Subgroups — C₂×C₅₃×#2459 #27242174

Order 13568.

3394 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	C₂²×#124×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2459	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#393	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₃×#392	C₂	1	1	yes	maximal, characteristic
8	C₂×C₅₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
20	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×#124×C₅₃	—	2	8	no	—
24	C₂×#124×C₅₃	C₂²	1	8	yes	complemented
25	C₂×C₄×D₄×C₅₃	—	2	8	no	—
26	C₂×C₄×D₄×C₅₃	C₂²	1	8	yes	complemented
27	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
46	C₅₃×#394	C₂²	1	8	yes	complemented
47	C₅₃×#394	C₂²	1	8	yes	complemented
48	C₅₃×#393	C₂²	1	8	yes	complemented
49	C₅₃×#392	C₂²	1	8	yes	—
50	C₅₃×#391	C₂²	1	8	yes	complemented
51	C₅₃×#388	C₂²	1	8	yes	complemented
52	C₅₃×#388	C₂²	1	8	yes	complemented
53	C₅₃×#388	C₂²	1	8	yes	complemented
54	C₅₃×#387	C₂²	1	8	yes	complemented
55	C₅₃×#386	C₂²	1	8	yes	complemented
56	C₅₃×#386	C₂²	1	8	yes	complemented
57	C₅₃×#381	C₂²	1	8	yes	complemented
58	C₄×C₂²⋊C₄×C₅₃	C₂²	1	8	yes	complemented
59	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
61	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
62	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
63	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
66	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
67	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
68	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
69	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
70	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
71	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₅₃	—	2	4	no	—
73	C₂²×Q₈×C₅₃	—	2	4	no	—
74	C₂²×Q₈×C₅₃	—	4	2	no	—
75	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
76	C₂²×D₄×C₅₃	—	2	4	no	—
77	C₂²×D₄×C₅₃	—	2	4	no	—
78	C₂²×D₄×C₅₃	—	2	4	no	—
79	C₂²×D₄×C₅₃	—	2	4	no	—
80	C₂²×D₄×C₅₃	—	2	4	no	—
81	C₂²×D₄×C₅₃	—	2	4	no	—
82	C₂²×D₄×C₅₃	—	4	2	no	—
83	C₂²×D₄×C₅₃	—	4	2	no	—
84	C₂²×D₄×C₅₃	—	4	2	no	—
85	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
86	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
87	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
88	C₂³×C₄×C₅₃	—	2	4	no	—
89	C₂³×C₄×C₅₃	—	2	4	no	—
90	C₂³×C₄×C₅₃	—	2	4	no	—
91	C₂³×C₄×C₅₃	—	2	4	no	—
92	C₂³×C₄×C₅₃	—	4	2	no	—
93	C₂³×C₄×C₅₃	—	4	2	no	—
94	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
102	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
103	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
108	#124×C₅₃	—	2	32	no	—
109	C₄×D₄×C₅₃	—	2	32	no	—
110	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
111	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
112	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
113	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
117	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
118	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
119	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
120	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
121	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
122	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
123	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
124	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
125	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
126	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
127	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
128	C₂×C₂²⋊C₄×C₅₃	D₄	1	8	yes	complemented
129	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
142	C₂×C₄²×C₅₃	—	2	4	no	—
143	C₂×C₄²×C₅₃	—	2	4	no	—
144	C₂×C₄²×C₅₃	—	4	2	no	—
145	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
146	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
147	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
148	#95×C₅₃	C₂³	1	4	yes	—
149	#95×C₅₃	C₂³	1	4	yes	—
150	#95×C₅₃	C₂³	1	4	yes	—
151	#95×C₅₃	C₂³	1	4	yes	—
152	#95×C₅₃	C₂³	1	4	yes	—
153	#95×C₅₃	C₂³	1	4	yes	—
154	#95×C₅₃	C₂³	1	4	yes	—
155	#95×C₅₃	C₂³	1	4	yes	—
156	#95×C₅₃	C₂³	1	4	yes	—
157	#95×C₅₃	C₂³	1	4	yes	—
158	C₂⁴×C₅₃	—	2	2	no	—
159	C₂⁴×C₅₃	—	2	2	no	—
160	C₂⁴×C₅₃	—	2	2	no	—
161	C₂⁴×C₅₃	—	2	2	no	—
162	C₂⁴×C₅₃	—	2	2	no	—
163	C₂⁴×C₅₃	—	2	2	no	—
164	C₂⁴×C₅₃	—	2	2	no	—
165	C₂⁴×C₅₃	—	2	2	no	—
166	C₂⁴×C₅₃	—	2	2	no	—
167	C₂⁴×C₅₃	—	2	2	no	—
168	C₂⁴×C₅₃	—	2	2	no	—
169	C₂⁴×C₅₃	—	2	2	no	—
170	C₂⁴×C₅₃	—	2	2	no	—
171	C₂⁴×C₅₃	—	2	2	no	—
172	C₂⁴×C₅₃	—	2	2	no	—
173	C₂⁴×C₅₃	—	2	2	no	—
174	C₂⁴×C₅₃	—	2	2	no	—
175	C₂⁴×C₅₃	—	2	2	no	—
176	C₂⁴×C₅₃	—	2	2	no	—
177	C₂⁴×C₅₃	C₂×D₄	1	4	yes	—
178	C₂⁴×C₅₃	#41	1	4	yes	—
179	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
180	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
181	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
182	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
183	C₂×Q₈×C₅₃	—	2	8	no	—
184	C₂×Q₈×C₅₃	—	2	8	no	—
185	C₂×Q₈×C₅₃	—	4	4	no	—
186	C₂×Q₈×C₅₃	—	4	16	no	—
187	C₂×D₄×C₅₃	—	2	32	no	—
188	C₂×D₄×C₅₃	—	2	8	no	—
189	C₂×D₄×C₅₃	—	2	8	no	—
190	C₂×D₄×C₅₃	—	2	8	no	—
191	C₂×D₄×C₅₃	—	2	8	no	—
192	C₂×D₄×C₅₃	—	2	8	no	—
193	C₂×D₄×C₅₃	—	2	8	no	—
194	C₂×D₄×C₅₃	—	4	4	no	—
195	C₂×D₄×C₅₃	—	4	4	no	—
196	C₂×D₄×C₅₃	—	4	4	no	—
197	C₂×D₄×C₅₃	—	4	16	no	—
198	C₂×D₄×C₅₃	—	4	16	no	—
199	C₂²×C₄×C₅₃	—	2	2	no	—
200	C₂²×C₄×C₅₃	—	2	2	no	—
201	C₂²×C₄×C₅₃	—	2	2	no	—
202	C₂²×C₄×C₅₃	—	2	2	no	—
203	C₂²×C₄×C₅₃	—	2	2	no	—
204	C₂²×C₄×C₅₃	—	2	2	no	—
205	C₂²×C₄×C₅₃	—	2	2	no	—
206	C₂²×C₄×C₅₃	—	2	2	no	—
207	C₂²×C₄×C₅₃	—	2	2	no	—
208	C₂²×C₄×C₅₃	—	2	2	no	—
209	C₂²×C₄×C₅₃	—	2	2	no	—
210	C₂²×C₄×C₅₃	—	2	2	no	—
211	C₂²×C₄×C₅₃	—	2	2	no	—
212	C₂²×C₄×C₅₃	—	2	8	no	—
213	C₂²×C₄×C₅₃	—	2	2	no	—
214	C₂²×C₄×C₅₃	—	2	2	no	—
215	C₂²×C₄×C₅₃	—	2	2	no	—
216	C₂²×C₄×C₅₃	—	2	2	no	—
217	C₂²×C₄×C₅₃	—	2	2	no	—
218	C₂²×C₄×C₅₃	—	2	2	no	—
219	C₂²×C₄×C₅₃	—	2	2	no	—
220	C₂²×C₄×C₅₃	—	2	2	no	—
221	C₂²×C₄×C₅₃	—	2	2	no	—
222	C₂²×C₄×C₅₃	—	2	2	no	—
223	C₂²×C₄×C₅₃	—	2	2	no	—
224	C₂²×C₄×C₅₃	—	2	2	no	—
225	C₂²×C₄×C₅₃	—	2	2	no	—
226	C₂²×C₄×C₅₃	—	2	2	no	—
227	C₂²×C₄×C₅₃	—	2	2	no	—
228	C₂²×C₄×C₅₃	—	2	2	no	—
229	C₂²×C₄×C₅₃	—	2	2	no	—
230	C₂²×C₄×C₅₃	—	2	2	no	—
231	C₂²×C₄×C₅₃	—	2	8	no	—
232	C₂²×C₄×C₅₃	—	2	8	no	—
233	C₂²×C₄×C₅₃	—	2	8	no	—
234	C₂²×C₄×C₅₃	—	4	4	no	—
235	C₂²×C₄×C₅₃	—	4	4	no	—
236	C₂²×C₄×C₅₃	—	4	16	no	—
237	C₂²×C₄×C₅₃	—	4	16	no	—
238	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₅₃	#41	1	4	yes	—
241	C₂²×C₄×C₅₃	#41	1	4	yes	—
242	C₂²×C₄×C₅₃	#41	1	4	yes	—
243	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₅₃	—	2	8	no	—
256	C₄⋊C₄×C₅₃	—	2	8	no	—
257	C₄⋊C₄×C₅₃	—	4	4	no	—
258	C₂²⋊C₄×C₅₃	—	2	8	no	—
259	C₂²⋊C₄×C₅₃	—	2	8	no	—
260	C₂²⋊C₄×C₅₃	—	2	8	no	—
261	C₂²⋊C₄×C₅₃	—	2	8	no	—
262	C₂²⋊C₄×C₅₃	—	2	8	no	—
263	C₂²⋊C₄×C₅₃	—	2	8	no	—
264	C₂²⋊C₄×C₅₃	—	2	8	no	—
265	C₂²⋊C₄×C₅₃	—	2	8	no	—
266	C₂²⋊C₄×C₅₃	—	4	4	no	—
267	C₂²⋊C₄×C₅₃	—	4	4	no	—
268	C₂²⋊C₄×C₅₃	—	4	4	no	—
269	C₂²⋊C₄×C₅₃	—	4	4	no	—
270	C₂²⋊C₄×C₅₃	C₂×D₄	1	16	yes	complemented
271	C₄²×C₅₃	—	2	8	no	—
272	C₄²×C₅₃	—	2	8	no	—
273	C₄²×C₅₃	—	4	4	no	—
274	C₂³×C₅₃	—	2	8	no	—
275	C₂³×C₅₃	—	2	8	no	—
276	C₂³×C₅₃	—	2	8	no	—
277	C₂³×C₅₃	—	2	8	no	—
278	C₂³×C₅₃	—	2	8	no	—
279	C₂³×C₅₃	—	2	8	no	—
280	C₂³×C₅₃	—	2	2	no	—
281	C₂³×C₅₃	—	2	2	no	—
282	C₂³×C₅₃	—	2	2	no	—
283	C₂³×C₅₃	—	2	2	no	—
284	C₂³×C₅₃	—	2	2	no	—
285	C₂³×C₅₃	—	2	2	no	—
286	C₂³×C₅₃	—	2	2	no	—
287	C₂³×C₅₃	—	2	2	no	—
288	C₂³×C₅₃	—	2	2	no	—
289	C₂³×C₅₃	—	2	2	no	—
290	C₂³×C₅₃	—	2	2	no	—
291	C₂³×C₅₃	—	2	2	no	—
292	C₂³×C₅₃	—	2	2	no	—
293	C₂³×C₅₃	—	2	2	no	—
294	C₂³×C₅₃	—	2	2	no	—
295	C₂³×C₅₃	—	2	2	no	—
296	C₂³×C₅₃	—	2	2	no	—
297	C₂³×C₅₃	—	2	2	no	—
298	C₂³×C₅₃	—	2	2	no	—
299	C₂³×C₅₃	—	4	4	no	—
300	C₂³×C₅₃	—	4	4	no	—
301	C₂³×C₅₃	—	4	4	no	—
302	C₂³×C₅₃	—	4	4	no	—
303	C₂³×C₅₃	—	4	4	no	—
304	C₂³×C₅₃	—	4	4	no	—
305	C₂³×C₅₃	—	4	4	no	—
306	C₂³×C₅₃	—	4	4	no	—
307	C₂³×C₅₃	—	4	4	no	—
308	C₂³×C₅₃	—	4	4	no	—
309	C₂³×C₅₃	—	4	4	no	—
310	C₂³×C₅₃	—	4	4	no	—
311	C₂³×C₅₃	—	4	4	no	—
312	C₂³×C₅₃	—	4	4	no	—
313	C₂³×C₅₃	—	4	4	no	—
314	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
315	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
316	C₂³×C₅₃	C₂×#41	1	4	yes	—
317	C₂³×C₅₃	C₂×#41	1	2	yes	—
318	C₂³×C₅₃	C₂×#41	1	2	yes	—
319	C₂³×C₅₃	C₂×#41	1	2	yes	—
320	C₂³×C₅₃	C₂×#41	1	2	yes	—
321	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
322	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
323	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
324	Q₈×C₅₃	—	4	16	no	—
325	D₄×C₅₃	—	2	32	no	—
326	D₄×C₅₃	—	4	16	no	—
327	D₄×C₅₃	—	4	16	no	—
328	C₂×C₄×C₅₃	—	2	8	no	—
329	C₂×C₄×C₅₃	—	2	8	no	—
330	C₂×C₄×C₅₃	—	2	8	no	—
331	C₂×C₄×C₅₃	—	2	8	no	—
332	C₂×C₄×C₅₃	—	2	8	no	—
333	C₂×C₄×C₅₃	—	2	2	no	—
334	C₂×C₄×C₅₃	—	2	2	no	—
335	C₂×C₄×C₅₃	—	2	2	no	—
336	C₂×C₄×C₅₃	—	2	2	no	—
337	C₂×C₄×C₅₃	—	2	2	no	—
338	C₂×C₄×C₅₃	—	2	2	no	—
339	C₂×C₄×C₅₃	—	2	2	no	—
340	C₂×C₄×C₅₃	—	2	2	no	—
341	C₂×C₄×C₅₃	—	2	2	no	—
342	C₂×C₄×C₅₃	—	2	2	no	—
343	C₂×C₄×C₅₃	—	2	2	no	—
344	C₂×C₄×C₅₃	—	2	2	no	—
345	C₂×C₄×C₅₃	—	2	2	no	—
346	C₂×C₄×C₅₃	—	2	2	no	—
347	C₂×C₄×C₅₃	—	2	2	no	—
348	C₂×C₄×C₅₃	—	2	2	no	—
349	C₂×C₄×C₅₃	—	2	2	no	—
350	C₂×C₄×C₅₃	—	2	2	no	—
351	C₂×C₄×C₅₃	—	2	2	no	—
352	C₂×C₄×C₅₃	—	2	2	no	—
353	C₂×C₄×C₅₃	—	2	2	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	2	no	—
358	C₂×C₄×C₅₃	—	2	2	no	—
359	C₂×C₄×C₅₃	—	2	2	no	—
360	C₂×C₄×C₅₃	—	2	2	no	—
361	C₂×C₄×C₅₃	—	2	2	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	2	no	—
364	C₂×C₄×C₅₃	—	4	16	no	—
365	C₂×C₄×C₅₃	—	4	16	no	—
366	C₂×C₄×C₅₃	—	4	4	no	—
367	C₂×C₄×C₅₃	—	4	4	no	—
368	C₂×C₄×C₅₃	—	4	4	no	—
369	C₂×C₄×C₅₃	—	4	4	no	—
370	C₂×C₄×C₅₃	—	4	4	no	—
371	C₂×C₄×C₅₃	—	4	4	no	—
372	C₂×C₄×C₅₃	—	4	4	no	—
373	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
374	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
375	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
376	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
377	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
378	C₂×#2459	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
379	C₂²×C₅₃	—	2	4	no	—
380	C₂²×C₅₃	—	2	4	no	—
381	C₂²×C₅₃	—	2	4	no	—
382	C₂²×C₅₃	—	2	4	no	—
383	C₂²×C₅₃	—	2	4	no	—
384	C₂²×C₅₃	—	2	4	no	—
385	C₂²×C₅₃	—	4	2	no	—
386	C₂²×C₅₃	—	4	2	no	—
387	C₂²×C₅₃	—	4	2	no	—
388	C₂²×C₅₃	—	4	2	no	—
389	C₂²×C₅₃	—	4	2	no	—
390	C₂²×C₅₃	—	4	2	no	—
391	C₂²×C₅₃	—	4	2	no	—
392	C₂²×C₅₃	—	4	2	no	—
393	C₂²×C₅₃	—	4	16	no	—
394	C₂²×C₅₃	—	4	16	no	—
395	C₂²×C₅₃	—	4	2	no	—
396	C₂²×C₅₃	—	4	2	no	—
397	C₂²×C₅₃	—	4	2	no	—
398	C₂²×C₅₃	—	4	2	no	—
399	C₂²×C₅₃	—	4	2	no	—
400	C₂²×C₅₃	—	4	2	no	—
401	C₂²×C₅₃	—	4	2	no	—
402	C₂²×C₅₃	—	8	8	no	—
403	C₂²×C₅₃	#525	1	4	yes	—
404	C₂²×C₅₃	#529	1	4	yes	—
405	C₂²×C₅₃	#538	1	4	yes	—
406	C₂²×C₅₃	#546	1	4	yes	—
407	C₂²×C₅₃	#546	1	4	yes	—
408	C₂²×C₅₃	#555	1	4	yes	—
409	C₂²×C₅₃	#559	1	4	yes	—
410	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
411	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
412	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
413	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
414	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
415	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
417	C₄×C₅₃	—	2	4	no	—
418	C₄×C₅₃	—	2	4	no	—
419	C₄×C₅₃	—	2	4	no	—
420	C₄×C₅₃	—	2	4	no	—
421	C₄×C₅₃	—	2	4	no	—
422	C₄×C₅₃	—	4	2	no	—
423	C₄×C₅₃	—	4	2	no	—
424	C₄×C₅₃	—	4	2	no	—
425	C₄×C₅₃	—	4	2	no	—
426	C₄×C₅₃	—	4	2	no	—
427	C₄×C₅₃	—	4	2	no	—
428	C₄×C₅₃	—	4	2	no	—
429	C₂²×#124	C₂×C₅₃	1	1	yes	characteristic, complemented
430	C₂²×C₄×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
431	#2459	C₂×C₅₃	1	16	yes	direct product factor
432	C₂×#394	C₂×C₅₃	1	1	yes	characteristic, complemented
433	C₂×#394	C₂×C₅₃	1	1	yes	characteristic, complemented
434	C₂×#393	C₂×C₅₃	1	1	yes	characteristic, complemented
435	C₂×#392	C₂×C₅₃	1	1	yes	characteristic
436	C₂×#391	C₂×C₅₃	1	1	yes	characteristic, complemented
437	C₂×#388	C₂×C₅₃	1	1	yes	characteristic, complemented
438	C₂×#388	C₂×C₅₃	1	1	yes	characteristic, complemented
439	C₂×#388	C₂×C₅₃	1	1	yes	characteristic, complemented
440	C₂×#387	C₂×C₅₃	1	1	yes	characteristic, complemented
441	C₂×#386	C₂×C₅₃	1	1	yes	characteristic, complemented
442	C₂×#386	C₂×C₅₃	1	1	yes	characteristic, complemented
443	C₂×#381	C₂×C₅₃	1	1	yes	characteristic, complemented
444	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
445	C₂×C₅₃	—	4	4	no	—
446	C₂×C₅₃	—	4	4	no	—
447	C₂×C₅₃	—	8	2	no	—
448	C₂×C₅₃	#2459	1	8	yes	direct product factor
449	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
450	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
451	C₂×C₅₃	C₂×#538	1	1	yes	characteristic
452	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
453	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
454	C₂×C₅₃	C₂×#555	1	1	yes	characteristic
455	C₂×C₅₃	C₂×#559	1	1	yes	characteristic
456	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic
457	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
458	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
459	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
460	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
461	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
462	C₂×#124	—	2	8	no	—
463	C₂×#124	C₂²×C₅₃	1	8	yes	complemented
464	C₂×C₄×D₄	—	2	8	no	—
465	C₂×C₄×D₄	C₂²×C₅₃	1	8	yes	complemented
466	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
467	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
468	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
469	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
470	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
471	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
472	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
473	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
474	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
475	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
476	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
477	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
478	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
479	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
480	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
481	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
482	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
483	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
484	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
485	#394	C₂²×C₅₃	1	8	yes	complemented
486	#394	C₂²×C₅₃	1	8	yes	complemented
487	#393	C₂²×C₅₃	1	8	yes	complemented
488	#392	C₂²×C₅₃	1	8	yes	—
489	#391	C₂²×C₅₃	1	8	yes	complemented
490	#388	C₂²×C₅₃	1	8	yes	complemented
491	#388	C₂²×C₅₃	1	8	yes	complemented
492	#388	C₂²×C₅₃	1	8	yes	complemented
493	#387	C₂²×C₅₃	1	8	yes	complemented
494	#386	C₂²×C₅₃	1	8	yes	complemented
495	#386	C₂²×C₅₃	1	8	yes	complemented
496	#381	C₂²×C₅₃	1	8	yes	complemented
497	C₄×C₂²⋊C₄	C₂²×C₅₃	1	8	yes	complemented
498	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
499	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
500	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
501	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
502	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
503	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
504	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
505	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
506	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
507	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
508	C₅₃	C₂×#2459	1	1	yes	characteristic, direct product factor, Sylow
509	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
510	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
511	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
512	C₂²×Q₈	—	2	4	no	—
513	C₂²×Q₈	—	2	4	no	—
514	C₂²×Q₈	—	4	2	no	—
515	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
516	C₂²×D₄	—	2	4	no	—
517	C₂²×D₄	—	2	4	no	—
518	C₂²×D₄	—	2	4	no	—
519	C₂²×D₄	—	2	4	no	—
520	C₂²×D₄	—	2	4	no	—
521	C₂²×D₄	—	2	4	no	—
522	C₂²×D₄	—	4	2	no	—
523	C₂²×D₄	—	4	2	no	—
524	C₂²×D₄	—	4	2	no	—
525	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
526	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
527	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
528	C₂³×C₄	—	2	4	no	—
529	C₂³×C₄	—	2	4	no	—
530	C₂³×C₄	—	2	4	no	—
531	C₂³×C₄	—	2	4	no	—
532	C₂³×C₄	—	4	2	no	—
533	C₂³×C₄	—	4	2	no	—
534	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
542	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
543	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
548	#124	—	2	32	no	—
549	C₄×D₄	—	2	32	no	—
550	C₂×C₄⋊C₄	—	2	4	no	—
551	C₂×C₄⋊C₄	—	2	4	no	—
552	C₂×C₄⋊C₄	—	4	2	no	—
553	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
554	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
555	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
556	C₂×C₂²⋊C₄	—	2	4	no	—
557	C₂×C₂²⋊C₄	—	2	4	no	—
558	C₂×C₂²⋊C₄	—	2	4	no	—
559	C₂×C₂²⋊C₄	—	2	4	no	—
560	C₂×C₂²⋊C₄	—	2	4	no	—
561	C₂×C₂²⋊C₄	—	2	4	no	—
562	C₂×C₂²⋊C₄	—	2	4	no	—
563	C₂×C₂²⋊C₄	—	2	4	no	—
564	C₂×C₂²⋊C₄	—	4	2	no	—
565	C₂×C₂²⋊C₄	—	4	2	no	—
566	C₂×C₂²⋊C₄	—	4	2	no	—
567	C₂×C₂²⋊C₄	—	4	2	no	—
568	C₂×C₂²⋊C₄	D₄×C₅₃	1	8	yes	complemented
569	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
582	C₂×C₄²	—	2	4	no	—
583	C₂×C₄²	—	2	4	no	—
584	C₂×C₄²	—	4	2	no	—
585	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
586	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
587	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
588	#95	C₂³×C₅₃	1	4	yes	—
589	#95	C₂³×C₅₃	1	4	yes	—
590	#95	C₂³×C₅₃	1	4	yes	—
591	#95	C₂³×C₅₃	1	4	yes	—
592	#95	C₂³×C₅₃	1	4	yes	—
593	#95	C₂³×C₅₃	1	4	yes	—
594	#95	C₂³×C₅₃	1	4	yes	—
595	#95	C₂³×C₅₃	1	4	yes	—
596	#95	C₂³×C₅₃	1	4	yes	—
597	#95	C₂³×C₅₃	1	4	yes	—
598	C₂⁴	—	2	2	no	—
599	C₂⁴	—	2	2	no	—
600	C₂⁴	—	2	2	no	—
601	C₂⁴	—	2	2	no	—
602	C₂⁴	—	2	2	no	—
603	C₂⁴	—	2	2	no	—
604	C₂⁴	—	2	2	no	—
605	C₂⁴	—	2	2	no	—
606	C₂⁴	—	2	2	no	—
607	C₂⁴	—	2	2	no	—
608	C₂⁴	—	2	2	no	—
609	C₂⁴	—	2	2	no	—
610	C₂⁴	—	2	2	no	—
611	C₂⁴	—	2	2	no	—
612	C₂⁴	—	2	2	no	—
613	C₂⁴	—	2	2	no	—
614	C₂⁴	—	2	2	no	—
615	C₂⁴	—	2	2	no	—
616	C₂⁴	—	2	2	no	—
617	C₂⁴	C₂×D₄×C₅₃	1	4	yes	—
618	C₂⁴	#41×C₅₃	1	4	yes	—
619	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
620	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
621	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
622	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
623	C₂×Q₈	—	2	8	no	—
624	C₂×Q₈	—	2	8	no	—
625	C₂×Q₈	—	4	4	no	—
626	C₂×Q₈	—	4	16	no	—
627	C₂×D₄	—	2	32	no	—
628	C₂×D₄	—	2	8	no	—
629	C₂×D₄	—	2	8	no	—
630	C₂×D₄	—	2	8	no	—
631	C₂×D₄	—	2	8	no	—
632	C₂×D₄	—	2	8	no	—
633	C₂×D₄	—	2	8	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	4	4	no	—
637	C₂×D₄	—	4	16	no	—
638	C₂×D₄	—	4	16	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	8	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	8	no	—
672	C₂²×C₄	—	2	8	no	—
673	C₂²×C₄	—	2	8	no	—
674	C₂²×C₄	—	4	4	no	—
675	C₂²×C₄	—	4	4	no	—
676	C₂²×C₄	—	4	16	no	—
677	C₂²×C₄	—	4	16	no	—
678	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
679	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
680	C₂²×C₄	#41×C₅₃	1	4	yes	—
681	C₂²×C₄	#41×C₅₃	1	4	yes	—
682	C₂²×C₄	#41×C₅₃	1	4	yes	—
683	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
695	C₄⋊C₄	—	2	8	no	—
696	C₄⋊C₄	—	2	8	no	—
697	C₄⋊C₄	—	4	4	no	—
698	C₂²⋊C₄	—	2	8	no	—
699	C₂²⋊C₄	—	2	8	no	—
700	C₂²⋊C₄	—	2	8	no	—
701	C₂²⋊C₄	—	2	8	no	—
702	C₂²⋊C₄	—	2	8	no	—
703	C₂²⋊C₄	—	2	8	no	—
704	C₂²⋊C₄	—	2	8	no	—
705	C₂²⋊C₄	—	2	8	no	—
706	C₂²⋊C₄	—	4	4	no	—
707	C₂²⋊C₄	—	4	4	no	—
708	C₂²⋊C₄	—	4	4	no	—
709	C₂²⋊C₄	—	4	4	no	—
710	C₂²⋊C₄	C₂×D₄×C₅₃	1	16	yes	complemented
711	C₄²	—	2	8	no	—
712	C₄²	—	2	8	no	—
713	C₄²	—	4	4	no	—
714	C₂³	—	2	8	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	2	8	no	—
717	C₂³	—	2	8	no	—
718	C₂³	—	2	8	no	—
719	C₂³	—	2	8	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	4	4	no	—
740	C₂³	—	4	4	no	—
741	C₂³	—	4	4	no	—
742	C₂³	—	4	4	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	4	no	—
745	C₂³	—	4	4	no	—
746	C₂³	—	4	4	no	—
747	C₂³	—	4	4	no	—
748	C₂³	—	4	4	no	—
749	C₂³	—	4	4	no	—
750	C₂³	—	4	4	no	—
751	C₂³	—	4	4	no	—
752	C₂³	—	4	4	no	—
753	C₂³	—	4	4	no	—
754	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
755	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
756	C₂³	C₂×#41×C₅₃	1	4	yes	—
757	C₂³	C₂×#41×C₅₃	1	2	yes	—
758	C₂³	C₂×#41×C₅₃	1	2	yes	—
759	C₂³	C₂×#41×C₅₃	1	2	yes	—
760	C₂³	C₂×#41×C₅₃	1	2	yes	—
761	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
762	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
763	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
764	Q₈	—	4	16	no	—
765	D₄	—	2	32	no	—
766	D₄	—	4	16	no	—
767	D₄	—	4	16	no	—
768	C₂×C₄	—	2	8	no	—
769	C₂×C₄	—	2	8	no	—
770	C₂×C₄	—	2	8	no	—
771	C₂×C₄	—	2	8	no	—
772	C₂×C₄	—	2	8	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	4	16	no	—
805	C₂×C₄	—	4	16	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
814	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
815	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
816	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
817	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
818	C₂²	—	2	4	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	16	no	—
832	C₂²	—	4	16	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	8	8	no	—
842	C₂²	C₅₃×#525	1	4	yes	—
843	C₂²	C₅₃×#529	1	4	yes	—
844	C₂²	C₅₃×#538	1	4	yes	—
845	C₂²	C₅₃×#546	1	4	yes	—
846	C₂²	C₅₃×#546	1	4	yes	—
847	C₂²	C₅₃×#555	1	4	yes	—
848	C₂²	C₅₃×#559	1	4	yes	—
849	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
850	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
851	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
852	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
853	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
854	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
855	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
856	C₄	—	2	4	no	—
857	C₄	—	2	4	no	—
858	C₄	—	2	4	no	—
859	C₄	—	2	4	no	—
860	C₄	—	2	4	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₂	—	4	4	no	—
869	C₂	—	4	4	no	—
870	C₂	—	8	2	no	—
871	C₂	C₅₃×#2459	1	8	yes	direct product factor
872	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
873	C₂	C₂×C₅₃×#529	1	1	yes	characteristic
874	C₂	C₂×C₅₃×#538	1	1	yes	characteristic
875	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
876	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
877	C₂	C₂×C₅₃×#555	1	1	yes	characteristic
878	C₂	C₂×C₅₃×#559	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂×C₅₃×#392	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#124×C₅₃	C₂	semidirect
2. C₂²×C₄×D₄×C₅₃	C₂	semidirect
3. C₅₃×#2459	C₂	direct (N × H)
4. C₂×C₅₃×#394	C₂	semidirect
5. C₂×C₅₃×#394	C₂	semidirect
6. C₂×C₅₃×#393	C₂	semidirect
8. C₂×C₅₃×#391	C₂	semidirect
9. C₂×C₅₃×#388	C₂	semidirect
10. C₂×C₅₃×#388	C₂	semidirect
11. C₂×C₅₃×#388	C₂	semidirect
12. C₂×C₅₃×#387	C₂	semidirect
13. C₂×C₅₃×#386	C₂	semidirect
14. C₂×C₅₃×#386	C₂	semidirect
15. C₂×C₅₃×#381	C₂	semidirect
16. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
24. C₂×#124×C₅₃	C₂²	semidirect
26. C₂×C₄×D₄×C₅₃	C₂²	semidirect
46. C₅₃×#394	C₂²	semidirect
47. C₅₃×#394	C₂²	semidirect
48. C₅₃×#393	C₂²	semidirect
50. C₅₃×#391	C₂²	semidirect
51. C₅₃×#388	C₂²	semidirect
52. C₅₃×#388	C₂²	semidirect
53. C₅₃×#388	C₂²	semidirect
54. C₅₃×#387	C₂²	semidirect
55. C₅₃×#386	C₂²	semidirect
56. C₅₃×#386	C₂²	semidirect
57. C₅₃×#381	C₂²	semidirect
58. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
128. C₂×C₂²⋊C₄×C₅₃	D₄	semidirect
270. C₂²⋊C₄×C₅₃	C₂×D₄	semidirect
378. C₂×#2459	C₅₃	direct (N × H)
429. C₂²×#124	C₂×C₅₃	semidirect
430. C₂²×C₄×D₄	C₂×C₅₃	semidirect
431. #2459	C₂×C₅₃	direct (N × H)
432. C₂×#394	C₂×C₅₃	semidirect
433. C₂×#394	C₂×C₅₃	semidirect
434. C₂×#393	C₂×C₅₃	semidirect
436. C₂×#391	C₂×C₅₃	semidirect
437. C₂×#388	C₂×C₅₃	semidirect
438. C₂×#388	C₂×C₅₃	semidirect
439. C₂×#388	C₂×C₅₃	semidirect
440. C₂×#387	C₂×C₅₃	semidirect
441. C₂×#386	C₂×C₅₃	semidirect
442. C₂×#386	C₂×C₅₃	semidirect
443. C₂×#381	C₂×C₅₃	semidirect
444. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
448. C₂×C₅₃	#2459	direct (N × H)
463. C₂×#124	C₂²×C₅₃	semidirect
465. C₂×C₄×D₄	C₂²×C₅₃	semidirect
485. #394	C₂²×C₅₃	semidirect
486. #394	C₂²×C₅₃	semidirect
487. #393	C₂²×C₅₃	semidirect
489. #391	C₂²×C₅₃	semidirect
490. #388	C₂²×C₅₃	semidirect
491. #388	C₂²×C₅₃	semidirect
492. #388	C₂²×C₅₃	semidirect
493. #387	C₂²×C₅₃	semidirect
494. #386	C₂²×C₅₃	semidirect
495. #386	C₂²×C₅₃	semidirect
496. #381	C₂²×C₅₃	semidirect
497. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
508. C₅₃	C₂×#2459	direct (N × H)
568. C₂×C₂²⋊C₄	D₄×C₅₃	semidirect
710. C₂²⋊C₄	C₂×D₄×C₅₃	semidirect
871. C₂	C₅₃×#2459	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₅₃	2
C₂²×C₄×D₄×C₅₃	2
C₅₃×#2459	2
C₂×C₅₃×#394	2
C₂×C₅₃×#393	2
C₂×C₅₃×#392	2
C₂×C₅₃×#391	2
C₂×C₅₃×#388	2
C₂×C₅₃×#387	2
C₂×C₅₃×#386	2
C₂×C₅₃×#381	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
C₂×#2459	53

Subgroups — C2×C53×#2459 #27242174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#2459 #27242174