Subgroups — C₂×#123×D₅₃ #20287945

Order 6784.

1968 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13133202	C₂	1	2	yes	maximal, complemented
4	C₂×#13133201	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13133200	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13133199	C₂	1	2	yes	maximal, complemented
7	C₂×#13133198	C₂	1	1	yes	maximal, characteristic, complemented
8	#123×D₅₃	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₄⋊C₄×D₅₃	C₂	1	2	yes	maximal, complemented
10	C₂×C₂²⋊C₄×D₅₃	C₂	1	2	yes	maximal, complemented
11	C₂×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₅₃	C₂²	1	1	yes	characteristic
14	C₂⁴×D₅₃	C₂²	1	1	yes	characteristic
15	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₅₃	—	2	8	no	—
19	C₂×D₄×D₅₃	C₂²	1	8	yes	—
20	C₂³×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₄×D₅₃	—	2	8	no	—
22	C₂²×C₄×D₅₃	C₂²	1	2	yes	—
23	C₂²×C₄×D₅₃	C₂²	1	2	yes	—
24	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₅₃	C₂²	1	8	yes	complemented
26	C₂²×C₄×D₅₃	C₂²	1	2	yes	complemented
27	#13133202	C₂²	1	16	yes	complemented
28	#13133201	C₂²	1	8	yes	complemented
29	#13133200	C₂²	1	8	yes	complemented
30	#13133199	C₂²	1	16	yes	complemented
31	#13133198	C₂²	1	8	yes	complemented
32	C₂×C₄⋊Dic₅₃	C₂²	1	2	yes	complemented
33	C₂×#11719919	C₂²	1	2	yes	complemented
34	C₂×#11719919	C₂²	1	2	yes	complemented
35	C₄⋊C₄×D₅₃	C₂²	1	16	yes	complemented
36	C₂×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
37	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#11719921	C₂²	1	2	yes	complemented
39	C₂×#11719921	C₂²	1	2	yes	complemented
40	C₂×#11719921	C₂²	1	2	yes	complemented
41	C₂²⋊C₄×D₅₃	C₂²	1	8	yes	complemented
42	C₂²⋊C₄×D₅₃	C₂²	1	16	yes	complemented
43	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
44	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	#123×C₅₃	C₂²	1	8	yes	complemented
46	C₂×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
47	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
48	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
49	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
50	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
51	C₂³×D₅₃	—	2	8	no	—
52	C₂³×D₅₃	—	2	4	no	—
53	C₂³×D₅₃	—	2	8	no	—
54	C₂³×D₅₃	D₄	1	8	yes	—
55	C₂³×D₅₃	C₂³	1	4	yes	—
56	C₂³×D₅₃	C₂³	1	1	yes	characteristic
57	C₂³×D₅₃	C₂³	1	4	yes	—
58	C₂³×D₅₃	C₂³	1	1	yes	characteristic
59	C₂³×D₅₃	C₂³	1	1	yes	characteristic
60	C₂×D₄×C₅₃	—	2	4	no	—
61	C₂×D₄×C₅₃	C₂³	1	4	yes	—
62	C₂²×C₄×C₅₃	—	2	4	no	—
63	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
64	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
65	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₅₃	C₂³	1	4	yes	complemented
67	C₂×C₂²⋊D₅₃	—	2	4	no	—
68	C₂×C₂²⋊D₅₃	—	2	4	no	—
69	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
70	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
71	C₂²×Dic₅₃	—	2	4	no	—
72	C₂²×Dic₅₃	C₂³	1	2	yes	—
73	C₂²×Dic₅₃	C₂³	1	2	yes	—
74	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
75	C₂²×Dic₅₃	C₂³	1	4	yes	complemented
76	D₄×D₅₃	—	2	32	no	—
77	C₂×D₂₁₂	—	2	4	no	—
78	C₂×D₂₁₂	C₂³	1	4	yes	—
79	C₂×C₄×D₅₃	—	2	8	no	—
80	C₂×C₄×D₅₃	—	2	32	no	—
81	C₂×C₄×D₅₃	—	2	8	no	—
82	C₂×C₄×D₅₃	—	2	4	no	—
83	C₂×C₄×D₅₃	—	2	8	no	—
84	C₂×C₄×D₅₃	C₂³	1	8	yes	—
85	C₂×C₄×D₅₃	C₂³	1	8	yes	—
86	C₂×C₄×D₅₃	C₂³	1	4	yes	—
87	C₂×C₄×D₅₃	C₂³	1	8	yes	complemented
88	C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
89	C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
90	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
91	C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
92	C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
93	#11719921	C₂³	1	8	yes	complemented
94	#11719921	C₂³	1	8	yes	complemented
95	#11719921	C₂³	1	8	yes	complemented
96	C₄⋊Dic₅₃	C₂³	1	8	yes	complemented
97	#11719919	C₂³	1	8	yes	complemented
98	#11719919	C₂³	1	8	yes	complemented
99	C₂³×C₅₃	—	2	4	no	—
100	C₂³×C₅₃	—	2	2	no	—
101	C₂³×C₅₃	—	2	4	no	—
102	C₂³×C₅₃	C₂×D₄	1	4	yes	—
103	C₂³×C₅₃	C₂⁴	1	2	yes	—
104	C₂³×C₅₃	C₂⁴	1	2	yes	—
105	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
106	C₂²×D₅₃	—	2	4	no	—
107	C₂²×D₅₃	—	2	32	no	—
108	C₂²×D₅₃	—	2	16	no	—
109	C₂²×D₅₃	—	2	2	no	—
110	C₂²×D₅₃	—	2	4	no	—
111	C₂²×D₅₃	—	2	8	no	—
112	C₂²×D₅₃	—	2	16	no	—
113	C₂²×D₅₃	—	4	16	no	—
114	C₂²×D₅₃	C₂×D₄	1	4	yes	—
115	C₂²×D₅₃	C₂×D₄	1	16	yes	—
116	C₂²×D₅₃	C₂×D₄	1	4	yes	—
117	C₂²×D₅₃	#41	1	8	yes	—
118	C₂²×D₅₃	C₂⁴	1	2	yes	—
119	C₂²×D₅₃	C₂⁴	1	2	yes	—
120	C₂²×D₅₃	C₂⁴	1	2	yes	—
121	D₄×C₅₃	—	2	8	no	—
122	C₂×C₄×C₅₃	—	2	4	no	—
123	C₂×C₄×C₅₃	—	2	8	no	—
124	C₂×C₄×C₅₃	—	2	2	no	—
125	C₂×C₄×C₅₃	—	2	4	no	—
126	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
127	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
128	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
129	C₂²⋊D₅₃	—	2	8	no	—
130	C₂²⋊D₅₃	—	2	8	no	—
131	C₂×Dic₅₃	—	2	4	no	—
132	C₂×Dic₅₃	—	2	8	no	—
133	C₂×Dic₅₃	—	2	2	no	—
134	C₂×Dic₅₃	—	2	4	no	—
135	C₂×Dic₅₃	C₂⁴	1	4	yes	—
136	C₂×Dic₅₃	C₂⁴	1	2	yes	—
137	C₂×Dic₅₃	C₂⁴	1	4	yes	—
138	D₂₁₂	—	2	8	no	—
139	C₄×D₅₃	—	2	16	no	—
140	C₄×D₅₃	—	2	16	no	—
141	C₄×D₅₃	—	2	8	no	—
142	C₄×D₅₃	—	2	16	no	—
143	C₂²×C₅₃	—	2	8	no	—
144	C₂²×C₅₃	—	2	4	no	—
145	C₂²×C₅₃	—	2	2	no	—
146	C₂²×C₅₃	—	2	4	no	—
147	C₂²×C₅₃	—	4	4	no	—
148	C₂²×C₅₃	C₂²×D₄	1	4	yes	—
149	C₂²×C₅₃	C₂²×D₄	1	2	yes	—
150	C₂²×C₅₃	C₂×#41	1	4	yes	—
151	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
152	C₂×D₅₃	—	2	8	no	—
153	C₂×D₅₃	—	2	4	no	—
154	C₂×D₅₃	—	2	32	no	—
155	C₂×D₅₃	—	2	2	no	—
156	C₂×D₅₃	—	2	4	no	—
157	C₂×D₅₃	—	4	4	no	—
158	C₂×D₅₃	—	4	16	no	—
159	C₂×D₅₃	#123	1	16	yes	direct product factor
160	C₂×D₅₃	C₂²×D₄	1	4	yes	—
161	C₂×D₅₃	C₂²×D₄	1	4	yes	—
162	C₂×D₅₃	C₂×#41	1	8	yes	—
163	C₄×C₅₃	—	2	4	no	—
164	C₄×C₅₃	—	2	2	no	—
165	C₄×C₅₃	—	2	4	no	—
166	Dic₅₃	—	2	4	no	—
167	Dic₅₃	—	2	2	no	—
168	Dic₅₃	—	2	4	no	—
169	C₂²×#123	—	53	1	no	maximal, Sylow
170	C₂×C₅₃	—	2	4	no	—
171	C₂×C₅₃	—	4	2	no	—
172	C₂×C₅₃	C₂×#123	1	4	yes	complemented
173	C₂×C₅₃	C₂³×D₄	1	1	yes	characteristic
174	C₂×C₅₃	C₂²×#41	1	2	yes	—
175	D₅₃	—	2	4	no	—
176	D₅₃	—	4	2	no	—
177	D₅₃	C₂×#123	1	8	yes	direct product factor
178	C₂³×D₄	—	53	1	no	—
179	C₂⁴×C₄	—	53	1	no	—
180	C₂×#123	—	53	1	no	—
181	C₂×#123	—	53	1	no	—
182	C₂×#123	—	53	16	no	—
183	C₂×#123	—	53	2	no	—
184	C₂×#123	—	53	2	no	—
185	C₂×#123	—	53	1	no	—
186	C₂×#123	D₅₃	1	1	yes	characteristic, direct product factor
187	C₂²×C₄⋊C₄	—	53	2	no	—
188	C₂²×C₂²⋊C₄	—	53	1	no	—
189	C₂²×C₂²⋊C₄	—	53	2	no	—
190	C₅₃	C₂²×#123	1	1	yes	characteristic, complemented, Sylow
191	C₂⁵	—	53	1	no	—
192	C₂⁵	—	53	1	no	—
193	C₂²×D₄	—	53	1	no	—
194	C₂²×D₄	—	53	1	no	—
195	C₂²×D₄	—	53	8	no	—
196	C₂²×D₄	—	53	1	no	—
197	C₂²×D₄	—	106	8	no	—
198	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic
199	C₂³×C₄	—	53	1	no	—
200	C₂³×C₄	—	53	2	no	—
201	C₂³×C₄	—	53	2	no	—
202	C₂³×C₄	—	53	1	no	—
203	C₂³×C₄	—	53	2	no	—
204	C₂³×C₄	—	53	8	no	—
205	C₂³×C₄	—	106	8	no	—
206	C₂³×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
207	#123	—	53	8	no	—
208	#123	—	53	8	no	—
209	#123	—	53	16	no	—
210	#123	—	53	16	no	—
211	#123	—	53	8	no	—
212	#123	C₂×D₅₃	1	8	yes	direct product factor
213	C₂×C₄⋊C₄	—	53	2	no	—
214	C₂×C₄⋊C₄	—	53	2	no	—
215	C₂×C₄⋊C₄	—	53	2	no	—
216	C₂×C₄⋊C₄	—	53	16	no	—
217	C₂×C₄⋊C₄	C₂×D₅₃	1	2	yes	complemented
218	C₂×C₂²⋊C₄	—	53	1	no	—
219	C₂×C₂²⋊C₄	—	53	2	no	—
220	C₂×C₂²⋊C₄	—	53	2	no	—
221	C₂×C₂²⋊C₄	—	53	2	no	—
222	C₂×C₂²⋊C₄	—	53	2	no	—
223	C₂×C₂²⋊C₄	—	53	8	no	—
224	C₂×C₂²⋊C₄	—	53	16	no	—
225	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
226	C₂×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
227	C₂⁴	—	53	1	no	—
228	C₂⁴	—	53	8	no	—
229	C₂⁴	—	53	4	no	—
230	C₂⁴	—	53	1	no	—
231	C₂⁴	—	53	4	no	—
232	C₂⁴	—	53	1	no	—
233	C₂⁴	—	106	8	no	—
234	C₂⁴	—	106	4	no	—
235	C₂⁴	—	106	8	no	—
236	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
237	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
238	C₂×D₄	—	2	4	no	—
239	C₂×D₄	—	53	4	no	—
240	C₂×D₄	—	53	4	no	—
241	C₂×D₄	—	53	4	no	—
242	C₂×D₄	—	106	4	no	—
243	C₂×D₄	—	106	32	no	—
244	C₂×D₄	—	106	4	no	—
245	C₂×D₄	—	106	4	no	—
246	C₂×D₄	C₂²×D₅₃	1	4	yes	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	53	4	no	—
249	C₂²×C₄	—	53	2	no	—
250	C₂²×C₄	—	53	2	no	—
251	C₂²×C₄	—	53	1	no	—
252	C₂²×C₄	—	53	8	no	—
253	C₂²×C₄	—	53	8	no	—
254	C₂²×C₄	—	53	4	no	—
255	C₂²×C₄	—	53	8	no	—
256	C₂²×C₄	—	106	8	no	—
257	C₂²×C₄	—	106	8	no	—
258	C₂²×C₄	—	106	8	no	—
259	C₂²×C₄	—	106	32	no	—
260	C₂²×C₄	—	106	4	no	—
261	C₂²×C₄	—	106	4	no	—
262	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
263	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
264	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
265	C₂²×C₄	C₂²×D₅₃	1	4	yes	complemented
266	C₄⋊C₄	—	53	8	no	—
267	C₄⋊C₄	—	53	8	no	—
268	C₄⋊C₄	—	53	8	no	—
269	C₄⋊C₄	C₂²×D₅₃	1	8	yes	complemented
270	C₂²⋊C₄	—	53	4	no	—
271	C₂²⋊C₄	—	53	8	no	—
272	C₂²⋊C₄	—	53	8	no	—
273	C₂²⋊C₄	—	53	8	no	—
274	C₂²⋊C₄	—	53	8	no	—
275	C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
276	C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
277	C₂³	—	2	4	no	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	4	no	—
280	C₂³	—	53	4	no	—
281	C₂³	—	53	8	no	—
282	C₂³	—	53	2	no	—
283	C₂³	—	53	16	no	—
284	C₂³	—	53	4	no	—
285	C₂³	—	53	2	no	—
286	C₂³	—	53	2	no	—
287	C₂³	—	106	32	no	—
288	C₂³	—	106	16	no	—
289	C₂³	—	106	8	no	—
290	C₂³	—	106	16	no	—
291	C₂³	—	106	4	no	—
292	C₂³	—	106	2	no	—
293	C₂³	—	106	4	no	—
294	C₂³	—	212	16	no	—
295	C₂³	D₄×D₅₃	1	4	yes	—
296	C₂³	C₂³×D₅₃	1	2	yes	—
297	C₂³	C₂³×D₅₃	1	2	yes	—
298	C₂³	C₂³×D₅₃	1	1	yes	characteristic
299	D₄	—	2	8	no	—
300	D₄	—	106	8	no	—
301	D₄	—	106	8	no	—
302	D₄	—	106	8	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	53	4	no	—
308	C₂×C₄	—	53	4	no	—
309	C₂×C₄	—	53	2	no	—
310	C₂×C₄	—	106	16	no	—
311	C₂×C₄	—	106	16	no	—
312	C₂×C₄	—	106	16	no	—
313	C₂×C₄	—	106	8	no	—
314	C₂×C₄	—	106	8	no	—
315	C₂×C₄	—	106	4	no	—
316	C₂×C₄	—	106	2	no	—
317	C₂×C₄	—	106	4	no	—
318	C₂×C₄	C₂³×D₅₃	1	4	yes	—
319	C₂×C₄	C₂³×D₅₃	1	4	yes	—
320	C₂×C₄	C₂³×D₅₃	1	2	yes	—
321	C₂²	—	2	8	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	4	4	no	—
326	C₂²	—	53	16	no	—
327	C₂²	—	53	4	no	—
328	C₂²	—	53	8	no	—
329	C₂²	—	53	4	no	—
330	C₂²	—	106	32	no	—
331	C₂²	—	106	8	no	—
332	C₂²	—	106	4	no	—
333	C₂²	—	106	2	no	—
334	C₂²	—	106	4	no	—
335	C₂²	—	212	16	no	—
336	C₂²	—	212	4	no	—
337	C₂²	C₂×D₄×D₅₃	1	4	yes	—
338	C₂²	C₂×D₄×D₅₃	1	2	yes	—
339	C₂²	#41×D₅₃	1	4	yes	—
340	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
341	C₄	—	2	4	no	—
342	C₄	—	2	2	no	—
343	C₄	—	2	4	no	—
344	C₄	—	106	4	no	—
345	C₄	—	106	2	no	—
346	C₄	—	106	4	no	—
347	C₂	—	2	4	no	—
348	C₂	—	4	2	no	—
349	C₂	—	53	8	no	—
350	C₂	—	106	4	no	—
351	C₂	—	212	2	no	—
352	C₂	#123×D₅₃	1	4	yes	direct product factor
353	C₂	C₂²×D₄×D₅₃	1	1	yes	characteristic
354	C₂	C₂×#41×D₅₃	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂³×D₅₃
commutator	C₂²×C₅₃	C₂⁵
Frattini	C₂²	C₂⁴×D₅₃
Fitting	C₂×#123×C₅₃	C₂
socle	C₂³×C₅₃	C₂⁴
hypercenter	C₂×#123	D₅₃
hypocenter	C₅₃	C₂²×#123
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#123

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄×D₅₃	C₂	semidirect
3. C₂×#13133202	C₂	semidirect
4. C₂×#13133201	C₂	semidirect
5. C₂×#13133200	C₂	semidirect
6. C₂×#13133199	C₂	semidirect
7. C₂×#13133198	C₂	semidirect
8. #123×D₅₃	C₂	direct (N × H)
9. C₂×C₄⋊C₄×D₅₃	C₂	semidirect
10. C₂×C₂²⋊C₄×D₅₃	C₂	semidirect
11. C₂×C₂²⋊C₄×D₅₃	C₂	semidirect
12. C₂×#123×C₅₃	C₂	semidirect
20. C₂³×Dic₅₃	C₂²	semidirect
25. C₂²×C₄×D₅₃	C₂²	semidirect
26. C₂²×C₄×D₅₃	C₂²	semidirect
27. #13133202	C₂²	semidirect
28. #13133201	C₂²	semidirect
29. #13133200	C₂²	semidirect
30. #13133199	C₂²	semidirect
31. #13133198	C₂²	semidirect
32. C₂×C₄⋊Dic₅₃	C₂²	semidirect
33. C₂×#11719919	C₂²	semidirect
34. C₂×#11719919	C₂²	semidirect
35. C₄⋊C₄×D₅₃	C₂²	semidirect
36. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
37. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
38. C₂×#11719921	C₂²	semidirect
39. C₂×#11719921	C₂²	semidirect
40. C₂×#11719921	C₂²	semidirect
41. C₂²⋊C₄×D₅₃	C₂²	semidirect
42. C₂²⋊C₄×D₅₃	C₂²	semidirect
44. C₂³×C₄×C₅₃	C₂²	semidirect
45. #123×C₅₃	C₂²	semidirect
46. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
47. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
48. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
66. C₂²×C₄×C₅₃	C₂³	semidirect
75. C₂²×Dic₅₃	C₂³	semidirect
87. C₂×C₄×D₅₃	C₂³	semidirect
88. C₄⋊C₄×C₅₃	C₂³	semidirect
89. C₂²⋊C₄×C₅₃	C₂³	semidirect
90. C₂²⋊C₄×C₅₃	C₂³	semidirect
91. C₂²⋊Dic₅₃	C₂³	semidirect
92. C₂²⋊Dic₅₃	C₂³	semidirect
93. #11719921	C₂³	semidirect
94. #11719921	C₂³	semidirect
95. #11719921	C₂³	semidirect
96. C₄⋊Dic₅₃	C₂³	semidirect
97. #11719919	C₂³	semidirect
98. #11719919	C₂³	semidirect
159. C₂×D₅₃	#123	direct (N × H)
172. C₂×C₅₃	C₂×#123	semidirect
177. D₅₃	C₂×#123	direct (N × H)
186. C₂×#123	D₅₃	direct (N × H)
190. C₅₃	C₂²×#123	semidirect
206. C₂³×C₄	C₂×D₅₃	semidirect
212. #123	C₂×D₅₃	direct (N × H)
217. C₂×C₄⋊C₄	C₂×D₅₃	semidirect
225. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect
226. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect
265. C₂²×C₄	C₂²×D₅₃	semidirect
269. C₄⋊C₄	C₂²×D₅₃	semidirect
275. C₂²⋊C₄	C₂²×D₅₃	semidirect
276. C₂²⋊C₄	C₂²×D₅₃	semidirect
352. C₂	#123×D₅₃	direct (N × H)

Subgroups — C2×#123×D53 #20287945

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#123×D₅₃ #20287945