Subgroups — #20288348

Order 6784.

1900 conjugacy classes of subgroups.

The subgroup lattice has 414 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	1	yes	maximal, characteristic, complemented
2	C₂³×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811269	C₂	1	4	yes	maximal, complemented
4	#16811264	C₂	1	4	yes	maximal, complemented
5	D₄×D₂₁₂	C₂	1	4	yes	maximal, complemented
6	#16811257	C₂	1	4	yes	maximal, complemented
7	#16811192	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811187	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811184	C₂	1	4	yes	maximal, complemented
10	#16811134	C₂	1	1	yes	maximal, characteristic, complemented
11	#120×D₅₃	C₂	1	4	yes	maximal, complemented
12	#16811097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂⁴×D₅₃	C₂²	1	2	yes	complemented
15	#13133263	—	2	8	no	—
16	C₂×#11719949	C₂²	1	2	yes	complemented
17	C₂×#11719945	C₂²	1	2	yes	complemented
18	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₂₁₂	—	2	8	no	—
20	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
21	C₂²×D₂₁₂	C₂²	1	4	yes	complemented
22	C₂²×D₂₁₂	C₂²	1	4	yes	complemented
23	C₂²×D₂₁₂	C₂²	1	2	yes	complemented
24	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
25	C₂²×D₂₁₂	C₂²	1	2	yes	complemented
26	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
27	C₂×D₄×D₅₃	C₂²	1	4	yes	complemented
28	C₂×D₄×D₅₃	C₂²	1	8	yes	complemented
29	#13133214	C₂²	1	2	yes	complemented
30	#13133213	C₂²	1	2	yes	complemented
31	#13133206	C₂²	1	2	yes	complemented
32	#13133205	C₂²	1	2	yes	complemented
33	#13133202	C₂²	1	8	yes	complemented
34	#13133200	C₂²	1	2	yes	complemented
35	#13133196	C₂²	1	2	yes	complemented
36	#13133192	C₂²	1	8	yes	complemented
37	#13133192	C₂²	1	4	yes	complemented
38	#13133191	C₂²	1	4	yes	complemented
39	#13133191	C₂²	1	2	yes	complemented
40	#13133190	C₂²	1	8	yes	complemented
41	#13133187	C₂²	1	8	yes	complemented
42	#13133187	C₂²	1	8	yes	complemented
43	#13133187	C₂²	1	4	yes	complemented
44	#13133186	C₂²	1	2	yes	complemented
45	#13133185	C₂²	1	8	yes	complemented
46	#13133185	C₂²	1	4	yes	complemented
47	C₄×D₂₁₂	C₂²	1	4	yes	complemented
48	#13133179	C₂²	1	4	yes	complemented
49	C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
50	#13133176	C₂²	1	1	yes	characteristic, complemented
51	C₂²⋊C₄×D₅₃	C₂²	1	8	yes	complemented
52	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
53	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	#123×C₅₃	C₂²	1	2	yes	complemented
56	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
57	#121×C₅₃	C₂²	1	2	yes	complemented
58	#120×C₅₃	C₂²	1	2	yes	complemented
59	C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
60	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
62	C₂³×D₅₃	—	2	8	no	—
63	C₂³×D₅₃	—	4	8	no	—
64	C₂³×D₅₃	C₂³	1	8	yes	—
65	C₂³×D₅₃	C₂³	1	2	yes	—
66	C₂³×D₅₃	C₂³	1	2	yes	—
67	C₂³×D₅₃	C₂³	1	4	yes	complemented
68	#41×C₅₃	—	2	4	no	—
69	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
70	C₂×D₄×C₅₃	C₂³	1	4	yes	—
71	C₂×D₄×C₅₃	C₂³	1	2	yes	—
72	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
73	C₂²×C₄×C₅₃	—	2	4	no	—
74	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
75	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
76	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	C₂³	1	2	yes	complemented
79	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
80	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
81	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
82	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
83	#11719949	—	2	8	no	—
84	D₄×D₅₃	—	2	16	no	—
85	D₄×D₅₃	—	2	8	no	—
86	D₄×D₅₃	—	4	16	no	—
87	#11719945	—	2	4	no	—
88	#11719945	—	2	8	no	—
89	C₂×D₂₁₂	—	2	8	no	—
90	C₂×D₂₁₂	—	2	4	no	—
91	C₂×D₂₁₂	—	2	16	no	—
92	C₂×D₂₁₂	—	2	16	no	—
93	C₂×D₂₁₂	—	2	8	no	—
94	C₂×D₂₁₂	D₄	1	8	yes	complemented
95	C₂×D₂₁₂	C₂³	1	8	yes	—
96	C₂×D₂₁₂	C₂³	1	2	yes	—
97	C₂×D₂₁₂	C₂³	1	2	yes	—
98	C₂×D₂₁₂	C₂³	1	2	yes	—
99	C₂×D₂₁₂	C₂³	1	2	yes	—
100	C₂×D₂₁₂	C₂³	1	4	yes	complemented
101	C₂×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
102	C₂×D₂₁₂	C₂³	1	8	yes	complemented
103	C₂×C₄×D₅₃	C₂³	1	4	yes	complemented
104	C₂×C₄×D₅₃	C₂³	1	2	yes	complemented
105	C₂×C₄×D₅₃	C₂³	1	8	yes	complemented
106	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
107	C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
108	C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
109	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
110	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
111	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
112	C₄²×C₅₃	C₂³	1	2	yes	complemented
113	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
114	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
115	#11719921	C₂³	1	8	yes	complemented
116	#11719921	C₂³	1	8	yes	complemented
117	#11719921	C₂³	1	8	yes	complemented
118	#11719921	C₂³	1	4	yes	complemented
119	C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
120	#11719919	C₂³	1	4	yes	complemented
121	C₄×Dic₅₃	C₂³	1	2	yes	complemented
122	C₂³×C₅₃	—	2	2	no	—
123	C₂³×C₅₃	—	2	4	no	—
124	C₂³×C₅₃	C₂⁴	1	2	yes	—
125	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
126	C₂³×C₅₃	C₂⁴	1	2	yes	—
127	C₂²×D₅₃	—	2	4	no	—
128	C₂²×D₅₃	—	2	16	no	—
129	C₂²×D₅₃	—	2	16	no	—
130	C₂²×D₅₃	—	2	8	no	—
131	C₂²×D₅₃	—	4	4	no	—
132	C₂²×D₅₃	—	4	8	no	—
133	C₂²×D₅₃	—	4	4	no	—
134	C₂²×D₅₃	—	4	8	no	—
135	C₂²×D₅₃	—	4	32	no	—
136	C₂²×D₅₃	C₂×D₄	1	8	yes	complemented
137	C₂²×D₅₃	C₂⁴	1	2	yes	—
138	C₂²×D₅₃	C₂⁴	1	4	yes	—
139	C₂²×D₅₃	C₂⁴	1	4	yes	—
140	Q₈×C₅₃	—	2	2	no	—
141	D₄×C₅₃	—	2	4	no	—
142	D₄×C₅₃	—	2	8	no	—
143	D₄×C₅₃	—	2	2	no	—
144	C₂×C₄×C₅₃	—	2	2	no	—
145	C₂×C₄×C₅₃	—	2	4	no	—
146	C₂×C₄×C₅₃	—	2	4	no	—
147	C₂×C₄×C₅₃	—	2	4	no	—
148	C₂×C₄×C₅₃	C₂×D₄	1	4	yes	complemented
149	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
150	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
151	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
152	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
153	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
154	C₂²⋊D₅₃	—	2	4	no	—
155	C₂²⋊D₅₃	—	2	8	no	—
156	C₂²⋊D₅₃	—	2	8	no	—
157	C₂²⋊D₅₃	—	4	8	no	—
158	C₂×Dic₅₃	C₂⁴	1	2	yes	—
159	C₂×Dic₅₃	C₂⁴	1	4	yes	—
160	D₂₁₂	—	2	16	no	—
161	D₂₁₂	—	2	8	no	—
162	D₂₁₂	—	2	4	no	—
163	D₂₁₂	—	2	4	no	—
164	D₂₁₂	—	2	2	no	—
165	D₂₁₂	—	4	8	no	—
166	D₂₁₂	C₂×D₄	1	8	yes	complemented
167	D₂₁₂	C₂×D₄	1	8	yes	complemented
168	C₄×D₅₃	—	2	8	no	—
169	C₄×D₅₃	—	2	4	no	—
170	C₄×D₅₃	—	4	8	no	—
171	Dic₁₀₆	—	2	2	no	—
172	C₂²×C₅₃	—	2	8	no	—
173	C₂²×C₅₃	—	2	2	no	—
174	C₂²×C₅₃	—	2	2	no	—
175	C₂²×C₅₃	—	2	2	no	—
176	C₂²×C₅₃	—	2	2	no	—
177	C₂²×C₅₃	—	2	4	no	—
178	C₂²×C₅₃	C₂²×D₄	1	2	yes	—
179	C₂²×C₅₃	H(5,𝔽₂)	1	4	yes	complemented
180	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
181	C₂×D₅₃	—	2	8	no	—
182	C₂×D₅₃	—	2	2	no	—
183	C₂×D₅₃	—	2	4	no	—
184	C₂×D₅₃	—	2	4	no	—
185	C₂×D₅₃	—	2	8	no	—
186	C₂×D₅₃	—	4	8	no	—
187	C₂×D₅₃	—	4	32	no	—
188	C₂×D₅₃	—	4	8	no	—
189	C₂×D₅₃	—	8	8	no	—
190	C₂×D₅₃	C₂²×D₄	1	8	yes	—
191	C₄×C₅₃	—	2	2	no	—
192	C₄×C₅₃	—	2	2	no	—
193	C₄×C₅₃	—	2	4	no	—
194	C₄×C₅₃	C₂²×D₄	1	2	yes	—
195	C₄×C₅₃	C₂²×D₄	1	2	yes	—
196	Dic₅₃	—	2	2	no	—
197	Dic₅₃	—	2	4	no	—
198	#3484	—	53	1	no	maximal, Sylow
199	C₂×C₅₃	—	2	2	no	—
200	C₂×C₅₃	—	2	4	no	—
201	C₂×C₅₃	—	4	2	no	—
202	C₂×C₅₃	C₂³×D₄	1	1	yes	characteristic
203	C₂×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
204	D₅₃	—	2	8	no	—
205	D₅₃	—	4	4	no	—
206	D₅₃	—	4	2	no	—
207	C₂×H(5,𝔽₂)	—	53	1	no	—
208	C₂³×D₄	—	53	1	no	—
209	#546	—	53	4	no	—
210	#546	—	53	4	no	—
211	D₄²	—	53	4	no	—
212	D₄²	—	53	4	no	—
213	#535	—	53	1	no	—
214	#535	—	53	1	no	—
215	#534	—	53	4	no	—
216	#525	—	53	1	no	—
217	#525	D₅₃	1	1	yes	characteristic, complemented
218	C₂×#120	—	53	4	no	—
219	#518	—	53	1	no	—
220	C₅₃	#3484	1	1	yes	characteristic, complemented, Sylow
221	C₂⁵	—	53	2	no	—
222	H(5,𝔽₂)	—	106	8	no	—
223	C₂×#41	—	53	2	no	—
224	C₂×#41	—	53	1	no	—
225	C₂×#41	—	53	2	no	—
226	C₂×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
227	C₂²×D₄	—	53	4	no	—
228	C₂²×D₄	—	53	2	no	—
229	C₂²×D₄	—	53	8	no	—
230	C₂²×D₄	—	53	1	no	—
231	C₂²×D₄	—	53	2	no	—
232	C₂²×D₄	—	53	1	no	—
233	C₂²×D₄	—	53	4	no	—
234	C₂²×D₄	—	53	4	no	—
235	C₂²×D₄	—	53	2	no	—
236	C₂²×D₄	—	106	8	no	—
237	C₂³×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
238	#127	—	53	2	no	—
239	#127	—	53	2	no	—
240	#124	—	53	2	no	—
241	#124	—	53	2	no	—
242	#123	—	53	2	no	—
243	#123	—	53	8	no	—
244	#123	C₂×D₅₃	1	2	yes	complemented
245	C₂²⋊Q₈	—	53	2	no	—
246	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
247	#121	—	53	2	no	—
248	#121	—	53	4	no	—
249	#121	—	53	8	no	—
250	#121	—	53	4	no	—
251	#121	—	53	8	no	—
252	#121	C₂×D₅₃	1	2	yes	complemented
253	#120	—	53	2	no	—
254	#120	—	53	4	no	—
255	#120	—	53	8	no	—
256	#120	—	53	4	no	—
257	#120	—	53	8	no	—
258	#120	—	53	8	no	—
259	#120	C₂×D₅₃	1	2	yes	complemented
260	C₄×D₄	—	53	4	no	—
261	C₄×D₄	—	53	4	no	—
262	C₄×D₄	—	53	4	no	—
263	C₄×D₄	C₂×D₅₃	1	4	yes	complemented
264	#117	—	53	1	no	—
265	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
266	C₂×C₂²⋊C₄	—	53	4	no	—
267	C₂×C₂²⋊C₄	—	53	8	no	—
268	C₂⁴	—	53	2	no	—
269	C₂⁴	—	53	8	no	—
270	C₂⁴	—	53	2	no	—
271	C₂⁴	—	53	4	no	—
272	C₂⁴	—	106	8	no	—
273	C₂⁴	—	212	8	no	—
274	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
275	#41	—	2	4	no	—
276	#41	—	106	8	no	—
277	#41	—	106	8	no	—
278	#41	—	106	4	no	—
279	C₂×Q₈	—	53	1	no	—
280	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
281	C₂×D₄	—	53	4	no	—
282	C₂×D₄	—	53	2	no	—
283	C₂×D₄	—	53	4	no	—
284	C₂×D₄	—	53	8	no	—
285	C₂×D₄	—	53	8	no	—
286	C₂×D₄	—	53	2	no	—
287	C₂×D₄	—	53	2	no	—
288	C₂×D₄	—	53	8	no	—
289	C₂×D₄	—	53	2	no	—
290	C₂×D₄	—	53	2	no	—
291	C₂×D₄	—	53	4	no	—
292	C₂×D₄	—	53	1	no	—
293	C₂×D₄	—	53	8	no	—
294	C₂×D₄	—	106	16	no	—
295	C₂×D₄	—	106	16	no	—
296	C₂×D₄	—	106	8	no	—
297	C₂×D₄	—	106	8	no	—
298	C₂×D₄	—	106	8	no	—
299	C₂×D₄	—	106	16	no	—
300	C₂×D₄	—	106	4	no	—
301	C₂×D₄	—	212	16	no	—
302	C₂×D₄	C₂²×D₅₃	1	4	yes	—
303	C₂×D₄	C₂²×D₅₃	1	2	yes	—
304	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	53	4	no	—
307	C₂²×C₄	—	53	2	no	—
308	C₂²×C₄	—	53	8	no	—
309	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
310	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
311	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
312	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
313	C₂²×C₄	C₂²×D₅₃	1	2	yes	complemented
314	C₄⋊C₄	—	53	2	no	—
315	C₄⋊C₄	—	53	4	no	—
316	C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
317	C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
318	C₂²⋊C₄	—	53	2	no	—
319	C₂²⋊C₄	—	53	4	no	—
320	C₂²⋊C₄	—	53	8	no	—
321	C₂²⋊C₄	—	53	8	no	—
322	C₂²⋊C₄	—	53	8	no	—
323	C₂²⋊C₄	—	53	4	no	—
324	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
325	C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
326	C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
327	C₄²	—	53	2	no	—
328	C₄²	C₂²×D₅₃	1	2	yes	complemented
329	C₂³	—	2	2	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	53	4	no	—
332	C₂³	—	53	8	no	—
333	C₂³	—	53	4	no	—
334	C₂³	—	53	2	no	—
335	C₂³	—	106	8	no	—
336	C₂³	—	106	16	no	—
337	C₂³	—	106	4	no	—
338	C₂³	—	106	16	no	—
339	C₂³	—	212	8	no	—
340	C₂³	—	212	4	no	—
341	C₂³	—	212	8	no	—
342	C₂³	—	212	4	no	—
343	C₂³	—	212	32	no	—
344	C₂³	C₂³×D₅₃	1	2	yes	—
345	C₂³	C₂³×D₅₃	1	1	yes	characteristic
346	C₂³	C₂³×D₅₃	1	2	yes	—
347	Q₈	—	2	2	no	—
348	Q₈	—	106	2	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	8	no	—
351	D₄	—	2	2	no	—
352	D₄	—	53	8	no	—
353	D₄	—	53	8	no	—
354	D₄	—	106	16	no	—
355	D₄	—	106	8	no	—
356	D₄	—	106	8	no	—
357	D₄	—	106	4	no	—
358	D₄	—	106	8	no	—
359	D₄	—	106	4	no	—
360	D₄	—	106	4	no	—
361	D₄	—	106	2	no	—
362	D₄	—	212	8	no	—
363	D₄	—	212	8	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	53	4	no	—
369	C₂×C₄	—	53	2	no	—
370	C₂×C₄	—	106	8	no	—
371	C₂×C₄	—	106	4	no	—
372	C₂×C₄	—	212	8	no	—
373	C₂×C₄	D₄×D₅₃	1	4	yes	complemented
374	C₂×C₄	C₂³×D₅₃	1	4	yes	—
375	C₂×C₄	C₂³×D₅₃	1	2	yes	—
376	C₂×C₄	C₂³×D₅₃	1	2	yes	—
377	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
379	C₂²	—	2	8	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	53	8	no	—
386	C₂²	—	106	8	no	—
387	C₂²	—	106	2	no	—
388	C₂²	—	106	4	no	—
389	C₂²	—	106	4	no	—
390	C₂²	—	106	8	no	—
391	C₂²	—	424	8	no	—
392	C₂²	—	212	8	no	—
393	C₂²	—	212	32	no	—
394	C₂²	—	212	8	no	—
395	C₂²	C₂×D₄×D₅₃	1	2	yes	—
396	C₂²	#13133263	1	4	yes	complemented
397	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	4	no	—
401	C₄	—	106	2	no	—
402	C₄	—	106	4	no	—
403	C₄	C₂×D₄×D₅₃	1	2	yes	—
404	C₄	C₂×D₄×D₅₃	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	2	4	no	—
407	C₂	—	4	2	no	—
408	C₂	—	106	8	no	—
409	C₂	—	212	2	no	—
410	C₂	—	212	4	no	—
411	C₂	C₂²×D₄×D₅₃	1	1	yes	characteristic
412	C₂	C₂×#13133263	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#525	C₂
hypercenter	#525	D₅₃
hypocenter	C₅₃	#3484
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂×#13133263	C₂	semidirect
2. C₂³×D₂₁₂	C₂	semidirect
3. #16811269	C₂	semidirect
4. #16811264	C₂	semidirect
5. D₄×D₂₁₂	C₂	semidirect
6. #16811257	C₂	semidirect
7. #16811192	C₂	semidirect
8. #16811187	C₂	semidirect
9. #16811184	C₂	semidirect
10. #16811134	C₂	semidirect
11. #120×D₅₃	C₂	semidirect
12. #16811097	C₂	semidirect
13. C₅₃×#525	C₂	semidirect
14. C₂⁴×D₅₃	C₂²	semidirect
16. C₂×#11719949	C₂²	semidirect
17. C₂×#11719945	C₂²	semidirect
18. C₂×#11719945	C₂²	semidirect
21. C₂²×D₂₁₂	C₂²	semidirect
22. C₂²×D₂₁₂	C₂²	semidirect
23. C₂²×D₂₁₂	C₂²	semidirect
24. C₂²×D₂₁₂	C₂²	semidirect
25. C₂²×D₂₁₂	C₂²	semidirect
26. C₂×D₄×D₅₃	C₂²	semidirect
27. C₂×D₄×D₅₃	C₂²	semidirect
28. C₂×D₄×D₅₃	C₂²	semidirect
29. #13133214	C₂²	semidirect
30. #13133213	C₂²	semidirect
31. #13133206	C₂²	semidirect
32. #13133205	C₂²	semidirect
33. #13133202	C₂²	semidirect
34. #13133200	C₂²	semidirect
35. #13133196	C₂²	semidirect
36. #13133192	C₂²	semidirect
37. #13133192	C₂²	semidirect
38. #13133191	C₂²	semidirect
39. #13133191	C₂²	semidirect
40. #13133190	C₂²	semidirect
41. #13133187	C₂²	semidirect
42. #13133187	C₂²	semidirect
43. #13133187	C₂²	semidirect
44. #13133186	C₂²	semidirect
45. #13133185	C₂²	semidirect
46. #13133185	C₂²	semidirect
47. C₄×D₂₁₂	C₂²	semidirect
48. #13133179	C₂²	semidirect
49. C₄×C₂²⋊D₅₃	C₂²	semidirect
50. #13133176	C₂²	semidirect
51. C₂²⋊C₄×D₅₃	C₂²	semidirect
52. C₂²⋊C₄×D₅₃	C₂²	semidirect
53. C₂×#41×C₅₃	C₂²	semidirect
54. C₂³×C₄×C₅₃	C₂²	semidirect
55. #123×C₅₃	C₂²	semidirect
56. C₂²⋊Q₈×C₅₃	C₂²	semidirect
57. #121×C₅₃	C₂²	semidirect
58. #120×C₅₃	C₂²	semidirect
59. C₄×D₄×C₅₃	C₂²	semidirect
60. #117×C₅₃	C₂²	semidirect
67. C₂³×D₅₃	C₂³	semidirect
69. C₂×Q₈×C₅₃	C₂³	semidirect
72. C₂×D₄×C₅₃	C₂³	semidirect
78. C₂²×C₄×C₅₃	C₂³	semidirect
81. C₂×C₂²⋊D₅₃	C₂³	semidirect
82. C₂×C₂²⋊D₅₃	C₂³	semidirect
94. C₂×D₂₁₂	D₄	semidirect
100. C₂×D₂₁₂	C₂³	semidirect
101. C₂×D₂₁₂	C₂³	semidirect
102. C₂×D₂₁₂	C₂³	semidirect
103. C₂×C₄×D₅₃	C₂³	semidirect
104. C₂×C₄×D₅₃	C₂³	semidirect
105. C₂×C₄×D₅₃	C₂³	semidirect
106. C₂×Dic₁₀₆	C₂³	semidirect
107. C₄⋊C₄×C₅₃	C₂³	semidirect
108. C₄⋊C₄×C₅₃	C₂³	semidirect
111. C₂²⋊C₄×C₅₃	C₂³	semidirect
112. C₄²×C₅₃	C₂³	semidirect
115. #11719921	C₂³	semidirect
116. #11719921	C₂³	semidirect
117. #11719921	C₂³	semidirect
118. #11719921	C₂³	semidirect
119. C₄⋊Dic₅₃	C₂³	semidirect
120. #11719919	C₂³	semidirect
121. C₄×Dic₅₃	C₂³	semidirect
136. C₂²×D₅₃	C₂×D₄	semidirect
148. C₂×C₄×C₅₃	C₂×D₄	semidirect
166. D₂₁₂	C₂×D₄	semidirect
167. D₂₁₂	C₂×D₄	semidirect
179. C₂²×C₅₃	H(5,𝔽₂)	semidirect
217. #525	D₅₃	semidirect
220. C₅₃	#3484	semidirect
226. C₂×#41	C₂×D₅₃	semidirect
237. C₂³×C₄	C₂×D₅₃	semidirect
244. #123	C₂×D₅₃	semidirect
246. C₂²⋊Q₈	C₂×D₅₃	semidirect
252. #121	C₂×D₅₃	semidirect
259. #120	C₂×D₅₃	semidirect
263. C₄×D₄	C₂×D₅₃	semidirect
265. #117	C₂×D₅₃	semidirect
280. C₂×Q₈	C₂²×D₅₃	semidirect
304. C₂×D₄	C₂²×D₅₃	semidirect
313. C₂²×C₄	C₂²×D₅₃	semidirect
316. C₄⋊C₄	C₂²×D₅₃	semidirect
317. C₄⋊C₄	C₂²×D₅₃	semidirect
326. C₂²⋊C₄	C₂²×D₅₃	semidirect
328. C₄²	C₂²×D₅₃	semidirect
373. C₂×C₄	D₄×D₅₃	semidirect
396. C₂²	#13133263	semidirect