Subgroups — C₅₃×#61223 #27268735

Order 13568.

2156 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3318	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3317	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3310	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3309	C₂	1	4	yes	maximal, complemented
7	C₂×C₅₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3096	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3062	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3012	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2897	C₂	1	2	yes	maximal, complemented
16	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	—
17	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
18	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#131×C₅₃	C₂²	1	2	yes	complemented
20	C₅₃×#553	—	2	4	no	—
21	C₅₃×#553	C₂²	1	4	yes	complemented
22	C₅₃×#552	C₂²	1	4	yes	complemented
23	C₅₃×#550	C₂²	1	4	yes	—
24	D₄²×C₅₃	—	2	4	no	—
25	D₄²×C₅₃	C₂²	1	4	yes	—
26	C₅₃×#541	—	2	1	no	—
27	C₅₃×#540	—	2	1	no	—
28	C₅₃×#537	C₂²	1	2	yes	complemented
29	C₅₃×#535	—	2	2	no	—
30	C₅₃×#535	C₂²	1	2	yes	—
31	C₅₃×#532	—	2	1	no	—
32	C₅₃×#532	C₂²	1	1	yes	characteristic
33	C₂×#127×C₅₃	—	2	1	no	—
34	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#529	—	2	2	no	—
36	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#520	C₂²	1	2	yes	complemented
38	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
39	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#490	C₂²	1	4	yes	complemented
41	C₅₃×#490	C₂²	1	4	yes	complemented
42	C₅₃×#482	C₂²	1	4	yes	complemented
43	C₅₃×#482	C₂²	1	4	yes	complemented
44	C₅₃×#481	C₂²	1	4	yes	complemented
45	C₅₃×#480	C₂²	1	4	yes	complemented
46	C₅₃×#479	C₂²	1	4	yes	complemented
47	C₅₃×#478	C₂²	1	4	yes	complemented
48	C₅₃×#469	C₂²	1	4	yes	complemented
49	C₅₃×#468	C₂²	1	4	yes	complemented
50	C₅₃×#466	C₂²	1	4	yes	complemented
51	C₅₃×#465	C₂²	1	4	yes	complemented
52	C₅₃×#460	C₂²	1	4	yes	complemented
53	C₅₃×#459	C₂²	1	4	yes	complemented
54	C₅₃×#452	C₂²	1	4	yes	complemented
55	C₅₃×#450	C₂²	1	4	yes	complemented
56	C₅₃×#449	C₂²	1	4	yes	complemented
57	C₅₃×#447	C₂²	1	4	yes	complemented
58	C₅₃×#442	C₂²	1	2	yes	complemented
59	C₅₃×#441	C₂²	1	2	yes	complemented
60	C₅₃×#440	C₂²	1	2	yes	complemented
61	C₅₃×#440	C₂²	1	2	yes	complemented
62	C₅₃×#435	C₂²	1	4	yes	complemented
63	C₅₃×#435	C₂²	1	4	yes	complemented
64	C₅₃×#428	C₂²	1	2	yes	complemented
65	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#418	C₂²	1	2	yes	complemented
68	C₅₃×#418	C₂²	1	4	yes	complemented
69	C₅₃×#417	C₂²	1	2	yes	—
70	C₅₃×#417	C₂²	1	4	yes	complemented
71	C₅₃×#416	C₂²	1	1	yes	characteristic
72	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#416	C₂²	1	4	yes	complemented
74	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
75	C₂×#102×C₅₃	C₂²	1	4	yes	complemented
76	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
77	C₅₃×#408	C₂²	1	2	yes	complemented
78	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
79	H(5,𝔽₂)×C₅₃	—	2	8	no	—
80	H(5,𝔽₂)×C₅₃	—	4	4	no	—
81	C₂×#41×C₅₃	—	2	2	no	—
82	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
83	C₂×#41×C₅₃	C₂³	1	4	yes	—
84	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
85	C₂×#41×C₅₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₅₃	—	2	2	no	—
87	C₂²×D₄×C₅₃	—	2	4	no	—
88	C₂²×D₄×C₅₃	—	2	4	no	—
89	C₂²×D₄×C₅₃	—	2	2	no	—
90	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
92	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
93	#135×C₅₃	—	2	4	no	—
94	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
95	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
96	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
98	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
99	C₂×D₈×C₅₃	C₂³	1	4	yes	—
100	#131×C₅₃	—	4	4	no	—
101	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
102	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
103	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
106	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
107	#127×C₅₃	—	2	1	no	—
108	#127×C₅₃	—	2	1	no	—
109	#127×C₅₃	—	2	2	no	—
110	#127×C₅₃	—	2	4	no	—
111	#127×C₅₃	D₄	1	1	yes	characteristic
112	#127×C₅₃	C₂³	1	4	yes	—
113	#126×C₅₃	—	2	4	no	—
114	#126×C₅₃	—	2	4	no	—
115	#125×C₅₃	—	2	4	no	—
116	#125×C₅₃	—	2	1	no	—
117	#125×C₅₃	—	2	1	no	—
118	#125×C₅₃	C₂³	1	4	yes	—
119	#124×C₅₃	—	2	2	no	—
120	#124×C₅₃	D₄	1	2	yes	—
121	#123×C₅₃	—	2	4	no	—
122	#123×C₅₃	—	2	4	no	—
123	C₂²⋊Q₈×C₅₃	—	2	2	no	—
124	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
125	#121×C₅₃	—	2	4	no	—
126	#121×C₅₃	—	2	4	no	—
127	#121×C₅₃	—	2	4	no	—
128	#121×C₅₃	—	2	2	no	—
129	#121×C₅₃	—	2	4	no	—
130	#121×C₅₃	—	2	4	no	—
131	#121×C₅₃	D₄	1	4	yes	—
132	#121×C₅₃	C₂³	1	4	yes	—
133	#121×C₅₃	C₂³	1	4	yes	—
134	#121×C₅₃	C₂³	1	4	yes	—
135	#120×C₅₃	—	2	4	no	—
136	#120×C₅₃	—	2	4	no	—
137	#120×C₅₃	—	2	4	no	—
138	C₄×Q₈×C₅₃	—	2	2	no	—
139	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
140	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
141	C₄×D₄×C₅₃	—	2	4	no	—
142	C₄×D₄×C₅₃	—	2	4	no	—
143	C₄×D₄×C₅₃	—	2	2	no	—
144	C₄×D₄×C₅₃	—	2	4	no	—
145	C₄×D₄×C₅₃	—	2	2	no	—
146	C₄×D₄×C₅₃	—	2	2	no	—
147	C₄×D₄×C₅₃	C₂³	1	2	yes	—
148	C₄×D₄×C₅₃	C₂³	1	2	yes	—
149	C₄×D₄×C₅₃	C₂³	1	4	yes	—
150	#117×C₅₃	—	2	4	no	—
151	#117×C₅₃	—	2	1	no	—
152	#117×C₅₃	—	2	1	no	—
153	#117×C₅₃	C₂³	1	1	yes	characteristic
154	#117×C₅₃	C₂³	1	1	yes	characteristic
155	#117×C₅₃	C₂³	1	4	yes	—
156	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
157	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
159	C₂×C₄²×C₅₃	—	2	1	no	—
160	C₂×C₄²×C₅₃	—	2	1	no	—
161	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
162	#107×C₅₃	C₂³	1	2	yes	—
163	#107×C₅₃	C₂³	1	4	yes	—
164	#106×C₅₃	C₂³	1	2	yes	—
165	#106×C₅₃	C₂³	1	4	yes	—
166	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
167	#103×C₅₃	C₂³	1	2	yes	—
168	#103×C₅₃	C₂³	1	4	yes	—
169	#103×C₅₃	C₂³	1	2	yes	—
170	#102×C₅₃	C₂³	1	4	yes	—
171	#102×C₅₃	C₂³	1	4	yes	—
172	#102×C₅₃	C₂³	1	4	yes	—
173	#102×C₅₃	C₂³	1	4	yes	—
174	#102×C₅₃	C₂³	1	2	yes	—
175	#102×C₅₃	C₂³	1	4	yes	—
176	#102×C₅₃	C₂³	1	4	yes	—
177	#102×C₅₃	C₂³	1	4	yes	—
178	#102×C₅₃	C₂³	1	2	yes	—
179	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
180	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
181	#97×C₅₃	C₂³	1	2	yes	—
182	#97×C₅₃	C₂³	1	2	yes	—
183	C₂⁴×C₅₃	—	2	4	no	—
184	C₂⁴×C₅₃	—	2	2	no	—
185	#41×C₅₃	—	2	4	no	—
186	#41×C₅₃	—	2	4	no	—
187	#41×C₅₃	—	2	2	no	—
188	#41×C₅₃	—	2	8	no	—
189	#41×C₅₃	—	2	2	no	—
190	#41×C₅₃	—	2	2	no	—
191	#41×C₅₃	—	4	4	no	—
192	#41×C₅₃	—	4	8	no	—
193	#41×C₅₃	#41	1	4	yes	—
194	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
195	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
196	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
197	C₂×D₄×C₅₃	—	2	1	no	—
198	C₂×D₄×C₅₃	—	2	8	no	—
199	C₂×D₄×C₅₃	—	2	1	no	—
200	C₂×D₄×C₅₃	—	2	4	no	—
201	C₂×D₄×C₅₃	—	2	4	no	—
202	C₂×D₄×C₅₃	—	2	4	no	—
203	C₂×D₄×C₅₃	—	2	4	no	—
204	C₂×D₄×C₅₃	—	2	4	no	—
205	C₂×D₄×C₅₃	—	2	4	no	—
206	C₂×D₄×C₅₃	—	2	2	no	—
207	C₂×D₄×C₅₃	—	2	4	no	—
208	C₂×D₄×C₅₃	—	2	4	no	—
209	C₂×D₄×C₅₃	—	2	4	no	—
210	C₂×D₄×C₅₃	—	4	4	no	—
211	C₂×D₄×C₅₃	—	4	8	no	—
212	C₂×D₄×C₅₃	—	4	16	no	—
213	C₂×D₄×C₅₃	—	8	4	no	—
214	C₂×D₄×C₅₃	—	8	8	no	—
215	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
216	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
218	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
219	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
220	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₅₃	—	2	1	no	—
222	C₂²×C₄×C₅₃	—	2	2	no	—
223	C₂²×C₄×C₅₃	—	2	4	no	—
224	C₂²×C₄×C₅₃	—	2	1	no	—
225	C₂²×C₄×C₅₃	—	2	2	no	—
226	C₂²×C₄×C₅₃	—	2	4	no	—
227	C₂²×C₄×C₅₃	—	2	2	no	—
228	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
230	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
231	Q₁₆×C₅₃	—	2	2	no	—
232	SD₁₆×C₅₃	—	2	2	no	—
233	SD₁₆×C₅₃	—	2	2	no	—
234	SD₁₆×C₅₃	—	4	4	no	—
235	D₈×C₅₃	—	2	2	no	—
236	D₈×C₅₃	—	4	4	no	—
237	M₁₆×C₅₃	—	2	4	no	—
238	M₁₆×C₅₃	—	4	4	no	—
239	C₂×C₈×C₅₃	—	2	2	no	—
240	C₂×C₈×C₅₃	—	2	2	no	—
241	C₂×C₈×C₅₃	—	4	4	no	—
242	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
245	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
246	C₄⋊C₄×C₅₃	—	2	4	no	—
247	C₄⋊C₄×C₅₃	—	2	4	no	—
248	C₄⋊C₄×C₅₃	—	2	2	no	—
249	C₄⋊C₄×C₅₃	—	2	4	no	—
250	C₄⋊C₄×C₅₃	—	2	2	no	—
251	C₄⋊C₄×C₅₃	—	2	2	no	—
252	C₄⋊C₄×C₅₃	—	2	4	no	—
253	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
254	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
256	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
257	C₂²⋊C₄×C₅₃	—	2	4	no	—
258	C₂²⋊C₄×C₅₃	—	2	1	no	—
259	C₂²⋊C₄×C₅₃	—	2	1	no	—
260	C₂²⋊C₄×C₅₃	—	2	4	no	—
261	C₂²⋊C₄×C₅₃	—	2	2	no	—
262	C₂²⋊C₄×C₅₃	—	2	2	no	—
263	C₂²⋊C₄×C₅₃	—	2	4	no	—
264	C₂²⋊C₄×C₅₃	—	2	4	no	—
265	C₂²⋊C₄×C₅₃	—	2	4	no	—
266	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
267	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
268	C₄²×C₅₃	—	2	2	no	—
269	C₄²×C₅₃	—	2	1	no	—
270	C₄²×C₅₃	—	2	1	no	—
271	C₄²×C₅₃	—	2	2	no	—
272	C₄²×C₅₃	—	2	4	no	—
273	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₅₃	C₂⁴	1	2	yes	—
276	C₂³×C₅₃	—	2	1	no	—
277	C₂³×C₅₃	—	2	1	no	—
278	C₂³×C₅₃	—	2	4	no	—
279	C₂³×C₅₃	—	4	8	no	—
280	C₂³×C₅₃	—	4	4	no	—
281	C₂³×C₅₃	—	8	2	no	—
282	C₂³×C₅₃	—	8	2	no	—
283	C₂³×C₅₃	—	8	4	no	—
284	C₂³×C₅₃	—	8	4	no	—
285	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
286	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
287	Q₈×C₅₃	—	2	4	no	—
288	Q₈×C₅₃	—	2	1	no	—
289	Q₈×C₅₃	—	2	1	no	—
290	Q₈×C₅₃	—	2	1	no	—
291	Q₈×C₅₃	C₂×#41	1	2	yes	—
292	D₄×C₅₃	—	2	4	no	—
293	D₄×C₅₃	—	2	8	no	—
294	D₄×C₅₃	—	2	4	no	—
295	D₄×C₅₃	—	2	4	no	—
296	D₄×C₅₃	—	2	1	no	—
297	D₄×C₅₃	—	2	1	no	—
298	D₄×C₅₃	—	2	4	no	—
299	D₄×C₅₃	—	2	1	no	—
300	D₄×C₅₃	—	4	4	no	—
301	D₄×C₅₃	—	4	8	no	—
302	D₄×C₅₃	—	4	8	no	—
303	D₄×C₅₃	—	4	8	no	—
304	D₄×C₅₃	—	4	2	no	—
305	D₄×C₅₃	—	4	4	no	—
306	D₄×C₅₃	—	8	4	no	—
307	D₄×C₅₃	—	8	4	no	—
308	D₄×C₅₃	—	8	4	no	—
309	D₄×C₅₃	—	8	4	no	—
310	D₄×C₅₃	C₂×#41	1	2	yes	—
311	C₂×C₄×C₅₃	—	2	1	no	—
312	C₂×C₄×C₅₃	—	2	4	no	—
313	C₂×C₄×C₅₃	—	2	4	no	—
314	C₂×C₄×C₅₃	—	2	4	no	—
315	C₂×C₄×C₅₃	—	2	2	no	—
316	C₂×C₄×C₅₃	—	2	4	no	—
317	C₂×C₄×C₅₃	—	2	2	no	—
318	C₂×C₄×C₅₃	—	2	1	no	—
319	C₂×C₄×C₅₃	—	4	2	no	—
320	C₂×C₄×C₅₃	—	4	8	no	—
321	C₂×C₄×C₅₃	—	4	4	no	—
322	C₂×C₄×C₅₃	—	4	2	no	—
323	C₂×C₄×C₅₃	—	8	2	no	—
324	C₂×C₄×C₅₃	—	8	4	no	—
325	C₂×C₄×C₅₃	—	8	2	no	—
326	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
329	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
331	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
332	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
333	C₈×C₅₃	—	2	1	no	—
334	C₈×C₅₃	—	2	1	no	—
335	C₈×C₅₃	—	2	2	no	—
336	C₈×C₅₃	—	2	4	no	—
337	#61223	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
338	C₂²×C₅₃	—	2	2	no	—
339	C₂²×C₅₃	—	2	4	no	—
340	C₂²×C₅₃	—	2	4	no	—
341	C₂²×C₅₃	—	2	4	no	—
342	C₂²×C₅₃	—	2	2	no	—
343	C₂²×C₅₃	—	4	2	no	—
344	C₂²×C₅₃	—	4	2	no	—
345	C₂²×C₅₃	—	4	4	no	—
346	C₂²×C₅₃	—	4	4	no	—
347	C₂²×C₅₃	—	4	4	no	—
348	C₂²×C₅₃	—	4	1	no	—
349	C₂²×C₅₃	—	16	4	no	—
350	C₂²×C₅₃	—	16	8	no	—
351	C₂²×C₅₃	#546	1	2	yes	—
352	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
353	C₄×C₅₃	—	2	2	no	—
354	C₄×C₅₃	—	2	2	no	—
355	C₄×C₅₃	—	2	2	no	—
356	C₄×C₅₃	—	2	4	no	—
357	C₄×C₅₃	—	4	2	no	—
358	C₄×C₅₃	—	4	2	no	—
359	C₄×C₅₃	—	4	4	no	—
360	C₄×C₅₃	—	4	1	no	—
361	C₄×C₅₃	#546	1	2	yes	—
362	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
363	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
364	#3512	C₂×C₅₃	1	1	yes	characteristic, complemented
365	#3498	C₂×C₅₃	1	1	yes	characteristic, complemented
366	#3318	C₂×C₅₃	1	4	yes	complemented
367	#3317	C₂×C₅₃	1	4	yes	complemented
368	#3310	C₂×C₅₃	1	4	yes	complemented
369	#3309	C₂×C₅₃	1	4	yes	complemented
370	C₂×#490	C₂×C₅₃	1	1	yes	characteristic, complemented
371	#3096	C₂×C₅₃	1	2	yes	complemented
372	#3080	C₂×C₅₃	1	1	yes	characteristic, complemented
373	#3062	C₂×C₅₃	1	2	yes	complemented
374	#3038	C₂×C₅₃	1	1	yes	characteristic, complemented
375	#3012	C₂×C₅₃	1	2	yes	complemented
376	#2943	C₂×C₅₃	1	1	yes	characteristic, complemented
377	#2932	C₂×C₅₃	1	1	yes	characteristic, complemented
378	#2897	C₂×C₅₃	1	2	yes	complemented
379	C₂×C₅₃	—	2	2	no	—
380	C₂×C₅₃	—	4	4	no	—
381	C₂×C₅₃	—	4	2	no	—
382	C₂×C₅₃	—	8	1	no	—
383	C₂×C₅₃	—	8	4	no	—
384	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
385	C₂×C₅₃	#3585	1	2	yes	—
386	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	2	yes	—
387	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
388	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
389	C₂×#131	C₂²×C₅₃	1	2	yes	complemented
390	#553	—	2	4	no	—
391	#553	C₂²×C₅₃	1	4	yes	complemented
392	#552	C₂²×C₅₃	1	4	yes	complemented
393	#550	C₂²×C₅₃	1	4	yes	—
394	D₄²	—	2	4	no	—
395	D₄²	C₂²×C₅₃	1	4	yes	—
396	#541	—	2	1	no	—
397	#540	—	2	1	no	—
398	#537	C₂²×C₅₃	1	2	yes	complemented
399	#535	—	2	2	no	—
400	#535	C₂²×C₅₃	1	2	yes	—
401	#532	—	2	1	no	—
402	#532	C₂²×C₅₃	1	1	yes	characteristic
403	C₂×#127	—	2	1	no	—
404	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
405	#529	—	2	2	no	—
406	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
407	#520	C₂²×C₅₃	1	2	yes	complemented
408	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
409	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
410	#490	C₂²×C₅₃	1	4	yes	complemented
411	#490	C₂²×C₅₃	1	4	yes	complemented
412	#482	C₂²×C₅₃	1	4	yes	complemented
413	#482	C₂²×C₅₃	1	4	yes	complemented
414	#481	C₂²×C₅₃	1	4	yes	complemented
415	#480	C₂²×C₅₃	1	4	yes	complemented
416	#479	C₂²×C₅₃	1	4	yes	complemented
417	#478	C₂²×C₅₃	1	4	yes	complemented
418	#469	C₂²×C₅₃	1	4	yes	complemented
419	#468	C₂²×C₅₃	1	4	yes	complemented
420	#466	C₂²×C₅₃	1	4	yes	complemented
421	#465	C₂²×C₅₃	1	4	yes	complemented
422	#460	C₂²×C₅₃	1	4	yes	complemented
423	#459	C₂²×C₅₃	1	4	yes	complemented
424	#452	C₂²×C₅₃	1	4	yes	complemented
425	#450	C₂²×C₅₃	1	4	yes	complemented
426	#449	C₂²×C₅₃	1	4	yes	complemented
427	#447	C₂²×C₅₃	1	4	yes	complemented
428	#442	C₂²×C₅₃	1	2	yes	complemented
429	#441	C₂²×C₅₃	1	2	yes	complemented
430	#440	C₂²×C₅₃	1	2	yes	complemented
431	#440	C₂²×C₅₃	1	2	yes	complemented
432	#435	C₂²×C₅₃	1	4	yes	complemented
433	#435	C₂²×C₅₃	1	4	yes	complemented
434	#428	C₂²×C₅₃	1	2	yes	complemented
435	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
436	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
437	#418	C₂²×C₅₃	1	2	yes	complemented
438	#418	C₂²×C₅₃	1	4	yes	complemented
439	#417	C₂²×C₅₃	1	2	yes	—
440	#417	C₂²×C₅₃	1	4	yes	complemented
441	#416	C₂²×C₅₃	1	1	yes	characteristic
442	#416	C₂²×C₅₃	1	4	yes	complemented
443	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
444	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
445	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
446	C₂×#102	C₂²×C₅₃	1	4	yes	complemented
447	#408	C₂²×C₅₃	1	2	yes	complemented
448	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
449	C₅₃	#61223	1	1	yes	characteristic, direct product factor, Sylow
450	H(5,𝔽₂)	—	2	8	no	—
451	H(5,𝔽₂)	—	4	4	no	—
452	C₂×#41	—	2	2	no	—
453	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
454	C₂×#41	C₂³×C₅₃	1	4	yes	—
455	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
456	C₂×#41	C₂³×C₅₃	1	2	yes	—
457	C₂²×D₄	—	2	2	no	—
458	C₂²×D₄	—	2	4	no	—
459	C₂²×D₄	—	2	4	no	—
460	C₂²×D₄	—	2	2	no	—
461	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
462	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
463	AGL(1,ℤ/8)	—	4	4	no	—
464	#135	—	2	4	no	—
465	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
466	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
467	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
468	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
469	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
470	C₂×D₈	C₂³×C₅₃	1	4	yes	—
471	#131	—	4	4	no	—
472	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
473	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
474	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
477	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
478	#127	—	2	2	no	—
479	#127	—	2	4	no	—
480	#127	—	2	1	no	—
481	#127	—	2	1	no	—
482	#127	D₄×C₅₃	1	1	yes	characteristic
483	#127	C₂³×C₅₃	1	4	yes	—
484	#126	—	2	4	no	—
485	#126	—	2	4	no	—
486	#125	—	2	4	no	—
487	#125	—	2	1	no	—
488	#125	—	2	1	no	—
489	#125	C₂³×C₅₃	1	4	yes	—
490	#124	—	2	2	no	—
491	#124	D₄×C₅₃	1	2	yes	—
492	#123	—	2	4	no	—
493	#123	—	2	4	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
496	#121	—	2	2	no	—
497	#121	—	2	4	no	—
498	#121	—	2	4	no	—
499	#121	—	2	4	no	—
500	#121	—	2	4	no	—
501	#121	—	2	4	no	—
502	#121	D₄×C₅₃	1	4	yes	—
503	#121	C₂³×C₅₃	1	4	yes	—
504	#121	C₂³×C₅₃	1	4	yes	—
505	#121	C₂³×C₅₃	1	4	yes	—
506	#120	—	2	4	no	—
507	#120	—	2	4	no	—
508	#120	—	2	4	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
511	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	2	4	no	—
517	C₄×D₄	—	2	4	no	—
518	C₄×D₄	C₂³×C₅₃	1	2	yes	—
519	C₄×D₄	C₂³×C₅₃	1	2	yes	—
520	C₄×D₄	C₂³×C₅₃	1	4	yes	—
521	#117	—	2	4	no	—
522	#117	—	2	1	no	—
523	#117	—	2	1	no	—
524	#117	C₂³×C₅₃	1	1	yes	characteristic
525	#117	C₂³×C₅₃	1	1	yes	characteristic
526	#117	C₂³×C₅₃	1	4	yes	—
527	C₂×C₄⋊C₄	—	2	2	no	—
528	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
530	C₂×C₄²	—	2	1	no	—
531	C₂×C₄²	—	2	1	no	—
532	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
533	#107	C₂³×C₅₃	1	2	yes	—
534	#107	C₂³×C₅₃	1	4	yes	—
535	#106	C₂³×C₅₃	1	2	yes	—
536	#106	C₂³×C₅₃	1	4	yes	—
537	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
538	#103	C₂³×C₅₃	1	2	yes	—
539	#103	C₂³×C₅₃	1	4	yes	—
540	#103	C₂³×C₅₃	1	2	yes	—
541	#102	C₂³×C₅₃	1	2	yes	—
542	#102	C₂³×C₅₃	1	4	yes	—
543	#102	C₂³×C₅₃	1	4	yes	—
544	#102	C₂³×C₅₃	1	4	yes	—
545	#102	C₂³×C₅₃	1	4	yes	—
546	#102	C₂³×C₅₃	1	4	yes	—
547	#102	C₂³×C₅₃	1	4	yes	—
548	#102	C₂³×C₅₃	1	4	yes	—
549	#102	C₂³×C₅₃	1	2	yes	—
550	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
551	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
552	#97	C₂³×C₅₃	1	2	yes	—
553	#97	C₂³×C₅₃	1	2	yes	—
554	C₂⁴	—	2	4	no	—
555	C₂⁴	—	2	2	no	—
556	#41	—	2	4	no	—
557	#41	—	2	4	no	—
558	#41	—	2	2	no	—
559	#41	—	2	8	no	—
560	#41	—	2	2	no	—
561	#41	—	2	2	no	—
562	#41	—	4	4	no	—
563	#41	—	4	8	no	—
564	#41	#41×C₅₃	1	4	yes	—
565	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
566	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
567	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	8	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	4	4	no	—
582	C₂×D₄	—	4	8	no	—
583	C₂×D₄	—	4	16	no	—
584	C₂×D₄	—	8	4	no	—
585	C₂×D₄	—	8	8	no	—
586	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
587	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
588	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
589	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
590	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
591	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
601	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
602	Q₁₆	—	2	2	no	—
603	SD₁₆	—	2	2	no	—
604	SD₁₆	—	2	2	no	—
605	SD₁₆	—	4	4	no	—
606	D₈	—	2	2	no	—
607	D₈	—	4	4	no	—
608	M₁₆	—	2	4	no	—
609	M₁₆	—	4	4	no	—
610	C₂×C₈	—	2	2	no	—
611	C₂×C₈	—	2	2	no	—
612	C₂×C₈	—	4	4	no	—
613	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
614	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
615	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
616	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
625	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
627	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
638	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	1	no	—
641	C₄²	—	2	1	no	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	4	no	—
644	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
645	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
646	C₄²	C₂⁴×C₅₃	1	2	yes	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	4	8	no	—
651	C₂³	—	4	4	no	—
652	C₂³	—	8	2	no	—
653	C₂³	—	8	2	no	—
654	C₂³	—	8	4	no	—
655	C₂³	—	8	4	no	—
656	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
657	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
658	Q₈	—	2	4	no	—
659	Q₈	—	2	1	no	—
660	Q₈	—	2	1	no	—
661	Q₈	—	2	1	no	—
662	Q₈	C₂×#41×C₅₃	1	2	yes	—
663	D₄	—	2	4	no	—
664	D₄	—	2	8	no	—
665	D₄	—	2	4	no	—
666	D₄	—	2	1	no	—
667	D₄	—	2	4	no	—
668	D₄	—	2	1	no	—
669	D₄	—	2	1	no	—
670	D₄	—	2	4	no	—
671	D₄	—	4	4	no	—
672	D₄	—	4	8	no	—
673	D₄	—	4	8	no	—
674	D₄	—	4	8	no	—
675	D₄	—	4	2	no	—
676	D₄	—	4	4	no	—
677	D₄	—	8	4	no	—
678	D₄	—	8	4	no	—
679	D₄	—	8	4	no	—
680	D₄	—	8	4	no	—
681	D₄	C₂×#41×C₅₃	1	2	yes	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	8	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	8	2	no	—
695	C₂×C₄	—	8	4	no	—
696	C₂×C₄	—	8	2	no	—
697	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
700	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
701	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
702	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
703	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
704	C₈	—	2	1	no	—
705	C₈	—	2	1	no	—
706	C₈	—	2	2	no	—
707	C₈	—	2	4	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	4	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	4	no	—
712	C₂²	—	2	4	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	4	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	4	no	—
718	C₂²	—	4	4	no	—
719	C₂²	—	16	4	no	—
720	C₂²	—	16	8	no	—
721	C₂²	C₅₃×#546	1	2	yes	—
722	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
723	C₄	—	2	2	no	—
724	C₄	—	2	4	no	—
725	C₄	—	2	2	no	—
726	C₄	—	2	2	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	4	no	—
731	C₄	C₅₃×#546	1	2	yes	—
732	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
733	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
734	C₂	—	2	2	no	—
735	C₂	—	4	4	no	—
736	C₂	—	4	2	no	—
737	C₂	—	8	4	no	—
738	C₂	—	8	1	no	—
739	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
740	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 ◁ C₅₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3512	C₂	semidirect
2. C₅₃×#3498	C₂	semidirect
3. C₅₃×#3318	C₂	semidirect
4. C₅₃×#3317	C₂	semidirect
5. C₅₃×#3310	C₂	semidirect
6. C₅₃×#3309	C₂	semidirect
7. C₂×C₅₃×#490	C₂	semidirect
8. C₅₃×#3096	C₂	semidirect
9. C₅₃×#3080	C₂	semidirect
10. C₅₃×#3062	C₂	semidirect
11. C₅₃×#3038	C₂	semidirect
12. C₅₃×#3012	C₂	semidirect
13. C₅₃×#2943	C₂	semidirect
14. C₅₃×#2932	C₂	semidirect
15. C₅₃×#2897	C₂	semidirect
17. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
19. C₂×#131×C₅₃	C₂²	semidirect
21. C₅₃×#553	C₂²	semidirect
22. C₅₃×#552	C₂²	semidirect
28. C₅₃×#537	C₂²	semidirect
36. C₂×#125×C₅₃	C₂²	semidirect
37. C₅₃×#520	C₂²	semidirect
39. C₄×#41×C₅₃	C₂²	semidirect
40. C₅₃×#490	C₂²	semidirect
41. C₅₃×#490	C₂²	semidirect
42. C₅₃×#482	C₂²	semidirect
43. C₅₃×#482	C₂²	semidirect
44. C₅₃×#481	C₂²	semidirect
45. C₅₃×#480	C₂²	semidirect
46. C₅₃×#479	C₂²	semidirect
47. C₅₃×#478	C₂²	semidirect
48. C₅₃×#469	C₂²	semidirect
49. C₅₃×#468	C₂²	semidirect
50. C₅₃×#466	C₂²	semidirect
51. C₅₃×#465	C₂²	semidirect
52. C₅₃×#460	C₂²	semidirect
53. C₅₃×#459	C₂²	semidirect
54. C₅₃×#452	C₂²	semidirect
55. C₅₃×#450	C₂²	semidirect
56. C₅₃×#449	C₂²	semidirect
57. C₅₃×#447	C₂²	semidirect
58. C₅₃×#442	C₂²	semidirect
59. C₅₃×#441	C₂²	semidirect
60. C₅₃×#440	C₂²	semidirect
61. C₅₃×#440	C₂²	semidirect
62. C₅₃×#435	C₂²	semidirect
63. C₅₃×#435	C₂²	semidirect
64. C₅₃×#428	C₂²	semidirect
65. C₅₃×#427	C₂²	semidirect
66. C₅₃×#423	C₂²	semidirect
67. C₅₃×#418	C₂²	semidirect
68. C₅₃×#418	C₂²	semidirect
70. C₅₃×#417	C₂²	semidirect
72. C₅₃×#416	C₂²	semidirect
73. C₅₃×#416	C₂²	semidirect
74. C₂×#102×C₅₃	C₂²	semidirect
75. C₂×#102×C₅₃	C₂²	semidirect
76. C₂×#102×C₅₃	C₂²	semidirect
77. C₅₃×#408	C₂²	semidirect
78. C₂×#97×C₅₃	C₂²	semidirect
337. #61223	C₅₃	direct (N × H)
364. #3512	C₂×C₅₃	semidirect
365. #3498	C₂×C₅₃	semidirect
366. #3318	C₂×C₅₃	semidirect
367. #3317	C₂×C₅₃	semidirect
368. #3310	C₂×C₅₃	semidirect
369. #3309	C₂×C₅₃	semidirect
370. C₂×#490	C₂×C₅₃	semidirect
371. #3096	C₂×C₅₃	semidirect
372. #3080	C₂×C₅₃	semidirect
373. #3062	C₂×C₅₃	semidirect
374. #3038	C₂×C₅₃	semidirect
375. #3012	C₂×C₅₃	semidirect
376. #2943	C₂×C₅₃	semidirect
377. #2932	C₂×C₅₃	semidirect
378. #2897	C₂×C₅₃	semidirect
387. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
389. C₂×#131	C₂²×C₅₃	semidirect
391. #553	C₂²×C₅₃	semidirect
392. #552	C₂²×C₅₃	semidirect
398. #537	C₂²×C₅₃	semidirect
406. C₂×#125	C₂²×C₅₃	semidirect
407. #520	C₂²×C₅₃	semidirect
409. C₄×#41	C₂²×C₅₃	semidirect
410. #490	C₂²×C₅₃	semidirect
411. #490	C₂²×C₅₃	semidirect
412. #482	C₂²×C₅₃	semidirect
413. #482	C₂²×C₅₃	semidirect
414. #481	C₂²×C₅₃	semidirect
415. #480	C₂²×C₅₃	semidirect
416. #479	C₂²×C₅₃	semidirect
417. #478	C₂²×C₅₃	semidirect
418. #469	C₂²×C₅₃	semidirect
419. #468	C₂²×C₅₃	semidirect
420. #466	C₂²×C₅₃	semidirect
421. #465	C₂²×C₅₃	semidirect
422. #460	C₂²×C₅₃	semidirect
423. #459	C₂²×C₅₃	semidirect
424. #452	C₂²×C₅₃	semidirect
425. #450	C₂²×C₅₃	semidirect
426. #449	C₂²×C₅₃	semidirect
427. #447	C₂²×C₅₃	semidirect
428. #442	C₂²×C₅₃	semidirect
429. #441	C₂²×C₅₃	semidirect
430. #440	C₂²×C₅₃	semidirect
431. #440	C₂²×C₅₃	semidirect
432. #435	C₂²×C₅₃	semidirect
433. #435	C₂²×C₅₃	semidirect
434. #428	C₂²×C₅₃	semidirect
435. #427	C₂²×C₅₃	semidirect
436. #423	C₂²×C₅₃	semidirect
437. #418	C₂²×C₅₃	semidirect
438. #418	C₂²×C₅₃	semidirect
440. #417	C₂²×C₅₃	semidirect
442. #416	C₂²×C₅₃	semidirect
443. #416	C₂²×C₅₃	semidirect
444. C₂×#102	C₂²×C₅₃	semidirect
445. C₂×#102	C₂²×C₅₃	semidirect
446. C₂×#102	C₂²×C₅₃	semidirect
447. #408	C₂²×C₅₃	semidirect
448. C₂×#97	C₂²×C₅₃	semidirect
449. C₅₃	#61223	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×#3512	2
C₅₃×#3498	2
C₅₃×#3318	2
C₅₃×#3317	2
C₅₃×#3310	2
C₅₃×#3309	2
C₂×C₅₃×#490	2
C₅₃×#3096	2
C₅₃×#3080	2
C₅₃×#3062	2
C₅₃×#3038	2
C₅₃×#3012	2
C₅₃×#2943	2
C₅₃×#2932	2
C₅₃×#2897	2
#61223	53

Subgroups — C53×#61223 #27268735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61223 #27268735