Subgroups — C₂×C₅₃×#3241 #27268367

Order 13568.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#540	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3241	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#544	—	2	4	no	—
18	C₅₃×#544	C₂²	1	8	yes	complemented
19	C₅₃×#540	—	2	4	no	—
20	C₅₃×#540	C₂²	1	8	yes	—
21	C₂×C₄⋊Q₈×C₅₃	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#125×C₅₃	—	2	1	no	—
26	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#123×C₅₃	—	2	1	no	—
30	C₂×#123×C₅₃	—	2	1	no	—
31	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
32	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
33	C₂×#121×C₅₃	—	2	1	no	—
34	C₂×#121×C₅₃	—	2	1	no	—
35	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
42	C₅₃×#501	C₂²	1	8	yes	complemented
43	C₅₃×#499	C₂²	1	8	yes	complemented
44	C₅₃×#490	C₂²	1	8	yes	complemented
45	C₅₃×#486	C₂²	1	8	yes	complemented
46	C₅₃×#482	C₂²	1	8	yes	complemented
47	C₅₃×#482	C₂²	1	8	yes	complemented
48	C₅₃×#481	C₂²	1	8	yes	complemented
49	C₅₃×#480	C₂²	1	8	yes	complemented
50	C₅₃×#478	C₂²	1	8	yes	complemented
51	C₅₃×#478	C₂²	1	8	yes	complemented
52	C₅₃×#476	C₂²	1	8	yes	complemented
53	C₅₃×#474	C₂²	1	8	yes	complemented
54	C₅₃×#433	C₂²	1	8	yes	complemented
55	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
56	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
57	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
58	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
61	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
62	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
66	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
67	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
68	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
69	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
70	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
71	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
72	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
73	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
75	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₅₃	—	2	1	no	—
78	C₂²×Q₈×C₅₃	—	2	1	no	—
79	C₂²×D₄×C₅₃	—	2	1	no	—
80	C₂²×D₄×C₅₃	—	2	1	no	—
81	C₂²×D₄×C₅₃	—	2	1	no	—
82	C₂²×D₄×C₅₃	—	2	1	no	—
83	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₅₃	—	2	1	no	—
86	C₂³×C₄×C₅₃	—	2	1	no	—
87	C₂³×C₄×C₅₃	—	2	1	no	—
88	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₄⋊Q₈×C₅₃	—	2	8	no	—
94	C₄⋊Q₈×C₅₃	—	2	2	no	—
95	C₄⋊Q₈×C₅₃	—	2	2	no	—
96	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
97	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
98	#127×C₅₃	—	2	2	no	—
99	#127×C₅₃	C₂³	1	4	yes	—
100	#125×C₅₃	—	2	8	no	—
101	#125×C₅₃	—	2	2	no	—
102	#125×C₅₃	—	2	2	no	—
103	#125×C₅₃	—	2	2	no	—
104	#125×C₅₃	C₂³	1	4	yes	—
105	#125×C₅₃	C₂³	1	4	yes	—
106	#125×C₅₃	C₂³	1	4	yes	—
107	#123×C₅₃	—	2	8	no	—
108	#123×C₅₃	—	2	8	no	—
109	C₂²⋊Q₈×C₅₃	—	2	8	no	—
110	C₂²⋊Q₈×C₅₃	—	2	8	no	—
111	#121×C₅₃	—	2	8	no	—
112	#121×C₅₃	—	2	8	no	—
113	#121×C₅₃	—	2	2	no	—
114	#121×C₅₃	—	2	2	no	—
115	#121×C₅₃	C₂³	1	4	yes	—
116	#121×C₅₃	C₂³	1	4	yes	—
117	C₄×D₄×C₅₃	—	2	2	no	—
118	C₄×D₄×C₅₃	—	2	2	no	—
119	C₄×D₄×C₅₃	C₂³	1	4	yes	—
120	C₄×D₄×C₅₃	C₂³	1	4	yes	—
121	#117×C₅₃	—	2	2	no	—
122	#117×C₅₃	D₄	1	4	yes	—
123	#117×C₅₃	C₂³	1	4	yes	—
124	#117×C₅₃	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
126	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
127	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
128	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
129	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
130	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
131	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
132	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
133	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
134	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
135	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
151	C₂×C₄²×C₅₃	—	2	1	no	—
152	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
154	#107×C₅₃	C₂³	1	4	yes	—
155	#107×C₅₃	C₂³	1	4	yes	—
156	#107×C₅₃	C₂³	1	4	yes	—
157	#107×C₅₃	C₂³	1	4	yes	—
158	#106×C₅₃	C₂³	1	4	yes	—
159	#106×C₅₃	C₂³	1	4	yes	—
160	#106×C₅₃	C₂³	1	4	yes	—
161	#106×C₅₃	C₂³	1	4	yes	—
162	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
163	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
164	#102×C₅₃	C₂³	1	4	yes	—
165	#102×C₅₃	C₂³	1	4	yes	—
166	#102×C₅₃	C₂³	1	4	yes	—
167	#102×C₅₃	C₂³	1	4	yes	—
168	#102×C₅₃	C₂³	1	4	yes	—
169	#102×C₅₃	C₂³	1	4	yes	—
170	#102×C₅₃	C₂³	1	4	yes	—
171	#102×C₅₃	C₂³	1	4	yes	—
172	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
173	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
174	#97×C₅₃	C₂³	1	4	yes	—
175	C₄×C₈×C₅₃	C₂³	1	4	yes	—
176	C₂⁴×C₅₃	—	2	1	no	—
177	C₂⁴×C₅₃	—	2	1	no	—
178	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
179	C₂×Q₈×C₅₃	—	2	4	no	—
180	C₂×Q₈×C₅₃	—	2	4	no	—
181	C₂×Q₈×C₅₃	—	8	2	no	—
182	C₂×Q₈×C₅₃	—	8	2	no	—
183	C₂×D₄×C₅₃	—	2	4	no	—
184	C₂×D₄×C₅₃	—	2	4	no	—
185	C₂×D₄×C₅₃	—	2	1	no	—
186	C₂×D₄×C₅₃	—	2	1	no	—
187	C₂×D₄×C₅₃	—	2	4	no	—
188	C₂×D₄×C₅₃	—	2	4	no	—
189	C₂×D₄×C₅₃	—	2	2	no	—
190	C₂×D₄×C₅₃	—	2	2	no	—
191	C₂×D₄×C₅₃	—	2	2	no	—
192	C₂×D₄×C₅₃	—	2	2	no	—
193	C₂×D₄×C₅₃	—	8	2	no	—
194	C₂×D₄×C₅₃	—	8	2	no	—
195	C₂×D₄×C₅₃	—	8	2	no	—
196	C₂×D₄×C₅₃	—	8	2	no	—
197	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
198	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₅₃	—	2	2	no	—
200	C₂²×C₄×C₅₃	—	2	2	no	—
201	C₂²×C₄×C₅₃	—	2	1	no	—
202	C₂²×C₄×C₅₃	—	2	1	no	—
203	C₂²×C₄×C₅₃	—	2	1	no	—
204	C₂²×C₄×C₅₃	—	2	1	no	—
205	C₂²×C₄×C₅₃	—	2	1	no	—
206	C₂²×C₄×C₅₃	—	2	1	no	—
207	C₂²×C₄×C₅₃	—	2	4	no	—
208	C₂²×C₄×C₅₃	—	2	4	no	—
209	C₂²×C₄×C₅₃	—	2	4	no	—
210	C₂²×C₄×C₅₃	—	8	2	no	—
211	C₂²×C₄×C₅₃	—	8	2	no	—
212	C₂²×C₄×C₅₃	—	8	2	no	—
213	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
221	C₂×C₈×C₅₃	—	2	2	no	—
222	C₂×C₈×C₅₃	—	2	2	no	—
223	C₂×C₈×C₅₃	—	2	2	no	—
224	C₂×C₈×C₅₃	—	2	2	no	—
225	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
226	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
227	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
228	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
229	C₄⋊C₄×C₅₃	—	2	4	no	—
230	C₄⋊C₄×C₅₃	—	2	1	no	—
231	C₄⋊C₄×C₅₃	—	2	1	no	—
232	C₄⋊C₄×C₅₃	—	2	4	no	—
233	C₄⋊C₄×C₅₃	—	2	4	no	—
234	C₄⋊C₄×C₅₃	—	2	4	no	—
235	C₄⋊C₄×C₅₃	—	2	4	no	—
236	C₄⋊C₄×C₅₃	—	2	4	no	—
237	C₄⋊C₄×C₅₃	—	2	4	no	—
238	C₄⋊C₄×C₅₃	—	2	4	no	—
239	C₄⋊C₄×C₅₃	—	2	4	no	—
240	C₄⋊C₄×C₅₃	—	2	1	no	—
241	C₄⋊C₄×C₅₃	—	2	1	no	—
242	C₄⋊C₄×C₅₃	—	2	1	no	—
243	C₄⋊C₄×C₅₃	—	2	1	no	—
244	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
245	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
246	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
247	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
248	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
249	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
250	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
252	C₂²⋊C₄×C₅₃	—	2	4	no	—
253	C₂²⋊C₄×C₅₃	—	2	4	no	—
254	C₂²⋊C₄×C₅₃	—	2	4	no	—
255	C₂²⋊C₄×C₅₃	—	2	4	no	—
256	C₂²⋊C₄×C₅₃	—	2	4	no	—
257	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
258	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
259	C₄²×C₅₃	—	2	4	no	—
260	C₄²×C₅₃	C₂×D₄	1	2	yes	—
261	C₄²×C₅₃	C₂×D₄	1	2	yes	—
262	C₄²×C₅₃	C₂⁴	1	2	yes	—
263	C₄²×C₅₃	C₂⁴	1	2	yes	—
264	C₂³×C₅₃	—	2	2	no	—
265	C₂³×C₅₃	—	2	2	no	—
266	C₂³×C₅₃	—	2	2	no	—
267	C₂³×C₅₃	—	2	2	no	—
268	C₂³×C₅₃	—	2	2	no	—
269	C₂³×C₅₃	—	4	2	no	—
270	C₂³×C₅₃	—	4	2	no	—
271	C₂³×C₅₃	—	4	2	no	—
272	C₂³×C₅₃	—	4	2	no	—
273	C₂³×C₅₃	—	4	2	no	—
274	C₂³×C₅₃	—	4	2	no	—
275	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
276	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
277	Q₈×C₅₃	—	8	4	no	—
278	Q₈×C₅₃	—	8	4	no	—
279	D₄×C₅₃	—	2	2	no	—
280	D₄×C₅₃	—	2	2	no	—
281	D₄×C₅₃	—	2	2	no	—
282	D₄×C₅₃	—	2	2	no	—
283	D₄×C₅₃	—	4	2	no	—
284	D₄×C₅₃	—	4	2	no	—
285	D₄×C₅₃	—	8	4	no	—
286	D₄×C₅₃	—	8	4	no	—
287	D₄×C₅₃	—	8	4	no	—
288	D₄×C₅₃	—	8	4	no	—
289	C₂×C₄×C₅₃	—	2	2	no	—
290	C₂×C₄×C₅₃	—	2	2	no	—
291	C₂×C₄×C₅₃	—	2	2	no	—
292	C₂×C₄×C₅₃	—	2	2	no	—
293	C₂×C₄×C₅₃	—	2	2	no	—
294	C₂×C₄×C₅₃	—	2	4	no	—
295	C₂×C₄×C₅₃	—	2	2	no	—
296	C₂×C₄×C₅₃	—	2	2	no	—
297	C₂×C₄×C₅₃	—	2	2	no	—
298	C₂×C₄×C₅₃	—	2	2	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	—	4	2	no	—
304	C₂×C₄×C₅₃	—	4	2	no	—
305	C₂×C₄×C₅₃	—	4	2	no	—
306	C₂×C₄×C₅₃	—	4	2	no	—
307	C₂×C₄×C₅₃	—	4	2	no	—
308	C₂×C₄×C₅₃	—	4	2	no	—
309	C₂×C₄×C₅₃	—	8	4	no	—
310	C₂×C₄×C₅₃	—	8	4	no	—
311	C₂×C₄×C₅₃	—	8	4	no	—
312	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
314	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
318	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
319	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
320	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
321	C₈×C₅₃	—	2	2	no	—
322	C₈×C₅₃	—	2	2	no	—
323	C₈×C₅₃	—	2	2	no	—
324	C₈×C₅₃	—	2	2	no	—
325	C₂×#3241	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
326	C₂²×C₅₃	—	2	2	no	—
327	C₂²×C₅₃	—	2	2	no	—
328	C₂²×C₅₃	—	2	2	no	—
329	C₂²×C₅₃	—	4	4	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	—	8	4	no	—
337	C₂²×C₅₃	—	8	4	no	—
338	C₂²×C₅₃	#536	1	2	yes	—
339	C₂²×C₅₃	#576	1	2	yes	—
340	C₂²×C₅₃	#577	1	2	yes	—
341	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
342	C₄×C₅₃	—	2	2	no	—
343	C₄×C₅₃	—	2	2	no	—
344	C₄×C₅₃	—	2	2	no	—
345	C₄×C₅₃	—	2	2	no	—
346	C₄×C₅₃	—	2	2	no	—
347	C₄×C₅₃	—	4	2	no	—
348	C₄×C₅₃	—	4	2	no	—
349	C₄×C₅₃	—	4	2	no	—
350	C₄×C₅₃	—	4	2	no	—
351	C₄×C₅₃	—	4	2	no	—
352	C₄×C₅₃	—	4	2	no	—
353	C₄×C₅₃	#536	1	2	yes	—
354	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
355	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
356	C₂×#544	C₂×C₅₃	1	1	yes	characteristic, complemented
357	C₂×#540	C₂×C₅₃	1	1	yes	characteristic
358	#3241	C₂×C₅₃	1	16	yes	direct product factor
359	C₂×#501	C₂×C₅₃	1	1	yes	characteristic, complemented
360	C₂×#499	C₂×C₅₃	1	1	yes	characteristic, complemented
361	C₂×#490	C₂×C₅₃	1	1	yes	characteristic, complemented
362	C₂×#486	C₂×C₅₃	1	1	yes	characteristic, complemented
363	C₂×#481	C₂×C₅₃	1	1	yes	characteristic, complemented
364	C₂×#482	C₂×C₅₃	1	1	yes	characteristic, complemented
365	C₂×#482	C₂×C₅₃	1	1	yes	characteristic, complemented
366	C₂×#480	C₂×C₅₃	1	1	yes	characteristic, complemented
367	C₂×#478	C₂×C₅₃	1	1	yes	characteristic, complemented
368	C₂×#478	C₂×C₅₃	1	1	yes	characteristic, complemented
369	C₂×#476	C₂×C₅₃	1	1	yes	characteristic, complemented
370	C₂×#474	C₂×C₅₃	1	1	yes	characteristic, complemented
371	C₂×#433	C₂×C₅₃	1	1	yes	characteristic, complemented
372	C₂×C₅₃	—	4	2	no	—
373	C₂×C₅₃	—	8	2	no	—
374	C₂×C₅₃	—	8	2	no	—
375	C₂×C₅₃	#3241	1	4	yes	direct product factor
376	C₂×C₅₃	C₂×#536	1	1	yes	characteristic
377	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
378	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
379	#544	—	2	4	no	—
380	#544	C₂²×C₅₃	1	8	yes	complemented
381	#540	—	2	4	no	—
382	#540	C₂²×C₅₃	1	8	yes	—
383	C₂×C₄⋊Q₈	—	2	1	no	—
384	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
385	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
386	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
387	C₂×#125	—	2	1	no	—
388	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
389	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
390	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
391	C₂×#123	—	2	1	no	—
392	C₂×#123	—	2	1	no	—
393	C₂×C₂²⋊Q₈	—	2	1	no	—
394	C₂×C₂²⋊Q₈	—	2	1	no	—
395	C₂×#121	—	2	1	no	—
396	C₂×#121	—	2	1	no	—
397	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
398	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
399	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
401	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
402	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
403	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
404	#501	C₂²×C₅₃	1	8	yes	complemented
405	#499	C₂²×C₅₃	1	8	yes	complemented
406	#490	C₂²×C₅₃	1	8	yes	complemented
407	#486	C₂²×C₅₃	1	8	yes	complemented
408	#482	C₂²×C₅₃	1	8	yes	complemented
409	#482	C₂²×C₅₃	1	8	yes	complemented
410	#481	C₂²×C₅₃	1	8	yes	complemented
411	#480	C₂²×C₅₃	1	8	yes	complemented
412	#478	C₂²×C₅₃	1	8	yes	complemented
413	#478	C₂²×C₅₃	1	8	yes	complemented
414	#476	C₂²×C₅₃	1	8	yes	complemented
415	#474	C₂²×C₅₃	1	8	yes	complemented
416	#433	C₂²×C₅₃	1	8	yes	complemented
417	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
418	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
419	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
420	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
421	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
422	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
423	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
424	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
425	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
426	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
427	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
428	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
429	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
430	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
431	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
432	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
433	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
434	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
435	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
436	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
437	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
438	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
439	C₅₃	C₂×#3241	1	1	yes	characteristic, direct product factor, Sylow
440	C₂²×Q₈	—	2	1	no	—
441	C₂²×Q₈	—	2	1	no	—
442	C₂²×D₄	—	2	1	no	—
443	C₂²×D₄	—	2	1	no	—
444	C₂²×D₄	—	2	1	no	—
445	C₂²×D₄	—	2	1	no	—
446	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
447	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
448	C₂³×C₄	—	2	1	no	—
449	C₂³×C₄	—	2	1	no	—
450	C₂³×C₄	—	2	1	no	—
451	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
455	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
456	C₄⋊Q₈	—	2	8	no	—
457	C₄⋊Q₈	—	2	2	no	—
458	C₄⋊Q₈	—	2	2	no	—
459	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
460	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
461	#127	—	2	2	no	—
462	#127	C₂³×C₅₃	1	4	yes	—
463	#125	—	2	8	no	—
464	#125	—	2	2	no	—
465	#125	—	2	2	no	—
466	#125	—	2	2	no	—
467	#125	C₂³×C₅₃	1	4	yes	—
468	#125	C₂³×C₅₃	1	4	yes	—
469	#125	C₂³×C₅₃	1	4	yes	—
470	#123	—	2	8	no	—
471	#123	—	2	8	no	—
472	C₂²⋊Q₈	—	2	8	no	—
473	C₂²⋊Q₈	—	2	8	no	—
474	#121	—	2	2	no	—
475	#121	—	2	2	no	—
476	#121	—	2	8	no	—
477	#121	—	2	8	no	—
478	#121	C₂³×C₅₃	1	4	yes	—
479	#121	C₂³×C₅₃	1	4	yes	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	C₂³×C₅₃	1	4	yes	—
483	C₄×D₄	C₂³×C₅₃	1	4	yes	—
484	#117	—	2	2	no	—
485	#117	D₄×C₅₃	1	4	yes	—
486	#117	C₂³×C₅₃	1	4	yes	—
487	#117	C₂³×C₅₃	1	4	yes	—
488	C₂×C₄⋊C₄	—	2	1	no	—
489	C₂×C₄⋊C₄	—	2	2	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
514	C₂×C₄²	—	2	1	no	—
515	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
516	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
517	#107	C₂³×C₅₃	1	4	yes	—
518	#107	C₂³×C₅₃	1	4	yes	—
519	#107	C₂³×C₅₃	1	4	yes	—
520	#107	C₂³×C₅₃	1	4	yes	—
521	#106	C₂³×C₅₃	1	4	yes	—
522	#106	C₂³×C₅₃	1	4	yes	—
523	#106	C₂³×C₅₃	1	4	yes	—
524	#106	C₂³×C₅₃	1	4	yes	—
525	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
526	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
527	#102	C₂³×C₅₃	1	4	yes	—
528	#102	C₂³×C₅₃	1	4	yes	—
529	#102	C₂³×C₅₃	1	4	yes	—
530	#102	C₂³×C₅₃	1	4	yes	—
531	#102	C₂³×C₅₃	1	4	yes	—
532	#102	C₂³×C₅₃	1	4	yes	—
533	#102	C₂³×C₅₃	1	4	yes	—
534	#102	C₂³×C₅₃	1	4	yes	—
535	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
536	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
537	#97	C₂³×C₅₃	1	4	yes	—
538	C₄×C₈	C₂³×C₅₃	1	4	yes	—
539	C₂⁴	—	2	1	no	—
540	C₂⁴	—	2	1	no	—
541	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
542	C₂×Q₈	—	2	4	no	—
543	C₂×Q₈	—	2	4	no	—
544	C₂×Q₈	—	8	2	no	—
545	C₂×Q₈	—	8	2	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	8	2	no	—
557	C₂×D₄	—	8	2	no	—
558	C₂×D₄	—	8	2	no	—
559	C₂×D₄	—	8	2	no	—
560	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
561	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	8	2	no	—
574	C₂²×C₄	—	8	2	no	—
575	C₂²×C₄	—	8	2	no	—
576	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
584	C₂×C₈	—	2	2	no	—
585	C₂×C₈	—	2	2	no	—
586	C₂×C₈	—	2	2	no	—
587	C₂×C₈	—	2	2	no	—
588	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
589	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
590	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
591	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
608	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
609	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
610	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
611	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
612	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
613	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
614	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
621	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
622	C₄²	—	2	4	no	—
623	C₄²	C₂×D₄×C₅₃	1	2	yes	—
624	C₄²	C₂×D₄×C₅₃	1	2	yes	—
625	C₄²	C₂⁴×C₅₃	1	2	yes	—
626	C₄²	C₂⁴×C₅₃	1	2	yes	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	4	2	no	—
633	C₂³	—	4	2	no	—
634	C₂³	—	4	2	no	—
635	C₂³	—	4	2	no	—
636	C₂³	—	4	2	no	—
637	C₂³	—	4	2	no	—
638	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
639	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
640	Q₈	—	8	4	no	—
641	Q₈	—	8	4	no	—
642	D₄	—	2	2	no	—
643	D₄	—	2	2	no	—
644	D₄	—	2	2	no	—
645	D₄	—	2	2	no	—
646	D₄	—	4	2	no	—
647	D₄	—	4	2	no	—
648	D₄	—	8	4	no	—
649	D₄	—	8	4	no	—
650	D₄	—	8	4	no	—
651	D₄	—	8	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	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	4	2	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	8	4	no	—
673	C₂×C₄	—	8	4	no	—
674	C₂×C₄	—	8	4	no	—
675	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
676	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
677	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
678	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
679	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
680	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
681	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
682	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
683	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
684	C₈	—	2	2	no	—
685	C₈	—	2	2	no	—
686	C₈	—	2	2	no	—
687	C₈	—	2	2	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	4	4	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	—	8	4	no	—
699	C₂²	—	8	4	no	—
700	C₂²	C₅₃×#536	1	2	yes	—
701	C₂²	C₅₃×#576	1	2	yes	—
702	C₂²	C₅₃×#577	1	2	yes	—
703	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	2	no	—
708	C₄	—	2	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	C₅₃×#536	1	2	yes	—
716	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
717	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
718	C₂	—	4	2	no	—
719	C₂	—	8	2	no	—
720	C₂	—	8	2	no	—
721	C₂	C₅₃×#3241	1	4	yes	direct product factor
722	C₂	C₂×C₅₃×#536	1	1	yes	characteristic
723	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
724	C₂	C₂×C₅₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₂×C₅₃×#540	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×#117×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#544	C₂	semidirect
3. C₅₃×#3241	C₂	direct (N × H)
4. C₂×C₅₃×#501	C₂	semidirect
5. C₂×C₅₃×#499	C₂	semidirect
6. C₂×C₅₃×#490	C₂	semidirect
7. C₂×C₅₃×#486	C₂	semidirect
8. C₂×C₅₃×#481	C₂	semidirect
9. C₂×C₅₃×#482	C₂	semidirect
10. C₂×C₅₃×#482	C₂	semidirect
11. C₂×C₅₃×#480	C₂	semidirect
12. C₂×C₅₃×#478	C₂	semidirect
13. C₂×C₅₃×#478	C₂	semidirect
14. C₂×C₅₃×#476	C₂	semidirect
15. C₂×C₅₃×#474	C₂	semidirect
16. C₂×C₅₃×#433	C₂	semidirect
18. C₅₃×#544	C₂²	semidirect
42. C₅₃×#501	C₂²	semidirect
43. C₅₃×#499	C₂²	semidirect
44. C₅₃×#490	C₂²	semidirect
45. C₅₃×#486	C₂²	semidirect
46. C₅₃×#482	C₂²	semidirect
47. C₅₃×#482	C₂²	semidirect
48. C₅₃×#481	C₂²	semidirect
49. C₅₃×#480	C₂²	semidirect
50. C₅₃×#478	C₂²	semidirect
51. C₅₃×#478	C₂²	semidirect
52. C₅₃×#476	C₂²	semidirect
53. C₅₃×#474	C₂²	semidirect
54. C₅₃×#433	C₂²	semidirect
325. C₂×#3241	C₅₃	direct (N × H)
356. C₂×#544	C₂×C₅₃	semidirect
358. #3241	C₂×C₅₃	direct (N × H)
359. C₂×#501	C₂×C₅₃	semidirect
360. C₂×#499	C₂×C₅₃	semidirect
361. C₂×#490	C₂×C₅₃	semidirect
362. C₂×#486	C₂×C₅₃	semidirect
363. C₂×#481	C₂×C₅₃	semidirect
364. C₂×#482	C₂×C₅₃	semidirect
365. C₂×#482	C₂×C₅₃	semidirect
366. C₂×#480	C₂×C₅₃	semidirect
367. C₂×#478	C₂×C₅₃	semidirect
368. C₂×#478	C₂×C₅₃	semidirect
369. C₂×#476	C₂×C₅₃	semidirect
370. C₂×#474	C₂×C₅₃	semidirect
371. C₂×#433	C₂×C₅₃	semidirect
375. C₂×C₅₃	#3241	direct (N × H)
380. #544	C₂²×C₅₃	semidirect
404. #501	C₂²×C₅₃	semidirect
405. #499	C₂²×C₅₃	semidirect
406. #490	C₂²×C₅₃	semidirect
407. #486	C₂²×C₅₃	semidirect
408. #482	C₂²×C₅₃	semidirect
409. #482	C₂²×C₅₃	semidirect
410. #481	C₂²×C₅₃	semidirect
411. #480	C₂²×C₅₃	semidirect
412. #478	C₂²×C₅₃	semidirect
413. #478	C₂²×C₅₃	semidirect
414. #476	C₂²×C₅₃	semidirect
415. #474	C₂²×C₅₃	semidirect
416. #433	C₂²×C₅₃	semidirect
439. C₅₃	C₂×#3241	direct (N × H)
721. C₂	C₅₃×#3241	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#544	2
C₂×C₅₃×#540	2
C₅₃×#3241	2
C₂×C₅₃×#501	2
C₂×C₅₃×#499	2
C₂×C₅₃×#490	2
C₂×C₅₃×#486	2
C₂×C₅₃×#481	2
C₂×C₅₃×#482	2
C₂×C₅₃×#480	2
C₂×C₅₃×#478	2
C₂×C₅₃×#476	2
C₂×C₅₃×#474	2
C₂×C₅₃×#433	2
C₂×#3241	53

Subgroups — C2×C53×#3241 #27268367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3241 #27268367