Subgroups — #20288397

Order 6784.

1328 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811304	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811303	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811302	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811302	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811301	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811300	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811299	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811296	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811270	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811267	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811263	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811262	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811262	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811261	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811260	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811248	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811209	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811207	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811205	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811205	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811183	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811133	C₂	1	1	yes	maximal, characteristic, complemented
23	#16811132	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811131	C₂	1	1	yes	maximal, characteristic, complemented
25	#16811130	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#13133185	C₂	1	1	yes	maximal, characteristic, complemented
27	#120×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
28	#16811096	C₂	1	1	yes	maximal, characteristic, complemented
29	#16811095	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×D₅₃	C₂²	1	1	yes	characteristic
33	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
34	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
35	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
39	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
43	#13133212	C₂²	1	1	yes	characteristic, complemented
44	#13133212	C₂²	1	1	yes	characteristic, complemented
45	#13133212	C₂²	1	1	yes	characteristic, complemented
46	#13133211	C₂²	1	1	yes	characteristic, complemented
47	#13133210	C₂²	1	1	yes	characteristic, complemented
48	#13133210	C₂²	1	1	yes	characteristic, complemented
49	#13133210	C₂²	1	1	yes	characteristic, complemented
50	#13133210	C₂²	1	1	yes	characteristic, complemented
51	#13133206	C₂²	1	1	yes	characteristic, complemented
52	#13133204	C₂²	1	1	yes	characteristic, complemented
53	#13133204	C₂²	1	1	yes	characteristic, complemented
54	#13133203	C₂²	1	1	yes	characteristic, complemented
55	#13133203	C₂²	1	1	yes	characteristic, complemented
56	#13133203	C₂²	1	1	yes	characteristic, complemented
57	#13133203	C₂²	1	1	yes	characteristic, complemented
58	#13133202	C₂²	1	1	yes	characteristic, complemented
59	#13133202	C₂²	1	1	yes	characteristic, complemented
60	#13133201	C₂²	1	1	yes	characteristic, complemented
61	#13133201	C₂²	1	1	yes	characteristic, complemented
62	#13133200	C₂²	1	1	yes	characteristic, complemented
63	#13133200	C₂²	1	1	yes	characteristic, complemented
64	#13133200	C₂²	1	1	yes	characteristic, complemented
65	#13133199	C₂²	1	1	yes	characteristic, complemented
66	#13133199	C₂²	1	1	yes	characteristic, complemented
67	#13133199	C₂²	1	1	yes	characteristic, complemented
68	#13133199	C₂²	1	1	yes	characteristic, complemented
69	#13133199	C₂²	1	1	yes	characteristic, complemented
70	#13133199	C₂²	1	1	yes	characteristic, complemented
71	#13133198	C₂²	1	1	yes	characteristic, complemented
72	#13133198	C₂²	1	1	yes	characteristic, complemented
73	#13133198	C₂²	1	1	yes	characteristic, complemented
74	#13133198	C₂²	1	1	yes	characteristic, complemented
75	#13133198	C₂²	1	1	yes	characteristic, complemented
76	#13133197	C₂²	1	1	yes	characteristic, complemented
77	#13133197	C₂²	1	1	yes	characteristic, complemented
78	#13133196	C₂²	1	1	yes	characteristic, complemented
79	#13133196	C₂²	1	1	yes	characteristic, complemented
80	#13133195	C₂²	1	1	yes	characteristic, complemented
81	#13133195	C₂²	1	1	yes	characteristic, complemented
82	#13133195	C₂²	1	1	yes	characteristic, complemented
83	#13133195	C₂²	1	1	yes	characteristic, complemented
84	#13133195	C₂²	1	1	yes	characteristic, complemented
85	#13133194	C₂²	1	1	yes	characteristic, complemented
86	#13133194	C₂²	1	1	yes	characteristic, complemented
87	#13133194	C₂²	1	1	yes	characteristic, complemented
88	#13133193	C₂²	1	1	yes	characteristic, complemented
89	#13133193	C₂²	1	1	yes	characteristic, complemented
90	#13133193	C₂²	1	1	yes	characteristic, complemented
91	#13133191	C₂²	1	1	yes	characteristic, complemented
92	#13133190	C₂²	1	1	yes	characteristic, complemented
93	#13133190	C₂²	1	1	yes	characteristic, complemented
94	#13133190	C₂²	1	1	yes	characteristic, complemented
95	#13133190	C₂²	1	1	yes	characteristic, complemented
96	#13133189	C₂²	1	1	yes	characteristic, complemented
97	#13133189	C₂²	1	1	yes	characteristic, complemented
98	#13133189	C₂²	1	1	yes	characteristic, complemented
99	#13133189	C₂²	1	1	yes	characteristic, complemented
100	#13133188	C₂²	1	1	yes	characteristic, complemented
101	#13133188	C₂²	1	1	yes	characteristic, complemented
102	#13133188	C₂²	1	1	yes	characteristic, complemented
103	#13133188	C₂²	1	1	yes	characteristic, complemented
104	#13133187	C₂²	1	1	yes	characteristic
105	#13133187	C₂²	1	1	yes	characteristic, complemented
106	#13133187	C₂²	1	1	yes	characteristic, complemented
107	#13133186	C₂²	1	1	yes	characteristic
108	#13133186	C₂²	1	1	yes	characteristic, complemented
109	#13133185	C₂²	1	1	yes	characteristic
110	#13133185	C₂²	1	1	yes	characteristic
111	#13133185	C₂²	1	1	yes	characteristic
112	#13133185	C₂²	1	1	yes	characteristic
113	#13133185	C₂²	1	1	yes	characteristic
114	#13133185	C₂²	1	1	yes	characteristic, complemented
115	#13133185	C₂²	1	1	yes	characteristic, complemented
116	#13133185	C₂²	1	1	yes	characteristic, complemented
117	#13133185	C₂²	1	1	yes	characteristic, complemented
118	#13133185	C₂²	1	1	yes	characteristic, complemented
119	#13133185	C₂²	1	1	yes	characteristic, complemented
120	#13133185	C₂²	1	1	yes	characteristic, complemented
121	#13133185	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
123	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
124	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
125	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
126	#13133179	C₂²	1	1	yes	characteristic, complemented
127	#13133179	C₂²	1	1	yes	characteristic, complemented
128	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
131	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
133	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
134	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
136	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
137	#13133177	C₂²	1	1	yes	characteristic, complemented
138	#13133177	C₂²	1	1	yes	characteristic, complemented
139	#13133177	C₂²	1	1	yes	characteristic, complemented
140	#13133177	C₂²	1	1	yes	characteristic, complemented
141	#13133177	C₂²	1	1	yes	characteristic, complemented
142	#13133177	C₂²	1	1	yes	characteristic, complemented
143	#13133177	C₂²	1	1	yes	characteristic, complemented
144	#13133176	C₂²	1	1	yes	characteristic, complemented
145	#13133175	C₂²	1	1	yes	characteristic, complemented
146	#13133175	C₂²	1	1	yes	characteristic, complemented
147	#13133174	C₂²	1	1	yes	characteristic, complemented
148	#13133174	C₂²	1	1	yes	characteristic, complemented
149	#13133173	C₂²	1	1	yes	characteristic, complemented
150	#13133173	C₂²	1	1	yes	characteristic, complemented
151	#13133173	C₂²	1	1	yes	characteristic, complemented
152	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
153	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
154	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
155	C₂×#11719921	C₂²	1	1	yes	characteristic
156	C₂×#11719921	C₂²	1	1	yes	characteristic, complemented
157	C₂×#11719921	C₂²	1	1	yes	characteristic, complemented
158	C₂×#11719921	C₂²	1	1	yes	characteristic, complemented
159	C₂×#11719921	C₂²	1	1	yes	characteristic, complemented
160	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
161	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
162	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
163	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
164	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
165	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
166	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
167	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
168	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
169	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
171	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
172	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
173	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
174	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
175	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
177	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	#120×C₅₃	C₂²	1	1	yes	characteristic
182	#120×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
188	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
189	C₂³×D₅₃	—	2	4	no	—
190	C₂³×D₅₃	—	4	2	no	—
191	C₂³×D₅₃	—	4	2	no	—
192	C₂³×D₅₃	C₂³	1	1	yes	characteristic
193	C₂³×D₅₃	C₂³	1	1	yes	characteristic
194	C₂³×D₅₃	C₂³	1	1	yes	characteristic
195	C₂³×D₅₃	C₂³	1	1	yes	characteristic
196	C₂³×D₅₃	C₂³	1	1	yes	characteristic
197	C₂³×D₅₃	C₂³	1	1	yes	characteristic
198	C₂³×D₅₃	C₂³	1	1	yes	characteristic
199	#41×C₅₃	—	4	2	no	—
200	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
201	C₂×D₄×C₅₃	—	4	2	no	—
202	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
210	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
211	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
215	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
216	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
217	C₂×C₂²⋊D₅₃	—	2	4	no	—
218	C₂×C₂²⋊D₅₃	—	4	2	no	—
219	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic, complemented
234	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic, complemented
235	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
236	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
237	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
238	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
239	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
240	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
241	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
242	#11719947	—	4	2	no	—
243	#11719947	—	4	2	no	—
244	D₄×D₅₃	—	2	4	no	—
245	D₄×D₅₃	—	4	2	no	—
246	D₄×D₅₃	—	4	2	no	—
247	#11719945	—	4	2	no	—
248	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
249	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
250	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₅₃	—	4	2	no	—
252	C₂×C₄×D₅₃	—	4	2	no	—
253	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic, complemented
265	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic, complemented
266	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
267	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
268	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
269	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
270	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
271	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
272	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
273	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
281	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
282	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
283	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
284	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
285	C₄²×C₅₃	C₂³	1	1	yes	characteristic, complemented
286	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
287	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
288	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
289	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
290	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
291	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
292	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
293	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
294	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
295	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
296	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
297	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
298	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
299	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
300	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
301	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
302	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
303	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
304	#11719921	C₂³	1	1	yes	characteristic
305	#11719921	C₂³	1	1	yes	characteristic
306	#11719921	C₂³	1	1	yes	characteristic
307	#11719921	C₂³	1	1	yes	characteristic
308	#11719921	C₂³	1	1	yes	characteristic
309	#11719921	C₂³	1	1	yes	characteristic
310	#11719921	C₂³	1	1	yes	characteristic
311	#11719921	C₂³	1	1	yes	characteristic
312	#11719921	C₂³	1	1	yes	characteristic
313	#11719921	C₂³	1	1	yes	characteristic
314	#11719921	C₂³	1	1	yes	characteristic
315	#11719921	C₂³	1	1	yes	characteristic
316	#11719921	C₂³	1	1	yes	characteristic
317	#11719921	C₂³	1	1	yes	characteristic
318	#11719921	C₂³	1	1	yes	characteristic
319	#11719921	C₂³	1	1	yes	characteristic
320	#11719921	C₂³	1	1	yes	characteristic
321	#11719921	C₂³	1	1	yes	characteristic
322	#11719921	C₂³	1	1	yes	characteristic
323	#11719921	C₂³	1	1	yes	characteristic
324	#11719921	C₂³	1	1	yes	characteristic
325	#11719921	C₂³	1	1	yes	characteristic
326	#11719921	C₂³	1	1	yes	characteristic, complemented
327	#11719921	C₂³	1	1	yes	characteristic, complemented
328	#11719921	C₂³	1	1	yes	characteristic, complemented
329	#11719921	C₂³	1	1	yes	characteristic, complemented
330	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
331	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
332	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
333	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
334	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
335	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
336	#11719919	C₂³	1	1	yes	characteristic, complemented
337	#11719919	C₂³	1	1	yes	characteristic, complemented
338	#11719919	C₂³	1	1	yes	characteristic, complemented
339	#11719919	C₂³	1	1	yes	characteristic, complemented
340	#11719919	C₂³	1	1	yes	characteristic, complemented
341	#11719919	C₂³	1	1	yes	characteristic, complemented
342	#11719919	C₂³	1	1	yes	characteristic, complemented
343	#11719919	C₂³	1	1	yes	characteristic, complemented
344	#11719919	C₂³	1	1	yes	characteristic, complemented
345	#11719919	C₂³	1	1	yes	characteristic, complemented
346	#11719919	C₂³	1	1	yes	characteristic, complemented
347	#11719919	C₂³	1	1	yes	characteristic, complemented
348	#11719919	C₂³	1	1	yes	characteristic, complemented
349	#11719919	C₂³	1	1	yes	characteristic, complemented
350	C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
351	C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
352	C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
353	C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
354	C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
355	C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
356	C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
357	C₂³×C₅₃	—	2	2	no	—
358	C₂³×C₅₃	—	2	2	no	—
359	C₂³×C₅₃	—	2	2	no	—
360	C₂³×C₅₃	—	4	1	no	—
361	C₂³×C₅₃	—	4	1	no	—
362	C₂³×C₅₃	—	4	1	no	—
363	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂²×D₅₃	—	2	2	no	—
370	C₂²×D₅₃	—	2	2	no	—
371	C₂²×D₅₃	—	2	2	no	—
372	C₂²×D₅₃	—	2	2	no	—
373	C₂²×D₅₃	—	2	2	no	—
374	C₂²×D₅₃	—	2	2	no	—
375	C₂²×D₅₃	—	2	2	no	—
376	C₂²×D₅₃	—	2	2	no	—
377	C₂²×D₅₃	—	2	2	no	—
378	C₂²×D₅₃	—	2	2	no	—
379	C₂²×D₅₃	—	2	2	no	—
380	C₂²×D₅₃	—	4	1	no	—
381	C₂²×D₅₃	—	4	1	no	—
382	C₂²×D₅₃	—	4	1	no	—
383	C₂²×D₅₃	—	4	1	no	—
384	C₂²×D₅₃	—	4	1	no	—
385	C₂²×D₅₃	—	4	1	no	—
386	C₂²×D₅₃	—	4	1	no	—
387	C₂²×D₅₃	—	4	1	no	—
388	C₂²×D₅₃	—	4	1	no	—
389	C₂²×D₅₃	—	4	16	no	—
390	C₂²×D₅₃	#41	1	4	yes	complemented
391	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
396	Q₈×C₅₃	—	4	1	no	—
397	D₄×C₅₃	—	2	2	no	—
398	D₄×C₅₃	—	2	2	no	—
399	D₄×C₅₃	—	2	2	no	—
400	D₄×C₅₃	—	2	2	no	—
401	D₄×C₅₃	—	4	1	no	—
402	D₄×C₅₃	—	4	1	no	—
403	D₄×C₅₃	—	4	1	no	—
404	D₄×C₅₃	—	4	1	no	—
405	D₄×C₅₃	—	4	1	no	—
406	C₂×C₄×C₅₃	—	2	2	no	—
407	C₂×C₄×C₅₃	—	4	1	no	—
408	C₂×C₄×C₅₃	—	4	1	no	—
409	C₂×C₄×C₅₃	—	4	1	no	—
410	C₂×C₄×C₅₃	—	4	1	no	—
411	C₂×C₄×C₅₃	—	4	1	no	—
412	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²⋊D₅₃	—	2	2	no	—
422	C₂²⋊D₅₃	—	2	2	no	—
423	C₂²⋊D₅₃	—	2	2	no	—
424	C₂²⋊D₅₃	—	2	2	no	—
425	C₂²⋊D₅₃	—	2	2	no	—
426	C₂²⋊D₅₃	—	2	2	no	—
427	C₂²⋊D₅₃	—	2	2	no	—
428	C₂²⋊D₅₃	—	2	2	no	—
429	C₂²⋊D₅₃	—	2	2	no	—
430	C₂²⋊D₅₃	—	2	2	no	—
431	C₂²⋊D₅₃	—	4	1	no	—
432	C₂²⋊D₅₃	—	4	1	no	—
433	C₂²⋊D₅₃	—	4	1	no	—
434	C₂²⋊D₅₃	—	4	1	no	—
435	C₂²⋊D₅₃	—	4	1	no	—
436	C₂²⋊D₅₃	—	4	1	no	—
437	C₂×Dic₅₃	—	2	2	no	—
438	C₂×Dic₅₃	—	2	2	no	—
439	C₂×Dic₅₃	—	4	1	no	—
440	C₂×Dic₅₃	—	4	1	no	—
441	C₂×Dic₅₃	—	4	1	no	—
442	C₂×Dic₅₃	—	4	1	no	—
443	C₂×Dic₅₃	—	4	1	no	—
444	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
445	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
446	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
447	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
448	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
449	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
450	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
451	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
452	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
453	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
454	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
455	D₂₁₂	—	2	2	no	—
456	D₂₁₂	—	2	2	no	—
457	D₂₁₂	—	4	1	no	—
458	C₄×D₅₃	—	2	2	no	—
459	C₄×D₅₃	—	2	2	no	—
460	C₄×D₅₃	—	2	2	no	—
461	C₄×D₅₃	—	4	1	no	—
462	C₄×D₅₃	—	4	1	no	—
463	C₄×D₅₃	—	4	1	no	—
464	C₄×D₅₃	—	4	1	no	—
465	C₄×D₅₃	—	4	1	no	—
466	C₄×D₅₃	—	4	1	no	—
467	C₄×D₅₃	—	4	1	no	—
468	C₄×D₅₃	—	4	1	no	—
469	C₄×D₅₃	—	4	1	no	—
470	C₄×D₅₃	—	4	1	no	—
471	Dic₁₀₆	—	4	1	no	—
472	Dic₁₀₆	—	4	1	no	—
473	Dic₁₀₆	—	4	1	no	—
474	C₂²×C₅₃	—	2	1	no	—
475	C₂²×C₅₃	—	2	1	no	—
476	C₂²×C₅₃	—	2	1	no	—
477	C₂²×C₅₃	—	2	1	no	—
478	C₂²×C₅₃	—	2	1	no	—
479	C₂²×C₅₃	—	2	1	no	—
480	C₂²×C₅₃	—	2	1	no	—
481	C₂²×C₅₃	—	2	1	no	—
482	C₂²×C₅₃	—	2	1	no	—
483	C₂²×C₅₃	—	2	1	no	—
484	C₂²×C₅₃	—	2	1	no	—
485	C₂²×C₅₃	—	2	1	no	—
486	C₂²×C₅₃	—	2	1	no	—
487	C₂²×C₅₃	—	2	1	no	—
488	C₂²×C₅₃	—	2	1	no	—
489	C₂²×C₅₃	—	2	1	no	—
490	C₂²×C₅₃	—	4	4	no	—
491	C₂²×C₅₃	—	8	2	no	—
492	C₂²×C₅₃	C₂×#41	1	2	yes	—
493	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
494	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
495	C₂×D₅₃	—	2	8	no	—
496	C₂×D₅₃	—	2	1	no	—
497	C₂×D₅₃	—	2	1	no	—
498	C₂×D₅₃	—	2	1	no	—
499	C₂×D₅₃	—	2	1	no	—
500	C₂×D₅₃	—	2	1	no	—
501	C₂×D₅₃	—	2	1	no	—
502	C₂×D₅₃	—	2	1	no	—
503	C₂×D₅₃	—	2	1	no	—
504	C₂×D₅₃	—	2	1	no	—
505	C₂×D₅₃	—	2	1	no	—
506	C₂×D₅₃	—	2	1	no	—
507	C₂×D₅₃	—	2	1	no	—
508	C₂×D₅₃	—	4	4	no	—
509	C₂×D₅₃	—	4	4	no	—
510	C₂×D₅₃	—	4	4	no	—
511	C₂×D₅₃	—	4	4	no	—
512	C₂×D₅₃	—	4	4	no	—
513	C₂×D₅₃	—	8	2	no	—
514	C₂×D₅₃	C₂×#41	1	2	yes	—
515	C₂×D₅₃	C₂×#41	1	2	yes	—
516	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	—
517	C₄×C₅₃	—	2	1	no	—
518	C₄×C₅₃	—	2	1	no	—
519	C₄×C₅₃	—	2	1	no	—
520	C₄×C₅₃	—	2	1	no	—
521	C₄×C₅₃	—	2	1	no	—
522	C₄×C₅₃	—	2	1	no	—
523	C₄×C₅₃	—	2	1	no	—
524	C₄×C₅₃	—	2	1	no	—
525	C₄×C₅₃	—	2	1	no	—
526	Dic₅₃	—	2	1	no	—
527	Dic₅₃	—	2	1	no	—
528	Dic₅₃	—	2	1	no	—
529	Dic₅₃	—	2	1	no	—
530	Dic₅₃	—	2	1	no	—
531	Dic₅₃	—	2	1	no	—
532	Dic₅₃	—	2	1	no	—
533	Dic₅₃	—	2	1	no	—
534	Dic₅₃	—	2	1	no	—
535	Dic₅₃	—	2	1	no	—
536	Dic₅₃	—	2	1	no	—
537	#3490	—	53	1	no	maximal, Sylow
538	C₂×C₅₃	—	2	2	no	—
539	C₂×C₅₃	—	2	2	no	—
540	C₂×C₅₃	—	4	1	no	—
541	C₂×C₅₃	—	4	1	no	—
542	C₂×C₅₃	—	4	1	no	—
543	C₂×C₅₃	—	4	1	no	—
544	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
545	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
546	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
547	D₅₃	—	2	2	no	—
548	D₅₃	—	2	2	no	—
549	D₅₃	—	2	2	no	—
550	D₅₃	—	4	1	no	—
551	D₅₃	—	4	1	no	—
552	#551	—	53	1	no	—
553	#551	—	53	1	no	—
554	#551	—	53	1	no	—
555	#551	—	53	1	no	—
556	#551	—	53	1	no	—
557	#551	—	53	1	no	—
558	#551	—	53	1	no	—
559	#551	—	53	1	no	—
560	#546	—	53	1	no	—
561	#546	—	53	1	no	—
562	#546	—	53	1	no	—
563	#546	—	53	1	no	—
564	#546	—	53	1	no	—
565	#546	—	53	1	no	—
566	#546	—	53	1	no	—
567	#546	D₅₃	1	1	yes	characteristic, complemented
568	#543	—	53	1	no	—
569	#538	—	53	1	no	—
570	#538	—	53	1	no	—
571	#538	—	53	1	no	—
572	#538	—	53	1	no	—
573	#534	—	53	1	no	—
574	#525	—	53	1	no	—
575	#525	—	53	1	no	—
576	#525	—	53	1	no	—
577	#525	—	53	1	no	—
578	C₂×#120	—	53	1	no	—
579	C₂×#120	—	53	1	no	—
580	#518	—	53	1	no	—
581	#518	—	53	1	no	—
582	C₂²×C₂²⋊C₄	—	53	1	no	—
583	C₅₃	#3490	1	1	yes	characteristic, complemented, Sylow
584	C₂⁵	—	53	1	no	—
585	C₂×#41	—	53	1	no	—
586	C₂×#41	—	53	1	no	—
587	C₂×#41	—	53	1	no	—
588	C₂×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
589	C₂²×D₄	—	53	1	no	—
590	C₂²×D₄	—	53	1	no	—
591	C₂²×D₄	—	53	1	no	—
592	C₂²×D₄	—	53	1	no	—
593	C₂²×D₄	—	53	1	no	—
594	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
595	C₂³×C₄	—	53	1	no	—
596	C₂³×C₄	—	53	1	no	—
597	#126	—	53	1	no	—
598	#126	—	53	1	no	—
599	#126	—	53	1	no	—
600	#126	—	53	1	no	—
601	#126	—	53	1	no	—
602	#126	—	53	1	no	—
603	#126	—	53	1	no	—
604	#126	—	53	1	no	—
605	#124	—	53	1	no	—
606	#124	—	53	1	no	—
607	#124	—	53	1	no	—
608	#124	—	53	1	no	—
609	#124	—	53	1	no	—
610	#124	—	53	1	no	—
611	#124	—	53	1	no	—
612	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
613	#123	—	53	1	no	—
614	#123	—	53	1	no	—
615	#123	—	53	1	no	—
616	#123	—	53	1	no	—
617	#123	—	53	1	no	—
618	#123	—	53	1	no	—
619	#123	—	53	1	no	—
620	#123	—	53	1	no	—
621	#123	—	53	1	no	—
622	#123	—	53	1	no	—
623	#123	—	53	1	no	—
624	#123	—	53	1	no	—
625	#123	—	53	1	no	—
626	#123	—	53	1	no	—
627	#123	—	53	1	no	—
628	#123	—	53	1	no	—
629	#123	—	53	1	no	—
630	#123	—	53	1	no	—
631	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
632	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
633	C₂²⋊Q₈	—	53	1	no	—
634	C₂²⋊Q₈	—	53	1	no	—
635	C₂²⋊Q₈	—	53	1	no	—
636	C₂²⋊Q₈	—	53	1	no	—
637	C₂²⋊Q₈	—	53	1	no	—
638	C₂²⋊Q₈	—	53	1	no	—
639	C₂²⋊Q₈	—	53	1	no	—
640	C₂²⋊Q₈	—	53	1	no	—
641	C₂²⋊Q₈	—	53	1	no	—
642	C₂²⋊Q₈	—	53	1	no	—
643	C₂²⋊Q₈	—	53	1	no	—
644	C₂²⋊Q₈	—	53	1	no	—
645	C₂²⋊Q₈	—	53	1	no	—
646	C₂²⋊Q₈	—	53	1	no	—
647	C₂²⋊Q₈	—	53	1	no	—
648	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
649	#121	—	53	1	no	—
650	#121	—	53	1	no	—
651	#121	—	53	1	no	—
652	#121	—	53	1	no	—
653	#121	—	53	1	no	—
654	#121	—	53	1	no	—
655	#121	—	53	1	no	—
656	#121	—	53	1	no	—
657	#121	—	53	1	no	—
658	#121	—	53	1	no	—
659	#121	—	53	1	no	—
660	#121	—	53	1	no	—
661	#121	—	53	1	no	—
662	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
663	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
664	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
665	#120	—	53	1	no	—
666	#120	—	53	1	no	—
667	#120	—	53	1	no	—
668	#120	—	53	1	no	—
669	#120	—	53	1	no	—
670	#120	—	53	1	no	—
671	#120	—	53	1	no	—
672	#120	—	53	1	no	—
673	#120	—	53	1	no	—
674	#120	—	53	1	no	—
675	#120	—	53	1	no	—
676	#120	—	53	1	no	—
677	#120	—	53	1	no	—
678	#120	—	53	1	no	—
679	#120	—	53	1	no	—
680	#120	—	53	1	no	—
681	#120	—	53	1	no	—
682	#120	—	53	1	no	—
683	#120	C₂×D₅₃	1	1	yes	characteristic
684	#120	C₂×D₅₃	1	1	yes	characteristic, complemented
685	C₄×D₄	—	53	1	no	—
686	C₄×D₄	—	53	1	no	—
687	C₄×D₄	—	53	1	no	—
688	C₄×D₄	—	53	1	no	—
689	C₄×D₄	—	53	1	no	—
690	C₄×D₄	—	53	1	no	—
691	C₄×D₄	—	53	1	no	—
692	C₄×D₄	—	53	1	no	—
693	C₄×D₄	—	53	1	no	—
694	C₄×D₄	—	53	1	no	—
695	C₄×D₄	—	53	1	no	—
696	C₄×D₄	—	53	1	no	—
697	C₄×D₄	—	53	1	no	—
698	C₄×D₄	—	53	1	no	—
699	C₄×D₄	—	53	1	no	—
700	C₄×D₄	—	53	1	no	—
701	C₄×D₄	—	53	1	no	—
702	C₄×D₄	—	53	1	no	—
703	C₄×D₄	—	53	1	no	—
704	C₄×D₄	—	53	1	no	—
705	C₄×D₄	—	53	1	no	—
706	C₄×D₄	—	53	1	no	—
707	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
708	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
709	#117	—	53	1	no	—
710	#117	—	53	1	no	—
711	#117	—	53	1	no	—
712	#117	—	53	1	no	—
713	#117	—	53	1	no	—
714	#117	—	53	1	no	—
715	#117	—	53	1	no	—
716	#117	—	53	1	no	—
717	C₂×C₂²⋊C₄	—	53	1	no	—
718	C₂×C₂²⋊C₄	—	53	1	no	—
719	C₂×C₂²⋊C₄	—	53	1	no	—
720	C₂×C₂²⋊C₄	—	53	1	no	—
721	C₂×C₂²⋊C₄	—	53	1	no	—
722	C₂×C₂²⋊C₄	—	53	1	no	—
723	C₂×C₂²⋊C₄	—	53	1	no	—
724	C₂×C₂²⋊C₄	—	53	1	no	—
725	C₂×C₂²⋊C₄	—	53	1	no	—
726	C₂×C₂²⋊C₄	—	53	1	no	—
727	C₂×C₂²⋊C₄	—	53	1	no	—
728	C₂×C₂²⋊C₄	—	53	1	no	—
729	C₂×C₂²⋊C₄	—	53	1	no	—
730	C₂×C₂²⋊C₄	—	53	1	no	—
731	C₂×C₂²⋊C₄	—	53	1	no	—
732	C₂×C₂²⋊C₄	—	53	1	no	—
733	C₂×C₂²⋊C₄	—	53	1	no	—
734	C₂×C₂²⋊C₄	—	53	1	no	—
735	C₂×C₂²⋊C₄	—	53	1	no	—
736	C₂×C₂²⋊C₄	—	53	1	no	—
737	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
738	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
739	C₂⁴	—	53	1	no	—
740	C₂⁴	—	53	1	no	—
741	C₂⁴	—	53	1	no	—
742	C₂⁴	—	53	1	no	—
743	C₂⁴	—	53	1	no	—
744	C₂⁴	—	53	1	no	—
745	C₂⁴	—	53	1	no	—
746	C₂⁴	—	106	4	no	—
747	C₂⁴	—	212	2	no	—
748	C₂⁴	—	212	2	no	—
749	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
750	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
751	#41	—	4	2	no	—
752	#41	—	212	2	no	—
753	#41	—	212	2	no	—
754	#41	—	212	2	no	—
755	C₂×Q₈	—	53	1	no	—
756	C₂×Q₈	—	53	1	no	—
757	C₂×Q₈	—	53	1	no	—
758	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
759	C₂×D₄	—	4	2	no	—
760	C₂×D₄	—	53	1	no	—
761	C₂×D₄	—	53	1	no	—
762	C₂×D₄	—	53	1	no	—
763	C₂×D₄	—	53	1	no	—
764	C₂×D₄	—	53	1	no	—
765	C₂×D₄	—	53	1	no	—
766	C₂×D₄	—	53	1	no	—
767	C₂×D₄	—	53	1	no	—
768	C₂×D₄	—	53	1	no	—
769	C₂×D₄	—	53	1	no	—
770	C₂×D₄	—	53	1	no	—
771	C₂×D₄	—	53	1	no	—
772	C₂×D₄	—	53	1	no	—
773	C₂×D₄	—	53	1	no	—
774	C₂×D₄	—	53	1	no	—
775	C₂×D₄	—	53	1	no	—
776	C₂×D₄	—	53	1	no	—
777	C₂×D₄	—	53	1	no	—
778	C₂×D₄	—	53	1	no	—
779	C₂×D₄	—	106	4	no	—
780	C₂×D₄	—	106	4	no	—
781	C₂×D₄	—	212	2	no	—
782	C₂×D₄	—	212	2	no	—
783	C₂×D₄	—	212	2	no	—
784	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
785	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
786	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
787	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
788	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
789	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
790	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
791	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
792	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
793	C₂²×C₄	—	53	1	no	—
794	C₂²×C₄	—	53	1	no	—
795	C₂²×C₄	—	53	1	no	—
796	C₂²×C₄	—	53	1	no	—
797	C₂²×C₄	—	53	1	no	—
798	C₂²×C₄	—	53	1	no	—
799	C₂²×C₄	—	53	1	no	—
800	C₂²×C₄	—	53	1	no	—
801	C₂²×C₄	—	53	1	no	—
802	C₂²×C₄	—	53	1	no	—
803	C₂²×C₄	—	53	1	no	—
804	C₂²×C₄	—	53	1	no	—
805	C₂²×C₄	—	53	1	no	—
806	C₂²×C₄	—	53	1	no	—
807	C₂²×C₄	—	53	1	no	—
808	C₂²×C₄	—	53	1	no	—
809	C₂²×C₄	—	53	1	no	—
810	C₂²×C₄	—	53	1	no	—
811	C₂²×C₄	—	53	1	no	—
812	C₂²×C₄	—	53	1	no	—
813	C₂²×C₄	—	212	2	no	—
814	C₂²×C₄	—	212	2	no	—
815	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
816	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
817	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
818	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
819	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
820	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
821	C₄⋊C₄	—	53	1	no	—
822	C₄⋊C₄	—	53	1	no	—
823	C₄⋊C₄	—	53	1	no	—
824	C₄⋊C₄	—	53	1	no	—
825	C₄⋊C₄	—	53	1	no	—
826	C₄⋊C₄	—	53	1	no	—
827	C₄⋊C₄	—	53	1	no	—
828	C₄⋊C₄	—	53	1	no	—
829	C₄⋊C₄	—	53	1	no	—
830	C₄⋊C₄	—	53	1	no	—
831	C₄⋊C₄	—	53	1	no	—
832	C₄⋊C₄	—	53	1	no	—
833	C₄⋊C₄	—	53	1	no	—
834	C₄⋊C₄	—	53	1	no	—
835	C₄⋊C₄	—	53	1	no	—
836	C₄⋊C₄	—	53	1	no	—
837	C₄⋊C₄	—	53	1	no	—
838	C₄⋊C₄	—	53	1	no	—
839	C₄⋊C₄	—	53	1	no	—
840	C₄⋊C₄	—	53	1	no	—
841	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
842	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
843	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
844	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
845	C₂²⋊C₄	—	53	1	no	—
846	C₂²⋊C₄	—	53	1	no	—
847	C₂²⋊C₄	—	53	1	no	—
848	C₂²⋊C₄	—	53	1	no	—
849	C₂²⋊C₄	—	53	1	no	—
850	C₂²⋊C₄	—	53	1	no	—
851	C₂²⋊C₄	—	53	1	no	—
852	C₂²⋊C₄	—	53	1	no	—
853	C₂²⋊C₄	—	53	1	no	—
854	C₂²⋊C₄	—	53	1	no	—
855	C₂²⋊C₄	—	53	1	no	—
856	C₂²⋊C₄	—	53	1	no	—
857	C₂²⋊C₄	—	53	1	no	—
858	C₂²⋊C₄	—	53	1	no	—
859	C₂²⋊C₄	—	53	1	no	—
860	C₂²⋊C₄	—	53	1	no	—
861	C₂²⋊C₄	—	53	1	no	—
862	C₂²⋊C₄	—	53	1	no	—
863	C₂²⋊C₄	—	53	1	no	—
864	C₂²⋊C₄	—	53	1	no	—
865	C₂²⋊C₄	—	53	1	no	—
866	C₂²⋊C₄	—	53	1	no	—
867	C₂²⋊C₄	—	53	1	no	—
868	C₂²⋊C₄	—	53	1	no	—
869	C₂²⋊C₄	—	53	1	no	—
870	C₂²⋊C₄	—	53	1	no	—
871	C₂²⋊C₄	—	53	1	no	—
872	C₂²⋊C₄	—	53	1	no	—
873	C₂²⋊C₄	—	53	1	no	—
874	C₂²⋊C₄	—	53	1	no	—
875	C₂²⋊C₄	—	53	1	no	—
876	C₂²⋊C₄	—	53	1	no	—
877	C₂²⋊C₄	—	53	1	no	—
878	C₂²⋊C₄	—	53	1	no	—
879	C₂²⋊C₄	—	53	1	no	—
880	C₂²⋊C₄	—	53	1	no	—
881	C₂²⋊C₄	—	53	1	no	—
882	C₂²⋊C₄	—	53	1	no	—
883	C₂²⋊C₄	—	53	1	no	—
884	C₂²⋊C₄	—	53	1	no	—
885	C₂²⋊C₄	—	53	1	no	—
886	C₂²⋊C₄	—	53	1	no	—
887	C₂²⋊C₄	—	53	1	no	—
888	C₂²⋊C₄	—	53	1	no	—
889	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
890	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
891	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
892	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
893	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
894	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
895	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
896	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
897	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
898	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
899	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
900	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
901	C₄²	—	53	1	no	—
902	C₄²	—	53	1	no	—
903	C₄²	—	53	1	no	—
904	C₄²	—	53	1	no	—
905	C₄²	—	53	1	no	—
906	C₄²	—	53	1	no	—
907	C₄²	—	53	1	no	—
908	C₄²	C₂²×D₅₃	1	1	yes	characteristic, complemented
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	4	1	no	—
913	C₂³	—	4	1	no	—
914	C₂³	—	4	1	no	—
915	C₂³	—	53	1	no	—
916	C₂³	—	53	1	no	—
917	C₂³	—	53	1	no	—
918	C₂³	—	53	4	no	—
919	C₂³	—	53	1	no	—
920	C₂³	—	53	1	no	—
921	C₂³	—	106	2	no	—
922	C₂³	—	106	2	no	—
923	C₂³	—	106	2	no	—
924	C₂³	—	106	2	no	—
925	C₂³	—	106	2	no	—
926	C₂³	—	106	2	no	—
927	C₂³	—	106	2	no	—
928	C₂³	—	106	2	no	—
929	C₂³	—	106	2	no	—
930	C₂³	—	106	2	no	—
931	C₂³	—	106	2	no	—
932	C₂³	—	212	1	no	—
933	C₂³	—	212	1	no	—
934	C₂³	—	212	1	no	—
935	C₂³	—	212	1	no	—
936	C₂³	—	212	1	no	—
937	C₂³	—	212	1	no	—
938	C₂³	—	212	1	no	—
939	C₂³	—	212	1	no	—
940	C₂³	—	212	1	no	—
941	C₂³	—	212	16	no	—
942	C₂³	C₂³×D₅₃	1	1	yes	characteristic
943	C₂³	C₂³×D₅₃	1	1	yes	characteristic
944	C₂³	C₂³×D₅₃	1	1	yes	characteristic
945	C₂³	C₂³×D₅₃	1	1	yes	characteristic
946	C₂³	C₂³×D₅₃	1	1	yes	characteristic
947	C₂³	C₂³×D₅₃	1	1	yes	characteristic
948	Q₈	—	4	1	no	—
949	Q₈	—	212	1	no	—
950	Q₈	—	212	1	no	—
951	Q₈	—	212	1	no	—
952	D₄	—	2	2	no	—
953	D₄	—	2	2	no	—
954	D₄	—	2	2	no	—
955	D₄	—	2	2	no	—
956	D₄	—	4	1	no	—
957	D₄	—	4	1	no	—
958	D₄	—	4	1	no	—
959	D₄	—	4	1	no	—
960	D₄	—	4	1	no	—
961	D₄	—	106	2	no	—
962	D₄	—	106	2	no	—
963	D₄	—	106	2	no	—
964	D₄	—	106	2	no	—
965	D₄	—	106	2	no	—
966	D₄	—	106	2	no	—
967	D₄	—	106	2	no	—
968	D₄	—	106	2	no	—
969	D₄	—	106	2	no	—
970	D₄	—	106	2	no	—
971	D₄	—	106	2	no	—
972	D₄	—	106	2	no	—
973	D₄	—	212	1	no	—
974	D₄	—	212	1	no	—
975	D₄	—	212	1	no	—
976	D₄	—	212	1	no	—
977	D₄	—	212	1	no	—
978	D₄	—	212	1	no	—
979	D₄	—	212	1	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	4	1	no	—
982	C₂×C₄	—	4	1	no	—
983	C₂×C₄	—	4	1	no	—
984	C₂×C₄	—	4	1	no	—
985	C₂×C₄	—	4	1	no	—
986	C₂×C₄	—	53	1	no	—
987	C₂×C₄	—	53	1	no	—
988	C₂×C₄	—	53	1	no	—
989	C₂×C₄	—	53	1	no	—
990	C₂×C₄	—	53	1	no	—
991	C₂×C₄	—	53	1	no	—
992	C₂×C₄	—	53	1	no	—
993	C₂×C₄	—	53	1	no	—
994	C₂×C₄	—	53	1	no	—
995	C₂×C₄	—	53	1	no	—
996	C₂×C₄	—	53	1	no	—
997	C₂×C₄	—	106	2	no	—
998	C₂×C₄	—	106	2	no	—
999	C₂×C₄	—	106	2	no	—
1000	C₂×C₄	—	106	2	no	—
1001	C₂×C₄	—	106	2	no	—
1002	C₂×C₄	—	212	1	no	—
1003	C₂×C₄	—	212	1	no	—
1004	C₂×C₄	—	212	1	no	—
1005	C₂×C₄	—	212	1	no	—
1006	C₂×C₄	—	212	1	no	—
1007	C₂×C₄	—	212	1	no	—
1008	C₂×C₄	—	212	1	no	—
1009	C₂×C₄	—	212	1	no	—
1010	C₂×C₄	—	212	1	no	—
1011	C₂×C₄	—	212	1	no	—
1012	C₂×C₄	—	212	1	no	—
1013	C₂×C₄	—	212	1	no	—
1014	C₂×C₄	—	212	1	no	—
1015	C₂×C₄	—	212	1	no	—
1016	C₂×C₄	—	212	1	no	—
1017	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1018	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1019	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1020	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1021	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1022	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1023	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1024	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1025	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1026	C₂²	—	2	1	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	2	1	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	2	1	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	1	no	—
1033	C₂²	—	2	1	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	4	4	no	—
1043	C₂²	—	8	2	no	—
1044	C₂²	—	53	2	no	—
1045	C₂²	—	53	2	no	—
1046	C₂²	—	53	2	no	—
1047	C₂²	—	106	8	no	—
1048	C₂²	—	106	1	no	—
1049	C₂²	—	106	1	no	—
1050	C₂²	—	106	1	no	—
1051	C₂²	—	106	1	no	—
1052	C₂²	—	106	1	no	—
1053	C₂²	—	106	1	no	—
1054	C₂²	—	106	1	no	—
1055	C₂²	—	106	1	no	—
1056	C₂²	—	106	1	no	—
1057	C₂²	—	106	1	no	—
1058	C₂²	—	106	1	no	—
1059	C₂²	—	106	1	no	—
1060	C₂²	—	424	2	no	—
1061	C₂²	—	212	4	no	—
1062	C₂²	—	212	4	no	—
1063	C₂²	—	212	4	no	—
1064	C₂²	—	212	4	no	—
1065	C₂²	—	212	4	no	—
1066	C₂²	#41×D₅₃	1	2	yes	—
1067	C₂²	#13133262	1	2	yes	—
1068	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
1069	C₄	—	2	1	no	—
1070	C₄	—	2	1	no	—
1071	C₄	—	2	1	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	106	1	no	—
1079	C₄	—	106	1	no	—
1080	C₄	—	106	1	no	—
1081	C₄	—	106	1	no	—
1082	C₄	—	106	1	no	—
1083	C₄	—	106	1	no	—
1084	C₄	—	106	1	no	—
1085	C₄	—	106	1	no	—
1086	C₄	—	106	1	no	—
1087	C₄	—	106	1	no	—
1088	C₄	—	106	1	no	—
1089	C₂	—	2	2	no	—
1090	C₂	—	2	2	no	—
1091	C₂	—	4	1	no	—
1092	C₂	—	4	1	no	—
1093	C₂	—	4	1	no	—
1094	C₂	—	4	1	no	—
1095	C₂	—	106	2	no	—
1096	C₂	—	106	2	no	—
1097	C₂	—	106	2	no	—
1098	C₂	—	212	1	no	—
1099	C₂	—	212	1	no	—
1100	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
1101	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1102	C₂	C₂×#13133262	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#546	C₂
hypercenter	#546	D₅₃
hypocenter	C₅₃	#3490
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #16811304	C₂	semidirect
2. #16811303	C₂	semidirect
3. #16811302	C₂	semidirect
4. #16811302	C₂	semidirect
5. #16811301	C₂	semidirect
6. #16811300	C₂	semidirect
7. #16811299	C₂	semidirect
8. #16811296	C₂	semidirect
9. #16811270	C₂	semidirect
10. #16811267	C₂	semidirect
11. #16811263	C₂	semidirect
12. #16811262	C₂	semidirect
13. #16811262	C₂	semidirect
14. #16811261	C₂	semidirect
15. #16811260	C₂	semidirect
16. #16811248	C₂	semidirect
17. #16811209	C₂	semidirect
18. #16811207	C₂	semidirect
19. #16811205	C₂	semidirect
20. #16811205	C₂	semidirect
21. #16811183	C₂	semidirect
22. #16811133	C₂	semidirect
23. #16811132	C₂	semidirect
24. #16811131	C₂	semidirect
25. #16811130	C₂	semidirect
26. C₂×#13133185	C₂	semidirect
27. #120×D₅₃	C₂	semidirect
28. #16811096	C₂	semidirect
29. #16811095	C₂	semidirect
30. C₂×C₂²⋊C₄×D₅₃	C₂	semidirect
31. C₅₃×#546	C₂	semidirect
33. C₂×#11719945	C₂²	semidirect
34. C₂×#11719947	C₂²	semidirect
35. C₂×#11719947	C₂²	semidirect
37. C₂²×C₂²⋊D₅₃	C₂²	semidirect
39. C₂×D₄×D₅₃	C₂²	semidirect
40. C₂×D₄×D₅₃	C₂²	semidirect
41. C₂²×C₄×D₅₃	C₂²	semidirect
42. C₂²×C₄×D₅₃	C₂²	semidirect
43. #13133212	C₂²	semidirect
44. #13133212	C₂²	semidirect
45. #13133212	C₂²	semidirect
46. #13133211	C₂²	semidirect
47. #13133210	C₂²	semidirect
48. #13133210	C₂²	semidirect
49. #13133210	C₂²	semidirect
50. #13133210	C₂²	semidirect
51. #13133206	C₂²	semidirect
52. #13133204	C₂²	semidirect
53. #13133204	C₂²	semidirect
54. #13133203	C₂²	semidirect
55. #13133203	C₂²	semidirect
56. #13133203	C₂²	semidirect
57. #13133203	C₂²	semidirect
58. #13133202	C₂²	semidirect
59. #13133202	C₂²	semidirect
60. #13133201	C₂²	semidirect
61. #13133201	C₂²	semidirect
62. #13133200	C₂²	semidirect
63. #13133200	C₂²	semidirect
64. #13133200	C₂²	semidirect
65. #13133199	C₂²	semidirect
66. #13133199	C₂²	semidirect
67. #13133199	C₂²	semidirect
68. #13133199	C₂²	semidirect
69. #13133199	C₂²	semidirect
70. #13133199	C₂²	semidirect
71. #13133198	C₂²	semidirect
72. #13133198	C₂²	semidirect
73. #13133198	C₂²	semidirect
74. #13133198	C₂²	semidirect
75. #13133198	C₂²	semidirect
76. #13133197	C₂²	semidirect
77. #13133197	C₂²	semidirect
78. #13133196	C₂²	semidirect
79. #13133196	C₂²	semidirect
80. #13133195	C₂²	semidirect
81. #13133195	C₂²	semidirect
82. #13133195	C₂²	semidirect
83. #13133195	C₂²	semidirect
84. #13133195	C₂²	semidirect
85. #13133194	C₂²	semidirect
86. #13133194	C₂²	semidirect
87. #13133194	C₂²	semidirect
88. #13133193	C₂²	semidirect
89. #13133193	C₂²	semidirect
90. #13133193	C₂²	semidirect
91. #13133191	C₂²	semidirect
92. #13133190	C₂²	semidirect
93. #13133190	C₂²	semidirect
94. #13133190	C₂²	semidirect
95. #13133190	C₂²	semidirect
96. #13133189	C₂²	semidirect
97. #13133189	C₂²	semidirect
98. #13133189	C₂²	semidirect
99. #13133189	C₂²	semidirect
100. #13133188	C₂²	semidirect
101. #13133188	C₂²	semidirect
102. #13133188	C₂²	semidirect
103. #13133188	C₂²	semidirect
105. #13133187	C₂²	semidirect
106. #13133187	C₂²	semidirect
108. #13133186	C₂²	semidirect
114. #13133185	C₂²	semidirect
115. #13133185	C₂²	semidirect
116. #13133185	C₂²	semidirect
117. #13133185	C₂²	semidirect
118. #13133185	C₂²	semidirect
119. #13133185	C₂²	semidirect
120. #13133185	C₂²	semidirect
121. #13133185	C₂²	semidirect
122. C₄×D₂₁₂	C₂²	semidirect
123. D₄×Dic₅₃	C₂²	semidirect
124. D₄×Dic₅₃	C₂²	semidirect
125. D₄×Dic₅₃	C₂²	semidirect
126. #13133179	C₂²	semidirect
127. #13133179	C₂²	semidirect
128. C₄×C₂²⋊D₅₃	C₂²	semidirect
129. C₄×C₂²⋊D₅₃	C₂²	semidirect
130. C₄×C₂²⋊D₅₃	C₂²	semidirect
131. C₄×C₂²⋊D₅₃	C₂²	semidirect
132. C₄×C₂²⋊D₅₃	C₂²	semidirect
133. C₄×C₂²⋊D₅₃	C₂²	semidirect
134. C₄×C₂²⋊D₅₃	C₂²	semidirect
135. C₄×C₂²⋊D₅₃	C₂²	semidirect
136. C₄×C₂²⋊D₅₃	C₂²	semidirect
137. #13133177	C₂²	semidirect
138. #13133177	C₂²	semidirect
139. #13133177	C₂²	semidirect
140. #13133177	C₂²	semidirect
141. #13133177	C₂²	semidirect
142. #13133177	C₂²	semidirect
143. #13133177	C₂²	semidirect
144. #13133176	C₂²	semidirect
145. #13133175	C₂²	semidirect
146. #13133175	C₂²	semidirect
147. #13133174	C₂²	semidirect
148. #13133174	C₂²	semidirect
149. #13133173	C₂²	semidirect
150. #13133173	C₂²	semidirect
151. #13133173	C₂²	semidirect
152. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
153. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
154. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
156. C₂×#11719921	C₂²	semidirect
157. C₂×#11719921	C₂²	semidirect
158. C₂×#11719921	C₂²	semidirect
159. C₂×#11719921	C₂²	semidirect
163. C₂²⋊C₄×D₅₃	C₂²	semidirect
164. C₂²⋊C₄×D₅₃	C₂²	semidirect
165. C₂²⋊C₄×D₅₃	C₂²	semidirect
166. C₂²⋊C₄×D₅₃	C₂²	semidirect
167. C₂²⋊C₄×D₅₃	C₂²	semidirect
168. C₂²⋊C₄×D₅₃	C₂²	semidirect
169. C₂²⋊C₄×D₅₃	C₂²	semidirect
170. C₂²⋊C₄×D₅₃	C₂²	semidirect
171. C₂²⋊C₄×D₅₃	C₂²	semidirect
172. C₂×#41×C₅₃	C₂²	semidirect
173. C₂²×D₄×C₅₃	C₂²	semidirect
174. #124×C₅₃	C₂²	semidirect
175. #123×C₅₃	C₂²	semidirect
176. #123×C₅₃	C₂²	semidirect
177. C₂²⋊Q₈×C₅₃	C₂²	semidirect
178. #121×C₅₃	C₂²	semidirect
179. #121×C₅₃	C₂²	semidirect
180. #121×C₅₃	C₂²	semidirect
182. #120×C₅₃	C₂²	semidirect
183. C₄×D₄×C₅₃	C₂²	semidirect
184. C₄×D₄×C₅₃	C₂²	semidirect
185. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
186. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
200. C₂×Q₈×C₅₃	C₂³	semidirect
209. C₂×D₄×C₅₃	C₂³	semidirect
210. C₂×D₄×C₅₃	C₂³	semidirect
214. C₂²×C₄×C₅₃	C₂³	semidirect
215. C₂²×C₄×C₅₃	C₂³	semidirect
216. C₂²×C₄×C₅₃	C₂³	semidirect
233. C₂×C₂²⋊D₅₃	C₂³	semidirect
234. C₂×C₂²⋊D₅₃	C₂³	semidirect
239. C₂²×Dic₅₃	C₂³	semidirect
240. C₂²×Dic₅₃	C₂³	semidirect
241. C₂²×Dic₅₃	C₂³	semidirect
264. C₂×C₄×D₅₃	C₂³	semidirect
265. C₂×C₄×D₅₃	C₂³	semidirect
266. C₂×Dic₁₀₆	C₂³	semidirect
267. C₂×Dic₁₀₆	C₂³	semidirect
268. C₂×Dic₁₀₆	C₂³	semidirect
269. C₄⋊C₄×C₅₃	C₂³	semidirect
270. C₄⋊C₄×C₅₃	C₂³	semidirect
271. C₄⋊C₄×C₅₃	C₂³	semidirect
272. C₄⋊C₄×C₅₃	C₂³	semidirect
280. C₂²⋊C₄×C₅₃	C₂³	semidirect
281. C₂²⋊C₄×C₅₃	C₂³	semidirect
282. C₂²⋊C₄×C₅₃	C₂³	semidirect
283. C₂²⋊C₄×C₅₃	C₂³	semidirect
284. C₂²⋊C₄×C₅₃	C₂³	semidirect
285. C₄²×C₅₃	C₂³	semidirect
297. C₂²⋊Dic₅₃	C₂³	semidirect
298. C₂²⋊Dic₅₃	C₂³	semidirect
299. C₂²⋊Dic₅₃	C₂³	semidirect
300. C₂²⋊Dic₅₃	C₂³	semidirect
301. C₂²⋊Dic₅₃	C₂³	semidirect
302. C₂²⋊Dic₅₃	C₂³	semidirect
303. C₂²⋊Dic₅₃	C₂³	semidirect
326. #11719921	C₂³	semidirect
327. #11719921	C₂³	semidirect
328. #11719921	C₂³	semidirect
329. #11719921	C₂³	semidirect
330. C₄⋊Dic₅₃	C₂³	semidirect
331. C₄⋊Dic₅₃	C₂³	semidirect
332. C₄⋊Dic₅₃	C₂³	semidirect
333. C₄⋊Dic₅₃	C₂³	semidirect
334. C₄⋊Dic₅₃	C₂³	semidirect
335. C₄⋊Dic₅₃	C₂³	semidirect
336. #11719919	C₂³	semidirect
337. #11719919	C₂³	semidirect
338. #11719919	C₂³	semidirect
339. #11719919	C₂³	semidirect
340. #11719919	C₂³	semidirect
341. #11719919	C₂³	semidirect
342. #11719919	C₂³	semidirect
343. #11719919	C₂³	semidirect
344. #11719919	C₂³	semidirect
345. #11719919	C₂³	semidirect
346. #11719919	C₂³	semidirect
347. #11719919	C₂³	semidirect
348. #11719919	C₂³	semidirect
349. #11719919	C₂³	semidirect
350. C₄×Dic₅₃	C₂³	semidirect
351. C₄×Dic₅₃	C₂³	semidirect
352. C₄×Dic₅₃	C₂³	semidirect
353. C₄×Dic₅₃	C₂³	semidirect
354. C₄×Dic₅₃	C₂³	semidirect
355. C₄×Dic₅₃	C₂³	semidirect
356. C₄×Dic₅₃	C₂³	semidirect
390. C₂²×D₅₃	#41	semidirect
567. #546	D₅₃	semidirect
583. C₅₃	#3490	semidirect
588. C₂×#41	C₂×D₅₃	semidirect
594. C₂²×D₄	C₂×D₅₃	semidirect
612. #124	C₂×D₅₃	semidirect
631. #123	C₂×D₅₃	semidirect
632. #123	C₂×D₅₃	semidirect
648. C₂²⋊Q₈	C₂×D₅₃	semidirect
662. #121	C₂×D₅₃	semidirect
663. #121	C₂×D₅₃	semidirect
664. #121	C₂×D₅₃	semidirect
684. #120	C₂×D₅₃	semidirect
707. C₄×D₄	C₂×D₅₃	semidirect
708. C₄×D₄	C₂×D₅₃	semidirect
737. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect
738. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect
758. C₂×Q₈	C₂²×D₅₃	semidirect
791. C₂×D₄	C₂²×D₅₃	semidirect
792. C₂×D₄	C₂²×D₅₃	semidirect
818. C₂²×C₄	C₂²×D₅₃	semidirect
819. C₂²×C₄	C₂²×D₅₃	semidirect
820. C₂²×C₄	C₂²×D₅₃	semidirect
841. C₄⋊C₄	C₂²×D₅₃	semidirect
842. C₄⋊C₄	C₂²×D₅₃	semidirect
843. C₄⋊C₄	C₂²×D₅₃	semidirect
844. C₄⋊C₄	C₂²×D₅₃	semidirect
896. C₂²⋊C₄	C₂²×D₅₃	semidirect
897. C₂²⋊C₄	C₂²×D₅₃	semidirect
898. C₂²⋊C₄	C₂²×D₅₃	semidirect
899. C₂²⋊C₄	C₂²×D₅₃	semidirect
900. C₂²⋊C₄	C₂²×D₅₃	semidirect
908. C₄²	C₂²×D₅₃	semidirect