Subgroups — #20288740

Order 6784.

1252 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811336	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811328	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811326	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811324	C₂	1	2	yes	maximal, complemented
5	#16811291	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811269	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811269	C₂	1	2	yes	maximal, complemented
8	#16811268	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811265	C₂	1	2	yes	maximal, complemented
10	#16811257	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811257	C₂	1	2	yes	maximal, complemented
12	#16811225	C₂	1	2	yes	maximal, complemented
13	#16811212	C₂	1	2	yes	maximal, complemented
14	#16811210	C₂	1	2	yes	maximal, complemented
15	#16811170	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811158	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811135	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811133	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#13133192	C₂	1	1	yes	maximal, characteristic, complemented
20	#121×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811095	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	2	yes	complemented
25	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
26	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₂₁₂	C₂²	1	2	yes	complemented
29	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
30	C₂×D₄×D₅₃	C₂²	1	2	yes	—
31	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
32	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
35	#13133216	C₂²	1	1	yes	characteristic, complemented
36	#13133213	C₂²	1	1	yes	characteristic, complemented
37	#13133213	C₂²	1	2	yes	complemented
38	#13133212	C₂²	1	2	yes	complemented
39	#13133212	C₂²	1	2	yes	complemented
40	#13133207	C₂²	1	2	yes	complemented
41	#13133205	C₂²	1	1	yes	characteristic, complemented
42	#13133205	C₂²	1	2	yes	complemented
43	#13133203	C₂²	1	2	yes	complemented
44	#13133203	C₂²	1	2	yes	complemented
45	#13133202	C₂²	1	2	yes	complemented
46	#13133202	C₂²	1	2	yes	complemented
47	#13133202	C₂²	1	2	yes	complemented
48	#13133201	C₂²	1	2	yes	complemented
49	#13133201	C₂²	1	2	yes	complemented
50	#13133199	C₂²	1	2	yes	complemented
51	#13133197	C₂²	1	1	yes	characteristic, complemented
52	#13133197	C₂²	1	1	yes	characteristic, complemented
53	#13133196	C₂²	1	1	yes	characteristic, complemented
54	#13133196	C₂²	1	2	yes	complemented
55	#13133195	C₂²	1	2	yes	complemented
56	#13133192	C₂²	1	1	yes	characteristic
57	#13133192	C₂²	1	2	yes	complemented
58	#13133192	C₂²	1	1	yes	characteristic, complemented
59	#13133192	C₂²	1	1	yes	characteristic, complemented
60	#13133192	C₂²	1	1	yes	characteristic, complemented
61	#13133192	C₂²	1	2	yes	complemented
62	#13133192	C₂²	1	1	yes	characteristic, complemented
63	#13133192	C₂²	1	2	yes	complemented
64	#13133191	C₂²	1	2	yes	complemented
65	#13133191	C₂²	1	1	yes	characteristic, complemented
66	#13133190	C₂²	1	2	yes	complemented
67	#13133190	C₂²	1	2	yes	complemented
68	#13133190	C₂²	1	2	yes	complemented
69	#13133190	C₂²	1	2	yes	complemented
70	#13133190	C₂²	1	2	yes	complemented
71	#13133190	C₂²	1	2	yes	complemented
72	#13133189	C₂²	1	2	yes	complemented
73	#13133189	C₂²	1	2	yes	complemented
74	#13133188	C₂²	1	1	yes	characteristic, complemented
75	#13133187	C₂²	1	2	yes	complemented
76	#13133187	C₂²	1	2	yes	complemented
77	#13133187	C₂²	1	2	yes	complemented
78	#13133185	C₂²	1	2	yes	complemented
79	#13133185	C₂²	1	2	yes	complemented
80	#13133185	C₂²	1	2	yes	complemented
81	#13133182	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₂₁₂	C₂²	1	2	yes	complemented
84	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
85	C₄×D₂₁₂	C₂²	1	2	yes	complemented
86	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
87	D₄×Dic₅₃	C₂²	1	2	yes	complemented
88	#13133179	C₂²	1	2	yes	complemented
89	#13133179	C₂²	1	2	yes	complemented
90	#13133179	C₂²	1	1	yes	characteristic, complemented
91	#13133179	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
96	#13133177	C₂²	1	1	yes	characteristic
97	#13133177	C₂²	1	2	yes	complemented
98	#13133177	C₂²	1	2	yes	complemented
99	#13133177	C₂²	1	1	yes	characteristic, complemented
100	#13133175	C₂²	1	1	yes	characteristic, complemented
101	#13133175	C₂²	1	2	yes	complemented
102	#13133174	C₂²	1	2	yes	complemented
103	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
104	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
105	C₂×#11719921	C₂²	1	2	yes	complemented
106	C₂×#11719921	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
108	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, 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	#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, complemented
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	1	yes	characteristic, complemented
120	C₄×D₄×C₅₃	C₂²	1	2	yes	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	1	yes	characteristic
124	C₂³×D₅₃	C₂³	1	1	yes	characteristic
125	C₂³×D₅₃	C₂³	1	2	yes	—
126	C₂³×D₅₃	C₂³	1	2	yes	—
127	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₅₃	C₂³	1	2	yes	—
129	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₅₃	C₂³	1	2	yes	—
131	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
137	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
144	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
145	C₂²×Dic₅₃	C₂³	1	2	yes	—
146	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
147	#11719947	—	4	2	no	—
148	D₄×D₅₃	—	2	4	no	—
149	D₄×D₅₃	—	2	8	no	—
150	D₄×D₅₃	—	4	2	no	—
151	D₄×D₅₃	—	4	4	no	—
152	#11719945	—	4	2	no	—
153	#11719945	—	4	4	no	—
154	C₂×D₂₁₂	—	4	2	no	—
155	C₂×D₂₁₂	—	4	4	no	—
156	C₂×D₂₁₂	C₂³	1	2	yes	—
157	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
158	C₂×D₂₁₂	C₂³	1	2	yes	—
159	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
160	C₂×D₂₁₂	C₂³	1	2	yes	—
161	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
162	C₂×D₂₁₂	C₂³	1	2	yes	—
163	C₂×D₂₁₂	C₂³	1	2	yes	—
164	C₂×D₂₁₂	C₂³	1	2	yes	—
165	C₂×C₄×D₅₃	—	4	2	no	—
166	C₂×C₄×D₅₃	—	4	2	no	—
167	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
171	C₂×C₄×D₅₃	C₂³	1	2	yes	—
172	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
174	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×D₅₃	C₂³	1	2	yes	—
176	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
177	C₂×C₄×D₅₃	C₂³	1	2	yes	—
178	C₂×C₄×D₅₃	C₂³	1	2	yes	—
179	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
180	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
181	C₂×Dic₁₀₆	C₂³	1	2	yes	—
182	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
183	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
184	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
186	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
187	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
195	C₄²×C₅₃	C₂³	1	2	yes	—
196	C₄²×C₅₃	C₂³	1	1	yes	characteristic
197	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
198	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
199	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
200	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
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	#11719921	C₂³	1	1	yes	characteristic
206	#11719921	C₂³	1	1	yes	characteristic
207	#11719921	C₂³	1	1	yes	characteristic
208	#11719921	C₂³	1	2	yes	—
209	#11719921	C₂³	1	2	yes	—
210	#11719921	C₂³	1	2	yes	—
211	#11719921	C₂³	1	2	yes	—
212	#11719921	C₂³	1	2	yes	—
213	#11719921	C₂³	1	2	yes	—
214	#11719921	C₂³	1	2	yes	—
215	#11719921	C₂³	1	2	yes	—
216	#11719921	C₂³	1	2	yes	—
217	#11719921	C₂³	1	2	yes	—
218	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₅₃	C₂³	1	2	yes	—
221	C₄⋊Dic₅₃	C₂³	1	2	yes	—
222	#11719919	C₂³	1	1	yes	characteristic
223	#11719919	C₂³	1	1	yes	characteristic
224	#11719919	C₂³	1	2	yes	—
225	#11719919	C₂³	1	2	yes	—
226	#11719919	C₂³	1	2	yes	—
227	#11719919	C₂³	1	2	yes	—
228	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
229	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
230	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
231	C₄×Dic₅₃	C₂³	1	2	yes	—
232	C₄×Dic₅₃	C₂³	1	2	yes	—
233	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
234	C₂³×C₅₃	C₂⁴	1	2	yes	—
235	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
236	C₂²×D₅₃	—	2	2	no	—
237	C₂²×D₅₃	—	2	4	no	—
238	C₂²×D₅₃	—	2	2	no	—
239	C₂²×D₅₃	—	2	2	no	—
240	C₂²×D₅₃	—	2	2	no	—
241	C₂²×D₅₃	—	2	4	no	—
242	C₂²×D₅₃	—	4	1	no	—
243	C₂²×D₅₃	—	4	1	no	—
244	C₂²×D₅₃	—	4	2	no	—
245	C₂²×D₅₃	—	4	2	no	—
246	C₂²×D₅₃	—	4	2	no	—
247	C₂²×D₅₃	—	4	2	no	—
248	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
249	C₂²×D₅₃	C₂⁴	1	2	yes	—
250	C₂²×D₅₃	C₂⁴	1	2	yes	—
251	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
252	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
253	D₄×C₅₃	—	2	2	no	—
254	D₄×C₅₃	—	2	4	no	—
255	D₄×C₅₃	—	2	2	no	—
256	D₄×C₅₃	—	4	2	no	—
257	C₂×C₄×C₅₃	—	2	2	no	—
258	C₂×C₄×C₅₃	—	2	2	no	—
259	C₂×C₄×C₅₃	—	4	2	no	—
260	C₂×C₄×C₅₃	—	4	2	no	—
261	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
262	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
266	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
268	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
269	C₂²⋊D₅₃	—	2	4	no	—
270	C₂²⋊D₅₃	—	2	2	no	—
271	C₂²⋊D₅₃	—	2	4	no	—
272	C₂²⋊D₅₃	—	4	2	no	—
273	C₂²⋊D₅₃	—	4	2	no	—
274	C₂²⋊D₅₃	—	4	2	no	—
275	C₂²⋊D₅₃	—	4	2	no	—
276	C₂²⋊D₅₃	—	4	2	no	—
277	C₂²⋊D₅₃	#41	1	4	yes	complemented
278	C₂×Dic₅₃	—	4	1	no	—
279	C₂×Dic₅₃	—	4	1	no	—
280	C₂×Dic₅₃	—	4	2	no	—
281	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₅₃	C₂⁴	1	2	yes	—
283	C₂×Dic₅₃	C₂⁴	1	2	yes	—
284	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
288	D₂₁₂	—	2	2	no	—
289	D₂₁₂	—	2	4	no	—
290	D₂₁₂	—	2	4	no	—
291	D₂₁₂	—	2	4	no	—
292	D₂₁₂	—	2	2	no	—
293	D₂₁₂	—	2	2	no	—
294	D₂₁₂	—	4	2	no	—
295	D₂₁₂	—	4	2	no	—
296	D₂₁₂	—	4	2	no	—
297	C₄×D₅₃	—	2	2	no	—
298	C₄×D₅₃	—	2	2	no	—
299	C₄×D₅₃	—	2	2	no	—
300	C₄×D₅₃	—	2	2	no	—
301	C₄×D₅₃	—	2	2	no	—
302	C₄×D₅₃	—	2	4	no	—
303	C₄×D₅₃	—	4	1	no	—
304	C₄×D₅₃	—	4	1	no	—
305	C₄×D₅₃	—	4	1	no	—
306	C₄×D₅₃	—	4	1	no	—
307	C₄×D₅₃	—	4	2	no	—
308	C₄×D₅₃	—	4	2	no	—
309	C₄×D₅₃	—	4	2	no	—
310	Dic₁₀₆	—	2	2	no	—
311	Dic₁₀₆	—	4	2	no	—
312	C₂²×C₅₃	—	2	1	no	—
313	C₂²×C₅₃	—	2	1	no	—
314	C₂²×C₅₃	—	2	1	no	—
315	C₂²×C₅₃	—	2	2	no	—
316	C₂²×C₅₃	—	2	1	no	—
317	C₂²×C₅₃	—	2	2	no	—
318	C₂²×C₅₃	—	2	2	no	—
319	C₂²×C₅₃	—	2	1	no	—
320	C₂²×C₅₃	C₂×#41	1	2	yes	—
321	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
322	C₂×D₅₃	—	2	1	no	—
323	C₂×D₅₃	—	2	1	no	—
324	C₂×D₅₃	—	2	1	no	—
325	C₂×D₅₃	—	2	1	no	—
326	C₂×D₅₃	—	2	2	no	—
327	C₂×D₅₃	—	2	1	no	—
328	C₂×D₅₃	—	2	2	no	—
329	C₂×D₅₃	—	2	1	no	—
330	C₂×D₅₃	—	2	2	no	—
331	C₂×D₅₃	—	2	2	no	—
332	C₂×D₅₃	—	2	2	no	—
333	C₂×D₅₃	—	2	2	no	—
334	C₂×D₅₃	—	2	1	no	—
335	C₂×D₅₃	—	4	4	no	—
336	C₂×D₅₃	—	4	4	no	—
337	C₂×D₅₃	—	8	4	no	—
338	C₂×D₅₃	—	8	4	no	—
339	C₂×D₅₃	C₂×#41	1	2	yes	—
340	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	—
341	C₄×C₅₃	—	2	1	no	—
342	C₄×C₅₃	—	2	2	no	—
343	C₄×C₅₃	—	2	2	no	—
344	C₄×C₅₃	—	2	1	no	—
345	C₄×C₅₃	—	2	1	no	—
346	C₄×C₅₃	—	2	1	no	—
347	C₄×C₅₃	—	2	2	no	—
348	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
349	Dic₅₃	—	2	2	no	—
350	Dic₅₃	—	2	1	no	—
351	Dic₅₃	—	2	2	no	—
352	Dic₅₃	—	2	1	no	—
353	Dic₅₃	—	2	1	no	—
354	Dic₅₃	—	2	1	no	—
355	Dic₅₃	C₂×#41	1	2	yes	—
356	#3519	—	53	1	no	maximal, Sylow
357	C₂×C₅₃	—	2	2	no	—
358	C₂×C₅₃	—	4	1	no	—
359	C₂×C₅₃	—	4	2	no	—
360	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
361	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	D₅₃	—	2	2	no	—
364	D₅₃	—	2	2	no	—
365	D₅₃	—	4	1	no	—
366	D₅₃	—	4	2	no	—
367	D₅₃	—	4	2	no	—
368	#555	—	53	1	no	—
369	#554	—	53	1	no	—
370	#553	—	53	2	no	—
371	#553	—	53	1	no	—
372	#553	D₅₃	1	1	yes	characteristic, complemented
373	#550	—	53	1	no	—
374	#546	—	53	2	no	—
375	#546	—	53	1	no	—
376	#546	—	53	2	no	—
377	#546	—	53	1	no	—
378	D₄²	—	53	1	no	—
379	D₄²	—	53	2	no	—
380	#540	—	53	2	no	—
381	#538	—	53	2	no	—
382	#538	—	53	2	no	—
383	#532	—	53	1	no	—
384	#529	—	53	1	no	—
385	#525	—	53	1	no	—
386	#525	—	53	1	no	—
387	C₂×#121	—	53	1	no	—
388	C₂×#121	—	53	1	no	—
389	#518	—	53	2	no	—
390	C₂×C₄×D₄	—	53	1	no	—
391	C₅₃	#3519	1	1	yes	characteristic, complemented, Sylow
392	C₂×#41	—	53	1	no	—
393	C₂×#41	—	53	1	no	—
394	C₂×#41	—	53	2	no	—
395	C₂²×D₄	—	53	1	no	—
396	C₂²×D₄	—	53	2	no	—
397	C₂²×D₄	—	53	1	no	—
398	C₂²×D₄	—	53	2	no	—
399	C₂²×D₄	—	53	1	no	—
400	C₂²×D₄	—	53	2	no	—
401	C₂³×C₄	—	53	1	no	—
402	C₂³×C₄	—	53	1	no	—
403	C₄⋊Q₈	—	53	1	no	—
404	#127	—	53	1	no	—
405	#127	—	53	2	no	—
406	#126	—	53	2	no	—
407	#126	—	53	2	no	—
408	#126	C₂×D₅₃	1	2	yes	complemented
409	#125	—	53	2	no	—
410	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
411	#124	—	53	2	no	—
412	#124	—	53	2	no	—
413	#124	—	53	1	no	—
414	#124	—	53	2	no	—
415	#123	—	53	2	no	—
416	#123	—	53	2	no	—
417	#123	—	53	2	no	—
418	#123	—	53	2	no	—
419	#123	—	53	2	no	—
420	#123	—	53	2	no	—
421	#123	C₂×D₅₃	1	2	yes	complemented
422	C₂²⋊Q₈	—	53	1	no	—
423	C₂²⋊Q₈	—	53	2	no	—
424	C₂²⋊Q₈	—	53	1	no	—
425	C₂²⋊Q₈	—	53	1	no	—
426	C₂²⋊Q₈	—	53	2	no	—
427	#121	—	53	1	no	—
428	#121	—	53	2	no	—
429	#121	—	53	2	no	—
430	#121	—	53	1	no	—
431	#121	—	53	2	no	—
432	#121	—	53	1	no	—
433	#121	—	53	1	no	—
434	#121	—	53	2	no	—
435	#121	—	53	2	no	—
436	#121	—	53	1	no	—
437	#121	—	53	1	no	—
438	#121	—	53	1	no	—
439	#121	—	53	2	no	—
440	#121	—	53	2	no	—
441	#121	—	53	2	no	—
442	#121	—	53	2	no	—
443	#121	—	53	2	no	—
444	#121	—	53	2	no	—
445	#121	—	53	2	no	—
446	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
447	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
448	#121	C₂×D₅₃	1	2	yes	complemented
449	#120	—	53	2	no	—
450	#120	—	53	2	no	—
451	#120	—	53	2	no	—
452	#120	—	53	2	no	—
453	#120	—	53	2	no	—
454	#120	—	53	2	no	—
455	C₄×Q₈	—	53	1	no	—
456	C₄×D₄	—	53	1	no	—
457	C₄×D₄	—	53	2	no	—
458	C₄×D₄	—	53	1	no	—
459	C₄×D₄	—	53	1	no	—
460	C₄×D₄	—	53	2	no	—
461	C₄×D₄	—	53	2	no	—
462	C₄×D₄	—	53	1	no	—
463	C₄×D₄	—	53	2	no	—
464	C₄×D₄	—	53	2	no	—
465	C₄×D₄	—	53	1	no	—
466	C₄×D₄	—	53	1	no	—
467	C₄×D₄	—	53	1	no	—
468	C₄×D₄	—	53	2	no	—
469	C₄×D₄	—	53	2	no	—
470	C₄×D₄	—	53	1	no	—
471	C₄×D₄	—	53	2	no	—
472	C₄×D₄	—	53	2	no	—
473	C₄×D₄	—	53	1	no	—
474	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
475	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
476	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
477	#117	—	53	2	no	—
478	#117	—	53	1	no	—
479	#117	—	53	2	no	—
480	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
481	C₂×C₄⋊C₄	—	53	1	no	—
482	C₂×C₄⋊C₄	—	53	1	no	—
483	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
484	C₂×C₂²⋊C₄	—	53	2	no	—
485	C₂×C₂²⋊C₄	—	53	2	no	—
486	C₂×C₂²⋊C₄	—	53	1	no	—
487	C₂×C₂²⋊C₄	—	53	1	no	—
488	C₂×C₂²⋊C₄	—	53	2	no	—
489	C₂×C₂²⋊C₄	—	53	2	no	—
490	C₂×C₄²	—	53	1	no	—
491	C₂⁴	—	53	1	no	—
492	C₂⁴	—	53	1	no	—
493	C₂⁴	—	53	2	no	—
494	C₂⁴	—	53	2	no	—
495	#41	—	212	2	no	—
496	#41	—	212	4	no	—
497	#41	—	212	2	no	—
498	C₂×Q₈	—	53	1	no	—
499	C₂×Q₈	—	53	2	no	—
500	C₂×D₄	—	53	1	no	—
501	C₂×D₄	—	53	1	no	—
502	C₂×D₄	—	53	2	no	—
503	C₂×D₄	—	53	2	no	—
504	C₂×D₄	—	53	2	no	—
505	C₂×D₄	—	53	2	no	—
506	C₂×D₄	—	53	2	no	—
507	C₂×D₄	—	53	2	no	—
508	C₂×D₄	—	53	2	no	—
509	C₂×D₄	—	53	1	no	—
510	C₂×D₄	—	53	2	no	—
511	C₂×D₄	—	53	2	no	—
512	C₂×D₄	—	53	2	no	—
513	C₂×D₄	—	53	1	no	—
514	C₂×D₄	—	53	1	no	—
515	C₂×D₄	—	53	2	no	—
516	C₂×D₄	—	53	2	no	—
517	C₂×D₄	—	53	2	no	—
518	C₂×D₄	—	106	8	no	—
519	C₂×D₄	—	106	4	no	—
520	C₂×D₄	—	212	2	no	—
521	C₂×D₄	—	212	4	no	—
522	C₂×D₄	—	212	2	no	—
523	C₂×D₄	—	212	4	no	—
524	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
525	C₂×D₄	C₂²×D₅₃	1	2	yes	—
526	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
527	C₂×D₄	C₂²×D₅₃	1	2	yes	—
528	C₂²×C₄	—	53	1	no	—
529	C₂²×C₄	—	53	2	no	—
530	C₂²×C₄	—	53	1	no	—
531	C₂²×C₄	—	53	1	no	—
532	C₂²×C₄	—	53	1	no	—
533	C₂²×C₄	—	53	1	no	—
534	C₂²×C₄	—	53	1	no	—
535	C₂²×C₄	—	53	2	no	—
536	C₂²×C₄	—	53	1	no	—
537	C₂²×C₄	—	53	1	no	—
538	C₂²×C₄	—	53	1	no	—
539	C₂²×C₄	—	53	1	no	—
540	C₂²×C₄	—	53	2	no	—
541	C₂²×C₄	—	53	2	no	—
542	C₂²×C₄	—	53	2	no	—
543	C₂²×C₄	—	53	1	no	—
544	C₂²×C₄	—	212	2	no	—
545	C₂²×C₄	—	212	2	no	—
546	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
547	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
548	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
549	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
550	C₄⋊C₄	—	53	1	no	—
551	C₄⋊C₄	—	53	1	no	—
552	C₄⋊C₄	—	53	1	no	—
553	C₄⋊C₄	—	53	1	no	—
554	C₄⋊C₄	—	53	2	no	—
555	C₄⋊C₄	—	53	2	no	—
556	C₄⋊C₄	—	53	2	no	—
557	C₄⋊C₄	—	53	2	no	—
558	C₄⋊C₄	—	53	2	no	—
559	C₄⋊C₄	—	53	2	no	—
560	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
561	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
562	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
563	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
564	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
565	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
566	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
567	C₂²⋊C₄	—	53	1	no	—
568	C₂²⋊C₄	—	53	2	no	—
569	C₂²⋊C₄	—	53	2	no	—
570	C₂²⋊C₄	—	53	1	no	—
571	C₂²⋊C₄	—	53	1	no	—
572	C₂²⋊C₄	—	53	2	no	—
573	C₂²⋊C₄	—	53	2	no	—
574	C₂²⋊C₄	—	53	2	no	—
575	C₂²⋊C₄	—	53	2	no	—
576	C₂²⋊C₄	—	53	1	no	—
577	C₂²⋊C₄	—	53	2	no	—
578	C₂²⋊C₄	—	53	2	no	—
579	C₂²⋊C₄	—	53	1	no	—
580	C₂²⋊C₄	—	53	2	no	—
581	C₂²⋊C₄	—	53	1	no	—
582	C₂²⋊C₄	—	53	2	no	—
583	C₂²⋊C₄	—	53	2	no	—
584	C₂²⋊C₄	—	53	2	no	—
585	C₂²⋊C₄	—	53	2	no	—
586	C₂²⋊C₄	—	53	2	no	—
587	C₂²⋊C₄	—	53	2	no	—
588	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
589	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
590	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
591	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
592	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
593	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
594	C₄²	—	53	1	no	—
595	C₄²	—	53	1	no	—
596	C₄²	—	53	1	no	—
597	C₄²	—	53	2	no	—
598	C₄²	—	53	2	no	—
599	C₄²	C₂²×D₅₃	1	1	yes	characteristic
600	C₄²	C₂²×D₅₃	1	2	yes	—
601	C₂³	—	53	1	no	—
602	C₂³	—	53	1	no	—
603	C₂³	—	53	2	no	—
604	C₂³	—	53	2	no	—
605	C₂³	—	53	1	no	—
606	C₂³	—	106	4	no	—
607	C₂³	—	106	2	no	—
608	C₂³	—	106	2	no	—
609	C₂³	—	106	2	no	—
610	C₂³	—	106	4	no	—
611	C₂³	—	106	2	no	—
612	C₂³	—	212	2	no	—
613	C₂³	—	212	2	no	—
614	C₂³	—	212	2	no	—
615	C₂³	—	212	2	no	—
616	C₂³	—	212	1	no	—
617	C₂³	—	212	1	no	—
618	C₂³	C₂³×D₅₃	1	2	yes	—
619	C₂³	C₂³×D₅₃	1	1	yes	characteristic
620	C₂³	C₂³×D₅₃	1	1	yes	characteristic
621	Q₈	—	106	2	no	—
622	Q₈	—	212	2	no	—
623	D₄	—	2	4	no	—
624	D₄	—	2	2	no	—
625	D₄	—	2	2	no	—
626	D₄	—	4	2	no	—
627	D₄	—	53	4	no	—
628	D₄	—	106	4	no	—
629	D₄	—	106	2	no	—
630	D₄	—	106	4	no	—
631	D₄	—	106	4	no	—
632	D₄	—	106	4	no	—
633	D₄	—	106	2	no	—
634	D₄	—	106	4	no	—
635	D₄	—	106	2	no	—
636	D₄	—	106	2	no	—
637	D₄	—	212	2	no	—
638	D₄	—	212	2	no	—
639	D₄	—	212	2	no	—
640	D₄	—	212	2	no	—
641	D₄	—	212	2	no	—
642	D₄	—	212	2	no	—
643	D₄	—	212	2	no	—
644	D₄	—	212	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	4	2	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	53	1	no	—
650	C₂×C₄	—	53	1	no	—
651	C₂×C₄	—	53	1	no	—
652	C₂×C₄	—	53	1	no	—
653	C₂×C₄	—	53	2	no	—
654	C₂×C₄	—	53	2	no	—
655	C₂×C₄	—	53	1	no	—
656	C₂×C₄	—	106	2	no	—
657	C₂×C₄	—	106	4	no	—
658	C₂×C₄	—	106	2	no	—
659	C₂×C₄	—	106	2	no	—
660	C₂×C₄	—	106	2	no	—
661	C₂×C₄	—	106	2	no	—
662	C₂×C₄	—	212	1	no	—
663	C₂×C₄	—	212	1	no	—
664	C₂×C₄	—	212	1	no	—
665	C₂×C₄	—	212	1	no	—
666	C₂×C₄	—	212	2	no	—
667	C₂×C₄	—	212	2	no	—
668	C₂×C₄	—	212	2	no	—
669	C₂×C₄	—	212	1	no	—
670	C₂×C₄	—	212	1	no	—
671	C₂×C₄	—	212	2	no	—
672	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
673	C₂×C₄	C₂³×D₅₃	1	2	yes	—
674	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
675	C₂×C₄	C₂³×D₅₃	1	2	yes	—
676	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
677	C₂×C₄	C₂³×D₅₃	1	2	yes	—
678	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
679	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
680	C₂²	—	2	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	53	2	no	—
689	C₂²	—	53	2	no	—
690	C₂²	—	106	1	no	—
691	C₂²	—	106	1	no	—
692	C₂²	—	106	1	no	—
693	C₂²	—	106	1	no	—
694	C₂²	—	106	2	no	—
695	C₂²	—	106	2	no	—
696	C₂²	—	106	1	no	—
697	C₂²	—	106	2	no	—
698	C₂²	—	106	2	no	—
699	C₂²	—	106	1	no	—
700	C₂²	—	106	1	no	—
701	C₂²	—	106	2	no	—
702	C₂²	—	106	2	no	—
703	C₂²	—	424	4	no	—
704	C₂²	—	424	4	no	—
705	C₂²	—	212	4	no	—
706	C₂²	—	212	4	no	—
707	C₂²	#41×D₅₃	1	2	yes	—
708	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
709	C₄	—	2	1	no	—
710	C₄	—	2	2	no	—
711	C₄	—	2	1	no	—
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	53	2	no	—
717	C₄	—	106	1	no	—
718	C₄	—	106	2	no	—
719	C₄	—	106	1	no	—
720	C₄	—	106	1	no	—
721	C₄	—	106	1	no	—
722	C₄	—	106	2	no	—
723	C₄	#13133263	1	2	yes	—
724	C₂	—	2	2	no	—
725	C₂	—	4	2	no	—
726	C₂	—	4	1	no	—
727	C₂	—	106	2	no	—
728	C₂	—	106	2	no	—
729	C₂	—	212	2	no	—
730	C₂	—	212	2	no	—
731	C₂	—	212	1	no	—
732	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
733	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
734	C₂	C₂×#13133263	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	#3519
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. #16811336	C₂	semidirect
2. #16811328	C₂	semidirect
3. #16811326	C₂	semidirect
4. #16811324	C₂	semidirect
5. #16811291	C₂	semidirect
6. #16811269	C₂	semidirect
7. #16811269	C₂	semidirect
8. #16811268	C₂	semidirect
9. #16811265	C₂	semidirect
10. #16811257	C₂	semidirect
11. #16811257	C₂	semidirect
12. #16811225	C₂	semidirect
13. #16811212	C₂	semidirect
14. #16811210	C₂	semidirect
15. #16811170	C₂	semidirect
16. #16811158	C₂	semidirect
17. #16811135	C₂	semidirect
18. #16811133	C₂	semidirect
19. C₂×#13133192	C₂	semidirect
20. #121×D₅₃	C₂	semidirect
21. #16811095	C₂	semidirect
22. C₄×D₄×D₅₃	C₂	semidirect
23. C₅₃×#553	C₂	semidirect
24. C₂×#11719945	C₂²	semidirect
25. C₂×#11719945	C₂²	semidirect
26. C₂×#11719947	C₂²	semidirect
27. C₂²×D₂₁₂	C₂²	semidirect
28. C₂²×D₂₁₂	C₂²	semidirect
31. C₂×D₄×D₅₃	C₂²	semidirect
32. C₂×D₄×D₅₃	C₂²	semidirect
33. C₂²×C₄×D₅₃	C₂²	semidirect
34. C₂²×C₄×D₅₃	C₂²	semidirect
35. #13133216	C₂²	semidirect
36. #13133213	C₂²	semidirect
37. #13133213	C₂²	semidirect
38. #13133212	C₂²	semidirect
39. #13133212	C₂²	semidirect
40. #13133207	C₂²	semidirect
41. #13133205	C₂²	semidirect
42. #13133205	C₂²	semidirect
43. #13133203	C₂²	semidirect
44. #13133203	C₂²	semidirect
45. #13133202	C₂²	semidirect
46. #13133202	C₂²	semidirect
47. #13133202	C₂²	semidirect
48. #13133201	C₂²	semidirect
49. #13133201	C₂²	semidirect
50. #13133199	C₂²	semidirect
51. #13133197	C₂²	semidirect
52. #13133197	C₂²	semidirect
53. #13133196	C₂²	semidirect
54. #13133196	C₂²	semidirect
55. #13133195	C₂²	semidirect
57. #13133192	C₂²	semidirect
58. #13133192	C₂²	semidirect
59. #13133192	C₂²	semidirect
60. #13133192	C₂²	semidirect
61. #13133192	C₂²	semidirect
62. #13133192	C₂²	semidirect
63. #13133192	C₂²	semidirect
64. #13133191	C₂²	semidirect
65. #13133191	C₂²	semidirect
66. #13133190	C₂²	semidirect
67. #13133190	C₂²	semidirect
68. #13133190	C₂²	semidirect
69. #13133190	C₂²	semidirect
70. #13133190	C₂²	semidirect
71. #13133190	C₂²	semidirect
72. #13133189	C₂²	semidirect
73. #13133189	C₂²	semidirect
74. #13133188	C₂²	semidirect
75. #13133187	C₂²	semidirect
76. #13133187	C₂²	semidirect
77. #13133187	C₂²	semidirect
78. #13133185	C₂²	semidirect
79. #13133185	C₂²	semidirect
80. #13133185	C₂²	semidirect
81. #13133182	C₂²	semidirect
82. C₄×D₂₁₂	C₂²	semidirect
83. C₄×D₂₁₂	C₂²	semidirect
84. C₄×D₂₁₂	C₂²	semidirect
85. C₄×D₂₁₂	C₂²	semidirect
86. D₄×Dic₅₃	C₂²	semidirect
87. D₄×Dic₅₃	C₂²	semidirect
88. #13133179	C₂²	semidirect
89. #13133179	C₂²	semidirect
90. #13133179	C₂²	semidirect
91. #13133179	C₂²	semidirect
94. C₄×C₂²⋊D₅₃	C₂²	semidirect
95. C₄×C₂²⋊D₅₃	C₂²	semidirect
97. #13133177	C₂²	semidirect
98. #13133177	C₂²	semidirect
99. #13133177	C₂²	semidirect
100. #13133175	C₂²	semidirect
101. #13133175	C₂²	semidirect
102. #13133174	C₂²	semidirect
103. C₄⋊C₄×D₅₃	C₂²	semidirect
104. C₄⋊C₄×D₅₃	C₂²	semidirect
105. C₂×#11719921	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. #126×C₅₃	C₂²	semidirect
113. #125×C₅₃	C₂²	semidirect
114. #123×C₅₃	C₂²	semidirect
115. #121×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
277. C₂²⋊D₅₃	#41	semidirect
372. #553	D₅₃	semidirect
391. C₅₃	#3519	semidirect
408. #126	C₂×D₅₃	semidirect
410. #125	C₂×D₅₃	semidirect
421. #123	C₂×D₅₃	semidirect
446. #121	C₂×D₅₃	semidirect
447. #121	C₂×D₅₃	semidirect
448. #121	C₂×D₅₃	semidirect
474. C₄×D₄	C₂×D₅₃	semidirect
475. C₄×D₄	C₂×D₅₃	semidirect
476. C₄×D₄	C₂×D₅₃	semidirect
480. #117	C₂×D₅₃	semidirect
483. C₂×C₄⋊C₄	C₂×D₅₃	semidirect