Subgroups — C₂×#16811205 #20288050

Order 6784.

1336 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811205	C₂	1	16	yes	maximal, direct product factor
2	C₂×#13133212	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13133210	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13133204	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13133203	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13133200	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#13133198	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13133195	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13133189	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13133188	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#13133185	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133185	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13133177	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁴×D₅₃	C₂²	1	1	yes	characteristic
18	C₂²×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
23	C₂³×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
26	#13133212	C₂²	1	8	yes	complemented
27	#13133210	C₂²	1	8	yes	complemented
28	#13133204	C₂²	1	8	yes	complemented
29	#13133203	C₂²	1	8	yes	complemented
30	#13133200	C₂²	1	8	yes	complemented
31	#13133198	C₂²	1	8	yes	complemented
32	#13133195	C₂²	1	8	yes	complemented
33	#13133189	C₂²	1	8	yes	complemented
34	#13133188	C₂²	1	8	yes	complemented
35	#13133185	C₂²	1	8	yes	complemented
36	#13133185	C₂²	1	8	yes	complemented
37	C₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
38	#13133177	C₂²	1	8	yes	complemented
39	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
41	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
42	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
43	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×#11719921	C₂²	1	1	yes	characteristic
51	C₂×#11719921	C₂²	1	1	yes	characteristic
52	C₂×#11719921	C₂²	1	1	yes	characteristic
53	C₂×#11719921	C₂²	1	1	yes	characteristic
54	C₂×#11719921	C₂²	1	1	yes	characteristic
55	C₂×#11719921	C₂²	1	1	yes	characteristic
56	C₂²⋊C₄×D₅₃	C₂²	1	8	yes	complemented
57	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	#121×C₅₃	C₂²	1	8	yes	complemented
64	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
68	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
69	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
70	C₂³×D₅₃	—	2	4	no	—
71	C₂³×D₅₃	—	4	2	no	—
72	C₂³×D₅₃	—	4	2	no	—
73	C₂³×D₅₃	C₂³	1	1	yes	characteristic
74	C₂³×D₅₃	C₂³	1	1	yes	characteristic
75	C₂³×D₅₃	C₂³	1	4	yes	—
76	C₂×D₄×C₅₃	—	4	2	no	—
77	C₂×D₄×C₅₃	—	4	2	no	—
78	C₂×D₄×C₅₃	—	4	2	no	—
79	C₂×D₄×C₅₃	C₂³	1	4	yes	—
80	C₂×D₄×C₅₃	C₂³	1	4	yes	—
81	C₂×D₄×C₅₃	C₂³	1	4	yes	complemented
82	C₂²×C₄×C₅₃	—	4	2	no	—
83	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₅₃	C₂³	1	4	yes	complemented
88	C₂×C₂²⋊D₅₃	—	2	4	no	—
89	C₂×C₂²⋊D₅₃	—	2	4	no	—
90	C₂×C₂²⋊D₅₃	—	4	2	no	—
91	C₂×C₂²⋊D₅₃	—	4	2	no	—
92	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
96	C₂²×Dic₅₃	—	4	2	no	—
97	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
98	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
99	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
100	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
101	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
102	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
103	C₂²×Dic₅₃	C₂³	1	4	yes	complemented
104	C₂×C₄×D₅₃	—	4	2	no	—
105	C₂×C₄×D₅₃	—	4	2	no	—
106	C₂×C₄×D₅₃	C₂³	1	4	yes	—
107	C₂×C₄×D₅₃	C₂³	1	4	yes	—
108	C₂×Dic₁₀₆	—	4	2	no	—
109	C₂×Dic₁₀₆	C₂³	1	4	yes	complemented
110	C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
111	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
112	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
113	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
114	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
115	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
116	C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
117	C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
118	C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
119	#11719921	C₂³	1	4	yes	—
120	#11719921	C₂³	1	4	yes	—
121	#11719921	C₂³	1	4	yes	—
122	#11719921	C₂³	1	4	yes	—
123	#11719921	C₂³	1	4	yes	—
124	#11719921	C₂³	1	4	yes	—
125	C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
126	#11719919	C₂³	1	4	yes	complemented
127	#11719919	C₂³	1	4	yes	complemented
128	#11719919	C₂³	1	4	yes	complemented
129	#11719919	C₂³	1	4	yes	complemented
130	C₄×Dic₅₃	C₂³	1	4	yes	complemented
131	C₄×Dic₅₃	C₂³	1	4	yes	complemented
132	C₂³×C₅₃	—	2	2	no	—
133	C₂³×C₅₃	—	2	2	no	—
134	C₂³×C₅₃	—	2	2	no	—
135	C₂³×C₅₃	—	2	2	no	—
136	C₂³×C₅₃	—	2	2	no	—
137	C₂³×C₅₃	—	2	2	no	—
138	C₂³×C₅₃	—	2	2	no	—
139	C₂³×C₅₃	—	2	2	no	—
140	C₂³×C₅₃	—	2	2	no	—
141	C₂³×C₅₃	C₂⁴	1	2	yes	—
142	C₂³×C₅₃	C₂⁴	1	2	yes	—
143	C₂³×C₅₃	C₂⁴	1	2	yes	—
144	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
145	C₂²×D₅₃	—	2	2	no	—
146	C₂²×D₅₃	—	2	2	no	—
147	C₂²×D₅₃	—	2	2	no	—
148	C₂²×D₅₃	—	2	2	no	—
149	C₂²×D₅₃	—	2	2	no	—
150	C₂²×D₅₃	—	2	8	no	—
151	C₂²×D₅₃	—	4	4	no	—
152	C₂²×D₅₃	—	4	4	no	—
153	C₂²×D₅₃	—	4	16	no	—
154	C₂²×D₅₃	#41	1	4	yes	—
155	C₂²×D₅₃	C₂⁴	1	2	yes	—
156	C₂²×D₅₃	C₂⁴	1	2	yes	—
157	D₄×C₅₃	—	4	4	no	—
158	D₄×C₅₃	—	4	4	no	—
159	D₄×C₅₃	—	4	4	no	—
160	C₂×C₄×C₅₃	—	2	2	no	—
161	C₂×C₄×C₅₃	—	2	2	no	—
162	C₂×C₄×C₅₃	—	2	2	no	—
163	C₂×C₄×C₅₃	—	2	2	no	—
164	C₂×C₄×C₅₃	—	4	4	no	—
165	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
166	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
169	C₂²⋊D₅₃	—	2	8	no	—
170	C₂²⋊D₅₃	—	2	8	no	—
171	C₂²⋊D₅₃	—	4	4	no	—
172	C₂²⋊D₅₃	—	4	4	no	—
173	C₂×Dic₅₃	—	2	2	no	—
174	C₂×Dic₅₃	—	2	2	no	—
175	C₂×Dic₅₃	—	2	2	no	—
176	C₂×Dic₅₃	—	2	2	no	—
177	C₂×Dic₅₃	—	2	2	no	—
178	C₂×Dic₅₃	—	2	2	no	—
179	C₂×Dic₅₃	—	4	4	no	—
180	C₂×Dic₅₃	C₂⁴	1	2	yes	—
181	C₂×Dic₅₃	C₂⁴	1	2	yes	—
182	C₂×Dic₅₃	C₂⁴	1	2	yes	—
183	C₂×Dic₅₃	C₂⁴	1	2	yes	—
184	C₂×Dic₅₃	C₂⁴	1	2	yes	—
185	C₂×Dic₅₃	C₂⁴	1	2	yes	—
186	C₄×D₅₃	—	4	4	no	—
187	C₄×D₅₃	—	4	4	no	—
188	Dic₁₀₆	—	4	4	no	—
189	C₂²×C₅₃	—	2	2	no	—
190	C₂²×C₅₃	—	2	2	no	—
191	C₂²×C₅₃	—	2	2	no	—
192	C₂²×C₅₃	—	2	2	no	—
193	C₂²×C₅₃	—	2	2	no	—
194	C₂²×C₅₃	—	2	2	no	—
195	C₂²×C₅₃	—	2	2	no	—
196	C₂²×C₅₃	—	2	2	no	—
197	C₂²×C₅₃	—	2	2	no	—
198	C₂²×C₅₃	—	4	4	no	—
199	C₂²×C₅₃	—	4	4	no	—
200	C₂²×C₅₃	—	4	4	no	—
201	C₂²×C₅₃	C₂×#41	1	2	yes	—
202	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
203	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
204	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
205	C₂×D₅₃	—	2	8	no	—
206	C₂×D₅₃	—	2	2	no	—
207	C₂×D₅₃	—	2	2	no	—
208	C₂×D₅₃	—	2	2	no	—
209	C₂×D₅₃	—	2	2	no	—
210	C₂×D₅₃	—	2	2	no	—
211	C₂×D₅₃	—	4	16	no	—
212	C₂×D₅₃	—	4	4	no	—
213	C₂×D₅₃	C₂×#41	1	4	yes	—
214	C₄×C₅₃	—	2	2	no	—
215	C₄×C₅₃	—	2	2	no	—
216	C₄×C₅₃	—	2	2	no	—
217	C₄×C₅₃	—	2	2	no	—
218	Dic₅₃	—	2	2	no	—
219	Dic₅₃	—	2	2	no	—
220	Dic₅₃	—	2	2	no	—
221	Dic₅₃	—	2	2	no	—
222	Dic₅₃	—	2	2	no	—
223	Dic₅₃	—	2	2	no	—
224	C₂×#538	—	53	1	no	maximal, Sylow
225	C₂×C₅₃	—	4	2	no	—
226	C₂×C₅₃	—	4	2	no	—
227	C₂×C₅₃	—	4	2	no	—
228	C₂×C₅₃	#538	1	4	yes	complemented
229	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
230	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
232	D₅₃	—	2	4	no	—
233	D₅₃	—	4	2	no	—
234	#538	—	53	16	no	—
235	C₂×#126	—	53	1	no	—
236	C₂×#126	—	53	1	no	—
237	C₂×#124	—	53	1	no	—
238	C₂×#124	—	53	1	no	—
239	C₂×#123	—	53	1	no	—
240	C₂×#123	—	53	1	no	—
241	C₂×C₂²⋊Q₈	—	53	1	no	—
242	C₂×#121	—	53	1	no	—
243	C₂×#121	—	53	1	no	—
244	C₂×#121	D₅₃	1	1	yes	characteristic, complemented
245	C₂×#120	—	53	1	no	—
246	C₂×#120	—	53	1	no	—
247	C₂×C₄×D₄	—	53	1	no	—
248	C₂×C₄×D₄	—	53	1	no	—
249	C₂²×C₂²⋊C₄	—	53	1	no	—
250	C₅₃	C₂×#538	1	1	yes	characteristic, complemented, Sylow
251	C₂⁵	—	53	1	no	—
252	C₂²×Q₈	—	53	1	no	—
253	C₂²×D₄	—	53	1	no	—
254	C₂²×D₄	—	53	1	no	—
255	C₂²×D₄	—	53	1	no	—
256	C₂²×D₄	—	53	1	no	—
257	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic
258	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic
259	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
260	C₂³×C₄	—	53	1	no	—
261	C₂³×C₄	—	53	1	no	—
262	C₂³×C₄	—	53	1	no	—
263	C₂³×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
264	#126	—	53	8	no	—
265	#126	—	53	8	no	—
266	#124	—	53	8	no	—
267	#124	—	53	8	no	—
268	#123	—	53	8	no	—
269	#123	—	53	8	no	—
270	C₂²⋊Q₈	—	53	8	no	—
271	#121	—	53	8	no	—
272	#121	—	53	8	no	—
273	#121	C₂×D₅₃	1	8	yes	complemented
274	#120	—	53	8	no	—
275	#120	—	53	8	no	—
276	C₄×D₄	—	53	8	no	—
277	C₄×D₄	—	53	8	no	—
278	C₂×C₄⋊C₄	—	53	1	no	—
279	C₂×C₄⋊C₄	—	53	1	no	—
280	C₂×C₄⋊C₄	—	53	1	no	—
281	C₂×C₄⋊C₄	—	53	1	no	—
282	C₂×C₄⋊C₄	—	53	1	no	—
283	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
284	C₂×C₂²⋊C₄	—	53	1	no	—
285	C₂×C₂²⋊C₄	—	53	1	no	—
286	C₂×C₂²⋊C₄	—	53	1	no	—
287	C₂×C₂²⋊C₄	—	53	1	no	—
288	C₂×C₂²⋊C₄	—	53	1	no	—
289	C₂×C₂²⋊C₄	—	53	1	no	—
290	C₂×C₂²⋊C₄	—	53	1	no	—
291	C₂×C₂²⋊C₄	—	53	1	no	—
292	C₂×C₂²⋊C₄	—	53	1	no	—
293	C₂×C₂²⋊C₄	—	53	1	no	—
294	C₂×C₂²⋊C₄	—	53	1	no	—
295	C₂×C₂²⋊C₄	—	53	1	no	—
296	C₂×C₂²⋊C₄	—	53	8	no	—
297	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
299	C₂×C₄²	—	53	1	no	—
300	C₂×C₄²	—	53	1	no	—
301	C₂⁴	—	53	1	no	—
302	C₂⁴	—	53	1	no	—
303	C₂⁴	—	53	4	no	—
304	C₂⁴	—	106	4	no	—
305	C₂⁴	—	212	2	no	—
306	C₂⁴	—	212	2	no	—
307	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
308	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
309	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
310	C₂×Q₈	—	53	4	no	—
311	C₂×Q₈	—	212	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	53	4	no	—
316	C₂×D₄	—	53	4	no	—
317	C₂×D₄	—	53	4	no	—
318	C₂×D₄	—	53	4	no	—
319	C₂×D₄	—	106	4	no	—
320	C₂×D₄	—	106	4	no	—
321	C₂×D₄	—	212	2	no	—
322	C₂×D₄	—	212	2	no	—
323	C₂×D₄	C₂²×D₅₃	1	4	yes	—
324	C₂×D₄	C₂²×D₅₃	1	4	yes	—
325	C₂×D₄	C₂²×D₅₃	1	4	yes	complemented
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	53	1	no	—
328	C₂²×C₄	—	53	1	no	—
329	C₂²×C₄	—	53	1	no	—
330	C₂²×C₄	—	53	1	no	—
331	C₂²×C₄	—	53	1	no	—
332	C₂²×C₄	—	53	1	no	—
333	C₂²×C₄	—	53	4	no	—
334	C₂²×C₄	—	53	4	no	—
335	C₂²×C₄	—	53	4	no	—
336	C₂²×C₄	—	212	2	no	—
337	C₂²×C₄	—	212	2	no	—
338	C₂²×C₄	—	212	2	no	—
339	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
341	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
342	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
343	C₂²×C₄	C₂²×D₅₃	1	4	yes	complemented
344	C₄⋊C₄	—	53	4	no	—
345	C₄⋊C₄	—	53	4	no	—
346	C₄⋊C₄	—	53	4	no	—
347	C₄⋊C₄	—	53	4	no	—
348	C₄⋊C₄	—	53	4	no	—
349	C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
350	C₂²⋊C₄	—	53	4	no	—
351	C₂²⋊C₄	—	53	4	no	—
352	C₂²⋊C₄	—	53	4	no	—
353	C₂²⋊C₄	—	53	4	no	—
354	C₂²⋊C₄	—	53	4	no	—
355	C₂²⋊C₄	—	53	4	no	—
356	C₂²⋊C₄	—	53	4	no	—
357	C₂²⋊C₄	—	53	4	no	—
358	C₂²⋊C₄	—	53	4	no	—
359	C₂²⋊C₄	—	53	4	no	—
360	C₂²⋊C₄	—	53	4	no	—
361	C₂²⋊C₄	—	53	4	no	—
362	C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
363	C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
364	C₄²	—	53	4	no	—
365	C₄²	—	53	4	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	53	4	no	—
376	C₂³	—	53	2	no	—
377	C₂³	—	53	2	no	—
378	C₂³	—	106	8	no	—
379	C₂³	—	106	2	no	—
380	C₂³	—	106	2	no	—
381	C₂³	—	106	2	no	—
382	C₂³	—	106	2	no	—
383	C₂³	—	106	2	no	—
384	C₂³	—	212	4	no	—
385	C₂³	—	212	4	no	—
386	C₂³	—	212	16	no	—
387	C₂³	C₂³×D₅₃	1	2	yes	—
388	C₂³	C₂³×D₅₃	1	2	yes	—
389	C₂³	C₂³×D₅₃	1	2	yes	—
390	C₂³	C₂³×D₅₃	1	1	yes	characteristic
391	Q₈	—	212	4	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	4	no	—
395	D₄	—	106	8	no	—
396	D₄	—	106	8	no	—
397	D₄	—	212	4	no	—
398	D₄	—	212	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	53	2	no	—
405	C₂×C₄	—	53	2	no	—
406	C₂×C₄	—	53	2	no	—
407	C₂×C₄	—	53	2	no	—
408	C₂×C₄	—	53	2	no	—
409	C₂×C₄	—	53	2	no	—
410	C₂×C₄	—	106	2	no	—
411	C₂×C₄	—	106	2	no	—
412	C₂×C₄	—	106	2	no	—
413	C₂×C₄	—	106	2	no	—
414	C₂×C₄	—	106	2	no	—
415	C₂×C₄	—	106	2	no	—
416	C₂×C₄	—	212	4	no	—
417	C₂×C₄	—	212	4	no	—
418	C₂×C₄	—	212	4	no	—
419	C₂×C₄	C₂³×D₅₃	1	2	yes	—
420	C₂×C₄	C₂³×D₅₃	1	2	yes	—
421	C₂×C₄	C₂³×D₅₃	1	2	yes	—
422	C₂×C₄	C₂³×D₅₃	1	2	yes	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	53	4	no	—
436	C₂²	—	106	2	no	—
437	C₂²	—	106	2	no	—
438	C₂²	—	106	8	no	—
439	C₂²	—	106	2	no	—
440	C₂²	—	106	2	no	—
441	C₂²	—	106	2	no	—
442	C₂²	—	212	16	no	—
443	C₂²	—	212	4	no	—
444	C₂²	#41×D₅₃	1	2	yes	—
445	C₂²	#13133262	1	2	yes	—
446	C₂²	#13133262	1	2	yes	—
447	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	106	2	no	—
453	C₄	—	106	2	no	—
454	C₄	—	106	2	no	—
455	C₄	—	106	2	no	—
456	C₄	—	106	2	no	—
457	C₄	—	106	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	4	2	no	—
460	C₂	—	4	2	no	—
461	C₂	—	106	4	no	—
462	C₂	—	212	2	no	—
463	C₂	#16811205	1	4	yes	direct product factor
464	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
465	C₂	C₂×#13133262	1	1	yes	characteristic
466	C₂	C₂×#13133262	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₅₃
commutator	C₂²×C₅₃	C₂⁵
Frattini	C₂²	C₂⁴×D₅₃
Fitting	C₂×#121×C₅₃	C₂
socle	C₂³×C₅₃	C₂⁴
hypercenter	C₂×#121	D₅₃
hypocenter	C₅₃	C₂×#538
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. #16811205	C₂	direct (N × H)
2. C₂×#13133212	C₂	semidirect
3. C₂×#13133210	C₂	semidirect
4. C₂×#13133204	C₂	semidirect
5. C₂×#13133203	C₂	semidirect
6. C₂×#13133200	C₂	semidirect
7. C₂×#13133198	C₂	semidirect
8. C₂×#13133195	C₂	semidirect
9. C₂×#13133189	C₂	semidirect
10. C₂×#13133188	C₂	semidirect
11. C₂×#13133185	C₂	semidirect
12. C₂×#13133185	C₂	semidirect
13. C₂×C₄×C₂²⋊D₅₃	C₂	semidirect
14. C₂×#13133177	C₂	semidirect
15. C₂×C₂²⋊C₄×D₅₃	C₂	semidirect
16. C₂×#121×C₅₃	C₂	semidirect
18. C₂²×Dic₁₀₆	C₂²	semidirect
23. C₂³×Dic₅₃	C₂²	semidirect
26. #13133212	C₂²	semidirect
27. #13133210	C₂²	semidirect
28. #13133204	C₂²	semidirect
29. #13133203	C₂²	semidirect
30. #13133200	C₂²	semidirect
31. #13133198	C₂²	semidirect
32. #13133195	C₂²	semidirect
33. #13133189	C₂²	semidirect
34. #13133188	C₂²	semidirect
35. #13133185	C₂²	semidirect
36. #13133185	C₂²	semidirect
37. C₄×C₂²⋊D₅₃	C₂²	semidirect
38. #13133177	C₂²	semidirect
39. C₂×C₄⋊Dic₅₃	C₂²	semidirect
40. C₂×#11719919	C₂²	semidirect
41. C₂×#11719919	C₂²	semidirect
42. C₂×#11719919	C₂²	semidirect
43. C₂×#11719919	C₂²	semidirect
47. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
48. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
49. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
56. C₂²⋊C₄×D₅₃	C₂²	semidirect
57. C₂×C₄×Dic₅₃	C₂²	semidirect
58. C₂×C₄×Dic₅₃	C₂²	semidirect
61. C₂²×D₄×C₅₃	C₂²	semidirect
62. C₂³×C₄×C₅₃	C₂²	semidirect
63. #121×C₅₃	C₂²	semidirect
64. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
66. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
81. C₂×D₄×C₅₃	C₂³	semidirect
87. C₂²×C₄×C₅₃	C₂³	semidirect
103. C₂²×Dic₅₃	C₂³	semidirect
109. C₂×Dic₁₀₆	C₂³	semidirect
110. C₄⋊C₄×C₅₃	C₂³	semidirect
112. C₂²⋊C₄×C₅₃	C₂³	semidirect
116. C₂²⋊Dic₅₃	C₂³	semidirect
117. C₂²⋊Dic₅₃	C₂³	semidirect
118. C₂²⋊Dic₅₃	C₂³	semidirect
125. C₄⋊Dic₅₃	C₂³	semidirect
126. #11719919	C₂³	semidirect
127. #11719919	C₂³	semidirect
128. #11719919	C₂³	semidirect
129. #11719919	C₂³	semidirect
130. C₄×Dic₅₃	C₂³	semidirect
131. C₄×Dic₅₃	C₂³	semidirect
228. C₂×C₅₃	#538	semidirect
244. C₂×#121	D₅₃	semidirect
250. C₅₃	C₂×#538	semidirect
259. C₂²×D₄	C₂×D₅₃	semidirect
263. C₂³×C₄	C₂×D₅₃	semidirect
273. #121	C₂×D₅₃	semidirect
283. C₂×C₄⋊C₄	C₂×D₅₃	semidirect
298. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect
325. C₂×D₄	C₂²×D₅₃	semidirect
343. C₂²×C₄	C₂²×D₅₃	semidirect
349. C₄⋊C₄	C₂²×D₅₃	semidirect
363. C₂²⋊C₄	C₂²×D₅₃	semidirect
463. C₂	#16811205	direct (N × H)

Subgroups — C2×#16811205 #20288050

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16811205 #20288050