Subgroups — C₅₃×#34681 #27242193

Order 13568.

3700 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#525	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2472	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2464	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2461	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2452	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2424	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2416	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2392	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2388	C₂	1	2	yes	maximal, complemented
18	C₄×#127×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#120×C₅₃	C₂	1	2	yes	maximal, complemented
22	C₅₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
25	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₅₃	C₂²	1	2	yes	—
27	C₅₃×#532	—	2	8	no	—
28	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
32	C₅₃×#525	—	2	16	no	—
33	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
34	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
35	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
37	C₂×#121×C₅₃	C₂²	1	2	yes	—
38	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
42	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
43	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×#120×C₅₃	C₂²	1	2	yes	—
45	C₂×#120×C₅₃	C₂²	1	2	yes	—
46	C₂×#120×C₅₃	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₅₃	—	2	8	no	—
48	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
52	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
54	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
59	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
61	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
62	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
63	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
64	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
65	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
66	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
67	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#398	C₂²	1	2	yes	complemented
69	C₅₃×#397	C₂²	1	2	yes	complemented
70	C₅₃×#396	C₂²	1	2	yes	complemented
71	C₅₃×#396	C₂²	1	2	yes	complemented
72	C₅₃×#395	C₂²	1	2	yes	complemented
73	C₅₃×#394	C₂²	1	2	yes	—
74	C₅₃×#394	C₂²	1	2	yes	complemented
75	C₅₃×#394	C₂²	1	2	yes	complemented
76	C₅₃×#394	C₂²	1	2	yes	complemented
77	C₅₃×#394	C₂²	1	2	yes	complemented
78	C₅₃×#394	C₂²	1	2	yes	complemented
79	C₅₃×#393	C₂²	1	2	yes	complemented
80	C₅₃×#392	C₂²	1	2	yes	—
81	C₅₃×#392	C₂²	1	2	yes	—
82	C₅₃×#392	C₂²	1	2	yes	—
83	C₅₃×#392	C₂²	1	2	yes	complemented
84	C₅₃×#390	C₂²	1	1	yes	characteristic
85	C₅₃×#390	C₂²	1	1	yes	characteristic
86	C₅₃×#390	C₂²	1	1	yes	characteristic
87	C₅₃×#390	C₂²	1	1	yes	characteristic
88	C₅₃×#390	C₂²	1	2	yes	complemented
89	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#390	C₂²	1	2	yes	complemented
92	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#388	C₂²	1	2	yes	complemented
97	C₅₃×#388	C₂²	1	2	yes	complemented
98	C₅₃×#388	C₂²	1	2	yes	complemented
99	C₅₃×#388	C₂²	1	2	yes	complemented
100	C₅₃×#386	C₂²	1	2	yes	—
101	C₅₃×#386	C₂²	1	2	yes	—
102	C₅₃×#386	C₂²	1	2	yes	complemented
103	C₅₃×#386	C₂²	1	2	yes	complemented
104	C₅₃×#386	C₂²	1	2	yes	complemented
105	C₅₃×#385	C₂²	1	2	yes	—
106	C₅₃×#385	C₂²	1	2	yes	complemented
107	C₅₃×#385	C₂²	1	2	yes	complemented
108	C₅₃×#384	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#380	C₂²	1	1	yes	characteristic
110	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#379	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
123	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
124	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
125	C₄³×C₅₃	C₂²	1	1	yes	characteristic, complemented
126	C₂⁵×C₅₃	C₂³	1	2	yes	—
127	C₂×#41×C₅₃	—	2	8	no	—
128	C₂×#41×C₅₃	—	2	8	no	—
129	C₂×#41×C₅₃	—	4	4	no	—
130	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
131	C₂²×D₄×C₅₃	—	2	4	no	—
132	C₂²×D₄×C₅₃	—	2	4	no	—
133	C₂²×D₄×C₅₃	—	2	4	no	—
134	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
135	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
136	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
138	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
140	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
142	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
143	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
144	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₅₃	—	2	8	no	—
148	C₂³×C₄×C₅₃	—	2	8	no	—
149	C₂³×C₄×C₅₃	—	4	4	no	—
150	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
152	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
153	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
156	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
157	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
158	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
159	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
160	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
161	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₅₃	—	2	4	no	—
163	#127×C₅₃	—	2	4	no	—
164	#127×C₅₃	—	2	4	no	—
165	#124×C₅₃	—	2	8	no	—
166	#123×C₅₃	—	2	8	no	—
167	#123×C₅₃	—	2	8	no	—
168	C₂²⋊Q₈×C₅₃	—	2	8	no	—
169	C₂²⋊Q₈×C₅₃	—	2	8	no	—
170	#121×C₅₃	—	2	4	no	—
171	#121×C₅₃	—	2	8	no	—
172	#121×C₅₃	—	2	8	no	—
173	#121×C₅₃	—	2	8	no	—
174	#121×C₅₃	—	2	4	no	—
175	#121×C₅₃	—	2	4	no	—
176	#121×C₅₃	—	2	4	no	—
177	#120×C₅₃	—	2	8	no	—
178	#120×C₅₃	—	2	8	no	—
179	#120×C₅₃	—	2	8	no	—
180	C₄×D₄×C₅₃	—	2	4	no	—
181	C₄×D₄×C₅₃	—	2	8	no	—
182	C₄×D₄×C₅₃	—	2	4	no	—
183	C₄×D₄×C₅₃	—	2	4	no	—
184	C₄×D₄×C₅₃	—	2	4	no	—
185	C₄×D₄×C₅₃	—	2	8	no	—
186	C₄×D₄×C₅₃	—	2	4	no	—
187	C₄×D₄×C₅₃	—	2	8	no	—
188	C₄×D₄×C₅₃	—	2	8	no	—
189	C₄×D₄×C₅₃	—	2	8	no	—
190	C₄×D₄×C₅₃	—	2	8	no	—
191	C₄×D₄×C₅₃	—	2	4	no	—
192	C₄×D₄×C₅₃	—	4	4	no	—
193	C₄×D₄×C₅₃	D₄	1	8	yes	complemented
194	C₄×D₄×C₅₃	D₄	1	8	yes	complemented
195	#117×C₅₃	—	2	8	no	—
196	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
197	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
207	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
211	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
214	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
233	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
234	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
235	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
236	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
238	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
239	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
240	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₅₃	—	2	4	no	—
244	C₂×C₄²×C₅₃	—	2	4	no	—
245	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
256	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
259	#95×C₅₃	C₂³	1	1	yes	characteristic
260	#95×C₅₃	C₂³	1	1	yes	characteristic
261	#95×C₅₃	C₂³	1	1	yes	characteristic
262	#95×C₅₃	C₂³	1	1	yes	characteristic
263	#95×C₅₃	C₂³	1	1	yes	characteristic
264	#95×C₅₃	C₂³	1	1	yes	characteristic
265	#95×C₅₃	C₂³	1	2	yes	—
266	#95×C₅₃	C₂³	1	2	yes	—
267	#95×C₅₃	C₂³	1	2	yes	—
268	#95×C₅₃	C₂³	1	2	yes	—
269	#95×C₅₃	C₂³	1	2	yes	—
270	#95×C₅₃	C₂³	1	2	yes	—
271	#95×C₅₃	C₂³	1	2	yes	—
272	C₂⁴×C₅₃	—	2	4	no	—
273	C₂⁴×C₅₃	—	2	4	no	—
274	C₂⁴×C₅₃	—	2	4	no	—
275	C₂⁴×C₅₃	—	2	4	no	—
276	C₂⁴×C₅₃	—	2	4	no	—
277	C₂⁴×C₅₃	—	4	2	no	—
278	C₂⁴×C₅₃	—	4	2	no	—
279	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
280	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
281	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
282	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
283	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
284	#41×C₅₃	—	4	32	no	—
285	C₂×Q₈×C₅₃	—	2	4	no	—
286	C₂×Q₈×C₅₃	—	2	4	no	—
287	C₂×Q₈×C₅₃	—	4	2	no	—
288	C₂×D₄×C₅₃	—	2	32	no	—
289	C₂×D₄×C₅₃	—	2	4	no	—
290	C₂×D₄×C₅₃	—	2	2	no	—
291	C₂×D₄×C₅₃	—	2	2	no	—
292	C₂×D₄×C₅₃	—	2	4	no	—
293	C₂×D₄×C₅₃	—	2	4	no	—
294	C₂×D₄×C₅₃	—	2	4	no	—
295	C₂×D₄×C₅₃	—	2	4	no	—
296	C₂×D₄×C₅₃	—	2	4	no	—
297	C₂×D₄×C₅₃	—	2	4	no	—
298	C₂×D₄×C₅₃	—	2	4	no	—
299	C₂×D₄×C₅₃	—	2	4	no	—
300	C₂×D₄×C₅₃	—	2	4	no	—
301	C₂×D₄×C₅₃	—	2	4	no	—
302	C₂×D₄×C₅₃	—	2	4	no	—
303	C₂×D₄×C₅₃	—	2	4	no	—
304	C₂×D₄×C₅₃	—	2	4	no	—
305	C₂×D₄×C₅₃	—	2	2	no	—
306	C₂×D₄×C₅₃	—	2	4	no	—
307	C₂×D₄×C₅₃	—	2	2	no	—
308	C₂×D₄×C₅₃	—	2	4	no	—
309	C₂×D₄×C₅₃	—	2	4	no	—
310	C₂×D₄×C₅₃	—	2	4	no	—
311	C₂×D₄×C₅₃	—	2	2	no	—
312	C₂×D₄×C₅₃	—	2	2	no	—
313	C₂×D₄×C₅₃	—	2	2	no	—
314	C₂×D₄×C₅₃	—	2	4	no	—
315	C₂×D₄×C₅₃	—	2	4	no	—
316	C₂×D₄×C₅₃	—	2	2	no	—
317	C₂×D₄×C₅₃	—	2	2	no	—
318	C₂×D₄×C₅₃	—	4	2	no	—
319	C₂×D₄×C₅₃	—	4	2	no	—
320	C₂×D₄×C₅₃	—	4	2	no	—
321	C₂×D₄×C₅₃	—	4	2	no	—
322	C₂×D₄×C₅₃	—	4	2	no	—
323	C₂×D₄×C₅₃	—	4	2	no	—
324	C₂×D₄×C₅₃	—	4	2	no	—
325	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
326	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
327	C₂×D₄×C₅₃	#41	1	4	yes	complemented
328	C₂²×C₄×C₅₃	—	2	2	no	—
329	C₂²×C₄×C₅₃	—	2	2	no	—
330	C₂²×C₄×C₅₃	—	2	2	no	—
331	C₂²×C₄×C₅₃	—	2	4	no	—
332	C₂²×C₄×C₅₃	—	2	2	no	—
333	C₂²×C₄×C₅₃	—	2	2	no	—
334	C₂²×C₄×C₅₃	—	2	4	no	—
335	C₂²×C₄×C₅₃	—	2	2	no	—
336	C₂²×C₄×C₅₃	—	2	4	no	—
337	C₂²×C₄×C₅₃	—	2	4	no	—
338	C₂²×C₄×C₅₃	—	2	2	no	—
339	C₂²×C₄×C₅₃	—	2	2	no	—
340	C₂²×C₄×C₅₃	—	2	2	no	—
341	C₂²×C₄×C₅₃	—	2	2	no	—
342	C₂²×C₄×C₅₃	—	2	4	no	—
343	C₂²×C₄×C₅₃	—	2	4	no	—
344	C₂²×C₄×C₅₃	—	2	4	no	—
345	C₂²×C₄×C₅₃	—	2	4	no	—
346	C₂²×C₄×C₅₃	—	2	4	no	—
347	C₂²×C₄×C₅₃	—	2	4	no	—
348	C₂²×C₄×C₅₃	—	2	4	no	—
349	C₂²×C₄×C₅₃	—	2	4	no	—
350	C₂²×C₄×C₅₃	—	2	2	no	—
351	C₂²×C₄×C₅₃	—	2	2	no	—
352	C₂²×C₄×C₅₃	—	2	2	no	—
353	C₂²×C₄×C₅₃	—	2	4	no	—
354	C₂²×C₄×C₅₃	—	2	4	no	—
355	C₂²×C₄×C₅₃	—	4	2	no	—
356	C₂²×C₄×C₅₃	—	4	2	no	—
357	C₂²×C₄×C₅₃	—	4	2	no	—
358	C₂²×C₄×C₅₃	—	4	1	no	—
359	C₂²×C₄×C₅₃	—	4	1	no	—
360	C₂²×C₄×C₅₃	—	4	32	no	—
361	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
362	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
363	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	complemented
364	C₂²×C₄×C₅₃	#41	1	4	yes	complemented
365	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
377	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₅₃	—	2	4	no	—
384	C₄⋊C₄×C₅₃	—	2	2	no	—
385	C₄⋊C₄×C₅₃	—	2	4	no	—
386	C₄⋊C₄×C₅₃	—	2	4	no	—
387	C₄⋊C₄×C₅₃	—	2	4	no	—
388	C₄⋊C₄×C₅₃	—	2	2	no	—
389	C₄⋊C₄×C₅₃	—	2	4	no	—
390	C₄⋊C₄×C₅₃	—	2	4	no	—
391	C₄⋊C₄×C₅₃	—	2	4	no	—
392	C₄⋊C₄×C₅₃	—	2	2	no	—
393	C₄⋊C₄×C₅₃	—	2	2	no	—
394	C₄⋊C₄×C₅₃	—	2	2	no	—
395	C₄⋊C₄×C₅₃	—	2	2	no	—
396	C₄⋊C₄×C₅₃	—	4	2	no	—
397	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
398	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	complemented
399	C₂²⋊C₄×C₅₃	—	2	4	no	—
400	C₂²⋊C₄×C₅₃	—	2	4	no	—
401	C₂²⋊C₄×C₅₃	—	2	4	no	—
402	C₂²⋊C₄×C₅₃	—	2	4	no	—
403	C₂²⋊C₄×C₅₃	—	2	2	no	—
404	C₂²⋊C₄×C₅₃	—	2	4	no	—
405	C₂²⋊C₄×C₅₃	—	2	4	no	—
406	C₂²⋊C₄×C₅₃	—	2	4	no	—
407	C₂²⋊C₄×C₅₃	—	2	4	no	—
408	C₂²⋊C₄×C₅₃	—	2	4	no	—
409	C₂²⋊C₄×C₅₃	—	2	4	no	—
410	C₂²⋊C₄×C₅₃	—	2	4	no	—
411	C₂²⋊C₄×C₅₃	—	2	4	no	—
412	C₂²⋊C₄×C₅₃	—	2	4	no	—
413	C₂²⋊C₄×C₅₃	—	2	4	no	—
414	C₂²⋊C₄×C₅₃	—	2	4	no	—
415	C₂²⋊C₄×C₅₃	—	2	2	no	—
416	C₂²⋊C₄×C₅₃	—	2	2	no	—
417	C₂²⋊C₄×C₅₃	—	2	4	no	—
418	C₂²⋊C₄×C₅₃	—	2	4	no	—
419	C₂²⋊C₄×C₅₃	—	2	4	no	—
420	C₂²⋊C₄×C₅₃	—	4	2	no	—
421	C₂²⋊C₄×C₅₃	—	4	2	no	—
422	C₂²⋊C₄×C₅₃	—	4	2	no	—
423	C₂²⋊C₄×C₅₃	—	4	2	no	—
424	C₂²⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
425	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
426	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	complemented
427	C₂²⋊C₄×C₅₃	#41	1	4	yes	complemented
428	C₄²×C₅₃	—	2	2	no	—
429	C₄²×C₅₃	—	2	2	no	—
430	C₄²×C₅₃	—	2	2	no	—
431	C₄²×C₅₃	—	2	2	no	—
432	C₄²×C₅₃	—	2	2	no	—
433	C₄²×C₅₃	—	2	2	no	—
434	C₄²×C₅₃	—	2	4	no	—
435	C₄²×C₅₃	—	2	2	no	—
436	C₄²×C₅₃	—	2	2	no	—
437	C₄²×C₅₃	—	2	2	no	—
438	C₄²×C₅₃	—	2	2	no	—
439	C₄²×C₅₃	—	4	1	no	—
440	C₄²×C₅₃	C₂×D₄	1	4	yes	—
441	C₄²×C₅₃	C₂×D₄	1	4	yes	complemented
442	C₂³×C₅₃	—	2	1	no	—
443	C₂³×C₅₃	—	2	1	no	—
444	C₂³×C₅₃	—	2	1	no	—
445	C₂³×C₅₃	—	2	1	no	—
446	C₂³×C₅₃	—	2	16	no	—
447	C₂³×C₅₃	—	2	1	no	—
448	C₂³×C₅₃	—	2	2	no	—
449	C₂³×C₅₃	—	2	2	no	—
450	C₂³×C₅₃	—	2	2	no	—
451	C₂³×C₅₃	—	2	1	no	—
452	C₂³×C₅₃	—	2	1	no	—
453	C₂³×C₅₃	—	2	1	no	—
454	C₂³×C₅₃	—	2	2	no	—
455	C₂³×C₅₃	—	2	2	no	—
456	C₂³×C₅₃	—	2	2	no	—
457	C₂³×C₅₃	—	2	2	no	—
458	C₂³×C₅₃	—	2	2	no	—
459	C₂³×C₅₃	—	2	2	no	—
460	C₂³×C₅₃	—	2	2	no	—
461	C₂³×C₅₃	—	2	1	no	—
462	C₂³×C₅₃	—	2	1	no	—
463	C₂³×C₅₃	—	2	2	no	—
464	C₂³×C₅₃	—	2	2	no	—
465	C₂³×C₅₃	—	2	2	no	—
466	C₂³×C₅₃	—	2	2	no	—
467	C₂³×C₅₃	—	2	2	no	—
468	C₂³×C₅₃	—	2	2	no	—
469	C₂³×C₅₃	—	2	2	no	—
470	C₂³×C₅₃	—	2	2	no	—
471	C₂³×C₅₃	—	2	2	no	—
472	C₂³×C₅₃	—	4	8	no	—
473	C₂³×C₅₃	—	4	8	no	—
474	C₂³×C₅₃	—	4	8	no	—
475	C₂³×C₅₃	—	4	8	no	—
476	C₂³×C₅₃	—	4	8	no	—
477	C₂³×C₅₃	—	4	8	no	—
478	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
479	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
480	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
481	C₂³×C₅₃	C₂×#41	1	4	yes	—
482	C₂³×C₅₃	C₂×#41	1	2	yes	—
483	C₂³×C₅₃	C₂×#41	1	2	yes	—
484	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
485	Q₈×C₅₃	—	4	8	no	—
486	D₄×C₅₃	—	2	16	no	—
487	D₄×C₅₃	—	2	8	no	—
488	D₄×C₅₃	—	2	8	no	—
489	D₄×C₅₃	—	2	8	no	—
490	D₄×C₅₃	—	4	8	no	—
491	D₄×C₅₃	—	4	8	no	—
492	D₄×C₅₃	—	4	8	no	—
493	D₄×C₅₃	—	4	8	no	—
494	D₄×C₅₃	—	4	8	no	—
495	D₄×C₅₃	—	4	8	no	—
496	D₄×C₅₃	—	4	8	no	—
497	D₄×C₅₃	—	4	8	no	—
498	D₄×C₅₃	—	4	4	no	—
499	C₂×C₄×C₅₃	—	2	1	no	—
500	C₂×C₄×C₅₃	—	2	2	no	—
501	C₂×C₄×C₅₃	—	2	1	no	—
502	C₂×C₄×C₅₃	—	2	1	no	—
503	C₂×C₄×C₅₃	—	2	1	no	—
504	C₂×C₄×C₅₃	—	2	1	no	—
505	C₂×C₄×C₅₃	—	2	1	no	—
506	C₂×C₄×C₅₃	—	2	1	no	—
507	C₂×C₄×C₅₃	—	2	1	no	—
508	C₂×C₄×C₅₃	—	2	1	no	—
509	C₂×C₄×C₅₃	—	2	1	no	—
510	C₂×C₄×C₅₃	—	2	1	no	—
511	C₂×C₄×C₅₃	—	2	2	no	—
512	C₂×C₄×C₅₃	—	2	1	no	—
513	C₂×C₄×C₅₃	—	2	1	no	—
514	C₂×C₄×C₅₃	—	2	1	no	—
515	C₂×C₄×C₅₃	—	2	1	no	—
516	C₂×C₄×C₅₃	—	2	1	no	—
517	C₂×C₄×C₅₃	—	2	8	no	—
518	C₂×C₄×C₅₃	—	2	8	no	—
519	C₂×C₄×C₅₃	—	2	16	no	—
520	C₂×C₄×C₅₃	—	2	8	no	—
521	C₂×C₄×C₅₃	—	2	2	no	—
522	C₂×C₄×C₅₃	—	2	2	no	—
523	C₂×C₄×C₅₃	—	2	2	no	—
524	C₂×C₄×C₅₃	—	2	2	no	—
525	C₂×C₄×C₅₃	—	2	1	no	—
526	C₂×C₄×C₅₃	—	2	1	no	—
527	C₂×C₄×C₅₃	—	2	2	no	—
528	C₂×C₄×C₅₃	—	2	2	no	—
529	C₂×C₄×C₅₃	—	2	1	no	—
530	C₂×C₄×C₅₃	—	2	1	no	—
531	C₂×C₄×C₅₃	—	2	1	no	—
532	C₂×C₄×C₅₃	—	2	2	no	—
533	C₂×C₄×C₅₃	—	2	2	no	—
534	C₂×C₄×C₅₃	—	2	2	no	—
535	C₂×C₄×C₅₃	—	2	1	no	—
536	C₂×C₄×C₅₃	—	2	2	no	—
537	C₂×C₄×C₅₃	—	2	2	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	2	no	—
541	C₂×C₄×C₅₃	—	2	1	no	—
542	C₂×C₄×C₅₃	—	4	4	no	—
543	C₂×C₄×C₅₃	—	4	8	no	—
544	C₂×C₄×C₅₃	—	4	4	no	—
545	C₂×C₄×C₅₃	—	4	8	no	—
546	C₂×C₄×C₅₃	—	4	8	no	—
547	C₂×C₄×C₅₃	—	4	4	no	—
548	C₂×C₄×C₅₃	—	4	8	no	—
549	C₂×C₄×C₅₃	—	4	8	no	—
550	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
552	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
553	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
554	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
557	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
558	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
559	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
560	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
561	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
562	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
563	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
564	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
565	#34681	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
566	C₂²×C₅₃	—	2	2	no	—
567	C₂²×C₅₃	—	2	2	no	—
568	C₂²×C₅₃	—	2	2	no	—
569	C₂²×C₅₃	—	2	2	no	—
570	C₂²×C₅₃	—	2	2	no	—
571	C₂²×C₅₃	—	2	2	no	—
572	C₂²×C₅₃	—	2	4	no	—
573	C₂²×C₅₃	—	2	4	no	—
574	C₂²×C₅₃	—	2	2	no	—
575	C₂²×C₅₃	—	2	4	no	—
576	C₂²×C₅₃	—	2	2	no	—
577	C₂²×C₅₃	—	2	4	no	—
578	C₂²×C₅₃	—	2	2	no	—
579	C₂²×C₅₃	—	2	4	no	—
580	C₂²×C₅₃	—	2	4	no	—
581	C₂²×C₅₃	—	4	32	no	—
582	C₂²×C₅₃	—	4	1	no	—
583	C₂²×C₅₃	—	4	2	no	—
584	C₂²×C₅₃	—	4	2	no	—
585	C₂²×C₅₃	—	4	1	no	—
586	C₂²×C₅₃	—	4	2	no	—
587	C₂²×C₅₃	—	4	2	no	—
588	C₂²×C₅₃	—	4	2	no	—
589	C₂²×C₅₃	—	4	1	no	—
590	C₂²×C₅₃	—	4	2	no	—
591	C₂²×C₅₃	—	4	2	no	—
592	C₂²×C₅₃	—	4	1	no	—
593	C₂²×C₅₃	—	4	2	no	—
594	C₂²×C₅₃	—	4	2	no	—
595	C₂²×C₅₃	—	4	2	no	—
596	C₂²×C₅₃	—	4	2	no	—
597	C₂²×C₅₃	—	4	2	no	—
598	C₂²×C₅₃	—	4	2	no	—
599	C₂²×C₅₃	—	4	2	no	—
600	C₂²×C₅₃	—	4	2	no	—
601	C₂²×C₅₃	#532	1	4	yes	complemented
602	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
603	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
604	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
605	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
606	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
607	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
608	C₂²×C₅₃	#585	1	1	yes	characteristic
609	C₄×C₅₃	—	2	2	no	—
610	C₄×C₅₃	—	2	2	no	—
611	C₄×C₅₃	—	2	2	no	—
612	C₄×C₅₃	—	2	4	no	—
613	C₄×C₅₃	—	2	2	no	—
614	C₄×C₅₃	—	2	2	no	—
615	C₄×C₅₃	—	2	2	no	—
616	C₄×C₅₃	—	2	2	no	—
617	C₄×C₅₃	—	2	2	no	—
618	C₄×C₅₃	—	4	1	no	—
619	C₄×C₅₃	—	4	2	no	—
620	C₄×C₅₃	—	4	1	no	—
621	C₄×C₅₃	—	4	2	no	—
622	C₄×C₅₃	—	4	2	no	—
623	C₄×C₅₃	—	4	1	no	—
624	C₄×C₅₃	—	4	2	no	—
625	C₄×C₅₃	#525	1	4	yes	complemented
626	C₄×C₅₃	D₄²	1	4	yes	—
627	C₂×#532	C₂×C₅₃	1	1	yes	characteristic, complemented
628	C₂×#525	C₂×C₅₃	1	2	yes	complemented
629	C₂²×C₄×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
630	#2472	C₂×C₅₃	1	2	yes	complemented
631	#2464	C₂×C₅₃	1	2	yes	complemented
632	#2461	C₂×C₅₃	1	2	yes	complemented
633	#2452	C₂×C₅₃	1	1	yes	characteristic, complemented
634	#2445	C₂×C₅₃	1	1	yes	characteristic, complemented
635	#2440	C₂×C₅₃	1	1	yes	characteristic, complemented
636	#2433	C₂×C₅₃	1	1	yes	characteristic, complemented
637	#2428	C₂×C₅₃	1	1	yes	characteristic, complemented
638	#2424	C₂×C₅₃	1	2	yes	complemented
639	#2422	C₂×C₅₃	1	1	yes	characteristic, complemented
640	#2416	C₂×C₅₃	1	1	yes	characteristic, complemented
641	#2408	C₂×C₅₃	1	1	yes	characteristic, complemented
642	#2392	C₂×C₅₃	1	2	yes	complemented
643	#2388	C₂×C₅₃	1	2	yes	complemented
644	C₄×#127	C₂×C₅₃	1	1	yes	characteristic, complemented
645	C₄×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
646	C₄×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
647	C₄×#120	C₂×C₅₃	1	2	yes	complemented
648	#2293	C₂×C₅₃	1	1	yes	characteristic, complemented
649	C₄²×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
650	C₂×C₅₃	—	2	4	no	—
651	C₂×C₅₃	—	4	2	no	—
652	C₂×C₅₃	—	4	4	no	—
653	C₂×C₅₃	—	4	4	no	—
654	C₂×C₅₃	—	8	2	no	—
655	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
656	C₂×C₅₃	C₂×#532	1	1	yes	characteristic
657	C₂×C₅₃	#3460	1	1	yes	characteristic
658	C₂×C₅₃	C₂×D₄²	1	1	yes	characteristic
659	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
660	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
661	C₂×C₅₃	#3481	1	1	yes	characteristic
662	C₂²×#41	C₂²×C₅₃	1	2	yes	complemented
663	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
664	C₂⁴×C₄	C₂²×C₅₃	1	2	yes	—
665	#532	—	2	8	no	—
666	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
667	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
668	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
669	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
670	#525	—	2	16	no	—
671	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
672	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
673	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
674	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
675	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
676	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
677	C₂×#121	C₂²×C₅₃	1	2	yes	—
678	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
679	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
680	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
682	C₂×#120	C₂²×C₅₃	1	2	yes	—
683	C₂×#120	C₂²×C₅₃	1	2	yes	—
684	C₂×#120	C₂²×C₅₃	1	2	yes	—
685	C₂×C₄×D₄	—	2	8	no	—
686	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
687	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
688	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
689	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
690	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
691	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
692	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
693	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
694	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
695	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
696	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
697	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
698	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
699	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
700	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
701	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
702	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
703	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
704	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
705	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
706	#398	C₂²×C₅₃	1	2	yes	complemented
707	#397	C₂²×C₅₃	1	2	yes	complemented
708	#396	C₂²×C₅₃	1	2	yes	complemented
709	#396	C₂²×C₅₃	1	2	yes	complemented
710	#395	C₂²×C₅₃	1	2	yes	complemented
711	#394	C₂²×C₅₃	1	2	yes	—
712	#394	C₂²×C₅₃	1	2	yes	complemented
713	#394	C₂²×C₅₃	1	2	yes	complemented
714	#394	C₂²×C₅₃	1	2	yes	complemented
715	#394	C₂²×C₅₃	1	2	yes	complemented
716	#394	C₂²×C₅₃	1	2	yes	complemented
717	#393	C₂²×C₅₃	1	2	yes	complemented
718	#392	C₂²×C₅₃	1	2	yes	—
719	#392	C₂²×C₅₃	1	2	yes	—
720	#392	C₂²×C₅₃	1	2	yes	—
721	#392	C₂²×C₅₃	1	2	yes	complemented
722	#390	C₂²×C₅₃	1	1	yes	characteristic
723	#390	C₂²×C₅₃	1	1	yes	characteristic
724	#390	C₂²×C₅₃	1	1	yes	characteristic
725	#390	C₂²×C₅₃	1	1	yes	characteristic
726	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
727	#390	C₂²×C₅₃	1	2	yes	complemented
728	#390	C₂²×C₅₃	1	2	yes	complemented
729	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
730	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
731	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
732	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
733	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
734	#388	C₂²×C₅₃	1	2	yes	complemented
735	#388	C₂²×C₅₃	1	2	yes	complemented
736	#388	C₂²×C₅₃	1	2	yes	complemented
737	#388	C₂²×C₅₃	1	2	yes	complemented
738	#386	C₂²×C₅₃	1	2	yes	—
739	#386	C₂²×C₅₃	1	2	yes	—
740	#386	C₂²×C₅₃	1	2	yes	complemented
741	#386	C₂²×C₅₃	1	2	yes	complemented
742	#386	C₂²×C₅₃	1	2	yes	complemented
743	#385	C₂²×C₅₃	1	2	yes	—
744	#385	C₂²×C₅₃	1	2	yes	complemented
745	#385	C₂²×C₅₃	1	2	yes	complemented
746	#384	C₂²×C₅₃	1	1	yes	characteristic, complemented
747	#380	C₂²×C₅₃	1	1	yes	characteristic
748	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
749	#379	C₂²×C₅₃	1	2	yes	—
750	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
751	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
752	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
753	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
754	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
755	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
756	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
757	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
758	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
759	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
760	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
761	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
762	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
763	C₄³	C₂²×C₅₃	1	1	yes	characteristic, complemented
764	C₅₃	#34681	1	1	yes	characteristic, direct product factor, Sylow
765	C₂⁵	C₂³×C₅₃	1	2	yes	—
766	C₂×#41	—	2	8	no	—
767	C₂×#41	—	2	8	no	—
768	C₂×#41	—	4	4	no	—
769	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
770	C₂²×D₄	—	2	4	no	—
771	C₂²×D₄	—	2	4	no	—
772	C₂²×D₄	—	2	4	no	—
773	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
774	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
775	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
776	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
777	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
778	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
779	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
780	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
781	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
782	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
783	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
784	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
785	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
786	C₂³×C₄	—	2	8	no	—
787	C₂³×C₄	—	2	8	no	—
788	C₂³×C₄	—	4	4	no	—
789	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
790	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
791	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
792	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
793	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
794	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
795	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
796	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
797	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
798	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
799	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
800	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
801	C₄⋊Q₈	—	2	4	no	—
802	#127	—	2	4	no	—
803	#127	—	2	4	no	—
804	#124	—	2	8	no	—
805	#123	—	2	8	no	—
806	#123	—	2	8	no	—
807	C₂²⋊Q₈	—	2	8	no	—
808	C₂²⋊Q₈	—	2	8	no	—
809	#121	—	2	8	no	—
810	#121	—	2	4	no	—
811	#121	—	2	4	no	—
812	#121	—	2	4	no	—
813	#121	—	2	4	no	—
814	#121	—	2	8	no	—
815	#121	—	2	8	no	—
816	#120	—	2	8	no	—
817	#120	—	2	8	no	—
818	#120	—	2	8	no	—
819	C₄×D₄	—	2	4	no	—
820	C₄×D₄	—	2	8	no	—
821	C₄×D₄	—	2	8	no	—
822	C₄×D₄	—	2	8	no	—
823	C₄×D₄	—	2	8	no	—
824	C₄×D₄	—	2	4	no	—
825	C₄×D₄	—	2	4	no	—
826	C₄×D₄	—	2	8	no	—
827	C₄×D₄	—	2	4	no	—
828	C₄×D₄	—	2	4	no	—
829	C₄×D₄	—	2	4	no	—
830	C₄×D₄	—	2	8	no	—
831	C₄×D₄	—	4	4	no	—
832	C₄×D₄	D₄×C₅₃	1	8	yes	complemented
833	C₄×D₄	D₄×C₅₃	1	8	yes	complemented
834	#117	—	2	8	no	—
835	C₂×C₄⋊C₄	—	2	4	no	—
836	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
837	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
838	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
839	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
840	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
841	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
845	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
846	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
847	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
848	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
849	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
850	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
851	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
852	C₂×C₂²⋊C₄	—	2	8	no	—
853	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
854	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
855	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
856	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
857	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
858	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
859	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
860	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
861	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
862	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
863	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
864	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
865	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
866	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
867	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
868	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
869	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
870	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
871	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
872	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
873	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
874	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
875	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
876	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
877	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
878	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
879	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
880	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
881	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
882	C₂×C₄²	—	2	4	no	—
883	C₂×C₄²	—	2	4	no	—
884	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
885	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
886	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
887	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
888	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
889	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
890	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
891	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
892	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
893	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
894	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
895	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
896	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
897	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
898	#95	C₂³×C₅₃	1	1	yes	characteristic
899	#95	C₂³×C₅₃	1	1	yes	characteristic
900	#95	C₂³×C₅₃	1	1	yes	characteristic
901	#95	C₂³×C₅₃	1	1	yes	characteristic
902	#95	C₂³×C₅₃	1	1	yes	characteristic
903	#95	C₂³×C₅₃	1	1	yes	characteristic
904	#95	C₂³×C₅₃	1	2	yes	—
905	#95	C₂³×C₅₃	1	2	yes	—
906	#95	C₂³×C₅₃	1	2	yes	—
907	#95	C₂³×C₅₃	1	2	yes	—
908	#95	C₂³×C₅₃	1	2	yes	—
909	#95	C₂³×C₅₃	1	2	yes	—
910	#95	C₂³×C₅₃	1	2	yes	—
911	C₂⁴	—	2	4	no	—
912	C₂⁴	—	2	4	no	—
913	C₂⁴	—	2	4	no	—
914	C₂⁴	—	2	4	no	—
915	C₂⁴	—	2	4	no	—
916	C₂⁴	—	4	2	no	—
917	C₂⁴	—	4	2	no	—
918	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
919	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
920	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
921	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
922	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
923	#41	—	4	32	no	—
924	C₂×Q₈	—	2	4	no	—
925	C₂×Q₈	—	2	4	no	—
926	C₂×Q₈	—	4	2	no	—
927	C₂×D₄	—	2	32	no	—
928	C₂×D₄	—	2	4	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	4	no	—
932	C₂×D₄	—	2	4	no	—
933	C₂×D₄	—	2	4	no	—
934	C₂×D₄	—	2	4	no	—
935	C₂×D₄	—	2	4	no	—
936	C₂×D₄	—	2	4	no	—
937	C₂×D₄	—	2	4	no	—
938	C₂×D₄	—	2	4	no	—
939	C₂×D₄	—	2	4	no	—
940	C₂×D₄	—	2	4	no	—
941	C₂×D₄	—	2	4	no	—
942	C₂×D₄	—	2	4	no	—
943	C₂×D₄	—	2	4	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	4	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	4	no	—
948	C₂×D₄	—	2	4	no	—
949	C₂×D₄	—	2	4	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	4	no	—
954	C₂×D₄	—	2	4	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	4	2	no	—
958	C₂×D₄	—	4	2	no	—
959	C₂×D₄	—	4	2	no	—
960	C₂×D₄	—	4	2	no	—
961	C₂×D₄	—	4	2	no	—
962	C₂×D₄	—	4	2	no	—
963	C₂×D₄	—	4	2	no	—
964	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
965	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
966	C₂×D₄	#41×C₅₃	1	4	yes	complemented
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	4	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	4	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	4	no	—
976	C₂²×C₄	—	2	4	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	4	no	—
982	C₂²×C₄	—	2	4	no	—
983	C₂²×C₄	—	2	4	no	—
984	C₂²×C₄	—	2	4	no	—
985	C₂²×C₄	—	2	4	no	—
986	C₂²×C₄	—	2	4	no	—
987	C₂²×C₄	—	2	4	no	—
988	C₂²×C₄	—	2	4	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	4	no	—
993	C₂²×C₄	—	2	4	no	—
994	C₂²×C₄	—	4	2	no	—
995	C₂²×C₄	—	4	2	no	—
996	C₂²×C₄	—	4	2	no	—
997	C₂²×C₄	—	4	1	no	—
998	C₂²×C₄	—	4	1	no	—
999	C₂²×C₄	—	4	32	no	—
1000	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
1001	C₂²×C₄	C₂×D₄×C₅₃	1	8	yes	—
1002	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	complemented
1003	C₂²×C₄	#41×C₅₃	1	4	yes	complemented
1004	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1006	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1007	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1008	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1009	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1010	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1011	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1016	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1017	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1019	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1022	C₄⋊C₄	—	2	4	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	4	no	—
1025	C₄⋊C₄	—	2	4	no	—
1026	C₄⋊C₄	—	2	4	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	4	no	—
1029	C₄⋊C₄	—	2	4	no	—
1030	C₄⋊C₄	—	2	4	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	4	2	no	—
1036	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
1037	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	complemented
1038	C₂²⋊C₄	—	2	4	no	—
1039	C₂²⋊C₄	—	2	4	no	—
1040	C₂²⋊C₄	—	2	4	no	—
1041	C₂²⋊C₄	—	2	4	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	4	no	—
1044	C₂²⋊C₄	—	2	4	no	—
1045	C₂²⋊C₄	—	2	4	no	—
1046	C₂²⋊C₄	—	2	4	no	—
1047	C₂²⋊C₄	—	2	4	no	—
1048	C₂²⋊C₄	—	2	4	no	—
1049	C₂²⋊C₄	—	2	4	no	—
1050	C₂²⋊C₄	—	2	4	no	—
1051	C₂²⋊C₄	—	2	4	no	—
1052	C₂²⋊C₄	—	2	4	no	—
1053	C₂²⋊C₄	—	2	4	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	4	no	—
1057	C₂²⋊C₄	—	2	4	no	—
1058	C₂²⋊C₄	—	2	4	no	—
1059	C₂²⋊C₄	—	4	2	no	—
1060	C₂²⋊C₄	—	4	2	no	—
1061	C₂²⋊C₄	—	4	2	no	—
1062	C₂²⋊C₄	—	4	2	no	—
1063	C₂²⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
1064	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
1065	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	complemented
1066	C₂²⋊C₄	#41×C₅₃	1	4	yes	complemented
1067	C₄²	—	2	2	no	—
1068	C₄²	—	2	2	no	—
1069	C₄²	—	2	2	no	—
1070	C₄²	—	2	2	no	—
1071	C₄²	—	2	2	no	—
1072	C₄²	—	2	2	no	—
1073	C₄²	—	2	4	no	—
1074	C₄²	—	2	2	no	—
1075	C₄²	—	2	2	no	—
1076	C₄²	—	2	2	no	—
1077	C₄²	—	2	2	no	—
1078	C₄²	—	4	1	no	—
1079	C₄²	C₂×D₄×C₅₃	1	4	yes	—
1080	C₄²	C₂×D₄×C₅₃	1	4	yes	complemented
1081	C₂³	—	2	1	no	—
1082	C₂³	—	2	1	no	—
1083	C₂³	—	2	1	no	—
1084	C₂³	—	2	1	no	—
1085	C₂³	—	2	16	no	—
1086	C₂³	—	2	2	no	—
1087	C₂³	—	2	2	no	—
1088	C₂³	—	2	2	no	—
1089	C₂³	—	2	1	no	—
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	2	2	no	—
1094	C₂³	—	2	1	no	—
1095	C₂³	—	2	2	no	—
1096	C₂³	—	2	2	no	—
1097	C₂³	—	2	2	no	—
1098	C₂³	—	2	2	no	—
1099	C₂³	—	2	2	no	—
1100	C₂³	—	2	1	no	—
1101	C₂³	—	2	2	no	—
1102	C₂³	—	2	1	no	—
1103	C₂³	—	2	2	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	2	2	no	—
1107	C₂³	—	2	2	no	—
1108	C₂³	—	2	2	no	—
1109	C₂³	—	2	2	no	—
1110	C₂³	—	2	2	no	—
1111	C₂³	—	4	8	no	—
1112	C₂³	—	4	8	no	—
1113	C₂³	—	4	8	no	—
1114	C₂³	—	4	8	no	—
1115	C₂³	—	4	8	no	—
1116	C₂³	—	4	8	no	—
1117	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
1118	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1119	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1120	C₂³	C₂×#41×C₅₃	1	4	yes	—
1121	C₂³	C₂×#41×C₅₃	1	2	yes	—
1122	C₂³	C₂×#41×C₅₃	1	2	yes	—
1123	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1124	Q₈	—	4	8	no	—
1125	D₄	—	2	16	no	—
1126	D₄	—	2	8	no	—
1127	D₄	—	2	8	no	—
1128	D₄	—	2	8	no	—
1129	D₄	—	4	8	no	—
1130	D₄	—	4	8	no	—
1131	D₄	—	4	8	no	—
1132	D₄	—	4	8	no	—
1133	D₄	—	4	8	no	—
1134	D₄	—	4	8	no	—
1135	D₄	—	4	8	no	—
1136	D₄	—	4	8	no	—
1137	D₄	—	4	4	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	8	no	—
1157	C₂×C₄	—	2	8	no	—
1158	C₂×C₄	—	2	16	no	—
1159	C₂×C₄	—	2	8	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	2	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	4	4	no	—
1182	C₂×C₄	—	4	8	no	—
1183	C₂×C₄	—	4	4	no	—
1184	C₂×C₄	—	4	8	no	—
1185	C₂×C₄	—	4	8	no	—
1186	C₂×C₄	—	4	4	no	—
1187	C₂×C₄	—	4	8	no	—
1188	C₂×C₄	—	4	8	no	—
1189	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1190	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1191	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1192	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
1193	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1194	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1195	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1196	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1197	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1198	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1199	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1200	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1201	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1202	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1203	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	2	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	2	no	—
1210	C₂²	—	2	4	no	—
1211	C₂²	—	2	2	no	—
1212	C₂²	—	2	4	no	—
1213	C₂²	—	2	2	no	—
1214	C₂²	—	2	4	no	—
1215	C₂²	—	2	4	no	—
1216	C₂²	—	2	4	no	—
1217	C₂²	—	2	4	no	—
1218	C₂²	—	2	2	no	—
1219	C₂²	—	4	32	no	—
1220	C₂²	—	4	2	no	—
1221	C₂²	—	4	2	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	2	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	2	no	—
1226	C₂²	—	4	2	no	—
1227	C₂²	—	4	2	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	2	no	—
1231	C₂²	—	4	2	no	—
1232	C₂²	—	4	2	no	—
1233	C₂²	—	4	2	no	—
1234	C₂²	—	4	2	no	—
1235	C₂²	—	4	2	no	—
1236	C₂²	—	4	2	no	—
1237	C₂²	—	4	2	no	—
1238	C₂²	—	4	2	no	—
1239	C₂²	C₅₃×#532	1	4	yes	complemented
1240	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1241	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1242	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1243	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1244	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1245	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1246	C₂²	C₅₃×#585	1	1	yes	characteristic
1247	C₄	—	2	2	no	—
1248	C₄	—	2	4	no	—
1249	C₄	—	2	2	no	—
1250	C₄	—	2	2	no	—
1251	C₄	—	2	2	no	—
1252	C₄	—	2	2	no	—
1253	C₄	—	2	2	no	—
1254	C₄	—	2	2	no	—
1255	C₄	—	2	2	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	2	no	—
1258	C₄	—	4	2	no	—
1259	C₄	—	4	1	no	—
1260	C₄	—	4	2	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	4	2	no	—
1263	C₄	C₅₃×#525	1	4	yes	complemented
1264	C₄	D₄²×C₅₃	1	4	yes	—
1265	C₂	—	2	4	no	—
1266	C₂	—	4	4	no	—
1267	C₂	—	4	4	no	—
1268	C₂	—	4	2	no	—
1269	C₂	—	8	2	no	—
1270	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
1271	C₂	C₂×C₅₃×#532	1	1	yes	characteristic
1272	C₂	C₅₃×#3460	1	1	yes	characteristic
1273	C₂	C₂×D₄²×C₅₃	1	1	yes	characteristic
1274	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1275	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1276	C₂	C₅₃×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
socle	C₂³×C₅₃	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#532	C₂	semidirect
2. C₂×C₅₃×#525	C₂	semidirect
3. C₂²×C₄×D₄×C₅₃	C₂	semidirect
4. C₅₃×#2472	C₂	semidirect
5. C₅₃×#2464	C₂	semidirect
6. C₅₃×#2461	C₂	semidirect
7. C₅₃×#2452	C₂	semidirect
8. C₅₃×#2445	C₂	semidirect
9. C₅₃×#2440	C₂	semidirect
10. C₅₃×#2433	C₂	semidirect
11. C₅₃×#2428	C₂	semidirect
12. C₅₃×#2424	C₂	semidirect
13. C₅₃×#2422	C₂	semidirect
14. C₅₃×#2416	C₂	semidirect
15. C₅₃×#2408	C₂	semidirect
16. C₅₃×#2392	C₂	semidirect
17. C₅₃×#2388	C₂	semidirect
18. C₄×#127×C₅₃	C₂	semidirect
19. C₄×#121×C₅₃	C₂	semidirect
20. C₄×#121×C₅₃	C₂	semidirect
21. C₄×#120×C₅₃	C₂	semidirect
22. C₅₃×#2293	C₂	semidirect
23. C₄²×D₄×C₅₃	C₂	semidirect
24. C₂²×#41×C₅₃	C₂²	semidirect
28. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
31. C₂×#124×C₅₃	C₂²	semidirect
33. C₂×#123×C₅₃	C₂²	semidirect
34. C₂×#123×C₅₃	C₂²	semidirect
36. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
41. C₂×#121×C₅₃	C₂²	semidirect
42. C₂×#121×C₅₃	C₂²	semidirect
43. C₂×#121×C₅₃	C₂²	semidirect
58. C₂×C₄×D₄×C₅₃	C₂²	semidirect
59. C₂×C₄×D₄×C₅₃	C₂²	semidirect
60. C₂×C₄×D₄×C₅₃	C₂²	semidirect
61. C₂×C₄×D₄×C₅₃	C₂²	semidirect
62. C₂×C₄×D₄×C₅₃	C₂²	semidirect
63. C₂×#117×C₅₃	C₂²	semidirect
67. C₂²×C₄²×C₅₃	C₂²	semidirect
68. C₅₃×#398	C₂²	semidirect
69. C₅₃×#397	C₂²	semidirect
70. C₅₃×#396	C₂²	semidirect
71. C₅₃×#396	C₂²	semidirect
72. C₅₃×#395	C₂²	semidirect
74. C₅₃×#394	C₂²	semidirect
75. C₅₃×#394	C₂²	semidirect
76. C₅₃×#394	C₂²	semidirect
77. C₅₃×#394	C₂²	semidirect
78. C₅₃×#394	C₂²	semidirect
79. C₅₃×#393	C₂²	semidirect
83. C₅₃×#392	C₂²	semidirect
88. C₅₃×#390	C₂²	semidirect
89. C₅₃×#390	C₂²	semidirect
90. C₅₃×#390	C₂²	semidirect
91. C₅₃×#390	C₂²	semidirect
92. C₅₃×#389	C₂²	semidirect
93. C₅₃×#389	C₂²	semidirect
94. C₅₃×#389	C₂²	semidirect
95. C₅₃×#389	C₂²	semidirect
96. C₅₃×#388	C₂²	semidirect
97. C₅₃×#388	C₂²	semidirect
98. C₅₃×#388	C₂²	semidirect
99. C₅₃×#388	C₂²	semidirect
102. C₅₃×#386	C₂²	semidirect
103. C₅₃×#386	C₂²	semidirect
104. C₅₃×#386	C₂²	semidirect
106. C₅₃×#385	C₂²	semidirect
107. C₅₃×#385	C₂²	semidirect
108. C₅₃×#384	C₂²	semidirect
110. C₅₃×#380	C₂²	semidirect
112. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
113. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
114. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
115. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
124. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
125. C₄³×C₅₃	C₂²	semidirect
193. C₄×D₄×C₅₃	D₄	semidirect
194. C₄×D₄×C₅₃	D₄	semidirect
327. C₂×D₄×C₅₃	#41	semidirect
363. C₂²×C₄×C₅₃	C₂×D₄	semidirect
364. C₂²×C₄×C₅₃	#41	semidirect
398. C₄⋊C₄×C₅₃	C₂×D₄	semidirect
426. C₂²⋊C₄×C₅₃	C₂×D₄	semidirect
427. C₂²⋊C₄×C₅₃	#41	semidirect
441. C₄²×C₅₃	C₂×D₄	semidirect
565. #34681	C₅₃	direct (N × H)
601. C₂²×C₅₃	#532	semidirect
625. C₄×C₅₃	#525	semidirect
627. C₂×#532	C₂×C₅₃	semidirect
628. C₂×#525	C₂×C₅₃	semidirect
629. C₂²×C₄×D₄	C₂×C₅₃	semidirect
630. #2472	C₂×C₅₃	semidirect
631. #2464	C₂×C₅₃	semidirect
632. #2461	C₂×C₅₃	semidirect
633. #2452	C₂×C₅₃	semidirect
634. #2445	C₂×C₅₃	semidirect
635. #2440	C₂×C₅₃	semidirect
636. #2433	C₂×C₅₃	semidirect
637. #2428	C₂×C₅₃	semidirect
638. #2424	C₂×C₅₃	semidirect
639. #2422	C₂×C₅₃	semidirect
640. #2416	C₂×C₅₃	semidirect
641. #2408	C₂×C₅₃	semidirect
642. #2392	C₂×C₅₃	semidirect
643. #2388	C₂×C₅₃	semidirect
644. C₄×#127	C₂×C₅₃	semidirect
645. C₄×#121	C₂×C₅₃	semidirect
646. C₄×#121	C₂×C₅₃	semidirect
647. C₄×#120	C₂×C₅₃	semidirect
648. #2293	C₂×C₅₃	semidirect
649. C₄²×D₄	C₂×C₅₃	semidirect
662. C₂²×#41	C₂²×C₅₃	semidirect
666. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
669. C₂×#124	C₂²×C₅₃	semidirect
671. C₂×#123	C₂²×C₅₃	semidirect
672. C₂×#123	C₂²×C₅₃	semidirect
674. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
679. C₂×#121	C₂²×C₅₃	semidirect
680. C₂×#121	C₂²×C₅₃	semidirect
681. C₂×#121	C₂²×C₅₃	semidirect
696. C₂×C₄×D₄	C₂²×C₅₃	semidirect
697. C₂×C₄×D₄	C₂²×C₅₃	semidirect
698. C₂×C₄×D₄	C₂²×C₅₃	semidirect
699. C₂×C₄×D₄	C₂²×C₅₃	semidirect
700. C₂×C₄×D₄	C₂²×C₅₃	semidirect
701. C₂×#117	C₂²×C₅₃	semidirect
705. C₂²×C₄²	C₂²×C₅₃	semidirect
706. #398	C₂²×C₅₃	semidirect
707. #397	C₂²×C₅₃	semidirect
708. #396	C₂²×C₅₃	semidirect
709. #396	C₂²×C₅₃	semidirect
710. #395	C₂²×C₅₃	semidirect
712. #394	C₂²×C₅₃	semidirect
713. #394	C₂²×C₅₃	semidirect
714. #394	C₂²×C₅₃	semidirect
715. #394	C₂²×C₅₃	semidirect
716. #394	C₂²×C₅₃	semidirect
717. #393	C₂²×C₅₃	semidirect
721. #392	C₂²×C₅₃	semidirect
726. #390	C₂²×C₅₃	semidirect
727. #390	C₂²×C₅₃	semidirect
728. #390	C₂²×C₅₃	semidirect
729. #390	C₂²×C₅₃	semidirect
730. #389	C₂²×C₅₃	semidirect
731. #389	C₂²×C₅₃	semidirect
732. #389	C₂²×C₅₃	semidirect
733. #389	C₂²×C₅₃	semidirect
734. #388	C₂²×C₅₃	semidirect
735. #388	C₂²×C₅₃	semidirect
736. #388	C₂²×C₅₃	semidirect
737. #388	C₂²×C₅₃	semidirect
740. #386	C₂²×C₅₃	semidirect
741. #386	C₂²×C₅₃	semidirect
742. #386	C₂²×C₅₃	semidirect
744. #385	C₂²×C₅₃	semidirect
745. #385	C₂²×C₅₃	semidirect
746. #384	C₂²×C₅₃	semidirect
748. #380	C₂²×C₅₃	semidirect
750. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
751. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
752. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
753. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
757. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
758. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
759. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
760. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
761. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
762. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
763. C₄³	C₂²×C₅₃	semidirect
764. C₅₃	#34681	direct (N × H)
832. C₄×D₄	D₄×C₅₃	semidirect
833. C₄×D₄	D₄×C₅₃	semidirect
966. C₂×D₄	#41×C₅₃	semidirect
1002. C₂²×C₄	C₂×D₄×C₅₃	semidirect
1003. C₂²×C₄	#41×C₅₃	semidirect
1037. C₄⋊C₄	C₂×D₄×C₅₃	semidirect
1065. C₂²⋊C₄	C₂×D₄×C₅₃	semidirect
1066. C₂²⋊C₄	#41×C₅₃	semidirect
1080. C₄²	C₂×D₄×C₅₃	semidirect
1239. C₂²	C₅₃×#532	semidirect
1263. C₄	C₅₃×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#532	2
C₂×C₅₃×#525	2
C₂²×C₄×D₄×C₅₃	2
C₅₃×#2472	2
C₅₃×#2464	2
C₅₃×#2461	2
C₅₃×#2452	2
C₅₃×#2445	2
C₅₃×#2440	2
C₅₃×#2433	2
C₅₃×#2428	2
C₅₃×#2424	2
C₅₃×#2422	2
C₅₃×#2416	2
C₅₃×#2408	2
C₅₃×#2392	2
C₅₃×#2388	2
C₄×#127×C₅₃	2
C₄×#121×C₅₃	2
C₄×#120×C₅₃	2
C₅₃×#2293	2
C₄²×D₄×C₅₃	2
#34681	53

Subgroups — C53×#34681 #27242193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34681 #27242193