Subgroups — #553×D₅₃ #20288230

Order 6784.

1252 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811326	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811325	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811324	C₂	1	2	yes	maximal, complemented
4	#16811323	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811322	C₂	1	2	yes	maximal, complemented
6	#16811321	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811320	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811319	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811318	C₂	1	2	yes	maximal, complemented
10	#16811317	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811316	C₂	1	2	yes	maximal, complemented
12	#126×D₅₃	C₂	1	2	yes	maximal, complemented
13	#125×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#123×D₅₃	C₂	1	2	yes	maximal, complemented
15	#121×D₅₃	C₂	1	2	yes	maximal, complemented
16	#121×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#121×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
20	C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#117×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₄×D₅₃	C₂²	1	2	yes	—
25	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₅₃	C₂²	1	2	yes	—
28	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₅₃	C₂²	1	2	yes	—
31	C₂²×C₄×D₅₃	C₂²	1	2	yes	—
32	#13133212	C₂²	1	2	yes	complemented
33	#13133212	C₂²	1	2	yes	complemented
34	#13133212	C₂²	1	2	yes	complemented
35	#13133211	C₂²	1	2	yes	complemented
36	#13133210	C₂²	1	2	yes	complemented
37	#13133210	C₂²	1	2	yes	complemented
38	#13133210	C₂²	1	2	yes	complemented
39	#13133209	C₂²	1	1	yes	characteristic, complemented
40	#13133208	C₂²	1	1	yes	characteristic, complemented
41	#13133208	C₂²	1	1	yes	characteristic, complemented
42	#13133207	C₂²	1	2	yes	complemented
43	#13133207	C₂²	1	2	yes	complemented
44	#13133202	C₂²	1	2	yes	complemented
45	#13133202	C₂²	1	2	yes	complemented
46	#13133201	C₂²	1	2	yes	complemented
47	#13133200	C₂²	1	2	yes	complemented
48	#13133199	C₂²	1	2	yes	complemented
49	#13133199	C₂²	1	2	yes	complemented
50	#13133198	C₂²	1	2	yes	complemented
51	#13133192	C₂²	1	1	yes	characteristic, complemented
52	#13133192	C₂²	1	1	yes	characteristic, complemented
53	#13133192	C₂²	1	2	yes	complemented
54	#13133191	C₂²	1	1	yes	characteristic, complemented
55	#13133191	C₂²	1	1	yes	characteristic, complemented
56	#13133191	C₂²	1	2	yes	complemented
57	#13133190	C₂²	1	2	yes	complemented
58	#13133190	C₂²	1	2	yes	complemented
59	#13133190	C₂²	1	2	yes	complemented
60	#13133190	C₂²	1	2	yes	complemented
61	#13133189	C₂²	1	2	yes	complemented
62	#13133189	C₂²	1	2	yes	complemented
63	#13133189	C₂²	1	2	yes	complemented
64	#13133189	C₂²	1	2	yes	complemented
65	#13133188	C₂²	1	2	yes	complemented
66	#13133188	C₂²	1	1	yes	characteristic, complemented
67	#13133188	C₂²	1	1	yes	characteristic, complemented
68	C₄×D₂₁₂	C₂²	1	2	yes	complemented
69	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
70	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
71	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
72	D₄×Dic₅₃	C₂²	1	2	yes	complemented
73	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
74	#13133179	C₂²	1	1	yes	characteristic, complemented
75	#13133179	C₂²	1	2	yes	complemented
76	#13133179	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
82	#13133177	C₂²	1	2	yes	complemented
83	#13133177	C₂²	1	1	yes	characteristic, complemented
84	#13133177	C₂²	1	2	yes	complemented
85	#13133177	C₂²	1	2	yes	complemented
86	#13133177	C₂²	1	1	yes	characteristic, complemented
87	#13133176	C₂²	1	1	yes	characteristic, complemented
88	#13133175	C₂²	1	1	yes	characteristic, complemented
89	#13133175	C₂²	1	1	yes	characteristic, complemented
90	#13133174	C₂²	1	2	yes	complemented
91	#13133173	C₂²	1	2	yes	complemented
92	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
93	C₂×#11719919	C₂²	1	2	yes	complemented
94	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
95	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
96	C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
97	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
98	C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
99	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
100	C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
101	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
102	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
103	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
104	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
105	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
106	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
109	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
110	C₄²×D₅₃	C₂²	1	2	yes	—
111	C₄²×D₅₃	C₂²	1	1	yes	characteristic
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	2	yes	complemented
116	#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	#121×C₅₃	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic
124	C₂³×D₅₃	C₂³	1	2	yes	—
125	C₂³×D₅₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₅₃	C₂³	1	2	yes	—
129	C₂×D₄×C₅₃	C₂³	1	2	yes	—
130	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
133	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
141	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
142	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
143	C₂²×Dic₅₃	C₂³	1	2	yes	—
144	C₂²×Dic₅₃	C₂³	1	2	yes	—
145	D₄×D₅₃	—	2	8	no	—
146	D₄×D₅₃	—	2	4	no	—
147	D₄×D₅₃	—	2	4	no	—
148	D₄×D₅₃	—	4	4	no	—
149	C₂×D₂₁₂	C₂³	1	2	yes	—
150	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
151	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
152	C₂×D₂₁₂	C₂³	1	2	yes	—
153	C₂×C₄×D₅₃	—	2	4	no	—
154	C₂×C₄×D₅₃	—	2	4	no	—
155	C₂×C₄×D₅₃	—	4	4	no	—
156	C₂×C₄×D₅₃	—	4	4	no	—
157	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₅₃	C₂³	1	2	yes	—
159	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₅₃	C₂³	1	2	yes	—
161	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₅₃	C₂³	1	2	yes	—
164	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₅₃	C₂³	1	2	yes	—
169	C₂×C₄×D₅₃	C₂³	1	2	yes	—
170	C₂×C₄×D₅₃	C₂³	1	2	yes	—
171	C₂×C₄×D₅₃	C₂³	1	2	yes	—
172	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
179	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
182	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
183	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
185	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₄²×C₅₃	C₂³	1	2	yes	—
187	C₄²×C₅₃	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
190	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
191	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
192	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
194	#11719921	C₂³	1	2	yes	—
195	#11719921	C₂³	1	2	yes	—
196	#11719921	C₂³	1	1	yes	characteristic
197	#11719921	C₂³	1	1	yes	characteristic
198	#11719921	C₂³	1	2	yes	—
199	#11719921	C₂³	1	2	yes	—
200	#11719921	C₂³	1	1	yes	characteristic
201	#11719921	C₂³	1	2	yes	—
202	#11719921	C₂³	1	2	yes	—
203	#11719921	C₂³	1	1	yes	characteristic
204	#11719921	C₂³	1	2	yes	—
205	#11719921	C₂³	1	2	yes	—
206	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₅₃	C₂³	1	2	yes	—
209	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₅₃	C₂³	1	2	yes	—
211	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₅₃	C₂³	1	2	yes	—
213	#11719919	C₂³	1	2	yes	—
214	#11719919	C₂³	1	2	yes	—
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	#11719919	C₂³	1	2	yes	—
220	#11719919	C₂³	1	1	yes	characteristic
221	#11719919	C₂³	1	1	yes	characteristic
222	#11719919	C₂³	1	2	yes	—
223	#11719919	C₂³	1	2	yes	—
224	C₄×Dic₅₃	C₂³	1	2	yes	—
225	C₄×Dic₅₃	C₂³	1	2	yes	—
226	C₄×Dic₅₃	C₂³	1	2	yes	—
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	2	no	—
234	C₂²×D₅₃	—	2	2	no	—
235	C₂²×D₅₃	—	2	2	no	—
236	C₂²×D₅₃	—	2	2	no	—
237	C₂²×D₅₃	—	2	4	no	—
238	C₂²×D₅₃	—	2	4	no	—
239	C₂²×D₅₃	—	2	4	no	—
240	C₂²×D₅₃	—	2	2	no	—
241	C₂²×D₅₃	#41	1	4	yes	—
242	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
243	C₂²×D₅₃	C₂⁴	1	2	yes	—
244	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
245	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
246	D₄×C₅₃	—	2	2	no	—
247	D₄×C₅₃	—	2	4	no	—
248	D₄×C₅₃	—	2	2	no	—
249	D₄×C₅₃	—	4	2	no	—
250	C₂×C₄×C₅₃	—	2	2	no	—
251	C₂×C₄×C₅₃	—	2	2	no	—
252	C₂×C₄×C₅₃	—	4	2	no	—
253	C₂×C₄×C₅₃	—	4	2	no	—
254	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
255	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
257	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
260	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
262	C₂²⋊D₅₃	—	2	4	no	—
263	C₂²⋊D₅₃	—	2	2	no	—
264	C₂²⋊D₅₃	—	2	2	no	—
265	C₂²⋊D₅₃	—	2	4	no	—
266	C₂²⋊D₅₃	—	2	4	no	—
267	C₂²⋊D₅₃	—	4	2	no	—
268	C₂²⋊D₅₃	—	4	2	no	—
269	C₂×Dic₅₃	—	2	2	no	—
270	C₂×Dic₅₃	—	2	2	no	—
271	C₂×Dic₅₃	—	4	2	no	—
272	C₂×Dic₅₃	—	4	2	no	—
273	C₂×Dic₅₃	C₂⁴	1	2	yes	—
274	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₅₃	C₂⁴	1	2	yes	—
276	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₅₃	C₂⁴	1	2	yes	—
279	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
281	D₂₁₂	—	2	4	no	—
282	D₂₁₂	—	2	2	no	—
283	D₂₁₂	—	2	2	no	—
284	D₂₁₂	—	4	2	no	—
285	C₄×D₅₃	—	2	2	no	—
286	C₄×D₅₃	—	2	2	no	—
287	C₄×D₅₃	—	2	4	no	—
288	C₄×D₅₃	—	2	2	no	—
289	C₄×D₅₃	—	2	2	no	—
290	C₄×D₅₃	—	2	4	no	—
291	C₄×D₅₃	—	2	4	no	—
292	C₄×D₅₃	—	2	2	no	—
293	C₄×D₅₃	—	2	2	no	—
294	C₄×D₅₃	—	2	2	no	—
295	C₄×D₅₃	—	2	2	no	—
296	C₄×D₅₃	—	4	2	no	—
297	C₄×D₅₃	—	4	2	no	—
298	C₄×D₅₃	—	4	2	no	—
299	C₄×D₅₃	—	4	2	no	—
300	C₄×D₅₃	#41	1	4	yes	—
301	C₂²×C₅₃	—	2	1	no	—
302	C₂²×C₅₃	—	2	1	no	—
303	C₂²×C₅₃	—	2	1	no	—
304	C₂²×C₅₃	—	2	1	no	—
305	C₂²×C₅₃	—	2	2	no	—
306	C₂²×C₅₃	—	2	2	no	—
307	C₂²×C₅₃	—	2	2	no	—
308	C₂²×C₅₃	—	2	1	no	—
309	C₂²×C₅₃	C₂×#41	1	2	yes	—
310	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
311	C₂×D₅₃	—	2	1	no	—
312	C₂×D₅₃	—	2	1	no	—
313	C₂×D₅₃	—	2	8	no	—
314	C₂×D₅₃	—	2	1	no	—
315	C₂×D₅₃	—	2	1	no	—
316	C₂×D₅₃	—	2	2	no	—
317	C₂×D₅₃	—	2	2	no	—
318	C₂×D₅₃	—	2	2	no	—
319	C₂×D₅₃	—	2	1	no	—
320	C₂×D₅₃	—	4	4	no	—
321	C₂×D₅₃	—	4	8	no	—
322	C₂×D₅₃	C₂×#41	1	2	yes	—
323	C₂×D₅₃	C₂×#41	1	2	yes	—
324	C₂×D₅₃	C₂×#41	1	2	yes	—
325	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	—
326	C₄×C₅₃	—	2	1	no	—
327	C₄×C₅₃	—	2	1	no	—
328	C₄×C₅₃	—	2	2	no	—
329	C₄×C₅₃	—	2	1	no	—
330	C₄×C₅₃	—	2	1	no	—
331	C₄×C₅₃	—	2	2	no	—
332	C₄×C₅₃	—	2	2	no	—
333	C₄×C₅₃	C₂×#41	1	2	yes	—
334	Dic₅₃	—	2	1	no	—
335	Dic₅₃	—	2	1	no	—
336	Dic₅₃	—	2	2	no	—
337	Dic₅₃	—	2	1	no	—
338	Dic₅₃	—	2	1	no	—
339	Dic₅₃	—	2	2	no	—
340	Dic₅₃	—	2	2	no	—
341	Dic₅₃	C₂×#41	1	2	yes	—
342	C₂×#553	—	53	1	no	maximal, Sylow
343	C₂×C₅₃	—	2	2	no	—
344	C₂×C₅₃	—	4	1	no	—
345	C₂×C₅₃	—	4	2	no	—
346	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
347	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
348	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	D₅₃	—	2	2	no	—
350	D₅₃	—	4	1	no	—
351	D₅₃	—	4	2	no	—
352	D₅₃	#553	1	4	yes	direct product factor
353	#553	—	53	2	no	—
354	#553	—	53	1	no	—
355	#553	—	53	2	no	—
356	#553	—	53	2	no	—
357	#553	—	53	1	no	—
358	#553	—	53	1	no	—
359	#553	—	53	1	no	—
360	#553	—	53	2	no	—
361	#553	—	53	1	no	—
362	#553	—	53	1	no	—
363	#553	—	53	1	no	—
364	#553	D₅₃	1	1	yes	characteristic, direct product factor
365	C₂×#126	—	53	2	no	—
366	C₂×#125	—	53	1	no	—
367	C₂×#123	—	53	2	no	—
368	C₂×#121	—	53	2	no	—
369	C₂×#121	—	53	1	no	—
370	C₂×#121	—	53	1	no	—
371	C₂×C₄×D₄	—	53	2	no	—
372	C₂×C₄×D₄	—	53	1	no	—
373	C₂×C₄×D₄	—	53	1	no	—
374	C₂×#117	—	53	1	no	—
375	C₂²×C₄⋊C₄	—	53	1	no	—
376	C₅₃	C₂×#553	1	1	yes	characteristic, complemented, Sylow
377	C₂²×D₄	—	53	1	no	—
378	C₂²×D₄	—	53	2	no	—
379	C₂²×D₄	—	53	1	no	—
380	C₂²×D₄	—	53	2	no	—
381	C₂³×C₄	—	53	1	no	—
382	C₂³×C₄	—	53	1	no	—
383	C₂³×C₄	—	53	2	no	—
384	C₂³×C₄	—	53	2	no	—
385	#126	—	53	2	no	—
386	#126	—	53	2	no	—
387	#126	—	53	2	no	—
388	#126	—	53	2	no	—
389	#126	—	53	2	no	—
390	#126	—	53	2	no	—
391	#126	—	53	2	no	—
392	#126	C₂×D₅₃	1	2	yes	complemented
393	#125	—	53	2	no	—
394	#125	—	53	2	no	—
395	#125	—	53	1	no	—
396	#125	—	53	1	no	—
397	#125	—	53	1	no	—
398	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
399	#123	—	53	2	no	—
400	#123	—	53	2	no	—
401	#123	—	53	2	no	—
402	#123	—	53	2	no	—
403	#123	—	53	2	no	—
404	#123	—	53	2	no	—
405	#123	—	53	2	no	—
406	#123	C₂×D₅₃	1	2	yes	complemented
407	#121	—	53	2	no	—
408	#121	—	53	1	no	—
409	#121	—	53	1	no	—
410	#121	—	53	2	no	—
411	#121	—	53	2	no	—
412	#121	—	53	2	no	—
413	#121	—	53	2	no	—
414	#121	—	53	2	no	—
415	#121	—	53	1	no	—
416	#121	—	53	1	no	—
417	#121	—	53	2	no	—
418	#121	—	53	1	no	—
419	#121	—	53	1	no	—
420	#121	—	53	2	no	—
421	#121	—	53	2	no	—
422	#121	—	53	2	no	—
423	#121	—	53	2	no	—
424	#121	C₂×D₅₃	1	2	yes	complemented
425	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
426	#121	C₂×D₅₃	1	1	yes	characteristic, complemented
427	C₄×D₄	—	53	2	no	—
428	C₄×D₄	—	53	1	no	—
429	C₄×D₄	—	53	1	no	—
430	C₄×D₄	—	53	2	no	—
431	C₄×D₄	—	53	2	no	—
432	C₄×D₄	—	53	1	no	—
433	C₄×D₄	—	53	2	no	—
434	C₄×D₄	—	53	1	no	—
435	C₄×D₄	—	53	2	no	—
436	C₄×D₄	—	53	1	no	—
437	C₄×D₄	—	53	1	no	—
438	C₄×D₄	—	53	2	no	—
439	C₄×D₄	—	53	2	no	—
440	C₄×D₄	—	53	1	no	—
441	C₄×D₄	—	53	2	no	—
442	C₄×D₄	—	53	1	no	—
443	C₄×D₄	—	53	2	no	—
444	C₄×D₄	—	53	1	no	—
445	C₄×D₄	—	53	1	no	—
446	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
447	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
448	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
449	#117	—	53	1	no	—
450	#117	—	53	1	no	—
451	#117	—	53	1	no	—
452	#117	—	53	2	no	—
453	#117	—	53	2	no	—
454	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
455	C₂×C₄⋊C₄	—	53	2	no	—
456	C₂×C₄⋊C₄	—	53	1	no	—
457	C₂×C₄⋊C₄	—	53	1	no	—
458	C₂×C₄⋊C₄	—	53	1	no	—
459	C₂×C₄⋊C₄	—	53	2	no	—
460	C₂×C₄⋊C₄	—	53	2	no	—
461	C₂×C₄⋊C₄	—	53	1	no	—
462	C₂×C₄⋊C₄	—	53	1	no	—
463	C₂×C₄⋊C₄	—	53	1	no	—
464	C₂×C₄⋊C₄	—	53	2	no	—
465	C₂×C₄⋊C₄	—	53	1	no	—
466	C₂×C₄⋊C₄	—	53	2	no	—
467	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
468	C₂×C₂²⋊C₄	—	53	2	no	—
469	C₂×C₂²⋊C₄	—	53	1	no	—
470	C₂×C₂²⋊C₄	—	53	2	no	—
471	C₂×C₂²⋊C₄	—	53	2	no	—
472	C₂×C₂²⋊C₄	—	53	1	no	—
473	C₂×C₂²⋊C₄	—	53	2	no	—
474	C₂×C₄²	—	53	2	no	—
475	C₂×C₄²	—	53	1	no	—
476	C₂⁴	—	53	1	no	—
477	C₂⁴	—	53	1	no	—
478	C₂⁴	—	53	2	no	—
479	C₂×D₄	—	53	2	no	—
480	C₂×D₄	—	53	2	no	—
481	C₂×D₄	—	53	1	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	2	no	—
487	C₂×D₄	—	53	1	no	—
488	C₂×D₄	—	53	1	no	—
489	C₂×D₄	—	53	2	no	—
490	C₂×D₄	—	106	4	no	—
491	C₂×D₄	—	106	8	no	—
492	C₂×D₄	—	106	4	no	—
493	C₂×D₄	—	212	4	no	—
494	C₂×D₄	C₂²×D₅₃	1	2	yes	—
495	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
496	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
497	C₂×D₄	C₂²×D₅₃	1	2	yes	—
498	C₂²×C₄	—	53	1	no	—
499	C₂²×C₄	—	53	1	no	—
500	C₂²×C₄	—	53	1	no	—
501	C₂²×C₄	—	53	2	no	—
502	C₂²×C₄	—	53	2	no	—
503	C₂²×C₄	—	53	1	no	—
504	C₂²×C₄	—	53	2	no	—
505	C₂²×C₄	—	53	1	no	—
506	C₂²×C₄	—	53	2	no	—
507	C₂²×C₄	—	53	1	no	—
508	C₂²×C₄	—	53	1	no	—
509	C₂²×C₄	—	53	2	no	—
510	C₂²×C₄	—	53	1	no	—
511	C₂²×C₄	—	53	1	no	—
512	C₂²×C₄	—	53	1	no	—
513	C₂²×C₄	—	53	1	no	—
514	C₂²×C₄	—	53	2	no	—
515	C₂²×C₄	—	53	2	no	—
516	C₂²×C₄	—	53	2	no	—
517	C₂²×C₄	—	53	2	no	—
518	C₂²×C₄	—	106	4	no	—
519	C₂²×C₄	—	106	4	no	—
520	C₂²×C₄	—	212	4	no	—
521	C₂²×C₄	—	212	4	no	—
522	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
523	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
525	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
526	C₄⋊C₄	—	53	2	no	—
527	C₄⋊C₄	—	53	1	no	—
528	C₄⋊C₄	—	53	2	no	—
529	C₄⋊C₄	—	53	1	no	—
530	C₄⋊C₄	—	53	2	no	—
531	C₄⋊C₄	—	53	2	no	—
532	C₄⋊C₄	—	53	2	no	—
533	C₄⋊C₄	—	53	2	no	—
534	C₄⋊C₄	—	53	1	no	—
535	C₄⋊C₄	—	53	2	no	—
536	C₄⋊C₄	—	53	2	no	—
537	C₄⋊C₄	—	53	2	no	—
538	C₄⋊C₄	—	53	1	no	—
539	C₄⋊C₄	—	53	1	no	—
540	C₄⋊C₄	—	53	1	no	—
541	C₄⋊C₄	—	53	2	no	—
542	C₄⋊C₄	—	53	2	no	—
543	C₄⋊C₄	—	53	2	no	—
544	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
546	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
547	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
548	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
549	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
550	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
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	1	no	—
556	C₂²⋊C₄	—	53	2	no	—
557	C₂²⋊C₄	—	53	2	no	—
558	C₂²⋊C₄	—	53	2	no	—
559	C₂²⋊C₄	—	53	1	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	1	no	—
566	C₂²⋊C₄	—	53	1	no	—
567	C₂²⋊C₄	—	53	2	no	—
568	C₂²⋊C₄	—	53	2	no	—
569	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
571	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
574	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
575	C₄²	—	53	2	no	—
576	C₄²	—	53	2	no	—
577	C₄²	—	53	2	no	—
578	C₄²	—	53	1	no	—
579	C₄²	—	53	1	no	—
580	C₄²	—	53	1	no	—
581	C₄²	C₂²×D₅₃	1	2	yes	—
582	C₄²	C₂²×D₅₃	1	1	yes	characteristic
583	C₂³	—	53	1	no	—
584	C₂³	—	53	4	no	—
585	C₂³	—	53	1	no	—
586	C₂³	—	53	1	no	—
587	C₂³	—	53	2	no	—
588	C₂³	—	106	2	no	—
589	C₂³	—	106	2	no	—
590	C₂³	—	106	2	no	—
591	C₂³	—	106	4	no	—
592	C₂³	—	106	4	no	—
593	C₂³	—	106	2	no	—
594	C₂³	—	106	4	no	—
595	C₂³	—	106	2	no	—
596	C₂³	C₂³×D₅₃	1	1	yes	characteristic
597	C₂³	C₂³×D₅₃	1	2	yes	—
598	C₂³	C₂³×D₅₃	1	1	yes	characteristic
599	D₄	—	2	4	no	—
600	D₄	—	2	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	4	2	no	—
603	D₄	—	106	4	no	—
604	D₄	—	106	2	no	—
605	D₄	—	106	4	no	—
606	D₄	—	106	4	no	—
607	D₄	—	106	2	no	—
608	D₄	—	106	4	no	—
609	D₄	—	106	2	no	—
610	D₄	—	106	2	no	—
611	D₄	—	212	2	no	—
612	D₄	—	212	2	no	—
613	D₄	—	212	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	53	1	no	—
619	C₂×C₄	—	53	4	no	—
620	C₂×C₄	—	53	1	no	—
621	C₂×C₄	—	53	2	no	—
622	C₂×C₄	—	53	1	no	—
623	C₂×C₄	—	53	2	no	—
624	C₂×C₄	—	53	1	no	—
625	C₂×C₄	—	53	1	no	—
626	C₂×C₄	—	53	2	no	—
627	C₂×C₄	—	106	2	no	—
628	C₂×C₄	—	106	2	no	—
629	C₂×C₄	—	106	2	no	—
630	C₂×C₄	—	106	2	no	—
631	C₂×C₄	—	106	4	no	—
632	C₂×C₄	—	106	2	no	—
633	C₂×C₄	—	106	4	no	—
634	C₂×C₄	—	106	4	no	—
635	C₂×C₄	—	106	2	no	—
636	C₂×C₄	—	106	2	no	—
637	C₂×C₄	—	106	2	no	—
638	C₂×C₄	—	106	2	no	—
639	C₂×C₄	—	106	2	no	—
640	C₂×C₄	—	212	2	no	—
641	C₂×C₄	—	212	2	no	—
642	C₂×C₄	—	212	2	no	—
643	C₂×C₄	—	212	2	no	—
644	C₂×C₄	—	212	2	no	—
645	C₂×C₄	—	212	2	no	—
646	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₅₃	1	2	yes	—
648	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₅₃	1	2	yes	—
650	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₅₃	1	2	yes	—
653	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	53	2	no	—
663	C₂²	—	53	2	no	—
664	C₂²	—	53	2	no	—
665	C₂²	—	53	2	no	—
666	C₂²	—	106	8	no	—
667	C₂²	—	106	1	no	—
668	C₂²	—	106	1	no	—
669	C₂²	—	106	1	no	—
670	C₂²	—	106	1	no	—
671	C₂²	—	106	2	no	—
672	C₂²	—	106	2	no	—
673	C₂²	—	106	2	no	—
674	C₂²	—	106	1	no	—
675	C₂²	—	212	4	no	—
676	C₂²	—	212	8	no	—
677	C₂²	#41×D₅₃	1	2	yes	—
678	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	53	2	no	—
687	C₄	—	106	1	no	—
688	C₄	—	106	1	no	—
689	C₄	—	106	2	no	—
690	C₄	—	106	1	no	—
691	C₄	—	106	2	no	—
692	C₄	—	106	1	no	—
693	C₄	—	106	2	no	—
694	C₄	#41×D₅₃	1	2	yes	—
695	C₂	—	2	2	no	—
696	C₂	—	4	1	no	—
697	C₂	—	4	2	no	—
698	C₂	—	53	4	no	—
699	C₂	—	106	2	no	—
700	C₂	—	212	1	no	—
701	C₂	—	212	2	no	—
702	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
703	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
704	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	C₂×#553
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. #16811326	C₂	semidirect
2. #16811325	C₂	semidirect
3. #16811324	C₂	semidirect
4. #16811323	C₂	semidirect
5. #16811322	C₂	semidirect
6. #16811321	C₂	semidirect
7. #16811320	C₂	semidirect
8. #16811319	C₂	semidirect
9. #16811318	C₂	semidirect
10. #16811317	C₂	semidirect
11. #16811316	C₂	semidirect
12. #126×D₅₃	C₂	semidirect
13. #125×D₅₃	C₂	semidirect
14. #123×D₅₃	C₂	semidirect
15. #121×D₅₃	C₂	semidirect
16. #121×D₅₃	C₂	semidirect
17. #121×D₅₃	C₂	semidirect
18. C₄×D₄×D₅₃	C₂	semidirect
19. C₄×D₄×D₅₃	C₂	semidirect
20. C₄×D₄×D₅₃	C₂	semidirect
21. #117×D₅₃	C₂	semidirect
22. C₂×C₄⋊C₄×D₅₃	C₂	semidirect
23. C₅₃×#553	C₂	semidirect
32. #13133212	C₂²	semidirect
33. #13133212	C₂²	semidirect
34. #13133212	C₂²	semidirect
35. #13133211	C₂²	semidirect
36. #13133210	C₂²	semidirect
37. #13133210	C₂²	semidirect
38. #13133210	C₂²	semidirect
39. #13133209	C₂²	semidirect
40. #13133208	C₂²	semidirect
41. #13133208	C₂²	semidirect
42. #13133207	C₂²	semidirect
43. #13133207	C₂²	semidirect
44. #13133202	C₂²	semidirect
45. #13133202	C₂²	semidirect
46. #13133201	C₂²	semidirect
47. #13133200	C₂²	semidirect
48. #13133199	C₂²	semidirect
49. #13133199	C₂²	semidirect
50. #13133198	C₂²	semidirect
51. #13133192	C₂²	semidirect
52. #13133192	C₂²	semidirect
53. #13133192	C₂²	semidirect
54. #13133191	C₂²	semidirect
55. #13133191	C₂²	semidirect
56. #13133191	C₂²	semidirect
57. #13133190	C₂²	semidirect
58. #13133190	C₂²	semidirect
59. #13133190	C₂²	semidirect
60. #13133190	C₂²	semidirect
61. #13133189	C₂²	semidirect
62. #13133189	C₂²	semidirect
63. #13133189	C₂²	semidirect
64. #13133189	C₂²	semidirect
65. #13133188	C₂²	semidirect
66. #13133188	C₂²	semidirect
67. #13133188	C₂²	semidirect
68. C₄×D₂₁₂	C₂²	semidirect
69. C₄×D₂₁₂	C₂²	semidirect
70. C₄×D₂₁₂	C₂²	semidirect
71. D₄×Dic₅₃	C₂²	semidirect
72. D₄×Dic₅₃	C₂²	semidirect
73. D₄×Dic₅₃	C₂²	semidirect
74. #13133179	C₂²	semidirect
75. #13133179	C₂²	semidirect
76. #13133179	C₂²	semidirect
77. C₄×C₂²⋊D₅₃	C₂²	semidirect
78. C₄×C₂²⋊D₅₃	C₂²	semidirect
79. C₄×C₂²⋊D₅₃	C₂²	semidirect
80. C₄×C₂²⋊D₅₃	C₂²	semidirect
81. C₄×C₂²⋊D₅₃	C₂²	semidirect
82. #13133177	C₂²	semidirect
83. #13133177	C₂²	semidirect
84. #13133177	C₂²	semidirect
85. #13133177	C₂²	semidirect
86. #13133177	C₂²	semidirect
87. #13133176	C₂²	semidirect
88. #13133175	C₂²	semidirect
89. #13133175	C₂²	semidirect
90. #13133174	C₂²	semidirect
91. #13133173	C₂²	semidirect
92. C₂×C₄⋊Dic₅₃	C₂²	semidirect
93. C₂×#11719919	C₂²	semidirect
101. C₄⋊C₄×D₅₃	C₂²	semidirect
102. C₄⋊C₄×D₅₃	C₂²	semidirect
103. C₄⋊C₄×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
352. D₅₃	#553	direct (N × H)
364. #553	D₅₃	direct (N × H)
376. C₅₃	C₂×#553	semidirect
392. #126	C₂×D₅₃	semidirect
398. #125	C₂×D₅₃	semidirect
406. #123	C₂×D₅₃	semidirect
424. #121	C₂×D₅₃	semidirect
425. #121	C₂×D₅₃	semidirect
426. #121	C₂×D₅₃	semidirect
446. C₄×D₄	C₂×D₅₃	semidirect
447. C₄×D₄	C₂×D₅₃	semidirect
448. C₄×D₄	C₂×D₅₃	semidirect
454. #117	C₂×D₅₃	semidirect
467. C₂×C₄⋊C₄	C₂×D₅₃	semidirect

Subgroups — #553×D53 #20288230

Conjugacy classes of subgroups

Complements

Subgroups — #553×D₅₃ #20288230