Subgroups — C₅₃×#34737 #27242249

Order 13568.

3578 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#117×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2417	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2416	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2415	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2414	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2413	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2412	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2411	C₂	1	2	yes	maximal, complemented
12	C₅₃×#2410	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2392	C₂	1	4	yes	maximal, complemented
14	C₄×#121×C₅₃	C₂	1	4	yes	maximal, complemented
15	C₅₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
22	C₅₃×#525	—	2	8	no	—
23	C₅₃×#525	—	2	8	no	—
24	C₂×#123×C₅₃	C₂²	1	2	yes	—
25	C₂×#123×C₅₃	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
28	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#121×C₅₃	C₂²	1	4	yes	—
30	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
32	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×#120×C₅₃	C₂²	1	2	yes	—
34	C₂×#120×C₅₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₅₃	—	2	8	no	—
36	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
41	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
42	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
43	C₂×#117×C₅₃	—	2	8	no	—
44	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×#117×C₅₃	C₂²	1	2	yes	—
47	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
49	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
50	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
51	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
52	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
53	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
54	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
56	C₂²×C₄²×C₅₃	C₂²	1	2	yes	complemented
57	C₅₃×#398	C₂²	1	4	yes	complemented
58	C₅₃×#397	C₂²	1	4	yes	complemented
59	C₅₃×#396	C₂²	1	4	yes	complemented
60	C₅₃×#396	C₂²	1	4	yes	complemented
61	C₅₃×#394	C₂²	1	4	yes	—
62	C₅₃×#394	C₂²	1	4	yes	complemented
63	C₅₃×#394	C₂²	1	4	yes	complemented
64	C₅₃×#392	C₂²	1	4	yes	—
65	C₅₃×#391	C₂²	1	2	yes	complemented
66	C₅₃×#390	C₂²	1	2	yes	complemented
67	C₅₃×#390	C₂²	1	4	yes	complemented
68	C₅₃×#389	C₂²	1	2	yes	complemented
69	C₅₃×#389	C₂²	1	2	yes	complemented
70	C₅₃×#389	C₂²	1	4	yes	complemented
71	C₅₃×#388	C₂²	1	4	yes	complemented
72	C₅₃×#388	C₂²	1	4	yes	complemented
73	C₅₃×#386	C₂²	1	2	yes	—
74	C₅₃×#386	C₂²	1	2	yes	—
75	C₅₃×#386	C₂²	1	4	yes	—
76	C₅₃×#386	C₂²	1	4	yes	complemented
77	C₅₃×#385	C₂²	1	2	yes	—
78	C₅₃×#385	C₂²	1	2	yes	—
79	C₅₃×#381	C₂²	1	2	yes	—
80	C₅₃×#380	C₂²	1	2	yes	complemented
81	C₅₃×#380	C₂²	1	2	yes	complemented
82	C₅₃×#380	C₂²	1	4	yes	complemented
83	C₅₃×#379	C₂²	1	2	yes	—
84	C₄×C₄⋊C₄×C₅₃	C₂²	1	4	yes	complemented
85	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	complemented
86	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	complemented
87	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
88	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
89	C₂×#41×C₅₃	—	2	4	no	—
90	C₂×#41×C₅₃	—	2	4	no	—
91	C₂×#41×C₅₃	—	2	4	no	—
92	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₅₃	—	2	4	no	—
94	C₂²×D₄×C₅₃	—	2	8	no	—
95	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
96	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
98	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
100	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
101	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
102	C₂³×C₄×C₅₃	—	2	4	no	—
103	C₂³×C₄×C₅₃	—	2	4	no	—
104	C₂³×C₄×C₅₃	—	2	4	no	—
105	C₂³×C₄×C₅₃	—	2	4	no	—
106	C₂³×C₄×C₅₃	—	2	4	no	—
107	C₂³×C₄×C₅₃	D₄	1	8	yes	complemented
108	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
113	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
114	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
121	#123×C₅₃	—	2	8	no	—
122	#123×C₅₃	—	2	8	no	—
123	C₂²⋊Q₈×C₅₃	—	2	8	no	—
124	C₂²⋊Q₈×C₅₃	—	2	4	no	—
125	C₂²⋊Q₈×C₅₃	—	2	4	no	—
126	#121×C₅₃	—	2	8	no	—
127	#121×C₅₃	—	2	16	no	—
128	#121×C₅₃	—	2	4	no	—
129	#121×C₅₃	—	2	4	no	—
130	#120×C₅₃	—	2	8	no	—
131	#120×C₅₃	—	2	8	no	—
132	C₄×D₄×C₅₃	—	2	16	no	—
133	C₄×D₄×C₅₃	—	2	8	no	—
134	C₄×D₄×C₅₃	—	2	8	no	—
135	C₄×D₄×C₅₃	—	2	8	no	—
136	C₄×D₄×C₅₃	—	2	8	no	—
137	C₄×D₄×C₅₃	—	2	8	no	—
138	C₄×D₄×C₅₃	—	2	8	no	—
139	#117×C₅₃	—	2	8	no	—
140	#117×C₅₃	—	2	8	no	—
141	#117×C₅₃	—	2	8	no	—
142	#117×C₅₃	—	2	4	no	—
143	#117×C₅₃	—	2	4	no	—
144	#117×C₅₃	D₄	1	8	yes	complemented
145	C₂×C₄⋊C₄×C₅₃	—	2	8	no	—
146	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
147	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
151	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
154	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
157	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
158	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
160	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
161	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
162	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
164	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
171	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
173	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
176	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
177	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
178	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
179	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₅₃	—	2	8	no	—
181	C₂×C₄²×C₅₃	—	2	4	no	—
182	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
183	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
184	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
188	#95×C₅₃	C₂³	1	4	yes	—
189	#95×C₅₃	C₂³	1	4	yes	—
190	#95×C₅₃	C₂³	1	4	yes	—
191	#95×C₅₃	C₂³	1	4	yes	—
192	#95×C₅₃	C₂³	1	4	yes	—
193	#95×C₅₃	C₂³	1	4	yes	—
194	C₂⁴×C₅₃	—	2	2	no	—
195	C₂⁴×C₅₃	—	2	2	no	—
196	C₂⁴×C₅₃	—	2	2	no	—
197	C₂⁴×C₅₃	—	2	4	no	—
198	C₂⁴×C₅₃	—	2	4	no	—
199	C₂⁴×C₅₃	—	2	2	no	—
200	C₂⁴×C₅₃	—	2	2	no	—
201	C₂⁴×C₅₃	—	4	2	no	—
202	C₂⁴×C₅₃	—	4	2	no	—
203	C₂⁴×C₅₃	C₂×D₄	1	4	yes	—
204	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
205	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
206	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
207	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
208	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
209	#41×C₅₃	—	4	16	no	—
210	C₂×Q₈×C₅₃	—	2	2	no	—
211	C₂×Q₈×C₅₃	—	2	2	no	—
212	C₂×Q₈×C₅₃	—	2	2	no	—
213	C₂×D₄×C₅₃	—	2	32	no	—
214	C₂×D₄×C₅₃	—	2	4	no	—
215	C₂×D₄×C₅₃	—	2	4	no	—
216	C₂×D₄×C₅₃	—	2	4	no	—
217	C₂×D₄×C₅₃	—	2	4	no	—
218	C₂×D₄×C₅₃	—	2	4	no	—
219	C₂×D₄×C₅₃	—	2	4	no	—
220	C₂×D₄×C₅₃	—	2	4	no	—
221	C₂×D₄×C₅₃	—	2	4	no	—
222	C₂×D₄×C₅₃	—	2	8	no	—
223	C₂×D₄×C₅₃	—	2	8	no	—
224	C₂×D₄×C₅₃	—	2	4	no	—
225	C₂×D₄×C₅₃	—	2	8	no	—
226	C₂×D₄×C₅₃	—	2	2	no	—
227	C₂×D₄×C₅₃	—	2	2	no	—
228	C₂×D₄×C₅₃	—	2	4	no	—
229	C₂×D₄×C₅₃	—	2	2	no	—
230	C₂×D₄×C₅₃	—	4	4	no	—
231	C₂×D₄×C₅₃	—	4	4	no	—
232	C₂×D₄×C₅₃	#41	1	8	yes	complemented
233	C₂²×C₄×C₅₃	—	2	2	no	—
234	C₂²×C₄×C₅₃	—	2	2	no	—
235	C₂²×C₄×C₅₃	—	2	2	no	—
236	C₂²×C₄×C₅₃	—	2	32	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	2	no	—
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	4	no	—
246	C₂²×C₄×C₅₃	—	2	2	no	—
247	C₂²×C₄×C₅₃	—	2	2	no	—
248	C₂²×C₄×C₅₃	—	2	2	no	—
249	C₂²×C₄×C₅₃	—	2	8	no	—
250	C₂²×C₄×C₅₃	—	2	2	no	—
251	C₂²×C₄×C₅₃	—	2	8	no	—
252	C₂²×C₄×C₅₃	—	2	4	no	—
253	C₂²×C₄×C₅₃	—	2	4	no	—
254	C₂²×C₄×C₅₃	—	2	4	no	—
255	C₂²×C₄×C₅₃	—	2	4	no	—
256	C₂²×C₄×C₅₃	—	2	4	no	—
257	C₂²×C₄×C₅₃	—	2	4	no	—
258	C₂²×C₄×C₅₃	—	2	4	no	—
259	C₂²×C₄×C₅₃	—	2	4	no	—
260	C₂²×C₄×C₅₃	—	2	4	no	—
261	C₂²×C₄×C₅₃	—	4	4	no	—
262	C₂²×C₄×C₅₃	—	4	2	no	—
263	C₂²×C₄×C₅₃	—	4	16	no	—
264	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
265	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
266	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
267	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
268	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
269	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
270	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
271	C₂²×C₄×C₅₃	#41	1	4	yes	—
272	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
274	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
279	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
284	C₄⋊C₄×C₅₃	—	2	8	no	—
285	C₄⋊C₄×C₅₃	—	2	4	no	—
286	C₄⋊C₄×C₅₃	—	2	4	no	—
287	C₄⋊C₄×C₅₃	—	2	4	no	—
288	C₄⋊C₄×C₅₃	—	2	2	no	—
289	C₄⋊C₄×C₅₃	—	2	2	no	—
290	C₄⋊C₄×C₅₃	—	2	8	no	—
291	C₄⋊C₄×C₅₃	—	2	4	no	—
292	C₄⋊C₄×C₅₃	—	2	4	no	—
293	C₄⋊C₄×C₅₃	—	2	8	no	—
294	C₄⋊C₄×C₅₃	—	4	4	no	—
295	C₄⋊C₄×C₅₃	C₂×D₄	1	8	yes	complemented
296	C₂²⋊C₄×C₅₃	—	2	4	no	—
297	C₂²⋊C₄×C₅₃	—	2	4	no	—
298	C₂²⋊C₄×C₅₃	—	2	4	no	—
299	C₂²⋊C₄×C₅₃	—	2	4	no	—
300	C₂²⋊C₄×C₅₃	—	2	4	no	—
301	C₂²⋊C₄×C₅₃	—	2	4	no	—
302	C₂²⋊C₄×C₅₃	—	2	8	no	—
303	C₂²⋊C₄×C₅₃	—	2	8	no	—
304	C₂²⋊C₄×C₅₃	—	2	4	no	—
305	C₂²⋊C₄×C₅₃	—	2	4	no	—
306	C₂²⋊C₄×C₅₃	—	2	8	no	—
307	C₂²⋊C₄×C₅₃	—	2	8	no	—
308	C₂²⋊C₄×C₅₃	—	2	4	no	—
309	C₂²⋊C₄×C₅₃	—	2	4	no	—
310	C₂²⋊C₄×C₅₃	—	2	8	no	—
311	C₂²⋊C₄×C₅₃	—	4	4	no	—
312	C₂²⋊C₄×C₅₃	—	4	4	no	—
313	C₂²⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
314	C₄²×C₅₃	—	2	8	no	—
315	C₄²×C₅₃	—	2	4	no	—
316	C₄²×C₅₃	—	2	4	no	—
317	C₄²×C₅₃	—	2	4	no	—
318	C₄²×C₅₃	—	2	4	no	—
319	C₄²×C₅₃	C₂×D₄	1	8	yes	complemented
320	C₂³×C₅₃	—	2	1	no	—
321	C₂³×C₅₃	—	2	1	no	—
322	C₂³×C₅₃	—	2	2	no	—
323	C₂³×C₅₃	—	2	2	no	—
324	C₂³×C₅₃	—	2	2	no	—
325	C₂³×C₅₃	—	2	8	no	—
326	C₂³×C₅₃	—	2	8	no	—
327	C₂³×C₅₃	—	2	8	no	—
328	C₂³×C₅₃	—	2	2	no	—
329	C₂³×C₅₃	—	2	2	no	—
330	C₂³×C₅₃	—	2	1	no	—
331	C₂³×C₅₃	—	2	1	no	—
332	C₂³×C₅₃	—	2	2	no	—
333	C₂³×C₅₃	—	2	2	no	—
334	C₂³×C₅₃	—	2	2	no	—
335	C₂³×C₅₃	—	2	2	no	—
336	C₂³×C₅₃	—	2	2	no	—
337	C₂³×C₅₃	—	2	2	no	—
338	C₂³×C₅₃	—	2	2	no	—
339	C₂³×C₅₃	—	2	2	no	—
340	C₂³×C₅₃	—	2	2	no	—
341	C₂³×C₅₃	—	2	4	no	—
342	C₂³×C₅₃	—	2	4	no	—
343	C₂³×C₅₃	—	4	4	no	—
344	C₂³×C₅₃	—	4	8	no	—
345	C₂³×C₅₃	—	4	8	no	—
346	C₂³×C₅₃	—	4	8	no	—
347	C₂³×C₅₃	—	4	8	no	—
348	C₂³×C₅₃	—	4	4	no	—
349	C₂³×C₅₃	—	4	4	no	—
350	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
351	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
352	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
353	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
354	C₂³×C₅₃	C₂×#41	1	4	yes	—
355	C₂³×C₅₃	C₂×#41	1	2	yes	—
356	C₂³×C₅₃	C₂×#41	1	4	yes	—
357	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
358	Q₈×C₅₃	—	4	4	no	—
359	D₄×C₅₃	—	2	16	no	—
360	D₄×C₅₃	—	2	16	no	—
361	D₄×C₅₃	—	4	16	no	—
362	D₄×C₅₃	—	4	8	no	—
363	D₄×C₅₃	—	4	8	no	—
364	D₄×C₅₃	—	4	8	no	—
365	D₄×C₅₃	—	4	4	no	—
366	C₂×C₄×C₅₃	—	2	8	no	—
367	C₂×C₄×C₅₃	—	2	8	no	—
368	C₂×C₄×C₅₃	—	2	1	no	—
369	C₂×C₄×C₅₃	—	2	1	no	—
370	C₂×C₄×C₅₃	—	2	2	no	—
371	C₂×C₄×C₅₃	—	2	1	no	—
372	C₂×C₄×C₅₃	—	2	1	no	—
373	C₂×C₄×C₅₃	—	2	2	no	—
374	C₂×C₄×C₅₃	—	2	4	no	—
375	C₂×C₄×C₅₃	—	2	4	no	—
376	C₂×C₄×C₅₃	—	2	8	no	—
377	C₂×C₄×C₅₃	—	2	8	no	—
378	C₂×C₄×C₅₃	—	2	8	no	—
379	C₂×C₄×C₅₃	—	2	8	no	—
380	C₂×C₄×C₅₃	—	2	2	no	—
381	C₂×C₄×C₅₃	—	2	2	no	—
382	C₂×C₄×C₅₃	—	2	2	no	—
383	C₂×C₄×C₅₃	—	2	2	no	—
384	C₂×C₄×C₅₃	—	2	2	no	—
385	C₂×C₄×C₅₃	—	2	4	no	—
386	C₂×C₄×C₅₃	—	2	2	no	—
387	C₂×C₄×C₅₃	—	2	2	no	—
388	C₂×C₄×C₅₃	—	2	2	no	—
389	C₂×C₄×C₅₃	—	2	2	no	—
390	C₂×C₄×C₅₃	—	2	4	no	—
391	C₂×C₄×C₅₃	—	2	4	no	—
392	C₂×C₄×C₅₃	—	2	2	no	—
393	C₂×C₄×C₅₃	—	2	4	no	—
394	C₂×C₄×C₅₃	—	2	2	no	—
395	C₂×C₄×C₅₃	—	2	4	no	—
396	C₂×C₄×C₅₃	—	4	16	no	—
397	C₂×C₄×C₅₃	—	4	4	no	—
398	C₂×C₄×C₅₃	—	4	4	no	—
399	C₂×C₄×C₅₃	—	4	8	no	—
400	C₂×C₄×C₅₃	—	4	8	no	—
401	C₂×C₄×C₅₃	—	4	8	no	—
402	C₂×C₄×C₅₃	#121	1	16	yes	complemented
403	C₂×C₄×C₅₃	C₂²×D₄	1	8	yes	—
404	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
411	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
412	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
413	#34737	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
414	C₂²×C₅₃	—	2	2	no	—
415	C₂²×C₅₃	—	2	2	no	—
416	C₂²×C₅₃	—	2	2	no	—
417	C₂²×C₅₃	—	2	2	no	—
418	C₂²×C₅₃	—	2	4	no	—
419	C₂²×C₅₃	—	2	4	no	—
420	C₂²×C₅₃	—	2	4	no	—
421	C₂²×C₅₃	—	2	4	no	—
422	C₂²×C₅₃	—	2	2	no	—
423	C₂²×C₅₃	—	2	2	no	—
424	C₂²×C₅₃	—	2	4	no	—
425	C₂²×C₅₃	—	2	2	no	—
426	C₂²×C₅₃	—	2	4	no	—
427	C₂²×C₅₃	—	2	4	no	—
428	C₂²×C₅₃	—	4	16	no	—
429	C₂²×C₅₃	—	4	16	no	—
430	C₂²×C₅₃	—	4	2	no	—
431	C₂²×C₅₃	—	4	2	no	—
432	C₂²×C₅₃	—	4	2	no	—
433	C₂²×C₅₃	—	4	2	no	—
434	C₂²×C₅₃	—	4	2	no	—
435	C₂²×C₅₃	—	4	2	no	—
436	C₂²×C₅₃	—	4	2	no	—
437	C₂²×C₅₃	—	4	2	no	—
438	C₂²×C₅₃	—	4	2	no	—
439	C₂²×C₅₃	—	4	4	no	—
440	C₂²×C₅₃	—	4	4	no	—
441	C₂²×C₅₃	C₂×#121	1	4	yes	—
442	C₂²×C₅₃	#525	1	4	yes	complemented
443	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
444	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
445	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
446	C₂²×C₅₃	C₂²×#41	1	2	yes	—
447	C₂²×C₅₃	#585	1	2	yes	—
448	C₄×C₅₃	—	2	2	no	—
449	C₄×C₅₃	—	2	2	no	—
450	C₄×C₅₃	—	2	4	no	—
451	C₄×C₅₃	—	2	8	no	—
452	C₄×C₅₃	—	4	2	no	—
453	C₄×C₅₃	—	4	2	no	—
454	C₄×C₅₃	—	4	2	no	—
455	C₄×C₅₃	—	4	2	no	—
456	C₄×C₅₃	—	4	2	no	—
457	C₄×C₅₃	—	4	4	no	—
458	C₄×C₅₃	C₂×#121	1	4	yes	—
459	C₄×C₅₃	C₂×#121	1	4	yes	—
460	C₂×#525	C₂×C₅₃	1	1	yes	characteristic, complemented
461	C₂×#525	C₂×C₅₃	1	1	yes	characteristic, complemented
462	C₂²×C₄×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
463	C₂²×#117	C₂×C₅₃	1	1	yes	characteristic, complemented
464	#2417	C₂×C₅₃	1	2	yes	complemented
465	#2416	C₂×C₅₃	1	2	yes	complemented
466	#2415	C₂×C₅₃	1	2	yes	complemented
467	#2414	C₂×C₅₃	1	2	yes	complemented
468	#2413	C₂×C₅₃	1	2	yes	complemented
469	#2412	C₂×C₅₃	1	2	yes	complemented
470	#2411	C₂×C₅₃	1	2	yes	complemented
471	#2410	C₂×C₅₃	1	2	yes	complemented
472	#2392	C₂×C₅₃	1	4	yes	complemented
473	C₄×#121	C₂×C₅₃	1	4	yes	complemented
474	#2297	C₂×C₅₃	1	1	yes	characteristic, complemented
475	#2296	C₂×C₅₃	1	1	yes	characteristic, complemented
476	#2280	C₂×C₅₃	1	1	yes	characteristic, complemented
477	C₂×C₅₃	—	2	4	no	—
478	C₂×C₅₃	—	2	4	no	—
479	C₂×C₅₃	—	4	2	no	—
480	C₂×C₅₃	—	4	4	no	—
481	C₂×C₅₃	—	8	2	no	—
482	C₂×C₅₃	C₂²×#121	1	1	yes	characteristic
483	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
484	C₂×C₅₃	#3449	1	1	yes	characteristic
485	C₂×C₅₃	D₄×#41	1	2	yes	—
486	C₂×C₅₃	#3475	1	2	yes	—
487	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
488	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
489	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
490	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
491	#525	—	2	8	no	—
492	#525	—	2	8	no	—
493	C₂×#123	C₂²×C₅₃	1	2	yes	—
494	C₂×#123	C₂²×C₅₃	1	2	yes	—
495	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
496	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
497	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
498	C₂×#121	C₂²×C₅₃	1	4	yes	—
499	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
500	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
501	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
502	C₂×#120	C₂²×C₅₃	1	2	yes	—
503	C₂×#120	C₂²×C₅₃	1	2	yes	—
504	C₂×C₄×D₄	—	2	8	no	—
505	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
506	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
507	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
508	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
509	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
510	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
511	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
512	C₂×#117	—	2	8	no	—
513	C₂×#117	C₂²×C₅₃	1	2	yes	—
514	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
515	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
516	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
517	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
518	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
519	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
520	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
521	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
522	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
523	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
524	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
525	C₂²×C₄²	C₂²×C₅₃	1	2	yes	complemented
526	#398	C₂²×C₅₃	1	4	yes	complemented
527	#397	C₂²×C₅₃	1	4	yes	complemented
528	#396	C₂²×C₅₃	1	4	yes	complemented
529	#396	C₂²×C₅₃	1	4	yes	complemented
530	#394	C₂²×C₅₃	1	4	yes	—
531	#394	C₂²×C₅₃	1	4	yes	complemented
532	#394	C₂²×C₅₃	1	4	yes	complemented
533	#392	C₂²×C₅₃	1	4	yes	—
534	#391	C₂²×C₅₃	1	2	yes	complemented
535	#390	C₂²×C₅₃	1	4	yes	complemented
536	#390	C₂²×C₅₃	1	2	yes	complemented
537	#389	C₂²×C₅₃	1	4	yes	complemented
538	#389	C₂²×C₅₃	1	2	yes	complemented
539	#389	C₂²×C₅₃	1	2	yes	complemented
540	#388	C₂²×C₅₃	1	4	yes	complemented
541	#388	C₂²×C₅₃	1	4	yes	complemented
542	#386	C₂²×C₅₃	1	2	yes	—
543	#386	C₂²×C₅₃	1	4	yes	—
544	#386	C₂²×C₅₃	1	2	yes	—
545	#386	C₂²×C₅₃	1	4	yes	complemented
546	#385	C₂²×C₅₃	1	2	yes	—
547	#385	C₂²×C₅₃	1	2	yes	—
548	#381	C₂²×C₅₃	1	2	yes	—
549	#380	C₂²×C₅₃	1	4	yes	complemented
550	#380	C₂²×C₅₃	1	2	yes	complemented
551	#380	C₂²×C₅₃	1	2	yes	complemented
552	#379	C₂²×C₅₃	1	2	yes	—
553	C₄×C₄⋊C₄	C₂²×C₅₃	1	4	yes	complemented
554	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	complemented
555	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	complemented
556	C₅₃	#34737	1	1	yes	characteristic, direct product factor, Sylow
557	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
558	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
559	C₂×#41	—	2	4	no	—
560	C₂×#41	—	2	4	no	—
561	C₂×#41	—	2	4	no	—
562	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
563	C₂²×D₄	—	2	4	no	—
564	C₂²×D₄	—	2	8	no	—
565	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
566	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
567	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
568	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
570	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
571	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
572	C₂³×C₄	—	2	4	no	—
573	C₂³×C₄	—	2	4	no	—
574	C₂³×C₄	—	2	4	no	—
575	C₂³×C₄	—	2	4	no	—
576	C₂³×C₄	—	2	4	no	—
577	C₂³×C₄	D₄×C₅₃	1	8	yes	complemented
578	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
581	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
582	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
583	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
584	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
591	#123	—	2	8	no	—
592	#123	—	2	8	no	—
593	C₂²⋊Q₈	—	2	4	no	—
594	C₂²⋊Q₈	—	2	4	no	—
595	C₂²⋊Q₈	—	2	8	no	—
596	#121	—	2	16	no	—
597	#121	—	2	4	no	—
598	#121	—	2	4	no	—
599	#121	—	2	8	no	—
600	#120	—	2	8	no	—
601	#120	—	2	8	no	—
602	C₄×D₄	—	2	8	no	—
603	C₄×D₄	—	2	8	no	—
604	C₄×D₄	—	2	8	no	—
605	C₄×D₄	—	2	8	no	—
606	C₄×D₄	—	2	8	no	—
607	C₄×D₄	—	2	8	no	—
608	C₄×D₄	—	2	16	no	—
609	#117	—	2	4	no	—
610	#117	—	2	4	no	—
611	#117	—	2	8	no	—
612	#117	—	2	8	no	—
613	#117	—	2	8	no	—
614	#117	D₄×C₅₃	1	8	yes	complemented
615	C₂×C₄⋊C₄	—	2	4	no	—
616	C₂×C₄⋊C₄	—	2	8	no	—
617	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
621	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
624	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
627	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
628	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
629	C₂×C₂²⋊C₄	—	2	4	no	—
630	C₂×C₂²⋊C₄	—	2	4	no	—
631	C₂×C₂²⋊C₄	—	2	8	no	—
632	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
650	C₂×C₄²	—	2	4	no	—
651	C₂×C₄²	—	2	8	no	—
652	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
653	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
654	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
655	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
656	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
657	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
658	#95	C₂³×C₅₃	1	4	yes	—
659	#95	C₂³×C₅₃	1	4	yes	—
660	#95	C₂³×C₅₃	1	4	yes	—
661	#95	C₂³×C₅₃	1	4	yes	—
662	#95	C₂³×C₅₃	1	4	yes	—
663	#95	C₂³×C₅₃	1	4	yes	—
664	C₂⁴	—	2	2	no	—
665	C₂⁴	—	2	2	no	—
666	C₂⁴	—	2	2	no	—
667	C₂⁴	—	2	4	no	—
668	C₂⁴	—	2	4	no	—
669	C₂⁴	—	2	2	no	—
670	C₂⁴	—	2	2	no	—
671	C₂⁴	—	4	2	no	—
672	C₂⁴	—	4	2	no	—
673	C₂⁴	C₂×D₄×C₅₃	1	4	yes	—
674	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
675	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
676	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
677	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
678	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
679	#41	—	4	16	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×D₄	—	2	32	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	8	no	—
693	C₂×D₄	—	2	8	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	8	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	4	4	no	—
701	C₂×D₄	—	4	4	no	—
702	C₂×D₄	#41×C₅₃	1	8	yes	complemented
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	32	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	8	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	8	no	—
722	C₂²×C₄	—	2	4	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	4	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	4	4	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	16	no	—
734	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
735	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
736	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
737	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
738	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
739	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
740	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
741	C₂²×C₄	#41×C₅₃	1	4	yes	—
742	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
744	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
749	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
754	C₄⋊C₄	—	2	8	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	4	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	8	no	—
763	C₄⋊C₄	—	2	8	no	—
764	C₄⋊C₄	—	4	4	no	—
765	C₄⋊C₄	C₂×D₄×C₅₃	1	8	yes	complemented
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	8	no	—
773	C₂²⋊C₄	—	2	8	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	8	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	8	no	—
780	C₂²⋊C₄	—	2	8	no	—
781	C₂²⋊C₄	—	4	4	no	—
782	C₂²⋊C₄	—	4	4	no	—
783	C₂²⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
784	C₄²	—	2	8	no	—
785	C₄²	—	2	4	no	—
786	C₄²	—	2	4	no	—
787	C₄²	—	2	4	no	—
788	C₄²	—	2	4	no	—
789	C₄²	C₂×D₄×C₅₃	1	8	yes	complemented
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	8	no	—
796	C₂³	—	2	8	no	—
797	C₂³	—	2	8	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	4	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	4	no	—
813	C₂³	—	4	4	no	—
814	C₂³	—	4	8	no	—
815	C₂³	—	4	8	no	—
816	C₂³	—	4	8	no	—
817	C₂³	—	4	8	no	—
818	C₂³	—	4	4	no	—
819	C₂³	—	4	4	no	—
820	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
821	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
822	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
823	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
824	C₂³	C₂×#41×C₅₃	1	4	yes	—
825	C₂³	C₂×#41×C₅₃	1	2	yes	—
826	C₂³	C₂×#41×C₅₃	1	4	yes	—
827	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
828	Q₈	—	4	4	no	—
829	D₄	—	2	16	no	—
830	D₄	—	2	16	no	—
831	D₄	—	4	16	no	—
832	D₄	—	4	8	no	—
833	D₄	—	4	8	no	—
834	D₄	—	4	8	no	—
835	D₄	—	4	4	no	—
836	C₂×C₄	—	2	8	no	—
837	C₂×C₄	—	2	8	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	4	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	4	no	—
846	C₂×C₄	—	2	8	no	—
847	C₂×C₄	—	2	8	no	—
848	C₂×C₄	—	2	8	no	—
849	C₂×C₄	—	2	8	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	4	no	—
859	C₂×C₄	—	2	4	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	4	no	—
864	C₂×C₄	—	2	4	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	4	16	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	8	no	—
870	C₂×C₄	—	4	8	no	—
871	C₂×C₄	—	4	8	no	—
872	C₂×C₄	#121×C₅₃	1	16	yes	complemented
873	C₂×C₄	C₂²×D₄×C₅₃	1	8	yes	—
874	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
875	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
876	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
878	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
879	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
880	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
881	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
882	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	4	no	—
897	C₂²	—	4	16	no	—
898	C₂²	—	4	16	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	4	no	—
907	C₂²	—	4	4	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	C₂×#121×C₅₃	1	4	yes	—
911	C₂²	C₅₃×#525	1	4	yes	complemented
912	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
913	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
914	C₂²	C₂²×#41×C₅₃	1	2	yes	—
915	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
916	C₂²	C₅₃×#585	1	2	yes	—
917	C₄	—	2	8	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	4	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	4	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	C₂×#121×C₅₃	1	4	yes	—
928	C₄	C₂×#121×C₅₃	1	4	yes	—
929	C₂	—	2	4	no	—
930	C₂	—	2	4	no	—
931	C₂	—	4	2	no	—
932	C₂	—	4	4	no	—
933	C₂	—	8	2	no	—
934	C₂	C₂²×#121×C₅₃	1	1	yes	characteristic
935	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
936	C₂	C₅₃×#3449	1	1	yes	characteristic
937	C₂	D₄×#41×C₅₃	1	2	yes	—
938	C₂	C₅₃×#3475	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
socle	C₂³×C₅₃	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#525	C₂	semidirect
2. C₂×C₅₃×#525	C₂	semidirect
3. C₂²×C₄×D₄×C₅₃	C₂	semidirect
4. C₂²×#117×C₅₃	C₂	semidirect
5. C₅₃×#2417	C₂	semidirect
6. C₅₃×#2416	C₂	semidirect
7. C₅₃×#2415	C₂	semidirect
8. C₅₃×#2414	C₂	semidirect
9. C₅₃×#2413	C₂	semidirect
10. C₅₃×#2412	C₂	semidirect
11. C₅₃×#2411	C₂	semidirect
12. C₅₃×#2410	C₂	semidirect
13. C₅₃×#2392	C₂	semidirect
14. C₄×#121×C₅₃	C₂	semidirect
15. C₅₃×#2297	C₂	semidirect
16. C₅₃×#2296	C₂	semidirect
17. C₅₃×#2280	C₂	semidirect
26. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
30. C₂×#121×C₅₃	C₂²	semidirect
31. C₂×#121×C₅₃	C₂²	semidirect
32. C₂×#121×C₅₃	C₂²	semidirect
40. C₂×C₄×D₄×C₅₃	C₂²	semidirect
41. C₂×C₄×D₄×C₅₃	C₂²	semidirect
42. C₂×C₄×D₄×C₅₃	C₂²	semidirect
48. C₂×#117×C₅₃	C₂²	semidirect
49. C₂×#117×C₅₃	C₂²	semidirect
51. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
56. C₂²×C₄²×C₅₃	C₂²	semidirect
57. C₅₃×#398	C₂²	semidirect
58. C₅₃×#397	C₂²	semidirect
59. C₅₃×#396	C₂²	semidirect
60. C₅₃×#396	C₂²	semidirect
62. C₅₃×#394	C₂²	semidirect
63. C₅₃×#394	C₂²	semidirect
65. C₅₃×#391	C₂²	semidirect
66. C₅₃×#390	C₂²	semidirect
67. C₅₃×#390	C₂²	semidirect
68. C₅₃×#389	C₂²	semidirect
69. C₅₃×#389	C₂²	semidirect
70. C₅₃×#389	C₂²	semidirect
71. C₅₃×#388	C₂²	semidirect
72. C₅₃×#388	C₂²	semidirect
76. C₅₃×#386	C₂²	semidirect
80. C₅₃×#380	C₂²	semidirect
81. C₅₃×#380	C₂²	semidirect
82. C₅₃×#380	C₂²	semidirect
84. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
85. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
86. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
107. C₂³×C₄×C₅₃	D₄	semidirect
144. #117×C₅₃	D₄	semidirect
232. C₂×D₄×C₅₃	#41	semidirect
295. C₄⋊C₄×C₅₃	C₂×D₄	semidirect
319. C₄²×C₅₃	C₂×D₄	semidirect
402. C₂×C₄×C₅₃	#121	semidirect
413. #34737	C₅₃	direct (N × H)
442. C₂²×C₅₃	#525	semidirect
460. C₂×#525	C₂×C₅₃	semidirect
461. C₂×#525	C₂×C₅₃	semidirect
462. C₂²×C₄×D₄	C₂×C₅₃	semidirect
463. C₂²×#117	C₂×C₅₃	semidirect
464. #2417	C₂×C₅₃	semidirect
465. #2416	C₂×C₅₃	semidirect
466. #2415	C₂×C₅₃	semidirect
467. #2414	C₂×C₅₃	semidirect
468. #2413	C₂×C₅₃	semidirect
469. #2412	C₂×C₅₃	semidirect
470. #2411	C₂×C₅₃	semidirect
471. #2410	C₂×C₅₃	semidirect
472. #2392	C₂×C₅₃	semidirect
473. C₄×#121	C₂×C₅₃	semidirect
474. #2297	C₂×C₅₃	semidirect
475. #2296	C₂×C₅₃	semidirect
476. #2280	C₂×C₅₃	semidirect
495. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
496. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
497. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
499. C₂×#121	C₂²×C₅₃	semidirect
500. C₂×#121	C₂²×C₅₃	semidirect
501. C₂×#121	C₂²×C₅₃	semidirect
509. C₂×C₄×D₄	C₂²×C₅₃	semidirect
510. C₂×C₄×D₄	C₂²×C₅₃	semidirect
511. C₂×C₄×D₄	C₂²×C₅₃	semidirect
517. C₂×#117	C₂²×C₅₃	semidirect
518. C₂×#117	C₂²×C₅₃	semidirect
520. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
525. C₂²×C₄²	C₂²×C₅₃	semidirect
526. #398	C₂²×C₅₃	semidirect
527. #397	C₂²×C₅₃	semidirect
528. #396	C₂²×C₅₃	semidirect
529. #396	C₂²×C₅₃	semidirect
531. #394	C₂²×C₅₃	semidirect
532. #394	C₂²×C₅₃	semidirect
534. #391	C₂²×C₅₃	semidirect
535. #390	C₂²×C₅₃	semidirect
536. #390	C₂²×C₅₃	semidirect
537. #389	C₂²×C₅₃	semidirect
538. #389	C₂²×C₅₃	semidirect
539. #389	C₂²×C₅₃	semidirect
540. #388	C₂²×C₅₃	semidirect
541. #388	C₂²×C₅₃	semidirect
545. #386	C₂²×C₅₃	semidirect
549. #380	C₂²×C₅₃	semidirect
550. #380	C₂²×C₅₃	semidirect
551. #380	C₂²×C₅₃	semidirect
553. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
554. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
555. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
556. C₅₃	#34737	direct (N × H)
577. C₂³×C₄	D₄×C₅₃	semidirect
614. #117	D₄×C₅₃	semidirect
702. C₂×D₄	#41×C₅₃	semidirect
765. C₄⋊C₄	C₂×D₄×C₅₃	semidirect
789. C₄²	C₂×D₄×C₅₃	semidirect
872. C₂×C₄	#121×C₅₃	semidirect
911. C₂²	C₅₃×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#525	2
C₂²×C₄×D₄×C₅₃	2
C₂²×#117×C₅₃	2
C₅₃×#2417	2
C₅₃×#2416	2
C₅₃×#2415	2
C₅₃×#2414	2
C₅₃×#2413	2
C₅₃×#2412	2
C₅₃×#2411	2
C₅₃×#2410	2
C₅₃×#2392	2
C₄×#121×C₅₃	2
C₅₃×#2297	2
C₅₃×#2296	2
C₅₃×#2280	2
#34737	53

Subgroups — C53×#34737 #27242249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34737 #27242249