Subgroups — C₅₃×#60764 #27268276

Order 13568.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3203	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3201	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3196	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3193	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3189	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3188	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3098	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3063	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3061	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3013	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
20	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
22	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
23	C₂×#131×C₅₃	C₂²	1	2	yes	complemented
24	D₄×Q₈×C₅₃	—	2	1	no	—
25	C₅₃×#548	—	2	1	no	—
26	C₅₃×#547	—	2	2	no	—
27	C₅₃×#547	—	2	1	no	—
28	C₅₃×#546	—	2	2	no	—
29	C₅₃×#546	—	2	1	no	—
30	C₅₃×#537	—	2	2	no	—
31	C₅₃×#537	—	2	1	no	—
32	C₅₃×#537	—	2	1	no	—
33	C₅₃×#537	C₂²	1	4	yes	—
34	C₅₃×#537	C₂²	1	2	yes	—
35	C₅₃×#537	C₂²	1	2	yes	—
36	C₅₃×#537	C₂²	1	2	yes	complemented
37	C₅₃×#537	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#536	C₂²	1	2	yes	complemented
39	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#525	C₂²	1	2	yes	—
41	C₅₃×#525	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
43	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
44	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
45	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×#121×C₅₃	—	2	1	no	—
47	C₂×#121×C₅₃	—	2	2	no	—
48	C₂×#121×C₅₃	C₂²	1	2	yes	—
49	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#485	C₂²	1	4	yes	complemented
52	C₅₃×#484	C₂²	1	2	yes	—
53	C₅₃×#484	C₂²	1	2	yes	—
54	C₅₃×#484	C₂²	1	2	yes	—
55	C₅₃×#484	C₂²	1	4	yes	complemented
56	C₅₃×#484	C₂²	1	4	yes	complemented
57	C₅₃×#483	C₂²	1	2	yes	complemented
58	C₅₃×#482	C₂²	1	4	yes	complemented
59	C₅₃×#481	C₂²	1	2	yes	—
60	C₅₃×#480	C₂²	1	4	yes	complemented
61	C₅₃×#480	C₂²	1	2	yes	complemented
62	C₅₃×#470	C₂²	1	4	yes	complemented
63	C₅₃×#468	C₂²	1	4	yes	complemented
64	C₅₃×#468	C₂²	1	4	yes	complemented
65	C₅₃×#468	C₂²	1	4	yes	complemented
66	C₅₃×#467	C₂²	1	4	yes	complemented
67	C₅₃×#467	C₂²	1	4	yes	complemented
68	C₅₃×#466	C₂²	1	4	yes	complemented
69	C₅₃×#465	C₂²	1	4	yes	complemented
70	C₅₃×#452	C₂²	1	4	yes	complemented
71	C₅₃×#452	C₂²	1	2	yes	complemented
72	C₅₃×#452	C₂²	1	4	yes	complemented
73	C₅₃×#451	C₂²	1	2	yes	—
74	C₅₃×#451	C₂²	1	1	yes	characteristic
75	C₅₃×#451	C₂²	1	4	yes	complemented
76	C₅₃×#450	C₂²	1	1	yes	characteristic
77	C₅₃×#450	C₂²	1	2	yes	—
78	C₅₃×#449	C₂²	1	2	yes	complemented
79	C₅₃×#449	C₂²	1	4	yes	complemented
80	C₅₃×#448	C₂²	1	1	yes	characteristic
81	C₅₃×#448	C₂²	1	4	yes	complemented
82	C₅₃×#447	C₂²	1	1	yes	characteristic
83	C₅₃×#428	C₂²	1	2	yes	complemented
84	C₂×#107×C₅₃	C₂²	1	2	yes	complemented
85	C₅₃×#417	C₂²	1	2	yes	complemented
86	C₅₃×#417	C₂²	1	2	yes	complemented
87	C₅₃×#416	C₂²	1	2	yes	complemented
88	C₂×#103×C₅₃	C₂²	1	2	yes	complemented
89	C₅₃×#408	C₂²	1	4	yes	complemented
90	C₅₃×#408	C₂²	1	2	yes	complemented
91	C₅₃×#407	C₂²	1	2	yes	—
92	C₅₃×#407	C₂²	1	1	yes	characteristic
93	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
94	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
95	2₋¹⁺⁴×C₅₃	—	4	4	no	—
96	C₂×#41×C₅₃	—	2	1	no	—
97	C₂×#41×C₅₃	—	2	2	no	—
98	C₂×#41×C₅₃	—	2	1	no	—
99	C₂×#41×C₅₃	—	2	1	no	—
100	C₂×#41×C₅₃	—	4	4	no	—
101	C₂×#41×C₅₃	—	4	4	no	—
102	C₂×#41×C₅₃	D₄	1	2	yes	—
103	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
104	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
105	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
106	C₂×#41×C₅₃	C₂³	1	2	yes	—
107	C₂×#41×C₅₃	C₂³	1	2	yes	—
108	C₂×#41×C₅₃	C₂³	1	2	yes	—
109	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
110	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
111	C₂×#41×C₅₃	C₂³	1	2	yes	—
112	C₂²×Q₈×C₅₃	—	2	1	no	—
113	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
114	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
115	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
116	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
117	C₂²×D₄×C₅₃	—	2	1	no	—
118	C₂²×D₄×C₅₃	—	2	2	no	—
119	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
120	C₂²×D₄×C₅₃	D₄	1	2	yes	—
121	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₅₃	—	2	1	no	—
123	C₂³×C₄×C₅₃	—	2	1	no	—
124	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
126	#137×C₅₃	—	4	4	no	—
127	#135×C₅₃	—	4	4	no	—
128	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
129	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
130	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
132	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
133	C₂×D₈×C₅₃	C₂³	1	2	yes	—
134	#131×C₅₃	—	4	4	no	—
135	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
136	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
137	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
138	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
139	C₄⋊Q₈×C₅₃	—	2	1	no	—
140	C₄⋊Q₈×C₅₃	—	2	2	no	—
141	#124×C₅₃	—	2	1	no	—
142	#124×C₅₃	—	2	2	no	—
143	#123×C₅₃	—	2	2	no	—
144	#123×C₅₃	—	2	2	no	—
145	#123×C₅₃	—	2	2	no	—
146	#123×C₅₃	—	2	1	no	—
147	#123×C₅₃	—	2	2	no	—
148	C₂²⋊Q₈×C₅₃	—	2	2	no	—
149	C₂²⋊Q₈×C₅₃	—	2	2	no	—
150	C₂²⋊Q₈×C₅₃	—	2	4	no	—
151	C₂²⋊Q₈×C₅₃	—	2	1	no	—
152	C₂²⋊Q₈×C₅₃	—	2	2	no	—
153	C₂²⋊Q₈×C₅₃	—	2	2	no	—
154	C₂²⋊Q₈×C₅₃	—	2	2	no	—
155	C₂²⋊Q₈×C₅₃	—	2	1	no	—
156	C₂²⋊Q₈×C₅₃	—	2	2	no	—
157	C₂²⋊Q₈×C₅₃	—	2	1	no	—
158	C₂²⋊Q₈×C₅₃	—	2	2	no	—
159	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
160	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
162	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
163	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
164	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
165	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
166	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
167	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
168	#121×C₅₃	—	2	4	no	—
169	#121×C₅₃	—	2	4	no	—
170	#121×C₅₃	—	2	4	no	—
171	#121×C₅₃	—	2	4	no	—
172	#121×C₅₃	—	2	2	no	—
173	#121×C₅₃	—	2	2	no	—
174	#121×C₅₃	—	2	4	no	—
175	#121×C₅₃	—	2	2	no	—
176	#121×C₅₃	—	2	2	no	—
177	#121×C₅₃	—	2	2	no	—
178	#121×C₅₃	—	2	1	no	—
179	#121×C₅₃	—	2	2	no	—
180	#121×C₅₃	—	2	2	no	—
181	#121×C₅₃	—	2	2	no	—
182	#121×C₅₃	C₂³	1	4	yes	—
183	#121×C₅₃	C₂³	1	4	yes	—
184	#121×C₅₃	C₂³	1	1	yes	characteristic
185	#121×C₅₃	C₂³	1	1	yes	characteristic
186	#121×C₅₃	C₂³	1	2	yes	—
187	#120×C₅₃	—	2	1	no	—
188	#120×C₅₃	—	2	2	no	—
189	C₄×Q₈×C₅₃	—	2	1	no	—
190	C₄×D₄×C₅₃	—	2	1	no	—
191	C₄×D₄×C₅₃	—	2	2	no	—
192	C₄×D₄×C₅₃	—	2	1	no	—
193	C₄×D₄×C₅₃	—	2	2	no	—
194	C₄×D₄×C₅₃	—	2	1	no	—
195	C₄×D₄×C₅₃	—	2	2	no	—
196	#117×C₅₃	C₂³	1	2	yes	—
197	#117×C₅₃	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
199	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
200	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
201	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
202	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
203	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
204	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
207	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
210	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
211	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
212	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
213	#107×C₅₃	C₂³	1	4	yes	—
214	#107×C₅₃	C₂³	1	4	yes	—
215	#107×C₅₃	C₂³	1	4	yes	—
216	#106×C₅₃	C₂³	1	4	yes	—
217	#103×C₅₃	C₂³	1	2	yes	—
218	#103×C₅₃	C₂³	1	4	yes	—
219	#103×C₅₃	C₂³	1	4	yes	—
220	#103×C₅₃	C₂³	1	4	yes	—
221	#103×C₅₃	C₂³	1	2	yes	—
222	#103×C₅₃	C₂³	1	4	yes	—
223	#102×C₅₃	C₂³	1	2	yes	—
224	#102×C₅₃	C₂³	1	2	yes	—
225	#102×C₅₃	C₂³	1	4	yes	—
226	#102×C₅₃	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
228	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
230	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
231	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
232	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
233	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
234	C₂⁴×C₅₃	—	2	1	no	—
235	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
236	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
237	#41×C₅₃	—	2	4	no	—
238	#41×C₅₃	—	2	4	no	—
239	#41×C₅₃	—	2	4	no	—
240	#41×C₅₃	—	2	4	no	—
241	#41×C₅₃	—	2	4	no	—
242	#41×C₅₃	—	4	4	no	—
243	#41×C₅₃	—	4	4	no	—
244	#41×C₅₃	—	4	2	no	—
245	#41×C₅₃	—	4	2	no	—
246	#41×C₅₃	—	4	2	no	—
247	#41×C₅₃	—	4	2	no	—
248	#41×C₅₃	—	4	4	no	—
249	#41×C₅₃	—	4	4	no	—
250	#41×C₅₃	—	4	4	no	—
251	#41×C₅₃	—	4	8	no	—
252	#41×C₅₃	—	4	4	no	—
253	C₂×Q₈×C₅₃	—	2	1	no	—
254	C₂×Q₈×C₅₃	—	2	2	no	—
255	C₂×Q₈×C₅₃	—	2	1	no	—
256	C₂×Q₈×C₅₃	—	2	4	no	—
257	C₂×Q₈×C₅₃	—	4	2	no	—
258	C₂×Q₈×C₅₃	—	4	2	no	—
259	C₂×Q₈×C₅₃	—	4	4	no	—
260	C₂×Q₈×C₅₃	—	4	4	no	—
261	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
262	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
263	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
264	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
265	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
266	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
267	C₂×D₄×C₅₃	—	2	1	no	—
268	C₂×D₄×C₅₃	—	2	2	no	—
269	C₂×D₄×C₅₃	—	2	1	no	—
270	C₂×D₄×C₅₃	—	2	2	no	—
271	C₂×D₄×C₅₃	—	2	2	no	—
272	C₂×D₄×C₅₃	—	2	1	no	—
273	C₂×D₄×C₅₃	—	2	2	no	—
274	C₂×D₄×C₅₃	—	2	4	no	—
275	C₂×D₄×C₅₃	—	2	4	no	—
276	C₂×D₄×C₅₃	—	2	1	no	—
277	C₂×D₄×C₅₃	—	4	2	no	—
278	C₂×D₄×C₅₃	—	4	2	no	—
279	C₂×D₄×C₅₃	—	4	4	no	—
280	C₂×D₄×C₅₃	—	4	4	no	—
281	C₂×D₄×C₅₃	—	8	4	no	—
282	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
283	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
284	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
285	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
286	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
287	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
288	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
289	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
290	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₅₃	—	2	4	no	—
292	C₂²×C₄×C₅₃	—	2	2	no	—
293	C₂²×C₄×C₅₃	—	2	1	no	—
294	C₂²×C₄×C₅₃	—	2	2	no	—
295	C₂²×C₄×C₅₃	—	2	1	no	—
296	C₂²×C₄×C₅₃	—	2	2	no	—
297	C₂²×C₄×C₅₃	—	2	1	no	—
298	C₂²×C₄×C₅₃	—	2	2	no	—
299	C₂²×C₄×C₅₃	—	2	2	no	—
300	C₂²×C₄×C₅₃	—	2	2	no	—
301	C₂²×C₄×C₅₃	—	2	1	no	—
302	C₂²×C₄×C₅₃	—	2	2	no	—
303	C₂²×C₄×C₅₃	—	2	2	no	—
304	C₂²×C₄×C₅₃	—	4	4	no	—
305	C₂²×C₄×C₅₃	—	4	4	no	—
306	C₂²×C₄×C₅₃	—	8	2	no	—
307	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
311	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
312	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
313	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
318	Q₁₆×C₅₃	—	4	2	no	—
319	Q₁₆×C₅₃	—	4	4	no	—
320	SD₁₆×C₅₃	—	4	2	no	—
321	SD₁₆×C₅₃	—	4	2	no	—
322	SD₁₆×C₅₃	—	4	4	no	—
323	D₈×C₅₃	—	4	2	no	—
324	M₁₆×C₅₃	—	2	4	no	—
325	M₁₆×C₅₃	—	4	4	no	—
326	C₂×C₈×C₅₃	—	2	4	no	—
327	C₂×C₈×C₅₃	—	4	4	no	—
328	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
329	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
330	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
331	C₄⋊C₄×C₅₃	—	2	2	no	—
332	C₄⋊C₄×C₅₃	—	2	2	no	—
333	C₄⋊C₄×C₅₃	—	2	2	no	—
334	C₄⋊C₄×C₅₃	—	2	2	no	—
335	C₄⋊C₄×C₅₃	—	2	1	no	—
336	C₄⋊C₄×C₅₃	—	2	4	no	—
337	C₄⋊C₄×C₅₃	—	2	4	no	—
338	C₄⋊C₄×C₅₃	—	2	2	no	—
339	C₄⋊C₄×C₅₃	—	2	2	no	—
340	C₄⋊C₄×C₅₃	—	2	2	no	—
341	C₄⋊C₄×C₅₃	—	2	2	no	—
342	C₄⋊C₄×C₅₃	—	2	1	no	—
343	C₄⋊C₄×C₅₃	—	2	1	no	—
344	C₄⋊C₄×C₅₃	—	2	2	no	—
345	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
346	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
349	C₂²⋊C₄×C₅₃	—	2	2	no	—
350	C₂²⋊C₄×C₅₃	—	2	1	no	—
351	C₂²⋊C₄×C₅₃	—	2	4	no	—
352	C₂²⋊C₄×C₅₃	—	2	4	no	—
353	C₂²⋊C₄×C₅₃	—	2	2	no	—
354	C₂²⋊C₄×C₅₃	—	2	2	no	—
355	C₂²⋊C₄×C₅₃	—	2	2	no	—
356	C₂²⋊C₄×C₅₃	—	2	2	no	—
357	C₂²⋊C₄×C₅₃	—	2	1	no	—
358	C₂²⋊C₄×C₅₃	—	2	1	no	—
359	C₂²⋊C₄×C₅₃	—	2	2	no	—
360	C₂²⋊C₄×C₅₃	—	2	4	no	—
361	C₂²⋊C₄×C₅₃	—	2	4	no	—
362	C₂²⋊C₄×C₅₃	—	2	1	no	—
363	C₂²⋊C₄×C₅₃	—	2	1	no	—
364	C₂²⋊C₄×C₅₃	—	2	2	no	—
365	C₄²×C₅₃	—	2	2	no	—
366	C₄²×C₅₃	—	2	1	no	—
367	C₂³×C₅₃	—	2	2	no	—
368	C₂³×C₅₃	—	2	2	no	—
369	C₂³×C₅₃	—	2	4	no	—
370	C₂³×C₅₃	—	2	1	no	—
371	C₂³×C₅₃	—	2	2	no	—
372	C₂³×C₅₃	—	4	1	no	—
373	C₂³×C₅₃	—	4	2	no	—
374	C₂³×C₅₃	—	4	2	no	—
375	C₂³×C₅₃	—	4	2	no	—
376	C₂³×C₅₃	—	4	2	no	—
377	C₂³×C₅₃	—	4	2	no	—
378	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
379	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
380	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
381	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
382	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
383	Q₈×C₅₃	—	2	2	no	—
384	Q₈×C₅₃	—	2	2	no	—
385	Q₈×C₅₃	—	2	4	no	—
386	Q₈×C₅₃	—	2	2	no	—
387	Q₈×C₅₃	—	2	2	no	—
388	Q₈×C₅₃	—	2	2	no	—
389	Q₈×C₅₃	—	4	2	no	—
390	Q₈×C₅₃	—	4	4	no	—
391	Q₈×C₅₃	—	4	2	no	—
392	Q₈×C₅₃	—	4	2	no	—
393	D₄×C₅₃	—	2	4	no	—
394	D₄×C₅₃	—	2	4	no	—
395	D₄×C₅₃	—	2	2	no	—
396	D₄×C₅₃	—	2	2	no	—
397	D₄×C₅₃	—	2	2	no	—
398	D₄×C₅₃	—	2	2	no	—
399	D₄×C₅₃	—	2	2	no	—
400	D₄×C₅₃	—	4	2	no	—
401	D₄×C₅₃	—	4	2	no	—
402	D₄×C₅₃	—	4	2	no	—
403	D₄×C₅₃	—	4	2	no	—
404	D₄×C₅₃	—	4	4	no	—
405	D₄×C₅₃	—	4	4	no	—
406	D₄×C₅₃	—	4	4	no	—
407	D₄×C₅₃	—	4	2	no	—
408	D₄×C₅₃	—	4	2	no	—
409	D₄×C₅₃	—	8	1	no	—
410	D₄×C₅₃	—	8	2	no	—
411	D₄×C₅₃	—	8	4	no	—
412	D₄×C₅₃	—	8	4	no	—
413	C₂×C₄×C₅₃	—	2	2	no	—
414	C₂×C₄×C₅₃	—	2	2	no	—
415	C₂×C₄×C₅₃	—	2	2	no	—
416	C₂×C₄×C₅₃	—	2	2	no	—
417	C₂×C₄×C₅₃	—	2	2	no	—
418	C₂×C₄×C₅₃	—	2	4	no	—
419	C₂×C₄×C₅₃	—	2	4	no	—
420	C₂×C₄×C₅₃	—	2	2	no	—
421	C₂×C₄×C₅₃	—	2	4	no	—
422	C₂×C₄×C₅₃	—	2	2	no	—
423	C₂×C₄×C₅₃	—	2	1	no	—
424	C₂×C₄×C₅₃	—	2	1	no	—
425	C₂×C₄×C₅₃	—	2	2	no	—
426	C₂×C₄×C₅₃	—	2	1	no	—
427	C₂×C₄×C₅₃	—	4	2	no	—
428	C₂×C₄×C₅₃	—	4	2	no	—
429	C₂×C₄×C₅₃	—	4	2	no	—
430	C₂×C₄×C₅₃	—	4	4	no	—
431	C₂×C₄×C₅₃	—	4	4	no	—
432	C₂×C₄×C₅₃	—	4	2	no	—
433	C₂×C₄×C₅₃	—	4	4	no	—
434	C₂×C₄×C₅₃	—	4	4	no	—
435	C₂×C₄×C₅₃	—	4	2	no	—
436	C₂×C₄×C₅₃	—	4	4	no	—
437	C₂×C₄×C₅₃	—	4	2	no	—
438	C₂×C₄×C₅₃	—	8	1	no	—
439	C₂×C₄×C₅₃	—	8	2	no	—
440	C₂×C₄×C₅₃	—	8	2	no	—
441	C₂×C₄×C₅₃	—	8	2	no	—
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	1	yes	characteristic
445	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
448	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
449	C₈×C₅₃	—	2	2	no	—
450	C₈×C₅₃	—	2	2	no	—
451	C₈×C₅₃	—	2	4	no	—
452	#60764	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂²×C₅₃	—	2	1	no	—
454	C₂²×C₅₃	—	2	1	no	—
455	C₂²×C₅₃	—	2	1	no	—
456	C₂²×C₅₃	—	2	1	no	—
457	C₂²×C₅₃	—	2	1	no	—
458	C₂²×C₅₃	—	2	2	no	—
459	C₂²×C₅₃	—	2	2	no	—
460	C₂²×C₅₃	—	2	1	no	—
461	C₂²×C₅₃	—	2	2	no	—
462	C₂²×C₅₃	—	2	2	no	—
463	C₂²×C₅₃	—	2	1	no	—
464	C₂²×C₅₃	—	2	2	no	—
465	C₂²×C₅₃	—	2	2	no	—
466	C₂²×C₅₃	—	4	4	no	—
467	C₂²×C₅₃	—	4	2	no	—
468	C₂²×C₅₃	—	4	1	no	—
469	C₂²×C₅₃	—	4	1	no	—
470	C₂²×C₅₃	—	4	2	no	—
471	C₂²×C₅₃	—	4	1	no	—
472	C₂²×C₅₃	—	4	2	no	—
473	C₂²×C₅₃	—	8	4	no	—
474	C₂²×C₅₃	—	8	4	no	—
475	C₂²×C₅₃	#534	1	2	yes	—
476	C₂²×C₅₃	#578	1	2	yes	—
477	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
478	C₄×C₅₃	—	2	1	no	—
479	C₄×C₅₃	—	2	1	no	—
480	C₄×C₅₃	—	2	2	no	—
481	C₄×C₅₃	—	2	2	no	—
482	C₄×C₅₃	—	4	4	no	—
483	C₄×C₅₃	—	4	2	no	—
484	C₄×C₅₃	—	4	1	no	—
485	C₄×C₅₃	—	4	2	no	—
486	C₄×C₅₃	—	4	2	no	—
487	C₄×C₅₃	—	4	1	no	—
488	C₄×C₅₃	—	4	1	no	—
489	C₄×C₅₃	#534	1	2	yes	—
490	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
491	#3489	C₂×C₅₃	1	1	yes	characteristic, complemented
492	C₂×#537	C₂×C₅₃	1	1	yes	characteristic, complemented
493	#3203	C₂×C₅₃	1	4	yes	complemented
494	#3201	C₂×C₅₃	1	4	yes	complemented
495	#3196	C₂×C₅₃	1	2	yes	complemented
496	#3193	C₂×C₅₃	1	2	yes	complemented
497	#3189	C₂×C₅₃	1	2	yes	complemented
498	#3188	C₂×C₅₃	1	2	yes	complemented
499	#3098	C₂×C₅₃	1	2	yes	complemented
500	#3092	C₂×C₅₃	1	1	yes	characteristic, complemented
501	C₂×#484	C₂×C₅₃	1	1	yes	characteristic, complemented
502	#3063	C₂×C₅₃	1	2	yes	complemented
503	#3061	C₂×C₅₃	1	2	yes	complemented
504	#3013	C₂×C₅₃	1	2	yes	complemented
505	#3007	C₂×C₅₃	1	1	yes	characteristic, complemented
506	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
507	#2880	C₂×C₅₃	1	1	yes	characteristic, complemented
508	C₂×C₅₃	—	2	2	no	—
509	C₂×C₅₃	—	2	2	no	—
510	C₂×C₅₃	—	4	1	no	—
511	C₂×C₅₃	—	4	2	no	—
512	C₂×C₅₃	—	4	2	no	—
513	C₂×C₅₃	—	8	1	no	—
514	C₂×C₅₃	—	8	2	no	—
515	C₂×C₅₃	C₂×#534	1	1	yes	characteristic
516	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
517	C₂×C₅₃	#3585	1	1	yes	characteristic
518	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic, complemented
519	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
520	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
521	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
522	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
523	C₂×#131	C₂²×C₅₃	1	2	yes	complemented
524	D₄×Q₈	—	2	1	no	—
525	#548	—	2	1	no	—
526	#547	—	2	2	no	—
527	#547	—	2	1	no	—
528	#546	—	2	2	no	—
529	#546	—	2	1	no	—
530	#537	—	2	2	no	—
531	#537	—	2	1	no	—
532	#537	—	2	1	no	—
533	#537	C₂²×C₅₃	1	2	yes	—
534	#537	C₂²×C₅₃	1	4	yes	—
535	#537	C₂²×C₅₃	1	2	yes	—
536	#537	C₂²×C₅₃	1	2	yes	complemented
537	#537	C₂²×C₅₃	1	1	yes	characteristic, complemented
538	#536	C₂²×C₅₃	1	2	yes	complemented
539	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
540	#525	C₂²×C₅₃	1	1	yes	characteristic
541	#525	C₂²×C₅₃	1	2	yes	—
542	C₂×C₂²⋊Q₈	—	2	1	no	—
543	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
544	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
545	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
546	C₂×#121	—	2	1	no	—
547	C₂×#121	—	2	2	no	—
548	C₂×#121	C₂²×C₅₃	1	2	yes	—
549	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
550	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
551	#485	C₂²×C₅₃	1	4	yes	complemented
552	#484	C₂²×C₅₃	1	2	yes	—
553	#484	C₂²×C₅₃	1	2	yes	—
554	#484	C₂²×C₅₃	1	2	yes	—
555	#484	C₂²×C₅₃	1	4	yes	complemented
556	#484	C₂²×C₅₃	1	4	yes	complemented
557	#483	C₂²×C₅₃	1	2	yes	complemented
558	#482	C₂²×C₅₃	1	4	yes	complemented
559	#481	C₂²×C₅₃	1	2	yes	—
560	#480	C₂²×C₅₃	1	2	yes	complemented
561	#480	C₂²×C₅₃	1	4	yes	complemented
562	#470	C₂²×C₅₃	1	4	yes	complemented
563	#468	C₂²×C₅₃	1	4	yes	complemented
564	#468	C₂²×C₅₃	1	4	yes	complemented
565	#468	C₂²×C₅₃	1	4	yes	complemented
566	#467	C₂²×C₅₃	1	4	yes	complemented
567	#467	C₂²×C₅₃	1	4	yes	complemented
568	#466	C₂²×C₅₃	1	4	yes	complemented
569	#465	C₂²×C₅₃	1	4	yes	complemented
570	#452	C₂²×C₅₃	1	4	yes	complemented
571	#452	C₂²×C₅₃	1	2	yes	complemented
572	#452	C₂²×C₅₃	1	4	yes	complemented
573	#451	C₂²×C₅₃	1	1	yes	characteristic
574	#451	C₂²×C₅₃	1	2	yes	—
575	#451	C₂²×C₅₃	1	4	yes	complemented
576	#450	C₂²×C₅₃	1	2	yes	—
577	#450	C₂²×C₅₃	1	1	yes	characteristic
578	#449	C₂²×C₅₃	1	4	yes	complemented
579	#449	C₂²×C₅₃	1	2	yes	complemented
580	#448	C₂²×C₅₃	1	1	yes	characteristic
581	#448	C₂²×C₅₃	1	4	yes	complemented
582	#447	C₂²×C₅₃	1	1	yes	characteristic
583	#428	C₂²×C₅₃	1	2	yes	complemented
584	C₂×#107	C₂²×C₅₃	1	2	yes	complemented
585	#417	C₂²×C₅₃	1	2	yes	complemented
586	#417	C₂²×C₅₃	1	2	yes	complemented
587	#416	C₂²×C₅₃	1	2	yes	complemented
588	C₂×#103	C₂²×C₅₃	1	2	yes	complemented
589	#408	C₂²×C₅₃	1	2	yes	complemented
590	#408	C₂²×C₅₃	1	4	yes	complemented
591	#407	C₂²×C₅₃	1	1	yes	characteristic
592	#407	C₂²×C₅₃	1	2	yes	—
593	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
594	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
595	C₅₃	#60764	1	1	yes	characteristic, direct product factor, Sylow
596	2₋¹⁺⁴	—	4	4	no	—
597	C₂×#41	—	2	1	no	—
598	C₂×#41	—	2	2	no	—
599	C₂×#41	—	2	1	no	—
600	C₂×#41	—	2	1	no	—
601	C₂×#41	—	4	4	no	—
602	C₂×#41	—	4	4	no	—
603	C₂×#41	D₄×C₅₃	1	2	yes	—
604	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
605	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
606	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
607	C₂×#41	C₂³×C₅₃	1	2	yes	—
608	C₂×#41	C₂³×C₅₃	1	2	yes	—
609	C₂×#41	C₂³×C₅₃	1	2	yes	—
610	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
611	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
612	C₂×#41	C₂³×C₅₃	1	2	yes	—
613	C₂²×Q₈	—	2	1	no	—
614	C₂²×Q₈	D₄×C₅₃	1	1	yes	characteristic
615	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
616	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
617	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
618	C₂²×D₄	—	2	1	no	—
619	C₂²×D₄	—	2	2	no	—
620	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
621	C₂²×D₄	D₄×C₅₃	1	2	yes	—
622	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
623	C₂³×C₄	—	2	1	no	—
624	C₂³×C₄	—	2	1	no	—
625	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
627	#137	—	4	4	no	—
628	#135	—	4	4	no	—
629	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
630	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
631	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
632	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
634	C₂×D₈	C₂³×C₅₃	1	2	yes	—
635	#131	—	4	4	no	—
636	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
637	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
638	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
639	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
640	C₄⋊Q₈	—	2	1	no	—
641	C₄⋊Q₈	—	2	2	no	—
642	#124	—	2	1	no	—
643	#124	—	2	2	no	—
644	#123	—	2	2	no	—
645	#123	—	2	2	no	—
646	#123	—	2	2	no	—
647	#123	—	2	1	no	—
648	#123	—	2	2	no	—
649	C₂²⋊Q₈	—	2	2	no	—
650	C₂²⋊Q₈	—	2	2	no	—
651	C₂²⋊Q₈	—	2	4	no	—
652	C₂²⋊Q₈	—	2	1	no	—
653	C₂²⋊Q₈	—	2	2	no	—
654	C₂²⋊Q₈	—	2	2	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	1	no	—
657	C₂²⋊Q₈	—	2	2	no	—
658	C₂²⋊Q₈	—	2	1	no	—
659	C₂²⋊Q₈	—	2	2	no	—
660	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
661	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
662	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
663	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
664	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
665	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
666	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
667	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
668	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
669	#121	—	2	2	no	—
670	#121	—	2	2	no	—
671	#121	—	2	4	no	—
672	#121	—	2	4	no	—
673	#121	—	2	4	no	—
674	#121	—	2	4	no	—
675	#121	—	2	4	no	—
676	#121	—	2	2	no	—
677	#121	—	2	2	no	—
678	#121	—	2	2	no	—
679	#121	—	2	1	no	—
680	#121	—	2	2	no	—
681	#121	—	2	2	no	—
682	#121	—	2	2	no	—
683	#121	C₂³×C₅₃	1	4	yes	—
684	#121	C₂³×C₅₃	1	4	yes	—
685	#121	C₂³×C₅₃	1	1	yes	characteristic
686	#121	C₂³×C₅₃	1	1	yes	characteristic
687	#121	C₂³×C₅₃	1	2	yes	—
688	#120	—	2	1	no	—
689	#120	—	2	2	no	—
690	C₄×Q₈	—	2	1	no	—
691	C₄×D₄	—	2	2	no	—
692	C₄×D₄	—	2	1	no	—
693	C₄×D₄	—	2	1	no	—
694	C₄×D₄	—	2	2	no	—
695	C₄×D₄	—	2	1	no	—
696	C₄×D₄	—	2	2	no	—
697	#117	C₂³×C₅₃	1	1	yes	characteristic
698	#117	C₂³×C₅₃	1	2	yes	—
699	C₂×C₄⋊C₄	—	2	1	no	—
700	C₂×C₄⋊C₄	—	2	1	no	—
701	C₂×C₄⋊C₄	—	2	1	no	—
702	C₂×C₄⋊C₄	—	2	2	no	—
703	C₂×C₄⋊C₄	—	2	1	no	—
704	C₂×C₄⋊C₄	—	2	2	no	—
705	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
706	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
707	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
708	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
710	C₂×C₂²⋊C₄	—	2	2	no	—
711	C₂×C₂²⋊C₄	—	2	1	no	—
712	C₂×C₂²⋊C₄	—	2	2	no	—
713	C₂×C₂²⋊C₄	—	2	2	no	—
714	#107	C₂³×C₅₃	1	4	yes	—
715	#107	C₂³×C₅₃	1	4	yes	—
716	#107	C₂³×C₅₃	1	4	yes	—
717	#106	C₂³×C₅₃	1	4	yes	—
718	#103	C₂³×C₅₃	1	4	yes	—
719	#103	C₂³×C₅₃	1	4	yes	—
720	#103	C₂³×C₅₃	1	2	yes	—
721	#103	C₂³×C₅₃	1	2	yes	—
722	#103	C₂³×C₅₃	1	4	yes	—
723	#103	C₂³×C₅₃	1	4	yes	—
724	#102	C₂³×C₅₃	1	2	yes	—
725	#102	C₂³×C₅₃	1	2	yes	—
726	#102	C₂³×C₅₃	1	4	yes	—
727	#102	C₂³×C₅₃	1	4	yes	—
728	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
729	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
730	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
731	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
732	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
733	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
734	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
735	C₂⁴	—	2	1	no	—
736	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
737	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
738	#41	—	2	4	no	—
739	#41	—	2	4	no	—
740	#41	—	2	4	no	—
741	#41	—	2	4	no	—
742	#41	—	2	4	no	—
743	#41	—	4	4	no	—
744	#41	—	4	4	no	—
745	#41	—	4	2	no	—
746	#41	—	4	2	no	—
747	#41	—	4	2	no	—
748	#41	—	4	2	no	—
749	#41	—	4	4	no	—
750	#41	—	4	4	no	—
751	#41	—	4	4	no	—
752	#41	—	4	8	no	—
753	#41	—	4	4	no	—
754	C₂×Q₈	—	2	1	no	—
755	C₂×Q₈	—	2	2	no	—
756	C₂×Q₈	—	2	1	no	—
757	C₂×Q₈	—	2	4	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×Q₈	—	4	2	no	—
760	C₂×Q₈	—	4	4	no	—
761	C₂×Q₈	—	4	4	no	—
762	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
763	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
764	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
765	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
766	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
767	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
768	C₂×D₄	—	2	1	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	1	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	1	no	—
775	C₂×D₄	—	2	4	no	—
776	C₂×D₄	—	2	4	no	—
777	C₂×D₄	—	2	1	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	—	4	2	no	—
780	C₂×D₄	—	4	4	no	—
781	C₂×D₄	—	4	4	no	—
782	C₂×D₄	—	8	4	no	—
783	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
784	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
785	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
786	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
787	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
788	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
789	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
790	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
791	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
792	C₂²×C₄	—	2	4	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	1	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	1	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	4	4	no	—
806	C₂²×C₄	—	4	4	no	—
807	C₂²×C₄	—	8	2	no	—
808	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
809	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
810	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
811	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
812	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
813	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
814	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
817	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
818	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
819	Q₁₆	—	4	2	no	—
820	Q₁₆	—	4	4	no	—
821	SD₁₆	—	4	2	no	—
822	SD₁₆	—	4	2	no	—
823	SD₁₆	—	4	4	no	—
824	D₈	—	4	2	no	—
825	M₁₆	—	2	4	no	—
826	M₁₆	—	4	4	no	—
827	C₂×C₈	—	2	4	no	—
828	C₂×C₈	—	4	4	no	—
829	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
830	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
831	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	1	no	—
837	C₄⋊C₄	—	2	4	no	—
838	C₄⋊C₄	—	2	4	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
847	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
848	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
849	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	1	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	4	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	—	2	1	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	1	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	1	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	1	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	1	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	4	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	4	1	no	—
874	C₂³	—	4	2	no	—
875	C₂³	—	4	2	no	—
876	C₂³	—	4	2	no	—
877	C₂³	—	4	2	no	—
878	C₂³	—	4	2	no	—
879	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
880	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
881	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
882	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
883	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
884	Q₈	—	2	2	no	—
885	Q₈	—	2	2	no	—
886	Q₈	—	2	4	no	—
887	Q₈	—	2	2	no	—
888	Q₈	—	2	2	no	—
889	Q₈	—	2	2	no	—
890	Q₈	—	4	2	no	—
891	Q₈	—	4	4	no	—
892	Q₈	—	4	2	no	—
893	Q₈	—	4	2	no	—
894	D₄	—	2	4	no	—
895	D₄	—	2	4	no	—
896	D₄	—	2	2	no	—
897	D₄	—	2	2	no	—
898	D₄	—	2	2	no	—
899	D₄	—	2	2	no	—
900	D₄	—	2	2	no	—
901	D₄	—	4	2	no	—
902	D₄	—	4	2	no	—
903	D₄	—	4	2	no	—
904	D₄	—	4	2	no	—
905	D₄	—	4	4	no	—
906	D₄	—	4	4	no	—
907	D₄	—	4	4	no	—
908	D₄	—	4	2	no	—
909	D₄	—	4	2	no	—
910	D₄	—	8	1	no	—
911	D₄	—	8	2	no	—
912	D₄	—	8	4	no	—
913	D₄	—	8	4	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	4	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	4	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	4	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	4	2	no	—
929	C₂×C₄	—	4	2	no	—
930	C₂×C₄	—	4	2	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	4	no	—
933	C₂×C₄	—	4	2	no	—
934	C₂×C₄	—	4	4	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	—	4	2	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	4	2	no	—
939	C₂×C₄	—	8	1	no	—
940	C₂×C₄	—	8	2	no	—
941	C₂×C₄	—	8	2	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
944	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
945	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
946	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
947	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
948	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
949	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
950	C₈	—	2	2	no	—
951	C₈	—	2	2	no	—
952	C₈	—	2	4	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	2	no	—
965	C₂²	—	2	2	no	—
966	C₂²	—	4	4	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	8	4	no	—
974	C₂²	—	8	4	no	—
975	C₂²	C₅₃×#534	1	2	yes	—
976	C₂²	C₅₃×#578	1	2	yes	—
977	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
978	C₄	—	2	1	no	—
979	C₄	—	2	1	no	—
980	C₄	—	2	2	no	—
981	C₄	—	2	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	4	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	1	no	—
989	C₄	C₅₃×#534	1	2	yes	—
990	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
991	C₂	—	2	2	no	—
992	C₂	—	2	2	no	—
993	C₂	—	4	1	no	—
994	C₂	—	4	2	no	—
995	C₂	—	4	2	no	—
996	C₂	—	8	2	no	—
997	C₂	—	8	1	no	—
998	C₂	C₂×C₅₃×#534	1	1	yes	characteristic
999	C₂	C₂×C₅₃×#578	1	1	yes	characteristic
1000	C₂	C₅₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂²×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3489	C₂	semidirect
2. C₂×C₅₃×#537	C₂	semidirect
3. C₅₃×#3203	C₂	semidirect
4. C₅₃×#3201	C₂	semidirect
5. C₅₃×#3196	C₂	semidirect
6. C₅₃×#3193	C₂	semidirect
7. C₅₃×#3189	C₂	semidirect
8. C₅₃×#3188	C₂	semidirect
9. C₅₃×#3098	C₂	semidirect
10. C₅₃×#3092	C₂	semidirect
11. C₂×C₅₃×#484	C₂	semidirect
12. C₅₃×#3063	C₂	semidirect
13. C₅₃×#3061	C₂	semidirect
14. C₅₃×#3013	C₂	semidirect
15. C₅₃×#3007	C₂	semidirect
16. C₅₃×#3002	C₂	semidirect
17. C₅₃×#2880	C₂	semidirect
18. C₂×2₋¹⁺⁴×C₅₃	C₂²	semidirect
21. C₂×#137×C₅₃	C₂²	semidirect
22. C₂×#135×C₅₃	C₂²	semidirect
23. C₂×#131×C₅₃	C₂²	semidirect
36. C₅₃×#537	C₂²	semidirect
37. C₅₃×#537	C₂²	semidirect
38. C₅₃×#536	C₂²	semidirect
39. C₅₃×#536	C₂²	semidirect
49. C₅₃×#520	C₂²	semidirect
51. C₅₃×#485	C₂²	semidirect
55. C₅₃×#484	C₂²	semidirect
56. C₅₃×#484	C₂²	semidirect
57. C₅₃×#483	C₂²	semidirect
58. C₅₃×#482	C₂²	semidirect
60. C₅₃×#480	C₂²	semidirect
61. C₅₃×#480	C₂²	semidirect
62. C₅₃×#470	C₂²	semidirect
63. C₅₃×#468	C₂²	semidirect
64. C₅₃×#468	C₂²	semidirect
65. C₅₃×#468	C₂²	semidirect
66. C₅₃×#467	C₂²	semidirect
67. C₅₃×#467	C₂²	semidirect
68. C₅₃×#466	C₂²	semidirect
69. C₅₃×#465	C₂²	semidirect
70. C₅₃×#452	C₂²	semidirect
71. C₅₃×#452	C₂²	semidirect
72. C₅₃×#452	C₂²	semidirect
75. C₅₃×#451	C₂²	semidirect
78. C₅₃×#449	C₂²	semidirect
79. C₅₃×#449	C₂²	semidirect
81. C₅₃×#448	C₂²	semidirect
83. C₅₃×#428	C₂²	semidirect
84. C₂×#107×C₅₃	C₂²	semidirect
85. C₅₃×#417	C₂²	semidirect
86. C₅₃×#417	C₂²	semidirect
87. C₅₃×#416	C₂²	semidirect
88. C₂×#103×C₅₃	C₂²	semidirect
89. C₅₃×#408	C₂²	semidirect
90. C₅₃×#408	C₂²	semidirect
452. #60764	C₅₃	direct (N × H)
491. #3489	C₂×C₅₃	semidirect
492. C₂×#537	C₂×C₅₃	semidirect
493. #3203	C₂×C₅₃	semidirect
494. #3201	C₂×C₅₃	semidirect
495. #3196	C₂×C₅₃	semidirect
496. #3193	C₂×C₅₃	semidirect
497. #3189	C₂×C₅₃	semidirect
498. #3188	C₂×C₅₃	semidirect
499. #3098	C₂×C₅₃	semidirect
500. #3092	C₂×C₅₃	semidirect
501. C₂×#484	C₂×C₅₃	semidirect
502. #3063	C₂×C₅₃	semidirect
503. #3061	C₂×C₅₃	semidirect
504. #3013	C₂×C₅₃	semidirect
505. #3007	C₂×C₅₃	semidirect
506. #3002	C₂×C₅₃	semidirect
507. #2880	C₂×C₅₃	semidirect
518. C₂×2₋¹⁺⁴	C₂²×C₅₃	semidirect
521. C₂×#137	C₂²×C₅₃	semidirect
522. C₂×#135	C₂²×C₅₃	semidirect
523. C₂×#131	C₂²×C₅₃	semidirect
536. #537	C₂²×C₅₃	semidirect
537. #537	C₂²×C₅₃	semidirect
538. #536	C₂²×C₅₃	semidirect
539. #536	C₂²×C₅₃	semidirect
549. #520	C₂²×C₅₃	semidirect
551. #485	C₂²×C₅₃	semidirect
555. #484	C₂²×C₅₃	semidirect
556. #484	C₂²×C₅₃	semidirect
557. #483	C₂²×C₅₃	semidirect
558. #482	C₂²×C₅₃	semidirect
560. #480	C₂²×C₅₃	semidirect
561. #480	C₂²×C₅₃	semidirect
562. #470	C₂²×C₅₃	semidirect
563. #468	C₂²×C₅₃	semidirect
564. #468	C₂²×C₅₃	semidirect
565. #468	C₂²×C₅₃	semidirect
566. #467	C₂²×C₅₃	semidirect
567. #467	C₂²×C₅₃	semidirect
568. #466	C₂²×C₅₃	semidirect
569. #465	C₂²×C₅₃	semidirect
570. #452	C₂²×C₅₃	semidirect
571. #452	C₂²×C₅₃	semidirect
572. #452	C₂²×C₅₃	semidirect
575. #451	C₂²×C₅₃	semidirect
578. #449	C₂²×C₅₃	semidirect
579. #449	C₂²×C₅₃	semidirect
581. #448	C₂²×C₅₃	semidirect
583. #428	C₂²×C₅₃	semidirect
584. C₂×#107	C₂²×C₅₃	semidirect
585. #417	C₂²×C₅₃	semidirect
586. #417	C₂²×C₅₃	semidirect
587. #416	C₂²×C₅₃	semidirect
588. C₂×#103	C₂²×C₅₃	semidirect
589. #408	C₂²×C₅₃	semidirect
590. #408	C₂²×C₅₃	semidirect
595. C₅₃	#60764	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×#3489	2
C₂×C₅₃×#537	2
C₅₃×#3203	2
C₅₃×#3201	2
C₅₃×#3196	2
C₅₃×#3193	2
C₅₃×#3189	2
C₅₃×#3188	2
C₅₃×#3098	2
C₅₃×#3092	2
C₂×C₅₃×#484	2
C₅₃×#3063	2
C₅₃×#3061	2
C₅₃×#3013	2
C₅₃×#3007	2
C₅₃×#3002	2
C₅₃×#2880	2
#60764	53

Subgroups — C53×#60764 #27268276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60764 #27268276