Subgroups — D₅₃×#3459 #28290835

Order 13568.

8146 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288127	C₂	1	1	yes	maximal, characteristic, complemented
2	#20288126	C₂	1	6	yes	maximal, complemented
3	#20288125	C₂	1	6	yes	maximal, complemented
4	#20288124	C₂	1	3	yes	maximal, complemented
5	#20288123	C₂	1	6	yes	maximal, complemented
6	#20288122	C₂	1	6	yes	maximal, complemented
7	#20288121	C₂	1	3	yes	maximal, complemented
8	#543×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#539×D₅₃	C₂	1	6	yes	maximal, complemented
10	#538×D₅₃	C₂	1	6	yes	maximal, complemented
11	#534×D₅₃	C₂	1	3	yes	maximal, complemented
12	#529×D₅₃	C₂	1	6	yes	maximal, complemented
13	#525×D₅₃	C₂	1	6	yes	maximal, complemented
14	C₂×C₄×D₄×D₅₃	C₂	1	3	yes	maximal, complemented
15	C₅₃×#3459	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×D₅₃	C₂²	1	2	yes	complemented
17	C₂²×D₄×D₅₃	C₂²	1	3	yes	—
18	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
19	C₂³×C₄×D₅₃	C₂²	1	3	yes	complemented
20	#16811249	C₂²	1	3	yes	complemented
21	#16811248	C₂²	1	6	yes	complemented
22	#16811248	C₂²	1	6	yes	complemented
23	#16811222	C₂²	1	6	yes	complemented
24	#16811221	C₂²	1	12	yes	complemented
25	#16811220	C₂²	1	6	yes	complemented
26	#16811219	C₂²	1	12	yes	complemented
27	#16811218	C₂²	1	6	yes	complemented
28	#16811217	C₂²	1	12	yes	complemented
29	#16811216	C₂²	1	12	yes	complemented
30	#16811215	C₂²	1	12	yes	complemented
31	#16811214	C₂²	1	12	yes	complemented
32	#16811213	C₂²	1	6	yes	complemented
33	#16811212	C₂²	1	12	yes	complemented
34	#16811211	C₂²	1	6	yes	complemented
35	#16811210	C₂²	1	6	yes	complemented
36	#16811209	C₂²	1	12	yes	complemented
37	#16811208	C₂²	1	12	yes	complemented
38	#16811207	C₂²	1	12	yes	complemented
39	#16811206	C₂²	1	12	yes	complemented
40	#16811205	C₂²	1	12	yes	complemented
41	#16811185	C₂²	1	3	yes	complemented
42	#16811184	C₂²	1	12	yes	complemented
43	#16811183	C₂²	1	12	yes	complemented
44	#16811182	C₂²	1	6	yes	complemented
45	#16811181	C₂²	1	6	yes	complemented
46	#16811181	C₂²	1	6	yes	complemented
47	#16811160	C₂²	1	6	yes	complemented
48	#16811159	C₂²	1	6	yes	complemented
49	#16811158	C₂²	1	6	yes	complemented
50	#16811157	C₂²	1	6	yes	complemented
51	#16811156	C₂²	1	12	yes	complemented
52	#16811155	C₂²	1	6	yes	complemented
53	#16811154	C₂²	1	6	yes	complemented
54	#16811153	C₂²	1	12	yes	complemented
55	#16811152	C₂²	1	6	yes	complemented
56	#16811151	C₂²	1	12	yes	complemented
57	#16811150	C₂²	1	12	yes	complemented
58	#126×D₅₃	C₂²	1	12	yes	complemented
59	#125×D₅₃	C₂²	1	6	yes	complemented
60	#124×D₅₃	C₂²	1	6	yes	complemented
61	#16811136	C₂²	1	6	yes	complemented
62	#16811136	C₂²	1	6	yes	complemented
63	#16811135	C₂²	1	6	yes	complemented
64	#16811134	C₂²	1	6	yes	complemented
65	#16811133	C₂²	1	6	yes	complemented
66	#16811133	C₂²	1	6	yes	complemented
67	#16811132	C₂²	1	12	yes	complemented
68	#16811132	C₂²	1	12	yes	complemented
69	#16811131	C₂²	1	12	yes	complemented
70	#16811130	C₂²	1	6	yes	complemented
71	#16811129	C₂²	1	12	yes	complemented
72	#123×D₅₃	C₂²	1	12	yes	complemented
73	#123×D₅₃	C₂²	1	12	yes	complemented
74	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
75	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
76	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
77	#121×D₅₃	C₂²	1	6	yes	—
78	#121×D₅₃	C₂²	1	6	yes	—
79	#121×D₅₃	C₂²	1	6	yes	complemented
80	#120×D₅₃	C₂²	1	12	yes	complemented
81	C₄×Q₈×D₅₃	C₂²	1	2	yes	complemented
82	C₂×C₄×D₂₁₂	C₂²	1	3	yes	complemented
83	C₂×D₄×Dic₅₃	C₂²	1	3	yes	complemented
84	C₂×#13133179	C₂²	1	3	yes	complemented
85	C₂×C₄×C₂²⋊D₅₃	C₂²	1	3	yes	complemented
86	C₂×C₄×C₂²⋊D₅₃	C₂²	1	3	yes	complemented
87	C₂×#13133177	C₂²	1	3	yes	complemented
88	C₂×#13133177	C₂²	1	3	yes	complemented
89	C₄×D₄×D₅₃	C₂²	1	12	yes	complemented
90	C₄×D₄×D₅₃	C₂²	1	12	yes	complemented
91	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
92	C₄×D₄×D₅₃	C₂²	1	12	yes	complemented
93	C₄×D₄×D₅₃	C₂²	1	12	yes	complemented
94	#117×D₅₃	C₂²	1	6	yes	complemented
95	C₂×C₄⋊C₄×D₅₃	C₂²	1	3	yes	complemented
96	C₂×C₂²⋊C₄×D₅₃	C₂²	1	3	yes	—
97	C₂×C₂²⋊C₄×D₅₃	C₂²	1	3	yes	complemented
98	C₂×C₄²×D₅₃	C₂²	1	3	yes	complemented
99	C₅₃×#543	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#539	C₂²	1	6	yes	complemented
101	C₅₃×#538	C₂²	1	6	yes	complemented
102	C₅₃×#534	C₂²	1	3	yes	complemented
103	C₅₃×#529	C₂²	1	6	yes	complemented
104	C₅₃×#525	C₂²	1	6	yes	complemented
105	C₂×C₄×D₄×C₅₃	C₂²	1	3	yes	complemented
106	C₂⁴×D₅₃	C₂³	1	3	yes	—
107	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
108	C₂×#11719949	C₂³	1	2	yes	complemented
109	C₂×#11719945	C₂³	1	6	yes	complemented
110	C₂×#11719947	C₂³	1	6	yes	complemented
111	#41×D₅₃	—	4	8	no	—
112	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
113	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
114	C₂²×D₂₁₂	C₂³	1	3	yes	—
115	C₂²×C₂²⋊D₅₃	C₂³	1	3	yes	—
116	C₂²×C₂²⋊D₅₃	C₂³	1	3	yes	—
117	C₂×D₄×D₅₃	—	2	24	no	—
118	C₂×D₄×D₅₃	C₂³	1	12	yes	—
119	C₂×D₄×D₅₃	C₂³	1	12	yes	—
120	C₂×D₄×D₅₃	C₂³	1	6	yes	—
121	C₂×D₄×D₅₃	C₂³	1	6	yes	—
122	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
123	C₂³×Dic₅₃	C₂³	1	3	yes	complemented
124	C₂²×C₄×D₅₃	—	4	4	no	—
125	C₂²×C₄×D₅₃	—	4	12	no	—
126	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
127	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
128	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
129	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
130	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
131	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
132	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
133	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
134	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
135	C₂²×C₄×D₅₃	C₂³	1	6	yes	complemented
136	C₂²×C₄×D₅₃	C₂³	1	6	yes	complemented
137	C₂²×C₄×D₅₃	C₂³	1	3	yes	complemented
138	C₂²×C₄×D₅₃	C₂³	1	3	yes	complemented
139	#13133212	C₂³	1	12	yes	complemented
140	#13133212	C₂³	1	12	yes	complemented
141	#13133212	C₂³	1	12	yes	complemented
142	#13133211	C₂³	1	12	yes	complemented
143	#13133210	C₂³	1	12	yes	complemented
144	#13133210	C₂³	1	12	yes	complemented
145	#13133210	C₂³	1	12	yes	complemented
146	#13133209	C₂³	1	6	yes	complemented
147	#13133208	C₂³	1	6	yes	complemented
148	#13133208	C₂³	1	6	yes	complemented
149	#13133207	C₂³	1	12	yes	complemented
150	#13133207	C₂³	1	12	yes	complemented
151	#13133206	C₂³	1	6	yes	complemented
152	#13133205	C₂³	1	6	yes	complemented
153	#13133204	C₂³	1	6	yes	complemented
154	#13133203	C₂³	1	12	yes	complemented
155	#13133203	C₂³	1	12	yes	complemented
156	#13133202	C₂³	1	12	yes	complemented
157	#13133202	C₂³	1	12	yes	complemented
158	#13133202	C₂³	1	12	yes	complemented
159	#13133202	C₂³	1	12	yes	complemented
160	#13133201	C₂³	1	12	yes	complemented
161	#13133201	C₂³	1	12	yes	complemented
162	#13133200	C₂³	1	12	yes	complemented
163	#13133200	C₂³	1	12	yes	complemented
164	#13133199	C₂³	1	12	yes	complemented
165	#13133199	C₂³	1	12	yes	complemented
166	#13133199	C₂³	1	12	yes	complemented
167	#13133199	C₂³	1	12	yes	complemented
168	#13133198	C₂³	1	12	yes	complemented
169	#13133198	C₂³	1	12	yes	complemented
170	#13133197	C₂³	1	6	yes	complemented
171	#13133197	C₂³	1	6	yes	complemented
172	#13133197	C₂³	1	6	yes	complemented
173	#13133196	C₂³	1	6	yes	complemented
174	#13133196	C₂³	1	6	yes	complemented
175	#13133196	C₂³	1	6	yes	complemented
176	#13133195	C₂³	1	12	yes	complemented
177	#13133195	C₂³	1	12	yes	complemented
178	#13133195	C₂³	1	12	yes	complemented
179	#13133194	C₂³	1	12	yes	complemented
180	#13133194	C₂³	1	12	yes	complemented
181	#13133194	C₂³	1	12	yes	complemented
182	#13133193	C₂³	1	6	yes	complemented
183	#13133193	C₂³	1	6	yes	complemented
184	#13133193	C₂³	1	6	yes	complemented
185	#13133192	C₂³	1	6	yes	—
186	#13133192	C₂³	1	6	yes	—
187	#13133192	C₂³	1	6	yes	complemented
188	#13133191	C₂³	1	6	yes	—
189	#13133191	C₂³	1	6	yes	—
190	#13133191	C₂³	1	6	yes	complemented
191	#13133190	C₂³	1	12	yes	—
192	#13133190	C₂³	1	12	yes	—
193	#13133190	C₂³	1	12	yes	complemented
194	#13133189	C₂³	1	12	yes	—
195	#13133189	C₂³	1	12	yes	—
196	#13133189	C₂³	1	12	yes	complemented
197	#13133188	C₂³	1	6	yes	—
198	#13133188	C₂³	1	6	yes	—
199	#13133188	C₂³	1	6	yes	complemented
200	#13133187	C₂³	1	12	yes	complemented
201	#13133187	C₂³	1	12	yes	complemented
202	#13133187	C₂³	1	12	yes	complemented
203	#13133186	C₂³	1	12	yes	complemented
204	#13133185	C₂³	1	12	yes	complemented
205	#13133185	C₂³	1	12	yes	complemented
206	#13133185	C₂³	1	12	yes	complemented
207	Q₈×Dic₅₃	C₂³	1	2	yes	complemented
208	C₄×Dic₁₀₆	C₂³	1	6	yes	complemented
209	#13133182	C₂³	1	6	yes	complemented
210	C₄×D₂₁₂	C₂³	1	12	yes	complemented
211	C₄×D₂₁₂	C₂³	1	12	yes	complemented
212	C₄×D₂₁₂	C₂³	1	6	yes	complemented
213	D₄×Dic₅₃	C₂³	1	12	yes	complemented
214	D₄×Dic₅₃	C₂³	1	12	yes	complemented
215	D₄×Dic₅₃	C₂³	1	6	yes	complemented
216	#13133179	C₂³	1	12	yes	complemented
217	#13133179	C₂³	1	12	yes	complemented
218	#13133179	C₂³	1	6	yes	complemented
219	C₄×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
220	C₄×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
221	C₄×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
222	C₄×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
223	C₄×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
224	#13133177	C₂³	1	12	yes	complemented
225	#13133177	C₂³	1	12	yes	complemented
226	#13133177	C₂³	1	12	yes	complemented
227	#13133177	C₂³	1	12	yes	complemented
228	#13133177	C₂³	1	12	yes	complemented
229	#13133176	C₂³	1	6	yes	complemented
230	#13133175	C₂³	1	6	yes	complemented
231	#13133175	C₂³	1	6	yes	complemented
232	#13133174	C₂³	1	12	yes	complemented
233	#13133173	C₂³	1	12	yes	complemented
234	C₂×C₄⋊Dic₅₃	C₂³	1	3	yes	complemented
235	C₂×#11719919	C₂³	1	3	yes	complemented
236	C₂×#11719919	C₂³	1	3	yes	complemented
237	C₄⋊C₄×D₅₃	C₂³	1	12	yes	—
238	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
239	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
240	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
241	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
242	C₄⋊C₄×D₅₃	C₂³	1	12	yes	complemented
243	C₂×C₂²⋊Dic₅₃	C₂³	1	3	yes	—
244	C₂×C₂²⋊Dic₅₃	C₂³	1	3	yes	complemented
245	C₂×#11719921	C₂³	1	3	yes	—
246	C₂×#11719921	C₂³	1	3	yes	—
247	C₂×#11719921	C₂³	1	3	yes	complemented
248	C₂×#11719921	C₂³	1	3	yes	complemented
249	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	—
250	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	—
251	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	—
252	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	—
253	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	—
254	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	complemented
255	C₂×C₄×Dic₅₃	C₂³	1	3	yes	complemented
256	C₂×C₄×Dic₅₃	C₂³	1	3	yes	complemented
257	C₂×C₄×Dic₅₃	C₂³	1	3	yes	complemented
258	C₄²×D₅₃	C₂³	1	6	yes	—
259	C₄²×D₅₃	C₂³	1	6	yes	—
260	C₄²×D₅₃	C₂³	1	6	yes	complemented
261	C₄²×D₅₃	C₂³	1	6	yes	complemented
262	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
263	C₂²×D₄×C₅₃	C₂³	1	3	yes	—
264	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂³×C₄×C₅₃	C₂³	1	3	yes	complemented
266	#126×C₅₃	C₂³	1	12	yes	complemented
267	#125×C₅₃	C₂³	1	6	yes	complemented
268	#124×C₅₃	C₂³	1	6	yes	complemented
269	#123×C₅₃	C₂³	1	12	yes	complemented
270	#123×C₅₃	C₂³	1	12	yes	complemented
271	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
272	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
273	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
274	#121×C₅₃	C₂³	1	6	yes	—
275	#121×C₅₃	C₂³	1	6	yes	—
276	#121×C₅₃	C₂³	1	6	yes	complemented
277	#120×C₅₃	C₂³	1	12	yes	complemented
278	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
279	C₄×D₄×C₅₃	C₂³	1	12	yes	complemented
280	C₄×D₄×C₅₃	C₂³	1	12	yes	complemented
281	C₄×D₄×C₅₃	C₂³	1	6	yes	complemented
282	#117×C₅₃	C₂³	1	6	yes	complemented
283	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	complemented
284	C₂×C₂²⋊C₄×C₅₃	C₂³	1	3	yes	—
285	C₂×C₂²⋊C₄×C₅₃	C₂³	1	3	yes	complemented
286	C₂×C₄²×C₅₃	C₂³	1	3	yes	complemented
287	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
288	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
289	C₂³×D₅₃	—	2	12	no	—
290	C₂³×D₅₃	—	4	2	no	—
291	C₂³×D₅₃	—	4	6	no	—
292	C₂³×D₅₃	—	4	2	no	—
293	C₂³×D₅₃	—	4	6	no	—
294	C₂³×D₅₃	#41	1	8	yes	complemented
295	C₂³×D₅₃	C₂⁴	1	6	yes	—
296	C₂³×D₅₃	C₂⁴	1	3	yes	—
297	C₂³×D₅₃	C₂⁴	1	6	yes	—
298	C₂³×D₅₃	C₂⁴	1	3	yes	—
299	C₂³×D₅₃	C₂⁴	1	3	yes	—
300	#41×C₅₃	—	4	4	no	—
301	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
302	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
303	C₂×D₄×C₅₃	—	2	12	no	—
304	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
305	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
306	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
307	C₂²×C₄×C₅₃	—	4	2	no	—
308	C₂²×C₄×C₅₃	—	4	6	no	—
309	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
310	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
311	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
312	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
313	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
314	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
315	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
316	C₂×C₂²⋊D₅₃	—	2	12	no	—
317	C₂×C₂²⋊D₅₃	—	2	12	no	—
318	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
319	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
320	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
321	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
322	C₂²×Dic₅₃	—	4	2	no	—
323	C₂²×Dic₅₃	—	4	6	no	—
324	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
325	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
326	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
327	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
328	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
329	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
330	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
331	#11719949	—	4	4	no	—
332	Q₈×D₅₃	—	4	4	no	—
333	Q₈×D₅₃	—	4	4	no	—
334	#11719947	—	4	12	no	—
335	D₄×D₅₃	—	2	48	no	—
336	D₄×D₅₃	—	2	48	no	—
337	D₄×D₅₃	—	4	12	no	—
338	D₄×D₅₃	—	4	12	no	—
339	#11719945	—	4	12	no	—
340	C₂×D₂₁₂	—	2	12	no	—
341	C₂×D₂₁₂	C₂⁴	1	12	yes	—
342	C₂×D₂₁₂	C₂⁴	1	6	yes	—
343	C₂×D₂₁₂	C₂⁴	1	6	yes	—
344	C₂×C₄×D₅₃	—	2	12	no	—
345	C₂×C₄×D₅₃	—	2	12	no	—
346	C₂×C₄×D₅₃	—	2	24	no	—
347	C₂×C₄×D₅₃	—	4	6	no	—
348	C₂×C₄×D₅₃	—	4	12	no	—
349	C₂×C₄×D₅₃	—	4	6	no	—
350	C₂×C₄×D₅₃	—	4	6	no	—
351	C₂×C₄×D₅₃	—	4	12	no	—
352	C₂×C₄×D₅₃	—	4	6	no	—
353	C₂×C₄×D₅₃	—	4	6	no	—
354	C₂×C₄×D₅₃	—	4	12	no	—
355	C₂×C₄×D₅₃	—	4	6	no	—
356	C₂×C₄×D₅₃	—	4	6	no	—
357	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
358	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
359	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
360	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
361	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
362	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
363	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
364	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
365	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
366	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
367	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
368	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
369	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
370	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
371	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
372	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
373	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
374	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
375	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
376	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
377	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
378	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
379	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
380	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
381	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
382	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
383	C₄²×C₅₃	C₂⁴	1	6	yes	—
384	C₄²×C₅₃	C₂⁴	1	6	yes	—
385	C₂²⋊Dic₅₃	C₂⁴	1	12	yes	—
386	C₂²⋊Dic₅₃	C₂⁴	1	12	yes	—
387	C₂²⋊Dic₅₃	C₂⁴	1	12	yes	—
388	C₂²⋊Dic₅₃	C₂⁴	1	12	yes	—
389	#11719921	C₂⁴	1	12	yes	—
390	#11719921	C₂⁴	1	12	yes	—
391	#11719921	C₂⁴	1	12	yes	—
392	#11719921	C₂⁴	1	12	yes	—
393	#11719921	C₂⁴	1	12	yes	—
394	#11719921	C₂⁴	1	12	yes	—
395	#11719921	C₂⁴	1	12	yes	—
396	#11719921	C₂⁴	1	12	yes	—
397	C₄⋊Dic₅₃	C₂⁴	1	12	yes	—
398	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
399	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
400	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
401	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
402	#11719919	C₂⁴	1	12	yes	—
403	#11719919	C₂⁴	1	12	yes	—
404	#11719919	C₂⁴	1	12	yes	—
405	#11719919	C₂⁴	1	12	yes	—
406	#11719919	C₂⁴	1	12	yes	—
407	#11719919	C₂⁴	1	12	yes	—
408	C₄×Dic₅₃	C₂⁴	1	6	yes	—
409	C₄×Dic₅₃	C₂⁴	1	6	yes	—
410	C₄×Dic₅₃	C₂⁴	1	6	yes	—
411	C₄×Dic₅₃	C₂⁴	1	6	yes	—
412	C₄×Dic₅₃	C₂⁴	1	6	yes	—
413	C₄×Dic₅₃	C₂⁴	1	6	yes	—
414	C₂³×C₅₃	—	2	6	no	—
415	C₂³×C₅₃	—	4	1	no	—
416	C₂³×C₅₃	—	4	3	no	—
417	C₂³×C₅₃	—	4	1	no	—
418	C₂³×C₅₃	—	4	3	no	—
419	C₂³×C₅₃	C₂×#41	1	4	yes	complemented
420	C₂³×C₅₃	C₂⁵	1	6	yes	—
421	C₂³×C₅₃	C₂⁵	1	3	yes	—
422	C₂²×D₅₃	—	2	6	no	—
423	C₂²×D₅₃	—	2	6	no	—
424	C₂²×D₅₃	—	2	6	no	—
425	C₂²×D₅₃	—	2	12	no	—
426	C₂²×D₅₃	—	2	12	no	—
427	C₂²×D₅₃	—	2	12	no	—
428	C₂²×D₅₃	—	2	12	no	—
429	C₂²×D₅₃	—	4	16	no	—
430	C₂²×D₅₃	—	4	3	no	—
431	C₂²×D₅₃	—	4	6	no	—
432	C₂²×D₅₃	—	4	3	no	—
433	C₂²×D₅₃	—	4	3	no	—
434	C₂²×D₅₃	—	4	6	no	—
435	C₂²×D₅₃	—	4	3	no	—
436	C₂²×D₅₃	—	4	48	no	—
437	C₂²×D₅₃	C₂×#41	1	12	yes	—
438	C₂²×D₅₃	C₂×#41	1	12	yes	complemented
439	C₂²×D₅₃	C₂⁵	1	6	yes	—
440	C₂²×D₅₃	C₂⁵	1	3	yes	—
441	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
442	Q₈×C₅₃	—	4	2	no	—
443	Q₈×C₅₃	—	4	2	no	—
444	D₄×C₅₃	—	2	24	no	—
445	D₄×C₅₃	—	4	6	no	—
446	D₄×C₅₃	—	4	6	no	—
447	C₂×C₄×C₅₃	—	2	6	no	—
448	C₂×C₄×C₅₃	—	2	6	no	—
449	C₂×C₄×C₅₃	—	2	12	no	—
450	C₂×C₄×C₅₃	—	4	3	no	—
451	C₂×C₄×C₅₃	—	4	6	no	—
452	C₂×C₄×C₅₃	—	4	3	no	—
453	C₂×C₄×C₅₃	—	4	3	no	—
454	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
455	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
456	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
457	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
458	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
459	C₂²⋊D₅₃	—	2	24	no	—
460	C₂²⋊D₅₃	—	2	24	no	—
461	C₂²⋊D₅₃	—	4	12	no	—
462	C₂²⋊D₅₃	—	4	12	no	—
463	C₂×Dic₅₃	—	2	6	no	—
464	C₂×Dic₅₃	—	2	6	no	—
465	C₂×Dic₅₃	—	2	12	no	—
466	C₂×Dic₅₃	—	4	3	no	—
467	C₂×Dic₅₃	—	4	6	no	—
468	C₂×Dic₅₃	—	4	3	no	—
469	C₂×Dic₅₃	—	4	3	no	—
470	C₂×Dic₅₃	C₂⁵	1	6	yes	—
471	C₂×Dic₅₃	C₂⁵	1	6	yes	—
472	C₂×Dic₅₃	C₂⁵	1	3	yes	—
473	C₂×Dic₅₃	C₂⁵	1	6	yes	—
474	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
475	D₂₁₂	—	2	24	no	—
476	D₂₁₂	—	4	6	no	—
477	D₂₁₂	—	4	6	no	—
478	C₄×D₅₃	—	2	12	no	—
479	C₄×D₅₃	—	2	12	no	—
480	C₄×D₅₃	—	2	6	no	—
481	C₄×D₅₃	—	2	12	no	—
482	C₄×D₅₃	—	2	12	no	—
483	C₄×D₅₃	—	2	6	no	—
484	C₄×D₅₃	—	2	12	no	—
485	C₄×D₅₃	—	2	6	no	—
486	C₄×D₅₃	—	2	12	no	—
487	C₄×D₅₃	—	4	6	no	—
488	C₄×D₅₃	—	4	6	no	—
489	C₄×D₅₃	—	4	6	no	—
490	C₄×D₅₃	—	4	6	no	—
491	C₄×D₅₃	—	4	6	no	—
492	C₄×D₅₃	H(5,𝔽₂)	1	4	yes	—
493	Dic₁₀₆	—	4	6	no	—
494	Dic₁₀₆	—	4	6	no	—
495	C₂×#3459	—	53	1	no	maximal, Sylow
496	C₂²×C₅₃	—	2	3	no	—
497	C₂²×C₅₃	—	2	3	no	—
498	C₂²×C₅₃	—	2	6	no	—
499	C₂²×C₅₃	—	2	6	no	—
500	C₂²×C₅₃	—	2	6	no	—
501	C₂²×C₅₃	—	4	4	no	—
502	C₂²×C₅₃	—	4	12	no	—
503	C₂²×C₅₃	C₂²×#41	1	6	yes	—
504	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
505	C₂×D₅₃	—	2	3	no	—
506	C₂×D₅₃	—	2	3	no	—
507	C₂×D₅₃	—	2	24	no	—
508	C₂×D₅₃	—	2	6	no	—
509	C₂×D₅₃	—	2	6	no	—
510	C₂×D₅₃	—	2	6	no	—
511	C₂×D₅₃	—	4	12	no	—
512	C₂×D₅₃	—	4	24	no	—
513	C₂×D₅₃	—	4	12	no	—
514	C₂×D₅₃	—	4	24	no	—
515	C₂×D₅₃	C₂²×#41	1	6	yes	—
516	C₂×D₅₃	C₂²×#41	1	2	yes	—
517	C₂×D₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
518	C₂×D₅₃	#585	1	2	yes	—
519	C₄×C₅₃	—	2	6	no	—
520	C₄×C₅₃	—	2	6	no	—
521	C₄×C₅₃	—	2	3	no	—
522	C₄×C₅₃	—	2	6	no	—
523	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
524	Dic₅₃	—	2	6	no	—
525	Dic₅₃	—	2	6	no	—
526	Dic₅₃	—	2	3	no	—
527	Dic₅₃	—	2	6	no	—
528	Dic₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
529	#3459	—	53	1	no	—
530	#3459	—	53	6	no	—
531	#3459	—	53	6	no	—
532	#3459	—	53	3	no	—
533	#3459	—	53	6	no	—
534	#3459	—	53	6	no	—
535	#3459	—	53	3	no	—
536	#3459	D₅₃	1	1	yes	characteristic, direct product factor
537	C₂×#543	—	53	1	no	—
538	C₂×#539	—	53	6	no	—
539	C₂×#538	—	53	6	no	—
540	C₂×#534	—	53	3	no	—
541	C₂×#529	—	53	6	no	—
542	C₂×#525	—	53	6	no	—
543	C₂²×C₄×D₄	—	53	3	no	—
544	C₂×C₅₃	—	2	6	no	—
545	C₂×C₅₃	—	4	6	no	—
546	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
547	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
549	D₅₃	—	2	6	no	—
550	D₅₃	—	4	6	no	—
551	D₅₃	#3459	1	4	yes	direct product factor
552	C₂²×#41	—	53	2	no	—
553	C₂³×D₄	—	53	3	no	—
554	C₂⁴×C₄	—	53	1	no	—
555	C₂⁴×C₄	—	53	3	no	—
556	#543	—	53	6	no	—
557	#543	—	53	6	no	—
558	#543	—	53	3	no	—
559	#543	C₂×D₅₃	1	1	yes	characteristic, complemented
560	#539	—	53	12	no	—
561	#539	—	53	12	no	—
562	#539	—	53	12	no	—
563	#539	—	53	12	no	—
564	#539	—	53	12	no	—
565	#539	—	53	6	no	—
566	#539	—	53	6	no	—
567	#539	—	53	12	no	—
568	#539	—	53	6	no	—
569	#539	C₂×D₅₃	1	6	yes	complemented
570	#538	—	53	12	no	—
571	#538	—	53	12	no	—
572	#538	—	53	12	no	—
573	#538	—	53	6	no	—
574	#538	—	53	6	no	—
575	#538	—	53	12	no	—
576	#538	—	53	12	no	—
577	#538	—	53	12	no	—
578	#538	—	53	6	no	—
579	#538	C₂×D₅₃	1	6	yes	complemented
580	#534	—	53	6	no	—
581	#534	—	53	12	no	—
582	#534	—	53	6	no	—
583	#534	—	53	6	no	—
584	#534	—	53	12	no	—
585	#534	—	53	3	no	—
586	#534	C₂×D₅₃	1	3	yes	complemented
587	#529	—	53	12	no	—
588	#529	—	53	6	no	—
589	#529	—	53	6	no	—
590	#529	—	53	12	no	—
591	#529	—	53	6	no	—
592	#529	—	53	6	no	—
593	#529	—	53	6	no	—
594	#529	—	53	12	no	—
595	#529	—	53	6	no	—
596	#529	—	53	12	no	—
597	#529	—	53	6	no	—
598	#529	C₂×D₅₃	1	6	yes	complemented
599	C₂×#126	—	53	12	no	—
600	C₂×#125	—	53	6	no	—
601	C₂×#124	—	53	6	no	—
602	#525	—	53	6	no	—
603	#525	—	53	6	no	—
604	#525	—	53	12	no	—
605	#525	—	53	6	no	—
606	#525	—	53	6	no	—
607	#525	—	53	6	no	—
608	#525	—	53	6	no	—
609	#525	—	53	12	no	—
610	#525	—	53	12	no	—
611	#525	—	53	12	no	—
612	#525	—	53	6	no	—
613	#525	C₂×D₅₃	1	6	yes	complemented
614	C₂×#123	—	53	12	no	—
615	C₂×#123	—	53	12	no	—
616	C₂×C₂²⋊Q₈	—	53	6	no	—
617	C₂×C₂²⋊Q₈	—	53	6	no	—
618	C₂×C₂²⋊Q₈	—	53	6	no	—
619	C₂×#121	—	53	6	no	—
620	C₂×#121	—	53	6	no	—
621	C₂×#121	—	53	6	no	—
622	C₂×#120	—	53	12	no	—
623	C₂×C₄×Q₈	—	53	2	no	—
624	C₂×C₄×D₄	—	53	3	no	—
625	C₂×C₄×D₄	—	53	3	no	—
626	C₂×C₄×D₄	—	53	3	no	—
627	C₂×C₄×D₄	—	53	12	no	—
628	C₂×C₄×D₄	—	53	12	no	—
629	C₂×C₄×D₄	—	53	12	no	—
630	C₂×C₄×D₄	—	53	12	no	—
631	C₂×C₄×D₄	—	53	6	no	—
632	C₂×C₄×D₄	—	53	3	no	—
633	C₂×C₄×D₄	—	53	3	no	—
634	C₂×C₄×D₄	—	53	3	no	—
635	C₂×C₄×D₄	—	53	3	no	—
636	C₂×C₄×D₄	C₂×D₅₃	1	3	yes	complemented
637	C₂×#117	—	53	6	no	—
638	C₂²×C₄⋊C₄	—	53	3	no	—
639	C₂²×C₂²⋊C₄	—	53	3	no	—
640	C₂²×C₂²⋊C₄	—	53	3	no	—
641	C₂²×C₄²	—	53	3	no	—
642	C₅₃	C₂×#3459	1	1	yes	characteristic, complemented, Sylow
643	C₂⁵	—	53	1	no	—
644	C₂⁵	—	53	3	no	—
645	C₂×#41	—	53	2	no	—
646	C₂×#41	—	53	6	no	—
647	C₂×#41	—	53	6	no	—
648	C₂×#41	—	212	8	no	—
649	C₂×#41	C₂²×D₅₃	1	2	yes	complemented
650	C₂²×Q₈	—	53	2	no	—
651	C₂²×Q₈	—	53	2	no	—
652	C₂²×D₄	—	53	3	no	—
653	C₂²×D₄	—	53	3	no	—
654	C₂²×D₄	—	53	12	no	—
655	C₂²×D₄	—	53	12	no	—
656	C₂²×D₄	—	53	6	no	—
657	C₂²×D₄	—	53	6	no	—
658	C₂²×D₄	—	53	3	no	—
659	C₂²×D₄	—	106	24	no	—
660	C₂²×D₄	C₂²×D₅₃	1	3	yes	—
661	C₂³×C₄	—	53	1	no	—
662	C₂³×C₄	—	53	3	no	—
663	C₂³×C₄	—	53	3	no	—
664	C₂³×C₄	—	53	6	no	—
665	C₂³×C₄	—	53	3	no	—
666	C₂³×C₄	—	53	3	no	—
667	C₂³×C₄	—	53	3	no	—
668	C₂³×C₄	—	53	3	no	—
669	C₂³×C₄	—	53	3	no	—
670	C₂³×C₄	—	53	3	no	—
671	C₂³×C₄	—	53	6	no	—
672	C₂³×C₄	—	53	3	no	—
673	C₂³×C₄	—	53	6	no	—
674	C₂³×C₄	—	53	3	no	—
675	C₂³×C₄	—	53	6	no	—
676	C₂³×C₄	—	212	4	no	—
677	C₂³×C₄	—	212	12	no	—
678	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
679	C₂³×C₄	C₂²×D₅₃	1	3	yes	complemented
680	#126	—	53	12	no	—
681	#126	—	53	12	no	—
682	#126	—	53	12	no	—
683	#126	—	53	12	no	—
684	#126	—	53	12	no	—
685	#126	—	53	12	no	—
686	#126	—	53	12	no	—
687	#126	C₂²×D₅₃	1	12	yes	complemented
688	#125	—	53	12	no	—
689	#125	—	53	12	no	—
690	#125	—	53	6	no	—
691	#125	—	53	6	no	—
692	#125	—	53	6	no	—
693	#125	C₂²×D₅₃	1	6	yes	complemented
694	#124	—	53	6	no	—
695	#124	—	53	6	no	—
696	#124	—	53	12	no	—
697	#124	—	53	12	no	—
698	#124	—	53	6	no	—
699	#124	C₂²×D₅₃	1	6	yes	complemented
700	#123	—	53	12	no	—
701	#123	—	53	12	no	—
702	#123	—	53	12	no	—
703	#123	—	53	12	no	—
704	#123	—	53	12	no	—
705	#123	—	53	12	no	—
706	#123	—	53	12	no	—
707	#123	—	53	12	no	—
708	#123	—	53	12	no	—
709	#123	—	53	12	no	—
710	#123	—	53	12	no	—
711	#123	—	53	12	no	—
712	#123	—	53	12	no	—
713	#123	—	53	12	no	—
714	#123	C₂²×D₅₃	1	12	yes	complemented
715	#123	C₂²×D₅₃	1	12	yes	complemented
716	C₂²⋊Q₈	—	53	6	no	—
717	C₂²⋊Q₈	—	53	6	no	—
718	C₂²⋊Q₈	—	53	6	no	—
719	C₂²⋊Q₈	—	53	6	no	—
720	C₂²⋊Q₈	—	53	6	no	—
721	C₂²⋊Q₈	—	53	6	no	—
722	C₂²⋊Q₈	—	53	12	no	—
723	C₂²⋊Q₈	—	53	6	no	—
724	C₂²⋊Q₈	—	53	12	no	—
725	C₂²⋊Q₈	—	53	6	no	—
726	C₂²⋊Q₈	—	53	12	no	—
727	C₂²⋊Q₈	—	53	6	no	—
728	C₂²⋊Q₈	—	53	12	no	—
729	C₂²⋊Q₈	—	53	12	no	—
730	C₂²⋊Q₈	—	53	12	no	—
731	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
732	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
733	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
734	#121	—	53	6	no	—
735	#121	—	53	12	no	—
736	#121	—	53	6	no	—
737	#121	—	53	12	no	—
738	#121	—	53	6	no	—
739	#121	—	53	12	no	—
740	#121	—	53	6	no	—
741	#121	—	53	6	no	—
742	#121	—	53	6	no	—
743	#121	—	53	6	no	—
744	#121	—	53	6	no	—
745	#121	—	53	6	no	—
746	#121	—	53	12	no	—
747	#121	—	53	12	no	—
748	#121	—	53	12	no	—
749	#121	C₂²×D₅₃	1	6	yes	—
750	#121	C₂²×D₅₃	1	6	yes	—
751	#121	C₂²×D₅₃	1	6	yes	complemented
752	#120	—	53	12	no	—
753	#120	—	53	12	no	—
754	#120	—	53	12	no	—
755	#120	—	53	12	no	—
756	#120	—	53	12	no	—
757	#120	—	53	12	no	—
758	#120	—	53	12	no	—
759	#120	C₂²×D₅₃	1	12	yes	complemented
760	C₄×Q₈	—	53	2	no	—
761	C₄×Q₈	—	53	6	no	—
762	C₄×Q₈	—	53	6	no	—
763	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
764	C₄×D₄	—	53	12	no	—
765	C₄×D₄	—	53	12	no	—
766	C₄×D₄	—	53	6	no	—
767	C₄×D₄	—	53	12	no	—
768	C₄×D₄	—	53	12	no	—
769	C₄×D₄	—	53	12	no	—
770	C₄×D₄	—	53	12	no	—
771	C₄×D₄	—	53	12	no	—
772	C₄×D₄	—	53	12	no	—
773	C₄×D₄	—	53	12	no	—
774	C₄×D₄	—	53	6	no	—
775	C₄×D₄	—	53	12	no	—
776	C₄×D₄	—	53	12	no	—
777	C₄×D₄	—	53	12	no	—
778	C₄×D₄	—	53	12	no	—
779	C₄×D₄	—	53	12	no	—
780	C₄×D₄	—	53	12	no	—
781	C₄×D₄	—	53	12	no	—
782	C₄×D₄	—	53	6	no	—
783	C₄×D₄	C₂²×D₅₃	1	12	yes	complemented
784	C₄×D₄	C₂²×D₅₃	1	12	yes	complemented
785	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
786	#117	—	53	6	no	—
787	#117	—	53	6	no	—
788	#117	—	53	6	no	—
789	#117	—	53	12	no	—
790	#117	—	53	12	no	—
791	#117	C₂²×D₅₃	1	6	yes	complemented
792	C₂×C₄⋊C₄	—	53	3	no	—
793	C₂×C₄⋊C₄	—	53	3	no	—
794	C₂×C₄⋊C₄	—	53	3	no	—
795	C₂×C₄⋊C₄	—	53	12	no	—
796	C₂×C₄⋊C₄	—	53	12	no	—
797	C₂×C₄⋊C₄	—	53	6	no	—
798	C₂×C₄⋊C₄	—	53	6	no	—
799	C₂×C₄⋊C₄	—	53	6	no	—
800	C₂×C₄⋊C₄	—	53	6	no	—
801	C₂×C₄⋊C₄	C₂²×D₅₃	1	3	yes	complemented
802	C₂×C₂²⋊C₄	—	53	3	no	—
803	C₂×C₂²⋊C₄	—	53	3	no	—
804	C₂×C₂²⋊C₄	—	53	3	no	—
805	C₂×C₂²⋊C₄	—	53	3	no	—
806	C₂×C₂²⋊C₄	—	53	3	no	—
807	C₂×C₂²⋊C₄	—	53	3	no	—
808	C₂×C₂²⋊C₄	—	53	12	no	—
809	C₂×C₂²⋊C₄	—	53	12	no	—
810	C₂×C₂²⋊C₄	—	53	12	no	—
811	C₂×C₂²⋊C₄	—	53	12	no	—
812	C₂×C₂²⋊C₄	—	53	12	no	—
813	C₂×C₂²⋊C₄	—	53	12	no	—
814	C₂×C₂²⋊C₄	C₂²×D₅₃	1	3	yes	—
815	C₂×C₂²⋊C₄	C₂²×D₅₃	1	3	yes	complemented
816	C₂×C₄²	—	53	3	no	—
817	C₂×C₄²	—	53	3	no	—
818	C₂×C₄²	—	53	3	no	—
819	C₂×C₄²	—	53	6	no	—
820	C₂×C₄²	—	53	6	no	—
821	C₂×C₄²	—	53	6	no	—
822	C₂×C₄²	—	53	6	no	—
823	C₂×C₄²	C₂²×D₅₃	1	3	yes	complemented
824	C₂⁴	—	53	3	no	—
825	C₂⁴	—	53	8	no	—
826	C₂⁴	—	53	3	no	—
827	C₂⁴	—	53	6	no	—
828	C₂⁴	—	53	6	no	—
829	C₂⁴	—	53	3	no	—
830	C₂⁴	—	106	12	no	—
831	C₂⁴	—	212	2	no	—
832	C₂⁴	—	212	6	no	—
833	C₂⁴	—	212	2	no	—
834	C₂⁴	—	212	6	no	—
835	C₂⁴	C₂³×D₅₃	1	3	yes	—
836	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
837	#41	—	4	4	no	—
838	#41	—	212	12	no	—
839	#41	—	212	12	no	—
840	#41	—	212	4	no	—
841	C₂×Q₈	—	53	6	no	—
842	C₂×Q₈	—	53	6	no	—
843	C₂×Q₈	—	212	4	no	—
844	C₂×Q₈	—	212	4	no	—
845	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
846	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
847	C₂×D₄	—	2	12	no	—
848	C₂×D₄	—	53	12	no	—
849	C₂×D₄	—	53	12	no	—
850	C₂×D₄	—	53	12	no	—
851	C₂×D₄	—	53	12	no	—
852	C₂×D₄	—	53	12	no	—
853	C₂×D₄	—	53	6	no	—
854	C₂×D₄	—	53	6	no	—
855	C₂×D₄	—	106	12	no	—
856	C₂×D₄	—	106	48	no	—
857	C₂×D₄	—	106	48	no	—
858	C₂×D₄	—	106	12	no	—
859	C₂×D₄	—	106	12	no	—
860	C₂×D₄	—	212	12	no	—
861	C₂×D₄	—	212	12	no	—
862	C₂×D₄	C₂³×D₅₃	1	12	yes	—
863	C₂×D₄	C₂³×D₅₃	1	6	yes	—
864	C₂×D₄	C₂³×D₅₃	1	6	yes	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	6	no	—
867	C₂²×C₄	—	53	1	no	—
868	C₂²×C₄	—	53	3	no	—
869	C₂²×C₄	—	53	3	no	—
870	C₂²×C₄	—	53	6	no	—
871	C₂²×C₄	—	53	3	no	—
872	C₂²×C₄	—	53	3	no	—
873	C₂²×C₄	—	53	3	no	—
874	C₂²×C₄	—	53	6	no	—
875	C₂²×C₄	—	53	6	no	—
876	C₂²×C₄	—	53	6	no	—
877	C₂²×C₄	—	53	3	no	—
878	C₂²×C₄	—	53	6	no	—
879	C₂²×C₄	—	53	3	no	—
880	C₂²×C₄	—	53	6	no	—
881	C₂²×C₄	—	53	6	no	—
882	C₂²×C₄	—	53	3	no	—
883	C₂²×C₄	—	53	6	no	—
884	C₂²×C₄	—	53	6	no	—
885	C₂²×C₄	—	53	6	no	—
886	C₂²×C₄	—	53	6	no	—
887	C₂²×C₄	—	53	6	no	—
888	C₂²×C₄	—	53	6	no	—
889	C₂²×C₄	—	106	12	no	—
890	C₂²×C₄	—	106	24	no	—
891	C₂²×C₄	—	106	12	no	—
892	C₂²×C₄	—	212	6	no	—
893	C₂²×C₄	—	212	6	no	—
894	C₂²×C₄	—	212	12	no	—
895	C₂²×C₄	—	212	6	no	—
896	C₂²×C₄	—	212	12	no	—
897	C₂²×C₄	—	212	6	no	—
898	C₂²×C₄	—	212	6	no	—
899	C₂²×C₄	—	212	6	no	—
900	C₂²×C₄	—	212	12	no	—
901	C₂²×C₄	—	212	6	no	—
902	C₂²×C₄	—	212	2	no	—
903	C₂²×C₄	—	212	6	no	—
904	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
905	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
906	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
907	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
908	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
909	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
910	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
911	C₄⋊C₄	—	53	12	no	—
912	C₄⋊C₄	—	53	12	no	—
913	C₄⋊C₄	—	53	12	no	—
914	C₄⋊C₄	—	53	12	no	—
915	C₄⋊C₄	—	53	6	no	—
916	C₄⋊C₄	—	53	12	no	—
917	C₄⋊C₄	—	53	6	no	—
918	C₄⋊C₄	—	53	12	no	—
919	C₄⋊C₄	—	53	6	no	—
920	C₄⋊C₄	—	53	12	no	—
921	C₄⋊C₄	—	53	6	no	—
922	C₄⋊C₄	C₂³×D₅₃	1	12	yes	—
923	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
924	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
925	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
926	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
927	C₂²⋊C₄	—	53	12	no	—
928	C₂²⋊C₄	—	53	12	no	—
929	C₂²⋊C₄	—	53	12	no	—
930	C₂²⋊C₄	—	53	12	no	—
931	C₂²⋊C₄	—	53	12	no	—
932	C₂²⋊C₄	—	53	12	no	—
933	C₂²⋊C₄	—	53	12	no	—
934	C₂²⋊C₄	—	53	12	no	—
935	C₂²⋊C₄	—	53	12	no	—
936	C₂²⋊C₄	—	53	12	no	—
937	C₂²⋊C₄	—	53	12	no	—
938	C₂²⋊C₄	—	53	12	no	—
939	C₂²⋊C₄	C₂³×D₅₃	1	12	yes	—
940	C₂²⋊C₄	C₂³×D₅₃	1	12	yes	—
941	C₂²⋊C₄	C₂³×D₅₃	1	12	yes	—
942	C₂²⋊C₄	C₂³×D₅₃	1	12	yes	—
943	C₄²	—	53	6	no	—
944	C₄²	—	53	6	no	—
945	C₄²	—	53	6	no	—
946	C₄²	—	53	6	no	—
947	C₄²	—	53	6	no	—
948	C₄²	—	53	6	no	—
949	C₄²	C₂³×D₅₃	1	6	yes	—
950	C₄²	C₂³×D₅₃	1	6	yes	—
951	C₂³	—	2	6	no	—
952	C₂³	—	4	1	no	—
953	C₂³	—	4	3	no	—
954	C₂³	—	4	1	no	—
955	C₂³	—	4	3	no	—
956	C₂³	—	53	1	no	—
957	C₂³	—	53	12	no	—
958	C₂³	—	53	3	no	—
959	C₂³	—	53	12	no	—
960	C₂³	—	53	6	no	—
961	C₂³	—	106	6	no	—
962	C₂³	—	106	6	no	—
963	C₂³	—	106	12	no	—
964	C₂³	—	106	12	no	—
965	C₂³	—	106	12	no	—
966	C₂³	—	106	12	no	—
967	C₂³	—	106	6	no	—
968	C₂³	—	212	3	no	—
969	C₂³	—	212	3	no	—
970	C₂³	—	212	6	no	—
971	C₂³	—	212	3	no	—
972	C₂³	—	212	3	no	—
973	C₂³	—	212	6	no	—
974	C₂³	—	212	16	no	—
975	C₂³	—	212	48	no	—
976	C₂³	#41×D₅₃	1	4	yes	complemented
977	C₂³	C₂⁴×D₅₃	1	6	yes	—
978	C₂³	C₂⁴×D₅₃	1	3	yes	—
979	Q₈	—	4	2	no	—
980	Q₈	—	4	2	no	—
981	Q₈	—	212	6	no	—
982	Q₈	—	212	6	no	—
983	D₄	—	2	24	no	—
984	D₄	—	4	6	no	—
985	D₄	—	4	6	no	—
986	D₄	—	106	24	no	—
987	D₄	—	106	24	no	—
988	D₄	—	106	24	no	—
989	D₄	—	212	6	no	—
990	D₄	—	212	6	no	—
991	D₄	—	212	12	no	—
992	D₄	—	212	12	no	—
993	C₂×C₄	—	2	6	no	—
994	C₂×C₄	—	2	6	no	—
995	C₂×C₄	—	2	12	no	—
996	C₂×C₄	—	4	3	no	—
997	C₂×C₄	—	4	6	no	—
998	C₂×C₄	—	4	3	no	—
999	C₂×C₄	—	4	3	no	—
1000	C₂×C₄	—	53	1	no	—
1001	C₂×C₄	—	53	4	no	—
1002	C₂×C₄	—	53	6	no	—
1003	C₂×C₄	—	53	6	no	—
1004	C₂×C₄	—	53	3	no	—
1005	C₂×C₄	—	53	6	no	—
1006	C₂×C₄	—	106	6	no	—
1007	C₂×C₄	—	106	12	no	—
1008	C₂×C₄	—	106	6	no	—
1009	C₂×C₄	—	106	12	no	—
1010	C₂×C₄	—	106	12	no	—
1011	C₂×C₄	—	106	12	no	—
1012	C₂×C₄	—	106	12	no	—
1013	C₂×C₄	—	106	6	no	—
1014	C₂×C₄	—	106	12	no	—
1015	C₂×C₄	—	106	6	no	—
1016	C₂×C₄	—	106	6	no	—
1017	C₂×C₄	—	106	12	no	—
1018	C₂×C₄	—	212	6	no	—
1019	C₂×C₄	—	212	6	no	—
1020	C₂×C₄	—	212	6	no	—
1021	C₂×C₄	—	212	6	no	—
1022	C₂×C₄	—	212	6	no	—
1023	C₂×C₄	—	212	3	no	—
1024	C₂×C₄	—	212	3	no	—
1025	C₂×C₄	—	212	6	no	—
1026	C₂×C₄	—	212	3	no	—
1027	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1028	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1029	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1030	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1031	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1032	C₂²	—	2	3	no	—
1033	C₂²	—	2	3	no	—
1034	C₂²	—	2	6	no	—
1035	C₂²	—	2	6	no	—
1036	C₂²	—	2	6	no	—
1037	C₂²	—	4	4	no	—
1038	C₂²	—	4	12	no	—
1039	C₂²	—	53	2	no	—
1040	C₂²	—	53	2	no	—
1041	C₂²	—	53	2	no	—
1042	C₂²	—	53	6	no	—
1043	C₂²	—	106	24	no	—
1044	C₂²	—	106	3	no	—
1045	C₂²	—	106	3	no	—
1046	C₂²	—	106	6	no	—
1047	C₂²	—	106	6	no	—
1048	C₂²	—	106	6	no	—
1049	C₂²	—	212	12	no	—
1050	C₂²	—	212	12	no	—
1051	C₂²	—	212	24	no	—
1052	C₂²	—	212	24	no	—
1053	C₂²	C₂×#41×D₅₃	1	6	yes	—
1054	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1055	C₄	—	2	6	no	—
1056	C₄	—	2	3	no	—
1057	C₄	—	2	6	no	—
1058	C₄	—	2	6	no	—
1059	C₄	—	53	2	no	—
1060	C₄	—	106	6	no	—
1061	C₄	—	106	3	no	—
1062	C₄	—	106	6	no	—
1063	C₄	—	106	6	no	—
1064	C₄	H(5,𝔽₂)×D₅₃	1	2	yes	—
1065	C₂	—	2	6	no	—
1066	C₂	—	4	6	no	—
1067	C₂	—	53	4	no	—
1068	C₂	—	106	6	no	—
1069	C₂	—	212	6	no	—
1070	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1071	C₂	C₂×H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1072	C₂	#585×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₅₃×#3459	C₂
hypercenter	#3459	D₅₃
hypocenter	C₅₃	C₂×#3459
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #3459

Complements

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

N	H ≅ G/N	type
1. #20288127	C₂	semidirect
2. #20288126	C₂	semidirect
3. #20288125	C₂	semidirect
4. #20288124	C₂	semidirect
5. #20288123	C₂	semidirect
6. #20288122	C₂	semidirect
7. #20288121	C₂	semidirect
8. #543×D₅₃	C₂	semidirect
9. #539×D₅₃	C₂	semidirect
10. #538×D₅₃	C₂	semidirect
11. #534×D₅₃	C₂	semidirect
12. #529×D₅₃	C₂	semidirect
13. #525×D₅₃	C₂	semidirect
14. C₂×C₄×D₄×D₅₃	C₂	semidirect
15. C₅₃×#3459	C₂	semidirect
16. C₂×#41×D₅₃	C₂²	semidirect
19. C₂³×C₄×D₅₃	C₂²	semidirect
20. #16811249	C₂²	semidirect
21. #16811248	C₂²	semidirect
22. #16811248	C₂²	semidirect
23. #16811222	C₂²	semidirect
24. #16811221	C₂²	semidirect
25. #16811220	C₂²	semidirect
26. #16811219	C₂²	semidirect
27. #16811218	C₂²	semidirect
28. #16811217	C₂²	semidirect
29. #16811216	C₂²	semidirect
30. #16811215	C₂²	semidirect
31. #16811214	C₂²	semidirect
32. #16811213	C₂²	semidirect
33. #16811212	C₂²	semidirect
34. #16811211	C₂²	semidirect
35. #16811210	C₂²	semidirect
36. #16811209	C₂²	semidirect
37. #16811208	C₂²	semidirect
38. #16811207	C₂²	semidirect
39. #16811206	C₂²	semidirect
40. #16811205	C₂²	semidirect
41. #16811185	C₂²	semidirect
42. #16811184	C₂²	semidirect
43. #16811183	C₂²	semidirect
44. #16811182	C₂²	semidirect
45. #16811181	C₂²	semidirect
46. #16811181	C₂²	semidirect
47. #16811160	C₂²	semidirect
48. #16811159	C₂²	semidirect
49. #16811158	C₂²	semidirect
50. #16811157	C₂²	semidirect
51. #16811156	C₂²	semidirect
52. #16811155	C₂²	semidirect
53. #16811154	C₂²	semidirect
54. #16811153	C₂²	semidirect
55. #16811152	C₂²	semidirect
56. #16811151	C₂²	semidirect
57. #16811150	C₂²	semidirect
58. #126×D₅₃	C₂²	semidirect
59. #125×D₅₃	C₂²	semidirect
60. #124×D₅₃	C₂²	semidirect
61. #16811136	C₂²	semidirect
62. #16811136	C₂²	semidirect
63. #16811135	C₂²	semidirect
64. #16811134	C₂²	semidirect
65. #16811133	C₂²	semidirect
66. #16811133	C₂²	semidirect
67. #16811132	C₂²	semidirect
68. #16811132	C₂²	semidirect
69. #16811131	C₂²	semidirect
70. #16811130	C₂²	semidirect
71. #16811129	C₂²	semidirect
72. #123×D₅₃	C₂²	semidirect
73. #123×D₅₃	C₂²	semidirect
74. C₂²⋊Q₈×D₅₃	C₂²	semidirect
75. C₂²⋊Q₈×D₅₃	C₂²	semidirect
76. C₂²⋊Q₈×D₅₃	C₂²	semidirect
79. #121×D₅₃	C₂²	semidirect
80. #120×D₅₃	C₂²	semidirect
81. C₄×Q₈×D₅₃	C₂²	semidirect
82. C₂×C₄×D₂₁₂	C₂²	semidirect
83. C₂×D₄×Dic₅₃	C₂²	semidirect
84. C₂×#13133179	C₂²	semidirect
85. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
86. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
87. C₂×#13133177	C₂²	semidirect
88. C₂×#13133177	C₂²	semidirect
89. C₄×D₄×D₅₃	C₂²	semidirect
90. C₄×D₄×D₅₃	C₂²	semidirect
91. C₄×D₄×D₅₃	C₂²	semidirect
92. C₄×D₄×D₅₃	C₂²	semidirect
93. C₄×D₄×D₅₃	C₂²	semidirect
94. #117×D₅₃	C₂²	semidirect
95. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
97. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
98. C₂×C₄²×D₅₃	C₂²	semidirect
99. C₅₃×#543	C₂²	semidirect
100. C₅₃×#539	C₂²	semidirect
101. C₅₃×#538	C₂²	semidirect
102. C₅₃×#534	C₂²	semidirect
103. C₅₃×#529	C₂²	semidirect
104. C₅₃×#525	C₂²	semidirect
105. C₂×C₄×D₄×C₅₃	C₂²	semidirect
108. C₂×#11719949	C₂³	semidirect
109. C₂×#11719945	C₂³	semidirect
110. C₂×#11719947	C₂³	semidirect
123. C₂³×Dic₅₃	C₂³	semidirect
135. C₂²×C₄×D₅₃	C₂³	semidirect
136. C₂²×C₄×D₅₃	C₂³	semidirect
137. C₂²×C₄×D₅₃	C₂³	semidirect
138. C₂²×C₄×D₅₃	C₂³	semidirect
139. #13133212	C₂³	semidirect
140. #13133212	C₂³	semidirect
141. #13133212	C₂³	semidirect
142. #13133211	C₂³	semidirect
143. #13133210	C₂³	semidirect
144. #13133210	C₂³	semidirect
145. #13133210	C₂³	semidirect
146. #13133209	C₂³	semidirect
147. #13133208	C₂³	semidirect
148. #13133208	C₂³	semidirect
149. #13133207	C₂³	semidirect
150. #13133207	C₂³	semidirect
151. #13133206	C₂³	semidirect
152. #13133205	C₂³	semidirect
153. #13133204	C₂³	semidirect
154. #13133203	C₂³	semidirect
155. #13133203	C₂³	semidirect
156. #13133202	C₂³	semidirect
157. #13133202	C₂³	semidirect
158. #13133202	C₂³	semidirect
159. #13133202	C₂³	semidirect
160. #13133201	C₂³	semidirect
161. #13133201	C₂³	semidirect
162. #13133200	C₂³	semidirect
163. #13133200	C₂³	semidirect
164. #13133199	C₂³	semidirect
165. #13133199	C₂³	semidirect
166. #13133199	C₂³	semidirect
167. #13133199	C₂³	semidirect
168. #13133198	C₂³	semidirect
169. #13133198	C₂³	semidirect
170. #13133197	C₂³	semidirect
171. #13133197	C₂³	semidirect
172. #13133197	C₂³	semidirect
173. #13133196	C₂³	semidirect
174. #13133196	C₂³	semidirect
175. #13133196	C₂³	semidirect
176. #13133195	C₂³	semidirect
177. #13133195	C₂³	semidirect
178. #13133195	C₂³	semidirect
179. #13133194	C₂³	semidirect
180. #13133194	C₂³	semidirect
181. #13133194	C₂³	semidirect
182. #13133193	C₂³	semidirect
183. #13133193	C₂³	semidirect
184. #13133193	C₂³	semidirect
187. #13133192	C₂³	semidirect
190. #13133191	C₂³	semidirect
193. #13133190	C₂³	semidirect
196. #13133189	C₂³	semidirect
199. #13133188	C₂³	semidirect
200. #13133187	C₂³	semidirect
201. #13133187	C₂³	semidirect
202. #13133187	C₂³	semidirect
203. #13133186	C₂³	semidirect
204. #13133185	C₂³	semidirect
205. #13133185	C₂³	semidirect
206. #13133185	C₂³	semidirect
207. Q₈×Dic₅₃	C₂³	semidirect
208. C₄×Dic₁₀₆	C₂³	semidirect
209. #13133182	C₂³	semidirect
210. C₄×D₂₁₂	C₂³	semidirect
211. C₄×D₂₁₂	C₂³	semidirect
212. C₄×D₂₁₂	C₂³	semidirect
213. D₄×Dic₅₃	C₂³	semidirect
214. D₄×Dic₅₃	C₂³	semidirect
215. D₄×Dic₅₃	C₂³	semidirect
216. #13133179	C₂³	semidirect
217. #13133179	C₂³	semidirect
218. #13133179	C₂³	semidirect
219. C₄×C₂²⋊D₅₃	C₂³	semidirect
220. C₄×C₂²⋊D₅₃	C₂³	semidirect
221. C₄×C₂²⋊D₅₃	C₂³	semidirect
222. C₄×C₂²⋊D₅₃	C₂³	semidirect
223. C₄×C₂²⋊D₅₃	C₂³	semidirect
224. #13133177	C₂³	semidirect
225. #13133177	C₂³	semidirect
226. #13133177	C₂³	semidirect
227. #13133177	C₂³	semidirect
228. #13133177	C₂³	semidirect
229. #13133176	C₂³	semidirect
230. #13133175	C₂³	semidirect
231. #13133175	C₂³	semidirect
232. #13133174	C₂³	semidirect
233. #13133173	C₂³	semidirect
234. C₂×C₄⋊Dic₅₃	C₂³	semidirect
235. C₂×#11719919	C₂³	semidirect
236. C₂×#11719919	C₂³	semidirect
242. C₄⋊C₄×D₅₃	C₂³	semidirect
244. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
247. C₂×#11719921	C₂³	semidirect
248. C₂×#11719921	C₂³	semidirect
254. C₂²⋊C₄×D₅₃	C₂³	semidirect
255. C₂×C₄×Dic₅₃	C₂³	semidirect
256. C₂×C₄×Dic₅₃	C₂³	semidirect
257. C₂×C₄×Dic₅₃	C₂³	semidirect
260. C₄²×D₅₃	C₂³	semidirect
261. C₄²×D₅₃	C₂³	semidirect
262. C₂×#41×C₅₃	C₂³	semidirect
265. C₂³×C₄×C₅₃	C₂³	semidirect
266. #126×C₅₃	C₂³	semidirect
267. #125×C₅₃	C₂³	semidirect
268. #124×C₅₃	C₂³	semidirect
269. #123×C₅₃	C₂³	semidirect
270. #123×C₅₃	C₂³	semidirect
271. C₂²⋊Q₈×C₅₃	C₂³	semidirect
272. C₂²⋊Q₈×C₅₃	C₂³	semidirect
273. C₂²⋊Q₈×C₅₃	C₂³	semidirect
276. #121×C₅₃	C₂³	semidirect
277. #120×C₅₃	C₂³	semidirect
278. C₄×Q₈×C₅₃	C₂³	semidirect
279. C₄×D₄×C₅₃	C₂³	semidirect
280. C₄×D₄×C₅₃	C₂³	semidirect
281. C₄×D₄×C₅₃	C₂³	semidirect
282. #117×C₅₃	C₂³	semidirect
283. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
285. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
286. C₂×C₄²×C₅₃	C₂³	semidirect
294. C₂³×D₅₃	#41	semidirect
419. C₂³×C₅₃	C₂×#41	semidirect
438. C₂²×D₅₃	C₂×#41	semidirect
536. #3459	D₅₃	direct (N × H)
551. D₅₃	#3459	direct (N × H)
559. #543	C₂×D₅₃	semidirect
569. #539	C₂×D₅₃	semidirect
579. #538	C₂×D₅₃	semidirect
586. #534	C₂×D₅₃	semidirect
598. #529	C₂×D₅₃	semidirect
613. #525	C₂×D₅₃	semidirect
636. C₂×C₄×D₄	C₂×D₅₃	semidirect
642. C₅₃	C₂×#3459	semidirect
649. C₂×#41	C₂²×D₅₃	semidirect
679. C₂³×C₄	C₂²×D₅₃	semidirect
687. #126	C₂²×D₅₃	semidirect
693. #125	C₂²×D₅₃	semidirect
699. #124	C₂²×D₅₃	semidirect
714. #123	C₂²×D₅₃	semidirect
715. #123	C₂²×D₅₃	semidirect
731. C₂²⋊Q₈	C₂²×D₅₃	semidirect
732. C₂²⋊Q₈	C₂²×D₅₃	semidirect
733. C₂²⋊Q₈	C₂²×D₅₃	semidirect
751. #121	C₂²×D₅₃	semidirect
759. #120	C₂²×D₅₃	semidirect
763. C₄×Q₈	C₂²×D₅₃	semidirect
783. C₄×D₄	C₂²×D₅₃	semidirect
784. C₄×D₄	C₂²×D₅₃	semidirect
785. C₄×D₄	C₂²×D₅₃	semidirect
791. #117	C₂²×D₅₃	semidirect
801. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
815. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
823. C₂×C₄²	C₂²×D₅₃	semidirect
976. C₂³	#41×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288127	2
#20288126	2
#20288125	2
#20288124	2
#20288123	2
#20288122	2
#20288121	2
#543×D₅₃	2
#539×D₅₃	2
#538×D₅₃	2
#534×D₅₃	2
#529×D₅₃	2
#525×D₅₃	2
C₂×C₄×D₄×D₅₃	2
C₅₃×#3459	2
C₂×#3459	53

Subgroups — D53×#3459 #28290835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3459 #28290835