Subgroups — C₅₃×#60834 #27268346

Order 13568.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3225	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3224	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3221	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3220	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3219	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3213	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3211	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3207	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3008	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₅₃×#548	—	2	1	no	—
35	C₅₃×#548	—	2	1	no	—
36	C₅₃×#546	—	2	2	no	—
37	C₅₃×#546	—	2	2	no	—
38	C₅₃×#546	—	2	1	no	—
39	C₅₃×#546	—	2	1	no	—
40	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#542	—	2	1	no	—
42	C₅₃×#542	C₂²	1	2	yes	complemented
43	C₅₃×#540	—	2	1	no	—
44	C₅₃×#540	C₂²	1	2	yes	complemented
45	C₅₃×#538	—	2	2	no	—
46	C₅₃×#537	C₂²	1	1	yes	characteristic
47	C₅₃×#536	C₂²	1	1	yes	characteristic
48	C₅₃×#536	C₂²	1	2	yes	complemented
49	C₅₃×#535	C₂²	1	1	yes	characteristic
50	C₅₃×#535	C₂²	1	1	yes	characteristic
51	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#535	C₂²	1	2	yes	complemented
53	C₅₃×#532	—	2	1	no	—
54	C₅₃×#532	C₂²	1	1	yes	characteristic
55	C₅₃×#532	C₂²	1	2	yes	complemented
56	C₅₃×#532	C₂²	1	2	yes	complemented
57	C₅₃×#529	—	2	1	no	—
58	C₅₃×#529	C₂²	1	2	yes	complemented
59	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
61	C₅₃×#525	—	2	2	no	—
62	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
63	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#497	C₂²	1	2	yes	complemented
66	C₅₃×#496	C₂²	1	2	yes	complemented
67	C₅₃×#496	C₂²	1	2	yes	complemented
68	C₅₃×#496	C₂²	1	2	yes	complemented
69	C₅₃×#495	C₂²	1	2	yes	complemented
70	C₅₃×#495	C₂²	1	2	yes	complemented
71	C₅₃×#493	C₂²	1	2	yes	complemented
72	C₅₃×#492	C₂²	1	2	yes	complemented
73	C₅₃×#491	C₂²	1	2	yes	complemented
74	C₅₃×#490	C₂²	1	2	yes	complemented
75	C₅₃×#489	C₂²	1	2	yes	complemented
76	C₅₃×#489	C₂²	1	2	yes	complemented
77	C₅₃×#488	C₂²	1	2	yes	complemented
78	C₅₃×#488	C₂²	1	2	yes	complemented
79	C₅₃×#487	C₂²	1	2	yes	complemented
80	C₅₃×#486	C₂²	1	2	yes	complemented
81	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#464	C₂²	1	2	yes	complemented
83	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#464	C₂²	1	2	yes	complemented
85	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#463	C₂²	1	2	yes	complemented
87	C₅₃×#463	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	2	yes	complemented
89	C₅₃×#463	C₂²	1	2	yes	complemented
90	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#463	C₂²	1	2	yes	complemented
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×#462	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#461	C₂²	1	2	yes	complemented
98	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#459	C₂²	1	2	yes	complemented
101	C₅₃×#452	C₂²	1	2	yes	complemented
102	C₅₃×#452	C₂²	1	2	yes	complemented
103	C₅₃×#451	C₂²	1	2	yes	complemented
104	C₅₃×#450	C₂²	1	2	yes	complemented
105	C₅₃×#449	C₂²	1	2	yes	—
106	C₅₃×#449	C₂²	1	2	yes	—
107	C₅₃×#449	C₂²	1	2	yes	complemented
108	C₅₃×#449	C₂²	1	2	yes	complemented
109	C₅₃×#449	C₂²	1	2	yes	complemented
110	C₅₃×#449	C₂²	1	2	yes	complemented
111	C₅₃×#448	C₂²	1	2	yes	complemented
112	C₅₃×#448	C₂²	1	2	yes	complemented
113	C₅₃×#448	C₂²	1	2	yes	complemented
114	C₅₃×#447	C₂²	1	2	yes	—
115	C₅₃×#447	C₂²	1	2	yes	—
116	C₅₃×#447	C₂²	1	2	yes	complemented
117	C₅₃×#433	C₂²	1	2	yes	complemented
118	C₅₃×#433	C₂²	1	2	yes	complemented
119	C₅₃×#432	C₂²	1	2	yes	complemented
120	C₅₃×#431	C₂²	1	2	yes	complemented
121	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#418	C₂²	1	1	yes	characteristic
125	C₅₃×#417	C₂²	1	1	yes	characteristic
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, complemented
129	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
131	C₅₃×#408	C₂²	1	1	yes	characteristic
132	C₅₃×#408	C₂²	1	1	yes	characteristic
133	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
135	2₋¹⁺⁴×C₅₃	—	4	2	no	—
136	2₋¹⁺⁴×C₅₃	—	4	2	no	—
137	H(5,𝔽₂)×C₅₃	—	4	2	no	—
138	H(5,𝔽₂)×C₅₃	—	4	2	no	—
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	2	no	—
141	C₂×#41×C₅₃	—	2	1	no	—
142	C₂×#41×C₅₃	—	2	2	no	—
143	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×#41×C₅₃	C₂³	1	2	yes	—
147	C₂×#41×C₅₃	C₂³	1	2	yes	—
148	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₅₃	—	2	1	no	—
150	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
152	C₂²×D₄×C₅₃	—	2	2	no	—
153	C₂²×D₄×C₅₃	—	2	1	no	—
154	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
155	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
156	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
157	C₂³×C₄×C₅₃	—	2	1	no	—
158	#137×C₅₃	—	4	2	no	—
159	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
160	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
161	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
162	#135×C₅₃	—	4	2	no	—
163	#135×C₅₃	—	4	2	no	—
164	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
165	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
167	C₂×SD₁₆×C₅₃	—	4	2	no	—
168	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
170	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
171	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
172	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
173	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
174	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
175	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
176	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
177	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
178	C₂×D₈×C₅₃	—	4	2	no	—
179	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
180	C₂×D₈×C₅₃	C₂³	1	2	yes	—
181	C₂×D₈×C₅₃	C₂³	1	2	yes	—
182	C₂×D₈×C₅₃	C₂³	1	2	yes	—
183	C₂×D₈×C₅₃	C₂³	1	2	yes	—
184	C₂×D₈×C₅₃	C₂³	1	2	yes	—
185	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
186	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
187	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
188	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
189	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₄⋊Q₈×C₅₃	—	2	1	no	—
191	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
192	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
193	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
194	#127×C₅₃	—	2	1	no	—
195	#127×C₅₃	C₂³	1	2	yes	—
196	#127×C₅₃	C₂³	1	2	yes	—
197	#127×C₅₃	C₂³	1	1	yes	characteristic
198	#126×C₅₃	—	2	2	no	—
199	#126×C₅₃	—	2	2	no	—
200	#125×C₅₃	—	2	1	no	—
201	#125×C₅₃	C₂³	1	2	yes	—
202	#124×C₅₃	—	2	2	no	—
203	#124×C₅₃	—	2	1	no	—
204	#124×C₅₃	—	2	1	no	—
205	#124×C₅₃	—	2	2	no	—
206	#124×C₅₃	—	2	2	no	—
207	#124×C₅₃	—	2	2	no	—
208	#124×C₅₃	—	2	1	no	—
209	#124×C₅₃	C₂³	1	2	yes	—
210	#124×C₅₃	C₂³	1	2	yes	—
211	#124×C₅₃	C₂³	1	2	yes	—
212	#124×C₅₃	C₂³	1	2	yes	—
213	#124×C₅₃	C₂³	1	2	yes	—
214	#124×C₅₃	C₂³	1	1	yes	characteristic
215	#124×C₅₃	C₂³	1	1	yes	characteristic
216	#123×C₅₃	—	2	2	no	—
217	#123×C₅₃	—	2	2	no	—
218	#123×C₅₃	—	2	2	no	—
219	#123×C₅₃	—	2	2	no	—
220	#123×C₅₃	—	2	2	no	—
221	#123×C₅₃	—	2	2	no	—
222	#123×C₅₃	—	2	2	no	—
223	C₂²⋊Q₈×C₅₃	—	2	2	no	—
224	C₂²⋊Q₈×C₅₃	—	2	1	no	—
225	C₂²⋊Q₈×C₅₃	—	2	1	no	—
226	C₂²⋊Q₈×C₅₃	—	2	2	no	—
227	C₂²⋊Q₈×C₅₃	—	2	2	no	—
228	C₂²⋊Q₈×C₅₃	—	2	2	no	—
229	C₂²⋊Q₈×C₅₃	—	2	1	no	—
230	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
231	#121×C₅₃	—	2	1	no	—
232	#121×C₅₃	—	2	1	no	—
233	#121×C₅₃	—	2	1	no	—
234	#121×C₅₃	—	2	1	no	—
235	#121×C₅₃	—	2	2	no	—
236	#121×C₅₃	—	2	2	no	—
237	#121×C₅₃	—	2	2	no	—
238	#121×C₅₃	—	2	2	no	—
239	#121×C₅₃	—	2	2	no	—
240	#121×C₅₃	—	2	1	no	—
241	#121×C₅₃	—	2	1	no	—
242	#121×C₅₃	—	2	1	no	—
243	#121×C₅₃	—	2	2	no	—
244	#121×C₅₃	—	2	2	no	—
245	#121×C₅₃	—	2	2	no	—
246	#121×C₅₃	C₂³	1	2	yes	—
247	#121×C₅₃	C₂³	1	2	yes	—
248	#121×C₅₃	C₂³	1	2	yes	—
249	#120×C₅₃	—	2	2	no	—
250	#120×C₅₃	—	2	2	no	—
251	#120×C₅₃	—	2	2	no	—
252	#120×C₅₃	—	2	2	no	—
253	#120×C₅₃	—	2	2	no	—
254	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
255	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
256	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
257	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₅₃	—	2	1	no	—
259	C₄×D₄×C₅₃	—	2	1	no	—
260	C₄×D₄×C₅₃	—	2	2	no	—
261	C₄×D₄×C₅₃	—	2	1	no	—
262	C₄×D₄×C₅₃	—	2	1	no	—
263	C₄×D₄×C₅₃	—	2	2	no	—
264	C₄×D₄×C₅₃	—	2	2	no	—
265	C₄×D₄×C₅₃	—	2	1	no	—
266	C₄×D₄×C₅₃	—	2	1	no	—
267	C₄×D₄×C₅₃	—	2	2	no	—
268	C₄×D₄×C₅₃	D₄	1	2	yes	—
269	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
270	C₄×D₄×C₅₃	D₄	1	2	yes	—
271	C₄×D₄×C₅₃	D₄	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	1	yes	characteristic
275	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
276	#117×C₅₃	—	2	1	no	—
277	#117×C₅₃	—	2	2	no	—
278	#117×C₅₃	C₂³	1	1	yes	characteristic
279	#117×C₅₃	C₂³	1	1	yes	characteristic
280	#117×C₅₃	C₂³	1	2	yes	—
281	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
283	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
284	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
285	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
286	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
287	C₂×C₄²×C₅₃	—	2	1	no	—
288	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
290	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
291	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
293	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
294	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
295	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	1	yes	characteristic
297	#103×C₅₃	C₂³	1	2	yes	—
298	#103×C₅₃	C₂³	1	2	yes	—
299	#103×C₅₃	C₂³	1	2	yes	—
300	#103×C₅₃	C₂³	1	1	yes	characteristic
301	#103×C₅₃	C₂³	1	2	yes	—
302	#103×C₅₃	C₂³	1	2	yes	—
303	#103×C₅₃	C₂³	1	1	yes	characteristic
304	#103×C₅₃	C₂³	1	2	yes	—
305	#103×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	1	yes	characteristic
307	#102×C₅₃	C₂³	1	2	yes	—
308	#102×C₅₃	C₂³	1	2	yes	—
309	#102×C₅₃	C₂³	1	2	yes	—
310	#102×C₅₃	C₂³	1	1	yes	characteristic
311	#102×C₅₃	C₂³	1	2	yes	—
312	#102×C₅₃	C₂³	1	2	yes	—
313	#102×C₅₃	C₂³	1	1	yes	characteristic
314	#102×C₅₃	C₂³	1	2	yes	—
315	#102×C₅₃	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
319	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
320	#97×C₅₃	C₂³	1	2	yes	—
321	#97×C₅₃	C₂³	1	2	yes	—
322	C₄×C₈×C₅₃	C₂³	1	2	yes	—
323	C₄×C₈×C₅₃	C₂³	1	2	yes	—
324	C₂⁴×C₅₃	—	2	2	no	—
325	C₂⁴×C₅₃	—	2	1	no	—
326	C₂⁴×C₅₃	—	2	1	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	—	2	2	no	—
332	#41×C₅₃	—	2	2	no	—
333	#41×C₅₃	—	2	2	no	—
334	#41×C₅₃	—	2	2	no	—
335	#41×C₅₃	—	4	2	no	—
336	#41×C₅₃	—	4	2	no	—
337	#41×C₅₃	—	4	2	no	—
338	#41×C₅₃	—	4	2	no	—
339	#41×C₅₃	—	4	8	no	—
340	#41×C₅₃	—	4	4	no	—
341	#41×C₅₃	—	4	4	no	—
342	#41×C₅₃	—	8	4	no	—
343	C₂×Q₈×C₅₃	—	2	2	no	—
344	C₂×Q₈×C₅₃	—	2	1	no	—
345	C₂×Q₈×C₅₃	—	2	2	no	—
346	C₂×Q₈×C₅₃	—	2	2	no	—
347	C₂×Q₈×C₅₃	—	2	2	no	—
348	C₂×Q₈×C₅₃	—	4	2	no	—
349	C₂×Q₈×C₅₃	—	4	2	no	—
350	C₂×Q₈×C₅₃	—	4	4	no	—
351	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
352	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
353	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
354	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₅₃	—	2	1	no	—
357	C₂×D₄×C₅₃	—	2	2	no	—
358	C₂×D₄×C₅₃	—	2	1	no	—
359	C₂×D₄×C₅₃	—	2	2	no	—
360	C₂×D₄×C₅₃	—	2	1	no	—
361	C₂×D₄×C₅₃	—	2	2	no	—
362	C₂×D₄×C₅₃	—	2	2	no	—
363	C₂×D₄×C₅₃	—	2	2	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	2	no	—
370	C₂×D₄×C₅₃	—	2	2	no	—
371	C₂×D₄×C₅₃	—	2	2	no	—
372	C₂×D₄×C₅₃	—	2	2	no	—
373	C₂×D₄×C₅₃	—	2	2	no	—
374	C₂×D₄×C₅₃	—	2	2	no	—
375	C₂×D₄×C₅₃	—	2	2	no	—
376	C₂×D₄×C₅₃	—	2	2	no	—
377	C₂×D₄×C₅₃	—	4	2	no	—
378	C₂×D₄×C₅₃	—	4	2	no	—
379	C₂×D₄×C₅₃	—	4	8	no	—
380	C₂×D₄×C₅₃	—	4	4	no	—
381	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
382	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
384	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
387	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	—	2	2	no	—
389	C₂²×C₄×C₅₃	—	2	1	no	—
390	C₂²×C₄×C₅₃	—	2	1	no	—
391	C₂²×C₄×C₅₃	—	2	1	no	—
392	C₂²×C₄×C₅₃	—	2	1	no	—
393	C₂²×C₄×C₅₃	—	2	2	no	—
394	C₂²×C₄×C₅₃	—	2	2	no	—
395	C₂²×C₄×C₅₃	—	2	1	no	—
396	C₂²×C₄×C₅₃	—	2	2	no	—
397	C₂²×C₄×C₅₃	—	2	1	no	—
398	C₂²×C₄×C₅₃	—	2	1	no	—
399	C₂²×C₄×C₅₃	—	2	2	no	—
400	C₂²×C₄×C₅₃	—	8	2	no	—
401	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
404	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
405	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	Q₁₆×C₅₃	—	4	1	no	—
408	Q₁₆×C₅₃	—	4	1	no	—
409	Q₁₆×C₅₃	—	4	2	no	—
410	SD₁₆×C₅₃	—	4	2	no	—
411	SD₁₆×C₅₃	—	4	2	no	—
412	SD₁₆×C₅₃	—	4	1	no	—
413	SD₁₆×C₅₃	—	4	1	no	—
414	SD₁₆×C₅₃	—	4	1	no	—
415	SD₁₆×C₅₃	—	4	1	no	—
416	SD₁₆×C₅₃	—	4	2	no	—
417	SD₁₆×C₅₃	—	4	2	no	—
418	SD₁₆×C₅₃	—	4	2	no	—
419	SD₁₆×C₅₃	—	4	2	no	—
420	D₈×C₅₃	—	4	2	no	—
421	D₈×C₅₃	—	4	2	no	—
422	D₈×C₅₃	—	4	1	no	—
423	D₈×C₅₃	—	4	1	no	—
424	D₈×C₅₃	—	4	2	no	—
425	D₈×C₅₃	—	4	2	no	—
426	D₈×C₅₃	—	4	2	no	—
427	M₁₆×C₅₃	—	2	2	no	—
428	M₁₆×C₅₃	—	2	2	no	—
429	C₂×C₈×C₅₃	—	2	2	no	—
430	C₂×C₈×C₅₃	—	2	2	no	—
431	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
433	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
434	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
435	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
436	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₅₃	—	2	1	no	—
438	C₄⋊C₄×C₅₃	—	2	1	no	—
439	C₄⋊C₄×C₅₃	—	2	1	no	—
440	C₄⋊C₄×C₅₃	—	2	2	no	—
441	C₄⋊C₄×C₅₃	—	2	2	no	—
442	C₄⋊C₄×C₅₃	—	2	1	no	—
443	C₄⋊C₄×C₅₃	—	2	1	no	—
444	C₄⋊C₄×C₅₃	—	2	2	no	—
445	C₄⋊C₄×C₅₃	—	2	2	no	—
446	C₄⋊C₄×C₅₃	—	2	2	no	—
447	C₄⋊C₄×C₅₃	—	2	2	no	—
448	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
451	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
452	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
453	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
455	C₂²⋊C₄×C₅₃	—	2	1	no	—
456	C₂²⋊C₄×C₅₃	—	2	2	no	—
457	C₂²⋊C₄×C₅₃	—	2	2	no	—
458	C₂²⋊C₄×C₅₃	—	2	1	no	—
459	C₂²⋊C₄×C₅₃	—	2	2	no	—
460	C₂²⋊C₄×C₅₃	—	2	1	no	—
461	C₂²⋊C₄×C₅₃	—	2	2	no	—
462	C₂²⋊C₄×C₅₃	—	2	2	no	—
463	C₂²⋊C₄×C₅₃	—	2	2	no	—
464	C₂²⋊C₄×C₅₃	—	2	2	no	—
465	C₂²⋊C₄×C₅₃	—	2	2	no	—
466	C₂²⋊C₄×C₅₃	—	2	2	no	—
467	C₂²⋊C₄×C₅₃	—	2	2	no	—
468	C₂²⋊C₄×C₅₃	—	2	2	no	—
469	C₂²⋊C₄×C₅₃	—	2	1	no	—
470	C₂²⋊C₄×C₅₃	—	2	1	no	—
471	C₂²⋊C₄×C₅₃	—	2	2	no	—
472	C₂²⋊C₄×C₅₃	—	2	2	no	—
473	C₂²⋊C₄×C₅₃	—	2	1	no	—
474	C₂²⋊C₄×C₅₃	—	2	1	no	—
475	C₂²⋊C₄×C₅₃	—	2	2	no	—
476	C₂²⋊C₄×C₅₃	—	2	2	no	—
477	C₂²⋊C₄×C₅₃	—	2	2	no	—
478	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
479	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
480	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
481	C₄²×C₅₃	—	2	1	no	—
482	C₄²×C₅₃	—	2	1	no	—
483	C₄²×C₅₃	—	2	1	no	—
484	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
485	C₄²×C₅₃	C₂×D₄	1	2	yes	—
486	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
487	C₄²×C₅₃	C₂×D₄	1	2	yes	—
488	C₄²×C₅₃	C₂⁴	1	2	yes	—
489	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
490	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
491	C₂³×C₅₃	—	2	1	no	—
492	C₂³×C₅₃	—	2	1	no	—
493	C₂³×C₅₃	—	2	2	no	—
494	C₂³×C₅₃	—	2	2	no	—
495	C₂³×C₅₃	—	2	1	no	—
496	C₂³×C₅₃	—	4	4	no	—
497	C₂³×C₅₃	—	4	2	no	—
498	C₂³×C₅₃	—	4	2	no	—
499	C₂³×C₅₃	—	8	1	no	—
500	C₂³×C₅₃	—	8	1	no	—
501	C₂³×C₅₃	—	8	1	no	—
502	C₂³×C₅₃	—	8	1	no	—
503	C₂³×C₅₃	—	8	2	no	—
504	C₂³×C₅₃	—	8	2	no	—
505	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
506	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
507	Q₈×C₅₃	—	2	2	no	—
508	Q₈×C₅₃	—	2	2	no	—
509	Q₈×C₅₃	—	2	2	no	—
510	Q₈×C₅₃	—	2	1	no	—
511	Q₈×C₅₃	—	2	1	no	—
512	Q₈×C₅₃	—	2	1	no	—
513	Q₈×C₅₃	—	2	1	no	—
514	Q₈×C₅₃	—	2	1	no	—
515	Q₈×C₅₃	—	2	1	no	—
516	Q₈×C₅₃	—	4	4	no	—
517	Q₈×C₅₃	—	4	2	no	—
518	Q₈×C₅₃	—	8	2	no	—
519	D₄×C₅₃	—	2	4	no	—
520	D₄×C₅₃	—	2	2	no	—
521	D₄×C₅₃	—	2	2	no	—
522	D₄×C₅₃	—	2	2	no	—
523	D₄×C₅₃	—	2	2	no	—
524	D₄×C₅₃	—	2	2	no	—
525	D₄×C₅₃	—	2	1	no	—
526	D₄×C₅₃	—	2	1	no	—
527	D₄×C₅₃	—	2	1	no	—
528	D₄×C₅₃	—	2	1	no	—
529	D₄×C₅₃	—	2	1	no	—
530	D₄×C₅₃	—	2	1	no	—
531	D₄×C₅₃	—	4	4	no	—
532	D₄×C₅₃	—	4	4	no	—
533	D₄×C₅₃	—	4	4	no	—
534	D₄×C₅₃	—	4	2	no	—
535	D₄×C₅₃	—	4	2	no	—
536	D₄×C₅₃	—	4	2	no	—
537	D₄×C₅₃	—	4	2	no	—
538	D₄×C₅₃	—	4	2	no	—
539	D₄×C₅₃	—	8	1	no	—
540	D₄×C₅₃	—	8	2	no	—
541	D₄×C₅₃	—	8	2	no	—
542	D₄×C₅₃	—	8	1	no	—
543	D₄×C₅₃	—	8	2	no	—
544	D₄×C₅₃	—	8	2	no	—
545	D₄×C₅₃	—	8	2	no	—
546	D₄×C₅₃	—	8	2	no	—
547	D₄×C₅₃	—	8	2	no	—
548	C₂×C₄×C₅₃	—	2	2	no	—
549	C₂×C₄×C₅₃	—	2	2	no	—
550	C₂×C₄×C₅₃	—	2	1	no	—
551	C₂×C₄×C₅₃	—	2	2	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	2	no	—
554	C₂×C₄×C₅₃	—	2	1	no	—
555	C₂×C₄×C₅₃	—	2	1	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	2	no	—
560	C₂×C₄×C₅₃	—	4	2	no	—
561	C₂×C₄×C₅₃	—	4	4	no	—
562	C₂×C₄×C₅₃	—	4	4	no	—
563	C₂×C₄×C₅₃	—	4	4	no	—
564	C₂×C₄×C₅₃	—	4	2	no	—
565	C₂×C₄×C₅₃	—	4	4	no	—
566	C₂×C₄×C₅₃	—	4	2	no	—
567	C₂×C₄×C₅₃	—	4	2	no	—
568	C₂×C₄×C₅₃	—	4	2	no	—
569	C₂×C₄×C₅₃	—	4	2	no	—
570	C₂×C₄×C₅₃	—	8	1	no	—
571	C₂×C₄×C₅₃	—	8	2	no	—
572	C₂×C₄×C₅₃	—	8	1	no	—
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	2	yes	—
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	2	yes	—
579	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
580	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
582	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
583	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
584	C₈×C₅₃	—	2	1	no	—
585	C₈×C₅₃	—	2	1	no	—
586	C₈×C₅₃	—	2	1	no	—
587	C₈×C₅₃	—	2	1	no	—
588	C₈×C₅₃	—	2	2	no	—
589	C₈×C₅₃	—	2	2	no	—
590	#60834	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
591	C₂²×C₅₃	—	2	1	no	—
592	C₂²×C₅₃	—	2	1	no	—
593	C₂²×C₅₃	—	2	2	no	—
594	C₂²×C₅₃	—	2	2	no	—
595	C₂²×C₅₃	—	2	2	no	—
596	C₂²×C₅₃	—	4	1	no	—
597	C₂²×C₅₃	—	4	1	no	—
598	C₂²×C₅₃	—	4	2	no	—
599	C₂²×C₅₃	—	4	2	no	—
600	C₂²×C₅₃	—	4	1	no	—
601	C₂²×C₅₃	—	4	2	no	—
602	C₂²×C₅₃	—	4	1	no	—
603	C₂²×C₅₃	—	4	1	no	—
604	C₂²×C₅₃	—	4	2	no	—
605	C₂²×C₅₃	—	4	1	no	—
606	C₂²×C₅₃	—	4	1	no	—
607	C₂²×C₅₃	—	4	2	no	—
608	C₂²×C₅₃	—	4	1	no	—
609	C₂²×C₅₃	—	4	1	no	—
610	C₂²×C₅₃	—	4	2	no	—
611	C₂²×C₅₃	—	8	4	no	—
612	C₂²×C₅₃	—	16	2	no	—
613	C₂²×C₅₃	—	16	4	no	—
614	C₂²×C₅₃	#535	1	2	yes	—
615	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
616	C₄×C₅₃	—	2	1	no	—
617	C₄×C₅₃	—	2	1	no	—
618	C₄×C₅₃	—	2	2	no	—
619	C₄×C₅₃	—	2	1	no	—
620	C₄×C₅₃	—	2	1	no	—
621	C₄×C₅₃	—	2	2	no	—
622	C₄×C₅₃	—	2	2	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	—	4	2	no	—
628	C₄×C₅₃	—	4	1	no	—
629	C₄×C₅₃	—	4	1	no	—
630	C₄×C₅₃	#535	1	2	yes	—
631	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
632	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
633	#3500	C₂×C₅₃	1	1	yes	characteristic, complemented
634	#3460	C₂×C₅₃	1	1	yes	characteristic, complemented
635	#3225	C₂×C₅₃	1	2	yes	complemented
636	#3224	C₂×C₅₃	1	2	yes	complemented
637	#3221	C₂×C₅₃	1	2	yes	complemented
638	#3220	C₂×C₅₃	1	2	yes	complemented
639	#3219	C₂×C₅₃	1	2	yes	complemented
640	#3213	C₂×C₅₃	1	2	yes	complemented
641	#3211	C₂×C₅₃	1	2	yes	complemented
642	#3207	C₂×C₅₃	1	2	yes	complemented
643	#3155	C₂×C₅₃	1	1	yes	characteristic, complemented
644	#3154	C₂×C₅₃	1	1	yes	characteristic, complemented
645	#3137	C₂×C₅₃	1	1	yes	characteristic, complemented
646	#3136	C₂×C₅₃	1	1	yes	characteristic, complemented
647	#3040	C₂×C₅₃	1	1	yes	characteristic, complemented
648	#3036	C₂×C₅₃	1	1	yes	characteristic, complemented
649	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
650	C₂×#463	C₂×C₅₃	1	1	yes	characteristic, complemented
651	#3013	C₂×C₅₃	1	1	yes	characteristic, complemented
652	#3012	C₂×C₅₃	1	1	yes	characteristic, complemented
653	#3010	C₂×C₅₃	1	1	yes	characteristic, complemented
654	#3008	C₂×C₅₃	1	1	yes	characteristic, complemented
655	#2925	C₂×C₅₃	1	1	yes	characteristic, complemented
656	C₂×C₅₃	—	2	2	no	—
657	C₂×C₅₃	—	4	2	no	—
658	C₂×C₅₃	—	8	1	no	—
659	C₂×C₅₃	—	8	1	no	—
660	C₂×C₅₃	—	8	2	no	—
661	C₂×C₅₃	—	8	2	no	—
662	C₂×C₅₃	—	8	1	no	—
663	C₂×C₅₃	C₂×#535	1	1	yes	characteristic
664	C₂×C₅₃	#3584	1	1	yes	characteristic
665	C₂×C₅₃	#3585	1	1	yes	characteristic
666	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic
667	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
668	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
669	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
670	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
671	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
672	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
673	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
674	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
675	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
676	#548	—	2	1	no	—
677	#548	—	2	1	no	—
678	#546	—	2	2	no	—
679	#546	—	2	2	no	—
680	#546	—	2	1	no	—
681	#546	—	2	1	no	—
682	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	#542	—	2	1	no	—
684	#542	C₂²×C₅₃	1	2	yes	complemented
685	#540	—	2	1	no	—
686	#540	C₂²×C₅₃	1	2	yes	complemented
687	#538	—	2	2	no	—
688	#537	C₂²×C₅₃	1	1	yes	characteristic
689	#536	C₂²×C₅₃	1	1	yes	characteristic
690	#536	C₂²×C₅₃	1	2	yes	complemented
691	#535	C₂²×C₅₃	1	1	yes	characteristic
692	#535	C₂²×C₅₃	1	1	yes	characteristic
693	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
694	#535	C₂²×C₅₃	1	2	yes	complemented
695	#532	—	2	1	no	—
696	#532	C₂²×C₅₃	1	1	yes	characteristic
697	#532	C₂²×C₅₃	1	2	yes	complemented
698	#532	C₂²×C₅₃	1	2	yes	complemented
699	#529	—	2	1	no	—
700	#529	C₂²×C₅₃	1	2	yes	complemented
701	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
702	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
703	#525	—	2	2	no	—
704	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
705	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
706	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	#497	C₂²×C₅₃	1	2	yes	complemented
708	#496	C₂²×C₅₃	1	2	yes	complemented
709	#496	C₂²×C₅₃	1	2	yes	complemented
710	#496	C₂²×C₅₃	1	2	yes	complemented
711	#495	C₂²×C₅₃	1	2	yes	complemented
712	#495	C₂²×C₅₃	1	2	yes	complemented
713	#493	C₂²×C₅₃	1	2	yes	complemented
714	#492	C₂²×C₅₃	1	2	yes	complemented
715	#491	C₂²×C₅₃	1	2	yes	complemented
716	#490	C₂²×C₅₃	1	2	yes	complemented
717	#489	C₂²×C₅₃	1	2	yes	complemented
718	#489	C₂²×C₅₃	1	2	yes	complemented
719	#488	C₂²×C₅₃	1	2	yes	complemented
720	#488	C₂²×C₅₃	1	2	yes	complemented
721	#487	C₂²×C₅₃	1	2	yes	complemented
722	#486	C₂²×C₅₃	1	2	yes	complemented
723	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
724	#464	C₂²×C₅₃	1	2	yes	complemented
725	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
726	#464	C₂²×C₅₃	1	2	yes	complemented
727	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
728	#463	C₂²×C₅₃	1	2	yes	complemented
729	#463	C₂²×C₅₃	1	2	yes	complemented
730	#463	C₂²×C₅₃	1	2	yes	complemented
731	#463	C₂²×C₅₃	1	2	yes	complemented
732	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
733	#463	C₂²×C₅₃	1	2	yes	complemented
734	#463	C₂²×C₅₃	1	2	yes	complemented
735	#463	C₂²×C₅₃	1	2	yes	complemented
736	#463	C₂²×C₅₃	1	2	yes	complemented
737	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
738	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
739	#461	C₂²×C₅₃	1	2	yes	complemented
740	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
741	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
742	#459	C₂²×C₅₃	1	2	yes	complemented
743	#452	C₂²×C₅₃	1	2	yes	complemented
744	#452	C₂²×C₅₃	1	2	yes	complemented
745	#451	C₂²×C₅₃	1	2	yes	complemented
746	#450	C₂²×C₅₃	1	2	yes	complemented
747	#449	C₂²×C₅₃	1	2	yes	—
748	#449	C₂²×C₅₃	1	2	yes	—
749	#449	C₂²×C₅₃	1	2	yes	complemented
750	#449	C₂²×C₅₃	1	2	yes	complemented
751	#449	C₂²×C₅₃	1	2	yes	complemented
752	#449	C₂²×C₅₃	1	2	yes	complemented
753	#448	C₂²×C₅₃	1	2	yes	complemented
754	#448	C₂²×C₅₃	1	2	yes	complemented
755	#448	C₂²×C₅₃	1	2	yes	complemented
756	#447	C₂²×C₅₃	1	2	yes	—
757	#447	C₂²×C₅₃	1	2	yes	—
758	#447	C₂²×C₅₃	1	2	yes	complemented
759	#433	C₂²×C₅₃	1	2	yes	complemented
760	#433	C₂²×C₅₃	1	2	yes	complemented
761	#432	C₂²×C₅₃	1	2	yes	complemented
762	#431	C₂²×C₅₃	1	2	yes	complemented
763	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
764	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
765	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
766	#418	C₂²×C₅₃	1	1	yes	characteristic
767	#417	C₂²×C₅₃	1	1	yes	characteristic
768	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
769	#416	C₂²×C₅₃	1	1	yes	characteristic
770	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
771	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
772	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
773	#408	C₂²×C₅₃	1	1	yes	characteristic
774	#408	C₂²×C₅₃	1	1	yes	characteristic
775	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
776	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
777	C₅₃	#60834	1	1	yes	characteristic, direct product factor, Sylow
778	2₋¹⁺⁴	—	4	2	no	—
779	2₋¹⁺⁴	—	4	2	no	—
780	H(5,𝔽₂)	—	4	2	no	—
781	H(5,𝔽₂)	—	4	2	no	—
782	C₂×#41	—	2	1	no	—
783	C₂×#41	—	2	2	no	—
784	C₂×#41	—	2	1	no	—
785	C₂×#41	—	2	2	no	—
786	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
787	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
788	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
789	C₂×#41	C₂³×C₅₃	1	2	yes	—
790	C₂×#41	C₂³×C₅₃	1	2	yes	—
791	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
792	C₂²×Q₈	—	2	1	no	—
793	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
794	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
795	C₂²×D₄	—	2	2	no	—
796	C₂²×D₄	—	2	1	no	—
797	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
798	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
799	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
800	C₂³×C₄	—	2	1	no	—
801	#137	—	4	2	no	—
802	AGL(1,ℤ/8)	—	4	2	no	—
803	AGL(1,ℤ/8)	—	4	2	no	—
804	AGL(1,ℤ/8)	—	4	2	no	—
805	#135	—	4	2	no	—
806	#135	—	4	2	no	—
807	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
808	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
809	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
810	C₂×SD₁₆	—	4	2	no	—
811	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
812	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
813	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
814	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
815	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
816	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
817	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
818	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
819	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
820	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
821	C₂×D₈	—	4	2	no	—
822	C₂×D₈	C₂³×C₅₃	1	2	yes	—
823	C₂×D₈	C₂³×C₅₃	1	2	yes	—
824	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
825	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
826	C₂×D₈	C₂³×C₅₃	1	2	yes	—
827	C₂×D₈	C₂³×C₅₃	1	2	yes	—
828	C₂×D₈	C₂³×C₅₃	1	2	yes	—
829	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
830	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
831	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
832	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
833	C₄⋊Q₈	—	2	1	no	—
834	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
835	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
836	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
837	#127	—	2	1	no	—
838	#127	C₂³×C₅₃	1	1	yes	characteristic
839	#127	C₂³×C₅₃	1	2	yes	—
840	#127	C₂³×C₅₃	1	2	yes	—
841	#126	—	2	2	no	—
842	#126	—	2	2	no	—
843	#125	—	2	1	no	—
844	#125	C₂³×C₅₃	1	2	yes	—
845	#124	—	2	1	no	—
846	#124	—	2	2	no	—
847	#124	—	2	1	no	—
848	#124	—	2	1	no	—
849	#124	—	2	2	no	—
850	#124	—	2	2	no	—
851	#124	—	2	2	no	—
852	#124	C₂³×C₅₃	1	2	yes	—
853	#124	C₂³×C₅₃	1	2	yes	—
854	#124	C₂³×C₅₃	1	1	yes	characteristic
855	#124	C₂³×C₅₃	1	2	yes	—
856	#124	C₂³×C₅₃	1	2	yes	—
857	#124	C₂³×C₅₃	1	2	yes	—
858	#124	C₂³×C₅₃	1	1	yes	characteristic
859	#123	—	2	2	no	—
860	#123	—	2	2	no	—
861	#123	—	2	2	no	—
862	#123	—	2	2	no	—
863	#123	—	2	2	no	—
864	#123	—	2	2	no	—
865	#123	—	2	2	no	—
866	C₂²⋊Q₈	—	2	1	no	—
867	C₂²⋊Q₈	—	2	2	no	—
868	C₂²⋊Q₈	—	2	1	no	—
869	C₂²⋊Q₈	—	2	1	no	—
870	C₂²⋊Q₈	—	2	2	no	—
871	C₂²⋊Q₈	—	2	2	no	—
872	C₂²⋊Q₈	—	2	2	no	—
873	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
874	#121	—	2	2	no	—
875	#121	—	2	1	no	—
876	#121	—	2	1	no	—
877	#121	—	2	1	no	—
878	#121	—	2	2	no	—
879	#121	—	2	2	no	—
880	#121	—	2	2	no	—
881	#121	—	2	1	no	—
882	#121	—	2	1	no	—
883	#121	—	2	1	no	—
884	#121	—	2	1	no	—
885	#121	—	2	2	no	—
886	#121	—	2	2	no	—
887	#121	—	2	2	no	—
888	#121	—	2	2	no	—
889	#121	C₂³×C₅₃	1	2	yes	—
890	#121	C₂³×C₅₃	1	2	yes	—
891	#121	C₂³×C₅₃	1	2	yes	—
892	#120	—	2	2	no	—
893	#120	—	2	2	no	—
894	#120	—	2	2	no	—
895	#120	—	2	2	no	—
896	#120	—	2	2	no	—
897	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
898	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
899	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
900	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	1	no	—
903	C₄×D₄	—	2	2	no	—
904	C₄×D₄	—	2	1	no	—
905	C₄×D₄	—	2	1	no	—
906	C₄×D₄	—	2	2	no	—
907	C₄×D₄	—	2	1	no	—
908	C₄×D₄	—	2	1	no	—
909	C₄×D₄	—	2	2	no	—
910	C₄×D₄	—	2	2	no	—
911	C₄×D₄	D₄×C₅₃	1	2	yes	—
912	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
913	C₄×D₄	D₄×C₅₃	1	2	yes	—
914	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
915	C₄×D₄	C₂³×C₅₃	1	2	yes	—
916	C₄×D₄	C₂³×C₅₃	1	2	yes	—
917	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
918	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
919	#117	—	2	1	no	—
920	#117	—	2	2	no	—
921	#117	C₂³×C₅₃	1	1	yes	characteristic
922	#117	C₂³×C₅₃	1	1	yes	characteristic
923	#117	C₂³×C₅₃	1	2	yes	—
924	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
925	C₂×C₂²⋊C₄	—	2	1	no	—
926	C₂×C₂²⋊C₄	—	2	1	no	—
927	C₂×C₂²⋊C₄	—	2	1	no	—
928	C₂×C₂²⋊C₄	—	2	2	no	—
929	C₂×C₂²⋊C₄	—	2	2	no	—
930	C₂×C₄²	—	2	1	no	—
931	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
932	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
933	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
934	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
935	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
936	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
937	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
938	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
939	#103	C₂³×C₅₃	1	2	yes	—
940	#103	C₂³×C₅₃	1	2	yes	—
941	#103	C₂³×C₅₃	1	1	yes	characteristic
942	#103	C₂³×C₅₃	1	1	yes	characteristic
943	#103	C₂³×C₅₃	1	1	yes	characteristic
944	#103	C₂³×C₅₃	1	1	yes	characteristic
945	#103	C₂³×C₅₃	1	2	yes	—
946	#103	C₂³×C₅₃	1	2	yes	—
947	#103	C₂³×C₅₃	1	2	yes	—
948	#103	C₂³×C₅₃	1	2	yes	—
949	#102	C₂³×C₅₃	1	2	yes	—
950	#102	C₂³×C₅₃	1	2	yes	—
951	#102	C₂³×C₅₃	1	1	yes	characteristic
952	#102	C₂³×C₅₃	1	1	yes	characteristic
953	#102	C₂³×C₅₃	1	1	yes	characteristic
954	#102	C₂³×C₅₃	1	1	yes	characteristic
955	#102	C₂³×C₅₃	1	2	yes	—
956	#102	C₂³×C₅₃	1	2	yes	—
957	#102	C₂³×C₅₃	1	2	yes	—
958	#102	C₂³×C₅₃	1	2	yes	—
959	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
960	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
961	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
962	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
963	#97	C₂³×C₅₃	1	2	yes	—
964	#97	C₂³×C₅₃	1	2	yes	—
965	C₄×C₈	C₂³×C₅₃	1	2	yes	—
966	C₄×C₈	C₂³×C₅₃	1	2	yes	—
967	C₂⁴	—	2	2	no	—
968	C₂⁴	—	2	1	no	—
969	C₂⁴	—	2	1	no	—
970	#41	—	2	2	no	—
971	#41	—	2	2	no	—
972	#41	—	2	2	no	—
973	#41	—	2	2	no	—
974	#41	—	2	2	no	—
975	#41	—	2	2	no	—
976	#41	—	2	2	no	—
977	#41	—	2	2	no	—
978	#41	—	4	2	no	—
979	#41	—	4	2	no	—
980	#41	—	4	2	no	—
981	#41	—	4	2	no	—
982	#41	—	4	8	no	—
983	#41	—	4	4	no	—
984	#41	—	4	4	no	—
985	#41	—	8	4	no	—
986	C₂×Q₈	—	2	2	no	—
987	C₂×Q₈	—	2	1	no	—
988	C₂×Q₈	—	2	2	no	—
989	C₂×Q₈	—	2	2	no	—
990	C₂×Q₈	—	2	2	no	—
991	C₂×Q₈	—	4	2	no	—
992	C₂×Q₈	—	4	2	no	—
993	C₂×Q₈	—	4	4	no	—
994	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
995	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
996	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
997	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
998	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	2	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	2	no	—
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	2	no	—
1018	C₂×D₄	—	2	2	no	—
1019	C₂×D₄	—	2	2	no	—
1020	C₂×D₄	—	4	2	no	—
1021	C₂×D₄	—	4	2	no	—
1022	C₂×D₄	—	4	8	no	—
1023	C₂×D₄	—	4	4	no	—
1024	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1025	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1026	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1027	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1028	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1029	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1030	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1031	C₂²×C₄	—	2	2	no	—
1032	C₂²×C₄	—	2	1	no	—
1033	C₂²×C₄	—	2	1	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	1	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	1	no	—
1042	C₂²×C₄	—	2	2	no	—
1043	C₂²×C₄	—	8	2	no	—
1044	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1045	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1046	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1047	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1048	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1049	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1050	Q₁₆	—	4	1	no	—
1051	Q₁₆	—	4	1	no	—
1052	Q₁₆	—	4	2	no	—
1053	SD₁₆	—	4	2	no	—
1054	SD₁₆	—	4	2	no	—
1055	SD₁₆	—	4	1	no	—
1056	SD₁₆	—	4	1	no	—
1057	SD₁₆	—	4	1	no	—
1058	SD₁₆	—	4	1	no	—
1059	SD₁₆	—	4	2	no	—
1060	SD₁₆	—	4	2	no	—
1061	SD₁₆	—	4	2	no	—
1062	SD₁₆	—	4	2	no	—
1063	D₈	—	4	2	no	—
1064	D₈	—	4	2	no	—
1065	D₈	—	4	1	no	—
1066	D₈	—	4	1	no	—
1067	D₈	—	4	2	no	—
1068	D₈	—	4	2	no	—
1069	D₈	—	4	2	no	—
1070	M₁₆	—	2	2	no	—
1071	M₁₆	—	2	2	no	—
1072	C₂×C₈	—	2	2	no	—
1073	C₂×C₈	—	2	2	no	—
1074	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1075	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1076	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1077	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1078	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1079	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	1	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1092	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1093	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1094	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1095	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1096	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1097	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1122	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1123	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	—	2	1	no	—
1127	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1128	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1129	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1130	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1131	C₄²	C₂⁴×C₅₃	1	2	yes	—
1132	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1133	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1134	C₂³	—	2	2	no	—
1135	C₂³	—	2	2	no	—
1136	C₂³	—	2	1	no	—
1137	C₂³	—	2	1	no	—
1138	C₂³	—	2	1	no	—
1139	C₂³	—	4	4	no	—
1140	C₂³	—	4	2	no	—
1141	C₂³	—	4	2	no	—
1142	C₂³	—	8	1	no	—
1143	C₂³	—	8	1	no	—
1144	C₂³	—	8	1	no	—
1145	C₂³	—	8	1	no	—
1146	C₂³	—	8	2	no	—
1147	C₂³	—	8	2	no	—
1148	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1149	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1150	Q₈	—	2	2	no	—
1151	Q₈	—	2	1	no	—
1152	Q₈	—	2	1	no	—
1153	Q₈	—	2	2	no	—
1154	Q₈	—	2	1	no	—
1155	Q₈	—	2	1	no	—
1156	Q₈	—	2	2	no	—
1157	Q₈	—	2	1	no	—
1158	Q₈	—	2	1	no	—
1159	Q₈	—	4	4	no	—
1160	Q₈	—	4	2	no	—
1161	Q₈	—	8	2	no	—
1162	D₄	—	2	4	no	—
1163	D₄	—	2	2	no	—
1164	D₄	—	2	2	no	—
1165	D₄	—	2	2	no	—
1166	D₄	—	2	1	no	—
1167	D₄	—	2	1	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	2	2	no	—
1172	D₄	—	2	1	no	—
1173	D₄	—	2	1	no	—
1174	D₄	—	4	4	no	—
1175	D₄	—	4	4	no	—
1176	D₄	—	4	4	no	—
1177	D₄	—	4	2	no	—
1178	D₄	—	4	2	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	8	1	no	—
1183	D₄	—	8	2	no	—
1184	D₄	—	8	2	no	—
1185	D₄	—	8	1	no	—
1186	D₄	—	8	2	no	—
1187	D₄	—	8	2	no	—
1188	D₄	—	8	2	no	—
1189	D₄	—	8	2	no	—
1190	D₄	—	8	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	4	1	no	—
1201	C₂×C₄	—	4	1	no	—
1202	C₂×C₄	—	4	2	no	—
1203	C₂×C₄	—	4	2	no	—
1204	C₂×C₄	—	4	4	no	—
1205	C₂×C₄	—	4	4	no	—
1206	C₂×C₄	—	4	4	no	—
1207	C₂×C₄	—	4	2	no	—
1208	C₂×C₄	—	4	4	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	4	2	no	—
1213	C₂×C₄	—	8	1	no	—
1214	C₂×C₄	—	8	2	no	—
1215	C₂×C₄	—	8	1	no	—
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	2	yes	—
1220	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1221	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1222	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1223	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1224	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1225	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1226	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1227	C₈	—	2	1	no	—
1228	C₈	—	2	1	no	—
1229	C₈	—	2	1	no	—
1230	C₈	—	2	1	no	—
1231	C₈	—	2	2	no	—
1232	C₈	—	2	2	no	—
1233	C₂²	—	2	1	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	2	no	—
1236	C₂²	—	2	2	no	—
1237	C₂²	—	2	2	no	—
1238	C₂²	—	4	1	no	—
1239	C₂²	—	4	1	no	—
1240	C₂²	—	4	2	no	—
1241	C₂²	—	4	2	no	—
1242	C₂²	—	4	1	no	—
1243	C₂²	—	4	2	no	—
1244	C₂²	—	4	1	no	—
1245	C₂²	—	4	1	no	—
1246	C₂²	—	4	2	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	1	no	—
1249	C₂²	—	4	2	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	8	4	no	—
1254	C₂²	—	16	2	no	—
1255	C₂²	—	16	4	no	—
1256	C₂²	C₅₃×#535	1	2	yes	—
1257	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1258	C₄	—	2	1	no	—
1259	C₄	—	2	1	no	—
1260	C₄	—	2	2	no	—
1261	C₄	—	2	1	no	—
1262	C₄	—	2	1	no	—
1263	C₄	—	2	2	no	—
1264	C₄	—	2	2	no	—
1265	C₄	—	4	1	no	—
1266	C₄	—	4	2	no	—
1267	C₄	—	4	1	no	—
1268	C₄	—	4	1	no	—
1269	C₄	—	4	2	no	—
1270	C₄	—	4	1	no	—
1271	C₄	—	4	1	no	—
1272	C₄	C₅₃×#535	1	2	yes	—
1273	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1274	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1275	C₂	—	2	2	no	—
1276	C₂	—	4	2	no	—
1277	C₂	—	8	2	no	—
1278	C₂	—	8	2	no	—
1279	C₂	—	8	1	no	—
1280	C₂	—	8	1	no	—
1281	C₂	—	8	1	no	—
1282	C₂	C₂×C₅₃×#535	1	1	yes	characteristic
1283	C₂	C₅₃×#3584	1	1	yes	characteristic
1284	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×#3500	C₂	semidirect
2. C₅₃×#3460	C₂	semidirect
3. C₅₃×#3225	C₂	semidirect
4. C₅₃×#3224	C₂	semidirect
5. C₅₃×#3221	C₂	semidirect
6. C₅₃×#3220	C₂	semidirect
7. C₅₃×#3219	C₂	semidirect
8. C₅₃×#3213	C₂	semidirect
9. C₅₃×#3211	C₂	semidirect
10. C₅₃×#3207	C₂	semidirect
11. C₅₃×#3155	C₂	semidirect
12. C₅₃×#3154	C₂	semidirect
13. C₅₃×#3137	C₂	semidirect
14. C₅₃×#3136	C₂	semidirect
15. C₅₃×#3040	C₂	semidirect
16. C₅₃×#3036	C₂	semidirect
17. C₅₃×#3035	C₂	semidirect
18. C₂×C₅₃×#463	C₂	semidirect
19. C₅₃×#3013	C₂	semidirect
20. C₅₃×#3012	C₂	semidirect
21. C₅₃×#3010	C₂	semidirect
22. C₅₃×#3008	C₂	semidirect
23. C₅₃×#2925	C₂	semidirect
26. C₂×#137×C₅₃	C₂²	semidirect
29. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
31. C₂×#135×C₅₃	C₂²	semidirect
32. C₂²×SD₁₆×C₅₃	C₂²	semidirect
40. C₅₃×#544	C₂²	semidirect
42. C₅₃×#542	C₂²	semidirect
44. C₅₃×#540	C₂²	semidirect
48. C₅₃×#536	C₂²	semidirect
51. C₅₃×#535	C₂²	semidirect
52. C₅₃×#535	C₂²	semidirect
55. C₅₃×#532	C₂²	semidirect
56. C₅₃×#532	C₂²	semidirect
58. C₅₃×#529	C₂²	semidirect
60. C₂×#124×C₅₃	C₂²	semidirect
63. C₄×#41×C₅₃	C₂²	semidirect
64. C₂×C₄×D₄×C₅₃	C₂²	semidirect
65. C₅₃×#497	C₂²	semidirect
66. C₅₃×#496	C₂²	semidirect
67. C₅₃×#496	C₂²	semidirect
68. C₅₃×#496	C₂²	semidirect
69. C₅₃×#495	C₂²	semidirect
70. C₅₃×#495	C₂²	semidirect
71. C₅₃×#493	C₂²	semidirect
72. C₅₃×#492	C₂²	semidirect
73. C₅₃×#491	C₂²	semidirect
74. C₅₃×#490	C₂²	semidirect
75. C₅₃×#489	C₂²	semidirect
76. C₅₃×#489	C₂²	semidirect
77. C₅₃×#488	C₂²	semidirect
78. C₅₃×#488	C₂²	semidirect
79. C₅₃×#487	C₂²	semidirect
80. C₅₃×#486	C₂²	semidirect
81. C₅₃×#464	C₂²	semidirect
82. C₅₃×#464	C₂²	semidirect
83. C₅₃×#464	C₂²	semidirect
84. C₅₃×#464	C₂²	semidirect
85. C₅₃×#463	C₂²	semidirect
86. C₅₃×#463	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#463	C₂²	semidirect
90. C₅₃×#463	C₂²	semidirect
91. C₅₃×#463	C₂²	semidirect
92. C₅₃×#463	C₂²	semidirect
93. C₅₃×#463	C₂²	semidirect
94. C₅₃×#463	C₂²	semidirect
95. C₅₃×#462	C₂²	semidirect
96. C₅₃×#461	C₂²	semidirect
97. C₅₃×#461	C₂²	semidirect
98. C₅₃×#460	C₂²	semidirect
99. C₅₃×#459	C₂²	semidirect
100. C₅₃×#459	C₂²	semidirect
101. C₅₃×#452	C₂²	semidirect
102. C₅₃×#452	C₂²	semidirect
103. C₅₃×#451	C₂²	semidirect
104. C₅₃×#450	C₂²	semidirect
107. C₅₃×#449	C₂²	semidirect
108. C₅₃×#449	C₂²	semidirect
109. C₅₃×#449	C₂²	semidirect
110. C₅₃×#449	C₂²	semidirect
111. C₅₃×#448	C₂²	semidirect
112. C₅₃×#448	C₂²	semidirect
113. C₅₃×#448	C₂²	semidirect
116. C₅₃×#447	C₂²	semidirect
117. C₅₃×#433	C₂²	semidirect
118. C₅₃×#433	C₂²	semidirect
119. C₅₃×#432	C₂²	semidirect
120. C₅₃×#431	C₂²	semidirect
121. C₅₃×#423	C₂²	semidirect
122. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
123. C₅₃×#419	C₂²	semidirect
126. C₅₃×#417	C₂²	semidirect
128. C₅₃×#416	C₂²	semidirect
129. C₂×#103×C₅₃	C₂²	semidirect
133. C₅₃×#405	C₂²	semidirect
134. C₅₃×#405	C₂²	semidirect
590. #60834	C₅₃	direct (N × H)
633. #3500	C₂×C₅₃	semidirect
634. #3460	C₂×C₅₃	semidirect
635. #3225	C₂×C₅₃	semidirect
636. #3224	C₂×C₅₃	semidirect
637. #3221	C₂×C₅₃	semidirect
638. #3220	C₂×C₅₃	semidirect
639. #3219	C₂×C₅₃	semidirect
640. #3213	C₂×C₅₃	semidirect
641. #3211	C₂×C₅₃	semidirect
642. #3207	C₂×C₅₃	semidirect
643. #3155	C₂×C₅₃	semidirect
644. #3154	C₂×C₅₃	semidirect
645. #3137	C₂×C₅₃	semidirect
646. #3136	C₂×C₅₃	semidirect
647. #3040	C₂×C₅₃	semidirect
648. #3036	C₂×C₅₃	semidirect
649. #3035	C₂×C₅₃	semidirect
650. C₂×#463	C₂×C₅₃	semidirect
651. #3013	C₂×C₅₃	semidirect
652. #3012	C₂×C₅₃	semidirect
653. #3010	C₂×C₅₃	semidirect
654. #3008	C₂×C₅₃	semidirect
655. #2925	C₂×C₅₃	semidirect
668. C₂×#137	C₂²×C₅₃	semidirect
671. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
673. C₂×#135	C₂²×C₅₃	semidirect
674. C₂²×SD₁₆	C₂²×C₅₃	semidirect
682. #544	C₂²×C₅₃	semidirect
684. #542	C₂²×C₅₃	semidirect
686. #540	C₂²×C₅₃	semidirect
690. #536	C₂²×C₅₃	semidirect
693. #535	C₂²×C₅₃	semidirect
694. #535	C₂²×C₅₃	semidirect
697. #532	C₂²×C₅₃	semidirect
698. #532	C₂²×C₅₃	semidirect
700. #529	C₂²×C₅₃	semidirect
702. C₂×#124	C₂²×C₅₃	semidirect
705. C₄×#41	C₂²×C₅₃	semidirect
706. C₂×C₄×D₄	C₂²×C₅₃	semidirect
707. #497	C₂²×C₅₃	semidirect
708. #496	C₂²×C₅₃	semidirect
709. #496	C₂²×C₅₃	semidirect
710. #496	C₂²×C₅₃	semidirect
711. #495	C₂²×C₅₃	semidirect
712. #495	C₂²×C₅₃	semidirect
713. #493	C₂²×C₅₃	semidirect
714. #492	C₂²×C₅₃	semidirect
715. #491	C₂²×C₅₃	semidirect
716. #490	C₂²×C₅₃	semidirect
717. #489	C₂²×C₅₃	semidirect
718. #489	C₂²×C₅₃	semidirect
719. #488	C₂²×C₅₃	semidirect
720. #488	C₂²×C₅₃	semidirect
721. #487	C₂²×C₅₃	semidirect
722. #486	C₂²×C₅₃	semidirect
723. #464	C₂²×C₅₃	semidirect
724. #464	C₂²×C₅₃	semidirect
725. #464	C₂²×C₅₃	semidirect
726. #464	C₂²×C₅₃	semidirect
727. #463	C₂²×C₅₃	semidirect
728. #463	C₂²×C₅₃	semidirect
729. #463	C₂²×C₅₃	semidirect
730. #463	C₂²×C₅₃	semidirect
731. #463	C₂²×C₅₃	semidirect
732. #463	C₂²×C₅₃	semidirect
733. #463	C₂²×C₅₃	semidirect
734. #463	C₂²×C₅₃	semidirect
735. #463	C₂²×C₅₃	semidirect
736. #463	C₂²×C₅₃	semidirect
737. #462	C₂²×C₅₃	semidirect
738. #461	C₂²×C₅₃	semidirect
739. #461	C₂²×C₅₃	semidirect
740. #460	C₂²×C₅₃	semidirect
741. #459	C₂²×C₅₃	semidirect
742. #459	C₂²×C₅₃	semidirect
743. #452	C₂²×C₅₃	semidirect
744. #452	C₂²×C₅₃	semidirect
745. #451	C₂²×C₅₃	semidirect
746. #450	C₂²×C₅₃	semidirect
749. #449	C₂²×C₅₃	semidirect
750. #449	C₂²×C₅₃	semidirect
751. #449	C₂²×C₅₃	semidirect
752. #449	C₂²×C₅₃	semidirect
753. #448	C₂²×C₅₃	semidirect
754. #448	C₂²×C₅₃	semidirect
755. #448	C₂²×C₅₃	semidirect
758. #447	C₂²×C₅₃	semidirect
759. #433	C₂²×C₅₃	semidirect
760. #433	C₂²×C₅₃	semidirect
761. #432	C₂²×C₅₃	semidirect
762. #431	C₂²×C₅₃	semidirect
763. #423	C₂²×C₅₃	semidirect
764. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
765. #419	C₂²×C₅₃	semidirect
768. #417	C₂²×C₅₃	semidirect
770. #416	C₂²×C₅₃	semidirect
771. C₂×#103	C₂²×C₅₃	semidirect
775. #405	C₂²×C₅₃	semidirect
776. #405	C₂²×C₅₃	semidirect
777. C₅₃	#60834	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×#3500	2
C₅₃×#3460	2
C₅₃×#3225	2
C₅₃×#3224	2
C₅₃×#3221	2
C₅₃×#3220	2
C₅₃×#3219	2
C₅₃×#3213	2
C₅₃×#3211	2
C₅₃×#3207	2
C₅₃×#3155	2
C₅₃×#3154	2
C₅₃×#3137	2
C₅₃×#3136	2
C₅₃×#3040	2
C₅₃×#3036	2
C₅₃×#3035	2
C₂×C₅₃×#463	2
C₅₃×#3013	2
C₅₃×#3012	2
C₅₃×#3010	2
C₅₃×#3008	2
C₅₃×#2925	2
#60834	53

Subgroups — C53×#60834 #27268346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60834 #27268346