Subgroups — C₅₃×#17412 #27224924

Order 13568.

1046 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#551	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2924	C₂	1	2	yes	maximal, complemented
3	C₅₃×#1473	C₂	1	2	yes	maximal, complemented
4	C₅₃×#1469	C₂	1	2	yes	maximal, complemented
5	C₅₃×#1468	C₂	1	2	yes	maximal, complemented
6	C₅₃×#1466	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1462	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#1460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#1458	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#323	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#551	—	2	2	no	—
13	C₅₃×#551	—	2	2	no	—
14	C₅₃×#551	—	2	2	no	—
15	C₅₃×#551	—	2	2	no	—
16	C₂×#126×C₅₃	C₄	1	1	yes	characteristic
17	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#123×C₅₃	C₄	1	1	yes	characteristic
20	C₂×#123×C₅₃	C₄	1	1	yes	characteristic
21	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₅₃	C₄	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₅₃	C₄	1	1	yes	characteristic
24	C₂×#120×C₅₃	C₄	1	1	yes	characteristic
25	C₂×C₄×D₄×C₅₃	C₄	1	1	yes	characteristic
26	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₅₃	C₄	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
31	C₅₃×#433	—	2	2	no	—
32	C₅₃×#433	—	2	2	no	—
33	C₅₃×#432	C₂²	1	2	yes	complemented
34	C₅₃×#432	C₂²	1	2	yes	complemented
35	C₅₃×#431	C₂²	1	2	yes	complemented
36	C₅₃×#431	C₂²	1	2	yes	complemented
37	C₅₃×#424	—	2	2	no	—
38	C₅₃×#407	C₂²	1	2	yes	—
39	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
40	C₅₃×#405	—	2	2	no	—
41	C₅₃×#324	C₂²	1	2	yes	complemented
42	C₅₃×#324	C₂²	1	2	yes	complemented
43	C₅₃×#323	C₂²	1	1	yes	characteristic
44	C₅₃×#323	C₂²	1	1	yes	characteristic
45	C₅₃×#323	C₂²	1	2	yes	—
46	C₅₃×#323	C₂²	1	1	yes	characteristic
47	C₅₃×#323	C₂²	1	1	yes	characteristic
48	C₅₃×#323	C₂²	1	2	yes	—
49	C₅₃×#323	C₂²	1	2	yes	complemented
50	C₅₃×#323	C₂²	1	2	yes	complemented
51	C₂⁵×C₅₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₅₃	—	2	2	no	—
62	C₂²×C₈×C₅₃	—	2	2	no	—
63	#126×C₅₃	—	2	2	no	—
64	#126×C₅₃	—	2	2	no	—
65	#126×C₅₃	—	2	2	no	—
66	#126×C₅₃	—	2	2	no	—
67	#124×C₅₃	—	2	2	no	—
68	#124×C₅₃	—	2	2	no	—
69	#123×C₅₃	—	2	2	no	—
70	#123×C₅₃	—	2	2	no	—
71	#123×C₅₃	—	2	2	no	—
72	#123×C₅₃	—	2	2	no	—
73	#123×C₅₃	—	2	2	no	—
74	#123×C₅₃	—	2	2	no	—
75	C₂²⋊Q₈×C₅₃	—	2	2	no	—
76	C₂²⋊Q₈×C₅₃	—	2	2	no	—
77	C₂²⋊Q₈×C₅₃	—	2	2	no	—
78	C₂²⋊Q₈×C₅₃	—	2	2	no	—
79	#120×C₅₃	—	2	2	no	—
80	#120×C₅₃	—	2	2	no	—
81	C₄×D₄×C₅₃	—	2	1	no	—
82	C₄×D₄×C₅₃	—	2	1	no	—
83	C₄×D₄×C₅₃	—	2	1	no	—
84	C₄×D₄×C₅₃	—	2	1	no	—
85	C₄×D₄×C₅₃	—	2	2	no	—
86	C₄×D₄×C₅₃	—	2	2	no	—
87	#117×C₅₃	—	2	2	no	—
88	#117×C₅₃	—	2	2	no	—
89	#117×C₅₃	D₄	1	2	yes	—
90	#117×C₅₃	D₄	1	2	yes	—
91	#117×C₅₃	D₄	1	2	yes	—
92	#117×C₅₃	D₄	1	2	yes	—
93	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
106	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
107	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₅₃	—	2	2	no	—
125	C₄⋊C₈×C₅₃	—	2	2	no	—
126	C₄⋊C₈×C₅₃	—	2	2	no	—
127	C₄⋊C₈×C₅₃	—	2	2	no	—
128	C₂²⋊C₈×C₅₃	—	2	2	no	—
129	C₂²⋊C₈×C₅₃	—	2	2	no	—
130	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
131	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
132	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
133	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
134	#97×C₅₃	—	2	2	no	—
135	#97×C₅₃	—	2	2	no	—
136	C₄×C₈×C₅₃	—	2	2	no	—
137	C₄×C₈×C₅₃	—	2	2	no	—
138	C₂⁴×C₅₃	—	2	1	no	—
139	C₂⁴×C₅₃	—	2	1	no	—
140	C₂⁴×C₅₃	—	2	2	no	—
141	C₂⁴×C₅₃	—	4	1	no	—
142	C₂⁴×C₅₃	—	4	2	no	—
143	C₂⁴×C₅₃	—	8	1	no	—
144	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
145	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
146	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
147	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×Q₈×C₅₃	—	2	2	no	—
149	C₂×Q₈×C₅₃	—	8	1	no	—
150	C₂×D₄×C₅₃	—	2	1	no	—
151	C₂×D₄×C₅₃	—	2	1	no	—
152	C₂×D₄×C₅₃	—	2	2	no	—
153	C₂×D₄×C₅₃	—	2	2	no	—
154	C₂×D₄×C₅₃	—	2	2	no	—
155	C₂×D₄×C₅₃	—	4	1	no	—
156	C₂×D₄×C₅₃	—	4	2	no	—
157	C₂×D₄×C₅₃	—	8	1	no	—
158	C₂²×C₄×C₅₃	—	2	2	no	—
159	C₂²×C₄×C₅₃	—	2	1	no	—
160	C₂²×C₄×C₅₃	—	2	1	no	—
161	C₂²×C₄×C₅₃	—	2	1	no	—
162	C₂²×C₄×C₅₃	—	2	1	no	—
163	C₂²×C₄×C₅₃	—	2	1	no	—
164	C₂²×C₄×C₅₃	—	2	1	no	—
165	C₂²×C₄×C₅₃	—	2	1	no	—
166	C₂²×C₄×C₅₃	—	2	1	no	—
167	C₂²×C₄×C₅₃	—	4	1	no	—
168	C₂²×C₄×C₅₃	—	4	2	no	—
169	C₂²×C₄×C₅₃	—	8	1	no	—
170	C₂²×C₄×C₅₃	—	8	1	no	—
171	C₂²×C₄×C₅₃	—	8	1	no	—
172	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
185	M₁₆×C₅₃	—	4	4	no	—
186	C₂×C₈×C₅₃	—	2	2	no	—
187	C₂×C₈×C₅₃	—	2	2	no	—
188	C₂×C₈×C₅₃	—	2	2	no	—
189	C₂×C₈×C₅₃	—	2	2	no	—
190	C₂×C₈×C₅₃	—	4	4	no	—
191	C₄⋊C₄×C₅₃	—	2	2	no	—
192	C₄⋊C₄×C₅₃	—	2	2	no	—
193	C₄⋊C₄×C₅₃	—	2	1	no	—
194	C₄⋊C₄×C₅₃	—	2	1	no	—
195	C₄⋊C₄×C₅₃	—	2	2	no	—
196	C₄⋊C₄×C₅₃	—	2	2	no	—
197	C₄⋊C₄×C₅₃	—	2	2	no	—
198	C₄⋊C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
199	C₄⋊C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
200	C₄⋊C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
201	C₄⋊C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
202	C₂²⋊C₄×C₅₃	—	2	1	no	—
203	C₂²⋊C₄×C₅₃	—	2	1	no	—
204	C₂²⋊C₄×C₅₃	—	2	2	no	—
205	C₂²⋊C₄×C₅₃	—	2	2	no	—
206	C₂²⋊C₄×C₅₃	—	2	1	no	—
207	C₂²⋊C₄×C₅₃	—	2	1	no	—
208	C₂²⋊C₄×C₅₃	—	2	1	no	—
209	C₂²⋊C₄×C₅₃	—	2	1	no	—
210	C₂²⋊C₄×C₅₃	—	2	2	no	—
211	C₂²⋊C₄×C₅₃	—	2	1	no	—
212	C₂²⋊C₄×C₅₃	—	2	1	no	—
213	C₂²⋊C₄×C₅₃	—	2	2	no	—
214	C₂²⋊C₄×C₅₃	—	2	2	no	—
215	C₂²⋊C₄×C₅₃	—	2	2	no	—
216	C₂²⋊C₄×C₅₃	—	2	2	no	—
217	C₂²⋊C₄×C₅₃	—	2	2	no	—
218	C₂²⋊C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
219	C₂²⋊C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
220	C₂²⋊C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
221	C₂²⋊C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
222	C₂²⋊C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
223	C₂²⋊C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
224	C₄²×C₅₃	—	2	1	no	—
225	C₄²×C₅₃	—	2	1	no	—
226	C₄²×C₅₃	C₂×D₄	1	2	yes	—
227	C₄²×C₅₃	C₂×D₄	1	2	yes	—
228	C₄²×C₅₃	C₂×D₄	1	2	yes	—
229	C₄²×C₅₃	C₂×D₄	1	2	yes	—
230	C₂³×C₅₃	—	2	1	no	—
231	C₂³×C₅₃	—	2	1	no	—
232	C₂³×C₅₃	—	2	1	no	—
233	C₂³×C₅₃	—	2	1	no	—
234	C₂³×C₅₃	—	2	2	no	—
235	C₂³×C₅₃	—	2	1	no	—
236	C₂³×C₅₃	—	2	1	no	—
237	C₂³×C₅₃	—	2	1	no	—
238	C₂³×C₅₃	—	2	1	no	—
239	C₂³×C₅₃	—	2	1	no	—
240	C₂³×C₅₃	—	2	1	no	—
241	C₂³×C₅₃	—	4	1	no	—
242	C₂³×C₅₃	—	4	2	no	—
243	C₂³×C₅₃	—	4	2	no	—
244	C₂³×C₅₃	—	4	1	no	—
245	C₂³×C₅₃	—	4	1	no	—
246	C₂³×C₅₃	—	4	2	no	—
247	C₂³×C₅₃	—	4	1	no	—
248	C₂³×C₅₃	—	4	1	no	—
249	C₂³×C₅₃	—	4	1	no	—
250	C₂³×C₅₃	—	4	1	no	—
251	C₂³×C₅₃	—	4	2	no	—
252	C₂³×C₅₃	—	8	1	no	—
253	C₂³×C₅₃	—	8	1	no	—
254	C₂³×C₅₃	—	8	4	no	—
255	C₂³×C₅₃	—	8	4	no	—
256	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂³×C₅₃	#131	1	2	yes	—
259	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
260	Q₈×C₅₃	—	8	2	no	—
261	D₄×C₅₃	—	4	4	no	—
262	D₄×C₅₃	—	4	2	no	—
263	D₄×C₅₃	—	4	2	no	—
264	D₄×C₅₃	—	8	2	no	—
265	C₂×C₄×C₅₃	—	2	1	no	—
266	C₂×C₄×C₅₃	—	2	1	no	—
267	C₂×C₄×C₅₃	—	2	1	no	—
268	C₂×C₄×C₅₃	—	2	1	no	—
269	C₂×C₄×C₅₃	—	2	4	no	—
270	C₂×C₄×C₅₃	—	2	1	no	—
271	C₂×C₄×C₅₃	—	2	1	no	—
272	C₂×C₄×C₅₃	—	2	1	no	—
273	C₂×C₄×C₅₃	—	2	1	no	—
274	C₂×C₄×C₅₃	—	2	1	no	—
275	C₂×C₄×C₅₃	—	2	1	no	—
276	C₂×C₄×C₅₃	—	2	1	no	—
277	C₂×C₄×C₅₃	—	4	1	no	—
278	C₂×C₄×C₅₃	—	4	2	no	—
279	C₂×C₄×C₅₃	—	4	1	no	—
280	C₂×C₄×C₅₃	—	4	1	no	—
281	C₂×C₄×C₅₃	—	4	1	no	—
282	C₂×C₄×C₅₃	—	4	2	no	—
283	C₂×C₄×C₅₃	—	4	2	no	—
284	C₂×C₄×C₅₃	—	4	1	no	—
285	C₂×C₄×C₅₃	—	4	1	no	—
286	C₂×C₄×C₅₃	—	4	1	no	—
287	C₂×C₄×C₅₃	—	4	1	no	—
288	C₂×C₄×C₅₃	—	8	1	no	—
289	C₂×C₄×C₅₃	—	8	1	no	—
290	C₂×C₄×C₅₃	—	8	1	no	—
291	C₂×C₄×C₅₃	—	8	1	no	—
292	C₂×C₄×C₅₃	—	8	1	no	—
293	C₂×C₄×C₅₃	—	8	1	no	—
294	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
295	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
296	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	2	yes	—
299	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	2	yes	—
300	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	2	yes	—
301	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
302	C₈×C₅₃	—	4	2	no	—
303	C₈×C₅₃	—	4	2	no	—
304	C₈×C₅₃	—	4	2	no	—
305	C₈×C₅₃	—	4	2	no	—
306	#17412	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
307	C₂²×C₅₃	—	2	1	no	—
308	C₂²×C₅₃	—	2	1	no	—
309	C₂²×C₅₃	—	2	1	no	—
310	C₂²×C₅₃	—	2	1	no	—
311	C₂²×C₅₃	—	2	2	no	—
312	C₂²×C₅₃	—	2	1	no	—
313	C₂²×C₅₃	—	2	1	no	—
314	C₂²×C₅₃	—	2	1	no	—
315	C₂²×C₅₃	—	4	2	no	—
316	C₂²×C₅₃	—	4	2	no	—
317	C₂²×C₅₃	—	4	2	no	—
318	C₂²×C₅₃	—	4	2	no	—
319	C₂²×C₅₃	—	4	1	no	—
320	C₂²×C₅₃	—	4	1	no	—
321	C₂²×C₅₃	—	4	1	no	—
322	C₂²×C₅₃	—	4	1	no	—
323	C₂²×C₅₃	—	4	1	no	—
324	C₂²×C₅₃	—	4	1	no	—
325	C₂²×C₅₃	—	4	1	no	—
326	C₂²×C₅₃	—	4	1	no	—
327	C₂²×C₅₃	—	8	4	no	—
328	C₂²×C₅₃	—	8	1	no	—
329	C₂²×C₅₃	—	8	1	no	—
330	C₂²×C₅₃	—	8	1	no	—
331	C₂²×C₅₃	—	8	1	no	—
332	C₂²×C₅₃	—	8	4	no	—
333	C₂²×C₅₃	#410	1	2	yes	—
334	C₂²×C₅₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
335	C₂²×C₅₃	C₂×#131	1	1	yes	characteristic
336	C₂²×C₅₃	#568	1	1	yes	characteristic
337	C₄×C₅₃	—	2	1	no	—
338	C₄×C₅₃	—	2	1	no	—
339	C₄×C₅₃	—	2	2	no	—
340	C₄×C₅₃	—	2	2	no	—
341	C₄×C₅₃	—	2	2	no	—
342	C₄×C₅₃	—	2	1	no	—
343	C₄×C₅₃	—	2	1	no	—
344	C₄×C₅₃	—	2	2	no	—
345	C₄×C₅₃	—	4	1	no	—
346	C₄×C₅₃	—	4	1	no	—
347	C₄×C₅₃	—	4	1	no	—
348	C₄×C₅₃	—	4	1	no	—
349	C₄×C₅₃	—	4	1	no	—
350	C₂×#551	C₂×C₅₃	1	1	yes	characteristic
351	#2924	C₂×C₅₃	1	2	yes	complemented
352	#1473	C₂×C₅₃	1	2	yes	complemented
353	#1469	C₂×C₅₃	1	2	yes	complemented
354	#1468	C₂×C₅₃	1	2	yes	complemented
355	#1466	C₂×C₅₃	1	1	yes	characteristic, complemented
356	#1464	C₂×C₅₃	1	1	yes	characteristic, complemented
357	#1462	C₂×C₅₃	1	1	yes	characteristic, complemented
358	#1460	C₂×C₅₃	1	1	yes	characteristic, complemented
359	#1458	C₂×C₅₃	1	1	yes	characteristic, complemented
360	C₂×#323	C₂×C₅₃	1	1	yes	characteristic, complemented
361	C₂×C₅₃	—	2	1	no	—
362	C₂×C₅₃	—	2	1	no	—
363	C₂×C₅₃	—	2	2	no	—
364	C₂×C₅₃	—	4	1	no	—
365	C₂×C₅₃	—	4	2	no	—
366	C₂×C₅₃	—	8	1	no	—
367	C₂×C₅₃	—	8	1	no	—
368	C₂×C₅₃	#2880	1	1	yes	characteristic
369	C₂×C₅₃	C₂×#410	1	1	yes	characteristic
370	C₂×C₅₃	#2888	1	1	yes	characteristic
371	#551	—	2	2	no	—
372	#551	—	2	2	no	—
373	#551	—	2	2	no	—
374	#551	—	2	2	no	—
375	C₂×#126	C₄×C₅₃	1	1	yes	characteristic
376	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
377	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
378	C₂×#123	C₄×C₅₃	1	1	yes	characteristic
379	C₂×#123	C₄×C₅₃	1	1	yes	characteristic
380	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
381	C₂×C₂²⋊Q₈	C₄×C₅₃	1	1	yes	characteristic
382	C₂×C₂²⋊Q₈	C₄×C₅₃	1	1	yes	characteristic
383	C₂×#120	C₄×C₅₃	1	1	yes	characteristic
384	C₂×C₄×D₄	C₄×C₅₃	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
386	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
387	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
388	C₂²×C₂²⋊C₄	C₄×C₅₃	1	1	yes	characteristic
389	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
390	#433	—	2	2	no	—
391	#433	—	2	2	no	—
392	#432	C₂²×C₅₃	1	2	yes	complemented
393	#432	C₂²×C₅₃	1	2	yes	complemented
394	#431	C₂²×C₅₃	1	2	yes	complemented
395	#431	C₂²×C₅₃	1	2	yes	complemented
396	#424	—	2	2	no	—
397	#407	C₂²×C₅₃	1	2	yes	—
398	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
399	#405	—	2	2	no	—
400	#324	C₂²×C₅₃	1	2	yes	complemented
401	#324	C₂²×C₅₃	1	2	yes	complemented
402	#323	C₂²×C₅₃	1	1	yes	characteristic
403	#323	C₂²×C₅₃	1	1	yes	characteristic
404	#323	C₂²×C₅₃	1	2	yes	—
405	#323	C₂²×C₅₃	1	1	yes	characteristic
406	#323	C₂²×C₅₃	1	1	yes	characteristic
407	#323	C₂²×C₅₃	1	2	yes	—
408	#323	C₂²×C₅₃	1	2	yes	complemented
409	#323	C₂²×C₅₃	1	2	yes	complemented
410	C₅₃	#17412	1	1	yes	characteristic, direct product factor, Sylow
411	C₂⁵	C₂×C₄×C₅₃	1	1	yes	characteristic
412	C₂²×Q₈	C₂×C₄×C₅₃	1	1	yes	characteristic
413	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
414	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
415	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
416	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
417	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
418	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
419	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
421	C₂×M₁₆	—	2	2	no	—
422	C₂²×C₈	—	2	2	no	—
423	#126	—	2	2	no	—
424	#126	—	2	2	no	—
425	#126	—	2	2	no	—
426	#126	—	2	2	no	—
427	#124	—	2	2	no	—
428	#124	—	2	2	no	—
429	#123	—	2	2	no	—
430	#123	—	2	2	no	—
431	#123	—	2	2	no	—
432	#123	—	2	2	no	—
433	#123	—	2	2	no	—
434	#123	—	2	2	no	—
435	C₂²⋊Q₈	—	2	2	no	—
436	C₂²⋊Q₈	—	2	2	no	—
437	C₂²⋊Q₈	—	2	2	no	—
438	C₂²⋊Q₈	—	2	2	no	—
439	#120	—	2	2	no	—
440	#120	—	2	2	no	—
441	C₄×D₄	—	2	1	no	—
442	C₄×D₄	—	2	1	no	—
443	C₄×D₄	—	2	1	no	—
444	C₄×D₄	—	2	1	no	—
445	C₄×D₄	—	2	2	no	—
446	C₄×D₄	—	2	2	no	—
447	#117	—	2	2	no	—
448	#117	—	2	2	no	—
449	#117	D₄×C₅₃	1	2	yes	—
450	#117	D₄×C₅₃	1	2	yes	—
451	#117	D₄×C₅₃	1	2	yes	—
452	#117	D₄×C₅₃	1	2	yes	—
453	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	—	2	2	no	—
462	C₂×C₂²⋊C₄	—	2	2	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
475	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
481	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
482	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
483	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
484	C₄⋊C₈	—	2	2	no	—
485	C₄⋊C₈	—	2	2	no	—
486	C₄⋊C₈	—	2	2	no	—
487	C₄⋊C₈	—	2	2	no	—
488	C₂²⋊C₈	—	2	2	no	—
489	C₂²⋊C₈	—	2	2	no	—
490	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
491	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
492	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
493	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
494	#97	—	2	2	no	—
495	#97	—	2	2	no	—
496	C₄×C₈	—	2	2	no	—
497	C₄×C₈	—	2	2	no	—
498	C₂⁴	—	2	1	no	—
499	C₂⁴	—	2	1	no	—
500	C₂⁴	—	2	2	no	—
501	C₂⁴	—	4	1	no	—
502	C₂⁴	—	4	2	no	—
503	C₂⁴	—	8	1	no	—
504	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
505	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
506	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
507	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
508	C₂×Q₈	—	2	2	no	—
509	C₂×Q₈	—	8	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	4	1	no	—
516	C₂×D₄	—	4	2	no	—
517	C₂×D₄	—	8	1	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	4	1	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	8	1	no	—
530	C₂²×C₄	—	8	1	no	—
531	C₂²×C₄	—	8	1	no	—
532	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
533	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
534	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
535	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
536	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
537	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
538	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
539	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
540	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
541	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
542	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
543	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
545	M₁₆	—	4	4	no	—
546	C₂×C₈	—	2	2	no	—
547	C₂×C₈	—	2	2	no	—
548	C₂×C₈	—	2	2	no	—
549	C₂×C₈	—	2	2	no	—
550	C₂×C₈	—	4	4	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	C₂²⋊C₄×C₅₃	1	2	yes	—
559	C₄⋊C₄	C₂²⋊C₄×C₅₃	1	2	yes	—
560	C₄⋊C₄	C₂²⋊C₄×C₅₃	1	2	yes	—
561	C₄⋊C₄	C₂²⋊C₄×C₅₃	1	2	yes	—
562	C₂²⋊C₄	—	2	1	no	—
563	C₂²⋊C₄	—	2	1	no	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	1	no	—
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	2	2	no	—
571	C₂²⋊C₄	—	2	1	no	—
572	C₂²⋊C₄	—	2	1	no	—
573	C₂²⋊C₄	—	2	2	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
579	C₂²⋊C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
580	C₂²⋊C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
581	C₂²⋊C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
582	C₂²⋊C₄	C₂²⋊C₄×C₅₃	1	2	yes	—
583	C₂²⋊C₄	C₂²⋊C₄×C₅₃	1	2	yes	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	C₂×D₄×C₅₃	1	2	yes	—
587	C₄²	C₂×D₄×C₅₃	1	2	yes	—
588	C₄²	C₂×D₄×C₅₃	1	2	yes	—
589	C₄²	C₂×D₄×C₅₃	1	2	yes	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	2	no	—
603	C₂³	—	4	2	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	2	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	2	no	—
612	C₂³	—	8	1	no	—
613	C₂³	—	8	1	no	—
614	C₂³	—	8	4	no	—
615	C₂³	—	8	4	no	—
616	C₂³	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
617	C₂³	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
618	C₂³	#131×C₅₃	1	2	yes	—
619	C₂³	C₂³×C₄×C₅₃	1	1	yes	characteristic
620	Q₈	—	8	2	no	—
621	D₄	—	4	4	no	—
622	D₄	—	4	2	no	—
623	D₄	—	4	2	no	—
624	D₄	—	8	2	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	2	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	8	1	no	—
649	C₂×C₄	—	8	1	no	—
650	C₂×C₄	—	8	1	no	—
651	C₂×C₄	—	8	1	no	—
652	C₂×C₄	—	8	1	no	—
653	C₂×C₄	—	8	1	no	—
654	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
655	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
656	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	2	yes	—
657	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
658	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
659	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	2	yes	—
660	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	2	yes	—
661	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
662	C₈	—	4	2	no	—
663	C₈	—	4	2	no	—
664	C₈	—	4	2	no	—
665	C₈	—	4	2	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	8	4	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	8	4	no	—
692	C₂²	C₅₃×#410	1	2	yes	—
693	C₂²	C₂²×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
694	C₂²	C₂×#131×C₅₃	1	1	yes	characteristic
695	C₂²	C₅₃×#568	1	1	yes	characteristic
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	1	no	—
702	C₄	—	2	1	no	—
703	C₄	—	2	2	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₂	—	2	1	no	—
710	C₂	—	2	1	no	—
711	C₂	—	2	2	no	—
712	C₂	—	4	1	no	—
713	C₂	—	4	2	no	—
714	C₂	—	8	1	no	—
715	C₂	—	8	1	no	—
716	C₂	C₅₃×#2880	1	1	yes	characteristic
717	C₂	C₂×C₅₃×#410	1	1	yes	characteristic
718	C₂	C₅₃×#2888	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂×#120×C₅₃	C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂×#117×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#2924	C₂	semidirect
3. C₅₃×#1473	C₂	semidirect
4. C₅₃×#1469	C₂	semidirect
5. C₅₃×#1468	C₂	semidirect
6. C₅₃×#1466	C₂	semidirect
7. C₅₃×#1464	C₂	semidirect
8. C₅₃×#1462	C₂	semidirect
9. C₅₃×#1460	C₂	semidirect
10. C₅₃×#1458	C₂	semidirect
11. C₂×C₅₃×#323	C₂	semidirect
33. C₅₃×#432	C₂²	semidirect
34. C₅₃×#432	C₂²	semidirect
35. C₅₃×#431	C₂²	semidirect
36. C₅₃×#431	C₂²	semidirect
41. C₅₃×#324	C₂²	semidirect
42. C₅₃×#324	C₂²	semidirect
49. C₅₃×#323	C₂²	semidirect
50. C₅₃×#323	C₂²	semidirect
306. #17412	C₅₃	direct (N × H)
351. #2924	C₂×C₅₃	semidirect
352. #1473	C₂×C₅₃	semidirect
353. #1469	C₂×C₅₃	semidirect
354. #1468	C₂×C₅₃	semidirect
355. #1466	C₂×C₅₃	semidirect
356. #1464	C₂×C₅₃	semidirect
357. #1462	C₂×C₅₃	semidirect
358. #1460	C₂×C₅₃	semidirect
359. #1458	C₂×C₅₃	semidirect
360. C₂×#323	C₂×C₅₃	semidirect
392. #432	C₂²×C₅₃	semidirect
393. #432	C₂²×C₅₃	semidirect
394. #431	C₂²×C₅₃	semidirect
395. #431	C₂²×C₅₃	semidirect
400. #324	C₂²×C₅₃	semidirect
401. #324	C₂²×C₅₃	semidirect
408. #323	C₂²×C₅₃	semidirect
409. #323	C₂²×C₅₃	semidirect
410. C₅₃	#17412	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×#551	2
C₅₃×#2924	2
C₅₃×#1473	2
C₅₃×#1469	2
C₅₃×#1468	2
C₅₃×#1466	2
C₅₃×#1464	2
C₅₃×#1462	2
C₅₃×#1460	2
C₅₃×#1458	2
C₂×C₅₃×#323	2
#17412	53

Subgroups — C53×#17412 #27224924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#17412 #27224924