Subgroups — C₅₃×#60782 #27268294

Order 13568.

2208 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3212	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3211	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3210	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3207	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3147	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3131	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3035	C₂	1	4	yes	maximal, complemented
14	C₅₃×#3002	C₂	1	4	yes	maximal, complemented
15	C₂×C₅₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₅₃	C₂²	1	2	yes	—
17	C₂×#135×C₅₃	C₂²	1	8	yes	complemented
18	C₅₃×#533	C₂²	1	1	yes	characteristic
19	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
20	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
21	C₅₃×#532	—	2	1	no	—
22	C₅₃×#532	—	2	1	no	—
23	C₅₃×#532	—	2	1	no	—
24	C₅₃×#532	—	2	1	no	—
25	C₅₃×#532	C₂²	1	2	yes	—
26	C₅₃×#532	C₂²	1	2	yes	—
27	C₅₃×#532	C₂²	1	2	yes	—
28	C₅₃×#532	C₂²	1	2	yes	—
29	C₅₃×#532	C₂²	1	1	yes	characteristic
30	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
34	C₅₃×#529	—	2	1	no	—
35	C₅₃×#529	—	2	1	no	—
36	C₅₃×#529	—	2	1	no	—
37	C₅₃×#529	—	2	1	no	—
38	C₅₃×#529	C₂²	1	2	yes	—
39	C₅₃×#529	C₂²	1	2	yes	complemented
40	C₂×#124×C₅₃	C₂²	1	2	yes	—
41	C₅₃×#525	—	2	1	no	—
42	C₅₃×#525	—	2	1	no	—
43	C₅₃×#525	C₂²	1	2	yes	—
44	C₂×#121×C₅₃	—	2	1	no	—
45	C₂×#121×C₅₃	—	2	1	no	—
46	C₄×#41×C₅₃	—	2	1	no	—
47	C₄×#41×C₅₃	—	2	1	no	—
48	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
49	C₂×C₄×D₄×C₅₃	—	2	1	no	—
50	C₂×C₄×D₄×C₅₃	—	2	1	no	—
51	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
52	C₅₃×#495	C₂²	1	8	yes	complemented
53	C₅₃×#494	C₂²	1	2	yes	complemented
54	C₅₃×#493	C₂²	1	2	yes	complemented
55	C₅₃×#492	C₂²	1	2	yes	complemented
56	C₅₃×#492	C₂²	1	2	yes	complemented
57	C₅₃×#488	C₂²	1	8	yes	complemented
58	C₅₃×#487	C₂²	1	2	yes	complemented
59	C₅₃×#487	C₂²	1	2	yes	complemented
60	C₅₃×#486	C₂²	1	2	yes	complemented
61	C₅₃×#486	C₂²	1	2	yes	complemented
62	C₅₃×#464	C₂²	1	8	yes	complemented
63	C₅₃×#463	C₂²	1	8	yes	complemented
64	C₅₃×#462	C₂²	1	4	yes	complemented
65	C₅₃×#461	C₂²	1	4	yes	complemented
66	C₅₃×#460	C₂²	1	4	yes	complemented
67	C₅₃×#459	C₂²	1	4	yes	complemented
68	C₅₃×#452	C₂²	1	8	yes	complemented
69	C₅₃×#451	C₂²	1	4	yes	—
70	C₅₃×#450	C₂²	1	4	yes	—
71	C₅₃×#449	C₂²	1	8	yes	complemented
72	C₅₃×#448	C₂²	1	4	yes	—
73	C₅₃×#447	C₂²	1	4	yes	—
74	C₅₃×#431	C₂²	1	1	yes	characteristic
75	C₅₃×#431	C₂²	1	1	yes	characteristic
76	C₅₃×#431	C₂²	1	2	yes	—
77	C₅₃×#431	C₂²	1	2	yes	complemented
78	C₅₃×#431	C₂²	1	2	yes	complemented
79	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	complemented
80	C₅₃×#416	C₂²	1	8	yes	complemented
81	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
82	C₂×C₄×C₈×C₅₃	C₂²	1	2	yes	complemented
83	C₂×#41×C₅₃	—	2	1	no	—
84	C₂×#41×C₅₃	—	2	1	no	—
85	C₂×#41×C₅₃	—	2	2	no	—
86	C₂×#41×C₅₃	—	2	2	no	—
87	C₂×#41×C₅₃	—	4	8	no	—
88	C₂×#41×C₅₃	C₂³	1	2	yes	—
89	C₂×#41×C₅₃	C₂³	1	4	yes	—
90	C₂×#41×C₅₃	C₂³	1	4	yes	—
91	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₅₃	—	2	2	no	—
93	C₂²×D₄×C₅₃	—	2	1	no	—
94	C₂²×D₄×C₅₃	—	2	1	no	—
95	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
96	C₂³×C₄×C₅₃	—	2	2	no	—
97	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
98	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
99	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
100	#135×C₅₃	—	4	16	no	—
101	C₂×Q₁₆×C₅₃	C₂³	1	8	yes	—
102	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	—
103	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	—
104	C₂×D₈×C₅₃	C₂³	1	8	yes	—
105	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
106	C₄⋊Q₈×C₅₃	—	2	1	no	—
107	C₄⋊Q₈×C₅₃	—	2	1	no	—
108	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
109	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
113	#127×C₅₃	—	2	1	no	—
114	#127×C₅₃	—	2	1	no	—
115	#127×C₅₃	C₂³	1	2	yes	—
116	#127×C₅₃	C₂³	1	1	yes	characteristic
117	#127×C₅₃	C₂³	1	2	yes	—
118	#126×C₅₃	—	2	2	no	—
119	#126×C₅₃	—	2	2	no	—
120	#125×C₅₃	—	2	1	no	—
121	#125×C₅₃	—	2	1	no	—
122	#125×C₅₃	C₂³	1	2	yes	—
123	#124×C₅₃	—	2	2	no	—
124	#124×C₅₃	—	2	2	no	—
125	#124×C₅₃	—	2	1	no	—
126	#124×C₅₃	—	2	1	no	—
127	#124×C₅₃	C₂³	1	4	yes	—
128	#124×C₅₃	C₂³	1	2	yes	—
129	#124×C₅₃	C₂³	1	4	yes	—
130	#123×C₅₃	—	2	2	no	—
131	#123×C₅₃	—	2	2	no	—
132	#123×C₅₃	—	2	2	no	—
133	C₂²⋊Q₈×C₅₃	—	2	1	no	—
134	C₂²⋊Q₈×C₅₃	—	2	1	no	—
135	C₂²⋊Q₈×C₅₃	—	2	1	no	—
136	C₂²⋊Q₈×C₅₃	—	2	1	no	—
137	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
138	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
139	#121×C₅₃	—	2	2	no	—
140	#121×C₅₃	—	2	2	no	—
141	#121×C₅₃	—	2	2	no	—
142	#121×C₅₃	—	2	2	no	—
143	#121×C₅₃	—	2	2	no	—
144	#121×C₅₃	—	2	2	no	—
145	#121×C₅₃	—	2	2	no	—
146	#121×C₅₃	—	2	2	no	—
147	#121×C₅₃	—	2	1	no	—
148	#121×C₅₃	—	2	1	no	—
149	#121×C₅₃	—	2	1	no	—
150	#121×C₅₃	—	2	1	no	—
151	#121×C₅₃	C₂³	1	2	yes	—
152	#121×C₅₃	C₂³	1	2	yes	—
153	#120×C₅₃	—	2	2	no	—
154	C₄×Q₈×C₅₃	—	2	1	no	—
155	C₄×Q₈×C₅₃	—	2	1	no	—
156	C₄×Q₈×C₅₃	—	2	1	no	—
157	C₄×Q₈×C₅₃	—	2	1	no	—
158	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
160	C₄×D₄×C₅₃	—	2	2	no	—
161	C₄×D₄×C₅₃	—	2	2	no	—
162	C₄×D₄×C₅₃	—	2	2	no	—
163	C₄×D₄×C₅₃	—	2	2	no	—
164	C₄×D₄×C₅₃	—	2	2	no	—
165	C₄×D₄×C₅₃	—	2	2	no	—
166	C₄×D₄×C₅₃	—	2	2	no	—
167	C₄×D₄×C₅₃	—	2	2	no	—
168	C₄×D₄×C₅₃	—	2	1	no	—
169	C₄×D₄×C₅₃	—	2	1	no	—
170	C₄×D₄×C₅₃	—	2	1	no	—
171	C₄×D₄×C₅₃	—	2	1	no	—
172	C₄×D₄×C₅₃	—	2	2	no	—
173	C₄×D₄×C₅₃	—	2	2	no	—
174	C₄×D₄×C₅₃	—	2	2	no	—
175	C₄×D₄×C₅₃	—	2	2	no	—
176	C₄×D₄×C₅₃	—	2	2	no	—
177	C₄×D₄×C₅₃	—	2	2	no	—
178	C₄×D₄×C₅₃	C₂³	1	2	yes	—
179	C₄×D₄×C₅₃	C₂³	1	2	yes	—
180	#117×C₅₃	—	2	2	no	—
181	#117×C₅₃	—	2	2	no	—
182	#117×C₅₃	—	2	2	no	—
183	#117×C₅₃	—	2	1	no	—
184	#117×C₅₃	—	2	1	no	—
185	#117×C₅₃	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
187	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
189	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
190	C₂×C₄²×C₅₃	—	2	2	no	—
191	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
195	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
196	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
197	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
203	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
204	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
205	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
206	#103×C₅₃	C₂³	1	8	yes	—
207	#103×C₅₃	C₂³	1	8	yes	—
208	#102×C₅₃	C₂³	1	8	yes	—
209	#102×C₅₃	C₂³	1	8	yes	—
210	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
211	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
213	C₄×C₈×C₅₃	C₂³	1	2	yes	—
214	C₄×C₈×C₅₃	C₂³	1	2	yes	—
215	C₄×C₈×C₅₃	C₂³	1	4	yes	—
216	C₂⁴×C₅₃	—	2	2	no	—
217	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
218	#41×C₅₃	—	2	8	no	—
219	#41×C₅₃	—	2	16	no	—
220	#41×C₅₃	—	4	8	no	—
221	#41×C₅₃	—	4	4	no	—
222	#41×C₅₃	—	4	8	no	—
223	#41×C₅₃	—	4	8	no	—
224	#41×C₅₃	—	4	4	no	—
225	C₂×Q₈×C₅₃	—	2	1	no	—
226	C₂×Q₈×C₅₃	—	2	1	no	—
227	C₂×Q₈×C₅₃	—	2	2	no	—
228	C₂×Q₈×C₅₃	—	4	4	no	—
229	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
230	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
231	C₂×D₄×C₅₃	—	2	2	no	—
232	C₂×D₄×C₅₃	—	2	2	no	—
233	C₂×D₄×C₅₃	—	2	2	no	—
234	C₂×D₄×C₅₃	—	2	4	no	—
235	C₂×D₄×C₅₃	—	2	4	no	—
236	C₂×D₄×C₅₃	—	2	1	no	—
237	C₂×D₄×C₅₃	—	2	1	no	—
238	C₂×D₄×C₅₃	—	2	2	no	—
239	C₂×D₄×C₅₃	—	2	2	no	—
240	C₂×D₄×C₅₃	—	2	2	no	—
241	C₂×D₄×C₅₃	—	2	2	no	—
242	C₂×D₄×C₅₃	—	2	2	no	—
243	C₂×D₄×C₅₃	—	4	4	no	—
244	C₂×D₄×C₅₃	—	4	4	no	—
245	C₂×D₄×C₅₃	—	4	8	no	—
246	C₂×D₄×C₅₃	—	4	4	no	—
247	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
248	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₅₃	—	2	4	no	—
250	C₂²×C₄×C₅₃	—	2	4	no	—
251	C₂²×C₄×C₅₃	—	2	2	no	—
252	C₂²×C₄×C₅₃	—	2	2	no	—
253	C₂²×C₄×C₅₃	—	2	2	no	—
254	C₂²×C₄×C₅₃	—	2	4	no	—
255	C₂²×C₄×C₅₃	—	2	2	no	—
256	C₂²×C₄×C₅₃	—	2	4	no	—
257	C₂²×C₄×C₅₃	—	4	2	no	—
258	C₂²×C₄×C₅₃	—	4	8	no	—
259	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
277	Q₁₆×C₅₃	—	4	8	no	—
278	SD₁₆×C₅₃	—	4	8	no	—
279	SD₁₆×C₅₃	—	4	8	no	—
280	D₈×C₅₃	—	4	8	no	—
281	C₂×C₈×C₅₃	—	2	8	no	—
282	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
283	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
284	C₄⋊C₄×C₅₃	—	2	2	no	—
285	C₄⋊C₄×C₅₃	—	2	2	no	—
286	C₄⋊C₄×C₅₃	—	2	2	no	—
287	C₄⋊C₄×C₅₃	—	2	2	no	—
288	C₄⋊C₄×C₅₃	—	2	1	no	—
289	C₄⋊C₄×C₅₃	—	2	1	no	—
290	C₄⋊C₄×C₅₃	—	2	1	no	—
291	C₄⋊C₄×C₅₃	—	2	1	no	—
292	C₄⋊C₄×C₅₃	—	2	2	no	—
293	C₄⋊C₄×C₅₃	—	2	2	no	—
294	C₄⋊C₄×C₅₃	—	2	2	no	—
295	C₄⋊C₄×C₅₃	—	2	2	no	—
296	C₄⋊C₄×C₅₃	—	2	2	no	—
297	C₄⋊C₄×C₅₃	—	2	2	no	—
298	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
300	C₂²⋊C₄×C₅₃	—	2	2	no	—
301	C₂²⋊C₄×C₅₃	—	2	2	no	—
302	C₂²⋊C₄×C₅₃	—	2	2	no	—
303	C₂²⋊C₄×C₅₃	—	2	4	no	—
304	C₂²⋊C₄×C₅₃	—	2	4	no	—
305	C₂²⋊C₄×C₅₃	—	2	4	no	—
306	C₂²⋊C₄×C₅₃	—	2	4	no	—
307	C₂²⋊C₄×C₅₃	—	2	2	no	—
308	C₂²⋊C₄×C₅₃	—	2	2	no	—
309	C₂²⋊C₄×C₅₃	—	2	2	no	—
310	C₂²⋊C₄×C₅₃	—	2	2	no	—
311	C₂²⋊C₄×C₅₃	—	2	2	no	—
312	C₂²⋊C₄×C₅₃	—	2	2	no	—
313	C₄²×C₅₃	—	2	2	no	—
314	C₄²×C₅₃	—	2	2	no	—
315	C₄²×C₅₃	—	2	2	no	—
316	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₂³×C₅₃	—	2	2	no	—
333	C₂³×C₅₃	—	2	2	no	—
334	C₂³×C₅₃	—	2	2	no	—
335	C₂³×C₅₃	—	2	4	no	—
336	C₂³×C₅₃	—	4	1	no	—
337	C₂³×C₅₃	—	4	4	no	—
338	C₂³×C₅₃	—	4	4	no	—
339	C₂³×C₅₃	—	4	4	no	—
340	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
341	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
342	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₅₃	—	2	8	no	—
344	Q₈×C₅₃	—	2	4	no	—
345	Q₈×C₅₃	—	4	4	no	—
346	Q₈×C₅₃	—	4	2	no	—
347	Q₈×C₅₃	—	4	2	no	—
348	D₄×C₅₃	—	2	8	no	—
349	D₄×C₅₃	—	2	4	no	—
350	D₄×C₅₃	—	4	4	no	—
351	D₄×C₅₃	—	4	4	no	—
352	D₄×C₅₃	—	4	8	no	—
353	D₄×C₅₃	—	4	4	no	—
354	D₄×C₅₃	—	4	8	no	—
355	D₄×C₅₃	—	4	4	no	—
356	D₄×C₅₃	—	4	4	no	—
357	D₄×C₅₃	—	4	4	no	—
358	D₄×C₅₃	—	4	4	no	—
359	D₄×C₅₃	—	4	2	no	—
360	D₄×C₅₃	—	4	4	no	—
361	D₄×C₅₃	—	4	2	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	2	no	—
364	C₂×C₄×C₅₃	—	2	2	no	—
365	C₂×C₄×C₅₃	—	2	2	no	—
366	C₂×C₄×C₅₃	—	2	2	no	—
367	C₂×C₄×C₅₃	—	2	2	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	2	no	—
371	C₂×C₄×C₅₃	—	2	2	no	—
372	C₂×C₄×C₅₃	—	2	2	no	—
373	C₂×C₄×C₅₃	—	2	2	no	—
374	C₂×C₄×C₅₃	—	2	2	no	—
375	C₂×C₄×C₅₃	—	2	4	no	—
376	C₂×C₄×C₅₃	—	2	2	no	—
377	C₂×C₄×C₅₃	—	2	2	no	—
378	C₂×C₄×C₅₃	—	2	2	no	—
379	C₂×C₄×C₅₃	—	4	1	no	—
380	C₂×C₄×C₅₃	—	4	1	no	—
381	C₂×C₄×C₅₃	—	4	1	no	—
382	C₂×C₄×C₅₃	—	4	8	no	—
383	C₂×C₄×C₅₃	—	4	4	no	—
384	C₂×C₄×C₅₃	—	4	4	no	—
385	C₂×C₄×C₅₃	—	4	8	no	—
386	C₂×C₄×C₅₃	—	4	4	no	—
387	C₂×C₄×C₅₃	—	4	4	no	—
388	C₂×C₄×C₅₃	#135	1	4	yes	complemented
389	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
401	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
402	C₈×C₅₃	—	2	4	no	—
403	C₈×C₅₃	—	2	4	no	—
404	#60782	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
405	C₂²×C₅₃	—	2	1	no	—
406	C₂²×C₅₃	—	2	1	no	—
407	C₂²×C₅₃	—	2	1	no	—
408	C₂²×C₅₃	—	2	1	no	—
409	C₂²×C₅₃	—	2	1	no	—
410	C₂²×C₅₃	—	2	1	no	—
411	C₂²×C₅₃	—	2	1	no	—
412	C₂²×C₅₃	—	4	4	no	—
413	C₂²×C₅₃	—	4	4	no	—
414	C₂²×C₅₃	—	4	2	no	—
415	C₂²×C₅₃	—	4	2	no	—
416	C₂²×C₅₃	—	4	4	no	—
417	C₂²×C₅₃	—	4	2	no	—
418	C₂²×C₅₃	—	4	4	no	—
419	C₂²×C₅₃	—	8	8	no	—
420	C₂²×C₅₃	#535	1	2	yes	—
421	C₂²×C₅₃	C₂×#135	1	2	yes	—
422	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
423	C₄×C₅₃	—	2	1	no	—
424	C₄×C₅₃	—	2	1	no	—
425	C₄×C₅₃	—	2	1	no	—
426	C₄×C₅₃	—	2	1	no	—
427	C₄×C₅₃	—	2	1	no	—
428	C₄×C₅₃	—	2	1	no	—
429	C₄×C₅₃	—	2	1	no	—
430	C₄×C₅₃	—	4	4	no	—
431	C₄×C₅₃	—	4	2	no	—
432	C₄×C₅₃	—	4	2	no	—
433	C₄×C₅₃	—	4	2	no	—
434	C₄×C₅₃	#535	1	2	yes	—
435	C₄×C₅₃	C₂×#135	1	2	yes	—
436	C₄×C₅₃	C₂×#135	1	2	yes	—
437	C₄×C₅₃	#575	1	2	yes	—
438	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
439	#3444	C₂×C₅₃	1	1	yes	characteristic, complemented
440	C₂×#532	C₂×C₅₃	1	1	yes	characteristic, complemented
441	#3212	C₂×C₅₃	1	4	yes	complemented
442	#3211	C₂×C₅₃	1	4	yes	complemented
443	#3210	C₂×C₅₃	1	2	yes	complemented
444	#3209	C₂×C₅₃	1	1	yes	characteristic, complemented
445	#3208	C₂×C₅₃	1	1	yes	characteristic, complemented
446	#3207	C₂×C₅₃	1	2	yes	complemented
447	#3206	C₂×C₅₃	1	1	yes	characteristic, complemented
448	#3205	C₂×C₅₃	1	1	yes	characteristic, complemented
449	#3147	C₂×C₅₃	1	2	yes	complemented
450	#3131	C₂×C₅₃	1	2	yes	complemented
451	#3035	C₂×C₅₃	1	4	yes	complemented
452	#3002	C₂×C₅₃	1	4	yes	complemented
453	C₂×#431	C₂×C₅₃	1	1	yes	characteristic, complemented
454	C₂×C₅₃	—	2	2	no	—
455	C₂×C₅₃	—	2	2	no	—
456	C₂×C₅₃	—	4	1	no	—
457	C₂×C₅₃	—	8	2	no	—
458	C₂×C₅₃	—	8	4	no	—
459	C₂×C₅₃	C₂×#535	1	1	yes	characteristic
460	C₂×C₅₃	C₂²×#135	1	1	yes	characteristic
461	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
462	C₂²×#41	C₂²×C₅₃	1	2	yes	—
463	C₂×#135	C₂²×C₅₃	1	8	yes	complemented
464	#533	C₂²×C₅₃	1	1	yes	characteristic
465	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
466	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
467	#532	—	2	1	no	—
468	#532	—	2	1	no	—
469	#532	—	2	1	no	—
470	#532	—	2	1	no	—
471	#532	C₂²×C₅₃	1	2	yes	—
472	#532	C₂²×C₅₃	1	2	yes	—
473	#532	C₂²×C₅₃	1	2	yes	—
474	#532	C₂²×C₅₃	1	2	yes	—
475	#532	C₂²×C₅₃	1	1	yes	characteristic
476	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
477	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
478	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
479	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
480	#529	—	2	1	no	—
481	#529	—	2	1	no	—
482	#529	—	2	1	no	—
483	#529	—	2	1	no	—
484	#529	C₂²×C₅₃	1	2	yes	—
485	#529	C₂²×C₅₃	1	2	yes	complemented
486	C₂×#124	C₂²×C₅₃	1	2	yes	—
487	#525	—	2	1	no	—
488	#525	—	2	1	no	—
489	#525	C₂²×C₅₃	1	2	yes	—
490	C₂×#121	—	2	1	no	—
491	C₂×#121	—	2	1	no	—
492	C₄×#41	—	2	1	no	—
493	C₄×#41	—	2	1	no	—
494	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
495	C₂×C₄×D₄	—	2	1	no	—
496	C₂×C₄×D₄	—	2	1	no	—
497	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
498	#495	C₂²×C₅₃	1	8	yes	complemented
499	#494	C₂²×C₅₃	1	2	yes	complemented
500	#493	C₂²×C₅₃	1	2	yes	complemented
501	#492	C₂²×C₅₃	1	2	yes	complemented
502	#492	C₂²×C₅₃	1	2	yes	complemented
503	#488	C₂²×C₅₃	1	8	yes	complemented
504	#487	C₂²×C₅₃	1	2	yes	complemented
505	#487	C₂²×C₅₃	1	2	yes	complemented
506	#486	C₂²×C₅₃	1	2	yes	complemented
507	#486	C₂²×C₅₃	1	2	yes	complemented
508	#464	C₂²×C₅₃	1	8	yes	complemented
509	#463	C₂²×C₅₃	1	8	yes	complemented
510	#462	C₂²×C₅₃	1	4	yes	complemented
511	#461	C₂²×C₅₃	1	4	yes	complemented
512	#460	C₂²×C₅₃	1	4	yes	complemented
513	#459	C₂²×C₅₃	1	4	yes	complemented
514	#452	C₂²×C₅₃	1	8	yes	complemented
515	#451	C₂²×C₅₃	1	4	yes	—
516	#450	C₂²×C₅₃	1	4	yes	—
517	#449	C₂²×C₅₃	1	8	yes	complemented
518	#448	C₂²×C₅₃	1	4	yes	—
519	#447	C₂²×C₅₃	1	4	yes	—
520	#431	C₂²×C₅₃	1	1	yes	characteristic
521	#431	C₂²×C₅₃	1	1	yes	characteristic
522	#431	C₂²×C₅₃	1	2	yes	—
523	#431	C₂²×C₅₃	1	2	yes	complemented
524	#431	C₂²×C₅₃	1	2	yes	complemented
525	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	complemented
526	#416	C₂²×C₅₃	1	8	yes	complemented
527	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
528	C₂×C₄×C₈	C₂²×C₅₃	1	2	yes	complemented
529	C₅₃	#60782	1	1	yes	characteristic, direct product factor, Sylow
530	C₂×#41	—	2	1	no	—
531	C₂×#41	—	2	1	no	—
532	C₂×#41	—	2	2	no	—
533	C₂×#41	—	2	2	no	—
534	C₂×#41	—	4	8	no	—
535	C₂×#41	C₂³×C₅₃	1	2	yes	—
536	C₂×#41	C₂³×C₅₃	1	4	yes	—
537	C₂×#41	C₂³×C₅₃	1	4	yes	—
538	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
539	C₂²×D₄	—	2	2	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	—	2	1	no	—
542	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
543	C₂³×C₄	—	2	2	no	—
544	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
545	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
547	#135	—	4	16	no	—
548	C₂×Q₁₆	C₂³×C₅₃	1	8	yes	—
549	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	—
550	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	—
551	C₂×D₈	C₂³×C₅₃	1	8	yes	—
552	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
553	C₄⋊Q₈	—	2	1	no	—
554	C₄⋊Q₈	—	2	1	no	—
555	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
556	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
557	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
558	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
559	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
560	#127	—	2	1	no	—
561	#127	—	2	1	no	—
562	#127	C₂³×C₅₃	1	2	yes	—
563	#127	C₂³×C₅₃	1	2	yes	—
564	#127	C₂³×C₅₃	1	1	yes	characteristic
565	#126	—	2	2	no	—
566	#126	—	2	2	no	—
567	#125	—	2	1	no	—
568	#125	—	2	1	no	—
569	#125	C₂³×C₅₃	1	2	yes	—
570	#124	—	2	2	no	—
571	#124	—	2	2	no	—
572	#124	—	2	1	no	—
573	#124	—	2	1	no	—
574	#124	C₂³×C₅₃	1	4	yes	—
575	#124	C₂³×C₅₃	1	4	yes	—
576	#124	C₂³×C₅₃	1	2	yes	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	2	no	—
580	C₂²⋊Q₈	—	2	1	no	—
581	C₂²⋊Q₈	—	2	1	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	—	2	1	no	—
584	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
585	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	2	no	—
594	#121	—	2	1	no	—
595	#121	—	2	1	no	—
596	#121	—	2	1	no	—
597	#121	—	2	1	no	—
598	#121	C₂³×C₅₃	1	2	yes	—
599	#121	C₂³×C₅₃	1	2	yes	—
600	#120	—	2	2	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
606	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	C₂³×C₅₃	1	2	yes	—
626	C₄×D₄	C₂³×C₅₃	1	2	yes	—
627	#117	—	2	1	no	—
628	#117	—	2	1	no	—
629	#117	—	2	2	no	—
630	#117	—	2	2	no	—
631	#117	—	2	2	no	—
632	#117	C₂³×C₅₃	1	2	yes	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	2	no	—
636	C₂×C₂²⋊C₄	—	2	2	no	—
637	C₂×C₄²	—	2	2	no	—
638	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
639	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
640	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
641	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
642	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
643	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
650	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
651	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
652	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
653	#103	C₂³×C₅₃	1	8	yes	—
654	#103	C₂³×C₅₃	1	8	yes	—
655	#102	C₂³×C₅₃	1	8	yes	—
656	#102	C₂³×C₅₃	1	8	yes	—
657	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
658	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
659	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
660	C₄×C₈	C₂³×C₅₃	1	2	yes	—
661	C₄×C₈	C₂³×C₅₃	1	2	yes	—
662	C₄×C₈	C₂³×C₅₃	1	4	yes	—
663	C₂⁴	—	2	2	no	—
664	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
665	#41	—	2	8	no	—
666	#41	—	2	16	no	—
667	#41	—	4	8	no	—
668	#41	—	4	4	no	—
669	#41	—	4	8	no	—
670	#41	—	4	8	no	—
671	#41	—	4	4	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	4	4	no	—
676	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
677	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	4	4	no	—
691	C₂×D₄	—	4	4	no	—
692	C₂×D₄	—	4	8	no	—
693	C₂×D₄	—	4	4	no	—
694	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
695	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	8	no	—
706	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
724	Q₁₆	—	4	8	no	—
725	SD₁₆	—	4	8	no	—
726	SD₁₆	—	4	8	no	—
727	D₈	—	4	8	no	—
728	C₂×C₈	—	2	8	no	—
729	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
730	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
746	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	2	no	—
763	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
765	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
772	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
773	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
775	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
776	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
777	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
778	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	4	no	—
783	C₂³	—	4	1	no	—
784	C₂³	—	4	4	no	—
785	C₂³	—	4	4	no	—
786	C₂³	—	4	4	no	—
787	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
788	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
789	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
790	Q₈	—	2	4	no	—
791	Q₈	—	2	8	no	—
792	Q₈	—	4	4	no	—
793	Q₈	—	4	2	no	—
794	Q₈	—	4	2	no	—
795	D₄	—	2	4	no	—
796	D₄	—	2	8	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	8	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	8	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	4	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	8	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	#135×C₅₃	1	4	yes	complemented
836	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
847	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
848	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
849	C₈	—	2	4	no	—
850	C₈	—	2	4	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	4	4	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	4	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	4	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	8	8	no	—
866	C₂²	C₅₃×#535	1	2	yes	—
867	C₂²	C₂×#135×C₅₃	1	2	yes	—
868	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	4	no	—
879	C₄	—	4	2	no	—
880	C₄	C₅₃×#535	1	2	yes	—
881	C₄	C₂×#135×C₅₃	1	2	yes	—
882	C₄	C₂×#135×C₅₃	1	2	yes	—
883	C₄	C₅₃×#575	1	2	yes	—
884	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
885	C₂	—	2	2	no	—
886	C₂	—	2	2	no	—
887	C₂	—	4	1	no	—
888	C₂	—	8	4	no	—
889	C₂	—	8	2	no	—
890	C₂	C₂×C₅₃×#535	1	1	yes	characteristic
891	C₂	C₂²×#135×C₅₃	1	1	yes	characteristic
892	C₂	C₂×C₅₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
socle	C₂²×C₅₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₂²×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3444	C₂	semidirect
2. C₂×C₅₃×#532	C₂	semidirect
3. C₅₃×#3212	C₂	semidirect
4. C₅₃×#3211	C₂	semidirect
5. C₅₃×#3210	C₂	semidirect
6. C₅₃×#3209	C₂	semidirect
7. C₅₃×#3208	C₂	semidirect
8. C₅₃×#3207	C₂	semidirect
9. C₅₃×#3206	C₂	semidirect
10. C₅₃×#3205	C₂	semidirect
11. C₅₃×#3147	C₂	semidirect
12. C₅₃×#3131	C₂	semidirect
13. C₅₃×#3035	C₂	semidirect
14. C₅₃×#3002	C₂	semidirect
15. C₂×C₅₃×#431	C₂	semidirect
17. C₂×#135×C₅₃	C₂²	semidirect
19. C₅₃×#533	C₂²	semidirect
20. C₅₃×#533	C₂²	semidirect
30. C₅₃×#532	C₂²	semidirect
31. C₅₃×#532	C₂²	semidirect
39. C₅₃×#529	C₂²	semidirect
48. C₄×#41×C₅₃	C₂²	semidirect
52. C₅₃×#495	C₂²	semidirect
53. C₅₃×#494	C₂²	semidirect
54. C₅₃×#493	C₂²	semidirect
55. C₅₃×#492	C₂²	semidirect
56. C₅₃×#492	C₂²	semidirect
57. C₅₃×#488	C₂²	semidirect
58. C₅₃×#487	C₂²	semidirect
59. C₅₃×#487	C₂²	semidirect
60. C₅₃×#486	C₂²	semidirect
61. C₅₃×#486	C₂²	semidirect
62. C₅₃×#464	C₂²	semidirect
63. C₅₃×#463	C₂²	semidirect
64. C₅₃×#462	C₂²	semidirect
65. C₅₃×#461	C₂²	semidirect
66. C₅₃×#460	C₂²	semidirect
67. C₅₃×#459	C₂²	semidirect
68. C₅₃×#452	C₂²	semidirect
71. C₅₃×#449	C₂²	semidirect
77. C₅₃×#431	C₂²	semidirect
78. C₅₃×#431	C₂²	semidirect
79. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
80. C₅₃×#416	C₂²	semidirect
82. C₂×C₄×C₈×C₅₃	C₂²	semidirect
388. C₂×C₄×C₅₃	#135	semidirect
404. #60782	C₅₃	direct (N × H)
439. #3444	C₂×C₅₃	semidirect
440. C₂×#532	C₂×C₅₃	semidirect
441. #3212	C₂×C₅₃	semidirect
442. #3211	C₂×C₅₃	semidirect
443. #3210	C₂×C₅₃	semidirect
444. #3209	C₂×C₅₃	semidirect
445. #3208	C₂×C₅₃	semidirect
446. #3207	C₂×C₅₃	semidirect
447. #3206	C₂×C₅₃	semidirect
448. #3205	C₂×C₅₃	semidirect
449. #3147	C₂×C₅₃	semidirect
450. #3131	C₂×C₅₃	semidirect
451. #3035	C₂×C₅₃	semidirect
452. #3002	C₂×C₅₃	semidirect
453. C₂×#431	C₂×C₅₃	semidirect
463. C₂×#135	C₂²×C₅₃	semidirect
465. #533	C₂²×C₅₃	semidirect
466. #533	C₂²×C₅₃	semidirect
476. #532	C₂²×C₅₃	semidirect
477. #532	C₂²×C₅₃	semidirect
485. #529	C₂²×C₅₃	semidirect
494. C₄×#41	C₂²×C₅₃	semidirect
498. #495	C₂²×C₅₃	semidirect
499. #494	C₂²×C₅₃	semidirect
500. #493	C₂²×C₅₃	semidirect
501. #492	C₂²×C₅₃	semidirect
502. #492	C₂²×C₅₃	semidirect
503. #488	C₂²×C₅₃	semidirect
504. #487	C₂²×C₅₃	semidirect
505. #487	C₂²×C₅₃	semidirect
506. #486	C₂²×C₅₃	semidirect
507. #486	C₂²×C₅₃	semidirect
508. #464	C₂²×C₅₃	semidirect
509. #463	C₂²×C₅₃	semidirect
510. #462	C₂²×C₅₃	semidirect
511. #461	C₂²×C₅₃	semidirect
512. #460	C₂²×C₅₃	semidirect
513. #459	C₂²×C₅₃	semidirect
514. #452	C₂²×C₅₃	semidirect
517. #449	C₂²×C₅₃	semidirect
523. #431	C₂²×C₅₃	semidirect
524. #431	C₂²×C₅₃	semidirect
525. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
526. #416	C₂²×C₅₃	semidirect
528. C₂×C₄×C₈	C₂²×C₅₃	semidirect
529. C₅₃	#60782	direct (N × H)
835. C₂×C₄	#135×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3444	2
C₂×C₅₃×#532	2
C₅₃×#3212	2
C₅₃×#3211	2
C₅₃×#3210	2
C₅₃×#3209	2
C₅₃×#3208	2
C₅₃×#3207	2
C₅₃×#3206	2
C₅₃×#3205	2
C₅₃×#3147	2
C₅₃×#3131	2
C₅₃×#3035	2
C₅₃×#3002	2
C₂×C₅₃×#431	2
#60782	53

Subgroups — C53×#60782 #27268294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60782 #27268294