Subgroups — #551×D₅₃ #20288208

Order 6784.

1328 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811304	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811303	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811302	C₂	1	2	yes	maximal, complemented
4	#16811301	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811300	C₂	1	2	yes	maximal, complemented
6	#16811299	C₂	1	2	yes	maximal, complemented
7	#16811298	C₂	1	2	yes	maximal, complemented
8	#16811297	C₂	1	2	yes	maximal, complemented
9	#16811296	C₂	1	2	yes	maximal, complemented
10	#126×D₅₃	C₂	1	2	yes	maximal, complemented
11	#124×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#123×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#123×D₅₃	C₂	1	2	yes	maximal, complemented
14	C₂²⋊Q₈×D₅₃	C₂	1	2	yes	maximal, complemented
15	#120×D₅₃	C₂	1	1	yes	maximal, characteristic
16	C₄×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
17	#117×D₅₃	C₂	1	2	yes	maximal, complemented
18	C₂×C₂²⋊C₄×D₅₃	C₂	1	2	yes	maximal, complemented
19	C₅₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₅₃	C₂²	1	1	yes	characteristic
21	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₄×D₅₃	C₂²	1	2	yes	—
23	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₅₃	C₂²	1	2	yes	—
25	C₂²×C₄×D₅₃	C₂²	1	2	yes	—
26	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
27	#13133212	C₂²	1	2	yes	complemented
28	#13133212	C₂²	1	2	yes	complemented
29	#13133212	C₂²	1	2	yes	complemented
30	#13133211	C₂²	1	2	yes	complemented
31	#13133210	C₂²	1	2	yes	complemented
32	#13133210	C₂²	1	2	yes	complemented
33	#13133210	C₂²	1	2	yes	complemented
34	#13133206	C₂²	1	1	yes	characteristic, complemented
35	#13133205	C₂²	1	1	yes	characteristic, complemented
36	#13133204	C₂²	1	1	yes	characteristic, complemented
37	#13133203	C₂²	1	2	yes	complemented
38	#13133203	C₂²	1	2	yes	complemented
39	#13133202	C₂²	1	2	yes	complemented
40	#13133202	C₂²	1	2	yes	complemented
41	#13133202	C₂²	1	2	yes	complemented
42	#13133201	C₂²	1	2	yes	complemented
43	#13133201	C₂²	1	1	yes	characteristic, complemented
44	#13133200	C₂²	1	2	yes	complemented
45	#13133200	C₂²	1	1	yes	characteristic, complemented
46	#13133199	C₂²	1	2	yes	complemented
47	#13133199	C₂²	1	2	yes	complemented
48	#13133199	C₂²	1	2	yes	complemented
49	#13133198	C₂²	1	2	yes	complemented
50	#13133198	C₂²	1	1	yes	characteristic, complemented
51	#13133197	C₂²	1	2	yes	complemented
52	#13133196	C₂²	1	2	yes	complemented
53	#13133195	C₂²	1	2	yes	complemented
54	#13133195	C₂²	1	2	yes	complemented
55	#13133194	C₂²	1	2	yes	complemented
56	#13133194	C₂²	1	2	yes	complemented
57	#13133193	C₂²	1	2	yes	complemented
58	#13133187	C₂²	1	2	yes	—
59	#13133187	C₂²	1	1	yes	characteristic
60	#13133186	C₂²	1	1	yes	characteristic
61	#13133185	C₂²	1	2	yes	—
62	#13133185	C₂²	1	1	yes	characteristic
63	C₄×D₂₁₂	C₂²	1	2	yes	complemented
64	D₄×Dic₅₃	C₂²	1	2	yes	complemented
65	#13133179	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
68	#13133177	C₂²	1	2	yes	complemented
69	#13133177	C₂²	1	2	yes	complemented
70	#13133176	C₂²	1	2	yes	complemented
71	#13133175	C₂²	1	2	yes	complemented
72	#13133175	C₂²	1	2	yes	complemented
73	#13133174	C₂²	1	2	yes	complemented
74	#13133174	C₂²	1	2	yes	complemented
75	#13133173	C₂²	1	2	yes	complemented
76	#13133173	C₂²	1	2	yes	complemented
77	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
78	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
79	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
80	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
81	C₂×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
82	C₂×#11719921	C₂²	1	2	yes	complemented
83	C₂×#11719921	C₂²	1	2	yes	complemented
84	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
85	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
86	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
87	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
88	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
89	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
90	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
91	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
93	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
96	C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
97	C₄²×D₅₃	C₂²	1	2	yes	complemented
98	#126×C₅₃	C₂²	1	2	yes	complemented
99	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
100	#123×C₅₃	C₂²	1	2	yes	complemented
101	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
102	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
103	#120×C₅₃	C₂²	1	1	yes	characteristic
104	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
105	#117×C₅₃	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
107	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
108	C₂³×D₅₃	—	2	8	no	—
109	C₂³×D₅₃	—	4	2	no	—
110	C₂³×D₅₃	C₂³	1	1	yes	characteristic
111	C₂³×D₅₃	C₂³	1	1	yes	characteristic
112	C₂³×D₅₃	C₂³	1	1	yes	characteristic
113	C₂³×D₅₃	C₂³	1	2	yes	—
114	C₂³×D₅₃	C₂³	1	2	yes	—
115	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
116	C₂×D₄×C₅₃	C₂³	1	2	yes	—
117	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
119	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
120	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
121	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
125	C₂²×Dic₅₃	C₂³	1	2	yes	—
126	C₂²×Dic₅₃	C₂³	1	2	yes	—
127	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
128	Q₈×D₅₃	—	4	2	no	—
129	D₄×D₅₃	—	2	8	no	—
130	D₄×D₅₃	—	4	2	no	—
131	C₂×D₂₁₂	C₂³	1	2	yes	—
132	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₅₃	—	2	8	no	—
134	C₂×C₄×D₅₃	—	4	4	no	—
135	C₂×C₄×D₅₃	—	4	2	no	—
136	C₂×C₄×D₅₃	C₂³	1	2	yes	—
137	C₂×C₄×D₅₃	C₂³	1	2	yes	—
138	C₂×C₄×D₅₃	C₂³	1	2	yes	—
139	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₅₃	C₂³	1	2	yes	—
141	C₂×C₄×D₅₃	C₂³	1	2	yes	—
142	C₂×C₄×D₅₃	C₂³	1	2	yes	—
143	C₂×C₄×D₅₃	C₂³	1	2	yes	—
144	C₂×C₄×D₅₃	C₂³	1	2	yes	—
145	C₂×C₄×D₅₃	C₂³	1	2	yes	—
146	C₂×C₄×D₅₃	C₂³	1	2	yes	complemented
147	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
148	C₂×Dic₁₀₆	C₂³	1	2	yes	complemented
149	C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
150	C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
151	C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
152	C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
153	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
157	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
159	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
160	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
161	C₄²×C₅₃	C₂³	1	1	yes	characteristic, complemented
162	C₄²×C₅₃	C₂³	1	2	yes	complemented
163	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
164	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
165	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
166	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
167	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
168	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
169	C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
170	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
171	#11719921	C₂³	1	2	yes	—
172	#11719921	C₂³	1	2	yes	—
173	#11719921	C₂³	1	2	yes	—
174	#11719921	C₂³	1	2	yes	—
175	#11719921	C₂³	1	2	yes	—
176	#11719921	C₂³	1	2	yes	—
177	#11719921	C₂³	1	2	yes	—
178	#11719921	C₂³	1	2	yes	—
179	#11719921	C₂³	1	2	yes	—
180	#11719921	C₂³	1	2	yes	—
181	#11719921	C₂³	1	2	yes	—
182	#11719921	C₂³	1	2	yes	complemented
183	#11719921	C₂³	1	2	yes	complemented
184	#11719921	C₂³	1	2	yes	complemented
185	C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
186	C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
187	C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
188	C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
189	#11719919	C₂³	1	2	yes	complemented
190	#11719919	C₂³	1	2	yes	complemented
191	#11719919	C₂³	1	2	yes	complemented
192	#11719919	C₂³	1	2	yes	complemented
193	#11719919	C₂³	1	2	yes	complemented
194	#11719919	C₂³	1	2	yes	complemented
195	#11719919	C₂³	1	2	yes	complemented
196	#11719919	C₂³	1	2	yes	complemented
197	C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
198	C₄×Dic₅₃	C₂³	1	2	yes	complemented
199	C₄×Dic₅₃	C₂³	1	2	yes	complemented
200	C₄×Dic₅₃	C₂³	1	2	yes	complemented
201	C₄×Dic₅₃	C₂³	1	2	yes	complemented
202	C₂³×C₅₃	—	2	4	no	—
203	C₂³×C₅₃	—	4	1	no	—
204	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
205	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
206	C₂³×C₅₃	C₂⁴	1	2	yes	—
207	C₂²×D₅₃	—	2	4	no	—
208	C₂²×D₅₃	—	2	4	no	—
209	C₂²×D₅₃	—	2	4	no	—
210	C₂²×D₅₃	—	2	4	no	—
211	C₂²×D₅₃	—	2	4	no	—
212	C₂²×D₅₃	—	2	4	no	—
213	C₂²×D₅₃	—	2	4	no	—
214	C₂²×D₅₃	—	2	2	no	—
215	C₂²×D₅₃	—	2	2	no	—
216	C₂²×D₅₃	—	4	1	no	—
217	C₂²×D₅₃	—	4	2	no	—
218	C₂²×D₅₃	—	4	16	no	—
219	C₂²×D₅₃	#41	1	8	yes	—
220	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
221	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
222	C₂²×D₅₃	C₂⁴	1	2	yes	—
223	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
224	Q₈×C₅₃	—	4	1	no	—
225	D₄×C₅₃	—	2	4	no	—
226	D₄×C₅₃	—	4	1	no	—
227	C₂×C₄×C₅₃	—	2	4	no	—
228	C₂×C₄×C₅₃	—	4	2	no	—
229	C₂×C₄×C₅₃	—	4	1	no	—
230	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
231	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
233	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
234	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
235	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
236	C₂²⋊D₅₃	—	2	4	no	—
237	C₂²⋊D₅₃	—	2	4	no	—
238	C₂²⋊D₅₃	—	4	1	no	—
239	C₂²⋊D₅₃	—	4	1	no	—
240	C₂×Dic₅₃	—	2	4	no	—
241	C₂×Dic₅₃	—	4	2	no	—
242	C₂×Dic₅₃	—	4	1	no	—
243	C₂×Dic₅₃	C₂⁴	1	2	yes	—
244	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₅₃	C₂⁴	1	2	yes	—
246	C₂×Dic₅₃	C₂⁴	1	2	yes	—
247	C₂×Dic₅₃	C₂⁴	1	2	yes	—
248	C₂×Dic₅₃	C₂⁴	1	2	yes	—
249	D₂₁₂	—	2	4	no	—
250	D₂₁₂	—	4	1	no	—
251	C₄×D₅₃	—	2	4	no	—
252	C₄×D₅₃	—	2	4	no	—
253	C₄×D₅₃	—	2	4	no	—
254	C₄×D₅₃	—	2	4	no	—
255	C₄×D₅₃	—	2	4	no	—
256	C₄×D₅₃	—	2	4	no	—
257	C₄×D₅₃	—	2	4	no	—
258	C₄×D₅₃	—	2	2	no	—
259	C₄×D₅₃	—	4	2	no	—
260	C₄×D₅₃	—	4	2	no	—
261	C₄×D₅₃	—	4	2	no	—
262	Dic₁₀₆	—	4	1	no	—
263	Dic₁₀₆	—	4	2	no	—
264	C₂²×C₅₃	—	2	2	no	—
265	C₂²×C₅₃	—	2	2	no	—
266	C₂²×C₅₃	—	2	2	no	—
267	C₂²×C₅₃	—	2	2	no	—
268	C₂²×C₅₃	—	2	1	no	—
269	C₂²×C₅₃	—	2	1	no	—
270	C₂²×C₅₃	—	4	4	no	—
271	C₂²×C₅₃	C₂×#41	1	4	yes	—
272	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
273	C₂×D₅₃	—	2	2	no	—
274	C₂×D₅₃	—	2	2	no	—
275	C₂×D₅₃	—	2	16	no	—
276	C₂×D₅₃	—	2	2	no	—
277	C₂×D₅₃	—	2	2	no	—
278	C₂×D₅₃	—	2	1	no	—
279	C₂×D₅₃	—	2	1	no	—
280	C₂×D₅₃	—	4	4	no	—
281	C₂×D₅₃	—	4	8	no	—
282	C₂×D₅₃	—	4	4	no	—
283	C₂×D₅₃	—	4	4	no	—
284	C₂×D₅₃	C₂×#41	1	4	yes	—
285	C₂×D₅₃	C₂×#41	1	4	yes	—
286	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	—
287	C₄×C₅₃	—	2	2	no	—
288	C₄×C₅₃	—	2	2	no	—
289	C₄×C₅₃	—	2	2	no	—
290	C₄×C₅₃	—	2	2	no	—
291	C₄×C₅₃	—	2	1	no	—
292	C₄×C₅₃	—	2	2	no	—
293	Dic₅₃	—	2	2	no	—
294	Dic₅₃	—	2	2	no	—
295	Dic₅₃	—	2	2	no	—
296	Dic₅₃	—	2	2	no	—
297	Dic₅₃	—	2	1	no	—
298	Dic₅₃	—	2	2	no	—
299	C₂×#551	—	53	1	no	maximal, Sylow
300	C₂×C₅₃	—	2	4	no	—
301	C₂×C₅₃	—	4	1	no	—
302	C₂×C₅₃	—	4	1	no	—
303	C₂×C₅₃	C₂²×#41	1	2	yes	—
304	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
305	D₅₃	—	2	4	no	—
306	D₅₃	—	4	1	no	—
307	D₅₃	—	4	1	no	—
308	D₅₃	#551	1	4	yes	direct product factor
309	#551	—	53	2	no	—
310	#551	—	53	1	no	—
311	#551	—	53	2	no	—
312	#551	—	53	1	no	—
313	#551	—	53	2	no	—
314	#551	—	53	1	no	—
315	#551	—	53	2	no	—
316	#551	—	53	2	no	—
317	#551	—	53	2	no	—
318	#551	D₅₃	1	1	yes	characteristic, direct product factor
319	C₂×#126	—	53	2	no	—
320	C₂×#124	—	53	1	no	—
321	C₂×#123	—	53	2	no	—
322	C₂×#123	—	53	1	no	—
323	C₂×C₂²⋊Q₈	—	53	2	no	—
324	C₂×#120	—	53	1	no	—
325	C₂×C₄×D₄	—	53	2	no	—
326	C₂×#117	—	53	2	no	—
327	C₂²×C₂²⋊C₄	—	53	2	no	—
328	C₅₃	C₂×#551	1	1	yes	characteristic, complemented, Sylow
329	C₂⁵	—	53	1	no	—
330	C₂²×Q₈	—	53	1	no	—
331	C₂²×D₄	—	53	2	no	—
332	C₂²×D₄	—	53	1	no	—
333	C₂³×C₄	—	53	2	no	—
334	C₂³×C₄	—	53	2	no	—
335	C₂³×C₄	—	53	1	no	—
336	#126	—	53	2	no	—
337	#126	—	53	2	no	—
338	#126	—	53	2	no	—
339	#126	—	53	2	no	—
340	#126	—	53	2	no	—
341	#126	—	53	2	no	—
342	#126	—	53	2	no	—
343	#126	C₂×D₅₃	1	2	yes	complemented
344	#124	—	53	1	no	—
345	#124	—	53	1	no	—
346	#124	—	53	2	no	—
347	#124	—	53	2	no	—
348	#124	—	53	1	no	—
349	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
350	#123	—	53	2	no	—
351	#123	—	53	1	no	—
352	#123	—	53	2	no	—
353	#123	—	53	1	no	—
354	#123	—	53	2	no	—
355	#123	—	53	2	no	—
356	#123	—	53	2	no	—
357	#123	—	53	2	no	—
358	#123	—	53	2	no	—
359	#123	—	53	2	no	—
360	#123	—	53	2	no	—
361	#123	—	53	1	no	—
362	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
363	#123	C₂×D₅₃	1	2	yes	complemented
364	C₂²⋊Q₈	—	53	2	no	—
365	C₂²⋊Q₈	—	53	2	no	—
366	C₂²⋊Q₈	—	53	2	no	—
367	C₂²⋊Q₈	—	53	2	no	—
368	C₂²⋊Q₈	—	53	2	no	—
369	C₂²⋊Q₈	—	53	2	no	—
370	C₂²⋊Q₈	—	53	2	no	—
371	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
372	#120	—	53	1	no	—
373	#120	—	53	2	no	—
374	#120	—	53	1	no	—
375	#120	—	53	1	no	—
376	#120	—	53	2	no	—
377	#120	C₂×D₅₃	1	1	yes	characteristic
378	C₄×D₄	—	53	2	no	—
379	C₄×D₄	—	53	2	no	—
380	C₄×D₄	—	53	2	no	—
381	C₄×D₄	—	53	2	no	—
382	C₄×D₄	—	53	2	no	—
383	C₄×D₄	—	53	2	no	—
384	C₄×D₄	—	53	2	no	—
385	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
386	#117	—	53	2	no	—
387	#117	—	53	2	no	—
388	#117	—	53	2	no	—
389	#117	—	53	2	no	—
390	#117	—	53	2	no	—
391	#117	—	53	2	no	—
392	#117	—	53	2	no	—
393	#117	C₂×D₅₃	1	2	yes	complemented
394	C₂×C₄⋊C₄	—	53	2	no	—
395	C₂×C₄⋊C₄	—	53	2	no	—
396	C₂×C₄⋊C₄	—	53	2	no	—
397	C₂×C₄⋊C₄	—	53	2	no	—
398	C₂×C₂²⋊C₄	—	53	2	no	—
399	C₂×C₂²⋊C₄	—	53	2	no	—
400	C₂×C₂²⋊C₄	—	53	2	no	—
401	C₂×C₂²⋊C₄	—	53	2	no	—
402	C₂×C₂²⋊C₄	—	53	2	no	—
403	C₂×C₂²⋊C₄	—	53	2	no	—
404	C₂×C₂²⋊C₄	—	53	2	no	—
405	C₂×C₂²⋊C₄	—	53	2	no	—
406	C₂×C₂²⋊C₄	—	53	2	no	—
407	C₂×C₂²⋊C₄	—	53	2	no	—
408	C₂×C₂²⋊C₄	—	53	2	no	—
409	C₂×C₂²⋊C₄	—	53	2	no	—
410	C₂×C₂²⋊C₄	—	53	1	no	—
411	C₂×C₂²⋊C₄	—	53	2	no	—
412	C₂×C₂²⋊C₄	—	53	1	no	—
413	C₂×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
414	C₂×C₄²	—	53	1	no	—
415	C₂×C₄²	—	53	2	no	—
416	C₂⁴	—	53	2	no	—
417	C₂⁴	—	53	1	no	—
418	C₂⁴	—	53	1	no	—
419	C₂⁴	—	53	1	no	—
420	C₂⁴	—	53	2	no	—
421	C₂⁴	—	106	8	no	—
422	C₂⁴	—	212	2	no	—
423	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
424	C₂×Q₈	—	53	2	no	—
425	C₂×Q₈	—	53	1	no	—
426	C₂×Q₈	—	212	2	no	—
427	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
428	C₂×D₄	—	53	2	no	—
429	C₂×D₄	—	53	2	no	—
430	C₂×D₄	—	53	1	no	—
431	C₂×D₄	—	53	1	no	—
432	C₂×D₄	—	53	2	no	—
433	C₂×D₄	—	53	1	no	—
434	C₂×D₄	—	106	8	no	—
435	C₂×D₄	—	212	2	no	—
436	C₂×D₄	C₂²×D₅₃	1	2	yes	—
437	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
438	C₂²×C₄	—	53	2	no	—
439	C₂²×C₄	—	53	2	no	—
440	C₂²×C₄	—	53	1	no	—
441	C₂²×C₄	—	53	2	no	—
442	C₂²×C₄	—	53	2	no	—
443	C₂²×C₄	—	53	2	no	—
444	C₂²×C₄	—	53	1	no	—
445	C₂²×C₄	—	53	2	no	—
446	C₂²×C₄	—	53	2	no	—
447	C₂²×C₄	—	53	2	no	—
448	C₂²×C₄	—	53	2	no	—
449	C₂²×C₄	—	53	2	no	—
450	C₂²×C₄	—	53	2	no	—
451	C₂²×C₄	—	53	2	no	—
452	C₂²×C₄	—	106	8	no	—
453	C₂²×C₄	—	212	4	no	—
454	C₂²×C₄	—	212	2	no	—
455	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
456	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
457	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
458	C₄⋊C₄	—	53	2	no	—
459	C₄⋊C₄	—	53	2	no	—
460	C₄⋊C₄	—	53	2	no	—
461	C₄⋊C₄	—	53	2	no	—
462	C₄⋊C₄	—	53	2	no	—
463	C₄⋊C₄	—	53	2	no	—
464	C₄⋊C₄	—	53	2	no	—
465	C₄⋊C₄	—	53	2	no	—
466	C₄⋊C₄	—	53	2	no	—
467	C₄⋊C₄	—	53	2	no	—
468	C₄⋊C₄	—	53	2	no	—
469	C₄⋊C₄	—	53	2	no	—
470	C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
471	C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
472	C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
473	C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
474	C₂²⋊C₄	—	53	2	no	—
475	C₂²⋊C₄	—	53	2	no	—
476	C₂²⋊C₄	—	53	2	no	—
477	C₂²⋊C₄	—	53	2	no	—
478	C₂²⋊C₄	—	53	2	no	—
479	C₂²⋊C₄	—	53	2	no	—
480	C₂²⋊C₄	—	53	1	no	—
481	C₂²⋊C₄	—	53	1	no	—
482	C₂²⋊C₄	—	53	2	no	—
483	C₂²⋊C₄	—	53	2	no	—
484	C₂²⋊C₄	—	53	2	no	—
485	C₂²⋊C₄	—	53	2	no	—
486	C₂²⋊C₄	—	53	2	no	—
487	C₂²⋊C₄	—	53	2	no	—
488	C₂²⋊C₄	—	53	2	no	—
489	C₂²⋊C₄	—	53	2	no	—
490	C₂²⋊C₄	—	53	2	no	—
491	C₂²⋊C₄	—	53	2	no	—
492	C₂²⋊C₄	—	53	2	no	—
493	C₂²⋊C₄	—	53	2	no	—
494	C₂²⋊C₄	—	53	2	no	—
495	C₂²⋊C₄	—	53	2	no	—
496	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
497	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
498	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
502	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
503	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
504	C₄²	—	53	1	no	—
505	C₄²	—	53	2	no	—
506	C₄²	—	53	2	no	—
507	C₄²	—	53	2	no	—
508	C₄²	—	53	2	no	—
509	C₄²	C₂²×D₅₃	1	1	yes	characteristic, complemented
510	C₄²	C₂²×D₅₃	1	2	yes	complemented
511	C₂³	—	2	4	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	53	1	no	—
514	C₂³	—	53	8	no	—
515	C₂³	—	53	2	no	—
516	C₂³	—	53	1	no	—
517	C₂³	—	53	1	no	—
518	C₂³	—	106	4	no	—
519	C₂³	—	106	4	no	—
520	C₂³	—	106	2	no	—
521	C₂³	—	106	4	no	—
522	C₂³	—	106	2	no	—
523	C₂³	—	106	4	no	—
524	C₂³	—	106	4	no	—
525	C₂³	—	106	4	no	—
526	C₂³	—	106	4	no	—
527	C₂³	—	212	2	no	—
528	C₂³	—	212	1	no	—
529	C₂³	—	212	16	no	—
530	C₂³	C₂³×D₅₃	1	1	yes	characteristic
531	C₂³	C₂³×D₅₃	1	1	yes	characteristic
532	C₂³	C₂³×D₅₃	1	2	yes	—
533	Q₈	—	4	1	no	—
534	Q₈	—	212	2	no	—
535	Q₈	—	212	1	no	—
536	D₄	—	2	4	no	—
537	D₄	—	4	1	no	—
538	D₄	—	106	4	no	—
539	D₄	—	106	4	no	—
540	D₄	—	106	4	no	—
541	D₄	—	212	1	no	—
542	D₄	—	212	1	no	—
543	D₄	—	212	1	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	53	2	no	—
548	C₂×C₄	—	53	2	no	—
549	C₂×C₄	—	53	2	no	—
550	C₂×C₄	—	53	1	no	—
551	C₂×C₄	—	53	2	no	—
552	C₂×C₄	—	53	2	no	—
553	C₂×C₄	—	106	4	no	—
554	C₂×C₄	—	106	4	no	—
555	C₂×C₄	—	106	4	no	—
556	C₂×C₄	—	106	4	no	—
557	C₂×C₄	—	106	4	no	—
558	C₂×C₄	—	106	4	no	—
559	C₂×C₄	—	106	4	no	—
560	C₂×C₄	—	106	2	no	—
561	C₂×C₄	—	106	4	no	—
562	C₂×C₄	—	212	2	no	—
563	C₂×C₄	—	212	2	no	—
564	C₂×C₄	—	212	2	no	—
565	C₂×C₄	—	212	1	no	—
566	C₂×C₄	—	212	2	no	—
567	C₂×C₄	C₂³×D₅₃	1	2	yes	—
568	C₂×C₄	C₂³×D₅₃	1	2	yes	—
569	C₂×C₄	C₂³×D₅₃	1	2	yes	—
570	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₅₃	1	2	yes	—
572	C₂×C₄	C₂³×D₅₃	1	2	yes	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	53	4	no	—
581	C₂²	—	53	2	no	—
582	C₂²	—	53	4	no	—
583	C₂²	—	106	16	no	—
584	C₂²	—	106	2	no	—
585	C₂²	—	106	2	no	—
586	C₂²	—	106	2	no	—
587	C₂²	—	106	2	no	—
588	C₂²	—	106	1	no	—
589	C₂²	—	106	1	no	—
590	C₂²	—	212	8	no	—
591	C₂²	—	212	4	no	—
592	C₂²	—	212	4	no	—
593	C₂²	—	212	4	no	—
594	C₂²	#41×D₅₃	1	4	yes	—
595	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	1	no	—
602	C₄	—	106	2	no	—
603	C₄	—	106	2	no	—
604	C₄	—	106	2	no	—
605	C₄	—	106	2	no	—
606	C₄	—	106	2	no	—
607	C₄	—	106	1	no	—
608	C₂	—	2	4	no	—
609	C₂	—	4	1	no	—
610	C₂	—	4	1	no	—
611	C₂	—	53	4	no	—
612	C₂	—	106	4	no	—
613	C₂	—	212	1	no	—
614	C₂	—	212	1	no	—
615	C₂	C₂×#41×D₅₃	1	2	yes	—
616	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#551	C₂
hypercenter	#551	D₅₃
hypocenter	C₅₃	C₂×#551
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #16811304	C₂	semidirect
2. #16811303	C₂	semidirect
3. #16811302	C₂	semidirect
4. #16811301	C₂	semidirect
5. #16811300	C₂	semidirect
6. #16811299	C₂	semidirect
7. #16811298	C₂	semidirect
8. #16811297	C₂	semidirect
9. #16811296	C₂	semidirect
10. #126×D₅₃	C₂	semidirect
11. #124×D₅₃	C₂	semidirect
12. #123×D₅₃	C₂	semidirect
13. #123×D₅₃	C₂	semidirect
14. C₂²⋊Q₈×D₅₃	C₂	semidirect
16. C₄×D₄×D₅₃	C₂	semidirect
17. #117×D₅₃	C₂	semidirect
18. C₂×C₂²⋊C₄×D₅₃	C₂	semidirect
19. C₅₃×#551	C₂	semidirect
21. C₂×Q₈×D₅₃	C₂²	semidirect
26. C₂²×C₄×D₅₃	C₂²	semidirect
27. #13133212	C₂²	semidirect
28. #13133212	C₂²	semidirect
29. #13133212	C₂²	semidirect
30. #13133211	C₂²	semidirect
31. #13133210	C₂²	semidirect
32. #13133210	C₂²	semidirect
33. #13133210	C₂²	semidirect
34. #13133206	C₂²	semidirect
35. #13133205	C₂²	semidirect
36. #13133204	C₂²	semidirect
37. #13133203	C₂²	semidirect
38. #13133203	C₂²	semidirect
39. #13133202	C₂²	semidirect
40. #13133202	C₂²	semidirect
41. #13133202	C₂²	semidirect
42. #13133201	C₂²	semidirect
43. #13133201	C₂²	semidirect
44. #13133200	C₂²	semidirect
45. #13133200	C₂²	semidirect
46. #13133199	C₂²	semidirect
47. #13133199	C₂²	semidirect
48. #13133199	C₂²	semidirect
49. #13133198	C₂²	semidirect
50. #13133198	C₂²	semidirect
51. #13133197	C₂²	semidirect
52. #13133196	C₂²	semidirect
53. #13133195	C₂²	semidirect
54. #13133195	C₂²	semidirect
55. #13133194	C₂²	semidirect
56. #13133194	C₂²	semidirect
57. #13133193	C₂²	semidirect
63. C₄×D₂₁₂	C₂²	semidirect
64. D₄×Dic₅₃	C₂²	semidirect
65. #13133179	C₂²	semidirect
66. C₄×C₂²⋊D₅₃	C₂²	semidirect
67. C₄×C₂²⋊D₅₃	C₂²	semidirect
68. #13133177	C₂²	semidirect
69. #13133177	C₂²	semidirect
70. #13133176	C₂²	semidirect
71. #13133175	C₂²	semidirect
72. #13133175	C₂²	semidirect
73. #13133174	C₂²	semidirect
74. #13133174	C₂²	semidirect
75. #13133173	C₂²	semidirect
76. #13133173	C₂²	semidirect
77. C₄⋊C₄×D₅₃	C₂²	semidirect
78. C₄⋊C₄×D₅₃	C₂²	semidirect
79. C₄⋊C₄×D₅₃	C₂²	semidirect
80. C₄⋊C₄×D₅₃	C₂²	semidirect
81. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
82. C₂×#11719921	C₂²	semidirect
83. C₂×#11719921	C₂²	semidirect
90. C₂²⋊C₄×D₅₃	C₂²	semidirect
91. C₂²⋊C₄×D₅₃	C₂²	semidirect
92. C₂²⋊C₄×D₅₃	C₂²	semidirect
93. C₂²⋊C₄×D₅₃	C₂²	semidirect
94. C₂²⋊C₄×D₅₃	C₂²	semidirect
95. C₂²⋊C₄×D₅₃	C₂²	semidirect
96. C₄²×D₅₃	C₂²	semidirect
97. C₄²×D₅₃	C₂²	semidirect
98. #126×C₅₃	C₂²	semidirect
99. #124×C₅₃	C₂²	semidirect
100. #123×C₅₃	C₂²	semidirect
101. #123×C₅₃	C₂²	semidirect
102. C₂²⋊Q₈×C₅₃	C₂²	semidirect
104. C₄×D₄×C₅₃	C₂²	semidirect
105. #117×C₅₃	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
115. C₂×Q₈×C₅₃	C₂³	semidirect
120. C₂²×C₄×C₅₃	C₂³	semidirect
127. C₂²×Dic₅₃	C₂³	semidirect
146. C₂×C₄×D₅₃	C₂³	semidirect
147. C₂×Dic₁₀₆	C₂³	semidirect
148. C₂×Dic₁₀₆	C₂³	semidirect
149. C₄⋊C₄×C₅₃	C₂³	semidirect
150. C₄⋊C₄×C₅₃	C₂³	semidirect
151. C₄⋊C₄×C₅₃	C₂³	semidirect
152. C₄⋊C₄×C₅₃	C₂³	semidirect
159. C₂²⋊C₄×C₅₃	C₂³	semidirect
160. C₂²⋊C₄×C₅₃	C₂³	semidirect
161. C₄²×C₅₃	C₂³	semidirect
162. C₄²×C₅₃	C₂³	semidirect
169. C₂²⋊Dic₅₃	C₂³	semidirect
170. C₂²⋊Dic₅₃	C₂³	semidirect
182. #11719921	C₂³	semidirect
183. #11719921	C₂³	semidirect
184. #11719921	C₂³	semidirect
185. C₄⋊Dic₅₃	C₂³	semidirect
186. C₄⋊Dic₅₃	C₂³	semidirect
187. C₄⋊Dic₅₃	C₂³	semidirect
188. C₄⋊Dic₅₃	C₂³	semidirect
189. #11719919	C₂³	semidirect
190. #11719919	C₂³	semidirect
191. #11719919	C₂³	semidirect
192. #11719919	C₂³	semidirect
193. #11719919	C₂³	semidirect
194. #11719919	C₂³	semidirect
195. #11719919	C₂³	semidirect
196. #11719919	C₂³	semidirect
197. C₄×Dic₅₃	C₂³	semidirect
198. C₄×Dic₅₃	C₂³	semidirect
199. C₄×Dic₅₃	C₂³	semidirect
200. C₄×Dic₅₃	C₂³	semidirect
201. C₄×Dic₅₃	C₂³	semidirect
308. D₅₃	#551	direct (N × H)
318. #551	D₅₃	direct (N × H)
328. C₅₃	C₂×#551	semidirect
343. #126	C₂×D₅₃	semidirect
349. #124	C₂×D₅₃	semidirect
362. #123	C₂×D₅₃	semidirect
363. #123	C₂×D₅₃	semidirect
371. C₂²⋊Q₈	C₂×D₅₃	semidirect
385. C₄×D₄	C₂×D₅₃	semidirect
393. #117	C₂×D₅₃	semidirect
413. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect
427. C₂×Q₈	C₂²×D₅₃	semidirect
457. C₂²×C₄	C₂²×D₅₃	semidirect
470. C₄⋊C₄	C₂²×D₅₃	semidirect
471. C₄⋊C₄	C₂²×D₅₃	semidirect
472. C₄⋊C₄	C₂²×D₅₃	semidirect
473. C₄⋊C₄	C₂²×D₅₃	semidirect
502. C₂²⋊C₄	C₂²×D₅₃	semidirect
503. C₂²⋊C₄	C₂²×D₅₃	semidirect
509. C₄²	C₂²×D₅₃	semidirect
510. C₄²	C₂²×D₅₃	semidirect

Subgroups — #551×D53 #20288208

Conjugacy classes of subgroups

Complements

Subgroups — #551×D₅₃ #20288208