Subgroups — #20283526

Order 6784.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133241	C₂	1	1	yes	maximal, characteristic
2	C₄×#11719947	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#16810733	C₂	1	1	yes	maximal, characteristic, complemented
5	#16810725	C₂	1	1	yes	maximal, characteristic, complemented
6	#16810723	C₂	1	1	yes	maximal, characteristic, complemented
7	#16810714	C₂	1	1	yes	maximal, characteristic, complemented
8	#16810710	C₂	1	1	yes	maximal, characteristic, complemented
9	D₈×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#16810703	C₂	1	1	yes	maximal, characteristic, complemented
11	#16810662	C₂	1	1	yes	maximal, characteristic, complemented
12	#16810626	C₂	1	1	yes	maximal, characteristic, complemented
13	#16810621	C₂	1	1	yes	maximal, characteristic, complemented
14	#16810575	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11719947	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₅₃	—	2	1	no	—
19	#13133241	C₄	1	8	yes	complemented
20	C₂×#11719913	C₂²	1	1	yes	characteristic
21	C₂×#11719923	C₂²	1	1	yes	characteristic
22	C₂×#11719922	C₂²	1	1	yes	characteristic
23	C₂×#11719912	C₂²	1	1	yes	characteristic
24	C₂×#11719912	C₂²	1	1	yes	characteristic
25	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
26	#13133182	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
28	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
29	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
30	#13133179	C₂²	1	1	yes	characteristic
31	C₄×C₂²⋊D₅₃	—	2	1	no	—
32	C₄×C₂²⋊D₅₃	—	2	1	no	—
33	#13133177	—	2	1	no	—
34	#13133177	—	2	1	no	—
35	#13133175	C₂²	1	1	yes	characteristic
36	#13133173	—	2	1	no	—
37	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
38	C₂²⋊C₄×D₅₃	—	2	1	no	—
39	C₂×C₄×Dic₅₃	—	2	1	no	—
40	C₄²×D₅₃	C₂²	1	1	yes	characteristic
41	#13133151	C₂²	1	1	yes	characteristic, complemented
42	#13133150	C₂²	1	1	yes	characteristic, complemented
43	#13133148	C₂²	1	1	yes	characteristic, complemented
44	#13133142	C₂²	1	1	yes	characteristic, complemented
45	#13133140	C₂²	1	1	yes	characteristic, complemented
46	#13133139	C₂²	1	1	yes	characteristic
47	#13133138	C₂²	1	1	yes	characteristic
48	#13133138	C₂²	1	1	yes	characteristic, complemented
49	#13133137	C₂²	1	1	yes	characteristic
50	#13133128	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×D₈×C₅₃	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
56	#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	#102×C₅₃	C₂²	1	1	yes	characteristic
58	#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₅₃	—	2	1	no	—
61	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₅₃	—	2	1	no	—
64	C₂²×C₄×C₅₃	—	2	1	no	—
65	C₂×C₂²⋊D₅₃	—	2	1	no	—
66	C₂×C₂²⋊D₅₃	—	2	1	no	—
67	C₂²×Dic₅₃	—	2	1	no	—
68	C₂²×Dic₅₃	—	2	1	no	—
69	C₂²×Dic₅₃	—	2	1	no	—
70	#11719947	—	2	2	no	—
71	#11719947	C₂×C₄	1	4	yes	complemented
72	D₄×D₅₃	—	2	2	no	—
73	D₄×D₅₃	C₂×C₄	1	4	yes	complemented
74	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
75	C₂×C₄×D₅₃	—	2	1	no	—
76	C₂×C₄×D₅₃	—	2	1	no	—
77	C₂×C₄×D₅₃	—	2	1	no	—
78	C₂×C₄×D₅₃	—	4	4	no	—
79	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
80	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
81	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
82	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
83	D₈×C₅₃	C₂×C₄	1	4	yes	complemented
84	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
88	C₂²⋊C₄×C₅₃	—	2	1	no	—
89	C₂²⋊C₄×C₅₃	—	2	1	no	—
90	C₄²×C₅₃	C₂³	1	1	yes	characteristic
91	C₂²⋊Dic₅₃	—	2	1	no	—
92	C₂²⋊Dic₅₃	—	2	1	no	—
93	#11719923	C₂×C₄	1	4	yes	complemented
94	#11719922	C₂×C₄	1	4	yes	complemented
95	#11719921	—	2	1	no	—
96	#11719921	—	2	1	no	—
97	#11719921	—	2	1	no	—
98	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
100	#11719919	—	2	1	no	—
101	#11719919	—	2	1	no	—
102	#11719919	—	2	1	no	—
103	C₄×Dic₅₃	—	2	1	no	—
104	C₄×Dic₅₃	—	2	1	no	—
105	C₄×Dic₅₃	—	2	1	no	—
106	C₄×Dic₅₃	D₄	1	1	yes	characteristic
107	C₄×Dic₅₃	D₄	1	1	yes	characteristic
108	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
109	C₂×#88322	C₂³	1	1	yes	characteristic
110	C₂×#88322	C₂³	1	1	yes	characteristic
111	#11719913	C₂×C₄	1	4	yes	complemented
112	#11719912	—	2	2	no	—
113	#11719912	C₂×C₄	1	4	yes	complemented
114	C₂³×C₅₃	—	2	1	no	—
115	C₂³×C₅₃	—	2	1	no	—
116	C₂²×D₅₃	—	2	1	no	—
117	C₂²×D₅₃	—	2	4	no	—
118	C₂²×D₅₃	—	4	2	no	—
119	C₂²×D₅₃	—	4	2	no	—
120	C₂²×D₅₃	C₂×D₄	1	1	yes	characteristic
121	D₄×C₅₃	—	2	1	no	—
122	D₄×C₅₃	—	2	1	no	—
123	D₄×C₅₃	C₂²×C₄	1	2	yes	—
124	D₄×C₅₃	C₂²×C₄	1	2	yes	complemented
125	C₂×C₄×C₅₃	—	2	1	no	—
126	C₂×C₄×C₅₃	—	2	1	no	—
127	C₂×C₄×C₅₃	—	4	2	no	—
128	C₂×C₄×C₅₃	—	4	2	no	—
129	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
132	C₂²⋊D₅₃	—	2	4	no	—
133	C₂²⋊D₅₃	—	2	4	no	—
134	C₂×Dic₅₃	—	2	1	no	—
135	C₂×Dic₅₃	—	2	4	no	—
136	C₂×Dic₅₃	—	2	1	no	—
137	C₂×Dic₅₃	—	2	1	no	—
138	C₂×Dic₅₃	—	4	2	no	—
139	C₂×Dic₅₃	—	4	2	no	—
140	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
141	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
142	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
143	D₂₁₂	—	2	1	no	—
144	D₂₁₂	C₂²×C₄	1	2	yes	—
145	C₄×D₅₃	—	2	2	no	—
146	C₄×D₅₃	—	4	1	no	—
147	C₄×D₅₃	—	4	2	no	—
148	C₄×D₅₃	—	4	2	no	—
149	C₄×D₅₃	—	4	2	no	—
150	C₄×D₅₃	C₂²×C₄	1	2	yes	—
151	C₄×D₅₃	#41	1	2	yes	—
152	Dic₁₀₆	—	2	1	no	—
153	Dic₁₀₆	C₂²×C₄	1	2	yes	complemented
154	C₈×C₅₃	—	2	1	no	—
155	C₈×C₅₃	C₂²×C₄	1	2	yes	complemented
156	#88322	—	2	1	no	—
157	#88322	C₂²×C₄	1	2	yes	complemented
158	C₂²×C₅₃	—	2	2	no	—
159	C₂²×C₅₃	—	2	2	no	—
160	C₂²×C₅₃	—	4	1	no	—
161	C₂²×C₅₃	—	4	1	no	—
162	C₂²×C₅₃	—	4	1	no	—
163	C₂²×C₅₃	—	4	1	no	—
164	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×D₅₃	—	2	1	no	—
166	C₂×D₅₃	—	2	1	no	—
167	C₂×D₅₃	—	2	2	no	—
168	C₂×D₅₃	—	4	8	no	—
169	C₂×D₅₃	—	4	1	no	—
170	C₂×D₅₃	—	4	1	no	—
171	C₂×D₅₃	C₄×D₄	1	2	yes	—
172	C₄×C₅₃	—	2	1	no	—
173	C₄×C₅₃	—	2	1	no	—
174	C₄×C₅₃	—	4	1	no	—
175	C₄×C₅₃	—	4	1	no	—
176	C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
177	C₄×C₅₃	C₂×#41	1	1	yes	characteristic
178	Dic₅₃	—	2	2	no	—
179	Dic₅₃	—	2	1	no	—
180	Dic₅₃	—	4	1	no	—
181	Dic₅₃	—	4	1	no	—
182	Dic₅₃	C₄×D₄	1	2	yes	—
183	Dic₅₃	AGL(1,ℤ/8)	1	2	yes	complemented
184	C₄×AGL(1,ℤ/8)	—	53	1	no	maximal, Sylow
185	C₂×C₅₃	—	4	2	no	—
186	C₂×C₅₃	—	4	2	no	—
187	C₂×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂×C₅₃	#575	1	1	yes	characteristic
190	D₅₃	—	2	2	no	—
191	D₅₃	—	4	2	no	—
192	C₂×AGL(1,ℤ/8)	—	53	1	no	—
193	C₄×#41	—	53	1	no	—
194	C₂×C₄×D₄	—	53	1	no	—
195	#442	—	53	1	no	—
196	#442	D₅₃	1	1	yes	characteristic, complemented
197	#440	—	53	1	no	—
198	#440	—	53	1	no	—
199	C₄×SD₁₆	—	53	1	no	—
200	C₄×SD₁₆	—	53	1	no	—
201	C₄×D₈	—	53	1	no	—
202	C₄×D₈	—	53	1	no	—
203	#428	—	53	1	no	—
204	#418	—	53	1	no	—
205	#417	—	53	1	no	—
206	C₄×M₁₆	—	53	1	no	—
207	C₅₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
208	C₂×#41	—	53	1	no	—
209	C₂²×D₄	—	53	1	no	—
210	C₂³×C₄	—	106	1	no	—
211	AGL(1,ℤ/8)	—	53	8	no	—
212	C₂×SD₁₆	—	53	1	no	—
213	C₂×SD₁₆	—	53	1	no	—
214	C₂×D₈	—	53	1	no	—
215	C₂×D₈	C₂×D₅₃	1	1	yes	characteristic
216	C₂×M₁₆	—	53	1	no	—
217	C₂×M₁₆	—	53	1	no	—
218	C₄×Q₈	—	53	1	no	—
219	C₄×Q₈	—	53	1	no	—
220	C₄×D₄	—	53	1	no	—
221	C₄×D₄	—	53	1	no	—
222	C₄×D₄	—	53	1	no	—
223	C₄×D₄	—	53	1	no	—
224	C₄×D₄	—	106	1	no	—
225	C₄×D₄	—	106	1	no	—
226	C₄×D₄	—	106	1	no	—
227	C₄×D₄	—	106	1	no	—
228	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
229	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
230	#117	—	53	1	no	—
231	#117	—	106	1	no	—
232	C₂×C₄⋊C₄	—	53	1	no	—
233	C₂×C₂²⋊C₄	—	106	1	no	—
234	C₂×C₄²	—	53	1	no	—
235	C₂×C₄²	—	106	1	no	—
236	#107	—	53	1	no	—
237	#107	—	53	1	no	—
238	#106	—	53	1	no	—
239	#106	C₂×D₅₃	1	1	yes	characteristic, complemented
240	#103	—	53	1	no	—
241	#103	—	53	1	no	—
242	#102	—	53	1	no	—
243	#102	—	53	1	no	—
244	#102	—	53	1	no	—
245	#102	—	53	1	no	—
246	#102	C₂×D₅₃	1	1	yes	characteristic
247	#102	C₂×D₅₃	1	1	yes	characteristic, complemented
248	#97	—	53	1	no	—
249	#97	C₂×D₅₃	1	1	yes	characteristic, complemented
250	C₄×C₈	—	53	1	no	—
251	C₄×C₈	—	53	1	no	—
252	C₂⁴	—	106	1	no	—
253	#41	—	53	4	no	—
254	#41	—	106	2	no	—
255	C₂×Q₈	—	53	1	no	—
256	C₂×D₄	—	53	4	no	—
257	C₂×D₄	—	53	1	no	—
258	C₂×D₄	—	106	2	no	—
259	C₂×D₄	—	106	1	no	—
260	C₂×D₄	—	106	1	no	—
261	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
262	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	53	1	no	—
266	C₂²×C₄	—	53	1	no	—
267	C₂²×C₄	—	53	1	no	—
268	C₂²×C₄	—	106	1	no	—
269	C₂²×C₄	—	106	1	no	—
270	C₂²×C₄	—	106	1	no	—
271	C₂²×C₄	—	106	1	no	—
272	C₂²×C₄	—	106	1	no	—
273	C₂²×C₄	—	106	1	no	—
274	C₂²×C₄	—	212	4	no	—
275	SD₁₆	—	53	4	no	—
276	SD₁₆	—	53	4	no	—
277	D₈	—	53	4	no	—
278	D₈	C₄×D₅₃	1	4	yes	complemented
279	M₁₆	—	53	4	no	—
280	M₁₆	—	106	2	no	—
281	C₂×C₈	—	53	1	no	—
282	C₂×C₈	—	53	1	no	—
283	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
284	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
285	C₄⋊C₄	—	53	1	no	—
286	C₄⋊C₄	—	53	1	no	—
287	C₄⋊C₄	—	106	1	no	—
288	C₄⋊C₄	—	106	1	no	—
289	C₄⋊C₄	—	106	1	no	—
290	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
291	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₂²⋊C₄	—	106	1	no	—
295	C₂²⋊C₄	—	106	1	no	—
296	C₂²⋊C₄	—	106	1	no	—
297	C₂²⋊C₄	—	106	1	no	—
298	C₂²⋊C₄	—	106	1	no	—
299	C₄²	—	53	1	no	—
300	C₄²	—	53	1	no	—
301	C₄²	—	53	1	no	—
302	C₄²	—	106	1	no	—
303	C₄²	—	106	1	no	—
304	C₄²	—	106	1	no	—
305	C₄²	C₂²×D₅₃	1	1	yes	characteristic
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	53	1	no	—
309	C₂³	—	106	4	no	—
310	C₂³	—	106	1	no	—
311	C₂³	—	212	2	no	—
312	C₂³	—	212	2	no	—
313	Q₈	—	53	2	no	—
314	Q₈	—	106	1	no	—
315	D₄	—	2	1	no	—
316	D₄	—	2	1	no	—
317	D₄	—	53	2	no	—
318	D₄	—	106	4	no	—
319	D₄	—	106	4	no	—
320	D₄	—	106	1	no	—
321	D₄	C₂×C₄×D₅₃	1	2	yes	—
322	D₄	C₂×C₄×D₅₃	1	2	yes	complemented
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	53	1	no	—
328	C₂×C₄	—	53	1	no	—
329	C₂×C₄	—	53	2	no	—
330	C₂×C₄	—	53	2	no	—
331	C₂×C₄	—	53	1	no	—
332	C₂×C₄	—	106	2	no	—
333	C₂×C₄	—	106	4	no	—
334	C₂×C₄	—	106	1	no	—
335	C₂×C₄	—	106	1	no	—
336	C₂×C₄	—	106	1	no	—
337	C₂×C₄	—	212	1	no	—
338	C₂×C₄	—	212	2	no	—
339	C₂×C₄	—	212	2	no	—
340	C₂×C₄	—	212	2	no	—
341	C₂×C₄	—	212	2	no	—
342	C₂×C₄	—	212	2	no	—
343	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
344	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
345	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
346	C₈	—	2	1	no	—
347	C₈	—	53	2	no	—
348	C₈	—	106	1	no	—
349	C₈	C₂×C₄×D₅₃	1	2	yes	complemented
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	53	2	no	—
357	C₂²	—	106	1	no	—
358	C₂²	—	106	1	no	—
359	C₂²	—	106	2	no	—
360	C₂²	—	212	8	no	—
361	C₂²	—	212	1	no	—
362	C₂²	—	212	1	no	—
363	C₂²	C₂×D₄×D₅₃	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	53	2	no	—
369	C₄	—	53	2	no	—
370	C₄	—	106	2	no	—
371	C₄	—	106	1	no	—
372	C₄	—	212	1	no	—
373	C₄	—	212	1	no	—
374	C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
375	C₄	#41×D₅₃	1	1	yes	characteristic
376	C₂	—	4	2	no	—
377	C₂	—	4	2	no	—
378	C₂	—	106	2	no	—
379	C₂	—	212	2	no	—
380	C₂	C₄×D₄×D₅₃	1	1	yes	characteristic
381	C₂	AGL(1,ℤ/8)×D₅₃	1	1	yes	characteristic
382	C₂	#16811419	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₅₃
commutator	C₄×C₅₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₅₃
Fitting	C₅₃×#442	C₂
socle	C₂²×C₅₃	C₂²×D₄
hypercenter	#442	D₅₃
hypocenter	C₅₃	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #442

Complements

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

N	H ≅ G/N	type
2. C₄×#11719947	C₂	semidirect
3. C₄×D₄×D₅₃	C₂	semidirect
4. #16810733	C₂	semidirect
5. #16810725	C₂	semidirect
6. #16810723	C₂	semidirect
7. #16810714	C₂	semidirect
8. #16810710	C₂	semidirect
9. D₈×Dic₅₃	C₂	semidirect
10. #16810703	C₂	semidirect
11. #16810662	C₂	semidirect
12. #16810626	C₂	semidirect
13. #16810621	C₂	semidirect
14. #16810575	C₂	semidirect
15. C₅₃×#442	C₂	semidirect
19. #13133241	C₄	semidirect
25. C₄×Dic₁₀₆	C₂²	semidirect
26. #13133182	C₂²	semidirect
29. D₄×Dic₅₃	C₂²	semidirect
41. #13133151	C₂²	semidirect
42. #13133150	C₂²	semidirect
43. #13133148	C₂²	semidirect
44. #13133142	C₂²	semidirect
45. #13133140	C₂²	semidirect
48. #13133138	C₂²	semidirect
50. #13133128	C₂²	semidirect
51. C₈×Dic₅₃	C₂²	semidirect
52. C₈×Dic₅₃	C₂²	semidirect
55. C₄×D₄×C₅₃	C₂²	semidirect
56. #106×C₅₃	C₂²	semidirect
58. #102×C₅₃	C₂²	semidirect
59. #97×C₅₃	C₂²	semidirect
71. #11719947	C₂×C₄	semidirect
73. D₄×D₅₃	C₂×C₄	semidirect
83. D₈×C₅₃	C₂×C₄	semidirect
93. #11719923	C₂×C₄	semidirect
94. #11719922	C₂×C₄	semidirect
111. #11719913	C₂×C₄	semidirect
113. #11719912	C₂×C₄	semidirect
124. D₄×C₅₃	C₂²×C₄	semidirect
153. Dic₁₀₆	C₂²×C₄	semidirect
155. C₈×C₅₃	C₂²×C₄	semidirect
157. #88322	C₂²×C₄	semidirect
183. Dic₅₃	AGL(1,ℤ/8)	semidirect
196. #442	D₅₃	semidirect
207. C₅₃	C₄×AGL(1,ℤ/8)	semidirect
229. C₄×D₄	C₂×D₅₃	semidirect
239. #106	C₂×D₅₃	semidirect
247. #102	C₂×D₅₃	semidirect
249. #97	C₂×D₅₃	semidirect
278. D₈	C₄×D₅₃	semidirect
322. D₄	C₂×C₄×D₅₃	semidirect
349. C₈	C₂×C₄×D₅₃	semidirect