Subgroups — #20288745

Order 6784.

1252 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811337	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811329	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811326	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811320	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811318	C₂	1	2	yes	maximal, complemented
6	#16811293	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811270	C₂	1	2	yes	maximal, complemented
8	#16811265	C₂	1	2	yes	maximal, complemented
9	#16811262	C₂	1	2	yes	maximal, complemented
10	#16811258	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811257	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811257	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811224	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811209	C₂	1	2	yes	maximal, complemented
15	#16811205	C₂	1	2	yes	maximal, complemented
16	#16811170	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811151	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811131	C₂	1	2	yes	maximal, complemented
19	#121×D₅₃	C₂	1	2	yes	maximal, complemented
20	#16811097	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811095	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11719945	C₂²	1	2	yes	complemented
25	C₂×#11719947	C₂²	1	2	yes	complemented
26	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
30	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
31	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
32	C₂²×C₄×D₅₃	C₂²	1	2	yes	complemented
33	#13133216	C₂²	1	1	yes	characteristic, complemented
34	#13133213	C₂²	1	1	yes	characteristic, complemented
35	#13133213	C₂²	1	1	yes	characteristic, complemented
36	#13133212	C₂²	1	2	yes	complemented
37	#13133212	C₂²	1	1	yes	characteristic, complemented
38	#13133210	C₂²	1	2	yes	complemented
39	#13133210	C₂²	1	1	yes	characteristic, complemented
40	#13133208	C₂²	1	1	yes	characteristic, complemented
41	#13133207	C₂²	1	1	yes	characteristic, complemented
42	#13133204	C₂²	1	2	yes	complemented
43	#13133203	C₂²	1	2	yes	complemented
44	#13133203	C₂²	1	1	yes	characteristic, complemented
45	#13133203	C₂²	1	2	yes	complemented
46	#13133202	C₂²	1	1	yes	characteristic, complemented
47	#13133202	C₂²	1	2	yes	complemented
48	#13133200	C₂²	1	2	yes	complemented
49	#13133199	C₂²	1	1	yes	characteristic, complemented
50	#13133199	C₂²	1	2	yes	complemented
51	#13133198	C₂²	1	2	yes	complemented
52	#13133197	C₂²	1	2	yes	complemented
53	#13133195	C₂²	1	2	yes	complemented
54	#13133195	C₂²	1	2	yes	complemented
55	#13133195	C₂²	1	1	yes	characteristic, complemented
56	#13133192	C₂²	1	2	yes	complemented
57	#13133192	C₂²	1	1	yes	characteristic, complemented
58	#13133192	C₂²	1	1	yes	characteristic, complemented
59	#13133191	C₂²	1	2	yes	complemented
60	#13133190	C₂²	1	1	yes	characteristic
61	#13133190	C₂²	1	2	yes	complemented
62	#13133190	C₂²	1	2	yes	complemented
63	#13133190	C₂²	1	2	yes	complemented
64	#13133190	C₂²	1	2	yes	complemented
65	#13133189	C₂²	1	2	yes	complemented
66	#13133189	C₂²	1	2	yes	complemented
67	#13133189	C₂²	1	2	yes	complemented
68	#13133188	C₂²	1	2	yes	complemented
69	#13133188	C₂²	1	2	yes	complemented
70	#13133188	C₂²	1	2	yes	complemented
71	#13133188	C₂²	1	1	yes	characteristic, complemented
72	#13133188	C₂²	1	1	yes	characteristic, complemented
73	#13133187	C₂²	1	2	yes	complemented
74	#13133187	C₂²	1	2	yes	complemented
75	#13133185	C₂²	1	2	yes	complemented
76	#13133185	C₂²	1	2	yes	complemented
77	#13133185	C₂²	1	2	yes	complemented
78	#13133185	C₂²	1	2	yes	complemented
79	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
81	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
82	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
85	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
86	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
87	#13133179	C₂²	1	1	yes	characteristic
88	#13133179	C₂²	1	1	yes	characteristic
89	#13133179	C₂²	1	2	yes	complemented
90	#13133179	C₂²	1	2	yes	complemented
91	#13133179	C₂²	1	2	yes	complemented
92	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
97	#13133177	C₂²	1	2	yes	complemented
98	#13133177	C₂²	1	2	yes	complemented
99	#13133177	C₂²	1	2	yes	complemented
100	#13133176	C₂²	1	1	yes	characteristic, complemented
101	#13133175	C₂²	1	1	yes	characteristic, complemented
102	#13133174	C₂²	1	1	yes	characteristic, complemented
103	#13133173	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
106	C₂×#11719921	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
111	C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
112	#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
114	#123×C₅₃	C₂²	1	2	yes	complemented
115	#123×C₅₃	C₂²	1	2	yes	complemented
116	#121×C₅₃	C₂²	1	2	yes	complemented
117	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	#121×C₅₃	C₂²	1	2	yes	complemented
120	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₅₃	C₂³	1	2	yes	—
124	C₂³×D₅₃	C₂³	1	2	yes	—
125	C₂³×D₅₃	C₂³	1	2	yes	—
126	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₅₃	C₂³	1	2	yes	—
129	C₂×D₄×C₅₃	C₂³	1	2	yes	—
130	C₂×D₄×C₅₃	C₂³	1	2	yes	—
131	C₂×D₄×C₅₃	C₂³	1	2	yes	—
132	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
145	C₂²×Dic₅₃	C₂³	1	2	yes	—
146	C₂²×Dic₅₃	C₂³	1	2	yes	—
147	#11719947	—	4	4	no	—
148	D₄×D₅₃	—	2	4	no	—
149	D₄×D₅₃	—	2	4	no	—
150	D₄×D₅₃	—	4	4	no	—
151	D₄×D₅₃	—	4	4	no	—
152	D₄×D₅₃	—	4	4	no	—
153	#11719945	—	4	4	no	—
154	C₂×D₂₁₂	—	2	4	no	—
155	C₂×D₂₁₂	C₂³	1	2	yes	—
156	C₂×D₂₁₂	C₂³	1	2	yes	—
157	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
158	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
159	C₂×D₂₁₂	C₂³	1	2	yes	—
160	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₅₃	—	4	4	no	—
162	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₅₃	C₂³	1	2	yes	—
166	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₅₃	C₂³	1	2	yes	—
168	C₂×C₄×D₅₃	C₂³	1	2	yes	—
169	C₂×C₄×D₅₃	C₂³	1	2	yes	—
170	C₂×C₄×D₅₃	C₂³	1	2	yes	—
171	C₂×C₄×D₅₃	C₂³	1	2	yes	—
172	C₂×C₄×D₅₃	C₂³	1	2	yes	—
173	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
174	C₂×Dic₁₀₆	C₂³	1	2	yes	—
175	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
176	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
177	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
179	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
180	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
182	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
183	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
187	C₄²×C₅₃	C₂³	1	1	yes	characteristic
188	C₄²×C₅₃	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
190	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
191	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
192	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
193	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
194	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
195	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
196	#11719921	C₂³	1	2	yes	—
197	#11719921	C₂³	1	1	yes	characteristic
198	#11719921	C₂³	1	2	yes	—
199	#11719921	C₂³	1	2	yes	—
200	#11719921	C₂³	1	2	yes	—
201	#11719921	C₂³	1	2	yes	—
202	#11719921	C₂³	1	2	yes	—
203	#11719921	C₂³	1	1	yes	characteristic
204	#11719921	C₂³	1	2	yes	—
205	#11719921	C₂³	1	1	yes	characteristic
206	#11719921	C₂³	1	2	yes	—
207	#11719921	C₂³	1	1	yes	characteristic
208	#11719921	C₂³	1	1	yes	characteristic
209	#11719921	C₂³	1	2	yes	—
210	#11719921	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₅₃	C₂³	1	2	yes	—
213	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
216	#11719919	C₂³	1	1	yes	characteristic
217	#11719919	C₂³	1	2	yes	—
218	#11719919	C₂³	1	2	yes	—
219	#11719919	C₂³	1	1	yes	characteristic
220	#11719919	C₂³	1	1	yes	characteristic
221	#11719919	C₂³	1	1	yes	characteristic
222	#11719919	C₂³	1	2	yes	—
223	#11719919	C₂³	1	1	yes	characteristic
224	#11719919	C₂³	1	1	yes	characteristic
225	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
228	C₄×Dic₅₃	C₂³	1	2	yes	—
229	C₄×Dic₅₃	C₂³	1	2	yes	—
230	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
231	C₂³×C₅₃	C₂⁴	1	2	yes	—
232	C₂³×C₅₃	C₂⁴	1	2	yes	—
233	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
234	C₂²×D₅₃	—	2	4	no	—
235	C₂²×D₅₃	—	2	4	no	—
236	C₂²×D₅₃	—	2	4	no	—
237	C₂²×D₅₃	—	2	4	no	—
238	C₂²×D₅₃	—	4	2	no	—
239	C₂²×D₅₃	—	4	2	no	—
240	C₂²×D₅₃	—	4	2	no	—
241	C₂²×D₅₃	—	4	2	no	—
242	C₂²×D₅₃	—	4	2	no	—
243	C₂²×D₅₃	C₂⁴	1	2	yes	—
244	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
245	C₂²×D₅₃	C₂⁴	1	2	yes	—
246	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
247	D₄×C₅₃	—	2	2	no	—
248	D₄×C₅₃	—	2	2	no	—
249	D₄×C₅₃	—	4	2	no	—
250	D₄×C₅₃	—	4	2	no	—
251	D₄×C₅₃	—	4	2	no	—
252	D₄×C₅₃	—	4	2	no	—
253	C₂×C₄×C₅₃	—	2	2	no	—
254	C₂×C₄×C₅₃	—	4	2	no	—
255	C₂×C₄×C₅₃	—	4	2	no	—
256	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
258	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
261	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
264	C₂²⋊D₅₃	—	2	4	no	—
265	C₂²⋊D₅₃	—	2	4	no	—
266	C₂²⋊D₅₃	—	2	4	no	—
267	C₂²⋊D₅₃	—	2	2	no	—
268	C₂²⋊D₅₃	—	2	2	no	—
269	C₂²⋊D₅₃	—	2	4	no	—
270	C₂²⋊D₅₃	—	4	2	no	—
271	C₂²⋊D₅₃	—	4	2	no	—
272	C₂²⋊D₅₃	—	4	2	no	—
273	C₂²⋊D₅₃	—	4	2	no	—
274	C₂×Dic₅₃	—	2	4	no	—
275	C₂×Dic₅₃	—	4	2	no	—
276	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₅₃	C₂⁴	1	2	yes	—
278	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₅₃	C₂⁴	1	2	yes	—
280	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
284	D₂₁₂	—	2	4	no	—
285	D₂₁₂	—	2	4	no	—
286	D₂₁₂	—	2	2	no	—
287	D₂₁₂	—	2	2	no	—
288	D₂₁₂	—	4	2	no	—
289	D₂₁₂	#41	1	4	yes	complemented
290	C₄×D₅₃	—	2	2	no	—
291	C₄×D₅₃	—	2	2	no	—
292	C₄×D₅₃	—	2	2	no	—
293	C₄×D₅₃	—	2	2	no	—
294	C₄×D₅₃	—	2	4	no	—
295	C₄×D₅₃	—	4	2	no	—
296	C₄×D₅₃	—	4	2	no	—
297	C₄×D₅₃	—	4	2	no	—
298	C₄×D₅₃	—	4	2	no	—
299	C₄×D₅₃	—	4	2	no	—
300	C₄×D₅₃	—	4	2	no	—
301	Dic₁₀₆	—	2	2	no	—
302	Dic₁₀₆	—	4	2	no	—
303	C₂²×C₅₃	—	2	2	no	—
304	C₂²×C₅₃	—	2	2	no	—
305	C₂²×C₅₃	—	2	1	no	—
306	C₂²×C₅₃	—	2	2	no	—
307	C₂²×C₅₃	—	2	2	no	—
308	C₂²×C₅₃	—	2	2	no	—
309	C₂²×C₅₃	—	2	1	no	—
310	C₂²×C₅₃	—	2	1	no	—
311	C₂²×C₅₃	—	2	2	no	—
312	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
313	C₂×D₅₃	—	2	1	no	—
314	C₂×D₅₃	—	2	1	no	—
315	C₂×D₅₃	—	2	2	no	—
316	C₂×D₅₃	—	2	2	no	—
317	C₂×D₅₃	—	2	1	no	—
318	C₂×D₅₃	—	2	2	no	—
319	C₂×D₅₃	—	2	2	no	—
320	C₂×D₅₃	—	2	2	no	—
321	C₂×D₅₃	—	2	1	no	—
322	C₂×D₅₃	—	2	1	no	—
323	C₂×D₅₃	—	4	8	no	—
324	C₂×D₅₃	—	8	4	no	—
325	C₂×D₅₃	—	8	4	no	—
326	C₂×D₅₃	C₂×#41	1	4	yes	—
327	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	—
328	C₄×C₅₃	—	2	1	no	—
329	C₄×C₅₃	—	2	1	no	—
330	C₄×C₅₃	—	2	2	no	—
331	C₄×C₅₃	—	2	1	no	—
332	C₄×C₅₃	—	2	1	no	—
333	C₄×C₅₃	—	2	2	no	—
334	C₄×C₅₃	—	2	1	no	—
335	C₄×C₅₃	C₂×#41	1	2	yes	—
336	Dic₅₃	—	2	1	no	—
337	Dic₅₃	—	2	1	no	—
338	Dic₅₃	—	2	1	no	—
339	Dic₅₃	—	2	1	no	—
340	Dic₅₃	—	2	2	no	—
341	Dic₅₃	—	2	2	no	—
342	Dic₅₃	—	2	1	no	—
343	Dic₅₃	H(5,𝔽₂)	1	2	yes	—
344	#3519	—	53	1	no	maximal, Sylow
345	C₂×C₅₃	—	4	2	no	—
346	C₂×C₅₃	—	4	1	no	—
347	C₂×C₅₃	—	4	2	no	—
348	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
349	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
350	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
351	D₅₃	—	2	2	no	—
352	D₅₃	—	2	4	no	—
353	D₅₃	—	4	2	no	—
354	D₅₃	—	4	1	no	—
355	#555	—	53	1	no	—
356	#554	—	53	1	no	—
357	#553	—	53	1	no	—
358	#553	—	53	2	no	—
359	#553	—	53	1	no	—
360	#550	—	53	1	no	—
361	#546	—	53	2	no	—
362	#546	—	53	2	no	—
363	#546	—	53	2	no	—
364	D₄²	—	53	1	no	—
365	D₄²	—	53	1	no	—
366	D₄²	—	53	1	no	—
367	#540	—	53	1	no	—
368	#540	D₅₃	1	1	yes	characteristic, complemented
369	#538	—	53	2	no	—
370	#538	—	53	2	no	—
371	#532	—	53	1	no	—
372	#529	—	53	1	no	—
373	#525	—	53	2	no	—
374	C₂×#121	—	53	2	no	—
375	#518	—	53	1	no	—
376	#518	—	53	1	no	—
377	C₂×C₄×D₄	—	53	1	no	—
378	C₅₃	#3519	1	1	yes	characteristic, complemented, Sylow
379	C₂×#41	—	53	2	no	—
380	C₂×#41	—	53	2	no	—
381	C₂²×D₄	—	53	1	no	—
382	C₂²×D₄	—	53	1	no	—
383	C₂²×D₄	—	53	2	no	—
384	C₂²×D₄	—	53	2	no	—
385	C₂²×D₄	—	53	2	no	—
386	C₂²×D₄	—	53	1	no	—
387	C₂³×C₄	—	53	2	no	—
388	C₄⋊Q₈	—	53	1	no	—
389	#127	—	53	1	no	—
390	#127	—	53	1	no	—
391	#127	C₂×D₅₃	1	1	yes	characteristic, complemented
392	#126	—	53	1	no	—
393	#126	—	53	2	no	—
394	#126	—	53	1	no	—
395	#126	—	53	2	no	—
396	#125	—	53	1	no	—
397	#125	—	53	1	no	—
398	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
399	#124	—	53	2	no	—
400	#124	—	53	1	no	—
401	#124	—	53	2	no	—
402	#124	—	53	2	no	—
403	#123	—	53	2	no	—
404	#123	—	53	2	no	—
405	#123	—	53	1	no	—
406	#123	—	53	2	no	—
407	#123	—	53	1	no	—
408	#123	—	53	2	no	—
409	#123	C₂×D₅₃	1	2	yes	complemented
410	#123	C₂×D₅₃	1	2	yes	complemented
411	C₂²⋊Q₈	—	53	1	no	—
412	C₂²⋊Q₈	—	53	2	no	—
413	C₂²⋊Q₈	—	53	2	no	—
414	C₂²⋊Q₈	—	53	2	no	—
415	#121	—	53	2	no	—
416	#121	—	53	2	no	—
417	#121	—	53	2	no	—
418	#121	—	53	1	no	—
419	#121	—	53	2	no	—
420	#121	—	53	2	no	—
421	#121	—	53	2	no	—
422	#121	—	53	1	no	—
423	#121	—	53	2	no	—
424	#121	—	53	2	no	—
425	#121	—	53	1	no	—
426	#121	—	53	1	no	—
427	#121	—	53	1	no	—
428	#121	—	53	2	no	—
429	#121	—	53	2	no	—
430	#121	—	53	2	no	—
431	#121	—	53	2	no	—
432	#121	C₂×D₅₃	1	2	yes	complemented
433	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
434	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
435	#121	C₂×D₅₃	1	2	yes	complemented
436	#120	—	53	2	no	—
437	#120	—	53	2	no	—
438	#120	—	53	2	no	—
439	#120	—	53	2	no	—
440	#120	—	53	2	no	—
441	#120	—	53	2	no	—
442	C₄×Q₈	—	53	1	no	—
443	C₄×D₄	—	53	1	no	—
444	C₄×D₄	—	53	1	no	—
445	C₄×D₄	—	53	2	no	—
446	C₄×D₄	—	53	2	no	—
447	C₄×D₄	—	53	1	no	—
448	C₄×D₄	—	53	1	no	—
449	C₄×D₄	—	53	2	no	—
450	C₄×D₄	—	53	1	no	—
451	C₄×D₄	—	53	2	no	—
452	C₄×D₄	—	53	1	no	—
453	C₄×D₄	—	53	2	no	—
454	C₄×D₄	—	53	2	no	—
455	C₄×D₄	—	53	2	no	—
456	C₄×D₄	—	53	2	no	—
457	C₄×D₄	—	53	2	no	—
458	C₄×D₄	—	53	1	no	—
459	C₄×D₄	—	53	1	no	—
460	C₄×D₄	—	53	1	no	—
461	C₄×D₄	—	53	1	no	—
462	C₄×D₄	—	53	1	no	—
463	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
464	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
465	#117	—	53	1	no	—
466	#117	—	53	1	no	—
467	#117	—	53	2	no	—
468	#117	—	53	1	no	—
469	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
470	C₂×C₄⋊C₄	—	53	1	no	—
471	C₂×C₄⋊C₄	—	53	2	no	—
472	C₂×C₂²⋊C₄	—	53	2	no	—
473	C₂×C₂²⋊C₄	—	53	2	no	—
474	C₂×C₂²⋊C₄	—	53	2	no	—
475	C₂×C₂²⋊C₄	—	53	2	no	—
476	C₂×C₂²⋊C₄	—	53	2	no	—
477	C₂×C₄²	—	53	1	no	—
478	C₂⁴	—	53	2	no	—
479	C₂⁴	—	53	2	no	—
480	C₂⁴	—	53	2	no	—
481	#41	—	212	4	no	—
482	#41	—	212	4	no	—
483	C₂×Q₈	—	53	1	no	—
484	C₂×Q₈	—	53	2	no	—
485	C₂×D₄	—	53	2	no	—
486	C₂×D₄	—	53	2	no	—
487	C₂×D₄	—	53	2	no	—
488	C₂×D₄	—	53	1	no	—
489	C₂×D₄	—	53	1	no	—
490	C₂×D₄	—	53	2	no	—
491	C₂×D₄	—	53	2	no	—
492	C₂×D₄	—	53	2	no	—
493	C₂×D₄	—	53	2	no	—
494	C₂×D₄	—	53	2	no	—
495	C₂×D₄	—	53	1	no	—
496	C₂×D₄	—	53	2	no	—
497	C₂×D₄	—	53	1	no	—
498	C₂×D₄	—	53	2	no	—
499	C₂×D₄	—	53	1	no	—
500	C₂×D₄	—	53	2	no	—
501	C₂×D₄	—	106	4	no	—
502	C₂×D₄	—	106	4	no	—
503	C₂×D₄	—	106	4	no	—
504	C₂×D₄	—	212	4	no	—
505	C₂×D₄	—	212	4	no	—
506	C₂×D₄	—	212	4	no	—
507	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
508	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
509	C₂×D₄	C₂²×D₅₃	1	2	yes	—
510	C₂×D₄	C₂²×D₅₃	1	2	yes	—
511	C₂×D₄	C₂²×D₅₃	1	2	yes	—
512	C₂×D₄	C₂²×D₅₃	1	2	yes	—
513	C₂²×C₄	—	53	2	no	—
514	C₂²×C₄	—	53	2	no	—
515	C₂²×C₄	—	53	1	no	—
516	C₂²×C₄	—	53	1	no	—
517	C₂²×C₄	—	53	1	no	—
518	C₂²×C₄	—	53	2	no	—
519	C₂²×C₄	—	53	1	no	—
520	C₂²×C₄	—	53	2	no	—
521	C₂²×C₄	—	53	2	no	—
522	C₂²×C₄	—	53	2	no	—
523	C₂²×C₄	—	53	2	no	—
524	C₂²×C₄	—	53	2	no	—
525	C₂²×C₄	—	53	2	no	—
526	C₂²×C₄	—	212	4	no	—
527	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
528	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
529	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
530	C₄⋊C₄	—	53	1	no	—
531	C₄⋊C₄	—	53	1	no	—
532	C₄⋊C₄	—	53	2	no	—
533	C₄⋊C₄	—	53	2	no	—
534	C₄⋊C₄	—	53	2	no	—
535	C₄⋊C₄	—	53	1	no	—
536	C₄⋊C₄	—	53	1	no	—
537	C₄⋊C₄	—	53	1	no	—
538	C₄⋊C₄	—	53	1	no	—
539	C₄⋊C₄	—	53	1	no	—
540	C₄⋊C₄	—	53	1	no	—
541	C₄⋊C₄	—	53	2	no	—
542	C₄⋊C₄	—	53	1	no	—
543	C₄⋊C₄	—	53	1	no	—
544	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
546	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
548	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
549	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
550	C₂²⋊C₄	—	53	2	no	—
551	C₂²⋊C₄	—	53	2	no	—
552	C₂²⋊C₄	—	53	2	no	—
553	C₂²⋊C₄	—	53	2	no	—
554	C₂²⋊C₄	—	53	1	no	—
555	C₂²⋊C₄	—	53	1	no	—
556	C₂²⋊C₄	—	53	2	no	—
557	C₂²⋊C₄	—	53	2	no	—
558	C₂²⋊C₄	—	53	1	no	—
559	C₂²⋊C₄	—	53	2	no	—
560	C₂²⋊C₄	—	53	1	no	—
561	C₂²⋊C₄	—	53	2	no	—
562	C₂²⋊C₄	—	53	2	no	—
563	C₂²⋊C₄	—	53	2	no	—
564	C₂²⋊C₄	—	53	2	no	—
565	C₂²⋊C₄	—	53	2	no	—
566	C₂²⋊C₄	—	53	1	no	—
567	C₂²⋊C₄	—	53	1	no	—
568	C₂²⋊C₄	—	53	1	no	—
569	C₂²⋊C₄	—	53	1	no	—
570	C₂²⋊C₄	—	53	2	no	—
571	C₂²⋊C₄	—	53	2	no	—
572	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
573	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
574	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
576	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
577	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
578	C₄²	—	53	1	no	—
579	C₄²	—	53	1	no	—
580	C₄²	—	53	1	no	—
581	C₄²	—	53	2	no	—
582	C₄²	—	53	2	no	—
583	C₄²	—	53	1	no	—
584	C₄²	C₂²×D₅₃	1	1	yes	characteristic
585	C₄²	C₂²×D₅₃	1	1	yes	characteristic
586	C₂³	—	53	2	no	—
587	C₂³	—	53	1	no	—
588	C₂³	—	53	1	no	—
589	C₂³	—	53	2	no	—
590	C₂³	—	106	4	no	—
591	C₂³	—	106	4	no	—
592	C₂³	—	106	4	no	—
593	C₂³	—	106	4	no	—
594	C₂³	—	212	2	no	—
595	C₂³	—	212	2	no	—
596	C₂³	—	212	2	no	—
597	C₂³	—	212	2	no	—
598	C₂³	—	212	2	no	—
599	C₂³	C₂³×D₅₃	1	1	yes	characteristic
600	C₂³	C₂³×D₅₃	1	2	yes	—
601	C₂³	C₂³×D₅₃	1	2	yes	—
602	Q₈	—	106	2	no	—
603	Q₈	—	212	2	no	—
604	D₄	—	2	2	no	—
605	D₄	—	2	2	no	—
606	D₄	—	4	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	4	2	no	—
609	D₄	—	4	2	no	—
610	D₄	—	53	4	no	—
611	D₄	—	106	4	no	—
612	D₄	—	106	2	no	—
613	D₄	—	106	4	no	—
614	D₄	—	106	2	no	—
615	D₄	—	106	4	no	—
616	D₄	—	106	4	no	—
617	D₄	—	106	4	no	—
618	D₄	—	106	2	no	—
619	D₄	—	106	4	no	—
620	D₄	—	106	2	no	—
621	D₄	—	212	2	no	—
622	D₄	—	212	2	no	—
623	D₄	—	212	2	no	—
624	D₄	—	212	2	no	—
625	D₄	—	212	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	53	1	no	—
630	C₂×C₄	—	53	1	no	—
631	C₂×C₄	—	53	1	no	—
632	C₂×C₄	—	53	2	no	—
633	C₂×C₄	—	53	1	no	—
634	C₂×C₄	—	53	2	no	—
635	C₂×C₄	—	53	1	no	—
636	C₂×C₄	—	53	1	no	—
637	C₂×C₄	—	106	2	no	—
638	C₂×C₄	—	106	4	no	—
639	C₂×C₄	—	106	2	no	—
640	C₂×C₄	—	106	4	no	—
641	C₂×C₄	—	106	2	no	—
642	C₂×C₄	—	106	2	no	—
643	C₂×C₄	—	212	2	no	—
644	C₂×C₄	—	212	2	no	—
645	C₂×C₄	—	212	2	no	—
646	C₂×C₄	—	212	2	no	—
647	C₂×C₄	—	212	2	no	—
648	C₂×C₄	—	212	2	no	—
649	C₂×C₄	—	212	2	no	—
650	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
653	C₂×C₄	C₂³×D₅₃	1	2	yes	—
654	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
655	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
656	C₂×C₄	C₂³×D₅₃	1	2	yes	—
657	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	53	4	no	—
668	C₂²	—	53	2	no	—
669	C₂²	—	106	1	no	—
670	C₂²	—	106	1	no	—
671	C₂²	—	106	2	no	—
672	C₂²	—	106	2	no	—
673	C₂²	—	106	1	no	—
674	C₂²	—	106	2	no	—
675	C₂²	—	106	2	no	—
676	C₂²	—	106	2	no	—
677	C₂²	—	106	1	no	—
678	C₂²	—	106	1	no	—
679	C₂²	—	424	4	no	—
680	C₂²	—	424	4	no	—
681	C₂²	—	212	8	no	—
682	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	1	no	—
689	C₄	—	2	1	no	—
690	C₄	—	53	2	no	—
691	C₄	—	106	1	no	—
692	C₄	—	106	1	no	—
693	C₄	—	106	2	no	—
694	C₄	—	106	1	no	—
695	C₄	—	106	1	no	—
696	C₄	—	106	2	no	—
697	C₄	—	106	1	no	—
698	C₄	#41×D₅₃	1	2	yes	—
699	C₂	—	4	1	no	—
700	C₂	—	4	2	no	—
701	C₂	—	4	2	no	—
702	C₂	—	106	4	no	—
703	C₂	—	106	2	no	—
704	C₂	—	212	1	no	—
705	C₂	—	212	2	no	—
706	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
707	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
708	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#540	C₂
hypercenter	#540	D₅₃
hypocenter	C₅₃	#3519
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #16811337	C₂	semidirect
2. #16811329	C₂	semidirect
3. #16811326	C₂	semidirect
4. #16811320	C₂	semidirect
5. #16811318	C₂	semidirect
6. #16811293	C₂	semidirect
7. #16811270	C₂	semidirect
8. #16811265	C₂	semidirect
9. #16811262	C₂	semidirect
10. #16811258	C₂	semidirect
11. #16811257	C₂	semidirect
12. #16811257	C₂	semidirect
13. #16811224	C₂	semidirect
14. #16811209	C₂	semidirect
15. #16811205	C₂	semidirect
16. #16811170	C₂	semidirect
17. #16811151	C₂	semidirect
18. #16811131	C₂	semidirect
19. #121×D₅₃	C₂	semidirect
20. #16811097	C₂	semidirect
21. #16811095	C₂	semidirect
22. C₄×D₄×D₅₃	C₂	semidirect
23. C₅₃×#540	C₂	semidirect
24. C₂×#11719945	C₂²	semidirect
25. C₂×#11719947	C₂²	semidirect
29. C₂×D₄×D₅₃	C₂²	semidirect
30. C₂×D₄×D₅₃	C₂²	semidirect
31. C₂×D₄×D₅₃	C₂²	semidirect
32. C₂²×C₄×D₅₃	C₂²	semidirect
33. #13133216	C₂²	semidirect
34. #13133213	C₂²	semidirect
35. #13133213	C₂²	semidirect
36. #13133212	C₂²	semidirect
37. #13133212	C₂²	semidirect
38. #13133210	C₂²	semidirect
39. #13133210	C₂²	semidirect
40. #13133208	C₂²	semidirect
41. #13133207	C₂²	semidirect
42. #13133204	C₂²	semidirect
43. #13133203	C₂²	semidirect
44. #13133203	C₂²	semidirect
45. #13133203	C₂²	semidirect
46. #13133202	C₂²	semidirect
47. #13133202	C₂²	semidirect
48. #13133200	C₂²	semidirect
49. #13133199	C₂²	semidirect
50. #13133199	C₂²	semidirect
51. #13133198	C₂²	semidirect
52. #13133197	C₂²	semidirect
53. #13133195	C₂²	semidirect
54. #13133195	C₂²	semidirect
55. #13133195	C₂²	semidirect
56. #13133192	C₂²	semidirect
57. #13133192	C₂²	semidirect
58. #13133192	C₂²	semidirect
59. #13133191	C₂²	semidirect
61. #13133190	C₂²	semidirect
62. #13133190	C₂²	semidirect
63. #13133190	C₂²	semidirect
64. #13133190	C₂²	semidirect
65. #13133189	C₂²	semidirect
66. #13133189	C₂²	semidirect
67. #13133189	C₂²	semidirect
68. #13133188	C₂²	semidirect
69. #13133188	C₂²	semidirect
70. #13133188	C₂²	semidirect
71. #13133188	C₂²	semidirect
72. #13133188	C₂²	semidirect
73. #13133187	C₂²	semidirect
74. #13133187	C₂²	semidirect
75. #13133185	C₂²	semidirect
76. #13133185	C₂²	semidirect
77. #13133185	C₂²	semidirect
78. #13133185	C₂²	semidirect
79. C₄×Dic₁₀₆	C₂²	semidirect
82. C₄×D₂₁₂	C₂²	semidirect
83. C₄×D₂₁₂	C₂²	semidirect
84. C₄×D₂₁₂	C₂²	semidirect
85. D₄×Dic₅₃	C₂²	semidirect
86. D₄×Dic₅₃	C₂²	semidirect
89. #13133179	C₂²	semidirect
90. #13133179	C₂²	semidirect
91. #13133179	C₂²	semidirect
92. C₄×C₂²⋊D₅₃	C₂²	semidirect
93. C₄×C₂²⋊D₅₃	C₂²	semidirect
94. C₄×C₂²⋊D₅₃	C₂²	semidirect
95. C₄×C₂²⋊D₅₃	C₂²	semidirect
96. C₄×C₂²⋊D₅₃	C₂²	semidirect
97. #13133177	C₂²	semidirect
98. #13133177	C₂²	semidirect
99. #13133177	C₂²	semidirect
100. #13133176	C₂²	semidirect
101. #13133175	C₂²	semidirect
102. #13133174	C₂²	semidirect
103. #13133173	C₂²	semidirect
104. C₄⋊C₄×D₅₃	C₂²	semidirect
105. C₄⋊C₄×D₅₃	C₂²	semidirect
106. C₂×#11719921	C₂²	semidirect
107. C₂²⋊C₄×D₅₃	C₂²	semidirect
108. C₂²⋊C₄×D₅₃	C₂²	semidirect
109. C₂²⋊C₄×D₅₃	C₂²	semidirect
110. C₂²⋊C₄×D₅₃	C₂²	semidirect
111. C₄²×D₅₃	C₂²	semidirect
112. #127×C₅₃	C₂²	semidirect
113. #125×C₅₃	C₂²	semidirect
114. #123×C₅₃	C₂²	semidirect
115. #123×C₅₃	C₂²	semidirect
116. #121×C₅₃	C₂²	semidirect
117. #121×C₅₃	C₂²	semidirect
118. #121×C₅₃	C₂²	semidirect
119. #121×C₅₃	C₂²	semidirect
120. C₄×D₄×C₅₃	C₂²	semidirect
121. C₄×D₄×C₅₃	C₂²	semidirect
122. #117×C₅₃	C₂²	semidirect
289. D₂₁₂	#41	semidirect
368. #540	D₅₃	semidirect
378. C₅₃	#3519	semidirect
391. #127	C₂×D₅₃	semidirect
398. #125	C₂×D₅₃	semidirect
409. #123	C₂×D₅₃	semidirect
410. #123	C₂×D₅₃	semidirect
432. #121	C₂×D₅₃	semidirect
433. #121	C₂×D₅₃	semidirect
434. #121	C₂×D₅₃	semidirect
435. #121	C₂×D₅₃	semidirect
463. C₄×D₄	C₂×D₅₃	semidirect
464. C₄×D₄	C₂×D₅₃	semidirect
469. #117	C₂×D₅₃	semidirect