Subgroups — C₅₃×#60711 #27268223

Order 13568.

1846 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3495	C₂	1	2	yes	maximal, complemented
2	C₅₃×#3185	C₂	1	2	yes	maximal, complemented
3	C₅₃×#3183	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3178	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3177	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3173	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3172	C₂	1	4	yes	maximal, complemented
8	C₅₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3137	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3056	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3054	C₂	1	1	yes	maximal, characteristic
13	C₂×C₅₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2947	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₅₃	C₂²	1	2	yes	—
19	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
23	C₅₃×#556	—	2	2	no	—
24	C₅₃×#554	—	2	2	no	—
25	C₅₃×#552	—	2	2	no	—
26	C₅₃×#552	—	2	4	no	—
27	C₅₃×#552	—	2	2	no	—
28	C₅₃×#551	—	2	4	no	—
29	C₅₃×#544	C₂²	1	2	yes	—
30	C₅₃×#542	C₂²	1	4	yes	—
31	C₅₃×#541	C₂²	1	4	yes	—
32	C₅₃×#536	C₂²	1	2	yes	—
33	C₅₃×#533	C₂²	1	4	yes	—
34	C₅₃×#529	C₂²	1	4	yes	—
35	C₅₃×#525	C₂²	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
37	C₅₃×#520	C₂²	1	2	yes	—
38	C₅₃×#519	C₂²	1	2	yes	—
39	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#501	C₂²	1	4	yes	complemented
41	C₅₃×#499	C₂²	1	2	yes	complemented
42	C₅₃×#498	C₂²	1	2	yes	complemented
43	C₅₃×#497	C₂²	1	4	yes	complemented
44	C₅₃×#495	C₂²	1	2	yes	complemented
45	C₅₃×#494	C₂²	1	2	yes	complemented
46	C₅₃×#491	C₂²	1	4	yes	complemented
47	C₅₃×#489	C₂²	1	4	yes	complemented
48	C₅₃×#488	C₂²	1	4	yes	complemented
49	C₅₃×#487	C₂²	1	4	yes	complemented
50	C₅₃×#470	C₂²	1	2	yes	—
51	C₅₃×#470	C₂²	1	2	yes	—
52	C₅₃×#470	C₂²	1	2	yes	—
53	C₅₃×#470	C₂²	1	2	yes	—
54	C₅₃×#470	C₂²	1	1	yes	characteristic
55	C₅₃×#470	C₂²	1	1	yes	characteristic
56	C₅₃×#470	C₂²	1	4	yes	—
57	C₅₃×#469	C₂²	1	1	yes	characteristic
58	C₅₃×#469	C₂²	1	1	yes	characteristic
59	C₅₃×#468	C₂²	1	2	yes	—
60	C₅₃×#468	C₂²	1	2	yes	—
61	C₅₃×#468	C₂²	1	4	yes	—
62	C₅₃×#467	C₂²	1	4	yes	—
63	C₅₃×#465	C₂²	1	4	yes	—
64	C₅₃×#442	C₂²	1	2	yes	complemented
65	C₅₃×#441	C₂²	1	4	yes	complemented
66	C₅₃×#441	C₂²	1	2	yes	complemented
67	C₅₃×#441	C₂²	1	2	yes	complemented
68	C₅₃×#441	C₂²	1	2	yes	complemented
69	C₅₃×#440	C₂²	1	4	yes	complemented
70	C₄×Q₁₆×C₅₃	C₂²	1	4	yes	complemented
71	C₄×Q₁₆×C₅₃	C₂²	1	4	yes	complemented
72	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	complemented
73	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	complemented
74	C₅₃×#428	C₂²	1	2	yes	—
75	C₅₃×#427	C₂²	1	1	yes	characteristic
76	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
77	C₅₃×#419	C₂²	1	2	yes	—
78	C₅₃×#417	C₂²	1	2	yes	—
79	C₅₃×#416	C₂²	1	2	yes	—
80	C₂×#103×C₅₃	C₂²	1	2	yes	—
81	C₅₃×#405	C₂²	1	1	yes	characteristic
82	C₅₃×#405	C₂²	1	1	yes	characteristic
83	C₅₃×#405	C₂²	1	1	yes	characteristic
84	C₅₃×#405	C₂²	1	1	yes	characteristic
85	C₅₃×#405	C₂²	1	2	yes	—
86	C₅₃×#405	C₂²	1	2	yes	—
87	C₄×M₁₆×C₅₃	C₂²	1	2	yes	—
88	C₄×M₁₆×C₅₃	C₂²	1	2	yes	—
89	C₂×#41×C₅₃	C₂³	1	2	yes	—
90	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
92	#137×C₅₃	—	2	8	no	—
93	#135×C₅₃	—	2	4	no	—
94	C₂×Q₁₆×C₅₃	—	2	4	no	—
95	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
96	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
98	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
99	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
101	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₅₃	—	2	4	no	—
103	C₂×M₁₆×C₅₃	—	2	4	no	—
104	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
106	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
110	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₅₃	—	2	2	no	—
115	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
116	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
117	#126×C₅₃	—	2	4	no	—
118	#126×C₅₃	—	2	4	no	—
119	#126×C₅₃	—	2	4	no	—
120	#126×C₅₃	—	2	4	no	—
121	#125×C₅₃	—	2	4	no	—
122	#125×C₅₃	—	2	4	no	—
123	#125×C₅₃	—	2	2	no	—
124	#125×C₅₃	—	2	4	no	—
125	#125×C₅₃	C₂³	1	4	yes	—
126	#124×C₅₃	—	2	4	no	—
127	#124×C₅₃	C₂³	1	4	yes	—
128	#123×C₅₃	—	2	4	no	—
129	#123×C₅₃	—	2	4	no	—
130	#123×C₅₃	—	2	2	no	—
131	#123×C₅₃	—	2	4	no	—
132	C₂²⋊Q₈×C₅₃	—	2	2	no	—
133	C₂²⋊Q₈×C₅₃	—	2	2	no	—
134	C₂²⋊Q₈×C₅₃	—	2	4	no	—
135	C₂²⋊Q₈×C₅₃	—	2	4	no	—
136	C₂²⋊Q₈×C₅₃	—	2	2	no	—
137	C₂²⋊Q₈×C₅₃	—	2	2	no	—
138	C₂²⋊Q₈×C₅₃	—	2	4	no	—
139	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
140	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
141	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
142	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
143	#121×C₅₃	C₂³	1	2	yes	—
144	#121×C₅₃	C₂³	1	2	yes	—
145	#120×C₅₃	—	2	2	no	—
146	C₄×Q₈×C₅₃	—	2	2	no	—
147	C₄×Q₈×C₅₃	—	2	2	no	—
148	C₄×Q₈×C₅₃	—	2	4	no	—
149	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
150	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
151	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
152	C₄×D₄×C₅₃	—	2	4	no	—
153	C₄×D₄×C₅₃	—	2	2	no	—
154	C₄×D₄×C₅₃	—	2	2	no	—
155	C₄×D₄×C₅₃	—	2	4	no	—
156	C₄×D₄×C₅₃	C₂³	1	4	yes	—
157	#117×C₅₃	—	2	2	no	—
158	#117×C₅₃	—	2	4	no	—
159	#117×C₅₃	—	2	4	no	—
160	#117×C₅₃	—	2	4	no	—
161	#117×C₅₃	D₄	1	2	yes	—
162	#117×C₅₃	D₄	1	2	yes	—
163	#117×C₅₃	C₂³	1	2	yes	—
164	#117×C₅₃	C₂³	1	1	yes	characteristic
165	#117×C₅₃	C₂³	1	1	yes	characteristic
166	#117×C₅₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
168	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
169	C₂×C₄⋊C₄×C₅₃	D₄	1	2	yes	—
170	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
172	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
173	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
174	#107×C₅₃	C₂³	1	4	yes	—
175	#107×C₅₃	C₂³	1	2	yes	—
176	#106×C₅₃	C₂³	1	1	yes	characteristic
177	#106×C₅₃	C₂³	1	2	yes	—
178	#106×C₅₃	C₂³	1	4	yes	—
179	#106×C₅₃	C₂³	1	1	yes	characteristic
180	#106×C₅₃	C₂³	1	2	yes	—
181	#103×C₅₃	C₂³	1	2	yes	—
182	#103×C₅₃	C₂³	1	4	yes	—
183	#103×C₅₃	C₂³	1	4	yes	—
184	#103×C₅₃	C₂³	1	4	yes	—
185	#103×C₅₃	C₂³	1	4	yes	—
186	#103×C₅₃	C₂³	1	4	yes	—
187	#103×C₅₃	C₂³	1	2	yes	—
188	#102×C₅₃	C₂³	1	2	yes	—
189	#102×C₅₃	C₂³	1	4	yes	—
190	#102×C₅₃	C₂³	1	2	yes	—
191	#97×C₅₃	C₂³	1	2	yes	—
192	#97×C₅₃	C₂³	1	2	yes	—
193	#97×C₅₃	C₂³	1	2	yes	—
194	#97×C₅₃	C₂³	1	2	yes	—
195	C₄×C₈×C₅₃	C₂³	1	2	yes	—
196	C₄×C₈×C₅₃	C₂³	1	2	yes	—
197	C₄×C₈×C₅₃	C₂³	1	2	yes	—
198	C₄×C₈×C₅₃	C₂³	1	2	yes	—
199	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
200	#41×C₅₃	—	2	4	no	—
201	#41×C₅₃	—	2	4	no	—
202	C₂×Q₈×C₅₃	—	2	2	no	—
203	C₂×Q₈×C₅₃	—	2	4	no	—
204	C₂×Q₈×C₅₃	—	2	4	no	—
205	C₂×Q₈×C₅₃	—	2	4	no	—
206	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
207	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
208	C₂×D₄×C₅₃	—	2	2	no	—
209	C₂×D₄×C₅₃	—	2	2	no	—
210	C₂×D₄×C₅₃	—	2	2	no	—
211	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₅₃	—	2	2	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	4	no	—
218	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	4	yes	—
222	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
225	Q₁₆×C₅₃	—	2	4	no	—
226	Q₁₆×C₅₃	—	2	4	no	—
227	Q₁₆×C₅₃	—	2	2	no	—
228	Q₁₆×C₅₃	—	2	8	no	—
229	SD₁₆×C₅₃	—	2	4	no	—
230	SD₁₆×C₅₃	—	2	8	no	—
231	D₈×C₅₃	—	2	2	no	—
232	M₁₆×C₅₃	—	2	2	no	—
233	M₁₆×C₅₃	—	2	4	no	—
234	M₁₆×C₅₃	—	2	2	no	—
235	M₁₆×C₅₃	—	2	2	no	—
236	M₁₆×C₅₃	—	2	2	no	—
237	M₁₆×C₅₃	—	2	2	no	—
238	M₁₆×C₅₃	#41	1	4	yes	—
239	C₂×C₈×C₅₃	—	2	2	no	—
240	C₂×C₈×C₅₃	—	2	4	no	—
241	C₂×C₈×C₅₃	#41	1	4	yes	—
242	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
247	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
248	C₄⋊C₄×C₅₃	—	2	2	no	—
249	C₄⋊C₄×C₅₃	—	2	4	no	—
250	C₄⋊C₄×C₅₃	—	2	4	no	—
251	C₄⋊C₄×C₅₃	—	2	4	no	—
252	C₄⋊C₄×C₅₃	—	2	4	no	—
253	C₄⋊C₄×C₅₃	—	2	4	no	—
254	C₄⋊C₄×C₅₃	—	2	4	no	—
255	C₄⋊C₄×C₅₃	—	2	4	no	—
256	C₄⋊C₄×C₅₃	—	2	4	no	—
257	C₄⋊C₄×C₅₃	—	2	2	no	—
258	C₄⋊C₄×C₅₃	—	2	4	no	—
259	C₄⋊C₄×C₅₃	—	2	2	no	—
260	C₄⋊C₄×C₅₃	—	2	4	no	—
261	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
264	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
265	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
267	C₂²⋊C₄×C₅₃	—	2	4	no	—
268	C₂²⋊C₄×C₅₃	—	2	4	no	—
269	C₂²⋊C₄×C₅₃	—	2	2	no	—
270	C₂²⋊C₄×C₅₃	—	2	2	no	—
271	C₂²⋊C₄×C₅₃	—	2	2	no	—
272	C₂²⋊C₄×C₅₃	—	2	2	no	—
273	C₂²⋊C₄×C₅₃	—	2	4	no	—
274	C₂²⋊C₄×C₅₃	—	2	4	no	—
275	C₂²⋊C₄×C₅₃	—	2	2	no	—
276	C₂²⋊C₄×C₅₃	—	2	4	no	—
277	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
278	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
279	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
280	C₄²×C₅₃	—	2	4	no	—
281	C₄²×C₅₃	—	2	4	no	—
282	C₄²×C₅₃	—	2	4	no	—
283	C₄²×C₅₃	—	2	2	no	—
284	C₄²×C₅₃	C₂×D₄	1	4	yes	—
285	C₄²×C₅₃	C₂⁴	1	2	yes	—
286	C₄²×C₅₃	C₂⁴	1	2	yes	—
287	C₂³×C₅₃	—	2	2	no	—
288	C₂³×C₅₃	—	2	2	no	—
289	C₂³×C₅₃	—	4	2	no	—
290	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
291	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
292	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
293	Q₈×C₅₃	—	2	4	no	—
294	Q₈×C₅₃	—	2	4	no	—
295	Q₈×C₅₃	—	2	2	no	—
296	Q₈×C₅₃	—	2	2	no	—
297	Q₈×C₅₃	—	4	4	no	—
298	Q₈×C₅₃	—	8	4	no	—
299	D₄×C₅₃	—	2	2	no	—
300	D₄×C₅₃	—	2	2	no	—
301	D₄×C₅₃	—	4	4	no	—
302	D₄×C₅₃	—	4	4	no	—
303	D₄×C₅₃	—	8	2	no	—
304	C₂×C₄×C₅₃	—	2	2	no	—
305	C₂×C₄×C₅₃	—	2	2	no	—
306	C₂×C₄×C₅₃	—	2	2	no	—
307	C₂×C₄×C₅₃	—	2	1	no	—
308	C₂×C₄×C₅₃	—	2	1	no	—
309	C₂×C₄×C₅₃	—	2	1	no	—
310	C₂×C₄×C₅₃	—	2	1	no	—
311	C₂×C₄×C₅₃	—	2	4	no	—
312	C₂×C₄×C₅₃	—	2	2	no	—
313	C₂×C₄×C₅₃	—	2	4	no	—
314	C₂×C₄×C₅₃	—	2	2	no	—
315	C₂×C₄×C₅₃	—	2	2	no	—
316	C₂×C₄×C₅₃	—	4	4	no	—
317	C₂×C₄×C₅₃	—	4	4	no	—
318	C₂×C₄×C₅₃	—	4	4	no	—
319	C₂×C₄×C₅₃	—	8	4	no	—
320	C₂×C₄×C₅₃	—	8	2	no	—
321	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
322	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
325	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
327	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
328	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
329	C₈×C₅₃	—	2	1	no	—
330	C₈×C₅₃	—	2	1	no	—
331	C₈×C₅₃	—	2	2	no	—
332	C₈×C₅₃	C₂×#41	1	4	yes	—
333	C₈×C₅₃	C₂×#41	1	2	yes	—
334	C₈×C₅₃	C₂×#41	1	2	yes	—
335	#60711	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂²×C₅₃	—	2	2	no	—
337	C₂²×C₅₃	—	2	2	no	—
338	C₂²×C₅₃	—	2	2	no	—
339	C₂²×C₅₃	—	2	1	no	—
340	C₂²×C₅₃	—	2	1	no	—
341	C₂²×C₅₃	—	4	2	no	—
342	C₂²×C₅₃	—	4	2	no	—
343	C₂²×C₅₃	—	4	2	no	—
344	C₂²×C₅₃	—	8	2	no	—
345	C₂²×C₅₃	#532	1	2	yes	—
346	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
347	C₄×C₅₃	—	2	4	no	—
348	C₄×C₅₃	—	2	4	no	—
349	C₄×C₅₃	—	2	1	no	—
350	C₄×C₅₃	—	2	1	no	—
351	C₄×C₅₃	—	4	4	no	—
352	C₄×C₅₃	—	4	2	no	—
353	C₄×C₅₃	—	4	2	no	—
354	C₄×C₅₃	—	4	2	no	—
355	C₄×C₅₃	—	4	4	no	—
356	C₄×C₅₃	#532	1	2	yes	—
357	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
358	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
359	#3495	C₂×C₅₃	1	2	yes	complemented
360	#3185	C₂×C₅₃	1	2	yes	complemented
361	#3183	C₂×C₅₃	1	2	yes	complemented
362	#3178	C₂×C₅₃	1	4	yes	complemented
363	#3177	C₂×C₅₃	1	2	yes	complemented
364	#3173	C₂×C₅₃	1	2	yes	complemented
365	#3172	C₂×C₅₃	1	4	yes	complemented
366	#3163	C₂×C₅₃	1	1	yes	characteristic, complemented
367	#3156	C₂×C₅₃	1	1	yes	characteristic, complemented
368	#3137	C₂×C₅₃	1	2	yes	complemented
369	#3056	C₂×C₅₃	1	2	yes	complemented
370	#3054	C₂×C₅₃	1	1	yes	characteristic
371	C₂×#470	C₂×C₅₃	1	1	yes	characteristic, complemented
372	#2952	C₂×C₅₃	1	1	yes	characteristic, complemented
373	#2950	C₂×C₅₃	1	1	yes	characteristic, complemented
374	#2947	C₂×C₅₃	1	2	yes	complemented
375	#2873	C₂×C₅₃	1	1	yes	characteristic, complemented
376	C₂×C₅₃	—	2	2	no	—
377	C₂×C₅₃	—	4	1	no	—
378	C₂×C₅₃	—	4	1	no	—
379	C₂×C₅₃	—	8	2	no	—
380	C₂×C₅₃	C₂×#532	1	1	yes	characteristic
381	C₂×C₅₃	#3586	1	2	yes	—
382	C₂×#137	C₂²×C₅₃	1	2	yes	—
383	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
384	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
385	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
386	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
387	#556	—	2	2	no	—
388	#554	—	2	2	no	—
389	#552	—	2	4	no	—
390	#552	—	2	2	no	—
391	#552	—	2	2	no	—
392	#551	—	2	4	no	—
393	#544	C₂²×C₅₃	1	2	yes	—
394	#542	C₂²×C₅₃	1	4	yes	—
395	#541	C₂²×C₅₃	1	4	yes	—
396	#536	C₂²×C₅₃	1	2	yes	—
397	#533	C₂²×C₅₃	1	4	yes	—
398	#529	C₂²×C₅₃	1	4	yes	—
399	#525	C₂²×C₅₃	1	2	yes	—
400	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
401	#520	C₂²×C₅₃	1	2	yes	—
402	#519	C₂²×C₅₃	1	2	yes	—
403	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
404	#501	C₂²×C₅₃	1	4	yes	complemented
405	#499	C₂²×C₅₃	1	2	yes	complemented
406	#498	C₂²×C₅₃	1	2	yes	complemented
407	#497	C₂²×C₅₃	1	4	yes	complemented
408	#495	C₂²×C₅₃	1	2	yes	complemented
409	#494	C₂²×C₅₃	1	2	yes	complemented
410	#491	C₂²×C₅₃	1	4	yes	complemented
411	#489	C₂²×C₅₃	1	4	yes	complemented
412	#488	C₂²×C₅₃	1	4	yes	complemented
413	#487	C₂²×C₅₃	1	4	yes	complemented
414	#470	C₂²×C₅₃	1	2	yes	—
415	#470	C₂²×C₅₃	1	4	yes	—
416	#470	C₂²×C₅₃	1	2	yes	—
417	#470	C₂²×C₅₃	1	1	yes	characteristic
418	#470	C₂²×C₅₃	1	2	yes	—
419	#470	C₂²×C₅₃	1	2	yes	—
420	#470	C₂²×C₅₃	1	1	yes	characteristic
421	#469	C₂²×C₅₃	1	1	yes	characteristic
422	#469	C₂²×C₅₃	1	1	yes	characteristic
423	#468	C₂²×C₅₃	1	2	yes	—
424	#468	C₂²×C₅₃	1	4	yes	—
425	#468	C₂²×C₅₃	1	2	yes	—
426	#467	C₂²×C₅₃	1	4	yes	—
427	#465	C₂²×C₅₃	1	4	yes	—
428	#442	C₂²×C₅₃	1	2	yes	complemented
429	#441	C₂²×C₅₃	1	2	yes	complemented
430	#441	C₂²×C₅₃	1	2	yes	complemented
431	#441	C₂²×C₅₃	1	2	yes	complemented
432	#441	C₂²×C₅₃	1	4	yes	complemented
433	#440	C₂²×C₅₃	1	4	yes	complemented
434	C₄×Q₁₆	C₂²×C₅₃	1	4	yes	complemented
435	C₄×Q₁₆	C₂²×C₅₃	1	4	yes	complemented
436	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	complemented
437	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	complemented
438	#428	C₂²×C₅₃	1	2	yes	—
439	#427	C₂²×C₅₃	1	1	yes	characteristic
440	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
441	#419	C₂²×C₅₃	1	2	yes	—
442	#417	C₂²×C₅₃	1	2	yes	—
443	#416	C₂²×C₅₃	1	2	yes	—
444	C₂×#103	C₂²×C₅₃	1	2	yes	—
445	#405	C₂²×C₅₃	1	1	yes	characteristic
446	#405	C₂²×C₅₃	1	1	yes	characteristic
447	#405	C₂²×C₅₃	1	2	yes	—
448	#405	C₂²×C₅₃	1	2	yes	—
449	#405	C₂²×C₅₃	1	1	yes	characteristic
450	#405	C₂²×C₅₃	1	1	yes	characteristic
451	C₄×M₁₆	C₂²×C₅₃	1	2	yes	—
452	C₄×M₁₆	C₂²×C₅₃	1	2	yes	—
453	C₅₃	#60711	1	1	yes	characteristic, direct product factor, Sylow
454	C₂×#41	C₂³×C₅₃	1	2	yes	—
455	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
456	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
457	#137	—	2	8	no	—
458	#135	—	2	4	no	—
459	C₂×Q₁₆	—	2	4	no	—
460	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
461	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
462	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
463	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
464	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
465	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
466	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
467	C₂×M₁₆	—	2	4	no	—
468	C₂×M₁₆	—	2	4	no	—
469	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
470	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
471	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
472	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
473	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
474	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
475	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
478	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
479	C₄⋊Q₈	—	2	2	no	—
480	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
481	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
482	#126	—	2	4	no	—
483	#126	—	2	4	no	—
484	#126	—	2	4	no	—
485	#126	—	2	4	no	—
486	#125	—	2	4	no	—
487	#125	—	2	4	no	—
488	#125	—	2	2	no	—
489	#125	—	2	4	no	—
490	#125	C₂³×C₅₃	1	4	yes	—
491	#124	—	2	4	no	—
492	#124	C₂³×C₅₃	1	4	yes	—
493	#123	—	2	2	no	—
494	#123	—	2	4	no	—
495	#123	—	2	4	no	—
496	#123	—	2	4	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
505	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
506	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
507	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
508	#121	C₂³×C₅₃	1	2	yes	—
509	#121	C₂³×C₅₃	1	2	yes	—
510	#120	—	2	2	no	—
511	C₄×Q₈	—	2	2	no	—
512	C₄×Q₈	—	2	2	no	—
513	C₄×Q₈	—	2	4	no	—
514	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
515	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
516	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	—	2	4	no	—
521	C₄×D₄	C₂³×C₅₃	1	4	yes	—
522	#117	—	2	4	no	—
523	#117	—	2	2	no	—
524	#117	—	2	4	no	—
525	#117	—	2	4	no	—
526	#117	D₄×C₅₃	1	2	yes	—
527	#117	D₄×C₅₃	1	2	yes	—
528	#117	C₂³×C₅₃	1	2	yes	—
529	#117	C₂³×C₅₃	1	1	yes	characteristic
530	#117	C₂³×C₅₃	1	1	yes	characteristic
531	#117	C₂³×C₅₃	1	2	yes	—
532	C₂×C₄⋊C₄	—	2	2	no	—
533	C₂×C₄⋊C₄	—	2	2	no	—
534	C₂×C₄⋊C₄	D₄×C₅₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
536	C₂×C₂²⋊C₄	—	2	2	no	—
537	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
538	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
539	#107	C₂³×C₅₃	1	2	yes	—
540	#107	C₂³×C₅₃	1	4	yes	—
541	#106	C₂³×C₅₃	1	2	yes	—
542	#106	C₂³×C₅₃	1	2	yes	—
543	#106	C₂³×C₅₃	1	1	yes	characteristic
544	#106	C₂³×C₅₃	1	1	yes	characteristic
545	#106	C₂³×C₅₃	1	4	yes	—
546	#103	C₂³×C₅₃	1	4	yes	—
547	#103	C₂³×C₅₃	1	4	yes	—
548	#103	C₂³×C₅₃	1	2	yes	—
549	#103	C₂³×C₅₃	1	2	yes	—
550	#103	C₂³×C₅₃	1	4	yes	—
551	#103	C₂³×C₅₃	1	4	yes	—
552	#103	C₂³×C₅₃	1	4	yes	—
553	#102	C₂³×C₅₃	1	2	yes	—
554	#102	C₂³×C₅₃	1	2	yes	—
555	#102	C₂³×C₅₃	1	4	yes	—
556	#97	C₂³×C₅₃	1	2	yes	—
557	#97	C₂³×C₅₃	1	2	yes	—
558	#97	C₂³×C₅₃	1	2	yes	—
559	#97	C₂³×C₅₃	1	2	yes	—
560	C₄×C₈	C₂³×C₅₃	1	2	yes	—
561	C₄×C₈	C₂³×C₅₃	1	2	yes	—
562	C₄×C₈	C₂³×C₅₃	1	2	yes	—
563	C₄×C₈	C₂³×C₅₃	1	2	yes	—
564	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
565	#41	—	2	4	no	—
566	#41	—	2	4	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	4	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
572	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
587	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
590	Q₁₆	—	2	4	no	—
591	Q₁₆	—	2	4	no	—
592	Q₁₆	—	2	2	no	—
593	Q₁₆	—	2	8	no	—
594	SD₁₆	—	2	4	no	—
595	SD₁₆	—	2	8	no	—
596	D₈	—	2	2	no	—
597	M₁₆	—	2	2	no	—
598	M₁₆	—	2	4	no	—
599	M₁₆	—	2	2	no	—
600	M₁₆	—	2	2	no	—
601	M₁₆	—	2	2	no	—
602	M₁₆	—	2	2	no	—
603	M₁₆	#41×C₅₃	1	4	yes	—
604	C₂×C₈	—	2	2	no	—
605	C₂×C₈	—	2	4	no	—
606	C₂×C₈	#41×C₅₃	1	4	yes	—
607	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
608	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
609	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
610	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
611	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
612	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
627	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
628	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
629	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
630	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
631	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
643	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
644	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
645	C₄²	—	2	4	no	—
646	C₄²	—	2	4	no	—
647	C₄²	—	2	4	no	—
648	C₄²	—	2	2	no	—
649	C₄²	C₂×D₄×C₅₃	1	4	yes	—
650	C₄²	C₂⁴×C₅₃	1	2	yes	—
651	C₄²	C₂⁴×C₅₃	1	2	yes	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	4	2	no	—
655	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
656	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
657	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
658	Q₈	—	2	4	no	—
659	Q₈	—	2	2	no	—
660	Q₈	—	2	4	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	4	4	no	—
663	Q₈	—	8	4	no	—
664	D₄	—	2	2	no	—
665	D₄	—	2	2	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	4	no	—
668	D₄	—	8	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	4	4	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	8	4	no	—
685	C₂×C₄	—	8	2	no	—
686	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
687	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
688	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
689	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
691	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
692	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
693	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
694	C₈	—	2	1	no	—
695	C₈	—	2	1	no	—
696	C₈	—	2	2	no	—
697	C₈	C₂×#41×C₅₃	1	4	yes	—
698	C₈	C₂×#41×C₅₃	1	2	yes	—
699	C₈	C₂×#41×C₅₃	1	2	yes	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	8	2	no	—
709	C₂²	C₅₃×#532	1	2	yes	—
710	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
711	C₄	—	2	4	no	—
712	C₄	—	2	4	no	—
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	4	4	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	4	no	—
720	C₄	C₅₃×#532	1	2	yes	—
721	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
722	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
723	C₂	—	2	2	no	—
724	C₂	—	4	1	no	—
725	C₂	—	4	1	no	—
726	C₂	—	8	2	no	—
727	C₂	C₂×C₅₃×#532	1	1	yes	characteristic
728	C₂	C₅₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ 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
1. C₅₃×#3495	C₂	semidirect
2. C₅₃×#3185	C₂	semidirect
3. C₅₃×#3183	C₂	semidirect
4. C₅₃×#3178	C₂	semidirect
5. C₅₃×#3177	C₂	semidirect
6. C₅₃×#3173	C₂	semidirect
7. C₅₃×#3172	C₂	semidirect
8. C₅₃×#3163	C₂	semidirect
9. C₅₃×#3156	C₂	semidirect
10. C₅₃×#3137	C₂	semidirect
11. C₅₃×#3056	C₂	semidirect
13. C₂×C₅₃×#470	C₂	semidirect
14. C₅₃×#2952	C₂	semidirect
15. C₅₃×#2950	C₂	semidirect
16. C₅₃×#2947	C₂	semidirect
17. C₅₃×#2873	C₂	semidirect
40. C₅₃×#501	C₂²	semidirect
41. C₅₃×#499	C₂²	semidirect
42. C₅₃×#498	C₂²	semidirect
43. C₅₃×#497	C₂²	semidirect
44. C₅₃×#495	C₂²	semidirect
45. C₅₃×#494	C₂²	semidirect
46. C₅₃×#491	C₂²	semidirect
47. C₅₃×#489	C₂²	semidirect
48. C₅₃×#488	C₂²	semidirect
49. C₅₃×#487	C₂²	semidirect
64. C₅₃×#442	C₂²	semidirect
65. C₅₃×#441	C₂²	semidirect
66. C₅₃×#441	C₂²	semidirect
67. C₅₃×#441	C₂²	semidirect
68. C₅₃×#441	C₂²	semidirect
69. C₅₃×#440	C₂²	semidirect
70. C₄×Q₁₆×C₅₃	C₂²	semidirect
71. C₄×Q₁₆×C₅₃	C₂²	semidirect
72. C₄×SD₁₆×C₅₃	C₂²	semidirect
73. C₄×SD₁₆×C₅₃	C₂²	semidirect
335. #60711	C₅₃	direct (N × H)
359. #3495	C₂×C₅₃	semidirect
360. #3185	C₂×C₅₃	semidirect
361. #3183	C₂×C₅₃	semidirect
362. #3178	C₂×C₅₃	semidirect
363. #3177	C₂×C₅₃	semidirect
364. #3173	C₂×C₅₃	semidirect
365. #3172	C₂×C₅₃	semidirect
366. #3163	C₂×C₅₃	semidirect
367. #3156	C₂×C₅₃	semidirect
368. #3137	C₂×C₅₃	semidirect
369. #3056	C₂×C₅₃	semidirect
371. C₂×#470	C₂×C₅₃	semidirect
372. #2952	C₂×C₅₃	semidirect
373. #2950	C₂×C₅₃	semidirect
374. #2947	C₂×C₅₃	semidirect
375. #2873	C₂×C₅₃	semidirect
404. #501	C₂²×C₅₃	semidirect
405. #499	C₂²×C₅₃	semidirect
406. #498	C₂²×C₅₃	semidirect
407. #497	C₂²×C₅₃	semidirect
408. #495	C₂²×C₅₃	semidirect
409. #494	C₂²×C₅₃	semidirect
410. #491	C₂²×C₅₃	semidirect
411. #489	C₂²×C₅₃	semidirect
412. #488	C₂²×C₅₃	semidirect
413. #487	C₂²×C₅₃	semidirect
428. #442	C₂²×C₅₃	semidirect
429. #441	C₂²×C₅₃	semidirect
430. #441	C₂²×C₅₃	semidirect
431. #441	C₂²×C₅₃	semidirect
432. #441	C₂²×C₅₃	semidirect
433. #440	C₂²×C₅₃	semidirect
434. C₄×Q₁₆	C₂²×C₅₃	semidirect
435. C₄×Q₁₆	C₂²×C₅₃	semidirect
436. C₄×SD₁₆	C₂²×C₅₃	semidirect
437. C₄×SD₁₆	C₂²×C₅₃	semidirect
453. C₅₃	#60711	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3495	2
C₅₃×#3185	2
C₅₃×#3183	2
C₅₃×#3178	2
C₅₃×#3177	2
C₅₃×#3173	2
C₅₃×#3172	2
C₅₃×#3163	2
C₅₃×#3156	2
C₅₃×#3137	2
C₅₃×#3056	2
C₅₃×#3054	2
C₂×C₅₃×#470	2
C₅₃×#2952	2
C₅₃×#2950	2
C₅₃×#2947	2
C₅₃×#2873	2
#60711	53

Subgroups — C53×#60711 #27268223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60711 #27268223