Subgroups — C₅₃×#61419 #27268931

Order 13568.

2028 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3403	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3399	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3399	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3397	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3394	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3391	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3155	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3045	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3041	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
21	C₂×#135×C₅₃	C₂²	1	2	yes	—
22	C₂²×D₈×C₅₃	C₂²	1	2	yes	—
23	C₅₃×#559	C₂²	1	4	yes	complemented
24	C₅₃×#559	C₂²	1	2	yes	complemented
25	C₅₃×#559	C₂²	1	2	yes	complemented
26	C₅₃×#556	C₂²	1	2	yes	complemented
27	C₅₃×#555	—	2	1	no	—
28	C₅₃×#553	—	2	2	no	—
29	C₅₃×#550	C₂²	1	2	yes	complemented
30	C₅₃×#550	C₂²	1	2	yes	complemented
31	C₅₃×#550	C₂²	1	2	yes	complemented
32	C₅₃×#547	—	2	1	no	—
33	C₅₃×#546	—	2	2	no	—
34	C₅₃×#546	—	2	2	no	—
35	C₅₃×#540	—	2	2	no	—
36	C₅₃×#538	—	2	2	no	—
37	C₅₃×#535	C₂²	1	2	yes	—
38	C₅₃×#535	C₂²	1	2	yes	—
39	C₅₃×#533	C₂²	1	1	yes	characteristic
40	C₅₃×#532	—	2	1	no	—
41	C₅₃×#532	—	2	1	no	—
42	C₅₃×#532	C₂²	1	1	yes	characteristic
43	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
44	C₅₃×#525	—	2	2	no	—
45	C₅₃×#520	C₂²	1	2	yes	—
46	C₅₃×#518	C₂²	1	2	yes	—
47	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₅₃×#496	C₂²	1	4	yes	complemented
50	C₅₃×#496	C₂²	1	4	yes	complemented
51	C₅₃×#496	C₂²	1	4	yes	complemented
52	C₅₃×#495	C₂²	1	4	yes	complemented
53	C₅₃×#493	C₂²	1	2	yes	complemented
54	C₅₃×#493	C₂²	1	4	yes	complemented
55	C₅₃×#492	C₂²	1	2	yes	complemented
56	C₅₃×#464	C₂²	1	2	yes	complemented
57	C₅₃×#464	C₂²	1	4	yes	complemented
58	C₅₃×#463	C₂²	1	2	yes	complemented
59	C₅₃×#463	C₂²	1	4	yes	complemented
60	C₅₃×#463	C₂²	1	4	yes	complemented
61	C₅₃×#463	C₂²	1	4	yes	complemented
62	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#460	C₂²	1	4	yes	complemented
66	C₅₃×#459	C₂²	1	2	yes	—
67	C₅₃×#459	C₂²	1	2	yes	—
68	C₅₃×#459	C₂²	1	4	yes	—
69	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#459	C₂²	1	4	yes	complemented
71	C₅₃×#459	C₂²	1	4	yes	complemented
72	C₅₃×#459	C₂²	1	4	yes	complemented
73	C₅₃×#446	C₂²	1	2	yes	complemented
74	C₅₃×#446	C₂²	1	4	yes	complemented
75	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
76	C₅₃×#442	C₂²	1	2	yes	complemented
77	C₅₃×#442	C₂²	1	4	yes	complemented
78	C₅₃×#440	C₂²	1	2	yes	complemented
79	C₅₃×#440	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
81	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	complemented
82	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
83	C₄×D₈×C₅₃	C₂²	1	4	yes	complemented
84	C₅₃×#428	C₂²	1	1	yes	characteristic
85	C₅₃×#424	C₂²	1	2	yes	—
86	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
87	C₅₃×#418	C₂²	1	1	yes	characteristic
88	C₅₃×#417	C₂²	1	1	yes	characteristic
89	C₅₃×#416	C₂²	1	2	yes	—
90	C₂×#102×C₅₃	C₂²	1	2	yes	—
91	C₅₃×#405	C₂²	1	2	yes	—
92	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
93	C₂×#41×C₅₃	—	2	2	no	—
94	C₂×#41×C₅₃	—	2	2	no	—
95	C₂×#41×C₅₃	—	2	2	no	—
96	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
97	C₂×#41×C₅₃	C₂³	1	2	yes	—
98	C₂²×D₄×C₅₃	—	2	1	no	—
99	C₂²×D₄×C₅₃	—	2	1	no	—
100	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
102	C₂³×C₄×C₅₃	—	2	1	no	—
103	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
104	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
105	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
106	#135×C₅₃	—	4	4	no	—
107	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
112	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
113	C₂×D₈×C₅₃	—	4	4	no	—
114	C₂×D₈×C₅₃	C₂³	1	2	yes	—
115	C₂×D₈×C₅₃	C₂³	1	4	yes	—
116	C₂×D₈×C₅₃	C₂³	1	2	yes	—
117	C₂×D₈×C₅₃	C₂³	1	4	yes	—
118	C₂×D₈×C₅₃	C₂³	1	4	yes	—
119	C₂×D₈×C₅₃	C₂³	1	4	yes	—
120	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
121	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
123	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
124	C₄⋊Q₈×C₅₃	D₄	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	C₂³	1	2	yes	—
129	#127×C₅₃	C₂³	1	1	yes	characteristic
130	#127×C₅₃	C₂³	1	4	yes	—
131	#127×C₅₃	C₂³	1	4	yes	—
132	#127×C₅₃	C₂³	1	2	yes	—
133	#126×C₅₃	—	2	4	no	—
134	#125×C₅₃	D₄	1	2	yes	—
135	#124×C₅₃	—	2	2	no	—
136	#124×C₅₃	—	2	2	no	—
137	#124×C₅₃	—	2	4	no	—
138	#124×C₅₃	C₂³	1	4	yes	—
139	#124×C₅₃	C₂³	1	4	yes	—
140	#124×C₅₃	C₂³	1	2	yes	—
141	#123×C₅₃	—	2	4	no	—
142	#123×C₅₃	—	2	4	no	—
143	#123×C₅₃	—	2	4	no	—
144	#123×C₅₃	—	2	4	no	—
145	C₂²⋊Q₈×C₅₃	—	2	2	no	—
146	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
147	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
148	#121×C₅₃	—	2	2	no	—
149	#121×C₅₃	—	2	2	no	—
150	#121×C₅₃	—	2	2	no	—
151	#121×C₅₃	—	2	2	no	—
152	#121×C₅₃	—	2	2	no	—
153	#121×C₅₃	—	2	2	no	—
154	#121×C₅₃	—	2	2	no	—
155	#121×C₅₃	—	2	4	no	—
156	#121×C₅₃	—	2	4	no	—
157	#121×C₅₃	—	2	4	no	—
158	#121×C₅₃	—	2	1	no	—
159	#121×C₅₃	—	2	1	no	—
160	#120×C₅₃	—	2	4	no	—
161	#120×C₅₃	—	2	4	no	—
162	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
163	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
167	C₄×D₄×C₅₃	—	2	2	no	—
168	C₄×D₄×C₅₃	—	2	2	no	—
169	C₄×D₄×C₅₃	—	2	4	no	—
170	C₄×D₄×C₅₃	—	2	2	no	—
171	C₄×D₄×C₅₃	—	2	2	no	—
172	C₄×D₄×C₅₃	—	2	4	no	—
173	C₄×D₄×C₅₃	—	2	1	no	—
174	C₄×D₄×C₅₃	—	2	1	no	—
175	C₄×D₄×C₅₃	—	2	1	no	—
176	C₄×D₄×C₅₃	—	2	1	no	—
177	C₄×D₄×C₅₃	—	2	1	no	—
178	C₄×D₄×C₅₃	—	2	1	no	—
179	C₄×D₄×C₅₃	C₂³	1	2	yes	—
180	C₄×D₄×C₅₃	C₂³	1	2	yes	—
181	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₅₃	C₂³	1	4	yes	—
184	C₄×D₄×C₅₃	C₂³	1	4	yes	—
185	C₄×D₄×C₅₃	C₂³	1	4	yes	—
186	#117×C₅₃	—	2	2	no	—
187	#117×C₅₃	—	2	2	no	—
188	#117×C₅₃	—	2	1	no	—
189	#117×C₅₃	C₂³	1	1	yes	characteristic
190	#117×C₅₃	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
194	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
195	C₂×C₄²×C₅₃	—	2	1	no	—
196	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
197	#107×C₅₃	C₂³	1	2	yes	—
198	#106×C₅₃	C₂³	1	2	yes	—
199	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
200	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
201	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
202	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
203	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
204	#103×C₅₃	C₂³	1	2	yes	—
205	#103×C₅₃	C₂³	1	2	yes	—
206	#103×C₅₃	C₂³	1	2	yes	—
207	#102×C₅₃	C₂³	1	4	yes	—
208	#102×C₅₃	C₂³	1	4	yes	—
209	#102×C₅₃	C₂³	1	2	yes	—
210	#102×C₅₃	C₂³	1	2	yes	—
211	#102×C₅₃	C₂³	1	2	yes	—
212	#102×C₅₃	C₂³	1	2	yes	—
213	#102×C₅₃	C₂³	1	2	yes	—
214	#97×C₅₃	C₂³	1	2	yes	—
215	#97×C₅₃	C₂³	1	4	yes	—
216	C₄×C₈×C₅₃	C₂³	1	2	yes	—
217	C₄×C₈×C₅₃	C₂³	1	4	yes	—
218	C₂⁴×C₅₃	—	2	2	no	—
219	C₂⁴×C₅₃	—	2	1	no	—
220	#41×C₅₃	—	2	2	no	—
221	#41×C₅₃	—	2	4	no	—
222	#41×C₅₃	—	2	2	no	—
223	#41×C₅₃	—	2	4	no	—
224	#41×C₅₃	—	8	4	no	—
225	#41×C₅₃	—	8	4	no	—
226	#41×C₅₃	—	8	4	no	—
227	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
230	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
231	C₂×D₄×C₅₃	—	2	1	no	—
232	C₂×D₄×C₅₃	—	2	2	no	—
233	C₂×D₄×C₅₃	—	2	1	no	—
234	C₂×D₄×C₅₃	—	2	2	no	—
235	C₂×D₄×C₅₃	—	2	1	no	—
236	C₂×D₄×C₅₃	—	2	2	no	—
237	C₂×D₄×C₅₃	—	2	2	no	—
238	C₂×D₄×C₅₃	—	2	4	no	—
239	C₂×D₄×C₅₃	—	2	1	no	—
240	C₂×D₄×C₅₃	—	2	4	no	—
241	C₂×D₄×C₅₃	—	2	4	no	—
242	C₂×D₄×C₅₃	—	2	4	no	—
243	C₂×D₄×C₅₃	—	2	2	no	—
244	C₂×D₄×C₅₃	—	2	2	no	—
245	C₂×D₄×C₅₃	—	2	2	no	—
246	C₂×D₄×C₅₃	—	2	4	no	—
247	C₂×D₄×C₅₃	—	2	2	no	—
248	C₂×D₄×C₅₃	—	2	4	no	—
249	C₂×D₄×C₅₃	—	8	2	no	—
250	C₂×D₄×C₅₃	—	8	2	no	—
251	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
252	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
253	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
254	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₅₃	—	2	1	no	—
256	C₂²×C₄×C₅₃	—	2	1	no	—
257	C₂²×C₄×C₅₃	—	2	1	no	—
258	C₂²×C₄×C₅₃	—	2	1	no	—
259	C₂²×C₄×C₅₃	—	2	2	no	—
260	C₂²×C₄×C₅₃	—	2	2	no	—
261	C₂²×C₄×C₅₃	—	2	4	no	—
262	C₂²×C₄×C₅₃	—	2	4	no	—
263	C₂²×C₄×C₅₃	—	2	4	no	—
264	C₂²×C₄×C₅₃	—	2	2	no	—
265	C₂²×C₄×C₅₃	—	8	2	no	—
266	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
269	Q₁₆×C₅₃	—	4	2	no	—
270	SD₁₆×C₅₃	—	2	8	no	—
271	SD₁₆×C₅₃	—	2	4	no	—
272	SD₁₆×C₅₃	—	4	2	no	—
273	SD₁₆×C₅₃	—	4	2	no	—
274	SD₁₆×C₅₃	—	4	4	no	—
275	D₈×C₅₃	—	2	4	no	—
276	D₈×C₅₃	—	2	8	no	—
277	D₈×C₅₃	—	4	4	no	—
278	D₈×C₅₃	—	4	4	no	—
279	D₈×C₅₃	—	4	2	no	—
280	D₈×C₅₃	—	4	4	no	—
281	M₁₆×C₅₃	—	2	2	no	—
282	M₁₆×C₅₃	#41	1	4	yes	complemented
283	C₂×C₈×C₅₃	—	2	4	no	—
284	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
285	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₅₃	—	2	1	no	—
289	C₄⋊C₄×C₅₃	—	2	4	no	—
290	C₄⋊C₄×C₅₃	—	2	1	no	—
291	C₄⋊C₄×C₅₃	—	2	1	no	—
292	C₄⋊C₄×C₅₃	—	2	1	no	—
293	C₄⋊C₄×C₅₃	—	2	1	no	—
294	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
298	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
300	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
303	C₂²⋊C₄×C₅₃	—	2	1	no	—
304	C₂²⋊C₄×C₅₃	—	2	4	no	—
305	C₂²⋊C₄×C₅₃	—	2	4	no	—
306	C₂²⋊C₄×C₅₃	—	2	2	no	—
307	C₂²⋊C₄×C₅₃	—	2	2	no	—
308	C₂²⋊C₄×C₅₃	—	2	1	no	—
309	C₂²⋊C₄×C₅₃	—	2	1	no	—
310	C₂²⋊C₄×C₅₃	—	2	4	no	—
311	C₂²⋊C₄×C₅₃	—	2	4	no	—
312	C₂²⋊C₄×C₅₃	—	2	2	no	—
313	C₂²⋊C₄×C₅₃	—	2	4	no	—
314	C₂²⋊C₄×C₅₃	—	2	4	no	—
315	C₂²⋊C₄×C₅₃	—	2	4	no	—
316	C₂²⋊C₄×C₅₃	—	2	2	no	—
317	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
318	C₄²×C₅₃	—	2	1	no	—
319	C₄²×C₅₃	—	2	1	no	—
320	C₄²×C₅₃	—	2	1	no	—
321	C₄²×C₅₃	—	2	4	no	—
322	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
325	C₄²×C₅₃	C₂⁴	1	4	yes	—
326	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
327	C₂³×C₅₃	—	2	1	no	—
328	C₂³×C₅₃	—	2	2	no	—
329	C₂³×C₅₃	—	2	4	no	—
330	C₂³×C₅₃	—	2	2	no	—
331	C₂³×C₅₃	—	4	2	no	—
332	C₂³×C₅₃	—	4	4	no	—
333	C₂³×C₅₃	—	8	1	no	—
334	C₂³×C₅₃	—	8	1	no	—
335	C₂³×C₅₃	—	8	2	no	—
336	C₂³×C₅₃	—	8	2	no	—
337	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
338	Q₈×C₅₃	—	2	4	no	—
339	Q₈×C₅₃	—	2	1	no	—
340	Q₈×C₅₃	—	2	2	no	—
341	Q₈×C₅₃	—	2	2	no	—
342	Q₈×C₅₃	—	2	1	no	—
343	Q₈×C₅₃	—	4	2	no	—
344	D₄×C₅₃	—	2	2	no	—
345	D₄×C₅₃	—	2	4	no	—
346	D₄×C₅₃	—	2	2	no	—
347	D₄×C₅₃	—	2	1	no	—
348	D₄×C₅₃	—	2	2	no	—
349	D₄×C₅₃	—	2	4	no	—
350	D₄×C₅₃	—	2	2	no	—
351	D₄×C₅₃	—	2	1	no	—
352	D₄×C₅₃	—	4	4	no	—
353	D₄×C₅₃	—	4	2	no	—
354	D₄×C₅₃	—	4	4	no	—
355	D₄×C₅₃	—	4	2	no	—
356	D₄×C₅₃	—	4	4	no	—
357	D₄×C₅₃	—	4	4	no	—
358	D₄×C₅₃	—	4	2	no	—
359	D₄×C₅₃	—	8	1	no	—
360	D₄×C₅₃	—	8	4	no	—
361	D₄×C₅₃	—	8	2	no	—
362	D₄×C₅₃	—	8	2	no	—
363	D₄×C₅₃	—	8	4	no	—
364	D₄×C₅₃	—	8	4	no	—
365	D₄×C₅₃	—	8	4	no	—
366	C₂×C₄×C₅₃	—	2	2	no	—
367	C₂×C₄×C₅₃	—	2	1	no	—
368	C₂×C₄×C₅₃	—	2	1	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	1	no	—
371	C₂×C₄×C₅₃	—	2	2	no	—
372	C₂×C₄×C₅₃	—	4	1	no	—
373	C₂×C₄×C₅₃	—	4	2	no	—
374	C₂×C₄×C₅₃	—	4	2	no	—
375	C₂×C₄×C₅₃	—	4	4	no	—
376	C₂×C₄×C₅₃	—	4	4	no	—
377	C₂×C₄×C₅₃	—	4	2	no	—
378	C₂×C₄×C₅₃	—	8	2	no	—
379	C₂×C₄×C₅₃	—	8	4	no	—
380	C₂×C₄×C₅₃	—	8	4	no	—
381	C₂×C₄×C₅₃	—	8	4	no	—
382	C₂×C₄×C₅₃	—	8	1	no	—
383	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
385	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
387	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
391	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
392	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
393	C₈×C₅₃	—	2	2	no	—
394	C₈×C₅₃	—	2	2	no	—
395	C₈×C₅₃	—	2	2	no	—
396	C₈×C₅₃	C₂×#41	1	4	yes	—
397	#61419	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
398	C₂²×C₅₃	—	2	1	no	—
399	C₂²×C₅₃	—	2	1	no	—
400	C₂²×C₅₃	—	4	1	no	—
401	C₂²×C₅₃	—	4	4	no	—
402	C₂²×C₅₃	—	4	2	no	—
403	C₂²×C₅₃	—	4	2	no	—
404	C₂²×C₅₃	—	4	2	no	—
405	C₂²×C₅₃	—	4	1	no	—
406	C₂²×C₅₃	—	4	2	no	—
407	C₂²×C₅₃	—	4	4	no	—
408	C₂²×C₅₃	—	4	2	no	—
409	C₂²×C₅₃	—	4	1	no	—
410	C₂²×C₅₃	—	4	2	no	—
411	C₂²×C₅₃	—	4	4	no	—
412	C₂²×C₅₃	—	8	4	no	—
413	C₂²×C₅₃	—	16	4	no	—
414	C₂²×C₅₃	#550	1	2	yes	—
415	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
416	C₄×C₅₃	—	2	1	no	—
417	C₄×C₅₃	—	2	1	no	—
418	C₄×C₅₃	—	2	4	no	—
419	C₄×C₅₃	—	2	1	no	—
420	C₄×C₅₃	—	2	4	no	—
421	C₄×C₅₃	—	4	1	no	—
422	C₄×C₅₃	—	4	1	no	—
423	C₄×C₅₃	—	4	2	no	—
424	C₄×C₅₃	—	4	1	no	—
425	C₄×C₅₃	—	4	2	no	—
426	C₄×C₅₃	#550	1	2	yes	—
427	C₄×C₅₃	#576	1	2	yes	—
428	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
429	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
430	#3508	C₂×C₅₃	1	1	yes	characteristic, complemented
431	#3506	C₂×C₅₃	1	1	yes	characteristic, complemented
432	#3403	C₂×C₅₃	1	4	yes	complemented
433	#3399	C₂×C₅₃	1	2	yes	complemented
434	#3399	C₂×C₅₃	1	4	yes	complemented
435	#3397	C₂×C₅₃	1	2	yes	complemented
436	#3394	C₂×C₅₃	1	2	yes	complemented
437	#3391	C₂×C₅₃	1	2	yes	complemented
438	#3155	C₂×C₅₃	1	2	yes	complemented
439	#3151	C₂×C₅₃	1	1	yes	characteristic, complemented
440	#3045	C₂×C₅₃	1	2	yes	complemented
441	#3041	C₂×C₅₃	1	2	yes	complemented
442	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
443	C₂×#459	C₂×C₅₃	1	1	yes	characteristic, complemented
444	#2962	C₂×C₅₃	1	1	yes	characteristic, complemented
445	#2946	C₂×C₅₃	1	2	yes	complemented
446	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	1	yes	characteristic, complemented
447	C₂×C₅₃	—	2	2	no	—
448	C₂×C₅₃	—	8	1	no	—
449	C₂×C₅₃	—	8	2	no	—
450	C₂×C₅₃	—	8	2	no	—
451	C₂×C₅₃	—	8	4	no	—
452	C₂×C₅₃	C₂×#550	1	1	yes	characteristic
453	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
454	C₂×C₅₃	#3585	1	1	yes	characteristic
455	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
456	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
457	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
458	C₂×#135	C₂²×C₅₃	1	2	yes	—
459	C₂²×D₈	C₂²×C₅₃	1	2	yes	—
460	#559	C₂²×C₅₃	1	2	yes	complemented
461	#559	C₂²×C₅₃	1	4	yes	complemented
462	#559	C₂²×C₅₃	1	2	yes	complemented
463	#556	C₂²×C₅₃	1	2	yes	complemented
464	#555	—	2	1	no	—
465	#553	—	2	2	no	—
466	#550	C₂²×C₅₃	1	2	yes	complemented
467	#550	C₂²×C₅₃	1	2	yes	complemented
468	#550	C₂²×C₅₃	1	2	yes	complemented
469	#547	—	2	1	no	—
470	#546	—	2	2	no	—
471	#546	—	2	2	no	—
472	#540	—	2	2	no	—
473	#538	—	2	2	no	—
474	#535	C₂²×C₅₃	1	2	yes	—
475	#535	C₂²×C₅₃	1	2	yes	—
476	#533	C₂²×C₅₃	1	1	yes	characteristic
477	#532	—	2	1	no	—
478	#532	—	2	1	no	—
479	#532	C₂²×C₅₃	1	1	yes	characteristic
480	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
481	#525	—	2	2	no	—
482	#520	C₂²×C₅₃	1	2	yes	—
483	#518	C₂²×C₅₃	1	2	yes	—
484	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
485	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
486	#496	C₂²×C₅₃	1	4	yes	complemented
487	#496	C₂²×C₅₃	1	4	yes	complemented
488	#496	C₂²×C₅₃	1	4	yes	complemented
489	#495	C₂²×C₅₃	1	4	yes	complemented
490	#493	C₂²×C₅₃	1	2	yes	complemented
491	#493	C₂²×C₅₃	1	4	yes	complemented
492	#492	C₂²×C₅₃	1	2	yes	complemented
493	#464	C₂²×C₅₃	1	4	yes	complemented
494	#464	C₂²×C₅₃	1	2	yes	complemented
495	#463	C₂²×C₅₃	1	4	yes	complemented
496	#463	C₂²×C₅₃	1	4	yes	complemented
497	#463	C₂²×C₅₃	1	2	yes	complemented
498	#463	C₂²×C₅₃	1	4	yes	complemented
499	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
500	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
501	#460	C₂²×C₅₃	1	4	yes	complemented
502	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
503	#459	C₂²×C₅₃	1	2	yes	—
504	#459	C₂²×C₅₃	1	2	yes	—
505	#459	C₂²×C₅₃	1	4	yes	—
506	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
507	#459	C₂²×C₅₃	1	4	yes	complemented
508	#459	C₂²×C₅₃	1	4	yes	complemented
509	#459	C₂²×C₅₃	1	4	yes	complemented
510	#446	C₂²×C₅₃	1	2	yes	complemented
511	#446	C₂²×C₅₃	1	4	yes	complemented
512	C₈×Q₈	C₂²×C₅₃	1	2	yes	complemented
513	#442	C₂²×C₅₃	1	2	yes	complemented
514	#442	C₂²×C₅₃	1	4	yes	complemented
515	#440	C₂²×C₅₃	1	4	yes	complemented
516	#440	C₂²×C₅₃	1	2	yes	complemented
517	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
518	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	complemented
519	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
520	C₄×D₈	C₂²×C₅₃	1	4	yes	complemented
521	#428	C₂²×C₅₃	1	1	yes	characteristic
522	#424	C₂²×C₅₃	1	2	yes	—
523	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
524	#418	C₂²×C₅₃	1	1	yes	characteristic
525	#417	C₂²×C₅₃	1	1	yes	characteristic
526	#416	C₂²×C₅₃	1	2	yes	—
527	C₂×#102	C₂²×C₅₃	1	2	yes	—
528	#405	C₂²×C₅₃	1	2	yes	—
529	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
530	C₅₃	#61419	1	1	yes	characteristic, direct product factor, Sylow
531	C₂×#41	—	2	2	no	—
532	C₂×#41	—	2	2	no	—
533	C₂×#41	—	2	2	no	—
534	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
535	C₂×#41	C₂³×C₅₃	1	2	yes	—
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	—	2	1	no	—
538	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
539	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
540	C₂³×C₄	—	2	1	no	—
541	AGL(1,ℤ/8)	—	2	8	no	—
542	AGL(1,ℤ/8)	—	2	4	no	—
543	AGL(1,ℤ/8)	—	4	4	no	—
544	#135	—	4	4	no	—
545	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
546	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
547	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
548	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
549	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
550	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
551	C₂×D₈	—	4	4	no	—
552	C₂×D₈	C₂³×C₅₃	1	2	yes	—
553	C₂×D₈	C₂³×C₅₃	1	4	yes	—
554	C₂×D₈	C₂³×C₅₃	1	4	yes	—
555	C₂×D₈	C₂³×C₅₃	1	4	yes	—
556	C₂×D₈	C₂³×C₅₃	1	2	yes	—
557	C₂×D₈	C₂³×C₅₃	1	4	yes	—
558	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
559	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
560	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
561	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
562	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
564	#127	—	2	1	no	—
565	#127	—	2	1	no	—
566	#127	C₂³×C₅₃	1	2	yes	—
567	#127	C₂³×C₅₃	1	2	yes	—
568	#127	C₂³×C₅₃	1	1	yes	characteristic
569	#127	C₂³×C₅₃	1	4	yes	—
570	#127	C₂³×C₅₃	1	4	yes	—
571	#126	—	2	4	no	—
572	#125	D₄×C₅₃	1	2	yes	—
573	#124	—	2	2	no	—
574	#124	—	2	2	no	—
575	#124	—	2	4	no	—
576	#124	C₂³×C₅₃	1	2	yes	—
577	#124	C₂³×C₅₃	1	4	yes	—
578	#124	C₂³×C₅₃	1	4	yes	—
579	#123	—	2	4	no	—
580	#123	—	2	4	no	—
581	#123	—	2	4	no	—
582	#123	—	2	4	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
585	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
586	#121	—	2	1	no	—
587	#121	—	2	1	no	—
588	#121	—	2	2	no	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	4	no	—
596	#121	—	2	4	no	—
597	#121	—	2	4	no	—
598	#120	—	2	4	no	—
599	#120	—	2	4	no	—
600	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
603	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
604	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	4	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	4	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	C₂³×C₅₃	1	2	yes	—
618	C₄×D₄	C₂³×C₅₃	1	2	yes	—
619	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₅₃	1	4	yes	—
622	C₄×D₄	C₂³×C₅₃	1	4	yes	—
623	C₄×D₄	C₂³×C₅₃	1	4	yes	—
624	#117	—	2	2	no	—
625	#117	—	2	2	no	—
626	#117	—	2	1	no	—
627	#117	C₂³×C₅₃	1	1	yes	characteristic
628	#117	C₂³×C₅₃	1	2	yes	—
629	C₂×C₄⋊C₄	—	2	2	no	—
630	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	4	no	—
633	C₂×C₄²	—	2	1	no	—
634	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
635	#107	C₂³×C₅₃	1	2	yes	—
636	#106	C₂³×C₅₃	1	2	yes	—
637	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
638	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
639	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
640	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
641	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
642	#103	C₂³×C₅₃	1	2	yes	—
643	#103	C₂³×C₅₃	1	2	yes	—
644	#103	C₂³×C₅₃	1	2	yes	—
645	#102	C₂³×C₅₃	1	4	yes	—
646	#102	C₂³×C₅₃	1	4	yes	—
647	#102	C₂³×C₅₃	1	2	yes	—
648	#102	C₂³×C₅₃	1	2	yes	—
649	#102	C₂³×C₅₃	1	2	yes	—
650	#102	C₂³×C₅₃	1	2	yes	—
651	#102	C₂³×C₅₃	1	2	yes	—
652	#97	C₂³×C₅₃	1	2	yes	—
653	#97	C₂³×C₅₃	1	4	yes	—
654	C₄×C₈	C₂³×C₅₃	1	2	yes	—
655	C₄×C₈	C₂³×C₅₃	1	4	yes	—
656	C₂⁴	—	2	2	no	—
657	C₂⁴	—	2	1	no	—
658	#41	—	2	2	no	—
659	#41	—	2	4	no	—
660	#41	—	2	2	no	—
661	#41	—	2	4	no	—
662	#41	—	8	4	no	—
663	#41	—	8	4	no	—
664	#41	—	8	4	no	—
665	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
666	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
667	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
668	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	8	2	no	—
688	C₂×D₄	—	8	2	no	—
689	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
690	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
691	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
692	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	8	2	no	—
704	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
707	Q₁₆	—	4	2	no	—
708	SD₁₆	—	2	8	no	—
709	SD₁₆	—	2	4	no	—
710	SD₁₆	—	4	2	no	—
711	SD₁₆	—	4	2	no	—
712	SD₁₆	—	4	4	no	—
713	D₈	—	2	8	no	—
714	D₈	—	2	4	no	—
715	D₈	—	4	4	no	—
716	D₈	—	4	4	no	—
717	D₈	—	4	2	no	—
718	D₈	—	4	4	no	—
719	M₁₆	—	2	2	no	—
720	M₁₆	#41×C₅₃	1	4	yes	complemented
721	C₂×C₈	—	2	4	no	—
722	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
723	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
724	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
725	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
733	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
734	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
735	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
736	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
737	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
738	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	4	no	—
760	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
761	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
762	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
763	C₄²	C₂⁴×C₅₃	1	4	yes	—
764	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	4	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	4	2	no	—
770	C₂³	—	4	4	no	—
771	C₂³	—	8	1	no	—
772	C₂³	—	8	1	no	—
773	C₂³	—	8	2	no	—
774	C₂³	—	8	2	no	—
775	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
776	Q₈	—	2	4	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	2	2	no	—
780	Q₈	—	2	1	no	—
781	Q₈	—	4	2	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	1	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	4	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	1	no	—
790	D₄	—	4	4	no	—
791	D₄	—	4	2	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	4	no	—
796	D₄	—	4	2	no	—
797	D₄	—	8	1	no	—
798	D₄	—	8	4	no	—
799	D₄	—	8	2	no	—
800	D₄	—	8	2	no	—
801	D₄	—	8	4	no	—
802	D₄	—	8	4	no	—
803	D₄	—	8	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	8	2	no	—
817	C₂×C₄	—	8	4	no	—
818	C₂×C₄	—	8	4	no	—
819	C₂×C₄	—	8	4	no	—
820	C₂×C₄	—	8	1	no	—
821	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
823	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
826	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
828	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
829	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
830	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
831	C₈	—	2	2	no	—
832	C₈	—	2	2	no	—
833	C₈	—	2	2	no	—
834	C₈	C₂×#41×C₅₃	1	4	yes	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	4	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	4	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	8	4	no	—
850	C₂²	—	16	4	no	—
851	C₂²	C₅₃×#550	1	2	yes	—
852	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
853	C₄	—	2	1	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	4	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	1	no	—
863	C₄	C₅₃×#550	1	2	yes	—
864	C₄	C₅₃×#576	1	2	yes	—
865	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
866	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
867	C₂	—	2	2	no	—
868	C₂	—	8	2	no	—
869	C₂	—	8	4	no	—
870	C₂	—	8	1	no	—
871	C₂	—	8	2	no	—
872	C₂	C₂×C₅₃×#550	1	1	yes	characteristic
873	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
874	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 ◁ C₅₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3508	C₂	semidirect
2. C₅₃×#3506	C₂	semidirect
3. C₅₃×#3403	C₂	semidirect
4. C₅₃×#3399	C₂	semidirect
5. C₅₃×#3399	C₂	semidirect
6. C₅₃×#3397	C₂	semidirect
7. C₅₃×#3394	C₂	semidirect
8. C₅₃×#3391	C₂	semidirect
9. C₅₃×#3155	C₂	semidirect
10. C₅₃×#3151	C₂	semidirect
11. C₅₃×#3045	C₂	semidirect
12. C₅₃×#3041	C₂	semidirect
13. C₅₃×#3035	C₂	semidirect
14. C₂×C₅₃×#459	C₂	semidirect
15. C₅₃×#2962	C₂	semidirect
16. C₅₃×#2946	C₂	semidirect
17. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
23. C₅₃×#559	C₂²	semidirect
24. C₅₃×#559	C₂²	semidirect
25. C₅₃×#559	C₂²	semidirect
26. C₅₃×#556	C₂²	semidirect
29. C₅₃×#550	C₂²	semidirect
30. C₅₃×#550	C₂²	semidirect
31. C₅₃×#550	C₂²	semidirect
49. C₅₃×#496	C₂²	semidirect
50. C₅₃×#496	C₂²	semidirect
51. C₅₃×#496	C₂²	semidirect
52. C₅₃×#495	C₂²	semidirect
53. C₅₃×#493	C₂²	semidirect
54. C₅₃×#493	C₂²	semidirect
55. C₅₃×#492	C₂²	semidirect
56. C₅₃×#464	C₂²	semidirect
57. C₅₃×#464	C₂²	semidirect
58. C₅₃×#463	C₂²	semidirect
59. C₅₃×#463	C₂²	semidirect
60. C₅₃×#463	C₂²	semidirect
61. C₅₃×#463	C₂²	semidirect
62. C₅₃×#462	C₂²	semidirect
63. C₅₃×#461	C₂²	semidirect
64. C₅₃×#460	C₂²	semidirect
65. C₅₃×#460	C₂²	semidirect
69. C₅₃×#459	C₂²	semidirect
70. C₅₃×#459	C₂²	semidirect
71. C₅₃×#459	C₂²	semidirect
72. C₅₃×#459	C₂²	semidirect
73. C₅₃×#446	C₂²	semidirect
74. C₅₃×#446	C₂²	semidirect
75. C₈×Q₈×C₅₃	C₂²	semidirect
76. C₅₃×#442	C₂²	semidirect
77. C₅₃×#442	C₂²	semidirect
78. C₅₃×#440	C₂²	semidirect
79. C₅₃×#440	C₂²	semidirect
80. C₄×SD₁₆×C₅₃	C₂²	semidirect
81. C₄×SD₁₆×C₅₃	C₂²	semidirect
82. C₄×D₈×C₅₃	C₂²	semidirect
83. C₄×D₈×C₅₃	C₂²	semidirect
282. M₁₆×C₅₃	#41	semidirect
397. #61419	C₅₃	direct (N × H)
430. #3508	C₂×C₅₃	semidirect
431. #3506	C₂×C₅₃	semidirect
432. #3403	C₂×C₅₃	semidirect
433. #3399	C₂×C₅₃	semidirect
434. #3399	C₂×C₅₃	semidirect
435. #3397	C₂×C₅₃	semidirect
436. #3394	C₂×C₅₃	semidirect
437. #3391	C₂×C₅₃	semidirect
438. #3155	C₂×C₅₃	semidirect
439. #3151	C₂×C₅₃	semidirect
440. #3045	C₂×C₅₃	semidirect
441. #3041	C₂×C₅₃	semidirect
442. #3035	C₂×C₅₃	semidirect
443. C₂×#459	C₂×C₅₃	semidirect
444. #2962	C₂×C₅₃	semidirect
445. #2946	C₂×C₅₃	semidirect
446. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
460. #559	C₂²×C₅₃	semidirect
461. #559	C₂²×C₅₃	semidirect
462. #559	C₂²×C₅₃	semidirect
463. #556	C₂²×C₅₃	semidirect
466. #550	C₂²×C₅₃	semidirect
467. #550	C₂²×C₅₃	semidirect
468. #550	C₂²×C₅₃	semidirect
486. #496	C₂²×C₅₃	semidirect
487. #496	C₂²×C₅₃	semidirect
488. #496	C₂²×C₅₃	semidirect
489. #495	C₂²×C₅₃	semidirect
490. #493	C₂²×C₅₃	semidirect
491. #493	C₂²×C₅₃	semidirect
492. #492	C₂²×C₅₃	semidirect
493. #464	C₂²×C₅₃	semidirect
494. #464	C₂²×C₅₃	semidirect
495. #463	C₂²×C₅₃	semidirect
496. #463	C₂²×C₅₃	semidirect
497. #463	C₂²×C₅₃	semidirect
498. #463	C₂²×C₅₃	semidirect
499. #462	C₂²×C₅₃	semidirect
500. #461	C₂²×C₅₃	semidirect
501. #460	C₂²×C₅₃	semidirect
502. #460	C₂²×C₅₃	semidirect
506. #459	C₂²×C₅₃	semidirect
507. #459	C₂²×C₅₃	semidirect
508. #459	C₂²×C₅₃	semidirect
509. #459	C₂²×C₅₃	semidirect
510. #446	C₂²×C₅₃	semidirect
511. #446	C₂²×C₅₃	semidirect
512. C₈×Q₈	C₂²×C₅₃	semidirect
513. #442	C₂²×C₅₃	semidirect
514. #442	C₂²×C₅₃	semidirect
515. #440	C₂²×C₅₃	semidirect
516. #440	C₂²×C₅₃	semidirect
517. C₄×SD₁₆	C₂²×C₅₃	semidirect
518. C₄×SD₁₆	C₂²×C₅₃	semidirect
519. C₄×D₈	C₂²×C₅₃	semidirect
520. C₄×D₈	C₂²×C₅₃	semidirect
530. C₅₃	#61419	direct (N × H)
720. M₁₆	#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×#3508	2
C₅₃×#3506	2
C₅₃×#3403	2
C₅₃×#3399	2
C₅₃×#3397	2
C₅₃×#3394	2
C₅₃×#3391	2
C₅₃×#3155	2
C₅₃×#3151	2
C₅₃×#3045	2
C₅₃×#3041	2
C₅₃×#3035	2
C₂×C₅₃×#459	2
C₅₃×#2962	2
C₅₃×#2946	2
C₄×AGL(1,ℤ/8)×C₅₃	2
#61419	53

Subgroups — C53×#61419 #27268931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61419 #27268931