Subgroups — C₅₃×#35023 #27242535

Order 13568.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2847	C₂	1	1	yes	maximal, characteristic
5	C₅₃×#2643	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2622	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2597	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2595	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2578	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2576	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2495	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2494	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2490	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2489	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2427	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2426	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2421	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2420	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2321	C₂	1	2	yes	maximal, complemented
20	C₅₃×#2318	C₂	1	2	yes	maximal, complemented
21	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#120×C₅₃	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#401	C₂²	1	2	yes	complemented
42	C₅₃×#400	C₂²	1	2	yes	complemented
43	C₅₃×#400	C₂²	1	2	yes	complemented
44	C₅₃×#400	C₂²	1	2	yes	complemented
45	C₅₃×#397	C₂²	1	2	yes	—
46	C₅₃×#397	C₂²	1	2	yes	—
47	C₅₃×#397	C₂²	1	2	yes	—
48	C₅₃×#397	C₂²	1	2	yes	—
49	C₅₃×#397	C₂²	1	2	yes	complemented
50	C₅₃×#397	C₂²	1	2	yes	complemented
51	C₅₃×#397	C₂²	1	2	yes	complemented
52	C₅₃×#396	C₂²	1	2	yes	complemented
53	C₅₃×#394	C₂²	1	2	yes	—
54	C₅₃×#394	C₂²	1	2	yes	—
55	C₅₃×#394	C₂²	1	2	yes	—
56	C₅₃×#394	C₂²	1	2	yes	—
57	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#390	C₂²	1	2	yes	—
60	C₅₃×#390	C₂²	1	2	yes	—
61	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#388	C₂²	1	2	yes	—
68	C₅₃×#388	C₂²	1	2	yes	—
69	C₅₃×#388	C₂²	1	2	yes	—
70	C₅₃×#388	C₂²	1	2	yes	—
71	C₅₃×#388	C₂²	1	2	yes	complemented
72	C₅₃×#388	C₂²	1	2	yes	complemented
73	C₅₃×#388	C₂²	1	2	yes	complemented
74	C₅₃×#388	C₂²	1	2	yes	complemented
75	C₅₃×#388	C₂²	1	2	yes	complemented
76	C₅₃×#387	C₂²	1	2	yes	complemented
77	C₅₃×#387	C₂²	1	2	yes	complemented
78	C₅₃×#387	C₂²	1	2	yes	complemented
79	C₅₃×#387	C₂²	1	2	yes	complemented
80	C₅₃×#387	C₂²	1	2	yes	complemented
81	C₅₃×#386	C₂²	1	2	yes	—
82	C₅₃×#386	C₂²	1	2	yes	—
83	C₅₃×#386	C₂²	1	2	yes	—
84	C₅₃×#386	C₂²	1	2	yes	—
85	C₅₃×#386	C₂²	1	2	yes	—
86	C₅₃×#386	C₂²	1	2	yes	—
87	C₅₃×#386	C₂²	1	2	yes	—
88	C₅₃×#386	C₂²	1	2	yes	—
89	C₅₃×#385	C₂²	1	2	yes	—
90	C₅₃×#385	C₂²	1	2	yes	—
91	C₅₃×#385	C₂²	1	2	yes	—
92	C₅₃×#385	C₂²	1	2	yes	—
93	C₅₃×#385	C₂²	1	2	yes	—
94	C₅₃×#385	C₂²	1	2	yes	—
95	C₅₃×#383	C₂²	1	2	yes	complemented
96	C₅₃×#382	C₂²	1	2	yes	complemented
97	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#381	C₂²	1	2	yes	complemented
100	C₅₃×#380	C₂²	1	1	yes	characteristic
101	C₅₃×#380	C₂²	1	1	yes	characteristic
102	C₅₃×#380	C₂²	1	1	yes	characteristic
103	C₅₃×#380	C₂²	1	1	yes	characteristic
104	C₅₃×#380	C₂²	1	1	yes	characteristic
105	C₅₃×#380	C₂²	1	1	yes	characteristic
106	C₅₃×#380	C₂²	1	2	yes	complemented
107	C₅₃×#379	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
109	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
110	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
111	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
112	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
121	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
122	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
123	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
128	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₅₃	—	2	4	no	—
130	C₂³×C₄×C₅₃	—	4	2	no	—
131	C₂³×C₄×C₅₃	—	4	2	no	—
132	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
139	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
143	#125×C₅₃	—	4	2	no	—
144	#124×C₅₃	—	4	2	no	—
145	C₂²⋊Q₈×C₅₃	—	2	4	no	—
146	C₂²⋊Q₈×C₅₃	—	4	2	no	—
147	C₂²⋊Q₈×C₅₃	—	4	2	no	—
148	#121×C₅₃	—	2	4	no	—
149	#121×C₅₃	—	4	2	no	—
150	#121×C₅₃	—	4	2	no	—
151	#120×C₅₃	—	2	8	no	—
152	C₄×Q₈×C₅₃	—	4	2	no	—
153	C₄×D₄×C₅₃	—	2	8	no	—
154	C₄×D₄×C₅₃	—	4	2	no	—
155	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
172	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
173	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
200	C₂×C₄²×C₅₃	—	4	2	no	—
201	C₂×C₄²×C₅₃	—	4	2	no	—
202	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
207	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
212	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
213	#95×C₅₃	C₂³	1	1	yes	characteristic
214	#95×C₅₃	C₂³	1	1	yes	characteristic
215	#95×C₅₃	C₂³	1	1	yes	characteristic
216	#95×C₅₃	C₂³	1	1	yes	characteristic
217	#95×C₅₃	C₂³	1	1	yes	characteristic
218	#95×C₅₃	C₂³	1	1	yes	characteristic
219	#95×C₅₃	C₂³	1	1	yes	characteristic
220	#95×C₅₃	C₂³	1	1	yes	characteristic
221	#95×C₅₃	C₂³	1	2	yes	—
222	#95×C₅₃	C₂³	1	2	yes	—
223	#95×C₅₃	C₂³	1	2	yes	—
224	#95×C₅₃	C₂³	1	2	yes	—
225	#95×C₅₃	C₂³	1	2	yes	—
226	#95×C₅₃	C₂³	1	2	yes	—
227	#95×C₅₃	C₂³	1	2	yes	—
228	#95×C₅₃	C₂³	1	2	yes	—
229	#95×C₅₃	C₂³	1	2	yes	—
230	#95×C₅₃	C₂³	1	2	yes	—
231	#95×C₅₃	C₂³	1	2	yes	—
232	#95×C₅₃	C₂³	1	2	yes	—
233	#95×C₅₃	C₂³	1	2	yes	—
234	#95×C₅₃	C₂³	1	2	yes	—
235	#95×C₅₃	C₂³	1	2	yes	—
236	#95×C₅₃	C₂³	1	2	yes	—
237	#95×C₅₃	C₂³	1	2	yes	—
238	#95×C₅₃	C₂³	1	2	yes	—
239	#95×C₅₃	C₂³	1	2	yes	—
240	#95×C₅₃	C₂³	1	2	yes	—
241	C₂⁴×C₅₃	—	2	2	no	—
242	C₂⁴×C₅₃	—	2	2	no	—
243	C₂⁴×C₅₃	—	4	1	no	—
244	C₂⁴×C₅₃	—	4	1	no	—
245	C₂⁴×C₅₃	—	4	1	no	—
246	C₂⁴×C₅₃	—	4	1	no	—
247	C₂⁴×C₅₃	#41	1	4	yes	—
248	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
249	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
250	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
252	C₂×Q₈×C₅₃	—	2	2	no	—
253	C₂×Q₈×C₅₃	—	2	2	no	—
254	C₂×Q₈×C₅₃	—	2	2	no	—
255	C₂×D₄×C₅₃	—	2	4	no	—
256	C₂×D₄×C₅₃	—	2	4	no	—
257	C₂×D₄×C₅₃	—	2	4	no	—
258	C₂×D₄×C₅₃	—	2	4	no	—
259	C₂×D₄×C₅₃	—	2	4	no	—
260	C₂×D₄×C₅₃	—	2	2	no	—
261	C₂×D₄×C₅₃	—	2	2	no	—
262	C₂×D₄×C₅₃	—	2	2	no	—
263	C₂×D₄×C₅₃	—	4	2	no	—
264	C₂×D₄×C₅₃	—	4	2	no	—
265	C₂×D₄×C₅₃	—	4	2	no	—
266	C₂×D₄×C₅₃	—	4	2	no	—
267	C₂²×C₄×C₅₃	—	2	2	no	—
268	C₂²×C₄×C₅₃	—	2	2	no	—
269	C₂²×C₄×C₅₃	—	2	2	no	—
270	C₂²×C₄×C₅₃	—	2	2	no	—
271	C₂²×C₄×C₅₃	—	2	2	no	—
272	C₂²×C₄×C₅₃	—	2	2	no	—
273	C₂²×C₄×C₅₃	—	2	2	no	—
274	C₂²×C₄×C₅₃	—	2	2	no	—
275	C₂²×C₄×C₅₃	—	2	2	no	—
276	C₂²×C₄×C₅₃	—	2	2	no	—
277	C₂²×C₄×C₅₃	—	2	2	no	—
278	C₂²×C₄×C₅₃	—	2	2	no	—
279	C₂²×C₄×C₅₃	—	2	2	no	—
280	C₂²×C₄×C₅₃	—	2	2	no	—
281	C₂²×C₄×C₅₃	—	2	4	no	—
282	C₂²×C₄×C₅₃	—	4	1	no	—
283	C₂²×C₄×C₅₃	—	4	1	no	—
284	C₂²×C₄×C₅₃	—	4	1	no	—
285	C₂²×C₄×C₅₃	—	4	1	no	—
286	C₂²×C₄×C₅₃	—	4	1	no	—
287	C₂²×C₄×C₅₃	—	4	1	no	—
288	C₂²×C₄×C₅₃	—	4	1	no	—
289	C₂²×C₄×C₅₃	—	4	1	no	—
290	C₂²×C₄×C₅₃	—	4	1	no	—
291	C₂²×C₄×C₅₃	—	4	1	no	—
292	C₂²×C₄×C₅₃	—	4	1	no	—
293	C₂²×C₄×C₅₃	—	4	1	no	—
294	C₂²×C₄×C₅₃	—	4	1	no	—
295	C₂²×C₄×C₅₃	—	4	1	no	—
296	C₂²×C₄×C₅₃	—	4	2	no	—
297	C₂²×C₄×C₅₃	—	4	2	no	—
298	C₂²×C₄×C₅₃	—	4	16	no	—
299	C₂²×C₄×C₅₃	#41	1	4	yes	—
300	C₂²×C₄×C₅₃	#41	1	4	yes	—
301	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
320	C₄⋊C₄×C₅₃	—	2	4	no	—
321	C₄⋊C₄×C₅₃	—	2	2	no	—
322	C₄⋊C₄×C₅₃	—	2	4	no	—
323	C₄⋊C₄×C₅₃	—	2	2	no	—
324	C₄⋊C₄×C₅₃	—	2	2	no	—
325	C₄⋊C₄×C₅₃	—	2	2	no	—
326	C₄⋊C₄×C₅₃	—	2	2	no	—
327	C₄⋊C₄×C₅₃	—	2	2	no	—
328	C₄⋊C₄×C₅₃	—	4	2	no	—
329	C₄⋊C₄×C₅₃	—	4	2	no	—
330	C₄⋊C₄×C₅₃	—	4	2	no	—
331	C₄⋊C₄×C₅₃	—	4	2	no	—
332	C₄⋊C₄×C₅₃	—	4	2	no	—
333	C₄⋊C₄×C₅₃	—	4	2	no	—
334	C₄⋊C₄×C₅₃	—	4	2	no	—
335	C₄⋊C₄×C₅₃	—	4	2	no	—
336	C₂²⋊C₄×C₅₃	—	2	2	no	—
337	C₂²⋊C₄×C₅₃	—	2	2	no	—
338	C₂²⋊C₄×C₅₃	—	2	2	no	—
339	C₂²⋊C₄×C₅₃	—	2	2	no	—
340	C₂²⋊C₄×C₅₃	—	2	4	no	—
341	C₂²⋊C₄×C₅₃	—	2	4	no	—
342	C₂²⋊C₄×C₅₃	—	2	4	no	—
343	C₂²⋊C₄×C₅₃	—	2	4	no	—
344	C₂²⋊C₄×C₅₃	—	2	4	no	—
345	C₂²⋊C₄×C₅₃	—	2	2	no	—
346	C₂²⋊C₄×C₅₃	—	2	2	no	—
347	C₂²⋊C₄×C₅₃	—	2	2	no	—
348	C₂²⋊C₄×C₅₃	—	2	2	no	—
349	C₂²⋊C₄×C₅₃	—	2	4	no	—
350	C₂²⋊C₄×C₅₃	—	2	4	no	—
351	C₂²⋊C₄×C₅₃	—	4	2	no	—
352	C₂²⋊C₄×C₅₃	—	4	2	no	—
353	C₂²⋊C₄×C₅₃	—	4	2	no	—
354	C₂²⋊C₄×C₅₃	—	4	2	no	—
355	C₂²⋊C₄×C₅₃	—	4	2	no	—
356	C₂²⋊C₄×C₅₃	—	4	2	no	—
357	C₂²⋊C₄×C₅₃	—	4	2	no	—
358	C₂²⋊C₄×C₅₃	—	4	2	no	—
359	C₂²⋊C₄×C₅₃	—	4	2	no	—
360	C₂²⋊C₄×C₅₃	—	4	2	no	—
361	C₂²⋊C₄×C₅₃	—	4	2	no	—
362	C₂²⋊C₄×C₅₃	—	4	2	no	—
363	C₄²×C₅₃	—	2	4	no	—
364	C₄²×C₅₃	—	2	2	no	—
365	C₄²×C₅₃	—	2	2	no	—
366	C₄²×C₅₃	—	2	2	no	—
367	C₄²×C₅₃	—	2	2	no	—
368	C₄²×C₅₃	—	4	1	no	—
369	C₄²×C₅₃	—	4	1	no	—
370	C₄²×C₅₃	—	4	1	no	—
371	C₄²×C₅₃	—	4	1	no	—
372	C₄²×C₅₃	—	4	2	no	—
373	C₄²×C₅₃	—	4	2	no	—
374	C₂³×C₅₃	—	2	1	no	—
375	C₂³×C₅₃	—	2	1	no	—
376	C₂³×C₅₃	—	2	1	no	—
377	C₂³×C₅₃	—	2	1	no	—
378	C₂³×C₅₃	—	2	8	no	—
379	C₂³×C₅₃	—	2	1	no	—
380	C₂³×C₅₃	—	2	1	no	—
381	C₂³×C₅₃	—	2	1	no	—
382	C₂³×C₅₃	—	2	1	no	—
383	C₂³×C₅₃	—	2	1	no	—
384	C₂³×C₅₃	—	2	1	no	—
385	C₂³×C₅₃	—	2	1	no	—
386	C₂³×C₅₃	—	2	1	no	—
387	C₂³×C₅₃	—	2	1	no	—
388	C₂³×C₅₃	—	2	1	no	—
389	C₂³×C₅₃	—	2	1	no	—
390	C₂³×C₅₃	—	2	1	no	—
391	C₂³×C₅₃	—	2	2	no	—
392	C₂³×C₅₃	—	2	2	no	—
393	C₂³×C₅₃	—	2	2	no	—
394	C₂³×C₅₃	—	2	2	no	—
395	C₂³×C₅₃	—	2	2	no	—
396	C₂³×C₅₃	—	2	2	no	—
397	C₂³×C₅₃	—	2	2	no	—
398	C₂³×C₅₃	—	4	4	no	—
399	C₂³×C₅₃	—	4	4	no	—
400	C₂³×C₅₃	—	4	4	no	—
401	C₂³×C₅₃	—	4	4	no	—
402	C₂³×C₅₃	—	4	4	no	—
403	C₂³×C₅₃	—	4	4	no	—
404	C₂³×C₅₃	C₂×#41	1	2	yes	—
405	C₂³×C₅₃	C₂×#41	1	2	yes	—
406	C₂³×C₅₃	C₂×#41	1	2	yes	—
407	C₂³×C₅₃	C₂×#41	1	2	yes	—
408	C₂³×C₅₃	C₂×#41	1	2	yes	—
409	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
410	Q₈×C₅₃	—	4	4	no	—
411	D₄×C₅₃	—	4	8	no	—
412	D₄×C₅₃	—	4	4	no	—
413	D₄×C₅₃	—	8	4	no	—
414	D₄×C₅₃	—	8	4	no	—
415	C₂×C₄×C₅₃	—	2	1	no	—
416	C₂×C₄×C₅₃	—	2	1	no	—
417	C₂×C₄×C₅₃	—	2	1	no	—
418	C₂×C₄×C₅₃	—	2	1	no	—
419	C₂×C₄×C₅₃	—	2	1	no	—
420	C₂×C₄×C₅₃	—	2	1	no	—
421	C₂×C₄×C₅₃	—	2	8	no	—
422	C₂×C₄×C₅₃	—	2	1	no	—
423	C₂×C₄×C₅₃	—	2	1	no	—
424	C₂×C₄×C₅₃	—	2	1	no	—
425	C₂×C₄×C₅₃	—	2	1	no	—
426	C₂×C₄×C₅₃	—	2	1	no	—
427	C₂×C₄×C₅₃	—	2	1	no	—
428	C₂×C₄×C₅₃	—	2	1	no	—
429	C₂×C₄×C₅₃	—	2	1	no	—
430	C₂×C₄×C₅₃	—	2	2	no	—
431	C₂×C₄×C₅₃	—	2	2	no	—
432	C₂×C₄×C₅₃	—	2	2	no	—
433	C₂×C₄×C₅₃	—	2	2	no	—
434	C₂×C₄×C₅₃	—	2	2	no	—
435	C₂×C₄×C₅₃	—	2	2	no	—
436	C₂×C₄×C₅₃	—	2	2	no	—
437	C₂×C₄×C₅₃	—	2	2	no	—
438	C₂×C₄×C₅₃	—	2	2	no	—
439	C₂×C₄×C₅₃	—	2	1	no	—
440	C₂×C₄×C₅₃	—	2	1	no	—
441	C₂×C₄×C₅₃	—	2	1	no	—
442	C₂×C₄×C₅₃	—	2	1	no	—
443	C₂×C₄×C₅₃	—	2	1	no	—
444	C₂×C₄×C₅₃	—	2	1	no	—
445	C₂×C₄×C₅₃	—	2	1	no	—
446	C₂×C₄×C₅₃	—	2	1	no	—
447	C₂×C₄×C₅₃	—	2	1	no	—
448	C₂×C₄×C₅₃	—	2	1	no	—
449	C₂×C₄×C₅₃	—	2	2	no	—
450	C₂×C₄×C₅₃	—	2	2	no	—
451	C₂×C₄×C₅₃	—	2	2	no	—
452	C₂×C₄×C₅₃	—	2	2	no	—
453	C₂×C₄×C₅₃	—	2	2	no	—
454	C₂×C₄×C₅₃	—	2	2	no	—
455	C₂×C₄×C₅₃	—	2	1	no	—
456	C₂×C₄×C₅₃	—	2	1	no	—
457	C₂×C₄×C₅₃	—	2	1	no	—
458	C₂×C₄×C₅₃	—	2	2	no	—
459	C₂×C₄×C₅₃	—	2	1	no	—
460	C₂×C₄×C₅₃	—	2	1	no	—
461	C₂×C₄×C₅₃	—	2	1	no	—
462	C₂×C₄×C₅₃	—	2	2	no	—
463	C₂×C₄×C₅₃	—	2	2	no	—
464	C₂×C₄×C₅₃	—	2	2	no	—
465	C₂×C₄×C₅₃	—	2	2	no	—
466	C₂×C₄×C₅₃	—	2	2	no	—
467	C₂×C₄×C₅₃	—	4	4	no	—
468	C₂×C₄×C₅₃	—	4	4	no	—
469	C₂×C₄×C₅₃	—	4	4	no	—
470	C₂×C₄×C₅₃	—	4	4	no	—
471	C₂×C₄×C₅₃	—	4	4	no	—
472	C₂×C₄×C₅₃	—	4	4	no	—
473	C₂×C₄×C₅₃	—	4	4	no	—
474	C₂×C₄×C₅₃	—	4	4	no	—
475	C₂×C₄×C₅₃	—	4	4	no	—
476	C₂×C₄×C₅₃	—	8	4	no	—
477	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
478	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
479	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
480	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
481	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
482	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
483	#35023	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
484	C₂²×C₅₃	—	2	2	no	—
485	C₂²×C₅₃	—	2	2	no	—
486	C₂²×C₅₃	—	2	2	no	—
487	C₂²×C₅₃	—	2	2	no	—
488	C₂²×C₅₃	—	2	2	no	—
489	C₂²×C₅₃	—	2	2	no	—
490	C₂²×C₅₃	—	2	2	no	—
491	C₂²×C₅₃	—	2	2	no	—
492	C₂²×C₅₃	—	2	2	no	—
493	C₂²×C₅₃	—	2	2	no	—
494	C₂²×C₅₃	—	2	2	no	—
495	C₂²×C₅₃	—	2	2	no	—
496	C₂²×C₅₃	—	4	16	no	—
497	C₂²×C₅₃	—	4	1	no	—
498	C₂²×C₅₃	—	4	1	no	—
499	C₂²×C₅₃	—	4	1	no	—
500	C₂²×C₅₃	—	4	1	no	—
501	C₂²×C₅₃	—	4	1	no	—
502	C₂²×C₅₃	—	4	1	no	—
503	C₂²×C₅₃	—	4	1	no	—
504	C₂²×C₅₃	—	4	1	no	—
505	C₂²×C₅₃	—	4	2	no	—
506	C₂²×C₅₃	—	4	2	no	—
507	C₂²×C₅₃	—	4	2	no	—
508	C₂²×C₅₃	—	4	2	no	—
509	C₂²×C₅₃	—	4	2	no	—
510	C₂²×C₅₃	—	4	2	no	—
511	C₂²×C₅₃	—	4	2	no	—
512	C₂²×C₅₃	#529	1	4	yes	—
513	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
514	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
515	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
516	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
518	C₂²×C₅₃	#585	1	1	yes	characteristic
519	C₂²×C₅₃	#585	1	1	yes	characteristic
520	C₄×C₅₃	—	2	2	no	—
521	C₄×C₅₃	—	2	2	no	—
522	C₄×C₅₃	—	2	2	no	—
523	C₄×C₅₃	—	4	2	no	—
524	C₄×C₅₃	—	4	1	no	—
525	C₄×C₅₃	—	4	1	no	—
526	C₄×C₅₃	—	4	2	no	—
527	C₄×C₅₃	—	4	2	no	—
528	C₄×C₅₃	—	4	1	no	—
529	C₄×C₅₃	—	4	1	no	—
530	C₄×C₅₃	—	4	1	no	—
531	C₄×C₅₃	—	4	1	no	—
532	C₄×C₅₃	—	4	2	no	—
533	C₄×C₅₃	—	4	2	no	—
534	C₄×C₅₃	—	4	2	no	—
535	C₄×C₅₃	—	4	2	no	—
536	C₄×C₅₃	—	4	1	no	—
537	C₄×C₅₃	—	4	1	no	—
538	C₄×C₅₃	#538	1	4	yes	—
539	#2851	C₂×C₅₃	1	1	yes	characteristic, complemented
540	#2850	C₂×C₅₃	1	1	yes	characteristic, complemented
541	#2848	C₂×C₅₃	1	1	yes	characteristic, complemented
542	#2847	C₂×C₅₃	1	1	yes	characteristic
543	#2643	C₂×C₅₃	1	2	yes	complemented
544	#2622	C₂×C₅₃	1	2	yes	complemented
545	#2597	C₂×C₅₃	1	2	yes	complemented
546	#2595	C₂×C₅₃	1	2	yes	complemented
547	#2578	C₂×C₅₃	1	2	yes	complemented
548	#2576	C₂×C₅₃	1	2	yes	complemented
549	#2495	C₂×C₅₃	1	1	yes	characteristic, complemented
550	#2494	C₂×C₅₃	1	1	yes	characteristic, complemented
551	#2490	C₂×C₅₃	1	1	yes	characteristic, complemented
552	#2489	C₂×C₅₃	1	1	yes	characteristic, complemented
553	#2427	C₂×C₅₃	1	1	yes	characteristic, complemented
554	#2426	C₂×C₅₃	1	1	yes	characteristic, complemented
555	#2421	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#2420	C₂×C₅₃	1	1	yes	characteristic, complemented
557	#2321	C₂×C₅₃	1	2	yes	complemented
558	#2318	C₂×C₅₃	1	2	yes	complemented
559	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
560	C₄×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
561	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
562	C₂×C₅₃	—	2	4	no	—
563	C₂×C₅₃	—	4	2	no	—
564	C₂×C₅₃	—	4	2	no	—
565	C₂×C₅₃	—	8	2	no	—
566	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
567	C₂×C₅₃	C₂×#538	1	1	yes	characteristic
568	C₂×C₅₃	#3455	1	1	yes	characteristic
569	C₂×C₅₃	#3505	1	1	yes	characteristic
570	C₂×C₅₃	#3505	1	1	yes	characteristic
571	C₂×C₅₃	#3505	1	1	yes	characteristic
572	C₂×C₅₃	#3506	1	1	yes	characteristic
573	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
574	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
575	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
576	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
577	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
578	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
579	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
580	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
581	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
582	C₂×#120	C₂²×C₅₃	1	2	yes	—
583	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
584	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
585	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
586	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
587	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
588	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
589	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
590	#401	C₂²×C₅₃	1	2	yes	complemented
591	#400	C₂²×C₅₃	1	2	yes	complemented
592	#400	C₂²×C₅₃	1	2	yes	complemented
593	#400	C₂²×C₅₃	1	2	yes	complemented
594	#397	C₂²×C₅₃	1	2	yes	—
595	#397	C₂²×C₅₃	1	2	yes	—
596	#397	C₂²×C₅₃	1	2	yes	—
597	#397	C₂²×C₅₃	1	2	yes	—
598	#397	C₂²×C₅₃	1	2	yes	complemented
599	#397	C₂²×C₅₃	1	2	yes	complemented
600	#397	C₂²×C₅₃	1	2	yes	complemented
601	#396	C₂²×C₅₃	1	2	yes	complemented
602	#394	C₂²×C₅₃	1	2	yes	—
603	#394	C₂²×C₅₃	1	2	yes	—
604	#394	C₂²×C₅₃	1	2	yes	—
605	#394	C₂²×C₅₃	1	2	yes	—
606	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
607	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
608	#390	C₂²×C₅₃	1	2	yes	—
609	#390	C₂²×C₅₃	1	2	yes	—
610	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
611	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
612	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
613	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
614	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
615	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
616	#388	C₂²×C₅₃	1	2	yes	—
617	#388	C₂²×C₅₃	1	2	yes	—
618	#388	C₂²×C₅₃	1	2	yes	—
619	#388	C₂²×C₅₃	1	2	yes	—
620	#388	C₂²×C₅₃	1	2	yes	complemented
621	#388	C₂²×C₅₃	1	2	yes	complemented
622	#388	C₂²×C₅₃	1	2	yes	complemented
623	#388	C₂²×C₅₃	1	2	yes	complemented
624	#388	C₂²×C₅₃	1	2	yes	complemented
625	#387	C₂²×C₅₃	1	2	yes	complemented
626	#387	C₂²×C₅₃	1	2	yes	complemented
627	#387	C₂²×C₅₃	1	2	yes	complemented
628	#387	C₂²×C₅₃	1	2	yes	complemented
629	#387	C₂²×C₅₃	1	2	yes	complemented
630	#386	C₂²×C₅₃	1	2	yes	—
631	#386	C₂²×C₅₃	1	2	yes	—
632	#386	C₂²×C₅₃	1	2	yes	—
633	#386	C₂²×C₅₃	1	2	yes	—
634	#386	C₂²×C₅₃	1	2	yes	—
635	#386	C₂²×C₅₃	1	2	yes	—
636	#386	C₂²×C₅₃	1	2	yes	—
637	#386	C₂²×C₅₃	1	2	yes	—
638	#385	C₂²×C₅₃	1	2	yes	—
639	#385	C₂²×C₅₃	1	2	yes	—
640	#385	C₂²×C₅₃	1	2	yes	—
641	#385	C₂²×C₅₃	1	2	yes	—
642	#385	C₂²×C₅₃	1	2	yes	—
643	#385	C₂²×C₅₃	1	2	yes	—
644	#383	C₂²×C₅₃	1	2	yes	complemented
645	#382	C₂²×C₅₃	1	2	yes	complemented
646	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
647	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
648	#381	C₂²×C₅₃	1	2	yes	complemented
649	#380	C₂²×C₅₃	1	1	yes	characteristic
650	#380	C₂²×C₅₃	1	1	yes	characteristic
651	#380	C₂²×C₅₃	1	1	yes	characteristic
652	#380	C₂²×C₅₃	1	1	yes	characteristic
653	#380	C₂²×C₅₃	1	1	yes	characteristic
654	#380	C₂²×C₅₃	1	1	yes	characteristic
655	#380	C₂²×C₅₃	1	2	yes	complemented
656	#379	C₂²×C₅₃	1	2	yes	—
657	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
658	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
660	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
661	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
662	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
663	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
664	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
665	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
666	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
667	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
668	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
669	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
670	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
671	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
672	C₅₃	#35023	1	1	yes	characteristic, direct product factor, Sylow
673	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
674	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
675	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
676	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
677	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
678	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
679	C₂³×C₄	—	2	4	no	—
680	C₂³×C₄	—	4	2	no	—
681	C₂³×C₄	—	4	2	no	—
682	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
684	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
685	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
686	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
687	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
688	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
689	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
690	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
691	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
692	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
693	#125	—	4	2	no	—
694	#124	—	4	2	no	—
695	C₂²⋊Q₈	—	2	4	no	—
696	C₂²⋊Q₈	—	4	2	no	—
697	C₂²⋊Q₈	—	4	2	no	—
698	#121	—	2	4	no	—
699	#121	—	4	2	no	—
700	#121	—	4	2	no	—
701	#120	—	2	8	no	—
702	C₄×Q₈	—	4	2	no	—
703	C₄×D₄	—	2	8	no	—
704	C₄×D₄	—	4	2	no	—
705	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
706	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
708	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
710	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
711	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
713	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
718	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
719	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
721	C₂×C₂²⋊C₄	—	2	4	no	—
722	C₂×C₂²⋊C₄	—	2	4	no	—
723	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
724	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
725	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
729	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
730	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
731	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
750	C₂×C₄²	—	4	2	no	—
751	C₂×C₄²	—	4	2	no	—
752	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
753	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
754	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
755	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
756	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
757	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
758	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
759	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
760	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
761	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
762	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
763	#95	C₂³×C₅₃	1	1	yes	characteristic
764	#95	C₂³×C₅₃	1	1	yes	characteristic
765	#95	C₂³×C₅₃	1	1	yes	characteristic
766	#95	C₂³×C₅₃	1	1	yes	characteristic
767	#95	C₂³×C₅₃	1	1	yes	characteristic
768	#95	C₂³×C₅₃	1	1	yes	characteristic
769	#95	C₂³×C₅₃	1	1	yes	characteristic
770	#95	C₂³×C₅₃	1	1	yes	characteristic
771	#95	C₂³×C₅₃	1	2	yes	—
772	#95	C₂³×C₅₃	1	2	yes	—
773	#95	C₂³×C₅₃	1	2	yes	—
774	#95	C₂³×C₅₃	1	2	yes	—
775	#95	C₂³×C₅₃	1	2	yes	—
776	#95	C₂³×C₅₃	1	2	yes	—
777	#95	C₂³×C₅₃	1	2	yes	—
778	#95	C₂³×C₅₃	1	2	yes	—
779	#95	C₂³×C₅₃	1	2	yes	—
780	#95	C₂³×C₅₃	1	2	yes	—
781	#95	C₂³×C₅₃	1	2	yes	—
782	#95	C₂³×C₅₃	1	2	yes	—
783	#95	C₂³×C₅₃	1	2	yes	—
784	#95	C₂³×C₅₃	1	2	yes	—
785	#95	C₂³×C₅₃	1	2	yes	—
786	#95	C₂³×C₅₃	1	2	yes	—
787	#95	C₂³×C₅₃	1	2	yes	—
788	#95	C₂³×C₅₃	1	2	yes	—
789	#95	C₂³×C₅₃	1	2	yes	—
790	#95	C₂³×C₅₃	1	2	yes	—
791	C₂⁴	—	2	2	no	—
792	C₂⁴	—	2	2	no	—
793	C₂⁴	—	4	1	no	—
794	C₂⁴	—	4	1	no	—
795	C₂⁴	—	4	1	no	—
796	C₂⁴	—	4	1	no	—
797	C₂⁴	#41×C₅₃	1	4	yes	—
798	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
799	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
800	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
801	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×D₄	—	2	4	no	—
806	C₂×D₄	—	2	4	no	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	4	no	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	4	2	no	—
814	C₂×D₄	—	4	2	no	—
815	C₂×D₄	—	4	2	no	—
816	C₂×D₄	—	4	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	4	no	—
832	C₂²×C₄	—	4	1	no	—
833	C₂²×C₄	—	4	1	no	—
834	C₂²×C₄	—	4	1	no	—
835	C₂²×C₄	—	4	1	no	—
836	C₂²×C₄	—	4	1	no	—
837	C₂²×C₄	—	4	1	no	—
838	C₂²×C₄	—	4	1	no	—
839	C₂²×C₄	—	4	1	no	—
840	C₂²×C₄	—	4	1	no	—
841	C₂²×C₄	—	4	1	no	—
842	C₂²×C₄	—	4	1	no	—
843	C₂²×C₄	—	4	1	no	—
844	C₂²×C₄	—	4	1	no	—
845	C₂²×C₄	—	4	1	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	4	16	no	—
849	C₂²×C₄	#41×C₅₃	1	4	yes	—
850	C₂²×C₄	#41×C₅₃	1	4	yes	—
851	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
863	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
865	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
866	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
870	C₄⋊C₄	—	2	4	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	4	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	4	2	no	—
879	C₄⋊C₄	—	4	2	no	—
880	C₄⋊C₄	—	4	2	no	—
881	C₄⋊C₄	—	4	2	no	—
882	C₄⋊C₄	—	4	2	no	—
883	C₄⋊C₄	—	4	2	no	—
884	C₄⋊C₄	—	4	2	no	—
885	C₄⋊C₄	—	4	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	4	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	4	no	—
894	C₂²⋊C₄	—	2	4	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	4	2	no	—
902	C₂²⋊C₄	—	4	2	no	—
903	C₂²⋊C₄	—	4	2	no	—
904	C₂²⋊C₄	—	4	2	no	—
905	C₂²⋊C₄	—	4	2	no	—
906	C₂²⋊C₄	—	4	2	no	—
907	C₂²⋊C₄	—	4	2	no	—
908	C₂²⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	4	2	no	—
910	C₂²⋊C₄	—	4	2	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₄²	—	2	4	no	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	2	no	—
916	C₄²	—	2	2	no	—
917	C₄²	—	2	2	no	—
918	C₄²	—	4	1	no	—
919	C₄²	—	4	1	no	—
920	C₄²	—	4	1	no	—
921	C₄²	—	4	1	no	—
922	C₄²	—	4	2	no	—
923	C₄²	—	4	2	no	—
924	C₂³	—	2	1	no	—
925	C₂³	—	2	1	no	—
926	C₂³	—	2	1	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	8	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	2	1	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	4	4	no	—
949	C₂³	—	4	4	no	—
950	C₂³	—	4	4	no	—
951	C₂³	—	4	4	no	—
952	C₂³	—	4	4	no	—
953	C₂³	—	4	4	no	—
954	C₂³	C₂×#41×C₅₃	1	2	yes	—
955	C₂³	C₂×#41×C₅₃	1	2	yes	—
956	C₂³	C₂×#41×C₅₃	1	2	yes	—
957	C₂³	C₂×#41×C₅₃	1	2	yes	—
958	C₂³	C₂×#41×C₅₃	1	2	yes	—
959	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
960	Q₈	—	4	4	no	—
961	D₄	—	4	8	no	—
962	D₄	—	4	4	no	—
963	D₄	—	8	4	no	—
964	D₄	—	8	4	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	8	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	4	4	no	—
1018	C₂×C₄	—	4	4	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	4	no	—
1022	C₂×C₄	—	4	4	no	—
1023	C₂×C₄	—	4	4	no	—
1024	C₂×C₄	—	4	4	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	8	4	no	—
1027	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1028	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1029	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1030	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1031	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1032	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	2	no	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	2	no	—
1041	C₂²	—	2	2	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	2	2	no	—
1044	C₂²	—	2	2	no	—
1045	C₂²	—	4	16	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	—	4	1	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	C₅₃×#529	1	4	yes	—
1062	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1063	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1064	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1065	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1066	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1067	C₂²	C₅₃×#585	1	1	yes	characteristic
1068	C₂²	C₅₃×#585	1	1	yes	characteristic
1069	C₄	—	2	2	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	2	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	2	no	—
1087	C₄	C₅₃×#538	1	4	yes	—
1088	C₂	—	2	4	no	—
1089	C₂	—	4	2	no	—
1090	C₂	—	4	2	no	—
1091	C₂	—	8	2	no	—
1092	C₂	C₂×C₅₃×#529	1	1	yes	characteristic
1093	C₂	C₂×C₅₃×#538	1	1	yes	characteristic
1094	C₂	C₅₃×#3455	1	1	yes	characteristic
1095	C₂	C₅₃×#3505	1	1	yes	characteristic
1096	C₂	C₅₃×#3505	1	1	yes	characteristic
1097	C₂	C₅₃×#3505	1	1	yes	characteristic
1098	C₂	C₅₃×#3506	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₅₃×#2847	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#2851	C₂	semidirect
2. C₅₃×#2850	C₂	semidirect
3. C₅₃×#2848	C₂	semidirect
5. C₅₃×#2643	C₂	semidirect
6. C₅₃×#2622	C₂	semidirect
7. C₅₃×#2597	C₂	semidirect
8. C₅₃×#2595	C₂	semidirect
9. C₅₃×#2578	C₂	semidirect
10. C₅₃×#2576	C₂	semidirect
11. C₅₃×#2495	C₂	semidirect
12. C₅₃×#2494	C₂	semidirect
13. C₅₃×#2490	C₂	semidirect
14. C₅₃×#2489	C₂	semidirect
15. C₅₃×#2427	C₂	semidirect
16. C₅₃×#2426	C₂	semidirect
17. C₅₃×#2421	C₂	semidirect
18. C₅₃×#2420	C₂	semidirect
19. C₅₃×#2321	C₂	semidirect
20. C₅₃×#2318	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
22. C₄×#121×C₅₃	C₂	semidirect
23. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
25. C₂×#125×C₅₃	C₂²	semidirect
26. C₂×#124×C₅₃	C₂²	semidirect
34. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
36. C₂×C₄×D₄×C₅₃	C₂²	semidirect
41. C₅₃×#401	C₂²	semidirect
42. C₅₃×#400	C₂²	semidirect
43. C₅₃×#400	C₂²	semidirect
44. C₅₃×#400	C₂²	semidirect
49. C₅₃×#397	C₂²	semidirect
50. C₅₃×#397	C₂²	semidirect
51. C₅₃×#397	C₂²	semidirect
52. C₅₃×#396	C₂²	semidirect
57. C₅₃×#391	C₂²	semidirect
58. C₅₃×#391	C₂²	semidirect
61. C₅₃×#390	C₂²	semidirect
62. C₅₃×#390	C₂²	semidirect
63. C₅₃×#389	C₂²	semidirect
64. C₅₃×#389	C₂²	semidirect
65. C₅₃×#389	C₂²	semidirect
66. C₅₃×#389	C₂²	semidirect
71. C₅₃×#388	C₂²	semidirect
72. C₅₃×#388	C₂²	semidirect
73. C₅₃×#388	C₂²	semidirect
74. C₅₃×#388	C₂²	semidirect
75. C₅₃×#388	C₂²	semidirect
76. C₅₃×#387	C₂²	semidirect
77. C₅₃×#387	C₂²	semidirect
78. C₅₃×#387	C₂²	semidirect
79. C₅₃×#387	C₂²	semidirect
80. C₅₃×#387	C₂²	semidirect
95. C₅₃×#383	C₂²	semidirect
96. C₅₃×#382	C₂²	semidirect
97. C₅₃×#382	C₂²	semidirect
98. C₅₃×#382	C₂²	semidirect
99. C₅₃×#381	C₂²	semidirect
106. C₅₃×#380	C₂²	semidirect
108. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
109. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
110. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
483. #35023	C₅₃	direct (N × H)
539. #2851	C₂×C₅₃	semidirect
540. #2850	C₂×C₅₃	semidirect
541. #2848	C₂×C₅₃	semidirect
543. #2643	C₂×C₅₃	semidirect
544. #2622	C₂×C₅₃	semidirect
545. #2597	C₂×C₅₃	semidirect
546. #2595	C₂×C₅₃	semidirect
547. #2578	C₂×C₅₃	semidirect
548. #2576	C₂×C₅₃	semidirect
549. #2495	C₂×C₅₃	semidirect
550. #2494	C₂×C₅₃	semidirect
551. #2490	C₂×C₅₃	semidirect
552. #2489	C₂×C₅₃	semidirect
553. #2427	C₂×C₅₃	semidirect
554. #2426	C₂×C₅₃	semidirect
555. #2421	C₂×C₅₃	semidirect
556. #2420	C₂×C₅₃	semidirect
557. #2321	C₂×C₅₃	semidirect
558. #2318	C₂×C₅₃	semidirect
559. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
560. C₄×#121	C₂×C₅₃	semidirect
561. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
574. C₂×#125	C₂²×C₅₃	semidirect
575. C₂×#124	C₂²×C₅₃	semidirect
583. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
585. C₂×C₄×D₄	C₂²×C₅₃	semidirect
590. #401	C₂²×C₅₃	semidirect
591. #400	C₂²×C₅₃	semidirect
592. #400	C₂²×C₅₃	semidirect
593. #400	C₂²×C₅₃	semidirect
598. #397	C₂²×C₅₃	semidirect
599. #397	C₂²×C₅₃	semidirect
600. #397	C₂²×C₅₃	semidirect
601. #396	C₂²×C₅₃	semidirect
606. #391	C₂²×C₅₃	semidirect
607. #391	C₂²×C₅₃	semidirect
610. #390	C₂²×C₅₃	semidirect
611. #390	C₂²×C₅₃	semidirect
612. #389	C₂²×C₅₃	semidirect
613. #389	C₂²×C₅₃	semidirect
614. #389	C₂²×C₅₃	semidirect
615. #389	C₂²×C₅₃	semidirect
620. #388	C₂²×C₅₃	semidirect
621. #388	C₂²×C₅₃	semidirect
622. #388	C₂²×C₅₃	semidirect
623. #388	C₂²×C₅₃	semidirect
624. #388	C₂²×C₅₃	semidirect
625. #387	C₂²×C₅₃	semidirect
626. #387	C₂²×C₅₃	semidirect
627. #387	C₂²×C₅₃	semidirect
628. #387	C₂²×C₅₃	semidirect
629. #387	C₂²×C₅₃	semidirect
644. #383	C₂²×C₅₃	semidirect
645. #382	C₂²×C₅₃	semidirect
646. #382	C₂²×C₅₃	semidirect
647. #382	C₂²×C₅₃	semidirect
648. #381	C₂²×C₅₃	semidirect
655. #380	C₂²×C₅₃	semidirect
657. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
658. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
659. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
669. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
672. C₅₃	#35023	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#2851	2
C₅₃×#2850	2
C₅₃×#2848	2
C₅₃×#2847	2
C₅₃×#2643	2
C₅₃×#2622	2
C₅₃×#2597	2
C₅₃×#2595	2
C₅₃×#2578	2
C₅₃×#2576	2
C₅₃×#2495	2
C₅₃×#2494	2
C₅₃×#2490	2
C₅₃×#2489	2
C₅₃×#2427	2
C₅₃×#2426	2
C₅₃×#2421	2
C₅₃×#2420	2
C₅₃×#2321	2
C₅₃×#2318	2
C₄×C₂²⋊Q₈×C₅₃	2
C₄×#121×C₅₃	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
#35023	53

Subgroups — C53×#35023 #27242535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#35023 #27242535