Subgroups — C₅₃×#60558 #27268070

Order 13568.

2570 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3114	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3110	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3109	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3105	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3101	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3100	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3092	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3077	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3036	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3003	C₂	1	2	yes	maximal, complemented
13	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	4	yes	maximal, complemented
14	C₅₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₅₃	—	2	1	no	—
17	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	4	yes	—
18	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
19	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
20	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
21	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
22	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
23	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
24	C₅₃×#529	—	2	1	no	—
25	C₅₃×#529	—	2	1	no	—
26	C₅₃×#529	—	2	1	no	—
27	C₅₃×#529	—	2	1	no	—
28	C₅₃×#529	C₂²	1	2	yes	complemented
29	C₅₃×#529	C₂²	1	2	yes	complemented
30	C₅₃×#525	—	2	1	no	—
31	C₅₃×#525	—	2	1	no	—
32	C₅₃×#525	C₂²	1	2	yes	—
33	C₄×#41×C₅₃	—	2	1	no	—
34	C₄×#41×C₅₃	—	2	1	no	—
35	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₅₃	—	2	1	no	—
37	C₂×C₄×D₄×C₅₃	—	2	1	no	—
38	C₂×C₄×D₄×C₅₃	—	2	1	no	—
39	C₂×C₄×D₄×C₅₃	—	2	1	no	—
40	C₂×C₄×D₄×C₅₃	—	2	1	no	—
41	C₂×C₄×D₄×C₅₃	—	2	1	no	—
42	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
45	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
48	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₅₃	—	2	1	no	—
50	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#484	C₂²	1	4	yes	complemented
52	C₅₃×#483	C₂²	1	4	yes	complemented
53	C₅₃×#481	C₂²	1	4	yes	complemented
54	C₅₃×#480	C₂²	1	4	yes	complemented
55	C₅₃×#478	C₂²	1	8	yes	complemented
56	C₅₃×#476	C₂²	1	4	yes	complemented
57	C₅₃×#474	C₂²	1	4	yes	complemented
58	C₅₃×#463	C₂²	1	8	yes	complemented
59	C₅₃×#461	C₂²	1	4	yes	complemented
60	C₅₃×#459	C₂²	1	4	yes	complemented
61	C₅₃×#450	C₂²	1	4	yes	—
62	C₅₃×#450	C₂²	1	4	yes	—
63	C₅₃×#447	C₂²	1	4	yes	—
64	C₅₃×#447	C₂²	1	4	yes	—
65	C₅₃×#442	C₂²	1	8	yes	complemented
66	C₅₃×#440	C₂²	1	8	yes	complemented
67	C₄×SD₁₆×C₅₃	C₂²	1	8	yes	complemented
68	C₄×D₈×C₅₃	C₂²	1	8	yes	complemented
69	C₅₃×#432	C₂²	1	2	yes	complemented
70	C₅₃×#432	C₂²	1	2	yes	complemented
71	C₅₃×#431	C₂²	1	2	yes	complemented
72	C₅₃×#431	C₂²	1	2	yes	complemented
73	C₅₃×#428	C₂²	1	4	yes	complemented
74	C₅₃×#423	C₂²	1	2	yes	complemented
75	C₅₃×#418	C₂²	1	4	yes	—
76	C₅₃×#417	C₂²	1	4	yes	complemented
77	C₅₃×#407	C₂²	1	2	yes	—
78	C₄×M₁₆×C₅₃	C₂²	1	2	yes	complemented
79	C₂⁵×C₅₃	—	2	1	no	—
80	C₂×#41×C₅₃	—	2	1	no	—
81	C₂×#41×C₅₃	—	2	1	no	—
82	C₂×#41×C₅₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₅₃	—	2	8	no	—
84	C₂²×D₄×C₅₃	—	2	1	no	—
85	C₂²×D₄×C₅₃	—	2	1	no	—
86	C₂²×D₄×C₅₃	—	2	1	no	—
87	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
89	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₅₃	—	2	1	no	—
91	C₂³×C₄×C₅₃	—	2	2	no	—
92	C₂³×C₄×C₅₃	—	2	2	no	—
93	C₂³×C₄×C₅₃	—	2	2	no	—
94	C₂³×C₄×C₅₃	—	2	2	no	—
95	C₂³×C₄×C₅₃	—	2	2	no	—
96	C₂³×C₄×C₅₃	—	2	2	no	—
97	C₂³×C₄×C₅₃	—	4	8	no	—
98	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
99	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
100	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
101	AGL(1,ℤ/8)×C₅₃	—	2	16	no	—
102	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	—
103	C₂×D₈×C₅₃	C₂³	1	8	yes	—
104	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
105	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
106	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
107	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
108	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
109	#126×C₅₃	—	2	2	no	—
110	#126×C₅₃	—	2	2	no	—
111	#125×C₅₃	—	2	1	no	—
112	#125×C₅₃	—	2	1	no	—
113	#125×C₅₃	C₂³	1	2	yes	complemented
114	#124×C₅₃	—	2	1	no	—
115	#124×C₅₃	—	2	1	no	—
116	#124×C₅₃	C₂³	1	2	yes	complemented
117	#123×C₅₃	—	2	2	no	—
118	#123×C₅₃	—	2	2	no	—
119	#123×C₅₃	—	2	2	no	—
120	C₂²⋊Q₈×C₅₃	—	2	1	no	—
121	C₂²⋊Q₈×C₅₃	—	2	1	no	—
122	C₂²⋊Q₈×C₅₃	—	2	1	no	—
123	C₂²⋊Q₈×C₅₃	—	2	1	no	—
124	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
125	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
126	#121×C₅₃	—	2	1	no	—
127	#121×C₅₃	—	2	1	no	—
128	#121×C₅₃	—	2	1	no	—
129	#121×C₅₃	—	2	1	no	—
130	#121×C₅₃	C₂³	1	2	yes	—
131	#121×C₅₃	C₂³	1	2	yes	—
132	#120×C₅₃	—	2	2	no	—
133	C₄×Q₈×C₅₃	—	2	1	no	—
134	C₄×Q₈×C₅₃	—	2	1	no	—
135	C₄×Q₈×C₅₃	—	2	1	no	—
136	C₄×Q₈×C₅₃	—	2	1	no	—
137	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
138	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
139	C₄×D₄×C₅₃	—	2	2	no	—
140	C₄×D₄×C₅₃	—	2	2	no	—
141	C₄×D₄×C₅₃	—	2	2	no	—
142	C₄×D₄×C₅₃	—	2	2	no	—
143	C₄×D₄×C₅₃	—	2	2	no	—
144	C₄×D₄×C₅₃	—	2	2	no	—
145	C₄×D₄×C₅₃	—	2	2	no	—
146	C₄×D₄×C₅₃	—	2	2	no	—
147	C₄×D₄×C₅₃	—	2	2	no	—
148	C₄×D₄×C₅₃	—	2	2	no	—
149	C₄×D₄×C₅₃	—	2	2	no	—
150	C₄×D₄×C₅₃	—	2	2	no	—
151	C₄×D₄×C₅₃	—	2	1	no	—
152	C₄×D₄×C₅₃	—	2	1	no	—
153	C₄×D₄×C₅₃	—	2	1	no	—
154	C₄×D₄×C₅₃	—	2	1	no	—
155	C₄×D₄×C₅₃	—	2	2	no	—
156	C₄×D₄×C₅₃	—	2	2	no	—
157	C₄×D₄×C₅₃	—	2	2	no	—
158	C₄×D₄×C₅₃	—	2	2	no	—
159	C₄×D₄×C₅₃	—	2	2	no	—
160	C₄×D₄×C₅₃	—	2	2	no	—
161	C₄×D₄×C₅₃	C₂³	1	4	yes	—
162	C₄×D₄×C₅₃	C₂³	1	4	yes	—
163	C₄×D₄×C₅₃	C₂³	1	4	yes	—
164	C₄×D₄×C₅₃	C₂³	1	4	yes	—
165	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
166	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
167	#117×C₅₃	—	2	2	no	—
168	#117×C₅₃	—	2	2	no	—
169	#117×C₅₃	—	2	2	no	—
170	#117×C₅₃	—	2	1	no	—
171	#117×C₅₃	—	2	1	no	—
172	#117×C₅₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
174	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
175	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
176	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
180	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
181	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
182	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
183	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
184	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
185	C₂×C₄²×C₅₃	—	2	2	no	—
186	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
198	#107×C₅₃	C₂³	1	8	yes	complemented
199	#106×C₅₃	C₂³	1	8	yes	complemented
200	C₄⋊C₈×C₅₃	C₂³	1	4	yes	complemented
201	C₄⋊C₈×C₅₃	C₂³	1	4	yes	complemented
202	#103×C₅₃	C₂³	1	8	yes	complemented
203	#102×C₅₃	C₂³	1	8	yes	—
204	#102×C₅₃	C₂³	1	8	yes	—
205	#102×C₅₃	C₂³	1	8	yes	complemented
206	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
207	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
208	#97×C₅₃	C₂³	1	4	yes	complemented
209	C₄×C₈×C₅₃	C₂³	1	4	yes	complemented
210	C₂⁴×C₅₃	—	2	8	no	—
211	C₂⁴×C₅₃	—	2	2	no	—
212	C₂⁴×C₅₃	—	2	2	no	—
213	C₂⁴×C₅₃	—	2	2	no	—
214	C₂⁴×C₅₃	—	4	4	no	—
215	C₂⁴×C₅₃	—	4	4	no	—
216	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
217	#41×C₅₃	—	2	8	no	—
218	#41×C₅₃	—	4	4	no	—
219	#41×C₅₃	—	4	4	no	—
220	C₂×Q₈×C₅₃	—	2	1	no	—
221	C₂×Q₈×C₅₃	—	2	1	no	—
222	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
223	C₂×D₄×C₅₃	—	2	8	no	—
224	C₂×D₄×C₅₃	—	2	8	no	—
225	C₂×D₄×C₅₃	—	2	8	no	—
226	C₂×D₄×C₅₃	—	2	8	no	—
227	C₂×D₄×C₅₃	—	2	8	no	—
228	C₂×D₄×C₅₃	—	2	2	no	—
229	C₂×D₄×C₅₃	—	2	2	no	—
230	C₂×D₄×C₅₃	—	2	2	no	—
231	C₂×D₄×C₅₃	—	2	2	no	—
232	C₂×D₄×C₅₃	—	2	2	no	—
233	C₂×D₄×C₅₃	—	2	2	no	—
234	C₂×D₄×C₅₃	—	2	1	no	—
235	C₂×D₄×C₅₃	—	2	1	no	—
236	C₂×D₄×C₅₃	—	2	4	no	—
237	C₂×D₄×C₅₃	#41	1	8	yes	complemented
238	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₅₃	—	2	4	no	—
241	C₂²×C₄×C₅₃	—	2	4	no	—
242	C₂²×C₄×C₅₃	—	2	2	no	—
243	C₂²×C₄×C₅₃	—	2	2	no	—
244	C₂²×C₄×C₅₃	—	2	2	no	—
245	C₂²×C₄×C₅₃	—	2	2	no	—
246	C₂²×C₄×C₅₃	—	2	2	no	—
247	C₂²×C₄×C₅₃	—	2	4	no	—
248	C₂²×C₄×C₅₃	—	2	4	no	—
249	C₂²×C₄×C₅₃	—	2	4	no	—
250	C₂²×C₄×C₅₃	—	2	2	no	—
251	C₂²×C₄×C₅₃	—	2	4	no	—
252	C₂²×C₄×C₅₃	—	4	2	no	—
253	C₂²×C₄×C₅₃	—	4	8	no	—
254	C₂²×C₄×C₅₃	—	4	8	no	—
255	C₂²×C₄×C₅₃	—	4	8	no	—
256	C₂²×C₄×C₅₃	—	4	8	no	—
257	C₂²×C₄×C₅₃	—	4	8	no	—
258	C₂²×C₄×C₅₃	—	4	4	no	—
259	C₂²×C₄×C₅₃	—	4	8	no	—
260	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
278	SD₁₆×C₅₃	—	2	16	no	—
279	D₈×C₅₃	—	2	16	no	—
280	M₁₆×C₅₃	—	2	8	no	—
281	C₂×C₈×C₅₃	C₂⁴	1	8	yes	—
282	C₄⋊C₄×C₅₃	—	2	2	no	—
283	C₄⋊C₄×C₅₃	—	2	2	no	—
284	C₄⋊C₄×C₅₃	—	2	2	no	—
285	C₄⋊C₄×C₅₃	—	2	1	no	—
286	C₄⋊C₄×C₅₃	—	2	1	no	—
287	C₄⋊C₄×C₅₃	—	2	1	no	—
288	C₄⋊C₄×C₅₃	—	2	1	no	—
289	C₄⋊C₄×C₅₃	—	2	2	no	—
290	C₄⋊C₄×C₅₃	—	2	2	no	—
291	C₄⋊C₄×C₅₃	—	2	2	no	—
292	C₄⋊C₄×C₅₃	—	2	2	no	—
293	C₄⋊C₄×C₅₃	—	2	2	no	—
294	C₄⋊C₄×C₅₃	—	2	2	no	—
295	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
296	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
298	C₂²⋊C₄×C₅₃	—	2	2	no	—
299	C₂²⋊C₄×C₅₃	—	2	2	no	—
300	C₂²⋊C₄×C₅₃	—	2	2	no	—
301	C₂²⋊C₄×C₅₃	—	2	4	no	—
302	C₂²⋊C₄×C₅₃	—	2	4	no	—
303	C₂²⋊C₄×C₅₃	—	2	4	no	—
304	C₂²⋊C₄×C₅₃	—	2	4	no	—
305	C₂²⋊C₄×C₅₃	—	2	2	no	—
306	C₂²⋊C₄×C₅₃	—	2	2	no	—
307	C₂²⋊C₄×C₅₃	—	2	2	no	—
308	C₂²⋊C₄×C₅₃	—	2	2	no	—
309	C₂²⋊C₄×C₅₃	—	2	2	no	—
310	C₂²⋊C₄×C₅₃	—	2	2	no	—
311	C₄²×C₅₃	—	2	2	no	—
312	C₄²×C₅₃	—	2	2	no	—
313	C₄²×C₅₃	—	2	2	no	—
314	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
327	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂³×C₅₃	—	2	2	no	—
331	C₂³×C₅₃	—	2	2	no	—
332	C₂³×C₅₃	—	2	2	no	—
333	C₂³×C₅₃	—	2	8	no	—
334	C₂³×C₅₃	—	2	8	no	—
335	C₂³×C₅₃	—	2	8	no	—
336	C₂³×C₅₃	—	2	4	no	—
337	C₂³×C₅₃	—	2	2	no	—
338	C₂³×C₅₃	—	4	4	no	—
339	C₂³×C₅₃	—	4	4	no	—
340	C₂³×C₅₃	—	4	32	no	—
341	C₂³×C₅₃	—	4	4	no	—
342	C₂³×C₅₃	—	4	4	no	—
343	C₂³×C₅₃	—	4	4	no	—
344	C₂³×C₅₃	—	4	4	no	—
345	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
346	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
347	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
348	Q₈×C₅₃	—	2	4	no	—
349	Q₈×C₅₃	—	4	2	no	—
350	Q₈×C₅₃	—	4	2	no	—
351	D₄×C₅₃	—	2	8	no	—
352	D₄×C₅₃	—	2	8	no	—
353	D₄×C₅₃	—	2	8	no	—
354	D₄×C₅₃	—	2	4	no	—
355	D₄×C₅₃	—	2	4	no	—
356	D₄×C₅₃	—	4	2	no	—
357	D₄×C₅₃	—	4	4	no	—
358	D₄×C₅₃	—	4	4	no	—
359	D₄×C₅₃	—	4	4	no	—
360	D₄×C₅₃	—	4	2	no	—
361	D₄×C₅₃	C₂×#41	1	8	yes	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	2	no	—
364	C₂×C₄×C₅₃	—	2	2	no	—
365	C₂×C₄×C₅₃	—	2	2	no	—
366	C₂×C₄×C₅₃	—	2	2	no	—
367	C₂×C₄×C₅₃	—	2	2	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	2	no	—
371	C₂×C₄×C₅₃	—	2	2	no	—
372	C₂×C₄×C₅₃	—	2	2	no	—
373	C₂×C₄×C₅₃	—	2	2	no	—
374	C₂×C₄×C₅₃	—	2	4	no	—
375	C₂×C₄×C₅₃	—	2	2	no	—
376	C₂×C₄×C₅₃	—	2	2	no	—
377	C₂×C₄×C₅₃	—	2	2	no	—
378	C₂×C₄×C₅₃	—	4	1	no	—
379	C₂×C₄×C₅₃	—	4	1	no	—
380	C₂×C₄×C₅₃	—	4	1	no	—
381	C₂×C₄×C₅₃	—	4	1	no	—
382	C₂×C₄×C₅₃	—	4	8	no	—
383	C₂×C₄×C₅₃	—	4	8	no	—
384	C₂×C₄×C₅₃	—	4	4	no	—
385	C₂×C₄×C₅₃	—	4	4	no	—
386	C₂×C₄×C₅₃	—	4	4	no	—
387	C₂×C₄×C₅₃	—	4	4	no	—
388	C₂×C₄×C₅₃	—	4	4	no	—
389	C₂×C₄×C₅₃	—	4	8	no	—
390	C₂×C₄×C₅₃	—	4	8	no	—
391	C₂×C₄×C₅₃	—	4	4	no	—
392	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	4	yes	complemented
393	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
405	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
406	C₈×C₅₃	—	2	8	no	—
407	#60558	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
408	C₂²×C₅₃	—	2	8	no	—
409	C₂²×C₅₃	—	2	1	no	—
410	C₂²×C₅₃	—	2	1	no	—
411	C₂²×C₅₃	—	2	1	no	—
412	C₂²×C₅₃	—	2	1	no	—
413	C₂²×C₅₃	—	2	1	no	—
414	C₂²×C₅₃	—	2	1	no	—
415	C₂²×C₅₃	—	2	8	no	—
416	C₂²×C₅₃	—	4	16	no	—
417	C₂²×C₅₃	—	4	16	no	—
418	C₂²×C₅₃	—	4	16	no	—
419	C₂²×C₅₃	—	4	4	no	—
420	C₂²×C₅₃	—	4	4	no	—
421	C₂²×C₅₃	—	4	2	no	—
422	C₂²×C₅₃	—	4	2	no	—
423	C₂²×C₅₃	—	4	2	no	—
424	C₂²×C₅₃	#525	1	2	yes	—
425	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
426	C₂²×C₅₃	#575	1	2	yes	—
427	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
428	C₄×C₅₃	—	2	1	no	—
429	C₄×C₅₃	—	2	1	no	—
430	C₄×C₅₃	—	2	1	no	—
431	C₄×C₅₃	—	2	1	no	—
432	C₄×C₅₃	—	2	1	no	—
433	C₄×C₅₃	—	2	1	no	—
434	C₄×C₅₃	—	2	1	no	—
435	C₄×C₅₃	—	2	1	no	—
436	C₄×C₅₃	—	4	2	no	—
437	C₄×C₅₃	—	4	4	no	—
438	C₄×C₅₃	—	4	2	no	—
439	C₄×C₅₃	—	4	2	no	—
440	C₄×C₅₃	#525	1	2	yes	—
441	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
442	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
443	C₄×C₅₃	C₂²×#41	1	2	yes	—
444	#3444	C₂×C₅₃	1	1	yes	characteristic, complemented
445	C₂²×C₄×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
446	#3114	C₂×C₅₃	1	4	yes	complemented
447	#3110	C₂×C₅₃	1	2	yes	complemented
448	#3109	C₂×C₅₃	1	2	yes	complemented
449	#3105	C₂×C₅₃	1	4	yes	complemented
450	#3101	C₂×C₅₃	1	2	yes	complemented
451	#3100	C₂×C₅₃	1	2	yes	complemented
452	#3092	C₂×C₅₃	1	2	yes	complemented
453	#3077	C₂×C₅₃	1	2	yes	complemented
454	#3036	C₂×C₅₃	1	2	yes	complemented
455	#3003	C₂×C₅₃	1	2	yes	complemented
456	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	4	yes	complemented
457	#2920	C₂×C₅₃	1	1	yes	characteristic, complemented
458	C₂×C₅₃	—	2	2	no	—
459	C₂×C₅₃	—	2	2	no	—
460	C₂×C₅₃	—	2	2	no	—
461	C₂×C₅₃	—	4	8	no	—
462	C₂×C₅₃	—	8	2	no	—
463	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
464	C₂×C₅₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
465	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
466	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
467	C₂⁴×C₄	—	2	1	no	—
468	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	4	yes	—
469	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
470	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
471	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
472	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
473	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
474	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
475	#529	—	2	1	no	—
476	#529	—	2	1	no	—
477	#529	—	2	1	no	—
478	#529	—	2	1	no	—
479	#529	C₂²×C₅₃	1	2	yes	complemented
480	#529	C₂²×C₅₃	1	2	yes	complemented
481	#525	—	2	1	no	—
482	#525	—	2	1	no	—
483	#525	C₂²×C₅₃	1	2	yes	—
484	C₄×#41	—	2	1	no	—
485	C₄×#41	—	2	1	no	—
486	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
487	C₂×C₄×D₄	—	2	1	no	—
488	C₂×C₄×D₄	—	2	1	no	—
489	C₂×C₄×D₄	—	2	1	no	—
490	C₂×C₄×D₄	—	2	1	no	—
491	C₂×C₄×D₄	—	2	1	no	—
492	C₂×C₄×D₄	—	2	1	no	—
493	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
494	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
495	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
496	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
497	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
498	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
499	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
500	C₂²×C₂²⋊C₄	—	2	1	no	—
501	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
502	#484	C₂²×C₅₃	1	4	yes	complemented
503	#483	C₂²×C₅₃	1	4	yes	complemented
504	#481	C₂²×C₅₃	1	4	yes	complemented
505	#480	C₂²×C₅₃	1	4	yes	complemented
506	#478	C₂²×C₅₃	1	8	yes	complemented
507	#476	C₂²×C₅₃	1	4	yes	complemented
508	#474	C₂²×C₅₃	1	4	yes	complemented
509	#463	C₂²×C₅₃	1	8	yes	complemented
510	#461	C₂²×C₅₃	1	4	yes	complemented
511	#459	C₂²×C₅₃	1	4	yes	complemented
512	#450	C₂²×C₅₃	1	4	yes	—
513	#450	C₂²×C₅₃	1	4	yes	—
514	#447	C₂²×C₅₃	1	4	yes	—
515	#447	C₂²×C₅₃	1	4	yes	—
516	#442	C₂²×C₅₃	1	8	yes	complemented
517	#440	C₂²×C₅₃	1	8	yes	complemented
518	C₄×SD₁₆	C₂²×C₅₃	1	8	yes	complemented
519	C₄×D₈	C₂²×C₅₃	1	8	yes	complemented
520	#432	C₂²×C₅₃	1	2	yes	complemented
521	#432	C₂²×C₅₃	1	2	yes	complemented
522	#431	C₂²×C₅₃	1	2	yes	complemented
523	#431	C₂²×C₅₃	1	2	yes	complemented
524	#428	C₂²×C₅₃	1	4	yes	complemented
525	#423	C₂²×C₅₃	1	2	yes	complemented
526	#418	C₂²×C₅₃	1	4	yes	—
527	#417	C₂²×C₅₃	1	4	yes	complemented
528	#407	C₂²×C₅₃	1	2	yes	—
529	C₄×M₁₆	C₂²×C₅₃	1	2	yes	complemented
530	C₅₃	#60558	1	1	yes	characteristic, direct product factor, Sylow
531	C₂⁵	—	2	1	no	—
532	C₂×#41	—	2	1	no	—
533	C₂×#41	—	2	1	no	—
534	C₂×#41	C₂³×C₅₃	1	2	yes	—
535	C₂²×D₄	—	2	8	no	—
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	—	2	1	no	—
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
540	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
541	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
542	C₂³×C₄	—	2	1	no	—
543	C₂³×C₄	—	2	2	no	—
544	C₂³×C₄	—	2	2	no	—
545	C₂³×C₄	—	2	2	no	—
546	C₂³×C₄	—	2	2	no	—
547	C₂³×C₄	—	2	2	no	—
548	C₂³×C₄	—	2	2	no	—
549	C₂³×C₄	—	4	8	no	—
550	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
551	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
553	AGL(1,ℤ/8)	—	2	16	no	—
554	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	—
555	C₂×D₈	C₂³×C₅₃	1	8	yes	—
556	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
557	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
558	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
559	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
560	#127	C₂³×C₅₃	1	1	yes	characteristic, complemented
561	#126	—	2	2	no	—
562	#126	—	2	2	no	—
563	#125	—	2	1	no	—
564	#125	—	2	1	no	—
565	#125	C₂³×C₅₃	1	2	yes	complemented
566	#124	—	2	1	no	—
567	#124	—	2	1	no	—
568	#124	C₂³×C₅₃	1	2	yes	complemented
569	#123	—	2	2	no	—
570	#123	—	2	2	no	—
571	#123	—	2	2	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
577	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
578	#121	—	2	1	no	—
579	#121	—	2	1	no	—
580	#121	—	2	1	no	—
581	#121	—	2	1	no	—
582	#121	C₂³×C₅₃	1	2	yes	—
583	#121	C₂³×C₅₃	1	2	yes	—
584	#120	—	2	2	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	C₂³×C₅₃	1	2	yes	complemented
590	C₄×Q₈	C₂³×C₅₃	1	2	yes	complemented
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	C₂³×C₅₃	1	4	yes	—
614	C₄×D₄	C₂³×C₅₃	1	4	yes	—
615	C₄×D₄	C₂³×C₅₃	1	4	yes	—
616	C₄×D₄	C₂³×C₅₃	1	4	yes	—
617	C₄×D₄	C₂³×C₅₃	1	2	yes	complemented
618	C₄×D₄	C₂³×C₅₃	1	2	yes	complemented
619	#117	—	2	1	no	—
620	#117	—	2	1	no	—
621	#117	—	2	2	no	—
622	#117	—	2	2	no	—
623	#117	—	2	2	no	—
624	#117	C₂³×C₅₃	1	2	yes	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
631	C₂×C₂²⋊C₄	—	2	2	no	—
632	C₂×C₂²⋊C₄	—	2	2	no	—
633	C₂×C₂²⋊C₄	—	2	2	no	—
634	C₂×C₂²⋊C₄	—	2	2	no	—
635	C₂×C₂²⋊C₄	—	2	2	no	—
636	C₂×C₂²⋊C₄	—	2	2	no	—
637	C₂×C₄²	—	2	2	no	—
638	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
639	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
640	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
641	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
642	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
643	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
650	#107	C₂³×C₅₃	1	8	yes	complemented
651	#106	C₂³×C₅₃	1	8	yes	complemented
652	C₄⋊C₈	C₂³×C₅₃	1	4	yes	complemented
653	C₄⋊C₈	C₂³×C₅₃	1	4	yes	complemented
654	#103	C₂³×C₅₃	1	8	yes	complemented
655	#102	C₂³×C₅₃	1	8	yes	—
656	#102	C₂³×C₅₃	1	8	yes	—
657	#102	C₂³×C₅₃	1	8	yes	complemented
658	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
659	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
660	#97	C₂³×C₅₃	1	4	yes	complemented
661	C₄×C₈	C₂³×C₅₃	1	4	yes	complemented
662	C₂⁴	—	2	8	no	—
663	C₂⁴	—	2	2	no	—
664	C₂⁴	—	2	2	no	—
665	C₂⁴	—	2	2	no	—
666	C₂⁴	—	4	4	no	—
667	C₂⁴	—	4	4	no	—
668	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
669	#41	—	2	8	no	—
670	#41	—	4	4	no	—
671	#41	—	4	4	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
675	C₂×D₄	—	2	8	no	—
676	C₂×D₄	—	2	8	no	—
677	C₂×D₄	—	2	8	no	—
678	C₂×D₄	—	2	8	no	—
679	C₂×D₄	—	2	8	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	#41×C₅₃	1	8	yes	complemented
690	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
691	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	8	no	—
706	C₂²×C₄	—	4	8	no	—
707	C₂²×C₄	—	4	8	no	—
708	C₂²×C₄	—	4	8	no	—
709	C₂²×C₄	—	4	8	no	—
710	C₂²×C₄	—	4	4	no	—
711	C₂²×C₄	—	4	8	no	—
712	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
723	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
725	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
726	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
730	SD₁₆	—	2	16	no	—
731	D₈	—	2	16	no	—
732	M₁₆	—	2	8	no	—
733	C₂×C₈	C₂⁴×C₅₃	1	8	yes	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
748	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
749	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
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	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
772	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
773	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
775	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
776	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
777	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
778	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
779	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
780	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
781	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	8	no	—
786	C₂³	—	2	8	no	—
787	C₂³	—	2	8	no	—
788	C₂³	—	2	4	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	4	4	no	—
791	C₂³	—	4	4	no	—
792	C₂³	—	4	32	no	—
793	C₂³	—	4	4	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	4	4	no	—
796	C₂³	—	4	4	no	—
797	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
798	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
799	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
800	Q₈	—	2	4	no	—
801	Q₈	—	4	2	no	—
802	Q₈	—	4	2	no	—
803	D₄	—	2	8	no	—
804	D₄	—	2	8	no	—
805	D₄	—	2	8	no	—
806	D₄	—	2	4	no	—
807	D₄	—	2	4	no	—
808	D₄	—	4	2	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	2	no	—
813	D₄	C₂×#41×C₅₃	1	8	yes	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	8	no	—
835	C₂×C₄	—	4	8	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	4	no	—
839	C₂×C₄	—	4	4	no	—
840	C₂×C₄	—	4	4	no	—
841	C₂×C₄	—	4	8	no	—
842	C₂×C₄	—	4	8	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	4	yes	complemented
845	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
847	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
852	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
855	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
856	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
857	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
858	C₈	—	2	8	no	—
859	C₂²	—	2	8	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	2	8	no	—
867	C₂²	—	4	16	no	—
868	C₂²	—	4	16	no	—
869	C₂²	—	4	16	no	—
870	C₂²	—	4	4	no	—
871	C₂²	—	4	4	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	C₅₃×#525	1	2	yes	—
876	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
877	C₂²	C₅₃×#575	1	2	yes	—
878	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	1	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	4	4	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	2	no	—
891	C₄	C₅₃×#525	1	2	yes	—
892	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
893	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
894	C₄	C₂²×#41×C₅₃	1	2	yes	—
895	C₂	—	2	2	no	—
896	C₂	—	2	2	no	—
897	C₂	—	2	2	no	—
898	C₂	—	4	8	no	—
899	C₂	—	8	2	no	—
900	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
901	C₂	C₂²×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
902	C₂	C₂×C₅₃×#575	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 ◁ C₂²×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3444	C₂	semidirect
2. C₂²×C₄×D₄×C₅₃	C₂	semidirect
3. C₅₃×#3114	C₂	semidirect
4. C₅₃×#3110	C₂	semidirect
5. C₅₃×#3109	C₂	semidirect
6. C₅₃×#3105	C₂	semidirect
7. C₅₃×#3101	C₂	semidirect
8. C₅₃×#3100	C₂	semidirect
9. C₅₃×#3092	C₂	semidirect
10. C₅₃×#3077	C₂	semidirect
11. C₅₃×#3036	C₂	semidirect
12. C₅₃×#3003	C₂	semidirect
13. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
14. C₅₃×#2920	C₂	semidirect
18. C₅₃×#533	C₂²	semidirect
19. C₅₃×#533	C₂²	semidirect
20. C₅₃×#533	C₂²	semidirect
21. C₅₃×#532	C₂²	semidirect
22. C₅₃×#532	C₂²	semidirect
23. C₅₃×#532	C₂²	semidirect
28. C₅₃×#529	C₂²	semidirect
29. C₅₃×#529	C₂²	semidirect
35. C₄×#41×C₅₃	C₂²	semidirect
51. C₅₃×#484	C₂²	semidirect
52. C₅₃×#483	C₂²	semidirect
53. C₅₃×#481	C₂²	semidirect
54. C₅₃×#480	C₂²	semidirect
55. C₅₃×#478	C₂²	semidirect
56. C₅₃×#476	C₂²	semidirect
57. C₅₃×#474	C₂²	semidirect
58. C₅₃×#463	C₂²	semidirect
59. C₅₃×#461	C₂²	semidirect
60. C₅₃×#459	C₂²	semidirect
65. C₅₃×#442	C₂²	semidirect
66. C₅₃×#440	C₂²	semidirect
67. C₄×SD₁₆×C₅₃	C₂²	semidirect
68. C₄×D₈×C₅₃	C₂²	semidirect
69. C₅₃×#432	C₂²	semidirect
70. C₅₃×#432	C₂²	semidirect
71. C₅₃×#431	C₂²	semidirect
72. C₅₃×#431	C₂²	semidirect
73. C₅₃×#428	C₂²	semidirect
74. C₅₃×#423	C₂²	semidirect
76. C₅₃×#417	C₂²	semidirect
78. C₄×M₁₆×C₅₃	C₂²	semidirect
105. C₄⋊Q₈×C₅₃	C₂³	semidirect
106. C₄⋊Q₈×C₅₃	C₂³	semidirect
107. C₄⋊Q₈×C₅₃	C₂³	semidirect
108. #127×C₅₃	C₂³	semidirect
113. #125×C₅₃	C₂³	semidirect
116. #124×C₅₃	C₂³	semidirect
137. C₄×Q₈×C₅₃	C₂³	semidirect
138. C₄×Q₈×C₅₃	C₂³	semidirect
165. C₄×D₄×C₅₃	C₂³	semidirect
166. C₄×D₄×C₅₃	C₂³	semidirect
198. #107×C₅₃	C₂³	semidirect
199. #106×C₅₃	C₂³	semidirect
200. C₄⋊C₈×C₅₃	C₂³	semidirect
201. C₄⋊C₈×C₅₃	C₂³	semidirect
202. #103×C₅₃	C₂³	semidirect
205. #102×C₅₃	C₂³	semidirect
208. #97×C₅₃	C₂³	semidirect
209. C₄×C₈×C₅₃	C₂³	semidirect
237. C₂×D₄×C₅₃	#41	semidirect
392. C₂×C₄×C₅₃	AGL(1,ℤ/8)	semidirect
407. #60558	C₅₃	direct (N × H)
444. #3444	C₂×C₅₃	semidirect
445. C₂²×C₄×D₄	C₂×C₅₃	semidirect
446. #3114	C₂×C₅₃	semidirect
447. #3110	C₂×C₅₃	semidirect
448. #3109	C₂×C₅₃	semidirect
449. #3105	C₂×C₅₃	semidirect
450. #3101	C₂×C₅₃	semidirect
451. #3100	C₂×C₅₃	semidirect
452. #3092	C₂×C₅₃	semidirect
453. #3077	C₂×C₅₃	semidirect
454. #3036	C₂×C₅₃	semidirect
455. #3003	C₂×C₅₃	semidirect
456. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
457. #2920	C₂×C₅₃	semidirect
469. #533	C₂²×C₅₃	semidirect
470. #533	C₂²×C₅₃	semidirect
471. #533	C₂²×C₅₃	semidirect
472. #532	C₂²×C₅₃	semidirect
473. #532	C₂²×C₅₃	semidirect
474. #532	C₂²×C₅₃	semidirect
479. #529	C₂²×C₅₃	semidirect
480. #529	C₂²×C₅₃	semidirect
486. C₄×#41	C₂²×C₅₃	semidirect
502. #484	C₂²×C₅₃	semidirect
503. #483	C₂²×C₅₃	semidirect
504. #481	C₂²×C₅₃	semidirect
505. #480	C₂²×C₅₃	semidirect
506. #478	C₂²×C₅₃	semidirect
507. #476	C₂²×C₅₃	semidirect
508. #474	C₂²×C₅₃	semidirect
509. #463	C₂²×C₅₃	semidirect
510. #461	C₂²×C₅₃	semidirect
511. #459	C₂²×C₅₃	semidirect
516. #442	C₂²×C₅₃	semidirect
517. #440	C₂²×C₅₃	semidirect
518. C₄×SD₁₆	C₂²×C₅₃	semidirect
519. C₄×D₈	C₂²×C₅₃	semidirect
520. #432	C₂²×C₅₃	semidirect
521. #432	C₂²×C₅₃	semidirect
522. #431	C₂²×C₅₃	semidirect
523. #431	C₂²×C₅₃	semidirect
524. #428	C₂²×C₅₃	semidirect
525. #423	C₂²×C₅₃	semidirect
527. #417	C₂²×C₅₃	semidirect
529. C₄×M₁₆	C₂²×C₅₃	semidirect
530. C₅₃	#60558	direct (N × H)
557. C₄⋊Q₈	C₂³×C₅₃	semidirect
558. C₄⋊Q₈	C₂³×C₅₃	semidirect
559. C₄⋊Q₈	C₂³×C₅₃	semidirect
560. #127	C₂³×C₅₃	semidirect
565. #125	C₂³×C₅₃	semidirect
568. #124	C₂³×C₅₃	semidirect
589. C₄×Q₈	C₂³×C₅₃	semidirect
590. C₄×Q₈	C₂³×C₅₃	semidirect
617. C₄×D₄	C₂³×C₅₃	semidirect
618. C₄×D₄	C₂³×C₅₃	semidirect
650. #107	C₂³×C₅₃	semidirect
651. #106	C₂³×C₅₃	semidirect
652. C₄⋊C₈	C₂³×C₅₃	semidirect
653. C₄⋊C₈	C₂³×C₅₃	semidirect
654. #103	C₂³×C₅₃	semidirect
657. #102	C₂³×C₅₃	semidirect
660. #97	C₂³×C₅₃	semidirect
661. C₄×C₈	C₂³×C₅₃	semidirect
689. C₂×D₄	#41×C₅₃	semidirect
844. C₂×C₄	AGL(1,ℤ/8)×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3444	2
C₂²×C₄×D₄×C₅₃	2
C₅₃×#3114	2
C₅₃×#3110	2
C₅₃×#3109	2
C₅₃×#3105	2
C₅₃×#3101	2
C₅₃×#3100	2
C₅₃×#3092	2
C₅₃×#3077	2
C₅₃×#3036	2
C₅₃×#3003	2
C₄×AGL(1,ℤ/8)×C₅₃	2
C₅₃×#2920	2
#60558	53

Subgroups — C53×#60558 #27268070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60558 #27268070