Subgroups — #28293104

Order 13568.

11770 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133263	C₂	1	2	yes	maximal, complemented
2	#20288478	C₂	1	8	yes	maximal, complemented
3	#20288477	C₂	1	8	yes	maximal, complemented
4	#20288358	C₂	1	8	yes	maximal, complemented
5	#20288357	C₂	1	8	yes	maximal, complemented
6	#20288349	C₂	1	8	yes	maximal, complemented
7	#20288348	C₂	1	8	yes	maximal, complemented
8	#20288048	C₂	1	1	yes	maximal, characteristic, complemented
9	#20288044	C₂	1	2	yes	maximal, complemented
10	#534×D₅₃	C₂	1	8	yes	maximal, complemented
11	C₂×#16811097	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13133263	—	2	32	no	—
14	C₂×#13133263	C₂²	1	8	yes	complemented
15	C₂×#13133263	C₂²	1	8	yes	complemented
16	C₂×#13133263	C₂²	1	8	yes	complemented
17	C₂×#13133263	C₂²	1	8	yes	complemented
18	C₂²×#11719949	C₂²	1	4	yes	complemented
19	C₂²×#11719945	C₂²	1	2	yes	complemented
20	C₂²×#11719945	C₂²	1	4	yes	complemented
21	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
22	C₂³×D₂₁₂	C₂²	1	4	yes	complemented
23	C₂²×D₄×D₅₃	C₂²	1	8	yes	complemented
24	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
25	#16811278	C₂²	1	16	yes	complemented
26	#16811276	C₂²	1	16	yes	complemented
27	#16811275	C₂²	1	32	yes	complemented
28	#16811270	C₂²	1	32	yes	complemented
29	#16811269	C₂²	1	32	yes	complemented
30	#16811266	C₂²	1	32	yes	complemented
31	#16811264	C₂²	1	32	yes	complemented
32	D₄×D₂₁₂	C₂²	1	16	yes	complemented
33	#16811258	C₂²	1	16	yes	complemented
34	#16811257	C₂²	1	32	yes	complemented
35	#16811204	C₂²	1	4	yes	complemented
36	#16811201	C₂²	1	8	yes	complemented
37	#16811199	C₂²	1	4	yes	complemented
38	#16811197	C₂²	1	4	yes	complemented
39	#16811194	C₂²	1	4	yes	complemented
40	#16811192	C₂²	1	4	yes	complemented
41	#16811190	C₂²	1	4	yes	complemented
42	#16811187	C₂²	1	4	yes	complemented
43	#16811185	C₂²	1	4	yes	complemented
44	#16811184	C₂²	1	32	yes	complemented
45	#16811183	C₂²	1	32	yes	complemented
46	#16811182	C₂²	1	8	yes	complemented
47	#16811181	C₂²	1	32	yes	complemented
48	#16811173	C₂²	1	4	yes	complemented
49	#16811169	C₂²	1	8	yes	complemented
50	#16811135	C₂²	1	8	yes	complemented
51	#16811134	C₂²	1	8	yes	complemented
52	#16811130	C₂²	1	8	yes	complemented
53	#123×D₅₃	C₂²	1	32	yes	complemented
54	#121×D₅₃	C₂²	1	32	yes	complemented
55	#120×D₅₃	C₂²	1	32	yes	complemented
56	#16811097	C₂²	1	8	yes	complemented
57	#16811097	C₂²	1	8	yes	complemented
58	C₂×C₄×D₂₁₂	C₂²	1	4	yes	complemented
59	C₂×#13133179	C₂²	1	4	yes	complemented
60	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
62	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
63	C₅₃×#537	C₂²	1	4	yes	complemented
64	C₅₃×#536	C₂²	1	4	yes	complemented
65	C₅₃×#535	C₂²	1	4	yes	complemented
66	C₅₃×#534	C₂²	1	4	yes	complemented
67	C₅₃×#532	C₂²	1	4	yes	complemented
68	C₅₃×#525	C₂²	1	8	yes	complemented
69	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
70	C₂⁴×D₅₃	C₂³	1	2	yes	—
71	C₂⁴×D₅₃	C₂³	1	8	yes	complemented
72	#13133263	—	2	64	no	—
73	#13133263	—	2	64	no	—
74	#13133263	—	2	64	no	—
75	#13133263	—	2	64	no	—
76	C₂×#11719949	—	2	32	no	—
77	C₂×#11719949	C₂³	1	16	yes	complemented
78	C₂×#11719949	C₂³	1	16	yes	complemented
79	C₂×#11719945	—	2	16	no	—
80	C₂×#11719945	—	2	32	no	—
81	C₂×#11719945	C₂³	1	4	yes	—
82	C₂×#11719945	C₂³	1	4	yes	—
83	C₂×#11719945	C₂³	1	16	yes	complemented
84	C₂×#11719945	C₂³	1	16	yes	complemented
85	C₂×#11719945	C₂³	1	4	yes	complemented
86	C₂×#11719945	C₂³	1	4	yes	complemented
87	C₂²×Dic₁₀₆	C₂³	1	2	yes	complemented
88	C₂²×D₂₁₂	—	2	32	no	—
89	C₂²×D₂₁₂	D₄	1	16	yes	complemented
90	C₂²×D₂₁₂	C₂³	1	2	yes	—
91	C₂²×D₂₁₂	C₂³	1	2	yes	—
92	C₂²×D₂₁₂	C₂³	1	4	yes	—
93	C₂²×D₂₁₂	C₂³	1	4	yes	—
94	C₂²×D₂₁₂	C₂³	1	16	yes	complemented
95	C₂²×D₂₁₂	C₂³	1	16	yes	complemented
96	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
97	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
98	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
99	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
100	C₂×D₄×D₅₃	—	2	64	no	—
101	C₂×D₄×D₅₃	—	2	32	no	—
102	C₂×D₄×D₅₃	C₂³	1	32	yes	—
103	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
104	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
105	C₂×D₄×D₅₃	C₂³	1	32	yes	complemented
106	C₂×D₄×D₅₃	C₂³	1	32	yes	complemented
107	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
108	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
109	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
110	#13133217	C₂³	1	4	yes	complemented
111	#13133215	C₂³	1	8	yes	complemented
112	#13133214	C₂³	1	4	yes	complemented
113	#13133213	C₂³	1	8	yes	complemented
114	#13133206	C₂³	1	8	yes	complemented
115	#13133205	C₂³	1	8	yes	complemented
116	#13133204	C₂³	1	8	yes	complemented
117	#13133202	C₂³	1	64	yes	complemented
118	#13133201	C₂³	1	16	yes	complemented
119	#13133200	C₂³	1	16	yes	complemented
120	#13133199	C₂³	1	64	yes	complemented
121	#13133198	C₂³	1	16	yes	complemented
122	#13133197	C₂³	1	16	yes	complemented
123	#13133196	C₂³	1	16	yes	complemented
124	#13133193	C₂³	1	16	yes	complemented
125	#13133192	C₂³	1	32	yes	complemented
126	#13133192	C₂³	1	16	yes	complemented
127	#13133191	C₂³	1	16	yes	complemented
128	#13133191	C₂³	1	16	yes	complemented
129	#13133190	C₂³	1	64	yes	complemented
130	#13133189	C₂³	1	32	yes	complemented
131	#13133188	C₂³	1	16	yes	complemented
132	#13133188	C₂³	1	32	yes	complemented
133	#13133187	C₂³	1	64	yes	complemented
134	#13133187	C₂³	1	16	yes	complemented
135	#13133186	C₂³	1	16	yes	complemented
136	#13133185	C₂³	1	64	yes	complemented
137	#13133185	C₂³	1	16	yes	complemented
138	C₄×D₂₁₂	C₂³	1	16	yes	complemented
139	C₄×D₂₁₂	C₂³	1	16	yes	complemented
140	C₄×D₂₁₂	C₂³	1	16	yes	complemented
141	#13133179	C₂³	1	32	yes	complemented
142	C₄×C₂²⋊D₅₃	C₂³	1	32	yes	complemented
143	#13133176	C₂³	1	4	yes	complemented
144	#13133176	C₂³	1	4	yes	complemented
145	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
146	C₄⋊C₄×D₅₃	C₂³	1	32	yes	complemented
147	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
148	C₂×#11719921	C₂³	1	8	yes	complemented
149	C₂²⋊C₄×D₅₃	C₂³	1	64	yes	complemented
150	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	complemented
151	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
152	C₂×#41×C₅₃	—	2	16	no	—
153	C₂×#41×C₅₃	C₂³	1	4	yes	—
154	C₂×#41×C₅₃	C₂³	1	4	yes	—
155	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
156	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
157	C₂²×Q₈×C₅₃	C₂³	1	2	yes	complemented
158	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
159	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
160	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
161	C₂³×C₄×C₅₃	C₂³	1	4	yes	complemented
162	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
163	#127×C₅₃	C₂³	1	4	yes	complemented
164	#124×C₅₃	C₂³	1	8	yes	complemented
165	#123×C₅₃	C₂³	1	16	yes	complemented
166	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
167	#121×C₅₃	C₂³	1	16	yes	complemented
168	#121×C₅₃	C₂³	1	16	yes	complemented
169	#120×C₅₃	C₂³	1	16	yes	complemented
170	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
171	#117×C₅₃	C₂³	1	4	yes	complemented
172	#117×C₅₃	C₂³	1	4	yes	complemented
173	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
174	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
176	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
177	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
178	C₂³×D₅₃	—	2	32	no	—
179	C₂³×D₅₃	—	8	4	no	—
180	C₂³×D₅₃	—	8	16	no	—
181	C₂³×D₅₃	C₂×D₄	1	16	yes	complemented
182	C₂³×D₅₃	C₂⁴	1	32	yes	—
183	C₂³×D₅₃	C₂⁴	1	4	yes	—
184	C₂³×D₅₃	C₂⁴	1	8	yes	—
185	C₂³×D₅₃	C₂⁴	1	4	yes	—
186	#41×C₅₃	—	2	16	no	—
187	#41×C₅₃	—	2	16	no	—
188	#41×C₅₃	—	2	16	no	—
189	#41×C₅₃	—	2	16	no	—
190	C₂×Q₈×C₅₃	—	2	8	no	—
191	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
192	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
193	C₂×D₄×C₅₃	—	2	16	no	—
194	C₂×D₄×C₅₃	—	2	8	no	—
195	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
196	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
197	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
198	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
199	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
200	C₂²×C₄×C₅₃	—	2	16	no	—
201	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	complemented
202	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
203	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
204	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
210	C₂×C₂²⋊D₅₃	—	2	16	no	—
211	C₂×C₂²⋊D₅₃	—	2	32	no	—
212	C₂×C₂²⋊D₅₃	C₂⁴	1	32	yes	—
213	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
214	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
215	C₂×C₂²⋊D₅₃	C₂⁴	1	32	yes	—
216	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
217	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
218	#11719949	—	2	64	no	—
219	#11719949	—	2	64	no	—
220	D₄×D₅₃	—	2	128	no	—
221	D₄×D₅₃	—	2	128	no	—
222	D₄×D₅₃	—	2	64	no	—
223	D₄×D₅₃	—	2	64	no	—
224	D₄×D₅₃	—	8	32	no	—
225	#11719945	—	2	16	no	—
226	#11719945	—	2	16	no	—
227	#11719945	—	2	16	no	—
228	#11719945	—	2	16	no	—
229	#11719945	—	2	64	no	—
230	#11719945	—	2	64	no	—
231	C₂×D₂₁₂	—	2	32	no	—
232	C₂×D₂₁₂	—	2	8	no	—
233	C₂×D₂₁₂	—	2	64	no	—
234	C₂×D₂₁₂	—	2	64	no	—
235	C₂×D₂₁₂	C₂×D₄	1	32	yes	complemented
236	C₂×D₂₁₂	C₂×D₄	1	32	yes	complemented
237	C₂×D₂₁₂	C₂×D₄	1	16	yes	complemented
238	C₂×D₂₁₂	C₂×D₄	1	16	yes	complemented
239	C₂×D₂₁₂	C₂⁴	1	32	yes	—
240	C₂×D₂₁₂	C₂⁴	1	4	yes	—
241	C₂×D₂₁₂	C₂⁴	1	4	yes	—
242	C₂×D₂₁₂	C₂⁴	1	16	yes	—
243	C₂×D₂₁₂	C₂⁴	1	8	yes	—
244	C₂×D₂₁₂	C₂⁴	1	4	yes	—
245	C₂×D₂₁₂	C₂⁴	1	4	yes	—
246	C₂×C₄×D₅₃	—	2	32	no	—
247	C₂×C₄×D₅₃	—	2	16	no	—
248	C₂×C₄×D₅₃	—	8	8	no	—
249	C₂×C₄×D₅₃	C₂⁴	1	32	yes	—
250	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
251	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
252	C₂×C₄×D₅₃	C₂⁴	1	32	yes	—
253	C₂×Dic₁₀₆	—	2	8	no	—
254	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
255	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
256	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
257	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
258	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
259	C₂²⋊C₄×C₅₃	C₂⁴	1	32	yes	—
260	C₄²×C₅₃	C₂⁴	1	4	yes	—
261	C₄²×C₅₃	C₂⁴	1	4	yes	—
262	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
263	C₂²⋊Dic₅₃	C₂⁴	1	32	yes	—
264	#11719921	C₂⁴	1	32	yes	—
265	#11719921	C₂⁴	1	32	yes	—
266	#11719921	C₂⁴	1	32	yes	—
267	C₄⋊Dic₅₃	C₂⁴	1	16	yes	—
268	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
269	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
270	#11719919	C₂⁴	1	32	yes	—
271	C₄×Dic₅₃	C₂⁴	1	8	yes	—
272	C₂³×C₅₃	—	2	8	no	—
273	C₂³×C₅₃	—	4	2	no	—
274	C₂³×C₅₃	—	4	8	no	—
275	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
276	C₂³×C₅₃	C₂⁵	1	8	yes	—
277	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
278	C₂³×C₅₃	C₂⁵	1	2	yes	—
279	C₂²×D₅₃	—	2	8	no	—
280	C₂²×D₅₃	—	2	64	no	—
281	C₂²×D₅₃	—	4	8	no	—
282	C₂²×D₅₃	—	4	16	no	—
283	C₂²×D₅₃	—	4	8	no	—
284	C₂²×D₅₃	—	4	64	no	—
285	C₂²×D₅₃	—	8	16	no	—
286	C₂²×D₅₃	—	8	64	no	—
287	C₂²×D₅₃	C₂²×D₄	1	32	yes	—
288	C₂²×D₅₃	C₂²×D₄	1	16	yes	—
289	C₂²×D₅₃	C₂⁵	1	8	yes	—
290	C₂²×D₅₃	C₂⁵	1	8	yes	—
291	Q₈×C₅₃	—	2	8	no	—
292	Q₈×C₅₃	—	2	8	no	—
293	D₄×C₅₃	—	2	16	no	—
294	D₄×C₅₃	—	2	16	no	—
295	D₄×C₅₃	—	2	8	no	—
296	D₄×C₅₃	—	2	8	no	—
297	D₄×C₅₃	—	4	16	no	—
298	C₂×C₄×C₅₃	—	2	8	no	—
299	C₂×C₄×C₅₃	—	2	16	no	—
300	C₂×C₄×C₅₃	—	2	16	no	—
301	C₂×C₄×C₅₃	—	4	4	no	—
302	C₂×C₄×C₅₃	C₂²×D₄	1	8	yes	—
303	C₂×C₄×C₅₃	C₂²×D₄	1	8	yes	—
304	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
305	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
306	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
307	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
308	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
309	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
310	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
311	C₂²⋊D₅₃	—	2	16	no	—
312	C₂²⋊D₅₃	—	2	16	no	—
313	C₂²⋊D₅₃	—	2	64	no	—
314	C₂²⋊D₅₃	—	4	32	no	—
315	C₂×Dic₅₃	—	2	8	no	—
316	C₂×Dic₅₃	—	4	4	no	—
317	C₂×Dic₅₃	C₂⁵	1	8	yes	—
318	C₂×Dic₅₃	C₂⁵	1	8	yes	—
319	D₂₁₂	—	2	64	no	—
320	D₂₁₂	—	2	8	no	—
321	D₂₁₂	—	2	8	no	—
322	D₂₁₂	—	4	16	no	—
323	D₂₁₂	C₂²×D₄	1	16	yes	—
324	D₂₁₂	C₂²×D₄	1	32	yes	—
325	D₂₁₂	C₂²×D₄	1	16	yes	—
326	C₄×D₅₃	—	2	64	no	—
327	C₄×D₅₃	—	2	16	no	—
328	C₄×D₅₃	—	2	16	no	—
329	C₄×D₅₃	—	4	32	no	—
330	Dic₁₀₆	—	2	8	no	—
331	Dic₁₀₆	—	2	8	no	—
332	#62842	—	53	1	no	maximal, Sylow
333	C₂²×C₅₃	—	2	2	no	—
334	C₂²×C₅₃	—	2	4	no	—
335	C₂²×C₅₃	—	2	8	no	—
336	C₂²×C₅₃	—	2	16	no	—
337	C₂²×C₅₃	—	4	4	no	—
338	C₂²×C₅₃	—	4	16	no	—
339	C₂²×C₅₃	C₂³×D₄	1	4	yes	—
340	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
341	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
342	C₂×D₅₃	—	2	16	no	—
343	C₂×D₅₃	—	2	8	no	—
344	C₂×D₅₃	—	2	16	no	—
345	C₂×D₅₃	—	4	32	no	—
346	C₂×D₅₃	—	4	16	no	—
347	C₂×D₅₃	—	4	16	no	—
348	C₂×D₅₃	—	8	64	no	—
349	C₂×D₅₃	C₂³×D₄	1	16	yes	—
350	C₄×C₅₃	—	2	8	no	—
351	C₄×C₅₃	—	2	8	no	—
352	C₄×C₅₃	C₂³×D₄	1	2	yes	—
353	C₄×C₅₃	C₂³×D₄	1	4	yes	—
354	C₄×C₅₃	C₂³×D₄	1	2	yes	—
355	Dic₅₃	—	2	8	no	—
356	Dic₅₃	—	2	8	no	—
357	C₂²×H(5,𝔽₂)	—	53	2	no	—
358	#3496	—	53	8	no	—
359	#3496	—	53	8	no	—
360	#3485	—	53	8	no	—
361	#3485	—	53	8	no	—
362	#3484	—	53	8	no	—
363	#3484	—	53	8	no	—
364	#3449	—	53	2	no	—
365	#3449	—	53	1	no	—
366	#3449	D₅₃	1	1	yes	characteristic, complemented
367	C₂×#534	—	53	8	no	—
368	C₂×#518	—	53	1	no	—
369	C₂×C₅₃	—	2	4	no	—
370	C₂×C₅₃	—	2	2	no	—
371	C₂×C₅₃	—	4	8	no	—
372	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
373	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
374	D₅₃	—	2	16	no	—
375	D₅₃	—	4	8	no	—
376	C₂×H(5,𝔽₂)	—	53	8	no	—
377	C₂×H(5,𝔽₂)	—	53	8	no	—
378	C₂×H(5,𝔽₂)	—	53	8	no	—
379	C₂×H(5,𝔽₂)	—	53	8	no	—
380	C₂×H(5,𝔽₂)	—	106	32	no	—
381	C₂²×#41	—	53	4	no	—
382	C₂²×#41	—	53	2	no	—
383	C₂²×#41	—	53	4	no	—
384	C₂²×#41	C₂×D₅₃	1	2	yes	complemented
385	C₂³×D₄	—	53	8	no	—
386	C₂³×D₄	—	53	4	no	—
387	C₂³×D₄	—	53	1	no	—
388	C₂³×D₄	—	53	4	no	—
389	#547	—	53	16	no	—
390	#547	—	53	32	no	—
391	#547	—	53	16	no	—
392	#546	—	53	32	no	—
393	#546	—	53	32	no	—
394	#546	—	53	32	no	—
395	#546	—	53	32	no	—
396	D₄²	—	53	16	no	—
397	D₄²	—	53	32	no	—
398	D₄²	—	53	16	no	—
399	#537	—	53	8	no	—
400	#537	—	53	4	no	—
401	#537	C₂×D₅₃	1	4	yes	complemented
402	#536	—	53	4	no	—
403	#536	—	53	4	no	—
404	#536	—	53	4	no	—
405	#536	C₂×D₅₃	1	4	yes	complemented
406	#535	—	53	4	no	—
407	#535	—	53	4	no	—
408	#535	—	53	4	no	—
409	#535	C₂×D₅₃	1	4	yes	complemented
410	#534	—	53	8	no	—
411	#534	—	53	32	no	—
412	#534	—	53	32	no	—
413	#534	—	53	32	no	—
414	#534	—	53	4	no	—
415	#534	C₂×D₅₃	1	4	yes	complemented
416	#532	—	53	8	no	—
417	#532	—	53	4	no	—
418	#532	C₂×D₅₃	1	4	yes	complemented
419	#525	—	53	8	no	—
420	#525	—	53	8	no	—
421	#525	—	53	8	no	—
422	#525	C₂×D₅₃	1	8	yes	complemented
423	C₂×#123	—	53	32	no	—
424	C₂×#121	—	53	32	no	—
425	C₂×#120	—	53	32	no	—
426	#518	—	53	8	no	—
427	#518	—	53	8	no	—
428	C₂×C₄×D₄	—	53	4	no	—
429	C₂×C₄×D₄	—	53	4	no	—
430	C₂×#117	—	53	1	no	—
431	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
432	C₂²×C₂²⋊C₄	—	53	4	no	—
433	C₅₃	#62842	1	1	yes	characteristic, complemented, Sylow
434	C₂⁵	—	53	2	no	—
435	C₂⁵	—	53	8	no	—
436	H(5,𝔽₂)	—	106	64	no	—
437	H(5,𝔽₂)	—	106	64	no	—
438	H(5,𝔽₂)	—	106	64	no	—
439	H(5,𝔽₂)	—	106	64	no	—
440	C₂×#41	—	2	16	no	—
441	C₂×#41	—	53	16	no	—
442	C₂×#41	—	53	16	no	—
443	C₂×#41	—	53	4	no	—
444	C₂×#41	—	53	4	no	—
445	C₂×#41	—	53	4	no	—
446	C₂×#41	—	53	4	no	—
447	C₂×#41	—	53	16	no	—
448	C₂×#41	—	53	16	no	—
449	C₂×#41	—	106	32	no	—
450	C₂×#41	—	106	32	no	—
451	C₂×#41	—	106	16	no	—
452	C₂×#41	C₂²×D₅₃	1	4	yes	—
453	C₂×#41	C₂²×D₅₃	1	4	yes	—
454	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
455	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
456	C₂²×Q₈	—	53	2	no	—
457	C₂²×Q₈	C₂²×D₅₃	1	2	yes	complemented
458	C₂²×D₄	—	53	4	no	—
459	C₂²×D₄	—	53	8	no	—
460	C₂²×D₄	—	53	32	no	—
461	C₂²×D₄	—	53	32	no	—
462	C₂²×D₄	—	53	16	no	—
463	C₂²×D₄	—	53	16	no	—
464	C₂²×D₄	—	53	32	no	—
465	C₂²×D₄	—	53	16	no	—
466	C₂²×D₄	—	53	2	no	—
467	C₂²×D₄	—	53	2	no	—
468	C₂²×D₄	—	53	4	no	—
469	C₂²×D₄	—	53	4	no	—
470	C₂²×D₄	—	53	8	no	—
471	C₂²×D₄	—	53	2	no	—
472	C₂²×D₄	—	53	16	no	—
473	C₂²×D₄	—	53	16	no	—
474	C₂²×D₄	—	106	32	no	—
475	C₂²×D₄	—	106	32	no	—
476	C₂²×D₄	—	106	64	no	—
477	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
478	C₂²×D₄	C₂²×D₅₃	1	2	yes	complemented
479	C₂³×C₄	—	53	8	no	—
480	C₂³×C₄	—	53	4	no	—
481	C₂³×C₄	—	53	8	no	—
482	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
483	C₂³×C₄	C₂²×D₅₃	1	4	yes	complemented
484	C₄⋊Q₈	—	53	8	no	—
485	C₄⋊Q₈	—	53	4	no	—
486	C₄⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
487	#127	—	53	8	no	—
488	#127	—	53	4	no	—
489	#127	C₂²×D₅₃	1	4	yes	complemented
490	#124	—	53	8	no	—
491	#124	—	53	8	no	—
492	#124	—	53	8	no	—
493	#124	C₂²×D₅₃	1	8	yes	complemented
494	#123	—	53	16	no	—
495	#123	—	53	16	no	—
496	#123	—	53	64	no	—
497	#123	—	53	16	no	—
498	#123	—	53	64	no	—
499	#123	C₂²×D₅₃	1	16	yes	complemented
500	C₂²⋊Q₈	—	53	16	no	—
501	C₂²⋊Q₈	—	53	16	no	—
502	C₂²⋊Q₈	—	53	16	no	—
503	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
504	#121	—	53	32	no	—
505	#121	—	53	32	no	—
506	#121	—	53	16	no	—
507	#121	—	53	16	no	—
508	#121	—	53	16	no	—
509	#121	—	53	32	no	—
510	#121	—	53	16	no	—
511	#121	—	53	64	no	—
512	#121	C₂²×D₅₃	1	16	yes	complemented
513	#121	C₂²×D₅₃	1	16	yes	complemented
514	#120	—	53	16	no	—
515	#120	—	53	16	no	—
516	#120	—	53	64	no	—
517	#120	—	53	16	no	—
518	#120	—	53	64	no	—
519	#120	C₂²×D₅₃	1	16	yes	complemented
520	C₄×D₄	—	53	32	no	—
521	C₄×D₄	—	53	32	no	—
522	C₄×D₄	—	53	16	no	—
523	C₄×D₄	—	53	16	no	—
524	C₄×D₄	—	53	16	no	—
525	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
526	#117	—	53	4	no	—
527	#117	—	53	4	no	—
528	#117	C₂²×D₅₃	1	4	yes	complemented
529	#117	C₂²×D₅₃	1	4	yes	complemented
530	C₂×C₄⋊C₄	—	53	2	no	—
531	C₂×C₄⋊C₄	—	53	32	no	—
532	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
533	C₂×C₂²⋊C₄	—	53	2	no	—
534	C₂×C₂²⋊C₄	—	53	8	no	—
535	C₂×C₂²⋊C₄	—	53	32	no	—
536	C₂×C₂²⋊C₄	—	53	64	no	—
537	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
538	C₂×C₄²	—	53	2	no	—
539	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
540	C₂⁴	—	53	16	no	—
541	C₂⁴	—	53	8	no	—
542	C₂⁴	—	53	4	no	—
543	C₂⁴	—	53	32	no	—
544	C₂⁴	—	53	4	no	—
545	C₂⁴	—	106	32	no	—
546	C₂⁴	—	424	16	no	—
547	C₂⁴	—	424	4	no	—
548	C₂⁴	C₂³×D₅₃	1	4	yes	—
549	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
550	#41	—	2	16	no	—
551	#41	—	2	16	no	—
552	#41	—	2	16	no	—
553	#41	—	2	16	no	—
554	#41	—	106	64	no	—
555	#41	—	106	64	no	—
556	#41	—	106	64	no	—
557	#41	—	106	64	no	—
558	#41	—	106	16	no	—
559	#41	—	106	16	no	—
560	#41	—	106	16	no	—
561	#41	—	106	16	no	—
562	C₂×Q₈	—	2	8	no	—
563	C₂×Q₈	—	53	4	no	—
564	C₂×Q₈	—	53	4	no	—
565	C₂×Q₈	—	106	8	no	—
566	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
567	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
568	C₂×D₄	—	2	16	no	—
569	C₂×D₄	—	2	8	no	—
570	C₂×D₄	—	53	8	no	—
571	C₂×D₄	—	53	32	no	—
572	C₂×D₄	—	53	8	no	—
573	C₂×D₄	—	53	32	no	—
574	C₂×D₄	—	53	32	no	—
575	C₂×D₄	—	53	32	no	—
576	C₂×D₄	—	53	16	no	—
577	C₂×D₄	—	53	16	no	—
578	C₂×D₄	—	53	8	no	—
579	C₂×D₄	—	53	4	no	—
580	C₂×D₄	—	53	4	no	—
581	C₂×D₄	—	53	32	no	—
582	C₂×D₄	—	53	4	no	—
583	C₂×D₄	—	53	4	no	—
584	C₂×D₄	—	53	16	no	—
585	C₂×D₄	—	106	64	no	—
586	C₂×D₄	—	106	64	no	—
587	C₂×D₄	—	106	32	no	—
588	C₂×D₄	—	106	64	no	—
589	C₂×D₄	—	106	64	no	—
590	C₂×D₄	—	106	128	no	—
591	C₂×D₄	—	106	128	no	—
592	C₂×D₄	—	106	32	no	—
593	C₂×D₄	—	106	16	no	—
594	C₂×D₄	—	106	8	no	—
595	C₂×D₄	—	424	32	no	—
596	C₂×D₄	C₂³×D₅₃	1	8	yes	—
597	C₂×D₄	C₂³×D₅₃	1	8	yes	—
598	C₂×D₄	C₂³×D₅₃	1	4	yes	—
599	C₂×D₄	C₂³×D₅₃	1	4	yes	—
600	C₂×D₄	C₂³×D₅₃	1	16	yes	—
601	C₂²×C₄	—	2	16	no	—
602	C₂²×C₄	—	53	4	no	—
603	C₂²×C₄	—	53	4	no	—
604	C₂²×C₄	—	53	32	no	—
605	C₂²×C₄	—	53	8	no	—
606	C₂²×C₄	—	53	8	no	—
607	C₂²×C₄	—	53	32	no	—
608	C₂²×C₄	—	106	32	no	—
609	C₂²×C₄	—	106	16	no	—
610	C₂²×C₄	—	424	8	no	—
611	C₂²×C₄	D₄×D₅₃	1	8	yes	complemented
612	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
613	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
614	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
615	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
616	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
617	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
618	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
619	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
620	C₄⋊C₄	—	53	32	no	—
621	C₄⋊C₄	—	53	16	no	—
622	C₄⋊C₄	—	53	4	no	—
623	C₄⋊C₄	—	53	4	no	—
624	C₄⋊C₄	C₂³×D₅₃	1	16	yes	—
625	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
626	C₂²⋊C₄	—	53	8	no	—
627	C₂²⋊C₄	—	53	32	no	—
628	C₂²⋊C₄	—	53	32	no	—
629	C₂²⋊C₄	—	53	32	no	—
630	C₂²⋊C₄	—	53	32	no	—
631	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
632	C₂²⋊C₄	C₂³×D₅₃	1	32	yes	—
633	C₄²	—	53	8	no	—
634	C₄²	C₂³×D₅₃	1	4	yes	—
635	C₄²	C₂³×D₅₃	1	4	yes	—
636	C₂³	—	2	8	no	—
637	C₂³	—	4	2	no	—
638	C₂³	—	4	8	no	—
639	C₂³	—	53	8	no	—
640	C₂³	—	53	32	no	—
641	C₂³	—	53	16	no	—
642	C₂³	—	53	8	no	—
643	C₂³	—	106	64	no	—
644	C₂³	—	106	8	no	—
645	C₂³	—	424	64	no	—
646	C₂³	—	424	16	no	—
647	C₂³	—	212	64	no	—
648	C₂³	—	212	8	no	—
649	C₂³	—	212	16	no	—
650	C₂³	—	212	8	no	—
651	C₂³	C₂×D₄×D₅₃	1	4	yes	—
652	C₂³	C₂⁴×D₅₃	1	8	yes	—
653	C₂³	C₂⁴×D₅₃	1	2	yes	—
654	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
655	Q₈	—	2	8	no	—
656	Q₈	—	2	8	no	—
657	Q₈	—	106	8	no	—
658	Q₈	—	106	8	no	—
659	D₄	—	2	16	no	—
660	D₄	—	2	16	no	—
661	D₄	—	2	8	no	—
662	D₄	—	2	8	no	—
663	D₄	—	4	16	no	—
664	D₄	—	53	16	no	—
665	D₄	—	53	32	no	—
666	D₄	—	53	16	no	—
667	D₄	—	106	64	no	—
668	D₄	—	106	64	no	—
669	D₄	—	106	16	no	—
670	D₄	—	106	16	no	—
671	D₄	—	106	8	no	—
672	D₄	—	106	8	no	—
673	D₄	—	212	16	no	—
674	D₄	—	212	32	no	—
675	C₂×C₄	—	2	8	no	—
676	C₂×C₄	—	2	16	no	—
677	C₂×C₄	—	2	16	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	—	53	8	no	—
680	C₂×C₄	—	53	8	no	—
681	C₂×C₄	—	106	64	no	—
682	C₂×C₄	—	106	8	no	—
683	C₂×C₄	—	106	16	no	—
684	C₂×C₄	—	106	16	no	—
685	C₂×C₄	—	212	32	no	—
686	C₂×C₄	—	212	4	no	—
687	C₂×C₄	C₂×D₄×D₅₃	1	8	yes	—
688	C₂×C₄	C₂×D₄×D₅₃	1	8	yes	—
689	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
690	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
691	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
692	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
693	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
694	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
695	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
696	C₂²	—	2	2	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	2	8	no	—
699	C₂²	—	2	16	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	16	no	—
702	C₂²	—	53	16	no	—
703	C₂²	—	106	16	no	—
704	C₂²	—	106	8	no	—
705	C₂²	—	106	16	no	—
706	C₂²	—	424	64	no	—
707	C₂²	—	212	32	no	—
708	C₂²	—	212	16	no	—
709	C₂²	—	212	16	no	—
710	C₂²	C₂²×D₄×D₅₃	1	4	yes	—
711	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
712	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
713	C₄	—	2	8	no	—
714	C₄	—	2	8	no	—
715	C₄	—	106	8	no	—
716	C₄	—	106	8	no	—
717	C₄	C₂²×D₄×D₅₃	1	2	yes	—
718	C₄	C₂²×D₄×D₅₃	1	4	yes	—
719	C₄	C₂²×D₄×D₅₃	1	2	yes	—
720	C₂	—	2	4	no	—
721	C₂	—	2	2	no	—
722	C₂	—	4	8	no	—
723	C₂	—	106	16	no	—
724	C₂	—	212	8	no	—
725	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
726	C₂	#20289526	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3449	C₂
hypercenter	#3449	D₅₃
hypocenter	C₅₃	#62842
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3449

Complements

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

N	H ≅ G/N	type
1. C₂²×#13133263	C₂	semidirect
2. #20288478	C₂	semidirect
3. #20288477	C₂	semidirect
4. #20288358	C₂	semidirect
5. #20288357	C₂	semidirect
6. #20288349	C₂	semidirect
7. #20288348	C₂	semidirect
8. #20288048	C₂	semidirect
9. #20288044	C₂	semidirect
10. #534×D₅₃	C₂	semidirect
11. C₂×#16811097	C₂	semidirect
12. C₅₃×#3449	C₂	semidirect
14. C₂×#13133263	C₂²	semidirect
15. C₂×#13133263	C₂²	semidirect
16. C₂×#13133263	C₂²	semidirect
17. C₂×#13133263	C₂²	semidirect
18. C₂²×#11719949	C₂²	semidirect
19. C₂²×#11719945	C₂²	semidirect
20. C₂²×#11719945	C₂²	semidirect
22. C₂³×D₂₁₂	C₂²	semidirect
23. C₂²×D₄×D₅₃	C₂²	semidirect
24. C₂²×D₄×D₅₃	C₂²	semidirect
25. #16811278	C₂²	semidirect
26. #16811276	C₂²	semidirect
27. #16811275	C₂²	semidirect
28. #16811270	C₂²	semidirect
29. #16811269	C₂²	semidirect
30. #16811266	C₂²	semidirect
31. #16811264	C₂²	semidirect
32. D₄×D₂₁₂	C₂²	semidirect
33. #16811258	C₂²	semidirect
34. #16811257	C₂²	semidirect
35. #16811204	C₂²	semidirect
36. #16811201	C₂²	semidirect
37. #16811199	C₂²	semidirect
38. #16811197	C₂²	semidirect
39. #16811194	C₂²	semidirect
40. #16811192	C₂²	semidirect
41. #16811190	C₂²	semidirect
42. #16811187	C₂²	semidirect
43. #16811185	C₂²	semidirect
44. #16811184	C₂²	semidirect
45. #16811183	C₂²	semidirect
46. #16811182	C₂²	semidirect
47. #16811181	C₂²	semidirect
48. #16811173	C₂²	semidirect
49. #16811169	C₂²	semidirect
50. #16811135	C₂²	semidirect
51. #16811134	C₂²	semidirect
52. #16811130	C₂²	semidirect
53. #123×D₅₃	C₂²	semidirect
54. #121×D₅₃	C₂²	semidirect
55. #120×D₅₃	C₂²	semidirect
56. #16811097	C₂²	semidirect
57. #16811097	C₂²	semidirect
58. C₂×C₄×D₂₁₂	C₂²	semidirect
59. C₂×#13133179	C₂²	semidirect
60. C₂×#13133176	C₂²	semidirect
61. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
62. C₂²×#41×C₅₃	C₂²	semidirect
63. C₅₃×#537	C₂²	semidirect
64. C₅₃×#536	C₂²	semidirect
65. C₅₃×#535	C₂²	semidirect
66. C₅₃×#534	C₂²	semidirect
67. C₅₃×#532	C₂²	semidirect
68. C₅₃×#525	C₂²	semidirect
69. C₂×#117×C₅₃	C₂²	semidirect
71. C₂⁴×D₅₃	C₂³	semidirect
77. C₂×#11719949	C₂³	semidirect
78. C₂×#11719949	C₂³	semidirect
83. C₂×#11719945	C₂³	semidirect
84. C₂×#11719945	C₂³	semidirect
85. C₂×#11719945	C₂³	semidirect
86. C₂×#11719945	C₂³	semidirect
87. C₂²×Dic₁₀₆	C₂³	semidirect
89. C₂²×D₂₁₂	D₄	semidirect
94. C₂²×D₂₁₂	C₂³	semidirect
95. C₂²×D₂₁₂	C₂³	semidirect
96. C₂²×D₂₁₂	C₂³	semidirect
97. C₂²×D₂₁₂	C₂³	semidirect
99. C₂²×C₂²⋊D₅₃	C₂³	semidirect
103. C₂×D₄×D₅₃	C₂³	semidirect
104. C₂×D₄×D₅₃	C₂³	semidirect
105. C₂×D₄×D₅₃	C₂³	semidirect
106. C₂×D₄×D₅₃	C₂³	semidirect
107. C₂²×C₄×D₅₃	C₂³	semidirect
108. C₂²×C₄×D₅₃	C₂³	semidirect
109. C₂²×C₄×D₅₃	C₂³	semidirect
110. #13133217	C₂³	semidirect
111. #13133215	C₂³	semidirect
112. #13133214	C₂³	semidirect
113. #13133213	C₂³	semidirect
114. #13133206	C₂³	semidirect
115. #13133205	C₂³	semidirect
116. #13133204	C₂³	semidirect
117. #13133202	C₂³	semidirect
118. #13133201	C₂³	semidirect
119. #13133200	C₂³	semidirect
120. #13133199	C₂³	semidirect
121. #13133198	C₂³	semidirect
122. #13133197	C₂³	semidirect
123. #13133196	C₂³	semidirect
124. #13133193	C₂³	semidirect
125. #13133192	C₂³	semidirect
126. #13133192	C₂³	semidirect
127. #13133191	C₂³	semidirect
128. #13133191	C₂³	semidirect
129. #13133190	C₂³	semidirect
130. #13133189	C₂³	semidirect
131. #13133188	C₂³	semidirect
132. #13133188	C₂³	semidirect
133. #13133187	C₂³	semidirect
134. #13133187	C₂³	semidirect
135. #13133186	C₂³	semidirect
136. #13133185	C₂³	semidirect
137. #13133185	C₂³	semidirect
138. C₄×D₂₁₂	C₂³	semidirect
139. C₄×D₂₁₂	C₂³	semidirect
140. C₄×D₂₁₂	C₂³	semidirect
141. #13133179	C₂³	semidirect
142. C₄×C₂²⋊D₅₃	C₂³	semidirect
143. #13133176	C₂³	semidirect
144. #13133176	C₂³	semidirect
145. C₂×C₄⋊Dic₅₃	C₂³	semidirect
146. C₄⋊C₄×D₅₃	C₂³	semidirect
148. C₂×#11719921	C₂³	semidirect
149. C₂²⋊C₄×D₅₃	C₂³	semidirect
150. C₂²⋊C₄×D₅₃	C₂³	semidirect
151. C₂×C₄×Dic₅₃	C₂³	semidirect
155. C₂×#41×C₅₃	C₂³	semidirect
156. C₂×#41×C₅₃	C₂³	semidirect
157. C₂²×Q₈×C₅₃	C₂³	semidirect
159. C₂²×D₄×C₅₃	C₂³	semidirect
161. C₂³×C₄×C₅₃	C₂³	semidirect
162. C₄⋊Q₈×C₅₃	C₂³	semidirect
163. #127×C₅₃	C₂³	semidirect
164. #124×C₅₃	C₂³	semidirect
165. #123×C₅₃	C₂³	semidirect
166. C₂²⋊Q₈×C₅₃	C₂³	semidirect
167. #121×C₅₃	C₂³	semidirect
168. #121×C₅₃	C₂³	semidirect
169. #120×C₅₃	C₂³	semidirect
170. C₄×D₄×C₅₃	C₂³	semidirect
171. #117×C₅₃	C₂³	semidirect
172. #117×C₅₃	C₂³	semidirect
173. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
175. C₂×C₄²×C₅₃	C₂³	semidirect
181. C₂³×D₅₃	C₂×D₄	semidirect
201. C₂²×C₄×C₅₃	C₂×D₄	semidirect
235. C₂×D₂₁₂	C₂×D₄	semidirect
236. C₂×D₂₁₂	C₂×D₄	semidirect
237. C₂×D₂₁₂	C₂×D₄	semidirect
238. C₂×D₂₁₂	C₂×D₄	semidirect
366. #3449	D₅₃	semidirect
384. C₂²×#41	C₂×D₅₃	semidirect
401. #537	C₂×D₅₃	semidirect
405. #536	C₂×D₅₃	semidirect
409. #535	C₂×D₅₃	semidirect
415. #534	C₂×D₅₃	semidirect
418. #532	C₂×D₅₃	semidirect
422. #525	C₂×D₅₃	semidirect
431. C₂×#117	C₂×D₅₃	semidirect
433. C₅₃	#62842	semidirect
454. C₂×#41	C₂²×D₅₃	semidirect
455. C₂×#41	C₂²×D₅₃	semidirect
457. C₂²×Q₈	C₂²×D₅₃	semidirect
478. C₂²×D₄	C₂²×D₅₃	semidirect
483. C₂³×C₄	C₂²×D₅₃	semidirect
486. C₄⋊Q₈	C₂²×D₅₃	semidirect
489. #127	C₂²×D₅₃	semidirect
493. #124	C₂²×D₅₃	semidirect
499. #123	C₂²×D₅₃	semidirect
503. C₂²⋊Q₈	C₂²×D₅₃	semidirect
512. #121	C₂²×D₅₃	semidirect
513. #121	C₂²×D₅₃	semidirect
519. #120	C₂²×D₅₃	semidirect
525. C₄×D₄	C₂²×D₅₃	semidirect
528. #117	C₂²×D₅₃	semidirect
529. #117	C₂²×D₅₃	semidirect
532. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
539. C₂×C₄²	C₂²×D₅₃	semidirect
611. C₂²×C₄	D₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13133263	2
#20288478	2
#20288477	2
#20288358	2
#20288357	2
#20288349	2
#20288348	2
#20288048	2
#20288044	2
#534×D₅₃	2
C₂×#16811097	2
C₅₃×#3449	2
#62842	53