Subgroups — C₅₃×#61594 #27269106

Order 13568.

2174 conjugacy classes of subgroups.

The subgroup lattice has 1420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3326	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3321	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3316	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3301	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3282	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3275	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3271	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3265	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3211	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3192	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3188	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
27	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
28	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
29	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
30	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
32	C₅₃×#553	—	2	1	no	—
33	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
34	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
35	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#548	—	2	1	no	—
37	C₅₃×#548	—	2	1	no	—
38	C₅₃×#548	—	2	1	no	—
39	C₅₃×#548	—	2	1	no	—
40	C₅₃×#548	C₂²	1	2	yes	—
41	C₅₃×#548	C₂²	1	2	yes	complemented
42	C₅₃×#548	C₂²	1	2	yes	complemented
43	C₅₃×#548	C₂²	1	2	yes	complemented
44	C₅₃×#546	—	2	1	no	—
45	C₅₃×#546	—	2	1	no	—
46	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
48	D₄²×C₅₃	—	2	1	no	—
49	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#540	—	2	1	no	—
51	C₅₃×#538	—	2	1	no	—
52	C₅₃×#538	—	2	1	no	—
53	C₅₃×#532	C₂²	1	1	yes	characteristic
54	C₅₃×#529	C₂²	1	1	yes	characteristic
55	C₂×#124×C₅₃	—	2	1	no	—
56	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#525	C₂²	1	1	yes	characteristic
58	C₅₃×#525	C₂²	1	1	yes	characteristic
59	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
60	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×#121×C₅₃	—	2	1	no	—
62	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
63	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#518	—	2	1	no	—
66	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₄×D₄×C₅₃	—	2	1	no	—
68	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
69	C₅₃×#496	C₂²	1	2	yes	complemented
70	C₅₃×#495	C₂²	1	2	yes	complemented
71	C₅₃×#489	C₂²	1	2	yes	complemented
72	C₅₃×#488	C₂²	1	2	yes	complemented
73	C₅₃×#485	C₂²	1	2	yes	complemented
74	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#483	C₂²	1	2	yes	complemented
76	C₅₃×#482	C₂²	1	2	yes	complemented
77	C₅₃×#481	C₂²	1	1	yes	characteristic
78	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#481	C₂²	1	2	yes	complemented
80	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#479	C₂²	1	2	yes	complemented
82	C₅₃×#475	C₂²	1	2	yes	complemented
83	C₅₃×#470	C₂²	1	2	yes	complemented
84	C₅₃×#469	C₂²	1	2	yes	complemented
85	C₅₃×#469	C₂²	1	2	yes	complemented
86	C₅₃×#468	C₂²	1	2	yes	complemented
87	C₅₃×#466	C₂²	1	2	yes	complemented
88	C₅₃×#465	C₂²	1	2	yes	complemented
89	C₅₃×#465	C₂²	1	2	yes	complemented
90	C₅₃×#465	C₂²	1	2	yes	complemented
91	C₅₃×#464	C₂²	1	2	yes	complemented
92	C₅₃×#464	C₂²	1	2	yes	complemented
93	C₅₃×#463	C₂²	1	2	yes	complemented
94	C₅₃×#463	C₂²	1	2	yes	complemented
95	C₅₃×#463	C₂²	1	2	yes	complemented
96	C₅₃×#460	C₂²	1	2	yes	complemented
97	C₅₃×#452	C₂²	1	2	yes	complemented
98	C₅₃×#452	C₂²	1	2	yes	complemented
99	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#451	C₂²	1	2	yes	complemented
102	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#450	C₂²	1	2	yes	complemented
104	C₅₃×#449	C₂²	1	2	yes	complemented
105	C₅₃×#449	C₂²	1	2	yes	complemented
106	C₅₃×#449	C₂²	1	2	yes	complemented
107	C₅₃×#449	C₂²	1	2	yes	complemented
108	C₅₃×#448	C₂²	1	1	yes	characteristic
109	C₅₃×#448	C₂²	1	1	yes	characteristic
110	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#448	C₂²	1	2	yes	complemented
114	C₅₃×#448	C₂²	1	2	yes	complemented
115	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#448	C₂²	1	2	yes	complemented
117	C₅₃×#447	C₂²	1	1	yes	characteristic
118	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#447	C₂²	1	2	yes	complemented
120	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#441	C₂²	1	2	yes	complemented
122	C₅₃×#440	C₂²	1	2	yes	complemented
123	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
124	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
125	C₅₃×#436	C₂²	1	2	yes	complemented
126	C₅₃×#435	C₂²	1	2	yes	complemented
127	C₅₃×#435	C₂²	1	2	yes	complemented
128	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
129	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#419	C₂²	1	2	yes	complemented
132	C₅₃×#417	C₂²	1	2	yes	complemented
133	C₅₃×#416	C₂²	1	2	yes	complemented
134	C₂×#103×C₅₃	C₂²	1	2	yes	complemented
135	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
138	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	1	no	—
141	C₂×#41×C₅₃	—	2	1	no	—
142	C₂×#41×C₅₃	—	4	4	no	—
143	C₂×#41×C₅₃	C₂³	1	2	yes	—
144	C₂×#41×C₅₃	C₂³	1	2	yes	—
145	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
147	C₂²×Q₈×C₅₃	—	2	1	no	—
148	C₂²×Q₈×C₅₃	—	2	1	no	—
149	C₂²×Q₈×C₅₃	—	2	1	no	—
150	C₂²×Q₈×C₅₃	—	4	4	no	—
151	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
152	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
153	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
154	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
155	C₂²×D₄×C₅₃	—	2	1	no	—
156	C₂²×D₄×C₅₃	—	2	1	no	—
157	C₂²×D₄×C₅₃	—	2	1	no	—
158	C₂²×D₄×C₅₃	—	2	1	no	—
159	C₂²×D₄×C₅₃	—	2	1	no	—
160	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
161	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
162	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
163	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
164	C₂³×C₄×C₅₃	—	2	1	no	—
165	C₂³×C₄×C₅₃	—	2	1	no	—
166	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
167	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
168	#137×C₅₃	—	4	4	no	—
169	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
170	#135×C₅₃	—	4	4	no	—
171	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
172	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
173	C₂×SD₁₆×C₅₃	—	4	4	no	—
174	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
175	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
176	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
177	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
178	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
179	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
180	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
181	C₂×D₈×C₅₃	C₂³	1	2	yes	—
182	C₂×D₈×C₅₃	C₂³	1	2	yes	—
183	C₂×D₈×C₅₃	C₂³	1	2	yes	—
184	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
185	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
186	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
187	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
188	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	#127×C₅₃	—	2	1	no	—
190	#127×C₅₃	C₂³	1	1	yes	characteristic
191	#126×C₅₃	—	2	1	no	—
192	#126×C₅₃	—	2	1	no	—
193	#126×C₅₃	—	2	1	no	—
194	#125×C₅₃	—	2	1	no	—
195	#125×C₅₃	C₂³	1	1	yes	characteristic
196	#124×C₅₃	—	2	2	no	—
197	#124×C₅₃	—	2	2	no	—
198	#124×C₅₃	—	2	2	no	—
199	#124×C₅₃	—	2	2	no	—
200	#124×C₅₃	—	2	1	no	—
201	#124×C₅₃	—	2	1	no	—
202	#124×C₅₃	—	2	1	no	—
203	#124×C₅₃	—	2	1	no	—
204	#124×C₅₃	—	2	1	no	—
205	#124×C₅₃	C₂³	1	2	yes	—
206	#124×C₅₃	C₂³	1	2	yes	—
207	#124×C₅₃	C₂³	1	1	yes	characteristic
208	#123×C₅₃	—	2	1	no	—
209	#123×C₅₃	—	2	1	no	—
210	#123×C₅₃	—	2	1	no	—
211	#123×C₅₃	—	2	1	no	—
212	#123×C₅₃	—	2	1	no	—
213	#123×C₅₃	—	2	1	no	—
214	#123×C₅₃	—	2	1	no	—
215	C₂²⋊Q₈×C₅₃	—	2	2	no	—
216	C₂²⋊Q₈×C₅₃	—	2	2	no	—
217	C₂²⋊Q₈×C₅₃	—	2	2	no	—
218	C₂²⋊Q₈×C₅₃	—	2	2	no	—
219	C₂²⋊Q₈×C₅₃	—	2	1	no	—
220	C₂²⋊Q₈×C₅₃	—	2	1	no	—
221	C₂²⋊Q₈×C₅₃	—	2	1	no	—
222	C₂²⋊Q₈×C₅₃	—	2	1	no	—
223	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
225	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	#121×C₅₃	—	2	1	no	—
229	#121×C₅₃	—	2	1	no	—
230	#121×C₅₃	—	2	1	no	—
231	#121×C₅₃	—	2	1	no	—
232	#121×C₅₃	—	2	1	no	—
233	#121×C₅₃	—	2	2	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	1	no	—
239	#121×C₅₃	—	2	1	no	—
240	#121×C₅₃	—	2	1	no	—
241	#121×C₅₃	—	2	1	no	—
242	#121×C₅₃	—	2	1	no	—
243	#121×C₅₃	—	2	1	no	—
244	#121×C₅₃	—	2	1	no	—
245	#121×C₅₃	—	2	1	no	—
246	#121×C₅₃	—	2	1	no	—
247	#121×C₅₃	C₂³	1	1	yes	characteristic
248	#121×C₅₃	C₂³	1	1	yes	characteristic
249	#121×C₅₃	C₂³	1	1	yes	characteristic
250	#121×C₅₃	C₂³	1	1	yes	characteristic
251	#121×C₅₃	C₂³	1	1	yes	characteristic
252	#121×C₅₃	C₂³	1	1	yes	characteristic
253	#121×C₅₃	C₂³	1	1	yes	characteristic
254	#121×C₅₃	C₂³	1	2	yes	—
255	#121×C₅₃	C₂³	1	2	yes	—
256	#121×C₅₃	C₂³	1	1	yes	characteristic
257	#121×C₅₃	C₂³	1	1	yes	characteristic
258	#120×C₅₃	—	2	1	no	—
259	#120×C₅₃	—	2	1	no	—
260	#120×C₅₃	—	2	1	no	—
261	#120×C₅₃	—	2	1	no	—
262	#120×C₅₃	—	2	1	no	—
263	#120×C₅₃	—	2	1	no	—
264	C₄×Q₈×C₅₃	—	2	1	no	—
265	C₄×Q₈×C₅₃	—	2	1	no	—
266	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
267	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
268	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
269	C₄×D₄×C₅₃	—	2	1	no	—
270	C₄×D₄×C₅₃	—	2	2	no	—
271	C₄×D₄×C₅₃	—	2	2	no	—
272	C₄×D₄×C₅₃	—	2	2	no	—
273	C₄×D₄×C₅₃	—	2	2	no	—
274	C₄×D₄×C₅₃	—	2	1	no	—
275	C₄×D₄×C₅₃	—	2	1	no	—
276	C₄×D₄×C₅₃	—	2	1	no	—
277	C₄×D₄×C₅₃	—	2	1	no	—
278	C₄×D₄×C₅₃	—	2	1	no	—
279	C₄×D₄×C₅₃	—	2	1	no	—
280	C₄×D₄×C₅₃	—	2	1	no	—
281	C₄×D₄×C₅₃	—	2	1	no	—
282	C₄×D₄×C₅₃	—	2	1	no	—
283	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
284	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
285	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
286	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
287	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
292	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
293	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
294	#117×C₅₃	—	2	1	no	—
295	#117×C₅₃	—	2	1	no	—
296	#117×C₅₃	C₂³	1	1	yes	characteristic
297	#117×C₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
299	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
300	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
301	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
305	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
306	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
307	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
308	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
309	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
310	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
311	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
312	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
313	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
314	C₂×C₄²×C₅₃	—	2	1	no	—
315	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
316	#107×C₅₃	C₂³	1	2	yes	—
317	#106×C₅₃	C₂³	1	2	yes	—
318	#106×C₅₃	C₂³	1	2	yes	—
319	#106×C₅₃	C₂³	1	2	yes	—
320	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
321	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
322	#103×C₅₃	C₂³	1	2	yes	—
323	#103×C₅₃	C₂³	1	2	yes	—
324	#103×C₅₃	C₂³	1	2	yes	—
325	#103×C₅₃	C₂³	1	2	yes	—
326	#103×C₅₃	C₂³	1	2	yes	—
327	#103×C₅₃	C₂³	1	2	yes	—
328	#103×C₅₃	C₂³	1	2	yes	—
329	#103×C₅₃	C₂³	1	2	yes	—
330	#103×C₅₃	C₂³	1	2	yes	—
331	#102×C₅₃	C₂³	1	2	yes	—
332	#102×C₅₃	C₂³	1	2	yes	—
333	#102×C₅₃	C₂³	1	2	yes	—
334	#102×C₅₃	C₂³	1	2	yes	—
335	#102×C₅₃	C₂³	1	2	yes	—
336	#102×C₅₃	C₂³	1	2	yes	—
337	#102×C₅₃	C₂³	1	2	yes	—
338	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
339	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
340	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
341	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
342	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
343	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
344	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
345	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
346	#97×C₅₃	C₂³	1	2	yes	—
347	C₄×C₈×C₅₃	C₂³	1	2	yes	—
348	C₂⁴×C₅₃	—	2	1	no	—
349	C₂⁴×C₅₃	—	2	1	no	—
350	C₂⁴×C₅₃	—	2	1	no	—
351	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
352	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
353	#41×C₅₃	—	2	4	no	—
354	#41×C₅₃	—	2	4	no	—
355	#41×C₅₃	—	4	2	no	—
356	#41×C₅₃	—	4	2	no	—
357	#41×C₅₃	—	4	2	no	—
358	#41×C₅₃	—	4	2	no	—
359	#41×C₅₃	—	4	4	no	—
360	#41×C₅₃	—	4	4	no	—
361	#41×C₅₃	—	8	2	no	—
362	C₂×Q₈×C₅₃	—	2	4	no	—
363	C₂×Q₈×C₅₃	—	2	1	no	—
364	C₂×Q₈×C₅₃	—	2	2	no	—
365	C₂×Q₈×C₅₃	—	2	2	no	—
366	C₂×Q₈×C₅₃	—	2	1	no	—
367	C₂×Q₈×C₅₃	—	2	1	no	—
368	C₂×Q₈×C₅₃	—	2	4	no	—
369	C₂×Q₈×C₅₃	—	2	4	no	—
370	C₂×Q₈×C₅₃	—	4	2	no	—
371	C₂×Q₈×C₅₃	—	4	2	no	—
372	C₂×Q₈×C₅₃	—	4	2	no	—
373	C₂×Q₈×C₅₃	—	4	4	no	—
374	C₂×Q₈×C₅₃	—	4	4	no	—
375	C₂×Q₈×C₅₃	—	4	4	no	—
376	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
377	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
379	C₂×D₄×C₅₃	—	2	1	no	—
380	C₂×D₄×C₅₃	—	2	1	no	—
381	C₂×D₄×C₅₃	—	2	2	no	—
382	C₂×D₄×C₅₃	—	2	2	no	—
383	C₂×D₄×C₅₃	—	2	1	no	—
384	C₂×D₄×C₅₃	—	2	1	no	—
385	C₂×D₄×C₅₃	—	2	1	no	—
386	C₂×D₄×C₅₃	—	2	2	no	—
387	C₂×D₄×C₅₃	—	2	2	no	—
388	C₂×D₄×C₅₃	—	2	1	no	—
389	C₂×D₄×C₅₃	—	2	1	no	—
390	C₂×D₄×C₅₃	—	2	1	no	—
391	C₂×D₄×C₅₃	—	2	1	no	—
392	C₂×D₄×C₅₃	—	2	1	no	—
393	C₂×D₄×C₅₃	—	2	1	no	—
394	C₂×D₄×C₅₃	—	2	1	no	—
395	C₂×D₄×C₅₃	—	2	1	no	—
396	C₂×D₄×C₅₃	—	2	1	no	—
397	C₂×D₄×C₅₃	—	2	1	no	—
398	C₂×D₄×C₅₃	—	2	1	no	—
399	C₂×D₄×C₅₃	—	4	2	no	—
400	C₂×D₄×C₅₃	—	4	2	no	—
401	C₂×D₄×C₅₃	—	4	2	no	—
402	C₂×D₄×C₅₃	—	4	4	no	—
403	C₂×D₄×C₅₃	—	4	2	no	—
404	C₂×D₄×C₅₃	—	4	4	no	—
405	C₂×D₄×C₅₃	—	4	4	no	—
406	C₂×D₄×C₅₃	—	8	2	no	—
407	C₂×D₄×C₅₃	—	8	2	no	—
408	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
409	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
410	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
411	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
412	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
413	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₅₃	—	2	1	no	—
417	C₂²×C₄×C₅₃	—	2	1	no	—
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	1	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	1	no	—
427	C₂²×C₄×C₅₃	—	2	1	no	—
428	C₂²×C₄×C₅₃	—	2	1	no	—
429	C₂²×C₄×C₅₃	—	2	1	no	—
430	C₂²×C₄×C₅₃	—	4	2	no	—
431	C₂²×C₄×C₅₃	—	4	2	no	—
432	C₂²×C₄×C₅₃	—	4	4	no	—
433	C₂²×C₄×C₅₃	—	4	4	no	—
434	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
435	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
436	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
437	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
438	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
442	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
447	Q₁₆×C₅₃	—	2	4	no	—
448	Q₁₆×C₅₃	—	4	2	no	—
449	SD₁₆×C₅₃	—	2	4	no	—
450	SD₁₆×C₅₃	—	2	4	no	—
451	SD₁₆×C₅₃	—	2	4	no	—
452	SD₁₆×C₅₃	—	4	2	no	—
453	SD₁₆×C₅₃	—	4	2	no	—
454	SD₁₆×C₅₃	—	4	2	no	—
455	SD₁₆×C₅₃	—	4	2	no	—
456	D₈×C₅₃	—	4	2	no	—
457	D₈×C₅₃	—	4	2	no	—
458	D₈×C₅₃	—	4	2	no	—
459	M₁₆×C₅₃	—	4	2	no	—
460	M₁₆×C₅₃	—	4	2	no	—
461	C₂×C₈×C₅₃	—	4	2	no	—
462	C₂×C₈×C₅₃	—	4	2	no	—
463	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
464	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
465	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
466	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
467	C₄⋊C₄×C₅₃	—	2	2	no	—
468	C₄⋊C₄×C₅₃	—	2	2	no	—
469	C₄⋊C₄×C₅₃	—	2	2	no	—
470	C₄⋊C₄×C₅₃	—	2	2	no	—
471	C₄⋊C₄×C₅₃	—	2	1	no	—
472	C₄⋊C₄×C₅₃	—	2	1	no	—
473	C₄⋊C₄×C₅₃	—	2	1	no	—
474	C₄⋊C₄×C₅₃	—	2	1	no	—
475	C₄⋊C₄×C₅₃	—	2	1	no	—
476	C₄⋊C₄×C₅₃	—	2	1	no	—
477	C₄⋊C₄×C₅₃	—	2	1	no	—
478	C₄⋊C₄×C₅₃	—	2	1	no	—
479	C₄⋊C₄×C₅₃	—	2	1	no	—
480	C₄⋊C₄×C₅₃	—	2	1	no	—
481	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
482	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
483	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
484	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
485	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
486	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
487	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
488	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
489	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
490	C₂²⋊C₄×C₅₃	—	2	1	no	—
491	C₂²⋊C₄×C₅₃	—	2	1	no	—
492	C₂²⋊C₄×C₅₃	—	2	2	no	—
493	C₂²⋊C₄×C₅₃	—	2	2	no	—
494	C₂²⋊C₄×C₅₃	—	2	1	no	—
495	C₂²⋊C₄×C₅₃	—	2	1	no	—
496	C₂²⋊C₄×C₅₃	—	2	1	no	—
497	C₂²⋊C₄×C₅₃	—	2	1	no	—
498	C₂²⋊C₄×C₅₃	—	2	1	no	—
499	C₂²⋊C₄×C₅₃	—	2	1	no	—
500	C₂²⋊C₄×C₅₃	—	2	1	no	—
501	C₂²⋊C₄×C₅₃	—	2	1	no	—
502	C₂²⋊C₄×C₅₃	—	2	1	no	—
503	C₂²⋊C₄×C₅₃	—	2	1	no	—
504	C₂²⋊C₄×C₅₃	—	2	1	no	—
505	C₂²⋊C₄×C₅₃	—	2	2	no	—
506	C₂²⋊C₄×C₅₃	—	2	2	no	—
507	C₂²⋊C₄×C₅₃	—	2	2	no	—
508	C₂²⋊C₄×C₅₃	—	2	2	no	—
509	C₂²⋊C₄×C₅₃	—	2	2	no	—
510	C₂²⋊C₄×C₅₃	—	2	2	no	—
511	C₂²⋊C₄×C₅₃	—	2	1	no	—
512	C₂²⋊C₄×C₅₃	—	2	1	no	—
513	C₂²⋊C₄×C₅₃	—	2	1	no	—
514	C₂²⋊C₄×C₅₃	—	2	1	no	—
515	C₂²⋊C₄×C₅₃	—	2	1	no	—
516	C₂²⋊C₄×C₅₃	—	2	1	no	—
517	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
518	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
519	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
520	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
521	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
522	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
523	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
524	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
525	C₄²×C₅₃	—	2	2	no	—
526	C₄²×C₅₃	—	2	2	no	—
527	C₄²×C₅₃	—	2	1	no	—
528	C₄²×C₅₃	—	2	1	no	—
529	C₄²×C₅₃	—	2	1	no	—
530	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
531	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
532	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
533	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
534	C₂³×C₅₃	—	2	2	no	—
535	C₂³×C₅₃	—	2	2	no	—
536	C₂³×C₅₃	—	2	2	no	—
537	C₂³×C₅₃	—	2	1	no	—
538	C₂³×C₅₃	—	2	1	no	—
539	C₂³×C₅₃	—	2	2	no	—
540	C₂³×C₅₃	—	2	1	no	—
541	C₂³×C₅₃	—	4	1	no	—
542	C₂³×C₅₃	—	4	1	no	—
543	C₂³×C₅₃	—	4	1	no	—
544	C₂³×C₅₃	—	4	2	no	—
545	C₂³×C₅₃	—	4	2	no	—
546	C₂³×C₅₃	—	4	2	no	—
547	C₂³×C₅₃	—	4	2	no	—
548	C₂³×C₅₃	—	4	2	no	—
549	C₂³×C₅₃	—	8	1	no	—
550	C₂³×C₅₃	—	8	1	no	—
551	C₂³×C₅₃	—	8	1	no	—
552	C₂³×C₅₃	—	8	1	no	—
553	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
554	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
555	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
556	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
557	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
558	Q₈×C₅₃	—	2	4	no	—
559	Q₈×C₅₃	—	2	2	no	—
560	Q₈×C₅₃	—	2	2	no	—
561	Q₈×C₅₃	—	2	2	no	—
562	Q₈×C₅₃	—	2	2	no	—
563	Q₈×C₅₃	—	4	4	no	—
564	Q₈×C₅₃	—	4	4	no	—
565	Q₈×C₅₃	—	4	2	no	—
566	Q₈×C₅₃	—	8	1	no	—
567	Q₈×C₅₃	H(5,𝔽₂)	1	4	yes	—
568	D₄×C₅₃	—	2	2	no	—
569	D₄×C₅₃	—	2	2	no	—
570	D₄×C₅₃	—	2	2	no	—
571	D₄×C₅₃	—	2	2	no	—
572	D₄×C₅₃	—	2	2	no	—
573	D₄×C₅₃	—	2	2	no	—
574	D₄×C₅₃	—	2	2	no	—
575	D₄×C₅₃	—	4	1	no	—
576	D₄×C₅₃	—	4	1	no	—
577	D₄×C₅₃	—	4	4	no	—
578	D₄×C₅₃	—	4	4	no	—
579	D₄×C₅₃	—	4	2	no	—
580	D₄×C₅₃	—	4	2	no	—
581	D₄×C₅₃	—	4	2	no	—
582	D₄×C₅₃	—	4	4	no	—
583	D₄×C₅₃	—	4	2	no	—
584	D₄×C₅₃	—	4	4	no	—
585	D₄×C₅₃	—	4	2	no	—
586	D₄×C₅₃	—	4	2	no	—
587	D₄×C₅₃	—	4	2	no	—
588	D₄×C₅₃	—	8	1	no	—
589	D₄×C₅₃	—	8	1	no	—
590	D₄×C₅₃	—	8	1	no	—
591	D₄×C₅₃	—	8	1	no	—
592	D₄×C₅₃	—	8	1	no	—
593	D₄×C₅₃	—	8	1	no	—
594	D₄×C₅₃	—	8	1	no	—
595	D₄×C₅₃	—	8	1	no	—
596	D₄×C₅₃	—	8	1	no	—
597	C₂×C₄×C₅₃	—	2	4	no	—
598	C₂×C₄×C₅₃	—	2	2	no	—
599	C₂×C₄×C₅₃	—	2	2	no	—
600	C₂×C₄×C₅₃	—	2	2	no	—
601	C₂×C₄×C₅₃	—	2	2	no	—
602	C₂×C₄×C₅₃	—	2	2	no	—
603	C₂×C₄×C₅₃	—	2	2	no	—
604	C₂×C₄×C₅₃	—	2	2	no	—
605	C₂×C₄×C₅₃	—	2	2	no	—
606	C₂×C₄×C₅₃	—	2	1	no	—
607	C₂×C₄×C₅₃	—	2	1	no	—
608	C₂×C₄×C₅₃	—	2	1	no	—
609	C₂×C₄×C₅₃	—	2	1	no	—
610	C₂×C₄×C₅₃	—	2	1	no	—
611	C₂×C₄×C₅₃	—	2	2	no	—
612	C₂×C₄×C₅₃	—	4	1	no	—
613	C₂×C₄×C₅₃	—	4	1	no	—
614	C₂×C₄×C₅₃	—	4	1	no	—
615	C₂×C₄×C₅₃	—	4	1	no	—
616	C₂×C₄×C₅₃	—	4	1	no	—
617	C₂×C₄×C₅₃	—	4	1	no	—
618	C₂×C₄×C₅₃	—	4	1	no	—
619	C₂×C₄×C₅₃	—	4	4	no	—
620	C₂×C₄×C₅₃	—	4	4	no	—
621	C₂×C₄×C₅₃	—	4	4	no	—
622	C₂×C₄×C₅₃	—	4	4	no	—
623	C₂×C₄×C₅₃	—	4	2	no	—
624	C₂×C₄×C₅₃	—	4	2	no	—
625	C₂×C₄×C₅₃	—	4	2	no	—
626	C₂×C₄×C₅₃	—	8	1	no	—
627	C₂×C₄×C₅₃	—	8	1	no	—
628	C₂×C₄×C₅₃	—	8	1	no	—
629	C₂×C₄×C₅₃	—	8	1	no	—
630	C₂×C₄×C₅₃	—	8	1	no	—
631	C₂×C₄×C₅₃	—	8	1	no	—
632	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
633	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
634	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
635	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
636	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
637	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
638	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
639	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
640	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
641	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
642	C₈×C₅₃	—	2	2	no	—
643	C₈×C₅₃	—	2	2	no	—
644	C₈×C₅₃	—	2	2	no	—
645	C₈×C₅₃	—	2	2	no	—
646	#61594	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
647	C₂²×C₅₃	—	2	1	no	—
648	C₂²×C₅₃	—	2	1	no	—
649	C₂²×C₅₃	—	2	1	no	—
650	C₂²×C₅₃	—	2	1	no	—
651	C₂²×C₅₃	—	2	1	no	—
652	C₂²×C₅₃	—	2	1	no	—
653	C₂²×C₅₃	—	2	1	no	—
654	C₂²×C₅₃	—	2	1	no	—
655	C₂²×C₅₃	—	2	1	no	—
656	C₂²×C₅₃	—	2	1	no	—
657	C₂²×C₅₃	—	2	1	no	—
658	C₂²×C₅₃	—	2	1	no	—
659	C₂²×C₅₃	—	2	1	no	—
660	C₂²×C₅₃	—	4	4	no	—
661	C₂²×C₅₃	—	4	2	no	—
662	C₂²×C₅₃	—	4	1	no	—
663	C₂²×C₅₃	—	4	1	no	—
664	C₂²×C₅₃	—	4	1	no	—
665	C₂²×C₅₃	—	4	1	no	—
666	C₂²×C₅₃	—	4	2	no	—
667	C₂²×C₅₃	—	4	1	no	—
668	C₂²×C₅₃	—	4	1	no	—
669	C₂²×C₅₃	—	4	1	no	—
670	C₂²×C₅₃	—	4	1	no	—
671	C₂²×C₅₃	—	4	1	no	—
672	C₂²×C₅₃	—	4	2	no	—
673	C₂²×C₅₃	—	8	2	no	—
674	C₂²×C₅₃	—	8	4	no	—
675	C₂²×C₅₃	—	16	2	no	—
676	C₂²×C₅₃	—	16	2	no	—
677	C₂²×C₅₃	#575	1	2	yes	—
678	C₂²×C₅₃	#577	1	2	yes	—
679	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
680	C₄×C₅₃	—	2	4	no	—
681	C₄×C₅₃	—	2	1	no	—
682	C₄×C₅₃	—	2	1	no	—
683	C₄×C₅₃	—	2	1	no	—
684	C₄×C₅₃	—	2	1	no	—
685	C₄×C₅₃	—	2	1	no	—
686	C₄×C₅₃	—	2	1	no	—
687	C₄×C₅₃	—	2	1	no	—
688	C₄×C₅₃	—	2	1	no	—
689	C₄×C₅₃	—	2	1	no	—
690	C₄×C₅₃	—	4	2	no	—
691	C₄×C₅₃	—	4	1	no	—
692	C₄×C₅₃	—	4	1	no	—
693	C₄×C₅₃	—	4	2	no	—
694	C₄×C₅₃	—	4	1	no	—
695	C₄×C₅₃	—	4	1	no	—
696	C₄×C₅₃	—	4	1	no	—
697	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
698	#3519	C₂×C₅₃	1	1	yes	characteristic, complemented
699	C₂×#548	C₂×C₅₃	1	1	yes	characteristic, complemented
700	#3326	C₂×C₅₃	1	2	yes	complemented
701	#3321	C₂×C₅₃	1	2	yes	complemented
702	#3316	C₂×C₅₃	1	2	yes	complemented
703	#3301	C₂×C₅₃	1	2	yes	complemented
704	#3282	C₂×C₅₃	1	2	yes	complemented
705	#3275	C₂×C₅₃	1	2	yes	complemented
706	#3271	C₂×C₅₃	1	2	yes	complemented
707	#3265	C₂×C₅₃	1	2	yes	complemented
708	#3213	C₂×C₅₃	1	1	yes	characteristic, complemented
709	#3211	C₂×C₅₃	1	1	yes	characteristic, complemented
710	#3196	C₂×C₅₃	1	1	yes	characteristic, complemented
711	#3192	C₂×C₅₃	1	1	yes	characteristic, complemented
712	#3188	C₂×C₅₃	1	1	yes	characteristic, complemented
713	#3187	C₂×C₅₃	1	1	yes	characteristic, complemented
714	#3117	C₂×C₅₃	1	1	yes	characteristic, complemented
715	#3103	C₂×C₅₃	1	1	yes	characteristic, complemented
716	#3006	C₂×C₅₃	1	1	yes	characteristic, complemented
717	#3004	C₂×C₅₃	1	1	yes	characteristic, complemented
718	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
719	C₂×#448	C₂×C₅₃	1	1	yes	characteristic, complemented
720	#2974	C₂×C₅₃	1	1	yes	characteristic, complemented
721	C₂×C₅₃	—	2	2	no	—
722	C₂×C₅₃	—	2	2	no	—
723	C₂×C₅₃	—	4	1	no	—
724	C₂×C₅₃	—	4	1	no	—
725	C₂×C₅₃	—	4	1	no	—
726	C₂×C₅₃	—	8	2	no	—
727	C₂×C₅₃	—	8	1	no	—
728	C₂×C₅₃	—	8	1	no	—
729	C₂×C₅₃	—	8	1	no	—
730	C₂×C₅₃	#3484	1	1	yes	characteristic
731	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
732	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
733	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
734	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
735	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
736	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
737	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
738	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
739	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
740	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
741	#553	—	2	1	no	—
742	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
743	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
744	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	#548	—	2	1	no	—
746	#548	—	2	1	no	—
747	#548	—	2	1	no	—
748	#548	—	2	1	no	—
749	#548	C₂²×C₅₃	1	2	yes	—
750	#548	C₂²×C₅₃	1	2	yes	complemented
751	#548	C₂²×C₅₃	1	2	yes	complemented
752	#548	C₂²×C₅₃	1	2	yes	complemented
753	#546	—	2	1	no	—
754	#546	—	2	1	no	—
755	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
756	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
757	D₄²	—	2	1	no	—
758	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
759	#540	—	2	1	no	—
760	#538	—	2	1	no	—
761	#538	—	2	1	no	—
762	#532	C₂²×C₅₃	1	1	yes	characteristic
763	#529	C₂²×C₅₃	1	1	yes	characteristic
764	C₂×#124	—	2	1	no	—
765	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
766	#525	C₂²×C₅₃	1	1	yes	characteristic
767	#525	C₂²×C₅₃	1	1	yes	characteristic
768	C₂×C₂²⋊Q₈	—	2	1	no	—
769	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
770	C₂×#121	—	2	1	no	—
771	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
772	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
773	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
774	#518	—	2	1	no	—
775	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
776	C₂×C₄×D₄	—	2	1	no	—
777	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
778	#496	C₂²×C₅₃	1	2	yes	complemented
779	#495	C₂²×C₅₃	1	2	yes	complemented
780	#489	C₂²×C₅₃	1	2	yes	complemented
781	#488	C₂²×C₅₃	1	2	yes	complemented
782	#485	C₂²×C₅₃	1	2	yes	complemented
783	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
784	#483	C₂²×C₅₃	1	2	yes	complemented
785	#482	C₂²×C₅₃	1	2	yes	complemented
786	#481	C₂²×C₅₃	1	1	yes	characteristic
787	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
788	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
789	#481	C₂²×C₅₃	1	2	yes	complemented
790	#479	C₂²×C₅₃	1	2	yes	complemented
791	#475	C₂²×C₅₃	1	2	yes	complemented
792	#470	C₂²×C₅₃	1	2	yes	complemented
793	#469	C₂²×C₅₃	1	2	yes	complemented
794	#469	C₂²×C₅₃	1	2	yes	complemented
795	#468	C₂²×C₅₃	1	2	yes	complemented
796	#466	C₂²×C₅₃	1	2	yes	complemented
797	#465	C₂²×C₅₃	1	2	yes	complemented
798	#465	C₂²×C₅₃	1	2	yes	complemented
799	#465	C₂²×C₅₃	1	2	yes	complemented
800	#464	C₂²×C₅₃	1	2	yes	complemented
801	#464	C₂²×C₅₃	1	2	yes	complemented
802	#463	C₂²×C₅₃	1	2	yes	complemented
803	#463	C₂²×C₅₃	1	2	yes	complemented
804	#463	C₂²×C₅₃	1	2	yes	complemented
805	#460	C₂²×C₅₃	1	2	yes	complemented
806	#452	C₂²×C₅₃	1	2	yes	complemented
807	#452	C₂²×C₅₃	1	2	yes	complemented
808	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
809	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
810	#451	C₂²×C₅₃	1	2	yes	complemented
811	#450	C₂²×C₅₃	1	2	yes	complemented
812	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
813	#449	C₂²×C₅₃	1	2	yes	complemented
814	#449	C₂²×C₅₃	1	2	yes	complemented
815	#449	C₂²×C₅₃	1	2	yes	complemented
816	#449	C₂²×C₅₃	1	2	yes	complemented
817	#448	C₂²×C₅₃	1	1	yes	characteristic
818	#448	C₂²×C₅₃	1	1	yes	characteristic
819	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
820	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
821	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
822	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
823	#448	C₂²×C₅₃	1	2	yes	complemented
824	#448	C₂²×C₅₃	1	2	yes	complemented
825	#448	C₂²×C₅₃	1	2	yes	complemented
826	#447	C₂²×C₅₃	1	1	yes	characteristic
827	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
828	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
829	#447	C₂²×C₅₃	1	2	yes	complemented
830	#441	C₂²×C₅₃	1	2	yes	complemented
831	#440	C₂²×C₅₃	1	2	yes	complemented
832	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
833	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
834	#436	C₂²×C₅₃	1	2	yes	complemented
835	#435	C₂²×C₅₃	1	2	yes	complemented
836	#435	C₂²×C₅₃	1	2	yes	complemented
837	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
838	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
839	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
840	#419	C₂²×C₅₃	1	2	yes	complemented
841	#417	C₂²×C₅₃	1	2	yes	complemented
842	#416	C₂²×C₅₃	1	2	yes	complemented
843	C₂×#103	C₂²×C₅₃	1	2	yes	complemented
844	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
845	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
846	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
847	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
848	C₅₃	#61594	1	1	yes	characteristic, direct product factor, Sylow
849	C₂×#41	—	2	1	no	—
850	C₂×#41	—	2	1	no	—
851	C₂×#41	—	2	1	no	—
852	C₂×#41	—	4	4	no	—
853	C₂×#41	C₂³×C₅₃	1	2	yes	—
854	C₂×#41	C₂³×C₅₃	1	2	yes	—
855	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
856	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
857	C₂²×Q₈	—	2	1	no	—
858	C₂²×Q₈	—	2	1	no	—
859	C₂²×Q₈	—	2	1	no	—
860	C₂²×Q₈	—	4	4	no	—
861	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
862	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
863	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
864	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
865	C₂²×D₄	—	2	1	no	—
866	C₂²×D₄	—	2	1	no	—
867	C₂²×D₄	—	2	1	no	—
868	C₂²×D₄	—	2	1	no	—
869	C₂²×D₄	—	2	1	no	—
870	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
871	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
872	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
873	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
874	C₂³×C₄	—	2	1	no	—
875	C₂³×C₄	—	2	1	no	—
876	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
877	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
878	#137	—	4	4	no	—
879	AGL(1,ℤ/8)	—	4	4	no	—
880	#135	—	4	4	no	—
881	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
882	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
883	C₂×SD₁₆	—	4	4	no	—
884	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
885	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
886	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
887	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
888	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
889	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
890	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
891	C₂×D₈	C₂³×C₅₃	1	2	yes	—
892	C₂×D₈	C₂³×C₅₃	1	2	yes	—
893	C₂×D₈	C₂³×C₅₃	1	2	yes	—
894	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
895	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
896	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
897	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
898	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
899	#127	—	2	1	no	—
900	#127	C₂³×C₅₃	1	1	yes	characteristic
901	#126	—	2	1	no	—
902	#126	—	2	1	no	—
903	#126	—	2	1	no	—
904	#125	—	2	1	no	—
905	#125	C₂³×C₅₃	1	1	yes	characteristic
906	#124	—	2	2	no	—
907	#124	—	2	2	no	—
908	#124	—	2	2	no	—
909	#124	—	2	2	no	—
910	#124	—	2	1	no	—
911	#124	—	2	1	no	—
912	#124	—	2	1	no	—
913	#124	—	2	1	no	—
914	#124	—	2	1	no	—
915	#124	C₂³×C₅₃	1	2	yes	—
916	#124	C₂³×C₅₃	1	2	yes	—
917	#124	C₂³×C₅₃	1	1	yes	characteristic
918	#123	—	2	1	no	—
919	#123	—	2	1	no	—
920	#123	—	2	1	no	—
921	#123	—	2	1	no	—
922	#123	—	2	1	no	—
923	#123	—	2	1	no	—
924	#123	—	2	1	no	—
925	C₂²⋊Q₈	—	2	1	no	—
926	C₂²⋊Q₈	—	2	1	no	—
927	C₂²⋊Q₈	—	2	2	no	—
928	C₂²⋊Q₈	—	2	2	no	—
929	C₂²⋊Q₈	—	2	2	no	—
930	C₂²⋊Q₈	—	2	2	no	—
931	C₂²⋊Q₈	—	2	1	no	—
932	C₂²⋊Q₈	—	2	1	no	—
933	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
934	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
935	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
936	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
937	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
938	#121	—	2	2	no	—
939	#121	—	2	2	no	—
940	#121	—	2	2	no	—
941	#121	—	2	2	no	—
942	#121	—	2	1	no	—
943	#121	—	2	1	no	—
944	#121	—	2	1	no	—
945	#121	—	2	1	no	—
946	#121	—	2	1	no	—
947	#121	—	2	1	no	—
948	#121	—	2	1	no	—
949	#121	—	2	1	no	—
950	#121	—	2	1	no	—
951	#121	—	2	1	no	—
952	#121	—	2	1	no	—
953	#121	—	2	1	no	—
954	#121	—	2	1	no	—
955	#121	—	2	1	no	—
956	#121	—	2	1	no	—
957	#121	C₂³×C₅₃	1	1	yes	characteristic
958	#121	C₂³×C₅₃	1	1	yes	characteristic
959	#121	C₂³×C₅₃	1	1	yes	characteristic
960	#121	C₂³×C₅₃	1	1	yes	characteristic
961	#121	C₂³×C₅₃	1	1	yes	characteristic
962	#121	C₂³×C₅₃	1	1	yes	characteristic
963	#121	C₂³×C₅₃	1	1	yes	characteristic
964	#121	C₂³×C₅₃	1	2	yes	—
965	#121	C₂³×C₅₃	1	2	yes	—
966	#121	C₂³×C₅₃	1	1	yes	characteristic
967	#121	C₂³×C₅₃	1	1	yes	characteristic
968	#120	—	2	1	no	—
969	#120	—	2	1	no	—
970	#120	—	2	1	no	—
971	#120	—	2	1	no	—
972	#120	—	2	1	no	—
973	#120	—	2	1	no	—
974	C₄×Q₈	—	2	1	no	—
975	C₄×Q₈	—	2	1	no	—
976	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
977	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
978	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
979	C₄×D₄	—	2	1	no	—
980	C₄×D₄	—	2	1	no	—
981	C₄×D₄	—	2	1	no	—
982	C₄×D₄	—	2	1	no	—
983	C₄×D₄	—	2	1	no	—
984	C₄×D₄	—	2	1	no	—
985	C₄×D₄	—	2	1	no	—
986	C₄×D₄	—	2	2	no	—
987	C₄×D₄	—	2	2	no	—
988	C₄×D₄	—	2	2	no	—
989	C₄×D₄	—	2	2	no	—
990	C₄×D₄	—	2	1	no	—
991	C₄×D₄	—	2	1	no	—
992	C₄×D₄	—	2	1	no	—
993	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
994	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
995	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
996	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
997	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
998	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
999	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1000	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1001	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1002	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1003	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1004	#117	—	2	1	no	—
1005	#117	—	2	1	no	—
1006	#117	C₂³×C₅₃	1	1	yes	characteristic
1007	#117	C₂³×C₅₃	1	1	yes	characteristic
1008	C₂×C₄⋊C₄	—	2	1	no	—
1009	C₂×C₄⋊C₄	—	2	1	no	—
1010	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1011	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1012	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1013	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1014	C₂×C₂²⋊C₄	—	2	1	no	—
1015	C₂×C₂²⋊C₄	—	2	1	no	—
1016	C₂×C₂²⋊C₄	—	2	1	no	—
1017	C₂×C₂²⋊C₄	—	2	1	no	—
1018	C₂×C₂²⋊C₄	—	2	1	no	—
1019	C₂×C₂²⋊C₄	—	2	1	no	—
1020	C₂×C₂²⋊C₄	—	2	1	no	—
1021	C₂×C₂²⋊C₄	—	2	1	no	—
1022	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1023	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1024	C₂×C₄²	—	2	1	no	—
1025	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1026	#107	C₂³×C₅₃	1	2	yes	—
1027	#106	C₂³×C₅₃	1	2	yes	—
1028	#106	C₂³×C₅₃	1	2	yes	—
1029	#106	C₂³×C₅₃	1	2	yes	—
1030	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
1031	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
1032	#103	C₂³×C₅₃	1	2	yes	—
1033	#103	C₂³×C₅₃	1	2	yes	—
1034	#103	C₂³×C₅₃	1	2	yes	—
1035	#103	C₂³×C₅₃	1	2	yes	—
1036	#103	C₂³×C₅₃	1	2	yes	—
1037	#103	C₂³×C₅₃	1	2	yes	—
1038	#103	C₂³×C₅₃	1	2	yes	—
1039	#103	C₂³×C₅₃	1	2	yes	—
1040	#103	C₂³×C₅₃	1	2	yes	—
1041	#102	C₂³×C₅₃	1	2	yes	—
1042	#102	C₂³×C₅₃	1	2	yes	—
1043	#102	C₂³×C₅₃	1	2	yes	—
1044	#102	C₂³×C₅₃	1	2	yes	—
1045	#102	C₂³×C₅₃	1	2	yes	—
1046	#102	C₂³×C₅₃	1	2	yes	—
1047	#102	C₂³×C₅₃	1	2	yes	—
1048	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1049	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1050	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1051	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1052	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1053	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1054	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1055	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1056	#97	C₂³×C₅₃	1	2	yes	—
1057	C₄×C₈	C₂³×C₅₃	1	2	yes	—
1058	C₂⁴	—	2	1	no	—
1059	C₂⁴	—	2	1	no	—
1060	C₂⁴	—	2	1	no	—
1061	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1062	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1063	#41	—	2	4	no	—
1064	#41	—	2	4	no	—
1065	#41	—	4	2	no	—
1066	#41	—	4	2	no	—
1067	#41	—	4	2	no	—
1068	#41	—	4	2	no	—
1069	#41	—	4	4	no	—
1070	#41	—	4	4	no	—
1071	#41	—	8	2	no	—
1072	C₂×Q₈	—	2	4	no	—
1073	C₂×Q₈	—	2	1	no	—
1074	C₂×Q₈	—	2	2	no	—
1075	C₂×Q₈	—	2	2	no	—
1076	C₂×Q₈	—	2	1	no	—
1077	C₂×Q₈	—	2	1	no	—
1078	C₂×Q₈	—	2	4	no	—
1079	C₂×Q₈	—	2	4	no	—
1080	C₂×Q₈	—	4	2	no	—
1081	C₂×Q₈	—	4	2	no	—
1082	C₂×Q₈	—	4	2	no	—
1083	C₂×Q₈	—	4	4	no	—
1084	C₂×Q₈	—	4	4	no	—
1085	C₂×Q₈	—	4	4	no	—
1086	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1087	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1088	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1089	C₂×D₄	—	2	1	no	—
1090	C₂×D₄	—	2	1	no	—
1091	C₂×D₄	—	2	2	no	—
1092	C₂×D₄	—	2	2	no	—
1093	C₂×D₄	—	2	1	no	—
1094	C₂×D₄	—	2	1	no	—
1095	C₂×D₄	—	2	1	no	—
1096	C₂×D₄	—	2	2	no	—
1097	C₂×D₄	—	2	2	no	—
1098	C₂×D₄	—	2	1	no	—
1099	C₂×D₄	—	2	1	no	—
1100	C₂×D₄	—	2	1	no	—
1101	C₂×D₄	—	2	1	no	—
1102	C₂×D₄	—	2	1	no	—
1103	C₂×D₄	—	2	1	no	—
1104	C₂×D₄	—	2	1	no	—
1105	C₂×D₄	—	2	1	no	—
1106	C₂×D₄	—	2	1	no	—
1107	C₂×D₄	—	2	1	no	—
1108	C₂×D₄	—	2	1	no	—
1109	C₂×D₄	—	4	2	no	—
1110	C₂×D₄	—	4	2	no	—
1111	C₂×D₄	—	4	2	no	—
1112	C₂×D₄	—	4	4	no	—
1113	C₂×D₄	—	4	2	no	—
1114	C₂×D₄	—	4	4	no	—
1115	C₂×D₄	—	4	4	no	—
1116	C₂×D₄	—	8	2	no	—
1117	C₂×D₄	—	8	2	no	—
1118	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1119	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1120	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1121	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1122	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1123	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1124	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1125	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1126	C₂²×C₄	—	2	1	no	—
1127	C₂²×C₄	—	2	1	no	—
1128	C₂²×C₄	—	2	1	no	—
1129	C₂²×C₄	—	2	2	no	—
1130	C₂²×C₄	—	2	2	no	—
1131	C₂²×C₄	—	2	1	no	—
1132	C₂²×C₄	—	2	1	no	—
1133	C₂²×C₄	—	2	1	no	—
1134	C₂²×C₄	—	2	2	no	—
1135	C₂²×C₄	—	2	2	no	—
1136	C₂²×C₄	—	2	1	no	—
1137	C₂²×C₄	—	2	1	no	—
1138	C₂²×C₄	—	2	1	no	—
1139	C₂²×C₄	—	2	1	no	—
1140	C₂²×C₄	—	4	2	no	—
1141	C₂²×C₄	—	4	2	no	—
1142	C₂²×C₄	—	4	4	no	—
1143	C₂²×C₄	—	4	4	no	—
1144	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1145	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1146	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1147	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1148	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1149	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1150	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1151	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1152	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1153	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1154	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1155	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1156	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1157	Q₁₆	—	2	4	no	—
1158	Q₁₆	—	4	2	no	—
1159	SD₁₆	—	2	4	no	—
1160	SD₁₆	—	2	4	no	—
1161	SD₁₆	—	2	4	no	—
1162	SD₁₆	—	4	2	no	—
1163	SD₁₆	—	4	2	no	—
1164	SD₁₆	—	4	2	no	—
1165	SD₁₆	—	4	2	no	—
1166	D₈	—	4	2	no	—
1167	D₈	—	4	2	no	—
1168	D₈	—	4	2	no	—
1169	M₁₆	—	4	2	no	—
1170	M₁₆	—	4	2	no	—
1171	C₂×C₈	—	4	2	no	—
1172	C₂×C₈	—	4	2	no	—
1173	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1174	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1175	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1176	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1177	C₄⋊C₄	—	2	2	no	—
1178	C₄⋊C₄	—	2	2	no	—
1179	C₄⋊C₄	—	2	2	no	—
1180	C₄⋊C₄	—	2	2	no	—
1181	C₄⋊C₄	—	2	1	no	—
1182	C₄⋊C₄	—	2	1	no	—
1183	C₄⋊C₄	—	2	1	no	—
1184	C₄⋊C₄	—	2	1	no	—
1185	C₄⋊C₄	—	2	1	no	—
1186	C₄⋊C₄	—	2	1	no	—
1187	C₄⋊C₄	—	2	1	no	—
1188	C₄⋊C₄	—	2	1	no	—
1189	C₄⋊C₄	—	2	1	no	—
1190	C₄⋊C₄	—	2	1	no	—
1191	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1192	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1193	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1194	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1195	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1196	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1197	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1198	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1199	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1200	C₂²⋊C₄	—	2	1	no	—
1201	C₂²⋊C₄	—	2	1	no	—
1202	C₂²⋊C₄	—	2	2	no	—
1203	C₂²⋊C₄	—	2	2	no	—
1204	C₂²⋊C₄	—	2	1	no	—
1205	C₂²⋊C₄	—	2	1	no	—
1206	C₂²⋊C₄	—	2	1	no	—
1207	C₂²⋊C₄	—	2	1	no	—
1208	C₂²⋊C₄	—	2	1	no	—
1209	C₂²⋊C₄	—	2	1	no	—
1210	C₂²⋊C₄	—	2	1	no	—
1211	C₂²⋊C₄	—	2	1	no	—
1212	C₂²⋊C₄	—	2	1	no	—
1213	C₂²⋊C₄	—	2	1	no	—
1214	C₂²⋊C₄	—	2	1	no	—
1215	C₂²⋊C₄	—	2	2	no	—
1216	C₂²⋊C₄	—	2	2	no	—
1217	C₂²⋊C₄	—	2	2	no	—
1218	C₂²⋊C₄	—	2	2	no	—
1219	C₂²⋊C₄	—	2	2	no	—
1220	C₂²⋊C₄	—	2	2	no	—
1221	C₂²⋊C₄	—	2	1	no	—
1222	C₂²⋊C₄	—	2	1	no	—
1223	C₂²⋊C₄	—	2	1	no	—
1224	C₂²⋊C₄	—	2	1	no	—
1225	C₂²⋊C₄	—	2	1	no	—
1226	C₂²⋊C₄	—	2	1	no	—
1227	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1228	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1229	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1230	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1231	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1232	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1233	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1234	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1235	C₄²	—	2	2	no	—
1236	C₄²	—	2	2	no	—
1237	C₄²	—	2	1	no	—
1238	C₄²	—	2	1	no	—
1239	C₄²	—	2	1	no	—
1240	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1241	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1242	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1243	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1244	C₂³	—	2	2	no	—
1245	C₂³	—	2	2	no	—
1246	C₂³	—	2	2	no	—
1247	C₂³	—	2	2	no	—
1248	C₂³	—	2	1	no	—
1249	C₂³	—	2	1	no	—
1250	C₂³	—	2	1	no	—
1251	C₂³	—	4	1	no	—
1252	C₂³	—	4	1	no	—
1253	C₂³	—	4	1	no	—
1254	C₂³	—	4	2	no	—
1255	C₂³	—	4	2	no	—
1256	C₂³	—	4	2	no	—
1257	C₂³	—	4	2	no	—
1258	C₂³	—	4	2	no	—
1259	C₂³	—	8	1	no	—
1260	C₂³	—	8	1	no	—
1261	C₂³	—	8	1	no	—
1262	C₂³	—	8	1	no	—
1263	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1264	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1265	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1266	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1267	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1268	Q₈	—	2	4	no	—
1269	Q₈	—	2	2	no	—
1270	Q₈	—	2	2	no	—
1271	Q₈	—	2	2	no	—
1272	Q₈	—	2	2	no	—
1273	Q₈	—	4	4	no	—
1274	Q₈	—	4	4	no	—
1275	Q₈	—	4	2	no	—
1276	Q₈	—	8	1	no	—
1277	Q₈	H(5,𝔽₂)×C₅₃	1	4	yes	—
1278	D₄	—	2	2	no	—
1279	D₄	—	2	2	no	—
1280	D₄	—	2	2	no	—
1281	D₄	—	2	2	no	—
1282	D₄	—	2	2	no	—
1283	D₄	—	2	2	no	—
1284	D₄	—	2	2	no	—
1285	D₄	—	4	1	no	—
1286	D₄	—	4	1	no	—
1287	D₄	—	4	4	no	—
1288	D₄	—	4	4	no	—
1289	D₄	—	4	2	no	—
1290	D₄	—	4	2	no	—
1291	D₄	—	4	2	no	—
1292	D₄	—	4	4	no	—
1293	D₄	—	4	2	no	—
1294	D₄	—	4	4	no	—
1295	D₄	—	4	2	no	—
1296	D₄	—	4	2	no	—
1297	D₄	—	4	2	no	—
1298	D₄	—	8	1	no	—
1299	D₄	—	8	1	no	—
1300	D₄	—	8	1	no	—
1301	D₄	—	8	1	no	—
1302	D₄	—	8	1	no	—
1303	D₄	—	8	1	no	—
1304	D₄	—	8	1	no	—
1305	D₄	—	8	1	no	—
1306	D₄	—	8	1	no	—
1307	C₂×C₄	—	2	4	no	—
1308	C₂×C₄	—	2	2	no	—
1309	C₂×C₄	—	2	2	no	—
1310	C₂×C₄	—	2	2	no	—
1311	C₂×C₄	—	2	2	no	—
1312	C₂×C₄	—	2	2	no	—
1313	C₂×C₄	—	2	2	no	—
1314	C₂×C₄	—	2	2	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	2	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	2	no	—
1322	C₂×C₄	—	4	1	no	—
1323	C₂×C₄	—	4	1	no	—
1324	C₂×C₄	—	4	1	no	—
1325	C₂×C₄	—	4	1	no	—
1326	C₂×C₄	—	4	1	no	—
1327	C₂×C₄	—	4	1	no	—
1328	C₂×C₄	—	4	1	no	—
1329	C₂×C₄	—	4	4	no	—
1330	C₂×C₄	—	4	4	no	—
1331	C₂×C₄	—	4	4	no	—
1332	C₂×C₄	—	4	4	no	—
1333	C₂×C₄	—	4	2	no	—
1334	C₂×C₄	—	4	2	no	—
1335	C₂×C₄	—	4	2	no	—
1336	C₂×C₄	—	8	1	no	—
1337	C₂×C₄	—	8	1	no	—
1338	C₂×C₄	—	8	1	no	—
1339	C₂×C₄	—	8	1	no	—
1340	C₂×C₄	—	8	1	no	—
1341	C₂×C₄	—	8	1	no	—
1342	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1343	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1344	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1345	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1346	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1347	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1348	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1349	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1350	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1351	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1352	C₈	—	2	2	no	—
1353	C₈	—	2	2	no	—
1354	C₈	—	2	2	no	—
1355	C₈	—	2	2	no	—
1356	C₂²	—	2	1	no	—
1357	C₂²	—	2	1	no	—
1358	C₂²	—	2	1	no	—
1359	C₂²	—	2	1	no	—
1360	C₂²	—	2	1	no	—
1361	C₂²	—	2	1	no	—
1362	C₂²	—	2	1	no	—
1363	C₂²	—	2	1	no	—
1364	C₂²	—	2	1	no	—
1365	C₂²	—	2	1	no	—
1366	C₂²	—	2	1	no	—
1367	C₂²	—	2	1	no	—
1368	C₂²	—	2	1	no	—
1369	C₂²	—	4	4	no	—
1370	C₂²	—	4	2	no	—
1371	C₂²	—	4	1	no	—
1372	C₂²	—	4	1	no	—
1373	C₂²	—	4	1	no	—
1374	C₂²	—	4	1	no	—
1375	C₂²	—	4	2	no	—
1376	C₂²	—	4	1	no	—
1377	C₂²	—	4	1	no	—
1378	C₂²	—	4	1	no	—
1379	C₂²	—	4	1	no	—
1380	C₂²	—	4	1	no	—
1381	C₂²	—	4	2	no	—
1382	C₂²	—	8	2	no	—
1383	C₂²	—	8	4	no	—
1384	C₂²	—	16	2	no	—
1385	C₂²	—	16	2	no	—
1386	C₂²	C₅₃×#575	1	2	yes	—
1387	C₂²	C₅₃×#577	1	2	yes	—
1388	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1389	C₄	—	2	4	no	—
1390	C₄	—	2	1	no	—
1391	C₄	—	2	1	no	—
1392	C₄	—	2	1	no	—
1393	C₄	—	2	1	no	—
1394	C₄	—	2	1	no	—
1395	C₄	—	2	1	no	—
1396	C₄	—	2	1	no	—
1397	C₄	—	2	1	no	—
1398	C₄	—	2	1	no	—
1399	C₄	—	4	2	no	—
1400	C₄	—	4	1	no	—
1401	C₄	—	4	1	no	—
1402	C₄	—	4	2	no	—
1403	C₄	—	4	1	no	—
1404	C₄	—	4	1	no	—
1405	C₄	—	4	1	no	—
1406	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1407	C₂	—	2	2	no	—
1408	C₂	—	2	2	no	—
1409	C₂	—	4	1	no	—
1410	C₂	—	4	1	no	—
1411	C₂	—	4	1	no	—
1412	C₂	—	8	2	no	—
1413	C₂	—	8	1	no	—
1414	C₂	—	8	1	no	—
1415	C₂	—	8	1	no	—
1416	C₂	C₅₃×#3484	1	1	yes	characteristic
1417	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1418	C₂	C₂×C₅₃×#577	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 ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3519	C₂	semidirect
2. C₂×C₅₃×#548	C₂	semidirect
3. C₅₃×#3326	C₂	semidirect
4. C₅₃×#3321	C₂	semidirect
5. C₅₃×#3316	C₂	semidirect
6. C₅₃×#3301	C₂	semidirect
7. C₅₃×#3282	C₂	semidirect
8. C₅₃×#3275	C₂	semidirect
9. C₅₃×#3271	C₂	semidirect
10. C₅₃×#3265	C₂	semidirect
11. C₅₃×#3213	C₂	semidirect
12. C₅₃×#3211	C₂	semidirect
13. C₅₃×#3196	C₂	semidirect
14. C₅₃×#3192	C₂	semidirect
15. C₅₃×#3188	C₂	semidirect
16. C₅₃×#3187	C₂	semidirect
17. C₅₃×#3117	C₂	semidirect
18. C₅₃×#3103	C₂	semidirect
19. C₅₃×#3006	C₂	semidirect
20. C₅₃×#3004	C₂	semidirect
21. C₅₃×#3002	C₂	semidirect
22. C₂×C₅₃×#448	C₂	semidirect
23. C₅₃×#2974	C₂	semidirect
24. C₂²×#41×C₅₃	C₂²	semidirect
25. C₂³×Q₈×C₅₃	C₂²	semidirect
26. C₂×#137×C₅₃	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
28. C₂×#135×C₅₃	C₂²	semidirect
29. C₂²×SD₁₆×C₅₃	C₂²	semidirect
30. C₅₃×#555	C₂²	semidirect
31. C₅₃×#554	C₂²	semidirect
33. C₅₃×#553	C₂²	semidirect
34. C₅₃×#553	C₂²	semidirect
35. C₅₃×#550	C₂²	semidirect
41. C₅₃×#548	C₂²	semidirect
42. C₅₃×#548	C₂²	semidirect
43. C₅₃×#548	C₂²	semidirect
46. C₅₃×#546	C₂²	semidirect
47. C₅₃×#546	C₂²	semidirect
49. D₄²×C₅₃	C₂²	semidirect
56. C₂×#124×C₅₃	C₂²	semidirect
60. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
64. C₂×#121×C₅₃	C₂²	semidirect
66. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
69. C₅₃×#496	C₂²	semidirect
70. C₅₃×#495	C₂²	semidirect
71. C₅₃×#489	C₂²	semidirect
72. C₅₃×#488	C₂²	semidirect
73. C₅₃×#485	C₂²	semidirect
74. C₅₃×#484	C₂²	semidirect
75. C₅₃×#483	C₂²	semidirect
76. C₅₃×#482	C₂²	semidirect
78. C₅₃×#481	C₂²	semidirect
79. C₅₃×#481	C₂²	semidirect
80. C₅₃×#481	C₂²	semidirect
81. C₅₃×#479	C₂²	semidirect
82. C₅₃×#475	C₂²	semidirect
83. C₅₃×#470	C₂²	semidirect
84. C₅₃×#469	C₂²	semidirect
85. C₅₃×#469	C₂²	semidirect
86. C₅₃×#468	C₂²	semidirect
87. C₅₃×#466	C₂²	semidirect
88. C₅₃×#465	C₂²	semidirect
89. C₅₃×#465	C₂²	semidirect
90. C₅₃×#465	C₂²	semidirect
91. C₅₃×#464	C₂²	semidirect
92. C₅₃×#464	C₂²	semidirect
93. C₅₃×#463	C₂²	semidirect
94. C₅₃×#463	C₂²	semidirect
95. C₅₃×#463	C₂²	semidirect
96. C₅₃×#460	C₂²	semidirect
97. C₅₃×#452	C₂²	semidirect
98. C₅₃×#452	C₂²	semidirect
99. C₅₃×#451	C₂²	semidirect
100. C₅₃×#451	C₂²	semidirect
101. C₅₃×#451	C₂²	semidirect
102. C₅₃×#450	C₂²	semidirect
103. C₅₃×#450	C₂²	semidirect
104. C₅₃×#449	C₂²	semidirect
105. C₅₃×#449	C₂²	semidirect
106. C₅₃×#449	C₂²	semidirect
107. C₅₃×#449	C₂²	semidirect
110. C₅₃×#448	C₂²	semidirect
111. C₅₃×#448	C₂²	semidirect
112. C₅₃×#448	C₂²	semidirect
113. C₅₃×#448	C₂²	semidirect
114. C₅₃×#448	C₂²	semidirect
115. C₅₃×#448	C₂²	semidirect
116. C₅₃×#448	C₂²	semidirect
118. C₅₃×#447	C₂²	semidirect
119. C₅₃×#447	C₂²	semidirect
120. C₅₃×#447	C₂²	semidirect
121. C₅₃×#441	C₂²	semidirect
122. C₅₃×#440	C₂²	semidirect
123. C₄×SD₁₆×C₅₃	C₂²	semidirect
124. C₄×SD₁₆×C₅₃	C₂²	semidirect
125. C₅₃×#436	C₂²	semidirect
126. C₅₃×#435	C₂²	semidirect
127. C₅₃×#435	C₂²	semidirect
128. C₈×D₄×C₅₃	C₂²	semidirect
129. C₅₃×#432	C₂²	semidirect
130. C₅₃×#431	C₂²	semidirect
131. C₅₃×#419	C₂²	semidirect
132. C₅₃×#417	C₂²	semidirect
133. C₅₃×#416	C₂²	semidirect
134. C₂×#103×C₅₃	C₂²	semidirect
135. C₅₃×#407	C₂²	semidirect
136. C₅₃×#407	C₂²	semidirect
137. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
138. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
646. #61594	C₅₃	direct (N × H)
698. #3519	C₂×C₅₃	semidirect
699. C₂×#548	C₂×C₅₃	semidirect
700. #3326	C₂×C₅₃	semidirect
701. #3321	C₂×C₅₃	semidirect
702. #3316	C₂×C₅₃	semidirect
703. #3301	C₂×C₅₃	semidirect
704. #3282	C₂×C₅₃	semidirect
705. #3275	C₂×C₅₃	semidirect
706. #3271	C₂×C₅₃	semidirect
707. #3265	C₂×C₅₃	semidirect
708. #3213	C₂×C₅₃	semidirect
709. #3211	C₂×C₅₃	semidirect
710. #3196	C₂×C₅₃	semidirect
711. #3192	C₂×C₅₃	semidirect
712. #3188	C₂×C₅₃	semidirect
713. #3187	C₂×C₅₃	semidirect
714. #3117	C₂×C₅₃	semidirect
715. #3103	C₂×C₅₃	semidirect
716. #3006	C₂×C₅₃	semidirect
717. #3004	C₂×C₅₃	semidirect
718. #3002	C₂×C₅₃	semidirect
719. C₂×#448	C₂×C₅₃	semidirect
720. #2974	C₂×C₅₃	semidirect
733. C₂²×#41	C₂²×C₅₃	semidirect
734. C₂³×Q₈	C₂²×C₅₃	semidirect
735. C₂×#137	C₂²×C₅₃	semidirect
736. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
737. C₂×#135	C₂²×C₅₃	semidirect
738. C₂²×SD₁₆	C₂²×C₅₃	semidirect
739. #555	C₂²×C₅₃	semidirect
740. #554	C₂²×C₅₃	semidirect
742. #553	C₂²×C₅₃	semidirect
743. #553	C₂²×C₅₃	semidirect
744. #550	C₂²×C₅₃	semidirect
750. #548	C₂²×C₅₃	semidirect
751. #548	C₂²×C₅₃	semidirect
752. #548	C₂²×C₅₃	semidirect
755. #546	C₂²×C₅₃	semidirect
756. #546	C₂²×C₅₃	semidirect
758. D₄²	C₂²×C₅₃	semidirect
765. C₂×#124	C₂²×C₅₃	semidirect
769. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
773. C₂×#121	C₂²×C₅₃	semidirect
775. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
778. #496	C₂²×C₅₃	semidirect
779. #495	C₂²×C₅₃	semidirect
780. #489	C₂²×C₅₃	semidirect
781. #488	C₂²×C₅₃	semidirect
782. #485	C₂²×C₅₃	semidirect
783. #484	C₂²×C₅₃	semidirect
784. #483	C₂²×C₅₃	semidirect
785. #482	C₂²×C₅₃	semidirect
787. #481	C₂²×C₅₃	semidirect
788. #481	C₂²×C₅₃	semidirect
789. #481	C₂²×C₅₃	semidirect
790. #479	C₂²×C₅₃	semidirect
791. #475	C₂²×C₅₃	semidirect
792. #470	C₂²×C₅₃	semidirect
793. #469	C₂²×C₅₃	semidirect
794. #469	C₂²×C₅₃	semidirect
795. #468	C₂²×C₅₃	semidirect
796. #466	C₂²×C₅₃	semidirect
797. #465	C₂²×C₅₃	semidirect
798. #465	C₂²×C₅₃	semidirect
799. #465	C₂²×C₅₃	semidirect
800. #464	C₂²×C₅₃	semidirect
801. #464	C₂²×C₅₃	semidirect
802. #463	C₂²×C₅₃	semidirect
803. #463	C₂²×C₅₃	semidirect
804. #463	C₂²×C₅₃	semidirect
805. #460	C₂²×C₅₃	semidirect
806. #452	C₂²×C₅₃	semidirect
807. #452	C₂²×C₅₃	semidirect
808. #451	C₂²×C₅₃	semidirect
809. #451	C₂²×C₅₃	semidirect
810. #451	C₂²×C₅₃	semidirect
811. #450	C₂²×C₅₃	semidirect
812. #450	C₂²×C₅₃	semidirect
813. #449	C₂²×C₅₃	semidirect
814. #449	C₂²×C₅₃	semidirect
815. #449	C₂²×C₅₃	semidirect
816. #449	C₂²×C₅₃	semidirect
819. #448	C₂²×C₅₃	semidirect
820. #448	C₂²×C₅₃	semidirect
821. #448	C₂²×C₅₃	semidirect
822. #448	C₂²×C₅₃	semidirect
823. #448	C₂²×C₅₃	semidirect
824. #448	C₂²×C₅₃	semidirect
825. #448	C₂²×C₅₃	semidirect
827. #447	C₂²×C₅₃	semidirect
828. #447	C₂²×C₅₃	semidirect
829. #447	C₂²×C₅₃	semidirect
830. #441	C₂²×C₅₃	semidirect
831. #440	C₂²×C₅₃	semidirect
832. C₄×SD₁₆	C₂²×C₅₃	semidirect
833. C₄×SD₁₆	C₂²×C₅₃	semidirect
834. #436	C₂²×C₅₃	semidirect
835. #435	C₂²×C₅₃	semidirect
836. #435	C₂²×C₅₃	semidirect
837. C₈×D₄	C₂²×C₅₃	semidirect
838. #432	C₂²×C₅₃	semidirect
839. #431	C₂²×C₅₃	semidirect
840. #419	C₂²×C₅₃	semidirect
841. #417	C₂²×C₅₃	semidirect
842. #416	C₂²×C₅₃	semidirect
843. C₂×#103	C₂²×C₅₃	semidirect
844. #407	C₂²×C₅₃	semidirect
845. #407	C₂²×C₅₃	semidirect
846. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
847. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
848. C₅₃	#61594	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×#3519	2
C₂×C₅₃×#548	2
C₅₃×#3326	2
C₅₃×#3321	2
C₅₃×#3316	2
C₅₃×#3301	2
C₅₃×#3282	2
C₅₃×#3275	2
C₅₃×#3271	2
C₅₃×#3265	2
C₅₃×#3213	2
C₅₃×#3211	2
C₅₃×#3196	2
C₅₃×#3192	2
C₅₃×#3188	2
C₅₃×#3187	2
C₅₃×#3117	2
C₅₃×#3103	2
C₅₃×#3006	2
C₅₃×#3004	2
C₅₃×#3002	2
C₂×C₅₃×#448	2
C₅₃×#2974	2
#61594	53

Subgroups — C53×#61594 #27269106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61594 #27269106