Subgroups — C₅₃×#62016 #27269528

Order 13568.

1902 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3397	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3376	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3321	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3320	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3297	C₂	1	2	yes	maximal, complemented
8	D₄×SD₁₆×C₅₃	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3265	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3264	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3257	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3221	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3042	C₂	1	2	yes	maximal, complemented
18	C₂×C₅₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
21	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
23	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₅₃×#563	—	2	1	no	—
25	C₅₃×#562	—	2	1	no	—
26	C₅₃×#556	C₂²	1	2	yes	complemented
27	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#553	—	2	1	no	—
30	C₅₃×#553	C₂²	1	2	yes	—
31	C₅₃×#551	—	2	2	no	—
32	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
33	D₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
34	C₅₃×#548	C₂²	1	2	yes	complemented
35	C₅₃×#546	—	2	1	no	—
36	C₅₃×#546	—	2	2	no	—
37	C₅₃×#546	C₂²	1	2	yes	complemented
38	D₄²×C₅₃	C₂²	1	2	yes	—
39	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#543	—	2	1	no	—
41	C₅₃×#542	—	2	2	no	—
42	C₅₃×#542	C₂²	1	2	yes	complemented
43	C₅₃×#540	C₂²	1	2	yes	complemented
44	C₅₃×#538	—	2	2	no	—
45	C₅₃×#538	—	2	1	no	—
46	C₅₃×#536	C₂²	1	2	yes	complemented
47	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#532	C₂²	1	1	yes	characteristic
49	C₅₃×#529	C₂²	1	1	yes	characteristic
50	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#525	—	2	1	no	—
52	C₂×#121×C₅₃	—	2	1	no	—
53	C₅₃×#518	C₂²	1	2	yes	complemented
54	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₅₃×#496	C₂²	1	2	yes	complemented
56	C₅₃×#496	C₂²	1	2	yes	complemented
57	C₅₃×#492	C₂²	1	2	yes	complemented
58	C₅₃×#491	C₂²	1	2	yes	complemented
59	C₅₃×#489	C₂²	1	2	yes	complemented
60	C₅₃×#488	C₂²	1	2	yes	complemented
61	C₅₃×#485	C₂²	1	2	yes	complemented
62	C₅₃×#484	C₂²	1	2	yes	complemented
63	C₅₃×#482	C₂²	1	2	yes	complemented
64	C₅₃×#479	C₂²	1	2	yes	complemented
65	C₅₃×#478	C₂²	1	2	yes	complemented
66	C₅₃×#476	C₂²	1	2	yes	complemented
67	C₅₃×#475	C₂²	1	2	yes	complemented
68	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#469	C₂²	1	2	yes	complemented
71	C₅₃×#468	C₂²	1	2	yes	complemented
72	C₅₃×#466	C₂²	1	2	yes	complemented
73	C₅₃×#465	C₂²	1	2	yes	complemented
74	C₅₃×#465	C₂²	1	2	yes	complemented
75	C₅₃×#465	C₂²	1	2	yes	complemented
76	C₅₃×#463	C₂²	1	2	yes	—
77	C₅₃×#463	C₂²	1	2	yes	—
78	C₅₃×#463	C₂²	1	2	yes	—
79	C₅₃×#463	C₂²	1	2	yes	complemented
80	C₅₃×#463	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×#461	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#461	C₂²	1	2	yes	complemented
86	C₅₃×#461	C₂²	1	2	yes	complemented
87	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#461	C₂²	1	2	yes	complemented
89	C₅₃×#460	C₂²	1	2	yes	complemented
90	C₅₃×#460	C₂²	1	2	yes	complemented
91	C₅₃×#459	C₂²	1	2	yes	complemented
92	C₅₃×#450	C₂²	1	2	yes	—
93	C₅₃×#450	C₂²	1	2	yes	complemented
94	C₅₃×#449	C₂²	1	2	yes	complemented
95	C₅₃×#449	C₂²	1	2	yes	complemented
96	C₅₃×#448	C₂²	1	2	yes	complemented
97	C₅₃×#448	C₂²	1	2	yes	complemented
98	C₅₃×#448	C₂²	1	2	yes	complemented
99	C₅₃×#447	C₂²	1	2	yes	—
100	C₅₃×#447	C₂²	1	2	yes	complemented
101	C₅₃×#446	C₂²	1	2	yes	complemented
102	C₅₃×#442	C₂²	1	2	yes	—
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×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
107	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
108	C₅₃×#435	C₂²	1	2	yes	complemented
109	C₅₃×#435	C₂²	1	2	yes	complemented
110	C₈×D₄×C₅₃	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	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#419	C₂²	1	2	yes	complemented
116	C₅₃×#416	C₂²	1	2	yes	complemented
117	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₅₃	—	2	1	no	—
120	C₂×#41×C₅₃	—	2	1	no	—
121	C₂×#41×C₅₃	C₂³	1	2	yes	—
122	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₅₃	—	2	2	no	—
125	C₂²×D₄×C₅₃	—	2	1	no	—
126	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
128	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅₃	—	2	1	no	—
130	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
131	C₂×SD₁₆×C₅₃	—	4	2	no	—
132	C₂×SD₁₆×C₅₃	—	4	4	no	—
133	C₂×SD₁₆×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	—	4	2	no	—
142	C₂×D₈×C₅₃	C₂³	1	2	yes	—
143	C₂×D₈×C₅₃	C₂³	1	2	yes	—
144	C₂×D₈×C₅₃	C₂³	1	2	yes	—
145	C₂×D₈×C₅₃	C₂³	1	2	yes	—
146	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
150	C₄⋊Q₈×C₅₃	—	2	2	no	—
151	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
155	#127×C₅₃	C₂³	1	2	yes	—
156	#127×C₅₃	C₂³	1	1	yes	characteristic
157	#126×C₅₃	—	2	2	no	—
158	#126×C₅₃	—	2	2	no	—
159	#126×C₅₃	—	2	2	no	—
160	#126×C₅₃	—	2	2	no	—
161	#126×C₅₃	D₄	1	2	yes	—
162	#125×C₅₃	—	2	1	no	—
163	#125×C₅₃	D₄	1	1	yes	characteristic
164	#125×C₅₃	C₂³	1	2	yes	—
165	#124×C₅₃	—	2	2	no	—
166	#124×C₅₃	—	2	2	no	—
167	#124×C₅₃	—	2	2	no	—
168	#124×C₅₃	—	2	1	no	—
169	#124×C₅₃	—	2	1	no	—
170	#124×C₅₃	—	2	1	no	—
171	#124×C₅₃	D₄	1	1	yes	characteristic
172	#124×C₅₃	C₂³	1	2	yes	—
173	#124×C₅₃	C₂³	1	2	yes	—
174	#124×C₅₃	C₂³	1	2	yes	—
175	#123×C₅₃	—	2	2	no	—
176	#123×C₅₃	—	2	2	no	—
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	D₄	1	2	yes	—
183	C₂²⋊Q₈×C₅₃	—	2	2	no	—
184	C₂²⋊Q₈×C₅₃	—	2	2	no	—
185	C₂²⋊Q₈×C₅₃	—	2	2	no	—
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	2	no	—
192	C₂²⋊Q₈×C₅₃	—	2	1	no	—
193	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
194	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
196	#121×C₅₃	—	2	1	no	—
197	#121×C₅₃	—	2	1	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	1	no	—
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	1	no	—
207	#121×C₅₃	D₄	1	1	yes	characteristic
208	#121×C₅₃	C₂³	1	2	yes	—
209	#121×C₅₃	C₂³	1	2	yes	—
210	#121×C₅₃	C₂³	1	2	yes	—
211	#121×C₅₃	C₂³	1	2	yes	—
212	#120×C₅₃	—	2	2	no	—
213	#120×C₅₃	—	2	2	no	—
214	#120×C₅₃	—	2	2	no	—
215	#120×C₅₃	—	2	2	no	—
216	C₄×Q₈×C₅₃	—	2	1	no	—
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×D₄×C₅₃	—	2	2	no	—
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	1	no	—
225	C₄×D₄×C₅₃	—	2	1	no	—
226	C₄×D₄×C₅₃	—	2	1	no	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
236	C₄×D₄×C₅₃	C₂³	1	2	yes	—
237	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
238	#117×C₅₃	—	2	1	no	—
239	#117×C₅₃	—	2	2	no	—
240	#117×C₅₃	—	2	1	no	—
241	#117×C₅₃	C₂³	1	2	yes	—
242	#117×C₅₃	C₂³	1	2	yes	—
243	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
244	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
246	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
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×C₂²⋊C₄×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	#106×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	#103×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	1	no	—
286	C₂⁴×C₅₃	—	2	2	no	—
287	#41×C₅₃	—	4	2	no	—
288	#41×C₅₃	—	4	2	no	—
289	#41×C₅₃	—	8	2	no	—
290	#41×C₅₃	—	8	2	no	—
291	C₂×Q₈×C₅₃	—	2	1	no	—
292	C₂×Q₈×C₅₃	—	2	2	no	—
293	C₂×Q₈×C₅₃	—	2	1	no	—
294	C₂×Q₈×C₅₃	—	2	1	no	—
295	C₂×Q₈×C₅₃	—	4	1	no	—
296	C₂×Q₈×C₅₃	—	4	2	no	—
297	C₂×Q₈×C₅₃	—	4	1	no	—
298	C₂×Q₈×C₅₃	—	4	2	no	—
299	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
300	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
301	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
302	C₂×D₄×C₅₃	—	2	2	no	—
303	C₂×D₄×C₅₃	—	2	4	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	2	no	—
309	C₂×D₄×C₅₃	—	2	2	no	—
310	C₂×D₄×C₅₃	—	2	1	no	—
311	C₂×D₄×C₅₃	—	2	1	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	1	no	—
316	C₂×D₄×C₅₃	—	4	1	no	—
317	C₂×D₄×C₅₃	—	4	2	no	—
318	C₂×D₄×C₅₃	—	4	1	no	—
319	C₂×D₄×C₅₃	—	4	1	no	—
320	C₂×D₄×C₅₃	—	8	2	no	—
321	C₂×D₄×C₅₃	—	8	4	no	—
322	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
323	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
324	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
325	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
327	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₅₃	—	2	1	no	—
329	C₂²×C₄×C₅₃	—	2	1	no	—
330	C₂²×C₄×C₅₃	—	2	2	no	—
331	C₂²×C₄×C₅₃	—	2	1	no	—
332	C₂²×C₄×C₅₃	—	2	1	no	—
333	C₂²×C₄×C₅₃	—	2	1	no	—
334	C₂²×C₄×C₅₃	—	2	2	no	—
335	C₂²×C₄×C₅₃	—	2	2	no	—
336	C₂²×C₄×C₅₃	—	2	2	no	—
337	C₂²×C₄×C₅₃	—	2	2	no	—
338	C₂²×C₄×C₅₃	—	2	2	no	—
339	C₂²×C₄×C₅₃	—	2	1	no	—
340	C₂²×C₄×C₅₃	—	8	2	no	—
341	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
345	SD₁₆×C₅₃	—	2	4	no	—
346	SD₁₆×C₅₃	—	2	4	no	—
347	SD₁₆×C₅₃	—	4	2	no	—
348	SD₁₆×C₅₃	—	4	2	no	—
349	SD₁₆×C₅₃	—	4	2	no	—
350	SD₁₆×C₅₃	—	4	2	no	—
351	SD₁₆×C₅₃	—	4	2	no	—
352	SD₁₆×C₅₃	—	4	2	no	—
353	D₈×C₅₃	—	2	4	no	—
354	D₈×C₅₃	—	4	2	no	—
355	D₈×C₅₃	—	4	2	no	—
356	D₈×C₅₃	—	4	2	no	—
357	M₁₆×C₅₃	—	4	2	no	—
358	C₂×C₈×C₅₃	—	4	1	no	—
359	C₂×C₈×C₅₃	—	4	1	no	—
360	C₂×C₈×C₅₃	—	4	2	no	—
361	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
362	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
363	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
364	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₅₃	—	2	1	no	—
366	C₄⋊C₄×C₅₃	—	2	2	no	—
367	C₄⋊C₄×C₅₃	—	2	1	no	—
368	C₄⋊C₄×C₅₃	—	2	2	no	—
369	C₄⋊C₄×C₅₃	—	2	1	no	—
370	C₄⋊C₄×C₅₃	—	2	1	no	—
371	C₄⋊C₄×C₅₃	—	2	2	no	—
372	C₄⋊C₄×C₅₃	—	2	2	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	1	no	—
376	C₄⋊C₄×C₅₃	—	2	2	no	—
377	C₄⋊C₄×C₅₃	—	2	2	no	—
378	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
381	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
382	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
383	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
384	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
386	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²⋊C₄×C₅₃	—	2	2	no	—
389	C₂²⋊C₄×C₅₃	—	2	2	no	—
390	C₂²⋊C₄×C₅₃	—	2	2	no	—
391	C₂²⋊C₄×C₅₃	—	2	1	no	—
392	C₂²⋊C₄×C₅₃	—	2	2	no	—
393	C₂²⋊C₄×C₅₃	—	2	1	no	—
394	C₂²⋊C₄×C₅₃	—	2	2	no	—
395	C₂²⋊C₄×C₅₃	—	2	2	no	—
396	C₂²⋊C₄×C₅₃	—	2	1	no	—
397	C₂²⋊C₄×C₅₃	—	2	2	no	—
398	C₂²⋊C₄×C₅₃	—	2	1	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	—	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	2	no	—
408	C₂²⋊C₄×C₅₃	—	2	2	no	—
409	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
410	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
411	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
412	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
413	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
414	C₄²×C₅₃	—	2	2	no	—
415	C₄²×C₅₃	—	2	2	no	—
416	C₄²×C₅₃	—	2	2	no	—
417	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
418	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
419	C₄²×C₅₃	C₂⁴	1	2	yes	—
420	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂³×C₅₃	—	2	1	no	—
423	C₂³×C₅₃	—	2	1	no	—
424	C₂³×C₅₃	—	2	2	no	—
425	C₂³×C₅₃	—	2	2	no	—
426	C₂³×C₅₃	—	4	2	no	—
427	C₂³×C₅₃	—	4	4	no	—
428	C₂³×C₅₃	—	4	2	no	—
429	C₂³×C₅₃	—	4	2	no	—
430	C₂³×C₅₃	—	8	1	no	—
431	C₂³×C₅₃	—	8	1	no	—
432	C₂³×C₅₃	—	8	2	no	—
433	C₂³×C₅₃	—	8	2	no	—
434	C₂³×C₅₃	—	8	1	no	—
435	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
436	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
437	Q₈×C₅₃	—	2	2	no	—
438	Q₈×C₅₃	—	2	2	no	—
439	Q₈×C₅₃	—	2	2	no	—
440	Q₈×C₅₃	—	2	2	no	—
441	Q₈×C₅₃	—	4	1	no	—
442	Q₈×C₅₃	—	8	1	no	—
443	Q₈×C₅₃	—	8	2	no	—
444	Q₈×C₅₃	—	8	1	no	—
445	Q₈×C₅₃	—	8	1	no	—
446	D₄×C₅₃	—	2	4	no	—
447	D₄×C₅₃	—	2	1	no	—
448	D₄×C₅₃	—	2	2	no	—
449	D₄×C₅₃	—	2	2	no	—
450	D₄×C₅₃	—	2	1	no	—
451	D₄×C₅₃	—	2	2	no	—
452	D₄×C₅₃	—	2	2	no	—
453	D₄×C₅₃	—	2	1	no	—
454	D₄×C₅₃	—	4	1	no	—
455	D₄×C₅₃	—	4	4	no	—
456	D₄×C₅₃	—	4	2	no	—
457	D₄×C₅₃	—	4	2	no	—
458	D₄×C₅₃	—	4	4	no	—
459	D₄×C₅₃	—	8	1	no	—
460	D₄×C₅₃	—	8	2	no	—
461	D₄×C₅₃	—	8	2	no	—
462	D₄×C₅₃	—	8	1	no	—
463	D₄×C₅₃	—	8	2	no	—
464	D₄×C₅₃	—	8	2	no	—
465	D₄×C₅₃	—	8	2	no	—
466	D₄×C₅₃	—	8	2	no	—
467	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
468	C₂×C₄×C₅₃	—	2	2	no	—
469	C₂×C₄×C₅₃	—	2	1	no	—
470	C₂×C₄×C₅₃	—	2	2	no	—
471	C₂×C₄×C₅₃	—	2	1	no	—
472	C₂×C₄×C₅₃	—	2	2	no	—
473	C₂×C₄×C₅₃	—	2	1	no	—
474	C₂×C₄×C₅₃	—	2	1	no	—
475	C₂×C₄×C₅₃	—	2	2	no	—
476	C₂×C₄×C₅₃	—	2	2	no	—
477	C₂×C₄×C₅₃	—	2	2	no	—
478	C₂×C₄×C₅₃	—	2	2	no	—
479	C₂×C₄×C₅₃	—	4	1	no	—
480	C₂×C₄×C₅₃	—	4	2	no	—
481	C₂×C₄×C₅₃	—	4	2	no	—
482	C₂×C₄×C₅₃	—	8	2	no	—
483	C₂×C₄×C₅₃	—	8	1	no	—
484	C₂×C₄×C₅₃	—	8	1	no	—
485	C₂×C₄×C₅₃	—	8	2	no	—
486	C₂×C₄×C₅₃	—	8	2	no	—
487	C₂×C₄×C₅₃	—	8	2	no	—
488	C₂×C₄×C₅₃	—	8	2	no	—
489	C₂×C₄×C₅₃	—	8	1	no	—
490	C₂×C₄×C₅₃	—	8	2	no	—
491	C₂×C₄×C₅₃	—	8	1	no	—
492	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
501	C₈×C₅₃	—	2	2	no	—
502	C₈×C₅₃	—	2	2	no	—
503	C₈×C₅₃	—	2	2	no	—
504	C₈×C₅₃	—	2	2	no	—
505	#62016	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
506	C₂²×C₅₃	—	2	1	no	—
507	C₂²×C₅₃	—	2	1	no	—
508	C₂²×C₅₃	—	2	2	no	—
509	C₂²×C₅₃	—	2	2	no	—
510	C₂²×C₅₃	—	2	2	no	—
511	C₂²×C₅₃	—	2	2	no	—
512	C₂²×C₅₃	—	4	1	no	—
513	C₂²×C₅₃	—	4	1	no	—
514	C₂²×C₅₃	—	4	1	no	—
515	C₂²×C₅₃	—	4	2	no	—
516	C₂²×C₅₃	—	4	2	no	—
517	C₂²×C₅₃	—	4	2	no	—
518	C₂²×C₅₃	—	4	1	no	—
519	C₂²×C₅₃	—	4	2	no	—
520	C₂²×C₅₃	—	4	2	no	—
521	C₂²×C₅₃	—	4	1	no	—
522	C₂²×C₅₃	—	4	2	no	—
523	C₂²×C₅₃	—	8	4	no	—
524	C₂²×C₅₃	—	16	2	no	—
525	C₂²×C₅₃	—	16	4	no	—
526	C₂²×C₅₃	#577	1	2	yes	—
527	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
528	C₄×C₅₃	—	2	1	no	—
529	C₄×C₅₃	—	2	1	no	—
530	C₄×C₅₃	—	2	2	no	—
531	C₄×C₅₃	—	2	2	no	—
532	C₄×C₅₃	—	2	1	no	—
533	C₄×C₅₃	—	2	1	no	—
534	C₄×C₅₃	—	2	1	no	—
535	C₄×C₅₃	—	2	2	no	—
536	C₄×C₅₃	—	4	1	no	—
537	C₄×C₅₃	—	4	1	no	—
538	C₄×C₅₃	—	4	2	no	—
539	C₄×C₅₃	—	4	2	no	—
540	C₄×C₅₃	—	4	2	no	—
541	C₄×C₅₃	—	4	2	no	—
542	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
543	C₄×C₅₃	#585	1	1	yes	characteristic
544	#3561	C₂×C₅₃	1	1	yes	characteristic, complemented
545	#3519	C₂×C₅₃	1	1	yes	characteristic, complemented
546	#3397	C₂×C₅₃	1	2	yes	complemented
547	#3376	C₂×C₅₃	1	2	yes	complemented
548	#3321	C₂×C₅₃	1	2	yes	complemented
549	#3320	C₂×C₅₃	1	2	yes	complemented
550	#3297	C₂×C₅₃	1	2	yes	complemented
551	D₄×SD₁₆	C₂×C₅₃	1	2	yes	complemented
552	#3265	C₂×C₅₃	1	2	yes	complemented
553	#3264	C₂×C₅₃	1	2	yes	complemented
554	#3257	C₂×C₅₃	1	2	yes	complemented
555	#3246	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#3221	C₂×C₅₃	1	2	yes	complemented
557	#3213	C₂×C₅₃	1	1	yes	characteristic, complemented
558	#3118	C₂×C₅₃	1	2	yes	complemented
559	#3110	C₂×C₅₃	1	1	yes	characteristic, complemented
560	#3042	C₂×C₅₃	1	2	yes	complemented
561	C₂×#463	C₂×C₅₃	1	1	yes	characteristic, complemented
562	#2992	C₂×C₅₃	1	1	yes	characteristic, complemented
563	C₂×C₅₃	—	2	2	no	—
564	C₂×C₅₃	—	4	2	no	—
565	C₂×C₅₃	—	4	2	no	—
566	C₂×C₅₃	—	8	1	no	—
567	C₂×C₅₃	—	8	2	no	—
568	C₂×C₅₃	—	8	2	no	—
569	C₂×C₅₃	#3488	1	1	yes	characteristic
570	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
571	C₂×C₅₃	#3585	1	1	yes	characteristic
572	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
573	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
574	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
575	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
576	#563	—	2	1	no	—
577	#562	—	2	1	no	—
578	#556	C₂²×C₅₃	1	2	yes	complemented
579	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
580	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
581	#553	—	2	1	no	—
582	#553	C₂²×C₅₃	1	2	yes	—
583	#551	—	2	2	no	—
584	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
585	D₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
586	#548	C₂²×C₅₃	1	2	yes	complemented
587	#546	—	2	1	no	—
588	#546	—	2	2	no	—
589	#546	C₂²×C₅₃	1	2	yes	complemented
590	D₄²	C₂²×C₅₃	1	2	yes	—
591	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
592	#543	—	2	1	no	—
593	#542	—	2	2	no	—
594	#542	C₂²×C₅₃	1	2	yes	complemented
595	#540	C₂²×C₅₃	1	2	yes	complemented
596	#538	—	2	2	no	—
597	#538	—	2	1	no	—
598	#536	C₂²×C₅₃	1	2	yes	complemented
599	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
600	#532	C₂²×C₅₃	1	1	yes	characteristic
601	#529	C₂²×C₅₃	1	1	yes	characteristic
602	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
603	#525	—	2	1	no	—
604	C₂×#121	—	2	1	no	—
605	#518	C₂²×C₅₃	1	2	yes	complemented
606	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
607	#496	C₂²×C₅₃	1	2	yes	complemented
608	#496	C₂²×C₅₃	1	2	yes	complemented
609	#492	C₂²×C₅₃	1	2	yes	complemented
610	#491	C₂²×C₅₃	1	2	yes	complemented
611	#489	C₂²×C₅₃	1	2	yes	complemented
612	#488	C₂²×C₅₃	1	2	yes	complemented
613	#485	C₂²×C₅₃	1	2	yes	complemented
614	#484	C₂²×C₅₃	1	2	yes	complemented
615	#482	C₂²×C₅₃	1	2	yes	complemented
616	#479	C₂²×C₅₃	1	2	yes	complemented
617	#478	C₂²×C₅₃	1	2	yes	complemented
618	#476	C₂²×C₅₃	1	2	yes	complemented
619	#475	C₂²×C₅₃	1	2	yes	complemented
620	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
621	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
622	#469	C₂²×C₅₃	1	2	yes	complemented
623	#468	C₂²×C₅₃	1	2	yes	complemented
624	#466	C₂²×C₅₃	1	2	yes	complemented
625	#465	C₂²×C₅₃	1	2	yes	complemented
626	#465	C₂²×C₅₃	1	2	yes	complemented
627	#465	C₂²×C₅₃	1	2	yes	complemented
628	#463	C₂²×C₅₃	1	2	yes	—
629	#463	C₂²×C₅₃	1	2	yes	—
630	#463	C₂²×C₅₃	1	2	yes	—
631	#463	C₂²×C₅₃	1	2	yes	complemented
632	#463	C₂²×C₅₃	1	2	yes	complemented
633	#463	C₂²×C₅₃	1	2	yes	complemented
634	#463	C₂²×C₅₃	1	2	yes	complemented
635	#463	C₂²×C₅₃	1	2	yes	complemented
636	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
637	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
638	#461	C₂²×C₅₃	1	2	yes	complemented
639	#461	C₂²×C₅₃	1	2	yes	complemented
640	#461	C₂²×C₅₃	1	2	yes	complemented
641	#460	C₂²×C₅₃	1	2	yes	complemented
642	#460	C₂²×C₅₃	1	2	yes	complemented
643	#459	C₂²×C₅₃	1	2	yes	complemented
644	#450	C₂²×C₅₃	1	2	yes	—
645	#450	C₂²×C₅₃	1	2	yes	complemented
646	#449	C₂²×C₅₃	1	2	yes	complemented
647	#449	C₂²×C₅₃	1	2	yes	complemented
648	#448	C₂²×C₅₃	1	2	yes	complemented
649	#448	C₂²×C₅₃	1	2	yes	complemented
650	#448	C₂²×C₅₃	1	2	yes	complemented
651	#447	C₂²×C₅₃	1	2	yes	—
652	#447	C₂²×C₅₃	1	2	yes	complemented
653	#446	C₂²×C₅₃	1	2	yes	complemented
654	#442	C₂²×C₅₃	1	2	yes	—
655	#440	C₂²×C₅₃	1	2	yes	complemented
656	#440	C₂²×C₅₃	1	2	yes	complemented
657	#440	C₂²×C₅₃	1	2	yes	complemented
658	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
659	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
660	#435	C₂²×C₅₃	1	2	yes	complemented
661	#435	C₂²×C₅₃	1	2	yes	complemented
662	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
663	#433	C₂²×C₅₃	1	2	yes	complemented
664	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
665	#424	C₂²×C₅₃	1	2	yes	complemented
666	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
667	#419	C₂²×C₅₃	1	2	yes	complemented
668	#416	C₂²×C₅₃	1	2	yes	complemented
669	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
670	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
671	C₅₃	#62016	1	1	yes	characteristic, direct product factor, Sylow
672	C₂×#41	—	2	1	no	—
673	C₂×#41	—	2	1	no	—
674	C₂×#41	C₂³×C₅₃	1	2	yes	—
675	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
676	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
677	C₂²×D₄	—	2	2	no	—
678	C₂²×D₄	—	2	1	no	—
679	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
680	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
681	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
682	C₂³×C₄	—	2	1	no	—
683	AGL(1,ℤ/8)	—	4	4	no	—
684	C₂×SD₁₆	—	4	2	no	—
685	C₂×SD₁₆	—	4	4	no	—
686	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
689	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
690	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
692	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
693	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
694	C₂×D₈	—	4	2	no	—
695	C₂×D₈	C₂³×C₅₃	1	2	yes	—
696	C₂×D₈	C₂³×C₅₃	1	2	yes	—
697	C₂×D₈	C₂³×C₅₃	1	2	yes	—
698	C₂×D₈	C₂³×C₅₃	1	2	yes	—
699	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
700	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
701	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
702	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
703	C₄⋊Q₈	—	2	2	no	—
704	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
708	#127	C₂³×C₅₃	1	1	yes	characteristic
709	#127	C₂³×C₅₃	1	2	yes	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	D₄×C₅₃	1	2	yes	—
715	#125	—	2	1	no	—
716	#125	D₄×C₅₃	1	1	yes	characteristic
717	#125	C₂³×C₅₃	1	2	yes	—
718	#124	—	2	2	no	—
719	#124	—	2	2	no	—
720	#124	—	2	2	no	—
721	#124	—	2	1	no	—
722	#124	—	2	1	no	—
723	#124	—	2	1	no	—
724	#124	D₄×C₅₃	1	1	yes	characteristic
725	#124	C₂³×C₅₃	1	2	yes	—
726	#124	C₂³×C₅₃	1	2	yes	—
727	#124	C₂³×C₅₃	1	2	yes	—
728	#123	—	2	2	no	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	—	2	2	no	—
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	#123	D₄×C₅₃	1	2	yes	—
736	C₂²⋊Q₈	—	2	1	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	1	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
747	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
748	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
749	#121	—	2	2	no	—
750	#121	—	2	1	no	—
751	#121	—	2	2	no	—
752	#121	—	2	1	no	—
753	#121	—	2	1	no	—
754	#121	—	2	1	no	—
755	#121	—	2	2	no	—
756	#121	—	2	2	no	—
757	#121	—	2	2	no	—
758	#121	—	2	2	no	—
759	#121	—	2	2	no	—
760	#121	D₄×C₅₃	1	1	yes	characteristic
761	#121	C₂³×C₅₃	1	2	yes	—
762	#121	C₂³×C₅₃	1	2	yes	—
763	#121	C₂³×C₅₃	1	2	yes	—
764	#121	C₂³×C₅₃	1	2	yes	—
765	#120	—	2	2	no	—
766	#120	—	2	2	no	—
767	#120	—	2	2	no	—
768	#120	—	2	2	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
771	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
772	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
782	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
783	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
784	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
785	C₄×D₄	C₂³×C₅₃	1	2	yes	—
786	C₄×D₄	C₂³×C₅₃	1	2	yes	—
787	C₄×D₄	C₂³×C₅₃	1	2	yes	—
788	C₄×D₄	C₂³×C₅₃	1	2	yes	—
789	C₄×D₄	C₂³×C₅₃	1	2	yes	—
790	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
791	#117	—	2	1	no	—
792	#117	—	2	1	no	—
793	#117	—	2	2	no	—
794	#117	C₂³×C₅₃	1	2	yes	—
795	#117	C₂³×C₅₃	1	2	yes	—
796	C₂×C₄⋊C₄	—	2	1	no	—
797	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
798	C₂×C₂²⋊C₄	—	2	1	no	—
799	C₂×C₂²⋊C₄	—	2	1	no	—
800	C₂×C₂²⋊C₄	—	2	1	no	—
801	C₂×C₂²⋊C₄	—	2	2	no	—
802	C₂×C₂²⋊C₄	—	2	2	no	—
803	C₂×C₂²⋊C₄	—	2	2	no	—
804	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
805	#107	C₂³×C₅₃	1	2	yes	—
806	#107	C₂³×C₅₃	1	2	yes	—
807	#106	C₂³×C₅₃	1	2	yes	—
808	#106	C₂³×C₅₃	1	2	yes	—
809	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
810	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
811	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
813	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
814	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
815	#103	C₂³×C₅₃	1	2	yes	—
816	#103	C₂³×C₅₃	1	2	yes	—
817	#103	C₂³×C₅₃	1	2	yes	—
818	#103	C₂³×C₅₃	1	2	yes	—
819	#103	C₂³×C₅₃	1	2	yes	—
820	#103	C₂³×C₅₃	1	2	yes	—
821	#103	C₂³×C₅₃	1	2	yes	—
822	#103	C₂³×C₅₃	1	2	yes	—
823	#102	C₂³×C₅₃	1	2	yes	—
824	#102	C₂³×C₅₃	1	2	yes	—
825	#102	C₂³×C₅₃	1	2	yes	—
826	#102	C₂³×C₅₃	1	2	yes	—
827	#102	C₂³×C₅₃	1	2	yes	—
828	#102	C₂³×C₅₃	1	2	yes	—
829	#102	C₂³×C₅₃	1	2	yes	—
830	#102	C₂³×C₅₃	1	2	yes	—
831	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
832	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
833	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
834	#97	C₂³×C₅₃	1	2	yes	—
835	#97	C₂³×C₅₃	1	2	yes	—
836	C₄×C₈	C₂³×C₅₃	1	2	yes	—
837	C₂⁴	—	2	1	no	—
838	C₂⁴	—	2	1	no	—
839	C₂⁴	—	2	2	no	—
840	#41	—	4	2	no	—
841	#41	—	4	2	no	—
842	#41	—	8	2	no	—
843	#41	—	8	2	no	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	2	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	2	1	no	—
848	C₂×Q₈	—	4	1	no	—
849	C₂×Q₈	—	4	2	no	—
850	C₂×Q₈	—	4	1	no	—
851	C₂×Q₈	—	4	2	no	—
852	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
853	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
854	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	4	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	2	2	no	—
863	C₂×D₄	—	2	1	no	—
864	C₂×D₄	—	2	1	no	—
865	C₂×D₄	—	2	2	no	—
866	C₂×D₄	—	2	1	no	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	—	4	1	no	—
870	C₂×D₄	—	4	2	no	—
871	C₂×D₄	—	4	1	no	—
872	C₂×D₄	—	4	1	no	—
873	C₂×D₄	—	8	2	no	—
874	C₂×D₄	—	8	4	no	—
875	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
876	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
877	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
878	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
879	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
880	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	1	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	8	2	no	—
894	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
895	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
898	SD₁₆	—	2	4	no	—
899	SD₁₆	—	2	4	no	—
900	SD₁₆	—	4	2	no	—
901	SD₁₆	—	4	2	no	—
902	SD₁₆	—	4	2	no	—
903	SD₁₆	—	4	2	no	—
904	SD₁₆	—	4	2	no	—
905	SD₁₆	—	4	2	no	—
906	D₈	—	2	4	no	—
907	D₈	—	4	2	no	—
908	D₈	—	4	2	no	—
909	D₈	—	4	2	no	—
910	M₁₆	—	4	2	no	—
911	C₂×C₈	—	4	1	no	—
912	C₂×C₈	—	4	1	no	—
913	C₂×C₈	—	4	2	no	—
914	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
915	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
916	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
917	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
932	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
933	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
934	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
935	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
936	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
937	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
938	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
939	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
963	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
964	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
965	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
966	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
967	C₄²	—	2	2	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	2	no	—
970	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
971	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
972	C₄²	C₂⁴×C₅₃	1	2	yes	—
973	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
974	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
975	C₂³	—	2	1	no	—
976	C₂³	—	2	2	no	—
977	C₂³	—	2	2	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	4	2	no	—
980	C₂³	—	4	4	no	—
981	C₂³	—	4	2	no	—
982	C₂³	—	4	2	no	—
983	C₂³	—	8	1	no	—
984	C₂³	—	8	1	no	—
985	C₂³	—	8	2	no	—
986	C₂³	—	8	2	no	—
987	C₂³	—	8	1	no	—
988	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
989	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
990	Q₈	—	2	2	no	—
991	Q₈	—	2	2	no	—
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	4	1	no	—
995	Q₈	—	8	1	no	—
996	Q₈	—	8	2	no	—
997	Q₈	—	8	1	no	—
998	Q₈	—	8	1	no	—
999	D₄	—	2	4	no	—
1000	D₄	—	2	2	no	—
1001	D₄	—	2	1	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	2	2	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	4	1	no	—
1008	D₄	—	4	4	no	—
1009	D₄	—	4	2	no	—
1010	D₄	—	4	2	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	8	1	no	—
1013	D₄	—	8	2	no	—
1014	D₄	—	8	1	no	—
1015	D₄	—	8	2	no	—
1016	D₄	—	8	2	no	—
1017	D₄	—	8	2	no	—
1018	D₄	—	8	2	no	—
1019	D₄	—	8	2	no	—
1020	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	4	1	no	—
1033	C₂×C₄	—	4	2	no	—
1034	C₂×C₄	—	4	2	no	—
1035	C₂×C₄	—	8	2	no	—
1036	C₂×C₄	—	8	1	no	—
1037	C₂×C₄	—	8	1	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	2	no	—
1042	C₂×C₄	—	8	1	no	—
1043	C₂×C₄	—	8	2	no	—
1044	C₂×C₄	—	8	1	no	—
1045	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1046	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1047	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1048	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1051	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1052	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1053	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1054	C₈	—	2	2	no	—
1055	C₈	—	2	2	no	—
1056	C₈	—	2	2	no	—
1057	C₈	—	2	2	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	2	2	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	8	4	no	—
1076	C₂²	—	16	2	no	—
1077	C₂²	—	16	4	no	—
1078	C₂²	C₅₃×#577	1	2	yes	—
1079	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1080	C₄	—	2	2	no	—
1081	C₄	—	2	1	no	—
1082	C₄	—	2	1	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	4	2	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1095	C₄	C₅₃×#585	1	1	yes	characteristic
1096	C₂	—	2	2	no	—
1097	C₂	—	4	2	no	—
1098	C₂	—	4	2	no	—
1099	C₂	—	8	1	no	—
1100	C₂	—	8	2	no	—
1101	C₂	—	8	2	no	—
1102	C₂	C₅₃×#3488	1	1	yes	characteristic
1103	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1104	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3561	C₂	semidirect
2. C₅₃×#3519	C₂	semidirect
3. C₅₃×#3397	C₂	semidirect
4. C₅₃×#3376	C₂	semidirect
5. C₅₃×#3321	C₂	semidirect
6. C₅₃×#3320	C₂	semidirect
7. C₅₃×#3297	C₂	semidirect
8. D₄×SD₁₆×C₅₃	C₂	semidirect
9. C₅₃×#3265	C₂	semidirect
10. C₅₃×#3264	C₂	semidirect
11. C₅₃×#3257	C₂	semidirect
12. C₅₃×#3246	C₂	semidirect
13. C₅₃×#3221	C₂	semidirect
14. C₅₃×#3213	C₂	semidirect
15. C₅₃×#3118	C₂	semidirect
16. C₅₃×#3110	C₂	semidirect
17. C₅₃×#3042	C₂	semidirect
18. C₂×C₅₃×#463	C₂	semidirect
19. C₅₃×#2992	C₂	semidirect
22. C₂²×SD₁₆×C₅₃	C₂²	semidirect
26. C₅₃×#556	C₂²	semidirect
27. C₅₃×#555	C₂²	semidirect
28. C₅₃×#554	C₂²	semidirect
32. C₅₃×#550	C₂²	semidirect
33. D₄×Q₈×C₅₃	C₂²	semidirect
34. C₅₃×#548	C₂²	semidirect
37. C₅₃×#546	C₂²	semidirect
39. D₄²×C₅₃	C₂²	semidirect
42. C₅₃×#542	C₂²	semidirect
43. C₅₃×#540	C₂²	semidirect
46. C₅₃×#536	C₂²	semidirect
47. C₅₃×#533	C₂²	semidirect
50. C₂×#124×C₅₃	C₂²	semidirect
53. C₅₃×#518	C₂²	semidirect
55. C₅₃×#496	C₂²	semidirect
56. C₅₃×#496	C₂²	semidirect
57. C₅₃×#492	C₂²	semidirect
58. C₅₃×#491	C₂²	semidirect
59. C₅₃×#489	C₂²	semidirect
60. C₅₃×#488	C₂²	semidirect
61. C₅₃×#485	C₂²	semidirect
62. C₅₃×#484	C₂²	semidirect
63. C₅₃×#482	C₂²	semidirect
64. C₅₃×#479	C₂²	semidirect
65. C₅₃×#478	C₂²	semidirect
66. C₅₃×#476	C₂²	semidirect
67. C₅₃×#475	C₂²	semidirect
68. C₅₃×#474	C₂²	semidirect
69. C₅₃×#474	C₂²	semidirect
70. C₅₃×#469	C₂²	semidirect
71. C₅₃×#468	C₂²	semidirect
72. C₅₃×#466	C₂²	semidirect
73. C₅₃×#465	C₂²	semidirect
74. C₅₃×#465	C₂²	semidirect
75. C₅₃×#465	C₂²	semidirect
79. C₅₃×#463	C₂²	semidirect
80. C₅₃×#463	C₂²	semidirect
81. C₅₃×#463	C₂²	semidirect
82. C₅₃×#463	C₂²	semidirect
83. C₅₃×#463	C₂²	semidirect
84. C₅₃×#461	C₂²	semidirect
85. C₅₃×#461	C₂²	semidirect
86. C₅₃×#461	C₂²	semidirect
87. C₅₃×#461	C₂²	semidirect
88. C₅₃×#461	C₂²	semidirect
89. C₅₃×#460	C₂²	semidirect
90. C₅₃×#460	C₂²	semidirect
91. C₅₃×#459	C₂²	semidirect
93. C₅₃×#450	C₂²	semidirect
94. C₅₃×#449	C₂²	semidirect
95. C₅₃×#449	C₂²	semidirect
96. C₅₃×#448	C₂²	semidirect
97. C₅₃×#448	C₂²	semidirect
98. C₅₃×#448	C₂²	semidirect
100. C₅₃×#447	C₂²	semidirect
101. C₅₃×#446	C₂²	semidirect
103. C₅₃×#440	C₂²	semidirect
104. C₅₃×#440	C₂²	semidirect
105. C₅₃×#440	C₂²	semidirect
106. C₄×SD₁₆×C₅₃	C₂²	semidirect
107. C₄×D₈×C₅₃	C₂²	semidirect
108. C₅₃×#435	C₂²	semidirect
109. C₅₃×#435	C₂²	semidirect
110. C₈×D₄×C₅₃	C₂²	semidirect
111. C₅₃×#433	C₂²	semidirect
112. C₅₃×#432	C₂²	semidirect
113. C₅₃×#424	C₂²	semidirect
114. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
115. C₅₃×#419	C₂²	semidirect
116. C₅₃×#416	C₂²	semidirect
117. C₂×#103×C₅₃	C₂²	semidirect
118. C₂×#102×C₅₃	C₂²	semidirect
505. #62016	C₅₃	direct (N × H)
544. #3561	C₂×C₅₃	semidirect
545. #3519	C₂×C₅₃	semidirect
546. #3397	C₂×C₅₃	semidirect
547. #3376	C₂×C₅₃	semidirect
548. #3321	C₂×C₅₃	semidirect
549. #3320	C₂×C₅₃	semidirect
550. #3297	C₂×C₅₃	semidirect
551. D₄×SD₁₆	C₂×C₅₃	semidirect
552. #3265	C₂×C₅₃	semidirect
553. #3264	C₂×C₅₃	semidirect
554. #3257	C₂×C₅₃	semidirect
555. #3246	C₂×C₅₃	semidirect
556. #3221	C₂×C₅₃	semidirect
557. #3213	C₂×C₅₃	semidirect
558. #3118	C₂×C₅₃	semidirect
559. #3110	C₂×C₅₃	semidirect
560. #3042	C₂×C₅₃	semidirect
561. C₂×#463	C₂×C₅₃	semidirect
562. #2992	C₂×C₅₃	semidirect
574. C₂²×SD₁₆	C₂²×C₅₃	semidirect
578. #556	C₂²×C₅₃	semidirect
579. #555	C₂²×C₅₃	semidirect
580. #554	C₂²×C₅₃	semidirect
584. #550	C₂²×C₅₃	semidirect
585. D₄×Q₈	C₂²×C₅₃	semidirect
586. #548	C₂²×C₅₃	semidirect
589. #546	C₂²×C₅₃	semidirect
591. D₄²	C₂²×C₅₃	semidirect
594. #542	C₂²×C₅₃	semidirect
595. #540	C₂²×C₅₃	semidirect
598. #536	C₂²×C₅₃	semidirect
599. #533	C₂²×C₅₃	semidirect
602. C₂×#124	C₂²×C₅₃	semidirect
605. #518	C₂²×C₅₃	semidirect
607. #496	C₂²×C₅₃	semidirect
608. #496	C₂²×C₅₃	semidirect
609. #492	C₂²×C₅₃	semidirect
610. #491	C₂²×C₅₃	semidirect
611. #489	C₂²×C₅₃	semidirect
612. #488	C₂²×C₅₃	semidirect
613. #485	C₂²×C₅₃	semidirect
614. #484	C₂²×C₅₃	semidirect
615. #482	C₂²×C₅₃	semidirect
616. #479	C₂²×C₅₃	semidirect
617. #478	C₂²×C₅₃	semidirect
618. #476	C₂²×C₅₃	semidirect
619. #475	C₂²×C₅₃	semidirect
620. #474	C₂²×C₅₃	semidirect
621. #474	C₂²×C₅₃	semidirect
622. #469	C₂²×C₅₃	semidirect
623. #468	C₂²×C₅₃	semidirect
624. #466	C₂²×C₅₃	semidirect
625. #465	C₂²×C₅₃	semidirect
626. #465	C₂²×C₅₃	semidirect
627. #465	C₂²×C₅₃	semidirect
631. #463	C₂²×C₅₃	semidirect
632. #463	C₂²×C₅₃	semidirect
633. #463	C₂²×C₅₃	semidirect
634. #463	C₂²×C₅₃	semidirect
635. #463	C₂²×C₅₃	semidirect
636. #461	C₂²×C₅₃	semidirect
637. #461	C₂²×C₅₃	semidirect
638. #461	C₂²×C₅₃	semidirect
639. #461	C₂²×C₅₃	semidirect
640. #461	C₂²×C₅₃	semidirect
641. #460	C₂²×C₅₃	semidirect
642. #460	C₂²×C₅₃	semidirect
643. #459	C₂²×C₅₃	semidirect
645. #450	C₂²×C₅₃	semidirect
646. #449	C₂²×C₅₃	semidirect
647. #449	C₂²×C₅₃	semidirect
648. #448	C₂²×C₅₃	semidirect
649. #448	C₂²×C₅₃	semidirect
650. #448	C₂²×C₅₃	semidirect
652. #447	C₂²×C₅₃	semidirect
653. #446	C₂²×C₅₃	semidirect
655. #440	C₂²×C₅₃	semidirect
656. #440	C₂²×C₅₃	semidirect
657. #440	C₂²×C₅₃	semidirect
658. C₄×SD₁₆	C₂²×C₅₃	semidirect
659. C₄×D₈	C₂²×C₅₃	semidirect
660. #435	C₂²×C₅₃	semidirect
661. #435	C₂²×C₅₃	semidirect
662. C₈×D₄	C₂²×C₅₃	semidirect
663. #433	C₂²×C₅₃	semidirect
664. #432	C₂²×C₅₃	semidirect
665. #424	C₂²×C₅₃	semidirect
666. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
667. #419	C₂²×C₅₃	semidirect
668. #416	C₂²×C₅₃	semidirect
669. C₂×#103	C₂²×C₅₃	semidirect
670. C₂×#102	C₂²×C₅₃	semidirect
671. C₅₃	#62016	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×#3561	2
C₅₃×#3519	2
C₅₃×#3397	2
C₅₃×#3376	2
C₅₃×#3321	2
C₅₃×#3320	2
C₅₃×#3297	2
D₄×SD₁₆×C₅₃	2
C₅₃×#3265	2
C₅₃×#3264	2
C₅₃×#3257	2
C₅₃×#3246	2
C₅₃×#3221	2
C₅₃×#3213	2
C₅₃×#3118	2
C₅₃×#3110	2
C₅₃×#3042	2
C₂×C₅₃×#463	2
C₅₃×#2992	2
#62016	53

Subgroups — C53×#62016 #27269528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62016 #27269528