Subgroups — C₅₃×#34407 #27241919

Order 13568.

2890 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#534	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2377	C₂	1	2	yes	maximal, complemented
3	C₅₃×#2376	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2375	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2363	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2359	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2359	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2358	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2342	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊C₄×C₅₃	C₂	1	2	yes	maximal, complemented
12	C₅₃×#2335	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2333	C₂	1	2	yes	maximal, complemented
14	C₅₃×#2324	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2321	C₂	1	2	yes	maximal, complemented
16	C₅₃×#2321	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2309	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#120×C₅₃	C₂	1	2	yes	maximal, complemented
19	C₂×C₅₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₅₃×#534	C₄	1	16	yes	complemented
24	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#123×C₅₃	C₂²	1	2	yes	—
26	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#121×C₅₃	C₂²	1	2	yes	—
28	C₂×#121×C₅₃	C₂²	1	2	yes	—
29	C₂×#120×C₅₃	C₂²	1	2	yes	—
30	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
36	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
39	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
40	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
43	C₅₃×#390	C₂²	1	2	yes	—
44	C₅₃×#390	C₂²	1	1	yes	characteristic
45	C₅₃×#390	C₂²	1	1	yes	characteristic
46	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#390	C₂²	1	2	yes	complemented
49	C₅₃×#390	C₂²	1	2	yes	complemented
50	C₅₃×#390	C₂²	1	2	yes	complemented
51	C₅₃×#390	C₂²	1	2	yes	complemented
52	C₅₃×#390	C₂²	1	2	yes	complemented
53	C₅₃×#389	C₂²	1	2	yes	complemented
54	C₅₃×#389	C₂²	1	2	yes	complemented
55	C₅₃×#388	C₂²	1	2	yes	complemented
56	C₅₃×#388	C₂²	1	2	yes	complemented
57	C₅₃×#388	C₂²	1	2	yes	complemented
58	C₅₃×#388	C₂²	1	2	yes	complemented
59	C₅₃×#388	C₂²	1	2	yes	complemented
60	C₅₃×#388	C₂²	1	2	yes	complemented
61	C₅₃×#388	C₂²	1	2	yes	complemented
62	C₅₃×#388	C₂²	1	2	yes	complemented
63	C₅₃×#388	C₂²	1	2	yes	complemented
64	C₅₃×#388	C₂²	1	2	yes	complemented
65	C₅₃×#388	C₂²	1	2	yes	complemented
66	C₅₃×#388	C₂²	1	2	yes	complemented
67	C₅₃×#387	C₂²	1	2	yes	complemented
68	C₅₃×#387	C₂²	1	2	yes	complemented
69	C₅₃×#387	C₂²	1	2	yes	complemented
70	C₅₃×#387	C₂²	1	2	yes	complemented
71	C₅₃×#386	C₂²	1	2	yes	—
72	C₅₃×#386	C₂²	1	1	yes	characteristic
73	C₅₃×#386	C₂²	1	1	yes	characteristic
74	C₅₃×#386	C₂²	1	2	yes	—
75	C₅₃×#386	C₂²	1	2	yes	—
76	C₅₃×#386	C₂²	1	2	yes	complemented
77	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#386	C₂²	1	2	yes	complemented
80	C₅₃×#386	C₂²	1	2	yes	complemented
81	C₅₃×#386	C₂²	1	2	yes	complemented
82	C₅₃×#386	C₂²	1	2	yes	complemented
83	C₅₃×#386	C₂²	1	2	yes	complemented
84	C₅₃×#386	C₂²	1	2	yes	complemented
85	C₅₃×#385	C₂²	1	2	yes	complemented
86	C₅₃×#385	C₂²	1	2	yes	complemented
87	C₅₃×#385	C₂²	1	2	yes	complemented
88	C₅₃×#385	C₂²	1	2	yes	complemented
89	C₅₃×#385	C₂²	1	2	yes	complemented
90	C₅₃×#385	C₂²	1	2	yes	complemented
91	C₅₃×#381	C₂²	1	2	yes	complemented
92	C₅₃×#380	C₂²	1	2	yes	complemented
93	C₅₃×#380	C₂²	1	2	yes	complemented
94	C₅₃×#379	C₂²	1	2	yes	—
95	C₅₃×#379	C₂²	1	2	yes	complemented
96	C₅₃×#379	C₂²	1	2	yes	complemented
97	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
98	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
106	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
107	C₂×#95×C₅₃	C₂²	1	2	yes	complemented
108	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
109	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
110	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₅₃	—	4	2	no	—
112	C₂²×D₄×C₅₃	—	4	2	no	—
113	C₂²×D₄×C₅₃	—	4	2	no	—
114	C₂²×D₄×C₅₃	—	4	2	no	—
115	C₂²×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
116	C₂²×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
117	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
119	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
120	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
123	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₅₃	—	4	4	no	—
126	C₂³×C₄×C₅₃	—	4	2	no	—
127	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
133	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
136	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
137	#123×C₅₃	C₂×C₄	1	16	yes	complemented
138	#123×C₅₃	C₂×C₄	1	8	yes	complemented
139	#123×C₅₃	C₂×C₄	1	8	yes	complemented
140	#121×C₅₃	C₂×C₄	1	16	yes	complemented
141	#121×C₅₃	C₂×C₄	1	16	yes	complemented
142	#120×C₅₃	C₂×C₄	1	16	yes	complemented
143	#120×C₅₃	C₂×C₄	1	8	yes	complemented
144	#120×C₅₃	C₂×C₄	1	8	yes	complemented
145	C₄×D₄×C₅₃	—	4	4	no	—
146	C₄×D₄×C₅₃	—	4	4	no	—
147	C₄×D₄×C₅₃	—	4	4	no	—
148	C₄×D₄×C₅₃	—	4	4	no	—
149	#117×C₅₃	—	4	2	no	—
150	#117×C₅₃	—	4	2	no	—
151	#117×C₅₃	—	4	4	no	—
152	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
164	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
165	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
166	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
167	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
180	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
187	C₂×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	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
200	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
206	#95×C₅₃	C₂³	1	2	yes	—
207	#95×C₅₃	C₂³	1	2	yes	—
208	#95×C₅₃	C₂³	1	2	yes	—
209	#95×C₅₃	C₂³	1	2	yes	—
210	#95×C₅₃	C₂³	1	2	yes	—
211	#95×C₅₃	C₂³	1	2	yes	—
212	#95×C₅₃	C₂³	1	2	yes	—
213	#95×C₅₃	C₂³	1	2	yes	—
214	#95×C₅₃	C₂³	1	2	yes	—
215	#95×C₅₃	C₂³	1	2	yes	—
216	#95×C₅₃	C₂³	1	2	yes	—
217	#95×C₅₃	C₂³	1	2	yes	—
218	#95×C₅₃	C₂³	1	2	yes	—
219	#95×C₅₃	C₂³	1	2	yes	—
220	#95×C₅₃	C₂³	1	2	yes	—
221	#95×C₅₃	C₂³	1	2	yes	—
222	C₂⁴×C₅₃	—	2	2	no	—
223	C₂⁴×C₅₃	—	2	2	no	—
224	C₂⁴×C₅₃	—	2	2	no	—
225	C₂⁴×C₅₃	—	2	2	no	—
226	C₂⁴×C₅₃	—	4	2	no	—
227	C₂⁴×C₅₃	—	4	2	no	—
228	C₂⁴×C₅₃	—	4	2	no	—
229	C₂⁴×C₅₃	—	4	2	no	—
230	C₂⁴×C₅₃	—	4	1	no	—
231	C₂⁴×C₅₃	—	4	1	no	—
232	C₂⁴×C₅₃	—	4	2	no	—
233	C₂⁴×C₅₃	—	4	2	no	—
234	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
235	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
236	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	complemented
237	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
239	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
240	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
241	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
243	C₂×D₄×C₅₃	—	2	4	no	—
244	C₂×D₄×C₅₃	—	2	4	no	—
245	C₂×D₄×C₅₃	—	4	2	no	—
246	C₂×D₄×C₅₃	—	4	2	no	—
247	C₂×D₄×C₅₃	—	4	16	no	—
248	C₂×D₄×C₅₃	—	4	1	no	—
249	C₂×D₄×C₅₃	—	4	1	no	—
250	C₂×D₄×C₅₃	—	4	1	no	—
251	C₂×D₄×C₅₃	—	4	1	no	—
252	C₂×D₄×C₅₃	—	4	1	no	—
253	C₂×D₄×C₅₃	—	4	1	no	—
254	C₂×D₄×C₅₃	—	4	1	no	—
255	C₂×D₄×C₅₃	—	4	1	no	—
256	C₂×D₄×C₅₃	—	4	2	no	—
257	C₂×D₄×C₅₃	—	4	2	no	—
258	C₂×D₄×C₅₃	—	4	2	no	—
259	C₂×D₄×C₅₃	—	4	2	no	—
260	C₂×D₄×C₅₃	—	4	16	no	—
261	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	—
262	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	—
263	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	—
264	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
265	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
266	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
267	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
268	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	complemented
269	C₂²×C₄×C₅₃	—	2	2	no	—
270	C₂²×C₄×C₅₃	—	2	2	no	—
271	C₂²×C₄×C₅₃	—	2	4	no	—
272	C₂²×C₄×C₅₃	—	2	4	no	—
273	C₂²×C₄×C₅₃	—	2	4	no	—
274	C₂²×C₄×C₅₃	—	2	4	no	—
275	C₂²×C₄×C₅₃	—	2	4	no	—
276	C₂²×C₄×C₅₃	—	2	4	no	—
277	C₂²×C₄×C₅₃	—	4	2	no	—
278	C₂²×C₄×C₅₃	—	4	1	no	—
279	C₂²×C₄×C₅₃	—	4	2	no	—
280	C₂²×C₄×C₅₃	—	4	2	no	—
281	C₂²×C₄×C₅₃	—	4	2	no	—
282	C₂²×C₄×C₅₃	—	4	2	no	—
283	C₂²×C₄×C₅₃	—	4	1	no	—
284	C₂²×C₄×C₅₃	—	4	2	no	—
285	C₂²×C₄×C₅₃	—	4	1	no	—
286	C₂²×C₄×C₅₃	—	4	1	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	—	4	2	no	—
293	C₂²×C₄×C₅₃	—	4	2	no	—
294	C₂²×C₄×C₅₃	—	4	16	no	—
295	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
296	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	complemented
297	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
298	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
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	2	yes	—
304	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₅₃	—	2	4	no	—
312	C₄⋊C₄×C₅₃	—	4	2	no	—
313	C₄⋊C₄×C₅₃	—	4	1	no	—
314	C₄⋊C₄×C₅₃	—	4	2	no	—
315	C₄⋊C₄×C₅₃	—	4	1	no	—
316	C₄⋊C₄×C₅₃	—	4	2	no	—
317	C₄⋊C₄×C₅₃	—	4	2	no	—
318	C₄⋊C₄×C₅₃	—	4	2	no	—
319	C₄⋊C₄×C₅₃	—	4	2	no	—
320	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	complemented
321	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	complemented
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	—	4	2	no	—
328	C₂²⋊C₄×C₅₃	—	4	2	no	—
329	C₂²⋊C₄×C₅₃	—	4	1	no	—
330	C₂²⋊C₄×C₅₃	—	4	2	no	—
331	C₂²⋊C₄×C₅₃	—	4	1	no	—
332	C₂²⋊C₄×C₅₃	—	4	2	no	—
333	C₂²⋊C₄×C₅₃	—	4	2	no	—
334	C₂²⋊C₄×C₅₃	—	4	2	no	—
335	C₂²⋊C₄×C₅₃	—	4	2	no	—
336	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	C₂²×C₄	1	8	yes	—
346	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
347	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
348	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
349	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	complemented
350	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	complemented
351	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	complemented
352	C₄²×C₅₃	—	2	4	no	—
353	C₄²×C₅₃	—	4	2	no	—
354	C₄²×C₅₃	—	4	1	no	—
355	C₄²×C₅₃	—	4	2	no	—
356	C₄²×C₅₃	—	4	1	no	—
357	C₄²×C₅₃	—	4	2	no	—
358	C₄²×C₅₃	—	4	2	no	—
359	C₄²×C₅₃	—	4	2	no	—
360	C₄²×C₅₃	—	4	2	no	—
361	C₂³×C₅₃	—	2	2	no	—
362	C₂³×C₅₃	—	2	2	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	1	no	—
368	C₂³×C₅₃	—	2	1	no	—
369	C₂³×C₅₃	—	2	2	no	—
370	C₂³×C₅₃	—	2	2	no	—
371	C₂³×C₅₃	—	2	1	no	—
372	C₂³×C₅₃	—	2	1	no	—
373	C₂³×C₅₃	—	2	2	no	—
374	C₂³×C₅₃	—	2	2	no	—
375	C₂³×C₅₃	—	2	1	no	—
376	C₂³×C₅₃	—	2	1	no	—
377	C₂³×C₅₃	—	2	1	no	—
378	C₂³×C₅₃	—	2	1	no	—
379	C₂³×C₅₃	—	2	2	no	—
380	C₂³×C₅₃	—	2	2	no	—
381	C₂³×C₅₃	—	2	2	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	8	no	—
387	C₂³×C₅₃	—	4	8	no	—
388	C₂³×C₅₃	—	4	4	no	—
389	C₂³×C₅₃	—	4	8	no	—
390	C₂³×C₅₃	—	4	8	no	—
391	C₂³×C₅₃	—	4	4	no	—
392	C₂³×C₅₃	—	4	4	no	—
393	C₂³×C₅₃	—	4	8	no	—
394	C₂³×C₅₃	—	8	2	no	—
395	C₂³×C₅₃	—	8	2	no	—
396	C₂³×C₅₃	—	8	4	no	—
397	C₂³×C₅₃	—	8	2	no	—
398	C₂³×C₅₃	—	8	2	no	—
399	C₂³×C₅₃	—	8	4	no	—
400	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
401	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
402	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
403	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
404	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
405	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
406	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
407	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
408	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
409	D₄×C₅₃	—	2	16	no	—
410	D₄×C₅₃	—	4	4	no	—
411	D₄×C₅₃	—	4	4	no	—
412	D₄×C₅₃	—	4	4	no	—
413	D₄×C₅₃	—	4	4	no	—
414	D₄×C₅₃	—	4	8	no	—
415	D₄×C₅₃	—	4	8	no	—
416	D₄×C₅₃	—	4	8	no	—
417	C₂×C₄×C₅₃	—	2	8	no	—
418	C₂×C₄×C₅₃	—	2	2	no	—
419	C₂×C₄×C₅₃	—	2	2	no	—
420	C₂×C₄×C₅₃	—	2	1	no	—
421	C₂×C₄×C₅₃	—	2	1	no	—
422	C₂×C₄×C₅₃	—	2	1	no	—
423	C₂×C₄×C₅₃	—	2	1	no	—
424	C₂×C₄×C₅₃	—	2	2	no	—
425	C₂×C₄×C₅₃	—	2	2	no	—
426	C₂×C₄×C₅₃	—	2	2	no	—
427	C₂×C₄×C₅₃	—	2	2	no	—
428	C₂×C₄×C₅₃	—	2	2	no	—
429	C₂×C₄×C₅₃	—	2	2	no	—
430	C₂×C₄×C₅₃	—	2	2	no	—
431	C₂×C₄×C₅₃	—	2	2	no	—
432	C₂×C₄×C₅₃	—	2	2	no	—
433	C₂×C₄×C₅₃	—	2	2	no	—
434	C₂×C₄×C₅₃	—	2	2	no	—
435	C₂×C₄×C₅₃	—	2	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	2	no	—
441	C₂×C₄×C₅₃	—	2	2	no	—
442	C₂×C₄×C₅₃	—	2	2	no	—
443	C₂×C₄×C₅₃	—	2	2	no	—
444	C₂×C₄×C₅₃	—	2	2	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	—	4	8	no	—
452	C₂×C₄×C₅₃	—	4	4	no	—
453	C₂×C₄×C₅₃	—	4	4	no	—
454	C₂×C₄×C₅₃	—	4	8	no	—
455	C₂×C₄×C₅₃	—	4	8	no	—
456	C₂×C₄×C₅₃	—	4	4	no	—
457	C₂×C₄×C₅₃	—	8	4	no	—
458	C₂×C₄×C₅₃	—	8	4	no	—
459	C₂×C₄×C₅₃	—	8	4	no	—
460	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
461	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
462	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
463	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
464	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
465	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
466	#34407	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
467	C₂²×C₅₃	—	2	4	no	—
468	C₂²×C₅₃	—	2	2	no	—
469	C₂²×C₅₃	—	2	2	no	—
470	C₂²×C₅₃	—	2	4	no	—
471	C₂²×C₅₃	—	2	2	no	—
472	C₂²×C₅₃	—	2	4	no	—
473	C₂²×C₅₃	—	2	2	no	—
474	C₂²×C₅₃	—	2	2	no	—
475	C₂²×C₅₃	—	2	2	no	—
476	C₂²×C₅₃	—	2	4	no	—
477	C₂²×C₅₃	—	2	4	no	—
478	C₂²×C₅₃	—	2	4	no	—
479	C₂²×C₅₃	—	2	4	no	—
480	C₂²×C₅₃	—	2	4	no	—
481	C₂²×C₅₃	—	2	4	no	—
482	C₂²×C₅₃	—	4	16	no	—
483	C₂²×C₅₃	—	4	1	no	—
484	C₂²×C₅₃	—	4	1	no	—
485	C₂²×C₅₃	—	4	2	no	—
486	C₂²×C₅₃	—	4	1	no	—
487	C₂²×C₅₃	—	4	1	no	—
488	C₂²×C₅₃	—	4	1	no	—
489	C₂²×C₅₃	—	4	1	no	—
490	C₂²×C₅₃	—	4	2	no	—
491	C₂²×C₅₃	—	4	1	no	—
492	C₂²×C₅₃	—	4	1	no	—
493	C₂²×C₅₃	—	4	2	no	—
494	C₂²×C₅₃	—	4	2	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	—	8	8	no	—
500	C₂²×C₅₃	—	8	8	no	—
501	C₂²×C₅₃	#518	1	4	yes	—
502	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
503	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
504	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
505	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
506	C₂²×C₅₃	#585	1	2	yes	—
507	C₄×C₅₃	—	2	2	no	—
508	C₄×C₅₃	—	2	2	no	—
509	C₄×C₅₃	—	2	4	no	—
510	C₄×C₅₃	—	2	4	no	—
511	C₄×C₅₃	—	2	4	no	—
512	C₄×C₅₃	—	2	4	no	—
513	C₄×C₅₃	—	4	2	no	—
514	C₄×C₅₃	—	4	2	no	—
515	C₄×C₅₃	—	4	2	no	—
516	C₄×C₅₃	—	4	2	no	—
517	C₄×C₅₃	—	4	2	no	—
518	C₄×C₅₃	—	4	2	no	—
519	C₄×C₅₃	—	4	2	no	—
520	C₂×#534	C₂×C₅₃	1	1	yes	characteristic
521	#2377	C₂×C₅₃	1	2	yes	complemented
522	#2376	C₂×C₅₃	1	1	yes	characteristic, complemented
523	#2375	C₂×C₅₃	1	1	yes	characteristic, complemented
524	#2374	C₂×C₅₃	1	1	yes	characteristic, complemented
525	#2363	C₂×C₅₃	1	2	yes	complemented
526	#2359	C₂×C₅₃	1	2	yes	complemented
527	#2359	C₂×C₅₃	1	2	yes	complemented
528	#2358	C₂×C₅₃	1	1	yes	characteristic, complemented
529	#2342	C₂×C₅₃	1	2	yes	complemented
530	D₄×C₂²⋊C₄	C₂×C₅₃	1	2	yes	complemented
531	#2335	C₂×C₅₃	1	2	yes	complemented
532	#2333	C₂×C₅₃	1	2	yes	complemented
533	#2324	C₂×C₅₃	1	2	yes	complemented
534	#2321	C₂×C₅₃	1	2	yes	complemented
535	#2321	C₂×C₅₃	1	2	yes	complemented
536	#2309	C₂×C₅₃	1	1	yes	characteristic, complemented
537	C₄×#120	C₂×C₅₃	1	2	yes	complemented
538	C₂×#386	C₂×C₅₃	1	1	yes	characteristic, complemented
539	C₂×C₅₃	—	2	4	no	—
540	C₂×C₅₃	—	4	2	no	—
541	C₂×C₅₃	—	4	2	no	—
542	C₂×C₅₃	—	4	4	no	—
543	C₂×C₅₃	—	4	2	no	—
544	C₂×C₅₃	—	4	2	no	—
545	C₂×C₅₃	C₂×#518	1	1	yes	characteristic
546	C₂×C₅₃	C₄×H(5,𝔽₂)	1	2	yes	—
547	C₂×C₅₃	#3532	1	1	yes	characteristic
548	C₂×C₅₃	#3533	1	1	yes	characteristic
549	C₂×C₅₃	#3542	1	2	yes	—
550	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
551	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
552	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
553	#534	C₄×C₅₃	1	16	yes	complemented
554	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
555	C₂×#123	C₂²×C₅₃	1	2	yes	—
556	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
557	C₂×#121	C₂²×C₅₃	1	2	yes	—
558	C₂×#121	C₂²×C₅₃	1	2	yes	—
559	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
560	C₂×#120	C₂²×C₅₃	1	2	yes	—
561	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
562	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
563	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
564	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
565	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
566	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
567	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
568	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
569	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
570	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
571	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
572	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
573	#390	C₂²×C₅₃	1	2	yes	—
574	#390	C₂²×C₅₃	1	1	yes	characteristic
575	#390	C₂²×C₅₃	1	1	yes	characteristic
576	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
577	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
578	#390	C₂²×C₅₃	1	2	yes	complemented
579	#390	C₂²×C₅₃	1	2	yes	complemented
580	#390	C₂²×C₅₃	1	2	yes	complemented
581	#390	C₂²×C₅₃	1	2	yes	complemented
582	#390	C₂²×C₅₃	1	2	yes	complemented
583	#389	C₂²×C₅₃	1	2	yes	complemented
584	#389	C₂²×C₅₃	1	2	yes	complemented
585	#388	C₂²×C₅₃	1	2	yes	complemented
586	#388	C₂²×C₅₃	1	2	yes	complemented
587	#388	C₂²×C₅₃	1	2	yes	complemented
588	#388	C₂²×C₅₃	1	2	yes	complemented
589	#388	C₂²×C₅₃	1	2	yes	complemented
590	#388	C₂²×C₅₃	1	2	yes	complemented
591	#388	C₂²×C₅₃	1	2	yes	complemented
592	#388	C₂²×C₅₃	1	2	yes	complemented
593	#388	C₂²×C₅₃	1	2	yes	complemented
594	#388	C₂²×C₅₃	1	2	yes	complemented
595	#388	C₂²×C₅₃	1	2	yes	complemented
596	#388	C₂²×C₅₃	1	2	yes	complemented
597	#387	C₂²×C₅₃	1	2	yes	complemented
598	#387	C₂²×C₅₃	1	2	yes	complemented
599	#387	C₂²×C₅₃	1	2	yes	complemented
600	#387	C₂²×C₅₃	1	2	yes	complemented
601	#386	C₂²×C₅₃	1	2	yes	—
602	#386	C₂²×C₅₃	1	2	yes	—
603	#386	C₂²×C₅₃	1	2	yes	—
604	#386	C₂²×C₅₃	1	1	yes	characteristic
605	#386	C₂²×C₅₃	1	1	yes	characteristic
606	#386	C₂²×C₅₃	1	2	yes	complemented
607	#386	C₂²×C₅₃	1	2	yes	complemented
608	#386	C₂²×C₅₃	1	2	yes	complemented
609	#386	C₂²×C₅₃	1	2	yes	complemented
610	#386	C₂²×C₅₃	1	2	yes	complemented
611	#386	C₂²×C₅₃	1	2	yes	complemented
612	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
613	#386	C₂²×C₅₃	1	2	yes	complemented
614	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
615	#385	C₂²×C₅₃	1	2	yes	complemented
616	#385	C₂²×C₅₃	1	2	yes	complemented
617	#385	C₂²×C₅₃	1	2	yes	complemented
618	#385	C₂²×C₅₃	1	2	yes	complemented
619	#385	C₂²×C₅₃	1	2	yes	complemented
620	#385	C₂²×C₅₃	1	2	yes	complemented
621	#381	C₂²×C₅₃	1	2	yes	complemented
622	#380	C₂²×C₅₃	1	2	yes	complemented
623	#380	C₂²×C₅₃	1	2	yes	complemented
624	#379	C₂²×C₅₃	1	2	yes	—
625	#379	C₂²×C₅₃	1	2	yes	complemented
626	#379	C₂²×C₅₃	1	2	yes	complemented
627	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
628	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
629	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
630	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
631	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
632	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
633	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
634	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
635	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
636	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
637	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
638	C₅₃	#34407	1	1	yes	characteristic, direct product factor, Sylow
639	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
640	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
641	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
642	C₂²×D₄	—	4	2	no	—
643	C₂²×D₄	—	4	2	no	—
644	C₂²×D₄	—	4	2	no	—
645	C₂²×D₄	—	4	2	no	—
646	C₂²×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
647	C₂²×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
648	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
649	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
650	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
651	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
652	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
653	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
654	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
655	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
656	C₂³×C₄	—	4	4	no	—
657	C₂³×C₄	—	4	2	no	—
658	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
659	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
660	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
661	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
662	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
663	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
664	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
665	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
666	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
667	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
668	#123	C₂×C₄×C₅₃	1	8	yes	complemented
669	#123	C₂×C₄×C₅₃	1	8	yes	complemented
670	#123	C₂×C₄×C₅₃	1	16	yes	complemented
671	#121	C₂×C₄×C₅₃	1	16	yes	complemented
672	#121	C₂×C₄×C₅₃	1	16	yes	complemented
673	#120	C₂×C₄×C₅₃	1	16	yes	complemented
674	#120	C₂×C₄×C₅₃	1	8	yes	complemented
675	#120	C₂×C₄×C₅₃	1	8	yes	complemented
676	C₄×D₄	—	4	4	no	—
677	C₄×D₄	—	4	4	no	—
678	C₄×D₄	—	4	4	no	—
679	C₄×D₄	—	4	4	no	—
680	#117	—	4	4	no	—
681	#117	—	4	2	no	—
682	#117	—	4	2	no	—
683	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
694	C₂×C₂²⋊C₄	—	4	4	no	—
695	C₂×C₂²⋊C₄	—	4	4	no	—
696	C₂×C₂²⋊C₄	—	4	2	no	—
697	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	complemented
698	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
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	1	yes	characteristic
708	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
728	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
729	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
730	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
731	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
732	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
734	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
735	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
736	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
737	#95	C₂³×C₅₃	1	2	yes	—
738	#95	C₂³×C₅₃	1	2	yes	—
739	#95	C₂³×C₅₃	1	2	yes	—
740	#95	C₂³×C₅₃	1	2	yes	—
741	#95	C₂³×C₅₃	1	2	yes	—
742	#95	C₂³×C₅₃	1	2	yes	—
743	#95	C₂³×C₅₃	1	2	yes	—
744	#95	C₂³×C₅₃	1	2	yes	—
745	#95	C₂³×C₅₃	1	2	yes	—
746	#95	C₂³×C₅₃	1	2	yes	—
747	#95	C₂³×C₅₃	1	2	yes	—
748	#95	C₂³×C₅₃	1	2	yes	—
749	#95	C₂³×C₅₃	1	2	yes	—
750	#95	C₂³×C₅₃	1	2	yes	—
751	#95	C₂³×C₅₃	1	2	yes	—
752	#95	C₂³×C₅₃	1	2	yes	—
753	C₂⁴	—	2	2	no	—
754	C₂⁴	—	2	2	no	—
755	C₂⁴	—	2	2	no	—
756	C₂⁴	—	2	2	no	—
757	C₂⁴	—	4	2	no	—
758	C₂⁴	—	4	2	no	—
759	C₂⁴	—	4	2	no	—
760	C₂⁴	—	4	2	no	—
761	C₂⁴	—	4	1	no	—
762	C₂⁴	—	4	1	no	—
763	C₂⁴	—	4	2	no	—
764	C₂⁴	—	4	2	no	—
765	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
766	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
767	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	complemented
768	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
769	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
770	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
771	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
772	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
773	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	4	no	—
776	C₂×D₄	—	4	2	no	—
777	C₂×D₄	—	4	2	no	—
778	C₂×D₄	—	4	16	no	—
779	C₂×D₄	—	4	1	no	—
780	C₂×D₄	—	4	1	no	—
781	C₂×D₄	—	4	1	no	—
782	C₂×D₄	—	4	1	no	—
783	C₂×D₄	—	4	2	no	—
784	C₂×D₄	—	4	2	no	—
785	C₂×D₄	—	4	1	no	—
786	C₂×D₄	—	4	1	no	—
787	C₂×D₄	—	4	1	no	—
788	C₂×D₄	—	4	1	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	4	16	no	—
792	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	—
793	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	—
794	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	—
795	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
796	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
797	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
798	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
799	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	complemented
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	2	4	no	—
804	C₂²×C₄	—	2	4	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	2	4	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	1	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	1	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	1	no	—
817	C₂²×C₄	—	4	1	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	—	4	2	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	16	no	—
826	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
827	C₂²×C₄	C₂²×C₄×C₅₃	1	8	yes	complemented
828	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
829	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
842	C₄⋊C₄	—	2	4	no	—
843	C₄⋊C₄	—	4	2	no	—
844	C₄⋊C₄	—	4	1	no	—
845	C₄⋊C₄	—	4	2	no	—
846	C₄⋊C₄	—	4	1	no	—
847	C₄⋊C₄	—	4	2	no	—
848	C₄⋊C₄	—	4	2	no	—
849	C₄⋊C₄	—	4	2	no	—
850	C₄⋊C₄	—	4	2	no	—
851	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	complemented
852	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	complemented
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	4	no	—
856	C₂²⋊C₄	—	2	4	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	1	no	—
861	C₂²⋊C₄	—	4	2	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	1	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₂²⋊C₄	—	4	2	no	—
869	C₂²⋊C₄	—	4	2	no	—
870	C₂²⋊C₄	—	4	2	no	—
871	C₂²⋊C₄	—	4	2	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
877	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
878	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
880	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	complemented
881	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	complemented
882	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	complemented
883	C₄²	—	2	4	no	—
884	C₄²	—	4	2	no	—
885	C₄²	—	4	1	no	—
886	C₄²	—	4	2	no	—
887	C₄²	—	4	1	no	—
888	C₄²	—	4	2	no	—
889	C₄²	—	4	2	no	—
890	C₄²	—	4	2	no	—
891	C₄²	—	4	2	no	—
892	C₂³	—	2	2	no	—
893	C₂³	—	2	2	no	—
894	C₂³	—	2	8	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	1	no	—
907	C₂³	—	2	1	no	—
908	C₂³	—	2	1	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	8	no	—
918	C₂³	—	4	8	no	—
919	C₂³	—	4	4	no	—
920	C₂³	—	4	8	no	—
921	C₂³	—	4	8	no	—
922	C₂³	—	4	4	no	—
923	C₂³	—	4	4	no	—
924	C₂³	—	4	8	no	—
925	C₂³	—	8	2	no	—
926	C₂³	—	8	2	no	—
927	C₂³	—	8	4	no	—
928	C₂³	—	8	2	no	—
929	C₂³	—	8	2	no	—
930	C₂³	—	8	4	no	—
931	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
932	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
933	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
934	C₂³	C₂³×C₄×C₅₃	1	4	yes	—
935	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
936	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
937	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
938	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
939	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
940	D₄	—	2	16	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	4	no	—
943	D₄	—	4	4	no	—
944	D₄	—	4	4	no	—
945	D₄	—	4	8	no	—
946	D₄	—	4	8	no	—
947	D₄	—	4	8	no	—
948	C₂×C₄	—	2	8	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	4	8	no	—
983	C₂×C₄	—	4	4	no	—
984	C₂×C₄	—	4	4	no	—
985	C₂×C₄	—	4	8	no	—
986	C₂×C₄	—	4	8	no	—
987	C₂×C₄	—	4	4	no	—
988	C₂×C₄	—	8	4	no	—
989	C₂×C₄	—	8	4	no	—
990	C₂×C₄	—	8	4	no	—
991	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
992	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
993	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
994	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
995	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
996	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	4	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	4	no	—
1007	C₂²	—	2	4	no	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	4	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	4	16	no	—
1013	C₂²	—	4	1	no	—
1014	C₂²	—	4	1	no	—
1015	C₂²	—	4	2	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	—	8	8	no	—
1030	C₂²	—	8	8	no	—
1031	C₂²	C₅₃×#518	1	4	yes	—
1032	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
1033	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1034	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1035	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1036	C₂²	C₅₃×#585	1	2	yes	—
1037	C₄	—	2	4	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	2	4	no	—
1041	C₄	—	2	4	no	—
1042	C₄	—	2	4	no	—
1043	C₄	—	4	2	no	—
1044	C₄	—	4	2	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	2	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	2	no	—
1050	C₂	—	2	4	no	—
1051	C₂	—	4	2	no	—
1052	C₂	—	4	2	no	—
1053	C₂	—	4	2	no	—
1054	C₂	—	4	4	no	—
1055	C₂	—	4	2	no	—
1056	C₂	C₂×C₅₃×#518	1	1	yes	characteristic
1057	C₂	C₄×H(5,𝔽₂)×C₅₃	1	2	yes	—
1058	C₂	C₅₃×#3532	1	1	yes	characteristic
1059	C₂	C₅₃×#3533	1	1	yes	characteristic
1060	C₂	C₅₃×#3542	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅₃
Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂×C₅₃×#534	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#2377	C₂	semidirect
3. C₅₃×#2376	C₂	semidirect
4. C₅₃×#2375	C₂	semidirect
5. C₅₃×#2374	C₂	semidirect
6. C₅₃×#2363	C₂	semidirect
7. C₅₃×#2359	C₂	semidirect
8. C₅₃×#2359	C₂	semidirect
9. C₅₃×#2358	C₂	semidirect
10. C₅₃×#2342	C₂	semidirect
11. D₄×C₂²⋊C₄×C₅₃	C₂	semidirect
12. C₅₃×#2335	C₂	semidirect
13. C₅₃×#2333	C₂	semidirect
14. C₅₃×#2324	C₂	semidirect
15. C₅₃×#2321	C₂	semidirect
16. C₅₃×#2321	C₂	semidirect
17. C₅₃×#2309	C₂	semidirect
18. C₄×#120×C₅₃	C₂	semidirect
19. C₂×C₅₃×#386	C₂	semidirect
22. C₂⁴×C₄×C₅₃	C₂²	semidirect
23. C₅₃×#534	C₄	semidirect
34. C₂×C₄×D₄×C₅₃	C₂²	semidirect
35. C₂×C₄×D₄×C₅₃	C₂²	semidirect
36. C₂×#117×C₅₃	C₂²	semidirect
37. C₂×#117×C₅₃	C₂²	semidirect
38. C₂×#117×C₅₃	C₂²	semidirect
41. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
46. C₅₃×#390	C₂²	semidirect
47. C₅₃×#390	C₂²	semidirect
48. C₅₃×#390	C₂²	semidirect
49. C₅₃×#390	C₂²	semidirect
50. C₅₃×#390	C₂²	semidirect
51. C₅₃×#390	C₂²	semidirect
52. C₅₃×#390	C₂²	semidirect
53. C₅₃×#389	C₂²	semidirect
54. C₅₃×#389	C₂²	semidirect
55. C₅₃×#388	C₂²	semidirect
56. C₅₃×#388	C₂²	semidirect
57. C₅₃×#388	C₂²	semidirect
58. C₅₃×#388	C₂²	semidirect
59. C₅₃×#388	C₂²	semidirect
60. C₅₃×#388	C₂²	semidirect
61. C₅₃×#388	C₂²	semidirect
62. C₅₃×#388	C₂²	semidirect
63. C₅₃×#388	C₂²	semidirect
64. C₅₃×#388	C₂²	semidirect
65. C₅₃×#388	C₂²	semidirect
66. C₅₃×#388	C₂²	semidirect
67. C₅₃×#387	C₂²	semidirect
68. C₅₃×#387	C₂²	semidirect
69. C₅₃×#387	C₂²	semidirect
70. C₅₃×#387	C₂²	semidirect
76. C₅₃×#386	C₂²	semidirect
77. C₅₃×#386	C₂²	semidirect
78. C₅₃×#386	C₂²	semidirect
79. C₅₃×#386	C₂²	semidirect
80. C₅₃×#386	C₂²	semidirect
81. C₅₃×#386	C₂²	semidirect
82. C₅₃×#386	C₂²	semidirect
83. C₅₃×#386	C₂²	semidirect
84. C₅₃×#386	C₂²	semidirect
85. C₅₃×#385	C₂²	semidirect
86. C₅₃×#385	C₂²	semidirect
87. C₅₃×#385	C₂²	semidirect
88. C₅₃×#385	C₂²	semidirect
89. C₅₃×#385	C₂²	semidirect
90. C₅₃×#385	C₂²	semidirect
91. C₅₃×#381	C₂²	semidirect
92. C₅₃×#380	C₂²	semidirect
93. C₅₃×#380	C₂²	semidirect
95. C₅₃×#379	C₂²	semidirect
96. C₅₃×#379	C₂²	semidirect
97. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
98. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
99. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
100. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
107. C₂×#95×C₅₃	C₂²	semidirect
115. C₂²×D₄×C₅₃	C₂×C₄	semidirect
116. C₂²×D₄×C₅₃	C₂×C₄	semidirect
137. #123×C₅₃	C₂×C₄	semidirect
138. #123×C₅₃	C₂×C₄	semidirect
139. #123×C₅₃	C₂×C₄	semidirect
140. #121×C₅₃	C₂×C₄	semidirect
141. #121×C₅₃	C₂×C₄	semidirect
142. #120×C₅₃	C₂×C₄	semidirect
143. #120×C₅₃	C₂×C₄	semidirect
144. #120×C₅₃	C₂×C₄	semidirect
166. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
236. C₂⁴×C₅₃	C₂²×C₄	semidirect
268. C₂×D₄×C₅₃	C₂²×C₄	semidirect
296. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
297. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
320. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
321. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
348. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
349. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
350. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
351. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
466. #34407	C₅₃	direct (N × H)
521. #2377	C₂×C₅₃	semidirect
522. #2376	C₂×C₅₃	semidirect
523. #2375	C₂×C₅₃	semidirect
524. #2374	C₂×C₅₃	semidirect
525. #2363	C₂×C₅₃	semidirect
526. #2359	C₂×C₅₃	semidirect
527. #2359	C₂×C₅₃	semidirect
528. #2358	C₂×C₅₃	semidirect
529. #2342	C₂×C₅₃	semidirect
530. D₄×C₂²⋊C₄	C₂×C₅₃	semidirect
531. #2335	C₂×C₅₃	semidirect
532. #2333	C₂×C₅₃	semidirect
533. #2324	C₂×C₅₃	semidirect
534. #2321	C₂×C₅₃	semidirect
535. #2321	C₂×C₅₃	semidirect
536. #2309	C₂×C₅₃	semidirect
537. C₄×#120	C₂×C₅₃	semidirect
538. C₂×#386	C₂×C₅₃	semidirect
552. C₂⁴×C₄	C₂²×C₅₃	semidirect
553. #534	C₄×C₅₃	semidirect
564. C₂×C₄×D₄	C₂²×C₅₃	semidirect
565. C₂×C₄×D₄	C₂²×C₅₃	semidirect
566. C₂×#117	C₂²×C₅₃	semidirect
567. C₂×#117	C₂²×C₅₃	semidirect
568. C₂×#117	C₂²×C₅₃	semidirect
571. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
572. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
576. #390	C₂²×C₅₃	semidirect
577. #390	C₂²×C₅₃	semidirect
578. #390	C₂²×C₅₃	semidirect
579. #390	C₂²×C₅₃	semidirect
580. #390	C₂²×C₅₃	semidirect
581. #390	C₂²×C₅₃	semidirect
582. #390	C₂²×C₅₃	semidirect
583. #389	C₂²×C₅₃	semidirect
584. #389	C₂²×C₅₃	semidirect
585. #388	C₂²×C₅₃	semidirect
586. #388	C₂²×C₅₃	semidirect
587. #388	C₂²×C₅₃	semidirect
588. #388	C₂²×C₅₃	semidirect
589. #388	C₂²×C₅₃	semidirect
590. #388	C₂²×C₅₃	semidirect
591. #388	C₂²×C₅₃	semidirect
592. #388	C₂²×C₅₃	semidirect
593. #388	C₂²×C₅₃	semidirect
594. #388	C₂²×C₅₃	semidirect
595. #388	C₂²×C₅₃	semidirect
596. #388	C₂²×C₅₃	semidirect
597. #387	C₂²×C₅₃	semidirect
598. #387	C₂²×C₅₃	semidirect
599. #387	C₂²×C₅₃	semidirect
600. #387	C₂²×C₅₃	semidirect
606. #386	C₂²×C₅₃	semidirect
607. #386	C₂²×C₅₃	semidirect
608. #386	C₂²×C₅₃	semidirect
609. #386	C₂²×C₅₃	semidirect
610. #386	C₂²×C₅₃	semidirect
611. #386	C₂²×C₅₃	semidirect
612. #386	C₂²×C₅₃	semidirect
613. #386	C₂²×C₅₃	semidirect
614. #386	C₂²×C₅₃	semidirect
615. #385	C₂²×C₅₃	semidirect
616. #385	C₂²×C₅₃	semidirect
617. #385	C₂²×C₅₃	semidirect
618. #385	C₂²×C₅₃	semidirect
619. #385	C₂²×C₅₃	semidirect
620. #385	C₂²×C₅₃	semidirect
621. #381	C₂²×C₅₃	semidirect
622. #380	C₂²×C₅₃	semidirect
623. #380	C₂²×C₅₃	semidirect
625. #379	C₂²×C₅₃	semidirect
626. #379	C₂²×C₅₃	semidirect
627. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
628. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
629. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
630. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
631. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
632. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
633. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
634. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
635. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
636. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
637. C₂×#95	C₂²×C₅₃	semidirect
638. C₅₃	#34407	direct (N × H)
646. C₂²×D₄	C₂×C₄×C₅₃	semidirect
647. C₂²×D₄	C₂×C₄×C₅₃	semidirect
668. #123	C₂×C₄×C₅₃	semidirect
669. #123	C₂×C₄×C₅₃	semidirect
670. #123	C₂×C₄×C₅₃	semidirect
671. #121	C₂×C₄×C₅₃	semidirect
672. #121	C₂×C₄×C₅₃	semidirect
673. #120	C₂×C₄×C₅₃	semidirect
674. #120	C₂×C₄×C₅₃	semidirect
675. #120	C₂×C₄×C₅₃	semidirect
697. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
767. C₂⁴	C₂²×C₄×C₅₃	semidirect
799. C₂×D₄	C₂²×C₄×C₅₃	semidirect
827. C₂²×C₄	C₂²×C₄×C₅₃	semidirect
828. C₂²×C₄	C₂²×C₄×C₅₃	semidirect
851. C₄⋊C₄	C₂²×C₄×C₅₃	semidirect
852. C₄⋊C₄	C₂²×C₄×C₅₃	semidirect
879. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
880. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
881. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
882. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#534	2
C₅₃×#2377	2
C₅₃×#2376	2
C₅₃×#2375	2
C₅₃×#2374	2
C₅₃×#2363	2
C₅₃×#2359	2
C₅₃×#2358	2
C₅₃×#2342	2
D₄×C₂²⋊C₄×C₅₃	2
C₅₃×#2335	2
C₅₃×#2333	2
C₅₃×#2324	2
C₅₃×#2321	2
C₅₃×#2309	2
C₄×#120×C₅₃	2
C₂×C₅₃×#386	2
#34407	53

Subgroups — C53×#34407 #27241919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34407 #27241919