Subgroups — C₂×C₅₃×#1282 #27215435

Order 13568.

1130 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#1282	C₂	1	4	yes	maximal, direct product factor
5	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
6	C₂³×C₈×C₅₃	—	2	1	no	—
7	C₂³×C₈×C₅₃	C₄	1	2	yes	complemented
8	C₂²×C₂²⋊C₄×C₅₃	C₄	1	2	yes	—
9	C₂²×C₄²×C₅₃	—	2	1	no	—
10	C₂×C₂²⋊C₈×C₅₃	—	2	1	no	—
11	C₂×C₂²⋊C₈×C₅₃	—	2	1	no	—
12	C₂×C₂²⋊C₈×C₅₃	—	2	1	no	—
13	C₂×C₂²⋊C₈×C₅₃	—	2	1	no	—
14	C₂×C₂²⋊C₈×C₅₃	—	2	1	no	—
15	C₂×C₂²⋊C₈×C₅₃	—	2	1	no	—
16	C₂×C₂²⋊C₈×C₅₃	—	2	1	no	—
17	C₂×C₂²⋊C₈×C₅₃	C₄	1	2	yes	complemented
18	C₂×C₂²⋊C₈×C₅₃	C₄	1	2	yes	complemented
19	C₂×C₂²⋊C₈×C₅₃	C₄	1	2	yes	complemented
20	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
22	C₄×C₂²⋊C₄×C₅₃	—	2	1	no	—
23	C₄×C₂²⋊C₄×C₅₃	—	2	1	no	—
24	C₄×C₂²⋊C₄×C₅₃	C₄	1	2	yes	—
25	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
26	C₂×#95×C₅₃	—	2	1	no	—
27	C₂⁵×C₅₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₅₃	—	2	2	no	—
29	C₂³×C₄×C₅₃	—	4	4	no	—
30	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₅₃	Q₈	1	1	yes	characteristic
42	C₂³×C₄×C₅₃	Q₈	1	1	yes	characteristic
43	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₅₃	—	2	2	no	—
45	C₂²×C₈×C₅₃	—	2	2	no	—
46	C₂²×C₈×C₅₃	—	2	2	no	—
47	C₂²×C₈×C₅₃	—	2	2	no	—
48	C₂²×C₈×C₅₃	—	2	2	no	—
49	C₂²×C₈×C₅₃	—	4	4	no	—
50	C₂²×C₈×C₅₃	—	4	4	no	—
51	C₂²×C₈×C₅₃	C₂×C₄	1	4	yes	complemented
52	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₅₃	C₈	1	8	yes	complemented
55	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	4	yes	—
56	C₂×C₄²×C₅₃	—	2	2	no	—
57	C₂×C₄²×C₅₃	—	2	2	no	—
58	C₂×C₄²×C₅₃	—	4	4	no	—
59	C₂²⋊C₈×C₅₃	—	2	2	no	—
60	C₂²⋊C₈×C₅₃	—	2	2	no	—
61	C₂²⋊C₈×C₅₃	—	2	2	no	—
62	C₂²⋊C₈×C₅₃	—	2	2	no	—
63	C₂²⋊C₈×C₅₃	—	2	2	no	—
64	C₂²⋊C₈×C₅₃	—	2	2	no	—
65	C₂²⋊C₈×C₅₃	—	2	2	no	—
66	C₂²⋊C₈×C₅₃	C₂×C₄	1	4	yes	complemented
67	#95×C₅₃	—	2	2	no	—
68	#95×C₅₃	—	2	2	no	—
69	C₂⁴×C₅₃	—	4	2	no	—
70	C₂⁴×C₅₃	—	4	2	no	—
71	C₂⁴×C₅₃	C₄²	1	1	yes	characteristic
72	C₂⁴×C₅₃	C₄²	1	1	yes	characteristic
73	C₂⁴×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂⁴×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂⁴×C₅₃	C₄⋊C₄	1	1	yes	characteristic
76	C₂⁴×C₅₃	C₄⋊C₄	1	1	yes	characteristic
77	C₂⁴×C₅₃	C₂×C₈	1	4	yes	—
78	C₂⁴×C₅₃	M₁₆	1	4	yes	—
79	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	—	2	4	no	—
81	C₂²×C₄×C₅₃	—	2	4	no	—
82	C₂²×C₄×C₅₃	—	2	4	no	—
83	C₂²×C₄×C₅₃	—	2	8	no	—
84	C₂²×C₄×C₅₃	—	2	4	no	—
85	C₂²×C₄×C₅₃	—	4	2	no	—
86	C₂²×C₄×C₅₃	—	4	2	no	—
87	C₂²×C₄×C₅₃	—	4	2	no	—
88	C₂²×C₄×C₅₃	—	4	2	no	—
89	C₂²×C₄×C₅₃	—	4	2	no	—
90	C₂²×C₄×C₅₃	—	4	2	no	—
91	C₂²×C₄×C₅₃	—	4	2	no	—
92	C₂²×C₄×C₅₃	—	4	2	no	—
93	C₂²×C₄×C₅₃	—	4	2	no	—
94	C₂²×C₄×C₅₃	—	4	2	no	—
95	C₂²×C₄×C₅₃	—	4	2	no	—
96	C₂²×C₄×C₅₃	—	4	4	no	—
97	C₂²×C₄×C₅₃	—	4	4	no	—
98	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
99	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
100	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
126	C₂×C₈×C₅₃	—	2	4	no	—
127	C₂×C₈×C₅₃	—	2	4	no	—
128	C₂×C₈×C₅₃	—	4	4	no	—
129	C₂×C₈×C₅₃	—	4	4	no	—
130	C₂×C₈×C₅₃	—	4	4	no	—
131	C₂×C₈×C₅₃	—	4	4	no	—
132	C₂×C₈×C₅₃	—	4	4	no	—
133	C₂×C₈×C₅₃	—	4	4	no	—
134	C₂²⋊C₄×C₅₃	—	2	8	no	—
135	C₂²⋊C₄×C₅₃	—	2	4	no	—
136	C₂²⋊C₄×C₅₃	C₂×C₈	1	8	yes	complemented
137	C₄²×C₅₃	—	4	4	no	—
138	C₄²×C₅₃	—	4	4	no	—
139	C₂³×C₅₃	—	2	2	no	—
140	C₂³×C₅₃	—	2	2	no	—
141	C₂³×C₅₃	—	2	2	no	—
142	C₂³×C₅₃	—	2	2	no	—
143	C₂³×C₅₃	—	2	2	no	—
144	C₂³×C₅₃	—	2	2	no	—
145	C₂³×C₅₃	—	4	1	no	—
146	C₂³×C₅₃	—	4	1	no	—
147	C₂³×C₅₃	—	4	1	no	—
148	C₂³×C₅₃	—	4	1	no	—
149	C₂³×C₅₃	—	4	1	no	—
150	C₂³×C₅₃	—	4	1	no	—
151	C₂³×C₅₃	—	4	1	no	—
152	C₂³×C₅₃	—	4	8	no	—
153	C₂³×C₅₃	—	4	8	no	—
154	C₂³×C₅₃	—	4	1	no	—
155	C₂³×C₅₃	#95	1	1	yes	characteristic
156	C₂³×C₅₃	#95	1	1	yes	characteristic
157	C₂³×C₅₃	#95	1	1	yes	characteristic
158	C₂³×C₅₃	#95	1	1	yes	characteristic
159	C₂³×C₅₃	C₄×C₈	1	2	yes	—
160	C₂³×C₅₃	C₄×C₈	1	2	yes	—
161	C₂³×C₅₃	#97	1	2	yes	—
162	C₂³×C₅₃	#97	1	2	yes	—
163	C₂³×C₅₃	C₂²⋊C₈	1	4	yes	—
164	C₂³×C₅₃	C₂²⋊C₈	1	4	yes	—
165	C₂³×C₅₃	C₄⋊C₈	1	4	yes	—
166	C₂³×C₅₃	C₄⋊C₈	1	4	yes	—
167	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
168	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂³×C₅₃	C₂²×C₈	1	2	yes	—
171	C₂³×C₅₃	C₂×M₁₆	1	2	yes	—
172	C₂×C₄×C₅₃	—	2	2	no	—
173	C₂×C₄×C₅₃	—	2	2	no	—
174	C₂×C₄×C₅₃	—	2	2	no	—
175	C₂×C₄×C₅₃	—	2	2	no	—
176	C₂×C₄×C₅₃	—	2	2	no	—
177	C₂×C₄×C₅₃	—	2	2	no	—
178	C₂×C₄×C₅₃	—	2	2	no	—
179	C₂×C₄×C₅₃	—	2	2	no	—
180	C₂×C₄×C₅₃	—	2	2	no	—
181	C₂×C₄×C₅₃	—	2	2	no	—
182	C₂×C₄×C₅₃	—	2	2	no	—
183	C₂×C₄×C₅₃	—	2	2	no	—
184	C₂×C₄×C₅₃	—	2	2	no	—
185	C₂×C₄×C₅₃	—	2	2	no	—
186	C₂×C₄×C₅₃	—	2	2	no	—
187	C₂×C₄×C₅₃	—	2	8	no	—
188	C₂×C₄×C₅₃	—	4	1	no	—
189	C₂×C₄×C₅₃	—	4	1	no	—
190	C₂×C₄×C₅₃	—	4	1	no	—
191	C₂×C₄×C₅₃	—	4	1	no	—
192	C₂×C₄×C₅₃	—	4	1	no	—
193	C₂×C₄×C₅₃	—	4	1	no	—
194	C₂×C₄×C₅₃	—	4	1	no	—
195	C₂×C₄×C₅₃	—	4	1	no	—
196	C₂×C₄×C₅₃	—	4	1	no	—
197	C₂×C₄×C₅₃	—	4	1	no	—
198	C₂×C₄×C₅₃	—	4	1	no	—
199	C₂×C₄×C₅₃	—	4	1	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	#95	1	1	yes	characteristic
204	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
205	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
206	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
207	C₂×C₄×C₅₃	#99	1	4	yes	—
208	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₈×C₅₃	—	4	4	no	—
213	C₈×C₅₃	—	4	4	no	—
214	C₂×#1282	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂²×C₅₃	—	2	8	no	—
216	C₂²×C₅₃	—	2	4	no	—
217	C₂²×C₅₃	—	2	4	no	—
218	C₂²×C₅₃	—	2	8	no	—
219	C₂²×C₅₃	—	2	1	no	—
220	C₂²×C₅₃	—	2	1	no	—
221	C₂²×C₅₃	—	2	1	no	—
222	C₂²×C₅₃	—	2	1	no	—
223	C₂²×C₅₃	—	2	1	no	—
224	C₂²×C₅₃	—	2	1	no	—
225	C₂²×C₅₃	—	2	1	no	—
226	C₂²×C₅₃	—	2	1	no	—
227	C₂²×C₅₃	—	2	1	no	—
228	C₂²×C₅₃	—	2	1	no	—
229	C₂²×C₅₃	—	2	1	no	—
230	C₂²×C₅₃	—	2	1	no	—
231	C₂²×C₅₃	—	4	2	no	—
232	C₂²×C₅₃	—	4	2	no	—
233	C₂²×C₅₃	—	4	4	no	—
234	C₂²×C₅₃	—	4	4	no	—
235	C₂²×C₅₃	—	4	2	no	—
236	C₂²×C₅₃	—	4	2	no	—
237	C₂²×C₅₃	#336	1	2	yes	—
238	C₂²×C₅₃	#336	1	2	yes	—
239	C₂²×C₅₃	#336	1	2	yes	—
240	C₂²×C₅₃	#336	1	2	yes	—
241	C₂²×C₅₃	#342	1	2	yes	—
242	C₂²×C₅₃	#344	1	2	yes	—
243	C₂²×C₅₃	C₂×#95	1	1	yes	characteristic
244	C₂²×C₅₃	C₂×C₄×C₈	1	1	yes	characteristic
245	C₂²×C₅₃	C₂×#97	1	1	yes	characteristic
246	C₂²×C₅₃	C₂×C₂²⋊C₈	1	2	yes	—
247	C₂²×C₅₃	C₂×C₄⋊C₈	1	2	yes	—
248	C₄×C₅₃	—	2	1	no	—
249	C₄×C₅₃	—	2	1	no	—
250	C₄×C₅₃	—	2	1	no	—
251	C₄×C₅₃	—	2	1	no	—
252	C₄×C₅₃	—	2	1	no	—
253	C₄×C₅₃	—	2	1	no	—
254	C₄×C₅₃	—	4	8	no	—
255	C₄×C₅₃	#342	1	2	yes	—
256	C₄×C₅₃	C₂×#99	1	2	yes	—
257	C₂²×C₂²⋊C₈	C₂×C₅₃	1	1	yes	characteristic
258	C₂²×C₂²⋊C₈	C₂×C₅₃	1	1	yes	characteristic
259	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic
260	#1282	C₂×C₅₃	1	4	yes	direct product factor
261	C₂×C₅₃	—	2	2	no	—
262	C₂×C₅₃	—	2	2	no	—
263	C₂×C₅₃	—	2	2	no	—
264	C₂×C₅₃	—	2	2	no	—
265	C₂×C₅₃	—	2	1	no	—
266	C₂×C₅₃	—	2	1	no	—
267	C₂×C₅₃	—	2	2	no	—
268	C₂×C₅₃	#1282	1	4	yes	direct product factor
269	C₂×C₅₃	C₂×#336	1	1	yes	characteristic
270	C₂×C₅₃	C₂×#342	1	1	yes	characteristic
271	C₂×C₅₃	C₂×#344	1	1	yes	characteristic
272	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
273	C₂³×C₈	—	2	1	no	—
274	C₂³×C₈	C₄×C₅₃	1	2	yes	complemented
275	C₂²×C₂²⋊C₄	C₄×C₅₃	1	2	yes	—
276	C₂²×C₄²	—	2	1	no	—
277	C₂×C₂²⋊C₈	—	2	1	no	—
278	C₂×C₂²⋊C₈	—	2	1	no	—
279	C₂×C₂²⋊C₈	—	2	1	no	—
280	C₂×C₂²⋊C₈	—	2	1	no	—
281	C₂×C₂²⋊C₈	—	2	1	no	—
282	C₂×C₂²⋊C₈	—	2	1	no	—
283	C₂×C₂²⋊C₈	—	2	1	no	—
284	C₂×C₂²⋊C₈	C₄×C₅₃	1	2	yes	complemented
285	C₂×C₂²⋊C₈	C₄×C₅₃	1	2	yes	complemented
286	C₂×C₂²⋊C₈	C₄×C₅₃	1	2	yes	complemented
287	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
288	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
289	C₄×C₂²⋊C₄	—	2	1	no	—
290	C₄×C₂²⋊C₄	—	2	1	no	—
291	C₄×C₂²⋊C₄	C₄×C₅₃	1	2	yes	—
292	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
293	C₂×#95	—	2	1	no	—
294	C₅₃	C₂×#1282	1	1	yes	characteristic, direct product factor, Sylow
295	C₂⁵	C₂×C₄×C₅₃	1	1	yes	characteristic
296	C₂³×C₄	—	2	2	no	—
297	C₂³×C₄	—	4	4	no	—
298	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
299	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
300	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
301	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
302	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
303	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
304	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
305	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
306	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
307	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
308	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
309	C₂³×C₄	Q₈×C₅₃	1	1	yes	characteristic
310	C₂³×C₄	Q₈×C₅₃	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	—	2	2	no	—
317	C₂²×C₈	—	4	4	no	—
318	C₂²×C₈	—	4	4	no	—
319	C₂²×C₈	C₂×C₄×C₅₃	1	4	yes	complemented
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	4	no	—
322	C₂×C₂²⋊C₄	C₈×C₅₃	1	8	yes	complemented
323	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	4	yes	—
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	—	2	2	no	—
326	C₂×C₄²	—	4	4	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	C₂²⋊C₈	—	2	2	no	—
329	C₂²⋊C₈	—	2	2	no	—
330	C₂²⋊C₈	—	2	2	no	—
331	C₂²⋊C₈	—	2	2	no	—
332	C₂²⋊C₈	—	2	2	no	—
333	C₂²⋊C₈	—	2	2	no	—
334	C₂²⋊C₈	C₂×C₄×C₅₃	1	4	yes	complemented
335	#95	—	2	2	no	—
336	#95	—	2	2	no	—
337	C₂⁴	—	4	2	no	—
338	C₂⁴	—	4	2	no	—
339	C₂⁴	C₄²×C₅₃	1	1	yes	characteristic
340	C₂⁴	C₄²×C₅₃	1	1	yes	characteristic
341	C₂⁴	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
342	C₂⁴	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
343	C₂⁴	C₄⋊C₄×C₅₃	1	1	yes	characteristic
344	C₂⁴	C₄⋊C₄×C₅₃	1	1	yes	characteristic
345	C₂⁴	C₂×C₈×C₅₃	1	4	yes	—
346	C₂⁴	M₁₆×C₅₃	1	4	yes	—
347	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	C₄²×C₅₃	1	1	yes	characteristic
367	C₂²×C₄	C₄²×C₅₃	1	1	yes	characteristic
368	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
369	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
370	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
371	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
372	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
373	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
374	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
375	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
376	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
377	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
378	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
379	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
380	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
381	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
382	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
383	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
384	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
385	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
386	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
387	C₂²×C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×Q₈×C₅₃	1	1	yes	characteristic
394	C₂×C₈	—	2	4	no	—
395	C₂×C₈	—	2	4	no	—
396	C₂×C₈	—	4	4	no	—
397	C₂×C₈	—	4	4	no	—
398	C₂×C₈	—	4	4	no	—
399	C₂×C₈	—	4	4	no	—
400	C₂×C₈	—	4	4	no	—
401	C₂×C₈	—	4	4	no	—
402	C₂²⋊C₄	—	2	8	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	C₂×C₈×C₅₃	1	8	yes	complemented
405	C₄²	—	4	4	no	—
406	C₄²	—	4	4	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	8	no	—
422	C₂³	—	4	8	no	—
423	C₂³	#95×C₅₃	1	1	yes	characteristic
424	C₂³	#95×C₅₃	1	1	yes	characteristic
425	C₂³	#95×C₅₃	1	1	yes	characteristic
426	C₂³	#95×C₅₃	1	1	yes	characteristic
427	C₂³	C₄×C₈×C₅₃	1	2	yes	—
428	C₂³	C₄×C₈×C₅₃	1	2	yes	—
429	C₂³	#97×C₅₃	1	2	yes	—
430	C₂³	#97×C₅₃	1	2	yes	—
431	C₂³	C₂²⋊C₈×C₅₃	1	4	yes	—
432	C₂³	C₂²⋊C₈×C₅₃	1	4	yes	—
433	C₂³	C₄⋊C₈×C₅₃	1	4	yes	—
434	C₂³	C₄⋊C₈×C₅₃	1	4	yes	—
435	C₂³	C₂×C₄²×C₅₃	1	1	yes	characteristic
436	C₂³	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
437	C₂³	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
438	C₂³	C₂²×C₈×C₅₃	1	2	yes	—
439	C₂³	C₂×M₁₆×C₅₃	1	2	yes	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	16	no	—
471	C₂×C₄	#95×C₅₃	1	1	yes	characteristic
472	C₂×C₄	#95×C₅₃	1	1	yes	characteristic
473	C₂×C₄	#95×C₅₃	1	1	yes	characteristic
474	C₂×C₄	#95×C₅₃	1	1	yes	characteristic
475	C₂×C₄	#99×C₅₃	1	4	yes	—
476	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
477	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
478	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
479	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
480	C₈	—	4	4	no	—
481	C₈	—	4	4	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	8	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	2	8	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	C₅₃×#336	1	2	yes	—
505	C₂²	C₅₃×#336	1	2	yes	—
506	C₂²	C₅₃×#336	1	2	yes	—
507	C₂²	C₅₃×#336	1	2	yes	—
508	C₂²	C₅₃×#342	1	2	yes	—
509	C₂²	C₅₃×#344	1	2	yes	—
510	C₂²	C₂×#95×C₅₃	1	1	yes	characteristic
511	C₂²	C₂×C₄×C₈×C₅₃	1	1	yes	characteristic
512	C₂²	C₂×#97×C₅₃	1	1	yes	characteristic
513	C₂²	C₂×C₂²⋊C₈×C₅₃	1	2	yes	—
514	C₂²	C₂×C₄⋊C₈×C₅₃	1	2	yes	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	4	8	no	—
522	C₄	C₅₃×#342	1	2	yes	—
523	C₄	C₂×#99×C₅₃	1	2	yes	—
524	C₂	—	2	2	no	—
525	C₂	—	2	2	no	—
526	C₂	—	2	2	no	—
527	C₂	—	2	2	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	2	2	no	—
531	C₂	C₅₃×#1282	1	4	yes	direct product factor
532	C₂	C₂×C₅₃×#336	1	1	yes	characteristic
533	C₂	C₂×C₅₃×#342	1	1	yes	characteristic
534	C₂	C₂×C₅₃×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂²⋊C₄
commutator	C₂²	C₂×C₄×C₈×C₅₃
Frattini, cosocle	C₂³×C₄	C₂³×C₅₃
socle	C₂³×C₅₃	#95
prime radical	C₂⁵×C₅₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ C₂⁴×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅₃×#1282	C₂	direct (N × H)
7. C₂³×C₈×C₅₃	C₄	semidirect
17. C₂×C₂²⋊C₈×C₅₃	C₄	semidirect
18. C₂×C₂²⋊C₈×C₅₃	C₄	semidirect
19. C₂×C₂²⋊C₈×C₅₃	C₄	semidirect
51. C₂²×C₈×C₅₃	C₂×C₄	semidirect
54. C₂×C₂²⋊C₄×C₅₃	C₈	semidirect
66. C₂²⋊C₈×C₅₃	C₂×C₄	semidirect
136. C₂²⋊C₄×C₅₃	C₂×C₈	semidirect
214. C₂×#1282	C₅₃	direct (N × H)
260. #1282	C₂×C₅₃	direct (N × H)
268. C₂×C₅₃	#1282	direct (N × H)
274. C₂³×C₈	C₄×C₅₃	semidirect
284. C₂×C₂²⋊C₈	C₄×C₅₃	semidirect
285. C₂×C₂²⋊C₈	C₄×C₅₃	semidirect
286. C₂×C₂²⋊C₈	C₄×C₅₃	semidirect
294. C₅₃	C₂×#1282	direct (N × H)
319. C₂²×C₈	C₂×C₄×C₅₃	semidirect
322. C₂×C₂²⋊C₄	C₈×C₅₃	semidirect
334. C₂²⋊C₈	C₂×C₄×C₅₃	semidirect
404. C₂²⋊C₄	C₂×C₈×C₅₃	semidirect
531. C₂	C₅₃×#1282	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊C₈×C₅₃	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
C₅₃×#1282	2
C₂×#1282	53

Subgroups — C2×C53×#1282 #27215435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#1282 #27215435