Subgroups — #27398017

Order 13568.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20285196	C₂	1	1	yes	maximal, characteristic
2	#20283633	C₂	1	1	yes	maximal, characteristic, complemented
3	#20275626	C₂	1	1	yes	maximal, characteristic, complemented
4	#20275611	C₂	1	1	yes	maximal, characteristic, complemented
5	#20275247	C₂	1	2	yes	maximal, complemented
6	#20275239	C₂	1	2	yes	maximal, complemented
7	#20275202	C₂	1	2	yes	maximal, complemented
8	#20275192	C₂	1	2	yes	maximal, complemented
9	#20274838	C₂	1	1	yes	maximal, characteristic, complemented
10	#20274470	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133243	C₂²	1	2	yes	—
13	C₂×#13133239	C₂²	1	1	yes	characteristic
14	#16811389	C₂²	1	2	yes	—
15	#16811190	C₂²	1	2	yes	—
16	#16811011	C₄	1	4	yes	complemented
17	#16811006	C₄	1	2	yes	complemented
18	#16810998	C₄	1	2	yes	complemented
19	#16810746	—	2	2	no	—
20	#16810741	—	2	2	no	—
21	C₂×#13133153	C₂²	1	1	yes	characteristic
22	#16810641	C₂²	1	2	yes	—
23	#16810641	C₂²	1	2	yes	—
24	#16810628	C₂²	1	2	yes	—
25	C₂×#13133134	C₂²	1	2	yes	—
26	#16810596	C₂²	1	2	yes	—
27	#16810578	C₂²	1	1	yes	characteristic
28	#16810578	C₂²	1	1	yes	characteristic
29	#16810393	C₂²	1	2	yes	—
30	#16810381	C₂²	1	1	yes	characteristic
31	#16810380	C₂²	1	1	yes	characteristic
32	#16810379	C₂²	1	1	yes	characteristic
33	#16810379	C₂²	1	1	yes	characteristic
34	#16810379	C₂²	1	2	yes	—
35	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
36	C₅₃×#518	C₂²	1	2	yes	—
37	C₅₃×#442	—	2	2	no	—
38	C₄×D₈×C₅₃	—	2	2	no	—
39	C₅₃×#427	C₂²	1	1	yes	characteristic
40	C₅₃×#418	C₂²	1	2	yes	—
41	C₅₃×#405	C₂²	1	1	yes	characteristic
42	C₂×#11719945	C₂³	1	2	yes	—
43	#13133243	—	4	2	no	—
44	#13133243	—	4	2	no	—
45	#13133239	—	2	1	no	—
46	#13133239	—	2	1	no	—
47	#13133239	—	2	1	no	—
48	#13133239	—	2	1	no	—
49	C₂×Dic₂₁₂	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂×#11719913	C₂×C₄	1	2	yes	complemented
51	C₂×#11719923	C₂×C₄	1	4	yes	complemented
52	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic, complemented
53	C₂×#11719922	C₂×C₄	1	4	yes	complemented
54	#13133225	—	4	2	no	—
55	#13133223	—	2	4	no	—
56	C₂×#11719917	C₂³	1	1	yes	characteristic
57	C₂×#11719917	C₂³	1	2	yes	—
58	C₂×#11719917	C₂³	1	1	yes	characteristic
59	M₁₆×D₅₃	—	4	2	no	—
60	#13133213	C₂×C₄	1	4	yes	complemented
61	#13133204	C₂×C₄	1	4	yes	complemented
62	#13133188	—	4	2	no	—
63	#13133186	—	4	2	no	—
64	#13133176	C₂³	1	1	yes	characteristic
65	#13133176	C₂³	1	1	yes	characteristic
66	#13133153	—	2	1	no	—
67	#13133153	—	2	1	no	—
68	#13133145	—	2	4	no	—
69	#13133145	—	4	2	no	—
70	#13133138	—	4	2	no	—
71	#13133134	—	4	2	no	—
72	#13133131	—	4	2	no	—
73	#13133127	—	2	1	no	—
74	#13133127	C₂×C₄	1	2	yes	complemented
75	C₈×Dic₅₃	—	2	1	no	—
76	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
77	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
78	C₂×D₈×C₅₃	—	2	1	no	—
79	C₂×D₈×C₅₃	—	2	1	no	—
80	C₂×D₈×C₅₃	—	2	1	no	—
81	C₂×D₈×C₅₃	—	2	1	no	—
82	C₂×D₈×C₅₃	C₂×C₄	1	2	yes	—
83	C₂×D₈×C₅₃	C₂×C₄	1	2	yes	—
84	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₄×D₄×C₅₃	—	2	4	no	—
87	C₄×D₄×C₅₃	—	4	2	no	—
88	#117×C₅₃	C₂³	1	2	yes	—
89	#117×C₅₃	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
91	#107×C₅₃	—	2	1	no	—
92	#106×C₅₃	—	2	1	no	—
93	#102×C₅₃	—	2	4	no	—
94	#97×C₅₃	D₄	1	2	yes	complemented
95	C₄×C₈×C₅₃	D₄	1	2	yes	complemented
96	C₂⁴×C₅₃	—	2	2	no	—
97	C₂×D₄×C₅₃	—	2	2	no	—
98	C₂×D₄×C₅₃	—	2	2	no	—
99	C₂×D₄×C₅₃	—	2	2	no	—
100	C₂×D₄×C₅₃	—	2	2	no	—
101	C₂×D₄×C₅₃	—	2	2	no	—
102	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₅₃	—	4	4	no	—
104	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
105	C₂×C₂²⋊D₅₃	—	2	2	no	—
106	C₂×C₂²⋊D₅₃	—	4	4	no	—
107	#11719945	—	2	2	no	—
108	#11719945	—	2	2	no	—
109	#11719945	—	2	2	no	—
110	#11719945	—	2	2	no	—
111	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₅₃	—	2	2	no	—
113	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
114	D₈×C₅₃	—	2	2	no	—
115	D₈×C₅₃	—	2	2	no	—
116	D₈×C₅₃	—	2	2	no	—
117	D₈×C₅₃	—	2	2	no	—
118	M₁₆×C₅₃	—	2	1	no	—
119	M₁₆×C₅₃	—	2	1	no	—
120	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
126	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
127	C₄⋊C₄×C₅₃	—	2	1	no	—
128	C₄⋊C₄×C₅₃	—	2	2	no	—
129	C₂²⋊C₄×C₅₃	—	2	1	no	—
130	C₂²⋊C₄×C₅₃	—	2	2	no	—
131	C₂²⋊C₄×C₅₃	—	4	4	no	—
132	C₄²×C₅₃	—	2	2	no	—
133	C₄²×C₅₃	C₂×D₄	1	2	yes	—
134	C₂²⋊Dic₅₃	—	2	1	no	—
135	C₂²⋊Dic₅₃	—	2	1	no	—
136	C₂²⋊Dic₅₃	—	4	4	no	—
137	#11719923	—	4	4	no	—
138	#11719922	—	4	4	no	—
139	C₄⋊Dic₅₃	—	2	1	no	—
140	C₄⋊Dic₅₃	—	2	1	no	—
141	C₄×Dic₅₃	—	2	1	no	—
142	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
143	#11719917	—	2	1	no	—
144	#11719917	—	2	1	no	—
145	#11719917	—	2	2	no	—
146	#11719917	—	2	1	no	—
147	#11719917	—	2	2	no	—
148	#11719917	—	2	1	no	—
149	C₂×#88322	—	2	1	no	—
150	C₂×#88322	—	2	2	no	—
151	C₂×#88322	C₂²×C₄	1	2	yes	—
152	Dic₂₁₂	—	2	1	no	—
153	Dic₂₁₂	—	2	1	no	—
154	D₄₂₄	—	2	1	no	—
155	D₄₂₄	—	2	1	no	—
156	#11719913	—	2	2	no	—
157	#11719913	—	2	2	no	—
158	#11719912	—	4	4	no	—
159	C₈×D₅₃	—	4	4	no	—
160	C₂³×C₅₃	—	2	4	no	—
161	C₂³×C₅₃	—	4	2	no	—
162	C₂³×C₅₃	—	4	2	no	—
163	C₂³×C₅₃	—	16	2	no	—
164	C₂³×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂²×D₅₃	—	2	2	no	—
166	D₄×C₅₃	—	2	4	no	—
167	D₄×C₅₃	—	2	4	no	—
168	D₄×C₅₃	—	4	2	no	—
169	D₄×C₅₃	—	4	2	no	—
170	C₂×C₄×C₅₃	—	2	2	no	—
171	C₂×C₄×C₅₃	—	4	2	no	—
172	C₂×C₄×C₅₃	—	16	4	no	—
173	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂²⋊D₅₃	—	4	2	no	—
180	C₂²⋊D₅₃	—	4	2	no	—
181	C₂²⋊D₅₃	—	16	4	no	—
182	C₂×Dic₅₃	—	2	2	no	—
183	C₂×Dic₅₃	—	2	2	no	—
184	C₂×Dic₅₃	—	4	1	no	—
185	D₂₁₂	—	2	2	no	—
186	D₂₁₂	—	2	2	no	—
187	C₄×D₅₃	—	4	2	no	—
188	C₄×D₅₃	—	4	2	no	—
189	Dic₁₀₆	—	2	2	no	—
190	Dic₁₀₆	—	2	2	no	—
191	C₈×C₅₃	—	2	2	no	—
192	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
193	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
194	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
195	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
196	#88322	—	2	2	no	—
197	#88322	—	4	2	no	—
198	#88322	—	4	1	no	—
199	#22286	—	53	1	no	maximal, Sylow
200	C₂²×C₅₃	—	4	1	no	—
201	C₂²×C₅₃	—	4	4	no	—
202	C₂²×C₅₃	—	8	4	no	—
203	C₂²×C₅₃	—	8	4	no	—
204	C₂²×C₅₃	—	16	2	no	—
205	C₂²×C₅₃	#518	1	1	yes	characteristic
206	C₂²×C₅₃	#535	1	1	yes	characteristic
207	C₂²×C₅₃	#540	1	1	yes	characteristic
208	C₂×D₅₃	—	4	2	no	—
209	C₂×D₅₃	—	8	2	no	—
210	C₄×C₅₃	—	4	2	no	—
211	C₄×C₅₃	—	8	2	no	—
212	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₄×C₅₃	#518	1	1	yes	characteristic
214	C₄×C₅₃	#535	1	1	yes	characteristic
215	C₄×C₅₃	#540	1	1	yes	characteristic
216	Dic₅₃	—	4	2	no	—
217	Dic₅₃	—	4	2	no	—
218	Dic₅₃	—	8	1	no	—
219	#3155	—	53	1	no	—
220	#2957	—	53	1	no	—
221	#2948	D₅₃	1	1	yes	characteristic, complemented
222	#1978	—	53	1	no	—
223	#1976	—	53	1	no	—
224	#1911	—	53	2	no	—
225	#1910	—	53	2	no	—
226	#1904	—	53	2	no	—
227	#1903	—	53	2	no	—
228	#1833	—	53	1	no	—
229	#1747	—	53	1	no	—
230	C₂×C₅₃	—	2	1	no	—
231	C₂×C₅₃	—	2	1	no	—
232	C₂×C₅₃	—	2	1	no	—
233	C₂×C₅₃	—	8	4	no	—
234	C₂×C₅₃	#2328	1	1	yes	characteristic
235	D₅₃	—	8	2	no	—
236	C₂×AGL(1,ℤ/8)	—	53	2	no	—
237	C₂×#135	—	53	1	no	—
238	C₂²×D₈	C₂×D₅₃	1	1	yes	characteristic
239	#568	—	53	2	no	—
240	#535	—	53	2	no	—
241	#518	C₂×D₅₃	1	2	yes	—
242	#496	—	53	4	no	—
243	#495	—	53	2	no	—
244	#493	—	53	2	no	—
245	#444	—	106	2	no	—
246	#443	—	106	2	no	—
247	#442	—	2	2	no	—
248	C₄×D₈	—	2	2	no	—
249	C₂×#108	—	53	1	no	—
250	#427	C₂×D₅₃	1	1	yes	characteristic
251	#421	—	53	2	no	—
252	#421	—	53	2	no	—
253	#418	—	53	2	no	—
254	#418	C₂×D₅₃	1	2	yes	—
255	C₂×#100	—	53	2	no	—
256	#410	—	53	2	no	—
257	#405	—	53	1	no	—
258	#405	—	53	1	no	—
259	#405	C₂×D₅₃	1	1	yes	characteristic
260	#344	—	53	2	no	—
261	#338	—	53	1	no	—
262	H(3,ℤ/4)	—	53	1	no	—
263	H(3,ℤ/4)	—	53	2	no	—
264	H(3,ℤ/4)	—	53	1	no	—
265	H(3,ℤ/4)	—	53	1	no	—
266	C₅₃	#22286	1	1	yes	characteristic, complemented, Sylow
267	C₂×#41	—	53	2	no	—
268	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
269	AGL(1,ℤ/8)	—	212	2	no	—
270	AGL(1,ℤ/8)	—	212	2	no	—
271	#135	—	106	1	no	—
272	#135	—	106	1	no	—
273	#135	—	106	1	no	—
274	#135	—	106	1	no	—
275	C₂×Q₁₆	—	53	1	no	—
276	C₂×SD₁₆	—	53	4	no	—
277	C₂×SD₁₆	—	53	2	no	—
278	C₂×D₈	—	2	1	no	—
279	C₂×D₈	—	2	1	no	—
280	C₂×D₈	—	2	1	no	—
281	C₂×D₈	—	2	1	no	—
282	C₂×D₈	—	53	4	no	—
283	C₂×D₈	—	53	1	no	—
284	C₂×D₈	C₄×D₅₃	1	2	yes	—
285	C₂×D₈	C₄×D₅₃	1	2	yes	—
286	#131	—	106	4	no	—
287	#131	—	212	2	no	—
288	C₂×M₁₆	—	53	1	no	—
289	C₂×M₁₆	—	53	2	no	—
290	C₂×M₁₆	—	53	1	no	—
291	C₂×M₁₆	—	212	2	no	—
292	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
294	#127	—	53	4	no	—
295	#124	—	53	4	no	—
296	#121	—	212	2	no	—
297	#120	—	212	2	no	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	4	2	no	—
300	#117	—	53	1	no	—
301	#117	—	53	1	no	—
302	#117	C₂²×D₅₃	1	2	yes	—
303	#117	C₂²×D₅₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	4	2	no	—
305	#108	—	106	1	no	—
306	#108	—	106	1	no	—
307	#107	—	2	1	no	—
308	#106	—	2	1	no	—
309	#104	—	106	4	no	—
310	#104	—	212	2	no	—
311	#102	—	2	4	no	—
312	#102	—	212	2	no	—
313	#100	—	212	2	no	—
314	#99	—	212	2	no	—
315	#97	—	53	2	no	—
316	#97	—	106	1	no	—
317	#97	C₂²⋊D₅₃	1	2	yes	complemented
318	C₄×C₈	—	53	2	no	—
319	C₄×C₈	—	106	1	no	—
320	C₄×C₈	C₂²⋊D₅₃	1	2	yes	complemented
321	C₂⁴	—	2	2	no	—
322	#41	—	106	2	no	—
323	#41	—	106	2	no	—
324	#41	—	106	2	no	—
325	#41	—	106	2	no	—
326	C₂×Q₈	—	53	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	53	2	no	—
333	C₂×D₄	—	106	2	no	—
334	C₂×D₄	—	212	4	no	—
335	C₂×D₄	C₂×C₄×D₅₃	1	4	yes	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	106	2	no	—
338	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
339	Q₁₆	—	106	1	no	—
340	Q₁₆	—	106	1	no	—
341	SD₁₆	—	106	2	no	—
342	SD₁₆	—	106	2	no	—
343	SD₁₆	—	212	4	no	—
344	D₈	—	2	2	no	—
345	D₈	—	2	2	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	2	no	—
348	D₈	—	106	1	no	—
349	D₈	—	106	1	no	—
350	D₈	—	212	4	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	106	1	no	—
354	M₁₆	—	106	1	no	—
355	M₁₆	—	106	2	no	—
356	M₁₆	—	106	1	no	—
357	M₁₆	—	106	1	no	—
358	M₁₆	—	106	2	no	—
359	M₁₆	—	212	4	no	—
360	C₂×C₈	—	53	2	no	—
361	C₂×C₈	—	106	1	no	—
362	C₂×C₈	—	106	2	no	—
363	C₂×C₈	—	212	4	no	—
364	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
365	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
366	C₂×C₈	#11719945	1	1	yes	characteristic
367	C₂×C₈	#11719945	1	1	yes	characteristic
368	C₂×C₈	C₂×C₂²⋊D₅₃	1	2	yes	—
369	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
370	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	106	1	no	—
374	C₄⋊C₄	—	106	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₂²⋊C₄	—	106	1	no	—
379	C₂²⋊C₄	—	106	1	no	—
380	C₂²⋊C₄	—	212	4	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	53	2	no	—
383	C₄²	—	106	1	no	—
384	C₄²	C₂×C₂²⋊D₅₃	1	2	yes	—
385	C₂³	—	2	4	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	16	2	no	—
389	C₂³	—	106	2	no	—
390	C₂³	#13133262	1	1	yes	characteristic
391	Q₈	—	106	2	no	—
392	Q₈	—	106	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	848	4	no	—
398	D₄	—	106	2	no	—
399	D₄	—	106	2	no	—
400	D₄	—	212	2	no	—
401	D₄	—	212	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	16	4	no	—
405	C₂×C₄	—	106	2	no	—
406	C₂×C₄	—	106	2	no	—
407	C₂×C₄	—	212	1	no	—
408	C₂×C₄	—	212	2	no	—
409	C₂×C₄	—	212	2	no	—
410	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
412	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
413	C₂×C₄	#13133262	1	1	yes	characteristic
414	C₂×C₄	#13133263	1	1	yes	characteristic
415	C₂×C₄	#13133263	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	106	2	no	—
418	C₈	—	212	2	no	—
419	C₈	—	212	1	no	—
420	C₈	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
421	C₈	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
422	C₈	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
423	C₈	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	8	4	no	—
427	C₂²	—	8	4	no	—
428	C₂²	—	16	2	no	—
429	C₂²	—	424	2	no	—
430	C₂²	—	212	2	no	—
431	C₂²	#16811095	1	1	yes	characteristic
432	C₂²	#16811190	1	1	yes	characteristic
433	C₂²	#16811224	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	8	2	no	—
436	C₄	—	424	1	no	—
437	C₄	—	212	2	no	—
438	C₄	—	212	2	no	—
439	C₄	C₂×C₄×C₂²⋊D₅₃	1	1	yes	characteristic
440	C₄	#16811095	1	1	yes	characteristic
441	C₄	#16811187	1	1	yes	characteristic
442	C₄	#16811224	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	8	4	no	—
447	C₂	—	424	2	no	—
448	C₂	#20277437	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20277437
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#2948	C₂
socle	C₂×C₅₃	#2328
prime radical	#20285196	C₂
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#2948	D₅₃
hypocenter	C₅₃	#22286
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2948

Complements

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

N	H ≅ G/N	type
2. #20283633	C₂	semidirect
3. #20275626	C₂	semidirect
4. #20275611	C₂	semidirect
5. #20275247	C₂	semidirect
6. #20275239	C₂	semidirect
7. #20275202	C₂	semidirect
8. #20275192	C₂	semidirect
9. #20274838	C₂	semidirect
10. #20274470	C₂	semidirect
11. C₅₃×#2948	C₂	semidirect
16. #16811011	C₄	semidirect
17. #16811006	C₄	semidirect
18. #16810998	C₄	semidirect
49. C₂×Dic₂₁₂	C₂×C₄	semidirect
50. C₂×#11719913	C₂×C₄	semidirect
51. C₂×#11719923	C₂×C₄	semidirect
52. C₂×D₄₂₄	C₂×C₄	semidirect
53. C₂×#11719922	C₂×C₄	semidirect
60. #13133213	C₂×C₄	semidirect
61. #13133204	C₂×C₄	semidirect
74. #13133127	C₂×C₄	semidirect
76. C₈×Dic₅₃	C₂×C₄	semidirect
94. #97×C₅₃	D₄	semidirect
95. C₄×C₈×C₅₃	D₄	semidirect
221. #2948	D₅₃	semidirect
266. C₅₃	#22286	semidirect
317. #97	C₂²⋊D₅₃	semidirect
320. C₄×C₈	C₂²⋊D₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20285196	2
#20283633	2
#20275626	2
#20275611	2
#20275247	2
#20275239	2
#20275202	2
#20275192	2
#20274838	2
#20274470	2
C₅₃×#2948	2
#22286	53