Subgroups — C₂×#20288344 #28291969

Order 13568.

14438 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133262	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288344	C₂	1	32	yes	maximal, direct product factor
4	C₂×#16811263	C₂	1	4	yes	maximal, complemented
5	C₂×#16811260	C₂	1	4	yes	maximal, complemented
6	C₂×D₄×C₂²⋊D₅₃	C₂	1	4	yes	maximal, complemented
7	C₂×#16811255	C₂	1	4	yes	maximal, complemented
8	C₂×#16811188	C₂	1	2	yes	maximal, complemented
9	C₂×#16811185	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811183	C₂	1	2	yes	maximal, complemented
11	C₂×#16811182	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16811129	C₂	1	2	yes	maximal, complemented
13	C₂²×#13133186	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#120×D₅₃	C₂	1	2	yes	maximal, complemented
15	C₂×#16811096	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, complemented
18	C₂×#13133262	—	2	16	no	—
19	C₂×#13133262	C₂²	1	16	yes	complemented
20	C₂²×#11719945	C₂²	1	2	yes	complemented
21	C₂²×#11719947	C₂²	1	2	yes	complemented
22	C₂²×#11719947	C₂²	1	2	yes	complemented
23	C₂³×C₂²⋊D₅₃	—	2	16	no	—
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	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂³×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
29	C₂³×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
30	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
32	C₂³×C₂²⋊D₅₃	C₂²	1	16	yes	complemented
33	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
34	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
35	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
36	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
37	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
38	#16811263	C₂²	1	64	yes	complemented
39	#16811260	C₂²	1	64	yes	complemented
40	D₄×C₂²⋊D₅₃	C₂²	1	64	yes	complemented
41	#16811255	C₂²	1	64	yes	complemented
42	#16811188	C₂²	1	32	yes	complemented
43	#16811185	C₂²	1	16	yes	complemented
44	#16811183	C₂²	1	32	yes	complemented
45	#16811182	C₂²	1	16	yes	complemented
46	C₂×#13133213	C₂²	1	4	yes	complemented
47	C₂×#13133203	C₂²	1	4	yes	complemented
48	#16811129	C₂²	1	32	yes	complemented
49	C₂×#13133201	C₂²	1	2	yes	complemented
50	C₂×#13133201	C₂²	1	2	yes	complemented
51	C₂×#13133200	C₂²	1	2	yes	complemented
52	C₂×#13133199	C₂²	1	4	yes	complemented
53	C₂×#13133198	C₂²	1	2	yes	complemented
54	C₂×#13133194	C₂²	1	4	yes	complemented
55	C₂×#13133191	C₂²	1	4	yes	complemented
56	C₂×#13133190	C₂²	1	4	yes	complemented
57	C₂×#13133190	C₂²	1	4	yes	complemented
58	C₂×#13133189	C₂²	1	4	yes	complemented
59	C₂×#13133189	C₂²	1	4	yes	complemented
60	C₂×#13133189	C₂²	1	4	yes	complemented
61	C₂×#13133188	C₂²	1	4	yes	complemented
62	C₂×#13133187	C₂²	1	2	yes	complemented
63	C₂×#13133187	C₂²	1	4	yes	complemented
64	C₂×#13133187	C₂²	1	2	yes	complemented
65	C₂×#13133186	C₂²	1	2	yes	complemented
66	C₂×#13133186	C₂²	1	2	yes	complemented
67	C₂×#13133186	C₂²	1	4	yes	complemented
68	C₂×#13133186	C₂²	1	2	yes	complemented
69	C₂×#13133186	C₂²	1	16	yes	complemented
70	C₂×#13133185	C₂²	1	2	yes	complemented
71	C₂×#13133185	C₂²	1	4	yes	complemented
72	C₂×#13133185	C₂²	1	4	yes	complemented
73	#120×D₅₃	C₂²	1	32	yes	complemented
74	#16811096	C₂²	1	16	yes	complemented
75	C₂×D₄×Dic₅₃	C₂²	1	4	yes	complemented
76	C₂×C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
77	C₂×#13133177	C₂²	1	4	yes	complemented
78	C₂×#13133177	C₂²	1	4	yes	complemented
79	C₂×#13133173	C₂²	1	2	yes	complemented
80	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₂²×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
82	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
83	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
84	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic, complemented
85	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
86	C₂³×D₄×C₅₃	C₂²	1	2	yes	complemented
87	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
88	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
89	C₂×#120×C₅₃	C₂²	1	4	yes	complemented
90	C₂×#120×C₅₃	C₂²	1	16	yes	complemented
91	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
92	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
93	C₂⁴×D₅₃	—	2	8	no	—
94	C₂⁴×D₅₃	—	4	8	no	—
95	C₂⁴×D₅₃	C₂³	1	4	yes	—
96	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
97	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
98	C₂⁴×D₅₃	C₂³	1	8	yes	complemented
99	C₂⁴×D₅₃	C₂³	1	2	yes	complemented
100	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic, complemented
101	#13133262	—	2	128	no	—
102	C₂×#11719945	—	2	16	no	—
103	C₂×#11719945	C₂³	1	16	yes	complemented
104	C₂×#11719947	—	2	16	no	—
105	C₂×#11719947	—	2	16	no	—
106	C₂×#11719947	C₂³	1	16	yes	complemented
107	C₂×#11719947	C₂³	1	16	yes	complemented
108	C₂²×Dic₁₀₆	C₂³	1	2	yes	complemented
109	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
110	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
111	C₂²×C₂²⋊D₅₃	—	2	8	no	—
112	C₂²×C₂²⋊D₅₃	—	2	8	no	—
113	C₂²×C₂²⋊D₅₃	—	2	8	no	—
114	C₂²×C₂²⋊D₅₃	—	2	32	no	—
115	C₂²×C₂²⋊D₅₃	—	2	32	no	—
116	C₂²×C₂²⋊D₅₃	—	2	128	no	—
117	C₂²×C₂²⋊D₅₃	—	2	16	no	—
118	C₂²×C₂²⋊D₅₃	—	2	8	no	—
119	C₂²×C₂²⋊D₅₃	—	4	8	no	—
120	C₂²×C₂²⋊D₅₃	D₄	1	16	yes	complemented
121	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
122	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
123	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
124	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
125	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
126	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
127	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
128	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
129	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
130	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
131	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
132	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
133	C₂²×C₂²⋊D₅₃	C₂³	1	32	yes	complemented
134	C₂²×C₂²⋊D₅₃	C₂³	1	32	yes	complemented
135	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
136	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
137	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
138	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
139	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
140	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
141	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
142	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
143	C₂×D₄×D₅₃	—	2	16	no	—
144	C₂×D₄×D₅₃	—	2	16	no	—
145	C₂×D₄×D₅₃	—	4	16	no	—
146	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
147	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
148	C₂×D₄×D₅₃	C₂³	1	32	yes	complemented
149	C₂³×Dic₅₃	—	2	8	no	—
150	C₂³×Dic₅₃	C₂³	1	4	yes	—
151	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
152	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
153	C₂³×Dic₅₃	C₂³	1	8	yes	complemented
154	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
155	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
156	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
157	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
158	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
159	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
160	#13133213	C₂³	1	32	yes	complemented
161	#13133203	C₂³	1	32	yes	complemented
162	#13133201	C₂³	1	16	yes	complemented
163	#13133201	C₂³	1	16	yes	complemented
164	#13133200	C₂³	1	16	yes	complemented
165	#13133199	C₂³	1	32	yes	complemented
166	#13133198	C₂³	1	16	yes	complemented
167	#13133194	C₂³	1	32	yes	complemented
168	#13133191	C₂³	1	32	yes	complemented
169	#13133190	C₂³	1	32	yes	complemented
170	#13133190	C₂³	1	32	yes	complemented
171	#13133189	C₂³	1	32	yes	complemented
172	#13133189	C₂³	1	32	yes	complemented
173	#13133189	C₂³	1	32	yes	complemented
174	#13133188	C₂³	1	32	yes	complemented
175	#13133187	C₂³	1	16	yes	complemented
176	#13133187	C₂³	1	32	yes	complemented
177	#13133187	C₂³	1	16	yes	complemented
178	#13133186	C₂³	1	16	yes	complemented
179	#13133186	C₂³	1	16	yes	complemented
180	#13133186	C₂³	1	32	yes	complemented
181	#13133186	C₂³	1	16	yes	complemented
182	#13133185	C₂³	1	32	yes	complemented
183	#13133185	C₂³	1	16	yes	complemented
184	#13133185	C₂³	1	32	yes	complemented
185	D₄×Dic₅₃	C₂³	1	32	yes	complemented
186	C₄×C₂²⋊D₅₃	C₂³	1	32	yes	complemented
187	#13133177	C₂³	1	32	yes	complemented
188	#13133177	C₂³	1	32	yes	complemented
189	#13133173	C₂³	1	16	yes	complemented
190	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
191	C₂×#11719919	C₂³	1	4	yes	complemented
192	C₂×#11719919	C₂³	1	4	yes	complemented
193	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
194	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
195	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
196	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
197	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
198	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
199	C₂×C₂²⋊Dic₅₃	C₂³	1	16	yes	complemented
200	C₂×#11719921	C₂³	1	4	yes	complemented
201	C₂×#11719921	C₂³	1	4	yes	complemented
202	C₂×#11719921	C₂³	1	4	yes	complemented
203	C₂×#11719921	C₂³	1	4	yes	complemented
204	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
205	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	complemented
206	C₂×C₄×Dic₅₃	C₂³	1	4	yes	complemented
207	C₂⁵×C₅₃	—	2	8	no	—
208	C₂⁵×C₅₃	—	4	8	no	—
209	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
210	C₂⁵×C₅₃	C₂³	1	2	yes	—
211	C₂⁵×C₅₃	C₂³	1	2	yes	—
212	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
213	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
214	C₂⁵×C₅₃	C₂³	1	8	yes	complemented
215	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic, complemented
216	C₂²×D₄×C₅₃	—	2	8	no	—
217	C₂²×D₄×C₅₃	—	4	8	no	—
218	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
219	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
220	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
221	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
222	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
223	C₂²×D₄×C₅₃	C₂³	1	16	yes	complemented
224	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
225	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
226	#120×C₅₃	C₂³	1	16	yes	complemented
227	#120×C₅₃	C₂³	1	16	yes	complemented
228	#120×C₅₃	C₂³	1	32	yes	complemented
229	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
231	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
232	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
233	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
234	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	complemented
235	C₂⁴×C₅₃	—	2	4	no	—
236	C₂⁴×C₅₃	—	2	8	no	—
237	C₂⁴×C₅₃	—	2	8	no	—
238	C₂⁴×C₅₃	—	2	8	no	—
239	C₂⁴×C₅₃	—	2	4	no	—
240	C₂⁴×C₅₃	—	2	32	no	—
241	C₂⁴×C₅₃	—	2	8	no	—
242	C₂⁴×C₅₃	—	2	8	no	—
243	C₂⁴×C₅₃	—	2	4	no	—
244	C₂⁴×C₅₃	—	4	4	no	—
245	C₂⁴×C₅₃	—	4	4	no	—
246	C₂⁴×C₅₃	—	4	4	no	—
247	C₂⁴×C₅₃	—	4	4	no	—
248	C₂⁴×C₅₃	—	4	32	no	—
249	C₂⁴×C₅₃	—	4	4	no	—
250	C₂⁴×C₅₃	—	4	64	no	—
251	C₂⁴×C₅₃	C₂×D₄	1	8	yes	complemented
252	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
253	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
254	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
255	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
256	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
257	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
258	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
259	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
260	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
261	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
262	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
263	C₂⁴×C₅₃	C₂⁴	1	4	yes	complemented
264	C₂³×D₅₃	—	2	4	no	—
265	C₂³×D₅₃	—	2	16	no	—
266	C₂³×D₅₃	—	2	4	no	—
267	C₂³×D₅₃	—	2	16	no	—
268	C₂³×D₅₃	—	2	32	no	—
269	C₂³×D₅₃	—	2	8	no	—
270	C₂³×D₅₃	—	4	4	no	—
271	C₂³×D₅₃	—	4	8	no	—
272	C₂³×D₅₃	—	4	4	no	—
273	C₂³×D₅₃	—	4	32	no	—
274	C₂³×D₅₃	—	4	8	no	—
275	C₂³×D₅₃	—	4	4	no	—
276	C₂³×D₅₃	—	4	64	no	—
277	C₂³×D₅₃	C₂×D₄	1	8	yes	complemented
278	C₂³×D₅₃	C₂⁴	1	2	yes	—
279	C₂³×D₅₃	C₂⁴	1	2	yes	—
280	C₂³×D₅₃	C₂⁴	1	16	yes	—
281	C₂³×D₅₃	C₂⁴	1	2	yes	—
282	C₂³×D₅₃	C₂⁴	1	4	yes	—
283	C₂³×D₅₃	C₂⁴	1	4	yes	—
284	C₂³×D₅₃	C₂⁴	1	8	yes	complemented
285	C₂³×D₅₃	C₂⁴	1	4	yes	complemented
286	C₂×D₄×C₅₃	—	2	8	no	—
287	C₂×D₄×C₅₃	—	2	8	no	—
288	C₂×D₄×C₅₃	—	2	32	no	—
289	C₂×D₄×C₅₃	—	2	16	no	—
290	C₂×D₄×C₅₃	—	4	8	no	—
291	C₂×D₄×C₅₃	—	4	32	no	—
292	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
293	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
294	C₂×D₄×C₅₃	C₂⁴	1	8	yes	complemented
295	C₂×D₄×C₅₃	C₂⁴	1	16	yes	complemented
296	C₂²×C₄×C₅₃	—	2	4	no	—
297	C₂²×C₄×C₅₃	—	4	4	no	—
298	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
299	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	complemented
301	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	complemented
302	C₂×C₂²⋊D₅₃	—	2	8	no	—
303	C₂×C₂²⋊D₅₃	—	2	8	no	—
304	C₂×C₂²⋊D₅₃	—	2	8	no	—
305	C₂×C₂²⋊D₅₃	—	2	8	no	—
306	C₂×C₂²⋊D₅₃	—	2	32	no	—
307	C₂×C₂²⋊D₅₃	—	2	32	no	—
308	C₂×C₂²⋊D₅₃	—	2	16	no	—
309	C₂×C₂²⋊D₅₃	—	2	8	no	—
310	C₂×C₂²⋊D₅₃	—	2	16	no	—
311	C₂×C₂²⋊D₅₃	—	2	32	no	—
312	C₂×C₂²⋊D₅₃	—	2	128	no	—
313	C₂×C₂²⋊D₅₃	—	2	128	no	—
314	C₂×C₂²⋊D₅₃	—	2	64	no	—
315	C₂×C₂²⋊D₅₃	—	2	8	no	—
316	C₂×C₂²⋊D₅₃	—	2	16	no	—
317	C₂×C₂²⋊D₅₃	—	2	32	no	—
318	C₂×C₂²⋊D₅₃	—	4	8	no	—
319	C₂×C₂²⋊D₅₃	—	4	8	no	—
320	C₂×C₂²⋊D₅₃	—	4	32	no	—
321	C₂×C₂²⋊D₅₃	C₂×D₄	1	16	yes	complemented
322	C₂×C₂²⋊D₅₃	C₂×D₄	1	16	yes	complemented
323	C₂×C₂²⋊D₅₃	C₂×D₄	1	64	yes	complemented
324	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
325	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
326	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
327	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
328	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
329	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
330	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
331	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
332	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
333	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
334	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
335	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	complemented
336	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	complemented
337	C₂²×Dic₅₃	—	2	4	no	—
338	C₂²×Dic₅₃	—	2	4	no	—
339	C₂²×Dic₅₃	—	2	16	no	—
340	C₂²×Dic₅₃	—	2	8	no	—
341	C₂²×Dic₅₃	—	2	32	no	—
342	C₂²×Dic₅₃	—	4	4	no	—
343	C₂²×Dic₅₃	C₂×D₄	1	8	yes	complemented
344	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
345	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
346	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
347	C₂²×Dic₅₃	C₂⁴	1	16	yes	—
348	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
349	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
350	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
351	C₂²×Dic₅₃	C₂⁴	1	4	yes	complemented
352	C₂²×Dic₅₃	C₂⁴	1	8	yes	complemented
353	C₂²×Dic₅₃	C₂⁴	1	8	yes	complemented
354	#11719947	—	2	64	no	—
355	#11719947	—	2	64	no	—
356	D₄×D₅₃	—	2	64	no	—
357	D₄×D₅₃	—	2	64	no	—
358	D₄×D₅₃	—	4	64	no	—
359	#11719945	—	2	64	no	—
360	C₂×D₂₁₂	—	2	8	no	—
361	C₂×D₂₁₂	—	4	8	no	—
362	C₂×D₂₁₂	C₂⁴	1	8	yes	complemented
363	C₂×D₂₁₂	C₂⁴	1	16	yes	complemented
364	C₂×C₄×D₅₃	—	2	8	no	—
365	C₂×C₄×D₅₃	—	2	8	no	—
366	C₂×C₄×D₅₃	—	4	8	no	—
367	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
368	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
369	C₂×C₄×D₅₃	C₂⁴	1	16	yes	complemented
370	C₂×Dic₁₀₆	—	2	8	no	—
371	C₂×Dic₁₀₆	C₂⁴	1	8	yes	complemented
372	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
373	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
374	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
375	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
376	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
377	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
378	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
379	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
380	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
381	#11719921	C₂⁴	1	16	yes	complemented
382	#11719921	C₂⁴	1	16	yes	complemented
383	#11719921	C₂⁴	1	16	yes	complemented
384	#11719921	C₂⁴	1	16	yes	complemented
385	C₄⋊Dic₅₃	C₂⁴	1	16	yes	complemented
386	#11719919	C₂⁴	1	16	yes	complemented
387	#11719919	C₂⁴	1	16	yes	complemented
388	C₄×Dic₅₃	C₂⁴	1	16	yes	complemented
389	C₂³×C₅₃	—	2	32	no	—
390	C₂³×C₅₃	—	2	8	no	—
391	C₂³×C₅₃	—	2	4	no	—
392	C₂³×C₅₃	—	2	4	no	—
393	C₂³×C₅₃	—	2	4	no	—
394	C₂³×C₅₃	—	2	4	no	—
395	C₂³×C₅₃	—	2	4	no	—
396	C₂³×C₅₃	—	2	16	no	—
397	C₂³×C₅₃	—	2	4	no	—
398	C₂³×C₅₃	—	2	16	no	—
399	C₂³×C₅₃	—	2	16	no	—
400	C₂³×C₅₃	—	2	8	no	—
401	C₂³×C₅₃	—	2	4	no	—
402	C₂³×C₅₃	—	2	4	no	—
403	C₂³×C₅₃	—	2	8	no	—
404	C₂³×C₅₃	—	2	4	no	—
405	C₂³×C₅₃	—	2	16	no	—
406	C₂³×C₅₃	—	2	16	no	—
407	C₂³×C₅₃	—	2	8	no	—
408	C₂³×C₅₃	—	4	16	no	—
409	C₂³×C₅₃	—	4	8	no	—
410	C₂³×C₅₃	—	4	8	no	—
411	C₂³×C₅₃	—	4	8	no	—
412	C₂³×C₅₃	—	4	8	no	—
413	C₂³×C₅₃	—	4	8	no	—
414	C₂³×C₅₃	—	4	32	no	—
415	C₂³×C₅₃	—	4	32	no	—
416	C₂³×C₅₃	—	4	128	no	—
417	C₂³×C₅₃	—	4	16	no	—
418	C₂³×C₅₃	—	8	8	no	—
419	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
420	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
421	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
422	C₂³×C₅₃	C₂²×D₄	1	16	yes	complemented
423	C₂³×C₅₃	H(5,𝔽₂)	1	8	yes	complemented
424	C₂³×C₅₃	C₂⁵	1	4	yes	—
425	C₂³×C₅₃	C₂⁵	1	4	yes	—
426	C₂³×C₅₃	C₂⁵	1	2	yes	—
427	C₂³×C₅₃	C₂⁵	1	2	yes	—
428	C₂³×C₅₃	C₂⁵	1	2	yes	—
429	C₂³×C₅₃	C₂⁵	1	4	yes	—
430	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
431	C₂²×D₅₃	—	2	8	no	—
432	C₂²×D₅₃	—	2	4	no	—
433	C₂²×D₅₃	—	2	8	no	—
434	C₂²×D₅₃	—	2	4	no	—
435	C₂²×D₅₃	—	2	8	no	—
436	C₂²×D₅₃	—	2	8	no	—
437	C₂²×D₅₃	—	2	32	no	—
438	C₂²×D₅₃	—	2	8	no	—
439	C₂²×D₅₃	—	2	32	no	—
440	C₂²×D₅₃	—	2	16	no	—
441	C₂²×D₅₃	—	4	16	no	—
442	C₂²×D₅₃	—	4	8	no	—
443	C₂²×D₅₃	—	4	16	no	—
444	C₂²×D₅₃	—	4	8	no	—
445	C₂²×D₅₃	—	4	16	no	—
446	C₂²×D₅₃	—	4	8	no	—
447	C₂²×D₅₃	—	4	64	no	—
448	C₂²×D₅₃	—	4	128	no	—
449	C₂²×D₅₃	—	4	16	no	—
450	C₂²×D₅₃	—	8	16	no	—
451	C₂²×D₅₃	—	8	8	no	—
452	C₂²×D₅₃	C₂²×D₄	1	8	yes	—
453	C₂²×D₅₃	C₂²×D₄	1	16	yes	complemented
454	C₂²×D₅₃	C₂⁵	1	4	yes	—
455	C₂²×D₅₃	C₂⁵	1	4	yes	—
456	C₂²×D₅₃	C₂⁵	1	4	yes	—
457	D₄×C₅₃	—	2	16	no	—
458	D₄×C₅₃	—	2	16	no	—
459	D₄×C₅₃	—	2	32	no	—
460	D₄×C₅₃	—	4	16	no	—
461	C₂×C₄×C₅₃	—	2	4	no	—
462	C₂×C₄×C₅₃	—	2	8	no	—
463	C₂×C₄×C₅₃	—	2	8	no	—
464	C₂×C₄×C₅₃	—	4	8	no	—
465	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
466	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
467	C₂²⋊D₅₃	—	2	16	no	—
468	C₂²⋊D₅₃	—	2	16	no	—
469	C₂²⋊D₅₃	—	2	16	no	—
470	C₂²⋊D₅₃	—	2	16	no	—
471	C₂²⋊D₅₃	—	2	32	no	—
472	C₂²⋊D₅₃	—	2	16	no	—
473	C₂²⋊D₅₃	—	2	32	no	—
474	C₂²⋊D₅₃	—	2	16	no	—
475	C₂²⋊D₅₃	—	2	32	no	—
476	C₂²⋊D₅₃	—	4	16	no	—
477	C₂²⋊D₅₃	—	4	16	no	—
478	C₂²⋊D₅₃	C₂²×D₄	1	32	yes	complemented
479	C₂²⋊D₅₃	C₂²×D₄	1	32	yes	complemented
480	C₂×Dic₅₃	—	2	4	no	—
481	C₂×Dic₅₃	—	2	8	no	—
482	C₂×Dic₅₃	—	2	8	no	—
483	C₂×Dic₅₃	—	2	4	no	—
484	C₂×Dic₅₃	—	2	8	no	—
485	C₂×Dic₅₃	—	2	16	no	—
486	C₂×Dic₅₃	—	2	32	no	—
487	C₂×Dic₅₃	—	4	8	no	—
488	C₂×Dic₅₃	C₂²×D₄	1	8	yes	—
489	C₂×Dic₅₃	C₂²×D₄	1	16	yes	complemented
490	C₂×Dic₅₃	C₂⁵	1	4	yes	—
491	C₂×Dic₅₃	C₂⁵	1	8	yes	—
492	C₂×Dic₅₃	C₂⁵	1	4	yes	—
493	C₂×Dic₅₃	C₂⁵	1	4	yes	—
494	D₂₁₂	—	2	16	no	—
495	D₂₁₂	—	4	16	no	—
496	C₄×D₅₃	—	2	16	no	—
497	C₄×D₅₃	—	2	16	no	—
498	C₄×D₅₃	—	4	16	no	—
499	Dic₁₀₆	—	2	16	no	—
500	C₂×#3484	—	53	1	no	maximal, Sylow
501	C₂²×C₅₃	—	2	32	no	—
502	C₂²×C₅₃	—	2	4	no	—
503	C₂²×C₅₃	—	2	4	no	—
504	C₂²×C₅₃	—	2	4	no	—
505	C₂²×C₅₃	—	2	4	no	—
506	C₂²×C₅₃	—	2	4	no	—
507	C₂²×C₅₃	—	2	8	no	—
508	C₂²×C₅₃	—	2	16	no	—
509	C₂²×C₅₃	—	2	8	no	—
510	C₂²×C₅₃	—	2	8	no	—
511	C₂²×C₅₃	—	2	4	no	—
512	C₂²×C₅₃	—	2	4	no	—
513	C₂²×C₅₃	—	2	4	no	—
514	C₂²×C₅₃	—	2	8	no	—
515	C₂²×C₅₃	—	2	4	no	—
516	C₂²×C₅₃	—	4	16	no	—
517	C₂²×C₅₃	—	4	32	no	—
518	C₂²×C₅₃	—	4	32	no	—
519	C₂²×C₅₃	—	4	16	no	—
520	C₂²×C₅₃	—	4	8	no	—
521	C₂²×C₅₃	—	4	8	no	—
522	C₂²×C₅₃	—	8	8	no	—
523	C₂²×C₅₃	C₂³×D₄	1	4	yes	—
524	C₂²×C₅₃	C₂³×D₄	1	4	yes	—
525	C₂²×C₅₃	C₂³×D₄	1	4	yes	—
526	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
527	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
528	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	8	yes	complemented
529	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
530	C₂×D₅₃	—	2	8	no	—
531	C₂×D₅₃	—	2	16	no	—
532	C₂×D₅₃	—	2	4	no	—
533	C₂×D₅₃	—	2	4	no	—
534	C₂×D₅₃	—	2	8	no	—
535	C₂×D₅₃	—	2	8	no	—
536	C₂×D₅₃	—	4	16	no	—
537	C₂×D₅₃	—	4	64	no	—
538	C₂×D₅₃	—	4	16	no	—
539	C₂×D₅₃	—	4	8	no	—
540	C₂×D₅₃	—	4	8	no	—
541	C₂×D₅₃	—	8	16	no	—
542	C₂×D₅₃	—	8	8	no	—
543	C₂×D₅₃	C₂³×D₄	1	8	yes	—
544	C₄×C₅₃	—	2	4	no	—
545	C₄×C₅₃	—	2	8	no	—
546	Dic₅₃	—	2	4	no	—
547	Dic₅₃	—	2	4	no	—
548	Dic₅₃	—	2	8	no	—
549	Dic₅₃	C₂³×D₄	1	8	yes	—
550	C₂²×H(5,𝔽₂)	—	53	1	no	—
551	C₂⁴×D₄	—	53	1	no	—
552	#3484	—	53	32	no	—
553	C₂×#546	—	53	4	no	—
554	C₂×#546	—	53	4	no	—
555	C₂×D₄²	—	53	4	no	—
556	C₂×D₄²	—	53	4	no	—
557	C₂×#535	—	53	2	no	—
558	C₂×#534	—	53	1	no	—
559	C₂×#534	—	53	2	no	—
560	C₂×#534	—	53	1	no	—
561	C₂×#525	—	53	2	no	—
562	C₂²×#120	—	53	1	no	—
563	C₂²×#120	—	53	2	no	—
564	C₂²×#120	D₅₃	1	1	yes	characteristic, complemented
565	C₂×#518	—	53	1	no	—
566	C₂×C₅₃	—	2	4	no	—
567	C₂×C₅₃	—	2	8	no	—
568	C₂×C₅₃	—	2	4	no	—
569	C₂×C₅₃	—	2	4	no	—
570	C₂×C₅₃	—	4	4	no	—
571	C₂×C₅₃	—	4	4	no	—
572	C₂×C₅₃	#3484	1	4	yes	complemented
573	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
574	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	2	yes	—
575	D₅₃	—	2	8	no	—
576	D₅₃	—	4	4	no	—
577	D₅₃	—	4	4	no	—
578	C₂⁶	—	53	1	no	—
579	C₂⁶	C₂×D₅₃	1	1	yes	characteristic, complemented
580	C₂×H(5,𝔽₂)	—	53	16	no	—
581	C₂×H(5,𝔽₂)	—	106	16	no	—
582	C₂²×#41	—	53	2	no	—
583	C₂²×#41	—	53	2	no	—
584	C₂²×#41	—	53	2	no	—
585	C₂³×D₄	—	53	1	no	—
586	C₂³×D₄	—	53	1	no	—
587	C₂³×D₄	—	53	1	no	—
588	C₂³×D₄	—	53	1	no	—
589	C₂³×D₄	—	53	4	no	—
590	C₂³×D₄	—	53	4	no	—
591	C₂³×D₄	—	53	1	no	—
592	C₂³×D₄	—	53	16	no	—
593	C₂³×D₄	—	53	2	no	—
594	C₂³×D₄	—	53	2	no	—
595	C₂³×D₄	—	53	2	no	—
596	C₂³×D₄	—	53	2	no	—
597	C₂³×D₄	—	53	4	no	—
598	C₂³×D₄	—	106	16	no	—
599	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
600	C₂³×D₄	C₂×D₅₃	1	2	yes	complemented
601	C₂⁴×C₄	—	53	1	no	—
602	#546	—	53	64	no	—
603	#546	—	53	64	no	—
604	D₄²	—	53	64	no	—
605	D₄²	—	53	64	no	—
606	#535	—	53	32	no	—
607	#534	—	53	16	no	—
608	#534	—	53	32	no	—
609	#534	—	53	16	no	—
610	C₂×#127	—	53	4	no	—
611	C₂×#124	—	53	4	no	—
612	#525	—	53	32	no	—
613	C₂×#123	—	53	2	no	—
614	C₂×#123	—	53	2	no	—
615	C₂×#123	—	53	2	no	—
616	C₂×#123	—	53	4	no	—
617	C₂×#123	—	53	2	no	—
618	C₂×C₂²⋊Q₈	—	53	4	no	—
619	C₂×#121	—	53	4	no	—
620	C₂×#121	—	53	4	no	—
621	C₂×#121	—	53	4	no	—
622	C₂×#121	—	53	4	no	—
623	C₂×#121	—	53	4	no	—
624	C₂×#121	—	53	4	no	—
625	C₂×#121	—	53	4	no	—
626	C₂×#120	—	53	2	no	—
627	C₂×#120	—	53	2	no	—
628	C₂×#120	—	53	4	no	—
629	C₂×#120	—	53	16	no	—
630	C₂×#120	—	53	2	no	—
631	C₂×#120	—	53	2	no	—
632	C₂×#120	—	53	4	no	—
633	C₂×#120	—	53	4	no	—
634	C₂×#120	—	53	32	no	—
635	C₂×#120	—	53	2	no	—
636	C₂×#120	—	53	4	no	—
637	C₂×#120	—	53	2	no	—
638	C₂×#120	C₂×D₅₃	1	2	yes	complemented
639	C₂×#120	C₂×D₅₃	1	2	yes	complemented
640	C₂×#120	C₂×D₅₃	1	4	yes	complemented
641	C₂×#120	C₂×D₅₃	1	16	yes	complemented
642	#518	—	53	16	no	—
643	C₂×C₄×D₄	—	53	4	no	—
644	C₂×C₄×D₄	—	53	4	no	—
645	C₂×C₄×D₄	—	53	4	no	—
646	C₂×C₄×D₄	—	53	4	no	—
647	C₂×#117	—	53	2	no	—
648	C₂²×C₂²⋊C₄	—	53	1	no	—
649	C₂²×C₂²⋊C₄	—	53	2	no	—
650	C₂²×C₂²⋊C₄	—	53	2	no	—
651	C₂²×C₂²⋊C₄	—	53	4	no	—
652	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
653	C₂²×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
654	C₅₃	C₂×#3484	1	1	yes	characteristic, complemented, Sylow
655	C₂⁵	—	2	8	no	—
656	C₂⁵	—	4	8	no	—
657	C₂⁵	—	53	1	no	—
658	C₂⁵	—	53	4	no	—
659	C₂⁵	—	53	1	no	—
660	C₂⁵	—	53	8	no	—
661	C₂⁵	—	53	2	no	—
662	C₂⁵	—	53	1	no	—
663	C₂⁵	—	106	8	no	—
664	C₂⁵	—	212	8	no	—
665	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
666	C₂⁵	C₂²×D₅₃	1	2	yes	—
667	C₂⁵	C₂²×D₅₃	1	2	yes	—
668	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
669	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
670	C₂⁵	C₂²×D₅₃	1	8	yes	complemented
671	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic, complemented
672	H(5,𝔽₂)	—	106	128	no	—
673	C₂×#41	—	53	16	no	—
674	C₂×#41	—	53	16	no	—
675	C₂×#41	—	53	16	no	—
676	C₂×#41	—	106	16	no	—
677	C₂×#41	—	106	16	no	—
678	C₂×#41	—	106	16	no	—
679	C₂²×Q₈	—	53	2	no	—
680	C₂²×D₄	—	2	8	no	—
681	C₂²×D₄	—	4	8	no	—
682	C₂²×D₄	—	53	16	no	—
683	C₂²×D₄	—	53	2	no	—
684	C₂²×D₄	—	53	2	no	—
685	C₂²×D₄	—	53	8	no	—
686	C₂²×D₄	—	53	4	no	—
687	C₂²×D₄	—	53	2	no	—
688	C₂²×D₄	—	53	2	no	—
689	C₂²×D₄	—	53	2	no	—
690	C₂²×D₄	—	53	8	no	—
691	C₂²×D₄	—	53	4	no	—
692	C₂²×D₄	—	53	2	no	—
693	C₂²×D₄	—	53	2	no	—
694	C₂²×D₄	—	53	4	no	—
695	C₂²×D₄	—	53	2	no	—
696	C₂²×D₄	—	53	8	no	—
697	C₂²×D₄	—	53	8	no	—
698	C₂²×D₄	—	53	8	no	—
699	C₂²×D₄	—	53	32	no	—
700	C₂²×D₄	—	53	32	no	—
701	C₂²×D₄	—	53	16	no	—
702	C₂²×D₄	—	53	4	no	—
703	C₂²×D₄	—	53	4	no	—
704	C₂²×D₄	—	53	16	no	—
705	C₂²×D₄	—	53	16	no	—
706	C₂²×D₄	—	53	16	no	—
707	C₂²×D₄	—	53	32	no	—
708	C₂²×D₄	—	53	2	no	—
709	C₂²×D₄	—	53	4	no	—
710	C₂²×D₄	—	106	8	no	—
711	C₂²×D₄	—	106	16	no	—
712	C₂²×D₄	—	106	16	no	—
713	C₂²×D₄	—	106	32	no	—
714	C₂²×D₄	—	106	32	no	—
715	C₂²×D₄	—	106	128	no	—
716	C₂²×D₄	—	106	16	no	—
717	C₂²×D₄	—	106	8	no	—
718	C₂²×D₄	—	106	8	no	—
719	C₂²×D₄	—	106	8	no	—
720	C₂²×D₄	—	212	16	no	—
721	C₂²×D₄	—	212	8	no	—
722	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
723	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
724	C₂²×D₄	C₂²×D₅₃	1	2	yes	complemented
725	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
726	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
727	C₂²×D₄	C₂²×D₅₃	1	16	yes	complemented
728	C₂³×C₄	—	53	1	no	—
729	C₂³×C₄	—	53	1	no	—
730	C₂³×C₄	—	53	2	no	—
731	C₂³×C₄	—	53	4	no	—
732	C₂³×C₄	—	53	1	no	—
733	C₂³×C₄	—	53	8	no	—
734	C₂³×C₄	—	53	2	no	—
735	C₂³×C₄	—	53	2	no	—
736	C₂³×C₄	—	53	2	no	—
737	C₂³×C₄	—	53	4	no	—
738	C₂³×C₄	—	106	8	no	—
739	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
740	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
741	#127	—	53	32	no	—
742	#124	—	53	32	no	—
743	#123	—	53	16	no	—
744	#123	—	53	16	no	—
745	#123	—	53	16	no	—
746	#123	—	53	32	no	—
747	#123	—	53	16	no	—
748	C₂²⋊Q₈	—	53	32	no	—
749	#121	—	53	32	no	—
750	#121	—	53	32	no	—
751	#121	—	53	32	no	—
752	#121	—	53	32	no	—
753	#121	—	53	32	no	—
754	#121	—	53	32	no	—
755	#121	—	53	32	no	—
756	#120	—	53	16	no	—
757	#120	—	53	16	no	—
758	#120	—	53	32	no	—
759	#120	—	53	16	no	—
760	#120	—	53	16	no	—
761	#120	—	53	32	no	—
762	#120	—	53	32	no	—
763	#120	—	53	16	no	—
764	#120	—	53	32	no	—
765	#120	—	53	16	no	—
766	#120	C₂²×D₅₃	1	16	yes	complemented
767	#120	C₂²×D₅₃	1	16	yes	complemented
768	#120	C₂²×D₅₃	1	32	yes	complemented
769	C₄×D₄	—	53	32	no	—
770	C₄×D₄	—	53	32	no	—
771	C₄×D₄	—	53	32	no	—
772	C₄×D₄	—	53	32	no	—
773	#117	—	53	16	no	—
774	C₂×C₄⋊C₄	—	53	4	no	—
775	C₂×C₄⋊C₄	—	53	4	no	—
776	C₂×C₄⋊C₄	—	53	4	no	—
777	C₂×C₂²⋊C₄	—	53	2	no	—
778	C₂×C₂²⋊C₄	—	53	4	no	—
779	C₂×C₂²⋊C₄	—	53	2	no	—
780	C₂×C₂²⋊C₄	—	53	8	no	—
781	C₂×C₂²⋊C₄	—	53	4	no	—
782	C₂×C₂²⋊C₄	—	53	16	no	—
783	C₂×C₂²⋊C₄	—	53	4	no	—
784	C₂×C₂²⋊C₄	—	53	4	no	—
785	C₂×C₂²⋊C₄	—	53	4	no	—
786	C₂×C₂²⋊C₄	—	53	4	no	—
787	C₂×C₂²⋊C₄	—	53	4	no	—
788	C₂×C₂²⋊C₄	—	53	16	no	—
789	C₂×C₂²⋊C₄	—	53	32	no	—
790	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
792	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
793	C₂×C₂²⋊C₄	C₂²×D₅₃	1	16	yes	complemented
794	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
795	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
796	C₂×C₄²	—	53	4	no	—
797	C₂⁴	—	2	4	no	—
798	C₂⁴	—	2	8	no	—
799	C₂⁴	—	2	8	no	—
800	C₂⁴	—	2	8	no	—
801	C₂⁴	—	2	4	no	—
802	C₂⁴	—	2	32	no	—
803	C₂⁴	—	2	8	no	—
804	C₂⁴	—	2	8	no	—
805	C₂⁴	—	2	4	no	—
806	C₂⁴	—	4	4	no	—
807	C₂⁴	—	4	4	no	—
808	C₂⁴	—	4	4	no	—
809	C₂⁴	—	4	4	no	—
810	C₂⁴	—	4	32	no	—
811	C₂⁴	—	4	4	no	—
812	C₂⁴	—	4	64	no	—
813	C₂⁴	—	53	2	no	—
814	C₂⁴	—	53	8	no	—
815	C₂⁴	—	53	4	no	—
816	C₂⁴	—	53	2	no	—
817	C₂⁴	—	53	2	no	—
818	C₂⁴	—	53	16	no	—
819	C₂⁴	—	53	4	no	—
820	C₂⁴	—	53	8	no	—
821	C₂⁴	—	53	4	no	—
822	C₂⁴	—	106	8	no	—
823	C₂⁴	—	106	16	no	—
824	C₂⁴	—	106	32	no	—
825	C₂⁴	—	106	4	no	—
826	C₂⁴	—	106	4	no	—
827	C₂⁴	—	106	16	no	—
828	C₂⁴	—	212	4	no	—
829	C₂⁴	—	212	8	no	—
830	C₂⁴	—	212	4	no	—
831	C₂⁴	—	212	8	no	—
832	C₂⁴	—	212	4	no	—
833	C₂⁴	—	212	32	no	—
834	C₂⁴	—	212	64	no	—
835	C₂⁴	D₄×D₅₃	1	8	yes	complemented
836	C₂⁴	C₂³×D₅₃	1	4	yes	—
837	C₂⁴	C₂³×D₅₃	1	2	yes	—
838	C₂⁴	C₂³×D₅₃	1	2	yes	—
839	C₂⁴	C₂³×D₅₃	1	8	yes	—
840	C₂⁴	C₂³×D₅₃	1	8	yes	—
841	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
842	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
843	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
844	C₂⁴	C₂³×D₅₃	1	2	yes	—
845	C₂⁴	C₂³×D₅₃	1	4	yes	—
846	C₂⁴	C₂³×D₅₃	1	4	yes	—
847	C₂⁴	C₂³×D₅₃	1	4	yes	complemented
848	#41	—	106	64	no	—
849	#41	—	106	64	no	—
850	#41	—	106	64	no	—
851	C₂×Q₈	—	53	8	no	—
852	C₂×Q₈	—	106	8	no	—
853	C₂×D₄	—	2	8	no	—
854	C₂×D₄	—	2	8	no	—
855	C₂×D₄	—	2	32	no	—
856	C₂×D₄	—	2	16	no	—
857	C₂×D₄	—	4	8	no	—
858	C₂×D₄	—	4	32	no	—
859	C₂×D₄	—	53	16	no	—
860	C₂×D₄	—	53	16	no	—
861	C₂×D₄	—	53	64	no	—
862	C₂×D₄	—	53	8	no	—
863	C₂×D₄	—	53	8	no	—
864	C₂×D₄	—	53	16	no	—
865	C₂×D₄	—	53	8	no	—
866	C₂×D₄	—	53	16	no	—
867	C₂×D₄	—	53	8	no	—
868	C₂×D₄	—	53	8	no	—
869	C₂×D₄	—	53	16	no	—
870	C₂×D₄	—	53	8	no	—
871	C₂×D₄	—	53	8	no	—
872	C₂×D₄	—	53	8	no	—
873	C₂×D₄	—	53	16	no	—
874	C₂×D₄	—	53	16	no	—
875	C₂×D₄	—	53	8	no	—
876	C₂×D₄	—	53	16	no	—
877	C₂×D₄	—	106	8	no	—
878	C₂×D₄	—	106	16	no	—
879	C₂×D₄	—	106	32	no	—
880	C₂×D₄	—	106	8	no	—
881	C₂×D₄	—	106	64	no	—
882	C₂×D₄	—	106	64	no	—
883	C₂×D₄	—	106	128	no	—
884	C₂×D₄	—	106	128	no	—
885	C₂×D₄	—	106	64	no	—
886	C₂×D₄	—	106	16	no	—
887	C₂×D₄	—	106	32	no	—
888	C₂×D₄	—	106	8	no	—
889	C₂×D₄	—	106	8	no	—
890	C₂×D₄	—	106	8	no	—
891	C₂×D₄	—	106	8	no	—
892	C₂×D₄	—	106	8	no	—
893	C₂×D₄	—	106	32	no	—
894	C₂×D₄	—	106	32	no	—
895	C₂×D₄	—	106	16	no	—
896	C₂×D₄	—	212	8	no	—
897	C₂×D₄	—	212	8	no	—
898	C₂×D₄	—	212	8	no	—
899	C₂×D₄	—	212	64	no	—
900	C₂×D₄	—	212	32	no	—
901	C₂×D₄	C₂³×D₅₃	1	16	yes	—
902	C₂×D₄	C₂³×D₅₃	1	8	yes	—
903	C₂×D₄	C₂³×D₅₃	1	8	yes	complemented
904	C₂×D₄	C₂³×D₅₃	1	16	yes	complemented
905	C₂²×C₄	—	2	4	no	—
906	C₂²×C₄	—	4	4	no	—
907	C₂²×C₄	—	53	8	no	—
908	C₂²×C₄	—	53	4	no	—
909	C₂²×C₄	—	53	2	no	—
910	C₂²×C₄	—	53	16	no	—
911	C₂²×C₄	—	53	4	no	—
912	C₂²×C₄	—	53	4	no	—
913	C₂²×C₄	—	53	8	no	—
914	C₂²×C₄	—	53	4	no	—
915	C₂²×C₄	—	53	2	no	—
916	C₂²×C₄	—	53	2	no	—
917	C₂²×C₄	—	53	8	no	—
918	C₂²×C₄	—	53	8	no	—
919	C₂²×C₄	—	53	8	no	—
920	C₂²×C₄	—	53	16	no	—
921	C₂²×C₄	—	106	8	no	—
922	C₂²×C₄	—	106	8	no	—
923	C₂²×C₄	—	106	16	no	—
924	C₂²×C₄	—	106	32	no	—
925	C₂²×C₄	—	106	8	no	—
926	C₂²×C₄	—	106	4	no	—
927	C₂²×C₄	—	106	4	no	—
928	C₂²×C₄	—	212	8	no	—
929	C₂²×C₄	—	212	4	no	—
930	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
931	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
932	C₂²×C₄	C₂³×D₅₃	1	4	yes	complemented
933	C₂²×C₄	C₂³×D₅₃	1	8	yes	complemented
934	C₄⋊C₄	—	53	16	no	—
935	C₄⋊C₄	—	53	16	no	—
936	C₄⋊C₄	—	53	16	no	—
937	C₂²⋊C₄	—	53	8	no	—
938	C₂²⋊C₄	—	53	16	no	—
939	C₂²⋊C₄	—	53	8	no	—
940	C₂²⋊C₄	—	53	16	no	—
941	C₂²⋊C₄	—	53	16	no	—
942	C₂²⋊C₄	—	53	16	no	—
943	C₂²⋊C₄	—	53	16	no	—
944	C₂²⋊C₄	—	53	16	no	—
945	C₂²⋊C₄	—	53	16	no	—
946	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
947	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
948	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
949	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	complemented
950	C₄²	—	53	16	no	—
951	C₂³	—	2	32	no	—
952	C₂³	—	2	8	no	—
953	C₂³	—	2	4	no	—
954	C₂³	—	2	4	no	—
955	C₂³	—	2	4	no	—
956	C₂³	—	2	4	no	—
957	C₂³	—	2	4	no	—
958	C₂³	—	2	16	no	—
959	C₂³	—	2	4	no	—
960	C₂³	—	2	16	no	—
961	C₂³	—	2	16	no	—
962	C₂³	—	2	8	no	—
963	C₂³	—	2	4	no	—
964	C₂³	—	2	8	no	—
965	C₂³	—	2	4	no	—
966	C₂³	—	2	4	no	—
967	C₂³	—	2	16	no	—
968	C₂³	—	2	16	no	—
969	C₂³	—	2	8	no	—
970	C₂³	—	4	16	no	—
971	C₂³	—	4	8	no	—
972	C₂³	—	4	8	no	—
973	C₂³	—	4	8	no	—
974	C₂³	—	4	8	no	—
975	C₂³	—	4	8	no	—
976	C₂³	—	4	32	no	—
977	C₂³	—	4	32	no	—
978	C₂³	—	4	128	no	—
979	C₂³	—	4	16	no	—
980	C₂³	—	8	8	no	—
981	C₂³	—	53	8	no	—
982	C₂³	—	53	4	no	—
983	C₂³	—	53	16	no	—
984	C₂³	—	53	4	no	—
985	C₂³	—	53	4	no	—
986	C₂³	—	106	16	no	—
987	C₂³	—	106	32	no	—
988	C₂³	—	106	8	no	—
989	C₂³	—	106	8	no	—
990	C₂³	—	106	4	no	—
991	C₂³	—	106	8	no	—
992	C₂³	—	106	4	no	—
993	C₂³	—	106	8	no	—
994	C₂³	—	106	8	no	—
995	C₂³	—	106	32	no	—
996	C₂³	—	424	8	no	—
997	C₂³	—	424	16	no	—
998	C₂³	—	212	8	no	—
999	C₂³	—	212	16	no	—
1000	C₂³	—	212	16	no	—
1001	C₂³	—	212	8	no	—
1002	C₂³	—	212	16	no	—
1003	C₂³	—	212	8	no	—
1004	C₂³	—	212	64	no	—
1005	C₂³	—	212	128	no	—
1006	C₂³	—	212	16	no	—
1007	C₂³	C₂×D₄×D₅₃	1	4	yes	—
1008	C₂³	C₂×D₄×D₅₃	1	4	yes	—
1009	C₂³	C₂×D₄×D₅₃	1	4	yes	—
1010	C₂³	C₂×D₄×D₅₃	1	16	yes	complemented
1011	C₂³	#13133262	1	8	yes	complemented
1012	C₂³	C₂⁴×D₅₃	1	4	yes	—
1013	C₂³	C₂⁴×D₅₃	1	4	yes	—
1014	C₂³	C₂⁴×D₅₃	1	2	yes	—
1015	C₂³	C₂⁴×D₅₃	1	2	yes	—
1016	C₂³	C₂⁴×D₅₃	1	2	yes	—
1017	C₂³	C₂⁴×D₅₃	1	4	yes	—
1018	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1019	Q₈	—	106	16	no	—
1020	D₄	—	2	16	no	—
1021	D₄	—	2	16	no	—
1022	D₄	—	2	32	no	—
1023	D₄	—	4	16	no	—
1024	D₄	—	53	32	no	—
1025	D₄	—	53	32	no	—
1026	D₄	—	106	16	no	—
1027	D₄	—	106	32	no	—
1028	D₄	—	106	16	no	—
1029	D₄	—	106	32	no	—
1030	D₄	—	106	16	no	—
1031	D₄	—	106	16	no	—
1032	D₄	—	106	16	no	—
1033	D₄	—	106	16	no	—
1034	D₄	—	106	16	no	—
1035	D₄	—	106	32	no	—
1036	D₄	—	212	16	no	—
1037	D₄	—	212	16	no	—
1038	D₄	—	212	16	no	—
1039	C₂×C₄	—	2	4	no	—
1040	C₂×C₄	—	2	8	no	—
1041	C₂×C₄	—	2	8	no	—
1042	C₂×C₄	—	4	8	no	—
1043	C₂×C₄	—	53	8	no	—
1044	C₂×C₄	—	53	16	no	—
1045	C₂×C₄	—	53	4	no	—
1046	C₂×C₄	—	53	8	no	—
1047	C₂×C₄	—	53	4	no	—
1048	C₂×C₄	—	53	4	no	—
1049	C₂×C₄	—	106	16	no	—
1050	C₂×C₄	—	106	16	no	—
1051	C₂×C₄	—	106	32	no	—
1052	C₂×C₄	—	106	16	no	—
1053	C₂×C₄	—	106	8	no	—
1054	C₂×C₄	—	106	4	no	—
1055	C₂×C₄	—	106	4	no	—
1056	C₂×C₄	—	106	8	no	—
1057	C₂×C₄	—	106	8	no	—
1058	C₂×C₄	—	212	16	no	—
1059	C₂×C₄	—	212	8	no	—
1060	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1061	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1062	C₂²	—	2	32	no	—
1063	C₂²	—	2	8	no	—
1064	C₂²	—	2	16	no	—
1065	C₂²	—	2	8	no	—
1066	C₂²	—	2	8	no	—
1067	C₂²	—	2	4	no	—
1068	C₂²	—	2	4	no	—
1069	C₂²	—	2	4	no	—
1070	C₂²	—	2	4	no	—
1071	C₂²	—	2	4	no	—
1072	C₂²	—	2	4	no	—
1073	C₂²	—	2	4	no	—
1074	C₂²	—	2	8	no	—
1075	C₂²	—	2	4	no	—
1076	C₂²	—	2	4	no	—
1077	C₂²	—	4	16	no	—
1078	C₂²	—	4	32	no	—
1079	C₂²	—	4	32	no	—
1080	C₂²	—	4	16	no	—
1081	C₂²	—	4	8	no	—
1082	C₂²	—	4	8	no	—
1083	C₂²	—	8	8	no	—
1084	C₂²	—	53	8	no	—
1085	C₂²	—	106	16	no	—
1086	C₂²	—	106	8	no	—
1087	C₂²	—	106	4	no	—
1088	C₂²	—	106	4	no	—
1089	C₂²	—	106	8	no	—
1090	C₂²	—	106	8	no	—
1091	C₂²	—	424	8	no	—
1092	C₂²	—	424	16	no	—
1093	C₂²	—	212	16	no	—
1094	C₂²	—	212	64	no	—
1095	C₂²	—	212	16	no	—
1096	C₂²	—	212	8	no	—
1097	C₂²	—	212	8	no	—
1098	C₂²	C₂²×D₄×D₅₃	1	4	yes	—
1099	C₂²	C₂²×D₄×D₅₃	1	4	yes	—
1100	C₂²	C₂²×D₄×D₅₃	1	4	yes	—
1101	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1102	C₂²	C₂×#13133262	1	4	yes	—
1103	C₂²	C₂×#13133262	1	8	yes	complemented
1104	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1105	C₄	—	2	4	no	—
1106	C₄	—	2	8	no	—
1107	C₄	—	53	8	no	—
1108	C₄	—	106	4	no	—
1109	C₄	—	106	4	no	—
1110	C₄	—	106	8	no	—
1111	C₂	—	2	4	no	—
1112	C₂	—	2	8	no	—
1113	C₂	—	2	4	no	—
1114	C₂	—	2	4	no	—
1115	C₂	—	4	4	no	—
1116	C₂	—	4	4	no	—
1117	C₂	—	106	8	no	—
1118	C₂	—	212	4	no	—
1119	C₂	—	212	4	no	—
1120	C₂	#20288344	1	4	yes	direct product factor
1121	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1122	C₂	C₂²×#13133262	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂²×#120×C₅₃	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂²×#120	D₅₃
hypocenter	C₅₃	C₂×#3484
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂²×#120

Complements

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

N	H ≅ G/N	type
1. C₂²×#13133262	C₂	semidirect
2. C₂⁴×C₂²⋊D₅₃	C₂	semidirect
3. #20288344	C₂	direct (N × H)
4. C₂×#16811263	C₂	semidirect
5. C₂×#16811260	C₂	semidirect
6. C₂×D₄×C₂²⋊D₅₃	C₂	semidirect
7. C₂×#16811255	C₂	semidirect
8. C₂×#16811188	C₂	semidirect
9. C₂×#16811185	C₂	semidirect
10. C₂×#16811183	C₂	semidirect
11. C₂×#16811182	C₂	semidirect
12. C₂×#16811129	C₂	semidirect
13. C₂²×#13133186	C₂	semidirect
14. C₂×#120×D₅₃	C₂	semidirect
15. C₂×#16811096	C₂	semidirect
16. C₂²×#120×C₅₃	C₂	semidirect
17. C₂⁵×D₅₃	C₂²	semidirect
19. C₂×#13133262	C₂²	semidirect
20. C₂²×#11719945	C₂²	semidirect
21. C₂²×#11719947	C₂²	semidirect
22. C₂²×#11719947	C₂²	semidirect
25. C₂³×C₂²⋊D₅₃	C₂²	semidirect
26. C₂³×C₂²⋊D₅₃	C₂²	semidirect
27. C₂³×C₂²⋊D₅₃	C₂²	semidirect
28. C₂³×C₂²⋊D₅₃	C₂²	semidirect
29. C₂³×C₂²⋊D₅₃	C₂²	semidirect
30. C₂³×C₂²⋊D₅₃	C₂²	semidirect
31. C₂³×C₂²⋊D₅₃	C₂²	semidirect
32. C₂³×C₂²⋊D₅₃	C₂²	semidirect
33. C₂³×C₂²⋊D₅₃	C₂²	semidirect
34. C₂²×D₄×D₅₃	C₂²	semidirect
35. C₂²×D₄×D₅₃	C₂²	semidirect
36. C₂²×D₄×D₅₃	C₂²	semidirect
37. C₂⁴×Dic₅₃	C₂²	semidirect
38. #16811263	C₂²	semidirect
39. #16811260	C₂²	semidirect
40. D₄×C₂²⋊D₅₃	C₂²	semidirect
41. #16811255	C₂²	semidirect
42. #16811188	C₂²	semidirect
43. #16811185	C₂²	semidirect
44. #16811183	C₂²	semidirect
45. #16811182	C₂²	semidirect
46. C₂×#13133213	C₂²	semidirect
47. C₂×#13133203	C₂²	semidirect
48. #16811129	C₂²	semidirect
49. C₂×#13133201	C₂²	semidirect
50. C₂×#13133201	C₂²	semidirect
51. C₂×#13133200	C₂²	semidirect
52. C₂×#13133199	C₂²	semidirect
53. C₂×#13133198	C₂²	semidirect
54. C₂×#13133194	C₂²	semidirect
55. C₂×#13133191	C₂²	semidirect
56. C₂×#13133190	C₂²	semidirect
57. C₂×#13133190	C₂²	semidirect
58. C₂×#13133189	C₂²	semidirect
59. C₂×#13133189	C₂²	semidirect
60. C₂×#13133189	C₂²	semidirect
61. C₂×#13133188	C₂²	semidirect
62. C₂×#13133187	C₂²	semidirect
63. C₂×#13133187	C₂²	semidirect
64. C₂×#13133187	C₂²	semidirect
65. C₂×#13133186	C₂²	semidirect
66. C₂×#13133186	C₂²	semidirect
67. C₂×#13133186	C₂²	semidirect
68. C₂×#13133186	C₂²	semidirect
69. C₂×#13133186	C₂²	semidirect
70. C₂×#13133185	C₂²	semidirect
71. C₂×#13133185	C₂²	semidirect
72. C₂×#13133185	C₂²	semidirect
73. #120×D₅₃	C₂²	semidirect
74. #16811096	C₂²	semidirect
75. C₂×D₄×Dic₅₃	C₂²	semidirect
76. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
77. C₂×#13133177	C₂²	semidirect
78. C₂×#13133177	C₂²	semidirect
79. C₂×#13133173	C₂²	semidirect
80. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
81. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
82. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
83. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
84. C₂⁶×C₅₃	C₂²	semidirect
85. C₂³×D₄×C₅₃	C₂²	semidirect
86. C₂³×D₄×C₅₃	C₂²	semidirect
87. C₂×#120×C₅₃	C₂²	semidirect
88. C₂×#120×C₅₃	C₂²	semidirect
89. C₂×#120×C₅₃	C₂²	semidirect
90. C₂×#120×C₅₃	C₂²	semidirect
91. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
92. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
98. C₂⁴×D₅₃	C₂³	semidirect
99. C₂⁴×D₅₃	C₂³	semidirect
100. C₂⁴×D₅₃	C₂³	semidirect
103. C₂×#11719945	C₂³	semidirect
106. C₂×#11719947	C₂³	semidirect
107. C₂×#11719947	C₂³	semidirect
108. C₂²×Dic₁₀₆	C₂³	semidirect
109. C₂²×D₂₁₂	C₂³	semidirect
110. C₂²×D₂₁₂	C₂³	semidirect
120. C₂²×C₂²⋊D₅₃	D₄	semidirect
130. C₂²×C₂²⋊D₅₃	C₂³	semidirect
131. C₂²×C₂²⋊D₅₃	C₂³	semidirect
132. C₂²×C₂²⋊D₅₃	C₂³	semidirect
133. C₂²×C₂²⋊D₅₃	C₂³	semidirect
134. C₂²×C₂²⋊D₅₃	C₂³	semidirect
135. C₂²×C₂²⋊D₅₃	C₂³	semidirect
136. C₂²×C₂²⋊D₅₃	C₂³	semidirect
137. C₂²×C₂²⋊D₅₃	C₂³	semidirect
138. C₂²×C₂²⋊D₅₃	C₂³	semidirect
139. C₂²×C₂²⋊D₅₃	C₂³	semidirect
140. C₂²×C₂²⋊D₅₃	C₂³	semidirect
141. C₂²×C₂²⋊D₅₃	C₂³	semidirect
142. C₂²×C₂²⋊D₅₃	C₂³	semidirect
146. C₂×D₄×D₅₃	C₂³	semidirect
147. C₂×D₄×D₅₃	C₂³	semidirect
148. C₂×D₄×D₅₃	C₂³	semidirect
153. C₂³×Dic₅₃	C₂³	semidirect
154. C₂³×Dic₅₃	C₂³	semidirect
155. C₂³×Dic₅₃	C₂³	semidirect
156. C₂³×Dic₅₃	C₂³	semidirect
157. C₂²×C₄×D₅₃	C₂³	semidirect
158. C₂²×C₄×D₅₃	C₂³	semidirect
159. C₂²×C₄×D₅₃	C₂³	semidirect
160. #13133213	C₂³	semidirect
161. #13133203	C₂³	semidirect
162. #13133201	C₂³	semidirect
163. #13133201	C₂³	semidirect
164. #13133200	C₂³	semidirect
165. #13133199	C₂³	semidirect
166. #13133198	C₂³	semidirect
167. #13133194	C₂³	semidirect
168. #13133191	C₂³	semidirect
169. #13133190	C₂³	semidirect
170. #13133190	C₂³	semidirect
171. #13133189	C₂³	semidirect
172. #13133189	C₂³	semidirect
173. #13133189	C₂³	semidirect
174. #13133188	C₂³	semidirect
175. #13133187	C₂³	semidirect
176. #13133187	C₂³	semidirect
177. #13133187	C₂³	semidirect
178. #13133186	C₂³	semidirect
179. #13133186	C₂³	semidirect
180. #13133186	C₂³	semidirect
181. #13133186	C₂³	semidirect
182. #13133185	C₂³	semidirect
183. #13133185	C₂³	semidirect
184. #13133185	C₂³	semidirect
185. D₄×Dic₅₃	C₂³	semidirect
186. C₄×C₂²⋊D₅₃	C₂³	semidirect
187. #13133177	C₂³	semidirect
188. #13133177	C₂³	semidirect
189. #13133173	C₂³	semidirect
190. C₂×C₄⋊Dic₅₃	C₂³	semidirect
191. C₂×#11719919	C₂³	semidirect
192. C₂×#11719919	C₂³	semidirect
195. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
196. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
197. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
198. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
199. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
200. C₂×#11719921	C₂³	semidirect
201. C₂×#11719921	C₂³	semidirect
202. C₂×#11719921	C₂³	semidirect
203. C₂×#11719921	C₂³	semidirect
204. C₂²⋊C₄×D₅₃	C₂³	semidirect
205. C₂²⋊C₄×D₅₃	C₂³	semidirect
206. C₂×C₄×Dic₅₃	C₂³	semidirect
214. C₂⁵×C₅₃	C₂³	semidirect
215. C₂⁵×C₅₃	C₂³	semidirect
220. C₂²×D₄×C₅₃	C₂³	semidirect
221. C₂²×D₄×C₅₃	C₂³	semidirect
222. C₂²×D₄×C₅₃	C₂³	semidirect
223. C₂²×D₄×C₅₃	C₂³	semidirect
224. C₂³×C₄×C₅₃	C₂³	semidirect
225. C₂³×C₄×C₅₃	C₂³	semidirect
226. #120×C₅₃	C₂³	semidirect
227. #120×C₅₃	C₂³	semidirect
228. #120×C₅₃	C₂³	semidirect
231. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
232. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
233. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
234. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
251. C₂⁴×C₅₃	C₂×D₄	semidirect
263. C₂⁴×C₅₃	C₂⁴	semidirect
277. C₂³×D₅₃	C₂×D₄	semidirect
284. C₂³×D₅₃	C₂⁴	semidirect
285. C₂³×D₅₃	C₂⁴	semidirect
294. C₂×D₄×C₅₃	C₂⁴	semidirect
295. C₂×D₄×C₅₃	C₂⁴	semidirect
300. C₂²×C₄×C₅₃	C₂⁴	semidirect
301. C₂²×C₄×C₅₃	C₂⁴	semidirect
321. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
322. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
323. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
332. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
333. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
334. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
335. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
336. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
343. C₂²×Dic₅₃	C₂×D₄	semidirect
351. C₂²×Dic₅₃	C₂⁴	semidirect
352. C₂²×Dic₅₃	C₂⁴	semidirect
353. C₂²×Dic₅₃	C₂⁴	semidirect
362. C₂×D₂₁₂	C₂⁴	semidirect
363. C₂×D₂₁₂	C₂⁴	semidirect
367. C₂×C₄×D₅₃	C₂⁴	semidirect
368. C₂×C₄×D₅₃	C₂⁴	semidirect
369. C₂×C₄×D₅₃	C₂⁴	semidirect
371. C₂×Dic₁₀₆	C₂⁴	semidirect
374. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
375. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
378. C₂²⋊Dic₅₃	C₂⁴	semidirect
379. C₂²⋊Dic₅₃	C₂⁴	semidirect
380. C₂²⋊Dic₅₃	C₂⁴	semidirect
381. #11719921	C₂⁴	semidirect
382. #11719921	C₂⁴	semidirect
383. #11719921	C₂⁴	semidirect
384. #11719921	C₂⁴	semidirect
385. C₄⋊Dic₅₃	C₂⁴	semidirect
386. #11719919	C₂⁴	semidirect
387. #11719919	C₂⁴	semidirect
388. C₄×Dic₅₃	C₂⁴	semidirect
422. C₂³×C₅₃	C₂²×D₄	semidirect
423. C₂³×C₅₃	H(5,𝔽₂)	semidirect
453. C₂²×D₅₃	C₂²×D₄	semidirect
478. C₂²⋊D₅₃	C₂²×D₄	semidirect
479. C₂²⋊D₅₃	C₂²×D₄	semidirect
489. C₂×Dic₅₃	C₂²×D₄	semidirect
528. C₂²×C₅₃	C₂×H(5,𝔽₂)	semidirect
564. C₂²×#120	D₅₃	semidirect
572. C₂×C₅₃	#3484	semidirect
579. C₂⁶	C₂×D₅₃	semidirect
599. C₂³×D₄	C₂×D₅₃	semidirect
600. C₂³×D₄	C₂×D₅₃	semidirect
638. C₂×#120	C₂×D₅₃	semidirect
639. C₂×#120	C₂×D₅₃	semidirect
640. C₂×#120	C₂×D₅₃	semidirect
641. C₂×#120	C₂×D₅₃	semidirect
652. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
653. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
654. C₅₃	C₂×#3484	semidirect
670. C₂⁵	C₂²×D₅₃	semidirect
671. C₂⁵	C₂²×D₅₃	semidirect
724. C₂²×D₄	C₂²×D₅₃	semidirect
725. C₂²×D₄	C₂²×D₅₃	semidirect
726. C₂²×D₄	C₂²×D₅₃	semidirect
727. C₂²×D₄	C₂²×D₅₃	semidirect
739. C₂³×C₄	C₂²×D₅₃	semidirect
740. C₂³×C₄	C₂²×D₅₃	semidirect
766. #120	C₂²×D₅₃	semidirect
767. #120	C₂²×D₅₃	semidirect
768. #120	C₂²×D₅₃	semidirect
792. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
793. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
794. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
795. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
835. C₂⁴	D₄×D₅₃	semidirect
847. C₂⁴	C₂³×D₅₃	semidirect
903. C₂×D₄	C₂³×D₅₃	semidirect
904. C₂×D₄	C₂³×D₅₃	semidirect
932. C₂²×C₄	C₂³×D₅₃	semidirect
933. C₂²×C₄	C₂³×D₅₃	semidirect
948. C₂²⋊C₄	C₂³×D₅₃	semidirect
949. C₂²⋊C₄	C₂³×D₅₃	semidirect
1010. C₂³	C₂×D₄×D₅₃	semidirect
1011. C₂³	#13133262	semidirect
1103. C₂²	C₂×#13133262	semidirect
1120. C₂	#20288344	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13133262	2
C₂⁴×C₂²⋊D₅₃	2
#20288344	2
C₂×#16811263	2
C₂×#16811260	2
C₂×D₄×C₂²⋊D₅₃	2
C₂×#16811255	2
C₂×#16811188	2
C₂×#16811185	2
C₂×#16811183	2
C₂×#16811182	2
C₂×#16811129	2
C₂²×#13133186	2
C₂×#120×D₅₃	2
C₂×#16811096	2
C₂²×#120×C₅₃	2
C₂×#3484	53

Subgroups — C2×#20288344 #28291969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20288344 #28291969