Subgroups — C₂×#525×D₅₃ #28290743

Order 13568.

14334 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811136	C₂	1	2	yes	maximal, complemented
4	C₂×#16811135	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16811134	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16811133	C₂	1	2	yes	maximal, complemented
7	C₂×#16811132	C₂	1	4	yes	maximal, complemented
8	C₂×#16811131	C₂	1	2	yes	maximal, complemented
9	C₂×#16811130	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811129	C₂	1	2	yes	maximal, complemented
11	#525×D₅₃	C₂	1	32	yes	maximal, direct product factor
12	C₂×#123×D₅₃	C₂	1	2	yes	maximal, complemented
13	C₂×C₂²⋊Q₈×D₅₃	C₂	1	2	yes	maximal, complemented
14	C₂×#121×D₅₃	C₂	1	2	yes	maximal, complemented
15	C₂×#120×D₅₃	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×D₄×D₅₃	C₂	1	4	yes	maximal, complemented
17	C₂×#117×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂⁵×D₅₃	C₂²	1	1	yes	characteristic
20	C₂²×#11719949	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#11719945	C₂²	1	2	yes	complemented
23	C₂²×#11719947	C₂²	1	2	yes	complemented
24	C₂²×#11719947	C₂²	1	1	yes	characteristic, complemented
25	C₂×#41×D₅₃	—	2	16	no	—
26	C₂×#41×D₅₃	C₂²	1	16	yes	complemented
27	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₄×D₅₃	C₂²	1	4	yes	—
29	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
30	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂³×C₄×D₅₃	—	2	16	no	—
33	C₂³×C₄×D₅₃	C₂²	1	2	yes	—
34	C₂³×C₄×D₅₃	C₂²	1	2	yes	—
35	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
36	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
37	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
40	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
41	C₂³×C₄×D₅₃	C₂²	1	16	yes	complemented
42	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
43	#16811136	C₂²	1	32	yes	complemented
44	#16811135	C₂²	1	16	yes	complemented
45	#16811134	C₂²	1	16	yes	complemented
46	#16811133	C₂²	1	32	yes	complemented
47	#16811132	C₂²	1	64	yes	complemented
48	#16811131	C₂²	1	32	yes	complemented
49	#16811130	C₂²	1	16	yes	complemented
50	#16811129	C₂²	1	32	yes	complemented
51	C₂×#13133202	C₂²	1	4	yes	complemented
52	C₂×#13133201	C₂²	1	2	yes	complemented
53	C₂×#13133200	C₂²	1	2	yes	complemented
54	C₂×#13133199	C₂²	1	4	yes	complemented
55	C₂×#13133198	C₂²	1	2	yes	complemented
56	#123×D₅₃	C₂²	1	32	yes	complemented
57	C₂×#13133197	C₂²	1	2	yes	complemented
58	C₂×#13133196	C₂²	1	2	yes	complemented
59	C₂×#13133195	C₂²	1	4	yes	complemented
60	C₂×#13133194	C₂²	1	4	yes	complemented
61	C₂×#13133193	C₂²	1	2	yes	complemented
62	C₂²⋊Q₈×D₅₃	C₂²	1	32	yes	complemented
63	C₂×#13133192	C₂²	1	2	yes	complemented
64	C₂×#13133191	C₂²	1	2	yes	complemented
65	C₂×#13133190	C₂²	1	4	yes	complemented
66	C₂×#13133189	C₂²	1	4	yes	complemented
67	C₂×#13133188	C₂²	1	2	yes	complemented
68	#121×D₅₃	C₂²	1	32	yes	complemented
69	C₂×#13133187	C₂²	1	2	yes	complemented
70	C₂×#13133187	C₂²	1	4	yes	complemented
71	C₂×#13133186	C₂²	1	2	yes	complemented
72	C₂×#13133185	C₂²	1	2	yes	complemented
73	C₂×#13133185	C₂²	1	4	yes	complemented
74	#120×D₅₃	C₂²	1	32	yes	complemented
75	C₂×C₄×D₂₁₂	C₂²	1	4	yes	complemented
76	C₂×D₄×Dic₅₃	C₂²	1	4	yes	complemented
77	C₂×#13133179	C₂²	1	4	yes	complemented
78	C₂×C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
79	C₂×C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
80	C₂×#13133177	C₂²	1	4	yes	complemented
81	C₂×#13133177	C₂²	1	4	yes	complemented
82	C₄×D₄×D₅₃	C₂²	1	64	yes	complemented
83	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
84	C₂×#13133175	C₂²	1	2	yes	complemented
85	C₂×#13133174	C₂²	1	2	yes	complemented
86	C₂×#13133173	C₂²	1	2	yes	complemented
87	#117×D₅₃	C₂²	1	16	yes	complemented
88	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
89	C₂×C₄⋊C₄×D₅₃	C₂²	1	4	yes	complemented
90	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
91	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	—
92	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
93	C₂×C₄²×D₅₃	C₂²	1	2	yes	complemented
94	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
95	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#525	C₂²	1	16	yes	complemented
97	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
98	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
99	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
100	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
101	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
102	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
103	C₂⁴×D₅₃	—	2	8	no	—
104	C₂⁴×D₅₃	—	2	16	no	—
105	C₂⁴×D₅₃	C₂³	1	2	yes	—
106	C₂⁴×D₅₃	C₂³	1	8	yes	—
107	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
108	C₂⁴×D₅₃	C₂³	1	2	yes	—
109	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
110	C₂⁴×D₅₃	C₂³	1	2	yes	—
111	C₂×#11719949	—	2	8	no	—
112	C₂×#11719949	C₂³	1	8	yes	complemented
113	C₂×#11719945	—	2	8	no	—
114	C₂×#11719945	—	2	16	no	—
115	C₂×#11719945	C₂³	1	16	yes	complemented
116	C₂×#11719945	C₂³	1	8	yes	complemented
117	C₂×#11719947	—	2	16	no	—
118	C₂×#11719947	—	2	8	no	—
119	C₂×#11719947	C₂³	1	8	yes	complemented
120	C₂×#11719947	C₂³	1	16	yes	complemented
121	#41×D₅₃	—	2	128	no	—
122	C₂²×Dic₁₀₆	C₂³	1	2	yes	complemented
123	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
124	C₂×Q₈×D₅₃	—	2	8	no	—
125	C₂×Q₈×D₅₃	C₂³	1	8	yes	complemented
126	C₂²×D₂₁₂	C₂³	1	4	yes	—
127	C₂²×D₂₁₂	C₂³	1	2	yes	—
128	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
129	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
130	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
131	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
132	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
133	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
134	C₂×D₄×D₅₃	—	2	16	no	—
135	C₂×D₄×D₅₃	—	2	32	no	—
136	C₂×D₄×D₅₃	—	2	8	no	—
137	C₂×D₄×D₅₃	C₂³	1	32	yes	—
138	C₂×D₄×D₅₃	C₂³	1	16	yes	—
139	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
140	C₂³×Dic₅₃	—	2	8	no	—
141	C₂³×Dic₅₃	C₂³	1	2	yes	—
142	C₂³×Dic₅₃	C₂³	1	2	yes	—
143	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
144	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
145	C₂³×Dic₅₃	C₂³	1	8	yes	complemented
146	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
147	C₂²×C₄×D₅₃	—	2	8	no	—
148	C₂²×C₄×D₅₃	—	2	8	no	—
149	C₂²×C₄×D₅₃	—	2	8	no	—
150	C₂²×C₄×D₅₃	—	2	16	no	—
151	C₂²×C₄×D₅₃	—	2	16	no	—
152	C₂²×C₄×D₅₃	—	2	16	no	—
153	C₂²×C₄×D₅₃	—	2	16	no	—
154	C₂²×C₄×D₅₃	—	2	16	no	—
155	C₂²×C₄×D₅₃	—	2	128	no	—
156	C₂²×C₄×D₅₃	D₄	1	16	yes	complemented
157	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
158	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
159	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
160	C₂²×C₄×D₅₃	C₂³	1	16	yes	—
161	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
162	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
163	C₂²×C₄×D₅₃	C₂³	1	16	yes	—
164	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
165	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
166	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
167	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
168	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
169	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
170	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
171	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
172	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
173	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
174	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
175	C₂²×C₄×D₅₃	C₂³	1	16	yes	complemented
176	C₂²×C₄×D₅₃	C₂³	1	16	yes	complemented
177	C₂²×C₄×D₅₃	C₂³	1	16	yes	complemented
178	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
179	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
180	#13133202	C₂³	1	32	yes	complemented
181	#13133201	C₂³	1	16	yes	complemented
182	#13133200	C₂³	1	16	yes	complemented
183	#13133199	C₂³	1	32	yes	complemented
184	#13133198	C₂³	1	16	yes	complemented
185	#13133197	C₂³	1	16	yes	complemented
186	#13133196	C₂³	1	16	yes	complemented
187	#13133195	C₂³	1	32	yes	complemented
188	#13133194	C₂³	1	32	yes	complemented
189	#13133193	C₂³	1	16	yes	complemented
190	#13133192	C₂³	1	16	yes	complemented
191	#13133191	C₂³	1	16	yes	complemented
192	#13133190	C₂³	1	32	yes	complemented
193	#13133189	C₂³	1	32	yes	complemented
194	#13133188	C₂³	1	16	yes	complemented
195	#13133187	C₂³	1	16	yes	complemented
196	#13133187	C₂³	1	32	yes	complemented
197	#13133186	C₂³	1	16	yes	complemented
198	#13133185	C₂³	1	16	yes	complemented
199	#13133185	C₂³	1	32	yes	complemented
200	C₄×D₂₁₂	C₂³	1	32	yes	complemented
201	D₄×Dic₅₃	C₂³	1	32	yes	complemented
202	#13133179	C₂³	1	32	yes	complemented
203	C₄×C₂²⋊D₅₃	C₂³	1	32	yes	complemented
204	C₄×C₂²⋊D₅₃	C₂³	1	32	yes	complemented
205	#13133177	C₂³	1	32	yes	complemented
206	#13133177	C₂³	1	32	yes	complemented
207	#13133176	C₂³	1	8	yes	complemented
208	#13133175	C₂³	1	16	yes	complemented
209	#13133174	C₂³	1	16	yes	complemented
210	#13133173	C₂³	1	16	yes	complemented
211	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
212	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
213	C₂×#11719919	C₂³	1	4	yes	complemented
214	C₂×#11719919	C₂³	1	4	yes	complemented
215	C₂×#11719919	C₂³	1	4	yes	complemented
216	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
217	C₄⋊C₄×D₅₃	C₂³	1	32	yes	complemented
218	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
219	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
220	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
221	C₂×#11719921	C₂³	1	4	yes	—
222	C₂×#11719921	C₂³	1	4	yes	—
223	C₂×#11719921	C₂³	1	4	yes	—
224	C₂×#11719921	C₂³	1	4	yes	complemented
225	C₂×#11719921	C₂³	1	4	yes	complemented
226	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
227	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	—
228	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	complemented
229	C₂×C₄×Dic₅₃	C₂³	1	4	yes	complemented
230	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
231	C₄²×D₅₃	C₂³	1	16	yes	complemented
232	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×#41×C₅₃	—	2	8	no	—
234	C₂×#41×C₅₃	C₂³	1	8	yes	complemented
235	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
236	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
237	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
238	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
239	C₂³×C₄×C₅₃	—	2	8	no	—
240	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
241	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
242	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₂³×C₄×C₅₃	C₂³	1	8	yes	complemented
245	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
246	#123×C₅₃	C₂³	1	16	yes	complemented
247	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
248	#121×C₅₃	C₂³	1	16	yes	complemented
249	#120×C₅₃	C₂³	1	16	yes	complemented
250	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
251	#117×C₅₃	C₂³	1	8	yes	complemented
252	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
253	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
254	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
255	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
256	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
257	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
258	C₂⁴×C₅₃	—	2	4	no	—
259	C₂⁴×C₅₃	—	2	8	no	—
260	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
261	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
262	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
264	C₂³×D₅₃	—	2	128	no	—
265	C₂³×D₅₃	—	2	4	no	—
266	C₂³×D₅₃	—	2	8	no	—
267	C₂³×D₅₃	—	2	8	no	—
268	C₂³×D₅₃	—	2	32	no	—
269	C₂³×D₅₃	—	2	8	no	—
270	C₂³×D₅₃	—	2	8	no	—
271	C₂³×D₅₃	—	2	8	no	—
272	C₂³×D₅₃	—	2	8	no	—
273	C₂³×D₅₃	—	2	8	no	—
274	C₂³×D₅₃	—	2	64	no	—
275	C₂³×D₅₃	—	2	8	no	—
276	C₂³×D₅₃	—	2	16	no	—
277	C₂³×D₅₃	C₂×D₄	1	8	yes	—
278	C₂³×D₅₃	#41	1	16	yes	complemented
279	C₂³×D₅₃	C₂⁴	1	8	yes	—
280	C₂³×D₅₃	C₂⁴	1	2	yes	—
281	C₂³×D₅₃	C₂⁴	1	4	yes	—
282	C₂³×D₅₃	C₂⁴	1	8	yes	—
283	C₂³×D₅₃	C₂⁴	1	4	yes	—
284	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
285	C₂³×D₅₃	C₂⁴	1	8	yes	—
286	C₂³×D₅₃	C₂⁴	1	2	yes	—
287	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
288	#41×C₅₃	—	2	32	no	—
289	C₂×Q₈×C₅₃	—	2	4	no	—
290	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	complemented
291	C₂×D₄×C₅₃	—	2	8	no	—
292	C₂×D₄×C₅₃	—	2	16	no	—
293	C₂×D₄×C₅₃	—	2	4	no	—
294	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
295	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
296	C₂×D₄×C₅₃	C₂⁴	1	4	yes	complemented
297	C₂²×C₄×C₅₃	—	2	4	no	—
298	C₂²×C₄×C₅₃	—	2	8	no	—
299	C₂²×C₄×C₅₃	—	2	8	no	—
300	C₂²×C₄×C₅₃	—	2	8	no	—
301	C₂²×C₄×C₅₃	—	2	32	no	—
302	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	complemented
303	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
304	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
307	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
308	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
309	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
312	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	complemented
313	C₂×C₂²⋊D₅₃	—	2	8	no	—
314	C₂×C₂²⋊D₅₃	—	2	16	no	—
315	C₂×C₂²⋊D₅₃	—	2	8	no	—
316	C₂×C₂²⋊D₅₃	—	2	16	no	—
317	C₂×C₂²⋊D₅₃	—	2	8	no	—
318	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
319	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
320	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
321	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
322	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
323	C₂²×Dic₅₃	—	2	4	no	—
324	C₂²×Dic₅₃	—	2	8	no	—
325	C₂²×Dic₅₃	—	2	8	no	—
326	C₂²×Dic₅₃	—	2	8	no	—
327	C₂²×Dic₅₃	—	2	32	no	—
328	C₂²×Dic₅₃	C₂×D₄	1	8	yes	complemented
329	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
330	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
331	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
332	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
333	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
334	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
335	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
336	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
337	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
338	C₂²×Dic₅₃	C₂⁴	1	8	yes	complemented
339	#11719949	—	2	32	no	—
340	Q₈×D₅₃	—	2	32	no	—
341	#11719947	—	2	64	no	—
342	#11719947	—	2	32	no	—
343	D₄×D₅₃	—	2	64	no	—
344	D₄×D₅₃	—	2	128	no	—
345	D₄×D₅₃	—	2	32	no	—
346	#11719945	—	2	32	no	—
347	#11719945	—	2	64	no	—
348	C₂×D₂₁₂	—	2	8	no	—
349	C₂×D₂₁₂	—	2	16	no	—
350	C₂×D₂₁₂	—	2	4	no	—
351	C₂×D₂₁₂	C₂⁴	1	16	yes	—
352	C₂×D₂₁₂	C₂⁴	1	8	yes	—
353	C₂×D₂₁₂	C₂⁴	1	4	yes	complemented
354	C₂×C₄×D₅₃	—	2	8	no	—
355	C₂×C₄×D₅₃	—	2	32	no	—
356	C₂×C₄×D₅₃	—	2	8	no	—
357	C₂×C₄×D₅₃	—	2	8	no	—
358	C₂×C₄×D₅₃	—	2	16	no	—
359	C₂×C₄×D₅₃	—	2	8	no	—
360	C₂×C₄×D₅₃	—	2	8	no	—
361	C₂×C₄×D₅₃	—	2	8	no	—
362	C₂×C₄×D₅₃	—	2	32	no	—
363	C₂×C₄×D₅₃	—	2	8	no	—
364	C₂×C₄×D₅₃	—	2	8	no	—
365	C₂×C₄×D₅₃	—	2	8	no	—
366	C₂×C₄×D₅₃	—	2	32	no	—
367	C₂×C₄×D₅₃	—	2	64	no	—
368	C₂×C₄×D₅₃	—	2	64	no	—
369	C₂×C₄×D₅₃	—	2	64	no	—
370	C₂×C₄×D₅₃	—	2	64	no	—
371	C₂×C₄×D₅₃	—	2	64	no	—
372	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	—
373	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	—
374	C₂×C₄×D₅₃	C₂×D₄	1	64	yes	complemented
375	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	complemented
376	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	complemented
377	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
378	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
379	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
380	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
381	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
382	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
383	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
384	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
385	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
386	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
387	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
388	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
389	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
390	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
391	C₂×Dic₁₀₆	—	2	4	no	—
392	C₂×Dic₁₀₆	—	2	8	no	—
393	C₂×Dic₁₀₆	C₂⁴	1	8	yes	complemented
394	C₂×Dic₁₀₆	C₂⁴	1	4	yes	complemented
395	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
396	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
397	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
398	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
399	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
400	C₄²×C₅₃	C₂⁴	1	8	yes	complemented
401	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
402	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
403	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
404	#11719921	C₂⁴	1	16	yes	—
405	#11719921	C₂⁴	1	16	yes	—
406	#11719921	C₂⁴	1	16	yes	—
407	#11719921	C₂⁴	1	16	yes	complemented
408	#11719921	C₂⁴	1	16	yes	complemented
409	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
410	C₄⋊Dic₅₃	C₂⁴	1	16	yes	complemented
411	#11719919	C₂⁴	1	16	yes	complemented
412	#11719919	C₂⁴	1	16	yes	complemented
413	#11719919	C₂⁴	1	16	yes	complemented
414	C₄×Dic₅₃	C₂⁴	1	16	yes	complemented
415	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
416	C₂³×C₅₃	—	2	32	no	—
417	C₂³×C₅₃	—	2	8	no	—
418	C₂³×C₅₃	—	2	4	no	—
419	C₂³×C₅₃	—	2	4	no	—
420	C₂³×C₅₃	—	2	4	no	—
421	C₂³×C₅₃	—	2	16	no	—
422	C₂³×C₅₃	—	2	4	no	—
423	C₂³×C₅₃	—	2	8	no	—
424	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
425	C₂³×C₅₃	C₂×#41	1	8	yes	complemented
426	C₂³×C₅₃	C₂⁵	1	4	yes	—
427	C₂³×C₅₃	C₂⁵	1	2	yes	—
428	C₂³×C₅₃	C₂⁵	1	4	yes	—
429	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
430	C₂²×D₅₃	—	2	64	no	—
431	C₂²×D₅₃	—	2	32	no	—
432	C₂²×D₅₃	—	2	256	no	—
433	C₂²×D₅₃	—	2	8	no	—
434	C₂²×D₅₃	—	2	4	no	—
435	C₂²×D₅₃	—	2	4	no	—
436	C₂²×D₅₃	—	2	4	no	—
437	C₂²×D₅₃	—	2	16	no	—
438	C₂²×D₅₃	—	2	32	no	—
439	C₂²×D₅₃	—	2	64	no	—
440	C₂²×D₅₃	—	2	16	no	—
441	C₂²×D₅₃	—	2	16	no	—
442	C₂²×D₅₃	—	2	16	no	—
443	C₂²×D₅₃	—	2	16	no	—
444	C₂²×D₅₃	—	2	16	no	—
445	C₂²×D₅₃	—	2	16	no	—
446	C₂²×D₅₃	—	2	4	no	—
447	C₂²×D₅₃	—	2	8	no	—
448	C₂²×D₅₃	—	2	16	no	—
449	C₂²×D₅₃	—	2	32	no	—
450	C₂²×D₅₃	—	4	32	no	—
451	C₂²×D₅₃	C₂²×D₄	1	4	yes	—
452	C₂²×D₅₃	C₂²×D₄	1	16	yes	—
453	C₂²×D₅₃	C₂²×D₄	1	4	yes	—
454	C₂²×D₅₃	C₂×#41	1	8	yes	—
455	C₂²×D₅₃	C₂×#41	1	32	yes	complemented
456	C₂²×D₅₃	C₂×#41	1	8	yes	complemented
457	C₂²×D₅₃	C₂⁵	1	4	yes	—
458	C₂²×D₅₃	C₂⁵	1	2	yes	—
459	C₂²×D₅₃	C₂⁵	1	4	yes	—
460	C₂²×D₅₃	C₂⁵	1	2	yes	—
461	Q₈×C₅₃	—	2	8	no	—
462	D₄×C₅₃	—	2	16	no	—
463	D₄×C₅₃	—	2	32	no	—
464	D₄×C₅₃	—	2	8	no	—
465	C₂×C₄×C₅₃	—	2	4	no	—
466	C₂×C₄×C₅₃	—	2	8	no	—
467	C₂×C₄×C₅₃	—	2	4	no	—
468	C₂×C₄×C₅₃	—	2	8	no	—
469	C₂×C₄×C₅₃	—	2	16	no	—
470	C₂×C₄×C₅₃	—	2	16	no	—
471	C₂×C₄×C₅₃	—	2	16	no	—
472	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
473	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
474	C₂×C₄×C₅₃	C₂²×D₄	1	16	yes	complemented
475	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
476	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
477	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
478	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
479	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
480	C₂²⋊D₅₃	—	2	16	no	—
481	C₂²⋊D₅₃	—	2	32	no	—
482	C₂²⋊D₅₃	—	2	16	no	—
483	C₂²⋊D₅₃	—	2	32	no	—
484	C₂²⋊D₅₃	—	2	16	no	—
485	C₂×Dic₅₃	—	2	4	no	—
486	C₂×Dic₅₃	—	2	8	no	—
487	C₂×Dic₅₃	—	2	4	no	—
488	C₂×Dic₅₃	—	2	8	no	—
489	C₂×Dic₅₃	—	2	16	no	—
490	C₂×Dic₅₃	—	2	16	no	—
491	C₂×Dic₅₃	—	2	16	no	—
492	C₂×Dic₅₃	C₂²×D₄	1	4	yes	—
493	C₂×Dic₅₃	C₂²×D₄	1	4	yes	—
494	C₂×Dic₅₃	C₂²×D₄	1	16	yes	complemented
495	C₂×Dic₅₃	C₂⁵	1	4	yes	—
496	C₂×Dic₅₃	C₂⁵	1	4	yes	—
497	C₂×Dic₅₃	C₂⁵	1	8	yes	—
498	C₂×Dic₅₃	C₂⁵	1	2	yes	—
499	C₂×Dic₅₃	C₂⁵	1	2	yes	—
500	D₂₁₂	—	2	16	no	—
501	D₂₁₂	—	2	32	no	—
502	D₂₁₂	—	2	8	no	—
503	C₄×D₅₃	—	2	16	no	—
504	C₄×D₅₃	—	2	16	no	—
505	C₄×D₅₃	—	2	16	no	—
506	C₄×D₅₃	—	2	32	no	—
507	C₄×D₅₃	—	2	16	no	—
508	C₄×D₅₃	—	2	16	no	—
509	C₄×D₅₃	—	2	16	no	—
510	C₄×D₅₃	—	2	16	no	—
511	C₄×D₅₃	—	2	16	no	—
512	C₄×D₅₃	—	2	16	no	—
513	C₄×D₅₃	C₂²×D₄	1	16	yes	—
514	C₄×D₅₃	C₂²×D₄	1	16	yes	—
515	C₄×D₅₃	C₂²×D₄	1	16	yes	complemented
516	C₄×D₅₃	C₂²×D₄	1	16	yes	complemented
517	Dic₁₀₆	—	2	8	no	—
518	Dic₁₀₆	—	2	16	no	—
519	C₂²×#525	—	53	1	no	maximal, Sylow
520	C₂²×C₅₃	—	2	32	no	—
521	C₂²×C₅₃	—	2	4	no	—
522	C₂²×C₅₃	—	2	4	no	—
523	C₂²×C₅₃	—	2	4	no	—
524	C₂²×C₅₃	—	2	8	no	—
525	C₂²×C₅₃	—	2	16	no	—
526	C₂²×C₅₃	—	2	4	no	—
527	C₂²×C₅₃	—	2	8	no	—
528	C₂²×C₅₃	—	4	8	no	—
529	C₂²×C₅₃	C₂³×D₄	1	4	yes	—
530	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
531	C₂²×C₅₃	C₂²×#41	1	4	yes	—
532	C₂²×C₅₃	C₂²×#41	1	8	yes	complemented
533	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
534	C₂×D₅₃	—	2	64	no	—
535	C₂×D₅₃	—	2	32	no	—
536	C₂×D₅₃	—	2	4	no	—
537	C₂×D₅₃	—	2	4	no	—
538	C₂×D₅₃	—	2	4	no	—
539	C₂×D₅₃	—	2	8	no	—
540	C₂×D₅₃	—	2	16	no	—
541	C₂×D₅₃	—	2	32	no	—
542	C₂×D₅₃	—	2	64	no	—
543	C₂×D₅₃	—	2	4	no	—
544	C₂×D₅₃	—	2	8	no	—
545	C₂×D₅₃	—	4	8	no	—
546	C₂×D₅₃	—	4	32	no	—
547	C₂×D₅₃	#525	1	16	yes	direct product factor
548	C₂×D₅₃	C₂³×D₄	1	4	yes	—
549	C₂×D₅₃	C₂³×D₄	1	4	yes	—
550	C₂×D₅₃	C₂²×#41	1	8	yes	—
551	C₂×D₅₃	C₂²×#41	1	8	yes	complemented
552	C₄×C₅₃	—	2	4	no	—
553	C₄×C₅₃	—	2	4	no	—
554	C₄×C₅₃	—	2	8	no	—
555	C₄×C₅₃	C₂³×D₄	1	4	yes	—
556	C₄×C₅₃	C₂³×D₄	1	4	yes	—
557	Dic₅₃	—	2	4	no	—
558	Dic₅₃	—	2	4	no	—
559	Dic₅₃	—	2	8	no	—
560	Dic₅₃	C₂³×D₄	1	4	yes	—
561	Dic₅₃	C₂³×D₄	1	4	yes	—
562	C₂³×#41	—	53	1	no	—
563	C₂⁵×C₄	—	53	1	no	—
564	C₂×#525	—	53	1	no	—
565	C₂×#525	—	53	1	no	—
566	C₂×#525	—	53	32	no	—
567	C₂×#525	—	53	2	no	—
568	C₂×#525	—	53	2	no	—
569	C₂×#525	—	53	2	no	—
570	C₂×#525	—	53	2	no	—
571	C₂×#525	—	53	4	no	—
572	C₂×#525	—	53	1	no	—
573	C₂×#525	D₅₃	1	1	yes	characteristic, direct product factor
574	C₂²×#123	—	53	2	no	—
575	C₂²×C₂²⋊Q₈	—	53	2	no	—
576	C₂²×#121	—	53	2	no	—
577	C₂²×#120	—	53	2	no	—
578	C₂²×C₄×D₄	—	53	4	no	—
579	C₂²×#117	—	53	1	no	—
580	C₂×C₅₃	—	2	4	no	—
581	C₂×C₅₃	—	2	8	no	—
582	C₂×C₅₃	—	4	4	no	—
583	C₂×C₅₃	C₂×#525	1	4	yes	complemented
584	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
585	C₂×C₅₃	C₂³×#41	1	2	yes	—
586	D₅₃	—	2	4	no	—
587	D₅₃	—	2	8	no	—
588	D₅₃	—	4	4	no	—
589	D₅₃	C₂×#525	1	8	yes	direct product factor
590	C₂⁶	—	53	1	no	—
591	C₂²×#41	—	53	16	no	—
592	C₂²×#41	—	53	1	no	—
593	C₂²×#41	—	53	2	no	—
594	C₂²×#41	—	53	1	no	—
595	C₂²×#41	—	53	1	no	—
596	C₂²×#41	—	53	2	no	—
597	C₂²×#41	—	106	16	no	—
598	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
599	C₂³×Q₈	—	53	1	no	—
600	C₂³×D₄	—	53	2	no	—
601	C₂³×D₄	—	53	4	no	—
602	C₂³×D₄	—	53	1	no	—
603	C₂⁴×C₄	—	53	1	no	—
604	C₂⁴×C₄	—	53	1	no	—
605	C₂⁴×C₄	—	53	2	no	—
606	C₂⁴×C₄	—	53	2	no	—
607	C₂⁴×C₄	—	53	1	no	—
608	C₂⁴×C₄	—	53	1	no	—
609	C₂⁴×C₄	—	53	2	no	—
610	C₂⁴×C₄	—	53	2	no	—
611	C₂⁴×C₄	—	53	1	no	—
612	C₂⁴×C₄	—	53	16	no	—
613	C₂⁴×C₄	—	53	2	no	—
614	C₂⁴×C₄	—	106	16	no	—
615	C₂⁴×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
616	#525	—	53	16	no	—
617	#525	—	53	16	no	—
618	#525	—	53	32	no	—
619	#525	—	53	32	no	—
620	#525	—	53	32	no	—
621	#525	—	53	32	no	—
622	#525	—	53	64	no	—
623	#525	—	53	16	no	—
624	#525	C₂×D₅₃	1	16	yes	direct product factor
625	C₂×#123	—	53	2	no	—
626	C₂×#123	—	53	2	no	—
627	C₂×#123	—	53	32	no	—
628	C₂×#123	—	53	4	no	—
629	C₂×#123	—	53	2	no	—
630	C₂×#123	—	53	4	no	—
631	C₂×#123	C₂×D₅₃	1	2	yes	complemented
632	C₂×C₂²⋊Q₈	—	53	2	no	—
633	C₂×C₂²⋊Q₈	—	53	2	no	—
634	C₂×C₂²⋊Q₈	—	53	32	no	—
635	C₂×C₂²⋊Q₈	—	53	4	no	—
636	C₂×C₂²⋊Q₈	—	53	2	no	—
637	C₂×C₂²⋊Q₈	—	53	4	no	—
638	C₂×C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
639	C₂×#121	—	53	4	no	—
640	C₂×#121	—	53	2	no	—
641	C₂×#121	—	53	2	no	—
642	C₂×#121	—	53	32	no	—
643	C₂×#121	—	53	2	no	—
644	C₂×#121	—	53	4	no	—
645	C₂×#121	C₂×D₅₃	1	2	yes	complemented
646	C₂×#120	—	53	2	no	—
647	C₂×#120	—	53	2	no	—
648	C₂×#120	—	53	4	no	—
649	C₂×#120	—	53	32	no	—
650	C₂×#120	—	53	4	no	—
651	C₂×#120	—	53	2	no	—
652	C₂×#120	C₂×D₅₃	1	2	yes	complemented
653	C₂×C₄×D₄	—	53	4	no	—
654	C₂×C₄×D₄	—	53	4	no	—
655	C₂×C₄×D₄	—	53	4	no	—
656	C₂×C₄×D₄	—	53	64	no	—
657	C₂×C₄×D₄	—	53	4	no	—
658	C₂×C₄×D₄	—	53	4	no	—
659	C₂×C₄×D₄	—	53	4	no	—
660	C₂×C₄×D₄	—	53	4	no	—
661	C₂×C₄×D₄	C₂×D₅₃	1	4	yes	complemented
662	C₂×#117	—	53	1	no	—
663	C₂×#117	—	53	16	no	—
664	C₂×#117	—	53	2	no	—
665	C₂×#117	—	53	2	no	—
666	C₂×#117	—	53	2	no	—
667	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
668	C₂²×C₄⋊C₄	—	53	2	no	—
669	C₂²×C₄⋊C₄	—	53	4	no	—
670	C₂²×C₂²⋊C₄	—	53	2	no	—
671	C₂²×C₂²⋊C₄	—	53	4	no	—
672	C₂²×C₂²⋊C₄	—	53	4	no	—
673	C₂²×C₄²	—	53	2	no	—
674	C₅₃	C₂²×#525	1	1	yes	characteristic, complemented, Sylow
675	C₂⁵	—	53	1	no	—
676	C₂⁵	—	53	2	no	—
677	C₂⁵	—	53	2	no	—
678	C₂⁵	—	53	8	no	—
679	C₂⁵	—	53	2	no	—
680	C₂⁵	—	53	1	no	—
681	C₂⁵	—	106	8	no	—
682	C₂⁵	—	106	16	no	—
683	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
684	C₂×#41	—	2	8	no	—
685	C₂×#41	—	53	8	no	—
686	C₂×#41	—	53	16	no	—
687	C₂×#41	—	53	8	no	—
688	C₂×#41	—	53	8	no	—
689	C₂×#41	—	53	16	no	—
690	C₂×#41	—	106	16	no	—
691	C₂×#41	—	106	16	no	—
692	C₂×#41	—	106	8	no	—
693	C₂×#41	—	106	8	no	—
694	C₂×#41	—	106	128	no	—
695	C₂×#41	—	106	8	no	—
696	C₂×#41	C₂²×D₅₃	1	8	yes	complemented
697	C₂²×Q₈	—	53	8	no	—
698	C₂²×Q₈	—	53	2	no	—
699	C₂²×Q₈	—	53	1	no	—
700	C₂²×Q₈	—	106	8	no	—
701	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
702	C₂²×D₄	—	53	4	no	—
703	C₂²×D₄	—	53	4	no	—
704	C₂²×D₄	—	53	2	no	—
705	C₂²×D₄	—	53	2	no	—
706	C₂²×D₄	—	53	2	no	—
707	C₂²×D₄	—	53	32	no	—
708	C₂²×D₄	—	53	16	no	—
709	C₂²×D₄	—	53	8	no	—
710	C₂²×D₄	—	53	4	no	—
711	C₂²×D₄	—	53	2	no	—
712	C₂²×D₄	—	53	1	no	—
713	C₂²×D₄	—	106	8	no	—
714	C₂²×D₄	—	106	16	no	—
715	C₂²×D₄	—	106	32	no	—
716	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
717	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
718	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
719	C₂³×C₄	—	2	8	no	—
720	C₂³×C₄	—	53	1	no	—
721	C₂³×C₄	—	53	16	no	—
722	C₂³×C₄	—	53	1	no	—
723	C₂³×C₄	—	53	1	no	—
724	C₂³×C₄	—	53	8	no	—
725	C₂³×C₄	—	53	1	no	—
726	C₂³×C₄	—	53	1	no	—
727	C₂³×C₄	—	53	2	no	—
728	C₂³×C₄	—	53	2	no	—
729	C₂³×C₄	—	53	2	no	—
730	C₂³×C₄	—	53	1	no	—
731	C₂³×C₄	—	53	8	no	—
732	C₂³×C₄	—	53	4	no	—
733	C₂³×C₄	—	53	2	no	—
734	C₂³×C₄	—	53	2	no	—
735	C₂³×C₄	—	53	2	no	—
736	C₂³×C₄	—	53	16	no	—
737	C₂³×C₄	—	53	2	no	—
738	C₂³×C₄	—	53	2	no	—
739	C₂³×C₄	—	53	16	no	—
740	C₂³×C₄	—	53	2	no	—
741	C₂³×C₄	—	53	2	no	—
742	C₂³×C₄	—	53	8	no	—
743	C₂³×C₄	—	53	8	no	—
744	C₂³×C₄	—	53	16	no	—
745	C₂³×C₄	—	53	16	no	—
746	C₂³×C₄	—	53	8	no	—
747	C₂³×C₄	—	53	2	no	—
748	C₂³×C₄	—	53	2	no	—
749	C₂³×C₄	—	53	16	no	—
750	C₂³×C₄	—	106	8	no	—
751	C₂³×C₄	—	106	16	no	—
752	C₂³×C₄	—	106	16	no	—
753	C₂³×C₄	—	106	16	no	—
754	C₂³×C₄	—	106	16	no	—
755	C₂³×C₄	—	106	128	no	—
756	C₂³×C₄	—	106	16	no	—
757	C₂³×C₄	—	106	8	no	—
758	C₂³×C₄	—	106	8	no	—
759	C₂³×C₄	—	106	8	no	—
760	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
761	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
762	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
763	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
764	C₂³×C₄	C₂²×D₅₃	1	8	yes	complemented
765	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
766	#123	—	53	16	no	—
767	#123	—	53	16	no	—
768	#123	—	53	32	no	—
769	#123	—	53	16	no	—
770	#123	—	53	32	no	—
771	#123	C₂²×D₅₃	1	16	yes	complemented
772	C₂²⋊Q₈	—	53	16	no	—
773	C₂²⋊Q₈	—	53	16	no	—
774	C₂²⋊Q₈	—	53	32	no	—
775	C₂²⋊Q₈	—	53	16	no	—
776	C₂²⋊Q₈	—	53	32	no	—
777	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
778	#121	—	53	32	no	—
779	#121	—	53	16	no	—
780	#121	—	53	16	no	—
781	#121	—	53	16	no	—
782	#121	—	53	32	no	—
783	#121	C₂²×D₅₃	1	16	yes	complemented
784	#120	—	53	16	no	—
785	#120	—	53	16	no	—
786	#120	—	53	32	no	—
787	#120	—	53	32	no	—
788	#120	—	53	16	no	—
789	#120	C₂²×D₅₃	1	16	yes	complemented
790	C₄×D₄	—	53	32	no	—
791	C₄×D₄	—	53	32	no	—
792	C₄×D₄	—	53	32	no	—
793	C₄×D₄	—	53	32	no	—
794	C₄×D₄	—	53	32	no	—
795	C₄×D₄	—	53	32	no	—
796	C₄×D₄	—	53	32	no	—
797	C₄×D₄	C₂²×D₅₃	1	32	yes	complemented
798	#117	—	53	8	no	—
799	#117	—	53	16	no	—
800	#117	—	53	16	no	—
801	#117	—	53	16	no	—
802	#117	C₂²×D₅₃	1	8	yes	complemented
803	C₂×C₄⋊C₄	—	53	4	no	—
804	C₂×C₄⋊C₄	—	53	2	no	—
805	C₂×C₄⋊C₄	—	53	4	no	—
806	C₂×C₄⋊C₄	—	53	4	no	—
807	C₂×C₄⋊C₄	—	53	4	no	—
808	C₂×C₄⋊C₄	—	53	16	no	—
809	C₂×C₄⋊C₄	—	53	32	no	—
810	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
811	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
812	C₂×C₂²⋊C₄	—	53	2	no	—
813	C₂×C₂²⋊C₄	—	53	4	no	—
814	C₂×C₂²⋊C₄	—	53	4	no	—
815	C₂×C₂²⋊C₄	—	53	4	no	—
816	C₂×C₂²⋊C₄	—	53	4	no	—
817	C₂×C₂²⋊C₄	—	53	4	no	—
818	C₂×C₂²⋊C₄	—	53	4	no	—
819	C₂×C₂²⋊C₄	—	53	4	no	—
820	C₂×C₂²⋊C₄	—	53	16	no	—
821	C₂×C₂²⋊C₄	—	53	32	no	—
822	C₂×C₂²⋊C₄	—	53	32	no	—
823	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
824	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
825	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
826	C₂×C₄²	—	53	4	no	—
827	C₂×C₄²	—	53	2	no	—
828	C₂×C₄²	—	53	16	no	—
829	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
830	C₂⁴	—	2	4	no	—
831	C₂⁴	—	2	8	no	—
832	C₂⁴	—	53	1	no	—
833	C₂⁴	—	53	8	no	—
834	C₂⁴	—	53	16	no	—
835	C₂⁴	—	53	4	no	—
836	C₂⁴	—	53	8	no	—
837	C₂⁴	—	53	1	no	—
838	C₂⁴	—	53	2	no	—
839	C₂⁴	—	53	8	no	—
840	C₂⁴	—	53	2	no	—
841	C₂⁴	—	53	8	no	—
842	C₂⁴	—	53	4	no	—
843	C₂⁴	—	106	8	no	—
844	C₂⁴	—	106	32	no	—
845	C₂⁴	—	106	8	no	—
846	C₂⁴	—	106	8	no	—
847	C₂⁴	—	106	8	no	—
848	C₂⁴	—	106	8	no	—
849	C₂⁴	—	106	8	no	—
850	C₂⁴	—	106	64	no	—
851	C₂⁴	—	106	8	no	—
852	C₂⁴	—	106	16	no	—
853	C₂⁴	—	106	128	no	—
854	C₂⁴	—	106	4	no	—
855	C₂⁴	—	106	8	no	—
856	C₂⁴	C₂³×D₅₃	1	2	yes	—
857	C₂⁴	C₂³×D₅₃	1	4	yes	—
858	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
859	C₂⁴	C₂³×D₅₃	1	2	yes	—
860	#41	—	2	32	no	—
861	#41	—	106	64	no	—
862	#41	—	106	64	no	—
863	#41	—	106	32	no	—
864	#41	—	106	32	no	—
865	#41	—	106	32	no	—
866	C₂×Q₈	—	2	4	no	—
867	C₂×Q₈	—	53	8	no	—
868	C₂×Q₈	—	53	4	no	—
869	C₂×Q₈	—	106	8	no	—
870	C₂×Q₈	—	106	32	no	—
871	C₂×Q₈	—	106	4	no	—
872	C₂×Q₈	C₂³×D₅₃	1	4	yes	complemented
873	C₂×D₄	—	2	8	no	—
874	C₂×D₄	—	2	16	no	—
875	C₂×D₄	—	2	4	no	—
876	C₂×D₄	—	53	16	no	—
877	C₂×D₄	—	53	16	no	—
878	C₂×D₄	—	53	8	no	—
879	C₂×D₄	—	53	8	no	—
880	C₂×D₄	—	53	8	no	—
881	C₂×D₄	—	53	16	no	—
882	C₂×D₄	—	53	8	no	—
883	C₂×D₄	—	53	4	no	—
884	C₂×D₄	—	106	16	no	—
885	C₂×D₄	—	106	8	no	—
886	C₂×D₄	—	106	32	no	—
887	C₂×D₄	—	106	8	no	—
888	C₂×D₄	—	106	128	no	—
889	C₂×D₄	—	106	64	no	—
890	C₂×D₄	—	106	16	no	—
891	C₂×D₄	—	106	8	no	—
892	C₂×D₄	—	106	8	no	—
893	C₂×D₄	—	106	16	no	—
894	C₂×D₄	—	106	4	no	—
895	C₂×D₄	C₂³×D₅₃	1	16	yes	—
896	C₂×D₄	C₂³×D₅₃	1	8	yes	—
897	C₂×D₄	C₂³×D₅₃	1	4	yes	complemented
898	C₂²×C₄	—	2	4	no	—
899	C₂²×C₄	—	2	8	no	—
900	C₂²×C₄	—	2	8	no	—
901	C₂²×C₄	—	2	8	no	—
902	C₂²×C₄	—	2	32	no	—
903	C₂²×C₄	—	53	8	no	—
904	C₂²×C₄	—	53	1	no	—
905	C₂²×C₄	—	53	1	no	—
906	C₂²×C₄	—	53	4	no	—
907	C₂²×C₄	—	53	8	no	—
908	C₂²×C₄	—	53	8	no	—
909	C₂²×C₄	—	53	8	no	—
910	C₂²×C₄	—	53	8	no	—
911	C₂²×C₄	—	53	64	no	—
912	C₂²×C₄	—	53	4	no	—
913	C₂²×C₄	—	53	4	no	—
914	C₂²×C₄	—	53	4	no	—
915	C₂²×C₄	—	53	4	no	—
916	C₂²×C₄	—	53	4	no	—
917	C₂²×C₄	—	53	2	no	—
918	C₂²×C₄	—	53	2	no	—
919	C₂²×C₄	—	53	8	no	—
920	C₂²×C₄	—	53	8	no	—
921	C₂²×C₄	—	53	4	no	—
922	C₂²×C₄	—	53	8	no	—
923	C₂²×C₄	—	53	16	no	—
924	C₂²×C₄	—	53	8	no	—
925	C₂²×C₄	—	53	8	no	—
926	C₂²×C₄	—	53	8	no	—
927	C₂²×C₄	—	53	8	no	—
928	C₂²×C₄	—	53	8	no	—
929	C₂²×C₄	—	53	8	no	—
930	C₂²×C₄	—	53	8	no	—
931	C₂²×C₄	—	53	8	no	—
932	C₂²×C₄	—	53	8	no	—
933	C₂²×C₄	—	106	8	no	—
934	C₂²×C₄	—	106	8	no	—
935	C₂²×C₄	—	106	32	no	—
936	C₂²×C₄	—	106	64	no	—
937	C₂²×C₄	—	106	64	no	—
938	C₂²×C₄	—	106	64	no	—
939	C₂²×C₄	—	106	64	no	—
940	C₂²×C₄	—	106	8	no	—
941	C₂²×C₄	—	106	64	no	—
942	C₂²×C₄	—	106	8	no	—
943	C₂²×C₄	—	106	32	no	—
944	C₂²×C₄	—	106	8	no	—
945	C₂²×C₄	—	106	8	no	—
946	C₂²×C₄	—	106	16	no	—
947	C₂²×C₄	—	106	8	no	—
948	C₂²×C₄	—	106	8	no	—
949	C₂²×C₄	—	106	32	no	—
950	C₂²×C₄	—	106	8	no	—
951	C₂²×C₄	—	106	4	no	—
952	C₂²×C₄	—	106	8	no	—
953	C₂²×C₄	—	106	8	no	—
954	C₂²×C₄	—	106	8	no	—
955	C₂²×C₄	—	106	32	no	—
956	C₂²×C₄	D₄×D₅₃	1	8	yes	complemented
957	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
958	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
959	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
960	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
961	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
962	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
963	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
964	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
965	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
966	C₂²×C₄	C₂³×D₅₃	1	8	yes	complemented
967	C₄⋊C₄	—	53	16	no	—
968	C₄⋊C₄	—	53	8	no	—
969	C₄⋊C₄	—	53	16	no	—
970	C₄⋊C₄	—	53	16	no	—
971	C₄⋊C₄	—	53	16	no	—
972	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
973	C₄⋊C₄	C₂³×D₅₃	1	16	yes	complemented
974	C₂²⋊C₄	—	53	8	no	—
975	C₂²⋊C₄	—	53	16	no	—
976	C₂²⋊C₄	—	53	16	no	—
977	C₂²⋊C₄	—	53	16	no	—
978	C₂²⋊C₄	—	53	16	no	—
979	C₂²⋊C₄	—	53	16	no	—
980	C₂²⋊C₄	—	53	16	no	—
981	C₂²⋊C₄	—	53	16	no	—
982	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
983	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
984	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	complemented
985	C₄²	—	53	16	no	—
986	C₄²	—	53	8	no	—
987	C₄²	C₂³×D₅₃	1	8	yes	complemented
988	C₂³	—	2	32	no	—
989	C₂³	—	2	8	no	—
990	C₂³	—	2	4	no	—
991	C₂³	—	2	4	no	—
992	C₂³	—	2	4	no	—
993	C₂³	—	2	16	no	—
994	C₂³	—	2	4	no	—
995	C₂³	—	2	8	no	—
996	C₂³	—	53	4	no	—
997	C₂³	—	53	8	no	—
998	C₂³	—	53	2	no	—
999	C₂³	—	53	16	no	—
1000	C₂³	—	53	4	no	—
1001	C₂³	—	53	8	no	—
1002	C₂³	—	53	32	no	—
1003	C₂³	—	53	2	no	—
1004	C₂³	—	53	4	no	—
1005	C₂³	—	53	4	no	—
1006	C₂³	—	106	16	no	—
1007	C₂³	—	106	16	no	—
1008	C₂³	—	106	32	no	—
1009	C₂³	—	106	64	no	—
1010	C₂³	—	106	16	no	—
1011	C₂³	—	106	16	no	—
1012	C₂³	—	106	16	no	—
1013	C₂³	—	106	16	no	—
1014	C₂³	—	106	16	no	—
1015	C₂³	—	106	32	no	—
1016	C₂³	—	106	256	no	—
1017	C₂³	—	106	32	no	—
1018	C₂³	—	106	64	no	—
1019	C₂³	—	106	8	no	—
1020	C₂³	—	106	4	no	—
1021	C₂³	—	106	4	no	—
1022	C₂³	—	106	4	no	—
1023	C₂³	—	106	16	no	—
1024	C₂³	—	106	4	no	—
1025	C₂³	—	106	8	no	—
1026	C₂³	—	212	32	no	—
1027	C₂³	C₂×D₄×D₅₃	1	4	yes	—
1028	C₂³	#41×D₅₃	1	8	yes	complemented
1029	C₂³	C₂⁴×D₅₃	1	4	yes	—
1030	C₂³	C₂⁴×D₅₃	1	2	yes	—
1031	C₂³	C₂⁴×D₅₃	1	4	yes	—
1032	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1033	Q₈	—	2	8	no	—
1034	Q₈	—	106	16	no	—
1035	Q₈	—	106	8	no	—
1036	D₄	—	2	16	no	—
1037	D₄	—	2	32	no	—
1038	D₄	—	2	8	no	—
1039	D₄	—	106	32	no	—
1040	D₄	—	106	16	no	—
1041	D₄	—	106	16	no	—
1042	D₄	—	106	32	no	—
1043	D₄	—	106	16	no	—
1044	D₄	—	106	16	no	—
1045	D₄	—	106	32	no	—
1046	D₄	—	106	8	no	—
1047	C₂×C₄	—	2	8	no	—
1048	C₂×C₄	—	2	4	no	—
1049	C₂×C₄	—	2	4	no	—
1050	C₂×C₄	—	2	8	no	—
1051	C₂×C₄	—	2	16	no	—
1052	C₂×C₄	—	2	16	no	—
1053	C₂×C₄	—	2	16	no	—
1054	C₂×C₄	—	53	4	no	—
1055	C₂×C₄	—	53	4	no	—
1056	C₂×C₄	—	53	16	no	—
1057	C₂×C₄	—	53	2	no	—
1058	C₂×C₄	—	53	2	no	—
1059	C₂×C₄	—	53	16	no	—
1060	C₂×C₄	—	53	16	no	—
1061	C₂×C₄	—	53	16	no	—
1062	C₂×C₄	—	53	16	no	—
1063	C₂×C₄	—	53	8	no	—
1064	C₂×C₄	—	53	4	no	—
1065	C₂×C₄	—	53	4	no	—
1066	C₂×C₄	—	106	16	no	—
1067	C₂×C₄	—	106	16	no	—
1068	C₂×C₄	—	106	16	no	—
1069	C₂×C₄	—	106	16	no	—
1070	C₂×C₄	—	106	16	no	—
1071	C₂×C₄	—	106	16	no	—
1072	C₂×C₄	—	106	32	no	—
1073	C₂×C₄	—	106	16	no	—
1074	C₂×C₄	—	106	16	no	—
1075	C₂×C₄	—	106	16	no	—
1076	C₂×C₄	—	106	8	no	—
1077	C₂×C₄	—	106	4	no	—
1078	C₂×C₄	—	106	4	no	—
1079	C₂×C₄	—	106	8	no	—
1080	C₂×C₄	—	106	16	no	—
1081	C₂×C₄	—	106	16	no	—
1082	C₂×C₄	—	106	16	no	—
1083	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1084	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1085	C₂×C₄	C₂×D₄×D₅₃	1	16	yes	complemented
1086	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1087	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1088	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1089	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1090	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1091	C₂²	—	2	32	no	—
1092	C₂²	—	2	8	no	—
1093	C₂²	—	2	16	no	—
1094	C₂²	—	2	4	no	—
1095	C₂²	—	2	4	no	—
1096	C₂²	—	2	4	no	—
1097	C₂²	—	2	4	no	—
1098	C₂²	—	2	8	no	—
1099	C₂²	—	4	8	no	—
1100	C₂²	—	53	16	no	—
1101	C₂²	—	53	4	no	—
1102	C₂²	—	53	8	no	—
1103	C₂²	—	53	4	no	—
1104	C₂²	—	53	8	no	—
1105	C₂²	—	106	32	no	—
1106	C₂²	—	106	64	no	—
1107	C₂²	—	106	32	no	—
1108	C₂²	—	106	64	no	—
1109	C₂²	—	106	8	no	—
1110	C₂²	—	106	16	no	—
1111	C₂²	—	106	4	no	—
1112	C₂²	—	106	4	no	—
1113	C₂²	—	106	4	no	—
1114	C₂²	—	106	4	no	—
1115	C₂²	—	106	8	no	—
1116	C₂²	—	212	32	no	—
1117	C₂²	—	212	8	no	—
1118	C₂²	C₂²×D₄×D₅₃	1	4	yes	—
1119	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1120	C₂²	C₂×#41×D₅₃	1	4	yes	—
1121	C₂²	C₂×#41×D₅₃	1	8	yes	complemented
1122	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1123	C₄	—	2	4	no	—
1124	C₄	—	2	4	no	—
1125	C₄	—	2	8	no	—
1126	C₄	—	53	4	no	—
1127	C₄	—	53	4	no	—
1128	C₄	—	106	4	no	—
1129	C₄	—	106	4	no	—
1130	C₄	—	106	8	no	—
1131	C₄	C₂²×D₄×D₅₃	1	4	yes	—
1132	C₄	C₂²×D₄×D₅₃	1	4	yes	—
1133	C₂	—	2	4	no	—
1134	C₂	—	2	8	no	—
1135	C₂	—	4	4	no	—
1136	C₂	—	53	8	no	—
1137	C₂	—	106	4	no	—
1138	C₂	—	106	8	no	—
1139	C₂	—	212	4	no	—
1140	C₂	#525×D₅₃	1	4	yes	direct product factor
1141	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1142	C₂	C₂²×#41×D₅₃	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×#41×D₅₃	C₂	semidirect
2. C₂⁴×C₄×D₅₃	C₂	semidirect
3. C₂×#16811136	C₂	semidirect
4. C₂×#16811135	C₂	semidirect
5. C₂×#16811134	C₂	semidirect
6. C₂×#16811133	C₂	semidirect
7. C₂×#16811132	C₂	semidirect
8. C₂×#16811131	C₂	semidirect
9. C₂×#16811130	C₂	semidirect
10. C₂×#16811129	C₂	semidirect
11. #525×D₅₃	C₂	direct (N × H)
12. C₂×#123×D₅₃	C₂	semidirect
13. C₂×C₂²⋊Q₈×D₅₃	C₂	semidirect
14. C₂×#121×D₅₃	C₂	semidirect
15. C₂×#120×D₅₃	C₂	semidirect
16. C₂×C₄×D₄×D₅₃	C₂	semidirect
17. C₂×#117×D₅₃	C₂	semidirect
18. C₂×C₅₃×#525	C₂	semidirect
20. C₂²×#11719949	C₂²	semidirect
21. C₂²×#11719945	C₂²	semidirect
22. C₂²×#11719945	C₂²	semidirect
23. C₂²×#11719947	C₂²	semidirect
24. C₂²×#11719947	C₂²	semidirect
26. C₂×#41×D₅₃	C₂²	semidirect
27. C₂²×Q₈×D₅₃	C₂²	semidirect
30. C₂²×D₄×D₅₃	C₂²	semidirect
31. C₂⁴×Dic₅₃	C₂²	semidirect
37. C₂³×C₄×D₅₃	C₂²	semidirect
38. C₂³×C₄×D₅₃	C₂²	semidirect
39. C₂³×C₄×D₅₃	C₂²	semidirect
40. C₂³×C₄×D₅₃	C₂²	semidirect
41. C₂³×C₄×D₅₃	C₂²	semidirect
42. C₂³×C₄×D₅₃	C₂²	semidirect
43. #16811136	C₂²	semidirect
44. #16811135	C₂²	semidirect
45. #16811134	C₂²	semidirect
46. #16811133	C₂²	semidirect
47. #16811132	C₂²	semidirect
48. #16811131	C₂²	semidirect
49. #16811130	C₂²	semidirect
50. #16811129	C₂²	semidirect
51. C₂×#13133202	C₂²	semidirect
52. C₂×#13133201	C₂²	semidirect
53. C₂×#13133200	C₂²	semidirect
54. C₂×#13133199	C₂²	semidirect
55. C₂×#13133198	C₂²	semidirect
56. #123×D₅₃	C₂²	semidirect
57. C₂×#13133197	C₂²	semidirect
58. C₂×#13133196	C₂²	semidirect
59. C₂×#13133195	C₂²	semidirect
60. C₂×#13133194	C₂²	semidirect
61. C₂×#13133193	C₂²	semidirect
62. C₂²⋊Q₈×D₅₃	C₂²	semidirect
63. C₂×#13133192	C₂²	semidirect
64. C₂×#13133191	C₂²	semidirect
65. C₂×#13133190	C₂²	semidirect
66. C₂×#13133189	C₂²	semidirect
67. C₂×#13133188	C₂²	semidirect
68. #121×D₅₃	C₂²	semidirect
69. C₂×#13133187	C₂²	semidirect
70. C₂×#13133187	C₂²	semidirect
71. C₂×#13133186	C₂²	semidirect
72. C₂×#13133185	C₂²	semidirect
73. C₂×#13133185	C₂²	semidirect
74. #120×D₅₃	C₂²	semidirect
75. C₂×C₄×D₂₁₂	C₂²	semidirect
76. C₂×D₄×Dic₅₃	C₂²	semidirect
77. C₂×#13133179	C₂²	semidirect
78. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
79. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
80. C₂×#13133177	C₂²	semidirect
81. C₂×#13133177	C₂²	semidirect
82. C₄×D₄×D₅₃	C₂²	semidirect
83. C₂×#13133176	C₂²	semidirect
84. C₂×#13133175	C₂²	semidirect
85. C₂×#13133174	C₂²	semidirect
86. C₂×#13133173	C₂²	semidirect
87. #117×D₅₃	C₂²	semidirect
88. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
89. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
92. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
93. C₂×C₄²×D₅₃	C₂²	semidirect
94. C₂²×#41×C₅₃	C₂²	semidirect
95. C₂⁴×C₄×C₅₃	C₂²	semidirect
96. C₅₃×#525	C₂²	semidirect
97. C₂×#123×C₅₃	C₂²	semidirect
98. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
99. C₂×#121×C₅₃	C₂²	semidirect
100. C₂×#120×C₅₃	C₂²	semidirect
101. C₂×C₄×D₄×C₅₃	C₂²	semidirect
102. C₂×#117×C₅₃	C₂²	semidirect
112. C₂×#11719949	C₂³	semidirect
115. C₂×#11719945	C₂³	semidirect
116. C₂×#11719945	C₂³	semidirect
119. C₂×#11719947	C₂³	semidirect
120. C₂×#11719947	C₂³	semidirect
122. C₂²×Dic₁₀₆	C₂³	semidirect
123. C₂²×Dic₁₀₆	C₂³	semidirect
125. C₂×Q₈×D₅₃	C₂³	semidirect
128. C₂²×D₂₁₂	C₂³	semidirect
133. C₂²×C₂²⋊D₅₃	C₂³	semidirect
139. C₂×D₄×D₅₃	C₂³	semidirect
145. C₂³×Dic₅₃	C₂³	semidirect
146. C₂³×Dic₅₃	C₂³	semidirect
156. C₂²×C₄×D₅₃	D₄	semidirect
173. C₂²×C₄×D₅₃	C₂³	semidirect
174. C₂²×C₄×D₅₃	C₂³	semidirect
175. C₂²×C₄×D₅₃	C₂³	semidirect
176. C₂²×C₄×D₅₃	C₂³	semidirect
177. C₂²×C₄×D₅₃	C₂³	semidirect
178. C₂²×C₄×D₅₃	C₂³	semidirect
179. C₂²×C₄×D₅₃	C₂³	semidirect
180. #13133202	C₂³	semidirect
181. #13133201	C₂³	semidirect
182. #13133200	C₂³	semidirect
183. #13133199	C₂³	semidirect
184. #13133198	C₂³	semidirect
185. #13133197	C₂³	semidirect
186. #13133196	C₂³	semidirect
187. #13133195	C₂³	semidirect
188. #13133194	C₂³	semidirect
189. #13133193	C₂³	semidirect
190. #13133192	C₂³	semidirect
191. #13133191	C₂³	semidirect
192. #13133190	C₂³	semidirect
193. #13133189	C₂³	semidirect
194. #13133188	C₂³	semidirect
195. #13133187	C₂³	semidirect
196. #13133187	C₂³	semidirect
197. #13133186	C₂³	semidirect
198. #13133185	C₂³	semidirect
199. #13133185	C₂³	semidirect
200. C₄×D₂₁₂	C₂³	semidirect
201. D₄×Dic₅₃	C₂³	semidirect
202. #13133179	C₂³	semidirect
203. C₄×C₂²⋊D₅₃	C₂³	semidirect
204. C₄×C₂²⋊D₅₃	C₂³	semidirect
205. #13133177	C₂³	semidirect
206. #13133177	C₂³	semidirect
207. #13133176	C₂³	semidirect
208. #13133175	C₂³	semidirect
209. #13133174	C₂³	semidirect
210. #13133173	C₂³	semidirect
211. C₂×C₄⋊Dic₅₃	C₂³	semidirect
212. C₂×C₄⋊Dic₅₃	C₂³	semidirect
213. C₂×#11719919	C₂³	semidirect
214. C₂×#11719919	C₂³	semidirect
215. C₂×#11719919	C₂³	semidirect
216. C₄⋊C₄×D₅₃	C₂³	semidirect
217. C₄⋊C₄×D₅₃	C₂³	semidirect
220. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
224. C₂×#11719921	C₂³	semidirect
225. C₂×#11719921	C₂³	semidirect
228. C₂²⋊C₄×D₅₃	C₂³	semidirect
229. C₂×C₄×Dic₅₃	C₂³	semidirect
230. C₂×C₄×Dic₅₃	C₂³	semidirect
231. C₄²×D₅₃	C₂³	semidirect
234. C₂×#41×C₅₃	C₂³	semidirect
235. C₂²×Q₈×C₅₃	C₂³	semidirect
238. C₂²×D₄×C₅₃	C₂³	semidirect
244. C₂³×C₄×C₅₃	C₂³	semidirect
245. C₂³×C₄×C₅₃	C₂³	semidirect
246. #123×C₅₃	C₂³	semidirect
247. C₂²⋊Q₈×C₅₃	C₂³	semidirect
248. #121×C₅₃	C₂³	semidirect
249. #120×C₅₃	C₂³	semidirect
250. C₄×D₄×C₅₃	C₂³	semidirect
251. #117×C₅₃	C₂³	semidirect
252. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
253. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
256. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
257. C₂×C₄²×C₅₃	C₂³	semidirect
278. C₂³×D₅₃	#41	semidirect
290. C₂×Q₈×C₅₃	C₂⁴	semidirect
296. C₂×D₄×C₅₃	C₂⁴	semidirect
302. C₂²×C₄×C₅₃	C₂×D₄	semidirect
312. C₂²×C₄×C₅₃	C₂⁴	semidirect
322. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
328. C₂²×Dic₅₃	C₂×D₄	semidirect
338. C₂²×Dic₅₃	C₂⁴	semidirect
353. C₂×D₂₁₂	C₂⁴	semidirect
374. C₂×C₄×D₅₃	C₂×D₄	semidirect
375. C₂×C₄×D₅₃	C₂×D₄	semidirect
376. C₂×C₄×D₅₃	C₂×D₄	semidirect
389. C₂×C₄×D₅₃	C₂⁴	semidirect
390. C₂×C₄×D₅₃	C₂⁴	semidirect
393. C₂×Dic₁₀₆	C₂⁴	semidirect
394. C₂×Dic₁₀₆	C₂⁴	semidirect
395. C₄⋊C₄×C₅₃	C₂⁴	semidirect
396. C₄⋊C₄×C₅₃	C₂⁴	semidirect
399. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
400. C₄²×C₅₃	C₂⁴	semidirect
403. C₂²⋊Dic₅₃	C₂⁴	semidirect
407. #11719921	C₂⁴	semidirect
408. #11719921	C₂⁴	semidirect
409. C₄⋊Dic₅₃	C₂⁴	semidirect
410. C₄⋊Dic₅₃	C₂⁴	semidirect
411. #11719919	C₂⁴	semidirect
412. #11719919	C₂⁴	semidirect
413. #11719919	C₂⁴	semidirect
414. C₄×Dic₅₃	C₂⁴	semidirect
415. C₄×Dic₅₃	C₂⁴	semidirect
425. C₂³×C₅₃	C₂×#41	semidirect
455. C₂²×D₅₃	C₂×#41	semidirect
456. C₂²×D₅₃	C₂×#41	semidirect
474. C₂×C₄×C₅₃	C₂²×D₄	semidirect
494. C₂×Dic₅₃	C₂²×D₄	semidirect
515. C₄×D₅₃	C₂²×D₄	semidirect
516. C₄×D₅₃	C₂²×D₄	semidirect
532. C₂²×C₅₃	C₂²×#41	semidirect
547. C₂×D₅₃	#525	direct (N × H)
551. C₂×D₅₃	C₂²×#41	semidirect
573. C₂×#525	D₅₃	direct (N × H)
583. C₂×C₅₃	C₂×#525	semidirect
589. D₅₃	C₂×#525	direct (N × H)
598. C₂²×#41	C₂×D₅₃	semidirect
615. C₂⁴×C₄	C₂×D₅₃	semidirect
624. #525	C₂×D₅₃	direct (N × H)
631. C₂×#123	C₂×D₅₃	semidirect
638. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
645. C₂×#121	C₂×D₅₃	semidirect
652. C₂×#120	C₂×D₅₃	semidirect
661. C₂×C₄×D₄	C₂×D₅₃	semidirect
667. C₂×#117	C₂×D₅₃	semidirect
674. C₅₃	C₂²×#525	semidirect
696. C₂×#41	C₂²×D₅₃	semidirect
701. C₂²×Q₈	C₂²×D₅₃	semidirect
718. C₂²×D₄	C₂²×D₅₃	semidirect
764. C₂³×C₄	C₂²×D₅₃	semidirect
765. C₂³×C₄	C₂²×D₅₃	semidirect
771. #123	C₂²×D₅₃	semidirect
777. C₂²⋊Q₈	C₂²×D₅₃	semidirect
783. #121	C₂²×D₅₃	semidirect
789. #120	C₂²×D₅₃	semidirect
797. C₄×D₄	C₂²×D₅₃	semidirect
802. #117	C₂²×D₅₃	semidirect
810. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
811. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
825. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
829. C₂×C₄²	C₂²×D₅₃	semidirect
872. C₂×Q₈	C₂³×D₅₃	semidirect
897. C₂×D₄	C₂³×D₅₃	semidirect
956. C₂²×C₄	D₄×D₅₃	semidirect
966. C₂²×C₄	C₂³×D₅₃	semidirect
972. C₄⋊C₄	C₂³×D₅₃	semidirect
973. C₄⋊C₄	C₂³×D₅₃	semidirect
984. C₂²⋊C₄	C₂³×D₅₃	semidirect
987. C₄²	C₂³×D₅₃	semidirect
1028. C₂³	#41×D₅₃	semidirect
1085. C₂×C₄	C₂×D₄×D₅₃	semidirect
1121. C₂²	C₂×#41×D₅₃	semidirect
1140. C₂	#525×D₅₃	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×#41×D₅₃	2
C₂⁴×C₄×D₅₃	2
C₂×#16811136	2
C₂×#16811135	2
C₂×#16811134	2
C₂×#16811133	2
C₂×#16811132	2
C₂×#16811131	2
C₂×#16811130	2
C₂×#16811129	2
#525×D₅₃	2
C₂×#123×D₅₃	2
C₂×C₂²⋊Q₈×D₅₃	2
C₂×#121×D₅₃	2
C₂×#120×D₅₃	2
C₂×C₄×D₄×D₅₃	2
C₂×#117×D₅₃	2
C₂×C₅₃×#525	2
C₂²×#525	53

Subgroups — C2×#525×D53 #28290743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#525×D₅₃ #28290743