Subgroups — C₂×C₅₃×#2358 #27241642

Order 13568.

5942 conjugacy classes of subgroups.

The subgroup lattice has 632 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	2	yes	maximal, complemented
3	C₂³×C₂²⋊C₄×C₅₃	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2358	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#388	C₂	1	2	yes	maximal, complemented
7	C₂×C₅₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₅₃×#385	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	2	yes	maximal, complemented
11	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₅₃	C₂²	1	2	yes	—
13	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₅₃	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₅₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
17	C₂×#120×C₅₃	C₄	1	16	yes	complemented
18	C₂×#120×C₅₃	C₂²	1	8	yes	—
19	C₂×C₄×D₄×C₅₃	—	2	16	no	—
20	C₂×C₄×D₄×C₅₃	C₂²	1	16	yes	complemented
21	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
22	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₂²⋊C₄×C₅₃	—	2	16	no	—
24	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	16	yes	complemented
31	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
32	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₄²×C₅₃	C₂²	1	2	yes	complemented
34	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₅₃×#390	C₂²	1	8	yes	complemented
36	C₅₃×#388	C₂²	1	16	yes	complemented
37	C₅₃×#386	C₂²	1	8	yes	complemented
38	C₅₃×#386	C₂²	1	16	yes	complemented
39	C₅₃×#385	C₂²	1	16	yes	complemented
40	C₄×C₂²⋊C₄×C₅₃	C₂²	1	16	yes	complemented
41	C₂×#95×C₅₃	C₂²	1	2	yes	complemented
42	C₂×#95×C₅₃	C₂²	1	2	yes	complemented
43	C₂×#95×C₅₃	C₂²	1	2	yes	complemented
44	C₂⁵×C₅₃	—	2	8	no	—
45	C₂⁵×C₅₃	—	2	8	no	—
46	C₂⁵×C₅₃	—	4	2	no	—
47	C₂⁵×C₅₃	—	4	2	no	—
48	C₂⁵×C₅₃	C₂×C₄	1	8	yes	complemented
49	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
50	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
51	C₂⁵×C₅₃	C₂³	1	4	yes	—
52	C₂⁵×C₅₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₅₃	—	2	8	no	—
54	C₂²×D₄×C₅₃	—	2	8	no	—
55	C₂²×D₄×C₅₃	—	4	2	no	—
56	C₂²×D₄×C₅₃	—	4	2	no	—
57	C₂²×D₄×C₅₃	C₂×C₄	1	16	yes	complemented
58	C₂²×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
59	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
60	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
61	C₂³×C₄×C₅₃	—	2	8	no	—
62	C₂³×C₄×C₅₃	—	2	8	no	—
63	C₂³×C₄×C₅₃	—	2	8	no	—
64	C₂³×C₄×C₅₃	—	2	8	no	—
65	C₂³×C₄×C₅₃	—	2	8	no	—
66	C₂³×C₄×C₅₃	—	4	4	no	—
67	C₂³×C₄×C₅₃	—	4	4	no	—
68	C₂³×C₄×C₅₃	—	4	2	no	—
69	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
71	C₂³×C₄×C₅₃	C₂³	1	8	yes	—
72	C₂³×C₄×C₅₃	C₂³	1	8	yes	—
73	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₅₃	C₂³	1	4	yes	complemented
78	#120×C₅₃	C₂×C₄	1	64	yes	complemented
79	C₄×D₄×C₅₃	—	2	64	no	—
80	C₂×C₄⋊C₄×C₅₃	—	2	8	no	—
81	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
82	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
83	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
84	C₂×C₂²⋊C₄×C₅₃	—	2	64	no	—
85	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
86	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
87	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
88	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
89	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
90	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
91	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	16	yes	complemented
92	C₂×C₂²⋊C₄×C₅₃	D₄	1	16	yes	complemented
93	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
94	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
95	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
96	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
97	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
99	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
100	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
101	C₂×C₄²×C₅₃	—	2	8	no	—
102	C₂×C₄²×C₅₃	—	4	2	no	—
103	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
104	C₂×C₄²×C₅₃	C₂³	1	4	yes	complemented
105	#95×C₅₃	C₂³	1	8	yes	complemented
106	#95×C₅₃	C₂³	1	8	yes	complemented
107	#95×C₅₃	C₂³	1	8	yes	complemented
108	C₂⁴×C₅₃	—	2	4	no	—
109	C₂⁴×C₅₃	—	2	4	no	—
110	C₂⁴×C₅₃	—	2	4	no	—
111	C₂⁴×C₅₃	—	2	4	no	—
112	C₂⁴×C₅₃	—	2	64	no	—
113	C₂⁴×C₅₃	—	2	16	no	—
114	C₂⁴×C₅₃	—	2	4	no	—
115	C₂⁴×C₅₃	—	2	4	no	—
116	C₂⁴×C₅₃	—	2	4	no	—
117	C₂⁴×C₅₃	—	2	16	no	—
118	C₂⁴×C₅₃	—	2	4	no	—
119	C₂⁴×C₅₃	—	2	2	no	—
120	C₂⁴×C₅₃	—	2	2	no	—
121	C₂⁴×C₅₃	—	2	2	no	—
122	C₂⁴×C₅₃	—	2	2	no	—
123	C₂⁴×C₅₃	—	4	16	no	—
124	C₂⁴×C₅₃	—	4	4	no	—
125	C₂⁴×C₅₃	—	4	4	no	—
126	C₂⁴×C₅₃	—	4	16	no	—
127	C₂⁴×C₅₃	—	4	32	no	—
128	C₂⁴×C₅₃	—	4	16	no	—
129	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
130	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
131	C₂⁴×C₅₃	C₂²×C₄	1	8	yes	—
132	C₂⁴×C₅₃	C₂²×C₄	1	16	yes	complemented
133	C₂⁴×C₅₃	C₂×D₄	1	8	yes	—
134	C₂⁴×C₅₃	#41	1	8	yes	—
135	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
136	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
137	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
138	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
139	C₂×D₄×C₅₃	—	2	64	no	—
140	C₂×D₄×C₅₃	—	2	16	no	—
141	C₂×D₄×C₅₃	—	2	16	no	—
142	C₂×D₄×C₅₃	—	4	16	no	—
143	C₂×D₄×C₅₃	—	4	4	no	—
144	C₂×D₄×C₅₃	—	4	4	no	—
145	C₂×D₄×C₅₃	C₂²×C₄	1	32	yes	complemented
146	C₂×D₄×C₅₃	C₂²×C₄	1	16	yes	complemented
147	C₂²×C₄×C₅₃	—	2	4	no	—
148	C₂²×C₄×C₅₃	—	2	4	no	—
149	C₂²×C₄×C₅₃	—	2	4	no	—
150	C₂²×C₄×C₅₃	—	2	4	no	—
151	C₂²×C₄×C₅₃	—	2	4	no	—
152	C₂²×C₄×C₅₃	—	2	2	no	—
153	C₂²×C₄×C₅₃	—	2	2	no	—
154	C₂²×C₄×C₅₃	—	2	4	no	—
155	C₂²×C₄×C₅₃	—	2	4	no	—
156	C₂²×C₄×C₅₃	—	2	4	no	—
157	C₂²×C₄×C₅₃	—	2	4	no	—
158	C₂²×C₄×C₅₃	—	2	16	no	—
159	C₂²×C₄×C₅₃	—	2	16	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	16	no	—
164	C₂²×C₄×C₅₃	—	2	16	no	—
165	C₂²×C₄×C₅₃	—	2	16	no	—
166	C₂²×C₄×C₅₃	—	4	8	no	—
167	C₂²×C₄×C₅₃	—	4	8	no	—
168	C₂²×C₄×C₅₃	—	4	4	no	—
169	C₂²×C₄×C₅₃	—	4	16	no	—
170	C₂²×C₄×C₅₃	—	4	32	no	—
171	C₂²×C₄×C₅₃	—	4	32	no	—
172	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	—
173	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
175	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
176	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
182	C₄⋊C₄×C₅₃	—	2	16	no	—
183	C₄⋊C₄×C₅₃	—	4	4	no	—
184	C₂²⋊C₄×C₅₃	—	2	16	no	—
185	C₂²⋊C₄×C₅₃	—	2	16	no	—
186	C₂²⋊C₄×C₅₃	—	2	16	no	—
187	C₂²⋊C₄×C₅₃	—	2	16	no	—
188	C₂²⋊C₄×C₅₃	—	4	4	no	—
189	C₂²⋊C₄×C₅₃	C₂²×C₄	1	16	yes	complemented
190	C₂²⋊C₄×C₅₃	C₂²×C₄	1	32	yes	complemented
191	C₂²⋊C₄×C₅₃	C₂×D₄	1	32	yes	complemented
192	C₄²×C₅₃	—	2	16	no	—
193	C₄²×C₅₃	—	4	4	no	—
194	C₂³×C₅₃	—	2	16	no	—
195	C₂³×C₅₃	—	2	16	no	—
196	C₂³×C₅₃	—	2	16	no	—
197	C₂³×C₅₃	—	2	16	no	—
198	C₂³×C₅₃	—	2	16	no	—
199	C₂³×C₅₃	—	2	16	no	—
200	C₂³×C₅₃	—	2	4	no	—
201	C₂³×C₅₃	—	2	4	no	—
202	C₂³×C₅₃	—	2	4	no	—
203	C₂³×C₅₃	—	2	4	no	—
204	C₂³×C₅₃	—	2	16	no	—
205	C₂³×C₅₃	—	2	16	no	—
206	C₂³×C₅₃	—	2	64	no	—
207	C₂³×C₅₃	—	2	8	no	—
208	C₂³×C₅₃	—	2	8	no	—
209	C₂³×C₅₃	—	2	4	no	—
210	C₂³×C₅₃	—	2	4	no	—
211	C₂³×C₅₃	—	2	4	no	—
212	C₂³×C₅₃	—	2	4	no	—
213	C₂³×C₅₃	—	2	2	no	—
214	C₂³×C₅₃	—	2	2	no	—
215	C₂³×C₅₃	—	2	2	no	—
216	C₂³×C₅₃	—	2	2	no	—
217	C₂³×C₅₃	—	4	16	no	—
218	C₂³×C₅₃	—	4	128	no	—
219	C₂³×C₅₃	—	4	16	no	—
220	C₂³×C₅₃	—	4	32	no	—
221	C₂³×C₅₃	—	4	16	no	—
222	C₂³×C₅₃	—	4	4	no	—
223	C₂³×C₅₃	—	4	4	no	—
224	C₂³×C₅₃	—	4	8	no	—
225	C₂³×C₅₃	—	4	8	no	—
226	C₂³×C₅₃	—	4	4	no	—
227	C₂³×C₅₃	—	4	4	no	—
228	C₂³×C₅₃	C₄×D₄	1	32	yes	complemented
229	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
230	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
231	C₂³×C₅₃	C₂³×C₄	1	8	yes	—
232	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
233	C₂³×C₅₃	C₂²×D₄	1	8	yes	—
234	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
235	C₂³×C₅₃	C₂×#41	1	8	yes	—
236	C₂³×C₅₃	C₂×#41	1	4	yes	—
237	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
238	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
239	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
240	D₄×C₅₃	—	2	64	no	—
241	D₄×C₅₃	—	4	16	no	—
242	C₂×C₄×C₅₃	—	2	16	no	—
243	C₂×C₄×C₅₃	—	2	8	no	—
244	C₂×C₄×C₅₃	—	2	16	no	—
245	C₂×C₄×C₅₃	—	2	16	no	—
246	C₂×C₄×C₅₃	—	2	4	no	—
247	C₂×C₄×C₅₃	—	2	4	no	—
248	C₂×C₄×C₅₃	—	2	4	no	—
249	C₂×C₄×C₅₃	—	2	4	no	—
250	C₂×C₄×C₅₃	—	2	4	no	—
251	C₂×C₄×C₅₃	—	2	4	no	—
252	C₂×C₄×C₅₃	—	2	2	no	—
253	C₂×C₄×C₅₃	—	2	2	no	—
254	C₂×C₄×C₅₃	—	2	4	no	—
255	C₂×C₄×C₅₃	—	2	4	no	—
256	C₂×C₄×C₅₃	—	2	4	no	—
257	C₂×C₄×C₅₃	—	2	4	no	—
258	C₂×C₄×C₅₃	—	2	4	no	—
259	C₂×C₄×C₅₃	—	2	4	no	—
260	C₂×C₄×C₅₃	—	4	16	no	—
261	C₂×C₄×C₅₃	—	4	32	no	—
262	C₂×C₄×C₅₃	—	4	32	no	—
263	C₂×C₄×C₅₃	—	4	8	no	—
264	C₂×C₄×C₅₃	—	4	8	no	—
265	C₂×C₄×C₅₃	C₂³×C₄	1	8	yes	—
266	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
267	C₂×C₄×C₅₃	C₂²×D₄	1	8	yes	—
268	C₂×C₄×C₅₃	C₂²×D₄	1	8	yes	—
269	C₂×#2358	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₂²×C₅₃	—	2	64	no	—
271	C₂²×C₅₃	—	2	8	no	—
272	C₂²×C₅₃	—	2	8	no	—
273	C₂²×C₅₃	—	2	8	no	—
274	C₂²×C₅₃	—	2	8	no	—
275	C₂²×C₅₃	—	2	8	no	—
276	C₂²×C₅₃	—	2	8	no	—
277	C₂²×C₅₃	—	2	8	no	—
278	C₂²×C₅₃	—	2	8	no	—
279	C₂²×C₅₃	—	2	4	no	—
280	C₂²×C₅₃	—	2	4	no	—
281	C₂²×C₅₃	—	4	64	no	—
282	C₂²×C₅₃	—	4	16	no	—
283	C₂²×C₅₃	—	4	16	no	—
284	C₂²×C₅₃	—	4	2	no	—
285	C₂²×C₅₃	—	4	2	no	—
286	C₂²×C₅₃	—	4	4	no	—
287	C₂²×C₅₃	—	4	4	no	—
288	C₂²×C₅₃	—	4	2	no	—
289	C₂²×C₅₃	—	4	2	no	—
290	C₂²×C₅₃	C₂×C₄×D₄	1	8	yes	—
291	C₂²×C₅₃	C₂×C₄×D₄	1	16	yes	complemented
292	C₂²×C₅₃	#518	1	4	yes	—
293	C₂²×C₅₃	D₄²	1	4	yes	—
294	C₂²×C₅₃	#546	1	8	yes	—
295	C₂²×C₅₃	#551	1	4	yes	—
296	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
297	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
298	C₂²×C₅₃	C₂²×#41	1	2	yes	—
299	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
300	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
301	C₄×C₅₃	—	2	8	no	—
302	C₄×C₅₃	—	2	4	no	—
303	C₄×C₅₃	—	2	8	no	—
304	C₄×C₅₃	—	2	8	no	—
305	C₄×C₅₃	—	4	4	no	—
306	C₄×C₅₃	—	4	4	no	—
307	C₂²×#120	C₂×C₅₃	1	1	yes	characteristic
308	C₂²×C₄×D₄	C₂×C₅₃	1	2	yes	complemented
309	C₂³×C₂²⋊C₄	C₂×C₅₃	1	2	yes	complemented
310	#2358	C₂×C₅₃	1	16	yes	direct product factor
311	C₂×#390	C₂×C₅₃	1	1	yes	characteristic, complemented
312	C₂×#388	C₂×C₅₃	1	2	yes	complemented
313	C₂×#386	C₂×C₅₃	1	1	yes	characteristic, complemented
314	C₂×#386	C₂×C₅₃	1	2	yes	complemented
315	C₂×#385	C₂×C₅₃	1	2	yes	complemented
316	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	2	yes	complemented
317	C₂×C₅₃	—	2	16	no	—
318	C₂×C₅₃	—	4	4	no	—
319	C₂×C₅₃	—	4	4	no	—
320	C₂×C₅₃	#2358	1	8	yes	direct product factor
321	C₂×C₅₃	C₂²×C₄×D₄	1	2	yes	—
322	C₂×C₅₃	C₂×#518	1	1	yes	characteristic
323	C₂×C₅₃	C₂×D₄²	1	1	yes	characteristic
324	C₂×C₅₃	C₂×#546	1	2	yes	—
325	C₂×C₅₃	C₂×#551	1	1	yes	characteristic
326	C₂⁶	C₂²×C₅₃	1	1	yes	characteristic
327	C₂³×D₄	C₂²×C₅₃	1	2	yes	—
328	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
329	C₂⁴×C₄	C₂²×C₅₃	1	2	yes	—
330	C₂⁴×C₄	C₂²×C₅₃	1	2	yes	—
331	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
332	C₂×#120	C₄×C₅₃	1	16	yes	complemented
333	C₂×#120	C₂²×C₅₃	1	8	yes	—
334	C₂×C₄×D₄	—	2	16	no	—
335	C₂×C₄×D₄	C₂²×C₅₃	1	16	yes	complemented
336	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
337	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
338	C₂²×C₂²⋊C₄	—	2	16	no	—
339	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
340	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
341	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
342	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
343	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
344	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
345	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	16	yes	complemented
346	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
347	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
348	C₂²×C₄²	C₂²×C₅₃	1	2	yes	complemented
349	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
350	#390	C₂²×C₅₃	1	8	yes	complemented
351	#388	C₂²×C₅₃	1	16	yes	complemented
352	#386	C₂²×C₅₃	1	8	yes	complemented
353	#386	C₂²×C₅₃	1	16	yes	complemented
354	#385	C₂²×C₅₃	1	16	yes	complemented
355	C₄×C₂²⋊C₄	C₂²×C₅₃	1	16	yes	complemented
356	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
357	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
358	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
359	C₅₃	C₂×#2358	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁵	—	2	8	no	—
361	C₂⁵	—	2	8	no	—
362	C₂⁵	—	4	2	no	—
363	C₂⁵	—	4	2	no	—
364	C₂⁵	C₂×C₄×C₅₃	1	8	yes	complemented
365	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
366	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
367	C₂⁵	C₂³×C₅₃	1	4	yes	—
368	C₂⁵	C₂³×C₅₃	1	2	yes	—
369	C₂²×D₄	—	2	8	no	—
370	C₂²×D₄	—	2	8	no	—
371	C₂²×D₄	—	4	2	no	—
372	C₂²×D₄	—	4	2	no	—
373	C₂²×D₄	C₂×C₄×C₅₃	1	16	yes	complemented
374	C₂²×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
375	C₂²×D₄	C₂³×C₅₃	1	8	yes	—
376	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
377	C₂³×C₄	—	2	8	no	—
378	C₂³×C₄	—	2	8	no	—
379	C₂³×C₄	—	2	8	no	—
380	C₂³×C₄	—	2	8	no	—
381	C₂³×C₄	—	2	8	no	—
382	C₂³×C₄	—	4	4	no	—
383	C₂³×C₄	—	4	4	no	—
384	C₂³×C₄	—	4	2	no	—
385	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
386	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
387	C₂³×C₄	C₂³×C₅₃	1	8	yes	—
388	C₂³×C₄	C₂³×C₅₃	1	8	yes	—
389	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
390	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
392	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
393	C₂³×C₄	C₂³×C₅₃	1	4	yes	complemented
394	#120	C₂×C₄×C₅₃	1	64	yes	complemented
395	C₄×D₄	—	2	64	no	—
396	C₂×C₄⋊C₄	—	2	8	no	—
397	C₂×C₄⋊C₄	—	4	2	no	—
398	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
399	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	complemented
400	C₂×C₂²⋊C₄	—	2	8	no	—
401	C₂×C₂²⋊C₄	—	2	8	no	—
402	C₂×C₂²⋊C₄	—	2	8	no	—
403	C₂×C₂²⋊C₄	—	2	8	no	—
404	C₂×C₂²⋊C₄	—	2	64	no	—
405	C₂×C₂²⋊C₄	—	4	2	no	—
406	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	complemented
407	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	16	yes	complemented
408	C₂×C₂²⋊C₄	D₄×C₅₃	1	16	yes	complemented
409	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	complemented
416	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	complemented
417	C₂×C₄²	—	2	8	no	—
418	C₂×C₄²	—	4	2	no	—
419	C₂×C₄²	C₂³×C₅₃	1	8	yes	complemented
420	C₂×C₄²	C₂³×C₅₃	1	4	yes	complemented
421	#95	C₂³×C₅₃	1	8	yes	complemented
422	#95	C₂³×C₅₃	1	8	yes	complemented
423	#95	C₂³×C₅₃	1	8	yes	complemented
424	C₂⁴	—	2	4	no	—
425	C₂⁴	—	2	4	no	—
426	C₂⁴	—	2	4	no	—
427	C₂⁴	—	2	4	no	—
428	C₂⁴	—	2	64	no	—
429	C₂⁴	—	2	16	no	—
430	C₂⁴	—	2	4	no	—
431	C₂⁴	—	2	4	no	—
432	C₂⁴	—	2	4	no	—
433	C₂⁴	—	2	16	no	—
434	C₂⁴	—	2	4	no	—
435	C₂⁴	—	2	2	no	—
436	C₂⁴	—	2	2	no	—
437	C₂⁴	—	2	2	no	—
438	C₂⁴	—	2	2	no	—
439	C₂⁴	—	4	16	no	—
440	C₂⁴	—	4	4	no	—
441	C₂⁴	—	4	4	no	—
442	C₂⁴	—	4	16	no	—
443	C₂⁴	—	4	32	no	—
444	C₂⁴	—	4	16	no	—
445	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
446	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
447	C₂⁴	C₂²×C₄×C₅₃	1	8	yes	—
448	C₂⁴	C₂²×C₄×C₅₃	1	16	yes	complemented
449	C₂⁴	C₂×D₄×C₅₃	1	8	yes	—
450	C₂⁴	#41×C₅₃	1	8	yes	—
451	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
452	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
453	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
454	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
455	C₂×D₄	—	2	64	no	—
456	C₂×D₄	—	2	16	no	—
457	C₂×D₄	—	2	16	no	—
458	C₂×D₄	—	4	16	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂×D₄	C₂²×C₄×C₅₃	1	32	yes	complemented
462	C₂×D₄	C₂²×C₄×C₅₃	1	16	yes	complemented
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	16	no	—
475	C₂²×C₄	—	2	16	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	16	no	—
480	C₂²×C₄	—	2	16	no	—
481	C₂²×C₄	—	2	16	no	—
482	C₂²×C₄	—	4	8	no	—
483	C₂²×C₄	—	4	8	no	—
484	C₂²×C₄	—	4	4	no	—
485	C₂²×C₄	—	4	16	no	—
486	C₂²×C₄	—	4	32	no	—
487	C₂²×C₄	—	4	32	no	—
488	C₂²×C₄	C₂²×C₄×C₅₃	1	8	yes	—
489	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
490	C₂²×C₄	C₂×D₄×C₅₃	1	8	yes	—
491	C₂²×C₄	C₂×D₄×C₅₃	1	8	yes	—
492	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
494	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
498	C₄⋊C₄	—	2	16	no	—
499	C₄⋊C₄	—	4	4	no	—
500	C₂²⋊C₄	—	2	16	no	—
501	C₂²⋊C₄	—	2	16	no	—
502	C₂²⋊C₄	—	2	16	no	—
503	C₂²⋊C₄	—	2	16	no	—
504	C₂²⋊C₄	—	4	4	no	—
505	C₂²⋊C₄	C₂²×C₄×C₅₃	1	16	yes	complemented
506	C₂²⋊C₄	C₂²×C₄×C₅₃	1	32	yes	complemented
507	C₂²⋊C₄	C₂×D₄×C₅₃	1	32	yes	complemented
508	C₄²	—	2	16	no	—
509	C₄²	—	4	4	no	—
510	C₂³	—	2	16	no	—
511	C₂³	—	2	16	no	—
512	C₂³	—	2	16	no	—
513	C₂³	—	2	16	no	—
514	C₂³	—	2	16	no	—
515	C₂³	—	2	16	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	4	no	—
520	C₂³	—	2	16	no	—
521	C₂³	—	2	16	no	—
522	C₂³	—	2	64	no	—
523	C₂³	—	2	8	no	—
524	C₂³	—	2	8	no	—
525	C₂³	—	2	4	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	4	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	4	16	no	—
534	C₂³	—	4	16	no	—
535	C₂³	—	4	32	no	—
536	C₂³	—	4	16	no	—
537	C₂³	—	4	128	no	—
538	C₂³	—	4	4	no	—
539	C₂³	—	4	4	no	—
540	C₂³	—	4	8	no	—
541	C₂³	—	4	8	no	—
542	C₂³	—	4	4	no	—
543	C₂³	—	4	4	no	—
544	C₂³	C₄×D₄×C₅₃	1	32	yes	complemented
545	C₂³	C₂³×C₄×C₅₃	1	4	yes	—
546	C₂³	C₂³×C₄×C₅₃	1	4	yes	—
547	C₂³	C₂³×C₄×C₅₃	1	8	yes	—
548	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
549	C₂³	C₂²×D₄×C₅₃	1	8	yes	—
550	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
551	C₂³	C₂×#41×C₅₃	1	8	yes	—
552	C₂³	C₂×#41×C₅₃	1	4	yes	—
553	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
554	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
555	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
556	D₄	—	2	64	no	—
557	D₄	—	4	16	no	—
558	C₂×C₄	—	2	16	no	—
559	C₂×C₄	—	2	8	no	—
560	C₂×C₄	—	2	16	no	—
561	C₂×C₄	—	2	16	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	4	16	no	—
577	C₂×C₄	—	4	32	no	—
578	C₂×C₄	—	4	32	no	—
579	C₂×C₄	—	4	8	no	—
580	C₂×C₄	—	4	8	no	—
581	C₂×C₄	C₂³×C₄×C₅₃	1	8	yes	—
582	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
583	C₂×C₄	C₂²×D₄×C₅₃	1	8	yes	—
584	C₂×C₄	C₂²×D₄×C₅₃	1	8	yes	—
585	C₂²	—	2	8	no	—
586	C₂²	—	2	8	no	—
587	C₂²	—	2	8	no	—
588	C₂²	—	2	8	no	—
589	C₂²	—	2	64	no	—
590	C₂²	—	2	8	no	—
591	C₂²	—	2	8	no	—
592	C₂²	—	2	8	no	—
593	C₂²	—	2	8	no	—
594	C₂²	—	2	4	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	4	64	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	4	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	16	no	—
604	C₂²	—	4	16	no	—
605	C₂²	C₂×C₄×D₄×C₅₃	1	8	yes	—
606	C₂²	C₂×C₄×D₄×C₅₃	1	16	yes	complemented
607	C₂²	C₅₃×#518	1	4	yes	—
608	C₂²	D₄²×C₅₃	1	4	yes	—
609	C₂²	C₅₃×#546	1	8	yes	—
610	C₂²	C₅₃×#551	1	4	yes	—
611	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
612	C₂²	C₂³×D₄×C₅₃	1	2	yes	—
613	C₂²	C₂²×#41×C₅₃	1	2	yes	—
614	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
615	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
616	C₄	—	2	8	no	—
617	C₄	—	2	8	no	—
618	C₄	—	2	8	no	—
619	C₄	—	2	4	no	—
620	C₄	—	4	4	no	—
621	C₄	—	4	4	no	—
622	C₂	—	2	16	no	—
623	C₂	—	4	4	no	—
624	C₂	—	4	4	no	—
625	C₂	C₅₃×#2358	1	8	yes	direct product factor
626	C₂	C₂²×C₄×D₄×C₅₃	1	2	yes	—
627	C₂	C₂×C₅₃×#518	1	1	yes	characteristic
628	C₂	C₂×D₄²×C₅₃	1	1	yes	characteristic
629	C₂	C₂×C₅₃×#546	1	2	yes	—
630	C₂	C₂×C₅₃×#551	1	1	yes	characteristic

	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×#2358	C₂	direct (N × H)
5. C₂×C₅₃×#390	C₂	semidirect
6. C₂×C₅₃×#388	C₂	semidirect
7. C₂×C₅₃×#386	C₂	semidirect
8. C₂×C₅₃×#386	C₂	semidirect
9. C₂×C₅₃×#385	C₂	semidirect
10. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
16. C₂⁴×C₄×C₅₃	C₂²	semidirect
17. C₂×#120×C₅₃	C₄	semidirect
20. C₂×C₄×D₄×C₅₃	C₂²	semidirect
21. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
22. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
30. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
31. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
32. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
33. C₂²×C₄²×C₅₃	C₂²	semidirect
34. C₂²×C₄²×C₅₃	C₂²	semidirect
35. C₅₃×#390	C₂²	semidirect
36. C₅₃×#388	C₂²	semidirect
37. C₅₃×#386	C₂²	semidirect
38. C₅₃×#386	C₂²	semidirect
39. C₅₃×#385	C₂²	semidirect
40. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
41. C₂×#95×C₅₃	C₂²	semidirect
42. C₂×#95×C₅₃	C₂²	semidirect
43. C₂×#95×C₅₃	C₂²	semidirect
48. C₂⁵×C₅₃	C₂×C₄	semidirect
57. C₂²×D₄×C₅₃	C₂×C₄	semidirect
58. C₂²×D₄×C₅₃	C₂×C₄	semidirect
77. C₂³×C₄×C₅₃	C₂³	semidirect
78. #120×C₅₃	C₂×C₄	semidirect
82. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
83. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
90. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
91. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
92. C₂×C₂²⋊C₄×C₅₃	D₄	semidirect
99. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
100. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
103. C₂×C₄²×C₅₃	C₂³	semidirect
104. C₂×C₄²×C₅₃	C₂³	semidirect
105. #95×C₅₃	C₂³	semidirect
106. #95×C₅₃	C₂³	semidirect
107. #95×C₅₃	C₂³	semidirect
132. C₂⁴×C₅₃	C₂²×C₄	semidirect
145. C₂×D₄×C₅₃	C₂²×C₄	semidirect
146. C₂×D₄×C₅₃	C₂²×C₄	semidirect
189. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
190. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
191. C₂²⋊C₄×C₅₃	C₂×D₄	semidirect
228. C₂³×C₅₃	C₄×D₄	semidirect
269. C₂×#2358	C₅₃	direct (N × H)
291. C₂²×C₅₃	C₂×C₄×D₄	semidirect
308. C₂²×C₄×D₄	C₂×C₅₃	semidirect
309. C₂³×C₂²⋊C₄	C₂×C₅₃	semidirect
310. #2358	C₂×C₅₃	direct (N × H)
311. C₂×#390	C₂×C₅₃	semidirect
312. C₂×#388	C₂×C₅₃	semidirect
313. C₂×#386	C₂×C₅₃	semidirect
314. C₂×#386	C₂×C₅₃	semidirect
315. C₂×#385	C₂×C₅₃	semidirect
316. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
320. C₂×C₅₃	#2358	direct (N × H)
331. C₂⁴×C₄	C₂²×C₅₃	semidirect
332. C₂×#120	C₄×C₅₃	semidirect
335. C₂×C₄×D₄	C₂²×C₅₃	semidirect
336. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
337. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
345. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
346. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
347. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
348. C₂²×C₄²	C₂²×C₅₃	semidirect
349. C₂²×C₄²	C₂²×C₅₃	semidirect
350. #390	C₂²×C₅₃	semidirect
351. #388	C₂²×C₅₃	semidirect
352. #386	C₂²×C₅₃	semidirect
353. #386	C₂²×C₅₃	semidirect
354. #385	C₂²×C₅₃	semidirect
355. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
356. C₂×#95	C₂²×C₅₃	semidirect
357. C₂×#95	C₂²×C₅₃	semidirect
358. C₂×#95	C₂²×C₅₃	semidirect
359. C₅₃	C₂×#2358	direct (N × H)
364. C₂⁵	C₂×C₄×C₅₃	semidirect
373. C₂²×D₄	C₂×C₄×C₅₃	semidirect
374. C₂²×D₄	C₂×C₄×C₅₃	semidirect
393. C₂³×C₄	C₂³×C₅₃	semidirect
394. #120	C₂×C₄×C₅₃	semidirect
398. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
399. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
406. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
407. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
408. C₂×C₂²⋊C₄	D₄×C₅₃	semidirect
415. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
416. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
419. C₂×C₄²	C₂³×C₅₃	semidirect
420. C₂×C₄²	C₂³×C₅₃	semidirect
421. #95	C₂³×C₅₃	semidirect
422. #95	C₂³×C₅₃	semidirect
423. #95	C₂³×C₅₃	semidirect
448. C₂⁴	C₂²×C₄×C₅₃	semidirect
461. C₂×D₄	C₂²×C₄×C₅₃	semidirect
462. C₂×D₄	C₂²×C₄×C₅₃	semidirect
505. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
506. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
507. C₂²⋊C₄	C₂×D₄×C₅₃	semidirect
544. C₂³	C₄×D₄×C₅₃	semidirect
606. C₂²	C₂×C₄×D₄×C₅₃	semidirect
625. C₂	C₅₃×#2358	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×#2358	2
C₂×C₅₃×#390	2
C₂×C₅₃×#388	2
C₂×C₅₃×#386	2
C₂×C₅₃×#385	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
C₂×#2358	53

Subgroups — C2×C53×#2358 #27241642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#2358 #27241642