Subgroups — #20284329

Order 6784.

548 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133244	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811136	C₂	1	1	yes	maximal, characteristic, complemented
4	#121×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#16810876	C₂	1	1	yes	maximal, characteristic, complemented
6	#16810874	C₂	1	1	yes	maximal, characteristic, complemented
7	#16810871	C₂	1	1	yes	maximal, characteristic, complemented
8	#16810860	C₂	1	1	yes	maximal, characteristic, complemented
9	#16810858	C₂	1	1	yes	maximal, characteristic, complemented
10	#16810855	C₂	1	1	yes	maximal, characteristic, complemented
11	#16810849	C₂	1	1	yes	maximal, characteristic, complemented
12	#16810664	C₂	1	1	yes	maximal, characteristic, complemented
13	#16810626	C₂	1	1	yes	maximal, characteristic, complemented
14	#16810623	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11719949	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₅₃	—	2	1	no	—
18	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
20	#13133244	—	2	4	no	—
21	C₂×#11719924	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₄₂₄	C₂²	1	1	yes	characteristic, complemented
23	C₂×#11719922	C₂²	1	1	yes	characteristic, complemented
24	C₂×#11719917	C₂²	1	1	yes	characteristic, complemented
25	C₂×#11719912	C₂²	1	1	yes	characteristic
26	C₂×#11719912	C₂²	1	1	yes	characteristic
27	M₁₆×D₅₃	—	2	4	no	—
28	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
30	#13133202	—	2	1	no	—
31	#13133193	C₂²	1	1	yes	characteristic, complemented
32	#13133192	C₂²	1	1	yes	characteristic
33	#13133192	C₂²	1	1	yes	characteristic, complemented
34	#13133191	C₂²	1	1	yes	characteristic
35	#13133191	C₂²	1	1	yes	characteristic, complemented
36	#13133190	—	2	1	no	—
37	#13133189	—	2	1	no	—
38	#13133188	C₂²	1	1	yes	characteristic
39	#13133187	—	2	1	no	—
40	#13133179	—	2	1	no	—
41	#13133177	—	2	1	no	—
42	#13133175	C₂²	1	1	yes	characteristic
43	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
44	C₂²⋊C₄×D₅₃	—	2	1	no	—
45	#13133150	C₂²	1	1	yes	characteristic, complemented
46	#13133149	C₂²	1	1	yes	characteristic, complemented
47	#13133148	C₂²	1	1	yes	characteristic, complemented
48	#13133141	C₂²	1	1	yes	characteristic, complemented
49	#13133139	C₂²	1	1	yes	characteristic, complemented
50	#13133139	C₂²	1	1	yes	characteristic, complemented
51	#13133138	C₂²	1	1	yes	characteristic, complemented
52	#13133137	C₂²	1	1	yes	characteristic, complemented
53	#13133137	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	#121×C₅₃	C₂²	1	1	yes	characteristic
58	#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₅₃	—	2	1	no	—
62	C₂³×D₅₃	D₄	1	1	yes	characteristic
63	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₅₃	—	2	1	no	—
65	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊D₅₃	—	2	1	no	—
68	C₂×C₂²⋊D₅₃	—	2	1	no	—
69	C₂×C₂²⋊D₅₃	—	2	1	no	—
70	C₂×C₂²⋊D₅₃	—	2	1	no	—
71	C₂²×Dic₅₃	D₄	1	1	yes	characteristic
72	#11719949	—	2	2	no	—
73	#11719949	—	2	2	no	—
74	D₄×D₅₃	—	2	2	no	—
75	D₄×D₅₃	—	2	2	no	—
76	D₄×D₅₃	—	4	4	no	—
77	C₂×D₂₁₂	—	2	1	no	—
78	C₂×D₂₁₂	—	2	1	no	—
79	C₂×D₂₁₂	—	2	1	no	—
80	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
81	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
82	C₂×C₄×D₅₃	—	2	2	no	—
83	C₂×C₄×D₅₃	—	2	2	no	—
84	C₂×C₄×D₅₃	—	2	1	no	—
85	C₂×C₄×D₅₃	—	2	1	no	—
86	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
87	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
88	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
90	SD₁₆×C₅₃	—	2	2	no	—
91	M₁₆×C₅₃	—	2	2	no	—
92	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	C₄⋊C₄×C₅₃	—	2	1	no	—
95	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
97	C₂²⋊C₄×C₅₃	—	2	1	no	—
98	C₂²⋊C₄×C₅₃	—	2	1	no	—
99	C₂²⋊Dic₅₃	—	2	1	no	—
100	#11719924	—	2	2	no	—
101	#11719922	—	2	2	no	—
102	#11719921	—	2	1	no	—
103	#11719921	—	2	1	no	—
104	#11719921	—	2	1	no	—
105	#11719921	—	2	1	no	—
106	#11719921	—	2	1	no	—
107	#11719921	—	2	1	no	—
108	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
109	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
110	#11719919	—	2	1	no	—
111	#11719919	—	2	1	no	—
112	C₄×Dic₅₃	—	2	1	no	—
113	#11719917	—	2	2	no	—
114	C₂×#88322	C₂³	1	1	yes	characteristic
115	C₂×#88322	C₂³	1	1	yes	characteristic
116	D₄₂₄	—	2	2	no	—
117	#11719912	—	2	2	no	—
118	#11719912	D₄	1	4	yes	complemented
119	C₈×D₅₃	—	2	2	no	—
120	C₈×D₅₃	—	2	2	no	—
121	C₂³×C₅₃	—	2	1	no	—
122	C₂³×C₅₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×D₅₃	—	2	2	no	—
124	C₂²×D₅₃	—	2	2	no	—
125	C₂²×D₅₃	—	2	1	no	—
126	C₂²×D₅₃	—	2	1	no	—
127	C₂²×D₅₃	—	4	1	no	—
128	C₂²×D₅₃	—	4	2	no	—
129	C₂²×D₅₃	—	4	2	no	—
130	C₂²×D₅₃	—	4	2	no	—
131	C₂²×D₅₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×D₅₃	C₂×D₄	1	1	yes	characteristic
133	Q₈×C₅₃	—	2	1	no	—
134	Q₈×C₅₃	—	2	1	no	—
135	D₄×C₅₃	—	2	1	no	—
136	D₄×C₅₃	—	2	1	no	—
137	D₄×C₅₃	—	4	2	no	—
138	C₂×C₄×C₅₃	—	2	1	no	—
139	C₂×C₄×C₅₃	—	2	1	no	—
140	C₂×C₄×C₅₃	—	2	1	no	—
141	C₂×C₄×C₅₃	—	2	1	no	—
142	C₂×C₄×C₅₃	—	2	1	no	—
143	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
145	C₂²⋊D₅₃	—	4	2	no	—
146	C₂²⋊D₅₃	—	4	2	no	—
147	C₂²⋊D₅₃	—	4	2	no	—
148	C₂²⋊D₅₃	—	4	2	no	—
149	C₂×Dic₅₃	—	2	2	no	—
150	C₂×Dic₅₃	—	2	1	no	—
151	C₂×Dic₅₃	—	2	1	no	—
152	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
153	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
154	D₂₁₂	—	2	1	no	—
155	D₂₁₂	—	2	1	no	—
156	D₂₁₂	—	2	1	no	—
157	D₂₁₂	—	2	1	no	—
158	D₂₁₂	—	4	2	no	—
159	D₂₁₂	—	4	2	no	—
160	D₂₁₂	—	4	2	no	—
161	C₄×D₅₃	—	2	2	no	—
162	C₄×D₅₃	—	2	1	no	—
163	C₄×D₅₃	—	2	1	no	—
164	C₄×D₅₃	—	2	2	no	—
165	C₄×D₅₃	—	4	2	no	—
166	C₄×D₅₃	—	4	2	no	—
167	C₄×D₅₃	C₂×D₄	1	2	yes	—
168	C₄×D₅₃	#41	1	2	yes	—
169	C₈×C₅₃	—	2	1	no	—
170	C₈×C₅₃	C₂×D₄	1	2	yes	complemented
171	#88322	—	2	1	no	—
172	#88322	C₂×D₄	1	2	yes	complemented
173	C₂²×C₅₃	—	2	1	no	—
174	C₂²×C₅₃	—	2	1	no	—
175	C₂²×C₅₃	—	2	1	no	—
176	C₂²×C₅₃	—	4	1	no	—
177	C₂²×C₅₃	—	4	1	no	—
178	C₂²×C₅₃	—	4	1	no	—
179	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×D₅₃	—	2	1	no	—
181	C₂×D₅₃	—	2	1	no	—
182	C₂×D₅₃	—	2	1	no	—
183	C₂×D₅₃	—	2	1	no	—
184	C₂×D₅₃	—	4	4	no	—
185	C₂×D₅₃	—	4	1	no	—
186	C₂×D₅₃	—	4	1	no	—
187	C₂×D₅₃	—	4	1	no	—
188	C₂×D₅₃	—	4	1	no	—
189	C₂×D₅₃	—	4	1	no	—
190	C₂×D₅₃	—	4	1	no	—
191	C₂×D₅₃	—	8	4	no	—
192	C₂×D₅₃	#121	1	2	yes	—
193	C₂×D₅₃	AGL(1,ℤ/8)	1	2	yes	complemented
194	C₄×C₅₃	—	2	1	no	—
195	C₄×C₅₃	—	4	1	no	—
196	C₄×C₅₃	—	4	1	no	—
197	C₄×C₅₃	—	4	1	no	—
198	C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
199	C₄×C₅₃	C₂×#41	1	1	yes	characteristic
200	Dic₅₃	—	2	1	no	—
201	Dic₅₃	—	4	1	no	—
202	Dic₅₃	—	4	1	no	—
203	Dic₅₃	#121	1	2	yes	—
204	#3055	—	53	1	no	maximal, Sylow
205	C₂×C₅₃	—	4	1	no	—
206	C₂×C₅₃	—	8	1	no	—
207	C₂×C₅₃	C₂×#121	1	1	yes	characteristic
208	C₂×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
209	C₂×C₅₃	#575	1	1	yes	characteristic
210	D₅₃	—	2	2	no	—
211	D₅₃	—	2	2	no	—
212	D₅₃	—	8	1	no	—
213	D₅₃	—	8	1	no	—
214	C₂×AGL(1,ℤ/8)	—	53	1	no	—
215	C₂²×M₁₆	—	53	1	no	—
216	#525	—	53	1	no	—
217	C₂×#121	—	53	1	no	—
218	#469	—	53	1	no	—
219	#469	—	53	1	no	—
220	#468	—	53	1	no	—
221	#468	D₅₃	1	1	yes	characteristic, complemented
222	#466	—	53	1	no	—
223	#466	—	53	1	no	—
224	#465	—	53	1	no	—
225	#465	—	53	1	no	—
226	#428	—	53	1	no	—
227	#418	—	53	1	no	—
228	#417	—	53	1	no	—
229	C₅₃	#3055	1	1	yes	characteristic, complemented, Sylow
230	C₂×#41	—	53	1	no	—
231	C₂²×D₄	—	53	1	no	—
232	C₂²×D₄	—	106	1	no	—
233	C₂³×C₄	—	53	1	no	—
234	AGL(1,ℤ/8)	—	106	4	no	—
235	C₂×SD₁₆	—	53	1	no	—
236	C₂×SD₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
237	C₂×D₈	—	53	1	no	—
238	C₂×D₈	—	53	1	no	—
239	C₂×M₁₆	—	53	1	no	—
240	C₂×M₁₆	—	53	1	no	—
241	C₂×M₁₆	—	53	1	no	—
242	C₂×M₁₆	—	106	4	no	—
243	C₂×M₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
244	C₂²×C₈	—	53	1	no	—
245	C₂²×C₈	—	53	1	no	—
246	#123	—	106	1	no	—
247	C₂²⋊Q₈	—	53	1	no	—
248	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
249	#121	—	53	1	no	—
250	#121	—	53	1	no	—
251	#121	—	53	1	no	—
252	#121	—	53	1	no	—
253	#121	—	53	1	no	—
254	#121	—	106	1	no	—
255	#121	—	106	1	no	—
256	#121	C₂×D₅₃	1	1	yes	characteristic
257	#120	—	106	1	no	—
258	C₄×D₄	—	106	1	no	—
259	C₄×D₄	—	106	1	no	—
260	#117	—	53	1	no	—
261	C₂×C₄⋊C₄	—	53	1	no	—
262	C₂×C₂²⋊C₄	—	106	1	no	—
263	#107	—	53	1	no	—
264	#107	C₂×D₅₃	1	1	yes	characteristic, complemented
265	#106	—	53	1	no	—
266	#106	—	53	1	no	—
267	#103	—	53	1	no	—
268	#103	C₂×D₅₃	1	1	yes	characteristic, complemented
269	#102	—	53	1	no	—
270	#102	—	53	1	no	—
271	#102	—	53	1	no	—
272	#102	—	53	1	no	—
273	#102	—	53	1	no	—
274	#102	C₂×D₅₃	1	1	yes	characteristic, complemented
275	C₂⁴	—	53	1	no	—
276	C₂⁴	—	106	1	no	—
277	#41	—	106	2	no	—
278	#41	—	106	2	no	—
279	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	53	1	no	—
282	C₂×D₄	—	53	1	no	—
283	C₂×D₄	—	106	1	no	—
284	C₂×D₄	—	106	1	no	—
285	C₂×D₄	—	106	1	no	—
286	C₂×D₄	—	106	2	no	—
287	C₂×D₄	—	106	2	no	—
288	C₂×D₄	—	106	1	no	—
289	C₂×D₄	—	106	1	no	—
290	C₂×D₄	—	106	1	no	—
291	C₂×D₄	—	106	1	no	—
292	C₂×D₄	—	212	4	no	—
293	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
294	C₂²×C₄	—	53	1	no	—
295	C₂²×C₄	—	53	1	no	—
296	C₂²×C₄	—	53	1	no	—
297	C₂²×C₄	—	53	1	no	—
298	C₂²×C₄	—	53	1	no	—
299	C₂²×C₄	—	106	2	no	—
300	C₂²×C₄	—	106	2	no	—
301	C₂²×C₄	—	106	1	no	—
302	C₂²×C₄	—	106	1	no	—
303	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
304	SD₁₆	—	2	2	no	—
305	SD₁₆	—	106	2	no	—
306	D₈	—	106	2	no	—
307	D₈	—	106	2	no	—
308	M₁₆	—	2	2	no	—
309	M₁₆	—	53	4	no	—
310	M₁₆	—	106	2	no	—
311	M₁₆	—	106	2	no	—
312	C₂×C₈	—	53	1	no	—
313	C₂×C₈	—	53	1	no	—
314	C₂×C₈	—	106	2	no	—
315	C₂×C₈	—	106	2	no	—
316	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
317	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	53	1	no	—
320	C₄⋊C₄	—	53	1	no	—
321	C₄⋊C₄	—	106	1	no	—
322	C₄⋊C₄	—	106	1	no	—
323	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
324	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
325	C₂²⋊C₄	—	2	1	no	—
326	C₂²⋊C₄	—	2	1	no	—
327	C₂²⋊C₄	—	106	1	no	—
328	C₂²⋊C₄	—	106	1	no	—
329	C₂²⋊C₄	—	106	1	no	—
330	C₂²⋊C₄	—	106	1	no	—
331	C₂²⋊C₄	—	106	1	no	—
332	C₂²⋊C₄	—	106	1	no	—
333	C₂²⋊C₄	—	106	1	no	—
334	C₄²	—	106	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	53	1	no	—
337	C₂³	—	53	1	no	—
338	C₂³	—	106	2	no	—
339	C₂³	—	106	2	no	—
340	C₂³	—	106	1	no	—
341	C₂³	—	106	1	no	—
342	C₂³	—	212	1	no	—
343	C₂³	—	212	2	no	—
344	C₂³	—	212	2	no	—
345	C₂³	—	212	2	no	—
346	C₂³	D₄×D₅₃	1	1	yes	characteristic
347	Q₈	—	2	1	no	—
348	Q₈	—	2	1	no	—
349	D₄	—	2	1	no	—
350	D₄	—	2	1	no	—
351	D₄	—	4	2	no	—
352	D₄	—	106	1	no	—
353	D₄	—	106	1	no	—
354	D₄	—	106	1	no	—
355	D₄	—	106	1	no	—
356	D₄	—	212	2	no	—
357	D₄	—	212	2	no	—
358	D₄	—	212	2	no	—
359	D₄	—	212	2	no	—
360	D₄	—	212	2	no	—
361	D₄	—	212	2	no	—
362	D₄	—	212	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	53	1	no	—
369	C₂×C₄	—	53	2	no	—
370	C₂×C₄	—	53	2	no	—
371	C₂×C₄	—	53	1	no	—
372	C₂×C₄	—	106	2	no	—
373	C₂×C₄	—	106	2	no	—
374	C₂×C₄	—	106	2	no	—
375	C₂×C₄	—	106	1	no	—
376	C₂×C₄	—	106	1	no	—
377	C₂×C₄	—	106	1	no	—
378	C₂×C₄	—	106	1	no	—
379	C₂×C₄	—	212	2	no	—
380	C₂×C₄	—	212	2	no	—
381	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
382	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	53	2	no	—
385	C₈	—	106	1	no	—
386	C₈	D₄×D₅₃	1	2	yes	complemented
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	53	2	no	—
394	C₂²	—	53	2	no	—
395	C₂²	—	106	1	no	—
396	C₂²	—	106	1	no	—
397	C₂²	—	106	1	no	—
398	C₂²	—	106	1	no	—
399	C₂²	—	424	4	no	—
400	C₂²	—	212	4	no	—
401	C₂²	—	212	1	no	—
402	C₂²	—	212	1	no	—
403	C₂²	—	212	1	no	—
404	C₂²	—	212	1	no	—
405	C₂²	—	212	1	no	—
406	C₂²	—	212	1	no	—
407	C₂²	C₂×D₄×D₅₃	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	53	2	no	—
413	C₄	—	106	1	no	—
414	C₄	—	212	1	no	—
415	C₄	—	212	1	no	—
416	C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
417	C₄	#41×D₅₃	1	1	yes	characteristic
418	C₂	—	4	1	no	—
419	C₂	—	8	1	no	—
420	C₂	—	106	2	no	—
421	C₂	—	106	2	no	—
422	C₂	—	424	1	no	—
423	C₂	—	424	1	no	—
424	C₂	#121×D₅₃	1	1	yes	characteristic
425	C₂	AGL(1,ℤ/8)×D₅₃	1	1	yes	characteristic
426	C₂	#16811422	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₃
Fitting	C₅₃×#468	C₂
socle	C₂²×C₅₃	C₂²×D₄
hypercenter	#468	D₅₃
hypocenter	C₅₃	#3055
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #468

Complements

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

N	H ≅ G/N	type
1. C₂×#13133244	C₂	semidirect
2. C₂×M₁₆×D₅₃	C₂	semidirect
3. #16811136	C₂	semidirect
4. #121×D₅₃	C₂	semidirect
5. #16810876	C₂	semidirect
6. #16810874	C₂	semidirect
7. #16810871	C₂	semidirect
8. #16810860	C₂	semidirect
9. #16810858	C₂	semidirect
10. #16810855	C₂	semidirect
11. #16810849	C₂	semidirect
12. #16810664	C₂	semidirect
13. #16810626	C₂	semidirect
14. #16810623	C₂	semidirect
15. C₅₃×#468	C₂	semidirect
21. C₂×#11719924	C₂²	semidirect
22. C₂×D₄₂₄	C₂²	semidirect
23. C₂×#11719922	C₂²	semidirect
24. C₂×#11719917	C₂²	semidirect
28. C₂×C₈×D₅₃	C₂²	semidirect
29. C₂×C₈×D₅₃	C₂²	semidirect
31. #13133193	C₂²	semidirect
33. #13133192	C₂²	semidirect
35. #13133191	C₂²	semidirect
45. #13133150	C₂²	semidirect
46. #13133149	C₂²	semidirect
47. #13133148	C₂²	semidirect
48. #13133141	C₂²	semidirect
49. #13133139	C₂²	semidirect
50. #13133139	C₂²	semidirect
51. #13133138	C₂²	semidirect
52. #13133137	C₂²	semidirect
53. #13133137	C₂²	semidirect
54. C₂×SD₁₆×C₅₃	C₂²	semidirect
55. C₂×M₁₆×C₅₃	C₂²	semidirect
56. C₂²⋊Q₈×C₅₃	C₂²	semidirect
58. #107×C₅₃	C₂²	semidirect
59. #103×C₅₃	C₂²	semidirect
60. #102×C₅₃	C₂²	semidirect
118. #11719912	D₄	semidirect
170. C₈×C₅₃	C₂×D₄	semidirect
172. #88322	C₂×D₄	semidirect
193. C₂×D₅₃	AGL(1,ℤ/8)	semidirect
221. #468	D₅₃	semidirect
229. C₅₃	#3055	semidirect
236. C₂×SD₁₆	C₂×D₅₃	semidirect
243. C₂×M₁₆	C₂×D₅₃	semidirect
248. C₂²⋊Q₈	C₂×D₅₃	semidirect
264. #107	C₂×D₅₃	semidirect
268. #103	C₂×D₅₃	semidirect
274. #102	C₂×D₅₃	semidirect
386. C₈	D₄×D₅₃	semidirect