Subgroups — C₅₃×#34223 #27241735

Order 13568.

2698 conjugacy classes of subgroups.

The subgroup lattice has 766 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
2	C₅₃×#2374	C₂	1	4	yes	maximal, complemented
3	C₅₃×#2363	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2362	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2357	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2353	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2346	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2321	C₂	1	4	yes	maximal, complemented
12	C₅₃×#2318	C₂	1	2	yes	maximal, complemented
13	C₄×C₂²⋊Q₈×C₅₃	C₂	1	2	yes	maximal, complemented
14	C₄×#121×C₅₃	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2275	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
20	C₅₃×#525	C₄	1	16	yes	complemented
21	C₂×#123×C₅₃	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#120×C₅₃	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
28	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
32	C₂×#117×C₅₃	C₂²	1	2	yes	—
33	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
35	C₂²×C₄²×C₅₃	C₂²	1	2	yes	—
36	C₅₃×#391	C₂²	1	2	yes	complemented
37	C₅₃×#390	C₂²	1	4	yes	—
38	C₅₃×#390	C₂²	1	4	yes	—
39	C₅₃×#390	C₂²	1	2	yes	complemented
40	C₅₃×#389	C₂²	1	2	yes	complemented
41	C₅₃×#389	C₂²	1	2	yes	complemented
42	C₅₃×#388	C₂²	1	4	yes	—
43	C₅₃×#388	C₂²	1	4	yes	—
44	C₅₃×#388	C₂²	1	4	yes	—
45	C₅₃×#388	C₂²	1	4	yes	—
46	C₅₃×#388	C₂²	1	4	yes	complemented
47	C₅₃×#388	C₂²	1	4	yes	complemented
48	C₅₃×#387	C₂²	1	4	yes	complemented
49	C₅₃×#387	C₂²	1	4	yes	complemented
50	C₅₃×#386	C₂²	1	4	yes	—
51	C₅₃×#386	C₂²	1	4	yes	—
52	C₅₃×#386	C₂²	1	4	yes	—
53	C₅₃×#385	C₂²	1	4	yes	—
54	C₅₃×#383	C₂²	1	2	yes	complemented
55	C₅₃×#382	C₂²	1	2	yes	complemented
56	C₅₃×#381	C₂²	1	2	yes	—
57	C₅₃×#381	C₂²	1	2	yes	complemented
58	C₅₃×#380	C₂²	1	2	yes	—
59	C₅₃×#380	C₂²	1	1	yes	characteristic
60	C₅₃×#380	C₂²	1	1	yes	characteristic
61	C₅₃×#380	C₂²	1	2	yes	complemented
62	C₅₃×#379	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
64	C₄×C₄⋊C₄×C₅₃	C₂²	1	4	yes	complemented
65	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
66	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
67	C₄×C₄⋊C₄×C₅₃	C₂²	1	4	yes	complemented
68	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	—
76	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	complemented
79	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	complemented
80	C₅₃×#376	C₂²	1	2	yes	complemented
81	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
82	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
83	C₂×#95×C₅₃	C₂²	1	2	yes	complemented
84	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
85	C₂×#41×C₅₃	—	4	4	no	—
86	C₂×#41×C₅₃	C₂×C₄	1	8	yes	complemented
87	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
89	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₅₃	—	4	4	no	—
93	C₂³×C₄×C₅₃	C₂×C₄	1	8	yes	complemented
94	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
98	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
99	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
102	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
104	#123×C₅₃	C₂×C₄	1	16	yes	complemented
105	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
106	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
107	#121×C₅₃	C₂×C₄	1	8	yes	—
108	#121×C₅₃	C₂×C₄	1	8	yes	complemented
109	#120×C₅₃	C₂×C₄	1	16	yes	complemented
110	C₄×Q₈×C₅₃	—	4	4	no	—
111	C₄×D₄×C₅₃	—	2	16	no	—
112	C₄×D₄×C₅₃	—	4	4	no	—
113	C₄×D₄×C₅₃	C₂×C₄	1	16	yes	complemented
114	C₄×D₄×C₅₃	C₂×C₄	1	16	yes	complemented
115	#117×C₅₃	—	4	4	no	—
116	#117×C₅₃	C₂×C₄	1	8	yes	complemented
117	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
127	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
143	C₂×C₄²×C₅₃	—	4	4	no	—
144	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
145	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
147	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
148	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
149	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
150	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
151	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
152	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
153	#95×C₅₃	C₂³	1	1	yes	characteristic
154	#95×C₅₃	C₂³	1	1	yes	characteristic
155	#95×C₅₃	C₂³	1	2	yes	—
156	#95×C₅₃	C₂³	1	1	yes	characteristic
157	#95×C₅₃	C₂³	1	1	yes	characteristic
158	#95×C₅₃	C₂³	1	2	yes	—
159	#95×C₅₃	C₂³	1	2	yes	—
160	#95×C₅₃	C₂³	1	4	yes	—
161	#95×C₅₃	C₂³	1	2	yes	—
162	#95×C₅₃	C₂³	1	4	yes	—
163	#95×C₅₃	C₂³	1	4	yes	—
164	#95×C₅₃	C₂³	1	4	yes	—
165	#95×C₅₃	C₂³	1	4	yes	—
166	#95×C₅₃	C₂³	1	4	yes	—
167	#95×C₅₃	C₂³	1	4	yes	—
168	C₂⁴×C₅₃	—	2	4	no	—
169	C₂⁴×C₅₃	—	4	2	no	—
170	C₂⁴×C₅₃	—	4	1	no	—
171	C₂⁴×C₅₃	—	4	1	no	—
172	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
173	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
174	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
175	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
176	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
177	#41×C₅₃	—	4	16	no	—
178	C₂×Q₈×C₅₃	—	2	4	no	—
179	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
180	C₂×D₄×C₅₃	—	2	8	no	—
181	C₂×D₄×C₅₃	—	2	4	no	—
182	C₂×D₄×C₅₃	—	4	2	no	—
183	C₂×D₄×C₅₃	—	4	2	no	—
184	C₂×D₄×C₅₃	—	4	4	no	—
185	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	—
186	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
187	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	—
188	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	—
189	C₂²×C₄×C₅₃	—	2	4	no	—
190	C₂²×C₄×C₅₃	—	2	4	no	—
191	C₂²×C₄×C₅₃	—	2	4	no	—
192	C₂²×C₄×C₅₃	—	2	4	no	—
193	C₂²×C₄×C₅₃	—	2	8	no	—
194	C₂²×C₄×C₅₃	—	4	16	no	—
195	C₂²×C₄×C₅₃	—	4	2	no	—
196	C₂²×C₄×C₅₃	—	4	2	no	—
197	C₂²×C₄×C₅₃	—	4	2	no	—
198	C₂²×C₄×C₅₃	—	4	2	no	—
199	C₂²×C₄×C₅₃	—	4	2	no	—
200	C₂²×C₄×C₅₃	—	4	2	no	—
201	C₂²×C₄×C₅₃	—	4	2	no	—
202	C₂²×C₄×C₅₃	—	4	4	no	—
203	C₂²×C₄×C₅₃	—	4	4	no	—
204	C₂²×C₄×C₅₃	—	4	4	no	—
205	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
206	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
207	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
208	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
209	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
210	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	—
211	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
212	C₂²×C₄×C₅₃	#41	1	8	yes	complemented
213	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
226	C₄⋊C₄×C₅₃	—	2	8	no	—
227	C₄⋊C₄×C₅₃	—	2	4	no	—
228	C₄⋊C₄×C₅₃	—	2	4	no	—
229	C₄⋊C₄×C₅₃	—	4	4	no	—
230	C₄⋊C₄×C₅₃	—	4	4	no	—
231	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
232	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
233	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
234	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
235	C₂²⋊C₄×C₅₃	—	2	8	no	—
236	C₂²⋊C₄×C₅₃	—	2	4	no	—
237	C₂²⋊C₄×C₅₃	—	2	4	no	—
238	C₂²⋊C₄×C₅₃	—	2	4	no	—
239	C₂²⋊C₄×C₅₃	—	2	4	no	—
240	C₂²⋊C₄×C₅₃	—	2	8	no	—
241	C₂²⋊C₄×C₅₃	—	4	2	no	—
242	C₂²⋊C₄×C₅₃	—	4	4	no	—
243	C₂²⋊C₄×C₅₃	—	4	2	no	—
244	C₂²⋊C₄×C₅₃	—	4	4	no	—
245	C₂²⋊C₄×C₅₃	—	4	4	no	—
246	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
247	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
248	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
249	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
250	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
251	C₄²×C₅₃	—	2	8	no	—
252	C₄²×C₅₃	—	2	4	no	—
253	C₄²×C₅₃	—	2	4	no	—
254	C₄²×C₅₃	—	4	2	no	—
255	C₄²×C₅₃	—	4	2	no	—
256	C₄²×C₅₃	—	4	4	no	—
257	C₄²×C₅₃	—	4	4	no	—
258	C₄²×C₅₃	—	4	4	no	—
259	C₄²×C₅₃	C₂²×C₄	1	8	yes	—
260	C₂³×C₅₃	—	2	2	no	—
261	C₂³×C₅₃	—	2	1	no	—
262	C₂³×C₅₃	—	2	1	no	—
263	C₂³×C₅₃	—	2	8	no	—
264	C₂³×C₅₃	—	2	4	no	—
265	C₂³×C₅₃	—	2	2	no	—
266	C₂³×C₅₃	—	2	2	no	—
267	C₂³×C₅₃	—	2	2	no	—
268	C₂³×C₅₃	—	2	2	no	—
269	C₂³×C₅₃	—	2	4	no	—
270	C₂³×C₅₃	—	2	2	no	—
271	C₂³×C₅₃	—	2	1	no	—
272	C₂³×C₅₃	—	2	1	no	—
273	C₂³×C₅₃	—	2	2	no	—
274	C₂³×C₅₃	—	2	1	no	—
275	C₂³×C₅₃	—	2	1	no	—
276	C₂³×C₅₃	—	4	4	no	—
277	C₂³×C₅₃	—	4	4	no	—
278	C₂³×C₅₃	—	4	8	no	—
279	C₂³×C₅₃	—	4	8	no	—
280	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
281	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
282	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
283	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
284	C₂³×C₅₃	C₂×#41	1	4	yes	—
285	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
286	Q₈×C₅₃	—	2	8	no	—
287	D₄×C₅₃	—	2	16	no	—
288	D₄×C₅₃	—	2	8	no	—
289	D₄×C₅₃	—	4	8	no	—
290	D₄×C₅₃	—	4	8	no	—
291	C₂×C₄×C₅₃	—	2	4	no	—
292	C₂×C₄×C₅₃	—	2	2	no	—
293	C₂×C₄×C₅₃	—	2	2	no	—
294	C₂×C₄×C₅₃	—	2	2	no	—
295	C₂×C₄×C₅₃	—	2	2	no	—
296	C₂×C₄×C₅₃	—	2	4	no	—
297	C₂×C₄×C₅₃	—	2	2	no	—
298	C₂×C₄×C₅₃	—	2	2	no	—
299	C₂×C₄×C₅₃	—	2	2	no	—
300	C₂×C₄×C₅₃	—	2	2	no	—
301	C₂×C₄×C₅₃	—	2	2	no	—
302	C₂×C₄×C₅₃	—	2	8	no	—
303	C₂×C₄×C₅₃	—	2	8	no	—
304	C₂×C₄×C₅₃	—	2	8	no	—
305	C₂×C₄×C₅₃	—	2	2	no	—
306	C₂×C₄×C₅₃	—	2	2	no	—
307	C₂×C₄×C₅₃	—	2	4	no	—
308	C₂×C₄×C₅₃	—	2	4	no	—
309	C₂×C₄×C₅₃	—	2	2	no	—
310	C₂×C₄×C₅₃	—	2	2	no	—
311	C₂×C₄×C₅₃	—	2	4	no	—
312	C₂×C₄×C₅₃	—	2	4	no	—
313	C₂×C₄×C₅₃	—	2	4	no	—
314	C₂×C₄×C₅₃	—	2	2	no	—
315	C₂×C₄×C₅₃	—	2	2	no	—
316	C₂×C₄×C₅₃	—	2	4	no	—
317	C₂×C₄×C₅₃	—	4	4	no	—
318	C₂×C₄×C₅₃	—	4	4	no	—
319	C₂×C₄×C₅₃	—	4	4	no	—
320	C₂×C₄×C₅₃	—	4	8	no	—
321	C₂×C₄×C₅₃	—	4	8	no	—
322	C₂×C₄×C₅₃	—	4	8	no	—
323	C₂×C₄×C₅₃	—	8	8	no	—
324	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
325	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
326	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
327	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
328	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
329	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
330	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
331	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
332	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
333	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
334	#34223	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂²×C₅₃	—	2	2	no	—
336	C₂²×C₅₃	—	2	2	no	—
337	C₂²×C₅₃	—	2	4	no	—
338	C₂²×C₅₃	—	2	4	no	—
339	C₂²×C₅₃	—	2	4	no	—
340	C₂²×C₅₃	—	2	2	no	—
341	C₂²×C₅₃	—	2	2	no	—
342	C₂²×C₅₃	—	2	2	no	—
343	C₂²×C₅₃	—	2	2	no	—
344	C₂²×C₅₃	—	2	4	no	—
345	C₂²×C₅₃	—	2	2	no	—
346	C₂²×C₅₃	—	2	4	no	—
347	C₂²×C₅₃	—	2	2	no	—
348	C₂²×C₅₃	—	4	16	no	—
349	C₂²×C₅₃	—	4	4	no	—
350	C₂²×C₅₃	—	4	2	no	—
351	C₂²×C₅₃	—	4	2	no	—
352	C₂²×C₅₃	—	4	4	no	—
353	C₂²×C₅₃	—	4	2	no	—
354	C₂²×C₅₃	—	4	2	no	—
355	C₂²×C₅₃	C₄×#41	1	4	yes	—
356	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
357	C₂²×C₅₃	C₂²×#41	1	2	yes	—
358	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
359	C₂²×C₅₃	#585	1	1	yes	characteristic
360	C₂²×C₅₃	#585	1	1	yes	characteristic
361	C₄×C₅₃	—	2	4	no	—
362	C₄×C₅₃	—	2	2	no	—
363	C₄×C₅₃	—	2	2	no	—
364	C₄×C₅₃	—	2	2	no	—
365	C₄×C₅₃	—	2	4	no	—
366	C₄×C₅₃	—	2	4	no	—
367	C₄×C₅₃	—	2	4	no	—
368	C₄×C₅₃	—	2	4	no	—
369	C₄×C₅₃	—	4	4	no	—
370	C₄×C₅₃	—	4	4	no	—
371	C₄×C₅₃	—	4	2	no	—
372	C₄×C₅₃	—	4	2	no	—
373	C₄×C₅₃	#518	1	4	yes	—
374	C₂×#525	C₂×C₅₃	1	1	yes	characteristic
375	#2374	C₂×C₅₃	1	4	yes	complemented
376	#2363	C₂×C₅₃	1	2	yes	complemented
377	#2362	C₂×C₅₃	1	2	yes	complemented
378	#2357	C₂×C₅₃	1	2	yes	complemented
379	#2353	C₂×C₅₃	1	2	yes	complemented
380	#2347	C₂×C₅₃	1	1	yes	characteristic, complemented
381	#2346	C₂×C₅₃	1	1	yes	characteristic, complemented
382	#2341	C₂×C₅₃	1	1	yes	characteristic, complemented
383	#2339	C₂×C₅₃	1	1	yes	characteristic, complemented
384	#2321	C₂×C₅₃	1	4	yes	complemented
385	#2318	C₂×C₅₃	1	2	yes	complemented
386	C₄×C₂²⋊Q₈	C₂×C₅₃	1	2	yes	complemented
387	C₄×#121	C₂×C₅₃	1	2	yes	complemented
388	#2280	C₂×C₅₃	1	1	yes	characteristic, complemented
389	#2275	C₂×C₅₃	1	2	yes	complemented
390	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
391	C₂×C₅₃	—	2	4	no	—
392	C₂×C₅₃	—	4	4	no	—
393	C₂×C₅₃	—	4	2	no	—
394	C₂×C₅₃	—	4	2	no	—
395	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
396	C₂×C₅₃	C₂×#518	1	1	yes	characteristic
397	C₂×C₅₃	#3428	1	1	yes	characteristic
398	C₂×C₅₃	#3505	1	2	yes	—
399	C₂×C₅₃	#3506	1	2	yes	—
400	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
401	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
402	#525	C₄×C₅₃	1	16	yes	complemented
403	C₂×#123	C₂²×C₅₃	1	2	yes	—
404	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
405	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
406	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
407	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
408	C₂×#120	C₂²×C₅₃	1	2	yes	—
409	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
410	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	—
411	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
412	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
413	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
414	C₂×#117	C₂²×C₅₃	1	2	yes	—
415	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
417	C₂²×C₄²	C₂²×C₅₃	1	2	yes	—
418	#391	C₂²×C₅₃	1	2	yes	complemented
419	#390	C₂²×C₅₃	1	4	yes	—
420	#390	C₂²×C₅₃	1	4	yes	—
421	#390	C₂²×C₅₃	1	2	yes	complemented
422	#389	C₂²×C₅₃	1	2	yes	complemented
423	#389	C₂²×C₅₃	1	2	yes	complemented
424	#388	C₂²×C₅₃	1	4	yes	—
425	#388	C₂²×C₅₃	1	4	yes	—
426	#388	C₂²×C₅₃	1	4	yes	—
427	#388	C₂²×C₅₃	1	4	yes	—
428	#388	C₂²×C₅₃	1	4	yes	complemented
429	#388	C₂²×C₅₃	1	4	yes	complemented
430	#387	C₂²×C₅₃	1	4	yes	complemented
431	#387	C₂²×C₅₃	1	4	yes	complemented
432	#386	C₂²×C₅₃	1	4	yes	—
433	#386	C₂²×C₅₃	1	4	yes	—
434	#386	C₂²×C₅₃	1	4	yes	—
435	#385	C₂²×C₅₃	1	4	yes	—
436	#383	C₂²×C₅₃	1	2	yes	complemented
437	#382	C₂²×C₅₃	1	2	yes	complemented
438	#381	C₂²×C₅₃	1	2	yes	—
439	#381	C₂²×C₅₃	1	2	yes	complemented
440	#380	C₂²×C₅₃	1	1	yes	characteristic
441	#380	C₂²×C₅₃	1	1	yes	characteristic
442	#380	C₂²×C₅₃	1	2	yes	—
443	#380	C₂²×C₅₃	1	2	yes	complemented
444	#379	C₂²×C₅₃	1	2	yes	—
445	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
446	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
447	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
448	C₄×C₄⋊C₄	C₂²×C₅₃	1	4	yes	complemented
449	C₄×C₄⋊C₄	C₂²×C₅₃	1	4	yes	complemented
450	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
451	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	—
452	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
453	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
454	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
455	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
456	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
457	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
460	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	complemented
461	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	complemented
462	#376	C₂²×C₅₃	1	2	yes	complemented
463	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
464	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
465	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
466	C₅₃	#34223	1	1	yes	characteristic, direct product factor, Sylow
467	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
468	C₂×#41	—	4	4	no	—
469	C₂×#41	C₂×C₄×C₅₃	1	8	yes	complemented
470	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
471	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
472	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
473	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
474	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
475	C₂³×C₄	—	4	4	no	—
476	C₂³×C₄	C₂×C₄×C₅₃	1	8	yes	complemented
477	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
481	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
482	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
485	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
487	#123	C₂×C₄×C₅₃	1	16	yes	complemented
488	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
489	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
490	#121	C₂×C₄×C₅₃	1	8	yes	—
491	#121	C₂×C₄×C₅₃	1	8	yes	complemented
492	#120	C₂×C₄×C₅₃	1	16	yes	complemented
493	C₄×Q₈	—	4	4	no	—
494	C₄×D₄	—	2	16	no	—
495	C₄×D₄	—	4	4	no	—
496	C₄×D₄	C₂×C₄×C₅₃	1	16	yes	complemented
497	C₄×D₄	C₂×C₄×C₅₃	1	16	yes	complemented
498	#117	—	4	4	no	—
499	#117	C₂×C₄×C₅₃	1	8	yes	complemented
500	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
509	C₂×C₂²⋊C₄	—	2	8	no	—
510	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
526	C₂×C₄²	—	4	4	no	—
527	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
528	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
529	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
530	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
531	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
532	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
533	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
534	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
535	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
536	#95	C₂³×C₅₃	1	1	yes	characteristic
537	#95	C₂³×C₅₃	1	1	yes	characteristic
538	#95	C₂³×C₅₃	1	2	yes	—
539	#95	C₂³×C₅₃	1	1	yes	characteristic
540	#95	C₂³×C₅₃	1	1	yes	characteristic
541	#95	C₂³×C₅₃	1	2	yes	—
542	#95	C₂³×C₅₃	1	2	yes	—
543	#95	C₂³×C₅₃	1	4	yes	—
544	#95	C₂³×C₅₃	1	2	yes	—
545	#95	C₂³×C₅₃	1	4	yes	—
546	#95	C₂³×C₅₃	1	4	yes	—
547	#95	C₂³×C₅₃	1	4	yes	—
548	#95	C₂³×C₅₃	1	4	yes	—
549	#95	C₂³×C₅₃	1	4	yes	—
550	#95	C₂³×C₅₃	1	4	yes	—
551	C₂⁴	—	2	4	no	—
552	C₂⁴	—	4	2	no	—
553	C₂⁴	—	4	1	no	—
554	C₂⁴	—	4	1	no	—
555	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
556	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
557	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
558	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
559	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
560	#41	—	4	16	no	—
561	C₂×Q₈	—	2	4	no	—
562	C₂×Q₈	C₂²×C₄×C₅₃	1	4	yes	—
563	C₂×D₄	—	2	8	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	—
569	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
570	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	—
571	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	8	no	—
577	C₂²×C₄	—	4	16	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	2	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	4	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
589	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
590	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
591	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
592	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
593	C₂²×C₄	C₂²×C₄×C₅₃	1	8	yes	—
594	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
595	C₂²×C₄	#41×C₅₃	1	8	yes	complemented
596	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
599	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
609	C₄⋊C₄	—	2	8	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	4	4	no	—
613	C₄⋊C₄	—	4	4	no	—
614	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
615	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
616	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
617	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
618	C₂²⋊C₄	—	2	8	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	8	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	4	4	no	—
626	C₂²⋊C₄	—	4	2	no	—
627	C₂²⋊C₄	—	4	2	no	—
628	C₂²⋊C₄	—	4	4	no	—
629	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
630	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
631	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
632	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
633	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
634	C₄²	—	2	8	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	4	2	no	—
638	C₄²	—	4	2	no	—
639	C₄²	—	4	4	no	—
640	C₄²	—	4	4	no	—
641	C₄²	—	4	4	no	—
642	C₄²	C₂²×C₄×C₅₃	1	8	yes	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	8	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	4	4	no	—
660	C₂³	—	4	4	no	—
661	C₂³	—	4	8	no	—
662	C₂³	—	4	8	no	—
663	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
664	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
665	C₂³	C₂³×C₄×C₅₃	1	4	yes	—
666	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
667	C₂³	C₂×#41×C₅₃	1	4	yes	—
668	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
669	Q₈	—	2	8	no	—
670	D₄	—	2	16	no	—
671	D₄	—	2	8	no	—
672	D₄	—	4	8	no	—
673	D₄	—	4	8	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	8	no	—
686	C₂×C₄	—	2	8	no	—
687	C₂×C₄	—	2	8	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	4	4	no	—
703	C₂×C₄	—	4	8	no	—
704	C₂×C₄	—	4	8	no	—
705	C₂×C₄	—	4	8	no	—
706	C₂×C₄	—	8	8	no	—
707	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
708	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
709	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
710	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
711	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
712	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
713	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
714	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
715	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
716	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
717	C₂²	—	2	4	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	4	16	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	4	no	—
737	C₂²	C₄×#41×C₅₃	1	4	yes	—
738	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
739	C₂²	C₂²×#41×C₅₃	1	2	yes	—
740	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
741	C₂²	C₅₃×#585	1	1	yes	characteristic
742	C₂²	C₅₃×#585	1	1	yes	characteristic
743	C₄	—	2	4	no	—
744	C₄	—	2	4	no	—
745	C₄	—	2	4	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	4	no	—
750	C₄	—	2	4	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	4	no	—
755	C₄	C₅₃×#518	1	4	yes	—
756	C₂	—	2	4	no	—
757	C₂	—	4	2	no	—
758	C₂	—	4	2	no	—
759	C₂	—	4	4	no	—
760	C₂	C₂×C₄×#41×C₅₃	1	1	yes	characteristic
761	C₂	C₂×C₅₃×#518	1	1	yes	characteristic
762	C₂	C₅₃×#3428	1	1	yes	characteristic
763	C₂	C₅₃×#3505	1	2	yes	—
764	C₂	C₅₃×#3506	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅₃
Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂×C₅₃×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#2374	C₂	semidirect
3. C₅₃×#2363	C₂	semidirect
4. C₅₃×#2362	C₂	semidirect
5. C₅₃×#2357	C₂	semidirect
6. C₅₃×#2353	C₂	semidirect
7. C₅₃×#2347	C₂	semidirect
8. C₅₃×#2346	C₂	semidirect
9. C₅₃×#2341	C₂	semidirect
10. C₅₃×#2339	C₂	semidirect
11. C₅₃×#2321	C₂	semidirect
12. C₅₃×#2318	C₂	semidirect
13. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
14. C₄×#121×C₅₃	C₂	semidirect
15. C₅₃×#2280	C₂	semidirect
16. C₅₃×#2275	C₂	semidirect
17. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
20. C₅₃×#525	C₄	semidirect
27. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
31. C₂×C₄×D₄×C₅₃	C₂²	semidirect
36. C₅₃×#391	C₂²	semidirect
39. C₅₃×#390	C₂²	semidirect
40. C₅₃×#389	C₂²	semidirect
41. C₅₃×#389	C₂²	semidirect
46. C₅₃×#388	C₂²	semidirect
47. C₅₃×#388	C₂²	semidirect
48. C₅₃×#387	C₂²	semidirect
49. C₅₃×#387	C₂²	semidirect
54. C₅₃×#383	C₂²	semidirect
55. C₅₃×#382	C₂²	semidirect
57. C₅₃×#381	C₂²	semidirect
61. C₅₃×#380	C₂²	semidirect
63. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
64. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
65. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
66. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
67. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
77. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
78. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
79. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
80. C₅₃×#376	C₂²	semidirect
83. C₂×#95×C₅₃	C₂²	semidirect
86. C₂×#41×C₅₃	C₂×C₄	semidirect
93. C₂³×C₄×C₅₃	C₂×C₄	semidirect
104. #123×C₅₃	C₂×C₄	semidirect
105. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
106. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
108. #121×C₅₃	C₂×C₄	semidirect
109. #120×C₅₃	C₂×C₄	semidirect
113. C₄×D₄×C₅₃	C₂×C₄	semidirect
114. C₄×D₄×C₅₃	C₂×C₄	semidirect
116. #117×C₅₃	C₂×C₄	semidirect
212. C₂²×C₄×C₅₃	#41	semidirect
334. #34223	C₅₃	direct (N × H)
375. #2374	C₂×C₅₃	semidirect
376. #2363	C₂×C₅₃	semidirect
377. #2362	C₂×C₅₃	semidirect
378. #2357	C₂×C₅₃	semidirect
379. #2353	C₂×C₅₃	semidirect
380. #2347	C₂×C₅₃	semidirect
381. #2346	C₂×C₅₃	semidirect
382. #2341	C₂×C₅₃	semidirect
383. #2339	C₂×C₅₃	semidirect
384. #2321	C₂×C₅₃	semidirect
385. #2318	C₂×C₅₃	semidirect
386. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
387. C₄×#121	C₂×C₅₃	semidirect
388. #2280	C₂×C₅₃	semidirect
389. #2275	C₂×C₅₃	semidirect
390. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
402. #525	C₄×C₅₃	semidirect
409. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
413. C₂×C₄×D₄	C₂²×C₅₃	semidirect
418. #391	C₂²×C₅₃	semidirect
421. #390	C₂²×C₅₃	semidirect
422. #389	C₂²×C₅₃	semidirect
423. #389	C₂²×C₅₃	semidirect
428. #388	C₂²×C₅₃	semidirect
429. #388	C₂²×C₅₃	semidirect
430. #387	C₂²×C₅₃	semidirect
431. #387	C₂²×C₅₃	semidirect
436. #383	C₂²×C₅₃	semidirect
437. #382	C₂²×C₅₃	semidirect
439. #381	C₂²×C₅₃	semidirect
443. #380	C₂²×C₅₃	semidirect
445. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
446. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
447. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
448. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
449. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
459. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
460. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
461. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
462. #376	C₂²×C₅₃	semidirect
465. C₂×#95	C₂²×C₅₃	semidirect
466. C₅₃	#34223	direct (N × H)
469. C₂×#41	C₂×C₄×C₅₃	semidirect
476. C₂³×C₄	C₂×C₄×C₅₃	semidirect
487. #123	C₂×C₄×C₅₃	semidirect
488. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
489. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
491. #121	C₂×C₄×C₅₃	semidirect
492. #120	C₂×C₄×C₅₃	semidirect
496. C₄×D₄	C₂×C₄×C₅₃	semidirect
497. C₄×D₄	C₂×C₄×C₅₃	semidirect
499. #117	C₂×C₄×C₅₃	semidirect
595. C₂²×C₄	#41×C₅₃	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
C₅₃×#2374	2
C₅₃×#2363	2
C₅₃×#2362	2
C₅₃×#2357	2
C₅₃×#2353	2
C₅₃×#2347	2
C₅₃×#2346	2
C₅₃×#2341	2
C₅₃×#2339	2
C₅₃×#2321	2
C₅₃×#2318	2
C₄×C₂²⋊Q₈×C₅₃	2
C₄×#121×C₅₃	2
C₅₃×#2280	2
C₅₃×#2275	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
#34223	53

Subgroups — C53×#34223 #27241735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34223 #27241735