Subgroups — C₅₃×#3566 #20272503

Order 6784.

954 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#562	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#562	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#560	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
32	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	#127×C₅₃	C₂²	1	1	yes	characteristic
36	#126×C₅₃	C₂²	1	1	yes	characteristic
37	#126×C₅₃	C₂²	1	1	yes	characteristic
38	#126×C₅₃	C₂²	1	1	yes	characteristic
39	#126×C₅₃	C₂²	1	1	yes	characteristic
40	#126×C₅₃	C₂²	1	1	yes	characteristic
41	#126×C₅₃	C₂²	1	1	yes	characteristic
42	#126×C₅₃	C₂²	1	1	yes	characteristic
43	#126×C₅₃	C₂²	1	1	yes	characteristic
44	#126×C₅₃	C₂²	1	1	yes	characteristic
45	#126×C₅₃	C₂²	1	1	yes	characteristic
46	#126×C₅₃	C₂²	1	1	yes	characteristic
47	#126×C₅₃	C₂²	1	1	yes	characteristic
48	#126×C₅₃	C₂²	1	1	yes	characteristic
49	#126×C₅₃	C₂²	1	1	yes	characteristic
50	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
52	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
56	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
66	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	#124×C₅₃	C₂²	1	1	yes	characteristic
69	#124×C₅₃	C₂²	1	1	yes	characteristic
70	#124×C₅₃	C₂²	1	1	yes	characteristic
71	#124×C₅₃	C₂²	1	1	yes	characteristic
72	#124×C₅₃	C₂²	1	1	yes	characteristic
73	#124×C₅₃	C₂²	1	1	yes	characteristic
74	#124×C₅₃	C₂²	1	1	yes	characteristic
75	#124×C₅₃	C₂²	1	1	yes	characteristic
76	#124×C₅₃	C₂²	1	1	yes	characteristic
77	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
78	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
79	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
80	#123×C₅₃	C₂²	1	1	yes	characteristic
81	#123×C₅₃	C₂²	1	1	yes	characteristic
82	#123×C₅₃	C₂²	1	1	yes	characteristic
83	#123×C₅₃	C₂²	1	1	yes	characteristic
84	#123×C₅₃	C₂²	1	1	yes	characteristic
85	#123×C₅₃	C₂²	1	1	yes	characteristic
86	#123×C₅₃	C₂²	1	1	yes	characteristic
87	#123×C₅₃	C₂²	1	1	yes	characteristic
88	#123×C₅₃	C₂²	1	1	yes	characteristic
89	#123×C₅₃	C₂²	1	1	yes	characteristic
90	#123×C₅₃	C₂²	1	1	yes	characteristic
91	#123×C₅₃	C₂²	1	1	yes	characteristic
92	#123×C₅₃	C₂²	1	1	yes	characteristic
93	#123×C₅₃	C₂²	1	1	yes	characteristic
94	#123×C₅₃	C₂²	1	1	yes	characteristic
95	#123×C₅₃	C₂²	1	1	yes	characteristic
96	#123×C₅₃	C₂²	1	1	yes	characteristic
97	#123×C₅₃	C₂²	1	1	yes	characteristic
98	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
99	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
100	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
101	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
102	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
103	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
104	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
105	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
106	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
107	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
108	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
109	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
110	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
111	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
112	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
113	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	#121×C₅₃	C₂²	1	1	yes	characteristic
123	#121×C₅₃	C₂²	1	1	yes	characteristic
124	#121×C₅₃	C₂²	1	1	yes	characteristic
125	#121×C₅₃	C₂²	1	1	yes	characteristic
126	#121×C₅₃	C₂²	1	1	yes	characteristic
127	#121×C₅₃	C₂²	1	1	yes	characteristic
128	#121×C₅₃	C₂²	1	1	yes	characteristic
129	#121×C₅₃	C₂²	1	1	yes	characteristic
130	#121×C₅₃	C₂²	1	1	yes	characteristic
131	#121×C₅₃	C₂²	1	1	yes	characteristic
132	#121×C₅₃	C₂²	1	1	yes	characteristic
133	#121×C₅₃	C₂²	1	1	yes	characteristic
134	#121×C₅₃	C₂²	1	1	yes	characteristic
135	#121×C₅₃	C₂²	1	1	yes	characteristic
136	#121×C₅₃	C₂²	1	1	yes	characteristic
137	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
138	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
140	#120×C₅₃	C₂²	1	1	yes	characteristic
141	#120×C₅₃	C₂²	1	1	yes	characteristic
142	#120×C₅₃	C₂²	1	1	yes	characteristic
143	#120×C₅₃	C₂²	1	1	yes	characteristic
144	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
145	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
146	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
147	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
148	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
149	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
150	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
151	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
152	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
153	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
154	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
155	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
156	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
157	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
158	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
159	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
160	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
161	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
162	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
163	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
164	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
165	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
166	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
167	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
168	#117×C₅₃	C₂²	1	1	yes	characteristic
169	#117×C₅₃	C₂²	1	1	yes	characteristic
170	#117×C₅₃	C₂²	1	1	yes	characteristic
171	#117×C₅₃	C₂²	1	1	yes	characteristic
172	#117×C₅₃	C₂²	1	1	yes	characteristic
173	#117×C₅₃	C₂²	1	1	yes	characteristic
174	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
175	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
177	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
188	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
192	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
193	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
216	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
217	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
218	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
219	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
220	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
221	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
222	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
223	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
224	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
225	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
226	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
227	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
292	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
293	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
294	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
295	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
296	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
297	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
298	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
299	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
300	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
301	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
302	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
303	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
305	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
307	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
310	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
311	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
312	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
313	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
314	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
315	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
316	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
317	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
318	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
319	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
320	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
321	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
322	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
323	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
324	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
325	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
326	C₄²×C₅₃	C₂³	1	1	yes	characteristic
327	C₄²×C₅₃	C₂³	1	1	yes	characteristic
328	C₄²×C₅₃	C₂³	1	1	yes	characteristic
329	C₄²×C₅₃	C₂³	1	1	yes	characteristic
330	C₄²×C₅₃	C₂³	1	1	yes	characteristic
331	C₄²×C₅₃	C₂³	1	1	yes	characteristic
332	C₄²×C₅₃	C₂³	1	1	yes	characteristic
333	C₄²×C₅₃	C₂³	1	1	yes	characteristic
334	C₄²×C₅₃	C₂³	1	1	yes	characteristic
335	C₄²×C₅₃	C₂³	1	1	yes	characteristic
336	C₄²×C₅₃	C₂³	1	1	yes	characteristic
337	C₄²×C₅₃	C₂³	1	1	yes	characteristic
338	C₄²×C₅₃	C₂³	1	1	yes	characteristic
339	C₄²×C₅₃	C₂³	1	1	yes	characteristic
340	C₄²×C₅₃	C₂³	1	1	yes	characteristic
341	C₄²×C₅₃	C₂³	1	1	yes	characteristic
342	C₂³×C₅₃	—	4	1	no	—
343	C₂³×C₅₃	—	4	1	no	—
344	C₂³×C₅₃	—	4	1	no	—
345	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
346	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
348	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
350	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
351	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
352	Q₈×C₅₃	—	4	1	no	—
353	Q₈×C₅₃	—	4	1	no	—
354	Q₈×C₅₃	—	4	1	no	—
355	Q₈×C₅₃	—	4	1	no	—
356	Q₈×C₅₃	—	4	1	no	—
357	Q₈×C₅₃	—	4	1	no	—
358	D₄×C₅₃	—	4	1	no	—
359	D₄×C₅₃	—	4	1	no	—
360	D₄×C₅₃	—	4	1	no	—
361	D₄×C₅₃	—	4	1	no	—
362	D₄×C₅₃	—	4	1	no	—
363	D₄×C₅₃	—	4	1	no	—
364	D₄×C₅₃	—	4	1	no	—
365	D₄×C₅₃	—	4	1	no	—
366	D₄×C₅₃	—	4	1	no	—
367	D₄×C₅₃	—	4	1	no	—
368	D₄×C₅₃	—	4	1	no	—
369	D₄×C₅₃	—	4	1	no	—
370	D₄×C₅₃	—	4	1	no	—
371	D₄×C₅₃	—	4	1	no	—
372	D₄×C₅₃	—	4	1	no	—
373	D₄×C₅₃	—	4	1	no	—
374	D₄×C₅₃	—	4	1	no	—
375	D₄×C₅₃	—	4	1	no	—
376	C₂×C₄×C₅₃	—	4	1	no	—
377	C₂×C₄×C₅₃	—	4	1	no	—
378	C₂×C₄×C₅₃	—	4	1	no	—
379	C₂×C₄×C₅₃	—	4	1	no	—
380	C₂×C₄×C₅₃	—	4	1	no	—
381	C₂×C₄×C₅₃	—	4	1	no	—
382	C₂×C₄×C₅₃	—	4	1	no	—
383	C₂×C₄×C₅₃	—	4	1	no	—
384	C₂×C₄×C₅₃	—	4	1	no	—
385	C₂×C₄×C₅₃	—	4	1	no	—
386	C₂×C₄×C₅₃	—	4	1	no	—
387	C₂×C₄×C₅₃	—	4	1	no	—
388	C₂×C₄×C₅₃	—	4	1	no	—
389	C₂×C₄×C₅₃	—	4	1	no	—
390	C₂×C₄×C₅₃	—	4	1	no	—
391	C₂×C₄×C₅₃	—	4	1	no	—
392	C₂×C₄×C₅₃	—	4	1	no	—
393	C₂×C₄×C₅₃	—	4	1	no	—
394	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
411	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×C₅₃	—	2	1	no	—
419	C₂²×C₅₃	—	2	1	no	—
420	C₂²×C₅₃	—	2	1	no	—
421	C₂²×C₅₃	—	2	1	no	—
422	C₂²×C₅₃	—	2	1	no	—
423	C₂²×C₅₃	—	2	1	no	—
424	C₂²×C₅₃	—	2	1	no	—
425	C₂²×C₅₃	—	2	1	no	—
426	C₂²×C₅₃	—	2	1	no	—
427	C₂²×C₅₃	—	2	1	no	—
428	C₂²×C₅₃	—	2	1	no	—
429	C₂²×C₅₃	—	2	1	no	—
430	C₂²×C₅₃	—	2	1	no	—
431	C₂²×C₅₃	—	2	1	no	—
432	C₂²×C₅₃	—	2	1	no	—
433	C₂²×C₅₃	—	2	1	no	—
434	C₂²×C₅₃	—	2	1	no	—
435	C₂²×C₅₃	—	2	1	no	—
436	C₂²×C₅₃	—	2	1	no	—
437	C₂²×C₅₃	—	2	1	no	—
438	C₂²×C₅₃	—	2	1	no	—
439	C₂²×C₅₃	—	8	2	no	—
440	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
441	C₄×C₅₃	—	2	1	no	—
442	C₄×C₅₃	—	2	1	no	—
443	C₄×C₅₃	—	2	1	no	—
444	C₄×C₅₃	—	2	1	no	—
445	C₄×C₅₃	—	2	1	no	—
446	C₄×C₅₃	—	2	1	no	—
447	C₄×C₅₃	—	2	1	no	—
448	C₄×C₅₃	—	2	1	no	—
449	C₄×C₅₃	—	2	1	no	—
450	C₄×C₅₃	—	2	1	no	—
451	C₄×C₅₃	—	2	1	no	—
452	C₄×C₅₃	—	2	1	no	—
453	C₄×C₅₃	—	2	1	no	—
454	C₄×C₅₃	—	2	1	no	—
455	C₄×C₅₃	—	2	1	no	—
456	C₄×C₅₃	—	2	1	no	—
457	C₄×C₅₃	—	2	1	no	—
458	C₄×C₅₃	—	2	1	no	—
459	C₄×C₅₃	—	2	1	no	—
460	C₄×C₅₃	—	2	1	no	—
461	C₄×C₅₃	—	2	1	no	—
462	C₄×C₅₃	—	2	1	no	—
463	C₄×C₅₃	—	2	1	no	—
464	C₄×C₅₃	—	2	1	no	—
465	#3566	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
466	C₂×C₅₃	—	4	1	no	—
467	C₂×C₅₃	—	4	1	no	—
468	C₂×C₅₃	—	4	1	no	—
469	C₂×C₅₃	—	4	1	no	—
470	C₂×C₅₃	—	4	1	no	—
471	C₂×C₅₃	—	4	1	no	—
472	C₂×C₅₃	—	4	1	no	—
473	C₂×C₅₃	#585	1	1	yes	characteristic
474	C₂×C₅₃	#585	1	1	yes	characteristic
475	C₂×C₅₃	#585	1	1	yes	characteristic
476	#563	C₂×C₅₃	1	1	yes	characteristic, complemented
477	#562	C₂×C₅₃	1	1	yes	characteristic, complemented
478	#562	C₂×C₅₃	1	1	yes	characteristic, complemented
479	#560	C₂×C₅₃	1	1	yes	characteristic, complemented
480	#559	C₂×C₅₃	1	1	yes	characteristic, complemented
481	#556	C₂×C₅₃	1	1	yes	characteristic, complemented
482	#555	C₂×C₅₃	1	1	yes	characteristic, complemented
483	#553	C₂×C₅₃	1	1	yes	characteristic, complemented
484	#553	C₂×C₅₃	1	1	yes	characteristic, complemented
485	#553	C₂×C₅₃	1	1	yes	characteristic, complemented
486	#552	C₂×C₅₃	1	1	yes	characteristic, complemented
487	#552	C₂×C₅₃	1	1	yes	characteristic, complemented
488	#552	C₂×C₅₃	1	1	yes	characteristic, complemented
489	#551	C₂×C₅₃	1	1	yes	characteristic, complemented
490	#551	C₂×C₅₃	1	1	yes	characteristic, complemented
491	#551	C₂×C₅₃	1	1	yes	characteristic, complemented
492	#542	C₂×C₅₃	1	1	yes	characteristic, complemented
493	#542	C₂×C₅₃	1	1	yes	characteristic, complemented
494	#542	C₂×C₅₃	1	1	yes	characteristic, complemented
495	#541	C₂×C₅₃	1	1	yes	characteristic, complemented
496	#541	C₂×C₅₃	1	1	yes	characteristic, complemented
497	#540	C₂×C₅₃	1	1	yes	characteristic, complemented
498	#539	C₂×C₅₃	1	1	yes	characteristic, complemented
499	#539	C₂×C₅₃	1	1	yes	characteristic, complemented
500	#539	C₂×C₅₃	1	1	yes	characteristic, complemented
501	#538	C₂×C₅₃	1	1	yes	characteristic, complemented
502	#538	C₂×C₅₃	1	1	yes	characteristic, complemented
503	#538	C₂×C₅₃	1	1	yes	characteristic, complemented
504	#529	C₂×C₅₃	1	1	yes	characteristic, complemented
505	#529	C₂×C₅₃	1	1	yes	characteristic, complemented
506	#529	C₂×C₅₃	1	1	yes	characteristic, complemented
507	C₅₃	#3566	1	1	yes	characteristic, direct product factor, Sylow
508	C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
509	C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
510	C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
511	#127	C₂²×C₅₃	1	1	yes	characteristic
512	#126	C₂²×C₅₃	1	1	yes	characteristic
513	#126	C₂²×C₅₃	1	1	yes	characteristic
514	#126	C₂²×C₅₃	1	1	yes	characteristic
515	#126	C₂²×C₅₃	1	1	yes	characteristic
516	#126	C₂²×C₅₃	1	1	yes	characteristic
517	#126	C₂²×C₅₃	1	1	yes	characteristic
518	#126	C₂²×C₅₃	1	1	yes	characteristic
519	#126	C₂²×C₅₃	1	1	yes	characteristic
520	#126	C₂²×C₅₃	1	1	yes	characteristic
521	#126	C₂²×C₅₃	1	1	yes	characteristic
522	#126	C₂²×C₅₃	1	1	yes	characteristic
523	#126	C₂²×C₅₃	1	1	yes	characteristic
524	#126	C₂²×C₅₃	1	1	yes	characteristic
525	#126	C₂²×C₅₃	1	1	yes	characteristic
526	#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
527	#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
528	#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
529	#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
530	#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
531	#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
532	#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
533	#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
534	#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
535	#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
536	#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
537	#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
538	#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
539	#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
540	#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
541	#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
542	#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
543	#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
544	#124	C₂²×C₅₃	1	1	yes	characteristic
545	#124	C₂²×C₅₃	1	1	yes	characteristic
546	#124	C₂²×C₅₃	1	1	yes	characteristic
547	#124	C₂²×C₅₃	1	1	yes	characteristic
548	#124	C₂²×C₅₃	1	1	yes	characteristic
549	#124	C₂²×C₅₃	1	1	yes	characteristic
550	#124	C₂²×C₅₃	1	1	yes	characteristic
551	#124	C₂²×C₅₃	1	1	yes	characteristic
552	#124	C₂²×C₅₃	1	1	yes	characteristic
553	#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
554	#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
555	#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
556	#123	C₂²×C₅₃	1	1	yes	characteristic
557	#123	C₂²×C₅₃	1	1	yes	characteristic
558	#123	C₂²×C₅₃	1	1	yes	characteristic
559	#123	C₂²×C₅₃	1	1	yes	characteristic
560	#123	C₂²×C₅₃	1	1	yes	characteristic
561	#123	C₂²×C₅₃	1	1	yes	characteristic
562	#123	C₂²×C₅₃	1	1	yes	characteristic
563	#123	C₂²×C₅₃	1	1	yes	characteristic
564	#123	C₂²×C₅₃	1	1	yes	characteristic
565	#123	C₂²×C₅₃	1	1	yes	characteristic
566	#123	C₂²×C₅₃	1	1	yes	characteristic
567	#123	C₂²×C₅₃	1	1	yes	characteristic
568	#123	C₂²×C₅₃	1	1	yes	characteristic
569	#123	C₂²×C₅₃	1	1	yes	characteristic
570	#123	C₂²×C₅₃	1	1	yes	characteristic
571	#123	C₂²×C₅₃	1	1	yes	characteristic
572	#123	C₂²×C₅₃	1	1	yes	characteristic
573	#123	C₂²×C₅₃	1	1	yes	characteristic
574	#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
575	#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
576	#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
577	#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
578	#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
579	#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
580	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
581	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
582	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
583	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
584	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
585	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
586	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
587	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
588	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
589	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
590	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
591	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
592	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
593	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
594	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
595	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
596	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
597	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
598	#121	C₂²×C₅₃	1	1	yes	characteristic
599	#121	C₂²×C₅₃	1	1	yes	characteristic
600	#121	C₂²×C₅₃	1	1	yes	characteristic
601	#121	C₂²×C₅₃	1	1	yes	characteristic
602	#121	C₂²×C₅₃	1	1	yes	characteristic
603	#121	C₂²×C₅₃	1	1	yes	characteristic
604	#121	C₂²×C₅₃	1	1	yes	characteristic
605	#121	C₂²×C₅₃	1	1	yes	characteristic
606	#121	C₂²×C₅₃	1	1	yes	characteristic
607	#121	C₂²×C₅₃	1	1	yes	characteristic
608	#121	C₂²×C₅₃	1	1	yes	characteristic
609	#121	C₂²×C₅₃	1	1	yes	characteristic
610	#121	C₂²×C₅₃	1	1	yes	characteristic
611	#121	C₂²×C₅₃	1	1	yes	characteristic
612	#121	C₂²×C₅₃	1	1	yes	characteristic
613	#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
614	#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
615	#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
616	#120	C₂²×C₅₃	1	1	yes	characteristic
617	#120	C₂²×C₅₃	1	1	yes	characteristic
618	#120	C₂²×C₅₃	1	1	yes	characteristic
619	#120	C₂²×C₅₃	1	1	yes	characteristic
620	C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
621	C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
622	C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
623	C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
624	C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
625	C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
626	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
627	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
628	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
629	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
630	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
631	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
632	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
633	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
634	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
635	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
636	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
637	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
638	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
639	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
640	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
641	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
642	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
643	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
644	#117	C₂²×C₅₃	1	1	yes	characteristic
645	#117	C₂²×C₅₃	1	1	yes	characteristic
646	#117	C₂²×C₅₃	1	1	yes	characteristic
647	#117	C₂²×C₅₃	1	1	yes	characteristic
648	#117	C₂²×C₅₃	1	1	yes	characteristic
649	#117	C₂²×C₅₃	1	1	yes	characteristic
650	#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
651	#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
652	#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
653	#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
654	#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
655	#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
657	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
658	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
661	C₂×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
662	C₂×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	C₂⁴	C₂³×C₅₃	1	1	yes	characteristic
664	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
665	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
666	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
667	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
668	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
669	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
670	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
671	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
672	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
673	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
674	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
675	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
676	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
677	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
678	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
679	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
680	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
681	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
682	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
683	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
684	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
685	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
686	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
687	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
688	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
689	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
690	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
691	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
692	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
693	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
694	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
695	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
696	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
697	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
698	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
699	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
700	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
701	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
702	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
703	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
704	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
705	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
706	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
707	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
708	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
709	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
710	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
711	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
712	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
713	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
714	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
715	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
716	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
717	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
718	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
719	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
720	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
721	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
722	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
723	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
724	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
725	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
730	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
731	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
735	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
737	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
741	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
742	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
743	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
744	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
745	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
746	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
750	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
751	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
752	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
754	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
755	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
756	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
757	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
758	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
759	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
760	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
761	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
762	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
763	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
764	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
765	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
766	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
767	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
768	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
769	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
770	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
771	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
772	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
773	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
774	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
775	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
776	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
777	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
778	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
779	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
780	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
781	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
782	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
783	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
784	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
785	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
786	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
787	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
788	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
789	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
790	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
791	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
792	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
793	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
794	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
795	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
796	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
797	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
798	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
799	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
800	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
801	C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
802	C₄²	C₂³×C₅₃	1	1	yes	characteristic
803	C₄²	C₂³×C₅₃	1	1	yes	characteristic
804	C₄²	C₂³×C₅₃	1	1	yes	characteristic
805	C₄²	C₂³×C₅₃	1	1	yes	characteristic
806	C₄²	C₂³×C₅₃	1	1	yes	characteristic
807	C₄²	C₂³×C₅₃	1	1	yes	characteristic
808	C₄²	C₂³×C₅₃	1	1	yes	characteristic
809	C₄²	C₂³×C₅₃	1	1	yes	characteristic
810	C₄²	C₂³×C₅₃	1	1	yes	characteristic
811	C₄²	C₂³×C₅₃	1	1	yes	characteristic
812	C₄²	C₂³×C₅₃	1	1	yes	characteristic
813	C₄²	C₂³×C₅₃	1	1	yes	characteristic
814	C₄²	C₂³×C₅₃	1	1	yes	characteristic
815	C₄²	C₂³×C₅₃	1	1	yes	characteristic
816	C₄²	C₂³×C₅₃	1	1	yes	characteristic
817	C₄²	C₂³×C₅₃	1	1	yes	characteristic
818	C₂³	—	4	1	no	—
819	C₂³	—	4	1	no	—
820	C₂³	—	4	1	no	—
821	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
822	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
823	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
824	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
825	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
826	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
827	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
828	Q₈	—	4	1	no	—
829	Q₈	—	4	1	no	—
830	Q₈	—	4	1	no	—
831	Q₈	—	4	1	no	—
832	Q₈	—	4	1	no	—
833	Q₈	—	4	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	1	no	—
836	D₄	—	4	1	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	4	1	no	—
840	D₄	—	4	1	no	—
841	D₄	—	4	1	no	—
842	D₄	—	4	1	no	—
843	D₄	—	4	1	no	—
844	D₄	—	4	1	no	—
845	D₄	—	4	1	no	—
846	D₄	—	4	1	no	—
847	D₄	—	4	1	no	—
848	D₄	—	4	1	no	—
849	D₄	—	4	1	no	—
850	D₄	—	4	1	no	—
851	D₄	—	4	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	4	1	no	—
861	C₂×C₄	—	4	1	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
871	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
872	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
873	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
874	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
875	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
876	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
877	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
878	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
879	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
880	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
881	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
882	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
883	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
884	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
885	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
886	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
887	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
888	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
889	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
890	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
891	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
892	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
893	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	8	2	no	—
916	C₂²	C₂⁵×C₅₃	1	1	yes	characteristic
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	2	1	no	—
930	C₄	—	2	1	no	—
931	C₄	—	2	1	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₂	—	4	1	no	—
942	C₂	—	4	1	no	—
943	C₂	—	4	1	no	—
944	C₂	—	4	1	no	—
945	C₂	—	4	1	no	—
946	C₂	—	4	1	no	—
947	C₂	—	4	1	no	—
948	C₂	C₅₃×#585	1	1	yes	characteristic
949	C₂	C₅₃×#585	1	1	yes	characteristic
950	C₂	C₅₃×#585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#563	C₂	semidirect
2. C₅₃×#562	C₂	semidirect
3. C₅₃×#562	C₂	semidirect
4. C₅₃×#560	C₂	semidirect
5. C₅₃×#559	C₂	semidirect
6. C₅₃×#556	C₂	semidirect
7. C₅₃×#555	C₂	semidirect
8. C₅₃×#553	C₂	semidirect
9. C₅₃×#553	C₂	semidirect
10. C₅₃×#553	C₂	semidirect
11. C₅₃×#552	C₂	semidirect
12. C₅₃×#552	C₂	semidirect
13. C₅₃×#552	C₂	semidirect
14. C₅₃×#551	C₂	semidirect
15. C₅₃×#551	C₂	semidirect
16. C₅₃×#551	C₂	semidirect
17. C₅₃×#542	C₂	semidirect
18. C₅₃×#542	C₂	semidirect
19. C₅₃×#542	C₂	semidirect
20. C₅₃×#541	C₂	semidirect
21. C₅₃×#541	C₂	semidirect
22. C₅₃×#540	C₂	semidirect
23. C₅₃×#539	C₂	semidirect
24. C₅₃×#539	C₂	semidirect
25. C₅₃×#539	C₂	semidirect
26. C₅₃×#538	C₂	semidirect
27. C₅₃×#538	C₂	semidirect
28. C₅₃×#538	C₂	semidirect
29. C₅₃×#529	C₂	semidirect
30. C₅₃×#529	C₂	semidirect
31. C₅₃×#529	C₂	semidirect
32. C₄⋊Q₈×C₅₃	C₂²	semidirect
33. C₄⋊Q₈×C₅₃	C₂²	semidirect
34. C₄⋊Q₈×C₅₃	C₂²	semidirect
50. #126×C₅₃	C₂²	semidirect
51. #126×C₅₃	C₂²	semidirect
52. #126×C₅₃	C₂²	semidirect
53. #126×C₅₃	C₂²	semidirect
54. #126×C₅₃	C₂²	semidirect
55. #126×C₅₃	C₂²	semidirect
56. #125×C₅₃	C₂²	semidirect
57. #125×C₅₃	C₂²	semidirect
58. #125×C₅₃	C₂²	semidirect
59. #125×C₅₃	C₂²	semidirect
60. #125×C₅₃	C₂²	semidirect
61. #125×C₅₃	C₂²	semidirect
62. #125×C₅₃	C₂²	semidirect
63. #125×C₅₃	C₂²	semidirect
64. #125×C₅₃	C₂²	semidirect
65. #125×C₅₃	C₂²	semidirect
66. #125×C₅₃	C₂²	semidirect
67. #125×C₅₃	C₂²	semidirect
77. #124×C₅₃	C₂²	semidirect
78. #124×C₅₃	C₂²	semidirect
79. #124×C₅₃	C₂²	semidirect
98. #123×C₅₃	C₂²	semidirect
99. #123×C₅₃	C₂²	semidirect
100. #123×C₅₃	C₂²	semidirect
101. #123×C₅₃	C₂²	semidirect
102. #123×C₅₃	C₂²	semidirect
103. #123×C₅₃	C₂²	semidirect
113. C₂²⋊Q₈×C₅₃	C₂²	semidirect
114. C₂²⋊Q₈×C₅₃	C₂²	semidirect
115. C₂²⋊Q₈×C₅₃	C₂²	semidirect
116. C₂²⋊Q₈×C₅₃	C₂²	semidirect
117. C₂²⋊Q₈×C₅₃	C₂²	semidirect
118. C₂²⋊Q₈×C₅₃	C₂²	semidirect
119. C₂²⋊Q₈×C₅₃	C₂²	semidirect
120. C₂²⋊Q₈×C₅₃	C₂²	semidirect
121. C₂²⋊Q₈×C₅₃	C₂²	semidirect
137. #121×C₅₃	C₂²	semidirect
138. #121×C₅₃	C₂²	semidirect
139. #121×C₅₃	C₂²	semidirect
144. C₄×Q₈×C₅₃	C₂²	semidirect
145. C₄×Q₈×C₅₃	C₂²	semidirect
146. C₄×Q₈×C₅₃	C₂²	semidirect
147. C₄×Q₈×C₅₃	C₂²	semidirect
148. C₄×Q₈×C₅₃	C₂²	semidirect
149. C₄×Q₈×C₅₃	C₂²	semidirect
162. C₄×D₄×C₅₃	C₂²	semidirect
163. C₄×D₄×C₅₃	C₂²	semidirect
164. C₄×D₄×C₅₃	C₂²	semidirect
165. C₄×D₄×C₅₃	C₂²	semidirect
166. C₄×D₄×C₅₃	C₂²	semidirect
167. C₄×D₄×C₅₃	C₂²	semidirect
174. #117×C₅₃	C₂²	semidirect
175. #117×C₅₃	C₂²	semidirect
176. #117×C₅₃	C₂²	semidirect
177. #117×C₅₃	C₂²	semidirect
178. #117×C₅₃	C₂²	semidirect
179. #117×C₅₃	C₂²	semidirect
180. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
181. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
182. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
186. C₂×C₄²×C₅₃	C₂²	semidirect
465. #3566	C₅₃	direct (N × H)
476. #563	C₂×C₅₃	semidirect
477. #562	C₂×C₅₃	semidirect
478. #562	C₂×C₅₃	semidirect
479. #560	C₂×C₅₃	semidirect
480. #559	C₂×C₅₃	semidirect
481. #556	C₂×C₅₃	semidirect
482. #555	C₂×C₅₃	semidirect
483. #553	C₂×C₅₃	semidirect
484. #553	C₂×C₅₃	semidirect
485. #553	C₂×C₅₃	semidirect
486. #552	C₂×C₅₃	semidirect
487. #552	C₂×C₅₃	semidirect
488. #552	C₂×C₅₃	semidirect
489. #551	C₂×C₅₃	semidirect
490. #551	C₂×C₅₃	semidirect
491. #551	C₂×C₅₃	semidirect
492. #542	C₂×C₅₃	semidirect
493. #542	C₂×C₅₃	semidirect
494. #542	C₂×C₅₃	semidirect
495. #541	C₂×C₅₃	semidirect
496. #541	C₂×C₅₃	semidirect
497. #540	C₂×C₅₃	semidirect
498. #539	C₂×C₅₃	semidirect
499. #539	C₂×C₅₃	semidirect
500. #539	C₂×C₅₃	semidirect
501. #538	C₂×C₅₃	semidirect
502. #538	C₂×C₅₃	semidirect
503. #538	C₂×C₅₃	semidirect
504. #529	C₂×C₅₃	semidirect
505. #529	C₂×C₅₃	semidirect
506. #529	C₂×C₅₃	semidirect
507. C₅₃	#3566	direct (N × H)
508. C₄⋊Q₈	C₂²×C₅₃	semidirect
509. C₄⋊Q₈	C₂²×C₅₃	semidirect
510. C₄⋊Q₈	C₂²×C₅₃	semidirect
526. #126	C₂²×C₅₃	semidirect
527. #126	C₂²×C₅₃	semidirect
528. #126	C₂²×C₅₃	semidirect
529. #126	C₂²×C₅₃	semidirect
530. #126	C₂²×C₅₃	semidirect
531. #126	C₂²×C₅₃	semidirect
532. #125	C₂²×C₅₃	semidirect
533. #125	C₂²×C₅₃	semidirect
534. #125	C₂²×C₅₃	semidirect
535. #125	C₂²×C₅₃	semidirect
536. #125	C₂²×C₅₃	semidirect
537. #125	C₂²×C₅₃	semidirect
538. #125	C₂²×C₅₃	semidirect
539. #125	C₂²×C₅₃	semidirect
540. #125	C₂²×C₅₃	semidirect
541. #125	C₂²×C₅₃	semidirect
542. #125	C₂²×C₅₃	semidirect
543. #125	C₂²×C₅₃	semidirect
553. #124	C₂²×C₅₃	semidirect
554. #124	C₂²×C₅₃	semidirect
555. #124	C₂²×C₅₃	semidirect
574. #123	C₂²×C₅₃	semidirect
575. #123	C₂²×C₅₃	semidirect
576. #123	C₂²×C₅₃	semidirect
577. #123	C₂²×C₅₃	semidirect
578. #123	C₂²×C₅₃	semidirect
579. #123	C₂²×C₅₃	semidirect
589. C₂²⋊Q₈	C₂²×C₅₃	semidirect
590. C₂²⋊Q₈	C₂²×C₅₃	semidirect
591. C₂²⋊Q₈	C₂²×C₅₃	semidirect
592. C₂²⋊Q₈	C₂²×C₅₃	semidirect
593. C₂²⋊Q₈	C₂²×C₅₃	semidirect
594. C₂²⋊Q₈	C₂²×C₅₃	semidirect
595. C₂²⋊Q₈	C₂²×C₅₃	semidirect
596. C₂²⋊Q₈	C₂²×C₅₃	semidirect
597. C₂²⋊Q₈	C₂²×C₅₃	semidirect
613. #121	C₂²×C₅₃	semidirect
614. #121	C₂²×C₅₃	semidirect
615. #121	C₂²×C₅₃	semidirect
620. C₄×Q₈	C₂²×C₅₃	semidirect
621. C₄×Q₈	C₂²×C₅₃	semidirect
622. C₄×Q₈	C₂²×C₅₃	semidirect
623. C₄×Q₈	C₂²×C₅₃	semidirect
624. C₄×Q₈	C₂²×C₅₃	semidirect
625. C₄×Q₈	C₂²×C₅₃	semidirect
638. C₄×D₄	C₂²×C₅₃	semidirect
639. C₄×D₄	C₂²×C₅₃	semidirect
640. C₄×D₄	C₂²×C₅₃	semidirect
641. C₄×D₄	C₂²×C₅₃	semidirect
642. C₄×D₄	C₂²×C₅₃	semidirect
643. C₄×D₄	C₂²×C₅₃	semidirect
650. #117	C₂²×C₅₃	semidirect
651. #117	C₂²×C₅₃	semidirect
652. #117	C₂²×C₅₃	semidirect
653. #117	C₂²×C₅₃	semidirect
654. #117	C₂²×C₅₃	semidirect
655. #117	C₂²×C₅₃	semidirect
656. C₂×C₄⋊C₄	C₂²×C₅₃	semidirect
657. C₂×C₄⋊C₄	C₂²×C₅₃	semidirect
658. C₂×C₄⋊C₄	C₂²×C₅₃	semidirect
662. C₂×C₄²	C₂²×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#563	2
C₅₃×#562	2
C₅₃×#560	2
C₅₃×#559	2
C₅₃×#556	2
C₅₃×#555	2
C₅₃×#553	2
C₅₃×#552	2
C₅₃×#551	2
C₅₃×#542	2
C₅₃×#541	2
C₅₃×#540	2
C₅₃×#539	2
C₅₃×#538	2
C₅₃×#529	2
#3566	53

Subgroups — C53×#3566 #20272503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#3566 #20272503