Subgroups — C₅₃×#62189 #27269701

Order 13568.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3520	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3356	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3344	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3323	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3311	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3258	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3244	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3120	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3084	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×#563	—	2	2	no	—
25	Q₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₅₃×#557	—	2	1	no	—
27	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×#556	—	2	1	no	—
29	C₅₃×#556	C₂²	1	1	yes	characteristic
30	C₅₃×#556	C₂²	1	2	yes	—
31	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
32	C₅₃×#554	C₂²	1	2	yes	—
33	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
34	C₅₃×#552	—	2	1	no	—
35	C₅₃×#552	C₂²	1	2	yes	—
36	C₅₃×#551	—	2	2	no	—
37	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#548	—	2	1	no	—
39	C₅₃×#547	C₂²	1	1	yes	characteristic
40	C₅₃×#547	C₂²	1	1	yes	characteristic
41	C₅₃×#546	C₂²	1	2	yes	—
42	C₅₃×#544	C₂²	1	2	yes	complemented
43	C₅₃×#542	—	2	1	no	—
44	C₅₃×#542	C₂²	1	2	yes	—
45	C₅₃×#541	—	2	2	no	—
46	C₅₃×#541	—	2	1	no	—
47	C₅₃×#541	C₂²	1	2	yes	complemented
48	C₅₃×#539	—	2	2	no	—
49	C₅₃×#533	C₂²	1	1	yes	characteristic
50	C₅₃×#533	C₂²	1	1	yes	characteristic
51	C₅₃×#533	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×#498	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#498	C₂²	1	2	yes	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×#483	C₂²	1	1	yes	characteristic
70	C₅₃×#483	C₂²	1	1	yes	characteristic
71	C₅₃×#483	C₂²	1	2	yes	complemented
72	C₅₃×#483	C₂²	1	2	yes	complemented
73	C₅₃×#482	C₂²	1	2	yes	—
74	C₅₃×#481	C₂²	1	2	yes	—
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×#476	C₂²	1	1	yes	characteristic
83	C₅₃×#476	C₂²	1	2	yes	—
84	C₅₃×#476	C₂²	1	1	yes	characteristic
85	C₅₃×#476	C₂²	1	1	yes	characteristic
86	C₅₃×#476	C₂²	1	1	yes	characteristic
87	C₅₃×#475	C₂²	1	2	yes	complemented
88	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#475	C₂²	1	2	yes	complemented
91	C₅₃×#475	C₂²	1	2	yes	complemented
92	C₅₃×#474	C₂²	1	1	yes	characteristic
93	C₅₃×#474	C₂²	1	1	yes	characteristic
94	C₅₃×#470	C₂²	1	2	yes	—
95	C₅₃×#470	C₂²	1	2	yes	—
96	C₅₃×#470	C₂²	1	2	yes	complemented
97	C₅₃×#468	C₂²	1	2	yes	—
98	C₅₃×#467	C₂²	1	2	yes	complemented
99	C₅₃×#465	C₂²	1	2	yes	—
100	C₅₃×#464	C₂²	1	2	yes	—
101	C₅₃×#464	C₂²	1	2	yes	—
102	C₅₃×#462	C₂²	1	2	yes	complemented
103	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#461	C₂²	1	1	yes	characteristic
106	C₅₃×#461	C₂²	1	1	yes	characteristic
107	C₅₃×#452	C₂²	1	2	yes	—
108	C₅₃×#452	C₂²	1	2	yes	—
109	C₅₃×#450	C₂²	1	1	yes	characteristic
110	C₅₃×#450	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×#441	C₂²	1	2	yes	complemented
114	C₅₃×#440	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×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×#106×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	C₂³	1	2	yes	—
137	C₂²×Q₈×C₅₃	—	2	1	no	—
138	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅₃	—	2	1	no	—
140	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
148	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₅₃	—	2	2	no	—
150	C₄⋊Q₈×C₅₃	—	2	1	no	—
151	C₄⋊Q₈×C₅₃	—	2	2	no	—
152	C₄⋊Q₈×C₅₃	—	2	1	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	C₄⋊Q₈×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	—	2	2	no	—
165	#126×C₅₃	—	2	2	no	—
166	#126×C₅₃	—	2	2	no	—
167	#126×C₅₃	—	2	2	no	—
168	#126×C₅₃	—	2	2	no	—
169	#126×C₅₃	D₄	1	2	yes	—
170	#125×C₅₃	—	2	2	no	—
171	#125×C₅₃	—	2	2	no	—
172	#125×C₅₃	—	2	2	no	—
173	#125×C₅₃	—	2	2	no	—
174	#125×C₅₃	—	2	1	no	—
175	#125×C₅₃	—	2	2	no	—
176	#125×C₅₃	—	2	2	no	—
177	#125×C₅₃	—	2	1	no	—
178	#125×C₅₃	—	2	1	no	—
179	#125×C₅₃	D₄	1	1	yes	characteristic
180	#125×C₅₃	C₂³	1	2	yes	—
181	#125×C₅₃	C₂³	1	2	yes	—
182	#124×C₅₃	—	2	2	no	—
183	#124×C₅₃	—	2	1	no	—
184	#124×C₅₃	—	2	2	no	—
185	#124×C₅₃	D₄	1	1	yes	characteristic
186	#124×C₅₃	C₂³	1	2	yes	—
187	#123×C₅₃	—	2	2	no	—
188	#123×C₅₃	—	2	2	no	—
189	#123×C₅₃	—	2	2	no	—
190	#123×C₅₃	—	2	2	no	—
191	#123×C₅₃	—	2	2	no	—
192	#123×C₅₃	D₄	1	2	yes	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	1	no	—
195	C₂²⋊Q₈×C₅₃	—	2	1	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	2	no	—
200	C₂²⋊Q₈×C₅₃	—	2	2	no	—
201	C₂²⋊Q₈×C₅₃	—	2	2	no	—
202	C₂²⋊Q₈×C₅₃	—	2	1	no	—
203	C₂²⋊Q₈×C₅₃	—	2	1	no	—
204	C₂²⋊Q₈×C₅₃	—	2	1	no	—
205	C₂²⋊Q₈×C₅₃	—	2	1	no	—
206	C₂²⋊Q₈×C₅₃	—	2	1	no	—
207	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
211	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
214	#121×C₅₃	—	2	2	no	—
215	#121×C₅₃	—	2	1	no	—
216	#121×C₅₃	D₄	1	1	yes	characteristic
217	#121×C₅₃	C₂³	1	2	yes	—
218	#120×C₅₃	—	2	2	no	—
219	C₄×Q₈×C₅₃	—	2	2	no	—
220	C₄×Q₈×C₅₃	—	2	1	no	—
221	C₄×Q₈×C₅₃	—	2	1	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	—	2	1	no	—
226	C₄×Q₈×C₅₃	—	2	1	no	—
227	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
229	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
230	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
233	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
234	C₄×D₄×C₅₃	—	2	2	no	—
235	C₄×D₄×C₅₃	—	2	2	no	—
236	C₄×D₄×C₅₃	—	2	1	no	—
237	C₄×D₄×C₅₃	—	2	1	no	—
238	C₄×D₄×C₅₃	—	2	2	no	—
239	C₄×D₄×C₅₃	—	2	1	no	—
240	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₅₃	C₂³	1	2	yes	—
245	C₄×D₄×C₅₃	C₂³	1	2	yes	—
246	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
252	#117×C₅₃	C₂³	1	2	yes	—
253	#117×C₅₃	C₂³	1	2	yes	—
254	#117×C₅₃	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₅₃	—	2	2	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	2	yes	—
266	#107×C₅₃	C₂³	1	2	yes	—
267	#106×C₅₃	C₂³	1	2	yes	—
268	#106×C₅₃	C₂³	1	2	yes	—
269	#106×C₅₃	C₂³	1	1	yes	characteristic
270	#106×C₅₃	C₂³	1	2	yes	—
271	#106×C₅₃	C₂³	1	2	yes	—
272	#106×C₅₃	C₂³	1	1	yes	characteristic
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	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	#103×C₅₃	C₂³	1	1	yes	characteristic
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	1	yes	characteristic
294	#103×C₅₃	C₂³	1	2	yes	—
295	#103×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	2	yes	—
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	1	yes	characteristic
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	C₂×Q₈×C₅₃	—	2	1	no	—
317	C₂×Q₈×C₅₃	—	2	1	no	—
318	C₂×Q₈×C₅₃	—	2	1	no	—
319	C₂×Q₈×C₅₃	—	2	1	no	—
320	C₂×Q₈×C₅₃	—	2	2	no	—
321	C₂×Q₈×C₅₃	—	2	2	no	—
322	C₂×Q₈×C₅₃	—	8	2	no	—
323	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₅₃	—	2	2	no	—
328	C₂×D₄×C₅₃	—	2	2	no	—
329	C₂×D₄×C₅₃	—	2	2	no	—
330	C₂×D₄×C₅₃	—	2	1	no	—
331	C₂×D₄×C₅₃	—	4	1	no	—
332	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
333	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₅₃	—	2	1	no	—
337	C₂²×C₄×C₅₃	—	2	2	no	—
338	C₂²×C₄×C₅₃	—	2	2	no	—
339	C₂²×C₄×C₅₃	—	2	2	no	—
340	C₂²×C₄×C₅₃	—	2	1	no	—
341	C₂²×C₄×C₅₃	—	2	1	no	—
342	C₂²×C₄×C₅₃	—	2	2	no	—
343	C₂²×C₄×C₅₃	—	2	1	no	—
344	C₂²×C₄×C₅₃	—	2	1	no	—
345	C₂²×C₄×C₅₃	—	8	2	no	—
346	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
350	Q₁₆×C₅₃	—	4	2	no	—
351	Q₁₆×C₅₃	—	4	2	no	—
352	SD₁₆×C₅₃	—	2	2	no	—
353	SD₁₆×C₅₃	—	2	2	no	—
354	SD₁₆×C₅₃	—	4	1	no	—
355	SD₁₆×C₅₃	—	4	1	no	—
356	M₁₆×C₅₃	—	4	2	no	—
357	M₁₆×C₅₃	—	4	2	no	—
358	C₂×C₈×C₅₃	—	4	2	no	—
359	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
362	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₅₃	—	2	2	no	—
366	C₄⋊C₄×C₅₃	—	2	1	no	—
367	C₄⋊C₄×C₅₃	—	2	2	no	—
368	C₄⋊C₄×C₅₃	—	2	2	no	—
369	C₄⋊C₄×C₅₃	—	2	2	no	—
370	C₄⋊C₄×C₅₃	—	2	1	no	—
371	C₄⋊C₄×C₅₃	—	2	2	no	—
372	C₄⋊C₄×C₅₃	—	2	1	no	—
373	C₄⋊C₄×C₅₃	—	2	1	no	—
374	C₄⋊C₄×C₅₃	—	2	1	no	—
375	C₄⋊C₄×C₅₃	—	2	2	no	—
376	C₄⋊C₄×C₅₃	—	2	1	no	—
377	C₄⋊C₄×C₅₃	—	2	1	no	—
378	C₄⋊C₄×C₅₃	—	2	1	no	—
379	C₄⋊C₄×C₅₃	—	2	2	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	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	1	no	—
391	C₄⋊C₄×C₅₃	—	2	1	no	—
392	C₄⋊C₄×C₅₃	—	2	2	no	—
393	C₄⋊C₄×C₅₃	—	2	2	no	—
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	1	yes	characteristic
398	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₅₃	C₂×D₄	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	2	yes	—
404	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
407	C₂²⋊C₄×C₅₃	—	2	2	no	—
408	C₂²⋊C₄×C₅₃	—	2	1	no	—
409	C₂²⋊C₄×C₅₃	—	2	1	no	—
410	C₂²⋊C₄×C₅₃	—	2	2	no	—
411	C₂²⋊C₄×C₅₃	—	2	2	no	—
412	C₂²⋊C₄×C₅₃	—	2	2	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
414	C₂²⋊C₄×C₅₃	—	2	2	no	—
415	C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂²⋊C₄×C₅₃	—	2	1	no	—
417	C₂²⋊C₄×C₅₃	—	2	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	2	no	—
423	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
428	C₄²×C₅₃	—	2	2	no	—
429	C₄²×C₅₃	—	2	2	no	—
430	C₄²×C₅₃	—	2	2	no	—
431	C₄²×C₅₃	—	2	1	no	—
432	C₄²×C₅₃	—	2	1	no	—
433	C₄²×C₅₃	—	2	2	no	—
434	C₄²×C₅₃	—	2	2	no	—
435	C₄²×C₅₃	—	2	2	no	—
436	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
439	C₄²×C₅₃	C₂⁴	1	2	yes	—
440	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₂³×C₅₃	—	2	1	no	—
442	C₂³×C₅₃	—	2	1	no	—
443	C₂³×C₅₃	—	4	2	no	—
444	C₂³×C₅₃	—	4	2	no	—
445	C₂³×C₅₃	—	8	1	no	—
446	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
447	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
448	Q₈×C₅₃	—	2	2	no	—
449	Q₈×C₅₃	—	2	2	no	—
450	Q₈×C₅₃	—	2	1	no	—
451	Q₈×C₅₃	—	2	1	no	—
452	Q₈×C₅₃	—	2	2	no	—
453	Q₈×C₅₃	—	2	1	no	—
454	Q₈×C₅₃	—	2	1	no	—
455	Q₈×C₅₃	—	4	2	no	—
456	Q₈×C₅₃	—	4	2	no	—
457	Q₈×C₅₃	—	8	1	no	—
458	Q₈×C₅₃	—	8	1	no	—
459	Q₈×C₅₃	—	8	2	no	—
460	Q₈×C₅₃	—	8	2	no	—
461	D₄×C₅₃	—	2	2	no	—
462	D₄×C₅₃	—	2	1	no	—
463	D₄×C₅₃	—	2	1	no	—
464	D₄×C₅₃	—	2	1	no	—
465	D₄×C₅₃	—	4	2	no	—
466	D₄×C₅₃	—	4	2	no	—
467	D₄×C₅₃	—	4	4	no	—
468	D₄×C₅₃	—	8	2	no	—
469	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
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	2	no	—
475	C₂×C₄×C₅₃	—	2	1	no	—
476	C₂×C₄×C₅₃	—	2	1	no	—
477	C₂×C₄×C₅₃	—	2	2	no	—
478	C₂×C₄×C₅₃	—	2	1	no	—
479	C₂×C₄×C₅₃	—	2	2	no	—
480	C₂×C₄×C₅₃	—	2	2	no	—
481	C₂×C₄×C₅₃	—	2	1	no	—
482	C₂×C₄×C₅₃	—	2	2	no	—
483	C₂×C₄×C₅₃	—	2	1	no	—
484	C₂×C₄×C₅₃	—	2	1	no	—
485	C₂×C₄×C₅₃	—	4	1	no	—
486	C₂×C₄×C₅₃	—	4	4	no	—
487	C₂×C₄×C₅₃	—	4	2	no	—
488	C₂×C₄×C₅₃	—	4	2	no	—
489	C₂×C₄×C₅₃	—	8	1	no	—
490	C₂×C₄×C₅₃	—	8	1	no	—
491	C₂×C₄×C₅₃	—	8	2	no	—
492	C₂×C₄×C₅₃	—	8	2	no	—
493	C₂×C₄×C₅₃	—	8	1	no	—
494	C₂×C₄×C₅₃	—	8	2	no	—
495	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
504	C₈×C₅₃	—	2	1	no	—
505	C₈×C₅₃	—	2	1	no	—
506	C₈×C₅₃	—	2	1	no	—
507	C₈×C₅₃	—	2	2	no	—
508	C₈×C₅₃	—	2	1	no	—
509	C₈×C₅₃	—	2	2	no	—
510	#62189	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
511	C₂²×C₅₃	—	2	1	no	—
512	C₂²×C₅₃	—	2	2	no	—
513	C₂²×C₅₃	—	2	2	no	—
514	C₂²×C₅₃	—	2	1	no	—
515	C₂²×C₅₃	—	2	2	no	—
516	C₂²×C₅₃	—	2	1	no	—
517	C₂²×C₅₃	—	2	2	no	—
518	C₂²×C₅₃	—	4	1	no	—
519	C₂²×C₅₃	—	4	1	no	—
520	C₂²×C₅₃	—	4	1	no	—
521	C₂²×C₅₃	—	4	1	no	—
522	C₂²×C₅₃	—	4	1	no	—
523	C₂²×C₅₃	—	8	4	no	—
524	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
525	C₄×C₅₃	—	2	1	no	—
526	C₄×C₅₃	—	2	1	no	—
527	C₄×C₅₃	—	2	2	no	—
528	C₄×C₅₃	—	2	2	no	—
529	C₄×C₅₃	—	2	1	no	—
530	C₄×C₅₃	—	2	1	no	—
531	C₄×C₅₃	—	2	2	no	—
532	C₄×C₅₃	—	4	1	no	—
533	C₄×C₅₃	—	4	2	no	—
534	C₄×C₅₃	—	4	1	no	—
535	C₄×C₅₃	—	4	2	no	—
536	C₄×C₅₃	—	4	1	no	—
537	C₄×C₅₃	—	4	1	no	—
538	C₄×C₅₃	—	4	1	no	—
539	C₄×C₅₃	—	4	1	no	—
540	C₄×C₅₃	—	4	2	no	—
541	C₄×C₅₃	—	4	2	no	—
542	C₄×C₅₃	#577	1	2	yes	—
543	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
544	C₄×C₅₃	#585	1	1	yes	characteristic
545	#3555	C₂×C₅₃	1	1	yes	characteristic, complemented
546	#3520	C₂×C₅₃	1	1	yes	characteristic
547	#3386	C₂×C₅₃	1	1	yes	characteristic, complemented
548	Q₈×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
549	#3369	C₂×C₅₃	1	1	yes	characteristic, complemented
550	#3364	C₂×C₅₃	1	1	yes	characteristic, complemented
551	#3356	C₂×C₅₃	1	2	yes	complemented
552	#3353	C₂×C₅₃	1	1	yes	characteristic, complemented
553	#3344	C₂×C₅₃	1	2	yes	complemented
554	#3335	C₂×C₅₃	1	1	yes	characteristic, complemented
555	#3331	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#3323	C₂×C₅₃	1	2	yes	complemented
557	#3311	C₂×C₅₃	1	2	yes	complemented
558	#3302	C₂×C₅₃	1	1	yes	characteristic, complemented
559	#3258	C₂×C₅₃	1	2	yes	complemented
560	#3255	C₂×C₅₃	1	1	yes	characteristic, complemented
561	#3244	C₂×C₅₃	1	2	yes	complemented
562	#3231	C₂×C₅₃	1	1	yes	characteristic, complemented
563	#3120	C₂×C₅₃	1	2	yes	complemented
564	#3101	C₂×C₅₃	1	1	yes	characteristic, complemented
565	#3084	C₂×C₅₃	1	2	yes	complemented
566	#3077	C₂×C₅₃	1	1	yes	characteristic, complemented
567	#2993	C₂×C₅₃	1	1	yes	characteristic, complemented
568	C₂×C₅₃	—	4	2	no	—
569	C₂×C₅₃	—	4	1	no	—
570	C₂×C₅₃	—	4	2	no	—
571	C₂×C₅₃	—	8	1	no	—
572	C₂×C₅₃	#3489	1	1	yes	characteristic
573	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
574	C₂×C₅₃	#3586	1	1	yes	characteristic
575	#563	—	2	2	no	—
576	Q₈²	C₂²×C₅₃	1	1	yes	characteristic, complemented
577	#557	—	2	1	no	—
578	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
579	#556	—	2	1	no	—
580	#556	C₂²×C₅₃	1	1	yes	characteristic
581	#556	C₂²×C₅₃	1	2	yes	—
582	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
583	#554	C₂²×C₅₃	1	2	yes	—
584	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
585	#552	—	2	1	no	—
586	#552	C₂²×C₅₃	1	2	yes	—
587	#551	—	2	2	no	—
588	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
589	#548	—	2	1	no	—
590	#547	C₂²×C₅₃	1	1	yes	characteristic
591	#547	C₂²×C₅₃	1	1	yes	characteristic
592	#546	C₂²×C₅₃	1	2	yes	—
593	#544	C₂²×C₅₃	1	2	yes	complemented
594	#542	—	2	1	no	—
595	#542	C₂²×C₅₃	1	2	yes	—
596	#541	—	2	2	no	—
597	#541	—	2	1	no	—
598	#541	C₂²×C₅₃	1	2	yes	complemented
599	#539	—	2	2	no	—
600	#533	C₂²×C₅₃	1	1	yes	characteristic
601	#533	C₂²×C₅₃	1	1	yes	characteristic
602	#533	C₂²×C₅₃	1	1	yes	characteristic
603	#529	C₂²×C₅₃	1	1	yes	characteristic
604	#525	—	2	1	no	—
605	C₂×C₂²⋊Q₈	—	2	1	no	—
606	#520	C₂²×C₅₃	1	2	yes	—
607	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
608	#501	C₂²×C₅₃	1	2	yes	complemented
609	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
610	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
611	#498	C₂²×C₅₃	1	2	yes	complemented
612	#489	C₂²×C₅₃	1	2	yes	—
613	#488	C₂²×C₅₃	1	2	yes	—
614	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
615	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
616	#485	C₂²×C₅₃	1	2	yes	—
617	#485	C₂²×C₅₃	1	2	yes	—
618	#485	C₂²×C₅₃	1	2	yes	complemented
619	#484	C₂²×C₅₃	1	2	yes	complemented
620	#483	C₂²×C₅₃	1	1	yes	characteristic
621	#483	C₂²×C₅₃	1	1	yes	characteristic
622	#483	C₂²×C₅₃	1	2	yes	complemented
623	#483	C₂²×C₅₃	1	2	yes	complemented
624	#482	C₂²×C₅₃	1	2	yes	—
625	#481	C₂²×C₅₃	1	2	yes	—
626	#479	C₂²×C₅₃	1	2	yes	complemented
627	#479	C₂²×C₅₃	1	2	yes	complemented
628	#479	C₂²×C₅₃	1	2	yes	complemented
629	#478	C₂²×C₅₃	1	2	yes	—
630	#478	C₂²×C₅₃	1	2	yes	—
631	#478	C₂²×C₅₃	1	2	yes	—
632	#477	C₂²×C₅₃	1	2	yes	complemented
633	#476	C₂²×C₅₃	1	1	yes	characteristic
634	#476	C₂²×C₅₃	1	1	yes	characteristic
635	#476	C₂²×C₅₃	1	1	yes	characteristic
636	#476	C₂²×C₅₃	1	2	yes	—
637	#476	C₂²×C₅₃	1	1	yes	characteristic
638	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
639	#475	C₂²×C₅₃	1	2	yes	complemented
640	#475	C₂²×C₅₃	1	2	yes	complemented
641	#475	C₂²×C₅₃	1	2	yes	complemented
642	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
643	#474	C₂²×C₅₃	1	1	yes	characteristic
644	#474	C₂²×C₅₃	1	1	yes	characteristic
645	#470	C₂²×C₅₃	1	2	yes	—
646	#470	C₂²×C₅₃	1	2	yes	—
647	#470	C₂²×C₅₃	1	2	yes	complemented
648	#468	C₂²×C₅₃	1	2	yes	—
649	#467	C₂²×C₅₃	1	2	yes	complemented
650	#465	C₂²×C₅₃	1	2	yes	—
651	#464	C₂²×C₅₃	1	2	yes	—
652	#464	C₂²×C₅₃	1	2	yes	—
653	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
654	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
655	#462	C₂²×C₅₃	1	2	yes	complemented
656	#461	C₂²×C₅₃	1	1	yes	characteristic
657	#461	C₂²×C₅₃	1	1	yes	characteristic
658	#452	C₂²×C₅₃	1	2	yes	—
659	#452	C₂²×C₅₃	1	2	yes	—
660	#450	C₂²×C₅₃	1	1	yes	characteristic
661	#450	C₂²×C₅₃	1	1	yes	characteristic
662	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
664	#441	C₂²×C₅₃	1	2	yes	complemented
665	#440	C₂²×C₅₃	1	2	yes	—
666	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
667	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
668	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
669	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
670	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
671	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
672	#436	C₂²×C₅₃	1	2	yes	—
673	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
674	#435	C₂²×C₅₃	1	2	yes	—
675	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
676	#433	C₂²×C₅₃	1	2	yes	complemented
677	#431	C₂²×C₅₃	1	1	yes	characteristic
678	#428	C₂²×C₅₃	1	2	yes	—
679	#428	C₂²×C₅₃	1	2	yes	complemented
680	C₂×#106	C₂²×C₅₃	1	2	yes	complemented
681	#424	C₂²×C₅₃	1	2	yes	complemented
682	#423	C₂²×C₅₃	1	1	yes	characteristic
683	#418	C₂²×C₅₃	1	2	yes	—
684	#417	C₂²×C₅₃	1	2	yes	—
685	#416	C₂²×C₅₃	1	2	yes	—
686	C₅₃	#62189	1	1	yes	characteristic, direct product factor, Sylow
687	C₂×#41	—	2	1	no	—
688	C₂×#41	C₂³×C₅₃	1	2	yes	—
689	C₂²×Q₈	—	2	1	no	—
690	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
691	C₂³×C₄	—	2	1	no	—
692	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
693	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
694	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
695	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
696	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
697	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
698	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
699	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
700	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	—	2	2	no	—
703	C₄⋊Q₈	—	2	1	no	—
704	C₄⋊Q₈	—	2	2	no	—
705	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
706	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
712	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	D₄×C₅₃	1	2	yes	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	1	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	1	no	—
730	#125	—	2	1	no	—
731	#125	D₄×C₅₃	1	1	yes	characteristic
732	#125	C₂³×C₅₃	1	2	yes	—
733	#125	C₂³×C₅₃	1	2	yes	—
734	#124	—	2	1	no	—
735	#124	—	2	2	no	—
736	#124	—	2	2	no	—
737	#124	D₄×C₅₃	1	1	yes	characteristic
738	#124	C₂³×C₅₃	1	2	yes	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	D₄×C₅₃	1	2	yes	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
760	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
762	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
763	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
765	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
766	#121	—	2	1	no	—
767	#121	—	2	2	no	—
768	#121	D₄×C₅₃	1	1	yes	characteristic
769	#121	C₂³×C₅₃	1	2	yes	—
770	#120	—	2	2	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
780	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
781	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
784	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
785	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
793	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₅₃	1	2	yes	—
797	C₄×D₄	C₂³×C₅₃	1	2	yes	—
798	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
799	#117	—	2	1	no	—
800	#117	—	2	1	no	—
801	#117	—	2	2	no	—
802	#117	—	2	1	no	—
803	#117	—	2	2	no	—
804	#117	C₂³×C₅₃	1	2	yes	—
805	#117	C₂³×C₅₃	1	2	yes	—
806	#117	C₂³×C₅₃	1	2	yes	—
807	C₂×C₄⋊C₄	—	2	2	no	—
808	C₂×C₄⋊C₄	—	2	1	no	—
809	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
810	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
811	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
812	C₂×C₂²⋊C₄	—	2	1	no	—
813	C₂×C₂²⋊C₄	—	2	2	no	—
814	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
815	#107	C₂³×C₅₃	1	2	yes	—
816	#107	C₂³×C₅₃	1	2	yes	—
817	#107	C₂³×C₅₃	1	2	yes	—
818	#107	C₂³×C₅₃	1	2	yes	—
819	#106	C₂³×C₅₃	1	1	yes	characteristic
820	#106	C₂³×C₅₃	1	2	yes	—
821	#106	C₂³×C₅₃	1	2	yes	—
822	#106	C₂³×C₅₃	1	2	yes	—
823	#106	C₂³×C₅₃	1	2	yes	—
824	#106	C₂³×C₅₃	1	1	yes	characteristic
825	#106	C₂³×C₅₃	1	2	yes	—
826	#106	C₂³×C₅₃	1	1	yes	characteristic
827	#106	C₂³×C₅₃	1	1	yes	characteristic
828	#106	C₂³×C₅₃	1	2	yes	—
829	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
830	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
834	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
835	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
836	#103	C₂³×C₅₃	1	2	yes	—
837	#103	C₂³×C₅₃	1	2	yes	—
838	#103	C₂³×C₅₃	1	2	yes	—
839	#103	C₂³×C₅₃	1	2	yes	—
840	#103	C₂³×C₅₃	1	1	yes	characteristic
841	#103	C₂³×C₅₃	1	1	yes	characteristic
842	#103	C₂³×C₅₃	1	1	yes	characteristic
843	#103	C₂³×C₅₃	1	1	yes	characteristic
844	#103	C₂³×C₅₃	1	2	yes	—
845	#103	C₂³×C₅₃	1	2	yes	—
846	#103	C₂³×C₅₃	1	2	yes	—
847	#103	C₂³×C₅₃	1	2	yes	—
848	#102	C₂³×C₅₃	1	1	yes	characteristic
849	#102	C₂³×C₅₃	1	2	yes	—
850	#102	C₂³×C₅₃	1	1	yes	characteristic
851	#102	C₂³×C₅₃	1	2	yes	—
852	#102	C₂³×C₅₃	1	2	yes	—
853	#102	C₂³×C₅₃	1	2	yes	—
854	#102	C₂³×C₅₃	1	1	yes	characteristic
855	#102	C₂³×C₅₃	1	1	yes	characteristic
856	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
857	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
858	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
859	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
860	#97	C₂³×C₅₃	1	2	yes	—
861	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
862	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₅₃	1	2	yes	—
864	C₂⁴	—	2	1	no	—
865	#41	—	2	4	no	—
866	#41	—	4	2	no	—
867	#41	—	8	2	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	2	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	8	2	no	—
875	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
876	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
877	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
878	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	1	no	—
883	C₂×D₄	—	4	1	no	—
884	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
885	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
886	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
887	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
888	C₂²×C₄	—	2	1	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	—	2	1	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	8	2	no	—
898	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
899	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
902	Q₁₆	—	4	2	no	—
903	Q₁₆	—	4	2	no	—
904	SD₁₆	—	2	2	no	—
905	SD₁₆	—	2	2	no	—
906	SD₁₆	—	4	1	no	—
907	SD₁₆	—	4	1	no	—
908	M₁₆	—	4	2	no	—
909	M₁₆	—	4	2	no	—
910	C₂×C₈	—	4	2	no	—
911	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
912	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
913	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
914	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
947	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
949	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
950	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
951	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
952	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
953	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
955	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
956	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
976	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
977	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
978	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
979	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
989	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
990	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
991	C₄²	C₂⁴×C₅₃	1	2	yes	—
992	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
993	C₂³	—	2	1	no	—
994	C₂³	—	2	1	no	—
995	C₂³	—	4	2	no	—
996	C₂³	—	4	2	no	—
997	C₂³	—	8	1	no	—
998	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
999	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1000	Q₈	—	2	2	no	—
1001	Q₈	—	2	1	no	—
1002	Q₈	—	2	1	no	—
1003	Q₈	—	2	2	no	—
1004	Q₈	—	2	1	no	—
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	2	no	—
1007	Q₈	—	4	2	no	—
1008	Q₈	—	4	2	no	—
1009	Q₈	—	8	1	no	—
1010	Q₈	—	8	1	no	—
1011	Q₈	—	8	2	no	—
1012	Q₈	—	8	2	no	—
1013	D₄	—	2	2	no	—
1014	D₄	—	2	1	no	—
1015	D₄	—	2	1	no	—
1016	D₄	—	2	1	no	—
1017	D₄	—	4	2	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	4	4	no	—
1020	D₄	—	8	2	no	—
1021	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	4	1	no	—
1038	C₂×C₄	—	4	4	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	4	2	no	—
1041	C₂×C₄	—	8	1	no	—
1042	C₂×C₄	—	8	1	no	—
1043	C₂×C₄	—	8	2	no	—
1044	C₂×C₄	—	8	2	no	—
1045	C₂×C₄	—	8	1	no	—
1046	C₂×C₄	—	8	2	no	—
1047	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1048	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1050	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1051	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1052	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1054	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1055	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	2	no	—
1060	C₈	—	2	1	no	—
1061	C₈	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	1	no	—
1074	C₂²	—	8	4	no	—
1075	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1076	C₄	—	2	2	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	1	no	—
1079	C₄	—	2	2	no	—
1080	C₄	—	2	1	no	—
1081	C₄	—	2	1	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	4	2	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	2	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	1	no	—
1093	C₄	C₅₃×#577	1	2	yes	—
1094	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1095	C₄	C₅₃×#585	1	1	yes	characteristic
1096	C₂	—	4	1	no	—
1097	C₂	—	4	2	no	—
1098	C₂	—	4	2	no	—
1099	C₂	—	8	1	no	—
1100	C₂	C₅₃×#3489	1	1	yes	characteristic
1101	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1102	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3520	C₂
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×#3555	C₂	semidirect
3. C₅₃×#3386	C₂	semidirect
4. Q₈×SD₁₆×C₅₃	C₂	semidirect
5. C₅₃×#3369	C₂	semidirect
6. C₅₃×#3364	C₂	semidirect
7. C₅₃×#3356	C₂	semidirect
8. C₅₃×#3353	C₂	semidirect
9. C₅₃×#3344	C₂	semidirect
10. C₅₃×#3335	C₂	semidirect
11. C₅₃×#3331	C₂	semidirect
12. C₅₃×#3323	C₂	semidirect
13. C₅₃×#3311	C₂	semidirect
14. C₅₃×#3302	C₂	semidirect
15. C₅₃×#3258	C₂	semidirect
16. C₅₃×#3255	C₂	semidirect
17. C₅₃×#3244	C₂	semidirect
18. C₅₃×#3231	C₂	semidirect
19. C₅₃×#3120	C₂	semidirect
20. C₅₃×#3101	C₂	semidirect
21. C₅₃×#3084	C₂	semidirect
22. C₅₃×#3077	C₂	semidirect
23. C₅₃×#2993	C₂	semidirect
25. Q₈²×C₅₃	C₂²	semidirect
27. C₅₃×#557	C₂²	semidirect
31. C₅₃×#556	C₂²	semidirect
33. C₅₃×#554	C₂²	semidirect
42. C₅₃×#544	C₂²	semidirect
47. C₅₃×#541	C₂²	semidirect
57. C₅₃×#501	C₂²	semidirect
58. C₅₃×#500	C₂²	semidirect
59. C₅₃×#498	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
71. C₅₃×#483	C₂²	semidirect
72. C₅₃×#483	C₂²	semidirect
75. C₅₃×#479	C₂²	semidirect
76. C₅₃×#479	C₂²	semidirect
77. C₅₃×#479	C₂²	semidirect
81. C₅₃×#477	C₂²	semidirect
87. C₅₃×#475	C₂²	semidirect
88. C₅₃×#475	C₂²	semidirect
89. C₅₃×#475	C₂²	semidirect
90. C₅₃×#475	C₂²	semidirect
91. C₅₃×#475	C₂²	semidirect
96. C₅₃×#470	C₂²	semidirect
98. C₅₃×#467	C₂²	semidirect
102. C₅₃×#462	C₂²	semidirect
103. C₅₃×#462	C₂²	semidirect
104. C₅₃×#462	C₂²	semidirect
111. C₅₃×#446	C₂²	semidirect
112. C₈×Q₈×C₅₃	C₂²	semidirect
113. C₅₃×#441	C₂²	semidirect
115. C₄×Q₁₆×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×#106×C₅₃	C₂²	semidirect
130. C₅₃×#424	C₂²	semidirect
510. #62189	C₅₃	direct (N × H)
545. #3555	C₂×C₅₃	semidirect
547. #3386	C₂×C₅₃	semidirect
548. Q₈×SD₁₆	C₂×C₅₃	semidirect
549. #3369	C₂×C₅₃	semidirect
550. #3364	C₂×C₅₃	semidirect
551. #3356	C₂×C₅₃	semidirect
552. #3353	C₂×C₅₃	semidirect
553. #3344	C₂×C₅₃	semidirect
554. #3335	C₂×C₅₃	semidirect
555. #3331	C₂×C₅₃	semidirect
556. #3323	C₂×C₅₃	semidirect
557. #3311	C₂×C₅₃	semidirect
558. #3302	C₂×C₅₃	semidirect
559. #3258	C₂×C₅₃	semidirect
560. #3255	C₂×C₅₃	semidirect
561. #3244	C₂×C₅₃	semidirect
562. #3231	C₂×C₅₃	semidirect
563. #3120	C₂×C₅₃	semidirect
564. #3101	C₂×C₅₃	semidirect
565. #3084	C₂×C₅₃	semidirect
566. #3077	C₂×C₅₃	semidirect
567. #2993	C₂×C₅₃	semidirect
576. Q₈²	C₂²×C₅₃	semidirect
578. #557	C₂²×C₅₃	semidirect
582. #556	C₂²×C₅₃	semidirect
584. #554	C₂²×C₅₃	semidirect
593. #544	C₂²×C₅₃	semidirect
598. #541	C₂²×C₅₃	semidirect
608. #501	C₂²×C₅₃	semidirect
609. #500	C₂²×C₅₃	semidirect
610. #498	C₂²×C₅₃	semidirect
611. #498	C₂²×C₅₃	semidirect
614. #487	C₂²×C₅₃	semidirect
615. #487	C₂²×C₅₃	semidirect
618. #485	C₂²×C₅₃	semidirect
619. #484	C₂²×C₅₃	semidirect
622. #483	C₂²×C₅₃	semidirect
623. #483	C₂²×C₅₃	semidirect
626. #479	C₂²×C₅₃	semidirect
627. #479	C₂²×C₅₃	semidirect
628. #479	C₂²×C₅₃	semidirect
632. #477	C₂²×C₅₃	semidirect
638. #475	C₂²×C₅₃	semidirect
639. #475	C₂²×C₅₃	semidirect
640. #475	C₂²×C₅₃	semidirect
641. #475	C₂²×C₅₃	semidirect
642. #475	C₂²×C₅₃	semidirect
647. #470	C₂²×C₅₃	semidirect
649. #467	C₂²×C₅₃	semidirect
653. #462	C₂²×C₅₃	semidirect
654. #462	C₂²×C₅₃	semidirect
655. #462	C₂²×C₅₃	semidirect
662. #446	C₂²×C₅₃	semidirect
663. C₈×Q₈	C₂²×C₅₃	semidirect
664. #441	C₂²×C₅₃	semidirect
666. C₄×Q₁₆	C₂²×C₅₃	semidirect
673. #436	C₂²×C₅₃	semidirect
675. C₈×D₄	C₂²×C₅₃	semidirect
676. #433	C₂²×C₅₃	semidirect
679. #428	C₂²×C₅₃	semidirect
680. C₂×#106	C₂²×C₅₃	semidirect
681. #424	C₂²×C₅₃	semidirect
686. C₅₃	#62189	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×#3555	2
C₅₃×#3520	2
C₅₃×#3386	2
Q₈×SD₁₆×C₅₃	2
C₅₃×#3369	2
C₅₃×#3364	2
C₅₃×#3356	2
C₅₃×#3353	2
C₅₃×#3344	2
C₅₃×#3335	2
C₅₃×#3331	2
C₅₃×#3323	2
C₅₃×#3311	2
C₅₃×#3302	2
C₅₃×#3258	2
C₅₃×#3255	2
C₅₃×#3244	2
C₅₃×#3231	2
C₅₃×#3120	2
C₅₃×#3101	2
C₅₃×#3084	2
C₅₃×#3077	2
C₅₃×#2993	2
#62189	53

Subgroups — C53×#62189 #27269701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62189 #27269701