Subgroups — #27353341

Order 13568.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283682	C₂	1	1	yes	maximal, characteristic
2	#20283381	C₂	1	1	yes	maximal, characteristic
3	#20273506	C₂	1	2	yes	maximal, complemented
4	#20273498	C₂	1	2	yes	maximal, complemented
5	#20273489	C₂	1	1	yes	maximal, characteristic, complemented
6	#20273487	C₂	1	1	yes	maximal, characteristic, complemented
7	#20273480	C₂	1	2	yes	maximal, complemented
8	#20273473	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273465	C₂	1	2	yes	maximal, complemented
10	C₂×#16810373	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2906	C₂	1	1	yes	maximal, characteristic
12	#16810754	C₄	1	1	yes	characteristic
13	#16810754	C₄	1	1	yes	characteristic
14	#16810701	C₄	1	1	yes	characteristic
15	#16810701	C₄	1	1	yes	characteristic
16	#16810695	C₄	1	2	yes	—
17	#16810695	C₄	1	2	yes	—
18	#16810684	—	2	2	no	—
19	#16810680	C₂²	1	2	yes	—
20	#16810676	C₂²	1	2	yes	—
21	#16810676	C₂²	1	1	yes	characteristic
22	#16810676	C₂²	1	2	yes	—
23	#16810647	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
25	#16810590	—	2	1	no	—
26	#16810579	—	2	1	no	—
27	C₄×#11719917	C₂²	1	2	yes	—
28	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
29	#16810375	C₂²	1	2	yes	—
30	#16810375	C₂²	1	2	yes	—
31	#16810375	C₂²	1	2	yes	—
32	#16810375	C₂²	1	2	yes	—
33	#16810373	C₂²	1	1	yes	characteristic
34	#16810373	C₂²	1	1	yes	characteristic
35	#16810373	C₂²	1	1	yes	characteristic
36	#16810373	C₂²	1	1	yes	characteristic
37	#16810373	C₂²	1	2	yes	—
38	#16810373	C₂²	1	2	yes	—
39	C₂×#131×C₅₃	—	2	1	no	—
40	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#424	—	2	1	no	—
42	C₅₃×#424	—	2	2	no	—
43	C₅₃×#423	C₂²	1	1	yes	characteristic
44	C₅₃×#423	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
47	C₂×#11719917	—	2	1	no	—
48	C₂×#11719917	C₂×C₄	1	2	yes	—
49	C₂×#11719917	C₂×C₄	1	2	yes	—
50	C₂²×#88322	—	2	1	no	—
51	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
52	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
53	C₄⋊#88322	—	2	1	no	—
54	C₄⋊#88322	—	2	1	no	—
55	C₄⋊#88322	C₂×C₄	1	2	yes	—
56	C₄⋊#88322	C₂×C₄	1	2	yes	—
57	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
58	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
59	C₄⋊#88322	C₂³	1	1	yes	characteristic
60	C₄⋊#88322	C₂³	1	1	yes	characteristic
61	C₄⋊#88322	C₂³	1	2	yes	—
62	C₂²⋊#88322	—	2	2	no	—
63	C₂²⋊#88322	—	2	2	no	—
64	C₂²⋊#88322	C₂×C₄	1	2	yes	—
65	C₂²⋊#88322	C₂×C₄	1	2	yes	—
66	C₂²⋊#88322	C₂×C₄	1	2	yes	—
67	#13133128	—	2	2	no	—
68	#13133128	C₂×C₄	1	2	yes	—
69	#13133128	C₂×C₄	1	2	yes	—
70	C₄×#88322	—	2	2	no	—
71	C₄×#88322	C₂×C₄	1	1	yes	characteristic
72	C₄×#88322	C₂×C₄	1	1	yes	characteristic
73	C₄×#88322	C₂³	1	1	yes	characteristic
74	C₄×#88322	C₂³	1	1	yes	characteristic
75	C₄×#88322	C₂³	1	2	yes	—
76	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
77	#131×C₅₃	—	4	4	no	—
78	C₂×M₁₆×C₅₃	—	2	2	no	—
79	C₂×M₁₆×C₅₃	—	2	1	no	—
80	C₂²×C₈×C₅₃	—	2	2	no	—
81	C₂²×C₈×C₅₃	—	2	1	no	—
82	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₅₃	Q₈	1	1	yes	characteristic
84	C₄×D₄×C₅₃	C₂×C₄	1	2	yes	—
85	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
86	C₄×D₄×C₅₃	Q₈	1	1	yes	characteristic
87	C₄×D₄×C₅₃	Q₈	1	2	yes	—
88	#117×C₅₃	D₄	1	1	yes	characteristic
89	#117×C₅₃	D₄	1	2	yes	—
90	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
92	C₄⋊C₈×C₅₃	—	2	2	no	—
93	C₄⋊C₈×C₅₃	—	2	1	no	—
94	C₄⋊C₈×C₅₃	—	2	2	no	—
95	C₄⋊C₈×C₅₃	—	2	1	no	—
96	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
99	#41×C₅₃	—	2	2	no	—
100	#41×C₅₃	—	2	2	no	—
101	C₂×Q₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×D₄×C₅₃	C₄⋊C₄	1	2	yes	—
103	C₂×D₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₃	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
110	M₁₆×C₅₃	—	4	4	no	—
111	M₁₆×C₅₃	—	4	2	no	—
112	C₂×C₈×C₅₃	—	2	1	no	—
113	C₂×C₈×C₅₃	—	2	2	no	—
114	C₂×C₈×C₅₃	—	2	1	no	—
115	C₂×C₈×C₅₃	—	4	4	no	—
116	C₂×C₈×C₅₃	—	4	2	no	—
117	C₄⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
118	C₄⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
119	C₄⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
120	C₄⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
121	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
122	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
123	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
124	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₅₃	C₂×D₄	1	2	yes	—
127	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
129	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
130	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
131	#11719917	—	2	4	no	—
132	#11719917	—	4	2	no	—
133	#11719917	—	4	2	no	—
134	C₂×#88322	—	2	2	no	—
135	C₂×#88322	—	2	1	no	—
136	C₂×#88322	—	2	2	no	—
137	C₂×#88322	—	2	1	no	—
138	C₂×#88322	—	4	1	no	—
139	C₂×#88322	—	4	2	no	—
140	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
141	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
142	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
143	C₂×#88322	C₂²×C₄	1	2	yes	—
144	C₂×#88322	C₂²×C₄	1	2	yes	—
145	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
146	C₂³×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
147	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	Q₈×C₅₃	—	2	2	no	—
149	D₄×C₅₃	—	2	4	no	—
150	D₄×C₅₃	—	2	2	no	—
151	C₂×C₄×C₅₃	—	2	1	no	—
152	C₂×C₄×C₅₃	—	2	2	no	—
153	C₂×C₄×C₅₃	—	2	1	no	—
154	C₂×C₄×C₅₃	—	2	2	no	—
155	C₂×C₄×C₅₃	—	2	2	no	—
156	C₂×C₄×C₅₃	—	2	2	no	—
157	C₂×C₄×C₅₃	—	4	1	no	—
158	C₂×C₄×C₅₃	—	4	2	no	—
159	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₅₃	#137	1	2	yes	—
167	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
170	C₈×C₅₃	—	4	1	no	—
171	C₈×C₅₃	—	4	2	no	—
172	C₈×C₅₃	—	4	1	no	—
173	#88322	—	2	1	no	—
174	#88322	—	2	2	no	—
175	#88322	—	2	1	no	—
176	#88322	—	2	1	no	—
177	#88322	—	2	2	no	—
178	#88322	—	4	2	no	—
179	#88322	—	4	1	no	—
180	#88322	—	4	1	no	—
181	#88322	#131	1	2	yes	complemented
182	#17830	—	53	1	no	maximal, Sylow
183	C₂²×C₅₃	—	2	1	no	—
184	C₂²×C₅₃	—	2	1	no	—
185	C₂²×C₅₃	—	2	2	no	—
186	C₂²×C₅₃	—	2	2	no	—
187	C₂²×C₅₃	—	2	2	no	—
188	C₂²×C₅₃	#428	1	2	yes	—
189	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
190	C₄×C₅₃	—	2	1	no	—
191	C₄×C₅₃	—	2	2	no	—
192	C₄×C₅₃	—	2	2	no	—
193	C₄×C₅₃	—	2	1	no	—
194	C₄×C₅₃	—	2	1	no	—
195	C₄×C₅₃	—	2	2	no	—
196	C₄×C₅₃	#428	1	2	yes	—
197	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
198	C₄×C₅₃	#568	1	1	yes	characteristic
199	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
201	#2965	—	53	1	no	—
202	#2925	—	53	1	no	—
203	#2906	D₅₃	1	1	yes	characteristic
204	#1574	—	53	2	no	—
205	#1573	—	53	2	no	—
206	#1571	—	53	1	no	—
207	#1570	—	53	1	no	—
208	#1569	—	53	2	no	—
209	#1567	—	53	1	no	—
210	#1565	—	53	2	no	—
211	C₂×#334	—	53	1	no	—
212	C₂×C₅₃	—	2	2	no	—
213	C₂×C₅₃	—	4	2	no	—
214	C₂×C₅₃	#2906	1	1	yes	characteristic
215	C₂×C₅₃	C₂×#428	1	1	yes	characteristic
216	C₂×C₅₃	#2916	1	1	yes	characteristic
217	C₂×#131	—	2	1	no	—
218	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
219	#446	—	53	1	no	—
220	#446	—	53	1	no	—
221	#436	—	53	1	no	—
222	#436	—	53	1	no	—
223	#435	—	53	2	no	—
224	#435	—	53	2	no	—
225	#433	—	106	2	no	—
226	#432	—	53	2	no	—
227	#431	—	53	1	no	—
228	#431	—	53	2	no	—
229	#431	—	53	2	no	—
230	#424	—	2	1	no	—
231	#424	—	2	2	no	—
232	#423	—	53	1	no	—
233	#423	C₂×D₅₃	1	1	yes	characteristic
234	#423	C₂×D₅₃	1	2	yes	—
235	C₂×C₄⋊C₈	—	53	1	no	—
236	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂×D₅₃	1	2	yes	—
238	#408	—	106	1	no	—
239	#405	—	106	1	no	—
240	C₄×M₁₆	—	53	2	no	—
241	C₂×C₄×C₈	—	53	1	no	—
242	#335	—	53	2	no	—
243	#335	—	53	2	no	—
244	#335	—	53	2	no	—
245	#335	—	53	2	no	—
246	#334	—	53	1	no	—
247	#334	—	53	1	no	—
248	#334	—	53	1	no	—
249	#334	—	53	1	no	—
250	#334	—	53	2	no	—
251	#334	—	53	2	no	—
252	C₅₃	#17830	1	1	yes	characteristic, complemented, Sylow
253	C₂×#41	C₂²⋊D₅₃	1	1	yes	characteristic
254	#131	—	4	4	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	53	2	no	—
258	C₂×M₁₆	—	53	2	no	—
259	C₂×M₁₆	—	106	1	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	53	1	no	—
263	C₂²×C₈	—	53	1	no	—
264	C₂²×C₈	—	106	1	no	—
265	C₄×Q₈	Dic₁₀₆	1	1	yes	characteristic
266	C₄×Q₈	C₄×D₅₃	1	1	yes	characteristic
267	C₄×D₄	Dic₁₀₆	1	2	yes	—
268	C₄×D₄	Dic₁₀₆	1	1	yes	characteristic
269	C₄×D₄	C₄×D₅₃	1	2	yes	—
270	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
271	#117	C₂²⋊D₅₃	1	1	yes	characteristic
272	#117	C₂²⋊D₅₃	1	2	yes	—
273	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	53	2	no	—
280	C₄⋊C₈	—	53	2	no	—
281	C₄⋊C₈	—	53	1	no	—
282	C₄⋊C₈	—	53	1	no	—
283	C₄⋊C₈	—	53	1	no	—
284	C₄⋊C₈	—	53	1	no	—
285	C₄⋊C₈	—	53	2	no	—
286	C₄⋊C₈	—	106	1	no	—
287	C₄⋊C₈	—	106	1	no	—
288	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
289	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
291	C₂²⋊C₈	—	53	2	no	—
292	C₂²⋊C₈	—	53	2	no	—
293	C₂²⋊C₈	—	53	2	no	—
294	C₂²⋊C₈	—	106	2	no	—
295	C₂²⋊C₈	—	106	2	no	—
296	#97	—	53	2	no	—
297	#97	—	53	2	no	—
298	#97	—	106	2	no	—
299	C₄×C₈	—	53	1	no	—
300	C₄×C₈	—	53	1	no	—
301	C₄×C₈	—	53	1	no	—
302	C₄×C₈	—	53	1	no	—
303	C₄×C₈	—	53	2	no	—
304	C₄×C₈	—	106	2	no	—
305	#41	—	2	2	no	—
306	#41	—	2	2	no	—
307	C₂×Q₈	#11719919	1	1	yes	characteristic
308	C₂×D₄	#11719919	1	2	yes	—
309	C₂×D₄	#11719919	1	1	yes	characteristic
310	C₂²×C₄	C₂×Dic₁₀₆	1	2	yes	—
311	C₂²×C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₄×D₅₃	1	2	yes	—
314	C₂²×C₄	C₂×C₂²⋊D₅₃	1	2	yes	—
315	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
316	M₁₆	—	4	4	no	—
317	M₁₆	—	4	2	no	—
318	M₁₆	—	106	4	no	—
319	M₁₆	—	212	2	no	—
320	M₁₆	—	212	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	4	4	no	—
325	C₂×C₈	—	4	2	no	—
326	C₂×C₈	—	53	1	no	—
327	C₂×C₈	—	53	1	no	—
328	C₂×C₈	—	53	1	no	—
329	C₂×C₈	—	53	1	no	—
330	C₂×C₈	—	53	2	no	—
331	C₂×C₈	—	53	2	no	—
332	C₂×C₈	—	106	2	no	—
333	C₂×C₈	—	106	1	no	—
334	C₂×C₈	—	106	2	no	—
335	C₂×C₈	—	106	1	no	—
336	C₂×C₈	—	212	1	no	—
337	C₂×C₈	—	212	2	no	—
338	C₄⋊C₄	#11719919	1	2	yes	—
339	C₄⋊C₄	#11719919	1	1	yes	characteristic
340	C₄⋊C₄	#11719919	1	2	yes	—
341	C₄⋊C₄	#11719919	1	1	yes	characteristic
342	C₂²⋊C₄	#11719919	1	2	yes	—
343	C₂²⋊C₄	#11719919	1	2	yes	—
344	C₂²⋊C₄	#11719919	1	2	yes	—
345	C₄²	C₂×Dic₁₀₆	1	2	yes	—
346	C₄²	C₂×Dic₁₀₆	1	1	yes	characteristic
347	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
348	C₄²	C₂×C₄×D₅₃	1	2	yes	—
349	C₄²	C₂×C₂²⋊D₅₃	1	2	yes	—
350	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
351	C₄²	C₂³×D₅₃	1	1	yes	characteristic
352	C₂³	C₂×#11719919	1	2	yes	—
353	C₂³	C₂×#11719919	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	C₂×#11719919	1	2	yes	—
366	C₂×C₄	C₂×#11719919	1	2	yes	—
367	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
368	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
369	C₂×C₄	C₂×#11719919	1	2	yes	—
370	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
371	C₂×C₄	#13133243	1	2	yes	—
372	C₂×C₄	#13133248	1	2	yes	—
373	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
375	C₂×C₄	C₂²×Dic₁₀₆	1	1	yes	characteristic
376	C₈	—	4	1	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	1	no	—
379	C₈	—	53	2	no	—
380	C₈	—	106	1	no	—
381	C₈	—	106	2	no	—
382	C₈	—	106	1	no	—
383	C₈	—	106	1	no	—
384	C₈	—	106	2	no	—
385	C₈	—	212	2	no	—
386	C₈	—	212	1	no	—
387	C₈	—	212	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	#16810663	1	2	yes	—
394	C₂²	C₂²×#11719919	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	#16810663	1	2	yes	—
402	C₄	#131×D₅₃	1	1	yes	characteristic
403	C₄	#16811388	1	1	yes	characteristic
404	C₄	C₂×#13133243	1	1	yes	characteristic
405	C₄	C₂×#13133248	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	4	2	no	—
408	C₂	#20283281	1	1	yes	characteristic
409	C₂	C₂×#16810663	1	1	yes	characteristic
410	C₂	#20283324	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#2906	C₂
socle	C₂²×C₅₃	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₅₃	D₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#2906	D₅₃
hypocenter	C₅₃	#17830
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2906

Complements

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

N	H ≅ G/N	type
3. #20273506	C₂	semidirect
4. #20273498	C₂	semidirect
5. #20273489	C₂	semidirect
6. #20273487	C₂	semidirect
7. #20273480	C₂	semidirect
8. #20273473	C₂	semidirect
9. #20273465	C₂	semidirect
10. C₂×#16810373	C₂	semidirect
181. #88322	#131	semidirect
252. C₅₃	#17830	semidirect

Maximal subgroups

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

subgroup	index
#20283682	2
#20283381	2
#20273506	2
#20273498	2
#20273489	2
#20273487	2
#20273480	2
#20273473	2
#20273465	2
C₂×#16810373	2
C₅₃×#2906	2
#17830	53