Subgroups — C₅₃×#36719 #27244231

Order 13568.

2490 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×#539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2847	C₂	1	1	yes	maximal, characteristic
5	C₅₃×#2704	C₂	1	4	yes	maximal, complemented
6	C₅₃×#2702	C₂	1	4	yes	maximal, complemented
7	C₅₃×#2683	C₂	1	4	yes	maximal, complemented
8	C₅₃×#2681	C₂	1	4	yes	maximal, complemented
9	C₅₃×#2627	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2618	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2534	C₂	1	2	yes	maximal, complemented
12	C₅₃×#2413	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2411	C₂	1	2	yes	maximal, complemented
14	C₅₃×#2409	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2316	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
18	C₅₃×#539	—	2	8	no	—
19	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
20	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
21	C₂×#123×C₅₃	C₂²	1	2	yes	—
22	C₂×#123×C₅₃	C₂²	1	2	yes	—
23	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₅₃	—	2	8	no	—
25	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
26	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
27	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	complemented
31	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×#121×C₅₃	C₂²	1	2	yes	—
33	C₂×#120×C₅₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
35	C₂×#117×C₅₃	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#400	C₂²	1	2	yes	complemented
42	C₅₃×#398	C₂²	1	4	yes	complemented
43	C₅₃×#398	C₂²	1	4	yes	complemented
44	C₅₃×#398	C₂²	1	2	yes	complemented
45	C₅₃×#396	C₂²	1	4	yes	—
46	C₅₃×#396	C₂²	1	4	yes	—
47	C₅₃×#396	C₂²	1	4	yes	complemented
48	C₅₃×#396	C₂²	1	4	yes	complemented
49	C₅₃×#395	C₂²	1	2	yes	complemented
50	C₅₃×#395	C₂²	1	4	yes	complemented
51	C₅₃×#394	C₂²	1	4	yes	—
52	C₅₃×#394	C₂²	1	4	yes	—
53	C₅₃×#394	C₂²	1	2	yes	complemented
54	C₅₃×#393	C₂²	1	4	yes	complemented
55	C₅₃×#391	C₂²	1	4	yes	complemented
56	C₅₃×#390	C₂²	1	4	yes	—
57	C₅₃×#389	C₂²	1	4	yes	complemented
58	C₅₃×#389	C₂²	1	4	yes	complemented
59	C₅₃×#389	C₂²	1	4	yes	complemented
60	C₅₃×#388	C₂²	1	4	yes	—
61	C₅₃×#388	C₂²	1	4	yes	—
62	C₅₃×#388	C₂²	1	4	yes	complemented
63	C₅₃×#386	C₂²	1	4	yes	—
64	C₅₃×#386	C₂²	1	4	yes	—
65	C₅₃×#386	C₂²	1	2	yes	—
66	C₅₃×#386	C₂²	1	2	yes	—
67	C₅₃×#385	C₂²	1	4	yes	—
68	C₅₃×#385	C₂²	1	2	yes	—
69	C₅₃×#385	C₂²	1	2	yes	—
70	C₅₃×#381	C₂²	1	2	yes	—
71	C₅₃×#380	C₂²	1	2	yes	—
72	C₅₃×#380	C₂²	1	2	yes	—
73	C₅₃×#380	C₂²	1	2	yes	—
74	C₅₃×#380	C₂²	1	1	yes	characteristic
75	C₅₃×#380	C₂²	1	1	yes	characteristic
76	C₅₃×#379	C₂²	1	2	yes	—
77	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₅₃	—	2	4	no	—
79	C₂²×Q₈×C₅₃	—	4	4	no	—
80	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
81	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
84	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₅₃	—	2	4	no	—
86	C₂³×C₄×C₅₃	—	4	4	no	—
87	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
94	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
96	#126×C₅₃	—	2	8	no	—
97	#125×C₅₃	—	2	8	no	—
98	#123×C₅₃	—	2	8	no	—
99	#123×C₅₃	—	2	8	no	—
100	#123×C₅₃	—	4	4	no	—
101	C₂²⋊Q₈×C₅₃	—	2	16	no	—
102	C₂²⋊Q₈×C₅₃	—	2	16	no	—
103	C₂²⋊Q₈×C₅₃	—	2	8	no	—
104	C₂²⋊Q₈×C₅₃	—	2	4	no	—
105	C₂²⋊Q₈×C₅₃	—	4	4	no	—
106	C₂²⋊Q₈×C₅₃	—	4	8	no	—
107	#121×C₅₃	—	2	4	no	—
108	#121×C₅₃	—	4	4	no	—
109	#120×C₅₃	—	4	4	no	—
110	C₄×D₄×C₅₃	—	2	8	no	—
111	#117×C₅₃	—	4	4	no	—
112	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
113	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
114	C₂×C₄⋊C₄×C₅₃	D₄	1	8	yes	complemented
115	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
150	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
151	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
152	#95×C₅₃	C₂³	1	4	yes	—
153	#95×C₅₃	C₂³	1	2	yes	—
154	#95×C₅₃	C₂³	1	2	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	#95×C₅₃	C₂³	1	4	yes	—
160	#95×C₅₃	C₂³	1	4	yes	—
161	C₂⁴×C₅₃	—	2	2	no	—
162	C₂⁴×C₅₃	—	2	4	no	—
163	C₂⁴×C₅₃	—	2	2	no	—
164	C₂⁴×C₅₃	—	2	2	no	—
165	C₂⁴×C₅₃	—	4	2	no	—
166	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
167	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
168	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
169	C₂×Q₈×C₅₃	—	2	8	no	—
170	C₂×Q₈×C₅₃	—	2	2	no	—
171	C₂×Q₈×C₅₃	—	2	8	no	—
172	C₂×Q₈×C₅₃	—	4	4	no	—
173	C₂×Q₈×C₅₃	—	4	2	no	—
174	C₂×Q₈×C₅₃	—	4	16	no	—
175	C₂×D₄×C₅₃	—	2	4	no	—
176	C₂×D₄×C₅₃	—	2	4	no	—
177	C₂×D₄×C₅₃	—	2	4	no	—
178	C₂×D₄×C₅₃	—	2	8	no	—
179	C₂×D₄×C₅₃	—	2	2	no	—
180	C₂×D₄×C₅₃	—	4	4	no	—
181	C₂×D₄×C₅₃	—	4	2	no	—
182	C₂×D₄×C₅₃	—	4	4	no	—
183	C₂²×C₄×C₅₃	—	2	2	no	—
184	C₂²×C₄×C₅₃	—	2	2	no	—
185	C₂²×C₄×C₅₃	—	2	2	no	—
186	C₂²×C₄×C₅₃	—	2	4	no	—
187	C₂²×C₄×C₅₃	—	2	2	no	—
188	C₂²×C₄×C₅₃	—	2	2	no	—
189	C₂²×C₄×C₅₃	—	2	2	no	—
190	C₂²×C₄×C₅₃	—	2	2	no	—
191	C₂²×C₄×C₅₃	—	2	4	no	—
192	C₂²×C₄×C₅₃	—	2	4	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	—	4	2	no	—
197	C₂²×C₄×C₅₃	—	4	2	no	—
198	C₂²×C₄×C₅₃	—	4	2	no	—
199	C₂²×C₄×C₅₃	—	4	2	no	—
200	C₂²×C₄×C₅₃	—	4	2	no	—
201	C₂²×C₄×C₅₃	—	4	4	no	—
202	C₂²×C₄×C₅₃	—	4	16	no	—
203	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
206	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
218	C₄⋊C₄×C₅₃	—	2	8	no	—
219	C₄⋊C₄×C₅₃	—	2	4	no	—
220	C₄⋊C₄×C₅₃	—	2	4	no	—
221	C₄⋊C₄×C₅₃	—	2	4	no	—
222	C₄⋊C₄×C₅₃	—	2	2	no	—
223	C₄⋊C₄×C₅₃	—	2	4	no	—
224	C₄⋊C₄×C₅₃	—	2	4	no	—
225	C₄⋊C₄×C₅₃	—	2	2	no	—
226	C₄⋊C₄×C₅₃	—	2	4	no	—
227	C₄⋊C₄×C₅₃	—	2	8	no	—
228	C₄⋊C₄×C₅₃	—	4	4	no	—
229	C₄⋊C₄×C₅₃	—	4	2	no	—
230	C₄⋊C₄×C₅₃	—	4	2	no	—
231	C₄⋊C₄×C₅₃	—	4	4	no	—
232	C₄⋊C₄×C₅₃	—	4	4	no	—
233	C₄⋊C₄×C₅₃	—	4	4	no	—
234	C₄⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
235	C₄⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
236	C₂²⋊C₄×C₅₃	—	2	4	no	—
237	C₂²⋊C₄×C₅₃	—	2	4	no	—
238	C₂²⋊C₄×C₅₃	—	2	4	no	—
239	C₂²⋊C₄×C₅₃	—	2	8	no	—
240	C₂²⋊C₄×C₅₃	—	2	8	no	—
241	C₂²⋊C₄×C₅₃	—	2	8	no	—
242	C₂²⋊C₄×C₅₃	—	2	4	no	—
243	C₂²⋊C₄×C₅₃	—	2	4	no	—
244	C₂²⋊C₄×C₅₃	—	2	4	no	—
245	C₂²⋊C₄×C₅₃	—	2	4	no	—
246	C₂²⋊C₄×C₅₃	—	2	8	no	—
247	C₂²⋊C₄×C₅₃	—	4	4	no	—
248	C₂²⋊C₄×C₅₃	—	4	4	no	—
249	C₂²⋊C₄×C₅₃	—	4	4	no	—
250	C₂²⋊C₄×C₅₃	—	4	4	no	—
251	C₄²×C₅₃	—	2	4	no	—
252	C₄²×C₅₃	—	4	4	no	—
253	C₂³×C₅₃	—	2	2	no	—
254	C₂³×C₅₃	—	2	2	no	—
255	C₂³×C₅₃	—	2	8	no	—
256	C₂³×C₅₃	—	2	2	no	—
257	C₂³×C₅₃	—	2	2	no	—
258	C₂³×C₅₃	—	2	2	no	—
259	C₂³×C₅₃	—	2	2	no	—
260	C₂³×C₅₃	—	2	2	no	—
261	C₂³×C₅₃	—	2	2	no	—
262	C₂³×C₅₃	—	2	2	no	—
263	C₂³×C₅₃	—	2	4	no	—
264	C₂³×C₅₃	—	2	2	no	—
265	C₂³×C₅₃	—	2	2	no	—
266	C₂³×C₅₃	—	2	4	no	—
267	C₂³×C₅₃	—	4	8	no	—
268	C₂³×C₅₃	—	4	8	no	—
269	C₂³×C₅₃	—	4	4	no	—
270	C₂³×C₅₃	—	4	4	no	—
271	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
272	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
273	C₂³×C₅₃	2₋¹⁺⁴	1	4	yes	—
274	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
275	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
276	Q₈×C₅₃	—	4	16	no	—
277	Q₈×C₅₃	—	8	2	no	—
278	D₄×C₅₃	—	4	8	no	—
279	D₄×C₅₃	—	8	2	no	—
280	D₄×C₅₃	—	8	8	no	—
281	C₂×C₄×C₅₃	—	2	8	no	—
282	C₂×C₄×C₅₃	—	2	8	no	—
283	C₂×C₄×C₅₃	—	2	2	no	—
284	C₂×C₄×C₅₃	—	2	2	no	—
285	C₂×C₄×C₅₃	—	2	2	no	—
286	C₂×C₄×C₅₃	—	2	2	no	—
287	C₂×C₄×C₅₃	—	2	2	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	2	no	—
295	C₂×C₄×C₅₃	—	2	2	no	—
296	C₂×C₄×C₅₃	—	2	4	no	—
297	C₂×C₄×C₅₃	—	2	4	no	—
298	C₂×C₄×C₅₃	—	2	2	no	—
299	C₂×C₄×C₅₃	—	2	4	no	—
300	C₂×C₄×C₅₃	—	2	4	no	—
301	C₂×C₄×C₅₃	—	2	4	no	—
302	C₂×C₄×C₅₃	—	2	4	no	—
303	C₂×C₄×C₅₃	—	2	2	no	—
304	C₂×C₄×C₅₃	—	2	2	no	—
305	C₂×C₄×C₅₃	—	2	4	no	—
306	C₂×C₄×C₅₃	—	2	4	no	—
307	C₂×C₄×C₅₃	—	2	4	no	—
308	C₂×C₄×C₅₃	—	4	4	no	—
309	C₂×C₄×C₅₃	—	4	4	no	—
310	C₂×C₄×C₅₃	—	4	8	no	—
311	C₂×C₄×C₅₃	—	4	8	no	—
312	C₂×C₄×C₅₃	—	4	4	no	—
313	C₂×C₄×C₅₃	—	4	4	no	—
314	C₂×C₄×C₅₃	—	8	4	no	—
315	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
318	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
319	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
320	#36719	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	4	no	—
328	C₂²×C₅₃	—	4	16	no	—
329	C₂²×C₅₃	—	4	2	no	—
330	C₂²×C₅₃	—	4	2	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	4	no	—
338	C₂²×C₅₃	#537	1	4	yes	—
339	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
340	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
341	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
342	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
343	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
344	C₄×C₅₃	—	2	4	no	—
345	C₄×C₅₃	—	2	4	no	—
346	C₄×C₅₃	—	2	2	no	—
347	C₄×C₅₃	—	2	2	no	—
348	C₄×C₅₃	—	2	4	no	—
349	C₄×C₅₃	—	4	2	no	—
350	C₄×C₅₃	—	4	2	no	—
351	C₄×C₅₃	—	4	2	no	—
352	C₄×C₅₃	—	4	2	no	—
353	C₄×C₅₃	—	4	2	no	—
354	C₄×C₅₃	—	4	4	no	—
355	C₄×C₅₃	—	4	4	no	—
356	C₂×#539	C₂×C₅₃	1	1	yes	characteristic, complemented
357	C₂²×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
358	#2848	C₂×C₅₃	1	1	yes	characteristic, complemented
359	#2847	C₂×C₅₃	1	1	yes	characteristic
360	#2704	C₂×C₅₃	1	4	yes	complemented
361	#2702	C₂×C₅₃	1	4	yes	complemented
362	#2683	C₂×C₅₃	1	4	yes	complemented
363	#2681	C₂×C₅₃	1	4	yes	complemented
364	#2627	C₂×C₅₃	1	1	yes	characteristic, complemented
365	#2618	C₂×C₅₃	1	1	yes	characteristic, complemented
366	#2534	C₂×C₅₃	1	2	yes	complemented
367	#2413	C₂×C₅₃	1	2	yes	complemented
368	#2411	C₂×C₅₃	1	2	yes	complemented
369	#2409	C₂×C₅₃	1	2	yes	complemented
370	#2316	C₂×C₅₃	1	1	yes	characteristic, complemented
371	C₂×C₅₃	—	2	4	no	—
372	C₂×C₅₃	—	4	4	no	—
373	C₂×C₅₃	—	8	2	no	—
374	C₂×C₅₃	C₂×#537	1	1	yes	characteristic
375	C₂×C₅₃	#3484	1	1	yes	characteristic
376	C₂×C₅₃	#3486	1	1	yes	characteristic
377	C₂×C₅₃	#3536	1	2	yes	—
378	C₂×C₅₃	#3538	1	2	yes	—
379	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic
380	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
381	#539	—	2	8	no	—
382	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
383	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
384	C₂×#123	C₂²×C₅₃	1	2	yes	—
385	C₂×#123	C₂²×C₅₃	1	2	yes	—
386	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
387	C₂×C₂²⋊Q₈	—	2	8	no	—
388	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
389	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
390	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
391	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
392	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
393	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	complemented
394	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
395	C₂×#121	C₂²×C₅₃	1	2	yes	—
396	C₂×#120	C₂²×C₅₃	1	2	yes	—
397	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
398	C₂×#117	C₂²×C₅₃	1	2	yes	—
399	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
400	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
401	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
402	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
403	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
404	#400	C₂²×C₅₃	1	2	yes	complemented
405	#398	C₂²×C₅₃	1	2	yes	complemented
406	#398	C₂²×C₅₃	1	4	yes	complemented
407	#398	C₂²×C₅₃	1	4	yes	complemented
408	#396	C₂²×C₅₃	1	4	yes	—
409	#396	C₂²×C₅₃	1	4	yes	—
410	#396	C₂²×C₅₃	1	4	yes	complemented
411	#396	C₂²×C₅₃	1	4	yes	complemented
412	#395	C₂²×C₅₃	1	2	yes	complemented
413	#395	C₂²×C₅₃	1	4	yes	complemented
414	#394	C₂²×C₅₃	1	4	yes	—
415	#394	C₂²×C₅₃	1	4	yes	—
416	#394	C₂²×C₅₃	1	2	yes	complemented
417	#393	C₂²×C₅₃	1	4	yes	complemented
418	#391	C₂²×C₅₃	1	4	yes	complemented
419	#390	C₂²×C₅₃	1	4	yes	—
420	#389	C₂²×C₅₃	1	4	yes	complemented
421	#389	C₂²×C₅₃	1	4	yes	complemented
422	#389	C₂²×C₅₃	1	4	yes	complemented
423	#388	C₂²×C₅₃	1	4	yes	—
424	#388	C₂²×C₅₃	1	4	yes	—
425	#388	C₂²×C₅₃	1	4	yes	complemented
426	#386	C₂²×C₅₃	1	2	yes	—
427	#386	C₂²×C₅₃	1	4	yes	—
428	#386	C₂²×C₅₃	1	2	yes	—
429	#386	C₂²×C₅₃	1	4	yes	—
430	#385	C₂²×C₅₃	1	2	yes	—
431	#385	C₂²×C₅₃	1	4	yes	—
432	#385	C₂²×C₅₃	1	2	yes	—
433	#381	C₂²×C₅₃	1	2	yes	—
434	#380	C₂²×C₅₃	1	1	yes	characteristic
435	#380	C₂²×C₅₃	1	1	yes	characteristic
436	#380	C₂²×C₅₃	1	2	yes	—
437	#380	C₂²×C₅₃	1	2	yes	—
438	#380	C₂²×C₅₃	1	2	yes	—
439	#379	C₂²×C₅₃	1	2	yes	—
440	C₅₃	#36719	1	1	yes	characteristic, direct product factor, Sylow
441	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
442	C₂²×Q₈	—	2	4	no	—
443	C₂²×Q₈	—	4	4	no	—
444	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
445	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
446	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
447	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
448	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
449	C₂³×C₄	—	2	4	no	—
450	C₂³×C₄	—	4	4	no	—
451	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
454	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
455	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
458	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
460	#126	—	2	8	no	—
461	#125	—	2	8	no	—
462	#123	—	2	8	no	—
463	#123	—	2	8	no	—
464	#123	—	4	4	no	—
465	C₂²⋊Q₈	—	2	4	no	—
466	C₂²⋊Q₈	—	2	16	no	—
467	C₂²⋊Q₈	—	2	16	no	—
468	C₂²⋊Q₈	—	2	8	no	—
469	C₂²⋊Q₈	—	4	8	no	—
470	C₂²⋊Q₈	—	4	4	no	—
471	#121	—	2	4	no	—
472	#121	—	4	4	no	—
473	#120	—	4	4	no	—
474	C₄×D₄	—	2	8	no	—
475	#117	—	4	4	no	—
476	C₂×C₄⋊C₄	—	2	4	no	—
477	C₂×C₄⋊C₄	—	2	4	no	—
478	C₂×C₄⋊C₄	D₄×C₅₃	1	8	yes	complemented
479	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
485	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
497	C₂×C₂²⋊C₄	—	2	4	no	—
498	C₂×C₂²⋊C₄	—	2	4	no	—
499	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
514	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
515	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
516	#95	C₂³×C₅₃	1	4	yes	—
517	#95	C₂³×C₅₃	1	2	yes	—
518	#95	C₂³×C₅₃	1	2	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	#95	C₂³×C₅₃	1	4	yes	—
524	#95	C₂³×C₅₃	1	4	yes	—
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	4	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	4	2	no	—
530	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
531	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
532	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
533	C₂×Q₈	—	2	8	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	8	no	—
536	C₂×Q₈	—	4	4	no	—
537	C₂×Q₈	—	4	2	no	—
538	C₂×Q₈	—	4	16	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	8	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	4	4	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	4	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	4	no	—
566	C₂²×C₄	—	4	16	no	—
567	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
568	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
569	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
570	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
572	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
573	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
582	C₄⋊C₄	—	2	8	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	8	no	—
592	C₄⋊C₄	—	4	4	no	—
593	C₄⋊C₄	—	4	2	no	—
594	C₄⋊C₄	—	4	2	no	—
595	C₄⋊C₄	—	4	4	no	—
596	C₄⋊C₄	—	4	4	no	—
597	C₄⋊C₄	—	4	4	no	—
598	C₄⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
599	C₄⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	8	no	—
605	C₂²⋊C₄	—	2	8	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	8	no	—
611	C₂²⋊C₄	—	4	4	no	—
612	C₂²⋊C₄	—	4	4	no	—
613	C₂²⋊C₄	—	4	4	no	—
614	C₂²⋊C₄	—	4	4	no	—
615	C₄²	—	2	4	no	—
616	C₄²	—	4	4	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	8	no	—
620	C₂³	—	2	2	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	2	no	—
627	C₂³	—	2	4	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	4	no	—
631	C₂³	—	4	8	no	—
632	C₂³	—	4	8	no	—
633	C₂³	—	4	4	no	—
634	C₂³	—	4	4	no	—
635	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
636	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
637	C₂³	2₋¹⁺⁴×C₅₃	1	4	yes	—
638	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
639	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
640	Q₈	—	4	16	no	—
641	Q₈	—	8	2	no	—
642	D₄	—	4	8	no	—
643	D₄	—	8	2	no	—
644	D₄	—	8	8	no	—
645	C₂×C₄	—	2	8	no	—
646	C₂×C₄	—	2	8	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	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	2	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	4	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	4	4	no	—
673	C₂×C₄	—	4	4	no	—
674	C₂×C₄	—	4	8	no	—
675	C₂×C₄	—	4	8	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	4	4	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
680	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
681	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
682	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
683	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	4	16	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	4	no	—
701	C₂²	C₅₃×#537	1	4	yes	—
702	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
703	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
704	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
705	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
706	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
707	C₄	—	2	4	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	2	no	—
711	C₄	—	2	4	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	4	no	—
718	C₄	—	4	4	no	—
719	C₂	—	2	4	no	—
720	C₂	—	4	4	no	—
721	C₂	—	8	2	no	—
722	C₂	C₂×C₅₃×#537	1	1	yes	characteristic
723	C₂	C₅₃×#3484	1	1	yes	characteristic
724	C₂	C₅₃×#3486	1	1	yes	characteristic
725	C₂	C₅₃×#3536	1	2	yes	—
726	C₂	C₅₃×#3538	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₅₃×#2847	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#539	C₂	semidirect
2. C₂²×C₂²⋊Q₈×C₅₃	C₂	semidirect
3. C₅₃×#2848	C₂	semidirect
5. C₅₃×#2704	C₂	semidirect
6. C₅₃×#2702	C₂	semidirect
7. C₅₃×#2683	C₂	semidirect
8. C₅₃×#2681	C₂	semidirect
9. C₅₃×#2627	C₂	semidirect
10. C₅₃×#2618	C₂	semidirect
11. C₅₃×#2534	C₂	semidirect
12. C₅₃×#2413	C₂	semidirect
13. C₅₃×#2411	C₂	semidirect
14. C₅₃×#2409	C₂	semidirect
15. C₅₃×#2316	C₂	semidirect
19. C₂×#126×C₅₃	C₂²	semidirect
20. C₂×#125×C₅₃	C₂²	semidirect
23. C₂×#123×C₅₃	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
41. C₅₃×#400	C₂²	semidirect
42. C₅₃×#398	C₂²	semidirect
43. C₅₃×#398	C₂²	semidirect
44. C₅₃×#398	C₂²	semidirect
47. C₅₃×#396	C₂²	semidirect
48. C₅₃×#396	C₂²	semidirect
49. C₅₃×#395	C₂²	semidirect
50. C₅₃×#395	C₂²	semidirect
53. C₅₃×#394	C₂²	semidirect
54. C₅₃×#393	C₂²	semidirect
55. C₅₃×#391	C₂²	semidirect
57. C₅₃×#389	C₂²	semidirect
58. C₅₃×#389	C₂²	semidirect
59. C₅₃×#389	C₂²	semidirect
62. C₅₃×#388	C₂²	semidirect
114. C₂×C₄⋊C₄×C₅₃	D₄	semidirect
320. #36719	C₅₃	direct (N × H)
356. C₂×#539	C₂×C₅₃	semidirect
357. C₂²×C₂²⋊Q₈	C₂×C₅₃	semidirect
358. #2848	C₂×C₅₃	semidirect
360. #2704	C₂×C₅₃	semidirect
361. #2702	C₂×C₅₃	semidirect
362. #2683	C₂×C₅₃	semidirect
363. #2681	C₂×C₅₃	semidirect
364. #2627	C₂×C₅₃	semidirect
365. #2618	C₂×C₅₃	semidirect
366. #2534	C₂×C₅₃	semidirect
367. #2413	C₂×C₅₃	semidirect
368. #2411	C₂×C₅₃	semidirect
369. #2409	C₂×C₅₃	semidirect
370. #2316	C₂×C₅₃	semidirect
382. C₂×#126	C₂²×C₅₃	semidirect
383. C₂×#125	C₂²×C₅₃	semidirect
386. C₂×#123	C₂²×C₅₃	semidirect
392. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
393. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
404. #400	C₂²×C₅₃	semidirect
405. #398	C₂²×C₅₃	semidirect
406. #398	C₂²×C₅₃	semidirect
407. #398	C₂²×C₅₃	semidirect
410. #396	C₂²×C₅₃	semidirect
411. #396	C₂²×C₅₃	semidirect
412. #395	C₂²×C₅₃	semidirect
413. #395	C₂²×C₅₃	semidirect
416. #394	C₂²×C₅₃	semidirect
417. #393	C₂²×C₅₃	semidirect
418. #391	C₂²×C₅₃	semidirect
420. #389	C₂²×C₅₃	semidirect
421. #389	C₂²×C₅₃	semidirect
422. #389	C₂²×C₅₃	semidirect
425. #388	C₂²×C₅₃	semidirect
440. C₅₃	#36719	direct (N × H)
478. C₂×C₄⋊C₄	D₄×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×#539	2
C₂²×C₂²⋊Q₈×C₅₃	2
C₅₃×#2848	2
C₅₃×#2847	2
C₅₃×#2704	2
C₅₃×#2702	2
C₅₃×#2683	2
C₅₃×#2681	2
C₅₃×#2627	2
C₅₃×#2618	2
C₅₃×#2534	2
C₅₃×#2413	2
C₅₃×#2411	2
C₅₃×#2409	2
C₅₃×#2316	2
#36719	53

Subgroups — C53×#36719 #27244231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36719 #27244231