Subgroups — C₅₃×#61591 #27269103

Order 13568.

2632 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3325	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3318	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3295	C₂	1	2	yes	maximal, complemented
6	D₄×D₈×C₅₃	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3274	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3264	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3192	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3188	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3003	C₂	1	2	yes	maximal, complemented
16	C₂×C₅₃×#447	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₄×C₅₃	—	2	1	no	—
19	C₂³×D₄×C₅₃	C₂²	1	2	yes	complemented
20	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	4	yes	complemented
21	C₂²×D₈×C₅₃	C₂²	1	4	yes	complemented
22	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
23	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
24	C₅₃×#553	—	2	1	no	—
25	C₅₃×#553	C₂²	1	2	yes	complemented
26	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
27	C₅₃×#546	—	2	2	no	—
28	C₅₃×#546	C₂²	1	2	yes	complemented
29	D₄²×C₅₃	—	2	1	no	—
30	D₄²×C₅₃	—	2	1	no	—
31	D₄²×C₅₃	—	2	2	no	—
32	D₄²×C₅₃	—	2	1	no	—
33	D₄²×C₅₃	C₂²	1	2	yes	—
34	D₄²×C₅₃	C₂²	1	4	yes	complemented
35	D₄²×C₅₃	C₂²	1	2	yes	complemented
36	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#540	—	2	1	no	—
38	C₅₃×#538	—	2	2	no	—
39	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
40	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#525	C₂²	1	2	yes	complemented
43	C₂×#121×C₅₃	—	2	1	no	—
44	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
45	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
46	C₂×#120×C₅₃	—	2	2	no	—
47	C₅₃×#518	—	2	1	no	—
48	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#496	C₂²	1	2	yes	complemented
51	C₅₃×#493	C₂²	1	2	yes	complemented
52	C₅₃×#490	C₂²	1	2	yes	complemented
53	C₅₃×#486	C₂²	1	2	yes	complemented
54	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#482	C₂²	1	4	yes	complemented
56	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#481	C₂²	1	2	yes	complemented
58	C₅₃×#481	C₂²	1	4	yes	complemented
59	C₅₃×#478	C₂²	1	2	yes	complemented
60	C₅₃×#476	C₂²	1	2	yes	complemented
61	C₅₃×#469	C₂²	1	4	yes	complemented
62	C₅₃×#469	C₂²	1	4	yes	complemented
63	C₅₃×#466	C₂²	1	4	yes	complemented
64	C₅₃×#465	C₂²	1	4	yes	complemented
65	C₅₃×#463	C₂²	1	2	yes	complemented
66	C₅₃×#460	C₂²	1	2	yes	complemented
67	C₅₃×#459	C₂²	1	2	yes	complemented
68	C₅₃×#459	C₂²	1	4	yes	complemented
69	C₅₃×#459	C₂²	1	2	yes	complemented
70	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#450	C₂²	1	2	yes	complemented
72	C₅₃×#450	C₂²	1	4	yes	complemented
73	C₅₃×#449	C₂²	1	4	yes	complemented
74	C₅₃×#447	C₂²	1	1	yes	characteristic
75	C₅₃×#447	C₂²	1	2	yes	complemented
76	C₅₃×#447	C₂²	1	2	yes	complemented
77	C₅₃×#447	C₂²	1	2	yes	complemented
78	C₅₃×#447	C₂²	1	2	yes	complemented
79	C₅₃×#447	C₂²	1	4	yes	complemented
80	C₅₃×#447	C₂²	1	4	yes	complemented
81	C₅₃×#447	C₂²	1	4	yes	complemented
82	C₅₃×#447	C₂²	1	4	yes	complemented
83	C₅₃×#442	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
85	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
86	C₅₃×#436	C₂²	1	2	yes	complemented
87	C₅₃×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
89	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#418	C₂²	1	4	yes	complemented
92	C₂×#102×C₅₃	C₂²	1	4	yes	complemented
93	C₅₃×#407	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	complemented
95	C₂⁵×C₅₃	—	2	2	no	—
96	C₂×#41×C₅₃	—	2	1	no	—
97	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
98	C₂²×D₄×C₅₃	—	2	2	no	—
99	C₂²×D₄×C₅₃	—	2	2	no	—
100	C₂²×D₄×C₅₃	—	2	1	no	—
101	C₂²×D₄×C₅₃	—	2	2	no	—
102	C₂²×D₄×C₅₃	—	2	4	no	—
103	C₂²×D₄×C₅₃	—	2	2	no	—
104	C₂²×D₄×C₅₃	—	2	2	no	—
105	C₂²×D₄×C₅₃	—	2	1	no	—
106	C₂²×D₄×C₅₃	—	2	2	no	—
107	C₂²×D₄×C₅₃	—	2	2	no	—
108	C₂²×D₄×C₅₃	—	2	1	no	—
109	C₂²×D₄×C₅₃	—	4	8	no	—
110	C₂²×D₄×C₅₃	—	4	8	no	—
111	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
112	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
114	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
115	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
117	C₂³×C₄×C₅₃	—	2	1	no	—
118	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
119	AGL(1,ℤ/8)×C₅₃	—	4	8	no	—
120	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
121	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	complemented
122	C₂×D₈×C₅₃	—	4	8	no	—
123	C₂×D₈×C₅₃	C₂³	1	2	yes	—
124	C₂×D₈×C₅₃	C₂³	1	4	yes	—
125	C₂×D₈×C₅₃	C₂³	1	4	yes	complemented
126	C₂×D₈×C₅₃	C₂³	1	4	yes	complemented
127	C₂×D₈×C₅₃	C₂³	1	4	yes	complemented
128	C₂×M₁₆×C₅₃	C₂³	1	4	yes	complemented
129	C₂²×C₈×C₅₃	C₂³	1	4	yes	complemented
130	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
131	#127×C₅₃	—	2	1	no	—
132	#127×C₅₃	—	2	1	no	—
133	#127×C₅₃	—	2	1	no	—
134	#127×C₅₃	C₂³	1	2	yes	—
135	#127×C₅₃	C₂³	1	2	yes	—
136	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
137	#126×C₅₃	—	2	2	no	—
138	#126×C₅₃	—	2	1	no	—
139	#125×C₅₃	—	2	1	no	—
140	#125×C₅₃	C₂³	1	1	yes	characteristic, complemented
141	#124×C₅₃	—	2	2	no	—
142	#124×C₅₃	—	2	1	no	—
143	#124×C₅₃	C₂³	1	1	yes	characteristic, complemented
144	#123×C₅₃	—	2	2	no	—
145	#123×C₅₃	—	2	2	no	—
146	#123×C₅₃	—	2	2	no	—
147	#123×C₅₃	—	2	1	no	—
148	C₂²⋊Q₈×C₅₃	—	2	2	no	—
149	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
151	#121×C₅₃	—	2	2	no	—
152	#121×C₅₃	—	2	2	no	—
153	#121×C₅₃	—	2	4	no	—
154	#121×C₅₃	—	2	1	no	—
155	#121×C₅₃	—	2	2	no	—
156	#121×C₅₃	—	2	2	no	—
157	#121×C₅₃	—	2	2	no	—
158	#121×C₅₃	—	2	1	no	—
159	#121×C₅₃	—	2	2	no	—
160	#121×C₅₃	—	2	2	no	—
161	#121×C₅₃	—	2	2	no	—
162	#121×C₅₃	—	2	2	no	—
163	#121×C₅₃	—	2	1	no	—
164	#121×C₅₃	C₂³	1	1	yes	characteristic
165	#121×C₅₃	C₂³	1	2	yes	—
166	#121×C₅₃	C₂³	1	4	yes	—
167	#121×C₅₃	C₂³	1	4	yes	—
168	#121×C₅₃	C₂³	1	2	yes	complemented
169	#121×C₅₃	C₂³	1	2	yes	complemented
170	#121×C₅₃	C₂³	1	2	yes	complemented
171	#120×C₅₃	—	2	4	no	—
172	#120×C₅₃	—	2	4	no	—
173	#120×C₅₃	—	2	4	no	—
174	#120×C₅₃	—	2	4	no	—
175	#120×C₅₃	—	2	2	no	—
176	#120×C₅₃	—	2	2	no	—
177	#120×C₅₃	—	2	2	no	—
178	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
179	C₄×D₄×C₅₃	—	2	1	no	—
180	C₄×D₄×C₅₃	—	2	2	no	—
181	C₄×D₄×C₅₃	—	2	1	no	—
182	C₄×D₄×C₅₃	—	2	1	no	—
183	C₄×D₄×C₅₃	—	2	1	no	—
184	C₄×D₄×C₅₃	—	2	1	no	—
185	C₄×D₄×C₅₃	—	2	2	no	—
186	C₄×D₄×C₅₃	—	2	2	no	—
187	C₄×D₄×C₅₃	—	2	1	no	—
188	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
189	C₄×D₄×C₅₃	D₄	1	2	yes	—
190	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
191	C₄×D₄×C₅₃	C₂³	1	2	yes	—
192	C₄×D₄×C₅₃	C₂³	1	2	yes	—
193	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₅₃	C₂³	1	2	yes	—
195	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
197	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
198	#117×C₅₃	—	2	1	no	—
199	#117×C₅₃	—	2	1	no	—
200	#117×C₅₃	C₂³	1	2	yes	complemented
201	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
204	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
206	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
207	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
208	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
209	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
210	#107×C₅₃	C₂³	1	2	yes	complemented
211	#106×C₅₃	C₂³	1	2	yes	complemented
212	#106×C₅₃	C₂³	1	4	yes	complemented
213	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
214	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
215	#103×C₅₃	C₂³	1	2	yes	complemented
216	#102×C₅₃	C₂³	1	2	yes	—
217	#102×C₅₃	C₂³	1	4	yes	—
218	#102×C₅₃	C₂³	1	2	yes	—
219	#102×C₅₃	C₂³	1	4	yes	complemented
220	#102×C₅₃	C₂³	1	4	yes	complemented
221	#102×C₅₃	C₂³	1	4	yes	complemented
222	#102×C₅₃	C₂³	1	4	yes	complemented
223	#102×C₅₃	C₂³	1	2	yes	complemented
224	#102×C₅₃	C₂³	1	4	yes	complemented
225	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
229	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
230	#97×C₅₃	C₂³	1	2	yes	complemented
231	C₄×C₈×C₅₃	C₂³	1	2	yes	complemented
232	C₂⁴×C₅₃	—	2	1	no	—
233	C₂⁴×C₅₃	—	2	2	no	—
234	C₂⁴×C₅₃	—	2	4	no	—
235	C₂⁴×C₅₃	—	2	4	no	—
236	C₂⁴×C₅₃	—	2	2	no	—
237	C₂⁴×C₅₃	—	4	8	no	—
238	C₂⁴×C₅₃	—	4	8	no	—
239	C₂⁴×C₅₃	—	8	4	no	—
240	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
241	#41×C₅₃	—	4	4	no	—
242	#41×C₅₃	—	8	2	no	—
243	C₂×Q₈×C₅₃	—	2	1	no	—
244	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₅₃	—	2	4	no	—
246	C₂×D₄×C₅₃	—	2	4	no	—
247	C₂×D₄×C₅₃	—	2	8	no	—
248	C₂×D₄×C₅₃	—	2	8	no	—
249	C₂×D₄×C₅₃	—	2	2	no	—
250	C₂×D₄×C₅₃	—	2	2	no	—
251	C₂×D₄×C₅₃	—	2	1	no	—
252	C₂×D₄×C₅₃	—	2	4	no	—
253	C₂×D₄×C₅₃	—	2	4	no	—
254	C₂×D₄×C₅₃	—	2	2	no	—
255	C₂×D₄×C₅₃	—	2	2	no	—
256	C₂×D₄×C₅₃	—	2	2	no	—
257	C₂×D₄×C₅₃	—	2	1	no	—
258	C₂×D₄×C₅₃	—	2	1	no	—
259	C₂×D₄×C₅₃	—	2	4	no	—
260	C₂×D₄×C₅₃	—	2	4	no	—
261	C₂×D₄×C₅₃	—	2	2	no	—
262	C₂×D₄×C₅₃	—	2	2	no	—
263	C₂×D₄×C₅₃	—	2	2	no	—
264	C₂×D₄×C₅₃	—	2	2	no	—
265	C₂×D₄×C₅₃	—	2	2	no	—
266	C₂×D₄×C₅₃	—	2	1	no	—
267	C₂×D₄×C₅₃	—	2	2	no	—
268	C₂×D₄×C₅₃	—	4	4	no	—
269	C₂×D₄×C₅₃	—	4	4	no	—
270	C₂×D₄×C₅₃	—	4	4	no	—
271	C₂×D₄×C₅₃	—	4	4	no	—
272	C₂×D₄×C₅₃	—	4	4	no	—
273	C₂×D₄×C₅₃	—	4	8	no	—
274	C₂×D₄×C₅₃	—	4	8	no	—
275	C₂×D₄×C₅₃	—	4	16	no	—
276	C₂×D₄×C₅₃	—	4	8	no	—
277	C₂×D₄×C₅₃	—	4	8	no	—
278	C₂×D₄×C₅₃	—	4	8	no	—
279	C₂×D₄×C₅₃	—	4	4	no	—
280	C₂×D₄×C₅₃	—	4	8	no	—
281	C₂×D₄×C₅₃	—	8	2	no	—
282	C₂×D₄×C₅₃	—	8	4	no	—
283	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
284	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
285	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
286	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
287	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
288	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
289	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₅₃	—	2	1	no	—
291	C₂²×C₄×C₅₃	—	2	2	no	—
292	C₂²×C₄×C₅₃	—	2	1	no	—
293	C₂²×C₄×C₅₃	—	2	2	no	—
294	C₂²×C₄×C₅₃	—	2	2	no	—
295	C₂²×C₄×C₅₃	—	2	2	no	—
296	C₂²×C₄×C₅₃	—	2	2	no	—
297	C₂²×C₄×C₅₃	—	4	4	no	—
298	C₂²×C₄×C₅₃	—	4	4	no	—
299	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
302	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
303	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
304	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
307	SD₁₆×C₅₃	—	2	4	no	—
308	SD₁₆×C₅₃	—	4	4	no	—
309	D₈×C₅₃	—	2	4	no	—
310	D₈×C₅₃	—	2	8	no	—
311	D₈×C₅₃	—	4	4	no	—
312	D₈×C₅₃	—	4	4	no	—
313	D₈×C₅₃	—	4	4	no	—
314	M₁₆×C₅₃	—	4	4	no	—
315	C₂×C₈×C₅₃	—	4	4	no	—
316	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
317	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
318	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₅₃	—	2	1	no	—
320	C₄⋊C₄×C₅₃	—	2	2	no	—
321	C₄⋊C₄×C₅₃	—	2	1	no	—
322	C₄⋊C₄×C₅₃	—	2	1	no	—
323	C₄⋊C₄×C₅₃	—	2	1	no	—
324	C₄⋊C₄×C₅₃	—	2	1	no	—
325	C₄⋊C₄×C₅₃	—	2	2	no	—
326	C₄⋊C₄×C₅₃	—	2	1	no	—
327	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
328	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
329	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
330	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
332	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
333	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
334	C₂²⋊C₄×C₅₃	—	2	2	no	—
335	C₂²⋊C₄×C₅₃	—	2	2	no	—
336	C₂²⋊C₄×C₅₃	—	2	1	no	—
337	C₂²⋊C₄×C₅₃	—	2	1	no	—
338	C₂²⋊C₄×C₅₃	—	2	1	no	—
339	C₂²⋊C₄×C₅₃	—	2	2	no	—
340	C₂²⋊C₄×C₅₃	—	2	2	no	—
341	C₂²⋊C₄×C₅₃	—	2	2	no	—
342	C₂²⋊C₄×C₅₃	—	2	2	no	—
343	C₂²⋊C₄×C₅₃	—	2	2	no	—
344	C₂²⋊C₄×C₅₃	—	2	4	no	—
345	C₂²⋊C₄×C₅₃	—	2	4	no	—
346	C₂²⋊C₄×C₅₃	—	2	1	no	—
347	C₂²⋊C₄×C₅₃	—	2	2	no	—
348	C₂²⋊C₄×C₅₃	—	2	1	no	—
349	C₂²⋊C₄×C₅₃	—	2	2	no	—
350	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
351	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
352	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
353	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
354	C₄²×C₅₃	—	2	2	no	—
355	C₄²×C₅₃	—	2	1	no	—
356	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
357	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
358	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂³×C₅₃	—	2	4	no	—
361	C₂³×C₅₃	—	2	4	no	—
362	C₂³×C₅₃	—	2	4	no	—
363	C₂³×C₅₃	—	2	2	no	—
364	C₂³×C₅₃	—	2	2	no	—
365	C₂³×C₅₃	—	2	1	no	—
366	C₂³×C₅₃	—	2	4	no	—
367	C₂³×C₅₃	—	4	2	no	—
368	C₂³×C₅₃	—	4	8	no	—
369	C₂³×C₅₃	—	4	8	no	—
370	C₂³×C₅₃	—	4	2	no	—
371	C₂³×C₅₃	—	4	4	no	—
372	C₂³×C₅₃	—	4	4	no	—
373	C₂³×C₅₃	—	4	8	no	—
374	C₂³×C₅₃	—	4	2	no	—
375	C₂³×C₅₃	—	4	8	no	—
376	C₂³×C₅₃	—	4	4	no	—
377	C₂³×C₅₃	—	4	4	no	—
378	C₂³×C₅₃	—	8	4	no	—
379	C₂³×C₅₃	—	8	4	no	—
380	C₂³×C₅₃	—	8	2	no	—
381	C₂³×C₅₃	—	8	2	no	—
382	C₂³×C₅₃	—	8	32	no	—
383	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
384	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
385	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
386	Q₈×C₅₃	—	2	2	no	—
387	Q₈×C₅₃	—	8	1	no	—
388	D₄×C₅₃	—	2	4	no	—
389	D₄×C₅₃	—	2	4	no	—
390	D₄×C₅₃	—	2	2	no	—
391	D₄×C₅₃	—	2	2	no	—
392	D₄×C₅₃	—	2	4	no	—
393	D₄×C₅₃	—	2	4	no	—
394	D₄×C₅₃	—	2	2	no	—
395	D₄×C₅₃	—	2	4	no	—
396	D₄×C₅₃	—	4	8	no	—
397	D₄×C₅₃	—	4	8	no	—
398	D₄×C₅₃	—	4	4	no	—
399	D₄×C₅₃	—	4	4	no	—
400	D₄×C₅₃	—	4	8	no	—
401	D₄×C₅₃	—	4	4	no	—
402	D₄×C₅₃	—	4	8	no	—
403	D₄×C₅₃	—	4	2	no	—
404	D₄×C₅₃	—	4	4	no	—
405	D₄×C₅₃	—	4	2	no	—
406	D₄×C₅₃	—	4	4	no	—
407	D₄×C₅₃	—	8	2	no	—
408	D₄×C₅₃	—	8	2	no	—
409	D₄×C₅₃	—	8	2	no	—
410	D₄×C₅₃	—	8	1	no	—
411	D₄×C₅₃	—	8	2	no	—
412	D₄×C₅₃	—	8	2	no	—
413	D₄×C₅₃	—	8	2	no	—
414	D₄×C₅₃	AGL(1,ℤ/8)	1	4	yes	complemented
415	D₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
416	C₂×C₄×C₅₃	—	2	2	no	—
417	C₂×C₄×C₅₃	—	2	2	no	—
418	C₂×C₄×C₅₃	—	2	2	no	—
419	C₂×C₄×C₅₃	—	2	4	no	—
420	C₂×C₄×C₅₃	—	2	4	no	—
421	C₂×C₄×C₅₃	—	2	2	no	—
422	C₂×C₄×C₅₃	—	2	1	no	—
423	C₂×C₄×C₅₃	—	2	2	no	—
424	C₂×C₄×C₅₃	—	2	1	no	—
425	C₂×C₄×C₅₃	—	2	1	no	—
426	C₂×C₄×C₅₃	—	4	2	no	—
427	C₂×C₄×C₅₃	—	4	2	no	—
428	C₂×C₄×C₅₃	—	4	2	no	—
429	C₂×C₄×C₅₃	—	4	4	no	—
430	C₂×C₄×C₅₃	—	4	2	no	—
431	C₂×C₄×C₅₃	—	4	4	no	—
432	C₂×C₄×C₅₃	—	4	2	no	—
433	C₂×C₄×C₅₃	—	8	2	no	—
434	C₂×C₄×C₅₃	—	8	2	no	—
435	C₂×C₄×C₅₃	—	8	2	no	—
436	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
444	C₈×C₅₃	—	2	2	no	—
445	C₈×C₅₃	—	2	4	no	—
446	C₈×C₅₃	—	2	2	no	—
447	#61591	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
448	C₂²×C₅₃	—	2	1	no	—
449	C₂²×C₅₃	—	2	2	no	—
450	C₂²×C₅₃	—	2	1	no	—
451	C₂²×C₅₃	—	2	2	no	—
452	C₂²×C₅₃	—	2	2	no	—
453	C₂²×C₅₃	—	2	4	no	—
454	C₂²×C₅₃	—	2	2	no	—
455	C₂²×C₅₃	—	2	2	no	—
456	C₂²×C₅₃	—	4	8	no	—
457	C₂²×C₅₃	—	4	8	no	—
458	C₂²×C₅₃	—	4	2	no	—
459	C₂²×C₅₃	—	4	2	no	—
460	C₂²×C₅₃	—	4	2	no	—
461	C₂²×C₅₃	—	4	4	no	—
462	C₂²×C₅₃	—	4	1	no	—
463	C₂²×C₅₃	—	4	1	no	—
464	C₂²×C₅₃	—	4	4	no	—
465	C₂²×C₅₃	—	4	2	no	—
466	C₂²×C₅₃	—	4	2	no	—
467	C₂²×C₅₃	—	4	1	no	—
468	C₂²×C₅₃	—	4	4	no	—
469	C₂²×C₅₃	—	8	16	no	—
470	C₂²×C₅₃	—	8	8	no	—
471	C₂²×C₅₃	—	8	16	no	—
472	C₂²×C₅₃	—	16	4	no	—
473	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
474	C₂²×C₅₃	#576	1	2	yes	—
475	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
476	C₄×C₅₃	—	2	1	no	—
477	C₄×C₅₃	—	2	2	no	—
478	C₄×C₅₃	—	2	2	no	—
479	C₄×C₅₃	—	2	1	no	—
480	C₄×C₅₃	—	2	1	no	—
481	C₄×C₅₃	—	2	1	no	—
482	C₄×C₅₃	—	4	1	no	—
483	C₄×C₅₃	—	4	2	no	—
484	C₄×C₅₃	—	4	1	no	—
485	C₄×C₅₃	—	4	1	no	—
486	C₄×C₅₃	—	4	2	no	—
487	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
488	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
489	#3519	C₂×C₅₃	1	1	yes	characteristic, complemented
490	C₂×D₄²	C₂×C₅₃	1	1	yes	characteristic, complemented
491	#3325	C₂×C₅₃	1	2	yes	complemented
492	#3318	C₂×C₅₃	1	4	yes	complemented
493	#3295	C₂×C₅₃	1	2	yes	complemented
494	D₄×D₈	C₂×C₅₃	1	2	yes	complemented
495	#3274	C₂×C₅₃	1	2	yes	complemented
496	#3264	C₂×C₅₃	1	4	yes	complemented
497	#3217	C₂×C₅₃	1	1	yes	characteristic, complemented
498	#3205	C₂×C₅₃	1	1	yes	characteristic, complemented
499	#3192	C₂×C₅₃	1	2	yes	complemented
500	#3188	C₂×C₅₃	1	2	yes	complemented
501	#3109	C₂×C₅₃	1	1	yes	characteristic, complemented
502	#3105	C₂×C₅₃	1	1	yes	characteristic, complemented
503	#3003	C₂×C₅₃	1	2	yes	complemented
504	C₂×#447	C₂×C₅₃	1	2	yes	complemented
505	#2974	C₂×C₅₃	1	1	yes	characteristic, complemented
506	C₂×C₅₃	—	2	2	no	—
507	C₂×C₅₃	—	2	4	no	—
508	C₂×C₅₃	—	4	2	no	—
509	C₂×C₅₃	—	4	4	no	—
510	C₂×C₅₃	—	8	4	no	—
511	C₂×C₅₃	—	8	2	no	—
512	C₂×C₅₃	—	8	1	no	—
513	C₂×C₅₃	#3484	1	1	yes	characteristic
514	C₂×C₅₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
515	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
516	C₂³×D₄	—	2	1	no	—
517	C₂³×D₄	C₂²×C₅₃	1	2	yes	complemented
518	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	4	yes	complemented
519	C₂²×D₈	C₂²×C₅₃	1	4	yes	complemented
520	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
521	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
522	#553	—	2	1	no	—
523	#553	C₂²×C₅₃	1	2	yes	complemented
524	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
525	#546	—	2	2	no	—
526	#546	C₂²×C₅₃	1	2	yes	complemented
527	D₄²	—	2	1	no	—
528	D₄²	—	2	1	no	—
529	D₄²	—	2	2	no	—
530	D₄²	—	2	1	no	—
531	D₄²	C₂²×C₅₃	1	2	yes	—
532	D₄²	C₂²×C₅₃	1	4	yes	complemented
533	D₄²	C₂²×C₅₃	1	2	yes	complemented
534	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
535	#540	—	2	1	no	—
536	#538	—	2	2	no	—
537	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
538	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic, complemented
539	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
540	#525	C₂²×C₅₃	1	2	yes	complemented
541	C₂×#121	—	2	1	no	—
542	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
543	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
544	C₂×#120	—	2	2	no	—
545	#518	—	2	1	no	—
546	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
547	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
548	#496	C₂²×C₅₃	1	2	yes	complemented
549	#493	C₂²×C₅₃	1	2	yes	complemented
550	#490	C₂²×C₅₃	1	2	yes	complemented
551	#486	C₂²×C₅₃	1	2	yes	complemented
552	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
553	#482	C₂²×C₅₃	1	4	yes	complemented
554	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
555	#481	C₂²×C₅₃	1	2	yes	complemented
556	#481	C₂²×C₅₃	1	4	yes	complemented
557	#478	C₂²×C₅₃	1	2	yes	complemented
558	#476	C₂²×C₅₃	1	2	yes	complemented
559	#469	C₂²×C₅₃	1	4	yes	complemented
560	#469	C₂²×C₅₃	1	4	yes	complemented
561	#466	C₂²×C₅₃	1	4	yes	complemented
562	#465	C₂²×C₅₃	1	4	yes	complemented
563	#463	C₂²×C₅₃	1	2	yes	complemented
564	#460	C₂²×C₅₃	1	2	yes	complemented
565	#459	C₂²×C₅₃	1	2	yes	complemented
566	#459	C₂²×C₅₃	1	4	yes	complemented
567	#459	C₂²×C₅₃	1	2	yes	complemented
568	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
569	#450	C₂²×C₅₃	1	2	yes	complemented
570	#450	C₂²×C₅₃	1	4	yes	complemented
571	#449	C₂²×C₅₃	1	4	yes	complemented
572	#447	C₂²×C₅₃	1	1	yes	characteristic
573	#447	C₂²×C₅₃	1	2	yes	complemented
574	#447	C₂²×C₅₃	1	2	yes	complemented
575	#447	C₂²×C₅₃	1	2	yes	complemented
576	#447	C₂²×C₅₃	1	2	yes	complemented
577	#447	C₂²×C₅₃	1	4	yes	complemented
578	#447	C₂²×C₅₃	1	4	yes	complemented
579	#447	C₂²×C₅₃	1	4	yes	complemented
580	#447	C₂²×C₅₃	1	4	yes	complemented
581	#442	C₂²×C₅₃	1	4	yes	complemented
582	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
583	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
584	#436	C₂²×C₅₃	1	2	yes	complemented
585	#435	C₂²×C₅₃	1	4	yes	complemented
586	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
587	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
588	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
589	#418	C₂²×C₅₃	1	4	yes	complemented
590	C₂×#102	C₂²×C₅₃	1	4	yes	complemented
591	#407	C₂²×C₅₃	1	2	yes	complemented
592	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	complemented
593	C₅₃	#61591	1	1	yes	characteristic, direct product factor, Sylow
594	C₂⁵	—	2	2	no	—
595	C₂×#41	—	2	1	no	—
596	C₂×#41	C₂³×C₅₃	1	2	yes	complemented
597	C₂²×D₄	—	2	2	no	—
598	C₂²×D₄	—	2	2	no	—
599	C₂²×D₄	—	2	1	no	—
600	C₂²×D₄	—	2	2	no	—
601	C₂²×D₄	—	2	4	no	—
602	C₂²×D₄	—	2	2	no	—
603	C₂²×D₄	—	2	2	no	—
604	C₂²×D₄	—	2	1	no	—
605	C₂²×D₄	—	2	2	no	—
606	C₂²×D₄	—	2	2	no	—
607	C₂²×D₄	—	2	1	no	—
608	C₂²×D₄	—	4	8	no	—
609	C₂²×D₄	—	4	8	no	—
610	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
611	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
612	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
613	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
614	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
615	C₂²×D₄	C₂³×C₅₃	1	2	yes	complemented
616	C₂³×C₄	—	2	1	no	—
617	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
618	AGL(1,ℤ/8)	—	4	8	no	—
619	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
620	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	complemented
621	C₂×D₈	—	4	8	no	—
622	C₂×D₈	C₂³×C₅₃	1	2	yes	—
623	C₂×D₈	C₂³×C₅₃	1	4	yes	—
624	C₂×D₈	C₂³×C₅₃	1	4	yes	complemented
625	C₂×D₈	C₂³×C₅₃	1	4	yes	complemented
626	C₂×D₈	C₂³×C₅₃	1	4	yes	complemented
627	C₂×M₁₆	C₂³×C₅₃	1	4	yes	complemented
628	C₂²×C₈	C₂³×C₅₃	1	4	yes	complemented
629	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
630	#127	—	2	1	no	—
631	#127	—	2	1	no	—
632	#127	—	2	1	no	—
633	#127	C₂³×C₅₃	1	2	yes	—
634	#127	C₂³×C₅₃	1	2	yes	—
635	#127	C₂³×C₅₃	1	1	yes	characteristic, complemented
636	#126	—	2	2	no	—
637	#126	—	2	1	no	—
638	#125	—	2	1	no	—
639	#125	C₂³×C₅₃	1	1	yes	characteristic, complemented
640	#124	—	2	2	no	—
641	#124	—	2	1	no	—
642	#124	C₂³×C₅₃	1	1	yes	characteristic, complemented
643	#123	—	2	2	no	—
644	#123	—	2	1	no	—
645	#123	—	2	2	no	—
646	#123	—	2	2	no	—
647	C₂²⋊Q₈	—	2	2	no	—
648	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
649	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
650	#121	—	2	2	no	—
651	#121	—	2	1	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	2	no	—
656	#121	—	2	1	no	—
657	#121	—	2	2	no	—
658	#121	—	2	2	no	—
659	#121	—	2	4	no	—
660	#121	—	2	1	no	—
661	#121	—	2	2	no	—
662	#121	—	2	2	no	—
663	#121	C₂³×C₅₃	1	1	yes	characteristic
664	#121	C₂³×C₅₃	1	2	yes	—
665	#121	C₂³×C₅₃	1	4	yes	—
666	#121	C₂³×C₅₃	1	4	yes	—
667	#121	C₂³×C₅₃	1	2	yes	complemented
668	#121	C₂³×C₅₃	1	2	yes	complemented
669	#121	C₂³×C₅₃	1	2	yes	complemented
670	#120	—	2	2	no	—
671	#120	—	2	2	no	—
672	#120	—	2	4	no	—
673	#120	—	2	4	no	—
674	#120	—	2	4	no	—
675	#120	—	2	4	no	—
676	#120	—	2	2	no	—
677	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
678	C₄×D₄	—	2	1	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	—	2	1	no	—
682	C₄×D₄	—	2	1	no	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	—	2	1	no	—
685	C₄×D₄	—	2	1	no	—
686	C₄×D₄	—	2	1	no	—
687	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
688	C₄×D₄	D₄×C₅₃	1	2	yes	—
689	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
690	C₄×D₄	C₂³×C₅₃	1	2	yes	—
691	C₄×D₄	C₂³×C₅₃	1	2	yes	—
692	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
693	C₄×D₄	C₂³×C₅₃	1	2	yes	—
694	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
695	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
696	C₄×D₄	C₂³×C₅₃	1	2	yes	complemented
697	#117	—	2	1	no	—
698	#117	—	2	1	no	—
699	#117	C₂³×C₅₃	1	2	yes	complemented
700	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
703	C₂×C₂²⋊C₄	—	2	1	no	—
704	C₂×C₂²⋊C₄	—	2	2	no	—
705	C₂×C₂²⋊C₄	—	2	2	no	—
706	C₂×C₂²⋊C₄	—	2	2	no	—
707	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
708	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
709	#107	C₂³×C₅₃	1	2	yes	complemented
710	#106	C₂³×C₅₃	1	2	yes	complemented
711	#106	C₂³×C₅₃	1	4	yes	complemented
712	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
713	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
714	#103	C₂³×C₅₃	1	2	yes	complemented
715	#102	C₂³×C₅₃	1	2	yes	—
716	#102	C₂³×C₅₃	1	4	yes	—
717	#102	C₂³×C₅₃	1	2	yes	—
718	#102	C₂³×C₅₃	1	4	yes	complemented
719	#102	C₂³×C₅₃	1	4	yes	complemented
720	#102	C₂³×C₅₃	1	4	yes	complemented
721	#102	C₂³×C₅₃	1	4	yes	complemented
722	#102	C₂³×C₅₃	1	2	yes	complemented
723	#102	C₂³×C₅₃	1	4	yes	complemented
724	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
725	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
726	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
727	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
728	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
729	#97	C₂³×C₅₃	1	2	yes	complemented
730	C₄×C₈	C₂³×C₅₃	1	2	yes	complemented
731	C₂⁴	—	2	1	no	—
732	C₂⁴	—	2	2	no	—
733	C₂⁴	—	2	4	no	—
734	C₂⁴	—	2	4	no	—
735	C₂⁴	—	2	2	no	—
736	C₂⁴	—	4	8	no	—
737	C₂⁴	—	4	8	no	—
738	C₂⁴	—	8	4	no	—
739	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
740	#41	—	4	4	no	—
741	#41	—	8	2	no	—
742	C₂×Q₈	—	2	1	no	—
743	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	8	no	—
747	C₂×D₄	—	2	8	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	1	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	2	4	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	1	no	—
757	C₂×D₄	—	2	1	no	—
758	C₂×D₄	—	2	4	no	—
759	C₂×D₄	—	2	4	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	4	4	no	—
768	C₂×D₄	—	4	4	no	—
769	C₂×D₄	—	4	4	no	—
770	C₂×D₄	—	4	4	no	—
771	C₂×D₄	—	4	4	no	—
772	C₂×D₄	—	4	8	no	—
773	C₂×D₄	—	4	8	no	—
774	C₂×D₄	—	4	16	no	—
775	C₂×D₄	—	4	8	no	—
776	C₂×D₄	—	4	8	no	—
777	C₂×D₄	—	4	8	no	—
778	C₂×D₄	—	4	4	no	—
779	C₂×D₄	—	4	8	no	—
780	C₂×D₄	—	8	2	no	—
781	C₂×D₄	—	8	4	no	—
782	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
783	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
784	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
785	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
786	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
787	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
788	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	4	4	no	—
797	C₂²×C₄	—	4	4	no	—
798	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
799	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
800	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
801	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
802	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
803	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
806	SD₁₆	—	2	4	no	—
807	SD₁₆	—	4	4	no	—
808	D₈	—	2	4	no	—
809	D₈	—	2	8	no	—
810	D₈	—	4	4	no	—
811	D₈	—	4	4	no	—
812	D₈	—	4	4	no	—
813	M₁₆	—	4	4	no	—
814	C₂×C₈	—	4	4	no	—
815	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
816	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
817	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	1	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
827	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
828	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
829	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
830	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
831	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
832	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	1	no	—
836	C₂²⋊C₄	—	2	1	no	—
837	C₂²⋊C₄	—	2	1	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	4	no	—
844	C₂²⋊C₄	—	2	4	no	—
845	C₂²⋊C₄	—	2	1	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	1	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
850	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
851	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
852	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	1	no	—
855	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
856	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
857	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
858	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
859	C₂³	—	2	4	no	—
860	C₂³	—	2	4	no	—
861	C₂³	—	2	4	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	4	no	—
866	C₂³	—	4	2	no	—
867	C₂³	—	4	8	no	—
868	C₂³	—	4	8	no	—
869	C₂³	—	4	2	no	—
870	C₂³	—	4	4	no	—
871	C₂³	—	4	4	no	—
872	C₂³	—	4	8	no	—
873	C₂³	—	4	2	no	—
874	C₂³	—	4	8	no	—
875	C₂³	—	4	4	no	—
876	C₂³	—	4	4	no	—
877	C₂³	—	8	4	no	—
878	C₂³	—	8	4	no	—
879	C₂³	—	8	2	no	—
880	C₂³	—	8	2	no	—
881	C₂³	—	8	32	no	—
882	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
883	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
884	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
885	Q₈	—	2	2	no	—
886	Q₈	—	8	1	no	—
887	D₄	—	2	4	no	—
888	D₄	—	2	4	no	—
889	D₄	—	2	2	no	—
890	D₄	—	2	2	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	4	no	—
893	D₄	—	2	4	no	—
894	D₄	—	2	4	no	—
895	D₄	—	4	8	no	—
896	D₄	—	4	8	no	—
897	D₄	—	4	4	no	—
898	D₄	—	4	4	no	—
899	D₄	—	4	8	no	—
900	D₄	—	4	4	no	—
901	D₄	—	4	8	no	—
902	D₄	—	4	2	no	—
903	D₄	—	4	4	no	—
904	D₄	—	4	2	no	—
905	D₄	—	4	4	no	—
906	D₄	—	8	2	no	—
907	D₄	—	8	2	no	—
908	D₄	—	8	2	no	—
909	D₄	—	8	1	no	—
910	D₄	—	8	2	no	—
911	D₄	—	8	2	no	—
912	D₄	—	8	2	no	—
913	D₄	AGL(1,ℤ/8)×C₅₃	1	4	yes	complemented
914	D₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	4	no	—
918	C₂×C₄	—	2	4	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	4	2	no	—
926	C₂×C₄	—	4	2	no	—
927	C₂×C₄	—	4	2	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	—	4	2	no	—
930	C₂×C₄	—	4	4	no	—
931	C₂×C₄	—	4	2	no	—
932	C₂×C₄	—	8	2	no	—
933	C₂×C₄	—	8	2	no	—
934	C₂×C₄	—	8	2	no	—
935	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
936	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
937	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
938	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
939	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
940	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
941	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
942	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
943	C₈	—	2	2	no	—
944	C₈	—	2	4	no	—
945	C₈	—	2	2	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	1	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	4	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	4	8	no	—
955	C₂²	—	4	8	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	4	no	—
960	C₂²	—	4	1	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	4	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	4	no	—
967	C₂²	—	8	16	no	—
968	C₂²	—	8	8	no	—
969	C₂²	—	8	16	no	—
970	C₂²	—	16	4	no	—
971	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	4	yes	—
972	C₂²	C₅₃×#576	1	2	yes	—
973	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
974	C₄	—	2	1	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	1	no	—
978	C₄	—	2	1	no	—
979	C₄	—	2	1	no	—
980	C₄	—	4	1	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	2	no	—
985	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
986	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
987	C₂	—	2	2	no	—
988	C₂	—	2	4	no	—
989	C₂	—	4	2	no	—
990	C₂	—	4	4	no	—
991	C₂	—	8	4	no	—
992	C₂	—	8	1	no	—
993	C₂	—	8	2	no	—
994	C₂	C₅₃×#3484	1	1	yes	characteristic
995	C₂	C₂²×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
996	C₂	C₂×C₅₃×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3519	C₂	semidirect
2. C₂×D₄²×C₅₃	C₂	semidirect
3. C₅₃×#3325	C₂	semidirect
4. C₅₃×#3318	C₂	semidirect
5. C₅₃×#3295	C₂	semidirect
6. D₄×D₈×C₅₃	C₂	semidirect
7. C₅₃×#3274	C₂	semidirect
8. C₅₃×#3264	C₂	semidirect
9. C₅₃×#3217	C₂	semidirect
10. C₅₃×#3205	C₂	semidirect
11. C₅₃×#3192	C₂	semidirect
12. C₅₃×#3188	C₂	semidirect
13. C₅₃×#3109	C₂	semidirect
14. C₅₃×#3105	C₂	semidirect
15. C₅₃×#3003	C₂	semidirect
16. C₂×C₅₃×#447	C₂	semidirect
17. C₅₃×#2974	C₂	semidirect
19. C₂³×D₄×C₅₃	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
21. C₂²×D₈×C₅₃	C₂²	semidirect
22. C₅₃×#555	C₂²	semidirect
23. C₅₃×#554	C₂²	semidirect
25. C₅₃×#553	C₂²	semidirect
26. C₅₃×#550	C₂²	semidirect
28. C₅₃×#546	C₂²	semidirect
34. D₄²×C₅₃	C₂²	semidirect
35. D₄²×C₅₃	C₂²	semidirect
36. D₄²×C₅₃	C₂²	semidirect
39. C₅₃×#532	C₂²	semidirect
40. C₂×#127×C₅₃	C₂²	semidirect
41. C₅₃×#529	C₂²	semidirect
42. C₅₃×#525	C₂²	semidirect
44. C₂×#121×C₅₃	C₂²	semidirect
45. C₂×#121×C₅₃	C₂²	semidirect
49. C₂×C₄×D₄×C₅₃	C₂²	semidirect
50. C₅₃×#496	C₂²	semidirect
51. C₅₃×#493	C₂²	semidirect
52. C₅₃×#490	C₂²	semidirect
53. C₅₃×#486	C₂²	semidirect
54. C₅₃×#484	C₂²	semidirect
55. C₅₃×#482	C₂²	semidirect
56. C₅₃×#481	C₂²	semidirect
57. C₅₃×#481	C₂²	semidirect
58. C₅₃×#481	C₂²	semidirect
59. C₅₃×#478	C₂²	semidirect
60. C₅₃×#476	C₂²	semidirect
61. C₅₃×#469	C₂²	semidirect
62. C₅₃×#469	C₂²	semidirect
63. C₅₃×#466	C₂²	semidirect
64. C₅₃×#465	C₂²	semidirect
65. C₅₃×#463	C₂²	semidirect
66. C₅₃×#460	C₂²	semidirect
67. C₅₃×#459	C₂²	semidirect
68. C₅₃×#459	C₂²	semidirect
69. C₅₃×#459	C₂²	semidirect
70. C₅₃×#450	C₂²	semidirect
71. C₅₃×#450	C₂²	semidirect
72. C₅₃×#450	C₂²	semidirect
73. C₅₃×#449	C₂²	semidirect
75. C₅₃×#447	C₂²	semidirect
76. C₅₃×#447	C₂²	semidirect
77. C₅₃×#447	C₂²	semidirect
78. C₅₃×#447	C₂²	semidirect
79. C₅₃×#447	C₂²	semidirect
80. C₅₃×#447	C₂²	semidirect
81. C₅₃×#447	C₂²	semidirect
82. C₅₃×#447	C₂²	semidirect
83. C₅₃×#442	C₂²	semidirect
84. C₄×SD₁₆×C₅₃	C₂²	semidirect
85. C₄×D₈×C₅₃	C₂²	semidirect
86. C₅₃×#436	C₂²	semidirect
87. C₅₃×#435	C₂²	semidirect
88. C₈×D₄×C₅₃	C₂²	semidirect
89. C₅₃×#432	C₂²	semidirect
90. C₅₃×#431	C₂²	semidirect
91. C₅₃×#418	C₂²	semidirect
92. C₂×#102×C₅₃	C₂²	semidirect
93. C₅₃×#407	C₂²	semidirect
94. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
97. C₂×#41×C₅₃	C₂³	semidirect
116. C₂²×D₄×C₅₃	C₂³	semidirect
121. C₂×SD₁₆×C₅₃	C₂³	semidirect
125. C₂×D₈×C₅₃	C₂³	semidirect
126. C₂×D₈×C₅₃	C₂³	semidirect
127. C₂×D₈×C₅₃	C₂³	semidirect
128. C₂×M₁₆×C₅₃	C₂³	semidirect
129. C₂²×C₈×C₅₃	C₂³	semidirect
130. C₄⋊Q₈×C₅₃	C₂³	semidirect
136. #127×C₅₃	C₂³	semidirect
140. #125×C₅₃	C₂³	semidirect
143. #124×C₅₃	C₂³	semidirect
150. C₂²⋊Q₈×C₅₃	C₂³	semidirect
168. #121×C₅₃	C₂³	semidirect
169. #121×C₅₃	C₂³	semidirect
170. #121×C₅₃	C₂³	semidirect
178. C₄×Q₈×C₅₃	C₂³	semidirect
196. C₄×D₄×C₅₃	C₂³	semidirect
197. C₄×D₄×C₅₃	C₂³	semidirect
200. #117×C₅₃	C₂³	semidirect
203. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
210. #107×C₅₃	C₂³	semidirect
211. #106×C₅₃	C₂³	semidirect
212. #106×C₅₃	C₂³	semidirect
213. C₄⋊C₈×C₅₃	C₂³	semidirect
214. C₄⋊C₈×C₅₃	C₂³	semidirect
215. #103×C₅₃	C₂³	semidirect
219. #102×C₅₃	C₂³	semidirect
220. #102×C₅₃	C₂³	semidirect
221. #102×C₅₃	C₂³	semidirect
222. #102×C₅₃	C₂³	semidirect
223. #102×C₅₃	C₂³	semidirect
224. #102×C₅₃	C₂³	semidirect
228. C₂²⋊C₈×C₅₃	C₂³	semidirect
229. C₂²⋊C₈×C₅₃	C₂³	semidirect
230. #97×C₅₃	C₂³	semidirect
231. C₄×C₈×C₅₃	C₂³	semidirect
414. D₄×C₅₃	AGL(1,ℤ/8)	semidirect
447. #61591	C₅₃	direct (N × H)
489. #3519	C₂×C₅₃	semidirect
490. C₂×D₄²	C₂×C₅₃	semidirect
491. #3325	C₂×C₅₃	semidirect
492. #3318	C₂×C₅₃	semidirect
493. #3295	C₂×C₅₃	semidirect
494. D₄×D₈	C₂×C₅₃	semidirect
495. #3274	C₂×C₅₃	semidirect
496. #3264	C₂×C₅₃	semidirect
497. #3217	C₂×C₅₃	semidirect
498. #3205	C₂×C₅₃	semidirect
499. #3192	C₂×C₅₃	semidirect
500. #3188	C₂×C₅₃	semidirect
501. #3109	C₂×C₅₃	semidirect
502. #3105	C₂×C₅₃	semidirect
503. #3003	C₂×C₅₃	semidirect
504. C₂×#447	C₂×C₅₃	semidirect
505. #2974	C₂×C₅₃	semidirect
517. C₂³×D₄	C₂²×C₅₃	semidirect
518. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
519. C₂²×D₈	C₂²×C₅₃	semidirect
520. #555	C₂²×C₅₃	semidirect
521. #554	C₂²×C₅₃	semidirect
523. #553	C₂²×C₅₃	semidirect
524. #550	C₂²×C₅₃	semidirect
526. #546	C₂²×C₅₃	semidirect
532. D₄²	C₂²×C₅₃	semidirect
533. D₄²	C₂²×C₅₃	semidirect
534. D₄²	C₂²×C₅₃	semidirect
537. #532	C₂²×C₅₃	semidirect
538. C₂×#127	C₂²×C₅₃	semidirect
539. #529	C₂²×C₅₃	semidirect
540. #525	C₂²×C₅₃	semidirect
542. C₂×#121	C₂²×C₅₃	semidirect
543. C₂×#121	C₂²×C₅₃	semidirect
547. C₂×C₄×D₄	C₂²×C₅₃	semidirect
548. #496	C₂²×C₅₃	semidirect
549. #493	C₂²×C₅₃	semidirect
550. #490	C₂²×C₅₃	semidirect
551. #486	C₂²×C₅₃	semidirect
552. #484	C₂²×C₅₃	semidirect
553. #482	C₂²×C₅₃	semidirect
554. #481	C₂²×C₅₃	semidirect
555. #481	C₂²×C₅₃	semidirect
556. #481	C₂²×C₅₃	semidirect
557. #478	C₂²×C₅₃	semidirect
558. #476	C₂²×C₅₃	semidirect
559. #469	C₂²×C₅₃	semidirect
560. #469	C₂²×C₅₃	semidirect
561. #466	C₂²×C₅₃	semidirect
562. #465	C₂²×C₅₃	semidirect
563. #463	C₂²×C₅₃	semidirect
564. #460	C₂²×C₅₃	semidirect
565. #459	C₂²×C₅₃	semidirect
566. #459	C₂²×C₅₃	semidirect
567. #459	C₂²×C₅₃	semidirect
568. #450	C₂²×C₅₃	semidirect
569. #450	C₂²×C₅₃	semidirect
570. #450	C₂²×C₅₃	semidirect
571. #449	C₂²×C₅₃	semidirect
573. #447	C₂²×C₅₃	semidirect
574. #447	C₂²×C₅₃	semidirect
575. #447	C₂²×C₅₃	semidirect
576. #447	C₂²×C₅₃	semidirect
577. #447	C₂²×C₅₃	semidirect
578. #447	C₂²×C₅₃	semidirect
579. #447	C₂²×C₅₃	semidirect
580. #447	C₂²×C₅₃	semidirect
581. #442	C₂²×C₅₃	semidirect
582. C₄×SD₁₆	C₂²×C₅₃	semidirect
583. C₄×D₈	C₂²×C₅₃	semidirect
584. #436	C₂²×C₅₃	semidirect
585. #435	C₂²×C₅₃	semidirect
586. C₈×D₄	C₂²×C₅₃	semidirect
587. #432	C₂²×C₅₃	semidirect
588. #431	C₂²×C₅₃	semidirect
589. #418	C₂²×C₅₃	semidirect
590. C₂×#102	C₂²×C₅₃	semidirect
591. #407	C₂²×C₅₃	semidirect
592. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
593. C₅₃	#61591	direct (N × H)
596. C₂×#41	C₂³×C₅₃	semidirect
615. C₂²×D₄	C₂³×C₅₃	semidirect
620. C₂×SD₁₆	C₂³×C₅₃	semidirect
624. C₂×D₈	C₂³×C₅₃	semidirect
625. C₂×D₈	C₂³×C₅₃	semidirect
626. C₂×D₈	C₂³×C₅₃	semidirect
627. C₂×M₁₆	C₂³×C₅₃	semidirect
628. C₂²×C₈	C₂³×C₅₃	semidirect
629. C₄⋊Q₈	C₂³×C₅₃	semidirect
635. #127	C₂³×C₅₃	semidirect
639. #125	C₂³×C₅₃	semidirect
642. #124	C₂³×C₅₃	semidirect
649. C₂²⋊Q₈	C₂³×C₅₃	semidirect
667. #121	C₂³×C₅₃	semidirect
668. #121	C₂³×C₅₃	semidirect
669. #121	C₂³×C₅₃	semidirect
677. C₄×Q₈	C₂³×C₅₃	semidirect
695. C₄×D₄	C₂³×C₅₃	semidirect
696. C₄×D₄	C₂³×C₅₃	semidirect
699. #117	C₂³×C₅₃	semidirect
702. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
709. #107	C₂³×C₅₃	semidirect
710. #106	C₂³×C₅₃	semidirect
711. #106	C₂³×C₅₃	semidirect
712. C₄⋊C₈	C₂³×C₅₃	semidirect
713. C₄⋊C₈	C₂³×C₅₃	semidirect
714. #103	C₂³×C₅₃	semidirect
718. #102	C₂³×C₅₃	semidirect
719. #102	C₂³×C₅₃	semidirect
720. #102	C₂³×C₅₃	semidirect
721. #102	C₂³×C₅₃	semidirect
722. #102	C₂³×C₅₃	semidirect
723. #102	C₂³×C₅₃	semidirect
727. C₂²⋊C₈	C₂³×C₅₃	semidirect
728. C₂²⋊C₈	C₂³×C₅₃	semidirect
729. #97	C₂³×C₅₃	semidirect
730. C₄×C₈	C₂³×C₅₃	semidirect
913. D₄	AGL(1,ℤ/8)×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3519	2
C₂×D₄²×C₅₃	2
C₅₃×#3325	2
C₅₃×#3318	2
C₅₃×#3295	2
D₄×D₈×C₅₃	2
C₅₃×#3274	2
C₅₃×#3264	2
C₅₃×#3217	2
C₅₃×#3205	2
C₅₃×#3192	2
C₅₃×#3188	2
C₅₃×#3109	2
C₅₃×#3105	2
C₅₃×#3003	2
C₂×C₅₃×#447	2
C₅₃×#2974	2
#61591	53

Subgroups — C53×#61591 #27269103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61591 #27269103