Subgroups — C₅₃×#60561 #27268073

Order 13568.

2428 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3115	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3112	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3109	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3106	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3103	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3100	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3094	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3079	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3038	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3006	C₂	1	2	yes	maximal, complemented
13	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	4	yes	maximal, complemented
14	C₅₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₅₃	—	2	1	no	—
16	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	4	yes	—
18	C₅₃×#532	—	2	1	no	—
19	C₅₃×#532	—	2	1	no	—
20	C₅₃×#532	—	2	1	no	—
21	C₅₃×#532	—	2	1	no	—
22	C₅₃×#532	C₂²	1	2	yes	—
23	C₅₃×#532	C₂²	1	2	yes	—
24	C₅₃×#532	C₂²	1	2	yes	complemented
25	C₅₃×#532	C₂²	1	2	yes	complemented
26	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#124×C₅₃	—	2	1	no	—
29	C₂×#121×C₅₃	—	2	1	no	—
30	C₂×#121×C₅₃	C₂²	1	2	yes	—
31	C₄×#41×C₅₃	—	2	1	no	—
32	C₄×#41×C₅₃	—	2	1	no	—
33	C₄×#41×C₅₃	—	2	1	no	—
34	C₄×#41×C₅₃	—	2	1	no	—
35	C₄×#41×C₅₃	C₂²	1	2	yes	—
36	C₄×#41×C₅₃	C₂²	1	2	yes	—
37	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
38	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
39	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₅₃	—	2	1	no	—
42	C₂×C₄×D₄×C₅₃	—	2	1	no	—
43	C₂×C₄×D₄×C₅₃	—	2	1	no	—
44	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₂×#117×C₅₃	—	2	1	no	—
48	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₅₃	—	2	1	no	—
50	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#482	C₂²	1	8	yes	complemented
52	C₅₃×#481	C₂²	1	4	yes	complemented
53	C₅₃×#480	C₂²	1	4	yes	complemented
54	C₅₃×#477	C₂²	1	4	yes	complemented
55	C₅₃×#476	C₂²	1	4	yes	complemented
56	C₅₃×#475	C₂²	1	4	yes	complemented
57	C₅₃×#474	C₂²	1	4	yes	complemented
58	C₅₃×#460	C₂²	1	4	yes	complemented
59	C₅₃×#460	C₂²	1	4	yes	complemented
60	C₅₃×#459	C₂²	1	4	yes	complemented
61	C₅₃×#459	C₂²	1	4	yes	complemented
62	C₅₃×#449	C₂²	1	8	yes	complemented
63	C₅₃×#448	C₂²	1	4	yes	complemented
64	C₅₃×#447	C₂²	1	4	yes	complemented
65	C₅₃×#442	C₂²	1	8	yes	complemented
66	C₅₃×#440	C₂²	1	8	yes	complemented
67	C₄×SD₁₆×C₅₃	C₂²	1	8	yes	complemented
68	C₄×D₈×C₅₃	C₂²	1	8	yes	complemented
69	C₅₃×#432	C₂²	1	2	yes	complemented
70	C₅₃×#432	C₂²	1	2	yes	complemented
71	C₅₃×#431	C₂²	1	2	yes	complemented
72	C₅₃×#431	C₂²	1	2	yes	complemented
73	C₅₃×#428	C₂²	1	4	yes	complemented
74	C₅₃×#423	C₂²	1	2	yes	complemented
75	C₅₃×#418	C₂²	1	4	yes	complemented
76	C₅₃×#417	C₂²	1	4	yes	—
77	C₅₃×#407	C₂²	1	2	yes	—
78	C₄×M₁₆×C₅₃	C₂²	1	2	yes	complemented
79	C₂×#41×C₅₃	—	2	8	no	—
80	C₂×#41×C₅₃	—	2	1	no	—
81	C₂×#41×C₅₃	—	2	1	no	—
82	C₂×#41×C₅₃	—	2	2	no	—
83	C₂×#41×C₅₃	—	2	2	no	—
84	C₂×#41×C₅₃	—	2	2	no	—
85	C₂×#41×C₅₃	—	2	2	no	—
86	C₂×#41×C₅₃	—	4	8	no	—
87	C₂×#41×C₅₃	C₂³	1	2	yes	—
88	C₂×#41×C₅₃	C₂³	1	2	yes	—
89	C₂²×Q₈×C₅₃	—	2	1	no	—
90	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₅₃	—	2	1	no	—
92	C₂²×D₄×C₅₃	—	2	2	no	—
93	C₂²×D₄×C₅₃	—	2	1	no	—
94	C₂²×D₄×C₅₃	—	2	1	no	—
95	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
97	C₂³×C₄×C₅₃	—	2	1	no	—
98	C₂³×C₄×C₅₃	—	2	1	no	—
99	C₂³×C₄×C₅₃	—	2	1	no	—
100	C₂³×C₄×C₅₃	—	2	2	no	—
101	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
102	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
103	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
104	AGL(1,ℤ/8)×C₅₃	—	2	16	no	—
105	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	—
106	C₂×D₈×C₅₃	C₂³	1	8	yes	—
107	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
108	C₄⋊Q₈×C₅₃	—	2	1	no	—
109	C₄⋊Q₈×C₅₃	—	2	1	no	—
110	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
112	#127×C₅₃	—	2	1	no	—
113	#127×C₅₃	—	2	1	no	—
114	#127×C₅₃	C₂³	1	2	yes	—
115	#127×C₅₃	C₂³	1	2	yes	—
116	#124×C₅₃	—	2	2	no	—
117	#124×C₅₃	—	2	2	no	—
118	#124×C₅₃	—	2	2	no	—
119	#124×C₅₃	—	2	2	no	—
120	#121×C₅₃	—	2	2	no	—
121	#121×C₅₃	—	2	2	no	—
122	#121×C₅₃	—	2	2	no	—
123	#121×C₅₃	—	2	2	no	—
124	#121×C₅₃	—	2	2	no	—
125	#121×C₅₃	—	2	2	no	—
126	#121×C₅₃	C₂³	1	4	yes	—
127	#121×C₅₃	C₂³	1	4	yes	—
128	C₄×Q₈×C₅₃	—	2	1	no	—
129	C₄×Q₈×C₅₃	—	2	1	no	—
130	C₄×Q₈×C₅₃	—	2	1	no	—
131	C₄×Q₈×C₅₃	—	2	1	no	—
132	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
133	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
134	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
135	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
136	C₄×D₄×C₅₃	—	2	2	no	—
137	C₄×D₄×C₅₃	—	2	2	no	—
138	C₄×D₄×C₅₃	—	2	2	no	—
139	C₄×D₄×C₅₃	—	2	2	no	—
140	C₄×D₄×C₅₃	—	2	1	no	—
141	C₄×D₄×C₅₃	—	2	1	no	—
142	C₄×D₄×C₅₃	—	2	1	no	—
143	C₄×D₄×C₅₃	—	2	1	no	—
144	C₄×D₄×C₅₃	—	2	2	no	—
145	C₄×D₄×C₅₃	—	2	2	no	—
146	C₄×D₄×C₅₃	—	2	2	no	—
147	C₄×D₄×C₅₃	—	2	2	no	—
148	C₄×D₄×C₅₃	—	2	2	no	—
149	C₄×D₄×C₅₃	—	2	2	no	—
150	C₄×D₄×C₅₃	—	2	2	no	—
151	C₄×D₄×C₅₃	—	2	2	no	—
152	C₄×D₄×C₅₃	—	2	2	no	—
153	C₄×D₄×C₅₃	—	2	2	no	—
154	C₄×D₄×C₅₃	C₂³	1	2	yes	—
155	C₄×D₄×C₅₃	C₂³	1	2	yes	—
156	C₄×D₄×C₅₃	C₂³	1	2	yes	—
157	C₄×D₄×C₅₃	C₂³	1	2	yes	—
158	C₄×D₄×C₅₃	C₂³	1	4	yes	—
159	C₄×D₄×C₅₃	C₂³	1	4	yes	—
160	#117×C₅₃	—	2	2	no	—
161	#117×C₅₃	—	2	2	no	—
162	#117×C₅₃	—	2	2	no	—
163	#117×C₅₃	—	2	2	no	—
164	#117×C₅₃	—	2	1	no	—
165	#117×C₅₃	—	2	1	no	—
166	#117×C₅₃	C₂³	1	2	yes	—
167	#117×C₅₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
169	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
170	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
171	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
175	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
178	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
179	C₂×C₄²×C₅₃	—	2	2	no	—
180	C₂×C₄²×C₅₃	—	2	2	no	—
181	C₂×C₄²×C₅₃	—	2	2	no	—
182	C₂×C₄²×C₅₃	—	2	2	no	—
183	C₂×C₄²×C₅₃	—	2	1	no	—
184	C₂×C₄²×C₅₃	—	2	1	no	—
185	C₂×C₄²×C₅₃	—	2	1	no	—
186	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
198	#107×C₅₃	C₂³	1	8	yes	—
199	#106×C₅₃	C₂³	1	8	yes	—
200	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
201	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
202	#103×C₅₃	C₂³	1	8	yes	—
203	#102×C₅₃	C₂³	1	8	yes	—
204	#102×C₅₃	C₂³	1	8	yes	—
205	#102×C₅₃	C₂³	1	8	yes	—
206	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
207	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
208	#97×C₅₃	C₂³	1	4	yes	—
209	C₄×C₈×C₅₃	C₂³	1	4	yes	—
210	C₂⁴×C₅₃	—	2	1	no	—
211	C₂⁴×C₅₃	—	2	2	no	—
212	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
213	#41×C₅₃	—	2	8	no	—
214	#41×C₅₃	—	2	8	no	—
215	#41×C₅₃	—	2	4	no	—
216	#41×C₅₃	—	2	4	no	—
217	#41×C₅₃	—	2	4	no	—
218	#41×C₅₃	—	4	8	no	—
219	#41×C₅₃	—	4	8	no	—
220	#41×C₅₃	—	4	8	no	—
221	#41×C₅₃	—	4	8	no	—
222	#41×C₅₃	#41	1	8	yes	complemented
223	C₂×Q₈×C₅₃	—	2	4	no	—
224	C₂×Q₈×C₅₃	—	2	1	no	—
225	C₂×Q₈×C₅₃	—	2	2	no	—
226	C₂×Q₈×C₅₃	—	2	2	no	—
227	C₂×Q₈×C₅₃	—	4	4	no	—
228	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
229	C₂×D₄×C₅₃	—	2	8	no	—
230	C₂×D₄×C₅₃	—	2	2	no	—
231	C₂×D₄×C₅₃	—	2	2	no	—
232	C₂×D₄×C₅₃	—	2	4	no	—
233	C₂×D₄×C₅₃	—	2	4	no	—
234	C₂×D₄×C₅₃	—	2	4	no	—
235	C₂×D₄×C₅₃	—	2	1	no	—
236	C₂×D₄×C₅₃	—	2	2	no	—
237	C₂×D₄×C₅₃	—	2	2	no	—
238	C₂×D₄×C₅₃	—	2	2	no	—
239	C₂×D₄×C₅₃	—	2	2	no	—
240	C₂×D₄×C₅₃	—	2	2	no	—
241	C₂×D₄×C₅₃	—	2	8	no	—
242	C₂×D₄×C₅₃	—	4	4	no	—
243	C₂×D₄×C₅₃	—	4	4	no	—
244	C₂×D₄×C₅₃	—	4	8	no	—
245	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
246	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₅₃	—	2	8	no	—
248	C₂²×C₄×C₅₃	—	2	1	no	—
249	C₂²×C₄×C₅₃	—	2	4	no	—
250	C₂²×C₄×C₅₃	—	2	2	no	—
251	C₂²×C₄×C₅₃	—	2	2	no	—
252	C₂²×C₄×C₅₃	—	2	4	no	—
253	C₂²×C₄×C₅₃	—	2	1	no	—
254	C₂²×C₄×C₅₃	—	2	1	no	—
255	C₂²×C₄×C₅₃	—	2	2	no	—
256	C₂²×C₄×C₅₃	—	2	2	no	—
257	C₂²×C₄×C₅₃	—	2	2	no	—
258	C₂²×C₄×C₅₃	—	2	2	no	—
259	C₂²×C₄×C₅₃	—	2	4	no	—
260	C₂²×C₄×C₅₃	—	2	2	no	—
261	C₂²×C₄×C₅₃	—	2	4	no	—
262	C₂²×C₄×C₅₃	—	4	2	no	—
263	C₂²×C₄×C₅₃	—	4	4	no	—
264	C₂²×C₄×C₅₃	—	4	8	no	—
265	C₂²×C₄×C₅₃	—	4	4	no	—
266	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
284	SD₁₆×C₅₃	—	2	16	no	—
285	D₈×C₅₃	—	2	16	no	—
286	M₁₆×C₅₃	—	2	8	no	—
287	C₂×C₈×C₅₃	C₂⁴	1	8	yes	—
288	C₄⋊C₄×C₅₃	—	2	2	no	—
289	C₄⋊C₄×C₅₃	—	2	2	no	—
290	C₄⋊C₄×C₅₃	—	2	2	no	—
291	C₄⋊C₄×C₅₃	—	2	2	no	—
292	C₄⋊C₄×C₅₃	—	2	2	no	—
293	C₄⋊C₄×C₅₃	—	2	2	no	—
294	C₄⋊C₄×C₅₃	—	2	1	no	—
295	C₄⋊C₄×C₅₃	—	2	1	no	—
296	C₄⋊C₄×C₅₃	—	2	2	no	—
297	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
300	C₂²⋊C₄×C₅₃	—	2	2	no	—
301	C₂²⋊C₄×C₅₃	—	2	2	no	—
302	C₂²⋊C₄×C₅₃	—	2	2	no	—
303	C₂²⋊C₄×C₅₃	—	2	2	no	—
304	C₂²⋊C₄×C₅₃	—	2	2	no	—
305	C₂²⋊C₄×C₅₃	—	2	2	no	—
306	C₂²⋊C₄×C₅₃	—	2	4	no	—
307	C₂²⋊C₄×C₅₃	—	2	4	no	—
308	C₂²⋊C₄×C₅₃	—	2	4	no	—
309	C₂²⋊C₄×C₅₃	—	2	4	no	—
310	C₄²×C₅₃	—	2	2	no	—
311	C₄²×C₅₃	—	2	2	no	—
312	C₄²×C₅₃	—	2	2	no	—
313	C₄²×C₅₃	—	2	2	no	—
314	C₄²×C₅₃	—	2	2	no	—
315	C₄²×C₅₃	—	2	2	no	—
316	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₂³×C₅₃	—	2	4	no	—
333	C₂³×C₅₃	—	2	2	no	—
334	C₂³×C₅₃	—	2	2	no	—
335	C₂³×C₅₃	—	2	2	no	—
336	C₂³×C₅₃	—	2	4	no	—
337	C₂³×C₅₃	—	4	1	no	—
338	C₂³×C₅₃	—	4	2	no	—
339	C₂³×C₅₃	—	4	4	no	—
340	C₂³×C₅₃	—	4	4	no	—
341	C₂³×C₅₃	—	4	2	no	—
342	C₂³×C₅₃	—	4	4	no	—
343	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
344	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
345	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
346	Q₈×C₅₃	—	2	4	no	—
347	Q₈×C₅₃	—	2	2	no	—
348	Q₈×C₅₃	—	4	4	no	—
349	Q₈×C₅₃	—	4	4	no	—
350	Q₈×C₅₃	C₂×#41	1	4	yes	complemented
351	D₄×C₅₃	—	2	8	no	—
352	D₄×C₅₃	—	2	4	no	—
353	D₄×C₅₃	—	2	8	no	—
354	D₄×C₅₃	—	2	2	no	—
355	D₄×C₅₃	—	2	8	no	—
356	D₄×C₅₃	—	4	4	no	—
357	D₄×C₅₃	—	4	4	no	—
358	D₄×C₅₃	—	4	8	no	—
359	D₄×C₅₃	—	4	8	no	—
360	D₄×C₅₃	—	4	4	no	—
361	D₄×C₅₃	—	4	4	no	—
362	D₄×C₅₃	—	4	4	no	—
363	D₄×C₅₃	C₂×#41	1	4	yes	complemented
364	C₂×C₄×C₅₃	—	2	4	no	—
365	C₂×C₄×C₅₃	—	2	8	no	—
366	C₂×C₄×C₅₃	—	2	2	no	—
367	C₂×C₄×C₅₃	—	2	2	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	8	no	—
371	C₂×C₄×C₅₃	—	2	2	no	—
372	C₂×C₄×C₅₃	—	2	2	no	—
373	C₂×C₄×C₅₃	—	2	2	no	—
374	C₂×C₄×C₅₃	—	2	2	no	—
375	C₂×C₄×C₅₃	—	2	2	no	—
376	C₂×C₄×C₅₃	—	2	2	no	—
377	C₂×C₄×C₅₃	—	2	2	no	—
378	C₂×C₄×C₅₃	—	2	2	no	—
379	C₂×C₄×C₅₃	—	2	2	no	—
380	C₂×C₄×C₅₃	—	2	2	no	—
381	C₂×C₄×C₅₃	—	2	4	no	—
382	C₂×C₄×C₅₃	—	2	2	no	—
383	C₂×C₄×C₅₃	—	2	2	no	—
384	C₂×C₄×C₅₃	—	4	1	no	—
385	C₂×C₄×C₅₃	—	4	1	no	—
386	C₂×C₄×C₅₃	—	4	1	no	—
387	C₂×C₄×C₅₃	—	4	4	no	—
388	C₂×C₄×C₅₃	—	4	8	no	—
389	C₂×C₄×C₅₃	—	4	2	no	—
390	C₂×C₄×C₅₃	—	4	4	no	—
391	C₂×C₄×C₅₃	—	4	2	no	—
392	C₂×C₄×C₅₃	—	4	4	no	—
393	C₂×C₄×C₅₃	—	4	4	no	—
394	C₂×C₄×C₅₃	—	4	8	no	—
395	C₂×C₄×C₅₃	—	4	4	no	—
396	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	4	yes	complemented
397	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
409	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
410	C₈×C₅₃	—	2	8	no	—
411	#60561	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₂²×C₅₃	—	2	1	no	—
413	C₂²×C₅₃	—	2	1	no	—
414	C₂²×C₅₃	—	2	1	no	—
415	C₂²×C₅₃	—	2	1	no	—
416	C₂²×C₅₃	—	2	1	no	—
417	C₂²×C₅₃	—	2	4	no	—
418	C₂²×C₅₃	—	2	1	no	—
419	C₂²×C₅₃	—	2	1	no	—
420	C₂²×C₅₃	—	4	4	no	—
421	C₂²×C₅₃	—	4	8	no	—
422	C₂²×C₅₃	—	4	2	no	—
423	C₂²×C₅₃	—	4	2	no	—
424	C₂²×C₅₃	—	4	4	no	—
425	C₂²×C₅₃	—	4	4	no	—
426	C₂²×C₅₃	—	4	4	no	—
427	C₂²×C₅₃	—	8	8	no	—
428	C₂²×C₅₃	#525	1	2	yes	—
429	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
430	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
431	C₄×C₅₃	—	2	1	no	—
432	C₄×C₅₃	—	2	4	no	—
433	C₄×C₅₃	—	2	1	no	—
434	C₄×C₅₃	—	2	1	no	—
435	C₄×C₅₃	—	2	1	no	—
436	C₄×C₅₃	—	2	1	no	—
437	C₄×C₅₃	—	2	1	no	—
438	C₄×C₅₃	—	2	1	no	—
439	C₄×C₅₃	—	4	2	no	—
440	C₄×C₅₃	—	4	4	no	—
441	C₄×C₅₃	—	4	2	no	—
442	C₄×C₅₃	#525	1	2	yes	—
443	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
444	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
445	C₄×C₅₃	#575	1	2	yes	—
446	C₄×C₅₃	C₂²×#41	1	2	yes	—
447	C₂×#532	C₂×C₅₃	1	1	yes	characteristic, complemented
448	C₂×C₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
449	#3115	C₂×C₅₃	1	4	yes	complemented
450	#3112	C₂×C₅₃	1	2	yes	complemented
451	#3109	C₂×C₅₃	1	2	yes	complemented
452	#3106	C₂×C₅₃	1	4	yes	complemented
453	#3103	C₂×C₅₃	1	2	yes	complemented
454	#3100	C₂×C₅₃	1	2	yes	complemented
455	#3094	C₂×C₅₃	1	2	yes	complemented
456	#3079	C₂×C₅₃	1	2	yes	complemented
457	#3038	C₂×C₅₃	1	2	yes	complemented
458	#3006	C₂×C₅₃	1	2	yes	complemented
459	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	4	yes	complemented
460	#2920	C₂×C₅₃	1	1	yes	characteristic, complemented
461	C₂×C₅₃	—	2	2	no	—
462	C₂×C₅₃	—	2	2	no	—
463	C₂×C₅₃	—	4	1	no	—
464	C₂×C₅₃	—	4	4	no	—
465	C₂×C₅₃	—	8	4	no	—
466	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
467	C₂×C₅₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
468	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
469	C₂²×#41	—	2	1	no	—
470	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
471	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	4	yes	—
472	#532	—	2	1	no	—
473	#532	—	2	1	no	—
474	#532	—	2	1	no	—
475	#532	—	2	1	no	—
476	#532	C₂²×C₅₃	1	2	yes	—
477	#532	C₂²×C₅₃	1	2	yes	—
478	#532	C₂²×C₅₃	1	2	yes	complemented
479	#532	C₂²×C₅₃	1	2	yes	complemented
480	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
481	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic, complemented
482	C₂×#124	—	2	1	no	—
483	C₂×#121	—	2	1	no	—
484	C₂×#121	C₂²×C₅₃	1	2	yes	—
485	C₄×#41	—	2	1	no	—
486	C₄×#41	—	2	1	no	—
487	C₄×#41	—	2	1	no	—
488	C₄×#41	—	2	1	no	—
489	C₄×#41	C₂²×C₅₃	1	2	yes	—
490	C₄×#41	C₂²×C₅₃	1	2	yes	—
491	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
492	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
493	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
494	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
495	C₂×C₄×D₄	—	2	1	no	—
496	C₂×C₄×D₄	—	2	1	no	—
497	C₂×C₄×D₄	—	2	1	no	—
498	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
499	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
500	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
501	C₂×#117	—	2	1	no	—
502	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
503	C₂²×C₄²	—	2	1	no	—
504	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
505	#482	C₂²×C₅₃	1	8	yes	complemented
506	#481	C₂²×C₅₃	1	4	yes	complemented
507	#480	C₂²×C₅₃	1	4	yes	complemented
508	#477	C₂²×C₅₃	1	4	yes	complemented
509	#476	C₂²×C₅₃	1	4	yes	complemented
510	#475	C₂²×C₅₃	1	4	yes	complemented
511	#474	C₂²×C₅₃	1	4	yes	complemented
512	#460	C₂²×C₅₃	1	4	yes	complemented
513	#460	C₂²×C₅₃	1	4	yes	complemented
514	#459	C₂²×C₅₃	1	4	yes	complemented
515	#459	C₂²×C₅₃	1	4	yes	complemented
516	#449	C₂²×C₅₃	1	8	yes	complemented
517	#448	C₂²×C₅₃	1	4	yes	complemented
518	#447	C₂²×C₅₃	1	4	yes	complemented
519	#442	C₂²×C₅₃	1	8	yes	complemented
520	#440	C₂²×C₅₃	1	8	yes	complemented
521	C₄×SD₁₆	C₂²×C₅₃	1	8	yes	complemented
522	C₄×D₈	C₂²×C₅₃	1	8	yes	complemented
523	#432	C₂²×C₅₃	1	2	yes	complemented
524	#432	C₂²×C₅₃	1	2	yes	complemented
525	#431	C₂²×C₅₃	1	2	yes	complemented
526	#431	C₂²×C₅₃	1	2	yes	complemented
527	#428	C₂²×C₅₃	1	4	yes	complemented
528	#423	C₂²×C₅₃	1	2	yes	complemented
529	#418	C₂²×C₅₃	1	4	yes	complemented
530	#417	C₂²×C₅₃	1	4	yes	—
531	#407	C₂²×C₅₃	1	2	yes	—
532	C₄×M₁₆	C₂²×C₅₃	1	2	yes	complemented
533	C₅₃	#60561	1	1	yes	characteristic, direct product factor, Sylow
534	C₂×#41	—	2	8	no	—
535	C₂×#41	—	2	1	no	—
536	C₂×#41	—	2	1	no	—
537	C₂×#41	—	2	2	no	—
538	C₂×#41	—	2	2	no	—
539	C₂×#41	—	2	2	no	—
540	C₂×#41	—	2	2	no	—
541	C₂×#41	—	4	8	no	—
542	C₂×#41	C₂³×C₅₃	1	2	yes	—
543	C₂×#41	C₂³×C₅₃	1	2	yes	—
544	C₂²×Q₈	—	2	1	no	—
545	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
546	C₂²×D₄	—	2	1	no	—
547	C₂²×D₄	—	2	2	no	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
551	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
552	C₂³×C₄	—	2	1	no	—
553	C₂³×C₄	—	2	2	no	—
554	C₂³×C₄	—	2	1	no	—
555	C₂³×C₄	—	2	1	no	—
556	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
557	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
559	AGL(1,ℤ/8)	—	2	16	no	—
560	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	—
561	C₂×D₈	C₂³×C₅₃	1	8	yes	—
562	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
563	C₄⋊Q₈	—	2	1	no	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
566	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
567	#127	—	2	1	no	—
568	#127	—	2	1	no	—
569	#127	C₂³×C₅₃	1	2	yes	—
570	#127	C₂³×C₅₃	1	2	yes	—
571	#124	—	2	2	no	—
572	#124	—	2	2	no	—
573	#124	—	2	2	no	—
574	#124	—	2	2	no	—
575	#121	—	2	2	no	—
576	#121	—	2	2	no	—
577	#121	—	2	2	no	—
578	#121	—	2	2	no	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	C₂³×C₅₃	1	4	yes	—
582	#121	C₂³×C₅₃	1	4	yes	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
588	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
589	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
590	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	C₂³×C₅₃	1	2	yes	—
610	C₄×D₄	C₂³×C₅₃	1	2	yes	—
611	C₄×D₄	C₂³×C₅₃	1	2	yes	—
612	C₄×D₄	C₂³×C₅₃	1	2	yes	—
613	C₄×D₄	C₂³×C₅₃	1	4	yes	—
614	C₄×D₄	C₂³×C₅₃	1	4	yes	—
615	#117	—	2	1	no	—
616	#117	—	2	1	no	—
617	#117	—	2	2	no	—
618	#117	—	2	2	no	—
619	#117	—	2	2	no	—
620	#117	—	2	2	no	—
621	#117	C₂³×C₅₃	1	2	yes	—
622	#117	C₂³×C₅₃	1	2	yes	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	2	no	—
633	C₂×C₂²⋊C₄	—	2	2	no	—
634	C₂×C₄²	—	2	1	no	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	—	2	2	no	—
638	C₂×C₄²	—	2	2	no	—
639	C₂×C₄²	—	2	2	no	—
640	C₂×C₄²	—	2	2	no	—
641	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
642	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
643	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
644	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
645	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
646	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
653	#107	C₂³×C₅₃	1	8	yes	—
654	#106	C₂³×C₅₃	1	8	yes	—
655	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
656	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
657	#103	C₂³×C₅₃	1	8	yes	—
658	#102	C₂³×C₅₃	1	8	yes	—
659	#102	C₂³×C₅₃	1	8	yes	—
660	#102	C₂³×C₅₃	1	8	yes	—
661	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
662	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
663	#97	C₂³×C₅₃	1	4	yes	—
664	C₄×C₈	C₂³×C₅₃	1	4	yes	—
665	C₂⁴	—	2	1	no	—
666	C₂⁴	—	2	2	no	—
667	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
668	#41	—	2	8	no	—
669	#41	—	2	8	no	—
670	#41	—	2	4	no	—
671	#41	—	2	4	no	—
672	#41	—	2	4	no	—
673	#41	—	4	8	no	—
674	#41	—	4	8	no	—
675	#41	—	4	8	no	—
676	#41	—	4	8	no	—
677	#41	#41×C₅₃	1	8	yes	complemented
678	C₂×Q₈	—	2	4	no	—
679	C₂×Q₈	—	2	1	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	4	4	no	—
683	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
684	C₂×D₄	—	2	8	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	8	no	—
697	C₂×D₄	—	4	4	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	8	no	—
700	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
701	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
702	C₂²×C₄	—	2	8	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	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	4	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	—	4	4	no	—
719	C₂²×C₄	—	4	8	no	—
720	C₂²×C₄	—	4	4	no	—
721	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
723	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
725	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
726	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
727	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
728	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
729	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
730	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
731	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
732	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
735	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
739	SD₁₆	—	2	16	no	—
740	D₈	—	2	16	no	—
741	M₁₆	—	2	8	no	—
742	C₂×C₈	C₂⁴×C₅₃	1	8	yes	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
753	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
754	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
772	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
773	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
775	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
776	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
777	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
778	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
779	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
782	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
783	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
784	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
785	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
786	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
787	C₂³	—	2	4	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	4	no	—
792	C₂³	—	4	1	no	—
793	C₂³	—	4	2	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	4	4	no	—
796	C₂³	—	4	2	no	—
797	C₂³	—	4	4	no	—
798	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
799	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
800	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
801	Q₈	—	2	4	no	—
802	Q₈	—	2	2	no	—
803	Q₈	—	4	4	no	—
804	Q₈	—	4	4	no	—
805	Q₈	C₂×#41×C₅₃	1	4	yes	complemented
806	D₄	—	2	8	no	—
807	D₄	—	2	4	no	—
808	D₄	—	2	8	no	—
809	D₄	—	2	2	no	—
810	D₄	—	2	8	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	8	no	—
814	D₄	—	4	8	no	—
815	D₄	—	4	4	no	—
816	D₄	—	4	4	no	—
817	D₄	—	4	4	no	—
818	D₄	C₂×#41×C₅₃	1	4	yes	complemented
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	8	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	8	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	4	1	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	—	4	8	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	2	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	4	yes	complemented
852	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
855	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
856	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
857	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
859	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
860	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
861	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
863	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
864	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
865	C₈	—	2	8	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	4	4	no	—
875	C₂²	—	4	8	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	4	no	—
879	C₂²	—	4	4	no	—
880	C₂²	—	4	4	no	—
881	C₂²	—	8	8	no	—
882	C₂²	C₅₃×#525	1	2	yes	—
883	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
884	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	1	no	—
893	C₄	—	4	4	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	C₅₃×#525	1	2	yes	—
897	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
898	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
899	C₄	C₅₃×#575	1	2	yes	—
900	C₄	C₂²×#41×C₅₃	1	2	yes	—
901	C₂	—	2	2	no	—
902	C₂	—	2	2	no	—
903	C₂	—	4	1	no	—
904	C₂	—	4	4	no	—
905	C₂	—	8	4	no	—
906	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
907	C₂	C₂²×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
908	C₂	C₂×C₅₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
socle	C₂²×C₅₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₂²×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#532	C₂	semidirect
2. C₂×C₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#3115	C₂	semidirect
4. C₅₃×#3112	C₂	semidirect
5. C₅₃×#3109	C₂	semidirect
6. C₅₃×#3106	C₂	semidirect
7. C₅₃×#3103	C₂	semidirect
8. C₅₃×#3100	C₂	semidirect
9. C₅₃×#3094	C₂	semidirect
10. C₅₃×#3079	C₂	semidirect
11. C₅₃×#3038	C₂	semidirect
12. C₅₃×#3006	C₂	semidirect
13. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
14. C₅₃×#2920	C₂	semidirect
24. C₅₃×#532	C₂²	semidirect
25. C₅₃×#532	C₂²	semidirect
26. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
27. C₂×#127×C₅₃	C₂²	semidirect
37. C₄×#41×C₅₃	C₂²	semidirect
38. C₄×#41×C₅₃	C₂²	semidirect
39. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
40. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
44. C₂×C₄×D₄×C₅₃	C₂²	semidirect
45. C₂×C₄×D₄×C₅₃	C₂²	semidirect
46. C₂×C₄×D₄×C₅₃	C₂²	semidirect
51. C₅₃×#482	C₂²	semidirect
52. C₅₃×#481	C₂²	semidirect
53. C₅₃×#480	C₂²	semidirect
54. C₅₃×#477	C₂²	semidirect
55. C₅₃×#476	C₂²	semidirect
56. C₅₃×#475	C₂²	semidirect
57. C₅₃×#474	C₂²	semidirect
58. C₅₃×#460	C₂²	semidirect
59. C₅₃×#460	C₂²	semidirect
60. C₅₃×#459	C₂²	semidirect
61. C₅₃×#459	C₂²	semidirect
62. C₅₃×#449	C₂²	semidirect
63. C₅₃×#448	C₂²	semidirect
64. C₅₃×#447	C₂²	semidirect
65. C₅₃×#442	C₂²	semidirect
66. C₅₃×#440	C₂²	semidirect
67. C₄×SD₁₆×C₅₃	C₂²	semidirect
68. C₄×D₈×C₅₃	C₂²	semidirect
69. C₅₃×#432	C₂²	semidirect
70. C₅₃×#432	C₂²	semidirect
71. C₅₃×#431	C₂²	semidirect
72. C₅₃×#431	C₂²	semidirect
73. C₅₃×#428	C₂²	semidirect
74. C₅₃×#423	C₂²	semidirect
75. C₅₃×#418	C₂²	semidirect
78. C₄×M₁₆×C₅₃	C₂²	semidirect
222. #41×C₅₃	#41	semidirect
350. Q₈×C₅₃	C₂×#41	semidirect
363. D₄×C₅₃	C₂×#41	semidirect
396. C₂×C₄×C₅₃	AGL(1,ℤ/8)	semidirect
411. #60561	C₅₃	direct (N × H)
447. C₂×#532	C₂×C₅₃	semidirect
448. C₂×C₄×#41	C₂×C₅₃	semidirect
449. #3115	C₂×C₅₃	semidirect
450. #3112	C₂×C₅₃	semidirect
451. #3109	C₂×C₅₃	semidirect
452. #3106	C₂×C₅₃	semidirect
453. #3103	C₂×C₅₃	semidirect
454. #3100	C₂×C₅₃	semidirect
455. #3094	C₂×C₅₃	semidirect
456. #3079	C₂×C₅₃	semidirect
457. #3038	C₂×C₅₃	semidirect
458. #3006	C₂×C₅₃	semidirect
459. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
460. #2920	C₂×C₅₃	semidirect
478. #532	C₂²×C₅₃	semidirect
479. #532	C₂²×C₅₃	semidirect
480. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
481. C₂×#127	C₂²×C₅₃	semidirect
491. C₄×#41	C₂²×C₅₃	semidirect
492. C₄×#41	C₂²×C₅₃	semidirect
493. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
494. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
498. C₂×C₄×D₄	C₂²×C₅₃	semidirect
499. C₂×C₄×D₄	C₂²×C₅₃	semidirect
500. C₂×C₄×D₄	C₂²×C₅₃	semidirect
505. #482	C₂²×C₅₃	semidirect
506. #481	C₂²×C₅₃	semidirect
507. #480	C₂²×C₅₃	semidirect
508. #477	C₂²×C₅₃	semidirect
509. #476	C₂²×C₅₃	semidirect
510. #475	C₂²×C₅₃	semidirect
511. #474	C₂²×C₅₃	semidirect
512. #460	C₂²×C₅₃	semidirect
513. #460	C₂²×C₅₃	semidirect
514. #459	C₂²×C₅₃	semidirect
515. #459	C₂²×C₅₃	semidirect
516. #449	C₂²×C₅₃	semidirect
517. #448	C₂²×C₅₃	semidirect
518. #447	C₂²×C₅₃	semidirect
519. #442	C₂²×C₅₃	semidirect
520. #440	C₂²×C₅₃	semidirect
521. C₄×SD₁₆	C₂²×C₅₃	semidirect
522. C₄×D₈	C₂²×C₅₃	semidirect
523. #432	C₂²×C₅₃	semidirect
524. #432	C₂²×C₅₃	semidirect
525. #431	C₂²×C₅₃	semidirect
526. #431	C₂²×C₅₃	semidirect
527. #428	C₂²×C₅₃	semidirect
528. #423	C₂²×C₅₃	semidirect
529. #418	C₂²×C₅₃	semidirect
532. C₄×M₁₆	C₂²×C₅₃	semidirect
533. C₅₃	#60561	direct (N × H)
677. #41	#41×C₅₃	semidirect
805. Q₈	C₂×#41×C₅₃	semidirect
818. D₄	C₂×#41×C₅₃	semidirect
851. C₂×C₄	AGL(1,ℤ/8)×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×#532	2
C₂×C₄×#41×C₅₃	2
C₅₃×#3115	2
C₅₃×#3112	2
C₅₃×#3109	2
C₅₃×#3106	2
C₅₃×#3103	2
C₅₃×#3100	2
C₅₃×#3094	2
C₅₃×#3079	2
C₅₃×#3038	2
C₅₃×#3006	2
C₄×AGL(1,ℤ/8)×C₅₃	2
C₅₃×#2920	2
#60561	53

Subgroups — C53×#60561 #27268073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60561 #27268073