Subgroups — C₂×C₅₃×#3198 #27268254

Order 13568.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3198	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
22	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
23	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₅₃×#537	—	2	4	no	—
27	C₅₃×#537	C₂²	1	8	yes	complemented
28	C₅₃×#535	—	2	4	no	—
29	C₅₃×#535	C₂²	1	8	yes	complemented
30	C₂×#127×C₅₃	—	2	1	no	—
31	C₂×#124×C₅₃	—	2	1	no	—
32	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
33	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×#121×C₅₃	—	2	1	no	—
36	C₂×#121×C₅₃	—	2	1	no	—
37	C₂×#121×C₅₃	—	2	1	no	—
38	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×#120×C₅₃	—	2	1	no	—
45	C₂×#120×C₅₃	—	2	1	no	—
46	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#485	C₂²	1	8	yes	complemented
49	C₅₃×#482	C₂²	1	8	yes	complemented
50	C₅₃×#481	C₂²	1	8	yes	complemented
51	C₅₃×#480	C₂²	1	8	yes	complemented
52	C₅₃×#469	C₂²	1	8	yes	complemented
53	C₅₃×#468	C₂²	1	8	yes	complemented
54	C₅₃×#466	C₂²	1	8	yes	complemented
55	C₅₃×#465	C₂²	1	8	yes	complemented
56	C₅₃×#450	C₂²	1	8	yes	complemented
57	C₅₃×#449	C₂²	1	8	yes	complemented
58	C₅₃×#449	C₂²	1	8	yes	complemented
59	C₅₃×#447	C₂²	1	8	yes	complemented
60	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
67	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
68	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
69	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
70	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
71	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#408	C₂²	1	8	yes	complemented
73	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
75	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₅₃	—	2	1	no	—
78	C₂×#41×C₅₃	—	2	2	no	—
79	C₂×#41×C₅₃	—	4	2	no	—
80	C₂×#41×C₅₃	—	4	2	no	—
81	C₂×#41×C₅₃	—	4	2	no	—
82	C₂×#41×C₅₃	—	4	2	no	—
83	C₂×#41×C₅₃	D₄	1	4	yes	—
84	C₂×#41×C₅₃	C₂³	1	4	yes	—
85	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
86	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
87	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₅₃	—	2	1	no	—
89	C₂²×D₄×C₅₃	—	2	1	no	—
90	C₂²×D₄×C₅₃	—	2	1	no	—
91	C₂²×D₄×C₅₃	—	2	1	no	—
92	C₂²×D₄×C₅₃	—	2	1	no	—
93	C₂²×D₄×C₅₃	—	2	1	no	—
94	C₂²×D₄×C₅₃	—	2	1	no	—
95	C₂²×D₄×C₅₃	—	2	1	no	—
96	C₂²×D₄×C₅₃	—	2	2	no	—
97	C₂²×D₄×C₅₃	—	4	2	no	—
98	C₂²×D₄×C₅₃	—	4	2	no	—
99	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
100	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
101	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
102	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
106	C₂³×C₄×C₅₃	—	2	1	no	—
107	C₂³×C₄×C₅₃	—	2	1	no	—
108	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
111	C₂×SD₁₆×C₅₃	—	4	2	no	—
112	C₂×SD₁₆×C₅₃	—	4	2	no	—
113	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
115	C₂×D₈×C₅₃	—	4	2	no	—
116	C₂×D₈×C₅₃	—	4	2	no	—
117	C₂×D₈×C₅₃	C₂³	1	4	yes	—
118	C₂×D₈×C₅₃	C₂³	1	4	yes	—
119	C₂×M₁₆×C₅₃	—	4	2	no	—
120	C₂×M₁₆×C₅₃	C₂³	1	4	yes	complemented
121	C₂²×C₈×C₅₃	—	4	2	no	—
122	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
125	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₅₃	C₂³	1	4	yes	complemented
127	#127×C₅₃	—	2	8	no	—
128	#124×C₅₃	—	2	8	no	—
129	C₂²⋊Q₈×C₅₃	—	2	8	no	—
130	C₂²⋊Q₈×C₅₃	—	2	2	no	—
131	C₂²⋊Q₈×C₅₃	—	2	2	no	—
132	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
133	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
134	#121×C₅₃	—	2	8	no	—
135	#121×C₅₃	—	2	8	no	—
136	#121×C₅₃	—	2	8	no	—
137	#121×C₅₃	—	2	2	no	—
138	#121×C₅₃	—	2	2	no	—
139	#121×C₅₃	—	2	2	no	—
140	#121×C₅₃	—	2	2	no	—
141	#121×C₅₃	—	2	2	no	—
142	#121×C₅₃	—	2	2	no	—
143	#121×C₅₃	C₂³	1	4	yes	—
144	#121×C₅₃	C₂³	1	4	yes	—
145	#121×C₅₃	C₂³	1	4	yes	—
146	#121×C₅₃	C₂³	1	4	yes	—
147	#121×C₅₃	C₂³	1	4	yes	—
148	#121×C₅₃	C₂³	1	4	yes	complemented
149	#120×C₅₃	—	2	8	no	—
150	#120×C₅₃	—	2	8	no	—
151	#117×C₅₃	—	2	2	no	—
152	#117×C₅₃	C₂³	1	4	yes	—
153	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
154	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
155	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
156	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
157	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
162	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
164	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
165	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
166	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
167	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
168	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
169	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
170	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
171	C₂×C₄²×C₅₃	—	2	1	no	—
172	#107×C₅₃	C₂³	1	4	yes	complemented
173	#107×C₅₃	C₂³	1	4	yes	complemented
174	#106×C₅₃	C₂³	1	4	yes	complemented
175	#106×C₅₃	C₂³	1	4	yes	complemented
176	#103×C₅₃	C₂³	1	4	yes	complemented
177	#103×C₅₃	C₂³	1	4	yes	complemented
178	#102×C₅₃	C₂³	1	4	yes	—
179	#102×C₅₃	C₂³	1	4	yes	—
180	#102×C₅₃	C₂³	1	4	yes	—
181	#102×C₅₃	C₂³	1	4	yes	—
182	#102×C₅₃	C₂³	1	4	yes	complemented
183	#102×C₅₃	C₂³	1	4	yes	complemented
184	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
185	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
186	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
187	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
188	C₂⁴×C₅₃	—	2	1	no	—
189	C₂⁴×C₅₃	—	2	1	no	—
190	C₂⁴×C₅₃	—	2	1	no	—
191	C₂⁴×C₅₃	—	2	4	no	—
192	C₂⁴×C₅₃	—	4	4	no	—
193	C₂⁴×C₅₃	—	8	2	no	—
194	C₂⁴×C₅₃	—	8	2	no	—
195	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
196	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
197	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
198	#41×C₅₃	—	4	8	no	—
199	#41×C₅₃	—	4	4	no	—
200	#41×C₅₃	—	4	4	no	—
201	#41×C₅₃	—	4	4	no	—
202	#41×C₅₃	—	4	4	no	—
203	#41×C₅₃	—	4	8	no	—
204	C₂×Q₈×C₅₃	—	2	1	no	—
205	C₂×Q₈×C₅₃	—	2	2	no	—
206	C₂×Q₈×C₅₃	—	2	2	no	—
207	C₂×Q₈×C₅₃	—	4	2	no	—
208	C₂×Q₈×C₅₃	C₂×D₄	1	4	yes	—
209	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
210	C₂×D₄×C₅₃	—	2	4	no	—
211	C₂×D₄×C₅₃	—	2	4	no	—
212	C₂×D₄×C₅₃	—	2	4	no	—
213	C₂×D₄×C₅₃	—	2	4	no	—
214	C₂×D₄×C₅₃	—	2	4	no	—
215	C₂×D₄×C₅₃	—	2	4	no	—
216	C₂×D₄×C₅₃	—	2	4	no	—
217	C₂×D₄×C₅₃	—	2	1	no	—
218	C₂×D₄×C₅₃	—	2	1	no	—
219	C₂×D₄×C₅₃	—	2	1	no	—
220	C₂×D₄×C₅₃	—	2	4	no	—
221	C₂×D₄×C₅₃	—	2	2	no	—
222	C₂×D₄×C₅₃	—	2	2	no	—
223	C₂×D₄×C₅₃	—	2	2	no	—
224	C₂×D₄×C₅₃	—	2	2	no	—
225	C₂×D₄×C₅₃	—	2	2	no	—
226	C₂×D₄×C₅₃	—	2	2	no	—
227	C₂×D₄×C₅₃	—	4	4	no	—
228	C₂×D₄×C₅₃	—	4	4	no	—
229	C₂×D₄×C₅₃	—	4	2	no	—
230	C₂×D₄×C₅₃	—	4	2	no	—
231	C₂×D₄×C₅₃	—	4	2	no	—
232	C₂×D₄×C₅₃	—	4	4	no	—
233	C₂×D₄×C₅₃	—	4	8	no	—
234	C₂×D₄×C₅₃	—	4	4	no	—
235	C₂×D₄×C₅₃	—	8	2	no	—
236	C₂×D₄×C₅₃	—	8	2	no	—
237	C₂×D₄×C₅₃	—	8	2	no	—
238	C₂×D₄×C₅₃	—	8	2	no	—
239	C₂×D₄×C₅₃	—	8	2	no	—
240	C₂×D₄×C₅₃	—	8	2	no	—
241	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
242	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
243	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
244	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
245	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
246	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₅₃	—	2	2	no	—
248	C₂²×C₄×C₅₃	—	2	2	no	—
249	C₂²×C₄×C₅₃	—	2	2	no	—
250	C₂²×C₄×C₅₃	—	2	2	no	—
251	C₂²×C₄×C₅₃	—	2	2	no	—
252	C₂²×C₄×C₅₃	—	2	2	no	—
253	C₂²×C₄×C₅₃	—	2	1	no	—
254	C₂²×C₄×C₅₃	—	2	1	no	—
255	C₂²×C₄×C₅₃	—	2	1	no	—
256	C₂²×C₄×C₅₃	—	2	1	no	—
257	C₂²×C₄×C₅₃	—	2	1	no	—
258	C₂²×C₄×C₅₃	—	2	4	no	—
259	C₂²×C₄×C₅₃	—	2	4	no	—
260	C₂²×C₄×C₅₃	—	4	4	no	—
261	C₂²×C₄×C₅₃	—	8	2	no	—
262	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
272	SD₁₆×C₅₃	—	4	4	no	—
273	SD₁₆×C₅₃	—	4	4	no	—
274	D₈×C₅₃	—	4	4	no	—
275	D₈×C₅₃	—	4	4	no	—
276	M₁₆×C₅₃	—	4	4	no	—
277	C₂×C₈×C₅₃	—	2	2	no	—
278	C₂×C₈×C₅₃	—	2	2	no	—
279	C₂×C₈×C₅₃	—	2	2	no	—
280	C₂×C₈×C₅₃	—	2	2	no	—
281	C₂×C₈×C₅₃	—	4	4	no	—
282	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
283	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
284	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
285	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₅₃	—	2	1	no	—
287	C₄⋊C₄×C₅₃	—	2	1	no	—
288	C₄⋊C₄×C₅₃	—	2	4	no	—
289	C₄⋊C₄×C₅₃	—	2	4	no	—
290	C₄⋊C₄×C₅₃	—	2	4	no	—
291	C₄⋊C₄×C₅₃	—	2	1	no	—
292	C₄⋊C₄×C₅₃	—	2	1	no	—
293	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
294	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
295	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
296	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
297	C₂²⋊C₄×C₅₃	—	2	4	no	—
298	C₂²⋊C₄×C₅₃	—	2	4	no	—
299	C₂²⋊C₄×C₅₃	—	2	4	no	—
300	C₂²⋊C₄×C₅₃	—	2	4	no	—
301	C₂²⋊C₄×C₅₃	—	2	4	no	—
302	C₂²⋊C₄×C₅₃	—	2	4	no	—
303	C₂²⋊C₄×C₅₃	—	2	4	no	—
304	C₂²⋊C₄×C₅₃	—	2	4	no	—
305	C₂²⋊C₄×C₅₃	—	2	4	no	—
306	C₄²×C₅₃	—	2	4	no	—
307	C₂³×C₅₃	—	2	2	no	—
308	C₂³×C₅₃	—	2	2	no	—
309	C₂³×C₅₃	—	2	2	no	—
310	C₂³×C₅₃	—	2	2	no	—
311	C₂³×C₅₃	—	2	2	no	—
312	C₂³×C₅₃	—	2	2	no	—
313	C₂³×C₅₃	—	2	2	no	—
314	C₂³×C₅₃	—	2	2	no	—
315	C₂³×C₅₃	—	2	2	no	—
316	C₂³×C₅₃	—	2	2	no	—
317	C₂³×C₅₃	—	2	2	no	—
318	C₂³×C₅₃	—	2	2	no	—
319	C₂³×C₅₃	—	4	8	no	—
320	C₂³×C₅₃	—	4	2	no	—
321	C₂³×C₅₃	—	4	2	no	—
322	C₂³×C₅₃	—	4	2	no	—
323	C₂³×C₅₃	—	4	2	no	—
324	C₂³×C₅₃	—	4	2	no	—
325	C₂³×C₅₃	—	4	2	no	—
326	C₂³×C₅₃	—	4	2	no	—
327	C₂³×C₅₃	—	4	2	no	—
328	C₂³×C₅₃	—	4	2	no	—
329	C₂³×C₅₃	—	8	4	no	—
330	C₂³×C₅₃	—	8	4	no	—
331	C₂³×C₅₃	—	8	16	no	—
332	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
333	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
334	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
335	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₅₃	—	2	2	no	—
337	Q₈×C₅₃	—	2	2	no	—
338	Q₈×C₅₃	—	4	4	no	—
339	Q₈×C₅₃	—	4	2	no	—
340	D₄×C₅₃	—	2	2	no	—
341	D₄×C₅₃	—	2	2	no	—
342	D₄×C₅₃	—	2	2	no	—
343	D₄×C₅₃	—	2	2	no	—
344	D₄×C₅₃	—	2	2	no	—
345	D₄×C₅₃	—	2	2	no	—
346	D₄×C₅₃	—	4	4	no	—
347	D₄×C₅₃	—	4	4	no	—
348	D₄×C₅₃	—	4	4	no	—
349	D₄×C₅₃	—	4	8	no	—
350	D₄×C₅₃	—	4	8	no	—
351	D₄×C₅₃	—	4	2	no	—
352	D₄×C₅₃	—	4	2	no	—
353	D₄×C₅₃	—	4	2	no	—
354	D₄×C₅₃	—	8	4	no	—
355	D₄×C₅₃	—	8	4	no	—
356	D₄×C₅₃	—	8	4	no	—
357	D₄×C₅₃	—	8	4	no	—
358	D₄×C₅₃	—	8	4	no	—
359	D₄×C₅₃	—	8	4	no	—
360	C₂×C₄×C₅₃	—	2	2	no	—
361	C₂×C₄×C₅₃	—	2	2	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	4	no	—
364	C₂×C₄×C₅₃	—	2	4	no	—
365	C₂×C₄×C₅₃	—	2	4	no	—
366	C₂×C₄×C₅₃	—	2	2	no	—
367	C₂×C₄×C₅₃	—	2	2	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	2	no	—
371	C₂×C₄×C₅₃	—	2	2	no	—
372	C₂×C₄×C₅₃	—	2	2	no	—
373	C₂×C₄×C₅₃	—	2	2	no	—
374	C₂×C₄×C₅₃	—	2	2	no	—
375	C₂×C₄×C₅₃	—	2	2	no	—
376	C₂×C₄×C₅₃	—	2	2	no	—
377	C₂×C₄×C₅₃	—	4	8	no	—
378	C₂×C₄×C₅₃	—	4	2	no	—
379	C₂×C₄×C₅₃	—	4	2	no	—
380	C₂×C₄×C₅₃	—	4	2	no	—
381	C₂×C₄×C₅₃	—	4	2	no	—
382	C₂×C₄×C₅₃	—	4	2	no	—
383	C₂×C₄×C₅₃	—	8	4	no	—
384	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
389	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
390	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
391	C₈×C₅₃	—	2	2	no	—
392	C₈×C₅₃	—	2	2	no	—
393	C₈×C₅₃	—	2	2	no	—
394	C₈×C₅₃	—	2	2	no	—
395	C₂×#3198	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₂²×C₅₃	—	2	2	no	—
397	C₂²×C₅₃	—	2	2	no	—
398	C₂²×C₅₃	—	2	2	no	—
399	C₂²×C₅₃	—	2	2	no	—
400	C₂²×C₅₃	—	2	2	no	—
401	C₂²×C₅₃	—	2	2	no	—
402	C₂²×C₅₃	—	2	2	no	—
403	C₂²×C₅₃	—	2	2	no	—
404	C₂²×C₅₃	—	2	2	no	—
405	C₂²×C₅₃	—	4	4	no	—
406	C₂²×C₅₃	—	4	4	no	—
407	C₂²×C₅₃	—	4	4	no	—
408	C₂²×C₅₃	—	4	2	no	—
409	C₂²×C₅₃	—	4	2	no	—
410	C₂²×C₅₃	—	4	2	no	—
411	C₂²×C₅₃	—	4	2	no	—
412	C₂²×C₅₃	—	4	2	no	—
413	C₂²×C₅₃	—	4	2	no	—
414	C₂²×C₅₃	—	4	2	no	—
415	C₂²×C₅₃	—	4	2	no	—
416	C₂²×C₅₃	—	4	2	no	—
417	C₂²×C₅₃	—	8	16	no	—
418	C₂²×C₅₃	—	8	4	no	—
419	C₂²×C₅₃	—	8	4	no	—
420	C₂²×C₅₃	—	8	4	no	—
421	C₂²×C₅₃	#534	1	2	yes	—
422	C₂²×C₅₃	#576	1	2	yes	—
423	C₂²×C₅₃	#577	1	2	yes	—
424	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
425	C₄×C₅₃	—	2	2	no	—
426	C₄×C₅₃	—	2	2	no	—
427	C₄×C₅₃	—	2	2	no	—
428	C₄×C₅₃	—	4	2	no	—
429	C₄×C₅₃	—	4	2	no	—
430	C₄×C₅₃	—	4	2	no	—
431	C₄×C₅₃	—	4	2	no	—
432	C₄×C₅₃	—	4	2	no	—
433	C₄×C₅₃	#534	1	2	yes	—
434	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
435	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂×#537	C₂×C₅₃	1	1	yes	characteristic, complemented
437	C₂×#535	C₂×C₅₃	1	1	yes	characteristic, complemented
438	#3198	C₂×C₅₃	1	16	yes	direct product factor
439	C₂×#481	C₂×C₅₃	1	1	yes	characteristic, complemented
440	C₂×#485	C₂×C₅₃	1	1	yes	characteristic, complemented
441	C₂×#482	C₂×C₅₃	1	1	yes	characteristic, complemented
442	C₂×#480	C₂×C₅₃	1	1	yes	characteristic, complemented
443	C₂×#469	C₂×C₅₃	1	1	yes	characteristic, complemented
444	C₂×#468	C₂×C₅₃	1	1	yes	characteristic, complemented
445	C₂×#466	C₂×C₅₃	1	1	yes	characteristic, complemented
446	C₂×#465	C₂×C₅₃	1	1	yes	characteristic, complemented
447	C₂×#449	C₂×C₅₃	1	1	yes	characteristic, complemented
448	C₂×#449	C₂×C₅₃	1	1	yes	characteristic, complemented
449	C₂×#450	C₂×C₅₃	1	1	yes	characteristic, complemented
450	C₂×#447	C₂×C₅₃	1	1	yes	characteristic, complemented
451	C₂×#408	C₂×C₅₃	1	1	yes	characteristic, complemented
452	C₂×C₅₃	—	4	2	no	—
453	C₂×C₅₃	—	4	2	no	—
454	C₂×C₅₃	—	4	2	no	—
455	C₂×C₅₃	—	8	2	no	—
456	C₂×C₅₃	—	8	2	no	—
457	C₂×C₅₃	—	8	2	no	—
458	C₂×C₅₃	#3198	1	4	yes	direct product factor
459	C₂×C₅₃	C₂×#534	1	1	yes	characteristic
460	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
461	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
462	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
463	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
464	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
465	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
466	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
467	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
468	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
469	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
470	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
471	#537	—	2	4	no	—
472	#537	C₂²×C₅₃	1	8	yes	complemented
473	#535	—	2	4	no	—
474	#535	C₂²×C₅₃	1	8	yes	complemented
475	C₂×#127	—	2	1	no	—
476	C₂×#124	—	2	1	no	—
477	C₂×C₂²⋊Q₈	—	2	1	no	—
478	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
479	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
480	C₂×#121	—	2	1	no	—
481	C₂×#121	—	2	1	no	—
482	C₂×#121	—	2	1	no	—
483	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
484	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
485	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
486	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
487	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
488	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
489	C₂×#120	—	2	1	no	—
490	C₂×#120	—	2	1	no	—
491	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
492	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
493	#485	C₂²×C₅₃	1	8	yes	complemented
494	#482	C₂²×C₅₃	1	8	yes	complemented
495	#481	C₂²×C₅₃	1	8	yes	complemented
496	#480	C₂²×C₅₃	1	8	yes	complemented
497	#469	C₂²×C₅₃	1	8	yes	complemented
498	#468	C₂²×C₅₃	1	8	yes	complemented
499	#466	C₂²×C₅₃	1	8	yes	complemented
500	#465	C₂²×C₅₃	1	8	yes	complemented
501	#450	C₂²×C₅₃	1	8	yes	complemented
502	#449	C₂²×C₅₃	1	8	yes	complemented
503	#449	C₂²×C₅₃	1	8	yes	complemented
504	#447	C₂²×C₅₃	1	8	yes	complemented
505	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
506	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
507	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
508	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
509	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
510	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
511	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
512	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
513	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
514	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
515	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
516	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
517	#408	C₂²×C₅₃	1	8	yes	complemented
518	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
519	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
520	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
521	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
522	C₅₃	C₂×#3198	1	1	yes	characteristic, direct product factor, Sylow
523	C₂⁵	—	2	1	no	—
524	C₂×#41	—	2	2	no	—
525	C₂×#41	—	4	2	no	—
526	C₂×#41	—	4	2	no	—
527	C₂×#41	—	4	2	no	—
528	C₂×#41	—	4	2	no	—
529	C₂×#41	D₄×C₅₃	1	4	yes	—
530	C₂×#41	C₂³×C₅₃	1	4	yes	—
531	C₂×#41	C₂³×C₅₃	1	4	yes	complemented
532	C₂²×Q₈	D₄×C₅₃	1	1	yes	characteristic
533	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
534	C₂²×D₄	—	2	1	no	—
535	C₂²×D₄	—	2	1	no	—
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	—	2	1	no	—
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	—	2	1	no	—
542	C₂²×D₄	—	2	2	no	—
543	C₂²×D₄	—	4	2	no	—
544	C₂²×D₄	—	4	2	no	—
545	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
546	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
547	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
548	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
549	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
550	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
551	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
552	C₂³×C₄	—	2	1	no	—
553	C₂³×C₄	—	2	1	no	—
554	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
557	C₂×SD₁₆	—	4	2	no	—
558	C₂×SD₁₆	—	4	2	no	—
559	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
560	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
561	C₂×D₈	—	4	2	no	—
562	C₂×D₈	—	4	2	no	—
563	C₂×D₈	C₂³×C₅₃	1	4	yes	—
564	C₂×D₈	C₂³×C₅₃	1	4	yes	—
565	C₂×M₁₆	—	4	2	no	—
566	C₂×M₁₆	C₂³×C₅₃	1	4	yes	complemented
567	C₂²×C₈	—	4	2	no	—
568	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
569	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
570	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
571	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
572	C₂²×C₈	C₂³×C₅₃	1	4	yes	complemented
573	#127	—	2	8	no	—
574	#124	—	2	8	no	—
575	C₂²⋊Q₈	—	2	8	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
579	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	complemented
580	#121	—	2	8	no	—
581	#121	—	2	8	no	—
582	#121	—	2	8	no	—
583	#121	—	2	2	no	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	C₂³×C₅₃	1	4	yes	—
590	#121	C₂³×C₅₃	1	4	yes	—
591	#121	C₂³×C₅₃	1	4	yes	—
592	#121	C₂³×C₅₃	1	4	yes	—
593	#121	C₂³×C₅₃	1	4	yes	—
594	#121	C₂³×C₅₃	1	4	yes	complemented
595	#120	—	2	8	no	—
596	#120	—	2	8	no	—
597	#117	—	2	2	no	—
598	#117	C₂³×C₅₃	1	4	yes	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	2	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	complemented
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₄²	—	2	1	no	—
618	#107	C₂³×C₅₃	1	4	yes	complemented
619	#107	C₂³×C₅₃	1	4	yes	complemented
620	#106	C₂³×C₅₃	1	4	yes	complemented
621	#106	C₂³×C₅₃	1	4	yes	complemented
622	#103	C₂³×C₅₃	1	4	yes	complemented
623	#103	C₂³×C₅₃	1	4	yes	complemented
624	#102	C₂³×C₅₃	1	4	yes	—
625	#102	C₂³×C₅₃	1	4	yes	—
626	#102	C₂³×C₅₃	1	4	yes	—
627	#102	C₂³×C₅₃	1	4	yes	—
628	#102	C₂³×C₅₃	1	4	yes	complemented
629	#102	C₂³×C₅₃	1	4	yes	complemented
630	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
631	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
632	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
633	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
634	C₂⁴	—	2	1	no	—
635	C₂⁴	—	2	1	no	—
636	C₂⁴	—	2	1	no	—
637	C₂⁴	—	2	4	no	—
638	C₂⁴	—	4	4	no	—
639	C₂⁴	—	8	2	no	—
640	C₂⁴	—	8	2	no	—
641	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
642	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
643	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
644	#41	—	4	8	no	—
645	#41	—	4	4	no	—
646	#41	—	4	4	no	—
647	#41	—	4	4	no	—
648	#41	—	4	4	no	—
649	#41	—	4	8	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	4	2	no	—
654	C₂×Q₈	C₂×D₄×C₅₃	1	4	yes	—
655	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	4	no	—
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	4	4	no	—
674	C₂×D₄	—	4	4	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	4	2	no	—
677	C₂×D₄	—	4	2	no	—
678	C₂×D₄	—	4	4	no	—
679	C₂×D₄	—	4	8	no	—
680	C₂×D₄	—	4	4	no	—
681	C₂×D₄	—	8	2	no	—
682	C₂×D₄	—	8	2	no	—
683	C₂×D₄	—	8	2	no	—
684	C₂×D₄	—	8	2	no	—
685	C₂×D₄	—	8	2	no	—
686	C₂×D₄	—	8	2	no	—
687	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
688	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
689	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
690	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
691	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
692	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	4	4	no	—
707	C₂²×C₄	—	8	2	no	—
708	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
712	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
713	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
718	SD₁₆	—	4	4	no	—
719	SD₁₆	—	4	4	no	—
720	D₈	—	4	4	no	—
721	D₈	—	4	4	no	—
722	M₁₆	—	4	4	no	—
723	C₂×C₈	—	2	2	no	—
724	C₂×C₈	—	2	2	no	—
725	C₂×C₈	—	2	2	no	—
726	C₂×C₈	—	2	2	no	—
727	C₂×C₈	—	4	4	no	—
728	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
729	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
730	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
731	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₄²	—	2	4	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	4	8	no	—
766	C₂³	—	4	2	no	—
767	C₂³	—	4	2	no	—
768	C₂³	—	4	2	no	—
769	C₂³	—	4	2	no	—
770	C₂³	—	4	2	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	4	2	no	—
773	C₂³	—	4	2	no	—
774	C₂³	—	4	2	no	—
775	C₂³	—	8	4	no	—
776	C₂³	—	8	4	no	—
777	C₂³	—	8	16	no	—
778	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
779	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
780	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
781	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
782	Q₈	—	2	2	no	—
783	Q₈	—	2	2	no	—
784	Q₈	—	4	4	no	—
785	Q₈	—	4	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	2	no	—
791	D₄	—	2	2	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	4	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	8	no	—
796	D₄	—	4	8	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	2	no	—
800	D₄	—	8	4	no	—
801	D₄	—	8	4	no	—
802	D₄	—	8	4	no	—
803	D₄	—	8	4	no	—
804	D₄	—	8	4	no	—
805	D₄	—	8	4	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	4	no	—
811	C₂×C₄	—	2	4	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	4	8	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	8	4	no	—
830	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
831	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
832	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
834	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
835	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
836	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
837	C₈	—	2	2	no	—
838	C₈	—	2	2	no	—
839	C₈	—	2	2	no	—
840	C₈	—	2	2	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	4	4	no	—
851	C₂²	—	4	4	no	—
852	C₂²	—	4	4	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	8	16	no	—
863	C₂²	—	8	4	no	—
864	C₂²	—	8	4	no	—
865	C₂²	—	8	4	no	—
866	C₂²	C₅₃×#534	1	2	yes	—
867	C₂²	C₅₃×#576	1	2	yes	—
868	C₂²	C₅₃×#577	1	2	yes	—
869	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
870	C₄	—	2	2	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	2	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	C₅₃×#534	1	2	yes	—
879	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
880	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
881	C₂	—	4	2	no	—
882	C₂	—	4	2	no	—
883	C₂	—	4	2	no	—
884	C₂	—	8	2	no	—
885	C₂	—	8	2	no	—
886	C₂	—	8	2	no	—
887	C₂	C₅₃×#3198	1	4	yes	direct product factor
888	C₂	C₂×C₅₃×#534	1	1	yes	characteristic
889	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
890	C₂	C₂×C₅₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂²×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#537	C₂	semidirect
2. C₂×C₅₃×#535	C₂	semidirect
3. C₅₃×#3198	C₂	direct (N × H)
4. C₂×C₅₃×#481	C₂	semidirect
5. C₂×C₅₃×#485	C₂	semidirect
6. C₂×C₅₃×#482	C₂	semidirect
7. C₂×C₅₃×#480	C₂	semidirect
8. C₂×C₅₃×#469	C₂	semidirect
9. C₂×C₅₃×#468	C₂	semidirect
10. C₂×C₅₃×#466	C₂	semidirect
11. C₂×C₅₃×#465	C₂	semidirect
12. C₂×C₅₃×#449	C₂	semidirect
13. C₂×C₅₃×#449	C₂	semidirect
14. C₂×C₅₃×#450	C₂	semidirect
15. C₂×C₅₃×#447	C₂	semidirect
16. C₂×C₅₃×#408	C₂	semidirect
18. C₂²×#41×C₅₃	C₂²	semidirect
24. C₂²×M₁₆×C₅₃	C₂²	semidirect
25. C₂³×C₈×C₅₃	C₂²	semidirect
27. C₅₃×#537	C₂²	semidirect
29. C₅₃×#535	C₂²	semidirect
34. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
43. C₂×#121×C₅₃	C₂²	semidirect
47. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
48. C₅₃×#485	C₂²	semidirect
49. C₅₃×#482	C₂²	semidirect
50. C₅₃×#481	C₂²	semidirect
51. C₅₃×#480	C₂²	semidirect
52. C₅₃×#469	C₂²	semidirect
53. C₅₃×#468	C₂²	semidirect
54. C₅₃×#466	C₂²	semidirect
55. C₅₃×#465	C₂²	semidirect
56. C₅₃×#450	C₂²	semidirect
57. C₅₃×#449	C₂²	semidirect
58. C₅₃×#449	C₂²	semidirect
59. C₅₃×#447	C₂²	semidirect
60. C₂×#107×C₅₃	C₂²	semidirect
61. C₂×#107×C₅₃	C₂²	semidirect
62. C₂×#106×C₅₃	C₂²	semidirect
63. C₂×#106×C₅₃	C₂²	semidirect
64. C₂×#103×C₅₃	C₂²	semidirect
65. C₂×#103×C₅₃	C₂²	semidirect
70. C₂×#102×C₅₃	C₂²	semidirect
71. C₂×#102×C₅₃	C₂²	semidirect
72. C₅₃×#408	C₂²	semidirect
75. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
76. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
85. C₂×#41×C₅₃	C₂³	semidirect
120. C₂×M₁₆×C₅₃	C₂³	semidirect
126. C₂²×C₈×C₅₃	C₂³	semidirect
133. C₂²⋊Q₈×C₅₃	C₂³	semidirect
148. #121×C₅₃	C₂³	semidirect
161. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
172. #107×C₅₃	C₂³	semidirect
173. #107×C₅₃	C₂³	semidirect
174. #106×C₅₃	C₂³	semidirect
175. #106×C₅₃	C₂³	semidirect
176. #103×C₅₃	C₂³	semidirect
177. #103×C₅₃	C₂³	semidirect
182. #102×C₅₃	C₂³	semidirect
183. #102×C₅₃	C₂³	semidirect
186. C₂²⋊C₈×C₅₃	C₂³	semidirect
187. C₂²⋊C₈×C₅₃	C₂³	semidirect
395. C₂×#3198	C₅₃	direct (N × H)
436. C₂×#537	C₂×C₅₃	semidirect
437. C₂×#535	C₂×C₅₃	semidirect
438. #3198	C₂×C₅₃	direct (N × H)
439. C₂×#481	C₂×C₅₃	semidirect
440. C₂×#485	C₂×C₅₃	semidirect
441. C₂×#482	C₂×C₅₃	semidirect
442. C₂×#480	C₂×C₅₃	semidirect
443. C₂×#469	C₂×C₅₃	semidirect
444. C₂×#468	C₂×C₅₃	semidirect
445. C₂×#466	C₂×C₅₃	semidirect
446. C₂×#465	C₂×C₅₃	semidirect
447. C₂×#449	C₂×C₅₃	semidirect
448. C₂×#449	C₂×C₅₃	semidirect
449. C₂×#450	C₂×C₅₃	semidirect
450. C₂×#447	C₂×C₅₃	semidirect
451. C₂×#408	C₂×C₅₃	semidirect
458. C₂×C₅₃	#3198	direct (N × H)
463. C₂²×#41	C₂²×C₅₃	semidirect
469. C₂²×M₁₆	C₂²×C₅₃	semidirect
470. C₂³×C₈	C₂²×C₅₃	semidirect
472. #537	C₂²×C₅₃	semidirect
474. #535	C₂²×C₅₃	semidirect
479. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
488. C₂×#121	C₂²×C₅₃	semidirect
492. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
493. #485	C₂²×C₅₃	semidirect
494. #482	C₂²×C₅₃	semidirect
495. #481	C₂²×C₅₃	semidirect
496. #480	C₂²×C₅₃	semidirect
497. #469	C₂²×C₅₃	semidirect
498. #468	C₂²×C₅₃	semidirect
499. #466	C₂²×C₅₃	semidirect
500. #465	C₂²×C₅₃	semidirect
501. #450	C₂²×C₅₃	semidirect
502. #449	C₂²×C₅₃	semidirect
503. #449	C₂²×C₅₃	semidirect
504. #447	C₂²×C₅₃	semidirect
505. C₂×#107	C₂²×C₅₃	semidirect
506. C₂×#107	C₂²×C₅₃	semidirect
507. C₂×#106	C₂²×C₅₃	semidirect
508. C₂×#106	C₂²×C₅₃	semidirect
509. C₂×#103	C₂²×C₅₃	semidirect
510. C₂×#103	C₂²×C₅₃	semidirect
515. C₂×#102	C₂²×C₅₃	semidirect
516. C₂×#102	C₂²×C₅₃	semidirect
517. #408	C₂²×C₅₃	semidirect
520. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
521. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
522. C₅₃	C₂×#3198	direct (N × H)
531. C₂×#41	C₂³×C₅₃	semidirect
566. C₂×M₁₆	C₂³×C₅₃	semidirect
572. C₂²×C₈	C₂³×C₅₃	semidirect
579. C₂²⋊Q₈	C₂³×C₅₃	semidirect
594. #121	C₂³×C₅₃	semidirect
607. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
618. #107	C₂³×C₅₃	semidirect
619. #107	C₂³×C₅₃	semidirect
620. #106	C₂³×C₅₃	semidirect
621. #106	C₂³×C₅₃	semidirect
622. #103	C₂³×C₅₃	semidirect
623. #103	C₂³×C₅₃	semidirect
628. #102	C₂³×C₅₃	semidirect
629. #102	C₂³×C₅₃	semidirect
632. C₂²⋊C₈	C₂³×C₅₃	semidirect
633. C₂²⋊C₈	C₂³×C₅₃	semidirect
887. C₂	C₅₃×#3198	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#537	2
C₂×C₅₃×#535	2
C₅₃×#3198	2
C₂×C₅₃×#481	2
C₂×C₅₃×#485	2
C₂×C₅₃×#482	2
C₂×C₅₃×#480	2
C₂×C₅₃×#469	2
C₂×C₅₃×#468	2
C₂×C₅₃×#466	2
C₂×C₅₃×#465	2
C₂×C₅₃×#449	2
C₂×C₅₃×#450	2
C₂×C₅₃×#447	2
C₂×C₅₃×#408	2
C₂×#3198	53

Subgroups — C2×C53×#3198 #27268254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3198 #27268254