Subgroups — C₅₃×#36750 #27244262

Order 13568.

1778 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2807	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2788	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2768	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2763	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2729	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2720	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2704	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2704	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2646	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2549	C₂	1	2	yes	maximal, complemented
14	C₅₃×#2442	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2437	C₂	1	2	yes	maximal
16	C₅₃×#2437	C₂	1	2	yes	maximal
17	C₅₃×#2315	C₂	1	1	yes	maximal, characteristic
18	C₅₃×#2312	C₂	1	1	yes	maximal, characteristic
19	C₂×C₅₃×#388	C₂	1	1	yes	maximal, characteristic
20	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
22	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
27	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
33	C₅₃×#400	C₂²	1	2	yes	complemented
34	C₅₃×#400	C₂²	1	2	yes	complemented
35	C₅₃×#400	C₂²	1	2	yes	complemented
36	C₅₃×#400	C₂²	1	2	yes	complemented
37	C₅₃×#399	C₂²	1	2	yes	—
38	C₅₃×#399	C₂²	1	2	yes	—
39	C₅₃×#398	C₂²	1	2	yes	complemented
40	C₅₃×#398	C₂²	1	2	yes	complemented
41	C₅₃×#398	C₂²	1	2	yes	complemented
42	C₅₃×#398	C₂²	1	2	yes	complemented
43	C₅₃×#398	C₂²	1	2	yes	complemented
44	C₅₃×#398	C₂²	1	2	yes	complemented
45	C₅₃×#398	C₂²	1	2	yes	complemented
46	C₅₃×#398	C₂²	1	2	yes	complemented
47	C₅₃×#396	C₂²	1	2	yes	—
48	C₅₃×#396	C₂²	1	2	yes	—
49	C₅₃×#396	C₂²	1	2	yes	—
50	C₅₃×#396	C₂²	1	2	yes	—
51	C₅₃×#395	C₂²	1	2	yes	complemented
52	C₅₃×#395	C₂²	1	2	yes	complemented
53	C₅₃×#395	C₂²	1	2	yes	complemented
54	C₅₃×#395	C₂²	1	2	yes	complemented
55	C₅₃×#393	C₂²	1	2	yes	—
56	C₅₃×#393	C₂²	1	2	yes	—
57	C₅₃×#391	C₂²	1	2	yes	complemented
58	C₅₃×#391	C₂²	1	2	yes	complemented
59	C₅₃×#391	C₂²	1	2	yes	complemented
60	C₅₃×#389	C₂²	1	2	yes	complemented
61	C₅₃×#389	C₂²	1	2	yes	complemented
62	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#389	C₂²	1	2	yes	complemented
64	C₅₃×#389	C₂²	1	2	yes	complemented
65	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#389	C₂²	1	2	yes	complemented
67	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#388	C₂²	1	2	yes	—
70	C₅₃×#388	C₂²	1	2	yes	—
71	C₅₃×#388	C₂²	1	2	yes	—
72	C₅₃×#388	C₂²	1	2	yes	—
73	C₅₃×#388	C₂²	1	2	yes	—
74	C₅₃×#388	C₂²	1	2	yes	—
75	C₅₃×#388	C₂²	1	2	yes	—
76	C₅₃×#388	C₂²	1	2	yes	—
77	C₅₃×#387	C₂²	1	2	yes	complemented
78	C₅₃×#387	C₂²	1	2	yes	complemented
79	C₅₃×#385	C₂²	1	2	yes	—
80	C₅₃×#385	C₂²	1	2	yes	—
81	C₅₃×#385	C₂²	1	2	yes	—
82	C₅₃×#385	C₂²	1	2	yes	—
83	C₅₃×#385	C₂²	1	2	yes	—
84	C₅₃×#385	C₂²	1	2	yes	—
85	C₅₃×#385	C₂²	1	2	yes	—
86	C₅₃×#385	C₂²	1	2	yes	—
87	C₅₃×#385	C₂²	1	2	yes	—
88	C₅₃×#385	C₂²	1	2	yes	—
89	C₅₃×#385	C₂²	1	2	yes	—
90	C₅₃×#385	C₂²	1	2	yes	—
91	C₅₃×#384	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#382	C₂²	1	2	yes	complemented
93	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#380	C₂²	1	2	yes	—
95	C₅₃×#380	C₂²	1	2	yes	—
96	C₅₃×#380	C₂²	1	2	yes	—
97	C₅₃×#380	C₂²	1	2	yes	—
98	C₅₃×#380	C₂²	1	2	yes	—
99	C₅₃×#380	C₂²	1	1	yes	characteristic
100	C₅₃×#380	C₂²	1	1	yes	characteristic
101	C₅₃×#380	C₂²	1	1	yes	characteristic
102	C₅₃×#380	C₂²	1	1	yes	characteristic
103	C₅₃×#379	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
105	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
106	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
107	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
109	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
116	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₅₃	—	4	2	no	—
119	#125×C₅₃	—	4	2	no	—
120	#125×C₅₃	—	4	4	no	—
121	C₂²⋊Q₈×C₅₃	—	4	4	no	—
122	C₂²⋊Q₈×C₅₃	—	4	4	no	—
123	C₂²⋊Q₈×C₅₃	—	4	4	no	—
124	C₂²⋊Q₈×C₅₃	—	4	4	no	—
125	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
126	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
157	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
158	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
159	C₂×C₂²⋊C₄×C₅₃	Q₈	1	8	yes	complemented
160	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₅₃	—	4	2	no	—
177	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
183	#95×C₅₃	C₂³	1	2	yes	—
184	#95×C₅₃	C₂³	1	2	yes	—
185	#95×C₅₃	C₂³	1	2	yes	—
186	#95×C₅₃	C₂³	1	2	yes	—
187	#95×C₅₃	C₂³	1	2	yes	—
188	#95×C₅₃	C₂³	1	2	yes	—
189	#95×C₅₃	C₂³	1	2	yes	—
190	#95×C₅₃	C₂³	1	2	yes	—
191	#95×C₅₃	C₂³	1	2	yes	—
192	#95×C₅₃	C₂³	1	2	yes	—
193	#95×C₅₃	C₂³	1	2	yes	—
194	#95×C₅₃	C₂³	1	2	yes	—
195	#95×C₅₃	C₂³	1	2	yes	—
196	#95×C₅₃	C₂³	1	2	yes	—
197	#95×C₅₃	C₂³	1	2	yes	—
198	#95×C₅₃	C₂³	1	2	yes	—
199	#95×C₅₃	C₂³	1	2	yes	—
200	#95×C₅₃	C₂³	1	2	yes	—
201	#95×C₅₃	C₂³	1	2	yes	—
202	#95×C₅₃	C₂³	1	2	yes	—
203	#95×C₅₃	C₂³	1	2	yes	—
204	#95×C₅₃	C₂³	1	2	yes	—
205	#95×C₅₃	C₂³	1	2	yes	—
206	#95×C₅₃	C₂³	1	2	yes	—
207	C₂⁴×C₅₃	—	2	2	no	—
208	C₂⁴×C₅₃	—	2	2	no	—
209	C₂⁴×C₅₃	—	4	1	no	—
210	C₂⁴×C₅₃	—	4	1	no	—
211	C₂⁴×C₅₃	—	4	1	no	—
212	C₂⁴×C₅₃	—	4	1	no	—
213	C₂⁴×C₅₃	C₂×Q₈	1	4	yes	—
214	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
215	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
216	C₂×Q₈×C₅₃	—	2	4	no	—
217	C₂×Q₈×C₅₃	—	4	2	no	—
218	C₂×Q₈×C₅₃	—	4	2	no	—
219	C₂×Q₈×C₅₃	—	4	2	no	—
220	C₂×Q₈×C₅₃	—	4	2	no	—
221	C₂×Q₈×C₅₃	—	4	2	no	—
222	C₂²×C₄×C₅₃	—	2	2	no	—
223	C₂²×C₄×C₅₃	—	2	2	no	—
224	C₂²×C₄×C₅₃	—	2	2	no	—
225	C₂²×C₄×C₅₃	—	2	2	no	—
226	C₂²×C₄×C₅₃	—	2	2	no	—
227	C₂²×C₄×C₅₃	—	2	2	no	—
228	C₂²×C₄×C₅₃	—	4	1	no	—
229	C₂²×C₄×C₅₃	—	4	1	no	—
230	C₂²×C₄×C₅₃	—	4	1	no	—
231	C₂²×C₄×C₅₃	—	4	1	no	—
232	C₂²×C₄×C₅₃	—	4	1	no	—
233	C₂²×C₄×C₅₃	—	4	1	no	—
234	C₂²×C₄×C₅₃	—	4	1	no	—
235	C₂²×C₄×C₅₃	—	4	2	no	—
236	C₂²×C₄×C₅₃	—	4	2	no	—
237	C₂²×C₄×C₅₃	—	4	1	no	—
238	C₂²×C₄×C₅₃	—	4	1	no	—
239	C₂²×C₄×C₅₃	—	4	2	no	—
240	C₂²×C₄×C₅₃	—	4	2	no	—
241	C₂²×C₄×C₅₃	—	4	1	no	—
242	C₂²×C₄×C₅₃	—	4	2	no	—
243	C₂²×C₄×C₅₃	—	4	2	no	—
244	C₂²×C₄×C₅₃	C₂×Q₈	1	4	yes	—
245	C₂²×C₄×C₅₃	C₂×Q₈	1	4	yes	—
246	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
263	C₄⋊C₄×C₅₃	—	2	4	no	—
264	C₄⋊C₄×C₅₃	—	2	4	no	—
265	C₄⋊C₄×C₅₃	—	2	4	no	—
266	C₄⋊C₄×C₅₃	—	2	4	no	—
267	C₄⋊C₄×C₅₃	—	4	2	no	—
268	C₄⋊C₄×C₅₃	—	4	2	no	—
269	C₄⋊C₄×C₅₃	—	4	1	no	—
270	C₄⋊C₄×C₅₃	—	4	1	no	—
271	C₄⋊C₄×C₅₃	—	4	1	no	—
272	C₄⋊C₄×C₅₃	—	4	1	no	—
273	C₄⋊C₄×C₅₃	—	4	2	no	—
274	C₄⋊C₄×C₅₃	—	4	2	no	—
275	C₄⋊C₄×C₅₃	—	4	2	no	—
276	C₄⋊C₄×C₅₃	—	4	2	no	—
277	C₄⋊C₄×C₅₃	—	4	2	no	—
278	C₄⋊C₄×C₅₃	—	4	2	no	—
279	C₄⋊C₄×C₅₃	—	4	2	no	—
280	C₄⋊C₄×C₅₃	—	4	2	no	—
281	C₄⋊C₄×C₅₃	—	4	2	no	—
282	C₄⋊C₄×C₅₃	—	4	2	no	—
283	C₄⋊C₄×C₅₃	—	4	2	no	—
284	C₄⋊C₄×C₅₃	—	4	1	no	—
285	C₄⋊C₄×C₅₃	—	4	1	no	—
286	C₄⋊C₄×C₅₃	—	4	2	no	—
287	C₄⋊C₄×C₅₃	—	4	2	no	—
288	C₄⋊C₄×C₅₃	—	4	2	no	—
289	C₄⋊C₄×C₅₃	—	4	2	no	—
290	C₄⋊C₄×C₅₃	—	4	1	no	—
291	C₄⋊C₄×C₅₃	—	4	2	no	—
292	C₄⋊C₄×C₅₃	—	4	1	no	—
293	C₂²⋊C₄×C₅₃	—	2	4	no	—
294	C₂²⋊C₄×C₅₃	—	2	4	no	—
295	C₂²⋊C₄×C₅₃	—	2	4	no	—
296	C₂²⋊C₄×C₅₃	—	2	4	no	—
297	C₂²⋊C₄×C₅₃	—	2	4	no	—
298	C₂²⋊C₄×C₅₃	—	2	4	no	—
299	C₂²⋊C₄×C₅₃	—	4	2	no	—
300	C₂²⋊C₄×C₅₃	—	4	2	no	—
301	C₂²⋊C₄×C₅₃	—	4	2	no	—
302	C₂²⋊C₄×C₅₃	—	4	2	no	—
303	C₂²⋊C₄×C₅₃	—	4	2	no	—
304	C₂²⋊C₄×C₅₃	—	4	2	no	—
305	C₂²⋊C₄×C₅₃	—	4	2	no	—
306	C₂²⋊C₄×C₅₃	—	4	2	no	—
307	C₂²⋊C₄×C₅₃	C₂×Q₈	1	8	yes	—
308	C₂²⋊C₄×C₅₃	C₂×Q₈	1	8	yes	—
309	C₄²×C₅₃	—	2	2	no	—
310	C₄²×C₅₃	—	2	2	no	—
311	C₄²×C₅₃	—	4	1	no	—
312	C₄²×C₅₃	—	4	1	no	—
313	C₄²×C₅₃	—	4	2	no	—
314	C₄²×C₅₃	—	4	2	no	—
315	C₂³×C₅₃	—	2	1	no	—
316	C₂³×C₅₃	—	2	1	no	—
317	C₂³×C₅₃	—	2	1	no	—
318	C₂³×C₅₃	—	2	1	no	—
319	C₂³×C₅₃	—	2	2	no	—
320	C₂³×C₅₃	—	2	2	no	—
321	C₂³×C₅₃	—	2	2	no	—
322	C₂³×C₅₃	—	2	2	no	—
323	C₂³×C₅₃	—	2	2	no	—
324	C₂³×C₅₃	—	2	2	no	—
325	C₂³×C₅₃	—	2	8	no	—
326	C₂³×C₅₃	—	4	4	no	—
327	C₂³×C₅₃	—	4	4	no	—
328	C₂³×C₅₃	—	8	2	no	—
329	C₂³×C₅₃	—	8	2	no	—
330	C₂³×C₅₃	—	8	2	no	—
331	C₂³×C₅₃	—	8	2	no	—
332	C₂³×C₅₃	C₂²×Q₈	1	4	yes	—
333	C₂³×C₅₃	C₂²×Q₈	1	2	yes	—
334	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
335	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
336	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
337	Q₈×C₅₃	—	8	4	no	—
338	Q₈×C₅₃	—	8	4	no	—
339	C₂×C₄×C₅₃	—	2	1	no	—
340	C₂×C₄×C₅₃	—	2	1	no	—
341	C₂×C₄×C₅₃	—	2	1	no	—
342	C₂×C₄×C₅₃	—	2	1	no	—
343	C₂×C₄×C₅₃	—	2	2	no	—
344	C₂×C₄×C₅₃	—	2	1	no	—
345	C₂×C₄×C₅₃	—	2	1	no	—
346	C₂×C₄×C₅₃	—	2	2	no	—
347	C₂×C₄×C₅₃	—	2	1	no	—
348	C₂×C₄×C₅₃	—	2	1	no	—
349	C₂×C₄×C₅₃	—	2	2	no	—
350	C₂×C₄×C₅₃	—	2	1	no	—
351	C₂×C₄×C₅₃	—	2	1	no	—
352	C₂×C₄×C₅₃	—	2	1	no	—
353	C₂×C₄×C₅₃	—	2	2	no	—
354	C₂×C₄×C₅₃	—	2	2	no	—
355	C₂×C₄×C₅₃	—	2	2	no	—
356	C₂×C₄×C₅₃	—	2	2	no	—
357	C₂×C₄×C₅₃	—	2	2	no	—
358	C₂×C₄×C₅₃	—	2	1	no	—
359	C₂×C₄×C₅₃	—	2	2	no	—
360	C₂×C₄×C₅₃	—	2	2	no	—
361	C₂×C₄×C₅₃	—	2	2	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	2	no	—
364	C₂×C₄×C₅₃	—	2	2	no	—
365	C₂×C₄×C₅₃	—	2	2	no	—
366	C₂×C₄×C₅₃	—	2	2	no	—
367	C₂×C₄×C₅₃	—	2	2	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	2	no	—
371	C₂×C₄×C₅₃	—	2	1	no	—
372	C₂×C₄×C₅₃	—	2	2	no	—
373	C₂×C₄×C₅₃	—	2	2	no	—
374	C₂×C₄×C₅₃	—	2	2	no	—
375	C₂×C₄×C₅₃	—	2	2	no	—
376	C₂×C₄×C₅₃	—	2	2	no	—
377	C₂×C₄×C₅₃	—	2	2	no	—
378	C₂×C₄×C₅₃	—	2	1	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	2	no	—
383	C₂×C₄×C₅₃	—	2	2	no	—
384	C₂×C₄×C₅₃	—	2	2	no	—
385	C₂×C₄×C₅₃	—	4	4	no	—
386	C₂×C₄×C₅₃	—	4	4	no	—
387	C₂×C₄×C₅₃	—	4	4	no	—
388	C₂×C₄×C₅₃	—	4	4	no	—
389	C₂×C₄×C₅₃	—	8	2	no	—
390	C₂×C₄×C₅₃	—	8	2	no	—
391	C₂×C₄×C₅₃	—	8	4	no	—
392	C₂×C₄×C₅₃	—	8	4	no	—
393	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
394	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
395	C₂×C₄×C₅₃	C₂²×Q₈	1	4	yes	—
396	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
397	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
398	#36750	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₂²×C₅₃	—	2	2	no	—
400	C₂²×C₅₃	—	2	2	no	—
401	C₂²×C₅₃	—	2	2	no	—
402	C₂²×C₅₃	—	2	2	no	—
403	C₂²×C₅₃	—	2	2	no	—
404	C₂²×C₅₃	—	2	2	no	—
405	C₂²×C₅₃	—	2	4	no	—
406	C₂²×C₅₃	—	2	4	no	—
407	C₂²×C₅₃	—	2	4	no	—
408	C₂²×C₅₃	—	4	2	no	—
409	C₂²×C₅₃	—	4	2	no	—
410	C₂²×C₅₃	—	4	2	no	—
411	C₂²×C₅₃	—	4	2	no	—
412	C₂²×C₅₃	—	8	8	no	—
413	C₂²×C₅₃	#544	1	4	yes	—
414	C₂²×C₅₃	C₂³×Q₈	1	1	yes	characteristic
415	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
417	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
419	C₂²×C₅₃	#585	1	1	yes	characteristic
420	C₂²×C₅₃	#585	1	1	yes	characteristic
421	C₄×C₅₃	—	2	2	no	—
422	C₄×C₅₃	—	2	2	no	—
423	C₄×C₅₃	—	2	4	no	—
424	C₄×C₅₃	—	2	2	no	—
425	C₄×C₅₃	—	2	2	no	—
426	C₄×C₅₃	—	4	1	no	—
427	C₄×C₅₃	—	4	2	no	—
428	C₄×C₅₃	—	4	2	no	—
429	C₄×C₅₃	—	4	2	no	—
430	C₄×C₅₃	—	4	2	no	—
431	C₄×C₅₃	—	4	1	no	—
432	C₄×C₅₃	—	4	2	no	—
433	C₄×C₅₃	—	4	2	no	—
434	C₄×C₅₃	—	4	2	no	—
435	C₄×C₅₃	—	4	2	no	—
436	C₄×C₅₃	—	4	2	no	—
437	C₄×C₅₃	—	4	2	no	—
438	#2857	C₂×C₅₃	1	1	yes	characteristic, complemented
439	#2851	C₂×C₅₃	1	1	yes	characteristic, complemented
440	#2807	C₂×C₅₃	1	2	yes	complemented
441	#2788	C₂×C₅₃	1	2	yes	complemented
442	#2768	C₂×C₅₃	1	2	yes	complemented
443	#2763	C₂×C₅₃	1	2	yes	complemented
444	#2729	C₂×C₅₃	1	2	yes	complemented
445	#2720	C₂×C₅₃	1	2	yes	complemented
446	#2704	C₂×C₅₃	1	2	yes	complemented
447	#2704	C₂×C₅₃	1	2	yes	complemented
448	#2659	C₂×C₅₃	1	1	yes	characteristic, complemented
449	#2646	C₂×C₅₃	1	1	yes	characteristic, complemented
450	#2549	C₂×C₅₃	1	2	yes	complemented
451	#2442	C₂×C₅₃	1	2	yes	complemented
452	#2437	C₂×C₅₃	1	2	yes	—
453	#2437	C₂×C₅₃	1	2	yes	—
454	#2315	C₂×C₅₃	1	1	yes	characteristic
455	#2312	C₂×C₅₃	1	1	yes	characteristic
456	C₂×#388	C₂×C₅₃	1	1	yes	characteristic
457	C₂×C₅₃	—	2	4	no	—
458	C₂×C₅₃	—	4	4	no	—
459	C₂×C₅₃	C₂×#544	1	1	yes	characteristic
460	C₂×C₅₃	#3501	1	1	yes	characteristic
461	C₂×C₅₃	#3501	1	1	yes	characteristic
462	C₂×C₅₃	#3534	1	1	yes	characteristic
463	C₂×C₅₃	#3536	1	1	yes	characteristic
464	C₂×C₅₃	#3558	1	1	yes	characteristic
465	C₂×C₅₃	#3564	1	1	yes	characteristic
466	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
467	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
468	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
469	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
470	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
471	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
472	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
473	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
474	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
475	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
476	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
477	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
478	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
479	#400	C₂²×C₅₃	1	2	yes	complemented
480	#400	C₂²×C₅₃	1	2	yes	complemented
481	#400	C₂²×C₅₃	1	2	yes	complemented
482	#400	C₂²×C₅₃	1	2	yes	complemented
483	#399	C₂²×C₅₃	1	2	yes	—
484	#399	C₂²×C₅₃	1	2	yes	—
485	#398	C₂²×C₅₃	1	2	yes	complemented
486	#398	C₂²×C₅₃	1	2	yes	complemented
487	#398	C₂²×C₅₃	1	2	yes	complemented
488	#398	C₂²×C₅₃	1	2	yes	complemented
489	#398	C₂²×C₅₃	1	2	yes	complemented
490	#398	C₂²×C₅₃	1	2	yes	complemented
491	#398	C₂²×C₅₃	1	2	yes	complemented
492	#398	C₂²×C₅₃	1	2	yes	complemented
493	#396	C₂²×C₅₃	1	2	yes	—
494	#396	C₂²×C₅₃	1	2	yes	—
495	#396	C₂²×C₅₃	1	2	yes	—
496	#396	C₂²×C₅₃	1	2	yes	—
497	#395	C₂²×C₅₃	1	2	yes	complemented
498	#395	C₂²×C₅₃	1	2	yes	complemented
499	#395	C₂²×C₅₃	1	2	yes	complemented
500	#395	C₂²×C₅₃	1	2	yes	complemented
501	#393	C₂²×C₅₃	1	2	yes	—
502	#393	C₂²×C₅₃	1	2	yes	—
503	#391	C₂²×C₅₃	1	2	yes	complemented
504	#391	C₂²×C₅₃	1	2	yes	complemented
505	#391	C₂²×C₅₃	1	2	yes	complemented
506	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
507	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
508	#389	C₂²×C₅₃	1	2	yes	complemented
509	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
510	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
511	#389	C₂²×C₅₃	1	2	yes	complemented
512	#389	C₂²×C₅₃	1	2	yes	complemented
513	#389	C₂²×C₅₃	1	2	yes	complemented
514	#389	C₂²×C₅₃	1	2	yes	complemented
515	#388	C₂²×C₅₃	1	2	yes	—
516	#388	C₂²×C₅₃	1	2	yes	—
517	#388	C₂²×C₅₃	1	2	yes	—
518	#388	C₂²×C₅₃	1	2	yes	—
519	#388	C₂²×C₅₃	1	2	yes	—
520	#388	C₂²×C₅₃	1	2	yes	—
521	#388	C₂²×C₅₃	1	2	yes	—
522	#388	C₂²×C₅₃	1	2	yes	—
523	#387	C₂²×C₅₃	1	2	yes	complemented
524	#387	C₂²×C₅₃	1	2	yes	complemented
525	#385	C₂²×C₅₃	1	2	yes	—
526	#385	C₂²×C₅₃	1	2	yes	—
527	#385	C₂²×C₅₃	1	2	yes	—
528	#385	C₂²×C₅₃	1	2	yes	—
529	#385	C₂²×C₅₃	1	2	yes	—
530	#385	C₂²×C₅₃	1	2	yes	—
531	#385	C₂²×C₅₃	1	2	yes	—
532	#385	C₂²×C₅₃	1	2	yes	—
533	#385	C₂²×C₅₃	1	2	yes	—
534	#385	C₂²×C₅₃	1	2	yes	—
535	#385	C₂²×C₅₃	1	2	yes	—
536	#385	C₂²×C₅₃	1	2	yes	—
537	#384	C₂²×C₅₃	1	1	yes	characteristic, complemented
538	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
539	#382	C₂²×C₅₃	1	2	yes	complemented
540	#380	C₂²×C₅₃	1	1	yes	characteristic
541	#380	C₂²×C₅₃	1	1	yes	characteristic
542	#380	C₂²×C₅₃	1	1	yes	characteristic
543	#380	C₂²×C₅₃	1	1	yes	characteristic
544	#380	C₂²×C₅₃	1	2	yes	—
545	#380	C₂²×C₅₃	1	2	yes	—
546	#380	C₂²×C₅₃	1	2	yes	—
547	#380	C₂²×C₅₃	1	2	yes	—
548	#380	C₂²×C₅₃	1	2	yes	—
549	#379	C₂²×C₅₃	1	2	yes	—
550	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
551	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
552	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
553	C₅₃	#36750	1	1	yes	characteristic, direct product factor, Sylow
554	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
555	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
556	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
557	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
561	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
562	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
563	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
564	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
565	C₄⋊Q₈	—	4	2	no	—
566	#125	—	4	2	no	—
567	#125	—	4	4	no	—
568	C₂²⋊Q₈	—	4	4	no	—
569	C₂²⋊Q₈	—	4	4	no	—
570	C₂²⋊Q₈	—	4	4	no	—
571	C₂²⋊Q₈	—	4	4	no	—
572	C₂×C₄⋊C₄	—	4	2	no	—
573	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
603	C₂×C₂²⋊C₄	—	4	2	no	—
604	C₂×C₂²⋊C₄	—	4	2	no	—
605	C₂×C₂²⋊C₄	—	4	4	no	—
606	C₂×C₂²⋊C₄	Q₈×C₅₃	1	8	yes	complemented
607	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
623	C₂×C₄²	—	4	2	no	—
624	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
627	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
628	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
630	#95	C₂³×C₅₃	1	2	yes	—
631	#95	C₂³×C₅₃	1	2	yes	—
632	#95	C₂³×C₅₃	1	2	yes	—
633	#95	C₂³×C₅₃	1	2	yes	—
634	#95	C₂³×C₅₃	1	2	yes	—
635	#95	C₂³×C₅₃	1	2	yes	—
636	#95	C₂³×C₅₃	1	2	yes	—
637	#95	C₂³×C₅₃	1	2	yes	—
638	#95	C₂³×C₅₃	1	2	yes	—
639	#95	C₂³×C₅₃	1	2	yes	—
640	#95	C₂³×C₅₃	1	2	yes	—
641	#95	C₂³×C₅₃	1	2	yes	—
642	#95	C₂³×C₅₃	1	2	yes	—
643	#95	C₂³×C₅₃	1	2	yes	—
644	#95	C₂³×C₅₃	1	2	yes	—
645	#95	C₂³×C₅₃	1	2	yes	—
646	#95	C₂³×C₅₃	1	2	yes	—
647	#95	C₂³×C₅₃	1	2	yes	—
648	#95	C₂³×C₅₃	1	2	yes	—
649	#95	C₂³×C₅₃	1	2	yes	—
650	#95	C₂³×C₅₃	1	2	yes	—
651	#95	C₂³×C₅₃	1	2	yes	—
652	#95	C₂³×C₅₃	1	2	yes	—
653	#95	C₂³×C₅₃	1	2	yes	—
654	C₂⁴	—	2	2	no	—
655	C₂⁴	—	2	2	no	—
656	C₂⁴	—	4	1	no	—
657	C₂⁴	—	4	1	no	—
658	C₂⁴	—	4	1	no	—
659	C₂⁴	—	4	1	no	—
660	C₂⁴	C₂×Q₈×C₅₃	1	4	yes	—
661	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
662	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
663	C₂×Q₈	—	2	4	no	—
664	C₂×Q₈	—	4	2	no	—
665	C₂×Q₈	—	4	2	no	—
666	C₂×Q₈	—	4	2	no	—
667	C₂×Q₈	—	4	2	no	—
668	C₂×Q₈	—	4	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	4	1	no	—
676	C₂²×C₄	—	4	1	no	—
677	C₂²×C₄	—	4	1	no	—
678	C₂²×C₄	—	4	1	no	—
679	C₂²×C₄	—	4	1	no	—
680	C₂²×C₄	—	4	1	no	—
681	C₂²×C₄	—	4	1	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	1	no	—
685	C₂²×C₄	—	4	1	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	1	no	—
691	C₂²×C₄	C₂×Q₈×C₅₃	1	4	yes	—
692	C₂²×C₄	C₂×Q₈×C₅₃	1	4	yes	—
693	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	1	no	—
725	C₄⋊C₄	—	4	1	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	1	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	1	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	1	no	—
735	C₄⋊C₄	—	4	1	no	—
736	C₄⋊C₄	—	4	1	no	—
737	C₄⋊C₄	—	4	1	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	C₂×Q₈×C₅₃	1	8	yes	—
755	C₂²⋊C₄	C₂×Q₈×C₅₃	1	8	yes	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	4	1	no	—
759	C₄²	—	4	1	no	—
760	C₄²	—	4	2	no	—
761	C₄²	—	4	2	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	8	no	—
773	C₂³	—	4	4	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	8	2	no	—
776	C₂³	—	8	2	no	—
777	C₂³	—	8	2	no	—
778	C₂³	—	8	2	no	—
779	C₂³	C₂²×Q₈×C₅₃	1	4	yes	—
780	C₂³	C₂²×Q₈×C₅₃	1	2	yes	—
781	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
782	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
783	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
784	Q₈	—	8	4	no	—
785	Q₈	—	8	4	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	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	—	4	4	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	—	8	4	no	—
839	C₂×C₄	—	8	4	no	—
840	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
841	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
842	C₂×C₄	C₂²×Q₈×C₅₃	1	4	yes	—
843	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
844	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	4	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	8	8	no	—
859	C₂²	C₅₃×#544	1	4	yes	—
860	C₂²	C₂³×Q₈×C₅₃	1	1	yes	characteristic
861	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
862	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
863	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
864	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
865	C₂²	C₅₃×#585	1	1	yes	characteristic
866	C₂²	C₅₃×#585	1	1	yes	characteristic
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	4	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₂	—	2	4	no	—
885	C₂	—	4	4	no	—
886	C₂	C₂×C₅₃×#544	1	1	yes	characteristic
887	C₂	C₅₃×#3501	1	1	yes	characteristic
888	C₂	C₅₃×#3501	1	1	yes	characteristic
889	C₂	C₅₃×#3534	1	1	yes	characteristic
890	C₂	C₅₃×#3536	1	1	yes	characteristic
891	C₂	C₅₃×#3558	1	1	yes	characteristic
892	C₂	C₅₃×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂⁵×C₅₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#2857	C₂	semidirect
2. C₅₃×#2851	C₂	semidirect
3. C₅₃×#2807	C₂	semidirect
4. C₅₃×#2788	C₂	semidirect
5. C₅₃×#2768	C₂	semidirect
6. C₅₃×#2763	C₂	semidirect
7. C₅₃×#2729	C₂	semidirect
8. C₅₃×#2720	C₂	semidirect
9. C₅₃×#2704	C₂	semidirect
10. C₅₃×#2704	C₂	semidirect
11. C₅₃×#2659	C₂	semidirect
12. C₅₃×#2646	C₂	semidirect
13. C₅₃×#2549	C₂	semidirect
14. C₅₃×#2442	C₂	semidirect
20. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
21. C₂×#125×C₅₃	C₂²	semidirect
22. C₂×#125×C₅₃	C₂²	semidirect
33. C₅₃×#400	C₂²	semidirect
34. C₅₃×#400	C₂²	semidirect
35. C₅₃×#400	C₂²	semidirect
36. C₅₃×#400	C₂²	semidirect
39. C₅₃×#398	C₂²	semidirect
40. C₅₃×#398	C₂²	semidirect
41. C₅₃×#398	C₂²	semidirect
42. C₅₃×#398	C₂²	semidirect
43. C₅₃×#398	C₂²	semidirect
44. C₅₃×#398	C₂²	semidirect
45. C₅₃×#398	C₂²	semidirect
46. C₅₃×#398	C₂²	semidirect
51. C₅₃×#395	C₂²	semidirect
52. C₅₃×#395	C₂²	semidirect
53. C₅₃×#395	C₂²	semidirect
54. C₅₃×#395	C₂²	semidirect
57. C₅₃×#391	C₂²	semidirect
58. C₅₃×#391	C₂²	semidirect
59. C₅₃×#391	C₂²	semidirect
60. C₅₃×#389	C₂²	semidirect
61. C₅₃×#389	C₂²	semidirect
62. C₅₃×#389	C₂²	semidirect
63. C₅₃×#389	C₂²	semidirect
64. C₅₃×#389	C₂²	semidirect
65. C₅₃×#389	C₂²	semidirect
66. C₅₃×#389	C₂²	semidirect
67. C₅₃×#389	C₂²	semidirect
68. C₅₃×#389	C₂²	semidirect
77. C₅₃×#387	C₂²	semidirect
78. C₅₃×#387	C₂²	semidirect
91. C₅₃×#384	C₂²	semidirect
92. C₅₃×#382	C₂²	semidirect
93. C₅₃×#382	C₂²	semidirect
159. C₂×C₂²⋊C₄×C₅₃	Q₈	semidirect
398. #36750	C₅₃	direct (N × H)
438. #2857	C₂×C₅₃	semidirect
439. #2851	C₂×C₅₃	semidirect
440. #2807	C₂×C₅₃	semidirect
441. #2788	C₂×C₅₃	semidirect
442. #2768	C₂×C₅₃	semidirect
443. #2763	C₂×C₅₃	semidirect
444. #2729	C₂×C₅₃	semidirect
445. #2720	C₂×C₅₃	semidirect
446. #2704	C₂×C₅₃	semidirect
447. #2704	C₂×C₅₃	semidirect
448. #2659	C₂×C₅₃	semidirect
449. #2646	C₂×C₅₃	semidirect
450. #2549	C₂×C₅₃	semidirect
451. #2442	C₂×C₅₃	semidirect
466. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
467. C₂×#125	C₂²×C₅₃	semidirect
468. C₂×#125	C₂²×C₅₃	semidirect
479. #400	C₂²×C₅₃	semidirect
480. #400	C₂²×C₅₃	semidirect
481. #400	C₂²×C₅₃	semidirect
482. #400	C₂²×C₅₃	semidirect
485. #398	C₂²×C₅₃	semidirect
486. #398	C₂²×C₅₃	semidirect
487. #398	C₂²×C₅₃	semidirect
488. #398	C₂²×C₅₃	semidirect
489. #398	C₂²×C₅₃	semidirect
490. #398	C₂²×C₅₃	semidirect
491. #398	C₂²×C₅₃	semidirect
492. #398	C₂²×C₅₃	semidirect
497. #395	C₂²×C₅₃	semidirect
498. #395	C₂²×C₅₃	semidirect
499. #395	C₂²×C₅₃	semidirect
500. #395	C₂²×C₅₃	semidirect
503. #391	C₂²×C₅₃	semidirect
504. #391	C₂²×C₅₃	semidirect
505. #391	C₂²×C₅₃	semidirect
506. #389	C₂²×C₅₃	semidirect
507. #389	C₂²×C₅₃	semidirect
508. #389	C₂²×C₅₃	semidirect
509. #389	C₂²×C₅₃	semidirect
510. #389	C₂²×C₅₃	semidirect
511. #389	C₂²×C₅₃	semidirect
512. #389	C₂²×C₅₃	semidirect
513. #389	C₂²×C₅₃	semidirect
514. #389	C₂²×C₅₃	semidirect
523. #387	C₂²×C₅₃	semidirect
524. #387	C₂²×C₅₃	semidirect
537. #384	C₂²×C₅₃	semidirect
538. #382	C₂²×C₅₃	semidirect
539. #382	C₂²×C₅₃	semidirect
553. C₅₃	#36750	direct (N × H)
606. C₂×C₂²⋊C₄	Q₈×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#2857	2
C₅₃×#2851	2
C₅₃×#2807	2
C₅₃×#2788	2
C₅₃×#2768	2
C₅₃×#2763	2
C₅₃×#2729	2
C₅₃×#2720	2
C₅₃×#2704	2
C₅₃×#2659	2
C₅₃×#2646	2
C₅₃×#2549	2
C₅₃×#2442	2
C₅₃×#2437	2
C₅₃×#2315	2
C₅₃×#2312	2
C₂×C₅₃×#388	2
#36750	53

Subgroups — C53×#36750 #27244262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36750 #27244262