Subgroups — C₅₃×#62168 #27269680

Order 13568.

1628 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3563	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#3523	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3390	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3374	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3349	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3344	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3336	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3312	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3312	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3299	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3261	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3242	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3127	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3082	C₂	1	2	yes	maximal, complemented
18	C₂×C₅₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2992	C₂	1	1	yes	maximal, characteristic
20	C₅₃×#564	—	2	1	no	—
21	C₅₃×#563	—	2	1	no	—
22	C₅₃×#557	—	2	1	no	—
23	C₅₃×#557	C₂²	1	1	yes	characteristic
24	C₅₃×#557	C₂²	1	1	yes	characteristic
25	C₅₃×#557	C₂²	1	2	yes	—
26	C₅₃×#556	—	2	1	no	—
27	C₅₃×#556	C₂²	1	1	yes	characteristic
28	C₅₃×#554	C₂²	1	2	yes	—
29	C₅₃×#552	—	2	2	no	—
30	C₅₃×#552	—	2	2	no	—
31	C₅₃×#552	C₂²	1	2	yes	—
32	C₅₃×#552	C₂²	1	2	yes	—
33	C₅₃×#552	C₂²	1	2	yes	—
34	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
35	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
36	C₅₃×#544	—	2	1	no	—
37	C₅₃×#544	C₂²	1	2	yes	—
38	C₅₃×#541	—	2	2	no	—
39	C₅₃×#541	—	2	2	no	—
40	C₅₃×#541	C₂²	1	2	yes	—
41	C₅₃×#541	C₂²	1	2	yes	—
42	C₅₃×#539	—	2	1	no	—
43	C₅₃×#533	—	2	1	no	—
44	C₅₃×#533	C₂²	1	1	yes	characteristic
45	C₅₃×#533	C₂²	1	1	yes	characteristic
46	C₅₃×#529	—	2	1	no	—
47	C₅₃×#529	C₂²	1	1	yes	characteristic
48	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
49	C₅₃×#519	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#501	C₂²	1	2	yes	—
52	C₅₃×#501	C₂²	1	2	yes	—
53	C₅₃×#499	C₂²	1	2	yes	—
54	C₅₃×#491	C₂²	1	2	yes	—
55	C₅₃×#491	C₂²	1	2	yes	—
56	C₅₃×#487	C₂²	1	2	yes	—
57	C₅₃×#485	C₂²	1	2	yes	—
58	C₅₃×#485	C₂²	1	2	yes	—
59	C₅₃×#485	C₂²	1	2	yes	—
60	C₅₃×#485	C₂²	1	2	yes	—
61	C₅₃×#484	C₂²	1	2	yes	—
62	C₅₃×#484	C₂²	1	2	yes	—
63	C₅₃×#483	C₂²	1	2	yes	—
64	C₅₃×#483	C₂²	1	2	yes	—
65	C₅₃×#483	C₂²	1	2	yes	—
66	C₅₃×#479	C₂²	1	2	yes	—
67	C₅₃×#479	C₂²	1	2	yes	—
68	C₅₃×#479	C₂²	1	2	yes	—
69	C₅₃×#479	C₂²	1	2	yes	—
70	C₅₃×#479	C₂²	1	2	yes	—
71	C₅₃×#479	C₂²	1	2	yes	—
72	C₅₃×#479	C₂²	1	2	yes	—
73	C₅₃×#479	C₂²	1	2	yes	—
74	C₅₃×#479	C₂²	1	2	yes	—
75	C₅₃×#479	C₂²	1	2	yes	—
76	C₅₃×#477	C₂²	1	2	yes	—
77	C₅₃×#477	C₂²	1	2	yes	—
78	C₅₃×#477	C₂²	1	2	yes	—
79	C₅₃×#475	C₂²	1	1	yes	characteristic
80	C₅₃×#475	C₂²	1	1	yes	characteristic
81	C₅₃×#475	C₂²	1	2	yes	—
82	C₅₃×#470	C₂²	1	2	yes	—
83	C₅₃×#470	C₂²	1	2	yes	—
84	C₅₃×#467	C₂²	1	2	yes	—
85	C₅₃×#467	C₂²	1	2	yes	—
86	C₅₃×#467	C₂²	1	2	yes	—
87	C₅₃×#467	C₂²	1	2	yes	—
88	C₅₃×#462	C₂²	1	2	yes	—
89	C₅₃×#462	C₂²	1	2	yes	—
90	C₅₃×#462	C₂²	1	1	yes	characteristic
91	C₅₃×#462	C₂²	1	2	yes	—
92	C₅₃×#462	C₂²	1	2	yes	—
93	C₅₃×#462	C₂²	1	1	yes	characteristic
94	C₅₃×#451	C₂²	1	2	yes	—
95	C₅₃×#451	C₂²	1	2	yes	—
96	C₅₃×#451	C₂²	1	2	yes	—
97	C₅₃×#446	C₂²	1	2	yes	—
98	C₅₃×#441	C₂²	1	2	yes	—
99	C₅₃×#441	C₂²	1	2	yes	—
100	C₅₃×#441	C₂²	1	2	yes	—
101	C₅₃×#441	C₂²	1	2	yes	—
102	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
103	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
104	C₅₃×#435	C₂²	1	2	yes	—
105	C₅₃×#435	C₂²	1	2	yes	—
106	C₈×D₄×C₅₃	C₂²	1	2	yes	—
107	C₅₃×#433	C₂²	1	2	yes	—
108	C₅₃×#432	C₂²	1	1	yes	characteristic
109	C₅₃×#428	C₂²	1	2	yes	—
110	C₅₃×#427	C₂²	1	2	yes	—
111	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
112	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
113	C₅₃×#424	C₂²	1	2	yes	—
114	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
115	C₅₃×#419	C₂²	1	2	yes	—
116	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
117	C₂×#103×C₅₃	C₂²	1	2	yes	—
118	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
119	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
120	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
121	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
125	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
126	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₅₃	—	2	1	no	—
130	C₄⋊Q₈×C₅₃	—	2	2	no	—
131	C₄⋊Q₈×C₅₃	—	2	2	no	—
132	C₄⋊Q₈×C₅₃	—	2	1	no	—
133	C₄⋊Q₈×C₅₃	—	2	2	no	—
134	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
137	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
138	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
139	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
140	#126×C₅₃	—	2	2	no	—
141	#126×C₅₃	—	2	2	no	—
142	#126×C₅₃	—	2	2	no	—
143	#126×C₅₃	—	2	2	no	—
144	#126×C₅₃	—	2	2	no	—
145	#126×C₅₃	—	2	2	no	—
146	#126×C₅₃	—	2	2	no	—
147	#126×C₅₃	—	2	2	no	—
148	#126×C₅₃	D₄	1	2	yes	—
149	#125×C₅₃	—	2	1	no	—
150	#125×C₅₃	—	2	2	no	—
151	#125×C₅₃	—	2	2	no	—
152	#125×C₅₃	—	2	2	no	—
153	#125×C₅₃	—	2	2	no	—
154	#125×C₅₃	—	2	2	no	—
155	#125×C₅₃	—	2	2	no	—
156	#125×C₅₃	—	2	2	no	—
157	#125×C₅₃	—	2	2	no	—
158	#125×C₅₃	—	2	2	no	—
159	#125×C₅₃	—	2	2	no	—
160	#125×C₅₃	—	2	2	no	—
161	#125×C₅₃	—	2	2	no	—
162	#125×C₅₃	—	2	2	no	—
163	#125×C₅₃	—	2	1	no	—
164	#125×C₅₃	—	2	1	no	—
165	#125×C₅₃	—	2	1	no	—
166	#125×C₅₃	—	2	1	no	—
167	#125×C₅₃	D₄	1	1	yes	characteristic
168	#125×C₅₃	C₂³	1	2	yes	—
169	#125×C₅₃	C₂³	1	2	yes	—
170	#125×C₅₃	C₂³	1	2	yes	—
171	#125×C₅₃	C₂³	1	2	yes	—
172	#124×C₅₃	—	2	1	no	—
173	#124×C₅₃	D₄	1	1	yes	characteristic
174	#123×C₅₃	—	2	2	no	—
175	#123×C₅₃	—	2	2	no	—
176	#123×C₅₃	—	2	2	no	—
177	#123×C₅₃	D₄	1	2	yes	—
178	C₂²⋊Q₈×C₅₃	—	2	2	no	—
179	C₂²⋊Q₈×C₅₃	—	2	2	no	—
180	C₂²⋊Q₈×C₅₃	—	2	2	no	—
181	C₂²⋊Q₈×C₅₃	—	2	2	no	—
182	C₂²⋊Q₈×C₅₃	—	2	2	no	—
183	C₂²⋊Q₈×C₅₃	—	2	2	no	—
184	C₂²⋊Q₈×C₅₃	—	2	2	no	—
185	C₂²⋊Q₈×C₅₃	—	2	1	no	—
186	C₂²⋊Q₈×C₅₃	—	2	1	no	—
187	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
188	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
189	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
190	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
191	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
192	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
193	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
194	#121×C₅₃	D₄	1	1	yes	characteristic
195	C₄×Q₈×C₅₃	—	2	2	no	—
196	C₄×Q₈×C₅₃	—	2	2	no	—
197	C₄×Q₈×C₅₃	—	2	1	no	—
198	C₄×Q₈×C₅₃	—	2	1	no	—
199	C₄×Q₈×C₅₃	—	2	2	no	—
200	C₄×Q₈×C₅₃	—	2	1	no	—
201	C₄×Q₈×C₅₃	—	2	1	no	—
202	C₄×Q₈×C₅₃	—	2	1	no	—
203	C₄×Q₈×C₅₃	—	2	1	no	—
204	C₄×Q₈×C₅₃	—	2	1	no	—
205	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
208	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
209	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
210	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
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×D₄×C₅₃	—	2	2	no	—
217	C₄×D₄×C₅₃	—	2	1	no	—
218	C₄×D₄×C₅₃	—	2	2	no	—
219	C₄×D₄×C₅₃	C₂³	1	2	yes	—
220	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
221	#117×C₅₃	—	2	2	no	—
222	#117×C₅₃	—	2	2	no	—
223	#117×C₅₃	—	2	2	no	—
224	#117×C₅₃	—	2	2	no	—
225	#117×C₅₃	—	2	2	no	—
226	#117×C₅₃	—	2	1	no	—
227	#117×C₅₃	—	2	1	no	—
228	#117×C₅₃	C₂³	1	2	yes	—
229	#117×C₅₃	C₂³	1	2	yes	—
230	#117×C₅₃	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
232	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
233	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
234	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
238	C₂×C₄²×C₅₃	—	2	1	no	—
239	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
240	#107×C₅₃	C₂³	1	2	yes	—
241	#107×C₅₃	C₂³	1	2	yes	—
242	#107×C₅₃	C₂³	1	2	yes	—
243	#107×C₅₃	C₂³	1	2	yes	—
244	#107×C₅₃	C₂³	1	2	yes	—
245	#107×C₅₃	C₂³	1	2	yes	—
246	#106×C₅₃	C₂³	1	2	yes	—
247	#106×C₅₃	C₂³	1	2	yes	—
248	#106×C₅₃	C₂³	1	2	yes	—
249	#106×C₅₃	C₂³	1	2	yes	—
250	#106×C₅₃	C₂³	1	2	yes	—
251	#106×C₅₃	C₂³	1	2	yes	—
252	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
253	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
254	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
255	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
256	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
257	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
258	#103×C₅₃	C₂³	1	2	yes	—
259	#103×C₅₃	C₂³	1	2	yes	—
260	#103×C₅₃	C₂³	1	2	yes	—
261	#103×C₅₃	C₂³	1	2	yes	—
262	#103×C₅₃	C₂³	1	2	yes	—
263	#103×C₅₃	C₂³	1	2	yes	—
264	#103×C₅₃	C₂³	1	2	yes	—
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	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
277	#97×C₅₃	C₂³	1	2	yes	—
278	#97×C₅₃	C₂³	1	2	yes	—
279	C₄×C₈×C₅₃	C₂³	1	2	yes	—
280	C₂×Q₈×C₅₃	—	2	1	no	—
281	C₂×Q₈×C₅₃	—	2	2	no	—
282	C₂×Q₈×C₅₃	—	2	1	no	—
283	C₂×Q₈×C₅₃	—	2	2	no	—
284	C₂×Q₈×C₅₃	—	2	1	no	—
285	C₂×Q₈×C₅₃	—	2	2	no	—
286	C₂×Q₈×C₅₃	—	2	4	no	—
287	C₂×Q₈×C₅₃	—	4	1	no	—
288	C₂×Q₈×C₅₃	—	4	2	no	—
289	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
290	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
291	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
292	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
294	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
295	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₅₃	—	2	1	no	—
297	C₂²×C₄×C₅₃	—	2	1	no	—
298	C₂²×C₄×C₅₃	—	2	1	no	—
299	C₂²×C₄×C₅₃	—	2	2	no	—
300	C₂²×C₄×C₅₃	—	2	1	no	—
301	C₂²×C₄×C₅₃	—	2	2	no	—
302	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
306	Q₁₆×C₅₃	—	2	4	no	—
307	Q₁₆×C₅₃	—	4	2	no	—
308	Q₁₆×C₅₃	—	4	2	no	—
309	Q₁₆×C₅₃	—	4	2	no	—
310	M₁₆×C₅₃	—	4	2	no	—
311	C₂×C₈×C₅₃	—	4	1	no	—
312	C₂×C₈×C₅₃	—	4	2	no	—
313	C₂×C₈×C₅₃	—	4	1	no	—
314	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
316	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
317	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
318	C₄⋊C₄×C₅₃	—	2	1	no	—
319	C₄⋊C₄×C₅₃	—	2	2	no	—
320	C₄⋊C₄×C₅₃	—	2	1	no	—
321	C₄⋊C₄×C₅₃	—	2	1	no	—
322	C₄⋊C₄×C₅₃	—	2	1	no	—
323	C₄⋊C₄×C₅₃	—	2	2	no	—
324	C₄⋊C₄×C₅₃	—	2	2	no	—
325	C₄⋊C₄×C₅₃	—	2	2	no	—
326	C₄⋊C₄×C₅₃	—	2	1	no	—
327	C₄⋊C₄×C₅₃	—	2	1	no	—
328	C₄⋊C₄×C₅₃	—	2	2	no	—
329	C₄⋊C₄×C₅₃	—	2	1	no	—
330	C₄⋊C₄×C₅₃	—	2	2	no	—
331	C₄⋊C₄×C₅₃	—	2	2	no	—
332	C₄⋊C₄×C₅₃	—	2	2	no	—
333	C₄⋊C₄×C₅₃	—	2	1	no	—
334	C₄⋊C₄×C₅₃	—	2	1	no	—
335	C₄⋊C₄×C₅₃	—	2	2	no	—
336	C₄⋊C₄×C₅₃	—	2	2	no	—
337	C₄⋊C₄×C₅₃	—	2	2	no	—
338	C₄⋊C₄×C₅₃	—	2	2	no	—
339	C₄⋊C₄×C₅₃	—	2	1	no	—
340	C₄⋊C₄×C₅₃	—	2	1	no	—
341	C₄⋊C₄×C₅₃	—	2	2	no	—
342	C₄⋊C₄×C₅₃	—	2	1	no	—
343	C₄⋊C₄×C₅₃	—	2	2	no	—
344	C₄⋊C₄×C₅₃	—	2	2	no	—
345	C₄⋊C₄×C₅₃	—	2	2	no	—
346	C₄⋊C₄×C₅₃	—	2	2	no	—
347	C₄⋊C₄×C₅₃	—	2	2	no	—
348	C₄⋊C₄×C₅₃	—	2	2	no	—
349	C₄⋊C₄×C₅₃	—	2	2	no	—
350	C₄⋊C₄×C₅₃	—	2	1	no	—
351	C₄⋊C₄×C₅₃	—	2	2	no	—
352	C₄⋊C₄×C₅₃	—	2	2	no	—
353	C₄⋊C₄×C₅₃	—	2	2	no	—
354	C₄⋊C₄×C₅₃	—	2	2	no	—
355	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
358	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
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	2	no	—
373	C₂²⋊C₄×C₅₃	—	2	2	no	—
374	C₂²⋊C₄×C₅₃	—	2	2	no	—
375	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
376	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
377	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
378	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
379	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
380	C₄²×C₅₃	—	2	1	no	—
381	C₄²×C₅₃	—	2	1	no	—
382	C₄²×C₅₃	—	2	1	no	—
383	C₄²×C₅₃	—	2	1	no	—
384	C₄²×C₅₃	—	2	2	no	—
385	C₄²×C₅₃	—	2	2	no	—
386	C₄²×C₅₃	—	2	2	no	—
387	C₄²×C₅₃	—	2	2	no	—
388	C₄²×C₅₃	—	2	2	no	—
389	C₄²×C₅₃	—	2	2	no	—
390	C₄²×C₅₃	—	2	2	no	—
391	C₄²×C₅₃	—	2	2	no	—
392	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₅₃	C₂⁴	1	2	yes	—
395	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
398	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
399	Q₈×C₅₃	—	2	1	no	—
400	Q₈×C₅₃	—	2	1	no	—
401	Q₈×C₅₃	—	2	2	no	—
402	Q₈×C₅₃	—	2	2	no	—
403	Q₈×C₅₃	—	2	1	no	—
404	Q₈×C₅₃	—	2	2	no	—
405	Q₈×C₅₃	—	2	2	no	—
406	Q₈×C₅₃	—	4	1	no	—
407	Q₈×C₅₃	—	4	2	no	—
408	Q₈×C₅₃	—	4	4	no	—
409	Q₈×C₅₃	—	4	2	no	—
410	Q₈×C₅₃	—	8	1	no	—
411	Q₈×C₅₃	—	8	2	no	—
412	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
413	D₄×C₅₃	—	2	4	no	—
414	D₄×C₅₃	—	4	1	no	—
415	C₂×C₄×C₅₃	—	2	2	no	—
416	C₂×C₄×C₅₃	—	2	1	no	—
417	C₂×C₄×C₅₃	—	2	1	no	—
418	C₂×C₄×C₅₃	—	2	2	no	—
419	C₂×C₄×C₅₃	—	2	1	no	—
420	C₂×C₄×C₅₃	—	2	2	no	—
421	C₂×C₄×C₅₃	—	2	2	no	—
422	C₂×C₄×C₅₃	—	2	2	no	—
423	C₂×C₄×C₅₃	—	2	1	no	—
424	C₂×C₄×C₅₃	—	2	2	no	—
425	C₂×C₄×C₅₃	—	2	1	no	—
426	C₂×C₄×C₅₃	—	2	1	no	—
427	C₂×C₄×C₅₃	—	2	2	no	—
428	C₂×C₄×C₅₃	—	2	2	no	—
429	C₂×C₄×C₅₃	—	2	2	no	—
430	C₂×C₄×C₅₃	—	4	1	no	—
431	C₂×C₄×C₅₃	—	4	2	no	—
432	C₂×C₄×C₅₃	—	4	4	no	—
433	C₂×C₄×C₅₃	—	4	2	no	—
434	C₂×C₄×C₅₃	—	4	2	no	—
435	C₂×C₄×C₅₃	—	8	1	no	—
436	C₂×C₄×C₅₃	—	8	2	no	—
437	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
442	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
446	C₈×C₅₃	—	2	2	no	—
447	C₈×C₅₃	—	2	2	no	—
448	C₈×C₅₃	—	2	2	no	—
449	C₈×C₅₃	—	2	2	no	—
450	#62168	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂²×C₅₃	—	2	1	no	—
452	C₂²×C₅₃	—	2	1	no	—
453	C₂²×C₅₃	—	2	2	no	—
454	C₂²×C₅₃	—	2	2	no	—
455	C₂²×C₅₃	—	2	2	no	—
456	C₂²×C₅₃	#578	1	2	yes	—
457	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
458	C₄×C₅₃	—	2	1	no	—
459	C₄×C₅₃	—	2	1	no	—
460	C₄×C₅₃	—	2	2	no	—
461	C₄×C₅₃	—	2	1	no	—
462	C₄×C₅₃	—	2	2	no	—
463	C₄×C₅₃	—	2	2	no	—
464	C₄×C₅₃	—	2	1	no	—
465	C₄×C₅₃	—	2	1	no	—
466	C₄×C₅₃	—	2	2	no	—
467	C₄×C₅₃	—	4	2	no	—
468	C₄×C₅₃	—	4	2	no	—
469	C₄×C₅₃	—	4	2	no	—
470	C₄×C₅₃	—	4	1	no	—
471	C₄×C₅₃	—	4	2	no	—
472	C₄×C₅₃	—	4	2	no	—
473	C₄×C₅₃	—	4	1	no	—
474	C₄×C₅₃	—	4	1	no	—
475	C₄×C₅₃	—	4	2	no	—
476	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
477	C₄×C₅₃	#585	1	1	yes	characteristic
478	#3563	C₂×C₅₃	1	1	yes	characteristic
479	#3523	C₂×C₅₃	1	1	yes	characteristic
480	#3390	C₂×C₅₃	1	2	yes	complemented
481	#3374	C₂×C₅₃	1	2	yes	complemented
482	#3349	C₂×C₅₃	1	2	yes	complemented
483	#3344	C₂×C₅₃	1	2	yes	complemented
484	#3336	C₂×C₅₃	1	2	yes	complemented
485	#3312	C₂×C₅₃	1	2	yes	complemented
486	#3312	C₂×C₅₃	1	2	yes	complemented
487	#3299	C₂×C₅₃	1	2	yes	complemented
488	#3261	C₂×C₅₃	1	2	yes	complemented
489	#3249	C₂×C₅₃	1	1	yes	characteristic, complemented
490	#3242	C₂×C₅₃	1	2	yes	complemented
491	#3236	C₂×C₅₃	1	1	yes	characteristic, complemented
492	#3127	C₂×C₅₃	1	2	yes	complemented
493	#3113	C₂×C₅₃	1	1	yes	characteristic, complemented
494	#3082	C₂×C₅₃	1	2	yes	complemented
495	C₂×#479	C₂×C₅₃	1	1	yes	characteristic, complemented
496	#2992	C₂×C₅₃	1	1	yes	characteristic
497	C₂×C₅₃	—	2	2	no	—
498	C₂×C₅₃	—	4	2	no	—
499	C₂×C₅₃	#3489	1	1	yes	characteristic
500	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
501	C₂×C₅₃	#3586	1	1	yes	characteristic
502	#564	—	2	1	no	—
503	#563	—	2	1	no	—
504	#557	—	2	1	no	—
505	#557	C₂²×C₅₃	1	1	yes	characteristic
506	#557	C₂²×C₅₃	1	2	yes	—
507	#557	C₂²×C₅₃	1	1	yes	characteristic
508	#556	—	2	1	no	—
509	#556	C₂²×C₅₃	1	1	yes	characteristic
510	#554	C₂²×C₅₃	1	2	yes	—
511	#552	—	2	2	no	—
512	#552	—	2	2	no	—
513	#552	C₂²×C₅₃	1	2	yes	—
514	#552	C₂²×C₅₃	1	2	yes	—
515	#552	C₂²×C₅₃	1	2	yes	—
516	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
517	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
518	#544	—	2	1	no	—
519	#544	C₂²×C₅₃	1	2	yes	—
520	#541	—	2	2	no	—
521	#541	—	2	2	no	—
522	#541	C₂²×C₅₃	1	2	yes	—
523	#541	C₂²×C₅₃	1	2	yes	—
524	#539	—	2	1	no	—
525	#533	—	2	1	no	—
526	#533	C₂²×C₅₃	1	1	yes	characteristic
527	#533	C₂²×C₅₃	1	1	yes	characteristic
528	#529	—	2	1	no	—
529	#529	C₂²×C₅₃	1	1	yes	characteristic
530	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
531	#519	C₂²×C₅₃	1	2	yes	—
532	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
533	#501	C₂²×C₅₃	1	2	yes	—
534	#501	C₂²×C₅₃	1	2	yes	—
535	#499	C₂²×C₅₃	1	2	yes	—
536	#491	C₂²×C₅₃	1	2	yes	—
537	#491	C₂²×C₅₃	1	2	yes	—
538	#487	C₂²×C₅₃	1	2	yes	—
539	#485	C₂²×C₅₃	1	2	yes	—
540	#485	C₂²×C₅₃	1	2	yes	—
541	#485	C₂²×C₅₃	1	2	yes	—
542	#485	C₂²×C₅₃	1	2	yes	—
543	#484	C₂²×C₅₃	1	2	yes	—
544	#484	C₂²×C₅₃	1	2	yes	—
545	#483	C₂²×C₅₃	1	2	yes	—
546	#483	C₂²×C₅₃	1	2	yes	—
547	#483	C₂²×C₅₃	1	2	yes	—
548	#479	C₂²×C₅₃	1	2	yes	—
549	#479	C₂²×C₅₃	1	2	yes	—
550	#479	C₂²×C₅₃	1	2	yes	—
551	#479	C₂²×C₅₃	1	2	yes	—
552	#479	C₂²×C₅₃	1	2	yes	—
553	#479	C₂²×C₅₃	1	2	yes	—
554	#479	C₂²×C₅₃	1	2	yes	—
555	#479	C₂²×C₅₃	1	2	yes	—
556	#479	C₂²×C₅₃	1	2	yes	—
557	#479	C₂²×C₅₃	1	2	yes	—
558	#477	C₂²×C₅₃	1	2	yes	—
559	#477	C₂²×C₅₃	1	2	yes	—
560	#477	C₂²×C₅₃	1	2	yes	—
561	#475	C₂²×C₅₃	1	1	yes	characteristic
562	#475	C₂²×C₅₃	1	2	yes	—
563	#475	C₂²×C₅₃	1	1	yes	characteristic
564	#470	C₂²×C₅₃	1	2	yes	—
565	#470	C₂²×C₅₃	1	2	yes	—
566	#467	C₂²×C₅₃	1	2	yes	—
567	#467	C₂²×C₅₃	1	2	yes	—
568	#467	C₂²×C₅₃	1	2	yes	—
569	#467	C₂²×C₅₃	1	2	yes	—
570	#462	C₂²×C₅₃	1	1	yes	characteristic
571	#462	C₂²×C₅₃	1	1	yes	characteristic
572	#462	C₂²×C₅₃	1	2	yes	—
573	#462	C₂²×C₅₃	1	2	yes	—
574	#462	C₂²×C₅₃	1	2	yes	—
575	#462	C₂²×C₅₃	1	2	yes	—
576	#451	C₂²×C₅₃	1	2	yes	—
577	#451	C₂²×C₅₃	1	2	yes	—
578	#451	C₂²×C₅₃	1	2	yes	—
579	#446	C₂²×C₅₃	1	2	yes	—
580	#441	C₂²×C₅₃	1	2	yes	—
581	#441	C₂²×C₅₃	1	2	yes	—
582	#441	C₂²×C₅₃	1	2	yes	—
583	#441	C₂²×C₅₃	1	2	yes	—
584	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
585	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
586	#435	C₂²×C₅₃	1	2	yes	—
587	#435	C₂²×C₅₃	1	2	yes	—
588	C₈×D₄	C₂²×C₅₃	1	2	yes	—
589	#433	C₂²×C₅₃	1	2	yes	—
590	#432	C₂²×C₅₃	1	1	yes	characteristic
591	#428	C₂²×C₅₃	1	2	yes	—
592	#427	C₂²×C₅₃	1	2	yes	—
593	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
594	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
595	#424	C₂²×C₅₃	1	2	yes	—
596	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
597	#419	C₂²×C₅₃	1	2	yes	—
598	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
599	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
600	C₂×#103	C₂²×C₅₃	1	2	yes	—
601	C₅₃	#62168	1	1	yes	characteristic, direct product factor, Sylow
602	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
603	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
604	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
605	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
606	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
607	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
608	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
609	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
610	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
611	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
612	C₄⋊Q₈	—	2	1	no	—
613	C₄⋊Q₈	—	2	2	no	—
614	C₄⋊Q₈	—	2	1	no	—
615	C₄⋊Q₈	—	2	2	no	—
616	C₄⋊Q₈	—	2	2	no	—
617	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
618	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
619	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
620	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
621	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
622	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
623	#126	—	2	2	no	—
624	#126	—	2	2	no	—
625	#126	—	2	2	no	—
626	#126	—	2	2	no	—
627	#126	—	2	2	no	—
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#126	D₄×C₅₃	1	2	yes	—
632	#125	—	2	1	no	—
633	#125	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	—	2	2	no	—
637	#125	—	2	2	no	—
638	#125	—	2	2	no	—
639	#125	—	2	2	no	—
640	#125	—	2	2	no	—
641	#125	—	2	2	no	—
642	#125	—	2	2	no	—
643	#125	—	2	2	no	—
644	#125	—	2	2	no	—
645	#125	—	2	2	no	—
646	#125	—	2	1	no	—
647	#125	—	2	1	no	—
648	#125	—	2	1	no	—
649	#125	—	2	1	no	—
650	#125	D₄×C₅₃	1	1	yes	characteristic
651	#125	C₂³×C₅₃	1	2	yes	—
652	#125	C₂³×C₅₃	1	2	yes	—
653	#125	C₂³×C₅₃	1	2	yes	—
654	#125	C₂³×C₅₃	1	2	yes	—
655	#124	—	2	1	no	—
656	#124	D₄×C₅₃	1	1	yes	characteristic
657	#123	—	2	2	no	—
658	#123	—	2	2	no	—
659	#123	—	2	2	no	—
660	#123	D₄×C₅₃	1	2	yes	—
661	C₂²⋊Q₈	—	2	1	no	—
662	C₂²⋊Q₈	—	2	1	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	—	2	2	no	—
666	C₂²⋊Q₈	—	2	2	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
671	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
672	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
673	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
674	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
675	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
676	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
677	#121	D₄×C₅₃	1	1	yes	characteristic
678	C₄×Q₈	—	2	1	no	—
679	C₄×Q₈	—	2	2	no	—
680	C₄×Q₈	—	2	2	no	—
681	C₄×Q₈	—	2	1	no	—
682	C₄×Q₈	—	2	1	no	—
683	C₄×Q₈	—	2	2	no	—
684	C₄×Q₈	—	2	1	no	—
685	C₄×Q₈	—	2	1	no	—
686	C₄×Q₈	—	2	1	no	—
687	C₄×Q₈	—	2	1	no	—
688	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
689	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
690	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
691	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
692	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
693	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
694	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
695	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
696	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
697	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
698	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
699	C₄×D₄	—	2	2	no	—
700	C₄×D₄	—	2	1	no	—
701	C₄×D₄	—	2	2	no	—
702	C₄×D₄	C₂³×C₅₃	1	2	yes	—
703	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
704	#117	—	2	1	no	—
705	#117	—	2	1	no	—
706	#117	—	2	2	no	—
707	#117	—	2	2	no	—
708	#117	—	2	2	no	—
709	#117	—	2	2	no	—
710	#117	—	2	2	no	—
711	#117	C₂³×C₅₃	1	2	yes	—
712	#117	C₂³×C₅₃	1	2	yes	—
713	#117	C₂³×C₅₃	1	2	yes	—
714	C₂×C₄⋊C₄	—	2	1	no	—
715	C₂×C₄⋊C₄	—	2	1	no	—
716	C₂×C₄⋊C₄	—	2	1	no	—
717	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
721	C₂×C₄²	—	2	1	no	—
722	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
723	#107	C₂³×C₅₃	1	2	yes	—
724	#107	C₂³×C₅₃	1	2	yes	—
725	#107	C₂³×C₅₃	1	2	yes	—
726	#107	C₂³×C₅₃	1	2	yes	—
727	#107	C₂³×C₅₃	1	2	yes	—
728	#107	C₂³×C₅₃	1	2	yes	—
729	#106	C₂³×C₅₃	1	2	yes	—
730	#106	C₂³×C₅₃	1	2	yes	—
731	#106	C₂³×C₅₃	1	2	yes	—
732	#106	C₂³×C₅₃	1	2	yes	—
733	#106	C₂³×C₅₃	1	2	yes	—
734	#106	C₂³×C₅₃	1	2	yes	—
735	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
736	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
737	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
738	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
739	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
740	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
741	#103	C₂³×C₅₃	1	2	yes	—
742	#103	C₂³×C₅₃	1	2	yes	—
743	#103	C₂³×C₅₃	1	2	yes	—
744	#103	C₂³×C₅₃	1	2	yes	—
745	#103	C₂³×C₅₃	1	2	yes	—
746	#103	C₂³×C₅₃	1	2	yes	—
747	#103	C₂³×C₅₃	1	2	yes	—
748	#103	C₂³×C₅₃	1	2	yes	—
749	#103	C₂³×C₅₃	1	2	yes	—
750	#103	C₂³×C₅₃	1	2	yes	—
751	#103	C₂³×C₅₃	1	2	yes	—
752	#103	C₂³×C₅₃	1	2	yes	—
753	#103	C₂³×C₅₃	1	2	yes	—
754	#103	C₂³×C₅₃	1	2	yes	—
755	#103	C₂³×C₅₃	1	2	yes	—
756	#103	C₂³×C₅₃	1	2	yes	—
757	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
758	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
759	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
760	#97	C₂³×C₅₃	1	2	yes	—
761	#97	C₂³×C₅₃	1	2	yes	—
762	C₄×C₈	C₂³×C₅₃	1	2	yes	—
763	C₂×Q₈	—	2	1	no	—
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	—	2	1	no	—
766	C₂×Q₈	—	2	1	no	—
767	C₂×Q₈	—	2	2	no	—
768	C₂×Q₈	—	2	2	no	—
769	C₂×Q₈	—	2	4	no	—
770	C₂×Q₈	—	4	1	no	—
771	C₂×Q₈	—	4	2	no	—
772	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
773	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
774	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
775	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
776	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
777	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
778	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
779	C₂²×C₄	—	2	1	no	—
780	C₂²×C₄	—	2	1	no	—
781	C₂²×C₄	—	2	1	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	1	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
789	Q₁₆	—	2	4	no	—
790	Q₁₆	—	4	2	no	—
791	Q₁₆	—	4	2	no	—
792	Q₁₆	—	4	2	no	—
793	M₁₆	—	4	2	no	—
794	C₂×C₈	—	4	1	no	—
795	C₂×C₈	—	4	2	no	—
796	C₂×C₈	—	4	1	no	—
797	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
798	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
799	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
800	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
801	C₄⋊C₄	—	2	1	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	1	no	—
804	C₄⋊C₄	—	2	1	no	—
805	C₄⋊C₄	—	2	1	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	1	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
839	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
840	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
841	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
842	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
843	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
844	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
845	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
846	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
847	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
848	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
849	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
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	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
859	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
860	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
861	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
862	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
863	C₄²	—	2	1	no	—
864	C₄²	—	2	1	no	—
865	C₄²	—	2	1	no	—
866	C₄²	—	2	1	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
876	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
877	C₄²	C₂⁴×C₅₃	1	2	yes	—
878	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
879	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
880	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
881	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
882	Q₈	—	2	1	no	—
883	Q₈	—	2	2	no	—
884	Q₈	—	2	1	no	—
885	Q₈	—	2	2	no	—
886	Q₈	—	2	2	no	—
887	Q₈	—	2	2	no	—
888	Q₈	—	2	1	no	—
889	Q₈	—	4	1	no	—
890	Q₈	—	4	2	no	—
891	Q₈	—	4	4	no	—
892	Q₈	—	4	2	no	—
893	Q₈	—	8	1	no	—
894	Q₈	—	8	2	no	—
895	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
896	D₄	—	2	4	no	—
897	D₄	—	4	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	2	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	2	no	—
917	C₂×C₄	—	4	2	no	—
918	C₂×C₄	—	8	1	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
921	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
922	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
923	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
924	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
925	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
926	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
927	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
928	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
929	C₈	—	2	2	no	—
930	C₈	—	2	2	no	—
931	C₈	—	2	2	no	—
932	C₈	—	2	2	no	—
933	C₂²	—	2	1	no	—
934	C₂²	—	2	1	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	C₅₃×#578	1	2	yes	—
939	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
940	C₄	—	2	1	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	1	no	—
944	C₄	—	2	1	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	2	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
959	C₄	C₅₃×#585	1	1	yes	characteristic
960	C₂	—	2	2	no	—
961	C₂	—	4	2	no	—
962	C₂	C₅₃×#3489	1	1	yes	characteristic
963	C₂	C₂×C₅₃×#578	1	1	yes	characteristic
964	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	#121×C₅₃	D₄
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
3. C₅₃×#3390	C₂	semidirect
4. C₅₃×#3374	C₂	semidirect
5. C₅₃×#3349	C₂	semidirect
6. C₅₃×#3344	C₂	semidirect
7. C₅₃×#3336	C₂	semidirect
8. C₅₃×#3312	C₂	semidirect
9. C₅₃×#3312	C₂	semidirect
10. C₅₃×#3299	C₂	semidirect
11. C₅₃×#3261	C₂	semidirect
12. C₅₃×#3249	C₂	semidirect
13. C₅₃×#3242	C₂	semidirect
14. C₅₃×#3236	C₂	semidirect
15. C₅₃×#3127	C₂	semidirect
16. C₅₃×#3113	C₂	semidirect
17. C₅₃×#3082	C₂	semidirect
18. C₂×C₅₃×#479	C₂	semidirect
450. #62168	C₅₃	direct (N × H)
480. #3390	C₂×C₅₃	semidirect
481. #3374	C₂×C₅₃	semidirect
482. #3349	C₂×C₅₃	semidirect
483. #3344	C₂×C₅₃	semidirect
484. #3336	C₂×C₅₃	semidirect
485. #3312	C₂×C₅₃	semidirect
486. #3312	C₂×C₅₃	semidirect
487. #3299	C₂×C₅₃	semidirect
488. #3261	C₂×C₅₃	semidirect
489. #3249	C₂×C₅₃	semidirect
490. #3242	C₂×C₅₃	semidirect
491. #3236	C₂×C₅₃	semidirect
492. #3127	C₂×C₅₃	semidirect
493. #3113	C₂×C₅₃	semidirect
494. #3082	C₂×C₅₃	semidirect
495. C₂×#479	C₂×C₅₃	semidirect
601. C₅₃	#62168	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×#3563	2
C₅₃×#3523	2
C₅₃×#3390	2
C₅₃×#3374	2
C₅₃×#3349	2
C₅₃×#3344	2
C₅₃×#3336	2
C₅₃×#3312	2
C₅₃×#3299	2
C₅₃×#3261	2
C₅₃×#3249	2
C₅₃×#3242	2
C₅₃×#3236	2
C₅₃×#3127	2
C₅₃×#3113	2
C₅₃×#3082	2
C₂×C₅₃×#479	2
C₅₃×#2992	2
#62168	53

Subgroups — C53×#62168 #27269680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62168 #27269680