Subgroups — C₂×C₅₃×#3310 #27268639

Order 13568.

2578 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3310	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#440	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×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×SD₁₆×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×#552	—	2	4	no	—
26	C₅₃×#552	C₂²	1	8	yes	complemented
27	D₄²×C₅₃	—	2	4	no	—
28	D₄²×C₅₃	C₂²	1	8	yes	—
29	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#126×C₅₃	—	2	1	no	—
31	C₂×#125×C₅₃	—	2	1	no	—
32	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×#123×C₅₃	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×#121×C₅₃	—	2	1	no	—
37	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#120×C₅₃	—	2	1	no	—
40	C₂×#120×C₅₃	—	2	1	no	—
41	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×#117×C₅₃	—	2	1	no	—
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×#480	C₂²	1	8	yes	complemented
50	C₅₃×#478	C₂²	1	8	yes	complemented
51	C₅₃×#468	C₂²	1	8	yes	complemented
52	C₅₃×#465	C₂²	1	8	yes	complemented
53	C₅₃×#460	C₂²	1	8	yes	complemented
54	C₅₃×#450	C₂²	1	8	yes	complemented
55	C₅₃×#450	C₂²	1	8	yes	complemented
56	C₅₃×#440	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×#107×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×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
66	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
67	C₂×#102×C₅₃	C₂²	1	8	yes	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×Q₈×C₅₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₅₃	—	2	4	no	—
81	C₂²×D₄×C₅₃	—	2	4	no	—
82	C₂²×D₄×C₅₃	—	2	1	no	—
83	C₂²×D₄×C₅₃	—	2	1	no	—
84	C₂²×D₄×C₅₃	—	2	8	no	—
85	C₂²×D₄×C₅₃	—	2	1	no	—
86	C₂²×D₄×C₅₃	—	2	1	no	—
87	C₂²×D₄×C₅₃	—	2	1	no	—
88	C₂²×D₄×C₅₃	—	2	2	no	—
89	C₂²×D₄×C₅₃	—	2	2	no	—
90	C₂²×D₄×C₅₃	—	2	1	no	—
91	C₂²×D₄×C₅₃	—	4	2	no	—
92	C₂²×D₄×C₅₃	—	4	2	no	—
93	C₂²×D₄×C₅₃	—	4	8	no	—
94	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
95	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
98	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
99	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₅₃	—	2	1	no	—
101	C₂³×C₄×C₅₃	—	2	1	no	—
102	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
104	C₂×SD₁₆×C₅₃	—	2	4	no	—
105	C₂×SD₁₆×C₅₃	—	4	2	no	—
106	C₂×SD₁₆×C₅₃	—	4	2	no	—
107	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	complemented
109	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	complemented
110	C₂×M₁₆×C₅₃	—	4	2	no	—
111	C₂×M₁₆×C₅₃	C₂³	1	4	yes	complemented
112	C₂²×C₈×C₅₃	—	4	2	no	—
113	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₅₃	C₂³	1	4	yes	complemented
118	#127×C₅₃	—	2	2	no	—
119	#127×C₅₃	C₂³	1	4	yes	—
120	#126×C₅₃	—	2	8	no	—
121	#125×C₅₃	—	2	8	no	—
122	#125×C₅₃	—	2	2	no	—
123	#125×C₅₃	C₂³	1	4	yes	complemented
124	#123×C₅₃	—	2	8	no	—
125	C₂²⋊Q₈×C₅₃	—	2	2	no	—
126	C₂²⋊Q₈×C₅₃	—	2	2	no	—
127	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
128	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
129	#121×C₅₃	—	2	8	no	—
130	#121×C₅₃	—	2	2	no	—
131	#121×C₅₃	—	2	2	no	—
132	#121×C₅₃	C₂³	1	4	yes	—
133	#121×C₅₃	C₂³	1	4	yes	—
134	#120×C₅₃	—	2	8	no	—
135	#120×C₅₃	—	2	8	no	—
136	C₄×Q₈×C₅₃	—	2	2	no	—
137	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
138	C₄×D₄×C₅₃	—	2	2	no	—
139	C₄×D₄×C₅₃	D₄	1	4	yes	—
140	C₄×D₄×C₅₃	C₂³	1	4	yes	—
141	C₄×D₄×C₅₃	C₂³	1	4	yes	—
142	#117×C₅₃	—	2	8	no	—
143	#117×C₅₃	—	2	2	no	—
144	#117×C₅₃	C₂³	1	4	yes	complemented
145	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
146	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
147	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
148	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
149	C₂×C₄⋊C₄×C₅₃	—	2	1	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	D₄	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₅₃	—	2	1	no	—
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	#107×C₅₃	C₂³	1	4	yes	complemented
171	#106×C₅₃	C₂³	1	4	yes	complemented
172	C₄⋊C₈×C₅₃	C₂³	1	4	yes	complemented
173	#103×C₅₃	C₂³	1	4	yes	complemented
174	#102×C₅₃	C₂³	1	4	yes	—
175	#102×C₅₃	C₂³	1	4	yes	—
176	#102×C₅₃	C₂³	1	4	yes	—
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	4	no	—
190	C₂⁴×C₅₃	—	2	4	no	—
191	C₂⁴×C₅₃	—	4	4	no	—
192	C₂⁴×C₅₃	—	4	4	no	—
193	C₂⁴×C₅₃	—	4	4	no	—
194	C₂⁴×C₅₃	—	4	4	no	—
195	C₂⁴×C₅₃	—	8	2	no	—
196	C₂⁴×C₅₃	—	8	2	no	—
197	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
198	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
199	C₂×Q₈×C₅₃	—	2	1	no	—
200	C₂×Q₈×C₅₃	—	2	2	no	—
201	C₂×Q₈×C₅₃	—	2	2	no	—
202	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
203	C₂×D₄×C₅₃	—	2	4	no	—
204	C₂×D₄×C₅₃	—	2	8	no	—
205	C₂×D₄×C₅₃	—	2	8	no	—
206	C₂×D₄×C₅₃	—	2	4	no	—
207	C₂×D₄×C₅₃	—	2	4	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	—	4	4	no	—
221	C₂×D₄×C₅₃	—	4	4	no	—
222	C₂×D₄×C₅₃	—	4	8	no	—
223	C₂×D₄×C₅₃	—	4	8	no	—
224	C₂×D₄×C₅₃	—	4	4	no	—
225	C₂×D₄×C₅₃	—	4	4	no	—
226	C₂×D₄×C₅₃	—	4	4	no	—
227	C₂×D₄×C₅₃	—	4	32	no	—
228	C₂×D₄×C₅₃	—	4	4	no	—
229	C₂×D₄×C₅₃	—	4	4	no	—
230	C₂×D₄×C₅₃	—	8	2	no	—
231	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
232	C₂×D₄×C₅₃	#41	1	4	yes	—
233	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
234	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
235	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₅₃	—	2	2	no	—
237	C₂²×C₄×C₅₃	—	2	2	no	—
238	C₂²×C₄×C₅₃	—	2	2	no	—
239	C₂²×C₄×C₅₃	—	2	2	no	—
240	C₂²×C₄×C₅₃	—	2	4	no	—
241	C₂²×C₄×C₅₃	—	2	1	no	—
242	C₂²×C₄×C₅₃	—	2	1	no	—
243	C₂²×C₄×C₅₃	—	2	1	no	—
244	C₂²×C₄×C₅₃	—	2	1	no	—
245	C₂²×C₄×C₅₃	—	2	1	no	—
246	C₂²×C₄×C₅₃	—	2	4	no	—
247	C₂²×C₄×C₅₃	—	4	4	no	—
248	C₂²×C₄×C₅₃	—	4	4	no	—
249	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
250	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
258	SD₁₆×C₅₃	—	2	8	no	—
259	SD₁₆×C₅₃	—	4	4	no	—
260	SD₁₆×C₅₃	—	4	4	no	—
261	M₁₆×C₅₃	—	4	4	no	—
262	C₂×C₈×C₅₃	—	2	2	no	—
263	C₂×C₈×C₅₃	—	2	2	no	—
264	C₂×C₈×C₅₃	—	2	2	no	—
265	C₂×C₈×C₅₃	—	2	2	no	—
266	C₂×C₈×C₅₃	—	4	4	no	—
267	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
268	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
269	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
270	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
271	C₄⋊C₄×C₅₃	—	2	1	no	—
272	C₄⋊C₄×C₅₃	—	2	1	no	—
273	C₄⋊C₄×C₅₃	—	2	4	no	—
274	C₄⋊C₄×C₅₃	—	2	4	no	—
275	C₄⋊C₄×C₅₃	—	2	4	no	—
276	C₄⋊C₄×C₅₃	—	2	4	no	—
277	C₄⋊C₄×C₅₃	—	2	4	no	—
278	C₄⋊C₄×C₅₃	—	2	4	no	—
279	C₄⋊C₄×C₅₃	—	2	1	no	—
280	C₄⋊C₄×C₅₃	—	2	1	no	—
281	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
282	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
286	C₂²⋊C₄×C₅₃	—	2	4	no	—
287	C₂²⋊C₄×C₅₃	—	2	4	no	—
288	C₂²⋊C₄×C₅₃	—	2	4	no	—
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	C₂×D₄	1	4	yes	—
293	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
294	C₄²×C₅₃	—	2	4	no	—
295	C₄²×C₅₃	—	2	4	no	—
296	C₄²×C₅₃	C₂×D₄	1	2	yes	—
297	C₄²×C₅₃	C₂⁴	1	2	yes	—
298	C₂³×C₅₃	—	2	2	no	—
299	C₂³×C₅₃	—	2	2	no	—
300	C₂³×C₅₃	—	2	2	no	—
301	C₂³×C₅₃	—	2	4	no	—
302	C₂³×C₅₃	—	2	2	no	—
303	C₂³×C₅₃	—	2	2	no	—
304	C₂³×C₅₃	—	2	2	no	—
305	C₂³×C₅₃	—	2	2	no	—
306	C₂³×C₅₃	—	2	2	no	—
307	C₂³×C₅₃	—	4	8	no	—
308	C₂³×C₅₃	—	4	8	no	—
309	C₂³×C₅₃	—	4	8	no	—
310	C₂³×C₅₃	—	4	2	no	—
311	C₂³×C₅₃	—	4	2	no	—
312	C₂³×C₅₃	—	4	2	no	—
313	C₂³×C₅₃	—	4	2	no	—
314	C₂³×C₅₃	—	4	8	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	—	8	4	no	—
320	C₂³×C₅₃	—	8	4	no	—
321	C₂³×C₅₃	—	8	16	no	—
322	C₂³×C₅₃	—	8	16	no	—
323	C₂³×C₅₃	AGL(1,ℤ/8)	1	4	yes	—
324	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
325	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
326	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
327	Q₈×C₅₃	—	2	2	no	—
328	Q₈×C₅₃	—	2	2	no	—
329	Q₈×C₅₃	—	4	2	no	—
330	D₄×C₅₃	—	2	8	no	—
331	D₄×C₅₃	—	2	4	no	—
332	D₄×C₅₃	—	2	2	no	—
333	D₄×C₅₃	—	2	2	no	—
334	D₄×C₅₃	—	2	2	no	—
335	D₄×C₅₃	—	2	2	no	—
336	D₄×C₅₃	—	2	2	no	—
337	D₄×C₅₃	—	4	8	no	—
338	D₄×C₅₃	—	4	8	no	—
339	D₄×C₅₃	—	4	8	no	—
340	D₄×C₅₃	—	4	8	no	—
341	D₄×C₅₃	—	4	8	no	—
342	D₄×C₅₃	—	4	2	no	—
343	D₄×C₅₃	—	4	2	no	—
344	D₄×C₅₃	—	8	4	no	—
345	D₄×C₅₃	C₂×#41	1	4	yes	—
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	4	no	—
351	C₂×C₄×C₅₃	—	2	4	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	—	4	8	no	—
362	C₂×C₄×C₅₃	—	4	2	no	—
363	C₂×C₄×C₅₃	—	4	8	no	—
364	C₂×C₄×C₅₃	—	4	2	no	—
365	C₂×C₄×C₅₃	—	4	2	no	—
366	C₂×C₄×C₅₃	—	4	2	no	—
367	C₂×C₄×C₅₃	—	4	2	no	—
368	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
374	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
375	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
376	C₈×C₅₃	—	2	2	no	—
377	C₈×C₅₃	—	2	2	no	—
378	C₈×C₅₃	—	2	2	no	—
379	C₈×C₅₃	—	2	2	no	—
380	C₂×#3310	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂²×C₅₃	—	2	2	no	—
382	C₂²×C₅₃	—	2	8	no	—
383	C₂²×C₅₃	—	2	2	no	—
384	C₂²×C₅₃	—	2	2	no	—
385	C₂²×C₅₃	—	2	4	no	—
386	C₂²×C₅₃	—	2	2	no	—
387	C₂²×C₅₃	—	2	2	no	—
388	C₂²×C₅₃	—	4	4	no	—
389	C₂²×C₅₃	—	4	8	no	—
390	C₂²×C₅₃	—	4	2	no	—
391	C₂²×C₅₃	—	4	2	no	—
392	C₂²×C₅₃	—	4	2	no	—
393	C₂²×C₅₃	—	4	2	no	—
394	C₂²×C₅₃	—	4	2	no	—
395	C₂²×C₅₃	—	4	2	no	—
396	C₂²×C₅₃	—	4	2	no	—
397	C₂²×C₅₃	—	4	2	no	—
398	C₂²×C₅₃	—	8	16	no	—
399	C₂²×C₅₃	—	8	16	no	—
400	C₂²×C₅₃	—	8	4	no	—
401	C₂²×C₅₃	—	8	4	no	—
402	C₂²×C₅₃	#546	1	2	yes	—
403	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
404	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
405	C₂²×C₅₃	#577	1	2	yes	—
406	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
407	C₄×C₅₃	—	2	2	no	—
408	C₄×C₅₃	—	2	2	no	—
409	C₄×C₅₃	—	2	2	no	—
410	C₄×C₅₃	—	2	2	no	—
411	C₄×C₅₃	—	4	2	no	—
412	C₄×C₅₃	—	4	2	no	—
413	C₄×C₅₃	—	4	2	no	—
414	C₄×C₅₃	—	4	2	no	—
415	C₄×C₅₃	—	4	2	no	—
416	C₄×C₅₃	#546	1	2	yes	—
417	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
418	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂×#552	C₂×C₅₃	1	1	yes	characteristic, complemented
420	C₂×D₄²	C₂×C₅₃	1	1	yes	characteristic
421	#3310	C₂×C₅₃	1	16	yes	direct product factor
422	C₂×#490	C₂×C₅₃	1	1	yes	characteristic, complemented
423	C₂×#482	C₂×C₅₃	1	1	yes	characteristic, complemented
424	C₂×#480	C₂×C₅₃	1	1	yes	characteristic, complemented
425	C₂×#478	C₂×C₅₃	1	1	yes	characteristic, complemented
426	C₂×#468	C₂×C₅₃	1	1	yes	characteristic, complemented
427	C₂×#465	C₂×C₅₃	1	1	yes	characteristic, complemented
428	C₂×#460	C₂×C₅₃	1	1	yes	characteristic, complemented
429	C₂×#450	C₂×C₅₃	1	1	yes	characteristic, complemented
430	C₂×#450	C₂×C₅₃	1	1	yes	characteristic, complemented
431	C₂×#440	C₂×C₅₃	1	1	yes	characteristic, complemented
432	C₂×#435	C₂×C₅₃	1	1	yes	characteristic, complemented
433	C₂×#418	C₂×C₅₃	1	1	yes	characteristic, complemented
434	C₂²×#102	C₂×C₅₃	1	1	yes	characteristic, complemented
435	C₂×C₅₃	—	2	4	no	—
436	C₂×C₅₃	—	4	2	no	—
437	C₂×C₅₃	—	4	4	no	—
438	C₂×C₅₃	—	8	2	no	—
439	C₂×C₅₃	—	8	2	no	—
440	C₂×C₅₃	#3310	1	4	yes	direct product factor
441	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
442	C₂×C₅₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
443	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
444	C₂³×D₄	—	2	1	no	—
445	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
446	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
447	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
448	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
449	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
450	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
451	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
452	#552	—	2	4	no	—
453	#552	C₂²×C₅₃	1	8	yes	complemented
454	D₄²	—	2	4	no	—
455	D₄²	C₂²×C₅₃	1	8	yes	—
456	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
457	C₂×#126	—	2	1	no	—
458	C₂×#125	—	2	1	no	—
459	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
460	C₂×#123	—	2	1	no	—
461	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
462	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
463	C₂×#121	—	2	1	no	—
464	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
465	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
466	C₂×#120	—	2	1	no	—
467	C₂×#120	—	2	1	no	—
468	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
469	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
470	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
471	C₂×#117	—	2	1	no	—
472	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
473	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
474	#490	C₂²×C₅₃	1	8	yes	complemented
475	#482	C₂²×C₅₃	1	8	yes	complemented
476	#480	C₂²×C₅₃	1	8	yes	complemented
477	#478	C₂²×C₅₃	1	8	yes	complemented
478	#468	C₂²×C₅₃	1	8	yes	complemented
479	#465	C₂²×C₅₃	1	8	yes	complemented
480	#460	C₂²×C₅₃	1	8	yes	complemented
481	#450	C₂²×C₅₃	1	8	yes	complemented
482	#450	C₂²×C₅₃	1	8	yes	complemented
483	#440	C₂²×C₅₃	1	8	yes	complemented
484	#435	C₂²×C₅₃	1	8	yes	complemented
485	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
486	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
487	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
488	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
489	#418	C₂²×C₅₃	1	8	yes	complemented
490	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
491	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
492	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
493	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
494	C₂×#102	C₂²×C₅₃	1	8	yes	complemented
495	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
496	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
497	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
498	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
499	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
500	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
501	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
502	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
503	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
504	C₅₃	C₂×#3310	1	1	yes	characteristic, direct product factor, Sylow
505	C₂⁵	—	2	1	no	—
506	C₂⁵	—	2	1	no	—
507	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
508	C₂²×D₄	—	2	4	no	—
509	C₂²×D₄	—	2	4	no	—
510	C₂²×D₄	—	2	1	no	—
511	C₂²×D₄	—	2	1	no	—
512	C₂²×D₄	—	2	8	no	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	—	2	1	no	—
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	—	2	2	no	—
517	C₂²×D₄	—	2	2	no	—
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	—	4	2	no	—
520	C₂²×D₄	—	4	2	no	—
521	C₂²×D₄	—	4	8	no	—
522	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
523	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
524	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
525	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
526	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
527	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
528	C₂³×C₄	—	2	1	no	—
529	C₂³×C₄	—	2	1	no	—
530	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
532	C₂×SD₁₆	—	2	4	no	—
533	C₂×SD₁₆	—	4	2	no	—
534	C₂×SD₁₆	—	4	2	no	—
535	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
536	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	complemented
537	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	complemented
538	C₂×M₁₆	—	4	2	no	—
539	C₂×M₁₆	C₂³×C₅₃	1	4	yes	complemented
540	C₂²×C₈	—	4	2	no	—
541	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
542	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
543	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
544	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
545	C₂²×C₈	C₂³×C₅₃	1	4	yes	complemented
546	#127	—	2	2	no	—
547	#127	C₂³×C₅₃	1	4	yes	—
548	#126	—	2	8	no	—
549	#125	—	2	8	no	—
550	#125	—	2	2	no	—
551	#125	C₂³×C₅₃	1	4	yes	complemented
552	#123	—	2	8	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	complemented
556	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	complemented
557	#121	—	2	2	no	—
558	#121	—	2	2	no	—
559	#121	—	2	8	no	—
560	#121	C₂³×C₅₃	1	4	yes	—
561	#121	C₂³×C₅₃	1	4	yes	—
562	#120	—	2	8	no	—
563	#120	—	2	8	no	—
564	C₄×Q₈	—	2	2	no	—
565	C₄×Q₈	C₂³×C₅₃	1	4	yes	complemented
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	D₄×C₅₃	1	4	yes	—
568	C₄×D₄	C₂³×C₅₃	1	4	yes	—
569	C₄×D₄	C₂³×C₅₃	1	4	yes	—
570	#117	—	2	2	no	—
571	#117	—	2	8	no	—
572	#117	C₂³×C₅₃	1	4	yes	complemented
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	2	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	complemented
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
593	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
594	C₂×C₄²	—	2	1	no	—
595	C₂×C₄²	—	2	1	no	—
596	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
597	#107	C₂³×C₅₃	1	4	yes	complemented
598	#107	C₂³×C₅₃	1	4	yes	complemented
599	#106	C₂³×C₅₃	1	4	yes	complemented
600	C₄⋊C₈	C₂³×C₅₃	1	4	yes	complemented
601	#103	C₂³×C₅₃	1	4	yes	complemented
602	#102	C₂³×C₅₃	1	4	yes	—
603	#102	C₂³×C₅₃	1	4	yes	—
604	#102	C₂³×C₅₃	1	4	yes	—
605	#102	C₂³×C₅₃	1	4	yes	complemented
606	#102	C₂³×C₅₃	1	4	yes	complemented
607	#102	C₂³×C₅₃	1	4	yes	complemented
608	#102	C₂³×C₅₃	1	4	yes	complemented
609	#102	C₂³×C₅₃	1	4	yes	complemented
610	#102	C₂³×C₅₃	1	4	yes	complemented
611	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
612	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
613	#97	C₂³×C₅₃	1	4	yes	complemented
614	C₂⁴	—	2	1	no	—
615	C₂⁴	—	2	1	no	—
616	C₂⁴	—	2	1	no	—
617	C₂⁴	—	2	4	no	—
618	C₂⁴	—	2	4	no	—
619	C₂⁴	—	4	4	no	—
620	C₂⁴	—	4	4	no	—
621	C₂⁴	—	4	4	no	—
622	C₂⁴	—	4	4	no	—
623	C₂⁴	—	8	2	no	—
624	C₂⁴	—	8	2	no	—
625	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
626	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	2	2	no	—
630	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	8	no	—
633	C₂×D₄	—	2	8	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	4	4	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	8	no	—
651	C₂×D₄	—	4	8	no	—
652	C₂×D₄	—	4	4	no	—
653	C₂×D₄	—	4	4	no	—
654	C₂×D₄	—	4	4	no	—
655	C₂×D₄	—	4	32	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	8	2	no	—
659	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
660	C₂×D₄	#41×C₅₃	1	4	yes	—
661	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
662	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
663	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
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	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	4	4	no	—
676	C₂²×C₄	—	4	4	no	—
677	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
682	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
686	SD₁₆	—	2	8	no	—
687	SD₁₆	—	4	4	no	—
688	SD₁₆	—	4	4	no	—
689	M₁₆	—	4	4	no	—
690	C₂×C₈	—	2	2	no	—
691	C₂×C₈	—	2	2	no	—
692	C₂×C₈	—	2	2	no	—
693	C₂×C₈	—	2	2	no	—
694	C₂×C₈	—	4	4	no	—
695	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
696	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
697	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
698	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
710	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
711	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
712	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
713	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
721	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
722	C₄²	—	2	4	no	—
723	C₄²	—	2	4	no	—
724	C₄²	C₂×D₄×C₅₃	1	2	yes	—
725	C₄²	C₂⁴×C₅₃	1	2	yes	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	4	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	—	4	8	no	—
736	C₂³	—	4	8	no	—
737	C₂³	—	4	8	no	—
738	C₂³	—	4	2	no	—
739	C₂³	—	4	2	no	—
740	C₂³	—	4	2	no	—
741	C₂³	—	4	2	no	—
742	C₂³	—	4	8	no	—
743	C₂³	—	4	2	no	—
744	C₂³	—	4	2	no	—
745	C₂³	—	4	2	no	—
746	C₂³	—	4	2	no	—
747	C₂³	—	8	4	no	—
748	C₂³	—	8	4	no	—
749	C₂³	—	8	16	no	—
750	C₂³	—	8	16	no	—
751	C₂³	AGL(1,ℤ/8)×C₅₃	1	4	yes	—
752	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
753	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
754	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
755	Q₈	—	2	2	no	—
756	Q₈	—	2	2	no	—
757	Q₈	—	4	2	no	—
758	D₄	—	2	8	no	—
759	D₄	—	2	4	no	—
760	D₄	—	2	2	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	2	no	—
763	D₄	—	2	2	no	—
764	D₄	—	2	2	no	—
765	D₄	—	4	8	no	—
766	D₄	—	4	8	no	—
767	D₄	—	4	8	no	—
768	D₄	—	4	8	no	—
769	D₄	—	4	8	no	—
770	D₄	—	4	2	no	—
771	D₄	—	4	2	no	—
772	D₄	—	8	4	no	—
773	D₄	C₂×#41×C₅₃	1	4	yes	—
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	4	no	—
779	C₂×C₄	—	2	4	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	—	4	8	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	4	8	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	2	no	—
796	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
797	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
798	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
799	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
801	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
802	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
803	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
804	C₈	—	2	2	no	—
805	C₈	—	2	2	no	—
806	C₈	—	2	2	no	—
807	C₈	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	8	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	4	4	no	—
816	C₂²	—	4	8	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	8	16	no	—
826	C₂²	—	8	16	no	—
827	C₂²	—	8	4	no	—
828	C₂²	—	8	4	no	—
829	C₂²	C₅₃×#546	1	2	yes	—
830	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	4	yes	—
831	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
832	C₂²	C₅₃×#577	1	2	yes	—
833	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
834	C₄	—	2	2	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	2	no	—
837	C₄	—	2	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	C₅₃×#546	1	2	yes	—
844	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
845	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
846	C₂	—	2	4	no	—
847	C₂	—	4	2	no	—
848	C₂	—	4	4	no	—
849	C₂	—	8	2	no	—
850	C₂	—	8	2	no	—
851	C₂	C₅₃×#3310	1	4	yes	direct product factor
852	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
853	C₂	C₂²×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
854	C₂	C₂×C₅₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₂×D₄²×C₅₃	C₂
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×#552	C₂	semidirect
3. C₅₃×#3310	C₂	direct (N × H)
4. C₂×C₅₃×#490	C₂	semidirect
5. C₂×C₅₃×#482	C₂	semidirect
6. C₂×C₅₃×#480	C₂	semidirect
7. C₂×C₅₃×#478	C₂	semidirect
8. C₂×C₅₃×#468	C₂	semidirect
9. C₂×C₅₃×#465	C₂	semidirect
10. C₂×C₅₃×#460	C₂	semidirect
11. C₂×C₅₃×#450	C₂	semidirect
12. C₂×C₅₃×#450	C₂	semidirect
13. C₂×C₅₃×#440	C₂	semidirect
14. C₂×C₅₃×#435	C₂	semidirect
15. C₂×C₅₃×#418	C₂	semidirect
16. C₂²×#102×C₅₃	C₂	semidirect
21. C₂²×SD₁₆×C₅₃	C₂²	semidirect
22. C₂²×SD₁₆×C₅₃	C₂²	semidirect
23. C₂²×M₁₆×C₅₃	C₂²	semidirect
24. C₂³×C₈×C₅₃	C₂²	semidirect
26. C₅₃×#552	C₂²	semidirect
32. C₂×#125×C₅₃	C₂²	semidirect
34. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
35. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
41. C₂×C₄×Q₈×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×#480	C₂²	semidirect
50. C₅₃×#478	C₂²	semidirect
51. C₅₃×#468	C₂²	semidirect
52. C₅₃×#465	C₂²	semidirect
53. C₅₃×#460	C₂²	semidirect
54. C₅₃×#450	C₂²	semidirect
55. C₅₃×#450	C₂²	semidirect
56. C₅₃×#440	C₂²	semidirect
57. C₅₃×#435	C₂²	semidirect
58. C₂×#107×C₅₃	C₂²	semidirect
59. C₂×#107×C₅₃	C₂²	semidirect
60. C₂×#106×C₅₃	C₂²	semidirect
61. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
62. C₅₃×#418	C₂²	semidirect
63. C₂×#103×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
108. C₂×SD₁₆×C₅₃	C₂³	semidirect
109. C₂×SD₁₆×C₅₃	C₂³	semidirect
111. C₂×M₁₆×C₅₃	C₂³	semidirect
117. C₂²×C₈×C₅₃	C₂³	semidirect
123. #125×C₅₃	C₂³	semidirect
127. C₂²⋊Q₈×C₅₃	C₂³	semidirect
128. C₂²⋊Q₈×C₅₃	C₂³	semidirect
137. C₄×Q₈×C₅₃	C₂³	semidirect
144. #117×C₅₃	C₂³	semidirect
157. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
169. #107×C₅₃	C₂³	semidirect
170. #107×C₅₃	C₂³	semidirect
171. #106×C₅₃	C₂³	semidirect
172. C₄⋊C₈×C₅₃	C₂³	semidirect
173. #103×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
380. C₂×#3310	C₅₃	direct (N × H)
419. C₂×#552	C₂×C₅₃	semidirect
421. #3310	C₂×C₅₃	direct (N × H)
422. C₂×#490	C₂×C₅₃	semidirect
423. C₂×#482	C₂×C₅₃	semidirect
424. C₂×#480	C₂×C₅₃	semidirect
425. C₂×#478	C₂×C₅₃	semidirect
426. C₂×#468	C₂×C₅₃	semidirect
427. C₂×#465	C₂×C₅₃	semidirect
428. C₂×#460	C₂×C₅₃	semidirect
429. C₂×#450	C₂×C₅₃	semidirect
430. C₂×#450	C₂×C₅₃	semidirect
431. C₂×#440	C₂×C₅₃	semidirect
432. C₂×#435	C₂×C₅₃	semidirect
433. C₂×#418	C₂×C₅₃	semidirect
434. C₂²×#102	C₂×C₅₃	semidirect
440. C₂×C₅₃	#3310	direct (N × H)
448. C₂²×SD₁₆	C₂²×C₅₃	semidirect
449. C₂²×SD₁₆	C₂²×C₅₃	semidirect
450. C₂²×M₁₆	C₂²×C₅₃	semidirect
451. C₂³×C₈	C₂²×C₅₃	semidirect
453. #552	C₂²×C₅₃	semidirect
459. C₂×#125	C₂²×C₅₃	semidirect
461. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
462. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
468. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
472. C₂×#117	C₂²×C₅₃	semidirect
473. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
474. #490	C₂²×C₅₃	semidirect
475. #482	C₂²×C₅₃	semidirect
476. #480	C₂²×C₅₃	semidirect
477. #478	C₂²×C₅₃	semidirect
478. #468	C₂²×C₅₃	semidirect
479. #465	C₂²×C₅₃	semidirect
480. #460	C₂²×C₅₃	semidirect
481. #450	C₂²×C₅₃	semidirect
482. #450	C₂²×C₅₃	semidirect
483. #440	C₂²×C₅₃	semidirect
484. #435	C₂²×C₅₃	semidirect
485. C₂×#107	C₂²×C₅₃	semidirect
486. C₂×#107	C₂²×C₅₃	semidirect
487. C₂×#106	C₂²×C₅₃	semidirect
488. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
489. #418	C₂²×C₅₃	semidirect
490. C₂×#103	C₂²×C₅₃	semidirect
494. C₂×#102	C₂²×C₅₃	semidirect
495. C₂×#102	C₂²×C₅₃	semidirect
496. C₂×#102	C₂²×C₅₃	semidirect
497. C₂×#102	C₂²×C₅₃	semidirect
498. C₂×#102	C₂²×C₅₃	semidirect
499. C₂×#102	C₂²×C₅₃	semidirect
500. C₂×#102	C₂²×C₅₃	semidirect
501. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
502. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
503. C₂×#97	C₂²×C₅₃	semidirect
504. C₅₃	C₂×#3310	direct (N × H)
536. C₂×SD₁₆	C₂³×C₅₃	semidirect
537. C₂×SD₁₆	C₂³×C₅₃	semidirect
539. C₂×M₁₆	C₂³×C₅₃	semidirect
545. C₂²×C₈	C₂³×C₅₃	semidirect
551. #125	C₂³×C₅₃	semidirect
555. C₂²⋊Q₈	C₂³×C₅₃	semidirect
556. C₂²⋊Q₈	C₂³×C₅₃	semidirect
565. C₄×Q₈	C₂³×C₅₃	semidirect
572. #117	C₂³×C₅₃	semidirect
585. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
597. #107	C₂³×C₅₃	semidirect
598. #107	C₂³×C₅₃	semidirect
599. #106	C₂³×C₅₃	semidirect
600. C₄⋊C₈	C₂³×C₅₃	semidirect
601. #103	C₂³×C₅₃	semidirect
605. #102	C₂³×C₅₃	semidirect
606. #102	C₂³×C₅₃	semidirect
607. #102	C₂³×C₅₃	semidirect
608. #102	C₂³×C₅₃	semidirect
609. #102	C₂³×C₅₃	semidirect
610. #102	C₂³×C₅₃	semidirect
611. C₂²⋊C₈	C₂³×C₅₃	semidirect
612. C₂²⋊C₈	C₂³×C₅₃	semidirect
613. #97	C₂³×C₅₃	semidirect
851. C₂	C₅₃×#3310	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×#552	2
C₂×D₄²×C₅₃	2
C₅₃×#3310	2
C₂×C₅₃×#490	2
C₂×C₅₃×#482	2
C₂×C₅₃×#480	2
C₂×C₅₃×#478	2
C₂×C₅₃×#468	2
C₂×C₅₃×#465	2
C₂×C₅₃×#460	2
C₂×C₅₃×#450	2
C₂×C₅₃×#440	2
C₂×C₅₃×#435	2
C₂×C₅₃×#418	2
C₂²×#102×C₅₃	2
C₂×#3310	53

Subgroups — C2×C53×#3310 #27268639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3310 #27268639