	—
280	#102×C₅₃	C₂³	1	2	yes	—
281	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	#97×C₅₃	C₂³	1	1	yes	characteristic
288	#97×C₅₃	C₂³	1	1	yes	characteristic
289	#97×C₅₃	C₂³	1	1	yes	characteristic
290	#97×C₅₃	C₂³	1	1	yes	characteristic
291	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
292	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
297	#41×C₅₃	—	2	4	no	—
298	#41×C₅₃	—	4	2	no	—
299	C₂×Q₈×C₅₃	—	2	2	no	—
300	C₂×Q₈×C₅₃	—	2	2	no	—
301	C₂×Q₈×C₅₃	—	2	2	no	—
302	C₂×Q₈×C₅₃	—	2	4	no	—
303	C₂×Q₈×C₅₃	—	2	4	no	—
304	C₂×Q₈×C₅₃	—	4	2	no	—
305	C₂×Q₈×C₅₃	—	4	2	no	—
306	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
307	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
308	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
309	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
310	C₂×D₄×C₅₃	—	2	2	no	—
311	C₂×D₄×C₅₃	—	2	2	no	—
312	C₂×D₄×C₅₃	—	2	2	no	—
313	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
314	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
315	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
316	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₅₃	—	2	2	no	—
318	C₂²×C₄×C₅₃	—	2	2	no	—
319	C₂²×C₄×C₅₃	—	2	2	no	—
320	C₂²×C₄×C₅₃	—	2	2	no	—
321	C₂²×C₄×C₅₃	—	2	2	no	—
322	C₂²×C₄×C₅₃	—	2	2	no	—
323	C₂²×C₄×C₅₃	—	2	2	no	—
324	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
329	Q₁₆×C₅₃	—	2	4	no	—
330	Q₁₆×C₅₃	—	2	4	no	—
331	Q₁₆×C₅₃	—	2	2	no	—
332	Q₁₆×C₅₃	—	2	2	no	—
333	Q₁₆×C₅₃	—	4	2	no	—
334	Q₁₆×C₅₃	#41	1	4	yes	—
335	SD₁₆×C₅₃	—	2	4	no	—
336	SD₁₆×C₅₃	—	4	2	no	—
337	SD₁₆×C₅₃	—	4	2	no	—
338	D₈×C₅₃	—	2	2	no	—
339	M₁₆×C₅₃	—	4	1	no	—
340	M₁₆×C₅₃	—	4	1	no	—
341	C₂×C₈×C₅₃	—	2	2	no	—
342	C₂×C₈×C₅₃	—	2	2	no	—
343	C₂×C₈×C₅₃	—	2	2	no	—
344	C₂×C₈×C₅₃	—	4	1	no	—
345	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
346	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₄⋊C₄×C₅₃	—	2	2	no	—
354	C₄⋊C₄×C₅₃	—	2	2	no	—
355	C₄⋊C₄×C₅₃	—	2	2	no	—
356	C₄⋊C₄×C₅₃	—	2	2	no	—
357	C₄⋊C₄×C₅₃	—	2	2	no	—
358	C₄⋊C₄×C₅₃	—	2	2	no	—
359	C₄⋊C₄×C₅₃	—	2	2	no	—
360	C₄⋊C₄×C₅₃	—	2	2	no	—
361	C₄⋊C₄×C₅₃	—	2	2	no	—
362	C₄⋊C₄×C₅₃	—	2	2	no	—
363	C₄⋊C₄×C₅₃	—	2	2	no	—
364	C₄⋊C₄×C₅₃	—	2	2	no	—
365	C₄⋊C₄×C₅₃	—	2	2	no	—
366	C₄⋊C₄×C₅₃	—	2	2	no	—
367	C₄⋊C₄×C₅₃	—	2	2	no	—
368	C₄⋊C₄×C₅₃	—	2	2	no	—
369	C₄⋊C₄×C₅₃	—	2	2	no	—
370	C₄⋊C₄×C₅₃	—	2	2	no	—
371	C₄⋊C₄×C₅₃	—	2	2	no	—
372	C₄⋊C₄×C₅₃	—	2	2	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
375	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
376	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
378	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
383	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
384	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
386	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
387	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
388	C₂²⋊C₄×C₅₃	—	2	2	no	—
389	C₂²⋊C₄×C₅₃	—	2	2	no	—
390	C₂²⋊C₄×C₅₃	—	2	2	no	—
391	C₂²⋊C₄×C₅₃	—	2	2	no	—
392	C₂²⋊C₄×C₅₃	—	2	2	no	—
393	C₂²⋊C₄×C₅₃	—	2	2	no	—
394	C₂²⋊C₄×C₅₃	—	2	2	no	—
395	C₂²⋊C₄×C₅₃	—	2	2	no	—
396	C₂²⋊C₄×C₅₃	—	2	2	no	—
397	C₂²⋊C₄×C₅₃	—	2	2	no	—
398	C₂²⋊C₄×C₅₃	—	2	2	no	—
399	C₂²⋊C₄×C₅₃	—	2	2	no	—
400	C₂²⋊C₄×C₅₃	—	2	2	no	—
401	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
402	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
403	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
404	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
405	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
406	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
407	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
408	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
409	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
410	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
411	C₄²×C₅₃	—	2	2	no	—
412	C₄²×C₅₃	—	2	2	no	—
413	C₄²×C₅₃	—	2	2	no	—
414	C₄²×C₅₃	—	2	2	no	—
415	C₄²×C₅₃	—	2	2	no	—
416	C₄²×C₅₃	—	2	2	no	—
417	C₄²×C₅₃	—	2	2	no	—
418	C₄²×C₅₃	—	2	2	no	—
419	C₄²×C₅₃	—	2	2	no	—
420	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
421	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
422	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
426	C₂³×C₅₃	—	2	2	no	—
427	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
428	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
429	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
430	Q₈×C₅₃	—	2	2	no	—
431	Q₈×C₅₃	—	2	2	no	—
432	Q₈×C₅₃	—	2	2	no	—
433	Q₈×C₅₃	—	2	2	no	—
434	Q₈×C₅₃	—	2	2	no	—
435	Q₈×C₅₃	—	4	1	no	—
436	Q₈×C₅₃	—	4	4	no	—
437	Q₈×C₅₃	—	4	4	no	—
438	Q₈×C₅₃	—	8	2	no	—
439	Q₈×C₅₃	C₂×#41	1	4	yes	—
440	D₄×C₅₃	—	2	2	no	—
441	D₄×C₅₃	—	2	2	no	—
442	D₄×C₅₃	—	2	2	no	—
443	D₄×C₅₃	—	2	2	no	—
444	D₄×C₅₃	—	4	1	no	—
445	D₄×C₅₃	—	4	4	no	—
446	D₄×C₅₃	—	4	4	no	—
447	D₄×C₅₃	—	8	2	no	—
448	C₂×C₄×C₅₃	—	2	2	no	—
449	C₂×C₄×C₅₃	—	2	2	no	—
450	C₂×C₄×C₅₃	—	2	1	no	—
451	C₂×C₄×C₅₃	—	2	1	no	—
452	C₂×C₄×C₅₃	—	2	1	no	—
453	C₂×C₄×C₅₃	—	2	1	no	—
454	C₂×C₄×C₅₃	—	2	1	no	—
455	C₂×C₄×C₅₃	—	2	1	no	—
456	C₂×C₄×C₅₃	—	2	2	no	—
457	C₂×C₄×C₅₃	—	2	2	no	—
458	C₂×C₄×C₅₃	—	2	2	no	—
459	C₂×C₄×C₅₃	—	2	2	no	—
460	C₂×C₄×C₅₃	—	2	2	no	—
461	C₂×C₄×C₅₃	—	2	2	no	—
462	C₂×C₄×C₅₃	—	4	1	no	—
463	C₂×C₄×C₅₃	—	4	4	no	—
464	C₂×C₄×C₅₃	—	4	4	no	—
465	C₂×C₄×C₅₃	—	4	4	no	—
466	C₂×C₄×C₅₃	—	8	2	no	—
467	C₂×C₄×C₅₃	—	8	2	no	—
468	C₂×C₄×C₅₃	—	8	2	no	—
469	C₂×C₄×C₅₃	—	8	2	no	—
470	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
482	C₈×C₅₃	—	2	1	no	—
483	C₈×C₅₃	—	2	1	no	—
484	C₈×C₅₃	—	2	1	no	—
485	C₈×C₅₃	—	2	1	no	—
486	C₈×C₅₃	—	2	1	no	—
487	C₈×C₅₃	—	2	1	no	—
488	C₈×C₅₃	—	2	1	no	—
489	C₈×C₅₃	C₂×#41	1	2	yes	—
490	#61473	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
491	C₂²×C₅₃	—	2	1	no	—
492	C₂²×C₅₃	—	2	1	no	—
493	C₂²×C₅₃	—	2	1	no	—
494	C₂²×C₅₃	—	2	1	no	—
495	C₂²×C₅₃	—	2	1	no	—
496	C₂²×C₅₃	—	2	1	no	—
497	C₂²×C₅₃	—	2	1	no	—
498	C₂²×C₅₃	—	2	1	no	—
499	C₂²×C₅₃	—	4	2	no	—
500	C₂²×C₅₃	—	4	2	no	—
501	C₂²×C₅₃	—	4	2	no	—
502	C₂²×C₅₃	#578	1	2	yes	—
503	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
504	C₄×C₅₃	—	2	1	no	—
505	C₄×C₅₃	—	2	1	no	—
506	C₄×C₅₃	—	2	1	no	—
507	C₄×C₅₃	—	2	1	no	—
508	C₄×C₅₃	—	2	1	no	—
509	C₄×C₅₃	—	2	1	no	—
510	C₄×C₅₃	—	2	1	no	—
511	C₄×C₅₃	—	2	4	no	—
512	C₄×C₅₃	—	2	1	no	—
513	C₄×C₅₃	—	2	1	no	—
514	C₄×C₅₃	—	2	1	no	—
515	C₄×C₅₃	—	2	1	no	—
516	C₄×C₅₃	—	4	2	no	—
517	C₄×C₅₃	—	4	2	no	—
518	C₄×C₅₃	—	4	2	no	—
519	C₄×C₅₃	—	4	2	no	—
520	C₄×C₅₃	—	4	2	no	—
521	C₄×C₅₃	—	4	2	no	—
522	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
523	C₄×C₅₃	#585	1	1	yes	characteristic
524	#3516	C₂×C₅₃	1	2	yes	complemented
525	#3393	C₂×C₅₃	1	1	yes	characteristic, complemented
526	#3383	C₂×C₅₃	1	1	yes	characteristic, complemented
527	#3377	C₂×C₅₃	1	2	yes	complemented
528	#3339	C₂×C₅₃	1	1	yes	characteristic, complemented
529	#3338	C₂×C₅₃	1	1	yes	characteristic, complemented
530	#3336	C₂×C₅₃	1	1	yes	characteristic, complemented
531	#3327	C₂×C₅₃	1	2	yes	complemented
532	#3320	C₂×C₅₃	1	2	yes	complemented
533	#3316	C₂×C₅₃	1	2	yes	complemented
534	D₄×Q₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
535	#3285	C₂×C₅₃	1	1	yes	characteristic, complemented
536	#3285	C₂×C₅₃	1	1	yes	characteristic, complemented
537	#3177	C₂×C₅₃	1	1	yes	characteristic, complemented
538	#3175	C₂×C₅₃	1	1	yes	characteristic, complemented
539	#3168	C₂×C₅₃	1	1	yes	characteristic, complemented
540	#3121	C₂×C₅₃	1	2	yes	complemented
541	#3120	C₂×C₅₃	1	2	yes	complemented
542	#3117	C₂×C₅₃	1	2	yes	complemented
543	#2966	C₂×C₅₃	1	1	yes	characteristic, complemented
544	#2951	C₂×C₅₃	1	1	yes	characteristic, complemented
545	#2950	C₂×C₅₃	1	1	yes	characteristic, complemented
546	C₂×C₄×Q₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
547	C₂×C₅₃	—	2	2	no	—
548	C₂×C₅₃	—	4	1	no	—
549	C₂×C₅₃	—	4	1	no	—
550	C₂×C₅₃	—	8	2	no	—
551	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
552	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
553	C₂×C₅₃	#3584	1	1	yes	characteristic
554	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
555	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
556	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
557	#557	C₂²×C₅₃	1	2	yes	—
558	#556	—	2	2	no	—
559	#556	C₂²×C₅₃	1	2	yes	—
560	#554	—	2	2	no	—
561	#554	C₂²×C₅₃	1	2	yes	—
562	#553	—	2	2	no	—
563	#553	C₂²×C₅₃	1	2	yes	—
564	#552	—	2	2	no	—
565	#552	C₂²×C₅₃	1	2	yes	—
566	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
567	#548	C₂²×C₅₃	1	2	yes	—
568	#548	C₂²×C₅₃	1	2	yes	—
569	#542	—	2	2	no	—
570	#542	C₂²×C₅₃	1	2	yes	—
571	#541	—	2	2	no	—
572	#541	C₂²×C₅₃	1	2	yes	—
573	#529	—	2	2	no	—
574	#529	—	2	2	no	—
575	#529	C₂²×C₅₃	1	2	yes	—
576	#529	C₂²×C₅₃	1	1	yes	characteristic
577	#520	C₂²×C₅₃	1	2	yes	—
578	#519	C₂²×C₅₃	1	2	yes	—
579	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
580	#500	C₂²×C₅₃	1	1	yes	characteristic
581	#499	C₂²×C₅₃	1	1	yes	characteristic
582	#499	C₂²×C₅₃	1	1	yes	characteristic
583	#495	C₂²×C₅₃	1	1	yes	characteristic
584	#495	C₂²×C₅₃	1	1	yes	characteristic
585	#494	C₂²×C₅₃	1	1	yes	characteristic
586	#491	C₂²×C₅₃	1	2	yes	—
587	#489	C₂²×C₅₃	1	2	yes	—
588	#488	C₂²×C₅₃	1	2	yes	—
589	#485	C₂²×C₅₃	1	2	yes	—
590	#484	C₂²×C₅₃	1	2	yes	—
591	#484	C₂²×C₅₃	1	2	yes	—
592	#483	C₂²×C₅₃	1	2	yes	—
593	#482	C₂²×C₅₃	1	2	yes	—
594	#481	C₂²×C₅₃	1	2	yes	—
595	#479	C₂²×C₅₃	1	2	yes	—
596	#479	C₂²×C₅₃	1	2	yes	—
597	#479	C₂²×C₅₃	1	2	yes	—
598	#478	C₂²×C₅₃	1	2	yes	—
599	#477	C₂²×C₅₃	1	2	yes	—
600	#475	C₂²×C₅₃	1	2	yes	—
601	#470	C₂²×C₅₃	1	2	yes	—
602	#468	C₂²×C₅₃	1	2	yes	—
603	#467	C₂²×C₅₃	1	1	yes	characteristic
604	#467	C₂²×C₅₃	1	1	yes	characteristic
605	#467	C₂²×C₅₃	1	1	yes	characteristic
606	#467	C₂²×C₅₃	1	1	yes	characteristic
607	#466	C₂²×C₅₃	1	1	yes	characteristic
608	#466	C₂²×C₅₃	1	1	yes	characteristic
609	#465	C₂²×C₅₃	1	2	yes	—
610	#464	C₂²×C₅₃	1	2	yes	—
611	#464	C₂²×C₅₃	1	2	yes	—
612	#464	C₂²×C₅₃	1	2	yes	—
613	#464	C₂²×C₅₃	1	2	yes	—
614	#462	C₂²×C₅₃	1	2	yes	—
615	#461	C₂²×C₅₃	1	2	yes	—
616	#452	C₂²×C₅₃	1	2	yes	—
617	#452	C₂²×C₅₃	1	2	yes	—
618	#451	C₂²×C₅₃	1	2	yes	—
619	#451	C₂²×C₅₃	1	2	yes	—
620	#448	C₂²×C₅₃	1	2	yes	—
621	#448	C₂²×C₅₃	1	2	yes	—
622	#446	C₂²×C₅₃	1	1	yes	characteristic
623	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
624	#441	C₂²×C₅₃	1	2	yes	—
625	#441	C₂²×C₅₃	1	2	yes	—
626	#441	C₂²×C₅₃	1	2	yes	—
627	#440	C₂²×C₅₃	1	2	yes	—
628	#440	C₂²×C₅₃	1	2	yes	—
629	#440	C₂²×C₅₃	1	2	yes	—
630	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
631	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
632	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
633	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
634	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
635	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
636	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
637	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
638	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
639	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
640	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
641	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
642	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
643	#436	C₂²×C₅₃	1	1	yes	characteristic
644	#435	C₂²×C₅₃	1	1	yes	characteristic
645	#435	C₂²×C₅₃	1	1	yes	characteristic
646	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
647	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
648	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
649	#433	C₂²×C₅₃	1	1	yes	characteristic
650	#433	C₂²×C₅₃	1	1	yes	characteristic
651	#432	C₂²×C₅₃	1	1	yes	characteristic
652	#427	C₂²×C₅₃	1	1	yes	characteristic
653	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
654	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
655	#419	C₂²×C₅₃	1	2	yes	—
656	#417	C₂²×C₅₃	1	2	yes	—
657	C₂×#103	C₂²×C₅₃	1	2	yes	—
658	#405	C₂²×C₅₃	1	1	yes	characteristic
659	#405	C₂²×C₅₃	1	1	yes	characteristic
660	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
661	C₅₃	#61473	1	1	yes	characteristic, direct product factor, Sylow
662	C₂×#41	C₂³×C₅₃	1	2	yes	—
663	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
664	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
665	#135	—	2	4	no	—
666	C₂×Q₁₆	—	2	4	no	—
667	C₂×Q₁₆	—	2	4	no	—
668	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
669	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
670	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
671	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
672	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
673	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
674	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
675	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
676	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
677	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
678	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
679	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
680	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
681	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
682	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
683	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
684	C₄⋊Q₈	—	2	2	no	—
685	C₄⋊Q₈	—	2	2	no	—
686	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
687	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
688	#126	—	2	2	no	—
689	#126	—	2	2	no	—
690	#126	—	2	2	no	—
691	#126	—	2	2	no	—
692	#126	—	2	2	no	—
693	#126	—	2	2	no	—
694	#126	—	2	2	no	—
695	#126	—	2	2	no	—
696	#126	D₄×C₅₃	1	1	yes	characteristic
697	#126	D₄×C₅₃	1	1	yes	characteristic
698	#125	—	2	2	no	—
699	#125	—	2	2	no	—
700	#125	—	2	2	no	—
701	#125	—	2	2	no	—
702	#125	—	2	2	no	—
703	#125	—	2	2	no	—
704	#125	D₄×C₅₃	1	1	yes	characteristic
705	#125	C₂³×C₅₃	1	2	yes	—
706	#125	C₂³×C₅₃	1	2	yes	—
707	#124	—	2	2	no	—
708	#124	—	2	2	no	—
709	#124	—	2	2	no	—
710	#124	D₄×C₅₃	1	1	yes	characteristic
711	#124	C₂³×C₅₃	1	2	yes	—
712	#124	C₂³×C₅₃	1	2	yes	—
713	#123	—	2	2	no	—
714	#123	—	2	2	no	—
715	#123	—	2	2	no	—
716	#123	—	2	2	no	—
717	#123	D₄×C₅₃	1	1	yes	characteristic
718	#123	D₄×C₅₃	1	1	yes	characteristic
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
728	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
729	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
730	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
731	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
732	#121	—	2	2	no	—
733	#121	—	2	2	no	—
734	#121	—	2	2	no	—
735	#121	D₄×C₅₃	1	1	yes	characteristic
736	#121	C₂³×C₅₃	1	2	yes	—
737	#121	C₂³×C₅₃	1	2	yes	—
738	C₄×Q₈	—	2	2	no	—
739	C₄×Q₈	—	2	2	no	—
740	C₄×Q₈	—	2	2	no	—
741	C₄×Q₈	—	2	2	no	—
742	C₄×Q₈	—	2	2	no	—
743	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
744	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
745	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
746	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
747	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
748	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
749	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
750	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
751	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
752	C₄×D₄	—	2	2	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	2	no	—
758	C₄×D₄	—	2	2	no	—
759	C₄×D₄	—	2	2	no	—
760	C₄×D₄	C₂³×C₅₃	1	2	yes	—
761	C₄×D₄	C₂³×C₅₃	1	2	yes	—
762	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
763	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
764	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
765	#117	—	2	2	no	—
766	#117	—	2	2	no	—
767	#117	—	2	2	no	—
768	#117	—	2	2	no	—
769	#117	—	2	2	no	—
770	#117	—	2	2	no	—
771	#117	C₂³×C₅₃	1	2	yes	—
772	#117	C₂³×C₅₃	1	1	yes	characteristic
773	#117	C₂³×C₅₃	1	1	yes	characteristic
774	C₂×C₄⋊C₄	—	2	2	no	—
775	C₂×C₄⋊C₄	—	2	2	no	—
776	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
777	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
778	C₂×C₄²	—	2	2	no	—
779	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
780	#107	C₂³×C₅₃	1	1	yes	characteristic
781	#107	C₂³×C₅₃	1	1	yes	characteristic
782	#107	C₂³×C₅₃	1	1	yes	characteristic
783	#107	C₂³×C₅₃	1	2	yes	—
784	#107	C₂³×C₅₃	1	2	yes	—
785	#107	C₂³×C₅₃	1	1	yes	characteristic
786	#107	C₂³×C₅₃	1	2	yes	—
787	#106	C₂³×C₅₃	1	2	yes	—
788	#106	C₂³×C₅₃	1	2	yes	—
789	#106	C₂³×C₅₃	1	2	yes	—
790	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
791	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
792	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
793	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
794	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
795	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
796	#103	C₂³×C₅₃	1	2	yes	—
797	#103	C₂³×C₅₃	1	2	yes	—
798	#103	C₂³×C₅₃	1	2	yes	—
799	#103	C₂³×C₅₃	1	2	yes	—
800	#103	C₂³×C₅₃	1	2	yes	—
801	#103	C₂³×C₅₃	1	2	yes	—
802	#103	C₂³×C₅₃	1	2	yes	—
803	#103	C₂³×C₅₃	1	2	yes	—
804	#103	C₂³×C₅₃	1	2	yes	—
805	#103	C₂³×C₅₃	1	2	yes	—
806	#103	C₂³×C₅₃	1	2	yes	—
807	#103	C₂³×C₅₃	1	2	yes	—
808	#102	C₂³×C₅₃	1	2	yes	—
809	#102	C₂³×C₅₃	1	2	yes	—
810	#102	C₂³×C₅₃	1	2	yes	—
811	#102	C₂³×C₅₃	1	2	yes	—
812	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
813	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
814	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
815	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
816	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
817	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
818	#97	C₂³×C₅₃	1	1	yes	characteristic
819	#97	C₂³×C₅₃	1	1	yes	characteristic
820	#97	C₂³×C₅₃	1	1	yes	characteristic
821	#97	C₂³×C₅₃	1	1	yes	characteristic
822	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
823	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
824	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
825	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
826	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
827	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
828	#41	—	2	4	no	—
829	#41	—	4	2	no	—
830	C₂×Q₈	—	2	2	no	—
831	C₂×Q₈	—	2	2	no	—
832	C₂×Q₈	—	2	2	no	—
833	C₂×Q₈	—	2	4	no	—
834	C₂×Q₈	—	2	4	no	—
835	C₂×Q₈	—	4	2	no	—
836	C₂×Q₈	—	4	2	no	—
837	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
838	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
839	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
840	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	2	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
845	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
846	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
847	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
856	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
860	Q₁₆	—	2	4	no	—
861	Q₁₆	—	2	4	no	—
862	Q₁₆	—	2	2	no	—
863	Q₁₆	—	2	2	no	—
864	Q₁₆	—	4	2	no	—
865	Q₁₆	#41×C₅₃	1	4	yes	—
866	SD₁₆	—	2	4	no	—
867	SD₁₆	—	4	2	no	—
868	SD₁₆	—	4	2	no	—
869	D₈	—	2	2	no	—
870	M₁₆	—	4	1	no	—
871	M₁₆	—	4	1	no	—
872	C₂×C₈	—	2	2	no	—
873	C₂×C₈	—	2	2	no	—
874	C₂×C₈	—	2	2	no	—
875	C₂×C₈	—	4	1	no	—
876	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
877	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
878	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
879	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
880	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
881	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
882	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
883	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
906	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
907	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
908	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
909	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
910	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
911	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
912	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
913	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
914	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
915	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
916	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
917	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
918	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
933	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
934	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
935	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
936	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
937	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
938	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
939	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
940	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
941	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
942	C₄²	—	2	2	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	—	2	2	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
952	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
953	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
954	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
955	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
956	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
957	C₂³	—	2	2	no	—
958	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
959	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
960	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
961	Q₈	—	2	2	no	—
962	Q₈	—	2	2	no	—
963	Q₈	—	2	2	no	—
964	Q₈	—	2	2	no	—
965	Q₈	—	2	2	no	—
966	Q₈	—	4	1	no	—
967	Q₈	—	4	4	no	—
968	Q₈	—	4	4	no	—
969	Q₈	—	8	2	no	—
970	Q₈	C₂×#41×C₅₃	1	4	yes	—
971	D₄	—	2	2	no	—
972	D₄	—	2	2	no	—
973	D₄	—	2	2	no	—
974	D₄	—	2	2	no	—
975	D₄	—	4	1	no	—
976	D₄	—	4	4	no	—
977	D₄	—	4	4	no	—
978	D₄	—	8	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	4	1	no	—
994	C₂×C₄	—	4	4	no	—
995	C₂×C₄	—	4	4	no	—
996	C₂×C₄	—	4	4	no	—
997	C₂×C₄	—	8	2	no	—
998	C₂×C₄	—	8	2	no	—
999	C₂×C₄	—	8	2	no	—
1000	C₂×C₄	—	8	2	no	—
1001	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1003	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1004	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1005	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1006	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1007	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1008	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1009	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1010	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1011	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1012	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1013	C₈	—	2	1	no	—
1014	C₈	—	2	1	no	—
1015	C₈	—	2	1	no	—
1016	C₈	—	2	1	no	—
1017	C₈	—	2	1	no	—
1018	C₈	—	2	1	no	—
1019	C₈	—	2	1	no	—
1020	C₈	C₂×#41×C₅₃	1	2	yes	—
1021	C₂²	—	2	1	no	—
1022	C₂²	—	2	1	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	1	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	2	1	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	C₅₃×#578	1	2	yes	—
1033	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1034	C₄	—	2	1	no	—
1035	C₄	—	2	1	no	—
1036	C₄	—	2	1	no	—
1037	C₄	—	2	4	no	—
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	1	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	1	no	—
1044	C₄	—	2	1	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	2	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	2	no	—
1052	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1053	C₄	C₅₃×#585	1	1	yes	characteristic
1054	C₂	—	2	2	no	—
1055	C₂	—	4	1	no	—
1056	C₂	—	4	1	no	—
1057	C₂	—	8	2	no	—
1058	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1059	C₂	C₂×C₅₃×#578	1	1	yes	characteristic
1060	C₂	C₅₃×#3584	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×#3516	C₂	semidirect
2. C₅₃×#3393	C₂	semidirect
3. C₅₃×#3383	C₂	semidirect
4. C₅₃×#3377	C₂	semidirect
5. C₅₃×#3339	C₂	semidirect
6. C₅₃×#3338	C₂	semidirect
7. C₅₃×#3336	C₂	semidirect
8. C₅₃×#3327	C₂	semidirect
9. C₅₃×#3320	C₂	semidirect
10. C₅₃×#3316	C₂	semidirect
11. D₄×Q₁₆×C₅₃	C₂	semidirect
12. C₅₃×#3285	C₂	semidirect
13. C₅₃×#3285	C₂	semidirect
14. C₅₃×#3177	C₂	semidirect
15. C₅₃×#3175	C₂	semidirect
16. C₅₃×#3168	C₂	semidirect
17. C₅₃×#3121	C₂	semidirect
18. C₅₃×#3120	C₂	semidirect
19. C₅₃×#3117	C₂	semidirect
20. C₅₃×#2966	C₂	semidirect
21. C₅₃×#2951	C₂	semidirect
22. C₅₃×#2950	C₂	semidirect
23. C₂×C₄×Q₁₆×C₅₃	C₂	semidirect
490. #61473	C₅₃	direct (N × H)
524. #3516	C₂×C₅₃	semidirect
525. #3393	C₂×C₅₃	semidirect
526. #3383	C₂×C₅₃	semidirect
527. #3377	C₂×C₅₃	semidirect
528. #3339	C₂×C₅₃	semidirect
529. #3338	C₂×C₅₃	semidirect
530. #3336	C₂×C₅₃	semidirect
531. #3327	C₂×C₅₃	semidirect
532. #3320	C₂×C₅₃	semidirect
533. #3316	C₂×C₅₃	semidirect
534. D₄×Q₁₆	C₂×C₅₃	semidirect
535. #3285	C₂×C₅₃	semidirect
536. #3285	C₂×C₅₃	semidirect
537. #3177	C₂×C₅₃	semidirect
538. #3175	C₂×C₅₃	semidirect
539. #3168	C₂×C₅₃	semidirect
540. #3121	C₂×C₅₃	semidirect
541. #3120	C₂×C₅₃	semidirect
542. #3117	C₂×C₅₃	semidirect
543. #2966	C₂×C₅₃	semidirect
544. #2951	C₂×C₅₃	semidirect
545. #2950	C₂×C₅₃	semidirect
546. C₂×C₄×Q₁₆	C₂×C₅₃	semidirect
661. C₅₃	#61473	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×#3516	2
C₅₃×#3393	2
C₅₃×#3383	2
C₅₃×#3377	2
C₅₃×#3339	2
C₅₃×#3338	2
C₅₃×#3336	2
C₅₃×#3327	2
C₅₃×#3320	2
C₅₃×#3316	2
D₄×Q₁₆×C₅₃	2
C₅₃×#3285	2
C₅₃×#3177	2
C₅₃×#3175	2
C₅₃×#3168	2
C₅₃×#3121	2
C₅₃×#3120	2
C₅₃×#3117	2
C₅₃×#2966	2
C₅₃×#2951	2
C₅₃×#2950	2
C₂×C₄×Q₁₆×C₅₃	2
#61473	53

Subgroups — C53×#61473 #27268985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61473 #27268985