Subgroups — C₅₃×#34742 #27242254

Order 13568.

2738 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2423	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2422	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2421	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2420	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2419	C₂	1	4	yes	maximal, complemented
8	C₅₃×#2418	C₂	1	4	yes	maximal, complemented
9	C₅₃×#2395	C₂	1	4	yes	maximal, complemented
10	C₄×#123×C₅₃	C₂	1	4	yes	maximal, complemented
11	C₅₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
18	C₅₃×#525	—	2	8	no	—
19	C₂×#123×C₅₃	C₂²	1	4	yes	—
20	C₂×#123×C₅₃	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
22	C₂×#121×C₅₃	C₂²	1	2	yes	—
23	C₂×#120×C₅₃	C₂²	1	2	yes	—
24	C₄×#41×C₅₃	—	2	8	no	—
25	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
26	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
29	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
34	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₅₃	C₂²	1	2	yes	complemented
37	C₅₃×#400	C₂²	1	4	yes	complemented
38	C₅₃×#399	C₂²	1	4	yes	—
39	C₅₃×#398	C₂²	1	4	yes	complemented
40	C₅₃×#397	C₂²	1	4	yes	—
41	C₅₃×#397	C₂²	1	4	yes	complemented
42	C₅₃×#397	C₂²	1	4	yes	complemented
43	C₅₃×#394	C₂²	1	4	yes	—
44	C₅₃×#394	C₂²	1	4	yes	—
45	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#389	C₂²	1	2	yes	complemented
50	C₅₃×#389	C₂²	1	2	yes	complemented
51	C₅₃×#388	C₂²	1	4	yes	—
52	C₅₃×#388	C₂²	1	4	yes	—
53	C₅₃×#387	C₂²	1	4	yes	complemented
54	C₅₃×#387	C₂²	1	4	yes	complemented
55	C₅₃×#386	C₂²	1	4	yes	—
56	C₅₃×#386	C₂²	1	4	yes	—
57	C₅₃×#385	C₂²	1	4	yes	—
58	C₅₃×#385	C₂²	1	4	yes	complemented
59	C₅₃×#384	C₂²	1	2	yes	complemented
60	C₅₃×#382	C₂²	1	2	yes	complemented
61	C₅₃×#381	C₂²	1	2	yes	—
62	C₅₃×#381	C₂²	1	4	yes	complemented
63	C₅₃×#380	C₂²	1	2	yes	—
64	C₅₃×#380	C₂²	1	2	yes	—
65	C₅₃×#380	C₂²	1	4	yes	—
66	C₅₃×#379	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₅₃	C₂²	1	4	yes	complemented
68	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
69	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	—
75	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	complemented
76	C₂×#95×C₅₃	C₂²	1	2	yes	—
77	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
78	C₂×#41×C₅₃	—	2	4	no	—
79	C₂×#41×C₅₃	—	2	4	no	—
80	C₂×#41×C₅₃	D₄	1	8	yes	—
81	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
83	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
84	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₅₃	—	2	4	no	—
86	C₂³×C₄×C₅₃	—	2	4	no	—
87	C₂³×C₄×C₅₃	—	2	4	no	—
88	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
89	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
94	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
96	#123×C₅₃	—	2	16	no	—
97	#123×C₅₃	—	2	8	no	—
98	C₂²⋊Q₈×C₅₃	—	2	8	no	—
99	#121×C₅₃	—	2	8	no	—
100	#120×C₅₃	—	2	8	no	—
101	C₄×Q₈×C₅₃	—	2	8	no	—
102	C₄×D₄×C₅₃	—	2	16	no	—
103	C₄×D₄×C₅₃	—	2	8	no	—
104	C₄×D₄×C₅₃	—	2	16	no	—
105	#117×C₅₃	—	2	4	no	—
106	#117×C₅₃	—	2	4	no	—
107	#117×C₅₃	—	2	8	no	—
108	#117×C₅₃	—	2	4	no	—
109	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
120	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
134	C₂×C₄²×C₅₃	—	2	4	no	—
135	C₂×C₄²×C₅₃	—	2	8	no	—
136	C₂×C₄²×C₅₃	—	2	4	no	—
137	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
138	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
141	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
145	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
147	#95×C₅₃	C₂³	1	2	yes	—
148	#95×C₅₃	C₂³	1	2	yes	—
149	#95×C₅₃	C₂³	1	2	yes	—
150	#95×C₅₃	C₂³	1	2	yes	—
151	#95×C₅₃	C₂³	1	4	yes	—
152	#95×C₅₃	C₂³	1	4	yes	—
153	#95×C₅₃	C₂³	1	4	yes	—
154	#95×C₅₃	C₂³	1	4	yes	—
155	#95×C₅₃	C₂³	1	4	yes	—
156	#95×C₅₃	C₂³	1	4	yes	—
157	#95×C₅₃	C₂³	1	4	yes	—
158	#95×C₅₃	C₂³	1	4	yes	—
159	C₂⁴×C₅₃	—	2	4	no	—
160	C₂⁴×C₅₃	—	2	2	no	—
161	C₂⁴×C₅₃	—	2	2	no	—
162	C₂⁴×C₅₃	—	2	2	no	—
163	C₂⁴×C₅₃	—	4	2	no	—
164	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
165	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
166	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
167	#41×C₅₃	—	2	32	no	—
168	C₂×Q₈×C₅₃	—	2	2	no	—
169	C₂×Q₈×C₅₃	—	2	2	no	—
170	C₂×Q₈×C₅₃	C₂×D₄	1	4	yes	—
171	C₂×D₄×C₅₃	—	2	4	no	—
172	C₂×D₄×C₅₃	—	2	4	no	—
173	C₂×D₄×C₅₃	—	2	8	no	—
174	C₂×D₄×C₅₃	—	2	8	no	—
175	C₂×D₄×C₅₃	—	2	2	no	—
176	C₂×D₄×C₅₃	—	2	2	no	—
177	C₂×D₄×C₅₃	—	4	4	no	—
178	C₂×D₄×C₅₃	C₂×D₄	1	8	yes	—
179	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₅₃	—	2	4	no	—
181	C₂²×C₄×C₅₃	—	2	4	no	—
182	C₂²×C₄×C₅₃	—	2	8	no	—
183	C₂²×C₄×C₅₃	—	2	4	no	—
184	C₂²×C₄×C₅₃	—	2	2	no	—
185	C₂²×C₄×C₅₃	—	2	4	no	—
186	C₂²×C₄×C₅₃	—	2	2	no	—
187	C₂²×C₄×C₅₃	—	2	2	no	—
188	C₂²×C₄×C₅₃	—	2	4	no	—
189	C₂²×C₄×C₅₃	—	2	4	no	—
190	C₂²×C₄×C₅₃	—	2	4	no	—
191	C₂²×C₄×C₅₃	—	2	4	no	—
192	C₂²×C₄×C₅₃	—	2	8	no	—
193	C₂²×C₄×C₅₃	—	2	4	no	—
194	C₂²×C₄×C₅₃	—	2	4	no	—
195	C₂²×C₄×C₅₃	—	2	4	no	—
196	C₂²×C₄×C₅₃	—	2	4	no	—
197	C₂²×C₄×C₅₃	—	4	4	no	—
198	C₂²×C₄×C₅₃	—	4	2	no	—
199	C₂²×C₄×C₅₃	—	4	2	no	—
200	C₂²×C₄×C₅₃	—	4	16	no	—
201	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
202	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₅₃	#41	1	4	yes	—
204	C₂²×C₄×C₅₃	#41	1	4	yes	—
205	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
217	C₄⋊C₄×C₅₃	—	2	8	no	—
218	C₄⋊C₄×C₅₃	—	2	4	no	—
219	C₄⋊C₄×C₅₃	—	2	4	no	—
220	C₄⋊C₄×C₅₃	—	2	8	no	—
221	C₄⋊C₄×C₅₃	—	2	2	no	—
222	C₄⋊C₄×C₅₃	—	2	2	no	—
223	C₄⋊C₄×C₅₃	—	2	8	no	—
224	C₄⋊C₄×C₅₃	—	2	8	no	—
225	C₄⋊C₄×C₅₃	—	4	4	no	—
226	C₄⋊C₄×C₅₃	—	4	4	no	—
227	C₂²⋊C₄×C₅₃	—	2	8	no	—
228	C₂²⋊C₄×C₅₃	—	2	4	no	—
229	C₂²⋊C₄×C₅₃	—	2	4	no	—
230	C₂²⋊C₄×C₅₃	—	2	8	no	—
231	C₂²⋊C₄×C₅₃	—	2	4	no	—
232	C₂²⋊C₄×C₅₃	—	2	4	no	—
233	C₂²⋊C₄×C₅₃	—	2	8	no	—
234	C₂²⋊C₄×C₅₃	—	2	8	no	—
235	C₂²⋊C₄×C₅₃	—	2	4	no	—
236	C₂²⋊C₄×C₅₃	—	2	4	no	—
237	C₂²⋊C₄×C₅₃	—	2	8	no	—
238	C₂²⋊C₄×C₅₃	—	4	4	no	—
239	C₂²⋊C₄×C₅₃	—	4	4	no	—
240	C₂²⋊C₄×C₅₃	#41	1	8	yes	complemented
241	C₄²×C₅₃	—	2	2	no	—
242	C₄²×C₅₃	—	2	2	no	—
243	C₄²×C₅₃	—	2	4	no	—
244	C₄²×C₅₃	—	2	8	no	—
245	C₄²×C₅₃	—	2	4	no	—
246	C₄²×C₅₃	—	2	4	no	—
247	C₄²×C₅₃	—	2	2	no	—
248	C₄²×C₅₃	—	2	4	no	—
249	C₄²×C₅₃	—	2	2	no	—
250	C₄²×C₅₃	—	2	4	no	—
251	C₂³×C₅₃	—	2	2	no	—
252	C₂³×C₅₃	—	2	2	no	—
253	C₂³×C₅₃	—	2	8	no	—
254	C₂³×C₅₃	—	2	2	no	—
255	C₂³×C₅₃	—	2	2	no	—
256	C₂³×C₅₃	—	2	2	no	—
257	C₂³×C₅₃	—	2	2	no	—
258	C₂³×C₅₃	—	2	2	no	—
259	C₂³×C₅₃	—	2	4	no	—
260	C₂³×C₅₃	—	2	2	no	—
261	C₂³×C₅₃	—	2	4	no	—
262	C₂³×C₅₃	—	2	2	no	—
263	C₂³×C₅₃	—	2	2	no	—
264	C₂³×C₅₃	—	4	8	no	—
265	C₂³×C₅₃	—	4	8	no	—
266	C₂³×C₅₃	—	4	4	no	—
267	C₂³×C₅₃	—	4	4	no	—
268	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
269	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
270	C₂³×C₅₃	C₂×#41	1	4	yes	—
271	C₂³×C₅₃	C₂×#41	1	2	yes	—
272	C₂³×C₅₃	C₂×#41	1	2	yes	—
273	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
274	Q₈×C₅₃	—	2	8	no	—
275	D₄×C₅₃	—	2	16	no	—
276	D₄×C₅₃	—	2	8	no	—
277	D₄×C₅₃	—	4	16	no	—
278	C₂×C₄×C₅₃	—	2	2	no	—
279	C₂×C₄×C₅₃	—	2	2	no	—
280	C₂×C₄×C₅₃	—	2	2	no	—
281	C₂×C₄×C₅₃	—	2	2	no	—
282	C₂×C₄×C₅₃	—	2	2	no	—
283	C₂×C₄×C₅₃	—	2	2	no	—
284	C₂×C₄×C₅₃	—	2	16	no	—
285	C₂×C₄×C₅₃	—	2	2	no	—
286	C₂×C₄×C₅₃	—	2	2	no	—
287	C₂×C₄×C₅₃	—	2	4	no	—
288	C₂×C₄×C₅₃	—	2	4	no	—
289	C₂×C₄×C₅₃	—	2	2	no	—
290	C₂×C₄×C₅₃	—	2	2	no	—
291	C₂×C₄×C₅₃	—	2	2	no	—
292	C₂×C₄×C₅₃	—	2	2	no	—
293	C₂×C₄×C₅₃	—	2	2	no	—
294	C₂×C₄×C₅₃	—	2	4	no	—
295	C₂×C₄×C₅₃	—	2	4	no	—
296	C₂×C₄×C₅₃	—	2	2	no	—
297	C₂×C₄×C₅₃	—	2	2	no	—
298	C₂×C₄×C₅₃	—	2	4	no	—
299	C₂×C₄×C₅₃	—	2	2	no	—
300	C₂×C₄×C₅₃	—	2	4	no	—
301	C₂×C₄×C₅₃	—	2	2	no	—
302	C₂×C₄×C₅₃	—	2	4	no	—
303	C₂×C₄×C₅₃	—	2	4	no	—
304	C₂×C₄×C₅₃	—	4	8	no	—
305	C₂×C₄×C₅₃	—	4	16	no	—
306	C₂×C₄×C₅₃	—	4	8	no	—
307	C₂×C₄×C₅₃	—	4	4	no	—
308	C₂×C₄×C₅₃	—	4	8	no	—
309	C₂×C₄×C₅₃	—	4	8	no	—
310	C₂×C₄×C₅₃	#123	1	16	yes	complemented
311	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
312	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
314	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
315	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
316	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
317	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
318	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
319	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
320	#34742	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
321	C₂²×C₅₃	—	2	2	no	—
322	C₂²×C₅₃	—	2	2	no	—
323	C₂²×C₅₃	—	2	4	no	—
324	C₂²×C₅₃	—	2	4	no	—
325	C₂²×C₅₃	—	2	4	no	—
326	C₂²×C₅₃	—	2	4	no	—
327	C₂²×C₅₃	—	2	8	no	—
328	C₂²×C₅₃	—	2	4	no	—
329	C₂²×C₅₃	—	2	4	no	—
330	C₂²×C₅₃	—	4	16	no	—
331	C₂²×C₅₃	—	4	2	no	—
332	C₂²×C₅₃	—	4	2	no	—
333	C₂²×C₅₃	—	4	2	no	—
334	C₂²×C₅₃	—	4	2	no	—
335	C₂²×C₅₃	—	4	2	no	—
336	C₂²×C₅₃	—	4	4	no	—
337	C₂²×C₅₃	—	4	2	no	—
338	C₂²×C₅₃	C₂×#123	1	4	yes	—
339	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
340	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
341	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
342	C₂²×C₅₃	C₂²×#41	1	2	yes	—
343	C₂²×C₅₃	#585	1	2	yes	—
344	C₄×C₅₃	—	2	4	no	—
345	C₄×C₅₃	—	2	4	no	—
346	C₄×C₅₃	—	2	4	no	—
347	C₄×C₅₃	—	4	2	no	—
348	C₄×C₅₃	—	4	2	no	—
349	C₄×C₅₃	—	4	2	no	—
350	C₄×C₅₃	—	4	2	no	—
351	C₄×C₅₃	—	4	4	no	—
352	C₄×C₅₃	—	4	4	no	—
353	C₄×C₅₃	—	4	2	no	—
354	C₄×C₅₃	C₂×#123	1	4	yes	—
355	C₄×C₅₃	C₂×#123	1	4	yes	—
356	C₂×#525	C₂×C₅₃	1	1	yes	characteristic
357	C₂×C₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
358	#2423	C₂×C₅₃	1	2	yes	complemented
359	#2422	C₂×C₅₃	1	2	yes	complemented
360	#2421	C₂×C₅₃	1	2	yes	complemented
361	#2420	C₂×C₅₃	1	2	yes	complemented
362	#2419	C₂×C₅₃	1	4	yes	complemented
363	#2418	C₂×C₅₃	1	4	yes	complemented
364	#2395	C₂×C₅₃	1	4	yes	complemented
365	C₄×#123	C₂×C₅₃	1	4	yes	complemented
366	#2297	C₂×C₅₃	1	1	yes	characteristic, complemented
367	#2296	C₂×C₅₃	1	1	yes	characteristic, complemented
368	#2285	C₂×C₅₃	1	1	yes	characteristic, complemented
369	#2280	C₂×C₅₃	1	1	yes	characteristic, complemented
370	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
371	C₂×C₅₃	—	2	4	no	—
372	C₂×C₅₃	—	4	4	no	—
373	C₂×C₅₃	—	4	4	no	—
374	C₂×C₅₃	C₂²×#123	1	1	yes	characteristic
375	C₂×C₅₃	#3444	1	1	yes	characteristic
376	C₂×C₅₃	#3455	1	1	yes	characteristic
377	C₂×C₅₃	D₄×#41	1	2	yes	—
378	C₂×C₅₃	#3475	1	2	yes	—
379	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
380	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
381	#525	—	2	8	no	—
382	C₂×#123	C₂²×C₅₃	1	2	yes	—
383	C₂×#123	C₂²×C₅₃	1	4	yes	—
384	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
385	C₂×#121	C₂²×C₅₃	1	2	yes	—
386	C₂×#120	C₂²×C₅₃	1	2	yes	—
387	C₄×#41	—	2	8	no	—
388	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
389	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	—
390	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	—
391	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
392	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
393	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
394	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
395	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
396	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
397	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
398	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
399	C₂²×C₄²	C₂²×C₅₃	1	2	yes	complemented
400	#400	C₂²×C₅₃	1	4	yes	complemented
401	#399	C₂²×C₅₃	1	4	yes	—
402	#398	C₂²×C₅₃	1	4	yes	complemented
403	#397	C₂²×C₅₃	1	4	yes	—
404	#397	C₂²×C₅₃	1	4	yes	complemented
405	#397	C₂²×C₅₃	1	4	yes	complemented
406	#394	C₂²×C₅₃	1	4	yes	—
407	#394	C₂²×C₅₃	1	4	yes	—
408	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
409	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
410	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
411	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
412	#389	C₂²×C₅₃	1	2	yes	complemented
413	#389	C₂²×C₅₃	1	2	yes	complemented
414	#388	C₂²×C₅₃	1	4	yes	—
415	#388	C₂²×C₅₃	1	4	yes	—
416	#387	C₂²×C₅₃	1	4	yes	complemented
417	#387	C₂²×C₅₃	1	4	yes	complemented
418	#386	C₂²×C₅₃	1	4	yes	—
419	#386	C₂²×C₅₃	1	4	yes	—
420	#385	C₂²×C₅₃	1	4	yes	—
421	#385	C₂²×C₅₃	1	4	yes	complemented
422	#384	C₂²×C₅₃	1	2	yes	complemented
423	#382	C₂²×C₅₃	1	2	yes	complemented
424	#381	C₂²×C₅₃	1	2	yes	—
425	#381	C₂²×C₅₃	1	4	yes	complemented
426	#380	C₂²×C₅₃	1	4	yes	—
427	#380	C₂²×C₅₃	1	2	yes	—
428	#380	C₂²×C₅₃	1	2	yes	—
429	#379	C₂²×C₅₃	1	2	yes	—
430	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
431	C₄×C₄⋊C₄	C₂²×C₅₃	1	4	yes	complemented
432	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
433	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
434	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	—
435	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
436	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
437	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
438	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	complemented
439	C₂×#95	C₂²×C₅₃	1	2	yes	—
440	C₅₃	#34742	1	1	yes	characteristic, direct product factor, Sylow
441	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
442	C₂×#41	—	2	4	no	—
443	C₂×#41	—	2	4	no	—
444	C₂×#41	D₄×C₅₃	1	8	yes	—
445	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
446	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
447	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
448	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
449	C₂³×C₄	—	2	4	no	—
450	C₂³×C₄	—	2	4	no	—
451	C₂³×C₄	—	2	4	no	—
452	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
453	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
454	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
456	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
457	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
458	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
459	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
460	#123	—	2	8	no	—
461	#123	—	2	16	no	—
462	C₂²⋊Q₈	—	2	8	no	—
463	#121	—	2	8	no	—
464	#120	—	2	8	no	—
465	C₄×Q₈	—	2	8	no	—
466	C₄×D₄	—	2	16	no	—
467	C₄×D₄	—	2	8	no	—
468	C₄×D₄	—	2	16	no	—
469	#117	—	2	4	no	—
470	#117	—	2	4	no	—
471	#117	—	2	8	no	—
472	#117	—	2	4	no	—
473	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
482	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
483	C₂×C₂²⋊C₄	—	2	8	no	—
484	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
498	C₂×C₄²	—	2	4	no	—
499	C₂×C₄²	—	2	8	no	—
500	C₂×C₄²	—	2	4	no	—
501	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
502	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
503	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
504	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
506	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
507	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
508	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
511	#95	C₂³×C₅₃	1	2	yes	—
512	#95	C₂³×C₅₃	1	2	yes	—
513	#95	C₂³×C₅₃	1	2	yes	—
514	#95	C₂³×C₅₃	1	2	yes	—
515	#95	C₂³×C₅₃	1	4	yes	—
516	#95	C₂³×C₅₃	1	4	yes	—
517	#95	C₂³×C₅₃	1	4	yes	—
518	#95	C₂³×C₅₃	1	4	yes	—
519	#95	C₂³×C₅₃	1	4	yes	—
520	#95	C₂³×C₅₃	1	4	yes	—
521	#95	C₂³×C₅₃	1	4	yes	—
522	#95	C₂³×C₅₃	1	4	yes	—
523	C₂⁴	—	2	4	no	—
524	C₂⁴	—	2	2	no	—
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	4	2	no	—
528	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
529	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
530	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
531	#41	—	2	32	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	C₂×D₄×C₅₃	1	4	yes	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	2	8	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂×D₄	C₂×D₄×C₅₃	1	8	yes	—
543	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	8	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	8	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	4	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	4	16	no	—
565	C₂²×C₄	C₂×D₄×C₅₃	1	8	yes	—
566	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
567	C₂²×C₄	#41×C₅₃	1	4	yes	—
568	C₂²×C₄	#41×C₅₃	1	4	yes	—
569	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
575	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
576	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
581	C₄⋊C₄	—	2	8	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	8	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	8	no	—
588	C₄⋊C₄	—	2	8	no	—
589	C₄⋊C₄	—	4	4	no	—
590	C₄⋊C₄	—	4	4	no	—
591	C₂²⋊C₄	—	2	8	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	8	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	8	no	—
598	C₂²⋊C₄	—	2	8	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	8	no	—
602	C₂²⋊C₄	—	4	4	no	—
603	C₂²⋊C₄	—	4	4	no	—
604	C₂²⋊C₄	#41×C₅₃	1	8	yes	complemented
605	C₄²	—	2	2	no	—
606	C₄²	—	2	2	no	—
607	C₄²	—	2	4	no	—
608	C₄²	—	2	8	no	—
609	C₄²	—	2	4	no	—
610	C₄²	—	2	4	no	—
611	C₄²	—	2	2	no	—
612	C₄²	—	2	4	no	—
613	C₄²	—	2	2	no	—
614	C₄²	—	2	4	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	8	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	4	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	4	8	no	—
629	C₂³	—	4	8	no	—
630	C₂³	—	4	4	no	—
631	C₂³	—	4	4	no	—
632	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
633	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
634	C₂³	C₂×#41×C₅₃	1	4	yes	—
635	C₂³	C₂×#41×C₅₃	1	2	yes	—
636	C₂³	C₂×#41×C₅₃	1	2	yes	—
637	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
638	Q₈	—	2	8	no	—
639	D₄	—	2	16	no	—
640	D₄	—	2	8	no	—
641	D₄	—	4	16	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	16	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	4	8	no	—
669	C₂×C₄	—	4	16	no	—
670	C₂×C₄	—	4	8	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	—	4	8	no	—
673	C₂×C₄	—	4	8	no	—
674	C₂×C₄	#123×C₅₃	1	16	yes	complemented
675	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
676	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
677	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
678	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
679	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
680	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
681	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
682	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
683	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	4	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	8	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	2	4	no	—
692	C₂²	—	2	4	no	—
693	C₂²	—	4	16	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	4	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	C₂×#123×C₅₃	1	4	yes	—
702	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
703	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
704	C₂²	C₂²×#41×C₅₃	1	2	yes	—
705	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
706	C₂²	C₅₃×#585	1	2	yes	—
707	C₄	—	2	4	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	4	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	4	no	—
713	C₄	—	4	4	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	C₂×#123×C₅₃	1	4	yes	—
718	C₄	C₂×#123×C₅₃	1	4	yes	—
719	C₂	—	2	4	no	—
720	C₂	—	4	4	no	—
721	C₂	—	4	4	no	—
722	C₂	C₂²×#123×C₅₃	1	1	yes	characteristic
723	C₂	C₅₃×#3444	1	1	yes	characteristic
724	C₂	C₅₃×#3455	1	1	yes	characteristic
725	C₂	D₄×#41×C₅₃	1	2	yes	—
726	C₂	C₅₃×#3475	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
socle	C₂³×C₅₃	C₂⁵
prime radical	C₂×C₅₃×#525	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#2423	C₂	semidirect
4. C₅₃×#2422	C₂	semidirect
5. C₅₃×#2421	C₂	semidirect
6. C₅₃×#2420	C₂	semidirect
7. C₅₃×#2419	C₂	semidirect
8. C₅₃×#2418	C₂	semidirect
9. C₅₃×#2395	C₂	semidirect
10. C₄×#123×C₅₃	C₂	semidirect
11. C₅₃×#2297	C₂	semidirect
12. C₅₃×#2296	C₂	semidirect
13. C₅₃×#2285	C₂	semidirect
14. C₅₃×#2280	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
25. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
28. C₂×C₄×D₄×C₅₃	C₂²	semidirect
32. C₂×#117×C₅₃	C₂²	semidirect
36. C₂²×C₄²×C₅₃	C₂²	semidirect
37. C₅₃×#400	C₂²	semidirect
39. C₅₃×#398	C₂²	semidirect
41. C₅₃×#397	C₂²	semidirect
42. C₅₃×#397	C₂²	semidirect
45. C₅₃×#391	C₂²	semidirect
46. C₅₃×#391	C₂²	semidirect
47. C₅₃×#390	C₂²	semidirect
48. C₅₃×#390	C₂²	semidirect
49. C₅₃×#389	C₂²	semidirect
50. C₅₃×#389	C₂²	semidirect
53. C₅₃×#387	C₂²	semidirect
54. C₅₃×#387	C₂²	semidirect
58. C₅₃×#385	C₂²	semidirect
59. C₅₃×#384	C₂²	semidirect
60. C₅₃×#382	C₂²	semidirect
62. C₅₃×#381	C₂²	semidirect
67. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
68. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
69. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
75. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
240. C₂²⋊C₄×C₅₃	#41	semidirect
310. C₂×C₄×C₅₃	#123	semidirect
320. #34742	C₅₃	direct (N × H)
357. C₂×C₄×#41	C₂×C₅₃	semidirect
358. #2423	C₂×C₅₃	semidirect
359. #2422	C₂×C₅₃	semidirect
360. #2421	C₂×C₅₃	semidirect
361. #2420	C₂×C₅₃	semidirect
362. #2419	C₂×C₅₃	semidirect
363. #2418	C₂×C₅₃	semidirect
364. #2395	C₂×C₅₃	semidirect
365. C₄×#123	C₂×C₅₃	semidirect
366. #2297	C₂×C₅₃	semidirect
367. #2296	C₂×C₅₃	semidirect
368. #2285	C₂×C₅₃	semidirect
369. #2280	C₂×C₅₃	semidirect
370. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
388. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
391. C₂×C₄×D₄	C₂²×C₅₃	semidirect
395. C₂×#117	C₂²×C₅₃	semidirect
399. C₂²×C₄²	C₂²×C₅₃	semidirect
400. #400	C₂²×C₅₃	semidirect
402. #398	C₂²×C₅₃	semidirect
404. #397	C₂²×C₅₃	semidirect
405. #397	C₂²×C₅₃	semidirect
408. #391	C₂²×C₅₃	semidirect
409. #391	C₂²×C₅₃	semidirect
410. #390	C₂²×C₅₃	semidirect
411. #390	C₂²×C₅₃	semidirect
412. #389	C₂²×C₅₃	semidirect
413. #389	C₂²×C₅₃	semidirect
416. #387	C₂²×C₅₃	semidirect
417. #387	C₂²×C₅₃	semidirect
421. #385	C₂²×C₅₃	semidirect
422. #384	C₂²×C₅₃	semidirect
423. #382	C₂²×C₅₃	semidirect
425. #381	C₂²×C₅₃	semidirect
430. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
431. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
432. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
438. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
440. C₅₃	#34742	direct (N × H)
604. C₂²⋊C₄	#41×C₅₃	semidirect
674. C₂×C₄	#123×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#525	2
C₂×C₄×#41×C₅₃	2
C₅₃×#2423	2
C₅₃×#2422	2
C₅₃×#2421	2
C₅₃×#2420	2
C₅₃×#2419	2
C₅₃×#2418	2
C₅₃×#2395	2
C₄×#123×C₅₃	2
C₅₃×#2297	2
C₅₃×#2296	2
C₅₃×#2285	2
C₅₃×#2280	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
#34742	53

Subgroups — C53×#34742 #27242254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34742 #27242254