Subgroups — C₅₃×#61494 #27269006

Order 13568.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3347	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3305	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3297	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3268	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3179	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3124	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3122	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2946	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
25	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
26	C₅₃×#559	C₂²	1	1	yes	characteristic
27	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×#556	C₂²	1	1	yes	characteristic
29	C₅₃×#555	C₂²	1	2	yes	—
30	C₅₃×#553	—	2	2	no	—
31	C₅₃×#553	C₂²	1	2	yes	complemented
32	C₅₃×#551	—	2	2	no	—
33	C₅₃×#550	—	2	1	no	—
34	C₅₃×#550	C₂²	1	1	yes	characteristic
35	C₅₃×#550	C₂²	1	2	yes	complemented
36	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
37	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#548	—	2	1	no	—
39	C₅₃×#547	—	2	1	no	—
40	C₅₃×#547	C₂²	1	1	yes	characteristic
41	C₅₃×#546	—	2	1	no	—
42	C₅₃×#546	C₂²	1	2	yes	—
43	D₄²×C₅₃	C₂²	1	1	yes	characteristic
44	C₅₃×#542	C₂²	1	2	yes	—
45	C₅₃×#540	—	2	2	no	—
46	C₅₃×#540	C₂²	1	2	yes	complemented
47	C₅₃×#538	—	2	2	no	—
48	C₅₃×#532	—	2	1	no	—
49	C₅₃×#532	C₂²	1	1	yes	characteristic
50	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#529	—	2	1	no	—
52	C₅₃×#529	—	2	1	no	—
53	C₅₃×#529	C₂²	1	1	yes	characteristic
54	C₂×#124×C₅₃	—	2	1	no	—
55	C₅₃×#520	C₂²	1	2	yes	complemented
56	C₅₃×#518	C₂²	1	2	yes	—
57	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
58	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#501	C₂²	1	2	yes	complemented
60	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#496	C₂²	1	2	yes	complemented
62	C₅₃×#493	C₂²	1	1	yes	characteristic
63	C₅₃×#488	C₂²	1	2	yes	complemented
64	C₅₃×#486	C₂²	1	1	yes	characteristic
65	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#486	C₂²	1	2	yes	complemented
67	C₅₃×#484	C₂²	1	2	yes	complemented
68	C₅₃×#482	C₂²	1	2	yes	complemented
69	C₅₃×#482	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#482	C₂²	1	2	yes	complemented
72	C₅₃×#480	C₂²	1	2	yes	—
73	C₅₃×#478	C₂²	1	2	yes	—
74	C₅₃×#478	C₂²	1	2	yes	complemented
75	C₅₃×#477	C₂²	1	2	yes	complemented
76	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#474	C₂²	1	1	yes	characteristic
79	C₅₃×#474	C₂²	1	2	yes	complemented
80	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#469	C₂²	1	2	yes	—
82	C₅₃×#468	C₂²	1	2	yes	complemented
83	C₅₃×#466	C₂²	1	2	yes	—
84	C₅₃×#466	C₂²	1	2	yes	complemented
85	C₅₃×#466	C₂²	1	2	yes	complemented
86	C₅₃×#465	C₂²	1	2	yes	complemented
87	C₅₃×#464	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	2	yes	complemented
89	C₅₃×#460	C₂²	1	1	yes	characteristic
90	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#459	C₂²	1	2	yes	—
92	C₅₃×#459	C₂²	1	1	yes	characteristic
93	C₅₃×#459	C₂²	1	1	yes	characteristic
94	C₅₃×#459	C₂²	1	2	yes	complemented
95	C₅₃×#452	C₂²	1	2	yes	complemented
96	C₅₃×#449	C₂²	1	2	yes	—
97	C₅₃×#449	C₂²	1	2	yes	—
98	C₅₃×#449	C₂²	1	2	yes	complemented
99	C₅₃×#447	C₂²	1	2	yes	—
100	C₅₃×#447	C₂²	1	2	yes	—
101	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#442	C₂²	1	2	yes	—
104	C₅₃×#442	C₂²	1	2	yes	complemented
105	C₅₃×#442	C₂²	1	2	yes	complemented
106	C₅₃×#440	C₂²	1	2	yes	—
107	C₅₃×#440	C₂²	1	2	yes	complemented
108	C₅₃×#440	C₂²	1	2	yes	complemented
109	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
110	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
113	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
116	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×D₈×C₅₃	C₂²	1	2	yes	—
119	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
120	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
121	C₅₃×#436	C₂²	1	1	yes	characteristic
122	C₅₃×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
125	C₅₃×#433	C₂²	1	2	yes	complemented
126	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#428	C₂²	1	2	yes	complemented
128	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#416	C₂²	1	1	yes	characteristic
130	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#416	C₂²	1	2	yes	complemented
132	C₂×#102×C₅₃	C₂²	1	2	yes	—
133	C₅₃×#405	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	1	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
140	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₅₃	C₂³	1	2	yes	—
142	C₂²×Q₈×C₅₃	—	2	1	no	—
143	C₂²×D₄×C₅₃	—	2	1	no	—
144	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
145	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
146	#135×C₅₃	—	2	4	no	—
147	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₅₃	C₂³	1	2	yes	—
153	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₅₃	C₂³	1	2	yes	—
155	C₂×D₈×C₅₃	C₂³	1	2	yes	—
156	C₂×D₈×C₅₃	C₂³	1	2	yes	—
157	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₅₃	—	2	1	no	—
162	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
165	#127×C₅₃	—	2	1	no	—
166	#127×C₅₃	—	2	2	no	—
167	#127×C₅₃	C₂³	1	1	yes	characteristic
168	#127×C₅₃	C₂³	1	1	yes	characteristic
169	#127×C₅₃	C₂³	1	2	yes	—
170	#126×C₅₃	—	2	2	no	—
171	#126×C₅₃	—	2	2	no	—
172	#126×C₅₃	—	2	2	no	—
173	#126×C₅₃	D₄	1	2	yes	—
174	#125×C₅₃	—	2	2	no	—
175	#125×C₅₃	D₄	1	1	yes	characteristic
176	#125×C₅₃	C₂³	1	2	yes	—
177	#124×C₅₃	—	2	2	no	—
178	#124×C₅₃	—	2	2	no	—
179	#124×C₅₃	—	2	2	no	—
180	#124×C₅₃	—	2	1	no	—
181	#124×C₅₃	—	2	1	no	—
182	#124×C₅₃	—	2	1	no	—
183	#124×C₅₃	—	2	1	no	—
184	#124×C₅₃	D₄	1	1	yes	characteristic
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	#123×C₅₃	D₄	1	2	yes	—
194	C₂²⋊Q₈×C₅₃	—	2	1	no	—
195	C₂²⋊Q₈×C₅₃	—	2	1	no	—
196	C₂²⋊Q₈×C₅₃	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	—	2	2	no	—
198	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
199	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
200	#121×C₅₃	—	2	1	no	—
201	#121×C₅₃	—	2	1	no	—
202	#121×C₅₃	—	2	2	no	—
203	#121×C₅₃	—	2	2	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	2	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	2	no	—
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	—	2	1	no	—
213	#121×C₅₃	D₄	1	1	yes	characteristic
214	#121×C₅₃	C₂³	1	2	yes	—
215	#121×C₅₃	C₂³	1	2	yes	—
216	#121×C₅₃	C₂³	1	2	yes	—
217	#121×C₅₃	C₂³	1	2	yes	—
218	#121×C₅₃	C₂³	1	2	yes	—
219	#120×C₅₃	—	2	2	no	—
220	#120×C₅₃	—	2	2	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×Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
229	C₄×D₄×C₅₃	—	2	2	no	—
230	C₄×D₄×C₅₃	—	2	2	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	2	no	—
234	C₄×D₄×C₅₃	—	2	2	no	—
235	C₄×D₄×C₅₃	—	2	2	no	—
236	C₄×D₄×C₅₃	—	2	2	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	1	no	—
241	C₄×D₄×C₅₃	—	2	1	no	—
242	C₄×D₄×C₅₃	—	2	1	no	—
243	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₅₃	C₂³	1	2	yes	—
248	C₄×D₄×C₅₃	C₂³	1	2	yes	—
249	C₄×D₄×C₅₃	C₂³	1	2	yes	—
250	C₄×D₄×C₅₃	C₂³	1	2	yes	—
251	C₄×D₄×C₅₃	C₂³	1	2	yes	—
252	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₅₃	C₂³	1	2	yes	—
254	#117×C₅₃	—	2	2	no	—
255	#117×C₅₃	—	2	2	no	—
256	#117×C₅₃	—	2	1	no	—
257	#117×C₅₃	—	2	1	no	—
258	#117×C₅₃	C₂³	1	1	yes	characteristic
259	#117×C₅₃	C₂³	1	1	yes	characteristic
260	#117×C₅₃	C₂³	1	2	yes	—
261	#117×C₅₃	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
263	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
267	C₂×C₄²×C₅₃	—	2	1	no	—
268	C₂×C₄²×C₅₃	—	2	1	no	—
269	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
270	#107×C₅₃	C₂³	1	2	yes	—
271	#107×C₅₃	C₂³	1	2	yes	—
272	#107×C₅₃	C₂³	1	2	yes	—
273	#107×C₅₃	C₂³	1	1	yes	characteristic
274	#107×C₅₃	C₂³	1	1	yes	characteristic
275	#107×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	1	yes	characteristic
277	#106×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
284	#103×C₅₃	C₂³	1	1	yes	characteristic
285	#103×C₅₃	C₂³	1	2	yes	—
286	#103×C₅₃	C₂³	1	1	yes	characteristic
287	#103×C₅₃	C₂³	1	1	yes	characteristic
288	#103×C₅₃	C₂³	1	1	yes	characteristic
289	#103×C₅₃	C₂³	1	2	yes	—
290	#102×C₅₃	C₂³	1	2	yes	—
291	#102×C₅₃	C₂³	1	2	yes	—
292	#102×C₅₃	C₂³	1	2	yes	—
293	#102×C₅₃	C₂³	1	1	yes	characteristic
294	#102×C₅₃	C₂³	1	2	yes	—
295	#102×C₅₃	C₂³	1	2	yes	—
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	1	yes	characteristic
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	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
307	#97×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₃	C₂³	1	2	yes	—
311	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₂⁴×C₅₃	—	2	2	no	—
315	#41×C₅₃	—	2	2	no	—
316	#41×C₅₃	—	2	4	no	—
317	#41×C₅₃	—	2	2	no	—
318	#41×C₅₃	—	4	2	no	—
319	#41×C₅₃	—	4	1	no	—
320	#41×C₅₃	—	4	1	no	—
321	#41×C₅₃	—	8	2	no	—
322	#41×C₅₃	—	8	2	no	—
323	#41×C₅₃	—	8	2	no	—
324	#41×C₅₃	—	8	2	no	—
325	C₂×Q₈×C₅₃	—	2	1	no	—
326	C₂×Q₈×C₅₃	—	2	1	no	—
327	C₂×Q₈×C₅₃	—	2	2	no	—
328	C₂×Q₈×C₅₃	—	8	2	no	—
329	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₅₃	—	2	4	no	—
333	C₂×D₄×C₅₃	—	2	1	no	—
334	C₂×D₄×C₅₃	—	2	2	no	—
335	C₂×D₄×C₅₃	—	2	1	no	—
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	—	2	2	no	—
338	C₂×D₄×C₅₃	—	2	2	no	—
339	C₂×D₄×C₅₃	—	2	2	no	—
340	C₂×D₄×C₅₃	—	2	2	no	—
341	C₂×D₄×C₅₃	—	2	2	no	—
342	C₂×D₄×C₅₃	—	2	1	no	—
343	C₂×D₄×C₅₃	—	2	1	no	—
344	C₂×D₄×C₅₃	—	2	1	no	—
345	C₂×D₄×C₅₃	—	2	1	no	—
346	C₂×D₄×C₅₃	—	2	2	no	—
347	C₂×D₄×C₅₃	—	2	2	no	—
348	C₂×D₄×C₅₃	—	4	2	no	—
349	C₂×D₄×C₅₃	—	8	2	no	—
350	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
353	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
354	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₅₃	—	2	2	no	—
357	C₂²×C₄×C₅₃	—	2	1	no	—
358	C₂²×C₄×C₅₃	—	2	1	no	—
359	C₂²×C₄×C₅₃	—	2	1	no	—
360	C₂²×C₄×C₅₃	—	2	1	no	—
361	C₂²×C₄×C₅₃	—	2	2	no	—
362	C₂²×C₄×C₅₃	—	2	1	no	—
363	C₂²×C₄×C₅₃	—	2	1	no	—
364	C₂²×C₄×C₅₃	—	2	2	no	—
365	C₂²×C₄×C₅₃	—	2	2	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	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
373	Q₁₆×C₅₃	—	2	2	no	—
374	SD₁₆×C₅₃	—	2	4	no	—
375	SD₁₆×C₅₃	—	2	2	no	—
376	SD₁₆×C₅₃	—	4	2	no	—
377	SD₁₆×C₅₃	#41	1	4	yes	complemented
378	D₈×C₅₃	—	2	2	no	—
379	D₈×C₅₃	—	2	4	no	—
380	D₈×C₅₃	—	2	4	no	—
381	D₈×C₅₃	—	4	2	no	—
382	D₈×C₅₃	—	4	2	no	—
383	M₁₆×C₅₃	—	2	4	no	—
384	C₂×C₈×C₅₃	—	2	2	no	—
385	C₂×C₈×C₅₃	—	4	1	no	—
386	C₂×C₈×C₅₃	—	4	2	no	—
387	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
391	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
392	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₄⋊C₄×C₅₃	—	2	1	no	—
394	C₄⋊C₄×C₅₃	—	2	2	no	—
395	C₄⋊C₄×C₅₃	—	2	2	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	1	no	—
402	C₄⋊C₄×C₅₃	—	2	2	no	—
403	C₄⋊C₄×C₅₃	—	2	2	no	—
404	C₄⋊C₄×C₅₃	—	2	2	no	—
405	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄×C₅₃	—	2	2	no	—
418	C₂²⋊C₄×C₅₃	—	2	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	1	no	—
420	C₂²⋊C₄×C₅₃	—	2	1	no	—
421	C₂²⋊C₄×C₅₃	—	2	1	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	2	no	—
426	C₂²⋊C₄×C₅₃	—	2	2	no	—
427	C₂²⋊C₄×C₅₃	—	2	1	no	—
428	C₂²⋊C₄×C₅₃	—	2	2	no	—
429	C₂²⋊C₄×C₅₃	—	2	1	no	—
430	C₂²⋊C₄×C₅₃	—	2	1	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	2	no	—
437	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
442	C₄²×C₅₃	—	2	1	no	—
443	C₄²×C₅₃	—	2	1	no	—
444	C₄²×C₅₃	—	2	1	no	—
445	C₄²×C₅₃	—	2	1	no	—
446	C₄²×C₅₃	—	2	1	no	—
447	C₄²×C₅₃	—	2	1	no	—
448	C₄²×C₅₃	—	2	2	no	—
449	C₄²×C₅₃	—	2	2	no	—
450	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₄²×C₅₃	C₂⁴	1	2	yes	—
455	C₂³×C₅₃	—	2	1	no	—
456	C₂³×C₅₃	—	2	1	no	—
457	C₂³×C₅₃	—	2	2	no	—
458	C₂³×C₅₃	—	2	2	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	2	yes	—
463	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
464	Q₈×C₅₃	—	2	2	no	—
465	Q₈×C₅₃	—	2	1	no	—
466	Q₈×C₅₃	—	2	1	no	—
467	Q₈×C₅₃	—	2	1	no	—
468	Q₈×C₅₃	—	4	2	no	—
469	Q₈×C₅₃	—	4	2	no	—
470	Q₈×C₅₃	—	8	2	no	—
471	Q₈×C₅₃	C₂×#41	1	2	yes	—
472	D₄×C₅₃	—	2	2	no	—
473	D₄×C₅₃	—	2	2	no	—
474	D₄×C₅₃	—	2	2	no	—
475	D₄×C₅₃	—	2	1	no	—
476	D₄×C₅₃	—	2	1	no	—
477	D₄×C₅₃	—	2	2	no	—
478	D₄×C₅₃	—	2	1	no	—
479	D₄×C₅₃	—	2	2	no	—
480	D₄×C₅₃	—	4	2	no	—
481	D₄×C₅₃	—	4	4	no	—
482	D₄×C₅₃	—	4	2	no	—
483	D₄×C₅₃	—	4	4	no	—
484	D₄×C₅₃	—	4	2	no	—
485	D₄×C₅₃	—	4	2	no	—
486	D₄×C₅₃	—	4	2	no	—
487	D₄×C₅₃	—	8	1	no	—
488	D₄×C₅₃	—	8	1	no	—
489	D₄×C₅₃	—	8	2	no	—
490	D₄×C₅₃	—	8	2	no	—
491	D₄×C₅₃	—	8	2	no	—
492	D₄×C₅₃	—	8	2	no	—
493	D₄×C₅₃	—	8	2	no	—
494	D₄×C₅₃	—	8	2	no	—
495	D₄×C₅₃	—	8	2	no	—
496	D₄×C₅₃	C₂×#41	1	2	yes	—
497	C₂×C₄×C₅₃	—	2	1	no	—
498	C₂×C₄×C₅₃	—	2	2	no	—
499	C₂×C₄×C₅₃	—	2	2	no	—
500	C₂×C₄×C₅₃	—	2	1	no	—
501	C₂×C₄×C₅₃	—	2	2	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	2	no	—
507	C₂×C₄×C₅₃	—	2	1	no	—
508	C₂×C₄×C₅₃	—	2	1	no	—
509	C₂×C₄×C₅₃	—	2	1	no	—
510	C₂×C₄×C₅₃	—	4	1	no	—
511	C₂×C₄×C₅₃	—	4	2	no	—
512	C₂×C₄×C₅₃	—	4	4	no	—
513	C₂×C₄×C₅₃	—	4	2	no	—
514	C₂×C₄×C₅₃	—	4	2	no	—
515	C₂×C₄×C₅₃	—	4	2	no	—
516	C₂×C₄×C₅₃	—	8	1	no	—
517	C₂×C₄×C₅₃	—	8	1	no	—
518	C₂×C₄×C₅₃	—	8	2	no	—
519	C₂×C₄×C₅₃	—	8	2	no	—
520	C₂×C₄×C₅₃	—	8	2	no	—
521	C₂×C₄×C₅₃	—	8	2	no	—
522	C₂×C₄×C₅₃	—	8	2	no	—
523	C₂×C₄×C₅₃	—	8	2	no	—
524	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
533	C₈×C₅₃	—	2	1	no	—
534	C₈×C₅₃	—	2	2	no	—
535	C₈×C₅₃	—	2	1	no	—
536	C₈×C₅₃	—	2	1	no	—
537	C₈×C₅₃	—	2	2	no	—
538	C₈×C₅₃	C₂×#41	1	2	yes	—
539	#61494	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
540	C₂²×C₅₃	—	2	1	no	—
541	C₂²×C₅₃	—	2	2	no	—
542	C₂²×C₅₃	—	2	1	no	—
543	C₂²×C₅₃	—	2	2	no	—
544	C₂²×C₅₃	—	2	2	no	—
545	C₂²×C₅₃	—	2	1	no	—
546	C₂²×C₅₃	—	2	2	no	—
547	C₂²×C₅₃	—	4	1	no	—
548	C₂²×C₅₃	—	4	1	no	—
549	C₂²×C₅₃	—	4	1	no	—
550	C₂²×C₅₃	—	4	2	no	—
551	C₂²×C₅₃	—	4	2	no	—
552	C₂²×C₅₃	—	4	2	no	—
553	C₂²×C₅₃	—	4	1	no	—
554	C₂²×C₅₃	—	4	2	no	—
555	C₂²×C₅₃	—	4	1	no	—
556	C₂²×C₅₃	—	4	2	no	—
557	C₂²×C₅₃	—	4	2	no	—
558	C₂²×C₅₃	—	16	4	no	—
559	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
560	C₄×C₅₃	—	2	1	no	—
561	C₄×C₅₃	—	2	1	no	—
562	C₄×C₅₃	—	2	2	no	—
563	C₄×C₅₃	—	2	1	no	—
564	C₄×C₅₃	—	2	2	no	—
565	C₄×C₅₃	—	2	2	no	—
566	C₄×C₅₃	—	2	1	no	—
567	C₄×C₅₃	—	2	2	no	—
568	C₄×C₅₃	—	4	1	no	—
569	C₄×C₅₃	—	4	1	no	—
570	C₄×C₅₃	—	4	1	no	—
571	C₄×C₅₃	—	4	1	no	—
572	C₄×C₅₃	—	4	1	no	—
573	C₄×C₅₃	—	4	2	no	—
574	C₄×C₅₃	—	4	2	no	—
575	C₄×C₅₃	#576	1	2	yes	—
576	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
577	C₄×C₅₃	#585	1	1	yes	characteristic
578	#3517	C₂×C₅₃	1	1	yes	characteristic, complemented
579	#3514	C₂×C₅₃	1	1	yes	characteristic, complemented
580	#3399	C₂×C₅₃	1	1	yes	characteristic, complemented
581	#3386	C₂×C₅₃	1	1	yes	characteristic, complemented
582	#3365	C₂×C₅₃	1	1	yes	characteristic, complemented
583	#3358	C₂×C₅₃	1	1	yes	characteristic, complemented
584	#3353	C₂×C₅₃	1	1	yes	characteristic, complemented
585	#3347	C₂×C₅₃	1	2	yes	complemented
586	#3305	C₂×C₅₃	1	2	yes	complemented
587	#3304	C₂×C₅₃	1	1	yes	characteristic, complemented
588	#3297	C₂×C₅₃	1	2	yes	complemented
589	#3294	C₂×C₅₃	1	1	yes	characteristic, complemented
590	#3274	C₂×C₅₃	1	1	yes	characteristic, complemented
591	#3268	C₂×C₅₃	1	2	yes	complemented
592	#3179	C₂×C₅₃	1	2	yes	complemented
593	#3169	C₂×C₅₃	1	1	yes	characteristic, complemented
594	#3124	C₂×C₅₃	1	2	yes	complemented
595	#3122	C₂×C₅₃	1	2	yes	complemented
596	#3115	C₂×C₅₃	1	1	yes	characteristic, complemented
597	#3115	C₂×C₅₃	1	1	yes	characteristic, complemented
598	#2966	C₂×C₅₃	1	1	yes	characteristic, complemented
599	#2946	C₂×C₅₃	1	2	yes	complemented
600	C₄×#135	C₂×C₅₃	1	1	yes	characteristic, complemented
601	C₂×C₅₃	—	4	1	no	—
602	C₂×C₅₃	—	4	2	no	—
603	C₂×C₅₃	—	4	2	no	—
604	C₂×C₅₃	—	8	1	no	—
605	C₂×C₅₃	—	8	2	no	—
606	C₂×C₅₃	—	8	2	no	—
607	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
608	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
609	C₂×C₅₃	#3584	1	1	yes	characteristic
610	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
611	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
612	#559	C₂²×C₅₃	1	1	yes	characteristic
613	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
614	#556	C₂²×C₅₃	1	1	yes	characteristic
615	#555	C₂²×C₅₃	1	2	yes	—
616	#553	—	2	2	no	—
617	#553	C₂²×C₅₃	1	2	yes	complemented
618	#551	—	2	2	no	—
619	#550	—	2	1	no	—
620	#550	C₂²×C₅₃	1	1	yes	characteristic
621	#550	C₂²×C₅₃	1	2	yes	complemented
622	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
623	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
624	#548	—	2	1	no	—
625	#547	—	2	1	no	—
626	#547	C₂²×C₅₃	1	1	yes	characteristic
627	#546	—	2	1	no	—
628	#546	C₂²×C₅₃	1	2	yes	—
629	D₄²	C₂²×C₅₃	1	1	yes	characteristic
630	#542	C₂²×C₅₃	1	2	yes	—
631	#540	—	2	2	no	—
632	#540	C₂²×C₅₃	1	2	yes	complemented
633	#538	—	2	2	no	—
634	#532	—	2	1	no	—
635	#532	C₂²×C₅₃	1	1	yes	characteristic
636	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
637	#529	—	2	1	no	—
638	#529	—	2	1	no	—
639	#529	C₂²×C₅₃	1	1	yes	characteristic
640	C₂×#124	—	2	1	no	—
641	#520	C₂²×C₅₃	1	2	yes	complemented
642	#518	C₂²×C₅₃	1	2	yes	—
643	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
644	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
645	#501	C₂²×C₅₃	1	2	yes	complemented
646	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
647	#496	C₂²×C₅₃	1	2	yes	complemented
648	#493	C₂²×C₅₃	1	1	yes	characteristic
649	#488	C₂²×C₅₃	1	2	yes	complemented
650	#486	C₂²×C₅₃	1	1	yes	characteristic
651	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
652	#486	C₂²×C₅₃	1	2	yes	complemented
653	#484	C₂²×C₅₃	1	2	yes	complemented
654	#482	C₂²×C₅₃	1	2	yes	complemented
655	#482	C₂²×C₅₃	1	2	yes	complemented
656	#482	C₂²×C₅₃	1	2	yes	complemented
657	#482	C₂²×C₅₃	1	2	yes	complemented
658	#480	C₂²×C₅₃	1	2	yes	—
659	#478	C₂²×C₅₃	1	2	yes	—
660	#478	C₂²×C₅₃	1	2	yes	complemented
661	#477	C₂²×C₅₃	1	2	yes	complemented
662	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
664	#474	C₂²×C₅₃	1	1	yes	characteristic
665	#474	C₂²×C₅₃	1	2	yes	complemented
666	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
667	#469	C₂²×C₅₃	1	2	yes	—
668	#468	C₂²×C₅₃	1	2	yes	complemented
669	#466	C₂²×C₅₃	1	2	yes	—
670	#466	C₂²×C₅₃	1	2	yes	complemented
671	#466	C₂²×C₅₃	1	2	yes	complemented
672	#465	C₂²×C₅₃	1	2	yes	complemented
673	#464	C₂²×C₅₃	1	2	yes	complemented
674	#463	C₂²×C₅₃	1	2	yes	complemented
675	#460	C₂²×C₅₃	1	1	yes	characteristic
676	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
677	#459	C₂²×C₅₃	1	1	yes	characteristic
678	#459	C₂²×C₅₃	1	2	yes	—
679	#459	C₂²×C₅₃	1	1	yes	characteristic
680	#459	C₂²×C₅₃	1	2	yes	complemented
681	#452	C₂²×C₅₃	1	2	yes	complemented
682	#449	C₂²×C₅₃	1	2	yes	—
683	#449	C₂²×C₅₃	1	2	yes	—
684	#449	C₂²×C₅₃	1	2	yes	complemented
685	#447	C₂²×C₅₃	1	2	yes	—
686	#447	C₂²×C₅₃	1	2	yes	—
687	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
688	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	#442	C₂²×C₅₃	1	2	yes	—
690	#442	C₂²×C₅₃	1	2	yes	complemented
691	#442	C₂²×C₅₃	1	2	yes	complemented
692	#440	C₂²×C₅₃	1	2	yes	—
693	#440	C₂²×C₅₃	1	2	yes	complemented
694	#440	C₂²×C₅₃	1	2	yes	complemented
695	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
697	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
698	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
699	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
700	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
701	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
702	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
703	C₄×D₈	C₂²×C₅₃	1	2	yes	—
704	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
705	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
706	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
707	#436	C₂²×C₅₃	1	1	yes	characteristic
708	#435	C₂²×C₅₃	1	2	yes	complemented
709	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
710	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
711	#433	C₂²×C₅₃	1	2	yes	complemented
712	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	#428	C₂²×C₅₃	1	2	yes	complemented
714	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
715	#416	C₂²×C₅₃	1	1	yes	characteristic
716	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
717	#416	C₂²×C₅₃	1	2	yes	complemented
718	C₂×#102	C₂²×C₅₃	1	2	yes	—
719	#405	C₂²×C₅₃	1	2	yes	complemented
720	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
721	C₅₃	#61494	1	1	yes	characteristic, direct product factor, Sylow
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	2	1	no	—
724	C₂×#41	—	2	1	no	—
725	C₂×#41	—	2	1	no	—
726	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
727	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
728	C₂×#41	C₂³×C₅₃	1	2	yes	—
729	C₂²×Q₈	—	2	1	no	—
730	C₂²×D₄	—	2	1	no	—
731	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
732	AGL(1,ℤ/8)	—	2	8	no	—
733	#135	—	2	4	no	—
734	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
736	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
739	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
740	C₂×D₈	C₂³×C₅₃	1	2	yes	—
741	C₂×D₈	C₂³×C₅₃	1	2	yes	—
742	C₂×D₈	C₂³×C₅₃	1	2	yes	—
743	C₂×D₈	C₂³×C₅₃	1	2	yes	—
744	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
745	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
746	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
747	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
748	C₄⋊Q₈	—	2	1	no	—
749	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
750	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
752	#127	—	2	1	no	—
753	#127	—	2	2	no	—
754	#127	C₂³×C₅₃	1	1	yes	characteristic
755	#127	C₂³×C₅₃	1	1	yes	characteristic
756	#127	C₂³×C₅₃	1	2	yes	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	D₄×C₅₃	1	2	yes	—
761	#125	—	2	2	no	—
762	#125	D₄×C₅₃	1	1	yes	characteristic
763	#125	C₂³×C₅₃	1	2	yes	—
764	#124	—	2	1	no	—
765	#124	—	2	1	no	—
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	—	2	1	no	—
770	#124	—	2	1	no	—
771	#124	D₄×C₅₃	1	1	yes	characteristic
772	#124	C₂³×C₅₃	1	2	yes	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	D₄×C₅₃	1	2	yes	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
786	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	1	no	—
790	#121	—	2	1	no	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	D₄×C₅₃	1	1	yes	characteristic
801	#121	C₂³×C₅₃	1	2	yes	—
802	#121	C₂³×C₅₃	1	2	yes	—
803	#121	C₂³×C₅₃	1	2	yes	—
804	#121	C₂³×C₅₃	1	2	yes	—
805	#121	C₂³×C₅₃	1	2	yes	—
806	#120	—	2	2	no	—
807	#120	—	2	2	no	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
813	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
814	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
815	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₅₃	1	2	yes	—
835	C₄×D₄	C₂³×C₅₃	1	2	yes	—
836	C₄×D₄	C₂³×C₅₃	1	2	yes	—
837	C₄×D₄	C₂³×C₅₃	1	2	yes	—
838	C₄×D₄	C₂³×C₅₃	1	2	yes	—
839	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₅₃	1	2	yes	—
841	#117	—	2	2	no	—
842	#117	—	2	2	no	—
843	#117	—	2	1	no	—
844	#117	—	2	1	no	—
845	#117	C₂³×C₅₃	1	1	yes	characteristic
846	#117	C₂³×C₅₃	1	1	yes	characteristic
847	#117	C₂³×C₅₃	1	2	yes	—
848	#117	C₂³×C₅₃	1	2	yes	—
849	C₂×C₄⋊C₄	—	2	2	no	—
850	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₂²⋊C₄	—	2	2	no	—
854	C₂×C₄²	—	2	1	no	—
855	C₂×C₄²	—	2	1	no	—
856	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
857	#107	C₂³×C₅₃	1	1	yes	characteristic
858	#107	C₂³×C₅₃	1	1	yes	characteristic
859	#107	C₂³×C₅₃	1	2	yes	—
860	#107	C₂³×C₅₃	1	2	yes	—
861	#107	C₂³×C₅₃	1	2	yes	—
862	#107	C₂³×C₅₃	1	2	yes	—
863	#106	C₂³×C₅₃	1	1	yes	characteristic
864	#106	C₂³×C₅₃	1	1	yes	characteristic
865	#106	C₂³×C₅₃	1	2	yes	—
866	#106	C₂³×C₅₃	1	2	yes	—
867	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
869	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
870	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
871	#103	C₂³×C₅₃	1	1	yes	characteristic
872	#103	C₂³×C₅₃	1	1	yes	characteristic
873	#103	C₂³×C₅₃	1	1	yes	characteristic
874	#103	C₂³×C₅₃	1	1	yes	characteristic
875	#103	C₂³×C₅₃	1	2	yes	—
876	#103	C₂³×C₅₃	1	2	yes	—
877	#102	C₂³×C₅₃	1	1	yes	characteristic
878	#102	C₂³×C₅₃	1	2	yes	—
879	#102	C₂³×C₅₃	1	2	yes	—
880	#102	C₂³×C₅₃	1	2	yes	—
881	#102	C₂³×C₅₃	1	1	yes	characteristic
882	#102	C₂³×C₅₃	1	2	yes	—
883	#102	C₂³×C₅₃	1	1	yes	characteristic
884	#102	C₂³×C₅₃	1	1	yes	characteristic
885	#102	C₂³×C₅₃	1	2	yes	—
886	#102	C₂³×C₅₃	1	2	yes	—
887	#102	C₂³×C₅₃	1	2	yes	—
888	#102	C₂³×C₅₃	1	2	yes	—
889	#102	C₂³×C₅₃	1	2	yes	—
890	#102	C₂³×C₅₃	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
893	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
894	#97	C₂³×C₅₃	1	2	yes	—
895	#97	C₂³×C₅₃	1	2	yes	—
896	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
898	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
899	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
900	C₄×C₈	C₂³×C₅₃	1	2	yes	—
901	C₂⁴	—	2	2	no	—
902	#41	—	2	2	no	—
903	#41	—	2	4	no	—
904	#41	—	2	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	1	no	—
907	#41	—	4	1	no	—
908	#41	—	8	2	no	—
909	#41	—	8	2	no	—
910	#41	—	8	2	no	—
911	#41	—	8	2	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	—	2	1	no	—
914	C₂×Q₈	—	2	2	no	—
915	C₂×Q₈	—	8	2	no	—
916	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
918	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
919	C₂×D₄	—	2	4	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	4	2	no	—
936	C₂×D₄	—	8	2	no	—
937	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
938	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
939	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
940	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
941	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
942	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
957	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
959	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
960	Q₁₆	—	2	2	no	—
961	SD₁₆	—	2	4	no	—
962	SD₁₆	—	2	2	no	—
963	SD₁₆	—	4	2	no	—
964	SD₁₆	#41×C₅₃	1	4	yes	complemented
965	D₈	—	2	2	no	—
966	D₈	—	2	4	no	—
967	D₈	—	2	4	no	—
968	D₈	—	4	2	no	—
969	D₈	—	4	2	no	—
970	M₁₆	—	2	4	no	—
971	C₂×C₈	—	2	2	no	—
972	C₂×C₈	—	4	1	no	—
973	C₂×C₈	—	4	2	no	—
974	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
978	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
979	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
997	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1038	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1040	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1041	C₄²	C₂⁴×C₅₃	1	2	yes	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	4	4	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	—	8	2	no	—
1049	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1050	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	4	2	no	—
1057	Q₈	—	8	2	no	—
1058	Q₈	C₂×#41×C₅₃	1	2	yes	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	4	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	4	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	1	no	—
1075	D₄	—	8	1	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	C₂×#41×C₅₃	1	2	yes	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	4	1	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	8	1	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	—	8	2	no	—
1108	C₂×C₄	—	8	2	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1113	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1114	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1115	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1117	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1118	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1119	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1120	C₈	—	2	1	no	—
1121	C₈	—	2	2	no	—
1122	C₈	—	2	1	no	—
1123	C₈	—	2	1	no	—
1124	C₈	—	2	2	no	—
1125	C₈	C₂×#41×C₅₃	1	2	yes	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	16	4	no	—
1145	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1146	C₄	—	2	1	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	2	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	1	no	—
1161	C₄	C₅₃×#576	1	2	yes	—
1162	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1163	C₄	C₅₃×#585	1	1	yes	characteristic
1164	C₂	—	4	2	no	—
1165	C₂	—	4	1	no	—
1166	C₂	—	4	2	no	—
1167	C₂	—	8	2	no	—
1168	C₂	—	8	1	no	—
1169	C₂	—	8	2	no	—
1170	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1171	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1172	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3517	C₂	semidirect
2. C₅₃×#3514	C₂	semidirect
3. C₅₃×#3399	C₂	semidirect
4. C₅₃×#3386	C₂	semidirect
5. C₅₃×#3365	C₂	semidirect
6. C₅₃×#3358	C₂	semidirect
7. C₅₃×#3353	C₂	semidirect
8. C₅₃×#3347	C₂	semidirect
9. C₅₃×#3305	C₂	semidirect
10. C₅₃×#3304	C₂	semidirect
11. C₅₃×#3297	C₂	semidirect
12. C₅₃×#3294	C₂	semidirect
13. C₅₃×#3274	C₂	semidirect
14. C₅₃×#3268	C₂	semidirect
15. C₅₃×#3179	C₂	semidirect
16. C₅₃×#3169	C₂	semidirect
17. C₅₃×#3124	C₂	semidirect
18. C₅₃×#3122	C₂	semidirect
19. C₅₃×#3115	C₂	semidirect
20. C₅₃×#3115	C₂	semidirect
21. C₅₃×#2966	C₂	semidirect
22. C₅₃×#2946	C₂	semidirect
23. C₄×#135×C₅₃	C₂	semidirect
27. C₅₃×#557	C₂²	semidirect
31. C₅₃×#553	C₂²	semidirect
35. C₅₃×#550	C₂²	semidirect
36. C₅₃×#550	C₂²	semidirect
46. C₅₃×#540	C₂²	semidirect
50. C₅₃×#532	C₂²	semidirect
55. C₅₃×#520	C₂²	semidirect
58. C₄×#41×C₅₃	C₂²	semidirect
59. C₅₃×#501	C₂²	semidirect
60. C₅₃×#500	C₂²	semidirect
61. C₅₃×#496	C₂²	semidirect
63. C₅₃×#488	C₂²	semidirect
65. C₅₃×#486	C₂²	semidirect
66. C₅₃×#486	C₂²	semidirect
67. C₅₃×#484	C₂²	semidirect
68. C₅₃×#482	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#477	C₂²	semidirect
76. C₅₃×#475	C₂²	semidirect
77. C₅₃×#475	C₂²	semidirect
79. C₅₃×#474	C₂²	semidirect
80. C₅₃×#474	C₂²	semidirect
82. C₅₃×#468	C₂²	semidirect
84. C₅₃×#466	C₂²	semidirect
85. C₅₃×#466	C₂²	semidirect
86. C₅₃×#465	C₂²	semidirect
87. C₅₃×#464	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
90. C₅₃×#460	C₂²	semidirect
94. C₅₃×#459	C₂²	semidirect
95. C₅₃×#452	C₂²	semidirect
98. C₅₃×#449	C₂²	semidirect
101. C₅₃×#446	C₂²	semidirect
102. C₈×Q₈×C₅₃	C₂²	semidirect
104. C₅₃×#442	C₂²	semidirect
105. C₅₃×#442	C₂²	semidirect
107. C₅₃×#440	C₂²	semidirect
108. C₅₃×#440	C₂²	semidirect
109. C₄×Q₁₆×C₅₃	C₂²	semidirect
110. C₄×Q₁₆×C₅₃	C₂²	semidirect
113. C₄×SD₁₆×C₅₃	C₂²	semidirect
114. C₄×SD₁₆×C₅₃	C₂²	semidirect
115. C₄×SD₁₆×C₅₃	C₂²	semidirect
119. C₄×D₈×C₅₃	C₂²	semidirect
120. C₄×D₈×C₅₃	C₂²	semidirect
122. C₅₃×#435	C₂²	semidirect
124. C₈×D₄×C₅₃	C₂²	semidirect
125. C₅₃×#433	C₂²	semidirect
126. C₅₃×#432	C₂²	semidirect
127. C₅₃×#428	C₂²	semidirect
128. C₅₃×#427	C₂²	semidirect
130. C₅₃×#416	C₂²	semidirect
131. C₅₃×#416	C₂²	semidirect
133. C₅₃×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₅₃	C₂²	semidirect
377. SD₁₆×C₅₃	#41	semidirect
539. #61494	C₅₃	direct (N × H)
578. #3517	C₂×C₅₃	semidirect
579. #3514	C₂×C₅₃	semidirect
580. #3399	C₂×C₅₃	semidirect
581. #3386	C₂×C₅₃	semidirect
582. #3365	C₂×C₅₃	semidirect
583. #3358	C₂×C₅₃	semidirect
584. #3353	C₂×C₅₃	semidirect
585. #3347	C₂×C₅₃	semidirect
586. #3305	C₂×C₅₃	semidirect
587. #3304	C₂×C₅₃	semidirect
588. #3297	C₂×C₅₃	semidirect
589. #3294	C₂×C₅₃	semidirect
590. #3274	C₂×C₅₃	semidirect
591. #3268	C₂×C₅₃	semidirect
592. #3179	C₂×C₅₃	semidirect
593. #3169	C₂×C₅₃	semidirect
594. #3124	C₂×C₅₃	semidirect
595. #3122	C₂×C₅₃	semidirect
596. #3115	C₂×C₅₃	semidirect
597. #3115	C₂×C₅₃	semidirect
598. #2966	C₂×C₅₃	semidirect
599. #2946	C₂×C₅₃	semidirect
600. C₄×#135	C₂×C₅₃	semidirect
613. #557	C₂²×C₅₃	semidirect
617. #553	C₂²×C₅₃	semidirect
621. #550	C₂²×C₅₃	semidirect
622. #550	C₂²×C₅₃	semidirect
632. #540	C₂²×C₅₃	semidirect
636. #532	C₂²×C₅₃	semidirect
641. #520	C₂²×C₅₃	semidirect
644. C₄×#41	C₂²×C₅₃	semidirect
645. #501	C₂²×C₅₃	semidirect
646. #500	C₂²×C₅₃	semidirect
647. #496	C₂²×C₅₃	semidirect
649. #488	C₂²×C₅₃	semidirect
651. #486	C₂²×C₅₃	semidirect
652. #486	C₂²×C₅₃	semidirect
653. #484	C₂²×C₅₃	semidirect
654. #482	C₂²×C₅₃	semidirect
655. #482	C₂²×C₅₃	semidirect
656. #482	C₂²×C₅₃	semidirect
657. #482	C₂²×C₅₃	semidirect
660. #478	C₂²×C₅₃	semidirect
661. #477	C₂²×C₅₃	semidirect
662. #475	C₂²×C₅₃	semidirect
663. #475	C₂²×C₅₃	semidirect
665. #474	C₂²×C₅₃	semidirect
666. #474	C₂²×C₅₃	semidirect
668. #468	C₂²×C₅₃	semidirect
670. #466	C₂²×C₅₃	semidirect
671. #466	C₂²×C₅₃	semidirect
672. #465	C₂²×C₅₃	semidirect
673. #464	C₂²×C₅₃	semidirect
674. #463	C₂²×C₅₃	semidirect
676. #460	C₂²×C₅₃	semidirect
680. #459	C₂²×C₅₃	semidirect
681. #452	C₂²×C₅₃	semidirect
684. #449	C₂²×C₅₃	semidirect
687. #446	C₂²×C₅₃	semidirect
688. C₈×Q₈	C₂²×C₅₃	semidirect
690. #442	C₂²×C₅₃	semidirect
691. #442	C₂²×C₅₃	semidirect
693. #440	C₂²×C₅₃	semidirect
694. #440	C₂²×C₅₃	semidirect
695. C₄×Q₁₆	C₂²×C₅₃	semidirect
696. C₄×Q₁₆	C₂²×C₅₃	semidirect
699. C₄×SD₁₆	C₂²×C₅₃	semidirect
700. C₄×SD₁₆	C₂²×C₅₃	semidirect
701. C₄×SD₁₆	C₂²×C₅₃	semidirect
705. C₄×D₈	C₂²×C₅₃	semidirect
706. C₄×D₈	C₂²×C₅₃	semidirect
708. #435	C₂²×C₅₃	semidirect
710. C₈×D₄	C₂²×C₅₃	semidirect
711. #433	C₂²×C₅₃	semidirect
712. #432	C₂²×C₅₃	semidirect
713. #428	C₂²×C₅₃	semidirect
714. #427	C₂²×C₅₃	semidirect
716. #416	C₂²×C₅₃	semidirect
717. #416	C₂²×C₅₃	semidirect
719. #405	C₂²×C₅₃	semidirect
720. C₂×C₄×C₈	C₂²×C₅₃	semidirect
721. C₅₃	#61494	direct (N × H)
964. SD₁₆	#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×#3517	2
C₅₃×#3514	2
C₅₃×#3399	2
C₅₃×#3386	2
C₅₃×#3365	2
C₅₃×#3358	2
C₅₃×#3353	2
C₅₃×#3347	2
C₅₃×#3305	2
C₅₃×#3304	2
C₅₃×#3297	2
C₅₃×#3294	2
C₅₃×#3274	2
C₅₃×#3268	2
C₅₃×#3179	2
C₅₃×#3169	2
C₅₃×#3124	2
C₅₃×#3122	2
C₅₃×#3115	2
C₅₃×#2966	2
C₅₃×#2946	2
C₄×#135×C₅₃	2
#61494	53

Subgroups — C53×#61494 #27269006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61494 #27269006