Subgroups — C₂×C₅₃×#2342 #27241615

Order 13568.

4990 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#2342	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅₃×#388	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₃×#388	C₂	1	2	yes	maximal, complemented
7	C₂×C₅₃×#385	C₂	1	2	yes	maximal, complemented
8	C₂×C₅₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#379	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₅₃	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×#117×C₅₃	—	2	8	no	—
18	C₂×#117×C₅₃	C₂²	1	8	yes	complemented
19	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
20	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊C₄×C₅₃	—	2	8	no	—
22	C₂²×C₂²⋊C₄×C₅₃	C₄	1	16	yes	complemented
23	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	8	yes	—
29	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	8	yes	—
35	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₅₃	C₂²	1	2	yes	complemented
37	C₂²×C₄²×C₅₃	C₂²	1	2	yes	complemented
38	C₅₃×#388	C₂²	1	16	yes	complemented
39	C₅₃×#388	C₂²	1	16	yes	complemented
40	C₅₃×#385	C₂²	1	16	yes	complemented
41	C₅₃×#381	C₂²	1	8	yes	complemented
42	C₅₃×#380	C₂²	1	8	yes	complemented
43	C₅₃×#379	C₂²	1	8	yes	—
44	C₄×C₂²⋊C₄×C₅₃	C₂²	1	16	yes	complemented
45	C₄×C₂²⋊C₄×C₅₃	C₂²	1	8	yes	complemented
46	C₂×#95×C₅₃	C₂²	1	2	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	8	no	—
52	C₂⁵×C₅₃	—	2	4	no	—
53	C₂⁵×C₅₃	—	4	4	no	—
54	C₂⁵×C₅₃	C₂×C₄	1	8	yes	—
55	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
56	C₂⁵×C₅₃	C₂³	1	4	yes	—
57	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
58	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₅₃	—	2	4	no	—
60	C₂³×C₄×C₅₃	—	2	4	no	—
61	C₂³×C₄×C₅₃	—	2	8	no	—
62	C₂³×C₄×C₅₃	—	2	8	no	—
63	C₂³×C₄×C₅₃	—	4	4	no	—
64	C₂³×C₄×C₅₃	—	4	4	no	—
65	C₂³×C₄×C₅₃	C₂×C₄	1	8	yes	complemented
66	C₂³×C₄×C₅₃	C₂×C₄	1	8	yes	complemented
67	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₅₃	C₂³	1	8	yes	—
71	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
76	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
78	#117×C₅₃	—	2	32	no	—
79	C₂×C₄⋊C₄×C₅₃	—	2	8	no	—
80	C₂×C₄⋊C₄×C₅₃	—	4	4	no	—
81	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
82	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
83	C₂×C₂²⋊C₄×C₅₃	—	2	32	no	—
84	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
87	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
89	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
90	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	—
91	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	—
92	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
93	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
94	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	64	yes	complemented
95	C₂×C₂²⋊C₄×C₅₃	D₄	1	8	yes	—
96	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
101	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
102	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	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	4	yes	—
106	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
107	C₂×C₄²×C₅₃	—	2	8	no	—
108	C₂×C₄²×C₅₃	—	4	4	no	—
109	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
110	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
111	#95×C₅₃	C₂³	1	8	yes	complemented
112	#95×C₅₃	C₂³	1	8	yes	complemented
113	#95×C₅₃	C₂³	1	8	yes	complemented
114	#95×C₅₃	C₂³	1	8	yes	complemented
115	C₂⁴×C₅₃	—	2	2	no	—
116	C₂⁴×C₅₃	—	2	4	no	—
117	C₂⁴×C₅₃	—	2	2	no	—
118	C₂⁴×C₅₃	—	2	4	no	—
119	C₂⁴×C₅₃	—	2	4	no	—
120	C₂⁴×C₅₃	—	2	32	no	—
121	C₂⁴×C₅₃	—	2	32	no	—
122	C₂⁴×C₅₃	—	2	8	no	—
123	C₂⁴×C₅₃	—	2	2	no	—
124	C₂⁴×C₅₃	—	2	16	no	—
125	C₂⁴×C₅₃	—	2	8	no	—
126	C₂⁴×C₅₃	—	2	4	no	—
127	C₂⁴×C₅₃	—	2	2	no	—
128	C₂⁴×C₅₃	—	2	4	no	—
129	C₂⁴×C₅₃	—	4	16	no	—
130	C₂⁴×C₅₃	—	4	8	no	—
131	C₂⁴×C₅₃	—	4	32	no	—
132	C₂⁴×C₅₃	—	4	32	no	—
133	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
134	C₂⁴×C₅₃	C₂²×C₄	1	16	yes	—
135	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
136	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
137	C₂⁴×C₅₃	C₂×D₄	1	4	yes	—
138	C₂⁴×C₅₃	#41	1	8	yes	—
139	C₂⁴×C₅₃	#41	1	4	yes	—
140	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
141	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
142	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
143	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₅₃	—	2	32	no	—
145	C₂²×C₄×C₅₃	—	2	2	no	—
146	C₂²×C₄×C₅₃	—	2	2	no	—
147	C₂²×C₄×C₅₃	—	2	8	no	—
148	C₂²×C₄×C₅₃	—	2	2	no	—
149	C₂²×C₄×C₅₃	—	2	2	no	—
150	C₂²×C₄×C₅₃	—	2	8	no	—
151	C₂²×C₄×C₅₃	—	2	4	no	—
152	C₂²×C₄×C₅₃	—	2	4	no	—
153	C₂²×C₄×C₅₃	—	2	4	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	4	no	—
159	C₂²×C₄×C₅₃	—	2	4	no	—
160	C₂²×C₄×C₅₃	—	2	16	no	—
161	C₂²×C₄×C₅₃	—	2	4	no	—
162	C₂²×C₄×C₅₃	—	2	4	no	—
163	C₂²×C₄×C₅₃	—	2	4	no	—
164	C₂²×C₄×C₅₃	—	2	4	no	—
165	C₂²×C₄×C₅₃	—	2	16	no	—
166	C₂²×C₄×C₅₃	—	4	16	no	—
167	C₂²×C₄×C₅₃	—	4	8	no	—
168	C₂²×C₄×C₅₃	—	4	8	no	—
169	C₂²×C₄×C₅₃	—	4	32	no	—
170	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
171	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
172	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₅₃	C₂²×C₄	1	16	yes	complemented
175	C₂²×C₄×C₅₃	C₂²×C₄	1	16	yes	complemented
176	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
177	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
185	C₄⋊C₄×C₅₃	—	2	16	no	—
186	C₄⋊C₄×C₅₃	—	4	8	no	—
187	C₂²⋊C₄×C₅₃	—	2	8	no	—
188	C₂²⋊C₄×C₅₃	—	2	8	no	—
189	C₂²⋊C₄×C₅₃	—	2	16	no	—
190	C₂²⋊C₄×C₅₃	—	2	8	no	—
191	C₂²⋊C₄×C₅₃	—	2	16	no	—
192	C₂²⋊C₄×C₅₃	—	4	8	no	—
193	C₂²⋊C₄×C₅₃	C₂²×C₄	1	16	yes	—
194	C₂²⋊C₄×C₅₃	C₂²×C₄	1	16	yes	—
195	C₂²⋊C₄×C₅₃	C₂²×C₄	1	16	yes	complemented
196	C₂²⋊C₄×C₅₃	C₂²×C₄	1	16	yes	complemented
197	C₂²⋊C₄×C₅₃	C₂×D₄	1	16	yes	—
198	C₄²×C₅₃	—	2	16	no	—
199	C₄²×C₅₃	—	4	8	no	—
200	C₂³×C₅₃	—	2	8	no	—
201	C₂³×C₅₃	—	2	8	no	—
202	C₂³×C₅₃	—	2	8	no	—
203	C₂³×C₅₃	—	2	8	no	—
204	C₂³×C₅₃	—	2	16	no	—
205	C₂³×C₅₃	—	2	16	no	—
206	C₂³×C₅₃	—	2	16	no	—
207	C₂³×C₅₃	—	2	16	no	—
208	C₂³×C₅₃	—	2	2	no	—
209	C₂³×C₅₃	—	2	4	no	—
210	C₂³×C₅₃	—	2	2	no	—
211	C₂³×C₅₃	—	2	4	no	—
212	C₂³×C₅₃	—	2	4	no	—
213	C₂³×C₅₃	—	2	8	no	—
214	C₂³×C₅₃	—	2	32	no	—
215	C₂³×C₅₃	—	2	32	no	—
216	C₂³×C₅₃	—	2	8	no	—
217	C₂³×C₅₃	—	2	8	no	—
218	C₂³×C₅₃	—	2	2	no	—
219	C₂³×C₅₃	—	2	4	no	—
220	C₂³×C₅₃	—	2	2	no	—
221	C₂³×C₅₃	—	2	4	no	—
222	C₂³×C₅₃	—	4	16	no	—
223	C₂³×C₅₃	—	4	128	no	—
224	C₂³×C₅₃	—	4	32	no	—
225	C₂³×C₅₃	—	4	32	no	—
226	C₂³×C₅₃	—	4	8	no	—
227	C₂³×C₅₃	—	4	8	no	—
228	C₂³×C₅₃	#117	1	16	yes	complemented
229	C₂³×C₅₃	C₄×D₄	1	16	yes	—
230	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
231	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
232	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
233	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
234	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
235	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
236	C₂³×C₅₃	C₂×#41	1	8	yes	—
237	C₂³×C₅₃	C₂×#41	1	4	yes	—
238	C₂³×C₅₃	C₂×#41	1	4	yes	—
239	C₂³×C₅₃	C₂×#41	1	2	yes	—
240	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
241	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
242	C₂×C₄×C₅₃	—	2	8	no	—
243	C₂×C₄×C₅₃	—	2	8	no	—
244	C₂×C₄×C₅₃	—	2	32	no	—
245	C₂×C₄×C₅₃	—	2	8	no	—
246	C₂×C₄×C₅₃	—	2	8	no	—
247	C₂×C₄×C₅₃	—	2	16	no	—
248	C₂×C₄×C₅₃	—	2	2	no	—
249	C₂×C₄×C₅₃	—	2	2	no	—
250	C₂×C₄×C₅₃	—	2	2	no	—
251	C₂×C₄×C₅₃	—	2	2	no	—
252	C₂×C₄×C₅₃	—	2	4	no	—
253	C₂×C₄×C₅₃	—	2	4	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	—	2	4	no	—
261	C₂×C₄×C₅₃	—	2	4	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	—	4	16	no	—
266	C₂×C₄×C₅₃	—	4	32	no	—
267	C₂×C₄×C₅₃	—	4	8	no	—
268	C₂×C₄×C₅₃	—	4	8	no	—
269	C₂×C₄×C₅₃	—	4	8	no	—
270	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
271	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
272	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
273	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
274	C₂×C₄×C₅₃	C₂²×D₄	1	8	yes	—
275	C₂×#2342	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂²×C₅₃	—	2	32	no	—
277	C₂²×C₅₃	—	2	32	no	—
278	C₂²×C₅₃	—	2	4	no	—
279	C₂²×C₅₃	—	2	4	no	—
280	C₂²×C₅₃	—	2	4	no	—
281	C₂²×C₅₃	—	2	4	no	—
282	C₂²×C₅₃	—	2	8	no	—
283	C₂²×C₅₃	—	2	8	no	—
284	C₂²×C₅₃	—	2	8	no	—
285	C₂²×C₅₃	—	2	8	no	—
286	C₂²×C₅₃	—	2	4	no	—
287	C₂²×C₅₃	—	2	4	no	—
288	C₂²×C₅₃	—	2	4	no	—
289	C₂²×C₅₃	—	4	64	no	—
290	C₂²×C₅₃	—	4	16	no	—
291	C₂²×C₅₃	—	4	4	no	—
292	C₂²×C₅₃	—	4	4	no	—
293	C₂²×C₅₃	C₂×#117	1	4	yes	—
294	C₂²×C₅₃	C₂×#117	1	8	yes	complemented
295	C₂²×C₅₃	C₂×C₄×D₄	1	8	yes	—
296	C₂²×C₅₃	C₂×C₄×D₄	1	4	yes	—
297	C₂²×C₅₃	#518	1	4	yes	—
298	C₂²×C₅₃	#546	1	8	yes	—
299	C₂²×C₅₃	#551	1	8	yes	—
300	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
301	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
302	C₂²×C₅₃	C₂²×#41	1	2	yes	—
303	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
304	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
305	C₄×C₅₃	—	2	4	no	—
306	C₄×C₅₃	—	2	4	no	—
307	C₄×C₅₃	—	2	4	no	—
308	C₄×C₅₃	—	2	4	no	—
309	C₄×C₅₃	—	2	8	no	—
310	C₄×C₅₃	—	4	4	no	—
311	C₄×C₅₃	—	4	4	no	—
312	C₄×C₅₃	—	4	4	no	—
313	C₂²×#117	C₂×C₅₃	1	1	yes	characteristic, complemented
314	C₂³×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic
315	C₂³×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic
316	#2342	C₂×C₅₃	1	16	yes	direct product factor
317	C₂×#388	C₂×C₅₃	1	2	yes	complemented
318	C₂×#388	C₂×C₅₃	1	2	yes	complemented
319	C₂×#385	C₂×C₅₃	1	2	yes	complemented
320	C₂×#381	C₂×C₅₃	1	1	yes	characteristic, complemented
321	C₂×#380	C₂×C₅₃	1	1	yes	characteristic, complemented
322	C₂×#379	C₂×C₅₃	1	1	yes	characteristic
323	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
324	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	2	yes	complemented
325	C₂×C₅₃	—	2	8	no	—
326	C₂×C₅₃	—	2	8	no	—
327	C₂×C₅₃	—	4	4	no	—
328	C₂×C₅₃	#2342	1	8	yes	direct product factor
329	C₂×C₅₃	C₂²×#117	1	1	yes	characteristic
330	C₂×C₅₃	C₂²×C₄×D₄	1	1	yes	characteristic
331	C₂×C₅₃	C₂×#518	1	1	yes	characteristic
332	C₂×C₅₃	C₂×#546	1	2	yes	—
333	C₂×C₅₃	C₂×#551	1	2	yes	—
334	C₂⁶	C₂²×C₅₃	1	1	yes	characteristic
335	C₂⁴×C₄	C₂²×C₅₃	1	2	yes	—
336	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
337	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
338	C₂×#117	—	2	8	no	—
339	C₂×#117	C₂²×C₅₃	1	8	yes	complemented
340	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
341	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
342	C₂²×C₂²⋊C₄	—	2	8	no	—
343	C₂²×C₂²⋊C₄	C₄×C₅₃	1	16	yes	complemented
344	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	8	yes	—
345	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
347	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
348	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
349	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
350	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
351	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
352	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
353	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	8	yes	—
354	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
355	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
356	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
357	C₂²×C₄²	C₂²×C₅₃	1	2	yes	complemented
358	C₂²×C₄²	C₂²×C₅₃	1	2	yes	complemented
359	#388	C₂²×C₅₃	1	16	yes	complemented
360	#388	C₂²×C₅₃	1	16	yes	complemented
361	#385	C₂²×C₅₃	1	16	yes	complemented
362	#381	C₂²×C₅₃	1	8	yes	complemented
363	#380	C₂²×C₅₃	1	8	yes	complemented
364	#379	C₂²×C₅₃	1	8	yes	—
365	C₄×C₂²⋊C₄	C₂²×C₅₃	1	16	yes	complemented
366	C₄×C₂²⋊C₄	C₂²×C₅₃	1	8	yes	complemented
367	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
368	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
369	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
370	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
371	C₅₃	C₂×#2342	1	1	yes	characteristic, direct product factor, Sylow
372	C₂⁵	—	2	4	no	—
373	C₂⁵	—	2	8	no	—
374	C₂⁵	—	2	4	no	—
375	C₂⁵	—	4	4	no	—
376	C₂⁵	C₂×C₄×C₅₃	1	8	yes	—
377	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
378	C₂⁵	C₂³×C₅₃	1	4	yes	—
379	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
380	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
381	C₂³×C₄	—	2	4	no	—
382	C₂³×C₄	—	2	4	no	—
383	C₂³×C₄	—	2	8	no	—
384	C₂³×C₄	—	2	8	no	—
385	C₂³×C₄	—	4	4	no	—
386	C₂³×C₄	—	4	4	no	—
387	C₂³×C₄	C₂×C₄×C₅₃	1	8	yes	complemented
388	C₂³×C₄	C₂×C₄×C₅₃	1	8	yes	complemented
389	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
390	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
391	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
392	C₂³×C₄	C₂³×C₅₃	1	8	yes	—
393	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
398	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
399	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
400	#117	—	2	32	no	—
401	C₂×C₄⋊C₄	—	2	8	no	—
402	C₂×C₄⋊C₄	—	4	4	no	—
403	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
404	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
405	C₂×C₂²⋊C₄	—	2	4	no	—
406	C₂×C₂²⋊C₄	—	2	4	no	—
407	C₂×C₂²⋊C₄	—	2	8	no	—
408	C₂×C₂²⋊C₄	—	2	4	no	—
409	C₂×C₂²⋊C₄	—	2	8	no	—
410	C₂×C₂²⋊C₄	—	2	32	no	—
411	C₂×C₂²⋊C₄	—	4	4	no	—
412	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	—
413	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	—
414	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	64	yes	complemented
415	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	complemented
416	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	complemented
417	C₂×C₂²⋊C₄	D₄×C₅₃	1	8	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
429	C₂×C₄²	—	2	8	no	—
430	C₂×C₄²	—	4	4	no	—
431	C₂×C₄²	C₂³×C₅₃	1	8	yes	complemented
432	C₂×C₄²	C₂³×C₅₃	1	8	yes	complemented
433	#95	C₂³×C₅₃	1	8	yes	complemented
434	#95	C₂³×C₅₃	1	8	yes	complemented
435	#95	C₂³×C₅₃	1	8	yes	complemented
436	#95	C₂³×C₅₃	1	8	yes	complemented
437	C₂⁴	—	2	2	no	—
438	C₂⁴	—	2	4	no	—
439	C₂⁴	—	2	2	no	—
440	C₂⁴	—	2	4	no	—
441	C₂⁴	—	2	4	no	—
442	C₂⁴	—	2	32	no	—
443	C₂⁴	—	2	32	no	—
444	C₂⁴	—	2	8	no	—
445	C₂⁴	—	2	2	no	—
446	C₂⁴	—	2	16	no	—
447	C₂⁴	—	2	8	no	—
448	C₂⁴	—	2	4	no	—
449	C₂⁴	—	2	2	no	—
450	C₂⁴	—	2	4	no	—
451	C₂⁴	—	4	16	no	—
452	C₂⁴	—	4	8	no	—
453	C₂⁴	—	4	32	no	—
454	C₂⁴	—	4	32	no	—
455	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
456	C₂⁴	C₂²×C₄×C₅₃	1	16	yes	—
457	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
458	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
459	C₂⁴	C₂×D₄×C₅₃	1	4	yes	—
460	C₂⁴	#41×C₅₃	1	8	yes	—
461	C₂⁴	#41×C₅₃	1	4	yes	—
462	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
463	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
464	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
465	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
466	C₂²×C₄	—	2	32	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	16	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	16	no	—
488	C₂²×C₄	—	4	16	no	—
489	C₂²×C₄	—	4	8	no	—
490	C₂²×C₄	—	4	8	no	—
491	C₂²×C₄	—	4	32	no	—
492	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
493	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
494	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
495	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
496	C₂²×C₄	C₂²×C₄×C₅₃	1	16	yes	complemented
497	C₂²×C₄	C₂²×C₄×C₅₃	1	16	yes	complemented
498	C₂²×C₄	C₂×D₄×C₅₃	1	8	yes	—
499	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
500	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
501	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
502	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
504	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
507	C₄⋊C₄	—	2	16	no	—
508	C₄⋊C₄	—	4	8	no	—
509	C₂²⋊C₄	—	2	8	no	—
510	C₂²⋊C₄	—	2	8	no	—
511	C₂²⋊C₄	—	2	16	no	—
512	C₂²⋊C₄	—	2	8	no	—
513	C₂²⋊C₄	—	2	16	no	—
514	C₂²⋊C₄	—	4	8	no	—
515	C₂²⋊C₄	C₂²×C₄×C₅₃	1	16	yes	—
516	C₂²⋊C₄	C₂²×C₄×C₅₃	1	16	yes	—
517	C₂²⋊C₄	C₂²×C₄×C₅₃	1	16	yes	complemented
518	C₂²⋊C₄	C₂²×C₄×C₅₃	1	16	yes	complemented
519	C₂²⋊C₄	C₂×D₄×C₅₃	1	16	yes	—
520	C₄²	—	2	16	no	—
521	C₄²	—	4	8	no	—
522	C₂³	—	2	8	no	—
523	C₂³	—	2	8	no	—
524	C₂³	—	2	8	no	—
525	C₂³	—	2	8	no	—
526	C₂³	—	2	16	no	—
527	C₂³	—	2	16	no	—
528	C₂³	—	2	16	no	—
529	C₂³	—	2	16	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	8	no	—
536	C₂³	—	2	32	no	—
537	C₂³	—	2	32	no	—
538	C₂³	—	2	8	no	—
539	C₂³	—	2	8	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	4	16	no	—
545	C₂³	—	4	32	no	—
546	C₂³	—	4	32	no	—
547	C₂³	—	4	128	no	—
548	C₂³	—	4	8	no	—
549	C₂³	—	4	8	no	—
550	C₂³	#117×C₅₃	1	16	yes	complemented
551	C₂³	C₄×D₄×C₅₃	1	16	yes	—
552	C₂³	C₂³×C₄×C₅₃	1	4	yes	—
553	C₂³	C₂³×C₄×C₅₃	1	4	yes	—
554	C₂³	C₂³×C₄×C₅₃	1	4	yes	—
555	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
556	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
557	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
558	C₂³	C₂×#41×C₅₃	1	8	yes	—
559	C₂³	C₂×#41×C₅₃	1	4	yes	—
560	C₂³	C₂×#41×C₅₃	1	4	yes	—
561	C₂³	C₂×#41×C₅₃	1	2	yes	—
562	C₂³	H(5,𝔽₂)×C₅₃	1	4	yes	—
563	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
564	C₂×C₄	—	2	8	no	—
565	C₂×C₄	—	2	8	no	—
566	C₂×C₄	—	2	32	no	—
567	C₂×C₄	—	2	8	no	—
568	C₂×C₄	—	2	8	no	—
569	C₂×C₄	—	2	16	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	4	16	no	—
588	C₂×C₄	—	4	32	no	—
589	C₂×C₄	—	4	8	no	—
590	C₂×C₄	—	4	8	no	—
591	C₂×C₄	—	4	8	no	—
592	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
593	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
594	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
595	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
596	C₂×C₄	C₂²×D₄×C₅₃	1	8	yes	—
597	C₂²	—	2	8	no	—
598	C₂²	—	2	8	no	—
599	C₂²	—	2	8	no	—
600	C₂²	—	2	8	no	—
601	C₂²	—	2	32	no	—
602	C₂²	—	2	32	no	—
603	C₂²	—	2	4	no	—
604	C₂²	—	2	4	no	—
605	C₂²	—	2	4	no	—
606	C₂²	—	2	4	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	2	4	no	—
609	C₂²	—	2	4	no	—
610	C₂²	—	4	64	no	—
611	C₂²	—	4	4	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	4	16	no	—
614	C₂²	C₂×#117×C₅₃	1	4	yes	—
615	C₂²	C₂×#117×C₅₃	1	8	yes	complemented
616	C₂²	C₂×C₄×D₄×C₅₃	1	8	yes	—
617	C₂²	C₂×C₄×D₄×C₅₃	1	4	yes	—
618	C₂²	C₅₃×#518	1	4	yes	—
619	C₂²	C₅₃×#546	1	8	yes	—
620	C₂²	C₅₃×#551	1	8	yes	—
621	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
622	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
623	C₂²	C₂²×#41×C₅₃	1	2	yes	—
624	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
625	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
626	C₄	—	2	8	no	—
627	C₄	—	2	4	no	—
628	C₄	—	2	4	no	—
629	C₄	—	2	4	no	—
630	C₄	—	2	4	no	—
631	C₄	—	4	4	no	—
632	C₄	—	4	4	no	—
633	C₄	—	4	4	no	—
634	C₂	—	2	8	no	—
635	C₂	—	2	8	no	—
636	C₂	—	4	4	no	—
637	C₂	C₅₃×#2342	1	8	yes	direct product factor
638	C₂	C₂²×#117×C₅₃	1	1	yes	characteristic
639	C₂	C₂²×C₄×D₄×C₅₃	1	1	yes	characteristic
640	C₂	C₂×C₅₃×#518	1	1	yes	characteristic
641	C₂	C₂×C₅₃×#546	1	2	yes	—
642	C₂	C₂×C₅₃×#551	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₅₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₅₃
Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂⁶×C₅₃	C₂²
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
1. C₂²×#117×C₅₃	C₂	semidirect
4. C₅₃×#2342	C₂	direct (N × H)
5. C₂×C₅₃×#388	C₂	semidirect
6. C₂×C₅₃×#388	C₂	semidirect
7. C₂×C₅₃×#385	C₂	semidirect
8. C₂×C₅₃×#381	C₂	semidirect
9. C₂×C₅₃×#380	C₂	semidirect
11. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
18. C₂×#117×C₅₃	C₂²	semidirect
19. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
20. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
22. C₂²×C₂²⋊C₄×C₅₃	C₄	semidirect
36. C₂²×C₄²×C₅₃	C₂²	semidirect
37. C₂²×C₄²×C₅₃	C₂²	semidirect
38. C₅₃×#388	C₂²	semidirect
39. C₅₃×#388	C₂²	semidirect
40. C₅₃×#385	C₂²	semidirect
41. C₅₃×#381	C₂²	semidirect
42. C₅₃×#380	C₂²	semidirect
44. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
45. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
46. C₂×#95×C₅₃	C₂²	semidirect
47. C₂×#95×C₅₃	C₂²	semidirect
48. C₂×#95×C₅₃	C₂²	semidirect
49. C₂×#95×C₅₃	C₂²	semidirect
65. C₂³×C₄×C₅₃	C₂×C₄	semidirect
66. C₂³×C₄×C₅₃	C₂×C₄	semidirect
81. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
82. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
92. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
93. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
94. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
109. C₂×C₄²×C₅₃	C₂³	semidirect
110. C₂×C₄²×C₅₃	C₂³	semidirect
111. #95×C₅₃	C₂³	semidirect
112. #95×C₅₃	C₂³	semidirect
113. #95×C₅₃	C₂³	semidirect
114. #95×C₅₃	C₂³	semidirect
174. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
175. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
195. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
196. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
228. C₂³×C₅₃	#117	semidirect
275. C₂×#2342	C₅₃	direct (N × H)
294. C₂²×C₅₃	C₂×#117	semidirect
313. C₂²×#117	C₂×C₅₃	semidirect
316. #2342	C₂×C₅₃	direct (N × H)
317. C₂×#388	C₂×C₅₃	semidirect
318. C₂×#388	C₂×C₅₃	semidirect
319. C₂×#385	C₂×C₅₃	semidirect
320. C₂×#381	C₂×C₅₃	semidirect
321. C₂×#380	C₂×C₅₃	semidirect
323. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
324. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
328. C₂×C₅₃	#2342	direct (N × H)
339. C₂×#117	C₂²×C₅₃	semidirect
340. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
341. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
343. C₂²×C₂²⋊C₄	C₄×C₅₃	semidirect
357. C₂²×C₄²	C₂²×C₅₃	semidirect
358. C₂²×C₄²	C₂²×C₅₃	semidirect
359. #388	C₂²×C₅₃	semidirect
360. #388	C₂²×C₅₃	semidirect
361. #385	C₂²×C₅₃	semidirect
362. #381	C₂²×C₅₃	semidirect
363. #380	C₂²×C₅₃	semidirect
365. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
366. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
367. C₂×#95	C₂²×C₅₃	semidirect
368. C₂×#95	C₂²×C₅₃	semidirect
369. C₂×#95	C₂²×C₅₃	semidirect
370. C₂×#95	C₂²×C₅₃	semidirect
371. C₅₃	C₂×#2342	direct (N × H)
387. C₂³×C₄	C₂×C₄×C₅₃	semidirect
388. C₂³×C₄	C₂×C₄×C₅₃	semidirect
403. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
404. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
414. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
415. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
416. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
431. C₂×C₄²	C₂³×C₅₃	semidirect
432. C₂×C₄²	C₂³×C₅₃	semidirect
433. #95	C₂³×C₅₃	semidirect
434. #95	C₂³×C₅₃	semidirect
435. #95	C₂³×C₅₃	semidirect
436. #95	C₂³×C₅₃	semidirect
496. C₂²×C₄	C₂²×C₄×C₅₃	semidirect
497. C₂²×C₄	C₂²×C₄×C₅₃	semidirect
517. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
518. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
550. C₂³	#117×C₅₃	semidirect
615. C₂²	C₂×#117×C₅₃	semidirect
637. C₂	C₅₃×#2342	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×#117×C₅₃	2
C₂³×C₂²⋊C₄×C₅₃	2
C₅₃×#2342	2
C₂×C₅₃×#388	2
C₂×C₅₃×#385	2
C₂×C₅₃×#381	2
C₂×C₅₃×#380	2
C₂×C₅₃×#379	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
C₂×#2342	53

Subgroups — C2×C53×#2342 #27241615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#2342 #27241615