Subgroups — C₂×#534×D₅₃ #28290806

Order 13568.

15230 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#534	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#534	D₅₃
hypocenter	C₅₃	C₂²×#534
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#534

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄×D₅₃	C₂	semidirect
2. C₂×#16811185	C₂	semidirect
3. C₂×#16811184	C₂	semidirect
4. C₂×#16811183	C₂	semidirect
5. C₂×#16811182	C₂	semidirect
6. C₂×#16811181	C₂	semidirect
7. #534×D₅₃	C₂	direct (N × H)
8. C₂×#123×D₅₃	C₂	semidirect
9. C₂×#121×D₅₃	C₂	semidirect
10. C₂×#120×D₅₃	C₂	semidirect
11. C₂²×C₂²⋊C₄×D₅₃	C₂	semidirect
12. C₂×C₅₃×#534	C₂	semidirect
14. C₂⁵×D₅₃	C₂²	semidirect
15. C₂³×D₂₁₂	C₂²	semidirect
16. C₂³×C₂²⋊D₅₃	C₂²	semidirect
17. C₂³×C₂²⋊D₅₃	C₂²	semidirect
20. C₂²×D₄×D₅₃	C₂²	semidirect
21. C₂²×D₄×D₅₃	C₂²	semidirect
22. C₂²×D₄×D₅₃	C₂²	semidirect
23. C₂²×D₄×D₅₃	C₂²	semidirect
24. C₂²×D₄×D₅₃	C₂²	semidirect
25. C₂³×C₄×D₅₃	C₂²	semidirect
26. C₂³×C₄×D₅₃	C₂²	semidirect
27. #16811185	C₂²	semidirect
28. #16811184	C₂²	semidirect
29. #16811183	C₂²	semidirect
30. #16811182	C₂²	semidirect
31. #16811181	C₂²	semidirect
32. C₂×#13133202	C₂²	semidirect
33. C₂×#13133201	C₂²	semidirect
34. C₂×#13133200	C₂²	semidirect
35. C₂×#13133199	C₂²	semidirect
36. C₂×#13133198	C₂²	semidirect
37. #123×D₅₃	C₂²	semidirect
38. C₂×#13133192	C₂²	semidirect
39. C₂×#13133191	C₂²	semidirect
40. C₂×#13133190	C₂²	semidirect
41. C₂×#13133189	C₂²	semidirect
42. C₂×#13133188	C₂²	semidirect
43. #121×D₅₃	C₂²	semidirect
44. C₂×#13133187	C₂²	semidirect
45. C₂×#13133187	C₂²	semidirect
46. C₂×#13133186	C₂²	semidirect
47. C₂×#13133185	C₂²	semidirect
48. C₂×#13133185	C₂²	semidirect
49. #120×D₅₃	C₂²	semidirect
50. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
51. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
52. C₂²×#11719921	C₂²	semidirect
53. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
54. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
55. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
56. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
57. C₂³×D₄×C₅₃	C₂²	semidirect
58. C₅₃×#534	C₂²	semidirect
59. C₂×#123×C₅₃	C₂²	semidirect
60. C₂×#121×C₅₃	C₂²	semidirect
61. C₂×#120×C₅₃	C₂²	semidirect
62. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
66. C₂⁴×D₅₃	D₄	semidirect
73. C₂⁴×D₅₃	C₂³	semidirect
74. C₂⁴×D₅₃	C₂³	semidirect
75. C₂⁴×D₅₃	C₂³	semidirect
78. C₂²×D₂₁₂	C₂³	semidirect
79. C₂²×D₂₁₂	C₂³	semidirect
80. C₂²×D₂₁₂	C₂³	semidirect
85. C₂²×C₂²⋊D₅₃	C₂³	semidirect
86. C₂²×C₂²⋊D₅₃	C₂³	semidirect
87. C₂²×C₂²⋊D₅₃	C₂³	semidirect
88. C₂²×C₂²⋊D₅₃	C₂³	semidirect
89. C₂²×C₂²⋊D₅₃	C₂³	semidirect
97. C₂×D₄×D₅₃	C₂³	semidirect
98. C₂×D₄×D₅₃	C₂³	semidirect
99. C₂×D₄×D₅₃	C₂³	semidirect
100. C₂×D₄×D₅₃	C₂³	semidirect
101. C₂³×Dic₅₃	C₂³	semidirect
102. C₂³×Dic₅₃	C₂³	semidirect
107. C₂²×C₄×D₅₃	C₂³	semidirect
108. C₂²×C₄×D₅₃	C₂³	semidirect
109. C₂²×C₄×D₅₃	C₂³	semidirect
110. C₂²×C₄×D₅₃	C₂³	semidirect
111. #13133202	C₂³	semidirect
112. #13133201	C₂³	semidirect
113. #13133200	C₂³	semidirect
114. #13133199	C₂³	semidirect
115. #13133198	C₂³	semidirect
116. #13133192	C₂³	semidirect
117. #13133191	C₂³	semidirect
118. #13133190	C₂³	semidirect
119. #13133189	C₂³	semidirect
120. #13133188	C₂³	semidirect
121. #13133187	C₂³	semidirect
122. #13133187	C₂³	semidirect
123. #13133186	C₂³	semidirect
124. #13133185	C₂³	semidirect
125. #13133185	C₂³	semidirect
126. C₂×C₄⋊Dic₅₃	C₂³	semidirect
127. C₂×#11719919	C₂³	semidirect
128. C₄⋊C₄×D₅₃	C₂³	semidirect
129. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
130. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
131. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
132. C₂×#11719921	C₂³	semidirect
133. C₂×#11719921	C₂³	semidirect
134. C₂×#11719921	C₂³	semidirect
135. C₂×#11719921	C₂³	semidirect
136. C₂²⋊C₄×D₅₃	C₂³	semidirect
137. C₂²⋊C₄×D₅₃	C₂³	semidirect
138. C₂²⋊C₄×D₅₃	C₂³	semidirect
140. C₂⁵×C₅₃	C₂³	semidirect
143. C₂²×D₄×C₅₃	C₂³	semidirect
144. C₂²×D₄×C₅₃	C₂³	semidirect
145. C₂²×D₄×C₅₃	C₂³	semidirect
146. C₂³×C₄×C₅₃	C₂³	semidirect
147. C₂³×C₄×C₅₃	C₂³	semidirect
148. #123×C₅₃	C₂³	semidirect
149. #121×C₅₃	C₂³	semidirect
150. #120×C₅₃	C₂³	semidirect
151. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
152. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
153. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
154. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
158. C₂⁴×C₅₃	C₂×D₄	semidirect
163. C₂⁴×C₅₃	C₂⁴	semidirect
181. C₂³×D₅₃	C₂×D₄	semidirect
182. C₂³×D₅₃	C₂×D₄	semidirect
183. C₂³×D₅₃	C₂×D₄	semidirect
193. C₂³×D₅₃	C₂⁴	semidirect
194. C₂³×D₅₃	C₂⁴	semidirect
200. C₂×D₄×C₅₃	C₂⁴	semidirect
201. C₂×D₄×C₅₃	C₂⁴	semidirect
206. C₂²×C₄×C₅₃	C₂⁴	semidirect
207. C₂²×C₄×C₅₃	C₂⁴	semidirect
217. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
218. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
219. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
224. C₂²×Dic₅₃	C₂⁴	semidirect
225. C₂²×Dic₅₃	C₂⁴	semidirect
236. C₂×D₂₁₂	C₂⁴	semidirect
237. C₂×D₂₁₂	C₂⁴	semidirect
246. C₂×C₄×D₅₃	C₂⁴	semidirect
247. C₂×C₄×D₅₃	C₂⁴	semidirect
248. C₄⋊C₄×C₅₃	C₂⁴	semidirect
249. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
250. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
251. C₂²⋊Dic₅₃	C₂⁴	semidirect
252. C₂²⋊Dic₅₃	C₂⁴	semidirect
253. #11719921	C₂⁴	semidirect
254. #11719921	C₂⁴	semidirect
255. #11719921	C₂⁴	semidirect
256. C₄⋊Dic₅₃	C₂⁴	semidirect
257. #11719919	C₂⁴	semidirect
269. C₂³×C₅₃	C₂²×D₄	semidirect
302. C₂²×D₅₃	C₂²×D₄	semidirect
303. C₂²×D₅₃	C₂²×D₄	semidirect
365. C₂×D₅₃	#534	direct (N × H)
381. C₂×#534	D₅₃	direct (N × H)
389. C₂×C₅₃	C₂×#534	semidirect
395. D₅₃	C₂×#534	direct (N × H)
408. C₂³×D₄	C₂×D₅₃	semidirect
416. #534	C₂×D₅₃	direct (N × H)
423. C₂×#123	C₂×D₅₃	semidirect
430. C₂×#121	C₂×D₅₃	semidirect
437. C₂×#120	C₂×D₅₃	semidirect
445. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
446. C₅₃	C₂²×#534	semidirect
461. C₂⁵	C₂²×D₅₃	semidirect
489. C₂²×D₄	C₂²×D₅₃	semidirect
490. C₂²×D₄	C₂²×D₅₃	semidirect
491. C₂²×D₄	C₂²×D₅₃	semidirect
502. C₂³×C₄	C₂²×D₅₃	semidirect
503. C₂³×C₄	C₂²×D₅₃	semidirect
509. #123	C₂²×D₅₃	semidirect
515. #121	C₂²×D₅₃	semidirect
521. #120	C₂²×D₅₃	semidirect
525. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
536. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
537. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
538. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
573. C₂⁴	D₄×D₅₃	semidirect
578. C₂⁴	C₂³×D₅₃	semidirect
608. C₂×D₄	C₂³×D₅₃	semidirect
609. C₂×D₄	C₂³×D₅₃	semidirect
630. C₂²×C₄	C₂³×D₅₃	semidirect
631. C₂²×C₄	C₂³×D₅₃	semidirect
634. C₄⋊C₄	C₂³×D₅₃	semidirect
640. C₂²⋊C₄	C₂³×D₅₃	semidirect
641. C₂²⋊C₄	C₂³×D₅₃	semidirect
688. C₂³	C₂×D₄×D₅₃	semidirect
764. C₂	#534×D₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄×D₅₃	2
C₂×#16811185	2
C₂×#16811184	2
C₂×#16811183	2
C₂×#16811182	2
C₂×#16811181	2
#534×D₅₃	2
C₂×#123×D₅₃	2
C₂×#121×D₅₃	2
C₂×#120×D₅₃	2
C₂²×C₂²⋊C₄×D₅₃	2
C₂×C₅₃×#534	2
C₂²×#534	53

Subgroups — C2×#534×D53 #28290806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#534×D₅₃ #28290806