Subgroups — C₅₃×#62015 #27269527

Order 13568.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3399	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3370	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3319	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3318	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3301	C₂	1	2	yes	maximal, complemented
8	D₄×D₈×C₅₃	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3265	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3264	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3257	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3220	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3041	C₂	1	2	yes	maximal, complemented
18	C₂×C₅₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
21	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
23	C₂²×D₈×C₅₃	C₂²	1	2	yes	complemented
24	C₅₃×#562	—	2	1	no	—
25	C₅₃×H(3,𝔽₄)	—	2	1	no	—
26	C₅₃×#559	C₂²	1	2	yes	complemented
27	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#553	—	2	1	no	—
30	C₅₃×#553	C₂²	1	2	yes	complemented
31	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
32	C₅₃×#548	C₂²	1	2	yes	complemented
33	C₅₃×#546	—	2	1	no	—
34	C₅₃×#546	—	2	2	no	—
35	C₅₃×#546	—	2	2	no	—
36	C₅₃×#546	C₂²	1	2	yes	complemented
37	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	D₄²×C₅₃	C₂²	1	2	yes	complemented
39	D₄²×C₅₃	C₂²	1	2	yes	complemented
40	C₅₃×#542	C₂²	1	2	yes	complemented
41	C₅₃×#540	C₂²	1	2	yes	complemented
42	C₅₃×#538	—	2	2	no	—
43	C₅₃×#538	—	2	2	no	—
44	C₅₃×#538	—	2	1	no	—
45	C₅₃×#535	C₂²	1	2	yes	complemented
46	C₅₃×#534	—	2	1	no	—
47	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#529	C₂²	1	1	yes	characteristic
50	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#525	—	2	1	no	—
52	C₂×#121×C₅₃	—	2	1	no	—
53	C₅₃×#518	C₂²	1	2	yes	complemented
54	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#496	C₂²	1	2	yes	complemented
56	C₅₃×#496	C₂²	1	2	yes	complemented
57	C₅₃×#493	C₂²	1	2	yes	complemented
58	C₅₃×#490	C₂²	1	2	yes	complemented
59	C₅₃×#489	C₂²	1	2	yes	complemented
60	C₅₃×#488	C₂²	1	2	yes	complemented
61	C₅₃×#485	C₂²	1	2	yes	complemented
62	C₅₃×#482	C₂²	1	2	yes	complemented
63	C₅₃×#481	C₂²	1	2	yes	complemented
64	C₅₃×#479	C₂²	1	2	yes	complemented
65	C₅₃×#478	C₂²	1	2	yes	complemented
66	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#474	C₂²	1	2	yes	complemented
69	C₅₃×#474	C₂²	1	2	yes	complemented
70	C₅₃×#469	C₂²	1	2	yes	complemented
71	C₅₃×#468	C₂²	1	2	yes	complemented
72	C₅₃×#466	C₂²	1	2	yes	complemented
73	C₅₃×#466	C₂²	1	2	yes	complemented
74	C₅₃×#466	C₂²	1	2	yes	complemented
75	C₅₃×#465	C₂²	1	2	yes	complemented
76	C₅₃×#463	C₂²	1	2	yes	complemented
77	C₅₃×#463	C₂²	1	2	yes	complemented
78	C₅₃×#463	C₂²	1	2	yes	complemented
79	C₅₃×#463	C₂²	1	2	yes	complemented
80	C₅₃×#463	C₂²	1	2	yes	complemented
81	C₅₃×#463	C₂²	1	2	yes	complemented
82	C₅₃×#463	C₂²	1	2	yes	complemented
83	C₅₃×#463	C₂²	1	2	yes	complemented
84	C₅₃×#460	C₂²	1	2	yes	complemented
85	C₅₃×#459	C₂²	1	2	yes	—
86	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#459	C₂²	1	2	yes	complemented
88	C₅₃×#459	C₂²	1	2	yes	complemented
89	C₅₃×#459	C₂²	1	2	yes	complemented
90	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#459	C₂²	1	2	yes	complemented
92	C₅₃×#450	C₂²	1	2	yes	complemented
93	C₅₃×#449	C₂²	1	2	yes	complemented
94	C₅₃×#449	C₂²	1	2	yes	complemented
95	C₅₃×#448	C₂²	1	2	yes	complemented
96	C₅₃×#447	C₂²	1	2	yes	—
97	C₅₃×#447	C₂²	1	2	yes	complemented
98	C₅₃×#447	C₂²	1	2	yes	complemented
99	C₅₃×#447	C₂²	1	2	yes	complemented
100	C₅₃×#447	C₂²	1	2	yes	complemented
101	C₅₃×#446	C₂²	1	2	yes	complemented
102	C₅₃×#442	C₂²	1	2	yes	complemented
103	C₅₃×#442	C₂²	1	2	yes	complemented
104	C₅₃×#442	C₂²	1	2	yes	complemented
105	C₅₃×#440	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
107	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
108	C₅₃×#435	C₂²	1	2	yes	complemented
109	C₅₃×#435	C₂²	1	2	yes	complemented
110	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
111	C₅₃×#433	C₂²	1	2	yes	complemented
112	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#424	C₂²	1	2	yes	complemented
114	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#418	C₂²	1	2	yes	complemented
116	C₅₃×#416	C₂²	1	2	yes	complemented
117	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₅₃	—	2	1	no	—
120	C₂×#41×C₅₃	—	2	1	no	—
121	C₂×#41×C₅₃	—	2	1	no	—
122	C₂×#41×C₅₃	C₂³	1	2	yes	—
123	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₅₃	—	2	1	no	—
125	C₂²×D₄×C₅₃	—	2	2	no	—
126	C₂²×D₄×C₅₃	—	2	2	no	—
127	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
129	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₅₃	—	2	1	no	—
132	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
133	C₂×SD₁₆×C₅₃	—	4	2	no	—
134	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
135	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
138	C₂×D₈×C₅₃	—	4	2	no	—
139	C₂×D₈×C₅₃	—	4	4	no	—
140	C₂×D₈×C₅₃	C₂³	1	2	yes	—
141	C₂×D₈×C₅₃	C₂³	1	2	yes	—
142	C₂×D₈×C₅₃	C₂³	1	2	yes	—
143	C₂×D₈×C₅₃	C₂³	1	2	yes	—
144	C₂×D₈×C₅₃	C₂³	1	2	yes	—
145	C₂×D₈×C₅₃	C₂³	1	2	yes	—
146	C₂×D₈×C₅₃	C₂³	1	2	yes	—
147	C₂×D₈×C₅₃	C₂³	1	2	yes	—
148	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
154	#127×C₅₃	C₂³	1	2	yes	—
155	#127×C₅₃	C₂³	1	2	yes	—
156	#127×C₅₃	C₂³	1	1	yes	characteristic
157	#127×C₅₃	C₂³	1	1	yes	characteristic
158	#126×C₅₃	—	2	2	no	—
159	#126×C₅₃	—	2	2	no	—
160	#126×C₅₃	D₄	1	2	yes	—
161	#125×C₅₃	D₄	1	1	yes	characteristic
162	#125×C₅₃	C₂³	1	2	yes	—
163	#124×C₅₃	—	2	2	no	—
164	#124×C₅₃	—	2	2	no	—
165	#124×C₅₃	—	2	2	no	—
166	#124×C₅₃	—	2	1	no	—
167	#124×C₅₃	—	2	1	no	—
168	#124×C₅₃	—	2	1	no	—
169	#124×C₅₃	—	2	1	no	—
170	#124×C₅₃	—	2	2	no	—
171	#124×C₅₃	D₄	1	1	yes	characteristic
172	#124×C₅₃	C₂³	1	2	yes	—
173	#124×C₅₃	C₂³	1	2	yes	—
174	#124×C₅₃	C₂³	1	2	yes	—
175	#123×C₅₃	—	2	2	no	—
176	#123×C₅₃	—	2	2	no	—
177	#123×C₅₃	—	2	2	no	—
178	#123×C₅₃	—	2	2	no	—
179	#123×C₅₃	—	2	2	no	—
180	#123×C₅₃	—	2	2	no	—
181	#123×C₅₃	—	2	2	no	—
182	#123×C₅₃	D₄	1	2	yes	—
183	C₂²⋊Q₈×C₅₃	—	2	2	no	—
184	C₂²⋊Q₈×C₅₃	—	2	2	no	—
185	C₂²⋊Q₈×C₅₃	—	2	2	no	—
186	C₂²⋊Q₈×C₅₃	—	2	1	no	—
187	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
188	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
189	#121×C₅₃	—	2	1	no	—
190	#121×C₅₃	—	2	1	no	—
191	#121×C₅₃	—	2	2	no	—
192	#121×C₅₃	—	2	2	no	—
193	#121×C₅₃	—	2	2	no	—
194	#121×C₅₃	—	2	2	no	—
195	#121×C₅₃	—	2	2	no	—
196	#121×C₅₃	—	2	2	no	—
197	#121×C₅₃	—	2	2	no	—
198	#121×C₅₃	—	2	2	no	—
199	#121×C₅₃	—	2	2	no	—
200	#121×C₅₃	—	2	1	no	—
201	#121×C₅₃	—	2	2	no	—
202	#121×C₅₃	—	2	1	no	—
203	#121×C₅₃	—	2	1	no	—
204	#121×C₅₃	D₄	1	1	yes	characteristic
205	#121×C₅₃	C₂³	1	2	yes	—
206	#121×C₅₃	C₂³	1	2	yes	—
207	#121×C₅₃	C₂³	1	2	yes	—
208	#121×C₅₃	C₂³	1	2	yes	—
209	#121×C₅₃	C₂³	1	2	yes	—
210	#120×C₅₃	—	2	2	no	—
211	#120×C₅₃	—	2	2	no	—
212	#120×C₅₃	—	2	2	no	—
213	#120×C₅₃	—	2	2	no	—
214	#120×C₅₃	—	2	2	no	—
215	#120×C₅₃	—	2	2	no	—
216	#120×C₅₃	—	2	2	no	—
217	#120×C₅₃	—	2	2	no	—
218	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
220	C₄×D₄×C₅₃	—	2	2	no	—
221	C₄×D₄×C₅₃	—	2	2	no	—
222	C₄×D₄×C₅₃	—	2	2	no	—
223	C₄×D₄×C₅₃	—	2	2	no	—
224	C₄×D₄×C₅₃	—	2	2	no	—
225	C₄×D₄×C₅₃	—	2	1	no	—
226	C₄×D₄×C₅₃	—	2	1	no	—
227	C₄×D₄×C₅₃	—	2	1	no	—
228	C₄×D₄×C₅₃	—	2	1	no	—
229	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₅₃	C₂³	1	2	yes	—
234	C₄×D₄×C₅₃	C₂³	1	2	yes	—
235	C₄×D₄×C₅₃	C₂³	1	2	yes	—
236	C₄×D₄×C₅₃	C₂³	1	2	yes	—
237	C₄×D₄×C₅₃	C₂³	1	2	yes	—
238	C₄×D₄×C₅₃	C₂³	1	2	yes	—
239	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
240	#117×C₅₃	—	2	1	no	—
241	#117×C₅₃	C₂³	1	2	yes	—
242	#117×C₅₃	C₂³	1	2	yes	—
243	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
244	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
246	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
247	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
248	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
250	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
251	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
252	#107×C₅₃	C₂³	1	2	yes	—
253	#107×C₅₃	C₂³	1	2	yes	—
254	#106×C₅₃	C₂³	1	2	yes	—
255	#106×C₅₃	C₂³	1	2	yes	—
256	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
257	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
258	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
259	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
260	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
261	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
262	#103×C₅₃	C₂³	1	2	yes	—
263	#103×C₅₃	C₂³	1	2	yes	—
264	#103×C₅₃	C₂³	1	2	yes	—
265	#103×C₅₃	C₂³	1	2	yes	—
266	#102×C₅₃	C₂³	1	2	yes	—
267	#102×C₅₃	C₂³	1	2	yes	—
268	#102×C₅₃	C₂³	1	2	yes	—
269	#102×C₅₃	C₂³	1	2	yes	—
270	#102×C₅₃	C₂³	1	2	yes	—
271	#102×C₅₃	C₂³	1	2	yes	—
272	#102×C₅₃	C₂³	1	2	yes	—
273	#102×C₅₃	C₂³	1	2	yes	—
274	#102×C₅₃	C₂³	1	2	yes	—
275	#102×C₅₃	C₂³	1	2	yes	—
276	#102×C₅₃	C₂³	1	2	yes	—
277	#102×C₅₃	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
280	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
281	#97×C₅₃	C₂³	1	2	yes	—
282	#97×C₅₃	C₂³	1	2	yes	—
283	C₄×C₈×C₅₃	C₂³	1	2	yes	—
284	C₂⁴×C₅₃	—	2	1	no	—
285	C₂⁴×C₅₃	—	2	2	no	—
286	C₂⁴×C₅₃	—	2	1	no	—
287	C₂⁴×C₅₃	—	2	2	no	—
288	#41×C₅₃	—	4	2	no	—
289	#41×C₅₃	—	4	2	no	—
290	#41×C₅₃	—	8	2	no	—
291	#41×C₅₃	—	8	2	no	—
292	#41×C₅₃	—	8	2	no	—
293	C₂×Q₈×C₅₃	—	2	1	no	—
294	C₂×Q₈×C₅₃	—	2	1	no	—
295	C₂×Q₈×C₅₃	—	2	1	no	—
296	C₂×Q₈×C₅₃	—	4	1	no	—
297	C₂×Q₈×C₅₃	—	4	1	no	—
298	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
299	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
300	C₂×D₄×C₅₃	—	2	2	no	—
301	C₂×D₄×C₅₃	—	2	4	no	—
302	C₂×D₄×C₅₃	—	2	2	no	—
303	C₂×D₄×C₅₃	—	2	2	no	—
304	C₂×D₄×C₅₃	—	2	2	no	—
305	C₂×D₄×C₅₃	—	2	2	no	—
306	C₂×D₄×C₅₃	—	2	2	no	—
307	C₂×D₄×C₅₃	—	2	2	no	—
308	C₂×D₄×C₅₃	—	2	2	no	—
309	C₂×D₄×C₅₃	—	2	1	no	—
310	C₂×D₄×C₅₃	—	2	1	no	—
311	C₂×D₄×C₅₃	—	2	2	no	—
312	C₂×D₄×C₅₃	—	2	1	no	—
313	C₂×D₄×C₅₃	—	2	2	no	—
314	C₂×D₄×C₅₃	—	2	1	no	—
315	C₂×D₄×C₅₃	—	2	1	no	—
316	C₂×D₄×C₅₃	—	2	1	no	—
317	C₂×D₄×C₅₃	—	2	2	no	—
318	C₂×D₄×C₅₃	—	2	2	no	—
319	C₂×D₄×C₅₃	—	2	2	no	—
320	C₂×D₄×C₅₃	—	4	1	no	—
321	C₂×D₄×C₅₃	—	4	2	no	—
322	C₂×D₄×C₅₃	—	4	1	no	—
323	C₂×D₄×C₅₃	—	4	2	no	—
324	C₂×D₄×C₅₃	—	4	1	no	—
325	C₂×D₄×C₅₃	—	4	2	no	—
326	C₂×D₄×C₅₃	—	8	2	no	—
327	C₂×D₄×C₅₃	—	8	4	no	—
328	C₂×D₄×C₅₃	—	8	4	no	—
329	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
330	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
331	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
332	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
333	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
334	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₅₃	—	2	1	no	—
337	C₂²×C₄×C₅₃	—	2	1	no	—
338	C₂²×C₄×C₅₃	—	2	1	no	—
339	C₂²×C₄×C₅₃	—	2	1	no	—
340	C₂²×C₄×C₅₃	—	2	1	no	—
341	C₂²×C₄×C₅₃	—	2	2	no	—
342	C₂²×C₄×C₅₃	—	2	2	no	—
343	C₂²×C₄×C₅₃	—	2	2	no	—
344	C₂²×C₄×C₅₃	—	2	2	no	—
345	C₂²×C₄×C₅₃	—	2	2	no	—
346	C₂²×C₄×C₅₃	—	2	1	no	—
347	C₂²×C₄×C₅₃	—	2	2	no	—
348	C₂²×C₄×C₅₃	—	8	2	no	—
349	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
353	SD₁₆×C₅₃	—	2	4	no	—
354	SD₁₆×C₅₃	—	4	2	no	—
355	SD₁₆×C₅₃	—	4	2	no	—
356	SD₁₆×C₅₃	—	4	2	no	—
357	D₈×C₅₃	—	2	4	no	—
358	D₈×C₅₃	—	2	4	no	—
359	D₈×C₅₃	—	4	2	no	—
360	D₈×C₅₃	—	4	2	no	—
361	D₈×C₅₃	—	4	2	no	—
362	D₈×C₅₃	—	4	2	no	—
363	D₈×C₅₃	—	4	2	no	—
364	D₈×C₅₃	—	4	2	no	—
365	M₁₆×C₅₃	—	4	2	no	—
366	C₂×C₈×C₅₃	—	4	1	no	—
367	C₂×C₈×C₅₃	—	4	2	no	—
368	C₂×C₈×C₅₃	—	4	1	no	—
369	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
370	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
371	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
372	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₅₃	—	2	1	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	1	no	—
376	C₄⋊C₄×C₅₃	—	2	2	no	—
377	C₄⋊C₄×C₅₃	—	2	2	no	—
378	C₄⋊C₄×C₅₃	—	2	1	no	—
379	C₄⋊C₄×C₅₃	—	2	2	no	—
380	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
383	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
384	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
385	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
386	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
389	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
390	C₂²⋊C₄×C₅₃	—	2	2	no	—
391	C₂²⋊C₄×C₅₃	—	2	2	no	—
392	C₂²⋊C₄×C₅₃	—	2	1	no	—
393	C₂²⋊C₄×C₅₃	—	2	2	no	—
394	C₂²⋊C₄×C₅₃	—	2	1	no	—
395	C₂²⋊C₄×C₅₃	—	2	2	no	—
396	C₂²⋊C₄×C₅₃	—	2	2	no	—
397	C₂²⋊C₄×C₅₃	—	2	1	no	—
398	C₂²⋊C₄×C₅₃	—	2	2	no	—
399	C₂²⋊C₄×C₅₃	—	2	1	no	—
400	C₂²⋊C₄×C₅₃	—	2	2	no	—
401	C₂²⋊C₄×C₅₃	—	2	2	no	—
402	C₂²⋊C₄×C₅₃	—	2	2	no	—
403	C₂²⋊C₄×C₅₃	—	2	2	no	—
404	C₂²⋊C₄×C₅₃	—	2	2	no	—
405	C₂²⋊C₄×C₅₃	—	2	2	no	—
406	C₂²⋊C₄×C₅₃	—	2	2	no	—
407	C₂²⋊C₄×C₅₃	—	2	2	no	—
408	C₂²⋊C₄×C₅₃	—	2	2	no	—
409	C₂²⋊C₄×C₅₃	—	2	2	no	—
410	C₂²⋊C₄×C₅₃	—	2	2	no	—
411	C₂²⋊C₄×C₅₃	—	2	2	no	—
412	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
413	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
414	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
415	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
416	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
417	C₄²×C₅₃	—	2	2	no	—
418	C₄²×C₅₃	—	2	2	no	—
419	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
420	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
421	C₄²×C₅₃	C₂⁴	1	2	yes	—
422	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₂³×C₅₃	—	2	1	no	—
425	C₂³×C₅₃	—	2	1	no	—
426	C₂³×C₅₃	—	2	2	no	—
427	C₂³×C₅₃	—	2	2	no	—
428	C₂³×C₅₃	—	2	2	no	—
429	C₂³×C₅₃	—	4	2	no	—
430	C₂³×C₅₃	—	4	4	no	—
431	C₂³×C₅₃	—	4	2	no	—
432	C₂³×C₅₃	—	4	2	no	—
433	C₂³×C₅₃	—	8	1	no	—
434	C₂³×C₅₃	—	8	1	no	—
435	C₂³×C₅₃	—	8	2	no	—
436	C₂³×C₅₃	—	8	2	no	—
437	C₂³×C₅₃	—	8	2	no	—
438	C₂³×C₅₃	—	8	2	no	—
439	C₂³×C₅₃	—	8	1	no	—
440	C₂³×C₅₃	—	8	2	no	—
441	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
442	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
443	Q₈×C₅₃	—	2	2	no	—
444	Q₈×C₅₃	—	2	2	no	—
445	Q₈×C₅₃	—	4	1	no	—
446	Q₈×C₅₃	—	8	1	no	—
447	Q₈×C₅₃	—	8	1	no	—
448	Q₈×C₅₃	—	8	1	no	—
449	D₄×C₅₃	—	2	4	no	—
450	D₄×C₅₃	—	2	2	no	—
451	D₄×C₅₃	—	2	1	no	—
452	D₄×C₅₃	—	2	2	no	—
453	D₄×C₅₃	—	2	2	no	—
454	D₄×C₅₃	—	2	1	no	—
455	D₄×C₅₃	—	2	2	no	—
456	D₄×C₅₃	—	2	2	no	—
457	D₄×C₅₃	—	2	1	no	—
458	D₄×C₅₃	—	2	2	no	—
459	D₄×C₅₃	—	4	1	no	—
460	D₄×C₅₃	—	4	4	no	—
461	D₄×C₅₃	—	4	2	no	—
462	D₄×C₅₃	—	4	2	no	—
463	D₄×C₅₃	—	4	4	no	—
464	D₄×C₅₃	—	4	4	no	—
465	D₄×C₅₃	—	8	1	no	—
466	D₄×C₅₃	—	8	2	no	—
467	D₄×C₅₃	—	8	2	no	—
468	D₄×C₅₃	—	8	1	no	—
469	D₄×C₅₃	—	8	2	no	—
470	D₄×C₅₃	—	8	2	no	—
471	D₄×C₅₃	—	8	2	no	—
472	D₄×C₅₃	—	8	1	no	—
473	D₄×C₅₃	—	8	1	no	—
474	D₄×C₅₃	—	8	2	no	—
475	D₄×C₅₃	—	8	2	no	—
476	D₄×C₅₃	—	8	2	no	—
477	D₄×C₅₃	—	8	2	no	—
478	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
479	C₂×C₄×C₅₃	—	2	2	no	—
480	C₂×C₄×C₅₃	—	2	1	no	—
481	C₂×C₄×C₅₃	—	2	2	no	—
482	C₂×C₄×C₅₃	—	2	1	no	—
483	C₂×C₄×C₅₃	—	2	2	no	—
484	C₂×C₄×C₅₃	—	2	1	no	—
485	C₂×C₄×C₅₃	—	2	1	no	—
486	C₂×C₄×C₅₃	—	2	2	no	—
487	C₂×C₄×C₅₃	—	2	2	no	—
488	C₂×C₄×C₅₃	—	2	2	no	—
489	C₂×C₄×C₅₃	—	4	1	no	—
490	C₂×C₄×C₅₃	—	4	2	no	—
491	C₂×C₄×C₅₃	—	4	2	no	—
492	C₂×C₄×C₅₃	—	8	1	no	—
493	C₂×C₄×C₅₃	—	8	1	no	—
494	C₂×C₄×C₅₃	—	8	2	no	—
495	C₂×C₄×C₅₃	—	8	2	no	—
496	C₂×C₄×C₅₃	—	8	2	no	—
497	C₂×C₄×C₅₃	—	8	2	no	—
498	C₂×C₄×C₅₃	—	8	2	no	—
499	C₂×C₄×C₅₃	—	8	2	no	—
500	C₂×C₄×C₅₃	—	8	1	no	—
501	C₂×C₄×C₅₃	—	8	1	no	—
502	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
511	C₈×C₅₃	—	2	2	no	—
512	C₈×C₅₃	—	2	2	no	—
513	C₈×C₅₃	—	2	2	no	—
514	C₈×C₅₃	—	2	2	no	—
515	#62015	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
516	C₂²×C₅₃	—	2	1	no	—
517	C₂²×C₅₃	—	2	1	no	—
518	C₂²×C₅₃	—	2	2	no	—
519	C₂²×C₅₃	—	2	2	no	—
520	C₂²×C₅₃	—	2	2	no	—
521	C₂²×C₅₃	—	2	2	no	—
522	C₂²×C₅₃	—	4	1	no	—
523	C₂²×C₅₃	—	4	1	no	—
524	C₂²×C₅₃	—	4	1	no	—
525	C₂²×C₅₃	—	4	2	no	—
526	C₂²×C₅₃	—	4	2	no	—
527	C₂²×C₅₃	—	4	2	no	—
528	C₂²×C₅₃	—	4	2	no	—
529	C₂²×C₅₃	—	4	1	no	—
530	C₂²×C₅₃	—	4	2	no	—
531	C₂²×C₅₃	—	4	2	no	—
532	C₂²×C₅₃	—	4	2	no	—
533	C₂²×C₅₃	—	4	2	no	—
534	C₂²×C₅₃	—	4	2	no	—
535	C₂²×C₅₃	—	4	1	no	—
536	C₂²×C₅₃	—	8	4	no	—
537	C₂²×C₅₃	—	16	2	no	—
538	C₂²×C₅₃	—	16	4	no	—
539	C₂²×C₅₃	—	16	4	no	—
540	C₂²×C₅₃	#576	1	2	yes	—
541	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
542	C₄×C₅₃	—	2	1	no	—
543	C₄×C₅₃	—	2	1	no	—
544	C₄×C₅₃	—	2	2	no	—
545	C₄×C₅₃	—	2	2	no	—
546	C₄×C₅₃	—	2	1	no	—
547	C₄×C₅₃	—	2	1	no	—
548	C₄×C₅₃	—	2	1	no	—
549	C₄×C₅₃	—	2	2	no	—
550	C₄×C₅₃	—	4	1	no	—
551	C₄×C₅₃	—	4	1	no	—
552	C₄×C₅₃	—	4	2	no	—
553	C₄×C₅₃	—	4	2	no	—
554	C₄×C₅₃	—	4	2	no	—
555	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
556	C₄×C₅₃	#585	1	1	yes	characteristic
557	#3558	C₂×C₅₃	1	1	yes	characteristic, complemented
558	#3519	C₂×C₅₃	1	1	yes	characteristic, complemented
559	#3399	C₂×C₅₃	1	2	yes	complemented
560	#3370	C₂×C₅₃	1	2	yes	complemented
561	#3319	C₂×C₅₃	1	2	yes	complemented
562	#3318	C₂×C₅₃	1	2	yes	complemented
563	#3301	C₂×C₅₃	1	2	yes	complemented
564	D₄×D₈	C₂×C₅₃	1	2	yes	complemented
565	#3265	C₂×C₅₃	1	2	yes	complemented
566	#3264	C₂×C₅₃	1	2	yes	complemented
567	#3257	C₂×C₅₃	1	2	yes	complemented
568	#3245	C₂×C₅₃	1	1	yes	characteristic, complemented
569	#3220	C₂×C₅₃	1	2	yes	complemented
570	#3213	C₂×C₅₃	1	1	yes	characteristic, complemented
571	#3118	C₂×C₅₃	1	2	yes	complemented
572	#3109	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#3041	C₂×C₅₃	1	2	yes	complemented
574	C₂×#463	C₂×C₅₃	1	1	yes	characteristic, complemented
575	#2992	C₂×C₅₃	1	1	yes	characteristic, complemented
576	C₂×C₅₃	—	2	2	no	—
577	C₂×C₅₃	—	4	2	no	—
578	C₂×C₅₃	—	4	2	no	—
579	C₂×C₅₃	—	8	1	no	—
580	C₂×C₅₃	—	8	2	no	—
581	C₂×C₅₃	—	8	2	no	—
582	C₂×C₅₃	—	8	2	no	—
583	C₂×C₅₃	#3488	1	1	yes	characteristic
584	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
585	C₂×C₅₃	#3585	1	1	yes	characteristic
586	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
587	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
588	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
589	C₂²×D₈	C₂²×C₅₃	1	2	yes	complemented
590	#562	—	2	1	no	—
591	H(3,𝔽₄)	—	2	1	no	—
592	#559	C₂²×C₅₃	1	2	yes	complemented
593	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
594	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
595	#553	—	2	1	no	—
596	#553	C₂²×C₅₃	1	2	yes	complemented
597	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
598	#548	C₂²×C₅₃	1	2	yes	complemented
599	#546	—	2	1	no	—
600	#546	—	2	2	no	—
601	#546	—	2	2	no	—
602	#546	C₂²×C₅₃	1	2	yes	complemented
603	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
604	D₄²	C₂²×C₅₃	1	2	yes	complemented
605	D₄²	C₂²×C₅₃	1	2	yes	complemented
606	#542	C₂²×C₅₃	1	2	yes	complemented
607	#540	C₂²×C₅₃	1	2	yes	complemented
608	#538	—	2	2	no	—
609	#538	—	2	2	no	—
610	#538	—	2	1	no	—
611	#535	C₂²×C₅₃	1	2	yes	complemented
612	#534	—	2	1	no	—
613	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
614	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
615	#529	C₂²×C₅₃	1	1	yes	characteristic
616	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
617	#525	—	2	1	no	—
618	C₂×#121	—	2	1	no	—
619	#518	C₂²×C₅₃	1	2	yes	complemented
620	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
621	#496	C₂²×C₅₃	1	2	yes	complemented
622	#496	C₂²×C₅₃	1	2	yes	complemented
623	#493	C₂²×C₅₃	1	2	yes	complemented
624	#490	C₂²×C₅₃	1	2	yes	complemented
625	#489	C₂²×C₅₃	1	2	yes	complemented
626	#488	C₂²×C₅₃	1	2	yes	complemented
627	#485	C₂²×C₅₃	1	2	yes	complemented
628	#482	C₂²×C₅₃	1	2	yes	complemented
629	#481	C₂²×C₅₃	1	2	yes	complemented
630	#479	C₂²×C₅₃	1	2	yes	complemented
631	#478	C₂²×C₅₃	1	2	yes	complemented
632	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
633	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
634	#474	C₂²×C₅₃	1	2	yes	complemented
635	#474	C₂²×C₅₃	1	2	yes	complemented
636	#469	C₂²×C₅₃	1	2	yes	complemented
637	#468	C₂²×C₅₃	1	2	yes	complemented
638	#466	C₂²×C₅₃	1	2	yes	complemented
639	#466	C₂²×C₅₃	1	2	yes	complemented
640	#466	C₂²×C₅₃	1	2	yes	complemented
641	#465	C₂²×C₅₃	1	2	yes	complemented
642	#463	C₂²×C₅₃	1	2	yes	complemented
643	#463	C₂²×C₅₃	1	2	yes	complemented
644	#463	C₂²×C₅₃	1	2	yes	complemented
645	#463	C₂²×C₅₃	1	2	yes	complemented
646	#463	C₂²×C₅₃	1	2	yes	complemented
647	#463	C₂²×C₅₃	1	2	yes	complemented
648	#463	C₂²×C₅₃	1	2	yes	complemented
649	#463	C₂²×C₅₃	1	2	yes	complemented
650	#460	C₂²×C₅₃	1	2	yes	complemented
651	#459	C₂²×C₅₃	1	2	yes	—
652	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
653	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
654	#459	C₂²×C₅₃	1	2	yes	complemented
655	#459	C₂²×C₅₃	1	2	yes	complemented
656	#459	C₂²×C₅₃	1	2	yes	complemented
657	#459	C₂²×C₅₃	1	2	yes	complemented
658	#450	C₂²×C₅₃	1	2	yes	complemented
659	#449	C₂²×C₅₃	1	2	yes	complemented
660	#449	C₂²×C₅₃	1	2	yes	complemented
661	#448	C₂²×C₅₃	1	2	yes	complemented
662	#447	C₂²×C₅₃	1	2	yes	—
663	#447	C₂²×C₅₃	1	2	yes	complemented
664	#447	C₂²×C₅₃	1	2	yes	complemented
665	#447	C₂²×C₅₃	1	2	yes	complemented
666	#447	C₂²×C₅₃	1	2	yes	complemented
667	#446	C₂²×C₅₃	1	2	yes	complemented
668	#442	C₂²×C₅₃	1	2	yes	complemented
669	#442	C₂²×C₅₃	1	2	yes	complemented
670	#442	C₂²×C₅₃	1	2	yes	complemented
671	#440	C₂²×C₅₃	1	2	yes	complemented
672	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
673	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
674	#435	C₂²×C₅₃	1	2	yes	complemented
675	#435	C₂²×C₅₃	1	2	yes	complemented
676	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
677	#433	C₂²×C₅₃	1	2	yes	complemented
678	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
679	#424	C₂²×C₅₃	1	2	yes	complemented
680	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	#418	C₂²×C₅₃	1	2	yes	complemented
682	#416	C₂²×C₅₃	1	2	yes	complemented
683	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
684	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
685	C₅₃	#62015	1	1	yes	characteristic, direct product factor, Sylow
686	C₂×#41	—	2	1	no	—
687	C₂×#41	—	2	1	no	—
688	C₂×#41	—	2	1	no	—
689	C₂×#41	C₂³×C₅₃	1	2	yes	—
690	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
691	C₂²×D₄	—	2	1	no	—
692	C₂²×D₄	—	2	2	no	—
693	C₂²×D₄	—	2	2	no	—
694	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
695	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
696	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
697	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
698	C₂³×C₄	—	2	1	no	—
699	AGL(1,ℤ/8)	—	4	4	no	—
700	C₂×SD₁₆	—	4	2	no	—
701	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
702	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
703	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
704	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
705	C₂×D₈	—	4	2	no	—
706	C₂×D₈	—	4	4	no	—
707	C₂×D₈	C₂³×C₅₃	1	2	yes	—
708	C₂×D₈	C₂³×C₅₃	1	2	yes	—
709	C₂×D₈	C₂³×C₅₃	1	2	yes	—
710	C₂×D₈	C₂³×C₅₃	1	2	yes	—
711	C₂×D₈	C₂³×C₅₃	1	2	yes	—
712	C₂×D₈	C₂³×C₅₃	1	2	yes	—
713	C₂×D₈	C₂³×C₅₃	1	2	yes	—
714	C₂×D₈	C₂³×C₅₃	1	2	yes	—
715	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
716	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
717	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
718	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
721	#127	C₂³×C₅₃	1	1	yes	characteristic
722	#127	C₂³×C₅₃	1	1	yes	characteristic
723	#127	C₂³×C₅₃	1	2	yes	—
724	#127	C₂³×C₅₃	1	2	yes	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	D₄×C₅₃	1	2	yes	—
728	#125	D₄×C₅₃	1	1	yes	characteristic
729	#125	C₂³×C₅₃	1	2	yes	—
730	#124	—	2	2	no	—
731	#124	—	2	2	no	—
732	#124	—	2	2	no	—
733	#124	—	2	2	no	—
734	#124	—	2	1	no	—
735	#124	—	2	1	no	—
736	#124	—	2	1	no	—
737	#124	—	2	1	no	—
738	#124	D₄×C₅₃	1	1	yes	characteristic
739	#124	C₂³×C₅₃	1	2	yes	—
740	#124	C₂³×C₅₃	1	2	yes	—
741	#124	C₂³×C₅₃	1	2	yes	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	D₄×C₅₃	1	2	yes	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
755	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
756	#121	—	2	2	no	—
757	#121	—	2	1	no	—
758	#121	—	2	2	no	—
759	#121	—	2	1	no	—
760	#121	—	2	1	no	—
761	#121	—	2	1	no	—
762	#121	—	2	1	no	—
763	#121	—	2	2	no	—
764	#121	—	2	2	no	—
765	#121	—	2	2	no	—
766	#121	—	2	2	no	—
767	#121	—	2	2	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	D₄×C₅₃	1	1	yes	characteristic
772	#121	C₂³×C₅₃	1	2	yes	—
773	#121	C₂³×C₅₃	1	2	yes	—
774	#121	C₂³×C₅₃	1	2	yes	—
775	#121	C₂³×C₅₃	1	2	yes	—
776	#121	C₂³×C₅₃	1	2	yes	—
777	#120	—	2	2	no	—
778	#120	—	2	2	no	—
779	#120	—	2	2	no	—
780	#120	—	2	2	no	—
781	#120	—	2	2	no	—
782	#120	—	2	2	no	—
783	#120	—	2	2	no	—
784	#120	—	2	2	no	—
785	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
786	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₅₃	1	2	yes	—
801	C₄×D₄	C₂³×C₅₃	1	2	yes	—
802	C₄×D₄	C₂³×C₅₃	1	2	yes	—
803	C₄×D₄	C₂³×C₅₃	1	2	yes	—
804	C₄×D₄	C₂³×C₅₃	1	2	yes	—
805	C₄×D₄	C₂³×C₅₃	1	2	yes	—
806	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
807	#117	—	2	1	no	—
808	#117	C₂³×C₅₃	1	2	yes	—
809	#117	C₂³×C₅₃	1	2	yes	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
812	C₂×C₂²⋊C₄	—	2	1	no	—
813	C₂×C₂²⋊C₄	—	2	1	no	—
814	C₂×C₂²⋊C₄	—	2	1	no	—
815	C₂×C₂²⋊C₄	—	2	2	no	—
816	C₂×C₂²⋊C₄	—	2	2	no	—
817	C₂×C₂²⋊C₄	—	2	2	no	—
818	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
819	#107	C₂³×C₅₃	1	2	yes	—
820	#107	C₂³×C₅₃	1	2	yes	—
821	#106	C₂³×C₅₃	1	2	yes	—
822	#106	C₂³×C₅₃	1	2	yes	—
823	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
824	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
825	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
827	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
828	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
829	#103	C₂³×C₅₃	1	2	yes	—
830	#103	C₂³×C₅₃	1	2	yes	—
831	#103	C₂³×C₅₃	1	2	yes	—
832	#103	C₂³×C₅₃	1	2	yes	—
833	#102	C₂³×C₅₃	1	2	yes	—
834	#102	C₂³×C₅₃	1	2	yes	—
835	#102	C₂³×C₅₃	1	2	yes	—
836	#102	C₂³×C₅₃	1	2	yes	—
837	#102	C₂³×C₅₃	1	2	yes	—
838	#102	C₂³×C₅₃	1	2	yes	—
839	#102	C₂³×C₅₃	1	2	yes	—
840	#102	C₂³×C₅₃	1	2	yes	—
841	#102	C₂³×C₅₃	1	2	yes	—
842	#102	C₂³×C₅₃	1	2	yes	—
843	#102	C₂³×C₅₃	1	2	yes	—
844	#102	C₂³×C₅₃	1	2	yes	—
845	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
846	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
847	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
848	#97	C₂³×C₅₃	1	2	yes	—
849	#97	C₂³×C₅₃	1	2	yes	—
850	C₄×C₈	C₂³×C₅₃	1	2	yes	—
851	C₂⁴	—	2	1	no	—
852	C₂⁴	—	2	2	no	—
853	C₂⁴	—	2	1	no	—
854	C₂⁴	—	2	2	no	—
855	#41	—	4	2	no	—
856	#41	—	4	2	no	—
857	#41	—	8	2	no	—
858	#41	—	8	2	no	—
859	#41	—	8	2	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	1	no	—
862	C₂×Q₈	—	2	1	no	—
863	C₂×Q₈	—	4	1	no	—
864	C₂×Q₈	—	4	1	no	—
865	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
866	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	—	2	4	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	—	2	2	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	1	no	—
877	C₂×D₄	—	2	1	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	1	no	—
883	C₂×D₄	—	2	1	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	4	1	no	—
888	C₂×D₄	—	4	2	no	—
889	C₂×D₄	—	4	1	no	—
890	C₂×D₄	—	4	2	no	—
891	C₂×D₄	—	4	1	no	—
892	C₂×D₄	—	4	2	no	—
893	C₂×D₄	—	8	2	no	—
894	C₂×D₄	—	8	4	no	—
895	C₂×D₄	—	8	4	no	—
896	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
897	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
898	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
899	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
900	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
901	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
902	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	8	2	no	—
916	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
920	SD₁₆	—	2	4	no	—
921	SD₁₆	—	4	2	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	2	no	—
924	D₈	—	2	4	no	—
925	D₈	—	2	4	no	—
926	D₈	—	4	2	no	—
927	D₈	—	4	2	no	—
928	D₈	—	4	2	no	—
929	D₈	—	4	2	no	—
930	D₈	—	4	2	no	—
931	D₈	—	4	2	no	—
932	M₁₆	—	4	2	no	—
933	C₂×C₈	—	4	1	no	—
934	C₂×C₈	—	4	2	no	—
935	C₂×C₈	—	4	1	no	—
936	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
937	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
938	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
939	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
949	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
950	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
951	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
952	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
953	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
954	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
955	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
956	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
980	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
981	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
982	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
983	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	2	no	—
986	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
987	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
988	C₄²	C₂⁴×C₅₃	1	2	yes	—
989	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
990	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
991	C₂³	—	2	1	no	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	4	2	no	—
997	C₂³	—	4	4	no	—
998	C₂³	—	4	2	no	—
999	C₂³	—	4	2	no	—
1000	C₂³	—	8	1	no	—
1001	C₂³	—	8	1	no	—
1002	C₂³	—	8	2	no	—
1003	C₂³	—	8	2	no	—
1004	C₂³	—	8	2	no	—
1005	C₂³	—	8	2	no	—
1006	C₂³	—	8	1	no	—
1007	C₂³	—	8	2	no	—
1008	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1009	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1010	Q₈	—	2	2	no	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	4	1	no	—
1013	Q₈	—	8	1	no	—
1014	Q₈	—	8	1	no	—
1015	Q₈	—	8	1	no	—
1016	D₄	—	2	4	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	2	2	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	1	no	—
1023	D₄	—	2	2	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	2	no	—
1026	D₄	—	4	1	no	—
1027	D₄	—	4	4	no	—
1028	D₄	—	4	2	no	—
1029	D₄	—	4	2	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	4	4	no	—
1032	D₄	—	8	1	no	—
1033	D₄	—	8	2	no	—
1034	D₄	—	8	2	no	—
1035	D₄	—	8	1	no	—
1036	D₄	—	8	2	no	—
1037	D₄	—	8	2	no	—
1038	D₄	—	8	1	no	—
1039	D₄	—	8	1	no	—
1040	D₄	—	8	2	no	—
1041	D₄	—	8	2	no	—
1042	D₄	—	8	2	no	—
1043	D₄	—	8	2	no	—
1044	D₄	—	8	2	no	—
1045	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	8	1	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	1	no	—
1068	C₂×C₄	—	8	1	no	—
1069	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1071	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1077	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1078	C₈	—	2	2	no	—
1079	C₈	—	2	2	no	—
1080	C₈	—	2	2	no	—
1081	C₈	—	2	2	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	8	4	no	—
1103	C₂²	—	16	2	no	—
1104	C₂²	—	16	4	no	—
1105	C₂²	—	16	4	no	—
1106	C₂²	C₅₃×#576	1	2	yes	—
1107	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1108	C₄	—	2	2	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	2	1	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	2	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1122	C₄	C₅₃×#585	1	1	yes	characteristic
1123	C₂	—	2	2	no	—
1124	C₂	—	4	2	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	8	1	no	—
1127	C₂	—	8	2	no	—
1128	C₂	—	8	2	no	—
1129	C₂	—	8	2	no	—
1130	C₂	C₅₃×#3488	1	1	yes	characteristic
1131	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1132	C₂	C₅₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3558	C₂	semidirect
2. C₅₃×#3519	C₂	semidirect
3. C₅₃×#3399	C₂	semidirect
4. C₅₃×#3370	C₂	semidirect
5. C₅₃×#3319	C₂	semidirect
6. C₅₃×#3318	C₂	semidirect
7. C₅₃×#3301	C₂	semidirect
8. D₄×D₈×C₅₃	C₂	semidirect
9. C₅₃×#3265	C₂	semidirect
10. C₅₃×#3264	C₂	semidirect
11. C₅₃×#3257	C₂	semidirect
12. C₅₃×#3245	C₂	semidirect
13. C₅₃×#3220	C₂	semidirect
14. C₅₃×#3213	C₂	semidirect
15. C₅₃×#3118	C₂	semidirect
16. C₅₃×#3109	C₂	semidirect
17. C₅₃×#3041	C₂	semidirect
18. C₂×C₅₃×#463	C₂	semidirect
19. C₅₃×#2992	C₂	semidirect
20. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
21. C₂²×SD₁₆×C₅₃	C₂²	semidirect
23. C₂²×D₈×C₅₃	C₂²	semidirect
26. C₅₃×#559	C₂²	semidirect
27. C₅₃×#555	C₂²	semidirect
28. C₅₃×#554	C₂²	semidirect
30. C₅₃×#553	C₂²	semidirect
31. C₅₃×#550	C₂²	semidirect
32. C₅₃×#548	C₂²	semidirect
36. C₅₃×#546	C₂²	semidirect
37. D₄²×C₅₃	C₂²	semidirect
38. D₄²×C₅₃	C₂²	semidirect
39. D₄²×C₅₃	C₂²	semidirect
40. C₅₃×#542	C₂²	semidirect
41. C₅₃×#540	C₂²	semidirect
45. C₅₃×#535	C₂²	semidirect
47. C₅₃×#532	C₂²	semidirect
48. C₅₃×#532	C₂²	semidirect
50. C₂×#124×C₅₃	C₂²	semidirect
53. C₅₃×#518	C₂²	semidirect
54. C₂×C₄×D₄×C₅₃	C₂²	semidirect
55. C₅₃×#496	C₂²	semidirect
56. C₅₃×#496	C₂²	semidirect
57. C₅₃×#493	C₂²	semidirect
58. C₅₃×#490	C₂²	semidirect
59. C₅₃×#489	C₂²	semidirect
60. C₅₃×#488	C₂²	semidirect
61. C₅₃×#485	C₂²	semidirect
62. C₅₃×#482	C₂²	semidirect
63. C₅₃×#481	C₂²	semidirect
64. C₅₃×#479	C₂²	semidirect
65. C₅₃×#478	C₂²	semidirect
66. C₅₃×#476	C₂²	semidirect
67. C₅₃×#476	C₂²	semidirect
68. C₅₃×#474	C₂²	semidirect
69. C₅₃×#474	C₂²	semidirect
70. C₅₃×#469	C₂²	semidirect
71. C₅₃×#468	C₂²	semidirect
72. C₅₃×#466	C₂²	semidirect
73. C₅₃×#466	C₂²	semidirect
74. C₅₃×#466	C₂²	semidirect
75. C₅₃×#465	C₂²	semidirect
76. C₅₃×#463	C₂²	semidirect
77. C₅₃×#463	C₂²	semidirect
78. C₅₃×#463	C₂²	semidirect
79. C₅₃×#463	C₂²	semidirect
80. C₅₃×#463	C₂²	semidirect
81. C₅₃×#463	C₂²	semidirect
82. C₅₃×#463	C₂²	semidirect
83. C₅₃×#463	C₂²	semidirect
84. C₅₃×#460	C₂²	semidirect
86. C₅₃×#459	C₂²	semidirect
87. C₅₃×#459	C₂²	semidirect
88. C₅₃×#459	C₂²	semidirect
89. C₅₃×#459	C₂²	semidirect
90. C₅₃×#459	C₂²	semidirect
91. C₅₃×#459	C₂²	semidirect
92. C₅₃×#450	C₂²	semidirect
93. C₅₃×#449	C₂²	semidirect
94. C₅₃×#449	C₂²	semidirect
95. C₅₃×#448	C₂²	semidirect
97. C₅₃×#447	C₂²	semidirect
98. C₅₃×#447	C₂²	semidirect
99. C₅₃×#447	C₂²	semidirect
100. C₅₃×#447	C₂²	semidirect
101. C₅₃×#446	C₂²	semidirect
102. C₅₃×#442	C₂²	semidirect
103. C₅₃×#442	C₂²	semidirect
104. C₅₃×#442	C₂²	semidirect
105. C₅₃×#440	C₂²	semidirect
106. C₄×SD₁₆×C₅₃	C₂²	semidirect
107. C₄×D₈×C₅₃	C₂²	semidirect
108. C₅₃×#435	C₂²	semidirect
109. C₅₃×#435	C₂²	semidirect
110. C₈×D₄×C₅₃	C₂²	semidirect
111. C₅₃×#433	C₂²	semidirect
112. C₅₃×#432	C₂²	semidirect
113. C₅₃×#424	C₂²	semidirect
114. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
115. C₅₃×#418	C₂²	semidirect
116. C₅₃×#416	C₂²	semidirect
117. C₂×#103×C₅₃	C₂²	semidirect
118. C₂×#102×C₅₃	C₂²	semidirect
515. #62015	C₅₃	direct (N × H)
557. #3558	C₂×C₅₃	semidirect
558. #3519	C₂×C₅₃	semidirect
559. #3399	C₂×C₅₃	semidirect
560. #3370	C₂×C₅₃	semidirect
561. #3319	C₂×C₅₃	semidirect
562. #3318	C₂×C₅₃	semidirect
563. #3301	C₂×C₅₃	semidirect
564. D₄×D₈	C₂×C₅₃	semidirect
565. #3265	C₂×C₅₃	semidirect
566. #3264	C₂×C₅₃	semidirect
567. #3257	C₂×C₅₃	semidirect
568. #3245	C₂×C₅₃	semidirect
569. #3220	C₂×C₅₃	semidirect
570. #3213	C₂×C₅₃	semidirect
571. #3118	C₂×C₅₃	semidirect
572. #3109	C₂×C₅₃	semidirect
573. #3041	C₂×C₅₃	semidirect
574. C₂×#463	C₂×C₅₃	semidirect
575. #2992	C₂×C₅₃	semidirect
586. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
587. C₂²×SD₁₆	C₂²×C₅₃	semidirect
589. C₂²×D₈	C₂²×C₅₃	semidirect
592. #559	C₂²×C₅₃	semidirect
593. #555	C₂²×C₅₃	semidirect
594. #554	C₂²×C₅₃	semidirect
596. #553	C₂²×C₅₃	semidirect
597. #550	C₂²×C₅₃	semidirect
598. #548	C₂²×C₅₃	semidirect
602. #546	C₂²×C₅₃	semidirect
603. D₄²	C₂²×C₅₃	semidirect
604. D₄²	C₂²×C₅₃	semidirect
605. D₄²	C₂²×C₅₃	semidirect
606. #542	C₂²×C₅₃	semidirect
607. #540	C₂²×C₅₃	semidirect
611. #535	C₂²×C₅₃	semidirect
613. #532	C₂²×C₅₃	semidirect
614. #532	C₂²×C₅₃	semidirect
616. C₂×#124	C₂²×C₅₃	semidirect
619. #518	C₂²×C₅₃	semidirect
620. C₂×C₄×D₄	C₂²×C₅₃	semidirect
621. #496	C₂²×C₅₃	semidirect
622. #496	C₂²×C₅₃	semidirect
623. #493	C₂²×C₅₃	semidirect
624. #490	C₂²×C₅₃	semidirect
625. #489	C₂²×C₅₃	semidirect
626. #488	C₂²×C₅₃	semidirect
627. #485	C₂²×C₅₃	semidirect
628. #482	C₂²×C₅₃	semidirect
629. #481	C₂²×C₅₃	semidirect
630. #479	C₂²×C₅₃	semidirect
631. #478	C₂²×C₅₃	semidirect
632. #476	C₂²×C₅₃	semidirect
633. #476	C₂²×C₅₃	semidirect
634. #474	C₂²×C₅₃	semidirect
635. #474	C₂²×C₅₃	semidirect
636. #469	C₂²×C₅₃	semidirect
637. #468	C₂²×C₅₃	semidirect
638. #466	C₂²×C₅₃	semidirect
639. #466	C₂²×C₅₃	semidirect
640. #466	C₂²×C₅₃	semidirect
641. #465	C₂²×C₅₃	semidirect
642. #463	C₂²×C₅₃	semidirect
643. #463	C₂²×C₅₃	semidirect
644. #463	C₂²×C₅₃	semidirect
645. #463	C₂²×C₅₃	semidirect
646. #463	C₂²×C₅₃	semidirect
647. #463	C₂²×C₅₃	semidirect
648. #463	C₂²×C₅₃	semidirect
649. #463	C₂²×C₅₃	semidirect
650. #460	C₂²×C₅₃	semidirect
652. #459	C₂²×C₅₃	semidirect
653. #459	C₂²×C₅₃	semidirect
654. #459	C₂²×C₅₃	semidirect
655. #459	C₂²×C₅₃	semidirect
656. #459	C₂²×C₅₃	semidirect
657. #459	C₂²×C₅₃	semidirect
658. #450	C₂²×C₅₃	semidirect
659. #449	C₂²×C₅₃	semidirect
660. #449	C₂²×C₅₃	semidirect
661. #448	C₂²×C₅₃	semidirect
663. #447	C₂²×C₅₃	semidirect
664. #447	C₂²×C₅₃	semidirect
665. #447	C₂²×C₅₃	semidirect
666. #447	C₂²×C₅₃	semidirect
667. #446	C₂²×C₅₃	semidirect
668. #442	C₂²×C₅₃	semidirect
669. #442	C₂²×C₅₃	semidirect
670. #442	C₂²×C₅₃	semidirect
671. #440	C₂²×C₅₃	semidirect
672. C₄×SD₁₆	C₂²×C₅₃	semidirect
673. C₄×D₈	C₂²×C₅₃	semidirect
674. #435	C₂²×C₅₃	semidirect
675. #435	C₂²×C₅₃	semidirect
676. C₈×D₄	C₂²×C₅₃	semidirect
677. #433	C₂²×C₅₃	semidirect
678. #432	C₂²×C₅₃	semidirect
679. #424	C₂²×C₅₃	semidirect
680. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
681. #418	C₂²×C₅₃	semidirect
682. #416	C₂²×C₅₃	semidirect
683. C₂×#103	C₂²×C₅₃	semidirect
684. C₂×#102	C₂²×C₅₃	semidirect
685. C₅₃	#62015	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×#3558	2
C₅₃×#3519	2
C₅₃×#3399	2
C₅₃×#3370	2
C₅₃×#3319	2
C₅₃×#3318	2
C₅₃×#3301	2
D₄×D₈×C₅₃	2
C₅₃×#3265	2
C₅₃×#3264	2
C₅₃×#3257	2
C₅₃×#3245	2
C₅₃×#3220	2
C₅₃×#3213	2
C₅₃×#3118	2
C₅₃×#3109	2
C₅₃×#3041	2
C₂×C₅₃×#463	2
C₅₃×#2992	2
#62015	53

Subgroups — C53×#62015 #27269527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62015 #27269527