Subgroups — C₅₃×#36605 #27244117

Order 13568.

1860 conjugacy classes of subgroups.

The subgroup lattice has 990 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×#2850	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#2850	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#2594	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2579	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2573	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2545	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2525	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2512	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2510	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2481	C₂	1	2	yes	maximal, complemented
14	C₅₃×#2447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2373	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2353	C₂	1	2	yes	maximal, complemented
20	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic
23	C₂×C₄×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#126×C₅₃	C₂²	1	2	yes	—
26	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#401	C₂²	1	2	yes	—
41	C₅₃×#400	C₂²	1	2	yes	—
42	C₅₃×#400	C₂²	1	2	yes	—
43	C₅₃×#400	C₂²	1	2	yes	—
44	C₅₃×#398	C₂²	1	2	yes	—
45	C₅₃×#398	C₂²	1	2	yes	—
46	C₅₃×#397	C₂²	1	2	yes	—
47	C₅₃×#397	C₂²	1	2	yes	—
48	C₅₃×#397	C₂²	1	2	yes	—
49	C₅₃×#396	C₂²	1	2	yes	—
50	C₅₃×#396	C₂²	1	2	yes	—
51	C₅₃×#396	C₂²	1	2	yes	—
52	C₅₃×#391	C₂²	1	1	yes	characteristic
53	C₅₃×#391	C₂²	1	1	yes	characteristic
54	C₅₃×#391	C₂²	1	1	yes	characteristic
55	C₅₃×#391	C₂²	1	1	yes	characteristic
56	C₅₃×#391	C₂²	1	1	yes	characteristic
57	C₅₃×#391	C₂²	1	1	yes	characteristic
58	C₅₃×#390	C₂²	1	1	yes	characteristic
59	C₅₃×#390	C₂²	1	1	yes	characteristic
60	C₅₃×#390	C₂²	1	1	yes	characteristic
61	C₅₃×#389	C₂²	1	1	yes	characteristic
62	C₅₃×#389	C₂²	1	1	yes	characteristic
63	C₅₃×#389	C₂²	1	1	yes	characteristic
64	C₅₃×#389	C₂²	1	2	yes	—
65	C₅₃×#389	C₂²	1	2	yes	—
66	C₅₃×#388	C₂²	1	2	yes	—
67	C₅₃×#388	C₂²	1	2	yes	—
68	C₅₃×#388	C₂²	1	2	yes	—
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×#387	C₂²	1	2	yes	—
77	C₅₃×#387	C₂²	1	2	yes	—
78	C₅₃×#387	C₂²	1	2	yes	—
79	C₅₃×#387	C₂²	1	2	yes	—
80	C₅₃×#387	C₂²	1	2	yes	—
81	C₅₃×#387	C₂²	1	2	yes	—
82	C₅₃×#387	C₂²	1	2	yes	—
83	C₅₃×#387	C₂²	1	2	yes	—
84	C₅₃×#387	C₂²	1	2	yes	—
85	C₅₃×#386	C₂²	1	2	yes	—
86	C₅₃×#386	C₂²	1	2	yes	—
87	C₅₃×#386	C₂²	1	2	yes	—
88	C₅₃×#386	C₂²	1	2	yes	—
89	C₅₃×#386	C₂²	1	2	yes	—
90	C₅₃×#385	C₂²	1	2	yes	—
91	C₅₃×#385	C₂²	1	2	yes	—
92	C₅₃×#385	C₂²	1	2	yes	—
93	C₅₃×#385	C₂²	1	2	yes	—
94	C₅₃×#384	C₂²	1	1	yes	characteristic
95	C₅₃×#383	C₂²	1	2	yes	—
96	C₅₃×#383	C₂²	1	2	yes	—
97	C₅₃×#382	C₂²	1	1	yes	characteristic
98	C₅₃×#382	C₂²	1	1	yes	characteristic
99	C₅₃×#381	C₂²	1	2	yes	—
100	C₅₃×#380	C₂²	1	2	yes	—
101	C₅₃×#380	C₂²	1	1	yes	characteristic
102	C₅₃×#380	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
120	C₅₃×#376	C₂²	1	2	yes	—
121	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
122	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₄⋊Q₈×C₅₃	—	4	2	no	—
136	#126×C₅₃	—	2	8	no	—
137	#124×C₅₃	—	2	4	no	—
138	#124×C₅₃	—	4	2	no	—
139	C₂²⋊Q₈×C₅₃	—	2	4	no	—
140	C₂²⋊Q₈×C₅₃	—	2	4	no	—
141	#121×C₅₃	—	2	4	no	—
142	C₄×Q₈×C₅₃	—	2	4	no	—
143	C₄×Q₈×C₅₃	—	4	2	no	—
144	C₄×D₄×C₅₃	—	2	8	no	—
145	C₄×D₄×C₅₃	—	4	2	no	—
146	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
147	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
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	1	yes	characteristic
154	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₅₃	—	2	4	no	—
188	C₂×C₄²×C₅₃	—	4	2	no	—
189	C₂×C₄²×C₅₃	—	4	2	no	—
190	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
200	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
206	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
207	#95×C₅₃	C₂³	1	1	yes	characteristic
208	#95×C₅₃	C₂³	1	1	yes	characteristic
209	#95×C₅₃	C₂³	1	1	yes	characteristic
210	#95×C₅₃	C₂³	1	1	yes	characteristic
211	#95×C₅₃	C₂³	1	1	yes	characteristic
212	#95×C₅₃	C₂³	1	1	yes	characteristic
213	#95×C₅₃	C₂³	1	1	yes	characteristic
214	#95×C₅₃	C₂³	1	1	yes	characteristic
215	#95×C₅₃	C₂³	1	2	yes	—
216	#95×C₅₃	C₂³	1	2	yes	—
217	#95×C₅₃	C₂³	1	2	yes	—
218	#95×C₅₃	C₂³	1	2	yes	—
219	#95×C₅₃	C₂³	1	2	yes	—
220	#95×C₅₃	C₂³	1	2	yes	—
221	#95×C₅₃	C₂³	1	2	yes	—
222	#95×C₅₃	C₂³	1	2	yes	—
223	#95×C₅₃	C₂³	1	2	yes	—
224	#95×C₅₃	C₂³	1	2	yes	—
225	#95×C₅₃	C₂³	1	2	yes	—
226	#95×C₅₃	C₂³	1	2	yes	—
227	#95×C₅₃	C₂³	1	2	yes	—
228	#95×C₅₃	C₂³	1	2	yes	—
229	#95×C₅₃	C₂³	1	2	yes	—
230	#95×C₅₃	C₂³	1	2	yes	—
231	#95×C₅₃	C₂³	1	2	yes	—
232	#95×C₅₃	C₂³	1	2	yes	—
233	#95×C₅₃	C₂³	1	2	yes	—
234	#95×C₅₃	C₂³	1	2	yes	—
235	#95×C₅₃	C₂³	1	2	yes	—
236	#95×C₅₃	C₂³	1	2	yes	—
237	#95×C₅₃	C₂³	1	2	yes	—
238	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
239	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
245	C₂×Q₈×C₅₃	—	2	2	no	—
246	C₂×D₄×C₅₃	—	2	4	no	—
247	C₂×D₄×C₅₃	—	2	4	no	—
248	C₂×D₄×C₅₃	—	2	4	no	—
249	C₂×D₄×C₅₃	—	2	2	no	—
250	C₂×D₄×C₅₃	—	2	2	no	—
251	C₂×D₄×C₅₃	—	2	2	no	—
252	C₂²×C₄×C₅₃	—	2	2	no	—
253	C₂²×C₄×C₅₃	—	2	2	no	—
254	C₂²×C₄×C₅₃	—	2	2	no	—
255	C₂²×C₄×C₅₃	—	2	2	no	—
256	C₂²×C₄×C₅₃	—	2	2	no	—
257	C₂²×C₄×C₅₃	—	2	2	no	—
258	C₂²×C₄×C₅₃	—	2	2	no	—
259	C₂²×C₄×C₅₃	—	2	2	no	—
260	C₂²×C₄×C₅₃	—	2	2	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	—	4	1	no	—
266	C₂²×C₄×C₅₃	—	4	1	no	—
267	C₂²×C₄×C₅₃	—	4	1	no	—
268	C₂²×C₄×C₅₃	—	4	1	no	—
269	C₂²×C₄×C₅₃	—	4	1	no	—
270	C₂²×C₄×C₅₃	—	4	1	no	—
271	C₂²×C₄×C₅₃	—	4	1	no	—
272	C₂²×C₄×C₅₃	—	4	2	no	—
273	C₂²×C₄×C₅₃	—	4	2	no	—
274	C₂²×C₄×C₅₃	#41	1	4	yes	—
275	C₂²×C₄×C₅₃	#41	1	4	yes	—
276	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
297	C₄⋊C₄×C₅₃	—	2	2	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	2	no	—
302	C₄⋊C₄×C₅₃	—	2	2	no	—
303	C₄⋊C₄×C₅₃	—	2	2	no	—
304	C₄⋊C₄×C₅₃	—	2	4	no	—
305	C₄⋊C₄×C₅₃	—	2	4	no	—
306	C₄⋊C₄×C₅₃	—	2	2	no	—
307	C₄⋊C₄×C₅₃	—	2	2	no	—
308	C₄⋊C₄×C₅₃	—	2	4	no	—
309	C₄⋊C₄×C₅₃	—	2	4	no	—
310	C₄⋊C₄×C₅₃	—	2	2	no	—
311	C₄⋊C₄×C₅₃	—	2	2	no	—
312	C₄⋊C₄×C₅₃	—	2	4	no	—
313	C₄⋊C₄×C₅₃	—	2	4	no	—
314	C₄⋊C₄×C₅₃	—	2	2	no	—
315	C₄⋊C₄×C₅₃	—	4	2	no	—
316	C₄⋊C₄×C₅₃	—	4	2	no	—
317	C₄⋊C₄×C₅₃	—	4	2	no	—
318	C₄⋊C₄×C₅₃	—	4	2	no	—
319	C₄⋊C₄×C₅₃	—	4	2	no	—
320	C₄⋊C₄×C₅₃	#41	1	4	yes	—
321	C₂²⋊C₄×C₅₃	—	2	4	no	—
322	C₂²⋊C₄×C₅₃	—	2	4	no	—
323	C₂²⋊C₄×C₅₃	—	2	4	no	—
324	C₂²⋊C₄×C₅₃	—	2	4	no	—
325	C₂²⋊C₄×C₅₃	—	2	4	no	—
326	C₂²⋊C₄×C₅₃	—	2	4	no	—
327	C₂²⋊C₄×C₅₃	—	2	4	no	—
328	C₂²⋊C₄×C₅₃	—	2	4	no	—
329	C₂²⋊C₄×C₅₃	—	2	4	no	—
330	C₂²⋊C₄×C₅₃	—	2	4	no	—
331	C₂²⋊C₄×C₅₃	—	4	2	no	—
332	C₂²⋊C₄×C₅₃	—	4	2	no	—
333	C₂²⋊C₄×C₅₃	—	4	2	no	—
334	C₂²⋊C₄×C₅₃	—	4	2	no	—
335	C₂²⋊C₄×C₅₃	—	4	2	no	—
336	C₄²×C₅₃	—	2	2	no	—
337	C₄²×C₅₃	—	2	2	no	—
338	C₄²×C₅₃	—	2	2	no	—
339	C₄²×C₅₃	—	2	4	no	—
340	C₄²×C₅₃	—	2	4	no	—
341	C₄²×C₅₃	—	2	4	no	—
342	C₄²×C₅₃	—	2	2	no	—
343	C₄²×C₅₃	—	2	2	no	—
344	C₄²×C₅₃	—	2	2	no	—
345	C₄²×C₅₃	—	2	2	no	—
346	C₄²×C₅₃	—	4	1	no	—
347	C₄²×C₅₃	—	4	1	no	—
348	C₄²×C₅₃	—	4	1	no	—
349	C₄²×C₅₃	—	4	1	no	—
350	C₄²×C₅₃	—	4	2	no	—
351	C₄²×C₅₃	—	4	2	no	—
352	C₄²×C₅₃	#41	1	4	yes	—
353	C₂³×C₅₃	—	2	1	no	—
354	C₂³×C₅₃	—	2	1	no	—
355	C₂³×C₅₃	—	2	1	no	—
356	C₂³×C₅₃	—	2	1	no	—
357	C₂³×C₅₃	—	2	2	no	—
358	C₂³×C₅₃	—	2	2	no	—
359	C₂³×C₅₃	—	2	2	no	—
360	C₂³×C₅₃	—	2	2	no	—
361	C₂³×C₅₃	—	2	2	no	—
362	C₂³×C₅₃	—	2	2	no	—
363	C₂³×C₅₃	—	2	2	no	—
364	C₂³×C₅₃	C₂×#41	1	2	yes	—
365	C₂³×C₅₃	C₂×#41	1	2	yes	—
366	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
367	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
368	Q₈×C₅₃	—	4	4	no	—
369	Q₈×C₅₃	—	4	4	no	—
370	D₄×C₅₃	—	4	8	no	—
371	D₄×C₅₃	—	4	4	no	—
372	C₂×C₄×C₅₃	—	2	8	no	—
373	C₂×C₄×C₅₃	—	2	1	no	—
374	C₂×C₄×C₅₃	—	2	1	no	—
375	C₂×C₄×C₅₃	—	2	1	no	—
376	C₂×C₄×C₅₃	—	2	1	no	—
377	C₂×C₄×C₅₃	—	2	1	no	—
378	C₂×C₄×C₅₃	—	2	1	no	—
379	C₂×C₄×C₅₃	—	2	1	no	—
380	C₂×C₄×C₅₃	—	2	1	no	—
381	C₂×C₄×C₅₃	—	2	1	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	1	no	—
386	C₂×C₄×C₅₃	—	2	1	no	—
387	C₂×C₄×C₅₃	—	2	1	no	—
388	C₂×C₄×C₅₃	—	2	1	no	—
389	C₂×C₄×C₅₃	—	2	8	no	—
390	C₂×C₄×C₅₃	—	2	1	no	—
391	C₂×C₄×C₅₃	—	2	2	no	—
392	C₂×C₄×C₅₃	—	2	1	no	—
393	C₂×C₄×C₅₃	—	2	1	no	—
394	C₂×C₄×C₅₃	—	2	1	no	—
395	C₂×C₄×C₅₃	—	2	1	no	—
396	C₂×C₄×C₅₃	—	2	2	no	—
397	C₂×C₄×C₅₃	—	2	2	no	—
398	C₂×C₄×C₅₃	—	2	2	no	—
399	C₂×C₄×C₅₃	—	2	2	no	—
400	C₂×C₄×C₅₃	—	2	2	no	—
401	C₂×C₄×C₅₃	—	2	2	no	—
402	C₂×C₄×C₅₃	—	2	2	no	—
403	C₂×C₄×C₅₃	—	2	2	no	—
404	C₂×C₄×C₅₃	—	2	2	no	—
405	C₂×C₄×C₅₃	—	2	2	no	—
406	C₂×C₄×C₅₃	—	2	2	no	—
407	C₂×C₄×C₅₃	—	2	2	no	—
408	C₂×C₄×C₅₃	—	2	2	no	—
409	C₂×C₄×C₅₃	—	2	1	no	—
410	C₂×C₄×C₅₃	—	2	1	no	—
411	C₂×C₄×C₅₃	—	2	1	no	—
412	C₂×C₄×C₅₃	—	2	1	no	—
413	C₂×C₄×C₅₃	—	2	2	no	—
414	C₂×C₄×C₅₃	—	2	2	no	—
415	C₂×C₄×C₅₃	—	2	2	no	—
416	C₂×C₄×C₅₃	—	2	1	no	—
417	C₂×C₄×C₅₃	—	2	1	no	—
418	C₂×C₄×C₅₃	—	2	1	no	—
419	C₂×C₄×C₅₃	—	2	2	no	—
420	C₂×C₄×C₅₃	—	2	2	no	—
421	C₂×C₄×C₅₃	—	2	1	no	—
422	C₂×C₄×C₅₃	—	2	1	no	—
423	C₂×C₄×C₅₃	—	2	1	no	—
424	C₂×C₄×C₅₃	—	2	2	no	—
425	C₂×C₄×C₅₃	—	2	2	no	—
426	C₂×C₄×C₅₃	—	4	4	no	—
427	C₂×C₄×C₅₃	—	4	4	no	—
428	C₂×C₄×C₅₃	—	4	4	no	—
429	C₂×C₄×C₅₃	—	4	4	no	—
430	C₂×C₄×C₅₃	—	4	4	no	—
431	C₂×C₄×C₅₃	—	8	4	no	—
432	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
433	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
434	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
435	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
436	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
437	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
438	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
439	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
440	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
441	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
442	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
443	#36605	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂²×C₅₃	—	2	2	no	—
445	C₂²×C₅₃	—	2	2	no	—
446	C₂²×C₅₃	—	2	2	no	—
447	C₂²×C₅₃	—	2	2	no	—
448	C₂²×C₅₃	—	2	2	no	—
449	C₂²×C₅₃	—	2	2	no	—
450	C₂²×C₅₃	—	4	2	no	—
451	C₂²×C₅₃	—	4	2	no	—
452	C₂²×C₅₃	—	4	2	no	—
453	C₂²×C₅₃	—	4	2	no	—
454	C₂²×C₅₃	—	4	2	no	—
455	C₂²×C₅₃	—	4	2	no	—
456	C₂²×C₅₃	—	4	2	no	—
457	C₂²×C₅₃	#556	1	4	yes	—
458	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
459	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
460	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
461	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
462	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
463	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
464	C₂²×C₅₃	#585	1	1	yes	characteristic
465	C₄×C₅₃	—	2	2	no	—
466	C₄×C₅₃	—	2	2	no	—
467	C₄×C₅₃	—	2	2	no	—
468	C₄×C₅₃	—	2	2	no	—
469	C₄×C₅₃	—	2	2	no	—
470	C₄×C₅₃	—	2	2	no	—
471	C₄×C₅₃	—	2	2	no	—
472	C₄×C₅₃	—	2	2	no	—
473	C₄×C₅₃	—	4	2	no	—
474	C₄×C₅₃	—	4	2	no	—
475	C₄×C₅₃	—	4	2	no	—
476	C₄×C₅₃	—	4	2	no	—
477	C₄×C₅₃	—	4	2	no	—
478	C₄×C₅₃	—	4	2	no	—
479	C₄×C₅₃	—	4	1	no	—
480	C₄×C₅₃	—	4	1	no	—
481	C₄×C₅₃	—	4	1	no	—
482	C₄×C₅₃	—	4	2	no	—
483	C₄×C₅₃	—	4	1	no	—
484	C₄×C₅₃	—	4	1	no	—
485	C₄×C₅₃	#553	1	4	yes	—
486	#2857	C₂×C₅₃	1	1	yes	characteristic, complemented
487	#2850	C₂×C₅₃	1	1	yes	characteristic
488	#2850	C₂×C₅₃	1	1	yes	characteristic
489	#2594	C₂×C₅₃	1	2	yes	complemented
490	#2579	C₂×C₅₃	1	2	yes	complemented
491	#2573	C₂×C₅₃	1	2	yes	complemented
492	#2570	C₂×C₅₃	1	1	yes	characteristic, complemented
493	#2545	C₂×C₅₃	1	1	yes	characteristic, complemented
494	#2525	C₂×C₅₃	1	2	yes	complemented
495	#2514	C₂×C₅₃	1	1	yes	characteristic, complemented
496	#2512	C₂×C₅₃	1	1	yes	characteristic, complemented
497	#2510	C₂×C₅₃	1	2	yes	complemented
498	#2481	C₂×C₅₃	1	2	yes	complemented
499	#2447	C₂×C₅₃	1	1	yes	characteristic, complemented
500	#2446	C₂×C₅₃	1	1	yes	characteristic, complemented
501	#2373	C₂×C₅₃	1	2	yes	complemented
502	#2367	C₂×C₅₃	1	1	yes	characteristic, complemented
503	#2356	C₂×C₅₃	1	1	yes	characteristic, complemented
504	#2353	C₂×C₅₃	1	2	yes	complemented
505	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
506	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
507	C₄×#121	C₂×C₅₃	1	1	yes	characteristic
508	C₂×C₄×C₄⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
509	C₂×C₅₃	—	2	4	no	—
510	C₂×C₅₃	—	8	2	no	—
511	C₂×C₅₃	#3444	1	1	yes	characteristic
512	C₂×C₅₃	C₂×#553	1	1	yes	characteristic
513	C₂×C₅₃	C₂×#556	1	1	yes	characteristic
514	C₂×C₅₃	#3480	1	1	yes	characteristic
515	C₂×C₅₃	#3495	1	1	yes	characteristic
516	C₂×C₅₃	#3505	1	1	yes	characteristic
517	C₂×C₅₃	#3520	1	1	yes	characteristic
518	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
519	C₂×#126	C₂²×C₅₃	1	2	yes	—
520	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
521	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
522	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
523	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
524	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
525	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
526	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
527	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
528	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
529	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
530	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
531	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
532	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
533	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
534	#401	C₂²×C₅₃	1	2	yes	—
535	#400	C₂²×C₅₃	1	2	yes	—
536	#400	C₂²×C₅₃	1	2	yes	—
537	#400	C₂²×C₅₃	1	2	yes	—
538	#398	C₂²×C₅₃	1	2	yes	—
539	#398	C₂²×C₅₃	1	2	yes	—
540	#397	C₂²×C₅₃	1	2	yes	—
541	#397	C₂²×C₅₃	1	2	yes	—
542	#397	C₂²×C₅₃	1	2	yes	—
543	#396	C₂²×C₅₃	1	2	yes	—
544	#396	C₂²×C₅₃	1	2	yes	—
545	#396	C₂²×C₅₃	1	2	yes	—
546	#391	C₂²×C₅₃	1	1	yes	characteristic
547	#391	C₂²×C₅₃	1	1	yes	characteristic
548	#391	C₂²×C₅₃	1	1	yes	characteristic
549	#391	C₂²×C₅₃	1	1	yes	characteristic
550	#391	C₂²×C₅₃	1	1	yes	characteristic
551	#391	C₂²×C₅₃	1	1	yes	characteristic
552	#390	C₂²×C₅₃	1	1	yes	characteristic
553	#390	C₂²×C₅₃	1	1	yes	characteristic
554	#390	C₂²×C₅₃	1	1	yes	characteristic
555	#389	C₂²×C₅₃	1	1	yes	characteristic
556	#389	C₂²×C₅₃	1	1	yes	characteristic
557	#389	C₂²×C₅₃	1	2	yes	—
558	#389	C₂²×C₅₃	1	2	yes	—
559	#389	C₂²×C₅₃	1	1	yes	characteristic
560	#388	C₂²×C₅₃	1	2	yes	—
561	#388	C₂²×C₅₃	1	2	yes	—
562	#388	C₂²×C₅₃	1	2	yes	—
563	#388	C₂²×C₅₃	1	2	yes	—
564	#388	C₂²×C₅₃	1	2	yes	—
565	#388	C₂²×C₅₃	1	2	yes	—
566	#388	C₂²×C₅₃	1	2	yes	—
567	#388	C₂²×C₅₃	1	2	yes	—
568	#388	C₂²×C₅₃	1	2	yes	—
569	#388	C₂²×C₅₃	1	2	yes	—
570	#387	C₂²×C₅₃	1	2	yes	—
571	#387	C₂²×C₅₃	1	2	yes	—
572	#387	C₂²×C₅₃	1	2	yes	—
573	#387	C₂²×C₅₃	1	2	yes	—
574	#387	C₂²×C₅₃	1	2	yes	—
575	#387	C₂²×C₅₃	1	2	yes	—
576	#387	C₂²×C₅₃	1	2	yes	—
577	#387	C₂²×C₅₃	1	2	yes	—
578	#387	C₂²×C₅₃	1	2	yes	—
579	#386	C₂²×C₅₃	1	2	yes	—
580	#386	C₂²×C₅₃	1	2	yes	—
581	#386	C₂²×C₅₃	1	2	yes	—
582	#386	C₂²×C₅₃	1	2	yes	—
583	#386	C₂²×C₅₃	1	2	yes	—
584	#385	C₂²×C₅₃	1	2	yes	—
585	#385	C₂²×C₅₃	1	2	yes	—
586	#385	C₂²×C₅₃	1	2	yes	—
587	#385	C₂²×C₅₃	1	2	yes	—
588	#384	C₂²×C₅₃	1	1	yes	characteristic
589	#383	C₂²×C₅₃	1	2	yes	—
590	#383	C₂²×C₅₃	1	2	yes	—
591	#382	C₂²×C₅₃	1	1	yes	characteristic
592	#382	C₂²×C₅₃	1	1	yes	characteristic
593	#381	C₂²×C₅₃	1	2	yes	—
594	#380	C₂²×C₅₃	1	2	yes	—
595	#380	C₂²×C₅₃	1	2	yes	—
596	#380	C₂²×C₅₃	1	1	yes	characteristic
597	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
598	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
599	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
600	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
601	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
602	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
603	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
604	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
605	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
606	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
607	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
608	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
609	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
610	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
611	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
612	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
613	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
614	#376	C₂²×C₅₃	1	2	yes	—
615	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
616	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
617	C₅₃	#36605	1	1	yes	characteristic, direct product factor, Sylow
618	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
619	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
620	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
621	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
622	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
624	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
628	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
629	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
630	C₄⋊Q₈	—	4	2	no	—
631	#126	—	2	8	no	—
632	#124	—	2	4	no	—
633	#124	—	4	2	no	—
634	C₂²⋊Q₈	—	2	4	no	—
635	C₂²⋊Q₈	—	2	4	no	—
636	#121	—	2	4	no	—
637	C₄×Q₈	—	2	4	no	—
638	C₄×Q₈	—	4	2	no	—
639	C₄×D₄	—	2	8	no	—
640	C₄×D₄	—	4	2	no	—
641	C₂×C₄⋊C₄	—	2	4	no	—
642	C₂×C₄⋊C₄	—	2	4	no	—
643	C₂×C₄⋊C₄	C₂³×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×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
682	C₂×C₄²	—	2	4	no	—
683	C₂×C₄²	—	4	2	no	—
684	C₂×C₄²	—	4	2	no	—
685	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
686	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
688	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
691	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
696	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
697	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
702	#95	C₂³×C₅₃	1	1	yes	characteristic
703	#95	C₂³×C₅₃	1	1	yes	characteristic
704	#95	C₂³×C₅₃	1	1	yes	characteristic
705	#95	C₂³×C₅₃	1	1	yes	characteristic
706	#95	C₂³×C₅₃	1	1	yes	characteristic
707	#95	C₂³×C₅₃	1	1	yes	characteristic
708	#95	C₂³×C₅₃	1	1	yes	characteristic
709	#95	C₂³×C₅₃	1	1	yes	characteristic
710	#95	C₂³×C₅₃	1	2	yes	—
711	#95	C₂³×C₅₃	1	2	yes	—
712	#95	C₂³×C₅₃	1	2	yes	—
713	#95	C₂³×C₅₃	1	2	yes	—
714	#95	C₂³×C₅₃	1	2	yes	—
715	#95	C₂³×C₅₃	1	2	yes	—
716	#95	C₂³×C₅₃	1	2	yes	—
717	#95	C₂³×C₅₃	1	2	yes	—
718	#95	C₂³×C₅₃	1	2	yes	—
719	#95	C₂³×C₅₃	1	2	yes	—
720	#95	C₂³×C₅₃	1	2	yes	—
721	#95	C₂³×C₅₃	1	2	yes	—
722	#95	C₂³×C₅₃	1	2	yes	—
723	#95	C₂³×C₅₃	1	2	yes	—
724	#95	C₂³×C₅₃	1	2	yes	—
725	#95	C₂³×C₅₃	1	2	yes	—
726	#95	C₂³×C₅₃	1	2	yes	—
727	#95	C₂³×C₅₃	1	2	yes	—
728	#95	C₂³×C₅₃	1	2	yes	—
729	#95	C₂³×C₅₃	1	2	yes	—
730	#95	C₂³×C₅₃	1	2	yes	—
731	#95	C₂³×C₅₃	1	2	yes	—
732	#95	C₂³×C₅₃	1	2	yes	—
733	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
734	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	2	no	—
738	C₂×Q₈	—	2	2	no	—
739	C₂×Q₈	—	2	2	no	—
740	C₂×Q₈	—	2	2	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	4	1	no	—
761	C₂²×C₄	—	4	1	no	—
762	C₂²×C₄	—	4	1	no	—
763	C₂²×C₄	—	4	1	no	—
764	C₂²×C₄	—	4	1	no	—
765	C₂²×C₄	—	4	1	no	—
766	C₂²×C₄	—	4	1	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	#41×C₅₃	1	4	yes	—
770	C₂²×C₄	#41×C₅₃	1	4	yes	—
771	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	4	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	4	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	#41×C₅₃	1	4	yes	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	4	no	—
835	C₄²	—	2	4	no	—
836	C₄²	—	2	4	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	4	1	no	—
842	C₄²	—	4	1	no	—
843	C₄²	—	4	1	no	—
844	C₄²	—	4	1	no	—
845	C₄²	—	4	2	no	—
846	C₄²	—	4	2	no	—
847	C₄²	#41×C₅₃	1	4	yes	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	C₂×#41×C₅₃	1	2	yes	—
860	C₂³	C₂×#41×C₅₃	1	2	yes	—
861	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
862	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
863	Q₈	—	4	4	no	—
864	Q₈	—	4	4	no	—
865	D₄	—	4	8	no	—
866	D₄	—	4	4	no	—
867	C₂×C₄	—	2	8	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	8	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	8	4	no	—
927	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
928	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
929	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
930	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
931	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
932	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
933	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
934	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
935	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
936	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
937	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	C₅₃×#556	1	4	yes	—
952	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
953	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
954	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
955	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
956	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
957	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
958	C₂²	C₅₃×#585	1	1	yes	characteristic
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	1	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	1	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	1	no	—
978	C₄	—	4	2	no	—
979	C₄	C₅₃×#553	1	4	yes	—
980	C₂	—	2	4	no	—
981	C₂	—	8	2	no	—
982	C₂	C₅₃×#3444	1	1	yes	characteristic
983	C₂	C₂×C₅₃×#553	1	1	yes	characteristic
984	C₂	C₂×C₅₃×#556	1	1	yes	characteristic
985	C₂	C₅₃×#3480	1	1	yes	characteristic
986	C₂	C₅₃×#3495	1	1	yes	characteristic
987	C₂	C₅₃×#3505	1	1	yes	characteristic
988	C₂	C₅₃×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂×#121×C₅₃	C₂²
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
4. C₅₃×#2594	C₂	semidirect
5. C₅₃×#2579	C₂	semidirect
6. C₅₃×#2573	C₂	semidirect
7. C₅₃×#2570	C₂	semidirect
8. C₅₃×#2545	C₂	semidirect
9. C₅₃×#2525	C₂	semidirect
10. C₅₃×#2514	C₂	semidirect
11. C₅₃×#2512	C₂	semidirect
12. C₅₃×#2510	C₂	semidirect
13. C₅₃×#2481	C₂	semidirect
14. C₅₃×#2447	C₂	semidirect
15. C₅₃×#2446	C₂	semidirect
16. C₅₃×#2373	C₂	semidirect
17. C₅₃×#2367	C₂	semidirect
18. C₅₃×#2356	C₂	semidirect
19. C₅₃×#2353	C₂	semidirect
20. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₅₃	C₂	semidirect
443. #36605	C₅₃	direct (N × H)
486. #2857	C₂×C₅₃	semidirect
489. #2594	C₂×C₅₃	semidirect
490. #2579	C₂×C₅₃	semidirect
491. #2573	C₂×C₅₃	semidirect
492. #2570	C₂×C₅₃	semidirect
493. #2545	C₂×C₅₃	semidirect
494. #2525	C₂×C₅₃	semidirect
495. #2514	C₂×C₅₃	semidirect
496. #2512	C₂×C₅₃	semidirect
497. #2510	C₂×C₅₃	semidirect
498. #2481	C₂×C₅₃	semidirect
499. #2447	C₂×C₅₃	semidirect
500. #2446	C₂×C₅₃	semidirect
501. #2373	C₂×C₅₃	semidirect
502. #2367	C₂×C₅₃	semidirect
503. #2356	C₂×C₅₃	semidirect
504. #2353	C₂×C₅₃	semidirect
505. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
506. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
508. C₂×C₄×C₄⋊C₄	C₂×C₅₃	semidirect
617. C₅₃	#36605	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×#2857	2
C₅₃×#2850	2
C₅₃×#2594	2
C₅₃×#2579	2
C₅₃×#2573	2
C₅₃×#2570	2
C₅₃×#2545	2
C₅₃×#2525	2
C₅₃×#2514	2
C₅₃×#2512	2
C₅₃×#2510	2
C₅₃×#2481	2
C₅₃×#2447	2
C₅₃×#2446	2
C₅₃×#2373	2
C₅₃×#2367	2
C₅₃×#2356	2
C₅₃×#2353	2
C₄×C₂²⋊Q₈×C₅₃	2
C₄×#121×C₅₃	2
C₂×C₄×C₄⋊C₄×C₅₃	2
#36605	53

Subgroups — C53×#36605 #27244117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36605 #27244117