Subgroups — C₅₃×#35007 #27242519

Order 13568.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#538	C₂	1	2	yes	maximal, complemented
2	C₅₃×#2860	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2856	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2662	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2661	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2555	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2554	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2512	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2491	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2472	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2424	C₂	1	2	yes	maximal, complemented
18	C₅₃×#2416	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2321	C₂	1	2	yes	maximal, complemented
21	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
25	C₅₃×#538	—	2	16	no	—
26	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
30	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
31	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
32	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
33	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
34	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
35	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
36	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
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	2	yes	complemented
44	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#120×C₅₃	C₂²	1	2	yes	—
46	C₂×#120×C₅₃	C₂²	1	2	yes	—
47	C₂×#120×C₅₃	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
54	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
55	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
56	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
57	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#398	C₂²	1	2	yes	complemented
59	C₅₃×#397	C₂²	1	2	yes	complemented
60	C₅₃×#396	C₂²	1	2	yes	complemented
61	C₅₃×#396	C₂²	1	2	yes	complemented
62	C₅₃×#395	C₂²	1	2	yes	complemented
63	C₅₃×#394	C₂²	1	2	yes	—
64	C₅₃×#394	C₂²	1	2	yes	complemented
65	C₅₃×#394	C₂²	1	2	yes	complemented
66	C₅₃×#394	C₂²	1	2	yes	complemented
67	C₅₃×#394	C₂²	1	2	yes	complemented
68	C₅₃×#394	C₂²	1	2	yes	complemented
69	C₅₃×#393	C₂²	1	2	yes	complemented
70	C₅₃×#392	C₂²	1	2	yes	—
71	C₅₃×#392	C₂²	1	2	yes	—
72	C₅₃×#392	C₂²	1	2	yes	—
73	C₅₃×#392	C₂²	1	2	yes	complemented
74	C₅₃×#390	C₂²	1	1	yes	characteristic
75	C₅₃×#390	C₂²	1	1	yes	characteristic
76	C₅₃×#390	C₂²	1	1	yes	characteristic
77	C₅₃×#390	C₂²	1	1	yes	characteristic
78	C₅₃×#390	C₂²	1	1	yes	characteristic
79	C₅₃×#390	C₂²	1	1	yes	characteristic
80	C₅₃×#390	C₂²	1	2	yes	—
81	C₅₃×#390	C₂²	1	1	yes	characteristic
82	C₅₃×#390	C₂²	1	1	yes	characteristic
83	C₅₃×#390	C₂²	1	2	yes	—
84	C₅₃×#390	C₂²	1	2	yes	complemented
85	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#390	C₂²	1	2	yes	complemented
87	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#390	C₂²	1	2	yes	complemented
89	C₅₃×#390	C₂²	1	2	yes	complemented
90	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#388	C₂²	1	2	yes	complemented
95	C₅₃×#388	C₂²	1	2	yes	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×#388	C₂²	1	2	yes	complemented
101	C₅₃×#388	C₂²	1	2	yes	complemented
102	C₅₃×#386	C₂²	1	2	yes	—
103	C₅₃×#386	C₂²	1	2	yes	—
104	C₅₃×#386	C₂²	1	2	yes	complemented
105	C₅₃×#386	C₂²	1	2	yes	complemented
106	C₅₃×#386	C₂²	1	2	yes	complemented
107	C₅₃×#385	C₂²	1	2	yes	—
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	C₄³×C₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₅₃	C₂³	1	2	yes	—
125	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₅₃	—	2	4	no	—
127	C₂²×D₄×C₅₃	—	4	2	no	—
128	C₂²×D₄×C₅₃	—	4	2	no	—
129	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
130	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
135	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
136	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
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	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
148	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
150	C₄⋊Q₈×C₅₃	—	4	2	no	—
151	#127×C₅₃	—	4	2	no	—
152	#127×C₅₃	—	4	2	no	—
153	#126×C₅₃	—	2	8	no	—
154	#126×C₅₃	—	2	8	no	—
155	#124×C₅₃	—	2	8	no	—
156	#124×C₅₃	—	2	8	no	—
157	#124×C₅₃	—	4	4	no	—
158	#123×C₅₃	—	2	8	no	—
159	#123×C₅₃	—	2	8	no	—
160	C₂²⋊Q₈×C₅₃	—	2	8	no	—
161	#121×C₅₃	—	2	8	no	—
162	#121×C₅₃	—	2	8	no	—
163	#121×C₅₃	—	2	8	no	—
164	#121×C₅₃	—	2	4	no	—
165	#121×C₅₃	—	4	2	no	—
166	#121×C₅₃	—	4	2	no	—
167	#121×C₅₃	—	4	2	no	—
168	#121×C₅₃	—	4	4	no	—
169	#120×C₅₃	—	2	8	no	—
170	#120×C₅₃	—	2	8	no	—
171	#120×C₅₃	—	2	8	no	—
172	C₄×D₄×C₅₃	—	2	4	no	—
173	C₄×D₄×C₅₃	—	2	8	no	—
174	C₄×D₄×C₅₃	—	2	4	no	—
175	C₄×D₄×C₅₃	—	4	2	no	—
176	C₄×D₄×C₅₃	D₄	1	8	yes	complemented
177	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
178	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
195	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
196	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
222	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
227	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₅₃	—	4	2	no	—
230	C₂×C₄²×C₅₃	—	4	2	no	—
231	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
235	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
245	#95×C₅₃	C₂³	1	1	yes	characteristic
246	#95×C₅₃	C₂³	1	1	yes	characteristic
247	#95×C₅₃	C₂³	1	1	yes	characteristic
248	#95×C₅₃	C₂³	1	1	yes	characteristic
249	#95×C₅₃	C₂³	1	1	yes	characteristic
250	#95×C₅₃	C₂³	1	1	yes	characteristic
251	#95×C₅₃	C₂³	1	2	yes	—
252	#95×C₅₃	C₂³	1	2	yes	—
253	#95×C₅₃	C₂³	1	2	yes	—
254	#95×C₅₃	C₂³	1	2	yes	—
255	#95×C₅₃	C₂³	1	2	yes	—
256	#95×C₅₃	C₂³	1	2	yes	—
257	#95×C₅₃	C₂³	1	2	yes	—
258	C₂⁴×C₅₃	—	2	4	no	—
259	C₂⁴×C₅₃	—	2	4	no	—
260	C₂⁴×C₅₃	—	2	4	no	—
261	C₂⁴×C₅₃	—	4	2	no	—
262	C₂⁴×C₅₃	—	4	2	no	—
263	C₂⁴×C₅₃	—	4	2	no	—
264	C₂⁴×C₅₃	—	4	2	no	—
265	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
266	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
267	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
268	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
269	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
270	C₂×Q₈×C₅₃	—	2	4	no	—
271	C₂×Q₈×C₅₃	—	4	2	no	—
272	C₂×Q₈×C₅₃	—	4	2	no	—
273	C₂×D₄×C₅₃	—	2	2	no	—
274	C₂×D₄×C₅₃	—	2	2	no	—
275	C₂×D₄×C₅₃	—	2	4	no	—
276	C₂×D₄×C₅₃	—	2	4	no	—
277	C₂×D₄×C₅₃	—	2	4	no	—
278	C₂×D₄×C₅₃	—	2	4	no	—
279	C₂×D₄×C₅₃	—	2	4	no	—
280	C₂×D₄×C₅₃	—	2	4	no	—
281	C₂×D₄×C₅₃	—	2	4	no	—
282	C₂×D₄×C₅₃	—	2	4	no	—
283	C₂×D₄×C₅₃	—	2	2	no	—
284	C₂×D₄×C₅₃	—	2	4	no	—
285	C₂×D₄×C₅₃	—	2	2	no	—
286	C₂×D₄×C₅₃	—	2	2	no	—
287	C₂×D₄×C₅₃	—	2	4	no	—
288	C₂×D₄×C₅₃	—	2	4	no	—
289	C₂×D₄×C₅₃	—	2	2	no	—
290	C₂×D₄×C₅₃	—	2	2	no	—
291	C₂×D₄×C₅₃	—	2	2	no	—
292	C₂×D₄×C₅₃	—	2	2	no	—
293	C₂×D₄×C₅₃	—	2	2	no	—
294	C₂×D₄×C₅₃	—	2	2	no	—
295	C₂×D₄×C₅₃	—	4	2	no	—
296	C₂×D₄×C₅₃	—	4	2	no	—
297	C₂×D₄×C₅₃	—	4	16	no	—
298	C₂×D₄×C₅₃	—	4	2	no	—
299	C₂×D₄×C₅₃	—	4	2	no	—
300	C₂×D₄×C₅₃	—	4	2	no	—
301	C₂×D₄×C₅₃	—	4	2	no	—
302	C₂×D₄×C₅₃	—	4	2	no	—
303	C₂×D₄×C₅₃	—	4	2	no	—
304	C₂×D₄×C₅₃	—	4	2	no	—
305	C₂×D₄×C₅₃	—	4	2	no	—
306	C₂×D₄×C₅₃	—	4	2	no	—
307	C₂×D₄×C₅₃	—	4	2	no	—
308	C₂×D₄×C₅₃	—	4	2	no	—
309	C₂×D₄×C₅₃	—	4	2	no	—
310	C₂×D₄×C₅₃	—	4	2	no	—
311	C₂×D₄×C₅₃	—	4	2	no	—
312	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
313	C₂²×C₄×C₅₃	—	2	2	no	—
314	C₂²×C₄×C₅₃	—	2	2	no	—
315	C₂²×C₄×C₅₃	—	2	2	no	—
316	C₂²×C₄×C₅₃	—	2	4	no	—
317	C₂²×C₄×C₅₃	—	2	2	no	—
318	C₂²×C₄×C₅₃	—	2	2	no	—
319	C₂²×C₄×C₅₃	—	2	2	no	—
320	C₂²×C₄×C₅₃	—	2	2	no	—
321	C₂²×C₄×C₅₃	—	2	2	no	—
322	C₂²×C₄×C₅₃	—	2	2	no	—
323	C₂²×C₄×C₅₃	—	2	4	no	—
324	C₂²×C₄×C₅₃	—	4	1	no	—
325	C₂²×C₄×C₅₃	—	4	1	no	—
326	C₂²×C₄×C₅₃	—	4	1	no	—
327	C₂²×C₄×C₅₃	—	4	1	no	—
328	C₂²×C₄×C₅₃	—	4	1	no	—
329	C₂²×C₄×C₅₃	—	4	1	no	—
330	C₂²×C₄×C₅₃	—	4	2	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	C₂×D₄	1	4	yes	—
335	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	complemented
336	C₂²×C₄×C₅₃	#41	1	4	yes	—
337	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₄⋊C₄×C₅₃	—	2	4	no	—
356	C₄⋊C₄×C₅₃	—	2	4	no	—
357	C₄⋊C₄×C₅₃	—	2	4	no	—
358	C₄⋊C₄×C₅₃	—	2	4	no	—
359	C₄⋊C₄×C₅₃	—	2	4	no	—
360	C₄⋊C₄×C₅₃	—	2	2	no	—
361	C₄⋊C₄×C₅₃	—	2	2	no	—
362	C₄⋊C₄×C₅₃	—	2	2	no	—
363	C₄⋊C₄×C₅₃	—	2	2	no	—
364	C₄⋊C₄×C₅₃	—	2	2	no	—
365	C₄⋊C₄×C₅₃	—	2	2	no	—
366	C₄⋊C₄×C₅₃	—	2	2	no	—
367	C₄⋊C₄×C₅₃	—	4	2	no	—
368	C₄⋊C₄×C₅₃	—	4	2	no	—
369	C₄⋊C₄×C₅₃	—	4	2	no	—
370	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	complemented
371	C₂²⋊C₄×C₅₃	—	2	4	no	—
372	C₂²⋊C₄×C₅₃	—	2	4	no	—
373	C₂²⋊C₄×C₅₃	—	2	2	no	—
374	C₂²⋊C₄×C₅₃	—	2	4	no	—
375	C₂²⋊C₄×C₅₃	—	2	4	no	—
376	C₂²⋊C₄×C₅₃	—	2	4	no	—
377	C₂²⋊C₄×C₅₃	—	2	4	no	—
378	C₂²⋊C₄×C₅₃	—	2	4	no	—
379	C₂²⋊C₄×C₅₃	—	2	4	no	—
380	C₂²⋊C₄×C₅₃	—	2	4	no	—
381	C₂²⋊C₄×C₅₃	—	2	4	no	—
382	C₂²⋊C₄×C₅₃	—	2	4	no	—
383	C₂²⋊C₄×C₅₃	—	2	4	no	—
384	C₂²⋊C₄×C₅₃	—	2	2	no	—
385	C₂²⋊C₄×C₅₃	—	2	2	no	—
386	C₂²⋊C₄×C₅₃	—	2	4	no	—
387	C₂²⋊C₄×C₅₃	—	2	4	no	—
388	C₂²⋊C₄×C₅₃	—	2	4	no	—
389	C₂²⋊C₄×C₅₃	—	2	4	no	—
390	C₂²⋊C₄×C₅₃	—	2	4	no	—
391	C₂²⋊C₄×C₅₃	—	2	4	no	—
392	C₂²⋊C₄×C₅₃	—	4	2	no	—
393	C₂²⋊C₄×C₅₃	—	4	2	no	—
394	C₂²⋊C₄×C₅₃	—	4	2	no	—
395	C₂²⋊C₄×C₅₃	—	4	2	no	—
396	C₂²⋊C₄×C₅₃	—	4	2	no	—
397	C₂²⋊C₄×C₅₃	—	4	2	no	—
398	C₂²⋊C₄×C₅₃	—	4	2	no	—
399	C₂²⋊C₄×C₅₃	—	4	2	no	—
400	C₂²⋊C₄×C₅₃	—	4	2	no	—
401	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
402	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	complemented
403	C₂²⋊C₄×C₅₃	#41	1	4	yes	—
404	C₄²×C₅₃	—	2	4	no	—
405	C₄²×C₅₃	—	2	2	no	—
406	C₄²×C₅₃	—	2	2	no	—
407	C₄²×C₅₃	—	2	2	no	—
408	C₄²×C₅₃	—	2	2	no	—
409	C₄²×C₅₃	—	2	2	no	—
410	C₄²×C₅₃	—	2	2	no	—
411	C₄²×C₅₃	—	2	2	no	—
412	C₄²×C₅₃	—	4	1	no	—
413	C₄²×C₅₃	—	4	1	no	—
414	C₄²×C₅₃	—	4	1	no	—
415	C₄²×C₅₃	—	4	1	no	—
416	C₄²×C₅₃	—	4	1	no	—
417	C₄²×C₅₃	C₂×D₄	1	4	yes	complemented
418	C₂³×C₅₃	—	2	1	no	—
419	C₂³×C₅₃	—	2	1	no	—
420	C₂³×C₅₃	—	2	1	no	—
421	C₂³×C₅₃	—	2	1	no	—
422	C₂³×C₅₃	—	2	1	no	—
423	C₂³×C₅₃	—	2	1	no	—
424	C₂³×C₅₃	—	2	1	no	—
425	C₂³×C₅₃	—	2	1	no	—
426	C₂³×C₅₃	—	2	1	no	—
427	C₂³×C₅₃	—	2	1	no	—
428	C₂³×C₅₃	—	2	2	no	—
429	C₂³×C₅₃	—	2	2	no	—
430	C₂³×C₅₃	—	2	2	no	—
431	C₂³×C₅₃	—	2	2	no	—
432	C₂³×C₅₃	—	2	2	no	—
433	C₂³×C₅₃	—	2	2	no	—
434	C₂³×C₅₃	—	2	2	no	—
435	C₂³×C₅₃	—	2	2	no	—
436	C₂³×C₅₃	—	2	2	no	—
437	C₂³×C₅₃	—	2	2	no	—
438	C₂³×C₅₃	—	2	2	no	—
439	C₂³×C₅₃	—	2	2	no	—
440	C₂³×C₅₃	—	2	2	no	—
441	C₂³×C₅₃	—	2	2	no	—
442	C₂³×C₅₃	—	2	2	no	—
443	C₂³×C₅₃	—	2	2	no	—
444	C₂³×C₅₃	—	2	2	no	—
445	C₂³×C₅₃	—	2	2	no	—
446	C₂³×C₅₃	—	2	2	no	—
447	C₂³×C₅₃	—	2	2	no	—
448	C₂³×C₅₃	—	2	2	no	—
449	C₂³×C₅₃	—	4	8	no	—
450	C₂³×C₅₃	—	4	8	no	—
451	C₂³×C₅₃	—	4	8	no	—
452	C₂³×C₅₃	—	8	4	no	—
453	C₂³×C₅₃	—	8	4	no	—
454	C₂³×C₅₃	—	8	4	no	—
455	C₂³×C₅₃	—	8	4	no	—
456	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
457	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
458	C₂³×C₅₃	C₂×#41	1	2	yes	—
459	C₂³×C₅₃	C₂×#41	1	2	yes	—
460	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
461	Q₈×C₅₃	—	8	4	no	—
462	D₄×C₅₃	—	2	8	no	—
463	D₄×C₅₃	—	4	8	no	—
464	D₄×C₅₃	—	4	8	no	—
465	D₄×C₅₃	—	4	4	no	—
466	D₄×C₅₃	—	4	4	no	—
467	D₄×C₅₃	—	4	4	no	—
468	D₄×C₅₃	—	8	4	no	—
469	D₄×C₅₃	—	8	4	no	—
470	D₄×C₅₃	—	8	4	no	—
471	D₄×C₅₃	—	8	4	no	—
472	D₄×C₅₃	—	8	4	no	—
473	D₄×C₅₃	—	8	4	no	—
474	D₄×C₅₃	—	8	4	no	—
475	C₂×C₄×C₅₃	—	2	1	no	—
476	C₂×C₄×C₅₃	—	2	1	no	—
477	C₂×C₄×C₅₃	—	2	1	no	—
478	C₂×C₄×C₅₃	—	2	1	no	—
479	C₂×C₄×C₅₃	—	2	1	no	—
480	C₂×C₄×C₅₃	—	2	1	no	—
481	C₂×C₄×C₅₃	—	2	1	no	—
482	C₂×C₄×C₅₃	—	2	1	no	—
483	C₂×C₄×C₅₃	—	2	1	no	—
484	C₂×C₄×C₅₃	—	2	1	no	—
485	C₂×C₄×C₅₃	—	2	1	no	—
486	C₂×C₄×C₅₃	—	2	1	no	—
487	C₂×C₄×C₅₃	—	2	1	no	—
488	C₂×C₄×C₅₃	—	2	1	no	—
489	C₂×C₄×C₅₃	—	2	1	no	—
490	C₂×C₄×C₅₃	—	2	1	no	—
491	C₂×C₄×C₅₃	—	2	1	no	—
492	C₂×C₄×C₅₃	—	2	1	no	—
493	C₂×C₄×C₅₃	—	2	8	no	—
494	C₂×C₄×C₅₃	—	2	2	no	—
495	C₂×C₄×C₅₃	—	2	2	no	—
496	C₂×C₄×C₅₃	—	2	2	no	—
497	C₂×C₄×C₅₃	—	2	2	no	—
498	C₂×C₄×C₅₃	—	2	2	no	—
499	C₂×C₄×C₅₃	—	2	1	no	—
500	C₂×C₄×C₅₃	—	2	1	no	—
501	C₂×C₄×C₅₃	—	2	2	no	—
502	C₂×C₄×C₅₃	—	2	2	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	2	no	—
508	C₂×C₄×C₅₃	—	2	2	no	—
509	C₂×C₄×C₅₃	—	2	2	no	—
510	C₂×C₄×C₅₃	—	2	2	no	—
511	C₂×C₄×C₅₃	—	2	2	no	—
512	C₂×C₄×C₅₃	—	2	1	no	—
513	C₂×C₄×C₅₃	—	2	2	no	—
514	C₂×C₄×C₅₃	—	2	2	no	—
515	C₂×C₄×C₅₃	—	2	1	no	—
516	C₂×C₄×C₅₃	—	2	2	no	—
517	C₂×C₄×C₅₃	—	2	1	no	—
518	C₂×C₄×C₅₃	—	4	4	no	—
519	C₂×C₄×C₅₃	—	4	4	no	—
520	C₂×C₄×C₅₃	—	4	4	no	—
521	C₂×C₄×C₅₃	—	4	4	no	—
522	C₂×C₄×C₅₃	—	4	4	no	—
523	C₂×C₄×C₅₃	—	8	4	no	—
524	C₂×C₄×C₅₃	—	8	4	no	—
525	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
531	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
532	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
533	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
534	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
535	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
536	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
537	#35007	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
538	C₂²×C₅₃	—	2	2	no	—
539	C₂²×C₅₃	—	2	2	no	—
540	C₂²×C₅₃	—	2	2	no	—
541	C₂²×C₅₃	—	2	2	no	—
542	C₂²×C₅₃	—	2	2	no	—
543	C₂²×C₅₃	—	2	2	no	—
544	C₂²×C₅₃	—	2	2	no	—
545	C₂²×C₅₃	—	2	2	no	—
546	C₂²×C₅₃	—	2	2	no	—
547	C₂²×C₅₃	—	4	1	no	—
548	C₂²×C₅₃	—	4	1	no	—
549	C₂²×C₅₃	—	4	1	no	—
550	C₂²×C₅₃	—	4	1	no	—
551	C₂²×C₅₃	—	4	2	no	—
552	C₂²×C₅₃	—	4	2	no	—
553	C₂²×C₅₃	—	4	2	no	—
554	C₂²×C₅₃	—	4	2	no	—
555	C₂²×C₅₃	—	4	2	no	—
556	C₂²×C₅₃	—	4	2	no	—
557	C₂²×C₅₃	—	4	2	no	—
558	C₂²×C₅₃	—	4	2	no	—
559	C₂²×C₅₃	—	4	2	no	—
560	C₂²×C₅₃	—	4	2	no	—
561	C₂²×C₅₃	—	4	2	no	—
562	C₂²×C₅₃	—	4	2	no	—
563	C₂²×C₅₃	—	4	2	no	—
564	C₂²×C₅₃	—	4	2	no	—
565	C₂²×C₅₃	—	4	2	no	—
566	C₂²×C₅₃	—	4	2	no	—
567	C₂²×C₅₃	—	4	2	no	—
568	C₂²×C₅₃	—	4	2	no	—
569	C₂²×C₅₃	—	4	2	no	—
570	C₂²×C₅₃	—	4	2	no	—
571	C₂²×C₅₃	—	4	2	no	—
572	C₂²×C₅₃	—	8	16	no	—
573	C₂²×C₅₃	#532	1	4	yes	—
574	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
575	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
576	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
577	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
578	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂²×C₅₃	#585	1	1	yes	characteristic
581	C₄×C₅₃	—	2	2	no	—
582	C₄×C₅₃	—	2	2	no	—
583	C₄×C₅₃	—	2	2	no	—
584	C₄×C₅₃	—	2	2	no	—
585	C₄×C₅₃	—	2	2	no	—
586	C₄×C₅₃	—	2	2	no	—
587	C₄×C₅₃	—	2	2	no	—
588	C₄×C₅₃	—	2	2	no	—
589	C₄×C₅₃	—	2	2	no	—
590	C₄×C₅₃	—	4	2	no	—
591	C₄×C₅₃	—	4	1	no	—
592	C₄×C₅₃	—	4	1	no	—
593	C₄×C₅₃	—	4	2	no	—
594	C₄×C₅₃	—	4	2	no	—
595	C₄×C₅₃	—	4	2	no	—
596	C₄×C₅₃	—	4	2	no	—
597	C₄×C₅₃	—	4	1	no	—
598	C₄×C₅₃	#538	1	4	yes	complemented
599	C₂×#538	C₂×C₅₃	1	2	yes	complemented
600	#2860	C₂×C₅₃	1	1	yes	characteristic, complemented
601	#2858	C₂×C₅₃	1	1	yes	characteristic, complemented
602	#2856	C₂×C₅₃	1	1	yes	characteristic, complemented
603	#2854	C₂×C₅₃	1	1	yes	characteristic, complemented
604	#2662	C₂×C₅₃	1	2	yes	complemented
605	#2661	C₂×C₅₃	1	2	yes	complemented
606	#2555	C₂×C₅₃	1	2	yes	complemented
607	#2554	C₂×C₅₃	1	2	yes	complemented
608	#2512	C₂×C₅₃	1	1	yes	characteristic, complemented
609	#2491	C₂×C₅₃	1	1	yes	characteristic, complemented
610	#2472	C₂×C₅₃	1	2	yes	complemented
611	#2445	C₂×C₅₃	1	1	yes	characteristic, complemented
612	#2440	C₂×C₅₃	1	1	yes	characteristic, complemented
613	#2433	C₂×C₅₃	1	1	yes	characteristic, complemented
614	#2428	C₂×C₅₃	1	1	yes	characteristic, complemented
615	#2424	C₂×C₅₃	1	2	yes	complemented
616	#2416	C₂×C₅₃	1	1	yes	characteristic, complemented
617	#2408	C₂×C₅₃	1	1	yes	characteristic, complemented
618	#2321	C₂×C₅₃	1	2	yes	complemented
619	C₄×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
620	C₂×#390	C₂×C₅₃	1	1	yes	characteristic, complemented
621	C₄²×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
622	C₂×C₅₃	—	2	4	no	—
623	C₂×C₅₃	—	4	2	no	—
624	C₂×C₅₃	—	8	2	no	—
625	C₂×C₅₃	—	8	2	no	—
626	C₂×C₅₃	—	8	2	no	—
627	C₂×C₅₃	C₂×#532	1	1	yes	characteristic
628	C₂×C₅₃	C₂×#538	1	1	yes	characteristic
629	C₂×C₅₃	#3460	1	1	yes	characteristic
630	C₂×C₅₃	#3496	1	1	yes	characteristic
631	C₂×C₅₃	#3498	1	1	yes	characteristic
632	C₂×C₅₃	#3514	1	1	yes	characteristic
633	C₂×C₅₃	#3519	1	1	yes	characteristic
634	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
635	#538	—	2	16	no	—
636	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
637	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
638	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
639	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
640	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
641	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
642	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
643	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
644	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
645	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
646	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
647	C₂×#121	C₂²×C₅₃	1	2	yes	—
648	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
649	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
650	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
651	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
652	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
653	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
654	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
655	C₂×#120	C₂²×C₅₃	1	2	yes	—
656	C₂×#120	C₂²×C₅₃	1	2	yes	—
657	C₂×#120	C₂²×C₅₃	1	2	yes	—
658	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
659	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
660	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
661	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
662	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
664	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
665	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
666	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
667	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
668	#398	C₂²×C₅₃	1	2	yes	complemented
669	#397	C₂²×C₅₃	1	2	yes	complemented
670	#396	C₂²×C₅₃	1	2	yes	complemented
671	#396	C₂²×C₅₃	1	2	yes	complemented
672	#395	C₂²×C₅₃	1	2	yes	complemented
673	#394	C₂²×C₅₃	1	2	yes	—
674	#394	C₂²×C₅₃	1	2	yes	complemented
675	#394	C₂²×C₅₃	1	2	yes	complemented
676	#394	C₂²×C₅₃	1	2	yes	complemented
677	#394	C₂²×C₅₃	1	2	yes	complemented
678	#394	C₂²×C₅₃	1	2	yes	complemented
679	#393	C₂²×C₅₃	1	2	yes	complemented
680	#392	C₂²×C₅₃	1	2	yes	—
681	#392	C₂²×C₅₃	1	2	yes	—
682	#392	C₂²×C₅₃	1	2	yes	—
683	#392	C₂²×C₅₃	1	2	yes	complemented
684	#390	C₂²×C₅₃	1	1	yes	characteristic
685	#390	C₂²×C₅₃	1	1	yes	characteristic
686	#390	C₂²×C₅₃	1	1	yes	characteristic
687	#390	C₂²×C₅₃	1	1	yes	characteristic
688	#390	C₂²×C₅₃	1	1	yes	characteristic
689	#390	C₂²×C₅₃	1	1	yes	characteristic
690	#390	C₂²×C₅₃	1	2	yes	—
691	#390	C₂²×C₅₃	1	1	yes	characteristic
692	#390	C₂²×C₅₃	1	1	yes	characteristic
693	#390	C₂²×C₅₃	1	2	yes	—
694	#390	C₂²×C₅₃	1	2	yes	complemented
695	#390	C₂²×C₅₃	1	2	yes	complemented
696	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
697	#390	C₂²×C₅₃	1	2	yes	complemented
698	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
699	#390	C₂²×C₅₃	1	2	yes	complemented
700	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
701	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
702	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
704	#388	C₂²×C₅₃	1	2	yes	complemented
705	#388	C₂²×C₅₃	1	2	yes	complemented
706	#388	C₂²×C₅₃	1	2	yes	complemented
707	#388	C₂²×C₅₃	1	2	yes	complemented
708	#388	C₂²×C₅₃	1	2	yes	complemented
709	#388	C₂²×C₅₃	1	2	yes	complemented
710	#388	C₂²×C₅₃	1	2	yes	complemented
711	#388	C₂²×C₅₃	1	2	yes	complemented
712	#386	C₂²×C₅₃	1	2	yes	—
713	#386	C₂²×C₅₃	1	2	yes	—
714	#386	C₂²×C₅₃	1	2	yes	complemented
715	#386	C₂²×C₅₃	1	2	yes	complemented
716	#386	C₂²×C₅₃	1	2	yes	complemented
717	#385	C₂²×C₅₃	1	2	yes	—
718	#384	C₂²×C₅₃	1	1	yes	characteristic, complemented
719	#380	C₂²×C₅₃	1	1	yes	characteristic
720	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
721	#379	C₂²×C₅₃	1	2	yes	—
722	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
724	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
725	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
726	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
727	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
728	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
729	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
730	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
731	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
732	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
733	C₄³	C₂²×C₅₃	1	1	yes	characteristic, complemented
734	C₅₃	#35007	1	1	yes	characteristic, direct product factor, Sylow
735	C₂⁵	C₂³×C₅₃	1	2	yes	—
736	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
737	C₂²×D₄	—	2	4	no	—
738	C₂²×D₄	—	4	2	no	—
739	C₂²×D₄	—	4	2	no	—
740	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
741	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
742	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
743	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
744	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
745	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
746	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
747	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
748	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
749	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
750	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
751	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
752	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
753	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
754	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
755	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
756	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
757	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
758	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
759	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
760	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
761	C₄⋊Q₈	—	4	2	no	—
762	#127	—	4	2	no	—
763	#127	—	4	2	no	—
764	#126	—	2	8	no	—
765	#126	—	2	8	no	—
766	#124	—	2	8	no	—
767	#124	—	2	8	no	—
768	#124	—	4	4	no	—
769	#123	—	2	8	no	—
770	#123	—	2	8	no	—
771	C₂²⋊Q₈	—	2	8	no	—
772	#121	—	2	8	no	—
773	#121	—	2	8	no	—
774	#121	—	2	4	no	—
775	#121	—	2	8	no	—
776	#121	—	4	4	no	—
777	#121	—	4	2	no	—
778	#121	—	4	2	no	—
779	#121	—	4	2	no	—
780	#120	—	2	8	no	—
781	#120	—	2	8	no	—
782	#120	—	2	8	no	—
783	C₄×D₄	—	2	8	no	—
784	C₄×D₄	—	2	4	no	—
785	C₄×D₄	—	2	4	no	—
786	C₄×D₄	—	4	2	no	—
787	C₄×D₄	D₄×C₅₃	1	8	yes	complemented
788	C₂×C₄⋊C₄	—	4	2	no	—
789	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
790	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
791	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
792	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
793	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
794	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
795	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
796	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
797	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
798	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
799	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
800	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
801	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
802	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
803	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
804	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
805	C₂×C₂²⋊C₄	—	2	8	no	—
806	C₂×C₂²⋊C₄	—	4	4	no	—
807	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
817	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
818	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
819	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
826	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
828	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
829	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
830	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
831	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
832	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
833	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
834	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
835	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
836	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
837	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
838	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
839	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
840	C₂×C₄²	—	4	2	no	—
841	C₂×C₄²	—	4	2	no	—
842	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
843	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
844	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
845	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
846	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
847	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
848	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
849	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
850	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
851	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
852	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
853	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
854	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
855	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
856	#95	C₂³×C₅₃	1	1	yes	characteristic
857	#95	C₂³×C₅₃	1	1	yes	characteristic
858	#95	C₂³×C₅₃	1	1	yes	characteristic
859	#95	C₂³×C₅₃	1	1	yes	characteristic
860	#95	C₂³×C₅₃	1	1	yes	characteristic
861	#95	C₂³×C₅₃	1	1	yes	characteristic
862	#95	C₂³×C₅₃	1	2	yes	—
863	#95	C₂³×C₅₃	1	2	yes	—
864	#95	C₂³×C₅₃	1	2	yes	—
865	#95	C₂³×C₅₃	1	2	yes	—
866	#95	C₂³×C₅₃	1	2	yes	—
867	#95	C₂³×C₅₃	1	2	yes	—
868	#95	C₂³×C₅₃	1	2	yes	—
869	C₂⁴	—	2	4	no	—
870	C₂⁴	—	2	4	no	—
871	C₂⁴	—	2	4	no	—
872	C₂⁴	—	4	2	no	—
873	C₂⁴	—	4	2	no	—
874	C₂⁴	—	4	2	no	—
875	C₂⁴	—	4	2	no	—
876	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
877	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
878	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
879	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
880	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
881	C₂×Q₈	—	2	4	no	—
882	C₂×Q₈	—	4	2	no	—
883	C₂×Q₈	—	4	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	4	no	—
887	C₂×D₄	—	2	4	no	—
888	C₂×D₄	—	2	4	no	—
889	C₂×D₄	—	2	4	no	—
890	C₂×D₄	—	2	4	no	—
891	C₂×D₄	—	2	4	no	—
892	C₂×D₄	—	2	4	no	—
893	C₂×D₄	—	2	4	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	4	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	4	no	—
899	C₂×D₄	—	2	4	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	4	2	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	—	4	16	no	—
909	C₂×D₄	—	4	2	no	—
910	C₂×D₄	—	4	2	no	—
911	C₂×D₄	—	4	2	no	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	4	2	no	—
915	C₂×D₄	—	4	2	no	—
916	C₂×D₄	—	4	2	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	2	no	—
919	C₂×D₄	—	4	2	no	—
920	C₂×D₄	—	4	2	no	—
921	C₂×D₄	—	4	2	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	4	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	4	no	—
935	C₂²×C₄	—	4	1	no	—
936	C₂²×C₄	—	4	1	no	—
937	C₂²×C₄	—	4	1	no	—
938	C₂²×C₄	—	4	1	no	—
939	C₂²×C₄	—	4	1	no	—
940	C₂²×C₄	—	4	1	no	—
941	C₂²×C₄	—	4	2	no	—
942	C₂²×C₄	—	4	2	no	—
943	C₂²×C₄	—	4	2	no	—
944	C₂²×C₄	—	4	2	no	—
945	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
946	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	complemented
947	C₂²×C₄	#41×C₅₃	1	4	yes	—
948	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
952	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
953	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
954	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
955	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
956	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
959	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
960	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
961	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
962	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
966	C₄⋊C₄	—	2	4	no	—
967	C₄⋊C₄	—	2	4	no	—
968	C₄⋊C₄	—	2	4	no	—
969	C₄⋊C₄	—	2	4	no	—
970	C₄⋊C₄	—	2	4	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	4	2	no	—
979	C₄⋊C₄	—	4	2	no	—
980	C₄⋊C₄	—	4	2	no	—
981	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	complemented
982	C₂²⋊C₄	—	2	4	no	—
983	C₂²⋊C₄	—	2	4	no	—
984	C₂²⋊C₄	—	2	2	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	4	no	—
990	C₂²⋊C₄	—	2	4	no	—
991	C₂²⋊C₄	—	2	4	no	—
992	C₂²⋊C₄	—	2	4	no	—
993	C₂²⋊C₄	—	2	4	no	—
994	C₂²⋊C₄	—	2	4	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	4	no	—
998	C₂²⋊C₄	—	2	4	no	—
999	C₂²⋊C₄	—	2	4	no	—
1000	C₂²⋊C₄	—	2	4	no	—
1001	C₂²⋊C₄	—	2	4	no	—
1002	C₂²⋊C₄	—	2	4	no	—
1003	C₂²⋊C₄	—	4	2	no	—
1004	C₂²⋊C₄	—	4	2	no	—
1005	C₂²⋊C₄	—	4	2	no	—
1006	C₂²⋊C₄	—	4	2	no	—
1007	C₂²⋊C₄	—	4	2	no	—
1008	C₂²⋊C₄	—	4	2	no	—
1009	C₂²⋊C₄	—	4	2	no	—
1010	C₂²⋊C₄	—	4	2	no	—
1011	C₂²⋊C₄	—	4	2	no	—
1012	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	complemented
1014	C₂²⋊C₄	#41×C₅₃	1	4	yes	—
1015	C₄²	—	2	4	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	4	1	no	—
1024	C₄²	—	4	1	no	—
1025	C₄²	—	4	1	no	—
1026	C₄²	—	4	1	no	—
1027	C₄²	—	4	1	no	—
1028	C₄²	C₂×D₄×C₅₃	1	4	yes	complemented
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	2	2	no	—
1051	C₂³	—	2	2	no	—
1052	C₂³	—	2	2	no	—
1053	C₂³	—	2	2	no	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	2	2	no	—
1059	C₂³	—	2	2	no	—
1060	C₂³	—	4	8	no	—
1061	C₂³	—	4	8	no	—
1062	C₂³	—	4	8	no	—
1063	C₂³	—	8	4	no	—
1064	C₂³	—	8	4	no	—
1065	C₂³	—	8	4	no	—
1066	C₂³	—	8	4	no	—
1067	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1068	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1069	C₂³	C₂×#41×C₅₃	1	2	yes	—
1070	C₂³	C₂×#41×C₅₃	1	2	yes	—
1071	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1072	Q₈	—	8	4	no	—
1073	D₄	—	2	8	no	—
1074	D₄	—	4	8	no	—
1075	D₄	—	4	8	no	—
1076	D₄	—	4	4	no	—
1077	D₄	—	4	4	no	—
1078	D₄	—	4	4	no	—
1079	D₄	—	8	4	no	—
1080	D₄	—	8	4	no	—
1081	D₄	—	8	4	no	—
1082	D₄	—	8	4	no	—
1083	D₄	—	8	4	no	—
1084	D₄	—	8	4	no	—
1085	D₄	—	8	4	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	8	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	4	4	no	—
1130	C₂×C₄	—	4	4	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	8	4	no	—
1135	C₂×C₄	—	8	4	no	—
1136	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1137	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1138	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1140	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1141	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1142	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1143	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1144	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1145	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1146	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1147	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1148	C₂²	—	2	2	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	8	16	no	—
1183	C₂²	C₅₃×#532	1	4	yes	—
1184	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1185	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1186	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1187	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1188	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1189	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1190	C₂²	C₅₃×#585	1	1	yes	characteristic
1191	C₄	—	2	2	no	—
1192	C₄	—	2	2	no	—
1193	C₄	—	2	2	no	—
1194	C₄	—	2	2	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	2	2	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	2	no	—
1203	C₄	—	4	2	no	—
1204	C₄	—	4	2	no	—
1205	C₄	—	4	2	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	2	no	—
1208	C₄	C₅₃×#538	1	4	yes	complemented
1209	C₂	—	2	4	no	—
1210	C₂	—	4	2	no	—
1211	C₂	—	8	2	no	—
1212	C₂	—	8	2	no	—
1213	C₂	—	8	2	no	—
1214	C₂	C₂×C₅₃×#532	1	1	yes	characteristic
1215	C₂	C₂×C₅₃×#538	1	1	yes	characteristic
1216	C₂	C₅₃×#3460	1	1	yes	characteristic
1217	C₂	C₅₃×#3496	1	1	yes	characteristic
1218	C₂	C₅₃×#3498	1	1	yes	characteristic
1219	C₂	C₅₃×#3514	1	1	yes	characteristic
1220	C₂	C₅₃×#3519	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. C₂×C₅₃×#538	C₂	semidirect
2. C₅₃×#2860	C₂	semidirect
3. C₅₃×#2858	C₂	semidirect
4. C₅₃×#2856	C₂	semidirect
5. C₅₃×#2854	C₂	semidirect
6. C₅₃×#2662	C₂	semidirect
7. C₅₃×#2661	C₂	semidirect
8. C₅₃×#2555	C₂	semidirect
9. C₅₃×#2554	C₂	semidirect
10. C₅₃×#2512	C₂	semidirect
11. C₅₃×#2491	C₂	semidirect
12. C₅₃×#2472	C₂	semidirect
13. C₅₃×#2445	C₂	semidirect
14. C₅₃×#2440	C₂	semidirect
15. C₅₃×#2433	C₂	semidirect
16. C₅₃×#2428	C₂	semidirect
17. C₅₃×#2424	C₂	semidirect
18. C₅₃×#2416	C₂	semidirect
19. C₅₃×#2408	C₂	semidirect
20. C₅₃×#2321	C₂	semidirect
21. C₄×#121×C₅₃	C₂	semidirect
22. C₂×C₅₃×#390	C₂	semidirect
23. C₄²×D₄×C₅₃	C₂	semidirect
26. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
29. C₂×#126×C₅₃	C₂²	semidirect
30. C₂×#126×C₅₃	C₂²	semidirect
31. C₂×#124×C₅₃	C₂²	semidirect
32. C₂×#124×C₅₃	C₂²	semidirect
33. C₂×#124×C₅₃	C₂²	semidirect
34. C₂×#123×C₅₃	C₂²	semidirect
35. C₂×#123×C₅₃	C₂²	semidirect
41. C₂×#121×C₅₃	C₂²	semidirect
42. C₂×#121×C₅₃	C₂²	semidirect
43. C₂×#121×C₅₃	C₂²	semidirect
44. C₂×#121×C₅₃	C₂²	semidirect
52. C₂×C₄×D₄×C₅₃	C₂²	semidirect
57. C₂²×C₄²×C₅₃	C₂²	semidirect
58. C₅₃×#398	C₂²	semidirect
59. C₅₃×#397	C₂²	semidirect
60. C₅₃×#396	C₂²	semidirect
61. C₅₃×#396	C₂²	semidirect
62. C₅₃×#395	C₂²	semidirect
64. C₅₃×#394	C₂²	semidirect
65. C₅₃×#394	C₂²	semidirect
66. C₅₃×#394	C₂²	semidirect
67. C₅₃×#394	C₂²	semidirect
68. C₅₃×#394	C₂²	semidirect
69. C₅₃×#393	C₂²	semidirect
73. C₅₃×#392	C₂²	semidirect
84. C₅₃×#390	C₂²	semidirect
85. C₅₃×#390	C₂²	semidirect
86. C₅₃×#390	C₂²	semidirect
87. C₅₃×#390	C₂²	semidirect
88. C₅₃×#390	C₂²	semidirect
89. C₅₃×#390	C₂²	semidirect
90. C₅₃×#389	C₂²	semidirect
91. C₅₃×#389	C₂²	semidirect
92. C₅₃×#389	C₂²	semidirect
93. C₅₃×#389	C₂²	semidirect
94. C₅₃×#388	C₂²	semidirect
95. C₅₃×#388	C₂²	semidirect
96. C₅₃×#388	C₂²	semidirect
97. C₅₃×#388	C₂²	semidirect
98. C₅₃×#388	C₂²	semidirect
99. C₅₃×#388	C₂²	semidirect
100. C₅₃×#388	C₂²	semidirect
101. C₅₃×#388	C₂²	semidirect
104. C₅₃×#386	C₂²	semidirect
105. C₅₃×#386	C₂²	semidirect
106. C₅₃×#386	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. C₄³×C₅₃	C₂²	semidirect
176. C₄×D₄×C₅₃	D₄	semidirect
335. C₂²×C₄×C₅₃	C₂×D₄	semidirect
370. C₄⋊C₄×C₅₃	C₂×D₄	semidirect
402. C₂²⋊C₄×C₅₃	C₂×D₄	semidirect
417. C₄²×C₅₃	C₂×D₄	semidirect
537. #35007	C₅₃	direct (N × H)
598. C₄×C₅₃	#538	semidirect
599. C₂×#538	C₂×C₅₃	semidirect
600. #2860	C₂×C₅₃	semidirect
601. #2858	C₂×C₅₃	semidirect
602. #2856	C₂×C₅₃	semidirect
603. #2854	C₂×C₅₃	semidirect
604. #2662	C₂×C₅₃	semidirect
605. #2661	C₂×C₅₃	semidirect
606. #2555	C₂×C₅₃	semidirect
607. #2554	C₂×C₅₃	semidirect
608. #2512	C₂×C₅₃	semidirect
609. #2491	C₂×C₅₃	semidirect
610. #2472	C₂×C₅₃	semidirect
611. #2445	C₂×C₅₃	semidirect
612. #2440	C₂×C₅₃	semidirect
613. #2433	C₂×C₅₃	semidirect
614. #2428	C₂×C₅₃	semidirect
615. #2424	C₂×C₅₃	semidirect
616. #2416	C₂×C₅₃	semidirect
617. #2408	C₂×C₅₃	semidirect
618. #2321	C₂×C₅₃	semidirect
619. C₄×#121	C₂×C₅₃	semidirect
620. C₂×#390	C₂×C₅₃	semidirect
621. C₄²×D₄	C₂×C₅₃	semidirect
636. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
639. C₂×#126	C₂²×C₅₃	semidirect
640. C₂×#126	C₂²×C₅₃	semidirect
641. C₂×#124	C₂²×C₅₃	semidirect
642. C₂×#124	C₂²×C₅₃	semidirect
643. C₂×#124	C₂²×C₅₃	semidirect
644. C₂×#123	C₂²×C₅₃	semidirect
645. C₂×#123	C₂²×C₅₃	semidirect
651. C₂×#121	C₂²×C₅₃	semidirect
652. C₂×#121	C₂²×C₅₃	semidirect
653. C₂×#121	C₂²×C₅₃	semidirect
654. C₂×#121	C₂²×C₅₃	semidirect
662. C₂×C₄×D₄	C₂²×C₅₃	semidirect
667. C₂²×C₄²	C₂²×C₅₃	semidirect
668. #398	C₂²×C₅₃	semidirect
669. #397	C₂²×C₅₃	semidirect
670. #396	C₂²×C₅₃	semidirect
671. #396	C₂²×C₅₃	semidirect
672. #395	C₂²×C₅₃	semidirect
674. #394	C₂²×C₅₃	semidirect
675. #394	C₂²×C₅₃	semidirect
676. #394	C₂²×C₅₃	semidirect
677. #394	C₂²×C₅₃	semidirect
678. #394	C₂²×C₅₃	semidirect
679. #393	C₂²×C₅₃	semidirect
683. #392	C₂²×C₅₃	semidirect
694. #390	C₂²×C₅₃	semidirect
695. #390	C₂²×C₅₃	semidirect
696. #390	C₂²×C₅₃	semidirect
697. #390	C₂²×C₅₃	semidirect
698. #390	C₂²×C₅₃	semidirect
699. #390	C₂²×C₅₃	semidirect
700. #389	C₂²×C₅₃	semidirect
701. #389	C₂²×C₅₃	semidirect
702. #389	C₂²×C₅₃	semidirect
703. #389	C₂²×C₅₃	semidirect
704. #388	C₂²×C₅₃	semidirect
705. #388	C₂²×C₅₃	semidirect
706. #388	C₂²×C₅₃	semidirect
707. #388	C₂²×C₅₃	semidirect
708. #388	C₂²×C₅₃	semidirect
709. #388	C₂²×C₅₃	semidirect
710. #388	C₂²×C₅₃	semidirect
711. #388	C₂²×C₅₃	semidirect
714. #386	C₂²×C₅₃	semidirect
715. #386	C₂²×C₅₃	semidirect
716. #386	C₂²×C₅₃	semidirect
718. #384	C₂²×C₅₃	semidirect
720. #380	C₂²×C₅₃	semidirect
722. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
723. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
724. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
725. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
729. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
730. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
731. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
732. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
733. C₄³	C₂²×C₅₃	semidirect
734. C₅₃	#35007	direct (N × H)
787. C₄×D₄	D₄×C₅₃	semidirect
946. C₂²×C₄	C₂×D₄×C₅₃	semidirect
981. C₄⋊C₄	C₂×D₄×C₅₃	semidirect
1013. C₂²⋊C₄	C₂×D₄×C₅₃	semidirect
1028. C₄²	C₂×D₄×C₅₃	semidirect
1208. C₄	C₅₃×#538	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#538	2
C₅₃×#2860	2
C₅₃×#2858	2
C₅₃×#2856	2
C₅₃×#2854	2
C₅₃×#2662	2
C₅₃×#2661	2
C₅₃×#2555	2
C₅₃×#2554	2
C₅₃×#2512	2
C₅₃×#2491	2
C₅₃×#2472	2
C₅₃×#2445	2
C₅₃×#2440	2
C₅₃×#2433	2
C₅₃×#2428	2
C₅₃×#2424	2
C₅₃×#2416	2
C₅₃×#2408	2
C₅₃×#2321	2
C₄×#121×C₅₃	2
C₂×C₅₃×#390	2
C₄²×D₄×C₅₃	2
#35007	53

Subgroups — C53×#35007 #27242519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#35007 #27242519