Subgroups — #20288501

Order 6784.

1540 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133264	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13133262	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811283	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811282	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811281	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811279	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811268	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811267	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811265	C₂	1	2	yes	maximal, complemented
10	#16811263	C₂	1	2	yes	maximal, complemented
11	#16811262	C₂	1	2	yes	maximal, complemented
12	#16811261	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811260	C₂	1	2	yes	maximal, complemented
14	#16811196	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811195	C₂	1	2	yes	maximal, complemented
16	#16811189	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811188	C₂	1	2	yes	maximal, complemented
18	#16811170	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811168	C₂	1	2	yes	maximal, complemented
20	C₂×#13133203	C₂	1	2	yes	maximal, complemented
21	#124×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#11719947	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
24	#13133264	—	2	8	no	—
25	#13133262	—	2	8	no	—
26	C₂×#11719945	C₂²	1	1	yes	characteristic
27	C₂×#11719945	C₂²	1	1	yes	characteristic
28	C₂×#11719945	C₂²	1	2	yes	complemented
29	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
30	C₂×#11719947	C₂²	1	1	yes	characteristic
31	C₂×#11719947	C₂²	1	2	yes	—
32	C₂×#11719947	C₂²	1	1	yes	characteristic
33	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
34	C₂×#11719947	C₂²	1	2	yes	complemented
35	C₂×#11719947	C₂²	1	2	yes	complemented
36	C₂²×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
37	C₂²×Dic₁₀₆	C₂²	1	2	yes	complemented
38	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	—
41	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	—
42	C₂×D₄×D₅₃	C₂²	1	2	yes	—
43	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
44	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
45	#13133216	C₂²	1	2	yes	complemented
46	#13133216	C₂²	1	1	yes	characteristic, complemented
47	#13133213	C₂²	1	2	yes	complemented
48	#13133213	C₂²	1	1	yes	characteristic, complemented
49	#13133206	C₂²	1	1	yes	characteristic, complemented
50	#13133205	C₂²	1	1	yes	characteristic, complemented
51	#13133204	C₂²	1	1	yes	characteristic, complemented
52	#13133203	C₂²	1	2	yes	complemented
53	#13133203	C₂²	1	2	yes	complemented
54	#13133203	C₂²	1	2	yes	complemented
55	#13133203	C₂²	1	2	yes	complemented
56	#13133203	C₂²	1	2	yes	complemented
57	#13133203	C₂²	1	2	yes	complemented
58	#13133203	C₂²	1	1	yes	characteristic, complemented
59	#13133203	C₂²	1	2	yes	complemented
60	#13133203	C₂²	1	2	yes	complemented
61	#13133203	C₂²	1	1	yes	characteristic, complemented
62	#13133202	C₂²	1	2	yes	complemented
63	#13133201	C₂²	1	2	yes	complemented
64	#13133200	C₂²	1	2	yes	complemented
65	#13133199	C₂²	1	2	yes	complemented
66	#13133198	C₂²	1	2	yes	complemented
67	#13133197	C₂²	1	1	yes	characteristic, complemented
68	#13133196	C₂²	1	1	yes	characteristic, complemented
69	#13133195	C₂²	1	2	yes	complemented
70	#13133195	C₂²	1	2	yes	complemented
71	#13133194	C₂²	1	2	yes	complemented
72	#13133194	C₂²	1	2	yes	complemented
73	#13133193	C₂²	1	1	yes	characteristic, complemented
74	#13133192	C₂²	1	1	yes	characteristic, complemented
75	#13133192	C₂²	1	1	yes	characteristic, complemented
76	#13133191	C₂²	1	2	yes	complemented
77	#13133191	C₂²	1	1	yes	characteristic, complemented
78	#13133190	C₂²	1	2	yes	complemented
79	#13133190	C₂²	1	2	yes	complemented
80	#13133190	C₂²	1	1	yes	characteristic, complemented
81	#13133190	C₂²	1	1	yes	characteristic, complemented
82	#13133189	C₂²	1	2	yes	complemented
83	#13133189	C₂²	1	2	yes	complemented
84	#13133189	C₂²	1	2	yes	complemented
85	#13133189	C₂²	1	2	yes	complemented
86	#13133188	C₂²	1	1	yes	characteristic, complemented
87	#13133188	C₂²	1	1	yes	characteristic, complemented
88	#13133187	C₂²	1	2	yes	complemented
89	#13133187	C₂²	1	2	yes	complemented
90	#13133186	C₂²	1	2	yes	complemented
91	#13133185	C₂²	1	2	yes	complemented
92	#13133185	C₂²	1	2	yes	complemented
93	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
94	#13133182	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
96	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
97	D₄×Dic₅₃	C₂²	1	2	yes	complemented
98	#13133179	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
102	#13133177	C₂²	1	2	yes	complemented
103	#13133177	C₂²	1	2	yes	complemented
104	#13133177	C₂²	1	2	yes	complemented
105	#13133175	C₂²	1	1	yes	characteristic, complemented
106	#13133173	C₂²	1	2	yes	complemented
107	C₂×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
108	C₂×#11719921	C₂²	1	2	yes	complemented
109	C₂×#11719921	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
112	C₂×C₄×Dic₅₃	C₂²	1	2	yes	complemented
113	C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
116	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	#123×C₅₃	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	#121×C₅₃	C₂²	1	2	yes	complemented
121	#120×C₅₃	C₂²	1	2	yes	complemented
122	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
125	C₂⁴×C₅₃	C₂³	1	2	yes	—
126	C₂³×D₅₃	C₂³	1	2	yes	—
127	C₂³×D₅₃	C₂³	1	2	yes	—
128	#41×C₅₃	—	2	4	no	—
129	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₅₃	—	2	4	no	—
131	C₂×D₄×C₅₃	C₂³	1	2	yes	—
132	C₂×D₄×C₅₃	C₂³	1	2	yes	—
133	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₂×D₄×C₅₃	C₂³	1	2	yes	—
136	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
138	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₅₃	—	2	8	no	—
142	C₂×C₂²⋊D₅₃	—	2	8	no	—
143	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
157	C₂²×Dic₅₃	C₂³	1	2	yes	—
158	C₂²×Dic₅₃	C₂³	1	2	yes	—
159	C₂²×Dic₅₃	C₂³	1	2	yes	—
160	C₂²×Dic₅₃	C₂³	1	2	yes	—
161	C₂²×Dic₅₃	C₂³	1	2	yes	—
162	Q₈×D₅₃	—	2	4	no	—
163	Q₈×D₅₃	—	2	4	no	—
164	#11719947	—	2	4	no	—
165	#11719947	—	2	8	no	—
166	#11719947	—	2	8	no	—
167	#11719947	—	2	8	no	—
168	#11719947	—	2	4	no	—
169	#11719947	D₄	1	8	yes	complemented
170	D₄×D₅₃	—	2	4	no	—
171	D₄×D₅₃	—	2	8	no	—
172	D₄×D₅₃	—	2	4	no	—
173	#11719945	—	2	8	no	—
174	#11719945	—	2	4	no	—
175	#11719945	—	2	4	no	—
176	#11719945	—	2	4	no	—
177	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
178	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
179	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
180	C₂×D₂₁₂	C₂³	1	2	yes	—
181	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
182	C₂×C₄×D₅₃	C₂³	1	2	yes	—
183	C₂×C₄×D₅₃	C₂³	1	2	yes	—
184	C₂×C₄×D₅₃	C₂³	1	2	yes	—
185	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
186	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
187	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
188	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
189	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
190	C₂×Dic₁₀₆	—	2	8	no	—
191	C₂×Dic₁₀₆	—	2	4	no	—
192	C₂×Dic₁₀₆	C₂³	1	2	yes	—
193	C₂×Dic₁₀₆	C₂³	1	2	yes	—
194	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
195	C₂×Dic₁₀₆	C₂³	1	2	yes	—
196	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
197	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
198	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
199	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
202	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
204	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
205	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
206	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
207	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
209	C₄²×C₅₃	C₂³	1	1	yes	characteristic
210	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
211	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
212	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
213	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
214	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
215	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
216	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
217	#11719921	C₂³	1	2	yes	—
218	#11719921	C₂³	1	2	yes	—
219	#11719921	C₂³	1	2	yes	—
220	#11719921	C₂³	1	2	yes	—
221	#11719921	C₂³	1	1	yes	characteristic
222	#11719921	C₂³	1	1	yes	characteristic
223	#11719921	C₂³	1	2	yes	—
224	#11719921	C₂³	1	2	yes	—
225	#11719921	C₂³	1	2	yes	—
226	#11719921	C₂³	1	2	yes	—
227	#11719921	C₂³	1	2	yes	—
228	#11719921	C₂³	1	1	yes	characteristic
229	#11719921	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
231	C₄⋊Dic₅₃	C₂³	1	2	yes	—
232	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
233	#11719919	C₂³	1	2	yes	—
234	#11719919	C₂³	1	2	yes	—
235	#11719919	C₂³	1	2	yes	—
236	#11719919	C₂³	1	2	yes	—
237	#11719919	C₂³	1	1	yes	characteristic
238	#11719919	C₂³	1	1	yes	characteristic
239	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
240	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
241	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
242	C₄×Dic₅₃	C₂³	1	2	yes	—
243	C₄×Dic₅₃	C₂³	1	2	yes	—
244	C₄×Dic₅₃	C₂³	1	2	yes	—
245	C₂³×C₅₃	—	2	4	no	—
246	C₂³×C₅₃	—	4	2	no	—
247	C₂³×C₅₃	—	4	2	no	—
248	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
249	C₂³×C₅₃	C₂⁴	1	2	yes	—
250	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
251	C₂³×C₅₃	C₂⁴	1	2	yes	—
252	C₂²×D₅₃	—	2	4	no	—
253	C₂²×D₅₃	—	2	4	no	—
254	C₂²×D₅₃	—	4	2	no	—
255	C₂²×D₅₃	—	4	2	no	—
256	C₂²×D₅₃	—	4	2	no	—
257	C₂²×D₅₃	—	4	2	no	—
258	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
259	C₂²×D₅₃	C₂⁴	1	2	yes	—
260	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
261	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
262	Q₈×C₅₃	—	2	2	no	—
263	D₄×C₅₃	—	2	4	no	—
264	D₄×C₅₃	—	2	4	no	—
265	D₄×C₅₃	—	2	2	no	—
266	D₄×C₅₃	—	4	1	no	—
267	D₄×C₅₃	—	4	2	no	—
268	D₄×C₅₃	C₂×D₄	1	4	yes	—
269	C₂×C₄×C₅₃	—	2	4	no	—
270	C₂×C₄×C₅₃	—	2	2	no	—
271	C₂×C₄×C₅₃	—	2	2	no	—
272	C₂×C₄×C₅₃	—	4	2	no	—
273	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
275	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
279	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
280	C₂²⋊D₅₃	—	2	4	no	—
281	C₂²⋊D₅₃	—	2	4	no	—
282	C₂²⋊D₅₃	—	2	2	no	—
283	C₂²⋊D₅₃	—	2	2	no	—
284	C₂²⋊D₅₃	—	2	2	no	—
285	C₂²⋊D₅₃	—	2	2	no	—
286	C₂²⋊D₅₃	—	2	4	no	—
287	C₂²⋊D₅₃	—	2	4	no	—
288	C₂²⋊D₅₃	—	2	4	no	—
289	C₂²⋊D₅₃	—	4	1	no	—
290	C₂²⋊D₅₃	—	4	1	no	—
291	C₂²⋊D₅₃	—	4	2	no	—
292	C₂²⋊D₅₃	—	4	2	no	—
293	C₂²⋊D₅₃	C₂×D₄	1	8	yes	—
294	C₂×Dic₅₃	—	2	4	no	—
295	C₂×Dic₅₃	—	2	4	no	—
296	C₂×Dic₅₃	—	2	4	no	—
297	C₂×Dic₅₃	—	4	2	no	—
298	C₂×Dic₅₃	C₂×D₄	1	8	yes	—
299	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₅₃	C₂⁴	1	2	yes	—
301	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
303	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
304	C₂×Dic₅₃	C₂⁴	1	2	yes	—
305	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
306	C₂×Dic₅₃	C₂⁴	1	2	yes	—
307	D₂₁₂	—	2	2	no	—
308	D₂₁₂	—	2	2	no	—
309	D₂₁₂	—	2	2	no	—
310	D₂₁₂	—	4	1	no	—
311	D₂₁₂	—	4	2	no	—
312	C₄×D₅₃	—	2	4	no	—
313	C₄×D₅₃	—	2	2	no	—
314	C₄×D₅₃	—	2	2	no	—
315	C₄×D₅₃	—	2	4	no	—
316	C₄×D₅₃	—	2	4	no	—
317	C₄×D₅₃	—	4	1	no	—
318	C₄×D₅₃	—	4	1	no	—
319	C₄×D₅₃	C₂×D₄	1	4	yes	—
320	Dic₁₀₆	—	2	2	no	—
321	Dic₁₀₆	—	2	2	no	—
322	Dic₁₀₆	—	2	4	no	—
323	Dic₁₀₆	—	2	4	no	—
324	Dic₁₀₆	—	2	4	no	—
325	Dic₁₀₆	—	2	2	no	—
326	Dic₁₀₆	C₂×D₄	1	4	yes	—
327	C₂²×C₅₃	—	2	2	no	—
328	C₂²×C₅₃	—	2	2	no	—
329	C₂²×C₅₃	—	2	1	no	—
330	C₂²×C₅₃	—	2	2	no	—
331	C₂²×C₅₃	—	2	1	no	—
332	C₂²×C₅₃	—	2	1	no	—
333	C₂²×C₅₃	—	2	1	no	—
334	C₂²×C₅₃	—	2	2	no	—
335	C₂²×C₅₃	—	2	1	no	—
336	C₂²×C₅₃	—	2	2	no	—
337	C₂²×C₅₃	—	2	1	no	—
338	C₂²×C₅₃	—	8	4	no	—
339	C₂²×C₅₃	C₂²×D₄	1	4	yes	—
340	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
341	C₂×D₅₃	—	2	1	no	—
342	C₂×D₅₃	—	2	1	no	—
343	C₂×D₅₃	—	2	1	no	—
344	C₂×D₅₃	—	2	1	no	—
345	C₂×D₅₃	—	2	2	no	—
346	C₂×D₅₃	—	2	1	no	—
347	C₂×D₅₃	—	2	1	no	—
348	C₂×D₅₃	—	2	2	no	—
349	C₂×D₅₃	—	2	1	no	—
350	C₂×D₅₃	—	2	1	no	—
351	C₂×D₅₃	—	2	2	no	—
352	C₂×D₅₃	—	8	4	no	—
353	C₂×D₅₃	—	8	4	no	—
354	C₂×D₅₃	C₂²×D₄	1	2	yes	—
355	C₄×C₅₃	—	2	1	no	—
356	C₄×C₅₃	—	2	2	no	—
357	C₄×C₅₃	—	2	1	no	—
358	C₄×C₅₃	—	2	1	no	—
359	C₄×C₅₃	—	2	1	no	—
360	C₄×C₅₃	—	2	2	no	—
361	C₄×C₅₃	C₂²×D₄	1	2	yes	—
362	Dic₅₃	—	2	2	no	—
363	Dic₅₃	—	2	1	no	—
364	Dic₅₃	—	2	1	no	—
365	Dic₅₃	—	2	1	no	—
366	Dic₅₃	—	2	1	no	—
367	Dic₅₃	—	2	2	no	—
368	Dic₅₃	C₂²×D₄	1	2	yes	—
369	Dic₅₃	C₂²×D₄	1	4	yes	—
370	#3500	—	53	1	no	maximal, Sylow
371	C₂×C₅₃	—	2	4	no	—
372	C₂×C₅₃	—	4	2	no	—
373	C₂×C₅₃	—	4	1	no	—
374	C₂×C₅₃	—	4	1	no	—
375	C₂×C₅₃	C₂³×D₄	1	1	yes	characteristic
376	C₂×C₅₃	#585	1	1	yes	characteristic
377	C₂×C₅₃	#585	1	1	yes	characteristic
378	D₅₃	—	2	2	no	—
379	D₅₃	—	4	1	no	—
380	D₅₃	—	4	2	no	—
381	D₅₃	—	4	1	no	—
382	C₂×2₋¹⁺⁴	—	53	1	no	—
383	C₂×H(5,𝔽₂)	—	53	1	no	—
384	#548	—	53	1	no	—
385	#548	—	53	1	no	—
386	#548	—	53	1	no	—
387	#548	—	53	1	no	—
388	#546	—	53	1	no	—
389	#546	—	53	1	no	—
390	#546	—	53	2	no	—
391	#546	—	53	2	no	—
392	#546	—	53	2	no	—
393	#546	—	53	1	no	—
394	#546	—	53	2	no	—
395	#546	D₅₃	1	1	yes	characteristic, complemented
396	#536	—	53	2	no	—
397	#536	—	53	1	no	—
398	#535	—	53	1	no	—
399	#535	—	53	2	no	—
400	#532	—	53	2	no	—
401	#532	—	53	1	no	—
402	C₂×#124	—	53	1	no	—
403	C₂×#124	—	53	2	no	—
404	C₄×#41	—	53	1	no	—
405	C₅₃	#3500	1	1	yes	characteristic, complemented, Sylow
406	2₋¹⁺⁴	—	106	8	no	—
407	H(5,𝔽₂)	—	106	8	no	—
408	C₂×#41	—	53	1	no	—
409	C₂×#41	—	53	2	no	—
410	C₂×#41	—	53	2	no	—
411	C₂×#41	—	53	1	no	—
412	C₂×#41	—	53	2	no	—
413	C₂×#41	—	53	1	no	—
414	C₂×#41	—	53	1	no	—
415	C₂×#41	—	53	1	no	—
416	C₂×#41	—	53	2	no	—
417	C₂×#41	—	53	1	no	—
418	C₂×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
419	C₂²×Q₈	—	53	1	no	—
420	C₂²×Q₈	—	53	1	no	—
421	C₂²×Q₈	—	53	2	no	—
422	C₂²×Q₈	—	53	1	no	—
423	C₂²×D₄	—	53	2	no	—
424	C₂²×D₄	—	53	2	no	—
425	C₂²×D₄	—	53	1	no	—
426	C₂²×D₄	—	53	2	no	—
427	C₂²×D₄	—	53	1	no	—
428	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic
429	C₄⋊Q₈	—	53	2	no	—
430	C₄⋊Q₈	—	53	1	no	—
431	#127	—	53	2	no	—
432	#127	—	53	1	no	—
433	#124	—	53	1	no	—
434	#124	—	53	1	no	—
435	#124	—	53	2	no	—
436	#124	—	53	1	no	—
437	#124	—	53	2	no	—
438	#124	—	53	2	no	—
439	#124	—	53	2	no	—
440	#124	—	53	2	no	—
441	#124	—	53	2	no	—
442	#124	—	53	2	no	—
443	#124	—	53	2	no	—
444	#124	—	53	1	no	—
445	#124	—	53	1	no	—
446	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
447	#123	—	53	2	no	—
448	#123	—	53	2	no	—
449	#123	—	53	2	no	—
450	#123	—	53	2	no	—
451	#123	—	53	2	no	—
452	#123	C₂×D₅₃	1	2	yes	complemented
453	C₂²⋊Q₈	—	53	1	no	—
454	C₂²⋊Q₈	—	53	1	no	—
455	C₂²⋊Q₈	—	53	2	no	—
456	C₂²⋊Q₈	—	53	2	no	—
457	C₂²⋊Q₈	—	53	1	no	—
458	C₂²⋊Q₈	—	53	2	no	—
459	C₂²⋊Q₈	—	53	2	no	—
460	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
461	#121	—	53	1	no	—
462	#121	—	53	2	no	—
463	#121	—	53	2	no	—
464	#121	—	53	1	no	—
465	#121	—	53	2	no	—
466	#121	—	53	2	no	—
467	#121	—	53	2	no	—
468	#121	—	53	1	no	—
469	#121	—	53	1	no	—
470	#121	—	53	1	no	—
471	#121	—	53	1	no	—
472	#121	—	53	1	no	—
473	#121	—	53	2	no	—
474	#121	—	53	2	no	—
475	#121	C₂×D₅₃	1	2	yes	complemented
476	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
477	#120	—	53	2	no	—
478	#120	—	53	2	no	—
479	#120	—	53	2	no	—
480	#120	—	53	2	no	—
481	#120	—	53	2	no	—
482	#120	C₂×D₅₃	1	2	yes	complemented
483	C₄×Q₈	—	53	1	no	—
484	C₄×Q₈	—	53	1	no	—
485	C₄×D₄	—	53	1	no	—
486	C₄×D₄	—	53	2	no	—
487	C₄×D₄	—	53	2	no	—
488	C₄×D₄	—	53	1	no	—
489	C₄×D₄	—	53	1	no	—
490	C₄×D₄	—	53	2	no	—
491	C₄×D₄	—	53	2	no	—
492	C₄×D₄	—	53	2	no	—
493	C₄×D₄	—	53	2	no	—
494	C₄×D₄	—	53	1	no	—
495	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
496	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
497	#117	—	53	1	no	—
498	#117	—	53	2	no	—
499	C₂×C₂²⋊C₄	—	53	2	no	—
500	C₂×C₂²⋊C₄	—	53	2	no	—
501	C₂×C₂²⋊C₄	—	53	2	no	—
502	C₂×C₂²⋊C₄	—	53	2	no	—
503	C₂×C₂²⋊C₄	—	53	2	no	—
504	C₂×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
505	C₂×C₄²	—	53	2	no	—
506	C₂×C₄²	—	53	1	no	—
507	C₂⁴	—	53	2	no	—
508	C₂⁴	—	53	2	no	—
509	C₂⁴	C₂²×D₅₃	1	2	yes	—
510	#41	—	2	4	no	—
511	#41	—	53	8	no	—
512	#41	—	106	4	no	—
513	#41	—	106	4	no	—
514	#41	—	106	8	no	—
515	#41	—	106	4	no	—
516	#41	—	106	8	no	—
517	#41	—	106	8	no	—
518	#41	—	106	8	no	—
519	#41	—	106	4	no	—
520	#41	—	106	4	no	—
521	C₂×Q₈	—	53	1	no	—
522	C₂×Q₈	—	53	2	no	—
523	C₂×Q₈	—	53	2	no	—
524	C₂×Q₈	—	53	1	no	—
525	C₂×Q₈	—	53	2	no	—
526	C₂×Q₈	—	53	1	no	—
527	C₂×Q₈	—	53	1	no	—
528	C₂×Q₈	—	106	8	no	—
529	C₂×Q₈	—	106	4	no	—
530	C₂×Q₈	—	106	4	no	—
531	C₂×Q₈	—	106	4	no	—
532	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	53	2	no	—
535	C₂×D₄	—	53	1	no	—
536	C₂×D₄	—	53	2	no	—
537	C₂×D₄	—	53	1	no	—
538	C₂×D₄	—	53	2	no	—
539	C₂×D₄	—	53	2	no	—
540	C₂×D₄	—	53	2	no	—
541	C₂×D₄	—	53	2	no	—
542	C₂×D₄	—	53	1	no	—
543	C₂×D₄	—	53	1	no	—
544	C₂×D₄	—	53	2	no	—
545	C₂×D₄	—	53	1	no	—
546	C₂×D₄	—	53	2	no	—
547	C₂×D₄	—	53	1	no	—
548	C₂×D₄	—	53	1	no	—
549	C₂×D₄	—	53	1	no	—
550	C₂×D₄	—	53	1	no	—
551	C₂×D₄	—	53	2	no	—
552	C₂×D₄	—	53	1	no	—
553	C₂×D₄	—	106	4	no	—
554	C₂×D₄	—	106	8	no	—
555	C₂×D₄	—	106	8	no	—
556	C₂×D₄	—	106	8	no	—
557	C₂×D₄	—	106	4	no	—
558	C₂×D₄	C₂²×D₅₃	1	2	yes	—
559	C₂×D₄	C₂²×D₅₃	1	2	yes	—
560	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
561	C₂×D₄	C₂²×D₅₃	1	2	yes	—
562	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
563	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
564	C₂²×C₄	—	53	2	no	—
565	C₂²×C₄	—	53	1	no	—
566	C₂²×C₄	—	53	2	no	—
567	C₂²×C₄	—	53	2	no	—
568	C₂²×C₄	—	53	2	no	—
569	C₂²×C₄	—	53	2	no	—
570	C₂²×C₄	—	53	2	no	—
571	C₂²×C₄	—	53	2	no	—
572	C₂²×C₄	—	53	1	no	—
573	C₂²×C₄	—	53	2	no	—
574	C₂²×C₄	—	53	1	no	—
575	C₂²×C₄	—	53	1	no	—
576	C₂²×C₄	—	53	1	no	—
577	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
578	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
579	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
580	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
581	C₄⋊C₄	—	53	2	no	—
582	C₄⋊C₄	—	53	2	no	—
583	C₄⋊C₄	—	53	1	no	—
584	C₄⋊C₄	—	53	1	no	—
585	C₄⋊C₄	—	53	2	no	—
586	C₄⋊C₄	—	53	2	no	—
587	C₄⋊C₄	—	53	1	no	—
588	C₄⋊C₄	—	53	2	no	—
589	C₄⋊C₄	—	53	1	no	—
590	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
591	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
592	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
593	C₂²⋊C₄	—	53	2	no	—
594	C₂²⋊C₄	—	53	1	no	—
595	C₂²⋊C₄	—	53	2	no	—
596	C₂²⋊C₄	—	53	2	no	—
597	C₂²⋊C₄	—	53	2	no	—
598	C₂²⋊C₄	—	53	2	no	—
599	C₂²⋊C₄	—	53	1	no	—
600	C₂²⋊C₄	—	53	2	no	—
601	C₂²⋊C₄	—	53	1	no	—
602	C₂²⋊C₄	—	53	1	no	—
603	C₂²⋊C₄	—	53	2	no	—
604	C₂²⋊C₄	—	53	2	no	—
605	C₂²⋊C₄	—	53	2	no	—
606	C₂²⋊C₄	—	53	2	no	—
607	C₂²⋊C₄	—	53	2	no	—
608	C₂²⋊C₄	—	53	2	no	—
609	C₂²⋊C₄	—	53	2	no	—
610	C₂²⋊C₄	—	53	2	no	—
611	C₂²⋊C₄	—	53	1	no	—
612	C₂²⋊C₄	—	53	1	no	—
613	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
614	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
615	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
616	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
617	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
618	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
619	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
620	C₄²	—	53	1	no	—
621	C₄²	—	53	2	no	—
622	C₄²	—	53	1	no	—
623	C₄²	—	53	2	no	—
624	C₄²	—	53	2	no	—
625	C₄²	—	53	1	no	—
626	C₄²	C₂²×D₅₃	1	1	yes	characteristic
627	C₂³	—	2	4	no	—
628	C₂³	—	4	2	no	—
629	C₂³	—	4	2	no	—
630	C₂³	—	53	1	no	—
631	C₂³	—	53	2	no	—
632	C₂³	—	53	1	no	—
633	C₂³	—	53	1	no	—
634	C₂³	—	106	4	no	—
635	C₂³	—	106	4	no	—
636	C₂³	—	212	2	no	—
637	C₂³	—	212	2	no	—
638	C₂³	—	212	2	no	—
639	C₂³	—	212	2	no	—
640	C₂³	C₂³×D₅₃	1	2	yes	—
641	C₂³	C₂³×D₅₃	1	1	yes	characteristic
642	C₂³	C₂³×D₅₃	1	1	yes	characteristic
643	C₂³	C₂³×D₅₃	1	2	yes	—
644	Q₈	—	2	2	no	—
645	Q₈	—	53	4	no	—
646	Q₈	—	106	2	no	—
647	Q₈	—	106	4	no	—
648	Q₈	—	106	4	no	—
649	Q₈	—	106	4	no	—
650	Q₈	—	106	2	no	—
651	Q₈	—	106	2	no	—
652	D₄	—	2	4	no	—
653	D₄	—	2	4	no	—
654	D₄	—	2	2	no	—
655	D₄	—	4	2	no	—
656	D₄	—	4	1	no	—
657	D₄	—	53	8	no	—
658	D₄	—	106	2	no	—
659	D₄	—	106	2	no	—
660	D₄	—	106	2	no	—
661	D₄	—	106	4	no	—
662	D₄	—	106	4	no	—
663	D₄	—	106	4	no	—
664	D₄	—	106	2	no	—
665	D₄	—	106	2	no	—
666	D₄	—	106	2	no	—
667	D₄	—	106	4	no	—
668	D₄	—	106	4	no	—
669	D₄	—	106	2	no	—
670	D₄	—	212	2	no	—
671	D₄	—	212	1	no	—
672	D₄	—	212	1	no	—
673	D₄	—	212	1	no	—
674	D₄	—	212	2	no	—
675	D₄	—	212	2	no	—
676	D₄	D₄×D₅₃	1	4	yes	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	4	2	no	—
681	C₂×C₄	—	53	8	no	—
682	C₂×C₄	—	53	1	no	—
683	C₂×C₄	—	53	2	no	—
684	C₂×C₄	—	53	4	no	—
685	C₂×C₄	—	53	1	no	—
686	C₂×C₄	—	53	1	no	—
687	C₂×C₄	—	53	2	no	—
688	C₂×C₄	—	53	1	no	—
689	C₂×C₄	—	53	2	no	—
690	C₂×C₄	—	53	1	no	—
691	C₂×C₄	—	106	4	no	—
692	C₂×C₄	—	106	4	no	—
693	C₂×C₄	—	106	4	no	—
694	C₂×C₄	—	106	4	no	—
695	C₂×C₄	—	106	4	no	—
696	C₂×C₄	—	106	4	no	—
697	C₂×C₄	—	106	2	no	—
698	C₂×C₄	—	106	2	no	—
699	C₂×C₄	—	212	1	no	—
700	C₂×C₄	—	212	1	no	—
701	C₂×C₄	—	212	2	no	—
702	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
703	C₂×C₄	C₂³×D₅₃	1	2	yes	—
704	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
705	C₂×C₄	C₂³×D₅₃	1	2	yes	—
706	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
707	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
708	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	8	4	no	—
721	C₂²	—	53	2	no	—
722	C₂²	—	106	1	no	—
723	C₂²	—	106	1	no	—
724	C₂²	—	106	1	no	—
725	C₂²	—	106	2	no	—
726	C₂²	—	106	1	no	—
727	C₂²	—	106	1	no	—
728	C₂²	—	106	2	no	—
729	C₂²	—	106	1	no	—
730	C₂²	—	106	1	no	—
731	C₂²	—	106	1	no	—
732	C₂²	—	106	2	no	—
733	C₂²	—	424	4	no	—
734	C₂²	—	424	4	no	—
735	C₂²	C₂×D₄×D₅₃	1	4	yes	—
736	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
737	C₄	—	2	1	no	—
738	C₄	—	2	1	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	1	no	—
741	C₄	—	2	2	no	—
742	C₄	—	2	1	no	—
743	C₄	—	53	2	no	—
744	C₄	—	53	4	no	—
745	C₄	—	106	1	no	—
746	C₄	—	106	2	no	—
747	C₄	—	106	1	no	—
748	C₄	—	106	1	no	—
749	C₄	—	106	1	no	—
750	C₄	—	106	2	no	—
751	C₄	C₂×D₄×D₅₃	1	2	yes	—
752	C₂	—	2	4	no	—
753	C₂	—	4	1	no	—
754	C₂	—	4	2	no	—
755	C₂	—	4	1	no	—
756	C₂	—	106	2	no	—
757	C₂	—	212	1	no	—
758	C₂	—	212	2	no	—
759	C₂	—	212	1	no	—
760	C₂	C₂²×D₄×D₅₃	1	1	yes	characteristic
761	C₂	#16811458	1	1	yes	characteristic
762	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#546	C₂
hypercenter	#546	D₅₃
hypocenter	C₅₃	#3500
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₂×#13133264	C₂	semidirect
2. C₂×#13133262	C₂	semidirect
3. #16811283	C₂	semidirect
4. #16811282	C₂	semidirect
5. #16811281	C₂	semidirect
6. #16811279	C₂	semidirect
7. #16811268	C₂	semidirect
8. #16811267	C₂	semidirect
9. #16811265	C₂	semidirect
10. #16811263	C₂	semidirect
11. #16811262	C₂	semidirect
12. #16811261	C₂	semidirect
13. #16811260	C₂	semidirect
14. #16811196	C₂	semidirect
15. #16811195	C₂	semidirect
16. #16811189	C₂	semidirect
17. #16811188	C₂	semidirect
18. #16811170	C₂	semidirect
19. #16811168	C₂	semidirect
20. C₂×#13133203	C₂	semidirect
21. #124×D₅₃	C₂	semidirect
22. C₄×#11719947	C₂	semidirect
23. C₅₃×#546	C₂	semidirect
28. C₂×#11719945	C₂²	semidirect
29. C₂×#11719945	C₂²	semidirect
33. C₂×#11719947	C₂²	semidirect
34. C₂×#11719947	C₂²	semidirect
35. C₂×#11719947	C₂²	semidirect
36. C₂²×Dic₁₀₆	C₂²	semidirect
37. C₂²×Dic₁₀₆	C₂²	semidirect
38. C₂×Q₈×D₅₃	C₂²	semidirect
39. C₂×Q₈×D₅₃	C₂²	semidirect
45. #13133216	C₂²	semidirect
46. #13133216	C₂²	semidirect
47. #13133213	C₂²	semidirect
48. #13133213	C₂²	semidirect
49. #13133206	C₂²	semidirect
50. #13133205	C₂²	semidirect
51. #13133204	C₂²	semidirect
52. #13133203	C₂²	semidirect
53. #13133203	C₂²	semidirect
54. #13133203	C₂²	semidirect
55. #13133203	C₂²	semidirect
56. #13133203	C₂²	semidirect
57. #13133203	C₂²	semidirect
58. #13133203	C₂²	semidirect
59. #13133203	C₂²	semidirect
60. #13133203	C₂²	semidirect
61. #13133203	C₂²	semidirect
62. #13133202	C₂²	semidirect
63. #13133201	C₂²	semidirect
64. #13133200	C₂²	semidirect
65. #13133199	C₂²	semidirect
66. #13133198	C₂²	semidirect
67. #13133197	C₂²	semidirect
68. #13133196	C₂²	semidirect
69. #13133195	C₂²	semidirect
70. #13133195	C₂²	semidirect
71. #13133194	C₂²	semidirect
72. #13133194	C₂²	semidirect
73. #13133193	C₂²	semidirect
74. #13133192	C₂²	semidirect
75. #13133192	C₂²	semidirect
76. #13133191	C₂²	semidirect
77. #13133191	C₂²	semidirect
78. #13133190	C₂²	semidirect
79. #13133190	C₂²	semidirect
80. #13133190	C₂²	semidirect
81. #13133190	C₂²	semidirect
82. #13133189	C₂²	semidirect
83. #13133189	C₂²	semidirect
84. #13133189	C₂²	semidirect
85. #13133189	C₂²	semidirect
86. #13133188	C₂²	semidirect
87. #13133188	C₂²	semidirect
88. #13133187	C₂²	semidirect
89. #13133187	C₂²	semidirect
90. #13133186	C₂²	semidirect
91. #13133185	C₂²	semidirect
92. #13133185	C₂²	semidirect
93. C₄×Dic₁₀₆	C₂²	semidirect
94. #13133182	C₂²	semidirect
95. C₄×D₂₁₂	C₂²	semidirect
96. D₄×Dic₅₃	C₂²	semidirect
97. D₄×Dic₅₃	C₂²	semidirect
98. #13133179	C₂²	semidirect
99. C₄×C₂²⋊D₅₃	C₂²	semidirect
100. C₄×C₂²⋊D₅₃	C₂²	semidirect
101. C₄×C₂²⋊D₅₃	C₂²	semidirect
102. #13133177	C₂²	semidirect
103. #13133177	C₂²	semidirect
104. #13133177	C₂²	semidirect
105. #13133175	C₂²	semidirect
106. #13133173	C₂²	semidirect
107. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
108. C₂×#11719921	C₂²	semidirect
109. C₂×#11719921	C₂²	semidirect
110. C₂²⋊C₄×D₅₃	C₂²	semidirect
111. C₂²⋊C₄×D₅₃	C₂²	semidirect
112. C₂×C₄×Dic₅₃	C₂²	semidirect
113. C₄²×D₅₃	C₂²	semidirect
114. C₂×#41×C₅₃	C₂²	semidirect
116. #124×C₅₃	C₂²	semidirect
117. #123×C₅₃	C₂²	semidirect
118. C₂²⋊Q₈×C₅₃	C₂²	semidirect
119. #121×C₅₃	C₂²	semidirect
120. #121×C₅₃	C₂²	semidirect
121. #120×C₅₃	C₂²	semidirect
122. C₄×D₄×C₅₃	C₂²	semidirect
123. C₄×D₄×C₅₃	C₂²	semidirect
124. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
169. #11719947	D₄	semidirect
395. #546	D₅₃	semidirect
405. C₅₃	#3500	semidirect
418. C₂×#41	C₂×D₅₃	semidirect
446. #124	C₂×D₅₃	semidirect
452. #123	C₂×D₅₃	semidirect
460. C₂²⋊Q₈	C₂×D₅₃	semidirect
475. #121	C₂×D₅₃	semidirect
476. #121	C₂×D₅₃	semidirect
482. #120	C₂×D₅₃	semidirect
495. C₄×D₄	C₂×D₅₃	semidirect
496. C₄×D₄	C₂×D₅₃	semidirect
504. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect