Subgroups — C₂²×#16811361 #28290959

Order 13568.

9606 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	C₂×#16811361	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#13133213	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#13133212	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13133210	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13133202	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13133201	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13133200	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13133191	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#13133190	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#13133189	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#13133189	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#13133188	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#13133187	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#13133185	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#13133185	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×D₂₁₂	C₂²	1	1	yes	characteristic
19	C₂³×D₂₁₂	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	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, complemented
26	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
29	#16811361	C₂²	1	256	yes	direct product factor
30	C₂×#13133213	C₂²	1	24	yes	complemented
31	C₂×#13133212	C₂²	1	24	yes	complemented
32	C₂×#13133210	C₂²	1	24	yes	complemented
33	C₂×#13133202	C₂²	1	24	yes	complemented
34	C₂×#13133201	C₂²	1	24	yes	complemented
35	C₂×#13133200	C₂²	1	24	yes	complemented
36	C₂×#13133191	C₂²	1	24	yes	complemented
37	C₂×#13133190	C₂²	1	24	yes	complemented
38	C₂×#13133189	C₂²	1	24	yes	complemented
39	C₂×#13133189	C₂²	1	24	yes	complemented
40	C₂×#13133188	C₂²	1	24	yes	complemented
41	C₂×#13133187	C₂²	1	24	yes	complemented
42	C₂×#13133185	C₂²	1	24	yes	complemented
43	C₂×#13133185	C₂²	1	24	yes	complemented
44	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
47	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
48	C₂²×#11719919	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
50	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
51	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
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	C₂²×#11719921	C₂²	1	1	yes	characteristic
58	C₂²×#11719921	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	—	4	4	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	1	yes	characteristic
74	C₂⁴×D₅₃	C₂³	1	12	yes	—
75	C₂²×D₂₁₂	—	4	4	no	—
76	C₂²×D₂₁₂	—	4	4	no	—
77	C₂²×D₂₁₂	C₂³	1	12	yes	—
78	C₂²×D₂₁₂	C₂³	1	12	yes	—
79	C₂²×C₂²⋊D₅₃	—	4	4	no	—
80	C₂²×C₂²⋊D₅₃	—	4	4	no	—
81	C₂²×C₂²⋊D₅₃	—	4	4	no	—
82	C₂²×C₂²⋊D₅₃	—	4	4	no	—
83	C₂²×C₂²⋊D₅₃	—	4	4	no	—
84	C₂²×C₂²⋊D₅₃	—	4	4	no	—
85	C₂²×C₂²⋊D₅₃	—	4	4	no	—
86	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
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	12	yes	complemented
92	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
93	C₂³×Dic₅₃	—	4	4	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	1	yes	characteristic
99	C₂³×Dic₅₃	C₂³	1	12	yes	complemented
100	C₂²×C₄×D₅₃	—	4	4	no	—
101	C₂²×C₄×D₅₃	C₂³	1	12	yes	complemented
102	#13133213	C₂³	1	64	yes	complemented
103	#13133212	C₂³	1	64	yes	complemented
104	#13133210	C₂³	1	64	yes	complemented
105	#13133202	C₂³	1	64	yes	complemented
106	#13133201	C₂³	1	64	yes	complemented
107	#13133200	C₂³	1	64	yes	complemented
108	#13133191	C₂³	1	64	yes	complemented
109	#13133190	C₂³	1	64	yes	complemented
110	#13133189	C₂³	1	64	yes	complemented
111	#13133189	C₂³	1	64	yes	complemented
112	#13133188	C₂³	1	64	yes	complemented
113	#13133187	C₂³	1	64	yes	complemented
114	#13133185	C₂³	1	64	yes	complemented
115	#13133185	C₂³	1	64	yes	complemented
116	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	complemented
117	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	complemented
118	C₂×#11719919	C₂³	1	12	yes	complemented
119	C₂×#11719919	C₂³	1	12	yes	complemented
120	C₂×#11719919	C₂³	1	12	yes	complemented
121	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	—
122	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	—
123	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	complemented
124	C₂×#11719921	C₂³	1	12	yes	—
125	C₂×#11719921	C₂³	1	12	yes	—
126	C₂×#11719921	C₂³	1	12	yes	—
127	C₂×#11719921	C₂³	1	12	yes	—
128	C₂×#11719921	C₂³	1	12	yes	—
129	C₂×#11719921	C₂³	1	12	yes	—
130	C₂×#11719921	C₂³	1	12	yes	complemented
131	C₂×C₄×Dic₅₃	C₂³	1	12	yes	complemented
132	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
133	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
134	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₅₃	—	4	4	no	—
136	C₂²×D₄×C₅₃	—	4	4	no	—
137	C₂²×D₄×C₅₃	—	4	4	no	—
138	C₂²×D₄×C₅₃	C₂³	1	12	yes	—
139	C₂²×D₄×C₅₃	C₂³	1	12	yes	—
140	C₂²×D₄×C₅₃	C₂³	1	12	yes	complemented
141	C₂³×C₄×C₅₃	—	4	4	no	—
142	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₅₃	C₂³	1	12	yes	complemented
147	#121×C₅₃	C₂³	1	64	yes	complemented
148	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	complemented
149	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	—
150	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	complemented
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	—	2	4	no	—
158	C₂⁴×C₅₃	—	2	4	no	—
159	C₂⁴×C₅₃	—	2	4	no	—
160	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
161	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
162	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
163	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
164	C₂³×D₅₃	—	2	4	no	—
165	C₂³×D₅₃	—	2	4	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	4	no	—
171	C₂³×D₅₃	—	2	4	no	—
172	C₂³×D₅₃	—	2	4	no	—
173	C₂³×D₅₃	—	4	24	no	—
174	C₂³×D₅₃	—	4	24	no	—
175	C₂³×D₅₃	—	4	24	no	—
176	C₂³×D₅₃	—	4	64	no	—
177	C₂³×D₅₃	C₂⁴	1	6	yes	—
178	C₂³×D₅₃	C₂⁴	1	6	yes	—
179	C₂³×D₅₃	C₂⁴	1	6	yes	—
180	C₂³×D₅₃	C₂⁴	1	16	yes	—
181	C₂×D₄×C₅₃	—	4	24	no	—
182	C₂×D₄×C₅₃	—	4	24	no	—
183	C₂×D₄×C₅₃	—	4	24	no	—
184	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
185	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
186	C₂×D₄×C₅₃	C₂⁴	1	16	yes	complemented
187	C₂²×C₄×C₅₃	—	2	4	no	—
188	C₂²×C₄×C₅₃	—	2	4	no	—
189	C₂²×C₄×C₅₃	—	2	4	no	—
190	C₂²×C₄×C₅₃	—	2	4	no	—
191	C₂²×C₄×C₅₃	—	4	24	no	—
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	6	yes	—
196	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	complemented
197	C₂×C₂²⋊D₅₃	—	4	24	no	—
198	C₂×C₂²⋊D₅₃	—	4	24	no	—
199	C₂×C₂²⋊D₅₃	—	4	24	no	—
200	C₂×C₂²⋊D₅₃	—	4	24	no	—
201	C₂×C₂²⋊D₅₃	—	4	24	no	—
202	C₂×C₂²⋊D₅₃	—	4	24	no	—
203	C₂×C₂²⋊D₅₃	—	4	24	no	—
204	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
205	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
206	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
207	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
208	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
209	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	complemented
210	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	complemented
211	C₂²×Dic₅₃	—	2	4	no	—
212	C₂²×Dic₅₃	—	2	4	no	—
213	C₂²×Dic₅₃	—	2	4	no	—
214	C₂²×Dic₅₃	—	2	4	no	—
215	C₂²×Dic₅₃	—	2	4	no	—
216	C₂²×Dic₅₃	—	4	24	no	—
217	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
218	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
219	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
220	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
221	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
222	C₂²×Dic₅₃	C₂⁴	1	16	yes	complemented
223	C₂×D₂₁₂	—	4	24	no	—
224	C₂×D₂₁₂	—	4	24	no	—
225	C₂×D₂₁₂	C₂⁴	1	16	yes	—
226	C₂×D₂₁₂	C₂⁴	1	16	yes	—
227	C₂×C₄×D₅₃	—	4	24	no	—
228	C₂×C₄×D₅₃	C₂⁴	1	16	yes	complemented
229	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
230	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
231	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
232	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
233	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
234	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
235	#11719921	C₂⁴	1	16	yes	—
236	#11719921	C₂⁴	1	16	yes	—
237	#11719921	C₂⁴	1	16	yes	—
238	#11719921	C₂⁴	1	16	yes	—
239	#11719921	C₂⁴	1	16	yes	—
240	#11719921	C₂⁴	1	16	yes	—
241	#11719921	C₂⁴	1	16	yes	complemented
242	C₄⋊Dic₅₃	C₂⁴	1	16	yes	complemented
243	C₄⋊Dic₅₃	C₂⁴	1	16	yes	complemented
244	#11719919	C₂⁴	1	16	yes	complemented
245	#11719919	C₂⁴	1	16	yes	complemented
246	#11719919	C₂⁴	1	16	yes	complemented
247	C₄×Dic₅₃	C₂⁴	1	16	yes	complemented
248	C₂³×C₅₃	—	2	12	no	—
249	C₂³×C₅₃	—	2	12	no	—
250	C₂³×C₅₃	—	2	12	no	—
251	C₂³×C₅₃	—	2	12	no	—
252	C₂³×C₅₃	—	2	12	no	—
253	C₂³×C₅₃	—	2	12	no	—
254	C₂³×C₅₃	—	2	12	no	—
255	C₂³×C₅₃	—	2	12	no	—
256	C₂³×C₅₃	—	2	12	no	—
257	C₂³×C₅₃	—	4	16	no	—
258	C₂³×C₅₃	—	4	16	no	—
259	C₂³×C₅₃	—	4	16	no	—
260	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
261	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
262	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
263	C₂³×C₅₃	C₂⁵	1	4	yes	—
264	C₂³×C₅₃	C₂⁵	1	4	yes	—
265	C₂³×C₅₃	C₂⁵	1	4	yes	—
266	C₂³×C₅₃	C₂⁵	1	3	yes	—
267	C₂²×D₅₃	—	2	12	no	—
268	C₂²×D₅₃	—	2	12	no	—
269	C₂²×D₅₃	—	2	12	no	—
270	C₂²×D₅₃	—	2	12	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	12	no	—
276	C₂²×D₅₃	—	4	16	no	—
277	C₂²×D₅₃	—	4	16	no	—
278	C₂²×D₅₃	—	4	16	no	—
279	C₂²×D₅₃	—	4	192	no	—
280	C₂²×D₅₃	—	4	16	no	—
281	C₂²×D₅₃	—	4	16	no	—
282	C₂²×D₅₃	—	4	16	no	—
283	C₂²×D₅₃	C₂⁵	1	4	yes	—
284	C₂²×D₅₃	C₂⁵	1	4	yes	—
285	C₂²×D₅₃	C₂⁵	1	4	yes	—
286	D₄×C₅₃	—	4	16	no	—
287	D₄×C₅₃	—	4	16	no	—
288	D₄×C₅₃	—	4	16	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	12	no	—
293	C₂×C₄×C₅₃	—	4	16	no	—
294	C₂×C₄×C₅₃	C₂⁵	1	4	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	C₂²⋊D₅₃	—	4	16	no	—
299	C₂²⋊D₅₃	—	4	16	no	—
300	C₂²⋊D₅₃	—	4	16	no	—
301	C₂²⋊D₅₃	—	4	16	no	—
302	C₂²⋊D₅₃	—	4	16	no	—
303	C₂²⋊D₅₃	—	4	16	no	—
304	C₂²⋊D₅₃	—	4	16	no	—
305	C₂×Dic₅₃	—	2	12	no	—
306	C₂×Dic₅₃	—	2	12	no	—
307	C₂×Dic₅₃	—	2	12	no	—
308	C₂×Dic₅₃	—	2	12	no	—
309	C₂×Dic₅₃	—	2	12	no	—
310	C₂×Dic₅₃	—	4	16	no	—
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	C₂×Dic₅₃	C₂⁵	1	4	yes	—
316	D₂₁₂	—	4	16	no	—
317	D₂₁₂	—	4	16	no	—
318	C₄×D₅₃	—	4	16	no	—
319	C₂²×#560	—	53	1	no	maximal, Sylow
320	C₂²×C₅₃	—	2	4	no	—
321	C₂²×C₅₃	—	2	4	no	—
322	C₂²×C₅₃	—	2	4	no	—
323	C₂²×C₅₃	—	2	4	no	—
324	C₂²×C₅₃	—	2	4	no	—
325	C₂²×C₅₃	—	2	4	no	—
326	C₂²×C₅₃	—	2	4	no	—
327	C₂²×C₅₃	—	2	4	no	—
328	C₂²×C₅₃	—	2	4	no	—
329	C₂²×C₅₃	—	4	24	no	—
330	C₂²×C₅₃	—	4	24	no	—
331	C₂²×C₅₃	—	4	24	no	—
332	C₂²×C₅₃	#560	1	16	yes	complemented
333	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
334	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
335	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
336	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
337	C₂×D₅₃	—	2	4	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	4	no	—
343	C₂×D₅₃	—	2	4	no	—
344	C₂×D₅₃	—	2	4	no	—
345	C₂×D₅₃	—	2	4	no	—
346	C₂×D₅₃	—	4	64	no	—
347	C₂×D₅₃	—	4	24	no	—
348	C₂×D₅₃	—	4	24	no	—
349	C₂×D₅₃	—	4	24	no	—
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	Dic₅₃	—	2	4	no	—
355	Dic₅₃	—	2	4	no	—
356	Dic₅₃	—	2	4	no	—
357	Dic₅₃	—	2	4	no	—
358	Dic₅₃	—	2	4	no	—
359	C₂×#560	—	53	48	no	—
360	C₂²×#127	—	53	1	no	—
361	C₂²×#126	—	53	1	no	—
362	C₂²×#126	—	53	1	no	—
363	C₂²×#123	—	53	1	no	—
364	C₂²×#123	—	53	1	no	—
365	C₂²×#123	—	53	1	no	—
366	C₂²×#121	—	53	1	no	—
367	C₂²×#121	—	53	1	no	—
368	C₂²×#121	—	53	1	no	—
369	C₂²×#121	—	53	1	no	—
370	C₂²×#121	—	53	1	no	—
371	C₂²×#121	D₅₃	1	1	yes	characteristic, complemented
372	C₂²×#120	—	53	1	no	—
373	C₂²×#120	—	53	1	no	—
374	C₂²×#120	—	53	1	no	—
375	C₂×C₅₃	—	4	4	no	—
376	C₂×C₅₃	—	4	4	no	—
377	C₂×C₅₃	—	4	4	no	—
378	C₂×C₅₃	C₂×#560	1	12	yes	complemented
379	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
381	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
382	D₅₃	—	4	4	no	—
383	D₅₃	—	4	4	no	—
384	D₅₃	—	4	4	no	—
385	C₂⁶	—	53	1	no	—
386	C₂³×D₄	—	53	1	no	—
387	C₂³×D₄	—	53	1	no	—
388	C₂³×D₄	—	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	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic
397	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
398	C₂⁴×C₄	—	53	1	no	—
399	C₂⁴×C₄	—	53	1	no	—
400	C₂⁴×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
401	#560	—	53	256	no	—
402	C₂×#127	—	53	24	no	—
403	C₂×#126	—	53	24	no	—
404	C₂×#126	—	53	24	no	—
405	C₂×#123	—	53	24	no	—
406	C₂×#123	—	53	24	no	—
407	C₂×#123	—	53	24	no	—
408	C₂×#121	—	53	24	no	—
409	C₂×#121	—	53	24	no	—
410	C₂×#121	—	53	24	no	—
411	C₂×#121	—	53	24	no	—
412	C₂×#121	—	53	24	no	—
413	C₂×#121	C₂×D₅₃	1	24	yes	complemented
414	C₂×#120	—	53	24	no	—
415	C₂×#120	—	53	24	no	—
416	C₂×#120	—	53	24	no	—
417	C₂²×C₄⋊C₄	—	53	1	no	—
418	C₂²×C₄⋊C₄	—	53	1	no	—
419	C₂²×C₄⋊C₄	—	53	1	no	—
420	C₂²×C₄⋊C₄	—	53	1	no	—
421	C₂²×C₄⋊C₄	—	53	1	no	—
422	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
423	C₂²×C₂²⋊C₄	—	53	1	no	—
424	C₂²×C₂²⋊C₄	—	53	1	no	—
425	C₂²×C₂²⋊C₄	—	53	1	no	—
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	C₂×D₅₃	1	1	yes	characteristic
434	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
435	C₂²×C₄²	—	53	1	no	—
436	C₅₃	C₂²×#560	1	1	yes	characteristic, complemented, Sylow
437	C₂⁵	—	53	1	no	—
438	C₂⁵	—	53	1	no	—
439	C₂⁵	—	53	1	no	—
440	C₂⁵	—	53	12	no	—
441	C₂⁵	—	212	4	no	—
442	C₂⁵	—	212	4	no	—
443	C₂⁵	—	212	4	no	—
444	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
445	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
446	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
447	C₂²×D₄	—	4	4	no	—
448	C₂²×D₄	—	4	4	no	—
449	C₂²×D₄	—	4	4	no	—
450	C₂²×D₄	—	53	12	no	—
451	C₂²×D₄	—	53	12	no	—
452	C₂²×D₄	—	53	12	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	—	212	4	no	—
460	C₂²×D₄	—	212	4	no	—
461	C₂²×D₄	—	212	4	no	—
462	C₂²×D₄	—	212	4	no	—
463	C₂²×D₄	—	212	4	no	—
464	C₂²×D₄	—	212	4	no	—
465	C₂²×D₄	—	212	4	no	—
466	C₂²×D₄	—	212	4	no	—
467	C₂²×D₄	—	212	4	no	—
468	C₂²×D₄	C₂²×D₅₃	1	12	yes	—
469	C₂²×D₄	C₂²×D₅₃	1	12	yes	—
470	C₂²×D₄	C₂²×D₅₃	1	12	yes	complemented
471	C₂³×C₄	—	4	4	no	—
472	C₂³×C₄	—	53	1	no	—
473	C₂³×C₄	—	53	1	no	—
474	C₂³×C₄	—	53	1	no	—
475	C₂³×C₄	—	53	1	no	—
476	C₂³×C₄	—	53	1	no	—
477	C₂³×C₄	—	53	12	no	—
478	C₂³×C₄	—	53	12	no	—
479	C₂³×C₄	—	212	4	no	—
480	C₂³×C₄	—	212	4	no	—
481	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
482	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
483	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
484	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
485	C₂³×C₄	C₂²×D₅₃	1	12	yes	complemented
486	#127	—	53	64	no	—
487	#126	—	53	64	no	—
488	#126	—	53	64	no	—
489	#123	—	53	64	no	—
490	#123	—	53	64	no	—
491	#123	—	53	64	no	—
492	#121	—	53	64	no	—
493	#121	—	53	64	no	—
494	#121	—	53	64	no	—
495	#121	—	53	64	no	—
496	#121	—	53	64	no	—
497	#121	C₂²×D₅₃	1	64	yes	complemented
498	#120	—	53	64	no	—
499	#120	—	53	64	no	—
500	#120	—	53	64	no	—
501	C₂×C₄⋊C₄	—	53	12	no	—
502	C₂×C₄⋊C₄	—	53	12	no	—
503	C₂×C₄⋊C₄	—	53	12	no	—
504	C₂×C₄⋊C₄	—	53	12	no	—
505	C₂×C₄⋊C₄	—	53	12	no	—
506	C₂×C₄⋊C₄	C₂²×D₅₃	1	12	yes	complemented
507	C₂×C₂²⋊C₄	—	53	12	no	—
508	C₂×C₂²⋊C₄	—	53	12	no	—
509	C₂×C₂²⋊C₄	—	53	12	no	—
510	C₂×C₂²⋊C₄	—	53	12	no	—
511	C₂×C₂²⋊C₄	—	53	12	no	—
512	C₂×C₂²⋊C₄	—	53	12	no	—
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	C₂²×D₅₃	1	12	yes	—
518	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	complemented
519	C₂×C₄²	—	53	12	no	—
520	C₂⁴	—	2	4	no	—
521	C₂⁴	—	2	4	no	—
522	C₂⁴	—	2	4	no	—
523	C₂⁴	—	2	4	no	—
524	C₂⁴	—	2	4	no	—
525	C₂⁴	—	2	4	no	—
526	C₂⁴	—	2	4	no	—
527	C₂⁴	—	2	4	no	—
528	C₂⁴	—	2	4	no	—
529	C₂⁴	—	53	6	no	—
530	C₂⁴	—	53	6	no	—
531	C₂⁴	—	53	6	no	—
532	C₂⁴	—	53	16	no	—
533	C₂⁴	—	106	4	no	—
534	C₂⁴	—	106	4	no	—
535	C₂⁴	—	106	4	no	—
536	C₂⁴	—	106	4	no	—
537	C₂⁴	—	106	4	no	—
538	C₂⁴	—	106	4	no	—
539	C₂⁴	—	106	4	no	—
540	C₂⁴	—	106	4	no	—
541	C₂⁴	—	106	4	no	—
542	C₂⁴	—	212	24	no	—
543	C₂⁴	—	212	24	no	—
544	C₂⁴	—	212	24	no	—
545	C₂⁴	—	212	64	no	—
546	C₂⁴	C₂³×D₅₃	1	6	yes	—
547	C₂⁴	C₂³×D₅₃	1	6	yes	—
548	C₂⁴	C₂³×D₅₃	1	6	yes	—
549	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
550	C₂×D₄	—	4	24	no	—
551	C₂×D₄	—	4	24	no	—
552	C₂×D₄	—	4	24	no	—
553	C₂×D₄	—	53	16	no	—
554	C₂×D₄	—	53	16	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	—	53	16	no	—
562	C₂×D₄	—	212	24	no	—
563	C₂×D₄	—	212	24	no	—
564	C₂×D₄	—	212	24	no	—
565	C₂×D₄	—	212	24	no	—
566	C₂×D₄	—	212	24	no	—
567	C₂×D₄	—	212	24	no	—
568	C₂×D₄	—	212	24	no	—
569	C₂×D₄	—	212	24	no	—
570	C₂×D₄	—	212	24	no	—
571	C₂×D₄	C₂³×D₅₃	1	16	yes	—
572	C₂×D₄	C₂³×D₅₃	1	16	yes	—
573	C₂×D₄	C₂³×D₅₃	1	16	yes	complemented
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	4	24	no	—
579	C₂²×C₄	—	53	6	no	—
580	C₂²×C₄	—	53	6	no	—
581	C₂²×C₄	—	53	6	no	—
582	C₂²×C₄	—	53	6	no	—
583	C₂²×C₄	—	53	6	no	—
584	C₂²×C₄	—	53	16	no	—
585	C₂²×C₄	—	53	16	no	—
586	C₂²×C₄	—	106	4	no	—
587	C₂²×C₄	—	106	4	no	—
588	C₂²×C₄	—	106	4	no	—
589	C₂²×C₄	—	106	4	no	—
590	C₂²×C₄	—	106	4	no	—
591	C₂²×C₄	—	212	24	no	—
592	C₂²×C₄	—	212	24	no	—
593	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
594	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
595	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
596	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
597	C₂²×C₄	C₂³×D₅₃	1	16	yes	complemented
598	C₄⋊C₄	—	53	16	no	—
599	C₄⋊C₄	—	53	16	no	—
600	C₄⋊C₄	—	53	16	no	—
601	C₄⋊C₄	—	53	16	no	—
602	C₄⋊C₄	—	53	16	no	—
603	C₄⋊C₄	C₂³×D₅₃	1	16	yes	complemented
604	C₂²⋊C₄	—	53	16	no	—
605	C₂²⋊C₄	—	53	16	no	—
606	C₂²⋊C₄	—	53	16	no	—
607	C₂²⋊C₄	—	53	16	no	—
608	C₂²⋊C₄	—	53	16	no	—
609	C₂²⋊C₄	—	53	16	no	—
610	C₂²⋊C₄	—	53	16	no	—
611	C₂²⋊C₄	—	53	16	no	—
612	C₂²⋊C₄	—	53	16	no	—
613	C₂²⋊C₄	—	53	16	no	—
614	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
615	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	complemented
616	C₄²	—	53	16	no	—
617	C₂³	—	2	12	no	—
618	C₂³	—	2	12	no	—
619	C₂³	—	2	12	no	—
620	C₂³	—	2	12	no	—
621	C₂³	—	2	12	no	—
622	C₂³	—	2	12	no	—
623	C₂³	—	2	12	no	—
624	C₂³	—	2	12	no	—
625	C₂³	—	2	12	no	—
626	C₂³	—	4	16	no	—
627	C₂³	—	4	16	no	—
628	C₂³	—	4	16	no	—
629	C₂³	—	53	4	no	—
630	C₂³	—	53	4	no	—
631	C₂³	—	53	4	no	—
632	C₂³	—	106	12	no	—
633	C₂³	—	106	12	no	—
634	C₂³	—	106	12	no	—
635	C₂³	—	106	12	no	—
636	C₂³	—	106	12	no	—
637	C₂³	—	106	12	no	—
638	C₂³	—	106	12	no	—
639	C₂³	—	106	12	no	—
640	C₂³	—	106	12	no	—
641	C₂³	—	212	16	no	—
642	C₂³	—	212	16	no	—
643	C₂³	—	212	16	no	—
644	C₂³	—	212	192	no	—
645	C₂³	—	212	16	no	—
646	C₂³	—	212	16	no	—
647	C₂³	—	212	16	no	—
648	C₂³	#13133262	1	4	yes	—
649	C₂³	#13133262	1	4	yes	—
650	C₂³	#13133263	1	4	yes	—
651	C₂³	C₂⁴×D₅₃	1	4	yes	—
652	C₂³	C₂⁴×D₅₃	1	4	yes	—
653	C₂³	C₂⁴×D₅₃	1	4	yes	—
654	C₂³	C₂⁴×D₅₃	1	3	yes	—
655	D₄	—	4	16	no	—
656	D₄	—	4	16	no	—
657	D₄	—	4	16	no	—
658	D₄	—	212	16	no	—
659	D₄	—	212	16	no	—
660	D₄	—	212	16	no	—
661	D₄	—	212	16	no	—
662	D₄	—	212	16	no	—
663	D₄	—	212	16	no	—
664	D₄	—	212	16	no	—
665	D₄	—	212	16	no	—
666	D₄	—	212	16	no	—
667	C₂×C₄	—	2	12	no	—
668	C₂×C₄	—	2	12	no	—
669	C₂×C₄	—	2	12	no	—
670	C₂×C₄	—	2	12	no	—
671	C₂×C₄	—	4	16	no	—
672	C₂×C₄	—	53	4	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	12	no	—
678	C₂×C₄	—	106	12	no	—
679	C₂×C₄	—	106	12	no	—
680	C₂×C₄	—	106	12	no	—
681	C₂×C₄	—	106	12	no	—
682	C₂×C₄	—	212	16	no	—
683	C₂×C₄	—	212	16	no	—
684	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
685	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
686	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
687	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	2	4	no	—
692	C₂²	—	2	4	no	—
693	C₂²	—	2	4	no	—
694	C₂²	—	2	4	no	—
695	C₂²	—	2	4	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	4	24	no	—
698	C₂²	—	4	24	no	—
699	C₂²	—	4	24	no	—
700	C₂²	—	106	4	no	—
701	C₂²	—	106	4	no	—
702	C₂²	—	106	4	no	—
703	C₂²	—	106	4	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	—	212	64	no	—
710	C₂²	—	212	24	no	—
711	C₂²	—	212	24	no	—
712	C₂²	—	212	24	no	—
713	C₂²	#16811361	1	16	yes	direct product factor
714	C₂²	C₂×#13133262	1	6	yes	—
715	C₂²	C₂×#13133262	1	6	yes	—
716	C₂²	C₂×#13133263	1	6	yes	—
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	—	106	4	no	—
723	C₄	—	106	4	no	—
724	C₄	—	106	4	no	—
725	C₄	—	106	4	no	—
726	C₄	—	106	4	no	—
727	C₂	—	4	4	no	—
728	C₂	—	4	4	no	—
729	C₂	—	4	4	no	—
730	C₂	—	212	4	no	—
731	C₂	—	212	4	no	—
732	C₂	—	212	4	no	—
733	C₂	C₂×#16811361	1	12	yes	direct product factor
734	C₂	C₂²×#13133262	1	1	yes	characteristic
735	C₂	C₂²×#13133262	1	1	yes	characteristic
736	C₂	C₂²×#13133263	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×#560
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×#16811361	C₂	direct (N × H)
2. C₂²×#13133213	C₂	semidirect
3. C₂²×#13133212	C₂	semidirect
4. C₂²×#13133210	C₂	semidirect
5. C₂²×#13133202	C₂	semidirect
6. C₂²×#13133201	C₂	semidirect
7. C₂²×#13133200	C₂	semidirect
8. C₂²×#13133191	C₂	semidirect
9. C₂²×#13133190	C₂	semidirect
10. C₂²×#13133189	C₂	semidirect
11. C₂²×#13133189	C₂	semidirect
12. C₂²×#13133188	C₂	semidirect
13. C₂²×#13133187	C₂	semidirect
14. C₂²×#13133185	C₂	semidirect
15. C₂²×#13133185	C₂	semidirect
16. C₂²×#121×C₅₃	C₂	semidirect
25. C₂³×C₂²⋊D₅₃	C₂²	semidirect
26. C₂³×C₂²⋊D₅₃	C₂²	semidirect
27. C₂⁴×Dic₅₃	C₂²	semidirect
28. C₂³×C₄×D₅₃	C₂²	semidirect
29. #16811361	C₂²	direct (N × H)
30. C₂×#13133213	C₂²	semidirect
31. C₂×#13133212	C₂²	semidirect
32. C₂×#13133210	C₂²	semidirect
33. C₂×#13133202	C₂²	semidirect
34. C₂×#13133201	C₂²	semidirect
35. C₂×#13133200	C₂²	semidirect
36. C₂×#13133191	C₂²	semidirect
37. C₂×#13133190	C₂²	semidirect
38. C₂×#13133189	C₂²	semidirect
39. C₂×#13133189	C₂²	semidirect
40. C₂×#13133188	C₂²	semidirect
41. C₂×#13133187	C₂²	semidirect
42. C₂×#13133185	C₂²	semidirect
43. C₂×#13133185	C₂²	semidirect
44. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
45. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
46. C₂²×#11719919	C₂²	semidirect
47. C₂²×#11719919	C₂²	semidirect
48. C₂²×#11719919	C₂²	semidirect
51. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
58. C₂²×#11719921	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
91. C₂²×C₂²⋊D₅₃	C₂³	semidirect
92. C₂²×C₂²⋊D₅₃	C₂³	semidirect
99. C₂³×Dic₅₃	C₂³	semidirect
101. C₂²×C₄×D₅₃	C₂³	semidirect
102. #13133213	C₂³	semidirect
103. #13133212	C₂³	semidirect
104. #13133210	C₂³	semidirect
105. #13133202	C₂³	semidirect
106. #13133201	C₂³	semidirect
107. #13133200	C₂³	semidirect
108. #13133191	C₂³	semidirect
109. #13133190	C₂³	semidirect
110. #13133189	C₂³	semidirect
111. #13133189	C₂³	semidirect
112. #13133188	C₂³	semidirect
113. #13133187	C₂³	semidirect
114. #13133185	C₂³	semidirect
115. #13133185	C₂³	semidirect
116. C₂×C₄⋊Dic₅₃	C₂³	semidirect
117. C₂×C₄⋊Dic₅₃	C₂³	semidirect
118. C₂×#11719919	C₂³	semidirect
119. C₂×#11719919	C₂³	semidirect
120. C₂×#11719919	C₂³	semidirect
123. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
130. C₂×#11719921	C₂³	semidirect
131. C₂×C₄×Dic₅₃	C₂³	semidirect
140. C₂²×D₄×C₅₃	C₂³	semidirect
146. C₂³×C₄×C₅₃	C₂³	semidirect
147. #121×C₅₃	C₂³	semidirect
148. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
150. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
186. C₂×D₄×C₅₃	C₂⁴	semidirect
196. C₂²×C₄×C₅₃	C₂⁴	semidirect
209. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
210. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
222. C₂²×Dic₅₃	C₂⁴	semidirect
228. C₂×C₄×D₅₃	C₂⁴	semidirect
229. C₄⋊C₄×C₅₃	C₂⁴	semidirect
231. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
234. C₂²⋊Dic₅₃	C₂⁴	semidirect
241. #11719921	C₂⁴	semidirect
242. C₄⋊Dic₅₃	C₂⁴	semidirect
243. C₄⋊Dic₅₃	C₂⁴	semidirect
244. #11719919	C₂⁴	semidirect
245. #11719919	C₂⁴	semidirect
246. #11719919	C₂⁴	semidirect
247. C₄×Dic₅₃	C₂⁴	semidirect
332. C₂²×C₅₃	#560	semidirect
371. C₂²×#121	D₅₃	semidirect
378. C₂×C₅₃	C₂×#560	semidirect
397. C₂³×D₄	C₂×D₅₃	semidirect
400. C₂⁴×C₄	C₂×D₅₃	semidirect
413. C₂×#121	C₂×D₅₃	semidirect
422. C₂²×C₄⋊C₄	C₂×D₅₃	semidirect
434. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
436. C₅₃	C₂²×#560	semidirect
470. C₂²×D₄	C₂²×D₅₃	semidirect
485. C₂³×C₄	C₂²×D₅₃	semidirect
497. #121	C₂²×D₅₃	semidirect
506. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
518. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
573. C₂×D₄	C₂³×D₅₃	semidirect
597. C₂²×C₄	C₂³×D₅₃	semidirect
603. C₄⋊C₄	C₂³×D₅₃	semidirect
615. C₂²⋊C₄	C₂³×D₅₃	semidirect
713. C₂²	#16811361	direct (N × H)
733. C₂	C₂×#16811361	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×#16811361	2
C₂²×#13133213	2
C₂²×#13133212	2
C₂²×#13133210	2
C₂²×#13133202	2
C₂²×#13133201	2
C₂²×#13133200	2
C₂²×#13133191	2
C₂²×#13133190	2
C₂²×#13133189	2
C₂²×#13133188	2
C₂²×#13133187	2
C₂²×#13133185	2
C₂²×#121×C₅₃	2
C₂²×#560	53

Subgroups — C22×#16811361 #28290959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#16811361 #28290959