Subgroups — C₅₃×#61669 #27269181

Order 13568.

2166 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3318	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3311	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3307	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3306	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3268	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3267	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3264	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3264	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3204	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3198	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3012	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3008	C₂	1	2	yes	maximal, complemented
19	C₅₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	complemented
21	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
22	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
23	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
24	C₂²×D₈×C₅₃	C₂²	1	2	yes	complemented
25	C₅₃×#560	—	2	2	no	—
26	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
27	C₅₃×#553	C₂²	1	2	yes	complemented
28	C₅₃×#550	—	2	1	no	—
29	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#547	—	2	1	no	—
31	C₅₃×#547	C₂²	1	2	yes	complemented
32	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#546	—	2	2	no	—
34	C₅₃×#546	—	2	1	no	—
35	C₅₃×#546	C₂²	1	2	yes	—
36	C₅₃×#546	C₂²	1	2	yes	complemented
37	C₅₃×#546	C₂²	1	2	yes	complemented
38	D₄²×C₅₃	—	2	1	no	—
39	D₄²×C₅₃	C₂²	1	2	yes	complemented
40	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#542	—	2	1	no	—
42	C₅₃×#538	—	2	2	no	—
43	C₅₃×#537	C₂²	1	2	yes	complemented
44	C₅₃×#537	C₂²	1	2	yes	complemented
45	C₅₃×#535	—	2	1	no	—
46	C₅₃×#535	C₂²	1	2	yes	complemented
47	C₅₃×#534	—	2	1	no	—
48	C₅₃×#534	—	2	1	no	—
49	C₅₃×#532	C₂²	1	1	yes	characteristic
50	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
53	C₂×#121×C₅₃	—	2	2	no	—
54	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#496	C₂²	1	2	yes	complemented
57	C₅₃×#496	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#489	C₂²	1	2	yes	complemented
61	C₅₃×#485	C₂²	1	2	yes	complemented
62	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#483	C₂²	1	2	yes	complemented
64	C₅₃×#482	C₂²	1	2	yes	complemented
65	C₅₃×#481	C₂²	1	2	yes	complemented
66	C₅₃×#481	C₂²	1	2	yes	complemented
67	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#478	C₂²	1	2	yes	complemented
69	C₅₃×#476	C₂²	1	2	yes	complemented
70	C₅₃×#470	C₂²	1	2	yes	complemented
71	C₅₃×#469	C₂²	1	2	yes	complemented
72	C₅₃×#469	C₂²	1	2	yes	complemented
73	C₅₃×#468	C₂²	1	2	yes	complemented
74	C₅₃×#466	C₂²	1	2	yes	complemented
75	C₅₃×#465	C₂²	1	2	yes	complemented
76	C₅₃×#465	C₂²	1	2	yes	complemented
77	C₅₃×#465	C₂²	1	2	yes	complemented
78	C₅₃×#464	C₂²	1	2	yes	complemented
79	C₅₃×#463	C₂²	1	2	yes	complemented
80	C₅₃×#463	C₂²	1	2	yes	complemented
81	C₅₃×#461	C₂²	1	2	yes	complemented
82	C₅₃×#459	C₂²	1	2	yes	complemented
83	C₅₃×#459	C₂²	1	2	yes	complemented
84	C₅₃×#452	C₂²	1	2	yes	complemented
85	C₅₃×#452	C₂²	1	2	yes	complemented
86	C₅₃×#452	C₂²	1	2	yes	complemented
87	C₅₃×#450	C₂²	1	2	yes	complemented
88	C₅₃×#450	C₂²	1	2	yes	complemented
89	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#449	C₂²	1	2	yes	complemented
91	C₅₃×#449	C₂²	1	2	yes	complemented
92	C₅₃×#449	C₂²	1	2	yes	complemented
93	C₅₃×#449	C₂²	1	2	yes	complemented
94	C₅₃×#449	C₂²	1	2	yes	complemented
95	C₅₃×#449	C₂²	1	2	yes	complemented
96	C₅₃×#449	C₂²	1	2	yes	complemented
97	C₅₃×#447	C₂²	1	1	yes	characteristic
98	C₅₃×#447	C₂²	1	2	yes	complemented
99	C₅₃×#447	C₂²	1	2	yes	complemented
100	C₅₃×#447	C₂²	1	2	yes	complemented
101	C₅₃×#447	C₂²	1	2	yes	complemented
102	C₅₃×#447	C₂²	1	2	yes	complemented
103	C₅₃×#442	C₂²	1	2	yes	complemented
104	C₅₃×#442	C₂²	1	2	yes	complemented
105	C₅₃×#442	C₂²	1	2	yes	complemented
106	C₅₃×#440	C₂²	1	2	yes	complemented
107	C₅₃×#435	C₂²	1	2	yes	complemented
108	C₅₃×#435	C₂²	1	2	yes	complemented
109	C₅₃×#435	C₂²	1	2	yes	complemented
110	C₅₃×#435	C₂²	1	2	yes	complemented
111	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#418	C₂²	1	2	yes	complemented
114	C₅₃×#417	C₂²	1	2	yes	complemented
115	C₅₃×#416	C₂²	1	2	yes	complemented
116	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
117	C₅₃×#408	C₂²	1	2	yes	complemented
118	C₅₃×#408	C₂²	1	2	yes	complemented
119	H(5,𝔽₂)×C₅₃	—	4	4	no	—
120	H(5,𝔽₂)×C₅₃	—	4	4	no	—
121	C₂×#41×C₅₃	—	2	2	no	—
122	C₂×#41×C₅₃	—	2	1	no	—
123	C₂×#41×C₅₃	—	2	1	no	—
124	C₂×#41×C₅₃	C₂³	1	2	yes	—
125	C₂×#41×C₅₃	C₂³	1	2	yes	—
126	C₂×#41×C₅₃	C₂³	1	2	yes	—
127	C₂×#41×C₅₃	C₂³	1	2	yes	—
128	C₂×#41×C₅₃	C₂³	1	2	yes	—
129	C₂²×D₄×C₅₃	—	2	2	no	—
130	C₂²×D₄×C₅₃	—	2	2	no	—
131	C₂²×D₄×C₅₃	—	2	2	no	—
132	C₂²×D₄×C₅₃	—	2	2	no	—
133	C₂²×D₄×C₅₃	—	2	1	no	—
134	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
136	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₅₃	—	2	1	no	—
139	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
140	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
141	#135×C₅₃	—	4	4	no	—
142	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
148	C₂×D₈×C₅₃	—	4	4	no	—
149	C₂×D₈×C₅₃	C₂³	1	2	yes	—
150	C₂×D₈×C₅₃	C₂³	1	2	yes	—
151	C₂×D₈×C₅₃	C₂³	1	2	yes	—
152	C₂×D₈×C₅₃	C₂³	1	2	yes	—
153	C₂×D₈×C₅₃	C₂³	1	2	yes	—
154	C₂×D₈×C₅₃	C₂³	1	2	yes	—
155	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
158	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
160	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
162	#127×C₅₃	—	2	1	no	—
163	#127×C₅₃	—	2	2	no	—
164	#127×C₅₃	D₄	1	1	yes	characteristic
165	#127×C₅₃	C₂³	1	1	yes	characteristic
166	#127×C₅₃	C₂³	1	1	yes	characteristic
167	#126×C₅₃	—	2	2	no	—
168	#126×C₅₃	—	2	2	no	—
169	#126×C₅₃	—	2	1	no	—
170	#125×C₅₃	C₂³	1	1	yes	characteristic
171	#124×C₅₃	—	2	1	no	—
172	#124×C₅₃	—	2	2	no	—
173	#124×C₅₃	—	2	1	no	—
174	#124×C₅₃	D₄	1	2	yes	—
175	#124×C₅₃	C₂³	1	2	yes	—
176	#124×C₅₃	C₂³	1	1	yes	characteristic
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	1	no	—
185	C₂²⋊Q₈×C₅₃	—	2	1	no	—
186	C₂²⋊Q₈×C₅₃	—	2	2	no	—
187	C₂²⋊Q₈×C₅₃	—	2	2	no	—
188	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
189	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
191	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
192	#121×C₅₃	—	2	2	no	—
193	#121×C₅₃	—	2	1	no	—
194	#121×C₅₃	—	2	2	no	—
195	#121×C₅₃	—	2	2	no	—
196	#121×C₅₃	—	2	2	no	—
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	2	no	—
202	#121×C₅₃	—	2	2	no	—
203	#121×C₅₃	—	2	2	no	—
204	#121×C₅₃	—	2	2	no	—
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	1	no	—
207	#121×C₅₃	—	2	1	no	—
208	#121×C₅₃	—	2	1	no	—
209	#121×C₅₃	D₄	1	2	yes	—
210	#121×C₅₃	D₄	1	1	yes	characteristic
211	#121×C₅₃	D₄	1	1	yes	characteristic
212	#121×C₅₃	C₂³	1	1	yes	characteristic
213	#121×C₅₃	C₂³	1	2	yes	—
214	#121×C₅₃	C₂³	1	2	yes	—
215	#121×C₅₃	C₂³	1	2	yes	—
216	#121×C₅₃	C₂³	1	2	yes	—
217	#121×C₅₃	C₂³	1	2	yes	—
218	#121×C₅₃	C₂³	1	2	yes	—
219	#120×C₅₃	—	2	2	no	—
220	#120×C₅₃	—	2	2	no	—
221	#120×C₅₃	—	2	2	no	—
222	#120×C₅₃	—	2	2	no	—
223	#120×C₅₃	—	2	2	no	—
224	#120×C₅₃	—	2	2	no	—
225	#120×C₅₃	—	2	2	no	—
226	#120×C₅₃	—	2	2	no	—
227	C₄×Q₈×C₅₃	—	2	1	no	—
228	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₅₃	—	2	1	no	—
230	C₄×D₄×C₅₃	—	2	2	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	1	no	—
235	C₄×D₄×C₅₃	—	2	1	no	—
236	C₄×D₄×C₅₃	—	2	1	no	—
237	C₄×D₄×C₅₃	C₂³	1	2	yes	—
238	C₄×D₄×C₅₃	C₂³	1	2	yes	—
239	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₃	C₂³	1	2	yes	—
243	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
244	#117×C₅₃	—	2	1	no	—
245	#117×C₅₃	C₂³	1	2	yes	—
246	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
247	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
249	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
250	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
251	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
252	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
253	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
254	#107×C₅₃	C₂³	1	2	yes	—
255	#106×C₅₃	C₂³	1	2	yes	—
256	#106×C₅₃	C₂³	1	2	yes	—
257	#106×C₅₃	C₂³	1	2	yes	—
258	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
259	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
260	#103×C₅₃	C₂³	1	2	yes	—
261	#103×C₅₃	C₂³	1	2	yes	—
262	#103×C₅₃	C₂³	1	2	yes	—
263	#103×C₅₃	C₂³	1	2	yes	—
264	#103×C₅₃	C₂³	1	2	yes	—
265	#102×C₅₃	C₂³	1	2	yes	—
266	#102×C₅₃	C₂³	1	2	yes	—
267	#102×C₅₃	C₂³	1	2	yes	—
268	#102×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	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
278	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
280	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
281	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
283	#97×C₅₃	C₂³	1	2	yes	—
284	#97×C₅₃	C₂³	1	1	yes	characteristic
285	#97×C₅₃	C₂³	1	1	yes	characteristic
286	C₂⁴×C₅₃	—	2	1	no	—
287	C₂⁴×C₅₃	—	2	2	no	—
288	C₂⁴×C₅₃	—	2	2	no	—
289	C₂⁴×C₅₃	—	2	2	no	—
290	#41×C₅₃	—	2	4	no	—
291	#41×C₅₃	—	2	4	no	—
292	#41×C₅₃	—	4	2	no	—
293	#41×C₅₃	—	4	2	no	—
294	#41×C₅₃	—	4	2	no	—
295	#41×C₅₃	—	4	2	no	—
296	#41×C₅₃	—	4	2	no	—
297	#41×C₅₃	—	4	2	no	—
298	#41×C₅₃	—	4	2	no	—
299	#41×C₅₃	—	4	2	no	—
300	#41×C₅₃	—	4	8	no	—
301	#41×C₅₃	—	8	2	no	—
302	#41×C₅₃	—	8	2	no	—
303	C₂×Q₈×C₅₃	—	2	1	no	—
304	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
305	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
306	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
307	C₂×D₄×C₅₃	—	2	4	no	—
308	C₂×D₄×C₅₃	—	2	4	no	—
309	C₂×D₄×C₅₃	—	2	4	no	—
310	C₂×D₄×C₅₃	—	2	2	no	—
311	C₂×D₄×C₅₃	—	2	2	no	—
312	C₂×D₄×C₅₃	—	2	2	no	—
313	C₂×D₄×C₅₃	—	2	1	no	—
314	C₂×D₄×C₅₃	—	2	2	no	—
315	C₂×D₄×C₅₃	—	2	2	no	—
316	C₂×D₄×C₅₃	—	2	2	no	—
317	C₂×D₄×C₅₃	—	2	2	no	—
318	C₂×D₄×C₅₃	—	2	2	no	—
319	C₂×D₄×C₅₃	—	2	2	no	—
320	C₂×D₄×C₅₃	—	2	2	no	—
321	C₂×D₄×C₅₃	—	2	1	no	—
322	C₂×D₄×C₅₃	—	2	1	no	—
323	C₂×D₄×C₅₃	—	2	1	no	—
324	C₂×D₄×C₅₃	—	2	2	no	—
325	C₂×D₄×C₅₃	—	2	2	no	—
326	C₂×D₄×C₅₃	—	2	1	no	—
327	C₂×D₄×C₅₃	—	2	1	no	—
328	C₂×D₄×C₅₃	—	2	2	no	—
329	C₂×D₄×C₅₃	—	4	2	no	—
330	C₂×D₄×C₅₃	—	4	2	no	—
331	C₂×D₄×C₅₃	—	4	2	no	—
332	C₂×D₄×C₅₃	—	4	2	no	—
333	C₂×D₄×C₅₃	—	4	8	no	—
334	C₂×D₄×C₅₃	—	4	8	no	—
335	C₂×D₄×C₅₃	—	4	8	no	—
336	C₂×D₄×C₅₃	—	8	4	no	—
337	C₂×D₄×C₅₃	—	8	2	no	—
338	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
339	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
345	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
347	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₅₃	—	2	1	no	—
349	C₂²×C₄×C₅₃	—	2	2	no	—
350	C₂²×C₄×C₅₃	—	2	2	no	—
351	C₂²×C₄×C₅₃	—	2	2	no	—
352	C₂²×C₄×C₅₃	—	2	2	no	—
353	C₂²×C₄×C₅₃	—	2	1	no	—
354	C₂²×C₄×C₅₃	—	2	2	no	—
355	C₂²×C₄×C₅₃	—	2	2	no	—
356	C₂²×C₄×C₅₃	—	2	2	no	—
357	C₂²×C₄×C₅₃	—	2	2	no	—
358	C₂²×C₄×C₅₃	—	8	2	no	—
359	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
364	Q₁₆×C₅₃	—	4	2	no	—
365	SD₁₆×C₅₃	—	2	4	no	—
366	SD₁₆×C₅₃	—	4	2	no	—
367	SD₁₆×C₅₃	—	4	2	no	—
368	SD₁₆×C₅₃	—	4	2	no	—
369	SD₁₆×C₅₃	—	4	2	no	—
370	D₈×C₅₃	—	2	4	no	—
371	D₈×C₅₃	—	2	4	no	—
372	D₈×C₅₃	—	2	4	no	—
373	D₈×C₅₃	—	4	2	no	—
374	D₈×C₅₃	—	4	2	no	—
375	D₈×C₅₃	—	4	2	no	—
376	M₁₆×C₅₃	—	4	2	no	—
377	M₁₆×C₅₃	—	4	2	no	—
378	C₂×C₈×C₅₃	—	4	2	no	—
379	C₂×C₈×C₅₃	—	4	2	no	—
380	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
381	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
382	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
383	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
384	C₄⋊C₄×C₅₃	—	2	1	no	—
385	C₄⋊C₄×C₅₃	—	2	2	no	—
386	C₄⋊C₄×C₅₃	—	2	2	no	—
387	C₄⋊C₄×C₅₃	—	2	1	no	—
388	C₄⋊C₄×C₅₃	—	2	2	no	—
389	C₄⋊C₄×C₅₃	—	2	1	no	—
390	C₄⋊C₄×C₅₃	—	2	1	no	—
391	C₄⋊C₄×C₅₃	—	2	1	no	—
392	C₄⋊C₄×C₅₃	—	2	1	no	—
393	C₄⋊C₄×C₅₃	—	2	1	no	—
394	C₄⋊C₄×C₅₃	—	2	2	no	—
395	C₄⋊C₄×C₅₃	—	2	1	no	—
396	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
403	C₂²⋊C₄×C₅₃	—	2	2	no	—
404	C₂²⋊C₄×C₅₃	—	2	2	no	—
405	C₂²⋊C₄×C₅₃	—	2	2	no	—
406	C₂²⋊C₄×C₅₃	—	2	2	no	—
407	C₂²⋊C₄×C₅₃	—	2	1	no	—
408	C₂²⋊C₄×C₅₃	—	2	2	no	—
409	C₂²⋊C₄×C₅₃	—	2	1	no	—
410	C₂²⋊C₄×C₅₃	—	2	2	no	—
411	C₂²⋊C₄×C₅₃	—	2	2	no	—
412	C₂²⋊C₄×C₅₃	—	2	2	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
414	C₂²⋊C₄×C₅₃	—	2	2	no	—
415	C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂²⋊C₄×C₅₃	—	2	1	no	—
417	C₂²⋊C₄×C₅₃	—	2	2	no	—
418	C₂²⋊C₄×C₅₃	—	2	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	1	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	no	—
423	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
427	C₄²×C₅₃	—	2	1	no	—
428	C₄²×C₅₃	—	2	2	no	—
429	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
430	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
433	C₂³×C₅₃	—	2	4	no	—
434	C₂³×C₅₃	—	2	2	no	—
435	C₂³×C₅₃	—	2	2	no	—
436	C₂³×C₅₃	—	2	2	no	—
437	C₂³×C₅₃	—	2	1	no	—
438	C₂³×C₅₃	—	4	4	no	—
439	C₂³×C₅₃	—	4	4	no	—
440	C₂³×C₅₃	—	8	1	no	—
441	C₂³×C₅₃	—	8	1	no	—
442	C₂³×C₅₃	—	8	2	no	—
443	C₂³×C₅₃	—	8	2	no	—
444	C₂³×C₅₃	—	8	2	no	—
445	C₂³×C₅₃	—	8	2	no	—
446	C₂³×C₅₃	—	8	2	no	—
447	C₂³×C₅₃	—	8	2	no	—
448	C₂³×C₅₃	—	8	2	no	—
449	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
450	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
451	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
452	Q₈×C₅₃	—	2	2	no	—
453	Q₈×C₅₃	—	2	2	no	—
454	Q₈×C₅₃	—	2	2	no	—
455	Q₈×C₅₃	—	4	2	no	—
456	Q₈×C₅₃	—	4	2	no	—
457	D₄×C₅₃	—	2	4	no	—
458	D₄×C₅₃	—	2	2	no	—
459	D₄×C₅₃	—	2	2	no	—
460	D₄×C₅₃	—	2	2	no	—
461	D₄×C₅₃	—	2	2	no	—
462	D₄×C₅₃	—	2	2	no	—
463	D₄×C₅₃	—	2	2	no	—
464	D₄×C₅₃	—	4	2	no	—
465	D₄×C₅₃	—	4	2	no	—
466	D₄×C₅₃	—	4	2	no	—
467	D₄×C₅₃	—	4	2	no	—
468	D₄×C₅₃	—	4	1	no	—
469	D₄×C₅₃	—	4	1	no	—
470	D₄×C₅₃	—	4	4	no	—
471	D₄×C₅₃	—	4	4	no	—
472	D₄×C₅₃	—	4	2	no	—
473	D₄×C₅₃	—	4	2	no	—
474	D₄×C₅₃	—	4	4	no	—
475	D₄×C₅₃	—	4	4	no	—
476	D₄×C₅₃	—	4	4	no	—
477	D₄×C₅₃	—	8	1	no	—
478	D₄×C₅₃	—	8	1	no	—
479	D₄×C₅₃	—	8	2	no	—
480	D₄×C₅₃	—	8	1	no	—
481	D₄×C₅₃	—	8	2	no	—
482	D₄×C₅₃	—	8	2	no	—
483	D₄×C₅₃	—	8	2	no	—
484	D₄×C₅₃	—	8	2	no	—
485	D₄×C₅₃	—	8	2	no	—
486	D₄×C₅₃	—	8	2	no	—
487	D₄×C₅₃	—	8	2	no	—
488	D₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
489	C₂×C₄×C₅₃	—	2	2	no	—
490	C₂×C₄×C₅₃	—	2	2	no	—
491	C₂×C₄×C₅₃	—	2	2	no	—
492	C₂×C₄×C₅₃	—	2	2	no	—
493	C₂×C₄×C₅₃	—	2	2	no	—
494	C₂×C₄×C₅₃	—	2	2	no	—
495	C₂×C₄×C₅₃	—	2	2	no	—
496	C₂×C₄×C₅₃	—	2	1	no	—
497	C₂×C₄×C₅₃	—	2	2	no	—
498	C₂×C₄×C₅₃	—	2	1	no	—
499	C₂×C₄×C₅₃	—	2	1	no	—
500	C₂×C₄×C₅₃	—	4	1	no	—
501	C₂×C₄×C₅₃	—	4	1	no	—
502	C₂×C₄×C₅₃	—	4	4	no	—
503	C₂×C₄×C₅₃	—	4	4	no	—
504	C₂×C₄×C₅₃	—	4	4	no	—
505	C₂×C₄×C₅₃	—	4	4	no	—
506	C₂×C₄×C₅₃	—	4	2	no	—
507	C₂×C₄×C₅₃	—	8	2	no	—
508	C₂×C₄×C₅₃	—	8	2	no	—
509	C₂×C₄×C₅₃	—	8	2	no	—
510	C₂×C₄×C₅₃	—	8	1	no	—
511	C₂×C₄×C₅₃	—	8	2	no	—
512	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
520	C₈×C₅₃	—	2	2	no	—
521	C₈×C₅₃	—	2	2	no	—
522	C₈×C₅₃	—	2	2	no	—
523	C₈×C₅₃	—	2	2	no	—
524	#61669	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
525	C₂²×C₅₃	—	2	1	no	—
526	C₂²×C₅₃	—	2	1	no	—
527	C₂²×C₅₃	—	2	2	no	—
528	C₂²×C₅₃	—	2	2	no	—
529	C₂²×C₅₃	—	2	2	no	—
530	C₂²×C₅₃	—	2	2	no	—
531	C₂²×C₅₃	—	2	1	no	—
532	C₂²×C₅₃	—	2	2	no	—
533	C₂²×C₅₃	—	2	2	no	—
534	C₂²×C₅₃	—	2	4	no	—
535	C₂²×C₅₃	—	4	2	no	—
536	C₂²×C₅₃	—	4	2	no	—
537	C₂²×C₅₃	—	4	1	no	—
538	C₂²×C₅₃	—	4	2	no	—
539	C₂²×C₅₃	—	4	2	no	—
540	C₂²×C₅₃	—	4	2	no	—
541	C₂²×C₅₃	—	4	2	no	—
542	C₂²×C₅₃	—	4	1	no	—
543	C₂²×C₅₃	—	4	2	no	—
544	C₂²×C₅₃	—	4	2	no	—
545	C₂²×C₅₃	—	4	1	no	—
546	C₂²×C₅₃	—	8	4	no	—
547	C₂²×C₅₃	—	16	4	no	—
548	C₂²×C₅₃	—	16	4	no	—
549	C₂²×C₅₃	—	16	4	no	—
550	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
551	C₄×C₅₃	—	2	1	no	—
552	C₄×C₅₃	—	2	1	no	—
553	C₄×C₅₃	—	2	1	no	—
554	C₄×C₅₃	—	2	1	no	—
555	C₄×C₅₃	—	2	1	no	—
556	C₄×C₅₃	—	2	2	no	—
557	C₄×C₅₃	—	2	2	no	—
558	C₄×C₅₃	—	4	2	no	—
559	C₄×C₅₃	—	4	1	no	—
560	C₄×C₅₃	—	4	2	no	—
561	C₄×C₅₃	—	4	1	no	—
562	C₄×C₅₃	—	4	2	no	—
563	C₄×C₅₃	—	4	1	no	—
564	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
565	#3546	C₂×C₅₃	1	1	yes	characteristic, complemented
566	#3496	C₂×C₅₃	1	1	yes	characteristic, complemented
567	#3318	C₂×C₅₃	1	2	yes	complemented
568	#3311	C₂×C₅₃	1	2	yes	complemented
569	#3307	C₂×C₅₃	1	2	yes	complemented
570	#3306	C₂×C₅₃	1	2	yes	complemented
571	#3268	C₂×C₅₃	1	2	yes	complemented
572	#3267	C₂×C₅₃	1	2	yes	complemented
573	#3264	C₂×C₅₃	1	2	yes	complemented
574	#3264	C₂×C₅₃	1	2	yes	complemented
575	#3219	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#3214	C₂×C₅₃	1	1	yes	characteristic, complemented
577	#3204	C₂×C₅₃	1	2	yes	complemented
578	#3198	C₂×C₅₃	1	2	yes	complemented
579	#3114	C₂×C₅₃	1	1	yes	characteristic, complemented
580	#3109	C₂×C₅₃	1	1	yes	characteristic, complemented
581	#3012	C₂×C₅₃	1	2	yes	complemented
582	#3008	C₂×C₅₃	1	2	yes	complemented
583	#2980	C₂×C₅₃	1	1	yes	characteristic, complemented
584	C₂×C₅₃	—	4	1	no	—
585	C₂×C₅₃	—	4	2	no	—
586	C₂×C₅₃	—	4	2	no	—
587	C₂×C₅₃	—	4	4	no	—
588	C₂×C₅₃	—	8	2	no	—
589	C₂×C₅₃	—	8	1	no	—
590	C₂×C₅₃	—	8	2	no	—
591	C₂×C₅₃	#3484	1	1	yes	characteristic
592	C₂×C₅₃	#3585	1	1	yes	characteristic
593	C₂×C₅₃	#3585	1	1	yes	characteristic
594	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	2	yes	complemented
595	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
596	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
597	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
598	C₂²×D₈	C₂²×C₅₃	1	2	yes	complemented
599	#560	—	2	2	no	—
600	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
601	#553	C₂²×C₅₃	1	2	yes	complemented
602	#550	—	2	1	no	—
603	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
604	#547	—	2	1	no	—
605	#547	C₂²×C₅₃	1	2	yes	complemented
606	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
607	#546	—	2	2	no	—
608	#546	—	2	1	no	—
609	#546	C₂²×C₅₃	1	2	yes	—
610	#546	C₂²×C₅₃	1	2	yes	complemented
611	#546	C₂²×C₅₃	1	2	yes	complemented
612	D₄²	—	2	1	no	—
613	D₄²	C₂²×C₅₃	1	2	yes	complemented
614	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
615	#542	—	2	1	no	—
616	#538	—	2	2	no	—
617	#537	C₂²×C₅₃	1	2	yes	complemented
618	#537	C₂²×C₅₃	1	2	yes	complemented
619	#535	—	2	1	no	—
620	#535	C₂²×C₅₃	1	2	yes	complemented
621	#534	—	2	1	no	—
622	#534	—	2	1	no	—
623	#532	C₂²×C₅₃	1	1	yes	characteristic
624	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
625	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
626	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
627	C₂×#121	—	2	2	no	—
628	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
629	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
630	#496	C₂²×C₅₃	1	2	yes	complemented
631	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
632	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
633	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
634	#489	C₂²×C₅₃	1	2	yes	complemented
635	#485	C₂²×C₅₃	1	2	yes	complemented
636	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
637	#483	C₂²×C₅₃	1	2	yes	complemented
638	#482	C₂²×C₅₃	1	2	yes	complemented
639	#481	C₂²×C₅₃	1	2	yes	complemented
640	#481	C₂²×C₅₃	1	2	yes	complemented
641	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
642	#478	C₂²×C₅₃	1	2	yes	complemented
643	#476	C₂²×C₅₃	1	2	yes	complemented
644	#470	C₂²×C₅₃	1	2	yes	complemented
645	#469	C₂²×C₅₃	1	2	yes	complemented
646	#469	C₂²×C₅₃	1	2	yes	complemented
647	#468	C₂²×C₅₃	1	2	yes	complemented
648	#466	C₂²×C₅₃	1	2	yes	complemented
649	#465	C₂²×C₅₃	1	2	yes	complemented
650	#465	C₂²×C₅₃	1	2	yes	complemented
651	#465	C₂²×C₅₃	1	2	yes	complemented
652	#464	C₂²×C₅₃	1	2	yes	complemented
653	#463	C₂²×C₅₃	1	2	yes	complemented
654	#463	C₂²×C₅₃	1	2	yes	complemented
655	#461	C₂²×C₅₃	1	2	yes	complemented
656	#459	C₂²×C₅₃	1	2	yes	complemented
657	#459	C₂²×C₅₃	1	2	yes	complemented
658	#452	C₂²×C₅₃	1	2	yes	complemented
659	#452	C₂²×C₅₃	1	2	yes	complemented
660	#452	C₂²×C₅₃	1	2	yes	complemented
661	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
662	#450	C₂²×C₅₃	1	2	yes	complemented
663	#450	C₂²×C₅₃	1	2	yes	complemented
664	#449	C₂²×C₅₃	1	2	yes	complemented
665	#449	C₂²×C₅₃	1	2	yes	complemented
666	#449	C₂²×C₅₃	1	2	yes	complemented
667	#449	C₂²×C₅₃	1	2	yes	complemented
668	#449	C₂²×C₅₃	1	2	yes	complemented
669	#449	C₂²×C₅₃	1	2	yes	complemented
670	#449	C₂²×C₅₃	1	2	yes	complemented
671	#447	C₂²×C₅₃	1	1	yes	characteristic
672	#447	C₂²×C₅₃	1	2	yes	complemented
673	#447	C₂²×C₅₃	1	2	yes	complemented
674	#447	C₂²×C₅₃	1	2	yes	complemented
675	#447	C₂²×C₅₃	1	2	yes	complemented
676	#447	C₂²×C₅₃	1	2	yes	complemented
677	#442	C₂²×C₅₃	1	2	yes	complemented
678	#442	C₂²×C₅₃	1	2	yes	complemented
679	#442	C₂²×C₅₃	1	2	yes	complemented
680	#440	C₂²×C₅₃	1	2	yes	complemented
681	#435	C₂²×C₅₃	1	2	yes	complemented
682	#435	C₂²×C₅₃	1	2	yes	complemented
683	#435	C₂²×C₅₃	1	2	yes	complemented
684	#435	C₂²×C₅₃	1	2	yes	complemented
685	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
686	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#418	C₂²×C₅₃	1	2	yes	complemented
688	#417	C₂²×C₅₃	1	2	yes	complemented
689	#416	C₂²×C₅₃	1	2	yes	complemented
690	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
691	#408	C₂²×C₅₃	1	2	yes	complemented
692	#408	C₂²×C₅₃	1	2	yes	complemented
693	C₅₃	#61669	1	1	yes	characteristic, direct product factor, Sylow
694	H(5,𝔽₂)	—	4	4	no	—
695	H(5,𝔽₂)	—	4	4	no	—
696	C₂×#41	—	2	2	no	—
697	C₂×#41	—	2	1	no	—
698	C₂×#41	—	2	1	no	—
699	C₂×#41	C₂³×C₅₃	1	2	yes	—
700	C₂×#41	C₂³×C₅₃	1	2	yes	—
701	C₂×#41	C₂³×C₅₃	1	2	yes	—
702	C₂×#41	C₂³×C₅₃	1	2	yes	—
703	C₂×#41	C₂³×C₅₃	1	2	yes	—
704	C₂²×D₄	—	2	2	no	—
705	C₂²×D₄	—	2	2	no	—
706	C₂²×D₄	—	2	2	no	—
707	C₂²×D₄	—	2	2	no	—
708	C₂²×D₄	—	2	1	no	—
709	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
710	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
711	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
712	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
713	C₂³×C₄	—	2	1	no	—
714	AGL(1,ℤ/8)	—	4	4	no	—
715	AGL(1,ℤ/8)	—	4	4	no	—
716	#135	—	4	4	no	—
717	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
723	C₂×D₈	—	4	4	no	—
724	C₂×D₈	C₂³×C₅₃	1	2	yes	—
725	C₂×D₈	C₂³×C₅₃	1	2	yes	—
726	C₂×D₈	C₂³×C₅₃	1	2	yes	—
727	C₂×D₈	C₂³×C₅₃	1	2	yes	—
728	C₂×D₈	C₂³×C₅₃	1	2	yes	—
729	C₂×D₈	C₂³×C₅₃	1	2	yes	—
730	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
731	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
732	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
733	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
734	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
737	#127	—	2	1	no	—
738	#127	—	2	2	no	—
739	#127	D₄×C₅₃	1	1	yes	characteristic
740	#127	C₂³×C₅₃	1	1	yes	characteristic
741	#127	C₂³×C₅₃	1	1	yes	characteristic
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	1	no	—
745	#125	C₂³×C₅₃	1	1	yes	characteristic
746	#124	—	2	2	no	—
747	#124	—	2	1	no	—
748	#124	—	2	1	no	—
749	#124	D₄×C₅₃	1	2	yes	—
750	#124	C₂³×C₅₃	1	1	yes	characteristic
751	#124	C₂³×C₅₃	1	2	yes	—
752	#123	—	2	1	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
764	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
765	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
766	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
767	#121	—	2	2	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	1	no	—
776	#121	—	2	1	no	—
777	#121	—	2	1	no	—
778	#121	—	2	2	no	—
779	#121	—	2	1	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	D₄×C₅₃	1	2	yes	—
785	#121	D₄×C₅₃	1	1	yes	characteristic
786	#121	D₄×C₅₃	1	1	yes	characteristic
787	#121	C₂³×C₅₃	1	1	yes	characteristic
788	#121	C₂³×C₅₃	1	2	yes	—
789	#121	C₂³×C₅₃	1	2	yes	—
790	#121	C₂³×C₅₃	1	2	yes	—
791	#121	C₂³×C₅₃	1	2	yes	—
792	#121	C₂³×C₅₃	1	2	yes	—
793	#121	C₂³×C₅₃	1	2	yes	—
794	#120	—	2	2	no	—
795	#120	—	2	2	no	—
796	#120	—	2	2	no	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	#120	—	2	2	no	—
800	#120	—	2	2	no	—
801	#120	—	2	2	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	C₂³×C₅₃	1	2	yes	—
813	C₄×D₄	C₂³×C₅₃	1	2	yes	—
814	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₅₃	1	2	yes	—
816	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₅₃	1	2	yes	—
818	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
819	#117	—	2	1	no	—
820	#117	C₂³×C₅₃	1	2	yes	—
821	C₂×C₄⋊C₄	—	2	2	no	—
822	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
823	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
824	C₂×C₂²⋊C₄	—	2	1	no	—
825	C₂×C₂²⋊C₄	—	2	2	no	—
826	C₂×C₂²⋊C₄	—	2	2	no	—
827	C₂×C₂²⋊C₄	—	2	2	no	—
828	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
829	#107	C₂³×C₅₃	1	2	yes	—
830	#106	C₂³×C₅₃	1	2	yes	—
831	#106	C₂³×C₅₃	1	2	yes	—
832	#106	C₂³×C₅₃	1	2	yes	—
833	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
834	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
835	#103	C₂³×C₅₃	1	2	yes	—
836	#103	C₂³×C₅₃	1	2	yes	—
837	#103	C₂³×C₅₃	1	2	yes	—
838	#103	C₂³×C₅₃	1	2	yes	—
839	#103	C₂³×C₅₃	1	2	yes	—
840	#102	C₂³×C₅₃	1	2	yes	—
841	#102	C₂³×C₅₃	1	2	yes	—
842	#102	C₂³×C₅₃	1	2	yes	—
843	#102	C₂³×C₅₃	1	2	yes	—
844	#102	C₂³×C₅₃	1	2	yes	—
845	#102	C₂³×C₅₃	1	2	yes	—
846	#102	C₂³×C₅₃	1	2	yes	—
847	#102	C₂³×C₅₃	1	2	yes	—
848	#102	C₂³×C₅₃	1	2	yes	—
849	#102	C₂³×C₅₃	1	2	yes	—
850	#102	C₂³×C₅₃	1	2	yes	—
851	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
852	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
853	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
854	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
855	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
856	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
857	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
858	#97	C₂³×C₅₃	1	2	yes	—
859	#97	C₂³×C₅₃	1	1	yes	characteristic
860	#97	C₂³×C₅₃	1	1	yes	characteristic
861	C₂⁴	—	2	1	no	—
862	C₂⁴	—	2	2	no	—
863	C₂⁴	—	2	2	no	—
864	C₂⁴	—	2	2	no	—
865	#41	—	2	4	no	—
866	#41	—	2	4	no	—
867	#41	—	4	2	no	—
868	#41	—	4	2	no	—
869	#41	—	4	2	no	—
870	#41	—	4	2	no	—
871	#41	—	4	2	no	—
872	#41	—	4	2	no	—
873	#41	—	4	2	no	—
874	#41	—	4	2	no	—
875	#41	—	4	8	no	—
876	#41	—	8	2	no	—
877	#41	—	8	2	no	—
878	C₂×Q₈	—	2	1	no	—
879	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
880	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
881	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
882	C₂×D₄	—	2	4	no	—
883	C₂×D₄	—	2	4	no	—
884	C₂×D₄	—	2	4	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	4	2	no	—
905	C₂×D₄	—	4	2	no	—
906	C₂×D₄	—	4	2	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	—	4	8	no	—
909	C₂×D₄	—	4	8	no	—
910	C₂×D₄	—	4	8	no	—
911	C₂×D₄	—	8	4	no	—
912	C₂×D₄	—	8	2	no	—
913	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
914	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
915	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
916	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
917	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
918	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
919	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
920	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
921	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
922	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	1	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	—	8	2	no	—
934	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
935	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
937	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
938	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
939	Q₁₆	—	4	2	no	—
940	SD₁₆	—	2	4	no	—
941	SD₁₆	—	4	2	no	—
942	SD₁₆	—	4	2	no	—
943	SD₁₆	—	4	2	no	—
944	SD₁₆	—	4	2	no	—
945	D₈	—	2	4	no	—
946	D₈	—	2	4	no	—
947	D₈	—	2	4	no	—
948	D₈	—	4	2	no	—
949	D₈	—	4	2	no	—
950	D₈	—	4	2	no	—
951	M₁₆	—	4	2	no	—
952	M₁₆	—	4	2	no	—
953	C₂×C₈	—	4	2	no	—
954	C₂×C₈	—	4	2	no	—
955	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
956	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
957	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
958	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
973	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
976	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1001	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1005	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1008	C₂³	—	2	4	no	—
1009	C₂³	—	2	2	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	2	no	—
1012	C₂³	—	2	2	no	—
1013	C₂³	—	4	4	no	—
1014	C₂³	—	4	4	no	—
1015	C₂³	—	8	1	no	—
1016	C₂³	—	8	1	no	—
1017	C₂³	—	8	2	no	—
1018	C₂³	—	8	2	no	—
1019	C₂³	—	8	2	no	—
1020	C₂³	—	8	2	no	—
1021	C₂³	—	8	2	no	—
1022	C₂³	—	8	2	no	—
1023	C₂³	—	8	2	no	—
1024	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1025	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1026	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1027	Q₈	—	2	2	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	4	2	no	—
1032	D₄	—	2	4	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	1	no	—
1044	D₄	—	4	1	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	4	4	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	4	no	—
1050	D₄	—	4	4	no	—
1051	D₄	—	4	4	no	—
1052	D₄	—	8	1	no	—
1053	D₄	—	8	1	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	1	no	—
1056	D₄	—	8	2	no	—
1057	D₄	—	8	2	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	2	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	2	no	—
1062	D₄	—	8	2	no	—
1063	D₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	4	1	no	—
1076	C₂×C₄	—	4	1	no	—
1077	C₂×C₄	—	4	4	no	—
1078	C₂×C₄	—	4	4	no	—
1079	C₂×C₄	—	4	4	no	—
1080	C₂×C₄	—	4	4	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	1	no	—
1086	C₂×C₄	—	8	2	no	—
1087	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1091	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1092	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1093	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1094	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1095	C₈	—	2	2	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	2	no	—
1098	C₈	—	2	2	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	4	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	8	4	no	—
1121	C₂²	—	16	4	no	—
1122	C₂²	—	16	4	no	—
1123	C₂²	—	16	4	no	—
1124	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1125	C₄	—	2	1	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	1	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	2	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	1	no	—
1138	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1139	C₂	—	4	1	no	—
1140	C₂	—	4	2	no	—
1141	C₂	—	4	2	no	—
1142	C₂	—	4	4	no	—
1143	C₂	—	8	2	no	—
1144	C₂	—	8	1	no	—
1145	C₂	—	8	2	no	—
1146	C₂	C₅₃×#3484	1	1	yes	characteristic
1147	C₂	C₅₃×#3585	1	1	yes	characteristic
1148	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3546	C₂	semidirect
2. C₅₃×#3496	C₂	semidirect
3. C₅₃×#3318	C₂	semidirect
4. C₅₃×#3311	C₂	semidirect
5. C₅₃×#3307	C₂	semidirect
6. C₅₃×#3306	C₂	semidirect
7. C₅₃×#3268	C₂	semidirect
8. C₅₃×#3267	C₂	semidirect
9. C₅₃×#3264	C₂	semidirect
10. C₅₃×#3264	C₂	semidirect
11. C₅₃×#3219	C₂	semidirect
12. C₅₃×#3214	C₂	semidirect
13. C₅₃×#3204	C₂	semidirect
14. C₅₃×#3198	C₂	semidirect
15. C₅₃×#3114	C₂	semidirect
16. C₅₃×#3109	C₂	semidirect
17. C₅₃×#3012	C₂	semidirect
18. C₅₃×#3008	C₂	semidirect
19. C₅₃×#2980	C₂	semidirect
20. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
21. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
22. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
23. C₂×#135×C₅₃	C₂²	semidirect
24. C₂²×D₈×C₅₃	C₂²	semidirect
26. C₅₃×#556	C₂²	semidirect
27. C₅₃×#553	C₂²	semidirect
29. C₅₃×#550	C₂²	semidirect
31. C₅₃×#547	C₂²	semidirect
32. C₅₃×#547	C₂²	semidirect
36. C₅₃×#546	C₂²	semidirect
37. C₅₃×#546	C₂²	semidirect
39. D₄²×C₅₃	C₂²	semidirect
40. D₄²×C₅₃	C₂²	semidirect
43. C₅₃×#537	C₂²	semidirect
44. C₅₃×#537	C₂²	semidirect
46. C₅₃×#535	C₂²	semidirect
50. C₅₃×#532	C₂²	semidirect
51. C₅₃×#532	C₂²	semidirect
52. C₅₃×#529	C₂²	semidirect
54. C₂×C₄×D₄×C₅₃	C₂²	semidirect
55. C₅₃×#497	C₂²	semidirect
56. C₅₃×#496	C₂²	semidirect
57. C₅₃×#496	C₂²	semidirect
58. C₅₃×#491	C₂²	semidirect
59. C₅₃×#490	C₂²	semidirect
60. C₅₃×#489	C₂²	semidirect
61. C₅₃×#485	C₂²	semidirect
62. C₅₃×#483	C₂²	semidirect
63. C₅₃×#483	C₂²	semidirect
64. C₅₃×#482	C₂²	semidirect
65. C₅₃×#481	C₂²	semidirect
66. C₅₃×#481	C₂²	semidirect
67. C₅₃×#480	C₂²	semidirect
68. C₅₃×#478	C₂²	semidirect
69. C₅₃×#476	C₂²	semidirect
70. C₅₃×#470	C₂²	semidirect
71. C₅₃×#469	C₂²	semidirect
72. C₅₃×#469	C₂²	semidirect
73. C₅₃×#468	C₂²	semidirect
74. C₅₃×#466	C₂²	semidirect
75. C₅₃×#465	C₂²	semidirect
76. C₅₃×#465	C₂²	semidirect
77. C₅₃×#465	C₂²	semidirect
78. C₅₃×#464	C₂²	semidirect
79. C₅₃×#463	C₂²	semidirect
80. C₅₃×#463	C₂²	semidirect
81. C₅₃×#461	C₂²	semidirect
82. C₅₃×#459	C₂²	semidirect
83. C₅₃×#459	C₂²	semidirect
84. C₅₃×#452	C₂²	semidirect
85. C₅₃×#452	C₂²	semidirect
86. C₅₃×#452	C₂²	semidirect
87. C₅₃×#450	C₂²	semidirect
88. C₅₃×#450	C₂²	semidirect
89. C₅₃×#450	C₂²	semidirect
90. C₅₃×#449	C₂²	semidirect
91. C₅₃×#449	C₂²	semidirect
92. C₅₃×#449	C₂²	semidirect
93. C₅₃×#449	C₂²	semidirect
94. C₅₃×#449	C₂²	semidirect
95. C₅₃×#449	C₂²	semidirect
96. C₅₃×#449	C₂²	semidirect
98. C₅₃×#447	C₂²	semidirect
99. C₅₃×#447	C₂²	semidirect
100. C₅₃×#447	C₂²	semidirect
101. C₅₃×#447	C₂²	semidirect
102. C₅₃×#447	C₂²	semidirect
103. C₅₃×#442	C₂²	semidirect
104. C₅₃×#442	C₂²	semidirect
105. C₅₃×#442	C₂²	semidirect
106. C₅₃×#440	C₂²	semidirect
107. C₅₃×#435	C₂²	semidirect
108. C₅₃×#435	C₂²	semidirect
109. C₅₃×#435	C₂²	semidirect
110. C₅₃×#435	C₂²	semidirect
111. C₅₃×#432	C₂²	semidirect
112. C₅₃×#432	C₂²	semidirect
113. C₅₃×#418	C₂²	semidirect
114. C₅₃×#417	C₂²	semidirect
115. C₅₃×#416	C₂²	semidirect
116. C₂×#102×C₅₃	C₂²	semidirect
117. C₅₃×#408	C₂²	semidirect
118. C₅₃×#408	C₂²	semidirect
524. #61669	C₅₃	direct (N × H)
565. #3546	C₂×C₅₃	semidirect
566. #3496	C₂×C₅₃	semidirect
567. #3318	C₂×C₅₃	semidirect
568. #3311	C₂×C₅₃	semidirect
569. #3307	C₂×C₅₃	semidirect
570. #3306	C₂×C₅₃	semidirect
571. #3268	C₂×C₅₃	semidirect
572. #3267	C₂×C₅₃	semidirect
573. #3264	C₂×C₅₃	semidirect
574. #3264	C₂×C₅₃	semidirect
575. #3219	C₂×C₅₃	semidirect
576. #3214	C₂×C₅₃	semidirect
577. #3204	C₂×C₅₃	semidirect
578. #3198	C₂×C₅₃	semidirect
579. #3114	C₂×C₅₃	semidirect
580. #3109	C₂×C₅₃	semidirect
581. #3012	C₂×C₅₃	semidirect
582. #3008	C₂×C₅₃	semidirect
583. #2980	C₂×C₅₃	semidirect
594. C₂×H(5,𝔽₂)	C₂²×C₅₃	semidirect
595. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
596. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
597. C₂×#135	C₂²×C₅₃	semidirect
598. C₂²×D₈	C₂²×C₅₃	semidirect
600. #556	C₂²×C₅₃	semidirect
601. #553	C₂²×C₅₃	semidirect
603. #550	C₂²×C₅₃	semidirect
605. #547	C₂²×C₅₃	semidirect
606. #547	C₂²×C₅₃	semidirect
610. #546	C₂²×C₅₃	semidirect
611. #546	C₂²×C₅₃	semidirect
613. D₄²	C₂²×C₅₃	semidirect
614. D₄²	C₂²×C₅₃	semidirect
617. #537	C₂²×C₅₃	semidirect
618. #537	C₂²×C₅₃	semidirect
620. #535	C₂²×C₅₃	semidirect
624. #532	C₂²×C₅₃	semidirect
625. #532	C₂²×C₅₃	semidirect
626. #529	C₂²×C₅₃	semidirect
628. C₂×C₄×D₄	C₂²×C₅₃	semidirect
629. #497	C₂²×C₅₃	semidirect
630. #496	C₂²×C₅₃	semidirect
631. #496	C₂²×C₅₃	semidirect
632. #491	C₂²×C₅₃	semidirect
633. #490	C₂²×C₅₃	semidirect
634. #489	C₂²×C₅₃	semidirect
635. #485	C₂²×C₅₃	semidirect
636. #483	C₂²×C₅₃	semidirect
637. #483	C₂²×C₅₃	semidirect
638. #482	C₂²×C₅₃	semidirect
639. #481	C₂²×C₅₃	semidirect
640. #481	C₂²×C₅₃	semidirect
641. #480	C₂²×C₅₃	semidirect
642. #478	C₂²×C₅₃	semidirect
643. #476	C₂²×C₅₃	semidirect
644. #470	C₂²×C₅₃	semidirect
645. #469	C₂²×C₅₃	semidirect
646. #469	C₂²×C₅₃	semidirect
647. #468	C₂²×C₅₃	semidirect
648. #466	C₂²×C₅₃	semidirect
649. #465	C₂²×C₅₃	semidirect
650. #465	C₂²×C₅₃	semidirect
651. #465	C₂²×C₅₃	semidirect
652. #464	C₂²×C₅₃	semidirect
653. #463	C₂²×C₅₃	semidirect
654. #463	C₂²×C₅₃	semidirect
655. #461	C₂²×C₅₃	semidirect
656. #459	C₂²×C₅₃	semidirect
657. #459	C₂²×C₅₃	semidirect
658. #452	C₂²×C₅₃	semidirect
659. #452	C₂²×C₅₃	semidirect
660. #452	C₂²×C₅₃	semidirect
661. #450	C₂²×C₅₃	semidirect
662. #450	C₂²×C₅₃	semidirect
663. #450	C₂²×C₅₃	semidirect
664. #449	C₂²×C₅₃	semidirect
665. #449	C₂²×C₅₃	semidirect
666. #449	C₂²×C₅₃	semidirect
667. #449	C₂²×C₅₃	semidirect
668. #449	C₂²×C₅₃	semidirect
669. #449	C₂²×C₅₃	semidirect
670. #449	C₂²×C₅₃	semidirect
672. #447	C₂²×C₅₃	semidirect
673. #447	C₂²×C₅₃	semidirect
674. #447	C₂²×C₅₃	semidirect
675. #447	C₂²×C₅₃	semidirect
676. #447	C₂²×C₅₃	semidirect
677. #442	C₂²×C₅₃	semidirect
678. #442	C₂²×C₅₃	semidirect
679. #442	C₂²×C₅₃	semidirect
680. #440	C₂²×C₅₃	semidirect
681. #435	C₂²×C₅₃	semidirect
682. #435	C₂²×C₅₃	semidirect
683. #435	C₂²×C₅₃	semidirect
684. #435	C₂²×C₅₃	semidirect
685. #432	C₂²×C₅₃	semidirect
686. #432	C₂²×C₅₃	semidirect
687. #418	C₂²×C₅₃	semidirect
688. #417	C₂²×C₅₃	semidirect
689. #416	C₂²×C₅₃	semidirect
690. C₂×#102	C₂²×C₅₃	semidirect
691. #408	C₂²×C₅₃	semidirect
692. #408	C₂²×C₅₃	semidirect
693. C₅₃	#61669	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×#3546	2
C₅₃×#3496	2
C₅₃×#3318	2
C₅₃×#3311	2
C₅₃×#3307	2
C₅₃×#3306	2
C₅₃×#3268	2
C₅₃×#3267	2
C₅₃×#3264	2
C₅₃×#3219	2
C₅₃×#3214	2
C₅₃×#3204	2
C₅₃×#3198	2
C₅₃×#3114	2
C₅₃×#3109	2
C₅₃×#3012	2
C₅₃×#3008	2
C₅₃×#2980	2
#61669	53

Subgroups — C53×#61669 #27269181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61669 #27269181