Subgroups — C₅₃×#62190 #27269702

Order 13568.

1748 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3357	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3346	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3322	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3319	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3257	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3243	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3119	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3083	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#562	—	2	2	no	—
25	C₅₃×#556	C₂²	1	1	yes	characteristic
26	C₅₃×#555	C₂²	1	2	yes	—
27	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×#554	C₂²	1	2	yes	—
29	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#553	C₂²	1	2	yes	—
31	C₅₃×#552	—	2	1	no	—
32	C₅₃×#552	—	2	1	no	—
33	C₅₃×#551	—	2	2	no	—
34	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#548	—	2	1	no	—
37	C₅₃×#548	—	2	1	no	—
38	C₅₃×#547	C₂²	1	1	yes	characteristic
39	C₅₃×#547	C₂²	1	1	yes	characteristic
40	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#546	C₂²	1	2	yes	—
42	C₅₃×#544	C₂²	1	2	yes	complemented
43	C₅₃×#542	—	2	2	no	—
44	C₅₃×#542	C₂²	1	2	yes	—
45	C₅₃×#540	C₂²	1	2	yes	complemented
46	C₅₃×#539	—	2	2	no	—
47	C₅₃×#537	—	2	1	no	—
48	C₅₃×#536	—	2	1	no	—
49	C₅₃×#533	C₂²	1	1	yes	characteristic
50	C₅₃×#533	C₂²	1	1	yes	characteristic
51	C₅₃×#532	C₂²	1	1	yes	characteristic
52	C₅₃×#529	C₂²	1	1	yes	characteristic
53	C₅₃×#525	—	2	1	no	—
54	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
55	C₅₃×#520	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#501	C₂²	1	2	yes	complemented
58	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#500	C₂²	1	2	yes	complemented
60	C₅₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#489	C₂²	1	2	yes	—
62	C₅₃×#488	C₂²	1	2	yes	—
63	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#485	C₂²	1	2	yes	—
66	C₅₃×#485	C₂²	1	2	yes	—
67	C₅₃×#485	C₂²	1	2	yes	complemented
68	C₅₃×#484	C₂²	1	2	yes	complemented
69	C₅₃×#482	C₂²	1	2	yes	—
70	C₅₃×#481	C₂²	1	2	yes	complemented
71	C₅₃×#480	C₂²	1	2	yes	—
72	C₅₃×#480	C₂²	1	1	yes	characteristic
73	C₅₃×#480	C₂²	1	1	yes	characteristic
74	C₅₃×#480	C₂²	1	2	yes	complemented
75	C₅₃×#479	C₂²	1	2	yes	complemented
76	C₅₃×#479	C₂²	1	2	yes	complemented
77	C₅₃×#479	C₂²	1	2	yes	complemented
78	C₅₃×#478	C₂²	1	2	yes	—
79	C₅₃×#478	C₂²	1	2	yes	—
80	C₅₃×#478	C₂²	1	2	yes	—
81	C₅₃×#477	C₂²	1	2	yes	complemented
82	C₅₃×#477	C₂²	1	2	yes	complemented
83	C₅₃×#476	C₂²	1	1	yes	characteristic
84	C₅₃×#476	C₂²	1	1	yes	characteristic
85	C₅₃×#476	C₂²	1	2	yes	complemented
86	C₅₃×#474	C₂²	1	1	yes	characteristic
87	C₅₃×#474	C₂²	1	2	yes	—
88	C₅₃×#474	C₂²	1	1	yes	characteristic
89	C₅₃×#474	C₂²	1	1	yes	characteristic
90	C₅₃×#474	C₂²	1	1	yes	characteristic
91	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#474	C₂²	1	2	yes	complemented
94	C₅₃×#469	C₂²	1	2	yes	—
95	C₅₃×#468	C₂²	1	2	yes	—
96	C₅₃×#468	C₂²	1	2	yes	—
97	C₅₃×#468	C₂²	1	2	yes	complemented
98	C₅₃×#466	C₂²	1	2	yes	—
99	C₅₃×#465	C₂²	1	2	yes	complemented
100	C₅₃×#463	C₂²	1	2	yes	—
101	C₅₃×#463	C₂²	1	2	yes	—
102	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#460	C₂²	1	2	yes	complemented
105	C₅₃×#459	C₂²	1	1	yes	characteristic
106	C₅₃×#459	C₂²	1	1	yes	characteristic
107	C₅₃×#449	C₂²	1	2	yes	—
108	C₅₃×#449	C₂²	1	2	yes	—
109	C₅₃×#447	C₂²	1	1	yes	characteristic
110	C₅₃×#447	C₂²	1	1	yes	characteristic
111	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#442	C₂²	1	2	yes	—
114	C₅₃×#440	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
116	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×D₈×C₅₃	C₂²	1	2	yes	—
118	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
121	C₅₃×#436	C₂²	1	2	yes	—
122	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#435	C₂²	1	2	yes	—
124	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#433	C₂²	1	2	yes	complemented
126	C₅₃×#431	C₂²	1	1	yes	characteristic
127	C₅₃×#428	C₂²	1	2	yes	—
128	C₅₃×#428	C₂²	1	2	yes	complemented
129	C₂×#107×C₅₃	C₂²	1	2	yes	complemented
130	C₅₃×#424	C₂²	1	2	yes	complemented
131	C₅₃×#423	C₂²	1	1	yes	characteristic
132	C₅₃×#418	C₂²	1	2	yes	—
133	C₅₃×#417	C₂²	1	2	yes	—
134	C₅₃×#416	C₂²	1	2	yes	—
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	1	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	C₂³	1	2	yes	—
139	C₂²×Q₈×C₅₃	—	2	1	no	—
140	C₂²×Q₈×C₅₃	—	2	1	no	—
141	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₅₃	—	2	1	no	—
143	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
145	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
150	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₅₃	—	2	2	no	—
153	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
160	#127×C₅₃	C₂³	1	1	yes	characteristic
161	#126×C₅₃	—	2	2	no	—
162	#126×C₅₃	—	2	2	no	—
163	#126×C₅₃	—	2	2	no	—
164	#126×C₅₃	D₄	1	2	yes	—
165	#125×C₅₃	—	2	2	no	—
166	#125×C₅₃	—	2	2	no	—
167	#125×C₅₃	—	2	1	no	—
168	#125×C₅₃	D₄	1	1	yes	characteristic
169	#125×C₅₃	C₂³	1	2	yes	—
170	#125×C₅₃	C₂³	1	2	yes	—
171	#124×C₅₃	—	2	2	no	—
172	#124×C₅₃	—	2	2	no	—
173	#124×C₅₃	—	2	2	no	—
174	#124×C₅₃	—	2	2	no	—
175	#124×C₅₃	—	2	1	no	—
176	#124×C₅₃	D₄	1	1	yes	characteristic
177	#124×C₅₃	C₂³	1	2	yes	—
178	#123×C₅₃	—	2	2	no	—
179	#123×C₅₃	—	2	2	no	—
180	#123×C₅₃	—	2	2	no	—
181	#123×C₅₃	—	2	2	no	—
182	#123×C₅₃	—	2	2	no	—
183	#123×C₅₃	—	2	2	no	—
184	#123×C₅₃	—	2	2	no	—
185	#123×C₅₃	—	2	2	no	—
186	#123×C₅₃	D₄	1	2	yes	—
187	C₂²⋊Q₈×C₅₃	—	2	2	no	—
188	C₂²⋊Q₈×C₅₃	—	2	1	no	—
189	C₂²⋊Q₈×C₅₃	—	2	1	no	—
190	C₂²⋊Q₈×C₅₃	—	2	1	no	—
191	C₂²⋊Q₈×C₅₃	—	2	1	no	—
192	C₂²⋊Q₈×C₅₃	—	2	2	no	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	2	no	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	—	2	2	no	—
198	C₂²⋊Q₈×C₅₃	—	2	2	no	—
199	C₂²⋊Q₈×C₅₃	—	2	1	no	—
200	C₂²⋊Q₈×C₅₃	—	2	1	no	—
201	C₂²⋊Q₈×C₅₃	—	2	1	no	—
202	C₂²⋊Q₈×C₅₃	—	2	1	no	—
203	C₂²⋊Q₈×C₅₃	—	2	1	no	—
204	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
205	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
207	#121×C₅₃	—	2	2	no	—
208	#121×C₅₃	—	2	2	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	1	no	—
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	—	2	2	no	—
213	#121×C₅₃	—	2	2	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	D₄	1	1	yes	characteristic
216	#121×C₅₃	C₂³	1	1	yes	characteristic
217	#121×C₅₃	C₂³	1	1	yes	characteristic
218	#121×C₅₃	C₂³	1	2	yes	—
219	#121×C₅₃	C₂³	1	2	yes	—
220	#121×C₅₃	C₂³	1	2	yes	—
221	#120×C₅₃	—	2	2	no	—
222	C₄×Q₈×C₅₃	—	2	1	no	—
223	C₄×Q₈×C₅₃	—	2	1	no	—
224	C₄×Q₈×C₅₃	—	2	1	no	—
225	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
227	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
228	C₄×D₄×C₅₃	—	2	2	no	—
229	C₄×D₄×C₅₃	—	2	2	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	2	no	—
235	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₅₃	C₂³	1	2	yes	—
240	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₃	C₂³	1	2	yes	—
243	C₄×D₄×C₅₃	C₂³	1	2	yes	—
244	C₄×D₄×C₅₃	C₂³	1	2	yes	—
245	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
246	#117×C₅₃	—	2	2	no	—
247	#117×C₅₃	—	2	1	no	—
248	#117×C₅₃	—	2	1	no	—
249	#117×C₅₃	—	2	2	no	—
250	#117×C₅₃	—	2	1	no	—
251	#117×C₅₃	C₂³	1	2	yes	—
252	#117×C₅₃	C₂³	1	2	yes	—
253	#117×C₅₃	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
255	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
260	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
262	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
263	#107×C₅₃	C₂³	1	2	yes	—
264	#107×C₅₃	C₂³	1	2	yes	—
265	#107×C₅₃	C₂³	1	1	yes	characteristic
266	#107×C₅₃	C₂³	1	2	yes	—
267	#107×C₅₃	C₂³	1	2	yes	—
268	#107×C₅₃	C₂³	1	1	yes	characteristic
269	#107×C₅₃	C₂³	1	2	yes	—
270	#107×C₅₃	C₂³	1	1	yes	characteristic
271	#107×C₅₃	C₂³	1	2	yes	—
272	#107×C₅₃	C₂³	1	1	yes	characteristic
273	#106×C₅₃	C₂³	1	2	yes	—
274	#106×C₅₃	C₂³	1	2	yes	—
275	#106×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	2	yes	—
277	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
278	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	#103×C₅₃	C₂³	1	2	yes	—
285	#103×C₅₃	C₂³	1	2	yes	—
286	#103×C₅₃	C₂³	1	2	yes	—
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#102×C₅₃	C₂³	1	1	yes	characteristic
291	#102×C₅₃	C₂³	1	2	yes	—
292	#102×C₅₃	C₂³	1	1	yes	characteristic
293	#102×C₅₃	C₂³	1	2	yes	—
294	#102×C₅₃	C₂³	1	1	yes	characteristic
295	#102×C₅₃	C₂³	1	2	yes	—
296	#102×C₅₃	C₂³	1	1	yes	characteristic
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	1	yes	characteristic
299	#102×C₅₃	C₂³	1	1	yes	characteristic
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₃	C₂³	1	2	yes	—
312	C₂⁴×C₅₃	—	2	1	no	—
313	#41×C₅₃	—	2	4	no	—
314	#41×C₅₃	—	4	2	no	—
315	#41×C₅₃	—	8	2	no	—
316	#41×C₅₃	—	8	2	no	—
317	#41×C₅₃	—	8	2	no	—
318	C₂×Q₈×C₅₃	—	2	1	no	—
319	C₂×Q₈×C₅₃	—	2	1	no	—
320	C₂×Q₈×C₅₃	—	2	1	no	—
321	C₂×Q₈×C₅₃	—	2	2	no	—
322	C₂×Q₈×C₅₃	—	2	2	no	—
323	C₂×Q₈×C₅₃	—	2	1	no	—
324	C₂×Q₈×C₅₃	—	8	2	no	—
325	C₂×Q₈×C₅₃	—	8	2	no	—
326	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
328	C₂×D₄×C₅₃	—	2	2	no	—
329	C₂×D₄×C₅₃	—	2	2	no	—
330	C₂×D₄×C₅₃	—	2	2	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	1	no	—
333	C₂×D₄×C₅₃	—	2	2	no	—
334	C₂×D₄×C₅₃	—	2	1	no	—
335	C₂×D₄×C₅₃	—	2	1	no	—
336	C₂×D₄×C₅₃	—	2	1	no	—
337	C₂×D₄×C₅₃	—	2	1	no	—
338	C₂×D₄×C₅₃	—	4	1	no	—
339	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₅₃	—	2	1	no	—
346	C₂²×C₄×C₅₃	—	2	2	no	—
347	C₂²×C₄×C₅₃	—	2	2	no	—
348	C₂²×C₄×C₅₃	—	2	2	no	—
349	C₂²×C₄×C₅₃	—	2	1	no	—
350	C₂²×C₄×C₅₃	—	2	1	no	—
351	C₂²×C₄×C₅₃	—	2	1	no	—
352	C₂²×C₄×C₅₃	—	2	1	no	—
353	C₂²×C₄×C₅₃	—	2	2	no	—
354	C₂²×C₄×C₅₃	—	2	1	no	—
355	C₂²×C₄×C₅₃	—	2	2	no	—
356	C₂²×C₄×C₅₃	—	2	2	no	—
357	C₂²×C₄×C₅₃	—	2	1	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	SD₁₆×C₅₃	—	4	2	no	—
364	SD₁₆×C₅₃	—	4	2	no	—
365	D₈×C₅₃	—	2	2	no	—
366	D₈×C₅₃	—	2	2	no	—
367	D₈×C₅₃	—	4	1	no	—
368	D₈×C₅₃	—	4	1	no	—
369	M₁₆×C₅₃	—	4	2	no	—
370	M₁₆×C₅₃	—	4	2	no	—
371	C₂×C₈×C₅₃	—	4	2	no	—
372	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
375	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
378	C₄⋊C₄×C₅₃	—	2	2	no	—
379	C₄⋊C₄×C₅₃	—	2	1	no	—
380	C₄⋊C₄×C₅₃	—	2	1	no	—
381	C₄⋊C₄×C₅₃	—	2	2	no	—
382	C₄⋊C₄×C₅₃	—	2	2	no	—
383	C₄⋊C₄×C₅₃	—	2	2	no	—
384	C₄⋊C₄×C₅₃	—	2	2	no	—
385	C₄⋊C₄×C₅₃	—	2	1	no	—
386	C₄⋊C₄×C₅₃	—	2	2	no	—
387	C₄⋊C₄×C₅₃	—	2	2	no	—
388	C₄⋊C₄×C₅₃	—	2	1	no	—
389	C₄⋊C₄×C₅₃	—	2	1	no	—
390	C₄⋊C₄×C₅₃	—	2	1	no	—
391	C₄⋊C₄×C₅₃	—	2	2	no	—
392	C₄⋊C₄×C₅₃	—	2	2	no	—
393	C₄⋊C₄×C₅₃	—	2	2	no	—
394	C₄⋊C₄×C₅₃	—	2	2	no	—
395	C₄⋊C₄×C₅₃	—	2	2	no	—
396	C₄⋊C₄×C₅₃	—	2	1	no	—
397	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
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	1	no	—
415	C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂²⋊C₄×C₅₃	—	2	1	no	—
417	C₂²⋊C₄×C₅₃	—	2	1	no	—
418	C₂²⋊C₄×C₅₃	—	2	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	1	no	—
421	C₂²⋊C₄×C₅₃	—	2	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	2	no	—
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	1	no	—
426	C₂²⋊C₄×C₅₃	—	2	2	no	—
427	C₂²⋊C₄×C₅₃	—	2	1	no	—
428	C₂²⋊C₄×C₅₃	—	2	2	no	—
429	C₂²⋊C₄×C₅₃	—	2	1	no	—
430	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
435	C₄²×C₅₃	—	2	2	no	—
436	C₄²×C₅₃	—	2	2	no	—
437	C₄²×C₅₃	—	2	2	no	—
438	C₄²×C₅₃	—	2	2	no	—
439	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₄²×C₅₃	C₂⁴	1	2	yes	—
443	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₂³×C₅₃	—	2	1	no	—
445	C₂³×C₅₃	—	2	1	no	—
446	C₂³×C₅₃	—	2	1	no	—
447	C₂³×C₅₃	—	2	1	no	—
448	C₂³×C₅₃	—	4	2	no	—
449	C₂³×C₅₃	—	4	2	no	—
450	C₂³×C₅₃	—	8	1	no	—
451	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
452	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
453	Q₈×C₅₃	—	2	2	no	—
454	Q₈×C₅₃	—	2	2	no	—
455	Q₈×C₅₃	—	2	2	no	—
456	Q₈×C₅₃	—	4	2	no	—
457	Q₈×C₅₃	—	4	2	no	—
458	Q₈×C₅₃	—	8	1	no	—
459	Q₈×C₅₃	—	8	2	no	—
460	Q₈×C₅₃	—	8	2	no	—
461	Q₈×C₅₃	—	8	1	no	—
462	D₄×C₅₃	—	2	2	no	—
463	D₄×C₅₃	—	2	1	no	—
464	D₄×C₅₃	—	2	1	no	—
465	D₄×C₅₃	—	2	1	no	—
466	D₄×C₅₃	—	2	1	no	—
467	D₄×C₅₃	—	2	1	no	—
468	D₄×C₅₃	—	2	1	no	—
469	D₄×C₅₃	—	2	1	no	—
470	D₄×C₅₃	—	4	2	no	—
471	D₄×C₅₃	—	4	2	no	—
472	D₄×C₅₃	—	4	4	no	—
473	D₄×C₅₃	—	8	1	no	—
474	D₄×C₅₃	—	8	1	no	—
475	D₄×C₅₃	—	8	2	no	—
476	D₄×C₅₃	—	8	1	no	—
477	D₄×C₅₃	—	8	1	no	—
478	D₄×C₅₃	—	8	2	no	—
479	D₄×C₅₃	—	8	2	no	—
480	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
481	C₂×C₄×C₅₃	—	2	2	no	—
482	C₂×C₄×C₅₃	—	2	1	no	—
483	C₂×C₄×C₅₃	—	2	2	no	—
484	C₂×C₄×C₅₃	—	2	1	no	—
485	C₂×C₄×C₅₃	—	2	2	no	—
486	C₂×C₄×C₅₃	—	2	1	no	—
487	C₂×C₄×C₅₃	—	2	1	no	—
488	C₂×C₄×C₅₃	—	2	1	no	—
489	C₂×C₄×C₅₃	—	2	2	no	—
490	C₂×C₄×C₅₃	—	2	2	no	—
491	C₂×C₄×C₅₃	—	2	1	no	—
492	C₂×C₄×C₅₃	—	2	2	no	—
493	C₂×C₄×C₅₃	—	2	2	no	—
494	C₂×C₄×C₅₃	—	4	1	no	—
495	C₂×C₄×C₅₃	—	4	4	no	—
496	C₂×C₄×C₅₃	—	4	2	no	—
497	C₂×C₄×C₅₃	—	4	2	no	—
498	C₂×C₄×C₅₃	—	4	2	no	—
499	C₂×C₄×C₅₃	—	4	2	no	—
500	C₂×C₄×C₅₃	—	8	2	no	—
501	C₂×C₄×C₅₃	—	8	1	no	—
502	C₂×C₄×C₅₃	—	8	1	no	—
503	C₂×C₄×C₅₃	—	8	2	no	—
504	C₂×C₄×C₅₃	—	8	2	no	—
505	C₂×C₄×C₅₃	—	8	1	no	—
506	C₂×C₄×C₅₃	—	8	2	no	—
507	C₂×C₄×C₅₃	—	8	2	no	—
508	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
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	C₂⁵	1	1	yes	characteristic
517	C₈×C₅₃	—	2	1	no	—
518	C₈×C₅₃	—	2	1	no	—
519	C₈×C₅₃	—	2	1	no	—
520	C₈×C₅₃	—	2	2	no	—
521	C₈×C₅₃	—	2	1	no	—
522	C₈×C₅₃	—	2	2	no	—
523	#62190	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
524	C₂²×C₅₃	—	2	1	no	—
525	C₂²×C₅₃	—	2	2	no	—
526	C₂²×C₅₃	—	2	2	no	—
527	C₂²×C₅₃	—	2	1	no	—
528	C₂²×C₅₃	—	2	2	no	—
529	C₂²×C₅₃	—	2	1	no	—
530	C₂²×C₅₃	—	2	2	no	—
531	C₂²×C₅₃	—	4	1	no	—
532	C₂²×C₅₃	—	4	1	no	—
533	C₂²×C₅₃	—	4	1	no	—
534	C₂²×C₅₃	—	4	1	no	—
535	C₂²×C₅₃	—	4	1	no	—
536	C₂²×C₅₃	—	4	1	no	—
537	C₂²×C₅₃	—	4	1	no	—
538	C₂²×C₅₃	—	4	1	no	—
539	C₂²×C₅₃	—	4	1	no	—
540	C₂²×C₅₃	—	4	1	no	—
541	C₂²×C₅₃	—	4	1	no	—
542	C₂²×C₅₃	—	8	4	no	—
543	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
544	C₄×C₅₃	—	2	1	no	—
545	C₄×C₅₃	—	2	1	no	—
546	C₄×C₅₃	—	2	2	no	—
547	C₄×C₅₃	—	2	2	no	—
548	C₄×C₅₃	—	2	1	no	—
549	C₄×C₅₃	—	2	1	no	—
550	C₄×C₅₃	—	2	2	no	—
551	C₄×C₅₃	—	4	2	no	—
552	C₄×C₅₃	—	4	2	no	—
553	C₄×C₅₃	—	4	1	no	—
554	C₄×C₅₃	—	4	1	no	—
555	C₄×C₅₃	—	4	1	no	—
556	C₄×C₅₃	—	4	1	no	—
557	C₄×C₅₃	—	4	2	no	—
558	C₄×C₅₃	—	4	2	no	—
559	C₄×C₅₃	#576	1	2	yes	—
560	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
561	C₄×C₅₃	#585	1	1	yes	characteristic
562	#3547	C₂×C₅₃	1	1	yes	characteristic, complemented
563	#3520	C₂×C₅₃	1	1	yes	characteristic, complemented
564	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
565	Q₈×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
566	#3367	C₂×C₅₃	1	1	yes	characteristic, complemented
567	#3360	C₂×C₅₃	1	1	yes	characteristic, complemented
568	#3357	C₂×C₅₃	1	2	yes	complemented
569	#3354	C₂×C₅₃	1	1	yes	characteristic, complemented
570	#3346	C₂×C₅₃	1	2	yes	complemented
571	#3334	C₂×C₅₃	1	1	yes	characteristic, complemented
572	#3330	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#3322	C₂×C₅₃	1	2	yes	complemented
574	#3319	C₂×C₅₃	1	2	yes	complemented
575	#3303	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#3257	C₂×C₅₃	1	2	yes	complemented
577	#3254	C₂×C₅₃	1	1	yes	characteristic, complemented
578	#3243	C₂×C₅₃	1	2	yes	complemented
579	#3231	C₂×C₅₃	1	1	yes	characteristic, complemented
580	#3119	C₂×C₅₃	1	2	yes	complemented
581	#3100	C₂×C₅₃	1	1	yes	characteristic, complemented
582	#3083	C₂×C₅₃	1	2	yes	complemented
583	#3077	C₂×C₅₃	1	1	yes	characteristic, complemented
584	#2993	C₂×C₅₃	1	1	yes	characteristic, complemented
585	C₂×C₅₃	—	4	2	no	—
586	C₂×C₅₃	—	4	1	no	—
587	C₂×C₅₃	—	4	2	no	—
588	C₂×C₅₃	—	8	1	no	—
589	C₂×C₅₃	—	8	1	no	—
590	C₂×C₅₃	—	8	1	no	—
591	C₂×C₅₃	#3489	1	1	yes	characteristic
592	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
593	C₂×C₅₃	#3586	1	1	yes	characteristic
594	#562	—	2	2	no	—
595	#556	C₂²×C₅₃	1	1	yes	characteristic
596	#555	C₂²×C₅₃	1	2	yes	—
597	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
598	#554	C₂²×C₅₃	1	2	yes	—
599	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
600	#553	C₂²×C₅₃	1	2	yes	—
601	#552	—	2	1	no	—
602	#552	—	2	1	no	—
603	#551	—	2	2	no	—
604	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
605	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
606	#548	—	2	1	no	—
607	#548	—	2	1	no	—
608	#547	C₂²×C₅₃	1	1	yes	characteristic
609	#547	C₂²×C₅₃	1	1	yes	characteristic
610	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
611	#546	C₂²×C₅₃	1	2	yes	—
612	#544	C₂²×C₅₃	1	2	yes	complemented
613	#542	—	2	2	no	—
614	#542	C₂²×C₅₃	1	2	yes	—
615	#540	C₂²×C₅₃	1	2	yes	complemented
616	#539	—	2	2	no	—
617	#537	—	2	1	no	—
618	#536	—	2	1	no	—
619	#533	C₂²×C₅₃	1	1	yes	characteristic
620	#533	C₂²×C₅₃	1	1	yes	characteristic
621	#532	C₂²×C₅₃	1	1	yes	characteristic
622	#529	C₂²×C₅₃	1	1	yes	characteristic
623	#525	—	2	1	no	—
624	C₂×C₂²⋊Q₈	—	2	1	no	—
625	#520	C₂²×C₅₃	1	2	yes	—
626	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
627	#501	C₂²×C₅₃	1	2	yes	complemented
628	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
629	#500	C₂²×C₅₃	1	2	yes	complemented
630	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
631	#489	C₂²×C₅₃	1	2	yes	—
632	#488	C₂²×C₅₃	1	2	yes	—
633	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
634	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
635	#485	C₂²×C₅₃	1	2	yes	—
636	#485	C₂²×C₅₃	1	2	yes	—
637	#485	C₂²×C₅₃	1	2	yes	complemented
638	#484	C₂²×C₅₃	1	2	yes	complemented
639	#482	C₂²×C₅₃	1	2	yes	—
640	#481	C₂²×C₅₃	1	2	yes	complemented
641	#480	C₂²×C₅₃	1	2	yes	—
642	#480	C₂²×C₅₃	1	1	yes	characteristic
643	#480	C₂²×C₅₃	1	1	yes	characteristic
644	#480	C₂²×C₅₃	1	2	yes	complemented
645	#479	C₂²×C₅₃	1	2	yes	complemented
646	#479	C₂²×C₅₃	1	2	yes	complemented
647	#479	C₂²×C₅₃	1	2	yes	complemented
648	#478	C₂²×C₅₃	1	2	yes	—
649	#478	C₂²×C₅₃	1	2	yes	—
650	#478	C₂²×C₅₃	1	2	yes	—
651	#477	C₂²×C₅₃	1	2	yes	complemented
652	#477	C₂²×C₅₃	1	2	yes	complemented
653	#476	C₂²×C₅₃	1	1	yes	characteristic
654	#476	C₂²×C₅₃	1	1	yes	characteristic
655	#476	C₂²×C₅₃	1	2	yes	complemented
656	#474	C₂²×C₅₃	1	1	yes	characteristic
657	#474	C₂²×C₅₃	1	1	yes	characteristic
658	#474	C₂²×C₅₃	1	1	yes	characteristic
659	#474	C₂²×C₅₃	1	2	yes	—
660	#474	C₂²×C₅₃	1	1	yes	characteristic
661	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
662	#474	C₂²×C₅₃	1	2	yes	complemented
663	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
664	#469	C₂²×C₅₃	1	2	yes	—
665	#468	C₂²×C₅₃	1	2	yes	—
666	#468	C₂²×C₅₃	1	2	yes	—
667	#468	C₂²×C₅₃	1	2	yes	complemented
668	#466	C₂²×C₅₃	1	2	yes	—
669	#465	C₂²×C₅₃	1	2	yes	complemented
670	#463	C₂²×C₅₃	1	2	yes	—
671	#463	C₂²×C₅₃	1	2	yes	—
672	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
674	#460	C₂²×C₅₃	1	2	yes	complemented
675	#459	C₂²×C₅₃	1	1	yes	characteristic
676	#459	C₂²×C₅₃	1	1	yes	characteristic
677	#449	C₂²×C₅₃	1	2	yes	—
678	#449	C₂²×C₅₃	1	2	yes	—
679	#447	C₂²×C₅₃	1	1	yes	characteristic
680	#447	C₂²×C₅₃	1	1	yes	characteristic
681	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
682	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	#442	C₂²×C₅₃	1	2	yes	—
684	#440	C₂²×C₅₃	1	2	yes	complemented
685	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
686	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
687	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
688	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
689	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
690	C₄×D₈	C₂²×C₅₃	1	2	yes	—
691	#436	C₂²×C₅₃	1	2	yes	—
692	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#435	C₂²×C₅₃	1	2	yes	—
694	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
695	#433	C₂²×C₅₃	1	2	yes	complemented
696	#431	C₂²×C₅₃	1	1	yes	characteristic
697	#428	C₂²×C₅₃	1	2	yes	—
698	#428	C₂²×C₅₃	1	2	yes	complemented
699	C₂×#107	C₂²×C₅₃	1	2	yes	complemented
700	#424	C₂²×C₅₃	1	2	yes	complemented
701	#423	C₂²×C₅₃	1	1	yes	characteristic
702	#418	C₂²×C₅₃	1	2	yes	—
703	#417	C₂²×C₅₃	1	2	yes	—
704	#416	C₂²×C₅₃	1	2	yes	—
705	C₅₃	#62190	1	1	yes	characteristic, direct product factor, Sylow
706	C₂×#41	—	2	1	no	—
707	C₂×#41	—	2	1	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	C₂³×C₅₃	1	2	yes	—
710	C₂²×Q₈	—	2	1	no	—
711	C₂²×Q₈	—	2	1	no	—
712	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
713	C₂³×C₄	—	2	1	no	—
714	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
716	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
717	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
718	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
719	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
720	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
721	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
722	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
723	C₄⋊Q₈	—	2	2	no	—
724	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
730	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
731	#127	C₂³×C₅₃	1	1	yes	characteristic
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	D₄×C₅₃	1	2	yes	—
736	#125	—	2	2	no	—
737	#125	—	2	2	no	—
738	#125	—	2	1	no	—
739	#125	D₄×C₅₃	1	1	yes	characteristic
740	#125	C₂³×C₅₃	1	2	yes	—
741	#125	C₂³×C₅₃	1	2	yes	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	—	2	1	no	—
747	#124	D₄×C₅₃	1	1	yes	characteristic
748	#124	C₂³×C₅₃	1	2	yes	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	D₄×C₅₃	1	2	yes	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
776	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
778	#121	—	2	1	no	—
779	#121	—	2	1	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	1	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	D₄×C₅₃	1	1	yes	characteristic
787	#121	C₂³×C₅₃	1	1	yes	characteristic
788	#121	C₂³×C₅₃	1	1	yes	characteristic
789	#121	C₂³×C₅₃	1	2	yes	—
790	#121	C₂³×C₅₃	1	2	yes	—
791	#121	C₂³×C₅₃	1	2	yes	—
792	#120	—	2	2	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
797	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
798	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₅₃	1	2	yes	—
811	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₅₃	1	2	yes	—
814	C₄×D₄	C₂³×C₅₃	1	2	yes	—
815	C₄×D₄	C₂³×C₅₃	1	2	yes	—
816	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
817	#117	—	2	1	no	—
818	#117	—	2	2	no	—
819	#117	—	2	1	no	—
820	#117	—	2	1	no	—
821	#117	—	2	2	no	—
822	#117	C₂³×C₅₃	1	2	yes	—
823	#117	C₂³×C₅₃	1	2	yes	—
824	#117	C₂³×C₅₃	1	2	yes	—
825	C₂×C₄⋊C₄	—	2	2	no	—
826	C₂×C₄⋊C₄	—	2	1	no	—
827	C₂×C₄⋊C₄	—	2	1	no	—
828	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
829	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
830	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
831	C₂×C₂²⋊C₄	—	2	1	no	—
832	C₂×C₂²⋊C₄	—	2	2	no	—
833	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
834	#107	C₂³×C₅₃	1	1	yes	characteristic
835	#107	C₂³×C₅₃	1	2	yes	—
836	#107	C₂³×C₅₃	1	2	yes	—
837	#107	C₂³×C₅₃	1	2	yes	—
838	#107	C₂³×C₅₃	1	2	yes	—
839	#107	C₂³×C₅₃	1	1	yes	characteristic
840	#107	C₂³×C₅₃	1	2	yes	—
841	#107	C₂³×C₅₃	1	1	yes	characteristic
842	#107	C₂³×C₅₃	1	1	yes	characteristic
843	#107	C₂³×C₅₃	1	2	yes	—
844	#106	C₂³×C₅₃	1	2	yes	—
845	#106	C₂³×C₅₃	1	2	yes	—
846	#106	C₂³×C₅₃	1	2	yes	—
847	#106	C₂³×C₅₃	1	2	yes	—
848	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
849	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
850	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
851	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
853	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
854	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
855	#103	C₂³×C₅₃	1	2	yes	—
856	#103	C₂³×C₅₃	1	2	yes	—
857	#103	C₂³×C₅₃	1	2	yes	—
858	#103	C₂³×C₅₃	1	2	yes	—
859	#103	C₂³×C₅₃	1	2	yes	—
860	#103	C₂³×C₅₃	1	2	yes	—
861	#102	C₂³×C₅₃	1	1	yes	characteristic
862	#102	C₂³×C₅₃	1	2	yes	—
863	#102	C₂³×C₅₃	1	1	yes	characteristic
864	#102	C₂³×C₅₃	1	2	yes	—
865	#102	C₂³×C₅₃	1	2	yes	—
866	#102	C₂³×C₅₃	1	2	yes	—
867	#102	C₂³×C₅₃	1	1	yes	characteristic
868	#102	C₂³×C₅₃	1	1	yes	characteristic
869	#102	C₂³×C₅₃	1	1	yes	characteristic
870	#102	C₂³×C₅₃	1	1	yes	characteristic
871	#102	C₂³×C₅₃	1	1	yes	characteristic
872	#102	C₂³×C₅₃	1	1	yes	characteristic
873	#102	C₂³×C₅₃	1	2	yes	—
874	#102	C₂³×C₅₃	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
879	#97	C₂³×C₅₃	1	2	yes	—
880	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
881	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₅₃	1	2	yes	—
883	C₂⁴	—	2	1	no	—
884	#41	—	2	4	no	—
885	#41	—	4	2	no	—
886	#41	—	8	2	no	—
887	#41	—	8	2	no	—
888	#41	—	8	2	no	—
889	C₂×Q₈	—	2	1	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	8	2	no	—
896	C₂×Q₈	—	8	2	no	—
897	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
898	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	1	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	4	1	no	—
910	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
911	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
912	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
913	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
914	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
915	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	8	2	no	—
930	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
931	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	2	no	—
936	D₈	—	2	2	no	—
937	D₈	—	2	2	no	—
938	D₈	—	4	1	no	—
939	D₈	—	4	1	no	—
940	M₁₆	—	4	2	no	—
941	M₁₆	—	4	2	no	—
942	C₂×C₈	—	4	2	no	—
943	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
945	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
946	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
947	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
973	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	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	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1002	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1003	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1004	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1005	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1011	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1012	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₅₃	1	2	yes	—
1014	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	4	2	no	—
1020	C₂³	—	4	2	no	—
1021	C₂³	—	8	1	no	—
1022	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1023	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1024	Q₈	—	2	2	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	4	2	no	—
1029	Q₈	—	8	1	no	—
1030	Q₈	—	8	2	no	—
1031	Q₈	—	8	2	no	—
1032	Q₈	—	8	1	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	8	1	no	—
1045	D₄	—	8	1	no	—
1046	D₄	—	8	2	no	—
1047	D₄	—	8	1	no	—
1048	D₄	—	8	1	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	4	1	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	1	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	1	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1082	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1086	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1087	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	1	no	—
1091	C₈	—	2	2	no	—
1092	C₈	—	2	1	no	—
1093	C₈	—	2	2	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	8	4	no	—
1113	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1114	C₄	—	2	2	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	2	no	—
1129	C₄	C₅₃×#576	1	2	yes	—
1130	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1131	C₄	C₅₃×#585	1	1	yes	characteristic
1132	C₂	—	4	1	no	—
1133	C₂	—	4	2	no	—
1134	C₂	—	4	2	no	—
1135	C₂	—	8	1	no	—
1136	C₂	—	8	1	no	—
1137	C₂	—	8	1	no	—
1138	C₂	C₅₃×#3489	1	1	yes	characteristic
1139	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1140	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3547	C₂	semidirect
2. C₅₃×#3520	C₂	semidirect
3. C₅₃×#3384	C₂	semidirect
4. Q₈×D₈×C₅₃	C₂	semidirect
5. C₅₃×#3367	C₂	semidirect
6. C₅₃×#3360	C₂	semidirect
7. C₅₃×#3357	C₂	semidirect
8. C₅₃×#3354	C₂	semidirect
9. C₅₃×#3346	C₂	semidirect
10. C₅₃×#3334	C₂	semidirect
11. C₅₃×#3330	C₂	semidirect
12. C₅₃×#3322	C₂	semidirect
13. C₅₃×#3319	C₂	semidirect
14. C₅₃×#3303	C₂	semidirect
15. C₅₃×#3257	C₂	semidirect
16. C₅₃×#3254	C₂	semidirect
17. C₅₃×#3243	C₂	semidirect
18. C₅₃×#3231	C₂	semidirect
19. C₅₃×#3119	C₂	semidirect
20. C₅₃×#3100	C₂	semidirect
21. C₅₃×#3083	C₂	semidirect
22. C₅₃×#3077	C₂	semidirect
23. C₅₃×#2993	C₂	semidirect
27. C₅₃×#555	C₂²	semidirect
29. C₅₃×#554	C₂²	semidirect
35. D₄×Q₈×C₅₃	C₂²	semidirect
40. C₅₃×#547	C₂²	semidirect
42. C₅₃×#544	C₂²	semidirect
45. C₅₃×#540	C₂²	semidirect
57. C₅₃×#501	C₂²	semidirect
58. C₅₃×#500	C₂²	semidirect
59. C₅₃×#500	C₂²	semidirect
60. C₅₃×#498	C₂²	semidirect
63. C₅₃×#487	C₂²	semidirect
64. C₅₃×#487	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#484	C₂²	semidirect
70. C₅₃×#481	C₂²	semidirect
74. C₅₃×#480	C₂²	semidirect
75. C₅₃×#479	C₂²	semidirect
76. C₅₃×#479	C₂²	semidirect
77. C₅₃×#479	C₂²	semidirect
81. C₅₃×#477	C₂²	semidirect
82. C₅₃×#477	C₂²	semidirect
85. C₅₃×#476	C₂²	semidirect
91. C₅₃×#474	C₂²	semidirect
92. C₅₃×#474	C₂²	semidirect
93. C₅₃×#474	C₂²	semidirect
97. C₅₃×#468	C₂²	semidirect
99. C₅₃×#465	C₂²	semidirect
102. C₅₃×#461	C₂²	semidirect
103. C₅₃×#461	C₂²	semidirect
104. C₅₃×#460	C₂²	semidirect
111. C₅₃×#446	C₂²	semidirect
112. C₈×Q₈×C₅₃	C₂²	semidirect
114. C₅₃×#440	C₂²	semidirect
115. C₄×SD₁₆×C₅₃	C₂²	semidirect
122. C₅₃×#436	C₂²	semidirect
124. C₈×D₄×C₅₃	C₂²	semidirect
125. C₅₃×#433	C₂²	semidirect
128. C₅₃×#428	C₂²	semidirect
129. C₂×#107×C₅₃	C₂²	semidirect
130. C₅₃×#424	C₂²	semidirect
523. #62190	C₅₃	direct (N × H)
562. #3547	C₂×C₅₃	semidirect
563. #3520	C₂×C₅₃	semidirect
564. #3384	C₂×C₅₃	semidirect
565. Q₈×D₈	C₂×C₅₃	semidirect
566. #3367	C₂×C₅₃	semidirect
567. #3360	C₂×C₅₃	semidirect
568. #3357	C₂×C₅₃	semidirect
569. #3354	C₂×C₅₃	semidirect
570. #3346	C₂×C₅₃	semidirect
571. #3334	C₂×C₅₃	semidirect
572. #3330	C₂×C₅₃	semidirect
573. #3322	C₂×C₅₃	semidirect
574. #3319	C₂×C₅₃	semidirect
575. #3303	C₂×C₅₃	semidirect
576. #3257	C₂×C₅₃	semidirect
577. #3254	C₂×C₅₃	semidirect
578. #3243	C₂×C₅₃	semidirect
579. #3231	C₂×C₅₃	semidirect
580. #3119	C₂×C₅₃	semidirect
581. #3100	C₂×C₅₃	semidirect
582. #3083	C₂×C₅₃	semidirect
583. #3077	C₂×C₅₃	semidirect
584. #2993	C₂×C₅₃	semidirect
597. #555	C₂²×C₅₃	semidirect
599. #554	C₂²×C₅₃	semidirect
605. D₄×Q₈	C₂²×C₅₃	semidirect
610. #547	C₂²×C₅₃	semidirect
612. #544	C₂²×C₅₃	semidirect
615. #540	C₂²×C₅₃	semidirect
627. #501	C₂²×C₅₃	semidirect
628. #500	C₂²×C₅₃	semidirect
629. #500	C₂²×C₅₃	semidirect
630. #498	C₂²×C₅₃	semidirect
633. #487	C₂²×C₅₃	semidirect
634. #487	C₂²×C₅₃	semidirect
637. #485	C₂²×C₅₃	semidirect
638. #484	C₂²×C₅₃	semidirect
640. #481	C₂²×C₅₃	semidirect
644. #480	C₂²×C₅₃	semidirect
645. #479	C₂²×C₅₃	semidirect
646. #479	C₂²×C₅₃	semidirect
647. #479	C₂²×C₅₃	semidirect
651. #477	C₂²×C₅₃	semidirect
652. #477	C₂²×C₅₃	semidirect
655. #476	C₂²×C₅₃	semidirect
661. #474	C₂²×C₅₃	semidirect
662. #474	C₂²×C₅₃	semidirect
663. #474	C₂²×C₅₃	semidirect
667. #468	C₂²×C₅₃	semidirect
669. #465	C₂²×C₅₃	semidirect
672. #461	C₂²×C₅₃	semidirect
673. #461	C₂²×C₅₃	semidirect
674. #460	C₂²×C₅₃	semidirect
681. #446	C₂²×C₅₃	semidirect
682. C₈×Q₈	C₂²×C₅₃	semidirect
684. #440	C₂²×C₅₃	semidirect
685. C₄×SD₁₆	C₂²×C₅₃	semidirect
692. #436	C₂²×C₅₃	semidirect
694. C₈×D₄	C₂²×C₅₃	semidirect
695. #433	C₂²×C₅₃	semidirect
698. #428	C₂²×C₅₃	semidirect
699. C₂×#107	C₂²×C₅₃	semidirect
700. #424	C₂²×C₅₃	semidirect
705. C₅₃	#62190	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×#3547	2
C₅₃×#3520	2
C₅₃×#3384	2
Q₈×D₈×C₅₃	2
C₅₃×#3367	2
C₅₃×#3360	2
C₅₃×#3357	2
C₅₃×#3354	2
C₅₃×#3346	2
C₅₃×#3334	2
C₅₃×#3330	2
C₅₃×#3322	2
C₅₃×#3319	2
C₅₃×#3303	2
C₅₃×#3257	2
C₅₃×#3254	2
C₅₃×#3243	2
C₅₃×#3231	2
C₅₃×#3119	2
C₅₃×#3100	2
C₅₃×#3083	2
C₅₃×#3077	2
C₅₃×#2993	2
#62190	53

Subgroups — C53×#62190 #27269702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62190 #27269702