Subgroups — C₅₃×#62091 #27269603

Order 13568.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3402	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3369	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3328	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3321	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3311	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3275	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3270	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3270	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3263	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3225	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3121	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3044	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2995	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×#137×C₅₃	C₂²	1	2	yes	—
22	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
23	C₂²×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
24	C₅₃×#563	—	2	1	no	—
25	C₅₃×#562	—	2	1	no	—
26	Q₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₅₃×#556	—	2	2	no	—
28	C₅₃×#556	—	2	1	no	—
29	C₅₃×#556	C₂²	1	2	yes	—
30	C₅₃×#556	C₂²	1	2	yes	—
31	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
32	C₅₃×#555	—	2	1	no	—
33	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
34	C₅₃×#551	—	2	2	no	—
35	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
36	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#548	C₂²	1	2	yes	—
38	C₅₃×#548	C₂²	1	2	yes	—
39	C₅₃×#546	C₂²	1	2	yes	—
40	C₅₃×#543	—	2	1	no	—
41	C₅₃×#542	—	2	2	no	—
42	C₅₃×#542	—	2	2	no	—
43	C₅₃×#542	C₂²	1	2	yes	—
44	C₅₃×#542	C₂²	1	2	yes	complemented
45	C₅₃×#538	—	2	1	no	—
46	C₅₃×#536	C₂²	1	2	yes	—
47	C₅₃×#533	—	2	1	no	—
48	C₅₃×#533	C₂²	1	1	yes	characteristic
49	C₅₃×#533	C₂²	1	1	yes	characteristic
50	C₅₃×#529	—	2	1	no	—
51	C₅₃×#529	C₂²	1	1	yes	characteristic
52	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
53	C₅₃×#519	C₂²	1	2	yes	complemented
54	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
55	C₅₃×#497	C₂²	1	2	yes	—
56	C₅₃×#497	C₂²	1	2	yes	complemented
57	C₅₃×#495	C₂²	1	2	yes	—
58	C₅₃×#489	C₂²	1	2	yes	—
59	C₅₃×#489	C₂²	1	2	yes	—
60	C₅₃×#487	C₂²	1	2	yes	complemented
61	C₅₃×#485	C₂²	1	2	yes	—
62	C₅₃×#485	C₂²	1	2	yes	complemented
63	C₅₃×#482	C₂²	1	2	yes	—
64	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#476	C₂²	1	2	yes	—
66	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#475	C₂²	1	2	yes	complemented
68	C₅₃×#475	C₂²	1	2	yes	complemented
69	C₅₃×#475	C₂²	1	2	yes	complemented
70	C₅₃×#470	C₂²	1	2	yes	—
71	C₅₃×#470	C₂²	1	2	yes	—
72	C₅₃×#470	C₂²	1	2	yes	complemented
73	C₅₃×#469	C₂²	1	2	yes	—
74	C₅₃×#465	C₂²	1	2	yes	—
75	C₅₃×#465	C₂²	1	2	yes	complemented
76	C₅₃×#464	C₂²	1	2	yes	—
77	C₅₃×#464	C₂²	1	2	yes	—
78	C₅₃×#464	C₂²	1	2	yes	—
79	C₅₃×#464	C₂²	1	2	yes	—
80	C₅₃×#464	C₂²	1	2	yes	—
81	C₅₃×#464	C₂²	1	2	yes	—
82	C₅₃×#464	C₂²	1	2	yes	complemented
83	C₅₃×#463	C₂²	1	2	yes	—
84	C₅₃×#463	C₂²	1	2	yes	—
85	C₅₃×#463	C₂²	1	2	yes	—
86	C₅₃×#462	C₂²	1	2	yes	complemented
87	C₅₃×#462	C₂²	1	2	yes	complemented
88	C₅₃×#462	C₂²	1	2	yes	complemented
89	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#462	C₂²	1	2	yes	complemented
91	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#452	C₂²	1	2	yes	—
93	C₅₃×#452	C₂²	1	2	yes	—
94	C₅₃×#451	C₂²	1	2	yes	—
95	C₅₃×#451	C₂²	1	2	yes	complemented
96	C₅₃×#451	C₂²	1	2	yes	complemented
97	C₅₃×#450	C₂²	1	2	yes	—
98	C₅₃×#449	C₂²	1	2	yes	—
99	C₅₃×#448	C₂²	1	2	yes	—
100	C₅₃×#448	C₂²	1	2	yes	complemented
101	C₅₃×#446	C₂²	1	2	yes	complemented
102	C₅₃×#441	C₂²	1	2	yes	complemented
103	C₅₃×#441	C₂²	1	2	yes	complemented
104	C₅₃×#440	C₂²	1	2	yes	—
105	C₅₃×#440	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
108	C₅₃×#436	C₂²	1	2	yes	—
109	C₅₃×#435	C₂²	1	2	yes	—
110	C₅₃×#435	C₂²	1	2	yes	complemented
111	C₅₃×#433	C₂²	1	2	yes	complemented
112	C₅₃×#432	C₂²	1	1	yes	characteristic
113	C₅₃×#424	C₂²	1	2	yes	complemented
114	C₅₃×#423	C₂²	1	1	yes	characteristic
115	C₅₃×#419	C₂²	1	1	yes	characteristic
116	C₅₃×#419	C₂²	1	2	yes	complemented
117	C₅₃×#418	C₂²	1	1	yes	characteristic
118	C₅₃×#416	C₂²	1	2	yes	—
119	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
120	C₂×#41×C₅₃	C₂³	1	2	yes	—
121	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
122	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
125	#137×C₅₃	—	4	4	no	—
126	#137×C₅₃	—	4	2	no	—
127	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
128	C₂×Q₁₆×C₅₃	—	4	4	no	—
129	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
130	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
131	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
132	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
133	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
134	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
135	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
140	C₂×D₈×C₅₃	C₂³	1	2	yes	—
141	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
144	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
145	C₄⋊Q₈×C₅₃	—	2	1	no	—
146	C₄⋊Q₈×C₅₃	—	2	1	no	—
147	C₄⋊Q₈×C₅₃	—	2	2	no	—
148	C₄⋊Q₈×C₅₃	—	2	2	no	—
149	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
150	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
153	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
155	#126×C₅₃	—	2	2	no	—
156	#126×C₅₃	—	2	2	no	—
157	#126×C₅₃	—	2	2	no	—
158	#126×C₅₃	—	2	2	no	—
159	#126×C₅₃	—	2	2	no	—
160	#126×C₅₃	—	2	2	no	—
161	#126×C₅₃	—	2	2	no	—
162	#126×C₅₃	D₄	1	2	yes	—
163	#125×C₅₃	—	2	1	no	—
164	#125×C₅₃	—	2	1	no	—
165	#125×C₅₃	D₄	1	1	yes	characteristic
166	#124×C₅₃	—	2	2	no	—
167	#124×C₅₃	—	2	2	no	—
168	#124×C₅₃	—	2	2	no	—
169	#124×C₅₃	—	2	2	no	—
170	#124×C₅₃	—	2	2	no	—
171	#124×C₅₃	—	2	1	no	—
172	#124×C₅₃	—	2	1	no	—
173	#124×C₅₃	—	2	2	no	—
174	#124×C₅₃	D₄	1	1	yes	characteristic
175	#124×C₅₃	C₂³	1	2	yes	—
176	#124×C₅₃	C₂³	1	2	yes	—
177	#124×C₅₃	C₂³	1	2	yes	—
178	#124×C₅₃	C₂³	1	2	yes	—
179	#123×C₅₃	—	2	2	no	—
180	#123×C₅₃	—	2	2	no	—
181	#123×C₅₃	—	2	2	no	—
182	#123×C₅₃	—	2	2	no	—
183	#123×C₅₃	—	2	2	no	—
184	#123×C₅₃	D₄	1	2	yes	—
185	C₂²⋊Q₈×C₅₃	—	2	2	no	—
186	C₂²⋊Q₈×C₅₃	—	2	2	no	—
187	C₂²⋊Q₈×C₅₃	—	2	2	no	—
188	C₂²⋊Q₈×C₅₃	—	2	2	no	—
189	C₂²⋊Q₈×C₅₃	—	2	2	no	—
190	C₂²⋊Q₈×C₅₃	—	2	2	no	—
191	C₂²⋊Q₈×C₅₃	—	2	2	no	—
192	C₂²⋊Q₈×C₅₃	—	2	2	no	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	1	no	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	1	no	—
197	C₂²⋊Q₈×C₅₃	—	2	1	no	—
198	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
199	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
203	#121×C₅₃	—	2	2	no	—
204	#121×C₅₃	—	2	1	no	—
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	2	no	—
207	#121×C₅₃	D₄	1	1	yes	characteristic
208	#121×C₅₃	C₂³	1	2	yes	—
209	#121×C₅₃	C₂³	1	2	yes	—
210	#120×C₅₃	—	2	2	no	—
211	C₄×Q₈×C₅₃	—	2	2	no	—
212	C₄×Q₈×C₅₃	—	2	2	no	—
213	C₄×Q₈×C₅₃	—	2	2	no	—
214	C₄×Q₈×C₅₃	—	2	1	no	—
215	C₄×Q₈×C₅₃	—	2	1	no	—
216	C₄×Q₈×C₅₃	—	2	1	no	—
217	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
221	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
225	C₄×D₄×C₅₃	—	2	2	no	—
226	C₄×D₄×C₅₃	—	2	2	no	—
227	C₄×D₄×C₅₃	—	2	1	no	—
228	C₄×D₄×C₅₃	—	2	2	no	—
229	C₄×D₄×C₅₃	—	2	1	no	—
230	C₄×D₄×C₅₃	—	2	1	no	—
231	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₅₃	C₂³	1	2	yes	—
234	C₄×D₄×C₅₃	C₂³	1	2	yes	—
235	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
236	#117×C₅₃	—	2	1	no	—
237	#117×C₅₃	—	2	1	no	—
238	#117×C₅₃	—	2	2	no	—
239	#117×C₅₃	—	2	2	no	—
240	#117×C₅₃	—	2	2	no	—
241	#117×C₅₃	—	2	1	no	—
242	#117×C₅₃	—	2	1	no	—
243	#117×C₅₃	—	2	1	no	—
244	#117×C₅₃	C₂³	1	1	yes	characteristic
245	#117×C₅₃	C₂³	1	2	yes	—
246	#117×C₅₃	C₂³	1	2	yes	—
247	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
248	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
250	C₂×C₄²×C₅₃	—	2	1	no	—
251	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
252	#107×C₅₃	C₂³	1	2	yes	—
253	#106×C₅₃	C₂³	1	2	yes	—
254	#106×C₅₃	C₂³	1	2	yes	—
255	#106×C₅₃	C₂³	1	2	yes	—
256	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
257	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
258	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
259	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
260	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
261	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
262	#103×C₅₃	C₂³	1	2	yes	—
263	#103×C₅₃	C₂³	1	2	yes	—
264	#103×C₅₃	C₂³	1	2	yes	—
265	#103×C₅₃	C₂³	1	2	yes	—
266	#103×C₅₃	C₂³	1	2	yes	—
267	#103×C₅₃	C₂³	1	2	yes	—
268	#103×C₅₃	C₂³	1	2	yes	—
269	#103×C₅₃	C₂³	1	2	yes	—
270	#103×C₅₃	C₂³	1	2	yes	—
271	#103×C₅₃	C₂³	1	2	yes	—
272	#103×C₅₃	C₂³	1	2	yes	—
273	#102×C₅₃	C₂³	1	2	yes	—
274	#102×C₅₃	C₂³	1	2	yes	—
275	#102×C₅₃	C₂³	1	2	yes	—
276	#102×C₅₃	C₂³	1	2	yes	—
277	#102×C₅₃	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
280	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
281	#97×C₅₃	C₂³	1	2	yes	—
282	#97×C₅₃	C₂³	1	2	yes	—
283	C₄×C₈×C₅₃	C₂³	1	2	yes	—
284	C₂⁴×C₅₃	—	2	1	no	—
285	#41×C₅₃	—	2	2	no	—
286	#41×C₅₃	—	4	1	no	—
287	#41×C₅₃	—	4	2	no	—
288	#41×C₅₃	—	4	2	no	—
289	C₂×Q₈×C₅₃	—	2	2	no	—
290	C₂×Q₈×C₅₃	—	2	1	no	—
291	C₂×Q₈×C₅₃	—	2	2	no	—
292	C₂×Q₈×C₅₃	—	2	1	no	—
293	C₂×Q₈×C₅₃	—	2	2	no	—
294	C₂×Q₈×C₅₃	—	2	1	no	—
295	C₂×Q₈×C₅₃	—	2	4	no	—
296	C₂×Q₈×C₅₃	—	4	2	no	—
297	C₂×Q₈×C₅₃	—	4	2	no	—
298	C₂×Q₈×C₅₃	—	4	1	no	—
299	C₂×Q₈×C₅₃	—	4	1	no	—
300	C₂×Q₈×C₅₃	—	4	2	no	—
301	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
302	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
303	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
305	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₅₃	—	2	1	no	—
307	C₂×D₄×C₅₃	—	2	2	no	—
308	C₂×D₄×C₅₃	—	2	2	no	—
309	C₂×D₄×C₅₃	—	2	2	no	—
310	C₂×D₄×C₅₃	—	2	1	no	—
311	C₂×D₄×C₅₃	—	4	1	no	—
312	C₂×D₄×C₅₃	—	4	1	no	—
313	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
314	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
315	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
316	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₅₃	—	2	2	no	—
318	C₂²×C₄×C₅₃	—	2	1	no	—
319	C₂²×C₄×C₅₃	—	2	2	no	—
320	C₂²×C₄×C₅₃	—	2	1	no	—
321	C₂²×C₄×C₅₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
329	Q₁₆×C₅₃	—	2	4	no	—
330	Q₁₆×C₅₃	—	2	4	no	—
331	Q₁₆×C₅₃	—	4	2	no	—
332	Q₁₆×C₅₃	—	4	2	no	—
333	Q₁₆×C₅₃	—	4	2	no	—
334	Q₁₆×C₅₃	—	4	2	no	—
335	SD₁₆×C₅₃	—	2	4	no	—
336	SD₁₆×C₅₃	—	4	2	no	—
337	SD₁₆×C₅₃	—	4	2	no	—
338	SD₁₆×C₅₃	—	4	2	no	—
339	SD₁₆×C₅₃	—	4	2	no	—
340	D₈×C₅₃	—	4	2	no	—
341	M₁₆×C₅₃	—	4	1	no	—
342	M₁₆×C₅₃	—	4	1	no	—
343	M₁₆×C₅₃	—	4	2	no	—
344	C₂×C₈×C₅₃	—	4	2	no	—
345	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
346	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
347	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
348	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
349	C₄⋊C₄×C₅₃	—	2	1	no	—
350	C₄⋊C₄×C₅₃	—	2	1	no	—
351	C₄⋊C₄×C₅₃	—	2	1	no	—
352	C₄⋊C₄×C₅₃	—	2	1	no	—
353	C₄⋊C₄×C₅₃	—	2	2	no	—
354	C₄⋊C₄×C₅₃	—	2	2	no	—
355	C₄⋊C₄×C₅₃	—	2	2	no	—
356	C₄⋊C₄×C₅₃	—	2	2	no	—
357	C₄⋊C₄×C₅₃	—	2	1	no	—
358	C₄⋊C₄×C₅₃	—	2	1	no	—
359	C₄⋊C₄×C₅₃	—	2	2	no	—
360	C₄⋊C₄×C₅₃	—	2	2	no	—
361	C₄⋊C₄×C₅₃	—	2	2	no	—
362	C₄⋊C₄×C₅₃	—	2	2	no	—
363	C₄⋊C₄×C₅₃	—	2	1	no	—
364	C₄⋊C₄×C₅₃	—	2	1	no	—
365	C₄⋊C₄×C₅₃	—	2	2	no	—
366	C₄⋊C₄×C₅₃	—	2	2	no	—
367	C₄⋊C₄×C₅₃	—	2	2	no	—
368	C₄⋊C₄×C₅₃	—	2	2	no	—
369	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
370	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
371	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
372	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
373	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
377	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
379	C₂²⋊C₄×C₅₃	—	2	2	no	—
380	C₂²⋊C₄×C₅₃	—	2	2	no	—
381	C₂²⋊C₄×C₅₃	—	2	2	no	—
382	C₂²⋊C₄×C₅₃	—	2	1	no	—
383	C₂²⋊C₄×C₅₃	—	2	2	no	—
384	C₂²⋊C₄×C₅₃	—	2	2	no	—
385	C₂²⋊C₄×C₅₃	—	2	2	no	—
386	C₂²⋊C₄×C₅₃	—	2	2	no	—
387	C₂²⋊C₄×C₅₃	—	2	2	no	—
388	C₂²⋊C₄×C₅₃	—	2	2	no	—
389	C₂²⋊C₄×C₅₃	—	2	2	no	—
390	C₂²⋊C₄×C₅₃	—	2	2	no	—
391	C₂²⋊C₄×C₅₃	—	2	1	no	—
392	C₂²⋊C₄×C₅₃	—	2	1	no	—
393	C₂²⋊C₄×C₅₃	—	2	2	no	—
394	C₂²⋊C₄×C₅₃	—	2	2	no	—
395	C₂²⋊C₄×C₅₃	—	2	2	no	—
396	C₂²⋊C₄×C₅₃	—	2	2	no	—
397	C₂²⋊C₄×C₅₃	—	2	2	no	—
398	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
399	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
400	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
401	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
402	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
403	C₄²×C₅₃	—	2	1	no	—
404	C₄²×C₅₃	—	2	1	no	—
405	C₄²×C₅₃	—	2	1	no	—
406	C₄²×C₅₃	—	2	2	no	—
407	C₄²×C₅₃	—	2	2	no	—
408	C₄²×C₅₃	—	2	2	no	—
409	C₄²×C₅₃	—	2	2	no	—
410	C₄²×C₅₃	—	2	2	no	—
411	C₄²×C₅₃	—	2	2	no	—
412	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
413	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
414	C₄²×C₅₃	C₂⁴	1	2	yes	—
415	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂³×C₅₃	—	2	1	no	—
418	C₂³×C₅₃	—	2	2	no	—
419	C₂³×C₅₃	—	4	2	no	—
420	C₂³×C₅₃	—	8	1	no	—
421	C₂³×C₅₃	—	8	1	no	—
422	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
423	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
424	Q₈×C₅₃	—	2	1	no	—
425	Q₈×C₅₃	—	2	2	no	—
426	Q₈×C₅₃	—	2	2	no	—
427	Q₈×C₅₃	—	2	2	no	—
428	Q₈×C₅₃	—	2	2	no	—
429	Q₈×C₅₃	—	2	2	no	—
430	Q₈×C₅₃	—	2	2	no	—
431	Q₈×C₅₃	—	4	1	no	—
432	Q₈×C₅₃	—	4	4	no	—
433	Q₈×C₅₃	—	8	1	no	—
434	Q₈×C₅₃	—	8	1	no	—
435	Q₈×C₅₃	—	8	2	no	—
436	Q₈×C₅₃	—	8	1	no	—
437	Q₈×C₅₃	—	8	2	no	—
438	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
439	D₄×C₅₃	—	2	2	no	—
440	D₄×C₅₃	—	2	1	no	—
441	D₄×C₅₃	—	2	2	no	—
442	D₄×C₅₃	—	2	1	no	—
443	D₄×C₅₃	—	4	1	no	—
444	D₄×C₅₃	—	4	2	no	—
445	D₄×C₅₃	—	4	2	no	—
446	D₄×C₅₃	—	8	1	no	—
447	D₄×C₅₃	—	8	2	no	—
448	D₄×C₅₃	—	8	2	no	—
449	D₄×C₅₃	—	8	2	no	—
450	C₂×C₄×C₅₃	—	2	1	no	—
451	C₂×C₄×C₅₃	—	2	1	no	—
452	C₂×C₄×C₅₃	—	2	2	no	—
453	C₂×C₄×C₅₃	—	2	1	no	—
454	C₂×C₄×C₅₃	—	2	2	no	—
455	C₂×C₄×C₅₃	—	2	2	no	—
456	C₂×C₄×C₅₃	—	2	2	no	—
457	C₂×C₄×C₅₃	—	2	2	no	—
458	C₂×C₄×C₅₃	—	2	1	no	—
459	C₂×C₄×C₅₃	—	2	2	no	—
460	C₂×C₄×C₅₃	—	2	1	no	—
461	C₂×C₄×C₅₃	—	2	2	no	—
462	C₂×C₄×C₅₃	—	4	1	no	—
463	C₂×C₄×C₅₃	—	4	1	no	—
464	C₂×C₄×C₅₃	—	4	2	no	—
465	C₂×C₄×C₅₃	—	4	4	no	—
466	C₂×C₄×C₅₃	—	4	2	no	—
467	C₂×C₄×C₅₃	—	8	1	no	—
468	C₂×C₄×C₅₃	—	8	2	no	—
469	C₂×C₄×C₅₃	—	8	2	no	—
470	C₂×C₄×C₅₃	—	8	2	no	—
471	C₂×C₄×C₅₃	—	8	1	no	—
472	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
477	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
481	C₈×C₅₃	—	2	2	no	—
482	C₈×C₅₃	—	2	2	no	—
483	C₈×C₅₃	—	2	2	no	—
484	C₈×C₅₃	—	2	2	no	—
485	#62091	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
486	C₂²×C₅₃	—	2	1	no	—
487	C₂²×C₅₃	—	2	1	no	—
488	C₂²×C₅₃	—	2	2	no	—
489	C₂²×C₅₃	—	2	2	no	—
490	C₂²×C₅₃	—	2	2	no	—
491	C₂²×C₅₃	—	2	1	no	—
492	C₂²×C₅₃	—	4	1	no	—
493	C₂²×C₅₃	—	4	1	no	—
494	C₂²×C₅₃	—	4	2	no	—
495	C₂²×C₅₃	—	4	2	no	—
496	C₂²×C₅₃	—	4	1	no	—
497	C₂²×C₅₃	—	4	2	no	—
498	C₂²×C₅₃	—	16	2	no	—
499	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
500	C₄×C₅₃	—	2	1	no	—
501	C₄×C₅₃	—	2	1	no	—
502	C₄×C₅₃	—	2	1	no	—
503	C₄×C₅₃	—	2	1	no	—
504	C₄×C₅₃	—	2	2	no	—
505	C₄×C₅₃	—	2	2	no	—
506	C₄×C₅₃	—	2	1	no	—
507	C₄×C₅₃	—	2	2	no	—
508	C₄×C₅₃	—	2	2	no	—
509	C₄×C₅₃	—	4	1	no	—
510	C₄×C₅₃	—	4	2	no	—
511	C₄×C₅₃	—	4	1	no	—
512	C₄×C₅₃	—	4	2	no	—
513	C₄×C₅₃	—	4	2	no	—
514	C₄×C₅₃	—	4	2	no	—
515	C₄×C₅₃	—	4	2	no	—
516	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
517	C₄×C₅₃	#585	1	1	yes	characteristic
518	#3561	C₂×C₅₃	1	1	yes	characteristic, complemented
519	#3518	C₂×C₅₃	1	1	yes	characteristic, complemented
520	#3402	C₂×C₅₃	1	2	yes	complemented
521	#3369	C₂×C₅₃	1	2	yes	complemented
522	#3328	C₂×C₅₃	1	2	yes	complemented
523	#3321	C₂×C₅₃	1	2	yes	complemented
524	#3311	C₂×C₅₃	1	2	yes	complemented
525	#3275	C₂×C₅₃	1	2	yes	complemented
526	#3270	C₂×C₅₃	1	2	yes	complemented
527	#3270	C₂×C₅₃	1	2	yes	complemented
528	#3263	C₂×C₅₃	1	2	yes	complemented
529	#3255	C₂×C₅₃	1	1	yes	characteristic, complemented
530	#3225	C₂×C₅₃	1	2	yes	complemented
531	#3215	C₂×C₅₃	1	1	yes	characteristic, complemented
532	#3121	C₂×C₅₃	1	2	yes	complemented
533	#3116	C₂×C₅₃	1	1	yes	characteristic, complemented
534	#3044	C₂×C₅₃	1	2	yes	complemented
535	#3040	C₂×C₅₃	1	1	yes	characteristic, complemented
536	#2995	C₂×C₅₃	1	1	yes	characteristic, complemented
537	C₂×C₅₃	—	4	2	no	—
538	C₂×C₅₃	—	4	1	no	—
539	C₂×C₅₃	—	8	1	no	—
540	C₂×C₅₃	—	8	2	no	—
541	C₂×C₅₃	#3488	1	1	yes	characteristic
542	C₂×C₅₃	#3586	1	1	yes	characteristic
543	C₂×C₅₃	#3586	1	1	yes	characteristic
544	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
545	C₂×#137	C₂²×C₅₃	1	2	yes	—
546	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
547	C₂²×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
548	#563	—	2	1	no	—
549	#562	—	2	1	no	—
550	Q₈²	C₂²×C₅₃	1	1	yes	characteristic, complemented
551	#556	—	2	2	no	—
552	#556	—	2	1	no	—
553	#556	C₂²×C₅₃	1	2	yes	—
554	#556	C₂²×C₅₃	1	2	yes	—
555	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
556	#555	—	2	1	no	—
557	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
558	#551	—	2	2	no	—
559	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
560	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
561	#548	C₂²×C₅₃	1	2	yes	—
562	#548	C₂²×C₅₃	1	2	yes	—
563	#546	C₂²×C₅₃	1	2	yes	—
564	#543	—	2	1	no	—
565	#542	—	2	2	no	—
566	#542	—	2	2	no	—
567	#542	C₂²×C₅₃	1	2	yes	—
568	#542	C₂²×C₅₃	1	2	yes	complemented
569	#538	—	2	1	no	—
570	#536	C₂²×C₅₃	1	2	yes	—
571	#533	—	2	1	no	—
572	#533	C₂²×C₅₃	1	1	yes	characteristic
573	#533	C₂²×C₅₃	1	1	yes	characteristic
574	#529	—	2	1	no	—
575	#529	C₂²×C₅₃	1	1	yes	characteristic
576	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
577	#519	C₂²×C₅₃	1	2	yes	complemented
578	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
579	#497	C₂²×C₅₃	1	2	yes	—
580	#497	C₂²×C₅₃	1	2	yes	complemented
581	#495	C₂²×C₅₃	1	2	yes	—
582	#489	C₂²×C₅₃	1	2	yes	—
583	#489	C₂²×C₅₃	1	2	yes	—
584	#487	C₂²×C₅₃	1	2	yes	complemented
585	#485	C₂²×C₅₃	1	2	yes	—
586	#485	C₂²×C₅₃	1	2	yes	complemented
587	#482	C₂²×C₅₃	1	2	yes	—
588	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
589	#476	C₂²×C₅₃	1	2	yes	—
590	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
591	#475	C₂²×C₅₃	1	2	yes	complemented
592	#475	C₂²×C₅₃	1	2	yes	complemented
593	#475	C₂²×C₅₃	1	2	yes	complemented
594	#470	C₂²×C₅₃	1	2	yes	—
595	#470	C₂²×C₅₃	1	2	yes	—
596	#470	C₂²×C₅₃	1	2	yes	complemented
597	#469	C₂²×C₅₃	1	2	yes	—
598	#465	C₂²×C₅₃	1	2	yes	—
599	#465	C₂²×C₅₃	1	2	yes	complemented
600	#464	C₂²×C₅₃	1	2	yes	—
601	#464	C₂²×C₅₃	1	2	yes	—
602	#464	C₂²×C₅₃	1	2	yes	—
603	#464	C₂²×C₅₃	1	2	yes	—
604	#464	C₂²×C₅₃	1	2	yes	—
605	#464	C₂²×C₅₃	1	2	yes	—
606	#464	C₂²×C₅₃	1	2	yes	complemented
607	#463	C₂²×C₅₃	1	2	yes	—
608	#463	C₂²×C₅₃	1	2	yes	—
609	#463	C₂²×C₅₃	1	2	yes	—
610	#462	C₂²×C₅₃	1	2	yes	complemented
611	#462	C₂²×C₅₃	1	2	yes	complemented
612	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
613	#462	C₂²×C₅₃	1	2	yes	complemented
614	#462	C₂²×C₅₃	1	2	yes	complemented
615	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
616	#452	C₂²×C₅₃	1	2	yes	—
617	#452	C₂²×C₅₃	1	2	yes	—
618	#451	C₂²×C₅₃	1	2	yes	—
619	#451	C₂²×C₅₃	1	2	yes	complemented
620	#451	C₂²×C₅₃	1	2	yes	complemented
621	#450	C₂²×C₅₃	1	2	yes	—
622	#449	C₂²×C₅₃	1	2	yes	—
623	#448	C₂²×C₅₃	1	2	yes	—
624	#448	C₂²×C₅₃	1	2	yes	complemented
625	#446	C₂²×C₅₃	1	2	yes	complemented
626	#441	C₂²×C₅₃	1	2	yes	complemented
627	#441	C₂²×C₅₃	1	2	yes	complemented
628	#440	C₂²×C₅₃	1	2	yes	—
629	#440	C₂²×C₅₃	1	2	yes	complemented
630	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
631	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
632	#436	C₂²×C₅₃	1	2	yes	—
633	#435	C₂²×C₅₃	1	2	yes	—
634	#435	C₂²×C₅₃	1	2	yes	complemented
635	#433	C₂²×C₅₃	1	2	yes	complemented
636	#432	C₂²×C₅₃	1	1	yes	characteristic
637	#424	C₂²×C₅₃	1	2	yes	complemented
638	#423	C₂²×C₅₃	1	1	yes	characteristic
639	#419	C₂²×C₅₃	1	1	yes	characteristic
640	#419	C₂²×C₅₃	1	2	yes	complemented
641	#418	C₂²×C₅₃	1	1	yes	characteristic
642	#416	C₂²×C₅₃	1	2	yes	—
643	C₅₃	#62091	1	1	yes	characteristic, direct product factor, Sylow
644	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
645	C₂×#41	C₂³×C₅₃	1	2	yes	—
646	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
647	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
648	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
649	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
650	#137	—	4	4	no	—
651	#137	—	4	2	no	—
652	AGL(1,ℤ/8)	—	4	2	no	—
653	C₂×Q₁₆	—	4	4	no	—
654	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
655	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
656	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
657	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
658	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
659	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
660	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
661	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
662	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
663	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
664	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
665	C₂×D₈	C₂³×C₅₃	1	2	yes	—
666	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
667	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
668	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
669	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
670	C₄⋊Q₈	—	2	1	no	—
671	C₄⋊Q₈	—	2	1	no	—
672	C₄⋊Q₈	—	2	2	no	—
673	C₄⋊Q₈	—	2	2	no	—
674	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
675	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
676	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
677	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
678	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
679	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
680	#126	—	2	2	no	—
681	#126	—	2	2	no	—
682	#126	—	2	2	no	—
683	#126	—	2	2	no	—
684	#126	—	2	2	no	—
685	#126	—	2	2	no	—
686	#126	—	2	2	no	—
687	#126	D₄×C₅₃	1	2	yes	—
688	#125	—	2	1	no	—
689	#125	—	2	1	no	—
690	#125	D₄×C₅₃	1	1	yes	characteristic
691	#124	—	2	2	no	—
692	#124	—	2	2	no	—
693	#124	—	2	2	no	—
694	#124	—	2	2	no	—
695	#124	—	2	2	no	—
696	#124	—	2	2	no	—
697	#124	—	2	1	no	—
698	#124	—	2	1	no	—
699	#124	D₄×C₅₃	1	1	yes	characteristic
700	#124	C₂³×C₅₃	1	2	yes	—
701	#124	C₂³×C₅₃	1	2	yes	—
702	#124	C₂³×C₅₃	1	2	yes	—
703	#124	C₂³×C₅₃	1	2	yes	—
704	#123	—	2	2	no	—
705	#123	—	2	2	no	—
706	#123	—	2	2	no	—
707	#123	—	2	2	no	—
708	#123	—	2	2	no	—
709	#123	D₄×C₅₃	1	2	yes	—
710	C₂²⋊Q₈	—	2	1	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	1	no	—
713	C₂²⋊Q₈	—	2	1	no	—
714	C₂²⋊Q₈	—	2	2	no	—
715	C₂²⋊Q₈	—	2	2	no	—
716	C₂²⋊Q₈	—	2	2	no	—
717	C₂²⋊Q₈	—	2	2	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
724	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
725	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
726	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
727	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
728	#121	—	2	1	no	—
729	#121	—	2	2	no	—
730	#121	—	2	2	no	—
731	#121	—	2	2	no	—
732	#121	D₄×C₅₃	1	1	yes	characteristic
733	#121	C₂³×C₅₃	1	2	yes	—
734	#121	C₂³×C₅₃	1	2	yes	—
735	#120	—	2	2	no	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	2	no	—
738	C₄×Q₈	—	2	2	no	—
739	C₄×Q₈	—	2	2	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	—	2	1	no	—
742	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
743	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
744	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
745	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
746	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
747	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
748	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
749	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
750	C₄×D₄	—	2	1	no	—
751	C₄×D₄	—	2	2	no	—
752	C₄×D₄	—	2	1	no	—
753	C₄×D₄	—	2	1	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
757	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
758	C₄×D₄	C₂³×C₅₃	1	2	yes	—
759	C₄×D₄	C₂³×C₅₃	1	2	yes	—
760	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
761	#117	—	2	1	no	—
762	#117	—	2	1	no	—
763	#117	—	2	1	no	—
764	#117	—	2	1	no	—
765	#117	—	2	2	no	—
766	#117	—	2	2	no	—
767	#117	—	2	2	no	—
768	#117	—	2	1	no	—
769	#117	C₂³×C₅₃	1	1	yes	characteristic
770	#117	C₂³×C₅₃	1	2	yes	—
771	#117	C₂³×C₅₃	1	2	yes	—
772	C₂×C₂²⋊C₄	—	2	1	no	—
773	C₂×C₂²⋊C₄	—	2	1	no	—
774	C₂×C₂²⋊C₄	—	2	2	no	—
775	C₂×C₄²	—	2	1	no	—
776	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
777	#107	C₂³×C₅₃	1	2	yes	—
778	#106	C₂³×C₅₃	1	2	yes	—
779	#106	C₂³×C₅₃	1	2	yes	—
780	#106	C₂³×C₅₃	1	2	yes	—
781	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
782	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
783	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
784	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
785	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
786	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
787	#103	C₂³×C₅₃	1	2	yes	—
788	#103	C₂³×C₅₃	1	2	yes	—
789	#103	C₂³×C₅₃	1	2	yes	—
790	#103	C₂³×C₅₃	1	2	yes	—
791	#103	C₂³×C₅₃	1	2	yes	—
792	#103	C₂³×C₅₃	1	2	yes	—
793	#103	C₂³×C₅₃	1	2	yes	—
794	#103	C₂³×C₅₃	1	2	yes	—
795	#103	C₂³×C₅₃	1	2	yes	—
796	#103	C₂³×C₅₃	1	2	yes	—
797	#103	C₂³×C₅₃	1	2	yes	—
798	#102	C₂³×C₅₃	1	2	yes	—
799	#102	C₂³×C₅₃	1	2	yes	—
800	#102	C₂³×C₅₃	1	2	yes	—
801	#102	C₂³×C₅₃	1	2	yes	—
802	#102	C₂³×C₅₃	1	2	yes	—
803	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
804	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
805	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
806	#97	C₂³×C₅₃	1	2	yes	—
807	#97	C₂³×C₅₃	1	2	yes	—
808	C₄×C₈	C₂³×C₅₃	1	2	yes	—
809	C₂⁴	—	2	1	no	—
810	#41	—	2	2	no	—
811	#41	—	4	1	no	—
812	#41	—	4	2	no	—
813	#41	—	4	2	no	—
814	C₂×Q₈	—	2	2	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	2	no	—
818	C₂×Q₈	—	2	2	no	—
819	C₂×Q₈	—	2	1	no	—
820	C₂×Q₈	—	2	4	no	—
821	C₂×Q₈	—	4	2	no	—
822	C₂×Q₈	—	4	2	no	—
823	C₂×Q₈	—	4	1	no	—
824	C₂×Q₈	—	4	1	no	—
825	C₂×Q₈	—	4	2	no	—
826	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
827	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
828	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
829	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
830	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	4	1	no	—
837	C₂×D₄	—	4	1	no	—
838	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
839	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
840	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
841	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
851	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
854	Q₁₆	—	2	4	no	—
855	Q₁₆	—	2	4	no	—
856	Q₁₆	—	4	2	no	—
857	Q₁₆	—	4	2	no	—
858	Q₁₆	—	4	2	no	—
859	Q₁₆	—	4	2	no	—
860	SD₁₆	—	2	4	no	—
861	SD₁₆	—	4	2	no	—
862	SD₁₆	—	4	2	no	—
863	SD₁₆	—	4	2	no	—
864	SD₁₆	—	4	2	no	—
865	D₈	—	4	2	no	—
866	M₁₆	—	4	1	no	—
867	M₁₆	—	4	1	no	—
868	M₁₆	—	4	2	no	—
869	C₂×C₈	—	4	2	no	—
870	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
871	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
872	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
873	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	1	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
895	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
896	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
897	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
898	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
899	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
900	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
901	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
902	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
903	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	1	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	1	no	—
917	C₂²⋊C₄	—	2	1	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
924	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
925	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
926	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
927	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
928	C₄²	—	2	1	no	—
929	C₄²	—	2	1	no	—
930	C₄²	—	2	1	no	—
931	C₄²	—	2	2	no	—
932	C₄²	—	2	2	no	—
933	C₄²	—	2	2	no	—
934	C₄²	—	2	2	no	—
935	C₄²	—	2	2	no	—
936	C₄²	—	2	2	no	—
937	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
938	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
939	C₄²	C₂⁴×C₅₃	1	2	yes	—
940	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
941	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
942	C₂³	—	2	1	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	4	2	no	—
945	C₂³	—	8	1	no	—
946	C₂³	—	8	1	no	—
947	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
948	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
949	Q₈	—	2	1	no	—
950	Q₈	—	2	2	no	—
951	Q₈	—	2	2	no	—
952	Q₈	—	2	2	no	—
953	Q₈	—	2	2	no	—
954	Q₈	—	2	2	no	—
955	Q₈	—	2	2	no	—
956	Q₈	—	4	1	no	—
957	Q₈	—	4	4	no	—
958	Q₈	—	8	1	no	—
959	Q₈	—	8	1	no	—
960	Q₈	—	8	2	no	—
961	Q₈	—	8	1	no	—
962	Q₈	—	8	2	no	—
963	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
964	D₄	—	2	1	no	—
965	D₄	—	2	2	no	—
966	D₄	—	2	1	no	—
967	D₄	—	2	2	no	—
968	D₄	—	4	1	no	—
969	D₄	—	4	2	no	—
970	D₄	—	4	2	no	—
971	D₄	—	8	1	no	—
972	D₄	—	8	2	no	—
973	D₄	—	8	2	no	—
974	D₄	—	8	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	4	1	no	—
988	C₂×C₄	—	4	1	no	—
989	C₂×C₄	—	4	2	no	—
990	C₂×C₄	—	4	4	no	—
991	C₂×C₄	—	4	2	no	—
992	C₂×C₄	—	8	1	no	—
993	C₂×C₄	—	8	2	no	—
994	C₂×C₄	—	8	2	no	—
995	C₂×C₄	—	8	2	no	—
996	C₂×C₄	—	8	1	no	—
997	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
998	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
999	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1000	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1001	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1003	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1004	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1005	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1006	C₈	—	2	2	no	—
1007	C₈	—	2	2	no	—
1008	C₈	—	2	2	no	—
1009	C₈	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	2	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	16	2	no	—
1023	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1024	C₄	—	2	1	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	1	no	—
1029	C₄	—	2	1	no	—
1030	C₄	—	2	1	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	2	no	—
1040	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1041	C₄	C₅₃×#585	1	1	yes	characteristic
1042	C₂	—	4	1	no	—
1043	C₂	—	4	2	no	—
1044	C₂	—	8	2	no	—
1045	C₂	—	8	1	no	—
1046	C₂	C₅₃×#3488	1	1	yes	characteristic
1047	C₂	C₅₃×#3586	1	1	yes	characteristic
1048	C₂	C₅₃×#3586	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 ◁ C₅₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3561	C₂	semidirect
2. C₅₃×#3518	C₂	semidirect
3. C₅₃×#3402	C₂	semidirect
4. C₅₃×#3369	C₂	semidirect
5. C₅₃×#3328	C₂	semidirect
6. C₅₃×#3321	C₂	semidirect
7. C₅₃×#3311	C₂	semidirect
8. C₅₃×#3275	C₂	semidirect
9. C₅₃×#3270	C₂	semidirect
10. C₅₃×#3270	C₂	semidirect
11. C₅₃×#3263	C₂	semidirect
12. C₅₃×#3255	C₂	semidirect
13. C₅₃×#3225	C₂	semidirect
14. C₅₃×#3215	C₂	semidirect
15. C₅₃×#3121	C₂	semidirect
16. C₅₃×#3116	C₂	semidirect
17. C₅₃×#3044	C₂	semidirect
18. C₅₃×#3040	C₂	semidirect
19. C₅₃×#2995	C₂	semidirect
23. C₂²×Q₁₆×C₅₃	C₂²	semidirect
26. Q₈²×C₅₃	C₂²	semidirect
31. C₅₃×#556	C₂²	semidirect
33. C₅₃×#555	C₂²	semidirect
36. D₄×Q₈×C₅₃	C₂²	semidirect
44. C₅₃×#542	C₂²	semidirect
53. C₅₃×#519	C₂²	semidirect
56. C₅₃×#497	C₂²	semidirect
60. C₅₃×#487	C₂²	semidirect
62. C₅₃×#485	C₂²	semidirect
64. C₅₃×#477	C₂²	semidirect
66. C₅₃×#476	C₂²	semidirect
67. C₅₃×#475	C₂²	semidirect
68. C₅₃×#475	C₂²	semidirect
69. C₅₃×#475	C₂²	semidirect
72. C₅₃×#470	C₂²	semidirect
75. C₅₃×#465	C₂²	semidirect
82. C₅₃×#464	C₂²	semidirect
86. C₅₃×#462	C₂²	semidirect
87. C₅₃×#462	C₂²	semidirect
88. C₅₃×#462	C₂²	semidirect
89. C₅₃×#462	C₂²	semidirect
90. C₅₃×#462	C₂²	semidirect
91. C₅₃×#461	C₂²	semidirect
95. C₅₃×#451	C₂²	semidirect
96. C₅₃×#451	C₂²	semidirect
100. C₅₃×#448	C₂²	semidirect
101. C₅₃×#446	C₂²	semidirect
102. C₅₃×#441	C₂²	semidirect
103. C₅₃×#441	C₂²	semidirect
105. C₅₃×#440	C₂²	semidirect
106. C₄×Q₁₆×C₅₃	C₂²	semidirect
110. C₅₃×#435	C₂²	semidirect
111. C₅₃×#433	C₂²	semidirect
113. C₅₃×#424	C₂²	semidirect
116. C₅₃×#419	C₂²	semidirect
485. #62091	C₅₃	direct (N × H)
518. #3561	C₂×C₅₃	semidirect
519. #3518	C₂×C₅₃	semidirect
520. #3402	C₂×C₅₃	semidirect
521. #3369	C₂×C₅₃	semidirect
522. #3328	C₂×C₅₃	semidirect
523. #3321	C₂×C₅₃	semidirect
524. #3311	C₂×C₅₃	semidirect
525. #3275	C₂×C₅₃	semidirect
526. #3270	C₂×C₅₃	semidirect
527. #3270	C₂×C₅₃	semidirect
528. #3263	C₂×C₅₃	semidirect
529. #3255	C₂×C₅₃	semidirect
530. #3225	C₂×C₅₃	semidirect
531. #3215	C₂×C₅₃	semidirect
532. #3121	C₂×C₅₃	semidirect
533. #3116	C₂×C₅₃	semidirect
534. #3044	C₂×C₅₃	semidirect
535. #3040	C₂×C₅₃	semidirect
536. #2995	C₂×C₅₃	semidirect
547. C₂²×Q₁₆	C₂²×C₅₃	semidirect
550. Q₈²	C₂²×C₅₃	semidirect
555. #556	C₂²×C₅₃	semidirect
557. #555	C₂²×C₅₃	semidirect
560. D₄×Q₈	C₂²×C₅₃	semidirect
568. #542	C₂²×C₅₃	semidirect
577. #519	C₂²×C₅₃	semidirect
580. #497	C₂²×C₅₃	semidirect
584. #487	C₂²×C₅₃	semidirect
586. #485	C₂²×C₅₃	semidirect
588. #477	C₂²×C₅₃	semidirect
590. #476	C₂²×C₅₃	semidirect
591. #475	C₂²×C₅₃	semidirect
592. #475	C₂²×C₅₃	semidirect
593. #475	C₂²×C₅₃	semidirect
596. #470	C₂²×C₅₃	semidirect
599. #465	C₂²×C₅₃	semidirect
606. #464	C₂²×C₅₃	semidirect
610. #462	C₂²×C₅₃	semidirect
611. #462	C₂²×C₅₃	semidirect
612. #462	C₂²×C₅₃	semidirect
613. #462	C₂²×C₅₃	semidirect
614. #462	C₂²×C₅₃	semidirect
615. #461	C₂²×C₅₃	semidirect
619. #451	C₂²×C₅₃	semidirect
620. #451	C₂²×C₅₃	semidirect
624. #448	C₂²×C₅₃	semidirect
625. #446	C₂²×C₅₃	semidirect
626. #441	C₂²×C₅₃	semidirect
627. #441	C₂²×C₅₃	semidirect
629. #440	C₂²×C₅₃	semidirect
630. C₄×Q₁₆	C₂²×C₅₃	semidirect
634. #435	C₂²×C₅₃	semidirect
635. #433	C₂²×C₅₃	semidirect
637. #424	C₂²×C₅₃	semidirect
640. #419	C₂²×C₅₃	semidirect
643. C₅₃	#62091	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3561	2
C₅₃×#3518	2
C₅₃×#3402	2
C₅₃×#3369	2
C₅₃×#3328	2
C₅₃×#3321	2
C₅₃×#3311	2
C₅₃×#3275	2
C₅₃×#3270	2
C₅₃×#3263	2
C₅₃×#3255	2
C₅₃×#3225	2
C₅₃×#3215	2
C₅₃×#3121	2
C₅₃×#3116	2
C₅₃×#3044	2
C₅₃×#3040	2
C₅₃×#2995	2
#62091	53

Subgroups — C53×#62091 #27269603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62091 #27269603