Subgroups — C₅₃×#60757 #27268269

Order 13568.

2310 conjugacy classes of subgroups.

The subgroup lattice has 1006 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×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3200	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3198	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3194	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3193	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3188	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3187	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3096	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3062	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3057	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3010	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#450	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	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
22	C₂²×SD₁₆×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	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#537	C₂²	1	2	yes	complemented
32	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#536	C₂²	1	2	yes	complemented
34	C₅₃×#535	—	2	2	no	—
35	C₅₃×#535	—	2	1	no	—
36	C₅₃×#535	—	2	1	no	—
37	C₅₃×#535	C₂²	1	4	yes	—
38	C₅₃×#535	C₂²	1	2	yes	—
39	C₅₃×#535	C₂²	1	2	yes	—
40	C₂×#127×C₅₃	—	2	1	no	—
41	C₂×#124×C₅₃	—	2	1	no	—
42	C₅₃×#525	C₂²	1	1	yes	characteristic
43	C₅₃×#525	C₂²	1	2	yes	complemented
44	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
46	C₂×#121×C₅₃	C₂²	1	2	yes	—
47	C₂×#121×C₅₃	C₂²	1	2	yes	—
48	C₂×#120×C₅₃	—	2	2	no	—
49	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
50	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#485	C₂²	1	4	yes	complemented
52	C₅₃×#485	C₂²	1	2	yes	complemented
53	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#484	C₂²	1	2	yes	complemented
55	C₅₃×#483	C₂²	1	2	yes	complemented
56	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#482	C₂²	1	2	yes	complemented
58	C₅₃×#482	C₂²	1	4	yes	complemented
59	C₅₃×#482	C₂²	1	4	yes	complemented
60	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#481	C₂²	1	4	yes	complemented
62	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#480	C₂²	1	4	yes	complemented
64	C₅₃×#469	C₂²	1	4	yes	complemented
65	C₅₃×#468	C₂²	1	4	yes	complemented
66	C₅₃×#468	C₂²	1	4	yes	complemented
67	C₅₃×#468	C₂²	1	4	yes	complemented
68	C₅₃×#466	C₂²	1	4	yes	complemented
69	C₅₃×#465	C₂²	1	4	yes	complemented
70	C₅₃×#465	C₂²	1	4	yes	complemented
71	C₅₃×#465	C₂²	1	4	yes	complemented
72	C₅₃×#450	C₂²	1	2	yes	—
73	C₅₃×#450	C₂²	1	2	yes	—
74	C₅₃×#450	C₂²	1	2	yes	—
75	C₅₃×#450	C₂²	1	4	yes	complemented
76	C₅₃×#450	C₂²	1	2	yes	complemented
77	C₅₃×#449	C₂²	1	4	yes	complemented
78	C₅₃×#449	C₂²	1	4	yes	complemented
79	C₅₃×#448	C₂²	1	4	yes	complemented
80	C₅₃×#448	C₂²	1	4	yes	complemented
81	C₅₃×#447	C₂²	1	2	yes	—
82	C₅₃×#447	C₂²	1	2	yes	complemented
83	C₅₃×#428	C₂²	1	2	yes	complemented
84	C₅₃×#427	C₂²	1	2	yes	complemented
85	C₅₃×#419	C₂²	1	2	yes	complemented
86	C₅₃×#418	C₂²	1	2	yes	complemented
87	C₅₃×#416	C₂²	1	2	yes	complemented
88	C₂×#102×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	1	yes	characteristic
92	C₅₃×#407	C₂²	1	2	yes	complemented
93	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
94	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	complemented
95	C₂⁵×C₅₃	—	2	1	no	—
96	2₋¹⁺⁴×C₅₃	—	4	4	no	—
97	C₂×#41×C₅₃	—	2	2	no	—
98	C₂×#41×C₅₃	—	2	1	no	—
99	C₂×#41×C₅₃	—	4	4	no	—
100	C₂×#41×C₅₃	D₄	1	2	yes	—
101	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
102	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
103	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
104	C₂×#41×C₅₃	C₂³	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	complemented
108	C₂²×Q₈×C₅₃	—	2	1	no	—
109	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
110	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₅₃	C₂³	1	2	yes	complemented
112	C₂²×D₄×C₅₃	—	2	2	no	—
113	C₂²×D₄×C₅₃	—	2	2	no	—
114	C₂²×D₄×C₅₃	—	2	1	no	—
115	C₂²×D₄×C₅₃	—	2	1	no	—
116	C₂²×D₄×C₅₃	—	2	1	no	—
117	C₂²×D₄×C₅₃	—	4	4	no	—
118	C₂²×D₄×C₅₃	D₄	1	2	yes	—
119	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
120	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
121	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
122	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
125	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
126	C₂×SD₁₆×C₅₃	—	4	4	no	—
127	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
128	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
129	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
130	C₂×D₈×C₅₃	C₂³	1	4	yes	—
131	#131×C₅₃	—	4	4	no	—
132	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
133	C₂×M₁₆×C₅₃	C₂³	1	4	yes	complemented
134	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
135	C₂²×C₈×C₅₃	C₂³	1	4	yes	complemented
136	C₄⋊Q₈×C₅₃	—	2	1	no	—
137	C₄⋊Q₈×C₅₃	—	2	2	no	—
138	#127×C₅₃	—	2	2	no	—
139	#127×C₅₃	—	2	2	no	—
140	#127×C₅₃	—	2	4	no	—
141	#124×C₅₃	—	2	2	no	—
142	#124×C₅₃	—	2	2	no	—
143	#124×C₅₃	—	2	4	no	—
144	#124×C₅₃	—	2	1	no	—
145	#124×C₅₃	—	2	2	no	—
146	#123×C₅₃	—	2	2	no	—
147	#123×C₅₃	—	2	2	no	—
148	#123×C₅₃	—	2	2	no	—
149	#123×C₅₃	—	2	1	no	—
150	#123×C₅₃	—	2	2	no	—
151	C₂²⋊Q₈×C₅₃	—	2	1	no	—
152	C₂²⋊Q₈×C₅₃	—	2	2	no	—
153	C₂²⋊Q₈×C₅₃	—	2	1	no	—
154	C₂²⋊Q₈×C₅₃	—	2	1	no	—
155	C₂²⋊Q₈×C₅₃	—	2	2	no	—
156	C₂²⋊Q₈×C₅₃	—	2	2	no	—
157	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
158	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
160	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
162	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
163	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
164	#121×C₅₃	—	2	2	no	—
165	#121×C₅₃	—	2	2	no	—
166	#121×C₅₃	—	2	2	no	—
167	#121×C₅₃	—	2	1	no	—
168	#121×C₅₃	—	2	2	no	—
169	#121×C₅₃	—	2	2	no	—
170	#121×C₅₃	—	2	2	no	—
171	#121×C₅₃	—	2	2	no	—
172	#121×C₅₃	—	2	2	no	—
173	#121×C₅₃	C₂³	1	4	yes	—
174	#121×C₅₃	C₂³	1	4	yes	—
175	#121×C₅₃	C₂³	1	4	yes	—
176	#121×C₅₃	C₂³	1	4	yes	—
177	#121×C₅₃	C₂³	1	1	yes	characteristic
178	#121×C₅₃	C₂³	1	1	yes	characteristic
179	#121×C₅₃	C₂³	1	2	yes	complemented
180	#120×C₅₃	—	2	1	no	—
181	#120×C₅₃	—	2	2	no	—
182	#120×C₅₃	—	2	4	no	—
183	#120×C₅₃	—	2	4	no	—
184	#120×C₅₃	—	2	4	no	—
185	#120×C₅₃	—	2	4	no	—
186	C₄×Q₈×C₅₃	—	2	1	no	—
187	C₄×D₄×C₅₃	—	2	2	no	—
188	C₄×D₄×C₅₃	—	2	1	no	—
189	C₄×D₄×C₅₃	—	2	1	no	—
190	C₄×D₄×C₅₃	—	2	1	no	—
191	C₄×D₄×C₅₃	—	2	2	no	—
192	C₄×D₄×C₅₃	—	2	2	no	—
193	#117×C₅₃	—	2	1	no	—
194	#117×C₅₃	—	2	1	no	—
195	#117×C₅₃	C₂³	1	2	yes	—
196	#117×C₅₃	C₂³	1	2	yes	—
197	#117×C₅₃	C₂³	1	1	yes	characteristic
198	#117×C₅₃	C₂³	1	2	yes	complemented
199	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
200	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
201	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
205	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
206	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
207	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
208	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
209	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
210	C₂×C₄²×C₅₃	—	2	1	no	—
211	#107×C₅₃	C₂³	1	2	yes	complemented
212	#107×C₅₃	C₂³	1	4	yes	complemented
213	#107×C₅₃	C₂³	1	2	yes	complemented
214	#106×C₅₃	C₂³	1	2	yes	complemented
215	#106×C₅₃	C₂³	1	4	yes	complemented
216	#106×C₅₃	C₂³	1	2	yes	complemented
217	#103×C₅₃	C₂³	1	2	yes	complemented
218	#103×C₅₃	C₂³	1	2	yes	complemented
219	#103×C₅₃	C₂³	1	4	yes	complemented
220	#103×C₅₃	C₂³	1	4	yes	complemented
221	#102×C₅₃	C₂³	1	4	yes	—
222	#102×C₅₃	C₂³	1	4	yes	—
223	#102×C₅₃	C₂³	1	4	yes	—
224	#102×C₅₃	C₂³	1	4	yes	—
225	#102×C₅₃	C₂³	1	2	yes	complemented
226	#102×C₅₃	C₂³	1	2	yes	complemented
227	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
228	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
229	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
230	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
232	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
233	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
234	C₂⁴×C₅₃	—	2	2	no	—
235	C₂⁴×C₅₃	—	2	2	no	—
236	C₂⁴×C₅₃	—	2	2	no	—
237	C₂⁴×C₅₃	—	4	4	no	—
238	C₂⁴×C₅₃	—	8	2	no	—
239	C₂⁴×C₅₃	—	8	2	no	—
240	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
241	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
242	#41×C₅₃	—	2	4	no	—
243	#41×C₅₃	—	2	4	no	—
244	#41×C₅₃	—	2	4	no	—
245	#41×C₅₃	—	4	4	no	—
246	#41×C₅₃	—	4	4	no	—
247	#41×C₅₃	—	4	2	no	—
248	#41×C₅₃	—	4	2	no	—
249	#41×C₅₃	—	4	4	no	—
250	#41×C₅₃	—	4	8	no	—
251	#41×C₅₃	—	4	4	no	—
252	C₂×Q₈×C₅₃	—	2	1	no	—
253	C₂×Q₈×C₅₃	—	2	2	no	—
254	C₂×Q₈×C₅₃	—	2	4	no	—
255	C₂×Q₈×C₅₃	—	4	2	no	—
256	C₂×Q₈×C₅₃	—	4	4	no	—
257	C₂×Q₈×C₅₃	—	4	4	no	—
258	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
259	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
260	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
261	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
262	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₅₃	—	2	1	no	—
264	C₂×D₄×C₅₃	—	2	1	no	—
265	C₂×D₄×C₅₃	—	2	2	no	—
266	C₂×D₄×C₅₃	—	2	1	no	—
267	C₂×D₄×C₅₃	—	2	2	no	—
268	C₂×D₄×C₅₃	—	2	4	no	—
269	C₂×D₄×C₅₃	—	2	4	no	—
270	C₂×D₄×C₅₃	—	2	4	no	—
271	C₂×D₄×C₅₃	—	2	4	no	—
272	C₂×D₄×C₅₃	—	2	2	no	—
273	C₂×D₄×C₅₃	—	2	2	no	—
274	C₂×D₄×C₅₃	—	2	2	no	—
275	C₂×D₄×C₅₃	—	2	4	no	—
276	C₂×D₄×C₅₃	—	2	4	no	—
277	C₂×D₄×C₅₃	—	4	4	no	—
278	C₂×D₄×C₅₃	—	4	4	no	—
279	C₂×D₄×C₅₃	—	4	2	no	—
280	C₂×D₄×C₅₃	—	4	4	no	—
281	C₂×D₄×C₅₃	—	4	4	no	—
282	C₂×D₄×C₅₃	—	4	4	no	—
283	C₂×D₄×C₅₃	—	4	4	no	—
284	C₂×D₄×C₅₃	—	8	4	no	—
285	C₂×D₄×C₅₃	—	8	4	no	—
286	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
287	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
288	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
289	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
290	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
291	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
292	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
293	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
294	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₅₃	—	2	4	no	—
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	—	2	1	no	—
303	C₂²×C₄×C₅₃	—	2	2	no	—
304	C₂²×C₄×C₅₃	—	4	4	no	—
305	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
309	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
310	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
311	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
316	SD₁₆×C₅₃	—	4	4	no	—
317	SD₁₆×C₅₃	—	4	4	no	—
318	SD₁₆×C₅₃	—	4	4	no	—
319	D₈×C₅₃	—	4	4	no	—
320	M₁₆×C₅₃	—	2	4	no	—
321	M₁₆×C₅₃	—	4	4	no	—
322	C₂×C₈×C₅₃	—	2	4	no	—
323	C₂×C₈×C₅₃	—	4	4	no	—
324	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
325	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
326	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
327	C₄⋊C₄×C₅₃	—	2	2	no	—
328	C₄⋊C₄×C₅₃	—	2	1	no	—
329	C₄⋊C₄×C₅₃	—	2	2	no	—
330	C₄⋊C₄×C₅₃	—	2	2	no	—
331	C₄⋊C₄×C₅₃	—	2	2	no	—
332	C₄⋊C₄×C₅₃	—	2	1	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	1	no	—
337	C₄⋊C₄×C₅₃	—	2	2	no	—
338	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
341	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
343	C₂²⋊C₄×C₅₃	—	2	2	no	—
344	C₂²⋊C₄×C₅₃	—	2	1	no	—
345	C₂²⋊C₄×C₅₃	—	2	2	no	—
346	C₂²⋊C₄×C₅₃	—	2	2	no	—
347	C₂²⋊C₄×C₅₃	—	2	2	no	—
348	C₂²⋊C₄×C₅₃	—	2	2	no	—
349	C₂²⋊C₄×C₅₃	—	2	2	no	—
350	C₂²⋊C₄×C₅₃	—	2	1	no	—
351	C₂²⋊C₄×C₅₃	—	2	2	no	—
352	C₂²⋊C₄×C₅₃	—	2	1	no	—
353	C₂²⋊C₄×C₅₃	—	2	2	no	—
354	C₂²⋊C₄×C₅₃	—	2	4	no	—
355	C₂²⋊C₄×C₅₃	—	2	4	no	—
356	C₂²⋊C₄×C₅₃	—	2	4	no	—
357	C₂²⋊C₄×C₅₃	—	2	4	no	—
358	C₂²⋊C₄×C₅₃	—	2	1	no	—
359	C₂²⋊C₄×C₅₃	—	2	1	no	—
360	C₂²⋊C₄×C₅₃	—	2	2	no	—
361	C₄²×C₅₃	—	2	2	no	—
362	C₄²×C₅₃	—	2	2	no	—
363	C₄²×C₅₃	—	2	1	no	—
364	C₄²×C₅₃	—	2	2	no	—
365	C₂³×C₅₃	—	2	2	no	—
366	C₂³×C₅₃	—	2	2	no	—
367	C₂³×C₅₃	—	2	4	no	—
368	C₂³×C₅₃	—	2	1	no	—
369	C₂³×C₅₃	—	2	4	no	—
370	C₂³×C₅₃	—	4	1	no	—
371	C₂³×C₅₃	—	4	2	no	—
372	C₂³×C₅₃	—	4	2	no	—
373	C₂³×C₅₃	—	4	4	no	—
374	C₂³×C₅₃	—	4	4	no	—
375	C₂³×C₅₃	—	4	4	no	—
376	C₂³×C₅₃	—	4	4	no	—
377	C₂³×C₅₃	—	4	4	no	—
378	C₂³×C₅₃	—	8	2	no	—
379	C₂³×C₅₃	—	8	2	no	—
380	C₂³×C₅₃	—	8	2	no	—
381	C₂³×C₅₃	—	8	2	no	—
382	C₂³×C₅₃	—	8	16	no	—
383	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
384	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
385	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
386	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
387	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
388	Q₈×C₅₃	—	2	2	no	—
389	Q₈×C₅₃	—	2	2	no	—
390	Q₈×C₅₃	—	2	4	no	—
391	Q₈×C₅₃	—	2	2	no	—
392	Q₈×C₅₃	—	4	2	no	—
393	Q₈×C₅₃	—	4	4	no	—
394	Q₈×C₅₃	—	4	2	no	—
395	D₄×C₅₃	—	2	4	no	—
396	D₄×C₅₃	—	2	4	no	—
397	D₄×C₅₃	—	2	2	no	—
398	D₄×C₅₃	—	2	2	no	—
399	D₄×C₅₃	—	2	4	no	—
400	D₄×C₅₃	—	2	4	no	—
401	D₄×C₅₃	—	2	2	no	—
402	D₄×C₅₃	—	4	2	no	—
403	D₄×C₅₃	—	4	2	no	—
404	D₄×C₅₃	—	4	2	no	—
405	D₄×C₅₃	—	4	4	no	—
406	D₄×C₅₃	—	4	4	no	—
407	D₄×C₅₃	—	4	4	no	—
408	D₄×C₅₃	—	4	2	no	—
409	D₄×C₅₃	—	4	2	no	—
410	D₄×C₅₃	—	4	4	no	—
411	D₄×C₅₃	—	8	2	no	—
412	D₄×C₅₃	—	8	1	no	—
413	D₄×C₅₃	—	8	4	no	—
414	D₄×C₅₃	—	8	4	no	—
415	D₄×C₅₃	—	8	4	no	—
416	D₄×C₅₃	—	8	4	no	—
417	C₂×C₄×C₅₃	—	2	2	no	—
418	C₂×C₄×C₅₃	—	2	2	no	—
419	C₂×C₄×C₅₃	—	2	2	no	—
420	C₂×C₄×C₅₃	—	2	2	no	—
421	C₂×C₄×C₅₃	—	2	2	no	—
422	C₂×C₄×C₅₃	—	2	4	no	—
423	C₂×C₄×C₅₃	—	2	4	no	—
424	C₂×C₄×C₅₃	—	2	2	no	—
425	C₂×C₄×C₅₃	—	2	1	no	—
426	C₂×C₄×C₅₃	—	2	2	no	—
427	C₂×C₄×C₅₃	—	2	1	no	—
428	C₂×C₄×C₅₃	—	2	2	no	—
429	C₂×C₄×C₅₃	—	2	2	no	—
430	C₂×C₄×C₅₃	—	2	1	no	—
431	C₂×C₄×C₅₃	—	4	2	no	—
432	C₂×C₄×C₅₃	—	4	2	no	—
433	C₂×C₄×C₅₃	—	4	2	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	—	4	2	no	—
439	C₂×C₄×C₅₃	—	4	2	no	—
440	C₂×C₄×C₅₃	—	8	1	no	—
441	C₂×C₄×C₅₃	—	8	2	no	—
442	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
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	#60757	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	2	no	—
458	C₂²×C₅₃	—	2	2	no	—
459	C₂²×C₅₃	—	2	1	no	—
460	C₂²×C₅₃	—	2	1	no	—
461	C₂²×C₅₃	—	2	2	no	—
462	C₂²×C₅₃	—	2	2	no	—
463	C₂²×C₅₃	—	2	2	no	—
464	C₂²×C₅₃	—	2	2	no	—
465	C₂²×C₅₃	—	2	1	no	—
466	C₂²×C₅₃	—	4	4	no	—
467	C₂²×C₅₃	—	4	1	no	—
468	C₂²×C₅₃	—	4	4	no	—
469	C₂²×C₅₃	—	4	1	no	—
470	C₂²×C₅₃	—	4	4	no	—
471	C₂²×C₅₃	—	4	1	no	—
472	C₂²×C₅₃	—	4	4	no	—
473	C₂²×C₅₃	—	8	4	no	—
474	C₂²×C₅₃	—	8	8	no	—
475	C₂²×C₅₃	—	8	8	no	—
476	C₂²×C₅₃	—	8	8	no	—
477	C₂²×C₅₃	#534	1	2	yes	—
478	C₂²×C₅₃	#577	1	2	yes	—
479	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
480	C₄×C₅₃	—	2	1	no	—
481	C₄×C₅₃	—	2	1	no	—
482	C₄×C₅₃	—	2	2	no	—
483	C₄×C₅₃	—	2	2	no	—
484	C₄×C₅₃	—	4	2	no	—
485	C₄×C₅₃	—	4	2	no	—
486	C₄×C₅₃	—	4	1	no	—
487	C₄×C₅₃	—	4	2	no	—
488	C₄×C₅₃	—	4	1	no	—
489	C₄×C₅₃	—	4	2	no	—
490	C₄×C₅₃	—	4	1	no	—
491	C₄×C₅₃	#534	1	2	yes	—
492	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
493	#3489	C₂×C₅₃	1	1	yes	characteristic, complemented
494	C₂×#535	C₂×C₅₃	1	1	yes	characteristic, complemented
495	#3200	C₂×C₅₃	1	4	yes	complemented
496	#3198	C₂×C₅₃	1	4	yes	complemented
497	#3194	C₂×C₅₃	1	2	yes	complemented
498	#3193	C₂×C₅₃	1	2	yes	complemented
499	#3188	C₂×C₅₃	1	2	yes	complemented
500	#3187	C₂×C₅₃	1	2	yes	complemented
501	#3096	C₂×C₅₃	1	2	yes	complemented
502	#3095	C₂×C₅₃	1	1	yes	characteristic, complemented
503	#3091	C₂×C₅₃	1	1	yes	characteristic, complemented
504	#3062	C₂×C₅₃	1	2	yes	complemented
505	#3057	C₂×C₅₃	1	2	yes	complemented
506	#3010	C₂×C₅₃	1	2	yes	complemented
507	#3003	C₂×C₅₃	1	1	yes	characteristic, complemented
508	C₂×#450	C₂×C₅₃	1	1	yes	characteristic, complemented
509	#2880	C₂×C₅₃	1	1	yes	characteristic, complemented
510	C₂×C₅₃	—	2	2	no	—
511	C₂×C₅₃	—	2	2	no	—
512	C₂×C₅₃	—	4	1	no	—
513	C₂×C₅₃	—	4	2	no	—
514	C₂×C₅₃	—	4	2	no	—
515	C₂×C₅₃	—	8	1	no	—
516	C₂×C₅₃	—	8	4	no	—
517	C₂×C₅₃	C₂×#534	1	1	yes	characteristic
518	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
519	C₂×C₅₃	#3585	1	1	yes	characteristic
520	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic, complemented
521	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
522	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
523	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
524	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
525	C₂×#131	C₂²×C₅₃	1	2	yes	complemented
526	D₄×Q₈	—	2	1	no	—
527	#548	—	2	1	no	—
528	#547	—	2	2	no	—
529	#547	—	2	1	no	—
530	#546	—	2	2	no	—
531	#546	—	2	1	no	—
532	#537	C₂²×C₅₃	1	1	yes	characteristic, complemented
533	#537	C₂²×C₅₃	1	2	yes	complemented
534	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
535	#536	C₂²×C₅₃	1	2	yes	complemented
536	#535	—	2	2	no	—
537	#535	—	2	1	no	—
538	#535	—	2	1	no	—
539	#535	C₂²×C₅₃	1	2	yes	—
540	#535	C₂²×C₅₃	1	4	yes	—
541	#535	C₂²×C₅₃	1	2	yes	—
542	C₂×#127	—	2	1	no	—
543	C₂×#124	—	2	1	no	—
544	#525	C₂²×C₅₃	1	1	yes	characteristic
545	#525	C₂²×C₅₃	1	2	yes	complemented
546	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
547	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
548	C₂×#121	C₂²×C₅₃	1	2	yes	—
549	C₂×#121	C₂²×C₅₃	1	2	yes	—
550	C₂×#120	—	2	2	no	—
551	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
552	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
553	#485	C₂²×C₅₃	1	2	yes	complemented
554	#485	C₂²×C₅₃	1	4	yes	complemented
555	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
556	#484	C₂²×C₅₃	1	2	yes	complemented
557	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
558	#483	C₂²×C₅₃	1	2	yes	complemented
559	#482	C₂²×C₅₃	1	2	yes	complemented
560	#482	C₂²×C₅₃	1	4	yes	complemented
561	#482	C₂²×C₅₃	1	4	yes	complemented
562	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
563	#481	C₂²×C₅₃	1	4	yes	complemented
564	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
565	#480	C₂²×C₅₃	1	4	yes	complemented
566	#469	C₂²×C₅₃	1	4	yes	complemented
567	#468	C₂²×C₅₃	1	4	yes	complemented
568	#468	C₂²×C₅₃	1	4	yes	complemented
569	#468	C₂²×C₅₃	1	4	yes	complemented
570	#466	C₂²×C₅₃	1	4	yes	complemented
571	#465	C₂²×C₅₃	1	4	yes	complemented
572	#465	C₂²×C₅₃	1	4	yes	complemented
573	#465	C₂²×C₅₃	1	4	yes	complemented
574	#450	C₂²×C₅₃	1	2	yes	—
575	#450	C₂²×C₅₃	1	2	yes	—
576	#450	C₂²×C₅₃	1	2	yes	—
577	#450	C₂²×C₅₃	1	4	yes	complemented
578	#450	C₂²×C₅₃	1	2	yes	complemented
579	#449	C₂²×C₅₃	1	4	yes	complemented
580	#449	C₂²×C₅₃	1	4	yes	complemented
581	#448	C₂²×C₅₃	1	4	yes	complemented
582	#448	C₂²×C₅₃	1	4	yes	complemented
583	#447	C₂²×C₅₃	1	2	yes	—
584	#447	C₂²×C₅₃	1	2	yes	complemented
585	#428	C₂²×C₅₃	1	2	yes	complemented
586	#427	C₂²×C₅₃	1	2	yes	complemented
587	#419	C₂²×C₅₃	1	2	yes	complemented
588	#418	C₂²×C₅₃	1	2	yes	complemented
589	#416	C₂²×C₅₃	1	2	yes	complemented
590	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
591	#408	C₂²×C₅₃	1	4	yes	complemented
592	#408	C₂²×C₅₃	1	2	yes	complemented
593	#407	C₂²×C₅₃	1	1	yes	characteristic
594	#407	C₂²×C₅₃	1	2	yes	complemented
595	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
596	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	complemented
597	C₅₃	#60757	1	1	yes	characteristic, direct product factor, Sylow
598	C₂⁵	—	2	1	no	—
599	2₋¹⁺⁴	—	4	4	no	—
600	C₂×#41	—	2	2	no	—
601	C₂×#41	—	2	1	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	1	yes	characteristic
608	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
609	C₂×#41	C₂³×C₅₃	1	2	yes	—
610	C₂×#41	C₂³×C₅₃	1	2	yes	complemented
611	C₂²×Q₈	—	2	1	no	—
612	C₂²×Q₈	D₄×C₅₃	1	1	yes	characteristic
613	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
614	C₂²×Q₈	C₂³×C₅₃	1	2	yes	complemented
615	C₂²×D₄	—	2	2	no	—
616	C₂²×D₄	—	2	2	no	—
617	C₂²×D₄	—	2	1	no	—
618	C₂²×D₄	—	2	1	no	—
619	C₂²×D₄	—	2	1	no	—
620	C₂²×D₄	—	4	4	no	—
621	C₂²×D₄	D₄×C₅₃	1	2	yes	—
622	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
623	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
624	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
625	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
626	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
628	AGL(1,ℤ/8)	—	4	4	no	—
629	C₂×SD₁₆	—	4	4	no	—
630	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
631	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
632	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
633	C₂×D₈	C₂³×C₅₃	1	4	yes	—
634	#131	—	4	4	no	—
635	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
636	C₂×M₁₆	C₂³×C₅₃	1	4	yes	complemented
637	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
638	C₂²×C₈	C₂³×C₅₃	1	4	yes	complemented
639	C₄⋊Q₈	—	2	1	no	—
640	C₄⋊Q₈	—	2	2	no	—
641	#127	—	2	2	no	—
642	#127	—	2	2	no	—
643	#127	—	2	4	no	—
644	#124	—	2	2	no	—
645	#124	—	2	2	no	—
646	#124	—	2	4	no	—
647	#124	—	2	1	no	—
648	#124	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	#123	—	2	1	no	—
653	#123	—	2	2	no	—
654	C₂²⋊Q₈	—	2	2	no	—
655	C₂²⋊Q₈	—	2	1	no	—
656	C₂²⋊Q₈	—	2	1	no	—
657	C₂²⋊Q₈	—	2	1	no	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	—	2	2	no	—
660	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
661	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
662	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
663	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
664	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
665	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
666	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
667	#121	—	2	2	no	—
668	#121	—	2	2	no	—
669	#121	—	2	2	no	—
670	#121	—	2	2	no	—
671	#121	—	2	1	no	—
672	#121	—	2	2	no	—
673	#121	—	2	2	no	—
674	#121	—	2	2	no	—
675	#121	—	2	2	no	—
676	#121	C₂³×C₅₃	1	4	yes	—
677	#121	C₂³×C₅₃	1	4	yes	—
678	#121	C₂³×C₅₃	1	4	yes	—
679	#121	C₂³×C₅₃	1	4	yes	—
680	#121	C₂³×C₅₃	1	1	yes	characteristic
681	#121	C₂³×C₅₃	1	1	yes	characteristic
682	#121	C₂³×C₅₃	1	2	yes	complemented
683	#120	—	2	1	no	—
684	#120	—	2	2	no	—
685	#120	—	2	4	no	—
686	#120	—	2	4	no	—
687	#120	—	2	4	no	—
688	#120	—	2	4	no	—
689	C₄×Q₈	—	2	1	no	—
690	C₄×D₄	—	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	2	no	—
696	#117	—	2	1	no	—
697	#117	—	2	1	no	—
698	#117	C₂³×C₅₃	1	2	yes	—
699	#117	C₂³×C₅₃	1	2	yes	—
700	#117	C₂³×C₅₃	1	1	yes	characteristic
701	#117	C₂³×C₅₃	1	2	yes	complemented
702	C₂×C₄⋊C₄	—	2	1	no	—
703	C₂×C₄⋊C₄	—	2	2	no	—
704	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
708	C₂×C₂²⋊C₄	—	2	1	no	—
709	C₂×C₂²⋊C₄	—	2	1	no	—
710	C₂×C₂²⋊C₄	—	2	2	no	—
711	C₂×C₂²⋊C₄	—	2	2	no	—
712	C₂×C₂²⋊C₄	—	2	2	no	—
713	C₂×C₄²	—	2	1	no	—
714	#107	C₂³×C₅₃	1	2	yes	complemented
715	#107	C₂³×C₅₃	1	2	yes	complemented
716	#107	C₂³×C₅₃	1	4	yes	complemented
717	#106	C₂³×C₅₃	1	2	yes	complemented
718	#106	C₂³×C₅₃	1	2	yes	complemented
719	#106	C₂³×C₅₃	1	4	yes	complemented
720	#103	C₂³×C₅₃	1	2	yes	complemented
721	#103	C₂³×C₅₃	1	2	yes	complemented
722	#103	C₂³×C₅₃	1	4	yes	complemented
723	#103	C₂³×C₅₃	1	4	yes	complemented
724	#102	C₂³×C₅₃	1	4	yes	—
725	#102	C₂³×C₅₃	1	4	yes	—
726	#102	C₂³×C₅₃	1	4	yes	—
727	#102	C₂³×C₅₃	1	4	yes	—
728	#102	C₂³×C₅₃	1	2	yes	complemented
729	#102	C₂³×C₅₃	1	2	yes	complemented
730	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
731	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
732	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
733	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
734	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
735	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
736	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
737	C₂⁴	—	2	2	no	—
738	C₂⁴	—	2	2	no	—
739	C₂⁴	—	2	2	no	—
740	C₂⁴	—	4	4	no	—
741	C₂⁴	—	8	2	no	—
742	C₂⁴	—	8	2	no	—
743	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
744	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
745	#41	—	2	4	no	—
746	#41	—	2	4	no	—
747	#41	—	2	4	no	—
748	#41	—	4	4	no	—
749	#41	—	4	4	no	—
750	#41	—	4	2	no	—
751	#41	—	4	2	no	—
752	#41	—	4	4	no	—
753	#41	—	4	8	no	—
754	#41	—	4	4	no	—
755	C₂×Q₈	—	2	1	no	—
756	C₂×Q₈	—	2	2	no	—
757	C₂×Q₈	—	2	4	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×Q₈	—	4	4	no	—
760	C₂×Q₈	—	4	4	no	—
761	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
762	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
763	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
764	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
765	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
766	C₂×D₄	—	2	1	no	—
767	C₂×D₄	—	2	1	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	1	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	4	no	—
772	C₂×D₄	—	2	4	no	—
773	C₂×D₄	—	2	4	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	4	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	4	4	no	—
781	C₂×D₄	—	4	4	no	—
782	C₂×D₄	—	4	2	no	—
783	C₂×D₄	—	4	4	no	—
784	C₂×D₄	—	4	4	no	—
785	C₂×D₄	—	4	4	no	—
786	C₂×D₄	—	4	4	no	—
787	C₂×D₄	—	8	4	no	—
788	C₂×D₄	—	8	4	no	—
789	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
790	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
791	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
792	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
793	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
794	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
795	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
796	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
797	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
798	C₂²×C₄	—	2	4	no	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	1	no	—
801	C₂²×C₄	—	2	1	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	4	4	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	SD₁₆	—	4	4	no	—
820	SD₁₆	—	4	4	no	—
821	SD₁₆	—	4	4	no	—
822	D₈	—	4	4	no	—
823	M₁₆	—	2	4	no	—
824	M₁₆	—	4	4	no	—
825	C₂×C₈	—	2	4	no	—
826	C₂×C₈	—	4	4	no	—
827	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
828	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
829	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	1	no	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
842	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
843	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
844	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
845	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	1	no	—
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	1	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	1	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	2	4	no	—
859	C₂²⋊C₄	—	2	4	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	1	no	—
862	C₂²⋊C₄	—	2	1	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	1	no	—
867	C₄²	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	4	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	4	no	—
873	C₂³	—	4	1	no	—
874	C₂³	—	4	2	no	—
875	C₂³	—	4	2	no	—
876	C₂³	—	4	4	no	—
877	C₂³	—	4	4	no	—
878	C₂³	—	4	4	no	—
879	C₂³	—	4	4	no	—
880	C₂³	—	4	4	no	—
881	C₂³	—	8	2	no	—
882	C₂³	—	8	2	no	—
883	C₂³	—	8	2	no	—
884	C₂³	—	8	2	no	—
885	C₂³	—	8	16	no	—
886	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
887	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
888	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
889	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
890	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
891	Q₈	—	2	2	no	—
892	Q₈	—	2	2	no	—
893	Q₈	—	2	4	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	4	2	no	—
896	Q₈	—	4	4	no	—
897	Q₈	—	4	2	no	—
898	D₄	—	2	4	no	—
899	D₄	—	2	4	no	—
900	D₄	—	2	2	no	—
901	D₄	—	2	2	no	—
902	D₄	—	2	2	no	—
903	D₄	—	2	4	no	—
904	D₄	—	2	4	no	—
905	D₄	—	4	2	no	—
906	D₄	—	4	2	no	—
907	D₄	—	4	2	no	—
908	D₄	—	4	4	no	—
909	D₄	—	4	4	no	—
910	D₄	—	4	4	no	—
911	D₄	—	4	2	no	—
912	D₄	—	4	2	no	—
913	D₄	—	4	4	no	—
914	D₄	—	8	2	no	—
915	D₄	—	8	1	no	—
916	D₄	—	8	4	no	—
917	D₄	—	8	4	no	—
918	D₄	—	8	4	no	—
919	D₄	—	8	4	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	4	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	4	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	4	2	no	—
935	C₂×C₄	—	4	2	no	—
936	C₂×C₄	—	4	2	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	4	2	no	—
939	C₂×C₄	—	4	4	no	—
940	C₂×C₄	—	4	2	no	—
941	C₂×C₄	—	4	2	no	—
942	C₂×C₄	—	4	2	no	—
943	C₂×C₄	—	8	1	no	—
944	C₂×C₄	—	8	2	no	—
945	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
946	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
947	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
948	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
949	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
950	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
951	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
952	C₈	—	2	2	no	—
953	C₈	—	2	2	no	—
954	C₈	—	2	4	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	2	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	2	2	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	4	4	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	4	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	4	no	—
973	C₂²	—	4	1	no	—
974	C₂²	—	4	4	no	—
975	C₂²	—	8	4	no	—
976	C₂²	—	8	8	no	—
977	C₂²	—	8	8	no	—
978	C₂²	—	8	8	no	—
979	C₂²	C₅₃×#534	1	2	yes	—
980	C₂²	C₅₃×#577	1	2	yes	—
981	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	2	no	—
985	C₄	—	2	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	1	no	—
993	C₄	C₅₃×#534	1	2	yes	—
994	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
995	C₂	—	2	2	no	—
996	C₂	—	2	2	no	—
997	C₂	—	4	1	no	—
998	C₂	—	4	2	no	—
999	C₂	—	4	2	no	—
1000	C₂	—	8	4	no	—
1001	C₂	—	8	1	no	—
1002	C₂	C₂×C₅₃×#534	1	1	yes	characteristic
1003	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1004	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×#535	C₂	semidirect
3. C₅₃×#3200	C₂	semidirect
4. C₅₃×#3198	C₂	semidirect
5. C₅₃×#3194	C₂	semidirect
6. C₅₃×#3193	C₂	semidirect
7. C₅₃×#3188	C₂	semidirect
8. C₅₃×#3187	C₂	semidirect
9. C₅₃×#3096	C₂	semidirect
10. C₅₃×#3095	C₂	semidirect
11. C₅₃×#3091	C₂	semidirect
12. C₅₃×#3062	C₂	semidirect
13. C₅₃×#3057	C₂	semidirect
14. C₅₃×#3010	C₂	semidirect
15. C₅₃×#3003	C₂	semidirect
16. C₂×C₅₃×#450	C₂	semidirect
17. C₅₃×#2880	C₂	semidirect
18. C₂×2₋¹⁺⁴×C₅₃	C₂²	semidirect
21. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
22. C₂²×SD₁₆×C₅₃	C₂²	semidirect
23. C₂×#131×C₅₃	C₂²	semidirect
30. C₅₃×#537	C₂²	semidirect
31. C₅₃×#537	C₂²	semidirect
32. C₅₃×#536	C₂²	semidirect
33. C₅₃×#536	C₂²	semidirect
43. C₅₃×#525	C₂²	semidirect
45. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
49. C₅₃×#520	C₂²	semidirect
51. C₅₃×#485	C₂²	semidirect
52. C₅₃×#485	C₂²	semidirect
53. C₅₃×#484	C₂²	semidirect
54. C₅₃×#484	C₂²	semidirect
55. C₅₃×#483	C₂²	semidirect
56. C₅₃×#483	C₂²	semidirect
57. C₅₃×#482	C₂²	semidirect
58. C₅₃×#482	C₂²	semidirect
59. C₅₃×#482	C₂²	semidirect
60. C₅₃×#481	C₂²	semidirect
61. C₅₃×#481	C₂²	semidirect
62. C₅₃×#480	C₂²	semidirect
63. C₅₃×#480	C₂²	semidirect
64. C₅₃×#469	C₂²	semidirect
65. C₅₃×#468	C₂²	semidirect
66. C₅₃×#468	C₂²	semidirect
67. C₅₃×#468	C₂²	semidirect
68. C₅₃×#466	C₂²	semidirect
69. C₅₃×#465	C₂²	semidirect
70. C₅₃×#465	C₂²	semidirect
71. C₅₃×#465	C₂²	semidirect
75. C₅₃×#450	C₂²	semidirect
76. C₅₃×#450	C₂²	semidirect
77. C₅₃×#449	C₂²	semidirect
78. C₅₃×#449	C₂²	semidirect
79. C₅₃×#448	C₂²	semidirect
80. C₅₃×#448	C₂²	semidirect
82. C₅₃×#447	C₂²	semidirect
83. C₅₃×#428	C₂²	semidirect
84. C₅₃×#427	C₂²	semidirect
85. C₅₃×#419	C₂²	semidirect
86. C₅₃×#418	C₂²	semidirect
87. C₅₃×#416	C₂²	semidirect
88. C₂×#102×C₅₃	C₂²	semidirect
89. C₅₃×#408	C₂²	semidirect
90. C₅₃×#408	C₂²	semidirect
92. C₅₃×#407	C₂²	semidirect
94. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
107. C₂×#41×C₅₃	C₂³	semidirect
111. C₂²×Q₈×C₅₃	C₂³	semidirect
133. C₂×M₁₆×C₅₃	C₂³	semidirect
135. C₂²×C₈×C₅₃	C₂³	semidirect
161. C₂²⋊Q₈×C₅₃	C₂³	semidirect
162. C₂²⋊Q₈×C₅₃	C₂³	semidirect
163. C₂²⋊Q₈×C₅₃	C₂³	semidirect
179. #121×C₅₃	C₂³	semidirect
198. #117×C₅₃	C₂³	semidirect
204. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
211. #107×C₅₃	C₂³	semidirect
212. #107×C₅₃	C₂³	semidirect
213. #107×C₅₃	C₂³	semidirect
214. #106×C₅₃	C₂³	semidirect
215. #106×C₅₃	C₂³	semidirect
216. #106×C₅₃	C₂³	semidirect
217. #103×C₅₃	C₂³	semidirect
218. #103×C₅₃	C₂³	semidirect
219. #103×C₅₃	C₂³	semidirect
220. #103×C₅₃	C₂³	semidirect
225. #102×C₅₃	C₂³	semidirect
226. #102×C₅₃	C₂³	semidirect
232. C₂²⋊C₈×C₅₃	C₂³	semidirect
233. C₂²⋊C₈×C₅₃	C₂³	semidirect
452. #60757	C₅₃	direct (N × H)
493. #3489	C₂×C₅₃	semidirect
494. C₂×#535	C₂×C₅₃	semidirect
495. #3200	C₂×C₅₃	semidirect
496. #3198	C₂×C₅₃	semidirect
497. #3194	C₂×C₅₃	semidirect
498. #3193	C₂×C₅₃	semidirect
499. #3188	C₂×C₅₃	semidirect
500. #3187	C₂×C₅₃	semidirect
501. #3096	C₂×C₅₃	semidirect
502. #3095	C₂×C₅₃	semidirect
503. #3091	C₂×C₅₃	semidirect
504. #3062	C₂×C₅₃	semidirect
505. #3057	C₂×C₅₃	semidirect
506. #3010	C₂×C₅₃	semidirect
507. #3003	C₂×C₅₃	semidirect
508. C₂×#450	C₂×C₅₃	semidirect
509. #2880	C₂×C₅₃	semidirect
520. C₂×2₋¹⁺⁴	C₂²×C₅₃	semidirect
523. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
524. C₂²×SD₁₆	C₂²×C₅₃	semidirect
525. C₂×#131	C₂²×C₅₃	semidirect
532. #537	C₂²×C₅₃	semidirect
533. #537	C₂²×C₅₃	semidirect
534. #536	C₂²×C₅₃	semidirect
535. #536	C₂²×C₅₃	semidirect
545. #525	C₂²×C₅₃	semidirect
547. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
551. #520	C₂²×C₅₃	semidirect
553. #485	C₂²×C₅₃	semidirect
554. #485	C₂²×C₅₃	semidirect
555. #484	C₂²×C₅₃	semidirect
556. #484	C₂²×C₅₃	semidirect
557. #483	C₂²×C₅₃	semidirect
558. #483	C₂²×C₅₃	semidirect
559. #482	C₂²×C₅₃	semidirect
560. #482	C₂²×C₅₃	semidirect
561. #482	C₂²×C₅₃	semidirect
562. #481	C₂²×C₅₃	semidirect
563. #481	C₂²×C₅₃	semidirect
564. #480	C₂²×C₅₃	semidirect
565. #480	C₂²×C₅₃	semidirect
566. #469	C₂²×C₅₃	semidirect
567. #468	C₂²×C₅₃	semidirect
568. #468	C₂²×C₅₃	semidirect
569. #468	C₂²×C₅₃	semidirect
570. #466	C₂²×C₅₃	semidirect
571. #465	C₂²×C₅₃	semidirect
572. #465	C₂²×C₅₃	semidirect
573. #465	C₂²×C₅₃	semidirect
577. #450	C₂²×C₅₃	semidirect
578. #450	C₂²×C₅₃	semidirect
579. #449	C₂²×C₅₃	semidirect
580. #449	C₂²×C₅₃	semidirect
581. #448	C₂²×C₅₃	semidirect
582. #448	C₂²×C₅₃	semidirect
584. #447	C₂²×C₅₃	semidirect
585. #428	C₂²×C₅₃	semidirect
586. #427	C₂²×C₅₃	semidirect
587. #419	C₂²×C₅₃	semidirect
588. #418	C₂²×C₅₃	semidirect
589. #416	C₂²×C₅₃	semidirect
590. C₂×#102	C₂²×C₅₃	semidirect
591. #408	C₂²×C₅₃	semidirect
592. #408	C₂²×C₅₃	semidirect
594. #407	C₂²×C₅₃	semidirect
596. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
597. C₅₃	#60757	direct (N × H)
610. C₂×#41	C₂³×C₅₃	semidirect
614. C₂²×Q₈	C₂³×C₅₃	semidirect
636. C₂×M₁₆	C₂³×C₅₃	semidirect
638. C₂²×C₈	C₂³×C₅₃	semidirect
664. C₂²⋊Q₈	C₂³×C₅₃	semidirect
665. C₂²⋊Q₈	C₂³×C₅₃	semidirect
666. C₂²⋊Q₈	C₂³×C₅₃	semidirect
682. #121	C₂³×C₅₃	semidirect
701. #117	C₂³×C₅₃	semidirect
707. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
714. #107	C₂³×C₅₃	semidirect
715. #107	C₂³×C₅₃	semidirect
716. #107	C₂³×C₅₃	semidirect
717. #106	C₂³×C₅₃	semidirect
718. #106	C₂³×C₅₃	semidirect
719. #106	C₂³×C₅₃	semidirect
720. #103	C₂³×C₅₃	semidirect
721. #103	C₂³×C₅₃	semidirect
722. #103	C₂³×C₅₃	semidirect
723. #103	C₂³×C₅₃	semidirect
728. #102	C₂³×C₅₃	semidirect
729. #102	C₂³×C₅₃	semidirect
735. C₂²⋊C₈	C₂³×C₅₃	semidirect
736. C₂²⋊C₈	C₂³×C₅₃	semidirect

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×#535	2
C₅₃×#3200	2
C₅₃×#3198	2
C₅₃×#3194	2
C₅₃×#3193	2
C₅₃×#3188	2
C₅₃×#3187	2
C₅₃×#3096	2
C₅₃×#3095	2
C₅₃×#3091	2
C₅₃×#3062	2
C₅₃×#3057	2
C₅₃×#3010	2
C₅₃×#3003	2
C₂×C₅₃×#450	2
C₅₃×#2880	2
#60757	53

Subgroups — C53×#60757 #27268269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60757 #27268269