Subgroups — C₅₃×#61991 #27269503

Order 13568.

1848 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3514	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3316	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3314	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×Q₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3270	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3266	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3252	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3248	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3215	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3117	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#464	C₂	1	2	yes	maximal, complemented
23	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
25	C₂²×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
27	C₅₃×#559	C₂²	1	1	yes	characteristic
28	Q₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#557	—	2	1	no	—
30	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#556	C₂²	1	1	yes	characteristic
32	C₅₃×#555	—	2	1	no	—
33	C₅₃×#554	—	2	1	no	—
34	C₅₃×#554	—	2	2	no	—
35	C₅₃×#554	C₂²	1	1	yes	characteristic
36	C₅₃×#554	C₂²	1	2	yes	complemented
37	C₅₃×#551	—	2	2	no	—
38	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
41	C₅₃×#548	C₂²	1	2	yes	—
42	C₅₃×#546	—	2	1	no	—
43	C₅₃×#546	C₂²	1	2	yes	—
44	D₄²×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#542	—	2	1	no	—
46	C₅₃×#538	—	2	2	no	—
47	C₅₃×#533	—	2	2	no	—
48	C₅₃×#533	—	2	1	no	—
49	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#533	C₂²	1	2	yes	complemented
51	C₅₃×#532	C₂²	1	1	yes	characteristic
52	C₅₃×#529	C₂²	1	2	yes	—
53	C₅₃×#529	C₂²	1	1	yes	characteristic
54	C₂×#124×C₅₃	C₂²	1	2	yes	—
55	C₅₃×#518	—	2	1	no	—
56	C₄×#41×C₅₃	—	2	1	no	—
57	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#497	C₂²	1	2	yes	—
61	C₅₃×#497	C₂²	1	2	yes	complemented
62	C₅₃×#494	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#492	C₂²	1	1	yes	characteristic
64	C₅₃×#489	C₂²	1	2	yes	—
65	C₅₃×#489	C₂²	1	2	yes	complemented
66	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#486	C₂²	1	1	yes	characteristic
68	C₅₃×#484	C₂²	1	2	yes	complemented
69	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#481	C₂²	1	2	yes	—
71	C₅₃×#480	C₂²	1	1	yes	characteristic
72	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#479	C₂²	1	2	yes	complemented
74	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#476	C₂²	1	1	yes	characteristic
77	C₅₃×#475	C₂²	1	2	yes	complemented
78	C₅₃×#474	C₂²	1	2	yes	complemented
79	C₅₃×#470	C₂²	1	2	yes	complemented
80	C₅₃×#468	C₂²	1	2	yes	—
81	C₅₃×#467	C₂²	1	2	yes	complemented
82	C₅₃×#467	C₂²	1	2	yes	complemented
83	C₅₃×#465	C₂²	1	2	yes	—
84	C₅₃×#465	C₂²	1	2	yes	—
85	C₅₃×#464	C₂²	1	1	yes	characteristic
86	C₅₃×#464	C₂²	1	2	yes	—
87	C₅₃×#464	C₂²	1	2	yes	—
88	C₅₃×#464	C₂²	1	1	yes	characteristic
89	C₅₃×#464	C₂²	1	2	yes	—
90	C₅₃×#464	C₂²	1	2	yes	complemented
91	C₅₃×#464	C₂²	1	2	yes	complemented
92	C₅₃×#464	C₂²	1	2	yes	complemented
93	C₅₃×#464	C₂²	1	2	yes	complemented
94	C₅₃×#464	C₂²	1	2	yes	complemented
95	C₅₃×#464	C₂²	1	2	yes	complemented
96	C₅₃×#462	C₂²	1	2	yes	complemented
97	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#461	C₂²	1	1	yes	characteristic
101	C₅₃×#461	C₂²	1	2	yes	complemented
102	C₅₃×#460	C₂²	1	1	yes	characteristic
103	C₅₃×#460	C₂²	1	1	yes	characteristic
104	C₅₃×#452	C₂²	1	2	yes	complemented
105	C₅₃×#452	C₂²	1	2	yes	complemented
106	C₅₃×#451	C₂²	1	2	yes	complemented
107	C₅₃×#451	C₂²	1	2	yes	complemented
108	C₅₃×#451	C₂²	1	2	yes	complemented
109	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#450	C₂²	1	2	yes	—
111	C₅₃×#450	C₂²	1	2	yes	—
112	C₅₃×#448	C₂²	1	1	yes	characteristic
113	C₅₃×#448	C₂²	1	2	yes	—
114	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#441	C₂²	1	2	yes	complemented
117	C₅₃×#441	C₂²	1	2	yes	complemented
118	C₅₃×#440	C₂²	1	2	yes	complemented
119	C₅₃×#440	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
124	C₅₃×#435	C₂²	1	2	yes	complemented
125	C₅₃×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
127	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
128	C₅₃×#432	C₂²	1	2	yes	complemented
129	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	complemented
132	C₅₃×#417	C₂²	1	2	yes	complemented
133	C₂×#103×C₅₃	C₂²	1	2	yes	complemented
134	C₂×#102×C₅₃	C₂²	1	2	yes	—
135	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
136	C₂×#41×C₅₃	C₂³	1	2	yes	—
137	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
138	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
140	C₂²×D₄×C₅₃	—	2	1	no	—
141	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
142	#137×C₅₃	—	4	4	no	—
143	C₂×Q₁₆×C₅₃	—	4	4	no	—
144	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₅₃	—	4	4	no	—
152	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
159	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
160	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
161	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₅₃	—	2	1	no	—
163	C₄⋊Q₈×C₅₃	—	2	2	no	—
164	C₄⋊Q₈×C₅₃	—	2	1	no	—
165	C₄⋊Q₈×C₅₃	—	2	2	no	—
166	C₄⋊Q₈×C₅₃	—	2	1	no	—
167	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
169	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
172	#127×C₅₃	C₂³	1	1	yes	characteristic
173	#126×C₅₃	—	2	2	no	—
174	#126×C₅₃	—	2	2	no	—
175	#126×C₅₃	—	2	1	no	—
176	#125×C₅₃	—	2	1	no	—
177	#125×C₅₃	—	2	2	no	—
178	#125×C₅₃	—	2	1	no	—
179	#125×C₅₃	—	2	2	no	—
180	#125×C₅₃	—	2	1	no	—
181	#125×C₅₃	—	2	2	no	—
182	#125×C₅₃	C₂³	1	1	yes	characteristic
183	#124×C₅₃	—	2	2	no	—
184	#124×C₅₃	—	2	2	no	—
185	#124×C₅₃	—	2	2	no	—
186	#124×C₅₃	—	2	1	no	—
187	#124×C₅₃	C₂³	1	2	yes	—
188	#124×C₅₃	C₂³	1	2	yes	—
189	#124×C₅₃	C₂³	1	1	yes	characteristic
190	#124×C₅₃	C₂³	1	2	yes	—
191	#123×C₅₃	—	2	2	no	—
192	#123×C₅₃	—	2	2	no	—
193	#123×C₅₃	—	2	1	no	—
194	#123×C₅₃	—	2	2	no	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	—	2	2	no	—
198	C₂²⋊Q₈×C₅₃	—	2	2	no	—
199	C₂²⋊Q₈×C₅₃	—	2	2	no	—
200	C₂²⋊Q₈×C₅₃	—	2	2	no	—
201	C₂²⋊Q₈×C₅₃	—	2	2	no	—
202	C₂²⋊Q₈×C₅₃	—	2	2	no	—
203	C₂²⋊Q₈×C₅₃	—	2	1	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	1	no	—
206	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	—	2	2	no	—
213	#121×C₅₃	—	2	2	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	—	2	1	no	—
216	#121×C₅₃	C₂³	1	2	yes	—
217	#121×C₅₃	C₂³	1	1	yes	characteristic
218	#120×C₅₃	—	2	2	no	—
219	#120×C₅₃	—	2	2	no	—
220	C₄×Q₈×C₅₃	—	2	2	no	—
221	C₄×Q₈×C₅₃	—	2	1	no	—
222	C₄×Q₈×C₅₃	—	2	1	no	—
223	C₄×Q₈×C₅₃	—	2	2	no	—
224	C₄×Q₈×C₅₃	—	2	2	no	—
225	C₄×Q₈×C₅₃	—	2	1	no	—
226	C₄×Q₈×C₅₃	—	2	1	no	—
227	C₄×Q₈×C₅₃	—	2	1	no	—
228	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
229	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
232	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
235	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
237	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
238	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₅₃	—	2	1	no	—
240	C₄×D₄×C₅₃	—	2	2	no	—
241	C₄×D₄×C₅₃	—	2	1	no	—
242	C₄×D₄×C₅₃	—	2	1	no	—
243	C₄×D₄×C₅₃	—	2	1	no	—
244	C₄×D₄×C₅₃	—	2	2	no	—
245	C₄×D₄×C₅₃	—	2	1	no	—
246	C₄×D₄×C₅₃	—	2	2	no	—
247	C₄×D₄×C₅₃	—	2	1	no	—
248	C₄×D₄×C₅₃	—	2	2	no	—
249	C₄×D₄×C₅₃	—	2	1	no	—
250	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
251	C₄×D₄×C₅₃	D₄	1	2	yes	—
252	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₅₃	C₂³	1	2	yes	—
254	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₅₃	C₂³	1	2	yes	—
256	#117×C₅₃	—	2	1	no	—
257	#117×C₅₃	—	2	1	no	—
258	#117×C₅₃	—	2	2	no	—
259	#117×C₅₃	—	2	2	no	—
260	#117×C₅₃	—	2	1	no	—
261	#117×C₅₃	D₄	1	2	yes	—
262	#117×C₅₃	D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
264	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
265	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
270	C₂×C₄²×C₅₃	—	2	2	no	—
271	C₂×C₄²×C₅₃	—	2	1	no	—
272	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
273	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
274	#107×C₅₃	C₂³	1	1	yes	characteristic
275	#107×C₅₃	C₂³	1	1	yes	characteristic
276	#107×C₅₃	C₂³	1	2	yes	—
277	#106×C₅₃	C₂³	1	1	yes	characteristic
278	#106×C₅₃	C₂³	1	1	yes	characteristic
279	#106×C₅₃	C₂³	1	2	yes	—
280	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
284	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	1	yes	characteristic
296	#103×C₅₃	C₂³	1	1	yes	characteristic
297	#103×C₅₃	C₂³	1	1	yes	characteristic
298	#103×C₅₃	C₂³	1	2	yes	—
299	#103×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	2	yes	—
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	2	yes	—
304	#102×C₅₃	C₂³	1	2	yes	—
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
311	#97×C₅₃	C₂³	1	2	yes	—
312	#97×C₅₃	C₂³	1	2	yes	—
313	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₂⁴×C₅₃	—	2	2	no	—
316	#41×C₅₃	—	2	4	no	—
317	#41×C₅₃	—	4	2	no	—
318	#41×C₅₃	—	4	2	no	—
319	C₂×Q₈×C₅₃	—	2	1	no	—
320	C₂×Q₈×C₅₃	—	2	2	no	—
321	C₂×Q₈×C₅₃	—	2	2	no	—
322	C₂×Q₈×C₅₃	—	2	1	no	—
323	C₂×Q₈×C₅₃	—	2	2	no	—
324	C₂×Q₈×C₅₃	—	2	4	no	—
325	C₂×Q₈×C₅₃	—	2	2	no	—
326	C₂×Q₈×C₅₃	—	4	2	no	—
327	C₂×Q₈×C₅₃	—	4	1	no	—
328	C₂×Q₈×C₅₃	—	4	2	no	—
329	C₂×Q₈×C₅₃	—	4	2	no	—
330	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	—	2	1	no	—
338	C₂×D₄×C₅₃	—	2	2	no	—
339	C₂×D₄×C₅₃	—	2	1	no	—
340	C₂×D₄×C₅₃	—	2	1	no	—
341	C₂×D₄×C₅₃	—	2	2	no	—
342	C₂×D₄×C₅₃	—	4	2	no	—
343	C₂×D₄×C₅₃	—	4	2	no	—
344	C₂×D₄×C₅₃	—	4	4	no	—
345	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₅₃	—	2	1	no	—
350	C₂²×C₄×C₅₃	—	2	2	no	—
351	C₂²×C₄×C₅₃	—	2	1	no	—
352	C₂²×C₄×C₅₃	—	2	2	no	—
353	C₂²×C₄×C₅₃	—	2	2	no	—
354	C₂²×C₄×C₅₃	—	2	1	no	—
355	C₂²×C₄×C₅₃	—	2	2	no	—
356	C₂²×C₄×C₅₃	—	2	2	no	—
357	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
360	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
363	Q₁₆×C₅₃	—	2	2	no	—
364	Q₁₆×C₅₃	—	2	4	no	—
365	Q₁₆×C₅₃	—	4	2	no	—
366	Q₁₆×C₅₃	—	4	2	no	—
367	Q₁₆×C₅₃	—	4	1	no	—
368	Q₁₆×C₅₃	—	4	2	no	—
369	Q₁₆×C₅₃	—	4	2	no	—
370	SD₁₆×C₅₃	—	2	2	no	—
371	SD₁₆×C₅₃	—	2	4	no	—
372	SD₁₆×C₅₃	—	4	2	no	—
373	SD₁₆×C₅₃	—	4	2	no	—
374	SD₁₆×C₅₃	—	4	2	no	—
375	SD₁₆×C₅₃	—	4	1	no	—
376	SD₁₆×C₅₃	—	4	2	no	—
377	M₁₆×C₅₃	—	4	2	no	—
378	C₂×C₈×C₅₃	—	4	2	no	—
379	C₂×C₈×C₅₃	—	4	2	no	—
380	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
385	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
386	C₄⋊C₄×C₅₃	—	2	1	no	—
387	C₄⋊C₄×C₅₃	—	2	2	no	—
388	C₄⋊C₄×C₅₃	—	2	1	no	—
389	C₄⋊C₄×C₅₃	—	2	2	no	—
390	C₄⋊C₄×C₅₃	—	2	1	no	—
391	C₄⋊C₄×C₅₃	—	2	2	no	—
392	C₄⋊C₄×C₅₃	—	2	1	no	—
393	C₄⋊C₄×C₅₃	—	2	1	no	—
394	C₄⋊C₄×C₅₃	—	2	2	no	—
395	C₄⋊C₄×C₅₃	—	2	1	no	—
396	C₄⋊C₄×C₅₃	—	2	1	no	—
397	C₄⋊C₄×C₅₃	—	2	1	no	—
398	C₄⋊C₄×C₅₃	—	2	1	no	—
399	C₄⋊C₄×C₅₃	—	2	2	no	—
400	C₄⋊C₄×C₅₃	—	2	1	no	—
401	C₄⋊C₄×C₅₃	—	2	2	no	—
402	C₄⋊C₄×C₅₃	—	2	1	no	—
403	C₄⋊C₄×C₅₃	—	2	2	no	—
404	C₄⋊C₄×C₅₃	—	2	1	no	—
405	C₄⋊C₄×C₅₃	—	2	2	no	—
406	C₄⋊C₄×C₅₃	—	2	1	no	—
407	C₄⋊C₄×C₅₃	—	2	2	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	C₂×D₄	1	1	yes	characteristic
413	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
418	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²⋊C₄×C₅₃	—	2	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	2	no	—
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	1	no	—
426	C₂²⋊C₄×C₅₃	—	2	2	no	—
427	C₂²⋊C₄×C₅₃	—	2	1	no	—
428	C₂²⋊C₄×C₅₃	—	2	1	no	—
429	C₂²⋊C₄×C₅₃	—	2	1	no	—
430	C₂²⋊C₄×C₅₃	—	2	2	no	—
431	C₂²⋊C₄×C₅₃	—	2	2	no	—
432	C₂²⋊C₄×C₅₃	—	2	2	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	1	no	—
437	C₂²⋊C₄×C₅₃	—	2	2	no	—
438	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
441	C₄²×C₅₃	—	2	1	no	—
442	C₄²×C₅₃	—	2	2	no	—
443	C₄²×C₅₃	—	2	1	no	—
444	C₄²×C₅₃	—	2	2	no	—
445	C₄²×C₅₃	—	2	1	no	—
446	C₄²×C₅₃	—	2	2	no	—
447	C₄²×C₅₃	—	2	1	no	—
448	C₄²×C₅₃	—	2	2	no	—
449	C₄²×C₅₃	—	2	1	no	—
450	C₄²×C₅₃	C₂×D₄	1	2	yes	—
451	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₅₃	C₂×D₄	1	2	yes	—
454	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
455	C₄²×C₅₃	C₂⁴	1	2	yes	—
456	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
457	C₂³×C₅₃	—	2	2	no	—
458	C₂³×C₅₃	—	2	1	no	—
459	C₂³×C₅₃	—	4	4	no	—
460	C₂³×C₅₃	—	8	2	no	—
461	C₂³×C₅₃	—	8	2	no	—
462	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
463	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
464	Q₈×C₅₃	—	2	2	no	—
465	Q₈×C₅₃	—	2	1	no	—
466	Q₈×C₅₃	—	2	2	no	—
467	Q₈×C₅₃	—	2	1	no	—
468	Q₈×C₅₃	—	2	1	no	—
469	Q₈×C₅₃	—	2	2	no	—
470	Q₈×C₅₃	—	2	1	no	—
471	Q₈×C₅₃	—	2	2	no	—
472	Q₈×C₅₃	—	2	2	no	—
473	Q₈×C₅₃	—	2	1	no	—
474	Q₈×C₅₃	—	4	2	no	—
475	Q₈×C₅₃	—	4	4	no	—
476	Q₈×C₅₃	—	8	2	no	—
477	Q₈×C₅₃	—	8	1	no	—
478	Q₈×C₅₃	—	8	2	no	—
479	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
480	D₄×C₅₃	—	2	4	no	—
481	D₄×C₅₃	—	2	1	no	—
482	D₄×C₅₃	—	2	2	no	—
483	D₄×C₅₃	—	2	1	no	—
484	D₄×C₅₃	—	2	2	no	—
485	D₄×C₅₃	—	4	4	no	—
486	D₄×C₅₃	—	4	2	no	—
487	D₄×C₅₃	—	8	1	no	—
488	D₄×C₅₃	—	8	2	no	—
489	D₄×C₅₃	—	8	1	no	—
490	D₄×C₅₃	—	8	2	no	—
491	D₄×C₅₃	#137	1	4	yes	complemented
492	C₂×C₄×C₅₃	—	2	4	no	—
493	C₂×C₄×C₅₃	—	2	1	no	—
494	C₂×C₄×C₅₃	—	2	2	no	—
495	C₂×C₄×C₅₃	—	2	2	no	—
496	C₂×C₄×C₅₃	—	2	1	no	—
497	C₂×C₄×C₅₃	—	2	2	no	—
498	C₂×C₄×C₅₃	—	2	1	no	—
499	C₂×C₄×C₅₃	—	2	1	no	—
500	C₂×C₄×C₅₃	—	2	2	no	—
501	C₂×C₄×C₅₃	—	2	1	no	—
502	C₂×C₄×C₅₃	—	2	1	no	—
503	C₂×C₄×C₅₃	—	2	1	no	—
504	C₂×C₄×C₅₃	—	2	1	no	—
505	C₂×C₄×C₅₃	—	2	2	no	—
506	C₂×C₄×C₅₃	—	2	1	no	—
507	C₂×C₄×C₅₃	—	2	2	no	—
508	C₂×C₄×C₅₃	—	4	2	no	—
509	C₂×C₄×C₅₃	—	4	1	no	—
510	C₂×C₄×C₅₃	—	4	4	no	—
511	C₂×C₄×C₅₃	—	4	2	no	—
512	C₂×C₄×C₅₃	—	4	2	no	—
513	C₂×C₄×C₅₃	—	8	2	no	—
514	C₂×C₄×C₅₃	—	8	2	no	—
515	C₂×C₄×C₅₃	—	8	2	no	—
516	C₂×C₄×C₅₃	—	8	1	no	—
517	C₂×C₄×C₅₃	—	8	2	no	—
518	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
527	C₈×C₅₃	—	2	1	no	—
528	C₈×C₅₃	—	2	1	no	—
529	C₈×C₅₃	—	2	2	no	—
530	C₈×C₅₃	—	2	2	no	—
531	C₈×C₅₃	—	2	1	no	—
532	C₈×C₅₃	—	2	1	no	—
533	#61991	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
534	C₂²×C₅₃	—	2	2	no	—
535	C₂²×C₅₃	—	2	2	no	—
536	C₂²×C₅₃	—	2	1	no	—
537	C₂²×C₅₃	—	2	1	no	—
538	C₂²×C₅₃	—	2	1	no	—
539	C₂²×C₅₃	—	4	2	no	—
540	C₂²×C₅₃	—	4	1	no	—
541	C₂²×C₅₃	—	4	2	no	—
542	C₂²×C₅₃	—	4	1	no	—
543	C₂²×C₅₃	—	4	1	no	—
544	C₂²×C₅₃	—	4	2	no	—
545	C₂²×C₅₃	—	16	4	no	—
546	C₂²×C₅₃	C₂×#137	1	4	yes	—
547	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
548	C₄×C₅₃	—	2	1	no	—
549	C₄×C₅₃	—	2	2	no	—
550	C₄×C₅₃	—	2	1	no	—
551	C₄×C₅₃	—	2	1	no	—
552	C₄×C₅₃	—	2	2	no	—
553	C₄×C₅₃	—	2	2	no	—
554	C₄×C₅₃	—	2	1	no	—
555	C₄×C₅₃	—	2	2	no	—
556	C₄×C₅₃	—	4	1	no	—
557	C₄×C₅₃	—	4	1	no	—
558	C₄×C₅₃	—	4	2	no	—
559	C₄×C₅₃	—	4	1	no	—
560	C₄×C₅₃	—	4	2	no	—
561	C₄×C₅₃	—	4	1	no	—
562	C₄×C₅₃	—	4	2	no	—
563	C₄×C₅₃	—	4	1	no	—
564	C₄×C₅₃	—	4	1	no	—
565	C₄×C₅₃	C₂×#137	1	2	yes	—
566	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
567	C₄×C₅₃	#585	1	1	yes	characteristic
568	#3514	C₂×C₅₃	1	1	yes	characteristic
569	Q₈×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
570	#3400	C₂×C₅₃	1	1	yes	characteristic, complemented
571	#3398	C₂×C₅₃	1	1	yes	characteristic, complemented
572	#3375	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#3369	C₂×C₅₃	1	1	yes	characteristic, complemented
574	#3316	C₂×C₅₃	1	2	yes	complemented
575	#3314	C₂×C₅₃	1	2	yes	complemented
576	#3299	C₂×C₅₃	1	1	yes	characteristic, complemented
577	#3295	C₂×C₅₃	1	1	yes	characteristic, complemented
578	D₄×Q₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
579	D₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
580	#3270	C₂×C₅₃	1	2	yes	complemented
581	#3266	C₂×C₅₃	1	2	yes	complemented
582	#3252	C₂×C₅₃	1	1	yes	characteristic, complemented
583	#3248	C₂×C₅₃	1	2	yes	complemented
584	#3215	C₂×C₅₃	1	2	yes	complemented
585	#3210	C₂×C₅₃	1	1	yes	characteristic, complemented
586	#3117	C₂×C₅₃	1	2	yes	complemented
587	#3108	C₂×C₅₃	1	1	yes	characteristic, complemented
588	#3037	C₂×C₅₃	1	1	yes	characteristic, complemented
589	C₂×#464	C₂×C₅₃	1	2	yes	complemented
590	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
591	C₂×C₅₃	—	2	4	no	—
592	C₂×C₅₃	—	4	1	no	—
593	C₂×C₅₃	—	8	2	no	—
594	C₂×C₅₃	—	8	1	no	—
595	C₂×C₅₃	#3488	1	1	yes	characteristic
596	C₂×C₅₃	C₂²×#137	1	1	yes	characteristic
597	C₂×C₅₃	#3584	1	1	yes	characteristic
598	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
599	C₂²×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
600	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
601	#559	C₂²×C₅₃	1	1	yes	characteristic
602	Q₈²	C₂²×C₅₃	1	1	yes	characteristic, complemented
603	#557	—	2	1	no	—
604	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
605	#556	C₂²×C₅₃	1	1	yes	characteristic
606	#555	—	2	1	no	—
607	#554	—	2	1	no	—
608	#554	—	2	2	no	—
609	#554	C₂²×C₅₃	1	1	yes	characteristic
610	#554	C₂²×C₅₃	1	2	yes	complemented
611	#551	—	2	2	no	—
612	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
613	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
614	D₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
615	#548	C₂²×C₅₃	1	2	yes	—
616	#546	—	2	1	no	—
617	#546	C₂²×C₅₃	1	2	yes	—
618	D₄²	C₂²×C₅₃	1	1	yes	characteristic
619	#542	—	2	1	no	—
620	#538	—	2	2	no	—
621	#533	—	2	2	no	—
622	#533	—	2	1	no	—
623	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
624	#533	C₂²×C₅₃	1	2	yes	complemented
625	#532	C₂²×C₅₃	1	1	yes	characteristic
626	#529	C₂²×C₅₃	1	1	yes	characteristic
627	#529	C₂²×C₅₃	1	2	yes	—
628	C₂×#124	C₂²×C₅₃	1	2	yes	—
629	#518	—	2	1	no	—
630	C₄×#41	—	2	1	no	—
631	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
632	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
633	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
634	#497	C₂²×C₅₃	1	2	yes	—
635	#497	C₂²×C₅₃	1	2	yes	complemented
636	#494	C₂²×C₅₃	1	1	yes	characteristic, complemented
637	#492	C₂²×C₅₃	1	1	yes	characteristic
638	#489	C₂²×C₅₃	1	2	yes	—
639	#489	C₂²×C₅₃	1	2	yes	complemented
640	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
641	#486	C₂²×C₅₃	1	1	yes	characteristic
642	#484	C₂²×C₅₃	1	2	yes	complemented
643	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
644	#481	C₂²×C₅₃	1	2	yes	—
645	#480	C₂²×C₅₃	1	1	yes	characteristic
646	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
647	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
648	#479	C₂²×C₅₃	1	2	yes	complemented
649	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
650	#476	C₂²×C₅₃	1	1	yes	characteristic
651	#475	C₂²×C₅₃	1	2	yes	complemented
652	#474	C₂²×C₅₃	1	2	yes	complemented
653	#470	C₂²×C₅₃	1	2	yes	complemented
654	#468	C₂²×C₅₃	1	2	yes	—
655	#467	C₂²×C₅₃	1	2	yes	complemented
656	#467	C₂²×C₅₃	1	2	yes	complemented
657	#465	C₂²×C₅₃	1	2	yes	—
658	#465	C₂²×C₅₃	1	2	yes	—
659	#464	C₂²×C₅₃	1	1	yes	characteristic
660	#464	C₂²×C₅₃	1	1	yes	characteristic
661	#464	C₂²×C₅₃	1	2	yes	—
662	#464	C₂²×C₅₃	1	2	yes	—
663	#464	C₂²×C₅₃	1	2	yes	—
664	#464	C₂²×C₅₃	1	2	yes	complemented
665	#464	C₂²×C₅₃	1	2	yes	complemented
666	#464	C₂²×C₅₃	1	2	yes	complemented
667	#464	C₂²×C₅₃	1	2	yes	complemented
668	#464	C₂²×C₅₃	1	2	yes	complemented
669	#464	C₂²×C₅₃	1	2	yes	complemented
670	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
671	#462	C₂²×C₅₃	1	2	yes	complemented
672	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
674	#461	C₂²×C₅₃	1	1	yes	characteristic
675	#461	C₂²×C₅₃	1	2	yes	complemented
676	#460	C₂²×C₅₃	1	1	yes	characteristic
677	#460	C₂²×C₅₃	1	1	yes	characteristic
678	#452	C₂²×C₅₃	1	2	yes	complemented
679	#452	C₂²×C₅₃	1	2	yes	complemented
680	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	#451	C₂²×C₅₃	1	2	yes	complemented
682	#451	C₂²×C₅₃	1	2	yes	complemented
683	#451	C₂²×C₅₃	1	2	yes	complemented
684	#450	C₂²×C₅₃	1	2	yes	—
685	#450	C₂²×C₅₃	1	2	yes	—
686	#448	C₂²×C₅₃	1	1	yes	characteristic
687	#448	C₂²×C₅₃	1	2	yes	—
688	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	#441	C₂²×C₅₃	1	2	yes	complemented
691	#441	C₂²×C₅₃	1	2	yes	complemented
692	#440	C₂²×C₅₃	1	2	yes	complemented
693	#440	C₂²×C₅₃	1	2	yes	complemented
694	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
695	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
697	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
698	#435	C₂²×C₅₃	1	2	yes	complemented
699	#435	C₂²×C₅₃	1	2	yes	complemented
700	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
701	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
702	#432	C₂²×C₅₃	1	2	yes	complemented
703	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
704	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
705	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	complemented
706	#417	C₂²×C₅₃	1	2	yes	complemented
707	C₂×#103	C₂²×C₅₃	1	2	yes	complemented
708	C₂×#102	C₂²×C₅₃	1	2	yes	—
709	C₅₃	#61991	1	1	yes	characteristic, direct product factor, Sylow
710	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
711	C₂×#41	C₂³×C₅₃	1	2	yes	—
712	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
713	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
714	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
715	C₂²×D₄	—	2	1	no	—
716	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
717	#137	—	4	4	no	—
718	C₂×Q₁₆	—	4	4	no	—
719	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
720	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
721	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
722	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
723	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
724	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
725	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
726	C₂×SD₁₆	—	4	4	no	—
727	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
728	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
734	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
735	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
736	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
737	C₄⋊Q₈	—	2	1	no	—
738	C₄⋊Q₈	—	2	2	no	—
739	C₄⋊Q₈	—	2	1	no	—
740	C₄⋊Q₈	—	2	2	no	—
741	C₄⋊Q₈	—	2	1	no	—
742	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
743	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
744	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
745	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
747	#127	C₂³×C₅₃	1	1	yes	characteristic
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#126	—	2	1	no	—
751	#125	—	2	1	no	—
752	#125	—	2	2	no	—
753	#125	—	2	1	no	—
754	#125	—	2	2	no	—
755	#125	—	2	1	no	—
756	#125	—	2	2	no	—
757	#125	C₂³×C₅₃	1	1	yes	characteristic
758	#124	—	2	1	no	—
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	C₂³×C₅₃	1	1	yes	characteristic
763	#124	C₂³×C₅₃	1	2	yes	—
764	#124	C₂³×C₅₃	1	2	yes	—
765	#124	C₂³×C₅₃	1	2	yes	—
766	#123	—	2	1	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
782	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
784	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
785	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
786	#121	—	2	2	no	—
787	#121	—	2	1	no	—
788	#121	—	2	1	no	—
789	#121	—	2	1	no	—
790	#121	—	2	2	no	—
791	#121	C₂³×C₅₃	1	2	yes	—
792	#121	C₂³×C₅₃	1	1	yes	characteristic
793	#120	—	2	2	no	—
794	#120	—	2	2	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	2	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	2	no	—
801	C₄×Q₈	—	2	2	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
807	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
809	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
811	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
812	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
813	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
826	C₄×D₄	D₄×C₅₃	1	2	yes	—
827	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₅₃	1	2	yes	—
829	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₅₃	1	2	yes	—
831	#117	—	2	2	no	—
832	#117	—	2	1	no	—
833	#117	—	2	1	no	—
834	#117	—	2	1	no	—
835	#117	—	2	2	no	—
836	#117	D₄×C₅₃	1	2	yes	—
837	#117	D₄×C₅₃	1	1	yes	characteristic
838	C₂×C₄⋊C₄	—	2	2	no	—
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
841	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
842	C₂×C₂²⋊C₄	—	2	2	no	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₄²	—	2	2	no	—
846	C₂×C₄²	—	2	1	no	—
847	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
848	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
849	#107	C₂³×C₅₃	1	1	yes	characteristic
850	#107	C₂³×C₅₃	1	1	yes	characteristic
851	#107	C₂³×C₅₃	1	2	yes	—
852	#106	C₂³×C₅₃	1	1	yes	characteristic
853	#106	C₂³×C₅₃	1	1	yes	characteristic
854	#106	C₂³×C₅₃	1	2	yes	—
855	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
856	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
857	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
858	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
859	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
862	#103	C₂³×C₅₃	1	1	yes	characteristic
863	#103	C₂³×C₅₃	1	2	yes	—
864	#103	C₂³×C₅₃	1	2	yes	—
865	#103	C₂³×C₅₃	1	2	yes	—
866	#103	C₂³×C₅₃	1	2	yes	—
867	#103	C₂³×C₅₃	1	1	yes	characteristic
868	#103	C₂³×C₅₃	1	1	yes	characteristic
869	#103	C₂³×C₅₃	1	1	yes	characteristic
870	#103	C₂³×C₅₃	1	1	yes	characteristic
871	#103	C₂³×C₅₃	1	1	yes	characteristic
872	#103	C₂³×C₅₃	1	2	yes	—
873	#103	C₂³×C₅₃	1	2	yes	—
874	#103	C₂³×C₅₃	1	2	yes	—
875	#102	C₂³×C₅₃	1	1	yes	characteristic
876	#102	C₂³×C₅₃	1	2	yes	—
877	#102	C₂³×C₅₃	1	2	yes	—
878	#102	C₂³×C₅₃	1	2	yes	—
879	#102	C₂³×C₅₃	1	2	yes	—
880	#102	C₂³×C₅₃	1	1	yes	characteristic
881	#102	C₂³×C₅₃	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
883	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
884	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
886	#97	C₂³×C₅₃	1	2	yes	—
887	#97	C₂³×C₅₃	1	2	yes	—
888	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
889	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
890	C₂⁴	—	2	2	no	—
891	#41	—	2	4	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	2	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	4	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	4	2	no	—
902	C₂×Q₈	—	4	1	no	—
903	C₂×Q₈	—	4	2	no	—
904	C₂×Q₈	—	4	2	no	—
905	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
906	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
907	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
908	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
910	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	2	no	—
919	C₂×D₄	—	4	4	no	—
920	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
921	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
922	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
933	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
934	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
935	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
937	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
938	Q₁₆	—	2	2	no	—
939	Q₁₆	—	2	4	no	—
940	Q₁₆	—	4	2	no	—
941	Q₁₆	—	4	2	no	—
942	Q₁₆	—	4	2	no	—
943	Q₁₆	—	4	1	no	—
944	Q₁₆	—	4	2	no	—
945	SD₁₆	—	2	2	no	—
946	SD₁₆	—	2	4	no	—
947	SD₁₆	—	4	2	no	—
948	SD₁₆	—	4	2	no	—
949	SD₁₆	—	4	2	no	—
950	SD₁₆	—	4	2	no	—
951	SD₁₆	—	4	1	no	—
952	M₁₆	—	4	2	no	—
953	C₂×C₈	—	4	2	no	—
954	C₂×C₈	—	4	2	no	—
955	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
956	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
957	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
958	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
960	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
988	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
989	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1014	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1026	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1027	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1028	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1029	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₅₃	1	2	yes	—
1031	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	4	4	no	—
1035	C₂³	—	8	2	no	—
1036	C₂³	—	8	2	no	—
1037	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1038	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	2	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	2	no	—
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	4	2	no	—
1050	Q₈	—	4	4	no	—
1051	Q₈	—	8	2	no	—
1052	Q₈	—	8	1	no	—
1053	Q₈	—	8	2	no	—
1054	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1055	D₄	—	2	4	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	4	4	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	8	1	no	—
1063	D₄	—	8	2	no	—
1064	D₄	—	8	1	no	—
1065	D₄	—	8	2	no	—
1066	D₄	#137×C₅₃	1	4	yes	complemented
1067	C₂×C₄	—	2	4	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	1	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	8	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	—	8	1	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1096	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1101	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1102	C₈	—	2	1	no	—
1103	C₈	—	2	1	no	—
1104	C₈	—	2	2	no	—
1105	C₈	—	2	2	no	—
1106	C₈	—	2	1	no	—
1107	C₈	—	2	1	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	16	4	no	—
1120	C₂²	C₂×#137×C₅₃	1	4	yes	—
1121	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1122	C₄	—	2	1	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	1	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	4	2	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	C₂×#137×C₅₃	1	2	yes	—
1140	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1141	C₄	C₅₃×#585	1	1	yes	characteristic
1142	C₂	—	2	4	no	—
1143	C₂	—	4	1	no	—
1144	C₂	—	8	1	no	—
1145	C₂	—	8	2	no	—
1146	C₂	C₅₃×#3488	1	1	yes	characteristic
1147	C₂	C₂²×#137×C₅₃	1	1	yes	characteristic
1148	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3514	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
2. Q₈×#41×C₅₃	C₂	semidirect
3. C₅₃×#3400	C₂	semidirect
4. C₅₃×#3398	C₂	semidirect
5. C₅₃×#3375	C₂	semidirect
6. C₅₃×#3369	C₂	semidirect
7. C₅₃×#3316	C₂	semidirect
8. C₅₃×#3314	C₂	semidirect
9. C₅₃×#3299	C₂	semidirect
10. C₅₃×#3295	C₂	semidirect
11. D₄×Q₁₆×C₅₃	C₂	semidirect
12. D₄×SD₁₆×C₅₃	C₂	semidirect
13. C₅₃×#3270	C₂	semidirect
14. C₅₃×#3266	C₂	semidirect
15. C₅₃×#3252	C₂	semidirect
16. C₅₃×#3248	C₂	semidirect
17. C₅₃×#3215	C₂	semidirect
18. C₅₃×#3210	C₂	semidirect
19. C₅₃×#3117	C₂	semidirect
20. C₅₃×#3108	C₂	semidirect
21. C₅₃×#3037	C₂	semidirect
22. C₂×C₅₃×#464	C₂	semidirect
23. C₅₃×#2990	C₂	semidirect
24. C₂×#137×C₅₃	C₂²	semidirect
25. C₂²×Q₁₆×C₅₃	C₂²	semidirect
28. Q₈²×C₅₃	C₂²	semidirect
30. C₅₃×#557	C₂²	semidirect
36. C₅₃×#554	C₂²	semidirect
40. D₄×Q₈×C₅₃	C₂²	semidirect
49. C₅₃×#533	C₂²	semidirect
50. C₅₃×#533	C₂²	semidirect
58. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
59. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
61. C₅₃×#497	C₂²	semidirect
62. C₅₃×#494	C₂²	semidirect
65. C₅₃×#489	C₂²	semidirect
66. C₅₃×#487	C₂²	semidirect
68. C₅₃×#484	C₂²	semidirect
69. C₅₃×#483	C₂²	semidirect
72. C₅₃×#479	C₂²	semidirect
73. C₅₃×#479	C₂²	semidirect
74. C₅₃×#479	C₂²	semidirect
75. C₅₃×#477	C₂²	semidirect
77. C₅₃×#475	C₂²	semidirect
78. C₅₃×#474	C₂²	semidirect
79. C₅₃×#470	C₂²	semidirect
81. C₅₃×#467	C₂²	semidirect
82. C₅₃×#467	C₂²	semidirect
90. C₅₃×#464	C₂²	semidirect
91. C₅₃×#464	C₂²	semidirect
92. C₅₃×#464	C₂²	semidirect
93. C₅₃×#464	C₂²	semidirect
94. C₅₃×#464	C₂²	semidirect
95. C₅₃×#464	C₂²	semidirect
96. C₅₃×#462	C₂²	semidirect
97. C₅₃×#462	C₂²	semidirect
98. C₅₃×#462	C₂²	semidirect
99. C₅₃×#462	C₂²	semidirect
101. C₅₃×#461	C₂²	semidirect
104. C₅₃×#452	C₂²	semidirect
105. C₅₃×#452	C₂²	semidirect
106. C₅₃×#451	C₂²	semidirect
107. C₅₃×#451	C₂²	semidirect
108. C₅₃×#451	C₂²	semidirect
109. C₅₃×#451	C₂²	semidirect
114. C₅₃×#446	C₂²	semidirect
115. C₅₃×#446	C₂²	semidirect
116. C₅₃×#441	C₂²	semidirect
117. C₅₃×#441	C₂²	semidirect
118. C₅₃×#440	C₂²	semidirect
119. C₅₃×#440	C₂²	semidirect
120. C₄×Q₁₆×C₅₃	C₂²	semidirect
121. C₄×Q₁₆×C₅₃	C₂²	semidirect
124. C₅₃×#435	C₂²	semidirect
125. C₅₃×#435	C₂²	semidirect
128. C₅₃×#432	C₂²	semidirect
129. C₅₃×#431	C₂²	semidirect
130. C₅₃×#423	C₂²	semidirect
131. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
132. C₅₃×#417	C₂²	semidirect
133. C₂×#103×C₅₃	C₂²	semidirect
491. D₄×C₅₃	#137	semidirect
533. #61991	C₅₃	direct (N × H)
569. Q₈×#41	C₂×C₅₃	semidirect
570. #3400	C₂×C₅₃	semidirect
571. #3398	C₂×C₅₃	semidirect
572. #3375	C₂×C₅₃	semidirect
573. #3369	C₂×C₅₃	semidirect
574. #3316	C₂×C₅₃	semidirect
575. #3314	C₂×C₅₃	semidirect
576. #3299	C₂×C₅₃	semidirect
577. #3295	C₂×C₅₃	semidirect
578. D₄×Q₁₆	C₂×C₅₃	semidirect
579. D₄×SD₁₆	C₂×C₅₃	semidirect
580. #3270	C₂×C₅₃	semidirect
581. #3266	C₂×C₅₃	semidirect
582. #3252	C₂×C₅₃	semidirect
583. #3248	C₂×C₅₃	semidirect
584. #3215	C₂×C₅₃	semidirect
585. #3210	C₂×C₅₃	semidirect
586. #3117	C₂×C₅₃	semidirect
587. #3108	C₂×C₅₃	semidirect
588. #3037	C₂×C₅₃	semidirect
589. C₂×#464	C₂×C₅₃	semidirect
590. #2990	C₂×C₅₃	semidirect
598. C₂×#137	C₂²×C₅₃	semidirect
599. C₂²×Q₁₆	C₂²×C₅₃	semidirect
602. Q₈²	C₂²×C₅₃	semidirect
604. #557	C₂²×C₅₃	semidirect
610. #554	C₂²×C₅₃	semidirect
614. D₄×Q₈	C₂²×C₅₃	semidirect
623. #533	C₂²×C₅₃	semidirect
624. #533	C₂²×C₅₃	semidirect
632. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
633. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
635. #497	C₂²×C₅₃	semidirect
636. #494	C₂²×C₅₃	semidirect
639. #489	C₂²×C₅₃	semidirect
640. #487	C₂²×C₅₃	semidirect
642. #484	C₂²×C₅₃	semidirect
643. #483	C₂²×C₅₃	semidirect
646. #479	C₂²×C₅₃	semidirect
647. #479	C₂²×C₅₃	semidirect
648. #479	C₂²×C₅₃	semidirect
649. #477	C₂²×C₅₃	semidirect
651. #475	C₂²×C₅₃	semidirect
652. #474	C₂²×C₅₃	semidirect
653. #470	C₂²×C₅₃	semidirect
655. #467	C₂²×C₅₃	semidirect
656. #467	C₂²×C₅₃	semidirect
664. #464	C₂²×C₅₃	semidirect
665. #464	C₂²×C₅₃	semidirect
666. #464	C₂²×C₅₃	semidirect
667. #464	C₂²×C₅₃	semidirect
668. #464	C₂²×C₅₃	semidirect
669. #464	C₂²×C₅₃	semidirect
670. #462	C₂²×C₅₃	semidirect
671. #462	C₂²×C₅₃	semidirect
672. #462	C₂²×C₅₃	semidirect
673. #462	C₂²×C₅₃	semidirect
675. #461	C₂²×C₅₃	semidirect
678. #452	C₂²×C₅₃	semidirect
679. #452	C₂²×C₅₃	semidirect
680. #451	C₂²×C₅₃	semidirect
681. #451	C₂²×C₅₃	semidirect
682. #451	C₂²×C₅₃	semidirect
683. #451	C₂²×C₅₃	semidirect
688. #446	C₂²×C₅₃	semidirect
689. #446	C₂²×C₅₃	semidirect
690. #441	C₂²×C₅₃	semidirect
691. #441	C₂²×C₅₃	semidirect
692. #440	C₂²×C₅₃	semidirect
693. #440	C₂²×C₅₃	semidirect
694. C₄×Q₁₆	C₂²×C₅₃	semidirect
695. C₄×Q₁₆	C₂²×C₅₃	semidirect
698. #435	C₂²×C₅₃	semidirect
699. #435	C₂²×C₅₃	semidirect
702. #432	C₂²×C₅₃	semidirect
703. #431	C₂²×C₅₃	semidirect
704. #423	C₂²×C₅₃	semidirect
705. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
706. #417	C₂²×C₅₃	semidirect
707. C₂×#103	C₂²×C₅₃	semidirect
709. C₅₃	#61991	direct (N × H)
1066. D₄	#137×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3514	2
Q₈×#41×C₅₃	2
C₅₃×#3400	2
C₅₃×#3398	2
C₅₃×#3375	2
C₅₃×#3369	2
C₅₃×#3316	2
C₅₃×#3314	2
C₅₃×#3299	2
C₅₃×#3295	2
D₄×Q₁₆×C₅₃	2
D₄×SD₁₆×C₅₃	2
C₅₃×#3270	2
C₅₃×#3266	2
C₅₃×#3252	2
C₅₃×#3248	2
C₅₃×#3215	2
C₅₃×#3210	2
C₅₃×#3117	2
C₅₃×#3108	2
C₅₃×#3037	2
C₂×C₅₃×#464	2
C₅₃×#2990	2
#61991	53

Subgroups — C53×#61991 #27269503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61991 #27269503