Subgroups — C₅₃×#61446 #27268958

Order 13568.

1830 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3482	C₂	1	2	yes	maximal, complemented
2	C₅₃×#3402	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3377	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3343	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3327	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3312	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3308	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3277	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3270	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3172	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3108	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3104	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3102	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#137×C₅₃	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×Q₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#137×C₅₃	C₂²	1	2	yes	—
21	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
22	C₅₃×#557	C₂²	1	2	yes	—
23	C₅₃×#556	—	2	2	no	—
24	C₅₃×#556	C₂²	1	2	yes	—
25	C₅₃×#552	—	2	2	no	—
26	C₅₃×#552	—	2	2	no	—
27	C₅₃×#552	C₂²	1	2	yes	—
28	C₅₃×#552	C₂²	1	2	yes	—
29	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
30	C₅₃×#548	C₂²	1	2	yes	—
31	C₅₃×#548	C₂²	1	2	yes	—
32	C₅₃×#547	—	2	2	no	—
33	C₅₃×#547	C₂²	1	2	yes	—
34	C₅₃×#533	—	2	2	no	—
35	C₅₃×#533	C₂²	1	2	yes	—
36	C₅₃×#529	—	2	2	no	—
37	C₅₃×#529	—	2	2	no	—
38	C₅₃×#529	C₂²	1	2	yes	—
39	C₅₃×#529	C₂²	1	2	yes	—
40	C₄×#41×C₅₃	—	2	2	no	—
41	C₄×#41×C₅₃	C₂²	1	2	yes	—
42	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
45	C₅₃×#501	C₂²	1	2	yes	—
46	C₅₃×#499	C₂²	1	1	yes	characteristic
47	C₅₃×#497	C₂²	1	2	yes	—
48	C₅₃×#495	C₂²	1	1	yes	characteristic
49	C₅₃×#491	C₂²	1	2	yes	—
50	C₅₃×#489	C₂²	1	2	yes	—
51	C₅₃×#488	C₂²	1	2	yes	—
52	C₅₃×#485	C₂²	1	2	yes	—
53	C₅₃×#484	C₂²	1	2	yes	—
54	C₅₃×#484	C₂²	1	2	yes	—
55	C₅₃×#483	C₂²	1	2	yes	—
56	C₅₃×#482	C₂²	1	2	yes	—
57	C₅₃×#480	C₂²	1	2	yes	—
58	C₅₃×#479	C₂²	1	2	yes	—
59	C₅₃×#479	C₂²	1	2	yes	—
60	C₅₃×#479	C₂²	1	2	yes	—
61	C₅₃×#478	C₂²	1	2	yes	—
62	C₅₃×#477	C₂²	1	2	yes	—
63	C₅₃×#477	C₂²	1	2	yes	—
64	C₅₃×#470	C₂²	1	2	yes	—
65	C₅₃×#470	C₂²	1	2	yes	—
66	C₅₃×#468	C₂²	1	2	yes	—
67	C₅₃×#468	C₂²	1	2	yes	—
68	C₅₃×#467	C₂²	1	1	yes	characteristic
69	C₅₃×#466	C₂²	1	1	yes	characteristic
70	C₅₃×#465	C₂²	1	2	yes	—
71	C₅₃×#464	C₂²	1	2	yes	—
72	C₅₃×#464	C₂²	1	2	yes	—
73	C₅₃×#464	C₂²	1	2	yes	—
74	C₅₃×#463	C₂²	1	2	yes	—
75	C₅₃×#462	C₂²	1	2	yes	—
76	C₅₃×#462	C₂²	1	2	yes	—
77	C₅₃×#452	C₂²	1	2	yes	—
78	C₅₃×#451	C₂²	1	2	yes	—
79	C₅₃×#451	C₂²	1	2	yes	—
80	C₅₃×#451	C₂²	1	2	yes	—
81	C₅₃×#449	C₂²	1	2	yes	—
82	C₅₃×#448	C₂²	1	2	yes	—
83	C₅₃×#446	C₂²	1	1	yes	characteristic
84	C₅₃×#446	C₂²	1	1	yes	characteristic
85	C₅₃×#441	C₂²	1	2	yes	—
86	C₅₃×#441	C₂²	1	2	yes	—
87	C₅₃×#440	C₂²	1	2	yes	—
88	C₅₃×#440	C₂²	1	2	yes	—
89	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
90	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
91	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
92	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
93	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
94	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
95	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
96	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
97	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
98	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
99	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
100	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
101	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
102	C₅₃×#436	C₂²	1	1	yes	characteristic
103	C₅₃×#436	C₂²	1	1	yes	characteristic
104	C₅₃×#435	C₂²	1	2	yes	—
105	C₅₃×#435	C₂²	1	2	yes	—
106	C₅₃×#431	C₂²	1	2	yes	—
107	C₅₃×#431	C₂²	1	1	yes	characteristic
108	C₅₃×#428	C₂²	1	2	yes	—
109	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
110	C₅₃×#419	C₂²	1	2	yes	—
111	C₅₃×#417	C₂²	1	2	yes	—
112	C₂×#103×C₅₃	C₂²	1	2	yes	—
113	C₄×M₁₆×C₅₃	C₂²	1	2	yes	—
114	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
115	C₂×#41×C₅₃	—	2	2	no	—
116	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
117	C₂×#41×C₅₃	C₂³	1	2	yes	—
118	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
119	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
120	#137×C₅₃	—	2	8	no	—
121	C₂×Q₁₆×C₅₃	—	2	4	no	—
122	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
123	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
127	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
128	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
131	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
133	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
134	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₅₃	—	2	2	no	—
137	C₄⋊Q₈×C₅₃	—	2	2	no	—
138	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
140	#126×C₅₃	—	2	2	no	—
141	#126×C₅₃	—	2	2	no	—
142	#126×C₅₃	—	2	2	no	—
143	#126×C₅₃	—	2	2	no	—
144	#126×C₅₃	—	2	2	no	—
145	#126×C₅₃	—	2	2	no	—
146	#125×C₅₃	—	2	2	no	—
147	#125×C₅₃	—	2	2	no	—
148	#125×C₅₃	—	2	2	no	—
149	#125×C₅₃	—	2	2	no	—
150	#125×C₅₃	—	2	2	no	—
151	#125×C₅₃	C₂³	1	2	yes	—
152	#125×C₅₃	C₂³	1	2	yes	—
153	#124×C₅₃	—	2	2	no	—
154	#124×C₅₃	—	2	2	no	—
155	#124×C₅₃	C₂³	1	2	yes	—
156	#124×C₅₃	C₂³	1	2	yes	—
157	#123×C₅₃	—	2	2	no	—
158	#123×C₅₃	—	2	2	no	—
159	#123×C₅₃	—	2	2	no	—
160	#123×C₅₃	—	2	2	no	—
161	#123×C₅₃	—	2	2	no	—
162	#123×C₅₃	—	2	2	no	—
163	C₂²⋊Q₈×C₅₃	—	2	2	no	—
164	C₂²⋊Q₈×C₅₃	—	2	2	no	—
165	C₂²⋊Q₈×C₅₃	—	2	2	no	—
166	C₂²⋊Q₈×C₅₃	—	2	2	no	—
167	C₂²⋊Q₈×C₅₃	—	2	2	no	—
168	C₂²⋊Q₈×C₅₃	—	2	2	no	—
169	C₂²⋊Q₈×C₅₃	—	2	2	no	—
170	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
171	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
172	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
173	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
174	#121×C₅₃	—	2	2	no	—
175	#121×C₅₃	—	2	2	no	—
176	#121×C₅₃	C₂³	1	2	yes	—
177	#121×C₅₃	C₂³	1	2	yes	—
178	C₄×Q₈×C₅₃	—	2	2	no	—
179	C₄×Q₈×C₅₃	—	2	2	no	—
180	C₄×Q₈×C₅₃	—	2	2	no	—
181	C₄×Q₈×C₅₃	—	2	2	no	—
182	C₄×Q₈×C₅₃	—	2	2	no	—
183	C₄×Q₈×C₅₃	—	2	2	no	—
184	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
185	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
186	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
187	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
188	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
189	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
190	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
191	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
192	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
193	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
194	C₄×D₄×C₅₃	—	2	2	no	—
195	C₄×D₄×C₅₃	—	2	2	no	—
196	C₄×D₄×C₅₃	—	2	2	no	—
197	C₄×D₄×C₅₃	—	2	2	no	—
198	C₄×D₄×C₅₃	—	2	2	no	—
199	C₄×D₄×C₅₃	—	2	2	no	—
200	C₄×D₄×C₅₃	—	2	2	no	—
201	C₄×D₄×C₅₃	D₄	1	2	yes	—
202	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
203	C₄×D₄×C₅₃	C₂³	1	2	yes	—
204	C₄×D₄×C₅₃	C₂³	1	2	yes	—
205	C₄×D₄×C₅₃	C₂³	1	2	yes	—
206	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
207	#117×C₅₃	—	2	2	no	—
208	#117×C₅₃	—	2	2	no	—
209	#117×C₅₃	—	2	2	no	—
210	#117×C₅₃	—	2	2	no	—
211	#117×C₅₃	—	2	2	no	—
212	#117×C₅₃	—	2	2	no	—
213	#117×C₅₃	—	2	2	no	—
214	#117×C₅₃	D₄	1	1	yes	characteristic
215	#117×C₅₃	D₄	1	2	yes	—
216	#117×C₅₃	C₂³	1	2	yes	—
217	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
218	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
219	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
220	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
221	C₂×C₄²×C₅₃	—	2	2	no	—
222	C₂×C₄²×C₅₃	—	2	2	no	—
223	C₂×C₄²×C₅₃	—	2	2	no	—
224	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
226	#107×C₅₃	C₂³	1	1	yes	characteristic
227	#107×C₅₃	C₂³	1	1	yes	characteristic
228	#107×C₅₃	C₂³	1	1	yes	characteristic
229	#107×C₅₃	C₂³	1	2	yes	—
230	#107×C₅₃	C₂³	1	1	yes	characteristic
231	#107×C₅₃	C₂³	1	2	yes	—
232	#107×C₅₃	C₂³	1	2	yes	—
233	#106×C₅₃	C₂³	1	2	yes	—
234	#106×C₅₃	C₂³	1	2	yes	—
235	#106×C₅₃	C₂³	1	2	yes	—
236	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
237	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
238	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
239	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
240	#103×C₅₃	C₂³	1	2	yes	—
241	#103×C₅₃	C₂³	1	2	yes	—
242	#103×C₅₃	C₂³	1	2	yes	—
243	#103×C₅₃	C₂³	1	2	yes	—
244	#103×C₅₃	C₂³	1	2	yes	—
245	#103×C₅₃	C₂³	1	2	yes	—
246	#103×C₅₃	C₂³	1	2	yes	—
247	#103×C₅₃	C₂³	1	2	yes	—
248	#103×C₅₃	C₂³	1	2	yes	—
249	#103×C₅₃	C₂³	1	2	yes	—
250	#103×C₅₃	C₂³	1	2	yes	—
251	#103×C₅₃	C₂³	1	2	yes	—
252	#102×C₅₃	C₂³	1	2	yes	—
253	#102×C₅₃	C₂³	1	2	yes	—
254	#102×C₅₃	C₂³	1	2	yes	—
255	#102×C₅₃	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
258	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
259	#97×C₅₃	C₂³	1	2	yes	—
260	#97×C₅₃	C₂³	1	2	yes	—
261	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₅₃	C₂³	1	2	yes	—
266	#41×C₅₃	—	2	4	no	—
267	#41×C₅₃	—	4	2	no	—
268	#41×C₅₃	—	4	2	no	—
269	#41×C₅₃	—	4	8	no	—
270	C₂×Q₈×C₅₃	—	2	2	no	—
271	C₂×Q₈×C₅₃	—	2	2	no	—
272	C₂×Q₈×C₅₃	—	2	2	no	—
273	C₂×Q₈×C₅₃	—	2	4	no	—
274	C₂×Q₈×C₅₃	—	2	4	no	—
275	C₂×Q₈×C₅₃	—	4	2	no	—
276	C₂×Q₈×C₅₃	—	4	2	no	—
277	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
278	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
279	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
280	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
281	C₂×D₄×C₅₃	—	2	2	no	—
282	C₂×D₄×C₅₃	—	2	2	no	—
283	C₂×D₄×C₅₃	—	2	2	no	—
284	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
285	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
286	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₅₃	—	2	2	no	—
288	C₂²×C₄×C₅₃	—	2	2	no	—
289	C₂²×C₄×C₅₃	—	2	2	no	—
290	C₂²×C₄×C₅₃	—	2	2	no	—
291	C₂²×C₄×C₅₃	—	2	2	no	—
292	C₂²×C₄×C₅₃	—	2	2	no	—
293	C₂²×C₄×C₅₃	—	2	2	no	—
294	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
298	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
300	Q₁₆×C₅₃	—	2	4	no	—
301	Q₁₆×C₅₃	—	2	4	no	—
302	Q₁₆×C₅₃	—	2	2	no	—
303	Q₁₆×C₅₃	—	4	1	no	—
304	Q₁₆×C₅₃	—	4	2	no	—
305	Q₁₆×C₅₃	#41	1	4	yes	complemented
306	SD₁₆×C₅₃	—	2	4	no	—
307	SD₁₆×C₅₃	—	2	4	no	—
308	SD₁₆×C₅₃	—	4	2	no	—
309	D₈×C₅₃	—	4	1	no	—
310	M₁₆×C₅₃	—	2	4	no	—
311	M₁₆×C₅₃	—	4	2	no	—
312	C₂×C₈×C₅₃	—	2	2	no	—
313	C₂×C₈×C₅₃	—	4	1	no	—
314	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
315	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
316	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
317	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
318	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
319	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
320	C₄⋊C₄×C₅₃	—	2	2	no	—
321	C₄⋊C₄×C₅₃	—	2	2	no	—
322	C₄⋊C₄×C₅₃	—	2	2	no	—
323	C₄⋊C₄×C₅₃	—	2	2	no	—
324	C₄⋊C₄×C₅₃	—	2	2	no	—
325	C₄⋊C₄×C₅₃	—	2	2	no	—
326	C₄⋊C₄×C₅₃	—	2	2	no	—
327	C₄⋊C₄×C₅₃	—	2	2	no	—
328	C₄⋊C₄×C₅₃	—	2	2	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	2	no	—
333	C₄⋊C₄×C₅₃	—	2	2	no	—
334	C₄⋊C₄×C₅₃	—	2	2	no	—
335	C₄⋊C₄×C₅₃	—	2	2	no	—
336	C₄⋊C₄×C₅₃	—	2	2	no	—
337	C₄⋊C₄×C₅₃	—	2	2	no	—
338	C₄⋊C₄×C₅₃	—	2	2	no	—
339	C₄⋊C₄×C₅₃	—	2	2	no	—
340	C₄⋊C₄×C₅₃	—	2	2	no	—
341	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
342	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
343	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
344	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
345	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
349	C₂²⋊C₄×C₅₃	—	2	2	no	—
350	C₂²⋊C₄×C₅₃	—	2	2	no	—
351	C₂²⋊C₄×C₅₃	—	2	2	no	—
352	C₂²⋊C₄×C₅₃	—	2	2	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	2	no	—
358	C₂²⋊C₄×C₅₃	—	2	2	no	—
359	C₂²⋊C₄×C₅₃	—	2	2	no	—
360	C₂²⋊C₄×C₅₃	—	2	2	no	—
361	C₂²⋊C₄×C₅₃	—	2	2	no	—
362	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
363	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
364	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
365	C₄²×C₅₃	—	2	2	no	—
366	C₄²×C₅₃	—	2	2	no	—
367	C₄²×C₅₃	—	2	2	no	—
368	C₄²×C₅₃	—	2	2	no	—
369	C₄²×C₅₃	—	2	2	no	—
370	C₄²×C₅₃	—	2	2	no	—
371	C₄²×C₅₃	—	2	2	no	—
372	C₄²×C₅₃	—	2	2	no	—
373	C₄²×C₅₃	—	2	2	no	—
374	C₄²×C₅₃	C₂×D₄	1	2	yes	—
375	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₅₃	C₂×D₄	1	2	yes	—
377	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₄²×C₅₃	C₂⁴	1	2	yes	—
380	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂³×C₅₃	—	2	2	no	—
382	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
383	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
384	Q₈×C₅₃	—	2	2	no	—
385	Q₈×C₅₃	—	2	2	no	—
386	Q₈×C₅₃	—	2	2	no	—
387	Q₈×C₅₃	—	2	2	no	—
388	Q₈×C₅₃	—	2	2	no	—
389	Q₈×C₅₃	—	4	1	no	—
390	Q₈×C₅₃	—	4	4	no	—
391	Q₈×C₅₃	—	4	4	no	—
392	Q₈×C₅₃	—	4	4	no	—
393	Q₈×C₅₃	C₂×#41	1	4	yes	—
394	D₄×C₅₃	—	2	4	no	—
395	D₄×C₅₃	—	2	2	no	—
396	D₄×C₅₃	—	2	2	no	—
397	D₄×C₅₃	—	4	1	no	—
398	D₄×C₅₃	—	4	4	no	—
399	D₄×C₅₃	—	4	4	no	—
400	D₄×C₅₃	—	4	4	no	—
401	C₂×C₄×C₅₃	—	2	2	no	—
402	C₂×C₄×C₅₃	—	2	2	no	—
403	C₂×C₄×C₅₃	—	2	2	no	—
404	C₂×C₄×C₅₃	—	2	4	no	—
405	C₂×C₄×C₅₃	—	2	1	no	—
406	C₂×C₄×C₅₃	—	2	2	no	—
407	C₂×C₄×C₅₃	—	2	1	no	—
408	C₂×C₄×C₅₃	—	2	2	no	—
409	C₂×C₄×C₅₃	—	2	2	no	—
410	C₂×C₄×C₅₃	—	2	2	no	—
411	C₂×C₄×C₅₃	—	2	2	no	—
412	C₂×C₄×C₅₃	—	2	2	no	—
413	C₂×C₄×C₅₃	—	2	2	no	—
414	C₂×C₄×C₅₃	—	2	2	no	—
415	C₂×C₄×C₅₃	—	4	2	no	—
416	C₂×C₄×C₅₃	—	4	4	no	—
417	C₂×C₄×C₅₃	—	4	4	no	—
418	C₂×C₄×C₅₃	—	4	4	no	—
419	C₂×C₄×C₅₃	—	4	4	no	—
420	C₂×C₄×C₅₃	—	4	4	no	—
421	C₂×C₄×C₅₃	—	4	4	no	—
422	C₂×C₄×C₅₃	—	4	4	no	—
423	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
432	C₈×C₅₃	—	2	1	no	—
433	C₈×C₅₃	—	2	2	no	—
434	C₈×C₅₃	—	2	1	no	—
435	C₈×C₅₃	—	2	1	no	—
436	C₈×C₅₃	—	2	2	no	—
437	C₈×C₅₃	C₂×#41	1	2	yes	—
438	#61446	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₂²×C₅₃	—	2	1	no	—
440	C₂²×C₅₃	—	2	1	no	—
441	C₂²×C₅₃	—	2	2	no	—
442	C₂²×C₅₃	—	2	2	no	—
443	C₂²×C₅₃	—	2	2	no	—
444	C₂²×C₅₃	—	4	2	no	—
445	C₂²×C₅₃	—	4	2	no	—
446	C₂²×C₅₃	—	4	2	no	—
447	C₂²×C₅₃	#575	1	2	yes	—
448	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
449	C₄×C₅₃	—	2	2	no	—
450	C₄×C₅₃	—	2	1	no	—
451	C₄×C₅₃	—	2	4	no	—
452	C₄×C₅₃	—	2	1	no	—
453	C₄×C₅₃	—	2	1	no	—
454	C₄×C₅₃	—	2	2	no	—
455	C₄×C₅₃	—	2	1	no	—
456	C₄×C₅₃	—	2	2	no	—
457	C₄×C₅₃	—	4	2	no	—
458	C₄×C₅₃	—	4	2	no	—
459	C₄×C₅₃	—	4	2	no	—
460	C₄×C₅₃	—	4	2	no	—
461	C₄×C₅₃	—	4	2	no	—
462	C₄×C₅₃	—	4	2	no	—
463	C₄×C₅₃	#578	1	2	yes	—
464	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
465	C₄×C₅₃	#585	1	1	yes	characteristic
466	#3482	C₂×C₅₃	1	2	yes	complemented
467	#3402	C₂×C₅₃	1	1	yes	characteristic, complemented
468	#3390	C₂×C₅₃	1	1	yes	characteristic, complemented
469	#3377	C₂×C₅₃	1	2	yes	complemented
470	#3352	C₂×C₅₃	1	1	yes	characteristic, complemented
471	#3343	C₂×C₅₃	1	2	yes	complemented
472	#3327	C₂×C₅₃	1	2	yes	complemented
473	#3312	C₂×C₅₃	1	2	yes	complemented
474	#3308	C₂×C₅₃	1	2	yes	complemented
475	#3277	C₂×C₅₃	1	1	yes	characteristic, complemented
476	#3270	C₂×C₅₃	1	2	yes	complemented
477	#3172	C₂×C₅₃	1	2	yes	complemented
478	#3168	C₂×C₅₃	1	1	yes	characteristic, complemented
479	#3108	C₂×C₅₃	1	2	yes	complemented
480	#3104	C₂×C₅₃	1	2	yes	complemented
481	#3102	C₂×C₅₃	1	2	yes	complemented
482	#2965	C₂×C₅₃	1	1	yes	characteristic, complemented
483	C₄×#137	C₂×C₅₃	1	2	yes	complemented
484	C₂×C₄×Q₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
485	C₂×C₅₃	—	2	2	no	—
486	C₂×C₅₃	—	4	2	no	—
487	C₂×C₅₃	—	8	2	no	—
488	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
489	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
490	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
491	C₂×#137	C₂²×C₅₃	1	2	yes	—
492	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
493	#557	C₂²×C₅₃	1	2	yes	—
494	#556	—	2	2	no	—
495	#556	C₂²×C₅₃	1	2	yes	—
496	#552	—	2	2	no	—
497	#552	—	2	2	no	—
498	#552	C₂²×C₅₃	1	2	yes	—
499	#552	C₂²×C₅₃	1	2	yes	—
500	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
501	#548	C₂²×C₅₃	1	2	yes	—
502	#548	C₂²×C₅₃	1	2	yes	—
503	#547	—	2	2	no	—
504	#547	C₂²×C₅₃	1	2	yes	—
505	#533	—	2	2	no	—
506	#533	C₂²×C₅₃	1	2	yes	—
507	#529	—	2	2	no	—
508	#529	—	2	2	no	—
509	#529	C₂²×C₅₃	1	2	yes	—
510	#529	C₂²×C₅₃	1	2	yes	—
511	C₄×#41	—	2	2	no	—
512	C₄×#41	C₂²×C₅₃	1	2	yes	—
513	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
514	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
515	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
516	#501	C₂²×C₅₃	1	2	yes	—
517	#499	C₂²×C₅₃	1	1	yes	characteristic
518	#497	C₂²×C₅₃	1	2	yes	—
519	#495	C₂²×C₅₃	1	1	yes	characteristic
520	#491	C₂²×C₅₃	1	2	yes	—
521	#489	C₂²×C₅₃	1	2	yes	—
522	#488	C₂²×C₅₃	1	2	yes	—
523	#485	C₂²×C₅₃	1	2	yes	—
524	#484	C₂²×C₅₃	1	2	yes	—
525	#484	C₂²×C₅₃	1	2	yes	—
526	#483	C₂²×C₅₃	1	2	yes	—
527	#482	C₂²×C₅₃	1	2	yes	—
528	#480	C₂²×C₅₃	1	2	yes	—
529	#479	C₂²×C₅₃	1	2	yes	—
530	#479	C₂²×C₅₃	1	2	yes	—
531	#479	C₂²×C₅₃	1	2	yes	—
532	#478	C₂²×C₅₃	1	2	yes	—
533	#477	C₂²×C₅₃	1	2	yes	—
534	#477	C₂²×C₅₃	1	2	yes	—
535	#470	C₂²×C₅₃	1	2	yes	—
536	#470	C₂²×C₅₃	1	2	yes	—
537	#468	C₂²×C₅₃	1	2	yes	—
538	#468	C₂²×C₅₃	1	2	yes	—
539	#467	C₂²×C₅₃	1	1	yes	characteristic
540	#466	C₂²×C₅₃	1	1	yes	characteristic
541	#465	C₂²×C₅₃	1	2	yes	—
542	#464	C₂²×C₅₃	1	2	yes	—
543	#464	C₂²×C₅₃	1	2	yes	—
544	#464	C₂²×C₅₃	1	2	yes	—
545	#463	C₂²×C₅₃	1	2	yes	—
546	#462	C₂²×C₅₃	1	2	yes	—
547	#462	C₂²×C₅₃	1	2	yes	—
548	#452	C₂²×C₅₃	1	2	yes	—
549	#451	C₂²×C₅₃	1	2	yes	—
550	#451	C₂²×C₅₃	1	2	yes	—
551	#451	C₂²×C₅₃	1	2	yes	—
552	#449	C₂²×C₅₃	1	2	yes	—
553	#448	C₂²×C₅₃	1	2	yes	—
554	#446	C₂²×C₅₃	1	1	yes	characteristic
555	#446	C₂²×C₅₃	1	1	yes	characteristic
556	#441	C₂²×C₅₃	1	2	yes	—
557	#441	C₂²×C₅₃	1	2	yes	—
558	#440	C₂²×C₅₃	1	2	yes	—
559	#440	C₂²×C₅₃	1	2	yes	—
560	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
561	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
562	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
563	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
564	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
565	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
566	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
567	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
568	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
569	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
570	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
571	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
572	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
573	#436	C₂²×C₅₃	1	1	yes	characteristic
574	#436	C₂²×C₅₃	1	1	yes	characteristic
575	#435	C₂²×C₅₃	1	2	yes	—
576	#435	C₂²×C₅₃	1	2	yes	—
577	#431	C₂²×C₅₃	1	2	yes	—
578	#431	C₂²×C₅₃	1	1	yes	characteristic
579	#428	C₂²×C₅₃	1	2	yes	—
580	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
581	#419	C₂²×C₅₃	1	2	yes	—
582	#417	C₂²×C₅₃	1	2	yes	—
583	C₂×#103	C₂²×C₅₃	1	2	yes	—
584	C₄×M₁₆	C₂²×C₅₃	1	2	yes	—
585	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
586	C₅₃	#61446	1	1	yes	characteristic, direct product factor, Sylow
587	C₂×#41	—	2	2	no	—
588	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
589	C₂×#41	C₂³×C₅₃	1	2	yes	—
590	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
591	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
592	#137	—	2	8	no	—
593	C₂×Q₁₆	—	2	4	no	—
594	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
595	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
596	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
597	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
598	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
599	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
600	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
601	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
602	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
603	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
604	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
605	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
606	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
607	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
608	C₄⋊Q₈	—	2	2	no	—
609	C₄⋊Q₈	—	2	2	no	—
610	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
611	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
612	#126	—	2	2	no	—
613	#126	—	2	2	no	—
614	#126	—	2	2	no	—
615	#126	—	2	2	no	—
616	#126	—	2	2	no	—
617	#126	—	2	2	no	—
618	#125	—	2	2	no	—
619	#125	—	2	2	no	—
620	#125	—	2	2	no	—
621	#125	—	2	2	no	—
622	#125	—	2	2	no	—
623	#125	C₂³×C₅₃	1	2	yes	—
624	#125	C₂³×C₅₃	1	2	yes	—
625	#124	—	2	2	no	—
626	#124	—	2	2	no	—
627	#124	C₂³×C₅₃	1	2	yes	—
628	#124	C₂³×C₅₃	1	2	yes	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
643	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	C₂³×C₅₃	1	2	yes	—
649	#121	C₂³×C₅₃	1	2	yes	—
650	C₄×Q₈	—	2	2	no	—
651	C₄×Q₈	—	2	2	no	—
652	C₄×Q₈	—	2	2	no	—
653	C₄×Q₈	—	2	2	no	—
654	C₄×Q₈	—	2	2	no	—
655	C₄×Q₈	—	2	2	no	—
656	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
657	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
658	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
659	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
660	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
661	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
662	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
663	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
664	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
665	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	D₄×C₅₃	1	2	yes	—
674	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
675	C₄×D₄	C₂³×C₅₃	1	2	yes	—
676	C₄×D₄	C₂³×C₅₃	1	2	yes	—
677	C₄×D₄	C₂³×C₅₃	1	2	yes	—
678	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
679	#117	—	2	2	no	—
680	#117	—	2	2	no	—
681	#117	—	2	2	no	—
682	#117	—	2	2	no	—
683	#117	—	2	2	no	—
684	#117	—	2	2	no	—
685	#117	—	2	2	no	—
686	#117	D₄×C₅₃	1	1	yes	characteristic
687	#117	D₄×C₅₃	1	2	yes	—
688	#117	C₂³×C₅₃	1	2	yes	—
689	C₂×C₄⋊C₄	—	2	2	no	—
690	C₂×C₄⋊C₄	—	2	2	no	—
691	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
693	C₂×C₄²	—	2	2	no	—
694	C₂×C₄²	—	2	2	no	—
695	C₂×C₄²	—	2	2	no	—
696	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
698	#107	C₂³×C₅₃	1	1	yes	characteristic
699	#107	C₂³×C₅₃	1	1	yes	characteristic
700	#107	C₂³×C₅₃	1	2	yes	—
701	#107	C₂³×C₅₃	1	2	yes	—
702	#107	C₂³×C₅₃	1	1	yes	characteristic
703	#107	C₂³×C₅₃	1	1	yes	characteristic
704	#107	C₂³×C₅₃	1	2	yes	—
705	#106	C₂³×C₅₃	1	2	yes	—
706	#106	C₂³×C₅₃	1	2	yes	—
707	#106	C₂³×C₅₃	1	2	yes	—
708	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
709	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
710	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
711	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
712	#103	C₂³×C₅₃	1	2	yes	—
713	#103	C₂³×C₅₃	1	2	yes	—
714	#103	C₂³×C₅₃	1	2	yes	—
715	#103	C₂³×C₅₃	1	2	yes	—
716	#103	C₂³×C₅₃	1	2	yes	—
717	#103	C₂³×C₅₃	1	2	yes	—
718	#103	C₂³×C₅₃	1	2	yes	—
719	#103	C₂³×C₅₃	1	2	yes	—
720	#103	C₂³×C₅₃	1	2	yes	—
721	#103	C₂³×C₅₃	1	2	yes	—
722	#103	C₂³×C₅₃	1	2	yes	—
723	#103	C₂³×C₅₃	1	2	yes	—
724	#102	C₂³×C₅₃	1	2	yes	—
725	#102	C₂³×C₅₃	1	2	yes	—
726	#102	C₂³×C₅₃	1	2	yes	—
727	#102	C₂³×C₅₃	1	2	yes	—
728	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
729	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
730	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
731	#97	C₂³×C₅₃	1	2	yes	—
732	#97	C₂³×C₅₃	1	2	yes	—
733	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
734	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
735	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
736	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
737	C₄×C₈	C₂³×C₅₃	1	2	yes	—
738	#41	—	2	4	no	—
739	#41	—	4	2	no	—
740	#41	—	4	2	no	—
741	#41	—	4	8	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	2	2	no	—
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	—	2	4	no	—
746	C₂×Q₈	—	2	4	no	—
747	C₂×Q₈	—	4	2	no	—
748	C₂×Q₈	—	4	2	no	—
749	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
750	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
751	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
752	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
757	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
758	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
767	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
768	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
769	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
772	Q₁₆	—	2	4	no	—
773	Q₁₆	—	2	4	no	—
774	Q₁₆	—	2	2	no	—
775	Q₁₆	—	4	1	no	—
776	Q₁₆	—	4	2	no	—
777	Q₁₆	#41×C₅₃	1	4	yes	complemented
778	SD₁₆	—	2	4	no	—
779	SD₁₆	—	2	4	no	—
780	SD₁₆	—	4	2	no	—
781	D₈	—	4	1	no	—
782	M₁₆	—	2	4	no	—
783	M₁₆	—	4	2	no	—
784	C₂×C₈	—	2	2	no	—
785	C₂×C₈	—	4	1	no	—
786	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
787	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
788	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
789	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
790	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
791	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
814	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
815	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
816	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
817	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
818	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
819	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
835	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
836	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	C₂×D₄×C₅₃	1	2	yes	—
847	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
848	C₄²	C₂×D₄×C₅₃	1	2	yes	—
849	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
850	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
851	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
852	C₄²	C₂⁴×C₅₃	1	2	yes	—
853	C₂³	—	2	2	no	—
854	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
855	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
856	Q₈	—	2	2	no	—
857	Q₈	—	2	2	no	—
858	Q₈	—	2	2	no	—
859	Q₈	—	2	2	no	—
860	Q₈	—	2	2	no	—
861	Q₈	—	4	1	no	—
862	Q₈	—	4	4	no	—
863	Q₈	—	4	4	no	—
864	Q₈	—	4	4	no	—
865	Q₈	C₂×#41×C₅₃	1	4	yes	—
866	D₄	—	2	4	no	—
867	D₄	—	2	2	no	—
868	D₄	—	2	2	no	—
869	D₄	—	4	1	no	—
870	D₄	—	4	4	no	—
871	D₄	—	4	4	no	—
872	D₄	—	4	4	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	4	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	4	2	no	—
888	C₂×C₄	—	4	4	no	—
889	C₂×C₄	—	4	4	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
896	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
897	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
903	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
904	C₈	—	2	1	no	—
905	C₈	—	2	2	no	—
906	C₈	—	2	1	no	—
907	C₈	—	2	1	no	—
908	C₈	—	2	2	no	—
909	C₈	C₂×#41×C₅₃	1	2	yes	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	C₅₃×#575	1	2	yes	—
919	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
920	C₄	—	2	2	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	4	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	2	no	—
934	C₄	C₅₃×#578	1	2	yes	—
935	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
936	C₄	C₅₃×#585	1	1	yes	characteristic
937	C₂	—	2	2	no	—
938	C₂	—	4	2	no	—
939	C₂	—	8	2	no	—
940	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
941	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
942	C₂	C₂×C₅₃×#578	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3482	C₂	semidirect
2. C₅₃×#3402	C₂	semidirect
3. C₅₃×#3390	C₂	semidirect
4. C₅₃×#3377	C₂	semidirect
5. C₅₃×#3352	C₂	semidirect
6. C₅₃×#3343	C₂	semidirect
7. C₅₃×#3327	C₂	semidirect
8. C₅₃×#3312	C₂	semidirect
9. C₅₃×#3308	C₂	semidirect
10. C₅₃×#3277	C₂	semidirect
11. C₅₃×#3270	C₂	semidirect
12. C₅₃×#3172	C₂	semidirect
13. C₅₃×#3168	C₂	semidirect
14. C₅₃×#3108	C₂	semidirect
15. C₅₃×#3104	C₂	semidirect
16. C₅₃×#3102	C₂	semidirect
17. C₅₃×#2965	C₂	semidirect
18. C₄×#137×C₅₃	C₂	semidirect
19. C₂×C₄×Q₁₆×C₅₃	C₂	semidirect
305. Q₁₆×C₅₃	#41	semidirect
438. #61446	C₅₃	direct (N × H)
466. #3482	C₂×C₅₃	semidirect
467. #3402	C₂×C₅₃	semidirect
468. #3390	C₂×C₅₃	semidirect
469. #3377	C₂×C₅₃	semidirect
470. #3352	C₂×C₅₃	semidirect
471. #3343	C₂×C₅₃	semidirect
472. #3327	C₂×C₅₃	semidirect
473. #3312	C₂×C₅₃	semidirect
474. #3308	C₂×C₅₃	semidirect
475. #3277	C₂×C₅₃	semidirect
476. #3270	C₂×C₅₃	semidirect
477. #3172	C₂×C₅₃	semidirect
478. #3168	C₂×C₅₃	semidirect
479. #3108	C₂×C₅₃	semidirect
480. #3104	C₂×C₅₃	semidirect
481. #3102	C₂×C₅₃	semidirect
482. #2965	C₂×C₅₃	semidirect
483. C₄×#137	C₂×C₅₃	semidirect
484. C₂×C₄×Q₁₆	C₂×C₅₃	semidirect
586. C₅₃	#61446	direct (N × H)
777. Q₁₆	#41×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3482	2
C₅₃×#3402	2
C₅₃×#3390	2
C₅₃×#3377	2
C₅₃×#3352	2
C₅₃×#3343	2
C₅₃×#3327	2
C₅₃×#3312	2
C₅₃×#3308	2
C₅₃×#3277	2
C₅₃×#3270	2
C₅₃×#3172	2
C₅₃×#3168	2
C₅₃×#3108	2
C₅₃×#3104	2
C₅₃×#3102	2
C₅₃×#2965	2
C₄×#137×C₅₃	2
C₂×C₄×Q₁₆×C₅₃	2
#61446	53

Subgroups — C53×#61446 #27268958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61446 #27268958