Subgroups — C₂×#576×D₅₃ #28297899

Order 13568.

11462 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×H(5,𝔽₂)×D₅₃	C₂	1	2	yes	maximal, complemented
2	C₂×#16811428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811427	C₂	1	6	yes	maximal, complemented
4	C₂×#16811426	C₂	1	2	yes	maximal, complemented
5	C₂×#16811425	C₂	1	3	yes	maximal, complemented
6	C₂×#16811424	C₂	1	3	yes	maximal, complemented
7	#576×D₅₃	C₂	1	32	yes	maximal, direct product factor
8	C₂×AGL(1,ℤ/8)×D₅₃	C₂	1	6	yes	maximal, complemented
9	C₂×#135×D₅₃	C₂	1	3	yes	maximal, complemented
10	C₂²×D₈×D₅₃	C₂	1	3	yes	maximal, complemented
11	C₂×#131×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13133263	—	2	2	no	—
14	C₂×#13133263	C₂²	1	2	yes	complemented
15	C₂×#13133263	C₂²	1	6	yes	complemented
16	C₂×#13133262	—	2	6	no	—
17	C₂×#13133262	C₂²	1	6	yes	complemented
18	H(5,𝔽₂)×D₅₃	—	2	16	no	—
19	H(5,𝔽₂)×D₅₃	C₂²	1	32	yes	complemented
20	C₂×#41×D₅₃	—	2	2	no	—
21	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
22	C₂×#41×D₅₃	C₂²	1	6	yes	complemented
23	C₂²×D₄×D₅₃	—	2	6	no	—
24	C₂²×D₄×D₅₃	C₂²	1	6	yes	complemented
25	#16811428	C₂²	1	16	yes	complemented
26	#16811427	C₂²	1	96	yes	complemented
27	#16811426	C₂²	1	32	yes	complemented
28	#16811425	C₂²	1	48	yes	complemented
29	#16811424	C₂²	1	48	yes	complemented
30	C₂×#13133245	C₂²	1	6	yes	complemented
31	C₂×#13133244	C₂²	1	12	yes	complemented
32	C₂×#13133243	C₂²	1	6	yes	complemented
33	C₂×#13133242	C₂²	1	6	yes	complemented
34	C₂×#13133241	C₂²	1	12	yes	complemented
35	AGL(1,ℤ/8)×D₅₃	C₂²	1	96	yes	complemented
36	C₂×#13133240	C₂²	1	3	yes	complemented
37	C₂×#13133239	C₂²	1	3	yes	complemented
38	C₂×#13133238	C₂²	1	6	yes	complemented
39	C₂×#13133237	C₂²	1	6	yes	complemented
40	C₂×#13133236	C₂²	1	3	yes	complemented
41	#135×D₅₃	C₂²	1	48	yes	complemented
42	C₂×Q₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×SD₁₆×D₅₃	C₂²	1	6	yes	complemented
44	C₂²×D₄₂₄	C₂²	1	3	yes	complemented
45	C₂²×#11719922	C₂²	1	6	yes	complemented
46	C₂×D₈×D₅₃	C₂²	1	3	yes	complemented
47	C₂×D₈×D₅₃	C₂²	1	6	yes	complemented
48	C₂×D₈×D₅₃	C₂²	1	48	yes	complemented
49	C₂×D₈×D₅₃	C₂²	1	6	yes	complemented
50	C₂×D₈×D₅₃	C₂²	1	6	yes	complemented
51	C₂×#13133225	C₂²	1	3	yes	complemented
52	C₂×#13133224	C₂²	1	1	yes	characteristic, complemented
53	C₂×#13133223	C₂²	1	3	yes	complemented
54	#131×D₅₃	C₂²	1	16	yes	complemented
55	C₂×M₁₆×D₅₃	C₂²	1	3	yes	complemented
56	C₂²×C₈×D₅₃	C₂²	1	3	yes	complemented
57	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	complemented
58	C₅₃×#576	C₂²	1	16	yes	complemented
59	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	6	yes	complemented
60	C₂×#135×C₅₃	C₂²	1	3	yes	complemented
61	C₂²×D₈×C₅₃	C₂²	1	3	yes	complemented
62	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₂⁴×D₅₃	—	2	6	no	—
64	#13133263	—	2	8	no	—
65	#13133263	—	2	32	no	—
66	#13133263	—	2	24	no	—
67	#13133263	C₂³	1	48	yes	complemented
68	#13133263	C₂³	1	16	yes	complemented
69	#13133262	—	2	96	no	—
70	#13133262	—	2	24	no	—
71	#13133262	C₂³	1	48	yes	complemented
72	C₂×#11719949	—	2	2	no	—
73	C₂×#11719949	D₄	1	1	yes	characteristic
74	C₂×#11719949	C₂³	1	6	yes	complemented
75	C₂×#11719945	—	2	6	no	—
76	C₂×#11719945	—	2	6	no	—
77	C₂×#11719945	C₂³	1	3	yes	—
78	C₂×#11719945	C₂³	1	6	yes	complemented
79	C₂×#11719947	—	2	6	no	—
80	C₂×#11719947	—	2	6	no	—
81	C₂×#11719947	D₄	1	3	yes	—
82	C₂×#11719947	C₂³	1	6	yes	complemented
83	#41×D₅₃	—	2	32	no	—
84	#41×D₅₃	—	2	24	no	—
85	#41×D₅₃	D₄	1	8	yes	—
86	#41×D₅₃	C₂³	1	8	yes	—
87	#41×D₅₃	C₂³	1	48	yes	complemented
88	C₂×Q₈×D₅₃	D₄	1	1	yes	characteristic
89	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
90	C₂²×D₂₁₂	—	2	6	no	—
91	C₂²×D₂₁₂	C₂³	1	6	yes	complemented
92	C₂²×C₂²⋊D₅₃	—	2	12	no	—
93	C₂²×C₂²⋊D₅₃	—	2	6	no	—
94	C₂×D₄×D₅₃	—	2	6	no	—
95	C₂×D₄×D₅₃	—	2	6	no	—
96	C₂×D₄×D₅₃	—	2	12	no	—
97	C₂×D₄×D₅₃	—	2	96	no	—
98	C₂×D₄×D₅₃	—	2	6	no	—
99	C₂×D₄×D₅₃	—	2	6	no	—
100	C₂×D₄×D₅₃	—	2	24	no	—
101	C₂×D₄×D₅₃	—	2	6	no	—
102	C₂×D₄×D₅₃	D₄	1	3	yes	—
103	C₂×D₄×D₅₃	C₂³	1	6	yes	—
104	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
105	C₂×D₄×D₅₃	C₂³	1	48	yes	complemented
106	C₂²×C₄×D₅₃	—	2	6	no	—
107	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
108	#13133245	C₂³	1	48	yes	complemented
109	#13133244	C₂³	1	96	yes	complemented
110	#13133243	C₂³	1	48	yes	complemented
111	#13133242	C₂³	1	48	yes	complemented
112	#13133241	C₂³	1	96	yes	complemented
113	#13133240	C₂³	1	24	yes	complemented
114	#13133239	C₂³	1	24	yes	complemented
115	#13133238	C₂³	1	48	yes	complemented
116	#13133237	C₂³	1	48	yes	complemented
117	#13133236	C₂³	1	24	yes	complemented
118	C₂×Dic₂₁₂	C₂³	1	1	yes	characteristic, complemented
119	C₂×#11719925	C₂³	1	2	yes	complemented
120	Q₁₆×D₅₃	C₂³	1	8	yes	complemented
121	C₂×#11719913	C₂³	1	6	yes	complemented
122	C₂×#11719923	C₂³	1	6	yes	complemented
123	C₂×#11719924	C₂³	1	6	yes	complemented
124	SD₁₆×D₅₃	C₂³	1	48	yes	complemented
125	C₂×D₄₂₄	C₂³	1	3	yes	complemented
126	C₂×D₄₂₄	C₂³	1	6	yes	complemented
127	C₂×D₄₂₄	C₂³	1	24	yes	complemented
128	C₂×#11719922	C₂³	1	6	yes	complemented
129	C₂×#11719922	C₂³	1	12	yes	complemented
130	C₂×#11719922	C₂³	1	48	yes	complemented
131	D₈×D₅₃	C₂³	1	24	yes	complemented
132	D₈×D₅₃	C₂³	1	48	yes	complemented
133	D₈×D₅₃	C₂³	1	48	yes	complemented
134	D₈×D₅₃	C₂³	1	48	yes	complemented
135	#13133225	C₂³	1	24	yes	complemented
136	#13133224	C₂³	1	8	yes	complemented
137	#13133223	C₂³	1	24	yes	complemented
138	C₂×#11719917	C₂³	1	3	yes	complemented
139	C₂×#11719912	C₂³	1	6	yes	complemented
140	M₁₆×D₅₃	C₂³	1	24	yes	complemented
141	C₂²×#88322	C₂³	1	3	yes	complemented
142	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
143	C₂×C₈×D₅₃	C₂³	1	3	yes	—
144	C₂×C₈×D₅₃	C₂³	1	24	yes	complemented
145	C₂×C₈×D₅₃	C₂³	1	3	yes	complemented
146	C₂×C₈×D₅₃	C₂³	1	3	yes	complemented
147	H(5,𝔽₂)×C₅₃	—	2	8	no	—
148	H(5,𝔽₂)×C₅₃	C₂³	1	16	yes	complemented
149	C₂×#41×C₅₃	—	2	2	no	—
150	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
151	C₂×#41×C₅₃	C₂³	1	6	yes	complemented
152	C₂²×D₄×C₅₃	—	2	6	no	—
153	C₂²×D₄×C₅₃	C₂³	1	6	yes	complemented
154	AGL(1,ℤ/8)×C₅₃	C₂³	1	48	yes	complemented
155	#135×C₅₃	C₂³	1	24	yes	complemented
156	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
157	C₂×SD₁₆×C₅₃	C₂³	1	6	yes	complemented
158	C₂×D₈×C₅₃	C₂³	1	3	yes	complemented
159	C₂×D₈×C₅₃	C₂³	1	6	yes	complemented
160	C₂×D₈×C₅₃	C₂³	1	24	yes	complemented
161	#131×C₅₃	C₂³	1	8	yes	complemented
162	C₂×M₁₆×C₅₃	C₂³	1	3	yes	complemented
163	C₂²×C₈×C₅₃	C₂³	1	3	yes	complemented
164	C₂⁴×C₅₃	—	2	6	no	—
165	C₂³×D₅₃	—	2	6	no	—
166	C₂³×D₅₃	—	2	6	no	—
167	C₂³×D₅₃	—	2	48	no	—
168	C₂³×D₅₃	—	2	12	no	—
169	C₂³×D₅₃	—	8	24	no	—
170	C₂³×D₅₃	C₂×D₄	1	3	yes	—
171	#41×C₅₃	—	2	16	no	—
172	#41×C₅₃	—	2	12	no	—
173	#41×C₅₃	C₂×D₄	1	4	yes	—
174	#41×C₅₃	C₂⁴	1	4	yes	—
175	#41×C₅₃	C₂⁴	1	24	yes	complemented
176	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
177	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
178	C₂×D₄×C₅₃	—	2	6	no	—
179	C₂×D₄×C₅₃	—	2	48	no	—
180	C₂×D₄×C₅₃	—	2	6	no	—
181	C₂×D₄×C₅₃	—	2	12	no	—
182	C₂×D₄×C₅₃	C₂×D₄	1	3	yes	—
183	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
184	C₂×D₄×C₅₃	C₂⁴	1	24	yes	complemented
185	C₂²×C₄×C₅₃	—	2	6	no	—
186	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
187	C₂×C₂²⋊D₅₃	—	2	6	no	—
188	C₂×C₂²⋊D₅₃	—	2	6	no	—
189	C₂×C₂²⋊D₅₃	—	2	96	no	—
190	C₂×C₂²⋊D₅₃	—	2	6	no	—
191	C₂×C₂²⋊D₅₃	—	2	12	no	—
192	C₂×C₂²⋊D₅₃	—	2	48	no	—
193	C₂×C₂²⋊D₅₃	C₂×D₄	1	6	yes	—
194	C₂²×Dic₅₃	—	2	6	no	—
195	C₂²×Dic₅₃	C₂×D₄	1	3	yes	—
196	#11719949	—	2	16	no	—
197	#11719949	—	2	12	no	—
198	#11719949	C₂×D₄	1	8	yes	—
199	#11719949	C₂⁴	1	24	yes	complemented
200	Q₈×D₅₃	—	2	4	no	—
201	Q₈×D₅₃	C₂×D₄	1	8	yes	—
202	Q₈×D₅₃	C₂⁴	1	8	yes	—
203	#11719947	—	2	48	no	—
204	#11719947	—	2	12	no	—
205	#11719947	—	2	48	no	—
206	#11719947	C₂×D₄	1	24	yes	—
207	#11719947	C₂⁴	1	24	yes	complemented
208	D₄×D₅₃	—	2	48	no	—
209	D₄×D₅₃	—	2	48	no	—
210	D₄×D₅₃	—	2	96	no	—
211	D₄×D₅₃	—	2	48	no	—
212	D₄×D₅₃	—	2	12	no	—
213	D₄×D₅₃	—	2	48	no	—
214	D₄×D₅₃	—	2	48	no	—
215	D₄×D₅₃	—	2	24	no	—
216	D₄×D₅₃	C₂×D₄	1	24	yes	—
217	D₄×D₅₃	C₂⁴	1	24	yes	—
218	D₄×D₅₃	C₂⁴	1	48	yes	complemented
219	#11719945	—	2	12	no	—
220	#11719945	—	2	48	no	—
221	#11719945	—	2	48	no	—
222	#11719945	C₂×D₄	1	12	yes	—
223	#11719945	C₂⁴	1	12	yes	—
224	#11719945	C₂⁴	1	24	yes	complemented
225	C₂×D₂₁₂	—	2	6	no	—
226	C₂×D₂₁₂	—	2	6	no	—
227	C₂×D₂₁₂	—	2	12	no	—
228	C₂×D₂₁₂	—	2	48	no	—
229	C₂×D₂₁₂	C₂×D₄	1	3	yes	—
230	C₂×D₂₁₂	C₂⁴	1	6	yes	—
231	C₂×D₂₁₂	C₂⁴	1	24	yes	complemented
232	C₂×C₄×D₅₃	—	2	2	no	—
233	C₂×C₄×D₅₃	—	2	6	no	—
234	C₂×C₄×D₅₃	—	2	6	no	—
235	C₂×C₄×D₅₃	—	2	48	no	—
236	C₂×C₄×D₅₃	C₂×D₄	1	3	yes	—
237	C₂×C₄×D₅₃	C₂×D₄	1	12	yes	—
238	C₂×C₄×D₅₃	C₂×D₄	1	3	yes	—
239	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
241	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
242	C₂×Dic₁₀₆	—	2	2	no	—
243	C₂×Dic₁₀₆	C₂×D₄	1	3	yes	—
244	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
245	Q₁₆×C₅₃	C₂⁴	1	4	yes	complemented
246	SD₁₆×C₅₃	C₂⁴	1	24	yes	complemented
247	D₈×C₅₃	C₂⁴	1	12	yes	complemented
248	D₈×C₅₃	C₂⁴	1	24	yes	complemented
249	M₁₆×C₅₃	C₂⁴	1	12	yes	complemented
250	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₅₃	C₂⁴	1	3	yes	—
252	C₂×C₈×C₅₃	C₂⁴	1	12	yes	complemented
253	#11719925	C₂⁴	1	8	yes	complemented
254	#11719924	C₂⁴	1	24	yes	complemented
255	#11719923	C₂⁴	1	24	yes	complemented
256	#11719922	C₂⁴	1	24	yes	complemented
257	#11719922	C₂⁴	1	48	yes	complemented
258	#11719917	C₂⁴	1	12	yes	complemented
259	C₂×#88322	C₂⁴	1	1	yes	characteristic
260	C₂×#88322	C₂⁴	1	3	yes	—
261	C₂×#88322	C₂⁴	1	12	yes	complemented
262	Dic₂₁₂	C₂⁴	1	4	yes	complemented
263	D₄₂₄	C₂⁴	1	12	yes	complemented
264	D₄₂₄	C₂⁴	1	24	yes	complemented
265	#11719913	C₂⁴	1	24	yes	complemented
266	#11719912	C₂⁴	1	24	yes	complemented
267	C₈×D₅₃	C₂⁴	1	4	yes	—
268	C₈×D₅₃	C₂⁴	1	12	yes	—
269	C₈×D₅₃	C₂⁴	1	12	yes	complemented
270	C₈×D₅₃	C₂⁴	1	12	yes	complemented
271	C₂³×C₅₃	—	2	6	no	—
272	C₂³×C₅₃	—	2	24	no	—
273	C₂³×C₅₃	—	8	12	no	—
274	C₂³×C₅₃	C₂²×D₄	1	3	yes	—
275	C₂²×D₅₃	—	2	12	no	—
276	C₂²×D₅₃	—	2	6	no	—
277	C₂²×D₅₃	—	2	24	no	—
278	C₂²×D₅₃	—	2	24	no	—
279	C₂²×D₅₃	—	2	48	no	—
280	C₂²×D₅₃	—	4	24	no	—
281	C₂²×D₅₃	—	8	96	no	—
282	C₂²×D₅₃	—	8	24	no	—
283	C₂²×D₅₃	—	8	12	no	—
284	C₂²×D₅₃	C₂²×D₄	1	3	yes	—
285	C₂²×D₅₃	C₂²×D₄	1	12	yes	—
286	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
287	Q₈×C₅₃	—	2	2	no	—
288	Q₈×C₅₃	C₂²×D₄	1	4	yes	—
289	Q₈×C₅₃	C₂⁵	1	4	yes	—
290	D₄×C₅₃	—	2	24	no	—
291	D₄×C₅₃	—	2	6	no	—
292	D₄×C₅₃	—	2	24	no	—
293	D₄×C₅₃	C₂²×D₄	1	12	yes	—
294	D₄×C₅₃	C₂⁵	1	12	yes	—
295	C₂×C₄×C₅₃	—	2	2	no	—
296	C₂×C₄×C₅₃	—	2	24	no	—
297	C₂×C₄×C₅₃	C₂²×D₄	1	3	yes	—
298	C₂×C₄×C₅₃	C₂²×D₄	1	6	yes	—
299	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
300	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
301	C₂²⋊D₅₃	—	2	24	no	—
302	C₂²⋊D₅₃	—	2	24	no	—
303	C₂²⋊D₅₃	—	2	24	no	—
304	C₂²⋊D₅₃	—	2	48	no	—
305	C₂²⋊D₅₃	C₂²×D₄	1	24	yes	—
306	C₂×Dic₅₃	—	2	2	no	—
307	C₂×Dic₅₃	—	2	24	no	—
308	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
309	C₂×Dic₅₃	C₂²×D₄	1	3	yes	—
310	C₂×Dic₅₃	C₂²×D₄	1	12	yes	—
311	D₂₁₂	—	2	24	no	—
312	D₂₁₂	—	2	6	no	—
313	D₂₁₂	—	2	24	no	—
314	D₂₁₂	C₂²×D₄	1	12	yes	—
315	D₂₁₂	C₂⁵	1	12	yes	—
316	C₄×D₅₃	—	2	8	no	—
317	C₄×D₅₃	—	2	24	no	—
318	C₄×D₅₃	—	2	24	no	—
319	C₄×D₅₃	C₂²×D₄	1	12	yes	—
320	C₄×D₅₃	C₂²×D₄	1	2	yes	—
321	C₄×D₅₃	C₂²×D₄	1	12	yes	—
322	C₄×D₅₃	C₂²×D₄	1	6	yes	—
323	C₄×D₅₃	C₂⁵	1	2	yes	—
324	C₄×D₅₃	C₂⁵	1	6	yes	—
325	Dic₁₀₆	—	2	2	no	—
326	Dic₁₀₆	—	2	8	no	—
327	Dic₁₀₆	C₂²×D₄	1	12	yes	—
328	Dic₁₀₆	C₂⁵	1	4	yes	—
329	C₈×C₅₃	C₂⁵	1	2	yes	—
330	C₈×C₅₃	C₂⁵	1	6	yes	—
331	#88322	C₂⁵	1	2	yes	—
332	#88322	C₂⁵	1	6	yes	—
333	C₂²×#576	—	53	1	no	maximal, Sylow
334	C₂²×C₅₃	—	2	6	no	—
335	C₂²×C₅₃	—	2	12	no	—
336	C₂²×C₅₃	—	4	12	no	—
337	C₂²×C₅₃	—	8	24	no	—
338	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
339	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
340	C₂×D₅₃	—	2	6	no	—
341	C₂×D₅₃	—	2	24	no	—
342	C₂×D₅₃	—	2	12	no	—
343	C₂×D₅₃	—	4	12	no	—
344	C₂×D₅₃	—	4	48	no	—
345	C₂×D₅₃	—	8	48	no	—
346	C₂×D₅₃	—	8	24	no	—
347	C₂×D₅₃	#576	1	4	yes	direct product factor
348	C₂×D₅₃	C₂³×D₄	1	6	yes	—
349	C₂×D₅₃	C₂³×D₄	1	2	yes	—
350	C₄×C₅₃	—	2	4	no	—
351	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
352	C₄×C₅₃	C₂³×D₄	1	6	yes	—
353	C₄×C₅₃	C₂⁶	1	1	yes	characteristic
354	Dic₅₃	—	2	4	no	—
355	Dic₅₃	C₂³×D₄	1	2	yes	—
356	Dic₅₃	C₂³×D₄	1	6	yes	—
357	C₂²×H(5,𝔽₂)	—	53	2	no	—
358	C₂×#576	—	53	2	no	—
359	C₂×#576	—	53	32	no	—
360	C₂×#576	—	53	6	no	—
361	C₂×#576	—	53	3	no	—
362	C₂×#576	—	53	3	no	—
363	C₂×#576	—	53	1	no	—
364	C₂×#576	D₅₃	1	1	yes	characteristic, direct product factor
365	C₂²×AGL(1,ℤ/8)	—	53	6	no	—
366	C₂²×#135	—	53	3	no	—
367	C₂³×D₈	—	53	3	no	—
368	C₂²×#131	—	53	1	no	—
369	C₂×C₅₃	—	2	6	no	—
370	C₂×C₅₃	—	4	12	no	—
371	C₂×C₅₃	C₂×#576	1	2	yes	complemented
372	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
373	D₅₃	—	2	6	no	—
374	D₅₃	—	4	12	no	—
375	D₅₃	C₂×#576	1	4	yes	direct product factor
376	C₂×H(5,𝔽₂)	—	53	32	no	—
377	C₂×H(5,𝔽₂)	—	53	2	no	—
378	C₂×H(5,𝔽₂)	—	53	6	no	—
379	C₂×H(5,𝔽₂)	—	53	6	no	—
380	C₂×H(5,𝔽₂)	—	106	6	no	—
381	C₂×H(5,𝔽₂)	—	106	2	no	—
382	C₂×H(5,𝔽₂)	—	106	16	no	—
383	C₂×H(5,𝔽₂)	C₂×D₅₃	1	2	yes	complemented
384	C₂²×#41	—	53	1	no	—
385	C₂²×#41	—	53	6	no	—
386	C₂²×#41	—	106	2	no	—
387	C₂³×D₄	—	53	6	no	—
388	C₂³×D₄	—	106	6	no	—
389	#576	—	53	32	no	—
390	#576	—	53	96	no	—
391	#576	—	53	48	no	—
392	#576	—	53	48	no	—
393	#576	—	53	16	no	—
394	#576	C₂×D₅₃	1	16	yes	direct product factor
395	C₂×AGL(1,ℤ/8)	—	53	6	no	—
396	C₂×AGL(1,ℤ/8)	—	53	6	no	—
397	C₂×AGL(1,ℤ/8)	—	53	96	no	—
398	C₂×AGL(1,ℤ/8)	—	53	12	no	—
399	C₂×AGL(1,ℤ/8)	—	53	12	no	—
400	C₂×AGL(1,ℤ/8)	—	53	6	no	—
401	C₂×AGL(1,ℤ/8)	C₂×D₅₃	1	6	yes	complemented
402	C₂×#135	—	53	6	no	—
403	C₂×#135	—	53	48	no	—
404	C₂×#135	—	53	3	no	—
405	C₂×#135	—	53	6	no	—
406	C₂×#135	—	53	3	no	—
407	C₂×#135	—	53	3	no	—
408	C₂×#135	C₂×D₅₃	1	3	yes	complemented
409	C₂²×Q₁₆	—	53	1	no	—
410	C₂²×SD₁₆	—	53	6	no	—
411	C₂²×D₈	—	53	6	no	—
412	C₂²×D₈	—	53	3	no	—
413	C₂²×D₈	—	53	6	no	—
414	C₂²×D₈	—	53	6	no	—
415	C₂²×D₈	—	53	6	no	—
416	C₂²×D₈	—	53	48	no	—
417	C₂²×D₈	—	53	3	no	—
418	C₂²×D₈	C₂×D₅₃	1	3	yes	complemented
419	C₂×#131	—	53	1	no	—
420	C₂×#131	—	53	16	no	—
421	C₂×#131	—	53	3	no	—
422	C₂×#131	—	53	3	no	—
423	C₂×#131	C₂×D₅₃	1	1	yes	characteristic, complemented
424	C₂²×M₁₆	—	53	3	no	—
425	C₂³×C₈	—	53	3	no	—
426	C₅₃	C₂²×#576	1	1	yes	characteristic, complemented, Sylow
427	C₂⁵	—	106	6	no	—
428	H(5,𝔽₂)	—	2	8	no	—
429	H(5,𝔽₂)	—	53	16	no	—
430	H(5,𝔽₂)	—	53	48	no	—
431	H(5,𝔽₂)	—	53	48	no	—
432	H(5,𝔽₂)	—	106	96	no	—
433	H(5,𝔽₂)	—	106	24	no	—
434	H(5,𝔽₂)	—	106	32	no	—
435	H(5,𝔽₂)	—	106	24	no	—
436	H(5,𝔽₂)	—	106	8	no	—
437	H(5,𝔽₂)	C₂²×D₅₃	1	16	yes	complemented
438	C₂×#41	—	2	2	no	—
439	C₂×#41	—	53	8	no	—
440	C₂×#41	—	53	8	no	—
441	C₂×#41	—	53	1	no	—
442	C₂×#41	—	53	3	no	—
443	C₂×#41	—	53	3	no	—
444	C₂×#41	—	53	48	no	—
445	C₂×#41	—	53	6	no	—
446	C₂×#41	—	53	6	no	—
447	C₂×#41	—	53	6	no	—
448	C₂×#41	—	106	6	no	—
449	C₂×#41	—	106	6	no	—
450	C₂×#41	—	106	6	no	—
451	C₂×#41	—	106	24	no	—
452	C₂×#41	—	106	6	no	—
453	C₂×#41	—	106	32	no	—
454	C₂×#41	—	106	2	no	—
455	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
456	C₂×#41	C₂²×D₅₃	1	6	yes	complemented
457	C₂²×Q₈	—	53	1	no	—
458	C₂²×Q₈	—	53	2	no	—
459	C₂²×D₄	—	2	6	no	—
460	C₂²×D₄	—	53	3	no	—
461	C₂²×D₄	—	53	6	no	—
462	C₂²×D₄	—	53	12	no	—
463	C₂²×D₄	—	53	48	no	—
464	C₂²×D₄	—	53	6	no	—
465	C₂²×D₄	—	106	6	no	—
466	C₂²×D₄	—	106	6	no	—
467	C₂²×D₄	—	106	6	no	—
468	C₂²×D₄	—	106	24	no	—
469	C₂²×D₄	—	106	6	no	—
470	C₂²×D₄	—	106	12	no	—
471	C₂²×D₄	—	106	96	no	—
472	C₂²×D₄	—	106	6	no	—
473	C₂²×D₄	—	106	6	no	—
474	C₂²×D₄	—	106	12	no	—
475	C₂²×D₄	—	106	6	no	—
476	C₂²×D₄	C₂²×D₅₃	1	6	yes	complemented
477	C₂³×C₄	—	53	3	no	—
478	C₂³×C₄	—	106	6	no	—
479	AGL(1,ℤ/8)	—	53	48	no	—
480	AGL(1,ℤ/8)	—	53	48	no	—
481	AGL(1,ℤ/8)	—	53	96	no	—
482	AGL(1,ℤ/8)	—	53	96	no	—
483	AGL(1,ℤ/8)	—	53	48	no	—
484	AGL(1,ℤ/8)	C₂²×D₅₃	1	48	yes	complemented
485	#135	—	53	48	no	—
486	#135	—	53	24	no	—
487	#135	—	53	48	no	—
488	#135	—	53	24	no	—
489	#135	—	53	24	no	—
490	#135	C₂²×D₅₃	1	24	yes	complemented
491	C₂×Q₁₆	—	53	2	no	—
492	C₂×Q₁₆	—	53	8	no	—
493	C₂×Q₁₆	—	53	1	no	—
494	C₂×Q₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
495	C₂×SD₁₆	—	53	6	no	—
496	C₂×SD₁₆	—	53	6	no	—
497	C₂×SD₁₆	—	53	48	no	—
498	C₂×SD₁₆	—	53	6	no	—
499	C₂×SD₁₆	C₂²×D₅₃	1	6	yes	complemented
500	C₂×D₈	—	53	6	no	—
501	C₂×D₈	—	53	12	no	—
502	C₂×D₈	—	53	48	no	—
503	C₂×D₈	—	53	24	no	—
504	C₂×D₈	—	53	48	no	—
505	C₂×D₈	—	53	48	no	—
506	C₂×D₈	—	53	48	no	—
507	C₂×D₈	—	53	3	no	—
508	C₂×D₈	—	53	6	no	—
509	C₂×D₈	—	53	24	no	—
510	C₂×D₈	C₂²×D₅₃	1	3	yes	complemented
511	C₂×D₈	C₂²×D₅₃	1	6	yes	complemented
512	C₂×D₈	C₂²×D₅₃	1	24	yes	complemented
513	#131	—	53	8	no	—
514	#131	—	53	24	no	—
515	#131	—	53	24	no	—
516	#131	C₂²×D₅₃	1	8	yes	complemented
517	C₂×M₁₆	—	53	3	no	—
518	C₂×M₁₆	—	53	24	no	—
519	C₂×M₁₆	—	53	6	no	—
520	C₂×M₁₆	C₂²×D₅₃	1	3	yes	complemented
521	C₂²×C₈	—	53	3	no	—
522	C₂²×C₈	—	53	1	no	—
523	C₂²×C₈	—	53	3	no	—
524	C₂²×C₈	—	53	3	no	—
525	C₂²×C₈	—	53	3	no	—
526	C₂²×C₈	—	53	24	no	—
527	C₂²×C₈	C₂²×D₅₃	1	3	yes	complemented
528	C₂⁴	—	2	6	no	—
529	C₂⁴	—	53	3	no	—
530	C₂⁴	—	106	12	no	—
531	C₂⁴	—	106	48	no	—
532	C₂⁴	—	106	6	no	—
533	C₂⁴	—	106	6	no	—
534	C₂⁴	—	424	24	no	—
535	#41	—	2	16	no	—
536	#41	—	2	12	no	—
537	#41	—	53	8	no	—
538	#41	—	53	24	no	—
539	#41	—	53	12	no	—
540	#41	—	53	12	no	—
541	#41	—	53	24	no	—
542	#41	—	53	24	no	—
543	#41	—	53	24	no	—
544	#41	—	106	48	no	—
545	#41	—	106	48	no	—
546	#41	—	106	48	no	—
547	#41	—	106	12	no	—
548	#41	—	106	12	no	—
549	#41	—	106	48	no	—
550	#41	—	106	16	no	—
551	#41	—	106	12	no	—
552	#41	D₄×D₅₃	1	4	yes	—
553	#41	C₂³×D₅₃	1	4	yes	—
554	#41	C₂³×D₅₃	1	24	yes	complemented
555	C₂×Q₈	—	53	8	no	—
556	C₂×Q₈	—	53	3	no	—
557	C₂×Q₈	—	53	8	no	—
558	C₂×Q₈	—	53	2	no	—
559	C₂×Q₈	—	106	2	no	—
560	C₂×Q₈	—	106	4	no	—
561	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
562	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
563	C₂×D₄	—	2	6	no	—
564	C₂×D₄	—	2	48	no	—
565	C₂×D₄	—	2	6	no	—
566	C₂×D₄	—	2	12	no	—
567	C₂×D₄	—	53	6	no	—
568	C₂×D₄	—	53	24	no	—
569	C₂×D₄	—	53	24	no	—
570	C₂×D₄	—	53	48	no	—
571	C₂×D₄	—	53	3	no	—
572	C₂×D₄	—	53	6	no	—
573	C₂×D₄	—	53	24	no	—
574	C₂×D₄	—	106	48	no	—
575	C₂×D₄	—	106	6	no	—
576	C₂×D₄	—	106	12	no	—
577	C₂×D₄	—	106	48	no	—
578	C₂×D₄	—	106	24	no	—
579	C₂×D₄	—	106	48	no	—
580	C₂×D₄	—	106	6	no	—
581	C₂×D₄	—	106	12	no	—
582	C₂×D₄	—	106	48	no	—
583	C₂×D₄	—	106	96	no	—
584	C₂×D₄	—	106	48	no	—
585	C₂×D₄	—	106	48	no	—
586	C₂×D₄	—	106	96	no	—
587	C₂×D₄	—	106	6	no	—
588	C₂×D₄	—	106	6	no	—
589	C₂×D₄	—	106	48	no	—
590	C₂×D₄	—	106	6	no	—
591	C₂×D₄	—	106	12	no	—
592	C₂×D₄	D₄×D₅₃	1	3	yes	—
593	C₂×D₄	C₂³×D₅₃	1	6	yes	—
594	C₂×D₄	C₂³×D₅₃	1	24	yes	complemented
595	C₂²×C₄	—	2	6	no	—
596	C₂²×C₄	—	53	3	no	—
597	C₂²×C₄	—	53	3	no	—
598	C₂²×C₄	—	53	12	no	—
599	C₂²×C₄	—	53	3	no	—
600	C₂²×C₄	—	53	1	no	—
601	C₂²×C₄	—	53	12	no	—
602	C₂²×C₄	—	53	3	no	—
603	C₂²×C₄	—	106	6	no	—
604	C₂²×C₄	—	106	48	no	—
605	C₂²×C₄	—	106	2	no	—
606	C₂²×C₄	—	106	6	no	—
607	C₂²×C₄	—	106	6	no	—
608	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
609	Q₁₆	—	53	8	no	—
610	Q₁₆	—	53	4	no	—
611	Q₁₆	C₂³×D₅₃	1	4	yes	complemented
612	SD₁₆	—	53	24	no	—
613	SD₁₆	—	53	24	no	—
614	SD₁₆	—	53	24	no	—
615	SD₁₆	C₂³×D₅₃	1	24	yes	complemented
616	D₈	—	53	24	no	—
617	D₈	—	53	48	no	—
618	D₈	—	53	12	no	—
619	D₈	—	53	24	no	—
620	D₈	C₂³×D₅₃	1	12	yes	complemented
621	D₈	C₂³×D₅₃	1	24	yes	complemented
622	M₁₆	—	53	12	no	—
623	M₁₆	—	53	24	no	—
624	M₁₆	C₂³×D₅₃	1	12	yes	complemented
625	C₂×C₈	—	53	1	no	—
626	C₂×C₈	—	53	3	no	—
627	C₂×C₈	—	53	12	no	—
628	C₂×C₈	—	53	4	no	—
629	C₂×C₈	—	53	12	no	—
630	C₂×C₈	—	53	12	no	—
631	C₂×C₈	—	53	12	no	—
632	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
633	C₂×C₈	C₂³×D₅₃	1	3	yes	—
634	C₂×C₈	C₂³×D₅₃	1	12	yes	complemented
635	C₂³	—	2	6	no	—
636	C₂³	—	2	24	no	—
637	C₂³	—	8	12	no	—
638	C₂³	—	53	1	no	—
639	C₂³	—	53	12	no	—
640	C₂³	—	53	3	no	—
641	C₂³	—	106	12	no	—
642	C₂³	—	106	48	no	—
643	C₂³	—	106	24	no	—
644	C₂³	—	106	24	no	—
645	C₂³	—	106	6	no	—
646	C₂³	—	424	12	no	—
647	C₂³	—	424	24	no	—
648	C₂³	—	424	96	no	—
649	C₂³	—	212	24	no	—
650	C₂³	C₂×D₄×D₅₃	1	3	yes	—
651	Q₈	—	2	2	no	—
652	Q₈	—	53	12	no	—
653	Q₈	—	53	4	no	—
654	Q₈	—	106	8	no	—
655	Q₈	—	106	2	no	—
656	Q₈	C₂×D₄×D₅₃	1	4	yes	—
657	Q₈	C₂⁴×D₅₃	1	4	yes	—
658	D₄	—	2	24	no	—
659	D₄	—	2	6	no	—
660	D₄	—	2	24	no	—
661	D₄	—	53	24	no	—
662	D₄	—	53	12	no	—
663	D₄	—	53	12	no	—
664	D₄	—	106	24	no	—
665	D₄	—	106	24	no	—
666	D₄	—	106	48	no	—
667	D₄	—	106	24	no	—
668	D₄	—	106	24	no	—
669	D₄	—	106	24	no	—
670	D₄	—	106	6	no	—
671	D₄	C₂×D₄×D₅₃	1	12	yes	—
672	D₄	C₂⁴×D₅₃	1	12	yes	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	24	no	—
675	C₂×C₄	—	53	12	no	—
676	C₂×C₄	—	53	1	no	—
677	C₂×C₄	—	53	3	no	—
678	C₂×C₄	—	53	2	no	—
679	C₂×C₄	—	53	12	no	—
680	C₂×C₄	—	53	12	no	—
681	C₂×C₄	—	53	6	no	—
682	C₂×C₄	—	53	2	no	—
683	C₂×C₄	—	53	6	no	—
684	C₂×C₄	—	106	24	no	—
685	C₂×C₄	—	106	8	no	—
686	C₂×C₄	—	106	24	no	—
687	C₂×C₄	—	106	2	no	—
688	C₂×C₄	—	106	24	no	—
689	C₂×C₄	C₂×D₄×D₅₃	1	6	yes	—
690	C₂×C₄	C₂×D₄×D₅₃	1	3	yes	—
691	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
692	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
693	C₈	—	53	2	no	—
694	C₈	—	53	6	no	—
695	C₈	C₂⁴×D₅₃	1	2	yes	—
696	C₈	C₂⁴×D₅₃	1	6	yes	—
697	C₂²	—	2	6	no	—
698	C₂²	—	2	12	no	—
699	C₂²	—	4	12	no	—
700	C₂²	—	8	24	no	—
701	C₂²	—	53	4	no	—
702	C₂²	—	53	2	no	—
703	C₂²	—	53	6	no	—
704	C₂²	—	106	24	no	—
705	C₂²	—	106	6	no	—
706	C₂²	—	106	12	no	—
707	C₂²	—	424	24	no	—
708	C₂²	—	424	48	no	—
709	C₂²	—	212	48	no	—
710	C₂²	—	212	12	no	—
711	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
712	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
713	C₄	—	2	4	no	—
714	C₄	—	53	2	no	—
715	C₄	—	53	6	no	—
716	C₄	—	106	4	no	—
717	C₄	C₂²×D₄×D₅₃	1	6	yes	—
718	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
719	C₄	C₂⁵×D₅₃	1	1	yes	characteristic
720	C₂	—	2	6	no	—
721	C₂	—	4	12	no	—
722	C₂	—	53	4	no	—
723	C₂	—	106	6	no	—
724	C₂	—	212	12	no	—
725	C₂	#576×D₅₃	1	2	yes	direct product factor
726	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₅₃
commutator, cosocle	C₄×C₅₃	C₂⁶
Frattini	C₄	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#576	C₂
socle	C₂²×C₅₃	C₂³×D₄
hypercenter	C₂×#576	D₅₃
hypocenter	C₅₃	C₂²×#576
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×#41 ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. C₂×H(5,𝔽₂)×D₅₃	C₂	semidirect
2. C₂×#16811428	C₂	semidirect
3. C₂×#16811427	C₂	semidirect
4. C₂×#16811426	C₂	semidirect
5. C₂×#16811425	C₂	semidirect
6. C₂×#16811424	C₂	semidirect
7. #576×D₅₃	C₂	direct (N × H)
8. C₂×AGL(1,ℤ/8)×D₅₃	C₂	semidirect
9. C₂×#135×D₅₃	C₂	semidirect
10. C₂²×D₈×D₅₃	C₂	semidirect
11. C₂×#131×D₅₃	C₂	semidirect
12. C₂×C₅₃×#576	C₂	semidirect
14. C₂×#13133263	C₂²	semidirect
15. C₂×#13133263	C₂²	semidirect
17. C₂×#13133262	C₂²	semidirect
19. H(5,𝔽₂)×D₅₃	C₂²	semidirect
22. C₂×#41×D₅₃	C₂²	semidirect
24. C₂²×D₄×D₅₃	C₂²	semidirect
25. #16811428	C₂²	semidirect
26. #16811427	C₂²	semidirect
27. #16811426	C₂²	semidirect
28. #16811425	C₂²	semidirect
29. #16811424	C₂²	semidirect
30. C₂×#13133245	C₂²	semidirect
31. C₂×#13133244	C₂²	semidirect
32. C₂×#13133243	C₂²	semidirect
33. C₂×#13133242	C₂²	semidirect
34. C₂×#13133241	C₂²	semidirect
35. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
36. C₂×#13133240	C₂²	semidirect
37. C₂×#13133239	C₂²	semidirect
38. C₂×#13133238	C₂²	semidirect
39. C₂×#13133237	C₂²	semidirect
40. C₂×#13133236	C₂²	semidirect
41. #135×D₅₃	C₂²	semidirect
42. C₂×Q₁₆×D₅₃	C₂²	semidirect
43. C₂×SD₁₆×D₅₃	C₂²	semidirect
44. C₂²×D₄₂₄	C₂²	semidirect
45. C₂²×#11719922	C₂²	semidirect
46. C₂×D₈×D₅₃	C₂²	semidirect
47. C₂×D₈×D₅₃	C₂²	semidirect
48. C₂×D₈×D₅₃	C₂²	semidirect
49. C₂×D₈×D₅₃	C₂²	semidirect
50. C₂×D₈×D₅₃	C₂²	semidirect
51. C₂×#13133225	C₂²	semidirect
52. C₂×#13133224	C₂²	semidirect
53. C₂×#13133223	C₂²	semidirect
54. #131×D₅₃	C₂²	semidirect
55. C₂×M₁₆×D₅₃	C₂²	semidirect
56. C₂²×C₈×D₅₃	C₂²	semidirect
57. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
58. C₅₃×#576	C₂²	semidirect
59. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
60. C₂×#135×C₅₃	C₂²	semidirect
61. C₂²×D₈×C₅₃	C₂²	semidirect
62. C₂×#131×C₅₃	C₂²	semidirect
67. #13133263	C₂³	semidirect
68. #13133263	C₂³	semidirect
71. #13133262	C₂³	semidirect
74. C₂×#11719949	C₂³	semidirect
78. C₂×#11719945	C₂³	semidirect
82. C₂×#11719947	C₂³	semidirect
87. #41×D₅₃	C₂³	semidirect
91. C₂²×D₂₁₂	C₂³	semidirect
104. C₂×D₄×D₅₃	C₂³	semidirect
105. C₂×D₄×D₅₃	C₂³	semidirect
108. #13133245	C₂³	semidirect
109. #13133244	C₂³	semidirect
110. #13133243	C₂³	semidirect
111. #13133242	C₂³	semidirect
112. #13133241	C₂³	semidirect
113. #13133240	C₂³	semidirect
114. #13133239	C₂³	semidirect
115. #13133238	C₂³	semidirect
116. #13133237	C₂³	semidirect
117. #13133236	C₂³	semidirect
118. C₂×Dic₂₁₂	C₂³	semidirect
119. C₂×#11719925	C₂³	semidirect
120. Q₁₆×D₅₃	C₂³	semidirect
121. C₂×#11719913	C₂³	semidirect
122. C₂×#11719923	C₂³	semidirect
123. C₂×#11719924	C₂³	semidirect
124. SD₁₆×D₅₃	C₂³	semidirect
125. C₂×D₄₂₄	C₂³	semidirect
126. C₂×D₄₂₄	C₂³	semidirect
127. C₂×D₄₂₄	C₂³	semidirect
128. C₂×#11719922	C₂³	semidirect
129. C₂×#11719922	C₂³	semidirect
130. C₂×#11719922	C₂³	semidirect
131. D₈×D₅₃	C₂³	semidirect
132. D₈×D₅₃	C₂³	semidirect
133. D₈×D₅₃	C₂³	semidirect
134. D₈×D₅₃	C₂³	semidirect
135. #13133225	C₂³	semidirect
136. #13133224	C₂³	semidirect
137. #13133223	C₂³	semidirect
138. C₂×#11719917	C₂³	semidirect
139. C₂×#11719912	C₂³	semidirect
140. M₁₆×D₅₃	C₂³	semidirect
141. C₂²×#88322	C₂³	semidirect
144. C₂×C₈×D₅₃	C₂³	semidirect
145. C₂×C₈×D₅₃	C₂³	semidirect
146. C₂×C₈×D₅₃	C₂³	semidirect
148. H(5,𝔽₂)×C₅₃	C₂³	semidirect
151. C₂×#41×C₅₃	C₂³	semidirect
153. C₂²×D₄×C₅₃	C₂³	semidirect
154. AGL(1,ℤ/8)×C₅₃	C₂³	semidirect
155. #135×C₅₃	C₂³	semidirect
156. C₂×Q₁₆×C₅₃	C₂³	semidirect
157. C₂×SD₁₆×C₅₃	C₂³	semidirect
158. C₂×D₈×C₅₃	C₂³	semidirect
159. C₂×D₈×C₅₃	C₂³	semidirect
160. C₂×D₈×C₅₃	C₂³	semidirect
161. #131×C₅₃	C₂³	semidirect
162. C₂×M₁₆×C₅₃	C₂³	semidirect
163. C₂²×C₈×C₅₃	C₂³	semidirect
175. #41×C₅₃	C₂⁴	semidirect
184. C₂×D₄×C₅₃	C₂⁴	semidirect
199. #11719949	C₂⁴	semidirect
207. #11719947	C₂⁴	semidirect
218. D₄×D₅₃	C₂⁴	semidirect
224. #11719945	C₂⁴	semidirect
231. C₂×D₂₁₂	C₂⁴	semidirect
245. Q₁₆×C₅₃	C₂⁴	semidirect
246. SD₁₆×C₅₃	C₂⁴	semidirect
247. D₈×C₅₃	C₂⁴	semidirect
248. D₈×C₅₃	C₂⁴	semidirect
249. M₁₆×C₅₃	C₂⁴	semidirect
252. C₂×C₈×C₅₃	C₂⁴	semidirect
253. #11719925	C₂⁴	semidirect
254. #11719924	C₂⁴	semidirect
255. #11719923	C₂⁴	semidirect
256. #11719922	C₂⁴	semidirect
257. #11719922	C₂⁴	semidirect
258. #11719917	C₂⁴	semidirect
261. C₂×#88322	C₂⁴	semidirect
262. Dic₂₁₂	C₂⁴	semidirect
263. D₄₂₄	C₂⁴	semidirect
264. D₄₂₄	C₂⁴	semidirect
265. #11719913	C₂⁴	semidirect
266. #11719912	C₂⁴	semidirect
269. C₈×D₅₃	C₂⁴	semidirect
270. C₈×D₅₃	C₂⁴	semidirect
347. C₂×D₅₃	#576	direct (N × H)
364. C₂×#576	D₅₃	direct (N × H)
371. C₂×C₅₃	C₂×#576	semidirect
375. D₅₃	C₂×#576	direct (N × H)
383. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
394. #576	C₂×D₅₃	direct (N × H)
401. C₂×AGL(1,ℤ/8)	C₂×D₅₃	semidirect
408. C₂×#135	C₂×D₅₃	semidirect
418. C₂²×D₈	C₂×D₅₃	semidirect
423. C₂×#131	C₂×D₅₃	semidirect
426. C₅₃	C₂²×#576	semidirect
437. H(5,𝔽₂)	C₂²×D₅₃	semidirect
456. C₂×#41	C₂²×D₅₃	semidirect
476. C₂²×D₄	C₂²×D₅₃	semidirect
484. AGL(1,ℤ/8)	C₂²×D₅₃	semidirect
490. #135	C₂²×D₅₃	semidirect
494. C₂×Q₁₆	C₂²×D₅₃	semidirect
499. C₂×SD₁₆	C₂²×D₅₃	semidirect
510. C₂×D₈	C₂²×D₅₃	semidirect
511. C₂×D₈	C₂²×D₅₃	semidirect
512. C₂×D₈	C₂²×D₅₃	semidirect
516. #131	C₂²×D₅₃	semidirect
520. C₂×M₁₆	C₂²×D₅₃	semidirect
527. C₂²×C₈	C₂²×D₅₃	semidirect
554. #41	C₂³×D₅₃	semidirect
594. C₂×D₄	C₂³×D₅₃	semidirect
611. Q₁₆	C₂³×D₅₃	semidirect
615. SD₁₆	C₂³×D₅₃	semidirect
620. D₈	C₂³×D₅₃	semidirect
621. D₈	C₂³×D₅₃	semidirect
624. M₁₆	C₂³×D₅₃	semidirect
634. C₂×C₈	C₂³×D₅₃	semidirect
725. C₂	#576×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
C₂×H(5,𝔽₂)×D₅₃	2
C₂×#16811428	2
C₂×#16811427	2
C₂×#16811426	2
C₂×#16811425	2
C₂×#16811424	2
#576×D₅₃	2
C₂×AGL(1,ℤ/8)×D₅₃	2
C₂×#135×D₅₃	2
C₂²×D₈×D₅₃	2
C₂×#131×D₅₃	2
C₂×C₅₃×#576	2
C₂²×#576	53

Subgroups — C2×#576×D53 #28297899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#576×D₅₃ #28297899