Subgroups — C₅₃×#61154 #27268666

Order 13568.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3327	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3326	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3323	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3322	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3091	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3054	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3002	C₂	1	2	yes	maximal, complemented
21	C₄×#135×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2896	C₂	1	2	yes	maximal, complemented
24	C₂²×#41×C₅₃	C₂²	1	2	yes	—
25	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
27	C₂²×M₁₆×C₅₃	C₂²	1	2	yes	complemented
28	C₅₃×#556	C₂²	1	1	yes	characteristic
29	C₅₃×#555	C₂²	1	1	yes	characteristic
30	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#553	C₂²	1	2	yes	complemented
32	C₅₃×#552	—	2	1	no	—
33	C₅₃×#552	C₂²	1	2	yes	complemented
34	C₅₃×#551	—	2	2	no	—
35	C₅₃×#550	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
37	C₅₃×#548	C₂²	1	2	yes	—
38	C₅₃×#547	—	2	1	no	—
39	C₅₃×#547	C₂²	1	1	yes	characteristic
40	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#546	—	2	1	no	—
42	C₅₃×#546	—	2	2	no	—
43	C₅₃×#546	C₂²	1	2	yes	—
44	D₄²×C₅₃	—	2	1	no	—
45	D₄²×C₅₃	C₂²	1	1	yes	characteristic
46	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#532	—	2	1	no	—
48	C₅₃×#532	C₂²	1	1	yes	characteristic
49	C₅₃×#529	—	2	1	no	—
50	C₅₃×#529	—	2	2	no	—
51	C₅₃×#525	—	2	2	no	—
52	C₅₃×#525	C₂²	1	2	yes	—
53	C₅₃×#525	C₂²	1	2	yes	complemented
54	C₄×#41×C₅₃	—	2	1	no	—
55	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
56	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₅₃	—	2	1	no	—
58	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
60	C₅₃×#488	C₂²	1	2	yes	complemented
61	C₅₃×#488	C₂²	1	2	yes	complemented
62	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#485	C₂²	1	2	yes	complemented
67	C₅₃×#485	C₂²	1	2	yes	complemented
68	C₅₃×#484	C₂²	1	2	yes	complemented
69	C₅₃×#483	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#482	C₂²	1	2	yes	complemented
72	C₅₃×#481	C₂²	1	2	yes	complemented
73	C₅₃×#480	C₂²	1	2	yes	complemented
74	C₅₃×#479	C₂²	1	2	yes	complemented
75	C₅₃×#478	C₂²	1	2	yes	complemented
76	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#470	C₂²	1	2	yes	complemented
81	C₅₃×#470	C₂²	1	2	yes	complemented
82	C₅₃×#469	C₂²	1	2	yes	complemented
83	C₅₃×#469	C₂²	1	2	yes	complemented
84	C₅₃×#468	C₂²	1	2	yes	complemented
85	C₅₃×#468	C₂²	1	2	yes	complemented
86	C₅₃×#468	C₂²	1	2	yes	complemented
87	C₅₃×#468	C₂²	1	2	yes	complemented
88	C₅₃×#464	C₂²	1	2	yes	complemented
89	C₅₃×#463	C₂²	1	2	yes	complemented
90	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#452	C₂²	1	2	yes	complemented
95	C₅₃×#452	C₂²	1	2	yes	complemented
96	C₅₃×#451	C₂²	1	2	yes	complemented
97	C₅₃×#450	C₂²	1	2	yes	complemented
98	C₅₃×#449	C₂²	1	2	yes	complemented
99	C₅₃×#449	C₂²	1	2	yes	complemented
100	C₅₃×#448	C₂²	1	2	yes	complemented
101	C₅₃×#447	C₂²	1	2	yes	complemented
102	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
103	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
104	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
105	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
106	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
107	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#436	C₂²	1	1	yes	characteristic
111	C₅₃×#436	C₂²	1	1	yes	characteristic
112	C₅₃×#436	C₂²	1	2	yes	complemented
113	C₅₃×#436	C₂²	1	2	yes	complemented
114	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#427	C₂²	1	2	yes	complemented
118	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#419	C₂²	1	2	yes	complemented
120	C₅₃×#419	C₂²	1	2	yes	complemented
121	C₅₃×#418	C₂²	1	2	yes	complemented
122	C₅₃×#418	C₂²	1	2	yes	complemented
123	C₅₃×#417	C₂²	1	2	yes	complemented
124	C₅₃×#417	C₂²	1	2	yes	complemented
125	C₅₃×#417	C₂²	1	2	yes	complemented
126	C₅₃×#417	C₂²	1	2	yes	complemented
127	C₅₃×#416	C₂²	1	1	yes	characteristic
128	C₅₃×#416	C₂²	1	2	yes	—
129	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#416	C₂²	1	2	yes	complemented
131	C₅₃×#416	C₂²	1	2	yes	complemented
132	C₅₃×#416	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	2	no	—
137	C₂×#41×C₅₃	—	2	2	no	—
138	C₂×#41×C₅₃	—	2	8	no	—
139	C₂×#41×C₅₃	—	4	4	no	—
140	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₅₃	C₂³	1	2	yes	—
142	C₂×#41×C₅₃	C₂³	1	2	yes	—
143	C₂×#41×C₅₃	C₂³	1	2	yes	—
144	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
146	C₂²×D₄×C₅₃	—	2	2	no	—
147	C₂²×D₄×C₅₃	—	2	1	no	—
148	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
149	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
150	C₂³×C₄×C₅₃	—	2	2	no	—
151	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
152	#135×C₅₃	—	2	4	no	—
153	#135×C₅₃	—	4	4	no	—
154	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
155	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
160	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₅₃	C₂³	1	2	yes	—
162	C₂×M₁₆×C₅₃	—	4	4	no	—
163	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
164	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
165	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
167	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
169	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₅₃	—	2	1	no	—
171	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
173	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
174	#127×C₅₃	—	2	1	no	—
175	#127×C₅₃	C₂³	1	1	yes	characteristic
176	#126×C₅₃	—	2	2	no	—
177	#126×C₅₃	—	2	2	no	—
178	#126×C₅₃	—	2	2	no	—
179	#125×C₅₃	—	2	2	no	—
180	#125×C₅₃	—	2	1	no	—
181	#125×C₅₃	C₂³	1	2	yes	—
182	#124×C₅₃	—	2	2	no	—
183	#124×C₅₃	—	2	2	no	—
184	#124×C₅₃	—	2	1	no	—
185	#124×C₅₃	C₂³	1	2	yes	—
186	#123×C₅₃	—	2	2	no	—
187	#123×C₅₃	—	2	2	no	—
188	#123×C₅₃	—	2	2	no	—
189	#123×C₅₃	—	2	2	no	—
190	#123×C₅₃	—	2	2	no	—
191	#123×C₅₃	—	2	2	no	—
192	#123×C₅₃	—	2	2	no	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	1	no	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	—	2	1	no	—
198	C₂²⋊Q₈×C₅₃	—	2	1	no	—
199	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
203	#121×C₅₃	—	2	1	no	—
204	#121×C₅₃	—	2	2	no	—
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	2	no	—
207	#121×C₅₃	—	2	2	no	—
208	#121×C₅₃	—	2	1	no	—
209	#121×C₅₃	—	2	1	no	—
210	#121×C₅₃	—	2	1	no	—
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	C₂³	1	2	yes	—
213	#121×C₅₃	C₂³	1	2	yes	—
214	#121×C₅₃	C₂³	1	2	yes	—
215	#121×C₅₃	C₂³	1	2	yes	—
216	#120×C₅₃	—	2	2	no	—
217	#120×C₅₃	—	2	2	no	—
218	#120×C₅₃	—	2	2	no	—
219	#120×C₅₃	—	2	2	no	—
220	C₄×Q₈×C₅₃	—	2	1	no	—
221	C₄×Q₈×C₅₃	—	2	1	no	—
222	C₄×Q₈×C₅₃	—	2	1	no	—
223	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₅₃	—	2	1	no	—
228	C₄×D₄×C₅₃	—	2	2	no	—
229	C₄×D₄×C₅₃	—	2	2	no	—
230	C₄×D₄×C₅₃	—	2	1	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	2	no	—
235	C₄×D₄×C₅₃	—	2	2	no	—
236	C₄×D₄×C₅₃	—	2	1	no	—
237	C₄×D₄×C₅₃	—	2	1	no	—
238	C₄×D₄×C₅₃	—	2	1	no	—
239	C₄×D₄×C₅₃	—	2	1	no	—
240	C₄×D₄×C₅₃	—	2	2	no	—
241	C₄×D₄×C₅₃	—	2	2	no	—
242	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
243	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
244	C₄×D₄×C₅₃	D₄	1	2	yes	—
245	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₅₃	C₂³	1	2	yes	—
251	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
252	#117×C₅₃	—	2	1	no	—
253	#117×C₅₃	—	2	2	no	—
254	#117×C₅₃	—	2	1	no	—
255	#117×C₅₃	—	2	1	no	—
256	#117×C₅₃	—	2	2	no	—
257	#117×C₅₃	—	2	2	no	—
258	#117×C₅₃	C₂³	1	2	yes	—
259	#117×C₅₃	C₂³	1	2	yes	—
260	#117×C₅₃	C₂³	1	1	yes	characteristic
261	#117×C₅₃	C₂³	1	2	yes	—
262	#117×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
264	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
267	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
270	C₂×C₄²×C₅₃	—	2	1	no	—
271	C₂×C₄²×C₅₃	—	2	1	no	—
272	C₂×C₄²×C₅₃	—	2	2	no	—
273	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
274	#107×C₅₃	C₂³	1	1	yes	characteristic
275	#107×C₅₃	C₂³	1	2	yes	—
276	#107×C₅₃	C₂³	1	1	yes	characteristic
277	#107×C₅₃	C₂³	1	2	yes	—
278	#106×C₅₃	C₂³	1	1	yes	characteristic
279	#106×C₅₃	C₂³	1	2	yes	—
280	#106×C₅₃	C₂³	1	1	yes	characteristic
281	#106×C₅₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
285	#103×C₅₃	C₂³	1	2	yes	—
286	#103×C₅₃	C₂³	1	2	yes	—
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	2	yes	—
295	#103×C₅₃	C₂³	1	1	yes	characteristic
296	#103×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	2	yes	—
304	#102×C₅₃	C₂³	1	2	yes	—
305	#102×C₅₃	C₂³	1	2	yes	—
306	#102×C₅₃	C₂³	1	2	yes	—
307	#102×C₅₃	C₂³	1	1	yes	characteristic
308	#102×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
313	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₂⁴×C₅₃	—	2	2	no	—
318	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
319	#41×C₅₃	—	2	2	no	—
320	#41×C₅₃	—	2	4	no	—
321	#41×C₅₃	—	2	4	no	—
322	#41×C₅₃	—	2	2	no	—
323	#41×C₅₃	—	2	4	no	—
324	#41×C₅₃	—	2	2	no	—
325	#41×C₅₃	—	2	4	no	—
326	#41×C₅₃	—	4	8	no	—
327	#41×C₅₃	—	4	2	no	—
328	#41×C₅₃	—	4	2	no	—
329	#41×C₅₃	—	4	8	no	—
330	#41×C₅₃	—	4	4	no	—
331	#41×C₅₃	#41	1	4	yes	complemented
332	C₂×Q₈×C₅₃	—	2	1	no	—
333	C₂×Q₈×C₅₃	—	2	2	no	—
334	C₂×Q₈×C₅₃	—	2	1	no	—
335	C₂×Q₈×C₅₃	—	2	4	no	—
336	C₂×Q₈×C₅₃	—	4	2	no	—
337	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
338	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₅₃	—	2	1	no	—
341	C₂×D₄×C₅₃	—	2	4	no	—
342	C₂×D₄×C₅₃	—	2	2	no	—
343	C₂×D₄×C₅₃	—	2	1	no	—
344	C₂×D₄×C₅₃	—	2	2	no	—
345	C₂×D₄×C₅₃	—	2	2	no	—
346	C₂×D₄×C₅₃	—	2	2	no	—
347	C₂×D₄×C₅₃	—	2	2	no	—
348	C₂×D₄×C₅₃	—	2	2	no	—
349	C₂×D₄×C₅₃	—	2	2	no	—
350	C₂×D₄×C₅₃	—	2	1	no	—
351	C₂×D₄×C₅₃	—	2	2	no	—
352	C₂×D₄×C₅₃	—	2	1	no	—
353	C₂×D₄×C₅₃	—	4	2	no	—
354	C₂×D₄×C₅₃	—	4	2	no	—
355	C₂×D₄×C₅₃	—	4	8	no	—
356	C₂×D₄×C₅₃	—	4	4	no	—
357	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
358	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
359	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
360	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
361	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₅₃	—	2	1	no	—
364	C₂²×C₄×C₅₃	—	2	4	no	—
365	C₂²×C₄×C₅₃	—	2	4	no	—
366	C₂²×C₄×C₅₃	—	2	2	no	—
367	C₂²×C₄×C₅₃	—	2	2	no	—
368	C₂²×C₄×C₅₃	—	2	2	no	—
369	C₂²×C₄×C₅₃	—	2	1	no	—
370	C₂²×C₄×C₅₃	—	2	1	no	—
371	C₂²×C₄×C₅₃	—	2	2	no	—
372	C₂²×C₄×C₅₃	—	2	2	no	—
373	C₂²×C₄×C₅₃	—	2	1	no	—
374	C₂²×C₄×C₅₃	—	2	2	no	—
375	C₂²×C₄×C₅₃	—	2	1	no	—
376	C₂²×C₄×C₅₃	—	2	1	no	—
377	C₂²×C₄×C₅₃	—	4	8	no	—
378	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
380	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
381	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
382	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
384	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	Q₁₆×C₅₃	—	2	2	no	—
387	Q₁₆×C₅₃	—	4	2	no	—
388	SD₁₆×C₅₃	—	2	2	no	—
389	SD₁₆×C₅₃	—	2	2	no	—
390	SD₁₆×C₅₃	—	4	2	no	—
391	SD₁₆×C₅₃	—	4	2	no	—
392	D₈×C₅₃	—	2	2	no	—
393	D₈×C₅₃	—	4	2	no	—
394	M₁₆×C₅₃	—	4	2	no	—
395	M₁₆×C₅₃	—	4	2	no	—
396	M₁₆×C₅₃	—	4	2	no	—
397	M₁₆×C₅₃	—	4	2	no	—
398	C₂×C₈×C₅₃	—	2	2	no	—
399	C₂×C₈×C₅₃	—	2	2	no	—
400	C₂×C₈×C₅₃	—	2	4	no	—
401	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
406	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₅₃	—	2	1	no	—
408	C₄⋊C₄×C₅₃	—	2	2	no	—
409	C₄⋊C₄×C₅₃	—	2	2	no	—
410	C₄⋊C₄×C₅₃	—	2	2	no	—
411	C₄⋊C₄×C₅₃	—	2	1	no	—
412	C₄⋊C₄×C₅₃	—	2	2	no	—
413	C₄⋊C₄×C₅₃	—	2	2	no	—
414	C₄⋊C₄×C₅₃	—	2	1	no	—
415	C₄⋊C₄×C₅₃	—	2	1	no	—
416	C₄⋊C₄×C₅₃	—	2	1	no	—
417	C₄⋊C₄×C₅₃	—	2	1	no	—
418	C₄⋊C₄×C₅₃	—	2	1	no	—
419	C₄⋊C₄×C₅₃	—	2	2	no	—
420	C₄⋊C₄×C₅₃	—	2	2	no	—
421	C₄⋊C₄×C₅₃	—	2	2	no	—
422	C₄⋊C₄×C₅₃	—	2	1	no	—
423	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
424	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
425	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
426	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
429	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
430	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₂²⋊C₄×C₅₃	—	2	1	no	—
433	C₂²⋊C₄×C₅₃	—	2	2	no	—
434	C₂²⋊C₄×C₅₃	—	2	2	no	—
435	C₂²⋊C₄×C₅₃	—	2	2	no	—
436	C₂²⋊C₄×C₅₃	—	2	2	no	—
437	C₂²⋊C₄×C₅₃	—	2	2	no	—
438	C₂²⋊C₄×C₅₃	—	2	1	no	—
439	C₂²⋊C₄×C₅₃	—	2	2	no	—
440	C₂²⋊C₄×C₅₃	—	2	2	no	—
441	C₂²⋊C₄×C₅₃	—	2	2	no	—
442	C₂²⋊C₄×C₅₃	—	2	2	no	—
443	C₂²⋊C₄×C₅₃	—	2	2	no	—
444	C₂²⋊C₄×C₅₃	—	2	1	no	—
445	C₂²⋊C₄×C₅₃	—	2	1	no	—
446	C₂²⋊C₄×C₅₃	—	2	1	no	—
447	C₂²⋊C₄×C₅₃	—	2	1	no	—
448	C₂²⋊C₄×C₅₃	—	2	2	no	—
449	C₂²⋊C₄×C₅₃	—	2	2	no	—
450	C₂²⋊C₄×C₅₃	—	2	2	no	—
451	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
453	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
454	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
455	C₄²×C₅₃	—	2	2	no	—
456	C₄²×C₅₃	—	2	1	no	—
457	C₄²×C₅₃	—	2	2	no	—
458	C₄²×C₅₃	—	2	1	no	—
459	C₄²×C₅₃	—	2	1	no	—
460	C₄²×C₅₃	—	2	1	no	—
461	C₄²×C₅₃	—	2	1	no	—
462	C₄²×C₅₃	—	2	1	no	—
463	C₄²×C₅₃	—	2	2	no	—
464	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
465	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
466	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
467	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
468	C₂³×C₅₃	—	2	1	no	—
469	C₂³×C₅₃	—	2	4	no	—
470	C₂³×C₅₃	—	2	1	no	—
471	C₂³×C₅₃	—	2	2	no	—
472	C₂³×C₅₃	—	4	2	no	—
473	C₂³×C₅₃	—	4	2	no	—
474	C₂³×C₅₃	—	4	4	no	—
475	C₂³×C₅₃	—	4	4	no	—
476	C₂³×C₅₃	—	8	2	no	—
477	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
478	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
479	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
480	Q₈×C₅₃	—	2	1	no	—
481	Q₈×C₅₃	—	2	2	no	—
482	Q₈×C₅₃	—	2	1	no	—
483	Q₈×C₅₃	—	2	2	no	—
484	Q₈×C₅₃	—	2	1	no	—
485	Q₈×C₅₃	—	4	4	no	—
486	Q₈×C₅₃	—	4	2	no	—
487	Q₈×C₅₃	—	8	1	no	—
488	Q₈×C₅₃	C₂×#41	1	2	yes	—
489	D₄×C₅₃	—	2	4	no	—
490	D₄×C₅₃	—	2	2	no	—
491	D₄×C₅₃	—	2	2	no	—
492	D₄×C₅₃	—	2	2	no	—
493	D₄×C₅₃	—	2	1	no	—
494	D₄×C₅₃	—	2	1	no	—
495	D₄×C₅₃	—	2	2	no	—
496	D₄×C₅₃	—	2	1	no	—
497	D₄×C₅₃	—	4	2	no	—
498	D₄×C₅₃	—	4	4	no	—
499	D₄×C₅₃	—	4	4	no	—
500	D₄×C₅₃	—	4	4	no	—
501	D₄×C₅₃	—	4	4	no	—
502	D₄×C₅₃	—	4	4	no	—
503	D₄×C₅₃	—	4	4	no	—
504	D₄×C₅₃	—	4	2	no	—
505	D₄×C₅₃	—	4	2	no	—
506	D₄×C₅₃	—	8	1	no	—
507	D₄×C₅₃	—	8	2	no	—
508	D₄×C₅₃	—	8	2	no	—
509	D₄×C₅₃	C₂×#41	1	2	yes	—
510	C₂×C₄×C₅₃	—	2	4	no	—
511	C₂×C₄×C₅₃	—	2	1	no	—
512	C₂×C₄×C₅₃	—	2	4	no	—
513	C₂×C₄×C₅₃	—	2	4	no	—
514	C₂×C₄×C₅₃	—	2	4	no	—
515	C₂×C₄×C₅₃	—	2	2	no	—
516	C₂×C₄×C₅₃	—	2	2	no	—
517	C₂×C₄×C₅₃	—	2	2	no	—
518	C₂×C₄×C₅₃	—	2	2	no	—
519	C₂×C₄×C₅₃	—	2	2	no	—
520	C₂×C₄×C₅₃	—	2	2	no	—
521	C₂×C₄×C₅₃	—	2	1	no	—
522	C₂×C₄×C₅₃	—	2	1	no	—
523	C₂×C₄×C₅₃	—	2	1	no	—
524	C₂×C₄×C₅₃	—	2	1	no	—
525	C₂×C₄×C₅₃	—	2	2	no	—
526	C₂×C₄×C₅₃	—	2	2	no	—
527	C₂×C₄×C₅₃	—	2	1	no	—
528	C₂×C₄×C₅₃	—	4	1	no	—
529	C₂×C₄×C₅₃	—	4	4	no	—
530	C₂×C₄×C₅₃	—	4	4	no	—
531	C₂×C₄×C₅₃	—	4	4	no	—
532	C₂×C₄×C₅₃	—	4	4	no	—
533	C₂×C₄×C₅₃	—	4	4	no	—
534	C₂×C₄×C₅₃	—	4	2	no	—
535	C₂×C₄×C₅₃	—	4	2	no	—
536	C₂×C₄×C₅₃	—	4	2	no	—
537	C₂×C₄×C₅₃	—	8	1	no	—
538	C₂×C₄×C₅₃	—	8	1	no	—
539	C₂×C₄×C₅₃	—	8	2	no	—
540	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
548	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
549	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
550	C₈×C₅₃	—	2	1	no	—
551	C₈×C₅₃	—	2	1	no	—
552	C₈×C₅₃	—	2	1	no	—
553	C₈×C₅₃	—	2	1	no	—
554	C₈×C₅₃	—	2	2	no	—
555	C₈×C₅₃	—	2	2	no	—
556	#61154	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
557	C₂²×C₅₃	—	2	1	no	—
558	C₂²×C₅₃	—	2	1	no	—
559	C₂²×C₅₃	—	2	2	no	—
560	C₂²×C₅₃	—	2	2	no	—
561	C₂²×C₅₃	—	2	2	no	—
562	C₂²×C₅₃	—	2	2	no	—
563	C₂²×C₅₃	—	2	2	no	—
564	C₂²×C₅₃	—	2	2	no	—
565	C₂²×C₅₃	—	2	2	no	—
566	C₂²×C₅₃	—	4	1	no	—
567	C₂²×C₅₃	—	4	1	no	—
568	C₂²×C₅₃	—	4	1	no	—
569	C₂²×C₅₃	—	4	2	no	—
570	C₂²×C₅₃	—	4	2	no	—
571	C₂²×C₅₃	—	4	1	no	—
572	C₂²×C₅₃	—	4	1	no	—
573	C₂²×C₅₃	—	4	2	no	—
574	C₂²×C₅₃	—	8	4	no	—
575	C₂²×C₅₃	—	8	8	no	—
576	C₂²×C₅₃	#546	1	2	yes	—
577	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
578	C₄×C₅₃	—	2	1	no	—
579	C₄×C₅₃	—	2	1	no	—
580	C₄×C₅₃	—	2	2	no	—
581	C₄×C₅₃	—	2	2	no	—
582	C₄×C₅₃	—	2	2	no	—
583	C₄×C₅₃	—	2	1	no	—
584	C₄×C₅₃	—	4	1	no	—
585	C₄×C₅₃	—	4	1	no	—
586	C₄×C₅₃	—	4	2	no	—
587	C₄×C₅₃	—	4	2	no	—
588	C₄×C₅₃	—	4	1	no	—
589	C₄×C₅₃	—	4	1	no	—
590	C₄×C₅₃	—	4	1	no	—
591	C₄×C₅₃	—	4	2	no	—
592	C₄×C₅₃	#546	1	2	yes	—
593	C₄×C₅₃	#575	1	2	yes	—
594	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
595	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
596	#3475	C₂×C₅₃	1	1	yes	characteristic, complemented
597	D₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
598	#3333	C₂×C₅₃	1	1	yes	characteristic, complemented
599	#3332	C₂×C₅₃	1	1	yes	characteristic, complemented
600	#3331	C₂×C₅₃	1	1	yes	characteristic, complemented
601	#3330	C₂×C₅₃	1	1	yes	characteristic, complemented
602	#3329	C₂×C₅₃	1	1	yes	characteristic, complemented
603	#3328	C₂×C₅₃	1	1	yes	characteristic, complemented
604	#3327	C₂×C₅₃	1	2	yes	complemented
605	#3326	C₂×C₅₃	1	2	yes	complemented
606	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
607	#3324	C₂×C₅₃	1	1	yes	characteristic, complemented
608	#3323	C₂×C₅₃	1	2	yes	complemented
609	#3322	C₂×C₅₃	1	2	yes	complemented
610	#3131	C₂×C₅₃	1	1	yes	characteristic, complemented
611	#3091	C₂×C₅₃	1	2	yes	complemented
612	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
613	#3054	C₂×C₅₃	1	2	yes	complemented
614	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
615	#3002	C₂×C₅₃	1	2	yes	complemented
616	C₄×#135	C₂×C₅₃	1	1	yes	characteristic, complemented
617	C₂×#436	C₂×C₅₃	1	1	yes	characteristic, complemented
618	#2896	C₂×C₅₃	1	2	yes	complemented
619	C₂×C₅₃	—	2	2	no	—
620	C₂×C₅₃	—	4	2	no	—
621	C₂×C₅₃	—	4	2	no	—
622	C₂×C₅₃	—	4	2	no	—
623	C₂×C₅₃	—	8	1	no	—
624	C₂×C₅₃	—	8	2	no	—
625	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
626	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
627	C₂×C₅₃	#3584	1	1	yes	characteristic
628	C₂²×#41	C₂²×C₅₃	1	2	yes	—
629	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
630	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
631	C₂²×M₁₆	C₂²×C₅₃	1	2	yes	complemented
632	#556	C₂²×C₅₃	1	1	yes	characteristic
633	#555	C₂²×C₅₃	1	1	yes	characteristic
634	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
635	#553	C₂²×C₅₃	1	2	yes	complemented
636	#552	—	2	1	no	—
637	#552	C₂²×C₅₃	1	2	yes	complemented
638	#551	—	2	2	no	—
639	#550	C₂²×C₅₃	1	1	yes	characteristic
640	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
641	#548	C₂²×C₅₃	1	2	yes	—
642	#547	—	2	1	no	—
643	#547	C₂²×C₅₃	1	1	yes	characteristic
644	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
645	#546	—	2	1	no	—
646	#546	—	2	2	no	—
647	#546	C₂²×C₅₃	1	2	yes	—
648	D₄²	—	2	1	no	—
649	D₄²	C₂²×C₅₃	1	1	yes	characteristic
650	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
651	#532	—	2	1	no	—
652	#532	C₂²×C₅₃	1	1	yes	characteristic
653	#529	—	2	2	no	—
654	#529	—	2	1	no	—
655	#525	—	2	2	no	—
656	#525	C₂²×C₅₃	1	2	yes	—
657	#525	C₂²×C₅₃	1	2	yes	complemented
658	C₄×#41	—	2	1	no	—
659	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
660	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
661	C₂×C₄×D₄	—	2	1	no	—
662	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
663	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
664	#488	C₂²×C₅₃	1	2	yes	complemented
665	#488	C₂²×C₅₃	1	2	yes	complemented
666	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
667	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
668	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
669	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
670	#485	C₂²×C₅₃	1	2	yes	complemented
671	#485	C₂²×C₅₃	1	2	yes	complemented
672	#484	C₂²×C₅₃	1	2	yes	complemented
673	#483	C₂²×C₅₃	1	2	yes	complemented
674	#482	C₂²×C₅₃	1	2	yes	complemented
675	#482	C₂²×C₅₃	1	2	yes	complemented
676	#481	C₂²×C₅₃	1	2	yes	complemented
677	#480	C₂²×C₅₃	1	2	yes	complemented
678	#479	C₂²×C₅₃	1	2	yes	complemented
679	#478	C₂²×C₅₃	1	2	yes	complemented
680	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
682	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
684	#470	C₂²×C₅₃	1	2	yes	complemented
685	#470	C₂²×C₅₃	1	2	yes	complemented
686	#469	C₂²×C₅₃	1	2	yes	complemented
687	#469	C₂²×C₅₃	1	2	yes	complemented
688	#468	C₂²×C₅₃	1	2	yes	complemented
689	#468	C₂²×C₅₃	1	2	yes	complemented
690	#468	C₂²×C₅₃	1	2	yes	complemented
691	#468	C₂²×C₅₃	1	2	yes	complemented
692	#464	C₂²×C₅₃	1	2	yes	complemented
693	#463	C₂²×C₅₃	1	2	yes	complemented
694	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
695	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
697	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
698	#452	C₂²×C₅₃	1	2	yes	complemented
699	#452	C₂²×C₅₃	1	2	yes	complemented
700	#451	C₂²×C₅₃	1	2	yes	complemented
701	#450	C₂²×C₅₃	1	2	yes	complemented
702	#449	C₂²×C₅₃	1	2	yes	complemented
703	#449	C₂²×C₅₃	1	2	yes	complemented
704	#448	C₂²×C₅₃	1	2	yes	complemented
705	#447	C₂²×C₅₃	1	2	yes	complemented
706	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
710	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
711	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
714	#436	C₂²×C₅₃	1	1	yes	characteristic
715	#436	C₂²×C₅₃	1	1	yes	characteristic
716	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
717	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
718	#436	C₂²×C₅₃	1	2	yes	complemented
719	#436	C₂²×C₅₃	1	2	yes	complemented
720	#427	C₂²×C₅₃	1	2	yes	complemented
721	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	#419	C₂²×C₅₃	1	2	yes	complemented
724	#419	C₂²×C₅₃	1	2	yes	complemented
725	#418	C₂²×C₅₃	1	2	yes	complemented
726	#418	C₂²×C₅₃	1	2	yes	complemented
727	#417	C₂²×C₅₃	1	2	yes	complemented
728	#417	C₂²×C₅₃	1	2	yes	complemented
729	#417	C₂²×C₅₃	1	2	yes	complemented
730	#417	C₂²×C₅₃	1	2	yes	complemented
731	#416	C₂²×C₅₃	1	2	yes	—
732	#416	C₂²×C₅₃	1	1	yes	characteristic
733	#416	C₂²×C₅₃	1	2	yes	complemented
734	#416	C₂²×C₅₃	1	2	yes	complemented
735	#416	C₂²×C₅₃	1	2	yes	complemented
736	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
737	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	complemented
738	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
739	C₅₃	#61154	1	1	yes	characteristic, direct product factor, Sylow
740	C₂×#41	—	2	1	no	—
741	C₂×#41	—	2	2	no	—
742	C₂×#41	—	2	2	no	—
743	C₂×#41	—	2	8	no	—
744	C₂×#41	—	4	4	no	—
745	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
746	C₂×#41	C₂³×C₅₃	1	2	yes	—
747	C₂×#41	C₂³×C₅₃	1	2	yes	—
748	C₂×#41	C₂³×C₅₃	1	2	yes	—
749	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
750	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
751	C₂²×D₄	—	2	2	no	—
752	C₂²×D₄	—	2	1	no	—
753	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
754	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
755	C₂³×C₄	—	2	2	no	—
756	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
757	#135	—	2	4	no	—
758	#135	—	4	4	no	—
759	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
760	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
761	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
762	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
763	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
764	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
765	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
766	C₂×D₈	C₂³×C₅₃	1	2	yes	—
767	C₂×M₁₆	—	4	4	no	—
768	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
769	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
770	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
771	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
772	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
773	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
774	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
775	C₄⋊Q₈	—	2	1	no	—
776	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
777	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
778	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
779	#127	—	2	1	no	—
780	#127	C₂³×C₅₃	1	1	yes	characteristic
781	#126	—	2	2	no	—
782	#126	—	2	2	no	—
783	#126	—	2	2	no	—
784	#125	—	2	2	no	—
785	#125	—	2	1	no	—
786	#125	C₂³×C₅₃	1	2	yes	—
787	#124	—	2	1	no	—
788	#124	—	2	2	no	—
789	#124	—	2	2	no	—
790	#124	C₂³×C₅₃	1	2	yes	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	C₂²⋊Q₈	—	2	1	no	—
799	C₂²⋊Q₈	—	2	1	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	—	2	1	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
805	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
806	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
807	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	1	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	—	2	1	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	C₂³×C₅₃	1	2	yes	—
818	#121	C₂³×C₅₃	1	2	yes	—
819	#121	C₂³×C₅₃	1	2	yes	—
820	#121	C₂³×C₅₃	1	2	yes	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	#120	—	2	2	no	—
825	C₄×Q₈	—	2	1	no	—
826	C₄×Q₈	—	2	1	no	—
827	C₄×Q₈	—	2	1	no	—
828	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
829	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
830	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
831	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	—	2	2	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
848	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
849	C₄×D₄	D₄×C₅₃	1	2	yes	—
850	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
851	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
852	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
853	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
855	C₄×D₄	C₂³×C₅₃	1	2	yes	—
856	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
857	#117	—	2	2	no	—
858	#117	—	2	2	no	—
859	#117	—	2	1	no	—
860	#117	—	2	2	no	—
861	#117	—	2	1	no	—
862	#117	—	2	1	no	—
863	#117	C₂³×C₅₃	1	1	yes	characteristic
864	#117	C₂³×C₅₃	1	2	yes	—
865	#117	C₂³×C₅₃	1	2	yes	—
866	#117	C₂³×C₅₃	1	2	yes	—
867	#117	C₂³×C₅₃	1	1	yes	characteristic
868	C₂×C₄⋊C₄	—	2	1	no	—
869	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
870	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
871	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
872	C₂×C₂²⋊C₄	—	2	2	no	—
873	C₂×C₂²⋊C₄	—	2	2	no	—
874	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
875	C₂×C₄²	—	2	2	no	—
876	C₂×C₄²	—	2	1	no	—
877	C₂×C₄²	—	2	1	no	—
878	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
879	#107	C₂³×C₅₃	1	1	yes	characteristic
880	#107	C₂³×C₅₃	1	1	yes	characteristic
881	#107	C₂³×C₅₃	1	2	yes	—
882	#107	C₂³×C₅₃	1	2	yes	—
883	#106	C₂³×C₅₃	1	1	yes	characteristic
884	#106	C₂³×C₅₃	1	1	yes	characteristic
885	#106	C₂³×C₅₃	1	2	yes	—
886	#106	C₂³×C₅₃	1	2	yes	—
887	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
888	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
889	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
890	#103	C₂³×C₅₃	1	1	yes	characteristic
891	#103	C₂³×C₅₃	1	1	yes	characteristic
892	#103	C₂³×C₅₃	1	2	yes	—
893	#103	C₂³×C₅₃	1	2	yes	—
894	#103	C₂³×C₅₃	1	2	yes	—
895	#103	C₂³×C₅₃	1	2	yes	—
896	#103	C₂³×C₅₃	1	2	yes	—
897	#103	C₂³×C₅₃	1	2	yes	—
898	#103	C₂³×C₅₃	1	1	yes	characteristic
899	#103	C₂³×C₅₃	1	1	yes	characteristic
900	#103	C₂³×C₅₃	1	2	yes	—
901	#103	C₂³×C₅₃	1	2	yes	—
902	#102	C₂³×C₅₃	1	1	yes	characteristic
903	#102	C₂³×C₅₃	1	1	yes	characteristic
904	#102	C₂³×C₅₃	1	2	yes	—
905	#102	C₂³×C₅₃	1	2	yes	—
906	#102	C₂³×C₅₃	1	2	yes	—
907	#102	C₂³×C₅₃	1	2	yes	—
908	#102	C₂³×C₅₃	1	2	yes	—
909	#102	C₂³×C₅₃	1	2	yes	—
910	#102	C₂³×C₅₃	1	1	yes	characteristic
911	#102	C₂³×C₅₃	1	1	yes	characteristic
912	#102	C₂³×C₅₃	1	2	yes	—
913	#102	C₂³×C₅₃	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
915	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
916	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
917	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
918	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
919	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
920	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
921	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
922	C₂⁴	—	2	2	no	—
923	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
924	#41	—	2	2	no	—
925	#41	—	2	4	no	—
926	#41	—	2	4	no	—
927	#41	—	2	2	no	—
928	#41	—	2	4	no	—
929	#41	—	2	2	no	—
930	#41	—	2	4	no	—
931	#41	—	4	8	no	—
932	#41	—	4	2	no	—
933	#41	—	4	2	no	—
934	#41	—	4	8	no	—
935	#41	—	4	4	no	—
936	#41	#41×C₅₃	1	4	yes	complemented
937	C₂×Q₈	—	2	1	no	—
938	C₂×Q₈	—	2	2	no	—
939	C₂×Q₈	—	2	1	no	—
940	C₂×Q₈	—	2	4	no	—
941	C₂×Q₈	—	4	2	no	—
942	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
943	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
944	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	4	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	1	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	4	2	no	—
959	C₂×D₄	—	4	2	no	—
960	C₂×D₄	—	4	8	no	—
961	C₂×D₄	—	4	4	no	—
962	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
963	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
964	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
965	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
966	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
967	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	4	no	—
970	C₂²×C₄	—	2	4	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	2	1	no	—
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	1	no	—
982	C₂²×C₄	—	4	8	no	—
983	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
984	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
985	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
986	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
987	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
988	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
989	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
990	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
991	Q₁₆	—	2	2	no	—
992	Q₁₆	—	4	2	no	—
993	SD₁₆	—	2	2	no	—
994	SD₁₆	—	2	2	no	—
995	SD₁₆	—	4	2	no	—
996	SD₁₆	—	4	2	no	—
997	D₈	—	2	2	no	—
998	D₈	—	4	2	no	—
999	M₁₆	—	4	2	no	—
1000	M₁₆	—	4	2	no	—
1001	M₁₆	—	4	2	no	—
1002	M₁₆	—	4	2	no	—
1003	C₂×C₈	—	2	2	no	—
1004	C₂×C₈	—	2	2	no	—
1005	C₂×C₈	—	2	4	no	—
1006	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1007	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1008	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1009	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1010	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1011	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	1	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1029	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1030	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1031	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1032	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1033	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1034	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1035	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1036	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1057	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1058	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1059	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1060	C₄²	—	2	1	no	—
1061	C₄²	—	2	2	no	—
1062	C₄²	—	2	1	no	—
1063	C₄²	—	2	1	no	—
1064	C₄²	—	2	2	no	—
1065	C₄²	—	2	2	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1070	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1071	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1072	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1073	C₂³	—	2	1	no	—
1074	C₂³	—	2	4	no	—
1075	C₂³	—	2	1	no	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	4	2	no	—
1078	C₂³	—	4	2	no	—
1079	C₂³	—	4	4	no	—
1080	C₂³	—	4	4	no	—
1081	C₂³	—	8	2	no	—
1082	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1083	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1084	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1085	Q₈	—	2	1	no	—
1086	Q₈	—	2	1	no	—
1087	Q₈	—	2	2	no	—
1088	Q₈	—	2	1	no	—
1089	Q₈	—	2	2	no	—
1090	Q₈	—	4	4	no	—
1091	Q₈	—	4	2	no	—
1092	Q₈	—	8	1	no	—
1093	Q₈	C₂×#41×C₅₃	1	2	yes	—
1094	D₄	—	2	4	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	2	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	2	2	no	—
1099	D₄	—	2	1	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	4	2	no	—
1103	D₄	—	4	4	no	—
1104	D₄	—	4	4	no	—
1105	D₄	—	4	4	no	—
1106	D₄	—	4	4	no	—
1107	D₄	—	4	4	no	—
1108	D₄	—	4	4	no	—
1109	D₄	—	4	2	no	—
1110	D₄	—	4	2	no	—
1111	D₄	—	8	1	no	—
1112	D₄	—	8	2	no	—
1113	D₄	—	8	2	no	—
1114	D₄	C₂×#41×C₅₃	1	2	yes	—
1115	C₂×C₄	—	2	4	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	4	no	—
1118	C₂×C₄	—	2	4	no	—
1119	C₂×C₄	—	2	4	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	4	no	—
1135	C₂×C₄	—	4	4	no	—
1136	C₂×C₄	—	4	4	no	—
1137	C₂×C₄	—	4	4	no	—
1138	C₂×C₄	—	4	4	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	8	1	no	—
1143	C₂×C₄	—	8	1	no	—
1144	C₂×C₄	—	8	2	no	—
1145	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1146	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1147	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1148	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1149	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1150	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1151	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1152	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1153	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1154	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1155	C₈	—	2	1	no	—
1156	C₈	—	2	1	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	2	2	no	—
1160	C₈	—	2	2	no	—
1161	C₂²	—	2	1	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	1	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	8	4	no	—
1179	C₂²	—	8	8	no	—
1180	C₂²	C₅₃×#546	1	2	yes	—
1181	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1182	C₄	—	2	2	no	—
1183	C₄	—	2	2	no	—
1184	C₄	—	2	2	no	—
1185	C₄	—	2	1	no	—
1186	C₄	—	2	1	no	—
1187	C₄	—	2	1	no	—
1188	C₄	—	4	2	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	2	no	—
1193	C₄	—	4	1	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	2	no	—
1196	C₄	C₅₃×#546	1	2	yes	—
1197	C₄	C₅₃×#575	1	2	yes	—
1198	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1199	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1200	C₂	—	2	2	no	—
1201	C₂	—	4	2	no	—
1202	C₂	—	4	2	no	—
1203	C₂	—	4	2	no	—
1204	C₂	—	8	2	no	—
1205	C₂	—	8	1	no	—
1206	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
1207	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1208	C₂	C₅₃×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3475	C₂	semidirect
2. D₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#3333	C₂	semidirect
4. C₅₃×#3332	C₂	semidirect
5. C₅₃×#3331	C₂	semidirect
6. C₅₃×#3330	C₂	semidirect
7. C₅₃×#3329	C₂	semidirect
8. C₅₃×#3328	C₂	semidirect
9. C₅₃×#3327	C₂	semidirect
10. C₅₃×#3326	C₂	semidirect
11. C₅₃×#3325	C₂	semidirect
12. C₅₃×#3324	C₂	semidirect
13. C₅₃×#3323	C₂	semidirect
14. C₅₃×#3322	C₂	semidirect
15. C₅₃×#3131	C₂	semidirect
16. C₅₃×#3091	C₂	semidirect
17. C₅₃×#3076	C₂	semidirect
18. C₅₃×#3054	C₂	semidirect
19. C₅₃×#3035	C₂	semidirect
20. C₅₃×#3002	C₂	semidirect
21. C₄×#135×C₅₃	C₂	semidirect
22. C₂×C₅₃×#436	C₂	semidirect
23. C₅₃×#2896	C₂	semidirect
26. C₂×#135×C₅₃	C₂²	semidirect
27. C₂²×M₁₆×C₅₃	C₂²	semidirect
30. C₅₃×#554	C₂²	semidirect
31. C₅₃×#553	C₂²	semidirect
33. C₅₃×#552	C₂²	semidirect
40. C₅₃×#547	C₂²	semidirect
46. C₅₃×#533	C₂²	semidirect
53. C₅₃×#525	C₂²	semidirect
56. C₄×#41×C₅₃	C₂²	semidirect
59. C₂×#117×C₅₃	C₂²	semidirect
60. C₅₃×#488	C₂²	semidirect
61. C₅₃×#488	C₂²	semidirect
62. C₅₃×#487	C₂²	semidirect
63. C₅₃×#487	C₂²	semidirect
64. C₅₃×#486	C₂²	semidirect
65. C₅₃×#486	C₂²	semidirect
66. C₅₃×#485	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#484	C₂²	semidirect
69. C₅₃×#483	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#481	C₂²	semidirect
73. C₅₃×#480	C₂²	semidirect
74. C₅₃×#479	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#477	C₂²	semidirect
77. C₅₃×#476	C₂²	semidirect
78. C₅₃×#475	C₂²	semidirect
79. C₅₃×#474	C₂²	semidirect
80. C₅₃×#470	C₂²	semidirect
81. C₅₃×#470	C₂²	semidirect
82. C₅₃×#469	C₂²	semidirect
83. C₅₃×#469	C₂²	semidirect
84. C₅₃×#468	C₂²	semidirect
85. C₅₃×#468	C₂²	semidirect
86. C₅₃×#468	C₂²	semidirect
87. C₅₃×#468	C₂²	semidirect
88. C₅₃×#464	C₂²	semidirect
89. C₅₃×#463	C₂²	semidirect
90. C₅₃×#462	C₂²	semidirect
91. C₅₃×#461	C₂²	semidirect
92. C₅₃×#460	C₂²	semidirect
93. C₅₃×#459	C₂²	semidirect
94. C₅₃×#452	C₂²	semidirect
95. C₅₃×#452	C₂²	semidirect
96. C₅₃×#451	C₂²	semidirect
97. C₅₃×#450	C₂²	semidirect
98. C₅₃×#449	C₂²	semidirect
99. C₅₃×#449	C₂²	semidirect
100. C₅₃×#448	C₂²	semidirect
101. C₅₃×#447	C₂²	semidirect
102. C₄×Q₁₆×C₅₃	C₂²	semidirect
103. C₄×Q₁₆×C₅₃	C₂²	semidirect
104. C₄×SD₁₆×C₅₃	C₂²	semidirect
105. C₄×SD₁₆×C₅₃	C₂²	semidirect
106. C₄×SD₁₆×C₅₃	C₂²	semidirect
107. C₄×SD₁₆×C₅₃	C₂²	semidirect
108. C₄×D₈×C₅₃	C₂²	semidirect
109. C₄×D₈×C₅₃	C₂²	semidirect
112. C₅₃×#436	C₂²	semidirect
113. C₅₃×#436	C₂²	semidirect
114. C₅₃×#436	C₂²	semidirect
115. C₅₃×#436	C₂²	semidirect
116. C₅₃×#427	C₂²	semidirect
117. C₅₃×#427	C₂²	semidirect
118. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
119. C₅₃×#419	C₂²	semidirect
120. C₅₃×#419	C₂²	semidirect
121. C₅₃×#418	C₂²	semidirect
122. C₅₃×#418	C₂²	semidirect
123. C₅₃×#417	C₂²	semidirect
124. C₅₃×#417	C₂²	semidirect
125. C₅₃×#417	C₂²	semidirect
126. C₅₃×#417	C₂²	semidirect
129. C₅₃×#416	C₂²	semidirect
130. C₅₃×#416	C₂²	semidirect
131. C₅₃×#416	C₂²	semidirect
132. C₅₃×#416	C₂²	semidirect
133. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
134. C₂×C₄×C₈×C₅₃	C₂²	semidirect
331. #41×C₅₃	#41	semidirect
556. #61154	C₅₃	direct (N × H)
596. #3475	C₂×C₅₃	semidirect
597. D₄×#41	C₂×C₅₃	semidirect
598. #3333	C₂×C₅₃	semidirect
599. #3332	C₂×C₅₃	semidirect
600. #3331	C₂×C₅₃	semidirect
601. #3330	C₂×C₅₃	semidirect
602. #3329	C₂×C₅₃	semidirect
603. #3328	C₂×C₅₃	semidirect
604. #3327	C₂×C₅₃	semidirect
605. #3326	C₂×C₅₃	semidirect
606. #3325	C₂×C₅₃	semidirect
607. #3324	C₂×C₅₃	semidirect
608. #3323	C₂×C₅₃	semidirect
609. #3322	C₂×C₅₃	semidirect
610. #3131	C₂×C₅₃	semidirect
611. #3091	C₂×C₅₃	semidirect
612. #3076	C₂×C₅₃	semidirect
613. #3054	C₂×C₅₃	semidirect
614. #3035	C₂×C₅₃	semidirect
615. #3002	C₂×C₅₃	semidirect
616. C₄×#135	C₂×C₅₃	semidirect
617. C₂×#436	C₂×C₅₃	semidirect
618. #2896	C₂×C₅₃	semidirect
630. C₂×#135	C₂²×C₅₃	semidirect
631. C₂²×M₁₆	C₂²×C₅₃	semidirect
634. #554	C₂²×C₅₃	semidirect
635. #553	C₂²×C₅₃	semidirect
637. #552	C₂²×C₅₃	semidirect
644. #547	C₂²×C₅₃	semidirect
650. #533	C₂²×C₅₃	semidirect
657. #525	C₂²×C₅₃	semidirect
660. C₄×#41	C₂²×C₅₃	semidirect
663. C₂×#117	C₂²×C₅₃	semidirect
664. #488	C₂²×C₅₃	semidirect
665. #488	C₂²×C₅₃	semidirect
666. #487	C₂²×C₅₃	semidirect
667. #487	C₂²×C₅₃	semidirect
668. #486	C₂²×C₅₃	semidirect
669. #486	C₂²×C₅₃	semidirect
670. #485	C₂²×C₅₃	semidirect
671. #485	C₂²×C₅₃	semidirect
672. #484	C₂²×C₅₃	semidirect
673. #483	C₂²×C₅₃	semidirect
674. #482	C₂²×C₅₃	semidirect
675. #482	C₂²×C₅₃	semidirect
676. #481	C₂²×C₅₃	semidirect
677. #480	C₂²×C₅₃	semidirect
678. #479	C₂²×C₅₃	semidirect
679. #478	C₂²×C₅₃	semidirect
680. #477	C₂²×C₅₃	semidirect
681. #476	C₂²×C₅₃	semidirect
682. #475	C₂²×C₅₃	semidirect
683. #474	C₂²×C₅₃	semidirect
684. #470	C₂²×C₅₃	semidirect
685. #470	C₂²×C₅₃	semidirect
686. #469	C₂²×C₅₃	semidirect
687. #469	C₂²×C₅₃	semidirect
688. #468	C₂²×C₅₃	semidirect
689. #468	C₂²×C₅₃	semidirect
690. #468	C₂²×C₅₃	semidirect
691. #468	C₂²×C₅₃	semidirect
692. #464	C₂²×C₅₃	semidirect
693. #463	C₂²×C₅₃	semidirect
694. #462	C₂²×C₅₃	semidirect
695. #461	C₂²×C₅₃	semidirect
696. #460	C₂²×C₅₃	semidirect
697. #459	C₂²×C₅₃	semidirect
698. #452	C₂²×C₅₃	semidirect
699. #452	C₂²×C₅₃	semidirect
700. #451	C₂²×C₅₃	semidirect
701. #450	C₂²×C₅₃	semidirect
702. #449	C₂²×C₅₃	semidirect
703. #449	C₂²×C₅₃	semidirect
704. #448	C₂²×C₅₃	semidirect
705. #447	C₂²×C₅₃	semidirect
706. C₄×Q₁₆	C₂²×C₅₃	semidirect
707. C₄×Q₁₆	C₂²×C₅₃	semidirect
708. C₄×SD₁₆	C₂²×C₅₃	semidirect
709. C₄×SD₁₆	C₂²×C₅₃	semidirect
710. C₄×SD₁₆	C₂²×C₅₃	semidirect
711. C₄×SD₁₆	C₂²×C₅₃	semidirect
712. C₄×D₈	C₂²×C₅₃	semidirect
713. C₄×D₈	C₂²×C₅₃	semidirect
716. #436	C₂²×C₅₃	semidirect
717. #436	C₂²×C₅₃	semidirect
718. #436	C₂²×C₅₃	semidirect
719. #436	C₂²×C₅₃	semidirect
720. #427	C₂²×C₅₃	semidirect
721. #427	C₂²×C₅₃	semidirect
722. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
723. #419	C₂²×C₅₃	semidirect
724. #419	C₂²×C₅₃	semidirect
725. #418	C₂²×C₅₃	semidirect
726. #418	C₂²×C₅₃	semidirect
727. #417	C₂²×C₅₃	semidirect
728. #417	C₂²×C₅₃	semidirect
729. #417	C₂²×C₅₃	semidirect
730. #417	C₂²×C₅₃	semidirect
733. #416	C₂²×C₅₃	semidirect
734. #416	C₂²×C₅₃	semidirect
735. #416	C₂²×C₅₃	semidirect
736. #416	C₂²×C₅₃	semidirect
737. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
738. C₂×C₄×C₈	C₂²×C₅₃	semidirect
739. C₅₃	#61154	direct (N × H)
936. #41	#41×C₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#3475	2
D₄×#41×C₅₃	2
C₅₃×#3333	2
C₅₃×#3332	2
C₅₃×#3331	2
C₅₃×#3330	2
C₅₃×#3329	2
C₅₃×#3328	2
C₅₃×#3327	2
C₅₃×#3326	2
C₅₃×#3325	2
C₅₃×#3324	2
C₅₃×#3323	2
C₅₃×#3322	2
C₅₃×#3131	2
C₅₃×#3091	2
C₅₃×#3076	2
C₅₃×#3054	2
C₅₃×#3035	2
C₅₃×#3002	2
C₄×#135×C₅₃	2
C₂×C₅₃×#436	2
C₅₃×#2896	2
#61154	53

Subgroups — C53×#61154 #27268666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61154 #27268666