Subgroups — #532×D₅₃ #20287992

Order 6784.

1728 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₅₃	C₂	1	2	yes	maximal, complemented
2	#16811174	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811173	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811172	C₂	1	2	yes	maximal, complemented
5	#16811171	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811170	C₂	1	4	yes	maximal, complemented
7	#16811169	C₂	1	2	yes	maximal, complemented
8	#16811168	C₂	1	4	yes	maximal, complemented
9	C₄⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#127×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#124×D₅₃	C₂	1	2	yes	maximal, complemented
12	#121×D₅₃	C₂	1	4	yes	maximal, complemented
13	C₄×D₄×D₅₃	C₂	1	4	yes	maximal, complemented
14	C₂×C₄²×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11719949	C₂²	1	2	yes	complemented
17	C₂×#11719945	C₂²	1	2	yes	complemented
18	C₂×#11719945	C₂²	1	4	yes	complemented
19	C₂×#11719947	C₂²	1	4	yes	complemented
20	C₂×#11719947	C₂²	1	2	yes	complemented
21	#41×D₅₃	—	2	16	no	—
22	C₂×Q₈×D₅₃	C₂²	1	2	yes	—
23	C₂×D₄×D₅₃	C₂²	1	4	yes	—
24	C₂×D₄×D₅₃	C₂²	1	4	yes	—
25	C₂×D₄×D₅₃	C₂²	1	2	yes	—
26	C₂²×C₄×D₅₃	C₂²	1	2	yes	—
27	C₂²×C₄×D₅₃	C₂²	1	4	yes	—
28	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
29	#13133217	C₂²	1	1	yes	characteristic, complemented
30	#13133216	C₂²	1	4	yes	complemented
31	#13133215	C₂²	1	2	yes	complemented
32	#13133214	C₂²	1	1	yes	characteristic, complemented
33	#13133213	C₂²	1	4	yes	complemented
34	#13133213	C₂²	1	2	yes	complemented
35	#13133206	C₂²	1	2	yes	complemented
36	#13133205	C₂²	1	2	yes	complemented
37	#13133204	C₂²	1	2	yes	complemented
38	#13133203	C₂²	1	8	yes	complemented
39	#13133192	C₂²	1	4	yes	complemented
40	#13133191	C₂²	1	4	yes	complemented
41	#13133190	C₂²	1	8	yes	complemented
42	#13133189	C₂²	1	8	yes	complemented
43	#13133188	C₂²	1	4	yes	complemented
44	C₄×D₂₁₂	C₂²	1	4	yes	complemented
45	D₄×Dic₅₃	C₂²	1	4	yes	complemented
46	#13133179	C₂²	1	4	yes	complemented
47	C₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
48	#13133177	C₂²	1	8	yes	complemented
49	C₄⋊C₄×D₅₃	C₂²	1	4	yes	—
50	C₂²⋊C₄×D₅₃	C₂²	1	8	yes	—
51	C₂×C₄×Dic₅₃	C₂²	1	2	yes	complemented
52	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₄²×D₅₃	C₂²	1	2	yes	—
54	C₄²×D₅₃	C₂²	1	1	yes	characteristic
55	C₄²×D₅₃	C₂²	1	1	yes	characteristic
56	C₄²×D₅₃	C₂²	1	2	yes	complemented
57	C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×#41×C₅₃	C₂²	1	2	yes	complemented
60	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	#124×C₅₃	C₂²	1	2	yes	complemented
63	#121×C₅₃	C₂²	1	4	yes	complemented
64	C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
65	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
66	C₂³×D₅₃	C₂³	1	4	yes	—
67	C₂³×D₅₃	C₂³	1	1	yes	characteristic
68	#41×C₅₃	—	2	8	no	—
69	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
70	C₂×D₄×C₅₃	C₂³	1	4	yes	—
71	C₂×D₄×C₅₃	C₂³	1	4	yes	—
72	C₂×D₄×C₅₃	C₂³	1	2	yes	—
73	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
74	C₂²×C₄×C₅₃	C₂³	1	4	yes	—
75	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	—
77	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
78	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
79	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
80	C₂²×Dic₅₃	C₂³	1	2	yes	—
81	C₂²×Dic₅₃	C₂³	1	4	yes	—
82	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
83	#11719949	—	2	8	no	—
84	Q₈×D₅₃	—	2	8	no	—
85	#11719947	—	2	16	no	—
86	#11719947	—	2	8	no	—
87	D₄×D₅₃	—	2	16	no	—
88	D₄×D₅₃	—	2	8	no	—
89	D₄×D₅₃	—	2	16	no	—
90	#11719945	—	2	8	no	—
91	#11719945	—	2	16	no	—
92	C₂×D₂₁₂	C₂³	1	4	yes	—
93	C₂×D₂₁₂	C₂³	1	4	yes	—
94	C₂×D₂₁₂	C₂³	1	2	yes	—
95	C₂×C₄×D₅₃	—	2	16	no	—
96	C₂×C₄×D₅₃	—	2	8	no	—
97	C₂×C₄×D₅₃	D₄	1	8	yes	complemented
98	C₂×C₄×D₅₃	C₂³	1	2	yes	—
99	C₂×C₄×D₅₃	C₂³	1	2	yes	—
100	C₂×C₄×D₅₃	C₂³	1	2	yes	—
101	C₂×C₄×D₅₃	C₂³	1	4	yes	—
102	C₂×C₄×D₅₃	C₂³	1	4	yes	—
103	C₂×C₄×D₅₃	C₂³	1	4	yes	—
104	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₅₃	C₂³	1	2	yes	—
109	C₂×Dic₁₀₆	C₂³	1	4	yes	—
110	C₂×Dic₁₀₆	C₂³	1	2	yes	—
111	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
112	C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
113	C₄²×C₅₃	C₂³	1	2	yes	—
114	C₄²×C₅₃	C₂³	1	1	yes	characteristic
115	C₄²×C₅₃	C₂³	1	1	yes	characteristic
116	C₂²⋊Dic₅₃	C₂³	1	8	yes	—
117	#11719921	C₂³	1	8	yes	—
118	#11719921	C₂³	1	8	yes	—
119	C₄⋊Dic₅₃	C₂³	1	4	yes	—
120	#11719919	C₂³	1	8	yes	—
121	C₄×Dic₅₃	C₂³	1	2	yes	—
122	C₄×Dic₅₃	C₂³	1	2	yes	—
123	C₄×Dic₅₃	C₂³	1	2	yes	—
124	C₄×Dic₅₃	C₂³	1	2	yes	—
125	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
126	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
127	C₄×Dic₅₃	C₂³	1	2	yes	—
128	C₂³×C₅₃	C₂⁴	1	4	yes	—
129	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
130	C₂²×D₅₃	—	2	4	no	—
131	C₂²×D₅₃	—	2	8	no	—
132	C₂²×D₅₃	—	2	16	no	—
133	C₂²×D₅₃	C₂×D₄	1	4	yes	—
134	C₂²×D₅₃	C₂⁴	1	4	yes	—
135	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
136	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
137	Q₈×C₅₃	—	2	4	no	—
138	D₄×C₅₃	—	2	8	no	—
139	D₄×C₅₃	—	2	4	no	—
140	D₄×C₅₃	—	2	8	no	—
141	C₂×C₄×C₅₃	—	2	8	no	—
142	C₂×C₄×C₅₃	—	2	4	no	—
143	C₂×C₄×C₅₃	C₂×D₄	1	4	yes	complemented
144	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
145	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
146	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
148	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
149	C₂²⋊D₅₃	—	2	8	no	—
150	C₂²⋊D₅₃	—	2	8	no	—
151	C₂²⋊D₅₃	—	2	8	no	—
152	C₂²⋊D₅₃	—	2	16	no	—
153	C₂×Dic₅₃	—	2	8	no	—
154	C₂×Dic₅₃	—	2	4	no	—
155	C₂×Dic₅₃	C₂×D₄	1	4	yes	complemented
156	C₂×Dic₅₃	C₂⁴	1	4	yes	—
157	C₂×Dic₅₃	C₂⁴	1	2	yes	—
158	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
159	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
160	C₂×Dic₅₃	C₂⁴	1	2	yes	—
161	D₂₁₂	—	2	8	no	—
162	D₂₁₂	—	2	4	no	—
163	D₂₁₂	—	2	8	no	—
164	C₄×D₅₃	—	2	8	no	—
165	C₄×D₅₃	—	2	4	no	—
166	C₄×D₅₃	—	2	8	no	—
167	C₄×D₅₃	—	2	4	no	—
168	C₄×D₅₃	—	2	8	no	—
169	C₄×D₅₃	—	2	4	no	—
170	C₄×D₅₃	C₂×D₄	1	4	yes	—
171	C₄×D₅₃	C₂×D₄	1	4	yes	—
172	C₄×D₅₃	C₂×D₄	1	4	yes	complemented
173	C₄×D₅₃	C₂×D₄	1	4	yes	complemented
174	C₄×D₅₃	#41	1	8	yes	complemented
175	Dic₁₀₆	—	2	4	no	—
176	Dic₁₀₆	—	2	8	no	—
177	C₂²×C₅₃	—	2	2	no	—
178	C₂²×C₅₃	—	2	4	no	—
179	C₂²×C₅₃	—	2	8	no	—
180	C₂²×C₅₃	C₂²×D₄	1	2	yes	—
181	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
182	C₂×D₅₃	—	2	2	no	—
183	C₂×D₅₃	—	2	8	no	—
184	C₂×D₅₃	—	2	4	no	—
185	C₂×D₅₃	—	2	8	no	—
186	C₂×D₅₃	—	4	16	no	—
187	C₂×D₅₃	C₂²×D₄	1	2	yes	—
188	C₂×D₅₃	C₂²×D₄	1	2	yes	—
189	C₂×D₅₃	C₂×#41	1	4	yes	—
190	C₄×C₅₃	—	2	4	no	—
191	C₄×C₅₃	—	2	2	no	—
192	C₄×C₅₃	C₂²×D₄	1	2	yes	—
193	C₄×C₅₃	C₂²×D₄	1	2	yes	—
194	C₄×C₅₃	C₂×#41	1	4	yes	complemented
195	Dic₅₃	—	2	4	no	—
196	Dic₅₃	—	2	2	no	—
197	Dic₅₃	C₂²×D₄	1	2	yes	—
198	Dic₅₃	C₂²×D₄	1	2	yes	—
199	Dic₅₃	C₂×#41	1	4	yes	complemented
200	C₂×#532	—	53	1	no	maximal, Sylow
201	C₂×C₅₃	—	2	2	no	—
202	C₂×C₅₃	—	4	4	no	—
203	C₂×C₅₃	C₂³×D₄	1	1	yes	characteristic
204	C₂×C₅₃	C₂²×#41	1	2	yes	—
205	D₅₃	—	2	2	no	—
206	D₅₃	—	4	4	no	—
207	D₅₃	#532	1	4	yes	direct product factor
208	C₂²×#41	—	53	2	no	—
209	#532	—	53	2	no	—
210	#532	—	53	1	no	—
211	#532	—	53	1	no	—
212	#532	—	53	2	no	—
213	#532	—	53	4	no	—
214	#532	—	53	4	no	—
215	#532	—	53	1	no	—
216	#532	D₅₃	1	1	yes	characteristic, direct product factor
217	C₂×C₄⋊Q₈	—	53	1	no	—
218	C₂×#127	—	53	1	no	—
219	C₂×#124	—	53	2	no	—
220	C₂×#121	—	53	4	no	—
221	C₂×C₄×D₄	—	53	4	no	—
222	C₂²×C₄²	—	53	1	no	—
223	C₅₃	C₂×#532	1	1	yes	characteristic, complemented, Sylow
224	C₂×#41	—	53	2	no	—
225	C₂×#41	—	53	4	no	—
226	C₂×#41	—	53	2	no	—
227	C₂×#41	—	53	4	no	—
228	C₂×#41	—	53	2	no	—
229	C₂×#41	—	106	16	no	—
230	C₂×#41	C₂×D₅₃	1	2	yes	complemented
231	C₂²×Q₈	—	53	2	no	—
232	C₂²×D₄	—	53	4	no	—
233	C₂²×D₄	—	53	4	no	—
234	C₂²×D₄	—	53	2	no	—
235	C₂³×C₄	—	53	1	no	—
236	C₂³×C₄	—	53	4	no	—
237	C₂³×C₄	—	53	2	no	—
238	C₄⋊Q₈	—	53	2	no	—
239	C₄⋊Q₈	—	53	4	no	—
240	C₄⋊Q₈	—	53	1	no	—
241	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
242	#127	—	53	2	no	—
243	#127	—	53	4	no	—
244	#127	—	53	1	no	—
245	#127	C₂×D₅₃	1	1	yes	characteristic, complemented
246	#124	—	53	2	no	—
247	#124	—	53	2	no	—
248	#124	—	53	8	no	—
249	#124	—	53	2	no	—
250	#124	C₂×D₅₃	1	2	yes	complemented
251	#121	—	53	4	no	—
252	#121	—	53	8	no	—
253	#121	—	53	4	no	—
254	#121	—	53	4	no	—
255	#121	—	53	8	no	—
256	#121	C₂×D₅₃	1	4	yes	complemented
257	C₄×D₄	—	53	4	no	—
258	C₄×D₄	—	53	8	no	—
259	C₄×D₄	—	53	4	no	—
260	C₄×D₄	—	53	8	no	—
261	C₄×D₄	—	53	4	no	—
262	C₄×D₄	C₂×D₅₃	1	4	yes	complemented
263	C₂×C₄⋊C₄	—	53	4	no	—
264	C₂×C₂²⋊C₄	—	53	8	no	—
265	C₂×C₄²	—	53	2	no	—
266	C₂×C₄²	—	53	1	no	—
267	C₂×C₄²	—	53	2	no	—
268	C₂×C₄²	—	53	1	no	—
269	C₂×C₄²	—	53	1	no	—
270	C₂×C₄²	—	53	1	no	—
271	C₂×C₄²	—	53	1	no	—
272	C₂×C₄²	—	53	2	no	—
273	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
274	C₂⁴	—	53	1	no	—
275	C₂⁴	—	53	4	no	—
276	#41	—	2	8	no	—
277	#41	—	106	16	no	—
278	#41	—	106	16	no	—
279	#41	—	106	8	no	—
280	#41	—	106	8	no	—
281	#41	—	106	8	no	—
282	C₂×Q₈	—	53	4	no	—
283	C₂×Q₈	—	53	2	no	—
284	C₂×Q₈	—	106	8	no	—
285	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
286	C₂×D₄	—	53	8	no	—
287	C₂×D₄	—	53	4	no	—
288	C₂×D₄	—	53	4	no	—
289	C₂×D₄	—	53	4	no	—
290	C₂×D₄	—	53	4	no	—
291	C₂×D₄	—	53	4	no	—
292	C₂×D₄	—	53	2	no	—
293	C₂×D₄	—	106	16	no	—
294	C₂×D₄	—	106	8	no	—
295	C₂×D₄	—	106	16	no	—
296	C₂×D₄	C₂²×D₅₃	1	4	yes	—
297	C₂×D₄	C₂²×D₅₃	1	4	yes	—
298	C₂×D₄	C₂²×D₅₃	1	2	yes	—
299	C₂²×C₄	—	53	1	no	—
300	C₂²×C₄	—	53	8	no	—
301	C₂²×C₄	—	53	2	no	—
302	C₂²×C₄	—	53	1	no	—
303	C₂²×C₄	—	53	1	no	—
304	C₂²×C₄	—	53	1	no	—
305	C₂²×C₄	—	53	1	no	—
306	C₂²×C₄	—	53	2	no	—
307	C₂²×C₄	—	53	4	no	—
308	C₂²×C₄	—	53	2	no	—
309	C₂²×C₄	—	53	2	no	—
310	C₂²×C₄	—	53	2	no	—
311	C₂²×C₄	—	53	4	no	—
312	C₂²×C₄	—	53	4	no	—
313	C₂²×C₄	—	53	4	no	—
314	C₂²×C₄	—	106	8	no	—
315	C₂²×C₄	—	106	16	no	—
316	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
317	C₂²×C₄	C₂²×D₅₃	1	4	yes	—
318	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
319	C₄⋊C₄	—	53	8	no	—
320	C₄⋊C₄	—	53	4	no	—
321	C₄⋊C₄	C₂²×D₅₃	1	4	yes	—
322	C₂²⋊C₄	—	53	8	no	—
323	C₂²⋊C₄	—	53	8	no	—
324	C₂²⋊C₄	—	53	8	no	—
325	C₂²⋊C₄	C₂²×D₅₃	1	8	yes	—
326	C₄²	—	53	2	no	—
327	C₄²	—	53	2	no	—
328	C₄²	—	53	2	no	—
329	C₄²	—	53	1	no	—
330	C₄²	—	53	1	no	—
331	C₄²	—	53	2	no	—
332	C₄²	—	53	2	no	—
333	C₄²	C₂²×D₅₃	1	1	yes	characteristic
334	C₄²	C₂²×D₅₃	1	1	yes	characteristic
335	C₄²	C₂²×D₅₃	1	2	yes	—
336	C₂³	—	53	1	no	—
337	C₂³	—	53	4	no	—
338	C₂³	—	53	1	no	—
339	C₂³	—	53	4	no	—
340	C₂³	—	106	4	no	—
341	C₂³	—	106	8	no	—
342	C₂³	—	106	16	no	—
343	C₂³	C₂³×D₅₃	1	4	yes	—
344	C₂³	C₂³×D₅₃	1	1	yes	characteristic
345	Q₈	—	2	4	no	—
346	Q₈	—	106	8	no	—
347	Q₈	—	106	4	no	—
348	D₄	—	2	8	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	8	no	—
351	D₄	—	106	8	no	—
352	D₄	—	106	16	no	—
353	D₄	—	106	8	no	—
354	D₄	—	106	8	no	—
355	D₄	—	106	8	no	—
356	D₄	—	106	4	no	—
357	D₄	—	106	8	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	53	4	no	—
361	C₂×C₄	—	53	2	no	—
362	C₂×C₄	—	53	1	no	—
363	C₂×C₄	—	53	1	no	—
364	C₂×C₄	—	53	4	no	—
365	C₂×C₄	—	53	4	no	—
366	C₂×C₄	—	53	4	no	—
367	C₂×C₄	—	53	4	no	—
368	C₂×C₄	—	53	8	no	—
369	C₂×C₄	—	53	2	no	—
370	C₂×C₄	—	53	4	no	—
371	C₂×C₄	—	106	4	no	—
372	C₂×C₄	—	106	8	no	—
373	C₂×C₄	—	106	4	no	—
374	C₂×C₄	—	106	8	no	—
375	C₂×C₄	—	106	4	no	—
376	C₂×C₄	—	106	8	no	—
377	C₂×C₄	—	106	8	no	—
378	C₂×C₄	—	106	4	no	—
379	C₂×C₄	D₄×D₅₃	1	4	yes	complemented
380	C₂×C₄	C₂³×D₅₃	1	2	yes	—
381	C₂×C₄	C₂³×D₅₃	1	4	yes	—
382	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
383	C₂×C₄	C₂³×D₅₃	1	2	yes	—
384	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
385	C₂²	—	2	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	53	2	no	—
389	C₂²	—	53	4	no	—
390	C₂²	—	53	2	no	—
391	C₂²	—	106	8	no	—
392	C₂²	—	106	2	no	—
393	C₂²	—	106	4	no	—
394	C₂²	—	106	8	no	—
395	C₂²	—	212	16	no	—
396	C₂²	C₂×D₄×D₅₃	1	2	yes	—
397	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
398	C₄	—	2	4	no	—
399	C₄	—	2	2	no	—
400	C₄	—	53	2	no	—
401	C₄	—	53	2	no	—
402	C₄	—	53	4	no	—
403	C₄	—	106	4	no	—
404	C₄	—	106	2	no	—
405	C₄	C₂×D₄×D₅₃	1	2	yes	—
406	C₄	C₂×D₄×D₅₃	1	2	yes	—
407	C₄	#41×D₅₃	1	4	yes	complemented
408	C₂	—	2	2	no	—
409	C₂	—	4	4	no	—
410	C₂	—	53	4	no	—
411	C₂	—	106	2	no	—
412	C₂	—	212	4	no	—
413	C₂	C₂²×D₄×D₅₃	1	1	yes	characteristic
414	C₂	C₂×#41×D₅₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Frattini	C₂²	C₂⁴×D₅₃
Fitting	C₅₃×#532	C₂
hypercenter	#532	D₅₃
hypocenter	C₅₃	C₂×#532
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₅₃	C₂	semidirect
2. #16811174	C₂	semidirect
3. #16811173	C₂	semidirect
4. #16811172	C₂	semidirect
5. #16811171	C₂	semidirect
6. #16811170	C₂	semidirect
7. #16811169	C₂	semidirect
8. #16811168	C₂	semidirect
9. C₄⋊Q₈×D₅₃	C₂	semidirect
10. #127×D₅₃	C₂	semidirect
11. #124×D₅₃	C₂	semidirect
12. #121×D₅₃	C₂	semidirect
13. C₄×D₄×D₅₃	C₂	semidirect
14. C₂×C₄²×D₅₃	C₂	semidirect
15. C₅₃×#532	C₂	semidirect
16. C₂×#11719949	C₂²	semidirect
17. C₂×#11719945	C₂²	semidirect
18. C₂×#11719945	C₂²	semidirect
19. C₂×#11719947	C₂²	semidirect
20. C₂×#11719947	C₂²	semidirect
29. #13133217	C₂²	semidirect
30. #13133216	C₂²	semidirect
31. #13133215	C₂²	semidirect
32. #13133214	C₂²	semidirect
33. #13133213	C₂²	semidirect
34. #13133213	C₂²	semidirect
35. #13133206	C₂²	semidirect
36. #13133205	C₂²	semidirect
37. #13133204	C₂²	semidirect
38. #13133203	C₂²	semidirect
39. #13133192	C₂²	semidirect
40. #13133191	C₂²	semidirect
41. #13133190	C₂²	semidirect
42. #13133189	C₂²	semidirect
43. #13133188	C₂²	semidirect
44. C₄×D₂₁₂	C₂²	semidirect
45. D₄×Dic₅₃	C₂²	semidirect
46. #13133179	C₂²	semidirect
47. C₄×C₂²⋊D₅₃	C₂²	semidirect
48. #13133177	C₂²	semidirect
51. C₂×C₄×Dic₅₃	C₂²	semidirect
52. C₂×C₄×Dic₅₃	C₂²	semidirect
56. C₄²×D₅₃	C₂²	semidirect
57. C₄²×D₅₃	C₂²	semidirect
58. C₄²×D₅₃	C₂²	semidirect
59. C₂×#41×C₅₃	C₂²	semidirect
60. C₄⋊Q₈×C₅₃	C₂²	semidirect
61. #127×C₅₃	C₂²	semidirect
62. #124×C₅₃	C₂²	semidirect
63. #121×C₅₃	C₂²	semidirect
64. C₄×D₄×C₅₃	C₂²	semidirect
65. C₂×C₄²×C₅₃	C₂²	semidirect
97. C₂×C₄×D₅₃	D₄	semidirect
143. C₂×C₄×C₅₃	C₂×D₄	semidirect
155. C₂×Dic₅₃	C₂×D₄	semidirect
172. C₄×D₅₃	C₂×D₄	semidirect
173. C₄×D₅₃	C₂×D₄	semidirect
174. C₄×D₅₃	#41	semidirect
194. C₄×C₅₃	C₂×#41	semidirect
199. Dic₅₃	C₂×#41	semidirect
207. D₅₃	#532	direct (N × H)
216. #532	D₅₃	direct (N × H)
223. C₅₃	C₂×#532	semidirect
230. C₂×#41	C₂×D₅₃	semidirect
241. C₄⋊Q₈	C₂×D₅₃	semidirect
245. #127	C₂×D₅₃	semidirect
250. #124	C₂×D₅₃	semidirect
256. #121	C₂×D₅₃	semidirect
262. C₄×D₄	C₂×D₅₃	semidirect
273. C₂×C₄²	C₂×D₅₃	semidirect
379. C₂×C₄	D₄×D₅₃	semidirect
407. C₄	#41×D₅₃	semidirect

Subgroups — #532×D53 #20287992

Conjugacy classes of subgroups

Complements

Subgroups — #532×D₅₃ #20287992