Subgroups — C₂×C₅₃×#3120 #27268061

Order 13568.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#520	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3120	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#452	C₂	1	1	yes	maximal, characteristic
11	C₂×C₅₃×#452	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×Q₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×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	C₅₃×#541	—	2	4	no	—
23	C₅₃×#541	C₂²	1	8	yes	complemented
24	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#126×C₅₃	—	2	1	no	—
26	C₂×#126×C₅₃	—	2	1	no	—
27	C₂×#125×C₅₃	—	2	1	no	—
28	C₂×#125×C₅₃	—	2	1	no	—
29	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₅₃×#520	—	2	4	no	—
33	C₅₃×#520	C₂²	1	8	yes	—
34	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₅₃	—	2	1	no	—
39	C₂×C₄×D₄×C₅₃	—	2	1	no	—
40	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#117×C₅₃	—	2	1	no	—
43	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₅₃	—	2	1	no	—
45	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
46	C₅₃×#484	C₂²	1	8	yes	complemented
47	C₅₃×#483	C₂²	1	8	yes	complemented
48	C₅₃×#479	C₂²	1	8	yes	complemented
49	C₅₃×#478	C₂²	1	8	yes	complemented
50	C₅₃×#462	C₂²	1	8	yes	complemented
51	C₅₃×#461	C₂²	1	8	yes	complemented
52	C₅₃×#452	C₂²	1	8	yes	—
53	C₅₃×#452	C₂²	1	8	yes	—
54	C₅₃×#441	C₂²	1	8	yes	complemented
55	C₅₃×#440	C₂²	1	8	yes	complemented
56	C₄×Q₁₆×C₅₃	C₂²	1	8	yes	complemented
57	C₄×SD₁₆×C₅₃	C₂²	1	8	yes	complemented
58	C₅₃×#433	C₂²	1	8	yes	complemented
59	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
61	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
62	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
66	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
67	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
68	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
69	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
70	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
71	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
72	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
73	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
75	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
77	C₂×#41×C₅₃	—	2	4	no	—
78	C₂×#41×C₅₃	—	2	4	no	—
79	C₂×#41×C₅₃	—	2	2	no	—
80	C₂×#41×C₅₃	C₂³	1	4	yes	—
81	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₅₃	—	2	1	no	—
85	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₅₃	—	2	1	no	—
87	C₂³×C₄×C₅₃	—	2	1	no	—
88	C₂³×C₄×C₅₃	—	2	1	no	—
89	C₂³×C₄×C₅₃	—	2	1	no	—
90	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
91	C₂×Q₁₆×C₅₃	—	2	4	no	—
92	C₂×Q₁₆×C₅₃	—	2	4	no	—
93	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
94	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
95	C₂×SD₁₆×C₅₃	—	2	4	no	—
96	C₂×SD₁₆×C₅₃	—	2	4	no	—
97	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
99	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₅₃	—	2	2	no	—
104	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
105	#126×C₅₃	—	2	8	no	—
106	#126×C₅₃	—	2	8	no	—
107	#125×C₅₃	—	2	8	no	—
108	#125×C₅₃	—	2	8	no	—
109	#125×C₅₃	—	2	2	no	—
110	#125×C₅₃	C₂³	1	4	yes	—
111	C₂²⋊Q₈×C₅₃	—	2	2	no	—
112	C₂²⋊Q₈×C₅₃	—	2	2	no	—
113	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
114	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
115	C₄×Q₈×C₅₃	—	2	2	no	—
116	C₄×Q₈×C₅₃	—	2	2	no	—
117	C₄×Q₈×C₅₃	—	2	2	no	—
118	C₄×Q₈×C₅₃	—	2	2	no	—
119	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
120	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
121	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
122	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
123	C₄×D₄×C₅₃	—	2	8	no	—
124	C₄×D₄×C₅₃	—	2	8	no	—
125	C₄×D₄×C₅₃	—	2	2	no	—
126	C₄×D₄×C₅₃	—	2	2	no	—
127	C₄×D₄×C₅₃	C₂³	1	4	yes	—
128	C₄×D₄×C₅₃	C₂³	1	4	yes	—
129	#117×C₅₃	—	2	8	no	—
130	#117×C₅₃	D₄	1	4	yes	—
131	#117×C₅₃	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₅₃	—	2	8	no	—
133	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
134	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
135	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
136	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
137	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
138	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
139	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
140	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
141	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
142	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
143	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
144	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
145	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
150	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
158	C₂×C₄²×C₅₃	—	2	1	no	—
159	C₂×C₄²×C₅₃	—	2	1	no	—
160	C₂×C₄²×C₅₃	—	2	1	no	—
161	C₂×C₄²×C₅₃	—	2	1	no	—
162	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
164	#107×C₅₃	C₂³	1	4	yes	—
165	#107×C₅₃	C₂³	1	4	yes	—
166	#106×C₅₃	C₂³	1	4	yes	—
167	#106×C₅₃	C₂³	1	4	yes	—
168	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
169	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
170	#103×C₅₃	C₂³	1	4	yes	—
171	#103×C₅₃	C₂³	1	4	yes	—
172	#103×C₅₃	C₂³	1	4	yes	—
173	#103×C₅₃	C₂³	1	4	yes	—
174	#103×C₅₃	C₂³	1	4	yes	—
175	#103×C₅₃	C₂³	1	4	yes	—
176	#102×C₅₃	C₂³	1	4	yes	—
177	#102×C₅₃	C₂³	1	4	yes	—
178	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
179	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
180	#97×C₅₃	C₂³	1	4	yes	—
181	C₄×C₈×C₅₃	C₂³	1	4	yes	—
182	C₂⁴×C₅₃	—	2	1	no	—
183	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
184	#41×C₅₃	—	2	16	no	—
185	#41×C₅₃	—	2	8	no	—
186	#41×C₅₃	—	2	8	no	—
187	C₂×Q₈×C₅₃	—	2	1	no	—
188	C₂×Q₈×C₅₃	—	2	1	no	—
189	C₂×Q₈×C₅₃	—	2	1	no	—
190	C₂×Q₈×C₅₃	—	2	2	no	—
191	C₂×Q₈×C₅₃	—	2	2	no	—
192	C₂×Q₈×C₅₃	—	2	2	no	—
193	C₂×Q₈×C₅₃	—	2	2	no	—
194	C₂×Q₈×C₅₃	—	2	2	no	—
195	C₂×Q₈×C₅₃	#41	1	4	yes	—
196	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
197	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
198	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
199	C₂×D₄×C₅₃	—	2	8	no	—
200	C₂×D₄×C₅₃	—	2	4	no	—
201	C₂×D₄×C₅₃	—	2	1	no	—
202	C₂×D₄×C₅₃	—	2	2	no	—
203	C₂×D₄×C₅₃	#41	1	4	yes	—
204	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₅₃	—	2	8	no	—
206	C₂²×C₄×C₅₃	—	2	1	no	—
207	C₂²×C₄×C₅₃	—	2	4	no	—
208	C₂²×C₄×C₅₃	—	2	2	no	—
209	C₂²×C₄×C₅₃	—	2	2	no	—
210	C₂²×C₄×C₅₃	—	2	1	no	—
211	C₂²×C₄×C₅₃	—	2	1	no	—
212	C₂²×C₄×C₅₃	—	2	1	no	—
213	C₂²×C₄×C₅₃	—	2	1	no	—
214	C₂²×C₄×C₅₃	—	2	1	no	—
215	C₂²×C₄×C₅₃	—	2	1	no	—
216	C₂²×C₄×C₅₃	—	2	4	no	—
217	C₂²×C₄×C₅₃	—	2	4	no	—
218	C₂²×C₄×C₅₃	—	2	4	no	—
219	C₂²×C₄×C₅₃	—	8	2	no	—
220	C₂²×C₄×C₅₃	—	8	2	no	—
221	C₂²×C₄×C₅₃	—	8	2	no	—
222	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
223	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
230	Q₁₆×C₅₃	—	2	8	no	—
231	Q₁₆×C₅₃	—	2	8	no	—
232	SD₁₆×C₅₃	—	2	8	no	—
233	SD₁₆×C₅₃	—	2	8	no	—
234	C₂×C₈×C₅₃	—	2	2	no	—
235	C₂×C₈×C₅₃	—	2	2	no	—
236	C₂×C₈×C₅₃	—	2	2	no	—
237	C₂×C₈×C₅₃	—	2	2	no	—
238	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
239	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
240	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
241	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
242	C₄⋊C₄×C₅₃	—	2	4	no	—
243	C₄⋊C₄×C₅₃	—	2	4	no	—
244	C₄⋊C₄×C₅₃	—	2	4	no	—
245	C₄⋊C₄×C₅₃	—	2	1	no	—
246	C₄⋊C₄×C₅₃	—	2	1	no	—
247	C₄⋊C₄×C₅₃	—	2	4	no	—
248	C₄⋊C₄×C₅₃	—	2	4	no	—
249	C₄⋊C₄×C₅₃	—	2	4	no	—
250	C₄⋊C₄×C₅₃	—	2	4	no	—
251	C₄⋊C₄×C₅₃	—	2	4	no	—
252	C₄⋊C₄×C₅₃	—	2	4	no	—
253	C₄⋊C₄×C₅₃	—	2	4	no	—
254	C₄⋊C₄×C₅₃	—	2	4	no	—
255	C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
258	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
259	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
263	C₂²⋊C₄×C₅₃	—	2	4	no	—
264	C₂²⋊C₄×C₅₃	—	2	4	no	—
265	C₂²⋊C₄×C₅₃	—	2	4	no	—
266	C₂²⋊C₄×C₅₃	—	2	4	no	—
267	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
268	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
269	C₄²×C₅₃	—	2	4	no	—
270	C₄²×C₅₃	—	2	4	no	—
271	C₄²×C₅₃	—	2	4	no	—
272	C₄²×C₅₃	—	2	4	no	—
273	C₄²×C₅₃	C₂×D₄	1	2	yes	—
274	C₄²×C₅₃	C₂×D₄	1	2	yes	—
275	C₄²×C₅₃	C₂⁴	1	2	yes	—
276	C₄²×C₅₃	C₂⁴	1	2	yes	—
277	C₂³×C₅₃	—	2	2	no	—
278	C₂³×C₅₃	—	2	4	no	—
279	C₂³×C₅₃	—	2	2	no	—
280	C₂³×C₅₃	—	2	2	no	—
281	C₂³×C₅₃	—	2	2	no	—
282	C₂³×C₅₃	—	4	2	no	—
283	C₂³×C₅₃	—	4	2	no	—
284	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
285	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
286	Q₈×C₅₃	—	2	4	no	—
287	Q₈×C₅₃	—	2	2	no	—
288	Q₈×C₅₃	—	2	2	no	—
289	Q₈×C₅₃	—	2	2	no	—
290	Q₈×C₅₃	—	2	2	no	—
291	Q₈×C₅₃	—	2	2	no	—
292	Q₈×C₅₃	—	4	2	no	—
293	Q₈×C₅₃	—	4	2	no	—
294	Q₈×C₅₃	C₂×#41	1	4	yes	—
295	D₄×C₅₃	—	2	16	no	—
296	D₄×C₅₃	—	2	4	no	—
297	D₄×C₅₃	—	2	2	no	—
298	D₄×C₅₃	C₂×#41	1	4	yes	—
299	C₂×C₄×C₅₃	—	2	16	no	—
300	C₂×C₄×C₅₃	—	2	2	no	—
301	C₂×C₄×C₅₃	—	2	4	no	—
302	C₂×C₄×C₅₃	—	2	2	no	—
303	C₂×C₄×C₅₃	—	2	2	no	—
304	C₂×C₄×C₅₃	—	2	2	no	—
305	C₂×C₄×C₅₃	—	2	2	no	—
306	C₂×C₄×C₅₃	—	2	2	no	—
307	C₂×C₄×C₅₃	—	2	4	no	—
308	C₂×C₄×C₅₃	—	2	2	no	—
309	C₂×C₄×C₅₃	—	2	2	no	—
310	C₂×C₄×C₅₃	—	2	2	no	—
311	C₂×C₄×C₅₃	—	2	2	no	—
312	C₂×C₄×C₅₃	—	2	2	no	—
313	C₂×C₄×C₅₃	—	2	2	no	—
314	C₂×C₄×C₅₃	—	2	2	no	—
315	C₂×C₄×C₅₃	—	2	2	no	—
316	C₂×C₄×C₅₃	—	4	2	no	—
317	C₂×C₄×C₅₃	—	4	2	no	—
318	C₂×C₄×C₅₃	—	4	2	no	—
319	C₂×C₄×C₅₃	—	4	2	no	—
320	C₂×C₄×C₅₃	—	4	2	no	—
321	C₂×C₄×C₅₃	—	4	2	no	—
322	C₂×C₄×C₅₃	—	8	4	no	—
323	C₂×C₄×C₅₃	—	8	4	no	—
324	C₂×C₄×C₅₃	—	8	4	no	—
325	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
332	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
333	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
334	C₈×C₅₃	—	2	2	no	—
335	C₈×C₅₃	—	2	2	no	—
336	C₈×C₅₃	—	2	2	no	—
337	C₈×C₅₃	—	2	2	no	—
338	C₂×#3120	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂²×C₅₃	—	2	2	no	—
340	C₂²×C₅₃	—	2	4	no	—
341	C₂²×C₅₃	—	2	2	no	—
342	C₂²×C₅₃	—	2	2	no	—
343	C₂²×C₅₃	—	4	4	no	—
344	C₂²×C₅₃	—	4	8	no	—
345	C₂²×C₅₃	—	4	2	no	—
346	C₂²×C₅₃	—	4	2	no	—
347	C₂²×C₅₃	#525	1	2	yes	—
348	C₂²×C₅₃	#577	1	2	yes	—
349	C₂²×C₅₃	#578	1	2	yes	—
350	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
351	C₄×C₅₃	—	2	2	no	—
352	C₄×C₅₃	—	2	4	no	—
353	C₄×C₅₃	—	2	2	no	—
354	C₄×C₅₃	—	2	2	no	—
355	C₄×C₅₃	—	2	2	no	—
356	C₄×C₅₃	—	2	2	no	—
357	C₄×C₅₃	—	4	2	no	—
358	C₄×C₅₃	—	4	2	no	—
359	C₄×C₅₃	—	4	2	no	—
360	C₄×C₅₃	—	4	2	no	—
361	C₄×C₅₃	—	4	2	no	—
362	C₄×C₅₃	—	4	2	no	—
363	C₄×C₅₃	#525	1	2	yes	—
364	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
365	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
366	C₂×#541	C₂×C₅₃	1	1	yes	characteristic, complemented
367	C₂×#520	C₂×C₅₃	1	1	yes	characteristic
368	#3120	C₂×C₅₃	1	16	yes	direct product factor
369	C₂×#484	C₂×C₅₃	1	1	yes	characteristic, complemented
370	C₂×#483	C₂×C₅₃	1	1	yes	characteristic, complemented
371	C₂×#479	C₂×C₅₃	1	1	yes	characteristic, complemented
372	C₂×#478	C₂×C₅₃	1	1	yes	characteristic, complemented
373	C₂×#462	C₂×C₅₃	1	1	yes	characteristic, complemented
374	C₂×#461	C₂×C₅₃	1	1	yes	characteristic, complemented
375	C₂×#452	C₂×C₅₃	1	1	yes	characteristic
376	C₂×#452	C₂×C₅₃	1	1	yes	characteristic
377	C₂×#441	C₂×C₅₃	1	1	yes	characteristic, complemented
378	C₂×#440	C₂×C₅₃	1	1	yes	characteristic, complemented
379	C₂×C₄×Q₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
380	C₂×C₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
381	C₂×#433	C₂×C₅₃	1	1	yes	characteristic, complemented
382	C₂×C₅₃	—	4	2	no	—
383	C₂×C₅₃	—	4	4	no	—
384	C₂×C₅₃	#3120	1	4	yes	direct product factor
385	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
386	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
387	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
388	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
389	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
390	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
391	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
392	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
393	#541	—	2	4	no	—
394	#541	C₂²×C₅₃	1	8	yes	complemented
395	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
396	C₂×#126	—	2	1	no	—
397	C₂×#126	—	2	1	no	—
398	C₂×#125	—	2	1	no	—
399	C₂×#125	—	2	1	no	—
400	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
402	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
403	#520	—	2	4	no	—
404	#520	C₂²×C₅₃	1	8	yes	—
405	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
407	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
408	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
409	C₂×C₄×D₄	—	2	1	no	—
410	C₂×C₄×D₄	—	2	1	no	—
411	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
412	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
413	C₂×#117	—	2	1	no	—
414	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
415	C₂²×C₄⋊C₄	—	2	1	no	—
416	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
417	#484	C₂²×C₅₃	1	8	yes	complemented
418	#483	C₂²×C₅₃	1	8	yes	complemented
419	#479	C₂²×C₅₃	1	8	yes	complemented
420	#478	C₂²×C₅₃	1	8	yes	complemented
421	#462	C₂²×C₅₃	1	8	yes	complemented
422	#461	C₂²×C₅₃	1	8	yes	complemented
423	#452	C₂²×C₅₃	1	8	yes	—
424	#452	C₂²×C₅₃	1	8	yes	—
425	#441	C₂²×C₅₃	1	8	yes	complemented
426	#440	C₂²×C₅₃	1	8	yes	complemented
427	C₄×Q₁₆	C₂²×C₅₃	1	8	yes	complemented
428	C₄×SD₁₆	C₂²×C₅₃	1	8	yes	complemented
429	#433	C₂²×C₅₃	1	8	yes	complemented
430	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
431	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
432	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
433	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
434	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
435	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
436	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
437	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
438	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
439	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
440	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
441	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
442	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
443	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
446	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
447	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
448	C₅₃	C₂×#3120	1	1	yes	characteristic, direct product factor, Sylow
449	C₂×#41	—	2	4	no	—
450	C₂×#41	—	2	4	no	—
451	C₂×#41	—	2	2	no	—
452	C₂×#41	C₂³×C₅₃	1	4	yes	—
453	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
454	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
455	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
456	C₂²×D₄	—	2	1	no	—
457	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
458	C₂³×C₄	—	2	1	no	—
459	C₂³×C₄	—	2	1	no	—
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
463	C₂×Q₁₆	—	2	4	no	—
464	C₂×Q₁₆	—	2	4	no	—
465	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
466	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
467	C₂×SD₁₆	—	2	4	no	—
468	C₂×SD₁₆	—	2	4	no	—
469	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
470	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
471	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
475	C₄⋊Q₈	—	2	2	no	—
476	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
477	#126	—	2	8	no	—
478	#126	—	2	8	no	—
479	#125	—	2	8	no	—
480	#125	—	2	8	no	—
481	#125	—	2	2	no	—
482	#125	C₂³×C₅₃	1	4	yes	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
486	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
487	C₄×Q₈	—	2	2	no	—
488	C₄×Q₈	—	2	2	no	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	—	2	2	no	—
491	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
492	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
493	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
494	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
495	C₄×D₄	—	2	8	no	—
496	C₄×D₄	—	2	8	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	C₂³×C₅₃	1	4	yes	—
500	C₄×D₄	C₂³×C₅₃	1	4	yes	—
501	#117	—	2	8	no	—
502	#117	D₄×C₅₃	1	4	yes	—
503	#117	C₂³×C₅₃	1	4	yes	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	—	2	2	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	—	2	1	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	—	2	8	no	—
517	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
522	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
530	C₂×C₄²	—	2	1	no	—
531	C₂×C₄²	—	2	1	no	—
532	C₂×C₄²	—	2	1	no	—
533	C₂×C₄²	—	2	1	no	—
534	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
536	#107	C₂³×C₅₃	1	4	yes	—
537	#107	C₂³×C₅₃	1	4	yes	—
538	#106	C₂³×C₅₃	1	4	yes	—
539	#106	C₂³×C₅₃	1	4	yes	—
540	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
541	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
542	#103	C₂³×C₅₃	1	4	yes	—
543	#103	C₂³×C₅₃	1	4	yes	—
544	#103	C₂³×C₅₃	1	4	yes	—
545	#103	C₂³×C₅₃	1	4	yes	—
546	#103	C₂³×C₅₃	1	4	yes	—
547	#103	C₂³×C₅₃	1	4	yes	—
548	#102	C₂³×C₅₃	1	4	yes	—
549	#102	C₂³×C₅₃	1	4	yes	—
550	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
551	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
552	#97	C₂³×C₅₃	1	4	yes	—
553	C₄×C₈	C₂³×C₅₃	1	4	yes	—
554	C₂⁴	—	2	1	no	—
555	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
556	#41	—	2	16	no	—
557	#41	—	2	8	no	—
558	#41	—	2	8	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	2	no	—
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	#41×C₅₃	1	4	yes	—
568	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
569	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
570	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
571	C₂×D₄	—	2	8	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	#41×C₅₃	1	4	yes	—
576	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
577	C₂²×C₄	—	2	8	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	8	2	no	—
592	C₂²×C₄	—	8	2	no	—
593	C₂²×C₄	—	8	2	no	—
594	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
602	Q₁₆	—	2	8	no	—
603	Q₁₆	—	2	8	no	—
604	SD₁₆	—	2	8	no	—
605	SD₁₆	—	2	8	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	2	no	—
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
611	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
612	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
613	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
630	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
631	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
632	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
633	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
634	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
640	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
641	C₄²	—	2	4	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	4	no	—
645	C₄²	C₂×D₄×C₅₃	1	2	yes	—
646	C₄²	C₂×D₄×C₅₃	1	2	yes	—
647	C₄²	C₂⁴×C₅₃	1	2	yes	—
648	C₄²	C₂⁴×C₅₃	1	2	yes	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	4	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	4	2	no	—
655	C₂³	—	4	2	no	—
656	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
657	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
658	Q₈	—	2	4	no	—
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	2	2	no	—
664	Q₈	—	4	2	no	—
665	Q₈	—	4	2	no	—
666	Q₈	C₂×#41×C₅₃	1	4	yes	—
667	D₄	—	2	16	no	—
668	D₄	—	2	4	no	—
669	D₄	—	2	2	no	—
670	D₄	C₂×#41×C₅₃	1	4	yes	—
671	C₂×C₄	—	2	16	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	8	4	no	—
695	C₂×C₄	—	8	4	no	—
696	C₂×C₄	—	8	4	no	—
697	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
700	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
703	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
704	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
705	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
706	C₈	—	2	2	no	—
707	C₈	—	2	2	no	—
708	C₈	—	2	2	no	—
709	C₈	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	4	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	4	no	—
717	C₂²	—	4	8	no	—
718	C₂²	C₅₃×#525	1	2	yes	—
719	C₂²	C₅₃×#577	1	2	yes	—
720	C₂²	C₅₃×#578	1	2	yes	—
721	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	2	2	no	—
727	C₄	—	2	4	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	C₅₃×#525	1	2	yes	—
735	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
736	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
737	C₂	—	4	2	no	—
738	C₂	—	4	4	no	—
739	C₂	C₅₃×#3120	1	4	yes	direct product factor
740	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
741	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
742	C₂	C₂×C₅₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₂²×#41×C₅₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×#117×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#541	C₂	semidirect
3. C₅₃×#3120	C₂	direct (N × H)
4. C₂×C₅₃×#484	C₂	semidirect
5. C₂×C₅₃×#483	C₂	semidirect
6. C₂×C₅₃×#479	C₂	semidirect
7. C₂×C₅₃×#478	C₂	semidirect
8. C₂×C₅₃×#462	C₂	semidirect
9. C₂×C₅₃×#461	C₂	semidirect
12. C₂×C₅₃×#441	C₂	semidirect
13. C₂×C₅₃×#440	C₂	semidirect
14. C₂×C₄×Q₁₆×C₅₃	C₂	semidirect
15. C₂×C₄×SD₁₆×C₅₃	C₂	semidirect
16. C₂×C₅₃×#433	C₂	semidirect
23. C₅₃×#541	C₂²	semidirect
46. C₅₃×#484	C₂²	semidirect
47. C₅₃×#483	C₂²	semidirect
48. C₅₃×#479	C₂²	semidirect
49. C₅₃×#478	C₂²	semidirect
50. C₅₃×#462	C₂²	semidirect
51. C₅₃×#461	C₂²	semidirect
54. C₅₃×#441	C₂²	semidirect
55. C₅₃×#440	C₂²	semidirect
56. C₄×Q₁₆×C₅₃	C₂²	semidirect
57. C₄×SD₁₆×C₅₃	C₂²	semidirect
58. C₅₃×#433	C₂²	semidirect
338. C₂×#3120	C₅₃	direct (N × H)
366. C₂×#541	C₂×C₅₃	semidirect
368. #3120	C₂×C₅₃	direct (N × H)
369. C₂×#484	C₂×C₅₃	semidirect
370. C₂×#483	C₂×C₅₃	semidirect
371. C₂×#479	C₂×C₅₃	semidirect
372. C₂×#478	C₂×C₅₃	semidirect
373. C₂×#462	C₂×C₅₃	semidirect
374. C₂×#461	C₂×C₅₃	semidirect
377. C₂×#441	C₂×C₅₃	semidirect
378. C₂×#440	C₂×C₅₃	semidirect
379. C₂×C₄×Q₁₆	C₂×C₅₃	semidirect
380. C₂×C₄×SD₁₆	C₂×C₅₃	semidirect
381. C₂×#433	C₂×C₅₃	semidirect
384. C₂×C₅₃	#3120	direct (N × H)
394. #541	C₂²×C₅₃	semidirect
417. #484	C₂²×C₅₃	semidirect
418. #483	C₂²×C₅₃	semidirect
419. #479	C₂²×C₅₃	semidirect
420. #478	C₂²×C₅₃	semidirect
421. #462	C₂²×C₅₃	semidirect
422. #461	C₂²×C₅₃	semidirect
425. #441	C₂²×C₅₃	semidirect
426. #440	C₂²×C₅₃	semidirect
427. C₄×Q₁₆	C₂²×C₅₃	semidirect
428. C₄×SD₁₆	C₂²×C₅₃	semidirect
429. #433	C₂²×C₅₃	semidirect
448. C₅₃	C₂×#3120	direct (N × H)
739. C₂	C₅₃×#3120	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×#541	2
C₂×C₅₃×#520	2
C₅₃×#3120	2
C₂×C₅₃×#484	2
C₂×C₅₃×#483	2
C₂×C₅₃×#479	2
C₂×C₅₃×#478	2
C₂×C₅₃×#462	2
C₂×C₅₃×#461	2
C₂×C₅₃×#452	2
C₂×C₅₃×#441	2
C₂×C₅₃×#440	2
C₂×C₄×Q₁₆×C₅₃	2
C₂×C₄×SD₁₆×C₅₃	2
C₂×C₅₃×#433	2
C₂×#3120	53

Subgroups — C2×C53×#3120 #27268061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3120 #27268061