Subgroups — C₂×#20289231 #28291429

Order 13568.

8122 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289231	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16811371	C₂	1	2	yes	maximal, complemented
3	C₂×#16811365	C₂	1	2	yes	maximal, complemented
4	C₂×#16811358	C₂	1	2	yes	maximal, complemented
5	C₂×#16811282	C₂	1	2	yes	maximal, complemented
6	C₂×#16811269	C₂	1	2	yes	maximal, complemented
7	C₂×#16811265	C₂	1	4	yes	maximal, complemented
8	C₂×D₄×D₂₁₂	C₂	1	2	yes	maximal, complemented
9	C₂×#16811244	C₂	1	2	yes	maximal, complemented
10	C₂×#16811213	C₂	1	2	yes	maximal, complemented
11	C₂×#16811212	C₂	1	4	yes	maximal, complemented
12	C₂×#16811192	C₂	1	2	yes	maximal, complemented
13	C₂×#16811181	C₂	1	2	yes	maximal, complemented
14	C₂×#16811173	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#13133205	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#11719945	C₂²	1	2	yes	complemented
18	C₂²×#11719945	C₂²	1	2	yes	complemented
19	C₂³×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
21	C₂³×D₂₁₂	C₂²	1	2	yes	complemented
22	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
23	#16811371	C₂²	1	32	yes	complemented
24	#16811365	C₂²	1	32	yes	complemented
25	#16811358	C₂²	1	32	yes	complemented
26	#16811282	C₂²	1	32	yes	complemented
27	#16811269	C₂²	1	32	yes	complemented
28	#16811265	C₂²	1	64	yes	complemented
29	D₄×D₂₁₂	C₂²	1	32	yes	complemented
30	#16811244	C₂²	1	32	yes	complemented
31	#16811213	C₂²	1	32	yes	complemented
32	#16811212	C₂²	1	64	yes	complemented
33	#16811192	C₂²	1	32	yes	complemented
34	#16811181	C₂²	1	32	yes	complemented
35	#16811173	C₂²	1	16	yes	complemented
36	C₂×#13133217	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13133214	C₂²	1	2	yes	—
38	C₂×#13133214	C₂²	1	1	yes	characteristic, complemented
39	C₂×#13133212	C₂²	1	4	yes	complemented
40	C₂×#13133206	C₂²	1	4	yes	complemented
41	C₂×#13133205	C₂²	1	2	yes	complemented
42	C₂×#13133205	C₂²	1	2	yes	complemented
43	C₂×#13133205	C₂²	1	2	yes	complemented
44	C₂×#13133205	C₂²	1	2	yes	complemented
45	C₂×#13133205	C₂²	1	2	yes	complemented
46	C₂×#13133205	C₂²	1	2	yes	complemented
47	C₂×#13133205	C₂²	1	16	yes	complemented
48	C₂×#13133203	C₂²	1	4	yes	complemented
49	C₂×#13133203	C₂²	1	4	yes	complemented
50	C₂×#13133202	C₂²	1	4	yes	complemented
51	C₂×#13133202	C₂²	1	4	yes	complemented
52	C₂×#13133202	C₂²	1	4	yes	complemented
53	C₂×#13133199	C₂²	1	4	yes	complemented
54	C₂×#13133196	C₂²	1	2	yes	complemented
55	C₂×#13133195	C₂²	1	4	yes	complemented
56	C₂×#13133195	C₂²	1	4	yes	complemented
57	C₂×#13133192	C₂²	1	4	yes	complemented
58	C₂×#13133192	C₂²	1	4	yes	complemented
59	C₂×#13133192	C₂²	1	4	yes	complemented
60	C₂×#13133191	C₂²	1	2	yes	—
61	C₂×#13133191	C₂²	1	2	yes	complemented
62	C₂×#13133191	C₂²	1	2	yes	complemented
63	C₂×#13133190	C₂²	1	4	yes	complemented
64	C₂×#13133189	C₂²	1	4	yes	complemented
65	C₂×#13133187	C₂²	1	4	yes	complemented
66	C₂×#13133187	C₂²	1	4	yes	complemented
67	C₂×#13133187	C₂²	1	4	yes	complemented
68	C₂×#13133187	C₂²	1	4	yes	complemented
69	C₂×#13133185	C₂²	1	4	yes	complemented
70	C₂×C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
71	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
72	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
73	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
74	C₂×#13133179	C₂²	1	4	yes	complemented
75	C₂×#13133177	C₂²	1	4	yes	complemented
76	C₂²×#11719921	C₂²	1	2	yes	complemented
77	C₂²×#11719921	C₂²	1	2	yes	complemented
78	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
79	C₅₃×#529	C₂²	1	16	yes	complemented
80	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
81	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
82	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
84	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
85	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
86	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
88	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
89	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
90	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
91	C₂⁴×D₅₃	C₂³	1	2	yes	—
92	C₂⁴×D₅₃	C₂³	1	4	yes	—
93	C₂×#11719945	—	4	8	no	—
94	C₂×#11719945	—	4	8	no	—
95	C₂×#11719945	C₂³	1	16	yes	complemented
96	C₂×#11719945	C₂³	1	16	yes	complemented
97	C₂²×Dic₁₀₆	—	4	4	no	—
98	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
99	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
100	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
101	C₂²×Dic₁₀₆	C₂³	1	8	yes	complemented
102	C₂²×D₂₁₂	—	4	4	no	—
103	C₂²×D₂₁₂	—	4	8	no	—
104	C₂²×D₂₁₂	C₂³	1	2	yes	—
105	C₂²×D₂₁₂	C₂³	1	2	yes	—
106	C₂²×D₂₁₂	C₂³	1	4	yes	—
107	C₂²×D₂₁₂	C₂³	1	2	yes	—
108	C₂²×D₂₁₂	C₂³	1	2	yes	—
109	C₂²×D₂₁₂	C₂³	1	2	yes	—
110	C₂²×D₂₁₂	C₂³	1	4	yes	—
111	C₂²×D₂₁₂	C₂³	1	4	yes	—
112	C₂²×D₂₁₂	C₂³	1	8	yes	—
113	C₂²×D₂₁₂	C₂³	1	16	yes	complemented
114	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
115	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
116	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
117	C₂×D₄×D₅₃	—	4	16	no	—
118	C₂×D₄×D₅₃	C₂³	1	32	yes	complemented
119	C₂³×Dic₅₃	C₂³	1	2	yes	—
120	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
121	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
122	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
123	#13133217	C₂³	1	8	yes	complemented
124	#13133214	C₂³	1	16	yes	—
125	#13133214	C₂³	1	8	yes	complemented
126	#13133212	C₂³	1	32	yes	complemented
127	#13133206	C₂³	1	32	yes	complemented
128	#13133205	C₂³	1	16	yes	complemented
129	#13133205	C₂³	1	16	yes	complemented
130	#13133205	C₂³	1	16	yes	complemented
131	#13133205	C₂³	1	16	yes	complemented
132	#13133205	C₂³	1	16	yes	complemented
133	#13133205	C₂³	1	16	yes	complemented
134	#13133203	C₂³	1	32	yes	complemented
135	#13133203	C₂³	1	32	yes	complemented
136	#13133202	C₂³	1	32	yes	complemented
137	#13133202	C₂³	1	32	yes	complemented
138	#13133202	C₂³	1	32	yes	complemented
139	#13133199	C₂³	1	32	yes	complemented
140	#13133196	C₂³	1	16	yes	complemented
141	#13133195	C₂³	1	32	yes	complemented
142	#13133195	C₂³	1	32	yes	complemented
143	#13133192	C₂³	1	32	yes	complemented
144	#13133192	C₂³	1	32	yes	complemented
145	#13133192	C₂³	1	32	yes	complemented
146	#13133191	C₂³	1	16	yes	—
147	#13133191	C₂³	1	16	yes	complemented
148	#13133191	C₂³	1	16	yes	complemented
149	#13133190	C₂³	1	32	yes	complemented
150	#13133189	C₂³	1	32	yes	complemented
151	#13133187	C₂³	1	32	yes	complemented
152	#13133187	C₂³	1	32	yes	complemented
153	#13133187	C₂³	1	32	yes	complemented
154	#13133187	C₂³	1	32	yes	complemented
155	#13133185	C₂³	1	32	yes	complemented
156	C₄×Dic₁₀₆	C₂³	1	16	yes	complemented
157	C₄×D₂₁₂	C₂³	1	16	yes	complemented
158	C₄×D₂₁₂	C₂³	1	16	yes	complemented
159	C₄×D₂₁₂	C₂³	1	16	yes	complemented
160	#13133179	C₂³	1	32	yes	complemented
161	#13133177	C₂³	1	32	yes	complemented
162	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
163	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
164	C₂×#11719919	C₂³	1	4	yes	—
165	C₂×#11719919	C₂³	1	4	yes	—
166	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
167	C₂×#11719921	C₂³	1	4	yes	—
168	C₂×#11719921	C₂³	1	4	yes	—
169	C₂×#11719921	C₂³	1	4	yes	—
170	C₂×#11719921	C₂³	1	4	yes	—
171	C₂×#11719921	C₂³	1	4	yes	—
172	C₂×#11719921	C₂³	1	4	yes	—
173	C₂×#11719921	C₂³	1	4	yes	—
174	C₂×#11719921	C₂³	1	4	yes	—
175	C₂×#11719921	C₂³	1	4	yes	—
176	C₂×#11719921	C₂³	1	4	yes	—
177	C₂×#11719921	C₂³	1	16	yes	complemented
178	C₂×#11719921	C₂³	1	16	yes	complemented
179	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	complemented
180	C₂×C₄×Dic₅₃	C₂³	1	4	yes	—
181	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
182	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
183	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
184	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
185	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
186	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
187	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
188	#126×C₅₃	C₂³	1	16	yes	complemented
189	#125×C₅₃	C₂³	1	8	yes	complemented
190	#124×C₅₃	C₂³	1	8	yes	complemented
191	#123×C₅₃	C₂³	1	16	yes	complemented
192	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
193	#121×C₅₃	C₂³	1	8	yes	—
194	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
195	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
196	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
197	#117×C₅₃	C₂³	1	16	yes	complemented
198	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
209	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
215	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
216	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
217	C₂³×D₅₃	—	2	8	no	—
218	C₂³×D₅₃	—	4	8	no	—
219	C₂³×D₅₃	—	4	8	no	—
220	C₂³×D₅₃	—	4	4	no	—
221	C₂³×D₅₃	—	4	8	no	—
222	C₂³×D₅₃	—	4	4	no	—
223	C₂³×D₅₃	C₂⁴	1	4	yes	—
224	C₂³×D₅₃	C₂⁴	1	4	yes	—
225	C₂³×D₅₃	C₂⁴	1	8	yes	—
226	C₂³×D₅₃	C₂⁴	1	16	yes	—
227	C₂×Q₈×C₅₃	—	4	2	no	—
228	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
229	C₂×D₄×C₅₃	—	2	8	no	—
230	C₂×D₄×C₅₃	—	4	2	no	—
231	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
232	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
233	C₂²×C₄×C₅₃	—	2	4	no	—
234	C₂²×C₄×C₅₃	—	2	4	no	—
235	C₂²×C₄×C₅₃	—	2	8	no	—
236	C₂²×C₄×C₅₃	—	4	2	no	—
237	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
248	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₂²⋊D₅₃	—	2	16	no	—
251	C₂×C₂²⋊D₅₃	—	4	8	no	—
252	C₂×C₂²⋊D₅₃	—	4	8	no	—
253	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
254	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
255	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
256	C₂²×Dic₅₃	—	4	4	no	—
257	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
258	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
259	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
260	D₄×D₅₃	—	4	64	no	—
261	#11719945	—	4	32	no	—
262	#11719945	—	4	32	no	—
263	C₂×D₂₁₂	—	2	8	no	—
264	C₂×D₂₁₂	—	2	8	no	—
265	C₂×D₂₁₂	—	4	16	no	—
266	C₂×D₂₁₂	—	4	32	no	—
267	C₂×D₂₁₂	—	4	8	no	—
268	C₂×D₂₁₂	—	4	4	no	—
269	C₂×D₂₁₂	—	4	8	no	—
270	C₂×D₂₁₂	—	4	4	no	—
271	C₂×D₂₁₂	—	4	8	no	—
272	C₂×D₂₁₂	—	4	4	no	—
273	C₂×D₂₁₂	C₂⁴	1	8	yes	—
274	C₂×D₂₁₂	C₂⁴	1	8	yes	—
275	C₂×D₂₁₂	C₂⁴	1	16	yes	—
276	C₂×D₂₁₂	C₂⁴	1	8	yes	—
277	C₂×D₂₁₂	C₂⁴	1	8	yes	—
278	C₂×D₂₁₂	C₂⁴	1	8	yes	—
279	C₂×D₂₁₂	C₂⁴	1	16	yes	—
280	C₂×D₂₁₂	C₂⁴	1	16	yes	—
281	C₂×C₄×D₅₃	—	4	8	no	—
282	C₂×C₄×D₅₃	—	4	8	no	—
283	C₂×C₄×D₅₃	—	4	8	no	—
284	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
285	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
286	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
287	C₂×Dic₁₀₆	—	2	8	no	—
288	C₂×Dic₁₀₆	—	4	16	no	—
289	C₂×Dic₁₀₆	—	4	4	no	—
290	C₂×Dic₁₀₆	—	4	4	no	—
291	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
292	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
293	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
294	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
295	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
296	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
297	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
298	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
299	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
300	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
301	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
302	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
303	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
304	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
305	C₄²×C₅₃	C₂⁴	1	4	yes	—
306	C₄²×C₅₃	C₂⁴	1	4	yes	—
307	C₄²×C₅₃	C₂⁴	1	4	yes	—
308	C₄²×C₅₃	C₂⁴	1	4	yes	—
309	C₄²×C₅₃	C₂⁴	1	8	yes	—
310	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
311	#11719921	C₂⁴	1	16	yes	—
312	#11719921	C₂⁴	1	16	yes	—
313	#11719921	C₂⁴	1	16	yes	—
314	#11719921	C₂⁴	1	16	yes	—
315	#11719921	C₂⁴	1	16	yes	—
316	#11719921	C₂⁴	1	16	yes	—
317	#11719921	C₂⁴	1	16	yes	—
318	#11719921	C₂⁴	1	16	yes	—
319	#11719921	C₂⁴	1	16	yes	—
320	#11719921	C₂⁴	1	16	yes	—
321	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
322	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
323	#11719919	C₂⁴	1	16	yes	—
324	#11719919	C₂⁴	1	16	yes	—
325	C₄×Dic₅₃	C₂⁴	1	16	yes	—
326	C₂³×C₅₃	—	2	2	no	—
327	C₂³×C₅₃	—	2	2	no	—
328	C₂³×C₅₃	—	2	4	no	—
329	C₂³×C₅₃	—	2	4	no	—
330	C₂³×C₅₃	—	2	4	no	—
331	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
332	C₂³×C₅₃	C₂⁵	1	4	yes	—
333	C₂³×C₅₃	C₂⁵	1	2	yes	—
334	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
335	C₂²×D₅₃	—	2	8	no	—
336	C₂²×D₅₃	—	2	8	no	—
337	C₂²×D₅₃	—	2	8	no	—
338	C₂²×D₅₃	—	2	8	no	—
339	C₂²×D₅₃	—	2	8	no	—
340	C₂²×D₅₃	—	2	8	no	—
341	C₂²×D₅₃	—	2	16	no	—
342	C₂²×D₅₃	—	4	16	no	—
343	C₂²×D₅₃	—	4	8	no	—
344	C₂²×D₅₃	—	4	16	no	—
345	C₂²×D₅₃	—	4	16	no	—
346	C₂²×D₅₃	—	4	8	no	—
347	C₂²×D₅₃	—	8	16	no	—
348	C₂²×D₅₃	—	8	32	no	—
349	C₂²×D₅₃	C₂⁵	1	8	yes	—
350	C₂²×D₅₃	C₂⁵	1	8	yes	—
351	Q₈×C₅₃	—	4	4	no	—
352	D₄×C₅₃	—	2	16	no	—
353	D₄×C₅₃	—	4	4	no	—
354	C₂×C₄×C₅₃	—	2	2	no	—
355	C₂×C₄×C₅₃	—	2	2	no	—
356	C₂×C₄×C₅₃	—	2	2	no	—
357	C₂×C₄×C₅₃	—	2	4	no	—
358	C₂×C₄×C₅₃	—	2	4	no	—
359	C₂×C₄×C₅₃	—	2	8	no	—
360	C₂×C₄×C₅₃	—	2	2	no	—
361	C₂×C₄×C₅₃	—	2	4	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	8	no	—
364	C₂×C₄×C₅₃	—	2	16	no	—
365	C₂×C₄×C₅₃	—	4	4	no	—
366	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
367	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
368	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
369	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
370	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
371	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
372	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
373	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
374	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
375	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
376	C₂²⋊D₅₃	—	2	32	no	—
377	C₂²⋊D₅₃	—	4	16	no	—
378	C₂²⋊D₅₃	—	4	16	no	—
379	C₂×Dic₅₃	—	2	8	no	—
380	C₂×Dic₅₃	—	2	8	no	—
381	C₂×Dic₅₃	—	4	8	no	—
382	C₂×Dic₅₃	C₂⁵	1	8	yes	—
383	C₂×Dic₅₃	C₂⁵	1	8	yes	—
384	D₂₁₂	—	2	16	no	—
385	D₂₁₂	—	2	16	no	—
386	D₂₁₂	—	4	8	no	—
387	D₂₁₂	—	4	16	no	—
388	D₂₁₂	—	4	8	no	—
389	D₂₁₂	—	4	16	no	—
390	D₂₁₂	—	4	8	no	—
391	D₂₁₂	—	4	16	no	—
392	C₄×D₅₃	—	4	16	no	—
393	C₄×D₅₃	—	4	16	no	—
394	C₄×D₅₃	—	4	16	no	—
395	Dic₁₀₆	—	2	16	no	—
396	Dic₁₀₆	—	4	8	no	—
397	Dic₁₀₆	—	4	8	no	—
398	C₂×#3558	—	53	1	no	maximal, Sylow
399	C₂²×C₅₃	—	2	2	no	—
400	C₂²×C₅₃	—	2	2	no	—
401	C₂²×C₅₃	—	2	8	no	—
402	C₂²×C₅₃	—	2	4	no	—
403	C₂²×C₅₃	—	2	4	no	—
404	C₂²×C₅₃	—	2	4	no	—
405	C₂²×C₅₃	—	4	8	no	—
406	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
407	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
408	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
409	C₂²×C₅₃	#585	1	2	yes	—
410	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
411	C₂×D₅₃	—	2	8	no	—
412	C₂×D₅₃	—	2	8	no	—
413	C₂×D₅₃	—	2	8	no	—
414	C₂×D₅₃	—	2	8	no	—
415	C₂×D₅₃	—	2	8	no	—
416	C₂×D₅₃	—	2	8	no	—
417	C₂×D₅₃	—	4	16	no	—
418	C₂×D₅₃	—	4	16	no	—
419	C₂×D₅₃	—	8	16	no	—
420	C₂×D₅₃	—	8	32	no	—
421	C₄×C₅₃	—	2	2	no	—
422	C₄×C₅₃	—	2	2	no	—
423	C₄×C₅₃	—	2	2	no	—
424	C₄×C₅₃	—	2	4	no	—
425	C₄×C₅₃	—	2	4	no	—
426	C₄×C₅₃	—	2	2	no	—
427	C₄×C₅₃	—	2	4	no	—
428	C₄×C₅₃	—	2	2	no	—
429	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
430	Dic₅₃	—	2	8	no	—
431	Dic₅₃	—	2	8	no	—
432	#3558	—	53	32	no	—
433	C₂×#562	—	53	2	no	—
434	C₂×H(3,𝔽₄)	—	53	2	no	—
435	C₂×#559	—	53	2	no	—
436	C₂×#548	—	53	2	no	—
437	C₂×#546	—	53	4	no	—
438	C₂×#546	—	53	2	no	—
439	C₂×D₄²	—	53	2	no	—
440	C₂×#542	—	53	2	no	—
441	C₂×#538	—	53	4	no	—
442	C₂×#538	—	53	2	no	—
443	C₂×#535	—	53	2	no	—
444	C₂×#534	—	53	2	no	—
445	C₂×#532	—	53	1	no	—
446	C₂×#529	D₅₃	1	1	yes	characteristic, complemented
447	C₂²×#124	—	53	1	no	—
448	C₂×C₅₃	—	2	4	no	—
449	C₂×C₅₃	—	4	4	no	—
450	C₂×C₅₃	#3558	1	4	yes	complemented
451	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
454	D₅₃	—	4	8	no	—
455	D₅₃	—	4	8	no	—
456	C₂²×#41	—	53	2	no	—
457	C₂²×#41	—	53	2	no	—
458	C₂³×Q₈	—	53	1	no	—
459	C₂³×D₄	—	53	4	no	—
460	C₂³×D₄	—	53	1	no	—
461	C₂³×D₄	—	53	2	no	—
462	#562	—	53	32	no	—
463	H(3,𝔽₄)	—	53	32	no	—
464	#559	—	53	32	no	—
465	#548	—	53	32	no	—
466	#546	—	53	64	no	—
467	#546	—	53	32	no	—
468	D₄²	—	53	32	no	—
469	#542	—	53	32	no	—
470	#538	—	53	64	no	—
471	#538	—	53	32	no	—
472	#535	—	53	32	no	—
473	#534	—	53	32	no	—
474	#532	—	53	16	no	—
475	C₂×C₄⋊Q₈	—	53	1	no	—
476	C₂×#127	—	53	1	no	—
477	C₂×#127	—	53	2	no	—
478	#529	C₂×D₅₃	1	16	yes	complemented
479	C₂×#126	—	53	4	no	—
480	C₂×#126	C₂×D₅₃	1	2	yes	complemented
481	C₂×#125	C₂×D₅₃	1	1	yes	characteristic, complemented
482	C₂×#124	—	53	4	no	—
483	C₂×#124	—	53	4	no	—
484	C₂×#124	—	53	4	no	—
485	C₂×#124	—	53	2	no	—
486	C₂×#124	—	53	2	no	—
487	C₂×#124	—	53	2	no	—
488	C₂×#124	—	53	2	no	—
489	C₂×#124	—	53	2	no	—
490	C₂×#124	—	53	2	no	—
491	C₂×#124	—	53	16	no	—
492	C₂×#124	C₂×D₅₃	1	1	yes	characteristic, complemented
493	C₂×#123	—	53	4	no	—
494	C₂×#123	—	53	4	no	—
495	C₂×#123	—	53	4	no	—
496	C₂×#123	—	53	4	no	—
497	C₂×#123	C₂×D₅₃	1	2	yes	complemented
498	C₂×C₂²⋊Q₈	—	53	2	no	—
499	C₂×C₂²⋊Q₈	—	53	4	no	—
500	C₂×C₂²⋊Q₈	—	53	4	no	—
501	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
502	C₂×#121	—	53	4	no	—
503	C₂×#121	—	53	2	no	—
504	C₂×#121	—	53	2	no	—
505	C₂×#121	—	53	2	no	—
506	C₂×#121	—	53	4	no	—
507	C₂×#121	—	53	4	no	—
508	C₂×#121	—	53	4	no	—
509	C₂×#121	—	53	4	no	—
510	C₂×#121	C₂×D₅₃	1	1	yes	characteristic
511	C₂×#120	—	53	4	no	—
512	C₂×#120	—	53	4	no	—
513	C₂×#120	—	53	4	no	—
514	C₂×#120	—	53	4	no	—
515	C₂×#120	—	53	4	no	—
516	C₂×C₄×Q₈	—	53	2	no	—
517	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
518	C₂×C₄×D₄	—	53	4	no	—
519	C₂×C₄×D₄	—	53	4	no	—
520	C₂×C₄×D₄	—	53	2	no	—
521	C₂×C₄×D₄	—	53	2	no	—
522	C₂×C₄×D₄	—	53	2	no	—
523	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
524	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
525	C₂×#117	C₂×D₅₃	1	2	yes	complemented
526	C₂²×C₂²⋊C₄	—	53	2	no	—
527	C₂²×C₂²⋊C₄	—	53	2	no	—
528	C₂²×C₂²⋊C₄	—	53	4	no	—
529	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
530	C₅₃	C₂×#3558	1	1	yes	characteristic, complemented, Sylow
531	C₂⁵	—	53	2	no	—
532	C₂⁵	—	53	4	no	—
533	C₂×#41	—	53	16	no	—
534	C₂×#41	—	53	16	no	—
535	C₂×#41	—	212	8	no	—
536	C₂×#41	—	212	8	no	—
537	C₂²×Q₈	—	53	2	no	—
538	C₂²×Q₈	—	53	2	no	—
539	C₂²×Q₈	—	53	2	no	—
540	C₂²×Q₈	—	53	8	no	—
541	C₂²×Q₈	—	212	4	no	—
542	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
543	C₂²×D₄	—	53	4	no	—
544	C₂²×D₄	—	53	4	no	—
545	C₂²×D₄	—	53	4	no	—
546	C₂²×D₄	—	53	32	no	—
547	C₂²×D₄	—	53	2	no	—
548	C₂²×D₄	—	53	2	no	—
549	C₂²×D₄	—	53	4	no	—
550	C₂²×D₄	—	53	2	no	—
551	C₂²×D₄	—	53	2	no	—
552	C₂²×D₄	—	53	2	no	—
553	C₂²×D₄	—	53	4	no	—
554	C₂²×D₄	—	53	4	no	—
555	C₂²×D₄	—	53	8	no	—
556	C₂²×D₄	—	53	16	no	—
557	C₂²×D₄	—	212	4	no	—
558	C₂²×D₄	—	212	8	no	—
559	C₂²×D₄	—	212	16	no	—
560	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
561	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
562	C₂³×C₄	—	53	2	no	—
563	C₂³×C₄	—	53	4	no	—
564	C₂³×C₄	—	53	4	no	—
565	C₂³×C₄	—	53	4	no	—
566	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
567	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
568	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
569	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
570	C₄⋊Q₈	—	53	8	no	—
571	#127	—	53	8	no	—
572	#127	—	53	16	no	—
573	#126	—	53	32	no	—
574	#126	C₂²×D₅₃	1	16	yes	complemented
575	#125	C₂²×D₅₃	1	8	yes	complemented
576	#124	—	53	32	no	—
577	#124	—	53	32	no	—
578	#124	—	53	32	no	—
579	#124	—	53	16	no	—
580	#124	—	53	16	no	—
581	#124	—	53	16	no	—
582	#124	—	53	16	no	—
583	#124	—	53	16	no	—
584	#124	—	53	16	no	—
585	#124	C₂²×D₅₃	1	8	yes	complemented
586	#123	—	53	32	no	—
587	#123	—	53	32	no	—
588	#123	—	53	32	no	—
589	#123	—	53	32	no	—
590	#123	C₂²×D₅₃	1	16	yes	complemented
591	C₂²⋊Q₈	—	53	16	no	—
592	C₂²⋊Q₈	—	53	32	no	—
593	C₂²⋊Q₈	—	53	32	no	—
594	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
595	#121	—	53	32	no	—
596	#121	—	53	16	no	—
597	#121	—	53	16	no	—
598	#121	—	53	16	no	—
599	#121	—	53	32	no	—
600	#121	—	53	32	no	—
601	#121	—	53	32	no	—
602	#121	—	53	32	no	—
603	#121	C₂²×D₅₃	1	8	yes	—
604	#120	—	53	32	no	—
605	#120	—	53	32	no	—
606	#120	—	53	32	no	—
607	#120	—	53	32	no	—
608	#120	—	53	32	no	—
609	C₄×Q₈	—	53	16	no	—
610	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
611	C₄×D₄	—	53	32	no	—
612	C₄×D₄	—	53	32	no	—
613	C₄×D₄	—	53	16	no	—
614	C₄×D₄	—	53	16	no	—
615	C₄×D₄	—	53	16	no	—
616	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
617	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
618	#117	C₂²×D₅₃	1	16	yes	complemented
619	C₂×C₄⋊C₄	—	53	2	no	—
620	C₂×C₄⋊C₄	—	53	4	no	—
621	C₂×C₄⋊C₄	—	53	2	no	—
622	C₂×C₄⋊C₄	—	53	4	no	—
623	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
627	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	—	53	4	no	—
630	C₂×C₂²⋊C₄	—	53	4	no	—
631	C₂×C₂²⋊C₄	—	53	4	no	—
632	C₂×C₂²⋊C₄	—	53	4	no	—
633	C₂×C₂²⋊C₄	—	53	4	no	—
634	C₂×C₂²⋊C₄	—	53	4	no	—
635	C₂×C₂²⋊C₄	—	53	16	no	—
636	C₂×C₂²⋊C₄	—	53	16	no	—
637	C₂×C₂²⋊C₄	—	53	4	no	—
638	C₂×C₂²⋊C₄	—	53	4	no	—
639	C₂×C₂²⋊C₄	—	53	4	no	—
640	C₂×C₂²⋊C₄	—	53	4	no	—
641	C₂×C₂²⋊C₄	—	53	4	no	—
642	C₂×C₂²⋊C₄	—	53	32	no	—
643	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
648	C₂×C₄²	—	53	4	no	—
649	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
650	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
651	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
652	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
653	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
654	C₂×C₄²	C₂²×D₅₃	1	8	yes	complemented
655	C₂⁴	—	53	4	no	—
656	C₂⁴	—	53	4	no	—
657	C₂⁴	—	53	8	no	—
658	C₂⁴	—	53	16	no	—
659	C₂⁴	—	106	8	no	—
660	C₂⁴	—	212	4	no	—
661	C₂⁴	—	212	8	no	—
662	C₂⁴	—	212	8	no	—
663	C₂⁴	—	212	4	no	—
664	C₂⁴	—	212	8	no	—
665	C₂⁴	C₂³×D₅₃	1	2	yes	—
666	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
667	#41	—	212	32	no	—
668	#41	—	212	32	no	—
669	C₂×Q₈	—	4	2	no	—
670	C₂×Q₈	—	53	8	no	—
671	C₂×Q₈	—	53	8	no	—
672	C₂×Q₈	—	53	8	no	—
673	C₂×Q₈	—	106	8	no	—
674	C₂×Q₈	—	212	4	no	—
675	C₂×Q₈	—	212	4	no	—
676	C₂×Q₈	—	212	16	no	—
677	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
678	C₂×D₄	—	2	8	no	—
679	C₂×D₄	—	4	2	no	—
680	C₂×D₄	—	53	16	no	—
681	C₂×D₄	—	53	16	no	—
682	C₂×D₄	—	53	16	no	—
683	C₂×D₄	—	53	8	no	—
684	C₂×D₄	—	53	8	no	—
685	C₂×D₄	—	53	16	no	—
686	C₂×D₄	—	53	8	no	—
687	C₂×D₄	—	53	8	no	—
688	C₂×D₄	—	53	8	no	—
689	C₂×D₄	—	53	16	no	—
690	C₂×D₄	—	53	16	no	—
691	C₂×D₄	—	106	16	no	—
692	C₂×D₄	—	106	8	no	—
693	C₂×D₄	—	106	8	no	—
694	C₂×D₄	—	212	16	no	—
695	C₂×D₄	—	212	32	no	—
696	C₂×D₄	—	212	4	no	—
697	C₂×D₄	—	212	8	no	—
698	C₂×D₄	—	212	8	no	—
699	C₂×D₄	—	212	4	no	—
700	C₂×D₄	—	212	8	no	—
701	C₂×D₄	—	212	4	no	—
702	C₂×D₄	—	212	8	no	—
703	C₂×D₄	—	212	8	no	—
704	C₂×D₄	—	212	64	no	—
705	C₂×D₄	C₂³×D₅₃	1	8	yes	—
706	C₂×D₄	C₂³×D₅₃	1	4	yes	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	8	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	53	4	no	—
712	C₂²×C₄	—	53	4	no	—
713	C₂²×C₄	—	53	8	no	—
714	C₂²×C₄	—	53	16	no	—
715	C₂²×C₄	—	53	16	no	—
716	C₂²×C₄	—	53	16	no	—
717	C₂²×C₄	—	212	8	no	—
718	C₂²×C₄	—	212	8	no	—
719	C₂²×C₄	—	212	8	no	—
720	C₂²×C₄	—	212	4	no	—
721	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
722	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
723	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
724	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
725	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
726	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
727	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
728	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
729	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
730	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
731	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
732	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
733	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
734	C₄⋊C₄	—	53	8	no	—
735	C₄⋊C₄	—	53	16	no	—
736	C₄⋊C₄	—	53	8	no	—
737	C₄⋊C₄	—	53	16	no	—
738	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
739	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
740	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
741	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
742	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
743	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
744	C₂²⋊C₄	—	53	16	no	—
745	C₂²⋊C₄	—	53	16	no	—
746	C₂²⋊C₄	—	53	16	no	—
747	C₂²⋊C₄	—	53	16	no	—
748	C₂²⋊C₄	—	53	16	no	—
749	C₂²⋊C₄	—	53	16	no	—
750	C₂²⋊C₄	—	53	16	no	—
751	C₂²⋊C₄	—	53	16	no	—
752	C₂²⋊C₄	—	53	16	no	—
753	C₂²⋊C₄	—	53	16	no	—
754	C₂²⋊C₄	—	53	16	no	—
755	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
756	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
757	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
758	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
759	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
760	C₄²	—	53	16	no	—
761	C₄²	C₂³×D₅₃	1	4	yes	—
762	C₄²	C₂³×D₅₃	1	4	yes	—
763	C₄²	C₂³×D₅₃	1	4	yes	—
764	C₄²	C₂³×D₅₃	1	4	yes	—
765	C₄²	C₂³×D₅₃	1	8	yes	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	2	4	no	—
770	C₂³	—	2	4	no	—
771	C₂³	—	53	8	no	—
772	C₂³	—	53	8	no	—
773	C₂³	—	106	16	no	—
774	C₂³	—	106	8	no	—
775	C₂³	—	106	8	no	—
776	C₂³	—	106	8	no	—
777	C₂³	—	106	8	no	—
778	C₂³	—	106	8	no	—
779	C₂³	—	106	8	no	—
780	C₂³	—	424	16	no	—
781	C₂³	—	424	32	no	—
782	C₂³	—	212	8	no	—
783	C₂³	—	212	16	no	—
784	C₂³	—	212	16	no	—
785	C₂³	—	212	8	no	—
786	C₂³	—	212	16	no	—
787	C₂³	#13133263	1	4	yes	—
788	C₂³	C₂⁴×D₅₃	1	4	yes	—
789	C₂³	C₂⁴×D₅₃	1	2	yes	—
790	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
791	Q₈	—	4	4	no	—
792	Q₈	—	106	16	no	—
793	Q₈	—	212	8	no	—
794	Q₈	—	212	8	no	—
795	D₄	—	2	16	no	—
796	D₄	—	4	4	no	—
797	D₄	—	106	32	no	—
798	D₄	—	106	16	no	—
799	D₄	—	106	16	no	—
800	D₄	—	212	8	no	—
801	D₄	—	212	16	no	—
802	D₄	—	212	16	no	—
803	D₄	—	212	8	no	—
804	D₄	—	212	16	no	—
805	D₄	—	212	8	no	—
806	D₄	—	212	16	no	—
807	D₄	—	212	16	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	8	no	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	8	no	—
818	C₂×C₄	—	2	16	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	53	8	no	—
821	C₂×C₄	—	53	8	no	—
822	C₂×C₄	—	106	8	no	—
823	C₂×C₄	—	106	8	no	—
824	C₂×C₄	—	212	16	no	—
825	C₂×C₄	—	212	16	no	—
826	C₂×C₄	—	212	16	no	—
827	C₂×C₄	—	212	8	no	—
828	C₂×C₄	#13133263	1	4	yes	—
829	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
830	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
831	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
832	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
833	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
834	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
835	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
836	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
837	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
838	C₂²	—	2	8	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	2	4	no	—
844	C₂²	—	4	8	no	—
845	C₂²	—	106	8	no	—
846	C₂²	—	106	8	no	—
847	C₂²	—	106	8	no	—
848	C₂²	—	106	8	no	—
849	C₂²	—	106	8	no	—
850	C₂²	—	106	8	no	—
851	C₂²	—	424	16	no	—
852	C₂²	—	424	32	no	—
853	C₂²	—	212	16	no	—
854	C₂²	—	212	16	no	—
855	C₂²	C₂×#13133263	1	4	yes	—
856	C₂²	C₂×#13133263	1	2	yes	—
857	C₂²	C₂×#13133263	1	2	yes	—
858	C₂²	#16811459	1	2	yes	—
859	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
860	C₄	—	2	2	no	—
861	C₄	—	2	4	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	4	no	—
865	C₄	—	2	2	no	—
866	C₄	—	2	2	no	—
867	C₄	—	2	4	no	—
868	C₄	—	106	8	no	—
869	C₄	—	106	8	no	—
870	C₄	C₂×#13133263	1	4	yes	—
871	C₂	—	2	4	no	—
872	C₂	—	4	4	no	—
873	C₂	—	212	8	no	—
874	C₂	—	212	8	no	—
875	C₂	#20289231	1	4	yes	direct product factor
876	C₂	C₂²×#13133263	1	1	yes	characteristic
877	C₂	C₂²×#13133263	1	1	yes	characteristic
878	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×#529	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#529	D₅₃
hypocenter	C₅₃	C₂×#3558
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #20289231	C₂	direct (N × H)
2. C₂×#16811371	C₂	semidirect
3. C₂×#16811365	C₂	semidirect
4. C₂×#16811358	C₂	semidirect
5. C₂×#16811282	C₂	semidirect
6. C₂×#16811269	C₂	semidirect
7. C₂×#16811265	C₂	semidirect
8. C₂×D₄×D₂₁₂	C₂	semidirect
9. C₂×#16811244	C₂	semidirect
10. C₂×#16811213	C₂	semidirect
11. C₂×#16811212	C₂	semidirect
12. C₂×#16811192	C₂	semidirect
13. C₂×#16811181	C₂	semidirect
14. C₂×#16811173	C₂	semidirect
15. C₂²×#13133205	C₂	semidirect
16. C₂×C₅₃×#529	C₂	semidirect
17. C₂²×#11719945	C₂²	semidirect
18. C₂²×#11719945	C₂²	semidirect
19. C₂³×Dic₁₀₆	C₂²	semidirect
21. C₂³×D₂₁₂	C₂²	semidirect
22. C₂²×D₄×D₅₃	C₂²	semidirect
23. #16811371	C₂²	semidirect
24. #16811365	C₂²	semidirect
25. #16811358	C₂²	semidirect
26. #16811282	C₂²	semidirect
27. #16811269	C₂²	semidirect
28. #16811265	C₂²	semidirect
29. D₄×D₂₁₂	C₂²	semidirect
30. #16811244	C₂²	semidirect
31. #16811213	C₂²	semidirect
32. #16811212	C₂²	semidirect
33. #16811192	C₂²	semidirect
34. #16811181	C₂²	semidirect
35. #16811173	C₂²	semidirect
36. C₂×#13133217	C₂²	semidirect
38. C₂×#13133214	C₂²	semidirect
39. C₂×#13133212	C₂²	semidirect
40. C₂×#13133206	C₂²	semidirect
41. C₂×#13133205	C₂²	semidirect
42. C₂×#13133205	C₂²	semidirect
43. C₂×#13133205	C₂²	semidirect
44. C₂×#13133205	C₂²	semidirect
45. C₂×#13133205	C₂²	semidirect
46. C₂×#13133205	C₂²	semidirect
47. C₂×#13133205	C₂²	semidirect
48. C₂×#13133203	C₂²	semidirect
49. C₂×#13133203	C₂²	semidirect
50. C₂×#13133202	C₂²	semidirect
51. C₂×#13133202	C₂²	semidirect
52. C₂×#13133202	C₂²	semidirect
53. C₂×#13133199	C₂²	semidirect
54. C₂×#13133196	C₂²	semidirect
55. C₂×#13133195	C₂²	semidirect
56. C₂×#13133195	C₂²	semidirect
57. C₂×#13133192	C₂²	semidirect
58. C₂×#13133192	C₂²	semidirect
59. C₂×#13133192	C₂²	semidirect
61. C₂×#13133191	C₂²	semidirect
62. C₂×#13133191	C₂²	semidirect
63. C₂×#13133190	C₂²	semidirect
64. C₂×#13133189	C₂²	semidirect
65. C₂×#13133187	C₂²	semidirect
66. C₂×#13133187	C₂²	semidirect
67. C₂×#13133187	C₂²	semidirect
68. C₂×#13133187	C₂²	semidirect
69. C₂×#13133185	C₂²	semidirect
70. C₂×C₄×Dic₁₀₆	C₂²	semidirect
71. C₂×C₄×D₂₁₂	C₂²	semidirect
72. C₂×C₄×D₂₁₂	C₂²	semidirect
73. C₂×C₄×D₂₁₂	C₂²	semidirect
74. C₂×#13133179	C₂²	semidirect
75. C₂×#13133177	C₂²	semidirect
76. C₂²×#11719921	C₂²	semidirect
77. C₂²×#11719921	C₂²	semidirect
78. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
79. C₅₃×#529	C₂²	semidirect
80. C₂×#126×C₅₃	C₂²	semidirect
81. C₂×#125×C₅₃	C₂²	semidirect
82. C₂×#124×C₅₃	C₂²	semidirect
83. C₂×#123×C₅₃	C₂²	semidirect
84. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
86. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
87. C₂×C₄×D₄×C₅₃	C₂²	semidirect
88. C₂×C₄×D₄×C₅₃	C₂²	semidirect
89. C₂×#117×C₅₃	C₂²	semidirect
90. C₂²×C₄²×C₅₃	C₂²	semidirect
95. C₂×#11719945	C₂³	semidirect
96. C₂×#11719945	C₂³	semidirect
101. C₂²×Dic₁₀₆	C₂³	semidirect
113. C₂²×D₂₁₂	C₂³	semidirect
118. C₂×D₄×D₅₃	C₂³	semidirect
123. #13133217	C₂³	semidirect
125. #13133214	C₂³	semidirect
126. #13133212	C₂³	semidirect
127. #13133206	C₂³	semidirect
128. #13133205	C₂³	semidirect
129. #13133205	C₂³	semidirect
130. #13133205	C₂³	semidirect
131. #13133205	C₂³	semidirect
132. #13133205	C₂³	semidirect
133. #13133205	C₂³	semidirect
134. #13133203	C₂³	semidirect
135. #13133203	C₂³	semidirect
136. #13133202	C₂³	semidirect
137. #13133202	C₂³	semidirect
138. #13133202	C₂³	semidirect
139. #13133199	C₂³	semidirect
140. #13133196	C₂³	semidirect
141. #13133195	C₂³	semidirect
142. #13133195	C₂³	semidirect
143. #13133192	C₂³	semidirect
144. #13133192	C₂³	semidirect
145. #13133192	C₂³	semidirect
147. #13133191	C₂³	semidirect
148. #13133191	C₂³	semidirect
149. #13133190	C₂³	semidirect
150. #13133189	C₂³	semidirect
151. #13133187	C₂³	semidirect
152. #13133187	C₂³	semidirect
153. #13133187	C₂³	semidirect
154. #13133187	C₂³	semidirect
155. #13133185	C₂³	semidirect
156. C₄×Dic₁₀₆	C₂³	semidirect
157. C₄×D₂₁₂	C₂³	semidirect
158. C₄×D₂₁₂	C₂³	semidirect
159. C₄×D₂₁₂	C₂³	semidirect
160. #13133179	C₂³	semidirect
161. #13133177	C₂³	semidirect
177. C₂×#11719921	C₂³	semidirect
178. C₂×#11719921	C₂³	semidirect
179. C₂²⋊C₄×D₅₃	C₂³	semidirect
188. #126×C₅₃	C₂³	semidirect
189. #125×C₅₃	C₂³	semidirect
190. #124×C₅₃	C₂³	semidirect
191. #123×C₅₃	C₂³	semidirect
192. C₂²⋊Q₈×C₅₃	C₂³	semidirect
194. C₄×Q₈×C₅₃	C₂³	semidirect
195. C₄×D₄×C₅₃	C₂³	semidirect
196. C₄×D₄×C₅₃	C₂³	semidirect
197. #117×C₅₃	C₂³	semidirect
214. C₂×C₄²×C₅₃	C₂³	semidirect
446. C₂×#529	D₅₃	semidirect
450. C₂×C₅₃	#3558	semidirect
478. #529	C₂×D₅₃	semidirect
480. C₂×#126	C₂×D₅₃	semidirect
481. C₂×#125	C₂×D₅₃	semidirect
492. C₂×#124	C₂×D₅₃	semidirect
497. C₂×#123	C₂×D₅₃	semidirect
501. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
517. C₂×C₄×Q₈	C₂×D₅₃	semidirect
523. C₂×C₄×D₄	C₂×D₅₃	semidirect
524. C₂×C₄×D₄	C₂×D₅₃	semidirect
525. C₂×#117	C₂×D₅₃	semidirect
529. C₂²×C₄²	C₂×D₅₃	semidirect
530. C₅₃	C₂×#3558	semidirect
574. #126	C₂²×D₅₃	semidirect
575. #125	C₂²×D₅₃	semidirect
585. #124	C₂²×D₅₃	semidirect
590. #123	C₂²×D₅₃	semidirect
594. C₂²⋊Q₈	C₂²×D₅₃	semidirect
610. C₄×Q₈	C₂²×D₅₃	semidirect
616. C₄×D₄	C₂²×D₅₃	semidirect
617. C₄×D₄	C₂²×D₅₃	semidirect
618. #117	C₂²×D₅₃	semidirect
654. C₂×C₄²	C₂²×D₅₃	semidirect
875. C₂	#20289231	direct (N × H)

Maximal subgroups

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

subgroup	index
#20289231	2
C₂×#16811371	2
C₂×#16811365	2
C₂×#16811358	2
C₂×#16811282	2
C₂×#16811269	2
C₂×#16811265	2
C₂×D₄×D₂₁₂	2
C₂×#16811244	2
C₂×#16811213	2
C₂×#16811212	2
C₂×#16811192	2
C₂×#16811181	2
C₂×#16811173	2
C₂²×#13133205	2
C₂×C₅₃×#529	2
C₂×#3558	53

Subgroups — C2×#20289231 #28291429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20289231 #28291429