Subgroups — C₂²×#16811260 #28291016

Order 13568.

14462 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11719947	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811260	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#13133203	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13133201	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13133199	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13133194	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13133189	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#13133189	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#13133188	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#13133185	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₄×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#13133177	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×C₂²⋊Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#120×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁵×D₅₃	C₂²	1	1	yes	characteristic
18	C₂²×#11719947	—	2	16	no	—
19	C₂²×#11719947	C₂²	1	24	yes	complemented
20	C₂³×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₂²⋊D₅₃	—	2	16	no	—
22	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
23	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
24	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
25	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
26	C₂³×C₂²⋊D₅₃	C₂²	1	24	yes	complemented
27	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic
30	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
35	#16811260	C₂²	1	256	yes	direct product factor
36	C₂×#13133203	C₂²	1	24	yes	complemented
37	C₂×#13133201	C₂²	1	24	yes	complemented
38	C₂×#13133199	C₂²	1	24	yes	complemented
39	C₂×#13133194	C₂²	1	24	yes	complemented
40	C₂×#13133189	C₂²	1	24	yes	complemented
41	C₂×#13133189	C₂²	1	24	yes	complemented
42	C₂×#13133188	C₂²	1	24	yes	complemented
43	C₂×#13133185	C₂²	1	24	yes	complemented
44	C₂×D₄×Dic₅₃	C₂²	1	24	yes	complemented
45	C₂×#13133177	C₂²	1	24	yes	complemented
46	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
48	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
49	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
51	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
52	C₂²×C₂²⋊Dic₅₃	C₂²	1	24	yes	complemented
53	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₂²×#11719921	C₂²	1	1	yes	characteristic, complemented
57	C₂²×#11719921	C₂²	1	1	yes	characteristic, complemented
58	C₂²×#11719921	C₂²	1	1	yes	characteristic, complemented
59	C₂²×#11719921	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂²⋊C₄×D₅₃	C₂²	1	24	yes	complemented
61	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic
63	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
64	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×#120×C₅₃	C₂²	1	24	yes	complemented
67	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
68	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
69	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
70	C₂⁴×D₅₃	—	2	8	no	—
71	C₂⁴×D₅₃	—	2	8	no	—
72	C₂⁴×D₅₃	—	4	4	no	—
73	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
74	C₂⁴×D₅₃	C₂³	1	12	yes	—
75	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
76	C₂×#11719947	—	2	192	no	—
77	C₂×#11719947	C₂³	1	64	yes	complemented
78	C₂²×Dic₁₀₆	—	2	8	no	—
79	C₂²×Dic₁₀₆	C₂³	1	12	yes	complemented
80	C₂²×C₂²⋊D₅₃	—	2	8	no	—
81	C₂²×C₂²⋊D₅₃	—	2	8	no	—
82	C₂²×C₂²⋊D₅₃	—	2	8	no	—
83	C₂²×C₂²⋊D₅₃	—	2	192	no	—
84	C₂²×C₂²⋊D₅₃	—	2	8	no	—
85	C₂²×C₂²⋊D₅₃	—	4	4	no	—
86	C₂²×C₂²⋊D₅₃	D₄	1	16	yes	complemented
87	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
88	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
89	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
90	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
91	C₂²×C₂²⋊D₅₃	C₂³	1	64	yes	complemented
92	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
93	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
94	C₂³×Dic₅₃	—	2	8	no	—
95	C₂³×Dic₅₃	—	2	8	no	—
96	C₂³×Dic₅₃	—	2	8	no	—
97	C₂³×Dic₅₃	—	4	4	no	—
98	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
99	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
100	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
101	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
102	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
103	C₂³×Dic₅₃	C₂³	1	12	yes	—
104	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
105	C₂³×Dic₅₃	C₂³	1	12	yes	complemented
106	C₂³×Dic₅₃	C₂³	1	12	yes	complemented
107	C₂³×Dic₅₃	C₂³	1	12	yes	complemented
108	C₂²×C₄×D₅₃	—	2	8	no	—
109	C₂²×C₄×D₅₃	—	4	4	no	—
110	C₂²×C₄×D₅₃	C₂³	1	12	yes	complemented
111	C₂²×C₄×D₅₃	C₂³	1	12	yes	complemented
112	#13133203	C₂³	1	64	yes	complemented
113	#13133201	C₂³	1	64	yes	complemented
114	#13133199	C₂³	1	64	yes	complemented
115	#13133194	C₂³	1	64	yes	complemented
116	#13133189	C₂³	1	64	yes	complemented
117	#13133189	C₂³	1	64	yes	complemented
118	#13133188	C₂³	1	64	yes	complemented
119	#13133185	C₂³	1	64	yes	complemented
120	D₄×Dic₅₃	C₂³	1	64	yes	complemented
121	#13133177	C₂³	1	64	yes	complemented
122	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	complemented
123	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	complemented
124	C₂×#11719919	C₂³	1	12	yes	complemented
125	C₂×#11719919	C₂³	1	12	yes	complemented
126	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	—
127	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	—
128	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	complemented
129	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	complemented
130	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	complemented
131	C₂×C₂²⋊Dic₅₃	C₂³	1	64	yes	complemented
132	C₂×#11719921	C₂³	1	12	yes	complemented
133	C₂×#11719921	C₂³	1	12	yes	complemented
134	C₂×#11719921	C₂³	1	12	yes	complemented
135	C₂×#11719921	C₂³	1	12	yes	complemented
136	C₂²⋊C₄×D₅₃	C₂³	1	64	yes	complemented
137	C₂×C₄×Dic₅₃	C₂³	1	12	yes	complemented
138	C₂⁵×C₅₃	—	2	8	no	—
139	C₂⁵×C₅₃	—	2	8	no	—
140	C₂⁵×C₅₃	—	4	4	no	—
141	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
142	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
143	C₂⁵×C₅₃	C₂³	1	12	yes	—
144	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
145	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₅₃	—	2	8	no	—
147	C₂²×D₄×C₅₃	—	2	8	no	—
148	C₂²×D₄×C₅₃	—	4	4	no	—
149	C₂²×D₄×C₅₃	C₂³	1	12	yes	—
150	C₂²×D₄×C₅₃	C₂³	1	12	yes	complemented
151	C₂²×D₄×C₅₃	C₂³	1	12	yes	complemented
152	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
153	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
155	#120×C₅₃	C₂³	1	64	yes	complemented
156	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	—
157	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	complemented
158	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	complemented
159	C₂⁴×C₅₃	—	2	4	no	—
160	C₂⁴×C₅₃	—	2	4	no	—
161	C₂⁴×C₅₃	—	2	4	no	—
162	C₂⁴×C₅₃	—	2	4	no	—
163	C₂⁴×C₅₃	—	2	4	no	—
164	C₂⁴×C₅₃	—	2	48	no	—
165	C₂⁴×C₅₃	—	2	4	no	—
166	C₂⁴×C₅₃	—	2	4	no	—
167	C₂⁴×C₅₃	—	2	4	no	—
168	C₂⁴×C₅₃	—	2	48	no	—
169	C₂⁴×C₅₃	—	2	4	no	—
170	C₂⁴×C₅₃	—	2	4	no	—
171	C₂⁴×C₅₃	—	4	24	no	—
172	C₂⁴×C₅₃	—	4	64	no	—
173	C₂⁴×C₅₃	C₂×D₄	1	8	yes	—
174	C₂⁴×C₅₃	#41	1	8	yes	complemented
175	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
176	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
177	C₂⁴×C₅₃	C₂⁴	1	16	yes	—
178	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
179	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
180	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
181	C₂³×D₅₃	—	2	4	no	—
182	C₂³×D₅₃	—	2	4	no	—
183	C₂³×D₅₃	—	2	4	no	—
184	C₂³×D₅₃	—	2	4	no	—
185	C₂³×D₅₃	—	2	48	no	—
186	C₂³×D₅₃	—	2	4	no	—
187	C₂³×D₅₃	—	2	48	no	—
188	C₂³×D₅₃	—	4	24	no	—
189	C₂³×D₅₃	—	4	64	no	—
190	C₂³×D₅₃	C₂×D₄	1	8	yes	—
191	C₂³×D₅₃	C₂⁴	1	6	yes	—
192	C₂³×D₅₃	C₂⁴	1	16	yes	—
193	C₂³×D₅₃	C₂⁴	1	6	yes	—
194	C₂×D₄×C₅₃	—	2	48	no	—
195	C₂×D₄×C₅₃	—	2	48	no	—
196	C₂×D₄×C₅₃	—	4	24	no	—
197	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
198	C₂×D₄×C₅₃	C₂⁴	1	16	yes	complemented
199	C₂×D₄×C₅₃	C₂⁴	1	16	yes	complemented
200	C₂²×C₄×C₅₃	—	2	4	no	—
201	C₂²×C₄×C₅₃	—	2	4	no	—
202	C₂²×C₄×C₅₃	—	2	4	no	—
203	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
204	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
205	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
206	C₂×C₂²⋊D₅₃	—	2	48	no	—
207	C₂×C₂²⋊D₅₃	—	2	48	no	—
208	C₂×C₂²⋊D₅₃	—	2	48	no	—
209	C₂×C₂²⋊D₅₃	—	2	256	no	—
210	C₂×C₂²⋊D₅₃	—	2	48	no	—
211	C₂×C₂²⋊D₅₃	—	4	24	no	—
212	C₂×C₂²⋊D₅₃	C₂×D₄	1	96	yes	complemented
213	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
214	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
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	C₂²×Dic₅₃	—	2	4	no	—
220	C₂²×Dic₅₃	—	2	4	no	—
221	C₂²×Dic₅₃	—	2	4	no	—
222	C₂²×Dic₅₃	—	2	48	no	—
223	C₂²×Dic₅₃	—	2	4	no	—
224	C₂²×Dic₅₃	—	2	4	no	—
225	C₂²×Dic₅₃	—	2	48	no	—
226	C₂²×Dic₅₃	—	2	48	no	—
227	C₂²×Dic₅₃	—	4	24	no	—
228	C₂²×Dic₅₃	C₂×D₄	1	8	yes	—
229	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
230	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
231	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
232	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
233	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
234	C₂²×Dic₅₃	C₂⁴	1	16	yes	—
235	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
236	C₂²×Dic₅₃	C₂⁴	1	16	yes	complemented
237	C₂²×Dic₅₃	C₂⁴	1	16	yes	complemented
238	C₂²×Dic₅₃	C₂⁴	1	16	yes	complemented
239	#11719947	—	2	256	no	—
240	C₂×C₄×D₅₃	—	2	48	no	—
241	C₂×C₄×D₅₃	—	4	24	no	—
242	C₂×C₄×D₅₃	C₂⁴	1	16	yes	complemented
243	C₂×C₄×D₅₃	C₂⁴	1	16	yes	complemented
244	C₂×Dic₁₀₆	—	2	48	no	—
245	C₂×Dic₁₀₆	C₂⁴	1	16	yes	complemented
246	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
247	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
248	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
249	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
250	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
251	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
252	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
253	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
254	#11719921	C₂⁴	1	16	yes	complemented
255	#11719921	C₂⁴	1	16	yes	complemented
256	#11719921	C₂⁴	1	16	yes	complemented
257	#11719921	C₂⁴	1	16	yes	complemented
258	C₄⋊Dic₅₃	C₂⁴	1	16	yes	complemented
259	C₄⋊Dic₅₃	C₂⁴	1	16	yes	complemented
260	#11719919	C₂⁴	1	16	yes	complemented
261	#11719919	C₂⁴	1	16	yes	complemented
262	C₄×Dic₅₃	C₂⁴	1	16	yes	complemented
263	C₂³×C₅₃	—	2	32	no	—
264	C₂³×C₅₃	—	2	32	no	—
265	C₂³×C₅₃	—	2	12	no	—
266	C₂³×C₅₃	—	2	12	no	—
267	C₂³×C₅₃	—	2	12	no	—
268	C₂³×C₅₃	—	2	12	no	—
269	C₂³×C₅₃	—	2	12	no	—
270	C₂³×C₅₃	—	2	32	no	—
271	C₂³×C₅₃	—	2	12	no	—
272	C₂³×C₅₃	—	2	12	no	—
273	C₂³×C₅₃	—	2	12	no	—
274	C₂³×C₅₃	—	2	32	no	—
275	C₂³×C₅₃	—	2	12	no	—
276	C₂³×C₅₃	—	2	12	no	—
277	C₂³×C₅₃	—	4	16	no	—
278	C₂³×C₅₃	—	4	192	no	—
279	C₂³×C₅₃	—	4	16	no	—
280	C₂³×C₅₃	—	4	16	no	—
281	C₂³×C₅₃	C₂²×D₄	1	24	yes	—
282	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
283	C₂³×C₅₃	C₂×#41	1	4	yes	—
284	C₂³×C₅₃	C₂×#41	1	24	yes	complemented
285	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
286	C₂³×C₅₃	C₂⁵	1	4	yes	—
287	C₂³×C₅₃	C₂⁵	1	4	yes	—
288	C₂³×C₅₃	C₂⁵	1	4	yes	—
289	C₂³×C₅₃	C₂⁵	1	4	yes	—
290	C₂³×C₅₃	C₂⁵	1	3	yes	—
291	C₂²×D₅₃	—	2	32	no	—
292	C₂²×D₅₃	—	2	12	no	—
293	C₂²×D₅₃	—	2	12	no	—
294	C₂²×D₅₃	—	2	12	no	—
295	C₂²×D₅₃	—	2	12	no	—
296	C₂²×D₅₃	—	2	32	no	—
297	C₂²×D₅₃	—	2	12	no	—
298	C₂²×D₅₃	—	2	32	no	—
299	C₂²×D₅₃	—	4	16	no	—
300	C₂²×D₅₃	—	4	192	no	—
301	C₂²×D₅₃	—	4	16	no	—
302	C₂²×D₅₃	C₂²×D₄	1	24	yes	—
303	C₂²×D₅₃	C₂⁵	1	4	yes	—
304	C₂²×D₅₃	C₂⁵	1	4	yes	—
305	D₄×C₅₃	—	2	32	no	—
306	D₄×C₅₃	—	2	32	no	—
307	D₄×C₅₃	—	4	16	no	—
308	C₂×C₄×C₅₃	—	2	12	no	—
309	C₂×C₄×C₅₃	—	2	12	no	—
310	C₂×C₄×C₅₃	—	2	12	no	—
311	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
312	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
313	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
314	C₂²⋊D₅₃	—	2	32	no	—
315	C₂²⋊D₅₃	—	2	32	no	—
316	C₂²⋊D₅₃	—	2	32	no	—
317	C₂²⋊D₅₃	—	2	32	no	—
318	C₂²⋊D₅₃	—	4	16	no	—
319	C₂²⋊D₅₃	C₂²×D₄	1	64	yes	complemented
320	C₂×Dic₅₃	—	2	12	no	—
321	C₂×Dic₅₃	—	2	12	no	—
322	C₂×Dic₅₃	—	2	32	no	—
323	C₂×Dic₅₃	—	2	12	no	—
324	C₂×Dic₅₃	—	2	12	no	—
325	C₂×Dic₅₃	—	2	12	no	—
326	C₂×Dic₅₃	—	2	32	no	—
327	C₂×Dic₅₃	—	2	32	no	—
328	C₂×Dic₅₃	—	4	16	no	—
329	C₂×Dic₅₃	C₂²×D₄	1	24	yes	—
330	C₂×Dic₅₃	C₂⁵	1	4	yes	—
331	C₂×Dic₅₃	C₂⁵	1	4	yes	—
332	C₂×Dic₅₃	C₂⁵	1	4	yes	—
333	C₂×Dic₅₃	C₂⁵	1	4	yes	—
334	C₂×Dic₅₃	C₂⁵	1	4	yes	—
335	C₂×Dic₅₃	C₂⁵	1	4	yes	—
336	C₄×D₅₃	—	2	32	no	—
337	C₄×D₅₃	—	4	16	no	—
338	Dic₁₀₆	—	2	32	no	—
339	C₂²×#546	—	53	1	no	maximal, Sylow
340	C₂²×C₅₃	—	2	4	no	—
341	C₂²×C₅₃	—	2	4	no	—
342	C₂²×C₅₃	—	2	4	no	—
343	C₂²×C₅₃	—	2	4	no	—
344	C₂²×C₅₃	—	2	48	no	—
345	C₂²×C₅₃	—	2	48	no	—
346	C₂²×C₅₃	—	2	4	no	—
347	C₂²×C₅₃	—	2	4	no	—
348	C₂²×C₅₃	—	2	4	no	—
349	C₂²×C₅₃	—	2	4	no	—
350	C₂²×C₅₃	—	2	4	no	—
351	C₂²×C₅₃	—	2	4	no	—
352	C₂²×C₅₃	—	4	64	no	—
353	C₂²×C₅₃	—	4	24	no	—
354	C₂²×C₅₃	—	4	24	no	—
355	C₂²×C₅₃	#546	1	16	yes	complemented
356	C₂²×C₅₃	C₂³×D₄	1	8	yes	—
357	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
358	C₂²×C₅₃	C₂²×#41	1	6	yes	—
359	C₂²×C₅₃	C₂²×#41	1	8	yes	complemented
360	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
361	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
362	C₂×D₅₃	—	2	4	no	—
363	C₂×D₅₃	—	2	4	no	—
364	C₂×D₅₃	—	2	48	no	—
365	C₂×D₅₃	—	2	4	no	—
366	C₂×D₅₃	—	2	4	no	—
367	C₂×D₅₃	—	2	4	no	—
368	C₂×D₅₃	—	4	64	no	—
369	C₂×D₅₃	—	4	24	no	—
370	C₂×D₅₃	C₂³×D₄	1	8	yes	—
371	C₄×C₅₃	—	2	4	no	—
372	C₄×C₅₃	—	2	4	no	—
373	C₄×C₅₃	—	2	4	no	—
374	Dic₅₃	—	2	4	no	—
375	Dic₅₃	—	2	4	no	—
376	Dic₅₃	—	2	4	no	—
377	Dic₅₃	—	2	4	no	—
378	Dic₅₃	—	2	4	no	—
379	Dic₅₃	C₂³×D₄	1	8	yes	—
380	C₂³×#41	—	53	1	no	—
381	C₂⁴×D₄	—	53	1	no	—
382	C₂×#546	—	53	48	no	—
383	C₂²×#124	—	53	1	no	—
384	C₂²×#123	—	53	1	no	—
385	C₂²×#123	—	53	1	no	—
386	C₂²×C₂²⋊Q₈	—	53	1	no	—
387	C₂²×#121	—	53	1	no	—
388	C₂²×#121	—	53	1	no	—
389	C₂²×#121	—	53	1	no	—
390	C₂²×#120	—	53	1	no	—
391	C₂²×#120	D₅₃	1	1	yes	characteristic, complemented
392	C₂²×C₄×D₄	—	53	1	no	—
393	C₂²×C₄×D₄	—	53	1	no	—
394	C₂³×C₂²⋊C₄	—	53	1	no	—
395	C₂³×C₂²⋊C₄	—	53	1	no	—
396	C₂×C₅₃	—	2	8	no	—
397	C₂×C₅₃	—	2	8	no	—
398	C₂×C₅₃	—	4	4	no	—
399	C₂×C₅₃	—	4	4	no	—
400	C₂×C₅₃	C₂×#546	1	12	yes	complemented
401	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
402	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
403	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
404	D₅₃	—	2	8	no	—
405	D₅₃	—	4	4	no	—
406	C₂⁶	—	53	1	no	—
407	C₂⁶	C₂×D₅₃	1	1	yes	characteristic
408	C₂²×#41	—	53	24	no	—
409	C₂²×#41	—	106	16	no	—
410	C₂³×Q₈	—	53	1	no	—
411	C₂³×D₄	—	53	1	no	—
412	C₂³×D₄	—	53	1	no	—
413	C₂³×D₄	—	53	1	no	—
414	C₂³×D₄	—	53	1	no	—
415	C₂³×D₄	—	53	24	no	—
416	C₂³×D₄	—	53	1	no	—
417	C₂³×D₄	—	53	1	no	—
418	C₂³×D₄	—	106	16	no	—
419	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic
420	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
421	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
422	C₂⁴×C₄	—	53	1	no	—
423	C₂⁴×C₄	—	53	1	no	—
424	C₂⁴×C₄	—	53	1	no	—
425	C₂⁴×C₄	—	53	1	no	—
426	C₂⁴×C₄	—	53	1	no	—
427	C₂⁴×C₄	—	53	1	no	—
428	#546	—	53	256	no	—
429	C₂×#124	—	53	24	no	—
430	C₂×#123	—	53	24	no	—
431	C₂×#123	—	53	24	no	—
432	C₂×C₂²⋊Q₈	—	53	24	no	—
433	C₂×#121	—	53	24	no	—
434	C₂×#121	—	53	24	no	—
435	C₂×#121	—	53	24	no	—
436	C₂×#120	—	53	24	no	—
437	C₂×#120	C₂×D₅₃	1	24	yes	complemented
438	C₂×C₄×D₄	—	53	24	no	—
439	C₂×C₄×D₄	—	53	24	no	—
440	C₂²×C₄⋊C₄	—	53	1	no	—
441	C₂²×C₄⋊C₄	—	53	1	no	—
442	C₂²×C₄⋊C₄	—	53	1	no	—
443	C₂²×C₄⋊C₄	—	53	1	no	—
444	C₂²×C₂²⋊C₄	—	53	1	no	—
445	C₂²×C₂²⋊C₄	—	53	1	no	—
446	C₂²×C₂²⋊C₄	—	53	1	no	—
447	C₂²×C₂²⋊C₄	—	53	1	no	—
448	C₂²×C₂²⋊C₄	—	53	24	no	—
449	C₂²×C₂²⋊C₄	—	53	1	no	—
450	C₂²×C₂²⋊C₄	—	53	1	no	—
451	C₂²×C₂²⋊C₄	—	53	1	no	—
452	C₂²×C₂²⋊C₄	—	53	1	no	—
453	C₂²×C₂²⋊C₄	—	53	1	no	—
454	C₂²×C₂²⋊C₄	—	53	24	no	—
455	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
456	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
457	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
458	C₂²×C₄²	—	53	1	no	—
459	C₅₃	C₂²×#546	1	1	yes	characteristic, complemented, Sylow
460	C₂⁵	—	2	8	no	—
461	C₂⁵	—	2	8	no	—
462	C₂⁵	—	4	4	no	—
463	C₂⁵	—	53	1	no	—
464	C₂⁵	—	53	1	no	—
465	C₂⁵	—	53	12	no	—
466	C₂⁵	—	106	8	no	—
467	C₂⁵	—	106	8	no	—
468	C₂⁵	—	212	4	no	—
469	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
470	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
471	C₂⁵	C₂²×D₅₃	1	12	yes	—
472	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
473	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
474	C₂×#41	—	53	64	no	—
475	C₂×#41	—	106	192	no	—
476	C₂²×Q₈	—	53	12	no	—
477	C₂²×Q₈	—	106	8	no	—
478	C₂²×D₄	—	2	8	no	—
479	C₂²×D₄	—	2	8	no	—
480	C₂²×D₄	—	4	4	no	—
481	C₂²×D₄	—	53	16	no	—
482	C₂²×D₄	—	53	12	no	—
483	C₂²×D₄	—	53	12	no	—
484	C₂²×D₄	—	53	12	no	—
485	C₂²×D₄	—	53	12	no	—
486	C₂²×D₄	—	53	12	no	—
487	C₂²×D₄	—	53	64	no	—
488	C₂²×D₄	—	53	12	no	—
489	C₂²×D₄	—	106	8	no	—
490	C₂²×D₄	—	106	192	no	—
491	C₂²×D₄	—	106	8	no	—
492	C₂²×D₄	—	106	8	no	—
493	C₂²×D₄	—	106	8	no	—
494	C₂²×D₄	—	212	4	no	—
495	C₂²×D₄	C₂²×D₅₃	1	12	yes	—
496	C₂²×D₄	C₂²×D₅₃	1	12	yes	complemented
497	C₂²×D₄	C₂²×D₅₃	1	12	yes	complemented
498	C₂³×C₄	—	53	1	no	—
499	C₂³×C₄	—	53	12	no	—
500	C₂³×C₄	—	53	12	no	—
501	C₂³×C₄	—	53	12	no	—
502	C₂³×C₄	—	53	1	no	—
503	C₂³×C₄	—	53	1	no	—
504	C₂³×C₄	—	53	1	no	—
505	C₂³×C₄	—	53	1	no	—
506	C₂³×C₄	—	53	1	no	—
507	C₂³×C₄	—	53	12	no	—
508	C₂³×C₄	—	53	12	no	—
509	C₂³×C₄	—	53	12	no	—
510	C₂³×C₄	—	106	8	no	—
511	C₂³×C₄	—	106	8	no	—
512	C₂³×C₄	—	106	8	no	—
513	C₂³×C₄	—	106	8	no	—
514	C₂³×C₄	—	212	4	no	—
515	C₂³×C₄	—	212	4	no	—
516	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
517	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
518	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
519	#124	—	53	64	no	—
520	#123	—	53	64	no	—
521	#123	—	53	64	no	—
522	C₂²⋊Q₈	—	53	64	no	—
523	#121	—	53	64	no	—
524	#121	—	53	64	no	—
525	#121	—	53	64	no	—
526	#120	—	53	64	no	—
527	#120	C₂²×D₅₃	1	64	yes	complemented
528	C₄×D₄	—	53	64	no	—
529	C₄×D₄	—	53	64	no	—
530	C₂×C₄⋊C₄	—	53	12	no	—
531	C₂×C₄⋊C₄	—	53	12	no	—
532	C₂×C₄⋊C₄	—	53	12	no	—
533	C₂×C₄⋊C₄	—	53	12	no	—
534	C₂×C₂²⋊C₄	—	53	12	no	—
535	C₂×C₂²⋊C₄	—	53	12	no	—
536	C₂×C₂²⋊C₄	—	53	12	no	—
537	C₂×C₂²⋊C₄	—	53	12	no	—
538	C₂×C₂²⋊C₄	—	53	64	no	—
539	C₂×C₂²⋊C₄	—	53	12	no	—
540	C₂×C₂²⋊C₄	—	53	12	no	—
541	C₂×C₂²⋊C₄	—	53	12	no	—
542	C₂×C₂²⋊C₄	—	53	12	no	—
543	C₂×C₂²⋊C₄	—	53	12	no	—
544	C₂×C₂²⋊C₄	—	53	64	no	—
545	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	—
546	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	complemented
547	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	complemented
548	C₂×C₄²	—	53	12	no	—
549	C₂⁴	—	2	4	no	—
550	C₂⁴	—	2	4	no	—
551	C₂⁴	—	2	4	no	—
552	C₂⁴	—	2	4	no	—
553	C₂⁴	—	2	4	no	—
554	C₂⁴	—	2	48	no	—
555	C₂⁴	—	2	4	no	—
556	C₂⁴	—	2	4	no	—
557	C₂⁴	—	2	4	no	—
558	C₂⁴	—	2	48	no	—
559	C₂⁴	—	2	4	no	—
560	C₂⁴	—	2	4	no	—
561	C₂⁴	—	4	24	no	—
562	C₂⁴	—	4	64	no	—
563	C₂⁴	—	53	8	no	—
564	C₂⁴	—	53	6	no	—
565	C₂⁴	—	53	6	no	—
566	C₂⁴	—	53	16	no	—
567	C₂⁴	—	106	48	no	—
568	C₂⁴	—	106	4	no	—
569	C₂⁴	—	106	4	no	—
570	C₂⁴	—	106	4	no	—
571	C₂⁴	—	106	4	no	—
572	C₂⁴	—	106	48	no	—
573	C₂⁴	—	106	4	no	—
574	C₂⁴	—	212	24	no	—
575	C₂⁴	—	212	64	no	—
576	C₂⁴	D₄×D₅₃	1	8	yes	—
577	C₂⁴	#11719947	1	8	yes	complemented
578	C₂⁴	C₂³×D₅₃	1	6	yes	—
579	C₂⁴	C₂³×D₅₃	1	6	yes	—
580	C₂⁴	C₂³×D₅₃	1	16	yes	—
581	C₂⁴	C₂³×D₅₃	1	6	yes	—
582	C₂⁴	C₂³×D₅₃	1	6	yes	—
583	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
584	#41	—	106	256	no	—
585	C₂×Q₈	—	53	16	no	—
586	C₂×Q₈	—	106	48	no	—
587	C₂×D₄	—	2	48	no	—
588	C₂×D₄	—	2	48	no	—
589	C₂×D₄	—	4	24	no	—
590	C₂×D₄	—	53	96	no	—
591	C₂×D₄	—	53	16	no	—
592	C₂×D₄	—	53	16	no	—
593	C₂×D₄	—	53	16	no	—
594	C₂×D₄	—	53	16	no	—
595	C₂×D₄	—	53	16	no	—
596	C₂×D₄	—	53	16	no	—
597	C₂×D₄	—	106	48	no	—
598	C₂×D₄	—	106	256	no	—
599	C₂×D₄	—	106	48	no	—
600	C₂×D₄	—	106	48	no	—
601	C₂×D₄	—	106	48	no	—
602	C₂×D₄	—	212	24	no	—
603	C₂×D₄	C₂³×D₅₃	1	16	yes	—
604	C₂×D₄	C₂³×D₅₃	1	16	yes	complemented
605	C₂×D₄	C₂³×D₅₃	1	16	yes	complemented
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	53	8	no	—
610	C₂²×C₄	—	53	6	no	—
611	C₂²×C₄	—	53	6	no	—
612	C₂²×C₄	—	53	6	no	—
613	C₂²×C₄	—	53	6	no	—
614	C₂²×C₄	—	53	6	no	—
615	C₂²×C₄	—	53	6	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	—	53	16	no	—
621	C₂²×C₄	—	53	16	no	—
622	C₂²×C₄	—	106	48	no	—
623	C₂²×C₄	—	106	48	no	—
624	C₂²×C₄	—	106	48	no	—
625	C₂²×C₄	—	106	4	no	—
626	C₂²×C₄	—	106	4	no	—
627	C₂²×C₄	—	106	4	no	—
628	C₂²×C₄	—	106	48	no	—
629	C₂²×C₄	—	106	4	no	—
630	C₂²×C₄	—	106	4	no	—
631	C₂²×C₄	—	212	24	no	—
632	C₂²×C₄	—	212	24	no	—
633	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
634	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
635	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
636	C₄⋊C₄	—	53	16	no	—
637	C₄⋊C₄	—	53	16	no	—
638	C₄⋊C₄	—	53	16	no	—
639	C₄⋊C₄	—	53	16	no	—
640	C₂²⋊C₄	—	53	16	no	—
641	C₂²⋊C₄	—	53	16	no	—
642	C₂²⋊C₄	—	53	16	no	—
643	C₂²⋊C₄	—	53	16	no	—
644	C₂²⋊C₄	—	53	16	no	—
645	C₂²⋊C₄	—	53	16	no	—
646	C₂²⋊C₄	—	53	16	no	—
647	C₂²⋊C₄	—	53	16	no	—
648	C₂²⋊C₄	—	53	16	no	—
649	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
650	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	complemented
651	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	complemented
652	C₄²	—	53	16	no	—
653	C₂³	—	2	12	no	—
654	C₂³	—	2	12	no	—
655	C₂³	—	2	12	no	—
656	C₂³	—	2	12	no	—
657	C₂³	—	2	32	no	—
658	C₂³	—	2	32	no	—
659	C₂³	—	2	12	no	—
660	C₂³	—	2	32	no	—
661	C₂³	—	2	12	no	—
662	C₂³	—	2	12	no	—
663	C₂³	—	2	12	no	—
664	C₂³	—	2	32	no	—
665	C₂³	—	2	12	no	—
666	C₂³	—	2	12	no	—
667	C₂³	—	4	16	no	—
668	C₂³	—	4	192	no	—
669	C₂³	—	4	16	no	—
670	C₂³	—	4	16	no	—
671	C₂³	—	53	24	no	—
672	C₂³	—	53	4	no	—
673	C₂³	—	53	4	no	—
674	C₂³	—	106	32	no	—
675	C₂³	—	106	12	no	—
676	C₂³	—	106	12	no	—
677	C₂³	—	106	32	no	—
678	C₂³	—	106	12	no	—
679	C₂³	—	106	12	no	—
680	C₂³	—	106	32	no	—
681	C₂³	—	106	12	no	—
682	C₂³	—	212	16	no	—
683	C₂³	—	212	192	no	—
684	C₂³	—	212	16	no	—
685	C₂³	C₂×D₄×D₅₃	1	24	yes	—
686	C₂³	C₂×D₄×D₅₃	1	4	yes	—
687	C₂³	C₂×#11719947	1	4	yes	—
688	C₂³	C₂×#11719947	1	24	yes	complemented
689	C₂³	#13133262	1	4	yes	—
690	C₂³	C₂⁴×D₅₃	1	4	yes	—
691	C₂³	C₂⁴×D₅₃	1	4	yes	—
692	C₂³	C₂⁴×D₅₃	1	4	yes	—
693	C₂³	C₂⁴×D₅₃	1	4	yes	—
694	C₂³	C₂⁴×D₅₃	1	3	yes	—
695	Q₈	—	106	32	no	—
696	D₄	—	2	32	no	—
697	D₄	—	2	32	no	—
698	D₄	—	4	16	no	—
699	D₄	—	53	64	no	—
700	D₄	—	106	32	no	—
701	D₄	—	106	32	no	—
702	D₄	—	106	32	no	—
703	D₄	—	106	32	no	—
704	D₄	—	212	16	no	—
705	C₂×C₄	—	2	12	no	—
706	C₂×C₄	—	2	12	no	—
707	C₂×C₄	—	2	12	no	—
708	C₂×C₄	—	53	24	no	—
709	C₂×C₄	—	53	4	no	—
710	C₂×C₄	—	53	4	no	—
711	C₂×C₄	—	53	4	no	—
712	C₂×C₄	—	53	4	no	—
713	C₂×C₄	—	53	4	no	—
714	C₂×C₄	—	53	4	no	—
715	C₂×C₄	—	106	32	no	—
716	C₂×C₄	—	106	32	no	—
717	C₂×C₄	—	106	32	no	—
718	C₂×C₄	—	106	12	no	—
719	C₂×C₄	—	106	12	no	—
720	C₂×C₄	—	106	12	no	—
721	C₂×C₄	—	106	32	no	—
722	C₂×C₄	—	106	12	no	—
723	C₂×C₄	—	106	12	no	—
724	C₂×C₄	—	212	16	no	—
725	C₂×C₄	—	212	16	no	—
726	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
727	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
728	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
729	C₂²	—	2	48	no	—
730	C₂²	—	2	48	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	4	64	no	—
742	C₂²	—	4	24	no	—
743	C₂²	—	4	24	no	—
744	C₂²	—	53	8	no	—
745	C₂²	—	106	48	no	—
746	C₂²	—	106	4	no	—
747	C₂²	—	106	4	no	—
748	C₂²	—	106	4	no	—
749	C₂²	—	106	4	no	—
750	C₂²	—	106	4	no	—
751	C₂²	—	212	64	no	—
752	C₂²	—	212	24	no	—
753	C₂²	#16811260	1	16	yes	direct product factor
754	C₂²	C₂²×D₄×D₅₃	1	8	yes	—
755	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
756	C₂²	C₂²×#11719947	1	6	yes	—
757	C₂²	C₂²×#11719947	1	8	yes	complemented
758	C₂²	C₂×#13133262	1	6	yes	—
759	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
760	C₄	—	2	4	no	—
761	C₄	—	2	4	no	—
762	C₄	—	2	4	no	—
763	C₄	—	53	8	no	—
764	C₄	—	106	4	no	—
765	C₄	—	106	4	no	—
766	C₄	—	106	4	no	—
767	C₄	—	106	4	no	—
768	C₄	—	106	4	no	—
769	C₂	—	2	8	no	—
770	C₂	—	2	8	no	—
771	C₂	—	4	4	no	—
772	C₂	—	4	4	no	—
773	C₂	—	106	8	no	—
774	C₂	—	212	4	no	—
775	C₂	C₂×#16811260	1	12	yes	direct product factor
776	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
777	C₂	C₂³×#11719947	1	1	yes	characteristic
778	C₂	C₂²×#13133262	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂²×#120×C₅₃	C₂
socle	C₂⁴×C₅₃	C₂⁴
hypercenter	C₂²×#120	D₅₃
hypocenter	C₅₃	C₂²×#546
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#120

Complements

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

N	H ≅ G/N	type
1. C₂³×#11719947	C₂	semidirect
2. C₂⁴×C₂²⋊D₅₃	C₂	semidirect
3. C₂×#16811260	C₂	direct (N × H)
4. C₂²×#13133203	C₂	semidirect
5. C₂²×#13133201	C₂	semidirect
6. C₂²×#13133199	C₂	semidirect
7. C₂²×#13133194	C₂	semidirect
8. C₂²×#13133189	C₂	semidirect
9. C₂²×#13133189	C₂	semidirect
10. C₂²×#13133188	C₂	semidirect
11. C₂²×#13133185	C₂	semidirect
12. C₂²×D₄×Dic₅₃	C₂	semidirect
13. C₂²×#13133177	C₂	semidirect
14. C₂³×C₂²⋊Dic₅₃	C₂	semidirect
15. C₂²×C₂²⋊C₄×D₅₃	C₂	semidirect
16. C₂²×#120×C₅₃	C₂	semidirect
19. C₂²×#11719947	C₂²	semidirect
20. C₂³×Dic₁₀₆	C₂²	semidirect
26. C₂³×C₂²⋊D₅₃	C₂²	semidirect
27. C₂³×C₂²⋊D₅₃	C₂²	semidirect
28. C₂³×C₂²⋊D₅₃	C₂²	semidirect
30. C₂⁴×Dic₅₃	C₂²	semidirect
31. C₂⁴×Dic₅₃	C₂²	semidirect
32. C₂⁴×Dic₅₃	C₂²	semidirect
33. C₂³×C₄×D₅₃	C₂²	semidirect
34. C₂³×C₄×D₅₃	C₂²	semidirect
35. #16811260	C₂²	direct (N × H)
36. C₂×#13133203	C₂²	semidirect
37. C₂×#13133201	C₂²	semidirect
38. C₂×#13133199	C₂²	semidirect
39. C₂×#13133194	C₂²	semidirect
40. C₂×#13133189	C₂²	semidirect
41. C₂×#13133189	C₂²	semidirect
42. C₂×#13133188	C₂²	semidirect
43. C₂×#13133185	C₂²	semidirect
44. C₂×D₄×Dic₅₃	C₂²	semidirect
45. C₂×#13133177	C₂²	semidirect
46. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
47. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
48. C₂²×#11719919	C₂²	semidirect
49. C₂²×#11719919	C₂²	semidirect
52. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
53. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
54. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
55. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
56. C₂²×#11719921	C₂²	semidirect
57. C₂²×#11719921	C₂²	semidirect
58. C₂²×#11719921	C₂²	semidirect
59. C₂²×#11719921	C₂²	semidirect
60. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
61. C₂²×C₄×Dic₅₃	C₂²	semidirect
64. C₂³×D₄×C₅₃	C₂²	semidirect
65. C₂³×D₄×C₅₃	C₂²	semidirect
66. C₂×#120×C₅₃	C₂²	semidirect
68. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
69. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
77. C₂×#11719947	C₂³	semidirect
79. C₂²×Dic₁₀₆	C₂³	semidirect
86. C₂²×C₂²⋊D₅₃	D₄	semidirect
91. C₂²×C₂²⋊D₅₃	C₂³	semidirect
92. C₂²×C₂²⋊D₅₃	C₂³	semidirect
93. C₂²×C₂²⋊D₅₃	C₂³	semidirect
105. C₂³×Dic₅₃	C₂³	semidirect
106. C₂³×Dic₅₃	C₂³	semidirect
107. C₂³×Dic₅₃	C₂³	semidirect
110. C₂²×C₄×D₅₃	C₂³	semidirect
111. C₂²×C₄×D₅₃	C₂³	semidirect
112. #13133203	C₂³	semidirect
113. #13133201	C₂³	semidirect
114. #13133199	C₂³	semidirect
115. #13133194	C₂³	semidirect
116. #13133189	C₂³	semidirect
117. #13133189	C₂³	semidirect
118. #13133188	C₂³	semidirect
119. #13133185	C₂³	semidirect
120. D₄×Dic₅₃	C₂³	semidirect
121. #13133177	C₂³	semidirect
122. C₂×C₄⋊Dic₅₃	C₂³	semidirect
123. C₂×C₄⋊Dic₅₃	C₂³	semidirect
124. C₂×#11719919	C₂³	semidirect
125. C₂×#11719919	C₂³	semidirect
128. C₂×C₂²⋊Dic₅₃	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. C₂×C₄×Dic₅₃	C₂³	semidirect
150. C₂²×D₄×C₅₃	C₂³	semidirect
151. C₂²×D₄×C₅₃	C₂³	semidirect
155. #120×C₅₃	C₂³	semidirect
157. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
158. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
174. C₂⁴×C₅₃	#41	semidirect
198. C₂×D₄×C₅₃	C₂⁴	semidirect
199. C₂×D₄×C₅₃	C₂⁴	semidirect
212. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
217. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
218. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
236. C₂²×Dic₅₃	C₂⁴	semidirect
237. C₂²×Dic₅₃	C₂⁴	semidirect
238. C₂²×Dic₅₃	C₂⁴	semidirect
242. C₂×C₄×D₅₃	C₂⁴	semidirect
243. C₂×C₄×D₅₃	C₂⁴	semidirect
245. C₂×Dic₁₀₆	C₂⁴	semidirect
247. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
248. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
251. C₂²⋊Dic₅₃	C₂⁴	semidirect
252. C₂²⋊Dic₅₃	C₂⁴	semidirect
253. C₂²⋊Dic₅₃	C₂⁴	semidirect
254. #11719921	C₂⁴	semidirect
255. #11719921	C₂⁴	semidirect
256. #11719921	C₂⁴	semidirect
257. #11719921	C₂⁴	semidirect
258. C₄⋊Dic₅₃	C₂⁴	semidirect
259. C₄⋊Dic₅₃	C₂⁴	semidirect
260. #11719919	C₂⁴	semidirect
261. #11719919	C₂⁴	semidirect
262. C₄×Dic₅₃	C₂⁴	semidirect
284. C₂³×C₅₃	C₂×#41	semidirect
319. C₂²⋊D₅₃	C₂²×D₄	semidirect
355. C₂²×C₅₃	#546	semidirect
359. C₂²×C₅₃	C₂²×#41	semidirect
391. C₂²×#120	D₅₃	semidirect
400. C₂×C₅₃	C₂×#546	semidirect
420. C₂³×D₄	C₂×D₅₃	semidirect
421. C₂³×D₄	C₂×D₅₃	semidirect
437. C₂×#120	C₂×D₅₃	semidirect
456. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
457. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
459. C₅₃	C₂²×#546	semidirect
496. C₂²×D₄	C₂²×D₅₃	semidirect
497. C₂²×D₄	C₂²×D₅₃	semidirect
527. #120	C₂²×D₅₃	semidirect
546. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
547. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
577. C₂⁴	#11719947	semidirect
604. C₂×D₄	C₂³×D₅₃	semidirect
605. C₂×D₄	C₂³×D₅₃	semidirect
650. C₂²⋊C₄	C₂³×D₅₃	semidirect
651. C₂²⋊C₄	C₂³×D₅₃	semidirect
688. C₂³	C₂×#11719947	semidirect
753. C₂²	#16811260	direct (N × H)
757. C₂²	C₂²×#11719947	semidirect
775. C₂	C₂×#16811260	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×#11719947	2
C₂⁴×C₂²⋊D₅₃	2
C₂×#16811260	2
C₂²×#13133203	2
C₂²×#13133201	2
C₂²×#13133199	2
C₂²×#13133194	2
C₂²×#13133189	2
C₂²×#13133188	2
C₂²×#13133185	2
C₂²×D₄×Dic₅₃	2
C₂²×#13133177	2
C₂³×C₂²⋊Dic₅₃	2
C₂²×C₂²⋊C₄×D₅₃	2
C₂²×#120×C₅₃	2
C₂²×#546	53

Subgroups — C22×#16811260 #28291016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#16811260 #28291016