Subgroups — C₅₃×#10060 #27217572

Order 13568.

638 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#476	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#2542	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₅₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊Q₈×C₅₃	—	2	2	no	—
11	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
12	C₅₃×#487	—	2	2	no	—
13	C₅₃×#487	—	2	2	no	—
14	C₅₃×#476	—	2	2	no	—
15	C₅₃×#476	—	2	2	no	—
16	C₂×#106×C₅₃	—	2	1	no	—
17	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#103×C₅₃	—	2	2	no	—
20	C₂×#102×C₅₃	—	2	1	no	—
21	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
22	C₅₃×#399	—	2	2	no	—
23	C₅₃×#390	—	2	1	no	—
24	C₅₃×#384	—	2	1	no	—
25	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₅₃×#340	—	2	2	no	—
27	C₅₃×#332	—	2	2	no	—
28	C₅₃×D₄⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₅₃	—	2	1	no	—
30	C₂²×Q₈×C₅₃	—	2	1	no	—
31	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₅₃	—	2	1	no	—
33	C₂²×C₈×C₅₃	—	2	1	no	—
34	C₂²×C₈×C₅₃	—	2	1	no	—
35	C₂²×C₈×C₅₃	—	2	1	no	—
36	C₄⋊Q₈×C₅₃	—	2	1	no	—
37	C₄⋊Q₈×C₅₃	—	2	1	no	—
38	C₄⋊Q₈×C₅₃	—	2	1	no	—
39	C₄⋊Q₈×C₅₃	—	2	1	no	—
40	C₄⋊Q₈×C₅₃	—	2	1	no	—
41	C₄⋊Q₈×C₅₃	—	2	1	no	—
42	C₄⋊Q₈×C₅₃	—	2	1	no	—
43	C₄⋊Q₈×C₅₃	D₄	1	2	yes	—
44	C₂²⋊Q₈×C₅₃	—	4	4	no	—
45	C₂²⋊Q₈×C₅₃	—	4	4	no	—
46	C₄×D₄×C₅₃	—	2	1	no	—
47	C₄×D₄×C₅₃	—	2	1	no	—
48	C₄×D₄×C₅₃	—	2	1	no	—
49	C₄×D₄×C₅₃	—	2	1	no	—
50	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
51	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
52	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
53	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
54	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₅₃	D₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₅₃	D₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
59	C₂×C₄²×C₅₃	—	2	1	no	—
60	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
61	#106×C₅₃	—	2	4	no	—
62	C₄⋊C₈×C₅₃	—	2	1	no	—
63	C₄⋊C₈×C₅₃	—	2	1	no	—
64	C₄⋊C₈×C₅₃	—	2	1	no	—
65	C₄⋊C₈×C₅₃	D₄	1	2	yes	—
66	#103×C₅₃	—	2	8	no	—
67	#102×C₅₃	—	2	4	no	—
68	C₄×C₈×C₅₃	—	2	1	no	—
69	C₄×C₈×C₅₃	D₄	1	2	yes	—
70	#95×C₅₃	—	2	1	no	—
71	C₂⁴×C₅₃	—	2	1	no	—
72	C₂×Q₈×C₅₃	—	2	2	no	—
73	C₂×Q₈×C₅₃	—	4	4	no	—
74	C₂×Q₈×C₅₃	—	4	1	no	—
75	C₂×Q₈×C₅₃	—	4	1	no	—
76	C₂×Q₈×C₅₃	—	4	1	no	—
77	C₂×Q₈×C₅₃	—	4	2	no	—
78	C₂×Q₈×C₅₃	—	4	2	no	—
79	C₂×D₄×C₅₃	—	2	1	no	—
80	C₂×D₄×C₅₃	—	2	1	no	—
81	C₂×D₄×C₅₃	—	2	1	no	—
82	C₂×D₄×C₅₃	—	2	1	no	—
83	C₂×D₄×C₅₃	—	2	1	no	—
84	C₂×D₄×C₅₃	Q₁₆	1	2	yes	—
85	C₂²×C₄×C₅₃	—	2	2	no	—
86	C₂²×C₄×C₅₃	—	2	2	no	—
87	C₂²×C₄×C₅₃	—	2	1	no	—
88	C₂²×C₄×C₅₃	—	4	1	no	—
89	C₂²×C₄×C₅₃	—	4	1	no	—
90	C₂²×C₄×C₅₃	—	4	1	no	—
91	C₂²×C₄×C₅₃	—	4	2	no	—
92	C₂²×C₄×C₅₃	—	4	2	no	—
93	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
96	C₂×C₈×C₅₃	—	2	2	no	—
97	C₂×C₈×C₅₃	—	2	2	no	—
98	C₂×C₈×C₅₃	—	4	2	no	—
99	C₂×C₈×C₅₃	—	4	1	no	—
100	C₂×C₈×C₅₃	—	4	1	no	—
101	C₂×C₈×C₅₃	—	4	1	no	—
102	C₂×C₈×C₅₃	—	4	2	no	—
103	C₄⋊C₄×C₅₃	—	2	2	no	—
104	C₄⋊C₄×C₅₃	—	2	2	no	—
105	C₄⋊C₄×C₅₃	—	2	2	no	—
106	C₄⋊C₄×C₅₃	—	2	1	no	—
107	C₄⋊C₄×C₅₃	—	2	2	no	—
108	C₄⋊C₄×C₅₃	—	2	1	no	—
109	C₄⋊C₄×C₅₃	—	2	2	no	—
110	C₄⋊C₄×C₅₃	—	4	8	no	—
111	C₄⋊C₄×C₅₃	—	4	1	no	—
112	C₄⋊C₄×C₅₃	—	4	1	no	—
113	C₄⋊C₄×C₅₃	—	4	1	no	—
114	C₄⋊C₄×C₅₃	—	4	1	no	—
115	C₄⋊C₄×C₅₃	SD₁₆	1	4	yes	—
116	C₂²⋊C₄×C₅₃	—	4	8	no	—
117	C₂²⋊C₄×C₅₃	—	4	1	no	—
118	C₂²⋊C₄×C₅₃	—	4	1	no	—
119	C₄²×C₅₃	—	4	1	no	—
120	C₄²×C₅₃	—	4	1	no	—
121	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₅₃	#41	1	1	yes	characteristic
125	C₂³×C₅₃	—	2	2	no	—
126	C₂³×C₅₃	—	4	1	no	—
127	C₂³×C₅₃	—	4	2	no	—
128	C₂³×C₅₃	—	4	1	no	—
129	C₂³×C₅₃	—	4	2	no	—
130	C₂³×C₅₃	#120	1	1	yes	characteristic
131	Q₈×C₅₃	—	4	4	no	—
132	Q₈×C₅₃	—	8	2	no	—
133	Q₈×C₅₃	—	8	2	no	—
134	Q₈×C₅₃	—	8	1	no	—
135	Q₈×C₅₃	—	8	1	no	—
136	D₄×C₅₃	—	2	2	no	—
137	D₄×C₅₃	—	2	2	no	—
138	D₄×C₅₃	—	4	1	no	—
139	D₄×C₅₃	—	4	1	no	—
140	C₂×C₄×C₅₃	—	2	2	no	—
141	C₂×C₄×C₅₃	—	2	4	no	—
142	C₂×C₄×C₅₃	—	4	2	no	—
143	C₂×C₄×C₅₃	—	4	2	no	—
144	C₂×C₄×C₅₃	—	4	1	no	—
145	C₂×C₄×C₅₃	—	4	2	no	—
146	C₂×C₄×C₅₃	—	4	2	no	—
147	C₂×C₄×C₅₃	—	4	2	no	—
148	C₂×C₄×C₅₃	—	4	4	no	—
149	C₂×C₄×C₅₃	—	8	2	no	—
150	C₂×C₄×C₅₃	—	8	2	no	—
151	C₂×C₄×C₅₃	—	8	1	no	—
152	C₂×C₄×C₅₃	—	8	1	no	—
153	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
154	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
155	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
156	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
157	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
158	C₂×C₄×C₅₃	#127	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₅₃	C₂×Q₁₆	1	1	yes	characteristic
161	C₂×C₄×C₅₃	#135	1	1	yes	characteristic
162	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
163	C₂×C₄×C₅₃	#137	1	1	yes	characteristic
164	C₂×C₄×C₅₃	#137	1	1	yes	characteristic
165	C₈×C₅₃	—	4	2	no	—
166	C₈×C₅₃	—	4	2	no	—
167	C₈×C₅₃	—	8	1	no	—
168	#10060	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂²×C₅₃	—	4	4	no	—
170	C₂²×C₅₃	—	4	2	no	—
171	C₂²×C₅₃	—	8	2	no	—
172	C₂²×C₅₃	—	8	1	no	—
173	C₂²×C₅₃	—	8	1	no	—
174	C₂²×C₅₃	#392	1	1	yes	characteristic
175	C₂²×C₅₃	#450	1	2	yes	—
176	C₂²×C₅₃	#451	1	1	yes	characteristic
177	C₂²×C₅₃	#452	1	1	yes	characteristic
178	C₂²×C₅₃	#454	1	2	yes	—
179	C₄×C₅₃	—	2	1	no	—
180	C₄×C₅₃	—	2	1	no	—
181	C₄×C₅₃	—	4	4	no	—
182	C₄×C₅₃	—	8	2	no	—
183	C₄×C₅₃	—	8	1	no	—
184	C₄×C₅₃	—	8	2	no	—
185	C₄×C₅₃	#451	1	1	yes	characteristic
186	C₄×C₅₃	#452	1	1	yes	characteristic
187	C₄×C₅₃	#460	1	2	yes	—
188	C₄×C₅₃	#467	1	1	yes	characteristic
189	C₄×C₅₃	#470	1	1	yes	characteristic
190	C₄×C₅₃	#492	1	1	yes	characteristic
191	C₄×C₅₃	#496	1	1	yes	characteristic
192	C₂×#487	C₂×C₅₃	1	1	yes	characteristic, complemented
193	C₂×#476	C₂×C₅₃	1	1	yes	characteristic
194	#2542	C₂×C₅₃	1	1	yes	characteristic
195	#1987	C₂×C₅₃	1	1	yes	characteristic, complemented
196	C₂×#332	C₂×C₅₃	1	1	yes	characteristic, complemented
197	C₂×D₄⋊C₈	C₂×C₅₃	1	1	yes	characteristic
198	#1279	C₂×C₅₃	1	1	yes	characteristic, complemented
199	C₂×C₅₃	—	8	2	no	—
200	C₂×C₅₃	#1635	1	2	yes	—
201	C₂×C₅₃	#1637	1	2	yes	—
202	C₂×C₅₃	#2001	1	1	yes	characteristic
203	C₂×C₅₃	#2003	1	1	yes	characteristic
204	C₂×C₅₃	#2014	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
206	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
207	C₂×C₂²⋊Q₈	—	2	2	no	—
208	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
209	#487	—	2	2	no	—
210	#487	—	2	2	no	—
211	#476	—	2	2	no	—
212	#476	—	2	2	no	—
213	C₂×#106	—	2	1	no	—
214	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
216	C₂×#103	—	2	2	no	—
217	C₂×#102	—	2	1	no	—
218	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
219	#399	—	2	2	no	—
220	#390	—	2	1	no	—
221	#384	—	2	1	no	—
222	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
223	#340	—	2	2	no	—
224	#332	—	2	2	no	—
225	D₄⋊C₈	—	2	2	no	—
226	C₅₃	#10060	1	1	yes	characteristic, direct product factor, Sylow
227	C₂²×Q₈	—	2	1	no	—
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
230	C₂³×C₄	—	2	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	D₄×C₅₃	1	2	yes	—
242	C₂²⋊Q₈	—	4	4	no	—
243	C₂²⋊Q₈	—	4	4	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
253	C₂×C₄⋊C₄	D₄×C₅₃	1	2	yes	—
254	C₂×C₄⋊C₄	D₄×C₅₃	1	2	yes	—
255	C₂×C₂²⋊C₄	—	2	4	no	—
256	C₂×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
259	#106	—	2	4	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	D₄×C₅₃	1	2	yes	—
264	#103	—	2	8	no	—
265	#102	—	2	4	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	D₄×C₅₃	1	2	yes	—
268	#95	—	2	1	no	—
269	C₂⁴	—	2	1	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	4	4	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂×Q₈	—	4	1	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×Q₈	—	4	2	no	—
276	C₂×Q₈	—	4	2	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	Q₁₆×C₅₃	1	2	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	4	2	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	8	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	SD₁₆×C₅₃	1	4	yes	—
314	C₂²⋊C₄	—	4	8	no	—
315	C₂²⋊C₄	—	4	1	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₄²	—	4	1	no	—
318	C₄²	—	4	1	no	—
319	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
320	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
321	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
322	C₄²	#41×C₅₃	1	1	yes	characteristic
323	C₂³	—	2	2	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	2	no	—
328	C₂³	#120×C₅₃	1	1	yes	characteristic
329	Q₈	—	4	4	no	—
330	Q₈	—	8	2	no	—
331	Q₈	—	8	1	no	—
332	Q₈	—	8	1	no	—
333	Q₈	—	8	2	no	—
334	D₄	—	2	2	no	—
335	D₄	—	2	2	no	—
336	D₄	—	4	1	no	—
337	D₄	—	4	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	8	1	no	—
349	C₂×C₄	—	8	1	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	#120×C₅₃	1	1	yes	characteristic
352	C₂×C₄	#120×C₅₃	1	1	yes	characteristic
353	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
354	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
355	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
356	C₂×C₄	#127×C₅₃	1	1	yes	characteristic
357	C₂×C₄	C₂×SD₁₆×C₅₃	1	2	yes	—
358	C₂×C₄	C₂×Q₁₆×C₅₃	1	1	yes	characteristic
359	C₂×C₄	#135×C₅₃	1	1	yes	characteristic
360	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	2	yes	—
361	C₂×C₄	#137×C₅₃	1	1	yes	characteristic
362	C₂×C₄	#137×C₅₃	1	1	yes	characteristic
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₈	—	8	1	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	2	no	—
371	C₂²	C₅₃×#392	1	1	yes	characteristic
372	C₂²	C₅₃×#450	1	2	yes	—
373	C₂²	C₅₃×#451	1	1	yes	characteristic
374	C₂²	C₅₃×#452	1	1	yes	characteristic
375	C₂²	C₅₃×#454	1	2	yes	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	4	4	no	—
379	C₄	—	8	2	no	—
380	C₄	—	8	1	no	—
381	C₄	—	8	2	no	—
382	C₄	C₅₃×#451	1	1	yes	characteristic
383	C₄	C₅₃×#452	1	1	yes	characteristic
384	C₄	C₅₃×#460	1	2	yes	—
385	C₄	C₅₃×#467	1	1	yes	characteristic
386	C₄	C₅₃×#470	1	1	yes	characteristic
387	C₄	C₅₃×#492	1	1	yes	characteristic
388	C₄	C₅₃×#496	1	1	yes	characteristic
389	C₂	—	8	2	no	—
390	C₂	C₅₃×#1635	1	2	yes	—
391	C₂	C₅₃×#1637	1	2	yes	—
392	C₂	C₅₃×#2001	1	1	yes	characteristic
393	C₂	C₅₃×#2003	1	1	yes	characteristic
394	C₂	C₅₃×#2014	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₃
prime radical	C₂²×D₄×C₅₃	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#487	C₂	semidirect
4. C₅₃×#1987	C₂	semidirect
5. C₂×C₅₃×#332	C₂	semidirect
7. C₅₃×#1279	C₂	semidirect
168. #10060	C₅₃	direct (N × H)
192. C₂×#487	C₂×C₅₃	semidirect
195. #1987	C₂×C₅₃	semidirect
196. C₂×#332	C₂×C₅₃	semidirect
198. #1279	C₂×C₅₃	semidirect
226. C₅₃	#10060	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#487	2
C₂×C₅₃×#476	2
C₅₃×#2542	2
C₅₃×#1987	2
C₂×C₅₃×#332	2
C₂×C₅₃×D₄⋊C₈	2
C₅₃×#1279	2
#10060	53

Subgroups — C53×#10060 #27217572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#10060 #27217572