Subgroups — C₂×#20275386 #27386675

Order 13568.

1046 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810672	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16810640	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13133144	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#20275386	C₂	1	8	yes	maximal, direct product factor
6	C₂×#16810395	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16810384	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#413	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11719917	C₂²	1	1	yes	characteristic
10	C₂²×#11719917	C₂²	1	1	yes	characteristic
11	C₂×#13133176	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
13	#16810672	—	2	2	no	—
14	#16810672	C₂²	1	4	yes	complemented
15	C₂×#13133153	—	2	2	no	—
16	#16810640	—	2	2	no	—
17	#16810640	C₂²	1	4	yes	—
18	C₂×#13133144	—	2	2	no	—
19	C₂×#13133144	—	2	1	no	—
20	C₂×#13133144	—	2	1	no	—
21	C₂×#13133144	—	2	2	no	—
22	C₂×#13133144	C₂²	1	4	yes	—
23	M₁₆×Dic₅₃	—	2	2	no	—
24	M₁₆×Dic₅₃	C₂²	1	4	yes	complemented
25	C₂×#13133127	—	2	1	no	—
26	C₂×C₈×Dic₅₃	—	2	1	no	—
27	#16810395	C₂²	1	4	yes	complemented
28	#16810384	C₂²	1	4	yes	complemented
29	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
32	C₅₃×#413	C₄	1	4	yes	complemented
33	C₅₃×#413	C₂²	1	4	yes	—
34	C₂×#101×C₅₃	C₄	1	2	yes	complemented
35	C₂×#100×C₅₃	C₄	1	2	yes	complemented
36	C₂³×Dic₅₃	—	2	1	no	—
37	C₂×#11719917	—	2	1	no	—
38	C₂×#11719917	—	2	1	no	—
39	C₂×#11719917	—	2	1	no	—
40	C₂×#11719917	—	2	1	no	—
41	C₂×#11719917	—	2	1	no	—
42	C₂×#11719917	—	2	1	no	—
43	C₂×#11719917	—	2	1	no	—
44	C₂×#11719917	—	2	1	no	—
45	C₂×#11719917	D₄	1	2	yes	—
46	C₂×#11719917	D₄	1	2	yes	—
47	C₂×#11719917	C₂³	1	2	yes	—
48	C₂×#11719917	C₂³	1	2	yes	—
49	C₂²×#88322	—	2	1	no	—
50	C₂²×#88322	—	2	1	no	—
51	#13133176	—	2	1	no	—
52	#13133176	—	2	1	no	—
53	#13133176	—	2	1	no	—
54	#13133176	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₅₃	—	2	1	no	—
56	C₂×C₂²⋊Dic₅₃	—	2	1	no	—
57	C₂×C₄×Dic₅₃	—	2	1	no	—
58	C₂×C₄×Dic₅₃	—	2	1	no	—
59	C₂×C₄×Dic₅₃	—	2	1	no	—
60	C₂×C₄×Dic₅₃	—	2	1	no	—
61	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
62	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
63	C₂×C₄×Dic₅₃	D₄	1	2	yes	—
64	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
65	#13133153	—	2	8	no	—
66	#13133144	—	2	4	no	—
67	#13133144	—	2	4	no	—
68	#13133144	—	2	8	no	—
69	#13133127	—	2	4	no	—
70	C₈×Dic₅₃	—	2	4	no	—
71	C₂×#41×C₅₃	—	2	1	no	—
72	C₂×#41×C₅₃	—	2	1	no	—
73	C₂×#41×C₅₃	—	2	1	no	—
74	C₂×#41×C₅₃	—	2	1	no	—
75	C₂×#41×C₅₃	—	2	1	no	—
76	C₂×#41×C₅₃	—	2	1	no	—
77	C₂×#41×C₅₃	—	2	1	no	—
78	C₂×#41×C₅₃	—	2	1	no	—
79	C₂×#41×C₅₃	—	2	1	no	—
80	C₂×#41×C₅₃	—	2	1	no	—
81	C₂×#41×C₅₃	C₂×C₄	1	2	yes	—
82	C₂×#41×C₅₃	C₂³	1	2	yes	—
83	C₂²×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
84	C₂²×D₄×C₅₃	—	2	1	no	—
85	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
86	C₂³×C₄×C₅₃	—	2	1	no	—
87	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₅₃	—	2	1	no	—
89	C₂×M₁₆×C₅₃	—	2	1	no	—
90	C₂×M₁₆×C₅₃	—	2	1	no	—
91	C₂×M₁₆×C₅₃	—	2	1	no	—
92	C₂×M₁₆×C₅₃	—	2	1	no	—
93	C₂×M₁₆×C₅₃	—	2	1	no	—
94	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
95	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
96	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
97	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
98	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
99	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
100	C₂²×C₈×C₅₃	—	2	1	no	—
101	C₂²×C₈×C₅₃	—	2	1	no	—
102	#101×C₅₃	C₂×C₄	1	8	yes	complemented
103	#100×C₅₃	C₂×C₄	1	8	yes	complemented
104	C₂⁴×C₅₃	—	2	1	no	—
105	C₂⁴×C₅₃	#41	1	1	yes	characteristic
106	#41×C₅₃	—	2	2	no	—
107	#41×C₅₃	—	2	2	no	—
108	#41×C₅₃	—	2	2	no	—
109	#41×C₅₃	—	2	2	no	—
110	#41×C₅₃	—	2	2	no	—
111	#41×C₅₃	—	2	2	no	—
112	#41×C₅₃	—	2	2	no	—
113	#41×C₅₃	—	2	2	no	—
114	#41×C₅₃	—	4	1	no	—
115	#41×C₅₃	—	4	1	no	—
116	#41×C₅₃	—	4	1	no	—
117	#41×C₅₃	—	4	1	no	—
118	#41×C₅₃	—	4	1	no	—
119	#41×C₅₃	—	4	1	no	—
120	#41×C₅₃	—	4	1	no	—
121	#41×C₅₃	—	4	1	no	—
122	C₂×Q₈×C₅₃	—	2	1	no	—
123	C₂×Q₈×C₅₃	—	2	1	no	—
124	C₂×Q₈×C₅₃	—	2	1	no	—
125	C₂×Q₈×C₅₃	—	2	1	no	—
126	C₂×Q₈×C₅₃	—	2	1	no	—
127	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
128	C₂×D₄×C₅₃	—	2	2	no	—
129	C₂×D₄×C₅₃	—	2	2	no	—
130	C₂×D₄×C₅₃	—	2	1	no	—
131	C₂×D₄×C₅₃	—	2	1	no	—
132	C₂×D₄×C₅₃	—	2	1	no	—
133	C₂×D₄×C₅₃	—	2	1	no	—
134	C₂×D₄×C₅₃	—	2	1	no	—
135	C₂×D₄×C₅₃	—	4	1	no	—
136	C₂×D₄×C₅₃	—	4	1	no	—
137	C₂×D₄×C₅₃	—	4	1	no	—
138	C₂×D₄×C₅₃	—	4	1	no	—
139	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₅₃	—	2	1	no	—
141	C₂²×C₄×C₅₃	—	2	2	no	—
142	C₂²×C₄×C₅₃	—	2	2	no	—
143	C₂²×C₄×C₅₃	—	4	1	no	—
144	C₂²×C₄×C₅₃	—	4	1	no	—
145	C₂²×C₄×C₅₃	—	4	1	no	—
146	C₂²×C₄×C₅₃	—	4	1	no	—
147	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
154	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
155	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
156	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
157	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
158	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
159	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
160	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
161	C₂²×Dic₅₃	—	2	1	no	—
162	C₂²×Dic₅₃	—	2	2	no	—
163	C₂²×Dic₅₃	—	2	1	no	—
164	C₂²×Dic₅₃	—	2	2	no	—
165	C₂²×Dic₅₃	—	4	4	no	—
166	C₂²×Dic₅₃	—	4	1	no	—
167	M₁₆×C₅₃	—	2	2	no	—
168	M₁₆×C₅₃	—	2	2	no	—
169	M₁₆×C₅₃	—	2	2	no	—
170	M₁₆×C₅₃	—	2	2	no	—
171	M₁₆×C₅₃	—	2	2	no	—
172	M₁₆×C₅₃	—	2	2	no	—
173	M₁₆×C₅₃	C₂²×C₄	1	4	yes	—
174	M₁₆×C₅₃	C₂²×C₄	1	4	yes	—
175	C₂×C₈×C₅₃	—	2	2	no	—
176	C₂×C₈×C₅₃	—	2	2	no	—
177	C₂×C₈×C₅₃	—	2	2	no	—
178	C₂×C₈×C₅₃	—	2	2	no	—
179	C₂×C₈×C₅₃	—	2	2	no	—
180	C₂×C₈×C₅₃	—	2	2	no	—
181	C₂²⋊Dic₅₃	—	2	2	no	—
182	C₂²⋊Dic₅₃	—	4	1	no	—
183	C₄⋊Dic₅₃	—	2	2	no	—
184	C₄⋊Dic₅₃	—	4	1	no	—
185	C₄×Dic₅₃	—	2	1	no	—
186	C₄×Dic₅₃	—	2	2	no	—
187	C₄×Dic₅₃	—	2	1	no	—
188	C₄×Dic₅₃	—	2	2	no	—
189	C₄×Dic₅₃	—	2	2	no	—
190	C₄×Dic₅₃	—	4	1	no	—
191	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
192	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
193	#11719917	—	2	2	no	—
194	#11719917	—	2	2	no	—
195	#11719917	—	2	2	no	—
196	#11719917	—	2	2	no	—
197	#11719917	—	2	2	no	—
198	#11719917	—	4	1	no	—
199	#11719917	—	4	1	no	—
200	#11719917	C₂×D₄	1	4	yes	—
201	C₂×#88322	—	2	2	no	—
202	C₂×#88322	—	2	2	no	—
203	C₂×#88322	—	2	2	no	—
204	C₂×#88322	—	2	2	no	—
205	C₂×#88322	—	4	1	no	—
206	C₂×#88322	—	4	1	no	—
207	C₂³×C₅₃	—	2	2	no	—
208	C₂³×C₅₃	—	4	2	no	—
209	C₂³×C₅₃	—	4	1	no	—
210	C₂³×C₅₃	—	4	1	no	—
211	C₂³×C₅₃	—	8	2	no	—
212	C₂³×C₅₃	#117	1	1	yes	characteristic
213	C₂³×C₅₃	#117	1	1	yes	characteristic
214	C₂³×C₅₃	#123	1	1	yes	characteristic
215	C₂³×C₅₃	#123	1	1	yes	characteristic
216	C₂³×C₅₃	#124	1	1	yes	characteristic
217	C₂³×C₅₃	#124	1	1	yes	characteristic
218	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
219	Q₈×C₅₃	—	2	2	no	—
220	Q₈×C₅₃	—	2	2	no	—
221	Q₈×C₅₃	—	4	1	no	—
222	Q₈×C₅₃	—	4	1	no	—
223	D₄×C₅₃	—	2	2	no	—
224	D₄×C₅₃	—	2	2	no	—
225	D₄×C₅₃	—	4	2	no	—
226	D₄×C₅₃	—	4	2	no	—
227	D₄×C₅₃	—	4	2	no	—
228	D₄×C₅₃	—	4	2	no	—
229	D₄×C₅₃	—	4	1	no	—
230	D₄×C₅₃	—	4	1	no	—
231	C₂×C₄×C₅₃	—	2	2	no	—
232	C₂×C₄×C₅₃	—	4	1	no	—
233	C₂×C₄×C₅₃	—	4	1	no	—
234	C₂×C₄×C₅₃	—	4	2	no	—
235	C₂×C₄×C₅₃	—	4	2	no	—
236	C₂×C₄×C₅₃	—	4	2	no	—
237	C₂×C₄×C₅₃	—	4	2	no	—
238	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
239	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
240	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
249	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
250	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
251	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
252	C₂×C₄×C₅₃	#123	1	1	yes	characteristic
253	C₂×C₄×C₅₃	#123	1	1	yes	characteristic
254	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
255	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
256	C₂×C₄×C₅₃	#126	1	1	yes	characteristic
257	C₂×C₄×C₅₃	#126	1	1	yes	characteristic
258	C₂×C₄×C₅₃	#126	1	1	yes	characteristic
259	C₂×C₄×C₅₃	#126	1	1	yes	characteristic
260	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
261	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
266	C₂×Dic₅₃	—	2	4	no	—
267	C₂×Dic₅₃	—	2	2	no	—
268	C₂×Dic₅₃	—	2	2	no	—
269	C₂×Dic₅₃	—	4	4	no	—
270	C₂×Dic₅₃	—	4	4	no	—
271	C₂×Dic₅₃	—	4	2	no	—
272	C₂×Dic₅₃	—	4	2	no	—
273	C₂×Dic₅₃	—	8	2	no	—
274	C₈×C₅₃	—	2	4	no	—
275	C₈×C₅₃	—	2	4	no	—
276	#88322	—	2	4	no	—
277	#88322	—	4	2	no	—
278	C₂×#1932	—	53	1	no	maximal, Sylow
279	C₂²×C₅₃	—	2	2	no	—
280	C₂²×C₅₃	—	2	2	no	—
281	C₂²×C₅₃	—	2	2	no	—
282	C₂²×C₅₃	—	4	1	no	—
283	C₂²×C₅₃	—	4	1	no	—
284	C₂²×C₅₃	—	4	1	no	—
285	C₂²×C₅₃	—	4	1	no	—
286	C₂²×C₅₃	—	4	2	no	—
287	C₂²×C₅₃	—	8	2	no	—
288	C₂²×C₅₃	—	8	2	no	—
289	C₂²×C₅₃	—	8	2	no	—
290	C₂²×C₅₃	#388	1	1	yes	characteristic
291	C₂²×C₅₃	#388	1	1	yes	characteristic
292	C₂²×C₅₃	#388	1	1	yes	characteristic
293	C₂²×C₅₃	#388	1	1	yes	characteristic
294	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
295	C₂²×C₅₃	C₂×#123	1	1	yes	characteristic
296	C₂²×C₅₃	C₂×#124	1	1	yes	characteristic
297	C₄×C₅₃	—	4	2	no	—
298	C₄×C₅₃	#388	1	1	yes	characteristic
299	C₄×C₅₃	#388	1	1	yes	characteristic
300	C₄×C₅₃	#388	1	1	yes	characteristic
301	C₄×C₅₃	#388	1	1	yes	characteristic
302	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
303	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
304	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
305	C₄×C₅₃	C₂×#126	1	1	yes	characteristic
306	Dic₅₃	—	2	4	no	—
307	Dic₅₃	—	4	2	no	—
308	Dic₅₃	—	8	2	no	—
309	C₂×#430	—	53	1	no	—
310	C₂×#421	—	53	1	no	—
311	C₂²×#104	—	53	1	no	—
312	C₂×#413	D₅₃	1	1	yes	characteristic
313	C₂×C₄×M₁₆	—	53	1	no	—
314	#1932	—	53	8	no	—
315	C₂×#344	—	53	1	no	—
316	C₂×#339	—	53	1	no	—
317	C₂×C₅₃	—	2	1	no	—
318	C₂×C₅₃	—	2	1	no	—
319	C₂×C₅₃	—	2	1	no	—
320	C₂×C₅₃	—	2	1	no	—
321	C₂×C₅₃	—	2	1	no	—
322	C₂×C₅₃	—	2	1	no	—
323	C₂×C₅₃	—	8	2	no	—
324	C₂×C₅₃	#1932	1	2	yes	complemented
325	C₂×C₅₃	C₂×#388	1	1	yes	characteristic
326	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic
327	C₂²×M₁₆	—	53	1	no	—
328	C₂²×M₁₆	—	53	1	no	—
329	C₂²×M₁₆	C₂×D₅₃	1	1	yes	characteristic
330	C₂²×M₁₆	C₂×D₅₃	1	1	yes	characteristic
331	C₂×#117	—	53	1	no	—
332	C₂²×C₄²	—	53	1	no	—
333	#430	—	53	4	no	—
334	#430	—	106	2	no	—
335	C₂×#108	—	106	2	no	—
336	#421	—	53	4	no	—
337	#421	—	106	2	no	—
338	C₂×#104	—	53	4	no	—
339	C₂×#104	—	106	1	no	—
340	C₂×#104	—	106	1	no	—
341	C₂×#104	—	106	2	no	—
342	C₂×#104	—	106	2	no	—
343	#413	Dic₅₃	1	4	yes	complemented
344	#413	C₂×D₅₃	1	4	yes	—
345	C₂×#101	Dic₅₃	1	2	yes	complemented
346	C₂×#100	Dic₅₃	1	2	yes	complemented
347	C₄×M₁₆	—	53	4	no	—
348	C₄×M₁₆	—	106	2	no	—
349	C₂×#97	—	106	1	no	—
350	C₂×C₄×C₈	—	106	1	no	—
351	#344	—	53	4	no	—
352	#339	—	53	4	no	—
353	C₅₃	C₂×#1932	1	1	yes	characteristic, complemented, Sylow
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	C₂×Dic₅₃	1	2	yes	—
365	C₂×#41	C₂²×D₅₃	1	2	yes	—
366	C₂²×Q₈	C₂×Dic₅₃	1	1	yes	characteristic
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	C₂×Dic₅₃	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	—	106	1	no	—
371	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	53	2	no	—
379	C₂×M₁₆	—	53	2	no	—
380	C₂×M₁₆	—	53	2	no	—
381	C₂×M₁₆	—	53	2	no	—
382	C₂×M₁₆	—	106	1	no	—
383	C₂×M₁₆	—	106	1	no	—
384	C₂×M₁₆	—	106	1	no	—
385	C₂×M₁₆	—	106	1	no	—
386	C₂×M₁₆	—	106	1	no	—
387	C₂×M₁₆	—	106	1	no	—
388	C₂×M₁₆	—	106	1	no	—
389	C₂×M₁₆	—	106	1	no	—
390	C₂×M₁₆	C₂×Dic₅₃	1	2	yes	—
391	C₂×M₁₆	C₂×Dic₅₃	1	2	yes	—
392	C₂×M₁₆	C₂×Dic₅₃	1	2	yes	—
393	C₂×M₁₆	C₂×Dic₅₃	1	2	yes	—
394	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
395	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
396	C₂²×C₈	—	2	1	no	—
397	C₂²×C₈	—	2	1	no	—
398	C₂²×C₈	—	106	1	no	—
399	C₂²×C₈	—	106	1	no	—
400	#117	—	53	2	no	—
401	#117	—	106	1	no	—
402	#117	—	106	1	no	—
403	#117	—	106	1	no	—
404	C₂×C₄⋊C₄	—	106	1	no	—
405	C₂×C₂²⋊C₄	—	106	1	no	—
406	C₂×C₄²	—	53	1	no	—
407	C₂×C₄²	—	53	1	no	—
408	C₂×C₄²	—	53	2	no	—
409	C₂×C₄²	—	53	2	no	—
410	C₂×C₄²	—	106	1	no	—
411	C₂×C₄²	—	106	1	no	—
412	C₂×C₄²	—	106	1	no	—
413	C₂×C₄²	—	106	1	no	—
414	#108	—	106	8	no	—
415	#104	—	106	4	no	—
416	#104	—	106	4	no	—
417	#104	—	106	8	no	—
418	#101	C₂×Dic₅₃	1	8	yes	complemented
419	#100	C₂×Dic₅₃	1	8	yes	complemented
420	#97	—	106	4	no	—
421	C₄×C₈	—	106	4	no	—
422	C₂⁴	—	2	1	no	—
423	C₂⁴	#11719945	1	1	yes	characteristic
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	4	1	no	—
433	#41	—	4	1	no	—
434	#41	—	4	1	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	1	no	—
439	#41	—	4	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	C₂²×Dic₅₃	1	2	yes	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	C₂²×Dic₅₃	1	2	yes	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	106	1	no	—
466	C₂²×C₄	—	106	2	no	—
467	C₂²×C₄	—	106	1	no	—
468	C₂²×C₄	—	106	2	no	—
469	C₂²×C₄	—	212	4	no	—
470	C₂²×C₄	—	212	1	no	—
471	C₂²×C₄	#11719945	1	1	yes	characteristic
472	C₂²×C₄	#11719945	1	1	yes	characteristic
473	C₂²×C₄	#11719945	1	1	yes	characteristic
474	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
475	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
476	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
477	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
478	C₂²×C₄	#11719947	1	1	yes	characteristic
479	C₂²×C₄	#11719947	1	1	yes	characteristic
480	C₂²×C₄	#11719947	1	1	yes	characteristic
481	C₂²×C₄	#11719947	1	1	yes	characteristic
482	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
483	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
484	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	2	2	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	2	2	no	—
491	M₁₆	—	53	4	no	—
492	M₁₆	—	106	2	no	—
493	M₁₆	—	106	2	no	—
494	M₁₆	—	106	2	no	—
495	M₁₆	—	106	2	no	—
496	M₁₆	—	106	2	no	—
497	M₁₆	—	212	1	no	—
498	M₁₆	—	212	1	no	—
499	M₁₆	C₂²×Dic₅₃	1	4	yes	—
500	M₁₆	C₂²×Dic₅₃	1	4	yes	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	106	2	no	—
508	C₂×C₈	—	106	2	no	—
509	C₂×C₈	—	106	2	no	—
510	C₂×C₈	—	106	2	no	—
511	C₂×C₈	—	212	1	no	—
512	C₂×C₈	—	212	1	no	—
513	C₄⋊C₄	—	106	2	no	—
514	C₄⋊C₄	—	212	1	no	—
515	C₂²⋊C₄	—	106	2	no	—
516	C₂²⋊C₄	—	212	1	no	—
517	C₄²	—	53	2	no	—
518	C₄²	—	53	2	no	—
519	C₄²	—	106	1	no	—
520	C₄²	—	106	2	no	—
521	C₄²	—	106	1	no	—
522	C₄²	—	106	2	no	—
523	C₄²	—	106	2	no	—
524	C₄²	—	212	1	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	8	2	no	—
530	C₂³	#13133176	1	1	yes	characteristic
531	C₂³	#13133176	1	1	yes	characteristic
532	C₂³	#13133199	1	1	yes	characteristic
533	C₂³	#13133199	1	1	yes	characteristic
534	C₂³	#13133203	1	1	yes	characteristic
535	C₂³	#13133203	1	1	yes	characteristic
536	C₂³	C₂×#11719945	1	1	yes	characteristic
537	Q₈	—	2	2	no	—
538	Q₈	—	2	2	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	D₄	—	2	2	no	—
542	D₄	—	2	2	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	106	4	no	—
557	C₂×C₄	—	106	2	no	—
558	C₂×C₄	—	106	2	no	—
559	C₂×C₄	—	424	2	no	—
560	C₂×C₄	—	212	4	no	—
561	C₂×C₄	—	212	4	no	—
562	C₂×C₄	—	212	2	no	—
563	C₂×C₄	—	212	2	no	—
564	C₂×C₄	#13133176	1	1	yes	characteristic
565	C₂×C₄	#13133176	1	1	yes	characteristic
566	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
567	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
568	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
569	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
570	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
571	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
572	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
573	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
574	C₂×C₄	#13133190	1	1	yes	characteristic
575	C₂×C₄	#13133190	1	1	yes	characteristic
576	C₂×C₄	#13133190	1	1	yes	characteristic
577	C₂×C₄	#13133190	1	1	yes	characteristic
578	C₂×C₄	#13133199	1	1	yes	characteristic
579	C₂×C₄	#13133199	1	1	yes	characteristic
580	C₂×C₄	#13133203	1	1	yes	characteristic
581	C₂×C₄	#13133203	1	1	yes	characteristic
582	C₂×C₄	#13133210	1	1	yes	characteristic
583	C₂×C₄	#13133210	1	1	yes	characteristic
584	C₂×C₄	#13133210	1	1	yes	characteristic
585	C₂×C₄	#13133210	1	1	yes	characteristic
586	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
587	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
588	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
589	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
590	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
591	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
592	C₈	—	2	4	no	—
593	C₈	—	2	4	no	—
594	C₈	—	106	4	no	—
595	C₈	—	212	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	8	2	no	—
605	C₂²	—	8	2	no	—
606	C₂²	—	8	2	no	—
607	C₂²	#16810516	1	1	yes	characteristic
608	C₂²	#16810516	1	1	yes	characteristic
609	C₂²	#16810516	1	1	yes	characteristic
610	C₂²	#16810516	1	1	yes	characteristic
611	C₂²	C₂×#13133176	1	1	yes	characteristic
612	C₂²	C₂×#13133199	1	1	yes	characteristic
613	C₂²	C₂×#13133203	1	1	yes	characteristic
614	C₄	—	4	2	no	—
615	C₄	—	106	4	no	—
616	C₄	—	424	2	no	—
617	C₄	—	212	2	no	—
618	C₄	#16810516	1	1	yes	characteristic
619	C₄	#16810516	1	1	yes	characteristic
620	C₄	#16810516	1	1	yes	characteristic
621	C₄	#16810516	1	1	yes	characteristic
622	C₄	C₂×D₄×Dic₅₃	1	1	yes	characteristic
623	C₄	C₂×D₄×Dic₅₃	1	1	yes	characteristic
624	C₄	C₂×#13133190	1	1	yes	characteristic
625	C₄	C₂×#13133210	1	1	yes	characteristic
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	8	2	no	—
633	C₂	#20275386	1	2	yes	direct product factor
634	C₂	C₂×#16810516	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13133190
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₂×C₅₃×#413	C₂
socle	C₂²×C₅₃	#388
prime radical	C₂²×#41×C₅₃	C₂²
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	C₂×#413	D₅₃
hypocenter	C₅₃	C₂×#1932
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#413

Complements

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

N	H ≅ G/N	type
1. C₂×#16810672	C₂	semidirect
4. C₂×M₁₆×Dic₅₃	C₂	semidirect
5. #20275386	C₂	direct (N × H)
6. C₂×#16810395	C₂	semidirect
7. C₂×#16810384	C₂	semidirect
14. #16810672	C₂²	semidirect
24. M₁₆×Dic₅₃	C₂²	semidirect
27. #16810395	C₂²	semidirect
28. #16810384	C₂²	semidirect
32. C₅₃×#413	C₄	semidirect
34. C₂×#101×C₅₃	C₄	semidirect
35. C₂×#100×C₅₃	C₄	semidirect
102. #101×C₅₃	C₂×C₄	semidirect
103. #100×C₅₃	C₂×C₄	semidirect
324. C₂×C₅₃	#1932	semidirect
343. #413	Dic₅₃	semidirect
345. C₂×#101	Dic₅₃	semidirect
346. C₂×#100	Dic₅₃	semidirect
353. C₅₃	C₂×#1932	semidirect
418. #101	C₂×Dic₅₃	semidirect
419. #100	C₂×Dic₅₃	semidirect
633. C₂	#20275386	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×#16810672	2
C₂×#16810640	2
C₂²×#13133144	2
C₂×M₁₆×Dic₅₃	2
#20275386	2
C₂×#16810395	2
C₂×#16810384	2
C₂×C₅₃×#413	2
C₂×#1932	53

Subgroups — C2×#20275386 #27386675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20275386 #27386675