Subgroups — C₂×C₅₃×#1703 #27226653

Order 13568.

694 conjugacy classes of subgroups.

The subgroup lattice has 384 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	C₂×C₅₃×#474	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₃×#436	C₂	1	1	yes	maximal, characteristic
5	C₅₃×#1703	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×M₁₆×C₅₃	—	2	1	no	—
10	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
13	C₅₃×#487	—	2	2	no	—
14	C₅₃×#487	C₂²	1	4	yes	complemented
15	C₅₃×#476	—	2	2	no	—
16	C₅₃×#476	C₂²	1	4	yes	—
17	C₅₃×#474	—	2	2	no	—
18	C₅₃×#474	C₂²	1	4	yes	—
19	C₅₃×#436	—	2	2	no	—
20	C₅₃×#436	C₂²	1	4	yes	—
21	C₂×#107×C₅₃	—	2	1	no	—
22	C₂×#106×C₅₃	—	2	1	no	—
23	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#103×C₅₃	—	2	1	no	—
27	C₂×#103×C₅₃	—	2	1	no	—
28	C₂×#102×C₅₃	—	2	1	no	—
29	C₂×#102×C₅₃	—	2	1	no	—
30	C₂×C₂²⋊C₈×C₅₃	—	2	1	no	—
31	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₅₃×#334	C₂²	1	4	yes	complemented
33	C₅₃×#333	C₂²	1	4	yes	complemented
34	C₅₃×#332	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₅₃	—	2	1	no	—
36	C₂²×Q₈×C₅₃	—	2	1	no	—
37	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₅₃	—	2	1	no	—
39	C₂×M₁₆×C₅₃	—	2	4	no	—
40	C₂×M₁₆×C₅₃	—	4	4	no	—
41	C₂²×C₈×C₅₃	—	2	1	no	—
42	C₂²×C₈×C₅₃	—	2	1	no	—
43	C₂²×C₈×C₅₃	—	2	1	no	—
44	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
46	C₄⋊Q₈×C₅₃	—	2	1	no	—
47	C₄⋊Q₈×C₅₃	—	2	1	no	—
48	C₄⋊Q₈×C₅₃	—	2	1	no	—
49	C₄⋊Q₈×C₅₃	—	2	1	no	—
50	C₄⋊Q₈×C₅₃	—	2	1	no	—
51	C₄⋊Q₈×C₅₃	—	2	1	no	—
52	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
54	C₄×D₄×C₅₃	—	2	1	no	—
55	C₄×D₄×C₅₃	—	2	1	no	—
56	C₄×D₄×C₅₃	D₄	1	2	yes	—
57	C₄×D₄×C₅₃	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
64	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
65	#107×C₅₃	—	2	4	no	—
66	#106×C₅₃	—	2	4	no	—
67	C₄⋊C₈×C₅₃	—	2	1	no	—
68	C₄⋊C₈×C₅₃	—	2	1	no	—
69	C₄⋊C₈×C₅₃	—	2	1	no	—
70	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
71	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
72	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
73	#103×C₅₃	—	2	4	no	—
74	#103×C₅₃	—	2	4	no	—
75	#102×C₅₃	—	2	4	no	—
76	#102×C₅₃	—	2	4	no	—
77	C₂²⋊C₈×C₅₃	—	2	4	no	—
78	C₄×C₈×C₅₃	D₄	1	2	yes	—
79	C₄×C₈×C₅₃	C₂³	1	2	yes	—
80	C₂⁴×C₅₃	—	2	1	no	—
81	C₂×Q₈×C₅₃	—	2	2	no	—
82	C₂×Q₈×C₅₃	—	2	2	no	—
83	C₂×Q₈×C₅₃	—	4	1	no	—
84	C₂×Q₈×C₅₃	—	4	1	no	—
85	C₂×Q₈×C₅₃	—	4	2	no	—
86	C₂×Q₈×C₅₃	—	4	2	no	—
87	C₂×Q₈×C₅₃	—	8	2	no	—
88	C₂×D₄×C₅₃	—	2	1	no	—
89	C₂×D₄×C₅₃	—	2	2	no	—
90	C₂×D₄×C₅₃	—	2	2	no	—
91	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₅₃	—	2	1	no	—
93	C₂²×C₄×C₅₃	—	2	2	no	—
94	C₂²×C₄×C₅₃	—	2	2	no	—
95	C₂²×C₄×C₅₃	—	4	2	no	—
96	C₂²×C₄×C₅₃	—	4	2	no	—
97	C₂²×C₄×C₅₃	—	4	1	no	—
98	C₂²×C₄×C₅₃	—	4	1	no	—
99	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
102	M₁₆×C₅₃	—	4	8	no	—
103	C₂×C₈×C₅₃	—	2	2	no	—
104	C₂×C₈×C₅₃	—	2	2	no	—
105	C₂×C₈×C₅₃	—	2	2	no	—
106	C₂×C₈×C₅₃	—	2	2	no	—
107	C₂×C₈×C₅₃	—	2	2	no	—
108	C₂×C₈×C₅₃	—	4	2	no	—
109	C₂×C₈×C₅₃	—	4	2	no	—
110	C₂×C₈×C₅₃	—	4	2	no	—
111	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
113	C₄⋊C₄×C₅₃	—	2	1	no	—
114	C₄⋊C₄×C₅₃	—	2	2	no	—
115	C₄⋊C₄×C₅₃	—	2	2	no	—
116	C₄⋊C₄×C₅₃	—	2	2	no	—
117	C₄⋊C₄×C₅₃	—	2	2	no	—
118	C₄⋊C₄×C₅₃	—	4	1	no	—
119	C₄⋊C₄×C₅₃	—	4	1	no	—
120	C₄⋊C₄×C₅₃	—	4	1	no	—
121	C₄⋊C₄×C₅₃	—	4	1	no	—
122	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
123	C₂²⋊C₄×C₅₃	—	2	2	no	—
124	C₂²⋊C₄×C₅₃	—	2	2	no	—
125	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₅₃	#41	1	1	yes	characteristic
128	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
129	C₂³×C₅₃	—	2	2	no	—
130	C₂³×C₅₃	—	4	2	no	—
131	C₂³×C₅₃	—	4	2	no	—
132	C₂³×C₅₃	—	4	2	no	—
133	C₂³×C₅₃	#121	1	1	yes	characteristic
134	Q₈×C₅₃	—	4	2	no	—
135	Q₈×C₅₃	—	4	2	no	—
136	Q₈×C₅₃	—	8	2	no	—
137	Q₈×C₅₃	—	8	2	no	—
138	Q₈×C₅₃	—	8	2	no	—
139	D₄×C₅₃	—	2	2	no	—
140	D₄×C₅₃	—	2	2	no	—
141	D₄×C₅₃	—	4	2	no	—
142	C₂×C₄×C₅₃	—	2	2	no	—
143	C₂×C₄×C₅₃	—	2	2	no	—
144	C₂×C₄×C₅₃	—	4	2	no	—
145	C₂×C₄×C₅₃	—	4	2	no	—
146	C₂×C₄×C₅₃	—	4	2	no	—
147	C₂×C₄×C₅₃	—	4	4	no	—
148	C₂×C₄×C₅₃	—	4	2	no	—
149	C₂×C₄×C₅₃	—	4	2	no	—
150	C₂×C₄×C₅₃	—	8	2	no	—
151	C₂×C₄×C₅₃	—	8	2	no	—
152	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
153	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
154	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
155	C₂×C₄×C₅₃	#135	1	2	yes	—
156	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
157	C₂×C₄×C₅₃	#137	1	2	yes	—
158	C₂×C₄×C₅₃	#137	1	2	yes	—
159	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
162	C₈×C₅₃	—	2	2	no	—
163	C₈×C₅₃	—	2	2	no	—
164	C₈×C₅₃	—	4	2	no	—
165	C₈×C₅₃	—	4	2	no	—
166	C₈×C₅₃	—	4	2	no	—
167	C₂×#1703	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂²×C₅₃	—	4	2	no	—
169	C₂²×C₅₃	—	4	2	no	—
170	C₂²×C₅₃	—	4	2	no	—
171	C₂²×C₅₃	—	8	4	no	—
172	C₂²×C₅₃	#463	1	2	yes	—
173	C₂²×C₅₃	#470	1	2	yes	—
174	C₂²×C₅₃	#471	1	2	yes	—
175	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
176	C₄×C₅₃	—	2	1	no	—
177	C₄×C₅₃	—	2	1	no	—
178	C₄×C₅₃	—	4	2	no	—
179	C₄×C₅₃	—	8	2	no	—
180	C₄×C₅₃	—	8	2	no	—
181	C₄×C₅₃	#463	1	2	yes	—
182	C₄×C₅₃	#470	1	2	yes	—
183	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
184	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
186	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
187	C₂×#487	C₂×C₅₃	1	1	yes	characteristic, complemented
188	C₂×#476	C₂×C₅₃	1	1	yes	characteristic
189	C₂×#474	C₂×C₅₃	1	1	yes	characteristic
190	C₂×#436	C₂×C₅₃	1	1	yes	characteristic
191	#1703	C₂×C₅₃	1	8	yes	direct product factor
192	C₂×#334	C₂×C₅₃	1	1	yes	characteristic, complemented
193	C₂×#333	C₂×C₅₃	1	1	yes	characteristic, complemented
194	C₂×#332	C₂×C₅₃	1	1	yes	characteristic, complemented
195	C₂×C₅₃	—	8	2	no	—
196	C₂×C₅₃	#1703	1	4	yes	direct product factor
197	C₂×C₅₃	C₂×#463	1	1	yes	characteristic
198	C₂×C₅₃	C₂×#470	1	1	yes	characteristic
199	C₂×C₅₃	C₂×#471	1	1	yes	characteristic
200	C₂²×M₁₆	—	2	1	no	—
201	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
202	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
203	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
204	#487	—	2	2	no	—
205	#487	C₂²×C₅₃	1	4	yes	complemented
206	#476	—	2	2	no	—
207	#476	C₂²×C₅₃	1	4	yes	—
208	#474	—	2	2	no	—
209	#474	C₂²×C₅₃	1	4	yes	—
210	#436	—	2	2	no	—
211	#436	C₂²×C₅₃	1	4	yes	—
212	C₂×#107	—	2	1	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×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
217	C₂×#103	—	2	1	no	—
218	C₂×#103	—	2	1	no	—
219	C₂×#102	—	2	1	no	—
220	C₂×#102	—	2	1	no	—
221	C₂×C₂²⋊C₈	—	2	1	no	—
222	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
223	#334	C₂²×C₅₃	1	4	yes	complemented
224	#333	C₂²×C₅₃	1	4	yes	complemented
225	#332	C₂²×C₅₃	1	4	yes	complemented
226	C₅₃	C₂×#1703	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	C₂×M₁₆	—	2	4	no	—
232	C₂×M₁₆	—	4	4	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	2	1	no	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	D₄×C₅₃	1	1	yes	characteristic
237	C₂²×C₈	D₄×C₅₃	1	1	yes	characteristic
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
245	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	D₄×C₅₃	1	2	yes	—
249	C₄×D₄	C₂³×C₅₃	1	2	yes	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
257	#107	—	2	4	no	—
258	#106	—	2	4	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
263	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
264	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
265	#103	—	2	4	no	—
266	#103	—	2	4	no	—
267	#102	—	2	4	no	—
268	#102	—	2	4	no	—
269	C₂²⋊C₈	—	2	4	no	—
270	C₄×C₈	D₄×C₅₃	1	2	yes	—
271	C₄×C₈	C₂³×C₅₃	1	2	yes	—
272	C₂⁴	—	2	1	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×Q₈	—	4	1	no	—
277	C₂×Q₈	—	4	2	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	—	8	2	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
293	C₂²×C₄	#41×C₅₃	1	1	yes	characteristic
294	M₁₆	—	4	8	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
304	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
319	C₄²	#41×C₅₃	1	1	yes	characteristic
320	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
321	C₂³	—	2	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	#121×C₅₃	1	1	yes	characteristic
326	Q₈	—	4	2	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	8	2	no	—
329	Q₈	—	8	2	no	—
330	Q₈	—	8	2	no	—
331	D₄	—	2	2	no	—
332	D₄	—	2	2	no	—
333	D₄	—	4	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
345	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
346	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
347	C₂×C₄	#135×C₅₃	1	2	yes	—
348	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	2	yes	—
349	C₂×C₄	#137×C₅₃	1	2	yes	—
350	C₂×C₄	#137×C₅₃	1	2	yes	—
351	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
352	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
353	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
354	C₈	—	2	2	no	—
355	C₈	—	2	2	no	—
356	C₈	—	4	2	no	—
357	C₈	—	4	2	no	—
358	C₈	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	8	4	no	—
363	C₂²	C₅₃×#463	1	2	yes	—
364	C₂²	C₅₃×#470	1	2	yes	—
365	C₂²	C₅₃×#471	1	2	yes	—
366	C₂²	C₂×#121×C₅₃	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	4	2	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	2	no	—
372	C₄	C₅₃×#463	1	2	yes	—
373	C₄	C₅₃×#470	1	2	yes	—
374	C₄	C₂×#135×C₅₃	1	1	yes	characteristic
375	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
376	C₄	C₂×#137×C₅₃	1	1	yes	characteristic
377	C₄	C₂×#137×C₅₃	1	1	yes	characteristic
378	C₂	—	8	2	no	—
379	C₂	C₅₃×#1703	1	4	yes	direct product factor
380	C₂	C₂×C₅₃×#463	1	1	yes	characteristic
381	C₂	C₂×C₅₃×#470	1	1	yes	characteristic
382	C₂	C₂×C₅₃×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₃
prime radical	C₂²×D₄×C₅₃	D₄
LCS	G ▷ 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
5. C₅₃×#1703	C₂	direct (N × H)
6. C₂×C₅₃×#334	C₂	semidirect
7. C₂×C₅₃×#333	C₂	semidirect
8. C₂×C₅₃×#332	C₂	semidirect
14. C₅₃×#487	C₂²	semidirect
32. C₅₃×#334	C₂²	semidirect
33. C₅₃×#333	C₂²	semidirect
34. C₅₃×#332	C₂²	semidirect
167. C₂×#1703	C₅₃	direct (N × H)
187. C₂×#487	C₂×C₅₃	semidirect
191. #1703	C₂×C₅₃	direct (N × H)
192. C₂×#334	C₂×C₅₃	semidirect
193. C₂×#333	C₂×C₅₃	semidirect
194. C₂×#332	C₂×C₅₃	semidirect
196. C₂×C₅₃	#1703	direct (N × H)
205. #487	C₂²×C₅₃	semidirect
223. #334	C₂²×C₅₃	semidirect
224. #333	C₂²×C₅₃	semidirect
225. #332	C₂²×C₅₃	semidirect
226. C₅₃	C₂×#1703	direct (N × H)
379. C₂	C₅₃×#1703	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
C₂×C₅₃×#474	2
C₂×C₅₃×#436	2
C₅₃×#1703	2
C₂×C₅₃×#334	2
C₂×C₅₃×#333	2
C₂×C₅₃×#332	2
C₂×#1703	53

Subgroups — C2×C53×#1703 #27226653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#1703 #27226653