Subgroups — C₅₃×#62128 #27269640

Order 13568.

2018 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3384	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3373	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3345	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3335	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3306	C₂	1	4	yes	maximal, complemented
8	C₅₃×#3294	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3247	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3238	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3109	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#476	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₅₃	—	2	1	no	—
19	C₅₃×#559	C₂²	1	1	yes	characteristic
20	C₅₃×#554	C₂²	1	1	yes	characteristic
21	C₅₃×#554	C₂²	1	1	yes	characteristic
22	C₅₃×#553	—	2	1	no	—
23	C₅₃×#553	C₂²	1	2	yes	—
24	C₅₃×#551	—	2	2	no	—
25	D₄×Q₈×C₅₃	—	2	1	no	—
26	D₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
27	C₅₃×#547	—	2	1	no	—
28	C₅₃×#547	—	2	2	no	—
29	C₅₃×#547	C₂²	1	2	yes	—
30	C₅₃×#547	C₂²	1	4	yes	complemented
31	C₅₃×#546	—	2	1	no	—
32	C₅₃×#546	C₂²	1	2	yes	—
33	D₄²×C₅₃	C₂²	1	1	yes	characteristic
34	C₅₃×#536	—	2	2	no	—
35	C₅₃×#536	—	2	1	no	—
36	C₅₃×#532	C₂²	1	1	yes	characteristic
37	C₅₃×#532	C₂²	1	2	yes	complemented
38	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
41	C₅₃×#529	—	2	1	no	—
42	C₅₃×#529	C₂²	1	2	yes	—
43	C₅₃×#525	—	2	2	no	—
44	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
45	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₅₃	—	2	1	no	—
47	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
48	C₅₃×#501	C₂²	1	4	yes	complemented
49	C₅₃×#498	C₂²	1	2	yes	complemented
50	C₅₃×#489	C₂²	1	4	yes	complemented
51	C₅₃×#486	C₂²	1	2	yes	—
52	C₅₃×#483	C₂²	1	4	yes	complemented
53	C₅₃×#482	C₂²	1	2	yes	complemented
54	C₅₃×#481	C₂²	1	4	yes	complemented
55	C₅₃×#481	C₂²	1	4	yes	complemented
56	C₅₃×#480	C₂²	1	4	yes	—
57	C₅₃×#478	C₂²	1	4	yes	complemented
58	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#477	C₂²	1	2	yes	complemented
60	C₅₃×#476	C₂²	1	4	yes	—
61	C₅₃×#476	C₂²	1	1	yes	characteristic
62	C₅₃×#476	C₂²	1	2	yes	—
63	C₅₃×#476	C₂²	1	2	yes	complemented
64	C₅₃×#476	C₂²	1	2	yes	complemented
65	C₅₃×#476	C₂²	1	2	yes	complemented
66	C₅₃×#476	C₂²	1	2	yes	complemented
67	C₅₃×#476	C₂²	1	4	yes	complemented
68	C₅₃×#475	C₂²	1	2	yes	complemented
69	C₅₃×#474	C₂²	1	2	yes	—
70	C₅₃×#469	C₂²	1	4	yes	complemented
71	C₅₃×#466	C₂²	1	4	yes	—
72	C₅₃×#465	C₂²	1	4	yes	complemented
73	C₅₃×#463	C₂²	1	4	yes	complemented
74	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#459	C₂²	1	2	yes	—
76	C₅₃×#459	C₂²	1	1	yes	characteristic
77	C₅₃×#459	C₂²	1	2	yes	complemented
78	C₅₃×#449	C₂²	1	2	yes	—
79	C₅₃×#447	C₂²	1	4	yes	—
80	C₅₃×#446	C₂²	1	2	yes	complemented
81	C₅₃×#442	C₂²	1	4	yes	—
82	C₅₃×#442	C₂²	1	4	yes	complemented
83	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
84	C₄×D₈×C₅₃	C₂²	1	2	yes	—
85	C₅₃×#435	C₂²	1	4	yes	complemented
86	C₈×D₄×C₅₃	C₂²	1	2	yes	—
87	C₅₃×#432	C₂²	1	2	yes	complemented
88	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#428	C₂²	1	2	yes	complemented
90	C₂×#106×C₅₃	C₂²	1	4	yes	complemented
91	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	complemented
93	C₅₃×#417	C₂²	1	2	yes	—
94	C₂×#102×C₅₃	C₂²	1	4	yes	—
95	2₋¹⁺⁴×C₅₃	—	4	8	no	—
96	C₂×#41×C₅₃	—	2	2	no	—
97	C₂×#41×C₅₃	—	2	4	no	—
98	C₂×#41×C₅₃	—	2	2	no	—
99	C₂×#41×C₅₃	—	2	1	no	—
100	C₂×#41×C₅₃	—	2	1	no	—
101	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
102	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₅₃	—	2	2	no	—
104	C₂²×Q₈×C₅₃	—	2	2	no	—
105	C₂²×Q₈×C₅₃	—	2	1	no	—
106	C₂²×D₄×C₅₃	—	2	1	no	—
107	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
108	C₂³×C₄×C₅₃	—	2	2	no	—
109	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
110	C₂×D₈×C₅₃	C₂³	1	2	yes	—
111	C₂×D₈×C₅₃	C₂³	1	4	yes	—
112	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
114	C₄⋊Q₈×C₅₃	—	2	1	no	—
115	C₄⋊Q₈×C₅₃	—	2	2	no	—
116	C₄⋊Q₈×C₅₃	—	2	1	no	—
117	C₄⋊Q₈×C₅₃	—	2	2	no	—
118	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
119	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
120	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
122	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
123	#127×C₅₃	C₂³	1	1	yes	characteristic
124	#127×C₅₃	C₂³	1	1	yes	characteristic
125	#126×C₅₃	—	2	2	no	—
126	#126×C₅₃	—	2	2	no	—
127	#125×C₅₃	—	2	1	no	—
128	#125×C₅₃	C₂³	1	2	yes	—
129	#124×C₅₃	—	2	1	no	—
130	#124×C₅₃	—	2	1	no	—
131	#124×C₅₃	—	2	2	no	—
132	#124×C₅₃	—	2	1	no	—
133	#124×C₅₃	C₂³	1	2	yes	—
134	#123×C₅₃	—	2	2	no	—
135	#123×C₅₃	—	2	2	no	—
136	#123×C₅₃	—	2	2	no	—
137	#123×C₅₃	—	2	4	no	—
138	#123×C₅₃	—	2	4	no	—
139	#123×C₅₃	—	2	4	no	—
140	#123×C₅₃	—	2	2	no	—
141	C₂²⋊Q₈×C₅₃	—	2	2	no	—
142	C₂²⋊Q₈×C₅₃	—	2	2	no	—
143	C₂²⋊Q₈×C₅₃	—	2	4	no	—
144	C₂²⋊Q₈×C₅₃	—	2	2	no	—
145	C₂²⋊Q₈×C₅₃	—	2	4	no	—
146	C₂²⋊Q₈×C₅₃	—	2	2	no	—
147	C₂²⋊Q₈×C₅₃	—	2	1	no	—
148	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
149	#121×C₅₃	—	2	1	no	—
150	#121×C₅₃	—	2	2	no	—
151	#121×C₅₃	—	2	2	no	—
152	#121×C₅₃	—	2	1	no	—
153	#121×C₅₃	—	2	2	no	—
154	#121×C₅₃	—	2	1	no	—
155	#121×C₅₃	C₂³	1	2	yes	—
156	#121×C₅₃	C₂³	1	2	yes	—
157	#121×C₅₃	C₂³	1	4	yes	—
158	#121×C₅₃	C₂³	1	2	yes	—
159	#120×C₅₃	—	2	2	no	—
160	#120×C₅₃	—	2	2	no	—
161	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
162	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
165	C₄×D₄×C₅₃	—	2	1	no	—
166	C₄×D₄×C₅₃	—	2	2	no	—
167	C₄×D₄×C₅₃	—	2	1	no	—
168	C₄×D₄×C₅₃	—	2	2	no	—
169	C₄×D₄×C₅₃	—	2	2	no	—
170	C₄×D₄×C₅₃	—	2	1	no	—
171	C₄×D₄×C₅₃	—	2	2	no	—
172	C₄×D₄×C₅₃	—	2	1	no	—
173	C₄×D₄×C₅₃	—	2	2	no	—
174	C₄×D₄×C₅₃	—	2	1	no	—
175	C₄×D₄×C₅₃	—	2	1	no	—
176	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
177	C₄×D₄×C₅₃	D₄	1	2	yes	—
178	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₅₃	C₂³	1	2	yes	—
180	C₄×D₄×C₅₃	C₂³	1	2	yes	—
181	C₄×D₄×C₅₃	C₂³	1	2	yes	—
182	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₅₃	C₂³	1	2	yes	—
184	C₄×D₄×C₅₃	C₂³	1	4	yes	—
185	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₅₃	C₂³	1	2	yes	—
187	#117×C₅₃	—	2	1	no	—
188	#117×C₅₃	—	2	2	no	—
189	#117×C₅₃	D₄	1	2	yes	—
190	#117×C₅₃	D₄	1	1	yes	characteristic
191	#117×C₅₃	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
193	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
194	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
195	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
197	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
200	C₂×C₄²×C₅₃	—	2	1	no	—
201	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
203	#107×C₅₃	C₂³	1	2	yes	—
204	#107×C₅₃	C₂³	1	4	yes	—
205	#106×C₅₃	C₂³	1	4	yes	—
206	#106×C₅₃	C₂³	1	4	yes	—
207	#106×C₅₃	C₂³	1	4	yes	—
208	#106×C₅₃	C₂³	1	2	yes	—
209	#106×C₅₃	C₂³	1	4	yes	—
210	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
211	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
212	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
213	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
214	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
215	#103×C₅₃	C₂³	1	2	yes	—
216	#103×C₅₃	C₂³	1	4	yes	—
217	#102×C₅₃	C₂³	1	4	yes	—
218	#102×C₅₃	C₂³	1	4	yes	—
219	#102×C₅₃	C₂³	1	4	yes	—
220	#102×C₅₃	C₂³	1	2	yes	—
221	#102×C₅₃	C₂³	1	4	yes	—
222	#102×C₅₃	C₂³	1	2	yes	—
223	#102×C₅₃	C₂³	1	2	yes	—
224	#102×C₅₃	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
226	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
227	#97×C₅₃	C₂³	1	4	yes	—
228	C₄×C₈×C₅₃	C₂³	1	2	yes	—
229	C₂⁴×C₅₃	—	2	2	no	—
230	#41×C₅₃	—	2	4	no	—
231	#41×C₅₃	—	2	2	no	—
232	#41×C₅₃	—	4	1	no	—
233	#41×C₅₃	—	4	8	no	—
234	#41×C₅₃	—	4	4	no	—
235	#41×C₅₃	—	4	16	no	—
236	#41×C₅₃	—	4	8	no	—
237	#41×C₅₃	—	8	2	no	—
238	C₂×Q₈×C₅₃	—	2	4	no	—
239	C₂×Q₈×C₅₃	—	2	2	no	—
240	C₂×Q₈×C₅₃	—	2	1	no	—
241	C₂×Q₈×C₅₃	—	2	2	no	—
242	C₂×Q₈×C₅₃	—	2	1	no	—
243	C₂×Q₈×C₅₃	—	4	8	no	—
244	C₂×Q₈×C₅₃	—	4	4	no	—
245	C₂×Q₈×C₅₃	—	4	8	no	—
246	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
247	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₅₃	—	2	4	no	—
249	C₂×D₄×C₅₃	—	2	1	no	—
250	C₂×D₄×C₅₃	—	2	2	no	—
251	C₂×D₄×C₅₃	—	2	2	no	—
252	C₂×D₄×C₅₃	—	2	4	no	—
253	C₂×D₄×C₅₃	—	2	2	no	—
254	C₂×D₄×C₅₃	—	2	1	no	—
255	C₂×D₄×C₅₃	—	2	2	no	—
256	C₂×D₄×C₅₃	—	2	1	no	—
257	C₂×D₄×C₅₃	—	2	1	no	—
258	C₂×D₄×C₅₃	—	2	1	no	—
259	C₂×D₄×C₅₃	—	4	2	no	—
260	C₂×D₄×C₅₃	—	4	4	no	—
261	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
263	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
264	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
265	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₅₃	—	2	2	no	—
267	C₂²×C₄×C₅₃	—	2	4	no	—
268	C₂²×C₄×C₅₃	—	2	2	no	—
269	C₂²×C₄×C₅₃	—	2	1	no	—
270	C₂²×C₄×C₅₃	—	2	1	no	—
271	C₂²×C₄×C₅₃	—	2	1	no	—
272	C₂²×C₄×C₅₃	—	2	2	no	—
273	C₂²×C₄×C₅₃	—	2	4	no	—
274	C₂²×C₄×C₅₃	—	2	2	no	—
275	C₂²×C₄×C₅₃	—	2	2	no	—
276	C₂²×C₄×C₅₃	—	2	2	no	—
277	C₂²×C₄×C₅₃	—	8	4	no	—
278	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
279	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
284	SD₁₆×C₅₃	—	4	2	no	—
285	D₈×C₅₃	—	2	4	no	—
286	D₈×C₅₃	—	4	4	no	—
287	M₁₆×C₅₃	—	4	2	no	—
288	C₂×C₈×C₅₃	—	4	4	no	—
289	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
290	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
291	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
292	C₄⋊C₄×C₅₃	—	2	1	no	—
293	C₄⋊C₄×C₅₃	—	2	2	no	—
294	C₄⋊C₄×C₅₃	—	2	1	no	—
295	C₄⋊C₄×C₅₃	—	2	2	no	—
296	C₄⋊C₄×C₅₃	—	2	4	no	—
297	C₄⋊C₄×C₅₃	—	2	2	no	—
298	C₄⋊C₄×C₅₃	—	2	2	no	—
299	C₄⋊C₄×C₅₃	—	2	2	no	—
300	C₄⋊C₄×C₅₃	—	2	4	no	—
301	C₄⋊C₄×C₅₃	—	2	1	no	—
302	C₄⋊C₄×C₅₃	—	2	1	no	—
303	C₄⋊C₄×C₅₃	—	2	2	no	—
304	C₄⋊C₄×C₅₃	—	2	2	no	—
305	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
306	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
307	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
308	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
310	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
314	C₂²⋊C₄×C₅₃	—	2	2	no	—
315	C₂²⋊C₄×C₅₃	—	2	1	no	—
316	C₂²⋊C₄×C₅₃	—	2	1	no	—
317	C₂²⋊C₄×C₅₃	—	2	2	no	—
318	C₂²⋊C₄×C₅₃	—	2	2	no	—
319	C₂²⋊C₄×C₅₃	—	2	2	no	—
320	C₂²⋊C₄×C₅₃	—	2	2	no	—
321	C₂²⋊C₄×C₅₃	—	2	2	no	—
322	C₂²⋊C₄×C₅₃	—	2	1	no	—
323	C₂²⋊C₄×C₅₃	—	2	2	no	—
324	C₂²⋊C₄×C₅₃	—	2	2	no	—
325	C₂²⋊C₄×C₅₃	—	2	2	no	—
326	C₂²⋊C₄×C₅₃	—	2	4	no	—
327	C₂²⋊C₄×C₅₃	—	2	4	no	—
328	C₂²⋊C₄×C₅₃	—	2	2	no	—
329	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
332	C₄²×C₅₃	—	2	1	no	—
333	C₄²×C₅₃	—	2	1	no	—
334	C₄²×C₅₃	—	2	1	no	—
335	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₅₃	C₂×D₄	1	2	yes	—
338	C₄²×C₅₃	C₂×D₄	1	2	yes	—
339	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₄²×C₅₃	C₂⁴	1	2	yes	—
341	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
342	C₂³×C₅₃	—	2	1	no	—
343	C₂³×C₅₃	—	2	2	no	—
344	C₂³×C₅₃	—	2	2	no	—
345	C₂³×C₅₃	—	4	4	no	—
346	C₂³×C₅₃	—	4	4	no	—
347	C₂³×C₅₃	—	8	2	no	—
348	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
349	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
350	Q₈×C₅₃	—	2	2	no	—
351	Q₈×C₅₃	—	2	1	no	—
352	Q₈×C₅₃	—	2	1	no	—
353	Q₈×C₅₃	—	4	4	no	—
354	Q₈×C₅₃	—	4	2	no	—
355	Q₈×C₅₃	—	4	8	no	—
356	Q₈×C₅₃	—	4	4	no	—
357	Q₈×C₅₃	—	8	1	no	—
358	D₄×C₅₃	—	2	4	no	—
359	D₄×C₅₃	—	2	2	no	—
360	D₄×C₅₃	—	2	2	no	—
361	D₄×C₅₃	—	2	1	no	—
362	D₄×C₅₃	—	2	2	no	—
363	D₄×C₅₃	—	2	2	no	—
364	D₄×C₅₃	—	4	4	no	—
365	D₄×C₅₃	—	4	2	no	—
366	D₄×C₅₃	—	4	2	no	—
367	D₄×C₅₃	—	4	4	no	—
368	D₄×C₅₃	—	4	4	no	—
369	D₄×C₅₃	—	4	8	no	—
370	D₄×C₅₃	—	4	2	no	—
371	D₄×C₅₃	—	4	2	no	—
372	D₄×C₅₃	—	8	1	no	—
373	D₄×C₅₃	—	8	2	no	—
374	D₄×C₅₃	AGL(1,ℤ/8)	1	4	yes	—
375	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	complemented
376	C₂×C₄×C₅₃	—	2	4	no	—
377	C₂×C₄×C₅₃	—	2	2	no	—
378	C₂×C₄×C₅₃	—	2	4	no	—
379	C₂×C₄×C₅₃	—	2	2	no	—
380	C₂×C₄×C₅₃	—	2	2	no	—
381	C₂×C₄×C₅₃	—	2	1	no	—
382	C₂×C₄×C₅₃	—	2	2	no	—
383	C₂×C₄×C₅₃	—	2	1	no	—
384	C₂×C₄×C₅₃	—	2	1	no	—
385	C₂×C₄×C₅₃	—	2	4	no	—
386	C₂×C₄×C₅₃	—	2	2	no	—
387	C₂×C₄×C₅₃	—	2	2	no	—
388	C₂×C₄×C₅₃	—	2	1	no	—
389	C₂×C₄×C₅₃	—	2	1	no	—
390	C₂×C₄×C₅₃	—	4	2	no	—
391	C₂×C₄×C₅₃	—	4	8	no	—
392	C₂×C₄×C₅₃	—	4	4	no	—
393	C₂×C₄×C₅₃	—	4	8	no	—
394	C₂×C₄×C₅₃	—	4	2	no	—
395	C₂×C₄×C₅₃	—	4	4	no	—
396	C₂×C₄×C₅₃	—	4	2	no	—
397	C₂×C₄×C₅₃	—	4	4	no	—
398	C₂×C₄×C₅₃	—	8	2	no	—
399	C₂×C₄×C₅₃	—	8	2	no	—
400	C₂×C₄×C₅₃	—	8	2	no	—
401	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
410	C₈×C₅₃	—	2	2	no	—
411	C₈×C₅₃	—	2	2	no	—
412	C₈×C₅₃	—	2	4	no	—
413	#62128	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
414	C₂²×C₅₃	—	2	2	no	—
415	C₂²×C₅₃	—	2	2	no	—
416	C₂²×C₅₃	—	2	1	no	—
417	C₂²×C₅₃	—	2	2	no	—
418	C₂²×C₅₃	—	2	1	no	—
419	C₂²×C₅₃	—	2	1	no	—
420	C₂²×C₅₃	—	4	1	no	—
421	C₂²×C₅₃	—	4	1	no	—
422	C₂²×C₅₃	—	4	2	no	—
423	C₂²×C₅₃	—	4	2	no	—
424	C₂²×C₅₃	—	4	2	no	—
425	C₂²×C₅₃	—	4	2	no	—
426	C₂²×C₅₃	—	4	2	no	—
427	C₂²×C₅₃	—	4	2	no	—
428	C₂²×C₅₃	—	8	8	no	—
429	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
430	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
431	C₄×C₅₃	—	2	1	no	—
432	C₄×C₅₃	—	2	2	no	—
433	C₄×C₅₃	—	2	1	no	—
434	C₄×C₅₃	—	2	2	no	—
435	C₄×C₅₃	—	2	2	no	—
436	C₄×C₅₃	—	2	1	no	—
437	C₄×C₅₃	—	4	1	no	—
438	C₄×C₅₃	—	4	4	no	—
439	C₄×C₅₃	—	4	2	no	—
440	C₄×C₅₃	—	4	1	no	—
441	C₄×C₅₃	—	4	1	no	—
442	C₄×C₅₃	—	4	2	no	—
443	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
444	C₄×C₅₃	#577	1	2	yes	—
445	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
446	C₄×C₅₃	#585	1	1	yes	characteristic
447	#3499	C₂×C₅₃	1	1	yes	characteristic, complemented
448	#3481	C₂×C₅₃	1	1	yes	characteristic, complemented
449	#3384	C₂×C₅₃	1	2	yes	complemented
450	#3373	C₂×C₅₃	1	2	yes	complemented
451	#3345	C₂×C₅₃	1	4	yes	complemented
452	#3335	C₂×C₅₃	1	2	yes	complemented
453	#3306	C₂×C₅₃	1	4	yes	complemented
454	#3294	C₂×C₅₃	1	2	yes	complemented
455	#3253	C₂×C₅₃	1	1	yes	characteristic, complemented
456	#3247	C₂×C₅₃	1	2	yes	complemented
457	#3238	C₂×C₅₃	1	2	yes	complemented
458	#3227	C₂×C₅₃	1	1	yes	characteristic, complemented
459	#3109	C₂×C₅₃	1	2	yes	complemented
460	#3106	C₂×C₅₃	1	1	yes	characteristic, complemented
461	#3079	C₂×C₅₃	1	1	yes	characteristic, complemented
462	C₂×#476	C₂×C₅₃	1	2	yes	complemented
463	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
464	C₂×C₅₃	—	2	4	no	—
465	C₂×C₅₃	—	4	1	no	—
466	C₂×C₅₃	—	4	2	no	—
467	C₂×C₅₃	—	8	2	no	—
468	C₂×C₅₃	—	8	2	no	—
469	C₂×C₅₃	#3489	1	1	yes	characteristic
470	C₂×C₅₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
471	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
472	C₂×2₋¹⁺⁴	—	2	1	no	—
473	#559	C₂²×C₅₃	1	1	yes	characteristic
474	#554	C₂²×C₅₃	1	1	yes	characteristic
475	#554	C₂²×C₅₃	1	1	yes	characteristic
476	#553	—	2	1	no	—
477	#553	C₂²×C₅₃	1	2	yes	—
478	#551	—	2	2	no	—
479	D₄×Q₈	—	2	1	no	—
480	D₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
481	#547	—	2	1	no	—
482	#547	—	2	2	no	—
483	#547	C₂²×C₅₃	1	2	yes	—
484	#547	C₂²×C₅₃	1	4	yes	complemented
485	#546	—	2	1	no	—
486	#546	C₂²×C₅₃	1	2	yes	—
487	D₄²	C₂²×C₅₃	1	1	yes	characteristic
488	#536	—	2	2	no	—
489	#536	—	2	1	no	—
490	#532	C₂²×C₅₃	1	1	yes	characteristic
491	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
492	#532	C₂²×C₅₃	1	2	yes	complemented
493	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
494	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
495	#529	—	2	1	no	—
496	#529	C₂²×C₅₃	1	2	yes	—
497	#525	—	2	2	no	—
498	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
499	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
500	C₂×C₄×D₄	—	2	1	no	—
501	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
502	#501	C₂²×C₅₃	1	4	yes	complemented
503	#498	C₂²×C₅₃	1	2	yes	complemented
504	#489	C₂²×C₅₃	1	4	yes	complemented
505	#486	C₂²×C₅₃	1	2	yes	—
506	#483	C₂²×C₅₃	1	4	yes	complemented
507	#482	C₂²×C₅₃	1	2	yes	complemented
508	#481	C₂²×C₅₃	1	4	yes	complemented
509	#481	C₂²×C₅₃	1	4	yes	complemented
510	#480	C₂²×C₅₃	1	4	yes	—
511	#478	C₂²×C₅₃	1	4	yes	complemented
512	#477	C₂²×C₅₃	1	2	yes	complemented
513	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
514	#476	C₂²×C₅₃	1	2	yes	—
515	#476	C₂²×C₅₃	1	1	yes	characteristic
516	#476	C₂²×C₅₃	1	4	yes	—
517	#476	C₂²×C₅₃	1	2	yes	complemented
518	#476	C₂²×C₅₃	1	4	yes	complemented
519	#476	C₂²×C₅₃	1	2	yes	complemented
520	#476	C₂²×C₅₃	1	2	yes	complemented
521	#476	C₂²×C₅₃	1	2	yes	complemented
522	#475	C₂²×C₅₃	1	2	yes	complemented
523	#474	C₂²×C₅₃	1	2	yes	—
524	#469	C₂²×C₅₃	1	4	yes	complemented
525	#466	C₂²×C₅₃	1	4	yes	—
526	#465	C₂²×C₅₃	1	4	yes	complemented
527	#463	C₂²×C₅₃	1	4	yes	complemented
528	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
529	#459	C₂²×C₅₃	1	1	yes	characteristic
530	#459	C₂²×C₅₃	1	2	yes	—
531	#459	C₂²×C₅₃	1	2	yes	complemented
532	#449	C₂²×C₅₃	1	2	yes	—
533	#447	C₂²×C₅₃	1	4	yes	—
534	#446	C₂²×C₅₃	1	2	yes	complemented
535	#442	C₂²×C₅₃	1	4	yes	—
536	#442	C₂²×C₅₃	1	4	yes	complemented
537	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
538	C₄×D₈	C₂²×C₅₃	1	2	yes	—
539	#435	C₂²×C₅₃	1	4	yes	complemented
540	C₈×D₄	C₂²×C₅₃	1	2	yes	—
541	#432	C₂²×C₅₃	1	2	yes	complemented
542	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
543	#428	C₂²×C₅₃	1	2	yes	complemented
544	C₂×#106	C₂²×C₅₃	1	4	yes	complemented
545	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
546	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	complemented
547	#417	C₂²×C₅₃	1	2	yes	—
548	C₂×#102	C₂²×C₅₃	1	4	yes	—
549	C₅₃	#62128	1	1	yes	characteristic, direct product factor, Sylow
550	2₋¹⁺⁴	—	4	8	no	—
551	C₂×#41	—	2	2	no	—
552	C₂×#41	—	2	4	no	—
553	C₂×#41	—	2	2	no	—
554	C₂×#41	—	2	1	no	—
555	C₂×#41	—	2	1	no	—
556	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
557	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
558	C₂²×Q₈	—	2	2	no	—
559	C₂²×Q₈	—	2	2	no	—
560	C₂²×Q₈	—	2	1	no	—
561	C₂²×D₄	—	2	1	no	—
562	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
563	C₂³×C₄	—	2	2	no	—
564	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
565	C₂×D₈	C₂³×C₅₃	1	2	yes	—
566	C₂×D₈	C₂³×C₅₃	1	4	yes	—
567	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
568	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
569	C₄⋊Q₈	—	2	1	no	—
570	C₄⋊Q₈	—	2	2	no	—
571	C₄⋊Q₈	—	2	1	no	—
572	C₄⋊Q₈	—	2	2	no	—
573	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
574	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
575	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
576	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
577	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
578	#127	C₂³×C₅₃	1	1	yes	characteristic
579	#127	C₂³×C₅₃	1	1	yes	characteristic
580	#126	—	2	2	no	—
581	#126	—	2	2	no	—
582	#125	—	2	1	no	—
583	#125	C₂³×C₅₃	1	2	yes	—
584	#124	—	2	1	no	—
585	#124	—	2	1	no	—
586	#124	—	2	1	no	—
587	#124	—	2	2	no	—
588	#124	C₂³×C₅₃	1	2	yes	—
589	#123	—	2	2	no	—
590	#123	—	2	2	no	—
591	#123	—	2	2	no	—
592	#123	—	2	2	no	—
593	#123	—	2	4	no	—
594	#123	—	2	4	no	—
595	#123	—	2	4	no	—
596	C₂²⋊Q₈	—	2	1	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	—	2	4	no	—
600	C₂²⋊Q₈	—	2	2	no	—
601	C₂²⋊Q₈	—	2	4	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
604	#121	—	2	2	no	—
605	#121	—	2	1	no	—
606	#121	—	2	2	no	—
607	#121	—	2	1	no	—
608	#121	—	2	1	no	—
609	#121	—	2	2	no	—
610	#121	C₂³×C₅₃	1	2	yes	—
611	#121	C₂³×C₅₃	1	2	yes	—
612	#121	C₂³×C₅₃	1	4	yes	—
613	#121	C₂³×C₅₃	1	2	yes	—
614	#120	—	2	2	no	—
615	#120	—	2	2	no	—
616	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
617	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
618	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
619	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
632	C₄×D₄	D₄×C₅₃	1	2	yes	—
633	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
634	C₄×D₄	C₂³×C₅₃	1	2	yes	—
635	C₄×D₄	C₂³×C₅₃	1	2	yes	—
636	C₄×D₄	C₂³×C₅₃	1	2	yes	—
637	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
638	C₄×D₄	C₂³×C₅₃	1	2	yes	—
639	C₄×D₄	C₂³×C₅₃	1	4	yes	—
640	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
641	C₄×D₄	C₂³×C₅₃	1	2	yes	—
642	#117	—	2	1	no	—
643	#117	—	2	2	no	—
644	#117	D₄×C₅₃	1	2	yes	—
645	#117	D₄×C₅₃	1	1	yes	characteristic
646	#117	C₂³×C₅₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	—	2	2	no	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
652	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
653	C₂×C₂²⋊C₄	—	2	2	no	—
654	C₂×C₂²⋊C₄	—	2	2	no	—
655	C₂×C₄²	—	2	1	no	—
656	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
657	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
658	#107	C₂³×C₅₃	1	4	yes	—
659	#107	C₂³×C₅₃	1	2	yes	—
660	#106	C₂³×C₅₃	1	2	yes	—
661	#106	C₂³×C₅₃	1	4	yes	—
662	#106	C₂³×C₅₃	1	4	yes	—
663	#106	C₂³×C₅₃	1	4	yes	—
664	#106	C₂³×C₅₃	1	4	yes	—
665	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
666	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
667	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
668	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
669	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
670	#103	C₂³×C₅₃	1	4	yes	—
671	#103	C₂³×C₅₃	1	2	yes	—
672	#102	C₂³×C₅₃	1	2	yes	—
673	#102	C₂³×C₅₃	1	4	yes	—
674	#102	C₂³×C₅₃	1	4	yes	—
675	#102	C₂³×C₅₃	1	4	yes	—
676	#102	C₂³×C₅₃	1	2	yes	—
677	#102	C₂³×C₅₃	1	2	yes	—
678	#102	C₂³×C₅₃	1	4	yes	—
679	#102	C₂³×C₅₃	1	4	yes	—
680	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
681	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
682	#97	C₂³×C₅₃	1	4	yes	—
683	C₄×C₈	C₂³×C₅₃	1	2	yes	—
684	C₂⁴	—	2	2	no	—
685	#41	—	2	4	no	—
686	#41	—	2	2	no	—
687	#41	—	4	1	no	—
688	#41	—	4	8	no	—
689	#41	—	4	4	no	—
690	#41	—	4	16	no	—
691	#41	—	4	8	no	—
692	#41	—	8	2	no	—
693	C₂×Q₈	—	2	4	no	—
694	C₂×Q₈	—	2	2	no	—
695	C₂×Q₈	—	2	1	no	—
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	—	2	1	no	—
698	C₂×Q₈	—	4	8	no	—
699	C₂×Q₈	—	4	4	no	—
700	C₂×Q₈	—	4	8	no	—
701	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
702	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	—	4	4	no	—
716	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
717	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
718	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
719	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
720	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	4	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	4	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	8	4	no	—
733	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
734	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
735	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
736	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
739	SD₁₆	—	4	2	no	—
740	D₈	—	2	4	no	—
741	D₈	—	4	4	no	—
742	M₁₆	—	4	2	no	—
743	C₂×C₈	—	4	4	no	—
744	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
745	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
746	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
761	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
762	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
763	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
764	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
765	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
766	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
767	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
768	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
785	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
786	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
787	C₄²	—	2	1	no	—
788	C₄²	—	2	1	no	—
789	C₄²	—	2	1	no	—
790	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
791	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
792	C₄²	C₂×D₄×C₅₃	1	2	yes	—
793	C₄²	C₂×D₄×C₅₃	1	2	yes	—
794	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
795	C₄²	C₂⁴×C₅₃	1	2	yes	—
796	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
797	C₂³	—	2	1	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	4	4	no	—
801	C₂³	—	4	4	no	—
802	C₂³	—	8	2	no	—
803	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
804	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
805	Q₈	—	2	2	no	—
806	Q₈	—	2	1	no	—
807	Q₈	—	2	1	no	—
808	Q₈	—	4	4	no	—
809	Q₈	—	4	2	no	—
810	Q₈	—	4	8	no	—
811	Q₈	—	4	4	no	—
812	Q₈	—	8	1	no	—
813	D₄	—	2	4	no	—
814	D₄	—	2	2	no	—
815	D₄	—	2	2	no	—
816	D₄	—	2	1	no	—
817	D₄	—	2	2	no	—
818	D₄	—	2	2	no	—
819	D₄	—	4	4	no	—
820	D₄	—	4	2	no	—
821	D₄	—	4	2	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	4	no	—
824	D₄	—	4	8	no	—
825	D₄	—	4	2	no	—
826	D₄	—	4	2	no	—
827	D₄	—	8	1	no	—
828	D₄	—	8	2	no	—
829	D₄	AGL(1,ℤ/8)×C₅₃	1	4	yes	—
830	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	complemented
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	4	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	4	8	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	2	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	8	2	no	—
854	C₂×C₄	—	8	2	no	—
855	C₂×C₄	—	8	2	no	—
856	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
857	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
859	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
860	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
861	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
862	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
863	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
864	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
865	C₈	—	2	2	no	—
866	C₈	—	2	2	no	—
867	C₈	—	2	4	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	8	8	no	—
883	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	4	yes	—
884	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
885	C₄	—	2	1	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	1	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	4	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
898	C₄	C₅₃×#577	1	2	yes	—
899	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
900	C₄	C₅₃×#585	1	1	yes	characteristic
901	C₂	—	2	4	no	—
902	C₂	—	4	1	no	—
903	C₂	—	4	2	no	—
904	C₂	—	8	2	no	—
905	C₂	—	8	2	no	—
906	C₂	C₅₃×#3489	1	1	yes	characteristic
907	C₂	C₂²×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
908	C₂	C₂×C₅₃×#577	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 ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3499	C₂	semidirect
2. C₅₃×#3481	C₂	semidirect
3. C₅₃×#3384	C₂	semidirect
4. C₅₃×#3373	C₂	semidirect
5. C₅₃×#3345	C₂	semidirect
6. C₅₃×#3335	C₂	semidirect
7. C₅₃×#3306	C₂	semidirect
8. C₅₃×#3294	C₂	semidirect
9. C₅₃×#3253	C₂	semidirect
10. C₅₃×#3247	C₂	semidirect
11. C₅₃×#3238	C₂	semidirect
12. C₅₃×#3227	C₂	semidirect
13. C₅₃×#3109	C₂	semidirect
14. C₅₃×#3106	C₂	semidirect
15. C₅₃×#3079	C₂	semidirect
16. C₂×C₅₃×#476	C₂	semidirect
17. C₅₃×#2990	C₂	semidirect
26. D₄×Q₈×C₅₃	C₂²	semidirect
30. C₅₃×#547	C₂²	semidirect
37. C₅₃×#532	C₂²	semidirect
38. C₅₃×#532	C₂²	semidirect
39. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
40. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
48. C₅₃×#501	C₂²	semidirect
49. C₅₃×#498	C₂²	semidirect
50. C₅₃×#489	C₂²	semidirect
52. C₅₃×#483	C₂²	semidirect
53. C₅₃×#482	C₂²	semidirect
54. C₅₃×#481	C₂²	semidirect
55. C₅₃×#481	C₂²	semidirect
57. C₅₃×#478	C₂²	semidirect
58. C₅₃×#477	C₂²	semidirect
59. C₅₃×#477	C₂²	semidirect
63. C₅₃×#476	C₂²	semidirect
64. C₅₃×#476	C₂²	semidirect
65. C₅₃×#476	C₂²	semidirect
66. C₅₃×#476	C₂²	semidirect
67. C₅₃×#476	C₂²	semidirect
68. C₅₃×#475	C₂²	semidirect
70. C₅₃×#469	C₂²	semidirect
72. C₅₃×#465	C₂²	semidirect
73. C₅₃×#463	C₂²	semidirect
74. C₅₃×#460	C₂²	semidirect
77. C₅₃×#459	C₂²	semidirect
80. C₅₃×#446	C₂²	semidirect
82. C₅₃×#442	C₂²	semidirect
83. C₄×SD₁₆×C₅₃	C₂²	semidirect
85. C₅₃×#435	C₂²	semidirect
87. C₅₃×#432	C₂²	semidirect
88. C₅₃×#431	C₂²	semidirect
89. C₅₃×#428	C₂²	semidirect
90. C₂×#106×C₅₃	C₂²	semidirect
91. C₅₃×#423	C₂²	semidirect
92. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
375. D₄×C₅₃	2₋¹⁺⁴	semidirect
413. #62128	C₅₃	direct (N × H)
447. #3499	C₂×C₅₃	semidirect
448. #3481	C₂×C₅₃	semidirect
449. #3384	C₂×C₅₃	semidirect
450. #3373	C₂×C₅₃	semidirect
451. #3345	C₂×C₅₃	semidirect
452. #3335	C₂×C₅₃	semidirect
453. #3306	C₂×C₅₃	semidirect
454. #3294	C₂×C₅₃	semidirect
455. #3253	C₂×C₅₃	semidirect
456. #3247	C₂×C₅₃	semidirect
457. #3238	C₂×C₅₃	semidirect
458. #3227	C₂×C₅₃	semidirect
459. #3109	C₂×C₅₃	semidirect
460. #3106	C₂×C₅₃	semidirect
461. #3079	C₂×C₅₃	semidirect
462. C₂×#476	C₂×C₅₃	semidirect
463. #2990	C₂×C₅₃	semidirect
480. D₄×Q₈	C₂²×C₅₃	semidirect
484. #547	C₂²×C₅₃	semidirect
491. #532	C₂²×C₅₃	semidirect
492. #532	C₂²×C₅₃	semidirect
493. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
494. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
502. #501	C₂²×C₅₃	semidirect
503. #498	C₂²×C₅₃	semidirect
504. #489	C₂²×C₅₃	semidirect
506. #483	C₂²×C₅₃	semidirect
507. #482	C₂²×C₅₃	semidirect
508. #481	C₂²×C₅₃	semidirect
509. #481	C₂²×C₅₃	semidirect
511. #478	C₂²×C₅₃	semidirect
512. #477	C₂²×C₅₃	semidirect
513. #477	C₂²×C₅₃	semidirect
517. #476	C₂²×C₅₃	semidirect
518. #476	C₂²×C₅₃	semidirect
519. #476	C₂²×C₅₃	semidirect
520. #476	C₂²×C₅₃	semidirect
521. #476	C₂²×C₅₃	semidirect
522. #475	C₂²×C₅₃	semidirect
524. #469	C₂²×C₅₃	semidirect
526. #465	C₂²×C₅₃	semidirect
527. #463	C₂²×C₅₃	semidirect
528. #460	C₂²×C₅₃	semidirect
531. #459	C₂²×C₅₃	semidirect
534. #446	C₂²×C₅₃	semidirect
536. #442	C₂²×C₅₃	semidirect
537. C₄×SD₁₆	C₂²×C₅₃	semidirect
539. #435	C₂²×C₅₃	semidirect
541. #432	C₂²×C₅₃	semidirect
542. #431	C₂²×C₅₃	semidirect
543. #428	C₂²×C₅₃	semidirect
544. C₂×#106	C₂²×C₅₃	semidirect
545. #423	C₂²×C₅₃	semidirect
546. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
549. C₅₃	#62128	direct (N × H)
830. D₄	2₋¹⁺⁴×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3499	2
C₅₃×#3481	2
C₅₃×#3384	2
C₅₃×#3373	2
C₅₃×#3345	2
C₅₃×#3335	2
C₅₃×#3306	2
C₅₃×#3294	2
C₅₃×#3253	2
C₅₃×#3247	2
C₅₃×#3238	2
C₅₃×#3227	2
C₅₃×#3109	2
C₅₃×#3106	2
C₅₃×#3079	2
C₂×C₅₃×#476	2
C₅₃×#2990	2
#62128	53

Subgroups — C53×#62128 #27269640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62128 #27269640