Subgroups — C₅₃×#62117 #27269629

Order 13568.

1762 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3388	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3370	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3355	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3350	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3347	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3326	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3321	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3309	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#559	—	2	1	no	—
25	C₅₃×#559	C₂²	1	1	yes	characteristic
26	C₅₃×#557	C₂²	1	1	yes	characteristic
27	C₅₃×#556	—	2	1	no	—
28	C₅₃×#556	—	2	1	no	—
29	C₅₃×#556	C₂²	1	1	yes	characteristic
30	C₅₃×#555	C₂²	1	2	yes	—
31	C₅₃×#554	C₂²	1	2	yes	—
32	C₅₃×#553	—	2	1	no	—
33	C₅₃×#553	—	2	1	no	—
34	C₅₃×#553	C₂²	1	1	yes	characteristic
35	C₅₃×#553	C₂²	1	1	yes	characteristic
36	C₅₃×#553	C₂²	1	2	yes	—
37	C₅₃×#553	C₂²	1	2	yes	—
38	C₅₃×#550	C₂²	1	1	yes	characteristic
39	C₅₃×#548	—	2	1	no	—
40	C₅₃×#548	—	2	1	no	—
41	C₅₃×#548	C₂²	1	1	yes	characteristic
42	C₅₃×#548	C₂²	1	1	yes	characteristic
43	C₅₃×#547	—	2	1	no	—
44	C₅₃×#542	—	2	1	no	—
45	C₅₃×#542	—	2	1	no	—
46	C₅₃×#537	—	2	1	no	—
47	C₅₃×#533	C₂²	1	1	yes	characteristic
48	C₅₃×#533	C₂²	1	1	yes	characteristic
49	C₅₃×#532	—	2	1	no	—
50	C₅₃×#532	C₂²	1	1	yes	characteristic
51	C₅₃×#532	C₂²	1	1	yes	characteristic
52	C₅₃×#532	C₂²	1	1	yes	characteristic
53	C₅₃×#532	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
55	C₅₃×#529	—	2	1	no	—
56	C₅₃×#529	—	2	1	no	—
57	C₅₃×#529	C₂²	1	1	yes	characteristic
58	C₅₃×#529	C₂²	1	1	yes	characteristic
59	C₅₃×#520	—	2	1	no	—
60	C₄×#41×C₅₃	—	2	1	no	—
61	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
62	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
63	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
65	C₅₃×#501	C₂²	1	2	yes	—
66	C₅₃×#501	C₂²	1	2	yes	—
67	C₅₃×#499	C₂²	1	2	yes	—
68	C₅₃×#490	C₂²	1	2	yes	—
69	C₅₃×#489	C₂²	1	2	yes	—
70	C₅₃×#488	C₂²	1	2	yes	—
71	C₅₃×#485	C₂²	1	2	yes	—
72	C₅₃×#483	C₂²	1	2	yes	—
73	C₅₃×#482	C₂²	1	2	yes	—
74	C₅₃×#482	C₂²	1	2	yes	—
75	C₅₃×#482	C₂²	1	2	yes	—
76	C₅₃×#482	C₂²	1	2	yes	—
77	C₅₃×#482	C₂²	1	2	yes	—
78	C₅₃×#480	C₂²	1	2	yes	—
79	C₅₃×#480	C₂²	1	2	yes	—
80	C₅₃×#479	C₂²	1	2	yes	—
81	C₅₃×#479	C₂²	1	2	yes	—
82	C₅₃×#479	C₂²	1	2	yes	—
83	C₅₃×#478	C₂²	1	2	yes	—
84	C₅₃×#478	C₂²	1	2	yes	—
85	C₅₃×#478	C₂²	1	2	yes	—
86	C₅₃×#477	C₂²	1	1	yes	characteristic
87	C₅₃×#477	C₂²	1	1	yes	characteristic
88	C₅₃×#477	C₂²	1	1	yes	characteristic
89	C₅₃×#477	C₂²	1	1	yes	characteristic
90	C₅₃×#476	C₂²	1	1	yes	characteristic
91	C₅₃×#476	C₂²	1	1	yes	characteristic
92	C₅₃×#476	C₂²	1	1	yes	characteristic
93	C₅₃×#476	C₂²	1	1	yes	characteristic
94	C₅₃×#476	C₂²	1	2	yes	—
95	C₅₃×#475	C₂²	1	1	yes	characteristic
96	C₅₃×#475	C₂²	1	2	yes	—
97	C₅₃×#475	C₂²	1	1	yes	characteristic
98	C₅₃×#474	C₂²	1	1	yes	characteristic
99	C₅₃×#474	C₂²	1	1	yes	characteristic
100	C₅₃×#474	C₂²	1	2	yes	—
101	C₅₃×#469	C₂²	1	2	yes	—
102	C₅₃×#469	C₂²	1	2	yes	—
103	C₅₃×#469	C₂²	1	2	yes	—
104	C₅₃×#468	C₂²	1	2	yes	—
105	C₅₃×#466	C₂²	1	2	yes	—
106	C₅₃×#465	C₂²	1	2	yes	—
107	C₅₃×#463	C₂²	1	2	yes	—
108	C₅₃×#463	C₂²	1	2	yes	—
109	C₅₃×#460	C₂²	1	1	yes	characteristic
110	C₅₃×#460	C₂²	1	1	yes	characteristic
111	C₅₃×#459	C₂²	1	1	yes	characteristic
112	C₅₃×#459	C₂²	1	1	yes	characteristic
113	C₅₃×#459	C₂²	1	2	yes	—
114	C₅₃×#449	C₂²	1	2	yes	—
115	C₅₃×#449	C₂²	1	2	yes	—
116	C₅₃×#448	C₂²	1	2	yes	—
117	C₅₃×#446	C₂²	1	2	yes	—
118	C₅₃×#442	C₂²	1	2	yes	—
119	C₅₃×#440	C₂²	1	2	yes	—
120	C₅₃×#440	C₂²	1	2	yes	—
121	C₅₃×#440	C₂²	1	2	yes	—
122	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
123	C₄×D₈×C₅₃	C₂²	1	2	yes	—
124	C₅₃×#436	C₂²	1	2	yes	—
125	C₅₃×#435	C₂²	1	2	yes	—
126	C₅₃×#435	C₂²	1	2	yes	—
127	C₅₃×#432	C₂²	1	1	yes	characteristic
128	C₅₃×#432	C₂²	1	1	yes	characteristic
129	C₅₃×#431	C₂²	1	1	yes	characteristic
130	C₅₃×#428	C₂²	1	2	yes	—
131	C₅₃×#428	C₂²	1	2	yes	—
132	C₅₃×#427	C₂²	1	2	yes	—
133	C₅₃×#423	C₂²	1	1	yes	characteristic
134	C₅₃×#423	C₂²	1	1	yes	characteristic
135	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
136	C₅₃×#419	C₂²	1	2	yes	—
137	C₅₃×#417	C₂²	1	2	yes	—
138	C₅₃×#416	C₂²	1	2	yes	—
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	1	no	—
141	C₂×#41×C₅₃	—	2	1	no	—
142	C₂×#41×C₅₃	—	2	1	no	—
143	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
144	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
146	C₂²×Q₈×C₅₃	—	2	1	no	—
147	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
150	C₂×D₈×C₅₃	C₂³	1	2	yes	—
151	C₂×D₈×C₅₃	C₂³	1	2	yes	—
152	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₅₃	—	2	1	no	—
156	C₄⋊Q₈×C₅₃	—	2	1	no	—
157	C₄⋊Q₈×C₅₃	—	2	1	no	—
158	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
163	#127×C₅₃	—	2	1	no	—
164	#127×C₅₃	C₂³	1	1	yes	characteristic
165	#127×C₅₃	C₂³	1	1	yes	characteristic
166	#126×C₅₃	—	2	1	no	—
167	#126×C₅₃	—	2	1	no	—
168	#126×C₅₃	—	2	2	no	—
169	#126×C₅₃	—	2	2	no	—
170	#126×C₅₃	—	2	1	no	—
171	#126×C₅₃	—	2	1	no	—
172	#126×C₅₃	—	2	1	no	—
173	#126×C₅₃	—	2	1	no	—
174	#125×C₅₃	—	2	1	no	—
175	#125×C₅₃	—	2	1	no	—
176	#125×C₅₃	C₂³	1	2	yes	—
177	#125×C₅₃	C₂³	1	2	yes	—
178	#125×C₅₃	C₂³	1	1	yes	characteristic
179	#125×C₅₃	C₂³	1	1	yes	characteristic
180	#124×C₅₃	—	2	1	no	—
181	#124×C₅₃	—	2	1	no	—
182	#124×C₅₃	—	2	2	no	—
183	#124×C₅₃	—	2	2	no	—
184	#124×C₅₃	—	2	1	no	—
185	#124×C₅₃	—	2	1	no	—
186	#124×C₅₃	—	2	1	no	—
187	#124×C₅₃	—	2	1	no	—
188	#124×C₅₃	—	2	1	no	—
189	#124×C₅₃	—	2	1	no	—
190	#124×C₅₃	C₂³	1	1	yes	characteristic
191	#124×C₅₃	C₂³	1	1	yes	characteristic
192	#123×C₅₃	—	2	1	no	—
193	#123×C₅₃	—	2	1	no	—
194	#123×C₅₃	—	2	1	no	—
195	#123×C₅₃	—	2	1	no	—
196	#123×C₅₃	—	2	2	no	—
197	#123×C₅₃	—	2	2	no	—
198	#123×C₅₃	—	2	1	no	—
199	#123×C₅₃	—	2	1	no	—
200	C₂²⋊Q₈×C₅₃	—	2	1	no	—
201	C₂²⋊Q₈×C₅₃	—	2	1	no	—
202	C₂²⋊Q₈×C₅₃	—	2	2	no	—
203	C₂²⋊Q₈×C₅₃	—	2	2	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	1	no	—
206	C₂²⋊Q₈×C₅₃	—	2	1	no	—
207	C₂²⋊Q₈×C₅₃	—	2	1	no	—
208	C₂²⋊Q₈×C₅₃	—	2	1	no	—
209	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
210	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	—	2	1	no	—
213	#121×C₅₃	—	2	1	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	—	2	1	no	—
216	#121×C₅₃	—	2	1	no	—
217	#121×C₅₃	—	2	2	no	—
218	#121×C₅₃	—	2	2	no	—
219	#121×C₅₃	—	2	2	no	—
220	#121×C₅₃	—	2	1	no	—
221	#121×C₅₃	—	2	1	no	—
222	#121×C₅₃	—	2	1	no	—
223	#121×C₅₃	—	2	1	no	—
224	#121×C₅₃	C₂³	1	1	yes	characteristic
225	#121×C₅₃	C₂³	1	1	yes	characteristic
226	#121×C₅₃	C₂³	1	1	yes	characteristic
227	#121×C₅₃	C₂³	1	1	yes	characteristic
228	#121×C₅₃	C₂³	1	2	yes	—
229	#121×C₅₃	C₂³	1	2	yes	—
230	#121×C₅₃	C₂³	1	2	yes	—
231	C₄×Q₈×C₅₃	—	2	1	no	—
232	C₄×Q₈×C₅₃	—	2	1	no	—
233	C₄×Q₈×C₅₃	—	2	1	no	—
234	C₄×Q₈×C₅₃	—	2	1	no	—
235	C₄×Q₈×C₅₃	—	2	1	no	—
236	C₄×Q₈×C₅₃	—	2	1	no	—
237	C₄×Q₈×C₅₃	—	2	1	no	—
238	C₄×Q₈×C₅₃	—	2	1	no	—
239	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
240	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₅₃	—	2	1	no	—
248	C₄×D₄×C₅₃	—	2	1	no	—
249	C₄×D₄×C₅₃	—	2	1	no	—
250	C₄×D₄×C₅₃	—	2	1	no	—
251	C₄×D₄×C₅₃	—	2	1	no	—
252	C₄×D₄×C₅₃	—	2	1	no	—
253	C₄×D₄×C₅₃	—	2	2	no	—
254	C₄×D₄×C₅₃	—	2	2	no	—
255	C₄×D₄×C₅₃	—	2	1	no	—
256	C₄×D₄×C₅₃	—	2	1	no	—
257	C₄×D₄×C₅₃	—	2	1	no	—
258	C₄×D₄×C₅₃	—	2	1	no	—
259	C₄×D₄×C₅₃	—	2	1	no	—
260	C₄×D₄×C₅₃	—	2	1	no	—
261	C₄×D₄×C₅₃	—	2	1	no	—
262	C₄×D₄×C₅₃	—	2	1	no	—
263	C₄×D₄×C₅₃	—	2	1	no	—
264	C₄×D₄×C₅₃	—	2	1	no	—
265	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
266	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
267	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
268	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₄×D₄×C₅₃	C₂³	1	2	yes	—
273	C₄×D₄×C₅₃	C₂³	1	2	yes	—
274	C₄×D₄×C₅₃	C₂³	1	2	yes	—
275	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
278	#117×C₅₃	—	2	2	no	—
279	#117×C₅₃	—	2	1	no	—
280	#117×C₅₃	—	2	1	no	—
281	#117×C₅₃	—	2	1	no	—
282	#117×C₅₃	—	2	1	no	—
283	#117×C₅₃	D₄	1	1	yes	characteristic
284	#117×C₅₃	D₄	1	1	yes	characteristic
285	#117×C₅₃	D₄	1	1	yes	characteristic
286	#117×C₅₃	C₂³	1	2	yes	—
287	#117×C₅₃	C₂³	1	1	yes	characteristic
288	#117×C₅₃	C₂³	1	1	yes	characteristic
289	#117×C₅₃	C₂³	1	2	yes	—
290	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
291	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
292	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
293	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
295	C₂×C₄²×C₅₃	—	2	1	no	—
296	C₂×C₄²×C₅₃	—	2	1	no	—
297	C₂×C₄²×C₅₃	—	2	1	no	—
298	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
301	#107×C₅₃	C₂³	1	2	yes	—
302	#107×C₅₃	C₂³	1	2	yes	—
303	#107×C₅₃	C₂³	1	2	yes	—
304	#107×C₅₃	C₂³	1	2	yes	—
305	#107×C₅₃	C₂³	1	2	yes	—
306	#107×C₅₃	C₂³	1	2	yes	—
307	#106×C₅₃	C₂³	1	2	yes	—
308	#106×C₅₃	C₂³	1	2	yes	—
309	#106×C₅₃	C₂³	1	2	yes	—
310	#106×C₅₃	C₂³	1	2	yes	—
311	#106×C₅₃	C₂³	1	2	yes	—
312	#106×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	2	yes	—
316	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
318	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
319	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
320	#103×C₅₃	C₂³	1	2	yes	—
321	#103×C₅₃	C₂³	1	2	yes	—
322	#103×C₅₃	C₂³	1	2	yes	—
323	#103×C₅₃	C₂³	1	2	yes	—
324	#103×C₅₃	C₂³	1	2	yes	—
325	#103×C₅₃	C₂³	1	2	yes	—
326	#102×C₅₃	C₂³	1	2	yes	—
327	#102×C₅₃	C₂³	1	2	yes	—
328	#102×C₅₃	C₂³	1	2	yes	—
329	#102×C₅₃	C₂³	1	2	yes	—
330	#102×C₅₃	C₂³	1	2	yes	—
331	#102×C₅₃	C₂³	1	2	yes	—
332	#102×C₅₃	C₂³	1	2	yes	—
333	#102×C₅₃	C₂³	1	2	yes	—
334	#102×C₅₃	C₂³	1	2	yes	—
335	#102×C₅₃	C₂³	1	2	yes	—
336	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
337	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
338	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
339	#97×C₅₃	C₂³	1	2	yes	—
340	#97×C₅₃	C₂³	1	2	yes	—
341	C₄×C₈×C₅₃	C₂³	1	2	yes	—
342	#41×C₅₃	—	2	2	no	—
343	#41×C₅₃	—	2	2	no	—
344	#41×C₅₃	—	4	2	no	—
345	#41×C₅₃	—	4	1	no	—
346	#41×C₅₃	—	4	1	no	—
347	#41×C₅₃	—	4	4	no	—
348	#41×C₅₃	—	4	4	no	—
349	#41×C₅₃	—	8	2	no	—
350	#41×C₅₃	—	8	2	no	—
351	C₂×Q₈×C₅₃	—	2	1	no	—
352	C₂×Q₈×C₅₃	—	2	1	no	—
353	C₂×Q₈×C₅₃	—	2	1	no	—
354	C₂×Q₈×C₅₃	—	2	1	no	—
355	C₂×Q₈×C₅₃	—	2	1	no	—
356	C₂×Q₈×C₅₃	—	2	2	no	—
357	C₂×Q₈×C₅₃	—	2	2	no	—
358	C₂×Q₈×C₅₃	—	4	1	no	—
359	C₂×Q₈×C₅₃	—	8	2	no	—
360	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
361	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₅₃	—	2	1	no	—
364	C₂×D₄×C₅₃	—	2	1	no	—
365	C₂×D₄×C₅₃	—	2	2	no	—
366	C₂×D₄×C₅₃	—	2	1	no	—
367	C₂×D₄×C₅₃	—	2	1	no	—
368	C₂×D₄×C₅₃	—	2	1	no	—
369	C₂×D₄×C₅₃	—	2	1	no	—
370	C₂×D₄×C₅₃	—	2	2	no	—
371	C₂×D₄×C₅₃	—	2	2	no	—
372	C₂×D₄×C₅₃	—	2	1	no	—
373	C₂×D₄×C₅₃	—	2	1	no	—
374	C₂×D₄×C₅₃	—	2	1	no	—
375	C₂×D₄×C₅₃	—	2	1	no	—
376	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
377	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
378	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
379	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
382	C₂²×C₄×C₅₃	—	2	1	no	—
383	C₂²×C₄×C₅₃	—	2	1	no	—
384	C₂²×C₄×C₅₃	—	2	2	no	—
385	C₂²×C₄×C₅₃	—	2	1	no	—
386	C₂²×C₄×C₅₃	—	2	1	no	—
387	C₂²×C₄×C₅₃	—	2	1	no	—
388	C₂²×C₄×C₅₃	—	2	1	no	—
389	C₂²×C₄×C₅₃	—	2	2	no	—
390	C₂²×C₄×C₅₃	—	2	1	no	—
391	C₂²×C₄×C₅₃	—	2	1	no	—
392	C₂²×C₄×C₅₃	—	2	2	no	—
393	C₂²×C₄×C₅₃	—	2	2	no	—
394	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	SD₁₆×C₅₃	—	2	4	no	—
404	SD₁₆×C₅₃	—	4	2	no	—
405	D₈×C₅₃	—	4	2	no	—
406	D₈×C₅₃	—	4	2	no	—
407	M₁₆×C₅₃	—	4	2	no	—
408	M₁₆×C₅₃	—	4	2	no	—
409	C₂×C₈×C₅₃	—	4	2	no	—
410	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
411	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
412	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
413	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₅₃	—	2	2	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	2	no	—
419	C₄⋊C₄×C₅₃	—	2	2	no	—
420	C₄⋊C₄×C₅₃	—	2	1	no	—
421	C₄⋊C₄×C₅₃	—	2	1	no	—
422	C₄⋊C₄×C₅₃	—	2	1	no	—
423	C₄⋊C₄×C₅₃	—	2	1	no	—
424	C₄⋊C₄×C₅₃	—	2	2	no	—
425	C₄⋊C₄×C₅₃	—	2	1	no	—
426	C₄⋊C₄×C₅₃	—	2	1	no	—
427	C₄⋊C₄×C₅₃	—	2	1	no	—
428	C₄⋊C₄×C₅₃	—	2	1	no	—
429	C₄⋊C₄×C₅₃	—	2	1	no	—
430	C₄⋊C₄×C₅₃	—	2	1	no	—
431	C₄⋊C₄×C₅₃	—	2	1	no	—
432	C₄⋊C₄×C₅₃	—	2	1	no	—
433	C₄⋊C₄×C₅₃	—	2	1	no	—
434	C₄⋊C₄×C₅₃	—	2	1	no	—
435	C₄⋊C₄×C₅₃	—	2	2	no	—
436	C₄⋊C₄×C₅₃	—	2	2	no	—
437	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
444	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
445	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
446	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
450	C₂²⋊C₄×C₅₃	—	2	1	no	—
451	C₂²⋊C₄×C₅₃	—	2	1	no	—
452	C₂²⋊C₄×C₅₃	—	2	2	no	—
453	C₂²⋊C₄×C₅₃	—	2	2	no	—
454	C₂²⋊C₄×C₅₃	—	2	1	no	—
455	C₂²⋊C₄×C₅₃	—	2	1	no	—
456	C₂²⋊C₄×C₅₃	—	2	1	no	—
457	C₂²⋊C₄×C₅₃	—	2	1	no	—
458	C₂²⋊C₄×C₅₃	—	2	2	no	—
459	C₂²⋊C₄×C₅₃	—	2	2	no	—
460	C₂²⋊C₄×C₅₃	—	2	1	no	—
461	C₂²⋊C₄×C₅₃	—	2	1	no	—
462	C₂²⋊C₄×C₅₃	—	2	1	no	—
463	C₂²⋊C₄×C₅₃	—	2	1	no	—
464	C₂²⋊C₄×C₅₃	—	2	1	no	—
465	C₂²⋊C₄×C₅₃	—	2	1	no	—
466	C₂²⋊C₄×C₅₃	—	2	1	no	—
467	C₂²⋊C₄×C₅₃	—	2	1	no	—
468	C₂²⋊C₄×C₅₃	—	2	1	no	—
469	C₂²⋊C₄×C₅₃	—	2	1	no	—
470	C₂²⋊C₄×C₅₃	—	2	2	no	—
471	C₂²⋊C₄×C₅₃	—	2	2	no	—
472	C₂²⋊C₄×C₅₃	—	2	2	no	—
473	C₂²⋊C₄×C₅₃	—	2	2	no	—
474	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
475	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
476	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
480	C₄²×C₅₃	—	2	1	no	—
481	C₄²×C₅₃	—	2	1	no	—
482	C₄²×C₅₃	—	2	1	no	—
483	C₄²×C₅₃	—	2	1	no	—
484	C₄²×C₅₃	—	2	1	no	—
485	C₄²×C₅₃	—	2	1	no	—
486	C₄²×C₅₃	—	2	1	no	—
487	C₄²×C₅₃	—	2	1	no	—
488	C₄²×C₅₃	—	2	2	no	—
489	C₄²×C₅₃	—	2	2	no	—
490	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
497	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
498	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
499	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
500	C₂³×C₅₃	—	2	2	no	—
501	C₂³×C₅₃	—	2	1	no	—
502	C₂³×C₅₃	—	2	1	no	—
503	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
504	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
505	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
506	Q₈×C₅₃	—	2	1	no	—
507	Q₈×C₅₃	—	2	1	no	—
508	Q₈×C₅₃	—	2	1	no	—
509	Q₈×C₅₃	—	4	1	no	—
510	Q₈×C₅₃	—	4	2	no	—
511	Q₈×C₅₃	—	4	2	no	—
512	Q₈×C₅₃	—	4	2	no	—
513	Q₈×C₅₃	—	4	2	no	—
514	Q₈×C₅₃	—	4	2	no	—
515	Q₈×C₅₃	—	8	2	no	—
516	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
517	D₄×C₅₃	—	2	1	no	—
518	D₄×C₅₃	—	2	1	no	—
519	D₄×C₅₃	—	2	2	no	—
520	D₄×C₅₃	—	2	1	no	—
521	D₄×C₅₃	—	2	1	no	—
522	D₄×C₅₃	—	2	2	no	—
523	D₄×C₅₃	—	4	1	no	—
524	D₄×C₅₃	—	4	1	no	—
525	D₄×C₅₃	—	4	1	no	—
526	D₄×C₅₃	—	4	2	no	—
527	D₄×C₅₃	—	4	2	no	—
528	D₄×C₅₃	—	4	2	no	—
529	D₄×C₅₃	—	4	2	no	—
530	D₄×C₅₃	—	4	4	no	—
531	D₄×C₅₃	—	4	2	no	—
532	D₄×C₅₃	—	4	2	no	—
533	D₄×C₅₃	—	4	2	no	—
534	D₄×C₅₃	—	8	1	no	—
535	D₄×C₅₃	—	8	1	no	—
536	D₄×C₅₃	—	8	1	no	—
537	D₄×C₅₃	—	8	2	no	—
538	D₄×C₅₃	—	8	2	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	2	no	—
541	C₂×C₄×C₅₃	—	2	2	no	—
542	C₂×C₄×C₅₃	—	2	2	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	1	no	—
546	C₂×C₄×C₅₃	—	2	1	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	2	1	no	—
549	C₂×C₄×C₅₃	—	2	1	no	—
550	C₂×C₄×C₅₃	—	2	2	no	—
551	C₂×C₄×C₅₃	—	2	2	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	1	no	—
554	C₂×C₄×C₅₃	—	2	1	no	—
555	C₂×C₄×C₅₃	—	2	2	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	4	1	no	—
558	C₂×C₄×C₅₃	—	4	1	no	—
559	C₂×C₄×C₅₃	—	4	1	no	—
560	C₂×C₄×C₅₃	—	4	2	no	—
561	C₂×C₄×C₅₃	—	4	2	no	—
562	C₂×C₄×C₅₃	—	4	2	no	—
563	C₂×C₄×C₅₃	—	4	4	no	—
564	C₂×C₄×C₅₃	—	4	2	no	—
565	C₂×C₄×C₅₃	—	4	2	no	—
566	C₂×C₄×C₅₃	—	8	1	no	—
567	C₂×C₄×C₅₃	—	8	1	no	—
568	C₂×C₄×C₅₃	—	8	2	no	—
569	C₂×C₄×C₅₃	—	8	2	no	—
570	C₂×C₄×C₅₃	—	8	1	no	—
571	C₂×C₄×C₅₃	—	8	2	no	—
572	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
584	C₈×C₅₃	—	2	2	no	—
585	C₈×C₅₃	—	2	2	no	—
586	C₈×C₅₃	—	2	2	no	—
587	C₈×C₅₃	—	2	2	no	—
588	#62117	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
589	C₂²×C₅₃	—	2	1	no	—
590	C₂²×C₅₃	—	2	1	no	—
591	C₂²×C₅₃	—	2	1	no	—
592	C₂²×C₅₃	—	2	1	no	—
593	C₂²×C₅₃	—	2	1	no	—
594	C₂²×C₅₃	—	2	1	no	—
595	C₂²×C₅₃	—	2	1	no	—
596	C₂²×C₅₃	—	2	1	no	—
597	C₂²×C₅₃	—	2	1	no	—
598	C₂²×C₅₃	—	4	2	no	—
599	C₂²×C₅₃	—	4	1	no	—
600	C₂²×C₅₃	—	4	1	no	—
601	C₂²×C₅₃	—	4	1	no	—
602	C₂²×C₅₃	—	4	1	no	—
603	C₂²×C₅₃	—	4	2	no	—
604	C₂²×C₅₃	—	4	2	no	—
605	C₂²×C₅₃	—	4	1	no	—
606	C₂²×C₅₃	—	4	1	no	—
607	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
608	C₄×C₅₃	—	2	1	no	—
609	C₄×C₅₃	—	2	1	no	—
610	C₄×C₅₃	—	2	1	no	—
611	C₄×C₅₃	—	2	1	no	—
612	C₄×C₅₃	—	2	1	no	—
613	C₄×C₅₃	—	2	1	no	—
614	C₄×C₅₃	—	2	1	no	—
615	C₄×C₅₃	—	2	2	no	—
616	C₄×C₅₃	—	2	1	no	—
617	C₄×C₅₃	—	2	1	no	—
618	C₄×C₅₃	—	2	1	no	—
619	C₄×C₅₃	—	4	1	no	—
620	C₄×C₅₃	—	4	2	no	—
621	C₄×C₅₃	—	4	2	no	—
622	C₄×C₅₃	—	4	1	no	—
623	C₄×C₅₃	—	4	1	no	—
624	C₄×C₅₃	—	4	2	no	—
625	C₄×C₅₃	—	4	1	no	—
626	C₄×C₅₃	—	4	1	no	—
627	C₄×C₅₃	#575	1	2	yes	—
628	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
629	C₄×C₅₃	#585	1	1	yes	characteristic
630	#3511	C₂×C₅₃	1	1	yes	characteristic, complemented
631	#3480	C₂×C₅₃	1	1	yes	characteristic, complemented
632	#3388	C₂×C₅₃	1	2	yes	complemented
633	#3370	C₂×C₅₃	1	2	yes	complemented
634	#3355	C₂×C₅₃	1	2	yes	complemented
635	#3350	C₂×C₅₃	1	2	yes	complemented
636	#3347	C₂×C₅₃	1	2	yes	complemented
637	#3326	C₂×C₅₃	1	2	yes	complemented
638	#3321	C₂×C₅₃	1	2	yes	complemented
639	#3309	C₂×C₅₃	1	2	yes	complemented
640	#3253	C₂×C₅₃	1	1	yes	characteristic, complemented
641	#3251	C₂×C₅₃	1	1	yes	characteristic, complemented
642	#3247	C₂×C₅₃	1	1	yes	characteristic, complemented
643	#3238	C₂×C₅₃	1	1	yes	characteristic, complemented
644	#3235	C₂×C₅₃	1	1	yes	characteristic, complemented
645	#3233	C₂×C₅₃	1	1	yes	characteristic, complemented
646	#3115	C₂×C₅₃	1	1	yes	characteristic, complemented
647	#3112	C₂×C₅₃	1	1	yes	characteristic, complemented
648	#3106	C₂×C₅₃	1	1	yes	characteristic, complemented
649	#3079	C₂×C₅₃	1	1	yes	characteristic, complemented
650	#3078	C₂×C₅₃	1	1	yes	characteristic, complemented
651	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
652	#2989	C₂×C₅₃	1	1	yes	characteristic, complemented
653	C₂×C₅₃	—	4	1	no	—
654	C₂×C₅₃	—	4	1	no	—
655	C₂×C₅₃	—	4	1	no	—
656	C₂×C₅₃	—	8	2	no	—
657	C₂×C₅₃	—	8	1	no	—
658	C₂×C₅₃	—	8	1	no	—
659	C₂×C₅₃	#3489	1	1	yes	characteristic
660	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
661	C₂×C₅₃	#3585	1	1	yes	characteristic
662	#559	—	2	1	no	—
663	#559	C₂²×C₅₃	1	1	yes	characteristic
664	#557	C₂²×C₅₃	1	1	yes	characteristic
665	#556	—	2	1	no	—
666	#556	—	2	1	no	—
667	#556	C₂²×C₅₃	1	1	yes	characteristic
668	#555	C₂²×C₅₃	1	2	yes	—
669	#554	C₂²×C₅₃	1	2	yes	—
670	#553	—	2	1	no	—
671	#553	—	2	1	no	—
672	#553	C₂²×C₅₃	1	1	yes	characteristic
673	#553	C₂²×C₅₃	1	2	yes	—
674	#553	C₂²×C₅₃	1	1	yes	characteristic
675	#553	C₂²×C₅₃	1	2	yes	—
676	#550	C₂²×C₅₃	1	1	yes	characteristic
677	#548	—	2	1	no	—
678	#548	—	2	1	no	—
679	#548	C₂²×C₅₃	1	1	yes	characteristic
680	#548	C₂²×C₅₃	1	1	yes	characteristic
681	#547	—	2	1	no	—
682	#542	—	2	1	no	—
683	#542	—	2	1	no	—
684	#537	—	2	1	no	—
685	#533	C₂²×C₅₃	1	1	yes	characteristic
686	#533	C₂²×C₅₃	1	1	yes	characteristic
687	#532	—	2	1	no	—
688	#532	C₂²×C₅₃	1	1	yes	characteristic
689	#532	C₂²×C₅₃	1	1	yes	characteristic
690	#532	C₂²×C₅₃	1	1	yes	characteristic
691	#532	C₂²×C₅₃	1	1	yes	characteristic
692	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
693	#529	—	2	1	no	—
694	#529	—	2	1	no	—
695	#529	C₂²×C₅₃	1	1	yes	characteristic
696	#529	C₂²×C₅₃	1	1	yes	characteristic
697	#520	—	2	1	no	—
698	C₄×#41	—	2	1	no	—
699	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
700	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
701	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
702	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
703	#501	C₂²×C₅₃	1	2	yes	—
704	#501	C₂²×C₅₃	1	2	yes	—
705	#499	C₂²×C₅₃	1	2	yes	—
706	#490	C₂²×C₅₃	1	2	yes	—
707	#489	C₂²×C₅₃	1	2	yes	—
708	#488	C₂²×C₅₃	1	2	yes	—
709	#485	C₂²×C₅₃	1	2	yes	—
710	#483	C₂²×C₅₃	1	2	yes	—
711	#482	C₂²×C₅₃	1	2	yes	—
712	#482	C₂²×C₅₃	1	2	yes	—
713	#482	C₂²×C₅₃	1	2	yes	—
714	#482	C₂²×C₅₃	1	2	yes	—
715	#482	C₂²×C₅₃	1	2	yes	—
716	#480	C₂²×C₅₃	1	2	yes	—
717	#480	C₂²×C₅₃	1	2	yes	—
718	#479	C₂²×C₅₃	1	2	yes	—
719	#479	C₂²×C₅₃	1	2	yes	—
720	#479	C₂²×C₅₃	1	2	yes	—
721	#478	C₂²×C₅₃	1	2	yes	—
722	#478	C₂²×C₅₃	1	2	yes	—
723	#478	C₂²×C₅₃	1	2	yes	—
724	#477	C₂²×C₅₃	1	1	yes	characteristic
725	#477	C₂²×C₅₃	1	1	yes	characteristic
726	#477	C₂²×C₅₃	1	1	yes	characteristic
727	#477	C₂²×C₅₃	1	1	yes	characteristic
728	#476	C₂²×C₅₃	1	1	yes	characteristic
729	#476	C₂²×C₅₃	1	1	yes	characteristic
730	#476	C₂²×C₅₃	1	1	yes	characteristic
731	#476	C₂²×C₅₃	1	2	yes	—
732	#476	C₂²×C₅₃	1	1	yes	characteristic
733	#475	C₂²×C₅₃	1	1	yes	characteristic
734	#475	C₂²×C₅₃	1	1	yes	characteristic
735	#475	C₂²×C₅₃	1	2	yes	—
736	#474	C₂²×C₅₃	1	1	yes	characteristic
737	#474	C₂²×C₅₃	1	2	yes	—
738	#474	C₂²×C₅₃	1	1	yes	characteristic
739	#469	C₂²×C₅₃	1	2	yes	—
740	#469	C₂²×C₅₃	1	2	yes	—
741	#469	C₂²×C₅₃	1	2	yes	—
742	#468	C₂²×C₅₃	1	2	yes	—
743	#466	C₂²×C₅₃	1	2	yes	—
744	#465	C₂²×C₅₃	1	2	yes	—
745	#463	C₂²×C₅₃	1	2	yes	—
746	#463	C₂²×C₅₃	1	2	yes	—
747	#460	C₂²×C₅₃	1	1	yes	characteristic
748	#460	C₂²×C₅₃	1	1	yes	characteristic
749	#459	C₂²×C₅₃	1	1	yes	characteristic
750	#459	C₂²×C₅₃	1	2	yes	—
751	#459	C₂²×C₅₃	1	1	yes	characteristic
752	#449	C₂²×C₅₃	1	2	yes	—
753	#449	C₂²×C₅₃	1	2	yes	—
754	#448	C₂²×C₅₃	1	2	yes	—
755	#446	C₂²×C₅₃	1	2	yes	—
756	#442	C₂²×C₅₃	1	2	yes	—
757	#440	C₂²×C₅₃	1	2	yes	—
758	#440	C₂²×C₅₃	1	2	yes	—
759	#440	C₂²×C₅₃	1	2	yes	—
760	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
761	C₄×D₈	C₂²×C₅₃	1	2	yes	—
762	#436	C₂²×C₅₃	1	2	yes	—
763	#435	C₂²×C₅₃	1	2	yes	—
764	#435	C₂²×C₅₃	1	2	yes	—
765	#432	C₂²×C₅₃	1	1	yes	characteristic
766	#432	C₂²×C₅₃	1	1	yes	characteristic
767	#431	C₂²×C₅₃	1	1	yes	characteristic
768	#428	C₂²×C₅₃	1	2	yes	—
769	#428	C₂²×C₅₃	1	2	yes	—
770	#427	C₂²×C₅₃	1	2	yes	—
771	#423	C₂²×C₅₃	1	1	yes	characteristic
772	#423	C₂²×C₅₃	1	1	yes	characteristic
773	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
774	#419	C₂²×C₅₃	1	2	yes	—
775	#417	C₂²×C₅₃	1	2	yes	—
776	#416	C₂²×C₅₃	1	2	yes	—
777	C₅₃	#62117	1	1	yes	characteristic, direct product factor, Sylow
778	C₂×#41	—	2	1	no	—
779	C₂×#41	—	2	1	no	—
780	C₂×#41	—	2	1	no	—
781	C₂×#41	—	2	1	no	—
782	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
783	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
784	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
785	C₂²×Q₈	—	2	1	no	—
786	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
787	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
788	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
789	C₂×D₈	C₂³×C₅₃	1	2	yes	—
790	C₂×D₈	C₂³×C₅₃	1	2	yes	—
791	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
792	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
793	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
794	C₄⋊Q₈	—	2	1	no	—
795	C₄⋊Q₈	—	2	1	no	—
796	C₄⋊Q₈	—	2	1	no	—
797	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
798	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
799	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
800	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
801	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
802	#127	—	2	1	no	—
803	#127	C₂³×C₅₃	1	1	yes	characteristic
804	#127	C₂³×C₅₃	1	1	yes	characteristic
805	#126	—	2	1	no	—
806	#126	—	2	1	no	—
807	#126	—	2	2	no	—
808	#126	—	2	2	no	—
809	#126	—	2	1	no	—
810	#126	—	2	1	no	—
811	#126	—	2	1	no	—
812	#126	—	2	1	no	—
813	#125	—	2	1	no	—
814	#125	—	2	1	no	—
815	#125	C₂³×C₅₃	1	1	yes	characteristic
816	#125	C₂³×C₅₃	1	1	yes	characteristic
817	#125	C₂³×C₅₃	1	2	yes	—
818	#125	C₂³×C₅₃	1	2	yes	—
819	#124	—	2	1	no	—
820	#124	—	2	1	no	—
821	#124	—	2	1	no	—
822	#124	—	2	1	no	—
823	#124	—	2	2	no	—
824	#124	—	2	2	no	—
825	#124	—	2	1	no	—
826	#124	—	2	1	no	—
827	#124	—	2	1	no	—
828	#124	—	2	1	no	—
829	#124	C₂³×C₅₃	1	1	yes	characteristic
830	#124	C₂³×C₅₃	1	1	yes	characteristic
831	#123	—	2	1	no	—
832	#123	—	2	1	no	—
833	#123	—	2	1	no	—
834	#123	—	2	1	no	—
835	#123	—	2	1	no	—
836	#123	—	2	1	no	—
837	#123	—	2	2	no	—
838	#123	—	2	2	no	—
839	C₂²⋊Q₈	—	2	2	no	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	—	2	2	no	—
847	C₂²⋊Q₈	—	2	2	no	—
848	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
849	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
850	#121	—	2	1	no	—
851	#121	—	2	1	no	—
852	#121	—	2	1	no	—
853	#121	—	2	1	no	—
854	#121	—	2	2	no	—
855	#121	—	2	2	no	—
856	#121	—	2	2	no	—
857	#121	—	2	1	no	—
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	1	no	—
862	#121	—	2	1	no	—
863	#121	C₂³×C₅₃	1	1	yes	characteristic
864	#121	C₂³×C₅₃	1	1	yes	characteristic
865	#121	C₂³×C₅₃	1	1	yes	characteristic
866	#121	C₂³×C₅₃	1	1	yes	characteristic
867	#121	C₂³×C₅₃	1	2	yes	—
868	#121	C₂³×C₅₃	1	2	yes	—
869	#121	C₂³×C₅₃	1	2	yes	—
870	C₄×Q₈	—	2	1	no	—
871	C₄×Q₈	—	2	1	no	—
872	C₄×Q₈	—	2	1	no	—
873	C₄×Q₈	—	2	1	no	—
874	C₄×Q₈	—	2	1	no	—
875	C₄×Q₈	—	2	1	no	—
876	C₄×Q₈	—	2	1	no	—
877	C₄×Q₈	—	2	1	no	—
878	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
879	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
880	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
881	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
882	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
883	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
884	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
885	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	1	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	2	no	—
899	C₄×D₄	—	2	2	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	1	no	—
903	C₄×D₄	—	2	1	no	—
904	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
905	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
906	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
907	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
908	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
909	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
910	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
911	C₄×D₄	C₂³×C₅₃	1	2	yes	—
912	C₄×D₄	C₂³×C₅₃	1	2	yes	—
913	C₄×D₄	C₂³×C₅₃	1	2	yes	—
914	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
915	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
916	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
917	#117	—	2	2	no	—
918	#117	—	2	1	no	—
919	#117	—	2	1	no	—
920	#117	—	2	1	no	—
921	#117	—	2	1	no	—
922	#117	D₄×C₅₃	1	1	yes	characteristic
923	#117	D₄×C₅₃	1	1	yes	characteristic
924	#117	D₄×C₅₃	1	1	yes	characteristic
925	#117	C₂³×C₅₃	1	1	yes	characteristic
926	#117	C₂³×C₅₃	1	1	yes	characteristic
927	#117	C₂³×C₅₃	1	2	yes	—
928	#117	C₂³×C₅₃	1	2	yes	—
929	C₂×C₄⋊C₄	—	2	1	no	—
930	C₂×C₄⋊C₄	—	2	1	no	—
931	C₂×C₄⋊C₄	—	2	2	no	—
932	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
934	C₂×C₄²	—	2	1	no	—
935	C₂×C₄²	—	2	1	no	—
936	C₂×C₄²	—	2	1	no	—
937	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
938	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
939	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
940	#107	C₂³×C₅₃	1	2	yes	—
941	#107	C₂³×C₅₃	1	2	yes	—
942	#107	C₂³×C₅₃	1	2	yes	—
943	#107	C₂³×C₅₃	1	2	yes	—
944	#107	C₂³×C₅₃	1	2	yes	—
945	#107	C₂³×C₅₃	1	2	yes	—
946	#106	C₂³×C₅₃	1	2	yes	—
947	#106	C₂³×C₅₃	1	2	yes	—
948	#106	C₂³×C₅₃	1	2	yes	—
949	#106	C₂³×C₅₃	1	2	yes	—
950	#106	C₂³×C₅₃	1	2	yes	—
951	#106	C₂³×C₅₃	1	2	yes	—
952	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
953	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
954	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
955	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
956	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
957	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
958	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
959	#103	C₂³×C₅₃	1	2	yes	—
960	#103	C₂³×C₅₃	1	2	yes	—
961	#103	C₂³×C₅₃	1	2	yes	—
962	#103	C₂³×C₅₃	1	2	yes	—
963	#103	C₂³×C₅₃	1	2	yes	—
964	#103	C₂³×C₅₃	1	2	yes	—
965	#102	C₂³×C₅₃	1	2	yes	—
966	#102	C₂³×C₅₃	1	2	yes	—
967	#102	C₂³×C₅₃	1	2	yes	—
968	#102	C₂³×C₅₃	1	2	yes	—
969	#102	C₂³×C₅₃	1	2	yes	—
970	#102	C₂³×C₅₃	1	2	yes	—
971	#102	C₂³×C₅₃	1	2	yes	—
972	#102	C₂³×C₅₃	1	2	yes	—
973	#102	C₂³×C₅₃	1	2	yes	—
974	#102	C₂³×C₅₃	1	2	yes	—
975	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
976	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
977	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
978	#97	C₂³×C₅₃	1	2	yes	—
979	#97	C₂³×C₅₃	1	2	yes	—
980	C₄×C₈	C₂³×C₅₃	1	2	yes	—
981	#41	—	2	2	no	—
982	#41	—	2	2	no	—
983	#41	—	4	2	no	—
984	#41	—	4	1	no	—
985	#41	—	4	1	no	—
986	#41	—	4	4	no	—
987	#41	—	4	4	no	—
988	#41	—	8	2	no	—
989	#41	—	8	2	no	—
990	C₂×Q₈	—	2	1	no	—
991	C₂×Q₈	—	2	1	no	—
992	C₂×Q₈	—	2	1	no	—
993	C₂×Q₈	—	2	1	no	—
994	C₂×Q₈	—	2	1	no	—
995	C₂×Q₈	—	2	2	no	—
996	C₂×Q₈	—	2	2	no	—
997	C₂×Q₈	—	4	1	no	—
998	C₂×Q₈	—	8	2	no	—
999	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1000	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1001	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	2	no	—
1005	C₂×D₄	—	2	1	no	—
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	1	no	—
1009	C₂×D₄	—	2	2	no	—
1010	C₂×D₄	—	2	2	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	2	1	no	—
1015	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1016	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1017	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1018	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1019	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1020	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	1	no	—
1023	C₂²×C₄	—	2	2	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	1	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	2	no	—
1029	C₂²×C₄	—	2	1	no	—
1030	C₂²×C₄	—	2	1	no	—
1031	C₂²×C₄	—	2	2	no	—
1032	C₂²×C₄	—	2	2	no	—
1033	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1034	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1035	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1036	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1037	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1038	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1039	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1040	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1041	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1042	SD₁₆	—	2	4	no	—
1043	SD₁₆	—	4	2	no	—
1044	D₈	—	4	2	no	—
1045	D₈	—	4	2	no	—
1046	M₁₆	—	4	2	no	—
1047	M₁₆	—	4	2	no	—
1048	C₂×C₈	—	4	2	no	—
1049	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1050	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1051	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1052	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1077	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1078	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1079	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1080	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1081	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1082	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1083	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1084	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1085	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1086	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1087	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1088	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1114	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1115	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1116	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1117	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1118	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1119	C₄²	—	2	1	no	—
1120	C₄²	—	2	1	no	—
1121	C₄²	—	2	1	no	—
1122	C₄²	—	2	1	no	—
1123	C₄²	—	2	1	no	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	—	2	1	no	—
1127	C₄²	—	2	2	no	—
1128	C₄²	—	2	2	no	—
1129	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1130	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1131	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1132	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1133	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1134	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1135	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1136	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1137	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1138	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1139	C₂³	—	2	1	no	—
1140	C₂³	—	2	1	no	—
1141	C₂³	—	2	2	no	—
1142	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1143	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1144	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1145	Q₈	—	2	1	no	—
1146	Q₈	—	2	1	no	—
1147	Q₈	—	2	1	no	—
1148	Q₈	—	4	1	no	—
1149	Q₈	—	4	2	no	—
1150	Q₈	—	4	2	no	—
1151	Q₈	—	4	2	no	—
1152	Q₈	—	4	2	no	—
1153	Q₈	—	4	2	no	—
1154	Q₈	—	8	2	no	—
1155	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
1156	D₄	—	2	2	no	—
1157	D₄	—	2	1	no	—
1158	D₄	—	2	1	no	—
1159	D₄	—	2	2	no	—
1160	D₄	—	2	1	no	—
1161	D₄	—	2	1	no	—
1162	D₄	—	4	1	no	—
1163	D₄	—	4	1	no	—
1164	D₄	—	4	1	no	—
1165	D₄	—	4	2	no	—
1166	D₄	—	4	2	no	—
1167	D₄	—	4	2	no	—
1168	D₄	—	4	2	no	—
1169	D₄	—	4	4	no	—
1170	D₄	—	4	2	no	—
1171	D₄	—	4	2	no	—
1172	D₄	—	4	2	no	—
1173	D₄	—	8	1	no	—
1174	D₄	—	8	1	no	—
1175	D₄	—	8	1	no	—
1176	D₄	—	8	2	no	—
1177	D₄	—	8	2	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	2	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	4	1	no	—
1197	C₂×C₄	—	4	1	no	—
1198	C₂×C₄	—	4	1	no	—
1199	C₂×C₄	—	4	2	no	—
1200	C₂×C₄	—	4	2	no	—
1201	C₂×C₄	—	4	2	no	—
1202	C₂×C₄	—	4	4	no	—
1203	C₂×C₄	—	4	2	no	—
1204	C₂×C₄	—	4	2	no	—
1205	C₂×C₄	—	8	1	no	—
1206	C₂×C₄	—	8	1	no	—
1207	C₂×C₄	—	8	2	no	—
1208	C₂×C₄	—	8	2	no	—
1209	C₂×C₄	—	8	1	no	—
1210	C₂×C₄	—	8	2	no	—
1211	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1212	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1213	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1214	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1215	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1216	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1217	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1218	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1219	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1220	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1221	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1222	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1223	C₈	—	2	2	no	—
1224	C₈	—	2	2	no	—
1225	C₈	—	2	2	no	—
1226	C₈	—	2	2	no	—
1227	C₂²	—	2	1	no	—
1228	C₂²	—	2	1	no	—
1229	C₂²	—	2	1	no	—
1230	C₂²	—	2	1	no	—
1231	C₂²	—	2	1	no	—
1232	C₂²	—	2	1	no	—
1233	C₂²	—	2	1	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	1	no	—
1236	C₂²	—	4	1	no	—
1237	C₂²	—	4	1	no	—
1238	C₂²	—	4	2	no	—
1239	C₂²	—	4	2	no	—
1240	C₂²	—	4	1	no	—
1241	C₂²	—	4	1	no	—
1242	C₂²	—	4	2	no	—
1243	C₂²	—	4	1	no	—
1244	C₂²	—	4	1	no	—
1245	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1246	C₄	—	2	1	no	—
1247	C₄	—	2	1	no	—
1248	C₄	—	2	1	no	—
1249	C₄	—	2	2	no	—
1250	C₄	—	2	1	no	—
1251	C₄	—	2	1	no	—
1252	C₄	—	2	1	no	—
1253	C₄	—	2	1	no	—
1254	C₄	—	2	1	no	—
1255	C₄	—	2	1	no	—
1256	C₄	—	2	1	no	—
1257	C₄	—	4	1	no	—
1258	C₄	—	4	2	no	—
1259	C₄	—	4	1	no	—
1260	C₄	—	4	1	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	4	2	no	—
1263	C₄	—	4	2	no	—
1264	C₄	—	4	1	no	—
1265	C₄	C₅₃×#575	1	2	yes	—
1266	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1267	C₄	C₅₃×#585	1	1	yes	characteristic
1268	C₂	—	4	1	no	—
1269	C₂	—	4	1	no	—
1270	C₂	—	4	1	no	—
1271	C₂	—	8	1	no	—
1272	C₂	—	8	1	no	—
1273	C₂	—	8	2	no	—
1274	C₂	C₅₃×#3489	1	1	yes	characteristic
1275	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1276	C₂	C₅₃×#3585	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 ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3511	C₂	semidirect
2. C₅₃×#3480	C₂	semidirect
3. C₅₃×#3388	C₂	semidirect
4. C₅₃×#3370	C₂	semidirect
5. C₅₃×#3355	C₂	semidirect
6. C₅₃×#3350	C₂	semidirect
7. C₅₃×#3347	C₂	semidirect
8. C₅₃×#3326	C₂	semidirect
9. C₅₃×#3321	C₂	semidirect
10. C₅₃×#3309	C₂	semidirect
11. C₅₃×#3253	C₂	semidirect
12. C₅₃×#3251	C₂	semidirect
13. C₅₃×#3247	C₂	semidirect
14. C₅₃×#3238	C₂	semidirect
15. C₅₃×#3235	C₂	semidirect
16. C₅₃×#3233	C₂	semidirect
17. C₅₃×#3115	C₂	semidirect
18. C₅₃×#3112	C₂	semidirect
19. C₅₃×#3106	C₂	semidirect
20. C₅₃×#3079	C₂	semidirect
21. C₅₃×#3078	C₂	semidirect
22. C₅₃×#3076	C₂	semidirect
23. C₅₃×#2989	C₂	semidirect
588. #62117	C₅₃	direct (N × H)
630. #3511	C₂×C₅₃	semidirect
631. #3480	C₂×C₅₃	semidirect
632. #3388	C₂×C₅₃	semidirect
633. #3370	C₂×C₅₃	semidirect
634. #3355	C₂×C₅₃	semidirect
635. #3350	C₂×C₅₃	semidirect
636. #3347	C₂×C₅₃	semidirect
637. #3326	C₂×C₅₃	semidirect
638. #3321	C₂×C₅₃	semidirect
639. #3309	C₂×C₅₃	semidirect
640. #3253	C₂×C₅₃	semidirect
641. #3251	C₂×C₅₃	semidirect
642. #3247	C₂×C₅₃	semidirect
643. #3238	C₂×C₅₃	semidirect
644. #3235	C₂×C₅₃	semidirect
645. #3233	C₂×C₅₃	semidirect
646. #3115	C₂×C₅₃	semidirect
647. #3112	C₂×C₅₃	semidirect
648. #3106	C₂×C₅₃	semidirect
649. #3079	C₂×C₅₃	semidirect
650. #3078	C₂×C₅₃	semidirect
651. #3076	C₂×C₅₃	semidirect
652. #2989	C₂×C₅₃	semidirect
777. C₅₃	#62117	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3511	2
C₅₃×#3480	2
C₅₃×#3388	2
C₅₃×#3370	2
C₅₃×#3355	2
C₅₃×#3350	2
C₅₃×#3347	2
C₅₃×#3326	2
C₅₃×#3321	2
C₅₃×#3309	2
C₅₃×#3253	2
C₅₃×#3251	2
C₅₃×#3247	2
C₅₃×#3238	2
C₅₃×#3235	2
C₅₃×#3233	2
C₅₃×#3115	2
C₅₃×#3112	2
C₅₃×#3106	2
C₅₃×#3079	2
C₅₃×#3078	2
C₅₃×#3076	2
C₅₃×#2989	2
#62117	53

Subgroups — C53×#62117 #27269629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62117 #27269629