Subgroups — C₅₃×#60750 #27268262

Order 13568.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3194	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3193	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3192	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3188	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3187	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3186	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3094	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3092	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3055	C₂	1	4	yes	maximal, complemented
12	C₅₃×#3006	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3003	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
16	C₂³×D₄×C₅₃	—	2	1	no	—
17	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
18	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	4	yes	complemented
20	C₂²×M₁₆×C₅₃	C₂²	1	2	yes	complemented
21	C₅₃×#525	—	2	1	no	—
22	C₅₃×#525	—	2	1	no	—
23	C₅₃×#525	—	2	1	no	—
24	C₅₃×#525	—	2	1	no	—
25	C₅₃×#525	C₂²	1	2	yes	—
26	C₅₃×#525	C₂²	1	2	yes	complemented
27	C₅₃×#525	C₂²	1	2	yes	complemented
28	C₅₃×#525	C₂²	1	2	yes	complemented
29	C₂×#123×C₅₃	—	2	1	no	—
30	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#121×C₅₃	—	2	1	no	—
33	C₂×#121×C₅₃	—	2	1	no	—
34	C₂×#121×C₅₃	—	2	1	no	—
35	C₂×#121×C₅₃	—	2	1	no	—
36	C₂×#121×C₅₃	—	2	1	no	—
37	C₂×#121×C₅₃	—	2	1	no	—
38	C₂×#121×C₅₃	C₂²	1	2	yes	—
39	C₂×#121×C₅₃	C₂²	1	2	yes	—
40	C₂×#121×C₅₃	C₂²	1	2	yes	—
41	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
42	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
43	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
44	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×#120×C₅₃	—	2	1	no	—
47	C₂×C₄×D₄×C₅₃	—	2	1	no	—
48	C₂×C₄×D₄×C₅₃	—	2	1	no	—
49	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₂²×C₂²⋊C₄×C₅₃	—	2	1	no	—
52	C₅₃×#484	C₂²	1	4	yes	complemented
53	C₅₃×#483	C₂²	1	4	yes	complemented
54	C₅₃×#482	C₂²	1	8	yes	complemented
55	C₅₃×#481	C₂²	1	4	yes	complemented
56	C₅₃×#481	C₂²	1	4	yes	complemented
57	C₅₃×#480	C₂²	1	4	yes	complemented
58	C₅₃×#480	C₂²	1	4	yes	complemented
59	C₅₃×#469	C₂²	1	8	yes	complemented
60	C₅₃×#468	C₂²	1	8	yes	complemented
61	C₅₃×#466	C₂²	1	8	yes	complemented
62	C₅₃×#465	C₂²	1	8	yes	complemented
63	C₅₃×#450	C₂²	1	4	yes	complemented
64	C₅₃×#450	C₂²	1	4	yes	complemented
65	C₅₃×#449	C₂²	1	8	yes	complemented
66	C₅₃×#448	C₂²	1	4	yes	complemented
67	C₅₃×#447	C₂²	1	4	yes	complemented
68	C₅₃×#447	C₂²	1	4	yes	complemented
69	C₅₃×#447	C₂²	1	4	yes	complemented
70	C₅₃×#428	C₂²	1	4	yes	complemented
71	C₅₃×#418	C₂²	1	4	yes	complemented
72	C₅₃×#417	C₂²	1	4	yes	complemented
73	C₅₃×#407	C₂²	1	2	yes	complemented
74	C₅₃×#407	C₂²	1	2	yes	complemented
75	C₅₃×#407	C₂²	1	2	yes	complemented
76	C₅₃×#407	C₂²	1	2	yes	complemented
77	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	complemented
78	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	complemented
79	C₂⁵×C₅₃	—	2	1	no	—
80	C₂⁵×C₅₃	D₄	1	1	yes	characteristic
81	C₂×#41×C₅₃	—	2	1	no	—
82	C₂×#41×C₅₃	—	2	1	no	—
83	C₂×#41×C₅₃	—	4	4	no	—
84	C₂×#41×C₅₃	C₂³	1	2	yes	—
85	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
86	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
87	C₂²×D₄×C₅₃	—	2	1	no	—
88	C₂²×D₄×C₅₃	—	2	1	no	—
89	C₂²×D₄×C₅₃	—	2	1	no	—
90	C₂²×D₄×C₅₃	—	2	2	no	—
91	C₂²×D₄×C₅₃	—	2	2	no	—
92	C₂²×D₄×C₅₃	—	2	2	no	—
93	C₂²×D₄×C₅₃	—	2	2	no	—
94	C₂²×D₄×C₅₃	—	2	2	no	—
95	C₂²×D₄×C₅₃	—	2	2	no	—
96	C₂²×D₄×C₅₃	—	2	1	no	—
97	C₂²×D₄×C₅₃	—	2	1	no	—
98	C₂²×D₄×C₅₃	—	2	1	no	—
99	C₂²×D₄×C₅₃	—	4	4	no	—
100	C₂²×D₄×C₅₃	—	4	8	no	—
101	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
102	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
103	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
104	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
105	C₂³×C₄×C₅₃	—	2	1	no	—
106	C₂³×C₄×C₅₃	—	2	1	no	—
107	C₂³×C₄×C₅₃	—	4	4	no	—
108	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
109	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
110	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
111	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
112	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
113	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
114	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
115	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
122	AGL(1,ℤ/8)×C₅₃	—	4	8	no	—
123	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	complemented
124	C₂×D₈×C₅₃	C₂³	1	8	yes	complemented
125	C₂×M₁₆×C₅₃	—	4	4	no	—
126	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
127	C₂×M₁₆×C₅₃	C₂³	1	4	yes	complemented
128	C₂²×C₈×C₅₃	C₂³	1	4	yes	complemented
129	#123×C₅₃	—	2	2	no	—
130	#123×C₅₃	—	2	2	no	—
131	#123×C₅₃	—	2	2	no	—
132	#123×C₅₃	—	2	2	no	—
133	C₂²⋊Q₈×C₅₃	—	2	1	no	—
134	C₂²⋊Q₈×C₅₃	—	2	1	no	—
135	C₂²⋊Q₈×C₅₃	—	2	1	no	—
136	C₂²⋊Q₈×C₅₃	—	2	1	no	—
137	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
138	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
139	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
140	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
141	#121×C₅₃	—	2	2	no	—
142	#121×C₅₃	—	2	2	no	—
143	#121×C₅₃	—	2	2	no	—
144	#121×C₅₃	—	2	2	no	—
145	#121×C₅₃	—	2	2	no	—
146	#121×C₅₃	—	2	2	no	—
147	#121×C₅₃	—	2	2	no	—
148	#121×C₅₃	—	2	2	no	—
149	#121×C₅₃	—	2	2	no	—
150	#121×C₅₃	—	2	2	no	—
151	#121×C₅₃	—	2	2	no	—
152	#121×C₅₃	—	2	2	no	—
153	#121×C₅₃	—	2	1	no	—
154	#121×C₅₃	—	2	1	no	—
155	#121×C₅₃	—	2	1	no	—
156	#121×C₅₃	—	2	1	no	—
157	#121×C₅₃	C₂³	1	4	yes	—
158	#121×C₅₃	C₂³	1	4	yes	—
159	#121×C₅₃	C₂³	1	4	yes	—
160	#121×C₅₃	C₂³	1	4	yes	—
161	#121×C₅₃	C₂³	1	2	yes	—
162	#121×C₅₃	C₂³	1	2	yes	—
163	#121×C₅₃	C₂³	1	2	yes	complemented
164	#121×C₅₃	C₂³	1	2	yes	complemented
165	#120×C₅₃	—	2	2	no	—
166	#120×C₅₃	—	2	2	no	—
167	#120×C₅₃	—	2	2	no	—
168	#120×C₅₃	—	2	2	no	—
169	C₄×D₄×C₅₃	—	2	2	no	—
170	C₄×D₄×C₅₃	—	2	2	no	—
171	C₄×D₄×C₅₃	—	2	2	no	—
172	C₄×D₄×C₅₃	—	2	2	no	—
173	C₄×D₄×C₅₃	—	2	2	no	—
174	C₄×D₄×C₅₃	—	2	2	no	—
175	C₄×D₄×C₅₃	—	2	2	no	—
176	C₄×D₄×C₅₃	—	2	2	no	—
177	#117×C₅₃	—	2	1	no	—
178	#117×C₅₃	—	2	1	no	—
179	#117×C₅₃	C₂³	1	2	yes	—
180	#117×C₅₃	C₂³	1	2	yes	complemented
181	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
182	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
183	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
184	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
185	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
186	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
190	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
191	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
195	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
197	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
201	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
202	C₂×C₄²×C₅₃	—	2	1	no	—
203	#107×C₅₃	C₂³	1	8	yes	complemented
204	#106×C₅₃	C₂³	1	8	yes	complemented
205	#103×C₅₃	C₂³	1	8	yes	complemented
206	#102×C₅₃	C₂³	1	8	yes	complemented
207	#102×C₅₃	C₂³	1	8	yes	complemented
208	#102×C₅₃	C₂³	1	8	yes	complemented
209	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
210	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
211	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
212	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
213	C₂⁴×C₅₃	—	2	4	no	—
214	C₂⁴×C₅₃	—	2	1	no	—
215	C₂⁴×C₅₃	—	2	2	no	—
216	C₂⁴×C₅₃	—	2	2	no	—
217	C₂⁴×C₅₃	—	2	2	no	—
218	C₂⁴×C₅₃	—	4	2	no	—
219	C₂⁴×C₅₃	—	4	2	no	—
220	C₂⁴×C₅₃	—	4	4	no	—
221	C₂⁴×C₅₃	—	4	4	no	—
222	C₂⁴×C₅₃	—	4	4	no	—
223	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
224	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
225	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
226	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
227	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
228	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
229	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
230	#41×C₅₃	—	2	8	no	—
231	#41×C₅₃	—	4	4	no	—
232	#41×C₅₃	—	4	4	no	—
233	#41×C₅₃	—	4	4	no	—
234	C₂×Q₈×C₅₃	—	2	1	no	—
235	C₂×Q₈×C₅₃	—	4	2	no	—
236	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
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	2	no	—
242	C₂×D₄×C₅₃	—	2	2	no	—
243	C₂×D₄×C₅₃	—	2	4	no	—
244	C₂×D₄×C₅₃	—	2	4	no	—
245	C₂×D₄×C₅₃	—	2	4	no	—
246	C₂×D₄×C₅₃	—	2	4	no	—
247	C₂×D₄×C₅₃	—	2	2	no	—
248	C₂×D₄×C₅₃	—	2	2	no	—
249	C₂×D₄×C₅₃	—	2	2	no	—
250	C₂×D₄×C₅₃	—	2	1	no	—
251	C₂×D₄×C₅₃	—	2	8	no	—
252	C₂×D₄×C₅₃	—	4	4	no	—
253	C₂×D₄×C₅₃	—	4	4	no	—
254	C₂×D₄×C₅₃	—	4	2	no	—
255	C₂×D₄×C₅₃	—	4	4	no	—
256	C₂×D₄×C₅₃	—	4	4	no	—
257	C₂×D₄×C₅₃	—	4	4	no	—
258	C₂×D₄×C₅₃	—	4	4	no	—
259	C₂×D₄×C₅₃	—	4	8	no	—
260	C₂×D₄×C₅₃	—	4	8	no	—
261	C₂×D₄×C₅₃	—	4	8	no	—
262	C₂×D₄×C₅₃	—	4	8	no	—
263	C₂×D₄×C₅₃	—	4	8	no	—
264	C₂×D₄×C₅₃	—	4	4	no	—
265	C₂×D₄×C₅₃	—	4	4	no	—
266	C₂×D₄×C₅₃	—	4	8	no	—
267	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
268	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₅₃	—	2	4	no	—
270	C₂²×C₄×C₅₃	—	2	4	no	—
271	C₂²×C₄×C₅₃	—	2	4	no	—
272	C₂²×C₄×C₅₃	—	2	1	no	—
273	C₂²×C₄×C₅₃	—	2	1	no	—
274	C₂²×C₄×C₅₃	—	2	1	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	—	4	2	no	—
281	C₂²×C₄×C₅₃	—	4	2	no	—
282	C₂²×C₄×C₅₃	—	4	2	no	—
283	C₂²×C₄×C₅₃	—	4	2	no	—
284	C₂²×C₄×C₅₃	—	4	2	no	—
285	C₂²×C₄×C₅₃	—	4	2	no	—
286	C₂²×C₄×C₅₃	—	4	2	no	—
287	C₂²×C₄×C₅₃	—	4	2	no	—
288	C₂²×C₄×C₅₃	—	4	2	no	—
289	C₂²×C₄×C₅₃	—	4	2	no	—
290	C₂²×C₄×C₅₃	—	4	2	no	—
291	C₂²×C₄×C₅₃	—	4	4	no	—
292	C₂²×C₄×C₅₃	—	4	4	no	—
293	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
321	SD₁₆×C₅₃	—	4	8	no	—
322	D₈×C₅₃	—	4	8	no	—
323	M₁₆×C₅₃	—	2	8	no	—
324	M₁₆×C₅₃	—	4	4	no	—
325	C₂×C₈×C₅₃	—	4	4	no	—
326	C₂×C₈×C₅₃	C₂⁴	1	8	yes	—
327	C₄⋊C₄×C₅₃	—	2	2	no	—
328	C₄⋊C₄×C₅₃	—	2	2	no	—
329	C₄⋊C₄×C₅₃	—	2	2	no	—
330	C₄⋊C₄×C₅₃	—	2	2	no	—
331	C₄⋊C₄×C₅₃	—	2	2	no	—
332	C₄⋊C₄×C₅₃	—	2	2	no	—
333	C₄⋊C₄×C₅₃	—	2	2	no	—
334	C₄⋊C₄×C₅₃	—	2	1	no	—
335	C₄⋊C₄×C₅₃	—	2	1	no	—
336	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
339	C₂²⋊C₄×C₅₃	—	2	2	no	—
340	C₂²⋊C₄×C₅₃	—	2	2	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	4	no	—
346	C₂²⋊C₄×C₅₃	—	2	4	no	—
347	C₂²⋊C₄×C₅₃	—	2	4	no	—
348	C₂²⋊C₄×C₅₃	—	2	4	no	—
349	C₂²⋊C₄×C₅₃	—	2	2	no	—
350	C₂²⋊C₄×C₅₃	—	2	2	no	—
351	C₂²⋊C₄×C₅₃	—	2	2	no	—
352	C₂²⋊C₄×C₅₃	—	2	2	no	—
353	C₄²×C₅₃	—	2	2	no	—
354	C₄²×C₅₃	—	2	2	no	—
355	C₂³×C₅₃	—	2	2	no	—
356	C₂³×C₅₃	—	2	2	no	—
357	C₂³×C₅₃	—	2	2	no	—
358	C₂³×C₅₃	—	2	2	no	—
359	C₂³×C₅₃	—	2	2	no	—
360	C₂³×C₅₃	—	2	2	no	—
361	C₂³×C₅₃	—	2	2	no	—
362	C₂³×C₅₃	—	2	2	no	—
363	C₂³×C₅₃	—	2	2	no	—
364	C₂³×C₅₃	—	2	2	no	—
365	C₂³×C₅₃	—	2	2	no	—
366	C₂³×C₅₃	—	2	2	no	—
367	C₂³×C₅₃	—	2	2	no	—
368	C₂³×C₅₃	—	2	4	no	—
369	C₂³×C₅₃	—	4	1	no	—
370	C₂³×C₅₃	—	4	1	no	—
371	C₂³×C₅₃	—	4	1	no	—
372	C₂³×C₅₃	—	4	1	no	—
373	C₂³×C₅₃	—	4	1	no	—
374	C₂³×C₅₃	—	4	1	no	—
375	C₂³×C₅₃	—	4	1	no	—
376	C₂³×C₅₃	—	4	1	no	—
377	C₂³×C₅₃	—	4	16	no	—
378	C₂³×C₅₃	—	4	2	no	—
379	C₂³×C₅₃	—	4	4	no	—
380	C₂³×C₅₃	—	4	4	no	—
381	C₂³×C₅₃	—	4	4	no	—
382	C₂³×C₅₃	—	4	4	no	—
383	C₂³×C₅₃	—	4	2	no	—
384	C₂³×C₅₃	—	4	4	no	—
385	C₂³×C₅₃	—	4	4	no	—
386	C₂³×C₅₃	—	4	4	no	—
387	C₂³×C₅₃	—	4	4	no	—
388	C₂³×C₅₃	—	4	2	no	—
389	C₂³×C₅₃	—	4	4	no	—
390	C₂³×C₅₃	—	8	16	no	—
391	C₂³×C₅₃	AGL(1,ℤ/8)	1	4	yes	complemented
392	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
393	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
394	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
395	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
396	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
397	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
398	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
399	Q₈×C₅₃	—	2	4	no	—
400	Q₈×C₅₃	—	4	2	no	—
401	D₄×C₅₃	—	2	8	no	—
402	D₄×C₅₃	—	2	4	no	—
403	D₄×C₅₃	—	4	4	no	—
404	D₄×C₅₃	—	4	4	no	—
405	D₄×C₅₃	—	4	2	no	—
406	D₄×C₅₃	—	4	4	no	—
407	D₄×C₅₃	—	4	8	no	—
408	D₄×C₅₃	—	4	8	no	—
409	D₄×C₅₃	—	4	4	no	—
410	D₄×C₅₃	—	4	4	no	—
411	D₄×C₅₃	—	4	4	no	—
412	D₄×C₅₃	—	4	4	no	—
413	D₄×C₅₃	—	4	8	no	—
414	D₄×C₅₃	—	4	8	no	—
415	D₄×C₅₃	—	4	4	no	—
416	D₄×C₅₃	—	4	4	no	—
417	C₂×C₄×C₅₃	—	2	2	no	—
418	C₂×C₄×C₅₃	—	2	2	no	—
419	C₂×C₄×C₅₃	—	2	2	no	—
420	C₂×C₄×C₅₃	—	2	2	no	—
421	C₂×C₄×C₅₃	—	2	2	no	—
422	C₂×C₄×C₅₃	—	2	2	no	—
423	C₂×C₄×C₅₃	—	2	2	no	—
424	C₂×C₄×C₅₃	—	2	2	no	—
425	C₂×C₄×C₅₃	—	2	2	no	—
426	C₂×C₄×C₅₃	—	2	2	no	—
427	C₂×C₄×C₅₃	—	2	2	no	—
428	C₂×C₄×C₅₃	—	2	2	no	—
429	C₂×C₄×C₅₃	—	2	2	no	—
430	C₂×C₄×C₅₃	—	2	2	no	—
431	C₂×C₄×C₅₃	—	2	2	no	—
432	C₂×C₄×C₅₃	—	2	4	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	—	4	1	no	—
437	C₂×C₄×C₅₃	—	4	1	no	—
438	C₂×C₄×C₅₃	—	4	1	no	—
439	C₂×C₄×C₅₃	—	4	1	no	—
440	C₂×C₄×C₅₃	—	4	1	no	—
441	C₂×C₄×C₅₃	—	4	1	no	—
442	C₂×C₄×C₅₃	—	4	1	no	—
443	C₂×C₄×C₅₃	—	4	1	no	—
444	C₂×C₄×C₅₃	—	4	1	no	—
445	C₂×C₄×C₅₃	—	4	1	no	—
446	C₂×C₄×C₅₃	—	4	1	no	—
447	C₂×C₄×C₅₃	—	4	1	no	—
448	C₂×C₄×C₅₃	—	4	4	no	—
449	C₂×C₄×C₅₃	—	4	4	no	—
450	C₂×C₄×C₅₃	—	4	4	no	—
451	C₂×C₄×C₅₃	—	4	2	no	—
452	C₂×C₄×C₅₃	—	4	2	no	—
453	C₂×C₄×C₅₃	—	4	4	no	—
454	C₂×C₄×C₅₃	—	4	2	no	—
455	C₂×C₄×C₅₃	—	4	4	no	—
456	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
464	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
465	C₈×C₅₃	—	2	8	no	—
466	#60750	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
467	C₂²×C₅₃	—	2	8	no	—
468	C₂²×C₅₃	—	2	1	no	—
469	C₂²×C₅₃	—	2	1	no	—
470	C₂²×C₅₃	—	2	1	no	—
471	C₂²×C₅₃	—	2	1	no	—
472	C₂²×C₅₃	—	2	1	no	—
473	C₂²×C₅₃	—	2	1	no	—
474	C₂²×C₅₃	—	2	1	no	—
475	C₂²×C₅₃	—	2	1	no	—
476	C₂²×C₅₃	—	2	1	no	—
477	C₂²×C₅₃	—	2	1	no	—
478	C₂²×C₅₃	—	2	1	no	—
479	C₂²×C₅₃	—	2	1	no	—
480	C₂²×C₅₃	—	2	1	no	—
481	C₂²×C₅₃	—	2	1	no	—
482	C₂²×C₅₃	—	2	1	no	—
483	C₂²×C₅₃	—	2	1	no	—
484	C₂²×C₅₃	—	4	4	no	—
485	C₂²×C₅₃	—	4	4	no	—
486	C₂²×C₅₃	—	4	4	no	—
487	C₂²×C₅₃	—	4	4	no	—
488	C₂²×C₅₃	—	4	4	no	—
489	C₂²×C₅₃	—	4	4	no	—
490	C₂²×C₅₃	—	4	2	no	—
491	C₂²×C₅₃	—	4	4	no	—
492	C₂²×C₅₃	—	4	4	no	—
493	C₂²×C₅₃	—	4	2	no	—
494	C₂²×C₅₃	—	4	2	no	—
495	C₂²×C₅₃	—	4	4	no	—
496	C₂²×C₅₃	—	8	4	no	—
497	C₂²×C₅₃	—	8	8	no	—
498	C₂²×C₅₃	—	8	8	no	—
499	C₂²×C₅₃	—	8	8	no	—
500	C₂²×C₅₃	#534	1	2	yes	—
501	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
502	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
503	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
504	C₂²×C₅₃	#575	1	2	yes	—
505	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
506	C₄×C₅₃	—	2	1	no	—
507	C₄×C₅₃	—	2	1	no	—
508	C₄×C₅₃	—	2	1	no	—
509	C₄×C₅₃	—	2	1	no	—
510	C₄×C₅₃	—	2	1	no	—
511	C₄×C₅₃	—	2	1	no	—
512	C₄×C₅₃	—	4	2	no	—
513	C₄×C₅₃	—	4	4	no	—
514	C₄×C₅₃	—	4	2	no	—
515	C₄×C₅₃	—	4	2	no	—
516	C₄×C₅₃	#534	1	2	yes	—
517	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
518	C₂×#525	C₂×C₅₃	1	1	yes	characteristic, complemented
519	C₂²×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
520	#3194	C₂×C₅₃	1	4	yes	complemented
521	#3193	C₂×C₅₃	1	2	yes	complemented
522	#3192	C₂×C₅₃	1	2	yes	complemented
523	#3188	C₂×C₅₃	1	4	yes	complemented
524	#3187	C₂×C₅₃	1	2	yes	complemented
525	#3186	C₂×C₅₃	1	2	yes	complemented
526	#3094	C₂×C₅₃	1	2	yes	complemented
527	#3092	C₂×C₅₃	1	2	yes	complemented
528	#3055	C₂×C₅₃	1	4	yes	complemented
529	#3006	C₂×C₅₃	1	2	yes	complemented
530	#3003	C₂×C₅₃	1	2	yes	complemented
531	C₂×#407	C₂×C₅₃	1	1	yes	characteristic, complemented
532	C₂×C₅₃	—	2	2	no	—
533	C₂×C₅₃	—	2	2	no	—
534	C₂×C₅₃	—	2	2	no	—
535	C₂×C₅₃	—	2	2	no	—
536	C₂×C₅₃	—	2	2	no	—
537	C₂×C₅₃	—	4	1	no	—
538	C₂×C₅₃	—	4	1	no	—
539	C₂×C₅₃	—	8	2	no	—
540	C₂×C₅₃	—	8	4	no	—
541	C₂×C₅₃	C₂×#534	1	1	yes	characteristic
542	C₂×C₅₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
543	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
544	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
545	C₂³×D₄	—	2	1	no	—
546	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
547	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
548	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	4	yes	complemented
549	C₂²×M₁₆	C₂²×C₅₃	1	2	yes	complemented
550	#525	—	2	1	no	—
551	#525	—	2	1	no	—
552	#525	—	2	1	no	—
553	#525	—	2	1	no	—
554	#525	C₂²×C₅₃	1	2	yes	—
555	#525	C₂²×C₅₃	1	2	yes	complemented
556	#525	C₂²×C₅₃	1	2	yes	complemented
557	#525	C₂²×C₅₃	1	2	yes	complemented
558	C₂×#123	—	2	1	no	—
559	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
560	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
561	C₂×#121	—	2	1	no	—
562	C₂×#121	—	2	1	no	—
563	C₂×#121	—	2	1	no	—
564	C₂×#121	—	2	1	no	—
565	C₂×#121	—	2	1	no	—
566	C₂×#121	—	2	1	no	—
567	C₂×#121	C₂²×C₅₃	1	2	yes	—
568	C₂×#121	C₂²×C₅₃	1	2	yes	—
569	C₂×#121	C₂²×C₅₃	1	2	yes	—
570	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
571	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
572	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
573	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
574	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
575	C₂×#120	—	2	1	no	—
576	C₂×C₄×D₄	—	2	1	no	—
577	C₂×C₄×D₄	—	2	1	no	—
578	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
579	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
580	C₂²×C₂²⋊C₄	—	2	1	no	—
581	#484	C₂²×C₅₃	1	4	yes	complemented
582	#483	C₂²×C₅₃	1	4	yes	complemented
583	#482	C₂²×C₅₃	1	8	yes	complemented
584	#481	C₂²×C₅₃	1	4	yes	complemented
585	#481	C₂²×C₅₃	1	4	yes	complemented
586	#480	C₂²×C₅₃	1	4	yes	complemented
587	#480	C₂²×C₅₃	1	4	yes	complemented
588	#469	C₂²×C₅₃	1	8	yes	complemented
589	#468	C₂²×C₅₃	1	8	yes	complemented
590	#466	C₂²×C₅₃	1	8	yes	complemented
591	#465	C₂²×C₅₃	1	8	yes	complemented
592	#450	C₂²×C₅₃	1	4	yes	complemented
593	#450	C₂²×C₅₃	1	4	yes	complemented
594	#449	C₂²×C₅₃	1	8	yes	complemented
595	#448	C₂²×C₅₃	1	4	yes	complemented
596	#447	C₂²×C₅₃	1	4	yes	complemented
597	#447	C₂²×C₅₃	1	4	yes	complemented
598	#447	C₂²×C₅₃	1	4	yes	complemented
599	#428	C₂²×C₅₃	1	4	yes	complemented
600	#418	C₂²×C₅₃	1	4	yes	complemented
601	#417	C₂²×C₅₃	1	4	yes	complemented
602	#407	C₂²×C₅₃	1	2	yes	complemented
603	#407	C₂²×C₅₃	1	2	yes	complemented
604	#407	C₂²×C₅₃	1	2	yes	complemented
605	#407	C₂²×C₅₃	1	2	yes	complemented
606	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	complemented
607	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	complemented
608	C₅₃	#60750	1	1	yes	characteristic, direct product factor, Sylow
609	C₂⁵	—	2	1	no	—
610	C₂⁵	D₄×C₅₃	1	1	yes	characteristic
611	C₂×#41	—	2	1	no	—
612	C₂×#41	—	2	1	no	—
613	C₂×#41	—	4	4	no	—
614	C₂×#41	C₂³×C₅₃	1	2	yes	—
615	C₂×#41	C₂³×C₅₃	1	2	yes	complemented
616	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
617	C₂²×D₄	—	2	1	no	—
618	C₂²×D₄	—	2	1	no	—
619	C₂²×D₄	—	2	1	no	—
620	C₂²×D₄	—	2	2	no	—
621	C₂²×D₄	—	2	2	no	—
622	C₂²×D₄	—	2	2	no	—
623	C₂²×D₄	—	2	2	no	—
624	C₂²×D₄	—	2	2	no	—
625	C₂²×D₄	—	2	2	no	—
626	C₂²×D₄	—	2	1	no	—
627	C₂²×D₄	—	2	1	no	—
628	C₂²×D₄	—	2	1	no	—
629	C₂²×D₄	—	4	4	no	—
630	C₂²×D₄	—	4	8	no	—
631	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
632	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
633	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
634	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
635	C₂³×C₄	—	2	1	no	—
636	C₂³×C₄	—	2	1	no	—
637	C₂³×C₄	—	4	4	no	—
638	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
639	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
640	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
641	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
642	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
643	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
644	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
645	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
646	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
647	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
648	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
649	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
650	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
651	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
652	AGL(1,ℤ/8)	—	4	8	no	—
653	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	complemented
654	C₂×D₈	C₂³×C₅₃	1	8	yes	complemented
655	C₂×M₁₆	—	4	4	no	—
656	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
657	C₂×M₁₆	C₂³×C₅₃	1	4	yes	complemented
658	C₂²×C₈	C₂³×C₅₃	1	4	yes	complemented
659	#123	—	2	2	no	—
660	#123	—	2	2	no	—
661	#123	—	2	2	no	—
662	#123	—	2	2	no	—
663	C₂²⋊Q₈	—	2	1	no	—
664	C₂²⋊Q₈	—	2	1	no	—
665	C₂²⋊Q₈	—	2	1	no	—
666	C₂²⋊Q₈	—	2	1	no	—
667	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
668	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
669	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
670	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
671	#121	—	2	2	no	—
672	#121	—	2	2	no	—
673	#121	—	2	2	no	—
674	#121	—	2	2	no	—
675	#121	—	2	2	no	—
676	#121	—	2	2	no	—
677	#121	—	2	2	no	—
678	#121	—	2	2	no	—
679	#121	—	2	2	no	—
680	#121	—	2	2	no	—
681	#121	—	2	2	no	—
682	#121	—	2	2	no	—
683	#121	—	2	1	no	—
684	#121	—	2	1	no	—
685	#121	—	2	1	no	—
686	#121	—	2	1	no	—
687	#121	C₂³×C₅₃	1	4	yes	—
688	#121	C₂³×C₅₃	1	4	yes	—
689	#121	C₂³×C₅₃	1	4	yes	—
690	#121	C₂³×C₅₃	1	4	yes	—
691	#121	C₂³×C₅₃	1	2	yes	—
692	#121	C₂³×C₅₃	1	2	yes	—
693	#121	C₂³×C₅₃	1	2	yes	complemented
694	#121	C₂³×C₅₃	1	2	yes	complemented
695	#120	—	2	2	no	—
696	#120	—	2	2	no	—
697	#120	—	2	2	no	—
698	#120	—	2	2	no	—
699	C₄×D₄	—	2	2	no	—
700	C₄×D₄	—	2	2	no	—
701	C₄×D₄	—	2	2	no	—
702	C₄×D₄	—	2	2	no	—
703	C₄×D₄	—	2	2	no	—
704	C₄×D₄	—	2	2	no	—
705	C₄×D₄	—	2	2	no	—
706	C₄×D₄	—	2	2	no	—
707	#117	—	2	1	no	—
708	#117	—	2	1	no	—
709	#117	C₂³×C₅₃	1	2	yes	—
710	#117	C₂³×C₅₃	1	2	yes	complemented
711	C₂×C₄⋊C₄	—	2	1	no	—
712	C₂×C₄⋊C₄	—	2	1	no	—
713	C₂×C₄⋊C₄	—	2	1	no	—
714	C₂×C₄⋊C₄	—	2	1	no	—
715	C₂×C₄⋊C₄	—	2	1	no	—
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	1	yes	characteristic, complemented
720	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
721	C₂×C₂²⋊C₄	—	2	1	no	—
722	C₂×C₂²⋊C₄	—	2	1	no	—
723	C₂×C₂²⋊C₄	—	2	1	no	—
724	C₂×C₂²⋊C₄	—	2	2	no	—
725	C₂×C₂²⋊C₄	—	2	2	no	—
726	C₂×C₂²⋊C₄	—	2	2	no	—
727	C₂×C₂²⋊C₄	—	2	2	no	—
728	C₂×C₂²⋊C₄	—	2	2	no	—
729	C₂×C₂²⋊C₄	—	2	2	no	—
730	C₂×C₂²⋊C₄	—	2	1	no	—
731	C₂×C₂²⋊C₄	—	2	1	no	—
732	C₂×C₄²	—	2	1	no	—
733	#107	C₂³×C₅₃	1	8	yes	complemented
734	#106	C₂³×C₅₃	1	8	yes	complemented
735	#103	C₂³×C₅₃	1	8	yes	complemented
736	#102	C₂³×C₅₃	1	8	yes	complemented
737	#102	C₂³×C₅₃	1	8	yes	complemented
738	#102	C₂³×C₅₃	1	8	yes	complemented
739	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
740	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
741	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
742	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
743	C₂⁴	—	2	4	no	—
744	C₂⁴	—	2	1	no	—
745	C₂⁴	—	2	2	no	—
746	C₂⁴	—	2	2	no	—
747	C₂⁴	—	2	2	no	—
748	C₂⁴	—	4	2	no	—
749	C₂⁴	—	4	2	no	—
750	C₂⁴	—	4	4	no	—
751	C₂⁴	—	4	4	no	—
752	C₂⁴	—	4	4	no	—
753	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
754	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
755	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
756	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
757	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
758	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
759	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
760	#41	—	2	8	no	—
761	#41	—	4	4	no	—
762	#41	—	4	4	no	—
763	#41	—	4	4	no	—
764	C₂×Q₈	—	2	1	no	—
765	C₂×Q₈	—	4	2	no	—
766	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	4	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	4	no	—
776	C₂×D₄	—	2	4	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	—	2	8	no	—
782	C₂×D₄	—	4	4	no	—
783	C₂×D₄	—	4	4	no	—
784	C₂×D₄	—	4	2	no	—
785	C₂×D₄	—	4	4	no	—
786	C₂×D₄	—	4	4	no	—
787	C₂×D₄	—	4	4	no	—
788	C₂×D₄	—	4	4	no	—
789	C₂×D₄	—	4	8	no	—
790	C₂×D₄	—	4	8	no	—
791	C₂×D₄	—	4	8	no	—
792	C₂×D₄	—	4	8	no	—
793	C₂×D₄	—	4	8	no	—
794	C₂×D₄	—	4	4	no	—
795	C₂×D₄	—	4	4	no	—
796	C₂×D₄	—	4	8	no	—
797	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
798	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
799	C₂²×C₄	—	2	4	no	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	2	1	no	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	—	4	4	no	—
822	C₂²×C₄	—	4	4	no	—
823	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
824	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
825	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
826	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
827	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
828	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
829	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
830	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
831	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
832	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
833	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
834	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
835	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
836	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
837	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
838	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
839	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
840	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
841	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
842	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
843	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
847	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
851	SD₁₆	—	4	8	no	—
852	D₈	—	4	8	no	—
853	M₁₆	—	2	8	no	—
854	M₁₆	—	4	4	no	—
855	C₂×C₈	—	4	4	no	—
856	C₂×C₈	C₂⁴×C₅₃	1	8	yes	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	1	no	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
867	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	4	no	—
876	C₂²⋊C₄	—	2	4	no	—
877	C₂²⋊C₄	—	2	4	no	—
878	C₂²⋊C₄	—	2	4	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	2	no	—
892	C₂³	—	2	2	no	—
893	C₂³	—	2	2	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	4	no	—
899	C₂³	—	4	1	no	—
900	C₂³	—	4	1	no	—
901	C₂³	—	4	1	no	—
902	C₂³	—	4	1	no	—
903	C₂³	—	4	1	no	—
904	C₂³	—	4	1	no	—
905	C₂³	—	4	1	no	—
906	C₂³	—	4	1	no	—
907	C₂³	—	4	16	no	—
908	C₂³	—	4	2	no	—
909	C₂³	—	4	4	no	—
910	C₂³	—	4	4	no	—
911	C₂³	—	4	4	no	—
912	C₂³	—	4	4	no	—
913	C₂³	—	4	2	no	—
914	C₂³	—	4	4	no	—
915	C₂³	—	4	4	no	—
916	C₂³	—	4	4	no	—
917	C₂³	—	4	4	no	—
918	C₂³	—	4	2	no	—
919	C₂³	—	4	4	no	—
920	C₂³	—	8	16	no	—
921	C₂³	AGL(1,ℤ/8)×C₅₃	1	4	yes	complemented
922	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
923	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
924	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
925	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
926	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
927	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
928	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
929	Q₈	—	2	4	no	—
930	Q₈	—	4	2	no	—
931	D₄	—	2	4	no	—
932	D₄	—	2	8	no	—
933	D₄	—	4	4	no	—
934	D₄	—	4	4	no	—
935	D₄	—	4	2	no	—
936	D₄	—	4	4	no	—
937	D₄	—	4	8	no	—
938	D₄	—	4	8	no	—
939	D₄	—	4	4	no	—
940	D₄	—	4	4	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	4	no	—
943	D₄	—	4	8	no	—
944	D₄	—	4	8	no	—
945	D₄	—	4	4	no	—
946	D₄	—	4	4	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	4	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	4	1	no	—
970	C₂×C₄	—	4	1	no	—
971	C₂×C₄	—	4	1	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	1	no	—
974	C₂×C₄	—	4	1	no	—
975	C₂×C₄	—	4	1	no	—
976	C₂×C₄	—	4	1	no	—
977	C₂×C₄	—	4	1	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	—	4	2	no	—
982	C₂×C₄	—	4	2	no	—
983	C₂×C₄	—	4	4	no	—
984	C₂×C₄	—	4	2	no	—
985	C₂×C₄	—	4	4	no	—
986	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
988	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
989	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
990	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
991	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
992	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
993	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
994	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
995	C₈	—	2	8	no	—
996	C₂²	—	2	8	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	1	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	1	no	—
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	4	4	no	—
1014	C₂²	—	4	4	no	—
1015	C₂²	—	4	4	no	—
1016	C₂²	—	4	4	no	—
1017	C₂²	—	4	4	no	—
1018	C₂²	—	4	4	no	—
1019	C₂²	—	4	4	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	4	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	4	no	—
1025	C₂²	—	8	8	no	—
1026	C₂²	—	8	8	no	—
1027	C₂²	—	8	8	no	—
1028	C₂²	—	8	4	no	—
1029	C₂²	C₅₃×#534	1	2	yes	—
1030	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
1031	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
1032	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
1033	C₂²	C₅₃×#575	1	2	yes	—
1034	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1035	C₄	—	2	1	no	—
1036	C₄	—	2	1	no	—
1037	C₄	—	2	1	no	—
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	1	no	—
1041	C₄	—	4	4	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	2	no	—
1044	C₄	—	4	2	no	—
1045	C₄	C₅₃×#534	1	2	yes	—
1046	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1047	C₂	—	2	2	no	—
1048	C₂	—	2	2	no	—
1049	C₂	—	2	2	no	—
1050	C₂	—	2	2	no	—
1051	C₂	—	2	2	no	—
1052	C₂	—	4	1	no	—
1053	C₂	—	4	1	no	—
1054	C₂	—	8	4	no	—
1055	C₂	—	8	2	no	—
1056	C₂	C₂×C₅₃×#534	1	1	yes	characteristic
1057	C₂	C₂²×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
1058	C₂	C₂×C₅₃×#575	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 ◁ C₂⁴×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#525	C₂	semidirect
2. C₂²×#121×C₅₃	C₂	semidirect
3. C₅₃×#3194	C₂	semidirect
4. C₅₃×#3193	C₂	semidirect
5. C₅₃×#3192	C₂	semidirect
6. C₅₃×#3188	C₂	semidirect
7. C₅₃×#3187	C₂	semidirect
8. C₅₃×#3186	C₂	semidirect
9. C₅₃×#3094	C₂	semidirect
10. C₅₃×#3092	C₂	semidirect
11. C₅₃×#3055	C₂	semidirect
12. C₅₃×#3006	C₂	semidirect
13. C₅₃×#3003	C₂	semidirect
14. C₂×C₅₃×#407	C₂	semidirect
15. C₂²×#41×C₅₃	C₂²	semidirect
17. C₂³×D₄×C₅₃	C₂²	semidirect
19. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
20. C₂²×M₁₆×C₅₃	C₂²	semidirect
26. C₅₃×#525	C₂²	semidirect
27. C₅₃×#525	C₂²	semidirect
28. C₅₃×#525	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
31. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
41. C₂×#121×C₅₃	C₂²	semidirect
42. C₂×#121×C₅₃	C₂²	semidirect
43. C₂×#121×C₅₃	C₂²	semidirect
44. C₂×#121×C₅₃	C₂²	semidirect
45. C₂×#121×C₅₃	C₂²	semidirect
49. C₂×#117×C₅₃	C₂²	semidirect
50. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
52. C₅₃×#484	C₂²	semidirect
53. C₅₃×#483	C₂²	semidirect
54. C₅₃×#482	C₂²	semidirect
55. C₅₃×#481	C₂²	semidirect
56. C₅₃×#481	C₂²	semidirect
57. C₅₃×#480	C₂²	semidirect
58. C₅₃×#480	C₂²	semidirect
59. C₅₃×#469	C₂²	semidirect
60. C₅₃×#468	C₂²	semidirect
61. C₅₃×#466	C₂²	semidirect
62. C₅₃×#465	C₂²	semidirect
63. C₅₃×#450	C₂²	semidirect
64. C₅₃×#450	C₂²	semidirect
65. C₅₃×#449	C₂²	semidirect
66. C₅₃×#448	C₂²	semidirect
67. C₅₃×#447	C₂²	semidirect
68. C₅₃×#447	C₂²	semidirect
69. C₅₃×#447	C₂²	semidirect
70. C₅₃×#428	C₂²	semidirect
71. C₅₃×#418	C₂²	semidirect
72. C₅₃×#417	C₂²	semidirect
73. C₅₃×#407	C₂²	semidirect
74. C₅₃×#407	C₂²	semidirect
75. C₅₃×#407	C₂²	semidirect
76. C₅₃×#407	C₂²	semidirect
77. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
78. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
85. C₂×#41×C₅₃	C₂³	semidirect
86. C₂²×Q₈×C₅₃	C₂³	semidirect
104. C₂²×D₄×C₅₃	C₂³	semidirect
123. C₂×SD₁₆×C₅₃	C₂³	semidirect
124. C₂×D₈×C₅₃	C₂³	semidirect
127. C₂×M₁₆×C₅₃	C₂³	semidirect
128. C₂²×C₈×C₅₃	C₂³	semidirect
139. C₂²⋊Q₈×C₅₃	C₂³	semidirect
140. C₂²⋊Q₈×C₅₃	C₂³	semidirect
163. #121×C₅₃	C₂³	semidirect
164. #121×C₅₃	C₂³	semidirect
180. #117×C₅₃	C₂³	semidirect
189. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
190. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
203. #107×C₅₃	C₂³	semidirect
204. #106×C₅₃	C₂³	semidirect
205. #103×C₅₃	C₂³	semidirect
206. #102×C₅₃	C₂³	semidirect
207. #102×C₅₃	C₂³	semidirect
208. #102×C₅₃	C₂³	semidirect
211. C₂²⋊C₈×C₅₃	C₂³	semidirect
212. C₂²⋊C₈×C₅₃	C₂³	semidirect
391. C₂³×C₅₃	AGL(1,ℤ/8)	semidirect
466. #60750	C₅₃	direct (N × H)
518. C₂×#525	C₂×C₅₃	semidirect
519. C₂²×#121	C₂×C₅₃	semidirect
520. #3194	C₂×C₅₃	semidirect
521. #3193	C₂×C₅₃	semidirect
522. #3192	C₂×C₅₃	semidirect
523. #3188	C₂×C₅₃	semidirect
524. #3187	C₂×C₅₃	semidirect
525. #3186	C₂×C₅₃	semidirect
526. #3094	C₂×C₅₃	semidirect
527. #3092	C₂×C₅₃	semidirect
528. #3055	C₂×C₅₃	semidirect
529. #3006	C₂×C₅₃	semidirect
530. #3003	C₂×C₅₃	semidirect
531. C₂×#407	C₂×C₅₃	semidirect
544. C₂²×#41	C₂²×C₅₃	semidirect
546. C₂³×D₄	C₂²×C₅₃	semidirect
548. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
549. C₂²×M₁₆	C₂²×C₅₃	semidirect
555. #525	C₂²×C₅₃	semidirect
556. #525	C₂²×C₅₃	semidirect
557. #525	C₂²×C₅₃	semidirect
559. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
560. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
570. C₂×#121	C₂²×C₅₃	semidirect
571. C₂×#121	C₂²×C₅₃	semidirect
572. C₂×#121	C₂²×C₅₃	semidirect
573. C₂×#121	C₂²×C₅₃	semidirect
574. C₂×#121	C₂²×C₅₃	semidirect
578. C₂×#117	C₂²×C₅₃	semidirect
579. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
581. #484	C₂²×C₅₃	semidirect
582. #483	C₂²×C₅₃	semidirect
583. #482	C₂²×C₅₃	semidirect
584. #481	C₂²×C₅₃	semidirect
585. #481	C₂²×C₅₃	semidirect
586. #480	C₂²×C₅₃	semidirect
587. #480	C₂²×C₅₃	semidirect
588. #469	C₂²×C₅₃	semidirect
589. #468	C₂²×C₅₃	semidirect
590. #466	C₂²×C₅₃	semidirect
591. #465	C₂²×C₅₃	semidirect
592. #450	C₂²×C₅₃	semidirect
593. #450	C₂²×C₅₃	semidirect
594. #449	C₂²×C₅₃	semidirect
595. #448	C₂²×C₅₃	semidirect
596. #447	C₂²×C₅₃	semidirect
597. #447	C₂²×C₅₃	semidirect
598. #447	C₂²×C₅₃	semidirect
599. #428	C₂²×C₅₃	semidirect
600. #418	C₂²×C₅₃	semidirect
601. #417	C₂²×C₅₃	semidirect
602. #407	C₂²×C₅₃	semidirect
603. #407	C₂²×C₅₃	semidirect
604. #407	C₂²×C₅₃	semidirect
605. #407	C₂²×C₅₃	semidirect
606. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
607. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
608. C₅₃	#60750	direct (N × H)
615. C₂×#41	C₂³×C₅₃	semidirect
616. C₂²×Q₈	C₂³×C₅₃	semidirect
634. C₂²×D₄	C₂³×C₅₃	semidirect
653. C₂×SD₁₆	C₂³×C₅₃	semidirect
654. C₂×D₈	C₂³×C₅₃	semidirect
657. C₂×M₁₆	C₂³×C₅₃	semidirect
658. C₂²×C₈	C₂³×C₅₃	semidirect
669. C₂²⋊Q₈	C₂³×C₅₃	semidirect
670. C₂²⋊Q₈	C₂³×C₅₃	semidirect
693. #121	C₂³×C₅₃	semidirect
694. #121	C₂³×C₅₃	semidirect
710. #117	C₂³×C₅₃	semidirect
719. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
720. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
733. #107	C₂³×C₅₃	semidirect
734. #106	C₂³×C₅₃	semidirect
735. #103	C₂³×C₅₃	semidirect
736. #102	C₂³×C₅₃	semidirect
737. #102	C₂³×C₅₃	semidirect
738. #102	C₂³×C₅₃	semidirect
741. C₂²⋊C₈	C₂³×C₅₃	semidirect
742. C₂²⋊C₈	C₂³×C₅₃	semidirect
921. C₂³	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×#525	2
C₂²×#121×C₅₃	2
C₅₃×#3194	2
C₅₃×#3193	2
C₅₃×#3192	2
C₅₃×#3188	2
C₅₃×#3187	2
C₅₃×#3186	2
C₅₃×#3094	2
C₅₃×#3092	2
C₅₃×#3055	2
C₅₃×#3006	2
C₅₃×#3003	2
C₂×C₅₃×#407	2
#60750	53

Subgroups — C53×#60750 #27268262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60750 #27268262