Subgroups — C₅₃×#34724 #27242236

Order 13568.

2540 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2478	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2470	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2466	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2455	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2453	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2447	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2441	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2432	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2415	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2407	C₂	1	1	yes	maximal, characteristic
15	C₅₃×#2395	C₂	1	2	yes	maximal, complemented
16	C₅₃×#2392	C₂	1	2	yes	maximal, complemented
17	C₄×C₄⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#123×C₅₃	C₂	1	2	yes	maximal, complemented
21	C₅₃×#2296	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	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₅₃×#529	—	2	8	no	—
27	C₂×#126×C₅₃	C₂²	1	2	yes	—
28	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#123×C₅₃	C₂²	1	2	yes	—
31	C₂×#123×C₅₃	C₂²	1	2	yes	—
32	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
36	C₄×#41×C₅₃	—	2	8	no	—
37	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×#117×C₅₃	C₂²	1	2	yes	—
50	C₂×#117×C₅₃	C₂²	1	2	yes	—
51	C₂×#117×C₅₃	C₂²	1	2	yes	—
52	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
54	C₂²×C₄²×C₅₃	C₂²	1	2	yes	—
55	C₅₃×#400	C₂²	1	2	yes	—
56	C₅₃×#399	C₂²	1	2	yes	—
57	C₅₃×#398	C₂²	1	2	yes	—
58	C₅₃×#398	C₂²	1	2	yes	—
59	C₅₃×#397	C₂²	1	2	yes	—
60	C₅₃×#397	C₂²	1	2	yes	—
61	C₅₃×#397	C₂²	1	2	yes	—
62	C₅₃×#397	C₂²	1	2	yes	—
63	C₅₃×#396	C₂²	1	2	yes	—
64	C₅₃×#396	C₂²	1	2	yes	—
65	C₅₃×#394	C₂²	1	2	yes	—
66	C₅₃×#394	C₂²	1	2	yes	—
67	C₅₃×#394	C₂²	1	2	yes	—
68	C₅₃×#394	C₂²	1	2	yes	—
69	C₅₃×#394	C₂²	1	2	yes	—
70	C₅₃×#392	C₂²	1	2	yes	—
71	C₅₃×#391	C₂²	1	1	yes	characteristic
72	C₅₃×#391	C₂²	1	1	yes	characteristic
73	C₅₃×#391	C₂²	1	1	yes	characteristic
74	C₅₃×#391	C₂²	1	1	yes	characteristic
75	C₅₃×#390	C₂²	1	1	yes	characteristic
76	C₅₃×#390	C₂²	1	1	yes	characteristic
77	C₅₃×#389	C₂²	1	1	yes	characteristic
78	C₅₃×#389	C₂²	1	2	yes	—
79	C₅₃×#389	C₂²	1	1	yes	characteristic
80	C₅₃×#389	C₂²	1	2	yes	—
81	C₅₃×#389	C₂²	1	2	yes	—
82	C₅₃×#389	C₂²	1	1	yes	characteristic
83	C₅₃×#389	C₂²	1	1	yes	characteristic
84	C₅₃×#389	C₂²	1	2	yes	—
85	C₅₃×#389	C₂²	1	2	yes	—
86	C₅₃×#389	C₂²	1	2	yes	—
87	C₅₃×#388	C₂²	1	2	yes	—
88	C₅₃×#388	C₂²	1	2	yes	—
89	C₅₃×#388	C₂²	1	2	yes	—
90	C₅₃×#388	C₂²	1	2	yes	—
91	C₅₃×#387	C₂²	1	2	yes	—
92	C₅₃×#387	C₂²	1	2	yes	—
93	C₅₃×#387	C₂²	1	2	yes	—
94	C₅₃×#387	C₂²	1	2	yes	—
95	C₅₃×#386	C₂²	1	2	yes	—
96	C₅₃×#385	C₂²	1	2	yes	—
97	C₅₃×#385	C₂²	1	2	yes	—
98	C₅₃×#385	C₂²	1	2	yes	—
99	C₅₃×#385	C₂²	1	2	yes	—
100	C₅₃×#385	C₂²	1	2	yes	—
101	C₅₃×#385	C₂²	1	2	yes	—
102	C₅₃×#385	C₂²	1	2	yes	—
103	C₅₃×#384	C₂²	1	1	yes	characteristic
104	C₅₃×#381	C₂²	1	2	yes	—
105	C₅₃×#380	C₂²	1	1	yes	characteristic
106	C₅₃×#380	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
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
120	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
123	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
124	C₄³×C₅₃	C₂²	1	1	yes	characteristic
125	C₂×#41×C₅₃	—	2	4	no	—
126	C₂×#41×C₅₃	—	2	4	no	—
127	C₂×#41×C₅₃	—	2	4	no	—
128	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
132	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
133	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
140	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₄⋊Q₈×C₅₃	—	2	4	no	—
144	#126×C₅₃	—	2	8	no	—
145	#125×C₅₃	—	2	4	no	—
146	#124×C₅₃	—	2	4	no	—
147	#123×C₅₃	—	2	8	no	—
148	#123×C₅₃	—	2	8	no	—
149	C₂²⋊Q₈×C₅₃	—	2	4	no	—
150	C₂²⋊Q₈×C₅₃	—	2	4	no	—
151	C₂²⋊Q₈×C₅₃	—	2	4	no	—
152	#121×C₅₃	—	2	4	no	—
153	C₄×Q₈×C₅₃	—	2	4	no	—
154	C₄×Q₈×C₅₃	—	2	4	no	—
155	C₄×Q₈×C₅₃	—	2	4	no	—
156	C₄×D₄×C₅₃	—	2	8	no	—
157	C₄×D₄×C₅₃	—	2	4	no	—
158	C₄×D₄×C₅₃	—	2	4	no	—
159	C₄×D₄×C₅₃	—	2	4	no	—
160	C₄×D₄×C₅₃	—	2	8	no	—
161	C₄×D₄×C₅₃	—	2	8	no	—
162	C₄×D₄×C₅₃	—	2	4	no	—
163	C₄×D₄×C₅₃	D₄	1	8	yes	complemented
164	#117×C₅₃	—	2	4	no	—
165	#117×C₅₃	—	2	8	no	—
166	#117×C₅₃	—	2	8	no	—
167	#117×C₅₃	—	2	8	no	—
168	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
184	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
213	C₂×C₄²×C₅₃	—	2	4	no	—
214	C₂×C₄²×C₅₃	—	2	4	no	—
215	C₂×C₄²×C₅₃	—	2	8	no	—
216	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
218	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
220	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
229	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
230	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
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	#95×C₅₃	C₂³	1	1	yes	characteristic
235	#95×C₅₃	C₂³	1	1	yes	characteristic
236	#95×C₅₃	C₂³	1	1	yes	characteristic
237	#95×C₅₃	C₂³	1	1	yes	characteristic
238	#95×C₅₃	C₂³	1	1	yes	characteristic
239	#95×C₅₃	C₂³	1	1	yes	characteristic
240	#95×C₅₃	C₂³	1	2	yes	—
241	#95×C₅₃	C₂³	1	2	yes	—
242	#95×C₅₃	C₂³	1	2	yes	—
243	#95×C₅₃	C₂³	1	2	yes	—
244	#95×C₅₃	C₂³	1	2	yes	—
245	#95×C₅₃	C₂³	1	2	yes	—
246	#95×C₅₃	C₂³	1	2	yes	—
247	#95×C₅₃	C₂³	1	2	yes	—
248	#95×C₅₃	C₂³	1	2	yes	—
249	#95×C₅₃	C₂³	1	2	yes	—
250	#95×C₅₃	C₂³	1	2	yes	—
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	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
256	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
257	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
258	#41×C₅₃	—	2	32	no	—
259	C₂×Q₈×C₅₃	—	2	2	no	—
260	C₂×Q₈×C₅₃	—	2	2	no	—
261	C₂×Q₈×C₅₃	—	2	2	no	—
262	C₂×Q₈×C₅₃	—	2	2	no	—
263	C₂×Q₈×C₅₃	—	2	2	no	—
264	C₂×Q₈×C₅₃	#41	1	4	yes	—
265	C₂×D₄×C₅₃	—	2	4	no	—
266	C₂×D₄×C₅₃	—	2	2	no	—
267	C₂×D₄×C₅₃	—	2	2	no	—
268	C₂×D₄×C₅₃	—	2	4	no	—
269	C₂×D₄×C₅₃	—	2	4	no	—
270	C₂×D₄×C₅₃	—	2	4	no	—
271	C₂×D₄×C₅₃	—	2	2	no	—
272	C₂×D₄×C₅₃	—	2	4	no	—
273	C₂×D₄×C₅₃	—	2	2	no	—
274	C₂×D₄×C₅₃	—	2	2	no	—
275	C₂×D₄×C₅₃	—	4	2	no	—
276	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
277	C₂²×C₄×C₅₃	—	2	4	no	—
278	C₂²×C₄×C₅₃	—	2	2	no	—
279	C₂²×C₄×C₅₃	—	2	4	no	—
280	C₂²×C₄×C₅₃	—	2	4	no	—
281	C₂²×C₄×C₅₃	—	2	4	no	—
282	C₂²×C₄×C₅₃	—	2	2	no	—
283	C₂²×C₄×C₅₃	—	2	4	no	—
284	C₂²×C₄×C₅₃	—	2	4	no	—
285	C₂²×C₄×C₅₃	—	2	2	no	—
286	C₂²×C₄×C₅₃	—	2	2	no	—
287	C₂²×C₄×C₅₃	—	2	2	no	—
288	C₂²×C₄×C₅₃	—	2	2	no	—
289	C₂²×C₄×C₅₃	—	2	2	no	—
290	C₂²×C₄×C₅₃	—	2	2	no	—
291	C₂²×C₄×C₅₃	—	2	2	no	—
292	C₂²×C₄×C₅₃	—	2	2	no	—
293	C₂²×C₄×C₅₃	—	2	2	no	—
294	C₂²×C₄×C₅₃	—	2	2	no	—
295	C₂²×C₄×C₅₃	—	2	2	no	—
296	C₂²×C₄×C₅₃	—	2	4	no	—
297	C₂²×C₄×C₅₃	—	2	2	no	—
298	C₂²×C₄×C₅₃	—	2	2	no	—
299	C₂²×C₄×C₅₃	—	4	1	no	—
300	C₂²×C₄×C₅₃	—	4	2	no	—
301	C₂²×C₄×C₅₃	—	4	1	no	—
302	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
303	C₂²×C₄×C₅₃	#41	1	4	yes	—
304	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
324	C₄⋊C₄×C₅₃	—	2	4	no	—
325	C₄⋊C₄×C₅₃	—	2	4	no	—
326	C₄⋊C₄×C₅₃	—	2	2	no	—
327	C₄⋊C₄×C₅₃	—	2	4	no	—
328	C₄⋊C₄×C₅₃	—	2	4	no	—
329	C₄⋊C₄×C₅₃	—	2	4	no	—
330	C₄⋊C₄×C₅₃	—	2	2	no	—
331	C₄⋊C₄×C₅₃	—	2	4	no	—
332	C₄⋊C₄×C₅₃	—	2	4	no	—
333	C₄⋊C₄×C₅₃	—	2	4	no	—
334	C₄⋊C₄×C₅₃	—	2	2	no	—
335	C₄⋊C₄×C₅₃	—	2	2	no	—
336	C₄⋊C₄×C₅₃	—	2	2	no	—
337	C₄⋊C₄×C₅₃	—	2	4	no	—
338	C₄⋊C₄×C₅₃	—	2	4	no	—
339	C₄⋊C₄×C₅₃	—	2	2	no	—
340	C₄⋊C₄×C₅₃	—	2	2	no	—
341	C₄⋊C₄×C₅₃	—	2	4	no	—
342	C₄⋊C₄×C₅₃	—	2	4	no	—
343	C₄⋊C₄×C₅₃	—	2	4	no	—
344	C₄⋊C₄×C₅₃	—	2	4	no	—
345	C₄⋊C₄×C₅₃	—	4	2	no	—
346	C₄⋊C₄×C₅₃	—	4	2	no	—
347	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
348	C₂²⋊C₄×C₅₃	—	2	4	no	—
349	C₂²⋊C₄×C₅₃	—	2	4	no	—
350	C₂²⋊C₄×C₅₃	—	2	4	no	—
351	C₂²⋊C₄×C₅₃	—	2	4	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	—	2	4	no	—
356	C₂²⋊C₄×C₅₃	—	2	4	no	—
357	C₂²⋊C₄×C₅₃	—	2	4	no	—
358	C₂²⋊C₄×C₅₃	—	2	4	no	—
359	C₂²⋊C₄×C₅₃	—	2	2	no	—
360	C₂²⋊C₄×C₅₃	—	2	2	no	—
361	C₂²⋊C₄×C₅₃	—	2	2	no	—
362	C₂²⋊C₄×C₅₃	—	2	2	no	—
363	C₂²⋊C₄×C₅₃	—	2	4	no	—
364	C₂²⋊C₄×C₅₃	—	2	4	no	—
365	C₂²⋊C₄×C₅₃	—	4	2	no	—
366	C₂²⋊C₄×C₅₃	—	4	2	no	—
367	C₂²⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
368	C₂²⋊C₄×C₅₃	#41	1	4	yes	complemented
369	C₄²×C₅₃	—	2	2	no	—
370	C₄²×C₅₃	—	2	2	no	—
371	C₄²×C₅₃	—	2	4	no	—
372	C₄²×C₅₃	—	2	2	no	—
373	C₄²×C₅₃	—	2	4	no	—
374	C₄²×C₅₃	—	2	2	no	—
375	C₄²×C₅₃	—	2	4	no	—
376	C₄²×C₅₃	—	2	2	no	—
377	C₄²×C₅₃	—	2	2	no	—
378	C₄²×C₅₃	—	2	4	no	—
379	C₄²×C₅₃	—	2	4	no	—
380	C₄²×C₅₃	—	2	2	no	—
381	C₄²×C₅₃	—	2	2	no	—
382	C₄²×C₅₃	—	2	2	no	—
383	C₄²×C₅₃	—	2	2	no	—
384	C₄²×C₅₃	—	4	1	no	—
385	C₄²×C₅₃	C₂×D₄	1	4	yes	—
386	C₄²×C₅₃	#41	1	4	yes	complemented
387	C₂³×C₅₃	—	2	1	no	—
388	C₂³×C₅₃	—	2	1	no	—
389	C₂³×C₅₃	—	2	2	no	—
390	C₂³×C₅₃	—	2	2	no	—
391	C₂³×C₅₃	—	2	1	no	—
392	C₂³×C₅₃	—	2	1	no	—
393	C₂³×C₅₃	—	2	1	no	—
394	C₂³×C₅₃	—	2	1	no	—
395	C₂³×C₅₃	—	2	1	no	—
396	C₂³×C₅₃	—	2	2	no	—
397	C₂³×C₅₃	—	2	2	no	—
398	C₂³×C₅₃	—	2	1	no	—
399	C₂³×C₅₃	—	2	1	no	—
400	C₂³×C₅₃	—	2	2	no	—
401	C₂³×C₅₃	—	2	1	no	—
402	C₂³×C₅₃	—	2	1	no	—
403	C₂³×C₅₃	—	2	2	no	—
404	C₂³×C₅₃	—	2	1	no	—
405	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
406	C₂³×C₅₃	C₂×#41	1	2	yes	—
407	C₂³×C₅₃	C₂×#41	1	2	yes	—
408	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
409	Q₈×C₅₃	—	2	8	no	—
410	Q₈×C₅₃	—	4	4	no	—
411	D₄×C₅₃	—	2	8	no	—
412	D₄×C₅₃	—	2	16	no	—
413	D₄×C₅₃	—	2	8	no	—
414	D₄×C₅₃	—	4	8	no	—
415	C₂×C₄×C₅₃	—	2	16	no	—
416	C₂×C₄×C₅₃	—	2	1	no	—
417	C₂×C₄×C₅₃	—	2	1	no	—
418	C₂×C₄×C₅₃	—	2	2	no	—
419	C₂×C₄×C₅₃	—	2	1	no	—
420	C₂×C₄×C₅₃	—	2	1	no	—
421	C₂×C₄×C₅₃	—	2	2	no	—
422	C₂×C₄×C₅₃	—	2	2	no	—
423	C₂×C₄×C₅₃	—	2	1	no	—
424	C₂×C₄×C₅₃	—	2	1	no	—
425	C₂×C₄×C₅₃	—	2	1	no	—
426	C₂×C₄×C₅₃	—	2	1	no	—
427	C₂×C₄×C₅₃	—	2	2	no	—
428	C₂×C₄×C₅₃	—	2	1	no	—
429	C₂×C₄×C₅₃	—	2	1	no	—
430	C₂×C₄×C₅₃	—	2	1	no	—
431	C₂×C₄×C₅₃	—	2	1	no	—
432	C₂×C₄×C₅₃	—	2	8	no	—
433	C₂×C₄×C₅₃	—	2	16	no	—
434	C₂×C₄×C₅₃	—	2	1	no	—
435	C₂×C₄×C₅₃	—	2	1	no	—
436	C₂×C₄×C₅₃	—	2	1	no	—
437	C₂×C₄×C₅₃	—	2	2	no	—
438	C₂×C₄×C₅₃	—	2	1	no	—
439	C₂×C₄×C₅₃	—	2	2	no	—
440	C₂×C₄×C₅₃	—	2	2	no	—
441	C₂×C₄×C₅₃	—	2	1	no	—
442	C₂×C₄×C₅₃	—	2	1	no	—
443	C₂×C₄×C₅₃	—	2	1	no	—
444	C₂×C₄×C₅₃	—	2	1	no	—
445	C₂×C₄×C₅₃	—	2	2	no	—
446	C₂×C₄×C₅₃	—	2	1	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	1	no	—
451	C₂×C₄×C₅₃	—	2	2	no	—
452	C₂×C₄×C₅₃	—	2	2	no	—
453	C₂×C₄×C₅₃	—	2	2	no	—
454	C₂×C₄×C₅₃	—	2	2	no	—
455	C₂×C₄×C₅₃	—	2	2	no	—
456	C₂×C₄×C₅₃	—	2	1	no	—
457	C₂×C₄×C₅₃	—	2	1	no	—
458	C₂×C₄×C₅₃	—	2	1	no	—
459	C₂×C₄×C₅₃	—	2	2	no	—
460	C₂×C₄×C₅₃	—	2	1	no	—
461	C₂×C₄×C₅₃	—	2	2	no	—
462	C₂×C₄×C₅₃	—	2	1	no	—
463	C₂×C₄×C₅₃	—	2	2	no	—
464	C₂×C₄×C₅₃	—	4	4	no	—
465	C₂×C₄×C₅₃	—	4	8	no	—
466	C₂×C₄×C₅₃	—	4	4	no	—
467	C₂×C₄×C₅₃	—	4	4	no	—
468	C₂×C₄×C₅₃	—	4	4	no	—
469	C₂×C₄×C₅₃	—	4	4	no	—
470	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
472	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
475	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
476	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
477	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
478	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
479	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
480	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
481	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
482	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
483	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
484	#34724	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
485	C₂²×C₅₃	—	2	4	no	—
486	C₂²×C₅₃	—	2	2	no	—
487	C₂²×C₅₃	—	2	2	no	—
488	C₂²×C₅₃	—	2	2	no	—
489	C₂²×C₅₃	—	2	2	no	—
490	C₂²×C₅₃	—	2	4	no	—
491	C₂²×C₅₃	—	2	2	no	—
492	C₂²×C₅₃	—	2	4	no	—
493	C₂²×C₅₃	—	2	2	no	—
494	C₂²×C₅₃	—	4	1	no	—
495	C₂²×C₅₃	—	4	2	no	—
496	C₂²×C₅₃	—	4	2	no	—
497	C₂²×C₅₃	—	4	1	no	—
498	C₂²×C₅₃	—	4	1	no	—
499	C₂²×C₅₃	—	4	1	no	—
500	C₂²×C₅₃	—	4	1	no	—
501	C₂²×C₅₃	—	4	1	no	—
502	C₂²×C₅₃	—	4	2	no	—
503	C₂²×C₅₃	—	4	1	no	—
504	C₂²×C₅₃	—	4	2	no	—
505	C₂²×C₅₃	—	4	1	no	—
506	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
507	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
508	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
509	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
510	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
511	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
512	C₂²×C₅₃	#585	1	1	yes	characteristic
513	C₄×C₅₃	—	2	2	no	—
514	C₄×C₅₃	—	2	4	no	—
515	C₄×C₅₃	—	2	2	no	—
516	C₄×C₅₃	—	2	4	no	—
517	C₄×C₅₃	—	2	2	no	—
518	C₄×C₅₃	—	2	2	no	—
519	C₄×C₅₃	—	2	2	no	—
520	C₄×C₅₃	—	2	2	no	—
521	C₄×C₅₃	—	4	1	no	—
522	C₄×C₅₃	—	4	2	no	—
523	C₄×C₅₃	—	4	2	no	—
524	C₄×C₅₃	—	4	1	no	—
525	C₄×C₅₃	—	4	1	no	—
526	C₄×C₅₃	—	4	1	no	—
527	C₄×C₅₃	—	4	2	no	—
528	C₄×C₅₃	—	4	1	no	—
529	C₄×C₅₃	—	4	2	no	—
530	C₄×C₅₃	—	4	2	no	—
531	C₄×C₅₃	#525	1	4	yes	—
532	C₄×C₅₃	#547	1	4	yes	—
533	C₂×#529	C₂×C₅₃	1	1	yes	characteristic, complemented
534	C₂×C₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
535	#2478	C₂×C₅₃	1	2	yes	complemented
536	#2470	C₂×C₅₃	1	2	yes	complemented
537	#2466	C₂×C₅₃	1	2	yes	complemented
538	#2455	C₂×C₅₃	1	2	yes	complemented
539	#2453	C₂×C₅₃	1	1	yes	characteristic, complemented
540	#2447	C₂×C₅₃	1	1	yes	characteristic, complemented
541	#2441	C₂×C₅₃	1	1	yes	characteristic, complemented
542	#2432	C₂×C₅₃	1	1	yes	characteristic, complemented
543	#2429	C₂×C₅₃	1	1	yes	characteristic, complemented
544	#2422	C₂×C₅₃	1	1	yes	characteristic, complemented
545	#2415	C₂×C₅₃	1	1	yes	characteristic, complemented
546	#2407	C₂×C₅₃	1	1	yes	characteristic
547	#2395	C₂×C₅₃	1	2	yes	complemented
548	#2392	C₂×C₅₃	1	2	yes	complemented
549	C₄×C₄⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
550	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
551	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
552	C₄×#123	C₂×C₅₃	1	2	yes	complemented
553	#2296	C₂×C₅₃	1	2	yes	complemented
554	#2293	C₂×C₅₃	1	1	yes	characteristic, complemented
555	C₄²×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
556	C₂×C₅₃	—	4	4	no	—
557	C₂×C₅₃	—	4	2	no	—
558	C₂×C₅₃	—	4	2	no	—
559	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
560	C₂×C₅₃	#3444	1	1	yes	characteristic
561	C₂×C₅₃	#3461	1	1	yes	characteristic
562	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
563	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
564	C₂×C₅₃	#3480	1	1	yes	characteristic
565	C₂×C₅₃	#3482	1	1	yes	characteristic
566	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
567	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
568	#529	—	2	8	no	—
569	C₂×#126	C₂²×C₅₃	1	2	yes	—
570	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
571	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
572	C₂×#123	C₂²×C₅₃	1	2	yes	—
573	C₂×#123	C₂²×C₅₃	1	2	yes	—
574	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
575	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
576	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
577	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
578	C₄×#41	—	2	8	no	—
579	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
580	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
581	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
582	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
583	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
584	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
585	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
586	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
587	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
588	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
589	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
590	C₂×#117	C₂²×C₅₃	1	2	yes	—
591	C₂×#117	C₂²×C₅₃	1	2	yes	—
592	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
593	C₂×#117	C₂²×C₅₃	1	2	yes	—
594	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
595	C₂²×C₄²	C₂²×C₅₃	1	2	yes	—
596	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
597	#400	C₂²×C₅₃	1	2	yes	—
598	#399	C₂²×C₅₃	1	2	yes	—
599	#398	C₂²×C₅₃	1	2	yes	—
600	#398	C₂²×C₅₃	1	2	yes	—
601	#397	C₂²×C₅₃	1	2	yes	—
602	#397	C₂²×C₅₃	1	2	yes	—
603	#397	C₂²×C₅₃	1	2	yes	—
604	#397	C₂²×C₅₃	1	2	yes	—
605	#396	C₂²×C₅₃	1	2	yes	—
606	#396	C₂²×C₅₃	1	2	yes	—
607	#394	C₂²×C₅₃	1	2	yes	—
608	#394	C₂²×C₅₃	1	2	yes	—
609	#394	C₂²×C₅₃	1	2	yes	—
610	#394	C₂²×C₅₃	1	2	yes	—
611	#394	C₂²×C₅₃	1	2	yes	—
612	#392	C₂²×C₅₃	1	2	yes	—
613	#391	C₂²×C₅₃	1	1	yes	characteristic
614	#391	C₂²×C₅₃	1	1	yes	characteristic
615	#391	C₂²×C₅₃	1	1	yes	characteristic
616	#391	C₂²×C₅₃	1	1	yes	characteristic
617	#390	C₂²×C₅₃	1	1	yes	characteristic
618	#390	C₂²×C₅₃	1	1	yes	characteristic
619	#389	C₂²×C₅₃	1	2	yes	—
620	#389	C₂²×C₅₃	1	2	yes	—
621	#389	C₂²×C₅₃	1	1	yes	characteristic
622	#389	C₂²×C₅₃	1	2	yes	—
623	#389	C₂²×C₅₃	1	1	yes	characteristic
624	#389	C₂²×C₅₃	1	1	yes	characteristic
625	#389	C₂²×C₅₃	1	2	yes	—
626	#389	C₂²×C₅₃	1	1	yes	characteristic
627	#389	C₂²×C₅₃	1	2	yes	—
628	#389	C₂²×C₅₃	1	2	yes	—
629	#388	C₂²×C₅₃	1	2	yes	—
630	#388	C₂²×C₅₃	1	2	yes	—
631	#388	C₂²×C₅₃	1	2	yes	—
632	#388	C₂²×C₅₃	1	2	yes	—
633	#387	C₂²×C₅₃	1	2	yes	—
634	#387	C₂²×C₅₃	1	2	yes	—
635	#387	C₂²×C₅₃	1	2	yes	—
636	#387	C₂²×C₅₃	1	2	yes	—
637	#386	C₂²×C₅₃	1	2	yes	—
638	#385	C₂²×C₅₃	1	2	yes	—
639	#385	C₂²×C₅₃	1	2	yes	—
640	#385	C₂²×C₅₃	1	2	yes	—
641	#385	C₂²×C₅₃	1	2	yes	—
642	#385	C₂²×C₅₃	1	2	yes	—
643	#385	C₂²×C₅₃	1	2	yes	—
644	#385	C₂²×C₅₃	1	2	yes	—
645	#384	C₂²×C₅₃	1	1	yes	characteristic
646	#381	C₂²×C₅₃	1	2	yes	—
647	#380	C₂²×C₅₃	1	1	yes	characteristic
648	#380	C₂²×C₅₃	1	1	yes	characteristic
649	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
650	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
651	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
652	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
653	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
654	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
655	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
656	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
657	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
658	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
659	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
660	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
661	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
662	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
663	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
664	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
665	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
666	C₄³	C₂²×C₅₃	1	1	yes	characteristic
667	C₅₃	#34724	1	1	yes	characteristic, direct product factor, Sylow
668	C₂×#41	—	2	4	no	—
669	C₂×#41	—	2	4	no	—
670	C₂×#41	—	2	4	no	—
671	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
672	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
673	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
674	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
675	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
676	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
677	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
678	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
679	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
680	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
681	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
682	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
683	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
684	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
685	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
686	C₄⋊Q₈	—	2	4	no	—
687	#126	—	2	8	no	—
688	#125	—	2	4	no	—
689	#124	—	2	4	no	—
690	#123	—	2	8	no	—
691	#123	—	2	8	no	—
692	C₂²⋊Q₈	—	2	4	no	—
693	C₂²⋊Q₈	—	2	4	no	—
694	C₂²⋊Q₈	—	2	4	no	—
695	#121	—	2	4	no	—
696	C₄×Q₈	—	2	4	no	—
697	C₄×Q₈	—	2	4	no	—
698	C₄×Q₈	—	2	4	no	—
699	C₄×D₄	—	2	4	no	—
700	C₄×D₄	—	2	8	no	—
701	C₄×D₄	—	2	8	no	—
702	C₄×D₄	—	2	4	no	—
703	C₄×D₄	—	2	8	no	—
704	C₄×D₄	—	2	4	no	—
705	C₄×D₄	—	2	4	no	—
706	C₄×D₄	D₄×C₅₃	1	8	yes	complemented
707	#117	—	2	8	no	—
708	#117	—	2	4	no	—
709	#117	—	2	8	no	—
710	#117	—	2	8	no	—
711	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
713	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
718	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
719	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
722	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
726	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
734	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
735	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
744	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
745	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
746	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
747	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
748	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
756	C₂×C₄²	—	2	8	no	—
757	C₂×C₄²	—	2	4	no	—
758	C₂×C₄²	—	2	4	no	—
759	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
760	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
761	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
762	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
763	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
764	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
765	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
767	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
768	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
774	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
775	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
776	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
777	#95	C₂³×C₅₃	1	1	yes	characteristic
778	#95	C₂³×C₅₃	1	1	yes	characteristic
779	#95	C₂³×C₅₃	1	1	yes	characteristic
780	#95	C₂³×C₅₃	1	1	yes	characteristic
781	#95	C₂³×C₅₃	1	1	yes	characteristic
782	#95	C₂³×C₅₃	1	1	yes	characteristic
783	#95	C₂³×C₅₃	1	2	yes	—
784	#95	C₂³×C₅₃	1	2	yes	—
785	#95	C₂³×C₅₃	1	2	yes	—
786	#95	C₂³×C₅₃	1	2	yes	—
787	#95	C₂³×C₅₃	1	2	yes	—
788	#95	C₂³×C₅₃	1	2	yes	—
789	#95	C₂³×C₅₃	1	2	yes	—
790	#95	C₂³×C₅₃	1	2	yes	—
791	#95	C₂³×C₅₃	1	2	yes	—
792	#95	C₂³×C₅₃	1	2	yes	—
793	#95	C₂³×C₅₃	1	2	yes	—
794	#95	C₂³×C₅₃	1	2	yes	—
795	#95	C₂³×C₅₃	1	2	yes	—
796	#95	C₂³×C₅₃	1	2	yes	—
797	#95	C₂³×C₅₃	1	2	yes	—
798	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
799	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
800	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
801	#41	—	2	32	no	—
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	2	2	no	—
806	C₂×Q₈	—	2	2	no	—
807	C₂×Q₈	#41×C₅₃	1	4	yes	—
808	C₂×D₄	—	2	4	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	4	no	—
812	C₂×D₄	—	2	4	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
820	C₂²×C₄	—	2	4	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	4	no	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	2	4	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	4	no	—
827	C₂²×C₄	—	2	4	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	4	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	4	1	no	—
843	C₂²×C₄	—	4	1	no	—
844	C₂²×C₄	—	4	2	no	—
845	C₂²×C₄	C₂×D₄×C₅₃	1	8	yes	—
846	C₂²×C₄	#41×C₅₃	1	4	yes	—
847	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
851	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
859	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
867	C₄⋊C₄	—	2	4	no	—
868	C₄⋊C₄	—	2	4	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	4	no	—
871	C₄⋊C₄	—	2	4	no	—
872	C₄⋊C₄	—	2	4	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	4	no	—
875	C₄⋊C₄	—	2	4	no	—
876	C₄⋊C₄	—	2	4	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	4	no	—
883	C₄⋊C₄	—	2	4	no	—
884	C₄⋊C₄	—	2	4	no	—
885	C₄⋊C₄	—	2	4	no	—
886	C₄⋊C₄	—	2	4	no	—
887	C₄⋊C₄	—	2	4	no	—
888	C₄⋊C₄	—	4	2	no	—
889	C₄⋊C₄	—	4	2	no	—
890	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	4	no	—
894	C₂²⋊C₄	—	2	4	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	4	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	4	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	4	no	—
907	C₂²⋊C₄	—	2	4	no	—
908	C₂²⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	4	2	no	—
910	C₂²⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
911	C₂²⋊C₄	#41×C₅₃	1	4	yes	complemented
912	C₄²	—	2	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	—	2	4	no	—
915	C₄²	—	2	2	no	—
916	C₄²	—	2	4	no	—
917	C₄²	—	2	2	no	—
918	C₄²	—	2	4	no	—
919	C₄²	—	2	2	no	—
920	C₄²	—	2	2	no	—
921	C₄²	—	2	4	no	—
922	C₄²	—	2	4	no	—
923	C₄²	—	2	2	no	—
924	C₄²	—	2	2	no	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	4	1	no	—
928	C₄²	C₂×D₄×C₅₃	1	4	yes	—
929	C₄²	#41×C₅₃	1	4	yes	complemented
930	C₂³	—	2	1	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	2	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	2	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	1	no	—
948	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
949	C₂³	C₂×#41×C₅₃	1	2	yes	—
950	C₂³	C₂×#41×C₅₃	1	2	yes	—
951	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
952	Q₈	—	2	8	no	—
953	Q₈	—	4	4	no	—
954	D₄	—	2	8	no	—
955	D₄	—	2	16	no	—
956	D₄	—	2	8	no	—
957	D₄	—	4	8	no	—
958	C₂×C₄	—	2	16	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	8	no	—
976	C₂×C₄	—	2	16	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	4	4	no	—
1008	C₂×C₄	—	4	8	no	—
1009	C₂×C₄	—	4	4	no	—
1010	C₂×C₄	—	4	4	no	—
1011	C₂×C₄	—	4	4	no	—
1012	C₂×C₄	—	4	4	no	—
1013	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1014	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
1015	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1016	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1017	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1018	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1019	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1020	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1021	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
1022	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1023	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1024	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1025	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1026	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	4	no	—
1029	C₂²	—	2	2	no	—
1030	C₂²	—	2	4	no	—
1031	C₂²	—	2	2	no	—
1032	C₂²	—	2	4	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	2	no	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	4	1	no	—
1037	C₂²	—	4	2	no	—
1038	C₂²	—	4	1	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1049	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1050	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1051	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1052	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1053	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1054	C₂²	C₅₃×#585	1	1	yes	characteristic
1055	C₄	—	2	4	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	4	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	4	2	no	—
1073	C₄	C₅₃×#525	1	4	yes	—
1074	C₄	C₅₃×#547	1	4	yes	—
1075	C₂	—	4	2	no	—
1076	C₂	—	4	4	no	—
1077	C₂	—	4	2	no	—
1078	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
1079	C₂	C₅₃×#3444	1	1	yes	characteristic
1080	C₂	C₅₃×#3461	1	1	yes	characteristic
1081	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
1082	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1083	C₂	C₅₃×#3480	1	1	yes	characteristic
1084	C₂	C₅₃×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
socle	C₂³×C₅₃	C₂⁵
prime radical	C₅₃×#2407	C₂
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×#529	C₂	semidirect
2. C₂×C₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#2478	C₂	semidirect
4. C₅₃×#2470	C₂	semidirect
5. C₅₃×#2466	C₂	semidirect
6. C₅₃×#2455	C₂	semidirect
7. C₅₃×#2453	C₂	semidirect
8. C₅₃×#2447	C₂	semidirect
9. C₅₃×#2441	C₂	semidirect
10. C₅₃×#2432	C₂	semidirect
11. C₅₃×#2429	C₂	semidirect
12. C₅₃×#2422	C₂	semidirect
13. C₅₃×#2415	C₂	semidirect
15. C₅₃×#2395	C₂	semidirect
16. C₅₃×#2392	C₂	semidirect
17. C₄×C₄⋊Q₈×C₅₃	C₂	semidirect
18. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
19. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
20. C₄×#123×C₅₃	C₂	semidirect
21. C₅₃×#2296	C₂	semidirect
22. C₅₃×#2293	C₂	semidirect
23. C₄²×D₄×C₅₃	C₂	semidirect
163. C₄×D₄×C₅₃	D₄	semidirect
368. C₂²⋊C₄×C₅₃	#41	semidirect
386. C₄²×C₅₃	#41	semidirect
484. #34724	C₅₃	direct (N × H)
533. C₂×#529	C₂×C₅₃	semidirect
534. C₂×C₄×#41	C₂×C₅₃	semidirect
535. #2478	C₂×C₅₃	semidirect
536. #2470	C₂×C₅₃	semidirect
537. #2466	C₂×C₅₃	semidirect
538. #2455	C₂×C₅₃	semidirect
539. #2453	C₂×C₅₃	semidirect
540. #2447	C₂×C₅₃	semidirect
541. #2441	C₂×C₅₃	semidirect
542. #2432	C₂×C₅₃	semidirect
543. #2429	C₂×C₅₃	semidirect
544. #2422	C₂×C₅₃	semidirect
545. #2415	C₂×C₅₃	semidirect
547. #2395	C₂×C₅₃	semidirect
548. #2392	C₂×C₅₃	semidirect
549. C₄×C₄⋊Q₈	C₂×C₅₃	semidirect
550. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
551. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
552. C₄×#123	C₂×C₅₃	semidirect
553. #2296	C₂×C₅₃	semidirect
554. #2293	C₂×C₅₃	semidirect
555. C₄²×D₄	C₂×C₅₃	semidirect
667. C₅₃	#34724	direct (N × H)
706. C₄×D₄	D₄×C₅₃	semidirect
911. C₂²⋊C₄	#41×C₅₃	semidirect
929. C₄²	#41×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×#529	2
C₂×C₄×#41×C₅₃	2
C₅₃×#2478	2
C₅₃×#2470	2
C₅₃×#2466	2
C₅₃×#2455	2
C₅₃×#2453	2
C₅₃×#2447	2
C₅₃×#2441	2
C₅₃×#2432	2
C₅₃×#2429	2
C₅₃×#2422	2
C₅₃×#2415	2
C₅₃×#2407	2
C₅₃×#2395	2
C₅₃×#2392	2
C₄×C₄⋊Q₈×C₅₃	2
C₄×C₂²⋊Q₈×C₅₃	2
C₄×#123×C₅₃	2
C₅₃×#2296	2
C₅₃×#2293	2
C₄²×D₄×C₅₃	2
#34724	53

Subgroups — C53×#34724 #27242236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34724 #27242236