Subgroups — C₂²×H(5,𝔽₂)×D₅₃ #28297977

Order 13568.

65726 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133263	C₂	1	6	yes	maximal, complemented
2	C₂²×#13133262	C₂	1	9	yes	maximal, complemented
3	C₂×H(5,𝔽₂)×D₅₃	C₂	1	96	yes	maximal, direct product factor
4	C₂²×#41×D₅₃	C₂	1	6	yes	maximal, complemented
5	C₂³×D₄×D₅₃	C₂	1	9	yes	maximal, complemented
6	C₂²×H(5,𝔽₂)×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁵×D₅₃	C₂²	1	6	yes	complemented
8	C₂×#13133263	C₂²	1	288	yes	complemented
9	C₂×#13133262	C₂²	1	432	yes	complemented
10	H(5,𝔽₂)×D₅₃	C₂²	1	1024	yes	direct product factor
11	C₂²×#11719949	C₂²	1	6	yes	complemented
12	C₂²×#11719945	C₂²	1	18	yes	complemented
13	C₂²×#11719947	C₂²	1	18	yes	complemented
14	C₂×#41×D₅₃	C₂²	1	288	yes	complemented
15	C₂²×Q₈×D₅₃	C₂²	1	2	yes	complemented
16	C₂³×D₂₁₂	C₂²	1	9	yes	complemented
17	C₂³×C₂²⋊D₅₃	C₂²	1	18	yes	complemented
18	C₂²×D₄×D₅₃	C₂²	1	18	yes	complemented
19	C₂²×D₄×D₅₃	C₂²	1	432	yes	complemented
20	C₂²×D₄×D₅₃	C₂²	1	36	yes	complemented
21	C₂³×C₄×D₅₃	C₂²	1	9	yes	complemented
22	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	48	yes	complemented
23	C₂²×#41×C₅₃	C₂²	1	6	yes	complemented
24	C₂³×D₄×C₅₃	C₂²	1	9	yes	complemented
25	C₂⁴×D₅₃	—	4	48	no	—
26	C₂⁴×D₅₃	C₂³	1	9	yes	—
27	C₂⁴×D₅₃	C₂³	1	144	yes	complemented
28	C₂⁴×D₅₃	C₂³	1	18	yes	complemented
29	#13133263	C₂³	1	1536	yes	complemented
30	#13133262	C₂³	1	2304	yes	complemented
31	C₂×#11719949	C₂³	1	144	yes	complemented
32	C₂×#11719945	C₂³	1	432	yes	complemented
33	C₂×#11719947	C₂³	1	432	yes	complemented
34	#41×D₅₃	C₂³	1	1536	yes	complemented
35	C₂²×Dic₁₀₆	C₂³	1	6	yes	complemented
36	C₂×Q₈×D₅₃	C₂³	1	48	yes	complemented
37	C₂²×D₂₁₂	C₂³	1	18	yes	complemented
38	C₂²×D₂₁₂	C₂³	1	216	yes	complemented
39	C₂²×C₂²⋊D₅₃	C₂³	1	36	yes	complemented
40	C₂²×C₂²⋊D₅₃	C₂³	1	432	yes	complemented
41	C₂×D₄×D₅₃	C₂³	1	432	yes	complemented
42	C₂×D₄×D₅₃	C₂³	1	2304	yes	complemented
43	C₂×D₄×D₅₃	C₂³	1	864	yes	complemented
44	C₂³×Dic₅₃	C₂³	1	9	yes	complemented
45	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
46	C₂²×C₄×D₅₃	C₂³	1	216	yes	complemented
47	C₂²×C₄×D₅₃	C₂³	1	18	yes	complemented
48	C₂⁵×C₅₃	C₂³	1	6	yes	complemented
49	H(5,𝔽₂)×C₅₃	C₂³	1	256	yes	complemented
50	C₂×#41×C₅₃	C₂³	1	144	yes	complemented
51	C₂²×Q₈×C₅₃	C₂³	1	2	yes	complemented
52	C₂²×D₄×C₅₃	C₂³	1	18	yes	complemented
53	C₂²×D₄×C₅₃	C₂³	1	216	yes	complemented
54	C₂³×C₄×C₅₃	C₂³	1	9	yes	complemented
55	C₂⁴×C₅₃	—	4	24	no	—
56	C₂⁴×C₅₃	C₂⁴	1	9	yes	—
57	C₂⁴×C₅₃	C₂⁴	1	72	yes	complemented
58	C₂³×D₅₃	—	2	72	no	—
59	C₂³×D₅₃	—	4	576	no	—
60	C₂³×D₅₃	—	4	72	no	—
61	C₂³×D₅₃	C₂⁴	1	108	yes	—
62	C₂³×D₅₃	C₂⁴	1	9	yes	—
63	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
64	C₂³×D₅₃	C₂⁴	1	384	yes	complemented
65	C₂³×D₅₃	C₂⁴	1	216	yes	complemented
66	#41×C₅₃	C₂⁴	1	384	yes	complemented
67	C₂×Q₈×C₅₃	C₂⁴	1	24	yes	complemented
68	C₂×D₄×C₅₃	C₂⁴	1	216	yes	complemented
69	C₂×D₄×C₅₃	C₂⁴	1	576	yes	complemented
70	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
71	C₂²×C₄×C₅₃	C₂⁴	1	108	yes	complemented
72	C₂×C₂²⋊D₅₃	C₂⁴	1	432	yes	complemented
73	C₂×C₂²⋊D₅₃	C₂⁴	1	1152	yes	complemented
74	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
75	C₂²×Dic₅₃	C₂⁴	1	108	yes	complemented
76	#11719949	C₂⁴	1	384	yes	complemented
77	Q₈×D₅₃	C₂⁴	1	128	yes	complemented
78	#11719947	C₂⁴	1	1152	yes	complemented
79	D₄×D₅₃	C₂⁴	1	1152	yes	complemented
80	D₄×D₅₃	C₂⁴	1	2304	yes	complemented
81	#11719945	C₂⁴	1	1152	yes	complemented
82	C₂×D₂₁₂	C₂⁴	1	216	yes	complemented
83	C₂×D₂₁₂	C₂⁴	1	576	yes	complemented
84	C₂×C₄×D₅₃	C₂⁴	1	72	yes	—
85	C₂×C₄×D₅₃	C₂⁴	1	576	yes	complemented
86	C₂×C₄×D₅₃	C₂⁴	1	216	yes	complemented
87	C₂×Dic₁₀₆	C₂⁴	1	72	yes	complemented
88	C₂³×C₅₃	—	2	36	no	—
89	C₂³×C₅₃	—	4	144	no	—
90	C₂³×C₅₃	C₂⁵	1	54	yes	—
91	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
92	C₂³×C₅₃	C₂⁵	1	96	yes	complemented
93	C₂²×D₅₃	—	2	36	no	—
94	C₂²×D₅₃	—	2	432	no	—
95	C₂²×D₅₃	—	4	768	no	—
96	C₂²×D₅₃	—	4	432	no	—
97	C₂²×D₅₃	H(5,𝔽₂)	1	8	yes	direct product factor
98	C₂²×D₅₃	C₂⁵	1	54	yes	—
99	C₂²×D₅₃	C₂⁵	1	144	yes	—
100	C₂²×D₅₃	C₂⁵	1	6	yes	—
101	C₂²×D₅₃	C₂⁵	1	288	yes	complemented
102	Q₈×C₅₃	C₂⁵	1	32	yes	complemented
103	D₄×C₅₃	C₂⁵	1	288	yes	complemented
104	C₂×C₄×C₅₃	C₂⁵	1	36	yes	—
105	C₂×C₄×C₅₃	C₂⁵	1	144	yes	complemented
106	C₂²⋊D₅₃	C₂⁵	1	576	yes	complemented
107	C₂×Dic₅₃	C₂⁵	1	36	yes	—
108	C₂×Dic₅₃	C₂⁵	1	144	yes	complemented
109	D₂₁₂	C₂⁵	1	288	yes	complemented
110	C₄×D₅₃	C₂⁵	1	96	yes	—
111	C₄×D₅₃	C₂⁵	1	288	yes	complemented
112	Dic₁₀₆	C₂⁵	1	96	yes	complemented
113	C₂³×H(5,𝔽₂)	—	53	1	no	maximal, Sylow
114	C₂²×C₅₃	—	2	108	no	—
115	C₂²×C₅₃	—	4	96	no	—
116	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
117	C₂²×C₅₃	C₂⁶	1	36	yes	—
118	C₂²×C₅₃	C₂⁶	1	3	yes	—
119	C₂×D₅₃	—	2	108	no	—
120	C₂×D₅₃	—	2	288	no	—
121	C₂×D₅₃	—	4	288	no	—
122	C₂×D₅₃	C₂×H(5,𝔽₂)	1	24	yes	direct product factor
123	C₂×D₅₃	C₂⁶	1	36	yes	—
124	C₂×D₅₃	C₂⁶	1	4	yes	—
125	C₄×C₅₃	C₂⁶	1	24	yes	—
126	Dic₅₃	C₂⁶	1	24	yes	—
127	C₂²×H(5,𝔽₂)	—	53	96	no	—
128	C₂²×H(5,𝔽₂)	—	53	6	no	—
129	C₂²×H(5,𝔽₂)	—	53	9	no	—
130	C₂²×H(5,𝔽₂)	D₅₃	1	1	yes	characteristic, direct product factor
131	C₂³×#41	—	53	6	no	—
132	C₂⁴×D₄	—	53	9	no	—
133	C₂×C₅₃	—	2	36	no	—
134	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	6	yes	complemented
135	C₂×C₅₃	C₂⁷	1	1	yes	characteristic
136	D₅₃	—	2	36	no	—
137	D₅₃	C₂²×H(5,𝔽₂)	1	8	yes	direct product factor
138	C₂⁶	—	53	6	no	—
139	C₂×H(5,𝔽₂)	—	53	1024	no	—
140	C₂×H(5,𝔽₂)	—	53	288	no	—
141	C₂×H(5,𝔽₂)	—	53	432	no	—
142	C₂×H(5,𝔽₂)	C₂×D₅₃	1	48	yes	direct product factor
143	C₂²×#41	—	53	288	no	—
144	C₂²×#41	—	53	6	no	—
145	C₂²×#41	—	53	18	no	—
146	C₂²×#41	—	53	18	no	—
147	C₂²×#41	C₂×D₅₃	1	6	yes	complemented
148	C₂³×Q₈	—	53	2	no	—
149	C₂³×D₄	—	53	18	no	—
150	C₂³×D₄	—	53	18	no	—
151	C₂³×D₄	—	53	36	no	—
152	C₂³×D₄	—	53	432	no	—
153	C₂³×D₄	—	53	9	no	—
154	C₂³×D₄	C₂×D₅₃	1	9	yes	complemented
155	C₂⁴×C₄	—	53	9	no	—
156	C₅₃	C₂³×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
157	C₂⁵	—	53	9	no	—
158	C₂⁵	—	53	18	no	—
159	C₂⁵	—	53	144	no	—
160	C₂⁵	—	212	48	no	—
161	C₂⁵	C₂²×D₅₃	1	6	yes	complemented
162	H(5,𝔽₂)	—	53	1536	no	—
163	H(5,𝔽₂)	—	53	2304	no	—
164	H(5,𝔽₂)	C₂²×D₅₃	1	256	yes	direct product factor
165	C₂×#41	—	53	1536	no	—
166	C₂×#41	—	53	144	no	—
167	C₂×#41	—	53	432	no	—
168	C₂×#41	—	53	432	no	—
169	C₂×#41	C₂²×D₅₃	1	144	yes	complemented
170	C₂²×Q₈	—	53	48	no	—
171	C₂²×Q₈	—	53	6	no	—
172	C₂²×Q₈	C₂²×D₅₃	1	2	yes	complemented
173	C₂²×D₄	—	53	36	no	—
174	C₂²×D₄	—	53	432	no	—
175	C₂²×D₄	—	53	432	no	—
176	C₂²×D₄	—	53	864	no	—
177	C₂²×D₄	—	53	2304	no	—
178	C₂²×D₄	—	53	18	no	—
179	C₂²×D₄	—	53	216	no	—
180	C₂²×D₄	C₂²×D₅₃	1	18	yes	complemented
181	C₂²×D₄	C₂²×D₅₃	1	216	yes	complemented
182	C₂³×C₄	—	53	9	no	—
183	C₂³×C₄	—	53	6	no	—
184	C₂³×C₄	—	53	18	no	—
185	C₂³×C₄	—	53	216	no	—
186	C₂³×C₄	C₂²×D₅₃	1	9	yes	complemented
187	C₂⁴	—	4	24	no	—
188	C₂⁴	—	53	1	no	—
189	C₂⁴	—	53	108	no	—
190	C₂⁴	—	53	9	no	—
191	C₂⁴	—	53	216	no	—
192	C₂⁴	—	53	384	no	—
193	C₂⁴	—	106	72	no	—
194	C₂⁴	—	212	72	no	—
195	C₂⁴	—	212	576	no	—
196	C₂⁴	C₂³×D₅₃	1	9	yes	—
197	C₂⁴	C₂³×D₅₃	1	72	yes	complemented
198	#41	—	53	384	no	—
199	#41	—	53	1152	no	—
200	#41	—	53	1152	no	—
201	#41	C₂³×D₅₃	1	384	yes	complemented
202	C₂×Q₈	—	53	128	no	—
203	C₂×Q₈	—	53	72	no	—
204	C₂×Q₈	C₂³×D₅₃	1	24	yes	complemented
205	C₂×D₄	—	53	432	no	—
206	C₂×D₄	—	53	1152	no	—
207	C₂×D₄	—	53	1152	no	—
208	C₂×D₄	—	53	2304	no	—
209	C₂×D₄	—	53	216	no	—
210	C₂×D₄	—	53	576	no	—
211	C₂×D₄	C₂³×D₅₃	1	216	yes	complemented
212	C₂×D₄	C₂³×D₅₃	1	576	yes	complemented
213	C₂²×C₄	—	53	108	no	—
214	C₂²×C₄	—	53	6	no	—
215	C₂²×C₄	—	53	72	no	—
216	C₂²×C₄	—	53	216	no	—
217	C₂²×C₄	—	53	576	no	—
218	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
219	C₂²×C₄	C₂³×D₅₃	1	108	yes	complemented
220	C₂³	—	2	36	no	—
221	C₂³	—	4	144	no	—
222	C₂³	—	53	8	no	—
223	C₂³	—	53	6	no	—
224	C₂³	—	53	144	no	—
225	C₂³	—	53	54	no	—
226	C₂³	—	53	288	no	—
227	C₂³	—	106	432	no	—
228	C₂³	—	106	36	no	—
229	C₂³	—	212	432	no	—
230	C₂³	—	212	768	no	—
231	C₂³	C₂⁴×D₅₃	1	54	yes	—
232	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
233	C₂³	C₂⁴×D₅₃	1	96	yes	complemented
234	Q₈	—	53	96	no	—
235	Q₈	C₂⁴×D₅₃	1	32	yes	complemented
236	D₄	—	53	576	no	—
237	D₄	—	53	288	no	—
238	D₄	C₂⁴×D₅₃	1	288	yes	complemented
239	C₂×C₄	—	53	36	no	—
240	C₂×C₄	—	53	144	no	—
241	C₂×C₄	—	53	96	no	—
242	C₂×C₄	—	53	288	no	—
243	C₂×C₄	C₂⁴×D₅₃	1	36	yes	—
244	C₂×C₄	C₂⁴×D₅₃	1	144	yes	complemented
245	C₂²	—	2	108	no	—
246	C₂²	—	4	96	no	—
247	C₂²	—	53	24	no	—
248	C₂²	—	53	4	no	—
249	C₂²	—	53	36	no	—
250	C₂²	—	106	288	no	—
251	C₂²	—	106	108	no	—
252	C₂²	—	212	288	no	—
253	C₂²	H(5,𝔽₂)×D₅₃	1	4	yes	direct product factor
254	C₂²	C₂⁵×D₅₃	1	36	yes	—
255	C₂²	C₂⁵×D₅₃	1	3	yes	—
256	C₄	—	53	24	no	—
257	C₄	C₂⁵×D₅₃	1	24	yes	—
258	C₂	—	2	36	no	—
259	C₂	—	53	8	no	—
260	C₂	—	106	36	no	—
261	C₂	C₂×H(5,𝔽₂)×D₅₃	1	6	yes	direct product factor
262	C₂	C₂⁶×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂×C₅₃	C₂⁷
Frattini	C₂	C₂⁶×D₅₃
Fitting	C₂²×H(5,𝔽₂)×C₅₃	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂²×H(5,𝔽₂)	D₅₃
hypocenter	C₅₃	C₂³×H(5,𝔽₂)
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂²×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. C₂²×#13133263	C₂	semidirect
2. C₂²×#13133262	C₂	semidirect
3. C₂×H(5,𝔽₂)×D₅₃	C₂	direct (N × H)
4. C₂²×#41×D₅₃	C₂	semidirect
5. C₂³×D₄×D₅₃	C₂	semidirect
6. C₂²×H(5,𝔽₂)×C₅₃	C₂	semidirect
7. C₂⁵×D₅₃	C₂²	semidirect
8. C₂×#13133263	C₂²	semidirect
9. C₂×#13133262	C₂²	semidirect
10. H(5,𝔽₂)×D₅₃	C₂²	direct (N × H)
11. C₂²×#11719949	C₂²	semidirect
12. C₂²×#11719945	C₂²	semidirect
13. C₂²×#11719947	C₂²	semidirect
14. C₂×#41×D₅₃	C₂²	semidirect
15. C₂²×Q₈×D₅₃	C₂²	semidirect
16. C₂³×D₂₁₂	C₂²	semidirect
17. C₂³×C₂²⋊D₅₃	C₂²	semidirect
18. C₂²×D₄×D₅₃	C₂²	semidirect
19. C₂²×D₄×D₅₃	C₂²	semidirect
20. C₂²×D₄×D₅₃	C₂²	semidirect
21. C₂³×C₄×D₅₃	C₂²	semidirect
22. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
23. C₂²×#41×C₅₃	C₂²	semidirect
24. C₂³×D₄×C₅₃	C₂²	semidirect
27. C₂⁴×D₅₃	C₂³	semidirect
28. C₂⁴×D₅₃	C₂³	semidirect
29. #13133263	C₂³	semidirect
30. #13133262	C₂³	semidirect
31. C₂×#11719949	C₂³	semidirect
32. C₂×#11719945	C₂³	semidirect
33. C₂×#11719947	C₂³	semidirect
34. #41×D₅₃	C₂³	semidirect
35. C₂²×Dic₁₀₆	C₂³	semidirect
36. C₂×Q₈×D₅₃	C₂³	semidirect
37. C₂²×D₂₁₂	C₂³	semidirect
38. C₂²×D₂₁₂	C₂³	semidirect
39. C₂²×C₂²⋊D₅₃	C₂³	semidirect
40. C₂²×C₂²⋊D₅₃	C₂³	semidirect
41. C₂×D₄×D₅₃	C₂³	semidirect
42. C₂×D₄×D₅₃	C₂³	semidirect
43. C₂×D₄×D₅₃	C₂³	semidirect
44. C₂³×Dic₅₃	C₂³	semidirect
46. C₂²×C₄×D₅₃	C₂³	semidirect
47. C₂²×C₄×D₅₃	C₂³	semidirect
48. C₂⁵×C₅₃	C₂³	semidirect
49. H(5,𝔽₂)×C₅₃	C₂³	semidirect
50. C₂×#41×C₅₃	C₂³	semidirect
51. C₂²×Q₈×C₅₃	C₂³	semidirect
52. C₂²×D₄×C₅₃	C₂³	semidirect
53. C₂²×D₄×C₅₃	C₂³	semidirect
54. C₂³×C₄×C₅₃	C₂³	semidirect
57. C₂⁴×C₅₃	C₂⁴	semidirect
64. C₂³×D₅₃	C₂⁴	semidirect
65. C₂³×D₅₃	C₂⁴	semidirect
66. #41×C₅₃	C₂⁴	semidirect
67. C₂×Q₈×C₅₃	C₂⁴	semidirect
68. C₂×D₄×C₅₃	C₂⁴	semidirect
69. C₂×D₄×C₅₃	C₂⁴	semidirect
71. C₂²×C₄×C₅₃	C₂⁴	semidirect
72. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
73. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
75. C₂²×Dic₅₃	C₂⁴	semidirect
76. #11719949	C₂⁴	semidirect
77. Q₈×D₅₃	C₂⁴	semidirect
78. #11719947	C₂⁴	semidirect
79. D₄×D₅₃	C₂⁴	semidirect
80. D₄×D₅₃	C₂⁴	semidirect
81. #11719945	C₂⁴	semidirect
82. C₂×D₂₁₂	C₂⁴	semidirect
83. C₂×D₂₁₂	C₂⁴	semidirect
85. C₂×C₄×D₅₃	C₂⁴	semidirect
86. C₂×C₄×D₅₃	C₂⁴	semidirect
87. C₂×Dic₁₀₆	C₂⁴	semidirect
92. C₂³×C₅₃	C₂⁵	semidirect
97. C₂²×D₅₃	H(5,𝔽₂)	direct (N × H)
101. C₂²×D₅₃	C₂⁵	semidirect
102. Q₈×C₅₃	C₂⁵	semidirect
103. D₄×C₅₃	C₂⁵	semidirect
105. C₂×C₄×C₅₃	C₂⁵	semidirect
106. C₂²⋊D₅₃	C₂⁵	semidirect
108. C₂×Dic₅₃	C₂⁵	semidirect
109. D₂₁₂	C₂⁵	semidirect
111. C₄×D₅₃	C₂⁵	semidirect
112. Dic₁₀₆	C₂⁵	semidirect
116. C₂²×C₅₃	C₂×H(5,𝔽₂)	semidirect
122. C₂×D₅₃	C₂×H(5,𝔽₂)	direct (N × H)
130. C₂²×H(5,𝔽₂)	D₅₃	direct (N × H)
134. C₂×C₅₃	C₂²×H(5,𝔽₂)	semidirect
137. D₅₃	C₂²×H(5,𝔽₂)	direct (N × H)
142. C₂×H(5,𝔽₂)	C₂×D₅₃	direct (N × H)
147. C₂²×#41	C₂×D₅₃	semidirect
154. C₂³×D₄	C₂×D₅₃	semidirect
156. C₅₃	C₂³×H(5,𝔽₂)	semidirect
161. C₂⁵	C₂²×D₅₃	semidirect
164. H(5,𝔽₂)	C₂²×D₅₃	direct (N × H)
169. C₂×#41	C₂²×D₅₃	semidirect
172. C₂²×Q₈	C₂²×D₅₃	semidirect
180. C₂²×D₄	C₂²×D₅₃	semidirect
181. C₂²×D₄	C₂²×D₅₃	semidirect
186. C₂³×C₄	C₂²×D₅₃	semidirect
197. C₂⁴	C₂³×D₅₃	semidirect
201. #41	C₂³×D₅₃	semidirect
204. C₂×Q₈	C₂³×D₅₃	semidirect
211. C₂×D₄	C₂³×D₅₃	semidirect
212. C₂×D₄	C₂³×D₅₃	semidirect
219. C₂²×C₄	C₂³×D₅₃	semidirect
233. C₂³	C₂⁴×D₅₃	semidirect
235. Q₈	C₂⁴×D₅₃	semidirect
238. D₄	C₂⁴×D₅₃	semidirect
244. C₂×C₄	C₂⁴×D₅₃	semidirect
253. C₂²	H(5,𝔽₂)×D₅₃	direct (N × H)
261. C₂	C₂×H(5,𝔽₂)×D₅₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#13133263	2
C₂²×#13133262	2
C₂×H(5,𝔽₂)×D₅₃	2
C₂²×#41×D₅₃	2
C₂³×D₄×D₅₃	2
C₂²×H(5,𝔽₂)×C₅₃	2
C₂³×H(5,𝔽₂)	53

Subgroups — C22×H(5,𝔽2)×D53 #28297977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×H(5,𝔽₂)×D₅₃ #28297977