Subgroups — C₅₃×#60765 #27268277

Order 13568.

2250 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3204	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3198	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3196	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3192	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3188	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3187	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3099	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3062	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3060	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3012	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
20	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
22	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
23	C₂×#131×C₅₃	C₂²	1	2	yes	complemented
24	C₅₃×#550	—	2	1	no	—
25	C₅₃×#548	—	2	1	no	—
26	C₅₃×#546	—	2	2	no	—
27	C₅₃×#546	—	2	1	no	—
28	D₄²×C₅₃	—	2	1	no	—
29	D₄²×C₅₃	—	2	2	no	—
30	C₅₃×#537	—	2	2	no	—
31	C₅₃×#537	—	2	1	no	—
32	C₅₃×#537	—	2	1	no	—
33	C₅₃×#537	C₂²	1	2	yes	—
34	C₅₃×#537	C₂²	1	4	yes	complemented
35	C₅₃×#537	C₂²	1	2	yes	complemented
36	C₅₃×#537	C₂²	1	2	yes	complemented
37	C₅₃×#537	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#535	C₂²	1	2	yes	complemented
39	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#525	C₂²	1	2	yes	—
41	C₅₃×#525	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
43	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
44	C₂×#121×C₅₃	—	2	1	no	—
45	C₂×#121×C₅₃	—	2	2	no	—
46	C₂×#121×C₅₃	C₂²	1	2	yes	—
47	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
49	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#485	C₂²	1	4	yes	complemented
52	C₅₃×#484	C₂²	1	2	yes	complemented
53	C₅₃×#483	C₂²	1	2	yes	complemented
54	C₅₃×#483	C₂²	1	4	yes	complemented
55	C₅₃×#482	C₂²	1	4	yes	complemented
56	C₅₃×#481	C₂²	1	2	yes	complemented
57	C₅₃×#481	C₂²	1	4	yes	complemented
58	C₅₃×#481	C₂²	1	2	yes	complemented
59	C₅₃×#481	C₂²	1	4	yes	complemented
60	C₅₃×#481	C₂²	1	2	yes	complemented
61	C₅₃×#480	C₂²	1	2	yes	complemented
62	C₅₃×#470	C₂²	1	4	yes	complemented
63	C₅₃×#469	C₂²	1	4	yes	complemented
64	C₅₃×#469	C₂²	1	4	yes	complemented
65	C₅₃×#468	C₂²	1	4	yes	complemented
66	C₅₃×#466	C₂²	1	4	yes	complemented
67	C₅₃×#465	C₂²	1	4	yes	complemented
68	C₅₃×#465	C₂²	1	4	yes	complemented
69	C₅₃×#465	C₂²	1	4	yes	complemented
70	C₅₃×#452	C₂²	1	4	yes	complemented
71	C₅₃×#452	C₂²	1	2	yes	complemented
72	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#450	C₂²	1	4	yes	complemented
74	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#449	C₂²	1	2	yes	complemented
76	C₅₃×#449	C₂²	1	4	yes	complemented
77	C₅₃×#449	C₂²	1	4	yes	complemented
78	C₅₃×#448	C₂²	1	2	yes	complemented
79	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#447	C₂²	1	4	yes	complemented
82	C₅₃×#447	C₂²	1	2	yes	complemented
83	C₅₃×#428	C₂²	1	2	yes	complemented
84	C₂×#106×C₅₃	C₂²	1	2	yes	complemented
85	C₅₃×#417	C₂²	1	2	yes	complemented
86	C₅₃×#417	C₂²	1	2	yes	complemented
87	C₅₃×#416	C₂²	1	2	yes	complemented
88	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
89	C₅₃×#408	C₂²	1	4	yes	complemented
90	C₅₃×#408	C₂²	1	2	yes	complemented
91	C₅₃×#407	C₂²	1	2	yes	complemented
92	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
93	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	complemented
95	H(5,𝔽₂)×C₅₃	—	4	4	no	—
96	C₂×#41×C₅₃	—	2	1	no	—
97	C₂×#41×C₅₃	—	2	1	no	—
98	C₂×#41×C₅₃	—	2	1	no	—
99	C₂×#41×C₅₃	—	4	4	no	—
100	C₂×#41×C₅₃	—	4	4	no	—
101	C₂×#41×C₅₃	D₄	1	2	yes	—
102	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
103	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
104	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
105	C₂×#41×C₅₃	C₂³	1	2	yes	—
106	C₂×#41×C₅₃	C₂³	1	2	yes	—
107	C₂×#41×C₅₃	C₂³	1	2	yes	—
108	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
109	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
110	C₂×#41×C₅₃	C₂³	1	2	yes	—
111	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
112	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₅₃	—	2	1	no	—
114	C₂²×D₄×C₅₃	—	2	2	no	—
115	C₂²×D₄×C₅₃	—	2	1	no	—
116	C₂²×D₄×C₅₃	—	2	2	no	—
117	C₂²×D₄×C₅₃	—	2	2	no	—
118	C₂²×D₄×C₅₃	—	2	1	no	—
119	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
120	C₂²×D₄×C₅₃	D₄	1	2	yes	—
121	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
123	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₅₃	—	2	1	no	—
125	C₂³×C₄×C₅₃	—	2	1	no	—
126	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
128	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
129	#135×C₅₃	—	4	4	no	—
130	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
132	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
133	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
134	C₂×D₈×C₅₃	C₂³	1	2	yes	—
135	C₂×D₈×C₅₃	C₂³	1	4	yes	—
136	#131×C₅₃	—	4	4	no	—
137	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
138	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
139	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
140	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
141	#127×C₅₃	—	2	1	no	—
142	#127×C₅₃	—	2	2	no	—
143	#124×C₅₃	—	2	1	no	—
144	#124×C₅₃	—	2	2	no	—
145	#123×C₅₃	—	2	1	no	—
146	#123×C₅₃	—	2	2	no	—
147	C₂²⋊Q₈×C₅₃	—	2	2	no	—
148	C₂²⋊Q₈×C₅₃	—	2	2	no	—
149	C₂²⋊Q₈×C₅₃	—	2	4	no	—
150	C₂²⋊Q₈×C₅₃	—	2	1	no	—
151	C₂²⋊Q₈×C₅₃	—	2	2	no	—
152	C₂²⋊Q₈×C₅₃	—	2	2	no	—
153	C₂²⋊Q₈×C₅₃	—	2	2	no	—
154	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
155	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
156	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
159	#121×C₅₃	—	2	4	no	—
160	#121×C₅₃	—	2	2	no	—
161	#121×C₅₃	—	2	4	no	—
162	#121×C₅₃	—	2	4	no	—
163	#121×C₅₃	—	2	4	no	—
164	#121×C₅₃	—	2	2	no	—
165	#121×C₅₃	—	2	4	no	—
166	#121×C₅₃	—	2	2	no	—
167	#121×C₅₃	—	2	2	no	—
168	#121×C₅₃	—	2	2	no	—
169	#121×C₅₃	—	2	1	no	—
170	#121×C₅₃	—	2	2	no	—
171	#121×C₅₃	—	2	1	no	—
172	#121×C₅₃	—	2	2	no	—
173	#121×C₅₃	—	2	1	no	—
174	#121×C₅₃	—	2	2	no	—
175	#121×C₅₃	—	2	2	no	—
176	#121×C₅₃	—	2	2	no	—
177	#121×C₅₃	C₂³	1	1	yes	characteristic
178	#121×C₅₃	C₂³	1	2	yes	—
179	#121×C₅₃	C₂³	1	2	yes	—
180	#121×C₅₃	C₂³	1	2	yes	—
181	#121×C₅₃	C₂³	1	2	yes	—
182	#121×C₅₃	C₂³	1	4	yes	—
183	#121×C₅₃	C₂³	1	4	yes	—
184	#121×C₅₃	C₂³	1	1	yes	characteristic
185	#121×C₅₃	C₂³	1	2	yes	—
186	#120×C₅₃	—	2	1	no	—
187	#120×C₅₃	—	2	2	no	—
188	#120×C₅₃	—	2	2	no	—
189	#120×C₅₃	—	2	2	no	—
190	#120×C₅₃	—	2	2	no	—
191	C₄×Q₈×C₅₃	—	2	1	no	—
192	C₄×D₄×C₅₃	—	2	1	no	—
193	C₄×D₄×C₅₃	—	2	2	no	—
194	C₄×D₄×C₅₃	—	2	1	no	—
195	C₄×D₄×C₅₃	—	2	2	no	—
196	C₄×D₄×C₅₃	—	2	1	no	—
197	C₄×D₄×C₅₃	—	2	2	no	—
198	#117×C₅₃	C₂³	1	2	yes	—
199	#117×C₅₃	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
201	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
202	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
203	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
204	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
207	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
210	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
211	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
212	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
213	#107×C₅₃	C₂³	1	4	yes	—
214	#106×C₅₃	C₂³	1	4	yes	—
215	#106×C₅₃	C₂³	1	4	yes	—
216	#106×C₅₃	C₂³	1	4	yes	—
217	#103×C₅₃	C₂³	1	2	yes	—
218	#103×C₅₃	C₂³	1	4	yes	—
219	#103×C₅₃	C₂³	1	2	yes	—
220	#103×C₅₃	C₂³	1	4	yes	—
221	#102×C₅₃	C₂³	1	4	yes	—
222	#102×C₅₃	C₂³	1	4	yes	—
223	#102×C₅₃	C₂³	1	2	yes	—
224	#102×C₅₃	C₂³	1	2	yes	—
225	#102×C₅₃	C₂³	1	4	yes	—
226	#102×C₅₃	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
228	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
230	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
232	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
233	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
234	C₂⁴×C₅₃	—	2	1	no	—
235	C₂⁴×C₅₃	—	2	2	no	—
236	C₂⁴×C₅₃	—	2	1	no	—
237	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
238	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
239	#41×C₅₃	—	2	4	no	—
240	#41×C₅₃	—	2	4	no	—
241	#41×C₅₃	—	2	4	no	—
242	#41×C₅₃	—	2	4	no	—
243	#41×C₅₃	—	2	4	no	—
244	#41×C₅₃	—	4	4	no	—
245	#41×C₅₃	—	4	4	no	—
246	#41×C₅₃	—	4	2	no	—
247	#41×C₅₃	—	4	2	no	—
248	#41×C₅₃	—	4	2	no	—
249	#41×C₅₃	—	4	2	no	—
250	#41×C₅₃	—	4	4	no	—
251	#41×C₅₃	—	4	4	no	—
252	#41×C₅₃	—	4	4	no	—
253	#41×C₅₃	—	4	4	no	—
254	C₂×Q₈×C₅₃	—	2	1	no	—
255	C₂×Q₈×C₅₃	—	4	2	no	—
256	C₂×Q₈×C₅₃	—	4	2	no	—
257	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
258	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
259	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
260	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
261	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
262	C₂×D₄×C₅₃	—	2	1	no	—
263	C₂×D₄×C₅₃	—	2	2	no	—
264	C₂×D₄×C₅₃	—	2	2	no	—
265	C₂×D₄×C₅₃	—	2	1	no	—
266	C₂×D₄×C₅₃	—	2	2	no	—
267	C₂×D₄×C₅₃	—	2	2	no	—
268	C₂×D₄×C₅₃	—	2	1	no	—
269	C₂×D₄×C₅₃	—	2	2	no	—
270	C₂×D₄×C₅₃	—	2	2	no	—
271	C₂×D₄×C₅₃	—	2	2	no	—
272	C₂×D₄×C₅₃	—	2	2	no	—
273	C₂×D₄×C₅₃	—	2	4	no	—
274	C₂×D₄×C₅₃	—	2	4	no	—
275	C₂×D₄×C₅₃	—	2	1	no	—
276	C₂×D₄×C₅₃	—	2	2	no	—
277	C₂×D₄×C₅₃	—	2	1	no	—
278	C₂×D₄×C₅₃	—	2	4	no	—
279	C₂×D₄×C₅₃	—	4	2	no	—
280	C₂×D₄×C₅₃	—	4	2	no	—
281	C₂×D₄×C₅₃	—	4	4	no	—
282	C₂×D₄×C₅₃	—	4	4	no	—
283	C₂×D₄×C₅₃	—	4	8	no	—
284	C₂×D₄×C₅₃	—	4	4	no	—
285	C₂×D₄×C₅₃	—	4	4	no	—
286	C₂×D₄×C₅₃	—	8	4	no	—
287	C₂×D₄×C₅₃	—	8	2	no	—
288	C₂×D₄×C₅₃	—	8	4	no	—
289	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
290	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
291	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
292	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
293	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
294	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
295	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
296	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
297	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
298	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅₃	—	2	4	no	—
300	C₂²×C₄×C₅₃	—	2	2	no	—
301	C₂²×C₄×C₅₃	—	2	1	no	—
302	C₂²×C₄×C₅₃	—	2	2	no	—
303	C₂²×C₄×C₅₃	—	2	1	no	—
304	C₂²×C₄×C₅₃	—	2	2	no	—
305	C₂²×C₄×C₅₃	—	2	2	no	—
306	C₂²×C₄×C₅₃	—	2	2	no	—
307	C₂²×C₄×C₅₃	—	2	1	no	—
308	C₂²×C₄×C₅₃	—	2	2	no	—
309	C₂²×C₄×C₅₃	—	2	2	no	—
310	C₂²×C₄×C₅₃	—	4	4	no	—
311	C₂²×C₄×C₅₃	—	4	4	no	—
312	C₂²×C₄×C₅₃	—	8	2	no	—
313	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
317	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
318	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
319	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
324	Q₁₆×C₅₃	—	4	2	no	—
325	SD₁₆×C₅₃	—	4	2	no	—
326	SD₁₆×C₅₃	—	4	2	no	—
327	SD₁₆×C₅₃	—	4	4	no	—
328	D₈×C₅₃	—	4	2	no	—
329	D₈×C₅₃	—	4	4	no	—
330	M₁₆×C₅₃	—	2	4	no	—
331	M₁₆×C₅₃	—	4	4	no	—
332	C₂×C₈×C₅₃	—	2	4	no	—
333	C₂×C₈×C₅₃	—	4	4	no	—
334	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
335	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
336	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
337	C₄⋊C₄×C₅₃	—	2	2	no	—
338	C₄⋊C₄×C₅₃	—	2	2	no	—
339	C₄⋊C₄×C₅₃	—	2	2	no	—
340	C₄⋊C₄×C₅₃	—	2	4	no	—
341	C₄⋊C₄×C₅₃	—	2	4	no	—
342	C₄⋊C₄×C₅₃	—	2	2	no	—
343	C₄⋊C₄×C₅₃	—	2	1	no	—
344	C₄⋊C₄×C₅₃	—	2	1	no	—
345	C₄⋊C₄×C₅₃	—	2	1	no	—
346	C₄⋊C₄×C₅₃	—	2	2	no	—
347	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
348	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
350	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
351	C₂²⋊C₄×C₅₃	—	2	4	no	—
352	C₂²⋊C₄×C₅₃	—	2	4	no	—
353	C₂²⋊C₄×C₅₃	—	2	2	no	—
354	C₂²⋊C₄×C₅₃	—	2	1	no	—
355	C₂²⋊C₄×C₅₃	—	2	1	no	—
356	C₂²⋊C₄×C₅₃	—	2	1	no	—
357	C₂²⋊C₄×C₅₃	—	2	2	no	—
358	C₂²⋊C₄×C₅₃	—	2	2	no	—
359	C₂²⋊C₄×C₅₃	—	2	1	no	—
360	C₂²⋊C₄×C₅₃	—	2	2	no	—
361	C₂²⋊C₄×C₅₃	—	2	2	no	—
362	C₂²⋊C₄×C₅₃	—	2	2	no	—
363	C₂²⋊C₄×C₅₃	—	2	4	no	—
364	C₂²⋊C₄×C₅₃	—	2	4	no	—
365	C₂²⋊C₄×C₅₃	—	2	1	no	—
366	C₂²⋊C₄×C₅₃	—	2	2	no	—
367	C₄²×C₅₃	—	2	2	no	—
368	C₄²×C₅₃	—	2	1	no	—
369	C₂³×C₅₃	—	2	2	no	—
370	C₂³×C₅₃	—	2	2	no	—
371	C₂³×C₅₃	—	2	4	no	—
372	C₂³×C₅₃	—	2	2	no	—
373	C₂³×C₅₃	—	2	2	no	—
374	C₂³×C₅₃	—	2	1	no	—
375	C₂³×C₅₃	—	4	1	no	—
376	C₂³×C₅₃	—	4	2	no	—
377	C₂³×C₅₃	—	4	2	no	—
378	C₂³×C₅₃	—	4	2	no	—
379	C₂³×C₅₃	—	4	2	no	—
380	C₂³×C₅₃	—	4	4	no	—
381	C₂³×C₅₃	—	4	2	no	—
382	C₂³×C₅₃	—	4	2	no	—
383	C₂³×C₅₃	—	8	1	no	—
384	C₂³×C₅₃	—	8	2	no	—
385	C₂³×C₅₃	—	8	1	no	—
386	C₂³×C₅₃	—	8	2	no	—
387	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
388	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
389	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
390	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
391	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
392	Q₈×C₅₃	—	2	2	no	—
393	Q₈×C₅₃	—	2	2	no	—
394	Q₈×C₅₃	—	2	2	no	—
395	Q₈×C₅₃	—	2	2	no	—
396	Q₈×C₅₃	—	2	2	no	—
397	Q₈×C₅₃	—	4	2	no	—
398	Q₈×C₅₃	—	4	2	no	—
399	D₄×C₅₃	—	2	4	no	—
400	D₄×C₅₃	—	2	4	no	—
401	D₄×C₅₃	—	2	2	no	—
402	D₄×C₅₃	—	2	2	no	—
403	D₄×C₅₃	—	2	4	no	—
404	D₄×C₅₃	—	2	2	no	—
405	D₄×C₅₃	—	2	2	no	—
406	D₄×C₅₃	—	2	2	no	—
407	D₄×C₅₃	—	4	2	no	—
408	D₄×C₅₃	—	4	2	no	—
409	D₄×C₅₃	—	4	2	no	—
410	D₄×C₅₃	—	4	4	no	—
411	D₄×C₅₃	—	4	2	no	—
412	D₄×C₅₃	—	4	4	no	—
413	D₄×C₅₃	—	4	4	no	—
414	D₄×C₅₃	—	4	2	no	—
415	D₄×C₅₃	—	4	4	no	—
416	D₄×C₅₃	—	4	4	no	—
417	D₄×C₅₃	—	4	2	no	—
418	D₄×C₅₃	—	4	2	no	—
419	D₄×C₅₃	—	8	1	no	—
420	D₄×C₅₃	—	8	2	no	—
421	D₄×C₅₃	—	8	4	no	—
422	D₄×C₅₃	—	8	4	no	—
423	D₄×C₅₃	—	8	2	no	—
424	D₄×C₅₃	—	8	2	no	—
425	D₄×C₅₃	—	8	2	no	—
426	C₂×C₄×C₅₃	—	2	2	no	—
427	C₂×C₄×C₅₃	—	2	2	no	—
428	C₂×C₄×C₅₃	—	2	2	no	—
429	C₂×C₄×C₅₃	—	2	2	no	—
430	C₂×C₄×C₅₃	—	2	2	no	—
431	C₂×C₄×C₅₃	—	2	4	no	—
432	C₂×C₄×C₅₃	—	2	4	no	—
433	C₂×C₄×C₅₃	—	2	1	no	—
434	C₂×C₄×C₅₃	—	2	2	no	—
435	C₂×C₄×C₅₃	—	2	4	no	—
436	C₂×C₄×C₅₃	—	2	1	no	—
437	C₂×C₄×C₅₃	—	2	2	no	—
438	C₂×C₄×C₅₃	—	2	1	no	—
439	C₂×C₄×C₅₃	—	4	2	no	—
440	C₂×C₄×C₅₃	—	4	2	no	—
441	C₂×C₄×C₅₃	—	4	2	no	—
442	C₂×C₄×C₅₃	—	4	4	no	—
443	C₂×C₄×C₅₃	—	4	4	no	—
444	C₂×C₄×C₅₃	—	4	2	no	—
445	C₂×C₄×C₅₃	—	4	4	no	—
446	C₂×C₄×C₅₃	—	4	4	no	—
447	C₂×C₄×C₅₃	—	4	2	no	—
448	C₂×C₄×C₅₃	—	8	2	no	—
449	C₂×C₄×C₅₃	—	8	2	no	—
450	C₂×C₄×C₅₃	—	8	1	no	—
451	C₂×C₄×C₅₃	—	8	2	no	—
452	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
458	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
459	C₈×C₅₃	—	2	2	no	—
460	C₈×C₅₃	—	2	2	no	—
461	C₈×C₅₃	—	2	4	no	—
462	#60765	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
463	C₂²×C₅₃	—	2	1	no	—
464	C₂²×C₅₃	—	2	1	no	—
465	C₂²×C₅₃	—	2	1	no	—
466	C₂²×C₅₃	—	2	1	no	—
467	C₂²×C₅₃	—	2	1	no	—
468	C₂²×C₅₃	—	2	2	no	—
469	C₂²×C₅₃	—	2	2	no	—
470	C₂²×C₅₃	—	2	1	no	—
471	C₂²×C₅₃	—	2	2	no	—
472	C₂²×C₅₃	—	2	2	no	—
473	C₂²×C₅₃	—	2	2	no	—
474	C₂²×C₅₃	—	2	1	no	—
475	C₂²×C₅₃	—	2	2	no	—
476	C₂²×C₅₃	—	4	4	no	—
477	C₂²×C₅₃	—	4	2	no	—
478	C₂²×C₅₃	—	4	2	no	—
479	C₂²×C₅₃	—	4	1	no	—
480	C₂²×C₅₃	—	4	2	no	—
481	C₂²×C₅₃	—	4	2	no	—
482	C₂²×C₅₃	—	4	1	no	—
483	C₂²×C₅₃	—	4	2	no	—
484	C₂²×C₅₃	—	4	1	no	—
485	C₂²×C₅₃	—	4	2	no	—
486	C₂²×C₅₃	—	8	4	no	—
487	C₂²×C₅₃	—	8	4	no	—
488	C₂²×C₅₃	—	16	2	no	—
489	C₂²×C₅₃	—	16	4	no	—
490	C₂²×C₅₃	#534	1	2	yes	—
491	C₂²×C₅₃	#577	1	2	yes	—
492	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
493	C₄×C₅₃	—	2	1	no	—
494	C₄×C₅₃	—	2	1	no	—
495	C₄×C₅₃	—	2	2	no	—
496	C₄×C₅₃	—	2	2	no	—
497	C₄×C₅₃	—	4	4	no	—
498	C₄×C₅₃	—	4	1	no	—
499	C₄×C₅₃	—	4	1	no	—
500	C₄×C₅₃	—	4	2	no	—
501	C₄×C₅₃	—	4	2	no	—
502	C₄×C₅₃	—	4	1	no	—
503	C₄×C₅₃	#534	1	2	yes	—
504	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
505	#3488	C₂×C₅₃	1	1	yes	characteristic, complemented
506	C₂×#537	C₂×C₅₃	1	1	yes	characteristic, complemented
507	#3204	C₂×C₅₃	1	4	yes	complemented
508	#3198	C₂×C₅₃	1	4	yes	complemented
509	#3196	C₂×C₅₃	1	2	yes	complemented
510	#3192	C₂×C₅₃	1	2	yes	complemented
511	#3188	C₂×C₅₃	1	2	yes	complemented
512	#3187	C₂×C₅₃	1	2	yes	complemented
513	#3099	C₂×C₅₃	1	2	yes	complemented
514	#3092	C₂×C₅₃	1	1	yes	characteristic, complemented
515	C₂×#481	C₂×C₅₃	1	1	yes	characteristic, complemented
516	#3062	C₂×C₅₃	1	2	yes	complemented
517	#3060	C₂×C₅₃	1	2	yes	complemented
518	#3012	C₂×C₅₃	1	2	yes	complemented
519	#3006	C₂×C₅₃	1	1	yes	characteristic, complemented
520	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
521	#2880	C₂×C₅₃	1	1	yes	characteristic, complemented
522	C₂×C₅₃	—	2	2	no	—
523	C₂×C₅₃	—	2	2	no	—
524	C₂×C₅₃	—	4	1	no	—
525	C₂×C₅₃	—	4	2	no	—
526	C₂×C₅₃	—	4	2	no	—
527	C₂×C₅₃	—	8	2	no	—
528	C₂×C₅₃	—	8	2	no	—
529	C₂×C₅₃	—	8	1	no	—
530	C₂×C₅₃	C₂×#534	1	1	yes	characteristic
531	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
532	C₂×C₅₃	#3585	1	1	yes	characteristic
533	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic, complemented
534	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
535	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
536	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
537	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
538	C₂×#131	C₂²×C₅₃	1	2	yes	complemented
539	#550	—	2	1	no	—
540	#548	—	2	1	no	—
541	#546	—	2	2	no	—
542	#546	—	2	1	no	—
543	D₄²	—	2	1	no	—
544	D₄²	—	2	2	no	—
545	#537	—	2	2	no	—
546	#537	—	2	1	no	—
547	#537	—	2	1	no	—
548	#537	C₂²×C₅₃	1	2	yes	—
549	#537	C₂²×C₅₃	1	4	yes	complemented
550	#537	C₂²×C₅₃	1	2	yes	complemented
551	#537	C₂²×C₅₃	1	2	yes	complemented
552	#537	C₂²×C₅₃	1	1	yes	characteristic, complemented
553	#535	C₂²×C₅₃	1	2	yes	complemented
554	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
555	#525	C₂²×C₅₃	1	1	yes	characteristic
556	#525	C₂²×C₅₃	1	2	yes	—
557	C₂×C₂²⋊Q₈	—	2	1	no	—
558	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
559	C₂×#121	—	2	1	no	—
560	C₂×#121	—	2	2	no	—
561	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
562	C₂×#121	C₂²×C₅₃	1	2	yes	—
563	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
564	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
565	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
566	#485	C₂²×C₅₃	1	4	yes	complemented
567	#484	C₂²×C₅₃	1	2	yes	complemented
568	#483	C₂²×C₅₃	1	2	yes	complemented
569	#483	C₂²×C₅₃	1	4	yes	complemented
570	#482	C₂²×C₅₃	1	4	yes	complemented
571	#481	C₂²×C₅₃	1	2	yes	complemented
572	#481	C₂²×C₅₃	1	2	yes	complemented
573	#481	C₂²×C₅₃	1	4	yes	complemented
574	#481	C₂²×C₅₃	1	2	yes	complemented
575	#481	C₂²×C₅₃	1	4	yes	complemented
576	#480	C₂²×C₅₃	1	2	yes	complemented
577	#470	C₂²×C₅₃	1	4	yes	complemented
578	#469	C₂²×C₅₃	1	4	yes	complemented
579	#469	C₂²×C₅₃	1	4	yes	complemented
580	#468	C₂²×C₅₃	1	4	yes	complemented
581	#466	C₂²×C₅₃	1	4	yes	complemented
582	#465	C₂²×C₅₃	1	4	yes	complemented
583	#465	C₂²×C₅₃	1	4	yes	complemented
584	#465	C₂²×C₅₃	1	4	yes	complemented
585	#452	C₂²×C₅₃	1	4	yes	complemented
586	#452	C₂²×C₅₃	1	2	yes	complemented
587	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
588	#450	C₂²×C₅₃	1	4	yes	complemented
589	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
590	#449	C₂²×C₅₃	1	4	yes	complemented
591	#449	C₂²×C₅₃	1	2	yes	complemented
592	#449	C₂²×C₅₃	1	4	yes	complemented
593	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
594	#448	C₂²×C₅₃	1	2	yes	complemented
595	#447	C₂²×C₅₃	1	2	yes	complemented
596	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
597	#447	C₂²×C₅₃	1	4	yes	complemented
598	#428	C₂²×C₅₃	1	2	yes	complemented
599	C₂×#106	C₂²×C₅₃	1	2	yes	complemented
600	#417	C₂²×C₅₃	1	2	yes	complemented
601	#417	C₂²×C₅₃	1	2	yes	complemented
602	#416	C₂²×C₅₃	1	2	yes	complemented
603	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
604	#408	C₂²×C₅₃	1	2	yes	complemented
605	#408	C₂²×C₅₃	1	4	yes	complemented
606	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
607	#407	C₂²×C₅₃	1	2	yes	complemented
608	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
609	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	complemented
610	C₅₃	#60765	1	1	yes	characteristic, direct product factor, Sylow
611	H(5,𝔽₂)	—	4	4	no	—
612	C₂×#41	—	2	1	no	—
613	C₂×#41	—	2	1	no	—
614	C₂×#41	—	2	1	no	—
615	C₂×#41	—	4	4	no	—
616	C₂×#41	—	4	4	no	—
617	C₂×#41	D₄×C₅₃	1	2	yes	—
618	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
619	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
620	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
621	C₂×#41	C₂³×C₅₃	1	2	yes	—
622	C₂×#41	C₂³×C₅₃	1	2	yes	—
623	C₂×#41	C₂³×C₅₃	1	2	yes	—
624	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
625	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
626	C₂×#41	C₂³×C₅₃	1	2	yes	—
627	C₂²×Q₈	D₄×C₅₃	1	1	yes	characteristic
628	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
629	C₂²×D₄	—	2	1	no	—
630	C₂²×D₄	—	2	2	no	—
631	C₂²×D₄	—	2	1	no	—
632	C₂²×D₄	—	2	2	no	—
633	C₂²×D₄	—	2	2	no	—
634	C₂²×D₄	—	2	1	no	—
635	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
636	C₂²×D₄	D₄×C₅₃	1	2	yes	—
637	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
638	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
639	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
640	C₂³×C₄	—	2	1	no	—
641	C₂³×C₄	—	2	1	no	—
642	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
643	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
644	AGL(1,ℤ/8)	—	4	4	no	—
645	#135	—	4	4	no	—
646	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
647	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
648	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
649	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
650	C₂×D₈	C₂³×C₅₃	1	2	yes	—
651	C₂×D₈	C₂³×C₅₃	1	4	yes	—
652	#131	—	4	4	no	—
653	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
654	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
655	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
656	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
657	#127	—	2	1	no	—
658	#127	—	2	2	no	—
659	#124	—	2	1	no	—
660	#124	—	2	2	no	—
661	#123	—	2	1	no	—
662	#123	—	2	2	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	—	2	4	no	—
666	C₂²⋊Q₈	—	2	1	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
671	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
672	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
673	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
674	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
675	#121	—	2	2	no	—
676	#121	—	2	4	no	—
677	#121	—	2	2	no	—
678	#121	—	2	4	no	—
679	#121	—	2	4	no	—
680	#121	—	2	4	no	—
681	#121	—	2	4	no	—
682	#121	—	2	2	no	—
683	#121	—	2	2	no	—
684	#121	—	2	2	no	—
685	#121	—	2	1	no	—
686	#121	—	2	2	no	—
687	#121	—	2	1	no	—
688	#121	—	2	2	no	—
689	#121	—	2	1	no	—
690	#121	—	2	2	no	—
691	#121	—	2	2	no	—
692	#121	—	2	2	no	—
693	#121	C₂³×C₅₃	1	2	yes	—
694	#121	C₂³×C₅₃	1	1	yes	characteristic
695	#121	C₂³×C₅₃	1	2	yes	—
696	#121	C₂³×C₅₃	1	2	yes	—
697	#121	C₂³×C₅₃	1	2	yes	—
698	#121	C₂³×C₅₃	1	4	yes	—
699	#121	C₂³×C₅₃	1	4	yes	—
700	#121	C₂³×C₅₃	1	1	yes	characteristic
701	#121	C₂³×C₅₃	1	2	yes	—
702	#120	—	2	1	no	—
703	#120	—	2	2	no	—
704	#120	—	2	2	no	—
705	#120	—	2	2	no	—
706	#120	—	2	2	no	—
707	C₄×Q₈	—	2	1	no	—
708	C₄×D₄	—	2	2	no	—
709	C₄×D₄	—	2	1	no	—
710	C₄×D₄	—	2	1	no	—
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	1	no	—
713	C₄×D₄	—	2	2	no	—
714	#117	C₂³×C₅₃	1	1	yes	characteristic
715	#117	C₂³×C₅₃	1	2	yes	—
716	C₂×C₄⋊C₄	—	2	1	no	—
717	C₂×C₄⋊C₄	—	2	1	no	—
718	C₂×C₄⋊C₄	—	2	1	no	—
719	C₂×C₄⋊C₄	—	2	2	no	—
720	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
724	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
725	C₂×C₂²⋊C₄	—	2	2	no	—
726	C₂×C₂²⋊C₄	—	2	2	no	—
727	C₂×C₂²⋊C₄	—	2	1	no	—
728	C₂×C₂²⋊C₄	—	2	2	no	—
729	#107	C₂³×C₅₃	1	4	yes	—
730	#106	C₂³×C₅₃	1	4	yes	—
731	#106	C₂³×C₅₃	1	4	yes	—
732	#106	C₂³×C₅₃	1	4	yes	—
733	#103	C₂³×C₅₃	1	2	yes	—
734	#103	C₂³×C₅₃	1	2	yes	—
735	#103	C₂³×C₅₃	1	4	yes	—
736	#103	C₂³×C₅₃	1	4	yes	—
737	#102	C₂³×C₅₃	1	4	yes	—
738	#102	C₂³×C₅₃	1	4	yes	—
739	#102	C₂³×C₅₃	1	2	yes	—
740	#102	C₂³×C₅₃	1	2	yes	—
741	#102	C₂³×C₅₃	1	4	yes	—
742	#102	C₂³×C₅₃	1	4	yes	—
743	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
744	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
745	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
746	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
747	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
748	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
749	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
750	C₂⁴	—	2	1	no	—
751	C₂⁴	—	2	2	no	—
752	C₂⁴	—	2	1	no	—
753	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
754	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
755	#41	—	2	4	no	—
756	#41	—	2	4	no	—
757	#41	—	2	4	no	—
758	#41	—	2	4	no	—
759	#41	—	2	4	no	—
760	#41	—	4	4	no	—
761	#41	—	4	4	no	—
762	#41	—	4	2	no	—
763	#41	—	4	2	no	—
764	#41	—	4	2	no	—
765	#41	—	4	2	no	—
766	#41	—	4	4	no	—
767	#41	—	4	4	no	—
768	#41	—	4	4	no	—
769	#41	—	4	4	no	—
770	C₂×Q₈	—	2	1	no	—
771	C₂×Q₈	—	4	2	no	—
772	C₂×Q₈	—	4	2	no	—
773	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
774	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
775	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
776	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
777	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
778	C₂×D₄	—	2	1	no	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	4	no	—
790	C₂×D₄	—	2	4	no	—
791	C₂×D₄	—	2	1	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	4	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂×D₄	—	4	2	no	—
797	C₂×D₄	—	4	4	no	—
798	C₂×D₄	—	4	4	no	—
799	C₂×D₄	—	4	8	no	—
800	C₂×D₄	—	4	4	no	—
801	C₂×D₄	—	4	4	no	—
802	C₂×D₄	—	8	4	no	—
803	C₂×D₄	—	8	2	no	—
804	C₂×D₄	—	8	4	no	—
805	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
806	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
807	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
808	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
809	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
810	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
811	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
812	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
813	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
814	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
815	C₂²×C₄	—	2	4	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	4	4	no	—
827	C₂²×C₄	—	4	4	no	—
828	C₂²×C₄	—	8	2	no	—
829	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
830	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
831	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
832	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
833	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
834	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
839	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
840	Q₁₆	—	4	2	no	—
841	SD₁₆	—	4	2	no	—
842	SD₁₆	—	4	2	no	—
843	SD₁₆	—	4	4	no	—
844	D₈	—	4	2	no	—
845	D₈	—	4	4	no	—
846	M₁₆	—	2	4	no	—
847	M₁₆	—	4	4	no	—
848	C₂×C₈	—	2	4	no	—
849	C₂×C₈	—	4	4	no	—
850	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
851	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
852	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	4	no	—
857	C₄⋊C₄	—	2	4	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
864	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
865	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
866	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	1	no	—
871	C₂²⋊C₄	—	2	1	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	1	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	1	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	4	no	—
880	C₂²⋊C₄	—	2	4	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	1	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	1	no	—
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	4	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	2	1	no	—
891	C₂³	—	4	1	no	—
892	C₂³	—	4	2	no	—
893	C₂³	—	4	2	no	—
894	C₂³	—	4	2	no	—
895	C₂³	—	4	2	no	—
896	C₂³	—	4	4	no	—
897	C₂³	—	4	2	no	—
898	C₂³	—	4	2	no	—
899	C₂³	—	8	1	no	—
900	C₂³	—	8	2	no	—
901	C₂³	—	8	1	no	—
902	C₂³	—	8	2	no	—
903	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
904	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
905	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
906	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
907	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
908	Q₈	—	2	2	no	—
909	Q₈	—	2	2	no	—
910	Q₈	—	2	2	no	—
911	Q₈	—	2	2	no	—
912	Q₈	—	2	2	no	—
913	Q₈	—	4	2	no	—
914	Q₈	—	4	2	no	—
915	D₄	—	2	4	no	—
916	D₄	—	2	4	no	—
917	D₄	—	2	2	no	—
918	D₄	—	2	2	no	—
919	D₄	—	2	2	no	—
920	D₄	—	2	4	no	—
921	D₄	—	2	2	no	—
922	D₄	—	2	2	no	—
923	D₄	—	4	2	no	—
924	D₄	—	4	2	no	—
925	D₄	—	4	2	no	—
926	D₄	—	4	4	no	—
927	D₄	—	4	2	no	—
928	D₄	—	4	4	no	—
929	D₄	—	4	4	no	—
930	D₄	—	4	2	no	—
931	D₄	—	4	4	no	—
932	D₄	—	4	4	no	—
933	D₄	—	4	2	no	—
934	D₄	—	4	2	no	—
935	D₄	—	8	1	no	—
936	D₄	—	8	2	no	—
937	D₄	—	8	2	no	—
938	D₄	—	8	2	no	—
939	D₄	—	8	2	no	—
940	D₄	—	8	4	no	—
941	D₄	—	8	4	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	4	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	4	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	4	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	—	4	2	no	—
958	C₂×C₄	—	4	4	no	—
959	C₂×C₄	—	4	4	no	—
960	C₂×C₄	—	4	2	no	—
961	C₂×C₄	—	4	4	no	—
962	C₂×C₄	—	4	4	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	8	2	no	—
965	C₂×C₄	—	8	2	no	—
966	C₂×C₄	—	8	1	no	—
967	C₂×C₄	—	8	2	no	—
968	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
969	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
970	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
971	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
972	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
973	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
974	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
975	C₈	—	2	2	no	—
976	C₈	—	2	2	no	—
977	C₈	—	2	4	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	1	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	4	4	no	—
992	C₂²	—	4	2	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	2	no	—
995	C₂²	—	4	2	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	8	4	no	—
1002	C₂²	—	8	4	no	—
1003	C₂²	—	16	2	no	—
1004	C₂²	—	16	4	no	—
1005	C₂²	C₅₃×#534	1	2	yes	—
1006	C₂²	C₅₃×#577	1	2	yes	—
1007	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1008	C₄	—	2	1	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	1	no	—
1014	C₄	—	4	4	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	2	no	—
1018	C₄	C₅₃×#534	1	2	yes	—
1019	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1020	C₂	—	2	2	no	—
1021	C₂	—	2	2	no	—
1022	C₂	—	4	1	no	—
1023	C₂	—	4	2	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	8	2	no	—
1026	C₂	—	8	2	no	—
1027	C₂	—	8	1	no	—
1028	C₂	C₂×C₅₃×#534	1	1	yes	characteristic
1029	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1030	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 ◁ C₂²×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3488	C₂	semidirect
2. C₂×C₅₃×#537	C₂	semidirect
3. C₅₃×#3204	C₂	semidirect
4. C₅₃×#3198	C₂	semidirect
5. C₅₃×#3196	C₂	semidirect
6. C₅₃×#3192	C₂	semidirect
7. C₅₃×#3188	C₂	semidirect
8. C₅₃×#3187	C₂	semidirect
9. C₅₃×#3099	C₂	semidirect
10. C₅₃×#3092	C₂	semidirect
11. C₂×C₅₃×#481	C₂	semidirect
12. C₅₃×#3062	C₂	semidirect
13. C₅₃×#3060	C₂	semidirect
14. C₅₃×#3012	C₂	semidirect
15. C₅₃×#3006	C₂	semidirect
16. C₅₃×#3002	C₂	semidirect
17. C₅₃×#2880	C₂	semidirect
18. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
20. C₂²×#41×C₅₃	C₂²	semidirect
21. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
22. C₂×#135×C₅₃	C₂²	semidirect
23. C₂×#131×C₅₃	C₂²	semidirect
34. C₅₃×#537	C₂²	semidirect
35. C₅₃×#537	C₂²	semidirect
36. C₅₃×#537	C₂²	semidirect
37. C₅₃×#537	C₂²	semidirect
38. C₅₃×#535	C₂²	semidirect
39. C₅₃×#535	C₂²	semidirect
43. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
48. C₂×#121×C₅₃	C₂²	semidirect
49. C₅₃×#520	C₂²	semidirect
50. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
51. C₅₃×#485	C₂²	semidirect
52. C₅₃×#484	C₂²	semidirect
53. C₅₃×#483	C₂²	semidirect
54. C₅₃×#483	C₂²	semidirect
55. C₅₃×#482	C₂²	semidirect
56. C₅₃×#481	C₂²	semidirect
57. C₅₃×#481	C₂²	semidirect
58. C₅₃×#481	C₂²	semidirect
59. C₅₃×#481	C₂²	semidirect
60. C₅₃×#481	C₂²	semidirect
61. C₅₃×#480	C₂²	semidirect
62. C₅₃×#470	C₂²	semidirect
63. C₅₃×#469	C₂²	semidirect
64. C₅₃×#469	C₂²	semidirect
65. C₅₃×#468	C₂²	semidirect
66. C₅₃×#466	C₂²	semidirect
67. C₅₃×#465	C₂²	semidirect
68. C₅₃×#465	C₂²	semidirect
69. C₅₃×#465	C₂²	semidirect
70. C₅₃×#452	C₂²	semidirect
71. C₅₃×#452	C₂²	semidirect
72. C₅₃×#451	C₂²	semidirect
73. C₅₃×#450	C₂²	semidirect
74. C₅₃×#450	C₂²	semidirect
75. C₅₃×#449	C₂²	semidirect
76. C₅₃×#449	C₂²	semidirect
77. C₅₃×#449	C₂²	semidirect
78. C₅₃×#448	C₂²	semidirect
79. C₅₃×#448	C₂²	semidirect
80. C₅₃×#447	C₂²	semidirect
81. C₅₃×#447	C₂²	semidirect
82. C₅₃×#447	C₂²	semidirect
83. C₅₃×#428	C₂²	semidirect
84. C₂×#106×C₅₃	C₂²	semidirect
85. C₅₃×#417	C₂²	semidirect
86. C₅₃×#417	C₂²	semidirect
87. C₅₃×#416	C₂²	semidirect
88. C₂×#102×C₅₃	C₂²	semidirect
89. C₅₃×#408	C₂²	semidirect
90. C₅₃×#408	C₂²	semidirect
91. C₅₃×#407	C₂²	semidirect
92. C₅₃×#407	C₂²	semidirect
93. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
94. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
462. #60765	C₅₃	direct (N × H)
505. #3488	C₂×C₅₃	semidirect
506. C₂×#537	C₂×C₅₃	semidirect
507. #3204	C₂×C₅₃	semidirect
508. #3198	C₂×C₅₃	semidirect
509. #3196	C₂×C₅₃	semidirect
510. #3192	C₂×C₅₃	semidirect
511. #3188	C₂×C₅₃	semidirect
512. #3187	C₂×C₅₃	semidirect
513. #3099	C₂×C₅₃	semidirect
514. #3092	C₂×C₅₃	semidirect
515. C₂×#481	C₂×C₅₃	semidirect
516. #3062	C₂×C₅₃	semidirect
517. #3060	C₂×C₅₃	semidirect
518. #3012	C₂×C₅₃	semidirect
519. #3006	C₂×C₅₃	semidirect
520. #3002	C₂×C₅₃	semidirect
521. #2880	C₂×C₅₃	semidirect
533. C₂×H(5,𝔽₂)	C₂²×C₅₃	semidirect
535. C₂²×#41	C₂²×C₅₃	semidirect
536. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
537. C₂×#135	C₂²×C₅₃	semidirect
538. C₂×#131	C₂²×C₅₃	semidirect
549. #537	C₂²×C₅₃	semidirect
550. #537	C₂²×C₅₃	semidirect
551. #537	C₂²×C₅₃	semidirect
552. #537	C₂²×C₅₃	semidirect
553. #535	C₂²×C₅₃	semidirect
554. #535	C₂²×C₅₃	semidirect
558. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
563. C₂×#121	C₂²×C₅₃	semidirect
564. #520	C₂²×C₅₃	semidirect
565. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
566. #485	C₂²×C₅₃	semidirect
567. #484	C₂²×C₅₃	semidirect
568. #483	C₂²×C₅₃	semidirect
569. #483	C₂²×C₅₃	semidirect
570. #482	C₂²×C₅₃	semidirect
571. #481	C₂²×C₅₃	semidirect
572. #481	C₂²×C₅₃	semidirect
573. #481	C₂²×C₅₃	semidirect
574. #481	C₂²×C₅₃	semidirect
575. #481	C₂²×C₅₃	semidirect
576. #480	C₂²×C₅₃	semidirect
577. #470	C₂²×C₅₃	semidirect
578. #469	C₂²×C₅₃	semidirect
579. #469	C₂²×C₅₃	semidirect
580. #468	C₂²×C₅₃	semidirect
581. #466	C₂²×C₅₃	semidirect
582. #465	C₂²×C₅₃	semidirect
583. #465	C₂²×C₅₃	semidirect
584. #465	C₂²×C₅₃	semidirect
585. #452	C₂²×C₅₃	semidirect
586. #452	C₂²×C₅₃	semidirect
587. #451	C₂²×C₅₃	semidirect
588. #450	C₂²×C₅₃	semidirect
589. #450	C₂²×C₅₃	semidirect
590. #449	C₂²×C₅₃	semidirect
591. #449	C₂²×C₅₃	semidirect
592. #449	C₂²×C₅₃	semidirect
593. #448	C₂²×C₅₃	semidirect
594. #448	C₂²×C₅₃	semidirect
595. #447	C₂²×C₅₃	semidirect
596. #447	C₂²×C₅₃	semidirect
597. #447	C₂²×C₅₃	semidirect
598. #428	C₂²×C₅₃	semidirect
599. C₂×#106	C₂²×C₅₃	semidirect
600. #417	C₂²×C₅₃	semidirect
601. #417	C₂²×C₅₃	semidirect
602. #416	C₂²×C₅₃	semidirect
603. C₂×#102	C₂²×C₅₃	semidirect
604. #408	C₂²×C₅₃	semidirect
605. #408	C₂²×C₅₃	semidirect
606. #407	C₂²×C₅₃	semidirect
607. #407	C₂²×C₅₃	semidirect
608. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
609. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
610. C₅₃	#60765	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×#3488	2
C₂×C₅₃×#537	2
C₅₃×#3204	2
C₅₃×#3198	2
C₅₃×#3196	2
C₅₃×#3192	2
C₅₃×#3188	2
C₅₃×#3187	2
C₅₃×#3099	2
C₅₃×#3092	2
C₂×C₅₃×#481	2
C₅₃×#3062	2
C₅₃×#3060	2
C₅₃×#3012	2
C₅₃×#3006	2
C₅₃×#3002	2
C₅₃×#2880	2
#60765	53

Subgroups — C53×#60765 #27268277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60765 #27268277