Subgroups — C₂²×#16811132 #28290747

Order 13568.

14334 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11719945	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811132	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#13133202	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13133199	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13133195	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13133194	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13133190	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#13133189	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#13133187	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#13133185	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₄×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₄×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#13133174	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁵×D₅₃	C₂²	1	1	yes	characteristic
18	C₂²×#11719945	—	2	16	no	—
19	C₂²×#11719945	C₂²	1	24	yes	complemented
20	C₂³×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
22	C₂³×D₂₁₂	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	1	yes	characteristic, complemented
27	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic
28	C₂³×C₄×D₅₃	—	2	16	no	—
29	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
30	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
31	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
32	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
33	C₂³×C₄×D₅₃	C₂²	1	24	yes	complemented
34	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
35	#16811132	C₂²	1	256	yes	direct product factor
36	C₂×#13133202	C₂²	1	24	yes	complemented
37	C₂×#13133199	C₂²	1	24	yes	complemented
38	C₂×#13133195	C₂²	1	24	yes	complemented
39	C₂×#13133194	C₂²	1	24	yes	complemented
40	C₂×#13133190	C₂²	1	24	yes	complemented
41	C₂×#13133189	C₂²	1	24	yes	complemented
42	C₂×#13133187	C₂²	1	24	yes	complemented
43	C₂×#13133185	C₂²	1	24	yes	complemented
44	C₂×C₄×D₂₁₂	C₂²	1	24	yes	complemented
45	C₂×C₄×C₂²⋊D₅₃	C₂²	1	24	yes	complemented
46	C₂×C₄×C₂²⋊D₅₃	C₂²	1	24	yes	complemented
47	C₂×#13133174	C₂²	1	24	yes	complemented
48	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
49	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
50	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
51	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
52	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
54	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₂²×#11719921	C₂²	1	1	yes	characteristic
56	C₂²×#11719921	C₂²	1	1	yes	characteristic
57	C₂²×#11719921	C₂²	1	1	yes	characteristic
58	C₂²×#11719921	C₂²	1	1	yes	characteristic
59	C₂²×#11719921	C₂²	1	1	yes	characteristic, complemented
60	C₂²×#11719921	C₂²	1	1	yes	characteristic, complemented
61	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
63	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
64	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×D₄×C₅₃	C₂²	1	24	yes	complemented
66	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
68	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
69	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
70	C₂⁴×D₅₃	—	2	8	no	—
71	C₂⁴×D₅₃	—	2	8	no	—
72	C₂⁴×D₅₃	—	2	8	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	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
77	C₂×#11719945	—	2	192	no	—
78	C₂×#11719945	C₂³	1	64	yes	complemented
79	C₂²×Dic₁₀₆	—	2	8	no	—
80	C₂²×Dic₁₀₆	C₂³	1	12	yes	complemented
81	C₂²×D₂₁₂	—	2	8	no	—
82	C₂²×D₂₁₂	—	2	8	no	—
83	C₂²×D₂₁₂	C₂³	1	12	yes	—
84	C₂²×D₂₁₂	C₂³	1	12	yes	—
85	C₂²×C₂²⋊D₅₃	—	2	8	no	—
86	C₂²×C₂²⋊D₅₃	—	2	8	no	—
87	C₂²×C₂²⋊D₅₃	—	2	8	no	—
88	C₂²×C₂²⋊D₅₃	—	2	8	no	—
89	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
90	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
91	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
92	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
93	C₂³×Dic₅₃	—	2	8	no	—
94	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
95	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
96	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
97	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
98	C₂³×Dic₅₃	C₂³	1	12	yes	—
99	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
100	C₂²×C₄×D₅₃	—	2	8	no	—
101	C₂²×C₄×D₅₃	—	2	8	no	—
102	C₂²×C₄×D₅₃	—	2	8	no	—
103	C₂²×C₄×D₅₃	—	2	8	no	—
104	C₂²×C₄×D₅₃	—	2	192	no	—
105	C₂²×C₄×D₅₃	D₄	1	16	yes	complemented
106	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
107	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
108	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
109	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
110	C₂²×C₄×D₅₃	C₂³	1	64	yes	complemented
111	C₂²×C₄×D₅₃	C₂³	1	12	yes	complemented
112	#13133202	C₂³	1	64	yes	complemented
113	#13133199	C₂³	1	64	yes	complemented
114	#13133195	C₂³	1	64	yes	complemented
115	#13133194	C₂³	1	64	yes	complemented
116	#13133190	C₂³	1	64	yes	complemented
117	#13133189	C₂³	1	64	yes	complemented
118	#13133187	C₂³	1	64	yes	complemented
119	#13133185	C₂³	1	64	yes	complemented
120	C₄×D₂₁₂	C₂³	1	64	yes	complemented
121	C₄×C₂²⋊D₅₃	C₂³	1	64	yes	complemented
122	C₄×C₂²⋊D₅₃	C₂³	1	64	yes	complemented
123	#13133174	C₂³	1	64	yes	complemented
124	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	complemented
125	C₂×#11719919	C₂³	1	12	yes	complemented
126	C₂×#11719919	C₂³	1	12	yes	complemented
127	C₂×#11719919	C₂³	1	12	yes	complemented
128	C₂×#11719919	C₂³	1	12	yes	complemented
129	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	—
130	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	complemented
131	C₂×#11719921	C₂³	1	12	yes	—
132	C₂×#11719921	C₂³	1	12	yes	—
133	C₂×#11719921	C₂³	1	12	yes	—
134	C₂×#11719921	C₂³	1	12	yes	—
135	C₂×#11719921	C₂³	1	12	yes	complemented
136	C₂×#11719921	C₂³	1	12	yes	complemented
137	C₂×C₄×Dic₅₃	C₂³	1	12	yes	complemented
138	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
139	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₅₃	—	2	8	no	—
141	C₂²×D₄×C₅₃	C₂³	1	12	yes	—
142	C₂³×C₄×C₅₃	—	2	8	no	—
143	C₂³×C₄×C₅₃	—	2	8	no	—
144	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₅₃	C₂³	1	12	yes	—
149	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₅₃	C₂³	1	12	yes	complemented
151	C₄×D₄×C₅₃	C₂³	1	64	yes	complemented
152	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	complemented
153	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	—
154	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	complemented
155	C₂×C₄²×C₅₃	C₂³	1	12	yes	complemented
156	C₂⁴×C₅₃	—	2	4	no	—
157	C₂⁴×C₅₃	—	2	4	no	—
158	C₂⁴×C₅₃	—	2	4	no	—
159	C₂⁴×C₅₃	—	2	4	no	—
160	C₂⁴×C₅₃	—	2	4	no	—
161	C₂⁴×C₅₃	#41	1	8	yes	complemented
162	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
163	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
164	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
165	C₂³×D₅₃	—	2	128	no	—
166	C₂³×D₅₃	—	2	4	no	—
167	C₂³×D₅₃	—	2	4	no	—
168	C₂³×D₅₃	—	2	4	no	—
169	C₂³×D₅₃	—	2	4	no	—
170	C₂³×D₅₃	—	2	48	no	—
171	C₂³×D₅₃	—	2	48	no	—
172	C₂³×D₅₃	—	2	48	no	—
173	C₂³×D₅₃	—	2	4	no	—
174	C₂³×D₅₃	—	2	4	no	—
175	C₂³×D₅₃	—	2	4	no	—
176	C₂³×D₅₃	C₂×D₄	1	8	yes	—
177	C₂³×D₅₃	#41	1	8	yes	complemented
178	C₂³×D₅₃	C₂⁴	1	6	yes	—
179	C₂³×D₅₃	C₂⁴	1	16	yes	—
180	C₂³×D₅₃	C₂⁴	1	6	yes	—
181	C₂³×D₅₃	C₂⁴	1	6	yes	—
182	C₂×D₄×C₅₃	—	2	48	no	—
183	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
184	C₂²×C₄×C₅₃	—	2	4	no	—
185	C₂²×C₄×C₅₃	—	2	4	no	—
186	C₂²×C₄×C₅₃	—	2	4	no	—
187	C₂²×C₄×C₅₃	—	2	4	no	—
188	C₂²×C₄×C₅₃	—	2	48	no	—
189	C₂²×C₄×C₅₃	—	2	48	no	—
190	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
191	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
192	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
193	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
194	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
195	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
196	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
197	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	complemented
198	C₂×C₂²⋊D₅₃	—	2	48	no	—
199	C₂×C₂²⋊D₅₃	—	2	48	no	—
200	C₂×C₂²⋊D₅₃	—	2	48	no	—
201	C₂×C₂²⋊D₅₃	—	2	48	no	—
202	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
203	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
204	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
205	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	complemented
206	C₂²×Dic₅₃	—	2	4	no	—
207	C₂²×Dic₅₃	—	2	4	no	—
208	C₂²×Dic₅₃	—	2	4	no	—
209	C₂²×Dic₅₃	—	2	4	no	—
210	C₂²×Dic₅₃	—	2	48	no	—
211	C₂²×Dic₅₃	C₂×D₄	1	8	yes	—
212	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
213	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
214	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
215	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
216	C₂²×Dic₅₃	C₂⁴	1	16	yes	—
217	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
218	#11719945	—	2	256	no	—
219	C₂×D₂₁₂	—	2	48	no	—
220	C₂×D₂₁₂	—	2	48	no	—
221	C₂×D₂₁₂	C₂⁴	1	16	yes	—
222	C₂×D₂₁₂	C₂⁴	1	16	yes	—
223	C₂×C₄×D₅₃	—	2	48	no	—
224	C₂×C₄×D₅₃	—	2	48	no	—
225	C₂×C₄×D₅₃	—	2	48	no	—
226	C₂×C₄×D₅₃	—	2	48	no	—
227	C₂×C₄×D₅₃	—	2	256	no	—
228	C₂×C₄×D₅₃	C₂×D₄	1	96	yes	complemented
229	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
230	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
231	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
232	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
233	C₂×C₄×D₅₃	C₂⁴	1	16	yes	complemented
234	C₂×Dic₁₀₆	—	2	48	no	—
235	C₂×Dic₁₀₆	C₂⁴	1	16	yes	complemented
236	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
237	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
238	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
239	C₄²×C₅₃	C₂⁴	1	16	yes	complemented
240	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
241	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
242	#11719921	C₂⁴	1	16	yes	—
243	#11719921	C₂⁴	1	16	yes	—
244	#11719921	C₂⁴	1	16	yes	—
245	#11719921	C₂⁴	1	16	yes	—
246	#11719921	C₂⁴	1	16	yes	complemented
247	#11719921	C₂⁴	1	16	yes	complemented
248	C₄⋊Dic₅₃	C₂⁴	1	16	yes	complemented
249	#11719919	C₂⁴	1	16	yes	complemented
250	#11719919	C₂⁴	1	16	yes	complemented
251	#11719919	C₂⁴	1	16	yes	complemented
252	#11719919	C₂⁴	1	16	yes	complemented
253	C₄×Dic₅₃	C₂⁴	1	16	yes	complemented
254	C₂³×C₅₃	—	2	32	no	—
255	C₂³×C₅₃	—	2	12	no	—
256	C₂³×C₅₃	—	2	12	no	—
257	C₂³×C₅₃	—	2	12	no	—
258	C₂³×C₅₃	—	2	12	no	—
259	C₂³×C₅₃	—	2	12	no	—
260	C₂³×C₅₃	—	4	16	no	—
261	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
262	C₂³×C₅₃	C₂×#41	1	4	yes	—
263	C₂³×C₅₃	C₂×#41	1	4	yes	—
264	C₂³×C₅₃	C₂×#41	1	24	yes	complemented
265	C₂³×C₅₃	C₂⁵	1	4	yes	—
266	C₂³×C₅₃	C₂⁵	1	4	yes	—
267	C₂³×C₅₃	C₂⁵	1	3	yes	—
268	C₂²×D₅₃	—	2	384	no	—
269	C₂²×D₅₃	—	2	32	no	—
270	C₂²×D₅₃	—	2	32	no	—
271	C₂²×D₅₃	—	2	12	no	—
272	C₂²×D₅₃	—	2	12	no	—
273	C₂²×D₅₃	—	2	12	no	—
274	C₂²×D₅₃	—	2	12	no	—
275	C₂²×D₅₃	—	2	32	no	—
276	C₂²×D₅₃	—	2	32	no	—
277	C₂²×D₅₃	—	2	32	no	—
278	C₂²×D₅₃	—	2	12	no	—
279	C₂²×D₅₃	—	2	12	no	—
280	C₂²×D₅₃	—	2	12	no	—
281	C₂²×D₅₃	—	4	16	no	—
282	C₂²×D₅₃	C₂²×D₄	1	24	yes	—
283	C₂²×D₅₃	C₂×#41	1	24	yes	complemented
284	C₂²×D₅₃	C₂⁵	1	4	yes	—
285	C₂²×D₅₃	C₂⁵	1	4	yes	—
286	C₂²×D₅₃	C₂⁵	1	4	yes	—
287	D₄×C₅₃	—	2	32	no	—
288	C₂×C₄×C₅₃	—	2	12	no	—
289	C₂×C₄×C₅₃	—	2	12	no	—
290	C₂×C₄×C₅₃	—	2	12	no	—
291	C₂×C₄×C₅₃	—	2	12	no	—
292	C₂×C₄×C₅₃	—	2	32	no	—
293	C₂×C₄×C₅₃	—	2	32	no	—
294	C₂×C₄×C₅₃	C₂²×D₄	1	24	yes	—
295	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
296	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
297	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
298	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
299	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
300	C₂²⋊D₅₃	—	2	32	no	—
301	C₂²⋊D₅₃	—	2	32	no	—
302	C₂²⋊D₅₃	—	2	32	no	—
303	C₂²⋊D₅₃	—	2	32	no	—
304	C₂×Dic₅₃	—	2	12	no	—
305	C₂×Dic₅₃	—	2	12	no	—
306	C₂×Dic₅₃	—	2	12	no	—
307	C₂×Dic₅₃	—	2	12	no	—
308	C₂×Dic₅₃	—	2	32	no	—
309	C₂×Dic₅₃	C₂²×D₄	1	24	yes	—
310	C₂×Dic₅₃	C₂⁵	1	4	yes	—
311	C₂×Dic₅₃	C₂⁵	1	4	yes	—
312	C₂×Dic₅₃	C₂⁵	1	4	yes	—
313	C₂×Dic₅₃	C₂⁵	1	4	yes	—
314	C₂×Dic₅₃	C₂⁵	1	4	yes	—
315	D₂₁₂	—	2	32	no	—
316	D₂₁₂	—	2	32	no	—
317	C₄×D₅₃	—	2	32	no	—
318	C₄×D₅₃	—	2	32	no	—
319	C₄×D₅₃	—	2	32	no	—
320	C₄×D₅₃	—	2	32	no	—
321	C₄×D₅₃	C₂²×D₄	1	64	yes	complemented
322	Dic₁₀₆	—	2	32	no	—
323	C₂²×#525	—	53	1	no	maximal, Sylow
324	C₂²×C₅₃	—	2	4	no	—
325	C₂²×C₅₃	—	2	4	no	—
326	C₂²×C₅₃	—	2	48	no	—
327	C₂²×C₅₃	—	2	4	no	—
328	C₂²×C₅₃	—	2	4	no	—
329	C₂²×C₅₃	—	2	4	no	—
330	C₂²×C₅₃	—	4	24	no	—
331	C₂²×C₅₃	#525	1	16	yes	complemented
332	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
333	C₂²×C₅₃	C₂²×#41	1	6	yes	—
334	C₂²×C₅₃	C₂²×#41	1	6	yes	—
335	C₂²×C₅₃	C₂²×#41	1	8	yes	complemented
336	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
337	C₂×D₅₃	—	2	128	no	—
338	C₂×D₅₃	—	2	4	no	—
339	C₂×D₅₃	—	2	4	no	—
340	C₂×D₅₃	—	2	4	no	—
341	C₂×D₅₃	—	2	4	no	—
342	C₂×D₅₃	—	2	48	no	—
343	C₂×D₅₃	—	2	48	no	—
344	C₂×D₅₃	—	2	4	no	—
345	C₂×D₅₃	—	2	4	no	—
346	C₂×D₅₃	—	2	4	no	—
347	C₂×D₅₃	—	4	24	no	—
348	C₂×D₅₃	C₂³×D₄	1	8	yes	—
349	C₂×D₅₃	C₂²×#41	1	8	yes	complemented
350	C₄×C₅₃	—	2	4	no	—
351	C₄×C₅₃	—	2	4	no	—
352	C₄×C₅₃	—	2	4	no	—
353	C₄×C₅₃	—	2	4	no	—
354	C₄×C₅₃	C₂³×D₄	1	8	yes	—
355	Dic₅₃	—	2	4	no	—
356	Dic₅₃	—	2	4	no	—
357	Dic₅₃	—	2	4	no	—
358	Dic₅₃	—	2	4	no	—
359	Dic₅₃	C₂³×D₄	1	8	yes	—
360	C₂³×#41	—	53	1	no	—
361	C₂⁵×C₄	—	53	1	no	—
362	C₂×#525	—	53	48	no	—
363	C₂²×#123	—	53	1	no	—
364	C₂²×#123	—	53	1	no	—
365	C₂²×C₂²⋊Q₈	—	53	1	no	—
366	C₂²×C₂²⋊Q₈	—	53	1	no	—
367	C₂²×#121	—	53	1	no	—
368	C₂²×#121	—	53	1	no	—
369	C₂²×#120	—	53	1	no	—
370	C₂²×#120	—	53	1	no	—
371	C₂²×C₄×D₄	—	53	1	no	—
372	C₂²×C₄×D₄	—	53	1	no	—
373	C₂²×C₄×D₄	—	53	1	no	—
374	C₂²×C₄×D₄	D₅₃	1	1	yes	characteristic, complemented
375	C₂²×#117	—	53	1	no	—
376	C₂×C₅₃	—	2	8	no	—
377	C₂×C₅₃	—	4	4	no	—
378	C₂×C₅₃	C₂×#525	1	12	yes	complemented
379	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
380	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
381	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
382	D₅₃	—	2	8	no	—
383	D₅₃	—	2	8	no	—
384	D₅₃	—	4	4	no	—
385	C₂⁶	—	53	1	no	—
386	C₂²×#41	—	53	24	no	—
387	C₂²×#41	—	106	16	no	—
388	C₂³×Q₈	—	53	1	no	—
389	C₂³×D₄	—	53	1	no	—
390	C₂³×D₄	—	53	1	no	—
391	C₂³×D₄	—	53	1	no	—
392	C₂³×D₄	—	53	1	no	—
393	C₂³×D₄	—	53	1	no	—
394	C₂³×D₄	—	53	1	no	—
395	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic
396	C₂⁴×C₄	—	53	1	no	—
397	C₂⁴×C₄	—	53	1	no	—
398	C₂⁴×C₄	—	53	1	no	—
399	C₂⁴×C₄	—	53	1	no	—
400	C₂⁴×C₄	—	53	24	no	—
401	C₂⁴×C₄	—	53	1	no	—
402	C₂⁴×C₄	—	53	1	no	—
403	C₂⁴×C₄	—	106	16	no	—
404	C₂⁴×C₄	C₂×D₅₃	1	1	yes	characteristic
405	C₂⁴×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
406	#525	—	53	256	no	—
407	C₂×#123	—	53	24	no	—
408	C₂×#123	—	53	24	no	—
409	C₂×C₂²⋊Q₈	—	53	24	no	—
410	C₂×C₂²⋊Q₈	—	53	24	no	—
411	C₂×#121	—	53	24	no	—
412	C₂×#121	—	53	24	no	—
413	C₂×#120	—	53	24	no	—
414	C₂×#120	—	53	24	no	—
415	C₂×C₄×D₄	—	53	24	no	—
416	C₂×C₄×D₄	—	53	24	no	—
417	C₂×C₄×D₄	—	53	24	no	—
418	C₂×C₄×D₄	C₂×D₅₃	1	24	yes	complemented
419	C₂×#117	—	53	24	no	—
420	C₂²×C₄⋊C₄	—	53	1	no	—
421	C₂²×C₄⋊C₄	—	53	1	no	—
422	C₂²×C₄⋊C₄	—	53	1	no	—
423	C₂²×C₄⋊C₄	—	53	1	no	—
424	C₂²×C₄⋊C₄	—	53	1	no	—
425	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
426	C₂²×C₂²⋊C₄	—	53	1	no	—
427	C₂²×C₂²⋊C₄	—	53	1	no	—
428	C₂²×C₂²⋊C₄	—	53	1	no	—
429	C₂²×C₂²⋊C₄	—	53	1	no	—
430	C₂²×C₂²⋊C₄	—	53	1	no	—
431	C₂²×C₂²⋊C₄	—	53	1	no	—
432	C₂²×C₂²⋊C₄	—	53	1	no	—
433	C₂²×C₂²⋊C₄	—	53	1	no	—
434	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
435	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
436	C₂²×C₄²	—	53	1	no	—
437	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
438	C₅₃	C₂²×#525	1	1	yes	characteristic, complemented, Sylow
439	C₂⁵	—	53	1	no	—
440	C₂⁵	—	53	1	no	—
441	C₂⁵	—	53	1	no	—
442	C₂⁵	—	53	12	no	—
443	C₂⁵	—	106	8	no	—
444	C₂⁵	—	106	8	no	—
445	C₂⁵	—	106	8	no	—
446	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
447	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
448	C₂×#41	—	53	64	no	—
449	C₂×#41	—	106	192	no	—
450	C₂²×Q₈	—	53	12	no	—
451	C₂²×Q₈	—	106	8	no	—
452	C₂²×D₄	—	2	8	no	—
453	C₂²×D₄	—	53	12	no	—
454	C₂²×D₄	—	53	12	no	—
455	C₂²×D₄	—	53	12	no	—
456	C₂²×D₄	—	53	12	no	—
457	C₂²×D₄	—	53	12	no	—
458	C₂²×D₄	—	53	12	no	—
459	C₂²×D₄	—	106	8	no	—
460	C₂²×D₄	—	106	8	no	—
461	C₂²×D₄	—	106	8	no	—
462	C₂²×D₄	—	106	8	no	—
463	C₂²×D₄	—	106	8	no	—
464	C₂²×D₄	—	106	8	no	—
465	C₂²×D₄	C₂²×D₅₃	1	12	yes	—
466	C₂³×C₄	—	2	8	no	—
467	C₂³×C₄	—	2	8	no	—
468	C₂³×C₄	—	53	1	no	—
469	C₂³×C₄	—	53	16	no	—
470	C₂³×C₄	—	53	12	no	—
471	C₂³×C₄	—	53	1	no	—
472	C₂³×C₄	—	53	1	no	—
473	C₂³×C₄	—	53	1	no	—
474	C₂³×C₄	—	53	1	no	—
475	C₂³×C₄	—	53	12	no	—
476	C₂³×C₄	—	53	12	no	—
477	C₂³×C₄	—	53	12	no	—
478	C₂³×C₄	—	53	12	no	—
479	C₂³×C₄	—	53	12	no	—
480	C₂³×C₄	—	53	64	no	—
481	C₂³×C₄	—	106	8	no	—
482	C₂³×C₄	—	106	192	no	—
483	C₂³×C₄	—	106	8	no	—
484	C₂³×C₄	—	106	8	no	—
485	C₂³×C₄	—	106	8	no	—
486	C₂³×C₄	—	106	8	no	—
487	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
488	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
489	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
490	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
491	C₂³×C₄	C₂²×D₅₃	1	12	yes	—
492	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
493	C₂³×C₄	C₂²×D₅₃	1	12	yes	complemented
494	#123	—	53	64	no	—
495	#123	—	53	64	no	—
496	C₂²⋊Q₈	—	53	64	no	—
497	C₂²⋊Q₈	—	53	64	no	—
498	#121	—	53	64	no	—
499	#121	—	53	64	no	—
500	#120	—	53	64	no	—
501	#120	—	53	64	no	—
502	C₄×D₄	—	53	64	no	—
503	C₄×D₄	—	53	64	no	—
504	C₄×D₄	—	53	64	no	—
505	C₄×D₄	C₂²×D₅₃	1	64	yes	complemented
506	#117	—	53	64	no	—
507	C₂×C₄⋊C₄	—	53	12	no	—
508	C₂×C₄⋊C₄	—	53	12	no	—
509	C₂×C₄⋊C₄	—	53	12	no	—
510	C₂×C₄⋊C₄	—	53	12	no	—
511	C₂×C₄⋊C₄	—	53	12	no	—
512	C₂×C₄⋊C₄	C₂²×D₅₃	1	12	yes	complemented
513	C₂×C₂²⋊C₄	—	53	12	no	—
514	C₂×C₂²⋊C₄	—	53	12	no	—
515	C₂×C₂²⋊C₄	—	53	12	no	—
516	C₂×C₂²⋊C₄	—	53	12	no	—
517	C₂×C₂²⋊C₄	—	53	12	no	—
518	C₂×C₂²⋊C₄	—	53	12	no	—
519	C₂×C₂²⋊C₄	—	53	12	no	—
520	C₂×C₂²⋊C₄	—	53	12	no	—
521	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	—
522	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	complemented
523	C₂×C₄²	—	53	12	no	—
524	C₂×C₄²	C₂²×D₅₃	1	12	yes	complemented
525	C₂⁴	—	2	4	no	—
526	C₂⁴	—	2	4	no	—
527	C₂⁴	—	2	4	no	—
528	C₂⁴	—	2	4	no	—
529	C₂⁴	—	2	4	no	—
530	C₂⁴	—	53	8	no	—
531	C₂⁴	—	53	8	no	—
532	C₂⁴	—	53	6	no	—
533	C₂⁴	—	53	6	no	—
534	C₂⁴	—	53	6	no	—
535	C₂⁴	—	53	16	no	—
536	C₂⁴	—	106	48	no	—
537	C₂⁴	—	106	48	no	—
538	C₂⁴	—	106	128	no	—
539	C₂⁴	—	106	4	no	—
540	C₂⁴	—	106	4	no	—
541	C₂⁴	—	106	4	no	—
542	C₂⁴	—	106	4	no	—
543	C₂⁴	—	106	48	no	—
544	C₂⁴	—	106	4	no	—
545	C₂⁴	—	106	4	no	—
546	C₂⁴	—	106	4	no	—
547	C₂⁴	#11719945	1	8	yes	complemented
548	C₂⁴	C₂³×D₅₃	1	6	yes	—
549	C₂⁴	C₂³×D₅₃	1	6	yes	—
550	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
551	#41	—	106	256	no	—
552	C₂×Q₈	—	53	16	no	—
553	C₂×Q₈	—	106	48	no	—
554	C₂×D₄	—	2	48	no	—
555	C₂×D₄	—	53	16	no	—
556	C₂×D₄	—	53	16	no	—
557	C₂×D₄	—	53	16	no	—
558	C₂×D₄	—	53	16	no	—
559	C₂×D₄	—	53	16	no	—
560	C₂×D₄	—	53	16	no	—
561	C₂×D₄	—	106	48	no	—
562	C₂×D₄	—	106	48	no	—
563	C₂×D₄	—	106	48	no	—
564	C₂×D₄	—	106	48	no	—
565	C₂×D₄	—	106	48	no	—
566	C₂×D₄	—	106	48	no	—
567	C₂×D₄	C₂³×D₅₃	1	16	yes	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	48	no	—
573	C₂²×C₄	—	2	48	no	—
574	C₂²×C₄	—	53	8	no	—
575	C₂²×C₄	—	53	6	no	—
576	C₂²×C₄	—	53	96	no	—
577	C₂²×C₄	—	53	16	no	—
578	C₂²×C₄	—	53	6	no	—
579	C₂²×C₄	—	53	6	no	—
580	C₂²×C₄	—	53	6	no	—
581	C₂²×C₄	—	53	6	no	—
582	C₂²×C₄	—	53	16	no	—
583	C₂²×C₄	—	53	16	no	—
584	C₂²×C₄	—	53	16	no	—
585	C₂²×C₄	—	53	16	no	—
586	C₂²×C₄	—	53	16	no	—
587	C₂²×C₄	—	106	48	no	—
588	C₂²×C₄	—	106	256	no	—
589	C₂²×C₄	—	106	48	no	—
590	C₂²×C₄	—	106	48	no	—
591	C₂²×C₄	—	106	4	no	—
592	C₂²×C₄	—	106	4	no	—
593	C₂²×C₄	—	106	4	no	—
594	C₂²×C₄	—	106	4	no	—
595	C₂²×C₄	—	106	48	no	—
596	C₂²×C₄	—	106	48	no	—
597	C₂²×C₄	D₄×D₅₃	1	8	yes	—
598	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
599	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
600	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
601	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
602	C₂²×C₄	C₂³×D₅₃	1	16	yes	—
603	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
604	C₂²×C₄	C₂³×D₅₃	1	16	yes	complemented
605	C₄⋊C₄	—	53	16	no	—
606	C₄⋊C₄	—	53	16	no	—
607	C₄⋊C₄	—	53	16	no	—
608	C₄⋊C₄	—	53	16	no	—
609	C₄⋊C₄	—	53	16	no	—
610	C₄⋊C₄	C₂³×D₅₃	1	16	yes	complemented
611	C₂²⋊C₄	—	53	16	no	—
612	C₂²⋊C₄	—	53	16	no	—
613	C₂²⋊C₄	—	53	16	no	—
614	C₂²⋊C₄	—	53	16	no	—
615	C₂²⋊C₄	—	53	16	no	—
616	C₂²⋊C₄	—	53	16	no	—
617	C₂²⋊C₄	—	53	16	no	—
618	C₂²⋊C₄	—	53	16	no	—
619	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
620	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	complemented
621	C₄²	—	53	16	no	—
622	C₄²	C₂³×D₅₃	1	16	yes	complemented
623	C₂³	—	2	32	no	—
624	C₂³	—	2	12	no	—
625	C₂³	—	2	12	no	—
626	C₂³	—	2	12	no	—
627	C₂³	—	2	12	no	—
628	C₂³	—	2	12	no	—
629	C₂³	—	4	16	no	—
630	C₂³	—	53	24	no	—
631	C₂³	—	53	24	no	—
632	C₂³	—	53	4	no	—
633	C₂³	—	53	4	no	—
634	C₂³	—	53	4	no	—
635	C₂³	—	106	32	no	—
636	C₂³	—	106	32	no	—
637	C₂³	—	106	384	no	—
638	C₂³	—	106	32	no	—
639	C₂³	—	106	32	no	—
640	C₂³	—	106	12	no	—
641	C₂³	—	106	12	no	—
642	C₂³	—	106	12	no	—
643	C₂³	—	106	12	no	—
644	C₂³	—	106	32	no	—
645	C₂³	—	106	12	no	—
646	C₂³	—	106	12	no	—
647	C₂³	—	106	12	no	—
648	C₂³	—	212	16	no	—
649	C₂³	C₂×D₄×D₅₃	1	4	yes	—
650	C₂³	#41×D₅₃	1	4	yes	—
651	C₂³	C₂×#11719945	1	4	yes	—
652	C₂³	C₂×#11719945	1	24	yes	complemented
653	C₂³	C₂⁴×D₅₃	1	4	yes	—
654	C₂³	C₂⁴×D₅₃	1	4	yes	—
655	C₂³	C₂⁴×D₅₃	1	3	yes	—
656	Q₈	—	106	32	no	—
657	D₄	—	2	32	no	—
658	D₄	—	106	32	no	—
659	D₄	—	106	32	no	—
660	D₄	—	106	32	no	—
661	D₄	—	106	32	no	—
662	D₄	—	106	32	no	—
663	D₄	—	106	32	no	—
664	C₂×C₄	—	2	12	no	—
665	C₂×C₄	—	2	12	no	—
666	C₂×C₄	—	2	12	no	—
667	C₂×C₄	—	2	12	no	—
668	C₂×C₄	—	2	32	no	—
669	C₂×C₄	—	2	32	no	—
670	C₂×C₄	—	53	24	no	—
671	C₂×C₄	—	53	4	no	—
672	C₂×C₄	—	53	64	no	—
673	C₂×C₄	—	53	4	no	—
674	C₂×C₄	—	53	4	no	—
675	C₂×C₄	—	53	4	no	—
676	C₂×C₄	—	53	4	no	—
677	C₂×C₄	—	106	32	no	—
678	C₂×C₄	—	106	32	no	—
679	C₂×C₄	—	106	32	no	—
680	C₂×C₄	—	106	12	no	—
681	C₂×C₄	—	106	12	no	—
682	C₂×C₄	—	106	12	no	—
683	C₂×C₄	—	106	12	no	—
684	C₂×C₄	—	106	32	no	—
685	C₂×C₄	—	106	32	no	—
686	C₂×C₄	C₂×D₄×D₅₃	1	24	yes	—
687	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
688	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
689	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
690	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
691	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
692	C₂²	—	2	48	no	—
693	C₂²	—	2	4	no	—
694	C₂²	—	2	4	no	—
695	C₂²	—	2	4	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	4	24	no	—
699	C₂²	—	53	8	no	—
700	C₂²	—	53	8	no	—
701	C₂²	—	106	128	no	—
702	C₂²	—	106	48	no	—
703	C₂²	—	106	48	no	—
704	C₂²	—	106	4	no	—
705	C₂²	—	106	4	no	—
706	C₂²	—	106	4	no	—
707	C₂²	—	106	4	no	—
708	C₂²	—	106	4	no	—
709	C₂²	—	106	4	no	—
710	C₂²	—	106	4	no	—
711	C₂²	—	212	24	no	—
712	C₂²	#16811132	1	16	yes	direct product factor
713	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
714	C₂²	C₂×#41×D₅₃	1	6	yes	—
715	C₂²	C₂²×#11719945	1	6	yes	—
716	C₂²	C₂²×#11719945	1	8	yes	complemented
717	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
718	C₄	—	2	4	no	—
719	C₄	—	2	4	no	—
720	C₄	—	2	4	no	—
721	C₄	—	2	4	no	—
722	C₄	—	53	8	no	—
723	C₄	—	106	4	no	—
724	C₄	—	106	4	no	—
725	C₄	—	106	4	no	—
726	C₄	—	106	4	no	—
727	C₄	C₂²×D₄×D₅₃	1	8	yes	—
728	C₂	—	2	8	no	—
729	C₂	—	4	4	no	—
730	C₂	—	106	8	no	—
731	C₂	—	106	8	no	—
732	C₂	—	212	4	no	—
733	C₂	C₂×#16811132	1	12	yes	direct product factor
734	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
735	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
736	C₂	C₂³×#11719945	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂²×C₄×D₄×C₅₃	C₂
socle	C₂⁴×C₅₃	C₂⁴
hypercenter	C₂²×C₄×D₄	D₅₃
hypocenter	C₅₃	C₂²×#525
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#11719945	C₂	semidirect
2. C₂⁴×C₄×D₅₃	C₂	semidirect
3. C₂×#16811132	C₂	direct (N × H)
4. C₂²×#13133202	C₂	semidirect
5. C₂²×#13133199	C₂	semidirect
6. C₂²×#13133195	C₂	semidirect
7. C₂²×#13133194	C₂	semidirect
8. C₂²×#13133190	C₂	semidirect
9. C₂²×#13133189	C₂	semidirect
10. C₂²×#13133187	C₂	semidirect
11. C₂²×#13133185	C₂	semidirect
12. C₂²×C₄×D₂₁₂	C₂	semidirect
13. C₂²×C₄×C₂²⋊D₅₃	C₂	semidirect
14. C₂²×C₄×C₂²⋊D₅₃	C₂	semidirect
15. C₂²×#13133174	C₂	semidirect
16. C₂²×C₄×D₄×C₅₃	C₂	semidirect
19. C₂²×#11719945	C₂²	semidirect
20. C₂³×Dic₁₀₆	C₂²	semidirect
26. C₂³×C₂²⋊D₅₃	C₂²	semidirect
33. C₂³×C₄×D₅₃	C₂²	semidirect
34. C₂³×C₄×D₅₃	C₂²	semidirect
35. #16811132	C₂²	direct (N × H)
36. C₂×#13133202	C₂²	semidirect
37. C₂×#13133199	C₂²	semidirect
38. C₂×#13133195	C₂²	semidirect
39. C₂×#13133194	C₂²	semidirect
40. C₂×#13133190	C₂²	semidirect
41. C₂×#13133189	C₂²	semidirect
42. C₂×#13133187	C₂²	semidirect
43. C₂×#13133185	C₂²	semidirect
44. C₂×C₄×D₂₁₂	C₂²	semidirect
45. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
46. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
47. C₂×#13133174	C₂²	semidirect
48. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
49. C₂²×#11719919	C₂²	semidirect
50. C₂²×#11719919	C₂²	semidirect
51. C₂²×#11719919	C₂²	semidirect
52. C₂²×#11719919	C₂²	semidirect
54. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
59. C₂²×#11719921	C₂²	semidirect
60. C₂²×#11719921	C₂²	semidirect
61. C₂²×C₄×Dic₅₃	C₂²	semidirect
64. C₂⁴×C₄×C₅₃	C₂²	semidirect
65. C₂×C₄×D₄×C₅₃	C₂²	semidirect
66. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
68. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
69. C₂²×C₄²×C₅₃	C₂²	semidirect
78. C₂×#11719945	C₂³	semidirect
80. C₂²×Dic₁₀₆	C₂³	semidirect
92. C₂²×C₂²⋊D₅₃	C₂³	semidirect
105. C₂²×C₄×D₅₃	D₄	semidirect
110. C₂²×C₄×D₅₃	C₂³	semidirect
111. C₂²×C₄×D₅₃	C₂³	semidirect
112. #13133202	C₂³	semidirect
113. #13133199	C₂³	semidirect
114. #13133195	C₂³	semidirect
115. #13133194	C₂³	semidirect
116. #13133190	C₂³	semidirect
117. #13133189	C₂³	semidirect
118. #13133187	C₂³	semidirect
119. #13133185	C₂³	semidirect
120. C₄×D₂₁₂	C₂³	semidirect
121. C₄×C₂²⋊D₅₃	C₂³	semidirect
122. C₄×C₂²⋊D₅₃	C₂³	semidirect
123. #13133174	C₂³	semidirect
124. C₂×C₄⋊Dic₅₃	C₂³	semidirect
125. C₂×#11719919	C₂³	semidirect
126. C₂×#11719919	C₂³	semidirect
127. C₂×#11719919	C₂³	semidirect
128. C₂×#11719919	C₂³	semidirect
130. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
135. C₂×#11719921	C₂³	semidirect
136. C₂×#11719921	C₂³	semidirect
137. C₂×C₄×Dic₅₃	C₂³	semidirect
150. C₂³×C₄×C₅₃	C₂³	semidirect
151. C₄×D₄×C₅₃	C₂³	semidirect
152. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
154. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
155. C₂×C₄²×C₅₃	C₂³	semidirect
161. C₂⁴×C₅₃	#41	semidirect
177. C₂³×D₅₃	#41	semidirect
197. C₂²×C₄×C₅₃	C₂⁴	semidirect
205. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
228. C₂×C₄×D₅₃	C₂×D₄	semidirect
233. C₂×C₄×D₅₃	C₂⁴	semidirect
235. C₂×Dic₁₀₆	C₂⁴	semidirect
236. C₄⋊C₄×C₅₃	C₂⁴	semidirect
238. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
239. C₄²×C₅₃	C₂⁴	semidirect
241. C₂²⋊Dic₅₃	C₂⁴	semidirect
246. #11719921	C₂⁴	semidirect
247. #11719921	C₂⁴	semidirect
248. C₄⋊Dic₅₃	C₂⁴	semidirect
249. #11719919	C₂⁴	semidirect
250. #11719919	C₂⁴	semidirect
251. #11719919	C₂⁴	semidirect
252. #11719919	C₂⁴	semidirect
253. C₄×Dic₅₃	C₂⁴	semidirect
264. C₂³×C₅₃	C₂×#41	semidirect
283. C₂²×D₅₃	C₂×#41	semidirect
321. C₄×D₅₃	C₂²×D₄	semidirect
331. C₂²×C₅₃	#525	semidirect
335. C₂²×C₅₃	C₂²×#41	semidirect
349. C₂×D₅₃	C₂²×#41	semidirect
374. C₂²×C₄×D₄	D₅₃	semidirect
378. C₂×C₅₃	C₂×#525	semidirect
405. C₂⁴×C₄	C₂×D₅₃	semidirect
418. C₂×C₄×D₄	C₂×D₅₃	semidirect
425. C₂²×C₄⋊C₄	C₂×D₅₃	semidirect
435. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
437. C₂²×C₄²	C₂×D₅₃	semidirect
438. C₅₃	C₂²×#525	semidirect
493. C₂³×C₄	C₂²×D₅₃	semidirect
505. C₄×D₄	C₂²×D₅₃	semidirect
512. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
522. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
524. C₂×C₄²	C₂²×D₅₃	semidirect
547. C₂⁴	#11719945	semidirect
604. C₂²×C₄	C₂³×D₅₃	semidirect
610. C₄⋊C₄	C₂³×D₅₃	semidirect
620. C₂²⋊C₄	C₂³×D₅₃	semidirect
622. C₄²	C₂³×D₅₃	semidirect
652. C₂³	C₂×#11719945	semidirect
712. C₂²	#16811132	direct (N × H)
716. C₂²	C₂²×#11719945	semidirect
733. C₂	C₂×#16811132	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×#11719945	2
C₂⁴×C₄×D₅₃	2
C₂×#16811132	2
C₂²×#13133202	2
C₂²×#13133199	2
C₂²×#13133195	2
C₂²×#13133194	2
C₂²×#13133190	2
C₂²×#13133189	2
C₂²×#13133187	2
C₂²×#13133185	2
C₂²×C₄×D₂₁₂	2
C₂²×C₄×C₂²⋊D₅₃	2
C₂²×#13133174	2
C₂²×C₄×D₄×C₅₃	2
C₂²×#525	53

Subgroups — C22×#16811132 #28290747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#16811132 #28290747