Subgroups — C₂×#20276113 #27412809

Order 13568.

1078 conjugacy classes of subgroups.

The subgroup lattice has 592 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×#16810671	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16810671	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13133134	C₂	1	1	yes	maximal, characteristic
5	C₂²×#13133134	C₂	1	1	yes	maximal, characteristic
6	#20276113	C₂	1	8	yes	maximal, direct product factor
7	C₂×#16810381	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#100×C₅₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11719917	C₂²	1	1	yes	characteristic
10	C₂²×#11719917	C₂²	1	1	yes	characteristic
11	C₂²×#11719917	C₂²	1	1	yes	characteristic
12	C₂²×#11719917	C₂²	1	1	yes	characteristic
13	#16810672	—	2	2	no	—
14	#16810672	C₂²	1	4	yes	complemented
15	#16810671	—	2	2	no	—
16	#16810671	—	2	2	no	—
17	#16810671	C₂²	1	4	yes	complemented
18	#16810671	C₂²	1	4	yes	complemented
19	C₂×#13133153	—	2	2	no	—
20	C₂×#13133152	—	2	2	no	—
21	C₂×#13133152	—	2	2	no	—
22	C₂×#13133134	—	2	2	no	—
23	C₂×#13133134	—	2	2	no	—
24	C₂×#13133134	—	2	2	no	—
25	C₂×#13133134	—	2	2	no	—
26	C₂×#13133134	C₂²	1	4	yes	—
27	C₂×#13133134	C₂²	1	4	yes	—
28	#16810381	C₂²	1	4	yes	complemented
29	C₂³×D₄×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	C₂×#100×C₅₃	—	2	2	no	—
33	C₂×#100×C₅₃	—	2	2	no	—
34	C₂×#100×C₅₃	C₂²	1	4	yes	—
35	C₂×#11719917	—	2	1	no	—
36	C₂×#11719917	—	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	—	2	1	no	—
46	C₂×#11719917	—	2	1	no	—
47	C₂×#11719917	—	2	1	no	—
48	C₂×#11719917	—	2	1	no	—
49	C₂×#11719917	—	2	1	no	—
50	C₂×#11719917	—	2	1	no	—
51	C₂×#11719917	D₄	1	2	yes	—
52	C₂×#11719917	D₄	1	2	yes	—
53	C₂×#11719917	D₄	1	2	yes	—
54	C₂×#11719917	D₄	1	2	yes	—
55	C₂×#11719917	C₂³	1	2	yes	—
56	C₂×#11719917	C₂³	1	2	yes	—
57	C₂×#11719917	C₂³	1	2	yes	—
58	C₂×#11719917	C₂³	1	2	yes	—
59	C₂²×#88322	—	2	1	no	—
60	C₂²×#88322	—	2	1	no	—
61	C₂²×#88322	—	2	1	no	—
62	C₂²×#88322	—	2	1	no	—
63	#13133153	—	2	8	no	—
64	#13133152	—	2	8	no	—
65	#13133152	—	2	8	no	—
66	#13133134	—	2	8	no	—
67	#13133134	—	2	8	no	—
68	C₂⁵×C₅₃	Q₈	1	2	yes	—
69	C₂²×D₄×C₅₃	—	2	1	no	—
70	C₂²×D₄×C₅₃	—	2	1	no	—
71	C₂²×D₄×C₅₃	—	2	1	no	—
72	C₂²×D₄×C₅₃	—	2	1	no	—
73	C₂²×D₄×C₅₃	—	2	1	no	—
74	C₂²×D₄×C₅₃	—	2	1	no	—
75	C₂²×D₄×C₅₃	—	2	1	no	—
76	C₂²×D₄×C₅₃	—	2	1	no	—
77	C₂²×D₄×C₅₃	—	2	1	no	—
78	C₂²×D₄×C₅₃	—	2	1	no	—
79	C₂²×D₄×C₅₃	—	2	1	no	—
80	C₂²×D₄×C₅₃	—	2	1	no	—
81	C₂²×D₄×C₅₃	Q₈	1	2	yes	—
82	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₅₃	—	2	1	no	—
85	C₂×M₁₆×C₅₃	—	2	1	no	—
86	C₂×M₁₆×C₅₃	—	2	1	no	—
87	C₂×M₁₆×C₅₃	—	2	1	no	—
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	D₄	1	2	yes	—
93	C₂×M₁₆×C₅₃	D₄	1	2	yes	—
94	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
95	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
96	C₂²×C₈×C₅₃	—	2	1	no	—
97	C₂²×C₈×C₅₃	—	2	1	no	—
98	#100×C₅₃	—	2	8	no	—
99	C₂⁴×C₅₃	—	2	2	no	—
100	C₂⁴×C₅₃	—	2	2	no	—
101	C₂⁴×C₅₃	—	2	2	no	—
102	C₂⁴×C₅₃	—	2	2	no	—
103	C₂⁴×C₅₃	—	2	2	no	—
104	C₂⁴×C₅₃	—	2	2	no	—
105	C₂⁴×C₅₃	—	8	4	no	—
106	C₂⁴×C₅₃	C₂×Q₈	1	4	yes	—
107	C₂⁴×C₅₃	C₂×Q₈	1	1	yes	characteristic
108	C₂×D₄×C₅₃	—	2	2	no	—
109	C₂×D₄×C₅₃	—	2	2	no	—
110	C₂×D₄×C₅₃	—	2	2	no	—
111	C₂×D₄×C₅₃	—	2	2	no	—
112	C₂×D₄×C₅₃	—	2	2	no	—
113	C₂×D₄×C₅₃	—	2	2	no	—
114	C₂×D₄×C₅₃	—	2	2	no	—
115	C₂×D₄×C₅₃	—	2	2	no	—
116	C₂×D₄×C₅₃	—	2	2	no	—
117	C₂×D₄×C₅₃	—	2	2	no	—
118	C₂×D₄×C₅₃	—	2	2	no	—
119	C₂×D₄×C₅₃	—	2	2	no	—
120	C₂×D₄×C₅₃	—	4	1	no	—
121	C₂×D₄×C₅₃	—	4	1	no	—
122	C₂×D₄×C₅₃	—	4	1	no	—
123	C₂×D₄×C₅₃	—	4	1	no	—
124	C₂×D₄×C₅₃	—	4	1	no	—
125	C₂×D₄×C₅₃	—	4	1	no	—
126	C₂×D₄×C₅₃	—	4	1	no	—
127	C₂×D₄×C₅₃	—	4	1	no	—
128	C₂×D₄×C₅₃	—	4	1	no	—
129	C₂×D₄×C₅₃	—	4	1	no	—
130	C₂×D₄×C₅₃	—	4	1	no	—
131	C₂×D₄×C₅₃	—	4	1	no	—
132	C₂×D₄×C₅₃	—	4	1	no	—
133	C₂×D₄×C₅₃	—	4	1	no	—
134	C₂×D₄×C₅₃	—	4	1	no	—
135	C₂×D₄×C₅₃	—	4	1	no	—
136	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
143	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
144	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
145	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
146	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
147	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
148	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
149	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
150	M₁₆×C₅₃	—	2	2	no	—
151	M₁₆×C₅₃	—	2	2	no	—
152	M₁₆×C₅₃	—	2	2	no	—
153	M₁₆×C₅₃	—	2	2	no	—
154	M₁₆×C₅₃	—	2	2	no	—
155	M₁₆×C₅₃	—	4	1	no	—
156	M₁₆×C₅₃	—	4	1	no	—
157	M₁₆×C₅₃	C₂×D₄	1	4	yes	—
158	C₂×C₈×C₅₃	—	2	2	no	—
159	C₂×C₈×C₅₃	—	2	2	no	—
160	C₂×C₈×C₅₃	—	2	2	no	—
161	C₂×C₈×C₅₃	—	2	2	no	—
162	C₂×C₈×C₅₃	—	4	1	no	—
163	C₂×C₈×C₅₃	—	4	1	no	—
164	#11719917	—	2	2	no	—
165	#11719917	—	2	2	no	—
166	#11719917	—	2	2	no	—
167	#11719917	—	2	2	no	—
168	#11719917	—	2	2	no	—
169	#11719917	—	2	2	no	—
170	#11719917	—	2	2	no	—
171	#11719917	—	2	2	no	—
172	#11719917	—	2	2	no	—
173	#11719917	—	2	2	no	—
174	#11719917	—	4	1	no	—
175	#11719917	—	4	1	no	—
176	#11719917	—	4	1	no	—
177	#11719917	—	4	1	no	—
178	#11719917	C₂×D₄	1	4	yes	—
179	#11719917	C₂×D₄	1	4	yes	—
180	C₂×#88322	—	2	2	no	—
181	C₂×#88322	—	2	2	no	—
182	C₂×#88322	—	2	2	no	—
183	C₂×#88322	—	2	2	no	—
184	C₂×#88322	—	2	2	no	—
185	C₂×#88322	—	2	2	no	—
186	C₂×#88322	—	2	2	no	—
187	C₂×#88322	—	2	2	no	—
188	C₂×#88322	—	4	1	no	—
189	C₂×#88322	—	4	1	no	—
190	C₂×#88322	—	4	1	no	—
191	C₂×#88322	—	4	1	no	—
192	C₂³×C₅₃	—	2	4	no	—
193	C₂³×C₅₃	—	2	4	no	—
194	C₂³×C₅₃	—	2	4	no	—
195	C₂³×C₅₃	—	4	2	no	—
196	C₂³×C₅₃	—	4	2	no	—
197	C₂³×C₅₃	—	4	2	no	—
198	C₂³×C₅₃	—	4	2	no	—
199	C₂³×C₅₃	—	4	2	no	—
200	C₂³×C₅₃	—	8	4	no	—
201	C₂³×C₅₃	—	8	4	no	—
202	C₂³×C₅₃	—	8	4	no	—
203	C₂³×C₅₃	—	8	4	no	—
204	C₂³×C₅₃	—	8	4	no	—
205	C₂³×C₅₃	—	8	4	no	—
206	C₂³×C₅₃	—	8	4	no	—
207	C₂³×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
208	C₂³×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
209	C₂³×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
210	C₂³×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
211	C₂³×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
212	C₂³×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
213	C₂³×C₅₃	C₂²×Q₈	1	1	yes	characteristic
214	D₄×C₅₃	—	4	2	no	—
215	D₄×C₅₃	—	4	2	no	—
216	D₄×C₅₃	—	4	2	no	—
217	D₄×C₅₃	—	4	2	no	—
218	D₄×C₅₃	—	4	2	no	—
219	D₄×C₅₃	—	4	2	no	—
220	D₄×C₅₃	—	4	2	no	—
221	D₄×C₅₃	—	4	2	no	—
222	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
223	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
224	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
225	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
226	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
227	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
228	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
229	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
230	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
231	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
232	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
233	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
234	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
235	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
236	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
237	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
238	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
239	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
240	C₂×C₄×C₅₃	#126	1	1	yes	characteristic
241	C₂×C₄×C₅₃	#126	1	1	yes	characteristic
242	C₂×C₄×C₅₃	#126	1	1	yes	characteristic
243	C₂×C₄×C₅₃	#126	1	1	yes	characteristic
244	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
250	C₈×C₅₃	—	2	4	no	—
251	C₈×C₅₃	—	4	2	no	—
252	#88322	—	2	4	no	—
253	#88322	—	2	4	no	—
254	#88322	—	4	2	no	—
255	#88322	—	4	2	no	—
256	C₂×#2069	—	53	1	no	maximal, Sylow
257	C₂²×C₅₃	—	2	2	no	—
258	C₂²×C₅₃	—	2	2	no	—
259	C₂²×C₅₃	—	2	2	no	—
260	C₂²×C₅₃	—	4	1	no	—
261	C₂²×C₅₃	—	4	1	no	—
262	C₂²×C₅₃	—	4	1	no	—
263	C₂²×C₅₃	—	4	1	no	—
264	C₂²×C₅₃	—	4	4	no	—
265	C₂²×C₅₃	—	8	4	no	—
266	C₂²×C₅₃	—	8	4	no	—
267	C₂²×C₅₃	—	8	4	no	—
268	C₂²×C₅₃	—	8	4	no	—
269	C₂²×C₅₃	—	8	4	no	—
270	C₂²×C₅₃	—	8	4	no	—
271	C₂²×C₅₃	—	8	4	no	—
272	C₂²×C₅₃	#396	1	1	yes	characteristic
273	C₂²×C₅₃	#396	1	1	yes	characteristic
274	C₂²×C₅₃	#396	1	1	yes	characteristic
275	C₂²×C₅₃	#396	1	1	yes	characteristic
276	C₂²×C₅₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
277	C₂²×C₅₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
278	C₂²×C₅₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
279	C₄×C₅₃	#396	1	1	yes	characteristic
280	C₄×C₅₃	#396	1	1	yes	characteristic
281	C₄×C₅₃	#396	1	1	yes	characteristic
282	C₄×C₅₃	#396	1	1	yes	characteristic
283	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
284	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
285	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
286	C₄×C₅₃	C₂×#126	1	1	yes	characteristic
287	C₂×#430	—	53	1	no	—
288	C₂×#430	—	53	1	no	—
289	C₂×#430	—	53	1	no	—
290	C₂²×#100	—	53	1	no	—
291	C₂²×#100	—	53	1	no	—
292	C₂²×#100	D₅₃	1	1	yes	characteristic
293	#2069	—	53	8	no	—
294	C₂×#338	—	53	1	no	—
295	C₂×C₅₃	—	2	1	no	—
296	C₂×C₅₃	—	2	1	no	—
297	C₂×C₅₃	—	2	1	no	—
298	C₂×C₅₃	—	2	1	no	—
299	C₂×C₅₃	—	2	1	no	—
300	C₂×C₅₃	—	2	1	no	—
301	C₂×C₅₃	—	8	4	no	—
302	C₂×C₅₃	#2069	1	2	yes	complemented
303	C₂×C₅₃	C₂×#396	1	1	yes	characteristic
304	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic
305	C₂²×M₁₆	—	53	1	no	—
306	C₂²×M₁₆	—	53	1	no	—
307	C₂²×M₁₆	—	53	1	no	—
308	C₂²×M₁₆	—	53	1	no	—
309	C₂²×M₁₆	C₂×D₅₃	1	1	yes	characteristic
310	C₂²×M₁₆	C₂×D₅₃	1	1	yes	characteristic
311	#430	—	53	4	no	—
312	#430	—	53	4	no	—
313	#430	—	53	4	no	—
314	#430	—	106	2	no	—
315	#430	—	106	2	no	—
316	#430	—	106	2	no	—
317	C₂×#108	—	106	2	no	—
318	C₂×#108	—	106	2	no	—
319	C₂×#108	—	106	2	no	—
320	C₂×#100	—	2	2	no	—
321	C₂×#100	—	2	2	no	—
322	C₂×#100	—	53	4	no	—
323	C₂×#100	—	53	4	no	—
324	C₂×#100	—	106	2	no	—
325	C₂×#100	—	106	2	no	—
326	C₂×#100	—	106	2	no	—
327	C₂×#100	—	106	2	no	—
328	C₂×#100	C₂×D₅₃	1	4	yes	—
329	#338	—	53	4	no	—
330	C₅₃	C₂×#2069	1	1	yes	characteristic, complemented, Sylow
331	C₂⁵	Dic₁₀₆	1	2	yes	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	—	2	1	no	—
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	Dic₁₀₆	1	2	yes	—
345	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
346	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	53	2	no	—
356	C₂×M₁₆	—	53	2	no	—
357	C₂×M₁₆	—	53	2	no	—
358	C₂×M₁₆	—	53	2	no	—
359	C₂×M₁₆	—	53	2	no	—
360	C₂×M₁₆	—	53	2	no	—
361	C₂×M₁₆	—	53	2	no	—
362	C₂×M₁₆	—	53	2	no	—
363	C₂×M₁₆	—	106	1	no	—
364	C₂×M₁₆	—	106	1	no	—
365	C₂×M₁₆	—	106	1	no	—
366	C₂×M₁₆	—	106	1	no	—
367	C₂×M₁₆	—	106	1	no	—
368	C₂×M₁₆	—	106	1	no	—
369	C₂×M₁₆	—	106	1	no	—
370	C₂×M₁₆	—	106	1	no	—
371	C₂×M₁₆	—	106	1	no	—
372	C₂×M₁₆	—	106	1	no	—
373	C₂×M₁₆	—	106	1	no	—
374	C₂×M₁₆	—	106	1	no	—
375	C₂×M₁₆	—	106	1	no	—
376	C₂×M₁₆	—	106	1	no	—
377	C₂×M₁₆	—	106	1	no	—
378	C₂×M₁₆	—	106	1	no	—
379	C₂×M₁₆	C₂²⋊D₅₃	1	2	yes	—
380	C₂×M₁₆	C₂²⋊D₅₃	1	2	yes	—
381	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
382	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
383	C₂²×C₈	—	2	1	no	—
384	C₂²×C₈	—	2	1	no	—
385	C₂²×C₈	—	106	1	no	—
386	C₂²×C₈	—	106	1	no	—
387	C₂²×C₈	—	106	1	no	—
388	C₂²×C₈	—	106	1	no	—
389	#108	—	106	8	no	—
390	#108	—	106	8	no	—
391	#108	—	106	8	no	—
392	#100	—	2	8	no	—
393	#100	—	106	8	no	—
394	#100	—	106	8	no	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	—	2	2	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	8	4	no	—
402	C₂⁴	C₂×Dic₁₀₆	1	4	yes	—
403	C₂⁴	C₂×Dic₁₀₆	1	1	yes	characteristic
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	4	1	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	1	no	—
425	C₂×D₄	—	4	1	no	—
426	C₂×D₄	—	4	1	no	—
427	C₂×D₄	—	4	1	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂²×C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
433	C₂²×C₄	#11719945	1	1	yes	characteristic
434	C₂²×C₄	#11719945	1	1	yes	characteristic
435	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
436	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
437	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
438	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
439	C₂²×C₄	#11719947	1	1	yes	characteristic
440	C₂²×C₄	#11719947	1	1	yes	characteristic
441	C₂²×C₄	#11719947	1	1	yes	characteristic
442	C₂²×C₄	#11719947	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
445	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
446	M₁₆	—	2	2	no	—
447	M₁₆	—	2	2	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	4	1	no	—
452	M₁₆	—	4	1	no	—
453	M₁₆	—	53	4	no	—
454	M₁₆	—	53	4	no	—
455	M₁₆	—	106	2	no	—
456	M₁₆	—	106	2	no	—
457	M₁₆	—	106	2	no	—
458	M₁₆	—	106	2	no	—
459	M₁₆	—	106	2	no	—
460	M₁₆	—	106	2	no	—
461	M₁₆	—	106	2	no	—
462	M₁₆	—	106	2	no	—
463	M₁₆	—	106	2	no	—
464	M₁₆	—	106	2	no	—
465	M₁₆	—	212	1	no	—
466	M₁₆	—	212	1	no	—
467	M₁₆	—	212	1	no	—
468	M₁₆	—	212	1	no	—
469	M₁₆	C₂×C₂²⋊D₅₃	1	4	yes	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	4	1	no	—
475	C₂×C₈	—	4	1	no	—
476	C₂×C₈	—	106	2	no	—
477	C₂×C₈	—	106	2	no	—
478	C₂×C₈	—	106	2	no	—
479	C₂×C₈	—	106	2	no	—
480	C₂×C₈	—	106	2	no	—
481	C₂×C₈	—	106	2	no	—
482	C₂×C₈	—	106	2	no	—
483	C₂×C₈	—	106	2	no	—
484	C₂×C₈	—	212	1	no	—
485	C₂×C₈	—	212	1	no	—
486	C₂×C₈	—	212	1	no	—
487	C₂×C₈	—	212	1	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	8	4	no	—
497	C₂³	—	8	4	no	—
498	C₂³	—	8	4	no	—
499	C₂³	—	8	4	no	—
500	C₂³	—	8	4	no	—
501	C₂³	—	8	4	no	—
502	C₂³	—	8	4	no	—
503	C₂³	#13133194	1	1	yes	characteristic
504	C₂³	#13133194	1	1	yes	characteristic
505	C₂³	#13133194	1	1	yes	characteristic
506	C₂³	#13133194	1	1	yes	characteristic
507	C₂³	#13133196	1	1	yes	characteristic
508	C₂³	#13133196	1	1	yes	characteristic
509	C₂³	C₂²×Dic₁₀₆	1	1	yes	characteristic
510	D₄	—	4	2	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	C₂×C₄	#13133188	1	1	yes	characteristic
519	C₂×C₄	#13133188	1	1	yes	characteristic
520	C₂×C₄	#13133188	1	1	yes	characteristic
521	C₂×C₄	#13133188	1	1	yes	characteristic
522	C₂×C₄	#13133189	1	1	yes	characteristic
523	C₂×C₄	#13133189	1	1	yes	characteristic
524	C₂×C₄	#13133189	1	1	yes	characteristic
525	C₂×C₄	#13133189	1	1	yes	characteristic
526	C₂×C₄	#13133190	1	1	yes	characteristic
527	C₂×C₄	#13133190	1	1	yes	characteristic
528	C₂×C₄	#13133190	1	1	yes	characteristic
529	C₂×C₄	#13133190	1	1	yes	characteristic
530	C₂×C₄	#13133194	1	1	yes	characteristic
531	C₂×C₄	#13133194	1	1	yes	characteristic
532	C₂×C₄	#13133194	1	1	yes	characteristic
533	C₂×C₄	#13133194	1	1	yes	characteristic
534	C₂×C₄	#13133196	1	1	yes	characteristic
535	C₂×C₄	#13133196	1	1	yes	characteristic
536	C₂×C₄	#13133210	1	1	yes	characteristic
537	C₂×C₄	#13133210	1	1	yes	characteristic
538	C₂×C₄	#13133210	1	1	yes	characteristic
539	C₂×C₄	#13133210	1	1	yes	characteristic
540	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
541	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
542	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
543	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
544	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
545	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
546	C₈	—	2	4	no	—
547	C₈	—	4	2	no	—
548	C₈	—	106	4	no	—
549	C₈	—	106	4	no	—
550	C₈	—	212	2	no	—
551	C₈	—	212	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	8	4	no	—
561	C₂²	—	8	4	no	—
562	C₂²	—	8	4	no	—
563	C₂²	—	8	4	no	—
564	C₂²	—	8	4	no	—
565	C₂²	—	8	4	no	—
566	C₂²	—	8	4	no	—
567	C₂²	#16810546	1	1	yes	characteristic
568	C₂²	#16810546	1	1	yes	characteristic
569	C₂²	#16810546	1	1	yes	characteristic
570	C₂²	#16810546	1	1	yes	characteristic
571	C₂²	C₂×#13133194	1	1	yes	characteristic
572	C₂²	C₂×#13133194	1	1	yes	characteristic
573	C₂²	C₂×#13133196	1	1	yes	characteristic
574	C₄	#16810546	1	1	yes	characteristic
575	C₄	#16810546	1	1	yes	characteristic
576	C₄	#16810546	1	1	yes	characteristic
577	C₄	#16810546	1	1	yes	characteristic
578	C₄	C₂×#13133188	1	1	yes	characteristic
579	C₄	C₂×#13133189	1	1	yes	characteristic
580	C₄	C₂×#13133190	1	1	yes	characteristic
581	C₄	C₂×#13133210	1	1	yes	characteristic
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	8	4	no	—
589	C₂	#20276113	1	2	yes	direct product factor
590	C₂	C₂×#16810546	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16810546
commutator, cosocle	C₂²×C₄×C₅₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₂²×#100×C₅₃	C₂
socle	C₂²×C₅₃	#396
prime radical	C₂³×D₄×C₅₃	C₂²
hypercenter	C₂²×#100	D₅₃
hypocenter	C₅₃	C₂×#2069
LCS	G ▷ C₂²×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#100

Complements

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

N	H ≅ G/N	type
1. C₂×#16810672	C₂	semidirect
2. C₂×#16810671	C₂	semidirect
3. C₂×#16810671	C₂	semidirect
6. #20276113	C₂	direct (N × H)
7. C₂×#16810381	C₂	semidirect
14. #16810672	C₂²	semidirect
17. #16810671	C₂²	semidirect
18. #16810671	C₂²	semidirect
28. #16810381	C₂²	semidirect
302. C₂×C₅₃	#2069	semidirect
330. C₅₃	C₂×#2069	semidirect
589. C₂	#20276113	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×#16810671	2
C₂²×#13133134	2
#20276113	2
C₂×#16810381	2
C₂²×#100×C₅₃	2
C₂×#2069	53

Subgroups — C2×#20276113 #27412809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20276113 #27412809