Subgroups — #20288322

Order 6784.

1242 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811356	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811329	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811328	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811318	C₂	1	2	yes	maximal, complemented
5	#16811317	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811302	C₂	1	2	yes	maximal, complemented
7	#16811298	C₂	1	2	yes	maximal, complemented
8	#16811270	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811269	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811262	C₂	1	2	yes	maximal, complemented
11	#16811257	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811168	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811158	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811156	C₂	1	2	yes	maximal, complemented
15	#16811154	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811133	C₂	1	2	yes	maximal, complemented
17	#16811131	C₂	1	2	yes	maximal, complemented
18	#16811091	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#11719947	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13133179	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11719945	C₂²	1	1	yes	characteristic
25	C₂×#11719947	C₂²	1	1	yes	characteristic
26	C₂×#11719947	C₂²	1	2	yes	complemented
27	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₅₃	C₂²	1	2	yes	—
30	C₂²×C₄×D₅₃	C₂²	1	2	yes	complemented
31	C₂²×C₄×D₅₃	C₂²	1	2	yes	complemented
32	#13133216	C₂²	1	1	yes	characteristic, complemented
33	#13133213	C₂²	1	1	yes	characteristic
34	#13133212	C₂²	1	2	yes	complemented
35	#13133211	C₂²	1	2	yes	complemented
36	#13133210	C₂²	1	2	yes	complemented
37	#13133208	C₂²	1	1	yes	characteristic, complemented
38	#13133207	C₂²	1	2	yes	complemented
39	#13133205	C₂²	1	1	yes	characteristic, complemented
40	#13133204	C₂²	1	1	yes	characteristic, complemented
41	#13133203	C₂²	1	2	yes	complemented
42	#13133203	C₂²	1	2	yes	complemented
43	#13133202	C₂²	1	2	yes	complemented
44	#13133202	C₂²	1	2	yes	complemented
45	#13133200	C₂²	1	2	yes	complemented
46	#13133199	C₂²	1	2	yes	complemented
47	#13133199	C₂²	1	2	yes	complemented
48	#13133199	C₂²	1	2	yes	complemented
49	#13133198	C₂²	1	2	yes	complemented
50	#13133197	C₂²	1	1	yes	characteristic, complemented
51	#13133197	C₂²	1	2	yes	complemented
52	#13133196	C₂²	1	1	yes	characteristic, complemented
53	#13133196	C₂²	1	2	yes	complemented
54	#13133195	C₂²	1	2	yes	complemented
55	#13133195	C₂²	1	2	yes	complemented
56	#13133195	C₂²	1	2	yes	complemented
57	#13133192	C₂²	1	1	yes	characteristic
58	#13133191	C₂²	1	1	yes	characteristic, complemented
59	#13133190	C₂²	1	2	yes	—
60	#13133190	C₂²	1	2	yes	complemented
61	#13133190	C₂²	1	2	yes	complemented
62	#13133189	C₂²	1	2	yes	complemented
63	#13133188	C₂²	1	2	yes	complemented
64	#13133187	C₂²	1	2	yes	—
65	#13133185	C₂²	1	2	yes	—
66	#13133185	C₂²	1	2	yes	complemented
67	#13133185	C₂²	1	2	yes	complemented
68	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
69	#13133182	C₂²	1	1	yes	characteristic, complemented
70	#13133182	C₂²	1	1	yes	characteristic, complemented
71	#13133182	C₂²	1	1	yes	characteristic, complemented
72	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
73	C₄×D₂₁₂	C₂²	1	2	yes	complemented
74	D₄×Dic₅₃	C₂²	1	2	yes	complemented
75	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
76	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
77	#13133179	C₂²	1	1	yes	characteristic
78	#13133179	C₂²	1	1	yes	characteristic
79	#13133179	C₂²	1	1	yes	characteristic
80	#13133179	C₂²	1	2	yes	complemented
81	#13133179	C₂²	1	1	yes	characteristic, complemented
82	#13133179	C₂²	1	2	yes	complemented
83	#13133179	C₂²	1	2	yes	complemented
84	#13133179	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
86	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
89	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
90	#13133177	C₂²	1	1	yes	characteristic
91	#13133177	C₂²	1	2	yes	complemented
92	#13133177	C₂²	1	2	yes	complemented
93	#13133177	C₂²	1	2	yes	complemented
94	#13133177	C₂²	1	1	yes	characteristic, complemented
95	#13133177	C₂²	1	2	yes	complemented
96	#13133175	C₂²	1	1	yes	characteristic, complemented
97	#13133175	C₂²	1	2	yes	complemented
98	#13133174	C₂²	1	2	yes	complemented
99	#13133173	C₂²	1	1	yes	characteristic, complemented
100	#13133173	C₂²	1	1	yes	characteristic, complemented
101	#13133173	C₂²	1	2	yes	complemented
102	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
103	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
104	C₂×#11719921	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
108	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
110	C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₅₃	C₂²	1	2	yes	complemented
112	#126×C₅₃	C₂²	1	2	yes	complemented
113	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
114	#123×C₅₃	C₂²	1	2	yes	complemented
115	#121×C₅₃	C₂²	1	1	yes	characteristic
116	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	#121×C₅₃	C₂²	1	2	yes	complemented
118	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
120	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₅₃	C₂³	1	2	yes	—
124	C₂³×D₅₃	C₂³	1	2	yes	—
125	C₂×D₄×C₅₃	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	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
132	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
140	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
141	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
142	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
143	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
144	C₂²×Dic₅₃	C₂³	1	2	yes	—
145	#11719947	—	2	4	no	—
146	#11719947	—	4	4	no	—
147	D₄×D₅₃	—	2	8	no	—
148	D₄×D₅₃	—	2	4	no	—
149	#11719945	—	2	4	no	—
150	C₂×D₂₁₂	—	2	4	no	—
151	C₂×D₂₁₂	C₂³	1	2	yes	—
152	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
153	C₂×D₂₁₂	C₂³	1	2	yes	—
154	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₅₃	—	4	4	no	—
156	C₂×C₄×D₅₃	—	4	4	no	—
157	C₂×C₄×D₅₃	C₂³	1	2	yes	—
158	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₅₃	C₂³	1	2	yes	—
160	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₅₃	C₂³	1	2	yes	—
163	C₂×C₄×D₅₃	C₂³	1	2	yes	—
164	C₂×C₄×D₅₃	C₂³	1	2	yes	—
165	C₂×C₄×D₅₃	C₂³	1	2	yes	—
166	C₂×C₄×D₅₃	C₂³	1	2	yes	—
167	C₂×C₄×D₅₃	C₂³	1	2	yes	—
168	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
169	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
170	C₂×Dic₁₀₆	C₂³	1	2	yes	—
171	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
174	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
176	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
177	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
180	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
182	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
183	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₄²×C₅₃	C₂³	1	2	yes	—
185	C₄²×C₅₃	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
187	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
188	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
190	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
191	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
192	#11719921	C₂³	1	1	yes	characteristic
193	#11719921	C₂³	1	2	yes	—
194	#11719921	C₂³	1	2	yes	—
195	#11719921	C₂³	1	2	yes	—
196	#11719921	C₂³	1	2	yes	—
197	#11719921	C₂³	1	2	yes	—
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	1	yes	characteristic
203	#11719921	C₂³	1	2	yes	—
204	#11719921	C₂³	1	2	yes	—
205	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₅₃	C₂³	1	2	yes	—
207	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₅₃	C₂³	1	2	yes	—
209	#11719919	C₂³	1	1	yes	characteristic
210	#11719919	C₂³	1	2	yes	—
211	#11719919	C₂³	1	2	yes	—
212	#11719919	C₂³	1	1	yes	characteristic
213	#11719919	C₂³	1	1	yes	characteristic
214	#11719919	C₂³	1	1	yes	characteristic
215	#11719919	C₂³	1	2	yes	—
216	#11719919	C₂³	1	2	yes	—
217	#11719919	C₂³	1	2	yes	—
218	#11719919	C₂³	1	2	yes	—
219	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₅₃	C₂³	1	2	yes	—
223	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
229	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
230	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
231	C₂³×C₅₃	C₂⁴	1	2	yes	—
232	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₅₃	—	2	4	no	—
234	C₂²×D₅₃	—	2	4	no	—
235	C₂²×D₅₃	—	2	4	no	—
236	C₂²×D₅₃	—	2	4	no	—
237	C₂²×D₅₃	—	4	2	no	—
238	C₂²×D₅₃	—	4	2	no	—
239	C₂²×D₅₃	C₂⁴	1	2	yes	—
240	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
241	C₂²×D₅₃	C₂⁴	1	2	yes	—
242	D₄×C₅₃	—	2	4	no	—
243	D₄×C₅₃	—	2	2	no	—
244	D₄×C₅₃	—	2	2	no	—
245	D₄×C₅₃	—	4	2	no	—
246	C₂×C₄×C₅₃	—	2	2	no	—
247	C₂×C₄×C₅₃	—	2	2	no	—
248	C₂×C₄×C₅₃	—	4	2	no	—
249	C₂×C₄×C₅₃	—	4	2	no	—
250	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
256	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₅₃	—	2	4	no	—
259	C₂²⋊D₅₃	—	2	4	no	—
260	C₂²⋊D₅₃	—	2	2	no	—
261	C₂²⋊D₅₃	—	2	4	no	—
262	C₂²⋊D₅₃	—	4	2	no	—
263	C₂²⋊D₅₃	—	4	2	no	—
264	C₂²⋊D₅₃	#41	1	4	yes	complemented
265	C₂×Dic₅₃	—	2	2	no	—
266	C₂×Dic₅₃	—	2	2	no	—
267	C₂×Dic₅₃	—	2	2	no	—
268	C₂×Dic₅₃	—	2	4	no	—
269	C₂×Dic₅₃	—	2	2	no	—
270	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₅₃	C₂⁴	1	2	yes	—
272	C₂×Dic₅₃	C₂⁴	1	2	yes	—
273	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
279	D₂₁₂	—	2	4	no	—
280	D₂₁₂	—	2	4	no	—
281	D₂₁₂	—	2	2	no	—
282	D₂₁₂	#41	1	4	yes	complemented
283	C₄×D₅₃	—	2	4	no	—
284	C₄×D₅₃	—	2	2	no	—
285	C₄×D₅₃	—	2	2	no	—
286	C₄×D₅₃	—	2	4	no	—
287	C₄×D₅₃	—	2	2	no	—
288	C₄×D₅₃	—	2	4	no	—
289	C₄×D₅₃	—	2	4	no	—
290	C₄×D₅₃	—	4	2	no	—
291	C₄×D₅₃	—	4	2	no	—
292	C₄×D₅₃	—	4	2	no	—
293	C₄×D₅₃	—	4	2	no	—
294	Dic₁₀₆	—	2	2	no	—
295	Dic₁₀₆	—	2	2	no	—
296	Dic₁₀₆	—	4	2	no	—
297	C₂²×C₅₃	—	2	1	no	—
298	C₂²×C₅₃	—	2	1	no	—
299	C₂²×C₅₃	—	2	1	no	—
300	C₂²×C₅₃	—	2	1	no	—
301	C₂²×C₅₃	—	2	2	no	—
302	C₂²×C₅₃	—	2	2	no	—
303	C₂²×C₅₃	—	2	1	no	—
304	C₂²×C₅₃	—	2	2	no	—
305	C₂²×C₅₃	C₂×#41	1	2	yes	—
306	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
307	C₂×D₅₃	—	2	1	no	—
308	C₂×D₅₃	—	2	2	no	—
309	C₂×D₅₃	—	2	1	no	—
310	C₂×D₅₃	—	2	2	no	—
311	C₂×D₅₃	—	2	2	no	—
312	C₂×D₅₃	—	2	2	no	—
313	C₂×D₅₃	—	2	2	no	—
314	C₂×D₅₃	—	4	8	no	—
315	C₂×D₅₃	—	4	8	no	—
316	C₂×D₅₃	C₂×#41	1	2	yes	—
317	C₂×D₅₃	C₂×#41	1	4	yes	—
318	C₄×C₅₃	—	2	1	no	—
319	C₄×C₅₃	—	2	1	no	—
320	C₄×C₅₃	—	2	2	no	—
321	C₄×C₅₃	—	2	1	no	—
322	C₄×C₅₃	—	2	2	no	—
323	C₄×C₅₃	—	2	1	no	—
324	C₄×C₅₃	—	2	2	no	—
325	C₄×C₅₃	C₂×#41	1	2	yes	—
326	Dic₅₃	—	2	2	no	—
327	Dic₅₃	—	2	1	no	—
328	Dic₅₃	—	2	1	no	—
329	Dic₅₃	—	2	1	no	—
330	Dic₅₃	—	2	1	no	—
331	Dic₅₃	—	2	2	no	—
332	Dic₅₃	—	2	1	no	—
333	Dic₅₃	C₂×#41	1	2	yes	—
334	Dic₅₃	H(5,𝔽₂)	1	2	yes	—
335	#3481	—	53	1	no	maximal, Sylow
336	C₂×C₅₃	—	2	2	no	—
337	C₂×C₅₃	—	4	2	no	—
338	C₂×C₅₃	—	4	1	no	—
339	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
340	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
341	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
342	D₅₃	—	2	2	no	—
343	D₅₃	—	2	4	no	—
344	D₅₃	—	4	2	no	—
345	#559	—	53	1	no	—
346	#554	—	53	1	no	—
347	#554	—	53	1	no	—
348	#553	—	53	2	no	—
349	#553	—	53	1	no	—
350	#553	D₅₃	1	1	yes	characteristic, complemented
351	#551	—	53	2	no	—
352	#551	—	53	2	no	—
353	#546	—	53	1	no	—
354	#546	—	53	2	no	—
355	#546	—	53	1	no	—
356	D₄²	—	53	1	no	—
357	#532	—	53	1	no	—
358	#529	—	53	2	no	—
359	#529	—	53	1	no	—
360	#529	—	53	1	no	—
361	#525	—	53	2	no	—
362	#525	—	53	2	no	—
363	C₄×#41	—	53	1	no	—
364	C₄×#41	—	53	1	no	—
365	C₂×C₄×D₄	—	53	2	no	—
366	C₂×C₄×D₄	—	53	1	no	—
367	C₂×C₄×D₄	—	53	1	no	—
368	C₅₃	#3481	1	1	yes	characteristic, complemented, Sylow
369	C₂×#41	—	53	1	no	—
370	C₂×#41	—	53	2	no	—
371	C₂×#41	—	53	1	no	—
372	C₂²×D₄	—	53	2	no	—
373	C₂²×D₄	—	53	1	no	—
374	C₂²×D₄	—	53	1	no	—
375	C₂³×C₄	—	53	2	no	—
376	C₂³×C₄	—	53	2	no	—
377	C₄⋊Q₈	—	53	1	no	—
378	#127	—	53	1	no	—
379	#126	—	53	2	no	—
380	#126	—	53	2	no	—
381	#126	—	53	2	no	—
382	#126	C₂×D₅₃	1	2	yes	complemented
383	#125	—	53	2	no	—
384	#125	—	53	1	no	—
385	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
386	#124	—	53	1	no	—
387	#124	—	53	2	no	—
388	#124	—	53	2	no	—
389	#124	—	53	1	no	—
390	#123	—	53	2	no	—
391	#123	—	53	2	no	—
392	#123	—	53	2	no	—
393	#123	—	53	2	no	—
394	#123	—	53	2	no	—
395	#123	—	53	2	no	—
396	#123	—	53	2	no	—
397	#123	C₂×D₅₃	1	2	yes	complemented
398	C₂²⋊Q₈	—	53	2	no	—
399	C₂²⋊Q₈	—	53	1	no	—
400	C₂²⋊Q₈	—	53	2	no	—
401	C₂²⋊Q₈	—	53	2	no	—
402	C₂²⋊Q₈	—	53	2	no	—
403	C₂²⋊Q₈	—	53	2	no	—
404	C₂²⋊Q₈	—	53	1	no	—
405	#121	—	53	2	no	—
406	#121	—	53	2	no	—
407	#121	—	53	1	no	—
408	#121	—	53	1	no	—
409	#121	—	53	2	no	—
410	#121	—	53	2	no	—
411	#121	—	53	2	no	—
412	#121	C₂×D₅₃	1	1	yes	characteristic
413	#121	C₂×D₅₃	1	2	yes	complemented
414	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
415	#120	—	53	2	no	—
416	#120	—	53	2	no	—
417	#120	—	53	2	no	—
418	#120	—	53	2	no	—
419	C₄×Q₈	—	53	1	no	—
420	C₄×Q₈	—	53	1	no	—
421	C₄×Q₈	—	53	1	no	—
422	C₄×Q₈	—	53	1	no	—
423	C₄×D₄	—	53	2	no	—
424	C₄×D₄	—	53	1	no	—
425	C₄×D₄	—	53	1	no	—
426	C₄×D₄	—	53	2	no	—
427	C₄×D₄	—	53	2	no	—
428	C₄×D₄	—	53	2	no	—
429	C₄×D₄	—	53	1	no	—
430	C₄×D₄	—	53	1	no	—
431	C₄×D₄	—	53	1	no	—
432	C₄×D₄	—	53	2	no	—
433	C₄×D₄	—	53	2	no	—
434	C₄×D₄	—	53	1	no	—
435	C₄×D₄	—	53	1	no	—
436	C₄×D₄	—	53	2	no	—
437	C₄×D₄	—	53	1	no	—
438	C₄×D₄	—	53	1	no	—
439	C₄×D₄	—	53	1	no	—
440	C₄×D₄	—	53	2	no	—
441	C₄×D₄	—	53	2	no	—
442	C₄×D₄	—	53	1	no	—
443	C₄×D₄	—	53	2	no	—
444	C₄×D₄	—	53	2	no	—
445	C₄×D₄	—	53	1	no	—
446	C₄×D₄	—	53	2	no	—
447	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
448	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
449	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
450	#117	—	53	1	no	—
451	#117	—	53	2	no	—
452	#117	—	53	1	no	—
453	#117	—	53	1	no	—
454	#117	—	53	2	no	—
455	#117	—	53	2	no	—
456	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
457	C₂×C₄⋊C₄	—	53	2	no	—
458	C₂×C₄⋊C₄	—	53	1	no	—
459	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
460	C₂×C₂²⋊C₄	—	53	2	no	—
461	C₂×C₂²⋊C₄	—	53	2	no	—
462	C₂×C₂²⋊C₄	—	53	2	no	—
463	C₂×C₂²⋊C₄	—	53	2	no	—
464	C₂×C₄²	—	53	1	no	—
465	C₂×C₄²	—	53	1	no	—
466	C₂×C₄²	—	53	1	no	—
467	C₂×C₄²	—	53	2	no	—
468	C₂⁴	—	53	2	no	—
469	C₂⁴	—	53	2	no	—
470	#41	—	106	4	no	—
471	#41	—	106	4	no	—
472	#41	—	212	4	no	—
473	C₂×Q₈	—	53	1	no	—
474	C₂×Q₈	—	53	1	no	—
475	C₂×Q₈	—	53	2	no	—
476	C₂×D₄	—	53	1	no	—
477	C₂×D₄	—	53	2	no	—
478	C₂×D₄	—	53	1	no	—
479	C₂×D₄	—	53	2	no	—
480	C₂×D₄	—	53	2	no	—
481	C₂×D₄	—	53	2	no	—
482	C₂×D₄	—	53	2	no	—
483	C₂×D₄	—	53	1	no	—
484	C₂×D₄	—	53	2	no	—
485	C₂×D₄	—	53	2	no	—
486	C₂×D₄	—	53	1	no	—
487	C₂×D₄	—	106	4	no	—
488	C₂×D₄	—	106	8	no	—
489	C₂×D₄	—	106	4	no	—
490	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
491	C₂×D₄	C₂²×D₅₃	1	2	yes	—
492	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
493	C₂×D₄	C₂²×D₅₃	1	2	yes	—
494	C₂²×C₄	—	53	1	no	—
495	C₂²×C₄	—	53	1	no	—
496	C₂²×C₄	—	53	1	no	—
497	C₂²×C₄	—	53	1	no	—
498	C₂²×C₄	—	53	2	no	—
499	C₂²×C₄	—	53	1	no	—
500	C₂²×C₄	—	53	2	no	—
501	C₂²×C₄	—	53	2	no	—
502	C₂²×C₄	—	53	1	no	—
503	C₂²×C₄	—	53	1	no	—
504	C₂²×C₄	—	53	2	no	—
505	C₂²×C₄	—	53	2	no	—
506	C₂²×C₄	—	53	2	no	—
507	C₂²×C₄	—	53	2	no	—
508	C₂²×C₄	—	53	2	no	—
509	C₂²×C₄	—	53	2	no	—
510	C₂²×C₄	—	212	4	no	—
511	C₂²×C₄	—	212	4	no	—
512	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
514	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
515	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
516	C₄⋊C₄	—	53	1	no	—
517	C₄⋊C₄	—	53	2	no	—
518	C₄⋊C₄	—	53	1	no	—
519	C₄⋊C₄	—	53	2	no	—
520	C₄⋊C₄	—	53	2	no	—
521	C₄⋊C₄	—	53	1	no	—
522	C₄⋊C₄	—	53	1	no	—
523	C₄⋊C₄	—	53	2	no	—
524	C₄⋊C₄	—	53	1	no	—
525	C₄⋊C₄	—	53	2	no	—
526	C₄⋊C₄	—	53	1	no	—
527	C₄⋊C₄	—	53	2	no	—
528	C₄⋊C₄	—	53	2	no	—
529	C₄⋊C₄	—	53	2	no	—
530	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
532	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
533	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
534	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
536	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
537	C₂²⋊C₄	—	53	2	no	—
538	C₂²⋊C₄	—	53	2	no	—
539	C₂²⋊C₄	—	53	2	no	—
540	C₂²⋊C₄	—	53	1	no	—
541	C₂²⋊C₄	—	53	1	no	—
542	C₂²⋊C₄	—	53	2	no	—
543	C₂²⋊C₄	—	53	2	no	—
544	C₂²⋊C₄	—	53	1	no	—
545	C₂²⋊C₄	—	53	2	no	—
546	C₂²⋊C₄	—	53	2	no	—
547	C₂²⋊C₄	—	53	2	no	—
548	C₂²⋊C₄	—	53	2	no	—
549	C₂²⋊C₄	—	53	2	no	—
550	C₂²⋊C₄	—	53	2	no	—
551	C₂²⋊C₄	—	53	2	no	—
552	C₂²⋊C₄	—	53	1	no	—
553	C₂²⋊C₄	—	53	2	no	—
554	C₂²⋊C₄	—	53	2	no	—
555	C₂²⋊C₄	—	53	2	no	—
556	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
557	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
562	C₄²	—	53	1	no	—
563	C₄²	—	53	1	no	—
564	C₄²	—	53	1	no	—
565	C₄²	—	53	1	no	—
566	C₄²	—	53	2	no	—
567	C₄²	—	53	1	no	—
568	C₄²	—	53	1	no	—
569	C₄²	—	53	1	no	—
570	C₄²	—	53	2	no	—
571	C₄²	—	53	1	no	—
572	C₄²	—	53	1	no	—
573	C₄²	C₂²×D₅₃	1	2	yes	—
574	C₄²	C₂²×D₅₃	1	1	yes	characteristic
575	C₂³	—	53	1	no	—
576	C₂³	—	53	2	no	—
577	C₂³	—	53	2	no	—
578	C₂³	—	106	4	no	—
579	C₂³	—	106	4	no	—
580	C₂³	—	106	4	no	—
581	C₂³	—	106	4	no	—
582	C₂³	—	212	2	no	—
583	C₂³	—	212	2	no	—
584	C₂³	C₂³×D₅₃	1	2	yes	—
585	C₂³	C₂³×D₅₃	1	1	yes	characteristic
586	C₂³	C₂³×D₅₃	1	1	yes	characteristic
587	Q₈	—	106	2	no	—
588	Q₈	—	106	2	no	—
589	Q₈	—	212	2	no	—
590	D₄	—	2	4	no	—
591	D₄	—	2	2	no	—
592	D₄	—	2	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	53	4	no	—
595	D₄	—	53	4	no	—
596	D₄	—	106	4	no	—
597	D₄	—	106	4	no	—
598	D₄	—	106	4	no	—
599	D₄	—	106	4	no	—
600	D₄	—	106	4	no	—
601	D₄	—	106	2	no	—
602	D₄	—	106	2	no	—
603	D₄	—	212	2	no	—
604	D₄	—	212	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	53	1	no	—
610	C₂×C₄	—	53	1	no	—
611	C₂×C₄	—	53	1	no	—
612	C₂×C₄	—	53	2	no	—
613	C₂×C₄	—	53	1	no	—
614	C₂×C₄	—	53	1	no	—
615	C₂×C₄	—	53	1	no	—
616	C₂×C₄	—	53	1	no	—
617	C₂×C₄	—	53	2	no	—
618	C₂×C₄	—	106	2	no	—
619	C₂×C₄	—	106	4	no	—
620	C₂×C₄	—	106	4	no	—
621	C₂×C₄	—	106	4	no	—
622	C₂×C₄	—	106	4	no	—
623	C₂×C₄	—	106	2	no	—
624	C₂×C₄	—	106	2	no	—
625	C₂×C₄	—	106	4	no	—
626	C₂×C₄	—	106	2	no	—
627	C₂×C₄	—	106	2	no	—
628	C₂×C₄	—	106	2	no	—
629	C₂×C₄	—	106	2	no	—
630	C₂×C₄	—	212	2	no	—
631	C₂×C₄	—	212	2	no	—
632	C₂×C₄	—	212	2	no	—
633	C₂×C₄	—	212	2	no	—
634	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₅₃	1	2	yes	—
638	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₅₃	1	2	yes	—
640	C₂×C₄	C₂³×D₅₃	1	2	yes	—
641	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	53	2	no	—
651	C₂²	—	53	4	no	—
652	C₂²	—	106	2	no	—
653	C₂²	—	106	1	no	—
654	C₂²	—	106	2	no	—
655	C₂²	—	106	1	no	—
656	C₂²	—	106	2	no	—
657	C₂²	—	106	2	no	—
658	C₂²	—	106	2	no	—
659	C₂²	—	212	8	no	—
660	C₂²	—	212	8	no	—
661	C₂²	#41×D₅₃	1	2	yes	—
662	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	53	2	no	—
671	C₄	—	53	2	no	—
672	C₄	—	106	1	no	—
673	C₄	—	106	1	no	—
674	C₄	—	106	1	no	—
675	C₄	—	106	2	no	—
676	C₄	—	106	1	no	—
677	C₄	—	106	2	no	—
678	C₄	—	106	1	no	—
679	C₄	#41×D₅₃	1	2	yes	—
680	C₂	—	2	2	no	—
681	C₂	—	4	2	no	—
682	C₂	—	4	1	no	—
683	C₂	—	106	4	no	—
684	C₂	—	106	2	no	—
685	C₂	—	212	2	no	—
686	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
687	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
688	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#553	C₂
hypercenter	#553	D₅₃
hypocenter	C₅₃	#3481
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #16811356	C₂	semidirect
2. #16811329	C₂	semidirect
3. #16811328	C₂	semidirect
4. #16811318	C₂	semidirect
5. #16811317	C₂	semidirect
6. #16811302	C₂	semidirect
7. #16811298	C₂	semidirect
8. #16811270	C₂	semidirect
9. #16811269	C₂	semidirect
10. #16811262	C₂	semidirect
11. #16811257	C₂	semidirect
12. #16811168	C₂	semidirect
13. #16811158	C₂	semidirect
14. #16811156	C₂	semidirect
15. #16811154	C₂	semidirect
16. #16811133	C₂	semidirect
17. #16811131	C₂	semidirect
18. #16811091	C₂	semidirect
19. C₄×#11719947	C₂	semidirect
20. C₂×#13133179	C₂	semidirect
21. C₄×D₄×D₅₃	C₂	semidirect
22. C₄×D₄×D₅₃	C₂	semidirect
23. C₅₃×#553	C₂	semidirect
26. C₂×#11719947	C₂²	semidirect
30. C₂²×C₄×D₅₃	C₂²	semidirect
31. C₂²×C₄×D₅₃	C₂²	semidirect
32. #13133216	C₂²	semidirect
34. #13133212	C₂²	semidirect
35. #13133211	C₂²	semidirect
36. #13133210	C₂²	semidirect
37. #13133208	C₂²	semidirect
38. #13133207	C₂²	semidirect
39. #13133205	C₂²	semidirect
40. #13133204	C₂²	semidirect
41. #13133203	C₂²	semidirect
42. #13133203	C₂²	semidirect
43. #13133202	C₂²	semidirect
44. #13133202	C₂²	semidirect
45. #13133200	C₂²	semidirect
46. #13133199	C₂²	semidirect
47. #13133199	C₂²	semidirect
48. #13133199	C₂²	semidirect
49. #13133198	C₂²	semidirect
50. #13133197	C₂²	semidirect
51. #13133197	C₂²	semidirect
52. #13133196	C₂²	semidirect
53. #13133196	C₂²	semidirect
54. #13133195	C₂²	semidirect
55. #13133195	C₂²	semidirect
56. #13133195	C₂²	semidirect
58. #13133191	C₂²	semidirect
60. #13133190	C₂²	semidirect
61. #13133190	C₂²	semidirect
62. #13133189	C₂²	semidirect
63. #13133188	C₂²	semidirect
66. #13133185	C₂²	semidirect
67. #13133185	C₂²	semidirect
68. C₄×Dic₁₀₆	C₂²	semidirect
69. #13133182	C₂²	semidirect
70. #13133182	C₂²	semidirect
71. #13133182	C₂²	semidirect
73. C₄×D₂₁₂	C₂²	semidirect
74. D₄×Dic₅₃	C₂²	semidirect
75. D₄×Dic₅₃	C₂²	semidirect
76. D₄×Dic₅₃	C₂²	semidirect
80. #13133179	C₂²	semidirect
81. #13133179	C₂²	semidirect
82. #13133179	C₂²	semidirect
83. #13133179	C₂²	semidirect
84. #13133179	C₂²	semidirect
87. C₄×C₂²⋊D₅₃	C₂²	semidirect
88. C₄×C₂²⋊D₅₃	C₂²	semidirect
89. C₄×C₂²⋊D₅₃	C₂²	semidirect
91. #13133177	C₂²	semidirect
92. #13133177	C₂²	semidirect
93. #13133177	C₂²	semidirect
94. #13133177	C₂²	semidirect
95. #13133177	C₂²	semidirect
96. #13133175	C₂²	semidirect
97. #13133175	C₂²	semidirect
98. #13133174	C₂²	semidirect
99. #13133173	C₂²	semidirect
100. #13133173	C₂²	semidirect
101. #13133173	C₂²	semidirect
102. C₄⋊C₄×D₅₃	C₂²	semidirect
103. C₄⋊C₄×D₅₃	C₂²	semidirect
104. C₂×#11719921	C₂²	semidirect
105. C₂²⋊C₄×D₅₃	C₂²	semidirect
106. C₂²⋊C₄×D₅₃	C₂²	semidirect
107. C₂²⋊C₄×D₅₃	C₂²	semidirect
108. C₂×C₄×Dic₅₃	C₂²	semidirect
109. C₂×C₄×Dic₅₃	C₂²	semidirect
110. C₄²×D₅₃	C₂²	semidirect
111. C₄²×D₅₃	C₂²	semidirect
112. #126×C₅₃	C₂²	semidirect
113. #125×C₅₃	C₂²	semidirect
114. #123×C₅₃	C₂²	semidirect
116. #121×C₅₃	C₂²	semidirect
117. #121×C₅₃	C₂²	semidirect
118. C₄×D₄×C₅₃	C₂²	semidirect
119. C₄×D₄×C₅₃	C₂²	semidirect
120. C₄×D₄×C₅₃	C₂²	semidirect
121. #117×C₅₃	C₂²	semidirect
122. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
264. C₂²⋊D₅₃	#41	semidirect
282. D₂₁₂	#41	semidirect
350. #553	D₅₃	semidirect
368. C₅₃	#3481	semidirect
382. #126	C₂×D₅₃	semidirect
385. #125	C₂×D₅₃	semidirect
397. #123	C₂×D₅₃	semidirect
413. #121	C₂×D₅₃	semidirect
414. #121	C₂×D₅₃	semidirect
447. C₄×D₄	C₂×D₅₃	semidirect
448. C₄×D₄	C₂×D₅₃	semidirect
449. C₄×D₄	C₂×D₅₃	semidirect
456. #117	C₂×D₅₃	semidirect
459. C₂×C₄⋊C₄	C₂×D₅₃	semidirect