Subgroups — #20288354

Order 6784.

1560 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133263	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811276	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811275	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811274	C₂	1	2	yes	maximal, complemented
6	#16811272	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811271	C₂	1	2	yes	maximal, complemented
8	#16811269	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811268	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811265	C₂	1	2	yes	maximal, complemented
11	#16811264	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811262	C₂	1	2	yes	maximal, complemented
13	#16811261	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811198	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811196	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811184	C₂	1	2	yes	maximal, complemented
17	#16811181	C₂	1	2	yes	maximal, complemented
18	#16811136	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811132	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13133202	C₂	1	2	yes	maximal, complemented
21	#123×D₅₃	C₂	1	2	yes	maximal, complemented
22	#16811095	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
24	#13133263	—	2	8	no	—
25	C₂×#11719949	C₂²	1	1	yes	characteristic
26	C₂×#11719949	C₂²	1	1	yes	characteristic, complemented
27	C₂×#11719949	C₂²	1	1	yes	characteristic, complemented
28	C₂×#11719945	C₂²	1	1	yes	characteristic
29	C₂×#11719945	C₂²	1	2	yes	complemented
30	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
31	C₂×#11719945	C₂²	1	2	yes	complemented
32	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
33	C₂×#11719947	C₂²	1	2	yes	complemented
34	#41×D₅₃	—	2	8	no	—
35	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂²×D₂₁₂	C₂²	1	2	yes	—
37	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×D₅₃	C₂²	1	2	yes	—
39	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
40	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
41	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
43	C₂²×C₄×D₅₃	C₂²	1	2	yes	complemented
44	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
45	#13133216	C₂²	1	2	yes	complemented
46	#13133215	C₂²	1	1	yes	characteristic, complemented
47	#13133206	C₂²	1	1	yes	characteristic, complemented
48	#13133205	C₂²	1	1	yes	characteristic, complemented
49	#13133203	C₂²	1	2	yes	complemented
50	#13133202	C₂²	1	2	yes	complemented
51	#13133202	C₂²	1	2	yes	complemented
52	#13133202	C₂²	1	2	yes	complemented
53	#13133202	C₂²	1	2	yes	complemented
54	#13133202	C₂²	1	2	yes	complemented
55	#13133202	C₂²	1	2	yes	complemented
56	#13133202	C₂²	1	2	yes	complemented
57	#13133202	C₂²	1	1	yes	characteristic, complemented
58	#13133202	C₂²	1	2	yes	complemented
59	#13133202	C₂²	1	2	yes	complemented
60	#13133201	C₂²	1	2	yes	complemented
61	#13133200	C₂²	1	2	yes	complemented
62	#13133200	C₂²	1	2	yes	complemented
63	#13133199	C₂²	1	2	yes	complemented
64	#13133199	C₂²	1	1	yes	characteristic, complemented
65	#13133199	C₂²	1	2	yes	complemented
66	#13133198	C₂²	1	2	yes	complemented
67	#13133197	C₂²	1	1	yes	characteristic, complemented
68	#13133196	C₂²	1	1	yes	characteristic, complemented
69	#13133195	C₂²	1	2	yes	complemented
70	#13133195	C₂²	1	1	yes	characteristic, complemented
71	#13133195	C₂²	1	2	yes	complemented
72	#13133194	C₂²	1	1	yes	characteristic, complemented
73	#13133193	C₂²	1	1	yes	characteristic, complemented
74	#13133193	C₂²	1	1	yes	characteristic, complemented
75	#13133192	C₂²	1	1	yes	characteristic, complemented
76	#13133192	C₂²	1	2	yes	complemented
77	#13133192	C₂²	1	2	yes	complemented
78	#13133191	C₂²	1	2	yes	complemented
79	#13133191	C₂²	1	1	yes	characteristic, complemented
80	#13133190	C₂²	1	1	yes	characteristic, complemented
81	#13133190	C₂²	1	2	yes	complemented
82	#13133190	C₂²	1	2	yes	complemented
83	#13133189	C₂²	1	2	yes	complemented
84	#13133189	C₂²	1	2	yes	complemented
85	#13133189	C₂²	1	1	yes	characteristic, complemented
86	#13133187	C₂²	1	2	yes	complemented
87	#13133187	C₂²	1	2	yes	complemented
88	#13133187	C₂²	1	1	yes	characteristic, complemented
89	#13133187	C₂²	1	2	yes	complemented
90	#13133185	C₂²	1	2	yes	complemented
91	#13133185	C₂²	1	1	yes	characteristic, complemented
92	#13133185	C₂²	1	2	yes	complemented
93	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
94	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
95	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
96	#13133179	C₂²	1	1	yes	characteristic, complemented
97	#13133179	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
101	#13133177	C₂²	1	2	yes	complemented
102	#13133177	C₂²	1	2	yes	complemented
103	#13133175	C₂²	1	1	yes	characteristic, complemented
104	#13133174	C₂²	1	1	yes	characteristic, complemented
105	C₂×#11719919	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
107	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
108	C₂×#11719921	C₂²	1	2	yes	complemented
109	C₂×#11719921	C₂²	1	2	yes	complemented
110	C₂×#11719921	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
112	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
113	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
114	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	#123×C₅₃	C₂²	1	2	yes	complemented
118	#123×C₅₃	C₂²	1	2	yes	complemented
119	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	#121×C₅₃	C₂²	1	2	yes	complemented
122	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
125	C₂³×D₅₃	C₂³	1	2	yes	—
126	C₂³×D₅₃	C₂³	1	2	yes	—
127	C₂³×D₅₃	C₂³	1	1	yes	characteristic
128	C₂³×D₅₃	C₂³	1	2	yes	—
129	#41×C₅₃	—	2	4	no	—
130	#41×C₅₃	—	2	4	no	—
131	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
132	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₅₃	C₂³	1	2	yes	—
134	C₂×D₄×C₅₃	C₂³	1	2	yes	—
135	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
136	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
138	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
139	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
151	C₂²×Dic₅₃	C₂³	1	2	yes	—
152	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
153	C₂²×Dic₅₃	C₂³	1	2	yes	—
154	#11719949	—	2	4	no	—
155	#11719949	—	2	4	no	—
156	#11719949	—	2	4	no	—
157	Q₈×D₅₃	—	2	4	no	—
158	#11719947	—	2	4	no	—
159	#11719947	—	2	8	no	—
160	D₄×D₅₃	—	2	8	no	—
161	D₄×D₅₃	—	2	8	no	—
162	D₄×D₅₃	—	2	4	no	—
163	D₄×D₅₃	—	2	8	no	—
164	D₄×D₅₃	D₄	1	8	yes	complemented
165	#11719945	—	2	8	no	—
166	#11719945	—	2	8	no	—
167	#11719945	—	2	4	no	—
168	#11719945	—	2	4	no	—
169	C₂×D₂₁₂	—	2	8	no	—
170	C₂×D₂₁₂	—	2	4	no	—
171	C₂×D₂₁₂	C₂³	1	2	yes	—
172	C₂×D₂₁₂	C₂³	1	2	yes	—
173	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
174	C₂×D₂₁₂	C₂³	1	2	yes	—
175	C₂×D₂₁₂	C₂³	1	2	yes	—
176	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
177	C₂×D₂₁₂	C₂³	1	2	yes	—
178	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
179	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₅₃	—	2	8	no	—
181	C₂×C₄×D₅₃	—	2	4	no	—
182	C₂×C₄×D₅₃	C₂³	1	2	yes	—
183	C₂×C₄×D₅₃	C₂³	1	2	yes	—
184	C₂×C₄×D₅₃	C₂³	1	2	yes	—
185	C₂×C₄×D₅₃	C₂³	1	2	yes	—
186	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
187	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
188	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
189	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
190	C₂×C₄×D₅₃	C₂³	1	2	yes	—
191	C₂×C₄×D₅₃	C₂³	1	2	yes	—
192	C₂×C₄×D₅₃	C₂³	1	2	yes	—
193	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
194	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
195	C₂×Dic₁₀₆	C₂³	1	2	yes	—
196	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
197	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
199	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
200	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
201	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
203	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
205	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
207	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
208	C₄²×C₅₃	C₂³	1	1	yes	characteristic
209	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
210	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
211	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
212	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
213	#11719921	C₂³	1	1	yes	characteristic
214	#11719921	C₂³	1	2	yes	—
215	#11719921	C₂³	1	2	yes	—
216	#11719921	C₂³	1	2	yes	—
217	#11719921	C₂³	1	2	yes	—
218	#11719921	C₂³	1	2	yes	—
219	#11719921	C₂³	1	1	yes	characteristic
220	#11719921	C₂³	1	1	yes	characteristic
221	#11719921	C₂³	1	1	yes	characteristic
222	#11719921	C₂³	1	2	yes	—
223	#11719921	C₂³	1	2	yes	—
224	#11719921	C₂³	1	2	yes	—
225	#11719921	C₂³	1	2	yes	—
226	#11719921	C₂³	1	2	yes	—
227	#11719921	C₂³	1	2	yes	—
228	#11719921	C₂³	1	1	yes	characteristic
229	#11719921	C₂³	1	2	yes	—
230	#11719921	C₂³	1	1	yes	characteristic
231	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₅₃	C₂³	1	2	yes	—
233	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
234	#11719919	C₂³	1	1	yes	characteristic
235	#11719919	C₂³	1	2	yes	—
236	#11719919	C₂³	1	2	yes	—
237	#11719919	C₂³	1	2	yes	—
238	#11719919	C₂³	1	1	yes	characteristic
239	#11719919	C₂³	1	2	yes	—
240	#11719919	C₂³	1	2	yes	—
241	#11719919	C₂³	1	1	yes	characteristic
242	#11719919	C₂³	1	1	yes	characteristic
243	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
244	C₄×Dic₅₃	C₂³	1	2	yes	—
245	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
246	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
247	C₂³×C₅₃	C₂⁴	1	2	yes	—
248	C₂²×D₅₃	—	2	4	no	—
249	C₂²×D₅₃	—	2	2	no	—
250	C₂²×D₅₃	—	2	4	no	—
251	C₂²×D₅₃	—	4	2	no	—
252	C₂²×D₅₃	—	4	2	no	—
253	C₂²×D₅₃	—	4	1	no	—
254	C₂²×D₅₃	—	4	1	no	—
255	C₂²×D₅₃	—	4	2	no	—
256	C₂²×D₅₃	—	4	2	no	—
257	C₂²×D₅₃	—	4	2	no	—
258	C₂²×D₅₃	—	4	2	no	—
259	C₂²×D₅₃	C₂×D₄	1	8	yes	—
260	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
261	C₂²×D₅₃	C₂⁴	1	2	yes	—
262	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
263	C₂²×D₅₃	C₂⁴	1	2	yes	—
264	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
265	Q₈×C₅₃	—	2	2	no	—
266	Q₈×C₅₃	—	2	2	no	—
267	D₄×C₅₃	—	2	4	no	—
268	D₄×C₅₃	—	2	4	no	—
269	D₄×C₅₃	—	4	1	no	—
270	D₄×C₅₃	C₂×D₄	1	4	yes	—
271	C₂×C₄×C₅₃	—	2	4	no	—
272	C₂×C₄×C₅₃	—	2	4	no	—
273	C₂×C₄×C₅₃	—	2	2	no	—
274	C₂×C₄×C₅₃	—	2	2	no	—
275	C₂×C₄×C₅₃	—	4	2	no	—
276	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
277	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
280	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
282	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
284	C₂²⋊D₅₃	—	2	4	no	—
285	C₂²⋊D₅₃	—	2	4	no	—
286	C₂²⋊D₅₃	—	2	2	no	—
287	C₂²⋊D₅₃	—	2	4	no	—
288	C₂²⋊D₅₃	—	2	2	no	—
289	C₂²⋊D₅₃	—	4	1	no	—
290	C₂²⋊D₅₃	—	4	2	no	—
291	C₂²⋊D₅₃	—	4	1	no	—
292	C₂²⋊D₅₃	C₂×D₄	1	8	yes	—
293	C₂×Dic₅₃	—	2	4	no	—
294	C₂×Dic₅₃	—	2	2	no	—
295	C₂×Dic₅₃	—	4	2	no	—
296	C₂×Dic₅₃	C₂⁴	1	2	yes	—
297	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
298	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
299	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₅₃	C₂⁴	1	2	yes	—
301	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
303	D₂₁₂	—	2	2	no	—
304	D₂₁₂	—	2	4	no	—
305	D₂₁₂	—	2	4	no	—
306	D₂₁₂	—	2	4	no	—
307	D₂₁₂	—	2	4	no	—
308	D₂₁₂	—	2	2	no	—
309	D₂₁₂	—	4	1	no	—
310	D₂₁₂	—	4	2	no	—
311	D₂₁₂	C₂×D₄	1	4	yes	—
312	C₄×D₅₃	—	2	2	no	—
313	C₄×D₅₃	—	2	4	no	—
314	C₄×D₅₃	—	2	4	no	—
315	C₄×D₅₃	—	2	4	no	—
316	C₄×D₅₃	—	2	4	no	—
317	C₄×D₅₃	—	2	2	no	—
318	C₄×D₅₃	—	2	2	no	—
319	C₄×D₅₃	—	2	2	no	—
320	C₄×D₅₃	—	2	4	no	—
321	C₄×D₅₃	—	4	2	no	—
322	C₄×D₅₃	—	4	2	no	—
323	C₄×D₅₃	C₂×D₄	1	4	yes	—
324	Dic₁₀₆	—	2	2	no	—
325	Dic₁₀₆	—	2	2	no	—
326	Dic₁₀₆	—	2	4	no	—
327	C₂²×C₅₃	—	2	2	no	—
328	C₂²×C₅₃	—	2	2	no	—
329	C₂²×C₅₃	—	2	1	no	—
330	C₂²×C₅₃	—	2	1	no	—
331	C₂²×C₅₃	—	2	1	no	—
332	C₂²×C₅₃	—	2	1	no	—
333	C₂²×C₅₃	—	2	1	no	—
334	C₂²×C₅₃	—	2	1	no	—
335	C₂²×C₅₃	C₂²×D₄	1	4	yes	—
336	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
337	C₂×D₅₃	—	2	2	no	—
338	C₂×D₅₃	—	2	2	no	—
339	C₂×D₅₃	—	2	1	no	—
340	C₂×D₅₃	—	2	1	no	—
341	C₂×D₅₃	—	2	1	no	—
342	C₂×D₅₃	—	2	1	no	—
343	C₂×D₅₃	—	2	2	no	—
344	C₂×D₅₃	—	2	1	no	—
345	C₂×D₅₃	—	2	1	no	—
346	C₂×D₅₃	—	2	2	no	—
347	C₂×D₅₃	—	2	1	no	—
348	C₂×D₅₃	—	2	1	no	—
349	C₂×D₅₃	—	2	2	no	—
350	C₂×D₅₃	—	4	8	no	—
351	C₂×D₅₃	—	4	4	no	—
352	C₂×D₅₃	—	8	4	no	—
353	C₂×D₅₃	—	8	4	no	—
354	C₂×D₅₃	C₂²×D₄	1	2	yes	—
355	C₂×D₅₃	C₂²×D₄	1	4	yes	—
356	C₄×C₅₃	—	2	2	no	—
357	C₄×C₅₃	—	2	1	no	—
358	C₄×C₅₃	—	2	1	no	—
359	C₄×C₅₃	—	2	2	no	—
360	C₄×C₅₃	—	2	1	no	—
361	C₄×C₅₃	—	2	2	no	—
362	C₄×C₅₃	—	2	1	no	—
363	C₄×C₅₃	C₂²×D₄	1	2	yes	—
364	Dic₅₃	—	2	2	no	—
365	Dic₅₃	—	2	1	no	—
366	Dic₅₃	—	2	1	no	—
367	Dic₅₃	—	2	1	no	—
368	Dic₅₃	—	2	2	no	—
369	Dic₅₃	—	2	1	no	—
370	Dic₅₃	C₂²×D₄	1	2	yes	—
371	#3485	—	53	1	no	maximal, Sylow
372	C₂×C₅₃	—	2	4	no	—
373	C₂×C₅₃	—	4	1	no	—
374	C₂×C₅₃	—	4	1	no	—
375	C₂×C₅₃	C₂³×D₄	1	1	yes	characteristic
376	C₂×C₅₃	#585	1	1	yes	characteristic
377	C₂×C₅₃	#585	1	1	yes	characteristic
378	D₅₃	—	2	2	no	—
379	D₅₃	—	2	4	no	—
380	D₅₃	—	4	1	no	—
381	D₅₃	—	4	2	no	—
382	D₅₃	—	4	1	no	—
383	C₂×H(5,𝔽₂)	—	53	1	no	—
384	C₂²×#41	—	53	1	no	—
385	#547	—	53	1	no	—
386	#547	—	53	1	no	—
387	#547	—	53	2	no	—
388	#547	—	53	1	no	—
389	#547	—	53	2	no	—
390	#547	D₅₃	1	1	yes	characteristic, complemented
391	#546	—	53	1	no	—
392	#546	—	53	2	no	—
393	#546	—	53	1	no	—
394	#546	—	53	2	no	—
395	#546	—	53	1	no	—
396	#546	—	53	1	no	—
397	#536	—	53	1	no	—
398	#536	—	53	1	no	—
399	#534	—	53	2	no	—
400	#534	—	53	2	no	—
401	#525	—	53	1	no	—
402	#525	—	53	1	no	—
403	C₂×#123	—	53	2	no	—
404	C₂×#123	—	53	2	no	—
405	#518	—	53	1	no	—
406	C₅₃	#3485	1	1	yes	characteristic, complemented, Sylow
407	H(5,𝔽₂)	—	106	8	no	—
408	C₂×#41	—	53	1	no	—
409	C₂×#41	—	53	1	no	—
410	C₂×#41	—	53	1	no	—
411	C₂×#41	—	53	1	no	—
412	C₂×#41	—	53	2	no	—
413	C₂×#41	—	53	1	no	—
414	C₂×#41	—	53	1	no	—
415	C₂×#41	—	53	2	no	—
416	C₂×#41	—	53	2	no	—
417	C₂×#41	—	106	8	no	—
418	C₂×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
419	C₂×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
420	C₂²×Q₈	—	53	1	no	—
421	C₂²×D₄	—	53	1	no	—
422	C₂²×D₄	—	53	2	no	—
423	C₂²×D₄	—	53	2	no	—
424	C₂²×D₄	—	53	2	no	—
425	C₂²×D₄	—	53	1	no	—
426	C₂²×D₄	—	53	2	no	—
427	C₂²×D₄	—	53	1	no	—
428	C₂³×C₄	—	53	2	no	—
429	C₂³×C₄	—	53	1	no	—
430	C₄⋊Q₈	—	53	1	no	—
431	C₄⋊Q₈	—	53	2	no	—
432	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
433	#124	—	53	1	no	—
434	#124	—	53	2	no	—
435	#124	—	53	1	no	—
436	#123	—	53	2	no	—
437	#123	—	53	2	no	—
438	#123	—	53	2	no	—
439	#123	—	53	2	no	—
440	#123	—	53	1	no	—
441	#123	—	53	2	no	—
442	#123	—	53	2	no	—
443	#123	—	53	2	no	—
444	#123	—	53	2	no	—
445	#123	—	53	2	no	—
446	#123	—	53	2	no	—
447	#123	—	53	2	no	—
448	#123	—	53	2	no	—
449	#123	—	53	1	no	—
450	#123	—	53	2	no	—
451	#123	—	53	2	no	—
452	#123	—	53	2	no	—
453	#123	C₂×D₅₃	1	2	yes	complemented
454	#123	C₂×D₅₃	1	2	yes	complemented
455	C₂²⋊Q₈	—	53	1	no	—
456	C₂²⋊Q₈	—	53	1	no	—
457	C₂²⋊Q₈	—	53	1	no	—
458	C₂²⋊Q₈	—	53	1	no	—
459	C₂²⋊Q₈	—	53	2	no	—
460	C₂²⋊Q₈	—	53	2	no	—
461	C₂²⋊Q₈	—	53	1	no	—
462	C₂²⋊Q₈	—	53	1	no	—
463	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
464	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
465	#121	—	53	1	no	—
466	#121	—	53	2	no	—
467	#121	—	53	2	no	—
468	#121	—	53	1	no	—
469	#121	—	53	2	no	—
470	#121	—	53	1	no	—
471	#121	—	53	2	no	—
472	#121	—	53	2	no	—
473	#121	—	53	1	no	—
474	#121	—	53	2	no	—
475	#121	—	53	2	no	—
476	#121	C₂×D₅₃	1	2	yes	complemented
477	#120	—	53	1	no	—
478	#120	—	53	2	no	—
479	#120	—	53	2	no	—
480	#120	—	53	2	no	—
481	#120	—	53	1	no	—
482	#120	—	53	2	no	—
483	#120	—	53	2	no	—
484	C₄×D₄	—	53	1	no	—
485	C₄×D₄	—	53	2	no	—
486	C₄×D₄	—	53	1	no	—
487	C₄×D₄	—	53	1	no	—
488	C₄×D₄	—	53	1	no	—
489	C₄×D₄	—	53	2	no	—
490	C₄×D₄	—	53	2	no	—
491	C₄×D₄	—	53	2	no	—
492	C₄×D₄	—	53	1	no	—
493	C₄×D₄	—	53	1	no	—
494	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
495	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
496	#117	—	53	1	no	—
497	#117	—	53	1	no	—
498	C₂×C₄⋊C₄	—	53	2	no	—
499	C₂×C₄⋊C₄	—	53	2	no	—
500	C₂×C₄⋊C₄	—	53	2	no	—
501	C₂×C₄⋊C₄	C₂×D₅₃	1	2	yes	complemented
502	C₂×C₂²⋊C₄	—	53	2	no	—
503	C₂×C₂²⋊C₄	—	53	2	no	—
504	C₂×C₂²⋊C₄	—	53	2	no	—
505	C₂×C₂²⋊C₄	—	53	2	no	—
506	C₂×C₂²⋊C₄	—	53	2	no	—
507	C₂×C₂²⋊C₄	—	53	2	no	—
508	C₂⁴	—	53	2	no	—
509	C₂⁴	—	53	2	no	—
510	C₂⁴	—	53	2	no	—
511	C₂⁴	—	53	1	no	—
512	#41	—	2	4	no	—
513	#41	—	2	4	no	—
514	#41	—	106	4	no	—
515	#41	—	106	8	no	—
516	#41	—	106	4	no	—
517	#41	—	106	8	no	—
518	#41	—	106	4	no	—
519	#41	—	106	8	no	—
520	#41	—	106	4	no	—
521	#41	—	106	4	no	—
522	#41	—	106	4	no	—
523	C₂×Q₈	—	53	2	no	—
524	C₂×Q₈	—	53	1	no	—
525	C₂×Q₈	—	53	1	no	—
526	C₂×Q₈	—	106	4	no	—
527	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
528	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
529	C₂×D₄	—	53	2	no	—
530	C₂×D₄	—	53	8	no	—
531	C₂×D₄	—	53	2	no	—
532	C₂×D₄	—	53	2	no	—
533	C₂×D₄	—	53	1	no	—
534	C₂×D₄	—	53	2	no	—
535	C₂×D₄	—	53	1	no	—
536	C₂×D₄	—	53	2	no	—
537	C₂×D₄	—	53	1	no	—
538	C₂×D₄	—	53	1	no	—
539	C₂×D₄	—	53	1	no	—
540	C₂×D₄	—	53	2	no	—
541	C₂×D₄	—	53	2	no	—
542	C₂×D₄	—	53	1	no	—
543	C₂×D₄	—	53	2	no	—
544	C₂×D₄	—	53	2	no	—
545	C₂×D₄	—	53	1	no	—
546	C₂×D₄	—	53	2	no	—
547	C₂×D₄	—	53	1	no	—
548	C₂×D₄	—	106	4	no	—
549	C₂×D₄	—	106	8	no	—
550	C₂×D₄	—	106	8	no	—
551	C₂×D₄	—	106	8	no	—
552	C₂×D₄	—	106	8	no	—
553	C₂×D₄	—	106	4	no	—
554	C₂×D₄	C₂²×D₅₃	1	2	yes	—
555	C₂×D₄	C₂²×D₅₃	1	2	yes	—
556	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
557	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
558	C₂²×C₄	—	53	1	no	—
559	C₂²×C₄	—	53	2	no	—
560	C₂²×C₄	—	53	1	no	—
561	C₂²×C₄	—	53	2	no	—
562	C₂²×C₄	—	53	2	no	—
563	C₂²×C₄	—	53	2	no	—
564	C₂²×C₄	—	53	2	no	—
565	C₂²×C₄	—	53	1	no	—
566	C₂²×C₄	—	53	1	no	—
567	C₂²×C₄	—	53	2	no	—
568	C₂²×C₄	—	53	1	no	—
569	C₂²×C₄	—	53	1	no	—
570	C₂²×C₄	—	53	2	no	—
571	C₂²×C₄	—	53	2	no	—
572	C₂²×C₄	—	53	2	no	—
573	C₂²×C₄	—	106	4	no	—
574	C₂²×C₄	—	106	8	no	—
575	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
576	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
577	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
578	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
579	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
580	C₄⋊C₄	—	53	2	no	—
581	C₄⋊C₄	—	53	1	no	—
582	C₄⋊C₄	—	53	1	no	—
583	C₄⋊C₄	—	53	1	no	—
584	C₄⋊C₄	—	53	2	no	—
585	C₄⋊C₄	—	53	2	no	—
586	C₄⋊C₄	—	53	2	no	—
587	C₄⋊C₄	—	53	2	no	—
588	C₄⋊C₄	—	53	2	no	—
589	C₄⋊C₄	—	53	1	no	—
590	C₄⋊C₄	—	53	1	no	—
591	C₄⋊C₄	—	53	1	no	—
592	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
593	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
594	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
595	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
596	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
597	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
598	C₂²⋊C₄	—	53	1	no	—
599	C₂²⋊C₄	—	53	2	no	—
600	C₂²⋊C₄	—	53	2	no	—
601	C₂²⋊C₄	—	53	1	no	—
602	C₂²⋊C₄	—	53	2	no	—
603	C₂²⋊C₄	—	53	1	no	—
604	C₂²⋊C₄	—	53	1	no	—
605	C₂²⋊C₄	—	53	1	no	—
606	C₂²⋊C₄	—	53	2	no	—
607	C₂²⋊C₄	—	53	2	no	—
608	C₂²⋊C₄	—	53	1	no	—
609	C₂²⋊C₄	—	53	2	no	—
610	C₂²⋊C₄	—	53	2	no	—
611	C₂²⋊C₄	—	53	2	no	—
612	C₂²⋊C₄	—	53	2	no	—
613	C₂²⋊C₄	—	53	2	no	—
614	C₂²⋊C₄	—	53	2	no	—
615	C₂²⋊C₄	—	53	2	no	—
616	C₂²⋊C₄	—	53	2	no	—
617	C₂²⋊C₄	—	53	2	no	—
618	C₂²⋊C₄	—	53	1	no	—
619	C₂²⋊C₄	—	53	1	no	—
620	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
621	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
622	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
623	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
624	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
625	C₄²	—	53	2	no	—
626	C₄²	—	53	1	no	—
627	C₄²	C₂²×D₅₃	1	1	yes	characteristic
628	C₂³	—	53	1	no	—
629	C₂³	—	53	2	no	—
630	C₂³	—	53	8	no	—
631	C₂³	—	53	2	no	—
632	C₂³	—	53	1	no	—
633	C₂³	—	53	1	no	—
634	C₂³	—	106	4	no	—
635	C₂³	—	106	2	no	—
636	C₂³	—	106	4	no	—
637	C₂³	—	212	2	no	—
638	C₂³	—	212	2	no	—
639	C₂³	—	212	2	no	—
640	C₂³	—	212	2	no	—
641	C₂³	—	212	2	no	—
642	C₂³	—	212	2	no	—
643	C₂³	—	212	1	no	—
644	C₂³	—	212	1	no	—
645	C₂³	C₂³×D₅₃	1	1	yes	characteristic
646	C₂³	C₂³×D₅₃	1	1	yes	characteristic
647	C₂³	C₂³×D₅₃	1	2	yes	—
648	Q₈	—	2	2	no	—
649	Q₈	—	2	2	no	—
650	Q₈	—	106	4	no	—
651	Q₈	—	106	2	no	—
652	Q₈	—	106	2	no	—
653	D₄	—	2	4	no	—
654	D₄	—	2	4	no	—
655	D₄	—	4	1	no	—
656	D₄	—	53	8	no	—
657	D₄	—	53	4	no	—
658	D₄	—	106	2	no	—
659	D₄	—	106	4	no	—
660	D₄	—	106	4	no	—
661	D₄	—	106	4	no	—
662	D₄	—	106	4	no	—
663	D₄	—	106	2	no	—
664	D₄	—	106	2	no	—
665	D₄	—	106	4	no	—
666	D₄	—	106	4	no	—
667	D₄	—	106	4	no	—
668	D₄	—	106	2	no	—
669	D₄	—	212	2	no	—
670	D₄	—	212	1	no	—
671	D₄	—	212	1	no	—
672	D₄	—	212	2	no	—
673	D₄	—	212	1	no	—
674	D₄	D₄×D₅₃	1	4	yes	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	53	1	no	—
681	C₂×C₄	—	53	4	no	—
682	C₂×C₄	—	53	1	no	—
683	C₂×C₄	—	53	2	no	—
684	C₂×C₄	—	53	1	no	—
685	C₂×C₄	—	53	1	no	—
686	C₂×C₄	—	53	2	no	—
687	C₂×C₄	—	53	1	no	—
688	C₂×C₄	—	106	2	no	—
689	C₂×C₄	—	106	4	no	—
690	C₂×C₄	—	106	2	no	—
691	C₂×C₄	—	106	4	no	—
692	C₂×C₄	—	106	4	no	—
693	C₂×C₄	—	106	4	no	—
694	C₂×C₄	—	106	4	no	—
695	C₂×C₄	—	106	2	no	—
696	C₂×C₄	—	106	4	no	—
697	C₂×C₄	—	106	2	no	—
698	C₂×C₄	—	106	2	no	—
699	C₂×C₄	—	212	2	no	—
700	C₂×C₄	—	212	2	no	—
701	C₂×C₄	—	212	2	no	—
702	C₂×C₄	C₂³×D₅₃	1	2	yes	—
703	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
704	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
705	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
706	C₂×C₄	C₂³×D₅₃	1	2	yes	—
707	C₂×C₄	C₂³×D₅₃	1	2	yes	—
708	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
709	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	53	2	no	—
719	C₂²	—	53	4	no	—
720	C₂²	—	106	2	no	—
721	C₂²	—	106	1	no	—
722	C₂²	—	106	2	no	—
723	C₂²	—	106	1	no	—
724	C₂²	—	106	1	no	—
725	C₂²	—	106	2	no	—
726	C₂²	—	106	1	no	—
727	C₂²	—	106	1	no	—
728	C₂²	—	106	2	no	—
729	C₂²	—	106	1	no	—
730	C₂²	—	106	1	no	—
731	C₂²	—	106	1	no	—
732	C₂²	—	106	2	no	—
733	C₂²	—	424	4	no	—
734	C₂²	—	424	4	no	—
735	C₂²	—	212	8	no	—
736	C₂²	—	212	4	no	—
737	C₂²	C₂×D₄×D₅₃	1	4	yes	—
738	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
739	C₄	—	2	1	no	—
740	C₄	—	2	1	no	—
741	C₄	—	2	2	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	1	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	1	no	—
746	C₄	—	53	2	no	—
747	C₄	—	106	1	no	—
748	C₄	—	106	1	no	—
749	C₄	—	106	2	no	—
750	C₄	—	106	1	no	—
751	C₄	—	106	2	no	—
752	C₄	—	106	1	no	—
753	C₄	C₂×D₄×D₅₃	1	2	yes	—
754	C₂	—	2	4	no	—
755	C₂	—	4	1	no	—
756	C₂	—	4	1	no	—
757	C₂	—	106	4	no	—
758	C₂	—	106	2	no	—
759	C₂	—	212	1	no	—
760	C₂	—	212	2	no	—
761	C₂	—	212	1	no	—
762	C₂	C₂²×D₄×D₅₃	1	1	yes	characteristic
763	C₂	#16811459	1	1	yes	characteristic
764	C₂	#16811460	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#547	C₂
hypercenter	#547	D₅₃
hypocenter	C₅₃	#3485
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. C₂×#13133263	C₂	semidirect
2. C₂×#41×D₅₃	C₂	semidirect
3. #16811276	C₂	semidirect
4. #16811275	C₂	semidirect
5. #16811274	C₂	semidirect
6. #16811272	C₂	semidirect
7. #16811271	C₂	semidirect
8. #16811269	C₂	semidirect
9. #16811268	C₂	semidirect
10. #16811265	C₂	semidirect
11. #16811264	C₂	semidirect
12. #16811262	C₂	semidirect
13. #16811261	C₂	semidirect
14. #16811198	C₂	semidirect
15. #16811196	C₂	semidirect
16. #16811184	C₂	semidirect
17. #16811181	C₂	semidirect
18. #16811136	C₂	semidirect
19. #16811132	C₂	semidirect
20. C₂×#13133202	C₂	semidirect
21. #123×D₅₃	C₂	semidirect
22. #16811095	C₂	semidirect
23. C₅₃×#547	C₂	semidirect
26. C₂×#11719949	C₂²	semidirect
27. C₂×#11719949	C₂²	semidirect
29. C₂×#11719945	C₂²	semidirect
30. C₂×#11719945	C₂²	semidirect
31. C₂×#11719945	C₂²	semidirect
32. C₂×#11719947	C₂²	semidirect
33. C₂×#11719947	C₂²	semidirect
35. C₂×Q₈×D₅₃	C₂²	semidirect
37. C₂²×D₂₁₂	C₂²	semidirect
40. C₂×D₄×D₅₃	C₂²	semidirect
41. C₂×D₄×D₅₃	C₂²	semidirect
42. C₂×D₄×D₅₃	C₂²	semidirect
43. C₂²×C₄×D₅₃	C₂²	semidirect
44. C₂²×C₄×D₅₃	C₂²	semidirect
45. #13133216	C₂²	semidirect
46. #13133215	C₂²	semidirect
47. #13133206	C₂²	semidirect
48. #13133205	C₂²	semidirect
49. #13133203	C₂²	semidirect
50. #13133202	C₂²	semidirect
51. #13133202	C₂²	semidirect
52. #13133202	C₂²	semidirect
53. #13133202	C₂²	semidirect
54. #13133202	C₂²	semidirect
55. #13133202	C₂²	semidirect
56. #13133202	C₂²	semidirect
57. #13133202	C₂²	semidirect
58. #13133202	C₂²	semidirect
59. #13133202	C₂²	semidirect
60. #13133201	C₂²	semidirect
61. #13133200	C₂²	semidirect
62. #13133200	C₂²	semidirect
63. #13133199	C₂²	semidirect
64. #13133199	C₂²	semidirect
65. #13133199	C₂²	semidirect
66. #13133198	C₂²	semidirect
67. #13133197	C₂²	semidirect
68. #13133196	C₂²	semidirect
69. #13133195	C₂²	semidirect
70. #13133195	C₂²	semidirect
71. #13133195	C₂²	semidirect
72. #13133194	C₂²	semidirect
73. #13133193	C₂²	semidirect
74. #13133193	C₂²	semidirect
75. #13133192	C₂²	semidirect
76. #13133192	C₂²	semidirect
77. #13133192	C₂²	semidirect
78. #13133191	C₂²	semidirect
79. #13133191	C₂²	semidirect
80. #13133190	C₂²	semidirect
81. #13133190	C₂²	semidirect
82. #13133190	C₂²	semidirect
83. #13133189	C₂²	semidirect
84. #13133189	C₂²	semidirect
85. #13133189	C₂²	semidirect
86. #13133187	C₂²	semidirect
87. #13133187	C₂²	semidirect
88. #13133187	C₂²	semidirect
89. #13133187	C₂²	semidirect
90. #13133185	C₂²	semidirect
91. #13133185	C₂²	semidirect
92. #13133185	C₂²	semidirect
93. C₄×D₂₁₂	C₂²	semidirect
94. C₄×D₂₁₂	C₂²	semidirect
95. D₄×Dic₅₃	C₂²	semidirect
96. #13133179	C₂²	semidirect
97. #13133179	C₂²	semidirect
98. C₄×C₂²⋊D₅₃	C₂²	semidirect
99. C₄×C₂²⋊D₅₃	C₂²	semidirect
100. C₄×C₂²⋊D₅₃	C₂²	semidirect
101. #13133177	C₂²	semidirect
102. #13133177	C₂²	semidirect
103. #13133175	C₂²	semidirect
104. #13133174	C₂²	semidirect
105. C₂×#11719919	C₂²	semidirect
106. C₄⋊C₄×D₅₃	C₂²	semidirect
107. C₄⋊C₄×D₅₃	C₂²	semidirect
108. C₂×#11719921	C₂²	semidirect
109. C₂×#11719921	C₂²	semidirect
110. C₂×#11719921	C₂²	semidirect
111. C₂²⋊C₄×D₅₃	C₂²	semidirect
112. C₂²⋊C₄×D₅₃	C₂²	semidirect
113. C₂²⋊C₄×D₅₃	C₂²	semidirect
114. C₂×#41×C₅₃	C₂²	semidirect
115. C₂×#41×C₅₃	C₂²	semidirect
116. C₄⋊Q₈×C₅₃	C₂²	semidirect
117. #123×C₅₃	C₂²	semidirect
118. #123×C₅₃	C₂²	semidirect
119. C₂²⋊Q₈×C₅₃	C₂²	semidirect
120. C₂²⋊Q₈×C₅₃	C₂²	semidirect
121. #121×C₅₃	C₂²	semidirect
122. C₄×D₄×C₅₃	C₂²	semidirect
123. C₄×D₄×C₅₃	C₂²	semidirect
124. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
164. D₄×D₅₃	D₄	semidirect
390. #547	D₅₃	semidirect
406. C₅₃	#3485	semidirect
418. C₂×#41	C₂×D₅₃	semidirect
419. C₂×#41	C₂×D₅₃	semidirect
432. C₄⋊Q₈	C₂×D₅₃	semidirect
453. #123	C₂×D₅₃	semidirect
454. #123	C₂×D₅₃	semidirect
463. C₂²⋊Q₈	C₂×D₅₃	semidirect
464. C₂²⋊Q₈	C₂×D₅₃	semidirect
476. #121	C₂×D₅₃	semidirect
494. C₄×D₄	C₂×D₅₃	semidirect
495. C₄×D₄	C₂×D₅₃	semidirect
501. C₂×C₄⋊C₄	C₂×D₅₃	semidirect