Subgroups — C₅₃×#62101 #27269613

Order 13568.

1728 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3480	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3383	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3365	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3342	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3337	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3304	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3300	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3248	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3233	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3107	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3076	C₂	1	2	yes	maximal, complemented
16	C₂×C₅₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#559	—	2	1	no	—
19	C₅₃×#559	C₂²	1	1	yes	characteristic
20	C₅₃×#557	—	2	1	no	—
21	C₅₃×#557	C₂²	1	1	yes	characteristic
22	C₅₃×#557	C₂²	1	2	yes	—
23	C₅₃×#556	—	2	1	no	—
24	C₅₃×#556	—	2	1	no	—
25	C₅₃×#556	C₂²	1	1	yes	characteristic
26	C₅₃×#556	C₂²	1	2	yes	—
27	C₅₃×#553	—	2	2	no	—
28	C₅₃×#553	C₂²	1	2	yes	—
29	C₅₃×#552	—	2	2	no	—
30	C₅₃×#552	C₂²	1	4	yes	—
31	C₅₃×#550	C₂²	1	1	yes	characteristic
32	C₅₃×#548	C₂²	1	2	yes	—
33	C₅₃×#541	—	2	2	no	—
34	C₅₃×#536	—	2	1	no	—
35	C₅₃×#533	C₂²	1	1	yes	characteristic
36	C₅₃×#533	C₂²	1	2	yes	—
37	C₅₃×#533	C₂²	1	2	yes	—
38	C₅₃×#532	—	2	1	no	—
39	C₅₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#529	—	2	2	no	—
42	C₅₃×#529	C₂²	1	2	yes	—
43	C₅₃×#519	—	2	1	no	—
44	C₄×#41×C₅₃	—	2	1	no	—
45	C₄×#41×C₅₃	C₂²	1	2	yes	—
46	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
48	C₅₃×#500	C₂²	1	2	yes	—
49	C₅₃×#499	C₂²	1	4	yes	—
50	C₅₃×#488	C₂²	1	4	yes	—
51	C₅₃×#486	C₂²	1	2	yes	—
52	C₅₃×#485	C₂²	1	4	yes	—
53	C₅₃×#485	C₂²	1	4	yes	—
54	C₅₃×#484	C₂²	1	2	yes	—
55	C₅₃×#482	C₂²	1	4	yes	—
56	C₅₃×#480	C₂²	1	4	yes	—
57	C₅₃×#479	C₂²	1	4	yes	—
58	C₅₃×#479	C₂²	1	4	yes	—
59	C₅₃×#478	C₂²	1	4	yes	—
60	C₅₃×#477	C₂²	1	1	yes	characteristic
61	C₅₃×#477	C₂²	1	1	yes	characteristic
62	C₅₃×#476	C₂²	1	2	yes	—
63	C₅₃×#475	C₂²	1	2	yes	—
64	C₅₃×#475	C₂²	1	2	yes	—
65	C₅₃×#475	C₂²	1	2	yes	—
66	C₅₃×#475	C₂²	1	2	yes	—
67	C₅₃×#475	C₂²	1	2	yes	—
68	C₅₃×#474	C₂²	1	2	yes	—
69	C₅₃×#474	C₂²	1	2	yes	—
70	C₅₃×#467	C₂²	1	4	yes	—
71	C₅₃×#465	C₂²	1	4	yes	—
72	C₅₃×#465	C₂²	1	4	yes	—
73	C₅₃×#464	C₂²	1	4	yes	—
74	C₅₃×#462	C₂²	1	1	yes	characteristic
75	C₅₃×#462	C₂²	1	1	yes	characteristic
76	C₅₃×#461	C₂²	1	2	yes	—
77	C₅₃×#460	C₂²	1	2	yes	—
78	C₅₃×#452	C₂²	1	4	yes	—
79	C₅₃×#451	C₂²	1	2	yes	—
80	C₈×Q₈×C₅₃	C₂²	1	2	yes	—
81	C₄×Q₁₆×C₅₃	C₂²	1	4	yes	—
82	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
83	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
84	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	—
85	C₈×D₄×C₅₃	C₂²	1	4	yes	—
86	C₈×D₄×C₅₃	C₂²	1	2	yes	—
87	C₅₃×#431	C₂²	1	1	yes	characteristic
88	C₅₃×#431	C₂²	1	2	yes	—
89	C₅₃×#427	C₂²	1	4	yes	—
90	C₂×#106×C₅₃	C₂²	1	2	yes	—
91	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
92	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
93	C₅₃×#416	C₂²	1	4	yes	—
94	C₂×#103×C₅₃	C₂²	1	2	yes	—
95	C₂×#41×C₅₃	—	2	1	no	—
96	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
97	C₂×#41×C₅₃	C₂³	1	2	yes	—
98	C₂²×Q₈×C₅₃	—	2	1	no	—
99	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
103	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
104	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
105	C₄⋊Q₈×C₅₃	—	2	1	no	—
106	C₄⋊Q₈×C₅₃	—	2	1	no	—
107	C₄⋊Q₈×C₅₃	—	2	1	no	—
108	C₄⋊Q₈×C₅₃	—	2	2	no	—
109	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
110	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
114	#127×C₅₃	—	2	1	no	—
115	#127×C₅₃	C₂³	1	1	yes	characteristic
116	#126×C₅₃	—	2	2	no	—
117	#126×C₅₃	—	2	2	no	—
118	#126×C₅₃	—	2	4	no	—
119	#126×C₅₃	—	2	4	no	—
120	#126×C₅₃	—	2	2	no	—
121	#125×C₅₃	—	2	2	no	—
122	#125×C₅₃	—	2	4	no	—
123	#125×C₅₃	—	2	4	no	—
124	#125×C₅₃	—	2	1	no	—
125	#125×C₅₃	—	2	2	no	—
126	#125×C₅₃	C₂³	1	4	yes	—
127	#125×C₅₃	C₂³	1	2	yes	—
128	#124×C₅₃	—	2	2	no	—
129	#124×C₅₃	—	2	1	no	—
130	#124×C₅₃	—	2	1	no	—
131	#124×C₅₃	—	2	1	no	—
132	#124×C₅₃	—	2	2	no	—
133	#124×C₅₃	C₂³	1	2	yes	—
134	#123×C₅₃	—	2	2	no	—
135	#123×C₅₃	—	2	2	no	—
136	#123×C₅₃	—	2	4	no	—
137	#123×C₅₃	—	2	2	no	—
138	C₂²⋊Q₈×C₅₃	—	2	2	no	—
139	C₂²⋊Q₈×C₅₃	—	2	2	no	—
140	C₂²⋊Q₈×C₅₃	—	2	2	no	—
141	C₂²⋊Q₈×C₅₃	—	2	1	no	—
142	C₂²⋊Q₈×C₅₃	—	2	2	no	—
143	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
144	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
145	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
146	#121×C₅₃	—	2	2	no	—
147	#121×C₅₃	—	2	2	no	—
148	#121×C₅₃	—	2	2	no	—
149	#121×C₅₃	—	2	1	no	—
150	#121×C₅₃	C₂³	1	2	yes	—
151	#121×C₅₃	C₂³	1	2	yes	—
152	C₄×Q₈×C₅₃	—	2	1	no	—
153	C₄×Q₈×C₅₃	—	2	1	no	—
154	C₄×Q₈×C₅₃	—	2	2	no	—
155	C₄×Q₈×C₅₃	—	2	2	no	—
156	C₄×Q₈×C₅₃	—	2	1	no	—
157	C₄×Q₈×C₅₃	—	2	1	no	—
158	C₄×Q₈×C₅₃	—	2	2	no	—
159	C₄×Q₈×C₅₃	—	2	2	no	—
160	C₄×Q₈×C₅₃	—	2	2	no	—
161	C₄×Q₈×C₅₃	—	2	1	no	—
162	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
170	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
171	C₄×D₄×C₅₃	—	2	1	no	—
172	C₄×D₄×C₅₃	—	2	1	no	—
173	C₄×D₄×C₅₃	—	2	2	no	—
174	C₄×D₄×C₅₃	—	2	2	no	—
175	C₄×D₄×C₅₃	—	2	1	no	—
176	C₄×D₄×C₅₃	—	2	2	no	—
177	C₄×D₄×C₅₃	—	2	2	no	—
178	C₄×D₄×C₅₃	—	2	2	no	—
179	C₄×D₄×C₅₃	D₄	1	2	yes	—
180	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
181	C₄×D₄×C₅₃	C₂³	1	2	yes	—
182	C₄×D₄×C₅₃	C₂³	1	2	yes	—
183	C₄×D₄×C₅₃	C₂³	1	2	yes	—
184	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
185	#117×C₅₃	—	2	4	no	—
186	#117×C₅₃	—	2	2	no	—
187	#117×C₅₃	—	2	2	no	—
188	#117×C₅₃	—	2	1	no	—
189	#117×C₅₃	—	2	2	no	—
190	#117×C₅₃	D₄	1	1	yes	characteristic
191	#117×C₅₃	D₄	1	2	yes	—
192	#117×C₅₃	C₂³	1	2	yes	—
193	#117×C₅₃	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
195	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
196	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₅₃	—	2	2	no	—
199	C₂×C₄²×C₅₃	—	2	1	no	—
200	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
202	#107×C₅₃	C₂³	1	4	yes	—
203	#107×C₅₃	C₂³	1	2	yes	—
204	#107×C₅₃	C₂³	1	4	yes	—
205	#107×C₅₃	C₂³	1	2	yes	—
206	#106×C₅₃	C₂³	1	4	yes	—
207	#106×C₅₃	C₂³	1	4	yes	—
208	#106×C₅₃	C₂³	1	4	yes	—
209	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
210	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
211	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
212	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
213	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
214	#103×C₅₃	C₂³	1	2	yes	—
215	#103×C₅₃	C₂³	1	2	yes	—
216	#103×C₅₃	C₂³	1	4	yes	—
217	#103×C₅₃	C₂³	1	4	yes	—
218	#103×C₅₃	C₂³	1	4	yes	—
219	#103×C₅₃	C₂³	1	2	yes	—
220	#103×C₅₃	C₂³	1	2	yes	—
221	#102×C₅₃	C₂³	1	4	yes	—
222	#102×C₅₃	C₂³	1	4	yes	—
223	#102×C₅₃	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
226	C₄×C₈×C₅₃	C₂³	1	2	yes	—
227	C₄×C₈×C₅₃	C₂³	1	4	yes	—
228	#41×C₅₃	—	2	4	no	—
229	#41×C₅₃	—	2	4	no	—
230	#41×C₅₃	—	4	2	no	—
231	#41×C₅₃	—	4	4	no	—
232	C₂×Q₈×C₅₃	—	2	1	no	—
233	C₂×Q₈×C₅₃	—	2	1	no	—
234	C₂×Q₈×C₅₃	—	2	2	no	—
235	C₂×Q₈×C₅₃	—	2	1	no	—
236	C₂×Q₈×C₅₃	—	2	2	no	—
237	C₂×Q₈×C₅₃	—	2	2	no	—
238	C₂×Q₈×C₅₃	—	4	1	no	—
239	C₂×Q₈×C₅₃	—	4	4	no	—
240	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
242	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₅₃	—	2	2	no	—
245	C₂×D₄×C₅₃	—	2	2	no	—
246	C₂×D₄×C₅₃	—	2	2	no	—
247	C₂×D₄×C₅₃	—	2	1	no	—
248	C₂×D₄×C₅₃	—	2	1	no	—
249	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
250	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₅₃	—	2	1	no	—
253	C₂²×C₄×C₅₃	—	2	2	no	—
254	C₂²×C₄×C₅₃	—	2	1	no	—
255	C₂²×C₄×C₅₃	—	2	2	no	—
256	C₂²×C₄×C₅₃	—	2	2	no	—
257	C₂²×C₄×C₅₃	—	2	2	no	—
258	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
264	Q₁₆×C₅₃	—	2	4	no	—
265	Q₁₆×C₅₃	—	4	2	no	—
266	SD₁₆×C₅₃	—	4	4	no	—
267	C₂×C₈×C₅₃	—	4	2	no	—
268	C₂×C₈×C₅₃	—	4	4	no	—
269	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
270	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
271	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
272	C₄⋊C₄×C₅₃	—	2	1	no	—
273	C₄⋊C₄×C₅₃	—	2	2	no	—
274	C₄⋊C₄×C₅₃	—	2	1	no	—
275	C₄⋊C₄×C₅₃	—	2	1	no	—
276	C₄⋊C₄×C₅₃	—	2	1	no	—
277	C₄⋊C₄×C₅₃	—	2	2	no	—
278	C₄⋊C₄×C₅₃	—	2	1	no	—
279	C₄⋊C₄×C₅₃	—	2	2	no	—
280	C₄⋊C₄×C₅₃	—	2	1	no	—
281	C₄⋊C₄×C₅₃	—	2	2	no	—
282	C₄⋊C₄×C₅₃	—	2	2	no	—
283	C₄⋊C₄×C₅₃	—	2	2	no	—
284	C₄⋊C₄×C₅₃	—	2	1	no	—
285	C₄⋊C₄×C₅₃	—	2	1	no	—
286	C₄⋊C₄×C₅₃	—	2	4	no	—
287	C₄⋊C₄×C₅₃	—	2	4	no	—
288	C₄⋊C₄×C₅₃	—	2	1	no	—
289	C₄⋊C₄×C₅₃	—	2	2	no	—
290	C₄⋊C₄×C₅₃	—	2	4	no	—
291	C₄⋊C₄×C₅₃	—	2	2	no	—
292	C₄⋊C₄×C₅₃	—	2	4	no	—
293	C₄⋊C₄×C₅₃	—	2	2	no	—
294	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
299	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
303	C₂²⋊C₄×C₅₃	—	2	2	no	—
304	C₂²⋊C₄×C₅₃	—	2	4	no	—
305	C₂²⋊C₄×C₅₃	—	2	2	no	—
306	C₂²⋊C₄×C₅₃	—	2	4	no	—
307	C₂²⋊C₄×C₅₃	—	2	2	no	—
308	C₂²⋊C₄×C₅₃	—	2	2	no	—
309	C₂²⋊C₄×C₅₃	—	2	2	no	—
310	C₂²⋊C₄×C₅₃	—	2	2	no	—
311	C₂²⋊C₄×C₅₃	—	2	2	no	—
312	C₂²⋊C₄×C₅₃	—	2	2	no	—
313	C₂²⋊C₄×C₅₃	—	2	2	no	—
314	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
315	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
316	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
317	C₄²×C₅₃	—	2	1	no	—
318	C₄²×C₅₃	—	2	1	no	—
319	C₄²×C₅₃	—	2	2	no	—
320	C₄²×C₅₃	—	2	2	no	—
321	C₄²×C₅₃	—	2	1	no	—
322	C₄²×C₅₃	—	2	1	no	—
323	C₄²×C₅₃	—	2	4	no	—
324	C₄²×C₅₃	—	2	4	no	—
325	C₄²×C₅₃	—	2	2	no	—
326	C₄²×C₅₃	C₂×D₄	1	2	yes	—
327	C₄²×C₅₃	C₂×D₄	1	2	yes	—
328	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₅₃	C₂⁴	1	2	yes	—
331	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
333	C₂³×C₅₃	—	2	2	no	—
334	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
335	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₅₃	—	2	2	no	—
337	Q₈×C₅₃	—	2	1	no	—
338	Q₈×C₅₃	—	2	1	no	—
339	Q₈×C₅₃	—	2	2	no	—
340	Q₈×C₅₃	—	2	1	no	—
341	Q₈×C₅₃	—	2	2	no	—
342	Q₈×C₅₃	—	4	2	no	—
343	Q₈×C₅₃	—	4	2	no	—
344	Q₈×C₅₃	—	4	4	no	—
345	Q₈×C₅₃	—	4	4	no	—
346	Q₈×C₅₃	—	4	2	no	—
347	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
348	D₄×C₅₃	—	2	4	no	—
349	D₄×C₅₃	—	2	2	no	—
350	D₄×C₅₃	—	2	2	no	—
351	D₄×C₅₃	—	2	2	no	—
352	D₄×C₅₃	—	4	4	no	—
353	D₄×C₅₃	—	4	4	no	—
354	D₄×C₅₃	—	4	2	no	—
355	D₄×C₅₃	—	8	1	no	—
356	D₄×C₅₃	—	8	2	no	—
357	C₂×C₄×C₅₃	—	2	1	no	—
358	C₂×C₄×C₅₃	—	2	4	no	—
359	C₂×C₄×C₅₃	—	2	1	no	—
360	C₂×C₄×C₅₃	—	2	2	no	—
361	C₂×C₄×C₅₃	—	2	1	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	1	no	—
364	C₂×C₄×C₅₃	—	2	1	no	—
365	C₂×C₄×C₅₃	—	2	2	no	—
366	C₂×C₄×C₅₃	—	2	4	no	—
367	C₂×C₄×C₅₃	—	2	1	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	4	2	no	—
371	C₂×C₄×C₅₃	—	4	1	no	—
372	C₂×C₄×C₅₃	—	4	4	no	—
373	C₂×C₄×C₅₃	—	4	2	no	—
374	C₂×C₄×C₅₃	—	4	4	no	—
375	C₂×C₄×C₅₃	—	4	4	no	—
376	C₂×C₄×C₅₃	—	8	2	no	—
377	C₂×C₄×C₅₃	—	8	1	no	—
378	C₂×C₄×C₅₃	#135	1	4	yes	—
379	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
388	C₈×C₅₃	—	2	2	no	—
389	C₈×C₅₃	—	2	4	no	—
390	C₈×C₅₃	—	2	2	no	—
391	#62101	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
392	C₂²×C₅₃	—	2	1	no	—
393	C₂²×C₅₃	—	2	1	no	—
394	C₂²×C₅₃	—	2	2	no	—
395	C₂²×C₅₃	—	2	2	no	—
396	C₂²×C₅₃	—	2	2	no	—
397	C₂²×C₅₃	—	4	2	no	—
398	C₂²×C₅₃	—	4	2	no	—
399	C₂²×C₅₃	—	4	2	no	—
400	C₂²×C₅₃	C₂×#135	1	2	yes	—
401	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
402	C₄×C₅₃	—	2	1	no	—
403	C₄×C₅₃	—	2	2	no	—
404	C₄×C₅₃	—	2	1	no	—
405	C₄×C₅₃	—	2	2	no	—
406	C₄×C₅₃	—	2	1	no	—
407	C₄×C₅₃	—	2	2	no	—
408	C₄×C₅₃	—	2	2	no	—
409	C₄×C₅₃	—	4	1	no	—
410	C₄×C₅₃	—	4	1	no	—
411	C₄×C₅₃	—	4	2	no	—
412	C₄×C₅₃	—	4	1	no	—
413	C₄×C₅₃	—	4	2	no	—
414	C₄×C₅₃	—	4	2	no	—
415	C₄×C₅₃	—	4	4	no	—
416	C₄×C₅₃	C₂×#135	1	2	yes	—
417	C₄×C₅₃	C₂×#135	1	2	yes	—
418	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
419	C₄×C₅₃	#585	1	1	yes	characteristic
420	#3509	C₂×C₅₃	1	1	yes	characteristic, complemented
421	#3480	C₂×C₅₃	1	1	yes	characteristic
422	#3383	C₂×C₅₃	1	2	yes	complemented
423	#3365	C₂×C₅₃	1	2	yes	complemented
424	#3342	C₂×C₅₃	1	2	yes	complemented
425	#3337	C₂×C₅₃	1	4	yes	complemented
426	#3304	C₂×C₅₃	1	2	yes	complemented
427	#3300	C₂×C₅₃	1	4	yes	complemented
428	#3248	C₂×C₅₃	1	2	yes	complemented
429	#3246	C₂×C₅₃	1	1	yes	characteristic, complemented
430	#3233	C₂×C₅₃	1	2	yes	complemented
431	#3226	C₂×C₅₃	1	1	yes	characteristic, complemented
432	#3107	C₂×C₅₃	1	2	yes	complemented
433	#3104	C₂×C₅₃	1	1	yes	characteristic, complemented
434	#3076	C₂×C₅₃	1	2	yes	complemented
435	C₂×#475	C₂×C₅₃	1	1	yes	characteristic, complemented
436	#2988	C₂×C₅₃	1	1	yes	characteristic, complemented
437	C₂×C₅₃	—	2	2	no	—
438	C₂×C₅₃	—	4	2	no	—
439	C₂×C₅₃	—	8	2	no	—
440	C₂×C₅₃	#3489	1	1	yes	characteristic
441	C₂×C₅₃	C₂²×#135	1	1	yes	characteristic
442	C₂×C₅₃	#3586	1	1	yes	characteristic
443	#559	—	2	1	no	—
444	#559	C₂²×C₅₃	1	1	yes	characteristic
445	#557	—	2	1	no	—
446	#557	C₂²×C₅₃	1	2	yes	—
447	#557	C₂²×C₅₃	1	1	yes	characteristic
448	#556	—	2	1	no	—
449	#556	—	2	1	no	—
450	#556	C₂²×C₅₃	1	1	yes	characteristic
451	#556	C₂²×C₅₃	1	2	yes	—
452	#553	—	2	2	no	—
453	#553	C₂²×C₅₃	1	2	yes	—
454	#552	—	2	2	no	—
455	#552	C₂²×C₅₃	1	4	yes	—
456	#550	C₂²×C₅₃	1	1	yes	characteristic
457	#548	C₂²×C₅₃	1	2	yes	—
458	#541	—	2	2	no	—
459	#536	—	2	1	no	—
460	#533	C₂²×C₅₃	1	1	yes	characteristic
461	#533	C₂²×C₅₃	1	2	yes	—
462	#533	C₂²×C₅₃	1	2	yes	—
463	#532	—	2	1	no	—
464	#532	C₂²×C₅₃	1	1	yes	characteristic
465	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
466	#529	—	2	2	no	—
467	#529	C₂²×C₅₃	1	2	yes	—
468	#519	—	2	1	no	—
469	C₄×#41	—	2	1	no	—
470	C₄×#41	C₂²×C₅₃	1	2	yes	—
471	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
472	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
473	#500	C₂²×C₅₃	1	2	yes	—
474	#499	C₂²×C₅₃	1	4	yes	—
475	#488	C₂²×C₅₃	1	4	yes	—
476	#486	C₂²×C₅₃	1	2	yes	—
477	#485	C₂²×C₅₃	1	4	yes	—
478	#485	C₂²×C₅₃	1	4	yes	—
479	#484	C₂²×C₅₃	1	2	yes	—
480	#482	C₂²×C₅₃	1	4	yes	—
481	#480	C₂²×C₅₃	1	4	yes	—
482	#479	C₂²×C₅₃	1	4	yes	—
483	#479	C₂²×C₅₃	1	4	yes	—
484	#478	C₂²×C₅₃	1	4	yes	—
485	#477	C₂²×C₅₃	1	1	yes	characteristic
486	#477	C₂²×C₅₃	1	1	yes	characteristic
487	#476	C₂²×C₅₃	1	2	yes	—
488	#475	C₂²×C₅₃	1	2	yes	—
489	#475	C₂²×C₅₃	1	2	yes	—
490	#475	C₂²×C₅₃	1	2	yes	—
491	#475	C₂²×C₅₃	1	2	yes	—
492	#475	C₂²×C₅₃	1	2	yes	—
493	#474	C₂²×C₅₃	1	2	yes	—
494	#474	C₂²×C₅₃	1	2	yes	—
495	#467	C₂²×C₅₃	1	4	yes	—
496	#465	C₂²×C₅₃	1	4	yes	—
497	#465	C₂²×C₅₃	1	4	yes	—
498	#464	C₂²×C₅₃	1	4	yes	—
499	#462	C₂²×C₅₃	1	1	yes	characteristic
500	#462	C₂²×C₅₃	1	1	yes	characteristic
501	#461	C₂²×C₅₃	1	2	yes	—
502	#460	C₂²×C₅₃	1	2	yes	—
503	#452	C₂²×C₅₃	1	4	yes	—
504	#451	C₂²×C₅₃	1	2	yes	—
505	C₈×Q₈	C₂²×C₅₃	1	2	yes	—
506	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
507	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
508	C₄×Q₁₆	C₂²×C₅₃	1	4	yes	—
509	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	—
510	C₈×D₄	C₂²×C₅₃	1	4	yes	—
511	C₈×D₄	C₂²×C₅₃	1	2	yes	—
512	#431	C₂²×C₅₃	1	1	yes	characteristic
513	#431	C₂²×C₅₃	1	2	yes	—
514	#427	C₂²×C₅₃	1	4	yes	—
515	C₂×#106	C₂²×C₅₃	1	2	yes	—
516	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
517	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
518	#416	C₂²×C₅₃	1	4	yes	—
519	C₂×#103	C₂²×C₅₃	1	2	yes	—
520	C₅₃	#62101	1	1	yes	characteristic, direct product factor, Sylow
521	C₂×#41	—	2	1	no	—
522	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
523	C₂×#41	C₂³×C₅₃	1	2	yes	—
524	C₂²×Q₈	—	2	1	no	—
525	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
526	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
527	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
528	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
529	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
530	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	—	2	2	no	—
533	C₄⋊Q₈	—	2	1	no	—
534	C₄⋊Q₈	—	2	1	no	—
535	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
536	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
537	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
538	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
539	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
540	#127	—	2	1	no	—
541	#127	C₂³×C₅₃	1	1	yes	characteristic
542	#126	—	2	2	no	—
543	#126	—	2	2	no	—
544	#126	—	2	4	no	—
545	#126	—	2	4	no	—
546	#126	—	2	2	no	—
547	#125	—	2	2	no	—
548	#125	—	2	4	no	—
549	#125	—	2	4	no	—
550	#125	—	2	1	no	—
551	#125	—	2	2	no	—
552	#125	C₂³×C₅₃	1	2	yes	—
553	#125	C₂³×C₅₃	1	4	yes	—
554	#124	—	2	1	no	—
555	#124	—	2	1	no	—
556	#124	—	2	2	no	—
557	#124	—	2	2	no	—
558	#124	—	2	1	no	—
559	#124	C₂³×C₅₃	1	2	yes	—
560	#123	—	2	4	no	—
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	#123	—	2	2	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
570	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
571	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	—	2	1	no	—
575	#121	—	2	2	no	—
576	#121	C₂³×C₅₃	1	2	yes	—
577	#121	C₂³×C₅₃	1	2	yes	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	2	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
589	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
590	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
594	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
595	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
596	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	D₄×C₅₃	1	2	yes	—
606	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
607	C₄×D₄	C₂³×C₅₃	1	2	yes	—
608	C₄×D₄	C₂³×C₅₃	1	2	yes	—
609	C₄×D₄	C₂³×C₅₃	1	2	yes	—
610	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
611	#117	—	2	1	no	—
612	#117	—	2	2	no	—
613	#117	—	2	4	no	—
614	#117	—	2	2	no	—
615	#117	—	2	2	no	—
616	#117	D₄×C₅₃	1	1	yes	characteristic
617	#117	D₄×C₅₃	1	2	yes	—
618	#117	C₂³×C₅₃	1	2	yes	—
619	#117	C₂³×C₅₃	1	4	yes	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
624	C₂×C₄²	—	2	1	no	—
625	C₂×C₄²	—	2	2	no	—
626	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
628	#107	C₂³×C₅₃	1	2	yes	—
629	#107	C₂³×C₅₃	1	4	yes	—
630	#107	C₂³×C₅₃	1	4	yes	—
631	#107	C₂³×C₅₃	1	2	yes	—
632	#106	C₂³×C₅₃	1	4	yes	—
633	#106	C₂³×C₅₃	1	4	yes	—
634	#106	C₂³×C₅₃	1	4	yes	—
635	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
636	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
637	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
638	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
639	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
640	#103	C₂³×C₅₃	1	4	yes	—
641	#103	C₂³×C₅₃	1	4	yes	—
642	#103	C₂³×C₅₃	1	2	yes	—
643	#103	C₂³×C₅₃	1	2	yes	—
644	#103	C₂³×C₅₃	1	2	yes	—
645	#103	C₂³×C₅₃	1	4	yes	—
646	#103	C₂³×C₅₃	1	2	yes	—
647	#102	C₂³×C₅₃	1	4	yes	—
648	#102	C₂³×C₅₃	1	4	yes	—
649	#102	C₂³×C₅₃	1	4	yes	—
650	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
651	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
652	C₄×C₈	C₂³×C₅₃	1	4	yes	—
653	C₄×C₈	C₂³×C₅₃	1	2	yes	—
654	#41	—	2	4	no	—
655	#41	—	2	4	no	—
656	#41	—	4	2	no	—
657	#41	—	4	4	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	—	4	1	no	—
665	C₂×Q₈	—	4	4	no	—
666	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
667	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
668	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
669	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
676	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
677	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
685	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
687	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
690	Q₁₆	—	2	4	no	—
691	Q₁₆	—	4	2	no	—
692	SD₁₆	—	4	4	no	—
693	C₂×C₈	—	4	2	no	—
694	C₂×C₈	—	4	4	no	—
695	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
696	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
697	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
721	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
722	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
723	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
725	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
741	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
742	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
743	C₄²	—	2	1	no	—
744	C₄²	—	2	1	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	1	no	—
748	C₄²	—	2	1	no	—
749	C₄²	—	2	4	no	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	2	no	—
752	C₄²	C₂×D₄×C₅₃	1	2	yes	—
753	C₄²	C₂×D₄×C₅₃	1	2	yes	—
754	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
755	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
756	C₄²	C₂⁴×C₅₃	1	2	yes	—
757	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
758	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
759	C₂³	—	2	2	no	—
760	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
761	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
762	Q₈	—	2	2	no	—
763	Q₈	—	2	1	no	—
764	Q₈	—	2	2	no	—
765	Q₈	—	2	1	no	—
766	Q₈	—	2	2	no	—
767	Q₈	—	2	1	no	—
768	Q₈	—	4	2	no	—
769	Q₈	—	4	2	no	—
770	Q₈	—	4	4	no	—
771	Q₈	—	4	4	no	—
772	Q₈	—	4	2	no	—
773	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
774	D₄	—	2	4	no	—
775	D₄	—	2	2	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	4	4	no	—
779	D₄	—	4	4	no	—
780	D₄	—	4	2	no	—
781	D₄	—	8	1	no	—
782	D₄	—	8	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	4	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	4	4	no	—
802	C₂×C₄	—	8	2	no	—
803	C₂×C₄	—	8	1	no	—
804	C₂×C₄	#135×C₅₃	1	4	yes	—
805	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
807	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
810	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
811	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
813	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
814	C₈	—	2	2	no	—
815	C₈	—	2	4	no	—
816	C₈	—	2	2	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	C₂×#135×C₅₃	1	2	yes	—
826	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
827	C₄	—	2	2	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	1	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	4	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	2	no	—
841	C₄	C₂×#135×C₅₃	1	2	yes	—
842	C₄	C₂×#135×C₅₃	1	2	yes	—
843	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
844	C₄	C₅₃×#585	1	1	yes	characteristic
845	C₂	—	2	2	no	—
846	C₂	—	4	2	no	—
847	C₂	—	8	2	no	—
848	C₂	C₅₃×#3489	1	1	yes	characteristic
849	C₂	C₂²×#135×C₅₃	1	1	yes	characteristic
850	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3480	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×#3509	C₂	semidirect
3. C₅₃×#3383	C₂	semidirect
4. C₅₃×#3365	C₂	semidirect
5. C₅₃×#3342	C₂	semidirect
6. C₅₃×#3337	C₂	semidirect
7. C₅₃×#3304	C₂	semidirect
8. C₅₃×#3300	C₂	semidirect
9. C₅₃×#3248	C₂	semidirect
10. C₅₃×#3246	C₂	semidirect
11. C₅₃×#3233	C₂	semidirect
12. C₅₃×#3226	C₂	semidirect
13. C₅₃×#3107	C₂	semidirect
14. C₅₃×#3104	C₂	semidirect
15. C₅₃×#3076	C₂	semidirect
16. C₂×C₅₃×#475	C₂	semidirect
17. C₅₃×#2988	C₂	semidirect
391. #62101	C₅₃	direct (N × H)
420. #3509	C₂×C₅₃	semidirect
422. #3383	C₂×C₅₃	semidirect
423. #3365	C₂×C₅₃	semidirect
424. #3342	C₂×C₅₃	semidirect
425. #3337	C₂×C₅₃	semidirect
426. #3304	C₂×C₅₃	semidirect
427. #3300	C₂×C₅₃	semidirect
428. #3248	C₂×C₅₃	semidirect
429. #3246	C₂×C₅₃	semidirect
430. #3233	C₂×C₅₃	semidirect
431. #3226	C₂×C₅₃	semidirect
432. #3107	C₂×C₅₃	semidirect
433. #3104	C₂×C₅₃	semidirect
434. #3076	C₂×C₅₃	semidirect
435. C₂×#475	C₂×C₅₃	semidirect
436. #2988	C₂×C₅₃	semidirect
520. C₅₃	#62101	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×#3509	2
C₅₃×#3480	2
C₅₃×#3383	2
C₅₃×#3365	2
C₅₃×#3342	2
C₅₃×#3337	2
C₅₃×#3304	2
C₅₃×#3300	2
C₅₃×#3248	2
C₅₃×#3246	2
C₅₃×#3233	2
C₅₃×#3226	2
C₅₃×#3107	2
C₅₃×#3104	2
C₅₃×#3076	2
C₂×C₅₃×#475	2
C₅₃×#2988	2
#62101	53

Subgroups — C53×#62101 #27269613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62101 #27269613