Subgroups — #20289044

Order 6784.

1260 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811363	C₂	1	2	yes	maximal, complemented
2	#16811361	C₂	1	2	yes	maximal, complemented
3	#16811356	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811294	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811291	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811270	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811268	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811265	C₂	1	2	yes	maximal, complemented
9	D₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811257	C₂	1	2	yes	maximal, complemented
11	#16811257	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811257	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811229	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811225	C₂	1	2	yes	maximal, complemented
15	#16811192	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811189	C₂	1	2	yes	maximal, complemented
17	#16811186	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811184	C₂	1	2	yes	maximal, complemented
19	#16811181	C₂	1	2	yes	maximal, complemented
20	#127×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811158	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811151	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×#11719945	C₂²	1	1	yes	characteristic, complemented
26	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₂₁₂	C₂²	1	2	yes	complemented
28	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
30	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
33	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
34	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
36	#13133214	C₂²	1	1	yes	characteristic, complemented
37	#13133214	C₂²	1	1	yes	characteristic, complemented
38	#13133213	C₂²	1	1	yes	characteristic
39	#13133213	C₂²	1	1	yes	characteristic, complemented
40	#13133213	C₂²	1	2	yes	complemented
41	#13133213	C₂²	1	1	yes	characteristic, complemented
42	#13133213	C₂²	1	2	yes	complemented
43	#13133213	C₂²	1	2	yes	complemented
44	#13133212	C₂²	1	2	yes	complemented
45	#13133212	C₂²	1	1	yes	characteristic, complemented
46	#13133210	C₂²	1	1	yes	characteristic, complemented
47	#13133207	C₂²	1	1	yes	characteristic, complemented
48	#13133205	C₂²	1	1	yes	characteristic, complemented
49	#13133205	C₂²	1	1	yes	characteristic, complemented
50	#13133204	C₂²	1	1	yes	characteristic, complemented
51	#13133203	C₂²	1	2	yes	complemented
52	#13133203	C₂²	1	1	yes	characteristic, complemented
53	#13133202	C₂²	1	2	yes	complemented
54	#13133202	C₂²	1	1	yes	characteristic, complemented
55	#13133202	C₂²	1	2	yes	complemented
56	#13133202	C₂²	1	2	yes	complemented
57	#13133201	C₂²	1	2	yes	complemented
58	#13133200	C₂²	1	2	yes	complemented
59	#13133199	C₂²	1	2	yes	complemented
60	#13133199	C₂²	1	2	yes	complemented
61	#13133199	C₂²	1	1	yes	characteristic, complemented
62	#13133197	C₂²	1	1	yes	characteristic, complemented
63	#13133195	C₂²	1	1	yes	characteristic, complemented
64	#13133192	C₂²	1	1	yes	characteristic
65	#13133192	C₂²	1	2	yes	complemented
66	#13133192	C₂²	1	1	yes	characteristic, complemented
67	#13133192	C₂²	1	1	yes	characteristic, complemented
68	#13133192	C₂²	1	2	yes	complemented
69	#13133192	C₂²	1	2	yes	complemented
70	#13133192	C₂²	1	2	yes	complemented
71	#13133191	C₂²	1	2	yes	complemented
72	#13133191	C₂²	1	2	yes	complemented
73	#13133191	C₂²	1	2	yes	complemented
74	#13133190	C₂²	1	1	yes	characteristic
75	#13133190	C₂²	1	2	yes	complemented
76	#13133190	C₂²	1	2	yes	complemented
77	#13133190	C₂²	1	2	yes	complemented
78	#13133190	C₂²	1	2	yes	complemented
79	#13133190	C₂²	1	2	yes	complemented
80	#13133189	C₂²	1	2	yes	complemented
81	#13133189	C₂²	1	2	yes	complemented
82	#13133189	C₂²	1	2	yes	complemented
83	#13133188	C₂²	1	2	yes	complemented
84	#13133187	C₂²	1	2	yes	complemented
85	#13133187	C₂²	1	2	yes	complemented
86	#13133187	C₂²	1	2	yes	complemented
87	#13133187	C₂²	1	2	yes	complemented
88	#13133187	C₂²	1	2	yes	complemented
89	#13133187	C₂²	1	2	yes	complemented
90	#13133187	C₂²	1	2	yes	complemented
91	#13133185	C₂²	1	2	yes	complemented
92	#13133185	C₂²	1	2	yes	complemented
93	#13133185	C₂²	1	2	yes	complemented
94	#13133185	C₂²	1	2	yes	complemented
95	#13133185	C₂²	1	2	yes	complemented
96	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
97	#13133182	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
99	#13133179	C₂²	1	2	yes	complemented
100	#13133179	C₂²	1	1	yes	characteristic, complemented
101	#13133179	C₂²	1	1	yes	characteristic, complemented
102	#13133179	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
106	#13133177	C₂²	1	2	yes	complemented
107	#13133175	C₂²	1	2	yes	complemented
108	#13133174	C₂²	1	1	yes	characteristic, complemented
109	C₂×#11719921	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	1	yes	characteristic, complemented
117	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	#121×C₅₃	C₂²	1	2	yes	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	C₂³×D₅₃	C₂³	1	2	yes	—
127	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
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	C₂×D₄×C₅₃	C₂³	1	2	yes	—
133	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
135	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
144	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
149	C₂²×Dic₅₃	C₂³	1	2	yes	—
150	#11719947	—	4	2	no	—
151	D₄×D₅₃	—	4	2	no	—
152	D₄×D₅₃	—	4	2	no	—
153	D₄×D₅₃	—	4	2	no	—
154	D₄×D₅₃	—	4	4	no	—
155	D₄×D₅₃	—	4	4	no	—
156	D₄×D₅₃	—	4	4	no	—
157	D₄×D₅₃	—	4	4	no	—
158	#11719945	—	4	4	no	—
159	#11719945	—	4	2	no	—
160	C₂×D₂₁₂	—	4	2	no	—
161	C₂×D₂₁₂	—	4	4	no	—
162	C₂×D₂₁₂	C₂³	1	2	yes	—
163	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
164	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
165	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
166	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
167	C₂×D₂₁₂	C₂³	1	2	yes	—
168	C₂×D₂₁₂	C₂³	1	2	yes	—
169	C₂×D₂₁₂	C₂³	1	2	yes	—
170	C₂×D₂₁₂	C₂³	1	2	yes	—
171	C₂×D₂₁₂	C₂³	1	2	yes	—
172	C₂×D₂₁₂	C₂³	1	2	yes	—
173	C₂×D₂₁₂	C₂³	1	2	yes	—
174	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
176	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
177	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
178	C₂×C₄×D₅₃	C₂³	1	2	yes	—
179	C₂×C₄×D₅₃	C₂³	1	2	yes	—
180	C₂×C₄×D₅₃	C₂³	1	2	yes	—
181	C₂×C₄×D₅₃	C₂³	1	2	yes	—
182	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
183	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
184	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
185	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
186	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
187	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
192	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
196	C₄²×C₅₃	C₂³	1	1	yes	characteristic
197	C₄²×C₅₃	C₂³	1	1	yes	characteristic
198	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
199	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
200	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
201	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
202	#11719921	C₂³	1	1	yes	characteristic
203	#11719921	C₂³	1	2	yes	—
204	#11719921	C₂³	1	1	yes	characteristic
205	#11719921	C₂³	1	2	yes	—
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	2	yes	—
211	#11719921	C₂³	1	2	yes	—
212	#11719921	C₂³	1	1	yes	characteristic
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	#11719921	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₅₃	C₂³	1	2	yes	—
220	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
222	#11719919	C₂³	1	1	yes	characteristic
223	#11719919	C₂³	1	1	yes	characteristic
224	#11719919	C₂³	1	1	yes	characteristic
225	#11719919	C₂³	1	1	yes	characteristic
226	#11719919	C₂³	1	1	yes	characteristic
227	#11719919	C₂³	1	2	yes	—
228	#11719919	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	1	yes	characteristic
232	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
233	C₄×Dic₅₃	C₂³	1	2	yes	—
234	C₂³×C₅₃	C₂⁴	1	2	yes	—
235	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
236	C₂³×C₅₃	C₂⁴	1	2	yes	—
237	C₂²×D₅₃	—	2	4	no	—
238	C₂²×D₅₃	—	2	4	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	—	4	2	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	—	4	2	no	—
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	2	yes	—
253	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
254	D₄×C₅₃	—	2	2	no	—
255	D₄×C₅₃	—	2	2	no	—
256	D₄×C₅₃	—	4	2	no	—
257	D₄×C₅₃	—	4	2	no	—
258	D₄×C₅₃	—	4	2	no	—
259	D₄×C₅₃	—	4	2	no	—
260	C₂×C₄×C₅₃	—	2	2	no	—
261	C₂×C₄×C₅₃	—	4	2	no	—
262	C₂×C₄×C₅₃	—	4	2	no	—
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	2	yes	—
267	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
271	C₂²⋊D₅₃	—	2	2	no	—
272	C₂²⋊D₅₃	—	2	4	no	—
273	C₂²⋊D₅₃	—	2	2	no	—
274	C₂²⋊D₅₃	—	2	4	no	—
275	C₂²⋊D₅₃	—	4	2	no	—
276	C₂²⋊D₅₃	—	4	2	no	—
277	C₂²⋊D₅₃	—	4	2	no	—
278	C₂²⋊D₅₃	—	4	2	no	—
279	C₂²⋊D₅₃	—	4	2	no	—
280	C₂²⋊D₅₃	—	4	2	no	—
281	C₂²⋊D₅₃	—	4	2	no	—
282	C₂²⋊D₅₃	—	4	2	no	—
283	C₂²⋊D₅₃	—	4	2	no	—
284	C₂×Dic₅₃	—	4	2	no	—
285	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₅₃	C₂⁴	1	2	yes	—
287	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
292	D₂₁₂	—	2	2	no	—
293	D₂₁₂	—	2	4	no	—
294	D₂₁₂	—	2	2	no	—
295	D₂₁₂	—	2	2	no	—
296	D₂₁₂	—	2	2	no	—
297	D₂₁₂	—	4	2	no	—
298	D₂₁₂	—	4	2	no	—
299	D₂₁₂	—	4	2	no	—
300	D₂₁₂	—	4	2	no	—
301	D₂₁₂	—	4	2	no	—
302	D₂₁₂	—	4	2	no	—
303	D₂₁₂	—	4	2	no	—
304	C₄×D₅₃	—	2	2	no	—
305	C₄×D₅₃	—	2	2	no	—
306	C₄×D₅₃	—	2	2	no	—
307	C₄×D₅₃	—	2	4	no	—
308	C₄×D₅₃	—	2	2	no	—
309	C₄×D₅₃	—	4	2	no	—
310	C₄×D₅₃	—	4	2	no	—
311	C₄×D₅₃	—	4	2	no	—
312	Dic₁₀₆	—	2	2	no	—
313	Dic₁₀₆	—	2	2	no	—
314	C₂²×C₅₃	—	2	2	no	—
315	C₂²×C₅₃	—	2	2	no	—
316	C₂²×C₅₃	—	2	1	no	—
317	C₂²×C₅₃	—	2	2	no	—
318	C₂²×C₅₃	—	2	1	no	—
319	C₂²×C₅₃	—	2	1	no	—
320	C₂²×C₅₃	—	2	2	no	—
321	C₂²×C₅₃	—	2	2	no	—
322	C₂²×C₅₃	—	2	2	no	—
323	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
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	2	no	—
330	C₂×D₅₃	—	2	2	no	—
331	C₂×D₅₃	—	2	1	no	—
332	C₂×D₅₃	—	2	2	no	—
333	C₂×D₅₃	—	2	2	no	—
334	C₂×D₅₃	—	2	2	no	—
335	C₂×D₅₃	—	2	2	no	—
336	C₂×D₅₃	—	2	1	no	—
337	C₂×D₅₃	—	2	2	no	—
338	C₂×D₅₃	—	8	4	no	—
339	C₂×D₅₃	—	8	4	no	—
340	C₂×D₅₃	—	8	4	no	—
341	C₂×D₅₃	—	8	4	no	—
342	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	—
343	C₄×C₅₃	—	2	1	no	—
344	C₄×C₅₃	—	2	2	no	—
345	C₄×C₅₃	—	2	1	no	—
346	C₄×C₅₃	—	2	1	no	—
347	C₄×C₅₃	—	2	1	no	—
348	C₄×C₅₃	—	2	2	no	—
349	C₄×C₅₃	—	2	1	no	—
350	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
351	Dic₅₃	—	2	1	no	—
352	Dic₅₃	—	2	2	no	—
353	Dic₅₃	—	2	1	no	—
354	Dic₅₃	—	2	1	no	—
355	Dic₅₃	—	2	1	no	—
356	Dic₅₃	—	2	1	no	—
357	Dic₅₃	H(5,𝔽₂)	1	2	yes	—
358	#3543	—	53	1	no	maximal, Sylow
359	C₂×C₅₃	—	4	2	no	—
360	C₂×C₅₃	—	4	1	no	—
361	C₂×C₅₃	—	4	2	no	—
362	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
365	D₅₃	—	2	2	no	—
366	D₅₃	—	4	2	no	—
367	D₅₃	—	4	2	no	—
368	D₅₃	—	4	1	no	—
369	D₅₃	—	4	2	no	—
370	#560	—	53	2	no	—
371	#560	—	53	2	no	—
372	#559	—	53	1	no	—
373	#550	—	53	1	no	—
374	#550	—	53	1	no	—
375	#546	—	53	2	no	—
376	#546	—	53	1	no	—
377	#546	—	53	1	no	—
378	D₄²	—	53	1	no	—
379	D₄²	—	53	1	no	—
380	D₄²	—	53	2	no	—
381	D₄²	—	53	1	no	—
382	#540	—	53	1	no	—
383	#540	—	53	2	no	—
384	#540	D₅₃	1	1	yes	characteristic, complemented
385	#535	—	53	1	no	—
386	#535	—	53	2	no	—
387	#535	—	53	1	no	—
388	#534	—	53	2	no	—
389	#534	—	53	2	no	—
390	C₂×#127	—	53	1	no	—
391	#529	—	53	1	no	—
392	#529	—	53	1	no	—
393	C₅₃	#3543	1	1	yes	characteristic, complemented, Sylow
394	C₂×#41	—	53	1	no	—
395	C₂×#41	—	53	2	no	—
396	C₂×#41	—	53	1	no	—
397	C₂²×D₄	—	53	2	no	—
398	C₂²×D₄	—	53	2	no	—
399	C₂²×D₄	—	53	1	no	—
400	C₂²×D₄	—	53	1	no	—
401	C₂²×D₄	—	53	2	no	—
402	C₂²×D₄	—	53	2	no	—
403	C₂²×D₄	—	53	1	no	—
404	C₂²×D₄	—	53	2	no	—
405	C₂²×D₄	—	53	1	no	—
406	#127	—	53	2	no	—
407	#127	—	53	1	no	—
408	#127	—	53	1	no	—
409	#127	—	53	2	no	—
410	#127	—	53	2	no	—
411	#127	—	53	1	no	—
412	#127	—	53	1	no	—
413	#127	—	53	1	no	—
414	#127	C₂×D₅₃	1	1	yes	characteristic, complemented
415	#126	—	53	2	no	—
416	#126	—	53	1	no	—
417	#126	—	53	1	no	—
418	#125	—	53	1	no	—
419	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
420	#124	—	53	1	no	—
421	#124	—	53	1	no	—
422	#124	—	53	2	no	—
423	#124	—	53	1	no	—
424	#124	—	53	1	no	—
425	#123	—	53	2	no	—
426	#123	—	53	2	no	—
427	#123	—	53	1	no	—
428	#123	—	53	2	no	—
429	#123	—	53	2	no	—
430	#123	—	53	1	no	—
431	#123	—	53	2	no	—
432	#123	—	53	2	no	—
433	#123	—	53	2	no	—
434	#123	C₂×D₅₃	1	2	yes	complemented
435	#123	C₂×D₅₃	1	2	yes	complemented
436	C₂²⋊Q₈	—	53	1	no	—
437	C₂²⋊Q₈	—	53	1	no	—
438	#121	—	53	2	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	1	no	—
446	#121	—	53	2	no	—
447	#121	—	53	2	no	—
448	#121	—	53	2	no	—
449	#121	—	53	1	no	—
450	#121	—	53	1	no	—
451	#121	—	53	2	no	—
452	#121	—	53	1	no	—
453	#121	—	53	2	no	—
454	#121	—	53	2	no	—
455	#121	—	53	2	no	—
456	#121	—	53	2	no	—
457	#121	—	53	2	no	—
458	#121	C₂×D₅₃	1	2	yes	complemented
459	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
460	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
461	#121	C₂×D₅₃	1	2	yes	complemented
462	#120	—	53	2	no	—
463	#120	—	53	2	no	—
464	#120	—	53	2	no	—
465	#120	—	53	2	no	—
466	#120	—	53	2	no	—
467	#120	—	53	2	no	—
468	#120	—	53	2	no	—
469	#120	—	53	2	no	—
470	#120	—	53	2	no	—
471	#120	—	53	2	no	—
472	#120	—	53	2	no	—
473	#120	—	53	2	no	—
474	C₄×Q₈	—	53	1	no	—
475	C₄×Q₈	—	53	1	no	—
476	C₄×D₄	—	53	1	no	—
477	C₄×D₄	—	53	1	no	—
478	C₄×D₄	—	53	2	no	—
479	C₄×D₄	—	53	2	no	—
480	C₄×D₄	—	53	1	no	—
481	C₄×D₄	—	53	1	no	—
482	C₄×D₄	—	53	1	no	—
483	C₄×D₄	—	53	2	no	—
484	C₄×D₄	—	53	1	no	—
485	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
486	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
487	#117	—	53	2	no	—
488	#117	—	53	1	no	—
489	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
490	C₂×C₂²⋊C₄	—	53	2	no	—
491	C₂×C₂²⋊C₄	—	53	2	no	—
492	C₂×C₄²	—	53	1	no	—
493	C₂⁴	—	53	2	no	—
494	C₂⁴	—	53	2	no	—
495	C₂⁴	—	53	2	no	—
496	C₂⁴	—	53	2	no	—
497	#41	—	212	2	no	—
498	#41	—	212	4	no	—
499	#41	—	212	2	no	—
500	C₂×Q₈	—	53	1	no	—
501	C₂×Q₈	—	53	1	no	—
502	C₂×D₄	—	53	1	no	—
503	C₂×D₄	—	53	1	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	2	no	—
510	C₂×D₄	—	53	2	no	—
511	C₂×D₄	—	53	2	no	—
512	C₂×D₄	—	53	2	no	—
513	C₂×D₄	—	53	2	no	—
514	C₂×D₄	—	53	2	no	—
515	C₂×D₄	—	53	2	no	—
516	C₂×D₄	—	53	1	no	—
517	C₂×D₄	—	53	1	no	—
518	C₂×D₄	—	53	1	no	—
519	C₂×D₄	—	53	1	no	—
520	C₂×D₄	—	53	2	no	—
521	C₂×D₄	—	53	2	no	—
522	C₂×D₄	—	53	2	no	—
523	C₂×D₄	—	53	2	no	—
524	C₂×D₄	—	53	2	no	—
525	C₂×D₄	—	53	2	no	—
526	C₂×D₄	—	53	2	no	—
527	C₂×D₄	—	212	2	no	—
528	C₂×D₄	—	212	4	no	—
529	C₂×D₄	—	212	2	no	—
530	C₂×D₄	—	212	2	no	—
531	C₂×D₄	—	212	2	no	—
532	C₂×D₄	—	212	4	no	—
533	C₂×D₄	—	212	4	no	—
534	C₂×D₄	—	212	4	no	—
535	C₂×D₄	—	212	4	no	—
536	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
537	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
538	C₂×D₄	C₂²×D₅₃	1	2	yes	—
539	C₂×D₄	C₂²×D₅₃	1	2	yes	—
540	C₂×D₄	C₂²×D₅₃	1	2	yes	—
541	C₂×D₄	C₂²×D₅₃	1	2	yes	—
542	C₂²×C₄	—	53	2	no	—
543	C₂²×C₄	—	53	1	no	—
544	C₂²×C₄	—	53	1	no	—
545	C₂²×C₄	—	53	1	no	—
546	C₂²×C₄	—	53	2	no	—
547	C₂²×C₄	—	53	1	no	—
548	C₂²×C₄	—	53	2	no	—
549	C₂²×C₄	—	53	2	no	—
550	C₂²×C₄	—	53	2	no	—
551	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
552	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
553	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
554	C₄⋊C₄	—	53	1	no	—
555	C₄⋊C₄	—	53	2	no	—
556	C₄⋊C₄	—	53	1	no	—
557	C₄⋊C₄	—	53	1	no	—
558	C₄⋊C₄	—	53	1	no	—
559	C₄⋊C₄	—	53	1	no	—
560	C₄⋊C₄	—	53	1	no	—
561	C₄⋊C₄	—	53	2	no	—
562	C₄⋊C₄	—	53	1	no	—
563	C₄⋊C₄	—	53	1	no	—
564	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
565	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
566	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
567	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
568	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
569	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
570	C₂²⋊C₄	—	53	2	no	—
571	C₂²⋊C₄	—	53	1	no	—
572	C₂²⋊C₄	—	53	1	no	—
573	C₂²⋊C₄	—	53	2	no	—
574	C₂²⋊C₄	—	53	2	no	—
575	C₂²⋊C₄	—	53	1	no	—
576	C₂²⋊C₄	—	53	1	no	—
577	C₂²⋊C₄	—	53	2	no	—
578	C₂²⋊C₄	—	53	2	no	—
579	C₂²⋊C₄	—	53	2	no	—
580	C₂²⋊C₄	—	53	1	no	—
581	C₂²⋊C₄	—	53	2	no	—
582	C₂²⋊C₄	—	53	1	no	—
583	C₂²⋊C₄	—	53	2	no	—
584	C₂²⋊C₄	—	53	1	no	—
585	C₂²⋊C₄	—	53	1	no	—
586	C₂²⋊C₄	—	53	2	no	—
587	C₂²⋊C₄	—	53	2	no	—
588	C₂²⋊C₄	—	53	2	no	—
589	C₂²⋊C₄	—	53	2	no	—
590	C₂²⋊C₄	—	53	2	no	—
591	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
592	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
593	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
594	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
595	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
596	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
597	C₄²	—	53	1	no	—
598	C₄²	—	53	1	no	—
599	C₄²	—	53	1	no	—
600	C₄²	—	53	2	no	—
601	C₄²	—	53	1	no	—
602	C₄²	C₂²×D₅₃	1	1	yes	characteristic
603	C₄²	C₂²×D₅₃	1	1	yes	characteristic
604	C₂³	—	53	1	no	—
605	C₂³	—	53	2	no	—
606	C₂³	—	53	2	no	—
607	C₂³	—	53	1	no	—
608	C₂³	—	53	2	no	—
609	C₂³	—	106	4	no	—
610	C₂³	—	106	4	no	—
611	C₂³	—	212	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	2	no	—
617	C₂³	—	212	2	no	—
618	C₂³	—	212	2	no	—
619	C₂³	—	212	2	no	—
620	C₂³	—	212	2	no	—
621	C₂³	C₂³×D₅₃	1	2	yes	—
622	C₂³	C₂³×D₅₃	1	1	yes	characteristic
623	C₂³	C₂³×D₅₃	1	2	yes	—
624	Q₈	—	106	2	no	—
625	Q₈	—	106	2	no	—
626	D₄	—	2	2	no	—
627	D₄	—	2	2	no	—
628	D₄	—	4	2	no	—
629	D₄	—	4	2	no	—
630	D₄	—	4	2	no	—
631	D₄	—	4	2	no	—
632	D₄	—	106	2	no	—
633	D₄	—	106	4	no	—
634	D₄	—	106	2	no	—
635	D₄	—	106	4	no	—
636	D₄	—	106	4	no	—
637	D₄	—	106	2	no	—
638	D₄	—	106	2	no	—
639	D₄	—	106	2	no	—
640	D₄	—	106	2	no	—
641	D₄	—	212	2	no	—
642	D₄	—	212	2	no	—
643	D₄	—	212	2	no	—
644	D₄	—	212	2	no	—
645	D₄	—	212	2	no	—
646	D₄	—	212	2	no	—
647	D₄	—	212	2	no	—
648	D₄	—	212	2	no	—
649	D₄	—	212	2	no	—
650	D₄	—	212	2	no	—
651	D₄	—	212	2	no	—
652	D₄	—	212	2	no	—
653	D₄	—	212	2	no	—
654	D₄	—	212	2	no	—
655	D₄	—	212	2	no	—
656	D₄	—	212	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	53	1	no	—
661	C₂×C₄	—	53	1	no	—
662	C₂×C₄	—	53	1	no	—
663	C₂×C₄	—	53	1	no	—
664	C₂×C₄	—	53	2	no	—
665	C₂×C₄	—	53	1	no	—
666	C₂×C₄	—	53	1	no	—
667	C₂×C₄	—	106	2	no	—
668	C₂×C₄	—	106	4	no	—
669	C₂×C₄	—	106	2	no	—
670	C₂×C₄	—	106	2	no	—
671	C₂×C₄	—	106	2	no	—
672	C₂×C₄	—	212	2	no	—
673	C₂×C₄	—	212	2	no	—
674	C₂×C₄	—	212	2	no	—
675	C₂×C₄	—	212	2	no	—
676	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
677	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
678	C₂×C₄	C₂³×D₅₃	1	2	yes	—
679	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
680	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
681	C₂×C₄	C₂³×D₅₃	1	2	yes	—
682	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
683	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	1	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	1	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	53	2	no	—
694	C₂²	—	106	1	no	—
695	C₂²	—	106	1	no	—
696	C₂²	—	106	2	no	—
697	C₂²	—	106	2	no	—
698	C₂²	—	106	2	no	—
699	C₂²	—	106	2	no	—
700	C₂²	—	106	1	no	—
701	C₂²	—	106	1	no	—
702	C₂²	—	106	2	no	—
703	C₂²	—	106	2	no	—
704	C₂²	—	106	1	no	—
705	C₂²	—	106	2	no	—
706	C₂²	—	106	2	no	—
707	C₂²	—	106	2	no	—
708	C₂²	—	424	4	no	—
709	C₂²	—	424	4	no	—
710	C₂²	—	424	4	no	—
711	C₂²	—	424	4	no	—
712	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	53	2	no	—
721	C₄	—	106	1	no	—
722	C₄	—	106	1	no	—
723	C₄	—	106	1	no	—
724	C₄	—	106	1	no	—
725	C₄	—	106	1	no	—
726	C₄	—	106	2	no	—
727	C₄	#13133263	1	2	yes	—
728	C₂	—	4	2	no	—
729	C₂	—	4	1	no	—
730	C₂	—	4	2	no	—
731	C₂	—	106	2	no	—
732	C₂	—	212	2	no	—
733	C₂	—	212	2	no	—
734	C₂	—	212	1	no	—
735	C₂	—	212	2	no	—
736	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
737	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
738	C₂	C₂×#13133263	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	#3543
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. #16811363	C₂	semidirect
2. #16811361	C₂	semidirect
3. #16811356	C₂	semidirect
4. #16811294	C₂	semidirect
5. #16811291	C₂	semidirect
6. #16811270	C₂	semidirect
7. #16811268	C₂	semidirect
8. #16811265	C₂	semidirect
9. D₄×D₂₁₂	C₂	semidirect
10. #16811257	C₂	semidirect
11. #16811257	C₂	semidirect
12. #16811257	C₂	semidirect
13. #16811229	C₂	semidirect
14. #16811225	C₂	semidirect
15. #16811192	C₂	semidirect
16. #16811189	C₂	semidirect
17. #16811186	C₂	semidirect
18. #16811184	C₂	semidirect
19. #16811181	C₂	semidirect
20. #127×D₅₃	C₂	semidirect
21. #16811158	C₂	semidirect
22. #16811151	C₂	semidirect
23. C₅₃×#540	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
29. C₂×D₄×D₅₃	C₂²	semidirect
30. C₂×D₄×D₅₃	C₂²	semidirect
31. C₂×D₄×D₅₃	C₂²	semidirect
32. C₂×D₄×D₅₃	C₂²	semidirect
33. C₂×D₄×D₅₃	C₂²	semidirect
34. C₂×D₄×D₅₃	C₂²	semidirect
35. C₂×D₄×D₅₃	C₂²	semidirect
36. #13133214	C₂²	semidirect
37. #13133214	C₂²	semidirect
39. #13133213	C₂²	semidirect
40. #13133213	C₂²	semidirect
41. #13133213	C₂²	semidirect
42. #13133213	C₂²	semidirect
43. #13133213	C₂²	semidirect
44. #13133212	C₂²	semidirect
45. #13133212	C₂²	semidirect
46. #13133210	C₂²	semidirect
47. #13133207	C₂²	semidirect
48. #13133205	C₂²	semidirect
49. #13133205	C₂²	semidirect
50. #13133204	C₂²	semidirect
51. #13133203	C₂²	semidirect
52. #13133203	C₂²	semidirect
53. #13133202	C₂²	semidirect
54. #13133202	C₂²	semidirect
55. #13133202	C₂²	semidirect
56. #13133202	C₂²	semidirect
57. #13133201	C₂²	semidirect
58. #13133200	C₂²	semidirect
59. #13133199	C₂²	semidirect
60. #13133199	C₂²	semidirect
61. #13133199	C₂²	semidirect
62. #13133197	C₂²	semidirect
63. #13133195	C₂²	semidirect
65. #13133192	C₂²	semidirect
66. #13133192	C₂²	semidirect
67. #13133192	C₂²	semidirect
68. #13133192	C₂²	semidirect
69. #13133192	C₂²	semidirect
70. #13133192	C₂²	semidirect
71. #13133191	C₂²	semidirect
72. #13133191	C₂²	semidirect
73. #13133191	C₂²	semidirect
75. #13133190	C₂²	semidirect
76. #13133190	C₂²	semidirect
77. #13133190	C₂²	semidirect
78. #13133190	C₂²	semidirect
79. #13133190	C₂²	semidirect
80. #13133189	C₂²	semidirect
81. #13133189	C₂²	semidirect
82. #13133189	C₂²	semidirect
83. #13133188	C₂²	semidirect
84. #13133187	C₂²	semidirect
85. #13133187	C₂²	semidirect
86. #13133187	C₂²	semidirect
87. #13133187	C₂²	semidirect
88. #13133187	C₂²	semidirect
89. #13133187	C₂²	semidirect
90. #13133187	C₂²	semidirect
91. #13133185	C₂²	semidirect
92. #13133185	C₂²	semidirect
93. #13133185	C₂²	semidirect
94. #13133185	C₂²	semidirect
95. #13133185	C₂²	semidirect
96. C₄×Dic₁₀₆	C₂²	semidirect
97. #13133182	C₂²	semidirect
98. C₄×D₂₁₂	C₂²	semidirect
99. #13133179	C₂²	semidirect
100. #13133179	C₂²	semidirect
101. #13133179	C₂²	semidirect
102. #13133179	C₂²	semidirect
103. C₄×C₂²⋊D₅₃	C₂²	semidirect
104. C₄×C₂²⋊D₅₃	C₂²	semidirect
105. C₄×C₂²⋊D₅₃	C₂²	semidirect
106. #13133177	C₂²	semidirect
107. #13133175	C₂²	semidirect
108. #13133174	C₂²	semidirect
109. C₂×#11719921	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
384. #540	D₅₃	semidirect
393. C₅₃	#3543	semidirect
414. #127	C₂×D₅₃	semidirect
419. #125	C₂×D₅₃	semidirect
434. #123	C₂×D₅₃	semidirect
435. #123	C₂×D₅₃	semidirect
458. #121	C₂×D₅₃	semidirect
459. #121	C₂×D₅₃	semidirect
460. #121	C₂×D₅₃	semidirect
461. #121	C₂×D₅₃	semidirect
485. C₄×D₄	C₂×D₅₃	semidirect
486. C₄×D₄	C₂×D₅₃	semidirect
489. #117	C₂×D₅₃	semidirect