Subgroups — C₅₃×#61871 #27269383

Order 13568.

1700 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3387	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3384	C₂	1	2	yes	maximal, complemented
5	Q₈×SD₁₆×C₅₃	C₂	1	2	yes	maximal, complemented
6	Q₈×SD₁₆×C₅₃	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3373	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3369	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3365	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3360	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3244	C₂	1	4	yes	maximal, complemented
12	C₅₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3125	C₂	1	4	yes	maximal, complemented
15	C₅₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3106	C₂	1	1	yes	maximal, characteristic
17	C₅₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#563	—	2	2	no	—
19	C₅₃×#559	C₂²	1	2	yes	—
20	Q₈²×C₅₃	C₂²	1	2	yes	—
21	Q₈²×C₅₃	C₂²	1	2	yes	—
22	C₅₃×#557	C₂²	1	2	yes	—
23	C₅₃×#556	—	2	1	no	—
24	C₅₃×#556	C₂²	1	2	yes	—
25	C₅₃×#554	—	2	2	no	—
26	C₅₃×#554	C₂²	1	2	yes	—
27	D₄×Q₈×C₅₃	—	2	1	no	—
28	D₄×Q₈×C₅₃	—	2	2	no	—
29	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
30	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
31	C₅₃×#544	—	2	2	no	—
32	C₅₃×#544	C₂²	1	2	yes	—
33	C₅₃×#542	—	2	2	no	—
34	C₅₃×#542	C₂²	1	4	yes	—
35	C₅₃×#536	—	2	2	no	—
36	C₅₃×#533	—	2	1	no	—
37	C₅₃×#533	C₂²	1	1	yes	characteristic
38	C₅₃×#533	C₂²	1	1	yes	characteristic
39	C₅₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₅₃	—	2	1	no	—
41	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
42	C₅₃×#520	C₂²	1	2	yes	—
43	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
44	C₅₃×#501	C₂²	1	4	yes	—
45	C₅₃×#498	C₂²	1	2	yes	—
46	C₅₃×#498	C₂²	1	2	yes	—
47	C₅₃×#498	C₂²	1	4	yes	—
48	C₅₃×#489	C₂²	1	4	yes	—
49	C₅₃×#488	C₂²	1	4	yes	—
50	C₅₃×#487	C₂²	1	2	yes	—
51	C₅₃×#486	C₂²	1	2	yes	—
52	C₅₃×#485	C₂²	1	2	yes	—
53	C₅₃×#483	C₂²	1	4	yes	—
54	C₅₃×#482	C₂²	1	2	yes	—
55	C₅₃×#481	C₂²	1	4	yes	—
56	C₅₃×#479	C₂²	1	4	yes	—
57	C₅₃×#478	C₂²	1	4	yes	—
58	C₅₃×#477	C₂²	1	1	yes	characteristic
59	C₅₃×#476	C₂²	1	2	yes	—
60	C₅₃×#476	C₂²	1	2	yes	—
61	C₅₃×#476	C₂²	1	4	yes	—
62	C₅₃×#476	C₂²	1	1	yes	characteristic
63	C₅₃×#476	C₂²	1	4	yes	—
64	C₅₃×#475	C₂²	1	2	yes	—
65	C₅₃×#475	C₂²	1	2	yes	—
66	C₅₃×#475	C₂²	1	4	yes	—
67	C₅₃×#475	C₂²	1	1	yes	characteristic
68	C₅₃×#475	C₂²	1	4	yes	—
69	C₅₃×#474	C₂²	1	1	yes	characteristic
70	C₅₃×#464	C₂²	1	4	yes	—
71	C₅₃×#463	C₂²	1	4	yes	—
72	C₅₃×#462	C₂²	1	1	yes	characteristic
73	C₅₃×#461	C₂²	1	1	yes	characteristic
74	C₅₃×#460	C₂²	1	1	yes	characteristic
75	C₅₃×#459	C₂²	1	1	yes	characteristic
76	C₅₃×#452	C₂²	1	2	yes	—
77	C₅₃×#449	C₂²	1	2	yes	—
78	C₅₃×#446	C₂²	1	2	yes	—
79	C₅₃×#446	C₂²	1	2	yes	—
80	C₈×Q₈×C₅₃	C₂²	1	2	yes	—
81	C₈×Q₈×C₅₃	C₂²	1	2	yes	—
82	C₅₃×#442	C₂²	1	4	yes	—
83	C₅₃×#441	C₂²	1	4	yes	—
84	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
85	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	—
86	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
87	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
88	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	—
89	C₄×D₈×C₅₃	C₂²	1	2	yes	—
90	C₅₃×#433	C₂²	1	4	yes	—
91	C₅₃×#431	C₂²	1	1	yes	characteristic
92	C₅₃×#431	C₂²	1	1	yes	characteristic
93	C₂×#41×C₅₃	—	2	1	no	—
94	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₅₃	—	2	2	no	—
96	C₂²×Q₈×C₅₃	—	2	2	no	—
97	C₂²×Q₈×C₅₃	—	2	1	no	—
98	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
99	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
101	C₂×D₈×C₅₃	C₂³	1	2	yes	—
102	C₄⋊Q₈×C₅₃	—	2	2	no	—
103	C₄⋊Q₈×C₅₃	—	2	2	no	—
104	C₄⋊Q₈×C₅₃	—	2	4	no	—
105	C₄⋊Q₈×C₅₃	—	2	2	no	—
106	C₄⋊Q₈×C₅₃	—	2	4	no	—
107	C₄⋊Q₈×C₅₃	—	2	1	no	—
108	C₄⋊Q₈×C₅₃	—	2	1	no	—
109	C₄⋊Q₈×C₅₃	—	2	2	no	—
110	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
112	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
115	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
118	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
119	#127×C₅₃	C₂³	1	1	yes	characteristic
120	#126×C₅₃	—	2	4	no	—
121	#126×C₅₃	—	2	4	no	—
122	#125×C₅₃	—	2	2	no	—
123	#125×C₅₃	—	2	4	no	—
124	#125×C₅₃	—	2	1	no	—
125	#125×C₅₃	D₄	1	2	yes	—
126	#125×C₅₃	C₂³	1	4	yes	—
127	#124×C₅₃	—	2	4	no	—
128	#124×C₅₃	—	2	1	no	—
129	#124×C₅₃	—	2	2	no	—
130	#124×C₅₃	C₂³	1	4	yes	—
131	#123×C₅₃	—	2	4	no	—
132	#123×C₅₃	—	2	4	no	—
133	C₂²⋊Q₈×C₅₃	—	2	2	no	—
134	C₂²⋊Q₈×C₅₃	—	2	2	no	—
135	C₂²⋊Q₈×C₅₃	—	2	4	no	—
136	C₂²⋊Q₈×C₅₃	—	2	4	no	—
137	C₂²⋊Q₈×C₅₃	—	2	4	no	—
138	C₂²⋊Q₈×C₅₃	—	2	4	no	—
139	C₂²⋊Q₈×C₅₃	—	2	4	no	—
140	C₂²⋊Q₈×C₅₃	—	2	2	no	—
141	C₂²⋊Q₈×C₅₃	—	2	2	no	—
142	C₂²⋊Q₈×C₅₃	—	2	1	no	—
143	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
144	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
145	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
146	#121×C₅₃	—	2	1	no	—
147	#121×C₅₃	C₂³	1	2	yes	—
148	C₄×Q₈×C₅₃	—	2	2	no	—
149	C₄×Q₈×C₅₃	—	2	1	no	—
150	C₄×Q₈×C₅₃	—	2	2	no	—
151	C₄×Q₈×C₅₃	—	2	2	no	—
152	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
153	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
154	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
155	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
157	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
159	C₄×D₄×C₅₃	—	2	2	no	—
160	C₄×D₄×C₅₃	—	2	4	no	—
161	C₄×D₄×C₅₃	—	2	1	no	—
162	C₄×D₄×C₅₃	—	2	1	no	—
163	C₄×D₄×C₅₃	—	2	1	no	—
164	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
165	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
166	C₄×D₄×C₅₃	C₂³	1	4	yes	—
167	C₄×D₄×C₅₃	C₂³	1	2	yes	—
168	C₄×D₄×C₅₃	C₂³	1	4	yes	—
169	#117×C₅₃	—	2	2	no	—
170	#117×C₅₃	—	2	2	no	—
171	#117×C₅₃	—	2	1	no	—
172	#117×C₅₃	—	2	1	no	—
173	#117×C₅₃	C₂³	1	1	yes	characteristic
174	#117×C₅₃	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
176	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
177	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
178	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₅₃	—	2	1	no	—
180	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
181	#107×C₅₃	C₂³	1	2	yes	—
182	#107×C₅₃	C₂³	1	2	yes	—
183	#106×C₅₃	C₂³	1	2	yes	—
184	#106×C₅₃	C₂³	1	2	yes	—
185	#106×C₅₃	C₂³	1	4	yes	—
186	#106×C₅₃	C₂³	1	4	yes	—
187	#106×C₅₃	C₂³	1	4	yes	—
188	#106×C₅₃	C₂³	1	4	yes	—
189	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
191	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
192	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
194	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
195	#103×C₅₃	C₂³	1	2	yes	—
196	#103×C₅₃	C₂³	1	2	yes	—
197	#103×C₅₃	C₂³	1	4	yes	—
198	#103×C₅₃	C₂³	1	4	yes	—
199	#103×C₅₃	C₂³	1	2	yes	—
200	#103×C₅₃	C₂³	1	2	yes	—
201	#102×C₅₃	C₂³	1	4	yes	—
202	#102×C₅₃	C₂³	1	4	yes	—
203	#102×C₅₃	C₂³	1	2	yes	—
204	#102×C₅₃	C₂³	1	2	yes	—
205	#102×C₅₃	C₂³	1	2	yes	—
206	#102×C₅₃	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
208	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
209	#97×C₅₃	C₂³	1	4	yes	—
210	C₄×C₈×C₅₃	C₂³	1	2	yes	—
211	C₄×C₈×C₅₃	C₂³	1	2	yes	—
212	C₄×C₈×C₅₃	C₂³	1	4	yes	—
213	#41×C₅₃	—	2	2	no	—
214	#41×C₅₃	—	2	2	no	—
215	#41×C₅₃	—	8	2	no	—
216	C₂×Q₈×C₅₃	—	2	1	no	—
217	C₂×Q₈×C₅₃	—	2	2	no	—
218	C₂×Q₈×C₅₃	—	2	4	no	—
219	C₂×Q₈×C₅₃	—	2	2	no	—
220	C₂×Q₈×C₅₃	—	2	4	no	—
221	C₂×Q₈×C₅₃	—	2	1	no	—
222	C₂×Q₈×C₅₃	—	8	2	no	—
223	C₂×Q₈×C₅₃	—	8	4	no	—
224	C₂×Q₈×C₅₃	—	8	4	no	—
225	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
229	C₂×D₄×C₅₃	—	2	1	no	—
230	C₂×D₄×C₅₃	—	2	2	no	—
231	C₂×D₄×C₅₃	—	2	1	no	—
232	C₂×D₄×C₅₃	—	2	1	no	—
233	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
234	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₅₃	—	2	1	no	—
236	C₂²×C₄×C₅₃	—	2	2	no	—
237	C₂²×C₄×C₅₃	—	2	1	no	—
238	C₂²×C₄×C₅₃	—	2	1	no	—
239	C₂²×C₄×C₅₃	—	2	2	no	—
240	C₂²×C₄×C₅₃	—	2	4	no	—
241	C₂²×C₄×C₅₃	—	2	4	no	—
242	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
245	Q₁₆×C₅₃	—	2	4	no	—
246	SD₁₆×C₅₃	—	2	4	no	—
247	SD₁₆×C₅₃	—	2	4	no	—
248	D₈×C₅₃	—	2	4	no	—
249	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
250	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
251	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
252	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₅₃	—	2	2	no	—
254	C₄⋊C₄×C₅₃	—	2	2	no	—
255	C₄⋊C₄×C₅₃	—	2	4	no	—
256	C₄⋊C₄×C₅₃	—	2	2	no	—
257	C₄⋊C₄×C₅₃	—	2	4	no	—
258	C₄⋊C₄×C₅₃	—	2	1	no	—
259	C₄⋊C₄×C₅₃	—	2	1	no	—
260	C₄⋊C₄×C₅₃	—	2	1	no	—
261	C₄⋊C₄×C₅₃	—	2	1	no	—
262	C₄⋊C₄×C₅₃	—	2	1	no	—
263	C₄⋊C₄×C₅₃	—	2	1	no	—
264	C₄⋊C₄×C₅₃	—	2	4	no	—
265	C₄⋊C₄×C₅₃	—	2	4	no	—
266	C₄⋊C₄×C₅₃	—	2	2	no	—
267	C₄⋊C₄×C₅₃	—	2	4	no	—
268	C₄⋊C₄×C₅₃	—	2	4	no	—
269	C₄⋊C₄×C₅₃	—	2	2	no	—
270	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
271	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
272	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
273	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
275	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
276	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
278	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
279	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
281	C₂²⋊C₄×C₅₃	—	2	2	no	—
282	C₂²⋊C₄×C₅₃	—	2	1	no	—
283	C₂²⋊C₄×C₅₃	—	2	4	no	—
284	C₂²⋊C₄×C₅₃	—	2	1	no	—
285	C₂²⋊C₄×C₅₃	—	2	1	no	—
286	C₂²⋊C₄×C₅₃	—	2	4	no	—
287	C₂²⋊C₄×C₅₃	—	2	2	no	—
288	C₂²⋊C₄×C₅₃	—	2	4	no	—
289	C₂²⋊C₄×C₅₃	—	2	2	no	—
290	C₂²⋊C₄×C₅₃	—	2	4	no	—
291	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
292	C₄²×C₅₃	—	2	1	no	—
293	C₄²×C₅₃	—	2	1	no	—
294	C₄²×C₅₃	—	2	1	no	—
295	C₄²×C₅₃	—	2	2	no	—
296	C₄²×C₅₃	—	2	4	no	—
297	C₄²×C₅₃	—	2	4	no	—
298	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
301	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
302	C₄²×C₅₃	C₂⁴	1	4	yes	—
303	C₂³×C₅₃	—	2	1	no	—
304	C₂³×C₅₃	—	2	2	no	—
305	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
306	Q₈×C₅₃	—	2	4	no	—
307	Q₈×C₅₃	—	2	4	no	—
308	Q₈×C₅₃	—	2	1	no	—
309	Q₈×C₅₃	—	2	2	no	—
310	Q₈×C₅₃	—	2	2	no	—
311	Q₈×C₅₃	—	4	2	no	—
312	Q₈×C₅₃	—	4	4	no	—
313	Q₈×C₅₃	—	8	2	no	—
314	Q₈×C₅₃	—	8	4	no	—
315	Q₈×C₅₃	—	8	4	no	—
316	Q₈×C₅₃	—	8	1	no	—
317	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
318	D₄×C₅₃	—	2	4	no	—
319	D₄×C₅₃	—	2	1	no	—
320	D₄×C₅₃	—	2	2	no	—
321	D₄×C₅₃	—	2	2	no	—
322	D₄×C₅₃	—	4	2	no	—
323	D₄×C₅₃	—	8	1	no	—
324	D₄×C₅₃	—	8	2	no	—
325	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
326	C₂×C₄×C₅₃	—	2	4	no	—
327	C₂×C₄×C₅₃	—	2	1	no	—
328	C₂×C₄×C₅₃	—	2	2	no	—
329	C₂×C₄×C₅₃	—	2	2	no	—
330	C₂×C₄×C₅₃	—	2	1	no	—
331	C₂×C₄×C₅₃	—	2	1	no	—
332	C₂×C₄×C₅₃	—	2	2	no	—
333	C₂×C₄×C₅₃	—	2	4	no	—
334	C₂×C₄×C₅₃	—	2	2	no	—
335	C₂×C₄×C₅₃	—	2	1	no	—
336	C₂×C₄×C₅₃	—	2	1	no	—
337	C₂×C₄×C₅₃	—	2	2	no	—
338	C₂×C₄×C₅₃	—	4	2	no	—
339	C₂×C₄×C₅₃	—	4	2	no	—
340	C₂×C₄×C₅₃	—	4	4	no	—
341	C₂×C₄×C₅₃	—	8	4	no	—
342	C₂×C₄×C₅₃	—	8	4	no	—
343	C₂×C₄×C₅₃	—	8	2	no	—
344	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
346	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
347	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
352	C₈×C₅₃	—	2	2	no	—
353	C₈×C₅₃	—	2	2	no	—
354	C₈×C₅₃	—	2	2	no	—
355	C₈×C₅₃	—	2	2	no	—
356	#61871	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
357	C₂²×C₅₃	—	2	1	no	—
358	C₂²×C₅₃	—	2	2	no	—
359	C₂²×C₅₃	—	2	1	no	—
360	C₂²×C₅₃	—	2	1	no	—
361	C₂²×C₅₃	—	4	1	no	—
362	C₂²×C₅₃	—	4	1	no	—
363	C₂²×C₅₃	—	4	2	no	—
364	C₂²×C₅₃	—	4	2	no	—
365	C₂²×C₅₃	—	4	2	no	—
366	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
367	C₄×C₅₃	—	2	1	no	—
368	C₄×C₅₃	—	2	2	no	—
369	C₄×C₅₃	—	2	1	no	—
370	C₄×C₅₃	—	2	1	no	—
371	C₄×C₅₃	—	2	4	no	—
372	C₄×C₅₃	—	2	4	no	—
373	C₄×C₅₃	—	4	2	no	—
374	C₄×C₅₃	—	4	1	no	—
375	C₄×C₅₃	—	4	2	no	—
376	C₄×C₅₃	—	4	1	no	—
377	C₄×C₅₃	—	4	2	no	—
378	C₄×C₅₃	—	4	4	no	—
379	C₄×C₅₃	#577	1	2	yes	—
380	C₄×C₅₃	#577	1	2	yes	—
381	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
382	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
383	#3550	C₂×C₅₃	1	1	yes	characteristic, complemented
384	#3503	C₂×C₅₃	1	1	yes	characteristic, complemented
385	#3387	C₂×C₅₃	1	2	yes	complemented
386	#3384	C₂×C₅₃	1	2	yes	complemented
387	Q₈×SD₁₆	C₂×C₅₃	1	2	yes	complemented
388	Q₈×SD₁₆	C₂×C₅₃	1	2	yes	complemented
389	#3373	C₂×C₅₃	1	2	yes	complemented
390	#3369	C₂×C₅₃	1	2	yes	complemented
391	#3365	C₂×C₅₃	1	2	yes	complemented
392	#3360	C₂×C₅₃	1	2	yes	complemented
393	#3244	C₂×C₅₃	1	4	yes	complemented
394	#3229	C₂×C₅₃	1	1	yes	characteristic, complemented
395	#3227	C₂×C₅₃	1	1	yes	characteristic, complemented
396	#3125	C₂×C₅₃	1	4	yes	complemented
397	#3107	C₂×C₅₃	1	1	yes	characteristic, complemented
398	#3106	C₂×C₅₃	1	1	yes	characteristic
399	#2986	C₂×C₅₃	1	1	yes	characteristic, complemented
400	C₂×C₅₃	—	4	1	no	—
401	C₂×C₅₃	—	4	2	no	—
402	C₂×C₅₃	—	8	2	no	—
403	C₂×C₅₃	#3486	1	1	yes	characteristic
404	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
405	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
406	#563	—	2	2	no	—
407	#559	C₂²×C₅₃	1	2	yes	—
408	Q₈²	C₂²×C₅₃	1	2	yes	—
409	Q₈²	C₂²×C₅₃	1	2	yes	—
410	#557	C₂²×C₅₃	1	2	yes	—
411	#556	—	2	1	no	—
412	#556	C₂²×C₅₃	1	2	yes	—
413	#554	—	2	2	no	—
414	#554	C₂²×C₅₃	1	2	yes	—
415	D₄×Q₈	—	2	1	no	—
416	D₄×Q₈	—	2	2	no	—
417	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
418	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
419	#544	—	2	2	no	—
420	#544	C₂²×C₅₃	1	2	yes	—
421	#542	—	2	2	no	—
422	#542	C₂²×C₅₃	1	4	yes	—
423	#536	—	2	2	no	—
424	#533	—	2	1	no	—
425	#533	C₂²×C₅₃	1	1	yes	characteristic
426	#533	C₂²×C₅₃	1	1	yes	characteristic
427	#532	C₂²×C₅₃	1	1	yes	characteristic
428	C₂×C₄⋊Q₈	—	2	1	no	—
429	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
430	#520	C₂²×C₅₃	1	2	yes	—
431	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
432	#501	C₂²×C₅₃	1	4	yes	—
433	#498	C₂²×C₅₃	1	4	yes	—
434	#498	C₂²×C₅₃	1	2	yes	—
435	#498	C₂²×C₅₃	1	2	yes	—
436	#489	C₂²×C₅₃	1	4	yes	—
437	#488	C₂²×C₅₃	1	4	yes	—
438	#487	C₂²×C₅₃	1	2	yes	—
439	#486	C₂²×C₅₃	1	2	yes	—
440	#485	C₂²×C₅₃	1	2	yes	—
441	#483	C₂²×C₅₃	1	4	yes	—
442	#482	C₂²×C₅₃	1	2	yes	—
443	#481	C₂²×C₅₃	1	4	yes	—
444	#479	C₂²×C₅₃	1	4	yes	—
445	#478	C₂²×C₅₃	1	4	yes	—
446	#477	C₂²×C₅₃	1	1	yes	characteristic
447	#476	C₂²×C₅₃	1	2	yes	—
448	#476	C₂²×C₅₃	1	1	yes	characteristic
449	#476	C₂²×C₅₃	1	2	yes	—
450	#476	C₂²×C₅₃	1	4	yes	—
451	#476	C₂²×C₅₃	1	4	yes	—
452	#475	C₂²×C₅₃	1	1	yes	characteristic
453	#475	C₂²×C₅₃	1	2	yes	—
454	#475	C₂²×C₅₃	1	4	yes	—
455	#475	C₂²×C₅₃	1	2	yes	—
456	#475	C₂²×C₅₃	1	4	yes	—
457	#474	C₂²×C₅₃	1	1	yes	characteristic
458	#464	C₂²×C₅₃	1	4	yes	—
459	#463	C₂²×C₅₃	1	4	yes	—
460	#462	C₂²×C₅₃	1	1	yes	characteristic
461	#461	C₂²×C₅₃	1	1	yes	characteristic
462	#460	C₂²×C₅₃	1	1	yes	characteristic
463	#459	C₂²×C₅₃	1	1	yes	characteristic
464	#452	C₂²×C₅₃	1	2	yes	—
465	#449	C₂²×C₅₃	1	2	yes	—
466	#446	C₂²×C₅₃	1	2	yes	—
467	#446	C₂²×C₅₃	1	2	yes	—
468	C₈×Q₈	C₂²×C₅₃	1	2	yes	—
469	C₈×Q₈	C₂²×C₅₃	1	2	yes	—
470	#442	C₂²×C₅₃	1	4	yes	—
471	#441	C₂²×C₅₃	1	4	yes	—
472	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
473	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	—
474	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
475	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
476	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	—
477	C₄×D₈	C₂²×C₅₃	1	2	yes	—
478	#433	C₂²×C₅₃	1	4	yes	—
479	#431	C₂²×C₅₃	1	1	yes	characteristic
480	#431	C₂²×C₅₃	1	1	yes	characteristic
481	C₅₃	#61871	1	1	yes	characteristic, direct product factor, Sylow
482	C₂×#41	—	2	1	no	—
483	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
484	C₂²×Q₈	—	2	2	no	—
485	C₂²×Q₈	—	2	2	no	—
486	C₂²×Q₈	—	2	1	no	—
487	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
488	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
489	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
490	C₂×D₈	C₂³×C₅₃	1	2	yes	—
491	C₄⋊Q₈	—	2	2	no	—
492	C₄⋊Q₈	—	2	2	no	—
493	C₄⋊Q₈	—	2	2	no	—
494	C₄⋊Q₈	—	2	4	no	—
495	C₄⋊Q₈	—	2	2	no	—
496	C₄⋊Q₈	—	2	4	no	—
497	C₄⋊Q₈	—	2	1	no	—
498	C₄⋊Q₈	—	2	1	no	—
499	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
500	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
501	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
502	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
503	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
504	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
507	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
508	#127	C₂³×C₅₃	1	1	yes	characteristic
509	#126	—	2	4	no	—
510	#126	—	2	4	no	—
511	#125	—	2	2	no	—
512	#125	—	2	4	no	—
513	#125	—	2	1	no	—
514	#125	D₄×C₅₃	1	2	yes	—
515	#125	C₂³×C₅₃	1	4	yes	—
516	#124	—	2	2	no	—
517	#124	—	2	4	no	—
518	#124	—	2	1	no	—
519	#124	C₂³×C₅₃	1	4	yes	—
520	#123	—	2	4	no	—
521	#123	—	2	4	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	—	2	1	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
533	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
534	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
535	#121	—	2	1	no	—
536	#121	C₂³×C₅₃	1	2	yes	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	2	2	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
542	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
543	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
544	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
545	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
546	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
547	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	4	no	—
552	C₄×D₄	—	2	1	no	—
553	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
554	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
555	C₄×D₄	C₂³×C₅₃	1	4	yes	—
556	C₄×D₄	C₂³×C₅₃	1	2	yes	—
557	C₄×D₄	C₂³×C₅₃	1	4	yes	—
558	#117	—	2	1	no	—
559	#117	—	2	2	no	—
560	#117	—	2	2	no	—
561	#117	—	2	1	no	—
562	#117	C₂³×C₅₃	1	1	yes	characteristic
563	#117	C₂³×C₅₃	1	2	yes	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	2	no	—
566	C₂×C₄⋊C₄	—	2	2	no	—
567	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
568	C₂×C₄²	—	2	1	no	—
569	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
570	#107	C₂³×C₅₃	1	2	yes	—
571	#107	C₂³×C₅₃	1	2	yes	—
572	#106	C₂³×C₅₃	1	2	yes	—
573	#106	C₂³×C₅₃	1	2	yes	—
574	#106	C₂³×C₅₃	1	4	yes	—
575	#106	C₂³×C₅₃	1	4	yes	—
576	#106	C₂³×C₅₃	1	4	yes	—
577	#106	C₂³×C₅₃	1	4	yes	—
578	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
579	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
580	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
581	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
582	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
583	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
584	#103	C₂³×C₅₃	1	2	yes	—
585	#103	C₂³×C₅₃	1	2	yes	—
586	#103	C₂³×C₅₃	1	2	yes	—
587	#103	C₂³×C₅₃	1	4	yes	—
588	#103	C₂³×C₅₃	1	2	yes	—
589	#103	C₂³×C₅₃	1	4	yes	—
590	#102	C₂³×C₅₃	1	2	yes	—
591	#102	C₂³×C₅₃	1	2	yes	—
592	#102	C₂³×C₅₃	1	2	yes	—
593	#102	C₂³×C₅₃	1	2	yes	—
594	#102	C₂³×C₅₃	1	4	yes	—
595	#102	C₂³×C₅₃	1	4	yes	—
596	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
597	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
598	#97	C₂³×C₅₃	1	4	yes	—
599	C₄×C₈	C₂³×C₅₃	1	2	yes	—
600	C₄×C₈	C₂³×C₅₃	1	2	yes	—
601	C₄×C₈	C₂³×C₅₃	1	4	yes	—
602	#41	—	2	2	no	—
603	#41	—	2	2	no	—
604	#41	—	8	2	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	2	4	no	—
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	8	2	no	—
612	C₂×Q₈	—	8	4	no	—
613	C₂×Q₈	—	8	4	no	—
614	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
615	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
616	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
617	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
623	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
634	Q₁₆	—	2	4	no	—
635	SD₁₆	—	2	4	no	—
636	SD₁₆	—	2	4	no	—
637	D₈	—	2	4	no	—
638	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
639	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
640	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
641	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
660	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
661	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
662	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
663	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
664	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
665	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
666	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
667	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
668	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	1	no	—
683	C₄²	—	2	1	no	—
684	C₄²	—	2	2	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
688	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
689	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
690	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
691	C₄²	C₂⁴×C₅₃	1	4	yes	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	2	no	—
694	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
695	Q₈	—	2	4	no	—
696	Q₈	—	2	4	no	—
697	Q₈	—	2	1	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	4	2	no	—
701	Q₈	—	4	4	no	—
702	Q₈	—	8	2	no	—
703	Q₈	—	8	4	no	—
704	Q₈	—	8	4	no	—
705	Q₈	—	8	1	no	—
706	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
707	D₄	—	2	4	no	—
708	D₄	—	2	1	no	—
709	D₄	—	2	2	no	—
710	D₄	—	2	2	no	—
711	D₄	—	4	2	no	—
712	D₄	—	8	1	no	—
713	D₄	—	8	2	no	—
714	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	4	4	no	—
730	C₂×C₄	—	8	4	no	—
731	C₂×C₄	—	8	4	no	—
732	C₂×C₄	—	8	2	no	—
733	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
735	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
736	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
738	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
739	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
740	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
741	C₈	—	2	2	no	—
742	C₈	—	2	2	no	—
743	C₈	—	2	2	no	—
744	C₈	—	2	2	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
755	C₄	—	2	1	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	1	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	1	no	—
764	C₄	—	4	1	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	4	no	—
767	C₄	C₅₃×#577	1	2	yes	—
768	C₄	C₅₃×#577	1	2	yes	—
769	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
770	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
771	C₂	—	4	1	no	—
772	C₂	—	4	2	no	—
773	C₂	—	8	2	no	—
774	C₂	C₅₃×#3486	1	1	yes	characteristic
775	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
776	C₂	C₂×C₅₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3106	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3550	C₂	semidirect
2. C₅₃×#3503	C₂	semidirect
3. C₅₃×#3387	C₂	semidirect
4. C₅₃×#3384	C₂	semidirect
5. Q₈×SD₁₆×C₅₃	C₂	semidirect
6. Q₈×SD₁₆×C₅₃	C₂	semidirect
7. C₅₃×#3373	C₂	semidirect
8. C₅₃×#3369	C₂	semidirect
9. C₅₃×#3365	C₂	semidirect
10. C₅₃×#3360	C₂	semidirect
11. C₅₃×#3244	C₂	semidirect
12. C₅₃×#3229	C₂	semidirect
13. C₅₃×#3227	C₂	semidirect
14. C₅₃×#3125	C₂	semidirect
15. C₅₃×#3107	C₂	semidirect
17. C₅₃×#2986	C₂	semidirect
356. #61871	C₅₃	direct (N × H)
383. #3550	C₂×C₅₃	semidirect
384. #3503	C₂×C₅₃	semidirect
385. #3387	C₂×C₅₃	semidirect
386. #3384	C₂×C₅₃	semidirect
387. Q₈×SD₁₆	C₂×C₅₃	semidirect
388. Q₈×SD₁₆	C₂×C₅₃	semidirect
389. #3373	C₂×C₅₃	semidirect
390. #3369	C₂×C₅₃	semidirect
391. #3365	C₂×C₅₃	semidirect
392. #3360	C₂×C₅₃	semidirect
393. #3244	C₂×C₅₃	semidirect
394. #3229	C₂×C₅₃	semidirect
395. #3227	C₂×C₅₃	semidirect
396. #3125	C₂×C₅₃	semidirect
397. #3107	C₂×C₅₃	semidirect
399. #2986	C₂×C₅₃	semidirect
481. C₅₃	#61871	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×#3550	2
C₅₃×#3503	2
C₅₃×#3387	2
C₅₃×#3384	2
Q₈×SD₁₆×C₅₃	2
C₅₃×#3373	2
C₅₃×#3369	2
C₅₃×#3365	2
C₅₃×#3360	2
C₅₃×#3244	2
C₅₃×#3229	2
C₅₃×#3227	2
C₅₃×#3125	2
C₅₃×#3107	2
C₅₃×#3106	2
C₅₃×#2986	2
#61871	53

Subgroups — C53×#61871 #27269383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61871 #27269383