Subgroups — C₂×#20289031 #28291225

Order 13568.

8122 conjugacy classes of subgroups.

The subgroup lattice has 1444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289031	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16811369	C₂	1	2	yes	maximal, complemented
3	C₂×#16811361	C₂	1	2	yes	maximal, complemented
4	C₂×#16811338	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16811319	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16811313	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16811300	C₂	1	2	yes	maximal, complemented
8	C₂×#16811294	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16811277	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811269	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16811269	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16811262	C₂	1	2	yes	maximal, complemented
13	C₂×D₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16811244	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16811228	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16811225	C₂	1	2	yes	maximal, complemented
17	C₂×#16811209	C₂	1	2	yes	maximal, complemented
18	C₂×#16811201	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#16811188	C₂	1	2	yes	maximal, complemented
20	C₂×#16811187	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#16811183	C₂	1	2	yes	maximal, complemented
22	C₂×#16811134	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂²×#13133191	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#11719947	C₂²	1	2	yes	complemented
28	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
29	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
31	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
32	#16811369	C₂²	1	32	yes	complemented
33	#16811361	C₂²	1	32	yes	complemented
34	#16811338	C₂²	1	16	yes	complemented
35	#16811319	C₂²	1	16	yes	complemented
36	#16811313	C₂²	1	16	yes	complemented
37	#16811300	C₂²	1	32	yes	complemented
38	#16811294	C₂²	1	16	yes	complemented
39	#16811277	C₂²	1	16	yes	complemented
40	#16811269	C₂²	1	16	yes	complemented
41	#16811269	C₂²	1	16	yes	complemented
42	#16811262	C₂²	1	32	yes	complemented
43	D₄×D₂₁₂	C₂²	1	16	yes	complemented
44	#16811244	C₂²	1	16	yes	complemented
45	#16811228	C₂²	1	16	yes	complemented
46	#16811225	C₂²	1	32	yes	complemented
47	#16811209	C₂²	1	32	yes	complemented
48	#16811201	C₂²	1	16	yes	complemented
49	#16811188	C₂²	1	32	yes	complemented
50	#16811187	C₂²	1	16	yes	complemented
51	#16811183	C₂²	1	32	yes	complemented
52	C₂×#13133217	C₂²	1	1	yes	characteristic, complemented
53	C₂×#13133214	C₂²	1	1	yes	characteristic, complemented
54	C₂×#13133213	C₂²	1	2	yes	complemented
55	C₂×#13133213	C₂²	1	2	yes	complemented
56	C₂×#13133212	C₂²	1	2	yes	complemented
57	C₂×#13133212	C₂²	1	2	yes	complemented
58	C₂×#13133210	C₂²	1	2	yes	complemented
59	C₂×#13133209	C₂²	1	1	yes	characteristic, complemented
60	C₂×#13133207	C₂²	1	2	yes	complemented
61	C₂×#13133206	C₂²	1	2	yes	complemented
62	C₂×#13133205	C₂²	1	1	yes	characteristic, complemented
63	C₂×#13133203	C₂²	1	2	yes	complemented
64	C₂×#13133203	C₂²	1	2	yes	complemented
65	C₂×#13133203	C₂²	1	2	yes	complemented
66	#16811134	C₂²	1	16	yes	complemented
67	C₂×#13133202	C₂²	1	2	yes	complemented
68	C₂×#13133202	C₂²	1	2	yes	complemented
69	C₂×#13133202	C₂²	1	2	yes	complemented
70	C₂×#13133202	C₂²	1	2	yes	complemented
71	C₂×#13133201	C₂²	1	2	yes	complemented
72	C₂×#13133201	C₂²	1	2	yes	complemented
73	C₂×#13133200	C₂²	1	2	yes	complemented
74	C₂×#13133199	C₂²	1	2	yes	complemented
75	C₂×#13133199	C₂²	1	2	yes	complemented
76	C₂×#13133198	C₂²	1	2	yes	—
77	C₂×#13133197	C₂²	1	2	yes	complemented
78	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
79	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
80	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
81	C₂×#13133195	C₂²	1	2	yes	complemented
82	C₂×#13133193	C₂²	1	2	yes	complemented
83	C₂×#13133192	C₂²	1	2	yes	complemented
84	C₂×#13133191	C₂²	1	1	yes	characteristic
85	C₂×#13133191	C₂²	1	1	yes	characteristic
86	C₂×#13133191	C₂²	1	1	yes	characteristic
87	C₂×#13133191	C₂²	1	1	yes	characteristic, complemented
88	C₂×#13133191	C₂²	1	1	yes	characteristic, complemented
89	C₂×#13133191	C₂²	1	1	yes	characteristic, complemented
90	C₂×#13133191	C₂²	1	1	yes	characteristic, complemented
91	C₂×#13133191	C₂²	1	1	yes	characteristic, complemented
92	C₂×#13133191	C₂²	1	2	yes	complemented
93	C₂×#13133191	C₂²	1	2	yes	complemented
94	C₂×#13133191	C₂²	1	1	yes	characteristic, complemented
95	C₂×#13133191	C₂²	1	16	yes	complemented
96	C₂×#13133190	C₂²	1	2	yes	complemented
97	C₂×#13133190	C₂²	1	2	yes	complemented
98	C₂×#13133190	C₂²	1	2	yes	complemented
99	C₂×#13133190	C₂²	1	2	yes	complemented
100	C₂×#13133190	C₂²	1	2	yes	complemented
101	C₂×#13133190	C₂²	1	2	yes	complemented
102	C₂×#13133189	C₂²	1	2	yes	complemented
103	C₂×#13133189	C₂²	1	2	yes	complemented
104	C₂×#13133189	C₂²	1	2	yes	complemented
105	C₂×#13133188	C₂²	1	2	yes	complemented
106	C₂×#13133188	C₂²	1	2	yes	complemented
107	C₂×#13133187	C₂²	1	2	yes	—
108	C₂×#13133187	C₂²	1	2	yes	complemented
109	C₂×#13133186	C₂²	1	2	yes	complemented
110	C₂×#13133185	C₂²	1	2	yes	complemented
111	C₂×#13133185	C₂²	1	2	yes	complemented
112	C₂×#13133185	C₂²	1	2	yes	complemented
113	C₂×#13133185	C₂²	1	2	yes	complemented
114	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
118	C₂×#13133179	C₂²	1	2	yes	complemented
119	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
120	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
121	C₂×#13133177	C₂²	1	2	yes	complemented
122	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
123	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
124	C₂×#13133175	C₂²	1	2	yes	complemented
125	C₂×#13133173	C₂²	1	2	yes	complemented
126	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
128	C₂²×#11719921	C₂²	1	2	yes	complemented
129	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
130	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
131	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#525	C₂²	1	16	yes	complemented
134	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
138	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
139	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
140	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
141	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic, complemented
142	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
143	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
144	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
145	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
146	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₅₃	C₂³	1	2	yes	—
148	C₂⁴×D₅₃	C₂³	1	2	yes	—
149	C₂×#11719945	—	4	4	no	—
150	C₂×#11719945	—	4	4	no	—
151	C₂×#11719945	C₂³	1	8	yes	complemented
152	C₂×#11719945	C₂³	1	8	yes	complemented
153	C₂×#11719947	—	4	8	no	—
154	C₂×#11719947	C₂³	1	16	yes	complemented
155	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
156	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
157	C₂²×D₂₁₂	—	4	4	no	—
158	C₂²×D₂₁₂	—	4	4	no	—
159	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
160	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
161	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
162	C₂²×D₂₁₂	C₂³	1	8	yes	—
163	C₂²×D₂₁₂	C₂³	1	2	yes	—
164	C₂²×D₂₁₂	C₂³	1	2	yes	—
165	C₂²×D₂₁₂	C₂³	1	2	yes	—
166	C₂²×D₂₁₂	C₂³	1	2	yes	—
167	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
168	C₂²×C₂²⋊D₅₃	—	4	8	no	—
169	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
170	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
171	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
172	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
173	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
174	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
175	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
176	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
177	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
178	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
179	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
180	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
181	C₂×D₄×D₅₃	—	4	8	no	—
182	C₂×D₄×D₅₃	C₂³	1	16	yes	—
183	C₂³×Dic₅₃	C₂³	1	2	yes	—
184	C₂³×Dic₅₃	C₂³	1	2	yes	—
185	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
186	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
187	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
188	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
189	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
190	#13133217	C₂³	1	8	yes	complemented
191	#13133214	C₂³	1	8	yes	complemented
192	#13133213	C₂³	1	16	yes	complemented
193	#13133213	C₂³	1	16	yes	complemented
194	#13133212	C₂³	1	16	yes	complemented
195	#13133212	C₂³	1	16	yes	complemented
196	#13133210	C₂³	1	16	yes	complemented
197	#13133209	C₂³	1	8	yes	complemented
198	#13133207	C₂³	1	16	yes	complemented
199	#13133206	C₂³	1	16	yes	complemented
200	#13133205	C₂³	1	8	yes	complemented
201	#13133203	C₂³	1	16	yes	complemented
202	#13133203	C₂³	1	16	yes	complemented
203	#13133203	C₂³	1	16	yes	complemented
204	#13133202	C₂³	1	16	yes	complemented
205	#13133202	C₂³	1	16	yes	complemented
206	#13133202	C₂³	1	16	yes	complemented
207	#13133202	C₂³	1	16	yes	complemented
208	#13133201	C₂³	1	16	yes	complemented
209	#13133201	C₂³	1	16	yes	complemented
210	#13133200	C₂³	1	16	yes	complemented
211	#13133199	C₂³	1	16	yes	complemented
212	#13133199	C₂³	1	16	yes	complemented
213	#13133198	C₂³	1	16	yes	—
214	#13133197	C₂³	1	16	yes	complemented
215	#13133196	C₂³	1	8	yes	complemented
216	#13133196	C₂³	1	8	yes	complemented
217	#13133196	C₂³	1	8	yes	complemented
218	#13133195	C₂³	1	16	yes	complemented
219	#13133193	C₂³	1	16	yes	complemented
220	#13133192	C₂³	1	16	yes	complemented
221	#13133191	C₂³	1	8	yes	—
222	#13133191	C₂³	1	8	yes	—
223	#13133191	C₂³	1	8	yes	—
224	#13133191	C₂³	1	8	yes	complemented
225	#13133191	C₂³	1	8	yes	complemented
226	#13133191	C₂³	1	8	yes	complemented
227	#13133191	C₂³	1	8	yes	complemented
228	#13133191	C₂³	1	16	yes	complemented
229	#13133191	C₂³	1	8	yes	complemented
230	#13133191	C₂³	1	16	yes	complemented
231	#13133191	C₂³	1	8	yes	complemented
232	#13133190	C₂³	1	16	yes	complemented
233	#13133190	C₂³	1	16	yes	complemented
234	#13133190	C₂³	1	16	yes	complemented
235	#13133190	C₂³	1	16	yes	complemented
236	#13133190	C₂³	1	16	yes	complemented
237	#13133190	C₂³	1	16	yes	complemented
238	#13133189	C₂³	1	16	yes	complemented
239	#13133189	C₂³	1	16	yes	complemented
240	#13133189	C₂³	1	16	yes	complemented
241	#13133188	C₂³	1	16	yes	complemented
242	#13133188	C₂³	1	16	yes	complemented
243	#13133187	C₂³	1	16	yes	—
244	#13133187	C₂³	1	16	yes	complemented
245	#13133186	C₂³	1	16	yes	complemented
246	#13133185	C₂³	1	16	yes	complemented
247	#13133185	C₂³	1	16	yes	complemented
248	#13133185	C₂³	1	16	yes	complemented
249	#13133185	C₂³	1	16	yes	complemented
250	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
251	C₄×D₂₁₂	C₂³	1	8	yes	complemented
252	C₄×D₂₁₂	C₂³	1	8	yes	complemented
253	C₄×D₂₁₂	C₂³	1	8	yes	complemented
254	#13133179	C₂³	1	16	yes	complemented
255	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
256	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
257	#13133177	C₂³	1	16	yes	complemented
258	#13133176	C₂³	1	8	yes	complemented
259	#13133176	C₂³	1	8	yes	complemented
260	#13133175	C₂³	1	16	yes	complemented
261	#13133173	C₂³	1	16	yes	complemented
262	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
266	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
267	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
268	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊Dic₅₃	C₂³	1	8	yes	complemented
270	C₂×C₄⋊Dic₅₃	C₂³	1	8	yes	complemented
271	C₂×#11719919	C₂³	1	2	yes	—
272	C₂×#11719919	C₂³	1	2	yes	—
273	C₂×#11719919	C₂³	1	2	yes	—
274	C₂×#11719919	C₂³	1	2	yes	—
275	C₂×#11719919	C₂³	1	2	yes	—
276	C₂×#11719919	C₂³	1	2	yes	—
277	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
278	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
279	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
280	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
281	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
282	C₂×#11719921	C₂³	1	2	yes	—
283	C₂×#11719921	C₂³	1	2	yes	—
284	C₂×#11719921	C₂³	1	2	yes	—
285	C₂×#11719921	C₂³	1	2	yes	—
286	C₂×#11719921	C₂³	1	2	yes	—
287	C₂×#11719921	C₂³	1	2	yes	—
288	C₂×#11719921	C₂³	1	2	yes	—
289	C₂×#11719921	C₂³	1	2	yes	—
290	C₂×#11719921	C₂³	1	2	yes	—
291	C₂×#11719921	C₂³	1	2	yes	—
292	C₂×#11719921	C₂³	1	2	yes	—
293	C₂×#11719921	C₂³	1	2	yes	—
294	C₂×#11719921	C₂³	1	2	yes	—
295	C₂×#11719921	C₂³	1	2	yes	—
296	C₂×#11719921	C₂³	1	16	yes	complemented
297	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
298	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
299	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
300	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
301	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
302	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×#41×C₅₃	—	4	4	no	—
304	C₂×#41×C₅₃	C₂³	1	8	yes	complemented
305	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
307	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
310	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
311	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
312	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
313	C₂³×C₄×C₅₃	—	4	4	no	—
314	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
315	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
316	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
317	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
318	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
319	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
320	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
321	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
322	C₂³×C₄×C₅₃	C₂³	1	8	yes	complemented
323	#123×C₅₃	C₂³	1	8	yes	complemented
324	#123×C₅₃	C₂³	1	8	yes	complemented
325	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
326	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
327	#121×C₅₃	C₂³	1	8	yes	—
328	#121×C₅₃	C₂³	1	8	yes	complemented
329	#120×C₅₃	C₂³	1	8	yes	—
330	#120×C₅₃	C₂³	1	8	yes	complemented
331	C₄×D₄×C₅₃	C₂³	1	8	yes	—
332	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
333	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
334	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
335	#117×C₅₃	C₂³	1	8	yes	complemented
336	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
354	C₂⁴×C₅₃	—	2	4	no	—
355	C₂⁴×C₅₃	—	4	2	no	—
356	C₂⁴×C₅₃	—	4	2	no	—
357	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
363	C₂³×D₅₃	—	2	8	no	—
364	C₂³×D₅₃	—	4	4	no	—
365	C₂³×D₅₃	—	4	4	no	—
366	C₂³×D₅₃	—	4	4	no	—
367	C₂³×D₅₃	—	4	4	no	—
368	C₂³×D₅₃	—	4	4	no	—
369	C₂³×D₅₃	C₂⁴	1	2	yes	—
370	C₂³×D₅₃	C₂⁴	1	2	yes	—
371	C₂³×D₅₃	C₂⁴	1	2	yes	—
372	C₂³×D₅₃	C₂⁴	1	8	yes	—
373	C₂³×D₅₃	C₂⁴	1	8	yes	—
374	#41×C₅₃	—	4	16	no	—
375	C₂×Q₈×C₅₃	—	4	2	no	—
376	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
377	C₂×D₄×C₅₃	—	2	4	no	—
378	C₂×D₄×C₅₃	—	2	4	no	—
379	C₂×D₄×C₅₃	—	4	2	no	—
380	C₂×D₄×C₅₃	—	4	2	no	—
381	C₂×D₄×C₅₃	—	4	2	no	—
382	C₂×D₄×C₅₃	—	4	2	no	—
383	C₂×D₄×C₅₃	—	4	2	no	—
384	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
385	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
386	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
387	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
388	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
389	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
390	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
391	C₂²×C₄×C₅₃	—	2	4	no	—
392	C₂²×C₄×C₅₃	—	2	4	no	—
393	C₂²×C₄×C₅₃	—	2	4	no	—
394	C₂²×C₄×C₅₃	—	2	4	no	—
395	C₂²×C₄×C₅₃	—	2	4	no	—
396	C₂²×C₄×C₅₃	—	4	16	no	—
397	C₂²×C₄×C₅₃	—	4	2	no	—
398	C₂²×C₄×C₅₃	—	4	2	no	—
399	C₂²×C₄×C₅₃	—	4	2	no	—
400	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
410	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
411	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
412	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
413	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
414	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
415	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
416	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
417	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₂²⋊D₅₃	—	2	8	no	—
419	C₂×C₂²⋊D₅₃	—	4	4	no	—
420	C₂×C₂²⋊D₅₃	—	4	4	no	—
421	C₂×C₂²⋊D₅₃	—	4	4	no	—
422	C₂×C₂²⋊D₅₃	—	4	4	no	—
423	C₂×C₂²⋊D₅₃	—	4	4	no	—
424	C₂×C₂²⋊D₅₃	—	4	32	no	—
425	C₂×C₂²⋊D₅₃	—	4	4	no	—
426	C₂×C₂²⋊D₅₃	—	4	4	no	—
427	C₂×C₂²⋊D₅₃	—	4	4	no	—
428	C₂×C₂²⋊D₅₃	—	4	4	no	—
429	C₂×C₂²⋊D₅₃	—	4	4	no	—
430	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
431	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
432	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
433	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
434	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
435	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
436	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
437	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
438	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
439	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
440	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
441	C₂²×Dic₅₃	—	2	8	no	—
442	C₂²×Dic₅₃	—	4	4	no	—
443	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
444	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
445	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
446	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
447	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
448	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
449	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
450	#11719947	—	4	32	no	—
451	D₄×D₅₃	—	4	32	no	—
452	#11719945	—	4	16	no	—
453	#11719945	—	4	16	no	—
454	C₂×D₂₁₂	—	2	4	no	—
455	C₂×D₂₁₂	—	2	4	no	—
456	C₂×D₂₁₂	—	2	4	no	—
457	C₂×D₂₁₂	—	4	16	no	—
458	C₂×D₂₁₂	—	4	16	no	—
459	C₂×D₂₁₂	—	4	4	no	—
460	C₂×D₂₁₂	—	4	4	no	—
461	C₂×D₂₁₂	—	4	4	no	—
462	C₂×D₂₁₂	—	4	4	no	—
463	C₂×D₂₁₂	C₂⁴	1	4	yes	—
464	C₂×D₂₁₂	C₂⁴	1	4	yes	—
465	C₂×D₂₁₂	C₂⁴	1	4	yes	—
466	C₂×D₂₁₂	C₂⁴	1	8	yes	—
467	C₂×D₂₁₂	C₂⁴	1	8	yes	—
468	C₂×D₂₁₂	C₂⁴	1	8	yes	—
469	C₂×D₂₁₂	C₂⁴	1	8	yes	—
470	C₂×C₄×D₅₃	—	4	4	no	—
471	C₂×C₄×D₅₃	—	4	4	no	—
472	C₂×C₄×D₅₃	—	4	4	no	—
473	C₂×C₄×D₅₃	—	4	4	no	—
474	C₂×C₄×D₅₃	—	4	4	no	—
475	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
476	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
477	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
478	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
479	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
480	C₂×Dic₁₀₆	—	2	4	no	—
481	C₂×Dic₁₀₆	—	4	4	no	—
482	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
483	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
484	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
485	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
486	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
487	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
488	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
489	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
490	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
491	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
492	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
493	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
494	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
495	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
496	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
497	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
498	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
499	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
500	C₄²×C₅₃	C₂⁴	1	4	yes	—
501	C₄²×C₅₃	C₂⁴	1	4	yes	—
502	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
503	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
504	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
505	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
506	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
507	#11719921	C₂⁴	1	8	yes	—
508	#11719921	C₂⁴	1	8	yes	—
509	#11719921	C₂⁴	1	8	yes	—
510	#11719921	C₂⁴	1	8	yes	—
511	#11719921	C₂⁴	1	8	yes	—
512	#11719921	C₂⁴	1	8	yes	—
513	#11719921	C₂⁴	1	8	yes	—
514	#11719921	C₂⁴	1	8	yes	—
515	#11719921	C₂⁴	1	8	yes	—
516	#11719921	C₂⁴	1	8	yes	—
517	#11719921	C₂⁴	1	8	yes	—
518	#11719921	C₂⁴	1	8	yes	—
519	#11719921	C₂⁴	1	8	yes	—
520	#11719921	C₂⁴	1	8	yes	—
521	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
522	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
523	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
524	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
525	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
526	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
527	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
528	#11719919	C₂⁴	1	8	yes	—
529	#11719919	C₂⁴	1	8	yes	—
530	#11719919	C₂⁴	1	8	yes	—
531	#11719919	C₂⁴	1	8	yes	—
532	#11719919	C₂⁴	1	8	yes	—
533	#11719919	C₂⁴	1	8	yes	—
534	C₄×Dic₅₃	C₂⁴	1	8	yes	—
535	C₄×Dic₅₃	C₂⁴	1	8	yes	—
536	C₄×Dic₅₃	C₂⁴	1	8	yes	—
537	C₂³×C₅₃	—	2	2	no	—
538	C₂³×C₅₃	—	2	2	no	—
539	C₂³×C₅₃	—	2	2	no	—
540	C₂³×C₅₃	—	2	8	no	—
541	C₂³×C₅₃	—	2	2	no	—
542	C₂³×C₅₃	—	2	2	no	—
543	C₂³×C₅₃	—	2	2	no	—
544	C₂³×C₅₃	—	2	2	no	—
545	C₂³×C₅₃	—	2	2	no	—
546	C₂³×C₅₃	—	2	2	no	—
547	C₂³×C₅₃	—	2	2	no	—
548	C₂³×C₅₃	—	2	2	no	—
549	C₂³×C₅₃	—	2	2	no	—
550	C₂³×C₅₃	—	2	2	no	—
551	C₂³×C₅₃	—	2	2	no	—
552	C₂³×C₅₃	—	4	4	no	—
553	C₂³×C₅₃	—	4	4	no	—
554	C₂³×C₅₃	—	4	16	no	—
555	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
556	C₂³×C₅₃	C₂⁵	1	2	yes	—
557	C₂³×C₅₃	C₂⁵	1	2	yes	—
558	C₂³×C₅₃	C₂⁵	1	2	yes	—
559	C₂³×C₅₃	C₂⁵	1	2	yes	—
560	C₂³×C₅₃	C₂⁵	1	2	yes	—
561	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
562	C₂²×D₅₃	—	2	4	no	—
563	C₂²×D₅₃	—	2	4	no	—
564	C₂²×D₅₃	—	2	4	no	—
565	C₂²×D₅₃	—	2	4	no	—
566	C₂²×D₅₃	—	2	4	no	—
567	C₂²×D₅₃	—	2	4	no	—
568	C₂²×D₅₃	—	2	4	no	—
569	C₂²×D₅₃	—	2	4	no	—
570	C₂²×D₅₃	—	2	4	no	—
571	C₂²×D₅₃	—	2	16	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	—	8	16	no	—
578	C₂²×D₅₃	—	8	16	no	—
579	C₂²×D₅₃	C₂⁵	1	4	yes	—
580	C₂²×D₅₃	C₂⁵	1	4	yes	—
581	C₂²×D₅₃	C₂⁵	1	4	yes	—
582	Q₈×C₅₃	—	4	4	no	—
583	D₄×C₅₃	—	2	8	no	—
584	D₄×C₅₃	—	2	8	no	—
585	D₄×C₅₃	—	4	4	no	—
586	D₄×C₅₃	—	4	4	no	—
587	D₄×C₅₃	—	4	4	no	—
588	D₄×C₅₃	—	4	4	no	—
589	D₄×C₅₃	—	4	4	no	—
590	C₂×C₄×C₅₃	—	2	2	no	—
591	C₂×C₄×C₅₃	—	2	2	no	—
592	C₂×C₄×C₅₃	—	2	2	no	—
593	C₂×C₄×C₅₃	—	2	2	no	—
594	C₂×C₄×C₅₃	—	2	2	no	—
595	C₂×C₄×C₅₃	—	2	2	no	—
596	C₂×C₄×C₅₃	—	2	2	no	—
597	C₂×C₄×C₅₃	—	2	2	no	—
598	C₂×C₄×C₅₃	—	2	2	no	—
599	C₂×C₄×C₅₃	—	2	8	no	—
600	C₂×C₄×C₅₃	—	2	8	no	—
601	C₂×C₄×C₅₃	—	2	8	no	—
602	C₂×C₄×C₅₃	—	2	8	no	—
603	C₂×C₄×C₅₃	—	2	8	no	—
604	C₂×C₄×C₅₃	—	4	4	no	—
605	C₂×C₄×C₅₃	—	4	4	no	—
606	C₂×C₄×C₅₃	—	4	4	no	—
607	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
608	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
609	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
610	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
611	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
612	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
613	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
614	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
615	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
616	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
617	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
618	C₂²⋊D₅₃	—	2	16	no	—
619	C₂²⋊D₅₃	—	4	8	no	—
620	C₂²⋊D₅₃	—	4	8	no	—
621	C₂²⋊D₅₃	—	4	8	no	—
622	C₂²⋊D₅₃	—	4	8	no	—
623	C₂²⋊D₅₃	—	4	8	no	—
624	C₂²⋊D₅₃	—	4	8	no	—
625	C₂²⋊D₅₃	—	4	8	no	—
626	C₂²⋊D₅₃	—	4	8	no	—
627	C₂²⋊D₅₃	—	4	8	no	—
628	C₂²⋊D₅₃	—	4	8	no	—
629	C₂×Dic₅₃	—	2	4	no	—
630	C₂×Dic₅₃	—	2	4	no	—
631	C₂×Dic₅₃	—	2	4	no	—
632	C₂×Dic₅₃	—	2	4	no	—
633	C₂×Dic₅₃	—	2	16	no	—
634	C₂×Dic₅₃	—	2	4	no	—
635	C₂×Dic₅₃	—	4	8	no	—
636	C₂×Dic₅₃	C₂⁵	1	4	yes	—
637	C₂×Dic₅₃	C₂⁵	1	4	yes	—
638	C₂×Dic₅₃	C₂⁵	1	4	yes	—
639	C₂×Dic₅₃	C₂⁵	1	4	yes	—
640	C₂×Dic₅₃	C₂⁵	1	4	yes	—
641	D₂₁₂	—	2	8	no	—
642	D₂₁₂	—	2	8	no	—
643	D₂₁₂	—	2	8	no	—
644	D₂₁₂	—	4	8	no	—
645	D₂₁₂	—	4	8	no	—
646	D₂₁₂	—	4	8	no	—
647	D₂₁₂	—	4	8	no	—
648	C₄×D₅₃	—	4	8	no	—
649	C₄×D₅₃	—	4	8	no	—
650	C₄×D₅₃	—	4	8	no	—
651	C₄×D₅₃	—	4	8	no	—
652	C₄×D₅₃	—	4	8	no	—
653	Dic₁₀₆	—	2	8	no	—
654	Dic₁₀₆	—	4	8	no	—
655	C₂×#3542	—	53	1	no	maximal, Sylow
656	C₂²×C₅₃	—	2	2	no	—
657	C₂²×C₅₃	—	2	2	no	—
658	C₂²×C₅₃	—	2	8	no	—
659	C₂²×C₅₃	—	2	2	no	—
660	C₂²×C₅₃	—	2	2	no	—
661	C₂²×C₅₃	—	2	2	no	—
662	C₂²×C₅₃	—	2	2	no	—
663	C₂²×C₅₃	—	2	2	no	—
664	C₂²×C₅₃	—	2	2	no	—
665	C₂²×C₅₃	—	2	2	no	—
666	C₂²×C₅₃	—	2	2	no	—
667	C₂²×C₅₃	—	2	2	no	—
668	C₂²×C₅₃	—	2	2	no	—
669	C₂²×C₅₃	—	2	2	no	—
670	C₂²×C₅₃	—	2	2	no	—
671	C₂²×C₅₃	—	4	16	no	—
672	C₂²×C₅₃	—	4	4	no	—
673	C₂²×C₅₃	—	4	4	no	—
674	C₂²×C₅₃	—	4	4	no	—
675	C₂²×C₅₃	—	4	4	no	—
676	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
677	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
678	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
679	C₂²×C₅₃	#585	1	2	yes	—
680	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
681	C₂×D₅₃	—	2	4	no	—
682	C₂×D₅₃	—	2	4	no	—
683	C₂×D₅₃	—	2	4	no	—
684	C₂×D₅₃	—	2	4	no	—
685	C₂×D₅₃	—	2	4	no	—
686	C₂×D₅₃	—	2	4	no	—
687	C₂×D₅₃	—	2	4	no	—
688	C₂×D₅₃	—	2	4	no	—
689	C₂×D₅₃	—	2	4	no	—
690	C₂×D₅₃	—	4	8	no	—
691	C₂×D₅₃	—	4	8	no	—
692	C₂×D₅₃	—	4	8	no	—
693	C₂×D₅₃	—	8	16	no	—
694	C₂×D₅₃	—	8	16	no	—
695	C₄×C₅₃	—	2	2	no	—
696	C₄×C₅₃	—	2	2	no	—
697	C₄×C₅₃	—	2	2	no	—
698	C₄×C₅₃	—	2	2	no	—
699	C₄×C₅₃	—	2	2	no	—
700	C₄×C₅₃	—	2	2	no	—
701	C₄×C₅₃	—	2	2	no	—
702	C₄×C₅₃	—	2	2	no	—
703	C₄×C₅₃	—	2	2	no	—
704	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
705	Dic₅₃	—	2	4	no	—
706	Dic₅₃	—	2	4	no	—
707	Dic₅₃	—	2	4	no	—
708	Dic₅₃	—	2	4	no	—
709	Dic₅₃	—	2	4	no	—
710	#3542	—	53	32	no	—
711	C₂×#562	—	53	2	no	—
712	C₂×#560	—	53	2	no	—
713	C₂×#555	—	53	1	no	—
714	C₂×#553	—	53	1	no	—
715	C₂×#552	—	53	1	no	—
716	C₂×#551	—	53	2	no	—
717	C₂×#550	—	53	1	no	—
718	C₂×#547	—	53	1	no	—
719	C₂×#546	—	53	2	no	—
720	C₂×#546	—	53	1	no	—
721	C₂×#546	—	53	1	no	—
722	C₂×D₄²	—	53	1	no	—
723	C₂×#542	—	53	1	no	—
724	C₂×#540	—	53	2	no	—
725	C₂×#540	—	53	1	no	—
726	C₂×#538	—	53	2	no	—
727	C₂×#537	—	53	1	no	—
728	C₂×#535	—	53	1	no	—
729	C₂×#535	—	53	2	no	—
730	C₂×#534	—	53	2	no	—
731	C₂×#525	—	53	1	no	—
732	C₂×#525	D₅₃	1	1	yes	characteristic, complemented
733	C₂²×#121	—	53	1	no	—
734	C₂×C₅₃	—	2	4	no	—
735	C₂×C₅₃	—	4	2	no	—
736	C₂×C₅₃	—	4	2	no	—
737	C₂×C₅₃	—	4	2	no	—
738	C₂×C₅₃	—	4	2	no	—
739	C₂×C₅₃	#3542	1	4	yes	complemented
740	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
741	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
742	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
743	D₅₃	—	4	4	no	—
744	D₅₃	—	4	4	no	—
745	D₅₃	—	4	4	no	—
746	C₂²×#41	—	53	2	no	—
747	C₂²×#41	—	53	1	no	—
748	C₂²×#41	—	53	1	no	—
749	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
750	C₂³×D₄	—	53	2	no	—
751	C₂³×D₄	—	53	2	no	—
752	C₂³×D₄	—	53	1	no	—
753	C₂³×D₄	—	53	1	no	—
754	C₂⁴×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
755	#562	—	53	32	no	—
756	#560	—	53	32	no	—
757	#555	—	53	16	no	—
758	#553	—	53	16	no	—
759	#552	—	53	16	no	—
760	#551	—	53	32	no	—
761	#550	—	53	16	no	—
762	#547	—	53	16	no	—
763	#546	—	53	32	no	—
764	#546	—	53	16	no	—
765	#546	—	53	16	no	—
766	D₄²	—	53	16	no	—
767	#542	—	53	16	no	—
768	#540	—	53	32	no	—
769	#540	—	53	16	no	—
770	#538	—	53	32	no	—
771	#537	—	53	16	no	—
772	#535	—	53	16	no	—
773	#535	—	53	32	no	—
774	#534	—	53	32	no	—
775	C₂×C₄⋊Q₈	—	53	1	no	—
776	C₂×#127	—	53	2	no	—
777	C₂×#127	—	53	2	no	—
778	C₂×#127	—	53	1	no	—
779	C₂×#126	—	53	2	no	—
780	C₂×#126	—	53	2	no	—
781	C₂×#126	—	53	2	no	—
782	C₂×#125	—	53	2	no	—
783	C₂×#125	—	53	1	no	—
784	C₂×#124	—	53	2	no	—
785	C₂×#124	—	53	2	no	—
786	C₂×#124	—	53	2	no	—
787	C₂×#124	—	53	2	no	—
788	C₂×#124	—	53	1	no	—
789	#525	—	53	16	no	—
790	#525	C₂×D₅₃	1	16	yes	complemented
791	C₂×#123	—	53	2	no	—
792	C₂×#123	—	53	2	no	—
793	C₂×#123	—	53	2	no	—
794	C₂×#123	—	53	2	no	—
795	C₂×#123	—	53	2	no	—
796	C₂×#123	—	53	2	no	—
797	C₂×#123	—	53	2	no	—
798	C₂×#123	—	53	2	no	—
799	C₂×#123	—	53	2	no	—
800	C₂×#123	—	53	2	no	—
801	C₂×#123	C₂×D₅₃	1	1	yes	characteristic, complemented
802	C₂×#123	C₂×D₅₃	1	1	yes	characteristic, complemented
803	C₂×C₂²⋊Q₈	—	53	2	no	—
804	C₂×C₂²⋊Q₈	—	53	1	no	—
805	C₂×C₂²⋊Q₈	—	53	1	no	—
806	C₂×C₂²⋊Q₈	—	53	1	no	—
807	C₂×C₂²⋊Q₈	—	53	2	no	—
808	C₂×C₂²⋊Q₈	—	53	2	no	—
809	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
810	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
811	C₂×#121	—	53	2	no	—
812	C₂×#121	—	53	2	no	—
813	C₂×#121	—	53	2	no	—
814	C₂×#121	—	53	2	no	—
815	C₂×#121	—	53	2	no	—
816	C₂×#121	—	53	1	no	—
817	C₂×#121	—	53	1	no	—
818	C₂×#121	—	53	1	no	—
819	C₂×#121	—	53	2	no	—
820	C₂×#121	—	53	1	no	—
821	C₂×#121	—	53	2	no	—
822	C₂×#121	—	53	1	no	—
823	C₂×#121	—	53	1	no	—
824	C₂×#121	—	53	1	no	—
825	C₂×#121	—	53	1	no	—
826	C₂×#121	—	53	1	no	—
827	C₂×#121	—	53	16	no	—
828	C₂×#121	—	53	2	no	—
829	C₂×#121	—	53	2	no	—
830	C₂×#121	—	53	2	no	—
831	C₂×#121	—	53	2	no	—
832	C₂×#121	—	53	2	no	—
833	C₂×#121	—	53	2	no	—
834	C₂×#121	—	53	2	no	—
835	C₂×#121	C₂×D₅₃	1	1	yes	characteristic
836	C₂×#121	C₂×D₅₃	1	1	yes	characteristic, complemented
837	C₂×#120	—	53	2	no	—
838	C₂×#120	—	53	2	no	—
839	C₂×#120	—	53	2	no	—
840	C₂×#120	—	53	2	no	—
841	C₂×#120	—	53	2	no	—
842	C₂×#120	—	53	2	no	—
843	C₂×#120	—	53	2	no	—
844	C₂×#120	C₂×D₅₃	1	1	yes	characteristic
845	C₂×#120	C₂×D₅₃	1	1	yes	characteristic, complemented
846	C₂×C₄×Q₈	—	53	1	no	—
847	C₂×C₄×D₄	—	53	2	no	—
848	C₂×C₄×D₄	—	53	2	no	—
849	C₂×C₄×D₄	—	53	2	no	—
850	C₂×C₄×D₄	—	53	2	no	—
851	C₂×C₄×D₄	—	53	1	no	—
852	C₂×C₄×D₄	—	53	1	no	—
853	C₂×C₄×D₄	—	53	1	no	—
854	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
855	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
856	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
857	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
858	C₂×#117	—	53	1	no	—
859	C₂×#117	—	53	1	no	—
860	C₂×#117	—	53	2	no	—
861	C₂×#117	—	53	2	no	—
862	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
863	C₂²×C₄⋊C₄	—	53	1	no	—
864	C₂²×C₄⋊C₄	—	53	1	no	—
865	C₂²×C₂²⋊C₄	—	53	2	no	—
866	C₂²×C₂²⋊C₄	—	53	2	no	—
867	C₂²×C₂²⋊C₄	—	53	2	no	—
868	C₅₃	C₂×#3542	1	1	yes	characteristic, complemented, Sylow
869	C₂⁵	—	53	2	no	—
870	C₂⁵	—	53	2	no	—
871	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
872	C₂×#41	—	4	4	no	—
873	C₂×#41	—	53	16	no	—
874	C₂×#41	—	53	8	no	—
875	C₂×#41	—	53	8	no	—
876	C₂×#41	—	212	4	no	—
877	C₂×#41	—	212	4	no	—
878	C₂×#41	—	212	8	no	—
879	C₂×#41	C₂²×D₅₃	1	8	yes	complemented
880	C₂²×Q₈	—	53	1	no	—
881	C₂²×Q₈	—	53	2	no	—
882	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
883	C₂²×D₄	—	53	2	no	—
884	C₂²×D₄	—	53	2	no	—
885	C₂²×D₄	—	53	2	no	—
886	C₂²×D₄	—	53	2	no	—
887	C₂²×D₄	—	53	2	no	—
888	C₂²×D₄	—	53	2	no	—
889	C₂²×D₄	—	53	2	no	—
890	C₂²×D₄	—	53	2	no	—
891	C₂²×D₄	—	53	2	no	—
892	C₂²×D₄	—	53	2	no	—
893	C₂²×D₄	—	53	2	no	—
894	C₂²×D₄	—	53	16	no	—
895	C₂²×D₄	—	53	16	no	—
896	C₂²×D₄	—	53	1	no	—
897	C₂²×D₄	—	53	1	no	—
898	C₂²×D₄	—	53	1	no	—
899	C₂²×D₄	—	53	2	no	—
900	C₂²×D₄	—	53	2	no	—
901	C₂²×D₄	—	53	2	no	—
902	C₂²×D₄	—	53	2	no	—
903	C₂²×D₄	—	53	8	no	—
904	C₂²×D₄	—	53	8	no	—
905	C₂²×D₄	—	212	4	no	—
906	C₂²×D₄	—	212	4	no	—
907	C₂²×D₄	—	212	8	no	—
908	C₂²×D₄	—	212	8	no	—
909	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
910	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
911	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
912	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
913	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
914	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
915	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
916	C₂³×C₄	—	4	4	no	—
917	C₂³×C₄	—	53	2	no	—
918	C₂³×C₄	—	53	2	no	—
919	C₂³×C₄	—	53	2	no	—
920	C₂³×C₄	—	53	2	no	—
921	C₂³×C₄	—	53	2	no	—
922	C₂³×C₄	—	53	2	no	—
923	C₂³×C₄	—	53	2	no	—
924	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
925	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
926	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
927	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
928	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
929	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
930	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
931	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
932	C₂³×C₄	C₂²×D₅₃	1	8	yes	complemented
933	C₄⋊Q₈	—	53	8	no	—
934	#127	—	53	16	no	—
935	#127	—	53	16	no	—
936	#127	—	53	8	no	—
937	#126	—	53	16	no	—
938	#126	—	53	16	no	—
939	#126	—	53	16	no	—
940	#125	—	53	16	no	—
941	#125	—	53	8	no	—
942	#124	—	53	16	no	—
943	#124	—	53	16	no	—
944	#124	—	53	16	no	—
945	#124	—	53	16	no	—
946	#124	—	53	8	no	—
947	#123	—	53	16	no	—
948	#123	—	53	16	no	—
949	#123	—	53	16	no	—
950	#123	—	53	16	no	—
951	#123	—	53	16	no	—
952	#123	—	53	16	no	—
953	#123	—	53	16	no	—
954	#123	—	53	16	no	—
955	#123	—	53	16	no	—
956	#123	—	53	16	no	—
957	#123	C₂²×D₅₃	1	8	yes	complemented
958	#123	C₂²×D₅₃	1	8	yes	complemented
959	C₂²⋊Q₈	—	53	16	no	—
960	C₂²⋊Q₈	—	53	8	no	—
961	C₂²⋊Q₈	—	53	8	no	—
962	C₂²⋊Q₈	—	53	8	no	—
963	C₂²⋊Q₈	—	53	16	no	—
964	C₂²⋊Q₈	—	53	16	no	—
965	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
966	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
967	#121	—	53	16	no	—
968	#121	—	53	16	no	—
969	#121	—	53	16	no	—
970	#121	—	53	16	no	—
971	#121	—	53	16	no	—
972	#121	—	53	8	no	—
973	#121	—	53	8	no	—
974	#121	—	53	16	no	—
975	#121	—	53	8	no	—
976	#121	—	53	8	no	—
977	#121	—	53	16	no	—
978	#121	—	53	8	no	—
979	#121	—	53	8	no	—
980	#121	—	53	8	no	—
981	#121	—	53	8	no	—
982	#121	—	53	8	no	—
983	#121	—	53	16	no	—
984	#121	—	53	16	no	—
985	#121	—	53	16	no	—
986	#121	—	53	16	no	—
987	#121	—	53	16	no	—
988	#121	—	53	16	no	—
989	#121	—	53	16	no	—
990	#121	C₂²×D₅₃	1	8	yes	—
991	#121	C₂²×D₅₃	1	8	yes	complemented
992	#120	—	53	16	no	—
993	#120	—	53	16	no	—
994	#120	—	53	16	no	—
995	#120	—	53	16	no	—
996	#120	—	53	16	no	—
997	#120	—	53	16	no	—
998	#120	—	53	16	no	—
999	#120	C₂²×D₅₃	1	8	yes	—
1000	#120	C₂²×D₅₃	1	8	yes	complemented
1001	C₄×Q₈	—	53	8	no	—
1002	C₄×D₄	—	53	16	no	—
1003	C₄×D₄	—	53	16	no	—
1004	C₄×D₄	—	53	16	no	—
1005	C₄×D₄	—	53	16	no	—
1006	C₄×D₄	—	53	8	no	—
1007	C₄×D₄	—	53	8	no	—
1008	C₄×D₄	—	53	8	no	—
1009	C₄×D₄	C₂²×D₅₃	1	8	yes	—
1010	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1011	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1012	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1013	#117	—	53	8	no	—
1014	#117	—	53	8	no	—
1015	#117	—	53	16	no	—
1016	#117	—	53	16	no	—
1017	#117	C₂²×D₅₃	1	8	yes	complemented
1018	C₂×C₄⋊C₄	—	53	1	no	—
1019	C₂×C₄⋊C₄	—	53	1	no	—
1020	C₂×C₄⋊C₄	—	53	1	no	—
1021	C₂×C₄⋊C₄	—	53	2	no	—
1022	C₂×C₄⋊C₄	—	53	8	no	—
1023	C₂×C₄⋊C₄	—	53	2	no	—
1024	C₂×C₄⋊C₄	—	53	8	no	—
1025	C₂×C₄⋊C₄	—	53	1	no	—
1026	C₂×C₄⋊C₄	—	53	2	no	—
1027	C₂×C₄⋊C₄	—	53	2	no	—
1028	C₂×C₄⋊C₄	—	53	2	no	—
1029	C₂×C₄⋊C₄	—	53	2	no	—
1030	C₂×C₄⋊C₄	—	53	2	no	—
1031	C₂×C₄⋊C₄	—	53	2	no	—
1032	C₂×C₄⋊C₄	—	53	2	no	—
1033	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1034	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1035	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1036	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1037	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1038	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1039	C₂×C₂²⋊C₄	—	53	2	no	—
1040	C₂×C₂²⋊C₄	—	53	2	no	—
1041	C₂×C₂²⋊C₄	—	53	2	no	—
1042	C₂×C₂²⋊C₄	—	53	2	no	—
1043	C₂×C₂²⋊C₄	—	53	2	no	—
1044	C₂×C₂²⋊C₄	—	53	2	no	—
1045	C₂×C₂²⋊C₄	—	53	2	no	—
1046	C₂×C₂²⋊C₄	—	53	2	no	—
1047	C₂×C₂²⋊C₄	—	53	2	no	—
1048	C₂×C₂²⋊C₄	—	53	2	no	—
1049	C₂×C₂²⋊C₄	—	53	2	no	—
1050	C₂×C₂²⋊C₄	—	53	2	no	—
1051	C₂×C₂²⋊C₄	—	53	16	no	—
1052	C₂×C₂²⋊C₄	—	53	2	no	—
1053	C₂×C₂²⋊C₄	—	53	2	no	—
1054	C₂×C₂²⋊C₄	—	53	2	no	—
1055	C₂×C₂²⋊C₄	—	53	2	no	—
1056	C₂×C₂²⋊C₄	—	53	2	no	—
1057	C₂×C₂²⋊C₄	—	53	2	no	—
1058	C₂×C₂²⋊C₄	—	53	2	no	—
1059	C₂×C₂²⋊C₄	—	53	16	no	—
1060	C₂×C₂²⋊C₄	—	53	16	no	—
1061	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1062	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1063	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1064	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1065	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1066	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1067	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1068	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1069	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1070	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1071	C₂×C₄²	—	53	2	no	—
1072	C₂×C₄²	—	53	2	no	—
1073	C₂×C₄²	—	53	2	no	—
1074	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1075	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1076	C₂⁴	—	2	4	no	—
1077	C₂⁴	—	4	2	no	—
1078	C₂⁴	—	4	2	no	—
1079	C₂⁴	—	53	2	no	—
1080	C₂⁴	—	53	2	no	—
1081	C₂⁴	—	53	2	no	—
1082	C₂⁴	—	53	8	no	—
1083	C₂⁴	—	53	8	no	—
1084	C₂⁴	—	106	8	no	—
1085	C₂⁴	—	212	4	no	—
1086	C₂⁴	—	212	4	no	—
1087	C₂⁴	—	212	4	no	—
1088	C₂⁴	—	212	4	no	—
1089	C₂⁴	—	212	4	no	—
1090	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1091	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1092	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1093	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1094	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1095	C₂⁴	C₂³×D₅₃	1	4	yes	—
1096	#41	—	4	16	no	—
1097	#41	—	212	16	no	—
1098	#41	—	212	16	no	—
1099	#41	—	212	32	no	—
1100	C₂×Q₈	—	4	2	no	—
1101	C₂×Q₈	—	53	4	no	—
1102	C₂×Q₈	—	53	8	no	—
1103	C₂×Q₈	—	106	4	no	—
1104	C₂×Q₈	—	212	4	no	—
1105	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1106	C₂×D₄	—	2	4	no	—
1107	C₂×D₄	—	2	4	no	—
1108	C₂×D₄	—	4	2	no	—
1109	C₂×D₄	—	4	2	no	—
1110	C₂×D₄	—	4	2	no	—
1111	C₂×D₄	—	4	2	no	—
1112	C₂×D₄	—	4	2	no	—
1113	C₂×D₄	—	53	8	no	—
1114	C₂×D₄	—	53	8	no	—
1115	C₂×D₄	—	53	8	no	—
1116	C₂×D₄	—	53	8	no	—
1117	C₂×D₄	—	53	8	no	—
1118	C₂×D₄	—	53	8	no	—
1119	C₂×D₄	—	53	8	no	—
1120	C₂×D₄	—	53	8	no	—
1121	C₂×D₄	—	53	8	no	—
1122	C₂×D₄	—	53	8	no	—
1123	C₂×D₄	—	53	8	no	—
1124	C₂×D₄	—	53	4	no	—
1125	C₂×D₄	—	53	4	no	—
1126	C₂×D₄	—	53	4	no	—
1127	C₂×D₄	—	53	8	no	—
1128	C₂×D₄	—	53	8	no	—
1129	C₂×D₄	—	53	8	no	—
1130	C₂×D₄	—	53	8	no	—
1131	C₂×D₄	—	106	8	no	—
1132	C₂×D₄	—	106	4	no	—
1133	C₂×D₄	—	106	4	no	—
1134	C₂×D₄	—	106	4	no	—
1135	C₂×D₄	—	212	16	no	—
1136	C₂×D₄	—	212	16	no	—
1137	C₂×D₄	—	212	4	no	—
1138	C₂×D₄	—	212	4	no	—
1139	C₂×D₄	—	212	4	no	—
1140	C₂×D₄	—	212	4	no	—
1141	C₂×D₄	—	212	4	no	—
1142	C₂×D₄	—	212	4	no	—
1143	C₂×D₄	—	212	4	no	—
1144	C₂×D₄	—	212	4	no	—
1145	C₂×D₄	—	212	4	no	—
1146	C₂×D₄	—	212	4	no	—
1147	C₂×D₄	—	212	32	no	—
1148	C₂×D₄	—	212	4	no	—
1149	C₂×D₄	—	212	4	no	—
1150	C₂×D₄	—	212	4	no	—
1151	C₂×D₄	—	212	4	no	—
1152	C₂×D₄	—	212	32	no	—
1153	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1154	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1155	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1156	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1157	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1158	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1159	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1160	C₂²×C₄	—	2	4	no	—
1161	C₂²×C₄	—	2	4	no	—
1162	C₂²×C₄	—	2	4	no	—
1163	C₂²×C₄	—	2	4	no	—
1164	C₂²×C₄	—	2	4	no	—
1165	C₂²×C₄	—	4	16	no	—
1166	C₂²×C₄	—	4	2	no	—
1167	C₂²×C₄	—	4	2	no	—
1168	C₂²×C₄	—	4	2	no	—
1169	C₂²×C₄	—	53	8	no	—
1170	C₂²×C₄	—	53	2	no	—
1171	C₂²×C₄	—	53	2	no	—
1172	C₂²×C₄	—	53	2	no	—
1173	C₂²×C₄	—	53	2	no	—
1174	C₂²×C₄	—	53	2	no	—
1175	C₂²×C₄	—	53	8	no	—
1176	C₂²×C₄	—	53	8	no	—
1177	C₂²×C₄	—	53	8	no	—
1178	C₂²×C₄	—	53	8	no	—
1179	C₂²×C₄	—	53	8	no	—
1180	C₂²×C₄	—	53	8	no	—
1181	C₂²×C₄	—	106	8	no	—
1182	C₂²×C₄	—	212	4	no	—
1183	C₂²×C₄	—	212	4	no	—
1184	C₂²×C₄	—	212	4	no	—
1185	C₂²×C₄	—	212	4	no	—
1186	C₂²×C₄	—	212	4	no	—
1187	C₂²×C₄	—	212	4	no	—
1188	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1189	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1190	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1191	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1192	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1193	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1194	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1195	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1196	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1197	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1198	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1199	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1200	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1201	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1202	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1203	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1204	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1205	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1206	C₄⋊C₄	—	53	4	no	—
1207	C₄⋊C₄	—	53	4	no	—
1208	C₄⋊C₄	—	53	4	no	—
1209	C₄⋊C₄	—	53	8	no	—
1210	C₄⋊C₄	—	53	8	no	—
1211	C₄⋊C₄	—	53	4	no	—
1212	C₄⋊C₄	—	53	8	no	—
1213	C₄⋊C₄	—	53	8	no	—
1214	C₄⋊C₄	—	53	8	no	—
1215	C₄⋊C₄	—	53	8	no	—
1216	C₄⋊C₄	—	53	8	no	—
1217	C₄⋊C₄	—	53	8	no	—
1218	C₄⋊C₄	—	53	8	no	—
1219	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1220	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1221	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1222	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1223	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1224	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1225	C₂²⋊C₄	—	53	8	no	—
1226	C₂²⋊C₄	—	53	8	no	—
1227	C₂²⋊C₄	—	53	8	no	—
1228	C₂²⋊C₄	—	53	8	no	—
1229	C₂²⋊C₄	—	53	8	no	—
1230	C₂²⋊C₄	—	53	8	no	—
1231	C₂²⋊C₄	—	53	8	no	—
1232	C₂²⋊C₄	—	53	8	no	—
1233	C₂²⋊C₄	—	53	8	no	—
1234	C₂²⋊C₄	—	53	8	no	—
1235	C₂²⋊C₄	—	53	8	no	—
1236	C₂²⋊C₄	—	53	8	no	—
1237	C₂²⋊C₄	—	53	8	no	—
1238	C₂²⋊C₄	—	53	8	no	—
1239	C₂²⋊C₄	—	53	8	no	—
1240	C₂²⋊C₄	—	53	8	no	—
1241	C₂²⋊C₄	—	53	8	no	—
1242	C₂²⋊C₄	—	53	8	no	—
1243	C₂²⋊C₄	—	53	8	no	—
1244	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1245	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1246	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1247	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1248	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1249	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1250	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1251	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1252	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1253	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1254	C₄²	—	53	8	no	—
1255	C₄²	—	53	8	no	—
1256	C₄²	—	53	8	no	—
1257	C₄²	C₂³×D₅₃	1	4	yes	—
1258	C₄²	C₂³×D₅₃	1	4	yes	—
1259	C₂³	—	2	2	no	—
1260	C₂³	—	2	2	no	—
1261	C₂³	—	2	2	no	—
1262	C₂³	—	2	2	no	—
1263	C₂³	—	2	2	no	—
1264	C₂³	—	2	2	no	—
1265	C₂³	—	2	2	no	—
1266	C₂³	—	2	2	no	—
1267	C₂³	—	2	8	no	—
1268	C₂³	—	2	2	no	—
1269	C₂³	—	2	2	no	—
1270	C₂³	—	2	2	no	—
1271	C₂³	—	2	2	no	—
1272	C₂³	—	2	2	no	—
1273	C₂³	—	2	2	no	—
1274	C₂³	—	4	4	no	—
1275	C₂³	—	4	4	no	—
1276	C₂³	—	4	16	no	—
1277	C₂³	—	53	4	no	—
1278	C₂³	—	53	4	no	—
1279	C₂³	—	53	4	no	—
1280	C₂³	—	106	16	no	—
1281	C₂³	—	106	4	no	—
1282	C₂³	—	106	4	no	—
1283	C₂³	—	106	4	no	—
1284	C₂³	—	106	4	no	—
1285	C₂³	—	106	4	no	—
1286	C₂³	—	106	4	no	—
1287	C₂³	—	106	4	no	—
1288	C₂³	—	106	4	no	—
1289	C₂³	—	106	4	no	—
1290	C₂³	—	424	16	no	—
1291	C₂³	—	424	16	no	—
1292	C₂³	—	212	8	no	—
1293	C₂³	—	212	8	no	—
1294	C₂³	—	212	8	no	—
1295	C₂³	—	212	8	no	—
1296	C₂³	—	212	8	no	—
1297	C₂³	#13133263	1	4	yes	—
1298	C₂³	C₂⁴×D₅₃	1	2	yes	—
1299	C₂³	C₂⁴×D₅₃	1	2	yes	—
1300	C₂³	C₂⁴×D₅₃	1	2	yes	—
1301	C₂³	C₂⁴×D₅₃	1	2	yes	—
1302	C₂³	C₂⁴×D₅₃	1	2	yes	—
1303	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1304	Q₈	—	4	4	no	—
1305	Q₈	—	106	8	no	—
1306	Q₈	—	212	8	no	—
1307	D₄	—	2	8	no	—
1308	D₄	—	2	8	no	—
1309	D₄	—	4	4	no	—
1310	D₄	—	4	4	no	—
1311	D₄	—	4	4	no	—
1312	D₄	—	4	4	no	—
1313	D₄	—	4	4	no	—
1314	D₄	—	106	16	no	—
1315	D₄	—	106	8	no	—
1316	D₄	—	106	8	no	—
1317	D₄	—	106	8	no	—
1318	D₄	—	212	8	no	—
1319	D₄	—	212	8	no	—
1320	D₄	—	212	8	no	—
1321	D₄	—	212	8	no	—
1322	D₄	—	212	8	no	—
1323	D₄	—	212	8	no	—
1324	D₄	—	212	8	no	—
1325	D₄	—	212	8	no	—
1326	D₄	—	212	8	no	—
1327	D₄	—	212	8	no	—
1328	D₄	—	212	8	no	—
1329	D₄	—	212	8	no	—
1330	D₄	—	212	8	no	—
1331	D₄	—	212	8	no	—
1332	C₂×C₄	—	2	2	no	—
1333	C₂×C₄	—	2	2	no	—
1334	C₂×C₄	—	2	2	no	—
1335	C₂×C₄	—	2	2	no	—
1336	C₂×C₄	—	2	2	no	—
1337	C₂×C₄	—	2	2	no	—
1338	C₂×C₄	—	2	2	no	—
1339	C₂×C₄	—	2	2	no	—
1340	C₂×C₄	—	2	2	no	—
1341	C₂×C₄	—	2	8	no	—
1342	C₂×C₄	—	2	8	no	—
1343	C₂×C₄	—	2	8	no	—
1344	C₂×C₄	—	2	8	no	—
1345	C₂×C₄	—	2	8	no	—
1346	C₂×C₄	—	4	4	no	—
1347	C₂×C₄	—	4	4	no	—
1348	C₂×C₄	—	4	4	no	—
1349	C₂×C₄	—	53	4	no	—
1350	C₂×C₄	—	53	4	no	—
1351	C₂×C₄	—	53	4	no	—
1352	C₂×C₄	—	53	4	no	—
1353	C₂×C₄	—	53	4	no	—
1354	C₂×C₄	—	106	4	no	—
1355	C₂×C₄	—	106	4	no	—
1356	C₂×C₄	—	106	4	no	—
1357	C₂×C₄	—	106	16	no	—
1358	C₂×C₄	—	106	4	no	—
1359	C₂×C₄	—	106	4	no	—
1360	C₂×C₄	—	212	8	no	—
1361	C₂×C₄	—	212	8	no	—
1362	C₂×C₄	—	212	8	no	—
1363	C₂×C₄	—	212	8	no	—
1364	C₂×C₄	—	212	8	no	—
1365	C₂×C₄	—	212	8	no	—
1366	C₂×C₄	#13133262	1	4	yes	—
1367	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1368	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1369	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1370	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1371	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1372	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1373	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1374	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1375	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1376	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1377	C₂²	—	2	8	no	—
1378	C₂²	—	2	2	no	—
1379	C₂²	—	2	2	no	—
1380	C₂²	—	2	2	no	—
1381	C₂²	—	2	2	no	—
1382	C₂²	—	2	2	no	—
1383	C₂²	—	2	2	no	—
1384	C₂²	—	2	2	no	—
1385	C₂²	—	2	2	no	—
1386	C₂²	—	2	2	no	—
1387	C₂²	—	2	2	no	—
1388	C₂²	—	2	2	no	—
1389	C₂²	—	2	2	no	—
1390	C₂²	—	2	2	no	—
1391	C₂²	—	2	2	no	—
1392	C₂²	—	4	16	no	—
1393	C₂²	—	4	4	no	—
1394	C₂²	—	4	4	no	—
1395	C₂²	—	4	4	no	—
1396	C₂²	—	4	4	no	—
1397	C₂²	—	106	4	no	—
1398	C₂²	—	106	4	no	—
1399	C₂²	—	106	4	no	—
1400	C₂²	—	106	4	no	—
1401	C₂²	—	106	4	no	—
1402	C₂²	—	106	4	no	—
1403	C₂²	—	106	4	no	—
1404	C₂²	—	106	4	no	—
1405	C₂²	—	106	4	no	—
1406	C₂²	—	424	16	no	—
1407	C₂²	—	424	16	no	—
1408	C₂²	—	212	8	no	—
1409	C₂²	—	212	8	no	—
1410	C₂²	—	212	8	no	—
1411	C₂²	C₂×#13133262	1	2	yes	—
1412	C₂²	C₂×#13133263	1	4	yes	—
1413	C₂²	C₂×#13133263	1	2	yes	—
1414	C₂²	#16811459	1	2	yes	—
1415	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1416	C₄	—	2	2	no	—
1417	C₄	—	2	2	no	—
1418	C₄	—	2	2	no	—
1419	C₄	—	2	2	no	—
1420	C₄	—	2	2	no	—
1421	C₄	—	2	2	no	—
1422	C₄	—	2	2	no	—
1423	C₄	—	2	2	no	—
1424	C₄	—	2	2	no	—
1425	C₄	—	106	4	no	—
1426	C₄	—	106	4	no	—
1427	C₄	—	106	4	no	—
1428	C₄	—	106	4	no	—
1429	C₄	—	106	4	no	—
1430	C₄	C₂×#13133262	1	4	yes	—
1431	C₂	—	2	4	no	—
1432	C₂	—	4	2	no	—
1433	C₂	—	4	2	no	—
1434	C₂	—	4	2	no	—
1435	C₂	—	4	2	no	—
1436	C₂	—	212	4	no	—
1437	C₂	—	212	4	no	—
1438	C₂	—	212	4	no	—
1439	C₂	#20289031	1	4	yes	direct product factor
1440	C₂	C₂²×#13133262	1	1	yes	characteristic
1441	C₂	C₂²×#13133263	1	1	yes	characteristic
1442	C₂	C₂×#16811459	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#525	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#525	D₅₃
hypocenter	C₅₃	C₂×#3542
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. #20289031	C₂	direct (N × H)
2. C₂×#16811369	C₂	semidirect
3. C₂×#16811361	C₂	semidirect
4. C₂×#16811338	C₂	semidirect
5. C₂×#16811319	C₂	semidirect
6. C₂×#16811313	C₂	semidirect
7. C₂×#16811300	C₂	semidirect
8. C₂×#16811294	C₂	semidirect
9. C₂×#16811277	C₂	semidirect
10. C₂×#16811269	C₂	semidirect
11. C₂×#16811269	C₂	semidirect
12. C₂×#16811262	C₂	semidirect
13. C₂×D₄×D₂₁₂	C₂	semidirect
14. C₂×#16811244	C₂	semidirect
15. C₂×#16811228	C₂	semidirect
16. C₂×#16811225	C₂	semidirect
17. C₂×#16811209	C₂	semidirect
18. C₂×#16811201	C₂	semidirect
19. C₂×#16811188	C₂	semidirect
20. C₂×#16811187	C₂	semidirect
21. C₂×#16811183	C₂	semidirect
22. C₂×#16811134	C₂	semidirect
23. C₂²×#13133191	C₂	semidirect
24. C₂×C₅₃×#525	C₂	semidirect
25. C₂²×#11719945	C₂²	semidirect
26. C₂²×#11719945	C₂²	semidirect
27. C₂²×#11719947	C₂²	semidirect
29. C₂³×D₂₁₂	C₂²	semidirect
30. C₂³×C₂²⋊D₅₃	C₂²	semidirect
32. #16811369	C₂²	semidirect
33. #16811361	C₂²	semidirect
34. #16811338	C₂²	semidirect
35. #16811319	C₂²	semidirect
36. #16811313	C₂²	semidirect
37. #16811300	C₂²	semidirect
38. #16811294	C₂²	semidirect
39. #16811277	C₂²	semidirect
40. #16811269	C₂²	semidirect
41. #16811269	C₂²	semidirect
42. #16811262	C₂²	semidirect
43. D₄×D₂₁₂	C₂²	semidirect
44. #16811244	C₂²	semidirect
45. #16811228	C₂²	semidirect
46. #16811225	C₂²	semidirect
47. #16811209	C₂²	semidirect
48. #16811201	C₂²	semidirect
49. #16811188	C₂²	semidirect
50. #16811187	C₂²	semidirect
51. #16811183	C₂²	semidirect
52. C₂×#13133217	C₂²	semidirect
53. C₂×#13133214	C₂²	semidirect
54. C₂×#13133213	C₂²	semidirect
55. C₂×#13133213	C₂²	semidirect
56. C₂×#13133212	C₂²	semidirect
57. C₂×#13133212	C₂²	semidirect
58. C₂×#13133210	C₂²	semidirect
59. C₂×#13133209	C₂²	semidirect
60. C₂×#13133207	C₂²	semidirect
61. C₂×#13133206	C₂²	semidirect
62. C₂×#13133205	C₂²	semidirect
63. C₂×#13133203	C₂²	semidirect
64. C₂×#13133203	C₂²	semidirect
65. C₂×#13133203	C₂²	semidirect
66. #16811134	C₂²	semidirect
67. C₂×#13133202	C₂²	semidirect
68. C₂×#13133202	C₂²	semidirect
69. C₂×#13133202	C₂²	semidirect
70. C₂×#13133202	C₂²	semidirect
71. C₂×#13133201	C₂²	semidirect
72. C₂×#13133201	C₂²	semidirect
73. C₂×#13133200	C₂²	semidirect
74. C₂×#13133199	C₂²	semidirect
75. C₂×#13133199	C₂²	semidirect
77. C₂×#13133197	C₂²	semidirect
78. C₂×#13133196	C₂²	semidirect
79. C₂×#13133196	C₂²	semidirect
80. C₂×#13133196	C₂²	semidirect
81. C₂×#13133195	C₂²	semidirect
82. C₂×#13133193	C₂²	semidirect
83. C₂×#13133192	C₂²	semidirect
87. C₂×#13133191	C₂²	semidirect
88. C₂×#13133191	C₂²	semidirect
89. C₂×#13133191	C₂²	semidirect
90. C₂×#13133191	C₂²	semidirect
91. C₂×#13133191	C₂²	semidirect
92. C₂×#13133191	C₂²	semidirect
93. C₂×#13133191	C₂²	semidirect
94. C₂×#13133191	C₂²	semidirect
95. C₂×#13133191	C₂²	semidirect
96. C₂×#13133190	C₂²	semidirect
97. C₂×#13133190	C₂²	semidirect
98. C₂×#13133190	C₂²	semidirect
99. C₂×#13133190	C₂²	semidirect
100. C₂×#13133190	C₂²	semidirect
101. C₂×#13133190	C₂²	semidirect
102. C₂×#13133189	C₂²	semidirect
103. C₂×#13133189	C₂²	semidirect
104. C₂×#13133189	C₂²	semidirect
105. C₂×#13133188	C₂²	semidirect
106. C₂×#13133188	C₂²	semidirect
108. C₂×#13133187	C₂²	semidirect
109. C₂×#13133186	C₂²	semidirect
110. C₂×#13133185	C₂²	semidirect
111. C₂×#13133185	C₂²	semidirect
112. C₂×#13133185	C₂²	semidirect
113. C₂×#13133185	C₂²	semidirect
114. C₂×C₄×Dic₁₀₆	C₂²	semidirect
115. C₂×C₄×D₂₁₂	C₂²	semidirect
116. C₂×C₄×D₂₁₂	C₂²	semidirect
117. C₂×C₄×D₂₁₂	C₂²	semidirect
118. C₂×#13133179	C₂²	semidirect
119. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
120. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
121. C₂×#13133177	C₂²	semidirect
122. C₂×#13133176	C₂²	semidirect
123. C₂×#13133176	C₂²	semidirect
124. C₂×#13133175	C₂²	semidirect
125. C₂×#13133173	C₂²	semidirect
126. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
127. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
128. C₂²×#11719921	C₂²	semidirect
129. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
130. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
131. C₂²×#41×C₅₃	C₂²	semidirect
132. C₂⁴×C₄×C₅₃	C₂²	semidirect
133. C₅₃×#525	C₂²	semidirect
134. C₂×#123×C₅₃	C₂²	semidirect
135. C₂×#123×C₅₃	C₂²	semidirect
136. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
137. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
139. C₂×#121×C₅₃	C₂²	semidirect
141. C₂×#120×C₅₃	C₂²	semidirect
143. C₂×C₄×D₄×C₅₃	C₂²	semidirect
144. C₂×C₄×D₄×C₅₃	C₂²	semidirect
145. C₂×C₄×D₄×C₅₃	C₂²	semidirect
146. C₂×#117×C₅₃	C₂²	semidirect
151. C₂×#11719945	C₂³	semidirect
152. C₂×#11719945	C₂³	semidirect
154. C₂×#11719947	C₂³	semidirect
167. C₂²×D₂₁₂	C₂³	semidirect
180. C₂²×C₂²⋊D₅₃	C₂³	semidirect
190. #13133217	C₂³	semidirect
191. #13133214	C₂³	semidirect
192. #13133213	C₂³	semidirect
193. #13133213	C₂³	semidirect
194. #13133212	C₂³	semidirect
195. #13133212	C₂³	semidirect
196. #13133210	C₂³	semidirect
197. #13133209	C₂³	semidirect
198. #13133207	C₂³	semidirect
199. #13133206	C₂³	semidirect
200. #13133205	C₂³	semidirect
201. #13133203	C₂³	semidirect
202. #13133203	C₂³	semidirect
203. #13133203	C₂³	semidirect
204. #13133202	C₂³	semidirect
205. #13133202	C₂³	semidirect
206. #13133202	C₂³	semidirect
207. #13133202	C₂³	semidirect
208. #13133201	C₂³	semidirect
209. #13133201	C₂³	semidirect
210. #13133200	C₂³	semidirect
211. #13133199	C₂³	semidirect
212. #13133199	C₂³	semidirect
214. #13133197	C₂³	semidirect
215. #13133196	C₂³	semidirect
216. #13133196	C₂³	semidirect
217. #13133196	C₂³	semidirect
218. #13133195	C₂³	semidirect
219. #13133193	C₂³	semidirect
220. #13133192	C₂³	semidirect
224. #13133191	C₂³	semidirect
225. #13133191	C₂³	semidirect
226. #13133191	C₂³	semidirect
227. #13133191	C₂³	semidirect
228. #13133191	C₂³	semidirect
229. #13133191	C₂³	semidirect
230. #13133191	C₂³	semidirect
231. #13133191	C₂³	semidirect
232. #13133190	C₂³	semidirect
233. #13133190	C₂³	semidirect
234. #13133190	C₂³	semidirect
235. #13133190	C₂³	semidirect
236. #13133190	C₂³	semidirect
237. #13133190	C₂³	semidirect
238. #13133189	C₂³	semidirect
239. #13133189	C₂³	semidirect
240. #13133189	C₂³	semidirect
241. #13133188	C₂³	semidirect
242. #13133188	C₂³	semidirect
244. #13133187	C₂³	semidirect
245. #13133186	C₂³	semidirect
246. #13133185	C₂³	semidirect
247. #13133185	C₂³	semidirect
248. #13133185	C₂³	semidirect
249. #13133185	C₂³	semidirect
250. C₄×Dic₁₀₆	C₂³	semidirect
251. C₄×D₂₁₂	C₂³	semidirect
252. C₄×D₂₁₂	C₂³	semidirect
253. C₄×D₂₁₂	C₂³	semidirect
254. #13133179	C₂³	semidirect
255. C₄×C₂²⋊D₅₃	C₂³	semidirect
256. C₄×C₂²⋊D₅₃	C₂³	semidirect
257. #13133177	C₂³	semidirect
258. #13133176	C₂³	semidirect
259. #13133176	C₂³	semidirect
260. #13133175	C₂³	semidirect
261. #13133173	C₂³	semidirect
269. C₂×C₄⋊Dic₅₃	C₂³	semidirect
270. C₂×C₄⋊Dic₅₃	C₂³	semidirect
296. C₂×#11719921	C₂³	semidirect
297. C₂²⋊C₄×D₅₃	C₂³	semidirect
298. C₂²⋊C₄×D₅₃	C₂³	semidirect
304. C₂×#41×C₅₃	C₂³	semidirect
322. C₂³×C₄×C₅₃	C₂³	semidirect
323. #123×C₅₃	C₂³	semidirect
324. #123×C₅₃	C₂³	semidirect
325. C₂²⋊Q₈×C₅₃	C₂³	semidirect
326. C₂²⋊Q₈×C₅₃	C₂³	semidirect
328. #121×C₅₃	C₂³	semidirect
330. #120×C₅₃	C₂³	semidirect
332. C₄×D₄×C₅₃	C₂³	semidirect
333. C₄×D₄×C₅₃	C₂³	semidirect
334. C₄×D₄×C₅₃	C₂³	semidirect
335. #117×C₅₃	C₂³	semidirect
732. C₂×#525	D₅₃	semidirect
739. C₂×C₅₃	#3542	semidirect
749. C₂²×#41	C₂×D₅₃	semidirect
754. C₂⁴×C₄	C₂×D₅₃	semidirect
790. #525	C₂×D₅₃	semidirect
801. C₂×#123	C₂×D₅₃	semidirect
802. C₂×#123	C₂×D₅₃	semidirect
809. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
810. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
836. C₂×#121	C₂×D₅₃	semidirect
845. C₂×#120	C₂×D₅₃	semidirect
855. C₂×C₄×D₄	C₂×D₅₃	semidirect
856. C₂×C₄×D₄	C₂×D₅₃	semidirect
857. C₂×C₄×D₄	C₂×D₅₃	semidirect
862. C₂×#117	C₂×D₅₃	semidirect
868. C₅₃	C₂×#3542	semidirect
879. C₂×#41	C₂²×D₅₃	semidirect
932. C₂³×C₄	C₂²×D₅₃	semidirect
957. #123	C₂²×D₅₃	semidirect
958. #123	C₂²×D₅₃	semidirect
965. C₂²⋊Q₈	C₂²×D₅₃	semidirect
966. C₂²⋊Q₈	C₂²×D₅₃	semidirect
991. #121	C₂²×D₅₃	semidirect
1000. #120	C₂²×D₅₃	semidirect
1010. C₄×D₄	C₂²×D₅₃	semidirect
1011. C₄×D₄	C₂²×D₅₃	semidirect
1012. C₄×D₄	C₂²×D₅₃	semidirect
1017. #117	C₂²×D₅₃	semidirect
1439. C₂	#20289031	direct (N × H)

Maximal subgroups

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

subgroup	index
#20289031	2
C₂×#16811369	2
C₂×#16811361	2
C₂×#16811338	2
C₂×#16811319	2
C₂×#16811313	2
C₂×#16811300	2
C₂×#16811294	2
C₂×#16811277	2
C₂×#16811269	2
C₂×#16811262	2
C₂×D₄×D₂₁₂	2
C₂×#16811244	2
C₂×#16811228	2
C₂×#16811225	2
C₂×#16811209	2
C₂×#16811201	2
C₂×#16811188	2
C₂×#16811187	2
C₂×#16811183	2
C₂×#16811134	2
C₂²×#13133191	2
C₂×C₅₃×#525	2
C₂×#3542	53

Subgroups — C2×#20289031 #28291225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20289031 #28291225