Subgroups — C₅₃×#62089 #27269601

Order 13568.

1842 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3400	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3370	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3327	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3314	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3310	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3272	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3269	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3267	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3258	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3222	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3124	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3045	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, complemented
21	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
23	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
24	C₅₃×#562	—	2	1	no	—
25	C₅₃×H(3,𝔽₄)	—	2	1	no	—
26	C₅₃×#559	C₂²	1	2	yes	—
27	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#553	—	2	1	no	—
31	C₅₃×#552	—	2	2	no	—
32	C₅₃×#552	—	2	1	no	—
33	C₅₃×#552	C₂²	1	2	yes	complemented
34	C₅₃×#548	C₂²	1	2	yes	—
35	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#547	C₂²	1	2	yes	complemented
37	C₅₃×#546	—	2	2	no	—
38	C₅₃×#546	C₂²	1	2	yes	—
39	D₄²×C₅₃	C₂²	1	2	yes	—
40	C₅₃×#542	C₂²	1	2	yes	—
41	C₅₃×#541	C₂²	1	2	yes	complemented
42	C₅₃×#539	—	2	2	no	—
43	C₅₃×#538	—	2	2	no	—
44	C₅₃×#538	—	2	1	no	—
45	C₅₃×#535	C₂²	1	2	yes	—
46	C₅₃×#534	—	2	1	no	—
47	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#532	C₂²	1	1	yes	characteristic
49	C₅₃×#529	—	2	1	no	—
50	C₅₃×#529	C₂²	1	1	yes	characteristic
51	C₂×#125×C₅₃	—	2	1	no	—
52	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
53	C₅₃×#520	C₂²	1	2	yes	complemented
54	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#497	C₂²	1	2	yes	complemented
56	C₅₃×#497	C₂²	1	2	yes	complemented
57	C₅₃×#492	C₂²	1	2	yes	—
58	C₅₃×#490	C₂²	1	2	yes	—
59	C₅₃×#489	C₂²	1	2	yes	complemented
60	C₅₃×#488	C₂²	1	2	yes	complemented
61	C₅₃×#484	C₂²	1	2	yes	complemented
62	C₅₃×#482	C₂²	1	2	yes	complemented
63	C₅₃×#480	C₂²	1	2	yes	—
64	C₅₃×#479	C₂²	1	2	yes	complemented
65	C₅₃×#478	C₂²	1	2	yes	complemented
66	C₅₃×#477	C₂²	1	2	yes	complemented
67	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#474	C₂²	1	2	yes	complemented
69	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#470	C₂²	1	2	yes	complemented
71	C₅₃×#468	C₂²	1	2	yes	—
72	C₅₃×#468	C₂²	1	2	yes	complemented
73	C₅₃×#468	C₂²	1	2	yes	complemented
74	C₅₃×#467	C₂²	1	2	yes	complemented
75	C₅₃×#465	C₂²	1	2	yes	—
76	C₅₃×#464	C₂²	1	2	yes	complemented
77	C₅₃×#464	C₂²	1	2	yes	complemented
78	C₅₃×#464	C₂²	1	2	yes	complemented
79	C₅₃×#464	C₂²	1	2	yes	complemented
80	C₅₃×#464	C₂²	1	2	yes	complemented
81	C₅₃×#463	C₂²	1	2	yes	complemented
82	C₅₃×#463	C₂²	1	2	yes	complemented
83	C₅₃×#463	C₂²	1	2	yes	complemented
84	C₅₃×#462	C₂²	1	2	yes	complemented
85	C₅₃×#461	C₂²	1	2	yes	complemented
86	C₅₃×#461	C₂²	1	2	yes	complemented
87	C₅₃×#460	C₂²	1	2	yes	—
88	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#460	C₂²	1	2	yes	complemented
90	C₅₃×#459	C₂²	1	2	yes	—
91	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#452	C₂²	1	2	yes	complemented
93	C₅₃×#452	C₂²	1	2	yes	complemented
94	C₅₃×#452	C₂²	1	2	yes	complemented
95	C₅₃×#451	C₂²	1	2	yes	complemented
96	C₅₃×#450	C₂²	1	2	yes	—
97	C₅₃×#450	C₂²	1	2	yes	complemented
98	C₅₃×#450	C₂²	1	2	yes	complemented
99	C₅₃×#449	C₂²	1	2	yes	—
100	C₅₃×#449	C₂²	1	2	yes	complemented
101	C₅₃×#446	C₂²	1	2	yes	complemented
102	C₅₃×#442	C₂²	1	2	yes	complemented
103	C₅₃×#440	C₂²	1	2	yes	complemented
104	C₅₃×#440	C₂²	1	2	yes	complemented
105	C₅₃×#440	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
107	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
108	C₅₃×#436	C₂²	1	2	yes	complemented
109	C₅₃×#435	C₂²	1	2	yes	complemented
110	C₅₃×#435	C₂²	1	2	yes	complemented
111	C₅₃×#433	C₂²	1	2	yes	complemented
112	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#424	C₂²	1	2	yes	complemented
114	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#418	C₂²	1	1	yes	characteristic
117	C₅₃×#417	C₂²	1	2	yes	complemented
118	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
119	C₂×#41×C₅₃	—	2	1	no	—
120	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
121	C₂×#41×C₅₃	C₂³	1	2	yes	—
122	C₂×#41×C₅₃	C₂³	1	2	yes	—
123	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₅₃	—	2	2	no	—
125	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
127	#137×C₅₃	—	4	2	no	—
128	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
129	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
130	#135×C₅₃	—	4	4	no	—
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×SD₁₆×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×SD₁₆×C₅₃	C₂³	1	2	yes	—
141	C₂×D₈×C₅₃	C₂³	1	2	yes	—
142	C₂×D₈×C₅₃	C₂³	1	2	yes	—
143	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
145	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
147	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
148	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
149	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
150	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
151	#127×C₅₃	C₂³	1	2	yes	—
152	#127×C₅₃	C₂³	1	1	yes	characteristic
153	#126×C₅₃	—	2	2	no	—
154	#126×C₅₃	—	2	2	no	—
155	#126×C₅₃	—	2	2	no	—
156	#126×C₅₃	—	2	2	no	—
157	#126×C₅₃	D₄	1	2	yes	—
158	#125×C₅₃	—	2	2	no	—
159	#125×C₅₃	—	2	2	no	—
160	#125×C₅₃	—	2	1	no	—
161	#125×C₅₃	—	2	1	no	—
162	#125×C₅₃	—	2	2	no	—
163	#125×C₅₃	—	2	2	no	—
164	#125×C₅₃	—	2	1	no	—
165	#125×C₅₃	D₄	1	1	yes	characteristic
166	#125×C₅₃	C₂³	1	2	yes	—
167	#124×C₅₃	—	2	2	no	—
168	#124×C₅₃	—	2	2	no	—
169	#124×C₅₃	—	2	1	no	—
170	#124×C₅₃	—	2	1	no	—
171	#124×C₅₃	—	2	1	no	—
172	#124×C₅₃	—	2	2	no	—
173	#124×C₅₃	D₄	1	1	yes	characteristic
174	#124×C₅₃	C₂³	1	2	yes	—
175	#124×C₅₃	C₂³	1	2	yes	—
176	#124×C₅₃	C₂³	1	2	yes	—
177	#123×C₅₃	—	2	2	no	—
178	#123×C₅₃	—	2	2	no	—
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	—	2	2	no	—
185	#123×C₅₃	D₄	1	2	yes	—
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	1	no	—
191	C₂²⋊Q₈×C₅₃	—	2	1	no	—
192	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
193	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
197	#121×C₅₃	—	2	2	no	—
198	#121×C₅₃	—	2	2	no	—
199	#121×C₅₃	—	2	2	no	—
200	#121×C₅₃	—	2	2	no	—
201	#121×C₅₃	—	2	1	no	—
202	#121×C₅₃	—	2	2	no	—
203	#121×C₅₃	—	2	2	no	—
204	#121×C₅₃	—	2	1	no	—
205	#121×C₅₃	D₄	1	1	yes	characteristic
206	#121×C₅₃	C₂³	1	2	yes	—
207	#121×C₅₃	C₂³	1	2	yes	—
208	#120×C₅₃	—	2	2	no	—
209	#120×C₅₃	—	2	2	no	—
210	#120×C₅₃	—	2	2	no	—
211	#120×C₅₃	—	2	2	no	—
212	#120×C₅₃	—	2	2	no	—
213	C₄×Q₈×C₅₃	—	2	1	no	—
214	C₄×Q₈×C₅₃	—	2	1	no	—
215	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
221	C₄×D₄×C₅₃	—	2	2	no	—
222	C₄×D₄×C₅₃	—	2	2	no	—
223	C₄×D₄×C₅₃	—	2	2	no	—
224	C₄×D₄×C₅₃	—	2	2	no	—
225	C₄×D₄×C₅₃	—	2	1	no	—
226	C₄×D₄×C₅₃	—	2	1	no	—
227	C₄×D₄×C₅₃	—	2	1	no	—
228	C₄×D₄×C₅₃	—	2	1	no	—
229	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₅₃	C₂³	1	2	yes	—
232	C₄×D₄×C₅₃	C₂³	1	2	yes	—
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	2	no	—
237	#117×C₅₃	—	2	2	no	—
238	#117×C₅₃	—	2	1	no	—
239	#117×C₅₃	—	2	1	no	—
240	#117×C₅₃	C₂³	1	1	yes	characteristic
241	#117×C₅₃	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
243	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
244	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
245	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
246	C₂×C₄⋊C₄×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	#107×C₅₃	C₂³	1	2	yes	—
254	#107×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	#102×C₅₃	C₂³	1	2	yes	—
270	#102×C₅₃	C₂³	1	2	yes	—
271	#102×C₅₃	C₂³	1	2	yes	—
272	#102×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	C₂⁴×C₅₃	—	2	2	no	—
286	#41×C₅₃	—	2	4	no	—
287	#41×C₅₃	—	2	2	no	—
288	#41×C₅₃	—	4	1	no	—
289	#41×C₅₃	—	4	2	no	—
290	#41×C₅₃	—	4	2	no	—
291	#41×C₅₃	—	4	2	no	—
292	#41×C₅₃	—	8	2	no	—
293	C₂×Q₈×C₅₃	—	2	1	no	—
294	C₂×Q₈×C₅₃	—	2	1	no	—
295	C₂×Q₈×C₅₃	—	2	1	no	—
296	C₂×Q₈×C₅₃	—	4	1	no	—
297	C₂×Q₈×C₅₃	—	4	1	no	—
298	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
299	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
300	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
301	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
302	C₂×D₄×C₅₃	—	2	1	no	—
303	C₂×D₄×C₅₃	—	2	2	no	—
304	C₂×D₄×C₅₃	—	2	2	no	—
305	C₂×D₄×C₅₃	—	2	2	no	—
306	C₂×D₄×C₅₃	—	2	2	no	—
307	C₂×D₄×C₅₃	—	2	2	no	—
308	C₂×D₄×C₅₃	—	2	1	no	—
309	C₂×D₄×C₅₃	—	2	1	no	—
310	C₂×D₄×C₅₃	—	2	1	no	—
311	C₂×D₄×C₅₃	—	2	2	no	—
312	C₂×D₄×C₅₃	—	2	2	no	—
313	C₂×D₄×C₅₃	—	4	1	no	—
314	C₂×D₄×C₅₃	—	4	2	no	—
315	C₂×D₄×C₅₃	—	4	1	no	—
316	C₂×D₄×C₅₃	—	4	2	no	—
317	C₂×D₄×C₅₃	—	8	4	no	—
318	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
319	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
320	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
321	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
322	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₅₃	—	2	1	no	—
324	C₂²×C₄×C₅₃	—	2	2	no	—
325	C₂²×C₄×C₅₃	—	2	1	no	—
326	C₂²×C₄×C₅₃	—	2	1	no	—
327	C₂²×C₄×C₅₃	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
337	Q₁₆×C₅₃	—	4	2	no	—
338	Q₁₆×C₅₃	—	4	2	no	—
339	Q₁₆×C₅₃	—	4	2	no	—
340	SD₁₆×C₅₃	—	2	4	no	—
341	SD₁₆×C₅₃	—	4	2	no	—
342	SD₁₆×C₅₃	—	4	2	no	—
343	SD₁₆×C₅₃	—	4	2	no	—
344	SD₁₆×C₅₃	—	4	2	no	—
345	SD₁₆×C₅₃	—	4	2	no	—
346	SD₁₆×C₅₃	—	4	2	no	—
347	D₈×C₅₃	—	2	4	no	—
348	D₈×C₅₃	—	2	4	no	—
349	M₁₆×C₅₃	—	4	2	no	—
350	M₁₆×C₅₃	—	4	1	no	—
351	M₁₆×C₅₃	—	4	1	no	—
352	C₂×C₈×C₅₃	—	4	2	no	—
353	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
354	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
355	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
356	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₅₃	—	2	2	no	—
358	C₄⋊C₄×C₅₃	—	2	1	no	—
359	C₄⋊C₄×C₅₃	—	2	1	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	2	no	—
364	C₄⋊C₄×C₅₃	—	2	2	no	—
365	C₄⋊C₄×C₅₃	—	2	2	no	—
366	C₄⋊C₄×C₅₃	—	2	2	no	—
367	C₄⋊C₄×C₅₃	—	2	1	no	—
368	C₄⋊C₄×C₅₃	—	2	1	no	—
369	C₄⋊C₄×C₅₃	—	2	2	no	—
370	C₄⋊C₄×C₅₃	—	2	2	no	—
371	C₄⋊C₄×C₅₃	—	2	1	no	—
372	C₄⋊C₄×C₅₃	—	2	1	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
378	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
380	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
381	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
384	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
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	1	no	—
389	C₂²⋊C₄×C₅₃	—	2	2	no	—
390	C₂²⋊C₄×C₅₃	—	2	2	no	—
391	C₂²⋊C₄×C₅₃	—	2	2	no	—
392	C₂²⋊C₄×C₅₃	—	2	2	no	—
393	C₂²⋊C₄×C₅₃	—	2	2	no	—
394	C₂²⋊C₄×C₅₃	—	2	2	no	—
395	C₂²⋊C₄×C₅₃	—	2	1	no	—
396	C₂²⋊C₄×C₅₃	—	2	2	no	—
397	C₂²⋊C₄×C₅₃	—	2	1	no	—
398	C₂²⋊C₄×C₅₃	—	2	2	no	—
399	C₂²⋊C₄×C₅₃	—	2	2	no	—
400	C₂²⋊C₄×C₅₃	—	2	2	no	—
401	C₂²⋊C₄×C₅₃	—	2	2	no	—
402	C₂²⋊C₄×C₅₃	—	2	2	no	—
403	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
404	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
405	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
406	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
407	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
408	C₄²×C₅₃	—	2	1	no	—
409	C₄²×C₅₃	—	2	1	no	—
410	C₄²×C₅₃	—	2	1	no	—
411	C₄²×C₅₃	—	2	2	no	—
412	C₄²×C₅₃	—	2	2	no	—
413	C₄²×C₅₃	—	2	2	no	—
414	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
415	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
416	C₄²×C₅₃	C₂⁴	1	2	yes	—
417	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂³×C₅₃	—	2	1	no	—
420	C₂³×C₅₃	—	2	2	no	—
421	C₂³×C₅₃	—	2	2	no	—
422	C₂³×C₅₃	—	4	2	no	—
423	C₂³×C₅₃	—	8	1	no	—
424	C₂³×C₅₃	—	8	2	no	—
425	C₂³×C₅₃	—	8	2	no	—
426	C₂³×C₅₃	—	8	1	no	—
427	C₂³×C₅₃	—	8	2	no	—
428	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
429	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
430	Q₈×C₅₃	—	2	2	no	—
431	Q₈×C₅₃	—	2	2	no	—
432	Q₈×C₅₃	—	2	1	no	—
433	Q₈×C₅₃	—	2	2	no	—
434	Q₈×C₅₃	—	2	1	no	—
435	Q₈×C₅₃	—	2	2	no	—
436	Q₈×C₅₃	—	4	1	no	—
437	Q₈×C₅₃	—	8	1	no	—
438	Q₈×C₅₃	—	8	1	no	—
439	Q₈×C₅₃	—	8	1	no	—
440	D₄×C₅₃	—	2	2	no	—
441	D₄×C₅₃	—	2	2	no	—
442	D₄×C₅₃	—	2	1	no	—
443	D₄×C₅₃	—	2	2	no	—
444	D₄×C₅₃	—	2	2	no	—
445	D₄×C₅₃	—	4	2	no	—
446	D₄×C₅₃	—	4	1	no	—
447	D₄×C₅₃	—	4	2	no	—
448	D₄×C₅₃	—	4	4	no	—
449	D₄×C₅₃	—	4	4	no	—
450	D₄×C₅₃	—	8	1	no	—
451	D₄×C₅₃	—	8	2	no	—
452	D₄×C₅₃	—	8	2	no	—
453	D₄×C₅₃	—	8	1	no	—
454	D₄×C₅₃	—	8	2	no	—
455	D₄×C₅₃	—	8	1	no	—
456	D₄×C₅₃	—	8	2	no	—
457	D₄×C₅₃	—	8	2	no	—
458	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
459	C₂×C₄×C₅₃	—	2	1	no	—
460	C₂×C₄×C₅₃	—	2	2	no	—
461	C₂×C₄×C₅₃	—	2	1	no	—
462	C₂×C₄×C₅₃	—	2	2	no	—
463	C₂×C₄×C₅₃	—	2	1	no	—
464	C₂×C₄×C₅₃	—	2	2	no	—
465	C₂×C₄×C₅₃	—	2	2	no	—
466	C₂×C₄×C₅₃	—	2	2	no	—
467	C₂×C₄×C₅₃	—	2	1	no	—
468	C₂×C₄×C₅₃	—	2	2	no	—
469	C₂×C₄×C₅₃	—	2	1	no	—
470	C₂×C₄×C₅₃	—	4	1	no	—
471	C₂×C₄×C₅₃	—	4	1	no	—
472	C₂×C₄×C₅₃	—	4	4	no	—
473	C₂×C₄×C₅₃	—	4	2	no	—
474	C₂×C₄×C₅₃	—	4	2	no	—
475	C₂×C₄×C₅₃	—	8	1	no	—
476	C₂×C₄×C₅₃	—	8	2	no	—
477	C₂×C₄×C₅₃	—	8	2	no	—
478	C₂×C₄×C₅₃	—	8	2	no	—
479	C₂×C₄×C₅₃	—	8	2	no	—
480	C₂×C₄×C₅₃	—	8	2	no	—
481	C₂×C₄×C₅₃	—	8	1	no	—
482	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
491	C₈×C₅₃	—	2	2	no	—
492	C₈×C₅₃	—	2	2	no	—
493	C₈×C₅₃	—	2	2	no	—
494	C₈×C₅₃	—	2	2	no	—
495	#62089	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
496	C₂²×C₅₃	—	2	1	no	—
497	C₂²×C₅₃	—	2	2	no	—
498	C₂²×C₅₃	—	2	1	no	—
499	C₂²×C₅₃	—	2	2	no	—
500	C₂²×C₅₃	—	2	1	no	—
501	C₂²×C₅₃	—	2	2	no	—
502	C₂²×C₅₃	—	2	2	no	—
503	C₂²×C₅₃	—	4	1	no	—
504	C₂²×C₅₃	—	4	1	no	—
505	C₂²×C₅₃	—	4	2	no	—
506	C₂²×C₅₃	—	4	2	no	—
507	C₂²×C₅₃	—	4	2	no	—
508	C₂²×C₅₃	—	4	2	no	—
509	C₂²×C₅₃	—	4	2	no	—
510	C₂²×C₅₃	—	4	2	no	—
511	C₂²×C₅₃	—	16	2	no	—
512	C₂²×C₅₃	—	16	4	no	—
513	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
514	C₄×C₅₃	—	2	1	no	—
515	C₄×C₅₃	—	2	1	no	—
516	C₄×C₅₃	—	2	2	no	—
517	C₄×C₅₃	—	2	1	no	—
518	C₄×C₅₃	—	2	1	no	—
519	C₄×C₅₃	—	2	2	no	—
520	C₄×C₅₃	—	2	2	no	—
521	C₄×C₅₃	—	2	1	no	—
522	C₄×C₅₃	—	4	1	no	—
523	C₄×C₅₃	—	4	2	no	—
524	C₄×C₅₃	—	4	2	no	—
525	C₄×C₅₃	—	4	1	no	—
526	C₄×C₅₃	—	4	2	no	—
527	C₄×C₅₃	—	4	1	no	—
528	C₄×C₅₃	—	4	2	no	—
529	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₄×C₅₃	#585	1	1	yes	characteristic
531	#3558	C₂×C₅₃	1	1	yes	characteristic, complemented
532	#3515	C₂×C₅₃	1	1	yes	characteristic, complemented
533	#3400	C₂×C₅₃	1	2	yes	complemented
534	#3370	C₂×C₅₃	1	2	yes	complemented
535	#3327	C₂×C₅₃	1	2	yes	complemented
536	#3314	C₂×C₅₃	1	2	yes	complemented
537	#3310	C₂×C₅₃	1	2	yes	complemented
538	#3272	C₂×C₅₃	1	2	yes	complemented
539	#3269	C₂×C₅₃	1	2	yes	complemented
540	#3267	C₂×C₅₃	1	2	yes	complemented
541	#3258	C₂×C₅₃	1	2	yes	complemented
542	#3254	C₂×C₅₃	1	1	yes	characteristic, complemented
543	#3222	C₂×C₅₃	1	2	yes	complemented
544	#3215	C₂×C₅₃	1	1	yes	characteristic, complemented
545	#3124	C₂×C₅₃	1	2	yes	complemented
546	#3115	C₂×C₅₃	1	1	yes	characteristic, complemented
547	#3045	C₂×C₅₃	1	2	yes	complemented
548	#3040	C₂×C₅₃	1	1	yes	characteristic, complemented
549	#2995	C₂×C₅₃	1	1	yes	characteristic, complemented
550	C₂×C₅₃	—	4	1	no	—
551	C₂×C₅₃	—	4	2	no	—
552	C₂×C₅₃	—	4	2	no	—
553	C₂×C₅₃	—	8	2	no	—
554	C₂×C₅₃	—	8	2	no	—
555	C₂×C₅₃	#3488	1	1	yes	characteristic
556	C₂×C₅₃	#3585	1	1	yes	characteristic
557	C₂×C₅₃	#3586	1	1	yes	characteristic
558	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
559	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
560	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
561	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
562	#562	—	2	1	no	—
563	H(3,𝔽₄)	—	2	1	no	—
564	#559	C₂²×C₅₃	1	2	yes	—
565	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
566	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
567	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
568	#553	—	2	1	no	—
569	#552	—	2	2	no	—
570	#552	—	2	1	no	—
571	#552	C₂²×C₅₃	1	2	yes	complemented
572	#548	C₂²×C₅₃	1	2	yes	—
573	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
574	#547	C₂²×C₅₃	1	2	yes	complemented
575	#546	—	2	2	no	—
576	#546	C₂²×C₅₃	1	2	yes	—
577	D₄²	C₂²×C₅₃	1	2	yes	—
578	#542	C₂²×C₅₃	1	2	yes	—
579	#541	C₂²×C₅₃	1	2	yes	complemented
580	#539	—	2	2	no	—
581	#538	—	2	2	no	—
582	#538	—	2	1	no	—
583	#535	C₂²×C₅₃	1	2	yes	—
584	#534	—	2	1	no	—
585	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
586	#532	C₂²×C₅₃	1	1	yes	characteristic
587	#529	—	2	1	no	—
588	#529	C₂²×C₅₃	1	1	yes	characteristic
589	C₂×#125	—	2	1	no	—
590	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
591	#520	C₂²×C₅₃	1	2	yes	complemented
592	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
593	#497	C₂²×C₅₃	1	2	yes	complemented
594	#497	C₂²×C₅₃	1	2	yes	complemented
595	#492	C₂²×C₅₃	1	2	yes	—
596	#490	C₂²×C₅₃	1	2	yes	—
597	#489	C₂²×C₅₃	1	2	yes	complemented
598	#488	C₂²×C₅₃	1	2	yes	complemented
599	#484	C₂²×C₅₃	1	2	yes	complemented
600	#482	C₂²×C₅₃	1	2	yes	complemented
601	#480	C₂²×C₅₃	1	2	yes	—
602	#479	C₂²×C₅₃	1	2	yes	complemented
603	#478	C₂²×C₅₃	1	2	yes	complemented
604	#477	C₂²×C₅₃	1	2	yes	complemented
605	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
606	#474	C₂²×C₅₃	1	2	yes	complemented
607	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
608	#470	C₂²×C₅₃	1	2	yes	complemented
609	#468	C₂²×C₅₃	1	2	yes	—
610	#468	C₂²×C₅₃	1	2	yes	complemented
611	#468	C₂²×C₅₃	1	2	yes	complemented
612	#467	C₂²×C₅₃	1	2	yes	complemented
613	#465	C₂²×C₅₃	1	2	yes	—
614	#464	C₂²×C₅₃	1	2	yes	complemented
615	#464	C₂²×C₅₃	1	2	yes	complemented
616	#464	C₂²×C₅₃	1	2	yes	complemented
617	#464	C₂²×C₅₃	1	2	yes	complemented
618	#464	C₂²×C₅₃	1	2	yes	complemented
619	#463	C₂²×C₅₃	1	2	yes	complemented
620	#463	C₂²×C₅₃	1	2	yes	complemented
621	#463	C₂²×C₅₃	1	2	yes	complemented
622	#462	C₂²×C₅₃	1	2	yes	complemented
623	#461	C₂²×C₅₃	1	2	yes	complemented
624	#461	C₂²×C₅₃	1	2	yes	complemented
625	#460	C₂²×C₅₃	1	2	yes	—
626	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
627	#460	C₂²×C₅₃	1	2	yes	complemented
628	#459	C₂²×C₅₃	1	2	yes	—
629	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
630	#452	C₂²×C₅₃	1	2	yes	complemented
631	#452	C₂²×C₅₃	1	2	yes	complemented
632	#452	C₂²×C₅₃	1	2	yes	complemented
633	#451	C₂²×C₅₃	1	2	yes	complemented
634	#450	C₂²×C₅₃	1	2	yes	—
635	#450	C₂²×C₅₃	1	2	yes	complemented
636	#450	C₂²×C₅₃	1	2	yes	complemented
637	#449	C₂²×C₅₃	1	2	yes	—
638	#449	C₂²×C₅₃	1	2	yes	complemented
639	#446	C₂²×C₅₃	1	2	yes	complemented
640	#442	C₂²×C₅₃	1	2	yes	complemented
641	#440	C₂²×C₅₃	1	2	yes	complemented
642	#440	C₂²×C₅₃	1	2	yes	complemented
643	#440	C₂²×C₅₃	1	2	yes	complemented
644	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
645	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
646	#436	C₂²×C₅₃	1	2	yes	complemented
647	#435	C₂²×C₅₃	1	2	yes	complemented
648	#435	C₂²×C₅₃	1	2	yes	complemented
649	#433	C₂²×C₅₃	1	2	yes	complemented
650	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
651	#424	C₂²×C₅₃	1	2	yes	complemented
652	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
653	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
654	#418	C₂²×C₅₃	1	1	yes	characteristic
655	#417	C₂²×C₅₃	1	2	yes	complemented
656	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
657	C₅₃	#62089	1	1	yes	characteristic, direct product factor, Sylow
658	C₂×#41	—	2	1	no	—
659	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
660	C₂×#41	C₂³×C₅₃	1	2	yes	—
661	C₂×#41	C₂³×C₅₃	1	2	yes	—
662	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
663	C₂²×D₄	—	2	2	no	—
664	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
665	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
666	#137	—	4	2	no	—
667	AGL(1,ℤ/8)	—	4	2	no	—
668	AGL(1,ℤ/8)	—	4	4	no	—
669	#135	—	4	4	no	—
670	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
671	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
672	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
673	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
674	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
675	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
676	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
677	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
680	C₂×D₈	C₂³×C₅₃	1	2	yes	—
681	C₂×D₈	C₂³×C₅₃	1	2	yes	—
682	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
683	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
684	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
685	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
686	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
687	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
688	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
689	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
690	#127	C₂³×C₅₃	1	1	yes	characteristic
691	#127	C₂³×C₅₃	1	2	yes	—
692	#126	—	2	2	no	—
693	#126	—	2	2	no	—
694	#126	—	2	2	no	—
695	#126	—	2	2	no	—
696	#126	D₄×C₅₃	1	2	yes	—
697	#125	—	2	2	no	—
698	#125	—	2	2	no	—
699	#125	—	2	1	no	—
700	#125	—	2	1	no	—
701	#125	—	2	2	no	—
702	#125	—	2	2	no	—
703	#125	—	2	1	no	—
704	#125	D₄×C₅₃	1	1	yes	characteristic
705	#125	C₂³×C₅₃	1	2	yes	—
706	#124	—	2	2	no	—
707	#124	—	2	2	no	—
708	#124	—	2	2	no	—
709	#124	—	2	1	no	—
710	#124	—	2	1	no	—
711	#124	—	2	1	no	—
712	#124	D₄×C₅₃	1	1	yes	characteristic
713	#124	C₂³×C₅₃	1	2	yes	—
714	#124	C₂³×C₅₃	1	2	yes	—
715	#124	C₂³×C₅₃	1	2	yes	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	—	2	2	no	—
722	#123	—	2	2	no	—
723	#123	—	2	2	no	—
724	#123	D₄×C₅₃	1	2	yes	—
725	C₂²⋊Q₈	—	2	1	no	—
726	C₂²⋊Q₈	—	2	1	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
732	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
733	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
734	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
735	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
736	#121	—	2	1	no	—
737	#121	—	2	2	no	—
738	#121	—	2	2	no	—
739	#121	—	2	1	no	—
740	#121	—	2	2	no	—
741	#121	—	2	2	no	—
742	#121	—	2	2	no	—
743	#121	—	2	2	no	—
744	#121	D₄×C₅₃	1	1	yes	characteristic
745	#121	C₂³×C₅₃	1	2	yes	—
746	#121	C₂³×C₅₃	1	2	yes	—
747	#120	—	2	2	no	—
748	#120	—	2	2	no	—
749	#120	—	2	2	no	—
750	#120	—	2	2	no	—
751	#120	—	2	2	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
757	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
758	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
759	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	1	no	—
762	C₄×D₄	—	2	1	no	—
763	C₄×D₄	—	2	2	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	1	no	—
768	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
769	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
770	C₄×D₄	C₂³×C₅₃	1	2	yes	—
771	C₄×D₄	C₂³×C₅₃	1	2	yes	—
772	C₄×D₄	C₂³×C₅₃	1	2	yes	—
773	C₄×D₄	C₂³×C₅₃	1	2	yes	—
774	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
775	#117	—	2	1	no	—
776	#117	—	2	2	no	—
777	#117	—	2	2	no	—
778	#117	—	2	1	no	—
779	#117	C₂³×C₅₃	1	1	yes	characteristic
780	#117	C₂³×C₅₃	1	2	yes	—
781	C₂×C₄⋊C₄	—	2	2	no	—
782	C₂×C₄⋊C₄	—	2	1	no	—
783	C₂×C₄⋊C₄	—	2	2	no	—
784	C₂×C₄⋊C₄	—	2	1	no	—
785	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
786	C₂×C₂²⋊C₄	—	2	1	no	—
787	C₂×C₂²⋊C₄	—	2	1	no	—
788	C₂×C₂²⋊C₄	—	2	2	no	—
789	C₂×C₄²	—	2	1	no	—
790	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
791	#107	C₂³×C₅₃	1	2	yes	—
792	#107	C₂³×C₅₃	1	2	yes	—
793	#107	C₂³×C₅₃	1	2	yes	—
794	#106	C₂³×C₅₃	1	2	yes	—
795	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
796	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
797	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
798	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
799	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
800	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
801	#103	C₂³×C₅₃	1	2	yes	—
802	#103	C₂³×C₅₃	1	2	yes	—
803	#103	C₂³×C₅₃	1	2	yes	—
804	#103	C₂³×C₅₃	1	2	yes	—
805	#103	C₂³×C₅₃	1	2	yes	—
806	#103	C₂³×C₅₃	1	2	yes	—
807	#103	C₂³×C₅₃	1	2	yes	—
808	#102	C₂³×C₅₃	1	2	yes	—
809	#102	C₂³×C₅₃	1	2	yes	—
810	#102	C₂³×C₅₃	1	2	yes	—
811	#102	C₂³×C₅₃	1	2	yes	—
812	#102	C₂³×C₅₃	1	2	yes	—
813	#102	C₂³×C₅₃	1	2	yes	—
814	#102	C₂³×C₅₃	1	2	yes	—
815	#102	C₂³×C₅₃	1	2	yes	—
816	#102	C₂³×C₅₃	1	2	yes	—
817	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
818	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
819	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
820	#97	C₂³×C₅₃	1	2	yes	—
821	#97	C₂³×C₅₃	1	2	yes	—
822	C₄×C₈	C₂³×C₅₃	1	2	yes	—
823	C₂⁴	—	2	1	no	—
824	C₂⁴	—	2	2	no	—
825	#41	—	2	4	no	—
826	#41	—	2	2	no	—
827	#41	—	4	1	no	—
828	#41	—	4	2	no	—
829	#41	—	4	2	no	—
830	#41	—	4	2	no	—
831	#41	—	8	2	no	—
832	C₂×Q₈	—	2	1	no	—
833	C₂×Q₈	—	2	1	no	—
834	C₂×Q₈	—	2	1	no	—
835	C₂×Q₈	—	4	1	no	—
836	C₂×Q₈	—	4	1	no	—
837	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
838	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
839	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
840	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	1	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	1	no	—
848	C₂×D₄	—	2	1	no	—
849	C₂×D₄	—	2	1	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	4	2	no	—
853	C₂×D₄	—	4	1	no	—
854	C₂×D₄	—	4	1	no	—
855	C₂×D₄	—	4	2	no	—
856	C₂×D₄	—	8	4	no	—
857	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
858	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
859	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
860	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
861	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
873	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
876	Q₁₆	—	4	2	no	—
877	Q₁₆	—	4	2	no	—
878	Q₁₆	—	4	2	no	—
879	SD₁₆	—	2	4	no	—
880	SD₁₆	—	4	2	no	—
881	SD₁₆	—	4	2	no	—
882	SD₁₆	—	4	2	no	—
883	SD₁₆	—	4	2	no	—
884	SD₁₆	—	4	2	no	—
885	SD₁₆	—	4	2	no	—
886	D₈	—	2	4	no	—
887	D₈	—	2	4	no	—
888	M₁₆	—	4	2	no	—
889	M₁₆	—	4	1	no	—
890	M₁₆	—	4	1	no	—
891	C₂×C₈	—	4	2	no	—
892	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
893	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
894	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
895	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
915	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
916	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
917	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
918	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
919	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
920	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
921	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
922	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
923	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	1	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	1	no	—
935	C₂²⋊C₄	—	2	1	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
943	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
944	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
945	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
946	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
947	C₄²	—	2	1	no	—
948	C₄²	—	2	1	no	—
949	C₄²	—	2	1	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
954	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
955	C₄²	C₂⁴×C₅₃	1	2	yes	—
956	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
957	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
958	C₂³	—	2	1	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	4	2	no	—
962	C₂³	—	8	1	no	—
963	C₂³	—	8	2	no	—
964	C₂³	—	8	2	no	—
965	C₂³	—	8	1	no	—
966	C₂³	—	8	2	no	—
967	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
968	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
969	Q₈	—	2	2	no	—
970	Q₈	—	2	2	no	—
971	Q₈	—	2	1	no	—
972	Q₈	—	2	1	no	—
973	Q₈	—	2	2	no	—
974	Q₈	—	2	2	no	—
975	Q₈	—	4	1	no	—
976	Q₈	—	8	1	no	—
977	Q₈	—	8	1	no	—
978	Q₈	—	8	1	no	—
979	D₄	—	2	2	no	—
980	D₄	—	2	2	no	—
981	D₄	—	2	1	no	—
982	D₄	—	2	2	no	—
983	D₄	—	2	2	no	—
984	D₄	—	4	2	no	—
985	D₄	—	4	1	no	—
986	D₄	—	4	2	no	—
987	D₄	—	4	4	no	—
988	D₄	—	4	4	no	—
989	D₄	—	8	1	no	—
990	D₄	—	8	2	no	—
991	D₄	—	8	2	no	—
992	D₄	—	8	1	no	—
993	D₄	—	8	2	no	—
994	D₄	—	8	1	no	—
995	D₄	—	8	2	no	—
996	D₄	—	8	2	no	—
997	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	4	1	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	4	4	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	8	1	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	—	8	2	no	—
1019	C₂×C₄	—	8	2	no	—
1020	C₂×C₄	—	8	1	no	—
1021	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1023	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1026	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1027	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1028	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1029	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1030	C₈	—	2	2	no	—
1031	C₈	—	2	2	no	—
1032	C₈	—	2	2	no	—
1033	C₈	—	2	2	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	2	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	16	2	no	—
1050	C₂²	—	16	4	no	—
1051	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1052	C₄	—	2	2	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	1	no	—
1067	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1068	C₄	C₅₃×#585	1	1	yes	characteristic
1069	C₂	—	4	1	no	—
1070	C₂	—	4	2	no	—
1071	C₂	—	4	2	no	—
1072	C₂	—	8	2	no	—
1073	C₂	—	8	2	no	—
1074	C₂	C₅₃×#3488	1	1	yes	characteristic
1075	C₂	C₅₃×#3585	1	1	yes	characteristic
1076	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×#3558	C₂	semidirect
2. C₅₃×#3515	C₂	semidirect
3. C₅₃×#3400	C₂	semidirect
4. C₅₃×#3370	C₂	semidirect
5. C₅₃×#3327	C₂	semidirect
6. C₅₃×#3314	C₂	semidirect
7. C₅₃×#3310	C₂	semidirect
8. C₅₃×#3272	C₂	semidirect
9. C₅₃×#3269	C₂	semidirect
10. C₅₃×#3267	C₂	semidirect
11. C₅₃×#3258	C₂	semidirect
12. C₅₃×#3254	C₂	semidirect
13. C₅₃×#3222	C₂	semidirect
14. C₅₃×#3215	C₂	semidirect
15. C₅₃×#3124	C₂	semidirect
16. C₅₃×#3115	C₂	semidirect
17. C₅₃×#3045	C₂	semidirect
18. C₅₃×#3040	C₂	semidirect
19. C₅₃×#2995	C₂	semidirect
20. C₂×#137×C₅₃	C₂²	semidirect
22. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
23. C₂×#135×C₅₃	C₂²	semidirect
27. C₅₃×#557	C₂²	semidirect
28. C₅₃×#554	C₂²	semidirect
29. C₅₃×#554	C₂²	semidirect
33. C₅₃×#552	C₂²	semidirect
35. C₅₃×#547	C₂²	semidirect
36. C₅₃×#547	C₂²	semidirect
41. C₅₃×#541	C₂²	semidirect
47. C₅₃×#533	C₂²	semidirect
53. C₅₃×#520	C₂²	semidirect
54. C₄×#41×C₅₃	C₂²	semidirect
55. C₅₃×#497	C₂²	semidirect
56. C₅₃×#497	C₂²	semidirect
59. C₅₃×#489	C₂²	semidirect
60. C₅₃×#488	C₂²	semidirect
61. C₅₃×#484	C₂²	semidirect
62. C₅₃×#482	C₂²	semidirect
64. C₅₃×#479	C₂²	semidirect
65. C₅₃×#478	C₂²	semidirect
66. C₅₃×#477	C₂²	semidirect
67. C₅₃×#475	C₂²	semidirect
68. C₅₃×#474	C₂²	semidirect
69. C₅₃×#474	C₂²	semidirect
70. C₅₃×#470	C₂²	semidirect
72. C₅₃×#468	C₂²	semidirect
73. C₅₃×#468	C₂²	semidirect
74. C₅₃×#467	C₂²	semidirect
76. C₅₃×#464	C₂²	semidirect
77. C₅₃×#464	C₂²	semidirect
78. C₅₃×#464	C₂²	semidirect
79. C₅₃×#464	C₂²	semidirect
80. C₅₃×#464	C₂²	semidirect
81. C₅₃×#463	C₂²	semidirect
82. C₅₃×#463	C₂²	semidirect
83. C₅₃×#463	C₂²	semidirect
84. C₅₃×#462	C₂²	semidirect
85. C₅₃×#461	C₂²	semidirect
86. C₅₃×#461	C₂²	semidirect
88. C₅₃×#460	C₂²	semidirect
89. C₅₃×#460	C₂²	semidirect
91. C₅₃×#459	C₂²	semidirect
92. C₅₃×#452	C₂²	semidirect
93. C₅₃×#452	C₂²	semidirect
94. C₅₃×#452	C₂²	semidirect
95. C₅₃×#451	C₂²	semidirect
97. C₅₃×#450	C₂²	semidirect
98. C₅₃×#450	C₂²	semidirect
100. C₅₃×#449	C₂²	semidirect
101. C₅₃×#446	C₂²	semidirect
102. C₅₃×#442	C₂²	semidirect
103. C₅₃×#440	C₂²	semidirect
104. C₅₃×#440	C₂²	semidirect
105. C₅₃×#440	C₂²	semidirect
106. C₄×Q₁₆×C₅₃	C₂²	semidirect
107. C₄×D₈×C₅₃	C₂²	semidirect
108. C₅₃×#436	C₂²	semidirect
109. C₅₃×#435	C₂²	semidirect
110. C₅₃×#435	C₂²	semidirect
111. C₅₃×#433	C₂²	semidirect
112. C₅₃×#432	C₂²	semidirect
113. C₅₃×#424	C₂²	semidirect
114. C₅₃×#423	C₂²	semidirect
115. C₅₃×#419	C₂²	semidirect
117. C₅₃×#417	C₂²	semidirect
118. C₂×#102×C₅₃	C₂²	semidirect
495. #62089	C₅₃	direct (N × H)
531. #3558	C₂×C₅₃	semidirect
532. #3515	C₂×C₅₃	semidirect
533. #3400	C₂×C₅₃	semidirect
534. #3370	C₂×C₅₃	semidirect
535. #3327	C₂×C₅₃	semidirect
536. #3314	C₂×C₅₃	semidirect
537. #3310	C₂×C₅₃	semidirect
538. #3272	C₂×C₅₃	semidirect
539. #3269	C₂×C₅₃	semidirect
540. #3267	C₂×C₅₃	semidirect
541. #3258	C₂×C₅₃	semidirect
542. #3254	C₂×C₅₃	semidirect
543. #3222	C₂×C₅₃	semidirect
544. #3215	C₂×C₅₃	semidirect
545. #3124	C₂×C₅₃	semidirect
546. #3115	C₂×C₅₃	semidirect
547. #3045	C₂×C₅₃	semidirect
548. #3040	C₂×C₅₃	semidirect
549. #2995	C₂×C₅₃	semidirect
558. C₂×#137	C₂²×C₅₃	semidirect
560. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
561. C₂×#135	C₂²×C₅₃	semidirect
565. #557	C₂²×C₅₃	semidirect
566. #554	C₂²×C₅₃	semidirect
567. #554	C₂²×C₅₃	semidirect
571. #552	C₂²×C₅₃	semidirect
573. #547	C₂²×C₅₃	semidirect
574. #547	C₂²×C₅₃	semidirect
579. #541	C₂²×C₅₃	semidirect
585. #533	C₂²×C₅₃	semidirect
591. #520	C₂²×C₅₃	semidirect
592. C₄×#41	C₂²×C₅₃	semidirect
593. #497	C₂²×C₅₃	semidirect
594. #497	C₂²×C₅₃	semidirect
597. #489	C₂²×C₅₃	semidirect
598. #488	C₂²×C₅₃	semidirect
599. #484	C₂²×C₅₃	semidirect
600. #482	C₂²×C₅₃	semidirect
602. #479	C₂²×C₅₃	semidirect
603. #478	C₂²×C₅₃	semidirect
604. #477	C₂²×C₅₃	semidirect
605. #475	C₂²×C₅₃	semidirect
606. #474	C₂²×C₅₃	semidirect
607. #474	C₂²×C₅₃	semidirect
608. #470	C₂²×C₅₃	semidirect
610. #468	C₂²×C₅₃	semidirect
611. #468	C₂²×C₅₃	semidirect
612. #467	C₂²×C₅₃	semidirect
614. #464	C₂²×C₅₃	semidirect
615. #464	C₂²×C₅₃	semidirect
616. #464	C₂²×C₅₃	semidirect
617. #464	C₂²×C₅₃	semidirect
618. #464	C₂²×C₅₃	semidirect
619. #463	C₂²×C₅₃	semidirect
620. #463	C₂²×C₅₃	semidirect
621. #463	C₂²×C₅₃	semidirect
622. #462	C₂²×C₅₃	semidirect
623. #461	C₂²×C₅₃	semidirect
624. #461	C₂²×C₅₃	semidirect
626. #460	C₂²×C₅₃	semidirect
627. #460	C₂²×C₅₃	semidirect
629. #459	C₂²×C₅₃	semidirect
630. #452	C₂²×C₅₃	semidirect
631. #452	C₂²×C₅₃	semidirect
632. #452	C₂²×C₅₃	semidirect
633. #451	C₂²×C₅₃	semidirect
635. #450	C₂²×C₅₃	semidirect
636. #450	C₂²×C₅₃	semidirect
638. #449	C₂²×C₅₃	semidirect
639. #446	C₂²×C₅₃	semidirect
640. #442	C₂²×C₅₃	semidirect
641. #440	C₂²×C₅₃	semidirect
642. #440	C₂²×C₅₃	semidirect
643. #440	C₂²×C₅₃	semidirect
644. C₄×Q₁₆	C₂²×C₅₃	semidirect
645. C₄×D₈	C₂²×C₅₃	semidirect
646. #436	C₂²×C₅₃	semidirect
647. #435	C₂²×C₅₃	semidirect
648. #435	C₂²×C₅₃	semidirect
649. #433	C₂²×C₅₃	semidirect
650. #432	C₂²×C₅₃	semidirect
651. #424	C₂²×C₅₃	semidirect
652. #423	C₂²×C₅₃	semidirect
653. #419	C₂²×C₅₃	semidirect
655. #417	C₂²×C₅₃	semidirect
656. C₂×#102	C₂²×C₅₃	semidirect
657. C₅₃	#62089	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×#3558	2
C₅₃×#3515	2
C₅₃×#3400	2
C₅₃×#3370	2
C₅₃×#3327	2
C₅₃×#3314	2
C₅₃×#3310	2
C₅₃×#3272	2
C₅₃×#3269	2
C₅₃×#3267	2
C₅₃×#3258	2
C₅₃×#3254	2
C₅₃×#3222	2
C₅₃×#3215	2
C₅₃×#3124	2
C₅₃×#3115	2
C₅₃×#3045	2
C₅₃×#3040	2
C₅₃×#2995	2
#62089	53

Subgroups — C53×#62089 #27269601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62089 #27269601