Subgroups — C₅₃×#62202 #27269714

Order 13568.

1744 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3544	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×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3344	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3335	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×#3306	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3296	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3263	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3244	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3125	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3084	C₂	1	2	yes	maximal, complemented
22	C₂×C₅₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#563	—	2	2	no	—
25	Q₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₅₃×#556	C₂²	1	1	yes	characteristic
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×#554	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#552	—	2	1	no	—
32	C₅₃×#552	—	2	1	no	—
33	C₅₃×#552	C₂²	1	2	yes	—
34	C₅₃×#551	—	2	2	no	—
35	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
36	C₅₃×#548	—	2	1	no	—
37	C₅₃×#547	—	2	1	no	—
38	C₅₃×#547	C₂²	1	1	yes	characteristic
39	C₅₃×#547	C₂²	1	1	yes	characteristic
40	C₅₃×#547	C₂²	1	2	yes	—
41	C₅₃×#546	C₂²	1	2	yes	—
42	C₅₃×#544	—	2	1	no	—
43	C₅₃×#544	C₂²	1	2	yes	complemented
44	C₅₃×#542	—	2	1	no	—
45	C₅₃×#542	C₂²	1	2	yes	—
46	C₅₃×#542	C₂²	1	2	yes	complemented
47	C₅₃×#539	—	2	2	no	—
48	C₅₃×#536	—	2	2	no	—
49	C₅₃×#533	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#529	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×#498	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	complemented
66	C₅₃×#484	C₂²	1	1	yes	characteristic
67	C₅₃×#483	C₂²	1	2	yes	—
68	C₅₃×#483	C₂²	1	2	yes	—
69	C₅₃×#483	C₂²	1	2	yes	complemented
70	C₅₃×#483	C₂²	1	2	yes	complemented
71	C₅₃×#482	C₂²	1	2	yes	—
72	C₅₃×#481	C₂²	1	2	yes	—
73	C₅₃×#481	C₂²	1	1	yes	characteristic
74	C₅₃×#481	C₂²	1	2	yes	complemented
75	C₅₃×#479	C₂²	1	2	yes	complemented
76	C₅₃×#479	C₂²	1	2	yes	complemented
77	C₅₃×#478	C₂²	1	1	yes	characteristic
78	C₅₃×#478	C₂²	1	2	yes	—
79	C₅₃×#478	C₂²	1	1	yes	characteristic
80	C₅₃×#476	C₂²	1	2	yes	—
81	C₅₃×#476	C₂²	1	1	yes	characteristic
82	C₅₃×#476	C₂²	1	2	yes	—
83	C₅₃×#476	C₂²	1	1	yes	characteristic
84	C₅₃×#476	C₂²	1	1	yes	characteristic
85	C₅₃×#476	C₂²	1	2	yes	—
86	C₅₃×#476	C₂²	1	1	yes	characteristic
87	C₅₃×#476	C₂²	1	2	yes	complemented
88	C₅₃×#475	C₂²	1	2	yes	complemented
89	C₅₃×#475	C₂²	1	2	yes	complemented
90	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#475	C₂²	1	2	yes	complemented
92	C₅₃×#475	C₂²	1	2	yes	complemented
93	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#470	C₂²	1	2	yes	complemented
95	C₅₃×#469	C₂²	1	2	yes	—
96	C₅₃×#467	C₂²	1	2	yes	—
97	C₅₃×#465	C₂²	1	2	yes	—
98	C₅₃×#465	C₂²	1	2	yes	—
99	C₅₃×#465	C₂²	1	2	yes	complemented
100	C₅₃×#464	C₂²	1	2	yes	—
101	C₅₃×#464	C₂²	1	2	yes	complemented
102	C₅₃×#463	C₂²	1	1	yes	characteristic
103	C₅₃×#463	C₂²	1	2	yes	—
104	C₅₃×#463	C₂²	1	1	yes	characteristic
105	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#452	C₂²	1	2	yes	—
108	C₅₃×#450	C₂²	1	1	yes	characteristic
109	C₅₃×#449	C₂²	1	2	yes	—
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×#441	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
121	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₅₃	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	complemented
128	C₂×#106×C₅₃	C₂²	1	2	yes	—
129	C₂×#106×C₅₃	C₂²	1	2	yes	complemented
130	C₅₃×#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
132	C₅₃×#417	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	2	no	—
137	C₂×#41×C₅₃	C₂³	1	2	yes	—
138	C₂²×Q₈×C₅₃	—	2	1	no	—
139	C₂²×Q₈×C₅₃	—	2	1	no	—
140	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅₃	—	2	1	no	—
142	C₂×Q₁₆×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×SD₁₆×C₅₃	C₂³	1	2	yes	—
146	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
150	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
151	C₄⋊Q₈×C₅₃	—	2	2	no	—
152	C₄⋊Q₈×C₅₃	—	2	2	no	—
153	C₄⋊Q₈×C₅₃	—	2	1	no	—
154	C₄⋊Q₈×C₅₃	—	2	1	no	—
155	C₄⋊Q₈×C₅₃	—	2	1	no	—
156	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	1	no	—
168	#126×C₅₃	D₄	1	2	yes	—
169	#125×C₅₃	—	2	2	no	—
170	#125×C₅₃	—	2	1	no	—
171	#125×C₅₃	—	2	2	no	—
172	#125×C₅₃	—	2	2	no	—
173	#125×C₅₃	—	2	1	no	—
174	#125×C₅₃	D₄	1	1	yes	characteristic
175	#125×C₅₃	C₂³	1	2	yes	—
176	#125×C₅₃	C₂³	1	1	yes	characteristic
177	#124×C₅₃	—	2	2	no	—
178	#124×C₅₃	—	2	2	no	—
179	#124×C₅₃	—	2	2	no	—
180	#124×C₅₃	D₄	1	1	yes	characteristic
181	#124×C₅₃	C₂³	1	2	yes	—
182	#124×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
189	#123×C₅₃	—	2	2	no	—
190	#123×C₅₃	—	2	2	no	—
191	#123×C₅₃	—	2	1	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	2	no	—
203	C₂²⋊Q₈×C₅₃	—	2	2	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	1	no	—
206	C₂²⋊Q₈×C₅₃	—	2	1	no	—
207	C₂²⋊Q₈×C₅₃	—	2	1	no	—
208	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
211	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
213	#121×C₅₃	—	2	2	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	—	2	1	no	—
216	#121×C₅₃	D₄	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	#120×C₅₃	—	2	2	no	—
221	C₄×Q₈×C₅₃	—	2	1	no	—
222	C₄×Q₈×C₅₃	—	2	1	no	—
223	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
225	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	1	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	2	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	1	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	2	yes	—
242	C₄×D₄×C₅₃	C₂³	1	2	yes	—
243	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
244	#117×C₅₃	—	2	2	no	—
245	#117×C₅₃	—	2	1	no	—
246	#117×C₅₃	—	2	1	no	—
247	#117×C₅₃	—	2	2	no	—
248	#117×C₅₃	—	2	1	no	—
249	#117×C₅₃	—	2	1	no	—
250	#117×C₅₃	C₂³	1	2	yes	—
251	#117×C₅₃	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
253	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
255	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
264	#107×C₅₃	C₂³	1	2	yes	—
265	#107×C₅₃	C₂³	1	1	yes	characteristic
266	#106×C₅₃	C₂³	1	2	yes	—
267	#106×C₅₃	C₂³	1	2	yes	—
268	#106×C₅₃	C₂³	1	1	yes	characteristic
269	#106×C₅₃	C₂³	1	2	yes	—
270	#106×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	2	yes	—
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	2	yes	—
293	#102×C₅₃	C₂³	1	1	yes	characteristic
294	#102×C₅₃	C₂³	1	2	yes	—
295	#102×C₅₃	C₂³	1	1	yes	characteristic
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	2	yes	—
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	1	no	—
313	#41×C₅₃	—	2	4	no	—
314	#41×C₅₃	—	4	2	no	—
315	#41×C₅₃	—	8	4	no	—
316	#41×C₅₃	—	8	2	no	—
317	C₂×Q₈×C₅₃	—	2	1	no	—
318	C₂×Q₈×C₅₃	—	2	2	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	—	2	1	no	—
323	C₂×Q₈×C₅₃	—	8	2	no	—
324	C₂×Q₈×C₅₃	—	8	2	no	—
325	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	2	no	—
333	C₂×D₄×C₅₃	—	2	1	no	—
334	C₂×D₄×C₅₃	—	4	1	no	—
335	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₅₃	—	2	2	no	—
341	C₂²×C₄×C₅₃	—	2	1	no	—
342	C₂²×C₄×C₅₃	—	2	2	no	—
343	C₂²×C₄×C₅₃	—	2	2	no	—
344	C₂²×C₄×C₅₃	—	2	2	no	—
345	C₂²×C₄×C₅₃	—	2	1	no	—
346	C₂²×C₄×C₅₃	—	2	1	no	—
347	C₂²×C₄×C₅₃	—	2	1	no	—
348	C₂²×C₄×C₅₃	—	2	2	no	—
349	C₂²×C₄×C₅₃	—	2	1	no	—
350	C₂²×C₄×C₅₃	—	2	2	no	—
351	C₂²×C₄×C₅₃	—	2	1	no	—
352	C₂²×C₄×C₅₃	—	8	2	no	—
353	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
357	Q₁₆×C₅₃	—	4	2	no	—
358	SD₁₆×C₅₃	—	2	2	no	—
359	SD₁₆×C₅₃	—	4	1	no	—
360	SD₁₆×C₅₃	—	4	2	no	—
361	D₈×C₅₃	—	2	2	no	—
362	D₈×C₅₃	—	4	1	no	—
363	M₁₆×C₅₃	—	4	2	no	—
364	C₂×C₈×C₅₃	—	4	2	no	—
365	C₂×C₈×C₅₃	—	4	2	no	—
366	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
370	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₅₃	—	2	1	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	—	2	1	no	—
375	C₄⋊C₄×C₅₃	—	2	1	no	—
376	C₄⋊C₄×C₅₃	—	2	2	no	—
377	C₄⋊C₄×C₅₃	—	2	2	no	—
378	C₄⋊C₄×C₅₃	—	2	2	no	—
379	C₄⋊C₄×C₅₃	—	2	2	no	—
380	C₄⋊C₄×C₅₃	—	2	2	no	—
381	C₄⋊C₄×C₅₃	—	2	1	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	1	no	—
389	C₄⋊C₄×C₅₃	—	2	1	no	—
390	C₄⋊C₄×C₅₃	—	2	2	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	—	2	1	no	—
395	C₄⋊C₄×C₅₃	—	2	2	no	—
396	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
409	C₂²⋊C₄×C₅₃	—	2	2	no	—
410	C₂²⋊C₄×C₅₃	—	2	1	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	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	1	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	2	no	—
434	C₄²×C₅₃	—	2	2	no	—
435	C₄²×C₅₃	—	2	2	no	—
436	C₄²×C₅₃	—	2	1	no	—
437	C₄²×C₅₃	—	2	2	no	—
438	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₄²×C₅₃	C₂⁴	1	2	yes	—
442	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₂³×C₅₃	—	2	1	no	—
444	C₂³×C₅₃	—	2	1	no	—
445	C₂³×C₅₃	—	2	1	no	—
446	C₂³×C₅₃	—	4	2	no	—
447	C₂³×C₅₃	—	4	2	no	—
448	C₂³×C₅₃	—	8	1	no	—
449	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
450	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
451	Q₈×C₅₃	—	2	2	no	—
452	Q₈×C₅₃	—	2	2	no	—
453	Q₈×C₅₃	—	2	1	no	—
454	Q₈×C₅₃	—	2	2	no	—
455	Q₈×C₅₃	—	2	1	no	—
456	Q₈×C₅₃	—	4	2	no	—
457	Q₈×C₅₃	—	8	1	no	—
458	Q₈×C₅₃	—	8	2	no	—
459	Q₈×C₅₃	—	8	1	no	—
460	Q₈×C₅₃	—	8	2	no	—
461	Q₈×C₅₃	—	8	2	no	—
462	D₄×C₅₃	—	2	4	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	1	no	—
468	D₄×C₅₃	—	2	1	no	—
469	D₄×C₅₃	—	4	2	no	—
470	D₄×C₅₃	—	4	4	no	—
471	D₄×C₅₃	—	4	2	no	—
472	D₄×C₅₃	—	8	2	no	—
473	D₄×C₅₃	—	8	2	no	—
474	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
475	C₂×C₄×C₅₃	—	2	2	no	—
476	C₂×C₄×C₅₃	—	2	2	no	—
477	C₂×C₄×C₅₃	—	2	1	no	—
478	C₂×C₄×C₅₃	—	2	2	no	—
479	C₂×C₄×C₅₃	—	2	1	no	—
480	C₂×C₄×C₅₃	—	2	2	no	—
481	C₂×C₄×C₅₃	—	2	1	no	—
482	C₂×C₄×C₅₃	—	2	1	no	—
483	C₂×C₄×C₅₃	—	2	2	no	—
484	C₂×C₄×C₅₃	—	2	2	no	—
485	C₂×C₄×C₅₃	—	2	1	no	—
486	C₂×C₄×C₅₃	—	2	2	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	—	4	4	no	—
491	C₂×C₄×C₅₃	—	4	4	no	—
492	C₂×C₄×C₅₃	—	4	2	no	—
493	C₂×C₄×C₅₃	—	4	2	no	—
494	C₂×C₄×C₅₃	—	4	2	no	—
495	C₂×C₄×C₅₃	—	8	1	no	—
496	C₂×C₄×C₅₃	—	8	1	no	—
497	C₂×C₄×C₅₃	—	8	2	no	—
498	C₂×C₄×C₅₃	—	8	2	no	—
499	C₂×C₄×C₅₃	—	8	1	no	—
500	C₂×C₄×C₅₃	—	8	2	no	—
501	C₂×C₄×C₅₃	—	8	2	no	—
502	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
511	C₈×C₅₃	—	2	1	no	—
512	C₈×C₅₃	—	2	1	no	—
513	C₈×C₅₃	—	2	1	no	—
514	C₈×C₅₃	—	2	2	no	—
515	C₈×C₅₃	—	2	2	no	—
516	C₈×C₅₃	—	2	1	no	—
517	#62202	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
518	C₂²×C₅₃	—	2	1	no	—
519	C₂²×C₅₃	—	2	1	no	—
520	C₂²×C₅₃	—	2	2	no	—
521	C₂²×C₅₃	—	2	2	no	—
522	C₂²×C₅₃	—	2	2	no	—
523	C₂²×C₅₃	—	2	2	no	—
524	C₂²×C₅₃	—	4	1	no	—
525	C₂²×C₅₃	—	4	1	no	—
526	C₂²×C₅₃	—	4	1	no	—
527	C₂²×C₅₃	—	4	1	no	—
528	C₂²×C₅₃	—	4	1	no	—
529	C₂²×C₅₃	—	4	1	no	—
530	C₂²×C₅₃	—	4	1	no	—
531	C₂²×C₅₃	—	4	1	no	—
532	C₂²×C₅₃	—	8	4	no	—
533	C₂²×C₅₃	#577	1	2	yes	—
534	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
535	C₄×C₅₃	—	2	2	no	—
536	C₄×C₅₃	—	2	1	no	—
537	C₄×C₅₃	—	2	1	no	—
538	C₄×C₅₃	—	2	1	no	—
539	C₄×C₅₃	—	2	1	no	—
540	C₄×C₅₃	—	2	2	no	—
541	C₄×C₅₃	—	2	2	no	—
542	C₄×C₅₃	—	4	2	no	—
543	C₄×C₅₃	—	4	1	no	—
544	C₄×C₅₃	—	4	1	no	—
545	C₄×C₅₃	—	4	1	no	—
546	C₄×C₅₃	—	4	2	no	—
547	C₄×C₅₃	—	4	1	no	—
548	C₄×C₅₃	—	4	2	no	—
549	C₄×C₅₃	—	4	1	no	—
550	C₄×C₅₃	—	4	2	no	—
551	C₄×C₅₃	#577	1	2	yes	—
552	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	C₄×C₅₃	#585	1	1	yes	characteristic
554	#3544	C₂×C₅₃	1	1	yes	characteristic, complemented
555	#3520	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
557	Q₈×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
558	#3369	C₂×C₅₃	1	1	yes	characteristic, complemented
559	#3360	C₂×C₅₃	1	1	yes	characteristic, complemented
560	#3354	C₂×C₅₃	1	1	yes	characteristic, complemented
561	#3344	C₂×C₅₃	1	2	yes	complemented
562	#3335	C₂×C₅₃	1	2	yes	complemented
563	#3335	C₂×C₅₃	1	1	yes	characteristic, complemented
564	#3331	C₂×C₅₃	1	1	yes	characteristic, complemented
565	#3306	C₂×C₅₃	1	2	yes	complemented
566	#3303	C₂×C₅₃	1	1	yes	characteristic, complemented
567	#3296	C₂×C₅₃	1	2	yes	complemented
568	#3263	C₂×C₅₃	1	2	yes	complemented
569	#3248	C₂×C₅₃	1	1	yes	characteristic, complemented
570	#3244	C₂×C₅₃	1	2	yes	complemented
571	#3229	C₂×C₅₃	1	1	yes	characteristic, complemented
572	#3125	C₂×C₅₃	1	2	yes	complemented
573	#3105	C₂×C₅₃	1	1	yes	characteristic, complemented
574	#3084	C₂×C₅₃	1	2	yes	complemented
575	C₂×#476	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#2994	C₂×C₅₃	1	1	yes	characteristic, complemented
577	C₂×C₅₃	—	2	2	no	—
578	C₂×C₅₃	—	4	2	no	—
579	C₂×C₅₃	—	4	2	no	—
580	C₂×C₅₃	—	8	1	no	—
581	C₂×C₅₃	—	8	1	no	—
582	C₂×C₅₃	#3489	1	1	yes	characteristic
583	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
584	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
585	#563	—	2	2	no	—
586	Q₈²	C₂²×C₅₃	1	1	yes	characteristic, complemented
587	#556	C₂²×C₅₃	1	1	yes	characteristic
588	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
589	#554	C₂²×C₅₃	1	2	yes	—
590	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
591	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
592	#552	—	2	1	no	—
593	#552	—	2	1	no	—
594	#552	C₂²×C₅₃	1	2	yes	—
595	#551	—	2	2	no	—
596	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
597	#548	—	2	1	no	—
598	#547	—	2	1	no	—
599	#547	C₂²×C₅₃	1	1	yes	characteristic
600	#547	C₂²×C₅₃	1	1	yes	characteristic
601	#547	C₂²×C₅₃	1	2	yes	—
602	#546	C₂²×C₅₃	1	2	yes	—
603	#544	—	2	1	no	—
604	#544	C₂²×C₅₃	1	2	yes	complemented
605	#542	—	2	1	no	—
606	#542	C₂²×C₅₃	1	2	yes	—
607	#542	C₂²×C₅₃	1	2	yes	complemented
608	#539	—	2	2	no	—
609	#536	—	2	2	no	—
610	#533	C₂²×C₅₃	1	1	yes	characteristic
611	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
612	#529	C₂²×C₅₃	1	1	yes	characteristic
613	#529	C₂²×C₅₃	1	1	yes	characteristic
614	#525	—	2	1	no	—
615	C₂×C₂²⋊Q₈	—	2	1	no	—
616	#520	C₂²×C₅₃	1	2	yes	—
617	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
618	#501	C₂²×C₅₃	1	2	yes	complemented
619	#498	C₂²×C₅₃	1	2	yes	complemented
620	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
621	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
622	#489	C₂²×C₅₃	1	2	yes	—
623	#488	C₂²×C₅₃	1	2	yes	—
624	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
625	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
626	#485	C₂²×C₅₃	1	2	yes	complemented
627	#484	C₂²×C₅₃	1	1	yes	characteristic
628	#483	C₂²×C₅₃	1	2	yes	—
629	#483	C₂²×C₅₃	1	2	yes	—
630	#483	C₂²×C₅₃	1	2	yes	complemented
631	#483	C₂²×C₅₃	1	2	yes	complemented
632	#482	C₂²×C₅₃	1	2	yes	—
633	#481	C₂²×C₅₃	1	1	yes	characteristic
634	#481	C₂²×C₅₃	1	2	yes	—
635	#481	C₂²×C₅₃	1	2	yes	complemented
636	#479	C₂²×C₅₃	1	2	yes	complemented
637	#479	C₂²×C₅₃	1	2	yes	complemented
638	#478	C₂²×C₅₃	1	1	yes	characteristic
639	#478	C₂²×C₅₃	1	2	yes	—
640	#478	C₂²×C₅₃	1	1	yes	characteristic
641	#476	C₂²×C₅₃	1	1	yes	characteristic
642	#476	C₂²×C₅₃	1	1	yes	characteristic
643	#476	C₂²×C₅₃	1	2	yes	—
644	#476	C₂²×C₅₃	1	2	yes	—
645	#476	C₂²×C₅₃	1	1	yes	characteristic
646	#476	C₂²×C₅₃	1	1	yes	characteristic
647	#476	C₂²×C₅₃	1	2	yes	—
648	#476	C₂²×C₅₃	1	2	yes	complemented
649	#475	C₂²×C₅₃	1	2	yes	complemented
650	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
651	#475	C₂²×C₅₃	1	2	yes	complemented
652	#475	C₂²×C₅₃	1	2	yes	complemented
653	#475	C₂²×C₅₃	1	2	yes	complemented
654	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
655	#470	C₂²×C₅₃	1	2	yes	complemented
656	#469	C₂²×C₅₃	1	2	yes	—
657	#467	C₂²×C₅₃	1	2	yes	—
658	#465	C₂²×C₅₃	1	2	yes	—
659	#465	C₂²×C₅₃	1	2	yes	—
660	#465	C₂²×C₅₃	1	2	yes	complemented
661	#464	C₂²×C₅₃	1	2	yes	—
662	#464	C₂²×C₅₃	1	2	yes	complemented
663	#463	C₂²×C₅₃	1	2	yes	—
664	#463	C₂²×C₅₃	1	1	yes	characteristic
665	#463	C₂²×C₅₃	1	1	yes	characteristic
666	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
667	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
668	#452	C₂²×C₅₃	1	2	yes	—
669	#450	C₂²×C₅₃	1	1	yes	characteristic
670	#449	C₂²×C₅₃	1	2	yes	—
671	#447	C₂²×C₅₃	1	1	yes	characteristic
672	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
674	#442	C₂²×C₅₃	1	2	yes	—
675	#441	C₂²×C₅₃	1	2	yes	complemented
676	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
677	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
678	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
679	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
680	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
681	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
682	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	#435	C₂²×C₅₃	1	2	yes	—
684	C₈×D₄	C₂²×C₅₃	1	2	yes	—
685	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
686	#433	C₂²×C₅₃	1	2	yes	complemented
687	#431	C₂²×C₅₃	1	1	yes	characteristic
688	#428	C₂²×C₅₃	1	2	yes	complemented
689	C₂×#106	C₂²×C₅₃	1	2	yes	—
690	C₂×#106	C₂²×C₅₃	1	2	yes	complemented
691	#424	C₂²×C₅₃	1	2	yes	complemented
692	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
693	#417	C₂²×C₅₃	1	2	yes	—
694	#416	C₂²×C₅₃	1	2	yes	—
695	C₂×#102	C₂²×C₅₃	1	2	yes	—
696	C₅₃	#62202	1	1	yes	characteristic, direct product factor, Sylow
697	C₂×#41	—	2	1	no	—
698	C₂×#41	—	2	2	no	—
699	C₂×#41	C₂³×C₅₃	1	2	yes	—
700	C₂²×Q₈	—	2	1	no	—
701	C₂²×Q₈	—	2	1	no	—
702	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
703	C₂³×C₄	—	2	1	no	—
704	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
705	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
708	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
709	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
710	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
711	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
712	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
713	C₄⋊Q₈	—	2	2	no	—
714	C₄⋊Q₈	—	2	2	no	—
715	C₄⋊Q₈	—	2	1	no	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
720	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
724	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	1	no	—
730	#126	D₄×C₅₃	1	2	yes	—
731	#125	—	2	2	no	—
732	#125	—	2	1	no	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	1	no	—
736	#125	D₄×C₅₃	1	1	yes	characteristic
737	#125	C₂³×C₅₃	1	1	yes	characteristic
738	#125	C₂³×C₅₃	1	2	yes	—
739	#124	—	2	2	no	—
740	#124	—	2	2	no	—
741	#124	—	2	2	no	—
742	#124	D₄×C₅₃	1	1	yes	characteristic
743	#124	C₂³×C₅₃	1	1	yes	characteristic
744	#124	C₂³×C₅₃	1	2	yes	—
745	#123	—	2	2	no	—
746	#123	—	2	1	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
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	D₄×C₅₃	1	2	yes	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
771	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
772	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
773	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
775	#121	—	2	1	no	—
776	#121	—	2	1	no	—
777	#121	—	2	2	no	—
778	#121	D₄×C₅₃	1	1	yes	characteristic
779	#121	C₂³×C₅₃	1	1	yes	characteristic
780	#121	C₂³×C₅₃	1	2	yes	—
781	#121	C₂³×C₅₃	1	2	yes	—
782	#120	—	2	2	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
786	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
787	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
789	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₅₃	1	2	yes	—
802	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₅₃	1	2	yes	—
804	C₄×D₄	C₂³×C₅₃	1	2	yes	—
805	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
806	#117	—	2	1	no	—
807	#117	—	2	2	no	—
808	#117	—	2	1	no	—
809	#117	—	2	1	no	—
810	#117	—	2	2	no	—
811	#117	—	2	1	no	—
812	#117	C₂³×C₅₃	1	2	yes	—
813	#117	C₂³×C₅₃	1	2	yes	—
814	C₂×C₄⋊C₄	—	2	1	no	—
815	C₂×C₄⋊C₄	—	2	2	no	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
819	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
820	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
821	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
822	C₂×C₂²⋊C₄	—	2	1	no	—
823	C₂×C₂²⋊C₄	—	2	2	no	—
824	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
825	#107	C₂³×C₅₃	1	1	yes	characteristic
826	#107	C₂³×C₅₃	1	2	yes	—
827	#107	C₂³×C₅₃	1	1	yes	characteristic
828	#106	C₂³×C₅₃	1	2	yes	—
829	#106	C₂³×C₅₃	1	2	yes	—
830	#106	C₂³×C₅₃	1	2	yes	—
831	#106	C₂³×C₅₃	1	2	yes	—
832	#106	C₂³×C₅₃	1	1	yes	characteristic
833	#106	C₂³×C₅₃	1	2	yes	—
834	#106	C₂³×C₅₃	1	2	yes	—
835	#106	C₂³×C₅₃	1	2	yes	—
836	#106	C₂³×C₅₃	1	2	yes	—
837	#106	C₂³×C₅₃	1	1	yes	characteristic
838	#106	C₂³×C₅₃	1	2	yes	—
839	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
840	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
844	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
845	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
846	#103	C₂³×C₅₃	1	2	yes	—
847	#103	C₂³×C₅₃	1	2	yes	—
848	#103	C₂³×C₅₃	1	2	yes	—
849	#103	C₂³×C₅₃	1	2	yes	—
850	#103	C₂³×C₅₃	1	1	yes	characteristic
851	#103	C₂³×C₅₃	1	1	yes	characteristic
852	#103	C₂³×C₅₃	1	2	yes	—
853	#103	C₂³×C₅₃	1	2	yes	—
854	#103	C₂³×C₅₃	1	2	yes	—
855	#102	C₂³×C₅₃	1	2	yes	—
856	#102	C₂³×C₅₃	1	2	yes	—
857	#102	C₂³×C₅₃	1	2	yes	—
858	#102	C₂³×C₅₃	1	2	yes	—
859	#102	C₂³×C₅₃	1	1	yes	characteristic
860	#102	C₂³×C₅₃	1	1	yes	characteristic
861	#102	C₂³×C₅₃	1	1	yes	characteristic
862	#102	C₂³×C₅₃	1	1	yes	characteristic
863	#102	C₂³×C₅₃	1	1	yes	characteristic
864	#102	C₂³×C₅₃	1	1	yes	characteristic
865	#102	C₂³×C₅₃	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
867	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
870	#97	C₂³×C₅₃	1	2	yes	—
871	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₅₃	1	2	yes	—
874	C₂⁴	—	2	1	no	—
875	#41	—	2	4	no	—
876	#41	—	4	2	no	—
877	#41	—	8	4	no	—
878	#41	—	8	2	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	8	2	no	—
886	C₂×Q₈	—	8	2	no	—
887	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
889	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	4	1	no	—
897	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
898	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
899	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
900	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
901	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	8	2	no	—
915	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
916	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
919	Q₁₆	—	4	2	no	—
920	SD₁₆	—	2	2	no	—
921	SD₁₆	—	4	2	no	—
922	SD₁₆	—	4	1	no	—
923	D₈	—	2	2	no	—
924	D₈	—	4	1	no	—
925	M₁₆	—	4	2	no	—
926	C₂×C₈	—	4	2	no	—
927	C₂×C₈	—	4	2	no	—
928	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
932	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	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	C₂×D₄×C₅₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
960	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
962	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
963	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
965	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
993	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
994	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1001	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1002	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1003	C₄²	C₂⁴×C₅₃	1	2	yes	—
1004	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1005	C₂³	—	2	1	no	—
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	4	2	no	—
1009	C₂³	—	4	2	no	—
1010	C₂³	—	8	1	no	—
1011	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1012	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1013	Q₈	—	2	2	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	4	2	no	—
1019	Q₈	—	8	1	no	—
1020	Q₈	—	8	2	no	—
1021	Q₈	—	8	1	no	—
1022	Q₈	—	8	2	no	—
1023	Q₈	—	8	2	no	—
1024	D₄	—	2	4	no	—
1025	D₄	—	2	2	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	2	1	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	4	4	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	8	2	no	—
1035	D₄	—	8	2	no	—
1036	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	4	4	no	—
1053	C₂×C₄	—	4	4	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	8	1	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	—	8	1	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1065	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1067	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1069	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1072	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1073	C₈	—	2	1	no	—
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	8	4	no	—
1094	C₂²	C₅₃×#577	1	2	yes	—
1095	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1096	C₄	—	2	2	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	C₅₃×#577	1	2	yes	—
1113	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1114	C₄	C₅₃×#585	1	1	yes	characteristic
1115	C₂	—	2	2	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	4	2	no	—
1118	C₂	—	8	1	no	—
1119	C₂	—	8	1	no	—
1120	C₂	C₅₃×#3489	1	1	yes	characteristic
1121	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1122	C₂	C₂×C₅₃×#577	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×#3544	C₂	semidirect
2. C₅₃×#3520	C₂	semidirect
3. C₅₃×#3384	C₂	semidirect
4. Q₈×SD₁₆×C₅₃	C₂	semidirect
5. C₅₃×#3369	C₂	semidirect
6. C₅₃×#3360	C₂	semidirect
7. C₅₃×#3354	C₂	semidirect
8. C₅₃×#3344	C₂	semidirect
9. C₅₃×#3335	C₂	semidirect
10. C₅₃×#3335	C₂	semidirect
11. C₅₃×#3331	C₂	semidirect
12. C₅₃×#3306	C₂	semidirect
13. C₅₃×#3303	C₂	semidirect
14. C₅₃×#3296	C₂	semidirect
15. C₅₃×#3263	C₂	semidirect
16. C₅₃×#3248	C₂	semidirect
17. C₅₃×#3244	C₂	semidirect
18. C₅₃×#3229	C₂	semidirect
19. C₅₃×#3125	C₂	semidirect
20. C₅₃×#3105	C₂	semidirect
21. C₅₃×#3084	C₂	semidirect
22. C₂×C₅₃×#476	C₂	semidirect
23. C₅₃×#2994	C₂	semidirect
25. Q₈²×C₅₃	C₂²	semidirect
27. C₅₃×#555	C₂²	semidirect
29. C₅₃×#554	C₂²	semidirect
30. C₅₃×#554	C₂²	semidirect
43. C₅₃×#544	C₂²	semidirect
46. C₅₃×#542	C₂²	semidirect
57. C₅₃×#501	C₂²	semidirect
58. C₅₃×#498	C₂²	semidirect
59. C₅₃×#498	C₂²	semidirect
60. C₅₃×#498	C₂²	semidirect
63. C₅₃×#487	C₂²	semidirect
64. C₅₃×#487	C₂²	semidirect
65. C₅₃×#485	C₂²	semidirect
69. C₅₃×#483	C₂²	semidirect
70. C₅₃×#483	C₂²	semidirect
74. C₅₃×#481	C₂²	semidirect
75. C₅₃×#479	C₂²	semidirect
76. C₅₃×#479	C₂²	semidirect
87. C₅₃×#476	C₂²	semidirect
88. C₅₃×#475	C₂²	semidirect
89. C₅₃×#475	C₂²	semidirect
90. C₅₃×#475	C₂²	semidirect
91. C₅₃×#475	C₂²	semidirect
92. C₅₃×#475	C₂²	semidirect
93. C₅₃×#474	C₂²	semidirect
94. C₅₃×#470	C₂²	semidirect
99. C₅₃×#465	C₂²	semidirect
101. C₅₃×#464	C₂²	semidirect
105. C₅₃×#462	C₂²	semidirect
106. C₅₃×#461	C₂²	semidirect
111. C₅₃×#446	C₂²	semidirect
112. C₈×Q₈×C₅₃	C₂²	semidirect
114. C₅₃×#441	C₂²	semidirect
118. C₄×SD₁₆×C₅₃	C₂²	semidirect
121. C₅₃×#436	C₂²	semidirect
124. C₈×D₄×C₅₃	C₂²	semidirect
125. C₅₃×#433	C₂²	semidirect
127. C₅₃×#428	C₂²	semidirect
129. C₂×#106×C₅₃	C₂²	semidirect
130. C₅₃×#424	C₂²	semidirect
517. #62202	C₅₃	direct (N × H)
554. #3544	C₂×C₅₃	semidirect
555. #3520	C₂×C₅₃	semidirect
556. #3384	C₂×C₅₃	semidirect
557. Q₈×SD₁₆	C₂×C₅₃	semidirect
558. #3369	C₂×C₅₃	semidirect
559. #3360	C₂×C₅₃	semidirect
560. #3354	C₂×C₅₃	semidirect
561. #3344	C₂×C₅₃	semidirect
562. #3335	C₂×C₅₃	semidirect
563. #3335	C₂×C₅₃	semidirect
564. #3331	C₂×C₅₃	semidirect
565. #3306	C₂×C₅₃	semidirect
566. #3303	C₂×C₅₃	semidirect
567. #3296	C₂×C₅₃	semidirect
568. #3263	C₂×C₅₃	semidirect
569. #3248	C₂×C₅₃	semidirect
570. #3244	C₂×C₅₃	semidirect
571. #3229	C₂×C₅₃	semidirect
572. #3125	C₂×C₅₃	semidirect
573. #3105	C₂×C₅₃	semidirect
574. #3084	C₂×C₅₃	semidirect
575. C₂×#476	C₂×C₅₃	semidirect
576. #2994	C₂×C₅₃	semidirect
586. Q₈²	C₂²×C₅₃	semidirect
588. #555	C₂²×C₅₃	semidirect
590. #554	C₂²×C₅₃	semidirect
591. #554	C₂²×C₅₃	semidirect
604. #544	C₂²×C₅₃	semidirect
607. #542	C₂²×C₅₃	semidirect
618. #501	C₂²×C₅₃	semidirect
619. #498	C₂²×C₅₃	semidirect
620. #498	C₂²×C₅₃	semidirect
621. #498	C₂²×C₅₃	semidirect
624. #487	C₂²×C₅₃	semidirect
625. #487	C₂²×C₅₃	semidirect
626. #485	C₂²×C₅₃	semidirect
630. #483	C₂²×C₅₃	semidirect
631. #483	C₂²×C₅₃	semidirect
635. #481	C₂²×C₅₃	semidirect
636. #479	C₂²×C₅₃	semidirect
637. #479	C₂²×C₅₃	semidirect
648. #476	C₂²×C₅₃	semidirect
649. #475	C₂²×C₅₃	semidirect
650. #475	C₂²×C₅₃	semidirect
651. #475	C₂²×C₅₃	semidirect
652. #475	C₂²×C₅₃	semidirect
653. #475	C₂²×C₅₃	semidirect
654. #474	C₂²×C₅₃	semidirect
655. #470	C₂²×C₅₃	semidirect
660. #465	C₂²×C₅₃	semidirect
662. #464	C₂²×C₅₃	semidirect
666. #462	C₂²×C₅₃	semidirect
667. #461	C₂²×C₅₃	semidirect
672. #446	C₂²×C₅₃	semidirect
673. C₈×Q₈	C₂²×C₅₃	semidirect
675. #441	C₂²×C₅₃	semidirect
679. C₄×SD₁₆	C₂²×C₅₃	semidirect
682. #436	C₂²×C₅₃	semidirect
685. C₈×D₄	C₂²×C₅₃	semidirect
686. #433	C₂²×C₅₃	semidirect
688. #428	C₂²×C₅₃	semidirect
690. C₂×#106	C₂²×C₅₃	semidirect
691. #424	C₂²×C₅₃	semidirect
696. C₅₃	#62202	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×#3544	2
C₅₃×#3520	2
C₅₃×#3384	2
Q₈×SD₁₆×C₅₃	2
C₅₃×#3369	2
C₅₃×#3360	2
C₅₃×#3354	2
C₅₃×#3344	2
C₅₃×#3335	2
C₅₃×#3331	2
C₅₃×#3306	2
C₅₃×#3303	2
C₅₃×#3296	2
C₅₃×#3263	2
C₅₃×#3248	2
C₅₃×#3244	2
C₅₃×#3229	2
C₅₃×#3125	2
C₅₃×#3105	2
C₅₃×#3084	2
C₂×C₅₃×#476	2
C₅₃×#2994	2
#62202	53

Subgroups — C53×#62202 #27269714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62202 #27269714