Subgroups — C₂×C₅₃×#3318 #27268640

Order 13568.

2642 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	C₂×C₅₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3318	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#102×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₄×C₅₃	—	2	1	no	—
18	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₅₃×#553	—	2	4	no	—
26	C₅₃×#553	C₂²	1	8	yes	complemented
27	D₄²×C₅₃	—	2	4	no	—
28	D₄²×C₅₃	C₂²	1	8	yes	complemented
29	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#126×C₅₃	—	2	1	no	—
31	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#123×C₅₃	—	2	1	no	—
33	C₂×#121×C₅₃	—	2	1	no	—
34	C₂×#121×C₅₃	—	2	1	no	—
35	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×#120×C₅₃	—	2	1	no	—
40	C₂×#120×C₅₃	—	2	1	no	—
41	C₂×C₄×D₄×C₅₃	—	2	1	no	—
42	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#490	C₂²	1	8	yes	complemented
48	C₅₃×#482	C₂²	1	8	yes	complemented
49	C₅₃×#481	C₂²	1	8	yes	complemented
50	C₅₃×#478	C₂²	1	8	yes	complemented
51	C₅₃×#469	C₂²	1	8	yes	complemented
52	C₅₃×#466	C₂²	1	8	yes	complemented
53	C₅₃×#459	C₂²	1	8	yes	complemented
54	C₅₃×#447	C₂²	1	8	yes	complemented
55	C₅₃×#447	C₂²	1	8	yes	complemented
56	C₅₃×#442	C₂²	1	8	yes	complemented
57	C₅₃×#435	C₂²	1	8	yes	complemented
58	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#418	C₂²	1	8	yes	complemented
63	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
66	C₂×#102×C₅₃	C₂²	1	8	yes	complemented
67	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
69	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
70	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
71	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
72	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
73	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₅₃	—	2	1	no	—
78	C₂⁵×C₅₃	—	2	1	no	—
79	C₂²×D₄×C₅₃	—	2	4	no	—
80	C₂²×D₄×C₅₃	—	2	4	no	—
81	C₂²×D₄×C₅₃	—	2	1	no	—
82	C₂²×D₄×C₅₃	—	2	1	no	—
83	C₂²×D₄×C₅₃	—	2	1	no	—
84	C₂²×D₄×C₅₃	—	2	1	no	—
85	C₂²×D₄×C₅₃	—	2	8	no	—
86	C₂²×D₄×C₅₃	—	2	1	no	—
87	C₂²×D₄×C₅₃	—	2	1	no	—
88	C₂²×D₄×C₅₃	—	2	1	no	—
89	C₂²×D₄×C₅₃	—	2	2	no	—
90	C₂²×D₄×C₅₃	—	2	2	no	—
91	C₂²×D₄×C₅₃	—	2	1	no	—
92	C₂²×D₄×C₅₃	—	4	2	no	—
93	C₂²×D₄×C₅₃	—	4	2	no	—
94	C₂²×D₄×C₅₃	—	4	8	no	—
95	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
96	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
100	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
101	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₅₃	—	2	1	no	—
103	C₂³×C₄×C₅₃	—	2	1	no	—
104	C₂³×C₄×C₅₃	—	2	1	no	—
105	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
107	C₂×D₈×C₅₃	—	2	4	no	—
108	C₂×D₈×C₅₃	—	4	2	no	—
109	C₂×D₈×C₅₃	—	4	2	no	—
110	C₂×D₈×C₅₃	C₂³	1	4	yes	—
111	C₂×D₈×C₅₃	C₂³	1	4	yes	complemented
112	C₂×D₈×C₅₃	C₂³	1	4	yes	complemented
113	C₂×M₁₆×C₅₃	—	4	2	no	—
114	C₂×M₁₆×C₅₃	C₂³	1	4	yes	complemented
115	C₂²×C₈×C₅₃	—	4	2	no	—
116	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₅₃	C₂³	1	4	yes	complemented
121	#127×C₅₃	—	2	2	no	—
122	#127×C₅₃	C₂³	1	4	yes	—
123	#126×C₅₃	—	2	8	no	—
124	#125×C₅₃	—	2	2	no	—
125	#125×C₅₃	C₂³	1	4	yes	complemented
126	#123×C₅₃	—	2	8	no	—
127	#121×C₅₃	—	2	8	no	—
128	#121×C₅₃	—	2	8	no	—
129	#121×C₅₃	—	2	2	no	—
130	#121×C₅₃	—	2	2	no	—
131	#121×C₅₃	—	2	2	no	—
132	#121×C₅₃	—	2	2	no	—
133	#121×C₅₃	C₂³	1	4	yes	—
134	#121×C₅₃	C₂³	1	4	yes	—
135	#121×C₅₃	C₂³	1	4	yes	complemented
136	#121×C₅₃	C₂³	1	4	yes	complemented
137	#120×C₅₃	—	2	8	no	—
138	#120×C₅₃	—	2	8	no	—
139	C₄×D₄×C₅₃	—	2	8	no	—
140	C₄×D₄×C₅₃	—	2	2	no	—
141	C₄×D₄×C₅₃	—	2	2	no	—
142	C₄×D₄×C₅₃	D₄	1	4	yes	—
143	C₄×D₄×C₅₃	C₂³	1	4	yes	—
144	C₄×D₄×C₅₃	C₂³	1	4	yes	—
145	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
146	#117×C₅₃	—	2	2	no	—
147	#117×C₅₃	C₂³	1	4	yes	complemented
148	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
149	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
150	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
151	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
152	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
158	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
164	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
165	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
167	C₂×C₄²×C₅₃	—	2	1	no	—
168	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
169	#107×C₅₃	C₂³	1	4	yes	complemented
170	#106×C₅₃	C₂³	1	4	yes	complemented
171	#106×C₅₃	C₂³	1	4	yes	complemented
172	C₄⋊C₈×C₅₃	C₂³	1	4	yes	complemented
173	#102×C₅₃	C₂³	1	4	yes	—
174	#102×C₅₃	C₂³	1	4	yes	—
175	#102×C₅₃	C₂³	1	4	yes	—
176	#102×C₅₃	C₂³	1	4	yes	complemented
177	#102×C₅₃	C₂³	1	4	yes	complemented
178	#102×C₅₃	C₂³	1	4	yes	complemented
179	#102×C₅₃	C₂³	1	4	yes	complemented
180	#102×C₅₃	C₂³	1	4	yes	complemented
181	#102×C₅₃	C₂³	1	4	yes	complemented
182	#102×C₅₃	C₂³	1	4	yes	complemented
183	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
184	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
185	#97×C₅₃	C₂³	1	4	yes	complemented
186	C₂⁴×C₅₃	—	2	1	no	—
187	C₂⁴×C₅₃	—	2	1	no	—
188	C₂⁴×C₅₃	—	2	1	no	—
189	C₂⁴×C₅₃	—	2	1	no	—
190	C₂⁴×C₅₃	—	2	4	no	—
191	C₂⁴×C₅₃	—	2	4	no	—
192	C₂⁴×C₅₃	—	4	4	no	—
193	C₂⁴×C₅₃	—	4	4	no	—
194	C₂⁴×C₅₃	—	4	4	no	—
195	C₂⁴×C₅₃	—	4	4	no	—
196	C₂⁴×C₅₃	—	8	2	no	—
197	C₂⁴×C₅₃	—	8	2	no	—
198	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
199	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
200	C₂×D₄×C₅₃	—	2	4	no	—
201	C₂×D₄×C₅₃	—	2	8	no	—
202	C₂×D₄×C₅₃	—	2	8	no	—
203	C₂×D₄×C₅₃	—	2	4	no	—
204	C₂×D₄×C₅₃	—	2	4	no	—
205	C₂×D₄×C₅₃	—	2	4	no	—
206	C₂×D₄×C₅₃	—	2	4	no	—
207	C₂×D₄×C₅₃	—	2	1	no	—
208	C₂×D₄×C₅₃	—	2	1	no	—
209	C₂×D₄×C₅₃	—	2	4	no	—
210	C₂×D₄×C₅₃	—	2	4	no	—
211	C₂×D₄×C₅₃	—	2	1	no	—
212	C₂×D₄×C₅₃	—	2	1	no	—
213	C₂×D₄×C₅₃	—	2	4	no	—
214	C₂×D₄×C₅₃	—	2	4	no	—
215	C₂×D₄×C₅₃	—	2	2	no	—
216	C₂×D₄×C₅₃	—	2	2	no	—
217	C₂×D₄×C₅₃	—	2	2	no	—
218	C₂×D₄×C₅₃	—	2	2	no	—
219	C₂×D₄×C₅₃	—	2	2	no	—
220	C₂×D₄×C₅₃	—	2	2	no	—
221	C₂×D₄×C₅₃	—	2	2	no	—
222	C₂×D₄×C₅₃	—	4	4	no	—
223	C₂×D₄×C₅₃	—	4	4	no	—
224	C₂×D₄×C₅₃	—	4	8	no	—
225	C₂×D₄×C₅₃	—	4	8	no	—
226	C₂×D₄×C₅₃	—	4	4	no	—
227	C₂×D₄×C₅₃	—	4	4	no	—
228	C₂×D₄×C₅₃	—	4	4	no	—
229	C₂×D₄×C₅₃	—	4	32	no	—
230	C₂×D₄×C₅₃	—	4	4	no	—
231	C₂×D₄×C₅₃	—	4	4	no	—
232	C₂×D₄×C₅₃	—	4	4	no	—
233	C₂×D₄×C₅₃	—	8	2	no	—
234	C₂×D₄×C₅₃	—	8	2	no	—
235	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
236	C₂×D₄×C₅₃	#41	1	4	yes	—
237	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
238	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₅₃	—	2	2	no	—
242	C₂²×C₄×C₅₃	—	2	2	no	—
243	C₂²×C₄×C₅₃	—	2	2	no	—
244	C₂²×C₄×C₅₃	—	2	2	no	—
245	C₂²×C₄×C₅₃	—	2	1	no	—
246	C₂²×C₄×C₅₃	—	2	1	no	—
247	C₂²×C₄×C₅₃	—	2	1	no	—
248	C₂²×C₄×C₅₃	—	2	1	no	—
249	C₂²×C₄×C₅₃	—	2	4	no	—
250	C₂²×C₄×C₅₃	—	2	4	no	—
251	C₂²×C₄×C₅₃	—	2	4	no	—
252	C₂²×C₄×C₅₃	—	4	4	no	—
253	C₂²×C₄×C₅₃	—	8	2	no	—
254	C₂²×C₄×C₅₃	—	8	2	no	—
255	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
256	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
264	D₈×C₅₃	—	2	8	no	—
265	D₈×C₅₃	—	4	4	no	—
266	D₈×C₅₃	—	4	4	no	—
267	M₁₆×C₅₃	—	4	4	no	—
268	C₂×C₈×C₅₃	—	2	2	no	—
269	C₂×C₈×C₅₃	—	2	2	no	—
270	C₂×C₈×C₅₃	—	2	2	no	—
271	C₂×C₈×C₅₃	—	2	2	no	—
272	C₂×C₈×C₅₃	—	4	4	no	—
273	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
274	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₅₃	—	2	1	no	—
278	C₄⋊C₄×C₅₃	—	2	1	no	—
279	C₄⋊C₄×C₅₃	—	2	4	no	—
280	C₄⋊C₄×C₅₃	—	2	4	no	—
281	C₄⋊C₄×C₅₃	—	2	4	no	—
282	C₄⋊C₄×C₅₃	—	2	1	no	—
283	C₄⋊C₄×C₅₃	—	2	1	no	—
284	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
285	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
289	C₂²⋊C₄×C₅₃	—	2	4	no	—
290	C₂²⋊C₄×C₅₃	—	2	4	no	—
291	C₂²⋊C₄×C₅₃	—	2	4	no	—
292	C₂²⋊C₄×C₅₃	—	2	4	no	—
293	C₂²⋊C₄×C₅₃	—	2	4	no	—
294	C₂²⋊C₄×C₅₃	—	2	4	no	—
295	C₂²⋊C₄×C₅₃	—	2	4	no	—
296	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
297	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
298	C₄²×C₅₃	—	2	4	no	—
299	C₄²×C₅₃	C₂×D₄	1	2	yes	—
300	C₄²×C₅₃	C₂⁴	1	2	yes	—
301	C₂³×C₅₃	—	2	2	no	—
302	C₂³×C₅₃	—	2	2	no	—
303	C₂³×C₅₃	—	2	2	no	—
304	C₂³×C₅₃	—	2	4	no	—
305	C₂³×C₅₃	—	2	2	no	—
306	C₂³×C₅₃	—	2	2	no	—
307	C₂³×C₅₃	—	2	2	no	—
308	C₂³×C₅₃	—	2	2	no	—
309	C₂³×C₅₃	—	2	2	no	—
310	C₂³×C₅₃	—	2	2	no	—
311	C₂³×C₅₃	—	4	8	no	—
312	C₂³×C₅₃	—	4	8	no	—
313	C₂³×C₅₃	—	4	8	no	—
314	C₂³×C₅₃	—	4	2	no	—
315	C₂³×C₅₃	—	4	2	no	—
316	C₂³×C₅₃	—	4	2	no	—
317	C₂³×C₅₃	—	4	2	no	—
318	C₂³×C₅₃	—	4	2	no	—
319	C₂³×C₅₃	—	4	8	no	—
320	C₂³×C₅₃	—	4	2	no	—
321	C₂³×C₅₃	—	4	2	no	—
322	C₂³×C₅₃	—	4	2	no	—
323	C₂³×C₅₃	—	4	2	no	—
324	C₂³×C₅₃	—	4	2	no	—
325	C₂³×C₅₃	—	4	2	no	—
326	C₂³×C₅₃	—	8	4	no	—
327	C₂³×C₅₃	—	8	4	no	—
328	C₂³×C₅₃	—	8	16	no	—
329	C₂³×C₅₃	—	8	16	no	—
330	C₂³×C₅₃	AGL(1,ℤ/8)	1	4	yes	—
331	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
332	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
333	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
334	D₄×C₅₃	—	2	8	no	—
335	D₄×C₅₃	—	2	4	no	—
336	D₄×C₅₃	—	2	2	no	—
337	D₄×C₅₃	—	2	2	no	—
338	D₄×C₅₃	—	2	2	no	—
339	D₄×C₅₃	—	2	2	no	—
340	D₄×C₅₃	—	2	2	no	—
341	D₄×C₅₃	—	2	2	no	—
342	D₄×C₅₃	—	2	2	no	—
343	D₄×C₅₃	—	4	8	no	—
344	D₄×C₅₃	—	4	8	no	—
345	D₄×C₅₃	—	4	8	no	—
346	D₄×C₅₃	—	4	8	no	—
347	D₄×C₅₃	—	4	8	no	—
348	D₄×C₅₃	—	4	8	no	—
349	D₄×C₅₃	—	4	2	no	—
350	D₄×C₅₃	—	4	2	no	—
351	D₄×C₅₃	—	4	2	no	—
352	D₄×C₅₃	—	8	4	no	—
353	D₄×C₅₃	—	8	4	no	—
354	D₄×C₅₃	C₂×#41	1	4	yes	—
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	4	no	—
360	C₂×C₄×C₅₃	—	2	4	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	—	2	2	no	—
365	C₂×C₄×C₅₃	—	2	2	no	—
366	C₂×C₄×C₅₃	—	2	2	no	—
367	C₂×C₄×C₅₃	—	2	2	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	4	8	no	—
370	C₂×C₄×C₅₃	—	4	2	no	—
371	C₂×C₄×C₅₃	—	4	2	no	—
372	C₂×C₄×C₅₃	—	4	2	no	—
373	C₂×C₄×C₅₃	—	4	2	no	—
374	C₂×C₄×C₅₃	—	8	4	no	—
375	C₂×C₄×C₅₃	—	8	4	no	—
376	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
382	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
383	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
384	C₈×C₅₃	—	2	2	no	—
385	C₈×C₅₃	—	2	2	no	—
386	C₈×C₅₃	—	2	2	no	—
387	C₈×C₅₃	—	2	2	no	—
388	C₂×#3318	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
389	C₂²×C₅₃	—	2	2	no	—
390	C₂²×C₅₃	—	2	8	no	—
391	C₂²×C₅₃	—	2	2	no	—
392	C₂²×C₅₃	—	2	2	no	—
393	C₂²×C₅₃	—	2	4	no	—
394	C₂²×C₅₃	—	2	2	no	—
395	C₂²×C₅₃	—	2	2	no	—
396	C₂²×C₅₃	—	4	4	no	—
397	C₂²×C₅₃	—	4	8	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	—	4	2	no	—
403	C₂²×C₅₃	—	4	2	no	—
404	C₂²×C₅₃	—	4	2	no	—
405	C₂²×C₅₃	—	4	2	no	—
406	C₂²×C₅₃	—	4	2	no	—
407	C₂²×C₅₃	—	4	2	no	—
408	C₂²×C₅₃	—	4	2	no	—
409	C₂²×C₅₃	—	8	16	no	—
410	C₂²×C₅₃	—	8	16	no	—
411	C₂²×C₅₃	—	8	4	no	—
412	C₂²×C₅₃	—	8	4	no	—
413	C₂²×C₅₃	—	8	4	no	—
414	C₂²×C₅₃	#546	1	2	yes	—
415	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
416	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
417	C₂²×C₅₃	#576	1	2	yes	—
418	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
419	C₄×C₅₃	—	2	2	no	—
420	C₄×C₅₃	—	2	2	no	—
421	C₄×C₅₃	—	2	2	no	—
422	C₄×C₅₃	—	2	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	#546	1	2	yes	—
428	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
429	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
430	C₂×#553	C₂×C₅₃	1	1	yes	characteristic, complemented
431	C₂×D₄²	C₂×C₅₃	1	1	yes	characteristic, complemented
432	#3318	C₂×C₅₃	1	16	yes	direct product factor
433	C₂×#490	C₂×C₅₃	1	1	yes	characteristic, complemented
434	C₂×#481	C₂×C₅₃	1	1	yes	characteristic, complemented
435	C₂×#482	C₂×C₅₃	1	1	yes	characteristic, complemented
436	C₂×#478	C₂×C₅₃	1	1	yes	characteristic, complemented
437	C₂×#469	C₂×C₅₃	1	1	yes	characteristic, complemented
438	C₂×#466	C₂×C₅₃	1	1	yes	characteristic, complemented
439	C₂×#459	C₂×C₅₃	1	1	yes	characteristic, complemented
440	C₂×#447	C₂×C₅₃	1	1	yes	characteristic, complemented
441	C₂×#447	C₂×C₅₃	1	1	yes	characteristic, complemented
442	C₂×#442	C₂×C₅₃	1	1	yes	characteristic, complemented
443	C₂×#435	C₂×C₅₃	1	1	yes	characteristic, complemented
444	C₂×#418	C₂×C₅₃	1	1	yes	characteristic, complemented
445	C₂²×#102	C₂×C₅₃	1	1	yes	characteristic, complemented
446	C₂×C₅₃	—	2	4	no	—
447	C₂×C₅₃	—	4	2	no	—
448	C₂×C₅₃	—	4	4	no	—
449	C₂×C₅₃	—	8	2	no	—
450	C₂×C₅₃	—	8	2	no	—
451	C₂×C₅₃	—	8	2	no	—
452	C₂×C₅₃	#3318	1	4	yes	direct product factor
453	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
454	C₂×C₅₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
455	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
456	C₂³×D₄	—	2	1	no	—
457	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
458	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
459	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
460	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
461	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
462	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
463	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
464	#553	—	2	4	no	—
465	#553	C₂²×C₅₃	1	8	yes	complemented
466	D₄²	—	2	4	no	—
467	D₄²	C₂²×C₅₃	1	8	yes	complemented
468	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
469	C₂×#126	—	2	1	no	—
470	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
471	C₂×#123	—	2	1	no	—
472	C₂×#121	—	2	1	no	—
473	C₂×#121	—	2	1	no	—
474	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
475	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
476	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
477	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
478	C₂×#120	—	2	1	no	—
479	C₂×#120	—	2	1	no	—
480	C₂×C₄×D₄	—	2	1	no	—
481	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
482	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
483	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
484	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
485	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
486	#490	C₂²×C₅₃	1	8	yes	complemented
487	#482	C₂²×C₅₃	1	8	yes	complemented
488	#481	C₂²×C₅₃	1	8	yes	complemented
489	#478	C₂²×C₅₃	1	8	yes	complemented
490	#469	C₂²×C₅₃	1	8	yes	complemented
491	#466	C₂²×C₅₃	1	8	yes	complemented
492	#459	C₂²×C₅₃	1	8	yes	complemented
493	#447	C₂²×C₅₃	1	8	yes	complemented
494	#447	C₂²×C₅₃	1	8	yes	complemented
495	#442	C₂²×C₅₃	1	8	yes	complemented
496	#435	C₂²×C₅₃	1	8	yes	complemented
497	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
498	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
499	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
500	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
501	#418	C₂²×C₅₃	1	8	yes	complemented
502	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
503	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
504	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
505	C₂×#102	C₂²×C₅₃	1	8	yes	complemented
506	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
507	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
508	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
509	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
510	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
511	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
512	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
513	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
514	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
515	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
516	C₅₃	C₂×#3318	1	1	yes	characteristic, direct product factor, Sylow
517	C₂⁵	—	2	1	no	—
518	C₂⁵	—	2	1	no	—
519	C₂²×D₄	—	2	4	no	—
520	C₂²×D₄	—	2	4	no	—
521	C₂²×D₄	—	2	1	no	—
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	—	2	8	no	—
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	—	2	1	no	—
528	C₂²×D₄	—	2	1	no	—
529	C₂²×D₄	—	2	2	no	—
530	C₂²×D₄	—	2	2	no	—
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	—	4	2	no	—
533	C₂²×D₄	—	4	2	no	—
534	C₂²×D₄	—	4	8	no	—
535	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
536	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
539	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
540	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
541	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
542	C₂³×C₄	—	2	1	no	—
543	C₂³×C₄	—	2	1	no	—
544	C₂³×C₄	—	2	1	no	—
545	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
547	C₂×D₈	—	2	4	no	—
548	C₂×D₈	—	4	2	no	—
549	C₂×D₈	—	4	2	no	—
550	C₂×D₈	C₂³×C₅₃	1	4	yes	—
551	C₂×D₈	C₂³×C₅₃	1	4	yes	complemented
552	C₂×D₈	C₂³×C₅₃	1	4	yes	complemented
553	C₂×M₁₆	—	4	2	no	—
554	C₂×M₁₆	C₂³×C₅₃	1	4	yes	complemented
555	C₂²×C₈	—	4	2	no	—
556	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
557	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
558	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
559	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
560	C₂²×C₈	C₂³×C₅₃	1	4	yes	complemented
561	#127	—	2	2	no	—
562	#127	C₂³×C₅₃	1	4	yes	—
563	#126	—	2	8	no	—
564	#125	—	2	2	no	—
565	#125	C₂³×C₅₃	1	4	yes	complemented
566	#123	—	2	8	no	—
567	#121	—	2	8	no	—
568	#121	—	2	2	no	—
569	#121	—	2	2	no	—
570	#121	—	2	2	no	—
571	#121	—	2	2	no	—
572	#121	—	2	8	no	—
573	#121	C₂³×C₅₃	1	4	yes	—
574	#121	C₂³×C₅₃	1	4	yes	—
575	#121	C₂³×C₅₃	1	4	yes	complemented
576	#121	C₂³×C₅₃	1	4	yes	complemented
577	#120	—	2	8	no	—
578	#120	—	2	8	no	—
579	C₄×D₄	—	2	8	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	D₄×C₅₃	1	4	yes	—
583	C₄×D₄	C₂³×C₅₃	1	4	yes	—
584	C₄×D₄	C₂³×C₅₃	1	4	yes	—
585	C₄×D₄	C₂³×C₅₃	1	4	yes	complemented
586	#117	—	2	2	no	—
587	#117	C₂³×C₅₃	1	4	yes	complemented
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	2	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	complemented
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₂²⋊C₄	—	2	1	no	—
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	—	2	1	no	—
602	C₂×C₂²⋊C₄	—	2	1	no	—
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
607	C₂×C₄²	—	2	1	no	—
608	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
609	#107	C₂³×C₅₃	1	4	yes	complemented
610	#106	C₂³×C₅₃	1	4	yes	complemented
611	#106	C₂³×C₅₃	1	4	yes	complemented
612	C₄⋊C₈	C₂³×C₅₃	1	4	yes	complemented
613	#102	C₂³×C₅₃	1	4	yes	—
614	#102	C₂³×C₅₃	1	4	yes	—
615	#102	C₂³×C₅₃	1	4	yes	—
616	#102	C₂³×C₅₃	1	4	yes	complemented
617	#102	C₂³×C₅₃	1	4	yes	complemented
618	#102	C₂³×C₅₃	1	4	yes	complemented
619	#102	C₂³×C₅₃	1	4	yes	complemented
620	#102	C₂³×C₅₃	1	4	yes	complemented
621	#102	C₂³×C₅₃	1	4	yes	complemented
622	#102	C₂³×C₅₃	1	4	yes	complemented
623	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
624	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
625	#97	C₂³×C₅₃	1	4	yes	complemented
626	C₂⁴	—	2	1	no	—
627	C₂⁴	—	2	1	no	—
628	C₂⁴	—	2	1	no	—
629	C₂⁴	—	2	1	no	—
630	C₂⁴	—	2	4	no	—
631	C₂⁴	—	2	4	no	—
632	C₂⁴	—	4	4	no	—
633	C₂⁴	—	4	4	no	—
634	C₂⁴	—	4	4	no	—
635	C₂⁴	—	4	4	no	—
636	C₂⁴	—	8	2	no	—
637	C₂⁴	—	8	2	no	—
638	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
639	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	8	no	—
642	C₂×D₄	—	2	8	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	4	4	no	—
663	C₂×D₄	—	4	4	no	—
664	C₂×D₄	—	4	8	no	—
665	C₂×D₄	—	4	8	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	—	4	4	no	—
668	C₂×D₄	—	4	4	no	—
669	C₂×D₄	—	4	32	no	—
670	C₂×D₄	—	4	4	no	—
671	C₂×D₄	—	4	4	no	—
672	C₂×D₄	—	4	4	no	—
673	C₂×D₄	—	8	2	no	—
674	C₂×D₄	—	8	2	no	—
675	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
676	C₂×D₄	#41×C₅₃	1	4	yes	—
677	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
678	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
679	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
680	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	4	4	no	—
693	C₂²×C₄	—	8	2	no	—
694	C₂²×C₄	—	8	2	no	—
695	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
700	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
704	D₈	—	2	8	no	—
705	D₈	—	4	4	no	—
706	D₈	—	4	4	no	—
707	M₁₆	—	4	4	no	—
708	C₂×C₈	—	2	2	no	—
709	C₂×C₈	—	2	2	no	—
710	C₂×C₈	—	2	2	no	—
711	C₂×C₈	—	2	2	no	—
712	C₂×C₈	—	4	4	no	—
713	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
714	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
715	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
716	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
725	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
728	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
737	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
738	C₄²	—	2	4	no	—
739	C₄²	C₂×D₄×C₅₃	1	2	yes	—
740	C₄²	C₂⁴×C₅₃	1	2	yes	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	4	8	no	—
752	C₂³	—	4	8	no	—
753	C₂³	—	4	8	no	—
754	C₂³	—	4	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	2	no	—
757	C₂³	—	4	2	no	—
758	C₂³	—	4	2	no	—
759	C₂³	—	4	8	no	—
760	C₂³	—	4	2	no	—
761	C₂³	—	4	2	no	—
762	C₂³	—	4	2	no	—
763	C₂³	—	4	2	no	—
764	C₂³	—	4	2	no	—
765	C₂³	—	4	2	no	—
766	C₂³	—	8	4	no	—
767	C₂³	—	8	4	no	—
768	C₂³	—	8	16	no	—
769	C₂³	—	8	16	no	—
770	C₂³	AGL(1,ℤ/8)×C₅₃	1	4	yes	—
771	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
772	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
773	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
774	D₄	—	2	8	no	—
775	D₄	—	2	4	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	2	2	no	—
782	D₄	—	2	2	no	—
783	D₄	—	4	8	no	—
784	D₄	—	4	8	no	—
785	D₄	—	4	8	no	—
786	D₄	—	4	8	no	—
787	D₄	—	4	8	no	—
788	D₄	—	4	8	no	—
789	D₄	—	4	2	no	—
790	D₄	—	4	2	no	—
791	D₄	—	4	2	no	—
792	D₄	—	8	4	no	—
793	D₄	—	8	4	no	—
794	D₄	C₂×#41×C₅₃	1	4	yes	—
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	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	4	8	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	8	4	no	—
815	C₂×C₄	—	8	4	no	—
816	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
821	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
822	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
823	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
824	C₈	—	2	2	no	—
825	C₈	—	2	2	no	—
826	C₈	—	2	2	no	—
827	C₈	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	8	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	4	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	8	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	8	16	no	—
849	C₂²	—	8	16	no	—
850	C₂²	—	8	4	no	—
851	C₂²	—	8	4	no	—
852	C₂²	—	8	4	no	—
853	C₂²	C₅₃×#546	1	2	yes	—
854	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	4	yes	—
855	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
856	C₂²	C₅₃×#576	1	2	yes	—
857	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	C₅₃×#546	1	2	yes	—
867	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
868	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
869	C₂	—	2	4	no	—
870	C₂	—	4	2	no	—
871	C₂	—	4	4	no	—
872	C₂	—	8	2	no	—
873	C₂	—	8	2	no	—
874	C₂	—	8	2	no	—
875	C₂	C₅₃×#3318	1	4	yes	direct product factor
876	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
877	C₂	C₂²×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
878	C₂	C₂×C₅₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#553	C₂	semidirect
2. C₂×D₄²×C₅₃	C₂	semidirect
3. C₅₃×#3318	C₂	direct (N × H)
4. C₂×C₅₃×#490	C₂	semidirect
5. C₂×C₅₃×#481	C₂	semidirect
6. C₂×C₅₃×#482	C₂	semidirect
7. C₂×C₅₃×#478	C₂	semidirect
8. C₂×C₅₃×#469	C₂	semidirect
9. C₂×C₅₃×#466	C₂	semidirect
10. C₂×C₅₃×#459	C₂	semidirect
11. C₂×C₅₃×#447	C₂	semidirect
12. C₂×C₅₃×#447	C₂	semidirect
13. C₂×C₅₃×#442	C₂	semidirect
14. C₂×C₅₃×#435	C₂	semidirect
15. C₂×C₅₃×#418	C₂	semidirect
16. C₂²×#102×C₅₃	C₂	semidirect
21. C₂²×D₈×C₅₃	C₂²	semidirect
22. C₂²×D₈×C₅₃	C₂²	semidirect
23. C₂²×M₁₆×C₅₃	C₂²	semidirect
24. C₂³×C₈×C₅₃	C₂²	semidirect
26. C₅₃×#553	C₂²	semidirect
28. D₄²×C₅₃	C₂²	semidirect
31. C₂×#125×C₅₃	C₂²	semidirect
37. C₂×#121×C₅₃	C₂²	semidirect
38. C₂×#121×C₅₃	C₂²	semidirect
44. C₂×C₄×D₄×C₅₃	C₂²	semidirect
45. C₂×#117×C₅₃	C₂²	semidirect
46. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
47. C₅₃×#490	C₂²	semidirect
48. C₅₃×#482	C₂²	semidirect
49. C₅₃×#481	C₂²	semidirect
50. C₅₃×#478	C₂²	semidirect
51. C₅₃×#469	C₂²	semidirect
52. C₅₃×#466	C₂²	semidirect
53. C₅₃×#459	C₂²	semidirect
54. C₅₃×#447	C₂²	semidirect
55. C₅₃×#447	C₂²	semidirect
56. C₅₃×#442	C₂²	semidirect
57. C₅₃×#435	C₂²	semidirect
58. C₂×#107×C₅₃	C₂²	semidirect
59. C₂×#106×C₅₃	C₂²	semidirect
60. C₂×#106×C₅₃	C₂²	semidirect
61. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
62. C₅₃×#418	C₂²	semidirect
66. C₂×#102×C₅₃	C₂²	semidirect
67. C₂×#102×C₅₃	C₂²	semidirect
68. C₂×#102×C₅₃	C₂²	semidirect
69. C₂×#102×C₅₃	C₂²	semidirect
70. C₂×#102×C₅₃	C₂²	semidirect
71. C₂×#102×C₅₃	C₂²	semidirect
72. C₂×#102×C₅₃	C₂²	semidirect
73. C₂×#102×C₅₃	C₂²	semidirect
74. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
75. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
76. C₂×#97×C₅₃	C₂²	semidirect
111. C₂×D₈×C₅₃	C₂³	semidirect
112. C₂×D₈×C₅₃	C₂³	semidirect
114. C₂×M₁₆×C₅₃	C₂³	semidirect
120. C₂²×C₈×C₅₃	C₂³	semidirect
125. #125×C₅₃	C₂³	semidirect
135. #121×C₅₃	C₂³	semidirect
136. #121×C₅₃	C₂³	semidirect
145. C₄×D₄×C₅₃	C₂³	semidirect
147. #117×C₅₃	C₂³	semidirect
157. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
169. #107×C₅₃	C₂³	semidirect
170. #106×C₅₃	C₂³	semidirect
171. #106×C₅₃	C₂³	semidirect
172. C₄⋊C₈×C₅₃	C₂³	semidirect
176. #102×C₅₃	C₂³	semidirect
177. #102×C₅₃	C₂³	semidirect
178. #102×C₅₃	C₂³	semidirect
179. #102×C₅₃	C₂³	semidirect
180. #102×C₅₃	C₂³	semidirect
181. #102×C₅₃	C₂³	semidirect
182. #102×C₅₃	C₂³	semidirect
183. C₂²⋊C₈×C₅₃	C₂³	semidirect
184. C₂²⋊C₈×C₅₃	C₂³	semidirect
185. #97×C₅₃	C₂³	semidirect
388. C₂×#3318	C₅₃	direct (N × H)
430. C₂×#553	C₂×C₅₃	semidirect
431. C₂×D₄²	C₂×C₅₃	semidirect
432. #3318	C₂×C₅₃	direct (N × H)
433. C₂×#490	C₂×C₅₃	semidirect
434. C₂×#481	C₂×C₅₃	semidirect
435. C₂×#482	C₂×C₅₃	semidirect
436. C₂×#478	C₂×C₅₃	semidirect
437. C₂×#469	C₂×C₅₃	semidirect
438. C₂×#466	C₂×C₅₃	semidirect
439. C₂×#459	C₂×C₅₃	semidirect
440. C₂×#447	C₂×C₅₃	semidirect
441. C₂×#447	C₂×C₅₃	semidirect
442. C₂×#442	C₂×C₅₃	semidirect
443. C₂×#435	C₂×C₅₃	semidirect
444. C₂×#418	C₂×C₅₃	semidirect
445. C₂²×#102	C₂×C₅₃	semidirect
452. C₂×C₅₃	#3318	direct (N × H)
460. C₂²×D₈	C₂²×C₅₃	semidirect
461. C₂²×D₈	C₂²×C₅₃	semidirect
462. C₂²×M₁₆	C₂²×C₅₃	semidirect
463. C₂³×C₈	C₂²×C₅₃	semidirect
465. #553	C₂²×C₅₃	semidirect
467. D₄²	C₂²×C₅₃	semidirect
470. C₂×#125	C₂²×C₅₃	semidirect
476. C₂×#121	C₂²×C₅₃	semidirect
477. C₂×#121	C₂²×C₅₃	semidirect
483. C₂×C₄×D₄	C₂²×C₅₃	semidirect
484. C₂×#117	C₂²×C₅₃	semidirect
485. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
486. #490	C₂²×C₅₃	semidirect
487. #482	C₂²×C₅₃	semidirect
488. #481	C₂²×C₅₃	semidirect
489. #478	C₂²×C₅₃	semidirect
490. #469	C₂²×C₅₃	semidirect
491. #466	C₂²×C₅₃	semidirect
492. #459	C₂²×C₅₃	semidirect
493. #447	C₂²×C₅₃	semidirect
494. #447	C₂²×C₅₃	semidirect
495. #442	C₂²×C₅₃	semidirect
496. #435	C₂²×C₅₃	semidirect
497. C₂×#107	C₂²×C₅₃	semidirect
498. C₂×#106	C₂²×C₅₃	semidirect
499. C₂×#106	C₂²×C₅₃	semidirect
500. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
501. #418	C₂²×C₅₃	semidirect
505. C₂×#102	C₂²×C₅₃	semidirect
506. C₂×#102	C₂²×C₅₃	semidirect
507. C₂×#102	C₂²×C₅₃	semidirect
508. C₂×#102	C₂²×C₅₃	semidirect
509. C₂×#102	C₂²×C₅₃	semidirect
510. C₂×#102	C₂²×C₅₃	semidirect
511. C₂×#102	C₂²×C₅₃	semidirect
512. C₂×#102	C₂²×C₅₃	semidirect
513. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
514. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
515. C₂×#97	C₂²×C₅₃	semidirect
516. C₅₃	C₂×#3318	direct (N × H)
551. C₂×D₈	C₂³×C₅₃	semidirect
552. C₂×D₈	C₂³×C₅₃	semidirect
554. C₂×M₁₆	C₂³×C₅₃	semidirect
560. C₂²×C₈	C₂³×C₅₃	semidirect
565. #125	C₂³×C₅₃	semidirect
575. #121	C₂³×C₅₃	semidirect
576. #121	C₂³×C₅₃	semidirect
585. C₄×D₄	C₂³×C₅₃	semidirect
587. #117	C₂³×C₅₃	semidirect
597. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
609. #107	C₂³×C₅₃	semidirect
610. #106	C₂³×C₅₃	semidirect
611. #106	C₂³×C₅₃	semidirect
612. C₄⋊C₈	C₂³×C₅₃	semidirect
616. #102	C₂³×C₅₃	semidirect
617. #102	C₂³×C₅₃	semidirect
618. #102	C₂³×C₅₃	semidirect
619. #102	C₂³×C₅₃	semidirect
620. #102	C₂³×C₅₃	semidirect
621. #102	C₂³×C₅₃	semidirect
622. #102	C₂³×C₅₃	semidirect
623. C₂²⋊C₈	C₂³×C₅₃	semidirect
624. C₂²⋊C₈	C₂³×C₅₃	semidirect
625. #97	C₂³×C₅₃	semidirect
875. C₂	C₅₃×#3318	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#553	2
C₂×D₄²×C₅₃	2
C₅₃×#3318	2
C₂×C₅₃×#490	2
C₂×C₅₃×#481	2
C₂×C₅₃×#482	2
C₂×C₅₃×#478	2
C₂×C₅₃×#469	2
C₂×C₅₃×#466	2
C₂×C₅₃×#459	2
C₂×C₅₃×#447	2
C₂×C₅₃×#442	2
C₂×C₅₃×#435	2
C₂×C₅₃×#418	2
C₂²×#102×C₅₃	2
C₂×#3318	53

Subgroups — C2×C53×#3318 #27268640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3318 #27268640