Subgroups — #20288583

Order 6784.

1232 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811357	C₂	1	2	yes	maximal, complemented
2	#16811356	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811355	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811292	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811291	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811291	C₂	1	2	yes	maximal, complemented
7	#16811269	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811267	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811264	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811263	C₂	1	2	yes	maximal, complemented
11	#16811260	C₂	1	2	yes	maximal, complemented
12	#16811225	C₂	1	2	yes	maximal, complemented
13	#16811223	C₂	1	2	yes	maximal, complemented
14	#16811188	C₂	1	2	yes	maximal, complemented
15	#16811175	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811172	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811170	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811169	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811168	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13133213	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811096	C₂	1	2	yes	maximal, complemented
22	C₄×#11719947	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11719949	C₂²	1	1	yes	characteristic, complemented
25	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
26	C₂×#11719945	C₂²	1	2	yes	complemented
27	C₂×#11719947	C₂²	1	1	yes	characteristic
28	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
29	C₂×#11719947	C₂²	1	2	yes	complemented
30	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	—
32	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	—
33	#13133216	C₂²	1	1	yes	characteristic, complemented
34	#13133215	C₂²	1	1	yes	characteristic, complemented
35	#13133213	C₂²	1	1	yes	characteristic
36	#13133213	C₂²	1	2	yes	—
37	#13133213	C₂²	1	1	yes	characteristic
38	#13133213	C₂²	1	1	yes	characteristic
39	#13133213	C₂²	1	1	yes	characteristic
40	#13133213	C₂²	1	2	yes	—
41	#13133213	C₂²	1	2	yes	complemented
42	#13133213	C₂²	1	2	yes	complemented
43	#13133207	C₂²	1	2	yes	complemented
44	#13133206	C₂²	1	1	yes	characteristic, complemented
45	#13133205	C₂²	1	1	yes	characteristic, complemented
46	#13133204	C₂²	1	1	yes	characteristic, complemented
47	#13133203	C₂²	1	2	yes	complemented
48	#13133203	C₂²	1	2	yes	complemented
49	#13133203	C₂²	1	2	yes	complemented
50	#13133203	C₂²	1	2	yes	complemented
51	#13133202	C₂²	1	2	yes	complemented
52	#13133202	C₂²	1	2	yes	complemented
53	#13133201	C₂²	1	2	yes	complemented
54	#13133200	C₂²	1	2	yes	complemented
55	#13133199	C₂²	1	2	yes	complemented
56	#13133199	C₂²	1	2	yes	complemented
57	#13133198	C₂²	1	2	yes	complemented
58	#13133196	C₂²	1	1	yes	characteristic
59	#13133194	C₂²	1	2	yes	—
60	#13133192	C₂²	1	1	yes	characteristic, complemented
61	#13133192	C₂²	1	2	yes	complemented
62	#13133191	C₂²	1	1	yes	characteristic, complemented
63	#13133191	C₂²	1	2	yes	complemented
64	#13133190	C₂²	1	2	yes	complemented
65	#13133190	C₂²	1	2	yes	complemented
66	#13133190	C₂²	1	2	yes	complemented
67	#13133190	C₂²	1	2	yes	complemented
68	#13133190	C₂²	1	2	yes	complemented
69	#13133189	C₂²	1	2	yes	complemented
70	#13133189	C₂²	1	2	yes	complemented
71	#13133189	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	#13133188	C₂²	1	2	yes	complemented
76	#13133187	C₂²	1	2	yes	—
77	#13133186	C₂²	1	2	yes	—
78	#13133185	C₂²	1	2	yes	—
79	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
81	#13133182	C₂²	1	1	yes	characteristic, complemented
82	#13133182	C₂²	1	2	yes	complemented
83	#13133182	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
85	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
86	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
87	#13133179	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₅₃	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	2	yes	complemented
95	#13133177	C₂²	1	1	yes	characteristic
96	#13133177	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	#13133177	C₂²	1	2	yes	complemented
101	#13133177	C₂²	1	2	yes	complemented
102	#13133175	C₂²	1	1	yes	characteristic, complemented
103	#13133173	C₂²	1	1	yes	characteristic
104	#13133173	C₂²	1	2	yes	—
105	#13133173	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊Dic₅₃	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
109	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
110	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
114	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	#123×C₅₃	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
117	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	#121×C₅₃	C₂²	1	2	yes	complemented
119	#120×C₅₃	C₂²	1	2	yes	—
120	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
123	C₂⁴×C₅₃	C₂³	1	2	yes	—
124	C₂³×D₅₃	C₂³	1	2	yes	—
125	#41×C₅₃	—	4	2	no	—
126	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₅₃	—	4	2	no	—
128	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₅₃	C₂³	1	2	yes	—
132	C₂×D₄×C₅₃	C₂³	1	2	yes	—
133	C₂×D₄×C₅₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
137	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₅₃	—	2	8	no	—
139	C₂×C₂²⋊D₅₃	—	4	4	no	—
140	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
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	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	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
154	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
155	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
156	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
157	C₂²×Dic₅₃	C₂³	1	2	yes	—
158	C₂²×Dic₅₃	C₂³	1	2	yes	—
159	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
160	#11719949	—	4	2	no	—
161	#11719947	—	2	4	no	—
162	#11719947	—	4	2	no	—
163	#11719947	—	4	4	no	—
164	#11719945	—	4	4	no	—
165	#11719945	—	4	2	no	—
166	C₂×D₂₁₂	—	4	2	no	—
167	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
168	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
169	C₂×D₂₁₂	C₂³	1	2	yes	—
170	C₂×D₂₁₂	C₂³	1	2	yes	—
171	C₂×D₂₁₂	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	2	yes	—
177	C₂×C₄×D₅₃	C₂³	1	2	yes	—
178	C₂×C₄×D₅₃	C₂³	1	2	yes	—
179	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
180	C₂×Dic₁₀₆	C₂³	1	2	yes	—
181	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
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	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
186	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
190	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
192	C₄²×C₅₃	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
194	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
195	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
196	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
197	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
198	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
199	C₂²⋊Dic₅₃	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	2	yes	—
204	#11719921	C₂³	1	1	yes	characteristic
205	#11719921	C₂³	1	1	yes	characteristic
206	#11719921	C₂³	1	2	yes	—
207	#11719921	C₂³	1	2	yes	—
208	#11719921	C₂³	1	2	yes	—
209	#11719921	C₂³	1	2	yes	—
210	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
218	#11719919	C₂³	1	1	yes	characteristic
219	#11719919	C₂³	1	2	yes	—
220	#11719919	C₂³	1	2	yes	—
221	#11719919	C₂³	1	2	yes	—
222	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₅₃	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	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	—	2	4	no	—
234	C₂³×C₅₃	—	4	2	no	—
235	C₂³×C₅₃	—	4	2	no	—
236	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
237	C₂³×C₅₃	C₂⁴	1	2	yes	—
238	C₂³×C₅₃	C₂⁴	1	2	yes	—
239	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
240	C₂²×D₅₃	—	2	4	no	—
241	C₂²×D₅₃	—	4	2	no	—
242	C₂²×D₅₃	—	4	2	no	—
243	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
244	C₂²×D₅₃	C₂⁴	1	2	yes	—
245	C₂²×D₅₃	C₂⁴	1	2	yes	—
246	Q₈×C₅₃	—	2	2	no	—
247	D₄×C₅₃	—	2	2	no	—
248	D₄×C₅₃	—	2	2	no	—
249	D₄×C₅₃	—	2	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	—	2	2	no	—
255	C₂×C₄×C₅₃	—	4	2	no	—
256	C₂×C₄×C₅₃	—	4	2	no	—
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	1	yes	characteristic
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	C₂²⋊D₅₃	—	2	2	no	—
265	C₂²⋊D₅₃	—	2	2	no	—
266	C₂²⋊D₅₃	—	2	4	no	—
267	C₂²⋊D₅₃	—	2	4	no	—
268	C₂²⋊D₅₃	—	2	4	no	—
269	C₂²⋊D₅₃	—	2	4	no	—
270	C₂²⋊D₅₃	—	2	4	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	—	4	2	no	—
278	C₂×Dic₅₃	—	2	2	no	—
279	C₂×Dic₅₃	—	2	2	no	—
280	C₂×Dic₅₃	—	2	2	no	—
281	C₂×Dic₅₃	—	4	2	no	—
282	C₂×Dic₅₃	—	4	2	no	—
283	C₂×Dic₅₃	#41	1	4	yes	complemented
284	C₂×Dic₅₃	C₂⁴	1	2	yes	—
285	C₂×Dic₅₃	C₂⁴	1	2	yes	—
286	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
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	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
293	D₂₁₂	—	2	2	no	—
294	D₂₁₂	—	2	2	no	—
295	D₂₁₂	—	4	2	no	—
296	D₂₁₂	—	4	2	no	—
297	D₂₁₂	—	4	2	no	—
298	C₄×D₅₃	—	2	2	no	—
299	C₄×D₅₃	—	2	2	no	—
300	C₄×D₅₃	—	2	2	no	—
301	C₄×D₅₃	—	4	2	no	—
302	C₄×D₅₃	—	4	2	no	—
303	C₄×D₅₃	—	4	2	no	—
304	C₄×D₅₃	—	4	2	no	—
305	Dic₁₀₆	—	2	2	no	—
306	Dic₁₀₆	—	2	2	no	—
307	Dic₁₀₆	—	2	4	no	—
308	C₂²×C₅₃	—	2	1	no	—
309	C₂²×C₅₃	—	2	1	no	—
310	C₂²×C₅₃	—	2	1	no	—
311	C₂²×C₅₃	—	2	2	no	—
312	C₂²×C₅₃	—	2	2	no	—
313	C₂²×C₅₃	—	2	1	no	—
314	C₂²×C₅₃	—	2	2	no	—
315	C₂²×C₅₃	—	2	2	no	—
316	C₂²×C₅₃	—	2	2	no	—
317	C₂²×C₅₃	—	2	1	no	—
318	C₂²×C₅₃	—	2	2	no	—
319	C₂²×C₅₃	—	8	4	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	2	no	—
324	C₂×D₅₃	—	2	2	no	—
325	C₂×D₅₃	—	2	1	no	—
326	C₂×D₅₃	—	2	1	no	—
327	C₂×D₅₃	—	2	2	no	—
328	C₂×D₅₃	—	2	2	no	—
329	C₂×D₅₃	—	2	2	no	—
330	C₂×D₅₃	—	2	2	no	—
331	C₂×D₅₃	—	8	4	no	—
332	C₄×C₅₃	—	2	1	no	—
333	C₄×C₅₃	—	2	2	no	—
334	C₄×C₅₃	—	2	1	no	—
335	C₄×C₅₃	—	2	1	no	—
336	C₄×C₅₃	—	2	2	no	—
337	C₄×C₅₃	—	2	1	no	—
338	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
339	Dic₅₃	—	2	1	no	—
340	Dic₅₃	—	2	2	no	—
341	Dic₅₃	—	2	2	no	—
342	Dic₅₃	—	2	1	no	—
343	Dic₅₃	—	2	1	no	—
344	Dic₅₃	—	2	1	no	—
345	Dic₅₃	C₂×#41	1	2	yes	—
346	Dic₅₃	C₂×#41	1	2	yes	—
347	Dic₅₃	H(5,𝔽₂)	1	2	yes	—
348	#3508	—	53	1	no	maximal, Sylow
349	C₂×C₅₃	—	2	2	no	—
350	C₂×C₅₃	—	4	1	no	—
351	C₂×C₅₃	—	4	2	no	—
352	C₂×C₅₃	—	4	2	no	—
353	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
354	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
356	D₅₃	—	4	1	no	—
357	D₅₃	—	4	2	no	—
358	D₅₃	—	4	2	no	—
359	#559	—	53	1	no	—
360	#559	—	53	2	no	—
361	#559	—	53	1	no	—
362	#550	—	53	1	no	—
363	#550	—	53	1	no	—
364	#550	—	53	2	no	—
365	#546	—	53	1	no	—
366	#546	—	53	1	no	—
367	#546	—	53	2	no	—
368	#546	—	53	1	no	—
369	#546	—	53	2	no	—
370	#546	D₅₃	1	1	yes	characteristic, complemented
371	#540	—	53	2	no	—
372	#540	—	53	2	no	—
373	#535	—	53	2	no	—
374	#533	—	53	1	no	—
375	#532	—	53	1	no	—
376	#532	—	53	1	no	—
377	#532	—	53	1	no	—
378	#532	—	53	1	no	—
379	C₂×#127	—	53	1	no	—
380	#518	—	53	2	no	—
381	C₄×#41	—	53	1	no	—
382	C₅₃	#3508	1	1	yes	characteristic, complemented, Sylow
383	C₂×#41	—	53	1	no	—
384	C₂×#41	—	53	1	no	—
385	C₂×#41	—	53	2	no	—
386	C₂×#41	—	53	1	no	—
387	C₂×#41	—	53	2	no	—
388	C₂×#41	—	53	1	no	—
389	C₂×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
390	C₂²×D₄	—	53	2	no	—
391	C₂²×D₄	—	53	2	no	—
392	C₂²×D₄	—	53	1	no	—
393	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic
394	C₄⋊Q₈	—	53	1	no	—
395	C₄⋊Q₈	—	53	1	no	—
396	#127	—	53	1	no	—
397	#127	—	53	1	no	—
398	#127	—	53	2	no	—
399	#127	—	53	2	no	—
400	#127	—	53	1	no	—
401	#127	—	53	1	no	—
402	#127	—	53	2	no	—
403	#127	—	53	2	no	—
404	#125	—	53	2	no	—
405	#124	—	53	1	no	—
406	#124	—	53	1	no	—
407	#124	—	53	2	no	—
408	#124	—	53	2	no	—
409	#124	—	53	2	no	—
410	#124	—	53	2	no	—
411	#124	—	53	1	no	—
412	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
413	#123	—	53	2	no	—
414	#123	—	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	C₂×D₅₃	1	2	yes	complemented
421	C₂²⋊Q₈	—	53	1	no	—
422	C₂²⋊Q₈	—	53	2	no	—
423	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
424	#121	—	53	2	no	—
425	#121	—	53	2	no	—
426	#121	—	53	1	no	—
427	#121	—	53	2	no	—
428	#121	—	53	2	no	—
429	#121	—	53	2	no	—
430	#121	—	53	2	no	—
431	#121	—	53	1	no	—
432	#121	—	53	2	no	—
433	#121	—	53	1	no	—
434	#121	—	53	2	no	—
435	#121	—	53	2	no	—
436	#121	—	53	2	no	—
437	#121	—	53	2	no	—
438	#121	—	53	2	no	—
439	#121	—	53	2	no	—
440	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
441	#121	C₂×D₅₃	1	2	yes	complemented
442	#120	—	53	2	no	—
443	#120	—	53	2	no	—
444	#120	—	53	2	no	—
445	#120	C₂×D₅₃	1	2	yes	—
446	C₄×Q₈	—	53	1	no	—
447	C₄×Q₈	—	53	1	no	—
448	C₄×Q₈	—	53	2	no	—
449	C₄×Q₈	—	53	1	no	—
450	C₄×Q₈	—	53	1	no	—
451	C₄×D₄	—	53	1	no	—
452	C₄×D₄	—	53	1	no	—
453	C₄×D₄	—	53	1	no	—
454	C₄×D₄	—	53	1	no	—
455	C₄×D₄	—	53	2	no	—
456	C₄×D₄	—	53	2	no	—
457	C₄×D₄	—	53	2	no	—
458	C₄×D₄	—	53	2	no	—
459	C₄×D₄	—	53	2	no	—
460	C₄×D₄	—	53	1	no	—
461	C₄×D₄	—	53	1	no	—
462	C₄×D₄	—	53	1	no	—
463	C₄×D₄	—	53	2	no	—
464	C₄×D₄	—	53	2	no	—
465	C₄×D₄	—	53	2	no	—
466	C₄×D₄	—	53	2	no	—
467	C₄×D₄	—	53	2	no	—
468	C₄×D₄	—	53	1	no	—
469	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
470	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
471	#117	—	53	1	no	—
472	#117	—	53	1	no	—
473	#117	—	53	1	no	—
474	#117	—	53	2	no	—
475	C₂×C₂²⋊C₄	—	53	2	no	—
476	C₂×C₂²⋊C₄	—	53	2	no	—
477	C₂×C₂²⋊C₄	—	53	2	no	—
478	C₂×C₂²⋊C₄	C₂×D₅₃	1	2	yes	—
479	C₂×C₄²	—	53	1	no	—
480	C₂×C₄²	—	53	1	no	—
481	C₂×C₄²	—	53	1	no	—
482	C₂⁴	—	53	2	no	—
483	C₂⁴	C₂²×D₅₃	1	2	yes	—
484	#41	—	4	2	no	—
485	#41	—	106	4	no	—
486	#41	—	212	2	no	—
487	#41	—	212	4	no	—
488	#41	—	212	2	no	—
489	#41	—	212	4	no	—
490	#41	—	212	2	no	—
491	C₂×Q₈	—	53	1	no	—
492	C₂×Q₈	—	53	2	no	—
493	C₂×Q₈	—	53	1	no	—
494	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	53	1	no	—
497	C₂×D₄	—	53	2	no	—
498	C₂×D₄	—	53	2	no	—
499	C₂×D₄	—	53	2	no	—
500	C₂×D₄	—	53	2	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	2	no	—
510	C₂×D₄	—	53	1	no	—
511	C₂×D₄	—	53	1	no	—
512	C₂×D₄	—	53	2	no	—
513	C₂×D₄	—	53	2	no	—
514	C₂×D₄	—	53	2	no	—
515	C₂×D₄	—	106	8	no	—
516	C₂×D₄	—	212	2	no	—
517	C₂×D₄	—	212	4	no	—
518	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
519	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
520	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
521	C₂×D₄	C₂²×D₅₃	1	2	yes	—
522	C₂×D₄	C₂²×D₅₃	1	2	yes	—
523	C₂×D₄	C₂²×D₅₃	1	2	yes	—
524	C₂²×C₄	—	53	1	no	—
525	C₂²×C₄	—	53	1	no	—
526	C₂²×C₄	—	53	1	no	—
527	C₂²×C₄	—	53	1	no	—
528	C₂²×C₄	—	53	2	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	2	no	—
534	C₂²×C₄	—	53	2	no	—
535	C₂²×C₄	—	53	2	no	—
536	C₂²×C₄	—	53	2	no	—
537	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
538	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
539	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
540	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
541	C₄⋊C₄	—	53	1	no	—
542	C₄⋊C₄	—	53	1	no	—
543	C₄⋊C₄	—	53	2	no	—
544	C₄⋊C₄	—	53	2	no	—
545	C₄⋊C₄	—	53	1	no	—
546	C₄⋊C₄	—	53	1	no	—
547	C₄⋊C₄	—	53	1	no	—
548	C₄⋊C₄	—	53	2	no	—
549	C₄⋊C₄	—	53	1	no	—
550	C₄⋊C₄	—	53	2	no	—
551	C₄⋊C₄	—	53	2	no	—
552	C₄⋊C₄	—	53	2	no	—
553	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
554	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
555	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
556	C₂²⋊C₄	—	53	1	no	—
557	C₂²⋊C₄	—	53	2	no	—
558	C₂²⋊C₄	—	53	2	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	2	no	—
567	C₂²⋊C₄	—	53	1	no	—
568	C₂²⋊C₄	—	53	1	no	—
569	C₂²⋊C₄	—	53	2	no	—
570	C₂²⋊C₄	—	53	2	no	—
571	C₂²⋊C₄	—	53	2	no	—
572	C₂²⋊C₄	—	53	2	no	—
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	1	yes	characteristic
578	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
579	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
580	C₄²	—	53	1	no	—
581	C₄²	—	53	1	no	—
582	C₄²	—	53	1	no	—
583	C₄²	—	53	1	no	—
584	C₄²	—	53	1	no	—
585	C₄²	—	53	1	no	—
586	C₄²	—	53	1	no	—
587	C₄²	—	53	1	no	—
588	C₄²	—	53	1	no	—
589	C₄²	—	53	2	no	—
590	C₄²	—	53	2	no	—
591	C₄²	C₂²×D₅₃	1	1	yes	characteristic
592	C₂³	—	2	4	no	—
593	C₂³	—	4	2	no	—
594	C₂³	—	4	2	no	—
595	C₂³	—	53	2	no	—
596	C₂³	—	53	2	no	—
597	C₂³	—	53	1	no	—
598	C₂³	—	106	4	no	—
599	C₂³	—	212	2	no	—
600	C₂³	—	212	2	no	—
601	C₂³	C₂³×D₅₃	1	2	yes	—
602	C₂³	C₂³×D₅₃	1	2	yes	—
603	C₂³	C₂³×D₅₃	1	1	yes	characteristic
604	C₂³	C₂³×D₅₃	1	1	yes	characteristic
605	Q₈	—	2	2	no	—
606	Q₈	—	106	2	no	—
607	Q₈	—	106	4	no	—
608	Q₈	—	106	2	no	—
609	D₄	—	2	2	no	—
610	D₄	—	2	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	4	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	106	4	no	—
616	D₄	—	106	4	no	—
617	D₄	—	106	4	no	—
618	D₄	—	106	4	no	—
619	D₄	—	106	4	no	—
620	D₄	—	106	4	no	—
621	D₄	—	106	2	no	—
622	D₄	—	106	2	no	—
623	D₄	—	106	2	no	—
624	D₄	—	106	2	no	—
625	D₄	—	212	2	no	—
626	D₄	—	212	2	no	—
627	D₄	—	212	2	no	—
628	D₄	—	212	2	no	—
629	D₄	—	212	2	no	—
630	D₄	—	212	2	no	—
631	D₄	—	212	2	no	—
632	D₄	—	212	2	no	—
633	D₄	—	212	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	2	no	—
638	C₂×C₄	—	53	4	no	—
639	C₂×C₄	—	53	1	no	—
640	C₂×C₄	—	53	1	no	—
641	C₂×C₄	—	53	1	no	—
642	C₂×C₄	—	53	1	no	—
643	C₂×C₄	—	53	1	no	—
644	C₂×C₄	—	53	1	no	—
645	C₂×C₄	—	53	1	no	—
646	C₂×C₄	—	53	2	no	—
647	C₂×C₄	—	53	2	no	—
648	C₂×C₄	—	106	2	no	—
649	C₂×C₄	—	106	2	no	—
650	C₂×C₄	—	106	2	no	—
651	C₂×C₄	—	106	2	no	—
652	C₂×C₄	—	106	2	no	—
653	C₂×C₄	—	106	2	no	—
654	C₂×C₄	—	212	2	no	—
655	C₂×C₄	—	212	2	no	—
656	C₂×C₄	—	212	2	no	—
657	C₂×C₄	—	212	2	no	—
658	C₂×C₄	—	212	2	no	—
659	C₂×C₄	—	212	2	no	—
660	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₅₃	1	2	yes	—
665	C₂×C₄	C₂³×D₅₃	1	2	yes	—
666	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	8	4	no	—
679	C₂²	—	106	1	no	—
680	C₂²	—	106	2	no	—
681	C₂²	—	106	2	no	—
682	C₂²	—	106	1	no	—
683	C₂²	—	106	2	no	—
684	C₂²	—	106	2	no	—
685	C₂²	—	106	1	no	—
686	C₂²	—	106	2	no	—
687	C₂²	—	106	2	no	—
688	C₂²	—	424	4	no	—
689	C₂²	#41×D₅₃	1	2	yes	—
690	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
691	C₄	—	2	1	no	—
692	C₄	—	2	1	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	2	no	—
697	C₄	—	53	2	no	—
698	C₄	—	53	2	no	—
699	C₄	—	53	2	no	—
700	C₄	—	106	1	no	—
701	C₄	—	106	1	no	—
702	C₄	—	106	1	no	—
703	C₄	—	106	2	no	—
704	C₄	—	106	1	no	—
705	C₄	—	106	2	no	—
706	C₄	#13133262	1	2	yes	—
707	C₂	—	2	2	no	—
708	C₂	—	4	2	no	—
709	C₂	—	4	2	no	—
710	C₂	—	4	1	no	—
711	C₂	—	212	2	no	—
712	C₂	—	212	2	no	—
713	C₂	—	212	1	no	—
714	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
715	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
716	C₂	C₂×#13133262	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#546	C₂
hypercenter	#546	D₅₃
hypocenter	C₅₃	#3508
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #16811357	C₂	semidirect
2. #16811356	C₂	semidirect
3. #16811355	C₂	semidirect
4. #16811292	C₂	semidirect
5. #16811291	C₂	semidirect
6. #16811291	C₂	semidirect
7. #16811269	C₂	semidirect
8. #16811267	C₂	semidirect
9. #16811264	C₂	semidirect
10. #16811263	C₂	semidirect
11. #16811260	C₂	semidirect
12. #16811225	C₂	semidirect
13. #16811223	C₂	semidirect
14. #16811188	C₂	semidirect
15. #16811175	C₂	semidirect
16. #16811172	C₂	semidirect
17. #16811170	C₂	semidirect
18. #16811169	C₂	semidirect
19. #16811168	C₂	semidirect
20. C₂×#13133213	C₂	semidirect
21. #16811096	C₂	semidirect
22. C₄×#11719947	C₂	semidirect
23. C₅₃×#546	C₂	semidirect
24. C₂×#11719949	C₂²	semidirect
25. C₂×#11719945	C₂²	semidirect
26. C₂×#11719945	C₂²	semidirect
28. C₂×#11719947	C₂²	semidirect
29. C₂×#11719947	C₂²	semidirect
33. #13133216	C₂²	semidirect
34. #13133215	C₂²	semidirect
41. #13133213	C₂²	semidirect
42. #13133213	C₂²	semidirect
43. #13133207	C₂²	semidirect
44. #13133206	C₂²	semidirect
45. #13133205	C₂²	semidirect
46. #13133204	C₂²	semidirect
47. #13133203	C₂²	semidirect
48. #13133203	C₂²	semidirect
49. #13133203	C₂²	semidirect
50. #13133203	C₂²	semidirect
51. #13133202	C₂²	semidirect
52. #13133202	C₂²	semidirect
53. #13133201	C₂²	semidirect
54. #13133200	C₂²	semidirect
55. #13133199	C₂²	semidirect
56. #13133199	C₂²	semidirect
57. #13133198	C₂²	semidirect
60. #13133192	C₂²	semidirect
61. #13133192	C₂²	semidirect
62. #13133191	C₂²	semidirect
63. #13133191	C₂²	semidirect
64. #13133190	C₂²	semidirect
65. #13133190	C₂²	semidirect
66. #13133190	C₂²	semidirect
67. #13133190	C₂²	semidirect
68. #13133190	C₂²	semidirect
69. #13133189	C₂²	semidirect
70. #13133189	C₂²	semidirect
71. #13133189	C₂²	semidirect
72. #13133189	C₂²	semidirect
73. #13133189	C₂²	semidirect
74. #13133188	C₂²	semidirect
75. #13133188	C₂²	semidirect
79. Q₈×Dic₅₃	C₂²	semidirect
80. C₄×Dic₁₀₆	C₂²	semidirect
81. #13133182	C₂²	semidirect
82. #13133182	C₂²	semidirect
83. #13133182	C₂²	semidirect
84. C₄×D₂₁₂	C₂²	semidirect
86. D₄×Dic₅₃	C₂²	semidirect
87. #13133179	C₂²	semidirect
89. C₄×C₂²⋊D₅₃	C₂²	semidirect
90. C₄×C₂²⋊D₅₃	C₂²	semidirect
91. C₄×C₂²⋊D₅₃	C₂²	semidirect
92. C₄×C₂²⋊D₅₃	C₂²	semidirect
93. C₄×C₂²⋊D₅₃	C₂²	semidirect
94. C₄×C₂²⋊D₅₃	C₂²	semidirect
96. #13133177	C₂²	semidirect
97. #13133177	C₂²	semidirect
98. #13133177	C₂²	semidirect
99. #13133177	C₂²	semidirect
100. #13133177	C₂²	semidirect
101. #13133177	C₂²	semidirect
102. #13133175	C₂²	semidirect
105. #13133173	C₂²	semidirect
110. C₂×C₄×Dic₅₃	C₂²	semidirect
111. C₄²×D₅₃	C₂²	semidirect
112. C₂×#41×C₅₃	C₂²	semidirect
114. #124×C₅₃	C₂²	semidirect
115. #123×C₅₃	C₂²	semidirect
117. #121×C₅₃	C₂²	semidirect
118. #121×C₅₃	C₂²	semidirect
121. C₄×D₄×C₅₃	C₂²	semidirect
283. C₂×Dic₅₃	#41	semidirect
370. #546	D₅₃	semidirect
382. C₅₃	#3508	semidirect
389. C₂×#41	C₂×D₅₃	semidirect
412. #124	C₂×D₅₃	semidirect
420. #123	C₂×D₅₃	semidirect
440. #121	C₂×D₅₃	semidirect
441. #121	C₂×D₅₃	semidirect
470. C₄×D₄	C₂×D₅₃	semidirect