Subgroups — C₂²×#16811205 #28290816

Order 13568.

9566 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811205	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#13133212	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#13133210	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13133204	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13133203	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13133200	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13133198	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13133195	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×#13133185	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₄×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#13133177	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁵×D₅₃	C₂²	1	1	yes	characteristic
18	C₂³×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
20	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
21	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
22	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
23	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
25	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
26	#16811205	C₂²	1	256	yes	direct product factor
27	C₂×#13133212	C₂²	1	24	yes	complemented
28	C₂×#13133210	C₂²	1	24	yes	complemented
29	C₂×#13133204	C₂²	1	24	yes	complemented
30	C₂×#13133203	C₂²	1	24	yes	complemented
31	C₂×#13133200	C₂²	1	24	yes	complemented
32	C₂×#13133198	C₂²	1	24	yes	complemented
33	C₂×#13133195	C₂²	1	24	yes	complemented
34	C₂×#13133189	C₂²	1	24	yes	complemented
35	C₂×#13133188	C₂²	1	24	yes	complemented
36	C₂×#13133185	C₂²	1	24	yes	complemented
37	C₂×#13133185	C₂²	1	24	yes	complemented
38	C₂×C₄×C₂²⋊D₅₃	C₂²	1	24	yes	complemented
39	C₂×#13133177	C₂²	1	24	yes	complemented
40	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
43	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
44	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
48	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₂²×#11719921	C₂²	1	1	yes	characteristic
52	C₂²×#11719921	C₂²	1	1	yes	characteristic
53	C₂²×#11719921	C₂²	1	1	yes	characteristic
54	C₂²×#11719921	C₂²	1	1	yes	characteristic
55	C₂²×#11719921	C₂²	1	1	yes	characteristic
56	C₂²×#11719921	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×D₅₃	C₂²	1	24	yes	complemented
58	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
61	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
62	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×#121×C₅₃	C₂²	1	24	yes	complemented
65	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
66	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
67	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₂⁴×D₅₃	—	2	8	no	—
69	C₂⁴×D₅₃	—	4	4	no	—
70	C₂⁴×D₅₃	—	4	4	no	—
71	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
72	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
73	C₂⁴×D₅₃	C₂³	1	12	yes	—
74	C₂²×Dic₁₀₆	—	4	4	no	—
75	C₂²×Dic₁₀₆	C₂³	1	12	yes	complemented
76	C₂²×C₂²⋊D₅₃	—	2	8	no	—
77	C₂²×C₂²⋊D₅₃	—	2	8	no	—
78	C₂²×C₂²⋊D₅₃	—	4	4	no	—
79	C₂²×C₂²⋊D₅₃	—	4	4	no	—
80	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
81	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
82	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
83	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
84	C₂³×Dic₅₃	—	4	4	no	—
85	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
86	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
87	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
88	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
89	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
90	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
91	C₂³×Dic₅₃	C₂³	1	12	yes	complemented
92	C₂²×C₄×D₅₃	—	4	4	no	—
93	C₂²×C₄×D₅₃	—	4	4	no	—
94	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
95	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
96	#13133212	C₂³	1	64	yes	complemented
97	#13133210	C₂³	1	64	yes	complemented
98	#13133204	C₂³	1	64	yes	complemented
99	#13133203	C₂³	1	64	yes	complemented
100	#13133200	C₂³	1	64	yes	complemented
101	#13133198	C₂³	1	64	yes	complemented
102	#13133195	C₂³	1	64	yes	complemented
103	#13133189	C₂³	1	64	yes	complemented
104	#13133188	C₂³	1	64	yes	complemented
105	#13133185	C₂³	1	64	yes	complemented
106	#13133185	C₂³	1	64	yes	complemented
107	C₄×C₂²⋊D₅₃	C₂³	1	64	yes	complemented
108	#13133177	C₂³	1	64	yes	complemented
109	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	complemented
110	C₂×#11719919	C₂³	1	12	yes	complemented
111	C₂×#11719919	C₂³	1	12	yes	complemented
112	C₂×#11719919	C₂³	1	12	yes	complemented
113	C₂×#11719919	C₂³	1	12	yes	complemented
114	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	—
115	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	—
116	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	—
117	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	complemented
118	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	complemented
119	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	complemented
120	C₂×#11719921	C₂³	1	12	yes	—
121	C₂×#11719921	C₂³	1	12	yes	—
122	C₂×#11719921	C₂³	1	12	yes	—
123	C₂×#11719921	C₂³	1	12	yes	—
124	C₂×#11719921	C₂³	1	12	yes	—
125	C₂×#11719921	C₂³	1	12	yes	—
126	C₂²⋊C₄×D₅₃	C₂³	1	64	yes	complemented
127	C₂×C₄×Dic₅₃	C₂³	1	12	yes	complemented
128	C₂×C₄×Dic₅₃	C₂³	1	12	yes	complemented
129	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
130	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
131	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₅₃	—	4	4	no	—
133	C₂²×D₄×C₅₃	—	4	4	no	—
134	C₂²×D₄×C₅₃	—	4	4	no	—
135	C₂²×D₄×C₅₃	C₂³	1	12	yes	—
136	C₂²×D₄×C₅₃	C₂³	1	12	yes	—
137	C₂²×D₄×C₅₃	C₂³	1	12	yes	complemented
138	C₂³×C₄×C₅₃	—	4	4	no	—
139	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₅₃	C₂³	1	12	yes	complemented
144	#121×C₅₃	C₂³	1	64	yes	complemented
145	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	complemented
146	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	—
147	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	complemented
148	C₂⁴×C₅₃	—	2	4	no	—
149	C₂⁴×C₅₃	—	2	4	no	—
150	C₂⁴×C₅₃	—	2	4	no	—
151	C₂⁴×C₅₃	—	2	4	no	—
152	C₂⁴×C₅₃	—	2	4	no	—
153	C₂⁴×C₅₃	—	2	4	no	—
154	C₂⁴×C₅₃	—	2	4	no	—
155	C₂⁴×C₅₃	—	2	4	no	—
156	C₂⁴×C₅₃	—	2	4	no	—
157	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
158	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
159	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
160	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
161	C₂³×D₅₃	—	2	4	no	—
162	C₂³×D₅₃	—	2	4	no	—
163	C₂³×D₅₃	—	2	4	no	—
164	C₂³×D₅₃	—	2	4	no	—
165	C₂³×D₅₃	—	2	4	no	—
166	C₂³×D₅₃	—	2	48	no	—
167	C₂³×D₅₃	—	4	24	no	—
168	C₂³×D₅₃	—	4	24	no	—
169	C₂³×D₅₃	—	4	64	no	—
170	C₂³×D₅₃	#41	1	8	yes	—
171	C₂³×D₅₃	C₂⁴	1	6	yes	—
172	C₂³×D₅₃	C₂⁴	1	6	yes	—
173	C₂³×D₅₃	C₂⁴	1	16	yes	—
174	C₂×D₄×C₅₃	—	4	24	no	—
175	C₂×D₄×C₅₃	—	4	24	no	—
176	C₂×D₄×C₅₃	—	4	24	no	—
177	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
178	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
179	C₂×D₄×C₅₃	C₂⁴	1	16	yes	complemented
180	C₂²×C₄×C₅₃	—	2	4	no	—
181	C₂²×C₄×C₅₃	—	2	4	no	—
182	C₂²×C₄×C₅₃	—	2	4	no	—
183	C₂²×C₄×C₅₃	—	2	4	no	—
184	C₂²×C₄×C₅₃	—	4	24	no	—
185	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
186	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
187	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
188	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
189	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	complemented
190	C₂×C₂²⋊D₅₃	—	2	48	no	—
191	C₂×C₂²⋊D₅₃	—	2	48	no	—
192	C₂×C₂²⋊D₅₃	—	4	24	no	—
193	C₂×C₂²⋊D₅₃	—	4	24	no	—
194	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
195	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
196	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
197	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
198	C₂²×Dic₅₃	—	2	4	no	—
199	C₂²×Dic₅₃	—	2	4	no	—
200	C₂²×Dic₅₃	—	2	4	no	—
201	C₂²×Dic₅₃	—	2	4	no	—
202	C₂²×Dic₅₃	—	2	4	no	—
203	C₂²×Dic₅₃	—	2	4	no	—
204	C₂²×Dic₅₃	—	4	24	no	—
205	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
206	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
207	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
208	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
209	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
210	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
211	C₂²×Dic₅₃	C₂⁴	1	16	yes	complemented
212	C₂×C₄×D₅₃	—	4	24	no	—
213	C₂×C₄×D₅₃	—	4	24	no	—
214	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
215	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
216	C₂×Dic₁₀₆	—	4	24	no	—
217	C₂×Dic₁₀₆	C₂⁴	1	16	yes	complemented
218	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
219	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
220	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
221	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
222	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
223	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
224	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
225	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
226	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
227	#11719921	C₂⁴	1	16	yes	—
228	#11719921	C₂⁴	1	16	yes	—
229	#11719921	C₂⁴	1	16	yes	—
230	#11719921	C₂⁴	1	16	yes	—
231	#11719921	C₂⁴	1	16	yes	—
232	#11719921	C₂⁴	1	16	yes	—
233	C₄⋊Dic₅₃	C₂⁴	1	16	yes	complemented
234	#11719919	C₂⁴	1	16	yes	complemented
235	#11719919	C₂⁴	1	16	yes	complemented
236	#11719919	C₂⁴	1	16	yes	complemented
237	#11719919	C₂⁴	1	16	yes	complemented
238	C₄×Dic₅₃	C₂⁴	1	16	yes	complemented
239	C₄×Dic₅₃	C₂⁴	1	16	yes	complemented
240	C₂³×C₅₃	—	2	12	no	—
241	C₂³×C₅₃	—	2	12	no	—
242	C₂³×C₅₃	—	2	12	no	—
243	C₂³×C₅₃	—	2	12	no	—
244	C₂³×C₅₃	—	2	12	no	—
245	C₂³×C₅₃	—	2	12	no	—
246	C₂³×C₅₃	—	2	12	no	—
247	C₂³×C₅₃	—	2	12	no	—
248	C₂³×C₅₃	—	2	12	no	—
249	C₂³×C₅₃	—	4	16	no	—
250	C₂³×C₅₃	—	4	16	no	—
251	C₂³×C₅₃	—	4	16	no	—
252	C₂³×C₅₃	C₂×#41	1	4	yes	—
253	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
254	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
255	C₂³×C₅₃	C₂⁵	1	4	yes	—
256	C₂³×C₅₃	C₂⁵	1	4	yes	—
257	C₂³×C₅₃	C₂⁵	1	4	yes	—
258	C₂³×C₅₃	C₂⁵	1	3	yes	—
259	C₂²×D₅₃	—	2	32	no	—
260	C₂²×D₅₃	—	2	12	no	—
261	C₂²×D₅₃	—	2	12	no	—
262	C₂²×D₅₃	—	2	12	no	—
263	C₂²×D₅₃	—	2	12	no	—
264	C₂²×D₅₃	—	2	12	no	—
265	C₂²×D₅₃	—	2	32	no	—
266	C₂²×D₅₃	—	4	16	no	—
267	C₂²×D₅₃	—	4	16	no	—
268	C₂²×D₅₃	—	4	192	no	—
269	C₂²×D₅₃	—	4	16	no	—
270	C₂²×D₅₃	C₂×#41	1	24	yes	—
271	C₂²×D₅₃	C₂⁵	1	4	yes	—
272	C₂²×D₅₃	C₂⁵	1	4	yes	—
273	D₄×C₅₃	—	4	16	no	—
274	D₄×C₅₃	—	4	16	no	—
275	D₄×C₅₃	—	4	16	no	—
276	C₂×C₄×C₅₃	—	2	12	no	—
277	C₂×C₄×C₅₃	—	2	12	no	—
278	C₂×C₄×C₅₃	—	2	12	no	—
279	C₂×C₄×C₅₃	—	2	12	no	—
280	C₂×C₄×C₅₃	—	4	16	no	—
281	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
282	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
283	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
284	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
285	C₂²⋊D₅₃	—	2	32	no	—
286	C₂²⋊D₅₃	—	2	32	no	—
287	C₂²⋊D₅₃	—	4	16	no	—
288	C₂²⋊D₅₃	—	4	16	no	—
289	C₂×Dic₅₃	—	2	12	no	—
290	C₂×Dic₅₃	—	2	12	no	—
291	C₂×Dic₅₃	—	2	12	no	—
292	C₂×Dic₅₃	—	2	12	no	—
293	C₂×Dic₅₃	—	2	12	no	—
294	C₂×Dic₅₃	—	2	12	no	—
295	C₂×Dic₅₃	—	4	16	no	—
296	C₂×Dic₅₃	C₂⁵	1	4	yes	—
297	C₂×Dic₅₃	C₂⁵	1	4	yes	—
298	C₂×Dic₅₃	C₂⁵	1	4	yes	—
299	C₂×Dic₅₃	C₂⁵	1	4	yes	—
300	C₂×Dic₅₃	C₂⁵	1	4	yes	—
301	C₂×Dic₅₃	C₂⁵	1	4	yes	—
302	C₄×D₅₃	—	4	16	no	—
303	C₄×D₅₃	—	4	16	no	—
304	Dic₁₀₆	—	4	16	no	—
305	C₂²×#538	—	53	1	no	maximal, Sylow
306	C₂²×C₅₃	—	2	4	no	—
307	C₂²×C₅₃	—	2	4	no	—
308	C₂²×C₅₃	—	2	4	no	—
309	C₂²×C₅₃	—	2	4	no	—
310	C₂²×C₅₃	—	2	4	no	—
311	C₂²×C₅₃	—	2	4	no	—
312	C₂²×C₅₃	—	2	4	no	—
313	C₂²×C₅₃	—	2	4	no	—
314	C₂²×C₅₃	—	2	4	no	—
315	C₂²×C₅₃	—	4	24	no	—
316	C₂²×C₅₃	—	4	24	no	—
317	C₂²×C₅₃	—	4	24	no	—
318	C₂²×C₅₃	#538	1	16	yes	complemented
319	C₂²×C₅₃	C₂²×#41	1	6	yes	—
320	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
321	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
322	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
323	C₂×D₅₃	—	2	4	no	—
324	C₂×D₅₃	—	2	4	no	—
325	C₂×D₅₃	—	2	48	no	—
326	C₂×D₅₃	—	2	4	no	—
327	C₂×D₅₃	—	2	4	no	—
328	C₂×D₅₃	—	2	4	no	—
329	C₂×D₅₃	—	4	64	no	—
330	C₂×D₅₃	—	4	24	no	—
331	C₂×D₅₃	C₂²×#41	1	8	yes	—
332	C₄×C₅₃	—	2	4	no	—
333	C₄×C₅₃	—	2	4	no	—
334	C₄×C₅₃	—	2	4	no	—
335	C₄×C₅₃	—	2	4	no	—
336	Dic₅₃	—	2	4	no	—
337	Dic₅₃	—	2	4	no	—
338	Dic₅₃	—	2	4	no	—
339	Dic₅₃	—	2	4	no	—
340	Dic₅₃	—	2	4	no	—
341	Dic₅₃	—	2	4	no	—
342	C₂×#538	—	53	48	no	—
343	C₂²×#126	—	53	1	no	—
344	C₂²×#126	—	53	1	no	—
345	C₂²×#124	—	53	1	no	—
346	C₂²×#124	—	53	1	no	—
347	C₂²×#123	—	53	1	no	—
348	C₂²×#123	—	53	1	no	—
349	C₂²×C₂²⋊Q₈	—	53	1	no	—
350	C₂²×#121	—	53	1	no	—
351	C₂²×#121	—	53	1	no	—
352	C₂²×#121	D₅₃	1	1	yes	characteristic, complemented
353	C₂²×#120	—	53	1	no	—
354	C₂²×#120	—	53	1	no	—
355	C₂²×C₄×D₄	—	53	1	no	—
356	C₂²×C₄×D₄	—	53	1	no	—
357	C₂³×C₂²⋊C₄	—	53	1	no	—
358	C₂×C₅₃	—	4	4	no	—
359	C₂×C₅₃	—	4	4	no	—
360	C₂×C₅₃	—	4	4	no	—
361	C₂×C₅₃	C₂×#538	1	12	yes	complemented
362	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
363	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
365	D₅₃	—	2	8	no	—
366	D₅₃	—	4	4	no	—
367	C₂⁶	—	53	1	no	—
368	C₂³×Q₈	—	53	1	no	—
369	C₂³×D₄	—	53	1	no	—
370	C₂³×D₄	—	53	1	no	—
371	C₂³×D₄	—	53	1	no	—
372	C₂³×D₄	—	53	1	no	—
373	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic
374	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic
375	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
376	C₂⁴×C₄	—	53	1	no	—
377	C₂⁴×C₄	—	53	1	no	—
378	C₂⁴×C₄	—	53	1	no	—
379	C₂⁴×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
380	#538	—	53	256	no	—
381	C₂×#126	—	53	24	no	—
382	C₂×#126	—	53	24	no	—
383	C₂×#124	—	53	24	no	—
384	C₂×#124	—	53	24	no	—
385	C₂×#123	—	53	24	no	—
386	C₂×#123	—	53	24	no	—
387	C₂×C₂²⋊Q₈	—	53	24	no	—
388	C₂×#121	—	53	24	no	—
389	C₂×#121	—	53	24	no	—
390	C₂×#121	C₂×D₅₃	1	24	yes	complemented
391	C₂×#120	—	53	24	no	—
392	C₂×#120	—	53	24	no	—
393	C₂×C₄×D₄	—	53	24	no	—
394	C₂×C₄×D₄	—	53	24	no	—
395	C₂²×C₄⋊C₄	—	53	1	no	—
396	C₂²×C₄⋊C₄	—	53	1	no	—
397	C₂²×C₄⋊C₄	—	53	1	no	—
398	C₂²×C₄⋊C₄	—	53	1	no	—
399	C₂²×C₄⋊C₄	—	53	1	no	—
400	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
401	C₂²×C₂²⋊C₄	—	53	1	no	—
402	C₂²×C₂²⋊C₄	—	53	1	no	—
403	C₂²×C₂²⋊C₄	—	53	1	no	—
404	C₂²×C₂²⋊C₄	—	53	1	no	—
405	C₂²×C₂²⋊C₄	—	53	1	no	—
406	C₂²×C₂²⋊C₄	—	53	1	no	—
407	C₂²×C₂²⋊C₄	—	53	1	no	—
408	C₂²×C₂²⋊C₄	—	53	1	no	—
409	C₂²×C₂²⋊C₄	—	53	1	no	—
410	C₂²×C₂²⋊C₄	—	53	1	no	—
411	C₂²×C₂²⋊C₄	—	53	1	no	—
412	C₂²×C₂²⋊C₄	—	53	1	no	—
413	C₂²×C₂²⋊C₄	—	53	24	no	—
414	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
416	C₂²×C₄²	—	53	1	no	—
417	C₂²×C₄²	—	53	1	no	—
418	C₅₃	C₂²×#538	1	1	yes	characteristic, complemented, Sylow
419	C₂⁵	—	53	1	no	—
420	C₂⁵	—	53	1	no	—
421	C₂⁵	—	53	12	no	—
422	C₂⁵	—	106	8	no	—
423	C₂⁵	—	212	4	no	—
424	C₂⁵	—	212	4	no	—
425	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
426	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
427	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
428	C₂²×Q₈	—	53	12	no	—
429	C₂²×Q₈	—	212	4	no	—
430	C₂²×D₄	—	4	4	no	—
431	C₂²×D₄	—	4	4	no	—
432	C₂²×D₄	—	4	4	no	—
433	C₂²×D₄	—	53	12	no	—
434	C₂²×D₄	—	53	12	no	—
435	C₂²×D₄	—	53	12	no	—
436	C₂²×D₄	—	53	12	no	—
437	C₂²×D₄	—	106	8	no	—
438	C₂²×D₄	—	106	8	no	—
439	C₂²×D₄	—	212	4	no	—
440	C₂²×D₄	—	212	4	no	—
441	C₂²×D₄	C₂²×D₅₃	1	12	yes	—
442	C₂²×D₄	C₂²×D₅₃	1	12	yes	—
443	C₂²×D₄	C₂²×D₅₃	1	12	yes	complemented
444	C₂³×C₄	—	4	4	no	—
445	C₂³×C₄	—	53	1	no	—
446	C₂³×C₄	—	53	1	no	—
447	C₂³×C₄	—	53	1	no	—
448	C₂³×C₄	—	53	1	no	—
449	C₂³×C₄	—	53	1	no	—
450	C₂³×C₄	—	53	1	no	—
451	C₂³×C₄	—	53	12	no	—
452	C₂³×C₄	—	53	12	no	—
453	C₂³×C₄	—	53	12	no	—
454	C₂³×C₄	—	212	4	no	—
455	C₂³×C₄	—	212	4	no	—
456	C₂³×C₄	—	212	4	no	—
457	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
458	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
459	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
460	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
461	C₂³×C₄	C₂²×D₅₃	1	12	yes	complemented
462	#126	—	53	64	no	—
463	#126	—	53	64	no	—
464	#124	—	53	64	no	—
465	#124	—	53	64	no	—
466	#123	—	53	64	no	—
467	#123	—	53	64	no	—
468	C₂²⋊Q₈	—	53	64	no	—
469	#121	—	53	64	no	—
470	#121	—	53	64	no	—
471	#121	C₂²×D₅₃	1	64	yes	complemented
472	#120	—	53	64	no	—
473	#120	—	53	64	no	—
474	C₄×D₄	—	53	64	no	—
475	C₄×D₄	—	53	64	no	—
476	C₂×C₄⋊C₄	—	53	12	no	—
477	C₂×C₄⋊C₄	—	53	12	no	—
478	C₂×C₄⋊C₄	—	53	12	no	—
479	C₂×C₄⋊C₄	—	53	12	no	—
480	C₂×C₄⋊C₄	—	53	12	no	—
481	C₂×C₄⋊C₄	C₂²×D₅₃	1	12	yes	complemented
482	C₂×C₂²⋊C₄	—	53	12	no	—
483	C₂×C₂²⋊C₄	—	53	12	no	—
484	C₂×C₂²⋊C₄	—	53	12	no	—
485	C₂×C₂²⋊C₄	—	53	12	no	—
486	C₂×C₂²⋊C₄	—	53	12	no	—
487	C₂×C₂²⋊C₄	—	53	12	no	—
488	C₂×C₂²⋊C₄	—	53	12	no	—
489	C₂×C₂²⋊C₄	—	53	12	no	—
490	C₂×C₂²⋊C₄	—	53	12	no	—
491	C₂×C₂²⋊C₄	—	53	12	no	—
492	C₂×C₂²⋊C₄	—	53	12	no	—
493	C₂×C₂²⋊C₄	—	53	12	no	—
494	C₂×C₂²⋊C₄	—	53	64	no	—
495	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	—
496	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	complemented
497	C₂×C₄²	—	53	12	no	—
498	C₂×C₄²	—	53	12	no	—
499	C₂⁴	—	2	4	no	—
500	C₂⁴	—	2	4	no	—
501	C₂⁴	—	2	4	no	—
502	C₂⁴	—	2	4	no	—
503	C₂⁴	—	2	4	no	—
504	C₂⁴	—	2	4	no	—
505	C₂⁴	—	2	4	no	—
506	C₂⁴	—	2	4	no	—
507	C₂⁴	—	2	4	no	—
508	C₂⁴	—	53	8	no	—
509	C₂⁴	—	53	6	no	—
510	C₂⁴	—	53	6	no	—
511	C₂⁴	—	53	16	no	—
512	C₂⁴	—	106	48	no	—
513	C₂⁴	—	106	4	no	—
514	C₂⁴	—	106	4	no	—
515	C₂⁴	—	106	4	no	—
516	C₂⁴	—	106	4	no	—
517	C₂⁴	—	106	4	no	—
518	C₂⁴	—	212	24	no	—
519	C₂⁴	—	212	24	no	—
520	C₂⁴	—	212	64	no	—
521	C₂⁴	C₂³×D₅₃	1	6	yes	—
522	C₂⁴	C₂³×D₅₃	1	6	yes	—
523	C₂⁴	C₂³×D₅₃	1	6	yes	—
524	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
525	C₂×Q₈	—	53	16	no	—
526	C₂×Q₈	—	212	24	no	—
527	C₂×D₄	—	4	24	no	—
528	C₂×D₄	—	4	24	no	—
529	C₂×D₄	—	4	24	no	—
530	C₂×D₄	—	53	16	no	—
531	C₂×D₄	—	53	16	no	—
532	C₂×D₄	—	53	16	no	—
533	C₂×D₄	—	53	16	no	—
534	C₂×D₄	—	106	48	no	—
535	C₂×D₄	—	106	48	no	—
536	C₂×D₄	—	212	24	no	—
537	C₂×D₄	—	212	24	no	—
538	C₂×D₄	C₂³×D₅₃	1	16	yes	—
539	C₂×D₄	C₂³×D₅₃	1	16	yes	—
540	C₂×D₄	C₂³×D₅₃	1	16	yes	complemented
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	4	24	no	—
546	C₂²×C₄	—	53	6	no	—
547	C₂²×C₄	—	53	6	no	—
548	C₂²×C₄	—	53	6	no	—
549	C₂²×C₄	—	53	6	no	—
550	C₂²×C₄	—	53	6	no	—
551	C₂²×C₄	—	53	6	no	—
552	C₂²×C₄	—	53	16	no	—
553	C₂²×C₄	—	53	16	no	—
554	C₂²×C₄	—	53	16	no	—
555	C₂²×C₄	—	106	4	no	—
556	C₂²×C₄	—	106	4	no	—
557	C₂²×C₄	—	106	4	no	—
558	C₂²×C₄	—	106	4	no	—
559	C₂²×C₄	—	106	4	no	—
560	C₂²×C₄	—	106	4	no	—
561	C₂²×C₄	—	212	24	no	—
562	C₂²×C₄	—	212	24	no	—
563	C₂²×C₄	—	212	24	no	—
564	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
565	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
566	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
567	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
568	C₂²×C₄	C₂³×D₅₃	1	16	yes	complemented
569	C₄⋊C₄	—	53	16	no	—
570	C₄⋊C₄	—	53	16	no	—
571	C₄⋊C₄	—	53	16	no	—
572	C₄⋊C₄	—	53	16	no	—
573	C₄⋊C₄	—	53	16	no	—
574	C₄⋊C₄	C₂³×D₅₃	1	16	yes	complemented
575	C₂²⋊C₄	—	53	16	no	—
576	C₂²⋊C₄	—	53	16	no	—
577	C₂²⋊C₄	—	53	16	no	—
578	C₂²⋊C₄	—	53	16	no	—
579	C₂²⋊C₄	—	53	16	no	—
580	C₂²⋊C₄	—	53	16	no	—
581	C₂²⋊C₄	—	53	16	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	C₂³×D₅₃	1	16	yes	—
588	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	complemented
589	C₄²	—	53	16	no	—
590	C₄²	—	53	16	no	—
591	C₂³	—	2	12	no	—
592	C₂³	—	2	12	no	—
593	C₂³	—	2	12	no	—
594	C₂³	—	2	12	no	—
595	C₂³	—	2	12	no	—
596	C₂³	—	2	12	no	—
597	C₂³	—	2	12	no	—
598	C₂³	—	2	12	no	—
599	C₂³	—	2	12	no	—
600	C₂³	—	4	16	no	—
601	C₂³	—	4	16	no	—
602	C₂³	—	4	16	no	—
603	C₂³	—	53	24	no	—
604	C₂³	—	53	4	no	—
605	C₂³	—	53	4	no	—
606	C₂³	—	106	32	no	—
607	C₂³	—	106	12	no	—
608	C₂³	—	106	12	no	—
609	C₂³	—	106	32	no	—
610	C₂³	—	106	12	no	—
611	C₂³	—	106	12	no	—
612	C₂³	—	106	12	no	—
613	C₂³	—	212	16	no	—
614	C₂³	—	212	16	no	—
615	C₂³	—	212	192	no	—
616	C₂³	—	212	16	no	—
617	C₂³	#41×D₅₃	1	4	yes	—
618	C₂³	#13133262	1	4	yes	—
619	C₂³	#13133262	1	4	yes	—
620	C₂³	C₂⁴×D₅₃	1	4	yes	—
621	C₂³	C₂⁴×D₅₃	1	4	yes	—
622	C₂³	C₂⁴×D₅₃	1	4	yes	—
623	C₂³	C₂⁴×D₅₃	1	3	yes	—
624	Q₈	—	212	16	no	—
625	D₄	—	4	16	no	—
626	D₄	—	4	16	no	—
627	D₄	—	4	16	no	—
628	D₄	—	106	32	no	—
629	D₄	—	106	32	no	—
630	D₄	—	212	16	no	—
631	D₄	—	212	16	no	—
632	C₂×C₄	—	2	12	no	—
633	C₂×C₄	—	2	12	no	—
634	C₂×C₄	—	2	12	no	—
635	C₂×C₄	—	2	12	no	—
636	C₂×C₄	—	4	16	no	—
637	C₂×C₄	—	53	4	no	—
638	C₂×C₄	—	53	4	no	—
639	C₂×C₄	—	53	4	no	—
640	C₂×C₄	—	53	4	no	—
641	C₂×C₄	—	53	4	no	—
642	C₂×C₄	—	53	4	no	—
643	C₂×C₄	—	106	12	no	—
644	C₂×C₄	—	106	12	no	—
645	C₂×C₄	—	106	12	no	—
646	C₂×C₄	—	106	12	no	—
647	C₂×C₄	—	106	12	no	—
648	C₂×C₄	—	106	12	no	—
649	C₂×C₄	—	212	16	no	—
650	C₂×C₄	—	212	16	no	—
651	C₂×C₄	—	212	16	no	—
652	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
653	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
654	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
655	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
656	C₂²	—	2	4	no	—
657	C₂²	—	2	4	no	—
658	C₂²	—	2	4	no	—
659	C₂²	—	2	4	no	—
660	C₂²	—	2	4	no	—
661	C₂²	—	2	4	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	4	24	no	—
666	C₂²	—	4	24	no	—
667	C₂²	—	4	24	no	—
668	C₂²	—	53	8	no	—
669	C₂²	—	106	48	no	—
670	C₂²	—	106	4	no	—
671	C₂²	—	106	4	no	—
672	C₂²	—	106	4	no	—
673	C₂²	—	106	4	no	—
674	C₂²	—	106	4	no	—
675	C₂²	—	212	64	no	—
676	C₂²	—	212	24	no	—
677	C₂²	#16811205	1	16	yes	direct product factor
678	C₂²	C₂×#41×D₅₃	1	6	yes	—
679	C₂²	C₂×#13133262	1	6	yes	—
680	C₂²	C₂×#13133262	1	6	yes	—
681	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
682	C₄	—	2	4	no	—
683	C₄	—	2	4	no	—
684	C₄	—	2	4	no	—
685	C₄	—	2	4	no	—
686	C₄	—	106	4	no	—
687	C₄	—	106	4	no	—
688	C₄	—	106	4	no	—
689	C₄	—	106	4	no	—
690	C₄	—	106	4	no	—
691	C₄	—	106	4	no	—
692	C₂	—	4	4	no	—
693	C₂	—	4	4	no	—
694	C₂	—	4	4	no	—
695	C₂	—	106	8	no	—
696	C₂	—	212	4	no	—
697	C₂	C₂×#16811205	1	12	yes	direct product factor
698	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
699	C₂	C₂²×#13133262	1	1	yes	characteristic
700	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×#121×C₅₃	C₂
socle	C₂⁴×C₅₃	C₂⁴
hypercenter	C₂²×#121	D₅₃
hypocenter	C₅₃	C₂²×#538
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#121

Complements

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

N	H ≅ G/N	type
1. C₂×#16811205	C₂	direct (N × H)
2. C₂²×#13133212	C₂	semidirect
3. C₂²×#13133210	C₂	semidirect
4. C₂²×#13133204	C₂	semidirect
5. C₂²×#13133203	C₂	semidirect
6. C₂²×#13133200	C₂	semidirect
7. C₂²×#13133198	C₂	semidirect
8. C₂²×#13133195	C₂	semidirect
9. C₂²×#13133189	C₂	semidirect
10. C₂²×#13133188	C₂	semidirect
11. C₂²×#13133185	C₂	semidirect
12. C₂²×#13133185	C₂	semidirect
13. C₂²×C₄×C₂²⋊D₅₃	C₂	semidirect
14. C₂²×#13133177	C₂	semidirect
15. C₂²×C₂²⋊C₄×D₅₃	C₂	semidirect
16. C₂²×#121×C₅₃	C₂	semidirect
18. C₂³×Dic₁₀₆	C₂²	semidirect
23. C₂⁴×Dic₅₃	C₂²	semidirect
26. #16811205	C₂²	direct (N × H)
27. C₂×#13133212	C₂²	semidirect
28. C₂×#13133210	C₂²	semidirect
29. C₂×#13133204	C₂²	semidirect
30. C₂×#13133203	C₂²	semidirect
31. C₂×#13133200	C₂²	semidirect
32. C₂×#13133198	C₂²	semidirect
33. C₂×#13133195	C₂²	semidirect
34. C₂×#13133189	C₂²	semidirect
35. C₂×#13133188	C₂²	semidirect
36. C₂×#13133185	C₂²	semidirect
37. C₂×#13133185	C₂²	semidirect
38. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
39. C₂×#13133177	C₂²	semidirect
40. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
41. C₂²×#11719919	C₂²	semidirect
42. C₂²×#11719919	C₂²	semidirect
43. C₂²×#11719919	C₂²	semidirect
44. C₂²×#11719919	C₂²	semidirect
48. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
49. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
50. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
57. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
58. C₂²×C₄×Dic₅₃	C₂²	semidirect
59. C₂²×C₄×Dic₅₃	C₂²	semidirect
62. C₂³×D₄×C₅₃	C₂²	semidirect
63. C₂⁴×C₄×C₅₃	C₂²	semidirect
64. C₂×#121×C₅₃	C₂²	semidirect
65. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
67. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
75. C₂²×Dic₁₀₆	C₂³	semidirect
91. C₂³×Dic₅₃	C₂³	semidirect
96. #13133212	C₂³	semidirect
97. #13133210	C₂³	semidirect
98. #13133204	C₂³	semidirect
99. #13133203	C₂³	semidirect
100. #13133200	C₂³	semidirect
101. #13133198	C₂³	semidirect
102. #13133195	C₂³	semidirect
103. #13133189	C₂³	semidirect
104. #13133188	C₂³	semidirect
105. #13133185	C₂³	semidirect
106. #13133185	C₂³	semidirect
107. C₄×C₂²⋊D₅₃	C₂³	semidirect
108. #13133177	C₂³	semidirect
109. C₂×C₄⋊Dic₅₃	C₂³	semidirect
110. C₂×#11719919	C₂³	semidirect
111. C₂×#11719919	C₂³	semidirect
112. C₂×#11719919	C₂³	semidirect
113. C₂×#11719919	C₂³	semidirect
117. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
118. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
119. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
126. C₂²⋊C₄×D₅₃	C₂³	semidirect
127. C₂×C₄×Dic₅₃	C₂³	semidirect
128. C₂×C₄×Dic₅₃	C₂³	semidirect
137. C₂²×D₄×C₅₃	C₂³	semidirect
143. C₂³×C₄×C₅₃	C₂³	semidirect
144. #121×C₅₃	C₂³	semidirect
145. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
147. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
179. C₂×D₄×C₅₃	C₂⁴	semidirect
189. C₂²×C₄×C₅₃	C₂⁴	semidirect
211. C₂²×Dic₅₃	C₂⁴	semidirect
217. C₂×Dic₁₀₆	C₂⁴	semidirect
218. C₄⋊C₄×C₅₃	C₂⁴	semidirect
220. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
224. C₂²⋊Dic₅₃	C₂⁴	semidirect
225. C₂²⋊Dic₅₃	C₂⁴	semidirect
226. C₂²⋊Dic₅₃	C₂⁴	semidirect
233. C₄⋊Dic₅₃	C₂⁴	semidirect
234. #11719919	C₂⁴	semidirect
235. #11719919	C₂⁴	semidirect
236. #11719919	C₂⁴	semidirect
237. #11719919	C₂⁴	semidirect
238. C₄×Dic₅₃	C₂⁴	semidirect
239. C₄×Dic₅₃	C₂⁴	semidirect
318. C₂²×C₅₃	#538	semidirect
352. C₂²×#121	D₅₃	semidirect
361. C₂×C₅₃	C₂×#538	semidirect
375. C₂³×D₄	C₂×D₅₃	semidirect
379. C₂⁴×C₄	C₂×D₅₃	semidirect
390. C₂×#121	C₂×D₅₃	semidirect
400. C₂²×C₄⋊C₄	C₂×D₅₃	semidirect
415. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
418. C₅₃	C₂²×#538	semidirect
443. C₂²×D₄	C₂²×D₅₃	semidirect
461. C₂³×C₄	C₂²×D₅₃	semidirect
471. #121	C₂²×D₅₃	semidirect
481. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
496. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
540. C₂×D₄	C₂³×D₅₃	semidirect
568. C₂²×C₄	C₂³×D₅₃	semidirect
574. C₄⋊C₄	C₂³×D₅₃	semidirect
588. C₂²⋊C₄	C₂³×D₅₃	semidirect
677. C₂²	#16811205	direct (N × H)
697. C₂	C₂×#16811205	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16811205	2
C₂²×#13133212	2
C₂²×#13133210	2
C₂²×#13133204	2
C₂²×#13133203	2
C₂²×#13133200	2
C₂²×#13133198	2
C₂²×#13133195	2
C₂²×#13133189	2
C₂²×#13133188	2
C₂²×#13133185	2
C₂²×C₄×C₂²⋊D₅₃	2
C₂²×#13133177	2
C₂²×C₂²⋊C₄×D₅₃	2
C₂²×#121×C₅₃	2
C₂²×#538	53

Subgroups — C22×#16811205 #28290816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#16811205 #28290816