Subgroups — C₅₃×#61160 #27268672

Order 13568.

2172 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3333	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3332	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3317	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3309	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3305	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3304	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3094	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3055	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3005	C₂	1	2	yes	maximal, complemented
15	C₄×#137×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×M₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2896	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₅₃	C₂²	1	2	yes	—
19	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
21	C₂²×M₁₆×C₅₃	C₂²	1	2	yes	—
22	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
23	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
24	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
25	C₅₃×#553	C₂²	1	2	yes	complemented
26	C₅₃×#552	—	2	1	no	—
27	C₅₃×#552	C₂²	1	2	yes	complemented
28	C₅₃×#551	—	2	2	no	—
29	C₅₃×#550	—	2	1	no	—
30	C₅₃×#550	—	2	1	no	—
31	C₅₃×#550	—	2	2	no	—
32	C₅₃×#550	C₂²	1	2	yes	—
33	C₅₃×#550	C₂²	1	4	yes	—
34	C₅₃×#550	C₂²	1	2	yes	—
35	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#546	—	2	1	no	—
37	C₅₃×#533	C₂²	1	1	yes	characteristic
38	C₂×#127×C₅₃	—	2	1	no	—
39	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#529	—	2	1	no	—
41	C₅₃×#529	—	2	2	no	—
42	C₅₃×#525	C₂²	1	2	yes	—
43	C₂×#121×C₅₃	—	2	2	no	—
44	C₂×#121×C₅₃	C₂²	1	2	yes	—
45	C₄×#41×C₅₃	—	2	1	no	—
46	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₅₃	—	2	1	no	—
49	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×#117×C₅₃	C₂²	1	2	yes	—
51	C₅₃×#490	C₂²	1	4	yes	complemented
52	C₅₃×#486	C₂²	1	2	yes	complemented
53	C₅₃×#486	C₂²	1	2	yes	complemented
54	C₅₃×#482	C₂²	1	4	yes	complemented
55	C₅₃×#482	C₂²	1	4	yes	complemented
56	C₅₃×#481	C₂²	1	4	yes	complemented
57	C₅₃×#480	C₂²	1	4	yes	complemented
58	C₅₃×#479	C₂²	1	4	yes	complemented
59	C₅₃×#477	C₂²	1	2	yes	complemented
60	C₅₃×#475	C₂²	1	2	yes	complemented
61	C₅₃×#469	C₂²	1	4	yes	complemented
62	C₅₃×#468	C₂²	1	4	yes	complemented
63	C₅₃×#466	C₂²	1	4	yes	complemented
64	C₅₃×#465	C₂²	1	4	yes	complemented
65	C₅₃×#460	C₂²	1	2	yes	complemented
66	C₅₃×#460	C₂²	1	2	yes	complemented
67	C₅₃×#459	C₂²	1	2	yes	complemented
68	C₅₃×#459	C₂²	1	2	yes	complemented
69	C₅₃×#452	C₂²	1	4	yes	complemented
70	C₅₃×#452	C₂²	1	4	yes	complemented
71	C₅₃×#449	C₂²	1	4	yes	complemented
72	C₅₃×#449	C₂²	1	4	yes	complemented
73	C₅₃×#441	C₂²	1	2	yes	complemented
74	C₅₃×#440	C₂²	1	2	yes	complemented
75	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
76	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
77	C₅₃×#436	C₂²	1	2	yes	complemented
78	C₅₃×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
80	C₅₃×#428	C₂²	1	1	yes	characteristic
81	C₅₃×#428	C₂²	1	2	yes	—
82	C₅₃×#423	C₂²	1	1	yes	characteristic
83	C₅₃×#419	C₂²	1	1	yes	characteristic
84	C₅₃×#419	C₂²	1	2	yes	—
85	C₅₃×#418	C₂²	1	2	yes	—
86	C₅₃×#418	C₂²	1	2	yes	—
87	C₅₃×#418	C₂²	1	2	yes	—
88	C₅₃×#417	C₂²	1	1	yes	characteristic
89	C₅₃×#417	C₂²	1	4	yes	complemented
90	C₅₃×#417	C₂²	1	4	yes	complemented
91	C₅₃×#416	C₂²	1	4	yes	complemented
92	C₅₃×#416	C₂²	1	4	yes	complemented
93	C₅₃×#407	C₂²	1	2	yes	—
94	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
95	C₂×#41×C₅₃	—	2	1	no	—
96	C₂×#41×C₅₃	—	2	2	no	—
97	C₂×#41×C₅₃	—	2	2	no	—
98	C₂×#41×C₅₃	—	2	8	no	—
99	C₂×#41×C₅₃	—	4	4	no	—
100	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
101	C₂×#41×C₅₃	C₂³	1	4	yes	—
102	C₂×#41×C₅₃	C₂³	1	4	yes	—
103	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₅₃	—	2	2	no	—
105	C₂²×D₄×C₅₃	—	2	2	no	—
106	C₂²×D₄×C₅₃	—	2	1	no	—
107	C₂²×D₄×C₅₃	—	2	1	no	—
108	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₅₃	—	2	2	no	—
111	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
112	#137×C₅₃	—	2	4	no	—
113	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
114	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
115	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
117	C₂×D₈×C₅₃	C₂³	1	4	yes	—
118	C₂×M₁₆×C₅₃	—	4	4	no	—
119	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
121	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
122	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
123	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
124	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
125	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
126	#127×C₅₃	—	2	1	no	—
127	#127×C₅₃	—	2	1	no	—
128	#127×C₅₃	—	2	2	no	—
129	#127×C₅₃	—	2	2	no	—
130	#127×C₅₃	—	2	4	no	—
131	#127×C₅₃	C₂³	1	2	yes	—
132	#127×C₅₃	C₂³	1	2	yes	—
133	#126×C₅₃	—	2	2	no	—
134	#126×C₅₃	—	2	2	no	—
135	#126×C₅₃	—	2	2	no	—
136	#125×C₅₃	—	2	2	no	—
137	#125×C₅₃	—	2	1	no	—
138	#125×C₅₃	C₂³	1	2	yes	—
139	#124×C₅₃	—	2	2	no	—
140	#124×C₅₃	—	2	1	no	—
141	#123×C₅₃	—	2	2	no	—
142	#123×C₅₃	—	2	2	no	—
143	#123×C₅₃	—	2	2	no	—
144	#123×C₅₃	—	2	2	no	—
145	C₂²⋊Q₈×C₅₃	—	2	1	no	—
146	C₂²⋊Q₈×C₅₃	—	2	2	no	—
147	C₂²⋊Q₈×C₅₃	—	2	1	no	—
148	C₂²⋊Q₈×C₅₃	—	2	1	no	—
149	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
150	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
151	#121×C₅₃	—	2	4	no	—
152	#121×C₅₃	—	2	4	no	—
153	#121×C₅₃	—	2	4	no	—
154	#121×C₅₃	—	2	4	no	—
155	#121×C₅₃	—	2	2	no	—
156	#121×C₅₃	—	2	1	no	—
157	#121×C₅₃	—	2	2	no	—
158	#121×C₅₃	—	2	2	no	—
159	#121×C₅₃	C₂³	1	4	yes	—
160	#121×C₅₃	C₂³	1	4	yes	—
161	#121×C₅₃	C₂³	1	2	yes	—
162	#121×C₅₃	C₂³	1	2	yes	—
163	#120×C₅₃	—	2	2	no	—
164	C₄×Q₈×C₅₃	—	2	1	no	—
165	C₄×Q₈×C₅₃	—	2	1	no	—
166	C₄×Q₈×C₅₃	—	2	1	no	—
167	C₄×Q₈×C₅₃	—	2	1	no	—
168	C₄×Q₈×C₅₃	—	2	1	no	—
169	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
171	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₅₃	—	2	2	no	—
174	C₄×D₄×C₅₃	—	2	2	no	—
175	C₄×D₄×C₅₃	—	2	4	no	—
176	C₄×D₄×C₅₃	—	2	2	no	—
177	C₄×D₄×C₅₃	—	2	1	no	—
178	C₄×D₄×C₅₃	—	2	2	no	—
179	C₄×D₄×C₅₃	—	2	1	no	—
180	C₄×D₄×C₅₃	—	2	1	no	—
181	C₄×D₄×C₅₃	—	2	2	no	—
182	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
183	C₄×D₄×C₅₃	D₄	1	2	yes	—
184	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
185	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₅₃	C₂³	1	2	yes	—
189	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
190	#117×C₅₃	—	2	1	no	—
191	#117×C₅₃	—	2	2	no	—
192	#117×C₅₃	—	2	1	no	—
193	#117×C₅₃	—	2	2	no	—
194	#117×C₅₃	—	2	2	no	—
195	#117×C₅₃	C₂³	1	1	yes	characteristic
196	#117×C₅₃	C₂³	1	2	yes	—
197	#117×C₅₃	C₂³	1	2	yes	—
198	#117×C₅₃	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
200	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
207	C₂×C₄²×C₅₃	—	2	1	no	—
208	C₂×C₄²×C₅₃	—	2	2	no	—
209	C₂×C₄²×C₅₃	—	2	1	no	—
210	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
211	#107×C₅₃	C₂³	1	2	yes	—
212	#107×C₅₃	C₂³	1	4	yes	—
213	#106×C₅₃	C₂³	1	2	yes	—
214	#106×C₅₃	C₂³	1	4	yes	—
215	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
216	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
217	#103×C₅₃	C₂³	1	2	yes	—
218	#103×C₅₃	C₂³	1	2	yes	—
219	#103×C₅₃	C₂³	1	4	yes	—
220	#103×C₅₃	C₂³	1	4	yes	—
221	#103×C₅₃	C₂³	1	2	yes	—
222	#102×C₅₃	C₂³	1	4	yes	—
223	#102×C₅₃	C₂³	1	4	yes	—
224	#102×C₅₃	C₂³	1	4	yes	—
225	#102×C₅₃	C₂³	1	4	yes	—
226	#102×C₅₃	C₂³	1	4	yes	—
227	#102×C₅₃	C₂³	1	4	yes	—
228	#102×C₅₃	C₂³	1	2	yes	—
229	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
230	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
231	#97×C₅₃	C₂³	1	2	yes	—
232	C₄×C₈×C₅₃	C₂³	1	2	yes	—
233	C₂⁴×C₅₃	—	2	2	no	—
234	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
235	#41×C₅₃	—	2	8	no	—
236	#41×C₅₃	—	2	8	no	—
237	#41×C₅₃	—	2	2	no	—
238	#41×C₅₃	—	2	2	no	—
239	#41×C₅₃	—	4	4	no	—
240	#41×C₅₃	—	4	4	no	—
241	#41×C₅₃	—	4	8	no	—
242	#41×C₅₃	—	4	8	no	—
243	#41×C₅₃	—	4	4	no	—
244	C₂×Q₈×C₅₃	—	2	1	no	—
245	C₂×Q₈×C₅₃	—	2	1	no	—
246	C₂×Q₈×C₅₃	—	2	1	no	—
247	C₂×Q₈×C₅₃	—	2	2	no	—
248	C₂×Q₈×C₅₃	#41	1	4	yes	complemented
249	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
250	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
251	C₂×D₄×C₅₃	—	2	1	no	—
252	C₂×D₄×C₅₃	—	2	2	no	—
253	C₂×D₄×C₅₃	—	2	4	no	—
254	C₂×D₄×C₅₃	—	2	4	no	—
255	C₂×D₄×C₅₃	—	2	2	no	—
256	C₂×D₄×C₅₃	—	2	4	no	—
257	C₂×D₄×C₅₃	—	2	4	no	—
258	C₂×D₄×C₅₃	—	2	2	no	—
259	C₂×D₄×C₅₃	—	2	2	no	—
260	C₂×D₄×C₅₃	—	2	2	no	—
261	C₂×D₄×C₅₃	—	2	2	no	—
262	C₂×D₄×C₅₃	—	2	2	no	—
263	C₂×D₄×C₅₃	—	2	4	no	—
264	C₂×D₄×C₅₃	—	2	4	no	—
265	C₂×D₄×C₅₃	—	4	2	no	—
266	C₂×D₄×C₅₃	—	4	8	no	—
267	C₂×D₄×C₅₃	—	4	4	no	—
268	C₂×D₄×C₅₃	—	8	2	no	—
269	C₂×D₄×C₅₃	—	8	4	no	—
270	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
271	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
272	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
273	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
274	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₅₃	—	2	1	no	—
276	C₂²×C₄×C₅₃	—	2	4	no	—
277	C₂²×C₄×C₅₃	—	2	4	no	—
278	C₂²×C₄×C₅₃	—	2	1	no	—
279	C₂²×C₄×C₅₃	—	2	2	no	—
280	C₂²×C₄×C₅₃	—	2	2	no	—
281	C₂²×C₄×C₅₃	—	2	1	no	—
282	C₂²×C₄×C₅₃	—	2	1	no	—
283	C₂²×C₄×C₅₃	—	2	4	no	—
284	C₂²×C₄×C₅₃	—	2	4	no	—
285	C₂²×C₄×C₅₃	—	2	1	no	—
286	C₂²×C₄×C₅₃	—	4	8	no	—
287	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
291	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
295	Q₁₆×C₅₃	—	2	4	no	—
296	SD₁₆×C₅₃	—	2	4	no	—
297	SD₁₆×C₅₃	—	4	4	no	—
298	D₈×C₅₃	—	4	4	no	—
299	M₁₆×C₅₃	—	2	2	no	—
300	M₁₆×C₅₃	—	2	2	no	—
301	M₁₆×C₅₃	—	2	4	no	—
302	M₁₆×C₅₃	—	4	4	no	—
303	C₂×C₈×C₅₃	—	4	4	no	—
304	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
305	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
306	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₅₃	—	2	2	no	—
308	C₄⋊C₄×C₅₃	—	2	2	no	—
309	C₄⋊C₄×C₅₃	—	2	2	no	—
310	C₄⋊C₄×C₅₃	—	2	2	no	—
311	C₄⋊C₄×C₅₃	—	2	1	no	—
312	C₄⋊C₄×C₅₃	—	2	1	no	—
313	C₄⋊C₄×C₅₃	—	2	2	no	—
314	C₄⋊C₄×C₅₃	—	2	2	no	—
315	C₄⋊C₄×C₅₃	—	2	1	no	—
316	C₄⋊C₄×C₅₃	—	2	1	no	—
317	C₄⋊C₄×C₅₃	—	2	2	no	—
318	C₄⋊C₄×C₅₃	—	2	2	no	—
319	C₄⋊C₄×C₅₃	—	2	1	no	—
320	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
321	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
322	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
323	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
324	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
325	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
326	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
327	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
328	C₂²⋊C₄×C₅₃	—	2	1	no	—
329	C₂²⋊C₄×C₅₃	—	2	2	no	—
330	C₂²⋊C₄×C₅₃	—	2	2	no	—
331	C₂²⋊C₄×C₅₃	—	2	2	no	—
332	C₂²⋊C₄×C₅₃	—	2	2	no	—
333	C₂²⋊C₄×C₅₃	—	2	2	no	—
334	C₂²⋊C₄×C₅₃	—	2	4	no	—
335	C₂²⋊C₄×C₅₃	—	2	4	no	—
336	C₂²⋊C₄×C₅₃	—	2	2	no	—
337	C₂²⋊C₄×C₅₃	—	2	1	no	—
338	C₂²⋊C₄×C₅₃	—	2	1	no	—
339	C₂²⋊C₄×C₅₃	—	2	2	no	—
340	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
341	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
342	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
343	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
344	C₄²×C₅₃	—	2	1	no	—
345	C₄²×C₅₃	—	2	2	no	—
346	C₄²×C₅₃	—	2	1	no	—
347	C₄²×C₅₃	—	2	2	no	—
348	C₄²×C₅₃	—	2	2	no	—
349	C₄²×C₅₃	—	2	1	no	—
350	C₄²×C₅₃	—	2	2	no	—
351	C₄²×C₅₃	—	2	2	no	—
352	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
353	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
354	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂³×C₅₃	—	2	4	no	—
357	C₂³×C₅₃	—	2	1	no	—
358	C₂³×C₅₃	—	2	4	no	—
359	C₂³×C₅₃	—	4	2	no	—
360	C₂³×C₅₃	—	4	2	no	—
361	C₂³×C₅₃	—	4	4	no	—
362	C₂³×C₅₃	—	4	4	no	—
363	C₂³×C₅₃	—	4	4	no	—
364	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
365	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
366	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
367	Q₈×C₅₃	—	2	4	no	—
368	Q₈×C₅₃	—	2	2	no	—
369	Q₈×C₅₃	—	2	1	no	—
370	Q₈×C₅₃	—	2	1	no	—
371	Q₈×C₅₃	—	4	2	no	—
372	Q₈×C₅₃	—	8	1	no	—
373	Q₈×C₅₃	C₂×#41	1	4	yes	—
374	D₄×C₅₃	—	2	2	no	—
375	D₄×C₅₃	—	2	2	no	—
376	D₄×C₅₃	—	2	4	no	—
377	D₄×C₅₃	—	2	1	no	—
378	D₄×C₅₃	—	2	4	no	—
379	D₄×C₅₃	—	2	1	no	—
380	D₄×C₅₃	—	4	2	no	—
381	D₄×C₅₃	—	4	8	no	—
382	D₄×C₅₃	—	4	8	no	—
383	D₄×C₅₃	—	4	4	no	—
384	D₄×C₅₃	—	4	4	no	—
385	D₄×C₅₃	—	4	2	no	—
386	D₄×C₅₃	—	4	4	no	—
387	D₄×C₅₃	—	4	4	no	—
388	D₄×C₅₃	—	8	2	no	—
389	D₄×C₅₃	—	8	2	no	—
390	D₄×C₅₃	—	8	2	no	—
391	D₄×C₅₃	—	8	4	no	—
392	D₄×C₅₃	—	8	4	no	—
393	C₂×C₄×C₅₃	—	2	4	no	—
394	C₂×C₄×C₅₃	—	2	4	no	—
395	C₂×C₄×C₅₃	—	2	2	no	—
396	C₂×C₄×C₅₃	—	2	4	no	—
397	C₂×C₄×C₅₃	—	2	4	no	—
398	C₂×C₄×C₅₃	—	2	2	no	—
399	C₂×C₄×C₅₃	—	2	2	no	—
400	C₂×C₄×C₅₃	—	2	2	no	—
401	C₂×C₄×C₅₃	—	2	2	no	—
402	C₂×C₄×C₅₃	—	2	2	no	—
403	C₂×C₄×C₅₃	—	2	1	no	—
404	C₂×C₄×C₅₃	—	2	1	no	—
405	C₂×C₄×C₅₃	—	2	2	no	—
406	C₂×C₄×C₅₃	—	2	2	no	—
407	C₂×C₄×C₅₃	—	2	2	no	—
408	C₂×C₄×C₅₃	—	2	1	no	—
409	C₂×C₄×C₅₃	—	4	1	no	—
410	C₂×C₄×C₅₃	—	4	8	no	—
411	C₂×C₄×C₅₃	—	4	8	no	—
412	C₂×C₄×C₅₃	—	4	2	no	—
413	C₂×C₄×C₅₃	—	4	4	no	—
414	C₂×C₄×C₅₃	—	4	2	no	—
415	C₂×C₄×C₅₃	—	4	2	no	—
416	C₂×C₄×C₅₃	—	8	1	no	—
417	C₂×C₄×C₅₃	—	8	2	no	—
418	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
426	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
427	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
428	C₈×C₅₃	—	2	2	no	—
429	C₈×C₅₃	—	2	2	no	—
430	C₈×C₅₃	—	2	4	no	—
431	#61160	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
432	C₂²×C₅₃	—	2	1	no	—
433	C₂²×C₅₃	—	2	1	no	—
434	C₂²×C₅₃	—	2	2	no	—
435	C₂²×C₅₃	—	2	2	no	—
436	C₂²×C₅₃	—	2	2	no	—
437	C₂²×C₅₃	—	2	2	no	—
438	C₂²×C₅₃	—	2	2	no	—
439	C₂²×C₅₃	—	2	2	no	—
440	C₂²×C₅₃	—	4	1	no	—
441	C₂²×C₅₃	—	4	4	no	—
442	C₂²×C₅₃	—	4	4	no	—
443	C₂²×C₅₃	—	4	1	no	—
444	C₂²×C₅₃	—	4	1	no	—
445	C₂²×C₅₃	—	4	4	no	—
446	C₂²×C₅₃	—	8	4	no	—
447	C₂²×C₅₃	—	8	8	no	—
448	C₂²×C₅₃	#546	1	2	yes	—
449	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
450	C₄×C₅₃	—	2	1	no	—
451	C₄×C₅₃	—	2	1	no	—
452	C₄×C₅₃	—	2	2	no	—
453	C₄×C₅₃	—	2	2	no	—
454	C₄×C₅₃	—	2	4	no	—
455	C₄×C₅₃	—	2	1	no	—
456	C₄×C₅₃	—	4	2	no	—
457	C₄×C₅₃	—	4	1	no	—
458	C₄×C₅₃	—	4	2	no	—
459	C₄×C₅₃	—	4	1	no	—
460	C₄×C₅₃	—	4	1	no	—
461	C₄×C₅₃	—	4	2	no	—
462	C₄×C₅₃	#546	1	2	yes	—
463	C₄×C₅₃	#575	1	2	yes	—
464	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
465	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
466	#3475	C₂×C₅₃	1	1	yes	characteristic, complemented
467	C₂×#550	C₂×C₅₃	1	1	yes	characteristic, complemented
468	#3333	C₂×C₅₃	1	2	yes	complemented
469	#3332	C₂×C₅₃	1	2	yes	complemented
470	#3317	C₂×C₅₃	1	4	yes	complemented
471	#3309	C₂×C₅₃	1	4	yes	complemented
472	#3305	C₂×C₅₃	1	2	yes	complemented
473	#3304	C₂×C₅₃	1	2	yes	complemented
474	#3138	C₂×C₅₃	1	1	yes	characteristic, complemented
475	#3094	C₂×C₅₃	1	2	yes	complemented
476	#3078	C₂×C₅₃	1	1	yes	characteristic, complemented
477	#3055	C₂×C₅₃	1	2	yes	complemented
478	#3038	C₂×C₅₃	1	1	yes	characteristic, complemented
479	#3005	C₂×C₅₃	1	2	yes	complemented
480	C₄×#137	C₂×C₅₃	1	1	yes	characteristic, complemented
481	D₄×M₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
482	#2896	C₂×C₅₃	1	2	yes	complemented
483	C₂×C₅₃	—	2	2	no	—
484	C₂×C₅₃	—	4	2	no	—
485	C₂×C₅₃	—	4	2	no	—
486	C₂×C₅₃	—	8	1	no	—
487	C₂×C₅₃	—	8	4	no	—
488	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
489	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
490	C₂×C₅₃	#3585	1	1	yes	characteristic
491	C₂²×#41	C₂²×C₅₃	1	2	yes	—
492	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
493	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
494	C₂²×M₁₆	C₂²×C₅₃	1	2	yes	—
495	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
496	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
497	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
498	#553	C₂²×C₅₃	1	2	yes	complemented
499	#552	—	2	1	no	—
500	#552	C₂²×C₅₃	1	2	yes	complemented
501	#551	—	2	2	no	—
502	#550	—	2	1	no	—
503	#550	—	2	1	no	—
504	#550	—	2	2	no	—
505	#550	C₂²×C₅₃	1	2	yes	—
506	#550	C₂²×C₅₃	1	2	yes	—
507	#550	C₂²×C₅₃	1	4	yes	—
508	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
509	#546	—	2	1	no	—
510	#533	C₂²×C₅₃	1	1	yes	characteristic
511	C₂×#127	—	2	1	no	—
512	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
513	#529	—	2	2	no	—
514	#529	—	2	1	no	—
515	#525	C₂²×C₅₃	1	2	yes	—
516	C₂×#121	—	2	2	no	—
517	C₂×#121	C₂²×C₅₃	1	2	yes	—
518	C₄×#41	—	2	1	no	—
519	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
520	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
521	C₂×C₄×D₄	—	2	1	no	—
522	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
523	C₂×#117	C₂²×C₅₃	1	2	yes	—
524	#490	C₂²×C₅₃	1	4	yes	complemented
525	#486	C₂²×C₅₃	1	2	yes	complemented
526	#486	C₂²×C₅₃	1	2	yes	complemented
527	#482	C₂²×C₅₃	1	4	yes	complemented
528	#482	C₂²×C₅₃	1	4	yes	complemented
529	#481	C₂²×C₅₃	1	4	yes	complemented
530	#480	C₂²×C₅₃	1	4	yes	complemented
531	#479	C₂²×C₅₃	1	4	yes	complemented
532	#477	C₂²×C₅₃	1	2	yes	complemented
533	#475	C₂²×C₅₃	1	2	yes	complemented
534	#469	C₂²×C₅₃	1	4	yes	complemented
535	#468	C₂²×C₅₃	1	4	yes	complemented
536	#466	C₂²×C₅₃	1	4	yes	complemented
537	#465	C₂²×C₅₃	1	4	yes	complemented
538	#460	C₂²×C₅₃	1	2	yes	complemented
539	#460	C₂²×C₅₃	1	2	yes	complemented
540	#459	C₂²×C₅₃	1	2	yes	complemented
541	#459	C₂²×C₅₃	1	2	yes	complemented
542	#452	C₂²×C₅₃	1	4	yes	complemented
543	#452	C₂²×C₅₃	1	4	yes	complemented
544	#449	C₂²×C₅₃	1	4	yes	complemented
545	#449	C₂²×C₅₃	1	4	yes	complemented
546	#441	C₂²×C₅₃	1	2	yes	complemented
547	#440	C₂²×C₅₃	1	2	yes	complemented
548	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
549	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
550	#436	C₂²×C₅₃	1	2	yes	complemented
551	#435	C₂²×C₅₃	1	4	yes	complemented
552	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
553	#428	C₂²×C₅₃	1	2	yes	—
554	#428	C₂²×C₅₃	1	1	yes	characteristic
555	#423	C₂²×C₅₃	1	1	yes	characteristic
556	#419	C₂²×C₅₃	1	2	yes	—
557	#419	C₂²×C₅₃	1	1	yes	characteristic
558	#418	C₂²×C₅₃	1	2	yes	—
559	#418	C₂²×C₅₃	1	2	yes	—
560	#418	C₂²×C₅₃	1	2	yes	—
561	#417	C₂²×C₅₃	1	1	yes	characteristic
562	#417	C₂²×C₅₃	1	4	yes	complemented
563	#417	C₂²×C₅₃	1	4	yes	complemented
564	#416	C₂²×C₅₃	1	4	yes	complemented
565	#416	C₂²×C₅₃	1	4	yes	complemented
566	#407	C₂²×C₅₃	1	2	yes	—
567	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
568	C₅₃	#61160	1	1	yes	characteristic, direct product factor, Sylow
569	C₂×#41	—	2	1	no	—
570	C₂×#41	—	2	2	no	—
571	C₂×#41	—	2	2	no	—
572	C₂×#41	—	2	8	no	—
573	C₂×#41	—	4	4	no	—
574	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
575	C₂×#41	C₂³×C₅₃	1	4	yes	—
576	C₂×#41	C₂³×C₅₃	1	4	yes	—
577	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
578	C₂²×D₄	—	2	2	no	—
579	C₂²×D₄	—	2	2	no	—
580	C₂²×D₄	—	2	1	no	—
581	C₂²×D₄	—	2	1	no	—
582	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
583	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
584	C₂³×C₄	—	2	2	no	—
585	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
586	#137	—	2	4	no	—
587	AGL(1,ℤ/8)	—	4	4	no	—
588	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
589	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
590	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
591	C₂×D₈	C₂³×C₅₃	1	4	yes	—
592	C₂×M₁₆	—	4	4	no	—
593	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
594	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
595	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
596	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
597	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
598	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
599	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
600	#127	—	2	2	no	—
601	#127	—	2	2	no	—
602	#127	—	2	4	no	—
603	#127	—	2	1	no	—
604	#127	—	2	1	no	—
605	#127	C₂³×C₅₃	1	2	yes	—
606	#127	C₂³×C₅₃	1	2	yes	—
607	#126	—	2	2	no	—
608	#126	—	2	2	no	—
609	#126	—	2	2	no	—
610	#125	—	2	2	no	—
611	#125	—	2	1	no	—
612	#125	C₂³×C₅₃	1	2	yes	—
613	#124	—	2	1	no	—
614	#124	—	2	2	no	—
615	#123	—	2	2	no	—
616	#123	—	2	2	no	—
617	#123	—	2	2	no	—
618	#123	—	2	2	no	—
619	C₂²⋊Q₈	—	2	1	no	—
620	C₂²⋊Q₈	—	2	1	no	—
621	C₂²⋊Q₈	—	2	1	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
624	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
625	#121	—	2	2	no	—
626	#121	—	2	1	no	—
627	#121	—	2	2	no	—
628	#121	—	2	2	no	—
629	#121	—	2	4	no	—
630	#121	—	2	4	no	—
631	#121	—	2	4	no	—
632	#121	—	2	4	no	—
633	#121	C₂³×C₅₃	1	4	yes	—
634	#121	C₂³×C₅₃	1	4	yes	—
635	#121	C₂³×C₅₃	1	2	yes	—
636	#121	C₂³×C₅₃	1	2	yes	—
637	#120	—	2	2	no	—
638	C₄×Q₈	—	2	1	no	—
639	C₄×Q₈	—	2	1	no	—
640	C₄×Q₈	—	2	1	no	—
641	C₄×Q₈	—	2	1	no	—
642	C₄×Q₈	—	2	1	no	—
643	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
644	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
645	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
646	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	1	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	2	no	—
654	C₄×D₄	—	2	4	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
657	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
658	C₄×D₄	D₄×C₅₃	1	2	yes	—
659	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
660	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
661	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
662	C₄×D₄	C₂³×C₅₃	1	2	yes	—
663	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
664	#117	—	2	2	no	—
665	#117	—	2	2	no	—
666	#117	—	2	1	no	—
667	#117	—	2	2	no	—
668	#117	—	2	1	no	—
669	#117	C₂³×C₅₃	1	1	yes	characteristic
670	#117	C₂³×C₅₃	1	2	yes	—
671	#117	C₂³×C₅₃	1	2	yes	—
672	#117	C₂³×C₅₃	1	2	yes	—
673	C₂×C₄⋊C₄	—	2	1	no	—
674	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
676	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	—	2	2	no	—
679	C₂×C₂²⋊C₄	—	2	2	no	—
680	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
681	C₂×C₄²	—	2	2	no	—
682	C₂×C₄²	—	2	1	no	—
683	C₂×C₄²	—	2	1	no	—
684	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
685	#107	C₂³×C₅₃	1	2	yes	—
686	#107	C₂³×C₅₃	1	4	yes	—
687	#106	C₂³×C₅₃	1	2	yes	—
688	#106	C₂³×C₅₃	1	4	yes	—
689	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
690	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
691	#103	C₂³×C₅₃	1	2	yes	—
692	#103	C₂³×C₅₃	1	2	yes	—
693	#103	C₂³×C₅₃	1	4	yes	—
694	#103	C₂³×C₅₃	1	4	yes	—
695	#103	C₂³×C₅₃	1	2	yes	—
696	#102	C₂³×C₅₃	1	4	yes	—
697	#102	C₂³×C₅₃	1	4	yes	—
698	#102	C₂³×C₅₃	1	4	yes	—
699	#102	C₂³×C₅₃	1	4	yes	—
700	#102	C₂³×C₅₃	1	2	yes	—
701	#102	C₂³×C₅₃	1	4	yes	—
702	#102	C₂³×C₅₃	1	4	yes	—
703	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
704	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
705	#97	C₂³×C₅₃	1	2	yes	—
706	C₄×C₈	C₂³×C₅₃	1	2	yes	—
707	C₂⁴	—	2	2	no	—
708	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
709	#41	—	2	8	no	—
710	#41	—	2	8	no	—
711	#41	—	2	2	no	—
712	#41	—	2	2	no	—
713	#41	—	4	4	no	—
714	#41	—	4	4	no	—
715	#41	—	4	8	no	—
716	#41	—	4	8	no	—
717	#41	—	4	4	no	—
718	C₂×Q₈	—	2	1	no	—
719	C₂×Q₈	—	2	1	no	—
720	C₂×Q₈	—	2	1	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	#41×C₅₃	1	4	yes	complemented
723	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
724	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	8	no	—
741	C₂×D₄	—	4	4	no	—
742	C₂×D₄	—	8	2	no	—
743	C₂×D₄	—	8	4	no	—
744	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
745	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
746	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
747	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
748	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	1	no	—
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	4	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	4	8	no	—
761	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
763	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
764	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
765	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
769	Q₁₆	—	2	4	no	—
770	SD₁₆	—	2	4	no	—
771	SD₁₆	—	4	4	no	—
772	D₈	—	4	4	no	—
773	M₁₆	—	2	2	no	—
774	M₁₆	—	2	2	no	—
775	M₁₆	—	2	4	no	—
776	M₁₆	—	4	4	no	—
777	C₂×C₈	—	4	4	no	—
778	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
779	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
780	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
795	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
796	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
797	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
798	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
799	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
800	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
801	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
802	C₂²⋊C₄	—	2	1	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	1	no	—
812	C₂²⋊C₄	—	2	1	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
815	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
816	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
817	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
818	C₄²	—	2	1	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	1	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	1	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
827	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
828	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
829	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
830	C₂³	—	2	4	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	4	no	—
833	C₂³	—	4	2	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	4	no	—
836	C₂³	—	4	4	no	—
837	C₂³	—	4	4	no	—
838	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
839	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
840	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
841	Q₈	—	2	4	no	—
842	Q₈	—	2	2	no	—
843	Q₈	—	2	1	no	—
844	Q₈	—	2	1	no	—
845	Q₈	—	4	2	no	—
846	Q₈	—	8	1	no	—
847	Q₈	C₂×#41×C₅₃	1	4	yes	—
848	D₄	—	2	2	no	—
849	D₄	—	2	2	no	—
850	D₄	—	2	1	no	—
851	D₄	—	2	4	no	—
852	D₄	—	2	1	no	—
853	D₄	—	2	4	no	—
854	D₄	—	4	2	no	—
855	D₄	—	4	8	no	—
856	D₄	—	4	8	no	—
857	D₄	—	4	4	no	—
858	D₄	—	4	4	no	—
859	D₄	—	4	2	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	4	no	—
862	D₄	—	8	2	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	2	no	—
865	D₄	—	8	4	no	—
866	D₄	—	8	4	no	—
867	C₂×C₄	—	2	4	no	—
868	C₂×C₄	—	2	4	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	4	no	—
871	C₂×C₄	—	2	4	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	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	—	4	1	no	—
884	C₂×C₄	—	4	8	no	—
885	C₂×C₄	—	4	8	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	4	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	8	1	no	—
891	C₂×C₄	—	8	2	no	—
892	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
893	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
894	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
898	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
899	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
900	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
901	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
902	C₈	—	2	2	no	—
903	C₈	—	2	2	no	—
904	C₈	—	2	4	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	4	4	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	4	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	4	no	—
919	C₂²	—	8	4	no	—
920	C₂²	—	8	8	no	—
921	C₂²	C₅₃×#546	1	2	yes	—
922	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
923	C₄	—	2	2	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	4	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	1	no	—
934	C₄	—	4	2	no	—
935	C₄	C₅₃×#546	1	2	yes	—
936	C₄	C₅₃×#575	1	2	yes	—
937	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
938	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
939	C₂	—	2	2	no	—
940	C₂	—	4	2	no	—
941	C₂	—	4	2	no	—
942	C₂	—	8	4	no	—
943	C₂	—	8	1	no	—
944	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
945	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
946	C₂	C₅₃×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3475	C₂	semidirect
2. C₂×C₅₃×#550	C₂	semidirect
3. C₅₃×#3333	C₂	semidirect
4. C₅₃×#3332	C₂	semidirect
5. C₅₃×#3317	C₂	semidirect
6. C₅₃×#3309	C₂	semidirect
7. C₅₃×#3305	C₂	semidirect
8. C₅₃×#3304	C₂	semidirect
9. C₅₃×#3138	C₂	semidirect
10. C₅₃×#3094	C₂	semidirect
11. C₅₃×#3078	C₂	semidirect
12. C₅₃×#3055	C₂	semidirect
13. C₅₃×#3038	C₂	semidirect
14. C₅₃×#3005	C₂	semidirect
15. C₄×#137×C₅₃	C₂	semidirect
16. D₄×M₁₆×C₅₃	C₂	semidirect
17. C₅₃×#2896	C₂	semidirect
22. C₅₃×#556	C₂²	semidirect
23. C₅₃×#555	C₂²	semidirect
24. C₅₃×#554	C₂²	semidirect
25. C₅₃×#553	C₂²	semidirect
27. C₅₃×#552	C₂²	semidirect
35. C₅₃×#547	C₂²	semidirect
51. C₅₃×#490	C₂²	semidirect
52. C₅₃×#486	C₂²	semidirect
53. C₅₃×#486	C₂²	semidirect
54. C₅₃×#482	C₂²	semidirect
55. C₅₃×#482	C₂²	semidirect
56. C₅₃×#481	C₂²	semidirect
57. C₅₃×#480	C₂²	semidirect
58. C₅₃×#479	C₂²	semidirect
59. C₅₃×#477	C₂²	semidirect
60. C₅₃×#475	C₂²	semidirect
61. C₅₃×#469	C₂²	semidirect
62. C₅₃×#468	C₂²	semidirect
63. C₅₃×#466	C₂²	semidirect
64. C₅₃×#465	C₂²	semidirect
65. C₅₃×#460	C₂²	semidirect
66. C₅₃×#460	C₂²	semidirect
67. C₅₃×#459	C₂²	semidirect
68. C₅₃×#459	C₂²	semidirect
69. C₅₃×#452	C₂²	semidirect
70. C₅₃×#452	C₂²	semidirect
71. C₅₃×#449	C₂²	semidirect
72. C₅₃×#449	C₂²	semidirect
73. C₅₃×#441	C₂²	semidirect
74. C₅₃×#440	C₂²	semidirect
75. C₄×Q₁₆×C₅₃	C₂²	semidirect
76. C₄×SD₁₆×C₅₃	C₂²	semidirect
77. C₅₃×#436	C₂²	semidirect
78. C₅₃×#435	C₂²	semidirect
79. C₈×D₄×C₅₃	C₂²	semidirect
89. C₅₃×#417	C₂²	semidirect
90. C₅₃×#417	C₂²	semidirect
91. C₅₃×#416	C₂²	semidirect
92. C₅₃×#416	C₂²	semidirect
248. C₂×Q₈×C₅₃	#41	semidirect
431. #61160	C₅₃	direct (N × H)
466. #3475	C₂×C₅₃	semidirect
467. C₂×#550	C₂×C₅₃	semidirect
468. #3333	C₂×C₅₃	semidirect
469. #3332	C₂×C₅₃	semidirect
470. #3317	C₂×C₅₃	semidirect
471. #3309	C₂×C₅₃	semidirect
472. #3305	C₂×C₅₃	semidirect
473. #3304	C₂×C₅₃	semidirect
474. #3138	C₂×C₅₃	semidirect
475. #3094	C₂×C₅₃	semidirect
476. #3078	C₂×C₅₃	semidirect
477. #3055	C₂×C₅₃	semidirect
478. #3038	C₂×C₅₃	semidirect
479. #3005	C₂×C₅₃	semidirect
480. C₄×#137	C₂×C₅₃	semidirect
481. D₄×M₁₆	C₂×C₅₃	semidirect
482. #2896	C₂×C₅₃	semidirect
495. #556	C₂²×C₅₃	semidirect
496. #555	C₂²×C₅₃	semidirect
497. #554	C₂²×C₅₃	semidirect
498. #553	C₂²×C₅₃	semidirect
500. #552	C₂²×C₅₃	semidirect
508. #547	C₂²×C₅₃	semidirect
524. #490	C₂²×C₅₃	semidirect
525. #486	C₂²×C₅₃	semidirect
526. #486	C₂²×C₅₃	semidirect
527. #482	C₂²×C₅₃	semidirect
528. #482	C₂²×C₅₃	semidirect
529. #481	C₂²×C₅₃	semidirect
530. #480	C₂²×C₅₃	semidirect
531. #479	C₂²×C₅₃	semidirect
532. #477	C₂²×C₅₃	semidirect
533. #475	C₂²×C₅₃	semidirect
534. #469	C₂²×C₅₃	semidirect
535. #468	C₂²×C₅₃	semidirect
536. #466	C₂²×C₅₃	semidirect
537. #465	C₂²×C₅₃	semidirect
538. #460	C₂²×C₅₃	semidirect
539. #460	C₂²×C₅₃	semidirect
540. #459	C₂²×C₅₃	semidirect
541. #459	C₂²×C₅₃	semidirect
542. #452	C₂²×C₅₃	semidirect
543. #452	C₂²×C₅₃	semidirect
544. #449	C₂²×C₅₃	semidirect
545. #449	C₂²×C₅₃	semidirect
546. #441	C₂²×C₅₃	semidirect
547. #440	C₂²×C₅₃	semidirect
548. C₄×Q₁₆	C₂²×C₅₃	semidirect
549. C₄×SD₁₆	C₂²×C₅₃	semidirect
550. #436	C₂²×C₅₃	semidirect
551. #435	C₂²×C₅₃	semidirect
552. C₈×D₄	C₂²×C₅₃	semidirect
562. #417	C₂²×C₅₃	semidirect
563. #417	C₂²×C₅₃	semidirect
564. #416	C₂²×C₅₃	semidirect
565. #416	C₂²×C₅₃	semidirect
568. C₅₃	#61160	direct (N × H)
722. C₂×Q₈	#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×#3475	2
C₂×C₅₃×#550	2
C₅₃×#3333	2
C₅₃×#3332	2
C₅₃×#3317	2
C₅₃×#3309	2
C₅₃×#3305	2
C₅₃×#3304	2
C₅₃×#3138	2
C₅₃×#3094	2
C₅₃×#3078	2
C₅₃×#3055	2
C₅₃×#3038	2
C₅₃×#3005	2
C₄×#137×C₅₃	2
D₄×M₁₆×C₅₃	2
C₅₃×#2896	2
#61160	53

Subgroups — C53×#61160 #27268672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61160 #27268672