Subgroups — C₅₃×#36725 #27244237

Order 13568.

3282 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2846	C₂	1	2	yes	maximal, complemented
2	C₅₃×#2736	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2735	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2735	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2697	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2685	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2685	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2684	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2678	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2670	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2668	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2626	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2617	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2480	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2472	C₂	1	2	yes	maximal, complemented
16	C₅₃×#2424	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2418	C₂	1	2	yes	maximal, complemented
18	C₅₃×#2321	C₂	1	2	yes	maximal, complemented
19	C₂×C₅₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
22	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
23	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
26	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×#120×C₅₃	C₂²	1	2	yes	—
28	C₂×#120×C₅₃	C₂²	1	2	yes	—
29	C₂×#120×C₅₃	C₂²	1	2	yes	—
30	C₂×#120×C₅₃	C₂²	1	2	yes	—
31	C₂×#120×C₅₃	C₂²	1	2	yes	—
32	C₂×#120×C₅₃	C₂²	1	2	yes	—
33	C₂×#120×C₅₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
35	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
37	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₅₃×#399	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#399	C₂²	1	2	yes	complemented
41	C₅₃×#399	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#397	C₂²	1	2	yes	complemented
43	C₅₃×#397	C₂²	1	2	yes	complemented
44	C₅₃×#397	C₂²	1	2	yes	complemented
45	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#397	C₂²	1	2	yes	complemented
47	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#397	C₂²	1	2	yes	complemented
49	C₅₃×#396	C₂²	1	2	yes	complemented
50	C₅₃×#396	C₂²	1	2	yes	complemented
51	C₅₃×#396	C₂²	1	2	yes	complemented
52	C₅₃×#396	C₂²	1	2	yes	complemented
53	C₅₃×#394	C₂²	1	2	yes	complemented
54	C₅₃×#394	C₂²	1	2	yes	complemented
55	C₅₃×#394	C₂²	1	2	yes	complemented
56	C₅₃×#394	C₂²	1	2	yes	complemented
57	C₅₃×#394	C₂²	1	2	yes	complemented
58	C₅₃×#394	C₂²	1	2	yes	complemented
59	C₅₃×#394	C₂²	1	2	yes	complemented
60	C₅₃×#394	C₂²	1	2	yes	complemented
61	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#393	C₂²	1	2	yes	complemented
63	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#392	C₂²	1	2	yes	complemented
65	C₅₃×#392	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#392	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#390	C₂²	1	2	yes	complemented
68	C₅₃×#390	C₂²	1	2	yes	complemented
69	C₅₃×#390	C₂²	1	2	yes	complemented
70	C₅₃×#390	C₂²	1	2	yes	complemented
71	C₅₃×#388	C₂²	1	2	yes	complemented
72	C₅₃×#388	C₂²	1	2	yes	complemented
73	C₅₃×#388	C₂²	1	2	yes	complemented
74	C₅₃×#388	C₂²	1	2	yes	complemented
75	C₅₃×#388	C₂²	1	2	yes	complemented
76	C₅₃×#388	C₂²	1	2	yes	complemented
77	C₅₃×#388	C₂²	1	2	yes	complemented
78	C₅₃×#388	C₂²	1	2	yes	complemented
79	C₅₃×#388	C₂²	1	2	yes	complemented
80	C₅₃×#388	C₂²	1	2	yes	complemented
81	C₅₃×#388	C₂²	1	2	yes	complemented
82	C₅₃×#388	C₂²	1	2	yes	complemented
83	C₅₃×#386	C₂²	1	2	yes	complemented
84	C₅₃×#386	C₂²	1	2	yes	complemented
85	C₅₃×#386	C₂²	1	2	yes	complemented
86	C₅₃×#386	C₂²	1	2	yes	complemented
87	C₅₃×#386	C₂²	1	2	yes	complemented
88	C₅₃×#386	C₂²	1	2	yes	complemented
89	C₅₃×#385	C₂²	1	2	yes	complemented
90	C₅₃×#385	C₂²	1	2	yes	complemented
91	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#379	C₂²	1	2	yes	—
94	C₅₃×#379	C₂²	1	2	yes	—
95	C₅₃×#379	C₂²	1	1	yes	characteristic
96	C₅₃×#379	C₂²	1	2	yes	—
97	C₅₃×#379	C₂²	1	2	yes	—
98	C₅₃×#379	C₂²	1	1	yes	characteristic
99	C₅₃×#379	C₂²	1	2	yes	—
100	C₅₃×#379	C₂²	1	2	yes	—
101	C₅₃×#379	C₂²	1	1	yes	characteristic
102	C₅₃×#379	C₂²	1	2	yes	—
103	C₅₃×#379	C₂²	1	2	yes	—
104	C₅₃×#379	C₂²	1	1	yes	characteristic
105	C₅₃×#379	C₂²	1	2	yes	—
106	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
107	C₂⁵×C₅₃	—	2	4	no	—
108	C₂⁵×C₅₃	—	4	4	no	—
109	C₂⁵×C₅₃	—	4	4	no	—
110	C₂⁵×C₅₃	—	4	2	no	—
111	C₂⁵×C₅₃	—	4	2	no	—
112	C₂⁵×C₅₃	C₂³	1	2	yes	—
113	C₂⁵×C₅₃	C₂³	1	2	yes	—
114	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
115	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
116	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
118	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
119	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
120	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
121	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
122	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
123	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
126	C₂³×C₄×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	2	yes	complemented
130	#126×C₅₃	—	4	4	no	—
131	#124×C₅₃	—	4	4	no	—
132	#123×C₅₃	—	4	4	no	—
133	C₂²⋊Q₈×C₅₃	—	4	2	no	—
134	#121×C₅₃	—	4	2	no	—
135	#121×C₅₃	—	4	4	no	—
136	#120×C₅₃	—	2	8	no	—
137	#120×C₅₃	—	4	4	no	—
138	#120×C₅₃	—	4	4	no	—
139	#120×C₅₃	—	4	4	no	—
140	#120×C₅₃	—	4	4	no	—
141	#120×C₅₃	—	4	4	no	—
142	#120×C₅₃	—	4	4	no	—
143	C₄×D₄×C₅₃	—	4	4	no	—
144	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
145	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
146	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
147	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
148	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
149	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
150	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
151	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
152	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
153	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
154	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
155	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
156	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
157	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
158	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
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	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	1	yes	characteristic
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	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
195	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
196	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
197	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
198	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
199	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
200	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
201	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
202	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
203	#95×C₅₃	C₂³	1	2	yes	complemented
204	#95×C₅₃	C₂³	1	2	yes	complemented
205	#95×C₅₃	C₂³	1	1	yes	characteristic, complemented
206	#95×C₅₃	C₂³	1	1	yes	characteristic, complemented
207	#95×C₅₃	C₂³	1	1	yes	characteristic, complemented
208	#95×C₅₃	C₂³	1	1	yes	characteristic, complemented
209	#95×C₅₃	C₂³	1	2	yes	complemented
210	#95×C₅₃	C₂³	1	2	yes	complemented
211	#95×C₅₃	C₂³	1	2	yes	complemented
212	#95×C₅₃	C₂³	1	2	yes	complemented
213	#95×C₅₃	C₂³	1	2	yes	complemented
214	#95×C₅₃	C₂³	1	2	yes	complemented
215	#95×C₅₃	C₂³	1	2	yes	complemented
216	#95×C₅₃	C₂³	1	2	yes	complemented
217	C₂⁴×C₅₃	—	2	4	no	—
218	C₂⁴×C₅₃	—	2	4	no	—
219	C₂⁴×C₅₃	—	2	4	no	—
220	C₂⁴×C₅₃	—	2	2	no	—
221	C₂⁴×C₅₃	—	2	2	no	—
222	C₂⁴×C₅₃	—	2	4	no	—
223	C₂⁴×C₅₃	—	2	2	no	—
224	C₂⁴×C₅₃	—	2	2	no	—
225	C₂⁴×C₅₃	—	2	4	no	—
226	C₂⁴×C₅₃	—	2	4	no	—
227	C₂⁴×C₅₃	—	2	4	no	—
228	C₂⁴×C₅₃	—	2	4	no	—
229	C₂⁴×C₅₃	—	2	4	no	—
230	C₂⁴×C₅₃	—	2	4	no	—
231	C₂⁴×C₅₃	—	4	2	no	—
232	C₂⁴×C₅₃	—	4	2	no	—
233	C₂⁴×C₅₃	—	4	2	no	—
234	C₂⁴×C₅₃	—	4	2	no	—
235	C₂⁴×C₅₃	—	4	2	no	—
236	C₂⁴×C₅₃	—	4	2	no	—
237	C₂⁴×C₅₃	—	4	2	no	—
238	C₂⁴×C₅₃	—	4	2	no	—
239	C₂⁴×C₅₃	—	4	2	no	—
240	C₂⁴×C₅₃	—	4	1	no	—
241	C₂⁴×C₅₃	—	4	1	no	—
242	C₂⁴×C₅₃	—	4	2	no	—
243	C₂⁴×C₅₃	—	4	1	no	—
244	C₂⁴×C₅₃	—	4	1	no	—
245	C₂⁴×C₅₃	—	4	32	no	—
246	C₂⁴×C₅₃	—	4	16	no	—
247	C₂⁴×C₅₃	—	4	32	no	—
248	C₂⁴×C₅₃	—	4	16	no	—
249	C₂⁴×C₅₃	—	4	16	no	—
250	C₂⁴×C₅₃	#41	1	4	yes	—
251	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
252	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
253	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
254	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
255	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
256	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
257	C₂×Q₈×C₅₃	—	4	1	no	—
258	C₂×Q₈×C₅₃	—	4	2	no	—
259	C₂×D₄×C₅₃	—	2	4	no	—
260	C₂×D₄×C₅₃	—	2	4	no	—
261	C₂×D₄×C₅₃	—	2	4	no	—
262	C₂×D₄×C₅₃	—	2	4	no	—
263	C₂×D₄×C₅₃	—	2	4	no	—
264	C₂×D₄×C₅₃	—	2	4	no	—
265	C₂×D₄×C₅₃	—	2	4	no	—
266	C₂×D₄×C₅₃	—	2	4	no	—
267	C₂×D₄×C₅₃	—	2	4	no	—
268	C₂×D₄×C₅₃	—	4	2	no	—
269	C₂×D₄×C₅₃	—	4	2	no	—
270	C₂×D₄×C₅₃	—	4	2	no	—
271	C₂×D₄×C₅₃	—	4	2	no	—
272	C₂×D₄×C₅₃	—	4	2	no	—
273	C₂×D₄×C₅₃	—	4	2	no	—
274	C₂×D₄×C₅₃	—	4	2	no	—
275	C₂×D₄×C₅₃	—	4	2	no	—
276	C₂×D₄×C₅₃	—	4	2	no	—
277	C₂×D₄×C₅₃	—	4	2	no	—
278	C₂×D₄×C₅₃	—	4	2	no	—
279	C₂×D₄×C₅₃	—	4	2	no	—
280	C₂×D₄×C₅₃	—	4	1	no	—
281	C₂×D₄×C₅₃	—	4	2	no	—
282	C₂²×C₄×C₅₃	—	2	4	no	—
283	C₂²×C₄×C₅₃	—	2	2	no	—
284	C₂²×C₄×C₅₃	—	2	2	no	—
285	C₂²×C₄×C₅₃	—	4	2	no	—
286	C₂²×C₄×C₅₃	—	4	2	no	—
287	C₂²×C₄×C₅₃	—	4	2	no	—
288	C₂²×C₄×C₅₃	—	4	2	no	—
289	C₂²×C₄×C₅₃	—	4	2	no	—
290	C₂²×C₄×C₅₃	—	4	2	no	—
291	C₂²×C₄×C₅₃	—	4	2	no	—
292	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₅₃	—	4	2	no	—
306	C₄⋊C₄×C₅₃	—	4	1	no	—
307	C₄⋊C₄×C₅₃	—	4	2	no	—
308	C₄⋊C₄×C₅₃	—	4	1	no	—
309	C₄⋊C₄×C₅₃	—	4	2	no	—
310	C₄⋊C₄×C₅₃	—	4	2	no	—
311	C₄⋊C₄×C₅₃	—	4	2	no	—
312	C₄⋊C₄×C₅₃	—	4	2	no	—
313	C₄⋊C₄×C₅₃	—	4	2	no	—
314	C₄⋊C₄×C₅₃	—	4	2	no	—
315	C₂²⋊C₄×C₅₃	—	2	4	no	—
316	C₂²⋊C₄×C₅₃	—	2	4	no	—
317	C₂²⋊C₄×C₅₃	—	2	4	no	—
318	C₂²⋊C₄×C₅₃	—	2	4	no	—
319	C₂²⋊C₄×C₅₃	—	2	4	no	—
320	C₂²⋊C₄×C₅₃	—	2	4	no	—
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	—	4	1	no	—
329	C₂²⋊C₄×C₅₃	—	4	2	no	—
330	C₂²⋊C₄×C₅₃	—	4	1	no	—
331	C₂²⋊C₄×C₅₃	—	4	1	no	—
332	C₂²⋊C₄×C₅₃	—	4	1	no	—
333	C₂²⋊C₄×C₅₃	—	4	1	no	—
334	C₂²⋊C₄×C₅₃	—	4	1	no	—
335	C₂²⋊C₄×C₅₃	—	4	2	no	—
336	C₂²⋊C₄×C₅₃	—	4	2	no	—
337	C₂²⋊C₄×C₅₃	—	4	2	no	—
338	C₂²⋊C₄×C₅₃	—	4	2	no	—
339	C₂²⋊C₄×C₅₃	—	4	2	no	—
340	C₂²⋊C₄×C₅₃	—	4	2	no	—
341	C₂²⋊C₄×C₅₃	—	4	2	no	—
342	C₂²⋊C₄×C₅₃	—	4	2	no	—
343	C₂²⋊C₄×C₅₃	—	4	2	no	—
344	C₂²⋊C₄×C₅₃	—	4	2	no	—
345	C₂²⋊C₄×C₅₃	—	4	2	no	—
346	C₂²⋊C₄×C₅₃	—	4	2	no	—
347	C₂²⋊C₄×C₅₃	—	4	2	no	—
348	C₂²⋊C₄×C₅₃	—	4	2	no	—
349	C₂²⋊C₄×C₅₃	—	4	2	no	—
350	C₂²⋊C₄×C₅₃	—	4	2	no	—
351	C₂²⋊C₄×C₅₃	—	4	2	no	—
352	C₂²⋊C₄×C₅₃	—	4	2	no	—
353	C₂²⋊C₄×C₅₃	—	4	2	no	—
354	C₂²⋊C₄×C₅₃	—	4	2	no	—
355	C₂²⋊C₄×C₅₃	—	4	2	no	—
356	C₂²⋊C₄×C₅₃	—	4	2	no	—
357	C₄²×C₅₃	—	4	2	no	—
358	C₄²×C₅₃	—	4	2	no	—
359	C₄²×C₅₃	—	4	2	no	—
360	C₂³×C₅₃	—	2	2	no	—
361	C₂³×C₅₃	—	2	2	no	—
362	C₂³×C₅₃	—	2	16	no	—
363	C₂³×C₅₃	—	2	8	no	—
364	C₂³×C₅₃	—	2	2	no	—
365	C₂³×C₅₃	—	2	2	no	—
366	C₂³×C₅₃	—	2	2	no	—
367	C₂³×C₅₃	—	2	2	no	—
368	C₂³×C₅₃	—	2	2	no	—
369	C₂³×C₅₃	—	2	2	no	—
370	C₂³×C₅₃	—	2	2	no	—
371	C₂³×C₅₃	—	2	2	no	—
372	C₂³×C₅₃	—	2	2	no	—
373	C₂³×C₅₃	—	2	2	no	—
374	C₂³×C₅₃	—	2	2	no	—
375	C₂³×C₅₃	—	2	2	no	—
376	C₂³×C₅₃	—	2	2	no	—
377	C₂³×C₅₃	—	2	2	no	—
378	C₂³×C₅₃	—	2	1	no	—
379	C₂³×C₅₃	—	2	1	no	—
380	C₂³×C₅₃	—	2	1	no	—
381	C₂³×C₅₃	—	2	1	no	—
382	C₂³×C₅₃	—	2	2	no	—
383	C₂³×C₅₃	—	2	2	no	—
384	C₂³×C₅₃	—	2	2	no	—
385	C₂³×C₅₃	—	2	2	no	—
386	C₂³×C₅₃	—	2	2	no	—
387	C₂³×C₅₃	—	2	2	no	—
388	C₂³×C₅₃	—	2	2	no	—
389	C₂³×C₅₃	—	2	2	no	—
390	C₂³×C₅₃	—	2	2	no	—
391	C₂³×C₅₃	—	4	8	no	—
392	C₂³×C₅₃	—	4	8	no	—
393	C₂³×C₅₃	—	4	8	no	—
394	C₂³×C₅₃	—	4	8	no	—
395	C₂³×C₅₃	—	4	8	no	—
396	C₂³×C₅₃	—	4	8	no	—
397	C₂³×C₅₃	—	4	8	no	—
398	C₂³×C₅₃	—	4	8	no	—
399	C₂³×C₅₃	—	4	8	no	—
400	C₂³×C₅₃	—	4	8	no	—
401	C₂³×C₅₃	—	4	4	no	—
402	C₂³×C₅₃	—	4	4	no	—
403	C₂³×C₅₃	—	4	8	no	—
404	C₂³×C₅₃	—	4	8	no	—
405	C₂³×C₅₃	—	4	4	no	—
406	C₂³×C₅₃	—	4	4	no	—
407	C₂³×C₅₃	—	4	8	no	—
408	C₂³×C₅₃	—	4	4	no	—
409	C₂³×C₅₃	—	4	4	no	—
410	C₂³×C₅₃	—	4	8	no	—
411	C₂³×C₅₃	—	4	8	no	—
412	C₂³×C₅₃	—	4	8	no	—
413	C₂³×C₅₃	—	4	8	no	—
414	C₂³×C₅₃	—	4	128	no	—
415	C₂³×C₅₃	—	4	8	no	—
416	C₂³×C₅₃	—	4	4	no	—
417	C₂³×C₅₃	—	4	4	no	—
418	C₂³×C₅₃	—	4	8	no	—
419	C₂³×C₅₃	C₂×#41	1	2	yes	—
420	C₂³×C₅₃	C₂×#41	1	2	yes	—
421	C₂³×C₅₃	C₂×#41	1	2	yes	—
422	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
423	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
424	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
425	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
426	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
427	Q₈×C₅₃	—	8	2	no	—
428	D₄×C₅₃	—	4	8	no	—
429	D₄×C₅₃	—	8	4	no	—
430	D₄×C₅₃	—	8	4	no	—
431	D₄×C₅₃	—	8	4	no	—
432	D₄×C₅₃	—	8	4	no	—
433	D₄×C₅₃	—	8	4	no	—
434	D₄×C₅₃	—	8	4	no	—
435	D₄×C₅₃	—	8	2	no	—
436	C₂×C₄×C₅₃	—	2	2	no	—
437	C₂×C₄×C₅₃	—	2	2	no	—
438	C₂×C₄×C₅₃	—	2	2	no	—
439	C₂×C₄×C₅₃	—	2	2	no	—
440	C₂×C₄×C₅₃	—	2	1	no	—
441	C₂×C₄×C₅₃	—	2	1	no	—
442	C₂×C₄×C₅₃	—	2	1	no	—
443	C₂×C₄×C₅₃	—	2	2	no	—
444	C₂×C₄×C₅₃	—	2	1	no	—
445	C₂×C₄×C₅₃	—	2	2	no	—
446	C₂×C₄×C₅₃	—	2	2	no	—
447	C₂×C₄×C₅₃	—	2	2	no	—
448	C₂×C₄×C₅₃	—	2	2	no	—
449	C₂×C₄×C₅₃	—	2	2	no	—
450	C₂×C₄×C₅₃	—	2	2	no	—
451	C₂×C₄×C₅₃	—	2	2	no	—
452	C₂×C₄×C₅₃	—	2	2	no	—
453	C₂×C₄×C₅₃	—	2	2	no	—
454	C₂×C₄×C₅₃	—	2	2	no	—
455	C₂×C₄×C₅₃	—	2	2	no	—
456	C₂×C₄×C₅₃	—	2	2	no	—
457	C₂×C₄×C₅₃	—	2	2	no	—
458	C₂×C₄×C₅₃	—	2	2	no	—
459	C₂×C₄×C₅₃	—	2	2	no	—
460	C₂×C₄×C₅₃	—	2	2	no	—
461	C₂×C₄×C₅₃	—	2	2	no	—
462	C₂×C₄×C₅₃	—	2	2	no	—
463	C₂×C₄×C₅₃	—	2	2	no	—
464	C₂×C₄×C₅₃	—	2	2	no	—
465	C₂×C₄×C₅₃	—	2	2	no	—
466	C₂×C₄×C₅₃	—	2	2	no	—
467	C₂×C₄×C₅₃	—	2	2	no	—
468	C₂×C₄×C₅₃	—	2	2	no	—
469	C₂×C₄×C₅₃	—	2	2	no	—
470	C₂×C₄×C₅₃	—	2	2	no	—
471	C₂×C₄×C₅₃	—	8	4	no	—
472	C₂×C₄×C₅₃	—	8	2	no	—
473	C₂×C₄×C₅₃	—	8	2	no	—
474	C₂×C₄×C₅₃	—	8	4	no	—
475	#36725	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
476	C₂²×C₅₃	—	2	4	no	—
477	C₂²×C₅₃	—	2	4	no	—
478	C₂²×C₅₃	—	2	2	no	—
479	C₂²×C₅₃	—	2	2	no	—
480	C₂²×C₅₃	—	2	2	no	—
481	C₂²×C₅₃	—	2	2	no	—
482	C₂²×C₅₃	—	2	4	no	—
483	C₂²×C₅₃	—	2	4	no	—
484	C₂²×C₅₃	—	2	4	no	—
485	C₂²×C₅₃	—	2	4	no	—
486	C₂²×C₅₃	—	2	4	no	—
487	C₂²×C₅₃	—	2	4	no	—
488	C₂²×C₅₃	—	2	4	no	—
489	C₂²×C₅₃	—	2	4	no	—
490	C₂²×C₅₃	—	4	32	no	—
491	C₂²×C₅₃	—	4	16	no	—
492	C₂²×C₅₃	—	4	32	no	—
493	C₂²×C₅₃	—	4	16	no	—
494	C₂²×C₅₃	—	4	16	no	—
495	C₂²×C₅₃	—	4	2	no	—
496	C₂²×C₅₃	—	4	2	no	—
497	C₂²×C₅₃	—	4	2	no	—
498	C₂²×C₅₃	—	4	2	no	—
499	C₂²×C₅₃	—	4	2	no	—
500	C₂²×C₅₃	—	4	1	no	—
501	C₂²×C₅₃	—	4	1	no	—
502	C₂²×C₅₃	—	4	2	no	—
503	C₂²×C₅₃	—	4	2	no	—
504	C₂²×C₅₃	—	4	2	no	—
505	C₂²×C₅₃	—	4	2	no	—
506	C₂²×C₅₃	—	4	2	no	—
507	C₂²×C₅₃	—	4	1	no	—
508	C₂²×C₅₃	—	4	1	no	—
509	C₂²×C₅₃	—	4	2	no	—
510	C₂²×C₅₃	—	4	2	no	—
511	C₂²×C₅₃	—	4	2	no	—
512	C₂²×C₅₃	—	4	2	no	—
513	C₂²×C₅₃	—	4	2	no	—
514	C₂²×C₅₃	—	4	2	no	—
515	C₂²×C₅₃	—	4	2	no	—
516	C₂²×C₅₃	#538	1	4	yes	—
517	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
518	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
520	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
521	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
522	C₄×C₅₃	—	4	2	no	—
523	C₄×C₅₃	—	4	2	no	—
524	C₄×C₅₃	—	4	2	no	—
525	C₄×C₅₃	—	4	1	no	—
526	C₄×C₅₃	—	4	2	no	—
527	C₄×C₅₃	—	4	1	no	—
528	C₄×C₅₃	—	4	2	no	—
529	C₄×C₅₃	—	4	1	no	—
530	C₄×C₅₃	—	4	2	no	—
531	C₄×C₅₃	—	4	1	no	—
532	C₄×C₅₃	—	4	2	no	—
533	C₄×C₅₃	—	4	2	no	—
534	C₄×C₅₃	—	4	2	no	—
535	#2846	C₂×C₅₃	1	2	yes	complemented
536	#2736	C₂×C₅₃	1	1	yes	characteristic, complemented
537	#2735	C₂×C₅₃	1	2	yes	complemented
538	#2735	C₂×C₅₃	1	1	yes	characteristic, complemented
539	#2697	C₂×C₅₃	1	2	yes	complemented
540	#2685	C₂×C₅₃	1	2	yes	complemented
541	#2685	C₂×C₅₃	1	2	yes	complemented
542	#2684	C₂×C₅₃	1	2	yes	complemented
543	#2678	C₂×C₅₃	1	2	yes	complemented
544	#2670	C₂×C₅₃	1	1	yes	characteristic, complemented
545	#2668	C₂×C₅₃	1	1	yes	characteristic, complemented
546	#2626	C₂×C₅₃	1	1	yes	characteristic, complemented
547	#2617	C₂×C₅₃	1	1	yes	characteristic, complemented
548	#2480	C₂×C₅₃	1	2	yes	complemented
549	#2472	C₂×C₅₃	1	2	yes	complemented
550	#2424	C₂×C₅₃	1	2	yes	complemented
551	#2418	C₂×C₅₃	1	2	yes	complemented
552	#2321	C₂×C₅₃	1	2	yes	complemented
553	C₂×#379	C₂×C₅₃	1	1	yes	characteristic, complemented
554	C₂×C₅₃	—	2	4	no	—
555	C₂×C₅₃	—	4	2	no	—
556	C₂×C₅₃	—	4	2	no	—
557	C₂×C₅₃	—	4	4	no	—
558	C₂×C₅₃	—	4	4	no	—
559	C₂×C₅₃	—	8	2	no	—
560	C₂×C₅₃	C₂×#538	1	1	yes	characteristic
561	C₂×C₅₃	#3490	1	2	yes	—
562	C₂×C₅₃	#3532	1	2	yes	—
563	C₂×C₅₃	#3532	1	1	yes	characteristic
564	C₂×C₅₃	#3532	1	1	yes	characteristic
565	C₂⁶	C₂²×C₅₃	1	1	yes	characteristic
566	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
567	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
568	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
569	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
570	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
571	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
572	C₂×#120	C₂²×C₅₃	1	2	yes	—
573	C₂×#120	C₂²×C₅₃	1	2	yes	—
574	C₂×#120	C₂²×C₅₃	1	2	yes	—
575	C₂×#120	C₂²×C₅₃	1	2	yes	—
576	C₂×#120	C₂²×C₅₃	1	2	yes	—
577	C₂×#120	C₂²×C₅₃	1	2	yes	—
578	C₂×#120	C₂²×C₅₃	1	2	yes	—
579	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
580	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
581	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
582	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
583	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
584	#399	C₂²×C₅₃	1	1	yes	characteristic, complemented
585	#399	C₂²×C₅₃	1	1	yes	characteristic, complemented
586	#399	C₂²×C₅₃	1	2	yes	complemented
587	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
588	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
589	#397	C₂²×C₅₃	1	2	yes	complemented
590	#397	C₂²×C₅₃	1	2	yes	complemented
591	#397	C₂²×C₅₃	1	2	yes	complemented
592	#397	C₂²×C₅₃	1	2	yes	complemented
593	#397	C₂²×C₅₃	1	2	yes	complemented
594	#396	C₂²×C₅₃	1	2	yes	complemented
595	#396	C₂²×C₅₃	1	2	yes	complemented
596	#396	C₂²×C₅₃	1	2	yes	complemented
597	#396	C₂²×C₅₃	1	2	yes	complemented
598	#394	C₂²×C₅₃	1	2	yes	complemented
599	#394	C₂²×C₅₃	1	2	yes	complemented
600	#394	C₂²×C₅₃	1	2	yes	complemented
601	#394	C₂²×C₅₃	1	2	yes	complemented
602	#394	C₂²×C₅₃	1	2	yes	complemented
603	#394	C₂²×C₅₃	1	2	yes	complemented
604	#394	C₂²×C₅₃	1	2	yes	complemented
605	#394	C₂²×C₅₃	1	2	yes	complemented
606	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
607	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
608	#393	C₂²×C₅₃	1	2	yes	complemented
609	#392	C₂²×C₅₃	1	1	yes	characteristic, complemented
610	#392	C₂²×C₅₃	1	1	yes	characteristic, complemented
611	#392	C₂²×C₅₃	1	2	yes	complemented
612	#390	C₂²×C₅₃	1	2	yes	complemented
613	#390	C₂²×C₅₃	1	2	yes	complemented
614	#390	C₂²×C₅₃	1	2	yes	complemented
615	#390	C₂²×C₅₃	1	2	yes	complemented
616	#388	C₂²×C₅₃	1	2	yes	complemented
617	#388	C₂²×C₅₃	1	2	yes	complemented
618	#388	C₂²×C₅₃	1	2	yes	complemented
619	#388	C₂²×C₅₃	1	2	yes	complemented
620	#388	C₂²×C₅₃	1	2	yes	complemented
621	#388	C₂²×C₅₃	1	2	yes	complemented
622	#388	C₂²×C₅₃	1	2	yes	complemented
623	#388	C₂²×C₅₃	1	2	yes	complemented
624	#388	C₂²×C₅₃	1	2	yes	complemented
625	#388	C₂²×C₅₃	1	2	yes	complemented
626	#388	C₂²×C₅₃	1	2	yes	complemented
627	#388	C₂²×C₅₃	1	2	yes	complemented
628	#386	C₂²×C₅₃	1	2	yes	complemented
629	#386	C₂²×C₅₃	1	2	yes	complemented
630	#386	C₂²×C₅₃	1	2	yes	complemented
631	#386	C₂²×C₅₃	1	2	yes	complemented
632	#386	C₂²×C₅₃	1	2	yes	complemented
633	#386	C₂²×C₅₃	1	2	yes	complemented
634	#385	C₂²×C₅₃	1	2	yes	complemented
635	#385	C₂²×C₅₃	1	2	yes	complemented
636	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
637	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
638	#379	C₂²×C₅₃	1	2	yes	—
639	#379	C₂²×C₅₃	1	2	yes	—
640	#379	C₂²×C₅₃	1	2	yes	—
641	#379	C₂²×C₅₃	1	2	yes	—
642	#379	C₂²×C₅₃	1	2	yes	—
643	#379	C₂²×C₅₃	1	2	yes	—
644	#379	C₂²×C₅₃	1	2	yes	—
645	#379	C₂²×C₅₃	1	1	yes	characteristic
646	#379	C₂²×C₅₃	1	1	yes	characteristic
647	#379	C₂²×C₅₃	1	2	yes	—
648	#379	C₂²×C₅₃	1	2	yes	—
649	#379	C₂²×C₅₃	1	1	yes	characteristic
650	#379	C₂²×C₅₃	1	1	yes	characteristic
651	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
652	C₅₃	#36725	1	1	yes	characteristic, direct product factor, Sylow
653	C₂⁵	—	2	4	no	—
654	C₂⁵	—	4	4	no	—
655	C₂⁵	—	4	4	no	—
656	C₂⁵	—	4	2	no	—
657	C₂⁵	—	4	2	no	—
658	C₂⁵	C₂³×C₅₃	1	2	yes	—
659	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
660	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
661	C₂⁵	C₂³×C₅₃	1	2	yes	—
662	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
663	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
664	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
665	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
666	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
667	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
668	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
669	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
670	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
671	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
672	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
673	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
674	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
675	C₂³×C₄	C₂³×C₅₃	1	2	yes	complemented
676	#126	—	4	4	no	—
677	#124	—	4	4	no	—
678	#123	—	4	4	no	—
679	C₂²⋊Q₈	—	4	2	no	—
680	#121	—	4	4	no	—
681	#121	—	4	2	no	—
682	#120	—	2	8	no	—
683	#120	—	4	4	no	—
684	#120	—	4	4	no	—
685	#120	—	4	4	no	—
686	#120	—	4	4	no	—
687	#120	—	4	4	no	—
688	#120	—	4	4	no	—
689	C₄×D₄	—	4	4	no	—
690	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
691	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
692	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
693	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
694	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
695	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
696	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
697	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
698	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
699	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
700	C₂×C₂²⋊C₄	—	4	4	no	—
701	C₂×C₂²⋊C₄	—	4	4	no	—
702	C₂×C₂²⋊C₄	—	4	2	no	—
703	C₂×C₂²⋊C₄	—	4	2	no	—
704	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
718	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
722	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
725	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	complemented
741	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	complemented
742	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	complemented
743	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	complemented
744	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	complemented
745	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	complemented
746	C₂×C₄²	C₂³×C₅₃	1	2	yes	complemented
747	C₂×C₄²	C₂³×C₅₃	1	2	yes	complemented
748	C₂×C₄²	C₂³×C₅₃	1	2	yes	complemented
749	#95	C₂³×C₅₃	1	2	yes	complemented
750	#95	C₂³×C₅₃	1	2	yes	complemented
751	#95	C₂³×C₅₃	1	1	yes	characteristic, complemented
752	#95	C₂³×C₅₃	1	1	yes	characteristic, complemented
753	#95	C₂³×C₅₃	1	1	yes	characteristic, complemented
754	#95	C₂³×C₅₃	1	1	yes	characteristic, complemented
755	#95	C₂³×C₅₃	1	2	yes	complemented
756	#95	C₂³×C₅₃	1	2	yes	complemented
757	#95	C₂³×C₅₃	1	2	yes	complemented
758	#95	C₂³×C₅₃	1	2	yes	complemented
759	#95	C₂³×C₅₃	1	2	yes	complemented
760	#95	C₂³×C₅₃	1	2	yes	complemented
761	#95	C₂³×C₅₃	1	2	yes	complemented
762	#95	C₂³×C₅₃	1	2	yes	complemented
763	C₂⁴	—	2	4	no	—
764	C₂⁴	—	2	4	no	—
765	C₂⁴	—	2	4	no	—
766	C₂⁴	—	2	2	no	—
767	C₂⁴	—	2	2	no	—
768	C₂⁴	—	2	2	no	—
769	C₂⁴	—	2	2	no	—
770	C₂⁴	—	2	4	no	—
771	C₂⁴	—	2	4	no	—
772	C₂⁴	—	2	4	no	—
773	C₂⁴	—	2	4	no	—
774	C₂⁴	—	2	4	no	—
775	C₂⁴	—	2	4	no	—
776	C₂⁴	—	2	4	no	—
777	C₂⁴	—	4	2	no	—
778	C₂⁴	—	4	2	no	—
779	C₂⁴	—	4	2	no	—
780	C₂⁴	—	4	2	no	—
781	C₂⁴	—	4	1	no	—
782	C₂⁴	—	4	1	no	—
783	C₂⁴	—	4	2	no	—
784	C₂⁴	—	4	2	no	—
785	C₂⁴	—	4	2	no	—
786	C₂⁴	—	4	2	no	—
787	C₂⁴	—	4	2	no	—
788	C₂⁴	—	4	1	no	—
789	C₂⁴	—	4	1	no	—
790	C₂⁴	—	4	2	no	—
791	C₂⁴	—	4	32	no	—
792	C₂⁴	—	4	16	no	—
793	C₂⁴	—	4	32	no	—
794	C₂⁴	—	4	16	no	—
795	C₂⁴	—	4	16	no	—
796	C₂⁴	#41×C₅₃	1	4	yes	—
797	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
798	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
799	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
800	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
801	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
802	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
803	C₂×Q₈	—	4	1	no	—
804	C₂×Q₈	—	4	2	no	—
805	C₂×D₄	—	2	4	no	—
806	C₂×D₄	—	2	4	no	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	4	no	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	4	no	—
811	C₂×D₄	—	2	4	no	—
812	C₂×D₄	—	2	4	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	4	2	no	—
815	C₂×D₄	—	4	2	no	—
816	C₂×D₄	—	4	2	no	—
817	C₂×D₄	—	4	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	2	no	—
820	C₂×D₄	—	4	2	no	—
821	C₂×D₄	—	4	2	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	—	4	2	no	—
824	C₂×D₄	—	4	2	no	—
825	C₂×D₄	—	4	2	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	—	4	1	no	—
828	C₂²×C₄	—	2	4	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	2	no	—
833	C₂²×C₄	—	4	2	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	2	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
839	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
840	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
846	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
851	C₄⋊C₄	—	4	2	no	—
852	C₄⋊C₄	—	4	2	no	—
853	C₄⋊C₄	—	4	1	no	—
854	C₄⋊C₄	—	4	1	no	—
855	C₄⋊C₄	—	4	2	no	—
856	C₄⋊C₄	—	4	2	no	—
857	C₄⋊C₄	—	4	2	no	—
858	C₄⋊C₄	—	4	2	no	—
859	C₄⋊C₄	—	4	2	no	—
860	C₄⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	4	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	2	4	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	1	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	—	4	1	no	—
881	C₂²⋊C₄	—	4	1	no	—
882	C₂²⋊C₄	—	4	1	no	—
883	C₂²⋊C₄	—	4	1	no	—
884	C₂²⋊C₄	—	4	1	no	—
885	C₂²⋊C₄	—	4	2	no	—
886	C₂²⋊C₄	—	4	2	no	—
887	C₂²⋊C₄	—	4	2	no	—
888	C₂²⋊C₄	—	4	2	no	—
889	C₂²⋊C₄	—	4	2	no	—
890	C₂²⋊C₄	—	4	2	no	—
891	C₂²⋊C₄	—	4	2	no	—
892	C₂²⋊C₄	—	4	2	no	—
893	C₂²⋊C₄	—	4	2	no	—
894	C₂²⋊C₄	—	4	2	no	—
895	C₂²⋊C₄	—	4	2	no	—
896	C₂²⋊C₄	—	4	2	no	—
897	C₂²⋊C₄	—	4	2	no	—
898	C₂²⋊C₄	—	4	2	no	—
899	C₂²⋊C₄	—	4	2	no	—
900	C₂²⋊C₄	—	4	2	no	—
901	C₂²⋊C₄	—	4	2	no	—
902	C₂²⋊C₄	—	4	2	no	—
903	C₄²	—	4	2	no	—
904	C₄²	—	4	2	no	—
905	C₄²	—	4	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	16	no	—
909	C₂³	—	2	8	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	2	2	no	—
928	C₂³	—	2	2	no	—
929	C₂³	—	2	2	no	—
930	C₂³	—	2	2	no	—
931	C₂³	—	2	2	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	2	no	—
934	C₂³	—	2	2	no	—
935	C₂³	—	2	2	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	4	8	no	—
938	C₂³	—	4	8	no	—
939	C₂³	—	4	8	no	—
940	C₂³	—	4	8	no	—
941	C₂³	—	4	8	no	—
942	C₂³	—	4	8	no	—
943	C₂³	—	4	8	no	—
944	C₂³	—	4	8	no	—
945	C₂³	—	4	8	no	—
946	C₂³	—	4	8	no	—
947	C₂³	—	4	4	no	—
948	C₂³	—	4	4	no	—
949	C₂³	—	4	8	no	—
950	C₂³	—	4	8	no	—
951	C₂³	—	4	4	no	—
952	C₂³	—	4	4	no	—
953	C₂³	—	4	4	no	—
954	C₂³	—	4	4	no	—
955	C₂³	—	4	8	no	—
956	C₂³	—	4	8	no	—
957	C₂³	—	4	8	no	—
958	C₂³	—	4	8	no	—
959	C₂³	—	4	8	no	—
960	C₂³	—	4	128	no	—
961	C₂³	—	4	8	no	—
962	C₂³	—	4	4	no	—
963	C₂³	—	4	4	no	—
964	C₂³	—	4	8	no	—
965	C₂³	C₂×#41×C₅₃	1	2	yes	—
966	C₂³	C₂×#41×C₅₃	1	2	yes	—
967	C₂³	C₂×#41×C₅₃	1	2	yes	—
968	C₂³	H(5,𝔽₂)×C₅₃	1	4	yes	—
969	C₂³	H(5,𝔽₂)×C₅₃	1	4	yes	—
970	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
971	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
972	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
973	Q₈	—	8	2	no	—
974	D₄	—	4	8	no	—
975	D₄	—	8	4	no	—
976	D₄	—	8	4	no	—
977	D₄	—	8	4	no	—
978	D₄	—	8	4	no	—
979	D₄	—	8	4	no	—
980	D₄	—	8	4	no	—
981	D₄	—	8	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	8	4	no	—
1018	C₂×C₄	—	8	2	no	—
1019	C₂×C₄	—	8	2	no	—
1020	C₂×C₄	—	8	4	no	—
1021	C₂²	—	2	4	no	—
1022	C₂²	—	2	4	no	—
1023	C₂²	—	2	2	no	—
1024	C₂²	—	2	2	no	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	4	no	—
1028	C₂²	—	2	4	no	—
1029	C₂²	—	2	4	no	—
1030	C₂²	—	2	4	no	—
1031	C₂²	—	2	4	no	—
1032	C₂²	—	2	4	no	—
1033	C₂²	—	2	4	no	—
1034	C₂²	—	2	4	no	—
1035	C₂²	—	4	32	no	—
1036	C₂²	—	4	16	no	—
1037	C₂²	—	4	32	no	—
1038	C₂²	—	4	16	no	—
1039	C₂²	—	4	16	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	4	2	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	—	4	1	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	—	4	2	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	C₅₃×#538	1	4	yes	—
1062	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1063	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1064	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1065	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1066	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	2	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	2	no	—
1080	C₂	—	2	4	no	—
1081	C₂	—	4	2	no	—
1082	C₂	—	4	2	no	—
1083	C₂	—	4	4	no	—
1084	C₂	—	4	4	no	—
1085	C₂	—	8	2	no	—
1086	C₂	C₂×C₅₃×#538	1	1	yes	characteristic
1087	C₂	C₅₃×#3490	1	2	yes	—
1088	C₂	C₅₃×#3532	1	2	yes	—
1089	C₂	C₅₃×#3532	1	1	yes	characteristic
1090	C₂	C₅₃×#3532	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
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×#2846	C₂	semidirect
2. C₅₃×#2736	C₂	semidirect
3. C₅₃×#2735	C₂	semidirect
4. C₅₃×#2735	C₂	semidirect
5. C₅₃×#2697	C₂	semidirect
6. C₅₃×#2685	C₂	semidirect
7. C₅₃×#2685	C₂	semidirect
8. C₅₃×#2684	C₂	semidirect
9. C₅₃×#2678	C₂	semidirect
10. C₅₃×#2670	C₂	semidirect
11. C₅₃×#2668	C₂	semidirect
12. C₅₃×#2626	C₂	semidirect
13. C₅₃×#2617	C₂	semidirect
14. C₅₃×#2480	C₂	semidirect
15. C₅₃×#2472	C₂	semidirect
16. C₅₃×#2424	C₂	semidirect
17. C₅₃×#2418	C₂	semidirect
18. C₅₃×#2321	C₂	semidirect
19. C₂×C₅₃×#379	C₂	semidirect
21. C₂×#126×C₅₃	C₂²	semidirect
22. C₂×#124×C₅₃	C₂²	semidirect
23. C₂×#123×C₅₃	C₂²	semidirect
24. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
25. C₂×#121×C₅₃	C₂²	semidirect
26. C₂×#121×C₅₃	C₂²	semidirect
34. C₂×C₄×D₄×C₅₃	C₂²	semidirect
39. C₅₃×#399	C₂²	semidirect
40. C₅₃×#399	C₂²	semidirect
41. C₅₃×#399	C₂²	semidirect
42. C₅₃×#397	C₂²	semidirect
43. C₅₃×#397	C₂²	semidirect
44. C₅₃×#397	C₂²	semidirect
45. C₅₃×#397	C₂²	semidirect
46. C₅₃×#397	C₂²	semidirect
47. C₅₃×#397	C₂²	semidirect
48. C₅₃×#397	C₂²	semidirect
49. C₅₃×#396	C₂²	semidirect
50. C₅₃×#396	C₂²	semidirect
51. C₅₃×#396	C₂²	semidirect
52. C₅₃×#396	C₂²	semidirect
53. C₅₃×#394	C₂²	semidirect
54. C₅₃×#394	C₂²	semidirect
55. C₅₃×#394	C₂²	semidirect
56. C₅₃×#394	C₂²	semidirect
57. C₅₃×#394	C₂²	semidirect
58. C₅₃×#394	C₂²	semidirect
59. C₅₃×#394	C₂²	semidirect
60. C₅₃×#394	C₂²	semidirect
61. C₅₃×#393	C₂²	semidirect
62. C₅₃×#393	C₂²	semidirect
63. C₅₃×#393	C₂²	semidirect
64. C₅₃×#392	C₂²	semidirect
65. C₅₃×#392	C₂²	semidirect
66. C₅₃×#392	C₂²	semidirect
67. C₅₃×#390	C₂²	semidirect
68. C₅₃×#390	C₂²	semidirect
69. C₅₃×#390	C₂²	semidirect
70. C₅₃×#390	C₂²	semidirect
71. C₅₃×#388	C₂²	semidirect
72. C₅₃×#388	C₂²	semidirect
73. C₅₃×#388	C₂²	semidirect
74. C₅₃×#388	C₂²	semidirect
75. C₅₃×#388	C₂²	semidirect
76. C₅₃×#388	C₂²	semidirect
77. C₅₃×#388	C₂²	semidirect
78. C₅₃×#388	C₂²	semidirect
79. C₅₃×#388	C₂²	semidirect
80. C₅₃×#388	C₂²	semidirect
81. C₅₃×#388	C₂²	semidirect
82. C₅₃×#388	C₂²	semidirect
83. C₅₃×#386	C₂²	semidirect
84. C₅₃×#386	C₂²	semidirect
85. C₅₃×#386	C₂²	semidirect
86. C₅₃×#386	C₂²	semidirect
87. C₅₃×#386	C₂²	semidirect
88. C₅₃×#386	C₂²	semidirect
89. C₅₃×#385	C₂²	semidirect
90. C₅₃×#385	C₂²	semidirect
91. C₅₃×#380	C₂²	semidirect
92. C₅₃×#380	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
117. C₂²×Q₈×C₅₃	C₂³	semidirect
125. C₂²×D₄×C₅₃	C₂³	semidirect
129. C₂³×C₄×C₅₃	C₂³	semidirect
144. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
145. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
146. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
147. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
148. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
149. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
150. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
151. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
152. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
153. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
194. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
195. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
196. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
197. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
198. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
199. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
200. C₂×C₄²×C₅₃	C₂³	semidirect
201. C₂×C₄²×C₅₃	C₂³	semidirect
202. C₂×C₄²×C₅₃	C₂³	semidirect
203. #95×C₅₃	C₂³	semidirect
204. #95×C₅₃	C₂³	semidirect
205. #95×C₅₃	C₂³	semidirect
206. #95×C₅₃	C₂³	semidirect
207. #95×C₅₃	C₂³	semidirect
208. #95×C₅₃	C₂³	semidirect
209. #95×C₅₃	C₂³	semidirect
210. #95×C₅₃	C₂³	semidirect
211. #95×C₅₃	C₂³	semidirect
212. #95×C₅₃	C₂³	semidirect
213. #95×C₅₃	C₂³	semidirect
214. #95×C₅₃	C₂³	semidirect
215. #95×C₅₃	C₂³	semidirect
216. #95×C₅₃	C₂³	semidirect
475. #36725	C₅₃	direct (N × H)
535. #2846	C₂×C₅₃	semidirect
536. #2736	C₂×C₅₃	semidirect
537. #2735	C₂×C₅₃	semidirect
538. #2735	C₂×C₅₃	semidirect
539. #2697	C₂×C₅₃	semidirect
540. #2685	C₂×C₅₃	semidirect
541. #2685	C₂×C₅₃	semidirect
542. #2684	C₂×C₅₃	semidirect
543. #2678	C₂×C₅₃	semidirect
544. #2670	C₂×C₅₃	semidirect
545. #2668	C₂×C₅₃	semidirect
546. #2626	C₂×C₅₃	semidirect
547. #2617	C₂×C₅₃	semidirect
548. #2480	C₂×C₅₃	semidirect
549. #2472	C₂×C₅₃	semidirect
550. #2424	C₂×C₅₃	semidirect
551. #2418	C₂×C₅₃	semidirect
552. #2321	C₂×C₅₃	semidirect
553. C₂×#379	C₂×C₅₃	semidirect
566. C₂×#126	C₂²×C₅₃	semidirect
567. C₂×#124	C₂²×C₅₃	semidirect
568. C₂×#123	C₂²×C₅₃	semidirect
569. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
570. C₂×#121	C₂²×C₅₃	semidirect
571. C₂×#121	C₂²×C₅₃	semidirect
579. C₂×C₄×D₄	C₂²×C₅₃	semidirect
584. #399	C₂²×C₅₃	semidirect
585. #399	C₂²×C₅₃	semidirect
586. #399	C₂²×C₅₃	semidirect
587. #397	C₂²×C₅₃	semidirect
588. #397	C₂²×C₅₃	semidirect
589. #397	C₂²×C₅₃	semidirect
590. #397	C₂²×C₅₃	semidirect
591. #397	C₂²×C₅₃	semidirect
592. #397	C₂²×C₅₃	semidirect
593. #397	C₂²×C₅₃	semidirect
594. #396	C₂²×C₅₃	semidirect
595. #396	C₂²×C₅₃	semidirect
596. #396	C₂²×C₅₃	semidirect
597. #396	C₂²×C₅₃	semidirect
598. #394	C₂²×C₅₃	semidirect
599. #394	C₂²×C₅₃	semidirect
600. #394	C₂²×C₅₃	semidirect
601. #394	C₂²×C₅₃	semidirect
602. #394	C₂²×C₅₃	semidirect
603. #394	C₂²×C₅₃	semidirect
604. #394	C₂²×C₅₃	semidirect
605. #394	C₂²×C₅₃	semidirect
606. #393	C₂²×C₅₃	semidirect
607. #393	C₂²×C₅₃	semidirect
608. #393	C₂²×C₅₃	semidirect
609. #392	C₂²×C₅₃	semidirect
610. #392	C₂²×C₅₃	semidirect
611. #392	C₂²×C₅₃	semidirect
612. #390	C₂²×C₅₃	semidirect
613. #390	C₂²×C₅₃	semidirect
614. #390	C₂²×C₅₃	semidirect
615. #390	C₂²×C₅₃	semidirect
616. #388	C₂²×C₅₃	semidirect
617. #388	C₂²×C₅₃	semidirect
618. #388	C₂²×C₅₃	semidirect
619. #388	C₂²×C₅₃	semidirect
620. #388	C₂²×C₅₃	semidirect
621. #388	C₂²×C₅₃	semidirect
622. #388	C₂²×C₅₃	semidirect
623. #388	C₂²×C₅₃	semidirect
624. #388	C₂²×C₅₃	semidirect
625. #388	C₂²×C₅₃	semidirect
626. #388	C₂²×C₅₃	semidirect
627. #388	C₂²×C₅₃	semidirect
628. #386	C₂²×C₅₃	semidirect
629. #386	C₂²×C₅₃	semidirect
630. #386	C₂²×C₅₃	semidirect
631. #386	C₂²×C₅₃	semidirect
632. #386	C₂²×C₅₃	semidirect
633. #386	C₂²×C₅₃	semidirect
634. #385	C₂²×C₅₃	semidirect
635. #385	C₂²×C₅₃	semidirect
636. #380	C₂²×C₅₃	semidirect
637. #380	C₂²×C₅₃	semidirect
651. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
652. C₅₃	#36725	direct (N × H)
663. C₂²×Q₈	C₂³×C₅₃	semidirect
671. C₂²×D₄	C₂³×C₅₃	semidirect
675. C₂³×C₄	C₂³×C₅₃	semidirect
690. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
691. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
692. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
693. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
694. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
695. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
696. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
697. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
698. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
699. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
740. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
741. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
742. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
743. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
744. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
745. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
746. C₂×C₄²	C₂³×C₅₃	semidirect
747. C₂×C₄²	C₂³×C₅₃	semidirect
748. C₂×C₄²	C₂³×C₅₃	semidirect
749. #95	C₂³×C₅₃	semidirect
750. #95	C₂³×C₅₃	semidirect
751. #95	C₂³×C₅₃	semidirect
752. #95	C₂³×C₅₃	semidirect
753. #95	C₂³×C₅₃	semidirect
754. #95	C₂³×C₅₃	semidirect
755. #95	C₂³×C₅₃	semidirect
756. #95	C₂³×C₅₃	semidirect
757. #95	C₂³×C₅₃	semidirect
758. #95	C₂³×C₅₃	semidirect
759. #95	C₂³×C₅₃	semidirect
760. #95	C₂³×C₅₃	semidirect
761. #95	C₂³×C₅₃	semidirect
762. #95	C₂³×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#2846	2
C₅₃×#2736	2
C₅₃×#2735	2
C₅₃×#2697	2
C₅₃×#2685	2
C₅₃×#2684	2
C₅₃×#2678	2
C₅₃×#2670	2
C₅₃×#2668	2
C₅₃×#2626	2
C₅₃×#2617	2
C₅₃×#2480	2
C₅₃×#2472	2
C₅₃×#2424	2
C₅₃×#2418	2
C₅₃×#2321	2
C₂×C₅₃×#379	2
#36725	53

Subgroups — C53×#36725 #27244237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36725 #27244237