Subgroups — C₂×#560×D₅₃ #28290957

Order 13568.

9606 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811364	C₂	1	2	yes	maximal, complemented
2	C₂×#16811363	C₂	1	3	yes	maximal, complemented
3	C₂×#16811362	C₂	1	3	yes	maximal, complemented
4	C₂×#16811361	C₂	1	6	yes	maximal, complemented
5	C₂×#16811360	C₂	1	1	yes	maximal, characteristic, complemented
6	#560×D₅₃	C₂	1	32	yes	maximal, direct product factor
7	C₂×#127×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#126×D₅₃	C₂	1	2	yes	maximal, complemented
9	C₂×#123×D₅₃	C₂	1	3	yes	maximal, complemented
10	C₂×#121×D₅₃	C₂	1	6	yes	maximal, complemented
11	C₂×#120×D₅₃	C₂	1	3	yes	maximal, complemented
12	C₂×C₅₃×#560	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁵×D₅₃	C₂²	1	1	yes	characteristic
14	C₂²×D₄×D₅₃	C₂²	1	6	yes	—
15	C₂²×D₄×D₅₃	C₂²	1	3	yes	—
16	C₂²×D₄×D₅₃	C₂²	1	3	yes	complemented
17	C₂³×C₄×D₅₃	C₂²	1	3	yes	complemented
18	#16811364	C₂²	1	32	yes	complemented
19	#16811363	C₂²	1	48	yes	complemented
20	#16811362	C₂²	1	48	yes	complemented
21	#16811361	C₂²	1	96	yes	complemented
22	#16811360	C₂²	1	16	yes	complemented
23	C₂×#13133214	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13133213	C₂²	1	3	yes	complemented
25	C₂×#13133213	C₂²	1	3	yes	complemented
26	#127×D₅₃	C₂²	1	16	yes	complemented
27	C₂×#13133212	C₂²	1	6	yes	complemented
28	C₂×#13133211	C₂²	1	2	yes	complemented
29	C₂×#13133210	C₂²	1	6	yes	complemented
30	#126×D₅₃	C₂²	1	32	yes	complemented
31	C₂×#13133202	C₂²	1	6	yes	complemented
32	C₂×#13133201	C₂²	1	3	yes	complemented
33	C₂×#13133200	C₂²	1	3	yes	complemented
34	C₂×#13133199	C₂²	1	6	yes	complemented
35	C₂×#13133198	C₂²	1	3	yes	complemented
36	#123×D₅₃	C₂²	1	48	yes	complemented
37	C₂×#13133192	C₂²	1	6	yes	complemented
38	C₂×#13133191	C₂²	1	6	yes	complemented
39	C₂×#13133190	C₂²	1	6	yes	complemented
40	C₂×#13133190	C₂²	1	6	yes	complemented
41	C₂×#13133189	C₂²	1	6	yes	complemented
42	C₂×#13133189	C₂²	1	6	yes	complemented
43	C₂×#13133188	C₂²	1	6	yes	complemented
44	#121×D₅₃	C₂²	1	96	yes	complemented
45	C₂×#13133187	C₂²	1	6	yes	complemented
46	C₂×#13133187	C₂²	1	3	yes	complemented
47	C₂×#13133186	C₂²	1	3	yes	complemented
48	C₂×#13133185	C₂²	1	3	yes	complemented
49	C₂×#13133185	C₂²	1	6	yes	complemented
50	#120×D₅₃	C₂²	1	48	yes	complemented
51	C₂×C₄⋊C₄×D₅₃	C₂²	1	6	yes	complemented
52	C₂×C₂²⋊C₄×D₅₃	C₂²	1	6	yes	—
53	C₂×C₂²⋊C₄×D₅₃	C₂²	1	3	yes	—
54	C₂×C₂²⋊C₄×D₅₃	C₂²	1	3	yes	complemented
55	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#560	C₂²	1	16	yes	complemented
57	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
59	C₂×#123×C₅₃	C₂²	1	3	yes	complemented
60	C₂×#121×C₅₃	C₂²	1	6	yes	complemented
61	C₂×#120×C₅₃	C₂²	1	3	yes	complemented
62	C₂⁴×D₅₃	—	4	12	no	—
63	C₂⁴×D₅₃	C₂³	1	2	yes	—
64	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
65	C₂⁴×D₅₃	C₂³	1	3	yes	—
66	C₂⁴×D₅₃	C₂³	1	8	yes	—
67	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
68	C₂⁴×D₅₃	C₂³	1	2	yes	—
69	C₂²×D₂₁₂	C₂³	1	6	yes	—
70	C₂²×D₂₁₂	C₂³	1	3	yes	—
71	C₂²×D₂₁₂	C₂³	1	3	yes	complemented
72	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	—
73	C₂²×C₂²⋊D₅₃	C₂³	1	3	yes	—
74	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	—
75	C₂²×C₂²⋊D₅₃	C₂³	1	3	yes	—
76	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
77	C₂×D₄×D₅₃	—	4	24	no	—
78	C₂×D₄×D₅₃	—	4	12	no	—
79	C₂×D₄×D₅₃	—	4	12	no	—
80	C₂×D₄×D₅₃	C₂³	1	48	yes	—
81	C₂×D₄×D₅₃	C₂³	1	24	yes	—
82	C₂×D₄×D₅₃	C₂³	1	24	yes	complemented
83	C₂³×Dic₅₃	C₂³	1	3	yes	complemented
84	C₂²×C₄×D₅₃	—	4	12	no	—
85	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
86	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
87	C₂²×C₄×D₅₃	C₂³	1	24	yes	complemented
88	C₂²×C₄×D₅₃	C₂³	1	6	yes	complemented
89	#13133214	C₂³	1	8	yes	complemented
90	#13133213	C₂³	1	24	yes	complemented
91	#13133213	C₂³	1	24	yes	complemented
92	#13133212	C₂³	1	48	yes	complemented
93	#13133211	C₂³	1	16	yes	complemented
94	#13133210	C₂³	1	48	yes	complemented
95	#13133202	C₂³	1	48	yes	complemented
96	#13133201	C₂³	1	24	yes	complemented
97	#13133200	C₂³	1	24	yes	complemented
98	#13133199	C₂³	1	48	yes	complemented
99	#13133198	C₂³	1	24	yes	complemented
100	#13133192	C₂³	1	48	yes	complemented
101	#13133191	C₂³	1	48	yes	complemented
102	#13133190	C₂³	1	48	yes	complemented
103	#13133190	C₂³	1	48	yes	complemented
104	#13133189	C₂³	1	48	yes	complemented
105	#13133189	C₂³	1	48	yes	complemented
106	#13133188	C₂³	1	48	yes	complemented
107	#13133187	C₂³	1	48	yes	complemented
108	#13133187	C₂³	1	24	yes	complemented
109	#13133186	C₂³	1	24	yes	complemented
110	#13133185	C₂³	1	24	yes	complemented
111	#13133185	C₂³	1	48	yes	complemented
112	C₂×C₄⋊Dic₅₃	C₂³	1	6	yes	complemented
113	C₂×#11719919	C₂³	1	6	yes	complemented
114	C₂×#11719919	C₂³	1	6	yes	complemented
115	C₄⋊C₄×D₅₃	C₂³	1	48	yes	complemented
116	C₂×C₂²⋊Dic₅₃	C₂³	1	6	yes	—
117	C₂×C₂²⋊Dic₅₃	C₂³	1	3	yes	—
118	C₂×C₂²⋊Dic₅₃	C₂³	1	3	yes	complemented
119	C₂×#11719921	C₂³	1	6	yes	—
120	C₂×#11719921	C₂³	1	6	yes	—
121	C₂×#11719921	C₂³	1	6	yes	—
122	C₂×#11719921	C₂³	1	6	yes	complemented
123	C₂²⋊C₄×D₅₃	C₂³	1	48	yes	—
124	C₂²⋊C₄×D₅₃	C₂³	1	24	yes	—
125	C₂²⋊C₄×D₅₃	C₂³	1	24	yes	complemented
126	C₂×C₄×Dic₅₃	C₂³	1	3	yes	complemented
127	C₄²×D₅₃	C₂³	1	8	yes	complemented
128	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₅₃	C₂³	1	6	yes	—
130	C₂²×D₄×C₅₃	C₂³	1	3	yes	—
131	C₂²×D₄×C₅₃	C₂³	1	3	yes	complemented
132	C₂³×C₄×C₅₃	C₂³	1	3	yes	complemented
133	#127×C₅₃	C₂³	1	8	yes	complemented
134	#126×C₅₃	C₂³	1	16	yes	complemented
135	#123×C₅₃	C₂³	1	24	yes	complemented
136	#121×C₅₃	C₂³	1	48	yes	complemented
137	#120×C₅₃	C₂³	1	24	yes	complemented
138	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	complemented
139	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	—
140	C₂×C₂²⋊C₄×C₅₃	C₂³	1	3	yes	—
141	C₂×C₂²⋊C₄×C₅₃	C₂³	1	3	yes	complemented
142	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic, complemented
143	C₂⁴×C₅₃	—	4	6	no	—
144	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
145	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
146	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
147	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
148	C₂³×D₅₃	—	2	12	no	—
149	C₂³×D₅₃	—	2	24	no	—
150	C₂³×D₅₃	—	2	24	no	—
151	C₂³×D₅₃	—	2	12	no	—
152	C₂³×D₅₃	—	4	48	no	—
153	C₂³×D₅₃	—	4	6	no	—
154	C₂³×D₅₃	—	4	12	no	—
155	C₂³×D₅₃	—	4	64	no	—
156	C₂³×D₅₃	C₂⁴	1	8	yes	—
157	C₂³×D₅₃	C₂⁴	1	4	yes	—
158	C₂³×D₅₃	C₂⁴	1	12	yes	—
159	C₂³×D₅₃	C₂⁴	1	2	yes	—
160	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
161	C₂³×D₅₃	C₂⁴	1	3	yes	—
162	C₂³×D₅₃	C₂⁴	1	4	yes	—
163	C₂³×D₅₃	C₂⁴	1	8	yes	—
164	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
165	C₂×D₄×C₅₃	—	4	12	no	—
166	C₂×D₄×C₅₃	—	4	6	no	—
167	C₂×D₄×C₅₃	—	4	6	no	—
168	C₂×D₄×C₅₃	C₂⁴	1	24	yes	—
169	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
170	C₂×D₄×C₅₃	C₂⁴	1	12	yes	complemented
171	C₂²×C₄×C₅₃	—	4	6	no	—
172	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
173	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
174	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	complemented
175	C₂×C₂²⋊D₅₃	—	4	12	no	—
176	C₂×C₂²⋊D₅₃	—	4	12	no	—
177	C₂×C₂²⋊D₅₃	—	4	6	no	—
178	C₂×C₂²⋊D₅₃	—	4	6	no	—
179	C₂×C₂²⋊D₅₃	—	4	12	no	—
180	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	—
181	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
182	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	—
183	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
184	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	complemented
185	C₂²×Dic₅₃	—	4	6	no	—
186	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
187	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
188	C₂²×Dic₅₃	C₂⁴	1	12	yes	complemented
189	D₄×D₅₃	—	4	96	no	—
190	D₄×D₅₃	—	4	48	no	—
191	D₄×D₅₃	—	4	48	no	—
192	C₂×D₂₁₂	—	4	12	no	—
193	C₂×D₂₁₂	—	4	6	no	—
194	C₂×D₂₁₂	—	4	6	no	—
195	C₂×D₂₁₂	C₂⁴	1	24	yes	—
196	C₂×D₂₁₂	C₂⁴	1	12	yes	—
197	C₂×D₂₁₂	C₂⁴	1	12	yes	complemented
198	C₂×C₄×D₅₃	—	2	24	no	—
199	C₂×C₄×D₅₃	—	2	12	no	—
200	C₂×C₄×D₅₃	—	4	48	no	—
201	C₂×C₄×D₅₃	—	4	12	no	—
202	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
203	C₂×C₄×D₅₃	C₂⁴	1	24	yes	—
204	C₂×C₄×D₅₃	C₂⁴	1	24	yes	complemented
205	C₄⋊C₄×C₅₃	C₂⁴	1	24	yes	complemented
206	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
207	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
208	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	complemented
209	C₄²×C₅₃	C₂⁴	1	4	yes	complemented
210	C₂²⋊Dic₅₃	C₂⁴	1	24	yes	—
211	C₂²⋊Dic₅₃	C₂⁴	1	12	yes	—
212	C₂²⋊Dic₅₃	C₂⁴	1	12	yes	complemented
213	#11719921	C₂⁴	1	24	yes	—
214	#11719921	C₂⁴	1	24	yes	—
215	#11719921	C₂⁴	1	24	yes	—
216	#11719921	C₂⁴	1	24	yes	complemented
217	C₄⋊Dic₅₃	C₂⁴	1	24	yes	complemented
218	#11719919	C₂⁴	1	24	yes	complemented
219	#11719919	C₂⁴	1	24	yes	complemented
220	C₄×Dic₅₃	C₂⁴	1	12	yes	complemented
221	C₂³×C₅₃	—	2	6	no	—
222	C₂³×C₅₃	—	2	12	no	—
223	C₂³×C₅₃	—	2	12	no	—
224	C₂³×C₅₃	—	2	6	no	—
225	C₂³×C₅₃	—	4	12	no	—
226	C₂³×C₅₃	—	4	16	no	—
227	C₂³×C₅₃	C₂⁵	1	6	yes	—
228	C₂³×C₅₃	C₂⁵	1	4	yes	—
229	C₂³×C₅₃	C₂⁵	1	2	yes	—
230	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
231	C₂²×D₅₃	—	2	6	no	—
232	C₂²×D₅₃	—	2	12	no	—
233	C₂²×D₅₃	—	2	12	no	—
234	C₂²×D₅₃	—	2	6	no	—
235	C₂²×D₅₃	—	2	24	no	—
236	C₂²×D₅₃	—	2	48	no	—
237	C₂²×D₅₃	—	2	48	no	—
238	C₂²×D₅₃	—	2	24	no	—
239	C₂²×D₅₃	—	4	12	no	—
240	C₂²×D₅₃	—	4	24	no	—
241	C₂²×D₅₃	—	4	16	no	—
242	C₂²×D₅₃	—	4	32	no	—
243	C₂²×D₅₃	—	4	128	no	—
244	C₂²×D₅₃	—	4	48	no	—
245	C₂²×D₅₃	—	4	32	no	—
246	C₂²×D₅₃	—	4	16	no	—
247	C₂²×D₅₃	H(5,𝔽₂)	1	12	yes	—
248	C₂²×D₅₃	C₂⁵	1	6	yes	—
249	C₂²×D₅₃	C₂⁵	1	4	yes	—
250	C₂²×D₅₃	C₂⁵	1	2	yes	—
251	C₂²×D₅₃	C₂⁵	1	2	yes	—
252	D₄×C₅₃	—	4	24	no	—
253	D₄×C₅₃	—	4	12	no	—
254	D₄×C₅₃	—	4	12	no	—
255	C₂×C₄×C₅₃	—	2	12	no	—
256	C₂×C₄×C₅₃	—	2	6	no	—
257	C₂×C₄×C₅₃	—	4	12	no	—
258	C₂×C₄×C₅₃	C₂⁵	1	12	yes	—
259	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
260	C₂²⋊D₅₃	—	4	24	no	—
261	C₂²⋊D₅₃	—	4	24	no	—
262	C₂²⋊D₅₃	—	4	12	no	—
263	C₂²⋊D₅₃	—	4	12	no	—
264	C₂²⋊D₅₃	—	4	24	no	—
265	C₂×Dic₅₃	—	2	12	no	—
266	C₂×Dic₅₃	—	2	6	no	—
267	C₂×Dic₅₃	—	4	12	no	—
268	C₂×Dic₅₃	C₂⁵	1	12	yes	—
269	C₂×Dic₅₃	C₂⁵	1	6	yes	—
270	D₂₁₂	—	4	24	no	—
271	D₂₁₂	—	4	12	no	—
272	D₂₁₂	—	4	12	no	—
273	C₄×D₅₃	—	2	48	no	—
274	C₄×D₅₃	—	2	24	no	—
275	C₄×D₅₃	—	4	24	no	—
276	C₂²×#560	—	53	1	no	maximal, Sylow
277	C₂²×C₅₃	—	2	6	no	—
278	C₂²×C₅₃	—	2	12	no	—
279	C₂²×C₅₃	—	2	12	no	—
280	C₂²×C₅₃	—	2	6	no	—
281	C₂²×C₅₃	—	4	16	no	—
282	C₂²×C₅₃	—	4	8	no	—
283	C₂²×C₅₃	—	4	4	no	—
284	C₂²×C₅₃	—	4	12	no	—
285	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
286	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
287	C₂×D₅₃	—	2	6	no	—
288	C₂×D₅₃	—	2	12	no	—
289	C₂×D₅₃	—	2	12	no	—
290	C₂×D₅₃	—	2	6	no	—
291	C₂×D₅₃	—	4	16	no	—
292	C₂×D₅₃	—	4	32	no	—
293	C₂×D₅₃	—	4	12	no	—
294	C₂×D₅₃	—	4	8	no	—
295	C₂×D₅₃	—	4	4	no	—
296	C₂×D₅₃	—	4	48	no	—
297	C₂×D₅₃	—	4	32	no	—
298	C₂×D₅₃	—	4	16	no	—
299	C₂×D₅₃	#560	1	16	yes	direct product factor
300	C₂×D₅₃	C₂×H(5,𝔽₂)	1	12	yes	—
301	C₄×C₅₃	—	2	12	no	—
302	C₄×C₅₃	—	2	6	no	—
303	Dic₅₃	—	2	12	no	—
304	Dic₅₃	—	2	6	no	—
305	C₂×#560	—	53	32	no	—
306	C₂×#560	—	53	1	no	—
307	C₂×#560	—	53	2	no	—
308	C₂×#560	—	53	3	no	—
309	C₂×#560	—	53	6	no	—
310	C₂×#560	—	53	3	no	—
311	C₂×#560	D₅₃	1	1	yes	characteristic, direct product factor
312	C₂²×#127	—	53	1	no	—
313	C₂²×#126	—	53	2	no	—
314	C₂²×#123	—	53	3	no	—
315	C₂²×#121	—	53	6	no	—
316	C₂²×#120	—	53	3	no	—
317	C₂×C₅₃	—	4	4	no	—
318	C₂×C₅₃	—	4	2	no	—
319	C₂×C₅₃	—	4	6	no	—
320	C₂×C₅₃	C₂×#560	1	4	yes	complemented
321	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	3	yes	—
322	D₅₃	—	4	6	no	—
323	D₅₃	—	4	4	no	—
324	D₅₃	—	4	2	no	—
325	D₅₃	C₂×#560	1	8	yes	direct product factor
326	C₂⁶	—	53	1	no	—
327	C₂³×D₄	—	53	6	no	—
328	C₂³×D₄	—	53	3	no	—
329	C₂³×D₄	—	53	3	no	—
330	C₂⁴×C₄	—	53	3	no	—
331	#560	—	53	16	no	—
332	#560	—	53	32	no	—
333	#560	—	53	48	no	—
334	#560	—	53	96	no	—
335	#560	—	53	48	no	—
336	#560	C₂×D₅₃	1	16	yes	direct product factor
337	C₂×#127	—	53	3	no	—
338	C₂×#127	—	53	3	no	—
339	C₂×#127	—	53	16	no	—
340	C₂×#127	—	53	1	no	—
341	C₂×#127	C₂×D₅₃	1	1	yes	characteristic, complemented
342	C₂×#126	—	53	32	no	—
343	C₂×#126	—	53	6	no	—
344	C₂×#126	—	53	6	no	—
345	C₂×#126	—	53	2	no	—
346	C₂×#126	C₂×D₅₃	1	2	yes	complemented
347	C₂×#123	—	53	3	no	—
348	C₂×#123	—	53	3	no	—
349	C₂×#123	—	53	48	no	—
350	C₂×#123	—	53	6	no	—
351	C₂×#123	—	53	6	no	—
352	C₂×#123	—	53	3	no	—
353	C₂×#123	C₂×D₅₃	1	3	yes	complemented
354	C₂×#121	—	53	6	no	—
355	C₂×#121	—	53	6	no	—
356	C₂×#121	—	53	6	no	—
357	C₂×#121	—	53	6	no	—
358	C₂×#121	—	53	96	no	—
359	C₂×#121	—	53	6	no	—
360	C₂×#121	—	53	6	no	—
361	C₂×#121	—	53	6	no	—
362	C₂×#121	C₂×D₅₃	1	6	yes	complemented
363	C₂×#120	—	53	3	no	—
364	C₂×#120	—	53	6	no	—
365	C₂×#120	—	53	3	no	—
366	C₂×#120	—	53	48	no	—
367	C₂×#120	—	53	3	no	—
368	C₂×#120	—	53	6	no	—
369	C₂×#120	C₂×D₅₃	1	3	yes	complemented
370	C₂²×C₄⋊C₄	—	53	6	no	—
371	C₂²×C₂²⋊C₄	—	53	6	no	—
372	C₂²×C₂²⋊C₄	—	53	3	no	—
373	C₂²×C₂²⋊C₄	—	53	3	no	—
374	C₂²×C₄²	—	53	1	no	—
375	C₅₃	C₂²×#560	1	1	yes	characteristic, complemented, Sylow
376	C₂⁵	—	53	2	no	—
377	C₂⁵	—	53	1	no	—
378	C₂⁵	—	53	3	no	—
379	C₂⁵	—	53	8	no	—
380	C₂⁵	—	53	1	no	—
381	C₂⁵	—	53	2	no	—
382	C₂⁵	—	212	12	no	—
383	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
384	C₂²×D₄	—	53	6	no	—
385	C₂²×D₄	—	53	6	no	—
386	C₂²×D₄	—	53	3	no	—
387	C₂²×D₄	—	53	3	no	—
388	C₂²×D₄	—	53	6	no	—
389	C₂²×D₄	—	53	48	no	—
390	C₂²×D₄	—	53	24	no	—
391	C₂²×D₄	—	53	24	no	—
392	C₂²×D₄	—	53	6	no	—
393	C₂²×D₄	—	53	3	no	—
394	C₂²×D₄	—	53	3	no	—
395	C₂²×D₄	—	212	24	no	—
396	C₂²×D₄	—	212	12	no	—
397	C₂²×D₄	—	212	12	no	—
398	C₂²×D₄	C₂²×D₅₃	1	6	yes	—
399	C₂²×D₄	C₂²×D₅₃	1	3	yes	—
400	C₂²×D₄	C₂²×D₅₃	1	3	yes	complemented
401	C₂³×C₄	—	53	3	no	—
402	C₂³×C₄	—	53	6	no	—
403	C₂³×C₄	—	53	3	no	—
404	C₂³×C₄	—	53	6	no	—
405	C₂³×C₄	—	53	24	no	—
406	C₂³×C₄	—	212	12	no	—
407	C₂³×C₄	C₂²×D₅₃	1	3	yes	complemented
408	#127	—	53	24	no	—
409	#127	—	53	24	no	—
410	#127	—	53	8	no	—
411	#127	C₂²×D₅₃	1	8	yes	complemented
412	#126	—	53	48	no	—
413	#126	—	53	48	no	—
414	#126	—	53	16	no	—
415	#126	C₂²×D₅₃	1	16	yes	complemented
416	#123	—	53	24	no	—
417	#123	—	53	24	no	—
418	#123	—	53	48	no	—
419	#123	—	53	48	no	—
420	#123	—	53	24	no	—
421	#123	C₂²×D₅₃	1	24	yes	complemented
422	#121	—	53	48	no	—
423	#121	—	53	48	no	—
424	#121	—	53	48	no	—
425	#121	—	53	48	no	—
426	#121	—	53	48	no	—
427	#121	—	53	48	no	—
428	#121	—	53	48	no	—
429	#121	C₂²×D₅₃	1	48	yes	complemented
430	#120	—	53	24	no	—
431	#120	—	53	48	no	—
432	#120	—	53	24	no	—
433	#120	—	53	24	no	—
434	#120	—	53	48	no	—
435	#120	C₂²×D₅₃	1	24	yes	complemented
436	C₂×C₄⋊C₄	—	53	6	no	—
437	C₂×C₄⋊C₄	—	53	6	no	—
438	C₂×C₄⋊C₄	—	53	6	no	—
439	C₂×C₄⋊C₄	—	53	48	no	—
440	C₂×C₄⋊C₄	C₂²×D₅₃	1	6	yes	complemented
441	C₂×C₂²⋊C₄	—	53	6	no	—
442	C₂×C₂²⋊C₄	—	53	3	no	—
443	C₂×C₂²⋊C₄	—	53	3	no	—
444	C₂×C₂²⋊C₄	—	53	6	no	—
445	C₂×C₂²⋊C₄	—	53	6	no	—
446	C₂×C₂²⋊C₄	—	53	6	no	—
447	C₂×C₂²⋊C₄	—	53	6	no	—
448	C₂×C₂²⋊C₄	—	53	48	no	—
449	C₂×C₂²⋊C₄	—	53	24	no	—
450	C₂×C₂²⋊C₄	—	53	24	no	—
451	C₂×C₂²⋊C₄	C₂²×D₅₃	1	6	yes	—
452	C₂×C₂²⋊C₄	C₂²×D₅₃	1	3	yes	—
453	C₂×C₂²⋊C₄	C₂²×D₅₃	1	3	yes	complemented
454	C₂×C₄²	—	53	3	no	—
455	C₂×C₄²	—	53	8	no	—
456	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic, complemented
457	C₂⁴	—	4	6	no	—
458	C₂⁴	—	53	1	no	—
459	C₂⁴	—	53	8	no	—
460	C₂⁴	—	53	4	no	—
461	C₂⁴	—	53	12	no	—
462	C₂⁴	—	53	2	no	—
463	C₂⁴	—	53	1	no	—
464	C₂⁴	—	53	3	no	—
465	C₂⁴	—	53	4	no	—
466	C₂⁴	—	53	8	no	—
467	C₂⁴	—	106	12	no	—
468	C₂⁴	—	106	24	no	—
469	C₂⁴	—	106	24	no	—
470	C₂⁴	—	106	12	no	—
471	C₂⁴	—	212	12	no	—
472	C₂⁴	—	212	6	no	—
473	C₂⁴	—	212	48	no	—
474	C₂⁴	—	212	64	no	—
475	C₂⁴	C₂³×D₅₃	1	2	yes	—
476	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
477	C₂⁴	C₂³×D₅₃	1	3	yes	—
478	C₂⁴	C₂³×D₅₃	1	4	yes	—
479	C₂×D₄	—	4	12	no	—
480	C₂×D₄	—	4	6	no	—
481	C₂×D₄	—	4	6	no	—
482	C₂×D₄	—	53	24	no	—
483	C₂×D₄	—	53	24	no	—
484	C₂×D₄	—	53	12	no	—
485	C₂×D₄	—	53	12	no	—
486	C₂×D₄	—	53	24	no	—
487	C₂×D₄	—	53	24	no	—
488	C₂×D₄	—	53	12	no	—
489	C₂×D₄	—	53	12	no	—
490	C₂×D₄	—	212	12	no	—
491	C₂×D₄	—	212	6	no	—
492	C₂×D₄	—	212	6	no	—
493	C₂×D₄	—	212	96	no	—
494	C₂×D₄	—	212	48	no	—
495	C₂×D₄	—	212	48	no	—
496	C₂×D₄	—	212	12	no	—
497	C₂×D₄	—	212	12	no	—
498	C₂×D₄	—	212	6	no	—
499	C₂×D₄	—	212	12	no	—
500	C₂×D₄	—	212	6	no	—
501	C₂×D₄	C₂³×D₅₃	1	24	yes	—
502	C₂×D₄	C₂³×D₅₃	1	12	yes	—
503	C₂×D₄	C₂³×D₅₃	1	12	yes	complemented
504	C₂²×C₄	—	4	6	no	—
505	C₂²×C₄	—	53	3	no	—
506	C₂²×C₄	—	53	6	no	—
507	C₂²×C₄	—	53	12	no	—
508	C₂²×C₄	—	53	12	no	—
509	C₂²×C₄	—	53	24	no	—
510	C₂²×C₄	—	53	24	no	—
511	C₂²×C₄	—	106	24	no	—
512	C₂²×C₄	—	106	12	no	—
513	C₂²×C₄	—	212	12	no	—
514	C₂²×C₄	—	212	48	no	—
515	C₂²×C₄	—	212	6	no	—
516	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
517	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
518	C₂²×C₄	C₂³×D₅₃	1	12	yes	complemented
519	C₄⋊C₄	—	53	24	no	—
520	C₄⋊C₄	—	53	24	no	—
521	C₄⋊C₄	—	53	24	no	—
522	C₄⋊C₄	C₂³×D₅₃	1	24	yes	complemented
523	C₂²⋊C₄	—	53	24	no	—
524	C₂²⋊C₄	—	53	12	no	—
525	C₂²⋊C₄	—	53	12	no	—
526	C₂²⋊C₄	—	53	24	no	—
527	C₂²⋊C₄	—	53	24	no	—
528	C₂²⋊C₄	—	53	24	no	—
529	C₂²⋊C₄	—	53	24	no	—
530	C₂²⋊C₄	C₂³×D₅₃	1	24	yes	—
531	C₂²⋊C₄	C₂³×D₅₃	1	12	yes	—
532	C₂²⋊C₄	C₂³×D₅₃	1	12	yes	complemented
533	C₄²	—	53	12	no	—
534	C₄²	C₂³×D₅₃	1	4	yes	complemented
535	C₂³	—	2	6	no	—
536	C₂³	—	2	12	no	—
537	C₂³	—	2	12	no	—
538	C₂³	—	2	6	no	—
539	C₂³	—	4	12	no	—
540	C₂³	—	4	16	no	—
541	C₂³	—	53	12	no	—
542	C₂³	—	53	2	no	—
543	C₂³	—	53	4	no	—
544	C₂³	—	53	2	no	—
545	C₂³	—	53	6	no	—
546	C₂³	—	106	24	no	—
547	C₂³	—	106	48	no	—
548	C₂³	—	106	48	no	—
549	C₂³	—	106	24	no	—
550	C₂³	—	106	6	no	—
551	C₂³	—	106	12	no	—
552	C₂³	—	106	12	no	—
553	C₂³	—	106	6	no	—
554	C₂³	—	212	24	no	—
555	C₂³	—	212	12	no	—
556	C₂³	—	212	48	no	—
557	C₂³	—	212	32	no	—
558	C₂³	—	212	16	no	—
559	C₂³	—	212	128	no	—
560	C₂³	—	212	32	no	—
561	C₂³	—	212	16	no	—
562	C₂³	C₂⁴×D₅₃	1	4	yes	—
563	C₂³	C₂⁴×D₅₃	1	2	yes	—
564	C₂³	C₂⁴×D₅₃	1	6	yes	—
565	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
566	D₄	—	4	24	no	—
567	D₄	—	4	12	no	—
568	D₄	—	4	12	no	—
569	D₄	—	212	24	no	—
570	D₄	—	212	12	no	—
571	D₄	—	212	12	no	—
572	D₄	—	212	24	no	—
573	D₄	—	212	24	no	—
574	D₄	—	212	12	no	—
575	D₄	—	212	24	no	—
576	D₄	—	212	12	no	—
577	C₂×C₄	—	2	12	no	—
578	C₂×C₄	—	2	6	no	—
579	C₂×C₄	—	4	12	no	—
580	C₂×C₄	—	53	6	no	—
581	C₂×C₄	—	53	12	no	—
582	C₂×C₄	—	106	48	no	—
583	C₂×C₄	—	106	24	no	—
584	C₂×C₄	—	106	12	no	—
585	C₂×C₄	—	106	6	no	—
586	C₂×C₄	—	212	24	no	—
587	C₂×C₄	—	212	12	no	—
588	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
589	C₂×C₄	C₂⁴×D₅₃	1	12	yes	—
590	C₂²	—	2	6	no	—
591	C₂²	—	2	12	no	—
592	C₂²	—	2	12	no	—
593	C₂²	—	2	6	no	—
594	C₂²	—	4	16	no	—
595	C₂²	—	4	8	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	4	12	no	—
598	C₂²	—	53	16	no	—
599	C₂²	—	53	12	no	—
600	C₂²	—	106	6	no	—
601	C₂²	—	106	12	no	—
602	C₂²	—	106	12	no	—
603	C₂²	—	106	6	no	—
604	C₂²	—	212	32	no	—
605	C₂²	—	212	16	no	—
606	C₂²	—	212	48	no	—
607	C₂²	—	212	32	no	—
608	C₂²	—	212	16	no	—
609	C₂²	—	212	8	no	—
610	C₂²	—	212	4	no	—
611	C₂²	—	212	12	no	—
612	C₂²	H(5,𝔽₂)×D₅₃	1	6	yes	—
613	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
614	C₄	—	2	12	no	—
615	C₄	—	2	6	no	—
616	C₄	—	106	12	no	—
617	C₄	—	106	6	no	—
618	C₂	—	4	4	no	—
619	C₂	—	4	2	no	—
620	C₂	—	4	6	no	—
621	C₂	—	53	8	no	—
622	C₂	—	212	4	no	—
623	C₂	—	212	2	no	—
624	C₂	—	212	6	no	—
625	C₂	#560×D₅₃	1	4	yes	direct product factor
626	C₂	C₂×H(5,𝔽₂)×D₅₃	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#560	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#560	D₅₃
hypocenter	C₅₃	C₂²×#560
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#560

Complements

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

N	H ≅ G/N	type
1. C₂×#16811364	C₂	semidirect
2. C₂×#16811363	C₂	semidirect
3. C₂×#16811362	C₂	semidirect
4. C₂×#16811361	C₂	semidirect
5. C₂×#16811360	C₂	semidirect
6. #560×D₅₃	C₂	direct (N × H)
7. C₂×#127×D₅₃	C₂	semidirect
8. C₂×#126×D₅₃	C₂	semidirect
9. C₂×#123×D₅₃	C₂	semidirect
10. C₂×#121×D₅₃	C₂	semidirect
11. C₂×#120×D₅₃	C₂	semidirect
12. C₂×C₅₃×#560	C₂	semidirect
16. C₂²×D₄×D₅₃	C₂²	semidirect
17. C₂³×C₄×D₅₃	C₂²	semidirect
18. #16811364	C₂²	semidirect
19. #16811363	C₂²	semidirect
20. #16811362	C₂²	semidirect
21. #16811361	C₂²	semidirect
22. #16811360	C₂²	semidirect
23. C₂×#13133214	C₂²	semidirect
24. C₂×#13133213	C₂²	semidirect
25. C₂×#13133213	C₂²	semidirect
26. #127×D₅₃	C₂²	semidirect
27. C₂×#13133212	C₂²	semidirect
28. C₂×#13133211	C₂²	semidirect
29. C₂×#13133210	C₂²	semidirect
30. #126×D₅₃	C₂²	semidirect
31. C₂×#13133202	C₂²	semidirect
32. C₂×#13133201	C₂²	semidirect
33. C₂×#13133200	C₂²	semidirect
34. C₂×#13133199	C₂²	semidirect
35. C₂×#13133198	C₂²	semidirect
36. #123×D₅₃	C₂²	semidirect
37. C₂×#13133192	C₂²	semidirect
38. C₂×#13133191	C₂²	semidirect
39. C₂×#13133190	C₂²	semidirect
40. C₂×#13133190	C₂²	semidirect
41. C₂×#13133189	C₂²	semidirect
42. C₂×#13133189	C₂²	semidirect
43. C₂×#13133188	C₂²	semidirect
44. #121×D₅₃	C₂²	semidirect
45. C₂×#13133187	C₂²	semidirect
46. C₂×#13133187	C₂²	semidirect
47. C₂×#13133186	C₂²	semidirect
48. C₂×#13133185	C₂²	semidirect
49. C₂×#13133185	C₂²	semidirect
50. #120×D₅₃	C₂²	semidirect
51. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
54. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
55. C₂×C₄²×D₅₃	C₂²	semidirect
56. C₅₃×#560	C₂²	semidirect
57. C₂×#127×C₅₃	C₂²	semidirect
58. C₂×#126×C₅₃	C₂²	semidirect
59. C₂×#123×C₅₃	C₂²	semidirect
60. C₂×#121×C₅₃	C₂²	semidirect
61. C₂×#120×C₅₃	C₂²	semidirect
71. C₂²×D₂₁₂	C₂³	semidirect
76. C₂²×C₂²⋊D₅₃	C₂³	semidirect
82. C₂×D₄×D₅₃	C₂³	semidirect
83. C₂³×Dic₅₃	C₂³	semidirect
87. C₂²×C₄×D₅₃	C₂³	semidirect
88. C₂²×C₄×D₅₃	C₂³	semidirect
89. #13133214	C₂³	semidirect
90. #13133213	C₂³	semidirect
91. #13133213	C₂³	semidirect
92. #13133212	C₂³	semidirect
93. #13133211	C₂³	semidirect
94. #13133210	C₂³	semidirect
95. #13133202	C₂³	semidirect
96. #13133201	C₂³	semidirect
97. #13133200	C₂³	semidirect
98. #13133199	C₂³	semidirect
99. #13133198	C₂³	semidirect
100. #13133192	C₂³	semidirect
101. #13133191	C₂³	semidirect
102. #13133190	C₂³	semidirect
103. #13133190	C₂³	semidirect
104. #13133189	C₂³	semidirect
105. #13133189	C₂³	semidirect
106. #13133188	C₂³	semidirect
107. #13133187	C₂³	semidirect
108. #13133187	C₂³	semidirect
109. #13133186	C₂³	semidirect
110. #13133185	C₂³	semidirect
111. #13133185	C₂³	semidirect
112. C₂×C₄⋊Dic₅₃	C₂³	semidirect
113. C₂×#11719919	C₂³	semidirect
114. C₂×#11719919	C₂³	semidirect
115. C₄⋊C₄×D₅₃	C₂³	semidirect
118. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
122. C₂×#11719921	C₂³	semidirect
125. C₂²⋊C₄×D₅₃	C₂³	semidirect
126. C₂×C₄×Dic₅₃	C₂³	semidirect
127. C₄²×D₅₃	C₂³	semidirect
131. C₂²×D₄×C₅₃	C₂³	semidirect
132. C₂³×C₄×C₅₃	C₂³	semidirect
133. #127×C₅₃	C₂³	semidirect
134. #126×C₅₃	C₂³	semidirect
135. #123×C₅₃	C₂³	semidirect
136. #121×C₅₃	C₂³	semidirect
137. #120×C₅₃	C₂³	semidirect
138. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
141. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
142. C₂×C₄²×C₅₃	C₂³	semidirect
170. C₂×D₄×C₅₃	C₂⁴	semidirect
174. C₂²×C₄×C₅₃	C₂⁴	semidirect
184. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
188. C₂²×Dic₅₃	C₂⁴	semidirect
197. C₂×D₂₁₂	C₂⁴	semidirect
204. C₂×C₄×D₅₃	C₂⁴	semidirect
205. C₄⋊C₄×C₅₃	C₂⁴	semidirect
208. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
209. C₄²×C₅₃	C₂⁴	semidirect
212. C₂²⋊Dic₅₃	C₂⁴	semidirect
216. #11719921	C₂⁴	semidirect
217. C₄⋊Dic₅₃	C₂⁴	semidirect
218. #11719919	C₂⁴	semidirect
219. #11719919	C₂⁴	semidirect
220. C₄×Dic₅₃	C₂⁴	semidirect
299. C₂×D₅₃	#560	direct (N × H)
311. C₂×#560	D₅₃	direct (N × H)
320. C₂×C₅₃	C₂×#560	semidirect
325. D₅₃	C₂×#560	direct (N × H)
336. #560	C₂×D₅₃	direct (N × H)
341. C₂×#127	C₂×D₅₃	semidirect
346. C₂×#126	C₂×D₅₃	semidirect
353. C₂×#123	C₂×D₅₃	semidirect
362. C₂×#121	C₂×D₅₃	semidirect
369. C₂×#120	C₂×D₅₃	semidirect
375. C₅₃	C₂²×#560	semidirect
400. C₂²×D₄	C₂²×D₅₃	semidirect
407. C₂³×C₄	C₂²×D₅₃	semidirect
411. #127	C₂²×D₅₃	semidirect
415. #126	C₂²×D₅₃	semidirect
421. #123	C₂²×D₅₃	semidirect
429. #121	C₂²×D₅₃	semidirect
435. #120	C₂²×D₅₃	semidirect
440. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
453. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
456. C₂×C₄²	C₂²×D₅₃	semidirect
503. C₂×D₄	C₂³×D₅₃	semidirect
518. C₂²×C₄	C₂³×D₅₃	semidirect
522. C₄⋊C₄	C₂³×D₅₃	semidirect
532. C₂²⋊C₄	C₂³×D₅₃	semidirect
534. C₄²	C₂³×D₅₃	semidirect
625. C₂	#560×D₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16811364	2
C₂×#16811363	2
C₂×#16811362	2
C₂×#16811361	2
C₂×#16811360	2
#560×D₅₃	2
C₂×#127×D₅₃	2
C₂×#126×D₅₃	2
C₂×#123×D₅₃	2
C₂×#121×D₅₃	2
C₂×#120×D₅₃	2
C₂×C₅₃×#560	2
C₂²×#560	53

Subgroups — C2×#560×D53 #28290957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#560×D₅₃ #28290957