Subgroups — C₅₃×#62215 #27269727

Order 13568.

1762 conjugacy classes of subgroups.

The subgroup lattice has 1144 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×#3514	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×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3347	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3341	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3319	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3297	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3257	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3243	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3122	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3081	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#562	—	2	2	no	—
25	C₅₃×#559	C₂²	1	1	yes	characteristic
26	C₅₃×#556	C₂²	1	1	yes	characteristic
27	C₅₃×#555	C₂²	1	2	yes	—
28	C₅₃×#555	C₂²	1	1	yes	characteristic
29	C₅₃×#555	C₂²	1	2	yes	complemented
30	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#553	C₂²	1	2	yes	complemented
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×#546	—	2	1	no	—
40	C₅₃×#546	C₂²	1	2	yes	—
41	D₄²×C₅₃	C₂²	1	1	yes	characteristic
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×#538	—	2	2	no	—
47	C₅₃×#537	—	2	1	no	—
48	C₅₃×#536	—	2	1	no	—
49	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#532	C₂²	1	1	yes	characteristic
51	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#529	—	2	1	no	—
53	C₅₃×#529	C₂²	1	1	yes	characteristic
54	C₂×#124×C₅₃	—	2	1	no	—
55	C₅₃×#518	C₂²	1	2	yes	—
56	C₄×#41×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	complemented
62	C₅₃×#488	C₂²	1	2	yes	complemented
63	C₅₃×#486	C₂²	1	1	yes	characteristic
64	C₅₃×#486	C₂²	1	1	yes	characteristic
65	C₅₃×#485	C₂²	1	2	yes	complemented
66	C₅₃×#484	C₂²	1	2	yes	complemented
67	C₅₃×#482	C₂²	1	2	yes	—
68	C₅₃×#482	C₂²	1	2	yes	complemented
69	C₅₃×#482	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#482	C₂²	1	2	yes	complemented
73	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
74	C₅₃×#480	C₂²	1	2	yes	—
75	C₅₃×#479	C₂²	1	2	yes	complemented
76	C₅₃×#478	C₂²	1	2	yes	—
77	C₅₃×#478	C₂²	1	2	yes	—
78	C₅₃×#478	C₂²	1	2	yes	complemented
79	C₅₃×#478	C₂²	1	2	yes	complemented
80	C₅₃×#478	C₂²	1	2	yes	complemented
81	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#477	C₂²	1	1	yes	characteristic, 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×#476	C₂²	1	2	yes	complemented
87	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#474	C₂²	1	1	yes	characteristic
89	C₅₃×#474	C₂²	1	2	yes	—
90	C₅₃×#474	C₂²	1	2	yes	complemented
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	complemented
96	C₅₃×#466	C₂²	1	2	yes	—
97	C₅₃×#466	C₂²	1	2	yes	complemented
98	C₅₃×#466	C₂²	1	2	yes	complemented
99	C₅₃×#465	C₂²	1	2	yes	complemented
100	C₅₃×#463	C₂²	1	2	yes	complemented
101	C₅₃×#463	C₂²	1	2	yes	complemented
102	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#459	C₂²	1	1	yes	characteristic
104	C₅₃×#459	C₂²	1	1	yes	characteristic
105	C₅₃×#459	C₂²	1	1	yes	characteristic
106	C₅₃×#459	C₂²	1	2	yes	complemented
107	C₅₃×#449	C₂²	1	1	yes	characteristic
108	C₅₃×#449	C₂²	1	1	yes	characteristic
109	C₅₃×#447	C₂²	1	2	yes	—
110	C₅₃×#447	C₂²	1	2	yes	—
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×#442	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×D₈×C₅₃	C₂²	1	2	yes	—
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
121	C₅₃×#436	C₂²	1	1	yes	characteristic
122	C₅₃×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
125	C₅₃×#433	C₂²	1	2	yes	complemented
126	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#428	C₂²	1	2	yes	complemented
128	C₅₃×#427	C₂²	1	2	yes	complemented
129	C₅₃×#427	C₂²	1	2	yes	complemented
130	C₅₃×#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#418	C₂²	1	2	yes	—
133	C₅₃×#416	C₂²	1	2	yes	—
134	C₂×#102×C₅₃	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	1	yes	characteristic
139	C₂²×Q₈×C₅₃	—	2	1	no	—
140	C₂²×Q₈×C₅₃	—	2	1	no	—
141	C₂²×D₄×C₅₃	—	2	1	no	—
142	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₅₃	C₂³	1	2	yes	—
148	C₂×D₈×C₅₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
150	C₂²×C₈×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	#127×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	D₄	1	1	yes	characteristic
167	#125×C₅₃	C₂³	1	2	yes	—
168	#125×C₅₃	C₂³	1	2	yes	—
169	#124×C₅₃	—	2	2	no	—
170	#124×C₅₃	—	2	2	no	—
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	—	2	1	no	—
177	#124×C₅₃	—	2	1	no	—
178	#124×C₅₃	—	2	1	no	—
179	#124×C₅₃	D₄	1	1	yes	characteristic
180	#124×C₅₃	C₂³	1	2	yes	—
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	—	2	2	no	—
187	#123×C₅₃	—	2	2	no	—
188	#123×C₅₃	D₄	1	2	yes	—
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	1	no	—
199	C₂²⋊Q₈×C₅₃	—	2	1	no	—
200	C₂²⋊Q₈×C₅₃	—	2	1	no	—
201	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
202	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
203	#121×C₅₃	—	2	1	no	—
204	#121×C₅₃	—	2	2	no	—
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	2	no	—
207	#121×C₅₃	—	2	1	no	—
208	#121×C₅₃	—	2	2	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	2	no	—
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	—	2	1	no	—
213	#121×C₅₃	D₄	1	1	yes	characteristic
214	#121×C₅₃	C₂³	1	2	yes	—
215	#121×C₅₃	C₂³	1	1	yes	characteristic
216	#121×C₅₃	C₂³	1	1	yes	characteristic
217	#121×C₅₃	C₂³	1	2	yes	—
218	#121×C₅₃	C₂³	1	2	yes	—
219	#121×C₅₃	C₂³	1	2	yes	—
220	#120×C₅₃	—	2	2	no	—
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	1	yes	characteristic
227	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₅₃	—	2	2	no	—
229	C₄×D₄×C₅₃	—	2	2	no	—
230	C₄×D₄×C₅₃	—	2	1	no	—
231	C₄×D₄×C₅₃	—	2	2	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	1	no	—
235	C₄×D₄×C₅₃	—	2	1	no	—
236	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₅₃	C₂³	1	2	yes	—
239	C₄×D₄×C₅₃	C₂³	1	2	yes	—
240	C₄×D₄×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
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	C₄×D₄×C₅₃	C₂³	1	2	yes	—
247	#117×C₅₃	—	2	2	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	1	yes	characteristic
253	#117×C₅₃	C₂³	1	2	yes	—
254	#117×C₅₃	C₂³	1	2	yes	—
255	#117×C₅₃	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
261	C₂×C₄²×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	1	yes	characteristic
265	#107×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
271	#106×C₅₃	C₂³	1	2	yes	—
272	#106×C₅₃	C₂³	1	2	yes	—
273	#106×C₅₃	C₂³	1	2	yes	—
274	#106×C₅₃	C₂³	1	1	yes	characteristic
275	#106×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
285	#103×C₅₃	C₂³	1	2	yes	—
286	#103×C₅₃	C₂³	1	1	yes	characteristic
287	#103×C₅₃	C₂³	1	2	yes	—
288	#102×C₅₃	C₂³	1	2	yes	—
289	#102×C₅₃	C₂³	1	2	yes	—
290	#102×C₅₃	C₂³	1	2	yes	—
291	#102×C₅₃	C₂³	1	2	yes	—
292	#102×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
297	#102×C₅₃	C₂³	1	1	yes	characteristic
298	#102×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
303	#102×C₅₃	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
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	2	no	—
313	#41×C₅₃	—	2	2	no	—
314	#41×C₅₃	—	4	1	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	1	yes	characteristic
328	C₂×D₄×C₅₃	—	2	4	no	—
329	C₂×D₄×C₅₃	—	2	1	no	—
330	C₂×D₄×C₅₃	—	2	2	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	2	no	—
333	C₂×D₄×C₅₃	—	2	1	no	—
334	C₂×D₄×C₅₃	—	2	2	no	—
335	C₂×D₄×C₅₃	—	2	1	no	—
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	—	2	1	no	—
338	C₂×D₄×C₅₃	—	2	1	no	—
339	C₂×D₄×C₅₃	—	2	1	no	—
340	C₂×D₄×C₅₃	—	2	1	no	—
341	C₂×D₄×C₅₃	—	4	2	no	—
342	C₂×D₄×C₅₃	—	8	2	no	—
343	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
346	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₅₃	—	2	2	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	1	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	2	no	—
358	C₂²×C₄×C₅₃	—	2	2	no	—
359	C₂²×C₄×C₅₃	—	2	2	no	—
360	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
364	SD₁₆×C₅₃	—	4	1	no	—
365	SD₁₆×C₅₃	—	4	1	no	—
366	D₈×C₅₃	—	2	2	no	—
367	D₈×C₅₃	—	2	2	no	—
368	D₈×C₅₃	—	4	2	no	—
369	D₈×C₅₃	—	4	2	no	—
370	M₁₆×C₅₃	—	4	2	no	—
371	C₂×C₈×C₅₃	—	4	2	no	—
372	C₂×C₈×C₅₃	—	4	2	no	—
373	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
379	C₄⋊C₄×C₅₃	—	2	1	no	—
380	C₄⋊C₄×C₅₃	—	2	2	no	—
381	C₄⋊C₄×C₅₃	—	2	2	no	—
382	C₄⋊C₄×C₅₃	—	2	1	no	—
383	C₄⋊C₄×C₅₃	—	2	1	no	—
384	C₄⋊C₄×C₅₃	—	2	2	no	—
385	C₄⋊C₄×C₅₃	—	2	2	no	—
386	C₄⋊C₄×C₅₃	—	2	1	no	—
387	C₄⋊C₄×C₅₃	—	2	1	no	—
388	C₄⋊C₄×C₅₃	—	2	2	no	—
389	C₄⋊C₄×C₅₃	—	2	2	no	—
390	C₄⋊C₄×C₅₃	—	2	2	no	—
391	C₄⋊C₄×C₅₃	—	2	2	no	—
392	C₄⋊C₄×C₅₃	—	2	1	no	—
393	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²⋊C₄×C₅₃	—	2	2	no	—
407	C₂²⋊C₄×C₅₃	—	2	2	no	—
408	C₂²⋊C₄×C₅₃	—	2	1	no	—
409	C₂²⋊C₄×C₅₃	—	2	2	no	—
410	C₂²⋊C₄×C₅₃	—	2	2	no	—
411	C₂²⋊C₄×C₅₃	—	2	1	no	—
412	C₂²⋊C₄×C₅₃	—	2	2	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
414	C₂²⋊C₄×C₅₃	—	2	2	no	—
415	C₂²⋊C₄×C₅₃	—	2	2	no	—
416	C₂²⋊C₄×C₅₃	—	2	2	no	—
417	C₂²⋊C₄×C₅₃	—	2	1	no	—
418	C₂²⋊C₄×C₅₃	—	2	1	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	1	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	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	C₄²×C₅₃	—	2	1	no	—
434	C₄²×C₅₃	—	2	1	no	—
435	C₄²×C₅₃	—	2	1	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	2	no	—
448	C₂³×C₅₃	—	4	4	no	—
449	C₂³×C₅₃	—	8	2	no	—
450	C₂³×C₅₃	—	8	2	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	1	no	—
455	Q₈×C₅₃	—	2	1	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	2	no	—
464	D₄×C₅₃	—	2	1	no	—
465	D₄×C₅₃	—	2	1	no	—
466	D₄×C₅₃	—	2	1	no	—
467	D₄×C₅₃	—	2	2	no	—
468	D₄×C₅₃	—	2	1	no	—
469	D₄×C₅₃	—	2	1	no	—
470	D₄×C₅₃	—	4	2	no	—
471	D₄×C₅₃	—	4	4	no	—
472	D₄×C₅₃	—	4	2	no	—
473	D₄×C₅₃	—	4	2	no	—
474	D₄×C₅₃	—	8	1	no	—
475	D₄×C₅₃	—	8	1	no	—
476	D₄×C₅₃	—	8	1	no	—
477	D₄×C₅₃	—	8	2	no	—
478	D₄×C₅₃	—	8	2	no	—
479	D₄×C₅₃	—	8	1	no	—
480	D₄×C₅₃	—	8	1	no	—
481	D₄×C₅₃	—	8	2	no	—
482	D₄×C₅₃	—	8	2	no	—
483	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
484	C₂×C₄×C₅₃	—	2	2	no	—
485	C₂×C₄×C₅₃	—	2	2	no	—
486	C₂×C₄×C₅₃	—	2	1	no	—
487	C₂×C₄×C₅₃	—	2	2	no	—
488	C₂×C₄×C₅₃	—	2	1	no	—
489	C₂×C₄×C₅₃	—	2	1	no	—
490	C₂×C₄×C₅₃	—	2	1	no	—
491	C₂×C₄×C₅₃	—	2	2	no	—
492	C₂×C₄×C₅₃	—	2	2	no	—
493	C₂×C₄×C₅₃	—	2	1	no	—
494	C₂×C₄×C₅₃	—	2	1	no	—
495	C₂×C₄×C₅₃	—	2	2	no	—
496	C₂×C₄×C₅₃	—	2	1	no	—
497	C₂×C₄×C₅₃	—	4	1	no	—
498	C₂×C₄×C₅₃	—	4	2	no	—
499	C₂×C₄×C₅₃	—	4	2	no	—
500	C₂×C₄×C₅₃	—	4	2	no	—
501	C₂×C₄×C₅₃	—	4	2	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	2	no	—
506	C₂×C₄×C₅₃	—	8	2	no	—
507	C₂×C₄×C₅₃	—	8	2	no	—
508	C₂×C₄×C₅₃	—	8	2	no	—
509	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
516	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
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	C₈×C₅₃	—	2	1	no	—
524	#62215	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
525	C₂²×C₅₃	—	2	1	no	—
526	C₂²×C₅₃	—	2	2	no	—
527	C₂²×C₅₃	—	2	1	no	—
528	C₂²×C₅₃	—	2	2	no	—
529	C₂²×C₅₃	—	2	2	no	—
530	C₂²×C₅₃	—	2	1	no	—
531	C₂²×C₅₃	—	2	2	no	—
532	C₂²×C₅₃	—	4	1	no	—
533	C₂²×C₅₃	—	4	1	no	—
534	C₂²×C₅₃	—	4	1	no	—
535	C₂²×C₅₃	—	4	2	no	—
536	C₂²×C₅₃	—	4	1	no	—
537	C₂²×C₅₃	—	4	2	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	—	4	2	no	—
543	C₂²×C₅₃	—	16	4	no	—
544	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
545	C₄×C₅₃	—	2	1	no	—
546	C₄×C₅₃	—	2	1	no	—
547	C₄×C₅₃	—	2	2	no	—
548	C₄×C₅₃	—	2	1	no	—
549	C₄×C₅₃	—	2	2	no	—
550	C₄×C₅₃	—	2	1	no	—
551	C₄×C₅₃	—	2	2	no	—
552	C₄×C₅₃	—	4	1	no	—
553	C₄×C₅₃	—	4	2	no	—
554	C₄×C₅₃	—	4	1	no	—
555	C₄×C₅₃	—	4	1	no	—
556	C₄×C₅₃	—	4	1	no	—
557	C₄×C₅₃	—	4	1	no	—
558	C₄×C₅₃	—	4	2	no	—
559	C₄×C₅₃	—	4	2	no	—
560	C₄×C₅₃	#576	1	2	yes	—
561	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
562	C₄×C₅₃	#585	1	1	yes	characteristic
563	#3547	C₂×C₅₃	1	1	yes	characteristic, complemented
564	#3514	C₂×C₅₃	1	1	yes	characteristic, complemented
565	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
566	Q₈×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
567	#3373	C₂×C₅₃	1	1	yes	characteristic, complemented
568	#3361	C₂×C₅₃	1	1	yes	characteristic, complemented
569	#3353	C₂×C₅₃	1	1	yes	characteristic, complemented
570	#3347	C₂×C₅₃	1	2	yes	complemented
571	#3341	C₂×C₅₃	1	2	yes	complemented
572	#3340	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
574	#3319	C₂×C₅₃	1	2	yes	complemented
575	#3297	C₂×C₅₃	1	2	yes	complemented
576	#3294	C₂×C₅₃	1	1	yes	characteristic, complemented
577	#3257	C₂×C₅₃	1	2	yes	complemented
578	#3245	C₂×C₅₃	1	1	yes	characteristic, complemented
579	#3243	C₂×C₅₃	1	2	yes	complemented
580	#3228	C₂×C₅₃	1	1	yes	characteristic, complemented
581	#3122	C₂×C₅₃	1	2	yes	complemented
582	#3106	C₂×C₅₃	1	1	yes	characteristic, complemented
583	#3081	C₂×C₅₃	1	2	yes	complemented
584	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
585	#2994	C₂×C₅₃	1	1	yes	characteristic, complemented
586	C₂×C₅₃	—	4	1	no	—
587	C₂×C₅₃	—	4	2	no	—
588	C₂×C₅₃	—	4	2	no	—
589	C₂×C₅₃	—	8	1	no	—
590	C₂×C₅₃	—	8	1	no	—
591	C₂×C₅₃	—	8	2	no	—
592	C₂×C₅₃	#3489	1	1	yes	characteristic
593	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
594	C₂×C₅₃	#3584	1	1	yes	characteristic
595	#562	—	2	2	no	—
596	#559	C₂²×C₅₃	1	1	yes	characteristic
597	#556	C₂²×C₅₃	1	1	yes	characteristic
598	#555	C₂²×C₅₃	1	1	yes	characteristic
599	#555	C₂²×C₅₃	1	2	yes	—
600	#555	C₂²×C₅₃	1	2	yes	complemented
601	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
602	#553	C₂²×C₅₃	1	2	yes	complemented
603	#552	—	2	1	no	—
604	#551	—	2	2	no	—
605	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
606	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
607	#548	—	2	1	no	—
608	#548	—	2	1	no	—
609	#547	C₂²×C₅₃	1	1	yes	characteristic
610	#546	—	2	1	no	—
611	#546	C₂²×C₅₃	1	2	yes	—
612	D₄²	C₂²×C₅₃	1	1	yes	characteristic
613	#544	C₂²×C₅₃	1	2	yes	complemented
614	#542	—	2	2	no	—
615	#542	C₂²×C₅₃	1	2	yes	—
616	#540	C₂²×C₅₃	1	2	yes	complemented
617	#538	—	2	2	no	—
618	#537	—	2	1	no	—
619	#536	—	2	1	no	—
620	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
621	#532	C₂²×C₅₃	1	1	yes	characteristic
622	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
623	#529	—	2	1	no	—
624	#529	C₂²×C₅₃	1	1	yes	characteristic
625	C₂×#124	—	2	1	no	—
626	#518	C₂²×C₅₃	1	2	yes	—
627	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
628	#501	C₂²×C₅₃	1	2	yes	complemented
629	#500	C₂²×C₅₃	1	2	yes	complemented
630	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
631	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
632	#489	C₂²×C₅₃	1	2	yes	complemented
633	#488	C₂²×C₅₃	1	2	yes	complemented
634	#486	C₂²×C₅₃	1	1	yes	characteristic
635	#486	C₂²×C₅₃	1	1	yes	characteristic
636	#485	C₂²×C₅₃	1	2	yes	complemented
637	#484	C₂²×C₅₃	1	2	yes	complemented
638	#482	C₂²×C₅₃	1	2	yes	—
639	#482	C₂²×C₅₃	1	2	yes	complemented
640	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
641	#482	C₂²×C₅₃	1	2	yes	complemented
642	#482	C₂²×C₅₃	1	2	yes	complemented
643	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
644	#482	C₂²×C₅₃	1	2	yes	complemented
645	#480	C₂²×C₅₃	1	2	yes	—
646	#479	C₂²×C₅₃	1	2	yes	complemented
647	#478	C₂²×C₅₃	1	2	yes	—
648	#478	C₂²×C₅₃	1	2	yes	—
649	#478	C₂²×C₅₃	1	2	yes	complemented
650	#478	C₂²×C₅₃	1	2	yes	complemented
651	#478	C₂²×C₅₃	1	2	yes	complemented
652	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
653	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
654	#476	C₂²×C₅₃	1	1	yes	characteristic
655	#476	C₂²×C₅₃	1	1	yes	characteristic
656	#476	C₂²×C₅₃	1	2	yes	complemented
657	#476	C₂²×C₅₃	1	2	yes	complemented
658	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	#474	C₂²×C₅₃	1	1	yes	characteristic
660	#474	C₂²×C₅₃	1	2	yes	—
661	#474	C₂²×C₅₃	1	2	yes	complemented
662	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	#474	C₂²×C₅₃	1	2	yes	complemented
664	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
665	#469	C₂²×C₅₃	1	2	yes	—
666	#468	C₂²×C₅₃	1	2	yes	complemented
667	#466	C₂²×C₅₃	1	2	yes	—
668	#466	C₂²×C₅₃	1	2	yes	complemented
669	#466	C₂²×C₅₃	1	2	yes	complemented
670	#465	C₂²×C₅₃	1	2	yes	complemented
671	#463	C₂²×C₅₃	1	2	yes	complemented
672	#463	C₂²×C₅₃	1	2	yes	complemented
673	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
674	#459	C₂²×C₅₃	1	1	yes	characteristic
675	#459	C₂²×C₅₃	1	1	yes	characteristic
676	#459	C₂²×C₅₃	1	1	yes	characteristic
677	#459	C₂²×C₅₃	1	2	yes	complemented
678	#449	C₂²×C₅₃	1	1	yes	characteristic
679	#449	C₂²×C₅₃	1	1	yes	characteristic
680	#447	C₂²×C₅₃	1	2	yes	—
681	#447	C₂²×C₅₃	1	2	yes	—
682	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
684	#442	C₂²×C₅₃	1	2	yes	—
685	#442	C₂²×C₅₃	1	2	yes	complemented
686	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
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	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
692	#436	C₂²×C₅₃	1	1	yes	characteristic
693	#435	C₂²×C₅₃	1	2	yes	complemented
694	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
695	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
696	#433	C₂²×C₅₃	1	2	yes	complemented
697	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
698	#428	C₂²×C₅₃	1	2	yes	complemented
699	#427	C₂²×C₅₃	1	2	yes	complemented
700	#427	C₂²×C₅₃	1	2	yes	complemented
701	#424	C₂²×C₅₃	1	2	yes	complemented
702	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	#418	C₂²×C₅₃	1	2	yes	—
704	#416	C₂²×C₅₃	1	2	yes	—
705	C₂×#102	C₂²×C₅₃	1	2	yes	—
706	C₅₃	#62215	1	1	yes	characteristic, direct product factor, Sylow
707	C₂×#41	—	2	1	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	—	2	1	no	—
710	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
711	C₂²×Q₈	—	2	1	no	—
712	C₂²×Q₈	—	2	1	no	—
713	C₂²×D₄	—	2	1	no	—
714	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
716	C₂×SD₁₆	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	2	yes	—
720	C₂×D₈	C₂³×C₅₃	1	2	yes	—
721	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
722	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
723	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
724	C₄⋊Q₈	—	2	2	no	—
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	#127	C₂³×C₅₃	1	1	yes	characteristic
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	D₄×C₅₃	1	2	yes	—
737	#125	—	2	2	no	—
738	#125	D₄×C₅₃	1	1	yes	characteristic
739	#125	C₂³×C₅₃	1	2	yes	—
740	#125	C₂³×C₅₃	1	2	yes	—
741	#124	—	2	1	no	—
742	#124	—	2	1	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	—	2	2	no	—
747	#124	—	2	2	no	—
748	#124	—	2	2	no	—
749	#124	—	2	1	no	—
750	#124	—	2	1	no	—
751	#124	D₄×C₅₃	1	1	yes	characteristic
752	#124	C₂³×C₅₃	1	2	yes	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	D₄×C₅₃	1	2	yes	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	2	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	D₄×C₅₃	1	1	yes	characteristic
774	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	—	2	1	no	—
780	#121	—	2	1	no	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	D₄×C₅₃	1	1	yes	characteristic
786	#121	C₂³×C₅₃	1	2	yes	—
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	#120	—	2	2	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
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	2	yes	—
812	C₄×D₄	C₂³×C₅₃	1	2	yes	—
813	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₅₃	1	2	yes	—
816	C₄×D₄	C₂³×C₅₃	1	2	yes	—
817	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₅₃	1	2	yes	—
819	#117	—	2	2	no	—
820	#117	—	2	1	no	—
821	#117	—	2	2	no	—
822	#117	—	2	1	no	—
823	#117	C₂³×C₅₃	1	1	yes	characteristic
824	#117	C₂³×C₅₃	1	2	yes	—
825	#117	C₂³×C₅₃	1	2	yes	—
826	#117	C₂³×C₅₃	1	2	yes	—
827	#117	C₂³×C₅₃	1	2	yes	—
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
830	C₂×C₂²⋊C₄	—	2	2	no	—
831	C₂×C₂²⋊C₄	—	2	2	no	—
832	C₂×C₂²⋊C₄	—	2	2	no	—
833	C₂×C₄²	—	2	1	no	—
834	C₂×C₄²	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	2	yes	—
840	#107	C₂³×C₅₃	1	1	yes	characteristic
841	#107	C₂³×C₅₃	1	1	yes	characteristic
842	#107	C₂³×C₅₃	1	2	yes	—
843	#106	C₂³×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
848	#106	C₂³×C₅₃	1	2	yes	—
849	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
850	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
851	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
854	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
855	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
856	#103	C₂³×C₅₃	1	2	yes	—
857	#103	C₂³×C₅₃	1	2	yes	—
858	#103	C₂³×C₅₃	1	1	yes	characteristic
859	#103	C₂³×C₅₃	1	1	yes	characteristic
860	#102	C₂³×C₅₃	1	1	yes	characteristic
861	#102	C₂³×C₅₃	1	2	yes	—
862	#102	C₂³×C₅₃	1	2	yes	—
863	#102	C₂³×C₅₃	1	2	yes	—
864	#102	C₂³×C₅₃	1	2	yes	—
865	#102	C₂³×C₅₃	1	1	yes	characteristic
866	#102	C₂³×C₅₃	1	2	yes	—
867	#102	C₂³×C₅₃	1	2	yes	—
868	#102	C₂³×C₅₃	1	2	yes	—
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	2	yes	—
873	#102	C₂³×C₅₃	1	1	yes	characteristic
874	#102	C₂³×C₅₃	1	2	yes	—
875	#102	C₂³×C₅₃	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
878	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
880	#97	C₂³×C₅₃	1	2	yes	—
881	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₅₃	1	2	yes	—
884	C₂⁴	—	2	2	no	—
885	#41	—	2	2	no	—
886	#41	—	4	1	no	—
887	#41	—	8	2	no	—
888	#41	—	8	2	no	—
889	#41	—	8	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	1	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	2	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	8	2	no	—
897	C₂×Q₈	—	8	2	no	—
898	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
899	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
900	C₂×D₄	—	2	4	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	8	2	no	—
915	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
916	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
917	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
918	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
920	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
933	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
936	SD₁₆	—	4	1	no	—
937	SD₁₆	—	4	1	no	—
938	D₈	—	2	2	no	—
939	D₈	—	2	2	no	—
940	D₈	—	4	2	no	—
941	D₈	—	4	2	no	—
942	M₁₆	—	4	2	no	—
943	C₂×C₈	—	4	2	no	—
944	C₂×C₈	—	4	2	no	—
945	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
947	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
950	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
966	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
967	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
970	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
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	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1012	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₅₃	1	2	yes	—
1015	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	—	4	4	no	—
1021	C₂³	—	8	2	no	—
1022	C₂³	—	8	2	no	—
1023	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1024	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	4	2	no	—
1029	Q₈	—	4	2	no	—
1030	Q₈	—	8	1	no	—
1031	Q₈	—	8	2	no	—
1032	Q₈	—	8	2	no	—
1033	Q₈	—	8	1	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	2	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	8	1	no	—
1047	D₄	—	8	1	no	—
1048	D₄	—	8	1	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	1	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	8	1	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1089	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1090	C₈	—	2	1	no	—
1091	C₈	—	2	1	no	—
1092	C₈	—	2	2	no	—
1093	C₈	—	2	1	no	—
1094	C₈	—	2	2	no	—
1095	C₈	—	2	1	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	16	4	no	—
1115	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	2	no	—
1131	C₄	C₅₃×#576	1	2	yes	—
1132	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1133	C₄	C₅₃×#585	1	1	yes	characteristic
1134	C₂	—	4	2	no	—
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	8	2	no	—
1138	C₂	—	8	1	no	—
1139	C₂	—	8	1	no	—
1140	C₂	C₅₃×#3489	1	1	yes	characteristic
1141	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1142	C₂	C₅₃×#3584	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×#3514	C₂	semidirect
3. C₅₃×#3384	C₂	semidirect
4. Q₈×D₈×C₅₃	C₂	semidirect
5. C₅₃×#3373	C₂	semidirect
6. C₅₃×#3361	C₂	semidirect
7. C₅₃×#3353	C₂	semidirect
8. C₅₃×#3347	C₂	semidirect
9. C₅₃×#3341	C₂	semidirect
10. C₅₃×#3340	C₂	semidirect
11. C₅₃×#3325	C₂	semidirect
12. C₅₃×#3319	C₂	semidirect
13. C₅₃×#3297	C₂	semidirect
14. C₅₃×#3294	C₂	semidirect
15. C₅₃×#3257	C₂	semidirect
16. C₅₃×#3245	C₂	semidirect
17. C₅₃×#3243	C₂	semidirect
18. C₅₃×#3228	C₂	semidirect
19. C₅₃×#3122	C₂	semidirect
20. C₅₃×#3106	C₂	semidirect
21. C₅₃×#3081	C₂	semidirect
22. C₅₃×#3076	C₂	semidirect
23. C₅₃×#2994	C₂	semidirect
29. C₅₃×#555	C₂²	semidirect
30. C₅₃×#554	C₂²	semidirect
31. C₅₃×#553	C₂²	semidirect
35. D₄×Q₈×C₅₃	C₂²	semidirect
42. C₅₃×#544	C₂²	semidirect
45. C₅₃×#540	C₂²	semidirect
49. C₅₃×#533	C₂²	semidirect
51. C₅₃×#532	C₂²	semidirect
57. C₅₃×#501	C₂²	semidirect
58. C₅₃×#500	C₂²	semidirect
59. C₅₃×#500	C₂²	semidirect
60. C₅₃×#498	C₂²	semidirect
61. C₅₃×#489	C₂²	semidirect
62. C₅₃×#488	C₂²	semidirect
65. C₅₃×#485	C₂²	semidirect
66. C₅₃×#484	C₂²	semidirect
68. C₅₃×#482	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#482	C₂²	semidirect
73. C₅₃×#482	C₂²	semidirect
75. C₅₃×#479	C₂²	semidirect
78. C₅₃×#478	C₂²	semidirect
79. C₅₃×#478	C₂²	semidirect
80. C₅₃×#478	C₂²	semidirect
81. C₅₃×#477	C₂²	semidirect
82. C₅₃×#477	C₂²	semidirect
85. C₅₃×#476	C₂²	semidirect
86. C₅₃×#476	C₂²	semidirect
87. C₅₃×#475	C₂²	semidirect
90. C₅₃×#474	C₂²	semidirect
91. C₅₃×#474	C₂²	semidirect
92. C₅₃×#474	C₂²	semidirect
93. C₅₃×#474	C₂²	semidirect
95. C₅₃×#468	C₂²	semidirect
97. C₅₃×#466	C₂²	semidirect
98. C₅₃×#466	C₂²	semidirect
99. C₅₃×#465	C₂²	semidirect
100. C₅₃×#463	C₂²	semidirect
101. C₅₃×#463	C₂²	semidirect
102. C₅₃×#460	C₂²	semidirect
106. C₅₃×#459	C₂²	semidirect
111. C₅₃×#446	C₂²	semidirect
112. C₈×Q₈×C₅₃	C₂²	semidirect
114. C₅₃×#442	C₂²	semidirect
115. C₄×SD₁₆×C₅₃	C₂²	semidirect
116. C₄×SD₁₆×C₅₃	C₂²	semidirect
120. C₄×D₈×C₅₃	C₂²	semidirect
122. C₅₃×#435	C₂²	semidirect
124. C₈×D₄×C₅₃	C₂²	semidirect
125. C₅₃×#433	C₂²	semidirect
126. C₅₃×#431	C₂²	semidirect
127. C₅₃×#428	C₂²	semidirect
128. C₅₃×#427	C₂²	semidirect
129. C₅₃×#427	C₂²	semidirect
130. C₅₃×#424	C₂²	semidirect
131. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
524. #62215	C₅₃	direct (N × H)
563. #3547	C₂×C₅₃	semidirect
564. #3514	C₂×C₅₃	semidirect
565. #3384	C₂×C₅₃	semidirect
566. Q₈×D₈	C₂×C₅₃	semidirect
567. #3373	C₂×C₅₃	semidirect
568. #3361	C₂×C₅₃	semidirect
569. #3353	C₂×C₅₃	semidirect
570. #3347	C₂×C₅₃	semidirect
571. #3341	C₂×C₅₃	semidirect
572. #3340	C₂×C₅₃	semidirect
573. #3325	C₂×C₅₃	semidirect
574. #3319	C₂×C₅₃	semidirect
575. #3297	C₂×C₅₃	semidirect
576. #3294	C₂×C₅₃	semidirect
577. #3257	C₂×C₅₃	semidirect
578. #3245	C₂×C₅₃	semidirect
579. #3243	C₂×C₅₃	semidirect
580. #3228	C₂×C₅₃	semidirect
581. #3122	C₂×C₅₃	semidirect
582. #3106	C₂×C₅₃	semidirect
583. #3081	C₂×C₅₃	semidirect
584. #3076	C₂×C₅₃	semidirect
585. #2994	C₂×C₅₃	semidirect
600. #555	C₂²×C₅₃	semidirect
601. #554	C₂²×C₅₃	semidirect
602. #553	C₂²×C₅₃	semidirect
606. D₄×Q₈	C₂²×C₅₃	semidirect
613. #544	C₂²×C₅₃	semidirect
616. #540	C₂²×C₅₃	semidirect
620. #533	C₂²×C₅₃	semidirect
622. #532	C₂²×C₅₃	semidirect
628. #501	C₂²×C₅₃	semidirect
629. #500	C₂²×C₅₃	semidirect
630. #500	C₂²×C₅₃	semidirect
631. #498	C₂²×C₅₃	semidirect
632. #489	C₂²×C₅₃	semidirect
633. #488	C₂²×C₅₃	semidirect
636. #485	C₂²×C₅₃	semidirect
637. #484	C₂²×C₅₃	semidirect
639. #482	C₂²×C₅₃	semidirect
640. #482	C₂²×C₅₃	semidirect
641. #482	C₂²×C₅₃	semidirect
642. #482	C₂²×C₅₃	semidirect
643. #482	C₂²×C₅₃	semidirect
644. #482	C₂²×C₅₃	semidirect
646. #479	C₂²×C₅₃	semidirect
649. #478	C₂²×C₅₃	semidirect
650. #478	C₂²×C₅₃	semidirect
651. #478	C₂²×C₅₃	semidirect
652. #477	C₂²×C₅₃	semidirect
653. #477	C₂²×C₅₃	semidirect
656. #476	C₂²×C₅₃	semidirect
657. #476	C₂²×C₅₃	semidirect
658. #475	C₂²×C₅₃	semidirect
661. #474	C₂²×C₅₃	semidirect
662. #474	C₂²×C₅₃	semidirect
663. #474	C₂²×C₅₃	semidirect
664. #474	C₂²×C₅₃	semidirect
666. #468	C₂²×C₅₃	semidirect
668. #466	C₂²×C₅₃	semidirect
669. #466	C₂²×C₅₃	semidirect
670. #465	C₂²×C₅₃	semidirect
671. #463	C₂²×C₅₃	semidirect
672. #463	C₂²×C₅₃	semidirect
673. #460	C₂²×C₅₃	semidirect
677. #459	C₂²×C₅₃	semidirect
682. #446	C₂²×C₅₃	semidirect
683. C₈×Q₈	C₂²×C₅₃	semidirect
685. #442	C₂²×C₅₃	semidirect
686. C₄×SD₁₆	C₂²×C₅₃	semidirect
687. C₄×SD₁₆	C₂²×C₅₃	semidirect
691. C₄×D₈	C₂²×C₅₃	semidirect
693. #435	C₂²×C₅₃	semidirect
695. C₈×D₄	C₂²×C₅₃	semidirect
696. #433	C₂²×C₅₃	semidirect
697. #431	C₂²×C₅₃	semidirect
698. #428	C₂²×C₅₃	semidirect
699. #427	C₂²×C₅₃	semidirect
700. #427	C₂²×C₅₃	semidirect
701. #424	C₂²×C₅₃	semidirect
702. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
706. C₅₃	#62215	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×#3514	2
C₅₃×#3384	2
Q₈×D₈×C₅₃	2
C₅₃×#3373	2
C₅₃×#3361	2
C₅₃×#3353	2
C₅₃×#3347	2
C₅₃×#3341	2
C₅₃×#3340	2
C₅₃×#3325	2
C₅₃×#3319	2
C₅₃×#3297	2
C₅₃×#3294	2
C₅₃×#3257	2
C₅₃×#3245	2
C₅₃×#3243	2
C₅₃×#3228	2
C₅₃×#3122	2
C₅₃×#3106	2
C₅₃×#3081	2
C₅₃×#3076	2
C₅₃×#2994	2
#62215	53

Subgroups — C53×#62215 #27269727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62215 #27269727