Subgroups — D₅₃×#3568 #28291518

Order 13568.

6726 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289412	C₂	1	3	yes	maximal, complemented
2	#20289411	C₂	1	3	yes	maximal, complemented
3	#20289410	C₂	1	6	yes	maximal, complemented
4	#20289409	C₂	1	1	yes	maximal, characteristic, complemented
5	#20289408	C₂	1	6	yes	maximal, complemented
6	#20289407	C₂	1	6	yes	maximal, complemented
7	#20289406	C₂	1	6	yes	maximal, complemented
8	#563×D₅₃	C₂	1	3	yes	maximal, complemented
9	H(3,𝔽₄)×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#556×D₅₃	C₂	1	6	yes	maximal, complemented
11	#551×D₅₃	C₂	1	6	yes	maximal, complemented
12	#542×D₅₃	C₂	1	6	yes	maximal, complemented
13	#538×D₅₃	C₂	1	6	yes	maximal, complemented
14	#529×D₅₃	C₂	1	3	yes	maximal, complemented
15	C₅₃×#3568	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811377	C₂²	1	3	yes	complemented
17	#16811377	C₂²	1	3	yes	complemented
18	#16811376	C₂²	1	6	yes	complemented
19	#16811375	C₂²	1	6	yes	complemented
20	#16811375	C₂²	1	6	yes	complemented
21	#16811374	C₂²	1	6	yes	complemented
22	#16811374	C₂²	1	6	yes	complemented
23	#16811373	C₂²	1	3	yes	complemented
24	#16811372	C₂²	1	6	yes	complemented
25	#16811366	C₂²	1	6	yes	complemented
26	#16811365	C₂²	1	6	yes	complemented
27	#16811365	C₂²	1	3	yes	complemented
28	#16811347	C₂²	1	6	yes	complemented
29	#16811346	C₂²	1	6	yes	complemented
30	#16811345	C₂²	1	6	yes	complemented
31	#16811345	C₂²	1	6	yes	complemented
32	#16811344	C₂²	1	6	yes	complemented
33	#16811344	C₂²	1	6	yes	complemented
34	#16811343	C₂²	1	6	yes	complemented
35	#16811342	C₂²	1	6	yes	complemented
36	#16811342	C₂²	1	6	yes	complemented
37	#16811341	C₂²	1	6	yes	complemented
38	#16811341	C₂²	1	6	yes	complemented
39	#16811340	C₂²	1	6	yes	complemented
40	#16811340	C₂²	1	6	yes	complemented
41	#16811340	C₂²	1	6	yes	complemented
42	#16811340	C₂²	1	6	yes	complemented
43	#16811304	C₂²	1	6	yes	complemented
44	#16811303	C₂²	1	6	yes	complemented
45	#16811302	C₂²	1	6	yes	complemented
46	#16811302	C₂²	1	6	yes	complemented
47	#16811301	C₂²	1	6	yes	complemented
48	#16811300	C₂²	1	6	yes	complemented
49	#16811300	C₂²	1	6	yes	complemented
50	#16811299	C₂²	1	6	yes	complemented
51	#16811299	C₂²	1	6	yes	complemented
52	#16811298	C₂²	1	6	yes	complemented
53	#16811298	C₂²	1	6	yes	complemented
54	#16811297	C₂²	1	6	yes	complemented
55	#16811297	C₂²	1	6	yes	complemented
56	#16811296	C₂²	1	6	yes	complemented
57	#16811296	C₂²	1	6	yes	complemented
58	#16811247	C₂²	1	6	yes	complemented
59	#16811246	C₂²	1	6	yes	complemented
60	#16811245	C₂²	1	6	yes	complemented
61	#16811244	C₂²	1	6	yes	complemented
62	#16811243	C₂²	1	6	yes	complemented
63	#16811243	C₂²	1	6	yes	complemented
64	#16811242	C₂²	1	6	yes	complemented
65	#16811241	C₂²	1	6	yes	complemented
66	#16811241	C₂²	1	6	yes	complemented
67	#16811240	C₂²	1	6	yes	complemented
68	#16811239	C₂²	1	6	yes	complemented
69	#16811239	C₂²	1	6	yes	complemented
70	#16811238	C₂²	1	6	yes	complemented
71	#16811237	C₂²	1	6	yes	complemented
72	#16811237	C₂²	1	6	yes	complemented
73	#16811213	C₂²	1	6	yes	complemented
74	#16811212	C₂²	1	6	yes	complemented
75	#16811212	C₂²	1	6	yes	complemented
76	#16811211	C₂²	1	6	yes	complemented
77	#16811210	C₂²	1	6	yes	complemented
78	#16811209	C₂²	1	6	yes	complemented
79	#16811209	C₂²	1	6	yes	complemented
80	#16811208	C₂²	1	6	yes	complemented
81	#16811208	C₂²	1	6	yes	complemented
82	#16811207	C₂²	1	6	yes	complemented
83	#16811207	C₂²	1	6	yes	complemented
84	#16811206	C₂²	1	6	yes	complemented
85	#16811206	C₂²	1	6	yes	complemented
86	#16811205	C₂²	1	6	yes	complemented
87	#16811205	C₂²	1	6	yes	complemented
88	C₄⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
89	#16811160	C₂²	1	3	yes	complemented
90	#16811159	C₂²	1	3	yes	complemented
91	#16811158	C₂²	1	3	yes	complemented
92	#16811157	C₂²	1	3	yes	complemented
93	#16811156	C₂²	1	6	yes	complemented
94	#16811155	C₂²	1	3	yes	complemented
95	#16811154	C₂²	1	3	yes	complemented
96	#16811153	C₂²	1	6	yes	complemented
97	#16811152	C₂²	1	3	yes	complemented
98	#16811151	C₂²	1	6	yes	complemented
99	#16811150	C₂²	1	6	yes	complemented
100	#126×D₅₃	C₂²	1	6	yes	complemented
101	#126×D₅₃	C₂²	1	6	yes	complemented
102	#126×D₅₃	C₂²	1	6	yes	complemented
103	#126×D₅₃	C₂²	1	6	yes	complemented
104	#126×D₅₃	C₂²	1	2	yes	complemented
105	#125×D₅₃	C₂²	1	3	yes	complemented
106	#124×D₅₃	C₂²	1	6	yes	—
107	#124×D₅₃	C₂²	1	6	yes	—
108	#124×D₅₃	C₂²	1	3	yes	—
109	#124×D₅₃	C₂²	1	6	yes	complemented
110	#123×D₅₃	C₂²	1	6	yes	—
111	#123×D₅₃	C₂²	1	6	yes	—
112	#123×D₅₃	C₂²	1	6	yes	complemented
113	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
114	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
115	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
116	C₂²⋊Q₈×D₅₃	C₂²	1	3	yes	complemented
117	#121×D₅₃	C₂²	1	6	yes	—
118	#121×D₅₃	C₂²	1	3	yes	—
119	#120×D₅₃	C₂²	1	6	yes	—
120	#120×D₅₃	C₂²	1	2	yes	complemented
121	C₄×Q₈×D₅₃	C₂²	1	6	yes	complemented
122	C₄×Q₈×D₅₃	C₂²	1	3	yes	complemented
123	C₄×D₄×D₅₃	C₂²	1	6	yes	—
124	C₄×D₄×D₅₃	C₂²	1	3	yes	—
125	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
126	#117×D₅₃	C₂²	1	6	yes	complemented
127	#117×D₅₃	C₂²	1	6	yes	complemented
128	C₂×C₂²⋊C₄×D₅₃	C₂²	1	6	yes	complemented
129	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#563	C₂²	1	3	yes	complemented
131	C₅₃×H(3,𝔽₄)	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#556	C₂²	1	6	yes	complemented
133	C₅₃×#551	C₂²	1	6	yes	complemented
134	C₅₃×#542	C₂²	1	6	yes	complemented
135	C₅₃×#538	C₂²	1	6	yes	complemented
136	C₅₃×#529	C₂²	1	3	yes	complemented
137	C₂⁴×D₅₃	C₂³	1	2	yes	—
138	C₂×Q₈×D₅₃	C₂³	1	6	yes	—
139	C₂×Q₈×D₅₃	C₂³	1	3	yes	—
140	C₂×D₄×D₅₃	C₂³	1	3	yes	—
141	C₂×D₄×D₅₃	C₂³	1	6	yes	—
142	C₂×D₄×D₅₃	C₂³	1	6	yes	—
143	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
144	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
145	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
146	#13133217	C₂³	1	6	yes	complemented
147	#13133216	C₂³	1	6	yes	complemented
148	#13133216	C₂³	1	6	yes	complemented
149	#13133216	C₂³	1	6	yes	complemented
150	#13133216	C₂³	1	6	yes	complemented
151	#13133215	C₂³	1	6	yes	complemented
152	#13133215	C₂³	1	6	yes	complemented
153	#13133212	C₂³	1	6	yes	complemented
154	#13133212	C₂³	1	6	yes	complemented
155	#13133212	C₂³	1	6	yes	complemented
156	#13133212	C₂³	1	6	yes	complemented
157	#13133212	C₂³	1	6	yes	complemented
158	#13133212	C₂³	1	6	yes	complemented
159	#13133212	C₂³	1	6	yes	complemented
160	#13133212	C₂³	1	6	yes	complemented
161	#13133212	C₂³	1	6	yes	complemented
162	#13133212	C₂³	1	6	yes	complemented
163	#13133212	C₂³	1	6	yes	complemented
164	#13133212	C₂³	1	6	yes	complemented
165	#13133212	C₂³	1	6	yes	complemented
166	#13133211	C₂³	1	6	yes	complemented
167	#13133211	C₂³	1	6	yes	complemented
168	#13133211	C₂³	1	6	yes	complemented
169	#13133211	C₂³	1	6	yes	complemented
170	#13133211	C₂³	1	2	yes	complemented
171	#13133210	C₂³	1	6	yes	complemented
172	#13133210	C₂³	1	6	yes	complemented
173	#13133210	C₂³	1	6	yes	complemented
174	#13133210	C₂³	1	6	yes	complemented
175	#13133210	C₂³	1	6	yes	complemented
176	#13133210	C₂³	1	6	yes	complemented
177	#13133210	C₂³	1	6	yes	complemented
178	#13133210	C₂³	1	6	yes	complemented
179	#13133210	C₂³	1	6	yes	complemented
180	#13133210	C₂³	1	6	yes	complemented
181	#13133210	C₂³	1	6	yes	complemented
182	#13133210	C₂³	1	6	yes	complemented
183	#13133210	C₂³	1	6	yes	complemented
184	#13133209	C₂³	1	3	yes	complemented
185	#13133208	C₂³	1	3	yes	complemented
186	#13133208	C₂³	1	3	yes	complemented
187	#13133207	C₂³	1	6	yes	complemented
188	#13133207	C₂³	1	6	yes	complemented
189	#13133206	C₂³	1	6	yes	—
190	#13133206	C₂³	1	6	yes	—
191	#13133206	C₂³	1	3	yes	—
192	#13133206	C₂³	1	6	yes	complemented
193	#13133205	C₂³	1	6	yes	—
194	#13133205	C₂³	1	6	yes	—
195	#13133205	C₂³	1	3	yes	—
196	#13133205	C₂³	1	6	yes	complemented
197	#13133204	C₂³	1	6	yes	—
198	#13133204	C₂³	1	6	yes	—
199	#13133204	C₂³	1	3	yes	—
200	#13133204	C₂³	1	6	yes	complemented
201	#13133203	C₂³	1	6	yes	—
202	#13133203	C₂³	1	6	yes	—
203	#13133203	C₂³	1	6	yes	—
204	#13133203	C₂³	1	6	yes	—
205	#13133203	C₂³	1	6	yes	—
206	#13133203	C₂³	1	6	yes	—
207	#13133203	C₂³	1	6	yes	—
208	#13133203	C₂³	1	6	yes	—
209	#13133203	C₂³	1	6	yes	—
210	#13133203	C₂³	1	6	yes	—
211	#13133203	C₂³	1	6	yes	complemented
212	#13133203	C₂³	1	6	yes	complemented
213	#13133203	C₂³	1	6	yes	complemented
214	#13133203	C₂³	1	6	yes	complemented
215	#13133202	C₂³	1	6	yes	—
216	#13133202	C₂³	1	6	yes	—
217	#13133202	C₂³	1	6	yes	—
218	#13133202	C₂³	1	6	yes	—
219	#13133202	C₂³	1	6	yes	complemented
220	#13133202	C₂³	1	6	yes	complemented
221	#13133201	C₂³	1	6	yes	—
222	#13133201	C₂³	1	6	yes	—
223	#13133201	C₂³	1	6	yes	complemented
224	#13133200	C₂³	1	6	yes	—
225	#13133200	C₂³	1	6	yes	—
226	#13133200	C₂³	1	6	yes	complemented
227	#13133199	C₂³	1	6	yes	—
228	#13133199	C₂³	1	6	yes	—
229	#13133199	C₂³	1	6	yes	—
230	#13133199	C₂³	1	6	yes	—
231	#13133199	C₂³	1	6	yes	complemented
232	#13133199	C₂³	1	6	yes	complemented
233	#13133198	C₂³	1	6	yes	—
234	#13133198	C₂³	1	6	yes	—
235	#13133198	C₂³	1	6	yes	complemented
236	#13133197	C₂³	1	6	yes	complemented
237	#13133197	C₂³	1	6	yes	complemented
238	#13133197	C₂³	1	6	yes	complemented
239	#13133197	C₂³	1	3	yes	complemented
240	#13133196	C₂³	1	6	yes	complemented
241	#13133196	C₂³	1	6	yes	complemented
242	#13133196	C₂³	1	6	yes	complemented
243	#13133196	C₂³	1	3	yes	complemented
244	#13133195	C₂³	1	6	yes	complemented
245	#13133195	C₂³	1	6	yes	complemented
246	#13133195	C₂³	1	6	yes	complemented
247	#13133195	C₂³	1	6	yes	complemented
248	#13133195	C₂³	1	6	yes	complemented
249	#13133195	C₂³	1	6	yes	complemented
250	#13133195	C₂³	1	6	yes	complemented
251	#13133194	C₂³	1	6	yes	complemented
252	#13133194	C₂³	1	6	yes	complemented
253	#13133194	C₂³	1	6	yes	complemented
254	#13133194	C₂³	1	6	yes	complemented
255	#13133194	C₂³	1	6	yes	complemented
256	#13133194	C₂³	1	6	yes	complemented
257	#13133194	C₂³	1	6	yes	complemented
258	#13133193	C₂³	1	6	yes	complemented
259	#13133193	C₂³	1	6	yes	complemented
260	#13133193	C₂³	1	6	yes	complemented
261	#13133193	C₂³	1	3	yes	complemented
262	#13133192	C₂³	1	3	yes	—
263	#13133192	C₂³	1	6	yes	—
264	#13133191	C₂³	1	3	yes	—
265	#13133191	C₂³	1	6	yes	—
266	#13133190	C₂³	1	6	yes	—
267	#13133190	C₂³	1	6	yes	—
268	#13133190	C₂³	1	6	yes	—
269	#13133189	C₂³	1	6	yes	—
270	#13133189	C₂³	1	6	yes	—
271	#13133189	C₂³	1	6	yes	—
272	#13133188	C₂³	1	3	yes	—
273	#13133188	C₂³	1	6	yes	—
274	#13133187	C₂³	1	6	yes	—
275	#13133187	C₂³	1	6	yes	—
276	#13133187	C₂³	1	6	yes	—
277	#13133187	C₂³	1	6	yes	complemented
278	#13133186	C₂³	1	6	yes	—
279	#13133186	C₂³	1	2	yes	complemented
280	#13133185	C₂³	1	6	yes	—
281	#13133185	C₂³	1	6	yes	—
282	#13133185	C₂³	1	6	yes	—
283	#13133185	C₂³	1	6	yes	complemented
284	Q₈×Dic₅₃	C₂³	1	3	yes	complemented
285	Q₈×Dic₅₃	C₂³	1	6	yes	complemented
286	C₄×Dic₁₀₆	C₂³	1	3	yes	complemented
287	C₄×Dic₁₀₆	C₂³	1	6	yes	complemented
288	C₄×Dic₁₀₆	C₂³	1	6	yes	complemented
289	C₄×Dic₁₀₆	C₂³	1	6	yes	complemented
290	C₄×Dic₁₀₆	C₂³	1	6	yes	complemented
291	#13133182	C₂³	1	6	yes	complemented
292	#13133182	C₂³	1	6	yes	complemented
293	#13133182	C₂³	1	3	yes	complemented
294	#13133182	C₂³	1	6	yes	complemented
295	#13133182	C₂³	1	6	yes	complemented
296	C₄×D₂₁₂	C₂³	1	3	yes	—
297	C₄×D₂₁₂	C₂³	1	6	yes	—
298	C₄×D₂₁₂	C₂³	1	6	yes	complemented
299	D₄×Dic₅₃	C₂³	1	3	yes	—
300	D₄×Dic₅₃	C₂³	1	6	yes	—
301	D₄×Dic₅₃	C₂³	1	6	yes	complemented
302	#13133179	C₂³	1	3	yes	—
303	#13133179	C₂³	1	6	yes	—
304	#13133179	C₂³	1	6	yes	complemented
305	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	—
306	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	—
307	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	—
308	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
309	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
310	#13133177	C₂³	1	6	yes	—
311	#13133177	C₂³	1	6	yes	—
312	#13133177	C₂³	1	6	yes	—
313	#13133177	C₂³	1	6	yes	complemented
314	#13133177	C₂³	1	6	yes	complemented
315	#13133176	C₂³	1	6	yes	complemented
316	#13133176	C₂³	1	6	yes	complemented
317	#13133175	C₂³	1	6	yes	complemented
318	#13133175	C₂³	1	6	yes	complemented
319	#13133175	C₂³	1	6	yes	complemented
320	#13133175	C₂³	1	6	yes	complemented
321	#13133174	C₂³	1	6	yes	complemented
322	#13133174	C₂³	1	6	yes	complemented
323	#13133174	C₂³	1	6	yes	complemented
324	#13133174	C₂³	1	6	yes	complemented
325	#13133173	C₂³	1	6	yes	complemented
326	#13133173	C₂³	1	6	yes	complemented
327	#13133173	C₂³	1	6	yes	complemented
328	#13133173	C₂³	1	6	yes	complemented
329	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
330	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
331	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
332	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
333	C₄⋊C₄×D₅₃	C₂³	1	3	yes	—
334	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
335	C₄⋊C₄×D₅₃	C₂³	1	3	yes	—
336	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
337	C₂×C₂²⋊Dic₅₃	C₂³	1	6	yes	complemented
338	C₂×#11719921	C₂³	1	6	yes	complemented
339	C₂×#11719921	C₂³	1	6	yes	complemented
340	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
341	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
342	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
343	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
344	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
345	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
346	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
347	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
348	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
349	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
350	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
351	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
352	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
353	C₂×C₄×Dic₅₃	C₂³	1	3	yes	complemented
354	C₄²×D₅₃	C₂³	1	3	yes	—
355	C₄²×D₅₃	C₂³	1	1	yes	characteristic
356	C₄²×D₅₃	C₂³	1	6	yes	—
357	C₄²×D₅₃	C₂³	1	6	yes	—
358	C₄²×D₅₃	C₂³	1	2	yes	—
359	C₄²×D₅₃	C₂³	1	3	yes	complemented
360	C₄²×D₅₃	C₂³	1	1	yes	characteristic, complemented
361	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
362	#126×C₅₃	C₂³	1	6	yes	complemented
363	#126×C₅₃	C₂³	1	6	yes	complemented
364	#126×C₅₃	C₂³	1	6	yes	complemented
365	#126×C₅₃	C₂³	1	6	yes	complemented
366	#126×C₅₃	C₂³	1	2	yes	complemented
367	#125×C₅₃	C₂³	1	3	yes	complemented
368	#124×C₅₃	C₂³	1	6	yes	—
369	#124×C₅₃	C₂³	1	3	yes	—
370	#124×C₅₃	C₂³	1	6	yes	—
371	#124×C₅₃	C₂³	1	6	yes	complemented
372	#123×C₅₃	C₂³	1	6	yes	—
373	#123×C₅₃	C₂³	1	6	yes	—
374	#123×C₅₃	C₂³	1	6	yes	complemented
375	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
376	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
377	C₂²⋊Q₈×C₅₃	C₂³	1	3	yes	complemented
378	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
379	#121×C₅₃	C₂³	1	3	yes	—
380	#121×C₅₃	C₂³	1	6	yes	—
381	#120×C₅₃	C₂³	1	6	yes	—
382	#120×C₅₃	C₂³	1	2	yes	complemented
383	C₄×Q₈×C₅₃	C₂³	1	3	yes	complemented
384	C₄×Q₈×C₅₃	C₂³	1	6	yes	complemented
385	C₄×D₄×C₅₃	C₂³	1	3	yes	—
386	C₄×D₄×C₅₃	C₂³	1	6	yes	—
387	C₄×D₄×C₅₃	C₂³	1	6	yes	complemented
388	#117×C₅₃	C₂³	1	6	yes	complemented
389	#117×C₅₃	C₂³	1	6	yes	complemented
390	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	complemented
391	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic, complemented
392	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
393	C₂³×D₅₃	—	4	12	no	—
394	C₂³×D₅₃	C₂⁴	1	6	yes	—
395	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
396	C₂³×D₅₃	C₂⁴	1	6	yes	—
397	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
398	C₂×Q₈×C₅₃	C₂⁴	1	3	yes	—
399	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
400	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
401	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
402	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
403	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
404	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
405	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
406	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
407	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
408	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
409	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
410	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
411	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
412	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
413	Q₈×D₅₃	—	4	12	no	—
414	Q₈×D₅₃	—	4	6	no	—
415	D₄×D₅₃	—	4	12	no	—
416	D₄×D₅₃	—	4	6	no	—
417	D₄×D₅₃	—	4	12	no	—
418	C₂×D₂₁₂	C₂⁴	1	6	yes	—
419	C₂×D₂₁₂	C₂⁴	1	3	yes	—
420	C₂×D₂₁₂	C₂⁴	1	6	yes	—
421	C₂×C₄×D₅₃	—	4	12	no	—
422	C₂×C₄×D₅₃	—	4	6	no	—
423	C₂×C₄×D₅₃	—	4	12	no	—
424	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
425	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
426	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
427	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
428	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
429	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
430	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
431	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
432	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
433	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
434	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
435	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
436	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
437	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
438	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
439	C₂×Dic₁₀₆	C₂⁴	1	3	yes	—
440	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
441	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
442	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
443	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
444	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
445	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
446	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
447	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
448	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
449	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
450	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
451	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
452	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
453	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
454	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
455	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
456	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
457	C₄²×C₅₃	C₂⁴	1	3	yes	—
458	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
459	C₄²×C₅₃	C₂⁴	1	6	yes	—
460	C₄²×C₅₃	C₂⁴	1	6	yes	—
461	C₄²×C₅₃	C₂⁴	1	2	yes	—
462	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
463	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
464	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
465	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
466	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
467	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
468	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
469	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
470	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
471	#11719921	C₂⁴	1	6	yes	—
472	#11719921	C₂⁴	1	6	yes	—
473	#11719921	C₂⁴	1	6	yes	—
474	#11719921	C₂⁴	1	6	yes	—
475	#11719921	C₂⁴	1	6	yes	—
476	#11719921	C₂⁴	1	6	yes	—
477	#11719921	C₂⁴	1	6	yes	—
478	#11719921	C₂⁴	1	6	yes	—
479	#11719921	C₂⁴	1	6	yes	—
480	#11719921	C₂⁴	1	6	yes	—
481	#11719921	C₂⁴	1	6	yes	—
482	#11719921	C₂⁴	1	6	yes	—
483	#11719921	C₂⁴	1	6	yes	—
484	#11719921	C₂⁴	1	6	yes	—
485	#11719921	C₂⁴	1	6	yes	—
486	#11719921	C₂⁴	1	6	yes	—
487	#11719921	C₂⁴	1	6	yes	—
488	#11719921	C₂⁴	1	6	yes	—
489	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
490	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
491	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
492	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
493	C₄⋊Dic₅₃	C₂⁴	1	3	yes	—
494	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
495	C₄⋊Dic₅₃	C₂⁴	1	3	yes	—
496	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
497	#11719919	C₂⁴	1	6	yes	—
498	#11719919	C₂⁴	1	6	yes	—
499	#11719919	C₂⁴	1	6	yes	—
500	#11719919	C₂⁴	1	6	yes	—
501	#11719919	C₂⁴	1	6	yes	—
502	#11719919	C₂⁴	1	6	yes	—
503	#11719919	C₂⁴	1	6	yes	—
504	#11719919	C₂⁴	1	6	yes	—
505	#11719919	C₂⁴	1	6	yes	—
506	#11719919	C₂⁴	1	6	yes	—
507	#11719919	C₂⁴	1	6	yes	—
508	#11719919	C₂⁴	1	6	yes	—
509	#11719919	C₂⁴	1	6	yes	—
510	#11719919	C₂⁴	1	6	yes	—
511	C₄×Dic₅₃	C₂⁴	1	3	yes	—
512	C₄×Dic₅₃	C₂⁴	1	3	yes	—
513	C₄×Dic₅₃	C₂⁴	1	3	yes	—
514	C₄×Dic₅₃	C₂⁴	1	3	yes	—
515	C₄×Dic₅₃	C₂⁴	1	6	yes	—
516	C₄×Dic₅₃	C₂⁴	1	6	yes	—
517	C₄×Dic₅₃	C₂⁴	1	6	yes	—
518	C₄×Dic₅₃	C₂⁴	1	6	yes	—
519	C₄×Dic₅₃	C₂⁴	1	6	yes	—
520	C₄×Dic₅₃	C₂⁴	1	6	yes	—
521	C₄×Dic₅₃	C₂⁴	1	6	yes	—
522	C₂³×C₅₃	—	4	6	no	—
523	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
524	C₂³×C₅₃	C₂⁵	1	6	yes	—
525	C₂²×D₅₃	—	2	6	no	—
526	C₂²×D₅₃	—	2	12	no	—
527	C₂²×D₅₃	—	2	12	no	—
528	C₂²×D₅₃	—	2	12	no	—
529	C₂²×D₅₃	—	4	6	no	—
530	C₂²×D₅₃	—	4	6	no	—
531	C₂²×D₅₃	—	4	6	no	—
532	C₂²×D₅₃	—	8	16	no	—
533	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
534	C₂²×D₅₃	C₂⁵	1	6	yes	—
535	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
536	Q₈×C₅₃	—	4	3	no	—
537	Q₈×C₅₃	—	4	6	no	—
538	D₄×C₅₃	—	4	6	no	—
539	D₄×C₅₃	—	4	6	no	—
540	D₄×C₅₃	—	4	3	no	—
541	C₂×C₄×C₅₃	—	4	6	no	—
542	C₂×C₄×C₅₃	—	4	6	no	—
543	C₂×C₄×C₅₃	—	4	3	no	—
544	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
545	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
546	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
547	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
548	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
549	C₂²⋊D₅₃	—	4	6	no	—
550	C₂²⋊D₅₃	—	4	6	no	—
551	C₂²⋊D₅₃	—	4	6	no	—
552	C₂²⋊D₅₃	—	4	6	no	—
553	C₂²⋊D₅₃	—	4	6	no	—
554	C₂×Dic₅₃	—	4	6	no	—
555	C₂×Dic₅₃	—	4	6	no	—
556	C₂×Dic₅₃	—	4	3	no	—
557	C₂×Dic₅₃	C₂⁵	1	6	yes	—
558	C₂×Dic₅₃	C₂⁵	1	6	yes	—
559	C₂×Dic₅₃	C₂⁵	1	6	yes	—
560	C₂×Dic₅₃	C₂⁵	1	3	yes	—
561	C₂×Dic₅₃	C₂⁵	1	3	yes	—
562	D₂₁₂	—	4	6	no	—
563	D₂₁₂	—	4	6	no	—
564	D₂₁₂	—	4	3	no	—
565	C₄×D₅₃	—	2	6	no	—
566	C₄×D₅₃	—	2	12	no	—
567	C₄×D₅₃	—	2	6	no	—
568	C₄×D₅₃	—	2	12	no	—
569	C₄×D₅₃	—	2	12	no	—
570	C₄×D₅₃	—	4	6	no	—
571	C₄×D₅₃	—	4	6	no	—
572	C₄×D₅₃	—	4	6	no	—
573	C₄×D₅₃	—	4	3	no	—
574	C₄×D₅₃	—	4	6	no	—
575	C₄×D₅₃	—	4	3	no	—
576	Dic₁₀₆	—	4	3	no	—
577	Dic₁₀₆	—	4	6	no	—
578	Dic₁₀₆	—	4	6	no	—
579	Dic₁₀₆	—	4	6	no	—
580	Dic₁₀₆	—	4	6	no	—
581	C₂×#3568	—	53	1	no	maximal, Sylow
582	C₂²×C₅₃	—	2	3	no	—
583	C₂²×C₅₃	—	2	6	no	—
584	C₂²×C₅₃	—	2	6	no	—
585	C₂²×C₅₃	—	2	6	no	—
586	C₂²×C₅₃	—	8	4	no	—
587	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
588	C₂×D₅₃	—	2	3	no	—
589	C₂×D₅₃	—	2	6	no	—
590	C₂×D₅₃	—	2	6	no	—
591	C₂×D₅₃	—	2	6	no	—
592	C₂×D₅₃	—	4	4	no	—
593	C₂×D₅₃	—	4	24	no	—
594	C₂×D₅₃	—	8	12	no	—
595	C₂×D₅₃	#585	1	6	yes	—
596	C₄×C₅₃	—	2	6	no	—
597	C₄×C₅₃	—	2	6	no	—
598	C₄×C₅₃	—	2	3	no	—
599	C₄×C₅₃	—	2	6	no	—
600	C₄×C₅₃	—	2	3	no	—
601	Dic₅₃	—	2	6	no	—
602	Dic₅₃	—	2	6	no	—
603	Dic₅₃	—	2	3	no	—
604	Dic₅₃	—	2	6	no	—
605	Dic₅₃	—	2	3	no	—
606	#3568	—	53	3	no	—
607	#3568	—	53	1	no	—
608	#3568	—	53	6	no	—
609	#3568	—	53	6	no	—
610	#3568	—	53	6	no	—
611	#3568	—	53	6	no	—
612	#3568	—	53	3	no	—
613	#3568	D₅₃	1	1	yes	characteristic, direct product factor
614	C₂×#563	—	53	3	no	—
615	C₂×H(3,𝔽₄)	—	53	1	no	—
616	C₂×#556	—	53	6	no	—
617	C₂×#551	—	53	6	no	—
618	C₂×#542	—	53	6	no	—
619	C₂×#538	—	53	6	no	—
620	C₂×#529	—	53	3	no	—
621	C₂×C₅₃	—	4	6	no	—
622	C₂×C₅₃	—	4	1	no	—
623	C₂×C₅₃	C₂×#585	1	3	yes	—
624	D₅₃	—	4	1	no	—
625	D₅₃	—	4	6	no	—
626	D₅₃	#3568	1	4	yes	direct product factor
627	#563	—	53	6	no	—
628	#563	—	53	6	no	—
629	#563	—	53	6	no	—
630	#563	—	53	3	no	—
631	#563	—	53	3	no	—
632	#563	—	53	3	no	—
633	#563	—	53	6	no	—
634	#563	—	53	6	no	—
635	#563	—	53	6	no	—
636	#563	C₂×D₅₃	1	3	yes	complemented
637	H(3,𝔽₄)	—	53	6	no	—
638	H(3,𝔽₄)	—	53	3	no	—
639	H(3,𝔽₄)	—	53	6	no	—
640	H(3,𝔽₄)	C₂×D₅₃	1	1	yes	characteristic, complemented
641	#556	—	53	6	no	—
642	#556	—	53	6	no	—
643	#556	—	53	6	no	—
644	#556	—	53	6	no	—
645	#556	—	53	6	no	—
646	#556	—	53	6	no	—
647	#556	—	53	6	no	—
648	#556	—	53	6	no	—
649	#556	—	53	6	no	—
650	#556	—	53	6	no	—
651	#556	—	53	6	no	—
652	#556	—	53	6	no	—
653	#556	—	53	6	no	—
654	#556	—	53	6	no	—
655	#556	—	53	6	no	—
656	#556	C₂×D₅₃	1	6	yes	complemented
657	#551	—	53	6	no	—
658	#551	—	53	6	no	—
659	#551	—	53	6	no	—
660	#551	—	53	6	no	—
661	#551	—	53	6	no	—
662	#551	—	53	6	no	—
663	#551	—	53	6	no	—
664	#551	—	53	6	no	—
665	#551	—	53	6	no	—
666	#551	—	53	6	no	—
667	#551	—	53	6	no	—
668	#551	—	53	6	no	—
669	#551	—	53	6	no	—
670	#551	—	53	6	no	—
671	#551	—	53	6	no	—
672	#551	C₂×D₅₃	1	6	yes	complemented
673	#542	—	53	6	no	—
674	#542	—	53	6	no	—
675	#542	—	53	6	no	—
676	#542	—	53	6	no	—
677	#542	—	53	6	no	—
678	#542	—	53	6	no	—
679	#542	—	53	6	no	—
680	#542	—	53	6	no	—
681	#542	—	53	6	no	—
682	#542	—	53	6	no	—
683	#542	—	53	6	no	—
684	#542	—	53	6	no	—
685	#542	—	53	6	no	—
686	#542	—	53	6	no	—
687	#542	—	53	6	no	—
688	#542	C₂×D₅₃	1	6	yes	complemented
689	#538	—	53	6	no	—
690	#538	—	53	6	no	—
691	#538	—	53	6	no	—
692	#538	—	53	6	no	—
693	#538	—	53	6	no	—
694	#538	—	53	6	no	—
695	#538	—	53	6	no	—
696	#538	—	53	6	no	—
697	#538	—	53	6	no	—
698	#538	—	53	6	no	—
699	#538	—	53	6	no	—
700	#538	—	53	6	no	—
701	#538	—	53	6	no	—
702	#538	—	53	6	no	—
703	#538	—	53	6	no	—
704	#538	C₂×D₅₃	1	6	yes	complemented
705	C₂×C₄⋊Q₈	—	53	6	no	—
706	#529	—	53	6	no	—
707	#529	—	53	3	no	—
708	#529	—	53	3	no	—
709	#529	—	53	6	no	—
710	#529	—	53	3	no	—
711	#529	—	53	3	no	—
712	#529	—	53	3	no	—
713	#529	—	53	3	no	—
714	#529	—	53	6	no	—
715	#529	—	53	6	no	—
716	#529	—	53	3	no	—
717	#529	C₂×D₅₃	1	3	yes	complemented
718	C₂×#126	—	53	6	no	—
719	C₂×#126	—	53	6	no	—
720	C₂×#126	—	53	6	no	—
721	C₂×#126	—	53	2	no	—
722	C₂×#126	—	53	6	no	—
723	C₂×#125	—	53	3	no	—
724	C₂×#124	—	53	3	no	—
725	C₂×#124	—	53	6	no	—
726	C₂×#124	—	53	6	no	—
727	C₂×#124	—	53	6	no	—
728	C₂×#123	—	53	6	no	—
729	C₂×#123	—	53	6	no	—
730	C₂×#123	—	53	6	no	—
731	C₂×C₂²⋊Q₈	—	53	3	no	—
732	C₂×C₂²⋊Q₈	—	53	6	no	—
733	C₂×C₂²⋊Q₈	—	53	6	no	—
734	C₂×C₂²⋊Q₈	—	53	6	no	—
735	C₂×#121	—	53	3	no	—
736	C₂×#121	—	53	6	no	—
737	C₂×#120	—	53	6	no	—
738	C₂×#120	—	53	2	no	—
739	C₂×C₄×Q₈	—	53	3	no	—
740	C₂×C₄×Q₈	—	53	6	no	—
741	C₂×C₄×D₄	—	53	3	no	—
742	C₂×C₄×D₄	—	53	6	no	—
743	C₂×C₄×D₄	—	53	6	no	—
744	C₂×#117	—	53	6	no	—
745	C₂×#117	—	53	6	no	—
746	C₂²×C₂²⋊C₄	—	53	6	no	—
747	C₂²×C₄²	—	53	1	no	—
748	C₅₃	C₂×#3568	1	1	yes	characteristic, complemented, Sylow
749	C₂⁵	—	53	2	no	—
750	C₂²×Q₈	—	53	6	no	—
751	C₂²×Q₈	—	53	3	no	—
752	C₂²×D₄	—	53	3	no	—
753	C₂²×D₄	—	53	6	no	—
754	C₂²×D₄	—	53	6	no	—
755	C₂³×C₄	—	53	6	no	—
756	C₂³×C₄	—	53	6	no	—
757	C₂³×C₄	—	53	3	no	—
758	C₄⋊Q₈	—	53	6	no	—
759	C₄⋊Q₈	—	53	6	no	—
760	C₄⋊Q₈	—	53	6	no	—
761	C₄⋊Q₈	—	53	6	no	—
762	C₄⋊Q₈	—	53	6	no	—
763	C₄⋊Q₈	—	53	6	no	—
764	C₄⋊Q₈	—	53	6	no	—
765	C₄⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
766	#126	—	53	6	no	—
767	#126	—	53	6	no	—
768	#126	—	53	6	no	—
769	#126	—	53	6	no	—
770	#126	—	53	6	no	—
771	#126	—	53	6	no	—
772	#126	—	53	6	no	—
773	#126	—	53	6	no	—
774	#126	—	53	6	no	—
775	#126	—	53	6	no	—
776	#126	—	53	6	no	—
777	#126	—	53	6	no	—
778	#126	—	53	6	no	—
779	#126	—	53	6	no	—
780	#126	—	53	6	no	—
781	#126	—	53	6	no	—
782	#126	—	53	6	no	—
783	#126	—	53	6	no	—
784	#126	—	53	6	no	—
785	#126	—	53	6	no	—
786	#126	—	53	6	no	—
787	#126	—	53	6	no	—
788	#126	—	53	6	no	—
789	#126	—	53	6	no	—
790	#126	—	53	6	no	—
791	#126	—	53	6	no	—
792	#126	—	53	6	no	—
793	#126	—	53	6	no	—
794	#126	—	53	6	no	—
795	#126	—	53	2	no	—
796	#126	—	53	6	no	—
797	#126	C₂²×D₅₃	1	6	yes	complemented
798	#126	C₂²×D₅₃	1	6	yes	complemented
799	#126	C₂²×D₅₃	1	6	yes	complemented
800	#126	C₂²×D₅₃	1	2	yes	complemented
801	#126	C₂²×D₅₃	1	6	yes	complemented
802	#125	—	53	6	no	—
803	#125	—	53	6	no	—
804	#125	—	53	3	no	—
805	#125	—	53	3	no	—
806	#125	—	53	3	no	—
807	#125	C₂²×D₅₃	1	3	yes	complemented
808	#124	—	53	3	no	—
809	#124	—	53	6	no	—
810	#124	—	53	6	no	—
811	#124	—	53	6	no	—
812	#124	—	53	3	no	—
813	#124	—	53	6	no	—
814	#124	—	53	6	no	—
815	#124	—	53	6	no	—
816	#124	—	53	6	no	—
817	#124	—	53	6	no	—
818	#124	—	53	6	no	—
819	#124	—	53	6	no	—
820	#124	—	53	6	no	—
821	#124	—	53	6	no	—
822	#124	—	53	6	no	—
823	#124	—	53	6	no	—
824	#124	—	53	6	no	—
825	#124	—	53	6	no	—
826	#124	—	53	6	no	—
827	#124	—	53	6	no	—
828	#124	—	53	6	no	—
829	#124	—	53	6	no	—
830	#124	—	53	3	no	—
831	#124	—	53	6	no	—
832	#124	—	53	6	no	—
833	#124	—	53	6	no	—
834	#124	C₂²×D₅₃	1	3	yes	—
835	#124	C₂²×D₅₃	1	6	yes	—
836	#124	C₂²×D₅₃	1	6	yes	—
837	#124	C₂²×D₅₃	1	6	yes	complemented
838	#123	—	53	6	no	—
839	#123	—	53	6	no	—
840	#123	—	53	6	no	—
841	#123	—	53	6	no	—
842	#123	—	53	6	no	—
843	#123	—	53	6	no	—
844	#123	—	53	6	no	—
845	#123	—	53	6	no	—
846	#123	—	53	6	no	—
847	#123	—	53	6	no	—
848	#123	—	53	6	no	—
849	#123	—	53	6	no	—
850	#123	—	53	6	no	—
851	#123	—	53	6	no	—
852	#123	—	53	6	no	—
853	#123	—	53	6	no	—
854	#123	—	53	6	no	—
855	#123	—	53	6	no	—
856	#123	—	53	6	no	—
857	#123	—	53	6	no	—
858	#123	—	53	6	no	—
859	#123	C₂²×D₅₃	1	6	yes	—
860	#123	C₂²×D₅₃	1	6	yes	—
861	#123	C₂²×D₅₃	1	6	yes	complemented
862	C₂²⋊Q₈	—	53	3	no	—
863	C₂²⋊Q₈	—	53	6	no	—
864	C₂²⋊Q₈	—	53	6	no	—
865	C₂²⋊Q₈	—	53	6	no	—
866	C₂²⋊Q₈	—	53	3	no	—
867	C₂²⋊Q₈	—	53	6	no	—
868	C₂²⋊Q₈	—	53	6	no	—
869	C₂²⋊Q₈	—	53	6	no	—
870	C₂²⋊Q₈	—	53	6	no	—
871	C₂²⋊Q₈	—	53	3	no	—
872	C₂²⋊Q₈	—	53	6	no	—
873	C₂²⋊Q₈	—	53	6	no	—
874	C₂²⋊Q₈	—	53	6	no	—
875	C₂²⋊Q₈	—	53	6	no	—
876	C₂²⋊Q₈	—	53	6	no	—
877	C₂²⋊Q₈	—	53	6	no	—
878	C₂²⋊Q₈	—	53	6	no	—
879	C₂²⋊Q₈	—	53	6	no	—
880	C₂²⋊Q₈	—	53	6	no	—
881	C₂²⋊Q₈	—	53	6	no	—
882	C₂²⋊Q₈	—	53	6	no	—
883	C₂²⋊Q₈	—	53	6	no	—
884	C₂²⋊Q₈	—	53	6	no	—
885	C₂²⋊Q₈	—	53	6	no	—
886	C₂²⋊Q₈	—	53	6	no	—
887	C₂²⋊Q₈	—	53	6	no	—
888	C₂²⋊Q₈	C₂²×D₅₃	1	3	yes	complemented
889	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
890	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
891	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
892	#121	—	53	3	no	—
893	#121	—	53	6	no	—
894	#121	—	53	6	no	—
895	#121	—	53	6	no	—
896	#121	—	53	6	no	—
897	#121	—	53	3	no	—
898	#121	—	53	6	no	—
899	#121	—	53	3	no	—
900	#121	—	53	6	no	—
901	#121	—	53	6	no	—
902	#121	—	53	6	no	—
903	#121	—	53	6	no	—
904	#121	C₂²×D₅₃	1	3	yes	—
905	#121	C₂²×D₅₃	1	6	yes	—
906	#120	—	53	2	no	—
907	#120	—	53	6	no	—
908	#120	—	53	6	no	—
909	#120	—	53	6	no	—
910	#120	—	53	6	no	—
911	#120	—	53	6	no	—
912	#120	—	53	6	no	—
913	#120	—	53	6	no	—
914	#120	—	53	6	no	—
915	#120	—	53	6	no	—
916	#120	C₂²×D₅₃	1	6	yes	—
917	#120	C₂²×D₅₃	1	2	yes	complemented
918	C₄×Q₈	—	53	3	no	—
919	C₄×Q₈	—	53	6	no	—
920	C₄×Q₈	—	53	3	no	—
921	C₄×Q₈	—	53	6	no	—
922	C₄×Q₈	—	53	6	no	—
923	C₄×Q₈	—	53	6	no	—
924	C₄×Q₈	—	53	6	no	—
925	C₄×Q₈	—	53	6	no	—
926	C₄×Q₈	—	53	3	no	—
927	C₄×Q₈	—	53	6	no	—
928	C₄×Q₈	—	53	6	no	—
929	C₄×Q₈	—	53	6	no	—
930	C₄×Q₈	C₂²×D₅₃	1	3	yes	complemented
931	C₄×Q₈	C₂²×D₅₃	1	6	yes	complemented
932	C₄×D₄	—	53	6	no	—
933	C₄×D₄	—	53	3	no	—
934	C₄×D₄	—	53	6	no	—
935	C₄×D₄	—	53	6	no	—
936	C₄×D₄	—	53	6	no	—
937	C₄×D₄	—	53	6	no	—
938	C₄×D₄	—	53	6	no	—
939	C₄×D₄	—	53	6	no	—
940	C₄×D₄	—	53	6	no	—
941	C₄×D₄	—	53	3	no	—
942	C₄×D₄	—	53	6	no	—
943	C₄×D₄	—	53	6	no	—
944	C₄×D₄	—	53	6	no	—
945	C₄×D₄	—	53	6	no	—
946	C₄×D₄	—	53	6	no	—
947	C₄×D₄	—	53	6	no	—
948	C₄×D₄	—	53	6	no	—
949	C₄×D₄	—	53	3	no	—
950	C₄×D₄	—	53	6	no	—
951	C₄×D₄	C₂²×D₅₃	1	3	yes	—
952	C₄×D₄	C₂²×D₅₃	1	6	yes	—
953	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
954	#117	—	53	6	no	—
955	#117	—	53	6	no	—
956	#117	—	53	6	no	—
957	#117	—	53	6	no	—
958	#117	—	53	6	no	—
959	#117	—	53	6	no	—
960	#117	—	53	6	no	—
961	#117	—	53	6	no	—
962	#117	—	53	6	no	—
963	#117	—	53	6	no	—
964	#117	—	53	6	no	—
965	#117	—	53	6	no	—
966	#117	—	53	6	no	—
967	#117	—	53	6	no	—
968	#117	C₂²×D₅₃	1	6	yes	complemented
969	#117	C₂²×D₅₃	1	6	yes	complemented
970	C₂×C₄⋊C₄	—	53	6	no	—
971	C₂×C₄⋊C₄	—	53	6	no	—
972	C₂×C₄⋊C₄	—	53	6	no	—
973	C₂×C₄⋊C₄	—	53	6	no	—
974	C₂×C₄⋊C₄	—	53	3	no	—
975	C₂×C₄⋊C₄	—	53	6	no	—
976	C₂×C₄⋊C₄	—	53	3	no	—
977	C₂×C₄⋊C₄	—	53	6	no	—
978	C₂×C₂²⋊C₄	—	53	6	no	—
979	C₂×C₂²⋊C₄	—	53	6	no	—
980	C₂×C₂²⋊C₄	—	53	6	no	—
981	C₂×C₂²⋊C₄	—	53	6	no	—
982	C₂×C₂²⋊C₄	—	53	6	no	—
983	C₂×C₂²⋊C₄	—	53	6	no	—
984	C₂×C₂²⋊C₄	—	53	6	no	—
985	C₂×C₂²⋊C₄	—	53	6	no	—
986	C₂×C₂²⋊C₄	—	53	6	no	—
987	C₂×C₂²⋊C₄	—	53	6	no	—
988	C₂×C₂²⋊C₄	—	53	6	no	—
989	C₂×C₂²⋊C₄	—	53	6	no	—
990	C₂×C₂²⋊C₄	—	53	6	no	—
991	C₂×C₂²⋊C₄	—	53	6	no	—
992	C₂×C₂²⋊C₄	—	53	6	no	—
993	C₂×C₂²⋊C₄	—	53	6	no	—
994	C₂×C₂²⋊C₄	C₂²×D₅₃	1	6	yes	complemented
995	C₂×C₄²	—	53	3	no	—
996	C₂×C₄²	—	53	6	no	—
997	C₂×C₄²	—	53	3	no	—
998	C₂×C₄²	—	53	6	no	—
999	C₂×C₄²	—	53	2	no	—
1000	C₂×C₄²	—	53	1	no	—
1001	C₂×C₄²	—	53	1	no	—
1002	C₂×C₄²	—	53	3	no	—
1003	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic, complemented
1004	C₂⁴	—	53	6	no	—
1005	C₂⁴	—	53	1	no	—
1006	C₂⁴	—	53	6	no	—
1007	C₂⁴	—	212	12	no	—
1008	C₂⁴	C₂³×D₅₃	1	2	yes	—
1009	C₂×Q₈	—	53	6	no	—
1010	C₂×Q₈	—	53	6	no	—
1011	C₂×Q₈	—	53	6	no	—
1012	C₂×Q₈	—	53	3	no	—
1013	C₂×Q₈	—	53	6	no	—
1014	C₂×Q₈	—	212	12	no	—
1015	C₂×Q₈	—	212	6	no	—
1016	C₂×Q₈	C₂³×D₅₃	1	6	yes	—
1017	C₂×Q₈	C₂³×D₅₃	1	3	yes	—
1018	C₂×D₄	—	53	6	no	—
1019	C₂×D₄	—	53	6	no	—
1020	C₂×D₄	—	53	6	no	—
1021	C₂×D₄	—	53	6	no	—
1022	C₂×D₄	—	53	6	no	—
1023	C₂×D₄	—	53	3	no	—
1024	C₂×D₄	—	53	6	no	—
1025	C₂×D₄	—	53	6	no	—
1026	C₂×D₄	—	212	12	no	—
1027	C₂×D₄	—	212	6	no	—
1028	C₂×D₄	—	212	12	no	—
1029	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1030	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1031	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1032	C₂²×C₄	—	53	3	no	—
1033	C₂²×C₄	—	53	6	no	—
1034	C₂²×C₄	—	53	6	no	—
1035	C₂²×C₄	—	53	3	no	—
1036	C₂²×C₄	—	53	6	no	—
1037	C₂²×C₄	—	53	6	no	—
1038	C₂²×C₄	—	53	3	no	—
1039	C₂²×C₄	—	53	6	no	—
1040	C₂²×C₄	—	53	3	no	—
1041	C₂²×C₄	—	53	3	no	—
1042	C₂²×C₄	—	53	6	no	—
1043	C₂²×C₄	—	53	6	no	—
1044	C₂²×C₄	—	53	6	no	—
1045	C₂²×C₄	—	53	6	no	—
1046	C₂²×C₄	—	212	12	no	—
1047	C₂²×C₄	—	212	6	no	—
1048	C₂²×C₄	—	212	12	no	—
1049	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1050	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1051	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1052	C₄⋊C₄	—	53	6	no	—
1053	C₄⋊C₄	—	53	6	no	—
1054	C₄⋊C₄	—	53	6	no	—
1055	C₄⋊C₄	—	53	6	no	—
1056	C₄⋊C₄	—	53	6	no	—
1057	C₄⋊C₄	—	53	6	no	—
1058	C₄⋊C₄	—	53	6	no	—
1059	C₄⋊C₄	—	53	6	no	—
1060	C₄⋊C₄	—	53	6	no	—
1061	C₄⋊C₄	—	53	6	no	—
1062	C₄⋊C₄	—	53	6	no	—
1063	C₄⋊C₄	—	53	6	no	—
1064	C₄⋊C₄	—	53	6	no	—
1065	C₄⋊C₄	—	53	3	no	—
1066	C₄⋊C₄	—	53	6	no	—
1067	C₄⋊C₄	—	53	6	no	—
1068	C₄⋊C₄	—	53	6	no	—
1069	C₄⋊C₄	—	53	6	no	—
1070	C₄⋊C₄	—	53	3	no	—
1071	C₄⋊C₄	—	53	6	no	—
1072	C₄⋊C₄	—	53	6	no	—
1073	C₄⋊C₄	—	53	6	no	—
1074	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1075	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1076	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1077	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1078	C₄⋊C₄	C₂³×D₅₃	1	3	yes	—
1079	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1080	C₄⋊C₄	C₂³×D₅₃	1	3	yes	—
1081	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1082	C₂²⋊C₄	—	53	6	no	—
1083	C₂²⋊C₄	—	53	6	no	—
1084	C₂²⋊C₄	—	53	6	no	—
1085	C₂²⋊C₄	—	53	6	no	—
1086	C₂²⋊C₄	—	53	6	no	—
1087	C₂²⋊C₄	—	53	6	no	—
1088	C₂²⋊C₄	—	53	6	no	—
1089	C₂²⋊C₄	—	53	6	no	—
1090	C₂²⋊C₄	—	53	6	no	—
1091	C₂²⋊C₄	—	53	6	no	—
1092	C₂²⋊C₄	—	53	6	no	—
1093	C₂²⋊C₄	—	53	6	no	—
1094	C₂²⋊C₄	—	53	6	no	—
1095	C₂²⋊C₄	—	53	6	no	—
1096	C₂²⋊C₄	—	53	6	no	—
1097	C₂²⋊C₄	—	53	6	no	—
1098	C₂²⋊C₄	—	53	6	no	—
1099	C₂²⋊C₄	—	53	6	no	—
1100	C₂²⋊C₄	—	53	6	no	—
1101	C₂²⋊C₄	—	53	6	no	—
1102	C₂²⋊C₄	—	53	6	no	—
1103	C₂²⋊C₄	—	53	6	no	—
1104	C₂²⋊C₄	—	53	6	no	—
1105	C₂²⋊C₄	—	53	6	no	—
1106	C₂²⋊C₄	—	53	6	no	—
1107	C₂²⋊C₄	—	53	6	no	—
1108	C₂²⋊C₄	—	53	6	no	—
1109	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1110	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1111	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1112	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1113	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1114	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1115	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1116	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1117	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1118	C₄²	—	53	3	no	—
1119	C₄²	—	53	3	no	—
1120	C₄²	—	53	3	no	—
1121	C₄²	—	53	3	no	—
1122	C₄²	—	53	6	no	—
1123	C₄²	—	53	6	no	—
1124	C₄²	—	53	6	no	—
1125	C₄²	—	53	6	no	—
1126	C₄²	—	53	6	no	—
1127	C₄²	—	53	6	no	—
1128	C₄²	—	53	6	no	—
1129	C₄²	C₂³×D₅₃	1	3	yes	—
1130	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1131	C₄²	C₂³×D₅₃	1	6	yes	—
1132	C₄²	C₂³×D₅₃	1	6	yes	—
1133	C₄²	C₂³×D₅₃	1	2	yes	—
1134	C₂³	—	4	6	no	—
1135	C₂³	—	53	1	no	—
1136	C₂³	—	53	6	no	—
1137	C₂³	—	53	1	no	—
1138	C₂³	—	106	6	no	—
1139	C₂³	—	106	12	no	—
1140	C₂³	—	106	12	no	—
1141	C₂³	—	106	12	no	—
1142	C₂³	—	424	16	no	—
1143	C₂³	—	212	6	no	—
1144	C₂³	—	212	6	no	—
1145	C₂³	—	212	6	no	—
1146	C₂³	C₂⁴×D₅₃	1	6	yes	—
1147	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1148	Q₈	—	4	6	no	—
1149	Q₈	—	4	3	no	—
1150	Q₈	—	212	6	no	—
1151	Q₈	—	212	6	no	—
1152	Q₈	—	212	3	no	—
1153	Q₈	—	212	6	no	—
1154	Q₈	—	212	6	no	—
1155	D₄	—	4	6	no	—
1156	D₄	—	4	3	no	—
1157	D₄	—	4	6	no	—
1158	D₄	—	212	6	no	—
1159	D₄	—	212	3	no	—
1160	D₄	—	212	6	no	—
1161	D₄	—	212	6	no	—
1162	D₄	—	212	6	no	—
1163	D₄	—	212	6	no	—
1164	D₄	—	212	6	no	—
1165	D₄	—	212	6	no	—
1166	C₂×C₄	—	4	6	no	—
1167	C₂×C₄	—	4	3	no	—
1168	C₂×C₄	—	4	6	no	—
1169	C₂×C₄	—	53	3	no	—
1170	C₂×C₄	—	53	6	no	—
1171	C₂×C₄	—	53	3	no	—
1172	C₂×C₄	—	53	6	no	—
1173	C₂×C₄	—	53	6	no	—
1174	C₂×C₄	—	106	6	no	—
1175	C₂×C₄	—	106	12	no	—
1176	C₂×C₄	—	106	12	no	—
1177	C₂×C₄	—	106	6	no	—
1178	C₂×C₄	—	106	12	no	—
1179	C₂×C₄	—	212	6	no	—
1180	C₂×C₄	—	212	3	no	—
1181	C₂×C₄	—	212	6	no	—
1182	C₂×C₄	—	212	6	no	—
1183	C₂×C₄	—	212	3	no	—
1184	C₂×C₄	—	212	6	no	—
1185	C₂×C₄	—	212	6	no	—
1186	C₂×C₄	—	212	3	no	—
1187	C₂×C₄	—	212	6	no	—
1188	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1189	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1190	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1191	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1192	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1193	C₂²	—	2	3	no	—
1194	C₂²	—	2	6	no	—
1195	C₂²	—	2	6	no	—
1196	C₂²	—	2	6	no	—
1197	C₂²	—	8	4	no	—
1198	C₂²	—	53	6	no	—
1199	C₂²	—	106	3	no	—
1200	C₂²	—	106	6	no	—
1201	C₂²	—	106	6	no	—
1202	C₂²	—	106	6	no	—
1203	C₂²	—	424	12	no	—
1204	C₂²	—	212	24	no	—
1205	C₂²	—	212	4	no	—
1206	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1207	C₄	—	2	3	no	—
1208	C₄	—	2	6	no	—
1209	C₄	—	2	3	no	—
1210	C₄	—	2	6	no	—
1211	C₄	—	2	6	no	—
1212	C₄	—	106	3	no	—
1213	C₄	—	106	6	no	—
1214	C₄	—	106	3	no	—
1215	C₄	—	106	6	no	—
1216	C₄	—	106	6	no	—
1217	C₂	—	4	6	no	—
1218	C₂	—	4	1	no	—
1219	C₂	—	53	4	no	—
1220	C₂	—	212	6	no	—
1221	C₂	—	212	1	no	—
1222	C₂	#585×D₅₃	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3568	C₂
hypercenter	#3568	D₅₃
hypocenter	C₅₃	C₂×#3568
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3568

Complements

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

N	H ≅ G/N	type
1. #20289412	C₂	semidirect
2. #20289411	C₂	semidirect
3. #20289410	C₂	semidirect
4. #20289409	C₂	semidirect
5. #20289408	C₂	semidirect
6. #20289407	C₂	semidirect
7. #20289406	C₂	semidirect
8. #563×D₅₃	C₂	semidirect
9. H(3,𝔽₄)×D₅₃	C₂	semidirect
10. #556×D₅₃	C₂	semidirect
11. #551×D₅₃	C₂	semidirect
12. #542×D₅₃	C₂	semidirect
13. #538×D₅₃	C₂	semidirect
14. #529×D₅₃	C₂	semidirect
15. C₅₃×#3568	C₂	semidirect
16. #16811377	C₂²	semidirect
17. #16811377	C₂²	semidirect
18. #16811376	C₂²	semidirect
19. #16811375	C₂²	semidirect
20. #16811375	C₂²	semidirect
21. #16811374	C₂²	semidirect
22. #16811374	C₂²	semidirect
23. #16811373	C₂²	semidirect
24. #16811372	C₂²	semidirect
25. #16811366	C₂²	semidirect
26. #16811365	C₂²	semidirect
27. #16811365	C₂²	semidirect
28. #16811347	C₂²	semidirect
29. #16811346	C₂²	semidirect
30. #16811345	C₂²	semidirect
31. #16811345	C₂²	semidirect
32. #16811344	C₂²	semidirect
33. #16811344	C₂²	semidirect
34. #16811343	C₂²	semidirect
35. #16811342	C₂²	semidirect
36. #16811342	C₂²	semidirect
37. #16811341	C₂²	semidirect
38. #16811341	C₂²	semidirect
39. #16811340	C₂²	semidirect
40. #16811340	C₂²	semidirect
41. #16811340	C₂²	semidirect
42. #16811340	C₂²	semidirect
43. #16811304	C₂²	semidirect
44. #16811303	C₂²	semidirect
45. #16811302	C₂²	semidirect
46. #16811302	C₂²	semidirect
47. #16811301	C₂²	semidirect
48. #16811300	C₂²	semidirect
49. #16811300	C₂²	semidirect
50. #16811299	C₂²	semidirect
51. #16811299	C₂²	semidirect
52. #16811298	C₂²	semidirect
53. #16811298	C₂²	semidirect
54. #16811297	C₂²	semidirect
55. #16811297	C₂²	semidirect
56. #16811296	C₂²	semidirect
57. #16811296	C₂²	semidirect
58. #16811247	C₂²	semidirect
59. #16811246	C₂²	semidirect
60. #16811245	C₂²	semidirect
61. #16811244	C₂²	semidirect
62. #16811243	C₂²	semidirect
63. #16811243	C₂²	semidirect
64. #16811242	C₂²	semidirect
65. #16811241	C₂²	semidirect
66. #16811241	C₂²	semidirect
67. #16811240	C₂²	semidirect
68. #16811239	C₂²	semidirect
69. #16811239	C₂²	semidirect
70. #16811238	C₂²	semidirect
71. #16811237	C₂²	semidirect
72. #16811237	C₂²	semidirect
73. #16811213	C₂²	semidirect
74. #16811212	C₂²	semidirect
75. #16811212	C₂²	semidirect
76. #16811211	C₂²	semidirect
77. #16811210	C₂²	semidirect
78. #16811209	C₂²	semidirect
79. #16811209	C₂²	semidirect
80. #16811208	C₂²	semidirect
81. #16811208	C₂²	semidirect
82. #16811207	C₂²	semidirect
83. #16811207	C₂²	semidirect
84. #16811206	C₂²	semidirect
85. #16811206	C₂²	semidirect
86. #16811205	C₂²	semidirect
87. #16811205	C₂²	semidirect
88. C₄⋊Q₈×D₅₃	C₂²	semidirect
89. #16811160	C₂²	semidirect
90. #16811159	C₂²	semidirect
91. #16811158	C₂²	semidirect
92. #16811157	C₂²	semidirect
93. #16811156	C₂²	semidirect
94. #16811155	C₂²	semidirect
95. #16811154	C₂²	semidirect
96. #16811153	C₂²	semidirect
97. #16811152	C₂²	semidirect
98. #16811151	C₂²	semidirect
99. #16811150	C₂²	semidirect
100. #126×D₅₃	C₂²	semidirect
101. #126×D₅₃	C₂²	semidirect
102. #126×D₅₃	C₂²	semidirect
103. #126×D₅₃	C₂²	semidirect
104. #126×D₅₃	C₂²	semidirect
105. #125×D₅₃	C₂²	semidirect
109. #124×D₅₃	C₂²	semidirect
112. #123×D₅₃	C₂²	semidirect
113. C₂²⋊Q₈×D₅₃	C₂²	semidirect
114. C₂²⋊Q₈×D₅₃	C₂²	semidirect
115. C₂²⋊Q₈×D₅₃	C₂²	semidirect
116. C₂²⋊Q₈×D₅₃	C₂²	semidirect
120. #120×D₅₃	C₂²	semidirect
121. C₄×Q₈×D₅₃	C₂²	semidirect
122. C₄×Q₈×D₅₃	C₂²	semidirect
125. C₄×D₄×D₅₃	C₂²	semidirect
126. #117×D₅₃	C₂²	semidirect
127. #117×D₅₃	C₂²	semidirect
128. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
129. C₂×C₄²×D₅₃	C₂²	semidirect
130. C₅₃×#563	C₂²	semidirect
131. C₅₃×H(3,𝔽₄)	C₂²	semidirect
132. C₅₃×#556	C₂²	semidirect
133. C₅₃×#551	C₂²	semidirect
134. C₅₃×#542	C₂²	semidirect
135. C₅₃×#538	C₂²	semidirect
136. C₅₃×#529	C₂²	semidirect
146. #13133217	C₂³	semidirect
147. #13133216	C₂³	semidirect
148. #13133216	C₂³	semidirect
149. #13133216	C₂³	semidirect
150. #13133216	C₂³	semidirect
151. #13133215	C₂³	semidirect
152. #13133215	C₂³	semidirect
153. #13133212	C₂³	semidirect
154. #13133212	C₂³	semidirect
155. #13133212	C₂³	semidirect
156. #13133212	C₂³	semidirect
157. #13133212	C₂³	semidirect
158. #13133212	C₂³	semidirect
159. #13133212	C₂³	semidirect
160. #13133212	C₂³	semidirect
161. #13133212	C₂³	semidirect
162. #13133212	C₂³	semidirect
163. #13133212	C₂³	semidirect
164. #13133212	C₂³	semidirect
165. #13133212	C₂³	semidirect
166. #13133211	C₂³	semidirect
167. #13133211	C₂³	semidirect
168. #13133211	C₂³	semidirect
169. #13133211	C₂³	semidirect
170. #13133211	C₂³	semidirect
171. #13133210	C₂³	semidirect
172. #13133210	C₂³	semidirect
173. #13133210	C₂³	semidirect
174. #13133210	C₂³	semidirect
175. #13133210	C₂³	semidirect
176. #13133210	C₂³	semidirect
177. #13133210	C₂³	semidirect
178. #13133210	C₂³	semidirect
179. #13133210	C₂³	semidirect
180. #13133210	C₂³	semidirect
181. #13133210	C₂³	semidirect
182. #13133210	C₂³	semidirect
183. #13133210	C₂³	semidirect
184. #13133209	C₂³	semidirect
185. #13133208	C₂³	semidirect
186. #13133208	C₂³	semidirect
187. #13133207	C₂³	semidirect
188. #13133207	C₂³	semidirect
192. #13133206	C₂³	semidirect
196. #13133205	C₂³	semidirect
200. #13133204	C₂³	semidirect
211. #13133203	C₂³	semidirect
212. #13133203	C₂³	semidirect
213. #13133203	C₂³	semidirect
214. #13133203	C₂³	semidirect
219. #13133202	C₂³	semidirect
220. #13133202	C₂³	semidirect
223. #13133201	C₂³	semidirect
226. #13133200	C₂³	semidirect
231. #13133199	C₂³	semidirect
232. #13133199	C₂³	semidirect
235. #13133198	C₂³	semidirect
236. #13133197	C₂³	semidirect
237. #13133197	C₂³	semidirect
238. #13133197	C₂³	semidirect
239. #13133197	C₂³	semidirect
240. #13133196	C₂³	semidirect
241. #13133196	C₂³	semidirect
242. #13133196	C₂³	semidirect
243. #13133196	C₂³	semidirect
244. #13133195	C₂³	semidirect
245. #13133195	C₂³	semidirect
246. #13133195	C₂³	semidirect
247. #13133195	C₂³	semidirect
248. #13133195	C₂³	semidirect
249. #13133195	C₂³	semidirect
250. #13133195	C₂³	semidirect
251. #13133194	C₂³	semidirect
252. #13133194	C₂³	semidirect
253. #13133194	C₂³	semidirect
254. #13133194	C₂³	semidirect
255. #13133194	C₂³	semidirect
256. #13133194	C₂³	semidirect
257. #13133194	C₂³	semidirect
258. #13133193	C₂³	semidirect
259. #13133193	C₂³	semidirect
260. #13133193	C₂³	semidirect
261. #13133193	C₂³	semidirect
277. #13133187	C₂³	semidirect
279. #13133186	C₂³	semidirect
283. #13133185	C₂³	semidirect
284. Q₈×Dic₅₃	C₂³	semidirect
285. Q₈×Dic₅₃	C₂³	semidirect
286. C₄×Dic₁₀₆	C₂³	semidirect
287. C₄×Dic₁₀₆	C₂³	semidirect
288. C₄×Dic₁₀₆	C₂³	semidirect
289. C₄×Dic₁₀₆	C₂³	semidirect
290. C₄×Dic₁₀₆	C₂³	semidirect
291. #13133182	C₂³	semidirect
292. #13133182	C₂³	semidirect
293. #13133182	C₂³	semidirect
294. #13133182	C₂³	semidirect
295. #13133182	C₂³	semidirect
298. C₄×D₂₁₂	C₂³	semidirect
301. D₄×Dic₅₃	C₂³	semidirect
304. #13133179	C₂³	semidirect
308. C₄×C₂²⋊D₅₃	C₂³	semidirect
309. C₄×C₂²⋊D₅₃	C₂³	semidirect
313. #13133177	C₂³	semidirect
314. #13133177	C₂³	semidirect
315. #13133176	C₂³	semidirect
316. #13133176	C₂³	semidirect
317. #13133175	C₂³	semidirect
318. #13133175	C₂³	semidirect
319. #13133175	C₂³	semidirect
320. #13133175	C₂³	semidirect
321. #13133174	C₂³	semidirect
322. #13133174	C₂³	semidirect
323. #13133174	C₂³	semidirect
324. #13133174	C₂³	semidirect
325. #13133173	C₂³	semidirect
326. #13133173	C₂³	semidirect
327. #13133173	C₂³	semidirect
328. #13133173	C₂³	semidirect
337. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
338. C₂×#11719921	C₂³	semidirect
339. C₂×#11719921	C₂³	semidirect
349. C₂²⋊C₄×D₅₃	C₂³	semidirect
350. C₂²⋊C₄×D₅₃	C₂³	semidirect
351. C₂²⋊C₄×D₅₃	C₂³	semidirect
352. C₂²⋊C₄×D₅₃	C₂³	semidirect
353. C₂×C₄×Dic₅₃	C₂³	semidirect
359. C₄²×D₅₃	C₂³	semidirect
360. C₄²×D₅₃	C₂³	semidirect
361. C₄⋊Q₈×C₅₃	C₂³	semidirect
362. #126×C₅₃	C₂³	semidirect
363. #126×C₅₃	C₂³	semidirect
364. #126×C₅₃	C₂³	semidirect
365. #126×C₅₃	C₂³	semidirect
366. #126×C₅₃	C₂³	semidirect
367. #125×C₅₃	C₂³	semidirect
371. #124×C₅₃	C₂³	semidirect
374. #123×C₅₃	C₂³	semidirect
375. C₂²⋊Q₈×C₅₃	C₂³	semidirect
376. C₂²⋊Q₈×C₅₃	C₂³	semidirect
377. C₂²⋊Q₈×C₅₃	C₂³	semidirect
378. C₂²⋊Q₈×C₅₃	C₂³	semidirect
382. #120×C₅₃	C₂³	semidirect
383. C₄×Q₈×C₅₃	C₂³	semidirect
384. C₄×Q₈×C₅₃	C₂³	semidirect
387. C₄×D₄×C₅₃	C₂³	semidirect
388. #117×C₅₃	C₂³	semidirect
389. #117×C₅₃	C₂³	semidirect
390. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
391. C₂×C₄²×C₅₃	C₂³	semidirect
613. #3568	D₅₃	direct (N × H)
626. D₅₃	#3568	direct (N × H)
636. #563	C₂×D₅₃	semidirect
640. H(3,𝔽₄)	C₂×D₅₃	semidirect
656. #556	C₂×D₅₃	semidirect
672. #551	C₂×D₅₃	semidirect
688. #542	C₂×D₅₃	semidirect
704. #538	C₂×D₅₃	semidirect
717. #529	C₂×D₅₃	semidirect
748. C₅₃	C₂×#3568	semidirect
765. C₄⋊Q₈	C₂²×D₅₃	semidirect
797. #126	C₂²×D₅₃	semidirect
798. #126	C₂²×D₅₃	semidirect
799. #126	C₂²×D₅₃	semidirect
800. #126	C₂²×D₅₃	semidirect
801. #126	C₂²×D₅₃	semidirect
807. #125	C₂²×D₅₃	semidirect
837. #124	C₂²×D₅₃	semidirect
861. #123	C₂²×D₅₃	semidirect
888. C₂²⋊Q₈	C₂²×D₅₃	semidirect
889. C₂²⋊Q₈	C₂²×D₅₃	semidirect
890. C₂²⋊Q₈	C₂²×D₅₃	semidirect
891. C₂²⋊Q₈	C₂²×D₅₃	semidirect
917. #120	C₂²×D₅₃	semidirect
930. C₄×Q₈	C₂²×D₅₃	semidirect
931. C₄×Q₈	C₂²×D₅₃	semidirect
953. C₄×D₄	C₂²×D₅₃	semidirect
968. #117	C₂²×D₅₃	semidirect
969. #117	C₂²×D₅₃	semidirect
994. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1003. C₂×C₄²	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20289412	2
#20289411	2
#20289410	2
#20289409	2
#20289408	2
#20289407	2
#20289406	2
#563×D₅₃	2
H(3,𝔽₄)×D₅₃	2
#556×D₅₃	2
#551×D₅₃	2
#542×D₅₃	2
#538×D₅₃	2
#529×D₅₃	2
C₅₃×#3568	2
C₂×#3568	53

Subgroups — D53×#3568 #28291518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3568 #28291518