Subgroups — #20288198

Order 6784.

1648 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11719945	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811291	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811286	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811283	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811279	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811275	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811271	C₂	1	2	yes	maximal, complemented
9	#16811270	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811265	C₂	1	2	yes	maximal, complemented
11	#16811264	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811260	C₂	1	2	yes	maximal, complemented
13	#16811257	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811255	C₂	1	2	yes	maximal, complemented
15	#16811170	C₂	1	2	yes	maximal, complemented
16	#16811169	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811135	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811132	C₂	1	2	yes	maximal, complemented
19	#16811132	C₂	1	2	yes	maximal, complemented
20	#16811091	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
23	C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11719949	C₂²	1	1	yes	characteristic, complemented
25	C₂×#11719945	—	2	8	no	—
26	C₂×#11719945	C₂²	1	1	yes	characteristic
27	C₂×#11719945	C₂²	1	2	yes	complemented
28	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
29	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
30	C₂×#11719945	C₂²	1	2	yes	complemented
31	C₂×#11719945	C₂²	1	2	yes	complemented
32	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
33	C₂×#11719947	C₂²	1	2	yes	complemented
34	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
35	#41×D₅₃	—	2	8	no	—
36	C₂²×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
37	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
41	C₂×D₄×D₅₃	C₂²	1	2	yes	—
42	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
43	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄×D₅₃	C₂²	1	2	yes	complemented
45	C₂²×C₄×D₅₃	C₂²	1	2	yes	complemented
46	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
47	#13133216	C₂²	1	2	yes	complemented
48	#13133215	C₂²	1	1	yes	characteristic, complemented
49	#13133213	C₂²	1	1	yes	characteristic, complemented
50	#13133213	C₂²	1	2	yes	complemented
51	#13133206	C₂²	1	1	yes	characteristic, complemented
52	#13133204	C₂²	1	1	yes	characteristic, complemented
53	#13133203	C₂²	1	2	yes	complemented
54	#13133203	C₂²	1	2	yes	complemented
55	#13133202	C₂²	1	2	yes	complemented
56	#13133202	C₂²	1	2	yes	complemented
57	#13133201	C₂²	1	2	yes	complemented
58	#13133199	C₂²	1	2	yes	complemented
59	#13133199	C₂²	1	2	yes	complemented
60	#13133197	C₂²	1	1	yes	characteristic, complemented
61	#13133197	C₂²	1	1	yes	characteristic, complemented
62	#13133195	C₂²	1	2	yes	complemented
63	#13133195	C₂²	1	2	yes	complemented
64	#13133194	C₂²	1	2	yes	complemented
65	#13133194	C₂²	1	2	yes	complemented
66	#13133192	C₂²	1	2	yes	complemented
67	#13133192	C₂²	1	1	yes	characteristic, complemented
68	#13133192	C₂²	1	1	yes	characteristic, complemented
69	#13133190	C₂²	1	2	yes	complemented
70	#13133190	C₂²	1	2	yes	complemented
71	#13133190	C₂²	1	2	yes	complemented
72	#13133190	C₂²	1	2	yes	complemented
73	#13133189	C₂²	1	2	yes	complemented
74	#13133189	C₂²	1	2	yes	complemented
75	#13133189	C₂²	1	2	yes	complemented
76	#13133189	C₂²	1	2	yes	complemented
77	#13133188	C₂²	1	2	yes	complemented
78	#13133187	C₂²	1	2	yes	complemented
79	#13133187	C₂²	1	2	yes	complemented
80	#13133187	C₂²	1	2	yes	complemented
81	#13133185	C₂²	1	2	yes	complemented
82	#13133185	C₂²	1	2	yes	complemented
83	#13133182	C₂²	1	1	yes	characteristic, complemented
84	#13133182	C₂²	1	1	yes	characteristic, complemented
85	C₄×D₂₁₂	C₂²	1	2	yes	complemented
86	C₄×D₂₁₂	C₂²	1	2	yes	complemented
87	D₄×Dic₅₃	C₂²	1	2	yes	complemented
88	#13133179	C₂²	1	1	yes	characteristic, complemented
89	#13133179	C₂²	1	2	yes	complemented
90	#13133179	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
101	#13133177	C₂²	1	2	yes	—
102	#13133177	C₂²	1	2	yes	complemented
103	#13133177	C₂²	1	2	yes	complemented
104	#13133177	C₂²	1	2	yes	complemented
105	#13133174	C₂²	1	2	yes	complemented
106	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
108	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
109	C₂×#11719921	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
113	C₄²×D₅₃	C₂²	1	2	yes	complemented
114	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	#123×C₅₃	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
121	#120×C₅₃	C₂²	1	2	yes	complemented
122	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
123	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
124	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
126	C₂³×D₅₃	C₂³	1	2	yes	—
127	C₂³×D₅₃	C₂³	1	2	yes	—
128	C₂³×D₅₃	C₂³	1	1	yes	characteristic
129	#41×C₅₃	—	2	4	no	—
130	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
135	C₂²×C₄×C₅₃	—	2	4	no	—
136	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
139	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₅₃	—	2	8	no	—
144	C₂×C₂²⋊D₅₃	—	2	4	no	—
145	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
157	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
158	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
159	C₂²×Dic₅₃	C₂³	1	2	yes	—
160	C₂²×Dic₅₃	C₂³	1	2	yes	—
161	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
162	#11719949	—	2	4	no	—
163	Q₈×D₅₃	—	2	4	no	—
164	#11719947	—	2	8	no	—
165	#11719947	—	2	4	no	—
166	D₄×D₅₃	—	2	8	no	—
167	D₄×D₅₃	—	2	8	no	—
168	D₄×D₅₃	—	2	4	no	—
169	#11719945	—	2	4	no	—
170	#11719945	—	2	8	no	—
171	#11719945	—	2	4	no	—
172	#11719945	—	2	8	no	—
173	#11719945	—	2	8	no	—
174	#11719945	—	2	4	no	—
175	#11719945	D₄	1	8	yes	complemented
176	C₂×D₂₁₂	—	2	4	no	—
177	C₂×D₂₁₂	C₂³	1	2	yes	—
178	C₂×D₂₁₂	C₂³	1	2	yes	—
179	C₂×D₂₁₂	C₂³	1	2	yes	—
180	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
181	C₂×D₂₁₂	C₂³	1	2	yes	—
182	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₅₃	—	2	4	no	—
184	C₂×C₄×D₅₃	—	2	8	no	—
185	C₂×C₄×D₅₃	—	2	8	no	—
186	C₂×C₄×D₅₃	C₂³	1	2	yes	—
187	C₂×C₄×D₅₃	C₂³	1	2	yes	—
188	C₂×C₄×D₅₃	C₂³	1	2	yes	—
189	C₂×C₄×D₅₃	C₂³	1	2	yes	—
190	C₂×C₄×D₅₃	C₂³	1	2	yes	—
191	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
192	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
193	C₂×C₄×D₅₃	C₂³	1	2	yes	—
194	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
195	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₄×D₅₃	C₂³	1	2	yes	—
197	C₂×C₄×D₅₃	C₂³	1	2	yes	—
198	C₂×Dic₁₀₆	—	2	4	no	—
199	C₂×Dic₁₀₆	C₂³	1	2	yes	—
200	C₂×Dic₁₀₆	C₂³	1	2	yes	—
201	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
202	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
203	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
206	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
207	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
208	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
209	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
210	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
211	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
212	C₄²×C₅₃	C₂³	1	2	yes	—
213	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
214	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
215	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
216	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
217	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
218	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
219	#11719921	C₂³	1	1	yes	characteristic
220	#11719921	C₂³	1	2	yes	—
221	#11719921	C₂³	1	2	yes	—
222	#11719921	C₂³	1	2	yes	—
223	#11719921	C₂³	1	1	yes	characteristic
224	#11719921	C₂³	1	1	yes	characteristic
225	#11719921	C₂³	1	1	yes	characteristic
226	#11719921	C₂³	1	2	yes	—
227	#11719921	C₂³	1	2	yes	—
228	#11719921	C₂³	1	2	yes	—
229	#11719921	C₂³	1	2	yes	—
230	#11719921	C₂³	1	2	yes	—
231	C₄⋊Dic₅₃	C₂³	1	2	yes	—
232	C₄⋊Dic₅₃	C₂³	1	2	yes	—
233	#11719919	C₂³	1	1	yes	characteristic
234	#11719919	C₂³	1	2	yes	—
235	#11719919	C₂³	1	1	yes	characteristic
236	#11719919	C₂³	1	1	yes	characteristic
237	#11719919	C₂³	1	1	yes	characteristic
238	#11719919	C₂³	1	2	yes	—
239	#11719919	C₂³	1	2	yes	—
240	#11719919	C₂³	1	2	yes	—
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	1	yes	characteristic
245	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
246	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
247	C₂³×C₅₃	—	2	2	no	—
248	C₂³×C₅₃	—	2	2	no	—
249	C₂³×C₅₃	—	4	1	no	—
250	C₂³×C₅₃	C₂⁴	1	2	yes	—
251	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
252	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
253	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
254	C₂²×D₅₃	—	2	2	no	—
255	C₂²×D₅₃	—	2	4	no	—
256	C₂²×D₅₃	—	2	4	no	—
257	C₂²×D₅₃	—	2	4	no	—
258	C₂²×D₅₃	—	2	4	no	—
259	C₂²×D₅₃	—	2	2	no	—
260	C₂²×D₅₃	—	4	2	no	—
261	C₂²×D₅₃	—	4	2	no	—
262	C₂²×D₅₃	—	4	1	no	—
263	C₂²×D₅₃	C₂⁴	1	2	yes	—
264	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
265	C₂²×D₅₃	C₂⁴	1	2	yes	—
266	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
267	Q₈×C₅₃	—	2	2	no	—
268	D₄×C₅₃	—	2	4	no	—
269	D₄×C₅₃	—	2	4	no	—
270	D₄×C₅₃	—	2	2	no	—
271	D₄×C₅₃	—	4	2	no	—
272	C₂×C₄×C₅₃	—	2	2	no	—
273	C₂×C₄×C₅₃	—	2	2	no	—
274	C₂×C₄×C₅₃	—	2	2	no	—
275	C₂×C₄×C₅₃	—	2	4	no	—
276	C₂×C₄×C₅₃	—	2	2	no	—
277	C₂×C₄×C₅₃	—	2	2	no	—
278	C₂×C₄×C₅₃	C₂×D₄	1	4	yes	complemented
279	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
281	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
283	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
284	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
286	C₂²⋊D₅₃	—	2	4	no	—
287	C₂²⋊D₅₃	—	2	2	no	—
288	C₂²⋊D₅₃	—	2	4	no	—
289	C₂²⋊D₅₃	—	2	4	no	—
290	C₂²⋊D₅₃	—	2	2	no	—
291	C₂²⋊D₅₃	—	2	4	no	—
292	C₂²⋊D₅₃	—	2	4	no	—
293	C₂²⋊D₅₃	—	2	4	no	—
294	C₂²⋊D₅₃	—	2	2	no	—
295	C₂²⋊D₅₃	—	4	2	no	—
296	C₂²⋊D₅₃	C₂×D₄	1	8	yes	complemented
297	C₂²⋊D₅₃	#41	1	4	yes	complemented
298	C₂×Dic₅₃	—	2	2	no	—
299	C₂×Dic₅₃	—	2	4	no	—
300	C₂×Dic₅₃	—	2	4	no	—
301	C₂×Dic₅₃	—	2	2	no	—
302	C₂×Dic₅₃	—	4	1	no	—
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	1	yes	characteristic
307	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
308	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
309	C₂×Dic₅₃	C₂⁴	1	2	yes	—
310	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
311	D₂₁₂	—	2	4	no	—
312	D₂₁₂	—	2	4	no	—
313	D₂₁₂	—	2	4	no	—
314	D₂₁₂	—	2	2	no	—
315	D₂₁₂	—	4	2	no	—
316	D₂₁₂	C₂×D₄	1	4	yes	complemented
317	C₄×D₅₃	—	2	4	no	—
318	C₄×D₅₃	—	2	4	no	—
319	C₄×D₅₃	—	2	2	no	—
320	C₄×D₅₃	—	2	2	no	—
321	C₄×D₅₃	—	2	4	no	—
322	C₄×D₅₃	—	2	2	no	—
323	C₄×D₅₃	—	2	2	no	—
324	C₄×D₅₃	—	2	4	no	—
325	C₄×D₅₃	—	2	4	no	—
326	C₄×D₅₃	—	2	4	no	—
327	C₄×D₅₃	—	4	2	no	—
328	C₄×D₅₃	C₂×D₄	1	8	yes	complemented
329	Dic₁₀₆	—	2	2	no	—
330	Dic₁₀₆	—	2	4	no	—
331	Dic₁₀₆	—	2	4	no	—
332	Dic₁₀₆	C₂×D₄	1	4	yes	complemented
333	C₂²×C₅₃	—	2	1	no	—
334	C₂²×C₅₃	—	2	1	no	—
335	C₂²×C₅₃	—	2	1	no	—
336	C₂²×C₅₃	—	2	1	no	—
337	C₂²×C₅₃	—	2	2	no	—
338	C₂²×C₅₃	—	2	1	no	—
339	C₂²×C₅₃	—	2	1	no	—
340	C₂²×C₅₃	—	2	2	no	—
341	C₂²×C₅₃	—	2	2	no	—
342	C₂²×C₅₃	—	2	1	no	—
343	C₂²×C₅₃	—	4	4	no	—
344	C₂²×C₅₃	C₂²×D₄	1	2	yes	—
345	C₂²×C₅₃	C₂×#41	1	2	yes	complemented
346	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
347	C₂×D₅₃	—	2	1	no	—
348	C₂×D₅₃	—	2	2	no	—
349	C₂×D₅₃	—	2	2	no	—
350	C₂×D₅₃	—	2	1	no	—
351	C₂×D₅₃	—	2	1	no	—
352	C₂×D₅₃	—	2	2	no	—
353	C₂×D₅₃	—	2	2	no	—
354	C₂×D₅₃	—	2	1	no	—
355	C₂×D₅₃	—	2	1	no	—
356	C₂×D₅₃	—	2	2	no	—
357	C₂×D₅₃	—	4	8	no	—
358	C₂×D₅₃	—	4	4	no	—
359	C₂×D₅₃	—	4	8	no	—
360	C₂×D₅₃	C₂²×D₄	1	4	yes	—
361	C₂×D₅₃	C₂×#41	1	2	yes	complemented
362	C₄×C₅₃	—	2	1	no	—
363	C₄×C₅₃	—	2	2	no	—
364	C₄×C₅₃	—	2	1	no	—
365	C₄×C₅₃	—	2	2	no	—
366	C₄×C₅₃	—	2	2	no	—
367	C₄×C₅₃	C₂²×D₄	1	2	yes	—
368	C₄×C₅₃	C₂²×D₄	1	2	yes	—
369	Dic₅₃	—	2	2	no	—
370	Dic₅₃	—	2	1	no	—
371	Dic₅₃	—	2	1	no	—
372	Dic₅₃	—	2	1	no	—
373	Dic₅₃	—	2	1	no	—
374	Dic₅₃	—	2	1	no	—
375	Dic₅₃	C₂²×D₄	1	4	yes	—
376	Dic₅₃	C₂×#41	1	2	yes	complemented
377	D₄×#41	—	53	1	no	maximal, Sylow
378	C₂×C₅₃	—	2	2	no	—
379	C₂×C₅₃	—	2	2	no	—
380	C₂×C₅₃	—	4	2	no	—
381	C₂×C₅₃	—	4	1	no	—
382	C₂×C₅₃	C₂³×D₄	1	1	yes	characteristic
383	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
384	C₂×C₅₃	#585	1	1	yes	characteristic
385	D₅₃	—	2	2	no	—
386	D₅₃	—	2	4	no	—
387	D₅₃	—	4	2	no	—
388	D₅₃	—	4	1	no	—
389	C₂²×#41	—	53	1	no	—
390	C₂²×#41	—	53	1	no	—
391	#550	—	53	1	no	—
392	D₄×Q₈	—	53	1	no	—
393	#548	—	53	1	no	—
394	#548	—	53	1	no	—
395	#547	—	53	2	no	—
396	#547	—	53	1	no	—
397	#546	—	53	2	no	—
398	#546	—	53	1	no	—
399	#546	—	53	1	no	—
400	#546	—	53	2	no	—
401	D₄²	—	53	1	no	—
402	D₄²	—	53	2	no	—
403	#532	—	53	1	no	—
404	#532	—	53	2	no	—
405	#525	—	53	2	no	—
406	#525	—	53	2	no	—
407	#525	—	53	1	no	—
408	#525	D₅₃	1	1	yes	characteristic, complemented
409	C₄×#41	—	53	1	no	—
410	C₂×C₄×D₄	—	53	1	no	—
411	C₂×C₄×D₄	—	53	2	no	—
412	C₅₃	D₄×#41	1	1	yes	characteristic, complemented, Sylow
413	C₂×#41	—	53	1	no	—
414	C₂×#41	—	53	2	no	—
415	C₂×#41	—	53	1	no	—
416	C₂×#41	—	53	1	no	—
417	C₂×#41	—	53	2	no	—
418	C₂×#41	—	53	2	no	—
419	C₂×#41	—	53	1	no	—
420	C₂×#41	—	53	1	no	—
421	C₂×#41	—	53	2	no	—
422	C₂×#41	—	53	1	no	—
423	C₂×#41	—	106	8	no	—
424	C₂×#41	—	106	8	no	—
425	C₂×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
426	C₂²×Q₈	—	53	1	no	—
427	C₂²×Q₈	—	53	1	no	—
428	C₂²×D₄	—	53	1	no	—
429	C₂²×D₄	—	53	2	no	—
430	C₂²×D₄	—	53	2	no	—
431	C₂²×D₄	—	53	2	no	—
432	C₂²×D₄	—	53	1	no	—
433	C₂²×D₄	—	53	1	no	—
434	C₂³×C₄	—	53	2	no	—
435	C₂³×C₄	—	53	2	no	—
436	C₂³×C₄	—	53	1	no	—
437	C₂³×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
438	C₄⋊Q₈	—	53	1	no	—
439	C₄⋊Q₈	—	53	2	no	—
440	#127	—	53	2	no	—
441	#127	—	53	1	no	—
442	#124	—	53	1	no	—
443	#124	—	53	1	no	—
444	#124	—	53	2	no	—
445	#124	—	53	2	no	—
446	#123	—	53	2	no	—
447	#123	—	53	2	no	—
448	#123	—	53	2	no	—
449	#123	—	53	2	no	—
450	#123	—	53	2	no	—
451	#123	C₂×D₅₃	1	2	yes	complemented
452	C₂²⋊Q₈	—	53	2	no	—
453	C₂²⋊Q₈	—	53	1	no	—
454	C₂²⋊Q₈	—	53	2	no	—
455	C₂²⋊Q₈	—	53	1	no	—
456	C₂²⋊Q₈	—	53	2	no	—
457	C₂²⋊Q₈	—	53	2	no	—
458	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
459	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
460	#121	—	53	2	no	—
461	#121	—	53	2	no	—
462	#121	—	53	2	no	—
463	#121	—	53	2	no	—
464	#121	—	53	2	no	—
465	#121	—	53	1	no	—
466	#121	—	53	1	no	—
467	#121	—	53	2	no	—
468	#121	—	53	2	no	—
469	#121	—	53	2	no	—
470	#121	—	53	2	no	—
471	#121	—	53	2	no	—
472	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
473	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
474	#120	—	53	2	no	—
475	#120	—	53	2	no	—
476	#120	—	53	2	no	—
477	#120	—	53	2	no	—
478	#120	—	53	2	no	—
479	#120	C₂×D₅₃	1	2	yes	complemented
480	C₄×Q₈	—	53	1	no	—
481	C₄×Q₈	—	53	1	no	—
482	C₄×D₄	—	53	2	no	—
483	C₄×D₄	—	53	1	no	—
484	C₄×D₄	—	53	1	no	—
485	C₄×D₄	—	53	1	no	—
486	C₄×D₄	—	53	2	no	—
487	C₄×D₄	—	53	1	no	—
488	C₄×D₄	—	53	1	no	—
489	C₄×D₄	—	53	1	no	—
490	C₄×D₄	—	53	1	no	—
491	C₄×D₄	—	53	1	no	—
492	C₄×D₄	—	53	2	no	—
493	C₄×D₄	—	53	2	no	—
494	C₄×D₄	—	53	1	no	—
495	C₄×D₄	—	53	1	no	—
496	C₄×D₄	—	53	2	no	—
497	C₄×D₄	—	53	2	no	—
498	C₄×D₄	—	53	2	no	—
499	C₄×D₄	—	53	2	no	—
500	C₄×D₄	—	53	2	no	—
501	C₄×D₄	—	53	2	no	—
502	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
503	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
504	#117	—	53	2	no	—
505	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
506	C₂×C₄⋊C₄	—	53	1	no	—
507	C₂×C₄⋊C₄	—	53	2	no	—
508	C₂×C₂²⋊C₄	—	53	1	no	—
509	C₂×C₂²⋊C₄	—	53	1	no	—
510	C₂×C₂²⋊C₄	—	53	2	no	—
511	C₂×C₂²⋊C₄	—	53	2	no	—
512	C₂×C₄²	—	53	1	no	—
513	C₂×C₄²	—	53	2	no	—
514	C₂⁴	—	53	2	no	—
515	C₂⁴	—	53	1	no	—
516	C₂⁴	—	53	2	no	—
517	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
518	#41	—	2	4	no	—
519	#41	—	53	8	no	—
520	#41	—	106	8	no	—
521	#41	—	106	8	no	—
522	#41	—	106	8	no	—
523	#41	—	106	4	no	—
524	#41	—	106	4	no	—
525	#41	—	106	8	no	—
526	#41	—	106	4	no	—
527	#41	—	106	4	no	—
528	#41	—	106	4	no	—
529	C₂×Q₈	—	53	1	no	—
530	C₂×Q₈	—	53	2	no	—
531	C₂×Q₈	—	53	2	no	—
532	C₂×Q₈	—	53	1	no	—
533	C₂×Q₈	—	106	4	no	—
534	C₂×Q₈	—	106	4	no	—
535	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
536	C₂×D₄	—	53	1	no	—
537	C₂×D₄	—	53	2	no	—
538	C₂×D₄	—	53	1	no	—
539	C₂×D₄	—	53	1	no	—
540	C₂×D₄	—	53	2	no	—
541	C₂×D₄	—	53	1	no	—
542	C₂×D₄	—	53	2	no	—
543	C₂×D₄	—	53	2	no	—
544	C₂×D₄	—	53	2	no	—
545	C₂×D₄	—	53	2	no	—
546	C₂×D₄	—	53	2	no	—
547	C₂×D₄	—	53	2	no	—
548	C₂×D₄	—	53	1	no	—
549	C₂×D₄	—	53	2	no	—
550	C₂×D₄	—	53	2	no	—
551	C₂×D₄	—	53	2	no	—
552	C₂×D₄	—	53	1	no	—
553	C₂×D₄	—	53	2	no	—
554	C₂×D₄	—	106	4	no	—
555	C₂×D₄	—	106	8	no	—
556	C₂×D₄	—	106	8	no	—
557	C₂×D₄	—	106	4	no	—
558	C₂×D₄	—	106	4	no	—
559	C₂×D₄	—	106	8	no	—
560	C₂×D₄	C₂²×D₅₃	1	2	yes	—
561	C₂×D₄	C₂²×D₅₃	1	2	yes	—
562	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
563	C₂×D₄	C₂²×D₅₃	1	2	yes	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	53	2	no	—
566	C₂²×C₄	—	53	1	no	—
567	C₂²×C₄	—	53	1	no	—
568	C₂²×C₄	—	53	2	no	—
569	C₂²×C₄	—	53	2	no	—
570	C₂²×C₄	—	53	1	no	—
571	C₂²×C₄	—	53	2	no	—
572	C₂²×C₄	—	53	2	no	—
573	C₂²×C₄	—	53	2	no	—
574	C₂²×C₄	—	53	2	no	—
575	C₂²×C₄	—	53	1	no	—
576	C₂²×C₄	—	53	2	no	—
577	C₂²×C₄	—	53	1	no	—
578	C₂²×C₄	—	53	1	no	—
579	C₂²×C₄	—	53	1	no	—
580	C₂²×C₄	—	53	2	no	—
581	C₂²×C₄	—	53	2	no	—
582	C₂²×C₄	—	106	8	no	—
583	C₂²×C₄	—	106	8	no	—
584	C₂²×C₄	—	106	4	no	—
585	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
586	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
587	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
588	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
589	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
590	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
591	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
592	C₄⋊C₄	—	53	1	no	—
593	C₄⋊C₄	—	53	2	no	—
594	C₄⋊C₄	—	53	1	no	—
595	C₄⋊C₄	—	53	1	no	—
596	C₄⋊C₄	—	53	1	no	—
597	C₄⋊C₄	—	53	2	no	—
598	C₄⋊C₄	—	53	2	no	—
599	C₄⋊C₄	—	53	2	no	—
600	C₄⋊C₄	—	53	2	no	—
601	C₄⋊C₄	—	53	2	no	—
602	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
603	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
604	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
605	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
606	C₂²⋊C₄	—	53	1	no	—
607	C₂²⋊C₄	—	53	1	no	—
608	C₂²⋊C₄	—	53	1	no	—
609	C₂²⋊C₄	—	53	2	no	—
610	C₂²⋊C₄	—	53	1	no	—
611	C₂²⋊C₄	—	53	2	no	—
612	C₂²⋊C₄	—	53	1	no	—
613	C₂²⋊C₄	—	53	1	no	—
614	C₂²⋊C₄	—	53	2	no	—
615	C₂²⋊C₄	—	53	1	no	—
616	C₂²⋊C₄	—	53	2	no	—
617	C₂²⋊C₄	—	53	2	no	—
618	C₂²⋊C₄	—	53	1	no	—
619	C₂²⋊C₄	—	53	2	no	—
620	C₂²⋊C₄	—	53	2	no	—
621	C₂²⋊C₄	—	53	2	no	—
622	C₂²⋊C₄	—	53	2	no	—
623	C₂²⋊C₄	—	53	2	no	—
624	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
625	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
626	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
627	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
628	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
629	C₄²	—	53	2	no	—
630	C₄²	—	53	1	no	—
631	C₄²	—	53	2	no	—
632	C₄²	—	53	1	no	—
633	C₄²	—	53	1	no	—
634	C₄²	—	53	1	no	—
635	C₄²	C₂²×D₅₃	1	2	yes	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	53	1	no	—
640	C₂³	—	53	2	no	—
641	C₂³	—	53	1	no	—
642	C₂³	—	53	2	no	—
643	C₂³	—	106	4	no	—
644	C₂³	—	106	4	no	—
645	C₂³	—	106	2	no	—
646	C₂³	—	106	4	no	—
647	C₂³	—	106	2	no	—
648	C₂³	—	106	4	no	—
649	C₂³	—	212	1	no	—
650	C₂³	—	212	2	no	—
651	C₂³	—	212	2	no	—
652	C₂³	C₂³×D₅₃	1	2	yes	—
653	C₂³	C₂³×D₅₃	1	1	yes	characteristic
654	C₂³	C₂³×D₅₃	1	1	yes	characteristic
655	C₂³	C₂³×D₅₃	1	1	yes	characteristic
656	Q₈	—	2	2	no	—
657	Q₈	—	53	4	no	—
658	Q₈	—	106	4	no	—
659	Q₈	—	106	4	no	—
660	Q₈	—	106	2	no	—
661	D₄	—	2	4	no	—
662	D₄	—	2	4	no	—
663	D₄	—	2	2	no	—
664	D₄	—	4	2	no	—
665	D₄	—	53	8	no	—
666	D₄	—	53	4	no	—
667	D₄	—	53	4	no	—
668	D₄	—	106	4	no	—
669	D₄	—	106	4	no	—
670	D₄	—	106	4	no	—
671	D₄	—	106	4	no	—
672	D₄	—	106	2	no	—
673	D₄	—	106	4	no	—
674	D₄	—	106	4	no	—
675	D₄	—	106	2	no	—
676	D₄	—	106	4	no	—
677	D₄	—	106	4	no	—
678	D₄	—	106	4	no	—
679	D₄	—	106	2	no	—
680	D₄	—	106	2	no	—
681	D₄	—	212	2	no	—
682	D₄	—	212	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	53	1	no	—
690	C₂×C₄	—	53	2	no	—
691	C₂×C₄	—	53	8	no	—
692	C₂×C₄	—	53	1	no	—
693	C₂×C₄	—	53	1	no	—
694	C₂×C₄	—	53	1	no	—
695	C₂×C₄	—	53	1	no	—
696	C₂×C₄	—	53	1	no	—
697	C₂×C₄	—	53	2	no	—
698	C₂×C₄	—	106	4	no	—
699	C₂×C₄	—	106	4	no	—
700	C₂×C₄	—	106	4	no	—
701	C₂×C₄	—	106	4	no	—
702	C₂×C₄	—	106	4	no	—
703	C₂×C₄	—	106	4	no	—
704	C₂×C₄	—	106	4	no	—
705	C₂×C₄	—	106	2	no	—
706	C₂×C₄	—	106	2	no	—
707	C₂×C₄	—	106	2	no	—
708	C₂×C₄	—	106	2	no	—
709	C₂×C₄	—	106	2	no	—
710	C₂×C₄	—	106	4	no	—
711	C₂×C₄	—	106	2	no	—
712	C₂×C₄	—	212	2	no	—
713	C₂×C₄	—	212	1	no	—
714	C₂×C₄	D₄×D₅₃	1	4	yes	complemented
715	C₂×C₄	C₂³×D₅₃	1	2	yes	—
716	C₂×C₄	C₂³×D₅₃	1	2	yes	—
717	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
718	C₂×C₄	C₂³×D₅₃	1	2	yes	—
719	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
720	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
721	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
722	C₂²	—	2	1	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	53	4	no	—
734	C₂²	—	53	2	no	—
735	C₂²	—	106	1	no	—
736	C₂²	—	106	2	no	—
737	C₂²	—	106	2	no	—
738	C₂²	—	106	1	no	—
739	C₂²	—	106	2	no	—
740	C₂²	—	106	1	no	—
741	C₂²	—	106	2	no	—
742	C₂²	—	106	1	no	—
743	C₂²	—	106	1	no	—
744	C₂²	—	106	2	no	—
745	C₂²	—	212	8	no	—
746	C₂²	—	212	4	no	—
747	C₂²	—	212	8	no	—
748	C₂²	C₂×D₄×D₅₃	1	2	yes	—
749	C₂²	#41×D₅₃	1	2	yes	complemented
750	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	53	4	no	—
757	C₄	—	53	2	no	—
758	C₄	—	106	1	no	—
759	C₄	—	106	2	no	—
760	C₄	—	106	1	no	—
761	C₄	—	106	1	no	—
762	C₄	—	106	1	no	—
763	C₄	—	106	1	no	—
764	C₄	C₂×D₄×D₅₃	1	2	yes	—
765	C₄	C₂×D₄×D₅₃	1	2	yes	—
766	C₂	—	2	2	no	—
767	C₂	—	2	2	no	—
768	C₂	—	4	1	no	—
769	C₂	—	4	2	no	—
770	C₂	—	106	2	no	—
771	C₂	—	106	4	no	—
772	C₂	—	212	2	no	—
773	C₂	—	212	1	no	—
774	C₂	C₂²×D₄×D₅₃	1	1	yes	characteristic
775	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
776	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Frattini	C₂²	C₂⁴×D₅₃
Fitting	C₅₃×#525	C₂
hypercenter	#525	D₅₃
hypocenter	C₅₃	D₄×#41
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂²×#11719945	C₂	semidirect
2. C₂×#41×D₅₃	C₂	semidirect
3. #16811291	C₂	semidirect
4. #16811286	C₂	semidirect
5. #16811283	C₂	semidirect
6. #16811279	C₂	semidirect
7. #16811275	C₂	semidirect
8. #16811271	C₂	semidirect
9. #16811270	C₂	semidirect
10. #16811265	C₂	semidirect
11. #16811264	C₂	semidirect
12. #16811260	C₂	semidirect
13. #16811257	C₂	semidirect
14. #16811255	C₂	semidirect
15. #16811170	C₂	semidirect
16. #16811169	C₂	semidirect
17. #16811135	C₂	semidirect
18. #16811132	C₂	semidirect
19. #16811132	C₂	semidirect
20. #16811091	C₂	semidirect
21. C₂×C₄×C₂²⋊D₅₃	C₂	semidirect
22. C₄×D₄×D₅₃	C₂	semidirect
23. C₅₃×#525	C₂	semidirect
24. C₂×#11719949	C₂²	semidirect
27. C₂×#11719945	C₂²	semidirect
28. C₂×#11719945	C₂²	semidirect
29. C₂×#11719945	C₂²	semidirect
30. C₂×#11719945	C₂²	semidirect
31. C₂×#11719945	C₂²	semidirect
32. C₂×#11719945	C₂²	semidirect
33. C₂×#11719947	C₂²	semidirect
34. C₂×#11719947	C₂²	semidirect
36. C₂²×Dic₁₀₆	C₂²	semidirect
37. C₂×Q₈×D₅₃	C₂²	semidirect
38. C₂²×D₂₁₂	C₂²	semidirect
40. C₂²×C₂²⋊D₅₃	C₂²	semidirect
42. C₂×D₄×D₅₃	C₂²	semidirect
43. C₂×D₄×D₅₃	C₂²	semidirect
44. C₂²×C₄×D₅₃	C₂²	semidirect
45. C₂²×C₄×D₅₃	C₂²	semidirect
46. C₂²×C₄×D₅₃	C₂²	semidirect
47. #13133216	C₂²	semidirect
48. #13133215	C₂²	semidirect
49. #13133213	C₂²	semidirect
50. #13133213	C₂²	semidirect
51. #13133206	C₂²	semidirect
52. #13133204	C₂²	semidirect
53. #13133203	C₂²	semidirect
54. #13133203	C₂²	semidirect
55. #13133202	C₂²	semidirect
56. #13133202	C₂²	semidirect
57. #13133201	C₂²	semidirect
58. #13133199	C₂²	semidirect
59. #13133199	C₂²	semidirect
60. #13133197	C₂²	semidirect
61. #13133197	C₂²	semidirect
62. #13133195	C₂²	semidirect
63. #13133195	C₂²	semidirect
64. #13133194	C₂²	semidirect
65. #13133194	C₂²	semidirect
66. #13133192	C₂²	semidirect
67. #13133192	C₂²	semidirect
68. #13133192	C₂²	semidirect
69. #13133190	C₂²	semidirect
70. #13133190	C₂²	semidirect
71. #13133190	C₂²	semidirect
72. #13133190	C₂²	semidirect
73. #13133189	C₂²	semidirect
74. #13133189	C₂²	semidirect
75. #13133189	C₂²	semidirect
76. #13133189	C₂²	semidirect
77. #13133188	C₂²	semidirect
78. #13133187	C₂²	semidirect
79. #13133187	C₂²	semidirect
80. #13133187	C₂²	semidirect
81. #13133185	C₂²	semidirect
82. #13133185	C₂²	semidirect
83. #13133182	C₂²	semidirect
84. #13133182	C₂²	semidirect
85. C₄×D₂₁₂	C₂²	semidirect
86. C₄×D₂₁₂	C₂²	semidirect
87. D₄×Dic₅₃	C₂²	semidirect
88. #13133179	C₂²	semidirect
89. #13133179	C₂²	semidirect
90. #13133179	C₂²	semidirect
93. C₄×C₂²⋊D₅₃	C₂²	semidirect
94. C₄×C₂²⋊D₅₃	C₂²	semidirect
95. C₄×C₂²⋊D₅₃	C₂²	semidirect
96. C₄×C₂²⋊D₅₃	C₂²	semidirect
97. C₄×C₂²⋊D₅₃	C₂²	semidirect
98. C₄×C₂²⋊D₅₃	C₂²	semidirect
99. C₄×C₂²⋊D₅₃	C₂²	semidirect
100. C₄×C₂²⋊D₅₃	C₂²	semidirect
102. #13133177	C₂²	semidirect
103. #13133177	C₂²	semidirect
104. #13133177	C₂²	semidirect
105. #13133174	C₂²	semidirect
106. C₂×#11719919	C₂²	semidirect
107. C₄⋊C₄×D₅₃	C₂²	semidirect
108. C₂×C₂²⋊Dic₅₃	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
115. C₂³×C₄×C₅₃	C₂²	semidirect
116. #123×C₅₃	C₂²	semidirect
117. C₂²⋊Q₈×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. #117×C₅₃	C₂²	semidirect
175. #11719945	D₄	semidirect
278. C₂×C₄×C₅₃	C₂×D₄	semidirect
296. C₂²⋊D₅₃	C₂×D₄	semidirect
297. C₂²⋊D₅₃	#41	semidirect
316. D₂₁₂	C₂×D₄	semidirect
328. C₄×D₅₃	C₂×D₄	semidirect
332. Dic₁₀₆	C₂×D₄	semidirect
345. C₂²×C₅₃	C₂×#41	semidirect
361. C₂×D₅₃	C₂×#41	semidirect
376. Dic₅₃	C₂×#41	semidirect
408. #525	D₅₃	semidirect
412. C₅₃	D₄×#41	semidirect
425. C₂×#41	C₂×D₅₃	semidirect
437. C₂³×C₄	C₂×D₅₃	semidirect
451. #123	C₂×D₅₃	semidirect
458. C₂²⋊Q₈	C₂×D₅₃	semidirect
459. C₂²⋊Q₈	C₂×D₅₃	semidirect
472. #121	C₂×D₅₃	semidirect
473. #121	C₂×D₅₃	semidirect
479. #120	C₂×D₅₃	semidirect
502. C₄×D₄	C₂×D₅₃	semidirect
503. C₄×D₄	C₂×D₅₃	semidirect
505. #117	C₂×D₅₃	semidirect
714. C₂×C₄	D₄×D₅₃	semidirect
749. C₂²	#41×D₅₃	semidirect