Subgroups — C₂×C₅₃×#3183 #27268202

Order 13568.

2018 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#529	C₂	1	2	yes	maximal, complemented
2	C₅₃×#3183	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#488	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₃×#469	C₂	1	1	yes	maximal, characteristic
8	C₂×C₅₃×#468	C₂	1	2	yes	maximal, complemented
9	C₂×C₅₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#440	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×M₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
15	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
18	C₅₃×#529	—	2	8	no	—
19	C₅₃×#529	C₂²	1	16	yes	complemented
20	C₂×#126×C₅₃	—	2	2	no	—
21	C₂×#125×C₅₃	C₂²	1	2	yes	—
22	C₂×#124×C₅₃	C₂²	1	2	yes	—
23	C₂×#123×C₅₃	—	2	2	no	—
24	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
25	C₂×#121×C₅₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₅₃	—	2	2	no	—
28	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
29	C₂×#117×C₅₃	—	2	2	no	—
30	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
31	C₅₃×#499	C₂²	1	8	yes	complemented
32	C₅₃×#495	C₂²	1	8	yes	complemented
33	C₅₃×#488	C₂²	1	16	yes	complemented
34	C₅₃×#470	C₂²	1	8	yes	complemented
35	C₅₃×#469	C₂²	1	8	yes	—
36	C₅₃×#468	C₂²	1	16	yes	complemented
37	C₅₃×#442	C₂²	1	8	yes	complemented
38	C₅₃×#441	C₂²	1	8	yes	complemented
39	C₅₃×#440	C₂²	1	16	yes	complemented
40	C₂×#107×C₅₃	C₂²	1	2	yes	—
41	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#103×C₅₃	C₂²	1	2	yes	—
44	C₂×#103×C₅₃	C₂²	1	2	yes	—
45	C₂×#102×C₅₃	C₂²	1	2	yes	—
46	C₂×#102×C₅₃	C₂²	1	2	yes	—
47	C₄×M₁₆×C₅₃	C₂²	1	8	yes	complemented
48	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₅₃	—	2	2	no	—
54	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₅₃	—	2	2	no	—
56	C₂³×C₄×C₅₃	D₄	1	2	yes	—
57	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
58	C₂×Q₁₆×C₅₃	—	2	4	no	—
59	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
60	C₂×SD₁₆×C₅₃	—	2	8	no	—
61	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	—
62	C₂×D₈×C₅₃	—	2	4	no	—
63	C₂×D₈×C₅₃	C₂³	1	4	yes	—
64	C₂×M₁₆×C₅₃	—	2	4	no	—
65	C₂×M₁₆×C₅₃	—	2	4	no	—
66	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
67	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
68	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
72	#126×C₅₃	—	2	16	no	—
73	#125×C₅₃	—	2	4	no	—
74	#125×C₅₃	C₂³	1	8	yes	—
75	#124×C₅₃	—	2	4	no	—
76	#124×C₅₃	C₂³	1	8	yes	—
77	#123×C₅₃	—	2	16	no	—
78	C₂²⋊Q₈×C₅₃	—	2	4	no	—
79	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
80	#121×C₅₃	—	2	4	no	—
81	#121×C₅₃	C₂³	1	8	yes	—
82	C₄×Q₈×C₅₃	—	2	4	no	—
83	C₄×Q₈×C₅₃	C₂³	1	8	yes	—
84	C₄×D₄×C₅₃	—	2	4	no	—
85	C₄×D₄×C₅₃	—	2	16	no	—
86	C₄×D₄×C₅₃	C₂³	1	8	yes	—
87	#117×C₅₃	—	2	16	no	—
88	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
89	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
90	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
91	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
92	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
94	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
99	C₂×C₄²×C₅₃	—	2	2	no	—
100	C₂×C₄²×C₅₃	D₄	1	2	yes	—
101	C₂×C₄²×C₅₃	D₄	1	4	yes	—
102	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
105	#107×C₅₃	C₂³	1	8	yes	—
106	#106×C₅₃	C₂³	1	4	yes	—
107	#106×C₅₃	C₂³	1	4	yes	—
108	#103×C₅₃	C₂³	1	8	yes	—
109	#103×C₅₃	C₂³	1	8	yes	—
110	#102×C₅₃	C₂³	1	8	yes	—
111	#102×C₅₃	C₂³	1	8	yes	—
112	#97×C₅₃	C₂³	1	4	yes	—
113	#97×C₅₃	C₂³	1	4	yes	—
114	C₄×C₈×C₅₃	C₂³	1	4	yes	—
115	C₄×C₈×C₅₃	C₂³	1	4	yes	—
116	C₂⁴×C₅₃	—	2	2	no	—
117	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
118	C₂×Q₈×C₅₃	—	2	2	no	—
119	C₂×Q₈×C₅₃	—	2	4	no	—
120	C₂×Q₈×C₅₃	—	2	4	no	—
121	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
122	C₂×D₄×C₅₃	—	2	8	no	—
123	C₂×D₄×C₅₃	—	2	2	no	—
124	C₂×D₄×C₅₃	—	2	4	no	—
125	C₂×D₄×C₅₃	—	2	4	no	—
126	C₂×D₄×C₅₃	—	4	8	no	—
127	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₅₃	—	2	2	no	—
129	C₂²×C₄×C₅₃	—	2	2	no	—
130	C₂²×C₄×C₅₃	—	2	2	no	—
131	C₂²×C₄×C₅₃	—	2	2	no	—
132	C₂²×C₄×C₅₃	—	2	2	no	—
133	C₂²×C₄×C₅₃	—	2	8	no	—
134	C₂²×C₄×C₅₃	—	4	4	no	—
135	C₂²×C₄×C₅₃	—	4	8	no	—
136	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
141	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
143	Q₁₆×C₅₃	—	2	8	no	—
144	SD₁₆×C₅₃	—	2	16	no	—
145	D₈×C₅₃	—	2	8	no	—
146	M₁₆×C₅₃	—	2	8	no	—
147	M₁₆×C₅₃	—	2	8	no	—
148	C₂×C₈×C₅₃	—	2	2	no	—
149	C₂×C₈×C₅₃	—	2	2	no	—
150	C₂×C₈×C₅₃	#41	1	4	yes	—
151	C₂×C₈×C₅₃	#41	1	4	yes	—
152	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
153	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
154	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
155	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
156	C₄⋊C₄×C₅₃	—	2	8	no	—
157	C₄⋊C₄×C₅₃	—	2	8	no	—
158	C₄⋊C₄×C₅₃	—	2	8	no	—
159	C₄⋊C₄×C₅₃	—	2	8	no	—
160	C₄⋊C₄×C₅₃	—	2	2	no	—
161	C₄⋊C₄×C₅₃	—	2	2	no	—
162	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
163	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
164	C₂²⋊C₄×C₅₃	—	2	8	no	—
165	C₂²⋊C₄×C₅₃	—	2	8	no	—
166	C₂²⋊C₄×C₅₃	—	2	8	no	—
167	C₂²⋊C₄×C₅₃	—	2	8	no	—
168	C₂²⋊C₄×C₅₃	—	2	8	no	—
169	C₄²×C₅₃	—	2	8	no	—
170	C₄²×C₅₃	C₂×D₄	1	8	yes	—
171	C₄²×C₅₃	C₂×D₄	1	2	yes	—
172	C₄²×C₅₃	C₂×D₄	1	2	yes	—
173	C₄²×C₅₃	C₂⁴	1	2	yes	—
174	C₄²×C₅₃	C₂⁴	1	2	yes	—
175	C₂³×C₅₃	—	2	2	no	—
176	C₂³×C₅₃	—	2	4	no	—
177	C₂³×C₅₃	—	2	4	no	—
178	C₂³×C₅₃	—	4	4	no	—
179	C₂³×C₅₃	—	4	4	no	—
180	C₂³×C₅₃	—	4	4	no	—
181	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
182	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₅₃	—	2	4	no	—
184	Q₈×C₅₃	—	2	4	no	—
185	Q₈×C₅₃	—	4	4	no	—
186	D₄×C₅₃	—	2	4	no	—
187	D₄×C₅₃	—	2	4	no	—
188	D₄×C₅₃	—	4	16	no	—
189	D₄×C₅₃	—	4	4	no	—
190	C₂×C₄×C₅₃	—	2	2	no	—
191	C₂×C₄×C₅₃	—	2	4	no	—
192	C₂×C₄×C₅₃	—	2	4	no	—
193	C₂×C₄×C₅₃	—	2	4	no	—
194	C₂×C₄×C₅₃	—	2	2	no	—
195	C₂×C₄×C₅₃	—	2	2	no	—
196	C₂×C₄×C₅₃	—	2	4	no	—
197	C₂×C₄×C₅₃	—	2	4	no	—
198	C₂×C₄×C₅₃	—	2	4	no	—
199	C₂×C₄×C₅₃	—	4	8	no	—
200	C₂×C₄×C₅₃	—	4	16	no	—
201	C₂×C₄×C₅₃	—	4	4	no	—
202	C₂×C₄×C₅₃	—	4	4	no	—
203	C₂×C₄×C₅₃	—	4	4	no	—
204	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
205	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
206	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
209	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
210	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
211	C₈×C₅₃	—	2	2	no	—
212	C₈×C₅₃	—	2	2	no	—
213	C₈×C₅₃	C₂×#41	1	4	yes	—
214	C₈×C₅₃	C₂×#41	1	4	yes	—
215	C₂×#3183	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂²×C₅₃	—	2	2	no	—
217	C₂²×C₅₃	—	2	4	no	—
218	C₂²×C₅₃	—	4	4	no	—
219	C₂²×C₅₃	—	4	4	no	—
220	C₂²×C₅₃	—	4	4	no	—
221	C₂²×C₅₃	—	4	4	no	—
222	C₂²×C₅₃	—	8	8	no	—
223	C₂²×C₅₃	#532	1	2	yes	—
224	C₂²×C₅₃	#575	1	4	yes	—
225	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
226	C₄×C₅₃	—	2	2	no	—
227	C₄×C₅₃	—	2	4	no	—
228	C₄×C₅₃	—	2	4	no	—
229	C₄×C₅₃	—	4	4	no	—
230	C₄×C₅₃	—	4	4	no	—
231	C₄×C₅₃	—	4	4	no	—
232	C₄×C₅₃	#532	1	2	yes	—
233	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
234	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
235	C₂×#529	C₂×C₅₃	1	2	yes	complemented
236	#3183	C₂×C₅₃	1	16	yes	direct product factor
237	C₂×#499	C₂×C₅₃	1	1	yes	characteristic, complemented
238	C₂×#495	C₂×C₅₃	1	1	yes	characteristic, complemented
239	C₂×#488	C₂×C₅₃	1	2	yes	complemented
240	C₂×#470	C₂×C₅₃	1	1	yes	characteristic, complemented
241	C₂×#469	C₂×C₅₃	1	1	yes	characteristic
242	C₂×#468	C₂×C₅₃	1	2	yes	complemented
243	C₂×#442	C₂×C₅₃	1	1	yes	characteristic, complemented
244	C₂×#441	C₂×C₅₃	1	1	yes	characteristic, complemented
245	C₂×#440	C₂×C₅₃	1	2	yes	complemented
246	C₂×C₄×M₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
247	C₂×C₅₃	—	4	2	no	—
248	C₂×C₅₃	—	8	4	no	—
249	C₂×C₅₃	#3183	1	4	yes	direct product factor
250	C₂×C₅₃	C₂×#532	1	1	yes	characteristic
251	C₂×C₅₃	C₂×#575	1	2	yes	—
252	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
253	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
254	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
255	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
256	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
257	#529	—	2	8	no	—
258	#529	C₂²×C₅₃	1	16	yes	complemented
259	C₂×#126	—	2	2	no	—
260	C₂×#125	C₂²×C₅₃	1	2	yes	—
261	C₂×#124	C₂²×C₅₃	1	2	yes	—
262	C₂×#123	—	2	2	no	—
263	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
264	C₂×#121	C₂²×C₅₃	1	2	yes	—
265	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
266	C₂×C₄×D₄	—	2	2	no	—
267	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
268	C₂×#117	—	2	2	no	—
269	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
270	#499	C₂²×C₅₃	1	8	yes	complemented
271	#495	C₂²×C₅₃	1	8	yes	complemented
272	#488	C₂²×C₅₃	1	16	yes	complemented
273	#470	C₂²×C₅₃	1	8	yes	complemented
274	#469	C₂²×C₅₃	1	8	yes	—
275	#468	C₂²×C₅₃	1	16	yes	complemented
276	#442	C₂²×C₅₃	1	8	yes	complemented
277	#441	C₂²×C₅₃	1	8	yes	complemented
278	#440	C₂²×C₅₃	1	16	yes	complemented
279	C₂×#107	C₂²×C₅₃	1	2	yes	—
280	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
281	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
282	C₂×#103	C₂²×C₅₃	1	2	yes	—
283	C₂×#103	C₂²×C₅₃	1	2	yes	—
284	C₂×#102	C₂²×C₅₃	1	2	yes	—
285	C₂×#102	C₂²×C₅₃	1	2	yes	—
286	C₄×M₁₆	C₂²×C₅₃	1	8	yes	complemented
287	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
288	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
289	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
290	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
291	C₅₃	C₂×#3183	1	1	yes	characteristic, direct product factor, Sylow
292	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
295	C₂³×C₄	—	2	2	no	—
296	C₂³×C₄	D₄×C₅₃	1	2	yes	—
297	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
298	C₂×Q₁₆	—	2	4	no	—
299	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
300	C₂×SD₁₆	—	2	8	no	—
301	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	—
302	C₂×D₈	—	2	4	no	—
303	C₂×D₈	C₂³×C₅₃	1	4	yes	—
304	C₂×M₁₆	—	2	4	no	—
305	C₂×M₁₆	—	2	4	no	—
306	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
307	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
308	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
312	#126	—	2	16	no	—
313	#125	—	2	4	no	—
314	#125	C₂³×C₅₃	1	8	yes	—
315	#124	—	2	4	no	—
316	#124	C₂³×C₅₃	1	8	yes	—
317	#123	—	2	16	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
320	#121	—	2	4	no	—
321	#121	C₂³×C₅₃	1	8	yes	—
322	C₄×Q₈	—	2	4	no	—
323	C₄×Q₈	C₂³×C₅₃	1	8	yes	—
324	C₄×D₄	—	2	16	no	—
325	C₄×D₄	—	2	4	no	—
326	C₄×D₄	C₂³×C₅₃	1	8	yes	—
327	#117	—	2	16	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₄²	—	2	2	no	—
340	C₂×C₄²	D₄×C₅₃	1	2	yes	—
341	C₂×C₄²	D₄×C₅₃	1	4	yes	—
342	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
345	#107	C₂³×C₅₃	1	8	yes	—
346	#106	C₂³×C₅₃	1	4	yes	—
347	#106	C₂³×C₅₃	1	4	yes	—
348	#103	C₂³×C₅₃	1	8	yes	—
349	#103	C₂³×C₅₃	1	8	yes	—
350	#102	C₂³×C₅₃	1	8	yes	—
351	#102	C₂³×C₅₃	1	8	yes	—
352	#97	C₂³×C₅₃	1	4	yes	—
353	#97	C₂³×C₅₃	1	4	yes	—
354	C₄×C₈	C₂³×C₅₃	1	4	yes	—
355	C₄×C₈	C₂³×C₅₃	1	4	yes	—
356	C₂⁴	—	2	2	no	—
357	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	4	8	no	—
367	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	8	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	—	4	8	no	—
376	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₅₃	1	8	yes	—
381	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
382	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
383	Q₁₆	—	2	8	no	—
384	SD₁₆	—	2	16	no	—
385	D₈	—	2	8	no	—
386	M₁₆	—	2	8	no	—
387	M₁₆	—	2	8	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	#41×C₅₃	1	4	yes	—
391	C₂×C₈	#41×C₅₃	1	4	yes	—
392	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
393	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
394	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
395	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
403	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₄²	—	2	8	no	—
410	C₄²	C₂×D₄×C₅₃	1	8	yes	—
411	C₄²	C₂×D₄×C₅₃	1	2	yes	—
412	C₄²	C₂×D₄×C₅₃	1	2	yes	—
413	C₄²	C₂⁴×C₅₃	1	2	yes	—
414	C₄²	C₂⁴×C₅₃	1	2	yes	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
422	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
423	Q₈	—	2	4	no	—
424	Q₈	—	2	4	no	—
425	Q₈	—	4	4	no	—
426	D₄	—	2	4	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	16	no	—
429	D₄	—	4	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	4	8	no	—
440	C₂×C₄	—	4	16	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
445	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
446	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
447	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
448	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
449	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
450	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	2	2	no	—
453	C₈	C₂×#41×C₅₃	1	4	yes	—
454	C₈	C₂×#41×C₅₃	1	4	yes	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	8	8	no	—
462	C₂²	C₅₃×#532	1	2	yes	—
463	C₂²	C₅₃×#575	1	4	yes	—
464	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
465	C₄	—	2	4	no	—
466	C₄	—	2	4	no	—
467	C₄	—	2	2	no	—
468	C₄	—	4	4	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	4	no	—
471	C₄	C₅₃×#532	1	2	yes	—
472	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
473	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
474	C₂	—	4	2	no	—
475	C₂	—	8	4	no	—
476	C₂	C₅₃×#3183	1	4	yes	direct product factor
477	C₂	C₂×C₅₃×#532	1	1	yes	characteristic
478	C₂	C₂×C₅₃×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₂×C₅₃×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂²×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#529	C₂	semidirect
2. C₅₃×#3183	C₂	direct (N × H)
3. C₂×C₅₃×#499	C₂	semidirect
4. C₂×C₅₃×#495	C₂	semidirect
5. C₂×C₅₃×#488	C₂	semidirect
6. C₂×C₅₃×#470	C₂	semidirect
8. C₂×C₅₃×#468	C₂	semidirect
9. C₂×C₅₃×#442	C₂	semidirect
10. C₂×C₅₃×#441	C₂	semidirect
11. C₂×C₅₃×#440	C₂	semidirect
12. C₂×C₄×M₁₆×C₅₃	C₂	semidirect
19. C₅₃×#529	C₂²	semidirect
31. C₅₃×#499	C₂²	semidirect
32. C₅₃×#495	C₂²	semidirect
33. C₅₃×#488	C₂²	semidirect
34. C₅₃×#470	C₂²	semidirect
36. C₅₃×#468	C₂²	semidirect
37. C₅₃×#442	C₂²	semidirect
38. C₅₃×#441	C₂²	semidirect
39. C₅₃×#440	C₂²	semidirect
47. C₄×M₁₆×C₅₃	C₂²	semidirect
215. C₂×#3183	C₅₃	direct (N × H)
235. C₂×#529	C₂×C₅₃	semidirect
236. #3183	C₂×C₅₃	direct (N × H)
237. C₂×#499	C₂×C₅₃	semidirect
238. C₂×#495	C₂×C₅₃	semidirect
239. C₂×#488	C₂×C₅₃	semidirect
240. C₂×#470	C₂×C₅₃	semidirect
242. C₂×#468	C₂×C₅₃	semidirect
243. C₂×#442	C₂×C₅₃	semidirect
244. C₂×#441	C₂×C₅₃	semidirect
245. C₂×#440	C₂×C₅₃	semidirect
246. C₂×C₄×M₁₆	C₂×C₅₃	semidirect
249. C₂×C₅₃	#3183	direct (N × H)
258. #529	C₂²×C₅₃	semidirect
270. #499	C₂²×C₅₃	semidirect
271. #495	C₂²×C₅₃	semidirect
272. #488	C₂²×C₅₃	semidirect
273. #470	C₂²×C₅₃	semidirect
275. #468	C₂²×C₅₃	semidirect
276. #442	C₂²×C₅₃	semidirect
277. #441	C₂²×C₅₃	semidirect
278. #440	C₂²×C₅₃	semidirect
286. C₄×M₁₆	C₂²×C₅₃	semidirect
291. C₅₃	C₂×#3183	direct (N × H)
476. C₂	C₅₃×#3183	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×#529	2
C₅₃×#3183	2
C₂×C₅₃×#499	2
C₂×C₅₃×#495	2
C₂×C₅₃×#488	2
C₂×C₅₃×#470	2
C₂×C₅₃×#469	2
C₂×C₅₃×#468	2
C₂×C₅₃×#442	2
C₂×C₅₃×#441	2
C₂×C₅₃×#440	2
C₂×C₄×M₁₆×C₅₃	2
C₂×#3183	53

Subgroups — C2×C53×#3183 #27268202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3183 #27268202