Subgroups — C₂×C₅₃×#2321 #27241573

Order 13568.

5094 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#120×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2321	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅₃×#390	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₃×#388	C₂	1	2	yes	maximal, complemented
7	C₂×C₅₃×#388	C₂	1	2	yes	maximal, complemented
8	C₂×C₅₃×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₅₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₅₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
19	C₂×#120×C₅₃	C₄	1	16	yes	complemented
20	C₂×#120×C₅₃	C₂²	1	8	yes	—
21	C₂×C₄×D₄×C₅₃	—	2	8	no	—
22	C₂×C₄×D₄×C₅₃	C₂²	1	8	yes	complemented
23	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
25	C₂²×C₂²⋊C₄×C₅₃	—	2	8	no	—
26	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
34	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	8	yes	complemented
35	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
37	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₄²×C₅₃	C₂²	1	2	yes	complemented
39	C₅₃×#390	C₂²	1	16	yes	complemented
40	C₅₃×#388	C₂²	1	16	yes	complemented
41	C₅₃×#388	C₂²	1	16	yes	complemented
42	C₅₃×#386	C₂²	1	16	yes	complemented
43	C₅₃×#386	C₂²	1	8	yes	complemented
44	C₅₃×#385	C₂²	1	8	yes	complemented
45	C₅₃×#379	C₂²	1	8	yes	complemented
46	C₄×C₂²⋊C₄×C₅₃	C₂²	1	8	yes	complemented
47	C₂×#95×C₅₃	C₂²	1	2	yes	complemented
48	C₂×#95×C₅₃	C₂²	1	2	yes	complemented
49	C₂×#95×C₅₃	C₂²	1	2	yes	complemented
50	C₂⁵×C₅₃	—	2	4	no	—
51	C₂⁵×C₅₃	—	2	4	no	—
52	C₂⁵×C₅₃	—	4	4	no	—
53	C₂⁵×C₅₃	—	4	4	no	—
54	C₂⁵×C₅₃	C₂×C₄	1	8	yes	complemented
55	C₂⁵×C₅₃	C₂³	1	2	yes	—
56	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
57	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
58	C₂⁵×C₅₃	C₂³	1	4	yes	—
59	C₂²×D₄×C₅₃	—	2	4	no	—
60	C₂²×D₄×C₅₃	—	2	4	no	—
61	C₂²×D₄×C₅₃	—	4	4	no	—
62	C₂²×D₄×C₅₃	—	4	4	no	—
63	C₂²×D₄×C₅₃	C₂×C₄	1	8	yes	—
64	C₂²×D₄×C₅₃	C₂×C₄	1	16	yes	complemented
65	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
66	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
67	C₂³×C₄×C₅₃	—	2	4	no	—
68	C₂³×C₄×C₅₃	—	2	4	no	—
69	C₂³×C₄×C₅₃	—	4	4	no	—
70	C₂³×C₄×C₅₃	—	4	4	no	—
71	C₂³×C₄×C₅₃	—	4	4	no	—
72	C₂³×C₄×C₅₃	D₄	1	8	yes	complemented
73	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
82	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
83	C₂³×C₄×C₅₃	C₂³	1	4	yes	complemented
84	#120×C₅₃	C₂×C₄	1	64	yes	complemented
85	C₄×D₄×C₅₃	—	2	32	no	—
86	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
87	C₂×C₄⋊C₄×C₅₃	—	4	4	no	—
88	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
89	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
90	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
91	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
92	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
93	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
94	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₅₃	—	2	32	no	—
96	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
97	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
98	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
99	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	16	yes	complemented
100	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
101	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
102	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
106	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
107	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
109	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
110	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
111	C₂×C₄²×C₅₃	—	2	4	no	—
112	C₂×C₄²×C₅₃	—	4	4	no	—
113	C₂×C₄²×C₅₃	C₂³	1	4	yes	complemented
114	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
115	#95×C₅₃	C₂³	1	8	yes	complemented
116	#95×C₅₃	C₂³	1	8	yes	complemented
117	#95×C₅₃	C₂³	1	8	yes	complemented
118	C₂⁴×C₅₃	—	2	4	no	—
119	C₂⁴×C₅₃	—	2	4	no	—
120	C₂⁴×C₅₃	—	2	32	no	—
121	C₂⁴×C₅₃	—	2	4	no	—
122	C₂⁴×C₅₃	—	2	8	no	—
123	C₂⁴×C₅₃	—	2	2	no	—
124	C₂⁴×C₅₃	—	2	2	no	—
125	C₂⁴×C₅₃	—	2	4	no	—
126	C₂⁴×C₅₃	—	2	8	no	—
127	C₂⁴×C₅₃	—	2	4	no	—
128	C₂⁴×C₅₃	—	2	4	no	—
129	C₂⁴×C₅₃	—	2	4	no	—
130	C₂⁴×C₅₃	—	2	4	no	—
131	C₂⁴×C₅₃	—	2	4	no	—
132	C₂⁴×C₅₃	—	2	4	no	—
133	C₂⁴×C₅₃	—	4	32	no	—
134	C₂⁴×C₅₃	—	4	8	no	—
135	C₂⁴×C₅₃	—	4	8	no	—
136	C₂⁴×C₅₃	—	4	16	no	—
137	C₂⁴×C₅₃	—	4	16	no	—
138	C₂⁴×C₅₃	—	4	32	no	—
139	C₂⁴×C₅₃	C₂²×C₄	1	8	yes	—
140	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
141	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
142	C₂⁴×C₅₃	C₂²×C₄	1	16	yes	complemented
143	C₂⁴×C₅₃	C₂×D₄	1	4	yes	—
144	C₂⁴×C₅₃	#41	1	4	yes	—
145	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
146	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
147	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
148	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
149	C₂×D₄×C₅₃	—	2	32	no	—
150	C₂×D₄×C₅₃	—	2	8	no	—
151	C₂×D₄×C₅₃	—	2	8	no	—
152	C₂×D₄×C₅₃	—	4	32	no	—
153	C₂×D₄×C₅₃	—	4	8	no	—
154	C₂×D₄×C₅₃	—	4	8	no	—
155	C₂×D₄×C₅₃	C₂²×C₄	1	16	yes	—
156	C₂×D₄×C₅₃	C₂²×C₄	1	32	yes	complemented
157	C₂²×C₄×C₅₃	—	2	2	no	—
158	C₂²×C₄×C₅₃	—	2	2	no	—
159	C₂²×C₄×C₅₃	—	2	4	no	—
160	C₂²×C₄×C₅₃	—	2	4	no	—
161	C₂²×C₄×C₅₃	—	2	4	no	—
162	C₂²×C₄×C₅₃	—	2	4	no	—
163	C₂²×C₄×C₅₃	—	2	2	no	—
164	C₂²×C₄×C₅₃	—	2	8	no	—
165	C₂²×C₄×C₅₃	—	2	4	no	—
166	C₂²×C₄×C₅₃	—	2	2	no	—
167	C₂²×C₄×C₅₃	—	2	4	no	—
168	C₂²×C₄×C₅₃	—	2	4	no	—
169	C₂²×C₄×C₅₃	—	2	4	no	—
170	C₂²×C₄×C₅₃	—	2	4	no	—
171	C₂²×C₄×C₅₃	—	2	4	no	—
172	C₂²×C₄×C₅₃	—	2	4	no	—
173	C₂²×C₄×C₅₃	—	2	4	no	—
174	C₂²×C₄×C₅₃	—	2	8	no	—
175	C₂²×C₄×C₅₃	—	4	16	no	—
176	C₂²×C₄×C₅₃	—	4	8	no	—
177	C₂²×C₄×C₅₃	—	4	8	no	—
178	C₂²×C₄×C₅₃	—	4	8	no	—
179	C₂²×C₄×C₅₃	—	4	16	no	—
180	C₂²×C₄×C₅₃	—	4	16	no	—
181	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	—
183	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
184	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
185	C₂²×C₄×C₅₃	C₂×D₄	1	16	yes	complemented
186	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
194	C₄⋊C₄×C₅₃	—	2	8	no	—
195	C₄⋊C₄×C₅₃	—	4	8	no	—
196	C₂²⋊C₄×C₅₃	—	2	8	no	—
197	C₂²⋊C₄×C₅₃	—	2	8	no	—
198	C₂²⋊C₄×C₅₃	—	2	16	no	—
199	C₂²⋊C₄×C₅₃	—	2	16	no	—
200	C₂²⋊C₄×C₅₃	—	2	8	no	—
201	C₂²⋊C₄×C₅₃	—	4	8	no	—
202	C₂²⋊C₄×C₅₃	—	4	8	no	—
203	C₂²⋊C₄×C₅₃	—	4	8	no	—
204	C₂²⋊C₄×C₅₃	C₂²×C₄	1	32	yes	complemented
205	C₂²⋊C₄×C₅₃	C₂²×C₄	1	16	yes	complemented
206	C₄²×C₅₃	—	2	8	no	—
207	C₄²×C₅₃	—	4	8	no	—
208	C₂³×C₅₃	—	2	16	no	—
209	C₂³×C₅₃	—	2	8	no	—
210	C₂³×C₅₃	—	2	8	no	—
211	C₂³×C₅₃	—	2	16	no	—
212	C₂³×C₅₃	—	2	4	no	—
213	C₂³×C₅₃	—	2	4	no	—
214	C₂³×C₅₃	—	2	8	no	—
215	C₂³×C₅₃	—	2	16	no	—
216	C₂³×C₅₃	—	2	32	no	—
217	C₂³×C₅₃	—	2	16	no	—
218	C₂³×C₅₃	—	2	16	no	—
219	C₂³×C₅₃	—	2	16	no	—
220	C₂³×C₅₃	—	2	2	no	—
221	C₂³×C₅₃	—	2	4	no	—
222	C₂³×C₅₃	—	2	2	no	—
223	C₂³×C₅₃	—	2	4	no	—
224	C₂³×C₅₃	—	2	4	no	—
225	C₂³×C₅₃	—	2	4	no	—
226	C₂³×C₅₃	—	2	4	no	—
227	C₂³×C₅₃	—	2	4	no	—
228	C₂³×C₅₃	—	2	4	no	—
229	C₂³×C₅₃	—	2	4	no	—
230	C₂³×C₅₃	—	4	32	no	—
231	C₂³×C₅₃	—	4	128	no	—
232	C₂³×C₅₃	—	4	16	no	—
233	C₂³×C₅₃	—	4	16	no	—
234	C₂³×C₅₃	—	4	32	no	—
235	C₂³×C₅₃	—	4	4	no	—
236	C₂³×C₅₃	—	4	8	no	—
237	C₂³×C₅₃	—	4	4	no	—
238	C₂³×C₅₃	—	4	8	no	—
239	C₂³×C₅₃	—	4	8	no	—
240	C₂³×C₅₃	—	4	8	no	—
241	C₂³×C₅₃	—	4	8	no	—
242	C₂³×C₅₃	C₄×D₄	1	16	yes	—
243	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
244	C₂³×C₅₃	C₂³×C₄	1	8	yes	—
245	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
246	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
247	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
248	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
249	C₂³×C₅₃	C₂×#41	1	4	yes	—
250	C₂³×C₅₃	C₂×#41	1	2	yes	—
251	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
252	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
253	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
254	D₄×C₅₃	—	2	32	no	—
255	D₄×C₅₃	—	4	32	no	—
256	C₂×C₄×C₅₃	—	2	8	no	—
257	C₂×C₄×C₅₃	—	2	16	no	—
258	C₂×C₄×C₅₃	—	2	8	no	—
259	C₂×C₄×C₅₃	—	2	8	no	—
260	C₂×C₄×C₅₃	—	2	2	no	—
261	C₂×C₄×C₅₃	—	2	2	no	—
262	C₂×C₄×C₅₃	—	2	4	no	—
263	C₂×C₄×C₅₃	—	2	4	no	—
264	C₂×C₄×C₅₃	—	2	4	no	—
265	C₂×C₄×C₅₃	—	2	4	no	—
266	C₂×C₄×C₅₃	—	2	4	no	—
267	C₂×C₄×C₅₃	—	2	2	no	—
268	C₂×C₄×C₅₃	—	2	2	no	—
269	C₂×C₄×C₅₃	—	2	4	no	—
270	C₂×C₄×C₅₃	—	2	4	no	—
271	C₂×C₄×C₅₃	—	2	4	no	—
272	C₂×C₄×C₅₃	—	2	4	no	—
273	C₂×C₄×C₅₃	—	2	4	no	—
274	C₂×C₄×C₅₃	—	2	4	no	—
275	C₂×C₄×C₅₃	—	2	4	no	—
276	C₂×C₄×C₅₃	—	4	16	no	—
277	C₂×C₄×C₅₃	—	4	16	no	—
278	C₂×C₄×C₅₃	—	4	16	no	—
279	C₂×C₄×C₅₃	—	4	4	no	—
280	C₂×C₄×C₅₃	—	4	4	no	—
281	C₂×C₄×C₅₃	—	4	8	no	—
282	C₂×C₄×C₅₃	—	4	8	no	—
283	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
284	C₂×C₄×C₅₃	C₂³×C₄	1	8	yes	—
285	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
286	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
287	C₂×#2321	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂²×C₅₃	—	2	32	no	—
289	C₂²×C₅₃	—	2	8	no	—
290	C₂²×C₅₃	—	2	4	no	—
291	C₂²×C₅₃	—	2	4	no	—
292	C₂²×C₅₃	—	2	8	no	—
293	C₂²×C₅₃	—	2	4	no	—
294	C₂²×C₅₃	—	2	8	no	—
295	C₂²×C₅₃	—	2	8	no	—
296	C₂²×C₅₃	—	2	8	no	—
297	C₂²×C₅₃	—	2	8	no	—
298	C₂²×C₅₃	—	4	64	no	—
299	C₂²×C₅₃	—	4	16	no	—
300	C₂²×C₅₃	—	4	32	no	—
301	C₂²×C₅₃	—	4	2	no	—
302	C₂²×C₅₃	—	4	4	no	—
303	C₂²×C₅₃	—	4	2	no	—
304	C₂²×C₅₃	—	4	4	no	—
305	C₂²×C₅₃	—	4	4	no	—
306	C₂²×C₅₃	—	4	4	no	—
307	C₂²×C₅₃	—	4	4	no	—
308	C₂²×C₅₃	C₂×C₄×D₄	1	8	yes	—
309	C₂²×C₅₃	C₂×C₄×D₄	1	4	yes	—
310	C₂²×C₅₃	#518	1	8	yes	—
311	C₂²×C₅₃	#534	1	4	yes	—
312	C₂²×C₅₃	#535	1	4	yes	—
313	C₂²×C₅₃	#538	1	8	yes	—
314	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
315	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
316	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
317	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
318	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
319	C₄×C₅₃	—	2	4	no	—
320	C₄×C₅₃	—	2	8	no	—
321	C₄×C₅₃	—	2	4	no	—
322	C₄×C₅₃	—	2	4	no	—
323	C₄×C₅₃	—	4	2	no	—
324	C₄×C₅₃	—	4	2	no	—
325	C₄×C₅₃	—	4	4	no	—
326	C₄×C₅₃	—	4	4	no	—
327	C₂²×#120	C₂×C₅₃	1	1	yes	characteristic
328	C₂²×C₄×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
329	C₂³×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
330	#2321	C₂×C₅₃	1	16	yes	direct product factor
331	C₂×#390	C₂×C₅₃	1	2	yes	complemented
332	C₂×#388	C₂×C₅₃	1	2	yes	complemented
333	C₂×#388	C₂×C₅₃	1	2	yes	complemented
334	C₂×#386	C₂×C₅₃	1	2	yes	complemented
335	C₂×#386	C₂×C₅₃	1	1	yes	characteristic, complemented
336	C₂×#385	C₂×C₅₃	1	1	yes	characteristic, complemented
337	C₂×#379	C₂×C₅₃	1	1	yes	characteristic, complemented
338	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
339	C₂×C₅₃	—	2	8	no	—
340	C₂×C₅₃	—	4	4	no	—
341	C₂×C₅₃	—	4	8	no	—
342	C₂×C₅₃	#2321	1	8	yes	direct product factor
343	C₂×C₅₃	C₂²×C₄×D₄	1	1	yes	characteristic
344	C₂×C₅₃	C₂×#518	1	2	yes	—
345	C₂×C₅₃	C₂×#534	1	1	yes	characteristic
346	C₂×C₅₃	C₂×#535	1	1	yes	characteristic
347	C₂×C₅₃	C₂×#538	1	2	yes	—
348	C₂⁶	C₂²×C₅₃	1	1	yes	characteristic
349	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
350	C₂³×D₄	C₂²×C₅₃	1	2	yes	—
351	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
352	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
353	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
354	C₂×#120	C₄×C₅₃	1	16	yes	complemented
355	C₂×#120	C₂²×C₅₃	1	8	yes	—
356	C₂×C₄×D₄	—	2	8	no	—
357	C₂×C₄×D₄	C₂²×C₅₃	1	8	yes	complemented
358	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
359	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
360	C₂²×C₂²⋊C₄	—	2	8	no	—
361	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
362	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
363	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
364	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
365	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
366	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
367	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
368	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
369	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	8	yes	complemented
370	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
371	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
372	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
373	C₂²×C₄²	C₂²×C₅₃	1	2	yes	complemented
374	#390	C₂²×C₅₃	1	16	yes	complemented
375	#388	C₂²×C₅₃	1	16	yes	complemented
376	#388	C₂²×C₅₃	1	16	yes	complemented
377	#386	C₂²×C₅₃	1	16	yes	complemented
378	#386	C₂²×C₅₃	1	8	yes	complemented
379	#385	C₂²×C₅₃	1	8	yes	complemented
380	#379	C₂²×C₅₃	1	8	yes	complemented
381	C₄×C₂²⋊C₄	C₂²×C₅₃	1	8	yes	complemented
382	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
383	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
384	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
385	C₅₃	C₂×#2321	1	1	yes	characteristic, direct product factor, Sylow
386	C₂⁵	—	2	4	no	—
387	C₂⁵	—	2	4	no	—
388	C₂⁵	—	4	4	no	—
389	C₂⁵	—	4	4	no	—
390	C₂⁵	C₂×C₄×C₅₃	1	8	yes	complemented
391	C₂⁵	C₂³×C₅₃	1	2	yes	—
392	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
393	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
394	C₂⁵	C₂³×C₅₃	1	4	yes	—
395	C₂²×D₄	—	2	4	no	—
396	C₂²×D₄	—	2	4	no	—
397	C₂²×D₄	—	4	4	no	—
398	C₂²×D₄	—	4	4	no	—
399	C₂²×D₄	C₂×C₄×C₅₃	1	8	yes	—
400	C₂²×D₄	C₂×C₄×C₅₃	1	16	yes	complemented
401	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
402	C₂²×D₄	C₂³×C₅₃	1	8	yes	—
403	C₂³×C₄	—	2	4	no	—
404	C₂³×C₄	—	2	4	no	—
405	C₂³×C₄	—	4	4	no	—
406	C₂³×C₄	—	4	4	no	—
407	C₂³×C₄	—	4	4	no	—
408	C₂³×C₄	D₄×C₅₃	1	8	yes	complemented
409	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
410	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
411	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
412	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
413	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
414	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
415	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
418	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
419	C₂³×C₄	C₂³×C₅₃	1	4	yes	complemented
420	#120	C₂×C₄×C₅₃	1	64	yes	complemented
421	C₄×D₄	—	2	32	no	—
422	C₂×C₄⋊C₄	—	2	4	no	—
423	C₂×C₄⋊C₄	—	4	4	no	—
424	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	complemented
425	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
426	C₂×C₂²⋊C₄	—	2	4	no	—
427	C₂×C₂²⋊C₄	—	2	4	no	—
428	C₂×C₂²⋊C₄	—	2	8	no	—
429	C₂×C₂²⋊C₄	—	2	8	no	—
430	C₂×C₂²⋊C₄	—	2	4	no	—
431	C₂×C₂²⋊C₄	—	2	32	no	—
432	C₂×C₂²⋊C₄	—	4	4	no	—
433	C₂×C₂²⋊C₄	—	4	4	no	—
434	C₂×C₂²⋊C₄	—	4	4	no	—
435	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	16	yes	complemented
436	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	complemented
437	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	complemented
446	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	complemented
447	C₂×C₄²	—	2	4	no	—
448	C₂×C₄²	—	4	4	no	—
449	C₂×C₄²	C₂³×C₅₃	1	4	yes	complemented
450	C₂×C₄²	C₂³×C₅₃	1	8	yes	complemented
451	#95	C₂³×C₅₃	1	8	yes	complemented
452	#95	C₂³×C₅₃	1	8	yes	complemented
453	#95	C₂³×C₅₃	1	8	yes	complemented
454	C₂⁴	—	2	4	no	—
455	C₂⁴	—	2	4	no	—
456	C₂⁴	—	2	32	no	—
457	C₂⁴	—	2	4	no	—
458	C₂⁴	—	2	8	no	—
459	C₂⁴	—	2	2	no	—
460	C₂⁴	—	2	2	no	—
461	C₂⁴	—	2	4	no	—
462	C₂⁴	—	2	8	no	—
463	C₂⁴	—	2	4	no	—
464	C₂⁴	—	2	4	no	—
465	C₂⁴	—	2	4	no	—
466	C₂⁴	—	2	4	no	—
467	C₂⁴	—	2	4	no	—
468	C₂⁴	—	2	4	no	—
469	C₂⁴	—	4	32	no	—
470	C₂⁴	—	4	8	no	—
471	C₂⁴	—	4	8	no	—
472	C₂⁴	—	4	16	no	—
473	C₂⁴	—	4	16	no	—
474	C₂⁴	—	4	32	no	—
475	C₂⁴	C₂²×C₄×C₅₃	1	8	yes	—
476	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
477	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
478	C₂⁴	C₂²×C₄×C₅₃	1	16	yes	complemented
479	C₂⁴	C₂×D₄×C₅₃	1	4	yes	—
480	C₂⁴	#41×C₅₃	1	4	yes	—
481	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
482	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
483	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
484	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
485	C₂×D₄	—	2	32	no	—
486	C₂×D₄	—	2	8	no	—
487	C₂×D₄	—	2	8	no	—
488	C₂×D₄	—	4	32	no	—
489	C₂×D₄	—	4	8	no	—
490	C₂×D₄	—	4	8	no	—
491	C₂×D₄	C₂²×C₄×C₅₃	1	16	yes	—
492	C₂×D₄	C₂²×C₄×C₅₃	1	32	yes	complemented
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	8	no	—
501	C₂²×C₄	—	2	4	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	8	no	—
511	C₂²×C₄	—	4	16	no	—
512	C₂²×C₄	—	4	8	no	—
513	C₂²×C₄	—	4	8	no	—
514	C₂²×C₄	—	4	8	no	—
515	C₂²×C₄	—	4	16	no	—
516	C₂²×C₄	—	4	16	no	—
517	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
518	C₂²×C₄	C₂²×C₄×C₅₃	1	8	yes	—
519	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
520	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
521	C₂²×C₄	C₂×D₄×C₅₃	1	16	yes	complemented
522	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
525	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
530	C₄⋊C₄	—	2	8	no	—
531	C₄⋊C₄	—	4	8	no	—
532	C₂²⋊C₄	—	2	8	no	—
533	C₂²⋊C₄	—	2	8	no	—
534	C₂²⋊C₄	—	2	16	no	—
535	C₂²⋊C₄	—	2	16	no	—
536	C₂²⋊C₄	—	2	8	no	—
537	C₂²⋊C₄	—	4	8	no	—
538	C₂²⋊C₄	—	4	8	no	—
539	C₂²⋊C₄	—	4	8	no	—
540	C₂²⋊C₄	C₂²×C₄×C₅₃	1	32	yes	complemented
541	C₂²⋊C₄	C₂²×C₄×C₅₃	1	16	yes	complemented
542	C₄²	—	2	8	no	—
543	C₄²	—	4	8	no	—
544	C₂³	—	2	16	no	—
545	C₂³	—	2	8	no	—
546	C₂³	—	2	8	no	—
547	C₂³	—	2	16	no	—
548	C₂³	—	2	4	no	—
549	C₂³	—	2	4	no	—
550	C₂³	—	2	8	no	—
551	C₂³	—	2	16	no	—
552	C₂³	—	2	32	no	—
553	C₂³	—	2	16	no	—
554	C₂³	—	2	16	no	—
555	C₂³	—	2	16	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	2	2	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	2	4	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	2	4	no	—
562	C₂³	—	2	4	no	—
563	C₂³	—	2	4	no	—
564	C₂³	—	2	4	no	—
565	C₂³	—	2	4	no	—
566	C₂³	—	4	32	no	—
567	C₂³	—	4	32	no	—
568	C₂³	—	4	128	no	—
569	C₂³	—	4	16	no	—
570	C₂³	—	4	16	no	—
571	C₂³	—	4	4	no	—
572	C₂³	—	4	8	no	—
573	C₂³	—	4	4	no	—
574	C₂³	—	4	8	no	—
575	C₂³	—	4	8	no	—
576	C₂³	—	4	8	no	—
577	C₂³	—	4	8	no	—
578	C₂³	C₄×D₄×C₅₃	1	16	yes	—
579	C₂³	C₂³×C₄×C₅₃	1	8	yes	—
580	C₂³	C₂³×C₄×C₅₃	1	4	yes	—
581	C₂³	C₂³×C₄×C₅₃	1	4	yes	—
582	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
583	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
584	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
585	C₂³	C₂×#41×C₅₃	1	4	yes	—
586	C₂³	C₂×#41×C₅₃	1	2	yes	—
587	C₂³	H(5,𝔽₂)×C₅₃	1	4	yes	—
588	C₂³	H(5,𝔽₂)×C₅₃	1	4	yes	—
589	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
590	D₄	—	2	32	no	—
591	D₄	—	4	32	no	—
592	C₂×C₄	—	2	8	no	—
593	C₂×C₄	—	2	16	no	—
594	C₂×C₄	—	2	8	no	—
595	C₂×C₄	—	2	8	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	4	16	no	—
613	C₂×C₄	—	4	16	no	—
614	C₂×C₄	—	4	16	no	—
615	C₂×C₄	—	4	4	no	—
616	C₂×C₄	—	4	4	no	—
617	C₂×C₄	—	4	8	no	—
618	C₂×C₄	—	4	8	no	—
619	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
620	C₂×C₄	C₂³×C₄×C₅₃	1	8	yes	—
621	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
622	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
623	C₂²	—	2	8	no	—
624	C₂²	—	2	32	no	—
625	C₂²	—	2	8	no	—
626	C₂²	—	2	4	no	—
627	C₂²	—	2	4	no	—
628	C₂²	—	2	4	no	—
629	C₂²	—	2	8	no	—
630	C₂²	—	2	8	no	—
631	C₂²	—	2	8	no	—
632	C₂²	—	2	8	no	—
633	C₂²	—	4	64	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	4	4	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	4	32	no	—
638	C₂²	—	4	16	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	4	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	2	no	—
643	C₂²	C₂×C₄×D₄×C₅₃	1	8	yes	—
644	C₂²	C₂×C₄×D₄×C₅₃	1	4	yes	—
645	C₂²	C₅₃×#518	1	8	yes	—
646	C₂²	C₅₃×#534	1	4	yes	—
647	C₂²	C₅₃×#535	1	4	yes	—
648	C₂²	C₅₃×#538	1	8	yes	—
649	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
650	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
651	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
652	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
653	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
654	C₄	—	2	4	no	—
655	C₄	—	2	8	no	—
656	C₄	—	2	4	no	—
657	C₄	—	2	4	no	—
658	C₄	—	4	4	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	4	no	—
661	C₄	—	4	2	no	—
662	C₂	—	2	8	no	—
663	C₂	—	4	8	no	—
664	C₂	—	4	4	no	—
665	C₂	C₅₃×#2321	1	8	yes	direct product factor
666	C₂	C₂²×C₄×D₄×C₅₃	1	1	yes	characteristic
667	C₂	C₂×C₅₃×#518	1	2	yes	—
668	C₂	C₂×C₅₃×#534	1	1	yes	characteristic
669	C₂	C₂×C₅₃×#535	1	1	yes	characteristic
670	C₂	C₂×C₅₃×#538	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₅₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₅₃
Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂²×#120×C₅₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₄×C₅₃	C₂	semidirect
3. C₂³×C₂²⋊C₄×C₅₃	C₂	semidirect
4. C₅₃×#2321	C₂	direct (N × H)
5. C₂×C₅₃×#390	C₂	semidirect
6. C₂×C₅₃×#388	C₂	semidirect
7. C₂×C₅₃×#388	C₂	semidirect
8. C₂×C₅₃×#386	C₂	semidirect
9. C₂×C₅₃×#386	C₂	semidirect
10. C₂×C₅₃×#385	C₂	semidirect
11. C₂×C₅₃×#379	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
18. C₂⁴×C₄×C₅₃	C₂²	semidirect
19. C₂×#120×C₅₃	C₄	semidirect
22. C₂×C₄×D₄×C₅₃	C₂²	semidirect
23. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
24. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
34. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
35. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
36. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
37. C₂²×C₄²×C₅₃	C₂²	semidirect
38. C₂²×C₄²×C₅₃	C₂²	semidirect
39. C₅₃×#390	C₂²	semidirect
40. C₅₃×#388	C₂²	semidirect
41. C₅₃×#388	C₂²	semidirect
42. C₅₃×#386	C₂²	semidirect
43. C₅₃×#386	C₂²	semidirect
44. C₅₃×#385	C₂²	semidirect
45. C₅₃×#379	C₂²	semidirect
46. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
47. C₂×#95×C₅₃	C₂²	semidirect
48. C₂×#95×C₅₃	C₂²	semidirect
49. C₂×#95×C₅₃	C₂²	semidirect
54. C₂⁵×C₅₃	C₂×C₄	semidirect
64. C₂²×D₄×C₅₃	C₂×C₄	semidirect
72. C₂³×C₄×C₅₃	D₄	semidirect
83. C₂³×C₄×C₅₃	C₂³	semidirect
84. #120×C₅₃	C₂×C₄	semidirect
88. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
89. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
99. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
100. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
109. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
110. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
113. C₂×C₄²×C₅₃	C₂³	semidirect
114. C₂×C₄²×C₅₃	C₂³	semidirect
115. #95×C₅₃	C₂³	semidirect
116. #95×C₅₃	C₂³	semidirect
117. #95×C₅₃	C₂³	semidirect
142. C₂⁴×C₅₃	C₂²×C₄	semidirect
156. C₂×D₄×C₅₃	C₂²×C₄	semidirect
185. C₂²×C₄×C₅₃	C₂×D₄	semidirect
204. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
205. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
287. C₂×#2321	C₅₃	direct (N × H)
328. C₂²×C₄×D₄	C₂×C₅₃	semidirect
329. C₂³×C₂²⋊C₄	C₂×C₅₃	semidirect
330. #2321	C₂×C₅₃	direct (N × H)
331. C₂×#390	C₂×C₅₃	semidirect
332. C₂×#388	C₂×C₅₃	semidirect
333. C₂×#388	C₂×C₅₃	semidirect
334. C₂×#386	C₂×C₅₃	semidirect
335. C₂×#386	C₂×C₅₃	semidirect
336. C₂×#385	C₂×C₅₃	semidirect
337. C₂×#379	C₂×C₅₃	semidirect
338. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
342. C₂×C₅₃	#2321	direct (N × H)
353. C₂⁴×C₄	C₂²×C₅₃	semidirect
354. C₂×#120	C₄×C₅₃	semidirect
357. C₂×C₄×D₄	C₂²×C₅₃	semidirect
358. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
359. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
369. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
370. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
371. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
372. C₂²×C₄²	C₂²×C₅₃	semidirect
373. C₂²×C₄²	C₂²×C₅₃	semidirect
374. #390	C₂²×C₅₃	semidirect
375. #388	C₂²×C₅₃	semidirect
376. #388	C₂²×C₅₃	semidirect
377. #386	C₂²×C₅₃	semidirect
378. #386	C₂²×C₅₃	semidirect
379. #385	C₂²×C₅₃	semidirect
380. #379	C₂²×C₅₃	semidirect
381. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
382. C₂×#95	C₂²×C₅₃	semidirect
383. C₂×#95	C₂²×C₅₃	semidirect
384. C₂×#95	C₂²×C₅₃	semidirect
385. C₅₃	C₂×#2321	direct (N × H)
390. C₂⁵	C₂×C₄×C₅₃	semidirect
400. C₂²×D₄	C₂×C₄×C₅₃	semidirect
408. C₂³×C₄	D₄×C₅₃	semidirect
419. C₂³×C₄	C₂³×C₅₃	semidirect
420. #120	C₂×C₄×C₅₃	semidirect
424. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
425. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
435. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
436. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
445. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
446. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
449. C₂×C₄²	C₂³×C₅₃	semidirect
450. C₂×C₄²	C₂³×C₅₃	semidirect
451. #95	C₂³×C₅₃	semidirect
452. #95	C₂³×C₅₃	semidirect
453. #95	C₂³×C₅₃	semidirect
478. C₂⁴	C₂²×C₄×C₅₃	semidirect
492. C₂×D₄	C₂²×C₄×C₅₃	semidirect
521. C₂²×C₄	C₂×D₄×C₅₃	semidirect
540. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
541. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
665. C₂	C₅₃×#2321	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#120×C₅₃	2
C₂²×C₄×D₄×C₅₃	2
C₂³×C₂²⋊C₄×C₅₃	2
C₅₃×#2321	2
C₂×C₅₃×#390	2
C₂×C₅₃×#388	2
C₂×C₅₃×#386	2
C₂×C₅₃×#385	2
C₂×C₅₃×#379	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
C₂×#2321	53

Subgroups — C2×C53×#2321 #27241573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#2321 #27241573