Subgroups — C₅₃×#60582 #27268094

Order 13568.

2058 conjugacy classes of subgroups.

The subgroup lattice has 898 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
2	C₂×C₅₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3126	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3121	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3117	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3112	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3108	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3103	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3082	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3043	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2949	C₂	1	2	yes	maximal, complemented
16	C₅₃×#2947	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#137×C₅₃	C₂²	1	2	yes	—
20	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
21	C₅₃×#555	—	2	1	no	—
22	C₅₃×#553	—	2	1	no	—
23	C₅₃×#553	—	2	1	no	—
24	C₅₃×#551	—	2	2	no	—
25	C₅₃×#547	—	2	1	no	—
26	C₅₃×#546	—	2	2	no	—
27	C₅₃×#544	C₂²	1	1	yes	characteristic
28	C₅₃×#542	C₂²	1	2	yes	—
29	C₅₃×#540	C₂²	1	2	yes	—
30	C₅₃×#535	C₂²	1	1	yes	characteristic
31	C₅₃×#532	C₂²	1	2	yes	—
32	C₅₃×#529	C₂²	1	2	yes	—
33	C₅₃×#525	C₂²	1	1	yes	characteristic
34	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#520	C₂²	1	1	yes	characteristic
36	C₅₃×#519	—	2	2	no	—
37	C₅₃×#519	—	2	1	no	—
38	C₅₃×#519	—	2	1	no	—
39	C₅₃×#519	C₂²	1	2	yes	—
40	C₅₃×#519	C₂²	1	2	yes	—
41	C₅₃×#519	C₂²	1	4	yes	complemented
42	C₅₃×#518	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₅₃	—	2	1	no	—
44	C₂×C₄×Q₈×C₅₃	—	2	1	no	—
45	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
46	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
47	C₂×#117×C₅₃	—	2	2	no	—
48	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
50	C₅₃×#485	C₂²	1	2	yes	complemented
51	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#482	C₂²	1	4	yes	—
54	C₅₃×#482	C₂²	1	2	yes	complemented
55	C₅₃×#481	C₂²	1	2	yes	—
56	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#480	C₂²	1	2	yes	—
58	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#479	C₂²	1	4	yes	complemented
60	C₅₃×#479	C₂²	1	4	yes	complemented
61	C₅₃×#477	C₂²	1	4	yes	complemented
62	C₅₃×#475	C₂²	1	4	yes	complemented
63	C₅₃×#464	C₂²	1	4	yes	complemented
64	C₅₃×#464	C₂²	1	4	yes	complemented
65	C₅₃×#460	C₂²	1	4	yes	complemented
66	C₅₃×#460	C₂²	1	4	yes	complemented
67	C₅₃×#451	C₂²	1	2	yes	complemented
68	C₅₃×#451	C₂²	1	2	yes	complemented
69	C₅₃×#448	C₂²	1	2	yes	—
70	C₅₃×#448	C₂²	1	2	yes	—
71	C₅₃×#448	C₂²	1	4	yes	—
72	C₅₃×#448	C₂²	1	2	yes	complemented
73	C₅₃×#448	C₂²	1	2	yes	complemented
74	C₅₃×#441	C₂²	1	4	yes	complemented
75	C₅₃×#440	C₂²	1	4	yes	complemented
76	C₅₃×#440	C₂²	1	4	yes	complemented
77	C₅₃×#440	C₂²	1	4	yes	complemented
78	C₄×Q₁₆×C₅₃	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	complemented
81	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	complemented
82	C₅₃×#433	C₂²	1	4	yes	complemented
83	C₅₃×#432	C₂²	1	2	yes	complemented
84	C₅₃×#431	C₂²	1	2	yes	complemented
85	C₅₃×#428	C₂²	1	2	yes	—
86	C₅₃×#427	C₂²	1	2	yes	—
87	C₅₃×#424	C₂²	1	2	yes	—
88	C₅₃×#419	C₂²	1	2	yes	—
89	C₅₃×#418	C₂²	1	2	yes	—
90	C₅₃×#416	C₂²	1	2	yes	—
91	C₂×#103×C₅₃	C₂²	1	2	yes	—
92	C₅₃×#407	C₂²	1	1	yes	characteristic
93	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
94	C₅₃×#405	C₂²	1	2	yes	—
95	C₂×#41×C₅₃	—	2	2	no	—
96	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₅₃	—	2	8	no	—
98	C₂²×Q₈×C₅₃	—	2	1	no	—
99	C₂²×Q₈×C₅₃	—	2	1	no	—
100	C₂²×Q₈×C₅₃	—	2	1	no	—
101	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
103	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
104	C₂²×D₄×C₅₃	—	2	1	no	—
105	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₅₃	—	2	1	no	—
107	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
108	#137×C₅₃	—	2	8	no	—
109	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₅₃	—	2	8	no	—
111	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
114	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
115	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
116	C₄⋊Q₈×C₅₃	—	2	1	no	—
117	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
118	#127×C₅₃	C₂³	1	2	yes	—
119	#126×C₅₃	—	2	2	no	—
120	#126×C₅₃	—	2	2	no	—
121	#125×C₅₃	—	2	1	no	—
122	#125×C₅₃	C₂³	1	2	yes	—
123	#124×C₅₃	—	2	2	no	—
124	#124×C₅₃	—	2	2	no	—
125	#124×C₅₃	C₂³	1	2	yes	—
126	#123×C₅₃	—	2	2	no	—
127	#123×C₅₃	—	2	2	no	—
128	#123×C₅₃	—	2	2	no	—
129	#123×C₅₃	—	2	1	no	—
130	#123×C₅₃	—	2	2	no	—
131	C₂²⋊Q₈×C₅₃	—	2	2	no	—
132	C₂²⋊Q₈×C₅₃	—	2	2	no	—
133	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
134	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
135	#121×C₅₃	—	2	1	no	—
136	#121×C₅₃	—	2	1	no	—
137	#121×C₅₃	—	2	2	no	—
138	#121×C₅₃	—	2	2	no	—
139	#121×C₅₃	—	2	1	no	—
140	#121×C₅₃	—	2	1	no	—
141	#121×C₅₃	—	2	2	no	—
142	#121×C₅₃	C₂³	1	2	yes	—
143	#121×C₅₃	C₂³	1	2	yes	—
144	#121×C₅₃	C₂³	1	1	yes	characteristic
145	#121×C₅₃	C₂³	1	1	yes	characteristic
146	#120×C₅₃	—	2	2	no	—
147	#120×C₅₃	—	2	1	no	—
148	C₄×Q₈×C₅₃	—	2	2	no	—
149	C₄×Q₈×C₅₃	—	2	2	no	—
150	C₄×Q₈×C₅₃	—	2	2	no	—
151	C₄×Q₈×C₅₃	—	2	2	no	—
152	C₄×Q₈×C₅₃	—	2	4	no	—
153	C₄×Q₈×C₅₃	—	2	4	no	—
154	C₄×Q₈×C₅₃	—	2	2	no	—
155	C₄×Q₈×C₅₃	—	2	2	no	—
156	C₄×Q₈×C₅₃	—	2	2	no	—
157	C₄×Q₈×C₅₃	—	2	2	no	—
158	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
159	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
160	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
161	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
162	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
163	C₄×D₄×C₅₃	—	2	1	no	—
164	C₄×D₄×C₅₃	—	2	1	no	—
165	C₄×D₄×C₅₃	—	2	2	no	—
166	C₄×D₄×C₅₃	—	2	2	no	—
167	C₄×D₄×C₅₃	—	2	1	no	—
168	C₄×D₄×C₅₃	—	2	1	no	—
169	C₄×D₄×C₅₃	—	2	2	no	—
170	C₄×D₄×C₅₃	C₂³	1	2	yes	—
171	C₄×D₄×C₅₃	C₂³	1	2	yes	—
172	C₄×D₄×C₅₃	C₂³	1	2	yes	—
173	#117×C₅₃	—	2	1	no	—
174	#117×C₅₃	—	2	4	no	—
175	#117×C₅₃	—	2	4	no	—
176	#117×C₅₃	—	2	4	no	—
177	#117×C₅₃	—	2	4	no	—
178	#117×C₅₃	—	2	2	no	—
179	#117×C₅₃	—	2	1	no	—
180	#117×C₅₃	—	2	1	no	—
181	#117×C₅₃	D₄	1	2	yes	—
182	#117×C₅₃	D₄	1	1	yes	characteristic
183	#117×C₅₃	D₄	1	1	yes	characteristic
184	#117×C₅₃	C₂³	1	2	yes	—
185	#117×C₅₃	C₂³	1	2	yes	—
186	#117×C₅₃	C₂³	1	1	yes	characteristic
187	#117×C₅₃	C₂³	1	1	yes	characteristic
188	#117×C₅₃	C₂³	1	1	yes	characteristic
189	#117×C₅₃	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
193	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
201	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
202	C₂×C₄²×C₅₃	—	2	2	no	—
203	C₂×C₄²×C₅₃	—	2	2	no	—
204	C₂×C₄²×C₅₃	—	2	1	no	—
205	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
206	#107×C₅₃	C₂³	1	2	yes	—
207	#107×C₅₃	C₂³	1	2	yes	—
208	#107×C₅₃	C₂³	1	4	yes	—
209	#106×C₅₃	C₂³	1	2	yes	—
210	#106×C₅₃	C₂³	1	2	yes	—
211	#106×C₅₃	C₂³	1	4	yes	—
212	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
213	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
214	#103×C₅₃	C₂³	1	2	yes	—
215	#103×C₅₃	C₂³	1	2	yes	—
216	#103×C₅₃	C₂³	1	4	yes	—
217	#103×C₅₃	C₂³	1	4	yes	—
218	#103×C₅₃	C₂³	1	4	yes	—
219	#103×C₅₃	C₂³	1	4	yes	—
220	#102×C₅₃	C₂³	1	2	yes	—
221	#102×C₅₃	C₂³	1	2	yes	—
222	#102×C₅₃	C₂³	1	4	yes	—
223	#102×C₅₃	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
225	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
228	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
229	#97×C₅₃	C₂³	1	4	yes	—
230	C₄×C₈×C₅₃	C₂³	1	4	yes	—
231	C₂⁴×C₅₃	—	2	1	no	—
232	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
233	#41×C₅₃	—	2	4	no	—
234	#41×C₅₃	—	8	4	no	—
235	C₂×Q₈×C₅₃	—	2	8	no	—
236	C₂×Q₈×C₅₃	—	2	8	no	—
237	C₂×Q₈×C₅₃	—	2	8	no	—
238	C₂×Q₈×C₅₃	—	2	8	no	—
239	C₂×Q₈×C₅₃	—	2	8	no	—
240	C₂×Q₈×C₅₃	—	2	2	no	—
241	C₂×Q₈×C₅₃	—	2	2	no	—
242	C₂×Q₈×C₅₃	—	2	2	no	—
243	C₂×Q₈×C₅₃	—	2	2	no	—
244	C₂×Q₈×C₅₃	—	2	4	no	—
245	C₂×Q₈×C₅₃	#41	1	8	yes	complemented
246	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
248	C₂×D₄×C₅₃	—	2	1	no	—
249	C₂×D₄×C₅₃	—	2	1	no	—
250	C₂×D₄×C₅₃	—	2	2	no	—
251	C₂×D₄×C₅₃	—	2	1	no	—
252	C₂×D₄×C₅₃	—	2	2	no	—
253	C₂×D₄×C₅₃	—	2	1	no	—
254	C₂×D₄×C₅₃	—	2	2	no	—
255	C₂×D₄×C₅₃	—	2	2	no	—
256	C₂×D₄×C₅₃	—	2	4	no	—
257	C₂×D₄×C₅₃	—	8	2	no	—
258	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
259	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₅₃	—	2	8	no	—
261	C₂²×C₄×C₅₃	—	2	2	no	—
262	C₂²×C₄×C₅₃	—	2	2	no	—
263	C₂²×C₄×C₅₃	—	2	2	no	—
264	C₂²×C₄×C₅₃	—	2	4	no	—
265	C₂²×C₄×C₅₃	—	2	1	no	—
266	C₂²×C₄×C₅₃	—	2	1	no	—
267	C₂²×C₄×C₅₃	—	2	1	no	—
268	C₂²×C₄×C₅₃	—	2	1	no	—
269	C₂²×C₄×C₅₃	—	2	2	no	—
270	C₂²×C₄×C₅₃	—	2	2	no	—
271	C₂²×C₄×C₅₃	—	2	2	no	—
272	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
280	Q₁₆×C₅₃	—	2	8	no	—
281	SD₁₆×C₅₃	—	2	8	no	—
282	SD₁₆×C₅₃	—	2	8	no	—
283	SD₁₆×C₅₃	—	2	8	no	—
284	M₁₆×C₅₃	—	2	4	no	—
285	C₂×C₈×C₅₃	—	2	4	no	—
286	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
288	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₅₃	—	2	1	no	—
290	C₄⋊C₄×C₅₃	—	2	4	no	—
291	C₄⋊C₄×C₅₃	—	2	4	no	—
292	C₄⋊C₄×C₅₃	—	2	4	no	—
293	C₄⋊C₄×C₅₃	—	2	4	no	—
294	C₄⋊C₄×C₅₃	—	2	2	no	—
295	C₄⋊C₄×C₅₃	—	2	1	no	—
296	C₄⋊C₄×C₅₃	—	2	1	no	—
297	C₄⋊C₄×C₅₃	—	2	1	no	—
298	C₄⋊C₄×C₅₃	—	2	2	no	—
299	C₄⋊C₄×C₅₃	—	2	2	no	—
300	C₄⋊C₄×C₅₃	—	2	2	no	—
301	C₄⋊C₄×C₅₃	—	2	1	no	—
302	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
305	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
306	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
307	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
309	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
313	C₂²⋊C₄×C₅₃	—	2	1	no	—
314	C₂²⋊C₄×C₅₃	—	2	2	no	—
315	C₂²⋊C₄×C₅₃	—	2	2	no	—
316	C₂²⋊C₄×C₅₃	—	2	1	no	—
317	C₂²⋊C₄×C₅₃	—	2	1	no	—
318	C₂²⋊C₄×C₅₃	—	2	2	no	—
319	C₂²⋊C₄×C₅₃	—	2	2	no	—
320	C₂²⋊C₄×C₅₃	—	2	2	no	—
321	C₂²⋊C₄×C₅₃	—	2	2	no	—
322	C₂²⋊C₄×C₅₃	—	2	2	no	—
323	C₂²⋊C₄×C₅₃	—	2	2	no	—
324	C₂²⋊C₄×C₅₃	—	2	1	no	—
325	C₂²⋊C₄×C₅₃	—	2	2	no	—
326	C₂²⋊C₄×C₅₃	—	2	1	no	—
327	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
329	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
331	C₄²×C₅₃	—	2	4	no	—
332	C₄²×C₅₃	—	2	4	no	—
333	C₄²×C₅₃	—	2	4	no	—
334	C₄²×C₅₃	—	2	4	no	—
335	C₄²×C₅₃	—	2	2	no	—
336	C₄²×C₅₃	—	2	2	no	—
337	C₄²×C₅₃	—	2	2	no	—
338	C₄²×C₅₃	—	2	1	no	—
339	C₄²×C₅₃	C₂×D₄	1	2	yes	—
340	C₄²×C₅₃	C₂×D₄	1	2	yes	—
341	C₄²×C₅₃	C₂⁴	1	2	yes	—
342	C₄²×C₅₃	C₂⁴	1	2	yes	—
343	C₂³×C₅₃	—	2	2	no	—
344	C₂³×C₅₃	—	2	2	no	—
345	C₂³×C₅₃	—	2	1	no	—
346	C₂³×C₅₃	—	2	2	no	—
347	C₂³×C₅₃	—	4	1	no	—
348	C₂³×C₅₃	—	4	2	no	—
349	C₂³×C₅₃	—	8	1	no	—
350	C₂³×C₅₃	—	8	1	no	—
351	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
352	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
353	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
354	Q₈×C₅₃	—	2	8	no	—
355	Q₈×C₅₃	—	2	8	no	—
356	Q₈×C₅₃	—	2	8	no	—
357	Q₈×C₅₃	—	2	4	no	—
358	Q₈×C₅₃	—	2	2	no	—
359	Q₈×C₅₃	—	8	2	no	—
360	Q₈×C₅₃	C₂×#41	1	8	yes	—
361	D₄×C₅₃	—	2	4	no	—
362	D₄×C₅₃	—	2	2	no	—
363	D₄×C₅₃	—	4	2	no	—
364	D₄×C₅₃	—	4	4	no	—
365	D₄×C₅₃	—	4	2	no	—
366	D₄×C₅₃	—	4	2	no	—
367	D₄×C₅₃	—	8	2	no	—
368	D₄×C₅₃	—	8	2	no	—
369	D₄×C₅₃	—	8	1	no	—
370	D₄×C₅₃	—	8	2	no	—
371	C₂×C₄×C₅₃	—	2	8	no	—
372	C₂×C₄×C₅₃	—	2	8	no	—
373	C₂×C₄×C₅₃	—	2	8	no	—
374	C₂×C₄×C₅₃	—	2	2	no	—
375	C₂×C₄×C₅₃	—	2	4	no	—
376	C₂×C₄×C₅₃	—	2	4	no	—
377	C₂×C₄×C₅₃	—	2	2	no	—
378	C₂×C₄×C₅₃	—	2	2	no	—
379	C₂×C₄×C₅₃	—	2	2	no	—
380	C₂×C₄×C₅₃	—	2	2	no	—
381	C₂×C₄×C₅₃	—	2	2	no	—
382	C₂×C₄×C₅₃	—	2	1	no	—
383	C₂×C₄×C₅₃	—	2	1	no	—
384	C₂×C₄×C₅₃	—	2	1	no	—
385	C₂×C₄×C₅₃	—	2	2	no	—
386	C₂×C₄×C₅₃	—	2	2	no	—
387	C₂×C₄×C₅₃	—	4	2	no	—
388	C₂×C₄×C₅₃	—	4	2	no	—
389	C₂×C₄×C₅₃	—	4	2	no	—
390	C₂×C₄×C₅₃	—	4	2	no	—
391	C₂×C₄×C₅₃	—	8	2	no	—
392	C₂×C₄×C₅₃	—	8	2	no	—
393	C₂×C₄×C₅₃	—	8	2	no	—
394	C₂×C₄×C₅₃	—	8	1	no	—
395	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
403	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
404	C₈×C₅₃	—	2	2	no	—
405	C₈×C₅₃	—	2	2	no	—
406	C₈×C₅₃	—	2	4	no	—
407	#60582	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
408	C₂²×C₅₃	—	2	1	no	—
409	C₂²×C₅₃	—	2	1	no	—
410	C₂²×C₅₃	—	2	1	no	—
411	C₂²×C₅₃	—	2	1	no	—
412	C₂²×C₅₃	—	2	1	no	—
413	C₂²×C₅₃	—	2	1	no	—
414	C₂²×C₅₃	—	2	1	no	—
415	C₂²×C₅₃	—	4	4	no	—
416	C₂²×C₅₃	—	4	2	no	—
417	C₂²×C₅₃	—	4	1	no	—
418	C₂²×C₅₃	—	4	1	no	—
419	C₂²×C₅₃	—	4	2	no	—
420	C₂²×C₅₃	—	4	1	no	—
421	C₂²×C₅₃	—	4	2	no	—
422	C₂²×C₅₃	—	16	2	no	—
423	C₂²×C₅₃	#525	1	2	yes	—
424	C₂²×C₅₃	#577	1	2	yes	—
425	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
426	C₄×C₅₃	—	2	2	no	—
427	C₄×C₅₃	—	2	2	no	—
428	C₄×C₅₃	—	2	8	no	—
429	C₄×C₅₃	—	2	1	no	—
430	C₄×C₅₃	—	2	1	no	—
431	C₄×C₅₃	—	2	2	no	—
432	C₄×C₅₃	—	2	2	no	—
433	C₄×C₅₃	—	4	2	no	—
434	C₄×C₅₃	—	4	1	no	—
435	C₄×C₅₃	—	4	1	no	—
436	C₄×C₅₃	—	4	2	no	—
437	C₄×C₅₃	—	4	2	no	—
438	C₄×C₅₃	—	4	1	no	—
439	C₄×C₅₃	#525	1	2	yes	—
440	C₄×C₅₃	C₂²×#41	1	2	yes	—
441	#3494	C₂×C₅₃	1	1	yes	characteristic
442	C₂×#519	C₂×C₅₃	1	1	yes	characteristic, complemented
443	#3126	C₂×C₅₃	1	4	yes	complemented
444	#3121	C₂×C₅₃	1	4	yes	complemented
445	#3117	C₂×C₅₃	1	2	yes	complemented
446	#3112	C₂×C₅₃	1	2	yes	complemented
447	#3108	C₂×C₅₃	1	2	yes	complemented
448	#3103	C₂×C₅₃	1	2	yes	complemented
449	#3094	C₂×C₅₃	1	1	yes	characteristic, complemented
450	#3091	C₂×C₅₃	1	1	yes	characteristic, complemented
451	#3082	C₂×C₅₃	1	2	yes	complemented
452	#3043	C₂×C₅₃	1	2	yes	complemented
453	#3004	C₂×C₅₃	1	1	yes	characteristic, complemented
454	C₂×#448	C₂×C₅₃	1	1	yes	characteristic, complemented
455	#2949	C₂×C₅₃	1	2	yes	complemented
456	#2947	C₂×C₅₃	1	2	yes	complemented
457	#2924	C₂×C₅₃	1	1	yes	characteristic, complemented
458	C₂×C₅₃	—	2	2	no	—
459	C₂×C₅₃	—	2	2	no	—
460	C₂×C₅₃	—	4	1	no	—
461	C₂×C₅₃	—	8	1	no	—
462	C₂×C₅₃	—	8	2	no	—
463	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
464	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
465	C₂×C₅₃	#3586	1	1	yes	characteristic
466	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic
467	C₂×#137	C₂²×C₅₃	1	2	yes	—
468	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
469	#555	—	2	1	no	—
470	#553	—	2	1	no	—
471	#553	—	2	1	no	—
472	#551	—	2	2	no	—
473	#547	—	2	1	no	—
474	#546	—	2	2	no	—
475	#544	C₂²×C₅₃	1	1	yes	characteristic
476	#542	C₂²×C₅₃	1	2	yes	—
477	#540	C₂²×C₅₃	1	2	yes	—
478	#535	C₂²×C₅₃	1	1	yes	characteristic
479	#532	C₂²×C₅₃	1	2	yes	—
480	#529	C₂²×C₅₃	1	2	yes	—
481	#525	C₂²×C₅₃	1	1	yes	characteristic
482	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
483	#520	C₂²×C₅₃	1	1	yes	characteristic
484	#519	—	2	2	no	—
485	#519	—	2	1	no	—
486	#519	—	2	1	no	—
487	#519	C₂²×C₅₃	1	2	yes	—
488	#519	C₂²×C₅₃	1	2	yes	—
489	#519	C₂²×C₅₃	1	4	yes	complemented
490	#518	C₂²×C₅₃	1	1	yes	characteristic
491	C₂×C₄×Q₈	—	2	1	no	—
492	C₂×C₄×Q₈	—	2	1	no	—
493	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
494	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
495	C₂×#117	—	2	2	no	—
496	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
497	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
498	#485	C₂²×C₅₃	1	2	yes	complemented
499	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
500	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
501	#482	C₂²×C₅₃	1	4	yes	—
502	#482	C₂²×C₅₃	1	2	yes	complemented
503	#481	C₂²×C₅₃	1	2	yes	—
504	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
505	#480	C₂²×C₅₃	1	2	yes	—
506	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
507	#479	C₂²×C₅₃	1	4	yes	complemented
508	#479	C₂²×C₅₃	1	4	yes	complemented
509	#477	C₂²×C₅₃	1	4	yes	complemented
510	#475	C₂²×C₅₃	1	4	yes	complemented
511	#464	C₂²×C₅₃	1	4	yes	complemented
512	#464	C₂²×C₅₃	1	4	yes	complemented
513	#460	C₂²×C₅₃	1	4	yes	complemented
514	#460	C₂²×C₅₃	1	4	yes	complemented
515	#451	C₂²×C₅₃	1	2	yes	complemented
516	#451	C₂²×C₅₃	1	2	yes	complemented
517	#448	C₂²×C₅₃	1	2	yes	—
518	#448	C₂²×C₅₃	1	2	yes	—
519	#448	C₂²×C₅₃	1	4	yes	—
520	#448	C₂²×C₅₃	1	2	yes	complemented
521	#448	C₂²×C₅₃	1	2	yes	complemented
522	#441	C₂²×C₅₃	1	4	yes	complemented
523	#440	C₂²×C₅₃	1	4	yes	complemented
524	#440	C₂²×C₅₃	1	4	yes	complemented
525	#440	C₂²×C₅₃	1	4	yes	complemented
526	C₄×Q₁₆	C₂²×C₅₃	1	4	yes	complemented
527	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	complemented
528	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	complemented
529	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	complemented
530	#433	C₂²×C₅₃	1	4	yes	complemented
531	#432	C₂²×C₅₃	1	2	yes	complemented
532	#431	C₂²×C₅₃	1	2	yes	complemented
533	#428	C₂²×C₅₃	1	2	yes	—
534	#427	C₂²×C₅₃	1	2	yes	—
535	#424	C₂²×C₅₃	1	2	yes	—
536	#419	C₂²×C₅₃	1	2	yes	—
537	#418	C₂²×C₅₃	1	2	yes	—
538	#416	C₂²×C₅₃	1	2	yes	—
539	C₂×#103	C₂²×C₅₃	1	2	yes	—
540	#407	C₂²×C₅₃	1	1	yes	characteristic
541	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
542	#405	C₂²×C₅₃	1	2	yes	—
543	C₅₃	#60582	1	1	yes	characteristic, direct product factor, Sylow
544	C₂×#41	—	2	2	no	—
545	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
546	C₂²×Q₈	—	2	8	no	—
547	C₂²×Q₈	—	2	1	no	—
548	C₂²×Q₈	—	2	1	no	—
549	C₂²×Q₈	—	2	1	no	—
550	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
551	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
552	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
555	C₂³×C₄	—	2	1	no	—
556	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
557	#137	—	2	8	no	—
558	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
559	C₂×SD₁₆	—	2	8	no	—
560	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
561	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
562	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
563	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
564	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
565	C₄⋊Q₈	—	2	1	no	—
566	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
567	#127	C₂³×C₅₃	1	2	yes	—
568	#126	—	2	2	no	—
569	#126	—	2	2	no	—
570	#125	—	2	1	no	—
571	#125	C₂³×C₅₃	1	2	yes	—
572	#124	—	2	2	no	—
573	#124	—	2	2	no	—
574	#124	C₂³×C₅₃	1	2	yes	—
575	#123	—	2	1	no	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
583	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
584	#121	—	2	1	no	—
585	#121	—	2	1	no	—
586	#121	—	2	2	no	—
587	#121	—	2	1	no	—
588	#121	—	2	1	no	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	C₂³×C₅₃	1	2	yes	—
592	#121	C₂³×C₅₃	1	2	yes	—
593	#121	C₂³×C₅₃	1	1	yes	characteristic
594	#121	C₂³×C₅₃	1	1	yes	characteristic
595	#120	—	2	1	no	—
596	#120	—	2	2	no	—
597	C₄×Q₈	—	2	2	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	2	2	no	—
601	C₄×Q₈	—	2	4	no	—
602	C₄×Q₈	—	2	4	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	—	2	2	no	—
606	C₄×Q₈	—	2	2	no	—
607	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
608	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
609	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
610	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
611	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	C₂³×C₅₃	1	2	yes	—
620	C₄×D₄	C₂³×C₅₃	1	2	yes	—
621	C₄×D₄	C₂³×C₅₃	1	2	yes	—
622	#117	—	2	1	no	—
623	#117	—	2	1	no	—
624	#117	—	2	1	no	—
625	#117	—	2	4	no	—
626	#117	—	2	4	no	—
627	#117	—	2	4	no	—
628	#117	—	2	4	no	—
629	#117	—	2	2	no	—
630	#117	D₄×C₅₃	1	2	yes	—
631	#117	D₄×C₅₃	1	1	yes	characteristic
632	#117	D₄×C₅₃	1	1	yes	characteristic
633	#117	C₂³×C₅₃	1	2	yes	—
634	#117	C₂³×C₅₃	1	2	yes	—
635	#117	C₂³×C₅₃	1	1	yes	characteristic
636	#117	C₂³×C₅₃	1	1	yes	characteristic
637	#117	C₂³×C₅₃	1	1	yes	characteristic
638	#117	C₂³×C₅₃	1	2	yes	—
639	C₂×C₄⋊C₄	—	2	2	no	—
640	C₂×C₄⋊C₄	—	2	2	no	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
643	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	2	2	no	—
650	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
651	C₂×C₄²	—	2	2	no	—
652	C₂×C₄²	—	2	2	no	—
653	C₂×C₄²	—	2	1	no	—
654	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
655	#107	C₂³×C₅₃	1	2	yes	—
656	#107	C₂³×C₅₃	1	2	yes	—
657	#107	C₂³×C₅₃	1	4	yes	—
658	#106	C₂³×C₅₃	1	2	yes	—
659	#106	C₂³×C₅₃	1	2	yes	—
660	#106	C₂³×C₅₃	1	4	yes	—
661	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
662	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
663	#103	C₂³×C₅₃	1	4	yes	—
664	#103	C₂³×C₅₃	1	4	yes	—
665	#103	C₂³×C₅₃	1	2	yes	—
666	#103	C₂³×C₅₃	1	2	yes	—
667	#103	C₂³×C₅₃	1	4	yes	—
668	#103	C₂³×C₅₃	1	4	yes	—
669	#102	C₂³×C₅₃	1	2	yes	—
670	#102	C₂³×C₅₃	1	2	yes	—
671	#102	C₂³×C₅₃	1	4	yes	—
672	#102	C₂³×C₅₃	1	4	yes	—
673	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
674	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
675	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
676	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
678	#97	C₂³×C₅₃	1	4	yes	—
679	C₄×C₈	C₂³×C₅₃	1	4	yes	—
680	C₂⁴	—	2	1	no	—
681	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
682	#41	—	2	4	no	—
683	#41	—	8	4	no	—
684	C₂×Q₈	—	2	8	no	—
685	C₂×Q₈	—	2	8	no	—
686	C₂×Q₈	—	2	8	no	—
687	C₂×Q₈	—	2	8	no	—
688	C₂×Q₈	—	2	8	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	—	2	2	no	—
693	C₂×Q₈	—	2	4	no	—
694	C₂×Q₈	#41×C₅₃	1	8	yes	complemented
695	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
696	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	8	2	no	—
707	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
708	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
709	C₂²×C₄	—	2	8	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
722	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
723	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
725	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
729	Q₁₆	—	2	8	no	—
730	SD₁₆	—	2	8	no	—
731	SD₁₆	—	2	8	no	—
732	SD₁₆	—	2	8	no	—
733	M₁₆	—	2	4	no	—
734	C₂×C₈	—	2	4	no	—
735	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
736	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
737	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
752	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
756	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
758	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
759	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
760	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
761	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
762	C₂²⋊C₄	—	2	1	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
777	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
778	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
779	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
780	C₄²	—	2	4	no	—
781	C₄²	—	2	4	no	—
782	C₄²	—	2	4	no	—
783	C₄²	—	2	4	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	1	no	—
788	C₄²	C₂×D₄×C₅₃	1	2	yes	—
789	C₄²	C₂×D₄×C₅₃	1	2	yes	—
790	C₄²	C₂⁴×C₅₃	1	2	yes	—
791	C₄²	C₂⁴×C₅₃	1	2	yes	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	4	1	no	—
797	C₂³	—	4	2	no	—
798	C₂³	—	8	1	no	—
799	C₂³	—	8	1	no	—
800	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
801	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
802	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
803	Q₈	—	2	8	no	—
804	Q₈	—	2	8	no	—
805	Q₈	—	2	8	no	—
806	Q₈	—	2	4	no	—
807	Q₈	—	2	2	no	—
808	Q₈	—	8	2	no	—
809	Q₈	C₂×#41×C₅₃	1	8	yes	—
810	D₄	—	2	4	no	—
811	D₄	—	2	2	no	—
812	D₄	—	4	2	no	—
813	D₄	—	4	4	no	—
814	D₄	—	4	2	no	—
815	D₄	—	4	2	no	—
816	D₄	—	8	2	no	—
817	D₄	—	8	2	no	—
818	D₄	—	8	1	no	—
819	D₄	—	8	2	no	—
820	C₂×C₄	—	2	8	no	—
821	C₂×C₄	—	2	8	no	—
822	C₂×C₄	—	2	8	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	4	2	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	—	8	2	no	—
842	C₂×C₄	—	8	2	no	—
843	C₂×C₄	—	8	1	no	—
844	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
845	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
846	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
851	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
852	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
853	C₈	—	2	2	no	—
854	C₈	—	2	2	no	—
855	C₈	—	2	4	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	16	2	no	—
871	C₂²	C₅₃×#525	1	2	yes	—
872	C₂²	C₅₃×#577	1	2	yes	—
873	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
874	C₄	—	2	2	no	—
875	C₄	—	2	2	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	8	no	—
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	1	no	—
887	C₄	C₅₃×#525	1	2	yes	—
888	C₄	C₂²×#41×C₅₃	1	2	yes	—
889	C₂	—	2	2	no	—
890	C₂	—	2	2	no	—
891	C₂	—	4	1	no	—
892	C₂	—	8	2	no	—
893	C₂	—	8	1	no	—
894	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
895	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
896	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3494	C₂
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
2. C₂×C₅₃×#519	C₂	semidirect
3. C₅₃×#3126	C₂	semidirect
4. C₅₃×#3121	C₂	semidirect
5. C₅₃×#3117	C₂	semidirect
6. C₅₃×#3112	C₂	semidirect
7. C₅₃×#3108	C₂	semidirect
8. C₅₃×#3103	C₂	semidirect
9. C₅₃×#3094	C₂	semidirect
10. C₅₃×#3091	C₂	semidirect
11. C₅₃×#3082	C₂	semidirect
12. C₅₃×#3043	C₂	semidirect
13. C₅₃×#3004	C₂	semidirect
14. C₂×C₅₃×#448	C₂	semidirect
15. C₅₃×#2949	C₂	semidirect
16. C₅₃×#2947	C₂	semidirect
17. C₅₃×#2924	C₂	semidirect
41. C₅₃×#519	C₂²	semidirect
45. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
46. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
50. C₅₃×#485	C₂²	semidirect
51. C₅₃×#484	C₂²	semidirect
52. C₅₃×#483	C₂²	semidirect
54. C₅₃×#482	C₂²	semidirect
56. C₅₃×#481	C₂²	semidirect
58. C₅₃×#480	C₂²	semidirect
59. C₅₃×#479	C₂²	semidirect
60. C₅₃×#479	C₂²	semidirect
61. C₅₃×#477	C₂²	semidirect
62. C₅₃×#475	C₂²	semidirect
63. C₅₃×#464	C₂²	semidirect
64. C₅₃×#464	C₂²	semidirect
65. C₅₃×#460	C₂²	semidirect
66. C₅₃×#460	C₂²	semidirect
67. C₅₃×#451	C₂²	semidirect
68. C₅₃×#451	C₂²	semidirect
72. C₅₃×#448	C₂²	semidirect
73. C₅₃×#448	C₂²	semidirect
74. C₅₃×#441	C₂²	semidirect
75. C₅₃×#440	C₂²	semidirect
76. C₅₃×#440	C₂²	semidirect
77. C₅₃×#440	C₂²	semidirect
78. C₄×Q₁₆×C₅₃	C₂²	semidirect
79. C₄×SD₁₆×C₅₃	C₂²	semidirect
80. C₄×SD₁₆×C₅₃	C₂²	semidirect
81. C₄×SD₁₆×C₅₃	C₂²	semidirect
82. C₅₃×#433	C₂²	semidirect
83. C₅₃×#432	C₂²	semidirect
84. C₅₃×#431	C₂²	semidirect
245. C₂×Q₈×C₅₃	#41	semidirect
407. #60582	C₅₃	direct (N × H)
442. C₂×#519	C₂×C₅₃	semidirect
443. #3126	C₂×C₅₃	semidirect
444. #3121	C₂×C₅₃	semidirect
445. #3117	C₂×C₅₃	semidirect
446. #3112	C₂×C₅₃	semidirect
447. #3108	C₂×C₅₃	semidirect
448. #3103	C₂×C₅₃	semidirect
449. #3094	C₂×C₅₃	semidirect
450. #3091	C₂×C₅₃	semidirect
451. #3082	C₂×C₅₃	semidirect
452. #3043	C₂×C₅₃	semidirect
453. #3004	C₂×C₅₃	semidirect
454. C₂×#448	C₂×C₅₃	semidirect
455. #2949	C₂×C₅₃	semidirect
456. #2947	C₂×C₅₃	semidirect
457. #2924	C₂×C₅₃	semidirect
489. #519	C₂²×C₅₃	semidirect
493. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
494. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
498. #485	C₂²×C₅₃	semidirect
499. #484	C₂²×C₅₃	semidirect
500. #483	C₂²×C₅₃	semidirect
502. #482	C₂²×C₅₃	semidirect
504. #481	C₂²×C₅₃	semidirect
506. #480	C₂²×C₅₃	semidirect
507. #479	C₂²×C₅₃	semidirect
508. #479	C₂²×C₅₃	semidirect
509. #477	C₂²×C₅₃	semidirect
510. #475	C₂²×C₅₃	semidirect
511. #464	C₂²×C₅₃	semidirect
512. #464	C₂²×C₅₃	semidirect
513. #460	C₂²×C₅₃	semidirect
514. #460	C₂²×C₅₃	semidirect
515. #451	C₂²×C₅₃	semidirect
516. #451	C₂²×C₅₃	semidirect
520. #448	C₂²×C₅₃	semidirect
521. #448	C₂²×C₅₃	semidirect
522. #441	C₂²×C₅₃	semidirect
523. #440	C₂²×C₅₃	semidirect
524. #440	C₂²×C₅₃	semidirect
525. #440	C₂²×C₅₃	semidirect
526. C₄×Q₁₆	C₂²×C₅₃	semidirect
527. C₄×SD₁₆	C₂²×C₅₃	semidirect
528. C₄×SD₁₆	C₂²×C₅₃	semidirect
529. C₄×SD₁₆	C₂²×C₅₃	semidirect
530. #433	C₂²×C₅₃	semidirect
531. #432	C₂²×C₅₃	semidirect
532. #431	C₂²×C₅₃	semidirect
543. C₅₃	#60582	direct (N × H)
694. C₂×Q₈	#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
C₂×C₅₃×#519	2
C₅₃×#3126	2
C₅₃×#3121	2
C₅₃×#3117	2
C₅₃×#3112	2
C₅₃×#3108	2
C₅₃×#3103	2
C₅₃×#3094	2
C₅₃×#3091	2
C₅₃×#3082	2
C₅₃×#3043	2
C₅₃×#3004	2
C₂×C₅₃×#448	2
C₅₃×#2949	2
C₅₃×#2947	2
C₅₃×#2924	2
#60582	53

Subgroups — C53×#60582 #27268094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60582 #27268094