Subgroups — C₅₃×#61644 #27269156

Order 13568.

2234 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3325	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3324	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3319	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3311	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3275	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3273	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×#3224	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3200	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3199	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3197	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3008	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3003	C₂	1	2	yes	maximal, complemented
19	C₅₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×H(3,𝔽₄)	—	2	1	no	—
29	C₅₃×#560	—	2	1	no	—
30	C₅₃×#559	—	2	1	no	—
31	C₅₃×#556	C₂²	1	2	yes	complemented
32	C₅₃×#555	C₂²	1	2	yes	complemented
33	C₅₃×#551	—	2	1	no	—
34	C₅₃×#548	C₂²	1	2	yes	complemented
35	C₅₃×#546	—	2	2	no	—
36	C₅₃×#546	C₂²	1	2	yes	—
37	C₅₃×#546	C₂²	1	2	yes	complemented
38	C₅₃×#546	C₂²	1	2	yes	complemented
39	D₄²×C₅₃	—	2	2	no	—
40	D₄²×C₅₃	C₂²	1	2	yes	—
41	D₄²×C₅₃	C₂²	1	2	yes	complemented
42	C₅₃×#542	—	2	2	no	—
43	C₅₃×#542	C₂²	1	2	yes	complemented
44	C₅₃×#538	—	2	2	no	—
45	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#535	C₂²	1	1	yes	characteristic
47	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#534	—	2	1	no	—
50	C₅₃×#534	—	2	1	no	—
51	C₅₃×#525	C₂²	1	1	yes	characteristic
52	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#525	C₂²	1	2	yes	complemented
54	C₂×#120×C₅₃	—	2	1	no	—
55	C₂×#120×C₅₃	—	2	1	no	—
56	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#496	C₂²	1	2	yes	complemented
58	C₅₃×#495	C₂²	1	2	yes	complemented
59	C₅₃×#489	C₂²	1	2	yes	complemented
60	C₅₃×#486	C₂²	1	2	yes	complemented
61	C₅₃×#485	C₂²	1	2	yes	complemented
62	C₅₃×#485	C₂²	1	2	yes	complemented
63	C₅₃×#482	C₂²	1	2	yes	complemented
64	C₅₃×#482	C₂²	1	2	yes	complemented
65	C₅₃×#482	C₂²	1	2	yes	complemented
66	C₅₃×#482	C₂²	1	2	yes	complemented
67	C₅₃×#476	C₂²	1	2	yes	complemented
68	C₅₃×#474	C₂²	1	2	yes	complemented
69	C₅₃×#470	C₂²	1	2	yes	complemented
70	C₅₃×#469	C₂²	1	2	yes	complemented
71	C₅₃×#469	C₂²	1	2	yes	complemented
72	C₅₃×#468	C₂²	1	2	yes	complemented
73	C₅₃×#468	C₂²	1	2	yes	complemented
74	C₅₃×#468	C₂²	1	2	yes	complemented
75	C₅₃×#466	C₂²	1	2	yes	complemented
76	C₅₃×#465	C₂²	1	2	yes	complemented
77	C₅₃×#464	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×#460	C₂²	1	2	yes	complemented
82	C₅₃×#459	C₂²	1	2	yes	complemented
83	C₅₃×#452	C₂²	1	2	yes	complemented
84	C₅₃×#452	C₂²	1	2	yes	complemented
85	C₅₃×#452	C₂²	1	2	yes	complemented
86	C₅₃×#450	C₂²	1	2	yes	complemented
87	C₅₃×#450	C₂²	1	2	yes	complemented
88	C₅₃×#450	C₂²	1	2	yes	complemented
89	C₅₃×#450	C₂²	1	2	yes	complemented
90	C₅₃×#450	C₂²	1	2	yes	complemented
91	C₅₃×#449	C₂²	1	2	yes	complemented
92	C₅₃×#449	C₂²	1	2	yes	complemented
93	C₅₃×#449	C₂²	1	2	yes	complemented
94	C₅₃×#448	C₂²	1	2	yes	complemented
95	C₅₃×#447	C₂²	1	2	yes	—
96	C₅₃×#447	C₂²	1	2	yes	complemented
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×#442	C₂²	1	2	yes	complemented
102	C₅₃×#440	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
104	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
105	C₅₃×#436	C₂²	1	2	yes	complemented
106	C₅₃×#436	C₂²	1	2	yes	complemented
107	C₅₃×#435	C₂²	1	2	yes	complemented
108	C₅₃×#435	C₂²	1	2	yes	complemented
109	C₅₃×#433	C₂²	1	2	yes	complemented
110	C₅₃×#418	C₂²	1	2	yes	complemented
111	C₅₃×#418	C₂²	1	2	yes	complemented
112	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#407	C₂²	1	2	yes	complemented
119	C₂⁵×C₅₃	—	2	1	no	—
120	H(5,𝔽₂)×C₅₃	—	4	2	no	—
121	H(5,𝔽₂)×C₅₃	—	4	2	no	—
122	C₂×#41×C₅₃	—	2	1	no	—
123	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
124	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
125	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×#41×C₅₃	C₂³	1	2	yes	—
127	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
129	C₂²×D₄×C₅₃	—	2	1	no	—
130	C₂²×D₄×C₅₃	—	2	1	no	—
131	C₂²×D₄×C₅₃	—	2	1	no	—
132	C₂²×D₄×C₅₃	—	2	2	no	—
133	C₂²×D₄×C₅₃	—	2	2	no	—
134	C₂²×D₄×C₅₃	—	2	1	no	—
135	C₂²×D₄×C₅₃	—	2	2	no	—
136	C₂²×D₄×C₅₃	—	4	2	no	—
137	C₂²×D₄×C₅₃	—	4	2	no	—
138	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
143	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
145	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
146	#137×C₅₃	—	4	2	no	—
147	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
148	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
149	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
150	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	complemented
151	C₂×SD₁₆×C₅₃	—	4	2	no	—
152	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	complemented
157	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	complemented
158	C₂×D₈×C₅₃	—	4	2	no	—
159	C₂×D₈×C₅₃	C₂³	1	2	yes	—
160	C₂×D₈×C₅₃	C₂³	1	2	yes	—
161	C₂×D₈×C₅₃	C₂³	1	2	yes	—
162	C₂×D₈×C₅₃	C₂³	1	2	yes	—
163	C₂×D₈×C₅₃	C₂³	1	2	yes	complemented
164	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
165	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
167	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
168	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
169	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
170	C₄⋊Q₈×C₅₃	—	2	1	no	—
171	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
172	#127×C₅₃	—	2	1	no	—
173	#127×C₅₃	—	2	1	no	—
174	#127×C₅₃	C₂³	1	2	yes	—
175	#126×C₅₃	—	2	2	no	—
176	#126×C₅₃	—	2	2	no	—
177	#126×C₅₃	—	2	2	no	—
178	#124×C₅₃	—	2	2	no	—
179	#124×C₅₃	—	2	2	no	—
180	#124×C₅₃	—	2	2	no	—
181	#124×C₅₃	—	2	2	no	—
182	#124×C₅₃	—	2	1	no	—
183	#124×C₅₃	—	2	1	no	—
184	#124×C₅₃	—	2	1	no	—
185	#124×C₅₃	—	2	2	no	—
186	#124×C₅₃	C₂³	1	2	yes	—
187	#124×C₅₃	C₂³	1	2	yes	complemented
188	#123×C₅₃	—	2	2	no	—
189	#123×C₅₃	—	2	2	no	—
190	#123×C₅₃	—	2	2	no	—
191	#123×C₅₃	—	2	2	no	—
192	#123×C₅₃	—	2	1	no	—
193	#123×C₅₃	—	2	1	no	—
194	#123×C₅₃	—	2	1	no	—
195	#123×C₅₃	—	2	2	no	—
196	#123×C₅₃	D₄	1	1	yes	characteristic
197	#123×C₅₃	D₄	1	1	yes	characteristic
198	C₂²⋊Q₈×C₅₃	—	2	2	no	—
199	C₂²⋊Q₈×C₅₃	—	2	2	no	—
200	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
201	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
203	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	2	no	—
207	#121×C₅₃	—	2	2	no	—
208	#121×C₅₃	—	2	2	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	2	no	—
211	#121×C₅₃	—	2	2	no	—
212	#121×C₅₃	—	2	2	no	—
213	#121×C₅₃	D₄	1	2	yes	—
214	#121×C₅₃	C₂³	1	2	yes	—
215	#121×C₅₃	C₂³	1	2	yes	—
216	#121×C₅₃	C₂³	1	2	yes	—
217	#121×C₅₃	C₂³	1	2	yes	—
218	#121×C₅₃	C₂³	1	2	yes	—
219	#121×C₅₃	C₂³	1	2	yes	complemented
220	#120×C₅₃	—	2	1	no	—
221	#120×C₅₃	—	2	1	no	—
222	#120×C₅₃	—	2	2	no	—
223	#120×C₅₃	—	2	2	no	—
224	#120×C₅₃	—	2	2	no	—
225	#120×C₅₃	—	2	2	no	—
226	#120×C₅₃	—	2	1	no	—
227	#120×C₅₃	—	2	2	no	—
228	#120×C₅₃	—	2	1	no	—
229	#120×C₅₃	—	2	1	no	—
230	#120×C₅₃	—	2	2	no	—
231	#120×C₅₃	—	2	2	no	—
232	#120×C₅₃	—	2	1	no	—
233	#120×C₅₃	—	2	1	no	—
234	#120×C₅₃	—	2	2	no	—
235	#120×C₅₃	D₄	1	1	yes	characteristic
236	#120×C₅₃	D₄	1	1	yes	characteristic
237	C₄×Q₈×C₅₃	—	2	2	no	—
238	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
239	C₄×D₄×C₅₃	—	2	2	no	—
240	C₄×D₄×C₅₃	—	2	2	no	—
241	C₄×D₄×C₅₃	—	2	2	no	—
242	C₄×D₄×C₅₃	—	2	2	no	—
243	C₄×D₄×C₅₃	—	2	2	no	—
244	C₄×D₄×C₅₃	C₂³	1	2	yes	—
245	C₄×D₄×C₅₃	C₂³	1	2	yes	—
246	C₄×D₄×C₅₃	C₂³	1	2	yes	—
247	C₄×D₄×C₅₃	C₂³	1	2	yes	—
248	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
249	#117×C₅₃	—	2	2	no	—
250	#117×C₅₃	C₂³	1	1	yes	characteristic
251	#117×C₅₃	C₂³	1	2	yes	—
252	#117×C₅₃	C₂³	1	1	yes	characteristic
253	#117×C₅₃	C₂³	1	1	yes	characteristic, complemented
254	#117×C₅₃	C₂³	1	1	yes	characteristic, complemented
255	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
256	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
258	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
260	#107×C₅₃	C₂³	1	2	yes	complemented
261	#107×C₅₃	C₂³	1	2	yes	complemented
262	#106×C₅₃	C₂³	1	2	yes	complemented
263	#106×C₅₃	C₂³	1	2	yes	complemented
264	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
265	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
266	#103×C₅₃	C₂³	1	2	yes	complemented
267	#103×C₅₃	C₂³	1	2	yes	complemented
268	#103×C₅₃	C₂³	1	2	yes	complemented
269	#103×C₅₃	C₂³	1	2	yes	complemented
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	#102×C₅₃	C₂³	1	2	yes	complemented
279	#102×C₅₃	C₂³	1	2	yes	complemented
280	#102×C₅₃	C₂³	1	2	yes	complemented
281	#102×C₅₃	C₂³	1	2	yes	complemented
282	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
285	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
286	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	complemented
287	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	complemented
288	#97×C₅₃	C₂³	1	2	yes	complemented
289	C₄×C₈×C₅₃	C₂³	1	2	yes	complemented
290	C₂⁴×C₅₃	—	2	1	no	—
291	C₂⁴×C₅₃	—	2	2	no	—
292	C₂⁴×C₅₃	—	2	2	no	—
293	C₂⁴×C₅₃	—	2	1	no	—
294	C₂⁴×C₅₃	—	2	1	no	—
295	C₂⁴×C₅₃	—	2	1	no	—
296	C₂⁴×C₅₃	—	2	1	no	—
297	C₂⁴×C₅₃	—	4	4	no	—
298	C₂⁴×C₅₃	—	8	4	no	—
299	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
300	#41×C₅₃	—	2	2	no	—
301	#41×C₅₃	—	2	2	no	—
302	#41×C₅₃	—	4	1	no	—
303	#41×C₅₃	—	4	1	no	—
304	#41×C₅₃	—	4	1	no	—
305	#41×C₅₃	—	4	1	no	—
306	#41×C₅₃	—	4	1	no	—
307	#41×C₅₃	—	4	1	no	—
308	#41×C₅₃	—	4	2	no	—
309	#41×C₅₃	—	4	2	no	—
310	#41×C₅₃	—	4	4	no	—
311	C₂×Q₈×C₅₃	—	2	2	no	—
312	C₂×Q₈×C₅₃	—	2	1	no	—
313	C₂×Q₈×C₅₃	—	4	1	no	—
314	C₂×Q₈×C₅₃	—	4	1	no	—
315	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
316	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
317	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
318	C₂×D₄×C₅₃	—	2	2	no	—
319	C₂×D₄×C₅₃	—	2	2	no	—
320	C₂×D₄×C₅₃	—	2	2	no	—
321	C₂×D₄×C₅₃	—	2	2	no	—
322	C₂×D₄×C₅₃	—	2	4	no	—
323	C₂×D₄×C₅₃	—	2	4	no	—
324	C₂×D₄×C₅₃	—	2	2	no	—
325	C₂×D₄×C₅₃	—	2	1	no	—
326	C₂×D₄×C₅₃	—	2	1	no	—
327	C₂×D₄×C₅₃	—	2	1	no	—
328	C₂×D₄×C₅₃	—	2	2	no	—
329	C₂×D₄×C₅₃	—	2	2	no	—
330	C₂×D₄×C₅₃	—	2	2	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	2	no	—
333	C₂×D₄×C₅₃	—	2	2	no	—
334	C₂×D₄×C₅₃	—	2	1	no	—
335	C₂×D₄×C₅₃	—	2	1	no	—
336	C₂×D₄×C₅₃	—	2	1	no	—
337	C₂×D₄×C₅₃	—	2	2	no	—
338	C₂×D₄×C₅₃	—	2	2	no	—
339	C₂×D₄×C₅₃	—	2	1	no	—
340	C₂×D₄×C₅₃	—	2	2	no	—
341	C₂×D₄×C₅₃	—	2	2	no	—
342	C₂×D₄×C₅₃	—	2	1	no	—
343	C₂×D₄×C₅₃	—	4	1	no	—
344	C₂×D₄×C₅₃	—	4	1	no	—
345	C₂×D₄×C₅₃	—	4	2	no	—
346	C₂×D₄×C₅₃	—	4	2	no	—
347	C₂×D₄×C₅₃	—	4	1	no	—
348	C₂×D₄×C₅₃	—	4	1	no	—
349	C₂×D₄×C₅₃	—	4	1	no	—
350	C₂×D₄×C₅₃	—	4	1	no	—
351	C₂×D₄×C₅₃	—	4	8	no	—
352	C₂×D₄×C₅₃	—	4	4	no	—
353	C₂×D₄×C₅₃	—	4	4	no	—
354	C₂×D₄×C₅₃	—	4	4	no	—
355	C₂×D₄×C₅₃	—	4	4	no	—
356	C₂×D₄×C₅₃	—	8	4	no	—
357	C₂×D₄×C₅₃	—	8	4	no	—
358	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
359	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
360	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
361	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
362	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
364	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
366	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₅₃	—	2	1	no	—
369	C₂²×C₄×C₅₃	—	2	1	no	—
370	C₂²×C₄×C₅₃	—	2	1	no	—
371	C₂²×C₄×C₅₃	—	2	1	no	—
372	C₂²×C₄×C₅₃	—	2	2	no	—
373	C₂²×C₄×C₅₃	—	2	2	no	—
374	C₂²×C₄×C₅₃	—	2	2	no	—
375	C₂²×C₄×C₅₃	—	2	2	no	—
376	C₂²×C₄×C₅₃	—	4	1	no	—
377	C₂²×C₄×C₅₃	—	4	1	no	—
378	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
379	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
382	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
384	Q₁₆×C₅₃	—	4	2	no	—
385	SD₁₆×C₅₃	—	2	4	no	—
386	SD₁₆×C₅₃	—	2	4	no	—
387	SD₁₆×C₅₃	—	4	2	no	—
388	SD₁₆×C₅₃	—	4	2	no	—
389	SD₁₆×C₅₃	—	4	2	no	—
390	SD₁₆×C₅₃	—	4	2	no	—
391	D₈×C₅₃	—	2	4	no	—
392	D₈×C₅₃	—	2	4	no	—
393	D₈×C₅₃	—	4	2	no	—
394	D₈×C₅₃	—	4	2	no	—
395	D₈×C₅₃	—	4	2	no	—
396	M₁₆×C₅₃	—	4	2	no	—
397	M₁₆×C₅₃	—	4	2	no	—
398	M₁₆×C₅₃	—	4	1	no	—
399	M₁₆×C₅₃	—	4	1	no	—
400	C₂×C₈×C₅₃	—	4	1	no	—
401	C₂×C₈×C₅₃	—	4	1	no	—
402	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
403	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
404	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
405	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₅₃	—	2	2	no	—
407	C₄⋊C₄×C₅₃	—	2	2	no	—
408	C₄⋊C₄×C₅₃	—	2	2	no	—
409	C₄⋊C₄×C₅₃	—	2	2	no	—
410	C₄⋊C₄×C₅₃	—	2	2	no	—
411	C₄⋊C₄×C₅₃	—	2	2	no	—
412	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
418	C₂²⋊C₄×C₅₃	—	2	1	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	1	no	—
423	C₂²⋊C₄×C₅₃	—	2	1	no	—
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	2	no	—
426	C₂²⋊C₄×C₅₃	—	2	2	no	—
427	C₂²⋊C₄×C₅₃	—	2	2	no	—
428	C₂²⋊C₄×C₅₃	—	2	2	no	—
429	C₂²⋊C₄×C₅₃	—	2	2	no	—
430	C₂²⋊C₄×C₅₃	—	2	2	no	—
431	C₂²⋊C₄×C₅₃	—	2	2	no	—
432	C₂²⋊C₄×C₅₃	—	2	2	no	—
433	C₂²⋊C₄×C₅₃	—	2	2	no	—
434	C₂²⋊C₄×C₅₃	—	2	2	no	—
435	C₂²⋊C₄×C₅₃	—	2	2	no	—
436	C₂²⋊C₄×C₅₃	—	2	2	no	—
437	C₂²⋊C₄×C₅₃	—	2	2	no	—
438	C₂²⋊C₄×C₅₃	—	2	2	no	—
439	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
440	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
441	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
445	C₄²×C₅₃	—	2	1	no	—
446	C₄²×C₅₃	—	2	2	no	—
447	C₄²×C₅₃	—	2	1	no	—
448	C₄²×C₅₃	—	2	1	no	—
449	C₄²×C₅₃	—	2	2	no	—
450	C₄²×C₅₃	C₂⁴	1	2	yes	—
451	C₂³×C₅₃	—	2	4	no	—
452	C₂³×C₅₃	—	2	1	no	—
453	C₂³×C₅₃	—	2	1	no	—
454	C₂³×C₅₃	—	2	2	no	—
455	C₂³×C₅₃	—	2	1	no	—
456	C₂³×C₅₃	—	2	2	no	—
457	C₂³×C₅₃	—	4	1	no	—
458	C₂³×C₅₃	—	4	2	no	—
459	C₂³×C₅₃	—	4	4	no	—
460	C₂³×C₅₃	—	4	4	no	—
461	C₂³×C₅₃	—	4	2	no	—
462	C₂³×C₅₃	—	4	2	no	—
463	C₂³×C₅₃	—	4	2	no	—
464	C₂³×C₅₃	—	4	4	no	—
465	C₂³×C₅₃	—	4	4	no	—
466	C₂³×C₅₃	—	8	2	no	—
467	C₂³×C₅₃	—	8	2	no	—
468	C₂³×C₅₃	—	8	2	no	—
469	C₂³×C₅₃	—	8	2	no	—
470	C₂³×C₅₃	—	8	1	no	—
471	C₂³×C₅₃	—	8	2	no	—
472	C₂³×C₅₃	—	8	2	no	—
473	C₂³×C₅₃	—	8	2	no	—
474	C₂³×C₅₃	—	8	16	no	—
475	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
476	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
477	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
478	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
479	Q₈×C₅₃	—	2	2	no	—
480	Q₈×C₅₃	—	2	2	no	—
481	Q₈×C₅₃	—	2	1	no	—
482	Q₈×C₅₃	—	2	1	no	—
483	Q₈×C₅₃	—	4	1	no	—
484	Q₈×C₅₃	—	8	2	no	—
485	Q₈×C₅₃	—	8	1	no	—
486	D₄×C₅₃	—	2	4	no	—
487	D₄×C₅₃	—	2	1	no	—
488	D₄×C₅₃	—	2	1	no	—
489	D₄×C₅₃	—	2	2	no	—
490	D₄×C₅₃	—	2	2	no	—
491	D₄×C₅₃	—	2	1	no	—
492	D₄×C₅₃	—	2	1	no	—
493	D₄×C₅₃	—	2	2	no	—
494	D₄×C₅₃	—	2	2	no	—
495	D₄×C₅₃	—	4	1	no	—
496	D₄×C₅₃	—	4	1	no	—
497	D₄×C₅₃	—	4	1	no	—
498	D₄×C₅₃	—	4	2	no	—
499	D₄×C₅₃	—	4	2	no	—
500	D₄×C₅₃	—	4	4	no	—
501	D₄×C₅₃	—	4	4	no	—
502	D₄×C₅₃	—	4	2	no	—
503	D₄×C₅₃	—	4	2	no	—
504	D₄×C₅₃	—	4	2	no	—
505	D₄×C₅₃	—	4	2	no	—
506	D₄×C₅₃	—	4	2	no	—
507	D₄×C₅₃	—	4	2	no	—
508	D₄×C₅₃	—	4	4	no	—
509	D₄×C₅₃	—	8	1	no	—
510	D₄×C₅₃	—	8	2	no	—
511	D₄×C₅₃	—	8	2	no	—
512	D₄×C₅₃	—	8	2	no	—
513	D₄×C₅₃	—	8	2	no	—
514	D₄×C₅₃	—	8	2	no	—
515	D₄×C₅₃	—	8	2	no	—
516	D₄×C₅₃	—	8	2	no	—
517	D₄×C₅₃	—	8	2	no	—
518	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
519	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
520	C₂×C₄×C₅₃	—	2	1	no	—
521	C₂×C₄×C₅₃	—	2	1	no	—
522	C₂×C₄×C₅₃	—	2	2	no	—
523	C₂×C₄×C₅₃	—	2	2	no	—
524	C₂×C₄×C₅₃	—	2	1	no	—
525	C₂×C₄×C₅₃	—	2	1	no	—
526	C₂×C₄×C₅₃	—	2	1	no	—
527	C₂×C₄×C₅₃	—	2	1	no	—
528	C₂×C₄×C₅₃	—	2	1	no	—
529	C₂×C₄×C₅₃	—	2	2	no	—
530	C₂×C₄×C₅₃	—	2	2	no	—
531	C₂×C₄×C₅₃	—	2	2	no	—
532	C₂×C₄×C₅₃	—	2	2	no	—
533	C₂×C₄×C₅₃	—	4	2	no	—
534	C₂×C₄×C₅₃	—	4	1	no	—
535	C₂×C₄×C₅₃	—	4	2	no	—
536	C₂×C₄×C₅₃	—	4	2	no	—
537	C₂×C₄×C₅₃	—	4	2	no	—
538	C₂×C₄×C₅₃	—	8	2	no	—
539	C₂×C₄×C₅₃	—	8	2	no	—
540	C₂×C₄×C₅₃	—	8	2	no	—
541	C₂×C₄×C₅₃	—	8	2	no	—
542	C₂×C₄×C₅₃	—	8	1	no	—
543	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
546	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
550	C₈×C₅₃	—	2	2	no	—
551	C₈×C₅₃	—	2	2	no	—
552	C₈×C₅₃	—	2	2	no	—
553	C₈×C₅₃	—	2	2	no	—
554	#61644	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
555	C₂²×C₅₃	—	2	2	no	—
556	C₂²×C₅₃	—	2	2	no	—
557	C₂²×C₅₃	—	2	2	no	—
558	C₂²×C₅₃	—	2	2	no	—
559	C₂²×C₅₃	—	2	2	no	—
560	C₂²×C₅₃	—	2	1	no	—
561	C₂²×C₅₃	—	2	2	no	—
562	C₂²×C₅₃	—	2	1	no	—
563	C₂²×C₅₃	—	2	1	no	—
564	C₂²×C₅₃	—	2	2	no	—
565	C₂²×C₅₃	—	2	2	no	—
566	C₂²×C₅₃	—	4	4	no	—
567	C₂²×C₅₃	—	4	2	no	—
568	C₂²×C₅₃	—	4	2	no	—
569	C₂²×C₅₃	—	4	2	no	—
570	C₂²×C₅₃	—	4	2	no	—
571	C₂²×C₅₃	—	4	2	no	—
572	C₂²×C₅₃	—	4	2	no	—
573	C₂²×C₅₃	—	4	2	no	—
574	C₂²×C₅₃	—	4	1	no	—
575	C₂²×C₅₃	—	4	2	no	—
576	C₂²×C₅₃	—	4	2	no	—
577	C₂²×C₅₃	—	8	4	no	—
578	C₂²×C₅₃	—	8	8	no	—
579	C₂²×C₅₃	—	8	8	no	—
580	C₂²×C₅₃	—	8	4	no	—
581	C₂²×C₅₃	—	16	2	no	—
582	C₂²×C₅₃	—	16	2	no	—
583	C₂²×C₅₃	—	16	2	no	—
584	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
585	C₄×C₅₃	—	2	2	no	—
586	C₄×C₅₃	—	2	2	no	—
587	C₄×C₅₃	—	2	1	no	—
588	C₄×C₅₃	—	2	2	no	—
589	C₄×C₅₃	—	2	1	no	—
590	C₄×C₅₃	—	2	1	no	—
591	C₄×C₅₃	—	4	2	no	—
592	C₄×C₅₃	—	4	2	no	—
593	C₄×C₅₃	—	4	2	no	—
594	C₄×C₅₃	—	4	1	no	—
595	C₄×C₅₃	—	4	2	no	—
596	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
597	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
598	#3540	C₂×C₅₃	1	1	yes	characteristic, complemented
599	#3484	C₂×C₅₃	1	1	yes	characteristic, complemented
600	#3325	C₂×C₅₃	1	2	yes	complemented
601	#3324	C₂×C₅₃	1	2	yes	complemented
602	#3319	C₂×C₅₃	1	2	yes	complemented
603	#3311	C₂×C₅₃	1	2	yes	complemented
604	#3275	C₂×C₅₃	1	2	yes	complemented
605	#3273	C₂×C₅₃	1	2	yes	complemented
606	#3265	C₂×C₅₃	1	2	yes	complemented
607	#3264	C₂×C₅₃	1	2	yes	complemented
608	#3224	C₂×C₅₃	1	2	yes	complemented
609	#3200	C₂×C₅₃	1	1	yes	characteristic, complemented
610	#3199	C₂×C₅₃	1	1	yes	characteristic, complemented
611	#3197	C₂×C₅₃	1	2	yes	complemented
612	#3118	C₂×C₅₃	1	2	yes	complemented
613	#3009	C₂×C₅₃	1	1	yes	characteristic, complemented
614	#3008	C₂×C₅₃	1	1	yes	characteristic, complemented
615	#3003	C₂×C₅₃	1	2	yes	complemented
616	#2978	C₂×C₅₃	1	1	yes	characteristic, complemented
617	C₂×C₅₃	—	4	2	no	—
618	C₂×C₅₃	—	4	1	no	—
619	C₂×C₅₃	—	4	1	no	—
620	C₂×C₅₃	—	4	1	no	—
621	C₂×C₅₃	—	4	2	no	—
622	C₂×C₅₃	—	4	2	no	—
623	C₂×C₅₃	—	8	2	no	—
624	C₂×C₅₃	—	8	2	no	—
625	C₂×C₅₃	—	8	1	no	—
626	C₂×C₅₃	#3484	1	1	yes	characteristic
627	C₂×C₅₃	#3585	1	2	yes	—
628	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
629	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
630	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
631	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
632	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
633	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
634	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
635	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
636	H(3,𝔽₄)	—	2	1	no	—
637	#560	—	2	1	no	—
638	#559	—	2	1	no	—
639	#556	C₂²×C₅₃	1	2	yes	complemented
640	#555	C₂²×C₅₃	1	2	yes	complemented
641	#551	—	2	1	no	—
642	#548	C₂²×C₅₃	1	2	yes	complemented
643	#546	—	2	2	no	—
644	#546	C₂²×C₅₃	1	2	yes	—
645	#546	C₂²×C₅₃	1	2	yes	complemented
646	#546	C₂²×C₅₃	1	2	yes	complemented
647	D₄²	—	2	2	no	—
648	D₄²	C₂²×C₅₃	1	2	yes	—
649	D₄²	C₂²×C₅₃	1	2	yes	complemented
650	#542	—	2	2	no	—
651	#542	C₂²×C₅₃	1	2	yes	complemented
652	#538	—	2	2	no	—
653	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
654	#535	C₂²×C₅₃	1	1	yes	characteristic
655	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
657	#534	—	2	1	no	—
658	#534	—	2	1	no	—
659	#525	C₂²×C₅₃	1	1	yes	characteristic
660	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
661	#525	C₂²×C₅₃	1	2	yes	complemented
662	C₂×#120	—	2	1	no	—
663	C₂×#120	—	2	1	no	—
664	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
665	#496	C₂²×C₅₃	1	2	yes	complemented
666	#495	C₂²×C₅₃	1	2	yes	complemented
667	#489	C₂²×C₅₃	1	2	yes	complemented
668	#486	C₂²×C₅₃	1	2	yes	complemented
669	#485	C₂²×C₅₃	1	2	yes	complemented
670	#485	C₂²×C₅₃	1	2	yes	complemented
671	#482	C₂²×C₅₃	1	2	yes	complemented
672	#482	C₂²×C₅₃	1	2	yes	complemented
673	#482	C₂²×C₅₃	1	2	yes	complemented
674	#482	C₂²×C₅₃	1	2	yes	complemented
675	#476	C₂²×C₅₃	1	2	yes	complemented
676	#474	C₂²×C₅₃	1	2	yes	complemented
677	#470	C₂²×C₅₃	1	2	yes	complemented
678	#469	C₂²×C₅₃	1	2	yes	complemented
679	#469	C₂²×C₅₃	1	2	yes	complemented
680	#468	C₂²×C₅₃	1	2	yes	complemented
681	#468	C₂²×C₅₃	1	2	yes	complemented
682	#468	C₂²×C₅₃	1	2	yes	complemented
683	#466	C₂²×C₅₃	1	2	yes	complemented
684	#465	C₂²×C₅₃	1	2	yes	complemented
685	#464	C₂²×C₅₃	1	2	yes	complemented
686	#463	C₂²×C₅₃	1	2	yes	complemented
687	#463	C₂²×C₅₃	1	2	yes	complemented
688	#463	C₂²×C₅₃	1	2	yes	complemented
689	#460	C₂²×C₅₃	1	2	yes	complemented
690	#459	C₂²×C₅₃	1	2	yes	complemented
691	#452	C₂²×C₅₃	1	2	yes	complemented
692	#452	C₂²×C₅₃	1	2	yes	complemented
693	#452	C₂²×C₅₃	1	2	yes	complemented
694	#450	C₂²×C₅₃	1	2	yes	complemented
695	#450	C₂²×C₅₃	1	2	yes	complemented
696	#450	C₂²×C₅₃	1	2	yes	complemented
697	#450	C₂²×C₅₃	1	2	yes	complemented
698	#450	C₂²×C₅₃	1	2	yes	complemented
699	#449	C₂²×C₅₃	1	2	yes	complemented
700	#449	C₂²×C₅₃	1	2	yes	complemented
701	#449	C₂²×C₅₃	1	2	yes	complemented
702	#448	C₂²×C₅₃	1	2	yes	complemented
703	#447	C₂²×C₅₃	1	2	yes	—
704	#447	C₂²×C₅₃	1	2	yes	complemented
705	#447	C₂²×C₅₃	1	2	yes	complemented
706	#447	C₂²×C₅₃	1	2	yes	complemented
707	#447	C₂²×C₅₃	1	2	yes	complemented
708	#447	C₂²×C₅₃	1	2	yes	complemented
709	#442	C₂²×C₅₃	1	2	yes	complemented
710	#440	C₂²×C₅₃	1	2	yes	complemented
711	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
712	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
713	#436	C₂²×C₅₃	1	2	yes	complemented
714	#436	C₂²×C₅₃	1	2	yes	complemented
715	#435	C₂²×C₅₃	1	2	yes	complemented
716	#435	C₂²×C₅₃	1	2	yes	complemented
717	#433	C₂²×C₅₃	1	2	yes	complemented
718	#418	C₂²×C₅₃	1	2	yes	complemented
719	#418	C₂²×C₅₃	1	2	yes	complemented
720	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
721	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
724	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
725	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
726	#407	C₂²×C₅₃	1	2	yes	complemented
727	C₅₃	#61644	1	1	yes	characteristic, direct product factor, Sylow
728	C₂⁵	—	2	1	no	—
729	H(5,𝔽₂)	—	4	2	no	—
730	H(5,𝔽₂)	—	4	2	no	—
731	C₂×#41	—	2	1	no	—
732	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
733	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
734	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
735	C₂×#41	C₂³×C₅₃	1	2	yes	—
736	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
737	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
738	C₂²×D₄	—	2	1	no	—
739	C₂²×D₄	—	2	1	no	—
740	C₂²×D₄	—	2	1	no	—
741	C₂²×D₄	—	2	2	no	—
742	C₂²×D₄	—	2	2	no	—
743	C₂²×D₄	—	2	1	no	—
744	C₂²×D₄	—	2	2	no	—
745	C₂²×D₄	—	4	2	no	—
746	C₂²×D₄	—	4	2	no	—
747	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
748	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
749	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
750	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
751	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
752	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
753	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
754	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
755	#137	—	4	2	no	—
756	AGL(1,ℤ/8)	—	4	2	no	—
757	AGL(1,ℤ/8)	—	4	4	no	—
758	AGL(1,ℤ/8)	—	4	4	no	—
759	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	complemented
760	C₂×SD₁₆	—	4	2	no	—
761	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
762	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
763	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
764	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
765	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	complemented
766	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	complemented
767	C₂×D₈	—	4	2	no	—
768	C₂×D₈	C₂³×C₅₃	1	2	yes	—
769	C₂×D₈	C₂³×C₅₃	1	2	yes	—
770	C₂×D₈	C₂³×C₅₃	1	2	yes	—
771	C₂×D₈	C₂³×C₅₃	1	2	yes	—
772	C₂×D₈	C₂³×C₅₃	1	2	yes	complemented
773	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
774	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
775	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic, complemented
776	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic, complemented
777	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
778	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
779	C₄⋊Q₈	—	2	1	no	—
780	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
781	#127	—	2	1	no	—
782	#127	—	2	1	no	—
783	#127	C₂³×C₅₃	1	2	yes	—
784	#126	—	2	2	no	—
785	#126	—	2	2	no	—
786	#126	—	2	2	no	—
787	#124	—	2	1	no	—
788	#124	—	2	1	no	—
789	#124	—	2	1	no	—
790	#124	—	2	2	no	—
791	#124	—	2	2	no	—
792	#124	—	2	2	no	—
793	#124	—	2	2	no	—
794	#124	—	2	2	no	—
795	#124	C₂³×C₅₃	1	2	yes	—
796	#124	C₂³×C₅₃	1	2	yes	complemented
797	#123	—	2	1	no	—
798	#123	—	2	1	no	—
799	#123	—	2	1	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	#123	—	2	2	no	—
803	#123	—	2	2	no	—
804	#123	—	2	2	no	—
805	#123	D₄×C₅₃	1	1	yes	characteristic
806	#123	D₄×C₅₃	1	1	yes	characteristic
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
810	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
811	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
812	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
813	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	—	2	2	no	—
819	#121	—	2	2	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	D₄×C₅₃	1	2	yes	—
823	#121	C₂³×C₅₃	1	2	yes	—
824	#121	C₂³×C₅₃	1	2	yes	—
825	#121	C₂³×C₅₃	1	2	yes	—
826	#121	C₂³×C₅₃	1	2	yes	—
827	#121	C₂³×C₅₃	1	2	yes	—
828	#121	C₂³×C₅₃	1	2	yes	complemented
829	#120	—	2	1	no	—
830	#120	—	2	2	no	—
831	#120	—	2	1	no	—
832	#120	—	2	1	no	—
833	#120	—	2	2	no	—
834	#120	—	2	2	no	—
835	#120	—	2	1	no	—
836	#120	—	2	1	no	—
837	#120	—	2	2	no	—
838	#120	—	2	1	no	—
839	#120	—	2	1	no	—
840	#120	—	2	2	no	—
841	#120	—	2	2	no	—
842	#120	—	2	2	no	—
843	#120	—	2	2	no	—
844	#120	D₄×C₅₃	1	1	yes	characteristic
845	#120	D₄×C₅₃	1	1	yes	characteristic
846	C₄×Q₈	—	2	2	no	—
847	C₄×Q₈	C₂³×C₅₃	1	2	yes	complemented
848	C₄×D₄	—	2	2	no	—
849	C₄×D₄	—	2	2	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	—	2	2	no	—
852	C₄×D₄	—	2	2	no	—
853	C₄×D₄	C₂³×C₅₃	1	2	yes	—
854	C₄×D₄	C₂³×C₅₃	1	2	yes	—
855	C₄×D₄	C₂³×C₅₃	1	2	yes	—
856	C₄×D₄	C₂³×C₅₃	1	2	yes	—
857	C₄×D₄	C₂³×C₅₃	1	2	yes	complemented
858	#117	—	2	2	no	—
859	#117	C₂³×C₅₃	1	1	yes	characteristic
860	#117	C₂³×C₅₃	1	2	yes	—
861	#117	C₂³×C₅₃	1	1	yes	characteristic
862	#117	C₂³×C₅₃	1	1	yes	characteristic, complemented
863	#117	C₂³×C₅₃	1	1	yes	characteristic, complemented
864	C₂×C₂²⋊C₄	—	2	1	no	—
865	C₂×C₂²⋊C₄	—	2	1	no	—
866	C₂×C₂²⋊C₄	—	2	2	no	—
867	C₂×C₂²⋊C₄	—	2	2	no	—
868	C₂×C₂²⋊C₄	—	2	2	no	—
869	#107	C₂³×C₅₃	1	2	yes	complemented
870	#107	C₂³×C₅₃	1	2	yes	complemented
871	#106	C₂³×C₅₃	1	2	yes	complemented
872	#106	C₂³×C₅₃	1	2	yes	complemented
873	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
874	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
875	#103	C₂³×C₅₃	1	2	yes	complemented
876	#103	C₂³×C₅₃	1	2	yes	complemented
877	#103	C₂³×C₅₃	1	2	yes	complemented
878	#103	C₂³×C₅₃	1	2	yes	complemented
879	#102	C₂³×C₅₃	1	2	yes	—
880	#102	C₂³×C₅₃	1	2	yes	—
881	#102	C₂³×C₅₃	1	2	yes	—
882	#102	C₂³×C₅₃	1	2	yes	—
883	#102	C₂³×C₅₃	1	2	yes	—
884	#102	C₂³×C₅₃	1	2	yes	—
885	#102	C₂³×C₅₃	1	2	yes	—
886	#102	C₂³×C₅₃	1	2	yes	—
887	#102	C₂³×C₅₃	1	2	yes	complemented
888	#102	C₂³×C₅₃	1	2	yes	complemented
889	#102	C₂³×C₅₃	1	2	yes	complemented
890	#102	C₂³×C₅₃	1	2	yes	complemented
891	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
893	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
894	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	complemented
896	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	complemented
897	#97	C₂³×C₅₃	1	2	yes	complemented
898	C₄×C₈	C₂³×C₅₃	1	2	yes	complemented
899	C₂⁴	—	2	1	no	—
900	C₂⁴	—	2	2	no	—
901	C₂⁴	—	2	2	no	—
902	C₂⁴	—	2	1	no	—
903	C₂⁴	—	2	1	no	—
904	C₂⁴	—	2	1	no	—
905	C₂⁴	—	2	1	no	—
906	C₂⁴	—	4	4	no	—
907	C₂⁴	—	8	4	no	—
908	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
909	#41	—	2	2	no	—
910	#41	—	2	2	no	—
911	#41	—	4	1	no	—
912	#41	—	4	1	no	—
913	#41	—	4	1	no	—
914	#41	—	4	1	no	—
915	#41	—	4	1	no	—
916	#41	—	4	1	no	—
917	#41	—	4	2	no	—
918	#41	—	4	2	no	—
919	#41	—	4	4	no	—
920	C₂×Q₈	—	2	2	no	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	4	1	no	—
923	C₂×Q₈	—	4	1	no	—
924	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
925	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	4	no	—
932	C₂×D₄	—	2	4	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	4	2	no	—
953	C₂×D₄	—	4	2	no	—
954	C₂×D₄	—	4	1	no	—
955	C₂×D₄	—	4	1	no	—
956	C₂×D₄	—	4	1	no	—
957	C₂×D₄	—	4	1	no	—
958	C₂×D₄	—	4	1	no	—
959	C₂×D₄	—	4	1	no	—
960	C₂×D₄	—	4	8	no	—
961	C₂×D₄	—	4	4	no	—
962	C₂×D₄	—	4	4	no	—
963	C₂×D₄	—	4	4	no	—
964	C₂×D₄	—	4	4	no	—
965	C₂×D₄	—	8	4	no	—
966	C₂×D₄	—	8	4	no	—
967	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
968	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
969	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
970	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
971	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
972	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
973	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
974	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
975	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
976	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
977	C₂²×C₄	—	2	1	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	2	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	4	1	no	—
986	C₂²×C₄	—	4	1	no	—
987	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
988	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
989	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
990	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
991	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
992	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
993	Q₁₆	—	4	2	no	—
994	SD₁₆	—	2	4	no	—
995	SD₁₆	—	2	4	no	—
996	SD₁₆	—	4	2	no	—
997	SD₁₆	—	4	2	no	—
998	SD₁₆	—	4	2	no	—
999	SD₁₆	—	4	2	no	—
1000	D₈	—	2	4	no	—
1001	D₈	—	2	4	no	—
1002	D₈	—	4	2	no	—
1003	D₈	—	4	2	no	—
1004	D₈	—	4	2	no	—
1005	M₁₆	—	4	2	no	—
1006	M₁₆	—	4	2	no	—
1007	M₁₆	—	4	1	no	—
1008	M₁₆	—	4	1	no	—
1009	C₂×C₈	—	4	1	no	—
1010	C₂×C₈	—	4	1	no	—
1011	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1012	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1013	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1014	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1022	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1023	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1024	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1025	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1026	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1049	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1050	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1051	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1052	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1053	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1054	C₄²	—	2	1	no	—
1055	C₄²	—	2	2	no	—
1056	C₄²	—	2	1	no	—
1057	C₄²	—	2	1	no	—
1058	C₄²	—	2	2	no	—
1059	C₄²	C₂⁴×C₅₃	1	2	yes	—
1060	C₂³	—	2	4	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	1	no	—
1063	C₂³	—	2	2	no	—
1064	C₂³	—	2	2	no	—
1065	C₂³	—	2	1	no	—
1066	C₂³	—	4	1	no	—
1067	C₂³	—	4	2	no	—
1068	C₂³	—	4	4	no	—
1069	C₂³	—	4	4	no	—
1070	C₂³	—	4	2	no	—
1071	C₂³	—	4	2	no	—
1072	C₂³	—	4	2	no	—
1073	C₂³	—	4	4	no	—
1074	C₂³	—	4	4	no	—
1075	C₂³	—	8	2	no	—
1076	C₂³	—	8	2	no	—
1077	C₂³	—	8	2	no	—
1078	C₂³	—	8	2	no	—
1079	C₂³	—	8	1	no	—
1080	C₂³	—	8	2	no	—
1081	C₂³	—	8	2	no	—
1082	C₂³	—	8	2	no	—
1083	C₂³	—	8	16	no	—
1084	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1085	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1086	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1087	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1088	Q₈	—	2	2	no	—
1089	Q₈	—	2	2	no	—
1090	Q₈	—	2	1	no	—
1091	Q₈	—	2	1	no	—
1092	Q₈	—	4	1	no	—
1093	Q₈	—	8	2	no	—
1094	Q₈	—	8	1	no	—
1095	D₄	—	2	4	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	2	2	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	2	2	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	4	1	no	—
1105	D₄	—	4	1	no	—
1106	D₄	—	4	1	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	2	no	—
1109	D₄	—	4	4	no	—
1110	D₄	—	4	4	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	4	2	no	—
1113	D₄	—	4	2	no	—
1114	D₄	—	4	2	no	—
1115	D₄	—	4	2	no	—
1116	D₄	—	4	2	no	—
1117	D₄	—	4	4	no	—
1118	D₄	—	8	1	no	—
1119	D₄	—	8	2	no	—
1120	D₄	—	8	2	no	—
1121	D₄	—	8	2	no	—
1122	D₄	—	8	2	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	8	2	no	—
1125	D₄	—	8	2	no	—
1126	D₄	—	8	2	no	—
1127	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1128	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	4	2	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	2	no	—
1145	C₂×C₄	—	4	2	no	—
1146	C₂×C₄	—	4	2	no	—
1147	C₂×C₄	—	8	2	no	—
1148	C₂×C₄	—	8	2	no	—
1149	C₂×C₄	—	8	2	no	—
1150	C₂×C₄	—	8	2	no	—
1151	C₂×C₄	—	8	1	no	—
1152	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1153	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1154	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1155	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1156	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1157	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1158	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1159	C₈	—	2	2	no	—
1160	C₈	—	2	2	no	—
1161	C₈	—	2	2	no	—
1162	C₈	—	2	2	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	1	no	—
1166	C₂²	—	2	1	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	2	no	—
1171	C₂²	—	2	2	no	—
1172	C₂²	—	2	2	no	—
1173	C₂²	—	2	2	no	—
1174	C₂²	—	4	4	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	1	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	4	2	no	—
1184	C₂²	—	4	2	no	—
1185	C₂²	—	8	4	no	—
1186	C₂²	—	8	8	no	—
1187	C₂²	—	8	8	no	—
1188	C₂²	—	8	4	no	—
1189	C₂²	—	16	2	no	—
1190	C₂²	—	16	2	no	—
1191	C₂²	—	16	2	no	—
1192	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1193	C₄	—	2	1	no	—
1194	C₄	—	2	2	no	—
1195	C₄	—	2	1	no	—
1196	C₄	—	2	1	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	2	no	—
1201	C₄	—	4	2	no	—
1202	C₄	—	4	2	no	—
1203	C₄	—	4	2	no	—
1204	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1205	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1206	C₂	—	4	1	no	—
1207	C₂	—	4	2	no	—
1208	C₂	—	4	1	no	—
1209	C₂	—	4	1	no	—
1210	C₂	—	4	2	no	—
1211	C₂	—	4	2	no	—
1212	C₂	—	8	2	no	—
1213	C₂	—	8	1	no	—
1214	C₂	—	8	2	no	—
1215	C₂	C₅₃×#3484	1	1	yes	characteristic
1216	C₂	C₅₃×#3585	1	2	yes	—

	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3540	C₂	semidirect
2. C₅₃×#3484	C₂	semidirect
3. C₅₃×#3325	C₂	semidirect
4. C₅₃×#3324	C₂	semidirect
5. C₅₃×#3319	C₂	semidirect
6. C₅₃×#3311	C₂	semidirect
7. C₅₃×#3275	C₂	semidirect
8. C₅₃×#3273	C₂	semidirect
9. C₅₃×#3265	C₂	semidirect
10. C₅₃×#3264	C₂	semidirect
11. C₅₃×#3224	C₂	semidirect
12. C₅₃×#3200	C₂	semidirect
13. C₅₃×#3199	C₂	semidirect
14. C₅₃×#3197	C₂	semidirect
15. C₅₃×#3118	C₂	semidirect
16. C₅₃×#3009	C₂	semidirect
17. C₅₃×#3008	C₂	semidirect
18. C₅₃×#3003	C₂	semidirect
19. C₅₃×#2978	C₂	semidirect
21. C₂³×D₄×C₅₃	C₂²	semidirect
22. C₂×#137×C₅₃	C₂²	semidirect
23. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
26. C₂²×SD₁₆×C₅₃	C₂²	semidirect
27. C₂²×D₈×C₅₃	C₂²	semidirect
31. C₅₃×#556	C₂²	semidirect
32. C₅₃×#555	C₂²	semidirect
34. C₅₃×#548	C₂²	semidirect
37. C₅₃×#546	C₂²	semidirect
38. C₅₃×#546	C₂²	semidirect
41. D₄²×C₅₃	C₂²	semidirect
43. C₅₃×#542	C₂²	semidirect
45. C₅₃×#536	C₂²	semidirect
47. C₅₃×#535	C₂²	semidirect
48. C₅₃×#535	C₂²	semidirect
52. C₅₃×#525	C₂²	semidirect
53. C₅₃×#525	C₂²	semidirect
56. C₅₃×#518	C₂²	semidirect
57. C₅₃×#496	C₂²	semidirect
58. C₅₃×#495	C₂²	semidirect
59. C₅₃×#489	C₂²	semidirect
60. C₅₃×#486	C₂²	semidirect
61. C₅₃×#485	C₂²	semidirect
62. C₅₃×#485	C₂²	semidirect
63. C₅₃×#482	C₂²	semidirect
64. C₅₃×#482	C₂²	semidirect
65. C₅₃×#482	C₂²	semidirect
66. C₅₃×#482	C₂²	semidirect
67. C₅₃×#476	C₂²	semidirect
68. C₅₃×#474	C₂²	semidirect
69. C₅₃×#470	C₂²	semidirect
70. C₅₃×#469	C₂²	semidirect
71. C₅₃×#469	C₂²	semidirect
72. C₅₃×#468	C₂²	semidirect
73. C₅₃×#468	C₂²	semidirect
74. C₅₃×#468	C₂²	semidirect
75. C₅₃×#466	C₂²	semidirect
76. C₅₃×#465	C₂²	semidirect
77. C₅₃×#464	C₂²	semidirect
78. C₅₃×#463	C₂²	semidirect
79. C₅₃×#463	C₂²	semidirect
80. C₅₃×#463	C₂²	semidirect
81. C₅₃×#460	C₂²	semidirect
82. C₅₃×#459	C₂²	semidirect
83. C₅₃×#452	C₂²	semidirect
84. C₅₃×#452	C₂²	semidirect
85. C₅₃×#452	C₂²	semidirect
86. C₅₃×#450	C₂²	semidirect
87. C₅₃×#450	C₂²	semidirect
88. C₅₃×#450	C₂²	semidirect
89. C₅₃×#450	C₂²	semidirect
90. C₅₃×#450	C₂²	semidirect
91. C₅₃×#449	C₂²	semidirect
92. C₅₃×#449	C₂²	semidirect
93. C₅₃×#449	C₂²	semidirect
94. C₅₃×#448	C₂²	semidirect
96. C₅₃×#447	C₂²	semidirect
97. C₅₃×#447	C₂²	semidirect
98. C₅₃×#447	C₂²	semidirect
99. C₅₃×#447	C₂²	semidirect
100. C₅₃×#447	C₂²	semidirect
101. C₅₃×#442	C₂²	semidirect
102. C₅₃×#440	C₂²	semidirect
103. C₄×SD₁₆×C₅₃	C₂²	semidirect
104. C₄×D₈×C₅₃	C₂²	semidirect
105. C₅₃×#436	C₂²	semidirect
106. C₅₃×#436	C₂²	semidirect
107. C₅₃×#435	C₂²	semidirect
108. C₅₃×#435	C₂²	semidirect
109. C₅₃×#433	C₂²	semidirect
110. C₅₃×#418	C₂²	semidirect
111. C₅₃×#418	C₂²	semidirect
112. C₅₃×#418	C₂²	semidirect
113. C₅₃×#418	C₂²	semidirect
114. C₅₃×#416	C₂²	semidirect
115. C₅₃×#416	C₂²	semidirect
116. C₅₃×#408	C₂²	semidirect
117. C₅₃×#408	C₂²	semidirect
118. C₅₃×#407	C₂²	semidirect
128. C₂²×Q₈×C₅₃	C₂³	semidirect
144. C₂²×D₄×C₅₃	C₂³	semidirect
150. C₂×Q₁₆×C₅₃	C₂³	semidirect
156. C₂×SD₁₆×C₅₃	C₂³	semidirect
157. C₂×SD₁₆×C₅₃	C₂³	semidirect
163. C₂×D₈×C₅₃	C₂³	semidirect
166. C₂×M₁₆×C₅₃	C₂³	semidirect
167. C₂×M₁₆×C₅₃	C₂³	semidirect
168. C₂²×C₈×C₅₃	C₂³	semidirect
169. C₂²×C₈×C₅₃	C₂³	semidirect
171. C₄⋊Q₈×C₅₃	C₂³	semidirect
187. #124×C₅₃	C₂³	semidirect
204. C₂²⋊Q₈×C₅₃	C₂³	semidirect
219. #121×C₅₃	C₂³	semidirect
238. C₄×Q₈×C₅₃	C₂³	semidirect
248. C₄×D₄×C₅₃	C₂³	semidirect
253. #117×C₅₃	C₂³	semidirect
254. #117×C₅₃	C₂³	semidirect
260. #107×C₅₃	C₂³	semidirect
261. #107×C₅₃	C₂³	semidirect
262. #106×C₅₃	C₂³	semidirect
263. #106×C₅₃	C₂³	semidirect
264. C₄⋊C₈×C₅₃	C₂³	semidirect
265. C₄⋊C₈×C₅₃	C₂³	semidirect
266. #103×C₅₃	C₂³	semidirect
267. #103×C₅₃	C₂³	semidirect
268. #103×C₅₃	C₂³	semidirect
269. #103×C₅₃	C₂³	semidirect
278. #102×C₅₃	C₂³	semidirect
279. #102×C₅₃	C₂³	semidirect
280. #102×C₅₃	C₂³	semidirect
281. #102×C₅₃	C₂³	semidirect
286. C₂²⋊C₈×C₅₃	C₂³	semidirect
287. C₂²⋊C₈×C₅₃	C₂³	semidirect
288. #97×C₅₃	C₂³	semidirect
289. C₄×C₈×C₅₃	C₂³	semidirect
554. #61644	C₅₃	direct (N × H)
598. #3540	C₂×C₅₃	semidirect
599. #3484	C₂×C₅₃	semidirect
600. #3325	C₂×C₅₃	semidirect
601. #3324	C₂×C₅₃	semidirect
602. #3319	C₂×C₅₃	semidirect
603. #3311	C₂×C₅₃	semidirect
604. #3275	C₂×C₅₃	semidirect
605. #3273	C₂×C₅₃	semidirect
606. #3265	C₂×C₅₃	semidirect
607. #3264	C₂×C₅₃	semidirect
608. #3224	C₂×C₅₃	semidirect
609. #3200	C₂×C₅₃	semidirect
610. #3199	C₂×C₅₃	semidirect
611. #3197	C₂×C₅₃	semidirect
612. #3118	C₂×C₅₃	semidirect
613. #3009	C₂×C₅₃	semidirect
614. #3008	C₂×C₅₃	semidirect
615. #3003	C₂×C₅₃	semidirect
616. #2978	C₂×C₅₃	semidirect
629. C₂³×D₄	C₂²×C₅₃	semidirect
630. C₂×#137	C₂²×C₅₃	semidirect
631. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
632. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
633. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
634. C₂²×SD₁₆	C₂²×C₅₃	semidirect
635. C₂²×D₈	C₂²×C₅₃	semidirect
639. #556	C₂²×C₅₃	semidirect
640. #555	C₂²×C₅₃	semidirect
642. #548	C₂²×C₅₃	semidirect
645. #546	C₂²×C₅₃	semidirect
646. #546	C₂²×C₅₃	semidirect
649. D₄²	C₂²×C₅₃	semidirect
651. #542	C₂²×C₅₃	semidirect
653. #536	C₂²×C₅₃	semidirect
655. #535	C₂²×C₅₃	semidirect
656. #535	C₂²×C₅₃	semidirect
660. #525	C₂²×C₅₃	semidirect
661. #525	C₂²×C₅₃	semidirect
664. #518	C₂²×C₅₃	semidirect
665. #496	C₂²×C₅₃	semidirect
666. #495	C₂²×C₅₃	semidirect
667. #489	C₂²×C₅₃	semidirect
668. #486	C₂²×C₅₃	semidirect
669. #485	C₂²×C₅₃	semidirect
670. #485	C₂²×C₅₃	semidirect
671. #482	C₂²×C₅₃	semidirect
672. #482	C₂²×C₅₃	semidirect
673. #482	C₂²×C₅₃	semidirect
674. #482	C₂²×C₅₃	semidirect
675. #476	C₂²×C₅₃	semidirect
676. #474	C₂²×C₅₃	semidirect
677. #470	C₂²×C₅₃	semidirect
678. #469	C₂²×C₅₃	semidirect
679. #469	C₂²×C₅₃	semidirect
680. #468	C₂²×C₅₃	semidirect
681. #468	C₂²×C₅₃	semidirect
682. #468	C₂²×C₅₃	semidirect
683. #466	C₂²×C₅₃	semidirect
684. #465	C₂²×C₅₃	semidirect
685. #464	C₂²×C₅₃	semidirect
686. #463	C₂²×C₅₃	semidirect
687. #463	C₂²×C₅₃	semidirect
688. #463	C₂²×C₅₃	semidirect
689. #460	C₂²×C₅₃	semidirect
690. #459	C₂²×C₅₃	semidirect
691. #452	C₂²×C₅₃	semidirect
692. #452	C₂²×C₅₃	semidirect
693. #452	C₂²×C₅₃	semidirect
694. #450	C₂²×C₅₃	semidirect
695. #450	C₂²×C₅₃	semidirect
696. #450	C₂²×C₅₃	semidirect
697. #450	C₂²×C₅₃	semidirect
698. #450	C₂²×C₅₃	semidirect
699. #449	C₂²×C₅₃	semidirect
700. #449	C₂²×C₅₃	semidirect
701. #449	C₂²×C₅₃	semidirect
702. #448	C₂²×C₅₃	semidirect
704. #447	C₂²×C₅₃	semidirect
705. #447	C₂²×C₅₃	semidirect
706. #447	C₂²×C₅₃	semidirect
707. #447	C₂²×C₅₃	semidirect
708. #447	C₂²×C₅₃	semidirect
709. #442	C₂²×C₅₃	semidirect
710. #440	C₂²×C₅₃	semidirect
711. C₄×SD₁₆	C₂²×C₅₃	semidirect
712. C₄×D₈	C₂²×C₅₃	semidirect
713. #436	C₂²×C₅₃	semidirect
714. #436	C₂²×C₅₃	semidirect
715. #435	C₂²×C₅₃	semidirect
716. #435	C₂²×C₅₃	semidirect
717. #433	C₂²×C₅₃	semidirect
718. #418	C₂²×C₅₃	semidirect
719. #418	C₂²×C₅₃	semidirect
720. #418	C₂²×C₅₃	semidirect
721. #418	C₂²×C₅₃	semidirect
722. #416	C₂²×C₅₃	semidirect
723. #416	C₂²×C₅₃	semidirect
724. #408	C₂²×C₅₃	semidirect
725. #408	C₂²×C₅₃	semidirect
726. #407	C₂²×C₅₃	semidirect
727. C₅₃	#61644	direct (N × H)
737. C₂²×Q₈	C₂³×C₅₃	semidirect
753. C₂²×D₄	C₂³×C₅₃	semidirect
759. C₂×Q₁₆	C₂³×C₅₃	semidirect
765. C₂×SD₁₆	C₂³×C₅₃	semidirect
766. C₂×SD₁₆	C₂³×C₅₃	semidirect
772. C₂×D₈	C₂³×C₅₃	semidirect
775. C₂×M₁₆	C₂³×C₅₃	semidirect
776. C₂×M₁₆	C₂³×C₅₃	semidirect
777. C₂²×C₈	C₂³×C₅₃	semidirect
778. C₂²×C₈	C₂³×C₅₃	semidirect
780. C₄⋊Q₈	C₂³×C₅₃	semidirect
796. #124	C₂³×C₅₃	semidirect
813. C₂²⋊Q₈	C₂³×C₅₃	semidirect
828. #121	C₂³×C₅₃	semidirect
847. C₄×Q₈	C₂³×C₅₃	semidirect
857. C₄×D₄	C₂³×C₅₃	semidirect
862. #117	C₂³×C₅₃	semidirect
863. #117	C₂³×C₅₃	semidirect
869. #107	C₂³×C₅₃	semidirect
870. #107	C₂³×C₅₃	semidirect
871. #106	C₂³×C₅₃	semidirect
872. #106	C₂³×C₅₃	semidirect
873. C₄⋊C₈	C₂³×C₅₃	semidirect
874. C₄⋊C₈	C₂³×C₅₃	semidirect
875. #103	C₂³×C₅₃	semidirect
876. #103	C₂³×C₅₃	semidirect
877. #103	C₂³×C₅₃	semidirect
878. #103	C₂³×C₅₃	semidirect
887. #102	C₂³×C₅₃	semidirect
888. #102	C₂³×C₅₃	semidirect
889. #102	C₂³×C₅₃	semidirect
890. #102	C₂³×C₅₃	semidirect
895. C₂²⋊C₈	C₂³×C₅₃	semidirect
896. C₂²⋊C₈	C₂³×C₅₃	semidirect
897. #97	C₂³×C₅₃	semidirect
898. C₄×C₈	C₂³×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3540	2
C₅₃×#3484	2
C₅₃×#3325	2
C₅₃×#3324	2
C₅₃×#3319	2
C₅₃×#3311	2
C₅₃×#3275	2
C₅₃×#3273	2
C₅₃×#3265	2
C₅₃×#3264	2
C₅₃×#3224	2
C₅₃×#3200	2
C₅₃×#3199	2
C₅₃×#3197	2
C₅₃×#3118	2
C₅₃×#3009	2
C₅₃×#3008	2
C₅₃×#3003	2
C₅₃×#2978	2
#61644	53

Subgroups — C53×#61644 #27269156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61644 #27269156