Subgroups — C₅₃×#60890 #27268402

Order 13568.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3460	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3244	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3243	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3241	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3241	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3240	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3234	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3232	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3228	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#557	—	2	1	no	—
25	C₅₃×#557	—	2	1	no	—
26	C₅₃×#554	—	2	2	no	—
27	C₅₃×#554	—	2	2	no	—
28	C₅₃×#554	—	2	1	no	—
29	C₅₃×#554	—	2	1	no	—
30	C₅₃×#544	C₂²	1	1	yes	characteristic
31	C₅₃×#544	C₂²	1	1	yes	characteristic
32	C₅₃×#544	C₂²	1	1	yes	characteristic
33	C₅₃×#544	C₂²	1	2	yes	complemented
34	C₅₃×#544	C₂²	1	2	yes	complemented
35	C₅₃×#542	—	2	1	no	—
36	C₅₃×#542	C₂²	1	2	yes	—
37	C₅₃×#540	—	2	1	no	—
38	C₅₃×#540	C₂²	1	2	yes	—
39	C₅₃×#538	—	2	2	no	—
40	C₅₃×#537	C₂²	1	1	yes	characteristic
41	C₅₃×#535	C₂²	1	1	yes	characteristic
42	C₅₃×#535	C₂²	1	1	yes	characteristic
43	C₅₃×#533	C₂²	1	1	yes	characteristic
44	C₅₃×#533	C₂²	1	2	yes	complemented
45	C₅₃×#532	—	2	1	no	—
46	C₅₃×#532	C₂²	1	2	yes	—
47	C₅₃×#529	—	2	1	no	—
48	C₅₃×#529	C₂²	1	2	yes	—
49	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
51	C₅₃×#525	—	2	2	no	—
52	C₅₃×#520	C₂²	1	1	yes	characteristic
53	C₅₃×#520	C₂²	1	1	yes	characteristic
54	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
55	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#501	C₂²	1	2	yes	complemented
58	C₅₃×#501	C₂²	1	2	yes	complemented
59	C₅₃×#501	C₂²	1	2	yes	complemented
60	C₅₃×#501	C₂²	1	2	yes	complemented
61	C₅₃×#500	C₂²	1	2	yes	complemented
62	C₅₃×#499	C₂²	1	2	yes	complemented
63	C₅₃×#499	C₂²	1	2	yes	complemented
64	C₅₃×#498	C₂²	1	2	yes	complemented
65	C₅₃×#490	C₂²	1	2	yes	—
66	C₅₃×#490	C₂²	1	2	yes	—
67	C₅₃×#489	C₂²	1	2	yes	—
68	C₅₃×#489	C₂²	1	2	yes	—
69	C₅₃×#488	C₂²	1	2	yes	—
70	C₅₃×#488	C₂²	1	2	yes	—
71	C₅₃×#486	C₂²	1	2	yes	—
72	C₅₃×#486	C₂²	1	2	yes	—
73	C₅₃×#485	C₂²	1	2	yes	complemented
74	C₅₃×#485	C₂²	1	2	yes	complemented
75	C₅₃×#484	C₂²	1	2	yes	complemented
76	C₅₃×#483	C₂²	1	2	yes	complemented
77	C₅₃×#482	C₂²	1	2	yes	—
78	C₅₃×#482	C₂²	1	2	yes	—
79	C₅₃×#482	C₂²	1	2	yes	—
80	C₅₃×#482	C₂²	1	2	yes	—
81	C₅₃×#482	C₂²	1	2	yes	complemented
82	C₅₃×#482	C₂²	1	2	yes	complemented
83	C₅₃×#481	C₂²	1	2	yes	—
84	C₅₃×#481	C₂²	1	2	yes	—
85	C₅₃×#481	C₂²	1	2	yes	complemented
86	C₅₃×#480	C₂²	1	2	yes	—
87	C₅₃×#480	C₂²	1	2	yes	—
88	C₅₃×#480	C₂²	1	2	yes	complemented
89	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#479	C₂²	1	2	yes	complemented
91	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#479	C₂²	1	2	yes	complemented
93	C₅₃×#478	C₂²	1	2	yes	—
94	C₅₃×#478	C₂²	1	2	yes	—
95	C₅₃×#478	C₂²	1	2	yes	—
96	C₅₃×#478	C₂²	1	2	yes	—
97	C₅₃×#478	C₂²	1	2	yes	—
98	C₅₃×#478	C₂²	1	2	yes	—
99	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#478	C₂²	1	2	yes	complemented
101	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#478	C₂²	1	2	yes	complemented
103	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#476	C₂²	1	2	yes	—
105	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#474	C₂²	1	2	yes	—
108	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#433	C₂²	1	2	yes	complemented
110	C₅₃×#433	C₂²	1	2	yes	complemented
111	C₅₃×#432	C₂²	1	2	yes	complemented
112	C₅₃×#431	C₂²	1	2	yes	complemented
113	C₅₃×#428	C₂²	1	1	yes	characteristic
114	C₅₃×#428	C₂²	1	1	yes	characteristic
115	C₅₃×#428	C₂²	1	1	yes	characteristic
116	C₅₃×#428	C₂²	1	1	yes	characteristic
117	C₅₃×#427	C₂²	1	1	yes	characteristic
118	C₅₃×#427	C₂²	1	1	yes	characteristic
119	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
120	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
121	C₅₃×#423	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
123	C₅₃×#418	C₂²	1	1	yes	characteristic
124	C₅₃×#418	C₂²	1	1	yes	characteristic
125	C₅₃×#417	C₂²	1	1	yes	characteristic
126	C₅₃×#417	C₂²	1	1	yes	characteristic
127	C₅₃×#416	C₂²	1	1	yes	characteristic
128	C₅₃×#416	C₂²	1	1	yes	characteristic
129	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
130	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
131	C₅₃×#408	C₂²	1	1	yes	characteristic
132	C₅₃×#408	C₂²	1	1	yes	characteristic
133	C₅₃×#405	C₂²	1	1	yes	characteristic
134	C₅₃×#405	C₂²	1	1	yes	characteristic
135	C₂×#41×C₅₃	—	2	2	no	—
136	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
137	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅₃	—	2	1	no	—
140	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈×C₅₃	—	2	1	no	—
145	C₄⋊Q₈×C₅₃	—	2	1	no	—
146	C₄⋊Q₈×C₅₃	—	2	1	no	—
147	C₄⋊Q₈×C₅₃	—	2	2	no	—
148	C₄⋊Q₈×C₅₃	—	2	2	no	—
149	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
150	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
151	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
154	#127×C₅₃	—	2	1	no	—
155	#127×C₅₃	C₂³	1	2	yes	—
156	#126×C₅₃	—	2	2	no	—
157	#126×C₅₃	—	2	2	no	—
158	#125×C₅₃	—	2	1	no	—
159	#125×C₅₃	—	2	1	no	—
160	#125×C₅₃	—	2	1	no	—
161	#125×C₅₃	—	2	2	no	—
162	#125×C₅₃	—	2	2	no	—
163	#125×C₅₃	—	2	1	no	—
164	#125×C₅₃	—	2	1	no	—
165	#125×C₅₃	—	2	2	no	—
166	#125×C₅₃	—	2	2	no	—
167	#125×C₅₃	C₂³	1	2	yes	—
168	#125×C₅₃	C₂³	1	2	yes	—
169	#125×C₅₃	C₂³	1	2	yes	—
170	#125×C₅₃	C₂³	1	2	yes	—
171	#125×C₅₃	C₂³	1	2	yes	—
172	#125×C₅₃	C₂³	1	1	yes	characteristic
173	#125×C₅₃	C₂³	1	1	yes	characteristic
174	#124×C₅₃	—	2	2	no	—
175	#124×C₅₃	—	2	2	no	—
176	#124×C₅₃	—	2	1	no	—
177	#124×C₅₃	C₂³	1	2	yes	—
178	#123×C₅₃	—	2	2	no	—
179	#123×C₅₃	—	2	2	no	—
180	#123×C₅₃	—	2	2	no	—
181	#123×C₅₃	—	2	2	no	—
182	C₂²⋊Q₈×C₅₃	—	2	2	no	—
183	C₂²⋊Q₈×C₅₃	—	2	2	no	—
184	C₂²⋊Q₈×C₅₃	—	2	2	no	—
185	C₂²⋊Q₈×C₅₃	—	2	2	no	—
186	C₂²⋊Q₈×C₅₃	—	2	2	no	—
187	C₂²⋊Q₈×C₅₃	—	2	2	no	—
188	C₂²⋊Q₈×C₅₃	—	2	2	no	—
189	C₂²⋊Q₈×C₅₃	—	2	2	no	—
190	C₂²⋊Q₈×C₅₃	—	2	1	no	—
191	C₂²⋊Q₈×C₅₃	—	2	1	no	—
192	C₂²⋊Q₈×C₅₃	—	2	1	no	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	2	no	—
195	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
196	#121×C₅₃	—	2	1	no	—
197	#121×C₅₃	—	2	1	no	—
198	#121×C₅₃	—	2	2	no	—
199	#121×C₅₃	—	2	2	no	—
200	#121×C₅₃	—	2	2	no	—
201	#121×C₅₃	—	2	1	no	—
202	#121×C₅₃	—	2	2	no	—
203	#121×C₅₃	C₂³	1	2	yes	—
204	#121×C₅₃	C₂³	1	2	yes	—
205	#121×C₅₃	C₂³	1	2	yes	—
206	#120×C₅₃	—	2	2	no	—
207	#120×C₅₃	—	2	2	no	—
208	C₄×Q₈×C₅₃	—	2	1	no	—
209	C₄×Q₈×C₅₃	—	2	1	no	—
210	C₄×Q₈×C₅₃	—	2	2	no	—
211	C₄×Q₈×C₅₃	—	2	2	no	—
212	C₄×Q₈×C₅₃	—	2	1	no	—
213	C₄×Q₈×C₅₃	—	2	1	no	—
214	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
215	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₅₃	—	2	1	no	—
219	C₄×D₄×C₅₃	—	2	1	no	—
220	C₄×D₄×C₅₃	—	2	2	no	—
221	C₄×D₄×C₅₃	—	2	2	no	—
222	C₄×D₄×C₅₃	—	2	2	no	—
223	C₄×D₄×C₅₃	—	2	1	no	—
224	C₄×D₄×C₅₃	—	2	1	no	—
225	C₄×D₄×C₅₃	—	2	1	no	—
226	C₄×D₄×C₅₃	—	2	1	no	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	D₄	1	2	yes	—
229	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
230	C₄×D₄×C₅₃	D₄	1	2	yes	—
231	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
232	C₄×D₄×C₅₃	C₂³	1	2	yes	—
233	C₄×D₄×C₅₃	C₂³	1	2	yes	—
234	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
236	#117×C₅₃	—	2	1	no	—
237	#117×C₅₃	—	2	2	no	—
238	#117×C₅₃	C₂³	1	2	yes	—
239	#117×C₅₃	C₂³	1	2	yes	—
240	#117×C₅₃	C₂³	1	1	yes	characteristic
241	#117×C₅₃	C₂³	1	1	yes	characteristic
242	#117×C₅₃	C₂³	1	1	yes	characteristic
243	#117×C₅₃	C₂³	1	1	yes	characteristic
244	#117×C₅₃	C₂³	1	2	yes	—
245	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
246	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
247	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
248	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
249	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
254	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
255	C₂×C₄²×C₅₃	—	2	1	no	—
256	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
258	#107×C₅₃	C₂³	1	2	yes	—
259	#107×C₅₃	C₂³	1	2	yes	—
260	#107×C₅₃	C₂³	1	1	yes	characteristic
261	#107×C₅₃	C₂³	1	2	yes	—
262	#107×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
267	#107×C₅₃	C₂³	1	1	yes	characteristic
268	#106×C₅₃	C₂³	1	2	yes	—
269	#106×C₅₃	C₂³	1	2	yes	—
270	#106×C₅₃	C₂³	1	1	yes	characteristic
271	#106×C₅₃	C₂³	1	2	yes	—
272	#106×C₅₃	C₂³	1	2	yes	—
273	#106×C₅₃	C₂³	1	1	yes	characteristic
274	#106×C₅₃	C₂³	1	2	yes	—
275	#106×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	1	yes	characteristic
277	#106×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
284	#103×C₅₃	C₂³	1	1	yes	characteristic
285	#103×C₅₃	C₂³	1	1	yes	characteristic
286	#103×C₅₃	C₂³	1	2	yes	—
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	1	yes	characteristic
289	#103×C₅₃	C₂³	1	1	yes	characteristic
290	#102×C₅₃	C₂³	1	1	yes	characteristic
291	#102×C₅₃	C₂³	1	1	yes	characteristic
292	#102×C₅₃	C₂³	1	2	yes	—
293	#102×C₅₃	C₂³	1	2	yes	—
294	#102×C₅₃	C₂³	1	2	yes	—
295	#102×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
300	#102×C₅₃	C₂³	1	2	yes	—
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	#97×C₅₃	C₂³	1	2	yes	—
310	C₄×C₈×C₅₃	C₂³	1	2	yes	—
311	C₄×C₈×C₅₃	C₂³	1	2	yes	—
312	C₂⁴×C₅₃	—	2	1	no	—
313	#41×C₅₃	—	2	2	no	—
314	#41×C₅₃	—	2	2	no	—
315	#41×C₅₃	—	2	2	no	—
316	#41×C₅₃	—	2	2	no	—
317	#41×C₅₃	—	8	4	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	—	2	2	no	—
323	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₅₃	—	2	1	no	—
326	C₂×D₄×C₅₃	—	2	2	no	—
327	C₂×D₄×C₅₃	—	2	2	no	—
328	C₂×D₄×C₅₃	—	2	2	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	2	no	—
334	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
337	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅₃	—	2	1	no	—
339	C₂²×C₄×C₅₃	—	2	2	no	—
340	C₂²×C₄×C₅₃	—	2	2	no	—
341	C₂²×C₄×C₅₃	—	2	1	no	—
342	C₂²×C₄×C₅₃	—	2	1	no	—
343	C₂²×C₄×C₅₃	—	2	1	no	—
344	C₂²×C₄×C₅₃	—	2	1	no	—
345	C₂²×C₄×C₅₃	—	2	2	no	—
346	C₂²×C₄×C₅₃	—	2	1	no	—
347	C₂²×C₄×C₅₃	—	2	2	no	—
348	C₂²×C₄×C₅₃	—	8	2	no	—
349	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
352	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
353	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
355	M₁₆×C₅₃	—	2	2	no	—
356	M₁₆×C₅₃	—	2	2	no	—
357	C₂×C₈×C₅₃	—	2	2	no	—
358	C₂×C₈×C₅₃	—	2	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	2	yes	—
363	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
369	C₄⋊C₄×C₅₃	—	2	2	no	—
370	C₄⋊C₄×C₅₃	—	2	2	no	—
371	C₄⋊C₄×C₅₃	—	2	2	no	—
372	C₄⋊C₄×C₅₃	—	2	2	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	1	no	—
376	C₄⋊C₄×C₅₃	—	2	2	no	—
377	C₄⋊C₄×C₅₃	—	2	2	no	—
378	C₄⋊C₄×C₅₃	—	2	1	no	—
379	C₄⋊C₄×C₅₃	—	2	1	no	—
380	C₄⋊C₄×C₅₃	—	2	1	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	2	no	—
392	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
396	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
397	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²⋊C₄×C₅₃	—	2	1	no	—
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	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	1	no	—
414	C₂²⋊C₄×C₅₃	—	2	1	no	—
415	C₂²⋊C₄×C₅₃	—	2	2	no	—
416	C₂²⋊C₄×C₅₃	—	2	2	no	—
417	C₂²⋊C₄×C₅₃	—	2	2	no	—
418	C₂²⋊C₄×C₅₃	—	2	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
421	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
423	C₄²×C₅₃	—	2	1	no	—
424	C₄²×C₅₃	—	2	1	no	—
425	C₄²×C₅₃	—	2	1	no	—
426	C₄²×C₅₃	—	2	2	no	—
427	C₄²×C₅₃	—	2	2	no	—
428	C₄²×C₅₃	—	2	1	no	—
429	C₄²×C₅₃	—	2	1	no	—
430	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₅₃	C₂×D₄	1	2	yes	—
432	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
433	C₄²×C₅₃	C₂×D₄	1	2	yes	—
434	C₄²×C₅₃	C₂⁴	1	2	yes	—
435	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
436	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
437	C₂³×C₅₃	—	2	1	no	—
438	C₂³×C₅₃	—	2	2	no	—
439	C₂³×C₅₃	—	4	2	no	—
440	C₂³×C₅₃	—	8	1	no	—
441	C₂³×C₅₃	—	8	1	no	—
442	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
443	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
444	Q₈×C₅₃	—	2	2	no	—
445	Q₈×C₅₃	—	2	1	no	—
446	Q₈×C₅₃	—	2	1	no	—
447	Q₈×C₅₃	—	8	1	no	—
448	Q₈×C₅₃	—	8	2	no	—
449	Q₈×C₅₃	—	8	1	no	—
450	Q₈×C₅₃	—	8	2	no	—
451	Q₈×C₅₃	—	8	2	no	—
452	D₄×C₅₃	—	2	4	no	—
453	D₄×C₅₃	—	2	2	no	—
454	D₄×C₅₃	—	2	2	no	—
455	D₄×C₅₃	—	2	2	no	—
456	D₄×C₅₃	—	2	1	no	—
457	D₄×C₅₃	—	2	1	no	—
458	D₄×C₅₃	—	4	2	no	—
459	D₄×C₅₃	—	4	2	no	—
460	D₄×C₅₃	—	8	2	no	—
461	D₄×C₅₃	—	8	2	no	—
462	D₄×C₅₃	—	8	2	no	—
463	D₄×C₅₃	—	8	2	no	—
464	D₄×C₅₃	—	8	2	no	—
465	C₂×C₄×C₅₃	—	2	2	no	—
466	C₂×C₄×C₅₃	—	2	2	no	—
467	C₂×C₄×C₅₃	—	2	2	no	—
468	C₂×C₄×C₅₃	—	2	1	no	—
469	C₂×C₄×C₅₃	—	2	2	no	—
470	C₂×C₄×C₅₃	—	2	1	no	—
471	C₂×C₄×C₅₃	—	2	2	no	—
472	C₂×C₄×C₅₃	—	2	1	no	—
473	C₂×C₄×C₅₃	—	2	1	no	—
474	C₂×C₄×C₅₃	—	2	1	no	—
475	C₂×C₄×C₅₃	—	2	1	no	—
476	C₂×C₄×C₅₃	—	2	1	no	—
477	C₂×C₄×C₅₃	—	4	1	no	—
478	C₂×C₄×C₅₃	—	4	1	no	—
479	C₂×C₄×C₅₃	—	4	2	no	—
480	C₂×C₄×C₅₃	—	4	2	no	—
481	C₂×C₄×C₅₃	—	4	4	no	—
482	C₂×C₄×C₅₃	—	4	2	no	—
483	C₂×C₄×C₅₃	—	4	2	no	—
484	C₂×C₄×C₅₃	—	8	1	no	—
485	C₂×C₄×C₅₃	—	8	2	no	—
486	C₂×C₄×C₅₃	—	8	1	no	—
487	C₂×C₄×C₅₃	—	8	2	no	—
488	C₂×C₄×C₅₃	—	8	1	no	—
489	C₂×C₄×C₅₃	—	8	2	no	—
490	C₂×C₄×C₅₃	—	8	1	no	—
491	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
500	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
501	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
502	C₈×C₅₃	—	2	1	no	—
503	C₈×C₅₃	—	2	1	no	—
504	C₈×C₅₃	—	2	1	no	—
505	C₈×C₅₃	—	2	1	no	—
506	C₈×C₅₃	—	2	2	no	—
507	C₈×C₅₃	—	2	2	no	—
508	#60890	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
509	C₂²×C₅₃	—	2	1	no	—
510	C₂²×C₅₃	—	2	1	no	—
511	C₂²×C₅₃	—	2	2	no	—
512	C₂²×C₅₃	—	2	2	no	—
513	C₂²×C₅₃	—	2	2	no	—
514	C₂²×C₅₃	—	4	1	no	—
515	C₂²×C₅₃	—	4	2	no	—
516	C₂²×C₅₃	—	4	2	no	—
517	C₂²×C₅₃	—	4	1	no	—
518	C₂²×C₅₃	—	4	1	no	—
519	C₂²×C₅₃	—	4	2	no	—
520	C₂²×C₅₃	—	8	4	no	—
521	C₂²×C₅₃	#536	1	2	yes	—
522	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
523	C₄×C₅₃	—	2	1	no	—
524	C₄×C₅₃	—	2	1	no	—
525	C₄×C₅₃	—	2	2	no	—
526	C₄×C₅₃	—	2	1	no	—
527	C₄×C₅₃	—	2	1	no	—
528	C₄×C₅₃	—	2	2	no	—
529	C₄×C₅₃	—	2	2	no	—
530	C₄×C₅₃	—	4	2	no	—
531	C₄×C₅₃	—	4	1	no	—
532	C₄×C₅₃	—	4	1	no	—
533	C₄×C₅₃	—	4	1	no	—
534	C₄×C₅₃	—	4	2	no	—
535	C₄×C₅₃	—	4	1	no	—
536	C₄×C₅₃	—	4	2	no	—
537	C₄×C₅₃	—	4	1	no	—
538	C₄×C₅₃	—	4	1	no	—
539	C₄×C₅₃	—	4	1	no	—
540	C₄×C₅₃	#536	1	2	yes	—
541	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
542	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
543	#3504	C₂×C₅₃	1	1	yes	characteristic, complemented
544	#3460	C₂×C₅₃	1	1	yes	characteristic
545	#3244	C₂×C₅₃	1	2	yes	complemented
546	#3243	C₂×C₅₃	1	2	yes	complemented
547	#3241	C₂×C₅₃	1	2	yes	complemented
548	#3241	C₂×C₅₃	1	2	yes	complemented
549	#3240	C₂×C₅₃	1	2	yes	complemented
550	#3234	C₂×C₅₃	1	2	yes	complemented
551	#3232	C₂×C₅₃	1	2	yes	complemented
552	#3228	C₂×C₅₃	1	2	yes	complemented
553	#3164	C₂×C₅₃	1	1	yes	characteristic, complemented
554	#3163	C₂×C₅₃	1	1	yes	characteristic, complemented
555	#3136	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#3136	C₂×C₅₃	1	1	yes	characteristic, complemented
557	#3099	C₂×C₅₃	1	1	yes	characteristic, complemented
558	#3098	C₂×C₅₃	1	1	yes	characteristic, complemented
559	#3096	C₂×C₅₃	1	1	yes	characteristic, complemented
560	#3096	C₂×C₅₃	1	1	yes	characteristic, complemented
561	#3080	C₂×C₅₃	1	1	yes	characteristic, complemented
562	#3077	C₂×C₅₃	1	1	yes	characteristic, complemented
563	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
564	C₂×#478	C₂×C₅₃	1	1	yes	characteristic, complemented
565	#2925	C₂×C₅₃	1	1	yes	characteristic, complemented
566	C₂×C₅₃	—	2	2	no	—
567	C₂×C₅₃	—	4	2	no	—
568	C₂×C₅₃	—	8	1	no	—
569	C₂×C₅₃	—	8	2	no	—
570	C₂×C₅₃	C₂×#536	1	1	yes	characteristic
571	C₂×C₅₃	#3584	1	1	yes	characteristic
572	C₂×C₅₃	#3585	1	1	yes	characteristic
573	#557	—	2	1	no	—
574	#557	—	2	1	no	—
575	#554	—	2	2	no	—
576	#554	—	2	2	no	—
577	#554	—	2	1	no	—
578	#554	—	2	1	no	—
579	#544	C₂²×C₅₃	1	1	yes	characteristic
580	#544	C₂²×C₅₃	1	1	yes	characteristic
581	#544	C₂²×C₅₃	1	1	yes	characteristic
582	#544	C₂²×C₅₃	1	2	yes	complemented
583	#544	C₂²×C₅₃	1	2	yes	complemented
584	#542	—	2	1	no	—
585	#542	C₂²×C₅₃	1	2	yes	—
586	#540	—	2	1	no	—
587	#540	C₂²×C₅₃	1	2	yes	—
588	#538	—	2	2	no	—
589	#537	C₂²×C₅₃	1	1	yes	characteristic
590	#535	C₂²×C₅₃	1	1	yes	characteristic
591	#535	C₂²×C₅₃	1	1	yes	characteristic
592	#533	C₂²×C₅₃	1	1	yes	characteristic
593	#533	C₂²×C₅₃	1	2	yes	complemented
594	#532	—	2	1	no	—
595	#532	C₂²×C₅₃	1	2	yes	—
596	#529	—	2	1	no	—
597	#529	C₂²×C₅₃	1	2	yes	—
598	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
599	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
600	#525	—	2	2	no	—
601	#520	C₂²×C₅₃	1	1	yes	characteristic
602	#520	C₂²×C₅₃	1	1	yes	characteristic
603	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
604	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
605	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
606	#501	C₂²×C₅₃	1	2	yes	complemented
607	#501	C₂²×C₅₃	1	2	yes	complemented
608	#501	C₂²×C₅₃	1	2	yes	complemented
609	#501	C₂²×C₅₃	1	2	yes	complemented
610	#500	C₂²×C₅₃	1	2	yes	complemented
611	#499	C₂²×C₅₃	1	2	yes	complemented
612	#499	C₂²×C₅₃	1	2	yes	complemented
613	#498	C₂²×C₅₃	1	2	yes	complemented
614	#490	C₂²×C₅₃	1	2	yes	—
615	#490	C₂²×C₅₃	1	2	yes	—
616	#489	C₂²×C₅₃	1	2	yes	—
617	#489	C₂²×C₅₃	1	2	yes	—
618	#488	C₂²×C₅₃	1	2	yes	—
619	#488	C₂²×C₅₃	1	2	yes	—
620	#486	C₂²×C₅₃	1	2	yes	—
621	#486	C₂²×C₅₃	1	2	yes	—
622	#485	C₂²×C₅₃	1	2	yes	complemented
623	#485	C₂²×C₅₃	1	2	yes	complemented
624	#484	C₂²×C₅₃	1	2	yes	complemented
625	#483	C₂²×C₅₃	1	2	yes	complemented
626	#482	C₂²×C₅₃	1	2	yes	—
627	#482	C₂²×C₅₃	1	2	yes	—
628	#482	C₂²×C₅₃	1	2	yes	—
629	#482	C₂²×C₅₃	1	2	yes	—
630	#482	C₂²×C₅₃	1	2	yes	complemented
631	#482	C₂²×C₅₃	1	2	yes	complemented
632	#481	C₂²×C₅₃	1	2	yes	—
633	#481	C₂²×C₅₃	1	2	yes	—
634	#481	C₂²×C₅₃	1	2	yes	complemented
635	#480	C₂²×C₅₃	1	2	yes	—
636	#480	C₂²×C₅₃	1	2	yes	—
637	#480	C₂²×C₅₃	1	2	yes	complemented
638	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
639	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
640	#479	C₂²×C₅₃	1	2	yes	complemented
641	#479	C₂²×C₅₃	1	2	yes	complemented
642	#478	C₂²×C₅₃	1	2	yes	—
643	#478	C₂²×C₅₃	1	2	yes	—
644	#478	C₂²×C₅₃	1	2	yes	—
645	#478	C₂²×C₅₃	1	2	yes	—
646	#478	C₂²×C₅₃	1	2	yes	—
647	#478	C₂²×C₅₃	1	2	yes	—
648	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
649	#478	C₂²×C₅₃	1	1	yes	characteristic, 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	#476	C₂²×C₅₃	1	2	yes	—
654	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
655	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	#474	C₂²×C₅₃	1	2	yes	—
657	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
658	#433	C₂²×C₅₃	1	2	yes	complemented
659	#433	C₂²×C₅₃	1	2	yes	complemented
660	#432	C₂²×C₅₃	1	2	yes	complemented
661	#431	C₂²×C₅₃	1	2	yes	complemented
662	#428	C₂²×C₅₃	1	1	yes	characteristic
663	#428	C₂²×C₅₃	1	1	yes	characteristic
664	#428	C₂²×C₅₃	1	1	yes	characteristic
665	#428	C₂²×C₅₃	1	1	yes	characteristic
666	#427	C₂²×C₅₃	1	1	yes	characteristic
667	#427	C₂²×C₅₃	1	1	yes	characteristic
668	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
669	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
670	#423	C₂²×C₅₃	1	1	yes	characteristic
671	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
672	#418	C₂²×C₅₃	1	1	yes	characteristic
673	#418	C₂²×C₅₃	1	1	yes	characteristic
674	#417	C₂²×C₅₃	1	1	yes	characteristic
675	#417	C₂²×C₅₃	1	1	yes	characteristic
676	#416	C₂²×C₅₃	1	1	yes	characteristic
677	#416	C₂²×C₅₃	1	1	yes	characteristic
678	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
679	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
680	#408	C₂²×C₅₃	1	1	yes	characteristic
681	#408	C₂²×C₅₃	1	1	yes	characteristic
682	#405	C₂²×C₅₃	1	1	yes	characteristic
683	#405	C₂²×C₅₃	1	1	yes	characteristic
684	C₅₃	#60890	1	1	yes	characteristic, direct product factor, Sylow
685	C₂×#41	—	2	2	no	—
686	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
687	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
688	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
689	C₂³×C₄	—	2	1	no	—
690	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
691	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
692	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
693	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	—	2	1	no	—
696	C₄⋊Q₈	—	2	1	no	—
697	C₄⋊Q₈	—	2	2	no	—
698	C₄⋊Q₈	—	2	2	no	—
699	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
700	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
703	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
704	#127	—	2	1	no	—
705	#127	C₂³×C₅₃	1	2	yes	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#125	—	2	1	no	—
709	#125	—	2	1	no	—
710	#125	—	2	1	no	—
711	#125	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	—	2	1	no	—
714	#125	—	2	1	no	—
715	#125	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	C₂³×C₅₃	1	2	yes	—
718	#125	C₂³×C₅₃	1	2	yes	—
719	#125	C₂³×C₅₃	1	1	yes	characteristic
720	#125	C₂³×C₅₃	1	2	yes	—
721	#125	C₂³×C₅₃	1	2	yes	—
722	#125	C₂³×C₅₃	1	2	yes	—
723	#125	C₂³×C₅₃	1	1	yes	characteristic
724	#124	—	2	1	no	—
725	#124	—	2	2	no	—
726	#124	—	2	2	no	—
727	#124	C₂³×C₅₃	1	2	yes	—
728	#123	—	2	2	no	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	—	2	2	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	1	no	—
734	C₂²⋊Q₈	—	2	1	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
746	#121	—	2	2	no	—
747	#121	—	2	1	no	—
748	#121	—	2	2	no	—
749	#121	—	2	1	no	—
750	#121	—	2	1	no	—
751	#121	—	2	2	no	—
752	#121	—	2	2	no	—
753	#121	C₂³×C₅₃	1	2	yes	—
754	#121	C₂³×C₅₃	1	2	yes	—
755	#121	C₂³×C₅₃	1	2	yes	—
756	#120	—	2	2	no	—
757	#120	—	2	2	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	2	no	—
763	C₄×Q₈	—	2	2	no	—
764	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
765	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
766	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	D₄×C₅₃	1	2	yes	—
779	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
780	C₄×D₄	D₄×C₅₃	1	2	yes	—
781	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
782	C₄×D₄	C₂³×C₅₃	1	2	yes	—
783	C₄×D₄	C₂³×C₅₃	1	2	yes	—
784	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
785	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
786	#117	—	2	1	no	—
787	#117	—	2	2	no	—
788	#117	C₂³×C₅₃	1	1	yes	characteristic
789	#117	C₂³×C₅₃	1	1	yes	characteristic
790	#117	C₂³×C₅₃	1	1	yes	characteristic
791	#117	C₂³×C₅₃	1	2	yes	—
792	#117	C₂³×C₅₃	1	2	yes	—
793	#117	C₂³×C₅₃	1	1	yes	characteristic
794	#117	C₂³×C₅₃	1	2	yes	—
795	C₂×C₄⋊C₄	—	2	1	no	—
796	C₂×C₄⋊C₄	—	2	1	no	—
797	C₂×C₄⋊C₄	—	2	2	no	—
798	C₂×C₄⋊C₄	—	2	2	no	—
799	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
800	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
802	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
803	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
804	C₂×C₂²⋊C₄	—	2	1	no	—
805	C₂×C₄²	—	2	1	no	—
806	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
807	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
808	#107	C₂³×C₅₃	1	2	yes	—
809	#107	C₂³×C₅₃	1	2	yes	—
810	#107	C₂³×C₅₃	1	1	yes	characteristic
811	#107	C₂³×C₅₃	1	1	yes	characteristic
812	#107	C₂³×C₅₃	1	1	yes	characteristic
813	#107	C₂³×C₅₃	1	1	yes	characteristic
814	#107	C₂³×C₅₃	1	2	yes	—
815	#107	C₂³×C₅₃	1	2	yes	—
816	#107	C₂³×C₅₃	1	2	yes	—
817	#107	C₂³×C₅₃	1	2	yes	—
818	#106	C₂³×C₅₃	1	2	yes	—
819	#106	C₂³×C₅₃	1	2	yes	—
820	#106	C₂³×C₅₃	1	1	yes	characteristic
821	#106	C₂³×C₅₃	1	1	yes	characteristic
822	#106	C₂³×C₅₃	1	1	yes	characteristic
823	#106	C₂³×C₅₃	1	1	yes	characteristic
824	#106	C₂³×C₅₃	1	2	yes	—
825	#106	C₂³×C₅₃	1	2	yes	—
826	#106	C₂³×C₅₃	1	2	yes	—
827	#106	C₂³×C₅₃	1	2	yes	—
828	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
833	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
834	#103	C₂³×C₅₃	1	1	yes	characteristic
835	#103	C₂³×C₅₃	1	1	yes	characteristic
836	#103	C₂³×C₅₃	1	1	yes	characteristic
837	#103	C₂³×C₅₃	1	1	yes	characteristic
838	#103	C₂³×C₅₃	1	2	yes	—
839	#103	C₂³×C₅₃	1	2	yes	—
840	#102	C₂³×C₅₃	1	2	yes	—
841	#102	C₂³×C₅₃	1	2	yes	—
842	#102	C₂³×C₅₃	1	2	yes	—
843	#102	C₂³×C₅₃	1	2	yes	—
844	#102	C₂³×C₅₃	1	1	yes	characteristic
845	#102	C₂³×C₅₃	1	1	yes	characteristic
846	#102	C₂³×C₅₃	1	1	yes	characteristic
847	#102	C₂³×C₅₃	1	1	yes	characteristic
848	#102	C₂³×C₅₃	1	2	yes	—
849	#102	C₂³×C₅₃	1	2	yes	—
850	#102	C₂³×C₅₃	1	2	yes	—
851	#102	C₂³×C₅₃	1	2	yes	—
852	#102	C₂³×C₅₃	1	2	yes	—
853	#102	C₂³×C₅₃	1	2	yes	—
854	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
855	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
856	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
857	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
858	#97	C₂³×C₅₃	1	2	yes	—
859	#97	C₂³×C₅₃	1	2	yes	—
860	C₄×C₈	C₂³×C₅₃	1	2	yes	—
861	C₄×C₈	C₂³×C₅₃	1	2	yes	—
862	C₂⁴	—	2	1	no	—
863	#41	—	2	2	no	—
864	#41	—	2	2	no	—
865	#41	—	2	2	no	—
866	#41	—	2	2	no	—
867	#41	—	8	4	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	2	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	2	no	—
872	C₂×Q₈	—	2	2	no	—
873	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
874	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
885	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
886	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
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	1	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	8	2	no	—
899	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
900	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
901	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
902	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
903	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
904	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
905	M₁₆	—	2	2	no	—
906	M₁₆	—	2	2	no	—
907	C₂×C₈	—	2	2	no	—
908	C₂×C₈	—	2	2	no	—
909	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
910	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
911	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
912	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
913	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
914	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
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	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	2	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	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
943	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
944	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
946	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
949	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
950	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
951	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
953	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
954	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
971	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
972	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	1	no	—
980	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
981	C₄²	C₂×D₄×C₅₃	1	2	yes	—
982	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
983	C₄²	C₂×D₄×C₅₃	1	2	yes	—
984	C₄²	C₂⁴×C₅₃	1	2	yes	—
985	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
986	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
987	C₂³	—	2	2	no	—
988	C₂³	—	2	1	no	—
989	C₂³	—	4	2	no	—
990	C₂³	—	8	1	no	—
991	C₂³	—	8	1	no	—
992	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
993	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
994	Q₈	—	2	2	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	8	1	no	—
998	Q₈	—	8	2	no	—
999	Q₈	—	8	1	no	—
1000	Q₈	—	8	2	no	—
1001	Q₈	—	8	2	no	—
1002	D₄	—	2	4	no	—
1003	D₄	—	2	2	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	2	2	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	4	2	no	—
1009	D₄	—	4	2	no	—
1010	D₄	—	8	2	no	—
1011	D₄	—	8	2	no	—
1012	D₄	—	8	2	no	—
1013	D₄	—	8	2	no	—
1014	D₄	—	8	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	4	1	no	—
1028	C₂×C₄	—	4	1	no	—
1029	C₂×C₄	—	4	2	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	4	4	no	—
1032	C₂×C₄	—	4	2	no	—
1033	C₂×C₄	—	4	2	no	—
1034	C₂×C₄	—	8	1	no	—
1035	C₂×C₄	—	8	2	no	—
1036	C₂×C₄	—	8	1	no	—
1037	C₂×C₄	—	8	2	no	—
1038	C₂×C₄	—	8	1	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	1	no	—
1041	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1042	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1043	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1045	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1046	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1048	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1049	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1050	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1051	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1052	C₈	—	2	1	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	1	no	—
1055	C₈	—	2	1	no	—
1056	C₈	—	2	2	no	—
1057	C₈	—	2	2	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	8	4	no	—
1070	C₂²	C₅₃×#536	1	2	yes	—
1071	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1072	C₄	—	2	2	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	—	4	1	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	2	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	C₅₃×#536	1	2	yes	—
1090	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1091	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1092	C₂	—	2	2	no	—
1093	C₂	—	4	2	no	—
1094	C₂	—	8	2	no	—
1095	C₂	—	8	1	no	—
1096	C₂	C₂×C₅₃×#536	1	1	yes	characteristic
1097	C₂	C₅₃×#3584	1	1	yes	characteristic
1098	C₂	C₅₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3460	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3504	C₂	semidirect
3. C₅₃×#3244	C₂	semidirect
4. C₅₃×#3243	C₂	semidirect
5. C₅₃×#3241	C₂	semidirect
6. C₅₃×#3241	C₂	semidirect
7. C₅₃×#3240	C₂	semidirect
8. C₅₃×#3234	C₂	semidirect
9. C₅₃×#3232	C₂	semidirect
10. C₅₃×#3228	C₂	semidirect
11. C₅₃×#3164	C₂	semidirect
12. C₅₃×#3163	C₂	semidirect
13. C₅₃×#3136	C₂	semidirect
14. C₅₃×#3136	C₂	semidirect
15. C₅₃×#3099	C₂	semidirect
16. C₅₃×#3098	C₂	semidirect
17. C₅₃×#3096	C₂	semidirect
18. C₅₃×#3096	C₂	semidirect
19. C₅₃×#3080	C₂	semidirect
20. C₅₃×#3077	C₂	semidirect
21. C₅₃×#3076	C₂	semidirect
22. C₂×C₅₃×#478	C₂	semidirect
23. C₅₃×#2925	C₂	semidirect
33. C₅₃×#544	C₂²	semidirect
34. C₅₃×#544	C₂²	semidirect
44. C₅₃×#533	C₂²	semidirect
50. C₂×#125×C₅₃	C₂²	semidirect
57. C₅₃×#501	C₂²	semidirect
58. C₅₃×#501	C₂²	semidirect
59. C₅₃×#501	C₂²	semidirect
60. C₅₃×#501	C₂²	semidirect
61. C₅₃×#500	C₂²	semidirect
62. C₅₃×#499	C₂²	semidirect
63. C₅₃×#499	C₂²	semidirect
64. C₅₃×#498	C₂²	semidirect
73. C₅₃×#485	C₂²	semidirect
74. C₅₃×#485	C₂²	semidirect
75. C₅₃×#484	C₂²	semidirect
76. C₅₃×#483	C₂²	semidirect
81. C₅₃×#482	C₂²	semidirect
82. C₅₃×#482	C₂²	semidirect
85. C₅₃×#481	C₂²	semidirect
88. C₅₃×#480	C₂²	semidirect
89. C₅₃×#479	C₂²	semidirect
90. C₅₃×#479	C₂²	semidirect
91. C₅₃×#479	C₂²	semidirect
92. C₅₃×#479	C₂²	semidirect
99. C₅₃×#478	C₂²	semidirect
100. C₅₃×#478	C₂²	semidirect
101. C₅₃×#478	C₂²	semidirect
102. C₅₃×#478	C₂²	semidirect
103. C₅₃×#477	C₂²	semidirect
105. C₅₃×#476	C₂²	semidirect
106. C₅₃×#475	C₂²	semidirect
108. C₅₃×#474	C₂²	semidirect
109. C₅₃×#433	C₂²	semidirect
110. C₅₃×#433	C₂²	semidirect
111. C₅₃×#432	C₂²	semidirect
112. C₅₃×#431	C₂²	semidirect
508. #60890	C₅₃	direct (N × H)
543. #3504	C₂×C₅₃	semidirect
545. #3244	C₂×C₅₃	semidirect
546. #3243	C₂×C₅₃	semidirect
547. #3241	C₂×C₅₃	semidirect
548. #3241	C₂×C₅₃	semidirect
549. #3240	C₂×C₅₃	semidirect
550. #3234	C₂×C₅₃	semidirect
551. #3232	C₂×C₅₃	semidirect
552. #3228	C₂×C₅₃	semidirect
553. #3164	C₂×C₅₃	semidirect
554. #3163	C₂×C₅₃	semidirect
555. #3136	C₂×C₅₃	semidirect
556. #3136	C₂×C₅₃	semidirect
557. #3099	C₂×C₅₃	semidirect
558. #3098	C₂×C₅₃	semidirect
559. #3096	C₂×C₅₃	semidirect
560. #3096	C₂×C₅₃	semidirect
561. #3080	C₂×C₅₃	semidirect
562. #3077	C₂×C₅₃	semidirect
563. #3076	C₂×C₅₃	semidirect
564. C₂×#478	C₂×C₅₃	semidirect
565. #2925	C₂×C₅₃	semidirect
582. #544	C₂²×C₅₃	semidirect
583. #544	C₂²×C₅₃	semidirect
593. #533	C₂²×C₅₃	semidirect
599. C₂×#125	C₂²×C₅₃	semidirect
606. #501	C₂²×C₅₃	semidirect
607. #501	C₂²×C₅₃	semidirect
608. #501	C₂²×C₅₃	semidirect
609. #501	C₂²×C₅₃	semidirect
610. #500	C₂²×C₅₃	semidirect
611. #499	C₂²×C₅₃	semidirect
612. #499	C₂²×C₅₃	semidirect
613. #498	C₂²×C₅₃	semidirect
622. #485	C₂²×C₅₃	semidirect
623. #485	C₂²×C₅₃	semidirect
624. #484	C₂²×C₅₃	semidirect
625. #483	C₂²×C₅₃	semidirect
630. #482	C₂²×C₅₃	semidirect
631. #482	C₂²×C₅₃	semidirect
634. #481	C₂²×C₅₃	semidirect
637. #480	C₂²×C₅₃	semidirect
638. #479	C₂²×C₅₃	semidirect
639. #479	C₂²×C₅₃	semidirect
640. #479	C₂²×C₅₃	semidirect
641. #479	C₂²×C₅₃	semidirect
648. #478	C₂²×C₅₃	semidirect
649. #478	C₂²×C₅₃	semidirect
650. #478	C₂²×C₅₃	semidirect
651. #478	C₂²×C₅₃	semidirect
652. #477	C₂²×C₅₃	semidirect
654. #476	C₂²×C₅₃	semidirect
655. #475	C₂²×C₅₃	semidirect
657. #474	C₂²×C₅₃	semidirect
658. #433	C₂²×C₅₃	semidirect
659. #433	C₂²×C₅₃	semidirect
660. #432	C₂²×C₅₃	semidirect
661. #431	C₂²×C₅₃	semidirect
684. C₅₃	#60890	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×#3504	2
C₅₃×#3460	2
C₅₃×#3244	2
C₅₃×#3243	2
C₅₃×#3241	2
C₅₃×#3240	2
C₅₃×#3234	2
C₅₃×#3232	2
C₅₃×#3228	2
C₅₃×#3164	2
C₅₃×#3163	2
C₅₃×#3136	2
C₅₃×#3099	2
C₅₃×#3098	2
C₅₃×#3096	2
C₅₃×#3080	2
C₅₃×#3077	2
C₅₃×#3076	2
C₂×C₅₃×#478	2
C₅₃×#2925	2
#60890	53

Subgroups — C53×#60890 #27268402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60890 #27268402