Subgroups — #20288477

Order 6784.

1660 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133263	C₂	1	2	yes	maximal, complemented
2	#16811278	C₂	1	2	yes	maximal, complemented
3	#16811276	C₂	1	2	yes	maximal, complemented
4	#16811269	C₂	1	4	yes	maximal, complemented
5	#16811266	C₂	1	4	yes	maximal, complemented
6	D₄×D₂₁₂	C₂	1	2	yes	maximal, complemented
7	#16811258	C₂	1	2	yes	maximal, complemented
8	#16811201	C₂	1	2	yes	maximal, complemented
9	#16811181	C₂	1	4	yes	maximal, complemented
10	#16811173	C₂	1	1	yes	maximal, characteristic, complemented
11	#121×D₅₃	C₂	1	4	yes	maximal, complemented
12	C₂×C₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
14	#13133263	—	2	16	no	—
15	C₂×#11719949	C₂²	1	4	yes	complemented
16	C₂×#11719945	C₂²	1	4	yes	complemented
17	C₂×#11719945	C₂²	1	2	yes	complemented
18	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
19	C₂²×D₂₁₂	C₂²	1	4	yes	complemented
20	C₂×D₄×D₅₃	C₂²	1	4	yes	complemented
21	C₂×D₄×D₅₃	C₂²	1	8	yes	complemented
22	C₂×D₄×D₅₃	C₂²	1	4	yes	complemented
23	C₂²×C₄×D₅₃	C₂²	1	2	yes	complemented
24	#13133217	C₂²	1	1	yes	characteristic, complemented
25	#13133214	C₂²	1	1	yes	characteristic, complemented
26	#13133205	C₂²	1	2	yes	complemented
27	#13133202	C₂²	1	8	yes	complemented
28	#13133199	C₂²	1	8	yes	complemented
29	#13133196	C₂²	1	4	yes	complemented
30	#13133193	C₂²	1	4	yes	complemented
31	#13133192	C₂²	1	4	yes	complemented
32	#13133191	C₂²	1	4	yes	complemented
33	#13133191	C₂²	1	2	yes	complemented
34	#13133191	C₂²	1	2	yes	complemented
35	#13133190	C₂²	1	8	yes	complemented
36	#13133189	C₂²	1	8	yes	complemented
37	#13133188	C₂²	1	4	yes	complemented
38	#13133188	C₂²	1	4	yes	complemented
39	#13133187	C₂²	1	8	yes	complemented
40	#13133185	C₂²	1	8	yes	complemented
41	C₄×D₂₁₂	C₂²	1	2	yes	complemented
42	C₄×D₂₁₂	C₂²	1	2	yes	complemented
43	C₄×D₂₁₂	C₂²	1	2	yes	complemented
44	C₄×D₂₁₂	C₂²	1	2	yes	complemented
45	C₄×D₂₁₂	C₂²	1	2	yes	complemented
46	C₄×D₂₁₂	C₂²	1	2	yes	complemented
47	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
48	C₄⋊C₄×D₅₃	C₂²	1	4	yes	complemented
49	C₂×#11719921	C₂²	1	2	yes	complemented
50	C₂²⋊C₄×D₅₃	C₂²	1	8	yes	complemented
51	C₂×#41×C₅₃	C₂²	1	2	yes	complemented
52	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	#124×C₅₃	C₂²	1	2	yes	complemented
55	#121×C₅₃	C₂²	1	2	yes	complemented
56	#121×C₅₃	C₂²	1	2	yes	complemented
57	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
58	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
59	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₅₃	C₂³	1	8	yes	—
61	C₂³×D₅₃	C₂³	1	2	yes	—
62	#41×C₅₃	—	2	8	no	—
63	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
64	C₂×D₄×C₅₃	C₂³	1	2	yes	—
65	C₂×D₄×C₅₃	C₂³	1	4	yes	—
66	C₂×D₄×C₅₃	C₂³	1	2	yes	—
67	C₂×D₄×C₅₃	C₂³	1	2	yes	—
68	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	C₂³	1	4	yes	—
70	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	—
73	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
74	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	—
75	C₂²×Dic₅₃	C₂³	1	2	yes	—
76	#11719949	—	2	16	no	—
77	D₄×D₅₃	—	2	32	no	—
78	D₄×D₅₃	—	2	16	no	—
79	D₄×D₅₃	—	4	8	no	—
80	#11719945	—	2	8	no	—
81	#11719945	—	2	16	no	—
82	C₂×D₂₁₂	—	2	16	no	—
83	C₂×D₂₁₂	D₄	1	8	yes	complemented
84	C₂×D₂₁₂	C₂³	1	2	yes	—
85	C₂×D₂₁₂	C₂³	1	8	yes	—
86	C₂×D₂₁₂	C₂³	1	2	yes	—
87	C₂×D₂₁₂	C₂³	1	2	yes	—
88	C₂×D₂₁₂	C₂³	1	2	yes	—
89	C₂×D₂₁₂	C₂³	1	2	yes	—
90	C₂×C₄×D₅₃	—	4	4	no	—
91	C₂×C₄×D₅₃	C₂³	1	8	yes	—
92	C₂×C₄×D₅₃	C₂³	1	4	yes	—
93	C₂×C₄×D₅₃	C₂³	1	4	yes	—
94	C₂×C₄×D₅₃	C₂³	1	4	yes	—
95	C₂×Dic₁₀₆	C₂³	1	2	yes	—
96	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
97	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
98	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
99	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
100	C₄²×C₅₃	C₂³	1	1	yes	characteristic
101	C₄²×C₅₃	C₂³	1	1	yes	characteristic
102	C₄²×C₅₃	C₂³	1	1	yes	characteristic
103	C₄²×C₅₃	C₂³	1	1	yes	characteristic
104	C₂²⋊Dic₅₃	C₂³	1	8	yes	—
105	#11719921	C₂³	1	4	yes	—
106	#11719921	C₂³	1	8	yes	—
107	#11719921	C₂³	1	4	yes	—
108	#11719921	C₂³	1	4	yes	—
109	#11719921	C₂³	1	4	yes	—
110	C₄⋊Dic₅₃	C₂³	1	2	yes	—
111	C₄⋊Dic₅₃	C₂³	1	2	yes	—
112	C₄⋊Dic₅₃	C₂³	1	2	yes	—
113	C₄⋊Dic₅₃	C₂³	1	2	yes	—
114	#11719919	C₂³	1	8	yes	—
115	C₂³×C₅₃	C₂⁴	1	4	yes	—
116	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
117	C₂²×D₅₃	—	2	16	no	—
118	C₂²×D₅₃	—	4	2	no	—
119	C₂²×D₅₃	—	4	2	no	—
120	C₂²×D₅₃	—	4	8	no	—
121	C₂²×D₅₃	—	4	8	no	—
122	C₂²×D₅₃	C₂×D₄	1	8	yes	complemented
123	C₂²×D₅₃	C₂⁴	1	4	yes	—
124	C₂²×D₅₃	C₂⁴	1	4	yes	—
125	Q₈×C₅₃	—	2	4	no	—
126	D₄×C₅₃	—	2	8	no	—
127	D₄×C₅₃	—	2	4	no	—
128	D₄×C₅₃	—	2	4	no	—
129	D₄×C₅₃	—	4	2	no	—
130	C₂×C₄×C₅₃	—	2	8	no	—
131	C₂×C₄×C₅₃	—	2	2	no	—
132	C₂×C₄×C₅₃	—	4	1	no	—
133	C₂×C₄×C₅₃	C₂×D₄	1	4	yes	complemented
134	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
135	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
136	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
137	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
138	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
139	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
140	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
141	C₂²⋊D₅₃	—	2	8	no	—
142	C₂²⋊D₅₃	—	2	16	no	—
143	C₂²⋊D₅₃	—	4	8	no	—
144	C₂×Dic₅₃	—	4	2	no	—
145	C₂×Dic₅₃	C₂⁴	1	4	yes	—
146	C₂×Dic₅₃	C₂⁴	1	4	yes	—
147	D₂₁₂	—	2	16	no	—
148	D₂₁₂	—	2	4	no	—
149	D₂₁₂	—	2	4	no	—
150	D₂₁₂	—	4	2	no	—
151	D₂₁₂	C₂×D₄	1	8	yes	complemented
152	D₂₁₂	C₂×D₄	1	8	yes	complemented
153	C₄×D₅₃	—	2	16	no	—
154	C₄×D₅₃	—	2	8	no	—
155	C₄×D₅₃	—	2	8	no	—
156	C₄×D₅₃	—	4	4	no	—
157	Dic₁₀₆	—	2	4	no	—
158	C₂²×C₅₃	—	2	1	no	—
159	C₂²×C₅₃	—	2	1	no	—
160	C₂²×C₅₃	—	2	4	no	—
161	C₂²×C₅₃	—	2	4	no	—
162	C₂²×C₅₃	—	2	4	no	—
163	C₂²×C₅₃	C₂²×D₄	1	2	yes	—
164	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
165	C₂×D₅₃	—	2	4	no	—
166	C₂×D₅₃	—	2	4	no	—
167	C₂×D₅₃	—	2	4	no	—
168	C₂×D₅₃	—	2	4	no	—
169	C₂×D₅₃	—	2	4	no	—
170	C₂×D₅₃	—	4	8	no	—
171	C₂×D₅₃	—	8	16	no	—
172	C₂×D₅₃	C₂²×D₄	1	8	yes	—
173	C₄×C₅₃	—	2	4	no	—
174	C₄×C₅₃	—	2	1	no	—
175	C₄×C₅₃	—	2	1	no	—
176	C₄×C₅₃	—	2	1	no	—
177	C₄×C₅₃	C₂²×D₄	1	2	yes	—
178	C₄×C₅₃	C₂²×D₄	1	2	yes	—
179	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	complemented
180	Dic₅₃	—	2	4	no	—
181	Dic₅₃	—	2	4	no	—
182	#3496	—	53	1	no	maximal, Sylow
183	C₂×C₅₃	—	2	2	no	—
184	C₂×C₅₃	—	4	4	no	—
185	C₂×C₅₃	C₂³×D₄	1	1	yes	characteristic
186	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₅₃	#585	1	1	yes	characteristic
188	D₅₃	—	2	8	no	—
189	D₅₃	—	4	4	no	—
190	C₂×H(5,𝔽₂)	—	53	2	no	—
191	#547	—	53	2	no	—
192	#547	—	53	2	no	—
193	#546	—	53	4	no	—
194	#546	—	53	4	no	—
195	D₄²	—	53	2	no	—
196	D₄²	—	53	2	no	—
197	#537	—	53	2	no	—
198	#534	—	53	4	no	—
199	#532	—	53	1	no	—
200	#532	D₅₃	1	1	yes	characteristic, complemented
201	C₂×#121	—	53	4	no	—
202	C₂×C₄×D₄	—	53	1	no	—
203	C₅₃	#3496	1	1	yes	characteristic, complemented, Sylow
204	H(5,𝔽₂)	—	106	16	no	—
205	C₂×#41	—	53	4	no	—
206	C₂×#41	—	53	2	no	—
207	C₂×#41	—	53	4	no	—
208	C₂×#41	C₂×D₅₃	1	2	yes	complemented
209	C₂²×D₄	—	53	8	no	—
210	C₂²×D₄	—	53	4	no	—
211	C₂²×D₄	—	53	4	no	—
212	C₂²×D₄	—	53	1	no	—
213	C₂²×D₄	—	53	4	no	—
214	C₂³×C₄	—	53	2	no	—
215	C₄⋊Q₈	—	53	1	no	—
216	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
217	#127	—	53	1	no	—
218	#127	C₂×D₅₃	1	1	yes	characteristic, complemented
219	#124	—	53	2	no	—
220	#124	C₂×D₅₃	1	2	yes	complemented
221	#123	—	53	8	no	—
222	#123	—	53	8	no	—
223	C₂²⋊Q₈	—	53	4	no	—
224	C₂²⋊Q₈	—	53	4	no	—
225	#121	—	53	8	no	—
226	#121	—	53	4	no	—
227	#121	—	53	4	no	—
228	#121	—	53	2	no	—
229	#121	—	53	2	no	—
230	#121	—	53	4	no	—
231	#121	—	53	4	no	—
232	#121	—	53	8	no	—
233	#121	C₂×D₅₃	1	2	yes	complemented
234	#121	C₂×D₅₃	1	2	yes	complemented
235	#120	—	53	8	no	—
236	#120	—	53	8	no	—
237	C₄×D₄	—	53	2	no	—
238	C₄×D₄	—	53	2	no	—
239	C₄×D₄	—	53	2	no	—
240	C₄×D₄	—	53	2	no	—
241	C₄×D₄	—	53	2	no	—
242	C₄×D₄	—	53	2	no	—
243	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
244	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
245	C₂×C₄⋊C₄	—	53	1	no	—
246	C₂×C₄⋊C₄	—	53	4	no	—
247	C₂×C₂²⋊C₄	—	53	2	no	—
248	C₂×C₂²⋊C₄	—	53	8	no	—
249	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
250	C₂⁴	—	53	2	no	—
251	C₂⁴	—	53	8	no	—
252	#41	—	2	8	no	—
253	#41	—	106	16	no	—
254	#41	—	106	16	no	—
255	#41	—	106	8	no	—
256	C₂×Q₈	—	53	2	no	—
257	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
258	C₂×D₄	—	53	8	no	—
259	C₂×D₄	—	53	4	no	—
260	C₂×D₄	—	53	8	no	—
261	C₂×D₄	—	53	8	no	—
262	C₂×D₄	—	53	2	no	—
263	C₂×D₄	—	53	2	no	—
264	C₂×D₄	—	53	2	no	—
265	C₂×D₄	—	53	8	no	—
266	C₂×D₄	—	53	2	no	—
267	C₂×D₄	—	53	2	no	—
268	C₂×D₄	—	106	16	no	—
269	C₂×D₄	—	106	16	no	—
270	C₂×D₄	—	106	32	no	—
271	C₂×D₄	—	212	8	no	—
272	C₂×D₄	C₂²×D₅₃	1	2	yes	—
273	C₂×D₄	C₂²×D₅₃	1	4	yes	—
274	C₂×D₄	C₂²×D₅₃	1	2	yes	—
275	C₂×D₄	C₂²×D₅₃	1	2	yes	—
276	C₂²×C₄	—	53	2	no	—
277	C₂²×C₄	—	53	8	no	—
278	C₂²×C₄	—	53	4	no	—
279	C₂²×C₄	—	53	4	no	—
280	C₂²×C₄	—	53	4	no	—
281	C₂²×C₄	—	212	4	no	—
282	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
283	C₂²×C₄	C₂²×D₅₃	1	4	yes	—
284	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
286	C₄⋊C₄	—	53	2	no	—
287	C₄⋊C₄	—	53	2	no	—
288	C₄⋊C₄	—	53	2	no	—
289	C₄⋊C₄	—	53	8	no	—
290	C₄⋊C₄	—	53	2	no	—
291	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
292	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
293	C₂²⋊C₄	—	53	8	no	—
294	C₂²⋊C₄	—	53	4	no	—
295	C₂²⋊C₄	—	53	4	no	—
296	C₂²⋊C₄	—	53	4	no	—
297	C₂²⋊C₄	—	53	8	no	—
298	C₂²⋊C₄	—	53	4	no	—
299	C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
300	C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
301	C₄²	C₂²×D₅₃	1	1	yes	characteristic
302	C₄²	C₂²×D₅₃	1	1	yes	characteristic
303	C₄²	C₂²×D₅₃	1	1	yes	characteristic
304	C₄²	C₂²×D₅₃	1	1	yes	characteristic
305	C₂³	—	53	4	no	—
306	C₂³	—	53	8	no	—
307	C₂³	—	53	4	no	—
308	C₂³	—	106	16	no	—
309	C₂³	—	212	8	no	—
310	C₂³	—	212	8	no	—
311	C₂³	—	212	2	no	—
312	C₂³	—	212	2	no	—
313	C₂³	C₂³×D₅₃	1	4	yes	—
314	C₂³	C₂³×D₅₃	1	1	yes	characteristic
315	Q₈	—	2	4	no	—
316	Q₈	—	106	4	no	—
317	D₄	—	2	8	no	—
318	D₄	—	2	4	no	—
319	D₄	—	2	4	no	—
320	D₄	—	4	2	no	—
321	D₄	—	53	8	no	—
322	D₄	—	53	8	no	—
323	D₄	—	106	16	no	—
324	D₄	—	106	16	no	—
325	D₄	—	106	8	no	—
326	D₄	—	106	4	no	—
327	D₄	—	106	4	no	—
328	D₄	—	212	2	no	—
329	D₄	—	212	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	53	4	no	—
334	C₂×C₄	—	53	4	no	—
335	C₂×C₄	—	106	16	no	—
336	C₂×C₄	—	106	8	no	—
337	C₂×C₄	—	106	8	no	—
338	C₂×C₄	—	212	4	no	—
339	C₂×C₄	—	212	2	no	—
340	C₂×C₄	D₄×D₅₃	1	4	yes	complemented
341	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
342	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
343	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
344	C₂×C₄	C₂³×D₅₃	1	4	yes	—
345	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
346	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
347	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	53	8	no	—
354	C₂²	—	106	4	no	—
355	C₂²	—	106	4	no	—
356	C₂²	—	106	4	no	—
357	C₂²	—	106	4	no	—
358	C₂²	—	106	4	no	—
359	C₂²	—	424	16	no	—
360	C₂²	—	212	8	no	—
361	C₂²	C₂×D₄×D₅₃	1	2	yes	—
362	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	106	4	no	—
368	C₄	—	106	4	no	—
369	C₄	C₂×D₄×D₅₃	1	2	yes	—
370	C₄	C₂×D₄×D₅₃	1	2	yes	—
371	C₄	#13133263	1	2	yes	complemented
372	C₂	—	2	2	no	—
373	C₂	—	4	4	no	—
374	C₂	—	106	8	no	—
375	C₂	—	212	4	no	—
376	C₂	C₂²×D₄×D₅₃	1	1	yes	characteristic
377	C₂	C₂×#13133263	1	1	yes	characteristic
378	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#532	C₂
hypercenter	#532	D₅₃
hypocenter	C₅₃	#3496
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₂×#13133263	C₂	semidirect
2. #16811278	C₂	semidirect
3. #16811276	C₂	semidirect
4. #16811269	C₂	semidirect
5. #16811266	C₂	semidirect
6. D₄×D₂₁₂	C₂	semidirect
7. #16811258	C₂	semidirect
8. #16811201	C₂	semidirect
9. #16811181	C₂	semidirect
10. #16811173	C₂	semidirect
11. #121×D₅₃	C₂	semidirect
12. C₂×C₄×D₂₁₂	C₂	semidirect
13. C₅₃×#532	C₂	semidirect
15. C₂×#11719949	C₂²	semidirect
16. C₂×#11719945	C₂²	semidirect
17. C₂×#11719945	C₂²	semidirect
19. C₂²×D₂₁₂	C₂²	semidirect
20. C₂×D₄×D₅₃	C₂²	semidirect
21. C₂×D₄×D₅₃	C₂²	semidirect
22. C₂×D₄×D₅₃	C₂²	semidirect
23. C₂²×C₄×D₅₃	C₂²	semidirect
24. #13133217	C₂²	semidirect
25. #13133214	C₂²	semidirect
26. #13133205	C₂²	semidirect
27. #13133202	C₂²	semidirect
28. #13133199	C₂²	semidirect
29. #13133196	C₂²	semidirect
30. #13133193	C₂²	semidirect
31. #13133192	C₂²	semidirect
32. #13133191	C₂²	semidirect
33. #13133191	C₂²	semidirect
34. #13133191	C₂²	semidirect
35. #13133190	C₂²	semidirect
36. #13133189	C₂²	semidirect
37. #13133188	C₂²	semidirect
38. #13133188	C₂²	semidirect
39. #13133187	C₂²	semidirect
40. #13133185	C₂²	semidirect
41. C₄×D₂₁₂	C₂²	semidirect
42. C₄×D₂₁₂	C₂²	semidirect
43. C₄×D₂₁₂	C₂²	semidirect
44. C₄×D₂₁₂	C₂²	semidirect
45. C₄×D₂₁₂	C₂²	semidirect
46. C₄×D₂₁₂	C₂²	semidirect
47. C₂×C₄⋊Dic₅₃	C₂²	semidirect
48. C₄⋊C₄×D₅₃	C₂²	semidirect
49. C₂×#11719921	C₂²	semidirect
50. C₂²⋊C₄×D₅₃	C₂²	semidirect
51. C₂×#41×C₅₃	C₂²	semidirect
52. C₄⋊Q₈×C₅₃	C₂²	semidirect
53. #127×C₅₃	C₂²	semidirect
54. #124×C₅₃	C₂²	semidirect
55. #121×C₅₃	C₂²	semidirect
56. #121×C₅₃	C₂²	semidirect
57. C₄×D₄×C₅₃	C₂²	semidirect
58. C₄×D₄×C₅₃	C₂²	semidirect
59. C₂×C₄²×C₅₃	C₂²	semidirect
83. C₂×D₂₁₂	D₄	semidirect
122. C₂²×D₅₃	C₂×D₄	semidirect
133. C₂×C₄×C₅₃	C₂×D₄	semidirect
151. D₂₁₂	C₂×D₄	semidirect
152. D₂₁₂	C₂×D₄	semidirect
179. C₄×C₅₃	H(5,𝔽₂)	semidirect
200. #532	D₅₃	semidirect
203. C₅₃	#3496	semidirect
208. C₂×#41	C₂×D₅₃	semidirect
216. C₄⋊Q₈	C₂×D₅₃	semidirect
218. #127	C₂×D₅₃	semidirect
220. #124	C₂×D₅₃	semidirect
233. #121	C₂×D₅₃	semidirect
234. #121	C₂×D₅₃	semidirect
243. C₄×D₄	C₂×D₅₃	semidirect
244. C₄×D₄	C₂×D₅₃	semidirect
249. C₂×C₄²	C₂×D₅₃	semidirect
340. C₂×C₄	D₄×D₅₃	semidirect
371. C₄	#13133263	semidirect