Subgroups — C₅₃×#60772 #27268284

Order 13568.

2186 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3203	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3201	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3200	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3198	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3197	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3196	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3194	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3193	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3056	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#550	—	2	1	no	—
34	D₄×Q₈×C₅₃	—	2	1	no	—
35	C₅₃×#548	—	2	1	no	—
36	C₅₃×#548	—	2	1	no	—
37	C₅₃×#547	—	2	2	no	—
38	C₅₃×#547	—	2	1	no	—
39	C₅₃×#546	—	2	2	no	—
40	C₅₃×#546	—	2	1	no	—
41	C₅₃×#546	—	2	2	no	—
42	C₅₃×#546	—	2	1	no	—
43	D₄²×C₅₃	—	2	2	no	—
44	D₄²×C₅₃	—	2	1	no	—
45	C₅₃×#537	C₂²	1	2	yes	—
46	C₅₃×#537	C₂²	1	1	yes	characteristic
47	C₅₃×#537	C₂²	1	1	yes	characteristic
48	C₅₃×#537	C₂²	1	2	yes	complemented
49	C₅₃×#536	C₂²	1	1	yes	characteristic
50	C₅₃×#536	C₂²	1	2	yes	complemented
51	C₅₃×#535	C₂²	1	2	yes	—
52	C₅₃×#535	C₂²	1	1	yes	characteristic
53	C₅₃×#525	C₂²	1	2	yes	—
54	C₅₃×#525	C₂²	1	1	yes	characteristic
55	C₅₃×#525	C₂²	1	2	yes	complemented
56	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
58	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×#121×C₅₃	C₂²	1	2	yes	—
60	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
61	C₅₃×#520	C₂²	1	1	yes	characteristic
62	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#485	C₂²	1	2	yes	complemented
64	C₅₃×#485	C₂²	1	2	yes	complemented
65	C₅₃×#485	C₂²	1	2	yes	complemented
66	C₅₃×#485	C₂²	1	2	yes	complemented
67	C₅₃×#484	C₂²	1	2	yes	complemented
68	C₅₃×#484	C₂²	1	2	yes	complemented
69	C₅₃×#484	C₂²	1	2	yes	complemented
70	C₅₃×#483	C₂²	1	2	yes	complemented
71	C₅₃×#482	C₂²	1	2	yes	complemented
72	C₅₃×#482	C₂²	1	2	yes	complemented
73	C₅₃×#482	C₂²	1	2	yes	complemented
74	C₅₃×#482	C₂²	1	2	yes	complemented
75	C₅₃×#481	C₂²	1	2	yes	complemented
76	C₅₃×#480	C₂²	1	2	yes	complemented
77	C₅₃×#480	C₂²	1	2	yes	complemented
78	C₅₃×#480	C₂²	1	2	yes	complemented
79	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#470	C₂²	1	2	yes	complemented
81	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#469	C₂²	1	2	yes	complemented
84	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#468	C₂²	1	2	yes	complemented
87	C₅₃×#468	C₂²	1	2	yes	complemented
88	C₅₃×#468	C₂²	1	2	yes	complemented
89	C₅₃×#468	C₂²	1	2	yes	complemented
90	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#468	C₂²	1	2	yes	complemented
92	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#468	C₂²	1	2	yes	complemented
94	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#467	C₂²	1	2	yes	complemented
96	C₅₃×#466	C₂²	1	2	yes	complemented
97	C₅₃×#465	C₂²	1	2	yes	complemented
98	C₅₃×#465	C₂²	1	2	yes	complemented
99	C₅₃×#452	C₂²	1	2	yes	complemented
100	C₅₃×#452	C₂²	1	2	yes	complemented
101	C₅₃×#452	C₂²	1	2	yes	complemented
102	C₅₃×#452	C₂²	1	2	yes	complemented
103	C₅₃×#451	C₂²	1	2	yes	complemented
104	C₅₃×#450	C₂²	1	2	yes	complemented
105	C₅₃×#450	C₂²	1	2	yes	complemented
106	C₅₃×#450	C₂²	1	2	yes	complemented
107	C₅₃×#449	C₂²	1	2	yes	complemented
108	C₅₃×#449	C₂²	1	2	yes	complemented
109	C₅₃×#449	C₂²	1	2	yes	complemented
110	C₅₃×#449	C₂²	1	2	yes	complemented
111	C₅₃×#448	C₂²	1	2	yes	complemented
112	C₅₃×#448	C₂²	1	2	yes	complemented
113	C₅₃×#448	C₂²	1	2	yes	complemented
114	C₅₃×#447	C₂²	1	2	yes	complemented
115	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
118	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
126	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#408	C₂²	1	1	yes	characteristic
128	C₅₃×#408	C₂²	1	1	yes	characteristic
129	C₅₃×#408	C₂²	1	2	yes	complemented
130	C₅₃×#408	C₂²	1	2	yes	complemented
131	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#407	C₂²	1	2	yes	complemented
134	C₅₃×#407	C₂²	1	2	yes	complemented
135	2₋¹⁺⁴×C₅₃	—	4	2	no	—
136	2₋¹⁺⁴×C₅₃	—	4	2	no	—
137	H(5,𝔽₂)×C₅₃	—	4	2	no	—
138	H(5,𝔽₂)×C₅₃	—	4	2	no	—
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	2	no	—
141	C₂×#41×C₅₃	—	2	1	no	—
142	C₂×#41×C₅₃	—	4	2	no	—
143	C₂×#41×C₅₃	—	4	2	no	—
144	C₂×#41×C₅₃	D₄	1	2	yes	—
145	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
146	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
147	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×#41×C₅₃	C₂³	1	2	yes	—
150	C₂×#41×C₅₃	C₂³	1	2	yes	—
151	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
153	C₂×#41×C₅₃	C₂³	1	2	yes	—
154	C₂²×Q₈×C₅₃	—	2	1	no	—
155	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
156	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
158	C₂²×D₄×C₅₃	—	2	1	no	—
159	C₂²×D₄×C₅₃	—	2	2	no	—
160	C₂²×D₄×C₅₃	—	2	2	no	—
161	C₂²×D₄×C₅₃	—	2	1	no	—
162	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
163	C₂²×D₄×C₅₃	D₄	1	2	yes	—
164	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
165	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
166	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
167	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
168	#137×C₅₃	—	4	2	no	—
169	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
170	#135×C₅₃	—	4	2	no	—
171	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
172	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
173	C₂×SD₁₆×C₅₃	—	4	2	no	—
174	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
175	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
176	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
177	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
178	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
179	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
180	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
181	C₂×D₈×C₅₃	C₂³	1	2	yes	—
182	C₂×M₁₆×C₅₃	—	4	2	no	—
183	C₂×M₁₆×C₅₃	—	4	2	no	—
184	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
185	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
186	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
187	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
188	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
189	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
190	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
191	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
192	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
193	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
194	C₄⋊Q₈×C₅₃	—	2	1	no	—
195	C₄⋊Q₈×C₅₃	—	2	2	no	—
196	#127×C₅₃	—	2	1	no	—
197	#127×C₅₃	—	2	2	no	—
198	#124×C₅₃	—	2	1	no	—
199	#124×C₅₃	—	2	2	no	—
200	#124×C₅₃	—	2	1	no	—
201	#124×C₅₃	—	2	2	no	—
202	#123×C₅₃	—	2	2	no	—
203	#123×C₅₃	—	2	2	no	—
204	#123×C₅₃	—	2	2	no	—
205	#123×C₅₃	—	2	1	no	—
206	#123×C₅₃	—	2	2	no	—
207	#123×C₅₃	—	2	1	no	—
208	#123×C₅₃	—	2	2	no	—
209	C₂²⋊Q₈×C₅₃	—	2	1	no	—
210	C₂²⋊Q₈×C₅₃	—	2	2	no	—
211	C₂²⋊Q₈×C₅₃	—	2	1	no	—
212	C₂²⋊Q₈×C₅₃	—	2	2	no	—
213	C₂²⋊Q₈×C₅₃	—	2	1	no	—
214	C₂²⋊Q₈×C₅₃	—	2	2	no	—
215	C₂²⋊Q₈×C₅₃	—	2	1	no	—
216	C₂²⋊Q₈×C₅₃	—	2	2	no	—
217	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
220	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
222	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
223	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	#121×C₅₃	—	2	2	no	—
228	#121×C₅₃	—	2	2	no	—
229	#121×C₅₃	—	2	2	no	—
230	#121×C₅₃	—	2	1	no	—
231	#121×C₅₃	—	2	2	no	—
232	#121×C₅₃	—	2	2	no	—
233	#121×C₅₃	—	2	1	no	—
234	#121×C₅₃	—	2	2	no	—
235	#121×C₅₃	—	2	2	no	—
236	#121×C₅₃	—	2	2	no	—
237	#121×C₅₃	—	2	1	no	—
238	#121×C₅₃	—	2	2	no	—
239	#121×C₅₃	—	2	1	no	—
240	#121×C₅₃	—	2	2	no	—
241	#121×C₅₃	C₂³	1	1	yes	characteristic
242	#121×C₅₃	C₂³	1	2	yes	—
243	#121×C₅₃	C₂³	1	2	yes	—
244	#121×C₅₃	C₂³	1	2	yes	—
245	#121×C₅₃	C₂³	1	2	yes	—
246	#121×C₅₃	C₂³	1	2	yes	—
247	#121×C₅₃	C₂³	1	1	yes	characteristic
248	#121×C₅₃	C₂³	1	1	yes	characteristic
249	#121×C₅₃	C₂³	1	2	yes	—
250	#121×C₅₃	C₂³	1	1	yes	characteristic
251	#120×C₅₃	—	2	1	no	—
252	#120×C₅₃	—	2	2	no	—
253	#120×C₅₃	—	2	1	no	—
254	#120×C₅₃	—	2	2	no	—
255	#120×C₅₃	—	2	2	no	—
256	#120×C₅₃	—	2	2	no	—
257	#120×C₅₃	—	2	2	no	—
258	C₄×Q₈×C₅₃	—	2	1	no	—
259	C₄×Q₈×C₅₃	—	2	1	no	—
260	C₄×D₄×C₅₃	—	2	2	no	—
261	C₄×D₄×C₅₃	—	2	1	no	—
262	C₄×D₄×C₅₃	—	2	2	no	—
263	C₄×D₄×C₅₃	—	2	1	no	—
264	C₄×D₄×C₅₃	—	2	1	no	—
265	C₄×D₄×C₅₃	—	2	2	no	—
266	C₄×D₄×C₅₃	—	2	1	no	—
267	C₄×D₄×C₅₃	—	2	2	no	—
268	C₄×D₄×C₅₃	—	2	1	no	—
269	C₄×D₄×C₅₃	—	2	2	no	—
270	C₄×D₄×C₅₃	—	2	1	no	—
271	C₄×D₄×C₅₃	—	2	2	no	—
272	#117×C₅₃	C₂³	1	2	yes	—
273	#117×C₅₃	C₂³	1	2	yes	—
274	#117×C₅₃	C₂³	1	1	yes	characteristic
275	#117×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
277	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
278	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
280	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
282	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
283	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
284	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
285	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
286	#107×C₅₃	C₂³	1	1	yes	characteristic
287	#107×C₅₃	C₂³	1	2	yes	—
288	#107×C₅₃	C₂³	1	2	yes	—
289	#107×C₅₃	C₂³	1	2	yes	—
290	#107×C₅₃	C₂³	1	1	yes	characteristic
291	#107×C₅₃	C₂³	1	2	yes	—
292	#106×C₅₃	C₂³	1	1	yes	characteristic
293	#106×C₅₃	C₂³	1	2	yes	—
294	#106×C₅₃	C₂³	1	2	yes	—
295	#106×C₅₃	C₂³	1	1	yes	characteristic
296	#103×C₅₃	C₂³	1	1	yes	characteristic
297	#103×C₅₃	C₂³	1	1	yes	characteristic
298	#103×C₅₃	C₂³	1	2	yes	—
299	#103×C₅₃	C₂³	1	2	yes	—
300	#103×C₅₃	C₂³	1	2	yes	—
301	#103×C₅₃	C₂³	1	2	yes	—
302	#103×C₅₃	C₂³	1	2	yes	—
303	#103×C₅₃	C₂³	1	1	yes	characteristic
304	#103×C₅₃	C₂³	1	1	yes	characteristic
305	#103×C₅₃	C₂³	1	2	yes	—
306	#102×C₅₃	C₂³	1	2	yes	—
307	#102×C₅₃	C₂³	1	2	yes	—
308	#102×C₅₃	C₂³	1	1	yes	characteristic
309	#102×C₅₃	C₂³	1	1	yes	characteristic
310	#102×C₅₃	C₂³	1	1	yes	characteristic
311	#102×C₅₃	C₂³	1	1	yes	characteristic
312	#102×C₅₃	C₂³	1	2	yes	—
313	#102×C₅₃	C₂³	1	2	yes	—
314	#102×C₅₃	C₂³	1	2	yes	—
315	#102×C₅₃	C₂³	1	2	yes	—
316	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
319	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
320	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
321	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
322	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
323	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
324	C₂⁴×C₅₃	—	2	2	no	—
325	C₂⁴×C₅₃	—	2	1	no	—
326	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
327	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
328	#41×C₅₃	—	2	2	no	—
329	#41×C₅₃	—	2	2	no	—
330	#41×C₅₃	—	2	2	no	—
331	#41×C₅₃	—	2	2	no	—
332	#41×C₅₃	—	2	2	no	—
333	#41×C₅₃	—	2	2	no	—
334	#41×C₅₃	—	2	2	no	—
335	#41×C₅₃	—	2	2	no	—
336	#41×C₅₃	—	4	2	no	—
337	#41×C₅₃	—	4	2	no	—
338	#41×C₅₃	—	4	4	no	—
339	#41×C₅₃	—	4	2	no	—
340	#41×C₅₃	—	4	2	no	—
341	#41×C₅₃	—	4	2	no	—
342	#41×C₅₃	—	4	2	no	—
343	#41×C₅₃	—	4	2	no	—
344	#41×C₅₃	—	4	2	no	—
345	#41×C₅₃	—	4	8	no	—
346	#41×C₅₃	—	4	4	no	—
347	#41×C₅₃	—	4	4	no	—
348	C₂×Q₈×C₅₃	—	2	2	no	—
349	C₂×Q₈×C₅₃	—	2	1	no	—
350	C₂×Q₈×C₅₃	—	2	2	no	—
351	C₂×Q₈×C₅₃	—	2	2	no	—
352	C₂×Q₈×C₅₃	—	4	2	no	—
353	C₂×Q₈×C₅₃	—	4	2	no	—
354	C₂×Q₈×C₅₃	—	4	2	no	—
355	C₂×Q₈×C₅₃	—	4	4	no	—
356	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
357	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
358	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
359	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
360	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₅₃	—	2	1	no	—
363	C₂×D₄×C₅₃	—	2	1	no	—
364	C₂×D₄×C₅₃	—	2	2	no	—
365	C₂×D₄×C₅₃	—	2	2	no	—
366	C₂×D₄×C₅₃	—	2	1	no	—
367	C₂×D₄×C₅₃	—	2	2	no	—
368	C₂×D₄×C₅₃	—	2	1	no	—
369	C₂×D₄×C₅₃	—	2	2	no	—
370	C₂×D₄×C₅₃	—	2	1	no	—
371	C₂×D₄×C₅₃	—	2	2	no	—
372	C₂×D₄×C₅₃	—	2	1	no	—
373	C₂×D₄×C₅₃	—	2	2	no	—
374	C₂×D₄×C₅₃	—	2	2	no	—
375	C₂×D₄×C₅₃	—	2	2	no	—
376	C₂×D₄×C₅₃	—	2	2	no	—
377	C₂×D₄×C₅₃	—	2	1	no	—
378	C₂×D₄×C₅₃	—	2	2	no	—
379	C₂×D₄×C₅₃	—	2	2	no	—
380	C₂×D₄×C₅₃	—	4	2	no	—
381	C₂×D₄×C₅₃	—	4	2	no	—
382	C₂×D₄×C₅₃	—	4	2	no	—
383	C₂×D₄×C₅₃	—	4	4	no	—
384	C₂×D₄×C₅₃	—	4	8	no	—
385	C₂×D₄×C₅₃	—	4	4	no	—
386	C₂×D₄×C₅₃	—	8	2	no	—
387	C₂×D₄×C₅₃	—	8	4	no	—
388	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
389	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
390	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
391	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
392	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
393	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
394	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
395	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
397	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₅₃	—	2	2	no	—
399	C₂²×C₄×C₅₃	—	2	2	no	—
400	C₂²×C₄×C₅₃	—	2	2	no	—
401	C₂²×C₄×C₅₃	—	2	1	no	—
402	C₂²×C₄×C₅₃	—	2	2	no	—
403	C₂²×C₄×C₅₃	—	2	1	no	—
404	C₂²×C₄×C₅₃	—	2	2	no	—
405	C₂²×C₄×C₅₃	—	2	1	no	—
406	C₂²×C₄×C₅₃	—	2	2	no	—
407	C₂²×C₄×C₅₃	—	2	1	no	—
408	C₂²×C₄×C₅₃	—	2	2	no	—
409	C₂²×C₄×C₅₃	—	2	1	no	—
410	C₂²×C₄×C₅₃	—	4	2	no	—
411	C₂²×C₄×C₅₃	—	4	2	no	—
412	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
413	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
414	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
415	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
416	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
417	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
418	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
419	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
420	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
423	Q₁₆×C₅₃	—	4	1	no	—
424	Q₁₆×C₅₃	—	4	2	no	—
425	SD₁₆×C₅₃	—	4	2	no	—
426	SD₁₆×C₅₃	—	4	2	no	—
427	SD₁₆×C₅₃	—	4	1	no	—
428	SD₁₆×C₅₃	—	4	1	no	—
429	SD₁₆×C₅₃	—	4	2	no	—
430	SD₁₆×C₅₃	—	4	2	no	—
431	D₈×C₅₃	—	4	1	no	—
432	D₈×C₅₃	—	4	2	no	—
433	M₁₆×C₅₃	—	2	2	no	—
434	M₁₆×C₅₃	—	2	2	no	—
435	M₁₆×C₅₃	—	4	1	no	—
436	M₁₆×C₅₃	—	4	1	no	—
437	M₁₆×C₅₃	—	4	1	no	—
438	M₁₆×C₅₃	—	4	1	no	—
439	M₁₆×C₅₃	—	4	2	no	—
440	C₂×C₈×C₅₃	—	2	2	no	—
441	C₂×C₈×C₅₃	—	2	2	no	—
442	C₂×C₈×C₅₃	—	4	2	no	—
443	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
444	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
447	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
448	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
449	C₄⋊C₄×C₅₃	—	2	2	no	—
450	C₄⋊C₄×C₅₃	—	2	1	no	—
451	C₄⋊C₄×C₅₃	—	2	2	no	—
452	C₄⋊C₄×C₅₃	—	2	2	no	—
453	C₄⋊C₄×C₅₃	—	2	2	no	—
454	C₄⋊C₄×C₅₃	—	2	2	no	—
455	C₄⋊C₄×C₅₃	—	2	1	no	—
456	C₄⋊C₄×C₅₃	—	2	2	no	—
457	C₄⋊C₄×C₅₃	—	2	1	no	—
458	C₄⋊C₄×C₅₃	—	2	1	no	—
459	C₄⋊C₄×C₅₃	—	2	2	no	—
460	C₄⋊C₄×C₅₃	—	2	1	no	—
461	C₄⋊C₄×C₅₃	—	2	2	no	—
462	C₄⋊C₄×C₅₃	—	2	1	no	—
463	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
464	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
465	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
466	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
467	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
468	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
469	C₂²⋊C₄×C₅₃	—	2	2	no	—
470	C₂²⋊C₄×C₅₃	—	2	1	no	—
471	C₂²⋊C₄×C₅₃	—	2	2	no	—
472	C₂²⋊C₄×C₅₃	—	2	2	no	—
473	C₂²⋊C₄×C₅₃	—	2	2	no	—
474	C₂²⋊C₄×C₅₃	—	2	2	no	—
475	C₂²⋊C₄×C₅₃	—	2	1	no	—
476	C₂²⋊C₄×C₅₃	—	2	2	no	—
477	C₂²⋊C₄×C₅₃	—	2	1	no	—
478	C₂²⋊C₄×C₅₃	—	2	1	no	—
479	C₂²⋊C₄×C₅₃	—	2	2	no	—
480	C₂²⋊C₄×C₅₃	—	2	1	no	—
481	C₂²⋊C₄×C₅₃	—	2	2	no	—
482	C₂²⋊C₄×C₅₃	—	2	1	no	—
483	C₂²⋊C₄×C₅₃	—	2	2	no	—
484	C₂²⋊C₄×C₅₃	—	2	1	no	—
485	C₂²⋊C₄×C₅₃	—	2	2	no	—
486	C₂²⋊C₄×C₅₃	—	2	2	no	—
487	C₂²⋊C₄×C₅₃	—	2	2	no	—
488	C₂²⋊C₄×C₅₃	—	2	1	no	—
489	C₂²⋊C₄×C₅₃	—	2	2	no	—
490	C₂²⋊C₄×C₅₃	—	2	1	no	—
491	C₂²⋊C₄×C₅₃	—	2	2	no	—
492	C₂²⋊C₄×C₅₃	—	2	1	no	—
493	C₄²×C₅₃	—	2	2	no	—
494	C₄²×C₅₃	—	2	1	no	—
495	C₄²×C₅₃	—	2	2	no	—
496	C₄²×C₅₃	—	2	1	no	—
497	C₂³×C₅₃	—	2	2	no	—
498	C₂³×C₅₃	—	2	1	no	—
499	C₂³×C₅₃	—	2	2	no	—
500	C₂³×C₅₃	—	2	1	no	—
501	C₂³×C₅₃	—	4	2	no	—
502	C₂³×C₅₃	—	4	1	no	—
503	C₂³×C₅₃	—	4	2	no	—
504	C₂³×C₅₃	—	4	1	no	—
505	C₂³×C₅₃	—	4	2	no	—
506	C₂³×C₅₃	—	4	4	no	—
507	C₂³×C₅₃	—	4	2	no	—
508	C₂³×C₅₃	—	8	1	no	—
509	C₂³×C₅₃	—	8	2	no	—
510	C₂³×C₅₃	—	8	1	no	—
511	C₂³×C₅₃	—	8	2	no	—
512	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
513	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
514	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
515	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
516	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
517	Q₈×C₅₃	—	2	2	no	—
518	Q₈×C₅₃	—	2	2	no	—
519	Q₈×C₅₃	—	2	2	no	—
520	Q₈×C₅₃	—	2	2	no	—
521	Q₈×C₅₃	—	2	1	no	—
522	Q₈×C₅₃	—	2	1	no	—
523	Q₈×C₅₃	—	2	1	no	—
524	Q₈×C₅₃	—	2	1	no	—
525	Q₈×C₅₃	—	4	2	no	—
526	Q₈×C₅₃	—	4	4	no	—
527	Q₈×C₅₃	—	4	2	no	—
528	D₄×C₅₃	—	2	4	no	—
529	D₄×C₅₃	—	2	4	no	—
530	D₄×C₅₃	—	2	2	no	—
531	D₄×C₅₃	—	2	2	no	—
532	D₄×C₅₃	—	2	2	no	—
533	D₄×C₅₃	—	2	2	no	—
534	D₄×C₅₃	—	2	1	no	—
535	D₄×C₅₃	—	2	1	no	—
536	D₄×C₅₃	—	2	1	no	—
537	D₄×C₅₃	—	2	1	no	—
538	D₄×C₅₃	—	4	2	no	—
539	D₄×C₅₃	—	4	2	no	—
540	D₄×C₅₃	—	4	2	no	—
541	D₄×C₅₃	—	4	4	no	—
542	D₄×C₅₃	—	4	2	no	—
543	D₄×C₅₃	—	4	4	no	—
544	D₄×C₅₃	—	4	4	no	—
545	D₄×C₅₃	—	4	2	no	—
546	D₄×C₅₃	—	4	4	no	—
547	D₄×C₅₃	—	4	2	no	—
548	D₄×C₅₃	—	4	2	no	—
549	D₄×C₅₃	—	4	2	no	—
550	D₄×C₅₃	—	8	2	no	—
551	D₄×C₅₃	—	8	1	no	—
552	D₄×C₅₃	—	8	2	no	—
553	D₄×C₅₃	—	8	1	no	—
554	D₄×C₅₃	—	8	2	no	—
555	D₄×C₅₃	—	8	2	no	—
556	D₄×C₅₃	—	8	2	no	—
557	C₂×C₄×C₅₃	—	2	2	no	—
558	C₂×C₄×C₅₃	—	2	2	no	—
559	C₂×C₄×C₅₃	—	2	2	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	1	no	—
563	C₂×C₄×C₅₃	—	2	1	no	—
564	C₂×C₄×C₅₃	—	2	2	no	—
565	C₂×C₄×C₅₃	—	2	2	no	—
566	C₂×C₄×C₅₃	—	2	2	no	—
567	C₂×C₄×C₅₃	—	2	2	no	—
568	C₂×C₄×C₅₃	—	2	1	no	—
569	C₂×C₄×C₅₃	—	2	2	no	—
570	C₂×C₄×C₅₃	—	2	1	no	—
571	C₂×C₄×C₅₃	—	2	1	no	—
572	C₂×C₄×C₅₃	—	2	2	no	—
573	C₂×C₄×C₅₃	—	2	1	no	—
574	C₂×C₄×C₅₃	—	2	2	no	—
575	C₂×C₄×C₅₃	—	2	1	no	—
576	C₂×C₄×C₅₃	—	2	1	no	—
577	C₂×C₄×C₅₃	—	4	2	no	—
578	C₂×C₄×C₅₃	—	4	2	no	—
579	C₂×C₄×C₅₃	—	4	2	no	—
580	C₂×C₄×C₅₃	—	4	4	no	—
581	C₂×C₄×C₅₃	—	4	4	no	—
582	C₂×C₄×C₅₃	—	4	4	no	—
583	C₂×C₄×C₅₃	—	4	2	no	—
584	C₂×C₄×C₅₃	—	4	2	no	—
585	C₂×C₄×C₅₃	—	4	2	no	—
586	C₂×C₄×C₅₃	—	8	1	no	—
587	C₂×C₄×C₅₃	—	8	2	no	—
588	C₂×C₄×C₅₃	—	8	1	no	—
589	C₂×C₄×C₅₃	—	8	2	no	—
590	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
591	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
592	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
595	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
596	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
597	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
598	C₈×C₅₃	—	2	1	no	—
599	C₈×C₅₃	—	2	1	no	—
600	C₈×C₅₃	—	2	1	no	—
601	C₈×C₅₃	—	2	1	no	—
602	C₈×C₅₃	—	2	2	no	—
603	C₈×C₅₃	—	2	2	no	—
604	#60772	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
605	C₂²×C₅₃	—	2	1	no	—
606	C₂²×C₅₃	—	2	1	no	—
607	C₂²×C₅₃	—	2	2	no	—
608	C₂²×C₅₃	—	2	2	no	—
609	C₂²×C₅₃	—	2	1	no	—
610	C₂²×C₅₃	—	2	1	no	—
611	C₂²×C₅₃	—	2	1	no	—
612	C₂²×C₅₃	—	2	2	no	—
613	C₂²×C₅₃	—	2	1	no	—
614	C₂²×C₅₃	—	2	2	no	—
615	C₂²×C₅₃	—	2	1	no	—
616	C₂²×C₅₃	—	2	1	no	—
617	C₂²×C₅₃	—	2	2	no	—
618	C₂²×C₅₃	—	2	2	no	—
619	C₂²×C₅₃	—	4	2	no	—
620	C₂²×C₅₃	—	4	1	no	—
621	C₂²×C₅₃	—	4	1	no	—
622	C₂²×C₅₃	—	4	1	no	—
623	C₂²×C₅₃	—	4	2	no	—
624	C₂²×C₅₃	—	4	1	no	—
625	C₂²×C₅₃	—	4	1	no	—
626	C₂²×C₅₃	—	4	2	no	—
627	C₂²×C₅₃	—	4	1	no	—
628	C₂²×C₅₃	—	8	2	no	—
629	C₂²×C₅₃	—	8	4	no	—
630	C₂²×C₅₃	—	16	2	no	—
631	C₂²×C₅₃	—	16	4	no	—
632	C₂²×C₅₃	#534	1	2	yes	—
633	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
634	C₄×C₅₃	—	2	1	no	—
635	C₄×C₅₃	—	2	1	no	—
636	C₄×C₅₃	—	2	2	no	—
637	C₄×C₅₃	—	2	2	no	—
638	C₄×C₅₃	—	4	2	no	—
639	C₄×C₅₃	—	4	1	no	—
640	C₄×C₅₃	—	4	2	no	—
641	C₄×C₅₃	—	4	1	no	—
642	C₄×C₅₃	—	4	1	no	—
643	C₄×C₅₃	—	4	1	no	—
644	C₄×C₅₃	—	4	1	no	—
645	C₄×C₅₃	—	4	2	no	—
646	C₄×C₅₃	—	4	1	no	—
647	C₄×C₅₃	#534	1	2	yes	—
648	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
649	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
650	#3489	C₂×C₅₃	1	1	yes	characteristic, complemented
651	#3488	C₂×C₅₃	1	1	yes	characteristic, complemented
652	#3203	C₂×C₅₃	1	2	yes	complemented
653	#3201	C₂×C₅₃	1	2	yes	complemented
654	#3200	C₂×C₅₃	1	2	yes	complemented
655	#3198	C₂×C₅₃	1	2	yes	complemented
656	#3197	C₂×C₅₃	1	2	yes	complemented
657	#3196	C₂×C₅₃	1	2	yes	complemented
658	#3194	C₂×C₅₃	1	2	yes	complemented
659	#3193	C₂×C₅₃	1	2	yes	complemented
660	#3098	C₂×C₅₃	1	1	yes	characteristic, complemented
661	#3098	C₂×C₅₃	1	1	yes	characteristic, complemented
662	#3097	C₂×C₅₃	1	1	yes	characteristic, complemented
663	#3096	C₂×C₅₃	1	1	yes	characteristic, complemented
664	#3056	C₂×C₅₃	1	1	yes	characteristic, complemented
665	#3055	C₂×C₅₃	1	1	yes	characteristic, complemented
666	#3054	C₂×C₅₃	1	1	yes	characteristic, complemented
667	C₂×#468	C₂×C₅₃	1	1	yes	characteristic, complemented
668	#3013	C₂×C₅₃	1	1	yes	characteristic, complemented
669	#3012	C₂×C₅₃	1	1	yes	characteristic, complemented
670	#3010	C₂×C₅₃	1	1	yes	characteristic, complemented
671	#3009	C₂×C₅₃	1	1	yes	characteristic, complemented
672	#2879	C₂×C₅₃	1	1	yes	characteristic, complemented
673	C₂×C₅₃	—	2	2	no	—
674	C₂×C₅₃	—	4	2	no	—
675	C₂×C₅₃	—	4	1	no	—
676	C₂×C₅₃	—	4	1	no	—
677	C₂×C₅₃	—	4	2	no	—
678	C₂×C₅₃	—	8	1	no	—
679	C₂×C₅₃	—	8	2	no	—
680	C₂×C₅₃	—	8	1	no	—
681	C₂×C₅₃	C₂×#534	1	1	yes	characteristic
682	C₂×C₅₃	#3585	1	1	yes	characteristic
683	C₂×C₅₃	#3586	1	1	yes	characteristic
684	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic, complemented
685	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
686	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
687	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
688	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
691	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#550	—	2	1	no	—
694	D₄×Q₈	—	2	1	no	—
695	#548	—	2	1	no	—
696	#548	—	2	1	no	—
697	#547	—	2	2	no	—
698	#547	—	2	1	no	—
699	#546	—	2	2	no	—
700	#546	—	2	1	no	—
701	#546	—	2	2	no	—
702	#546	—	2	1	no	—
703	D₄²	—	2	2	no	—
704	D₄²	—	2	1	no	—
705	#537	C₂²×C₅₃	1	1	yes	characteristic
706	#537	C₂²×C₅₃	1	1	yes	characteristic
707	#537	C₂²×C₅₃	1	2	yes	—
708	#537	C₂²×C₅₃	1	2	yes	complemented
709	#536	C₂²×C₅₃	1	1	yes	characteristic
710	#536	C₂²×C₅₃	1	2	yes	complemented
711	#535	C₂²×C₅₃	1	1	yes	characteristic
712	#535	C₂²×C₅₃	1	2	yes	—
713	#525	C₂²×C₅₃	1	2	yes	—
714	#525	C₂²×C₅₃	1	1	yes	characteristic
715	#525	C₂²×C₅₃	1	2	yes	complemented
716	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
717	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
718	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
719	C₂×#121	C₂²×C₅₃	1	2	yes	—
720	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
721	#520	C₂²×C₅₃	1	1	yes	characteristic
722	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	#485	C₂²×C₅₃	1	2	yes	complemented
724	#485	C₂²×C₅₃	1	2	yes	complemented
725	#485	C₂²×C₅₃	1	2	yes	complemented
726	#485	C₂²×C₅₃	1	2	yes	complemented
727	#484	C₂²×C₅₃	1	2	yes	complemented
728	#484	C₂²×C₅₃	1	2	yes	complemented
729	#484	C₂²×C₅₃	1	2	yes	complemented
730	#483	C₂²×C₅₃	1	2	yes	complemented
731	#482	C₂²×C₅₃	1	2	yes	complemented
732	#482	C₂²×C₅₃	1	2	yes	complemented
733	#482	C₂²×C₅₃	1	2	yes	complemented
734	#482	C₂²×C₅₃	1	2	yes	complemented
735	#481	C₂²×C₅₃	1	2	yes	complemented
736	#480	C₂²×C₅₃	1	2	yes	complemented
737	#480	C₂²×C₅₃	1	2	yes	complemented
738	#480	C₂²×C₅₃	1	2	yes	complemented
739	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
740	#470	C₂²×C₅₃	1	2	yes	complemented
741	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
742	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
743	#469	C₂²×C₅₃	1	2	yes	complemented
744	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
746	#468	C₂²×C₅₃	1	2	yes	complemented
747	#468	C₂²×C₅₃	1	2	yes	complemented
748	#468	C₂²×C₅₃	1	2	yes	complemented
749	#468	C₂²×C₅₃	1	2	yes	complemented
750	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
751	#468	C₂²×C₅₃	1	2	yes	complemented
752	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
753	#468	C₂²×C₅₃	1	2	yes	complemented
754	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
755	#467	C₂²×C₅₃	1	2	yes	complemented
756	#466	C₂²×C₅₃	1	2	yes	complemented
757	#465	C₂²×C₅₃	1	2	yes	complemented
758	#465	C₂²×C₅₃	1	2	yes	complemented
759	#452	C₂²×C₅₃	1	2	yes	complemented
760	#452	C₂²×C₅₃	1	2	yes	complemented
761	#452	C₂²×C₅₃	1	2	yes	complemented
762	#452	C₂²×C₅₃	1	2	yes	complemented
763	#451	C₂²×C₅₃	1	2	yes	complemented
764	#450	C₂²×C₅₃	1	2	yes	complemented
765	#450	C₂²×C₅₃	1	2	yes	complemented
766	#450	C₂²×C₅₃	1	2	yes	complemented
767	#449	C₂²×C₅₃	1	2	yes	complemented
768	#449	C₂²×C₅₃	1	2	yes	complemented
769	#449	C₂²×C₅₃	1	2	yes	complemented
770	#449	C₂²×C₅₃	1	2	yes	complemented
771	#448	C₂²×C₅₃	1	2	yes	complemented
772	#448	C₂²×C₅₃	1	2	yes	complemented
773	#448	C₂²×C₅₃	1	2	yes	complemented
774	#447	C₂²×C₅₃	1	2	yes	complemented
775	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
776	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
777	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
778	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
779	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
780	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
781	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
782	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
783	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
784	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
785	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
786	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
787	#408	C₂²×C₅₃	1	1	yes	characteristic
788	#408	C₂²×C₅₃	1	1	yes	characteristic
789	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
790	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
791	#408	C₂²×C₅₃	1	2	yes	complemented
792	#408	C₂²×C₅₃	1	2	yes	complemented
793	#407	C₂²×C₅₃	1	2	yes	complemented
794	#407	C₂²×C₅₃	1	2	yes	complemented
795	C₅₃	#60772	1	1	yes	characteristic, direct product factor, Sylow
796	2₋¹⁺⁴	—	4	2	no	—
797	2₋¹⁺⁴	—	4	2	no	—
798	H(5,𝔽₂)	—	4	2	no	—
799	H(5,𝔽₂)	—	4	2	no	—
800	C₂×#41	—	2	1	no	—
801	C₂×#41	—	2	2	no	—
802	C₂×#41	—	2	1	no	—
803	C₂×#41	—	4	2	no	—
804	C₂×#41	—	4	2	no	—
805	C₂×#41	D₄×C₅₃	1	2	yes	—
806	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
807	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
808	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
809	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
810	C₂×#41	C₂³×C₅₃	1	2	yes	—
811	C₂×#41	C₂³×C₅₃	1	2	yes	—
812	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
813	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
814	C₂×#41	C₂³×C₅₃	1	2	yes	—
815	C₂²×Q₈	—	2	1	no	—
816	C₂²×Q₈	D₄×C₅₃	1	1	yes	characteristic
817	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
818	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
819	C₂²×D₄	—	2	1	no	—
820	C₂²×D₄	—	2	2	no	—
821	C₂²×D₄	—	2	2	no	—
822	C₂²×D₄	—	2	1	no	—
823	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
824	C₂²×D₄	D₄×C₅₃	1	2	yes	—
825	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
826	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
827	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
828	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
829	#137	—	4	2	no	—
830	AGL(1,ℤ/8)	—	4	2	no	—
831	#135	—	4	2	no	—
832	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
833	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
834	C₂×SD₁₆	—	4	2	no	—
835	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
836	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
837	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
838	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
839	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
840	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
841	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
842	C₂×D₈	C₂³×C₅₃	1	2	yes	—
843	C₂×M₁₆	—	4	2	no	—
844	C₂×M₁₆	—	4	2	no	—
845	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
846	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
847	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
848	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
849	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
850	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
851	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
852	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
853	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
854	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
855	C₄⋊Q₈	—	2	1	no	—
856	C₄⋊Q₈	—	2	2	no	—
857	#127	—	2	1	no	—
858	#127	—	2	2	no	—
859	#124	—	2	1	no	—
860	#124	—	2	2	no	—
861	#124	—	2	1	no	—
862	#124	—	2	2	no	—
863	#123	—	2	2	no	—
864	#123	—	2	2	no	—
865	#123	—	2	2	no	—
866	#123	—	2	1	no	—
867	#123	—	2	2	no	—
868	#123	—	2	1	no	—
869	#123	—	2	2	no	—
870	C₂²⋊Q₈	—	2	1	no	—
871	C₂²⋊Q₈	—	2	2	no	—
872	C₂²⋊Q₈	—	2	1	no	—
873	C₂²⋊Q₈	—	2	2	no	—
874	C₂²⋊Q₈	—	2	1	no	—
875	C₂²⋊Q₈	—	2	2	no	—
876	C₂²⋊Q₈	—	2	1	no	—
877	C₂²⋊Q₈	—	2	2	no	—
878	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
879	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
880	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
881	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
882	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
883	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
884	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
885	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
886	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
887	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
888	#121	—	2	2	no	—
889	#121	—	2	2	no	—
890	#121	—	2	2	no	—
891	#121	—	2	1	no	—
892	#121	—	2	2	no	—
893	#121	—	2	2	no	—
894	#121	—	2	1	no	—
895	#121	—	2	2	no	—
896	#121	—	2	2	no	—
897	#121	—	2	2	no	—
898	#121	—	2	1	no	—
899	#121	—	2	2	no	—
900	#121	—	2	1	no	—
901	#121	—	2	2	no	—
902	#121	C₂³×C₅₃	1	1	yes	characteristic
903	#121	C₂³×C₅₃	1	2	yes	—
904	#121	C₂³×C₅₃	1	2	yes	—
905	#121	C₂³×C₅₃	1	2	yes	—
906	#121	C₂³×C₅₃	1	2	yes	—
907	#121	C₂³×C₅₃	1	2	yes	—
908	#121	C₂³×C₅₃	1	1	yes	characteristic
909	#121	C₂³×C₅₃	1	1	yes	characteristic
910	#121	C₂³×C₅₃	1	2	yes	—
911	#121	C₂³×C₅₃	1	1	yes	characteristic
912	#120	—	2	1	no	—
913	#120	—	2	2	no	—
914	#120	—	2	1	no	—
915	#120	—	2	2	no	—
916	#120	—	2	2	no	—
917	#120	—	2	2	no	—
918	#120	—	2	2	no	—
919	C₄×Q₈	—	2	1	no	—
920	C₄×Q₈	—	2	1	no	—
921	C₄×D₄	—	2	2	no	—
922	C₄×D₄	—	2	1	no	—
923	C₄×D₄	—	2	2	no	—
924	C₄×D₄	—	2	1	no	—
925	C₄×D₄	—	2	1	no	—
926	C₄×D₄	—	2	2	no	—
927	C₄×D₄	—	2	1	no	—
928	C₄×D₄	—	2	2	no	—
929	C₄×D₄	—	2	1	no	—
930	C₄×D₄	—	2	2	no	—
931	C₄×D₄	—	2	1	no	—
932	C₄×D₄	—	2	2	no	—
933	#117	C₂³×C₅₃	1	1	yes	characteristic
934	#117	C₂³×C₅₃	1	2	yes	—
935	#117	C₂³×C₅₃	1	1	yes	characteristic
936	#117	C₂³×C₅₃	1	2	yes	—
937	C₂×C₄⋊C₄	—	2	1	no	—
938	C₂×C₄⋊C₄	—	2	2	no	—
939	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
940	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
941	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
943	C₂×C₂²⋊C₄	—	2	1	no	—
944	C₂×C₂²⋊C₄	—	2	2	no	—
945	C₂×C₂²⋊C₄	—	2	1	no	—
946	C₂×C₂²⋊C₄	—	2	2	no	—
947	#107	C₂³×C₅₃	1	2	yes	—
948	#107	C₂³×C₅₃	1	2	yes	—
949	#107	C₂³×C₅₃	1	1	yes	characteristic
950	#107	C₂³×C₅₃	1	1	yes	characteristic
951	#107	C₂³×C₅₃	1	2	yes	—
952	#107	C₂³×C₅₃	1	2	yes	—
953	#106	C₂³×C₅₃	1	1	yes	characteristic
954	#106	C₂³×C₅₃	1	1	yes	characteristic
955	#106	C₂³×C₅₃	1	2	yes	—
956	#106	C₂³×C₅₃	1	2	yes	—
957	#103	C₂³×C₅₃	1	2	yes	—
958	#103	C₂³×C₅₃	1	2	yes	—
959	#103	C₂³×C₅₃	1	1	yes	characteristic
960	#103	C₂³×C₅₃	1	1	yes	characteristic
961	#103	C₂³×C₅₃	1	1	yes	characteristic
962	#103	C₂³×C₅₃	1	1	yes	characteristic
963	#103	C₂³×C₅₃	1	2	yes	—
964	#103	C₂³×C₅₃	1	2	yes	—
965	#103	C₂³×C₅₃	1	2	yes	—
966	#103	C₂³×C₅₃	1	2	yes	—
967	#102	C₂³×C₅₃	1	2	yes	—
968	#102	C₂³×C₅₃	1	2	yes	—
969	#102	C₂³×C₅₃	1	1	yes	characteristic
970	#102	C₂³×C₅₃	1	1	yes	characteristic
971	#102	C₂³×C₅₃	1	1	yes	characteristic
972	#102	C₂³×C₅₃	1	1	yes	characteristic
973	#102	C₂³×C₅₃	1	2	yes	—
974	#102	C₂³×C₅₃	1	2	yes	—
975	#102	C₂³×C₅₃	1	2	yes	—
976	#102	C₂³×C₅₃	1	2	yes	—
977	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
978	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
979	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
980	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
981	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
982	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
983	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
984	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
985	C₂⁴	—	2	2	no	—
986	C₂⁴	—	2	1	no	—
987	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
988	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
989	#41	—	2	2	no	—
990	#41	—	2	2	no	—
991	#41	—	2	2	no	—
992	#41	—	2	2	no	—
993	#41	—	2	2	no	—
994	#41	—	2	2	no	—
995	#41	—	2	2	no	—
996	#41	—	2	2	no	—
997	#41	—	4	2	no	—
998	#41	—	4	2	no	—
999	#41	—	4	4	no	—
1000	#41	—	4	2	no	—
1001	#41	—	4	2	no	—
1002	#41	—	4	2	no	—
1003	#41	—	4	2	no	—
1004	#41	—	4	2	no	—
1005	#41	—	4	2	no	—
1006	#41	—	4	8	no	—
1007	#41	—	4	4	no	—
1008	#41	—	4	4	no	—
1009	C₂×Q₈	—	2	2	no	—
1010	C₂×Q₈	—	2	1	no	—
1011	C₂×Q₈	—	2	2	no	—
1012	C₂×Q₈	—	2	2	no	—
1013	C₂×Q₈	—	4	2	no	—
1014	C₂×Q₈	—	4	2	no	—
1015	C₂×Q₈	—	4	2	no	—
1016	C₂×Q₈	—	4	4	no	—
1017	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1018	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1019	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
1020	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1021	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1022	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1023	C₂×D₄	—	2	1	no	—
1024	C₂×D₄	—	2	1	no	—
1025	C₂×D₄	—	2	2	no	—
1026	C₂×D₄	—	2	2	no	—
1027	C₂×D₄	—	2	1	no	—
1028	C₂×D₄	—	2	2	no	—
1029	C₂×D₄	—	2	1	no	—
1030	C₂×D₄	—	2	1	no	—
1031	C₂×D₄	—	2	2	no	—
1032	C₂×D₄	—	2	2	no	—
1033	C₂×D₄	—	2	1	no	—
1034	C₂×D₄	—	2	2	no	—
1035	C₂×D₄	—	2	2	no	—
1036	C₂×D₄	—	2	2	no	—
1037	C₂×D₄	—	2	2	no	—
1038	C₂×D₄	—	2	1	no	—
1039	C₂×D₄	—	2	2	no	—
1040	C₂×D₄	—	2	2	no	—
1041	C₂×D₄	—	4	2	no	—
1042	C₂×D₄	—	4	2	no	—
1043	C₂×D₄	—	4	2	no	—
1044	C₂×D₄	—	4	4	no	—
1045	C₂×D₄	—	4	8	no	—
1046	C₂×D₄	—	4	4	no	—
1047	C₂×D₄	—	8	2	no	—
1048	C₂×D₄	—	8	4	no	—
1049	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1050	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1051	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1052	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1053	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1054	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1055	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1056	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1057	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1058	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1059	C₂²×C₄	—	2	2	no	—
1060	C₂²×C₄	—	2	2	no	—
1061	C₂²×C₄	—	2	2	no	—
1062	C₂²×C₄	—	2	1	no	—
1063	C₂²×C₄	—	2	2	no	—
1064	C₂²×C₄	—	2	1	no	—
1065	C₂²×C₄	—	2	2	no	—
1066	C₂²×C₄	—	2	1	no	—
1067	C₂²×C₄	—	2	2	no	—
1068	C₂²×C₄	—	2	1	no	—
1069	C₂²×C₄	—	2	2	no	—
1070	C₂²×C₄	—	2	1	no	—
1071	C₂²×C₄	—	4	2	no	—
1072	C₂²×C₄	—	4	2	no	—
1073	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1074	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1075	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1076	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1077	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1078	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1079	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1080	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1081	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1082	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1083	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1084	Q₁₆	—	4	1	no	—
1085	Q₁₆	—	4	2	no	—
1086	SD₁₆	—	4	2	no	—
1087	SD₁₆	—	4	2	no	—
1088	SD₁₆	—	4	1	no	—
1089	SD₁₆	—	4	1	no	—
1090	SD₁₆	—	4	2	no	—
1091	SD₁₆	—	4	2	no	—
1092	D₈	—	4	1	no	—
1093	D₈	—	4	2	no	—
1094	M₁₆	—	2	2	no	—
1095	M₁₆	—	2	2	no	—
1096	M₁₆	—	4	1	no	—
1097	M₁₆	—	4	1	no	—
1098	M₁₆	—	4	1	no	—
1099	M₁₆	—	4	1	no	—
1100	M₁₆	—	4	2	no	—
1101	C₂×C₈	—	2	2	no	—
1102	C₂×C₈	—	2	2	no	—
1103	C₂×C₈	—	4	2	no	—
1104	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1105	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1106	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1107	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1108	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1109	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1110	C₄⋊C₄	—	2	2	no	—
1111	C₄⋊C₄	—	2	1	no	—
1112	C₄⋊C₄	—	2	2	no	—
1113	C₄⋊C₄	—	2	2	no	—
1114	C₄⋊C₄	—	2	2	no	—
1115	C₄⋊C₄	—	2	2	no	—
1116	C₄⋊C₄	—	2	1	no	—
1117	C₄⋊C₄	—	2	2	no	—
1118	C₄⋊C₄	—	2	1	no	—
1119	C₄⋊C₄	—	2	1	no	—
1120	C₄⋊C₄	—	2	2	no	—
1121	C₄⋊C₄	—	2	1	no	—
1122	C₄⋊C₄	—	2	2	no	—
1123	C₄⋊C₄	—	2	1	no	—
1124	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1125	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1126	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1127	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1128	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1129	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1130	C₂²⋊C₄	—	2	2	no	—
1131	C₂²⋊C₄	—	2	1	no	—
1132	C₂²⋊C₄	—	2	2	no	—
1133	C₂²⋊C₄	—	2	2	no	—
1134	C₂²⋊C₄	—	2	2	no	—
1135	C₂²⋊C₄	—	2	2	no	—
1136	C₂²⋊C₄	—	2	1	no	—
1137	C₂²⋊C₄	—	2	2	no	—
1138	C₂²⋊C₄	—	2	1	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	1	no	—
1141	C₂²⋊C₄	—	2	2	no	—
1142	C₂²⋊C₄	—	2	2	no	—
1143	C₂²⋊C₄	—	2	1	no	—
1144	C₂²⋊C₄	—	2	2	no	—
1145	C₂²⋊C₄	—	2	1	no	—
1146	C₂²⋊C₄	—	2	2	no	—
1147	C₂²⋊C₄	—	2	2	no	—
1148	C₂²⋊C₄	—	2	2	no	—
1149	C₂²⋊C₄	—	2	1	no	—
1150	C₂²⋊C₄	—	2	2	no	—
1151	C₂²⋊C₄	—	2	1	no	—
1152	C₂²⋊C₄	—	2	2	no	—
1153	C₂²⋊C₄	—	2	1	no	—
1154	C₄²	—	2	2	no	—
1155	C₄²	—	2	1	no	—
1156	C₄²	—	2	2	no	—
1157	C₄²	—	2	1	no	—
1158	C₂³	—	2	2	no	—
1159	C₂³	—	2	1	no	—
1160	C₂³	—	2	2	no	—
1161	C₂³	—	2	1	no	—
1162	C₂³	—	4	2	no	—
1163	C₂³	—	4	1	no	—
1164	C₂³	—	4	2	no	—
1165	C₂³	—	4	1	no	—
1166	C₂³	—	4	2	no	—
1167	C₂³	—	4	4	no	—
1168	C₂³	—	4	2	no	—
1169	C₂³	—	8	1	no	—
1170	C₂³	—	8	2	no	—
1171	C₂³	—	8	1	no	—
1172	C₂³	—	8	2	no	—
1173	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1174	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1175	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1176	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1177	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1178	Q₈	—	2	2	no	—
1179	Q₈	—	2	2	no	—
1180	Q₈	—	2	2	no	—
1181	Q₈	—	2	1	no	—
1182	Q₈	—	2	2	no	—
1183	Q₈	—	2	1	no	—
1184	Q₈	—	2	1	no	—
1185	Q₈	—	2	1	no	—
1186	Q₈	—	4	2	no	—
1187	Q₈	—	4	4	no	—
1188	Q₈	—	4	2	no	—
1189	D₄	—	2	4	no	—
1190	D₄	—	2	4	no	—
1191	D₄	—	2	2	no	—
1192	D₄	—	2	2	no	—
1193	D₄	—	2	1	no	—
1194	D₄	—	2	2	no	—
1195	D₄	—	2	1	no	—
1196	D₄	—	2	1	no	—
1197	D₄	—	2	2	no	—
1198	D₄	—	2	1	no	—
1199	D₄	—	4	2	no	—
1200	D₄	—	4	2	no	—
1201	D₄	—	4	2	no	—
1202	D₄	—	4	4	no	—
1203	D₄	—	4	2	no	—
1204	D₄	—	4	4	no	—
1205	D₄	—	4	4	no	—
1206	D₄	—	4	2	no	—
1207	D₄	—	4	4	no	—
1208	D₄	—	4	2	no	—
1209	D₄	—	4	2	no	—
1210	D₄	—	4	2	no	—
1211	D₄	—	8	2	no	—
1212	D₄	—	8	1	no	—
1213	D₄	—	8	1	no	—
1214	D₄	—	8	2	no	—
1215	D₄	—	8	2	no	—
1216	D₄	—	8	2	no	—
1217	D₄	—	8	2	no	—
1218	C₂×C₄	—	2	2	no	—
1219	C₂×C₄	—	2	2	no	—
1220	C₂×C₄	—	2	2	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	1	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	2	no	—
1226	C₂×C₄	—	2	2	no	—
1227	C₂×C₄	—	2	2	no	—
1228	C₂×C₄	—	2	2	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	2	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	2	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	2	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	4	2	no	—
1239	C₂×C₄	—	4	2	no	—
1240	C₂×C₄	—	4	2	no	—
1241	C₂×C₄	—	4	4	no	—
1242	C₂×C₄	—	4	4	no	—
1243	C₂×C₄	—	4	4	no	—
1244	C₂×C₄	—	4	2	no	—
1245	C₂×C₄	—	4	2	no	—
1246	C₂×C₄	—	4	2	no	—
1247	C₂×C₄	—	8	1	no	—
1248	C₂×C₄	—	8	2	no	—
1249	C₂×C₄	—	8	1	no	—
1250	C₂×C₄	—	8	2	no	—
1251	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1252	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1253	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1254	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1255	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1256	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1257	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1258	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1259	C₈	—	2	1	no	—
1260	C₈	—	2	1	no	—
1261	C₈	—	2	1	no	—
1262	C₈	—	2	1	no	—
1263	C₈	—	2	2	no	—
1264	C₈	—	2	2	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	2	no	—
1268	C₂²	—	2	2	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	2	no	—
1274	C₂²	—	2	2	no	—
1275	C₂²	—	2	1	no	—
1276	C₂²	—	2	1	no	—
1277	C₂²	—	2	2	no	—
1278	C₂²	—	2	2	no	—
1279	C₂²	—	4	2	no	—
1280	C₂²	—	4	1	no	—
1281	C₂²	—	4	1	no	—
1282	C₂²	—	4	1	no	—
1283	C₂²	—	4	2	no	—
1284	C₂²	—	4	1	no	—
1285	C₂²	—	4	1	no	—
1286	C₂²	—	4	2	no	—
1287	C₂²	—	4	1	no	—
1288	C₂²	—	8	2	no	—
1289	C₂²	—	8	4	no	—
1290	C₂²	—	16	2	no	—
1291	C₂²	—	16	4	no	—
1292	C₂²	C₅₃×#534	1	2	yes	—
1293	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1294	C₄	—	2	1	no	—
1295	C₄	—	2	1	no	—
1296	C₄	—	2	2	no	—
1297	C₄	—	2	2	no	—
1298	C₄	—	4	2	no	—
1299	C₄	—	4	1	no	—
1300	C₄	—	4	2	no	—
1301	C₄	—	4	1	no	—
1302	C₄	—	4	1	no	—
1303	C₄	—	4	1	no	—
1304	C₄	—	4	1	no	—
1305	C₄	—	4	2	no	—
1306	C₄	—	4	1	no	—
1307	C₄	C₅₃×#534	1	2	yes	—
1308	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1309	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1310	C₂	—	2	2	no	—
1311	C₂	—	4	1	no	—
1312	C₂	—	4	2	no	—
1313	C₂	—	4	2	no	—
1314	C₂	—	4	1	no	—
1315	C₂	—	8	2	no	—
1316	C₂	—	8	1	no	—
1317	C₂	—	8	1	no	—
1318	C₂	C₂×C₅₃×#534	1	1	yes	characteristic
1319	C₂	C₅₃×#3585	1	1	yes	characteristic
1320	C₂	C₅₃×#3586	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 ◁ C₂²×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3489	C₂	semidirect
2. C₅₃×#3488	C₂	semidirect
3. C₅₃×#3203	C₂	semidirect
4. C₅₃×#3201	C₂	semidirect
5. C₅₃×#3200	C₂	semidirect
6. C₅₃×#3198	C₂	semidirect
7. C₅₃×#3197	C₂	semidirect
8. C₅₃×#3196	C₂	semidirect
9. C₅₃×#3194	C₂	semidirect
10. C₅₃×#3193	C₂	semidirect
11. C₅₃×#3098	C₂	semidirect
12. C₅₃×#3098	C₂	semidirect
13. C₅₃×#3097	C₂	semidirect
14. C₅₃×#3096	C₂	semidirect
15. C₅₃×#3056	C₂	semidirect
16. C₅₃×#3055	C₂	semidirect
17. C₅₃×#3054	C₂	semidirect
18. C₂×C₅₃×#468	C₂	semidirect
19. C₅₃×#3013	C₂	semidirect
20. C₅₃×#3012	C₂	semidirect
21. C₅₃×#3010	C₂	semidirect
22. C₅₃×#3009	C₂	semidirect
23. C₅₃×#2879	C₂	semidirect
24. C₂×2₋¹⁺⁴×C₅₃	C₂²	semidirect
27. C₂×#137×C₅₃	C₂²	semidirect
28. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
29. C₂×#135×C₅₃	C₂²	semidirect
30. C₂²×SD₁₆×C₅₃	C₂²	semidirect
31. C₂²×M₁₆×C₅₃	C₂²	semidirect
32. C₂²×M₁₆×C₅₃	C₂²	semidirect
48. C₅₃×#537	C₂²	semidirect
50. C₅₃×#536	C₂²	semidirect
55. C₅₃×#525	C₂²	semidirect
56. C₅₃×#525	C₂²	semidirect
57. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
58. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
62. C₅₃×#520	C₂²	semidirect
63. C₅₃×#485	C₂²	semidirect
64. C₅₃×#485	C₂²	semidirect
65. C₅₃×#485	C₂²	semidirect
66. C₅₃×#485	C₂²	semidirect
67. C₅₃×#484	C₂²	semidirect
68. C₅₃×#484	C₂²	semidirect
69. C₅₃×#484	C₂²	semidirect
70. C₅₃×#483	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#482	C₂²	semidirect
73. C₅₃×#482	C₂²	semidirect
74. C₅₃×#482	C₂²	semidirect
75. C₅₃×#481	C₂²	semidirect
76. C₅₃×#480	C₂²	semidirect
77. C₅₃×#480	C₂²	semidirect
78. C₅₃×#480	C₂²	semidirect
79. C₅₃×#470	C₂²	semidirect
80. C₅₃×#470	C₂²	semidirect
81. C₅₃×#470	C₂²	semidirect
82. C₅₃×#469	C₂²	semidirect
83. C₅₃×#469	C₂²	semidirect
84. C₅₃×#469	C₂²	semidirect
85. C₅₃×#468	C₂²	semidirect
86. C₅₃×#468	C₂²	semidirect
87. C₅₃×#468	C₂²	semidirect
88. C₅₃×#468	C₂²	semidirect
89. C₅₃×#468	C₂²	semidirect
90. C₅₃×#468	C₂²	semidirect
91. C₅₃×#468	C₂²	semidirect
92. C₅₃×#468	C₂²	semidirect
93. C₅₃×#468	C₂²	semidirect
94. C₅₃×#468	C₂²	semidirect
95. C₅₃×#467	C₂²	semidirect
96. C₅₃×#466	C₂²	semidirect
97. C₅₃×#465	C₂²	semidirect
98. C₅₃×#465	C₂²	semidirect
99. C₅₃×#452	C₂²	semidirect
100. C₅₃×#452	C₂²	semidirect
101. C₅₃×#452	C₂²	semidirect
102. C₅₃×#452	C₂²	semidirect
103. C₅₃×#451	C₂²	semidirect
104. C₅₃×#450	C₂²	semidirect
105. C₅₃×#450	C₂²	semidirect
106. C₅₃×#450	C₂²	semidirect
107. C₅₃×#449	C₂²	semidirect
108. C₅₃×#449	C₂²	semidirect
109. C₅₃×#449	C₂²	semidirect
110. C₅₃×#449	C₂²	semidirect
111. C₅₃×#448	C₂²	semidirect
112. C₅₃×#448	C₂²	semidirect
113. C₅₃×#448	C₂²	semidirect
114. C₅₃×#447	C₂²	semidirect
115. C₅₃×#428	C₂²	semidirect
116. C₅₃×#428	C₂²	semidirect
117. C₅₃×#427	C₂²	semidirect
118. C₂×#107×C₅₃	C₂²	semidirect
119. C₅₃×#419	C₂²	semidirect
120. C₅₃×#418	C₂²	semidirect
121. C₅₃×#417	C₂²	semidirect
122. C₅₃×#417	C₂²	semidirect
123. C₅₃×#416	C₂²	semidirect
124. C₅₃×#416	C₂²	semidirect
125. C₂×#103×C₅₃	C₂²	semidirect
126. C₂×#102×C₅₃	C₂²	semidirect
129. C₅₃×#408	C₂²	semidirect
130. C₅₃×#408	C₂²	semidirect
131. C₅₃×#408	C₂²	semidirect
132. C₅₃×#408	C₂²	semidirect
133. C₅₃×#407	C₂²	semidirect
134. C₅₃×#407	C₂²	semidirect
604. #60772	C₅₃	direct (N × H)
650. #3489	C₂×C₅₃	semidirect
651. #3488	C₂×C₅₃	semidirect
652. #3203	C₂×C₅₃	semidirect
653. #3201	C₂×C₅₃	semidirect
654. #3200	C₂×C₅₃	semidirect
655. #3198	C₂×C₅₃	semidirect
656. #3197	C₂×C₅₃	semidirect
657. #3196	C₂×C₅₃	semidirect
658. #3194	C₂×C₅₃	semidirect
659. #3193	C₂×C₅₃	semidirect
660. #3098	C₂×C₅₃	semidirect
661. #3098	C₂×C₅₃	semidirect
662. #3097	C₂×C₅₃	semidirect
663. #3096	C₂×C₅₃	semidirect
664. #3056	C₂×C₅₃	semidirect
665. #3055	C₂×C₅₃	semidirect
666. #3054	C₂×C₅₃	semidirect
667. C₂×#468	C₂×C₅₃	semidirect
668. #3013	C₂×C₅₃	semidirect
669. #3012	C₂×C₅₃	semidirect
670. #3010	C₂×C₅₃	semidirect
671. #3009	C₂×C₅₃	semidirect
672. #2879	C₂×C₅₃	semidirect
684. C₂×2₋¹⁺⁴	C₂²×C₅₃	semidirect
687. C₂×#137	C₂²×C₅₃	semidirect
688. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
689. C₂×#135	C₂²×C₅₃	semidirect
690. C₂²×SD₁₆	C₂²×C₅₃	semidirect
691. C₂²×M₁₆	C₂²×C₅₃	semidirect
692. C₂²×M₁₆	C₂²×C₅₃	semidirect
708. #537	C₂²×C₅₃	semidirect
710. #536	C₂²×C₅₃	semidirect
715. #525	C₂²×C₅₃	semidirect
716. #525	C₂²×C₅₃	semidirect
717. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
718. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
722. #520	C₂²×C₅₃	semidirect
723. #485	C₂²×C₅₃	semidirect
724. #485	C₂²×C₅₃	semidirect
725. #485	C₂²×C₅₃	semidirect
726. #485	C₂²×C₅₃	semidirect
727. #484	C₂²×C₅₃	semidirect
728. #484	C₂²×C₅₃	semidirect
729. #484	C₂²×C₅₃	semidirect
730. #483	C₂²×C₅₃	semidirect
731. #482	C₂²×C₅₃	semidirect
732. #482	C₂²×C₅₃	semidirect
733. #482	C₂²×C₅₃	semidirect
734. #482	C₂²×C₅₃	semidirect
735. #481	C₂²×C₅₃	semidirect
736. #480	C₂²×C₅₃	semidirect
737. #480	C₂²×C₅₃	semidirect
738. #480	C₂²×C₅₃	semidirect
739. #470	C₂²×C₅₃	semidirect
740. #470	C₂²×C₅₃	semidirect
741. #470	C₂²×C₅₃	semidirect
742. #469	C₂²×C₅₃	semidirect
743. #469	C₂²×C₅₃	semidirect
744. #469	C₂²×C₅₃	semidirect
745. #468	C₂²×C₅₃	semidirect
746. #468	C₂²×C₅₃	semidirect
747. #468	C₂²×C₅₃	semidirect
748. #468	C₂²×C₅₃	semidirect
749. #468	C₂²×C₅₃	semidirect
750. #468	C₂²×C₅₃	semidirect
751. #468	C₂²×C₅₃	semidirect
752. #468	C₂²×C₅₃	semidirect
753. #468	C₂²×C₅₃	semidirect
754. #468	C₂²×C₅₃	semidirect
755. #467	C₂²×C₅₃	semidirect
756. #466	C₂²×C₅₃	semidirect
757. #465	C₂²×C₅₃	semidirect
758. #465	C₂²×C₅₃	semidirect
759. #452	C₂²×C₅₃	semidirect
760. #452	C₂²×C₅₃	semidirect
761. #452	C₂²×C₅₃	semidirect
762. #452	C₂²×C₅₃	semidirect
763. #451	C₂²×C₅₃	semidirect
764. #450	C₂²×C₅₃	semidirect
765. #450	C₂²×C₅₃	semidirect
766. #450	C₂²×C₅₃	semidirect
767. #449	C₂²×C₅₃	semidirect
768. #449	C₂²×C₅₃	semidirect
769. #449	C₂²×C₅₃	semidirect
770. #449	C₂²×C₅₃	semidirect
771. #448	C₂²×C₅₃	semidirect
772. #448	C₂²×C₅₃	semidirect
773. #448	C₂²×C₅₃	semidirect
774. #447	C₂²×C₅₃	semidirect
775. #428	C₂²×C₅₃	semidirect
776. #428	C₂²×C₅₃	semidirect
777. #427	C₂²×C₅₃	semidirect
778. C₂×#107	C₂²×C₅₃	semidirect
779. #419	C₂²×C₅₃	semidirect
780. #418	C₂²×C₅₃	semidirect
781. #417	C₂²×C₅₃	semidirect
782. #417	C₂²×C₅₃	semidirect
783. #416	C₂²×C₅₃	semidirect
784. #416	C₂²×C₅₃	semidirect
785. C₂×#103	C₂²×C₅₃	semidirect
786. C₂×#102	C₂²×C₅₃	semidirect
789. #408	C₂²×C₅₃	semidirect
790. #408	C₂²×C₅₃	semidirect
791. #408	C₂²×C₅₃	semidirect
792. #408	C₂²×C₅₃	semidirect
793. #407	C₂²×C₅₃	semidirect
794. #407	C₂²×C₅₃	semidirect
795. C₅₃	#60772	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×#3489	2
C₅₃×#3488	2
C₅₃×#3203	2
C₅₃×#3201	2
C₅₃×#3200	2
C₅₃×#3198	2
C₅₃×#3197	2
C₅₃×#3196	2
C₅₃×#3194	2
C₅₃×#3193	2
C₅₃×#3098	2
C₅₃×#3097	2
C₅₃×#3096	2
C₅₃×#3056	2
C₅₃×#3055	2
C₅₃×#3054	2
C₂×C₅₃×#468	2
C₅₃×#3013	2
C₅₃×#3012	2
C₅₃×#3010	2
C₅₃×#3009	2
C₅₃×#2879	2
#60772	53

Subgroups — C53×#60772 #27268284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60772 #27268284