Subgroups — C₂×#20288871 #28291216

Order 13568.

9542 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288871	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16811365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811364	C₂	1	2	yes	maximal, complemented
4	C₂×#16811363	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16811297	C₂	1	2	yes	maximal, complemented
6	C₂×#16811265	C₂	1	2	yes	maximal, complemented
7	C₂×#16811264	C₂	1	2	yes	maximal, complemented
8	C₂×#16811263	C₂	1	2	yes	maximal, complemented
9	C₂×D₄×D₂₁₂	C₂	1	2	yes	maximal, complemented
10	C₂×#16811255	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16811213	C₂	1	2	yes	maximal, complemented
12	C₂×#16811212	C₂	1	2	yes	maximal, complemented
13	C₂×#16811206	C₂	1	2	yes	maximal, complemented
14	C₂×#16811192	C₂	1	2	yes	maximal, complemented
15	C₂×#16811191	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16811184	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#16811184	C₂	1	2	yes	maximal, complemented
18	C₂²×#13133187	C₂	1	2	yes	maximal, complemented
19	C₂×#120×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₅₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂⁵×D₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#11719949	C₂²	1	1	yes	characteristic, complemented
23	C₂²×#11719945	C₂²	1	2	yes	complemented
24	C₂³×D₂₁₂	C₂²	1	2	yes	complemented
25	C₂³×D₂₁₂	C₂²	1	2	yes	complemented
26	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
27	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
28	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
30	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
31	#16811365	C₂²	1	16	yes	complemented
32	#16811364	C₂²	1	32	yes	complemented
33	#16811363	C₂²	1	16	yes	complemented
34	#16811297	C₂²	1	32	yes	complemented
35	#16811265	C₂²	1	32	yes	complemented
36	#16811264	C₂²	1	32	yes	complemented
37	#16811263	C₂²	1	32	yes	complemented
38	D₄×D₂₁₂	C₂²	1	32	yes	complemented
39	#16811255	C₂²	1	16	yes	complemented
40	#16811213	C₂²	1	32	yes	complemented
41	#16811212	C₂²	1	32	yes	complemented
42	#16811206	C₂²	1	32	yes	complemented
43	#16811192	C₂²	1	32	yes	complemented
44	#16811191	C₂²	1	16	yes	complemented
45	#16811184	C₂²	1	32	yes	complemented
46	#16811184	C₂²	1	16	yes	complemented
47	C₂×#13133214	C₂²	1	1	yes	characteristic, complemented
48	C₂×#13133214	C₂²	1	2	yes	complemented
49	C₂×#13133213	C₂²	1	1	yes	characteristic, complemented
50	C₂×#13133212	C₂²	1	2	yes	complemented
51	C₂×#13133212	C₂²	1	2	yes	complemented
52	C₂×#13133211	C₂²	1	2	yes	complemented
53	C₂×#13133206	C₂²	1	1	yes	characteristic, complemented
54	C₂×#13133206	C₂²	1	2	yes	complemented
55	C₂×#13133205	C₂²	1	2	yes	complemented
56	C₂×#13133205	C₂²	1	2	yes	complemented
57	C₂×#13133203	C₂²	1	2	yes	complemented
58	C₂×#13133203	C₂²	1	2	yes	complemented
59	C₂×#13133202	C₂²	1	2	yes	complemented
60	C₂×#13133202	C₂²	1	2	yes	complemented
61	C₂×#13133202	C₂²	1	2	yes	complemented
62	C₂×#13133202	C₂²	1	2	yes	complemented
63	C₂×#13133202	C₂²	1	2	yes	complemented
64	C₂×#13133200	C₂²	1	2	yes	complemented
65	C₂×#13133200	C₂²	1	1	yes	characteristic, complemented
66	C₂×#13133199	C₂²	1	2	yes	complemented
67	C₂×#13133195	C₂²	1	2	yes	complemented
68	C₂×#13133194	C₂²	1	2	yes	complemented
69	C₂×#13133192	C₂²	1	2	yes	complemented
70	C₂×#13133192	C₂²	1	2	yes	complemented
71	C₂×#13133192	C₂²	1	2	yes	complemented
72	C₂×#13133192	C₂²	1	2	yes	complemented
73	C₂×#13133192	C₂²	1	2	yes	complemented
74	C₂×#13133192	C₂²	1	2	yes	complemented
75	C₂×#13133192	C₂²	1	2	yes	complemented
76	C₂×#13133191	C₂²	1	2	yes	complemented
77	C₂×#13133191	C₂²	1	2	yes	complemented
78	C₂×#13133190	C₂²	1	2	yes	complemented
79	C₂×#13133190	C₂²	1	2	yes	complemented
80	C₂×#13133190	C₂²	1	2	yes	complemented
81	C₂×#13133190	C₂²	1	2	yes	complemented
82	C₂×#13133190	C₂²	1	2	yes	complemented
83	C₂×#13133189	C₂²	1	2	yes	complemented
84	C₂×#13133187	C₂²	1	2	yes	—
85	C₂×#13133187	C₂²	1	2	yes	complemented
86	C₂×#13133187	C₂²	1	2	yes	complemented
87	C₂×#13133187	C₂²	1	2	yes	complemented
88	C₂×#13133187	C₂²	1	2	yes	complemented
89	C₂×#13133187	C₂²	1	2	yes	complemented
90	C₂×#13133187	C₂²	1	2	yes	complemented
91	C₂×#13133187	C₂²	1	1	yes	characteristic, complemented
92	C₂×#13133187	C₂²	1	2	yes	complemented
93	C₂×#13133187	C₂²	1	2	yes	complemented
94	C₂×#13133187	C₂²	1	2	yes	complemented
95	C₂×#13133187	C₂²	1	2	yes	complemented
96	C₂×#13133187	C₂²	1	2	yes	complemented
97	C₂×#13133187	C₂²	1	32	yes	complemented
98	C₂×#13133187	C₂²	1	1	yes	characteristic, complemented
99	C₂×#13133187	C₂²	1	2	yes	complemented
100	C₂×#13133186	C₂²	1	1	yes	characteristic, complemented
101	C₂×#13133185	C₂²	1	2	yes	complemented
102	C₂×#13133185	C₂²	1	1	yes	characteristic, complemented
103	C₂×#13133185	C₂²	1	1	yes	characteristic, complemented
104	#120×D₅₃	C₂²	1	16	yes	complemented
105	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
106	C₂×#13133179	C₂²	1	2	yes	complemented
107	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
108	C₂×#13133177	C₂²	1	2	yes	complemented
109	C₂×#13133177	C₂²	1	2	yes	complemented
110	C₂×#13133174	C₂²	1	1	yes	characteristic, complemented
111	C₂²×#11719921	C₂²	1	2	yes	complemented
112	C₂²×#11719921	C₂²	1	2	yes	complemented
113	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
115	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
116	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#551	C₂²	1	16	yes	complemented
118	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
119	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
122	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
123	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
124	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
125	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
126	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
127	C₂⁴×D₅₃	—	4	4	no	—
128	C₂⁴×D₅₃	—	4	8	no	—
129	C₂⁴×D₅₃	C₂³	1	2	yes	—
130	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
131	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
132	C₂⁴×D₅₃	C₂³	1	2	yes	—
133	C₂⁴×D₅₃	C₂³	1	2	yes	—
134	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
135	C₂⁴×D₅₃	C₂³	1	8	yes	complemented
136	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic, complemented
137	C₂×#11719949	—	4	4	no	—
138	C₂×#11719949	C₂³	1	8	yes	complemented
139	C₂×#11719945	—	4	8	no	—
140	C₂×#11719945	C₂³	1	16	yes	complemented
141	C₂²×Dic₁₀₆	C₂³	1	2	yes	complemented
142	C₂²×D₂₁₂	—	4	4	no	—
143	C₂²×D₂₁₂	—	4	8	no	—
144	C₂²×D₂₁₂	—	4	8	no	—
145	C₂²×D₂₁₂	C₂³	1	2	yes	—
146	C₂²×D₂₁₂	C₂³	1	2	yes	—
147	C₂²×D₂₁₂	C₂³	1	2	yes	—
148	C₂²×D₂₁₂	C₂³	1	2	yes	—
149	C₂²×D₂₁₂	C₂³	1	2	yes	—
150	C₂²×D₂₁₂	C₂³	1	2	yes	—
151	C₂²×D₂₁₂	C₂³	1	2	yes	—
152	C₂²×D₂₁₂	C₂³	1	2	yes	—
153	C₂²×D₂₁₂	C₂³	1	2	yes	—
154	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
155	C₂²×D₂₁₂	C₂³	1	16	yes	complemented
156	C₂²×D₂₁₂	C₂³	1	16	yes	complemented
157	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
158	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
159	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
160	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
161	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
162	C₂²×C₂²⋊D₅₃	—	4	8	no	—
163	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
164	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
165	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
166	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
167	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
168	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
169	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
170	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
171	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
172	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
173	C₂×D₄×D₅₃	—	4	4	no	—
174	C₂×D₄×D₅₃	—	4	8	no	—
175	C₂×D₄×D₅₃	—	4	8	no	—
176	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
177	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
178	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
179	C₂³×Dic₅₃	C₂³	1	2	yes	—
180	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
181	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
182	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
183	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
184	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
185	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
186	#13133214	C₂³	1	16	yes	complemented
187	#13133214	C₂³	1	8	yes	complemented
188	#13133213	C₂³	1	8	yes	complemented
189	#13133212	C₂³	1	16	yes	complemented
190	#13133212	C₂³	1	16	yes	complemented
191	#13133211	C₂³	1	16	yes	complemented
192	#13133206	C₂³	1	16	yes	complemented
193	#13133206	C₂³	1	8	yes	complemented
194	#13133205	C₂³	1	16	yes	complemented
195	#13133205	C₂³	1	16	yes	complemented
196	#13133203	C₂³	1	16	yes	complemented
197	#13133203	C₂³	1	16	yes	complemented
198	#13133202	C₂³	1	16	yes	complemented
199	#13133202	C₂³	1	16	yes	complemented
200	#13133202	C₂³	1	16	yes	complemented
201	#13133202	C₂³	1	16	yes	complemented
202	#13133202	C₂³	1	16	yes	complemented
203	#13133200	C₂³	1	16	yes	complemented
204	#13133200	C₂³	1	8	yes	complemented
205	#13133199	C₂³	1	16	yes	complemented
206	#13133195	C₂³	1	16	yes	complemented
207	#13133194	C₂³	1	16	yes	complemented
208	#13133192	C₂³	1	16	yes	complemented
209	#13133192	C₂³	1	16	yes	complemented
210	#13133192	C₂³	1	16	yes	complemented
211	#13133192	C₂³	1	16	yes	complemented
212	#13133192	C₂³	1	16	yes	complemented
213	#13133192	C₂³	1	16	yes	complemented
214	#13133192	C₂³	1	16	yes	complemented
215	#13133191	C₂³	1	16	yes	complemented
216	#13133191	C₂³	1	16	yes	complemented
217	#13133190	C₂³	1	16	yes	complemented
218	#13133190	C₂³	1	16	yes	complemented
219	#13133190	C₂³	1	16	yes	complemented
220	#13133190	C₂³	1	16	yes	complemented
221	#13133190	C₂³	1	16	yes	complemented
222	#13133189	C₂³	1	16	yes	complemented
223	#13133187	C₂³	1	16	yes	—
224	#13133187	C₂³	1	16	yes	complemented
225	#13133187	C₂³	1	8	yes	complemented
226	#13133187	C₂³	1	16	yes	complemented
227	#13133187	C₂³	1	16	yes	complemented
228	#13133187	C₂³	1	16	yes	complemented
229	#13133187	C₂³	1	16	yes	complemented
230	#13133187	C₂³	1	16	yes	complemented
231	#13133187	C₂³	1	16	yes	complemented
232	#13133187	C₂³	1	16	yes	complemented
233	#13133187	C₂³	1	16	yes	complemented
234	#13133187	C₂³	1	8	yes	complemented
235	#13133187	C₂³	1	16	yes	complemented
236	#13133187	C₂³	1	16	yes	complemented
237	#13133187	C₂³	1	16	yes	complemented
238	#13133186	C₂³	1	8	yes	complemented
239	#13133185	C₂³	1	8	yes	complemented
240	#13133185	C₂³	1	16	yes	complemented
241	#13133185	C₂³	1	8	yes	complemented
242	C₄×D₂₁₂	C₂³	1	16	yes	complemented
243	#13133179	C₂³	1	16	yes	complemented
244	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
245	#13133177	C₂³	1	16	yes	complemented
246	#13133177	C₂³	1	16	yes	complemented
247	#13133174	C₂³	1	8	yes	complemented
248	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
249	C₂×#11719919	C₂³	1	2	yes	complemented
250	C₂×#11719919	C₂³	1	2	yes	complemented
251	C₂×#11719919	C₂³	1	2	yes	complemented
252	C₂×#11719919	C₂³	1	2	yes	complemented
253	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
254	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
256	C₂×#11719921	C₂³	1	2	yes	—
257	C₂×#11719921	C₂³	1	2	yes	—
258	C₂×#11719921	C₂³	1	2	yes	—
259	C₂×#11719921	C₂³	1	2	yes	—
260	C₂×#11719921	C₂³	1	2	yes	—
261	C₂×#11719921	C₂³	1	2	yes	—
262	C₂×#11719921	C₂³	1	2	yes	—
263	C₂×#11719921	C₂³	1	2	yes	—
264	C₂×#11719921	C₂³	1	2	yes	—
265	C₂×#11719921	C₂³	1	2	yes	—
266	C₂×#11719921	C₂³	1	2	yes	—
267	C₂×#11719921	C₂³	1	16	yes	complemented
268	C₂×#11719921	C₂³	1	16	yes	complemented
269	C₂×#11719921	C₂³	1	2	yes	complemented
270	C₂×#11719921	C₂³	1	2	yes	complemented
271	C₂×#11719921	C₂³	1	2	yes	complemented
272	C₂×#11719921	C₂³	1	2	yes	complemented
273	C₂×#11719921	C₂³	1	2	yes	complemented
274	C₂×#11719921	C₂³	1	2	yes	complemented
275	C₂×#11719921	C₂³	1	2	yes	complemented
276	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
277	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
278	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
279	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
280	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
281	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
282	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
283	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
284	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
285	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
287	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
288	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
289	#126×C₅₃	C₂³	1	16	yes	complemented
290	#124×C₅₃	C₂³	1	8	yes	complemented
291	#123×C₅₃	C₂³	1	16	yes	complemented
292	#123×C₅₃	C₂³	1	8	yes	complemented
293	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
294	#120×C₅₃	C₂³	1	8	yes	—
295	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
296	#117×C₅₃	C₂³	1	16	yes	complemented
297	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
298	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
299	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
300	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
301	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
302	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
303	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
304	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
305	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
306	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	complemented
308	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
309	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
310	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic, complemented
311	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
312	C₂⁴×C₅₃	—	2	8	no	—
313	C₂⁴×C₅₃	—	4	2	no	—
314	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
315	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
316	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
317	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
318	C₂³×D₅₃	—	2	8	no	—
319	C₂³×D₅₃	—	2	8	no	—
320	C₂³×D₅₃	—	2	8	no	—
321	C₂³×D₅₃	—	2	4	no	—
322	C₂³×D₅₃	—	2	8	no	—
323	C₂³×D₅₃	—	2	4	no	—
324	C₂³×D₅₃	—	4	16	no	—
325	C₂³×D₅₃	—	4	4	no	—
326	C₂³×D₅₃	—	4	4	no	—
327	C₂³×D₅₃	—	4	2	no	—
328	C₂³×D₅₃	—	4	4	no	—
329	C₂³×D₅₃	—	4	4	no	—
330	C₂³×D₅₃	—	4	4	no	—
331	C₂³×D₅₃	—	4	32	no	—
332	C₂³×D₅₃	—	4	4	no	—
333	C₂³×D₅₃	—	4	4	no	—
334	C₂³×D₅₃	—	4	4	no	—
335	C₂³×D₅₃	—	4	4	no	—
336	C₂³×D₅₃	—	4	2	no	—
337	C₂³×D₅₃	—	4	64	no	—
338	C₂³×D₅₃	C₂⁴	1	2	yes	—
339	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
340	C₂³×D₅₃	C₂⁴	1	2	yes	—
341	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
342	C₂³×D₅₃	C₂⁴	1	2	yes	—
343	C₂³×D₅₃	C₂⁴	1	8	yes	—
344	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
345	C₂³×D₅₃	C₂⁴	1	4	yes	—
346	C₂³×D₅₃	C₂⁴	1	4	yes	—
347	C₂³×D₅₃	C₂⁴	1	8	yes	—
348	C₂³×D₅₃	C₂⁴	1	8	yes	—
349	C₂³×D₅₃	C₂⁴	1	4	yes	—
350	C₂³×D₅₃	C₂⁴	1	4	yes	complemented
351	C₂×Q₈×C₅₃	—	4	2	no	—
352	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	complemented
353	C₂×D₄×C₅₃	—	2	8	no	—
354	C₂×D₄×C₅₃	—	4	2	no	—
355	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
356	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
357	C₂²×C₄×C₅₃	—	2	8	no	—
358	C₂²×C₄×C₅₃	—	4	4	no	—
359	C₂²×C₄×C₅₃	—	4	2	no	—
360	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
365	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
366	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
367	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
368	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	complemented
369	C₂×C₂²⋊D₅₃	—	2	8	no	—
370	C₂×C₂²⋊D₅₃	—	2	8	no	—
371	C₂×C₂²⋊D₅₃	—	2	8	no	—
372	C₂×C₂²⋊D₅₃	—	4	4	no	—
373	C₂×C₂²⋊D₅₃	—	4	2	no	—
374	C₂×C₂²⋊D₅₃	—	4	2	no	—
375	C₂×C₂²⋊D₅₃	—	4	4	no	—
376	C₂×C₂²⋊D₅₃	—	4	4	no	—
377	C₂×C₂²⋊D₅₃	—	4	4	no	—
378	C₂×C₂²⋊D₅₃	—	4	32	no	—
379	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
380	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
381	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
382	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
383	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
384	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
385	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
386	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
387	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
388	C₂²×Dic₅₃	—	4	4	no	—
389	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
390	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
391	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
392	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
394	#11719949	—	4	16	no	—
395	D₄×D₅₃	—	4	16	no	—
396	D₄×D₅₃	—	4	32	no	—
397	D₄×D₅₃	—	4	32	no	—
398	#11719945	—	4	32	no	—
399	C₂×D₂₁₂	—	2	8	no	—
400	C₂×D₂₁₂	—	2	8	no	—
401	C₂×D₂₁₂	—	4	16	no	—
402	C₂×D₂₁₂	—	4	32	no	—
403	C₂×D₂₁₂	—	4	2	no	—
404	C₂×D₂₁₂	—	4	4	no	—
405	C₂×D₂₁₂	—	4	4	no	—
406	C₂×D₂₁₂	—	4	4	no	—
407	C₂×D₂₁₂	—	4	4	no	—
408	C₂×D₂₁₂	—	4	4	no	—
409	C₂×D₂₁₂	—	4	4	no	—
410	C₂×D₂₁₂	—	4	4	no	—
411	C₂×D₂₁₂	—	4	4	no	—
412	C₂×D₂₁₂	—	4	32	no	—
413	C₂×D₂₁₂	—	4	4	no	—
414	C₂×D₂₁₂	—	4	4	no	—
415	C₂×D₂₁₂	—	4	2	no	—
416	C₂×D₂₁₂	C₂⁴	1	8	yes	—
417	C₂×D₂₁₂	C₂⁴	1	8	yes	—
418	C₂×D₂₁₂	C₂⁴	1	8	yes	—
419	C₂×D₂₁₂	C₂⁴	1	8	yes	—
420	C₂×D₂₁₂	C₂⁴	1	8	yes	—
421	C₂×D₂₁₂	C₂⁴	1	8	yes	—
422	C₂×D₂₁₂	C₂⁴	1	8	yes	—
423	C₂×D₂₁₂	C₂⁴	1	8	yes	—
424	C₂×D₂₁₂	C₂⁴	1	8	yes	—
425	C₂×D₂₁₂	C₂⁴	1	4	yes	—
426	C₂×D₂₁₂	C₂⁴	1	8	yes	complemented
427	C₂×D₂₁₂	C₂⁴	1	4	yes	complemented
428	C₂×D₂₁₂	C₂⁴	1	8	yes	complemented
429	C₂×D₂₁₂	C₂⁴	1	8	yes	complemented
430	C₂×C₄×D₅₃	—	2	4	no	—
431	C₂×C₄×D₅₃	—	4	4	no	—
432	C₂×C₄×D₅₃	—	4	4	no	—
433	C₂×C₄×D₅₃	—	4	4	no	—
434	C₂×C₄×D₅₃	—	4	4	no	—
435	C₂×C₄×D₅₃	—	4	4	no	—
436	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
437	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
438	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
439	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
440	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
441	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
442	C₂×Dic₁₀₆	—	4	4	no	—
443	C₂×Dic₁₀₆	C₂⁴	1	8	yes	complemented
444	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
445	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
446	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
447	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
448	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
449	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
450	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
451	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
452	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
453	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
454	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
455	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	complemented
456	C₄²×C₅₃	C₂⁴	1	4	yes	complemented
457	C₄²×C₅₃	C₂⁴	1	8	yes	complemented
458	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
459	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
460	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	complemented
461	#11719921	C₂⁴	1	8	yes	—
462	#11719921	C₂⁴	1	8	yes	—
463	#11719921	C₂⁴	1	8	yes	—
464	#11719921	C₂⁴	1	8	yes	—
465	#11719921	C₂⁴	1	8	yes	—
466	#11719921	C₂⁴	1	8	yes	—
467	#11719921	C₂⁴	1	8	yes	—
468	#11719921	C₂⁴	1	8	yes	—
469	#11719921	C₂⁴	1	8	yes	—
470	#11719921	C₂⁴	1	8	yes	—
471	#11719921	C₂⁴	1	8	yes	—
472	#11719921	C₂⁴	1	8	yes	complemented
473	#11719921	C₂⁴	1	8	yes	complemented
474	#11719921	C₂⁴	1	8	yes	complemented
475	#11719921	C₂⁴	1	8	yes	complemented
476	#11719921	C₂⁴	1	8	yes	complemented
477	#11719921	C₂⁴	1	8	yes	complemented
478	#11719921	C₂⁴	1	8	yes	complemented
479	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
480	#11719919	C₂⁴	1	8	yes	complemented
481	#11719919	C₂⁴	1	8	yes	complemented
482	#11719919	C₂⁴	1	8	yes	complemented
483	#11719919	C₂⁴	1	8	yes	complemented
484	C₄×Dic₅₃	C₂⁴	1	4	yes	complemented
485	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
486	C₂³×C₅₃	—	2	4	no	—
487	C₂³×C₅₃	—	2	4	no	—
488	C₂³×C₅₃	—	2	4	no	—
489	C₂³×C₅₃	—	2	16	no	—
490	C₂³×C₅₃	—	2	4	no	—
491	C₂³×C₅₃	—	2	2	no	—
492	C₂³×C₅₃	—	2	2	no	—
493	C₂³×C₅₃	—	4	4	no	—
494	C₂³×C₅₃	—	4	16	no	—
495	C₂³×C₅₃	H(5,𝔽₂)	1	8	yes	—
496	C₂³×C₅₃	C₂⁵	1	2	yes	—
497	C₂³×C₅₃	C₂⁵	1	2	yes	—
498	C₂³×C₅₃	C₂⁵	1	4	yes	—
499	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
500	C₂²×D₅₃	—	2	4	no	—
501	C₂²×D₅₃	—	2	4	no	—
502	C₂²×D₅₃	—	2	4	no	—
503	C₂²×D₅₃	—	2	4	no	—
504	C₂²×D₅₃	—	2	4	no	—
505	C₂²×D₅₃	—	2	4	no	—
506	C₂²×D₅₃	—	2	2	no	—
507	C₂²×D₅₃	—	2	4	no	—
508	C₂²×D₅₃	—	2	4	no	—
509	C₂²×D₅₃	—	2	16	no	—
510	C₂²×D₅₃	—	2	4	no	—
511	C₂²×D₅₃	—	2	4	no	—
512	C₂²×D₅₃	—	2	4	no	—
513	C₂²×D₅₃	—	2	2	no	—
514	C₂²×D₅₃	—	2	4	no	—
515	C₂²×D₅₃	—	2	16	no	—
516	C₂²×D₅₃	—	2	16	no	—
517	C₂²×D₅₃	—	2	16	no	—
518	C₂²×D₅₃	—	2	8	no	—
519	C₂²×D₅₃	—	2	8	no	—
520	C₂²×D₅₃	—	4	8	no	—
521	C₂²×D₅₃	—	4	8	no	—
522	C₂²×D₅₃	—	4	4	no	—
523	C₂²×D₅₃	—	4	8	no	—
524	C₂²×D₅₃	—	4	8	no	—
525	C₂²×D₅₃	—	4	8	no	—
526	C₂²×D₅₃	—	4	8	no	—
527	C₂²×D₅₃	—	4	4	no	—
528	C₂²×D₅₃	—	4	8	no	—
529	C₂²×D₅₃	—	4	8	no	—
530	C₂²×D₅₃	—	4	8	no	—
531	C₂²×D₅₃	—	4	32	no	—
532	C₂²×D₅₃	—	4	16	no	—
533	C₂²×D₅₃	—	4	32	no	—
534	C₂²×D₅₃	—	4	128	no	—
535	C₂²×D₅₃	—	4	16	no	—
536	C₂²×D₅₃	—	8	8	no	—
537	C₂²×D₅₃	—	8	16	no	—
538	C₂²×D₅₃	—	8	8	no	—
539	C₂²×D₅₃	H(5,𝔽₂)	1	4	yes	—
540	C₂²×D₅₃	C₂⁵	1	4	yes	—
541	C₂²×D₅₃	C₂⁵	1	2	yes	—
542	C₂²×D₅₃	C₂⁵	1	4	yes	—
543	C₂²×D₅₃	C₂⁵	1	4	yes	—
544	C₂²×D₅₃	C₂⁵	1	2	yes	—
545	C₂²×D₅₃	C₂⁵	1	2	yes	—
546	Q₈×C₅₃	—	4	4	no	—
547	D₄×C₅₃	—	2	16	no	—
548	D₄×C₅₃	—	4	4	no	—
549	C₂×C₄×C₅₃	—	2	4	no	—
550	C₂×C₄×C₅₃	—	2	2	no	—
551	C₂×C₄×C₅₃	—	2	4	no	—
552	C₂×C₄×C₅₃	—	2	4	no	—
553	C₂×C₄×C₅₃	—	2	4	no	—
554	C₂×C₄×C₅₃	—	2	4	no	—
555	C₂×C₄×C₅₃	—	2	16	no	—
556	C₂×C₄×C₅₃	—	4	8	no	—
557	C₂×C₄×C₅₃	—	4	4	no	—
558	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
559	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
560	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
561	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
562	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
563	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
564	C₂²⋊D₅₃	—	2	16	no	—
565	C₂²⋊D₅₃	—	2	16	no	—
566	C₂²⋊D₅₃	—	2	16	no	—
567	C₂²⋊D₅₃	—	4	8	no	—
568	C₂²⋊D₅₃	—	4	4	no	—
569	C₂²⋊D₅₃	—	4	4	no	—
570	C₂²⋊D₅₃	—	4	8	no	—
571	C₂²⋊D₅₃	—	4	8	no	—
572	C₂²⋊D₅₃	—	4	8	no	—
573	C₂×Dic₅₃	—	2	4	no	—
574	C₂×Dic₅₃	—	2	4	no	—
575	C₂×Dic₅₃	—	2	2	no	—
576	C₂×Dic₅₃	—	2	4	no	—
577	C₂×Dic₅₃	—	4	8	no	—
578	C₂×Dic₅₃	C₂⁵	1	4	yes	—
579	C₂×Dic₅₃	C₂⁵	1	4	yes	—
580	C₂×Dic₅₃	C₂⁵	1	2	yes	—
581	C₂×Dic₅₃	C₂⁵	1	4	yes	—
582	D₂₁₂	—	2	16	no	—
583	D₂₁₂	—	2	16	no	—
584	D₂₁₂	—	4	8	no	—
585	D₂₁₂	—	4	8	no	—
586	D₂₁₂	—	4	8	no	—
587	D₂₁₂	—	4	8	no	—
588	D₂₁₂	—	4	8	no	—
589	D₂₁₂	—	4	8	no	—
590	D₂₁₂	—	4	8	no	—
591	D₂₁₂	—	4	4	no	—
592	D₂₁₂	—	4	8	no	—
593	D₂₁₂	—	4	8	no	—
594	D₂₁₂	—	4	8	no	—
595	D₂₁₂	—	4	4	no	—
596	C₄×D₅₃	—	2	8	no	—
597	C₄×D₅₃	—	4	8	no	—
598	C₄×D₅₃	—	4	8	no	—
599	C₄×D₅₃	—	4	8	no	—
600	C₄×D₅₃	—	4	8	no	—
601	C₄×D₅₃	—	4	8	no	—
602	Dic₁₀₆	—	4	8	no	—
603	C₂×#3532	—	53	1	no	maximal, Sylow
604	C₂²×C₅₃	—	2	4	no	—
605	C₂²×C₅₃	—	2	4	no	—
606	C₂²×C₅₃	—	2	16	no	—
607	C₂²×C₅₃	—	2	4	no	—
608	C₂²×C₅₃	—	2	4	no	—
609	C₂²×C₅₃	—	2	2	no	—
610	C₂²×C₅₃	—	2	2	no	—
611	C₂²×C₅₃	—	4	16	no	—
612	C₂²×C₅₃	—	4	4	no	—
613	C₂²×C₅₃	—	4	4	no	—
614	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
615	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	8	yes	—
616	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
617	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
618	C₂×D₅₃	—	2	4	no	—
619	C₂×D₅₃	—	2	8	no	—
620	C₂×D₅₃	—	2	4	no	—
621	C₂×D₅₃	—	2	4	no	—
622	C₂×D₅₃	—	2	4	no	—
623	C₂×D₅₃	—	2	4	no	—
624	C₂×D₅₃	—	2	4	no	—
625	C₂×D₅₃	—	2	2	no	—
626	C₂×D₅₃	—	2	4	no	—
627	C₂×D₅₃	—	2	4	no	—
628	C₂×D₅₃	—	2	4	no	—
629	C₂×D₅₃	—	2	4	no	—
630	C₂×D₅₃	—	2	4	no	—
631	C₂×D₅₃	—	2	2	no	—
632	C₂×D₅₃	—	2	4	no	—
633	C₂×D₅₃	—	4	32	no	—
634	C₂×D₅₃	—	4	16	no	—
635	C₂×D₅₃	—	4	32	no	—
636	C₂×D₅₃	—	4	16	no	—
637	C₂×D₅₃	—	4	8	no	—
638	C₂×D₅₃	—	4	4	no	—
639	C₂×D₅₃	—	4	8	no	—
640	C₂×D₅₃	—	4	4	no	—
641	C₂×D₅₃	—	4	8	no	—
642	C₂×D₅₃	—	8	8	no	—
643	C₂×D₅₃	—	8	16	no	—
644	C₂×D₅₃	—	8	8	no	—
645	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
646	C₄×C₅₃	—	2	4	no	—
647	C₄×C₅₃	—	2	2	no	—
648	C₄×C₅₃	—	2	4	no	—
649	C₄×C₅₃	—	2	4	no	—
650	C₄×C₅₃	—	2	4	no	—
651	C₄×C₅₃	—	2	4	no	—
652	Dic₅₃	—	2	4	no	—
653	Dic₅₃	—	2	4	no	—
654	Dic₅₃	—	2	2	no	—
655	Dic₅₃	—	2	4	no	—
656	#3532	—	53	32	no	—
657	C₂×H(3,𝔽₄)	—	53	1	no	—
658	C₂×#560	—	53	2	no	—
659	C₂×#560	—	53	1	no	—
660	C₂×#551	—	53	2	no	—
661	C₂×#551	D₅₃	1	1	yes	characteristic, complemented
662	C₂×#546	—	53	2	no	—
663	C₂×#546	—	53	2	no	—
664	C₂×#546	—	53	2	no	—
665	C₂×D₄²	—	53	1	no	—
666	C₂×D₄²	—	53	2	no	—
667	C₂×#538	—	53	2	no	—
668	C₂×#538	—	53	2	no	—
669	C₂×#538	—	53	2	no	—
670	C₂×#535	—	53	1	no	—
671	C₂×#535	—	53	2	no	—
672	C₂×#534	—	53	2	no	—
673	C₂×#534	—	53	1	no	—
674	C₂²×#120	—	53	1	no	—
675	C₂²×#120	—	53	2	no	—
676	C₂×C₅₃	—	2	8	no	—
677	C₂×C₅₃	—	4	2	no	—
678	C₂×C₅₃	—	4	2	no	—
679	C₂×C₅₃	#3532	1	4	yes	complemented
680	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
681	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	2	yes	—
682	D₅₃	—	2	4	no	—
683	D₅₃	—	4	4	no	—
684	D₅₃	—	4	2	no	—
685	D₅₃	—	4	4	no	—
686	D₅₃	—	4	2	no	—
687	D₅₃	—	4	4	no	—
688	C₂⁶	—	53	1	no	—
689	C₂²×#41	—	53	1	no	—
690	C₂²×#41	—	53	2	no	—
691	C₂³×D₄	—	53	2	no	—
692	C₂³×D₄	—	53	1	no	—
693	C₂³×D₄	—	53	2	no	—
694	C₂³×D₄	—	53	2	no	—
695	C₂³×D₄	—	53	2	no	—
696	C₂³×D₄	—	53	2	no	—
697	C₂³×D₄	—	53	1	no	—
698	H(3,𝔽₄)	—	53	16	no	—
699	#560	—	53	32	no	—
700	#560	—	53	16	no	—
701	#551	—	53	32	no	—
702	#551	C₂×D₅₃	1	16	yes	complemented
703	#546	—	53	32	no	—
704	#546	—	53	32	no	—
705	#546	—	53	32	no	—
706	D₄²	—	53	16	no	—
707	D₄²	—	53	32	no	—
708	#538	—	53	32	no	—
709	#538	—	53	32	no	—
710	#538	—	53	32	no	—
711	#535	—	53	16	no	—
712	#535	—	53	32	no	—
713	#534	—	53	32	no	—
714	#534	—	53	16	no	—
715	C₂×#127	—	53	1	no	—
716	C₂×#127	—	53	1	no	—
717	C₂×#127	—	53	2	no	—
718	C₂×#126	—	53	2	no	—
719	C₂×#126	—	53	2	no	—
720	C₂×#126	—	53	2	no	—
721	C₂×#126	C₂×D₅₃	1	2	yes	complemented
722	C₂×#124	—	53	1	no	—
723	C₂×#124	—	53	2	no	—
724	C₂×#124	—	53	2	no	—
725	C₂×#124	—	53	2	no	—
726	C₂×#124	—	53	2	no	—
727	C₂×#124	—	53	2	no	—
728	C₂×#124	C₂×D₅₃	1	1	yes	characteristic, complemented
729	C₂×#123	—	53	2	no	—
730	C₂×#123	—	53	1	no	—
731	C₂×#123	—	53	2	no	—
732	C₂×#123	—	53	2	no	—
733	C₂×#123	—	53	2	no	—
734	C₂×#123	—	53	2	no	—
735	C₂×#123	—	53	2	no	—
736	C₂×#123	—	53	2	no	—
737	C₂×#123	C₂×D₅₃	1	1	yes	characteristic, complemented
738	C₂×#123	C₂×D₅₃	1	2	yes	complemented
739	C₂×C₂²⋊Q₈	—	53	2	no	—
740	C₂×C₂²⋊Q₈	—	53	2	no	—
741	C₂×C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
742	C₂×#121	—	53	2	no	—
743	C₂×#121	—	53	2	no	—
744	C₂×#121	—	53	2	no	—
745	C₂×#121	—	53	2	no	—
746	C₂×#121	—	53	2	no	—
747	C₂×#121	—	53	2	no	—
748	C₂×#121	—	53	2	no	—
749	C₂×#121	—	53	2	no	—
750	C₂×#121	—	53	2	no	—
751	C₂×#121	—	53	2	no	—
752	C₂×#121	—	53	2	no	—
753	C₂×#121	—	53	2	no	—
754	C₂×#121	—	53	2	no	—
755	C₂×#121	—	53	2	no	—
756	C₂×#121	—	53	2	no	—
757	C₂×#120	—	53	1	no	—
758	C₂×#120	—	53	2	no	—
759	C₂×#120	—	53	1	no	—
760	C₂×#120	—	53	1	no	—
761	C₂×#120	—	53	16	no	—
762	C₂×#120	—	53	2	no	—
763	C₂×#120	—	53	2	no	—
764	C₂×#120	—	53	2	no	—
765	C₂×#120	—	53	2	no	—
766	C₂×#120	—	53	2	no	—
767	C₂×#120	—	53	2	no	—
768	C₂×#120	—	53	2	no	—
769	C₂×#120	—	53	2	no	—
770	C₂×#120	—	53	1	no	—
771	C₂×#120	—	53	2	no	—
772	C₂×#120	—	53	2	no	—
773	C₂×#120	—	53	2	no	—
774	C₂×#120	—	53	32	no	—
775	C₂×#120	—	53	1	no	—
776	C₂×#120	—	53	2	no	—
777	C₂×#120	—	53	2	no	—
778	C₂×#120	C₂×D₅₃	1	1	yes	characteristic
779	C₂×C₄×D₄	—	53	2	no	—
780	C₂×C₄×D₄	—	53	2	no	—
781	C₂×C₄×D₄	—	53	2	no	—
782	C₂×C₄×D₄	—	53	2	no	—
783	C₂×C₄×D₄	—	53	2	no	—
784	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
785	C₂×#117	—	53	1	no	—
786	C₂×#117	C₂×D₅₃	1	2	yes	complemented
787	C₂²×C₂²⋊C₄	—	53	2	no	—
788	C₂²×C₂²⋊C₄	—	53	2	no	—
789	C₂²×C₂²⋊C₄	—	53	1	no	—
790	C₂²×C₂²⋊C₄	—	53	2	no	—
791	C₂²×C₂²⋊C₄	—	53	2	no	—
792	C₂²×C₂²⋊C₄	—	53	1	no	—
793	C₂²×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
794	C₅₃	C₂×#3532	1	1	yes	characteristic, complemented, Sylow
795	C₂⁵	—	53	2	no	—
796	C₂⁵	—	53	1	no	—
797	C₂⁵	—	53	2	no	—
798	C₂⁵	—	53	1	no	—
799	C₂⁵	—	53	2	no	—
800	C₂⁵	—	53	1	no	—
801	C₂⁵	—	53	8	no	—
802	C₂⁵	—	53	1	no	—
803	C₂⁵	—	212	8	no	—
804	C₂⁵	—	212	4	no	—
805	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
806	C₂×#41	—	53	8	no	—
807	C₂×#41	—	53	16	no	—
808	C₂×#41	—	212	8	no	—
809	C₂×#41	—	212	4	no	—
810	C₂²×Q₈	—	53	2	no	—
811	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
812	C₂²×D₄	—	53	2	no	—
813	C₂²×D₄	—	53	2	no	—
814	C₂²×D₄	—	53	2	no	—
815	C₂²×D₄	—	53	1	no	—
816	C₂²×D₄	—	53	2	no	—
817	C₂²×D₄	—	53	2	no	—
818	C₂²×D₄	—	53	1	no	—
819	C₂²×D₄	—	53	2	no	—
820	C₂²×D₄	—	53	16	no	—
821	C₂²×D₄	—	53	2	no	—
822	C₂²×D₄	—	53	8	no	—
823	C₂²×D₄	—	53	16	no	—
824	C₂²×D₄	—	53	16	no	—
825	C₂²×D₄	—	53	2	no	—
826	C₂²×D₄	—	53	2	no	—
827	C₂²×D₄	—	53	2	no	—
828	C₂²×D₄	—	53	2	no	—
829	C₂²×D₄	—	53	2	no	—
830	C₂²×D₄	—	53	2	no	—
831	C₂²×D₄	—	53	2	no	—
832	C₂²×D₄	—	53	2	no	—
833	C₂²×D₄	—	53	1	no	—
834	C₂²×D₄	—	53	2	no	—
835	C₂²×D₄	—	53	1	no	—
836	C₂²×D₄	—	53	2	no	—
837	C₂²×D₄	—	53	16	no	—
838	C₂²×D₄	—	53	16	no	—
839	C₂²×D₄	—	53	2	no	—
840	C₂²×D₄	—	53	2	no	—
841	C₂²×D₄	—	53	8	no	—
842	C₂²×D₄	—	212	8	no	—
843	C₂²×D₄	—	212	8	no	—
844	C₂²×D₄	—	212	4	no	—
845	C₂²×D₄	—	212	4	no	—
846	C₂²×D₄	—	212	8	no	—
847	C₂²×D₄	—	212	8	no	—
848	C₂²×D₄	—	212	8	no	—
849	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
850	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
851	C₂³×C₄	—	53	2	no	—
852	C₂³×C₄	—	53	1	no	—
853	C₂³×C₄	—	53	2	no	—
854	C₂³×C₄	—	53	2	no	—
855	C₂³×C₄	—	53	2	no	—
856	C₂³×C₄	—	53	2	no	—
857	C₂³×C₄	—	53	2	no	—
858	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
859	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
860	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
861	#127	—	53	8	no	—
862	#127	—	53	8	no	—
863	#127	—	53	16	no	—
864	#126	—	53	16	no	—
865	#126	—	53	16	no	—
866	#126	—	53	16	no	—
867	#126	C₂²×D₅₃	1	16	yes	complemented
868	#124	—	53	8	no	—
869	#124	—	53	16	no	—
870	#124	—	53	16	no	—
871	#124	—	53	16	no	—
872	#124	—	53	16	no	—
873	#124	—	53	16	no	—
874	#124	C₂²×D₅₃	1	8	yes	complemented
875	#123	—	53	16	no	—
876	#123	—	53	8	no	—
877	#123	—	53	16	no	—
878	#123	—	53	16	no	—
879	#123	—	53	16	no	—
880	#123	—	53	16	no	—
881	#123	—	53	16	no	—
882	#123	—	53	16	no	—
883	#123	C₂²×D₅₃	1	8	yes	complemented
884	#123	C₂²×D₅₃	1	16	yes	complemented
885	C₂²⋊Q₈	—	53	16	no	—
886	C₂²⋊Q₈	—	53	16	no	—
887	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
888	#121	—	53	16	no	—
889	#121	—	53	16	no	—
890	#121	—	53	16	no	—
891	#121	—	53	16	no	—
892	#121	—	53	16	no	—
893	#121	—	53	16	no	—
894	#121	—	53	16	no	—
895	#121	—	53	16	no	—
896	#121	—	53	16	no	—
897	#121	—	53	16	no	—
898	#121	—	53	16	no	—
899	#121	—	53	16	no	—
900	#121	—	53	16	no	—
901	#121	—	53	16	no	—
902	#121	—	53	16	no	—
903	#120	—	53	8	no	—
904	#120	—	53	16	no	—
905	#120	—	53	8	no	—
906	#120	—	53	8	no	—
907	#120	—	53	16	no	—
908	#120	—	53	16	no	—
909	#120	—	53	16	no	—
910	#120	—	53	16	no	—
911	#120	—	53	16	no	—
912	#120	—	53	16	no	—
913	#120	—	53	16	no	—
914	#120	—	53	16	no	—
915	#120	—	53	8	no	—
916	#120	—	53	16	no	—
917	#120	—	53	16	no	—
918	#120	—	53	16	no	—
919	#120	—	53	8	no	—
920	#120	—	53	16	no	—
921	#120	—	53	16	no	—
922	#120	C₂²×D₅₃	1	8	yes	—
923	C₄×D₄	—	53	16	no	—
924	C₄×D₄	—	53	16	no	—
925	C₄×D₄	—	53	16	no	—
926	C₄×D₄	—	53	16	no	—
927	C₄×D₄	—	53	16	no	—
928	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
929	#117	—	53	8	no	—
930	#117	C₂²×D₅₃	1	16	yes	complemented
931	C₂×C₄⋊C₄	—	53	2	no	—
932	C₂×C₄⋊C₄	—	53	2	no	—
933	C₂×C₄⋊C₄	—	53	2	no	—
934	C₂×C₄⋊C₄	—	53	2	no	—
935	C₂×C₄⋊C₄	—	53	2	no	—
936	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
937	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
938	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
939	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
940	C₂×C₂²⋊C₄	—	53	2	no	—
941	C₂×C₂²⋊C₄	—	53	1	no	—
942	C₂×C₂²⋊C₄	—	53	1	no	—
943	C₂×C₂²⋊C₄	—	53	2	no	—
944	C₂×C₂²⋊C₄	—	53	2	no	—
945	C₂×C₂²⋊C₄	—	53	2	no	—
946	C₂×C₂²⋊C₄	—	53	2	no	—
947	C₂×C₂²⋊C₄	—	53	2	no	—
948	C₂×C₂²⋊C₄	—	53	2	no	—
949	C₂×C₂²⋊C₄	—	53	2	no	—
950	C₂×C₂²⋊C₄	—	53	2	no	—
951	C₂×C₂²⋊C₄	—	53	2	no	—
952	C₂×C₂²⋊C₄	—	53	2	no	—
953	C₂×C₂²⋊C₄	—	53	2	no	—
954	C₂×C₂²⋊C₄	—	53	16	no	—
955	C₂×C₂²⋊C₄	—	53	16	no	—
956	C₂×C₂²⋊C₄	—	53	2	no	—
957	C₂×C₂²⋊C₄	—	53	2	no	—
958	C₂×C₂²⋊C₄	—	53	2	no	—
959	C₂×C₂²⋊C₄	—	53	2	no	—
960	C₂×C₂²⋊C₄	—	53	2	no	—
961	C₂×C₂²⋊C₄	—	53	2	no	—
962	C₂×C₂²⋊C₄	—	53	2	no	—
963	C₂×C₂²⋊C₄	—	53	8	no	—
964	C₂×C₂²⋊C₄	—	53	16	no	—
965	C₂×C₂²⋊C₄	—	53	16	no	—
966	C₂×C₂²⋊C₄	—	53	8	no	—
967	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
968	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
969	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
970	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
971	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
972	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
973	C₂×C₂²⋊C₄	C₂²×D₅₃	1	16	yes	complemented
974	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
975	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
976	C₂×C₄²	—	53	1	no	—
977	C₂×C₄²	—	53	2	no	—
978	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic, complemented
979	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
980	C₂⁴	—	2	8	no	—
981	C₂⁴	—	4	2	no	—
982	C₂⁴	—	53	1	no	—
983	C₂⁴	—	53	2	no	—
984	C₂⁴	—	53	1	no	—
985	C₂⁴	—	53	2	no	—
986	C₂⁴	—	53	2	no	—
987	C₂⁴	—	53	1	no	—
988	C₂⁴	—	53	8	no	—
989	C₂⁴	—	53	4	no	—
990	C₂⁴	—	53	8	no	—
991	C₂⁴	—	53	4	no	—
992	C₂⁴	—	53	8	no	—
993	C₂⁴	—	53	4	no	—
994	C₂⁴	—	53	4	no	—
995	C₂⁴	—	106	4	no	—
996	C₂⁴	—	106	8	no	—
997	C₂⁴	—	106	4	no	—
998	C₂⁴	—	106	8	no	—
999	C₂⁴	—	106	8	no	—
1000	C₂⁴	—	106	8	no	—
1001	C₂⁴	—	212	4	no	—
1002	C₂⁴	—	212	4	no	—
1003	C₂⁴	—	212	2	no	—
1004	C₂⁴	—	212	4	no	—
1005	C₂⁴	—	212	4	no	—
1006	C₂⁴	—	212	4	no	—
1007	C₂⁴	—	212	4	no	—
1008	C₂⁴	—	212	4	no	—
1009	C₂⁴	—	212	2	no	—
1010	C₂⁴	—	212	4	no	—
1011	C₂⁴	—	212	4	no	—
1012	C₂⁴	—	212	32	no	—
1013	C₂⁴	—	212	16	no	—
1014	C₂⁴	—	212	64	no	—
1015	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1016	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1017	C₂⁴	C₂³×D₅₃	1	4	yes	—
1018	C₂⁴	C₂³×D₅₃	1	2	yes	—
1019	#41	—	212	32	no	—
1020	#41	—	212	16	no	—
1021	C₂×Q₈	—	4	2	no	—
1022	C₂×Q₈	—	53	8	no	—
1023	C₂×Q₈	—	212	4	no	—
1024	C₂×Q₈	C₂³×D₅₃	1	4	yes	complemented
1025	C₂×D₄	—	2	8	no	—
1026	C₂×D₄	—	4	2	no	—
1027	C₂×D₄	—	53	8	no	—
1028	C₂×D₄	—	53	8	no	—
1029	C₂×D₄	—	53	8	no	—
1030	C₂×D₄	—	53	4	no	—
1031	C₂×D₄	—	53	8	no	—
1032	C₂×D₄	—	53	8	no	—
1033	C₂×D₄	—	53	4	no	—
1034	C₂×D₄	—	53	8	no	—
1035	C₂×D₄	—	53	8	no	—
1036	C₂×D₄	—	53	8	no	—
1037	C₂×D₄	—	53	8	no	—
1038	C₂×D₄	—	53	8	no	—
1039	C₂×D₄	—	53	8	no	—
1040	C₂×D₄	—	53	8	no	—
1041	C₂×D₄	—	53	8	no	—
1042	C₂×D₄	—	53	8	no	—
1043	C₂×D₄	—	53	8	no	—
1044	C₂×D₄	—	53	4	no	—
1045	C₂×D₄	—	53	8	no	—
1046	C₂×D₄	—	53	4	no	—
1047	C₂×D₄	—	53	8	no	—
1048	C₂×D₄	—	53	8	no	—
1049	C₂×D₄	—	53	8	no	—
1050	C₂×D₄	—	106	8	no	—
1051	C₂×D₄	—	106	8	no	—
1052	C₂×D₄	—	106	8	no	—
1053	C₂×D₄	—	106	8	no	—
1054	C₂×D₄	—	106	8	no	—
1055	C₂×D₄	—	212	4	no	—
1056	C₂×D₄	—	212	4	no	—
1057	C₂×D₄	—	212	4	no	—
1058	C₂×D₄	—	212	2	no	—
1059	C₂×D₄	—	212	4	no	—
1060	C₂×D₄	—	212	4	no	—
1061	C₂×D₄	—	212	4	no	—
1062	C₂×D₄	—	212	4	no	—
1063	C₂×D₄	—	212	32	no	—
1064	C₂×D₄	—	212	4	no	—
1065	C₂×D₄	—	212	4	no	—
1066	C₂×D₄	—	212	2	no	—
1067	C₂×D₄	—	212	4	no	—
1068	C₂×D₄	—	212	32	no	—
1069	C₂×D₄	—	212	16	no	—
1070	C₂×D₄	—	212	16	no	—
1071	C₂×D₄	—	212	2	no	—
1072	C₂×D₄	—	212	2	no	—
1073	C₂×D₄	—	212	4	no	—
1074	C₂×D₄	—	212	4	no	—
1075	C₂×D₄	—	212	4	no	—
1076	C₂×D₄	—	212	4	no	—
1077	C₂×D₄	—	212	32	no	—
1078	C₂×D₄	—	212	32	no	—
1079	C₂×D₄	—	212	32	no	—
1080	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1081	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1082	C₂²×C₄	—	2	8	no	—
1083	C₂²×C₄	—	4	4	no	—
1084	C₂²×C₄	—	4	2	no	—
1085	C₂²×C₄	—	53	2	no	—
1086	C₂²×C₄	—	53	2	no	—
1087	C₂²×C₄	—	53	2	no	—
1088	C₂²×C₄	—	53	1	no	—
1089	C₂²×C₄	—	53	8	no	—
1090	C₂²×C₄	—	53	4	no	—
1091	C₂²×C₄	—	53	8	no	—
1092	C₂²×C₄	—	53	8	no	—
1093	C₂²×C₄	—	53	8	no	—
1094	C₂²×C₄	—	53	8	no	—
1095	C₂²×C₄	—	53	8	no	—
1096	C₂²×C₄	—	106	4	no	—
1097	C₂²×C₄	—	212	4	no	—
1098	C₂²×C₄	—	212	4	no	—
1099	C₂²×C₄	—	212	4	no	—
1100	C₂²×C₄	—	212	4	no	—
1101	C₂²×C₄	—	212	4	no	—
1102	C₂²×C₄	—	212	4	no	—
1103	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1104	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1105	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1106	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1107	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1108	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1109	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1110	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1111	C₂²×C₄	C₂³×D₅₃	1	4	yes	complemented
1112	C₄⋊C₄	—	53	8	no	—
1113	C₄⋊C₄	—	53	8	no	—
1114	C₄⋊C₄	—	53	8	no	—
1115	C₄⋊C₄	—	53	8	no	—
1116	C₄⋊C₄	—	53	8	no	—
1117	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1118	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1119	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1120	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1121	C₂²⋊C₄	—	53	8	no	—
1122	C₂²⋊C₄	—	53	4	no	—
1123	C₂²⋊C₄	—	53	4	no	—
1124	C₂²⋊C₄	—	53	8	no	—
1125	C₂²⋊C₄	—	53	8	no	—
1126	C₂²⋊C₄	—	53	8	no	—
1127	C₂²⋊C₄	—	53	8	no	—
1128	C₂²⋊C₄	—	53	8	no	—
1129	C₂²⋊C₄	—	53	8	no	—
1130	C₂²⋊C₄	—	53	8	no	—
1131	C₂²⋊C₄	—	53	8	no	—
1132	C₂²⋊C₄	—	53	8	no	—
1133	C₂²⋊C₄	—	53	8	no	—
1134	C₂²⋊C₄	—	53	8	no	—
1135	C₂²⋊C₄	—	53	8	no	—
1136	C₂²⋊C₄	—	53	8	no	—
1137	C₂²⋊C₄	—	53	8	no	—
1138	C₂²⋊C₄	—	53	8	no	—
1139	C₂²⋊C₄	—	53	8	no	—
1140	C₂²⋊C₄	—	53	8	no	—
1141	C₂²⋊C₄	—	53	8	no	—
1142	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1143	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1144	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1145	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1146	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1147	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1148	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	complemented
1149	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1150	C₄²	—	53	4	no	—
1151	C₄²	—	53	8	no	—
1152	C₄²	C₂³×D₅₃	1	4	yes	complemented
1153	C₄²	C₂³×D₅₃	1	8	yes	complemented
1154	C₂³	—	2	4	no	—
1155	C₂³	—	2	4	no	—
1156	C₂³	—	2	2	no	—
1157	C₂³	—	2	2	no	—
1158	C₂³	—	2	4	no	—
1159	C₂³	—	2	16	no	—
1160	C₂³	—	2	4	no	—
1161	C₂³	—	4	4	no	—
1162	C₂³	—	4	16	no	—
1163	C₂³	—	53	4	no	—
1164	C₂³	—	53	2	no	—
1165	C₂³	—	53	4	no	—
1166	C₂³	—	53	2	no	—
1167	C₂³	—	53	4	no	—
1168	C₂³	—	53	4	no	—
1169	C₂³	—	53	2	no	—
1170	C₂³	—	106	8	no	—
1171	C₂³	—	106	16	no	—
1172	C₂³	—	106	8	no	—
1173	C₂³	—	106	4	no	—
1174	C₂³	—	106	16	no	—
1175	C₂³	—	106	4	no	—
1176	C₂³	—	106	4	no	—
1177	C₂³	—	106	2	no	—
1178	C₂³	—	106	4	no	—
1179	C₂³	—	106	2	no	—
1180	C₂³	—	106	4	no	—
1181	C₂³	—	106	4	no	—
1182	C₂³	—	106	4	no	—
1183	C₂³	—	106	4	no	—
1184	C₂³	—	106	4	no	—
1185	C₂³	—	106	16	no	—
1186	C₂³	—	106	16	no	—
1187	C₂³	—	106	4	no	—
1188	C₂³	—	106	4	no	—
1189	C₂³	—	106	4	no	—
1190	C₂³	—	424	16	no	—
1191	C₂³	—	424	8	no	—
1192	C₂³	—	424	8	no	—
1193	C₂³	—	212	8	no	—
1194	C₂³	—	212	8	no	—
1195	C₂³	—	212	4	no	—
1196	C₂³	—	212	8	no	—
1197	C₂³	—	212	8	no	—
1198	C₂³	—	212	8	no	—
1199	C₂³	—	212	8	no	—
1200	C₂³	—	212	8	no	—
1201	C₂³	—	212	4	no	—
1202	C₂³	—	212	8	no	—
1203	C₂³	—	212	8	no	—
1204	C₂³	—	212	32	no	—
1205	C₂³	—	212	32	no	—
1206	C₂³	—	212	16	no	—
1207	C₂³	—	212	128	no	—
1208	C₂³	—	212	16	no	—
1209	C₂³	#13133263	1	8	yes	—
1210	C₂³	C₂⁴×D₅₃	1	2	yes	—
1211	C₂³	C₂⁴×D₅₃	1	2	yes	—
1212	C₂³	C₂⁴×D₅₃	1	4	yes	—
1213	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1214	Q₈	—	4	4	no	—
1215	Q₈	—	212	8	no	—
1216	D₄	—	2	16	no	—
1217	D₄	—	4	4	no	—
1218	D₄	—	106	16	no	—
1219	D₄	—	106	16	no	—
1220	D₄	—	106	16	no	—
1221	D₄	—	106	16	no	—
1222	D₄	—	106	16	no	—
1223	D₄	—	212	8	no	—
1224	D₄	—	212	8	no	—
1225	D₄	—	212	8	no	—
1226	D₄	—	212	4	no	—
1227	D₄	—	212	8	no	—
1228	D₄	—	212	8	no	—
1229	D₄	—	212	8	no	—
1230	D₄	—	212	8	no	—
1231	D₄	—	212	8	no	—
1232	D₄	—	212	8	no	—
1233	D₄	—	212	4	no	—
1234	D₄	—	212	8	no	—
1235	D₄	—	212	4	no	—
1236	D₄	—	212	4	no	—
1237	D₄	—	212	8	no	—
1238	D₄	—	212	8	no	—
1239	D₄	—	212	8	no	—
1240	D₄	—	212	8	no	—
1241	C₂×C₄	—	2	4	no	—
1242	C₂×C₄	—	2	4	no	—
1243	C₂×C₄	—	2	2	no	—
1244	C₂×C₄	—	2	4	no	—
1245	C₂×C₄	—	2	4	no	—
1246	C₂×C₄	—	2	16	no	—
1247	C₂×C₄	—	2	4	no	—
1248	C₂×C₄	—	4	8	no	—
1249	C₂×C₄	—	4	4	no	—
1250	C₂×C₄	—	53	4	no	—
1251	C₂×C₄	—	53	4	no	—
1252	C₂×C₄	—	53	4	no	—
1253	C₂×C₄	—	53	2	no	—
1254	C₂×C₄	—	106	8	no	—
1255	C₂×C₄	—	106	2	no	—
1256	C₂×C₄	—	106	4	no	—
1257	C₂×C₄	—	106	4	no	—
1258	C₂×C₄	—	106	4	no	—
1259	C₂×C₄	—	212	8	no	—
1260	C₂×C₄	—	212	8	no	—
1261	C₂×C₄	—	212	8	no	—
1262	C₂×C₄	—	212	8	no	—
1263	C₂×C₄	—	212	8	no	—
1264	C₂×C₄	—	212	8	no	—
1265	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1266	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1267	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1268	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1269	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1270	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1271	C₂²	—	2	16	no	—
1272	C₂²	—	2	4	no	—
1273	C₂²	—	2	4	no	—
1274	C₂²	—	2	2	no	—
1275	C₂²	—	2	2	no	—
1276	C₂²	—	2	4	no	—
1277	C₂²	—	2	4	no	—
1278	C₂²	—	4	16	no	—
1279	C₂²	—	4	4	no	—
1280	C₂²	—	4	4	no	—
1281	C₂²	—	53	4	no	—
1282	C₂²	—	106	8	no	—
1283	C₂²	—	106	4	no	—
1284	C₂²	—	106	4	no	—
1285	C₂²	—	106	4	no	—
1286	C₂²	—	106	2	no	—
1287	C₂²	—	106	4	no	—
1288	C₂²	—	106	2	no	—
1289	C₂²	—	106	4	no	—
1290	C₂²	—	106	4	no	—
1291	C₂²	—	106	4	no	—
1292	C₂²	—	106	4	no	—
1293	C₂²	—	106	4	no	—
1294	C₂²	—	106	4	no	—
1295	C₂²	—	106	4	no	—
1296	C₂²	—	106	4	no	—
1297	C₂²	—	424	16	no	—
1298	C₂²	—	424	8	no	—
1299	C₂²	—	424	8	no	—
1300	C₂²	—	212	32	no	—
1301	C₂²	—	212	32	no	—
1302	C₂²	—	212	16	no	—
1303	C₂²	—	212	16	no	—
1304	C₂²	—	212	8	no	—
1305	C₂²	—	212	8	no	—
1306	C₂²	—	212	4	no	—
1307	C₂²	—	212	8	no	—
1308	C₂²	—	212	4	no	—
1309	C₂²	H(5,𝔽₂)×D₅₃	1	2	yes	—
1310	C₂²	C₂×#13133263	1	8	yes	—
1311	C₂²	C₂×#13133263	1	4	yes	—
1312	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1313	C₄	—	2	4	no	—
1314	C₄	—	2	4	no	—
1315	C₄	—	2	2	no	—
1316	C₄	—	2	4	no	—
1317	C₄	—	2	4	no	—
1318	C₄	—	2	4	no	—
1319	C₄	—	106	2	no	—
1320	C₄	—	106	4	no	—
1321	C₄	—	106	4	no	—
1322	C₄	—	106	4	no	—
1323	C₂	—	2	8	no	—
1324	C₂	—	4	2	no	—
1325	C₂	—	4	2	no	—
1326	C₂	—	106	4	no	—
1327	C₂	—	212	4	no	—
1328	C₂	—	212	4	no	—
1329	C₂	—	212	2	no	—
1330	C₂	—	212	4	no	—
1331	C₂	—	212	2	no	—
1332	C₂	#20288871	1	4	yes	direct product factor
1333	C₂	C₂×H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1334	C₂	C₂²×#13133263	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#551	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#551	D₅₃
hypocenter	C₅₃	C₂×#3532
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#551

Complements

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

N	H ≅ G/N	type
1. #20288871	C₂	direct (N × H)
2. C₂×#16811365	C₂	semidirect
3. C₂×#16811364	C₂	semidirect
4. C₂×#16811363	C₂	semidirect
5. C₂×#16811297	C₂	semidirect
6. C₂×#16811265	C₂	semidirect
7. C₂×#16811264	C₂	semidirect
8. C₂×#16811263	C₂	semidirect
9. C₂×D₄×D₂₁₂	C₂	semidirect
10. C₂×#16811255	C₂	semidirect
11. C₂×#16811213	C₂	semidirect
12. C₂×#16811212	C₂	semidirect
13. C₂×#16811206	C₂	semidirect
14. C₂×#16811192	C₂	semidirect
15. C₂×#16811191	C₂	semidirect
16. C₂×#16811184	C₂	semidirect
17. C₂×#16811184	C₂	semidirect
18. C₂²×#13133187	C₂	semidirect
19. C₂×#120×D₅₃	C₂	semidirect
20. C₂×C₅₃×#551	C₂	semidirect
21. C₂⁵×D₅₃	C₂²	semidirect
22. C₂²×#11719949	C₂²	semidirect
23. C₂²×#11719945	C₂²	semidirect
24. C₂³×D₂₁₂	C₂²	semidirect
25. C₂³×D₂₁₂	C₂²	semidirect
26. C₂³×D₂₁₂	C₂²	semidirect
27. C₂³×C₂²⋊D₅₃	C₂²	semidirect
28. C₂²×D₄×D₅₃	C₂²	semidirect
29. C₂²×D₄×D₅₃	C₂²	semidirect
30. C₂²×D₄×D₅₃	C₂²	semidirect
31. #16811365	C₂²	semidirect
32. #16811364	C₂²	semidirect
33. #16811363	C₂²	semidirect
34. #16811297	C₂²	semidirect
35. #16811265	C₂²	semidirect
36. #16811264	C₂²	semidirect
37. #16811263	C₂²	semidirect
38. D₄×D₂₁₂	C₂²	semidirect
39. #16811255	C₂²	semidirect
40. #16811213	C₂²	semidirect
41. #16811212	C₂²	semidirect
42. #16811206	C₂²	semidirect
43. #16811192	C₂²	semidirect
44. #16811191	C₂²	semidirect
45. #16811184	C₂²	semidirect
46. #16811184	C₂²	semidirect
47. C₂×#13133214	C₂²	semidirect
48. C₂×#13133214	C₂²	semidirect
49. C₂×#13133213	C₂²	semidirect
50. C₂×#13133212	C₂²	semidirect
51. C₂×#13133212	C₂²	semidirect
52. C₂×#13133211	C₂²	semidirect
53. C₂×#13133206	C₂²	semidirect
54. C₂×#13133206	C₂²	semidirect
55. C₂×#13133205	C₂²	semidirect
56. C₂×#13133205	C₂²	semidirect
57. C₂×#13133203	C₂²	semidirect
58. C₂×#13133203	C₂²	semidirect
59. C₂×#13133202	C₂²	semidirect
60. C₂×#13133202	C₂²	semidirect
61. C₂×#13133202	C₂²	semidirect
62. C₂×#13133202	C₂²	semidirect
63. C₂×#13133202	C₂²	semidirect
64. C₂×#13133200	C₂²	semidirect
65. C₂×#13133200	C₂²	semidirect
66. C₂×#13133199	C₂²	semidirect
67. C₂×#13133195	C₂²	semidirect
68. C₂×#13133194	C₂²	semidirect
69. C₂×#13133192	C₂²	semidirect
70. C₂×#13133192	C₂²	semidirect
71. C₂×#13133192	C₂²	semidirect
72. C₂×#13133192	C₂²	semidirect
73. C₂×#13133192	C₂²	semidirect
74. C₂×#13133192	C₂²	semidirect
75. C₂×#13133192	C₂²	semidirect
76. C₂×#13133191	C₂²	semidirect
77. C₂×#13133191	C₂²	semidirect
78. C₂×#13133190	C₂²	semidirect
79. C₂×#13133190	C₂²	semidirect
80. C₂×#13133190	C₂²	semidirect
81. C₂×#13133190	C₂²	semidirect
82. C₂×#13133190	C₂²	semidirect
83. C₂×#13133189	C₂²	semidirect
85. C₂×#13133187	C₂²	semidirect
86. C₂×#13133187	C₂²	semidirect
87. C₂×#13133187	C₂²	semidirect
88. C₂×#13133187	C₂²	semidirect
89. C₂×#13133187	C₂²	semidirect
90. C₂×#13133187	C₂²	semidirect
91. C₂×#13133187	C₂²	semidirect
92. C₂×#13133187	C₂²	semidirect
93. C₂×#13133187	C₂²	semidirect
94. C₂×#13133187	C₂²	semidirect
95. C₂×#13133187	C₂²	semidirect
96. C₂×#13133187	C₂²	semidirect
97. C₂×#13133187	C₂²	semidirect
98. C₂×#13133187	C₂²	semidirect
99. C₂×#13133187	C₂²	semidirect
100. C₂×#13133186	C₂²	semidirect
101. C₂×#13133185	C₂²	semidirect
102. C₂×#13133185	C₂²	semidirect
103. C₂×#13133185	C₂²	semidirect
104. #120×D₅₃	C₂²	semidirect
105. C₂×C₄×D₂₁₂	C₂²	semidirect
106. C₂×#13133179	C₂²	semidirect
107. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
108. C₂×#13133177	C₂²	semidirect
109. C₂×#13133177	C₂²	semidirect
110. C₂×#13133174	C₂²	semidirect
111. C₂²×#11719921	C₂²	semidirect
112. C₂²×#11719921	C₂²	semidirect
113. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
114. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
115. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
116. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
117. C₅₃×#551	C₂²	semidirect
118. C₂×#126×C₅₃	C₂²	semidirect
119. C₂×#124×C₅₃	C₂²	semidirect
120. C₂×#123×C₅₃	C₂²	semidirect
121. C₂×#123×C₅₃	C₂²	semidirect
122. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
124. C₂×C₄×D₄×C₅₃	C₂²	semidirect
125. C₂×#117×C₅₃	C₂²	semidirect
126. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
135. C₂⁴×D₅₃	C₂³	semidirect
136. C₂⁴×D₅₃	C₂³	semidirect
138. C₂×#11719949	C₂³	semidirect
140. C₂×#11719945	C₂³	semidirect
141. C₂²×Dic₁₀₆	C₂³	semidirect
155. C₂²×D₂₁₂	C₂³	semidirect
156. C₂²×D₂₁₂	C₂³	semidirect
157. C₂²×D₂₁₂	C₂³	semidirect
158. C₂²×D₂₁₂	C₂³	semidirect
159. C₂²×D₂₁₂	C₂³	semidirect
160. C₂²×D₂₁₂	C₂³	semidirect
161. C₂²×D₂₁₂	C₂³	semidirect
171. C₂²×C₂²⋊D₅₃	C₂³	semidirect
172. C₂²×C₂²⋊D₅₃	C₂³	semidirect
176. C₂×D₄×D₅₃	C₂³	semidirect
177. C₂×D₄×D₅₃	C₂³	semidirect
178. C₂×D₄×D₅₃	C₂³	semidirect
182. C₂²×C₄×D₅₃	C₂³	semidirect
183. C₂²×C₄×D₅₃	C₂³	semidirect
184. C₂²×C₄×D₅₃	C₂³	semidirect
185. C₂²×C₄×D₅₃	C₂³	semidirect
186. #13133214	C₂³	semidirect
187. #13133214	C₂³	semidirect
188. #13133213	C₂³	semidirect
189. #13133212	C₂³	semidirect
190. #13133212	C₂³	semidirect
191. #13133211	C₂³	semidirect
192. #13133206	C₂³	semidirect
193. #13133206	C₂³	semidirect
194. #13133205	C₂³	semidirect
195. #13133205	C₂³	semidirect
196. #13133203	C₂³	semidirect
197. #13133203	C₂³	semidirect
198. #13133202	C₂³	semidirect
199. #13133202	C₂³	semidirect
200. #13133202	C₂³	semidirect
201. #13133202	C₂³	semidirect
202. #13133202	C₂³	semidirect
203. #13133200	C₂³	semidirect
204. #13133200	C₂³	semidirect
205. #13133199	C₂³	semidirect
206. #13133195	C₂³	semidirect
207. #13133194	C₂³	semidirect
208. #13133192	C₂³	semidirect
209. #13133192	C₂³	semidirect
210. #13133192	C₂³	semidirect
211. #13133192	C₂³	semidirect
212. #13133192	C₂³	semidirect
213. #13133192	C₂³	semidirect
214. #13133192	C₂³	semidirect
215. #13133191	C₂³	semidirect
216. #13133191	C₂³	semidirect
217. #13133190	C₂³	semidirect
218. #13133190	C₂³	semidirect
219. #13133190	C₂³	semidirect
220. #13133190	C₂³	semidirect
221. #13133190	C₂³	semidirect
222. #13133189	C₂³	semidirect
224. #13133187	C₂³	semidirect
225. #13133187	C₂³	semidirect
226. #13133187	C₂³	semidirect
227. #13133187	C₂³	semidirect
228. #13133187	C₂³	semidirect
229. #13133187	C₂³	semidirect
230. #13133187	C₂³	semidirect
231. #13133187	C₂³	semidirect
232. #13133187	C₂³	semidirect
233. #13133187	C₂³	semidirect
234. #13133187	C₂³	semidirect
235. #13133187	C₂³	semidirect
236. #13133187	C₂³	semidirect
237. #13133187	C₂³	semidirect
238. #13133186	C₂³	semidirect
239. #13133185	C₂³	semidirect
240. #13133185	C₂³	semidirect
241. #13133185	C₂³	semidirect
242. C₄×D₂₁₂	C₂³	semidirect
243. #13133179	C₂³	semidirect
244. C₄×C₂²⋊D₅₃	C₂³	semidirect
245. #13133177	C₂³	semidirect
246. #13133177	C₂³	semidirect
247. #13133174	C₂³	semidirect
248. C₂×C₄⋊Dic₅₃	C₂³	semidirect
249. C₂×#11719919	C₂³	semidirect
250. C₂×#11719919	C₂³	semidirect
251. C₂×#11719919	C₂³	semidirect
252. C₂×#11719919	C₂³	semidirect
255. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
267. C₂×#11719921	C₂³	semidirect
268. C₂×#11719921	C₂³	semidirect
269. C₂×#11719921	C₂³	semidirect
270. C₂×#11719921	C₂³	semidirect
271. C₂×#11719921	C₂³	semidirect
272. C₂×#11719921	C₂³	semidirect
273. C₂×#11719921	C₂³	semidirect
274. C₂×#11719921	C₂³	semidirect
275. C₂×#11719921	C₂³	semidirect
276. C₂²⋊C₄×D₅₃	C₂³	semidirect
277. C₂²⋊C₄×D₅₃	C₂³	semidirect
278. C₂²⋊C₄×D₅₃	C₂³	semidirect
279. C₂²⋊C₄×D₅₃	C₂³	semidirect
280. C₂×C₄×Dic₅₃	C₂³	semidirect
281. C₂×C₄×Dic₅₃	C₂³	semidirect
283. C₂²×Q₈×C₅₃	C₂³	semidirect
288. C₂³×C₄×C₅₃	C₂³	semidirect
289. #126×C₅₃	C₂³	semidirect
290. #124×C₅₃	C₂³	semidirect
291. #123×C₅₃	C₂³	semidirect
292. #123×C₅₃	C₂³	semidirect
293. C₂²⋊Q₈×C₅₃	C₂³	semidirect
295. C₄×D₄×C₅₃	C₂³	semidirect
296. #117×C₅₃	C₂³	semidirect
297. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
298. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
299. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
300. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
307. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
308. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
309. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
310. C₂×C₄²×C₅₃	C₂³	semidirect
311. C₂×C₄²×C₅₃	C₂³	semidirect
350. C₂³×D₅₃	C₂⁴	semidirect
352. C₂×Q₈×C₅₃	C₂⁴	semidirect
368. C₂²×C₄×C₅₃	C₂⁴	semidirect
387. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
426. C₂×D₂₁₂	C₂⁴	semidirect
427. C₂×D₂₁₂	C₂⁴	semidirect
428. C₂×D₂₁₂	C₂⁴	semidirect
429. C₂×D₂₁₂	C₂⁴	semidirect
438. C₂×C₄×D₅₃	C₂⁴	semidirect
439. C₂×C₄×D₅₃	C₂⁴	semidirect
440. C₂×C₄×D₅₃	C₂⁴	semidirect
441. C₂×C₄×D₅₃	C₂⁴	semidirect
443. C₂×Dic₁₀₆	C₂⁴	semidirect
444. C₄⋊C₄×C₅₃	C₂⁴	semidirect
445. C₄⋊C₄×C₅₃	C₂⁴	semidirect
446. C₄⋊C₄×C₅₃	C₂⁴	semidirect
447. C₄⋊C₄×C₅₃	C₂⁴	semidirect
454. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
455. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
456. C₄²×C₅₃	C₂⁴	semidirect
457. C₄²×C₅₃	C₂⁴	semidirect
460. C₂²⋊Dic₅₃	C₂⁴	semidirect
472. #11719921	C₂⁴	semidirect
473. #11719921	C₂⁴	semidirect
474. #11719921	C₂⁴	semidirect
475. #11719921	C₂⁴	semidirect
476. #11719921	C₂⁴	semidirect
477. #11719921	C₂⁴	semidirect
478. #11719921	C₂⁴	semidirect
479. C₄⋊Dic₅₃	C₂⁴	semidirect
480. #11719919	C₂⁴	semidirect
481. #11719919	C₂⁴	semidirect
482. #11719919	C₂⁴	semidirect
483. #11719919	C₂⁴	semidirect
484. C₄×Dic₅₃	C₂⁴	semidirect
485. C₄×Dic₅₃	C₂⁴	semidirect
661. C₂×#551	D₅₃	semidirect
679. C₂×C₅₃	#3532	semidirect
702. #551	C₂×D₅₃	semidirect
721. C₂×#126	C₂×D₅₃	semidirect
728. C₂×#124	C₂×D₅₃	semidirect
737. C₂×#123	C₂×D₅₃	semidirect
738. C₂×#123	C₂×D₅₃	semidirect
741. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
784. C₂×C₄×D₄	C₂×D₅₃	semidirect
786. C₂×#117	C₂×D₅₃	semidirect
793. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
794. C₅₃	C₂×#3532	semidirect
811. C₂²×Q₈	C₂²×D₅₃	semidirect
860. C₂³×C₄	C₂²×D₅₃	semidirect
867. #126	C₂²×D₅₃	semidirect
874. #124	C₂²×D₅₃	semidirect
883. #123	C₂²×D₅₃	semidirect
884. #123	C₂²×D₅₃	semidirect
887. C₂²⋊Q₈	C₂²×D₅₃	semidirect
928. C₄×D₄	C₂²×D₅₃	semidirect
930. #117	C₂²×D₅₃	semidirect
936. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
937. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
938. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
939. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
973. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
974. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
975. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
978. C₂×C₄²	C₂²×D₅₃	semidirect
979. C₂×C₄²	C₂²×D₅₃	semidirect
1024. C₂×Q₈	C₂³×D₅₃	semidirect
1111. C₂²×C₄	C₂³×D₅₃	semidirect
1117. C₄⋊C₄	C₂³×D₅₃	semidirect
1118. C₄⋊C₄	C₂³×D₅₃	semidirect
1119. C₄⋊C₄	C₂³×D₅₃	semidirect
1120. C₄⋊C₄	C₂³×D₅₃	semidirect
1148. C₂²⋊C₄	C₂³×D₅₃	semidirect
1149. C₂²⋊C₄	C₂³×D₅₃	semidirect
1152. C₄²	C₂³×D₅₃	semidirect
1153. C₄²	C₂³×D₅₃	semidirect
1332. C₂	#20288871	direct (N × H)

Maximal subgroups

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

subgroup	index
#20288871	2
C₂×#16811365	2
C₂×#16811364	2
C₂×#16811363	2
C₂×#16811297	2
C₂×#16811265	2
C₂×#16811264	2
C₂×#16811263	2
C₂×D₄×D₂₁₂	2
C₂×#16811255	2
C₂×#16811213	2
C₂×#16811212	2
C₂×#16811206	2
C₂×#16811192	2
C₂×#16811191	2
C₂×#16811184	2
C₂²×#13133187	2
C₂×#120×D₅₃	2
C₂×C₅₃×#551	2
C₂×#3532	53

Subgroups — C2×#20288871 #28291216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20288871 #28291216