Subgroups — C₅₃×#61975 #27269487

Order 13568.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1186 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, complemented
2	C₅₃×#3483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3397	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×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3321	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3319	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3271	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3268	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3251	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3213	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3111	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3040	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
26	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
27	C₅₃×#559	C₂²	1	1	yes	characteristic
28	Q₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#556	C₂²	1	1	yes	characteristic
30	C₅₃×#555	—	2	1	no	—
31	C₅₃×#555	—	2	2	no	—
32	C₅₃×#555	—	2	1	no	—
33	C₅₃×#555	C₂²	1	1	yes	characteristic
34	C₅₃×#555	C₂²	1	2	yes	complemented
35	C₅₃×#551	—	2	2	no	—
36	C₅₃×#550	—	2	1	no	—
37	C₅₃×#550	C₂²	1	1	yes	characteristic
38	C₅₃×#550	C₂²	1	2	yes	complemented
39	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
40	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
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×#532	—	2	1	no	—
48	C₅₃×#532	—	2	2	no	—
49	C₅₃×#532	C₂²	1	1	yes	characteristic
50	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#532	C₂²	1	2	yes	complemented
52	C₅₃×#529	C₂²	1	1	yes	characteristic
53	C₅₃×#529	C₂²	1	2	yes	—
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	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
60	C₅₃×#496	C₂²	1	2	yes	—
61	C₅₃×#496	C₂²	1	2	yes	complemented
62	C₅₃×#493	C₂²	1	1	yes	characteristic
63	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
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×#485	C₂²	1	2	yes	complemented
69	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#482	C₂²	1	1	yes	characteristic
71	C₅₃×#482	C₂²	1	2	yes	—
72	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#478	C₂²	1	2	yes	complemented
74	C₅₃×#478	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×#469	C₂²	1	2	yes	—
80	C₅₃×#469	C₂²	1	2	yes	—
81	C₅₃×#468	C₂²	1	2	yes	complemented
82	C₅₃×#468	C₂²	1	2	yes	complemented
83	C₅₃×#466	C₂²	1	2	yes	—
84	C₅₃×#465	C₂²	1	2	yes	complemented
85	C₅₃×#464	C₂²	1	2	yes	—
86	C₅₃×#464	C₂²	1	1	yes	characteristic
87	C₅₃×#464	C₂²	1	2	yes	complemented
88	C₅₃×#464	C₂²	1	2	yes	complemented
89	C₅₃×#463	C₂²	1	1	yes	characteristic
90	C₅₃×#463	C₂²	1	2	yes	—
91	C₅₃×#463	C₂²	1	2	yes	—
92	C₅₃×#463	C₂²	1	2	yes	complemented
93	C₅₃×#463	C₂²	1	2	yes	complemented
94	C₅₃×#463	C₂²	1	2	yes	complemented
95	C₅₃×#463	C₂²	1	2	yes	complemented
96	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#460	C₂²	1	1	yes	characteristic
99	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#460	C₂²	1	2	yes	complemented
101	C₅₃×#459	C₂²	1	1	yes	characteristic
102	C₅₃×#459	C₂²	1	1	yes	characteristic
103	C₅₃×#459	C₂²	1	2	yes	complemented
104	C₅₃×#452	C₂²	1	2	yes	complemented
105	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#449	C₂²	1	1	yes	characteristic
107	C₅₃×#449	C₂²	1	2	yes	—
108	C₅₃×#449	C₂²	1	2	yes	complemented
109	C₅₃×#449	C₂²	1	2	yes	complemented
110	C₅₃×#448	C₂²	1	2	yes	complemented
111	C₅₃×#448	C₂²	1	2	yes	complemented
112	C₅₃×#447	C₂²	1	2	yes	—
113	C₅₃×#447	C₂²	1	2	yes	—
114	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#442	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×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
122	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
124	C₅₃×#436	C₂²	1	1	yes	characteristic
125	C₅₃×#436	C₂²	1	1	yes	characteristic
126	C₅₃×#435	C₂²	1	2	yes	complemented
127	C₅₃×#435	C₂²	1	2	yes	complemented
128	C₅₃×#432	C₂²	1	2	yes	complemented
129	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#423	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#419	C₂²	1	2	yes	complemented
133	C₅₃×#418	C₂²	1	2	yes	—
134	C₅₃×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	2	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
139	C₂×#41×C₅₃	C₂³	1	2	yes	—
140	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₅₃	C₂³	1	2	yes	—
142	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
143	C₂²×D₄×C₅₃	—	2	1	no	—
144	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
145	#137×C₅₃	—	4	4	no	—
146	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
147	#135×C₅₃	—	4	4	no	—
148	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂×D₈×C₅₃	C₂³	1	2	yes	—
158	C₂×D₈×C₅₃	C₂³	1	2	yes	—
159	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×D₈×C₅₃	C₂³	1	2	yes	—
161	C₂×D₈×C₅₃	C₂³	1	2	yes	—
162	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
163	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
164	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₅₃	—	2	1	no	—
166	C₄⋊Q₈×C₅₃	—	2	2	no	—
167	C₄⋊Q₈×C₅₃	—	2	1	no	—
168	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
170	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
171	#127×C₅₃	—	2	1	no	—
172	#127×C₅₃	—	2	2	no	—
173	#127×C₅₃	C₂³	1	1	yes	characteristic
174	#127×C₅₃	C₂³	1	1	yes	characteristic
175	#127×C₅₃	C₂³	1	2	yes	—
176	#126×C₅₃	—	2	2	no	—
177	#126×C₅₃	—	2	2	no	—
178	#126×C₅₃	—	2	1	no	—
179	#125×C₅₃	C₂³	1	1	yes	characteristic
180	#124×C₅₃	—	2	2	no	—
181	#124×C₅₃	—	2	2	no	—
182	#124×C₅₃	—	2	2	no	—
183	#124×C₅₃	—	2	2	no	—
184	#124×C₅₃	—	2	2	no	—
185	#124×C₅₃	—	2	2	no	—
186	#124×C₅₃	—	2	2	no	—
187	#124×C₅₃	—	2	1	no	—
188	#124×C₅₃	—	2	1	no	—
189	#124×C₅₃	C₂³	1	2	yes	—
190	#124×C₅₃	C₂³	1	2	yes	—
191	#124×C₅₃	C₂³	1	1	yes	characteristic
192	#124×C₅₃	C₂³	1	2	yes	—
193	#123×C₅₃	—	2	2	no	—
194	#123×C₅₃	—	2	2	no	—
195	#123×C₅₃	—	2	1	no	—
196	#123×C₅₃	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	—	2	2	no	—
198	C₂²⋊Q₈×C₅₃	—	2	2	no	—
199	C₂²⋊Q₈×C₅₃	—	2	1	no	—
200	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
202	#121×C₅₃	—	2	1	no	—
203	#121×C₅₃	—	2	2	no	—
204	#121×C₅₃	—	2	1	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	1	no	—
210	#121×C₅₃	—	2	2	no	—
211	#121×C₅₃	—	2	2	no	—
212	#121×C₅₃	—	2	1	no	—
213	#121×C₅₃	—	2	1	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	—	2	2	no	—
216	#121×C₅₃	C₂³	1	2	yes	—
217	#121×C₅₃	C₂³	1	1	yes	characteristic
218	#121×C₅₃	C₂³	1	2	yes	—
219	#121×C₅₃	C₂³	1	2	yes	—
220	#121×C₅₃	C₂³	1	2	yes	—
221	#120×C₅₃	—	2	2	no	—
222	#120×C₅₃	—	2	2	no	—
223	C₄×Q₈×C₅₃	—	2	1	no	—
224	C₄×Q₈×C₅₃	D₄	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×Q₈×C₅₃	C₂³	1	2	yes	—
230	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	2	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	2	no	—
235	C₄×D₄×C₅₃	—	2	1	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	2	no	—
241	C₄×D₄×C₅₃	—	2	1	no	—
242	C₄×D₄×C₅₃	—	2	1	no	—
243	C₄×D₄×C₅₃	—	2	2	no	—
244	C₄×D₄×C₅₃	—	2	2	no	—
245	C₄×D₄×C₅₃	—	2	1	no	—
246	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
247	C₄×D₄×C₅₃	D₄	1	2	yes	—
248	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₅₃	C₂³	1	2	yes	—
250	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
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	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	2	no	—
258	#117×C₅₃	—	2	1	no	—
259	#117×C₅₃	—	2	2	no	—
260	#117×C₅₃	—	2	1	no	—
261	#117×C₅₃	—	2	1	no	—
262	#117×C₅₃	—	2	2	no	—
263	#117×C₅₃	D₄	1	2	yes	—
264	#117×C₅₃	D₄	1	1	yes	characteristic
265	#117×C₅₃	C₂³	1	2	yes	—
266	#117×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	1	no	—
271	C₂×C₄²×C₅₃	—	2	2	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	2	yes	—
276	#107×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
281	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
285	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	2	yes	—
306	#102×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
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	2	no	—
317	#41×C₅₃	—	2	4	no	—
318	#41×C₅₃	—	4	2	no	—
319	#41×C₅₃	—	4	2	no	—
320	#41×C₅₃	—	4	1	no	—
321	#41×C₅₃	—	4	2	no	—
322	#41×C₅₃	—	4	2	no	—
323	#41×C₅₃	—	4	4	no	—
324	#41×C₅₃	—	8	4	no	—
325	#41×C₅₃	—	8	2	no	—
326	C₂×Q₈×C₅₃	—	2	2	no	—
327	C₂×Q₈×C₅₃	—	2	2	no	—
328	C₂×Q₈×C₅₃	—	2	1	no	—
329	C₂×Q₈×C₅₃	—	4	2	no	—
330	C₂×Q₈×C₅₃	—	4	2	no	—
331	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₅₃	—	2	2	no	—
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	—	2	1	no	—
338	C₂×D₄×C₅₃	—	2	1	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	2	no	—
343	C₂×D₄×C₅₃	—	2	1	no	—
344	C₂×D₄×C₅₃	—	2	2	no	—
345	C₂×D₄×C₅₃	—	2	1	no	—
346	C₂×D₄×C₅₃	—	2	1	no	—
347	C₂×D₄×C₅₃	—	2	2	no	—
348	C₂×D₄×C₅₃	—	2	2	no	—
349	C₂×D₄×C₅₃	—	2	1	no	—
350	C₂×D₄×C₅₃	—	4	2	no	—
351	C₂×D₄×C₅₃	—	4	2	no	—
352	C₂×D₄×C₅₃	—	4	4	no	—
353	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
354	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
355	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
357	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₅₃	—	2	2	no	—
360	C₂²×C₄×C₅₃	—	2	1	no	—
361	C₂²×C₄×C₅₃	—	2	2	no	—
362	C₂²×C₄×C₅₃	—	2	2	no	—
363	C₂²×C₄×C₅₃	—	2	1	no	—
364	C₂²×C₄×C₅₃	—	2	1	no	—
365	C₂²×C₄×C₅₃	—	2	2	no	—
366	C₂²×C₄×C₅₃	—	2	1	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	2	yes	—
371	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
372	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
375	Q₁₆×C₅₃	—	2	4	no	—
376	Q₁₆×C₅₃	—	2	2	no	—
377	SD₁₆×C₅₃	—	2	4	no	—
378	SD₁₆×C₅₃	—	2	2	no	—
379	SD₁₆×C₅₃	—	4	1	no	—
380	SD₁₆×C₅₃	—	4	2	no	—
381	SD₁₆×C₅₃	—	4	2	no	—
382	SD₁₆×C₅₃	—	4	2	no	—
383	SD₁₆×C₅₃	—	4	2	no	—
384	D₈×C₅₃	—	4	2	no	—
385	D₈×C₅₃	—	4	1	no	—
386	D₈×C₅₃	—	4	2	no	—
387	D₈×C₅₃	—	4	2	no	—
388	D₈×C₅₃	—	4	2	no	—
389	M₁₆×C₅₃	—	4	2	no	—
390	M₁₆×C₅₃	—	4	2	no	—
391	C₂×C₈×C₅₃	—	4	2	no	—
392	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
397	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₅₃	—	2	1	no	—
399	C₄⋊C₄×C₅₃	—	2	1	no	—
400	C₄⋊C₄×C₅₃	—	2	1	no	—
401	C₄⋊C₄×C₅₃	—	2	1	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	1	no	—
409	C₄⋊C₄×C₅₃	—	2	2	no	—
410	C₄⋊C₄×C₅₃	—	2	1	no	—
411	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
415	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	1	no	—
423	C₂²⋊C₄×C₅₃	—	2	1	no	—
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	1	no	—
426	C₂²⋊C₄×C₅₃	—	2	1	no	—
427	C₂²⋊C₄×C₅₃	—	2	1	no	—
428	C₂²⋊C₄×C₅₃	—	2	2	no	—
429	C₂²⋊C₄×C₅₃	—	2	2	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	2	no	—
437	C₂²⋊C₄×C₅₃	—	2	1	no	—
438	C₂²⋊C₄×C₅₃	—	2	2	no	—
439	C₂²⋊C₄×C₅₃	—	2	1	no	—
440	C₂²⋊C₄×C₅₃	—	2	2	no	—
441	C₂²⋊C₄×C₅₃	—	2	1	no	—
442	C₂²⋊C₄×C₅₃	—	2	2	no	—
443	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
451	C₄²×C₅₃	—	2	2	no	—
452	C₄²×C₅₃	—	2	1	no	—
453	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₅₃	C₂×D₄	1	2	yes	—
455	C₄²×C₅₃	C₂×D₄	1	2	yes	—
456	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
458	C₄²×C₅₃	C₂⁴	1	2	yes	—
459	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
460	C₂³×C₅₃	—	2	2	no	—
461	C₂³×C₅₃	—	2	1	no	—
462	C₂³×C₅₃	—	2	2	no	—
463	C₂³×C₅₃	—	2	1	no	—
464	C₂³×C₅₃	—	4	4	no	—
465	C₂³×C₅₃	—	8	2	no	—
466	C₂³×C₅₃	—	8	2	no	—
467	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
468	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
469	Q₈×C₅₃	—	2	2	no	—
470	Q₈×C₅₃	—	2	1	no	—
471	Q₈×C₅₃	—	2	1	no	—
472	Q₈×C₅₃	—	2	2	no	—
473	Q₈×C₅₃	—	2	1	no	—
474	Q₈×C₅₃	—	2	2	no	—
475	Q₈×C₅₃	—	8	2	no	—
476	Q₈×C₅₃	—	8	2	no	—
477	Q₈×C₅₃	—	8	1	no	—
478	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
479	D₄×C₅₃	—	2	2	no	—
480	D₄×C₅₃	—	2	1	no	—
481	D₄×C₅₃	—	2	2	no	—
482	D₄×C₅₃	—	2	1	no	—
483	D₄×C₅₃	—	2	2	no	—
484	D₄×C₅₃	—	2	1	no	—
485	D₄×C₅₃	—	2	2	no	—
486	D₄×C₅₃	—	2	1	no	—
487	D₄×C₅₃	—	2	2	no	—
488	D₄×C₅₃	—	4	2	no	—
489	D₄×C₅₃	—	4	4	no	—
490	D₄×C₅₃	—	4	2	no	—
491	D₄×C₅₃	—	4	4	no	—
492	D₄×C₅₃	—	4	4	no	—
493	D₄×C₅₃	—	4	2	no	—
494	D₄×C₅₃	—	4	2	no	—
495	D₄×C₅₃	—	8	1	no	—
496	D₄×C₅₃	—	8	2	no	—
497	D₄×C₅₃	—	8	2	no	—
498	D₄×C₅₃	—	8	1	no	—
499	D₄×C₅₃	—	8	1	no	—
500	D₄×C₅₃	—	8	2	no	—
501	D₄×C₅₃	—	8	2	no	—
502	D₄×C₅₃	—	8	2	no	—
503	D₄×C₅₃	—	8	2	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	2	no	—
509	C₂×C₄×C₅₃	—	2	1	no	—
510	C₂×C₄×C₅₃	—	2	1	no	—
511	C₂×C₄×C₅₃	—	2	2	no	—
512	C₂×C₄×C₅₃	—	2	1	no	—
513	C₂×C₄×C₅₃	—	2	1	no	—
514	C₂×C₄×C₅₃	—	2	1	no	—
515	C₂×C₄×C₅₃	—	2	2	no	—
516	C₂×C₄×C₅₃	—	2	1	no	—
517	C₂×C₄×C₅₃	—	4	2	no	—
518	C₂×C₄×C₅₃	—	4	2	no	—
519	C₂×C₄×C₅₃	—	4	1	no	—
520	C₂×C₄×C₅₃	—	4	2	no	—
521	C₂×C₄×C₅₃	—	4	4	no	—
522	C₂×C₄×C₅₃	—	4	4	no	—
523	C₂×C₄×C₅₃	—	4	4	no	—
524	C₂×C₄×C₅₃	—	4	2	no	—
525	C₂×C₄×C₅₃	—	4	2	no	—
526	C₂×C₄×C₅₃	—	4	2	no	—
527	C₂×C₄×C₅₃	—	8	2	no	—
528	C₂×C₄×C₅₃	—	8	2	no	—
529	C₂×C₄×C₅₃	—	8	2	no	—
530	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
539	C₈×C₅₃	—	2	2	no	—
540	C₈×C₅₃	—	2	2	no	—
541	C₈×C₅₃	—	2	1	no	—
542	C₈×C₅₃	—	2	1	no	—
543	C₈×C₅₃	—	2	1	no	—
544	C₈×C₅₃	—	2	1	no	—
545	#61975	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
546	C₂²×C₅₃	—	2	1	no	—
547	C₂²×C₅₃	—	2	2	no	—
548	C₂²×C₅₃	—	2	2	no	—
549	C₂²×C₅₃	—	2	1	no	—
550	C₂²×C₅₃	—	2	1	no	—
551	C₂²×C₅₃	—	2	2	no	—
552	C₂²×C₅₃	—	4	1	no	—
553	C₂²×C₅₃	—	4	2	no	—
554	C₂²×C₅₃	—	4	2	no	—
555	C₂²×C₅₃	—	4	1	no	—
556	C₂²×C₅₃	—	4	1	no	—
557	C₂²×C₅₃	—	4	2	no	—
558	C₂²×C₅₃	—	4	2	no	—
559	C₂²×C₅₃	—	4	1	no	—
560	C₂²×C₅₃	—	4	2	no	—
561	C₂²×C₅₃	—	4	1	no	—
562	C₂²×C₅₃	—	4	1	no	—
563	C₂²×C₅₃	—	4	2	no	—
564	C₂²×C₅₃	—	16	4	no	—
565	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
566	C₄×C₅₃	—	2	1	no	—
567	C₄×C₅₃	—	2	2	no	—
568	C₄×C₅₃	—	2	1	no	—
569	C₄×C₅₃	—	2	1	no	—
570	C₄×C₅₃	—	2	2	no	—
571	C₄×C₅₃	—	2	2	no	—
572	C₄×C₅₃	—	2	1	no	—
573	C₄×C₅₃	—	2	2	no	—
574	C₄×C₅₃	—	4	2	no	—
575	C₄×C₅₃	—	4	1	no	—
576	C₄×C₅₃	—	4	1	no	—
577	C₄×C₅₃	—	4	2	no	—
578	C₄×C₅₃	—	4	1	no	—
579	C₄×C₅₃	—	4	1	no	—
580	C₄×C₅₃	—	4	1	no	—
581	C₄×C₅₃	#575	1	2	yes	—
582	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
583	C₄×C₅₃	#585	1	1	yes	characteristic
584	#3514	C₂×C₅₃	1	1	yes	characteristic, complemented
585	#3483	C₂×C₅₃	1	1	yes	characteristic, complemented
586	#3399	C₂×C₅₃	1	1	yes	characteristic, complemented
587	#3397	C₂×C₅₃	1	1	yes	characteristic, complemented
588	#3375	C₂×C₅₃	1	1	yes	characteristic, complemented
589	#3369	C₂×C₅₃	1	1	yes	characteristic, complemented
590	#3329	C₂×C₅₃	1	1	yes	characteristic, complemented
591	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
592	#3321	C₂×C₅₃	1	2	yes	complemented
593	#3319	C₂×C₅₃	1	2	yes	complemented
594	#3278	C₂×C₅₃	1	1	yes	characteristic, complemented
595	#3274	C₂×C₅₃	1	1	yes	characteristic, complemented
596	#3271	C₂×C₅₃	1	2	yes	complemented
597	#3268	C₂×C₅₃	1	2	yes	complemented
598	#3251	C₂×C₅₃	1	2	yes	complemented
599	#3247	C₂×C₅₃	1	1	yes	characteristic, complemented
600	#3213	C₂×C₅₃	1	2	yes	complemented
601	#3207	C₂×C₅₃	1	1	yes	characteristic, complemented
602	#3111	C₂×C₅₃	1	2	yes	complemented
603	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
604	#3040	C₂×C₅₃	1	2	yes	complemented
605	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
606	#2989	C₂×C₅₃	1	1	yes	characteristic, complemented
607	C₂×C₅₃	—	4	1	no	—
608	C₂×C₅₃	—	4	2	no	—
609	C₂×C₅₃	—	8	2	no	—
610	C₂×C₅₃	—	8	1	no	—
611	C₂×C₅₃	—	8	2	no	—
612	C₂×C₅₃	—	8	1	no	—
613	C₂×C₅₃	#3488	1	1	yes	characteristic
614	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
615	C₂×C₅₃	#3585	1	1	yes	characteristic
616	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
617	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
618	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
619	#559	C₂²×C₅₃	1	1	yes	characteristic
620	Q₈²	C₂²×C₅₃	1	1	yes	characteristic, complemented
621	#556	C₂²×C₅₃	1	1	yes	characteristic
622	#555	—	2	1	no	—
623	#555	—	2	2	no	—
624	#555	—	2	1	no	—
625	#555	C₂²×C₅₃	1	1	yes	characteristic
626	#555	C₂²×C₅₃	1	2	yes	complemented
627	#551	—	2	2	no	—
628	#550	—	2	1	no	—
629	#550	C₂²×C₅₃	1	1	yes	characteristic
630	#550	C₂²×C₅₃	1	2	yes	complemented
631	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
632	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
633	#548	C₂²×C₅₃	1	2	yes	—
634	#546	—	2	1	no	—
635	#546	C₂²×C₅₃	1	2	yes	—
636	D₄²	C₂²×C₅₃	1	1	yes	characteristic
637	#542	—	2	1	no	—
638	#538	—	2	2	no	—
639	#532	—	2	1	no	—
640	#532	—	2	2	no	—
641	#532	C₂²×C₅₃	1	1	yes	characteristic
642	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
643	#532	C₂²×C₅₃	1	2	yes	complemented
644	#529	C₂²×C₅₃	1	1	yes	characteristic
645	#529	C₂²×C₅₃	1	2	yes	—
646	C₂×#124	C₂²×C₅₃	1	2	yes	—
647	#518	—	2	1	no	—
648	C₄×#41	—	2	1	no	—
649	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
650	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
651	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
652	#496	C₂²×C₅₃	1	2	yes	—
653	#496	C₂²×C₅₃	1	2	yes	complemented
654	#493	C₂²×C₅₃	1	1	yes	characteristic
655	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	#489	C₂²×C₅₃	1	2	yes	—
657	#489	C₂²×C₅₃	1	2	yes	complemented
658	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	#486	C₂²×C₅₃	1	1	yes	characteristic
660	#485	C₂²×C₅₃	1	2	yes	complemented
661	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
662	#482	C₂²×C₅₃	1	1	yes	characteristic
663	#482	C₂²×C₅₃	1	2	yes	—
664	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
665	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
666	#478	C₂²×C₅₃	1	2	yes	complemented
667	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
668	#476	C₂²×C₅₃	1	1	yes	characteristic
669	#475	C₂²×C₅₃	1	2	yes	complemented
670	#474	C₂²×C₅₃	1	2	yes	complemented
671	#469	C₂²×C₅₃	1	2	yes	—
672	#469	C₂²×C₅₃	1	2	yes	—
673	#468	C₂²×C₅₃	1	2	yes	complemented
674	#468	C₂²×C₅₃	1	2	yes	complemented
675	#466	C₂²×C₅₃	1	2	yes	—
676	#465	C₂²×C₅₃	1	2	yes	complemented
677	#464	C₂²×C₅₃	1	1	yes	characteristic
678	#464	C₂²×C₅₃	1	2	yes	—
679	#464	C₂²×C₅₃	1	2	yes	complemented
680	#464	C₂²×C₅₃	1	2	yes	complemented
681	#463	C₂²×C₅₃	1	1	yes	characteristic
682	#463	C₂²×C₅₃	1	2	yes	—
683	#463	C₂²×C₅₃	1	2	yes	—
684	#463	C₂²×C₅₃	1	2	yes	complemented
685	#463	C₂²×C₅₃	1	2	yes	complemented
686	#463	C₂²×C₅₃	1	2	yes	complemented
687	#463	C₂²×C₅₃	1	2	yes	complemented
688	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	#460	C₂²×C₅₃	1	1	yes	characteristic
691	#460	C₂²×C₅₃	1	2	yes	complemented
692	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#459	C₂²×C₅₃	1	1	yes	characteristic
694	#459	C₂²×C₅₃	1	1	yes	characteristic
695	#459	C₂²×C₅₃	1	2	yes	complemented
696	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
697	#452	C₂²×C₅₃	1	2	yes	complemented
698	#449	C₂²×C₅₃	1	1	yes	characteristic
699	#449	C₂²×C₅₃	1	2	yes	—
700	#449	C₂²×C₅₃	1	2	yes	complemented
701	#449	C₂²×C₅₃	1	2	yes	complemented
702	#448	C₂²×C₅₃	1	2	yes	complemented
703	#448	C₂²×C₅₃	1	2	yes	complemented
704	#447	C₂²×C₅₃	1	2	yes	—
705	#447	C₂²×C₅₃	1	2	yes	—
706	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	#442	C₂²×C₅₃	1	2	yes	complemented
709	#441	C₂²×C₅₃	1	2	yes	complemented
710	#440	C₂²×C₅₃	1	2	yes	complemented
711	#440	C₂²×C₅₃	1	2	yes	complemented
712	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
714	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
715	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
716	#436	C₂²×C₅₃	1	1	yes	characteristic
717	#436	C₂²×C₅₃	1	1	yes	characteristic
718	#435	C₂²×C₅₃	1	2	yes	complemented
719	#435	C₂²×C₅₃	1	2	yes	complemented
720	#432	C₂²×C₅₃	1	2	yes	complemented
721	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	#423	C₂²×C₅₃	1	2	yes	complemented
723	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
724	#419	C₂²×C₅₃	1	2	yes	complemented
725	#418	C₂²×C₅₃	1	2	yes	—
726	#416	C₂²×C₅₃	1	2	yes	complemented
727	C₅₃	#61975	1	1	yes	characteristic, direct product factor, Sylow
728	C₂×#41	—	2	1	no	—
729	C₂×#41	—	2	2	no	—
730	C₂×#41	—	2	1	no	—
731	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
732	C₂×#41	C₂³×C₅₃	1	2	yes	—
733	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
734	C₂×#41	C₂³×C₅₃	1	2	yes	—
735	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
736	C₂²×D₄	—	2	1	no	—
737	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
738	#137	—	4	4	no	—
739	AGL(1,ℤ/8)	—	4	4	no	—
740	#135	—	4	4	no	—
741	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
742	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
745	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
749	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
750	C₂×D₈	C₂³×C₅₃	1	2	yes	—
751	C₂×D₈	C₂³×C₅₃	1	2	yes	—
752	C₂×D₈	C₂³×C₅₃	1	2	yes	—
753	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
754	C₂×D₈	C₂³×C₅₃	1	2	yes	—
755	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
756	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
757	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
758	C₄⋊Q₈	—	2	1	no	—
759	C₄⋊Q₈	—	2	2	no	—
760	C₄⋊Q₈	—	2	1	no	—
761	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
762	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
763	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
764	#127	—	2	1	no	—
765	#127	—	2	2	no	—
766	#127	C₂³×C₅₃	1	1	yes	characteristic
767	#127	C₂³×C₅₃	1	1	yes	characteristic
768	#127	C₂³×C₅₃	1	2	yes	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#126	—	2	1	no	—
772	#125	C₂³×C₅₃	1	1	yes	characteristic
773	#124	—	2	1	no	—
774	#124	—	2	2	no	—
775	#124	—	2	2	no	—
776	#124	—	2	2	no	—
777	#124	—	2	2	no	—
778	#124	—	2	2	no	—
779	#124	—	2	2	no	—
780	#124	—	2	2	no	—
781	#124	—	2	1	no	—
782	#124	C₂³×C₅₃	1	1	yes	characteristic
783	#124	C₂³×C₅₃	1	2	yes	—
784	#124	C₂³×C₅₃	1	2	yes	—
785	#124	C₂³×C₅₃	1	2	yes	—
786	#123	—	2	1	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	1	no	—
801	#121	—	2	2	no	—
802	#121	—	2	1	no	—
803	#121	—	2	2	no	—
804	#121	—	2	1	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	C₂³×C₅₃	1	2	yes	—
810	#121	C₂³×C₅₃	1	1	yes	characteristic
811	#121	C₂³×C₅₃	1	2	yes	—
812	#121	C₂³×C₅₃	1	2	yes	—
813	#121	C₂³×C₅₃	1	2	yes	—
814	#120	—	2	2	no	—
815	#120	—	2	2	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
820	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
821	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
822	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
823	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
840	C₄×D₄	D₄×C₅₃	1	2	yes	—
841	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₅₃	1	2	yes	—
843	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₅₃	1	2	yes	—
845	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₅₃	1	2	yes	—
847	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
848	C₄×D₄	C₂³×C₅₃	1	2	yes	—
849	#117	—	2	1	no	—
850	#117	—	2	2	no	—
851	#117	—	2	1	no	—
852	#117	—	2	2	no	—
853	#117	—	2	1	no	—
854	#117	—	2	1	no	—
855	#117	—	2	2	no	—
856	#117	D₄×C₅₃	1	2	yes	—
857	#117	D₄×C₅₃	1	1	yes	characteristic
858	#117	C₂³×C₅₃	1	2	yes	—
859	#117	C₂³×C₅₃	1	1	yes	characteristic
860	C₂×C₂²⋊C₄	—	2	2	no	—
861	C₂×C₂²⋊C₄	—	2	2	no	—
862	C₂×C₂²⋊C₄	—	2	2	no	—
863	C₂×C₄²	—	2	1	no	—
864	C₂×C₄²	—	2	2	no	—
865	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
866	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
867	#107	C₂³×C₅₃	1	1	yes	characteristic
868	#107	C₂³×C₅₃	1	1	yes	characteristic
869	#107	C₂³×C₅₃	1	2	yes	—
870	#106	C₂³×C₅₃	1	1	yes	characteristic
871	#106	C₂³×C₅₃	1	1	yes	characteristic
872	#106	C₂³×C₅₃	1	2	yes	—
873	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
874	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
875	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
877	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
878	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
879	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
880	#103	C₂³×C₅₃	1	2	yes	—
881	#103	C₂³×C₅₃	1	2	yes	—
882	#103	C₂³×C₅₃	1	1	yes	characteristic
883	#103	C₂³×C₅₃	1	2	yes	—
884	#103	C₂³×C₅₃	1	2	yes	—
885	#103	C₂³×C₅₃	1	1	yes	characteristic
886	#103	C₂³×C₅₃	1	1	yes	characteristic
887	#103	C₂³×C₅₃	1	1	yes	characteristic
888	#103	C₂³×C₅₃	1	2	yes	—
889	#102	C₂³×C₅₃	1	2	yes	—
890	#102	C₂³×C₅₃	1	2	yes	—
891	#102	C₂³×C₅₃	1	1	yes	characteristic
892	#102	C₂³×C₅₃	1	2	yes	—
893	#102	C₂³×C₅₃	1	2	yes	—
894	#102	C₂³×C₅₃	1	1	yes	characteristic
895	#102	C₂³×C₅₃	1	1	yes	characteristic
896	#102	C₂³×C₅₃	1	1	yes	characteristic
897	#102	C₂³×C₅₃	1	2	yes	—
898	#102	C₂³×C₅₃	1	2	yes	—
899	#102	C₂³×C₅₃	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
901	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
902	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
904	#97	C₂³×C₅₃	1	2	yes	—
905	#97	C₂³×C₅₃	1	2	yes	—
906	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
907	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
908	C₂⁴	—	2	2	no	—
909	#41	—	2	2	no	—
910	#41	—	2	4	no	—
911	#41	—	4	2	no	—
912	#41	—	4	2	no	—
913	#41	—	4	1	no	—
914	#41	—	4	2	no	—
915	#41	—	4	2	no	—
916	#41	—	4	4	no	—
917	#41	—	8	4	no	—
918	#41	—	8	2	no	—
919	C₂×Q₈	—	2	2	no	—
920	C₂×Q₈	—	2	2	no	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	4	2	no	—
923	C₂×Q₈	—	4	2	no	—
924	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
925	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
927	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	4	2	no	—
944	C₂×D₄	—	4	2	no	—
945	C₂×D₄	—	4	4	no	—
946	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
947	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
948	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
949	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
950	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
951	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
963	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
964	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
965	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
967	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
968	Q₁₆	—	2	4	no	—
969	Q₁₆	—	2	2	no	—
970	SD₁₆	—	2	4	no	—
971	SD₁₆	—	2	2	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	SD₁₆	—	4	1	no	—
976	SD₁₆	—	4	2	no	—
977	D₈	—	4	2	no	—
978	D₈	—	4	2	no	—
979	D₈	—	4	2	no	—
980	D₈	—	4	2	no	—
981	D₈	—	4	1	no	—
982	M₁₆	—	4	2	no	—
983	M₁₆	—	4	2	no	—
984	C₂×C₈	—	4	2	no	—
985	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
986	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
989	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
990	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1005	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1006	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1007	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1008	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1009	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1010	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1011	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1012	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1037	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1038	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	2	no	—
1042	C₄²	—	2	2	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1047	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1048	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1049	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1050	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₅₃	1	2	yes	—
1052	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	4	4	no	—
1058	C₂³	—	8	2	no	—
1059	C₂³	—	8	2	no	—
1060	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1061	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	1	no	—
1065	Q₈	—	2	2	no	—
1066	Q₈	—	2	1	no	—
1067	Q₈	—	2	2	no	—
1068	Q₈	—	8	2	no	—
1069	Q₈	—	8	2	no	—
1070	Q₈	—	8	1	no	—
1071	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	1	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	2	1	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	1	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	4	2	no	—
1082	D₄	—	4	4	no	—
1083	D₄	—	4	2	no	—
1084	D₄	—	4	4	no	—
1085	D₄	—	4	4	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	8	1	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	1	no	—
1092	D₄	—	8	1	no	—
1093	D₄	—	8	2	no	—
1094	D₄	—	8	2	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	1	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	4	4	no	—
1115	C₂×C₄	—	4	4	no	—
1116	C₂×C₄	—	4	4	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	2	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1126	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1127	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1128	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1129	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1130	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1131	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1132	C₈	—	2	2	no	—
1133	C₈	—	2	2	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	1	no	—
1137	C₈	—	2	1	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	1	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	2	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	4	2	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	16	4	no	—
1157	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1158	C₄	—	2	1	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	1	no	—
1166	C₄	—	4	2	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	2	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	1	no	—
1173	C₄	C₅₃×#575	1	2	yes	—
1174	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1175	C₄	C₅₃×#585	1	1	yes	characteristic
1176	C₂	—	4	2	no	—
1177	C₂	—	4	1	no	—
1178	C₂	—	8	1	no	—
1179	C₂	—	8	2	no	—
1180	C₂	—	8	2	no	—
1181	C₂	—	8	1	no	—
1182	C₂	C₅₃×#3488	1	1	yes	characteristic
1183	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1184	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×#3514	C₂	semidirect
2. C₅₃×#3483	C₂	semidirect
3. C₅₃×#3399	C₂	semidirect
4. C₅₃×#3397	C₂	semidirect
5. C₅₃×#3375	C₂	semidirect
6. C₅₃×#3369	C₂	semidirect
7. C₅₃×#3329	C₂	semidirect
8. C₅₃×#3325	C₂	semidirect
9. C₅₃×#3321	C₂	semidirect
10. C₅₃×#3319	C₂	semidirect
11. C₅₃×#3278	C₂	semidirect
12. C₅₃×#3274	C₂	semidirect
13. C₅₃×#3271	C₂	semidirect
14. C₅₃×#3268	C₂	semidirect
15. C₅₃×#3251	C₂	semidirect
16. C₅₃×#3247	C₂	semidirect
17. C₅₃×#3213	C₂	semidirect
18. C₅₃×#3207	C₂	semidirect
19. C₅₃×#3111	C₂	semidirect
20. C₅₃×#3102	C₂	semidirect
21. C₅₃×#3040	C₂	semidirect
22. C₅₃×#3035	C₂	semidirect
23. C₅₃×#2989	C₂	semidirect
24. C₂×#137×C₅₃	C₂²	semidirect
26. C₂×#135×C₅₃	C₂²	semidirect
28. Q₈²×C₅₃	C₂²	semidirect
34. C₅₃×#555	C₂²	semidirect
38. C₅₃×#550	C₂²	semidirect
39. C₅₃×#550	C₂²	semidirect
50. C₅₃×#532	C₂²	semidirect
51. C₅₃×#532	C₂²	semidirect
58. C₄×#41×C₅₃	C₂²	semidirect
59. C₄×#41×C₅₃	C₂²	semidirect
61. C₅₃×#496	C₂²	semidirect
63. C₅₃×#492	C₂²	semidirect
65. C₅₃×#489	C₂²	semidirect
66. C₅₃×#487	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
69. C₅₃×#485	C₂²	semidirect
72. C₅₃×#479	C₂²	semidirect
73. C₅₃×#478	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#477	C₂²	semidirect
77. C₅₃×#475	C₂²	semidirect
78. C₅₃×#474	C₂²	semidirect
81. C₅₃×#468	C₂²	semidirect
82. C₅₃×#468	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
87. C₅₃×#464	C₂²	semidirect
88. C₅₃×#464	C₂²	semidirect
92. C₅₃×#463	C₂²	semidirect
93. C₅₃×#463	C₂²	semidirect
94. C₅₃×#463	C₂²	semidirect
95. C₅₃×#463	C₂²	semidirect
96. C₅₃×#462	C₂²	semidirect
97. C₅₃×#461	C₂²	semidirect
99. C₅₃×#460	C₂²	semidirect
100. C₅₃×#460	C₂²	semidirect
103. C₅₃×#459	C₂²	semidirect
104. C₅₃×#452	C₂²	semidirect
105. C₅₃×#452	C₂²	semidirect
108. C₅₃×#449	C₂²	semidirect
109. C₅₃×#449	C₂²	semidirect
110. C₅₃×#448	C₂²	semidirect
111. C₅₃×#448	C₂²	semidirect
114. C₅₃×#446	C₂²	semidirect
115. C₅₃×#446	C₂²	semidirect
116. C₅₃×#442	C₂²	semidirect
117. C₅₃×#441	C₂²	semidirect
118. C₅₃×#440	C₂²	semidirect
119. C₅₃×#440	C₂²	semidirect
120. C₄×Q₁₆×C₅₃	C₂²	semidirect
122. C₄×SD₁₆×C₅₃	C₂²	semidirect
126. C₅₃×#435	C₂²	semidirect
127. 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×#419	C₂²	semidirect
134. C₅₃×#416	C₂²	semidirect
545. #61975	C₅₃	direct (N × H)
584. #3514	C₂×C₅₃	semidirect
585. #3483	C₂×C₅₃	semidirect
586. #3399	C₂×C₅₃	semidirect
587. #3397	C₂×C₅₃	semidirect
588. #3375	C₂×C₅₃	semidirect
589. #3369	C₂×C₅₃	semidirect
590. #3329	C₂×C₅₃	semidirect
591. #3325	C₂×C₅₃	semidirect
592. #3321	C₂×C₅₃	semidirect
593. #3319	C₂×C₅₃	semidirect
594. #3278	C₂×C₅₃	semidirect
595. #3274	C₂×C₅₃	semidirect
596. #3271	C₂×C₅₃	semidirect
597. #3268	C₂×C₅₃	semidirect
598. #3251	C₂×C₅₃	semidirect
599. #3247	C₂×C₅₃	semidirect
600. #3213	C₂×C₅₃	semidirect
601. #3207	C₂×C₅₃	semidirect
602. #3111	C₂×C₅₃	semidirect
603. #3102	C₂×C₅₃	semidirect
604. #3040	C₂×C₅₃	semidirect
605. #3035	C₂×C₅₃	semidirect
606. #2989	C₂×C₅₃	semidirect
616. C₂×#137	C₂²×C₅₃	semidirect
618. C₂×#135	C₂²×C₅₃	semidirect
620. Q₈²	C₂²×C₅₃	semidirect
626. #555	C₂²×C₅₃	semidirect
630. #550	C₂²×C₅₃	semidirect
631. #550	C₂²×C₅₃	semidirect
642. #532	C₂²×C₅₃	semidirect
643. #532	C₂²×C₅₃	semidirect
650. C₄×#41	C₂²×C₅₃	semidirect
651. C₄×#41	C₂²×C₅₃	semidirect
653. #496	C₂²×C₅₃	semidirect
655. #492	C₂²×C₅₃	semidirect
657. #489	C₂²×C₅₃	semidirect
658. #487	C₂²×C₅₃	semidirect
660. #485	C₂²×C₅₃	semidirect
661. #485	C₂²×C₅₃	semidirect
664. #479	C₂²×C₅₃	semidirect
665. #478	C₂²×C₅₃	semidirect
666. #478	C₂²×C₅₃	semidirect
667. #477	C₂²×C₅₃	semidirect
669. #475	C₂²×C₅₃	semidirect
670. #474	C₂²×C₅₃	semidirect
673. #468	C₂²×C₅₃	semidirect
674. #468	C₂²×C₅₃	semidirect
676. #465	C₂²×C₅₃	semidirect
679. #464	C₂²×C₅₃	semidirect
680. #464	C₂²×C₅₃	semidirect
684. #463	C₂²×C₅₃	semidirect
685. #463	C₂²×C₅₃	semidirect
686. #463	C₂²×C₅₃	semidirect
687. #463	C₂²×C₅₃	semidirect
688. #462	C₂²×C₅₃	semidirect
689. #461	C₂²×C₅₃	semidirect
691. #460	C₂²×C₅₃	semidirect
692. #460	C₂²×C₅₃	semidirect
695. #459	C₂²×C₅₃	semidirect
696. #452	C₂²×C₅₃	semidirect
697. #452	C₂²×C₅₃	semidirect
700. #449	C₂²×C₅₃	semidirect
701. #449	C₂²×C₅₃	semidirect
702. #448	C₂²×C₅₃	semidirect
703. #448	C₂²×C₅₃	semidirect
706. #446	C₂²×C₅₃	semidirect
707. #446	C₂²×C₅₃	semidirect
708. #442	C₂²×C₅₃	semidirect
709. #441	C₂²×C₅₃	semidirect
710. #440	C₂²×C₅₃	semidirect
711. #440	C₂²×C₅₃	semidirect
712. C₄×Q₁₆	C₂²×C₅₃	semidirect
714. C₄×SD₁₆	C₂²×C₅₃	semidirect
718. #435	C₂²×C₅₃	semidirect
719. #435	C₂²×C₅₃	semidirect
720. #432	C₂²×C₅₃	semidirect
721. #431	C₂²×C₅₃	semidirect
722. #423	C₂²×C₅₃	semidirect
723. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
724. #419	C₂²×C₅₃	semidirect
726. #416	C₂²×C₅₃	semidirect
727. C₅₃	#61975	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×#3514	2
C₅₃×#3483	2
C₅₃×#3399	2
C₅₃×#3397	2
C₅₃×#3375	2
C₅₃×#3369	2
C₅₃×#3329	2
C₅₃×#3325	2
C₅₃×#3321	2
C₅₃×#3319	2
C₅₃×#3278	2
C₅₃×#3274	2
C₅₃×#3271	2
C₅₃×#3268	2
C₅₃×#3251	2
C₅₃×#3247	2
C₅₃×#3213	2
C₅₃×#3207	2
C₅₃×#3111	2
C₅₃×#3102	2
C₅₃×#3040	2
C₅₃×#3035	2
C₅₃×#2989	2
#61975	53

Subgroups — C53×#61975 #27269487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61975 #27269487