Subgroups — C₂×C₅₃×#3321 #27268652

Order 13568.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3321	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅₃×#489	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×#475	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₅₃×#555	—	2	4	no	—
25	C₅₃×#555	C₂²	1	8	yes	complemented
26	C₅₃×#548	—	2	4	no	—
27	C₅₃×#548	C₂²	1	8	yes	complemented
28	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#124×C₅₃	—	2	1	no	—
30	C₂×#124×C₅₃	—	2	1	no	—
31	C₂×#124×C₅₃	—	2	1	no	—
32	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#121×C₅₃	—	2	1	no	—
36	C₂×#121×C₅₃	—	2	1	no	—
37	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₅₃	—	2	1	no	—
42	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×#117×C₅₃	—	2	1	no	—
45	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
47	C₅₃×#489	C₂²	1	8	yes	complemented
48	C₅₃×#485	C₂²	1	8	yes	complemented
49	C₅₃×#482	C₂²	1	8	yes	complemented
50	C₅₃×#475	C₂²	1	8	yes	complemented
51	C₅₃×#469	C₂²	1	8	yes	complemented
52	C₅₃×#465	C₂²	1	8	yes	complemented
53	C₅₃×#463	C₂²	1	8	yes	complemented
54	C₅₃×#449	C₂²	1	8	yes	complemented
55	C₅₃×#448	C₂²	1	8	yes	complemented
56	C₅₃×#440	C₂²	1	8	yes	complemented
57	C₅₃×#435	C₂²	1	8	yes	complemented
58	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
62	C₅₃×#419	C₂²	1	8	yes	complemented
63	C₅₃×#416	C₂²	1	8	yes	complemented
64	C₂×#103×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×#102×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×#102×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
76	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
77	C₂×#41×C₅₃	—	2	2	no	—
78	C₂×#41×C₅₃	—	2	4	no	—
79	C₂×#41×C₅₃	—	4	2	no	—
80	C₂×#41×C₅₃	C₂³	1	4	yes	—
81	C₂²×Q₈×C₅₃	—	2	1	no	—
82	C₂²×Q₈×C₅₃	—	2	2	no	—
83	C₂²×Q₈×C₅₃	—	2	1	no	—
84	C₂²×Q₈×C₅₃	—	2	4	no	—
85	C₂²×Q₈×C₅₃	—	4	2	no	—
86	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
88	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
94	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₅₃	—	2	1	no	—
97	C₂³×C₄×C₅₃	—	2	1	no	—
98	C₂³×C₄×C₅₃	—	2	1	no	—
99	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
101	C₂×SD₁₆×C₅₃	—	2	4	no	—
102	C₂×SD₁₆×C₅₃	—	4	2	no	—
103	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
105	C₂×D₈×C₅₃	—	4	2	no	—
106	C₂×D₈×C₅₃	C₂³	1	4	yes	—
107	C₂×M₁₆×C₅₃	—	4	2	no	—
108	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
109	C₂²×C₈×C₅₃	—	4	2	no	—
110	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
115	C₄⋊Q₈×C₅₃	—	2	2	no	—
116	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
117	#124×C₅₃	—	2	8	no	—
118	#124×C₅₃	—	2	8	no	—
119	#124×C₅₃	—	2	8	no	—
120	#124×C₅₃	—	2	2	no	—
121	#124×C₅₃	C₂³	1	4	yes	—
122	C₂²⋊Q₈×C₅₃	—	2	8	no	—
123	C₂²⋊Q₈×C₅₃	—	2	2	no	—
124	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
125	#121×C₅₃	—	2	8	no	—
126	#121×C₅₃	—	2	8	no	—
127	#121×C₅₃	—	2	2	no	—
128	#121×C₅₃	—	2	2	no	—
129	#121×C₅₃	—	2	2	no	—
130	#121×C₅₃	C₂³	1	4	yes	—
131	#121×C₅₃	C₂³	1	4	yes	—
132	#121×C₅₃	C₂³	1	4	yes	—
133	C₄×Q₈×C₅₃	—	2	2	no	—
134	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
135	C₄×D₄×C₅₃	—	2	8	no	—
136	C₄×D₄×C₅₃	—	2	2	no	—
137	C₄×D₄×C₅₃	D₄	1	4	yes	—
138	C₄×D₄×C₅₃	C₂³	1	4	yes	—
139	C₄×D₄×C₅₃	C₂³	1	4	yes	—
140	#117×C₅₃	—	2	8	no	—
141	#117×C₅₃	—	2	2	no	—
142	#117×C₅₃	—	2	2	no	—
143	#117×C₅₃	C₂³	1	4	yes	—
144	#117×C₅₃	C₂³	1	4	yes	—
145	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
146	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
147	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
148	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₅₃	—	2	1	no	—
165	C₂×C₄²×C₅₃	—	2	1	no	—
166	C₂×C₄²×C₅₃	—	2	1	no	—
167	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
168	#107×C₅₃	C₂³	1	4	yes	—
169	#106×C₅₃	C₂³	1	4	yes	—
170	#106×C₅₃	C₂³	1	4	yes	—
171	C₄⋊C₈×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	#103×C₅₃	C₂³	1	4	yes	—
177	#103×C₅₃	C₂³	1	4	yes	—
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	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
183	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
184	#97×C₅₃	C₂³	1	4	yes	—
185	C₂⁴×C₅₃	—	2	1	no	—
186	C₂⁴×C₅₃	—	2	1	no	—
187	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
189	#41×C₅₃	—	2	8	no	—
190	#41×C₅₃	—	4	4	no	—
191	#41×C₅₃	—	4	8	no	—
192	C₂×Q₈×C₅₃	—	2	1	no	—
193	C₂×Q₈×C₅₃	—	2	4	no	—
194	C₂×Q₈×C₅₃	—	2	1	no	—
195	C₂×Q₈×C₅₃	—	2	4	no	—
196	C₂×Q₈×C₅₃	—	2	2	no	—
197	C₂×Q₈×C₅₃	—	2	8	no	—
198	C₂×Q₈×C₅₃	—	2	2	no	—
199	C₂×Q₈×C₅₃	—	2	2	no	—
200	C₂×Q₈×C₅₃	—	4	4	no	—
201	C₂×Q₈×C₅₃	—	4	4	no	—
202	C₂×Q₈×C₅₃	—	4	8	no	—
203	C₂×Q₈×C₅₃	—	8	2	no	—
204	C₂×Q₈×C₅₃	#41	1	4	yes	—
205	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
206	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
207	C₂×D₄×C₅₃	—	2	4	no	—
208	C₂×D₄×C₅₃	—	2	4	no	—
209	C₂×D₄×C₅₃	—	2	4	no	—
210	C₂×D₄×C₅₃	—	2	4	no	—
211	C₂×D₄×C₅₃	—	2	1	no	—
212	C₂×D₄×C₅₃	—	2	1	no	—
213	C₂×D₄×C₅₃	—	2	2	no	—
214	C₂×D₄×C₅₃	—	2	2	no	—
215	C₂×D₄×C₅₃	—	2	2	no	—
216	C₂×D₄×C₅₃	—	2	2	no	—
217	C₂×D₄×C₅₃	—	4	2	no	—
218	C₂×D₄×C₅₃	—	4	4	no	—
219	C₂×D₄×C₅₃	—	4	4	no	—
220	C₂×D₄×C₅₃	—	8	2	no	—
221	C₂×D₄×C₅₃	—	8	2	no	—
222	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
223	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
224	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₅₃	—	2	1	no	—
226	C₂²×C₄×C₅₃	—	2	2	no	—
227	C₂²×C₄×C₅₃	—	2	2	no	—
228	C₂²×C₄×C₅₃	—	2	2	no	—
229	C₂²×C₄×C₅₃	—	2	2	no	—
230	C₂²×C₄×C₅₃	—	2	4	no	—
231	C₂²×C₄×C₅₃	—	2	1	no	—
232	C₂²×C₄×C₅₃	—	2	1	no	—
233	C₂²×C₄×C₅₃	—	2	1	no	—
234	C₂²×C₄×C₅₃	—	2	1	no	—
235	C₂²×C₄×C₅₃	—	2	1	no	—
236	C₂²×C₄×C₅₃	—	2	4	no	—
237	C₂²×C₄×C₅₃	—	2	4	no	—
238	C₂²×C₄×C₅₃	—	4	4	no	—
239	C₂²×C₄×C₅₃	—	4	4	no	—
240	C₂²×C₄×C₅₃	—	4	4	no	—
241	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
242	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
243	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
250	SD₁₆×C₅₃	—	2	8	no	—
251	SD₁₆×C₅₃	—	4	4	no	—
252	D₈×C₅₃	—	4	4	no	—
253	M₁₆×C₅₃	—	4	4	no	—
254	C₂×C₈×C₅₃	—	2	2	no	—
255	C₂×C₈×C₅₃	—	2	2	no	—
256	C₂×C₈×C₅₃	—	2	2	no	—
257	C₂×C₈×C₅₃	—	2	2	no	—
258	C₂×C₈×C₅₃	—	4	4	no	—
259	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
260	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
261	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
262	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₅₃	—	2	4	no	—
264	C₄⋊C₄×C₅₃	—	2	4	no	—
265	C₄⋊C₄×C₅₃	—	2	4	no	—
266	C₄⋊C₄×C₅₃	—	2	1	no	—
267	C₄⋊C₄×C₅₃	—	2	1	no	—
268	C₄⋊C₄×C₅₃	—	2	1	no	—
269	C₄⋊C₄×C₅₃	—	2	1	no	—
270	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
271	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
272	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
273	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
274	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
275	C₂²⋊C₄×C₅₃	—	2	4	no	—
276	C₂²⋊C₄×C₅₃	—	2	4	no	—
277	C₂²⋊C₄×C₅₃	—	2	4	no	—
278	C₂²⋊C₄×C₅₃	—	2	4	no	—
279	C₂²⋊C₄×C₅₃	—	2	4	no	—
280	C₂²⋊C₄×C₅₃	—	2	4	no	—
281	C₂²⋊C₄×C₅₃	—	2	4	no	—
282	C₂²⋊C₄×C₅₃	—	2	4	no	—
283	C₂²⋊C₄×C₅₃	—	2	4	no	—
284	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
285	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
286	C₄²×C₅₃	—	2	4	no	—
287	C₄²×C₅₃	—	2	4	no	—
288	C₄²×C₅₃	—	2	4	no	—
289	C₄²×C₅₃	C₂×D₄	1	2	yes	—
290	C₄²×C₅₃	C₂⁴	1	2	yes	—
291	C₂³×C₅₃	—	2	2	no	—
292	C₂³×C₅₃	—	2	2	no	—
293	C₂³×C₅₃	—	2	2	no	—
294	C₂³×C₅₃	—	2	2	no	—
295	C₂³×C₅₃	—	2	2	no	—
296	C₂³×C₅₃	—	2	2	no	—
297	C₂³×C₅₃	—	2	2	no	—
298	C₂³×C₅₃	—	2	2	no	—
299	C₂³×C₅₃	—	4	2	no	—
300	C₂³×C₅₃	—	4	2	no	—
301	C₂³×C₅₃	—	4	2	no	—
302	C₂³×C₅₃	—	4	2	no	—
303	C₂³×C₅₃	—	4	2	no	—
304	C₂³×C₅₃	—	4	2	no	—
305	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
306	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
307	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
308	Q₈×C₅₃	—	2	4	no	—
309	Q₈×C₅₃	—	2	2	no	—
310	Q₈×C₅₃	—	2	2	no	—
311	Q₈×C₅₃	—	2	2	no	—
312	Q₈×C₅₃	—	4	8	no	—
313	Q₈×C₅₃	—	4	2	no	—
314	Q₈×C₅₃	—	8	4	no	—
315	Q₈×C₅₃	C₂×#41	1	4	yes	—
316	D₄×C₅₃	—	2	2	no	—
317	D₄×C₅₃	—	2	2	no	—
318	D₄×C₅₃	—	2	2	no	—
319	D₄×C₅₃	—	2	2	no	—
320	D₄×C₅₃	—	4	4	no	—
321	D₄×C₅₃	—	4	8	no	—
322	D₄×C₅₃	—	4	8	no	—
323	D₄×C₅₃	—	4	2	no	—
324	D₄×C₅₃	—	4	2	no	—
325	D₄×C₅₃	—	8	4	no	—
326	D₄×C₅₃	—	8	4	no	—
327	C₂×C₄×C₅₃	—	2	2	no	—
328	C₂×C₄×C₅₃	—	2	2	no	—
329	C₂×C₄×C₅₃	—	2	4	no	—
330	C₂×C₄×C₅₃	—	2	2	no	—
331	C₂×C₄×C₅₃	—	2	2	no	—
332	C₂×C₄×C₅₃	—	2	2	no	—
333	C₂×C₄×C₅₃	—	2	4	no	—
334	C₂×C₄×C₅₃	—	2	4	no	—
335	C₂×C₄×C₅₃	—	2	2	no	—
336	C₂×C₄×C₅₃	—	2	2	no	—
337	C₂×C₄×C₅₃	—	2	2	no	—
338	C₂×C₄×C₅₃	—	2	2	no	—
339	C₂×C₄×C₅₃	—	2	2	no	—
340	C₂×C₄×C₅₃	—	2	2	no	—
341	C₂×C₄×C₅₃	—	2	2	no	—
342	C₂×C₄×C₅₃	—	2	2	no	—
343	C₂×C₄×C₅₃	—	2	2	no	—
344	C₂×C₄×C₅₃	—	4	8	no	—
345	C₂×C₄×C₅₃	—	4	8	no	—
346	C₂×C₄×C₅₃	—	4	8	no	—
347	C₂×C₄×C₅₃	—	4	2	no	—
348	C₂×C₄×C₅₃	—	4	2	no	—
349	C₂×C₄×C₅₃	—	4	2	no	—
350	C₂×C₄×C₅₃	—	4	2	no	—
351	C₂×C₄×C₅₃	—	4	2	no	—
352	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
354	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
358	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
359	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
360	C₈×C₅₃	—	2	2	no	—
361	C₈×C₅₃	—	2	2	no	—
362	C₈×C₅₃	—	2	2	no	—
363	C₈×C₅₃	—	2	2	no	—
364	C₂×#3321	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
365	C₂²×C₅₃	—	2	2	no	—
366	C₂²×C₅₃	—	2	2	no	—
367	C₂²×C₅₃	—	2	2	no	—
368	C₂²×C₅₃	—	2	2	no	—
369	C₂²×C₅₃	—	2	2	no	—
370	C₂²×C₅₃	—	2	2	no	—
371	C₂²×C₅₃	—	4	4	no	—
372	C₂²×C₅₃	—	4	4	no	—
373	C₂²×C₅₃	—	4	2	no	—
374	C₂²×C₅₃	—	4	2	no	—
375	C₂²×C₅₃	—	4	2	no	—
376	C₂²×C₅₃	—	4	2	no	—
377	C₂²×C₅₃	—	4	2	no	—
378	C₂²×C₅₃	—	4	2	no	—
379	C₂²×C₅₃	—	8	4	no	—
380	C₂²×C₅₃	—	8	4	no	—
381	C₂²×C₅₃	#546	1	2	yes	—
382	C₂²×C₅₃	#575	1	2	yes	—
383	C₂²×C₅₃	#577	1	2	yes	—
384	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
385	C₄×C₅₃	—	2	2	no	—
386	C₄×C₅₃	—	2	2	no	—
387	C₄×C₅₃	—	2	4	no	—
388	C₄×C₅₃	—	2	2	no	—
389	C₄×C₅₃	—	2	2	no	—
390	C₄×C₅₃	—	4	2	no	—
391	C₄×C₅₃	—	4	2	no	—
392	C₄×C₅₃	—	4	2	no	—
393	C₄×C₅₃	—	4	2	no	—
394	C₄×C₅₃	—	4	2	no	—
395	C₄×C₅₃	#546	1	2	yes	—
396	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
397	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂×#555	C₂×C₅₃	1	1	yes	characteristic, complemented
399	C₂×#548	C₂×C₅₃	1	1	yes	characteristic, complemented
400	#3321	C₂×C₅₃	1	16	yes	direct product factor
401	C₂×#489	C₂×C₅₃	1	1	yes	characteristic, complemented
402	C₂×#485	C₂×C₅₃	1	1	yes	characteristic, complemented
403	C₂×#482	C₂×C₅₃	1	1	yes	characteristic, complemented
404	C₂×#475	C₂×C₅₃	1	1	yes	characteristic, complemented
405	C₂×#469	C₂×C₅₃	1	1	yes	characteristic, complemented
406	C₂×#465	C₂×C₅₃	1	1	yes	characteristic, complemented
407	C₂×#463	C₂×C₅₃	1	1	yes	characteristic, complemented
408	C₂×#449	C₂×C₅₃	1	1	yes	characteristic, complemented
409	C₂×#448	C₂×C₅₃	1	1	yes	characteristic, complemented
410	C₂×#440	C₂×C₅₃	1	1	yes	characteristic, complemented
411	C₂×#435	C₂×C₅₃	1	1	yes	characteristic, complemented
412	C₂×#419	C₂×C₅₃	1	1	yes	characteristic, complemented
413	C₂×#416	C₂×C₅₃	1	1	yes	characteristic, complemented
414	C₂×C₅₃	—	4	2	no	—
415	C₂×C₅₃	—	4	2	no	—
416	C₂×C₅₃	—	8	2	no	—
417	C₂×C₅₃	—	8	2	no	—
418	C₂×C₅₃	#3321	1	4	yes	direct product factor
419	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
420	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
421	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
422	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
423	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic
424	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
425	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
426	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
427	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
428	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
429	#555	—	2	4	no	—
430	#555	C₂²×C₅₃	1	8	yes	complemented
431	#548	—	2	4	no	—
432	#548	C₂²×C₅₃	1	8	yes	complemented
433	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
434	C₂×#124	—	2	1	no	—
435	C₂×#124	—	2	1	no	—
436	C₂×#124	—	2	1	no	—
437	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
438	C₂×C₂²⋊Q₈	—	2	1	no	—
439	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
440	C₂×#121	—	2	1	no	—
441	C₂×#121	—	2	1	no	—
442	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
443	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
444	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
445	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
446	C₂×C₄×D₄	—	2	1	no	—
447	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
448	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
449	C₂×#117	—	2	1	no	—
450	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
451	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
452	#489	C₂²×C₅₃	1	8	yes	complemented
453	#485	C₂²×C₅₃	1	8	yes	complemented
454	#482	C₂²×C₅₃	1	8	yes	complemented
455	#475	C₂²×C₅₃	1	8	yes	complemented
456	#469	C₂²×C₅₃	1	8	yes	complemented
457	#465	C₂²×C₅₃	1	8	yes	complemented
458	#463	C₂²×C₅₃	1	8	yes	complemented
459	#449	C₂²×C₅₃	1	8	yes	complemented
460	#448	C₂²×C₅₃	1	8	yes	complemented
461	#440	C₂²×C₅₃	1	8	yes	complemented
462	#435	C₂²×C₅₃	1	8	yes	complemented
463	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
464	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
465	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
466	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
467	#419	C₂²×C₅₃	1	8	yes	complemented
468	#416	C₂²×C₅₃	1	8	yes	complemented
469	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
470	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
471	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
472	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
473	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
474	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
475	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
476	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
477	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
478	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
479	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
480	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
481	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
482	C₅₃	C₂×#3321	1	1	yes	characteristic, direct product factor, Sylow
483	C₂×#41	—	2	2	no	—
484	C₂×#41	—	2	4	no	—
485	C₂×#41	—	4	2	no	—
486	C₂×#41	C₂³×C₅₃	1	4	yes	—
487	C₂²×Q₈	—	2	1	no	—
488	C₂²×Q₈	—	2	2	no	—
489	C₂²×Q₈	—	2	1	no	—
490	C₂²×Q₈	—	2	4	no	—
491	C₂²×Q₈	—	4	2	no	—
492	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
493	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
494	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
507	C₂×SD₁₆	—	2	4	no	—
508	C₂×SD₁₆	—	4	2	no	—
509	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
510	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
511	C₂×D₈	—	4	2	no	—
512	C₂×D₈	C₂³×C₅₃	1	4	yes	—
513	C₂×M₁₆	—	4	2	no	—
514	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
515	C₂²×C₈	—	4	2	no	—
516	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
517	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
518	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
519	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
520	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
521	C₄⋊Q₈	—	2	2	no	—
522	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
523	#124	—	2	8	no	—
524	#124	—	2	8	no	—
525	#124	—	2	8	no	—
526	#124	—	2	2	no	—
527	#124	C₂³×C₅₃	1	4	yes	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	8	no	—
530	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
531	#121	—	2	8	no	—
532	#121	—	2	8	no	—
533	#121	—	2	2	no	—
534	#121	—	2	2	no	—
535	#121	—	2	2	no	—
536	#121	C₂³×C₅₃	1	4	yes	—
537	#121	C₂³×C₅₃	1	4	yes	—
538	#121	C₂³×C₅₃	1	4	yes	—
539	C₄×Q₈	—	2	2	no	—
540	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
541	C₄×D₄	—	2	8	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	D₄×C₅₃	1	4	yes	—
544	C₄×D₄	C₂³×C₅₃	1	4	yes	—
545	C₄×D₄	C₂³×C₅₃	1	4	yes	—
546	#117	—	2	2	no	—
547	#117	—	2	2	no	—
548	#117	—	2	8	no	—
549	#117	C₂³×C₅₃	1	4	yes	—
550	#117	C₂³×C₅₃	1	4	yes	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	—	2	1	no	—
561	C₂×C₂²⋊C₄	—	2	1	no	—
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
569	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
570	C₂×C₄²	—	2	1	no	—
571	C₂×C₄²	—	2	1	no	—
572	C₂×C₄²	—	2	1	no	—
573	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
574	#107	C₂³×C₅₃	1	4	yes	—
575	#106	C₂³×C₅₃	1	4	yes	—
576	#106	C₂³×C₅₃	1	4	yes	—
577	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
578	#103	C₂³×C₅₃	1	4	yes	—
579	#103	C₂³×C₅₃	1	4	yes	—
580	#103	C₂³×C₅₃	1	4	yes	—
581	#103	C₂³×C₅₃	1	4	yes	—
582	#103	C₂³×C₅₃	1	4	yes	—
583	#103	C₂³×C₅₃	1	4	yes	—
584	#102	C₂³×C₅₃	1	4	yes	—
585	#102	C₂³×C₅₃	1	4	yes	—
586	#102	C₂³×C₅₃	1	4	yes	—
587	#102	C₂³×C₅₃	1	4	yes	—
588	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
589	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
590	#97	C₂³×C₅₃	1	4	yes	—
591	C₂⁴	—	2	1	no	—
592	C₂⁴	—	2	1	no	—
593	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
594	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
595	#41	—	2	8	no	—
596	#41	—	4	4	no	—
597	#41	—	4	8	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	4	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	4	no	—
602	C₂×Q₈	—	2	2	no	—
603	C₂×Q₈	—	2	8	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	4	4	no	—
607	C₂×Q₈	—	4	4	no	—
608	C₂×Q₈	—	4	8	no	—
609	C₂×Q₈	—	8	2	no	—
610	C₂×Q₈	#41×C₅₃	1	4	yes	—
611	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
612	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	4	2	no	—
624	C₂×D₄	—	4	4	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	—	8	2	no	—
627	C₂×D₄	—	8	2	no	—
628	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
629	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
630	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	4	4	no	—
645	C₂²×C₄	—	4	4	no	—
646	C₂²×C₄	—	4	4	no	—
647	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
652	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
656	SD₁₆	—	2	8	no	—
657	SD₁₆	—	4	4	no	—
658	D₈	—	4	4	no	—
659	M₁₆	—	4	4	no	—
660	C₂×C₈	—	2	2	no	—
661	C₂×C₈	—	2	2	no	—
662	C₂×C₈	—	2	2	no	—
663	C₂×C₈	—	2	2	no	—
664	C₂×C₈	—	4	4	no	—
665	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
666	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
667	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
668	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
677	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
678	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
679	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
691	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	4	no	—
695	C₄²	C₂×D₄×C₅₃	1	2	yes	—
696	C₄²	C₂⁴×C₅₃	1	2	yes	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	4	2	no	—
706	C₂³	—	4	2	no	—
707	C₂³	—	4	2	no	—
708	C₂³	—	4	2	no	—
709	C₂³	—	4	2	no	—
710	C₂³	—	4	2	no	—
711	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
712	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
713	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
714	Q₈	—	2	4	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	4	8	no	—
719	Q₈	—	4	2	no	—
720	Q₈	—	8	4	no	—
721	Q₈	C₂×#41×C₅₃	1	4	yes	—
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	4	4	no	—
727	D₄	—	4	8	no	—
728	D₄	—	4	8	no	—
729	D₄	—	4	2	no	—
730	D₄	—	4	2	no	—
731	D₄	—	8	4	no	—
732	D₄	—	8	4	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	4	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	4	8	no	—
751	C₂×C₄	—	4	8	no	—
752	C₂×C₄	—	4	8	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
759	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
760	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
761	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
762	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
763	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
764	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
765	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
766	C₈	—	2	2	no	—
767	C₈	—	2	2	no	—
768	C₈	—	2	2	no	—
769	C₈	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	4	4	no	—
777	C₂²	—	4	4	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	8	4	no	—
785	C₂²	—	8	4	no	—
786	C₂²	C₅₃×#546	1	2	yes	—
787	C₂²	C₅₃×#575	1	2	yes	—
788	C₂²	C₅₃×#577	1	2	yes	—
789	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	4	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	C₅₃×#546	1	2	yes	—
801	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
802	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
803	C₂	—	4	2	no	—
804	C₂	—	4	2	no	—
805	C₂	—	8	2	no	—
806	C₂	—	8	2	no	—
807	C₂	C₅₃×#3321	1	4	yes	direct product factor
808	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
809	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
810	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 ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#555	C₂	semidirect
2. C₂×C₅₃×#548	C₂	semidirect
3. C₅₃×#3321	C₂	direct (N × H)
4. C₂×C₅₃×#489	C₂	semidirect
5. C₂×C₅₃×#485	C₂	semidirect
6. C₂×C₅₃×#482	C₂	semidirect
7. C₂×C₅₃×#475	C₂	semidirect
8. C₂×C₅₃×#469	C₂	semidirect
9. C₂×C₅₃×#465	C₂	semidirect
10. C₂×C₅₃×#463	C₂	semidirect
11. C₂×C₅₃×#449	C₂	semidirect
12. C₂×C₅₃×#448	C₂	semidirect
13. C₂×C₅₃×#440	C₂	semidirect
14. C₂×C₅₃×#435	C₂	semidirect
15. C₂×C₅₃×#419	C₂	semidirect
16. C₂×C₅₃×#416	C₂	semidirect
25. C₅₃×#555	C₂²	semidirect
27. C₅₃×#548	C₂²	semidirect
47. C₅₃×#489	C₂²	semidirect
48. C₅₃×#485	C₂²	semidirect
49. C₅₃×#482	C₂²	semidirect
50. C₅₃×#475	C₂²	semidirect
51. C₅₃×#469	C₂²	semidirect
52. C₅₃×#465	C₂²	semidirect
53. C₅₃×#463	C₂²	semidirect
54. C₅₃×#449	C₂²	semidirect
55. C₅₃×#448	C₂²	semidirect
56. C₅₃×#440	C₂²	semidirect
57. C₅₃×#435	C₂²	semidirect
62. C₅₃×#419	C₂²	semidirect
63. C₅₃×#416	C₂²	semidirect
364. C₂×#3321	C₅₃	direct (N × H)
398. C₂×#555	C₂×C₅₃	semidirect
399. C₂×#548	C₂×C₅₃	semidirect
400. #3321	C₂×C₅₃	direct (N × H)
401. C₂×#489	C₂×C₅₃	semidirect
402. C₂×#485	C₂×C₅₃	semidirect
403. C₂×#482	C₂×C₅₃	semidirect
404. C₂×#475	C₂×C₅₃	semidirect
405. C₂×#469	C₂×C₅₃	semidirect
406. C₂×#465	C₂×C₅₃	semidirect
407. C₂×#463	C₂×C₅₃	semidirect
408. C₂×#449	C₂×C₅₃	semidirect
409. C₂×#448	C₂×C₅₃	semidirect
410. C₂×#440	C₂×C₅₃	semidirect
411. C₂×#435	C₂×C₅₃	semidirect
412. C₂×#419	C₂×C₅₃	semidirect
413. C₂×#416	C₂×C₅₃	semidirect
418. C₂×C₅₃	#3321	direct (N × H)
430. #555	C₂²×C₅₃	semidirect
432. #548	C₂²×C₅₃	semidirect
452. #489	C₂²×C₅₃	semidirect
453. #485	C₂²×C₅₃	semidirect
454. #482	C₂²×C₅₃	semidirect
455. #475	C₂²×C₅₃	semidirect
456. #469	C₂²×C₅₃	semidirect
457. #465	C₂²×C₅₃	semidirect
458. #463	C₂²×C₅₃	semidirect
459. #449	C₂²×C₅₃	semidirect
460. #448	C₂²×C₅₃	semidirect
461. #440	C₂²×C₅₃	semidirect
462. #435	C₂²×C₅₃	semidirect
467. #419	C₂²×C₅₃	semidirect
468. #416	C₂²×C₅₃	semidirect
482. C₅₃	C₂×#3321	direct (N × H)
807. C₂	C₅₃×#3321	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×#555	2
C₂×C₅₃×#548	2
C₅₃×#3321	2
C₂×C₅₃×#489	2
C₂×C₅₃×#485	2
C₂×C₅₃×#482	2
C₂×C₅₃×#475	2
C₂×C₅₃×#469	2
C₂×C₅₃×#465	2
C₂×C₅₃×#463	2
C₂×C₅₃×#449	2
C₂×C₅₃×#448	2
C₂×C₅₃×#440	2
C₂×C₅₃×#435	2
C₂×C₅₃×#419	2
C₂×C₅₃×#416	2
C₂×#3321	53

Subgroups — C2×C53×#3321 #27268652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3321 #27268652