Subgroups — C₅₃×#34691 #27242203

Order 13568.

2464 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2473	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2465	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2462	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2451	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2449	C₂	1	2	yes	maximal
8	C₅₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2423	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2417	C₂	1	1	yes	maximal, characteristic
14	C₅₃×#2409	C₂	1	1	yes	maximal, characteristic
15	C₅₃×#2399	C₂	1	2	yes	maximal, complemented
16	C₅₃×#2396	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×C₂²⋊Q₈×C₅₃	C₂	1	2	yes	maximal, complemented
21	C₅₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2290	C₂	1	2	yes	maximal
23	C₄²×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic
24	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₅₃×#533	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#125×C₅₃	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
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	2	yes	—
35	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×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	2	yes	—
40	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
43	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×#117×C₅₃	C₂²	1	2	yes	—
49	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
50	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
51	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₅₃	C₂²	1	2	yes	—
54	C₅₃×#400	C₂²	1	2	yes	—
55	C₅₃×#399	C₂²	1	2	yes	—
56	C₅₃×#398	C₂²	1	2	yes	—
57	C₅₃×#398	C₂²	1	2	yes	—
58	C₅₃×#398	C₂²	1	2	yes	—
59	C₅₃×#398	C₂²	1	2	yes	—
60	C₅₃×#398	C₂²	1	2	yes	—
61	C₅₃×#398	C₂²	1	2	yes	—
62	C₅₃×#396	C₂²	1	2	yes	—
63	C₅₃×#396	C₂²	1	2	yes	—
64	C₅₃×#395	C₂²	1	2	yes	—
65	C₅₃×#395	C₂²	1	2	yes	—
66	C₅₃×#395	C₂²	1	2	yes	—
67	C₅₃×#395	C₂²	1	2	yes	—
68	C₅₃×#395	C₂²	1	2	yes	—
69	C₅₃×#393	C₂²	1	2	yes	—
70	C₅₃×#391	C₂²	1	1	yes	characteristic
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×#391	C₂²	1	2	yes	—
76	C₅₃×#391	C₂²	1	1	yes	characteristic
77	C₅₃×#389	C₂²	1	1	yes	characteristic
78	C₅₃×#389	C₂²	1	1	yes	characteristic
79	C₅₃×#389	C₂²	1	2	yes	—
80	C₅₃×#389	C₂²	1	1	yes	characteristic
81	C₅₃×#389	C₂²	1	2	yes	—
82	C₅₃×#389	C₂²	1	1	yes	characteristic
83	C₅₃×#389	C₂²	1	2	yes	—
84	C₅₃×#388	C₂²	1	2	yes	—
85	C₅₃×#388	C₂²	1	2	yes	—
86	C₅₃×#387	C₂²	1	2	yes	—
87	C₅₃×#387	C₂²	1	2	yes	—
88	C₅₃×#387	C₂²	1	2	yes	—
89	C₅₃×#387	C₂²	1	2	yes	—
90	C₅₃×#387	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×#386	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×#384	C₂²	1	1	yes	characteristic
103	C₅₃×#380	C₂²	1	1	yes	characteristic
104	C₅₃×#380	C₂²	1	1	yes	characteristic
105	C₅₃×#380	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₅₃	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	2	yes	—
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	C₅₃×#376	C₂²	1	2	yes	—
124	C₄³×C₅₃	C₂²	1	1	yes	characteristic
125	C₂²×Q₈×C₅₃	—	2	4	no	—
126	C₂²×Q₈×C₅₃	—	2	4	no	—
127	C₂²×Q₈×C₅₃	—	2	4	no	—
128	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
129	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
130	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
131	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
138	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₅₃	—	2	4	no	—
143	C₄⋊Q₈×C₅₃	—	2	4	no	—
144	C₄⋊Q₈×C₅₃	—	2	4	no	—
145	#125×C₅₃	—	2	8	no	—
146	C₂²⋊Q₈×C₅₃	—	2	4	no	—
147	C₂²⋊Q₈×C₅₃	—	2	8	no	—
148	C₂²⋊Q₈×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	C₄×Q₈×C₅₃	—	2	8	no	—
153	C₄×Q₈×C₅₃	—	2	4	no	—
154	C₄×Q₈×C₅₃	—	2	4	no	—
155	C₄×Q₈×C₅₃	—	2	8	no	—
156	C₄×Q₈×C₅₃	—	2	8	no	—
157	C₄×Q₈×C₅₃	—	2	4	no	—
158	C₄×Q₈×C₅₃	—	2	4	no	—
159	C₄×Q₈×C₅₃	D₄	1	8	yes	complemented
160	C₄×D₄×C₅₃	—	2	4	no	—
161	C₄×D₄×C₅₃	—	2	4	no	—
162	C₄×D₄×C₅₃	Q₈	1	8	yes	complemented
163	#117×C₅₃	—	2	8	no	—
164	C₂×C₄⋊C₄×C₅₃	—	2	8	no	—
165	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
166	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
174	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
192	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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×C₄²×C₅₃	—	2	4	no	—
208	C₂×C₄²×C₅₃	—	2	8	no	—
209	C₂×C₄²×C₅₃	—	2	4	no	—
210	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
213	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
223	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
224	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
226	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
228	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
229	#95×C₅₃	C₂³	1	2	yes	—
230	#95×C₅₃	C₂³	1	2	yes	—
231	#95×C₅₃	C₂³	1	2	yes	—
232	#95×C₅₃	C₂³	1	2	yes	—
233	#95×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	2	yes	—
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	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
255	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
256	C₂×Q₈×C₅₃	—	2	32	no	—
257	C₂×Q₈×C₅₃	—	2	4	no	—
258	C₂×Q₈×C₅₃	—	2	2	no	—
259	C₂×Q₈×C₅₃	—	2	4	no	—
260	C₂×Q₈×C₅₃	—	2	2	no	—
261	C₂×Q₈×C₅₃	—	2	4	no	—
262	C₂×Q₈×C₅₃	—	2	4	no	—
263	C₂×Q₈×C₅₃	—	2	2	no	—
264	C₂×Q₈×C₅₃	—	2	2	no	—
265	C₂×Q₈×C₅₃	—	2	2	no	—
266	C₂×Q₈×C₅₃	—	2	4	no	—
267	C₂×Q₈×C₅₃	—	2	2	no	—
268	C₂×Q₈×C₅₃	—	2	2	no	—
269	C₂×Q₈×C₅₃	—	4	2	no	—
270	C₂×Q₈×C₅₃	C₂×D₄	1	4	yes	—
271	C₂×Q₈×C₅₃	#41	1	4	yes	—
272	C₂×D₄×C₅₃	—	2	2	no	—
273	C₂×D₄×C₅₃	—	2	2	no	—
274	C₂×D₄×C₅₃	C₂×Q₈	1	4	yes	—
275	C₂²×C₄×C₅₃	—	2	4	no	—
276	C₂²×C₄×C₅₃	—	2	2	no	—
277	C₂²×C₄×C₅₃	—	2	4	no	—
278	C₂²×C₄×C₅₃	—	2	2	no	—
279	C₂²×C₄×C₅₃	—	2	2	no	—
280	C₂²×C₄×C₅₃	—	2	4	no	—
281	C₂²×C₄×C₅₃	—	2	2	no	—
282	C₂²×C₄×C₅₃	—	2	2	no	—
283	C₂²×C₄×C₅₃	—	2	2	no	—
284	C₂²×C₄×C₅₃	—	2	2	no	—
285	C₂²×C₄×C₅₃	—	2	4	no	—
286	C₂²×C₄×C₅₃	—	2	2	no	—
287	C₂²×C₄×C₅₃	—	2	4	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	—	4	1	no	—
294	C₂²×C₄×C₅₃	—	4	1	no	—
295	C₂²×C₄×C₅₃	—	4	2	no	—
296	C₂²×C₄×C₅₃	C₂×Q₈	1	4	yes	—
297	C₂²×C₄×C₅₃	C₂×Q₈	1	4	yes	complemented
298	C₂²×C₄×C₅₃	#41	1	4	yes	—
299	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
308	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₅₃	—	2	4	no	—
321	C₄⋊C₄×C₅₃	—	2	4	no	—
322	C₄⋊C₄×C₅₃	—	2	4	no	—
323	C₄⋊C₄×C₅₃	—	2	4	no	—
324	C₄⋊C₄×C₅₃	—	2	2	no	—
325	C₄⋊C₄×C₅₃	—	2	4	no	—
326	C₄⋊C₄×C₅₃	—	2	4	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	4	no	—
331	C₄⋊C₄×C₅₃	—	2	2	no	—
332	C₄⋊C₄×C₅₃	—	2	2	no	—
333	C₄⋊C₄×C₅₃	—	2	2	no	—
334	C₄⋊C₄×C₅₃	—	2	4	no	—
335	C₄⋊C₄×C₅₃	—	2	4	no	—
336	C₄⋊C₄×C₅₃	—	2	4	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	—	4	2	no	—
344	C₄⋊C₄×C₅₃	—	4	2	no	—
345	C₄⋊C₄×C₅₃	—	4	2	no	—
346	C₄⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
347	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
348	C₄⋊C₄×C₅₃	C₂×Q₈	1	4	yes	complemented
349	C₂²⋊C₄×C₅₃	—	2	2	no	—
350	C₂²⋊C₄×C₅₃	—	2	4	no	—
351	C₂²⋊C₄×C₅₃	—	2	4	no	—
352	C₂²⋊C₄×C₅₃	—	2	4	no	—
353	C₂²⋊C₄×C₅₃	—	2	4	no	—
354	C₂²⋊C₄×C₅₃	—	2	2	no	—
355	C₂²⋊C₄×C₅₃	—	2	2	no	—
356	C₂²⋊C₄×C₅₃	—	2	4	no	—
357	C₂²⋊C₄×C₅₃	—	4	2	no	—
358	C₂²⋊C₄×C₅₃	C₂×Q₈	1	4	yes	—
359	C₂²⋊C₄×C₅₃	C₂×Q₈	1	4	yes	complemented
360	C₂²⋊C₄×C₅₃	#41	1	4	yes	—
361	C₄²×C₅₃	—	2	2	no	—
362	C₄²×C₅₃	—	2	4	no	—
363	C₄²×C₅₃	—	2	2	no	—
364	C₄²×C₅₃	—	2	4	no	—
365	C₄²×C₅₃	—	2	2	no	—
366	C₄²×C₅₃	—	2	4	no	—
367	C₄²×C₅₃	—	2	2	no	—
368	C₄²×C₅₃	—	2	2	no	—
369	C₄²×C₅₃	—	2	2	no	—
370	C₄²×C₅₃	—	2	4	no	—
371	C₄²×C₅₃	—	2	2	no	—
372	C₄²×C₅₃	—	2	2	no	—
373	C₄²×C₅₃	—	2	2	no	—
374	C₄²×C₅₃	—	2	2	no	—
375	C₄²×C₅₃	—	2	4	no	—
376	C₄²×C₅₃	—	4	1	no	—
377	C₄²×C₅₃	C₂×D₄	1	4	yes	—
378	C₄²×C₅₃	C₂×D₄	1	8	yes	—
379	C₄²×C₅₃	C₂×Q₈	1	4	yes	complemented
380	C₂³×C₅₃	—	2	1	no	—
381	C₂³×C₅₃	—	2	1	no	—
382	C₂³×C₅₃	—	2	1	no	—
383	C₂³×C₅₃	—	2	1	no	—
384	C₂³×C₅₃	—	2	1	no	—
385	C₂³×C₅₃	—	2	1	no	—
386	C₂³×C₅₃	—	2	1	no	—
387	C₂³×C₅₃	—	2	1	no	—
388	C₂³×C₅₃	—	2	1	no	—
389	C₂³×C₅₃	—	2	1	no	—
390	C₂³×C₅₃	C₂²×Q₈	1	2	yes	—
391	C₂³×C₅₃	C₂²×Q₈	1	2	yes	—
392	C₂³×C₅₃	C₂×#41	1	2	yes	—
393	C₂³×C₅₃	C₂×#41	1	2	yes	—
394	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
395	Q₈×C₅₃	—	2	16	no	—
396	Q₈×C₅₃	—	2	8	no	—
397	Q₈×C₅₃	—	2	8	no	—
398	Q₈×C₅₃	—	4	8	no	—
399	Q₈×C₅₃	—	4	4	no	—
400	D₄×C₅₃	—	2	8	no	—
401	C₂×C₄×C₅₃	—	2	16	no	—
402	C₂×C₄×C₅₃	—	2	2	no	—
403	C₂×C₄×C₅₃	—	2	1	no	—
404	C₂×C₄×C₅₃	—	2	1	no	—
405	C₂×C₄×C₅₃	—	2	1	no	—
406	C₂×C₄×C₅₃	—	2	1	no	—
407	C₂×C₄×C₅₃	—	2	1	no	—
408	C₂×C₄×C₅₃	—	2	2	no	—
409	C₂×C₄×C₅₃	—	2	2	no	—
410	C₂×C₄×C₅₃	—	2	2	no	—
411	C₂×C₄×C₅₃	—	2	1	no	—
412	C₂×C₄×C₅₃	—	2	2	no	—
413	C₂×C₄×C₅₃	—	2	1	no	—
414	C₂×C₄×C₅₃	—	2	1	no	—
415	C₂×C₄×C₅₃	—	2	1	no	—
416	C₂×C₄×C₅₃	—	2	1	no	—
417	C₂×C₄×C₅₃	—	2	1	no	—
418	C₂×C₄×C₅₃	—	2	1	no	—
419	C₂×C₄×C₅₃	—	2	1	no	—
420	C₂×C₄×C₅₃	—	2	1	no	—
421	C₂×C₄×C₅₃	—	2	1	no	—
422	C₂×C₄×C₅₃	—	2	2	no	—
423	C₂×C₄×C₅₃	—	2	1	no	—
424	C₂×C₄×C₅₃	—	2	8	no	—
425	C₂×C₄×C₅₃	—	2	8	no	—
426	C₂×C₄×C₅₃	—	2	8	no	—
427	C₂×C₄×C₅₃	—	2	1	no	—
428	C₂×C₄×C₅₃	—	2	1	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	1	no	—
433	C₂×C₄×C₅₃	—	2	1	no	—
434	C₂×C₄×C₅₃	—	2	1	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	1	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	1	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	1	no	—
448	C₂×C₄×C₅₃	—	2	2	no	—
449	C₂×C₄×C₅₃	—	2	1	no	—
450	C₂×C₄×C₅₃	—	2	2	no	—
451	C₂×C₄×C₅₃	—	4	4	no	—
452	C₂×C₄×C₅₃	—	4	4	no	—
453	C₂×C₄×C₅₃	—	4	8	no	—
454	C₂×C₄×C₅₃	—	4	4	no	—
455	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
457	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
458	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
461	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
462	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
463	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
464	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
465	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
466	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
467	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
468	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
469	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
470	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
471	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
472	#34691	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
473	C₂²×C₅₃	—	2	2	no	—
474	C₂²×C₅₃	—	2	2	no	—
475	C₂²×C₅₃	—	2	2	no	—
476	C₂²×C₅₃	—	2	2	no	—
477	C₂²×C₅₃	—	2	2	no	—
478	C₂²×C₅₃	—	2	2	no	—
479	C₂²×C₅₃	—	2	2	no	—
480	C₂²×C₅₃	—	2	2	no	—
481	C₂²×C₅₃	—	2	2	no	—
482	C₂²×C₅₃	—	4	1	no	—
483	C₂²×C₅₃	—	4	1	no	—
484	C₂²×C₅₃	—	4	1	no	—
485	C₂²×C₅₃	—	4	1	no	—
486	C₂²×C₅₃	#533	1	4	yes	complemented
487	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
488	C₂²×C₅₃	C₂³×Q₈	1	1	yes	characteristic
489	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
490	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
491	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
492	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
493	C₂²×C₅₃	#585	1	1	yes	characteristic
494	C₄×C₅₃	—	2	4	no	—
495	C₄×C₅₃	—	2	4	no	—
496	C₄×C₅₃	—	2	2	no	—
497	C₄×C₅₃	—	2	2	no	—
498	C₄×C₅₃	—	2	2	no	—
499	C₄×C₅₃	—	2	2	no	—
500	C₄×C₅₃	—	2	2	no	—
501	C₄×C₅₃	—	2	4	no	—
502	C₄×C₅₃	—	2	2	no	—
503	C₄×C₅₃	—	2	2	no	—
504	C₄×C₅₃	—	2	2	no	—
505	C₄×C₅₃	—	4	1	no	—
506	C₄×C₅₃	—	4	2	no	—
507	C₄×C₅₃	—	4	1	no	—
508	C₄×C₅₃	—	4	2	no	—
509	C₄×C₅₃	—	4	1	no	—
510	C₄×C₅₃	—	4	2	no	—
511	C₄×C₅₃	—	4	2	no	—
512	C₄×C₅₃	—	4	2	no	—
513	C₄×C₅₃	#525	1	4	yes	—
514	C₄×C₅₃	D₄×Q₈	1	4	yes	—
515	C₂×#533	C₂×C₅₃	1	1	yes	characteristic, complemented
516	C₂²×C₄×Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
517	#2473	C₂×C₅₃	1	2	yes	complemented
518	#2465	C₂×C₅₃	1	2	yes	complemented
519	#2462	C₂×C₅₃	1	2	yes	complemented
520	#2451	C₂×C₅₃	1	1	yes	characteristic, complemented
521	#2449	C₂×C₅₃	1	2	yes	—
522	#2446	C₂×C₅₃	1	1	yes	characteristic, complemented
523	#2440	C₂×C₅₃	1	1	yes	characteristic, complemented
524	#2434	C₂×C₅₃	1	1	yes	characteristic, complemented
525	#2429	C₂×C₅₃	1	1	yes	characteristic, complemented
526	#2423	C₂×C₅₃	1	1	yes	characteristic, complemented
527	#2417	C₂×C₅₃	1	1	yes	characteristic
528	#2409	C₂×C₅₃	1	1	yes	characteristic
529	#2399	C₂×C₅₃	1	2	yes	complemented
530	#2396	C₂×C₅₃	1	2	yes	complemented
531	C₄×C₄⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
532	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
533	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
534	C₄×C₂²⋊Q₈	C₂×C₅₃	1	2	yes	complemented
535	#2295	C₂×C₅₃	1	1	yes	characteristic, complemented
536	#2290	C₂×C₅₃	1	2	yes	—
537	C₄²×D₄	C₂×C₅₃	1	1	yes	characteristic
538	C₂×C₅₃	—	2	4	no	—
539	C₂×C₅₃	—	4	2	no	—
540	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
541	C₂×C₅₃	C₂×#533	1	1	yes	characteristic
542	C₂×C₅₃	#3461	1	1	yes	characteristic
543	C₂×C₅₃	C₂×D₄×Q₈	1	1	yes	characteristic
544	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
545	C₂×C₅₃	Q₈×#41	1	1	yes	characteristic
546	C₂×C₅₃	#3482	1	1	yes	characteristic
547	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic
548	#533	—	2	8	no	—
549	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
550	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
551	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
552	C₂×#125	C₂²×C₅₃	1	2	yes	—
553	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
554	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
555	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
556	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
557	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
558	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
559	C₂×C₄×Q₈	—	2	8	no	—
560	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
561	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
562	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
563	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
564	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
565	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
566	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
567	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
568	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
569	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
570	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
571	C₂×#117	C₂²×C₅₃	1	2	yes	—
572	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
573	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
574	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
575	C₂²×C₄²	C₂²×C₅₃	1	2	yes	—
576	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
577	#400	C₂²×C₅₃	1	2	yes	—
578	#399	C₂²×C₅₃	1	2	yes	—
579	#398	C₂²×C₅₃	1	2	yes	—
580	#398	C₂²×C₅₃	1	2	yes	—
581	#398	C₂²×C₅₃	1	2	yes	—
582	#398	C₂²×C₅₃	1	2	yes	—
583	#398	C₂²×C₅₃	1	2	yes	—
584	#398	C₂²×C₅₃	1	2	yes	—
585	#396	C₂²×C₅₃	1	2	yes	—
586	#396	C₂²×C₅₃	1	2	yes	—
587	#395	C₂²×C₅₃	1	2	yes	—
588	#395	C₂²×C₅₃	1	2	yes	—
589	#395	C₂²×C₅₃	1	2	yes	—
590	#395	C₂²×C₅₃	1	2	yes	—
591	#395	C₂²×C₅₃	1	2	yes	—
592	#393	C₂²×C₅₃	1	2	yes	—
593	#391	C₂²×C₅₃	1	1	yes	characteristic
594	#391	C₂²×C₅₃	1	1	yes	characteristic
595	#391	C₂²×C₅₃	1	1	yes	characteristic
596	#391	C₂²×C₅₃	1	1	yes	characteristic
597	#391	C₂²×C₅₃	1	1	yes	characteristic
598	#391	C₂²×C₅₃	1	1	yes	characteristic
599	#391	C₂²×C₅₃	1	2	yes	—
600	#389	C₂²×C₅₃	1	2	yes	—
601	#389	C₂²×C₅₃	1	2	yes	—
602	#389	C₂²×C₅₃	1	1	yes	characteristic
603	#389	C₂²×C₅₃	1	1	yes	characteristic
604	#389	C₂²×C₅₃	1	1	yes	characteristic
605	#389	C₂²×C₅₃	1	2	yes	—
606	#389	C₂²×C₅₃	1	1	yes	characteristic
607	#388	C₂²×C₅₃	1	2	yes	—
608	#388	C₂²×C₅₃	1	2	yes	—
609	#387	C₂²×C₅₃	1	2	yes	—
610	#387	C₂²×C₅₃	1	2	yes	—
611	#387	C₂²×C₅₃	1	2	yes	—
612	#387	C₂²×C₅₃	1	2	yes	—
613	#387	C₂²×C₅₃	1	2	yes	—
614	#387	C₂²×C₅₃	1	2	yes	—
615	#387	C₂²×C₅₃	1	2	yes	—
616	#387	C₂²×C₅₃	1	2	yes	—
617	#386	C₂²×C₅₃	1	2	yes	—
618	#386	C₂²×C₅₃	1	2	yes	—
619	#385	C₂²×C₅₃	1	2	yes	—
620	#385	C₂²×C₅₃	1	2	yes	—
621	#385	C₂²×C₅₃	1	2	yes	—
622	#385	C₂²×C₅₃	1	2	yes	—
623	#385	C₂²×C₅₃	1	2	yes	—
624	#385	C₂²×C₅₃	1	2	yes	—
625	#384	C₂²×C₅₃	1	1	yes	characteristic
626	#380	C₂²×C₅₃	1	1	yes	characteristic
627	#380	C₂²×C₅₃	1	1	yes	characteristic
628	#380	C₂²×C₅₃	1	2	yes	—
629	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
630	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
631	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
632	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
633	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
634	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
635	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
636	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
637	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
638	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
639	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
640	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
641	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
642	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
643	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
644	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
645	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
646	#376	C₂²×C₅₃	1	2	yes	—
647	C₄³	C₂²×C₅₃	1	1	yes	characteristic
648	C₅₃	#34691	1	1	yes	characteristic, direct product factor, Sylow
649	C₂²×Q₈	—	2	4	no	—
650	C₂²×Q₈	—	2	4	no	—
651	C₂²×Q₈	—	2	4	no	—
652	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
653	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
654	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
655	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
656	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
657	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
663	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
664	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
665	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
666	C₄⋊Q₈	—	2	4	no	—
667	C₄⋊Q₈	—	2	4	no	—
668	C₄⋊Q₈	—	2	4	no	—
669	#125	—	2	8	no	—
670	C₂²⋊Q₈	—	2	4	no	—
671	C₂²⋊Q₈	—	2	4	no	—
672	C₂²⋊Q₈	—	2	4	no	—
673	C₂²⋊Q₈	—	2	4	no	—
674	C₂²⋊Q₈	—	2	8	no	—
675	C₂²⋊Q₈	—	2	8	no	—
676	C₄×Q₈	—	2	4	no	—
677	C₄×Q₈	—	2	8	no	—
678	C₄×Q₈	—	2	4	no	—
679	C₄×Q₈	—	2	4	no	—
680	C₄×Q₈	—	2	8	no	—
681	C₄×Q₈	—	2	8	no	—
682	C₄×Q₈	—	2	4	no	—
683	C₄×Q₈	D₄×C₅₃	1	8	yes	complemented
684	C₄×D₄	—	2	4	no	—
685	C₄×D₄	—	2	4	no	—
686	C₄×D₄	Q₈×C₅₃	1	8	yes	complemented
687	#117	—	2	8	no	—
688	C₂×C₄⋊C₄	—	2	8	no	—
689	C₂×C₄⋊C₄	—	2	4	no	—
690	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
699	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
707	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
708	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
709	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
710	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
711	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
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	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
719	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
722	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
723	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
724	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
729	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
730	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
731	C₂×C₄²	—	2	4	no	—
732	C₂×C₄²	—	2	8	no	—
733	C₂×C₄²	—	2	4	no	—
734	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
735	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
738	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
740	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
743	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
744	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
745	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
746	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
747	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
748	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
749	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
750	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
751	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
753	#95	C₂³×C₅₃	1	2	yes	—
754	#95	C₂³×C₅₃	1	2	yes	—
755	#95	C₂³×C₅₃	1	2	yes	—
756	#95	C₂³×C₅₃	1	2	yes	—
757	#95	C₂³×C₅₃	1	1	yes	characteristic
758	#95	C₂³×C₅₃	1	1	yes	characteristic
759	#95	C₂³×C₅₃	1	1	yes	characteristic
760	#95	C₂³×C₅₃	1	1	yes	characteristic
761	#95	C₂³×C₅₃	1	1	yes	characteristic
762	#95	C₂³×C₅₃	1	1	yes	characteristic
763	#95	C₂³×C₅₃	1	2	yes	—
764	#95	C₂³×C₅₃	1	2	yes	—
765	#95	C₂³×C₅₃	1	2	yes	—
766	#95	C₂³×C₅₃	1	2	yes	—
767	#95	C₂³×C₅₃	1	2	yes	—
768	#95	C₂³×C₅₃	1	2	yes	—
769	#95	C₂³×C₅₃	1	2	yes	—
770	#95	C₂³×C₅₃	1	2	yes	—
771	#95	C₂³×C₅₃	1	2	yes	—
772	#95	C₂³×C₅₃	1	2	yes	—
773	#95	C₂³×C₅₃	1	2	yes	—
774	#95	C₂³×C₅₃	1	2	yes	—
775	#95	C₂³×C₅₃	1	2	yes	—
776	#95	C₂³×C₅₃	1	2	yes	—
777	#95	C₂³×C₅₃	1	2	yes	—
778	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
779	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
780	C₂×Q₈	—	2	32	no	—
781	C₂×Q₈	—	2	4	no	—
782	C₂×Q₈	—	2	2	no	—
783	C₂×Q₈	—	2	4	no	—
784	C₂×Q₈	—	2	2	no	—
785	C₂×Q₈	—	2	4	no	—
786	C₂×Q₈	—	2	4	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	2	2	no	—
789	C₂×Q₈	—	2	2	no	—
790	C₂×Q₈	—	2	4	no	—
791	C₂×Q₈	—	2	2	no	—
792	C₂×Q₈	—	2	2	no	—
793	C₂×Q₈	—	4	2	no	—
794	C₂×Q₈	C₂×D₄×C₅₃	1	4	yes	—
795	C₂×Q₈	#41×C₅₃	1	4	yes	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	C₂×Q₈×C₅₃	1	4	yes	—
799	C₂²×C₄	—	2	4	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	4	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	4	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	4	1	no	—
818	C₂²×C₄	—	4	1	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	C₂×Q₈×C₅₃	1	4	yes	—
821	C₂²×C₄	C₂×Q₈×C₅₃	1	4	yes	complemented
822	C₂²×C₄	#41×C₅₃	1	4	yes	—
823	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
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	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
840	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
844	C₄⋊C₄	—	2	4	no	—
845	C₄⋊C₄	—	2	4	no	—
846	C₄⋊C₄	—	2	4	no	—
847	C₄⋊C₄	—	2	4	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	4	no	—
850	C₄⋊C₄	—	2	4	no	—
851	C₄⋊C₄	—	2	4	no	—
852	C₄⋊C₄	—	2	4	no	—
853	C₄⋊C₄	—	2	4	no	—
854	C₄⋊C₄	—	2	4	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	4	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	4	no	—
862	C₄⋊C₄	—	2	4	no	—
863	C₄⋊C₄	—	2	4	no	—
864	C₄⋊C₄	—	2	4	no	—
865	C₄⋊C₄	—	2	4	no	—
866	C₄⋊C₄	—	2	4	no	—
867	C₄⋊C₄	—	4	2	no	—
868	C₄⋊C₄	—	4	2	no	—
869	C₄⋊C₄	—	4	2	no	—
870	C₄⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
871	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
872	C₄⋊C₄	C₂×Q₈×C₅₃	1	4	yes	complemented
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	4	no	—
875	C₂²⋊C₄	—	2	4	no	—
876	C₂²⋊C₄	—	2	4	no	—
877	C₂²⋊C₄	—	2	4	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	4	no	—
881	C₂²⋊C₄	—	4	2	no	—
882	C₂²⋊C₄	C₂×Q₈×C₅₃	1	4	yes	—
883	C₂²⋊C₄	C₂×Q₈×C₅₃	1	4	yes	complemented
884	C₂²⋊C₄	#41×C₅₃	1	4	yes	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	4	no	—
887	C₄²	—	2	4	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	—	2	4	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	4	no	—
895	C₄²	—	2	2	no	—
896	C₄²	—	2	2	no	—
897	C₄²	—	2	2	no	—
898	C₄²	—	2	2	no	—
899	C₄²	—	2	4	no	—
900	C₄²	—	4	1	no	—
901	C₄²	C₂×D₄×C₅₃	1	4	yes	—
902	C₄²	C₂×D₄×C₅₃	1	8	yes	—
903	C₄²	C₂×Q₈×C₅₃	1	4	yes	complemented
904	C₂³	—	2	1	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	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	1	no	—
914	C₂³	C₂²×Q₈×C₅₃	1	2	yes	—
915	C₂³	C₂²×Q₈×C₅₃	1	2	yes	—
916	C₂³	C₂×#41×C₅₃	1	2	yes	—
917	C₂³	C₂×#41×C₅₃	1	2	yes	—
918	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
919	Q₈	—	2	16	no	—
920	Q₈	—	2	8	no	—
921	Q₈	—	2	8	no	—
922	Q₈	—	4	8	no	—
923	Q₈	—	4	4	no	—
924	D₄	—	2	8	no	—
925	C₂×C₄	—	2	16	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	8	no	—
949	C₂×C₄	—	2	8	no	—
950	C₂×C₄	—	2	8	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	4	4	no	—
977	C₂×C₄	—	4	8	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
980	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
981	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
982	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
983	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
984	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
985	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
986	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
987	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
988	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
989	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
990	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
991	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
992	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
993	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
994	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
995	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	C₅₃×#533	1	4	yes	complemented
1010	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1011	C₂²	C₂³×Q₈×C₅₃	1	1	yes	characteristic
1012	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1013	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1014	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1015	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1016	C₂²	C₅₃×#585	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	2	no	—
1020	C₄	—	2	4	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	2	4	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	2	no	—
1028	C₄	—	4	1	no	—
1029	C₄	—	4	2	no	—
1030	C₄	—	4	1	no	—
1031	C₄	—	4	2	no	—
1032	C₄	—	4	2	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	2	no	—
1036	C₄	C₅₃×#525	1	4	yes	—
1037	C₄	D₄×Q₈×C₅₃	1	4	yes	—
1038	C₂	—	2	4	no	—
1039	C₂	—	4	2	no	—
1040	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
1041	C₂	C₂×C₅₃×#533	1	1	yes	characteristic
1042	C₂	C₅₃×#3461	1	1	yes	characteristic
1043	C₂	C₂×D₄×Q₈×C₅₃	1	1	yes	characteristic
1044	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1045	C₂	Q₈×#41×C₅₃	1	1	yes	characteristic
1046	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	C₂²×D₄×C₅₃	C₂³
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×#533	C₂	semidirect
2. C₂²×C₄×Q₈×C₅₃	C₂	semidirect
3. C₅₃×#2473	C₂	semidirect
4. C₅₃×#2465	C₂	semidirect
5. C₅₃×#2462	C₂	semidirect
6. C₅₃×#2451	C₂	semidirect
8. C₅₃×#2446	C₂	semidirect
9. C₅₃×#2440	C₂	semidirect
10. C₅₃×#2434	C₂	semidirect
11. C₅₃×#2429	C₂	semidirect
12. C₅₃×#2423	C₂	semidirect
15. C₅₃×#2399	C₂	semidirect
16. C₅₃×#2396	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×C₂²⋊Q₈×C₅₃	C₂	semidirect
21. C₅₃×#2295	C₂	semidirect
159. C₄×Q₈×C₅₃	D₄	semidirect
162. C₄×D₄×C₅₃	Q₈	semidirect
297. C₂²×C₄×C₅₃	C₂×Q₈	semidirect
348. C₄⋊C₄×C₅₃	C₂×Q₈	semidirect
359. C₂²⋊C₄×C₅₃	C₂×Q₈	semidirect
379. C₄²×C₅₃	C₂×Q₈	semidirect
472. #34691	C₅₃	direct (N × H)
486. C₂²×C₅₃	#533	semidirect
515. C₂×#533	C₂×C₅₃	semidirect
516. C₂²×C₄×Q₈	C₂×C₅₃	semidirect
517. #2473	C₂×C₅₃	semidirect
518. #2465	C₂×C₅₃	semidirect
519. #2462	C₂×C₅₃	semidirect
520. #2451	C₂×C₅₃	semidirect
522. #2446	C₂×C₅₃	semidirect
523. #2440	C₂×C₅₃	semidirect
524. #2434	C₂×C₅₃	semidirect
525. #2429	C₂×C₅₃	semidirect
526. #2423	C₂×C₅₃	semidirect
529. #2399	C₂×C₅₃	semidirect
530. #2396	C₂×C₅₃	semidirect
531. C₄×C₄⋊Q₈	C₂×C₅₃	semidirect
532. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
533. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
534. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
535. #2295	C₂×C₅₃	semidirect
648. C₅₃	#34691	direct (N × H)
683. C₄×Q₈	D₄×C₅₃	semidirect
686. C₄×D₄	Q₈×C₅₃	semidirect
821. C₂²×C₄	C₂×Q₈×C₅₃	semidirect
872. C₄⋊C₄	C₂×Q₈×C₅₃	semidirect
883. C₂²⋊C₄	C₂×Q₈×C₅₃	semidirect
903. C₄²	C₂×Q₈×C₅₃	semidirect
1009. C₂²	C₅₃×#533	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#533	2
C₂²×C₄×Q₈×C₅₃	2
C₅₃×#2473	2
C₅₃×#2465	2
C₅₃×#2462	2
C₅₃×#2451	2
C₅₃×#2449	2
C₅₃×#2446	2
C₅₃×#2440	2
C₅₃×#2434	2
C₅₃×#2429	2
C₅₃×#2423	2
C₅₃×#2417	2
C₅₃×#2409	2
C₅₃×#2399	2
C₅₃×#2396	2
C₄×C₄⋊Q₈×C₅₃	2
C₄×C₂²⋊Q₈×C₅₃	2
C₅₃×#2295	2
C₅₃×#2290	2
C₄²×D₄×C₅₃	2
#34691	53

Subgroups — C53×#34691 #27242203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34691 #27242203