Subgroups — #20288908

Order 6784.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811370	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811369	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811364	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811363	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811324	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811317	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811297	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811269	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811266	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811265	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811264	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811263	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811263	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811255	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811228	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811224	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811222	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811215	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811214	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811212	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811209	C₂	1	1	yes	maximal, characteristic, complemented
23	#16811207	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811203	C₂	1	1	yes	maximal, characteristic, complemented
25	#16811185	C₂	1	1	yes	maximal, characteristic, complemented
26	#16811184	C₂	1	1	yes	maximal, characteristic, complemented
27	#16811183	C₂	1	1	yes	maximal, characteristic, complemented
28	#16811135	C₂	1	1	yes	maximal, characteristic, complemented
29	#123×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#13133190	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#11719949	C₂²	1	1	yes	characteristic, complemented
33	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
34	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
35	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
36	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
41	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
44	#13133214	C₂²	1	1	yes	characteristic, complemented
45	#13133213	C₂²	1	1	yes	characteristic, complemented
46	#13133212	C₂²	1	1	yes	characteristic, complemented
47	#13133212	C₂²	1	1	yes	characteristic, complemented
48	#13133212	C₂²	1	1	yes	characteristic, complemented
49	#13133211	C₂²	1	1	yes	characteristic, complemented
50	#13133211	C₂²	1	1	yes	characteristic, complemented
51	#13133210	C₂²	1	1	yes	characteristic, complemented
52	#13133209	C₂²	1	1	yes	characteristic, complemented
53	#13133208	C₂²	1	1	yes	characteristic, complemented
54	#13133208	C₂²	1	1	yes	characteristic, complemented
55	#13133207	C₂²	1	1	yes	characteristic, complemented
56	#13133206	C₂²	1	1	yes	characteristic, complemented
57	#13133205	C₂²	1	1	yes	characteristic, complemented
58	#13133203	C₂²	1	1	yes	characteristic, complemented
59	#13133203	C₂²	1	1	yes	characteristic, complemented
60	#13133203	C₂²	1	1	yes	characteristic, complemented
61	#13133202	C₂²	1	1	yes	characteristic, complemented
62	#13133202	C₂²	1	1	yes	characteristic, complemented
63	#13133202	C₂²	1	1	yes	characteristic, complemented
64	#13133202	C₂²	1	1	yes	characteristic, complemented
65	#13133202	C₂²	1	1	yes	characteristic, complemented
66	#13133202	C₂²	1	1	yes	characteristic, complemented
67	#13133202	C₂²	1	1	yes	characteristic, complemented
68	#13133202	C₂²	1	1	yes	characteristic, complemented
69	#13133202	C₂²	1	1	yes	characteristic, complemented
70	#13133201	C₂²	1	1	yes	characteristic, complemented
71	#13133201	C₂²	1	1	yes	characteristic, complemented
72	#13133201	C₂²	1	1	yes	characteristic, complemented
73	#13133201	C₂²	1	1	yes	characteristic, complemented
74	#13133201	C₂²	1	1	yes	characteristic, complemented
75	#13133200	C₂²	1	1	yes	characteristic, complemented
76	#13133200	C₂²	1	1	yes	characteristic, complemented
77	#13133200	C₂²	1	1	yes	characteristic, complemented
78	#13133199	C₂²	1	1	yes	characteristic, complemented
79	#13133199	C₂²	1	1	yes	characteristic, complemented
80	#13133199	C₂²	1	1	yes	characteristic, complemented
81	#13133199	C₂²	1	1	yes	characteristic, complemented
82	#13133199	C₂²	1	1	yes	characteristic, complemented
83	#13133199	C₂²	1	1	yes	characteristic, complemented
84	#13133199	C₂²	1	1	yes	characteristic, complemented
85	#13133198	C₂²	1	1	yes	characteristic, complemented
86	#13133197	C₂²	1	1	yes	characteristic, complemented
87	#13133197	C₂²	1	1	yes	characteristic, complemented
88	#13133196	C₂²	1	1	yes	characteristic, complemented
89	#13133195	C₂²	1	1	yes	characteristic, complemented
90	#13133195	C₂²	1	1	yes	characteristic, complemented
91	#13133195	C₂²	1	1	yes	characteristic, complemented
92	#13133194	C₂²	1	1	yes	characteristic, complemented
93	#13133194	C₂²	1	1	yes	characteristic, complemented
94	#13133193	C₂²	1	1	yes	characteristic, complemented
95	#13133193	C₂²	1	1	yes	characteristic, complemented
96	#13133192	C₂²	1	1	yes	characteristic, complemented
97	#13133192	C₂²	1	1	yes	characteristic, complemented
98	#13133192	C₂²	1	1	yes	characteristic, complemented
99	#13133192	C₂²	1	1	yes	characteristic, complemented
100	#13133192	C₂²	1	1	yes	characteristic, complemented
101	#13133192	C₂²	1	1	yes	characteristic, complemented
102	#13133192	C₂²	1	1	yes	characteristic, complemented
103	#13133192	C₂²	1	1	yes	characteristic, complemented
104	#13133191	C₂²	1	1	yes	characteristic
105	#13133191	C₂²	1	1	yes	characteristic, complemented
106	#13133191	C₂²	1	1	yes	characteristic, complemented
107	#13133191	C₂²	1	1	yes	characteristic, complemented
108	#13133191	C₂²	1	1	yes	characteristic, complemented
109	#13133191	C₂²	1	1	yes	characteristic, complemented
110	#13133191	C₂²	1	1	yes	characteristic, complemented
111	#13133190	C₂²	1	1	yes	characteristic
112	#13133190	C₂²	1	1	yes	characteristic, complemented
113	#13133190	C₂²	1	1	yes	characteristic, complemented
114	#13133190	C₂²	1	1	yes	characteristic, complemented
115	#13133190	C₂²	1	1	yes	characteristic, complemented
116	#13133190	C₂²	1	1	yes	characteristic, complemented
117	#13133190	C₂²	1	1	yes	characteristic, complemented
118	#13133190	C₂²	1	1	yes	characteristic, complemented
119	#13133190	C₂²	1	1	yes	characteristic, complemented
120	#13133190	C₂²	1	1	yes	characteristic, complemented
121	#13133190	C₂²	1	1	yes	characteristic, complemented
122	#13133190	C₂²	1	1	yes	characteristic, complemented
123	#13133190	C₂²	1	1	yes	characteristic, complemented
124	#13133190	C₂²	1	1	yes	characteristic, complemented
125	#13133190	C₂²	1	1	yes	characteristic, complemented
126	#13133190	C₂²	1	1	yes	characteristic, complemented
127	#13133190	C₂²	1	1	yes	characteristic, complemented
128	#13133189	C₂²	1	1	yes	characteristic
129	#13133189	C₂²	1	1	yes	characteristic, complemented
130	#13133188	C₂²	1	1	yes	characteristic, complemented
131	#13133188	C₂²	1	1	yes	characteristic, complemented
132	#13133187	C₂²	1	1	yes	characteristic
133	#13133187	C₂²	1	1	yes	characteristic, complemented
134	#13133187	C₂²	1	1	yes	characteristic, complemented
135	#13133187	C₂²	1	1	yes	characteristic, complemented
136	#13133187	C₂²	1	1	yes	characteristic, complemented
137	#13133187	C₂²	1	1	yes	characteristic, complemented
138	#13133187	C₂²	1	1	yes	characteristic, complemented
139	#13133187	C₂²	1	1	yes	characteristic, complemented
140	#13133187	C₂²	1	1	yes	characteristic, complemented
141	#13133187	C₂²	1	1	yes	characteristic, complemented
142	#13133187	C₂²	1	1	yes	characteristic, complemented
143	#13133186	C₂²	1	1	yes	characteristic, complemented
144	#13133185	C₂²	1	1	yes	characteristic, complemented
145	#13133185	C₂²	1	1	yes	characteristic, complemented
146	#13133185	C₂²	1	1	yes	characteristic, complemented
147	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
148	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
149	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
150	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
151	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
152	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
153	#13133179	C₂²	1	1	yes	characteristic, complemented
154	#13133179	C₂²	1	1	yes	characteristic, complemented
155	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
156	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
157	#13133177	C₂²	1	1	yes	characteristic, complemented
158	#13133177	C₂²	1	1	yes	characteristic, complemented
159	#13133177	C₂²	1	1	yes	characteristic, complemented
160	#13133177	C₂²	1	1	yes	characteristic, complemented
161	#13133174	C₂²	1	1	yes	characteristic, complemented
162	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
163	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
164	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
165	C₂×#11719921	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	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
173	#126×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	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	#120×C₅₃	C₂²	1	1	yes	characteristic
181	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	#117×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	C₂³×D₅₃	C₂³	1	1	yes	characteristic
189	C₂³×D₅₃	C₂³	1	1	yes	characteristic
190	C₂³×D₅₃	C₂³	1	1	yes	characteristic
191	C₂³×D₅₃	C₂³	1	1	yes	characteristic
192	C₂³×D₅₃	C₂³	1	1	yes	characteristic
193	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₅₃	—	4	2	no	—
203	C₂×C₂²⋊D₅₃	—	4	2	no	—
204	C₂×C₂²⋊D₅₃	—	4	2	no	—
205	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
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	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
224	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
225	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
226	#11719949	—	4	2	no	—
227	D₄×D₅₃	—	4	2	no	—
228	D₄×D₅₃	—	4	2	no	—
229	D₄×D₅₃	—	4	2	no	—
230	#11719945	—	4	2	no	—
231	#11719945	—	4	2	no	—
232	C₂×D₂₁₂	—	4	2	no	—
233	C₂×D₂₁₂	—	4	2	no	—
234	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
235	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
236	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
237	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
238	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
239	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
240	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
241	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
242	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
243	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
244	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
245	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
246	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
247	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
248	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
249	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₅₃	—	4	2	no	—
251	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
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
265	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
266	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
267	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
268	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₄⋊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
281	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₄²×C₅₃	C₂³	1	1	yes	characteristic
291	C₄²×C₅₃	C₂³	1	1	yes	characteristic
292	C₄²×C₅₃	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
298	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
299	#11719921	C₂³	1	1	yes	characteristic
300	#11719921	C₂³	1	1	yes	characteristic
301	#11719921	C₂³	1	1	yes	characteristic
302	#11719921	C₂³	1	1	yes	characteristic
303	#11719921	C₂³	1	1	yes	characteristic
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
327	#11719921	C₂³	1	1	yes	characteristic
328	#11719921	C₂³	1	1	yes	characteristic
329	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
330	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
331	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
332	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
333	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
334	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
335	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
336	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
337	#11719919	C₂³	1	1	yes	characteristic
338	#11719919	C₂³	1	1	yes	characteristic
339	#11719919	C₂³	1	1	yes	characteristic
340	#11719919	C₂³	1	1	yes	characteristic
341	#11719919	C₂³	1	1	yes	characteristic
342	#11719919	C₂³	1	1	yes	characteristic
343	#11719919	C₂³	1	1	yes	characteristic
344	#11719919	C₂³	1	1	yes	characteristic
345	#11719919	C₂³	1	1	yes	characteristic
346	#11719919	C₂³	1	1	yes	characteristic
347	#11719919	C₂³	1	1	yes	characteristic
348	#11719919	C₂³	1	1	yes	characteristic
349	#11719919	C₂³	1	1	yes	characteristic
350	#11719919	C₂³	1	1	yes	characteristic
351	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
352	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
353	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
354	C₂³×C₅₃	—	2	2	no	—
355	C₂³×C₅₃	—	4	1	no	—
356	C₂³×C₅₃	—	4	1	no	—
357	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂²×D₅₃	—	2	2	no	—
362	C₂²×D₅₃	—	2	2	no	—
363	C₂²×D₅₃	—	2	2	no	—
364	C₂²×D₅₃	—	2	2	no	—
365	C₂²×D₅₃	—	4	1	no	—
366	C₂²×D₅₃	—	4	1	no	—
367	C₂²×D₅₃	—	4	1	no	—
368	C₂²×D₅₃	—	4	1	no	—
369	C₂²×D₅₃	—	4	1	no	—
370	C₂²×D₅₃	—	4	1	no	—
371	C₂²×D₅₃	—	4	1	no	—
372	C₂²×D₅₃	—	4	1	no	—
373	C₂²×D₅₃	—	4	1	no	—
374	C₂²×D₅₃	—	4	1	no	—
375	C₂²×D₅₃	—	4	1	no	—
376	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
377	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
378	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
383	Q₈×C₅₃	—	4	1	no	—
384	D₄×C₅₃	—	2	2	no	—
385	D₄×C₅₃	—	4	1	no	—
386	D₄×C₅₃	—	4	1	no	—
387	C₂×C₄×C₅₃	—	2	2	no	—
388	C₂×C₄×C₅₃	—	4	1	no	—
389	C₂×C₄×C₅₃	—	4	1	no	—
390	C₂×C₄×C₅₃	—	4	1	no	—
391	C₂×C₄×C₅₃	—	4	1	no	—
392	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²⋊D₅₃	—	2	2	no	—
404	C₂²⋊D₅₃	—	2	2	no	—
405	C₂²⋊D₅₃	—	2	2	no	—
406	C₂²⋊D₅₃	—	2	2	no	—
407	C₂²⋊D₅₃	—	2	2	no	—
408	C₂²⋊D₅₃	—	4	1	no	—
409	C₂²⋊D₅₃	—	4	1	no	—
410	C₂²⋊D₅₃	—	4	1	no	—
411	C₂²⋊D₅₃	—	4	1	no	—
412	C₂²⋊D₅₃	—	4	1	no	—
413	C₂²⋊D₅₃	—	4	1	no	—
414	C₂²⋊D₅₃	—	4	1	no	—
415	C₂²⋊D₅₃	—	4	1	no	—
416	C₂²⋊D₅₃	—	4	1	no	—
417	C₂²⋊D₅₃	—	4	1	no	—
418	C₂²⋊D₅₃	—	4	1	no	—
419	C₂²⋊D₅₃	—	4	1	no	—
420	C₂²⋊D₅₃	—	4	1	no	—
421	C₂×Dic₅₃	—	2	2	no	—
422	C₂×Dic₅₃	—	4	1	no	—
423	C₂×Dic₅₃	—	4	1	no	—
424	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
425	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
426	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
427	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
428	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
429	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
430	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
431	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
432	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
433	D₂₁₂	—	2	2	no	—
434	D₂₁₂	—	2	2	no	—
435	D₂₁₂	—	2	2	no	—
436	D₂₁₂	—	2	2	no	—
437	D₂₁₂	—	4	1	no	—
438	D₂₁₂	—	4	1	no	—
439	D₂₁₂	—	4	1	no	—
440	D₂₁₂	—	4	1	no	—
441	D₂₁₂	—	4	1	no	—
442	D₂₁₂	—	4	1	no	—
443	D₂₁₂	—	4	1	no	—
444	D₂₁₂	—	4	1	no	—
445	D₂₁₂	—	4	1	no	—
446	D₂₁₂	—	4	1	no	—
447	D₂₁₂	—	4	1	no	—
448	D₂₁₂	—	4	1	no	—
449	C₄×D₅₃	—	2	2	no	—
450	C₄×D₅₃	—	4	1	no	—
451	C₄×D₅₃	—	4	1	no	—
452	C₄×D₅₃	—	4	1	no	—
453	C₄×D₅₃	—	4	1	no	—
454	C₄×D₅₃	—	4	1	no	—
455	C₄×D₅₃	—	4	1	no	—
456	C₄×D₅₃	—	4	1	no	—
457	C₄×D₅₃	—	4	1	no	—
458	C₄×D₅₃	—	4	1	no	—
459	C₄×D₅₃	—	4	1	no	—
460	C₄×D₅₃	—	4	1	no	—
461	C₄×D₅₃	—	4	1	no	—
462	C₄×D₅₃	—	4	1	no	—
463	C₄×D₅₃	—	4	1	no	—
464	Dic₁₀₆	—	4	1	no	—
465	Dic₁₀₆	—	4	1	no	—
466	C₂²×C₅₃	—	2	1	no	—
467	C₂²×C₅₃	—	2	1	no	—
468	C₂²×C₅₃	—	2	1	no	—
469	C₂²×C₅₃	—	2	1	no	—
470	C₂²×C₅₃	—	2	1	no	—
471	C₂²×C₅₃	—	2	1	no	—
472	C₂²×C₅₃	—	2	1	no	—
473	C₂²×C₅₃	—	2	1	no	—
474	C₂²×C₅₃	—	2	1	no	—
475	C₂²×C₅₃	—	2	1	no	—
476	C₂²×C₅₃	—	2	1	no	—
477	C₂²×C₅₃	—	8	2	no	—
478	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
479	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
480	C₂×D₅₃	—	2	1	no	—
481	C₂×D₅₃	—	2	1	no	—
482	C₂×D₅₃	—	2	1	no	—
483	C₂×D₅₃	—	2	1	no	—
484	C₂×D₅₃	—	2	1	no	—
485	C₂×D₅₃	—	2	1	no	—
486	C₂×D₅₃	—	2	1	no	—
487	C₂×D₅₃	—	2	1	no	—
488	C₂×D₅₃	—	2	1	no	—
489	C₂×D₅₃	—	2	1	no	—
490	C₂×D₅₃	—	2	1	no	—
491	C₂×D₅₃	—	2	1	no	—
492	C₂×D₅₃	—	2	1	no	—
493	C₂×D₅₃	—	2	1	no	—
494	C₂×D₅₃	—	2	1	no	—
495	C₂×D₅₃	—	2	1	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	—	4	4	no	—
501	C₂×D₅₃	—	8	2	no	—
502	C₂×D₅₃	—	8	2	no	—
503	C₂×D₅₃	—	8	2	no	—
504	C₂×D₅₃	—	8	2	no	—
505	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	—
506	C₄×C₅₃	—	2	1	no	—
507	C₄×C₅₃	—	2	1	no	—
508	C₄×C₅₃	—	2	1	no	—
509	C₄×C₅₃	—	2	1	no	—
510	C₄×C₅₃	—	2	1	no	—
511	C₄×C₅₃	—	2	1	no	—
512	C₄×C₅₃	—	2	1	no	—
513	C₄×C₅₃	—	2	1	no	—
514	C₄×C₅₃	—	2	1	no	—
515	C₄×C₅₃	—	2	1	no	—
516	C₄×C₅₃	—	2	1	no	—
517	Dic₅₃	—	2	1	no	—
518	Dic₅₃	—	2	1	no	—
519	Dic₅₃	—	2	1	no	—
520	Dic₅₃	—	2	1	no	—
521	Dic₅₃	—	2	1	no	—
522	Dic₅₃	—	2	1	no	—
523	Dic₅₃	—	2	1	no	—
524	Dic₅₃	—	2	1	no	—
525	Dic₅₃	—	2	1	no	—
526	#3534	—	53	1	no	maximal, Sylow
527	C₂×C₅₃	—	2	2	no	—
528	C₂×C₅₃	—	4	1	no	—
529	C₂×C₅₃	—	4	1	no	—
530	C₂×C₅₃	—	4	1	no	—
531	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
533	C₂×C₅₃	#585	1	1	yes	characteristic
534	D₅₃	—	2	2	no	—
535	D₅₃	—	4	1	no	—
536	D₅₃	—	4	1	no	—
537	D₅₃	—	4	1	no	—
538	D₅₃	—	4	1	no	—
539	D₅₃	—	4	1	no	—
540	D₅₃	—	4	1	no	—
541	#562	—	53	1	no	—
542	#562	—	53	1	no	—
543	#560	—	53	1	no	—
544	#560	—	53	1	no	—
545	#553	—	53	1	no	—
546	#553	—	53	1	no	—
547	#551	—	53	1	no	—
548	#551	D₅₃	1	1	yes	characteristic, complemented
549	#546	—	53	1	no	—
550	#546	—	53	1	no	—
551	#546	—	53	1	no	—
552	#546	—	53	1	no	—
553	#546	—	53	1	no	—
554	#546	—	53	1	no	—
555	D₄²	—	53	1	no	—
556	D₄²	—	53	1	no	—
557	#540	—	53	1	no	—
558	#540	—	53	1	no	—
559	#539	—	53	1	no	—
560	#539	—	53	1	no	—
561	#539	—	53	1	no	—
562	#538	—	53	1	no	—
563	#538	—	53	1	no	—
564	#538	—	53	1	no	—
565	#537	—	53	1	no	—
566	#534	—	53	1	no	—
567	#534	—	53	1	no	—
568	#534	—	53	1	no	—
569	#525	—	53	1	no	—
570	C₂×#123	—	53	1	no	—
571	C₂×#121	—	53	1	no	—
572	C₅₃	#3534	1	1	yes	characteristic, complemented, Sylow
573	C₂×#41	—	53	1	no	—
574	C₂×#41	—	53	1	no	—
575	C₂×#41	—	53	1	no	—
576	C₂²×D₄	—	53	1	no	—
577	C₂²×D₄	—	53	1	no	—
578	C₂²×D₄	—	53	1	no	—
579	C₂²×D₄	—	53	1	no	—
580	C₂²×D₄	—	53	1	no	—
581	C₂²×D₄	—	53	1	no	—
582	C₂²×D₄	—	53	1	no	—
583	C₂²×D₄	—	53	1	no	—
584	C₂³×C₄	—	53	1	no	—
585	#127	—	53	1	no	—
586	#127	—	53	1	no	—
587	#126	—	53	1	no	—
588	#126	—	53	1	no	—
589	#126	—	53	1	no	—
590	#126	—	53	1	no	—
591	#126	—	53	1	no	—
592	#126	—	53	1	no	—
593	#126	C₂×D₅₃	1	1	yes	characteristic, complemented
594	#126	C₂×D₅₃	1	1	yes	characteristic, complemented
595	#125	—	53	1	no	—
596	#125	—	53	1	no	—
597	#125	—	53	1	no	—
598	#125	—	53	1	no	—
599	#124	—	53	1	no	—
600	#124	—	53	1	no	—
601	#124	—	53	1	no	—
602	#124	—	53	1	no	—
603	#124	—	53	1	no	—
604	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
605	#123	—	53	1	no	—
606	#123	—	53	1	no	—
607	#123	—	53	1	no	—
608	#123	—	53	1	no	—
609	#123	—	53	1	no	—
610	#123	—	53	1	no	—
611	#123	—	53	1	no	—
612	#123	—	53	1	no	—
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	C₂×D₅₃	1	1	yes	characteristic, complemented
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	C₂×D₅₃	1	1	yes	characteristic, complemented
644	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
645	#121	—	53	1	no	—
646	#121	—	53	1	no	—
647	#121	—	53	1	no	—
648	#121	—	53	1	no	—
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	—	53	1	no	—
663	#121	—	53	1	no	—
664	#121	—	53	1	no	—
665	#121	—	53	1	no	—
666	#121	—	53	1	no	—
667	#121	—	53	1	no	—
668	#121	—	53	1	no	—
669	#121	—	53	1	no	—
670	#121	—	53	1	no	—
671	#121	—	53	1	no	—
672	#121	—	53	1	no	—
673	#121	—	53	1	no	—
674	#121	—	53	1	no	—
675	#121	—	53	1	no	—
676	#121	—	53	1	no	—
677	#121	—	53	1	no	—
678	#121	—	53	1	no	—
679	#121	—	53	1	no	—
680	#121	—	53	1	no	—
681	#120	—	53	1	no	—
682	#120	—	53	1	no	—
683	#120	—	53	1	no	—
684	#120	—	53	1	no	—
685	#120	—	53	1	no	—
686	#120	—	53	1	no	—
687	#120	—	53	1	no	—
688	#120	—	53	1	no	—
689	#120	—	53	1	no	—
690	#120	—	53	1	no	—
691	#120	—	53	1	no	—
692	#120	—	53	1	no	—
693	#120	—	53	1	no	—
694	#120	—	53	1	no	—
695	#120	—	53	1	no	—
696	#120	C₂×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
708	C₄×D₄	—	53	1	no	—
709	C₄×D₄	—	53	1	no	—
710	C₄×D₄	—	53	1	no	—
711	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
712	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
713	#117	—	53	1	no	—
714	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
715	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
716	C₂×C₄⋊C₄	—	53	1	no	—
717	C₂×C₄⋊C₄	—	53	1	no	—
718	C₂×C₄⋊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	C₂×D₅₃	1	1	yes	characteristic, complemented
727	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
728	C₂⁴	—	53	1	no	—
729	C₂⁴	—	53	1	no	—
730	C₂⁴	—	53	1	no	—
731	C₂⁴	—	53	1	no	—
732	C₂⁴	—	53	1	no	—
733	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
734	#41	—	212	2	no	—
735	#41	—	212	2	no	—
736	#41	—	212	2	no	—
737	C₂×Q₈	—	53	1	no	—
738	C₂×Q₈	—	53	1	no	—
739	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
740	C₂×D₄	—	53	1	no	—
741	C₂×D₄	—	53	1	no	—
742	C₂×D₄	—	53	1	no	—
743	C₂×D₄	—	53	1	no	—
744	C₂×D₄	—	53	1	no	—
745	C₂×D₄	—	53	1	no	—
746	C₂×D₄	—	53	1	no	—
747	C₂×D₄	—	53	1	no	—
748	C₂×D₄	—	53	1	no	—
749	C₂×D₄	—	53	1	no	—
750	C₂×D₄	—	53	1	no	—
751	C₂×D₄	—	53	1	no	—
752	C₂×D₄	—	53	1	no	—
753	C₂×D₄	—	53	1	no	—
754	C₂×D₄	—	53	1	no	—
755	C₂×D₄	—	53	1	no	—
756	C₂×D₄	—	53	1	no	—
757	C₂×D₄	—	53	1	no	—
758	C₂×D₄	—	53	1	no	—
759	C₂×D₄	—	53	1	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	—	212	2	no	—
775	C₂×D₄	—	212	2	no	—
776	C₂×D₄	—	212	2	no	—
777	C₂×D₄	—	212	2	no	—
778	C₂×D₄	—	212	2	no	—
779	C₂×D₄	—	212	2	no	—
780	C₂×D₄	—	212	2	no	—
781	C₂×D₄	—	212	2	no	—
782	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
783	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
784	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
785	C₂²×C₄	—	53	1	no	—
786	C₂²×C₄	—	53	1	no	—
787	C₂²×C₄	—	53	1	no	—
788	C₂²×C₄	—	53	1	no	—
789	C₂²×C₄	—	53	1	no	—
790	C₂²×C₄	—	53	1	no	—
791	C₂²×C₄	—	53	1	no	—
792	C₂²×C₄	—	53	1	no	—
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	—	212	2	no	—
804	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
805	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
806	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
807	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
808	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
809	C₄⋊C₄	—	53	1	no	—
810	C₄⋊C₄	—	53	1	no	—
811	C₄⋊C₄	—	53	1	no	—
812	C₄⋊C₄	—	53	1	no	—
813	C₄⋊C₄	—	53	1	no	—
814	C₄⋊C₄	—	53	1	no	—
815	C₄⋊C₄	—	53	1	no	—
816	C₄⋊C₄	—	53	1	no	—
817	C₄⋊C₄	—	53	1	no	—
818	C₄⋊C₄	—	53	1	no	—
819	C₄⋊C₄	—	53	1	no	—
820	C₄⋊C₄	—	53	1	no	—
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	C₂²×D₅₃	1	1	yes	characteristic
832	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
833	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
834	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
835	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
836	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
837	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
838	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
839	C₂²⋊C₄	—	53	1	no	—
840	C₂²⋊C₄	—	53	1	no	—
841	C₂²⋊C₄	—	53	1	no	—
842	C₂²⋊C₄	—	53	1	no	—
843	C₂²⋊C₄	—	53	1	no	—
844	C₂²⋊C₄	—	53	1	no	—
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	C₂²×D₅₃	1	1	yes	characteristic
876	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
877	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
878	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
879	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
880	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
881	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
882	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
883	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
884	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
885	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
886	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
887	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
888	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
889	C₄²	—	53	1	no	—
890	C₄²	—	53	1	no	—
891	C₄²	—	53	1	no	—
892	C₄²	C₂²×D₅₃	1	1	yes	characteristic
893	C₄²	C₂²×D₅₃	1	1	yes	characteristic
894	C₄²	C₂²×D₅₃	1	1	yes	characteristic
895	C₂³	—	2	2	no	—
896	C₂³	—	4	1	no	—
897	C₂³	—	4	1	no	—
898	C₂³	—	53	1	no	—
899	C₂³	—	53	1	no	—
900	C₂³	—	53	1	no	—
901	C₂³	—	53	1	no	—
902	C₂³	—	53	1	no	—
903	C₂³	—	53	1	no	—
904	C₂³	—	53	1	no	—
905	C₂³	—	106	2	no	—
906	C₂³	—	106	2	no	—
907	C₂³	—	106	2	no	—
908	C₂³	—	106	2	no	—
909	C₂³	—	212	1	no	—
910	C₂³	—	212	1	no	—
911	C₂³	—	212	1	no	—
912	C₂³	—	212	1	no	—
913	C₂³	—	212	1	no	—
914	C₂³	—	212	1	no	—
915	C₂³	—	212	1	no	—
916	C₂³	—	212	1	no	—
917	C₂³	—	212	1	no	—
918	C₂³	—	212	1	no	—
919	C₂³	—	212	1	no	—
920	C₂³	C₂³×D₅₃	1	1	yes	characteristic
921	C₂³	C₂³×D₅₃	1	1	yes	characteristic
922	C₂³	C₂³×D₅₃	1	1	yes	characteristic
923	C₂³	C₂³×D₅₃	1	1	yes	characteristic
924	Q₈	—	4	1	no	—
925	Q₈	—	212	1	no	—
926	Q₈	—	212	1	no	—
927	D₄	—	2	2	no	—
928	D₄	—	4	1	no	—
929	D₄	—	4	1	no	—
930	D₄	—	106	2	no	—
931	D₄	—	106	2	no	—
932	D₄	—	106	2	no	—
933	D₄	—	106	2	no	—
934	D₄	—	106	2	no	—
935	D₄	—	106	2	no	—
936	D₄	—	106	2	no	—
937	D₄	—	106	2	no	—
938	D₄	—	106	2	no	—
939	D₄	—	212	1	no	—
940	D₄	—	212	1	no	—
941	D₄	—	212	1	no	—
942	D₄	—	212	1	no	—
943	D₄	—	212	1	no	—
944	D₄	—	212	1	no	—
945	D₄	—	212	1	no	—
946	D₄	—	212	1	no	—
947	D₄	—	212	1	no	—
948	D₄	—	212	1	no	—
949	D₄	—	212	1	no	—
950	D₄	—	212	1	no	—
951	D₄	—	212	1	no	—
952	D₄	—	212	1	no	—
953	D₄	—	212	1	no	—
954	D₄	—	212	1	no	—
955	D₄	—	212	1	no	—
956	D₄	—	212	1	no	—
957	D₄	—	212	1	no	—
958	D₄	—	212	1	no	—
959	D₄	—	212	1	no	—
960	D₄	—	212	1	no	—
961	D₄	—	212	1	no	—
962	D₄	—	212	1	no	—
963	D₄	—	212	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	53	1	no	—
970	C₂×C₄	—	53	1	no	—
971	C₂×C₄	—	53	1	no	—
972	C₂×C₄	—	53	1	no	—
973	C₂×C₄	—	53	1	no	—
974	C₂×C₄	—	53	1	no	—
975	C₂×C₄	—	53	1	no	—
976	C₂×C₄	—	53	1	no	—
977	C₂×C₄	—	53	1	no	—
978	C₂×C₄	—	106	2	no	—
979	C₂×C₄	—	106	2	no	—
980	C₂×C₄	—	212	1	no	—
981	C₂×C₄	—	212	1	no	—
982	C₂×C₄	—	212	1	no	—
983	C₂×C₄	—	212	1	no	—
984	C₂×C₄	—	212	1	no	—
985	C₂×C₄	—	212	1	no	—
986	C₂×C₄	—	212	1	no	—
987	C₂×C₄	—	212	1	no	—
988	C₂×C₄	—	212	1	no	—
989	C₂×C₄	—	212	1	no	—
990	C₂×C₄	—	212	1	no	—
991	C₂×C₄	—	212	1	no	—
992	C₂×C₄	—	212	1	no	—
993	C₂×C₄	—	212	1	no	—
994	C₂×C₄	—	212	1	no	—
995	C₂×C₄	—	212	1	no	—
996	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
997	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
998	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
999	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1000	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1001	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1002	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1003	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1004	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1005	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1006	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	1	no	—
1016	C₂²	—	2	1	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	8	2	no	—
1019	C₂²	—	53	2	no	—
1020	C₂²	—	106	1	no	—
1021	C₂²	—	106	1	no	—
1022	C₂²	—	106	1	no	—
1023	C₂²	—	106	1	no	—
1024	C₂²	—	106	1	no	—
1025	C₂²	—	106	1	no	—
1026	C₂²	—	106	1	no	—
1027	C₂²	—	106	1	no	—
1028	C₂²	—	106	1	no	—
1029	C₂²	—	106	1	no	—
1030	C₂²	—	106	1	no	—
1031	C₂²	—	106	1	no	—
1032	C₂²	—	106	1	no	—
1033	C₂²	—	106	1	no	—
1034	C₂²	—	106	1	no	—
1035	C₂²	—	106	1	no	—
1036	C₂²	—	106	1	no	—
1037	C₂²	—	106	1	no	—
1038	C₂²	—	106	1	no	—
1039	C₂²	—	106	1	no	—
1040	C₂²	—	424	2	no	—
1041	C₂²	—	424	2	no	—
1042	C₂²	—	424	2	no	—
1043	C₂²	—	424	2	no	—
1044	C₂²	—	212	4	no	—
1045	C₂²	#13133263	1	2	yes	—
1046	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	106	1	no	—
1059	C₄	—	106	1	no	—
1060	C₄	—	106	1	no	—
1061	C₄	—	106	1	no	—
1062	C₄	—	106	1	no	—
1063	C₄	—	106	1	no	—
1064	C₄	—	106	1	no	—
1065	C₄	—	106	1	no	—
1066	C₄	—	106	1	no	—
1067	C₂	—	2	2	no	—
1068	C₂	—	4	1	no	—
1069	C₂	—	4	1	no	—
1070	C₂	—	4	1	no	—
1071	C₂	—	106	2	no	—
1072	C₂	—	212	1	no	—
1073	C₂	—	212	1	no	—
1074	C₂	—	212	1	no	—
1075	C₂	—	212	1	no	—
1076	C₂	—	212	1	no	—
1077	C₂	—	212	1	no	—
1078	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1079	C₂	C₂×#13133263	1	1	yes	characteristic
1080	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#551	C₂
hypercenter	#551	D₅₃
hypocenter	C₅₃	#3534
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #16811370	C₂	semidirect
2. #16811369	C₂	semidirect
3. #16811364	C₂	semidirect
4. #16811363	C₂	semidirect
5. #16811324	C₂	semidirect
6. #16811317	C₂	semidirect
7. #16811297	C₂	semidirect
8. #16811269	C₂	semidirect
9. #16811266	C₂	semidirect
10. #16811265	C₂	semidirect
11. #16811264	C₂	semidirect
12. #16811263	C₂	semidirect
13. #16811263	C₂	semidirect
14. D₄×D₂₁₂	C₂	semidirect
15. #16811255	C₂	semidirect
16. #16811228	C₂	semidirect
17. #16811224	C₂	semidirect
18. #16811222	C₂	semidirect
19. #16811215	C₂	semidirect
20. #16811214	C₂	semidirect
21. #16811212	C₂	semidirect
22. #16811209	C₂	semidirect
23. #16811207	C₂	semidirect
24. #16811203	C₂	semidirect
25. #16811185	C₂	semidirect
26. #16811184	C₂	semidirect
27. #16811183	C₂	semidirect
28. #16811135	C₂	semidirect
29. #123×D₅₃	C₂	semidirect
30. C₂×#13133190	C₂	semidirect
31. C₅₃×#551	C₂	semidirect
32. C₂×#11719949	C₂²	semidirect
33. C₂×#11719945	C₂²	semidirect
34. C₂×#11719945	C₂²	semidirect
35. C₂²×D₂₁₂	C₂²	semidirect
36. C₂²×D₂₁₂	C₂²	semidirect
37. C₂²×C₂²⋊D₅₃	C₂²	semidirect
38. C₂²×C₂²⋊D₅₃	C₂²	semidirect
39. C₂²×C₂²⋊D₅₃	C₂²	semidirect
41. C₂×D₄×D₅₃	C₂²	semidirect
42. C₂×D₄×D₅₃	C₂²	semidirect
43. C₂²×C₄×D₅₃	C₂²	semidirect
44. #13133214	C₂²	semidirect
45. #13133213	C₂²	semidirect
46. #13133212	C₂²	semidirect
47. #13133212	C₂²	semidirect
48. #13133212	C₂²	semidirect
49. #13133211	C₂²	semidirect
50. #13133211	C₂²	semidirect
51. #13133210	C₂²	semidirect
52. #13133209	C₂²	semidirect
53. #13133208	C₂²	semidirect
54. #13133208	C₂²	semidirect
55. #13133207	C₂²	semidirect
56. #13133206	C₂²	semidirect
57. #13133205	C₂²	semidirect
58. #13133203	C₂²	semidirect
59. #13133203	C₂²	semidirect
60. #13133203	C₂²	semidirect
61. #13133202	C₂²	semidirect
62. #13133202	C₂²	semidirect
63. #13133202	C₂²	semidirect
64. #13133202	C₂²	semidirect
65. #13133202	C₂²	semidirect
66. #13133202	C₂²	semidirect
67. #13133202	C₂²	semidirect
68. #13133202	C₂²	semidirect
69. #13133202	C₂²	semidirect
70. #13133201	C₂²	semidirect
71. #13133201	C₂²	semidirect
72. #13133201	C₂²	semidirect
73. #13133201	C₂²	semidirect
74. #13133201	C₂²	semidirect
75. #13133200	C₂²	semidirect
76. #13133200	C₂²	semidirect
77. #13133200	C₂²	semidirect
78. #13133199	C₂²	semidirect
79. #13133199	C₂²	semidirect
80. #13133199	C₂²	semidirect
81. #13133199	C₂²	semidirect
82. #13133199	C₂²	semidirect
83. #13133199	C₂²	semidirect
84. #13133199	C₂²	semidirect
85. #13133198	C₂²	semidirect
86. #13133197	C₂²	semidirect
87. #13133197	C₂²	semidirect
88. #13133196	C₂²	semidirect
89. #13133195	C₂²	semidirect
90. #13133195	C₂²	semidirect
91. #13133195	C₂²	semidirect
92. #13133194	C₂²	semidirect
93. #13133194	C₂²	semidirect
94. #13133193	C₂²	semidirect
95. #13133193	C₂²	semidirect
96. #13133192	C₂²	semidirect
97. #13133192	C₂²	semidirect
98. #13133192	C₂²	semidirect
99. #13133192	C₂²	semidirect
100. #13133192	C₂²	semidirect
101. #13133192	C₂²	semidirect
102. #13133192	C₂²	semidirect
103. #13133192	C₂²	semidirect
105. #13133191	C₂²	semidirect
106. #13133191	C₂²	semidirect
107. #13133191	C₂²	semidirect
108. #13133191	C₂²	semidirect
109. #13133191	C₂²	semidirect
110. #13133191	C₂²	semidirect
112. #13133190	C₂²	semidirect
113. #13133190	C₂²	semidirect
114. #13133190	C₂²	semidirect
115. #13133190	C₂²	semidirect
116. #13133190	C₂²	semidirect
117. #13133190	C₂²	semidirect
118. #13133190	C₂²	semidirect
119. #13133190	C₂²	semidirect
120. #13133190	C₂²	semidirect
121. #13133190	C₂²	semidirect
122. #13133190	C₂²	semidirect
123. #13133190	C₂²	semidirect
124. #13133190	C₂²	semidirect
125. #13133190	C₂²	semidirect
126. #13133190	C₂²	semidirect
127. #13133190	C₂²	semidirect
129. #13133189	C₂²	semidirect
130. #13133188	C₂²	semidirect
131. #13133188	C₂²	semidirect
133. #13133187	C₂²	semidirect
134. #13133187	C₂²	semidirect
135. #13133187	C₂²	semidirect
136. #13133187	C₂²	semidirect
137. #13133187	C₂²	semidirect
138. #13133187	C₂²	semidirect
139. #13133187	C₂²	semidirect
140. #13133187	C₂²	semidirect
141. #13133187	C₂²	semidirect
142. #13133187	C₂²	semidirect
143. #13133186	C₂²	semidirect
144. #13133185	C₂²	semidirect
145. #13133185	C₂²	semidirect
146. #13133185	C₂²	semidirect
147. C₄×D₂₁₂	C₂²	semidirect
148. C₄×D₂₁₂	C₂²	semidirect
149. C₄×D₂₁₂	C₂²	semidirect
150. C₄×D₂₁₂	C₂²	semidirect
151. C₄×D₂₁₂	C₂²	semidirect
152. C₄×D₂₁₂	C₂²	semidirect
153. #13133179	C₂²	semidirect
154. #13133179	C₂²	semidirect
155. C₄×C₂²⋊D₅₃	C₂²	semidirect
156. C₄×C₂²⋊D₅₃	C₂²	semidirect
157. #13133177	C₂²	semidirect
158. #13133177	C₂²	semidirect
159. #13133177	C₂²	semidirect
160. #13133177	C₂²	semidirect
161. #13133174	C₂²	semidirect
162. C₂×#11719919	C₂²	semidirect
163. C₄⋊C₄×D₅₃	C₂²	semidirect
164. C₄⋊C₄×D₅₃	C₂²	semidirect
165. C₂×#11719921	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. #126×C₅₃	C₂²	semidirect
173. #126×C₅₃	C₂²	semidirect
174. #124×C₅₃	C₂²	semidirect
175. #123×C₅₃	C₂²	semidirect
176. #123×C₅₃	C₂²	semidirect
177. #123×C₅₃	C₂²	semidirect
178. C₂²⋊Q₈×C₅₃	C₂²	semidirect
179. C₂²⋊Q₈×C₅₃	C₂²	semidirect
181. C₄×D₄×C₅₃	C₂²	semidirect
182. C₄×D₄×C₅₃	C₂²	semidirect
183. #117×C₅₃	C₂²	semidirect
184. #117×C₅₃	C₂²	semidirect
185. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
186. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
548. #551	D₅₃	semidirect
572. C₅₃	#3534	semidirect
593. #126	C₂×D₅₃	semidirect
594. #126	C₂×D₅₃	semidirect
604. #124	C₂×D₅₃	semidirect
630. #123	C₂×D₅₃	semidirect
631. #123	C₂×D₅₃	semidirect
632. #123	C₂×D₅₃	semidirect
643. C₂²⋊Q₈	C₂×D₅₃	semidirect
644. C₂²⋊Q₈	C₂×D₅₃	semidirect
711. C₄×D₄	C₂×D₅₃	semidirect
712. C₄×D₄	C₂×D₅₃	semidirect
714. #117	C₂×D₅₃	semidirect
715. #117	C₂×D₅₃	semidirect
726. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect
727. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect