Subgroups — C₅₃×#60753 #27268265

Order 13568.

2322 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3200	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3199	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3198	C₂	1	8	yes	maximal, complemented
6	C₅₃×#3094	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3093	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3055	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3006	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3003	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
15	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	4	yes	—
16	C₂²×M₁₆×C₅₃	C₂²	1	2	yes	complemented
17	C₅₃×#537	C₂²	1	4	yes	complemented
18	C₅₃×#536	—	2	1	no	—
19	C₅₃×#536	C₂²	1	2	yes	complemented
20	C₅₃×#535	—	2	2	no	—
21	C₅₃×#535	—	2	2	no	—
22	C₅₃×#535	—	2	1	no	—
23	C₅₃×#535	C₂²	1	4	yes	—
24	C₅₃×#535	C₂²	1	4	yes	complemented
25	C₅₃×#535	C₂²	1	2	yes	complemented
26	C₅₃×#534	—	2	1	no	—
27	C₅₃×#534	—	2	1	no	—
28	C₅₃×#532	—	2	2	no	—
29	C₂×#127×C₅₃	—	2	1	no	—
30	C₂×#124×C₅₃	—	2	1	no	—
31	C₅₃×#525	—	2	2	no	—
32	C₅₃×#525	C₂²	1	2	yes	—
33	C₅₃×#525	C₂²	1	2	yes	complemented
34	C₂×#121×C₅₃	C₂²	1	2	yes	—
35	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
36	C₂×#120×C₅₃	—	2	1	no	—
37	C₂×#120×C₅₃	—	2	1	no	—
38	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#485	C₂²	1	8	yes	complemented
41	C₅₃×#482	C₂²	1	8	yes	complemented
42	C₅₃×#482	C₂²	1	8	yes	complemented
43	C₅₃×#481	C₂²	1	4	yes	complemented
44	C₅₃×#480	C₂²	1	4	yes	complemented
45	C₅₃×#469	C₂²	1	8	yes	complemented
46	C₅₃×#468	C₂²	1	8	yes	complemented
47	C₅₃×#466	C₂²	1	8	yes	complemented
48	C₅₃×#465	C₂²	1	8	yes	complemented
49	C₅₃×#450	C₂²	1	8	yes	complemented
50	C₅₃×#449	C₂²	1	8	yes	complemented
51	C₅₃×#448	C₂²	1	4	yes	complemented
52	C₅₃×#447	C₂²	1	8	yes	complemented
53	C₅₃×#447	C₂²	1	4	yes	complemented
54	C₅₃×#428	C₂²	1	4	yes	complemented
55	C₅₃×#418	C₂²	1	4	yes	complemented
56	C₅₃×#417	C₂²	1	4	yes	complemented
57	C₅₃×#408	C₂²	1	4	yes	complemented
58	C₅₃×#408	C₂²	1	4	yes	complemented
59	C₅₃×#407	C₂²	1	2	yes	complemented
60	C₅₃×#407	C₂²	1	2	yes	complemented
61	C₂⁵×C₅₃	—	2	1	no	—
62	C₂×#41×C₅₃	—	2	1	no	—
63	C₂×#41×C₅₃	—	2	1	no	—
64	C₂×#41×C₅₃	—	4	4	no	—
65	C₂×#41×C₅₃	—	4	4	no	—
66	C₂×#41×C₅₃	D₄	1	2	yes	—
67	C₂×#41×C₅₃	D₄	1	2	yes	—
68	C₂×#41×C₅₃	C₂³	1	2	yes	—
69	C₂×#41×C₅₃	C₂³	1	2	yes	—
70	C₂×#41×C₅₃	C₂³	1	2	yes	—
71	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
72	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
73	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
74	C₂²×D₄×C₅₃	—	2	1	no	—
75	C₂²×D₄×C₅₃	—	2	2	no	—
76	C₂²×D₄×C₅₃	—	2	2	no	—
77	C₂²×D₄×C₅₃	—	2	1	no	—
78	C₂²×D₄×C₅₃	—	2	2	no	—
79	C₂²×D₄×C₅₃	—	4	4	no	—
80	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
83	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
84	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
85	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
86	C₂³×C₄×C₅₃	—	2	1	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	1	yes	characteristic
90	AGL(1,ℤ/8)×C₅₃	—	4	8	no	—
91	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	—
92	C₂×D₈×C₅₃	C₂³	1	8	yes	—
93	C₂×M₁₆×C₅₃	—	4	4	no	—
94	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
95	C₂×M₁₆×C₅₃	C₂³	1	4	yes	complemented
96	C₂²×C₈×C₅₃	C₂³	1	4	yes	complemented
97	C₄⋊Q₈×C₅₃	—	2	2	no	—
98	#127×C₅₃	—	2	4	no	—
99	#127×C₅₃	—	2	4	no	—
100	#127×C₅₃	—	2	2	no	—
101	#124×C₅₃	—	2	4	no	—
102	#124×C₅₃	—	2	4	no	—
103	#124×C₅₃	—	2	2	no	—
104	#124×C₅₃	—	2	2	no	—
105	#123×C₅₃	—	2	2	no	—
106	#123×C₅₃	—	2	2	no	—
107	#123×C₅₃	—	2	2	no	—
108	#123×C₅₃	—	2	2	no	—
109	C₂²⋊Q₈×C₅₃	—	2	4	no	—
110	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
111	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
112	#121×C₅₃	—	2	4	no	—
113	#121×C₅₃	—	2	4	no	—
114	#121×C₅₃	—	2	4	no	—
115	#121×C₅₃	—	2	2	no	—
116	#121×C₅₃	—	2	2	no	—
117	#121×C₅₃	—	2	4	no	—
118	#121×C₅₃	C₂³	1	4	yes	—
119	#121×C₅₃	C₂³	1	4	yes	—
120	#121×C₅₃	C₂³	1	8	yes	—
121	#121×C₅₃	C₂³	1	4	yes	—
122	#121×C₅₃	C₂³	1	4	yes	complemented
123	#120×C₅₃	—	2	2	no	—
124	#120×C₅₃	—	2	2	no	—
125	#120×C₅₃	—	2	4	no	—
126	#120×C₅₃	—	2	4	no	—
127	#120×C₅₃	—	2	4	no	—
128	#120×C₅₃	—	2	4	no	—
129	#120×C₅₃	—	2	2	no	—
130	#120×C₅₃	—	2	2	no	—
131	C₄×D₄×C₅₃	—	2	4	no	—
132	C₄×D₄×C₅₃	—	2	4	no	—
133	#117×C₅₃	—	2	1	no	—
134	#117×C₅₃	—	2	2	no	—
135	#117×C₅₃	—	2	1	no	—
136	#117×C₅₃	C₂³	1	4	yes	—
137	#117×C₅₃	C₂³	1	2	yes	—
138	#117×C₅₃	C₂³	1	2	yes	complemented
139	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
141	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
144	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
145	C₂×C₄²×C₅₃	—	2	1	no	—
146	C₂×C₄²×C₅₃	—	2	1	no	—
147	#107×C₅₃	C₂³	1	8	yes	complemented
148	#106×C₅₃	C₂³	1	8	yes	complemented
149	#103×C₅₃	C₂³	1	8	yes	complemented
150	#102×C₅₃	C₂³	1	8	yes	—
151	#102×C₅₃	C₂³	1	8	yes	—
152	#102×C₅₃	C₂³	1	8	yes	complemented
153	C₂²⋊C₈×C₅₃	C₂³	1	8	yes	—
154	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
155	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
156	C₂⁴×C₅₃	—	2	2	no	—
157	C₂⁴×C₅₃	—	2	1	no	—
158	C₂⁴×C₅₃	—	2	4	no	—
159	C₂⁴×C₅₃	—	4	4	no	—
160	C₂⁴×C₅₃	—	8	4	no	—
161	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
162	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
163	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
164	#41×C₅₃	—	2	8	no	—
165	#41×C₅₃	—	4	4	no	—
166	#41×C₅₃	—	4	4	no	—
167	#41×C₅₃	—	4	2	no	—
168	#41×C₅₃	—	4	2	no	—
169	#41×C₅₃	—	4	2	no	—
170	#41×C₅₃	—	4	2	no	—
171	#41×C₅₃	—	4	4	no	—
172	#41×C₅₃	—	4	4	no	—
173	#41×C₅₃	—	4	4	no	—
174	C₂×Q₈×C₅₃	—	2	1	no	—
175	C₂×Q₈×C₅₃	—	4	2	no	—
176	C₂×Q₈×C₅₃	—	4	2	no	—
177	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
178	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
179	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
180	C₂×D₄×C₅₃	—	2	2	no	—
181	C₂×D₄×C₅₃	—	2	2	no	—
182	C₂×D₄×C₅₃	—	2	4	no	—
183	C₂×D₄×C₅₃	—	2	4	no	—
184	C₂×D₄×C₅₃	—	2	4	no	—
185	C₂×D₄×C₅₃	—	2	4	no	—
186	C₂×D₄×C₅₃	—	2	8	no	—
187	C₂×D₄×C₅₃	—	2	2	no	—
188	C₂×D₄×C₅₃	—	2	4	no	—
189	C₂×D₄×C₅₃	—	2	1	no	—
190	C₂×D₄×C₅₃	—	2	8	no	—
191	C₂×D₄×C₅₃	—	4	4	no	—
192	C₂×D₄×C₅₃	—	4	4	no	—
193	C₂×D₄×C₅₃	—	4	2	no	—
194	C₂×D₄×C₅₃	—	4	2	no	—
195	C₂×D₄×C₅₃	—	4	2	no	—
196	C₂×D₄×C₅₃	—	4	2	no	—
197	C₂×D₄×C₅₃	—	4	4	no	—
198	C₂×D₄×C₅₃	—	4	8	no	—
199	C₂×D₄×C₅₃	—	4	4	no	—
200	C₂×D₄×C₅₃	—	8	4	no	—
201	C₂×D₄×C₅₃	—	8	4	no	—
202	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
203	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
205	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
206	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
207	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
209	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₅₃	—	2	4	no	—
211	C₂²×C₄×C₅₃	—	2	4	no	—
212	C₂²×C₄×C₅₃	—	2	4	no	—
213	C₂²×C₄×C₅₃	—	2	2	no	—
214	C₂²×C₄×C₅₃	—	2	1	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	—	4	4	no	—
219	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
231	SD₁₆×C₅₃	—	4	8	no	—
232	D₈×C₅₃	—	4	8	no	—
233	M₁₆×C₅₃	—	2	8	no	—
234	M₁₆×C₅₃	—	4	4	no	—
235	C₂×C₈×C₅₃	—	4	4	no	—
236	C₂×C₈×C₅₃	C₂⁴	1	8	yes	—
237	C₄⋊C₄×C₅₃	—	2	2	no	—
238	C₄⋊C₄×C₅₃	—	2	2	no	—
239	C₄⋊C₄×C₅₃	—	2	4	no	—
240	C₄⋊C₄×C₅₃	—	2	4	no	—
241	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
242	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
243	C₂²⋊C₄×C₅₃	—	2	4	no	—
244	C₂²⋊C₄×C₅₃	—	2	2	no	—
245	C₂²⋊C₄×C₅₃	—	2	2	no	—
246	C₂²⋊C₄×C₅₃	—	2	4	no	—
247	C₂²⋊C₄×C₅₃	—	2	4	no	—
248	C₂²⋊C₄×C₅₃	—	2	4	no	—
249	C₂²⋊C₄×C₅₃	—	2	4	no	—
250	C₂²⋊C₄×C₅₃	—	2	8	no	—
251	C₂²⋊C₄×C₅₃	—	2	4	no	—
252	C₂²⋊C₄×C₅₃	—	2	4	no	—
253	C₄²×C₅₃	—	2	2	no	—
254	C₄²×C₅₃	—	2	4	no	—
255	C₄²×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	2	no	—
260	C₂³×C₅₃	—	2	4	no	—
261	C₂³×C₅₃	—	4	2	no	—
262	C₂³×C₅₃	—	4	2	no	—
263	C₂³×C₅₃	—	4	2	no	—
264	C₂³×C₅₃	—	4	2	no	—
265	C₂³×C₅₃	—	4	8	no	—
266	C₂³×C₅₃	—	4	4	no	—
267	C₂³×C₅₃	—	4	4	no	—
268	C₂³×C₅₃	—	4	4	no	—
269	C₂³×C₅₃	—	8	2	no	—
270	C₂³×C₅₃	—	8	8	no	—
271	C₂³×C₅₃	—	8	16	no	—
272	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
273	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
274	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
275	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
276	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
277	Q₈×C₅₃	—	2	4	no	—
278	Q₈×C₅₃	—	4	2	no	—
279	Q₈×C₅₃	—	4	2	no	—
280	Q₈×C₅₃	—	4	2	no	—
281	D₄×C₅₃	—	2	8	no	—
282	D₄×C₅₃	—	2	4	no	—
283	D₄×C₅₃	—	4	2	no	—
284	D₄×C₅₃	—	4	2	no	—
285	D₄×C₅₃	—	4	2	no	—
286	D₄×C₅₃	—	4	2	no	—
287	D₄×C₅₃	—	4	2	no	—
288	D₄×C₅₃	—	4	2	no	—
289	D₄×C₅₃	—	4	8	no	—
290	D₄×C₅₃	—	4	2	no	—
291	D₄×C₅₃	—	4	4	no	—
292	D₄×C₅₃	—	4	4	no	—
293	D₄×C₅₃	—	4	4	no	—
294	D₄×C₅₃	—	8	4	no	—
295	D₄×C₅₃	—	8	4	no	—
296	D₄×C₅₃	—	8	4	no	—
297	D₄×C₅₃	—	8	8	no	—
298	D₄×C₅₃	—	8	4	no	—
299	C₂×C₄×C₅₃	—	2	2	no	—
300	C₂×C₄×C₅₃	—	2	2	no	—
301	C₂×C₄×C₅₃	—	2	2	no	—
302	C₂×C₄×C₅₃	—	2	2	no	—
303	C₂×C₄×C₅₃	—	2	4	no	—
304	C₂×C₄×C₅₃	—	2	4	no	—
305	C₂×C₄×C₅₃	—	2	2	no	—
306	C₂×C₄×C₅₃	—	2	2	no	—
307	C₂×C₄×C₅₃	—	2	2	no	—
308	C₂×C₄×C₅₃	—	2	2	no	—
309	C₂×C₄×C₅₃	—	2	2	no	—
310	C₂×C₄×C₅₃	—	2	2	no	—
311	C₂×C₄×C₅₃	—	2	2	no	—
312	C₂×C₄×C₅₃	—	2	2	no	—
313	C₂×C₄×C₅₃	—	2	4	no	—
314	C₂×C₄×C₅₃	—	2	4	no	—
315	C₂×C₄×C₅₃	—	4	4	no	—
316	C₂×C₄×C₅₃	—	4	2	no	—
317	C₂×C₄×C₅₃	—	4	4	no	—
318	C₂×C₄×C₅₃	—	4	4	no	—
319	C₂×C₄×C₅₃	—	8	2	no	—
320	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
326	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
327	C₈×C₅₃	—	2	8	no	—
328	#60753	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂²×C₅₃	—	2	2	no	—
330	C₂²×C₅₃	—	2	2	no	—
331	C₂²×C₅₃	—	2	4	no	—
332	C₂²×C₅₃	—	2	2	no	—
333	C₂²×C₅₃	—	2	4	no	—
334	C₂²×C₅₃	—	2	1	no	—
335	C₂²×C₅₃	—	2	1	no	—
336	C₂²×C₅₃	—	2	2	no	—
337	C₂²×C₅₃	—	2	2	no	—
338	C₂²×C₅₃	—	4	4	no	—
339	C₂²×C₅₃	—	4	4	no	—
340	C₂²×C₅₃	—	4	4	no	—
341	C₂²×C₅₃	—	4	4	no	—
342	C₂²×C₅₃	—	4	2	no	—
343	C₂²×C₅₃	—	4	4	no	—
344	C₂²×C₅₃	—	8	2	no	—
345	C₂²×C₅₃	—	8	2	no	—
346	C₂²×C₅₃	—	8	8	no	—
347	C₂²×C₅₃	—	8	4	no	—
348	C₂²×C₅₃	—	8	16	no	—
349	C₂²×C₅₃	#534	1	2	yes	—
350	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
351	C₄×C₅₃	—	2	1	no	—
352	C₄×C₅₃	—	2	2	no	—
353	C₄×C₅₃	—	2	1	no	—
354	C₄×C₅₃	—	2	2	no	—
355	C₄×C₅₃	—	4	4	no	—
356	C₄×C₅₃	—	4	4	no	—
357	C₄×C₅₃	—	4	2	no	—
358	C₄×C₅₃	#534	1	2	yes	—
359	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
360	#3449	C₂×C₅₃	1	1	yes	characteristic, complemented
361	C₂×#535	C₂×C₅₃	1	1	yes	characteristic, complemented
362	#3200	C₂×C₅₃	1	4	yes	complemented
363	#3199	C₂×C₅₃	1	4	yes	complemented
364	#3198	C₂×C₅₃	1	8	yes	complemented
365	#3094	C₂×C₅₃	1	2	yes	complemented
366	#3093	C₂×C₅₃	1	2	yes	complemented
367	#3055	C₂×C₅₃	1	4	yes	complemented
368	#3006	C₂×C₅₃	1	2	yes	complemented
369	#3003	C₂×C₅₃	1	2	yes	complemented
370	#2879	C₂×C₅₃	1	1	yes	characteristic, complemented
371	C₂×C₅₃	—	2	2	no	—
372	C₂×C₅₃	—	4	2	no	—
373	C₂×C₅₃	—	4	1	no	—
374	C₂×C₅₃	—	4	2	no	—
375	C₂×C₅₃	—	4	1	no	—
376	C₂×C₅₃	—	8	2	no	—
377	C₂×C₅₃	—	8	4	no	—
378	C₂×C₅₃	C₂×#534	1	1	yes	characteristic
379	C₂×C₅₃	#3585	1	2	yes	—
380	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
381	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
382	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
383	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	4	yes	—
384	C₂²×M₁₆	C₂²×C₅₃	1	2	yes	complemented
385	#537	C₂²×C₅₃	1	4	yes	complemented
386	#536	—	2	1	no	—
387	#536	C₂²×C₅₃	1	2	yes	complemented
388	#535	—	2	2	no	—
389	#535	—	2	2	no	—
390	#535	—	2	1	no	—
391	#535	C₂²×C₅₃	1	4	yes	—
392	#535	C₂²×C₅₃	1	4	yes	complemented
393	#535	C₂²×C₅₃	1	2	yes	complemented
394	#534	—	2	1	no	—
395	#534	—	2	1	no	—
396	#532	—	2	2	no	—
397	C₂×#127	—	2	1	no	—
398	C₂×#124	—	2	1	no	—
399	#525	—	2	2	no	—
400	#525	C₂²×C₅₃	1	2	yes	—
401	#525	C₂²×C₅₃	1	2	yes	complemented
402	C₂×#121	C₂²×C₅₃	1	2	yes	—
403	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
404	C₂×#120	—	2	1	no	—
405	C₂×#120	—	2	1	no	—
406	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
407	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
408	#485	C₂²×C₅₃	1	8	yes	complemented
409	#482	C₂²×C₅₃	1	8	yes	complemented
410	#482	C₂²×C₅₃	1	8	yes	complemented
411	#481	C₂²×C₅₃	1	4	yes	complemented
412	#480	C₂²×C₅₃	1	4	yes	complemented
413	#469	C₂²×C₅₃	1	8	yes	complemented
414	#468	C₂²×C₅₃	1	8	yes	complemented
415	#466	C₂²×C₅₃	1	8	yes	complemented
416	#465	C₂²×C₅₃	1	8	yes	complemented
417	#450	C₂²×C₅₃	1	8	yes	complemented
418	#449	C₂²×C₅₃	1	8	yes	complemented
419	#448	C₂²×C₅₃	1	4	yes	complemented
420	#447	C₂²×C₅₃	1	8	yes	complemented
421	#447	C₂²×C₅₃	1	4	yes	complemented
422	#428	C₂²×C₅₃	1	4	yes	complemented
423	#418	C₂²×C₅₃	1	4	yes	complemented
424	#417	C₂²×C₅₃	1	4	yes	complemented
425	#408	C₂²×C₅₃	1	4	yes	complemented
426	#408	C₂²×C₅₃	1	4	yes	complemented
427	#407	C₂²×C₅₃	1	2	yes	complemented
428	#407	C₂²×C₅₃	1	2	yes	complemented
429	C₅₃	#60753	1	1	yes	characteristic, direct product factor, Sylow
430	C₂⁵	—	2	1	no	—
431	C₂×#41	—	2	1	no	—
432	C₂×#41	—	2	1	no	—
433	C₂×#41	—	4	4	no	—
434	C₂×#41	—	4	4	no	—
435	C₂×#41	D₄×C₅₃	1	2	yes	—
436	C₂×#41	D₄×C₅₃	1	2	yes	—
437	C₂×#41	C₂³×C₅₃	1	2	yes	—
438	C₂×#41	C₂³×C₅₃	1	2	yes	—
439	C₂×#41	C₂³×C₅₃	1	2	yes	—
440	C₂×#41	C₂³×C₅₃	1	2	yes	complemented
441	C₂²×Q₈	D₄×C₅₃	1	1	yes	characteristic
442	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
443	C₂²×D₄	—	2	1	no	—
444	C₂²×D₄	—	2	2	no	—
445	C₂²×D₄	—	2	2	no	—
446	C₂²×D₄	—	2	1	no	—
447	C₂²×D₄	—	2	2	no	—
448	C₂²×D₄	—	4	4	no	—
449	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
450	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
451	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
452	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
453	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
454	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
455	C₂³×C₄	—	2	1	no	—
456	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
459	AGL(1,ℤ/8)	—	4	8	no	—
460	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	—
461	C₂×D₈	C₂³×C₅₃	1	8	yes	—
462	C₂×M₁₆	—	4	4	no	—
463	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
464	C₂×M₁₆	C₂³×C₅₃	1	4	yes	complemented
465	C₂²×C₈	C₂³×C₅₃	1	4	yes	complemented
466	C₄⋊Q₈	—	2	2	no	—
467	#127	—	2	4	no	—
468	#127	—	2	4	no	—
469	#127	—	2	2	no	—
470	#124	—	2	4	no	—
471	#124	—	2	4	no	—
472	#124	—	2	2	no	—
473	#124	—	2	2	no	—
474	#123	—	2	2	no	—
475	#123	—	2	2	no	—
476	#123	—	2	2	no	—
477	#123	—	2	2	no	—
478	C₂²⋊Q₈	—	2	4	no	—
479	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
480	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	complemented
481	#121	—	2	4	no	—
482	#121	—	2	4	no	—
483	#121	—	2	4	no	—
484	#121	—	2	2	no	—
485	#121	—	2	2	no	—
486	#121	—	2	4	no	—
487	#121	C₂³×C₅₃	1	4	yes	—
488	#121	C₂³×C₅₃	1	4	yes	—
489	#121	C₂³×C₅₃	1	8	yes	—
490	#121	C₂³×C₅₃	1	4	yes	—
491	#121	C₂³×C₅₃	1	4	yes	complemented
492	#120	—	2	2	no	—
493	#120	—	2	2	no	—
494	#120	—	2	4	no	—
495	#120	—	2	4	no	—
496	#120	—	2	4	no	—
497	#120	—	2	4	no	—
498	#120	—	2	2	no	—
499	#120	—	2	2	no	—
500	C₄×D₄	—	2	4	no	—
501	C₄×D₄	—	2	4	no	—
502	#117	—	2	1	no	—
503	#117	—	2	2	no	—
504	#117	—	2	1	no	—
505	#117	C₂³×C₅₃	1	2	yes	—
506	#117	C₂³×C₅₃	1	4	yes	—
507	#117	C₂³×C₅₃	1	2	yes	complemented
508	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	2	no	—
513	C₂×C₂²⋊C₄	—	2	2	no	—
514	C₂×C₄²	—	2	1	no	—
515	C₂×C₄²	—	2	1	no	—
516	#107	C₂³×C₅₃	1	8	yes	complemented
517	#106	C₂³×C₅₃	1	8	yes	complemented
518	#103	C₂³×C₅₃	1	8	yes	complemented
519	#102	C₂³×C₅₃	1	8	yes	—
520	#102	C₂³×C₅₃	1	8	yes	—
521	#102	C₂³×C₅₃	1	8	yes	complemented
522	C₂²⋊C₈	C₂³×C₅₃	1	8	yes	—
523	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
524	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	1	no	—
527	C₂⁴	—	2	4	no	—
528	C₂⁴	—	4	4	no	—
529	C₂⁴	—	8	4	no	—
530	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
531	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
532	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
533	#41	—	2	8	no	—
534	#41	—	4	4	no	—
535	#41	—	4	4	no	—
536	#41	—	4	2	no	—
537	#41	—	4	2	no	—
538	#41	—	4	2	no	—
539	#41	—	4	2	no	—
540	#41	—	4	4	no	—
541	#41	—	4	4	no	—
542	#41	—	4	4	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	4	2	no	—
545	C₂×Q₈	—	4	2	no	—
546	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
547	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
548	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	2	8	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	8	no	—
560	C₂×D₄	—	4	4	no	—
561	C₂×D₄	—	4	4	no	—
562	C₂×D₄	—	4	2	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	—	4	8	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	8	4	no	—
570	C₂×D₄	—	8	4	no	—
571	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
572	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
573	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
574	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
575	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
576	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
577	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
578	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
593	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
600	SD₁₆	—	4	8	no	—
601	D₈	—	4	8	no	—
602	M₁₆	—	2	8	no	—
603	M₁₆	—	4	4	no	—
604	C₂×C₈	—	4	4	no	—
605	C₂×C₈	C₂⁴×C₅₃	1	8	yes	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
611	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	8	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₄²	—	2	2	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	4	no	—
630	C₂³	—	4	2	no	—
631	C₂³	—	4	2	no	—
632	C₂³	—	4	2	no	—
633	C₂³	—	4	2	no	—
634	C₂³	—	4	8	no	—
635	C₂³	—	4	4	no	—
636	C₂³	—	4	4	no	—
637	C₂³	—	4	4	no	—
638	C₂³	—	8	2	no	—
639	C₂³	—	8	8	no	—
640	C₂³	—	8	16	no	—
641	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
642	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
643	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
644	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
645	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
646	Q₈	—	2	4	no	—
647	Q₈	—	4	2	no	—
648	Q₈	—	4	2	no	—
649	Q₈	—	4	2	no	—
650	D₄	—	2	4	no	—
651	D₄	—	2	8	no	—
652	D₄	—	4	2	no	—
653	D₄	—	4	2	no	—
654	D₄	—	4	2	no	—
655	D₄	—	4	2	no	—
656	D₄	—	4	2	no	—
657	D₄	—	4	2	no	—
658	D₄	—	4	8	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	4	no	—
661	D₄	—	4	4	no	—
662	D₄	—	4	4	no	—
663	D₄	—	8	4	no	—
664	D₄	—	8	4	no	—
665	D₄	—	8	4	no	—
666	D₄	—	8	8	no	—
667	D₄	—	8	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	8	2	no	—
689	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
692	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
694	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
695	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
696	C₈	—	2	8	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	4	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	4	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	4	4	no	—
707	C₂²	—	4	4	no	—
708	C₂²	—	4	4	no	—
709	C₂²	—	4	4	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	4	no	—
712	C₂²	—	8	2	no	—
713	C₂²	—	8	2	no	—
714	C₂²	—	8	8	no	—
715	C₂²	—	8	16	no	—
716	C₂²	—	8	4	no	—
717	C₂²	C₅₃×#534	1	2	yes	—
718	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
719	C₄	—	2	1	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	1	no	—
722	C₄	—	2	2	no	—
723	C₄	—	4	4	no	—
724	C₄	—	4	4	no	—
725	C₄	—	4	2	no	—
726	C₄	C₅₃×#534	1	2	yes	—
727	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
728	C₂	—	2	2	no	—
729	C₂	—	4	2	no	—
730	C₂	—	4	1	no	—
731	C₂	—	4	1	no	—
732	C₂	—	4	2	no	—
733	C₂	—	8	4	no	—
734	C₂	—	8	2	no	—
735	C₂	C₂×C₅₃×#534	1	1	yes	characteristic
736	C₂	C₅₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂²×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3449	C₂	semidirect
2. C₂×C₅₃×#535	C₂	semidirect
3. C₅₃×#3200	C₂	semidirect
4. C₅₃×#3199	C₂	semidirect
5. C₅₃×#3198	C₂	semidirect
6. C₅₃×#3094	C₂	semidirect
7. C₅₃×#3093	C₂	semidirect
8. C₅₃×#3055	C₂	semidirect
9. C₅₃×#3006	C₂	semidirect
10. C₅₃×#3003	C₂	semidirect
11. C₅₃×#2879	C₂	semidirect
13. C₂²×#41×C₅₃	C₂²	semidirect
14. C₂³×D₄×C₅₃	C₂²	semidirect
16. C₂²×M₁₆×C₅₃	C₂²	semidirect
17. C₅₃×#537	C₂²	semidirect
19. C₅₃×#536	C₂²	semidirect
24. C₅₃×#535	C₂²	semidirect
25. C₅₃×#535	C₂²	semidirect
33. C₅₃×#525	C₂²	semidirect
35. C₂×#121×C₅₃	C₂²	semidirect
38. C₂×#117×C₅₃	C₂²	semidirect
39. C₂×#117×C₅₃	C₂²	semidirect
40. C₅₃×#485	C₂²	semidirect
41. C₅₃×#482	C₂²	semidirect
42. C₅₃×#482	C₂²	semidirect
43. C₅₃×#481	C₂²	semidirect
44. C₅₃×#480	C₂²	semidirect
45. C₅₃×#469	C₂²	semidirect
46. C₅₃×#468	C₂²	semidirect
47. C₅₃×#466	C₂²	semidirect
48. C₅₃×#465	C₂²	semidirect
49. C₅₃×#450	C₂²	semidirect
50. C₅₃×#449	C₂²	semidirect
51. C₅₃×#448	C₂²	semidirect
52. C₅₃×#447	C₂²	semidirect
53. C₅₃×#447	C₂²	semidirect
54. C₅₃×#428	C₂²	semidirect
55. C₅₃×#418	C₂²	semidirect
56. C₅₃×#417	C₂²	semidirect
57. C₅₃×#408	C₂²	semidirect
58. C₅₃×#408	C₂²	semidirect
59. C₅₃×#407	C₂²	semidirect
60. C₅₃×#407	C₂²	semidirect
71. C₂×#41×C₅₃	C₂³	semidirect
73. C₂²×Q₈×C₅₃	C₂³	semidirect
85. C₂²×D₄×C₅₃	C₂³	semidirect
95. C₂×M₁₆×C₅₃	C₂³	semidirect
96. C₂²×C₈×C₅₃	C₂³	semidirect
111. C₂²⋊Q₈×C₅₃	C₂³	semidirect
122. #121×C₅₃	C₂³	semidirect
138. #117×C₅₃	C₂³	semidirect
140. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
147. #107×C₅₃	C₂³	semidirect
148. #106×C₅₃	C₂³	semidirect
149. #103×C₅₃	C₂³	semidirect
152. #102×C₅₃	C₂³	semidirect
154. C₂²⋊C₈×C₅₃	C₂³	semidirect
155. C₂²⋊C₈×C₅₃	C₂³	semidirect
328. #60753	C₅₃	direct (N × H)
360. #3449	C₂×C₅₃	semidirect
361. C₂×#535	C₂×C₅₃	semidirect
362. #3200	C₂×C₅₃	semidirect
363. #3199	C₂×C₅₃	semidirect
364. #3198	C₂×C₅₃	semidirect
365. #3094	C₂×C₅₃	semidirect
366. #3093	C₂×C₅₃	semidirect
367. #3055	C₂×C₅₃	semidirect
368. #3006	C₂×C₅₃	semidirect
369. #3003	C₂×C₅₃	semidirect
370. #2879	C₂×C₅₃	semidirect
381. C₂²×#41	C₂²×C₅₃	semidirect
382. C₂³×D₄	C₂²×C₅₃	semidirect
384. C₂²×M₁₆	C₂²×C₅₃	semidirect
385. #537	C₂²×C₅₃	semidirect
387. #536	C₂²×C₅₃	semidirect
392. #535	C₂²×C₅₃	semidirect
393. #535	C₂²×C₅₃	semidirect
401. #525	C₂²×C₅₃	semidirect
403. C₂×#121	C₂²×C₅₃	semidirect
406. C₂×#117	C₂²×C₅₃	semidirect
407. C₂×#117	C₂²×C₅₃	semidirect
408. #485	C₂²×C₅₃	semidirect
409. #482	C₂²×C₅₃	semidirect
410. #482	C₂²×C₅₃	semidirect
411. #481	C₂²×C₅₃	semidirect
412. #480	C₂²×C₅₃	semidirect
413. #469	C₂²×C₅₃	semidirect
414. #468	C₂²×C₅₃	semidirect
415. #466	C₂²×C₅₃	semidirect
416. #465	C₂²×C₅₃	semidirect
417. #450	C₂²×C₅₃	semidirect
418. #449	C₂²×C₅₃	semidirect
419. #448	C₂²×C₅₃	semidirect
420. #447	C₂²×C₅₃	semidirect
421. #447	C₂²×C₅₃	semidirect
422. #428	C₂²×C₅₃	semidirect
423. #418	C₂²×C₅₃	semidirect
424. #417	C₂²×C₅₃	semidirect
425. #408	C₂²×C₅₃	semidirect
426. #408	C₂²×C₅₃	semidirect
427. #407	C₂²×C₅₃	semidirect
428. #407	C₂²×C₅₃	semidirect
429. C₅₃	#60753	direct (N × H)
440. C₂×#41	C₂³×C₅₃	semidirect
442. C₂²×Q₈	C₂³×C₅₃	semidirect
454. C₂²×D₄	C₂³×C₅₃	semidirect
464. C₂×M₁₆	C₂³×C₅₃	semidirect
465. C₂²×C₈	C₂³×C₅₃	semidirect
480. C₂²⋊Q₈	C₂³×C₅₃	semidirect
491. #121	C₂³×C₅₃	semidirect
507. #117	C₂³×C₅₃	semidirect
509. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
516. #107	C₂³×C₅₃	semidirect
517. #106	C₂³×C₅₃	semidirect
518. #103	C₂³×C₅₃	semidirect
521. #102	C₂³×C₅₃	semidirect
523. C₂²⋊C₈	C₂³×C₅₃	semidirect
524. C₂²⋊C₈	C₂³×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3449	2
C₂×C₅₃×#535	2
C₅₃×#3200	2
C₅₃×#3199	2
C₅₃×#3198	2
C₅₃×#3094	2
C₅₃×#3093	2
C₅₃×#3055	2
C₅₃×#3006	2
C₅₃×#3003	2
C₅₃×#2879	2
#60753	53

Subgroups — C53×#60753 #27268265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60753 #27268265