Subgroups — C₂×#20288870 #28291214

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	#20288870	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16811366	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811362	C₂	1	2	yes	maximal, complemented
4	C₂×#16811362	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16811304	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16811299	C₂	1	2	yes	maximal, complemented
7	C₂×#16811267	C₂	1	2	yes	maximal, complemented
8	C₂×#16811263	C₂	1	2	yes	maximal, complemented
9	C₂×#16811260	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×C₂²⋊D₅₃	C₂	1	2	yes	maximal, complemented
11	C₂×#16811255	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16811211	C₂	1	2	yes	maximal, complemented
13	C₂×#16811208	C₂	1	2	yes	maximal, complemented
14	C₂×#16811208	C₂	1	2	yes	maximal, complemented
15	C₂×#16811190	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16811188	C₂	1	2	yes	maximal, complemented
17	C₂×#16811183	C₂	1	2	yes	maximal, complemented
18	C₂×#16811182	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#13133186	C₂	1	2	yes	maximal, complemented
20	C₂²×#120×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#11719947	C₂²	1	2	yes	complemented
23	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
24	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
25	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
26	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
28	#16811366	C₂²	1	16	yes	complemented
29	#16811362	C₂²	1	32	yes	complemented
30	#16811362	C₂²	1	16	yes	complemented
31	#16811304	C₂²	1	16	yes	complemented
32	#16811299	C₂²	1	32	yes	complemented
33	#16811267	C₂²	1	32	yes	complemented
34	#16811263	C₂²	1	32	yes	complemented
35	#16811260	C₂²	1	32	yes	complemented
36	D₄×C₂²⋊D₅₃	C₂²	1	32	yes	complemented
37	#16811255	C₂²	1	16	yes	complemented
38	#16811211	C₂²	1	32	yes	complemented
39	#16811208	C₂²	1	32	yes	complemented
40	#16811208	C₂²	1	32	yes	complemented
41	#16811190	C₂²	1	16	yes	complemented
42	#16811188	C₂²	1	32	yes	complemented
43	#16811183	C₂²	1	32	yes	complemented
44	#16811182	C₂²	1	16	yes	complemented
45	C₂×#13133213	C₂²	1	1	yes	characteristic, complemented
46	C₂×#13133213	C₂²	1	2	yes	complemented
47	C₂×#13133213	C₂²	1	1	yes	characteristic, complemented
48	C₂×#13133210	C₂²	1	2	yes	complemented
49	C₂×#13133210	C₂²	1	2	yes	complemented
50	C₂×#13133210	C₂²	1	2	yes	complemented
51	C₂×#13133210	C₂²	1	2	yes	complemented
52	C₂×#13133204	C₂²	1	1	yes	characteristic, complemented
53	C₂×#13133204	C₂²	1	1	yes	characteristic, complemented
54	C₂×#13133204	C₂²	1	2	yes	complemented
55	C₂×#13133203	C₂²	1	2	yes	complemented
56	C₂×#13133203	C₂²	1	2	yes	complemented
57	C₂×#13133203	C₂²	1	2	yes	complemented
58	C₂×#13133203	C₂²	1	2	yes	complemented
59	C₂×#13133201	C₂²	1	2	yes	complemented
60	C₂×#13133200	C₂²	1	2	yes	complemented
61	C₂×#13133199	C₂²	1	2	yes	complemented
62	C₂×#13133199	C₂²	1	2	yes	complemented
63	C₂×#13133199	C₂²	1	2	yes	complemented
64	C₂×#13133199	C₂²	1	2	yes	complemented
65	C₂×#13133198	C₂²	1	1	yes	characteristic, complemented
66	C₂×#13133198	C₂²	1	1	yes	characteristic, complemented
67	C₂×#13133198	C₂²	1	2	yes	complemented
68	C₂×#13133198	C₂²	1	2	yes	complemented
69	C₂×#13133196	C₂²	1	2	yes	complemented
70	C₂×#13133194	C₂²	1	2	yes	complemented
71	C₂×#13133194	C₂²	1	2	yes	complemented
72	C₂×#13133191	C₂²	1	2	yes	complemented
73	C₂×#13133190	C₂²	1	2	yes	complemented
74	C₂×#13133190	C₂²	1	2	yes	complemented
75	C₂×#13133190	C₂²	1	2	yes	complemented
76	C₂×#13133190	C₂²	1	2	yes	complemented
77	C₂×#13133189	C₂²	1	2	yes	complemented
78	C₂×#13133189	C₂²	1	2	yes	complemented
79	C₂×#13133189	C₂²	1	2	yes	complemented
80	C₂×#13133189	C₂²	1	2	yes	complemented
81	C₂×#13133189	C₂²	1	2	yes	complemented
82	C₂×#13133189	C₂²	1	2	yes	complemented
83	C₂×#13133188	C₂²	1	2	yes	complemented
84	C₂×#13133188	C₂²	1	2	yes	complemented
85	C₂×#13133188	C₂²	1	2	yes	complemented
86	C₂×#13133188	C₂²	1	2	yes	complemented
87	C₂×#13133187	C₂²	1	2	yes	complemented
88	C₂×#13133186	C₂²	1	2	yes	—
89	C₂×#13133186	C₂²	1	2	yes	complemented
90	C₂×#13133186	C₂²	1	2	yes	complemented
91	C₂×#13133186	C₂²	1	2	yes	complemented
92	C₂×#13133186	C₂²	1	2	yes	complemented
93	C₂×#13133186	C₂²	1	2	yes	complemented
94	C₂×#13133186	C₂²	1	2	yes	complemented
95	C₂×#13133186	C₂²	1	2	yes	complemented
96	C₂×#13133186	C₂²	1	2	yes	complemented
97	C₂×#13133186	C₂²	1	32	yes	complemented
98	C₂×#13133185	C₂²	1	2	yes	complemented
99	C₂×#13133185	C₂²	1	1	yes	characteristic, complemented
100	C₂×#13133185	C₂²	1	1	yes	characteristic, complemented
101	C₂×#13133185	C₂²	1	2	yes	complemented
102	C₂×D₄×Dic₅₃	C₂²	1	2	yes	complemented
103	C₂×D₄×Dic₅₃	C₂²	1	2	yes	complemented
104	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
105	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
106	C₂×#13133177	C₂²	1	2	yes	complemented
107	C₂×#13133177	C₂²	1	2	yes	complemented
108	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
109	C₂×#13133173	C₂²	1	2	yes	complemented
110	C₂²×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
111	C₂²×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
112	C₂²×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
113	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
115	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	C₂³×D₄×C₅₃	C₂²	1	2	yes	complemented
118	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
119	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
120	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
121	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₂×#120×C₅₃	C₂²	1	16	yes	complemented
125	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
126	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
127	C₂⁴×D₅₃	C₂³	1	2	yes	—
128	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic, complemented
129	C₂×#11719945	—	4	4	no	—
130	C₂×#11719945	C₂³	1	8	yes	complemented
131	C₂×#11719947	—	4	8	no	—
132	C₂×#11719947	C₂³	1	16	yes	complemented
133	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
134	C₂²×Dic₁₀₆	C₂³	1	2	yes	complemented
135	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
136	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
137	C₂²×C₂²⋊D₅₃	—	4	8	no	—
138	C₂²×C₂²⋊D₅₃	—	4	8	no	—
139	C₂²×C₂²⋊D₅₃	—	4	8	no	—
140	C₂²×C₂²⋊D₅₃	—	4	4	no	—
141	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
142	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
143	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
144	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
145	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
146	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
147	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
148	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
149	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
150	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
151	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
152	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
153	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
154	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
155	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
156	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
157	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
158	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
159	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
160	C₂×D₄×D₅₃	—	4	8	no	—
161	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
162	C₂³×Dic₅₃	C₂³	1	2	yes	—
163	C₂³×Dic₅₃	C₂³	1	2	yes	—
164	C₂³×Dic₅₃	C₂³	1	2	yes	—
165	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
166	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
167	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
168	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
169	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
170	#13133213	C₂³	1	16	yes	complemented
171	#13133213	C₂³	1	8	yes	complemented
172	#13133213	C₂³	1	8	yes	complemented
173	#13133210	C₂³	1	16	yes	complemented
174	#13133210	C₂³	1	16	yes	complemented
175	#13133210	C₂³	1	16	yes	complemented
176	#13133210	C₂³	1	16	yes	complemented
177	#13133204	C₂³	1	16	yes	complemented
178	#13133204	C₂³	1	8	yes	complemented
179	#13133204	C₂³	1	8	yes	complemented
180	#13133203	C₂³	1	16	yes	complemented
181	#13133203	C₂³	1	16	yes	complemented
182	#13133203	C₂³	1	16	yes	complemented
183	#13133203	C₂³	1	16	yes	complemented
184	#13133201	C₂³	1	16	yes	complemented
185	#13133200	C₂³	1	16	yes	complemented
186	#13133199	C₂³	1	16	yes	complemented
187	#13133199	C₂³	1	16	yes	complemented
188	#13133199	C₂³	1	16	yes	complemented
189	#13133199	C₂³	1	16	yes	complemented
190	#13133198	C₂³	1	16	yes	complemented
191	#13133198	C₂³	1	16	yes	complemented
192	#13133198	C₂³	1	8	yes	complemented
193	#13133198	C₂³	1	8	yes	complemented
194	#13133196	C₂³	1	16	yes	complemented
195	#13133194	C₂³	1	16	yes	complemented
196	#13133194	C₂³	1	16	yes	complemented
197	#13133191	C₂³	1	16	yes	complemented
198	#13133190	C₂³	1	16	yes	complemented
199	#13133190	C₂³	1	16	yes	complemented
200	#13133190	C₂³	1	16	yes	complemented
201	#13133190	C₂³	1	16	yes	complemented
202	#13133189	C₂³	1	16	yes	complemented
203	#13133189	C₂³	1	16	yes	complemented
204	#13133189	C₂³	1	16	yes	complemented
205	#13133189	C₂³	1	16	yes	complemented
206	#13133189	C₂³	1	16	yes	complemented
207	#13133189	C₂³	1	16	yes	complemented
208	#13133188	C₂³	1	16	yes	complemented
209	#13133188	C₂³	1	16	yes	complemented
210	#13133188	C₂³	1	16	yes	complemented
211	#13133188	C₂³	1	16	yes	complemented
212	#13133187	C₂³	1	16	yes	complemented
213	#13133186	C₂³	1	16	yes	—
214	#13133186	C₂³	1	16	yes	complemented
215	#13133186	C₂³	1	16	yes	complemented
216	#13133186	C₂³	1	16	yes	complemented
217	#13133186	C₂³	1	16	yes	complemented
218	#13133186	C₂³	1	16	yes	complemented
219	#13133186	C₂³	1	16	yes	complemented
220	#13133186	C₂³	1	16	yes	complemented
221	#13133186	C₂³	1	16	yes	complemented
222	#13133185	C₂³	1	8	yes	complemented
223	#13133185	C₂³	1	16	yes	complemented
224	#13133185	C₂³	1	8	yes	complemented
225	#13133185	C₂³	1	16	yes	complemented
226	D₄×Dic₅₃	C₂³	1	16	yes	complemented
227	D₄×Dic₅₃	C₂³	1	16	yes	complemented
228	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
229	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
230	#13133177	C₂³	1	16	yes	complemented
231	#13133177	C₂³	1	16	yes	complemented
232	#13133176	C₂³	1	8	yes	complemented
233	#13133173	C₂³	1	16	yes	complemented
234	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
235	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
236	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
237	C₂×#11719919	C₂³	1	2	yes	complemented
238	C₂×#11719919	C₂³	1	2	yes	complemented
239	C₂×#11719919	C₂³	1	2	yes	complemented
240	C₂×#11719919	C₂³	1	2	yes	complemented
241	C₂×#11719919	C₂³	1	2	yes	complemented
242	C₂×#11719919	C₂³	1	2	yes	complemented
243	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
244	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
245	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
246	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
247	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
248	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
249	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
250	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
251	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
252	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
253	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
254	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
255	C₂×C₂²⋊Dic₅₃	C₂³	1	16	yes	complemented
256	C₂×C₂²⋊Dic₅₃	C₂³	1	16	yes	complemented
257	C₂×C₂²⋊Dic₅₃	C₂³	1	16	yes	complemented
258	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
259	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
260	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
261	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
262	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
263	C₂×#11719921	C₂³	1	2	yes	complemented
264	C₂×#11719921	C₂³	1	2	yes	complemented
265	C₂×#11719921	C₂³	1	2	yes	complemented
266	C₂×#11719921	C₂³	1	2	yes	complemented
267	C₂×#11719921	C₂³	1	2	yes	complemented
268	C₂×#11719921	C₂³	1	2	yes	complemented
269	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
270	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
271	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
272	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
273	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
274	C₂⁵×C₅₃	—	4	8	no	—
275	C₂⁵×C₅₃	—	4	4	no	—
276	C₂⁵×C₅₃	C₂³	1	2	yes	—
277	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
278	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
279	C₂⁵×C₅₃	C₂³	1	2	yes	—
280	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
281	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
282	C₂⁵×C₅₃	C₂³	1	8	yes	complemented
283	C₂²×D₄×C₅₃	—	4	4	no	—
284	C₂²×D₄×C₅₃	—	4	8	no	—
285	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
286	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
287	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
290	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
292	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
293	C₂²×D₄×C₅₃	C₂³	1	16	yes	complemented
294	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
295	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
296	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
297	#120×C₅₃	C₂³	1	8	yes	—
298	#120×C₅₃	C₂³	1	8	yes	complemented
299	#120×C₅₃	C₂³	1	8	yes	complemented
300	#120×C₅₃	C₂³	1	16	yes	complemented
301	#120×C₅₃	C₂³	1	16	yes	complemented
302	#120×C₅₃	C₂³	1	8	yes	complemented
303	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
304	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
306	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
307	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
308	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
309	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	complemented
311	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
312	C₂⁴×C₅₃	—	2	8	no	—
313	C₂⁴×C₅₃	—	2	4	no	—
314	C₂⁴×C₅₃	—	2	8	no	—
315	C₂⁴×C₅₃	—	2	8	no	—
316	C₂⁴×C₅₃	—	2	8	no	—
317	C₂⁴×C₅₃	—	2	4	no	—
318	C₂⁴×C₅₃	—	4	2	no	—
319	C₂⁴×C₅₃	—	4	4	no	—
320	C₂⁴×C₅₃	—	4	4	no	—
321	C₂⁴×C₅₃	—	4	4	no	—
322	C₂⁴×C₅₃	—	4	4	no	—
323	C₂⁴×C₅₃	—	4	2	no	—
324	C₂⁴×C₅₃	—	4	4	no	—
325	C₂⁴×C₅₃	—	4	32	no	—
326	C₂⁴×C₅₃	—	4	16	no	—
327	C₂⁴×C₅₃	—	4	4	no	—
328	C₂⁴×C₅₃	—	4	64	no	—
329	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
331	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
333	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
334	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
335	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
336	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
337	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
339	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
340	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
341	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
342	C₂³×D₅₃	—	2	8	no	—
343	C₂³×D₅₃	—	4	4	no	—
344	C₂³×D₅₃	—	4	4	no	—
345	C₂³×D₅₃	—	4	4	no	—
346	C₂³×D₅₃	—	4	2	no	—
347	C₂³×D₅₃	C₂⁴	1	2	yes	—
348	C₂³×D₅₃	C₂⁴	1	2	yes	—
349	C₂³×D₅₃	C₂⁴	1	8	yes	—
350	C₂³×D₅₃	C₂⁴	1	4	yes	complemented
351	C₂×D₄×C₅₃	—	2	8	no	—
352	C₂×D₄×C₅₃	—	2	8	no	—
353	C₂×D₄×C₅₃	—	4	4	no	—
354	C₂×D₄×C₅₃	—	4	2	no	—
355	C₂×D₄×C₅₃	—	4	2	no	—
356	C₂×D₄×C₅₃	—	4	2	no	—
357	C₂×D₄×C₅₃	—	4	2	no	—
358	C₂×D₄×C₅₃	—	4	4	no	—
359	C₂×D₄×C₅₃	—	4	16	no	—
360	C₂×D₄×C₅₃	—	4	32	no	—
361	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
362	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
363	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
364	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
365	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
366	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
367	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
368	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
369	C₂²×C₄×C₅₃	—	2	4	no	—
370	C₂²×C₄×C₅₃	—	4	4	no	—
371	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
373	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
376	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
377	C₂×C₂²⋊D₅₃	—	2	8	no	—
378	C₂×C₂²⋊D₅₃	—	2	8	no	—
379	C₂×C₂²⋊D₅₃	—	2	8	no	—
380	C₂×C₂²⋊D₅₃	—	2	8	no	—
381	C₂×C₂²⋊D₅₃	—	4	4	no	—
382	C₂×C₂²⋊D₅₃	—	4	4	no	—
383	C₂×C₂²⋊D₅₃	—	4	4	no	—
384	C₂×C₂²⋊D₅₃	—	4	4	no	—
385	C₂×C₂²⋊D₅₃	—	4	4	no	—
386	C₂×C₂²⋊D₅₃	—	4	4	no	—
387	C₂×C₂²⋊D₅₃	—	4	4	no	—
388	C₂×C₂²⋊D₅₃	—	4	4	no	—
389	C₂×C₂²⋊D₅₃	—	4	4	no	—
390	C₂×C₂²⋊D₅₃	—	4	32	no	—
391	C₂×C₂²⋊D₅₃	—	4	4	no	—
392	C₂×C₂²⋊D₅₃	—	4	4	no	—
393	C₂×C₂²⋊D₅₃	—	4	32	no	—
394	C₂×C₂²⋊D₅₃	—	4	32	no	—
395	C₂×C₂²⋊D₅₃	—	4	16	no	—
396	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
397	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
398	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
399	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
400	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
401	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
402	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
403	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
404	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
405	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
406	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
407	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
408	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
409	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
410	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
411	C₂²×Dic₅₃	—	2	8	no	—
412	C₂²×Dic₅₃	—	4	4	no	—
413	C₂²×Dic₅₃	—	4	4	no	—
414	C₂²×Dic₅₃	—	4	2	no	—
415	C₂²×Dic₅₃	—	4	4	no	—
416	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
417	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
418	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
419	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
420	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
421	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
422	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
423	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
424	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
425	C₂²×Dic₅₃	C₂⁴	1	8	yes	complemented
426	C₂²×Dic₅₃	C₂⁴	1	4	yes	complemented
427	#11719947	—	4	32	no	—
428	D₄×D₅₃	—	4	32	no	—
429	#11719945	—	4	16	no	—
430	C₂×D₂₁₂	—	4	4	no	—
431	C₂×D₂₁₂	—	4	2	no	—
432	C₂×D₂₁₂	C₂⁴	1	4	yes	complemented
433	C₂×D₂₁₂	C₂⁴	1	8	yes	complemented
434	C₂×C₄×D₅₃	—	4	4	no	—
435	C₂×C₄×D₅₃	—	4	4	no	—
436	C₂×C₄×D₅₃	—	4	4	no	—
437	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
438	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
439	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
440	C₂×Dic₁₀₆	—	4	4	no	—
441	C₂×Dic₁₀₆	—	4	2	no	—
442	C₂×Dic₁₀₆	C₂⁴	1	4	yes	complemented
443	C₂×Dic₁₀₆	C₂⁴	1	8	yes	complemented
444	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
445	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
446	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
447	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
448	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
449	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
450	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
451	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
452	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
453	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
454	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
455	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
456	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
457	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
458	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
459	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
460	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
461	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
462	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
463	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	complemented
464	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	complemented
465	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
466	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
467	#11719921	C₂⁴	1	8	yes	complemented
468	#11719921	C₂⁴	1	8	yes	complemented
469	#11719921	C₂⁴	1	8	yes	complemented
470	#11719921	C₂⁴	1	8	yes	complemented
471	#11719921	C₂⁴	1	8	yes	complemented
472	#11719921	C₂⁴	1	8	yes	complemented
473	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
474	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
475	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
476	#11719919	C₂⁴	1	8	yes	complemented
477	#11719919	C₂⁴	1	8	yes	complemented
478	#11719919	C₂⁴	1	8	yes	complemented
479	#11719919	C₂⁴	1	8	yes	complemented
480	#11719919	C₂⁴	1	8	yes	complemented
481	#11719919	C₂⁴	1	8	yes	complemented
482	C₄×Dic₅₃	C₂⁴	1	4	yes	complemented
483	C₄×Dic₅₃	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	4	no	—
490	C₂³×C₅₃	—	2	2	no	—
491	C₂³×C₅₃	—	2	2	no	—
492	C₂³×C₅₃	—	2	16	no	—
493	C₂³×C₅₃	—	2	16	no	—
494	C₂³×C₅₃	—	2	16	no	—
495	C₂³×C₅₃	—	2	4	no	—
496	C₂³×C₅₃	—	2	4	no	—
497	C₂³×C₅₃	—	2	4	no	—
498	C₂³×C₅₃	—	2	4	no	—
499	C₂³×C₅₃	—	2	4	no	—
500	C₂³×C₅₃	—	2	16	no	—
501	C₂³×C₅₃	—	2	8	no	—
502	C₂³×C₅₃	—	2	2	no	—
503	C₂³×C₅₃	—	2	4	no	—
504	C₂³×C₅₃	—	2	2	no	—
505	C₂³×C₅₃	—	2	8	no	—
506	C₂³×C₅₃	—	4	4	no	—
507	C₂³×C₅₃	—	4	8	no	—
508	C₂³×C₅₃	—	4	8	no	—
509	C₂³×C₅₃	—	4	8	no	—
510	C₂³×C₅₃	—	4	8	no	—
511	C₂³×C₅₃	—	4	4	no	—
512	C₂³×C₅₃	—	4	8	no	—
513	C₂³×C₅₃	—	4	8	no	—
514	C₂³×C₅₃	—	4	16	no	—
515	C₂³×C₅₃	—	4	32	no	—
516	C₂³×C₅₃	—	4	32	no	—
517	C₂³×C₅₃	—	4	16	no	—
518	C₂³×C₅₃	—	4	128	no	—
519	C₂³×C₅₃	—	4	16	no	—
520	C₂³×C₅₃	—	8	8	no	—
521	C₂³×C₅₃	H(5,𝔽₂)	1	8	yes	—
522	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
523	C₂³×C₅₃	C₂⁵	1	2	yes	—
524	C₂³×C₅₃	C₂⁵	1	2	yes	—
525	C₂³×C₅₃	C₂⁵	1	4	yes	—
526	C₂³×C₅₃	C₂⁵	1	2	yes	—
527	C₂³×C₅₃	C₂⁵	1	2	yes	—
528	C₂³×C₅₃	C₂⁵	1	4	yes	—
529	C₂³×C₅₃	C₂⁵	1	2	yes	—
530	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
531	C₂²×D₅₃	—	2	4	no	—
532	C₂²×D₅₃	—	2	4	no	—
533	C₂²×D₅₃	—	2	4	no	—
534	C₂²×D₅₃	—	2	4	no	—
535	C₂²×D₅₃	—	2	4	no	—
536	C₂²×D₅₃	—	2	4	no	—
537	C₂²×D₅₃	—	2	16	no	—
538	C₂²×D₅₃	—	4	8	no	—
539	C₂²×D₅₃	—	4	8	no	—
540	C₂²×D₅₃	—	4	8	no	—
541	C₂²×D₅₃	—	4	4	no	—
542	C₂²×D₅₃	—	8	16	no	—
543	C₂²×D₅₃	—	8	8	no	—
544	C₂²×D₅₃	C₂⁵	1	4	yes	—
545	C₂²×D₅₃	C₂⁵	1	4	yes	—
546	D₄×C₅₃	—	2	16	no	—
547	D₄×C₅₃	—	2	16	no	—
548	D₄×C₅₃	—	4	8	no	—
549	D₄×C₅₃	—	4	4	no	—
550	D₄×C₅₃	—	4	4	no	—
551	D₄×C₅₃	—	4	4	no	—
552	D₄×C₅₃	—	4	4	no	—
553	D₄×C₅₃	—	4	8	no	—
554	C₂×C₄×C₅₃	—	2	4	no	—
555	C₂×C₄×C₅₃	—	2	2	no	—
556	C₂×C₄×C₅₃	—	2	2	no	—
557	C₂×C₄×C₅₃	—	2	4	no	—
558	C₂×C₄×C₅₃	—	2	8	no	—
559	C₂×C₄×C₅₃	—	4	8	no	—
560	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
561	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
562	C₂×C₄×C₅₃	C₂⁵	1	2	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	—	2	16	no	—
568	C₂²⋊D₅₃	—	4	8	no	—
569	C₂²⋊D₅₃	—	4	8	no	—
570	C₂²⋊D₅₃	—	4	8	no	—
571	C₂²⋊D₅₃	—	4	8	no	—
572	C₂²⋊D₅₃	—	4	8	no	—
573	C₂²⋊D₅₃	—	4	8	no	—
574	C₂²⋊D₅₃	—	4	8	no	—
575	C₂²⋊D₅₃	—	4	8	no	—
576	C₂²⋊D₅₃	—	4	8	no	—
577	C₂²⋊D₅₃	—	4	8	no	—
578	C₂²⋊D₅₃	—	4	8	no	—
579	C₂×Dic₅₃	—	2	4	no	—
580	C₂×Dic₅₃	—	2	4	no	—
581	C₂×Dic₅₃	—	2	4	no	—
582	C₂×Dic₅₃	—	2	4	no	—
583	C₂×Dic₅₃	—	2	4	no	—
584	C₂×Dic₅₃	—	2	16	no	—
585	C₂×Dic₅₃	—	2	4	no	—
586	C₂×Dic₅₃	—	4	8	no	—
587	C₂×Dic₅₃	—	4	8	no	—
588	C₂×Dic₅₃	—	4	8	no	—
589	C₂×Dic₅₃	—	4	4	no	—
590	C₂×Dic₅₃	C₂⁵	1	4	yes	—
591	C₂×Dic₅₃	C₂⁵	1	4	yes	—
592	C₂×Dic₅₃	C₂⁵	1	4	yes	—
593	C₂×Dic₅₃	C₂⁵	1	4	yes	—
594	C₂×Dic₅₃	C₂⁵	1	4	yes	—
595	C₂×Dic₅₃	C₂⁵	1	4	yes	—
596	D₂₁₂	—	4	4	no	—
597	D₂₁₂	—	4	8	no	—
598	C₄×D₅₃	—	4	8	no	—
599	C₄×D₅₃	—	4	8	no	—
600	C₄×D₅₃	—	4	8	no	—
601	Dic₁₀₆	—	4	4	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	4	no	—
607	C₂²×C₅₃	—	2	16	no	—
608	C₂²×C₅₃	—	2	8	no	—
609	C₂²×C₅₃	—	2	4	no	—
610	C₂²×C₅₃	—	2	2	no	—
611	C₂²×C₅₃	—	2	2	no	—
612	C₂²×C₅₃	—	2	4	no	—
613	C₂²×C₅₃	—	2	4	no	—
614	C₂²×C₅₃	—	2	4	no	—
615	C₂²×C₅₃	—	2	4	no	—
616	C₂²×C₅₃	—	2	4	no	—
617	C₂²×C₅₃	—	2	2	no	—
618	C₂²×C₅₃	—	2	4	no	—
619	C₂²×C₅₃	—	2	2	no	—
620	C₂²×C₅₃	—	4	16	no	—
621	C₂²×C₅₃	—	4	32	no	—
622	C₂²×C₅₃	—	4	32	no	—
623	C₂²×C₅₃	—	4	16	no	—
624	C₂²×C₅₃	—	4	16	no	—
625	C₂²×C₅₃	—	4	4	no	—
626	C₂²×C₅₃	—	4	4	no	—
627	C₂²×C₅₃	—	4	8	no	—
628	C₂²×C₅₃	—	4	4	no	—
629	C₂²×C₅₃	—	4	4	no	—
630	C₂²×C₅₃	—	8	8	no	—
631	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	8	yes	—
632	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
633	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
634	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
635	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
636	C₂×D₅₃	—	2	4	no	—
637	C₂×D₅₃	—	2	4	no	—
638	C₂×D₅₃	—	2	4	no	—
639	C₂×D₅₃	—	2	4	no	—
640	C₂×D₅₃	—	2	4	no	—
641	C₂×D₅₃	—	2	4	no	—
642	C₂×D₅₃	—	4	8	no	—
643	C₂×D₅₃	—	4	8	no	—
644	C₂×D₅₃	—	8	16	no	—
645	C₂×D₅₃	—	8	8	no	—
646	C₄×C₅₃	—	2	4	no	—
647	C₄×C₅₃	—	2	2	no	—
648	C₄×C₅₃	—	2	2	no	—
649	C₄×C₅₃	—	2	4	no	—
650	Dic₅₃	—	2	4	no	—
651	Dic₅₃	—	2	4	no	—
652	Dic₅₃	—	2	4	no	—
653	Dic₅₃	—	2	4	no	—
654	Dic₅₃	—	2	4	no	—
655	Dic₅₃	—	2	4	no	—
656	#3532	—	53	32	no	—
657	C₂×H(3,𝔽₄)	—	53	1	no	—
658	C₂×#560	—	53	1	no	—
659	C₂×#560	—	53	2	no	—
660	C₂×#551	—	53	1	no	—
661	C₂×#551	—	53	2	no	—
662	C₂×#546	—	53	2	no	—
663	C₂×#546	—	53	2	no	—
664	C₂×#546	—	53	2	no	—
665	C₂×D₄²	—	53	2	no	—
666	C₂×D₄²	—	53	1	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	1	no	—
673	C₂×#534	—	53	2	no	—
674	C₂²×#120	—	53	2	no	—
675	C₂²×#120	D₅₃	1	1	yes	characteristic, complemented
676	C₂×C₅₃	—	2	8	no	—
677	C₂×C₅₃	—	2	4	no	—
678	C₂×C₅₃	—	4	2	no	—
679	C₂×C₅₃	—	4	2	no	—
680	C₂×C₅₃	—	4	4	no	—
681	C₂×C₅₃	—	4	2	no	—
682	C₂×C₅₃	—	4	2	no	—
683	C₂×C₅₃	#3532	1	4	yes	complemented
684	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
685	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	2	yes	—
686	D₅₃	—	4	4	no	—
687	D₅₃	—	4	4	no	—
688	C₂⁶	C₂×D₅₃	1	1	yes	characteristic, complemented
689	C₂²×#41	—	53	2	no	—
690	C₂²×#41	—	53	1	no	—
691	C₂³×D₄	—	53	2	no	—
692	C₂³×D₄	—	53	2	no	—
693	C₂³×D₄	—	53	2	no	—
694	C₂³×D₄	—	53	1	no	—
695	C₂³×D₄	—	53	2	no	—
696	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
697	C₂³×D₄	C₂×D₅₃	1	2	yes	complemented
698	H(3,𝔽₄)	—	53	16	no	—
699	#560	—	53	16	no	—
700	#560	—	53	32	no	—
701	#551	—	53	16	no	—
702	#551	—	53	32	no	—
703	#546	—	53	32	no	—
704	#546	—	53	32	no	—
705	#546	—	53	32	no	—
706	D₄²	—	53	32	no	—
707	D₄²	—	53	16	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	16	no	—
714	#534	—	53	32	no	—
715	C₂×#127	—	53	1	no	—
716	C₂×#127	—	53	2	no	—
717	C₂×#127	—	53	1	no	—
718	C₂×#126	—	53	2	no	—
719	C₂×#126	—	53	2	no	—
720	C₂×#126	—	53	2	no	—
721	C₂×#126	—	53	2	no	—
722	C₂×#124	—	53	1	no	—
723	C₂×#124	—	53	1	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	—	53	2	no	—
729	C₂×#123	—	53	1	no	—
730	C₂×#123	—	53	2	no	—
731	C₂×#123	—	53	1	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	—	53	2	no	—
738	C₂×#123	—	53	2	no	—
739	C₂×C₂²⋊Q₈	—	53	2	no	—
740	C₂×C₂²⋊Q₈	—	53	2	no	—
741	C₂×C₂²⋊Q₈	—	53	2	no	—
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	2	no	—
758	C₂×#120	—	53	2	no	—
759	C₂×#120	—	53	2	no	—
760	C₂×#120	—	53	2	no	—
761	C₂×#120	—	53	2	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	32	no	—
767	C₂×#120	—	53	1	no	—
768	C₂×#120	—	53	1	no	—
769	C₂×#120	—	53	2	no	—
770	C₂×#120	—	53	2	no	—
771	C₂×#120	—	53	2	no	—
772	C₂×#120	C₂×D₅₃	1	1	yes	characteristic
773	C₂×#120	C₂×D₅₃	1	2	yes	complemented
774	C₂×#120	C₂×D₅₃	1	2	yes	complemented
775	C₂×#120	C₂×D₅₃	1	1	yes	characteristic, complemented
776	C₂×#120	C₂×D₅₃	1	1	yes	characteristic, complemented
777	C₂×#120	C₂×D₅₃	1	1	yes	characteristic, complemented
778	C₂×#120	C₂×D₅₃	1	16	yes	complemented
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	—	53	2	no	—
785	C₂×#117	—	53	1	no	—
786	C₂×#117	—	53	2	no	—
787	C₂²×C₂²⋊C₄	—	53	2	no	—
788	C₂²×C₂²⋊C₄	—	53	2	no	—
789	C₂²×C₂²⋊C₄	—	53	2	no	—
790	C₂²×C₂²⋊C₄	—	53	1	no	—
791	C₂²×C₂²⋊C₄	—	53	2	no	—
792	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
793	C₂²×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
794	C₅₃	C₂×#3532	1	1	yes	characteristic, complemented, Sylow
795	C₂⁵	—	4	8	no	—
796	C₂⁵	—	4	4	no	—
797	C₂⁵	—	53	2	no	—
798	C₂⁵	—	53	1	no	—
799	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
800	C₂⁵	C₂²×D₅₃	1	2	yes	—
801	C₂⁵	C₂²×D₅₃	1	2	yes	—
802	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
803	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
804	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
805	C₂⁵	C₂²×D₅₃	1	8	yes	complemented
806	C₂×#41	—	53	16	no	—
807	C₂×#41	—	53	8	no	—
808	C₂×#41	—	212	4	no	—
809	C₂×#41	—	212	8	no	—
810	C₂²×Q₈	—	53	2	no	—
811	C₂²×Q₈	—	53	1	no	—
812	C₂²×D₄	—	4	4	no	—
813	C₂²×D₄	—	4	8	no	—
814	C₂²×D₄	—	53	2	no	—
815	C₂²×D₄	—	53	2	no	—
816	C₂²×D₄	—	53	2	no	—
817	C₂²×D₄	—	53	2	no	—
818	C₂²×D₄	—	53	2	no	—
819	C₂²×D₄	—	53	2	no	—
820	C₂²×D₄	—	53	2	no	—
821	C₂²×D₄	—	53	2	no	—
822	C₂²×D₄	—	53	2	no	—
823	C₂²×D₄	—	53	2	no	—
824	C₂²×D₄	—	53	2	no	—
825	C₂²×D₄	—	53	2	no	—
826	C₂²×D₄	—	53	2	no	—
827	C₂²×D₄	—	53	16	no	—
828	C₂²×D₄	—	53	16	no	—
829	C₂²×D₄	—	53	16	no	—
830	C₂²×D₄	—	53	2	no	—
831	C₂²×D₄	—	53	2	no	—
832	C₂²×D₄	—	53	8	no	—
833	C₂²×D₄	—	53	16	no	—
834	C₂²×D₄	—	53	1	no	—
835	C₂²×D₄	—	53	2	no	—
836	C₂²×D₄	—	212	8	no	—
837	C₂²×D₄	—	212	8	no	—
838	C₂²×D₄	—	212	4	no	—
839	C₂²×D₄	—	212	8	no	—
840	C₂²×D₄	—	212	8	no	—
841	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
842	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
843	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
844	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
845	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
846	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
847	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
848	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
849	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
850	C₂²×D₄	C₂²×D₅₃	1	16	yes	complemented
851	C₂³×C₄	—	53	2	no	—
852	C₂³×C₄	—	53	2	no	—
853	C₂³×C₄	—	53	2	no	—
854	C₂³×C₄	—	53	2	no	—
855	C₂³×C₄	—	53	1	no	—
856	C₂³×C₄	—	53	2	no	—
857	C₂³×C₄	—	53	2	no	—
858	C₂³×C₄	—	53	2	no	—
859	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
860	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
861	#127	—	53	8	no	—
862	#127	—	53	16	no	—
863	#127	—	53	8	no	—
864	#126	—	53	16	no	—
865	#126	—	53	16	no	—
866	#126	—	53	16	no	—
867	#126	—	53	16	no	—
868	#124	—	53	8	no	—
869	#124	—	53	8	no	—
870	#124	—	53	16	no	—
871	#124	—	53	16	no	—
872	#124	—	53	16	no	—
873	#124	—	53	16	no	—
874	#124	—	53	16	no	—
875	#123	—	53	8	no	—
876	#123	—	53	16	no	—
877	#123	—	53	8	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	—	53	16	no	—
884	#123	—	53	16	no	—
885	C₂²⋊Q₈	—	53	16	no	—
886	C₂²⋊Q₈	—	53	16	no	—
887	C₂²⋊Q₈	—	53	16	no	—
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	16	no	—
904	#120	—	53	16	no	—
905	#120	—	53	16	no	—
906	#120	—	53	16	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	8	no	—
913	#120	—	53	8	no	—
914	#120	—	53	16	no	—
915	#120	—	53	16	no	—
916	#120	—	53	16	no	—
917	#120	C₂²×D₅₃	1	8	yes	—
918	#120	C₂²×D₅₃	1	16	yes	complemented
919	#120	C₂²×D₅₃	1	16	yes	complemented
920	#120	C₂²×D₅₃	1	8	yes	complemented
921	#120	C₂²×D₅₃	1	8	yes	complemented
922	#120	C₂²×D₅₃	1	8	yes	complemented
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	—	53	16	no	—
929	#117	—	53	8	no	—
930	#117	—	53	16	no	—
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	—	53	2	no	—
937	C₂×C₄⋊C₄	—	53	2	no	—
938	C₂×C₄⋊C₄	—	53	2	no	—
939	C₂×C₄⋊C₄	—	53	2	no	—
940	C₂×C₂²⋊C₄	—	53	2	no	—
941	C₂×C₂²⋊C₄	—	53	2	no	—
942	C₂×C₂²⋊C₄	—	53	2	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	16	no	—
953	C₂×C₂²⋊C₄	—	53	16	no	—
954	C₂×C₂²⋊C₄	—	53	16	no	—
955	C₂×C₂²⋊C₄	—	53	1	no	—
956	C₂×C₂²⋊C₄	—	53	1	no	—
957	C₂×C₂²⋊C₄	—	53	8	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	2	no	—
964	C₂×C₂²⋊C₄	—	53	2	no	—
965	C₂×C₂²⋊C₄	—	53	2	no	—
966	C₂×C₂²⋊C₄	—	53	16	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	1	yes	characteristic
974	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
975	C₂×C₂²⋊C₄	C₂²×D₅₃	1	16	yes	complemented
976	C₂×C₄²	—	53	1	no	—
977	C₂×C₄²	—	53	2	no	—
978	C₂×C₄²	—	53	1	no	—
979	C₂×C₄²	—	53	2	no	—
980	C₂⁴	—	2	8	no	—
981	C₂⁴	—	2	4	no	—
982	C₂⁴	—	2	8	no	—
983	C₂⁴	—	2	8	no	—
984	C₂⁴	—	2	8	no	—
985	C₂⁴	—	2	4	no	—
986	C₂⁴	—	4	4	no	—
987	C₂⁴	—	4	4	no	—
988	C₂⁴	—	4	2	no	—
989	C₂⁴	—	4	4	no	—
990	C₂⁴	—	4	4	no	—
991	C₂⁴	—	4	2	no	—
992	C₂⁴	—	4	4	no	—
993	C₂⁴	—	4	32	no	—
994	C₂⁴	—	4	16	no	—
995	C₂⁴	—	4	4	no	—
996	C₂⁴	—	4	64	no	—
997	C₂⁴	—	53	2	no	—
998	C₂⁴	—	53	2	no	—
999	C₂⁴	—	53	8	no	—
1000	C₂⁴	—	53	4	no	—
1001	C₂⁴	—	106	8	no	—
1002	C₂⁴	—	212	4	no	—
1003	C₂⁴	—	212	4	no	—
1004	C₂⁴	—	212	2	no	—
1005	C₂⁴	—	212	4	no	—
1006	C₂⁴	C₂³×D₅₃	1	2	yes	—
1007	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1008	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1009	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1010	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1011	C₂⁴	C₂³×D₅₃	1	4	yes	—
1012	C₂⁴	C₂³×D₅₃	1	8	yes	—
1013	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1014	C₂⁴	C₂³×D₅₃	1	2	yes	—
1015	C₂⁴	C₂³×D₅₃	1	8	yes	—
1016	C₂⁴	C₂³×D₅₃	1	4	yes	—
1017	C₂⁴	C₂³×D₅₃	1	4	yes	—
1018	C₂⁴	C₂³×D₅₃	1	4	yes	—
1019	#41	—	212	16	no	—
1020	#41	—	212	32	no	—
1021	C₂×Q₈	—	53	8	no	—
1022	C₂×Q₈	—	53	4	no	—
1023	C₂×Q₈	—	212	2	no	—
1024	C₂×Q₈	—	212	4	no	—
1025	C₂×D₄	—	2	8	no	—
1026	C₂×D₄	—	2	8	no	—
1027	C₂×D₄	—	4	2	no	—
1028	C₂×D₄	—	4	2	no	—
1029	C₂×D₄	—	4	2	no	—
1030	C₂×D₄	—	4	2	no	—
1031	C₂×D₄	—	4	4	no	—
1032	C₂×D₄	—	4	4	no	—
1033	C₂×D₄	—	4	16	no	—
1034	C₂×D₄	—	4	32	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	8	no	—
1045	C₂×D₄	—	53	8	no	—
1046	C₂×D₄	—	53	8	no	—
1047	C₂×D₄	—	53	8	no	—
1048	C₂×D₄	—	53	8	no	—
1049	C₂×D₄	—	53	8	no	—
1050	C₂×D₄	—	53	4	no	—
1051	C₂×D₄	—	53	8	no	—
1052	C₂×D₄	—	106	8	no	—
1053	C₂×D₄	—	106	8	no	—
1054	C₂×D₄	—	106	8	no	—
1055	C₂×D₄	—	106	8	no	—
1056	C₂×D₄	—	212	4	no	—
1057	C₂×D₄	—	212	2	no	—
1058	C₂×D₄	—	212	4	no	—
1059	C₂×D₄	—	212	4	no	—
1060	C₂×D₄	—	212	4	no	—
1061	C₂×D₄	—	212	4	no	—
1062	C₂×D₄	—	212	32	no	—
1063	C₂×D₄	—	212	4	no	—
1064	C₂×D₄	—	212	4	no	—
1065	C₂×D₄	—	212	4	no	—
1066	C₂×D₄	—	212	4	no	—
1067	C₂×D₄	—	212	4	no	—
1068	C₂×D₄	—	212	4	no	—
1069	C₂×D₄	—	212	4	no	—
1070	C₂×D₄	—	212	32	no	—
1071	C₂×D₄	—	212	16	no	—
1072	C₂×D₄	—	212	32	no	—
1073	C₂×D₄	—	212	32	no	—
1074	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1075	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1076	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1077	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1078	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1079	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1080	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1081	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1082	C₂²×C₄	—	2	4	no	—
1083	C₂²×C₄	—	4	4	no	—
1084	C₂²×C₄	—	53	8	no	—
1085	C₂²×C₄	—	53	2	no	—
1086	C₂²×C₄	—	53	2	no	—
1087	C₂²×C₄	—	53	2	no	—
1088	C₂²×C₄	—	53	2	no	—
1089	C₂²×C₄	—	53	2	no	—
1090	C₂²×C₄	—	53	2	no	—
1091	C₂²×C₄	—	53	8	no	—
1092	C₂²×C₄	—	53	8	no	—
1093	C₂²×C₄	—	53	8	no	—
1094	C₂²×C₄	—	53	4	no	—
1095	C₂²×C₄	—	53	8	no	—
1096	C₂²×C₄	—	53	8	no	—
1097	C₂²×C₄	—	53	8	no	—
1098	C₂²×C₄	—	106	8	no	—
1099	C₂²×C₄	—	212	4	no	—
1100	C₂²×C₄	—	212	4	no	—
1101	C₂²×C₄	—	212	4	no	—
1102	C₂²×C₄	—	212	2	no	—
1103	C₂²×C₄	—	212	4	no	—
1104	C₂²×C₄	—	212	4	no	—
1105	C₂²×C₄	—	212	4	no	—
1106	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1107	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1108	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1109	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1110	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1111	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
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	—	53	8	no	—
1118	C₄⋊C₄	—	53	8	no	—
1119	C₄⋊C₄	—	53	8	no	—
1120	C₄⋊C₄	—	53	8	no	—
1121	C₂²⋊C₄	—	53	8	no	—
1122	C₂²⋊C₄	—	53	8	no	—
1123	C₂²⋊C₄	—	53	8	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	4	no	—
1134	C₂²⋊C₄	—	53	4	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	—	53	8	no	—
1143	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1144	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1145	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1146	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1147	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1148	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1149	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1150	C₄²	—	53	4	no	—
1151	C₄²	—	53	8	no	—
1152	C₄²	—	53	4	no	—
1153	C₄²	—	53	8	no	—
1154	C₂³	—	2	4	no	—
1155	C₂³	—	2	4	no	—
1156	C₂³	—	2	4	no	—
1157	C₂³	—	2	4	no	—
1158	C₂³	—	2	2	no	—
1159	C₂³	—	2	4	no	—
1160	C₂³	—	2	2	no	—
1161	C₂³	—	2	16	no	—
1162	C₂³	—	2	8	no	—
1163	C₂³	—	2	2	no	—
1164	C₂³	—	2	4	no	—
1165	C₂³	—	2	2	no	—
1166	C₂³	—	2	16	no	—
1167	C₂³	—	2	16	no	—
1168	C₂³	—	2	16	no	—
1169	C₂³	—	2	4	no	—
1170	C₂³	—	2	4	no	—
1171	C₂³	—	2	4	no	—
1172	C₂³	—	2	4	no	—
1173	C₂³	—	2	8	no	—
1174	C₂³	—	4	8	no	—
1175	C₂³	—	4	8	no	—
1176	C₂³	—	4	4	no	—
1177	C₂³	—	4	8	no	—
1178	C₂³	—	4	8	no	—
1179	C₂³	—	4	4	no	—
1180	C₂³	—	4	8	no	—
1181	C₂³	—	4	8	no	—
1182	C₂³	—	4	32	no	—
1183	C₂³	—	4	16	no	—
1184	C₂³	—	4	16	no	—
1185	C₂³	—	4	32	no	—
1186	C₂³	—	4	128	no	—
1187	C₂³	—	4	16	no	—
1188	C₂³	—	8	8	no	—
1189	C₂³	—	53	4	no	—
1190	C₂³	—	53	4	no	—
1191	C₂³	—	106	16	no	—
1192	C₂³	—	106	4	no	—
1193	C₂³	—	106	4	no	—
1194	C₂³	—	106	4	no	—
1195	C₂³	—	106	4	no	—
1196	C₂³	—	106	4	no	—
1197	C₂³	—	106	4	no	—
1198	C₂³	—	424	16	no	—
1199	C₂³	—	424	8	no	—
1200	C₂³	—	212	8	no	—
1201	C₂³	—	212	8	no	—
1202	C₂³	—	212	4	no	—
1203	C₂³	—	212	8	no	—
1204	C₂³	#13133262	1	4	yes	—
1205	C₂³	#13133262	1	8	yes	—
1206	C₂³	C₂⁴×D₅₃	1	4	yes	—
1207	C₂³	C₂⁴×D₅₃	1	2	yes	—
1208	C₂³	C₂⁴×D₅₃	1	2	yes	—
1209	C₂³	C₂⁴×D₅₃	1	2	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	—	212	4	no	—
1215	Q₈	—	212	8	no	—
1216	D₄	—	2	16	no	—
1217	D₄	—	2	16	no	—
1218	D₄	—	4	4	no	—
1219	D₄	—	4	4	no	—
1220	D₄	—	4	4	no	—
1221	D₄	—	4	4	no	—
1222	D₄	—	4	8	no	—
1223	D₄	—	4	8	no	—
1224	D₄	—	106	16	no	—
1225	D₄	—	106	16	no	—
1226	D₄	—	106	16	no	—
1227	D₄	—	106	16	no	—
1228	D₄	—	212	8	no	—
1229	D₄	—	212	4	no	—
1230	D₄	—	212	8	no	—
1231	D₄	—	212	8	no	—
1232	D₄	—	212	8	no	—
1233	D₄	—	212	8	no	—
1234	D₄	—	212	8	no	—
1235	D₄	—	212	8	no	—
1236	D₄	—	212	8	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	2	no	—
1242	C₂×C₄	—	2	2	no	—
1243	C₂×C₄	—	2	8	no	—
1244	C₂×C₄	—	2	4	no	—
1245	C₂×C₄	—	2	4	no	—
1246	C₂×C₄	—	4	8	no	—
1247	C₂×C₄	—	53	4	no	—
1248	C₂×C₄	—	53	4	no	—
1249	C₂×C₄	—	53	4	no	—
1250	C₂×C₄	—	53	4	no	—
1251	C₂×C₄	—	53	4	no	—
1252	C₂×C₄	—	53	4	no	—
1253	C₂×C₄	—	106	4	no	—
1254	C₂×C₄	—	106	4	no	—
1255	C₂×C₄	—	106	16	no	—
1256	C₂×C₄	—	106	4	no	—
1257	C₂×C₄	—	106	4	no	—
1258	C₂×C₄	—	106	4	no	—
1259	C₂×C₄	—	106	4	no	—
1260	C₂×C₄	—	212	8	no	—
1261	C₂×C₄	—	212	8	no	—
1262	C₂×C₄	—	212	8	no	—
1263	C₂×C₄	—	212	4	no	—
1264	C₂×C₄	—	212	8	no	—
1265	C₂×C₄	—	212	8	no	—
1266	C₂×C₄	—	212	8	no	—
1267	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1268	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1269	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1270	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1271	C₂²	—	2	8	no	—
1272	C₂²	—	2	16	no	—
1273	C₂²	—	2	4	no	—
1274	C₂²	—	2	4	no	—
1275	C₂²	—	2	4	no	—
1276	C₂²	—	2	4	no	—
1277	C₂²	—	2	2	no	—
1278	C₂²	—	2	4	no	—
1279	C₂²	—	2	2	no	—
1280	C₂²	—	2	2	no	—
1281	C₂²	—	2	4	no	—
1282	C₂²	—	2	2	no	—
1283	C₂²	—	2	4	no	—
1284	C₂²	—	2	4	no	—
1285	C₂²	—	2	4	no	—
1286	C₂²	—	2	4	no	—
1287	C₂²	—	4	32	no	—
1288	C₂²	—	4	16	no	—
1289	C₂²	—	4	16	no	—
1290	C₂²	—	4	32	no	—
1291	C₂²	—	4	16	no	—
1292	C₂²	—	4	8	no	—
1293	C₂²	—	4	4	no	—
1294	C₂²	—	4	4	no	—
1295	C₂²	—	4	4	no	—
1296	C₂²	—	4	4	no	—
1297	C₂²	—	8	8	no	—
1298	C₂²	—	106	4	no	—
1299	C₂²	—	106	4	no	—
1300	C₂²	—	106	4	no	—
1301	C₂²	—	106	4	no	—
1302	C₂²	—	106	4	no	—
1303	C₂²	—	106	4	no	—
1304	C₂²	—	424	16	no	—
1305	C₂²	—	424	8	no	—
1306	C₂²	—	212	8	no	—
1307	C₂²	—	212	8	no	—
1308	C₂²	C₂×#13133262	1	4	yes	—
1309	C₂²	C₂×#13133262	1	8	yes	—
1310	C₂²	C₂×#13133262	1	2	yes	—
1311	C₂²	C₂×#13133262	1	4	yes	—
1312	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1313	C₄	—	2	2	no	—
1314	C₄	—	2	2	no	—
1315	C₄	—	2	4	no	—
1316	C₄	—	2	4	no	—
1317	C₄	—	106	4	no	—
1318	C₄	—	106	4	no	—
1319	C₄	—	106	4	no	—
1320	C₄	—	106	4	no	—
1321	C₄	—	106	4	no	—
1322	C₄	—	106	4	no	—
1323	C₂	—	2	4	no	—
1324	C₂	—	2	8	no	—
1325	C₂	—	4	4	no	—
1326	C₂	—	4	2	no	—
1327	C₂	—	4	2	no	—
1328	C₂	—	4	2	no	—
1329	C₂	—	4	2	no	—
1330	C₂	—	212	4	no	—
1331	C₂	—	212	4	no	—
1332	C₂	#20288870	1	4	yes	direct product factor
1333	C₂	C₂²×#13133262	1	1	yes	characteristic
1334	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×#3532
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. #20288870	C₂	direct (N × H)
2. C₂×#16811366	C₂	semidirect
3. C₂×#16811362	C₂	semidirect
4. C₂×#16811362	C₂	semidirect
5. C₂×#16811304	C₂	semidirect
6. C₂×#16811299	C₂	semidirect
7. C₂×#16811267	C₂	semidirect
8. C₂×#16811263	C₂	semidirect
9. C₂×#16811260	C₂	semidirect
10. C₂×D₄×C₂²⋊D₅₃	C₂	semidirect
11. C₂×#16811255	C₂	semidirect
12. C₂×#16811211	C₂	semidirect
13. C₂×#16811208	C₂	semidirect
14. C₂×#16811208	C₂	semidirect
15. C₂×#16811190	C₂	semidirect
16. C₂×#16811188	C₂	semidirect
17. C₂×#16811183	C₂	semidirect
18. C₂×#16811182	C₂	semidirect
19. C₂²×#13133186	C₂	semidirect
20. C₂²×#120×C₅₃	C₂	semidirect
21. C₂²×#11719945	C₂²	semidirect
22. C₂²×#11719947	C₂²	semidirect
23. C₂³×C₂²⋊D₅₃	C₂²	semidirect
24. C₂³×C₂²⋊D₅₃	C₂²	semidirect
25. C₂³×C₂²⋊D₅₃	C₂²	semidirect
26. C₂³×C₂²⋊D₅₃	C₂²	semidirect
27. C₂²×D₄×D₅₃	C₂²	semidirect
28. #16811366	C₂²	semidirect
29. #16811362	C₂²	semidirect
30. #16811362	C₂²	semidirect
31. #16811304	C₂²	semidirect
32. #16811299	C₂²	semidirect
33. #16811267	C₂²	semidirect
34. #16811263	C₂²	semidirect
35. #16811260	C₂²	semidirect
36. D₄×C₂²⋊D₅₃	C₂²	semidirect
37. #16811255	C₂²	semidirect
38. #16811211	C₂²	semidirect
39. #16811208	C₂²	semidirect
40. #16811208	C₂²	semidirect
41. #16811190	C₂²	semidirect
42. #16811188	C₂²	semidirect
43. #16811183	C₂²	semidirect
44. #16811182	C₂²	semidirect
45. C₂×#13133213	C₂²	semidirect
46. C₂×#13133213	C₂²	semidirect
47. C₂×#13133213	C₂²	semidirect
48. C₂×#13133210	C₂²	semidirect
49. C₂×#13133210	C₂²	semidirect
50. C₂×#13133210	C₂²	semidirect
51. C₂×#13133210	C₂²	semidirect
52. C₂×#13133204	C₂²	semidirect
53. C₂×#13133204	C₂²	semidirect
54. C₂×#13133204	C₂²	semidirect
55. C₂×#13133203	C₂²	semidirect
56. C₂×#13133203	C₂²	semidirect
57. C₂×#13133203	C₂²	semidirect
58. C₂×#13133203	C₂²	semidirect
59. C₂×#13133201	C₂²	semidirect
60. C₂×#13133200	C₂²	semidirect
61. C₂×#13133199	C₂²	semidirect
62. C₂×#13133199	C₂²	semidirect
63. C₂×#13133199	C₂²	semidirect
64. C₂×#13133199	C₂²	semidirect
65. C₂×#13133198	C₂²	semidirect
66. C₂×#13133198	C₂²	semidirect
67. C₂×#13133198	C₂²	semidirect
68. C₂×#13133198	C₂²	semidirect
69. C₂×#13133196	C₂²	semidirect
70. C₂×#13133194	C₂²	semidirect
71. C₂×#13133194	C₂²	semidirect
72. C₂×#13133191	C₂²	semidirect
73. C₂×#13133190	C₂²	semidirect
74. C₂×#13133190	C₂²	semidirect
75. C₂×#13133190	C₂²	semidirect
76. C₂×#13133190	C₂²	semidirect
77. C₂×#13133189	C₂²	semidirect
78. C₂×#13133189	C₂²	semidirect
79. C₂×#13133189	C₂²	semidirect
80. C₂×#13133189	C₂²	semidirect
81. C₂×#13133189	C₂²	semidirect
82. C₂×#13133189	C₂²	semidirect
83. C₂×#13133188	C₂²	semidirect
84. C₂×#13133188	C₂²	semidirect
85. C₂×#13133188	C₂²	semidirect
86. C₂×#13133188	C₂²	semidirect
87. C₂×#13133187	C₂²	semidirect
89. C₂×#13133186	C₂²	semidirect
90. C₂×#13133186	C₂²	semidirect
91. C₂×#13133186	C₂²	semidirect
92. C₂×#13133186	C₂²	semidirect
93. C₂×#13133186	C₂²	semidirect
94. C₂×#13133186	C₂²	semidirect
95. C₂×#13133186	C₂²	semidirect
96. C₂×#13133186	C₂²	semidirect
97. C₂×#13133186	C₂²	semidirect
98. C₂×#13133185	C₂²	semidirect
99. C₂×#13133185	C₂²	semidirect
100. C₂×#13133185	C₂²	semidirect
101. C₂×#13133185	C₂²	semidirect
102. C₂×D₄×Dic₅₃	C₂²	semidirect
103. C₂×D₄×Dic₅₃	C₂²	semidirect
104. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
105. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
106. C₂×#13133177	C₂²	semidirect
107. C₂×#13133177	C₂²	semidirect
108. C₂×#13133176	C₂²	semidirect
109. C₂×#13133173	C₂²	semidirect
110. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
111. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
112. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
113. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
114. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
115. C₂⁶×C₅₃	C₂²	semidirect
116. C₂³×D₄×C₅₃	C₂²	semidirect
117. C₂³×D₄×C₅₃	C₂²	semidirect
119. C₂×#120×C₅₃	C₂²	semidirect
120. C₂×#120×C₅₃	C₂²	semidirect
121. C₂×#120×C₅₃	C₂²	semidirect
122. C₂×#120×C₅₃	C₂²	semidirect
123. C₂×#120×C₅₃	C₂²	semidirect
124. C₂×#120×C₅₃	C₂²	semidirect
125. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
126. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
128. C₂⁴×D₅₃	C₂³	semidirect
130. C₂×#11719945	C₂³	semidirect
132. C₂×#11719947	C₂³	semidirect
133. C₂²×Dic₁₀₆	C₂³	semidirect
134. C₂²×Dic₁₀₆	C₂³	semidirect
135. C₂²×D₂₁₂	C₂³	semidirect
136. C₂²×D₂₁₂	C₂³	semidirect
153. C₂²×C₂²⋊D₅₃	C₂³	semidirect
154. C₂²×C₂²⋊D₅₃	C₂³	semidirect
155. C₂²×C₂²⋊D₅₃	C₂³	semidirect
156. C₂²×C₂²⋊D₅₃	C₂³	semidirect
157. C₂²×C₂²⋊D₅₃	C₂³	semidirect
158. C₂²×C₂²⋊D₅₃	C₂³	semidirect
159. C₂²×C₂²⋊D₅₃	C₂³	semidirect
161. C₂×D₄×D₅₃	C₂³	semidirect
165. C₂³×Dic₅₃	C₂³	semidirect
166. C₂³×Dic₅₃	C₂³	semidirect
167. C₂²×C₄×D₅₃	C₂³	semidirect
168. C₂²×C₄×D₅₃	C₂³	semidirect
169. C₂²×C₄×D₅₃	C₂³	semidirect
170. #13133213	C₂³	semidirect
171. #13133213	C₂³	semidirect
172. #13133213	C₂³	semidirect
173. #13133210	C₂³	semidirect
174. #13133210	C₂³	semidirect
175. #13133210	C₂³	semidirect
176. #13133210	C₂³	semidirect
177. #13133204	C₂³	semidirect
178. #13133204	C₂³	semidirect
179. #13133204	C₂³	semidirect
180. #13133203	C₂³	semidirect
181. #13133203	C₂³	semidirect
182. #13133203	C₂³	semidirect
183. #13133203	C₂³	semidirect
184. #13133201	C₂³	semidirect
185. #13133200	C₂³	semidirect
186. #13133199	C₂³	semidirect
187. #13133199	C₂³	semidirect
188. #13133199	C₂³	semidirect
189. #13133199	C₂³	semidirect
190. #13133198	C₂³	semidirect
191. #13133198	C₂³	semidirect
192. #13133198	C₂³	semidirect
193. #13133198	C₂³	semidirect
194. #13133196	C₂³	semidirect
195. #13133194	C₂³	semidirect
196. #13133194	C₂³	semidirect
197. #13133191	C₂³	semidirect
198. #13133190	C₂³	semidirect
199. #13133190	C₂³	semidirect
200. #13133190	C₂³	semidirect
201. #13133190	C₂³	semidirect
202. #13133189	C₂³	semidirect
203. #13133189	C₂³	semidirect
204. #13133189	C₂³	semidirect
205. #13133189	C₂³	semidirect
206. #13133189	C₂³	semidirect
207. #13133189	C₂³	semidirect
208. #13133188	C₂³	semidirect
209. #13133188	C₂³	semidirect
210. #13133188	C₂³	semidirect
211. #13133188	C₂³	semidirect
212. #13133187	C₂³	semidirect
214. #13133186	C₂³	semidirect
215. #13133186	C₂³	semidirect
216. #13133186	C₂³	semidirect
217. #13133186	C₂³	semidirect
218. #13133186	C₂³	semidirect
219. #13133186	C₂³	semidirect
220. #13133186	C₂³	semidirect
221. #13133186	C₂³	semidirect
222. #13133185	C₂³	semidirect
223. #13133185	C₂³	semidirect
224. #13133185	C₂³	semidirect
225. #13133185	C₂³	semidirect
226. D₄×Dic₅₃	C₂³	semidirect
227. D₄×Dic₅₃	C₂³	semidirect
228. C₄×C₂²⋊D₅₃	C₂³	semidirect
229. C₄×C₂²⋊D₅₃	C₂³	semidirect
230. #13133177	C₂³	semidirect
231. #13133177	C₂³	semidirect
232. #13133176	C₂³	semidirect
233. #13133173	C₂³	semidirect
234. C₂×C₄⋊Dic₅₃	C₂³	semidirect
235. C₂×C₄⋊Dic₅₃	C₂³	semidirect
236. C₂×C₄⋊Dic₅₃	C₂³	semidirect
237. C₂×#11719919	C₂³	semidirect
238. C₂×#11719919	C₂³	semidirect
239. C₂×#11719919	C₂³	semidirect
240. C₂×#11719919	C₂³	semidirect
241. C₂×#11719919	C₂³	semidirect
242. C₂×#11719919	C₂³	semidirect
255. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
256. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
257. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
258. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
259. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
260. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
261. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
262. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
263. C₂×#11719921	C₂³	semidirect
264. C₂×#11719921	C₂³	semidirect
265. C₂×#11719921	C₂³	semidirect
266. C₂×#11719921	C₂³	semidirect
267. C₂×#11719921	C₂³	semidirect
268. C₂×#11719921	C₂³	semidirect
269. C₂²⋊C₄×D₅₃	C₂³	semidirect
270. C₂×C₄×Dic₅₃	C₂³	semidirect
271. C₂×C₄×Dic₅₃	C₂³	semidirect
272. C₂×C₄×Dic₅₃	C₂³	semidirect
273. C₂×C₄×Dic₅₃	C₂³	semidirect
282. C₂⁵×C₅₃	C₂³	semidirect
293. C₂²×D₄×C₅₃	C₂³	semidirect
294. C₂²×D₄×C₅₃	C₂³	semidirect
298. #120×C₅₃	C₂³	semidirect
299. #120×C₅₃	C₂³	semidirect
300. #120×C₅₃	C₂³	semidirect
301. #120×C₅₃	C₂³	semidirect
302. #120×C₅₃	C₂³	semidirect
310. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
311. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
350. C₂³×D₅₃	C₂⁴	semidirect
408. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
409. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
410. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
425. C₂²×Dic₅₃	C₂⁴	semidirect
426. C₂²×Dic₅₃	C₂⁴	semidirect
432. C₂×D₂₁₂	C₂⁴	semidirect
433. C₂×D₂₁₂	C₂⁴	semidirect
437. C₂×C₄×D₅₃	C₂⁴	semidirect
438. C₂×C₄×D₅₃	C₂⁴	semidirect
439. C₂×C₄×D₅₃	C₂⁴	semidirect
442. C₂×Dic₁₀₆	C₂⁴	semidirect
443. C₂×Dic₁₀₆	C₂⁴	semidirect
463. C₂²⋊Dic₅₃	C₂⁴	semidirect
464. C₂²⋊Dic₅₃	C₂⁴	semidirect
465. C₂²⋊Dic₅₃	C₂⁴	semidirect
466. C₂²⋊Dic₅₃	C₂⁴	semidirect
467. #11719921	C₂⁴	semidirect
468. #11719921	C₂⁴	semidirect
469. #11719921	C₂⁴	semidirect
470. #11719921	C₂⁴	semidirect
471. #11719921	C₂⁴	semidirect
472. #11719921	C₂⁴	semidirect
473. C₄⋊Dic₅₃	C₂⁴	semidirect
474. C₄⋊Dic₅₃	C₂⁴	semidirect
475. C₄⋊Dic₅₃	C₂⁴	semidirect
476. #11719919	C₂⁴	semidirect
477. #11719919	C₂⁴	semidirect
478. #11719919	C₂⁴	semidirect
479. #11719919	C₂⁴	semidirect
480. #11719919	C₂⁴	semidirect
481. #11719919	C₂⁴	semidirect
482. C₄×Dic₅₃	C₂⁴	semidirect
483. C₄×Dic₅₃	C₂⁴	semidirect
484. C₄×Dic₅₃	C₂⁴	semidirect
485. C₄×Dic₅₃	C₂⁴	semidirect
675. C₂²×#120	D₅₃	semidirect
683. C₂×C₅₃	#3532	semidirect
688. C₂⁶	C₂×D₅₃	semidirect
696. C₂³×D₄	C₂×D₅₃	semidirect
697. C₂³×D₄	C₂×D₅₃	semidirect
773. C₂×#120	C₂×D₅₃	semidirect
774. C₂×#120	C₂×D₅₃	semidirect
775. C₂×#120	C₂×D₅₃	semidirect
776. C₂×#120	C₂×D₅₃	semidirect
777. C₂×#120	C₂×D₅₃	semidirect
778. C₂×#120	C₂×D₅₃	semidirect
792. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
793. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
794. C₅₃	C₂×#3532	semidirect
805. C₂⁵	C₂²×D₅₃	semidirect
849. C₂²×D₄	C₂²×D₅₃	semidirect
850. C₂²×D₄	C₂²×D₅₃	semidirect
918. #120	C₂²×D₅₃	semidirect
919. #120	C₂²×D₅₃	semidirect
920. #120	C₂²×D₅₃	semidirect
921. #120	C₂²×D₅₃	semidirect
922. #120	C₂²×D₅₃	semidirect
974. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
975. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1332. C₂	#20288870	direct (N × H)

Maximal subgroups

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

subgroup	index
#20288870	2
C₂×#16811366	2
C₂×#16811362	2
C₂×#16811304	2
C₂×#16811299	2
C₂×#16811267	2
C₂×#16811263	2
C₂×#16811260	2
C₂×D₄×C₂²⋊D₅₃	2
C₂×#16811255	2
C₂×#16811211	2
C₂×#16811208	2
C₂×#16811190	2
C₂×#16811188	2
C₂×#16811183	2
C₂×#16811182	2
C₂²×#13133186	2
C₂²×#120×C₅₃	2
C₂×#3532	53

Subgroups — C2×#20288870 #28291214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20288870 #28291214