Subgroups — C₅₃×#60587 #27268099

Order 13568.

2084 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3126	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3122	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3121	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3115	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3111	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3106	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3102	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
29	C₅₃×#555	—	2	1	no	—
30	C₅₃×#553	—	2	1	no	—
31	C₅₃×#553	—	2	1	no	—
32	C₅₃×#551	—	2	2	no	—
33	C₅₃×#547	—	2	1	no	—
34	C₅₃×#546	—	2	2	no	—
35	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#542	C₂²	1	2	yes	—
37	C₅₃×#540	C₂²	1	2	yes	—
38	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#532	C₂²	1	2	yes	complemented
40	C₅₃×#529	C₂²	1	2	yes	complemented
41	C₅₃×#525	C₂²	1	1	yes	characteristic
42	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#520	—	2	1	no	—
44	C₅₃×#520	—	2	1	no	—
45	C₅₃×#520	C₂²	1	1	yes	characteristic
46	C₅₃×#520	C₂²	1	1	yes	characteristic
47	C₅₃×#520	C₂²	1	1	yes	characteristic
48	C₅₃×#520	C₂²	1	1	yes	characteristic
49	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#519	C₂²	1	2	yes	complemented
51	C₅₃×#518	—	2	2	no	—
52	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#518	C₂²	1	2	yes	complemented
54	C₄×#41×C₅₃	—	2	2	no	—
55	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
56	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
57	C₂×#117×C₅₃	—	2	1	no	—
58	C₂×#117×C₅₃	—	2	1	no	—
59	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
61	C₅₃×#485	C₂²	1	2	yes	complemented
62	C₅₃×#485	C₂²	1	2	yes	complemented
63	C₅₃×#482	C₂²	1	2	yes	—
64	C₅₃×#482	C₂²	1	2	yes	—
65	C₅₃×#482	C₂²	1	2	yes	complemented
66	C₅₃×#482	C₂²	1	2	yes	complemented
67	C₅₃×#482	C₂²	1	2	yes	complemented
68	C₅₃×#482	C₂²	1	2	yes	complemented
69	C₅₃×#479	C₂²	1	2	yes	complemented
70	C₅₃×#479	C₂²	1	2	yes	complemented
71	C₅₃×#478	C₂²	1	2	yes	complemented
72	C₅₃×#478	C₂²	1	2	yes	complemented
73	C₅₃×#477	C₂²	1	2	yes	complemented
74	C₅₃×#476	C₂²	1	2	yes	complemented
75	C₅₃×#475	C₂²	1	2	yes	complemented
76	C₅₃×#474	C₂²	1	2	yes	complemented
77	C₅₃×#464	C₂²	1	2	yes	complemented
78	C₅₃×#464	C₂²	1	2	yes	complemented
79	C₅₃×#463	C₂²	1	2	yes	complemented
80	C₅₃×#463	C₂²	1	2	yes	complemented
81	C₅₃×#460	C₂²	1	2	yes	complemented
82	C₅₃×#460	C₂²	1	2	yes	complemented
83	C₅₃×#459	C₂²	1	2	yes	complemented
84	C₅₃×#459	C₂²	1	2	yes	complemented
85	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#449	C₂²	1	2	yes	—
90	C₅₃×#449	C₂²	1	2	yes	—
91	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#448	C₂²	1	2	yes	—
94	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#447	C₂²	1	2	yes	—
96	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#442	C₂²	1	2	yes	complemented
98	C₅₃×#442	C₂²	1	2	yes	complemented
99	C₅₃×#442	C₂²	1	2	yes	complemented
100	C₅₃×#441	C₂²	1	2	yes	complemented
101	C₅₃×#440	C₂²	1	2	yes	complemented
102	C₅₃×#440	C₂²	1	2	yes	complemented
103	C₅₃×#440	C₂²	1	2	yes	complemented
104	C₅₃×#440	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
110	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
111	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
112	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
113	C₅₃×#433	C₂²	1	2	yes	complemented
114	C₅₃×#433	C₂²	1	2	yes	complemented
115	C₅₃×#432	C₂²	1	2	yes	complemented
116	C₅₃×#431	C₂²	1	2	yes	complemented
117	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
119	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#417	C₂²	1	1	yes	characteristic
124	C₅₃×#417	C₂²	1	1	yes	characteristic
125	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#416	C₂²	1	1	yes	characteristic
128	C₅₃×#416	C₂²	1	1	yes	characteristic
129	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#407	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
133	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₅₃	—	2	4	no	—
136	C₂×#41×C₅₃	—	2	4	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	—	2	2	no	—
140	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₅₃	—	2	1	no	—
147	C₂²×D₄×C₅₃	—	2	1	no	—
148	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₅₃	—	2	1	no	—
151	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
152	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
153	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
154	#135×C₅₃	—	2	4	no	—
155	#135×C₅₃	—	2	4	no	—
156	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
159	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
164	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
165	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
166	C₂×D₈×C₅₃	C₂³	1	2	yes	—
167	C₂×D₈×C₅₃	C₂³	1	2	yes	—
168	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
170	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
171	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈×C₅₃	—	2	1	no	—
173	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
174	#127×C₅₃	C₂³	1	2	yes	—
175	#126×C₅₃	—	2	2	no	—
176	#126×C₅₃	—	2	2	no	—
177	#125×C₅₃	—	2	1	no	—
178	#125×C₅₃	C₂³	1	2	yes	—
179	#124×C₅₃	—	2	2	no	—
180	#124×C₅₃	—	2	2	no	—
181	#124×C₅₃	C₂³	1	2	yes	—
182	#123×C₅₃	—	2	2	no	—
183	#123×C₅₃	—	2	2	no	—
184	#123×C₅₃	—	2	2	no	—
185	#123×C₅₃	—	2	1	no	—
186	#123×C₅₃	—	2	2	no	—
187	C₂²⋊Q₈×C₅₃	—	2	2	no	—
188	C₂²⋊Q₈×C₅₃	—	2	2	no	—
189	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
191	#121×C₅₃	—	2	1	no	—
192	#121×C₅₃	—	2	1	no	—
193	#121×C₅₃	—	2	2	no	—
194	#121×C₅₃	—	2	2	no	—
195	#121×C₅₃	—	2	1	no	—
196	#121×C₅₃	—	2	1	no	—
197	#121×C₅₃	—	2	2	no	—
198	#121×C₅₃	C₂³	1	2	yes	—
199	#121×C₅₃	C₂³	1	2	yes	—
200	#121×C₅₃	C₂³	1	1	yes	characteristic
201	#121×C₅₃	C₂³	1	1	yes	characteristic
202	#120×C₅₃	—	2	2	no	—
203	#120×C₅₃	—	2	1	no	—
204	C₄×Q₈×C₅₃	—	2	2	no	—
205	C₄×Q₈×C₅₃	—	2	2	no	—
206	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
207	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
208	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
209	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
210	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
211	C₄×D₄×C₅₃	—	2	2	no	—
212	C₄×D₄×C₅₃	—	2	2	no	—
213	C₄×D₄×C₅₃	—	2	1	no	—
214	C₄×D₄×C₅₃	—	2	1	no	—
215	C₄×D₄×C₅₃	—	2	2	no	—
216	C₄×D₄×C₅₃	—	2	2	no	—
217	C₄×D₄×C₅₃	—	2	2	no	—
218	C₄×D₄×C₅₃	—	2	2	no	—
219	C₄×D₄×C₅₃	—	2	2	no	—
220	C₄×D₄×C₅₃	—	2	2	no	—
221	C₄×D₄×C₅₃	—	2	2	no	—
222	C₄×D₄×C₅₃	—	2	2	no	—
223	C₄×D₄×C₅₃	—	2	2	no	—
224	C₄×D₄×C₅₃	—	2	2	no	—
225	C₄×D₄×C₅₃	—	2	1	no	—
226	C₄×D₄×C₅₃	—	2	1	no	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	C₂³	1	2	yes	—
229	C₄×D₄×C₅₃	C₂³	1	2	yes	—
230	C₄×D₄×C₅₃	C₂³	1	2	yes	—
231	C₄×D₄×C₅₃	C₂³	1	2	yes	—
232	C₄×D₄×C₅₃	C₂³	1	2	yes	—
233	C₄×D₄×C₅₃	C₂³	1	2	yes	—
234	C₄×D₄×C₅₃	C₂³	1	2	yes	—
235	#117×C₅₃	—	2	1	no	—
236	#117×C₅₃	—	2	1	no	—
237	#117×C₅₃	—	2	1	no	—
238	#117×C₅₃	—	2	1	no	—
239	#117×C₅₃	—	2	1	no	—
240	#117×C₅₃	—	2	2	no	—
241	#117×C₅₃	—	2	2	no	—
242	#117×C₅₃	—	2	2	no	—
243	#117×C₅₃	—	2	2	no	—
244	#117×C₅₃	—	2	2	no	—
245	#117×C₅₃	—	2	1	no	—
246	#117×C₅₃	—	2	1	no	—
247	#117×C₅₃	D₄	1	1	yes	characteristic
248	#117×C₅₃	D₄	1	1	yes	characteristic
249	#117×C₅₃	D₄	1	2	yes	—
250	#117×C₅₃	C₂³	1	2	yes	—
251	#117×C₅₃	C₂³	1	2	yes	—
252	#117×C₅₃	C₂³	1	1	yes	characteristic
253	#117×C₅₃	C₂³	1	2	yes	—
254	#117×C₅₃	C₂³	1	1	yes	characteristic
255	#117×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
258	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
259	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
260	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
261	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
270	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
272	C₂×C₄²×C₅₃	—	2	2	no	—
273	C₂×C₄²×C₅₃	—	2	2	no	—
274	C₂×C₄²×C₅₃	—	2	1	no	—
275	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
276	#107×C₅₃	C₂³	1	2	yes	—
277	#107×C₅₃	C₂³	1	2	yes	—
278	#107×C₅₃	C₂³	1	2	yes	—
279	#107×C₅₃	C₂³	1	2	yes	—
280	#106×C₅₃	C₂³	1	2	yes	—
281	#106×C₅₃	C₂³	1	2	yes	—
282	#106×C₅₃	C₂³	1	2	yes	—
283	#106×C₅₃	C₂³	1	2	yes	—
284	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
285	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
287	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	1	yes	characteristic
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	1	yes	characteristic
294	#103×C₅₃	C₂³	1	2	yes	—
295	#103×C₅₃	C₂³	1	2	yes	—
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	2	yes	—
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	2	yes	—
305	#102×C₅₃	C₂³	1	2	yes	—
306	#102×C₅₃	C₂³	1	2	yes	—
307	#102×C₅₃	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
314	#97×C₅₃	C₂³	1	2	yes	—
315	#97×C₅₃	C₂³	1	2	yes	—
316	C₄×C₈×C₅₃	C₂³	1	2	yes	—
317	C₄×C₈×C₅₃	C₂³	1	2	yes	—
318	C₂⁴×C₅₃	—	2	1	no	—
319	C₂⁴×C₅₃	—	2	1	no	—
320	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
321	#41×C₅₃	—	2	8	no	—
322	#41×C₅₃	—	2	8	no	—
323	#41×C₅₃	—	2	2	no	—
324	#41×C₅₃	—	2	2	no	—
325	#41×C₅₃	—	2	2	no	—
326	#41×C₅₃	—	2	2	no	—
327	#41×C₅₃	—	2	2	no	—
328	#41×C₅₃	—	2	2	no	—
329	#41×C₅₃	—	2	2	no	—
330	#41×C₅₃	—	2	2	no	—
331	#41×C₅₃	—	8	4	no	—
332	#41×C₅₃	#41	1	4	yes	complemented
333	#41×C₅₃	#41	1	4	yes	complemented
334	C₂×Q₈×C₅₃	—	2	2	no	—
335	C₂×Q₈×C₅₃	—	2	2	no	—
336	C₂×Q₈×C₅₃	—	2	1	no	—
337	C₂×Q₈×C₅₃	—	2	2	no	—
338	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₅₃	—	2	8	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	—	2	1	no	—
349	C₂×D₄×C₅₃	—	2	1	no	—
350	C₂×D₄×C₅₃	—	2	2	no	—
351	C₂×D₄×C₅₃	—	2	1	no	—
352	C₂×D₄×C₅₃	—	2	2	no	—
353	C₂×D₄×C₅₃	—	2	1	no	—
354	C₂×D₄×C₅₃	—	2	1	no	—
355	C₂×D₄×C₅₃	—	2	2	no	—
356	C₂×D₄×C₅₃	—	2	2	no	—
357	C₂×D₄×C₅₃	—	2	2	no	—
358	C₂×D₄×C₅₃	—	2	2	no	—
359	C₂×D₄×C₅₃	—	8	2	no	—
360	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
361	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₅₃	—	2	8	no	—
365	C₂²×C₄×C₅₃	—	2	1	no	—
366	C₂²×C₄×C₅₃	—	2	1	no	—
367	C₂²×C₄×C₅₃	—	2	1	no	—
368	C₂²×C₄×C₅₃	—	2	1	no	—
369	C₂²×C₄×C₅₃	—	2	1	no	—
370	C₂²×C₄×C₅₃	—	2	2	no	—
371	C₂²×C₄×C₅₃	—	2	2	no	—
372	C₂²×C₄×C₅₃	—	2	1	no	—
373	C₂²×C₄×C₅₃	—	2	1	no	—
374	C₂²×C₄×C₅₃	—	2	1	no	—
375	C₂²×C₄×C₅₃	—	2	1	no	—
376	C₂²×C₄×C₅₃	—	2	2	no	—
377	C₂²×C₄×C₅₃	—	2	2	no	—
378	C₂²×C₄×C₅₃	—	2	2	no	—
379	C₂²×C₄×C₅₃	—	2	2	no	—
380	C₂²×C₄×C₅₃	—	2	2	no	—
381	C₂²×C₄×C₅₃	—	2	2	no	—
382	C₂²×C₄×C₅₃	—	2	2	no	—
383	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
387	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
388	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	Q₁₆×C₅₃	—	2	2	no	—
392	Q₁₆×C₅₃	—	2	2	no	—
393	SD₁₆×C₅₃	—	2	2	no	—
394	SD₁₆×C₅₃	—	2	2	no	—
395	SD₁₆×C₅₃	—	2	4	no	—
396	SD₁₆×C₅₃	—	2	4	no	—
397	SD₁₆×C₅₃	—	2	2	no	—
398	SD₁₆×C₅₃	—	2	2	no	—
399	D₈×C₅₃	—	2	2	no	—
400	D₈×C₅₃	—	2	2	no	—
401	D₈×C₅₃	—	2	4	no	—
402	D₈×C₅₃	—	2	4	no	—
403	M₁₆×C₅₃	—	2	2	no	—
404	M₁₆×C₅₃	—	2	2	no	—
405	C₂×C₈×C₅₃	—	2	2	no	—
406	C₂×C₈×C₅₃	—	2	2	no	—
407	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
410	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
411	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₅₃	—	2	1	no	—
414	C₄⋊C₄×C₅₃	—	2	1	no	—
415	C₄⋊C₄×C₅₃	—	2	1	no	—
416	C₄⋊C₄×C₅₃	—	2	2	no	—
417	C₄⋊C₄×C₅₃	—	2	2	no	—
418	C₄⋊C₄×C₅₃	—	2	2	no	—
419	C₄⋊C₄×C₅₃	—	2	2	no	—
420	C₄⋊C₄×C₅₃	—	2	2	no	—
421	C₄⋊C₄×C₅₃	—	2	1	no	—
422	C₄⋊C₄×C₅₃	—	2	2	no	—
423	C₄⋊C₄×C₅₃	—	2	2	no	—
424	C₄⋊C₄×C₅₃	—	2	2	no	—
425	C₄⋊C₄×C₅₃	—	2	1	no	—
426	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
427	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
428	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
429	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
430	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
431	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
432	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
433	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
434	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
435	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
437	C₂²⋊C₄×C₅₃	—	2	2	no	—
438	C₂²⋊C₄×C₅₃	—	2	1	no	—
439	C₂²⋊C₄×C₅₃	—	2	2	no	—
440	C₂²⋊C₄×C₅₃	—	2	1	no	—
441	C₂²⋊C₄×C₅₃	—	2	1	no	—
442	C₂²⋊C₄×C₅₃	—	2	2	no	—
443	C₂²⋊C₄×C₅₃	—	2	2	no	—
444	C₂²⋊C₄×C₅₃	—	2	2	no	—
445	C₂²⋊C₄×C₅₃	—	2	2	no	—
446	C₂²⋊C₄×C₅₃	—	2	2	no	—
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	—	2	2	no	—
449	C₂²⋊C₄×C₅₃	—	2	2	no	—
450	C₂²⋊C₄×C₅₃	—	2	2	no	—
451	C₂²⋊C₄×C₅₃	—	2	2	no	—
452	C₂²⋊C₄×C₅₃	—	2	1	no	—
453	C₂²⋊C₄×C₅₃	—	2	2	no	—
454	C₂²⋊C₄×C₅₃	—	2	1	no	—
455	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
456	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
457	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
458	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
459	C₄²×C₅₃	—	2	2	no	—
460	C₄²×C₅₃	—	2	2	no	—
461	C₄²×C₅₃	—	2	2	no	—
462	C₄²×C₅₃	—	2	2	no	—
463	C₄²×C₅₃	—	2	2	no	—
464	C₄²×C₅₃	—	2	2	no	—
465	C₄²×C₅₃	—	2	2	no	—
466	C₄²×C₅₃	—	2	1	no	—
467	C₄²×C₅₃	C₂×D₄	1	2	yes	—
468	C₄²×C₅₃	C₂×D₄	1	2	yes	—
469	C₄²×C₅₃	C₂⁴	1	2	yes	—
470	C₄²×C₅₃	C₂⁴	1	2	yes	—
471	C₂³×C₅₃	—	2	4	no	—
472	C₂³×C₅₃	—	2	1	no	—
473	C₂³×C₅₃	—	2	1	no	—
474	C₂³×C₅₃	—	2	2	no	—
475	C₂³×C₅₃	—	2	1	no	—
476	C₂³×C₅₃	—	2	2	no	—
477	C₂³×C₅₃	—	4	1	no	—
478	C₂³×C₅₃	—	4	1	no	—
479	C₂³×C₅₃	—	4	2	no	—
480	C₂³×C₅₃	—	8	1	no	—
481	C₂³×C₅₃	—	8	1	no	—
482	C₂³×C₅₃	—	8	1	no	—
483	C₂³×C₅₃	—	8	1	no	—
484	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
485	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
486	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
487	Q₈×C₅₃	—	2	4	no	—
488	Q₈×C₅₃	—	2	1	no	—
489	Q₈×C₅₃	—	2	1	no	—
490	Q₈×C₅₃	—	2	1	no	—
491	Q₈×C₅₃	—	2	1	no	—
492	Q₈×C₅₃	—	8	2	no	—
493	Q₈×C₅₃	C₂×#41	1	2	yes	—
494	Q₈×C₅₃	C₂×#41	1	2	yes	—
495	D₄×C₅₃	—	2	4	no	—
496	D₄×C₅₃	—	2	4	no	—
497	D₄×C₅₃	—	2	4	no	—
498	D₄×C₅₃	—	2	4	no	—
499	D₄×C₅₃	—	2	4	no	—
500	D₄×C₅₃	—	2	1	no	—
501	D₄×C₅₃	—	2	1	no	—
502	D₄×C₅₃	—	2	2	no	—
503	D₄×C₅₃	—	2	2	no	—
504	D₄×C₅₃	—	2	1	no	—
505	D₄×C₅₃	—	2	1	no	—
506	D₄×C₅₃	—	4	4	no	—
507	D₄×C₅₃	—	4	2	no	—
508	D₄×C₅₃	—	4	2	no	—
509	D₄×C₅₃	—	4	2	no	—
510	D₄×C₅₃	—	8	2	no	—
511	D₄×C₅₃	—	8	2	no	—
512	D₄×C₅₃	—	8	1	no	—
513	D₄×C₅₃	—	8	2	no	—
514	D₄×C₅₃	C₂×#41	1	2	yes	—
515	D₄×C₅₃	C₂×#41	1	2	yes	—
516	C₂×C₄×C₅₃	—	2	4	no	—
517	C₂×C₄×C₅₃	—	2	4	no	—
518	C₂×C₄×C₅₃	—	2	4	no	—
519	C₂×C₄×C₅₃	—	2	2	no	—
520	C₂×C₄×C₅₃	—	2	1	no	—
521	C₂×C₄×C₅₃	—	2	1	no	—
522	C₂×C₄×C₅₃	—	2	2	no	—
523	C₂×C₄×C₅₃	—	2	4	no	—
524	C₂×C₄×C₅₃	—	2	4	no	—
525	C₂×C₄×C₅₃	—	2	2	no	—
526	C₂×C₄×C₅₃	—	2	1	no	—
527	C₂×C₄×C₅₃	—	2	1	no	—
528	C₂×C₄×C₅₃	—	2	1	no	—
529	C₂×C₄×C₅₃	—	2	1	no	—
530	C₂×C₄×C₅₃	—	2	2	no	—
531	C₂×C₄×C₅₃	—	2	2	no	—
532	C₂×C₄×C₅₃	—	2	2	no	—
533	C₂×C₄×C₅₃	—	2	1	no	—
534	C₂×C₄×C₅₃	—	2	1	no	—
535	C₂×C₄×C₅₃	—	2	1	no	—
536	C₂×C₄×C₅₃	—	4	2	no	—
537	C₂×C₄×C₅₃	—	4	2	no	—
538	C₂×C₄×C₅₃	—	4	2	no	—
539	C₂×C₄×C₅₃	—	8	2	no	—
540	C₂×C₄×C₅₃	—	8	2	no	—
541	C₂×C₄×C₅₃	—	8	2	no	—
542	C₂×C₄×C₅₃	—	8	2	no	—
543	C₂×C₄×C₅₃	—	8	2	no	—
544	C₂×C₄×C₅₃	—	8	2	no	—
545	C₂×C₄×C₅₃	—	8	2	no	—
546	C₂×C₄×C₅₃	—	8	1	no	—
547	C₂×C₄×C₅₃	—	8	1	no	—
548	C₂×C₄×C₅₃	—	8	1	no	—
549	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
552	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
553	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
554	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
557	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
558	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
559	C₈×C₅₃	—	2	1	no	—
560	C₈×C₅₃	—	2	1	no	—
561	C₈×C₅₃	—	2	1	no	—
562	C₈×C₅₃	—	2	1	no	—
563	C₈×C₅₃	—	2	2	no	—
564	C₈×C₅₃	—	2	2	no	—
565	#60587	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
566	C₂²×C₅₃	—	2	1	no	—
567	C₂²×C₅₃	—	2	1	no	—
568	C₂²×C₅₃	—	2	1	no	—
569	C₂²×C₅₃	—	2	1	no	—
570	C₂²×C₅₃	—	2	1	no	—
571	C₂²×C₅₃	—	2	1	no	—
572	C₂²×C₅₃	—	2	1	no	—
573	C₂²×C₅₃	—	2	1	no	—
574	C₂²×C₅₃	—	2	2	no	—
575	C₂²×C₅₃	—	2	2	no	—
576	C₂²×C₅₃	—	4	1	no	—
577	C₂²×C₅₃	—	4	1	no	—
578	C₂²×C₅₃	—	4	1	no	—
579	C₂²×C₅₃	—	4	1	no	—
580	C₂²×C₅₃	—	4	2	no	—
581	C₂²×C₅₃	—	4	1	no	—
582	C₂²×C₅₃	—	4	1	no	—
583	C₂²×C₅₃	—	4	2	no	—
584	C₂²×C₅₃	—	4	1	no	—
585	C₂²×C₅₃	—	4	2	no	—
586	C₂²×C₅₃	—	8	2	no	—
587	C₂²×C₅₃	—	8	4	no	—
588	C₂²×C₅₃	—	16	2	no	—
589	C₂²×C₅₃	#525	1	2	yes	—
590	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
591	C₄×C₅₃	—	2	2	no	—
592	C₄×C₅₃	—	2	2	no	—
593	C₄×C₅₃	—	2	2	no	—
594	C₄×C₅₃	—	2	2	no	—
595	C₄×C₅₃	—	2	1	no	—
596	C₄×C₅₃	—	2	2	no	—
597	C₄×C₅₃	—	2	2	no	—
598	C₄×C₅₃	—	2	1	no	—
599	C₄×C₅₃	—	4	2	no	—
600	C₄×C₅₃	—	4	1	no	—
601	C₄×C₅₃	—	4	2	no	—
602	C₄×C₅₃	—	4	2	no	—
603	C₄×C₅₃	—	4	1	no	—
604	C₄×C₅₃	—	4	1	no	—
605	C₄×C₅₃	#525	1	2	yes	—
606	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
607	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
608	#3494	C₂×C₅₃	1	1	yes	characteristic, complemented
609	#3428	C₂×C₅₃	1	1	yes	characteristic, complemented
610	#3126	C₂×C₅₃	1	2	yes	complemented
611	#3122	C₂×C₅₃	1	2	yes	complemented
612	#3121	C₂×C₅₃	1	2	yes	complemented
613	#3118	C₂×C₅₃	1	2	yes	complemented
614	#3115	C₂×C₅₃	1	2	yes	complemented
615	#3111	C₂×C₅₃	1	2	yes	complemented
616	#3106	C₂×C₅₃	1	2	yes	complemented
617	#3102	C₂×C₅₃	1	2	yes	complemented
618	#3093	C₂×C₅₃	1	1	yes	characteristic, complemented
619	C₂×#482	C₂×C₅₃	1	1	yes	characteristic, complemented
620	#3084	C₂×C₅₃	1	1	yes	characteristic, complemented
621	#3083	C₂×C₅₃	1	1	yes	characteristic, complemented
622	#3045	C₂×C₅₃	1	1	yes	characteristic, complemented
623	#3045	C₂×C₅₃	1	1	yes	characteristic, complemented
624	#3006	C₂×C₅₃	1	1	yes	characteristic, complemented
625	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
626	#2952	C₂×C₅₃	1	1	yes	characteristic, complemented
627	#2951	C₂×C₅₃	1	1	yes	characteristic, complemented
628	#2946	C₂×C₅₃	1	1	yes	characteristic, complemented
629	#2946	C₂×C₅₃	1	1	yes	characteristic, complemented
630	#2924	C₂×C₅₃	1	1	yes	characteristic, complemented
631	C₂×C₅₃	—	2	2	no	—
632	C₂×C₅₃	—	4	1	no	—
633	C₂×C₅₃	—	4	1	no	—
634	C₂×C₅₃	—	4	2	no	—
635	C₂×C₅₃	—	4	2	no	—
636	C₂×C₅₃	—	8	1	no	—
637	C₂×C₅₃	—	8	2	no	—
638	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
639	C₂×C₅₃	#3584	1	1	yes	characteristic
640	C₂×C₅₃	#3585	1	1	yes	characteristic
641	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
642	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
643	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
644	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
645	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
646	#555	—	2	1	no	—
647	#553	—	2	1	no	—
648	#553	—	2	1	no	—
649	#551	—	2	2	no	—
650	#547	—	2	1	no	—
651	#546	—	2	2	no	—
652	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
653	#542	C₂²×C₅₃	1	2	yes	—
654	#540	C₂²×C₅₃	1	2	yes	—
655	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	#532	C₂²×C₅₃	1	2	yes	complemented
657	#529	C₂²×C₅₃	1	2	yes	complemented
658	#525	C₂²×C₅₃	1	1	yes	characteristic
659	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
660	#520	—	2	1	no	—
661	#520	—	2	1	no	—
662	#520	C₂²×C₅₃	1	1	yes	characteristic
663	#520	C₂²×C₅₃	1	1	yes	characteristic
664	#520	C₂²×C₅₃	1	1	yes	characteristic
665	#520	C₂²×C₅₃	1	1	yes	characteristic
666	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
667	#519	C₂²×C₅₃	1	2	yes	complemented
668	#518	—	2	2	no	—
669	#518	C₂²×C₅₃	1	2	yes	complemented
670	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
671	C₄×#41	—	2	2	no	—
672	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
673	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
674	C₂×#117	—	2	1	no	—
675	C₂×#117	—	2	1	no	—
676	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
677	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
678	#485	C₂²×C₅₃	1	2	yes	complemented
679	#485	C₂²×C₅₃	1	2	yes	complemented
680	#482	C₂²×C₅₃	1	2	yes	—
681	#482	C₂²×C₅₃	1	2	yes	—
682	#482	C₂²×C₅₃	1	2	yes	complemented
683	#482	C₂²×C₅₃	1	2	yes	complemented
684	#482	C₂²×C₅₃	1	2	yes	complemented
685	#482	C₂²×C₅₃	1	2	yes	complemented
686	#479	C₂²×C₅₃	1	2	yes	complemented
687	#479	C₂²×C₅₃	1	2	yes	complemented
688	#478	C₂²×C₅₃	1	2	yes	complemented
689	#478	C₂²×C₅₃	1	2	yes	complemented
690	#477	C₂²×C₅₃	1	2	yes	complemented
691	#476	C₂²×C₅₃	1	2	yes	complemented
692	#475	C₂²×C₅₃	1	2	yes	complemented
693	#474	C₂²×C₅₃	1	2	yes	complemented
694	#464	C₂²×C₅₃	1	2	yes	complemented
695	#464	C₂²×C₅₃	1	2	yes	complemented
696	#463	C₂²×C₅₃	1	2	yes	complemented
697	#463	C₂²×C₅₃	1	2	yes	complemented
698	#460	C₂²×C₅₃	1	2	yes	complemented
699	#460	C₂²×C₅₃	1	2	yes	complemented
700	#459	C₂²×C₅₃	1	2	yes	complemented
701	#459	C₂²×C₅₃	1	2	yes	complemented
702	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
704	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
705	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
706	#449	C₂²×C₅₃	1	2	yes	—
707	#449	C₂²×C₅₃	1	2	yes	—
708	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
710	#448	C₂²×C₅₃	1	2	yes	—
711	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	#447	C₂²×C₅₃	1	2	yes	—
713	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
714	#442	C₂²×C₅₃	1	2	yes	complemented
715	#442	C₂²×C₅₃	1	2	yes	complemented
716	#442	C₂²×C₅₃	1	2	yes	complemented
717	#441	C₂²×C₅₃	1	2	yes	complemented
718	#440	C₂²×C₅₃	1	2	yes	complemented
719	#440	C₂²×C₅₃	1	2	yes	complemented
720	#440	C₂²×C₅₃	1	2	yes	complemented
721	#440	C₂²×C₅₃	1	2	yes	complemented
722	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
723	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
724	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
725	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
726	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
727	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
728	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
729	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
730	#433	C₂²×C₅₃	1	2	yes	complemented
731	#433	C₂²×C₅₃	1	2	yes	complemented
732	#432	C₂²×C₅₃	1	2	yes	complemented
733	#431	C₂²×C₅₃	1	2	yes	complemented
734	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
735	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
736	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
737	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
738	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
739	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
740	#417	C₂²×C₅₃	1	1	yes	characteristic
741	#417	C₂²×C₅₃	1	1	yes	characteristic
742	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
743	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
744	#416	C₂²×C₅₃	1	1	yes	characteristic
745	#416	C₂²×C₅₃	1	1	yes	characteristic
746	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
747	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
748	#407	C₂²×C₅₃	1	1	yes	characteristic
749	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
750	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
751	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
752	C₅₃	#60587	1	1	yes	characteristic, direct product factor, Sylow
753	C₂×#41	—	2	4	no	—
754	C₂×#41	—	2	4	no	—
755	C₂×#41	—	2	1	no	—
756	C₂×#41	—	2	1	no	—
757	C₂×#41	—	2	2	no	—
758	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
759	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
760	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
761	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
762	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
763	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
764	C₂²×D₄	—	2	1	no	—
765	C₂²×D₄	—	2	1	no	—
766	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
767	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
768	C₂³×C₄	—	2	1	no	—
769	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
770	AGL(1,ℤ/8)	—	2	4	no	—
771	AGL(1,ℤ/8)	—	2	4	no	—
772	#135	—	2	4	no	—
773	#135	—	2	4	no	—
774	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
775	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
776	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
777	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
778	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
779	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
780	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
781	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
782	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
783	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
784	C₂×D₈	C₂³×C₅₃	1	2	yes	—
785	C₂×D₈	C₂³×C₅₃	1	2	yes	—
786	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
787	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
788	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
789	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
790	C₄⋊Q₈	—	2	1	no	—
791	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
792	#127	C₂³×C₅₃	1	2	yes	—
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#125	—	2	1	no	—
796	#125	C₂³×C₅₃	1	2	yes	—
797	#124	—	2	2	no	—
798	#124	—	2	2	no	—
799	#124	C₂³×C₅₃	1	2	yes	—
800	#123	—	2	1	no	—
801	#123	—	2	2	no	—
802	#123	—	2	2	no	—
803	#123	—	2	2	no	—
804	#123	—	2	2	no	—
805	C₂²⋊Q₈	—	2	2	no	—
806	C₂²⋊Q₈	—	2	2	no	—
807	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
808	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
809	#121	—	2	1	no	—
810	#121	—	2	1	no	—
811	#121	—	2	2	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	C₂³×C₅₃	1	2	yes	—
817	#121	C₂³×C₅₃	1	2	yes	—
818	#121	C₂³×C₅₃	1	1	yes	characteristic
819	#121	C₂³×C₅₃	1	1	yes	characteristic
820	#120	—	2	1	no	—
821	#120	—	2	2	no	—
822	C₄×Q₈	—	2	2	no	—
823	C₄×Q₈	—	2	2	no	—
824	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
825	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
826	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
827	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
828	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	—	2	2	no	—
842	C₄×D₄	—	2	2	no	—
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	—	2	2	no	—
846	C₄×D₄	C₂³×C₅₃	1	2	yes	—
847	C₄×D₄	C₂³×C₅₃	1	2	yes	—
848	C₄×D₄	C₂³×C₅₃	1	2	yes	—
849	C₄×D₄	C₂³×C₅₃	1	2	yes	—
850	C₄×D₄	C₂³×C₅₃	1	2	yes	—
851	C₄×D₄	C₂³×C₅₃	1	2	yes	—
852	C₄×D₄	C₂³×C₅₃	1	2	yes	—
853	#117	—	2	1	no	—
854	#117	—	2	1	no	—
855	#117	—	2	1	no	—
856	#117	—	2	1	no	—
857	#117	—	2	1	no	—
858	#117	—	2	1	no	—
859	#117	—	2	1	no	—
860	#117	—	2	2	no	—
861	#117	—	2	2	no	—
862	#117	—	2	2	no	—
863	#117	—	2	2	no	—
864	#117	—	2	2	no	—
865	#117	D₄×C₅₃	1	1	yes	characteristic
866	#117	D₄×C₅₃	1	1	yes	characteristic
867	#117	D₄×C₅₃	1	2	yes	—
868	#117	C₂³×C₅₃	1	2	yes	—
869	#117	C₂³×C₅₃	1	2	yes	—
870	#117	C₂³×C₅₃	1	1	yes	characteristic
871	#117	C₂³×C₅₃	1	2	yes	—
872	#117	C₂³×C₅₃	1	1	yes	characteristic
873	#117	C₂³×C₅₃	1	1	yes	characteristic
874	C₂×C₄⋊C₄	—	2	1	no	—
875	C₂×C₄⋊C₄	—	2	1	no	—
876	C₂×C₄⋊C₄	—	2	1	no	—
877	C₂×C₄⋊C₄	—	2	1	no	—
878	C₂×C₄⋊C₄	—	2	1	no	—
879	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
880	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
884	C₂×C₂²⋊C₄	—	2	1	no	—
885	C₂×C₂²⋊C₄	—	2	1	no	—
886	C₂×C₂²⋊C₄	—	2	2	no	—
887	C₂×C₂²⋊C₄	—	2	2	no	—
888	C₂×C₂²⋊C₄	—	2	2	no	—
889	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
890	C₂×C₄²	—	2	1	no	—
891	C₂×C₄²	—	2	2	no	—
892	C₂×C₄²	—	2	2	no	—
893	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
894	#107	C₂³×C₅₃	1	2	yes	—
895	#107	C₂³×C₅₃	1	2	yes	—
896	#107	C₂³×C₅₃	1	2	yes	—
897	#107	C₂³×C₅₃	1	2	yes	—
898	#106	C₂³×C₅₃	1	2	yes	—
899	#106	C₂³×C₅₃	1	2	yes	—
900	#106	C₂³×C₅₃	1	2	yes	—
901	#106	C₂³×C₅₃	1	2	yes	—
902	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
903	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
904	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
905	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
906	#103	C₂³×C₅₃	1	1	yes	characteristic
907	#103	C₂³×C₅₃	1	1	yes	characteristic
908	#103	C₂³×C₅₃	1	1	yes	characteristic
909	#103	C₂³×C₅₃	1	1	yes	characteristic
910	#103	C₂³×C₅₃	1	2	yes	—
911	#103	C₂³×C₅₃	1	2	yes	—
912	#103	C₂³×C₅₃	1	2	yes	—
913	#103	C₂³×C₅₃	1	2	yes	—
914	#102	C₂³×C₅₃	1	2	yes	—
915	#102	C₂³×C₅₃	1	2	yes	—
916	#102	C₂³×C₅₃	1	2	yes	—
917	#102	C₂³×C₅₃	1	2	yes	—
918	#102	C₂³×C₅₃	1	1	yes	characteristic
919	#102	C₂³×C₅₃	1	1	yes	characteristic
920	#102	C₂³×C₅₃	1	1	yes	characteristic
921	#102	C₂³×C₅₃	1	1	yes	characteristic
922	#102	C₂³×C₅₃	1	2	yes	—
923	#102	C₂³×C₅₃	1	2	yes	—
924	#102	C₂³×C₅₃	1	2	yes	—
925	#102	C₂³×C₅₃	1	2	yes	—
926	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
927	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
928	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
929	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
930	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
931	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
932	#97	C₂³×C₅₃	1	2	yes	—
933	#97	C₂³×C₅₃	1	2	yes	—
934	C₄×C₈	C₂³×C₅₃	1	2	yes	—
935	C₄×C₈	C₂³×C₅₃	1	2	yes	—
936	C₂⁴	—	2	1	no	—
937	C₂⁴	—	2	1	no	—
938	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
939	#41	—	2	8	no	—
940	#41	—	2	8	no	—
941	#41	—	2	2	no	—
942	#41	—	2	2	no	—
943	#41	—	2	2	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	2	2	no	—
947	#41	—	2	2	no	—
948	#41	—	2	2	no	—
949	#41	—	8	4	no	—
950	#41	#41×C₅₃	1	4	yes	complemented
951	#41	#41×C₅₃	1	4	yes	complemented
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	2	no	—
954	C₂×Q₈	—	2	1	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
957	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
958	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
959	C₂×D₄	—	2	8	no	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	1	no	—
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	1	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	8	2	no	—
978	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
979	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
980	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
981	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
982	C₂²×C₄	—	2	8	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	1	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1002	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1003	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1004	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1005	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1006	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1007	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1008	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1009	Q₁₆	—	2	2	no	—
1010	Q₁₆	—	2	2	no	—
1011	SD₁₆	—	2	2	no	—
1012	SD₁₆	—	2	2	no	—
1013	SD₁₆	—	2	4	no	—
1014	SD₁₆	—	2	4	no	—
1015	SD₁₆	—	2	2	no	—
1016	SD₁₆	—	2	2	no	—
1017	D₈	—	2	2	no	—
1018	D₈	—	2	2	no	—
1019	D₈	—	2	4	no	—
1020	D₈	—	2	4	no	—
1021	M₁₆	—	2	2	no	—
1022	M₁₆	—	2	2	no	—
1023	C₂×C₈	—	2	2	no	—
1024	C₂×C₈	—	2	2	no	—
1025	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1026	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1027	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1028	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1029	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1030	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1045	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1046	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1047	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1048	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1049	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1050	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1052	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1053	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1054	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1074	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1077	C₄²	—	2	2	no	—
1078	C₄²	—	2	2	no	—
1079	C₄²	—	2	2	no	—
1080	C₄²	—	2	2	no	—
1081	C₄²	—	2	2	no	—
1082	C₄²	—	2	2	no	—
1083	C₄²	—	2	2	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1086	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1087	C₄²	C₂⁴×C₅₃	1	2	yes	—
1088	C₄²	C₂⁴×C₅₃	1	2	yes	—
1089	C₂³	—	2	4	no	—
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	2	2	no	—
1094	C₂³	—	2	1	no	—
1095	C₂³	—	4	1	no	—
1096	C₂³	—	4	1	no	—
1097	C₂³	—	4	2	no	—
1098	C₂³	—	8	1	no	—
1099	C₂³	—	8	1	no	—
1100	C₂³	—	8	1	no	—
1101	C₂³	—	8	1	no	—
1102	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1103	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1104	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1105	Q₈	—	2	4	no	—
1106	Q₈	—	2	1	no	—
1107	Q₈	—	2	1	no	—
1108	Q₈	—	2	1	no	—
1109	Q₈	—	2	1	no	—
1110	Q₈	—	8	2	no	—
1111	Q₈	C₂×#41×C₅₃	1	2	yes	—
1112	Q₈	C₂×#41×C₅₃	1	2	yes	—
1113	D₄	—	2	4	no	—
1114	D₄	—	2	4	no	—
1115	D₄	—	2	4	no	—
1116	D₄	—	2	4	no	—
1117	D₄	—	2	4	no	—
1118	D₄	—	2	1	no	—
1119	D₄	—	2	1	no	—
1120	D₄	—	2	2	no	—
1121	D₄	—	2	2	no	—
1122	D₄	—	2	1	no	—
1123	D₄	—	2	1	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	8	2	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	1	no	—
1131	D₄	—	8	2	no	—
1132	D₄	C₂×#41×C₅₃	1	2	yes	—
1133	D₄	C₂×#41×C₅₃	1	2	yes	—
1134	C₂×C₄	—	2	4	no	—
1135	C₂×C₄	—	2	4	no	—
1136	C₂×C₄	—	2	4	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	4	no	—
1142	C₂×C₄	—	2	4	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	4	2	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	8	2	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	2	no	—
1161	C₂×C₄	—	8	2	no	—
1162	C₂×C₄	—	8	2	no	—
1163	C₂×C₄	—	8	2	no	—
1164	C₂×C₄	—	8	1	no	—
1165	C₂×C₄	—	8	1	no	—
1166	C₂×C₄	—	8	1	no	—
1167	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1168	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1169	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1170	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1171	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1172	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1173	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1174	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1175	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1176	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1177	C₈	—	2	1	no	—
1178	C₈	—	2	1	no	—
1179	C₈	—	2	1	no	—
1180	C₈	—	2	1	no	—
1181	C₈	—	2	2	no	—
1182	C₈	—	2	2	no	—
1183	C₂²	—	2	1	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	1	no	—
1186	C₂²	—	2	1	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	1	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	2	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	2	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	2	no	—
1203	C₂²	—	8	2	no	—
1204	C₂²	—	8	4	no	—
1205	C₂²	—	16	2	no	—
1206	C₂²	C₅₃×#525	1	2	yes	—
1207	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1208	C₄	—	2	2	no	—
1209	C₄	—	2	2	no	—
1210	C₄	—	2	2	no	—
1211	C₄	—	2	2	no	—
1212	C₄	—	2	1	no	—
1213	C₄	—	2	2	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	2	1	no	—
1216	C₄	—	4	2	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	4	2	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	1	no	—
1222	C₄	C₅₃×#525	1	2	yes	—
1223	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1224	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1225	C₂	—	2	2	no	—
1226	C₂	—	4	1	no	—
1227	C₂	—	4	1	no	—
1228	C₂	—	4	2	no	—
1229	C₂	—	4	2	no	—
1230	C₂	—	8	2	no	—
1231	C₂	—	8	1	no	—
1232	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
1233	C₂	C₅₃×#3584	1	1	yes	characteristic
1234	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 ◁ C₂×#117×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3494	C₂	semidirect
2. C₅₃×#3428	C₂	semidirect
3. C₅₃×#3126	C₂	semidirect
4. C₅₃×#3122	C₂	semidirect
5. C₅₃×#3121	C₂	semidirect
6. C₅₃×#3118	C₂	semidirect
7. C₅₃×#3115	C₂	semidirect
8. C₅₃×#3111	C₂	semidirect
9. C₅₃×#3106	C₂	semidirect
10. C₅₃×#3102	C₂	semidirect
11. C₅₃×#3093	C₂	semidirect
12. C₂×C₅₃×#482	C₂	semidirect
13. C₅₃×#3084	C₂	semidirect
14. C₅₃×#3083	C₂	semidirect
15. C₅₃×#3045	C₂	semidirect
16. C₅₃×#3045	C₂	semidirect
17. C₅₃×#3006	C₂	semidirect
18. C₅₃×#3002	C₂	semidirect
19. C₅₃×#2952	C₂	semidirect
20. C₅₃×#2951	C₂	semidirect
21. C₅₃×#2946	C₂	semidirect
22. C₅₃×#2946	C₂	semidirect
23. C₅₃×#2924	C₂	semidirect
35. C₅₃×#544	C₂²	semidirect
38. C₅₃×#535	C₂²	semidirect
39. C₅₃×#532	C₂²	semidirect
40. C₅₃×#529	C₂²	semidirect
49. C₅₃×#520	C₂²	semidirect
50. C₅₃×#519	C₂²	semidirect
52. C₅₃×#518	C₂²	semidirect
53. C₅₃×#518	C₂²	semidirect
55. C₄×#41×C₅₃	C₂²	semidirect
56. C₄×#41×C₅₃	C₂²	semidirect
61. C₅₃×#485	C₂²	semidirect
62. C₅₃×#485	C₂²	semidirect
65. C₅₃×#482	C₂²	semidirect
66. C₅₃×#482	C₂²	semidirect
67. C₅₃×#482	C₂²	semidirect
68. C₅₃×#482	C₂²	semidirect
69. C₅₃×#479	C₂²	semidirect
70. C₅₃×#479	C₂²	semidirect
71. C₅₃×#478	C₂²	semidirect
72. C₅₃×#478	C₂²	semidirect
73. C₅₃×#477	C₂²	semidirect
74. C₅₃×#476	C₂²	semidirect
75. C₅₃×#475	C₂²	semidirect
76. C₅₃×#474	C₂²	semidirect
77. C₅₃×#464	C₂²	semidirect
78. C₅₃×#464	C₂²	semidirect
79. C₅₃×#463	C₂²	semidirect
80. C₅₃×#463	C₂²	semidirect
81. C₅₃×#460	C₂²	semidirect
82. C₅₃×#460	C₂²	semidirect
83. C₅₃×#459	C₂²	semidirect
84. C₅₃×#459	C₂²	semidirect
85. C₅₃×#452	C₂²	semidirect
86. C₅₃×#452	C₂²	semidirect
87. C₅₃×#451	C₂²	semidirect
88. C₅₃×#450	C₂²	semidirect
91. C₅₃×#449	C₂²	semidirect
92. C₅₃×#449	C₂²	semidirect
94. C₅₃×#448	C₂²	semidirect
96. C₅₃×#447	C₂²	semidirect
97. C₅₃×#442	C₂²	semidirect
98. C₅₃×#442	C₂²	semidirect
99. C₅₃×#442	C₂²	semidirect
100. C₅₃×#441	C₂²	semidirect
101. C₅₃×#440	C₂²	semidirect
102. C₅₃×#440	C₂²	semidirect
103. C₅₃×#440	C₂²	semidirect
104. C₅₃×#440	C₂²	semidirect
105. C₄×Q₁₆×C₅₃	C₂²	semidirect
106. C₄×SD₁₆×C₅₃	C₂²	semidirect
107. C₄×SD₁₆×C₅₃	C₂²	semidirect
108. C₄×SD₁₆×C₅₃	C₂²	semidirect
109. C₄×SD₁₆×C₅₃	C₂²	semidirect
110. C₄×D₈×C₅₃	C₂²	semidirect
111. C₄×D₈×C₅₃	C₂²	semidirect
112. C₄×D₈×C₅₃	C₂²	semidirect
113. C₅₃×#433	C₂²	semidirect
114. C₅₃×#433	C₂²	semidirect
115. C₅₃×#432	C₂²	semidirect
116. C₅₃×#431	C₂²	semidirect
117. C₅₃×#428	C₂²	semidirect
118. C₅₃×#428	C₂²	semidirect
119. C₂×#107×C₅₃	C₂²	semidirect
120. C₂×#106×C₅₃	C₂²	semidirect
121. C₅₃×#424	C₂²	semidirect
122. C₅₃×#424	C₂²	semidirect
125. C₅₃×#417	C₂²	semidirect
126. C₅₃×#417	C₂²	semidirect
129. C₂×#102×C₅₃	C₂²	semidirect
130. C₂×#102×C₅₃	C₂²	semidirect
133. C₅₃×#405	C₂²	semidirect
134. C₅₃×#405	C₂²	semidirect
332. #41×C₅₃	#41	semidirect
333. #41×C₅₃	#41	semidirect
565. #60587	C₅₃	direct (N × H)
608. #3494	C₂×C₅₃	semidirect
609. #3428	C₂×C₅₃	semidirect
610. #3126	C₂×C₅₃	semidirect
611. #3122	C₂×C₅₃	semidirect
612. #3121	C₂×C₅₃	semidirect
613. #3118	C₂×C₅₃	semidirect
614. #3115	C₂×C₅₃	semidirect
615. #3111	C₂×C₅₃	semidirect
616. #3106	C₂×C₅₃	semidirect
617. #3102	C₂×C₅₃	semidirect
618. #3093	C₂×C₅₃	semidirect
619. C₂×#482	C₂×C₅₃	semidirect
620. #3084	C₂×C₅₃	semidirect
621. #3083	C₂×C₅₃	semidirect
622. #3045	C₂×C₅₃	semidirect
623. #3045	C₂×C₅₃	semidirect
624. #3006	C₂×C₅₃	semidirect
625. #3002	C₂×C₅₃	semidirect
626. #2952	C₂×C₅₃	semidirect
627. #2951	C₂×C₅₃	semidirect
628. #2946	C₂×C₅₃	semidirect
629. #2946	C₂×C₅₃	semidirect
630. #2924	C₂×C₅₃	semidirect
652. #544	C₂²×C₅₃	semidirect
655. #535	C₂²×C₅₃	semidirect
656. #532	C₂²×C₅₃	semidirect
657. #529	C₂²×C₅₃	semidirect
666. #520	C₂²×C₅₃	semidirect
667. #519	C₂²×C₅₃	semidirect
669. #518	C₂²×C₅₃	semidirect
670. #518	C₂²×C₅₃	semidirect
672. C₄×#41	C₂²×C₅₃	semidirect
673. C₄×#41	C₂²×C₅₃	semidirect
678. #485	C₂²×C₅₃	semidirect
679. #485	C₂²×C₅₃	semidirect
682. #482	C₂²×C₅₃	semidirect
683. #482	C₂²×C₅₃	semidirect
684. #482	C₂²×C₅₃	semidirect
685. #482	C₂²×C₅₃	semidirect
686. #479	C₂²×C₅₃	semidirect
687. #479	C₂²×C₅₃	semidirect
688. #478	C₂²×C₅₃	semidirect
689. #478	C₂²×C₅₃	semidirect
690. #477	C₂²×C₅₃	semidirect
691. #476	C₂²×C₅₃	semidirect
692. #475	C₂²×C₅₃	semidirect
693. #474	C₂²×C₅₃	semidirect
694. #464	C₂²×C₅₃	semidirect
695. #464	C₂²×C₅₃	semidirect
696. #463	C₂²×C₅₃	semidirect
697. #463	C₂²×C₅₃	semidirect
698. #460	C₂²×C₅₃	semidirect
699. #460	C₂²×C₅₃	semidirect
700. #459	C₂²×C₅₃	semidirect
701. #459	C₂²×C₅₃	semidirect
702. #452	C₂²×C₅₃	semidirect
703. #452	C₂²×C₅₃	semidirect
704. #451	C₂²×C₅₃	semidirect
705. #450	C₂²×C₅₃	semidirect
708. #449	C₂²×C₅₃	semidirect
709. #449	C₂²×C₅₃	semidirect
711. #448	C₂²×C₅₃	semidirect
713. #447	C₂²×C₅₃	semidirect
714. #442	C₂²×C₅₃	semidirect
715. #442	C₂²×C₅₃	semidirect
716. #442	C₂²×C₅₃	semidirect
717. #441	C₂²×C₅₃	semidirect
718. #440	C₂²×C₅₃	semidirect
719. #440	C₂²×C₅₃	semidirect
720. #440	C₂²×C₅₃	semidirect
721. #440	C₂²×C₅₃	semidirect
722. C₄×Q₁₆	C₂²×C₅₃	semidirect
723. C₄×SD₁₆	C₂²×C₅₃	semidirect
724. C₄×SD₁₆	C₂²×C₅₃	semidirect
725. C₄×SD₁₆	C₂²×C₅₃	semidirect
726. C₄×SD₁₆	C₂²×C₅₃	semidirect
727. C₄×D₈	C₂²×C₅₃	semidirect
728. C₄×D₈	C₂²×C₅₃	semidirect
729. C₄×D₈	C₂²×C₅₃	semidirect
730. #433	C₂²×C₅₃	semidirect
731. #433	C₂²×C₅₃	semidirect
732. #432	C₂²×C₅₃	semidirect
733. #431	C₂²×C₅₃	semidirect
734. #428	C₂²×C₅₃	semidirect
735. #428	C₂²×C₅₃	semidirect
736. C₂×#107	C₂²×C₅₃	semidirect
737. C₂×#106	C₂²×C₅₃	semidirect
738. #424	C₂²×C₅₃	semidirect
739. #424	C₂²×C₅₃	semidirect
742. #417	C₂²×C₅₃	semidirect
743. #417	C₂²×C₅₃	semidirect
746. C₂×#102	C₂²×C₅₃	semidirect
747. C₂×#102	C₂²×C₅₃	semidirect
750. #405	C₂²×C₅₃	semidirect
751. #405	C₂²×C₅₃	semidirect
752. C₅₃	#60587	direct (N × H)
950. #41	#41×C₅₃	semidirect
951. #41	#41×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3494	2
C₅₃×#3428	2
C₅₃×#3126	2
C₅₃×#3122	2
C₅₃×#3121	2
C₅₃×#3118	2
C₅₃×#3115	2
C₅₃×#3111	2
C₅₃×#3106	2
C₅₃×#3102	2
C₅₃×#3093	2
C₂×C₅₃×#482	2
C₅₃×#3084	2
C₅₃×#3083	2
C₅₃×#3045	2
C₅₃×#3006	2
C₅₃×#3002	2
C₅₃×#2952	2
C₅₃×#2951	2
C₅₃×#2946	2
C₅₃×#2924	2
#60587	53

Subgroups — C53×#60587 #27268099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60587 #27268099