Subgroups — #20288668

Order 6784.

1142 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811357	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811340	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811337	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811335	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811304	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811300	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811298	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811296	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811286	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811281	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811279	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	#16811260	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811260	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811255	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811239	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811237	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811209	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811206	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811205	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811168	C₂	1	1	yes	maximal, characteristic, complemented
23	#16811156	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811153	C₂	1	1	yes	maximal, characteristic, complemented
25	#16811150	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#13133203	C₂	1	1	yes	maximal, characteristic, complemented
27	#124×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	C₄×#11719947	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#11719947	C₂²	1	1	yes	characteristic
33	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
34	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
35	C₂²×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
36	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
39	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
40	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
41	#13133216	C₂²	1	1	yes	characteristic, complemented
42	#13133216	C₂²	1	1	yes	characteristic, complemented
43	#13133215	C₂²	1	1	yes	characteristic, complemented
44	#13133213	C₂²	1	1	yes	characteristic
45	#13133212	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	#13133210	C₂²	1	1	yes	characteristic, complemented
51	#13133210	C₂²	1	1	yes	characteristic, complemented
52	#13133210	C₂²	1	1	yes	characteristic, complemented
53	#13133207	C₂²	1	1	yes	characteristic, complemented
54	#13133206	C₂²	1	1	yes	characteristic, complemented
55	#13133205	C₂²	1	1	yes	characteristic, complemented
56	#13133204	C₂²	1	1	yes	characteristic, complemented
57	#13133204	C₂²	1	1	yes	characteristic, complemented
58	#13133203	C₂²	1	1	yes	characteristic
59	#13133203	C₂²	1	1	yes	characteristic
60	#13133203	C₂²	1	1	yes	characteristic
61	#13133203	C₂²	1	1	yes	characteristic, complemented
62	#13133203	C₂²	1	1	yes	characteristic, complemented
63	#13133203	C₂²	1	1	yes	characteristic, complemented
64	#13133203	C₂²	1	1	yes	characteristic, complemented
65	#13133203	C₂²	1	1	yes	characteristic, complemented
66	#13133203	C₂²	1	1	yes	characteristic, complemented
67	#13133203	C₂²	1	1	yes	characteristic, complemented
68	#13133203	C₂²	1	1	yes	characteristic, complemented
69	#13133203	C₂²	1	1	yes	characteristic, complemented
70	#13133203	C₂²	1	1	yes	characteristic, complemented
71	#13133203	C₂²	1	1	yes	characteristic, complemented
72	#13133203	C₂²	1	1	yes	characteristic, complemented
73	#13133202	C₂²	1	1	yes	characteristic, complemented
74	#13133202	C₂²	1	1	yes	characteristic, complemented
75	#13133202	C₂²	1	1	yes	characteristic, complemented
76	#13133202	C₂²	1	1	yes	characteristic, complemented
77	#13133201	C₂²	1	1	yes	characteristic, complemented
78	#13133201	C₂²	1	1	yes	characteristic, complemented
79	#13133200	C₂²	1	1	yes	characteristic, complemented
80	#13133199	C₂²	1	1	yes	characteristic, complemented
81	#13133199	C₂²	1	1	yes	characteristic, complemented
82	#13133198	C₂²	1	1	yes	characteristic, complemented
83	#13133198	C₂²	1	1	yes	characteristic, complemented
84	#13133198	C₂²	1	1	yes	characteristic, complemented
85	#13133197	C₂²	1	1	yes	characteristic, complemented
86	#13133197	C₂²	1	1	yes	characteristic, complemented
87	#13133195	C₂²	1	1	yes	characteristic, complemented
88	#13133195	C₂²	1	1	yes	characteristic, complemented
89	#13133195	C₂²	1	1	yes	characteristic, complemented
90	#13133194	C₂²	1	1	yes	characteristic, complemented
91	#13133194	C₂²	1	1	yes	characteristic, complemented
92	#13133194	C₂²	1	1	yes	characteristic, complemented
93	#13133194	C₂²	1	1	yes	characteristic, complemented
94	#13133194	C₂²	1	1	yes	characteristic, complemented
95	#13133194	C₂²	1	1	yes	characteristic, complemented
96	#13133193	C₂²	1	1	yes	characteristic, complemented
97	#13133191	C₂²	1	1	yes	characteristic, complemented
98	#13133190	C₂²	1	1	yes	characteristic
99	#13133190	C₂²	1	1	yes	characteristic
100	#13133190	C₂²	1	1	yes	characteristic, complemented
101	#13133190	C₂²	1	1	yes	characteristic, complemented
102	#13133189	C₂²	1	1	yes	characteristic
103	#13133189	C₂²	1	1	yes	characteristic
104	#13133189	C₂²	1	1	yes	characteristic
105	#13133189	C₂²	1	1	yes	characteristic, complemented
106	#13133189	C₂²	1	1	yes	characteristic, complemented
107	#13133189	C₂²	1	1	yes	characteristic, complemented
108	#13133189	C₂²	1	1	yes	characteristic, complemented
109	#13133188	C₂²	1	1	yes	characteristic, complemented
110	#13133188	C₂²	1	1	yes	characteristic, complemented
111	#13133187	C₂²	1	1	yes	characteristic
112	#13133187	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	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
119	#13133182	C₂²	1	1	yes	characteristic, complemented
120	#13133182	C₂²	1	1	yes	characteristic, complemented
121	#13133182	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	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
127	#13133179	C₂²	1	1	yes	characteristic, complemented
128	#13133179	C₂²	1	1	yes	characteristic, complemented
129	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
130	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
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	#13133177	C₂²	1	1	yes	characteristic
137	#13133177	C₂²	1	1	yes	characteristic
138	#13133177	C₂²	1	1	yes	characteristic
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	#13133177	C₂²	1	1	yes	characteristic, complemented
145	#13133177	C₂²	1	1	yes	characteristic, complemented
146	#13133177	C₂²	1	1	yes	characteristic, complemented
147	#13133176	C₂²	1	1	yes	characteristic, complemented
148	#13133175	C₂²	1	1	yes	characteristic, complemented
149	#13133175	C₂²	1	1	yes	characteristic, complemented
150	#13133175	C₂²	1	1	yes	characteristic, complemented
151	#13133174	C₂²	1	1	yes	characteristic, complemented
152	#13133174	C₂²	1	1	yes	characteristic, complemented
153	#13133173	C₂²	1	1	yes	characteristic, complemented
154	#13133173	C₂²	1	1	yes	characteristic, complemented
155	#13133173	C₂²	1	1	yes	characteristic, complemented
156	#13133173	C₂²	1	1	yes	characteristic, complemented
157	#13133173	C₂²	1	1	yes	characteristic, complemented
158	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
159	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
160	C₂×#11719921	C₂²	1	1	yes	characteristic, complemented
161	C₂×#11719921	C₂²	1	1	yes	characteristic, complemented
162	C₂×#11719921	C₂²	1	1	yes	characteristic, complemented
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	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
170	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
171	C₄²×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	#124×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	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	#120×C₅₃	C₂²	1	1	yes	characteristic
183	#120×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₄×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	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
193	C₂×D₄×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	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂×D₄×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	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₅₃	—	2	4	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	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
220	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
221	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
222	C₂²×Dic₅₃	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	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
227	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
228	Q₈×D₅₃	—	4	2	no	—
229	#11719947	—	2	4	no	—
230	#11719947	—	4	2	no	—
231	#11719947	—	4	2	no	—
232	D₄×D₅₃	—	2	4	no	—
233	D₄×D₅₃	—	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×C₄×D₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
247	C₂×Dic₁₀₆	—	4	2	no	—
248	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
249	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
250	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
251	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
252	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
253	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
254	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
255	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₄²×C₅₃	C₂³	1	1	yes	characteristic
276	C₄²×C₅₃	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
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	#11719921	C₂³	1	1	yes	characteristic
292	#11719921	C₂³	1	1	yes	characteristic
293	#11719921	C₂³	1	1	yes	characteristic
294	#11719921	C₂³	1	1	yes	characteristic
295	#11719921	C₂³	1	1	yes	characteristic
296	#11719921	C₂³	1	1	yes	characteristic
297	#11719921	C₂³	1	1	yes	characteristic
298	#11719921	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	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
316	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
317	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
318	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
319	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
320	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
321	#11719919	C₂³	1	1	yes	characteristic
322	#11719919	C₂³	1	1	yes	characteristic
323	#11719919	C₂³	1	1	yes	characteristic
324	#11719919	C₂³	1	1	yes	characteristic
325	#11719919	C₂³	1	1	yes	characteristic
326	#11719919	C₂³	1	1	yes	characteristic
327	#11719919	C₂³	1	1	yes	characteristic
328	#11719919	C₂³	1	1	yes	characteristic
329	#11719919	C₂³	1	1	yes	characteristic
330	#11719919	C₂³	1	1	yes	characteristic
331	#11719919	C₂³	1	1	yes	characteristic
332	#11719919	C₂³	1	1	yes	characteristic
333	#11719919	C₂³	1	1	yes	characteristic
334	#11719919	C₂³	1	1	yes	characteristic
335	#11719919	C₂³	1	1	yes	characteristic
336	#11719919	C₂³	1	1	yes	characteristic
337	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
338	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
339	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
340	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
341	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
342	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
343	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
344	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
345	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
346	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
347	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
348	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
349	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
350	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
351	C₂³×C₅₃	—	2	2	no	—
352	C₂³×C₅₃	—	4	1	no	—
353	C₂³×C₅₃	—	4	1	no	—
354	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂²×D₅₃	—	2	2	no	—
360	C₂²×D₅₃	—	2	2	no	—
361	C₂²×D₅₃	—	2	2	no	—
362	C₂²×D₅₃	—	4	1	no	—
363	C₂²×D₅₃	—	4	1	no	—
364	C₂²×D₅₃	—	4	1	no	—
365	C₂²×D₅₃	—	4	1	no	—
366	C₂²×D₅₃	—	4	1	no	—
367	C₂²×D₅₃	—	4	1	no	—
368	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
369	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
370	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
371	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
372	Q₈×C₅₃	—	4	1	no	—
373	D₄×C₅₃	—	2	2	no	—
374	D₄×C₅₃	—	2	2	no	—
375	D₄×C₅₃	—	4	1	no	—
376	D₄×C₅₃	—	4	1	no	—
377	D₄×C₅₃	—	4	1	no	—
378	D₄×C₅₃	—	4	1	no	—
379	D₄×C₅₃	—	4	1	no	—
380	C₂×C₄×C₅₃	—	4	1	no	—
381	C₂×C₄×C₅₃	—	4	1	no	—
382	C₂×C₄×C₅₃	—	4	1	no	—
383	C₂×C₄×C₅₃	—	4	1	no	—
384	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²⋊D₅₃	—	2	2	no	—
395	C₂²⋊D₅₃	—	2	2	no	—
396	C₂²⋊D₅₃	—	2	2	no	—
397	C₂²⋊D₅₃	—	2	2	no	—
398	C₂²⋊D₅₃	—	2	2	no	—
399	C₂²⋊D₅₃	—	2	2	no	—
400	C₂²⋊D₅₃	—	2	2	no	—
401	C₂²⋊D₅₃	—	2	2	no	—
402	C₂²⋊D₅₃	—	4	1	no	—
403	C₂²⋊D₅₃	—	4	1	no	—
404	C₂²⋊D₅₃	—	4	1	no	—
405	C₂²⋊D₅₃	—	4	1	no	—
406	C₂²⋊D₅₃	—	4	1	no	—
407	C₂²⋊D₅₃	#41	1	4	yes	complemented
408	C₂×Dic₅₃	—	2	2	no	—
409	C₂×Dic₅₃	—	2	2	no	—
410	C₂×Dic₅₃	—	2	2	no	—
411	C₂×Dic₅₃	—	2	2	no	—
412	C₂×Dic₅₃	—	2	2	no	—
413	C₂×Dic₅₃	—	4	1	no	—
414	C₂×Dic₅₃	—	4	1	no	—
415	C₂×Dic₅₃	—	4	1	no	—
416	C₂×Dic₅₃	—	4	1	no	—
417	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
418	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
419	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
420	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
421	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
422	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
423	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
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	D₂₁₂	—	2	2	no	—
430	D₂₁₂	—	4	1	no	—
431	D₂₁₂	—	4	1	no	—
432	C₄×D₅₃	—	2	2	no	—
433	C₄×D₅₃	—	2	2	no	—
434	C₄×D₅₃	—	2	2	no	—
435	C₄×D₅₃	—	4	1	no	—
436	C₄×D₅₃	—	4	1	no	—
437	C₄×D₅₃	—	4	1	no	—
438	C₄×D₅₃	—	4	1	no	—
439	C₄×D₅₃	—	4	1	no	—
440	C₄×D₅₃	—	4	1	no	—
441	C₄×D₅₃	—	4	1	no	—
442	Dic₁₀₆	—	2	2	no	—
443	Dic₁₀₆	—	2	2	no	—
444	Dic₁₀₆	—	2	2	no	—
445	Dic₁₀₆	—	2	2	no	—
446	Dic₁₀₆	—	4	1	no	—
447	Dic₁₀₆	—	4	1	no	—
448	Dic₁₀₆	—	4	1	no	—
449	C₂²×C₅₃	—	2	1	no	—
450	C₂²×C₅₃	—	2	1	no	—
451	C₂²×C₅₃	—	2	1	no	—
452	C₂²×C₅₃	—	2	1	no	—
453	C₂²×C₅₃	—	2	1	no	—
454	C₂²×C₅₃	—	2	1	no	—
455	C₂²×C₅₃	—	2	1	no	—
456	C₂²×C₅₃	—	2	1	no	—
457	C₂²×C₅₃	—	2	1	no	—
458	C₂²×C₅₃	—	2	1	no	—
459	C₂²×C₅₃	—	2	1	no	—
460	C₂²×C₅₃	—	2	1	no	—
461	C₂²×C₅₃	—	2	1	no	—
462	C₂²×C₅₃	—	2	1	no	—
463	C₂²×C₅₃	—	8	2	no	—
464	C₂²×C₅₃	C₂×#41	1	2	yes	—
465	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
466	C₂×D₅₃	—	2	1	no	—
467	C₂×D₅₃	—	2	1	no	—
468	C₂×D₅₃	—	2	1	no	—
469	C₂×D₅₃	—	2	1	no	—
470	C₂×D₅₃	—	2	1	no	—
471	C₂×D₅₃	—	2	1	no	—
472	C₂×D₅₃	—	2	1	no	—
473	C₂×D₅₃	—	2	1	no	—
474	C₂×D₅₃	—	2	1	no	—
475	C₂×D₅₃	—	2	1	no	—
476	C₂×D₅₃	—	2	1	no	—
477	C₂×D₅₃	—	8	2	no	—
478	C₂×D₅₃	—	8	2	no	—
479	C₂×D₅₃	—	8	2	no	—
480	C₂×D₅₃	C₂×#41	1	2	yes	—
481	C₄×C₅₃	—	2	1	no	—
482	C₄×C₅₃	—	2	1	no	—
483	C₄×C₅₃	—	2	1	no	—
484	C₄×C₅₃	—	2	1	no	—
485	C₄×C₅₃	—	2	1	no	—
486	C₄×C₅₃	—	2	1	no	—
487	C₄×C₅₃	—	2	1	no	—
488	C₄×C₅₃	—	2	1	no	—
489	C₄×C₅₃	—	2	1	no	—
490	C₄×C₅₃	—	2	1	no	—
491	Dic₅₃	—	2	1	no	—
492	Dic₅₃	—	2	1	no	—
493	Dic₅₃	—	2	1	no	—
494	Dic₅₃	—	2	1	no	—
495	Dic₅₃	—	2	1	no	—
496	Dic₅₃	—	2	1	no	—
497	Dic₅₃	—	2	1	no	—
498	Dic₅₃	—	2	1	no	—
499	Dic₅₃	—	2	1	no	—
500	Dic₅₃	—	2	1	no	—
501	Dic₅₃	C₂×#41	1	2	yes	—
502	Dic₅₃	H(5,𝔽₂)	1	2	yes	—
503	#3514	—	53	1	no	maximal, Sylow
504	C₂×C₅₃	—	2	2	no	—
505	C₂×C₅₃	—	4	1	no	—
506	C₂×C₅₃	—	4	1	no	—
507	C₂×C₅₃	—	4	1	no	—
508	C₂×C₅₃	—	4	1	no	—
509	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
510	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
511	C₂×C₅₃	#585	1	1	yes	characteristic
512	D₅₃	—	2	2	no	—
513	D₅₃	—	4	1	no	—
514	D₅₃	—	4	1	no	—
515	D₅₃	—	4	1	no	—
516	#559	—	53	1	no	—
517	#556	—	53	1	no	—
518	#555	—	53	1	no	—
519	#555	—	53	1	no	—
520	#551	—	53	1	no	—
521	#551	—	53	1	no	—
522	#551	—	53	1	no	—
523	#551	—	53	1	no	—
524	D₄×Q₈	—	53	1	no	—
525	#548	—	53	1	no	—
526	#548	—	53	1	no	—
527	#546	—	53	1	no	—
528	#546	—	53	1	no	—
529	#546	—	53	1	no	—
530	#546	—	53	1	no	—
531	D₄²	—	53	1	no	—
532	#542	—	53	1	no	—
533	#542	—	53	1	no	—
534	#538	—	53	1	no	—
535	#538	—	53	1	no	—
536	#538	—	53	1	no	—
537	#538	D₅₃	1	1	yes	characteristic, complemented
538	#532	—	53	1	no	—
539	#529	—	53	1	no	—
540	#529	—	53	1	no	—
541	#529	—	53	1	no	—
542	C₂×#124	—	53	1	no	—
543	C₂×#124	—	53	1	no	—
544	#518	—	53	1	no	—
545	#518	—	53	1	no	—
546	C₄×#41	—	53	1	no	—
547	C₅₃	#3514	1	1	yes	characteristic, complemented, Sylow
548	C₂×#41	—	53	1	no	—
549	C₂×#41	—	53	1	no	—
550	C₂×#41	—	53	1	no	—
551	C₂²×Q₈	—	53	1	no	—
552	C₂²×Q₈	—	53	1	no	—
553	C₂²×D₄	—	53	1	no	—
554	C₂²×D₄	—	53	1	no	—
555	C₂²×D₄	—	53	1	no	—
556	C₂²×D₄	—	53	1	no	—
557	C₄⋊Q₈	—	53	1	no	—
558	C₄⋊Q₈	—	53	1	no	—
559	C₄⋊Q₈	—	53	1	no	—
560	#127	—	53	1	no	—
561	#126	—	53	1	no	—
562	#126	—	53	1	no	—
563	#126	—	53	1	no	—
564	#126	—	53	1	no	—
565	#126	—	53	1	no	—
566	#126	—	53	1	no	—
567	#126	—	53	1	no	—
568	#126	—	53	1	no	—
569	#126	C₂×D₅₃	1	1	yes	characteristic, complemented
570	#126	C₂×D₅₃	1	1	yes	characteristic, complemented
571	#125	—	53	1	no	—
572	#124	—	53	1	no	—
573	#124	—	53	1	no	—
574	#124	—	53	1	no	—
575	#124	—	53	1	no	—
576	#124	—	53	1	no	—
577	#124	—	53	1	no	—
578	#124	—	53	1	no	—
579	#124	—	53	1	no	—
580	#124	—	53	1	no	—
581	#124	—	53	1	no	—
582	#124	—	53	1	no	—
583	#124	—	53	1	no	—
584	#124	—	53	1	no	—
585	#124	—	53	1	no	—
586	#124	—	53	1	no	—
587	#124	—	53	1	no	—
588	#124	—	53	1	no	—
589	#124	—	53	1	no	—
590	#124	—	53	1	no	—
591	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
592	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
593	#123	—	53	1	no	—
594	#123	—	53	1	no	—
595	#123	—	53	1	no	—
596	#123	—	53	1	no	—
597	#123	—	53	1	no	—
598	#123	—	53	1	no	—
599	#123	—	53	1	no	—
600	#123	—	53	1	no	—
601	#123	—	53	1	no	—
602	#123	—	53	1	no	—
603	#123	—	53	1	no	—
604	#123	—	53	1	no	—
605	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
606	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
607	C₂²⋊Q₈	—	53	1	no	—
608	C₂²⋊Q₈	—	53	1	no	—
609	C₂²⋊Q₈	—	53	1	no	—
610	C₂²⋊Q₈	—	53	1	no	—
611	C₂²⋊Q₈	—	53	1	no	—
612	C₂²⋊Q₈	—	53	1	no	—
613	C₂²⋊Q₈	—	53	1	no	—
614	C₂²⋊Q₈	—	53	1	no	—
615	C₂²⋊Q₈	—	53	1	no	—
616	C₂²⋊Q₈	—	53	1	no	—
617	C₂²⋊Q₈	—	53	1	no	—
618	C₂²⋊Q₈	—	53	1	no	—
619	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
620	#121	—	53	1	no	—
621	#121	—	53	1	no	—
622	#121	—	53	1	no	—
623	#121	—	53	1	no	—
624	#121	—	53	1	no	—
625	#121	—	53	1	no	—
626	#121	—	53	1	no	—
627	#121	—	53	1	no	—
628	#121	—	53	1	no	—
629	#121	—	53	1	no	—
630	#121	—	53	1	no	—
631	#121	—	53	1	no	—
632	#121	—	53	1	no	—
633	#121	—	53	1	no	—
634	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
635	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
636	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
637	#120	—	53	1	no	—
638	#120	—	53	1	no	—
639	#120	—	53	1	no	—
640	#120	—	53	1	no	—
641	#120	—	53	1	no	—
642	#120	—	53	1	no	—
643	#120	C₂×D₅₃	1	1	yes	characteristic
644	#120	C₂×D₅₃	1	1	yes	characteristic, complemented
645	C₄×Q₈	—	53	1	no	—
646	C₄×Q₈	—	53	1	no	—
647	C₄×Q₈	—	53	1	no	—
648	C₄×Q₈	—	53	1	no	—
649	C₄×Q₈	—	53	1	no	—
650	C₄×D₄	—	53	1	no	—
651	C₄×D₄	—	53	1	no	—
652	C₄×D₄	—	53	1	no	—
653	C₄×D₄	—	53	1	no	—
654	C₄×D₄	—	53	1	no	—
655	C₄×D₄	—	53	1	no	—
656	C₄×D₄	—	53	1	no	—
657	C₄×D₄	—	53	1	no	—
658	C₄×D₄	—	53	1	no	—
659	C₄×D₄	—	53	1	no	—
660	C₄×D₄	—	53	1	no	—
661	C₄×D₄	—	53	1	no	—
662	C₄×D₄	—	53	1	no	—
663	C₄×D₄	—	53	1	no	—
664	C₄×D₄	—	53	1	no	—
665	C₄×D₄	—	53	1	no	—
666	C₄×D₄	—	53	1	no	—
667	C₄×D₄	—	53	1	no	—
668	C₄×D₄	—	53	1	no	—
669	C₄×D₄	—	53	1	no	—
670	C₄×D₄	—	53	1	no	—
671	C₄×D₄	—	53	1	no	—
672	C₄×D₄	—	53	1	no	—
673	C₄×D₄	—	53	1	no	—
674	C₄×D₄	—	53	1	no	—
675	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
676	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
677	#117	—	53	1	no	—
678	#117	—	53	1	no	—
679	#117	—	53	1	no	—
680	#117	—	53	1	no	—
681	#117	—	53	1	no	—
682	#117	—	53	1	no	—
683	#117	—	53	1	no	—
684	#117	—	53	1	no	—
685	#117	—	53	1	no	—
686	#117	—	53	1	no	—
687	#117	—	53	1	no	—
688	C₂×C₂²⋊C₄	—	53	1	no	—
689	C₂×C₂²⋊C₄	—	53	1	no	—
690	C₂×C₂²⋊C₄	—	53	1	no	—
691	C₂×C₂²⋊C₄	—	53	1	no	—
692	C₂×C₂²⋊C₄	—	53	1	no	—
693	C₂×C₂²⋊C₄	—	53	1	no	—
694	C₂×C₂²⋊C₄	—	53	1	no	—
695	C₂×C₂²⋊C₄	—	53	1	no	—
696	C₂×C₂²⋊C₄	—	53	1	no	—
697	C₂×C₂²⋊C₄	—	53	1	no	—
698	C₂×C₂²⋊C₄	—	53	1	no	—
699	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
700	C₂×C₄²	—	53	1	no	—
701	C₂×C₄²	—	53	1	no	—
702	C₂×C₄²	—	53	1	no	—
703	C₂⁴	—	53	1	no	—
704	C₂⁴	—	53	1	no	—
705	C₂⁴	—	53	1	no	—
706	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
707	#41	—	106	4	no	—
708	#41	—	212	2	no	—
709	#41	—	212	2	no	—
710	C₂×Q₈	—	53	1	no	—
711	C₂×Q₈	—	53	1	no	—
712	C₂×Q₈	—	53	1	no	—
713	C₂×Q₈	—	53	1	no	—
714	C₂×Q₈	—	53	1	no	—
715	C₂×Q₈	—	53	1	no	—
716	C₂×Q₈	—	53	1	no	—
717	C₂×Q₈	—	212	2	no	—
718	C₂×Q₈	—	212	2	no	—
719	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
720	C₂×D₄	—	53	1	no	—
721	C₂×D₄	—	53	1	no	—
722	C₂×D₄	—	53	1	no	—
723	C₂×D₄	—	53	1	no	—
724	C₂×D₄	—	53	1	no	—
725	C₂×D₄	—	53	1	no	—
726	C₂×D₄	—	53	1	no	—
727	C₂×D₄	—	53	1	no	—
728	C₂×D₄	—	53	1	no	—
729	C₂×D₄	—	53	1	no	—
730	C₂×D₄	—	53	1	no	—
731	C₂×D₄	—	53	1	no	—
732	C₂×D₄	—	53	1	no	—
733	C₂×D₄	—	53	1	no	—
734	C₂×D₄	—	53	1	no	—
735	C₂×D₄	—	53	1	no	—
736	C₂×D₄	—	53	1	no	—
737	C₂×D₄	—	106	4	no	—
738	C₂×D₄	—	106	4	no	—
739	C₂×D₄	—	212	2	no	—
740	C₂×D₄	—	212	2	no	—
741	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
742	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
743	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
744	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
745	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
746	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
747	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
748	C₂²×C₄	—	53	1	no	—
749	C₂²×C₄	—	53	1	no	—
750	C₂²×C₄	—	53	1	no	—
751	C₂²×C₄	—	53	1	no	—
752	C₂²×C₄	—	53	1	no	—
753	C₂²×C₄	—	53	1	no	—
754	C₂²×C₄	—	53	1	no	—
755	C₂²×C₄	—	53	1	no	—
756	C₂²×C₄	—	53	1	no	—
757	C₂²×C₄	—	53	1	no	—
758	C₂²×C₄	—	53	1	no	—
759	C₂²×C₄	—	53	1	no	—
760	C₂²×C₄	—	53	1	no	—
761	C₂²×C₄	—	53	1	no	—
762	C₂²×C₄	—	53	1	no	—
763	C₂²×C₄	—	53	1	no	—
764	C₂²×C₄	—	53	1	no	—
765	C₂²×C₄	—	53	1	no	—
766	C₂²×C₄	—	53	1	no	—
767	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
768	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
769	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
770	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
771	C₄⋊C₄	—	53	1	no	—
772	C₄⋊C₄	—	53	1	no	—
773	C₄⋊C₄	—	53	1	no	—
774	C₄⋊C₄	—	53	1	no	—
775	C₄⋊C₄	—	53	1	no	—
776	C₄⋊C₄	—	53	1	no	—
777	C₄⋊C₄	—	53	1	no	—
778	C₄⋊C₄	—	53	1	no	—
779	C₄⋊C₄	—	53	1	no	—
780	C₄⋊C₄	—	53	1	no	—
781	C₄⋊C₄	—	53	1	no	—
782	C₄⋊C₄	—	53	1	no	—
783	C₄⋊C₄	—	53	1	no	—
784	C₄⋊C₄	—	53	1	no	—
785	C₄⋊C₄	—	53	1	no	—
786	C₄⋊C₄	—	53	1	no	—
787	C₄⋊C₄	—	53	1	no	—
788	C₄⋊C₄	—	53	1	no	—
789	C₄⋊C₄	—	53	1	no	—
790	C₄⋊C₄	—	53	1	no	—
791	C₄⋊C₄	—	53	1	no	—
792	C₄⋊C₄	—	53	1	no	—
793	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
795	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
796	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
797	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
798	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
814	C₂²⋊C₄	—	53	1	no	—
815	C₂²⋊C₄	—	53	1	no	—
816	C₂²⋊C₄	—	53	1	no	—
817	C₂²⋊C₄	—	53	1	no	—
818	C₂²⋊C₄	—	53	1	no	—
819	C₂²⋊C₄	—	53	1	no	—
820	C₂²⋊C₄	—	53	1	no	—
821	C₂²⋊C₄	—	53	1	no	—
822	C₂²⋊C₄	—	53	1	no	—
823	C₂²⋊C₄	—	53	1	no	—
824	C₂²⋊C₄	—	53	1	no	—
825	C₂²⋊C₄	—	53	1	no	—
826	C₂²⋊C₄	—	53	1	no	—
827	C₂²⋊C₄	—	53	1	no	—
828	C₂²⋊C₄	—	53	1	no	—
829	C₂²⋊C₄	—	53	1	no	—
830	C₂²⋊C₄	—	53	1	no	—
831	C₂²⋊C₄	—	53	1	no	—
832	C₂²⋊C₄	—	53	1	no	—
833	C₂²⋊C₄	—	53	1	no	—
834	C₂²⋊C₄	—	53	1	no	—
835	C₂²⋊C₄	—	53	1	no	—
836	C₂²⋊C₄	—	53	1	no	—
837	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
842	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
843	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
844	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
845	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
846	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
847	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
848	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
849	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
850	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
851	C₄²	—	53	1	no	—
852	C₄²	—	53	1	no	—
853	C₄²	—	53	1	no	—
854	C₄²	—	53	1	no	—
855	C₄²	—	53	1	no	—
856	C₄²	—	53	1	no	—
857	C₄²	—	53	1	no	—
858	C₄²	—	53	1	no	—
859	C₄²	—	53	1	no	—
860	C₄²	—	53	1	no	—
861	C₄²	—	53	1	no	—
862	C₄²	—	53	1	no	—
863	C₄²	—	53	1	no	—
864	C₄²	—	53	1	no	—
865	C₄²	C₂²×D₅₃	1	1	yes	characteristic
866	C₄²	C₂²×D₅₃	1	1	yes	characteristic
867	C₂³	—	2	2	no	—
868	C₂³	—	4	1	no	—
869	C₂³	—	4	1	no	—
870	C₂³	—	53	1	no	—
871	C₂³	—	53	1	no	—
872	C₂³	—	53	1	no	—
873	C₂³	—	53	1	no	—
874	C₂³	—	106	2	no	—
875	C₂³	—	106	2	no	—
876	C₂³	—	106	2	no	—
877	C₂³	—	212	1	no	—
878	C₂³	—	212	1	no	—
879	C₂³	—	212	1	no	—
880	C₂³	—	212	1	no	—
881	C₂³	—	212	1	no	—
882	C₂³	—	212	1	no	—
883	C₂³	C₂³×D₅₃	1	1	yes	characteristic
884	C₂³	C₂³×D₅₃	1	1	yes	characteristic
885	C₂³	C₂³×D₅₃	1	1	yes	characteristic
886	C₂³	C₂³×D₅₃	1	1	yes	characteristic
887	C₂³	C₂³×D₅₃	1	1	yes	characteristic
888	Q₈	—	4	1	no	—
889	Q₈	—	106	2	no	—
890	Q₈	—	106	2	no	—
891	Q₈	—	106	2	no	—
892	Q₈	—	106	2	no	—
893	Q₈	—	212	1	no	—
894	Q₈	—	212	1	no	—
895	Q₈	—	212	1	no	—
896	D₄	—	2	2	no	—
897	D₄	—	2	2	no	—
898	D₄	—	4	1	no	—
899	D₄	—	4	1	no	—
900	D₄	—	4	1	no	—
901	D₄	—	4	1	no	—
902	D₄	—	4	1	no	—
903	D₄	—	53	4	no	—
904	D₄	—	106	2	no	—
905	D₄	—	106	2	no	—
906	D₄	—	106	2	no	—
907	D₄	—	106	2	no	—
908	D₄	—	106	2	no	—
909	D₄	—	106	2	no	—
910	D₄	—	106	2	no	—
911	D₄	—	106	2	no	—
912	D₄	—	106	2	no	—
913	D₄	—	212	1	no	—
914	D₄	—	212	1	no	—
915	D₄	—	212	1	no	—
916	D₄	—	212	1	no	—
917	D₄	—	212	1	no	—
918	D₄	—	212	1	no	—
919	D₄	—	212	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	4	1	no	—
924	C₂×C₄	—	53	1	no	—
925	C₂×C₄	—	53	1	no	—
926	C₂×C₄	—	53	1	no	—
927	C₂×C₄	—	53	1	no	—
928	C₂×C₄	—	53	1	no	—
929	C₂×C₄	—	53	1	no	—
930	C₂×C₄	—	53	1	no	—
931	C₂×C₄	—	53	1	no	—
932	C₂×C₄	—	53	1	no	—
933	C₂×C₄	—	53	1	no	—
934	C₂×C₄	—	53	1	no	—
935	C₂×C₄	—	53	1	no	—
936	C₂×C₄	—	106	2	no	—
937	C₂×C₄	—	106	2	no	—
938	C₂×C₄	—	106	2	no	—
939	C₂×C₄	—	106	2	no	—
940	C₂×C₄	—	106	2	no	—
941	C₂×C₄	—	106	2	no	—
942	C₂×C₄	—	106	2	no	—
943	C₂×C₄	—	106	2	no	—
944	C₂×C₄	—	212	1	no	—
945	C₂×C₄	—	212	1	no	—
946	C₂×C₄	—	212	1	no	—
947	C₂×C₄	—	212	1	no	—
948	C₂×C₄	—	212	1	no	—
949	C₂×C₄	—	212	1	no	—
950	C₂×C₄	—	212	1	no	—
951	C₂×C₄	—	212	1	no	—
952	C₂×C₄	—	212	1	no	—
953	C₂×C₄	—	212	1	no	—
954	C₂×C₄	—	212	1	no	—
955	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
956	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
957	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
958	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
959	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
960	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
961	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
962	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
963	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
964	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	8	2	no	—
980	C₂²	—	53	2	no	—
981	C₂²	—	106	1	no	—
982	C₂²	—	106	1	no	—
983	C₂²	—	106	1	no	—
984	C₂²	—	106	1	no	—
985	C₂²	—	106	1	no	—
986	C₂²	—	106	1	no	—
987	C₂²	—	106	1	no	—
988	C₂²	—	106	1	no	—
989	C₂²	—	106	1	no	—
990	C₂²	—	106	1	no	—
991	C₂²	—	106	1	no	—
992	C₂²	—	424	2	no	—
993	C₂²	—	424	2	no	—
994	C₂²	—	424	2	no	—
995	C₂²	#41×D₅₃	1	2	yes	—
996	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	53	2	no	—
1008	C₄	—	53	2	no	—
1009	C₄	—	106	1	no	—
1010	C₄	—	106	1	no	—
1011	C₄	—	106	1	no	—
1012	C₄	—	106	1	no	—
1013	C₄	—	106	1	no	—
1014	C₄	—	106	1	no	—
1015	C₄	—	106	1	no	—
1016	C₄	—	106	1	no	—
1017	C₄	—	106	1	no	—
1018	C₄	—	106	1	no	—
1019	C₂	—	2	2	no	—
1020	C₂	—	4	1	no	—
1021	C₂	—	4	1	no	—
1022	C₂	—	4	1	no	—
1023	C₂	—	4	1	no	—
1024	C₂	—	106	2	no	—
1025	C₂	—	212	1	no	—
1026	C₂	—	212	1	no	—
1027	C₂	—	212	1	no	—
1028	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
1029	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1030	C₂	#16811458	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#538	C₂
hypercenter	#538	D₅₃
hypocenter	C₅₃	#3514
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #16811357	C₂	semidirect
2. #16811340	C₂	semidirect
3. #16811337	C₂	semidirect
4. #16811335	C₂	semidirect
5. #16811304	C₂	semidirect
6. #16811300	C₂	semidirect
7. #16811298	C₂	semidirect
8. #16811296	C₂	semidirect
9. #16811286	C₂	semidirect
10. #16811281	C₂	semidirect
11. #16811279	C₂	semidirect
12. #16811262	C₂	semidirect
13. #16811262	C₂	semidirect
14. #16811260	C₂	semidirect
15. #16811260	C₂	semidirect
16. #16811255	C₂	semidirect
17. #16811239	C₂	semidirect
18. #16811237	C₂	semidirect
19. #16811209	C₂	semidirect
20. #16811206	C₂	semidirect
21. #16811205	C₂	semidirect
22. #16811168	C₂	semidirect
23. #16811156	C₂	semidirect
24. #16811153	C₂	semidirect
25. #16811150	C₂	semidirect
26. C₂×#13133203	C₂	semidirect
27. #124×D₅₃	C₂	semidirect
28. #16811096	C₂	semidirect
29. #16811095	C₂	semidirect
30. C₄×#11719947	C₂	semidirect
31. C₅₃×#538	C₂	semidirect
33. C₂×#11719947	C₂²	semidirect
34. C₂×#11719947	C₂²	semidirect
35. C₂²×Dic₁₀₆	C₂²	semidirect
36. C₂×Q₈×D₅₃	C₂²	semidirect
41. #13133216	C₂²	semidirect
42. #13133216	C₂²	semidirect
43. #13133215	C₂²	semidirect
45. #13133212	C₂²	semidirect
46. #13133212	C₂²	semidirect
47. #13133212	C₂²	semidirect
48. #13133212	C₂²	semidirect
49. #13133211	C₂²	semidirect
50. #13133210	C₂²	semidirect
51. #13133210	C₂²	semidirect
52. #13133210	C₂²	semidirect
53. #13133207	C₂²	semidirect
54. #13133206	C₂²	semidirect
55. #13133205	C₂²	semidirect
56. #13133204	C₂²	semidirect
57. #13133204	C₂²	semidirect
61. #13133203	C₂²	semidirect
62. #13133203	C₂²	semidirect
63. #13133203	C₂²	semidirect
64. #13133203	C₂²	semidirect
65. #13133203	C₂²	semidirect
66. #13133203	C₂²	semidirect
67. #13133203	C₂²	semidirect
68. #13133203	C₂²	semidirect
69. #13133203	C₂²	semidirect
70. #13133203	C₂²	semidirect
71. #13133203	C₂²	semidirect
72. #13133203	C₂²	semidirect
73. #13133202	C₂²	semidirect
74. #13133202	C₂²	semidirect
75. #13133202	C₂²	semidirect
76. #13133202	C₂²	semidirect
77. #13133201	C₂²	semidirect
78. #13133201	C₂²	semidirect
79. #13133200	C₂²	semidirect
80. #13133199	C₂²	semidirect
81. #13133199	C₂²	semidirect
82. #13133198	C₂²	semidirect
83. #13133198	C₂²	semidirect
84. #13133198	C₂²	semidirect
85. #13133197	C₂²	semidirect
86. #13133197	C₂²	semidirect
87. #13133195	C₂²	semidirect
88. #13133195	C₂²	semidirect
89. #13133195	C₂²	semidirect
90. #13133194	C₂²	semidirect
91. #13133194	C₂²	semidirect
92. #13133194	C₂²	semidirect
93. #13133194	C₂²	semidirect
94. #13133194	C₂²	semidirect
95. #13133194	C₂²	semidirect
96. #13133193	C₂²	semidirect
97. #13133191	C₂²	semidirect
100. #13133190	C₂²	semidirect
101. #13133190	C₂²	semidirect
105. #13133189	C₂²	semidirect
106. #13133189	C₂²	semidirect
107. #13133189	C₂²	semidirect
108. #13133189	C₂²	semidirect
109. #13133188	C₂²	semidirect
110. #13133188	C₂²	semidirect
114. #13133185	C₂²	semidirect
115. #13133185	C₂²	semidirect
116. #13133185	C₂²	semidirect
117. C₄×Dic₁₀₆	C₂²	semidirect
118. C₄×Dic₁₀₆	C₂²	semidirect
119. #13133182	C₂²	semidirect
120. #13133182	C₂²	semidirect
121. #13133182	C₂²	semidirect
122. C₄×D₂₁₂	C₂²	semidirect
123. D₄×Dic₅₃	C₂²	semidirect
124. D₄×Dic₅₃	C₂²	semidirect
125. D₄×Dic₅₃	C₂²	semidirect
126. D₄×Dic₅₃	C₂²	semidirect
127. #13133179	C₂²	semidirect
128. #13133179	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
139. #13133177	C₂²	semidirect
140. #13133177	C₂²	semidirect
141. #13133177	C₂²	semidirect
142. #13133177	C₂²	semidirect
143. #13133177	C₂²	semidirect
144. #13133177	C₂²	semidirect
145. #13133177	C₂²	semidirect
146. #13133177	C₂²	semidirect
147. #13133176	C₂²	semidirect
148. #13133175	C₂²	semidirect
149. #13133175	C₂²	semidirect
150. #13133175	C₂²	semidirect
151. #13133174	C₂²	semidirect
152. #13133174	C₂²	semidirect
153. #13133173	C₂²	semidirect
154. #13133173	C₂²	semidirect
155. #13133173	C₂²	semidirect
156. #13133173	C₂²	semidirect
157. #13133173	C₂²	semidirect
158. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
159. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
160. C₂×#11719921	C₂²	semidirect
161. C₂×#11719921	C₂²	semidirect
162. 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. C₂×C₄×Dic₅₃	C₂²	semidirect
170. C₂×C₄×Dic₅₃	C₂²	semidirect
171. C₄²×D₅₃	C₂²	semidirect
172. #126×C₅₃	C₂²	semidirect
173. #126×C₅₃	C₂²	semidirect
174. #124×C₅₃	C₂²	semidirect
175. #124×C₅₃	C₂²	semidirect
176. #123×C₅₃	C₂²	semidirect
177. #123×C₅₃	C₂²	semidirect
178. C₂²⋊Q₈×C₅₃	C₂²	semidirect
179. #121×C₅₃	C₂²	semidirect
180. #121×C₅₃	C₂²	semidirect
181. #121×C₅₃	C₂²	semidirect
183. #120×C₅₃	C₂²	semidirect
184. C₄×D₄×C₅₃	C₂²	semidirect
185. C₄×D₄×C₅₃	C₂²	semidirect
186. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
407. C₂²⋊D₅₃	#41	semidirect
537. #538	D₅₃	semidirect
547. C₅₃	#3514	semidirect
569. #126	C₂×D₅₃	semidirect
570. #126	C₂×D₅₃	semidirect
591. #124	C₂×D₅₃	semidirect
592. #124	C₂×D₅₃	semidirect
605. #123	C₂×D₅₃	semidirect
606. #123	C₂×D₅₃	semidirect
619. C₂²⋊Q₈	C₂×D₅₃	semidirect
634. #121	C₂×D₅₃	semidirect
635. #121	C₂×D₅₃	semidirect
636. #121	C₂×D₅₃	semidirect
644. #120	C₂×D₅₃	semidirect
675. C₄×D₄	C₂×D₅₃	semidirect
676. C₄×D₄	C₂×D₅₃	semidirect
699. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect