Subgroups — C₅₃×#62127 #27269639

Order 13568.

1810 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3481	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3385	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3375	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3346	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3338	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3314	C₂	1	4	yes	maximal, complemented
8	C₅₃×#3295	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3248	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3239	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3110	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#474	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#559	C₂²	1	1	yes	characteristic
19	Q₈²×C₅₃	C₂²	1	2	yes	complemented
20	C₅₃×#557	—	2	1	no	—
21	C₅₃×#554	C₂²	1	1	yes	characteristic
22	C₅₃×#554	C₂²	1	1	yes	characteristic
23	C₅₃×#554	C₂²	1	2	yes	—
24	C₅₃×#554	C₂²	1	4	yes	complemented
25	C₅₃×#553	—	2	1	no	—
26	C₅₃×#553	C₂²	1	2	yes	—
27	C₅₃×#551	—	2	2	no	—
28	D₄×Q₈×C₅₃	—	2	1	no	—
29	D₄×Q₈×C₅₃	—	2	2	no	—
30	C₅₃×#546	—	2	1	no	—
31	C₅₃×#546	C₂²	1	2	yes	—
32	D₄²×C₅₃	C₂²	1	1	yes	characteristic
33	C₅₃×#544	—	2	2	no	—
34	C₅₃×#544	—	2	1	no	—
35	C₅₃×#533	C₂²	1	2	yes	complemented
36	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#532	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
40	C₅₃×#529	—	2	1	no	—
41	C₅₃×#529	C₂²	1	2	yes	—
42	C₅₃×#525	—	2	2	no	—
43	C₅₃×#520	—	2	1	no	—
44	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
45	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₅₃	—	2	1	no	—
47	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
48	C₅₃×#501	C₂²	1	4	yes	complemented
49	C₅₃×#500	C₂²	1	2	yes	complemented
50	C₅₃×#489	C₂²	1	4	yes	complemented
51	C₅₃×#486	C₂²	1	2	yes	—
52	C₅₃×#485	C₂²	1	2	yes	complemented
53	C₅₃×#484	C₂²	1	4	yes	complemented
54	C₅₃×#484	C₂²	1	4	yes	complemented
55	C₅₃×#481	C₂²	1	4	yes	—
56	C₅₃×#480	C₂²	1	4	yes	complemented
57	C₅₃×#479	C₂²	1	4	yes	complemented
58	C₅₃×#477	C₂²	1	2	yes	complemented
59	C₅₃×#477	C₂²	1	2	yes	complemented
60	C₅₃×#476	C₂²	1	2	yes	—
61	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#475	C₂²	1	2	yes	complemented
63	C₅₃×#474	C₂²	1	4	yes	—
64	C₅₃×#474	C₂²	1	1	yes	characteristic
65	C₅₃×#474	C₂²	1	2	yes	—
66	C₅₃×#474	C₂²	1	2	yes	complemented
67	C₅₃×#474	C₂²	1	2	yes	complemented
68	C₅₃×#474	C₂²	1	2	yes	complemented
69	C₅₃×#474	C₂²	1	4	yes	complemented
70	C₅₃×#468	C₂²	1	4	yes	complemented
71	C₅₃×#467	C₂²	1	4	yes	complemented
72	C₅₃×#465	C₂²	1	4	yes	—
73	C₅₃×#464	C₂²	1	4	yes	complemented
74	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#461	C₂²	1	1	yes	characteristic
76	C₅₃×#461	C₂²	1	2	yes	complemented
77	C₅₃×#460	C₂²	1	2	yes	—
78	C₅₃×#452	C₂²	1	2	yes	—
79	C₅₃×#450	C₂²	1	4	yes	—
80	C₅₃×#446	C₂²	1	2	yes	complemented
81	C₅₃×#440	C₂²	1	4	yes	—
82	C₅₃×#440	C₂²	1	4	yes	complemented
83	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
85	C₅₃×#435	C₂²	1	4	yes	complemented
86	C₈×D₄×C₅₃	C₂²	1	2	yes	—
87	C₅₃×#432	C₂²	1	2	yes	complemented
88	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#428	C₂²	1	2	yes	complemented
90	C₂×#107×C₅₃	C₂²	1	4	yes	complemented
91	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	complemented
93	C₅₃×#417	C₂²	1	2	yes	—
94	C₂×#102×C₅₃	C₂²	1	4	yes	—
95	C₂×#41×C₅₃	—	2	1	no	—
96	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
97	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₅₃	—	2	2	no	—
99	C₂²×Q₈×C₅₃	—	2	1	no	—
100	C₂²×D₄×C₅₃	—	2	1	no	—
101	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
102	C₂³×C₄×C₅₃	—	2	2	no	—
103	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
106	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
107	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
108	C₄⋊Q₈×C₅₃	—	2	2	no	—
109	C₄⋊Q₈×C₅₃	—	2	4	no	—
110	C₄⋊Q₈×C₅₃	—	2	1	no	—
111	C₄⋊Q₈×C₅₃	—	2	2	no	—
112	C₄⋊Q₈×C₅₃	—	2	1	no	—
113	C₄⋊Q₈×C₅₃	—	2	2	no	—
114	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
116	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
120	#127×C₅₃	C₂³	1	1	yes	characteristic
121	#126×C₅₃	—	2	2	no	—
122	#126×C₅₃	—	2	2	no	—
123	#125×C₅₃	—	2	1	no	—
124	#125×C₅₃	—	2	2	no	—
125	#125×C₅₃	—	2	4	no	—
126	#125×C₅₃	—	2	1	no	—
127	#125×C₅₃	—	2	2	no	—
128	#125×C₅₃	C₂³	1	2	yes	—
129	#124×C₅₃	—	2	1	no	—
130	#124×C₅₃	—	2	1	no	—
131	#124×C₅₃	C₂³	1	2	yes	—
132	#123×C₅₃	—	2	2	no	—
133	#123×C₅₃	—	2	2	no	—
134	#123×C₅₃	—	2	2	no	—
135	#123×C₅₃	—	2	2	no	—
136	C₂²⋊Q₈×C₅₃	—	2	2	no	—
137	C₂²⋊Q₈×C₅₃	—	2	2	no	—
138	C₂²⋊Q₈×C₅₃	—	2	4	no	—
139	C₂²⋊Q₈×C₅₃	—	2	4	no	—
140	C₂²⋊Q₈×C₅₃	—	2	4	no	—
141	C₂²⋊Q₈×C₅₃	—	2	1	no	—
142	C₂²⋊Q₈×C₅₃	—	2	2	no	—
143	C₂²⋊Q₈×C₅₃	—	2	1	no	—
144	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
145	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
146	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
147	#121×C₅₃	—	2	1	no	—
148	#121×C₅₃	—	2	2	no	—
149	#121×C₅₃	—	2	2	no	—
150	#121×C₅₃	—	2	1	no	—
151	#121×C₅₃	C₂³	1	2	yes	—
152	#121×C₅₃	C₂³	1	2	yes	—
153	#120×C₅₃	—	2	2	no	—
154	#120×C₅₃	—	2	2	no	—
155	C₄×Q₈×C₅₃	—	2	1	no	—
156	C₄×Q₈×C₅₃	—	2	2	no	—
157	C₄×Q₈×C₅₃	—	2	2	no	—
158	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
159	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
160	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
163	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
164	C₄×D₄×C₅₃	—	2	1	no	—
165	C₄×D₄×C₅₃	—	2	2	no	—
166	C₄×D₄×C₅₃	—	2	1	no	—
167	C₄×D₄×C₅₃	—	2	2	no	—
168	C₄×D₄×C₅₃	—	2	2	no	—
169	C₄×D₄×C₅₃	—	2	1	no	—
170	C₄×D₄×C₅₃	—	2	2	no	—
171	C₄×D₄×C₅₃	—	2	4	no	—
172	C₄×D₄×C₅₃	—	2	2	no	—
173	C₄×D₄×C₅₃	—	2	1	no	—
174	C₄×D₄×C₅₃	—	2	1	no	—
175	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
176	C₄×D₄×C₅₃	D₄	1	2	yes	—
177	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₅₃	C₂³	1	2	yes	—
179	C₄×D₄×C₅₃	C₂³	1	2	yes	—
180	C₄×D₄×C₅₃	C₂³	1	2	yes	—
181	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₅₃	C₂³	1	2	yes	—
184	#117×C₅₃	—	2	1	no	—
185	#117×C₅₃	—	2	2	no	—
186	#117×C₅₃	—	2	2	no	—
187	#117×C₅₃	—	2	1	no	—
188	#117×C₅₃	D₄	1	2	yes	—
189	#117×C₅₃	D₄	1	1	yes	characteristic
190	#117×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
192	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
193	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
194	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
196	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
199	C₂×C₄²×C₅₃	—	2	1	no	—
200	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
202	#107×C₅₃	C₂³	1	2	yes	—
203	#107×C₅₃	C₂³	1	4	yes	—
204	#107×C₅₃	C₂³	1	4	yes	—
205	#107×C₅₃	C₂³	1	4	yes	—
206	#107×C₅₃	C₂³	1	4	yes	—
207	#106×C₅₃	C₂³	1	2	yes	—
208	#106×C₅₃	C₂³	1	4	yes	—
209	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
210	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
211	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
212	C₄⋊C₈×C₅₃	C₂³	1	2	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	2	yes	—
217	#103×C₅₃	C₂³	1	4	yes	—
218	#103×C₅₃	C₂³	1	4	yes	—
219	#102×C₅₃	C₂³	1	4	yes	—
220	#102×C₅₃	C₂³	1	4	yes	—
221	#102×C₅₃	C₂³	1	4	yes	—
222	#102×C₅₃	C₂³	1	2	yes	—
223	#102×C₅₃	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
225	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
226	#97×C₅₃	C₂³	1	4	yes	—
227	C₄×C₈×C₅₃	C₂³	1	2	yes	—
228	C₂⁴×C₅₃	—	2	2	no	—
229	#41×C₅₃	—	2	4	no	—
230	#41×C₅₃	—	2	2	no	—
231	#41×C₅₃	—	4	1	no	—
232	#41×C₅₃	—	8	2	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	4	no	—
237	C₂×Q₈×C₅₃	—	2	2	no	—
238	C₂×Q₈×C₅₃	—	8	4	no	—
239	C₂×Q₈×C₅₃	—	8	2	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×D₄×C₅₃	—	2	4	no	—
244	C₂×D₄×C₅₃	—	2	1	no	—
245	C₂×D₄×C₅₃	—	2	2	no	—
246	C₂×D₄×C₅₃	—	2	2	no	—
247	C₂×D₄×C₅₃	—	2	2	no	—
248	C₂×D₄×C₅₃	—	2	1	no	—
249	C₂×D₄×C₅₃	—	2	1	no	—
250	C₂×D₄×C₅₃	—	4	2	no	—
251	C₂×D₄×C₅₃	—	4	4	no	—
252	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
254	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
255	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₅₃	—	2	2	no	—
257	C₂²×C₄×C₅₃	—	2	2	no	—
258	C₂²×C₄×C₅₃	—	2	4	no	—
259	C₂²×C₄×C₅₃	—	2	1	no	—
260	C₂²×C₄×C₅₃	—	2	1	no	—
261	C₂²×C₄×C₅₃	—	2	1	no	—
262	C₂²×C₄×C₅₃	—	2	2	no	—
263	C₂²×C₄×C₅₃	—	2	2	no	—
264	C₂²×C₄×C₅₃	—	2	2	no	—
265	C₂²×C₄×C₅₃	—	8	4	no	—
266	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
272	Q₁₆×C₅₃	—	4	2	no	—
273	SD₁₆×C₅₃	—	2	4	no	—
274	SD₁₆×C₅₃	—	4	4	no	—
275	M₁₆×C₅₃	—	4	2	no	—
276	C₂×C₈×C₅₃	—	4	4	no	—
277	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
278	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
279	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
280	C₄⋊C₄×C₅₃	—	2	1	no	—
281	C₄⋊C₄×C₅₃	—	2	2	no	—
282	C₄⋊C₄×C₅₃	—	2	1	no	—
283	C₄⋊C₄×C₅₃	—	2	2	no	—
284	C₄⋊C₄×C₅₃	—	2	4	no	—
285	C₄⋊C₄×C₅₃	—	2	2	no	—
286	C₄⋊C₄×C₅₃	—	2	2	no	—
287	C₄⋊C₄×C₅₃	—	2	2	no	—
288	C₄⋊C₄×C₅₃	—	2	4	no	—
289	C₄⋊C₄×C₅₃	—	2	1	no	—
290	C₄⋊C₄×C₅₃	—	2	1	no	—
291	C₄⋊C₄×C₅₃	—	2	1	no	—
292	C₄⋊C₄×C₅₃	—	2	2	no	—
293	C₄⋊C₄×C₅₃	—	2	2	no	—
294	C₄⋊C₄×C₅₃	—	2	1	no	—
295	C₄⋊C₄×C₅₃	—	2	2	no	—
296	C₄⋊C₄×C₅₃	—	2	4	no	—
297	C₄⋊C₄×C₅₃	—	2	4	no	—
298	C₄⋊C₄×C₅₃	—	2	2	no	—
299	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
302	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
305	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
307	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
308	C₂²⋊C₄×C₅₃	—	2	2	no	—
309	C₂²⋊C₄×C₅₃	—	2	2	no	—
310	C₂²⋊C₄×C₅₃	—	2	4	no	—
311	C₂²⋊C₄×C₅₃	—	2	1	no	—
312	C₂²⋊C₄×C₅₃	—	2	1	no	—
313	C₂²⋊C₄×C₅₃	—	2	2	no	—
314	C₂²⋊C₄×C₅₃	—	2	2	no	—
315	C₂²⋊C₄×C₅₃	—	2	2	no	—
316	C₂²⋊C₄×C₅₃	—	2	2	no	—
317	C₂²⋊C₄×C₅₃	—	2	2	no	—
318	C₂²⋊C₄×C₅₃	—	2	1	no	—
319	C₂²⋊C₄×C₅₃	—	2	2	no	—
320	C₂²⋊C₄×C₅₃	—	2	2	no	—
321	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
324	C₄²×C₅₃	—	2	1	no	—
325	C₄²×C₅₃	—	2	1	no	—
326	C₄²×C₅₃	—	2	1	no	—
327	C₄²×C₅₃	—	2	4	no	—
328	C₄²×C₅₃	—	2	2	no	—
329	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₅₃	C₂×D₄	1	2	yes	—
332	C₄²×C₅₃	C₂×D₄	1	2	yes	—
333	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
334	C₄²×C₅₃	C₂⁴	1	2	yes	—
335	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
336	C₂³×C₅₃	—	2	1	no	—
337	C₂³×C₅₃	—	2	2	no	—
338	C₂³×C₅₃	—	4	4	no	—
339	C₂³×C₅₃	—	4	4	no	—
340	C₂³×C₅₃	—	8	2	no	—
341	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
342	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
343	Q₈×C₅₃	—	2	2	no	—
344	Q₈×C₅₃	—	2	1	no	—
345	Q₈×C₅₃	—	2	2	no	—
346	Q₈×C₅₃	—	2	1	no	—
347	Q₈×C₅₃	—	2	2	no	—
348	Q₈×C₅₃	—	4	2	no	—
349	Q₈×C₅₃	—	4	4	no	—
350	Q₈×C₅₃	—	8	4	no	—
351	Q₈×C₅₃	—	8	2	no	—
352	Q₈×C₅₃	—	8	1	no	—
353	D₄×C₅₃	—	2	4	no	—
354	D₄×C₅₃	—	2	2	no	—
355	D₄×C₅₃	—	2	1	no	—
356	D₄×C₅₃	—	2	2	no	—
357	D₄×C₅₃	—	4	4	no	—
358	D₄×C₅₃	—	4	2	no	—
359	D₄×C₅₃	—	4	4	no	—
360	D₄×C₅₃	—	4	2	no	—
361	D₄×C₅₃	—	8	1	no	—
362	D₄×C₅₃	—	8	2	no	—
363	D₄×C₅₃	#137	1	4	yes	—
364	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
365	C₂×C₄×C₅₃	—	2	4	no	—
366	C₂×C₄×C₅₃	—	2	2	no	—
367	C₂×C₄×C₅₃	—	2	4	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	1	no	—
371	C₂×C₄×C₅₃	—	2	2	no	—
372	C₂×C₄×C₅₃	—	2	1	no	—
373	C₂×C₄×C₅₃	—	2	1	no	—
374	C₂×C₄×C₅₃	—	2	2	no	—
375	C₂×C₄×C₅₃	—	2	4	no	—
376	C₂×C₄×C₅₃	—	2	2	no	—
377	C₂×C₄×C₅₃	—	2	1	no	—
378	C₂×C₄×C₅₃	—	2	1	no	—
379	C₂×C₄×C₅₃	—	2	2	no	—
380	C₂×C₄×C₅₃	—	4	2	no	—
381	C₂×C₄×C₅₃	—	4	2	no	—
382	C₂×C₄×C₅₃	—	4	2	no	—
383	C₂×C₄×C₅₃	—	4	4	no	—
384	C₂×C₄×C₅₃	—	8	2	no	—
385	C₂×C₄×C₅₃	—	8	2	no	—
386	C₂×C₄×C₅₃	—	8	2	no	—
387	C₂×C₄×C₅₃	—	8	4	no	—
388	C₂×C₄×C₅₃	—	8	2	no	—
389	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
398	C₈×C₅₃	—	2	2	no	—
399	C₈×C₅₃	—	2	2	no	—
400	C₈×C₅₃	—	2	4	no	—
401	#62127	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
402	C₂²×C₅₃	—	2	2	no	—
403	C₂²×C₅₃	—	2	2	no	—
404	C₂²×C₅₃	—	2	1	no	—
405	C₂²×C₅₃	—	2	2	no	—
406	C₂²×C₅₃	—	2	1	no	—
407	C₂²×C₅₃	—	2	1	no	—
408	C₂²×C₅₃	—	4	1	no	—
409	C₂²×C₅₃	—	4	1	no	—
410	C₂²×C₅₃	—	4	2	no	—
411	C₂²×C₅₃	—	4	2	no	—
412	C₂²×C₅₃	—	4	2	no	—
413	C₂²×C₅₃	—	8	8	no	—
414	C₂²×C₅₃	C₂×#137	1	4	yes	—
415	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
416	C₄×C₅₃	—	2	1	no	—
417	C₄×C₅₃	—	2	2	no	—
418	C₄×C₅₃	—	2	1	no	—
419	C₄×C₅₃	—	2	2	no	—
420	C₄×C₅₃	—	2	2	no	—
421	C₄×C₅₃	—	2	1	no	—
422	C₄×C₅₃	—	4	1	no	—
423	C₄×C₅₃	—	4	2	no	—
424	C₄×C₅₃	—	4	1	no	—
425	C₄×C₅₃	—	4	1	no	—
426	C₄×C₅₃	—	4	2	no	—
427	C₄×C₅₃	—	4	2	no	—
428	C₄×C₅₃	—	4	4	no	—
429	C₄×C₅₃	C₂×#137	1	2	yes	—
430	C₄×C₅₃	#576	1	2	yes	—
431	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
432	C₄×C₅₃	#585	1	1	yes	characteristic
433	#3503	C₂×C₅₃	1	1	yes	characteristic, complemented
434	#3481	C₂×C₅₃	1	1	yes	characteristic
435	#3385	C₂×C₅₃	1	2	yes	complemented
436	#3375	C₂×C₅₃	1	2	yes	complemented
437	#3346	C₂×C₅₃	1	4	yes	complemented
438	#3338	C₂×C₅₃	1	2	yes	complemented
439	#3314	C₂×C₅₃	1	4	yes	complemented
440	#3295	C₂×C₅₃	1	2	yes	complemented
441	#3254	C₂×C₅₃	1	1	yes	characteristic, complemented
442	#3248	C₂×C₅₃	1	2	yes	complemented
443	#3239	C₂×C₅₃	1	2	yes	complemented
444	#3226	C₂×C₅₃	1	1	yes	characteristic, complemented
445	#3110	C₂×C₅₃	1	2	yes	complemented
446	#3107	C₂×C₅₃	1	1	yes	characteristic, complemented
447	#3079	C₂×C₅₃	1	1	yes	characteristic, complemented
448	C₂×#474	C₂×C₅₃	1	2	yes	complemented
449	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
450	C₂×C₅₃	—	2	4	no	—
451	C₂×C₅₃	—	4	1	no	—
452	C₂×C₅₃	—	4	2	no	—
453	C₂×C₅₃	—	8	2	no	—
454	C₂×C₅₃	#3489	1	1	yes	characteristic
455	C₂×C₅₃	C₂²×#137	1	1	yes	characteristic
456	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
457	#559	C₂²×C₅₃	1	1	yes	characteristic
458	Q₈²	C₂²×C₅₃	1	2	yes	complemented
459	#557	—	2	1	no	—
460	#554	C₂²×C₅₃	1	1	yes	characteristic
461	#554	C₂²×C₅₃	1	1	yes	characteristic
462	#554	C₂²×C₅₃	1	2	yes	—
463	#554	C₂²×C₅₃	1	4	yes	complemented
464	#553	—	2	1	no	—
465	#553	C₂²×C₅₃	1	2	yes	—
466	#551	—	2	2	no	—
467	D₄×Q₈	—	2	1	no	—
468	D₄×Q₈	—	2	2	no	—
469	#546	—	2	1	no	—
470	#546	C₂²×C₅₃	1	2	yes	—
471	D₄²	C₂²×C₅₃	1	1	yes	characteristic
472	#544	—	2	2	no	—
473	#544	—	2	1	no	—
474	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
475	#533	C₂²×C₅₃	1	2	yes	complemented
476	#532	C₂²×C₅₃	1	1	yes	characteristic
477	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
478	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
479	#529	—	2	1	no	—
480	#529	C₂²×C₅₃	1	2	yes	—
481	#525	—	2	2	no	—
482	#520	—	2	1	no	—
483	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
484	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
485	C₂×C₄×D₄	—	2	1	no	—
486	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
487	#501	C₂²×C₅₃	1	4	yes	complemented
488	#500	C₂²×C₅₃	1	2	yes	complemented
489	#489	C₂²×C₅₃	1	4	yes	complemented
490	#486	C₂²×C₅₃	1	2	yes	—
491	#485	C₂²×C₅₃	1	2	yes	complemented
492	#484	C₂²×C₅₃	1	4	yes	complemented
493	#484	C₂²×C₅₃	1	4	yes	complemented
494	#481	C₂²×C₅₃	1	4	yes	—
495	#480	C₂²×C₅₃	1	4	yes	complemented
496	#479	C₂²×C₅₃	1	4	yes	complemented
497	#477	C₂²×C₅₃	1	2	yes	complemented
498	#477	C₂²×C₅₃	1	2	yes	complemented
499	#476	C₂²×C₅₃	1	2	yes	—
500	#475	C₂²×C₅₃	1	2	yes	complemented
501	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
502	#474	C₂²×C₅₃	1	2	yes	—
503	#474	C₂²×C₅₃	1	1	yes	characteristic
504	#474	C₂²×C₅₃	1	4	yes	—
505	#474	C₂²×C₅₃	1	4	yes	complemented
506	#474	C₂²×C₅₃	1	2	yes	complemented
507	#474	C₂²×C₅₃	1	2	yes	complemented
508	#474	C₂²×C₅₃	1	2	yes	complemented
509	#468	C₂²×C₅₃	1	4	yes	complemented
510	#467	C₂²×C₅₃	1	4	yes	complemented
511	#465	C₂²×C₅₃	1	4	yes	—
512	#464	C₂²×C₅₃	1	4	yes	complemented
513	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
514	#461	C₂²×C₅₃	1	1	yes	characteristic
515	#461	C₂²×C₅₃	1	2	yes	complemented
516	#460	C₂²×C₅₃	1	2	yes	—
517	#452	C₂²×C₅₃	1	2	yes	—
518	#450	C₂²×C₅₃	1	4	yes	—
519	#446	C₂²×C₅₃	1	2	yes	complemented
520	#440	C₂²×C₅₃	1	4	yes	—
521	#440	C₂²×C₅₃	1	4	yes	complemented
522	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
523	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
524	#435	C₂²×C₅₃	1	4	yes	complemented
525	C₈×D₄	C₂²×C₅₃	1	2	yes	—
526	#432	C₂²×C₅₃	1	2	yes	complemented
527	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
528	#428	C₂²×C₅₃	1	2	yes	complemented
529	C₂×#107	C₂²×C₅₃	1	4	yes	complemented
530	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
531	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	complemented
532	#417	C₂²×C₅₃	1	2	yes	—
533	C₂×#102	C₂²×C₅₃	1	4	yes	—
534	C₅₃	#62127	1	1	yes	characteristic, direct product factor, Sylow
535	C₂×#41	—	2	1	no	—
536	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
537	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
538	C₂²×Q₈	—	2	2	no	—
539	C₂²×Q₈	—	2	1	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
542	C₂³×C₄	—	2	2	no	—
543	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
544	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
545	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
546	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
547	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
548	C₄⋊Q₈	—	2	2	no	—
549	C₄⋊Q₈	—	2	4	no	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	2	no	—
552	C₄⋊Q₈	—	2	1	no	—
553	C₄⋊Q₈	—	2	2	no	—
554	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
555	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
556	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
557	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
558	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
559	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
560	#127	C₂³×C₅₃	1	1	yes	characteristic
561	#126	—	2	2	no	—
562	#126	—	2	2	no	—
563	#125	—	2	1	no	—
564	#125	—	2	2	no	—
565	#125	—	2	4	no	—
566	#125	—	2	1	no	—
567	#125	—	2	2	no	—
568	#125	C₂³×C₅₃	1	2	yes	—
569	#124	—	2	1	no	—
570	#124	—	2	1	no	—
571	#124	C₂³×C₅₃	1	2	yes	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	#123	—	2	2	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₂²⋊Q₈	—	2	4	no	—
583	C₂²⋊Q₈	—	2	4	no	—
584	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
585	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
586	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
587	#121	—	2	2	no	—
588	#121	—	2	1	no	—
589	#121	—	2	1	no	—
590	#121	—	2	2	no	—
591	#121	C₂³×C₅₃	1	2	yes	—
592	#121	C₂³×C₅₃	1	2	yes	—
593	#120	—	2	2	no	—
594	#120	—	2	2	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	2	no	—
598	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
602	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
603	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	4	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
616	C₄×D₄	D₄×C₅₃	1	2	yes	—
617	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₅₃	1	2	yes	—
619	C₄×D₄	C₂³×C₅₃	1	2	yes	—
620	C₄×D₄	C₂³×C₅₃	1	2	yes	—
621	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
622	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
623	C₄×D₄	C₂³×C₅₃	1	2	yes	—
624	#117	—	2	2	no	—
625	#117	—	2	1	no	—
626	#117	—	2	1	no	—
627	#117	—	2	2	no	—
628	#117	D₄×C₅₃	1	2	yes	—
629	#117	D₄×C₅₃	1	1	yes	characteristic
630	#117	C₂³×C₅₃	1	1	yes	characteristic
631	C₂×C₄⋊C₄	—	2	2	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
636	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₂²⋊C₄	—	2	2	no	—
639	C₂×C₄²	—	2	1	no	—
640	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
641	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
642	#107	C₂³×C₅₃	1	2	yes	—
643	#107	C₂³×C₅₃	1	4	yes	—
644	#107	C₂³×C₅₃	1	4	yes	—
645	#107	C₂³×C₅₃	1	4	yes	—
646	#107	C₂³×C₅₃	1	4	yes	—
647	#106	C₂³×C₅₃	1	4	yes	—
648	#106	C₂³×C₅₃	1	2	yes	—
649	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
650	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
651	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
652	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
653	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
654	#103	C₂³×C₅₃	1	4	yes	—
655	#103	C₂³×C₅₃	1	2	yes	—
656	#103	C₂³×C₅₃	1	2	yes	—
657	#103	C₂³×C₅₃	1	2	yes	—
658	#103	C₂³×C₅₃	1	4	yes	—
659	#102	C₂³×C₅₃	1	2	yes	—
660	#102	C₂³×C₅₃	1	4	yes	—
661	#102	C₂³×C₅₃	1	4	yes	—
662	#102	C₂³×C₅₃	1	4	yes	—
663	#102	C₂³×C₅₃	1	4	yes	—
664	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
665	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
666	#97	C₂³×C₅₃	1	4	yes	—
667	C₄×C₈	C₂³×C₅₃	1	2	yes	—
668	C₂⁴	—	2	2	no	—
669	#41	—	2	4	no	—
670	#41	—	2	2	no	—
671	#41	—	4	1	no	—
672	#41	—	8	2	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	4	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	8	4	no	—
679	C₂×Q₈	—	8	2	no	—
680	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
681	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
682	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	4	no	—
692	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
693	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
694	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
695	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	8	4	no	—
706	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
707	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
709	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
712	Q₁₆	—	4	2	no	—
713	SD₁₆	—	2	4	no	—
714	SD₁₆	—	4	4	no	—
715	M₁₆	—	4	2	no	—
716	C₂×C₈	—	4	4	no	—
717	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
718	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
719	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
741	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
742	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
743	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
745	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
746	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
762	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
763	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	4	no	—
768	C₄²	—	2	2	no	—
769	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₅₃	1	2	yes	—
772	C₄²	C₂×D₄×C₅₃	1	2	yes	—
773	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
774	C₄²	C₂⁴×C₅₃	1	2	yes	—
775	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
776	C₂³	—	2	1	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	4	4	no	—
779	C₂³	—	4	4	no	—
780	C₂³	—	8	2	no	—
781	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
782	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
783	Q₈	—	2	2	no	—
784	Q₈	—	2	2	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	2	2	no	—
787	Q₈	—	2	1	no	—
788	Q₈	—	4	2	no	—
789	Q₈	—	4	4	no	—
790	Q₈	—	8	4	no	—
791	Q₈	—	8	2	no	—
792	Q₈	—	8	1	no	—
793	D₄	—	2	4	no	—
794	D₄	—	2	2	no	—
795	D₄	—	2	1	no	—
796	D₄	—	2	2	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	2	no	—
801	D₄	—	8	1	no	—
802	D₄	—	8	2	no	—
803	D₄	#137×C₅₃	1	4	yes	—
804	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	4	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	—	8	2	no	—
826	C₂×C₄	—	8	2	no	—
827	C₂×C₄	—	8	4	no	—
828	C₂×C₄	—	8	2	no	—
829	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
830	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
831	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
834	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
837	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
838	C₈	—	2	2	no	—
839	C₈	—	2	2	no	—
840	C₈	—	2	4	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	1	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	8	8	no	—
853	C₂²	C₂×#137×C₅₃	1	4	yes	—
854	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
855	C₄	—	2	1	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	4	no	—
868	C₄	C₂×#137×C₅₃	1	2	yes	—
869	C₄	C₅₃×#576	1	2	yes	—
870	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
871	C₄	C₅₃×#585	1	1	yes	characteristic
872	C₂	—	2	4	no	—
873	C₂	—	4	1	no	—
874	C₂	—	4	2	no	—
875	C₂	—	8	2	no	—
876	C₂	C₅₃×#3489	1	1	yes	characteristic
877	C₂	C₂²×#137×C₅₃	1	1	yes	characteristic
878	C₂	C₂×C₅₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3481	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×#3503	C₂	semidirect
3. C₅₃×#3385	C₂	semidirect
4. C₅₃×#3375	C₂	semidirect
5. C₅₃×#3346	C₂	semidirect
6. C₅₃×#3338	C₂	semidirect
7. C₅₃×#3314	C₂	semidirect
8. C₅₃×#3295	C₂	semidirect
9. C₅₃×#3254	C₂	semidirect
10. C₅₃×#3248	C₂	semidirect
11. C₅₃×#3239	C₂	semidirect
12. C₅₃×#3226	C₂	semidirect
13. C₅₃×#3110	C₂	semidirect
14. C₅₃×#3107	C₂	semidirect
15. C₅₃×#3079	C₂	semidirect
16. C₂×C₅₃×#474	C₂	semidirect
17. C₅₃×#2990	C₂	semidirect
19. Q₈²×C₅₃	C₂²	semidirect
24. C₅₃×#554	C₂²	semidirect
35. C₅₃×#533	C₂²	semidirect
36. C₅₃×#533	C₂²	semidirect
38. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
39. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
48. C₅₃×#501	C₂²	semidirect
49. C₅₃×#500	C₂²	semidirect
50. C₅₃×#489	C₂²	semidirect
52. C₅₃×#485	C₂²	semidirect
53. C₅₃×#484	C₂²	semidirect
54. C₅₃×#484	C₂²	semidirect
56. C₅₃×#480	C₂²	semidirect
57. C₅₃×#479	C₂²	semidirect
58. C₅₃×#477	C₂²	semidirect
59. C₅₃×#477	C₂²	semidirect
61. C₅₃×#475	C₂²	semidirect
62. C₅₃×#475	C₂²	semidirect
66. C₅₃×#474	C₂²	semidirect
67. C₅₃×#474	C₂²	semidirect
68. C₅₃×#474	C₂²	semidirect
69. C₅₃×#474	C₂²	semidirect
70. C₅₃×#468	C₂²	semidirect
71. C₅₃×#467	C₂²	semidirect
73. C₅₃×#464	C₂²	semidirect
74. C₅₃×#462	C₂²	semidirect
76. C₅₃×#461	C₂²	semidirect
80. C₅₃×#446	C₂²	semidirect
82. C₅₃×#440	C₂²	semidirect
83. C₄×Q₁₆×C₅₃	C₂²	semidirect
85. C₅₃×#435	C₂²	semidirect
87. C₅₃×#432	C₂²	semidirect
88. C₅₃×#431	C₂²	semidirect
89. C₅₃×#428	C₂²	semidirect
90. C₂×#107×C₅₃	C₂²	semidirect
91. C₅₃×#423	C₂²	semidirect
92. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
401. #62127	C₅₃	direct (N × H)
433. #3503	C₂×C₅₃	semidirect
435. #3385	C₂×C₅₃	semidirect
436. #3375	C₂×C₅₃	semidirect
437. #3346	C₂×C₅₃	semidirect
438. #3338	C₂×C₅₃	semidirect
439. #3314	C₂×C₅₃	semidirect
440. #3295	C₂×C₅₃	semidirect
441. #3254	C₂×C₅₃	semidirect
442. #3248	C₂×C₅₃	semidirect
443. #3239	C₂×C₅₃	semidirect
444. #3226	C₂×C₅₃	semidirect
445. #3110	C₂×C₅₃	semidirect
446. #3107	C₂×C₅₃	semidirect
447. #3079	C₂×C₅₃	semidirect
448. C₂×#474	C₂×C₅₃	semidirect
449. #2990	C₂×C₅₃	semidirect
458. Q₈²	C₂²×C₅₃	semidirect
463. #554	C₂²×C₅₃	semidirect
474. #533	C₂²×C₅₃	semidirect
475. #533	C₂²×C₅₃	semidirect
477. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
478. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
487. #501	C₂²×C₅₃	semidirect
488. #500	C₂²×C₅₃	semidirect
489. #489	C₂²×C₅₃	semidirect
491. #485	C₂²×C₅₃	semidirect
492. #484	C₂²×C₅₃	semidirect
493. #484	C₂²×C₅₃	semidirect
495. #480	C₂²×C₅₃	semidirect
496. #479	C₂²×C₅₃	semidirect
497. #477	C₂²×C₅₃	semidirect
498. #477	C₂²×C₅₃	semidirect
500. #475	C₂²×C₅₃	semidirect
501. #475	C₂²×C₅₃	semidirect
505. #474	C₂²×C₅₃	semidirect
506. #474	C₂²×C₅₃	semidirect
507. #474	C₂²×C₅₃	semidirect
508. #474	C₂²×C₅₃	semidirect
509. #468	C₂²×C₅₃	semidirect
510. #467	C₂²×C₅₃	semidirect
512. #464	C₂²×C₅₃	semidirect
513. #462	C₂²×C₅₃	semidirect
515. #461	C₂²×C₅₃	semidirect
519. #446	C₂²×C₅₃	semidirect
521. #440	C₂²×C₅₃	semidirect
522. C₄×Q₁₆	C₂²×C₅₃	semidirect
524. #435	C₂²×C₅₃	semidirect
526. #432	C₂²×C₅₃	semidirect
527. #431	C₂²×C₅₃	semidirect
528. #428	C₂²×C₅₃	semidirect
529. C₂×#107	C₂²×C₅₃	semidirect
530. #423	C₂²×C₅₃	semidirect
531. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
534. C₅₃	#62127	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×#3503	2
C₅₃×#3481	2
C₅₃×#3385	2
C₅₃×#3375	2
C₅₃×#3346	2
C₅₃×#3338	2
C₅₃×#3314	2
C₅₃×#3295	2
C₅₃×#3254	2
C₅₃×#3248	2
C₅₃×#3239	2
C₅₃×#3226	2
C₅₃×#3110	2
C₅₃×#3107	2
C₅₃×#3079	2
C₂×C₅₃×#474	2
C₅₃×#2990	2
#62127	53

Subgroups — C53×#62127 #27269639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62127 #27269639