Subgroups — C₂×D₄×C₂²⋊D₅₃ #20288152

Order 6784.

2536 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊D₅₃	C₂	1	2	yes	maximal, complemented
2	C₂²×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₅₃	C₂	1	16	yes	maximal, direct product factor
4	C₂×#13133213	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13133191	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13133189	C₂	1	2	yes	maximal, complemented
7	C₂×#13133188	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13133186	C₂	1	2	yes	maximal, complemented
9	C₂×#13133185	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₅₃	C₂²	1	2	yes	complemented
14	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₂²⋊D₅₃	—	2	16	no	—
16	C₂²×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
18	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
19	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
20	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
22	C₂²×C₂²⋊D₅₃	C₂²	1	16	yes	complemented
23	C₂×D₄×D₅₃	—	2	8	no	—
24	C₂×D₄×D₅₃	C₂²	1	8	yes	complemented
25	C₂³×Dic₅₃	C₂²	1	2	yes	complemented
26	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
27	#13133213	C₂²	1	8	yes	complemented
28	#13133191	C₂²	1	8	yes	complemented
29	#13133189	C₂²	1	16	yes	complemented
30	#13133188	C₂²	1	8	yes	complemented
31	#13133186	C₂²	1	16	yes	complemented
32	#13133185	C₂²	1	16	yes	complemented
33	D₄×Dic₅₃	C₂²	1	8	yes	complemented
34	C₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
35	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
39	C₂×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
40	C₂×#11719921	C₂²	1	1	yes	characteristic, complemented
41	C₂×#11719921	C₂²	1	2	yes	complemented
42	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₂⁵×C₅₃	C₂²	1	2	yes	complemented
44	C₂²×D₄×C₅₃	—	2	8	no	—
45	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
46	C₂²×D₄×C₅₃	C₂²	1	2	yes	complemented
47	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
48	C₂²×D₄×C₅₃	C₂²	1	8	yes	complemented
49	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
50	C₂⁴×C₅₃	—	2	8	no	—
51	C₂⁴×C₅₃	—	2	8	no	—
52	C₂⁴×C₅₃	—	4	4	no	—
53	C₂⁴×C₅₃	C₂³	1	2	yes	—
54	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
55	C₂⁴×C₅₃	C₂³	1	2	yes	—
56	C₂⁴×C₅₃	C₂³	1	8	yes	complemented
57	C₂³×D₅₃	—	2	8	no	—
58	C₂³×D₅₃	—	2	8	no	—
59	C₂³×D₅₃	—	4	4	no	—
60	C₂³×D₅₃	C₂³	1	2	yes	—
61	C₂³×D₅₃	C₂³	1	1	yes	characteristic
62	C₂³×D₅₃	C₂³	1	8	yes	complemented
63	C₂×D₄×C₅₃	—	2	8	no	—
64	C₂×D₄×C₅₃	—	2	32	no	—
65	C₂×D₄×C₅₃	—	2	4	no	—
66	C₂×D₄×C₅₃	D₄	1	8	yes	complemented
67	C₂×D₄×C₅₃	C₂³	1	4	yes	—
68	C₂×D₄×C₅₃	C₂³	1	8	yes	complemented
69	C₂×D₄×C₅₃	C₂³	1	4	yes	complemented
70	C₂²×C₄×C₅₃	—	2	4	no	—
71	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	C₂³	1	4	yes	complemented
74	C₂×C₂²⋊D₅₃	—	2	8	no	—
75	C₂×C₂²⋊D₅₃	—	2	8	no	—
76	C₂×C₂²⋊D₅₃	—	2	8	no	—
77	C₂×C₂²⋊D₅₃	—	2	64	no	—
78	C₂×C₂²⋊D₅₃	—	2	8	no	—
79	C₂×C₂²⋊D₅₃	—	4	4	no	—
80	C₂×C₂²⋊D₅₃	D₄	1	8	yes	direct product factor
81	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
82	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
83	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
84	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
85	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
86	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
87	C₂²×Dic₅₃	—	2	8	no	—
88	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
89	C₂²×Dic₅₃	C₂³	1	2	yes	—
90	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
91	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
92	C₂²×Dic₅₃	C₂³	1	8	yes	complemented
93	D₄×D₅₃	—	2	32	no	—
94	C₂×D₂₁₂	—	2	4	no	—
95	C₂×D₂₁₂	C₂³	1	4	yes	complemented
96	C₂×C₄×D₅₃	—	2	4	no	—
97	C₂×C₄×D₅₃	C₂³	1	4	yes	complemented
98	C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
99	C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
100	C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
101	#11719921	C₂³	1	4	yes	complemented
102	#11719921	C₂³	1	8	yes	complemented
103	C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
104	#11719919	C₂³	1	4	yes	complemented
105	C₄×Dic₅₃	C₂³	1	4	yes	complemented
106	C₂³×C₅₃	—	2	4	no	—
107	C₂³×C₅₃	—	2	2	no	—
108	C₂³×C₅₃	—	2	4	no	—
109	C₂³×C₅₃	—	2	2	no	—
110	C₂³×C₅₃	—	2	4	no	—
111	C₂³×C₅₃	—	2	4	no	—
112	C₂³×C₅₃	—	2	16	no	—
113	C₂³×C₅₃	—	2	16	no	—
114	C₂³×C₅₃	—	2	4	no	—
115	C₂³×C₅₃	—	4	8	no	—
116	C₂³×C₅₃	—	4	32	no	—
117	C₂³×C₅₃	C₂×D₄	1	4	yes	complemented
118	C₂³×C₅₃	C₂×D₄	1	8	yes	complemented
119	C₂³×C₅₃	C₂⁴	1	4	yes	—
120	C₂³×C₅₃	C₂⁴	1	4	yes	—
121	C₂³×C₅₃	C₂⁴	1	2	yes	—
122	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
123	C₂²×D₅₃	—	2	2	no	—
124	C₂²×D₅₃	—	2	2	no	—
125	C₂²×D₅₃	—	2	4	no	—
126	C₂²×D₅₃	—	2	4	no	—
127	C₂²×D₅₃	—	2	16	no	—
128	C₂²×D₅₃	—	2	4	no	—
129	C₂²×D₅₃	—	2	16	no	—
130	C₂²×D₅₃	—	4	8	no	—
131	C₂²×D₅₃	—	4	32	no	—
132	C₂²×D₅₃	C₂×D₄	1	4	yes	complemented
133	C₂²×D₅₃	C₂⁴	1	4	yes	—
134	C₂²×D₅₃	C₂⁴	1	2	yes	—
135	D₄×C₅₃	—	2	16	no	—
136	D₄×C₅₃	—	2	8	no	—
137	D₄×C₅₃	C₂×D₄	1	16	yes	complemented
138	C₂×C₄×C₅₃	—	2	2	no	—
139	C₂×C₄×C₅₃	—	2	8	no	—
140	C₂×C₄×C₅₃	C₂×D₄	1	4	yes	complemented
141	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
142	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
143	C₂²⋊D₅₃	—	2	16	no	—
144	C₂²⋊D₅₃	—	2	16	no	—
145	C₂²⋊D₅₃	—	2	16	no	—
146	C₂²⋊D₅₃	—	2	16	no	—
147	C₂²⋊D₅₃	—	4	8	no	—
148	C₂²⋊D₅₃	C₂×D₄	1	16	yes	direct product factor
149	C₂×Dic₅₃	—	2	2	no	—
150	C₂×Dic₅₃	—	2	4	no	—
151	C₂×Dic₅₃	—	2	2	no	—
152	C₂×Dic₅₃	—	2	16	no	—
153	C₂×Dic₅₃	C₂×D₄	1	4	yes	complemented
154	C₂×Dic₅₃	C₂⁴	1	2	yes	—
155	C₂×Dic₅₃	C₂⁴	1	4	yes	—
156	C₂×Dic₅₃	C₂⁴	1	2	yes	—
157	C₂×Dic₅₃	C₂⁴	1	2	yes	—
158	D₂₁₂	—	2	8	no	—
159	C₄×D₅₃	—	2	8	no	—
160	C₂²×C₅₃	—	2	16	no	—
161	C₂²×C₅₃	—	2	8	no	—
162	C₂²×C₅₃	—	2	4	no	—
163	C₂²×C₅₃	—	2	2	no	—
164	C₂²×C₅₃	—	2	4	no	—
165	C₂²×C₅₃	—	2	2	no	—
166	C₂²×C₅₃	—	2	4	no	—
167	C₂²×C₅₃	—	2	4	no	—
168	C₂²×C₅₃	—	2	4	no	—
169	C₂²×C₅₃	—	4	32	no	—
170	C₂²×C₅₃	—	4	8	no	—
171	C₂²×C₅₃	C₂²×D₄	1	2	yes	—
172	C₂²×C₅₃	C₂²×D₄	1	2	yes	—
173	C₂²×C₅₃	C₂²×D₄	1	4	yes	complemented
174	C₂²×C₅₃	C₂²×D₄	1	8	yes	complemented
175	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
176	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
177	C₂×D₅₃	—	2	8	no	—
178	C₂×D₅₃	—	2	2	no	—
179	C₂×D₅₃	—	2	2	no	—
180	C₂×D₅₃	—	2	4	no	—
181	C₂×D₅₃	—	2	4	no	—
182	C₂×D₅₃	—	2	4	no	—
183	C₂×D₅₃	—	4	32	no	—
184	C₂×D₅₃	—	4	8	no	—
185	C₂×D₅₃	C₂²×D₄	1	4	yes	complemented
186	C₄×C₅₃	—	2	2	no	—
187	C₄×C₅₃	C₂²×D₄	1	4	yes	complemented
188	Dic₅₃	—	2	2	no	—
189	Dic₅₃	—	2	4	no	—
190	Dic₅₃	—	2	2	no	—
191	Dic₅₃	C₂²×D₄	1	4	yes	complemented
192	C₂×D₄²	—	53	1	no	maximal, Sylow
193	C₂×C₅₃	—	2	8	no	—
194	C₂×C₅₃	—	2	4	no	—
195	C₂×C₅₃	—	4	4	no	—
196	C₂×C₅₃	D₄²	1	4	yes	complemented
197	C₂×C₅₃	C₂³×D₄	1	1	yes	characteristic
198	C₂×C₅₃	C₂³×D₄	1	1	yes	characteristic
199	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
200	D₅₃	—	2	4	no	—
201	D₅₃	—	4	4	no	—
202	C₂³×D₄	—	53	2	no	—
203	C₂³×D₄	—	53	1	no	—
204	C₂³×D₄	D₅₃	1	1	yes	characteristic, complemented
205	D₄²	—	53	16	no	—
206	C₂×#127	—	53	1	no	—
207	C₂×#121	—	53	1	no	—
208	C₂×#121	—	53	2	no	—
209	C₂×#121	—	53	1	no	—
210	C₂×#120	—	53	2	no	—
211	C₂×#120	—	53	2	no	—
212	C₂×C₄×D₄	—	53	1	no	—
213	C₂×C₄×D₄	—	53	1	no	—
214	C₅₃	C₂×D₄²	1	1	yes	characteristic, complemented, Sylow
215	C₂⁵	—	53	2	no	—
216	C₂⁵	C₂×D₅₃	1	2	yes	complemented
217	C₂²×D₄	—	2	8	no	—
218	C₂²×D₄	—	53	1	no	—
219	C₂²×D₄	—	53	2	no	—
220	C₂²×D₄	—	53	2	no	—
221	C₂²×D₄	—	53	2	no	—
222	C₂²×D₄	—	53	2	no	—
223	C₂²×D₄	—	53	16	no	—
224	C₂²×D₄	—	53	2	no	—
225	C₂²×D₄	—	53	8	no	—
226	C₂²×D₄	—	53	1	no	—
227	C₂²×D₄	—	106	16	no	—
228	C₂²×D₄	—	106	8	no	—
229	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic
230	C₂²×D₄	C₂×D₅₃	1	2	yes	complemented
231	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
232	C₂²×D₄	C₂×D₅₃	1	8	yes	complemented
233	C₂³×C₄	—	53	2	no	—
234	C₂³×C₄	—	53	1	no	—
235	C₂³×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
236	#127	—	53	8	no	—
237	#121	—	53	8	no	—
238	#121	—	53	16	no	—
239	#121	—	53	8	no	—
240	#120	—	53	16	no	—
241	#120	—	53	16	no	—
242	C₄×D₄	—	53	8	no	—
243	C₄×D₄	—	53	8	no	—
244	C₂×C₄⋊C₄	—	53	1	no	—
245	C₂×C₄⋊C₄	—	53	1	no	—
246	C₂×C₂²⋊C₄	—	53	1	no	—
247	C₂×C₂²⋊C₄	—	53	2	no	—
248	C₂×C₂²⋊C₄	—	53	2	no	—
249	C₂×C₂²⋊C₄	—	53	1	no	—
250	C₂×C₂²⋊C₄	—	53	2	no	—
251	C₂×C₄²	—	53	1	no	—
252	C₂⁴	—	2	8	no	—
253	C₂⁴	—	2	8	no	—
254	C₂⁴	—	4	4	no	—
255	C₂⁴	—	53	1	no	—
256	C₂⁴	—	53	2	no	—
257	C₂⁴	—	53	8	no	—
258	C₂⁴	—	106	8	no	—
259	C₂⁴	—	106	8	no	—
260	C₂⁴	—	212	4	no	—
261	C₂⁴	C₂²×D₅₃	1	2	yes	—
262	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
263	C₂⁴	C₂²×D₅₃	1	2	yes	—
264	C₂⁴	C₂²×D₅₃	1	8	yes	complemented
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	32	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	53	8	no	—
269	C₂×D₄	—	53	4	no	—
270	C₂×D₄	—	53	8	no	—
271	C₂×D₄	—	53	8	no	—
272	C₂×D₄	—	53	8	no	—
273	C₂×D₄	—	53	8	no	—
274	C₂×D₄	—	53	8	no	—
275	C₂×D₄	—	53	4	no	—
276	C₂×D₄	—	106	8	no	—
277	C₂×D₄	—	106	64	no	—
278	C₂×D₄	—	106	8	no	—
279	C₂×D₄	—	106	8	no	—
280	C₂×D₄	—	106	8	no	—
281	C₂×D₄	—	106	32	no	—
282	C₂×D₄	—	106	4	no	—
283	C₂×D₄	—	212	4	no	—
284	C₂×D₄	C₂²⋊D₅₃	1	8	yes	direct product factor
285	C₂×D₄	C₂²×D₅₃	1	4	yes	—
286	C₂×D₄	C₂²×D₅₃	1	8	yes	complemented
287	C₂×D₄	C₂²×D₅₃	1	4	yes	complemented
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	53	1	no	—
290	C₂²×C₄	—	53	8	no	—
291	C₂²×C₄	—	53	1	no	—
292	C₂²×C₄	—	53	2	no	—
293	C₂²×C₄	—	53	1	no	—
294	C₂²×C₄	—	53	4	no	—
295	C₂²×C₄	—	106	8	no	—
296	C₂²×C₄	—	106	4	no	—
297	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²×D₅₃	1	4	yes	complemented
300	C₄⋊C₄	—	53	4	no	—
301	C₄⋊C₄	—	53	4	no	—
302	C₂²⋊C₄	—	53	4	no	—
303	C₂²⋊C₄	—	53	8	no	—
304	C₂²⋊C₄	—	53	8	no	—
305	C₂²⋊C₄	—	53	4	no	—
306	C₂²⋊C₄	—	53	8	no	—
307	C₄²	—	53	4	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	4	no	—
312	C₂³	—	2	4	no	—
313	C₂³	—	2	16	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	16	no	—
316	C₂³	—	2	4	no	—
317	C₂³	—	4	8	no	—
318	C₂³	—	4	32	no	—
319	C₂³	—	53	4	no	—
320	C₂³	—	53	2	no	—
321	C₂³	—	53	4	no	—
322	C₂³	—	106	16	no	—
323	C₂³	—	106	2	no	—
324	C₂³	—	106	2	no	—
325	C₂³	—	106	4	no	—
326	C₂³	—	106	4	no	—
327	C₂³	—	106	16	no	—
328	C₂³	—	106	4	no	—
329	C₂³	—	212	8	no	—
330	C₂³	—	212	32	no	—
331	C₂³	D₄×D₅₃	1	4	yes	complemented
332	C₂³	C₂×C₂²⋊D₅₃	1	8	yes	complemented
333	C₂³	C₂³×D₅₃	1	4	yes	—
334	C₂³	C₂³×D₅₃	1	2	yes	—
335	C₂³	C₂³×D₅₃	1	4	yes	—
336	C₂³	C₂³×D₅₃	1	1	yes	characteristic
337	D₄	—	2	16	no	—
338	D₄	—	2	8	no	—
339	D₄	—	53	16	no	—
340	D₄	—	106	16	no	—
341	D₄	—	106	16	no	—
342	D₄	—	106	16	no	—
343	D₄	—	106	16	no	—
344	D₄	—	106	8	no	—
345	D₄	—	212	8	no	—
346	D₄	C₂×C₂²⋊D₅₃	1	16	yes	direct product factor
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	53	4	no	—
350	C₂×C₄	—	53	2	no	—
351	C₂×C₄	—	53	2	no	—
352	C₂×C₄	—	53	4	no	—
353	C₂×C₄	—	53	2	no	—
354	C₂×C₄	—	106	16	no	—
355	C₂×C₄	—	106	4	no	—
356	C₂×C₄	—	106	2	no	—
357	C₂×C₄	—	106	2	no	—
358	C₂×C₄	—	106	8	no	—
359	C₂×C₄	C₂×C₂²⋊D₅₃	1	4	yes	complemented
360	C₂×C₄	C₂³×D₅₃	1	2	yes	—
361	C₂×C₄	C₂³×D₅₃	1	2	yes	—
362	C₂²	—	2	4	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	8	no	—
367	C₂²	—	2	16	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	4	no	—
371	C₂²	—	4	32	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	53	4	no	—
374	C₂²	—	106	2	no	—
375	C₂²	—	106	2	no	—
376	C₂²	—	106	8	no	—
377	C₂²	—	106	4	no	—
378	C₂²	—	106	4	no	—
379	C₂²	—	106	4	no	—
380	C₂²	—	212	32	no	—
381	C₂²	—	212	8	no	—
382	C₂²	C₂×D₄×D₅₃	1	2	yes	—
383	C₂²	C₂×D₄×D₅₃	1	4	yes	complemented
384	C₂²	C₂²×C₂²⋊D₅₃	1	2	yes	—
385	C₂²	C₂²×C₂²⋊D₅₃	1	8	yes	complemented
386	C₂²	#13133262	1	2	yes	—
387	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	53	4	no	—
390	C₄	—	106	4	no	—
391	C₄	—	106	2	no	—
392	C₄	—	106	2	no	—
393	C₄	C₂²×C₂²⋊D₅₃	1	4	yes	complemented
394	C₂	—	2	4	no	—
395	C₂	—	2	8	no	—
396	C₂	—	4	4	no	—
397	C₂	—	106	4	no	—
398	C₂	—	212	4	no	—
399	C₂	D₄×C₂²⋊D₅₃	1	4	yes	direct product factor
400	C₂	C₂²×D₄×D₅₃	1	1	yes	characteristic
401	C₂	C₂³×C₂²⋊D₅₃	1	1	yes	characteristic
402	C₂	C₂×#13133262	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₅₃
commutator	C₂²×C₅₃	C₂⁵
Frattini	C₂²	C₂⁴×D₅₃
Fitting	C₂³×D₄×C₅₃	C₂
socle	C₂³×C₅₃	C₂⁴
hypercenter	C₂³×D₄	D₅₃
hypocenter	C₅₃	C₂×D₄²
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂³×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₂²⋊D₅₃	C₂	semidirect
2. C₂²×D₄×D₅₃	C₂	semidirect
3. D₄×C₂²⋊D₅₃	C₂	direct (N × H)
4. C₂×#13133213	C₂	semidirect
5. C₂×#13133191	C₂	semidirect
6. C₂×#13133189	C₂	semidirect
7. C₂×#13133188	C₂	semidirect
8. C₂×#13133186	C₂	semidirect
9. C₂×#13133185	C₂	semidirect
10. C₂×D₄×Dic₅₃	C₂	semidirect
11. C₂×C₄×C₂²⋊D₅₃	C₂	semidirect
12. C₂³×D₄×C₅₃	C₂	semidirect
13. C₂⁴×D₅₃	C₂²	semidirect
14. C₂²×D₂₁₂	C₂²	semidirect
17. C₂²×C₂²⋊D₅₃	C₂²	semidirect
18. C₂²×C₂²⋊D₅₃	C₂²	semidirect
19. C₂²×C₂²⋊D₅₃	C₂²	semidirect
20. C₂²×C₂²⋊D₅₃	C₂²	semidirect
21. C₂²×C₂²⋊D₅₃	C₂²	semidirect
22. C₂²×C₂²⋊D₅₃	C₂²	semidirect
24. C₂×D₄×D₅₃	C₂²	semidirect
25. C₂³×Dic₅₃	C₂²	semidirect
26. C₂²×C₄×D₅₃	C₂²	semidirect
27. #13133213	C₂²	semidirect
28. #13133191	C₂²	semidirect
29. #13133189	C₂²	semidirect
30. #13133188	C₂²	semidirect
31. #13133186	C₂²	semidirect
32. #13133185	C₂²	semidirect
33. D₄×Dic₅₃	C₂²	semidirect
34. C₄×C₂²⋊D₅₃	C₂²	semidirect
35. C₂×C₄⋊Dic₅₃	C₂²	semidirect
36. C₂×#11719919	C₂²	semidirect
37. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
38. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
39. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
40. C₂×#11719921	C₂²	semidirect
41. C₂×#11719921	C₂²	semidirect
42. C₂×C₄×Dic₅₃	C₂²	semidirect
43. C₂⁵×C₅₃	C₂²	semidirect
46. C₂²×D₄×C₅₃	C₂²	semidirect
47. C₂²×D₄×C₅₃	C₂²	semidirect
48. C₂²×D₄×C₅₃	C₂²	semidirect
49. C₂³×C₄×C₅₃	C₂²	semidirect
56. C₂⁴×C₅₃	C₂³	semidirect
62. C₂³×D₅₃	C₂³	semidirect
66. C₂×D₄×C₅₃	D₄	semidirect
68. C₂×D₄×C₅₃	C₂³	semidirect
69. C₂×D₄×C₅₃	C₂³	semidirect
73. C₂²×C₄×C₅₃	C₂³	semidirect
80. C₂×C₂²⋊D₅₃	D₄	direct (N × H)
82. C₂×C₂²⋊D₅₃	C₂³	semidirect
83. C₂×C₂²⋊D₅₃	C₂³	semidirect
84. C₂×C₂²⋊D₅₃	C₂³	semidirect
85. C₂×C₂²⋊D₅₃	C₂³	semidirect
86. C₂×C₂²⋊D₅₃	C₂³	semidirect
92. C₂²×Dic₅₃	C₂³	semidirect
95. C₂×D₂₁₂	C₂³	semidirect
97. C₂×C₄×D₅₃	C₂³	semidirect
98. C₂²⋊Dic₅₃	C₂³	semidirect
99. C₂²⋊Dic₅₃	C₂³	semidirect
100. C₂²⋊Dic₅₃	C₂³	semidirect
101. #11719921	C₂³	semidirect
102. #11719921	C₂³	semidirect
103. C₄⋊Dic₅₃	C₂³	semidirect
104. #11719919	C₂³	semidirect
105. C₄×Dic₅₃	C₂³	semidirect
117. C₂³×C₅₃	C₂×D₄	semidirect
118. C₂³×C₅₃	C₂×D₄	semidirect
132. C₂²×D₅₃	C₂×D₄	semidirect
137. D₄×C₅₃	C₂×D₄	semidirect
140. C₂×C₄×C₅₃	C₂×D₄	semidirect
148. C₂²⋊D₅₃	C₂×D₄	direct (N × H)
153. C₂×Dic₅₃	C₂×D₄	semidirect
173. C₂²×C₅₃	C₂²×D₄	semidirect
174. C₂²×C₅₃	C₂²×D₄	semidirect
185. C₂×D₅₃	C₂²×D₄	semidirect
187. C₄×C₅₃	C₂²×D₄	semidirect
191. Dic₅₃	C₂²×D₄	semidirect
196. C₂×C₅₃	D₄²	semidirect
204. C₂³×D₄	D₅₃	semidirect
214. C₅₃	C₂×D₄²	semidirect
216. C₂⁵	C₂×D₅₃	semidirect
230. C₂²×D₄	C₂×D₅₃	semidirect
231. C₂²×D₄	C₂×D₅₃	semidirect
232. C₂²×D₄	C₂×D₅₃	semidirect
235. C₂³×C₄	C₂×D₅₃	semidirect
264. C₂⁴	C₂²×D₅₃	semidirect
284. C₂×D₄	C₂²⋊D₅₃	direct (N × H)
286. C₂×D₄	C₂²×D₅₃	semidirect
287. C₂×D₄	C₂²×D₅₃	semidirect
299. C₂²×C₄	C₂²×D₅₃	semidirect
331. C₂³	D₄×D₅₃	semidirect
332. C₂³	C₂×C₂²⋊D₅₃	semidirect
346. D₄	C₂×C₂²⋊D₅₃	direct (N × H)
359. C₂×C₄	C₂×C₂²⋊D₅₃	semidirect
383. C₂²	C₂×D₄×D₅₃	semidirect
385. C₂²	C₂²×C₂²⋊D₅₃	semidirect
393. C₄	C₂²×C₂²⋊D₅₃	semidirect
399. C₂	D₄×C₂²⋊D₅₃	direct (N × H)

Subgroups — C2×D4×C22⋊D53 #20288152

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₄×C₂²⋊D₅₃ #20288152