Subgroups — C₂×#20289493 #28297931

Order 13568.

11138 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×H(5,𝔽₂)×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20289493	C₂	1	32	yes	maximal, direct product factor
4	C₂×#16811432	C₂	1	3	yes	maximal, complemented
5	C₂×#16811431	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16811429	C₂	1	3	yes	maximal, complemented
7	C₂×#16811428	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16811427	C₂	1	3	yes	maximal, complemented
9	C₂×#16811426	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811425	C₂	1	3	yes	maximal, complemented
11	C₂×#16811422	C₂	1	3	yes	maximal, complemented
12	C₂×#16811420	C₂	1	3	yes	maximal, complemented
13	C₂²×#13133244	C₂	1	3	yes	maximal, complemented
14	C₂×AGL(1,ℤ/8)×D₅₃	C₂	1	3	yes	maximal, complemented
15	C₂×#16811388	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#577	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811460	—	2	8	no	—
18	#16811460	C₂²	1	16	yes	complemented
19	C₂×#13133265	—	2	1	no	—
20	C₂×#13133265	C₂²	1	3	yes	complemented
21	C₂×#13133263	—	2	1	no	—
22	C₂×#13133263	—	2	3	no	—
23	C₂×#13133263	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13133263	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13133263	C₂²	1	3	yes	complemented
26	C₂×#13133263	C₂²	1	3	yes	complemented
27	C₂×#13133262	—	2	3	no	—
28	C₂×#13133262	C₂²	1	3	yes	complemented
29	H(5,𝔽₂)×D₅₃	—	2	8	no	—
30	H(5,𝔽₂)×D₅₃	C₂²	1	16	yes	complemented
31	C₂²×#11719949	—	2	1	no	—
32	C₂²×#11719949	C₂²	1	3	yes	complemented
33	C₂×#41×D₅₃	—	2	3	no	—
34	C₂×#41×D₅₃	—	2	1	no	—
35	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
36	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
37	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
38	C₂²×D₄×D₅₃	—	2	3	no	—
39	C₂²×D₄×D₅₃	C₂²	1	3	yes	complemented
40	#16811432	C₂²	1	48	yes	complemented
41	#16811431	C₂²	1	16	yes	complemented
42	#16811429	C₂²	1	48	yes	complemented
43	#16811428	C₂²	1	16	yes	complemented
44	#16811427	C₂²	1	48	yes	complemented
45	#16811426	C₂²	1	16	yes	complemented
46	#16811425	C₂²	1	48	yes	complemented
47	#16811422	C₂²	1	48	yes	complemented
48	#16811420	C₂²	1	48	yes	complemented
49	C₂×#13133249	C₂²	1	3	yes	complemented
50	C₂×#13133249	C₂²	1	3	yes	complemented
51	C₂×#13133248	C₂²	1	3	yes	complemented
52	C₂×#13133246	C₂²	1	1	yes	characteristic, complemented
53	C₂×#13133246	C₂²	1	3	yes	complemented
54	C₂×#13133245	C₂²	1	3	yes	complemented
55	C₂×#13133245	C₂²	1	3	yes	complemented
56	C₂×#13133244	C₂²	1	6	yes	complemented
57	C₂×#13133244	C₂²	1	3	yes	complemented
58	C₂×#13133244	C₂²	1	6	yes	complemented
59	C₂×#13133244	C₂²	1	6	yes	complemented
60	C₂×#13133244	C₂²	1	3	yes	complemented
61	C₂×#13133244	C₂²	1	48	yes	complemented
62	C₂×#13133243	C₂²	1	3	yes	complemented
63	C₂×#13133242	C₂²	1	3	yes	complemented
64	C₂×#13133242	C₂²	1	3	yes	complemented
65	C₂×#13133241	C₂²	1	3	yes	complemented
66	C₂×#13133241	C₂²	1	3	yes	complemented
67	AGL(1,ℤ/8)×D₅₃	C₂²	1	48	yes	complemented
68	C₂×#13133240	C₂²	1	6	yes	complemented
69	C₂×#13133239	C₂²	1	3	yes	complemented
70	C₂×#13133238	C₂²	1	6	yes	complemented
71	C₂×#13133237	C₂²	1	3	yes	complemented
72	C₂×#13133237	C₂²	1	3	yes	complemented
73	C₂²×#11719924	C₂²	1	3	yes	complemented
74	C₂×SD₁₆×D₅₃	C₂²	1	6	yes	complemented
75	C₂²×D₄₂₄	C₂²	1	3	yes	complemented
76	C₂²×#11719922	C₂²	1	3	yes	complemented
77	C₂×D₈×D₅₃	C₂²	1	6	yes	complemented
78	#16811388	C₂²	1	16	yes	complemented
79	C₂×#13133225	C₂²	1	3	yes	complemented
80	C₂×#13133224	C₂²	1	1	yes	characteristic, complemented
81	C₂×#13133223	C₂²	1	3	yes	complemented
82	C₂²×#11719912	C₂²	1	3	yes	complemented
83	C₂×M₁₆×D₅₃	C₂²	1	3	yes	complemented
84	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic, complemented
85	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#577	C₂²	1	16	yes	complemented
87	C₂×#137×C₅₃	C₂²	1	3	yes	complemented
88	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	3	yes	complemented
89	C₂×#135×C₅₃	C₂²	1	3	yes	complemented
90	C₂²×SD₁₆×C₅₃	C₂²	1	3	yes	complemented
91	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
92	C₂⁴×D₅₃	—	2	3	no	—
93	#13133265	—	2	16	no	—
94	#13133265	—	2	12	no	—
95	#13133265	C₂³	1	24	yes	complemented
96	#13133263	—	2	4	no	—
97	#13133263	—	2	4	no	—
98	#13133263	—	2	16	no	—
99	#13133263	—	2	48	no	—
100	#13133263	—	2	12	no	—
101	#13133263	—	2	12	no	—
102	#13133263	C₂³	1	24	yes	complemented
103	#13133263	C₂³	1	24	yes	complemented
104	#13133263	C₂³	1	8	yes	complemented
105	#13133263	C₂³	1	8	yes	complemented
106	#13133262	—	2	48	no	—
107	#13133262	—	2	12	no	—
108	#13133262	C₂³	1	24	yes	complemented
109	C₂×#11719949	—	2	1	no	—
110	C₂×#11719949	—	2	1	no	—
111	C₂×#11719949	—	2	16	no	—
112	C₂×#11719949	—	2	3	no	—
113	C₂×#11719949	—	2	3	no	—
114	C₂×#11719949	—	2	3	no	—
115	C₂×#11719949	—	2	12	no	—
116	C₂×#11719949	D₄	1	1	yes	characteristic
117	C₂×#11719949	C₂³	1	3	yes	—
118	C₂×#11719949	C₂³	1	3	yes	—
119	C₂×#11719949	C₂³	1	6	yes	complemented
120	C₂×#11719949	C₂³	1	24	yes	complemented
121	C₂×#11719945	—	2	6	no	—
122	C₂×#11719945	—	2	3	no	—
123	C₂×#11719945	—	2	3	no	—
124	C₂×#11719945	—	2	3	no	—
125	C₂×#11719945	—	2	3	no	—
126	C₂×#11719945	C₂³	1	3	yes	—
127	C₂×#11719945	C₂³	1	3	yes	—
128	C₂×#11719945	C₂³	1	3	yes	complemented
129	C₂×#11719947	—	2	3	no	—
130	C₂×#11719947	—	2	3	no	—
131	C₂×#11719947	—	2	3	no	—
132	C₂×#11719947	D₄	1	3	yes	—
133	C₂×#11719947	C₂³	1	3	yes	—
134	C₂×#11719947	C₂³	1	1	yes	characteristic
135	#41×D₅₃	—	2	16	no	—
136	#41×D₅₃	—	2	48	no	—
137	#41×D₅₃	—	2	12	no	—
138	#41×D₅₃	—	2	12	no	—
139	#41×D₅₃	D₄	1	8	yes	—
140	#41×D₅₃	C₂³	1	8	yes	—
141	#41×D₅₃	C₂³	1	24	yes	complemented
142	#41×D₅₃	C₂³	1	24	yes	complemented
143	C₂×Q₈×D₅₃	—	2	3	no	—
144	C₂×Q₈×D₅₃	D₄	1	1	yes	characteristic
145	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
146	C₂×Q₈×D₅₃	C₂³	1	3	yes	complemented
147	C₂²×D₂₁₂	—	2	3	no	—
148	C₂²×D₂₁₂	—	2	3	no	—
149	C₂²×D₂₁₂	—	2	3	no	—
150	C₂²×D₂₁₂	C₂³	1	3	yes	—
151	C₂²×D₂₁₂	C₂³	1	3	yes	complemented
152	C₂²×C₂²⋊D₅₃	—	2	6	no	—
153	C₂²×C₂²⋊D₅₃	—	2	3	no	—
154	C₂×D₄×D₅₃	—	2	3	no	—
155	C₂×D₄×D₅₃	—	2	3	no	—
156	C₂×D₄×D₅₃	—	2	3	no	—
157	C₂×D₄×D₅₃	—	2	3	no	—
158	C₂×D₄×D₅₃	—	2	6	no	—
159	C₂×D₄×D₅₃	—	2	6	no	—
160	C₂×D₄×D₅₃	—	2	48	no	—
161	C₂×D₄×D₅₃	—	2	3	no	—
162	C₂×D₄×D₅₃	—	2	3	no	—
163	C₂×D₄×D₅₃	—	2	12	no	—
164	C₂×D₄×D₅₃	—	2	3	no	—
165	C₂×D₄×D₅₃	D₄	1	3	yes	—
166	C₂×D₄×D₅₃	C₂³	1	6	yes	—
167	C₂×D₄×D₅₃	C₂³	1	3	yes	—
168	C₂×D₄×D₅₃	C₂³	1	24	yes	complemented
169	C₂×D₄×D₅₃	C₂³	1	3	yes	complemented
170	C₂²×C₄×D₅₃	—	2	3	no	—
171	C₂²×C₄×D₅₃	—	2	3	no	—
172	C₂²×C₄×D₅₃	—	2	3	no	—
173	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
174	#13133249	C₂³	1	24	yes	complemented
175	#13133249	C₂³	1	24	yes	complemented
176	#13133248	C₂³	1	24	yes	complemented
177	#13133246	C₂³	1	8	yes	complemented
178	#13133246	C₂³	1	24	yes	complemented
179	#13133245	C₂³	1	24	yes	complemented
180	#13133245	C₂³	1	24	yes	complemented
181	#13133244	C₂³	1	48	yes	complemented
182	#13133244	C₂³	1	24	yes	complemented
183	#13133244	C₂³	1	48	yes	complemented
184	#13133244	C₂³	1	48	yes	complemented
185	#13133244	C₂³	1	24	yes	complemented
186	#13133243	C₂³	1	24	yes	complemented
187	#13133242	C₂³	1	24	yes	complemented
188	#13133242	C₂³	1	24	yes	complemented
189	#13133241	C₂³	1	24	yes	complemented
190	#13133241	C₂³	1	24	yes	complemented
191	#13133240	C₂³	1	48	yes	complemented
192	#13133239	C₂³	1	24	yes	complemented
193	#13133238	C₂³	1	48	yes	complemented
194	#13133237	C₂³	1	24	yes	complemented
195	#13133237	C₂³	1	24	yes	complemented
196	C₂×Dic₂₁₂	C₂³	1	1	yes	characteristic, complemented
197	C₂×#11719925	C₂³	1	1	yes	characteristic, complemented
198	C₂×#11719925	C₂³	1	3	yes	complemented
199	C₂×#11719913	C₂³	1	3	yes	complemented
200	C₂×#11719913	C₂³	1	3	yes	complemented
201	C₂×#11719923	C₂³	1	3	yes	complemented
202	C₂×#11719923	C₂³	1	1	yes	characteristic, complemented
203	C₂×#11719924	C₂³	1	6	yes	complemented
204	C₂×#11719924	C₂³	1	3	yes	complemented
205	C₂×#11719924	C₂³	1	3	yes	complemented
206	C₂×#11719924	C₂³	1	24	yes	complemented
207	SD₁₆×D₅₃	C₂³	1	48	yes	complemented
208	C₂×D₄₂₄	C₂³	1	6	yes	complemented
209	C₂×D₄₂₄	C₂³	1	3	yes	complemented
210	C₂×D₄₂₄	C₂³	1	24	yes	complemented
211	C₂×#11719922	C₂³	1	3	yes	complemented
212	C₂×#11719922	C₂³	1	6	yes	complemented
213	C₂×#11719922	C₂³	1	3	yes	complemented
214	C₂×#11719922	C₂³	1	24	yes	complemented
215	D₈×D₅₃	C₂³	1	48	yes	complemented
216	#13133225	C₂³	1	24	yes	complemented
217	#13133224	C₂³	1	8	yes	complemented
218	#13133223	C₂³	1	24	yes	complemented
219	C₂×#11719917	C₂³	1	3	yes	complemented
220	C₂×#11719912	C₂³	1	3	yes	—
221	C₂×#11719912	C₂³	1	1	yes	characteristic
222	C₂×#11719912	C₂³	1	24	yes	complemented
223	C₂×#11719912	C₂³	1	3	yes	complemented
224	C₂×#11719912	C₂³	1	3	yes	complemented
225	M₁₆×D₅₃	C₂³	1	24	yes	complemented
226	C₂²×#88322	C₂³	1	3	yes	complemented
227	C₂×C₈×D₅₃	C₂³	1	6	yes	complemented
228	2₋¹⁺⁴×C₅₃	—	2	4	no	—
229	2₋¹⁺⁴×C₅₃	C₂³	1	8	yes	complemented
230	H(5,𝔽₂)×C₅₃	—	2	4	no	—
231	H(5,𝔽₂)×C₅₃	C₂³	1	8	yes	complemented
232	C₂×#41×C₅₃	—	2	1	no	—
233	C₂×#41×C₅₃	—	2	3	no	—
234	C₂×#41×C₅₃	C₂³	1	3	yes	—
235	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×#41×C₅₃	C₂³	1	3	yes	complemented
237	C₂²×Q₈×C₅₃	—	2	1	no	—
238	C₂²×Q₈×C₅₃	C₂³	1	3	yes	complemented
239	C₂²×D₄×C₅₃	—	2	3	no	—
240	C₂²×D₄×C₅₃	C₂³	1	3	yes	—
241	#137×C₅₃	C₂³	1	24	yes	complemented
242	AGL(1,ℤ/8)×C₅₃	C₂³	1	24	yes	complemented
243	#135×C₅₃	C₂³	1	24	yes	complemented
244	C₂×Q₁₆×C₅₃	C₂³	1	3	yes	complemented
245	C₂×SD₁₆×C₅₃	C₂³	1	3	yes	complemented
246	C₂×SD₁₆×C₅₃	C₂³	1	6	yes	complemented
247	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
248	C₂×SD₁₆×C₅₃	C₂³	1	24	yes	complemented
249	C₂×D₈×C₅₃	C₂³	1	3	yes	complemented
250	#131×C₅₃	C₂³	1	8	yes	complemented
251	C₂×M₁₆×C₅₃	C₂³	1	3	yes	complemented
252	C₂²×C₈×C₅₃	C₂³	1	3	yes	complemented
253	C₂⁴×C₅₃	—	2	3	no	—
254	C₂³×D₅₃	—	2	3	no	—
255	C₂³×D₅₃	—	2	3	no	—
256	C₂³×D₅₃	—	2	3	no	—
257	C₂³×D₅₃	—	2	3	no	—
258	C₂³×D₅₃	—	2	24	no	—
259	C₂³×D₅₃	—	2	6	no	—
260	C₂³×D₅₃	—	8	12	no	—
261	C₂³×D₅₃	C₂×D₄	1	3	yes	—
262	#41×C₅₃	—	2	8	no	—
263	#41×C₅₃	—	2	24	no	—
264	#41×C₅₃	—	2	6	no	—
265	#41×C₅₃	—	2	6	no	—
266	#41×C₅₃	C₂×D₄	1	4	yes	—
267	#41×C₅₃	C₂⁴	1	12	yes	—
268	#41×C₅₃	C₂⁴	1	4	yes	—
269	#41×C₅₃	C₂⁴	1	12	yes	complemented
270	C₂×Q₈×C₅₃	—	2	8	no	—
271	C₂×Q₈×C₅₃	—	2	3	no	—
272	C₂×Q₈×C₅₃	—	2	6	no	—
273	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
274	C₂×Q₈×C₅₃	C₂⁴	1	3	yes	—
275	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
276	C₂×Q₈×C₅₃	C₂⁴	1	12	yes	complemented
277	C₂×D₄×C₅₃	—	2	3	no	—
278	C₂×D₄×C₅₃	—	2	3	no	—
279	C₂×D₄×C₅₃	—	2	24	no	—
280	C₂×D₄×C₅₃	—	2	3	no	—
281	C₂×D₄×C₅₃	—	2	6	no	—
282	C₂×D₄×C₅₃	C₂×D₄	1	3	yes	—
283	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
284	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
285	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
286	C₂²×C₄×C₅₃	—	2	3	no	—
287	C₂²×C₄×C₅₃	—	2	3	no	—
288	C₂²×C₄×C₅₃	—	2	3	no	—
289	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
290	C₂×C₂²⋊D₅₃	—	2	3	no	—
291	C₂×C₂²⋊D₅₃	—	2	3	no	—
292	C₂×C₂²⋊D₅₃	—	2	3	no	—
293	C₂×C₂²⋊D₅₃	—	2	1	no	—
294	C₂×C₂²⋊D₅₃	—	2	48	no	—
295	C₂×C₂²⋊D₅₃	—	2	6	no	—
296	C₂×C₂²⋊D₅₃	—	2	3	no	—
297	C₂×C₂²⋊D₅₃	—	2	3	no	—
298	C₂×C₂²⋊D₅₃	—	2	24	no	—
299	C₂×C₂²⋊D₅₃	C₂×D₄	1	6	yes	—
300	C₂²×Dic₅₃	—	2	1	no	—
301	C₂²×Dic₅₃	—	2	3	no	—
302	C₂²×Dic₅₃	C₂×D₄	1	3	yes	—
303	#11719949	—	2	8	no	—
304	#11719949	—	2	8	no	—
305	#11719949	—	2	24	no	—
306	#11719949	—	2	6	no	—
307	#11719949	—	2	24	no	—
308	#11719949	—	2	6	no	—
309	#11719949	—	2	24	no	—
310	#11719949	—	2	12	no	—
311	#11719949	C₂×D₄	1	8	yes	—
312	#11719949	C₂⁴	1	12	yes	—
313	#11719949	C₂⁴	1	12	yes	—
314	#11719949	C₂⁴	1	24	yes	complemented
315	Q₈×D₅₃	—	2	2	no	—
316	Q₈×D₅₃	—	2	6	no	—
317	Q₈×D₅₃	—	2	24	no	—
318	Q₈×D₅₃	C₂×D₄	1	8	yes	—
319	Q₈×D₅₃	C₂⁴	1	4	yes	—
320	Q₈×D₅₃	C₂⁴	1	12	yes	complemented
321	#11719947	—	2	24	no	—
322	#11719947	—	2	24	no	—
323	#11719947	—	2	2	no	—
324	#11719947	—	2	6	no	—
325	#11719947	—	2	24	no	—
326	#11719947	C₂×D₄	1	24	yes	—
327	#11719947	C₂⁴	1	12	yes	—
328	#11719947	C₂⁴	1	4	yes	—
329	D₄×D₅₃	—	2	24	no	—
330	D₄×D₅₃	—	2	24	no	—
331	D₄×D₅₃	—	2	24	no	—
332	D₄×D₅₃	—	2	24	no	—
333	D₄×D₅₃	—	2	48	no	—
334	D₄×D₅₃	—	2	48	no	—
335	D₄×D₅₃	—	2	24	no	—
336	D₄×D₅₃	—	2	6	no	—
337	D₄×D₅₃	—	2	24	no	—
338	D₄×D₅₃	—	2	12	no	—
339	D₄×D₅₃	—	2	24	no	—
340	D₄×D₅₃	—	2	6	no	—
341	D₄×D₅₃	C₂×D₄	1	24	yes	—
342	D₄×D₅₃	C₂⁴	1	24	yes	—
343	D₄×D₅₃	C₂⁴	1	12	yes	—
344	D₄×D₅₃	C₂⁴	1	12	yes	complemented
345	#11719945	—	2	6	no	—
346	#11719945	—	2	6	no	—
347	#11719945	—	2	48	no	—
348	#11719945	—	2	24	no	—
349	#11719945	—	2	24	no	—
350	#11719945	—	2	24	no	—
351	#11719945	—	2	24	no	—
352	#11719945	C₂×D₄	1	12	yes	—
353	#11719945	C₂⁴	1	12	yes	—
354	#11719945	C₂⁴	1	12	yes	—
355	#11719945	C₂⁴	1	12	yes	complemented
356	C₂×D₂₁₂	—	2	3	no	—
357	C₂×D₂₁₂	—	2	3	no	—
358	C₂×D₂₁₂	—	2	6	no	—
359	C₂×D₂₁₂	—	2	24	no	—
360	C₂×D₂₁₂	—	2	3	no	—
361	C₂×D₂₁₂	—	2	6	no	—
362	C₂×D₂₁₂	—	2	3	no	—
363	C₂×D₂₁₂	—	2	6	no	—
364	C₂×D₂₁₂	—	2	24	no	—
365	C₂×D₂₁₂	—	2	24	no	—
366	C₂×D₂₁₂	C₂×D₄	1	3	yes	—
367	C₂×D₂₁₂	C₂⁴	1	3	yes	—
368	C₂×D₂₁₂	C₂⁴	1	3	yes	—
369	C₂×D₂₁₂	C₂⁴	1	12	yes	—
370	C₂×D₂₁₂	C₂⁴	1	12	yes	complemented
371	C₂×C₄×D₅₃	—	2	1	no	—
372	C₂×C₄×D₅₃	—	2	3	no	—
373	C₂×C₄×D₅₃	—	2	3	no	—
374	C₂×C₄×D₅₃	—	2	3	no	—
375	C₂×C₄×D₅₃	—	2	3	no	—
376	C₂×C₄×D₅₃	—	2	3	no	—
377	C₂×C₄×D₅₃	—	2	6	no	—
378	C₂×C₄×D₅₃	—	2	24	no	—
379	C₂×C₄×D₅₃	—	2	24	no	—
380	C₂×C₄×D₅₃	—	2	24	no	—
381	C₂×C₄×D₅₃	C₂×D₄	1	3	yes	—
382	C₂×C₄×D₅₃	C₂×D₄	1	3	yes	—
383	C₂×C₄×D₅₃	C₂×D₄	1	12	yes	—
384	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
385	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
386	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
387	C₂×Dic₁₀₆	—	2	3	no	—
388	C₂×Dic₁₀₆	—	2	1	no	—
389	C₂×Dic₁₀₆	C₂×D₄	1	3	yes	—
390	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
392	Q₁₆×C₅₃	C₂⁴	1	12	yes	complemented
393	SD₁₆×C₅₃	C₂⁴	1	12	yes	complemented
394	SD₁₆×C₅₃	C₂⁴	1	24	yes	complemented
395	SD₁₆×C₅₃	C₂⁴	1	4	yes	complemented
396	D₈×C₅₃	C₂⁴	1	12	yes	complemented
397	M₁₆×C₅₃	C₂⁴	1	12	yes	complemented
398	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₅₃	C₂⁴	1	3	yes	—
400	C₂×C₈×C₅₃	C₂⁴	1	12	yes	complemented
401	#11719925	C₂⁴	1	4	yes	complemented
402	#11719925	C₂⁴	1	12	yes	complemented
403	#11719924	C₂⁴	1	24	yes	complemented
404	#11719924	C₂⁴	1	12	yes	complemented
405	#11719924	C₂⁴	1	12	yes	complemented
406	#11719923	C₂⁴	1	12	yes	complemented
407	#11719923	C₂⁴	1	4	yes	complemented
408	#11719922	C₂⁴	1	12	yes	complemented
409	#11719922	C₂⁴	1	24	yes	complemented
410	#11719922	C₂⁴	1	12	yes	complemented
411	#11719917	C₂⁴	1	12	yes	complemented
412	C₂×#88322	C₂⁴	1	3	yes	—
413	C₂×#88322	C₂⁴	1	1	yes	characteristic
414	C₂×#88322	C₂⁴	1	12	yes	complemented
415	Dic₂₁₂	C₂⁴	1	4	yes	complemented
416	D₄₂₄	C₂⁴	1	24	yes	complemented
417	D₄₂₄	C₂⁴	1	12	yes	complemented
418	#11719913	C₂⁴	1	12	yes	complemented
419	#11719913	C₂⁴	1	12	yes	complemented
420	#11719912	C₂⁴	1	12	yes	—
421	#11719912	C₂⁴	1	4	yes	—
422	#11719912	C₂⁴	1	12	yes	complemented
423	#11719912	C₂⁴	1	12	yes	complemented
424	C₈×D₅₃	C₂⁴	1	24	yes	complemented
425	C₂³×C₅₃	—	2	1	no	—
426	C₂³×C₅₃	—	2	3	no	—
427	C₂³×C₅₃	—	2	12	no	—
428	C₂³×C₅₃	—	8	6	no	—
429	C₂³×C₅₃	C₂²×D₄	1	3	yes	—
430	C₂²×D₅₃	—	2	3	no	—
431	C₂²×D₅₃	—	2	3	no	—
432	C₂²×D₅₃	—	2	12	no	—
433	C₂²×D₅₃	—	2	12	no	—
434	C₂²×D₅₃	—	2	12	no	—
435	C₂²×D₅₃	—	2	12	no	—
436	C₂²×D₅₃	—	2	24	no	—
437	C₂²×D₅₃	—	4	6	no	—
438	C₂²×D₅₃	—	4	12	no	—
439	C₂²×D₅₃	—	8	6	no	—
440	C₂²×D₅₃	—	8	12	no	—
441	C₂²×D₅₃	—	8	48	no	—
442	C₂²×D₅₃	—	8	6	no	—
443	C₂²×D₅₃	—	8	6	no	—
444	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
445	C₂²×D₅₃	C₂²×D₄	1	3	yes	—
446	C₂²×D₅₃	C₂²×D₄	1	12	yes	—
447	Q₈×C₅₃	—	2	3	no	—
448	Q₈×C₅₃	—	2	12	no	—
449	Q₈×C₅₃	—	2	1	no	—
450	Q₈×C₅₃	C₂²×D₄	1	4	yes	—
451	Q₈×C₅₃	C₂⁵	1	2	yes	—
452	Q₈×C₅₃	C₂⁵	1	6	yes	—
453	D₄×C₅₃	—	2	12	no	—
454	D₄×C₅₃	—	2	12	no	—
455	D₄×C₅₃	—	2	3	no	—
456	D₄×C₅₃	—	2	12	no	—
457	D₄×C₅₃	—	2	1	no	—
458	D₄×C₅₃	C₂²×D₄	1	12	yes	—
459	D₄×C₅₃	C₂⁵	1	6	yes	—
460	D₄×C₅₃	C₂⁵	1	2	yes	—
461	C₂×C₄×C₅₃	—	2	1	no	—
462	C₂×C₄×C₅₃	—	2	3	no	—
463	C₂×C₄×C₅₃	—	2	12	no	—
464	C₂×C₄×C₅₃	—	2	12	no	—
465	C₂×C₄×C₅₃	—	2	12	no	—
466	C₂×C₄×C₅₃	C₂²×D₄	1	3	yes	—
467	C₂×C₄×C₅₃	C₂²×D₄	1	6	yes	—
468	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
469	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
470	C₂²⋊D₅₃	—	2	12	no	—
471	C₂²⋊D₅₃	—	2	12	no	—
472	C₂²⋊D₅₃	—	2	4	no	—
473	C₂²⋊D₅₃	—	2	12	no	—
474	C₂²⋊D₅₃	—	2	12	no	—
475	C₂²⋊D₅₃	—	2	24	no	—
476	C₂²⋊D₅₃	—	2	12	no	—
477	C₂²⋊D₅₃	C₂²×D₄	1	24	yes	—
478	C₂×Dic₅₃	—	2	1	no	—
479	C₂×Dic₅₃	—	2	1	no	—
480	C₂×Dic₅₃	—	2	4	no	—
481	C₂×Dic₅₃	—	2	12	no	—
482	C₂×Dic₅₃	C₂²×D₄	1	3	yes	—
483	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×Dic₅₃	C₂²×D₄	1	12	yes	—
485	D₂₁₂	—	2	12	no	—
486	D₂₁₂	—	2	12	no	—
487	D₂₁₂	—	2	24	no	—
488	D₂₁₂	—	2	3	no	—
489	D₂₁₂	—	2	12	no	—
490	D₂₁₂	—	2	3	no	—
491	D₂₁₂	—	2	12	no	—
492	D₂₁₂	C₂²×D₄	1	12	yes	—
493	D₂₁₂	C₂⁵	1	6	yes	—
494	D₂₁₂	C₂⁵	1	6	yes	—
495	C₄×D₅₃	—	2	4	no	—
496	C₄×D₅₃	—	2	12	no	—
497	C₄×D₅₃	—	2	12	no	—
498	C₄×D₅₃	—	2	12	no	—
499	C₄×D₅₃	—	2	12	no	—
500	C₄×D₅₃	—	2	12	no	—
501	C₄×D₅₃	—	2	24	no	—
502	C₄×D₅₃	C₂²×D₄	1	12	yes	—
503	C₄×D₅₃	C₂²×D₄	1	12	yes	—
504	C₄×D₅₃	C₂²×D₄	1	2	yes	—
505	C₄×D₅₃	C₂²×D₄	1	6	yes	—
506	C₄×D₅₃	C₂⁵	1	2	yes	—
507	C₄×D₅₃	C₂⁵	1	6	yes	—
508	Dic₁₀₆	—	2	1	no	—
509	Dic₁₀₆	—	2	1	no	—
510	Dic₁₀₆	—	2	4	no	—
511	Dic₁₀₆	—	2	12	no	—
512	Dic₁₀₆	C₂²×D₄	1	12	yes	—
513	Dic₁₀₆	C₂⁵	1	2	yes	—
514	Dic₁₀₆	C₂⁵	1	2	yes	—
515	C₈×C₅₃	C₂⁵	1	6	yes	—
516	C₈×C₅₃	C₂⁵	1	2	yes	—
517	#88322	C₂⁵	1	6	yes	—
518	#88322	C₂⁵	1	2	yes	—
519	C₂×#3585	—	53	1	no	maximal, Sylow
520	C₂²×C₅₃	—	2	6	no	—
521	C₂²×C₅₃	—	2	2	no	—
522	C₂²×C₅₃	—	2	6	no	—
523	C₂²×C₅₃	—	4	6	no	—
524	C₂²×C₅₃	—	4	2	no	—
525	C₂²×C₅₃	—	8	12	no	—
526	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
527	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
528	C₂×D₅₃	—	2	2	no	—
529	C₂×D₅₃	—	2	6	no	—
530	C₂×D₅₃	—	2	6	no	—
531	C₂×D₅₃	—	2	6	no	—
532	C₂×D₅₃	—	4	12	no	—
533	C₂×D₅₃	—	4	24	no	—
534	C₂×D₅₃	—	4	6	no	—
535	C₂×D₅₃	—	4	6	no	—
536	C₂×D₅₃	—	8	12	no	—
537	C₂×D₅₃	—	8	24	no	—
538	C₂×D₅₃	—	8	12	no	—
539	C₂×D₅₃	—	8	12	no	—
540	C₂×D₅₃	C₂³×D₄	1	2	yes	—
541	C₂×D₅₃	C₂³×D₄	1	6	yes	—
542	C₄×C₅₃	—	2	2	no	—
543	C₄×C₅₃	—	2	6	no	—
544	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
545	C₄×C₅₃	C₂³×D₄	1	6	yes	—
546	C₄×C₅₃	C₂⁶	1	1	yes	characteristic
547	Dic₅₃	—	2	2	no	—
548	Dic₅₃	—	2	2	no	—
549	Dic₅₃	C₂³×D₄	1	6	yes	—
550	Dic₅₃	C₂³×D₄	1	2	yes	—
551	C₂×#585	—	53	1	no	—
552	C₂²×H(5,𝔽₂)	—	53	1	no	—
553	#3585	—	53	32	no	—
554	C₂×#577	—	53	1	no	—
555	C₂×#577	—	53	3	no	—
556	C₂×#577	—	53	3	no	—
557	C₂×#577	D₅₃	1	1	yes	characteristic, complemented
558	C₂×#576	—	53	1	no	—
559	C₂×#576	—	53	3	no	—
560	C₂×#576	—	53	3	no	—
561	C₂×#576	—	53	1	no	—
562	C₂×#575	—	53	3	no	—
563	C₂×#575	—	53	3	no	—
564	C₂²×AGL(1,ℤ/8)	—	53	3	no	—
565	C₂²×AGL(1,ℤ/8)	—	53	3	no	—
566	C₂×#568	—	53	1	no	—
567	C₂×C₅₃	—	2	6	no	—
568	C₂×C₅₃	—	4	6	no	—
569	C₂×C₅₃	—	4	2	no	—
570	C₂×C₅₃	#3585	1	2	yes	complemented
571	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
572	D₅₃	—	2	2	no	—
573	D₅₃	—	2	6	no	—
574	D₅₃	—	4	6	no	—
575	D₅₃	—	4	6	no	—
576	#585	—	53	16	no	—
577	#585	—	106	8	no	—
578	C₂×2₋¹⁺⁴	—	53	3	no	—
579	C₂×2₋¹⁺⁴	—	106	1	no	—
580	C₂×2₋¹⁺⁴	C₂×D₅₃	1	1	yes	characteristic, complemented
581	C₂×H(5,𝔽₂)	—	53	16	no	—
582	C₂×H(5,𝔽₂)	—	53	3	no	—
583	C₂×H(5,𝔽₂)	—	53	1	no	—
584	C₂×H(5,𝔽₂)	—	53	1	no	—
585	C₂×H(5,𝔽₂)	—	53	3	no	—
586	C₂×H(5,𝔽₂)	—	53	3	no	—
587	C₂×H(5,𝔽₂)	—	106	3	no	—
588	C₂×H(5,𝔽₂)	—	106	3	no	—
589	C₂×H(5,𝔽₂)	—	106	1	no	—
590	C₂×H(5,𝔽₂)	—	106	8	no	—
591	C₂×H(5,𝔽₂)	C₂×D₅₃	1	1	yes	characteristic, complemented
592	C₂²×#41	—	53	1	no	—
593	C₂²×#41	—	53	3	no	—
594	C₂²×#41	—	53	3	no	—
595	C₂²×#41	—	53	3	no	—
596	C₂²×#41	—	106	1	no	—
597	C₂²×#41	—	106	1	no	—
598	C₂²×#41	—	106	3	no	—
599	C₂³×D₄	—	53	3	no	—
600	C₂³×D₄	—	106	3	no	—
601	#577	—	53	16	no	—
602	#577	—	53	48	no	—
603	#577	—	53	48	no	—
604	#577	C₂×D₅₃	1	16	yes	complemented
605	#576	—	53	16	no	—
606	#576	—	53	48	no	—
607	#576	—	53	48	no	—
608	#576	—	53	16	no	—
609	#575	—	53	48	no	—
610	#575	—	53	48	no	—
611	C₂×#137	—	53	3	no	—
612	C₂×#137	—	53	3	no	—
613	C₂×#137	—	53	3	no	—
614	C₂×#137	—	53	1	no	—
615	C₂×#137	—	53	3	no	—
616	C₂×#137	C₂×D₅₃	1	3	yes	complemented
617	C₂×AGL(1,ℤ/8)	—	53	3	no	—
618	C₂×AGL(1,ℤ/8)	—	53	3	no	—
619	C₂×AGL(1,ℤ/8)	—	53	3	no	—
620	C₂×AGL(1,ℤ/8)	—	53	48	no	—
621	C₂×AGL(1,ℤ/8)	—	53	48	no	—
622	C₂×AGL(1,ℤ/8)	—	53	6	no	—
623	C₂×AGL(1,ℤ/8)	—	53	3	no	—
624	C₂×AGL(1,ℤ/8)	—	53	6	no	—
625	C₂×AGL(1,ℤ/8)	—	53	6	no	—
626	C₂×AGL(1,ℤ/8)	—	53	3	no	—
627	C₂×AGL(1,ℤ/8)	—	53	3	no	—
628	C₂×AGL(1,ℤ/8)	—	53	3	no	—
629	C₂×AGL(1,ℤ/8)	—	53	3	no	—
630	C₂×AGL(1,ℤ/8)	—	53	3	no	—
631	C₂×AGL(1,ℤ/8)	C₂×D₅₃	1	3	yes	complemented
632	C₂×#135	—	53	3	no	—
633	C₂×#135	—	53	3	no	—
634	C₂×#135	—	53	6	no	—
635	C₂×#135	—	53	6	no	—
636	C₂×#135	—	53	3	no	—
637	C₂×#135	C₂×D₅₃	1	3	yes	complemented
638	C₂²×SD₁₆	—	53	3	no	—
639	C₂²×SD₁₆	—	53	6	no	—
640	C₂²×SD₁₆	C₂×D₅₃	1	3	yes	complemented
641	C₂²×D₈	—	53	3	no	—
642	C₂²×D₈	—	53	6	no	—
643	C₂²×D₈	—	53	3	no	—
644	#568	—	53	16	no	—
645	C₂×#131	—	53	1	no	—
646	C₂×#131	—	53	3	no	—
647	C₂×#131	—	53	3	no	—
648	C₂×#131	C₂×D₅₃	1	1	yes	characteristic, complemented
649	C₂²×M₁₆	—	53	3	no	—
650	C₂²×M₁₆	—	53	3	no	—
651	C₅₃	C₂×#3585	1	1	yes	characteristic, complemented, Sylow
652	C₂⁵	—	106	3	no	—
653	2₋¹⁺⁴	—	2	4	no	—
654	2₋¹⁺⁴	—	53	24	no	—
655	2₋¹⁺⁴	—	106	16	no	—
656	2₋¹⁺⁴	—	106	12	no	—
657	2₋¹⁺⁴	C₂²×D₅₃	1	8	yes	complemented
658	H(5,𝔽₂)	—	2	4	no	—
659	H(5,𝔽₂)	—	53	8	no	—
660	H(5,𝔽₂)	—	53	24	no	—
661	H(5,𝔽₂)	—	53	8	no	—
662	H(5,𝔽₂)	—	53	24	no	—
663	H(5,𝔽₂)	—	53	24	no	—
664	H(5,𝔽₂)	—	106	48	no	—
665	H(5,𝔽₂)	—	106	12	no	—
666	H(5,𝔽₂)	—	106	48	no	—
667	H(5,𝔽₂)	—	106	16	no	—
668	H(5,𝔽₂)	—	106	12	no	—
669	H(5,𝔽₂)	—	106	12	no	—
670	H(5,𝔽₂)	—	106	4	no	—
671	H(5,𝔽₂)	—	106	4	no	—
672	H(5,𝔽₂)	C₂²×D₅₃	1	8	yes	complemented
673	C₂×#41	—	2	1	no	—
674	C₂×#41	—	2	3	no	—
675	C₂×#41	—	53	8	no	—
676	C₂×#41	—	53	8	no	—
677	C₂×#41	—	53	1	no	—
678	C₂×#41	—	53	3	no	—
679	C₂×#41	—	53	3	no	—
680	C₂×#41	—	53	24	no	—
681	C₂×#41	—	53	24	no	—
682	C₂×#41	—	53	6	no	—
683	C₂×#41	—	53	3	no	—
684	C₂×#41	—	53	3	no	—
685	C₂×#41	—	53	24	no	—
686	C₂×#41	—	53	3	no	—
687	C₂×#41	—	53	1	no	—
688	C₂×#41	—	53	3	no	—
689	C₂×#41	—	53	3	no	—
690	C₂×#41	—	106	3	no	—
691	C₂×#41	—	106	3	no	—
692	C₂×#41	—	106	6	no	—
693	C₂×#41	—	106	3	no	—
694	C₂×#41	—	106	3	no	—
695	C₂×#41	—	106	3	no	—
696	C₂×#41	—	106	3	no	—
697	C₂×#41	—	106	3	no	—
698	C₂×#41	—	106	3	no	—
699	C₂×#41	—	106	12	no	—
700	C₂×#41	—	106	12	no	—
701	C₂×#41	—	106	12	no	—
702	C₂×#41	—	106	3	no	—
703	C₂×#41	—	106	3	no	—
704	C₂×#41	—	106	16	no	—
705	C₂×#41	—	106	16	no	—
706	C₂×#41	—	106	48	no	—
707	C₂×#41	—	106	1	no	—
708	C₂×#41	—	106	1	no	—
709	C₂×#41	C₂²×D₅₃	1	3	yes	—
710	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
711	C₂×#41	C₂²×D₅₃	1	3	yes	complemented
712	C₂²×Q₈	—	2	1	no	—
713	C₂²×Q₈	—	53	1	no	—
714	C₂²×Q₈	—	53	3	no	—
715	C₂²×Q₈	—	53	1	no	—
716	C₂²×Q₈	—	106	3	no	—
717	C₂²×Q₈	C₂²×D₅₃	1	3	yes	complemented
718	C₂²×D₄	—	2	3	no	—
719	C₂²×D₄	—	53	3	no	—
720	C₂²×D₄	—	53	3	no	—
721	C₂²×D₄	—	53	6	no	—
722	C₂²×D₄	—	53	3	no	—
723	C₂²×D₄	—	53	24	no	—
724	C₂²×D₄	—	53	3	no	—
725	C₂²×D₄	—	53	3	no	—
726	C₂²×D₄	—	106	3	no	—
727	C₂²×D₄	—	106	3	no	—
728	C₂²×D₄	—	106	3	no	—
729	C₂²×D₄	—	106	3	no	—
730	C₂²×D₄	—	106	3	no	—
731	C₂²×D₄	—	106	12	no	—
732	C₂²×D₄	—	106	3	no	—
733	C₂²×D₄	—	106	6	no	—
734	C₂²×D₄	—	106	48	no	—
735	C₂²×D₄	—	106	3	no	—
736	C₂²×D₄	—	106	6	no	—
737	C₂²×D₄	—	106	3	no	—
738	C₂²×D₄	—	106	3	no	—
739	C₂²×D₄	—	106	6	no	—
740	C₂²×D₄	—	106	3	no	—
741	C₂²×D₄	—	106	3	no	—
742	C₂²×D₄	C₂²×D₅₃	1	3	yes	—
743	C₂³×C₄	—	53	3	no	—
744	C₂³×C₄	—	106	3	no	—
745	C₂³×C₄	—	106	3	no	—
746	C₂³×C₄	—	106	3	no	—
747	#137	—	53	24	no	—
748	#137	—	53	24	no	—
749	#137	—	53	24	no	—
750	#137	—	53	8	no	—
751	#137	—	53	24	no	—
752	#137	C₂²×D₅₃	1	24	yes	complemented
753	AGL(1,ℤ/8)	—	53	24	no	—
754	AGL(1,ℤ/8)	—	53	24	no	—
755	AGL(1,ℤ/8)	—	53	24	no	—
756	AGL(1,ℤ/8)	—	53	48	no	—
757	AGL(1,ℤ/8)	—	53	24	no	—
758	AGL(1,ℤ/8)	—	53	48	no	—
759	AGL(1,ℤ/8)	—	53	48	no	—
760	AGL(1,ℤ/8)	—	53	24	no	—
761	AGL(1,ℤ/8)	—	53	24	no	—
762	AGL(1,ℤ/8)	—	53	24	no	—
763	AGL(1,ℤ/8)	—	53	24	no	—
764	AGL(1,ℤ/8)	—	53	24	no	—
765	AGL(1,ℤ/8)	C₂²×D₅₃	1	24	yes	complemented
766	#135	—	53	24	no	—
767	#135	—	53	24	no	—
768	#135	—	53	48	no	—
769	#135	—	53	48	no	—
770	#135	—	53	24	no	—
771	#135	C₂²×D₅₃	1	24	yes	complemented
772	C₂×Q₁₆	—	53	1	no	—
773	C₂×Q₁₆	—	53	3	no	—
774	C₂×Q₁₆	—	53	1	no	—
775	C₂×Q₁₆	C₂²×D₅₃	1	3	yes	complemented
776	C₂×SD₁₆	—	53	3	no	—
777	C₂×SD₁₆	—	53	6	no	—
778	C₂×SD₁₆	—	53	3	no	—
779	C₂×SD₁₆	—	53	24	no	—
780	C₂×SD₁₆	—	53	3	no	—
781	C₂×SD₁₆	—	53	1	no	—
782	C₂×SD₁₆	—	53	48	no	—
783	C₂×SD₁₆	—	53	3	no	—
784	C₂×SD₁₆	—	53	3	no	—
785	C₂×SD₁₆	C₂²×D₅₃	1	6	yes	complemented
786	C₂×SD₁₆	C₂²×D₅₃	1	3	yes	complemented
787	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
788	C₂×SD₁₆	C₂²×D₅₃	1	24	yes	complemented
789	C₂×D₈	—	53	3	no	—
790	C₂×D₈	—	53	6	no	—
791	C₂×D₈	—	53	3	no	—
792	C₂×D₈	—	53	24	no	—
793	C₂×D₈	—	53	48	no	—
794	C₂×D₈	—	53	6	no	—
795	C₂×D₈	—	53	3	no	—
796	C₂×D₈	—	53	24	no	—
797	C₂×D₈	C₂²×D₅₃	1	3	yes	complemented
798	#131	—	53	8	no	—
799	#131	—	53	24	no	—
800	#131	—	53	24	no	—
801	#131	C₂²×D₅₃	1	8	yes	complemented
802	C₂×M₁₆	—	53	3	no	—
803	C₂×M₁₆	—	53	24	no	—
804	C₂×M₁₆	—	53	3	no	—
805	C₂×M₁₆	—	53	1	no	—
806	C₂×M₁₆	—	53	3	no	—
807	C₂×M₁₆	—	53	3	no	—
808	C₂×M₁₆	—	53	24	no	—
809	C₂×M₁₆	C₂²×D₅₃	1	3	yes	complemented
810	C₂²×C₈	—	53	3	no	—
811	C₂²×C₈	—	53	6	no	—
812	C₂²×C₈	C₂²×D₅₃	1	3	yes	complemented
813	C₂⁴	—	2	3	no	—
814	C₂⁴	—	53	3	no	—
815	C₂⁴	—	106	3	no	—
816	C₂⁴	—	106	6	no	—
817	C₂⁴	—	106	24	no	—
818	C₂⁴	—	106	3	no	—
819	C₂⁴	—	106	3	no	—
820	C₂⁴	—	106	3	no	—
821	C₂⁴	—	424	12	no	—
822	#41	—	2	8	no	—
823	#41	—	2	24	no	—
824	#41	—	2	6	no	—
825	#41	—	2	6	no	—
826	#41	—	53	8	no	—
827	#41	—	53	24	no	—
828	#41	—	53	12	no	—
829	#41	—	53	12	no	—
830	#41	—	53	12	no	—
831	#41	—	53	12	no	—
832	#41	—	53	24	no	—
833	#41	—	53	12	no	—
834	#41	—	53	4	no	—
835	#41	—	53	12	no	—
836	#41	—	53	12	no	—
837	#41	—	106	24	no	—
838	#41	—	106	24	no	—
839	#41	—	106	48	no	—
840	#41	—	106	24	no	—
841	#41	—	106	24	no	—
842	#41	—	106	24	no	—
843	#41	—	106	2	no	—
844	#41	—	106	24	no	—
845	#41	—	106	6	no	—
846	#41	—	106	6	no	—
847	#41	—	106	24	no	—
848	#41	—	106	6	no	—
849	#41	—	106	24	no	—
850	#41	—	106	12	no	—
851	#41	—	106	24	no	—
852	#41	—	106	24	no	—
853	#41	—	106	8	no	—
854	#41	—	106	8	no	—
855	#41	—	106	6	no	—
856	#41	—	106	6	no	—
857	#41	D₄×D₅₃	1	4	yes	—
858	#41	C₂³×D₅₃	1	12	yes	—
859	#41	C₂³×D₅₃	1	4	yes	—
860	#41	C₂³×D₅₃	1	12	yes	complemented
861	C₂×Q₈	—	2	8	no	—
862	C₂×Q₈	—	2	3	no	—
863	C₂×Q₈	—	2	6	no	—
864	C₂×Q₈	—	53	8	no	—
865	C₂×Q₈	—	53	3	no	—
866	C₂×Q₈	—	53	4	no	—
867	C₂×Q₈	—	53	12	no	—
868	C₂×Q₈	—	53	1	no	—
869	C₂×Q₈	—	53	1	no	—
870	C₂×Q₈	—	106	3	no	—
871	C₂×Q₈	—	106	1	no	—
872	C₂×Q₈	—	106	2	no	—
873	C₂×Q₈	—	106	6	no	—
874	C₂×Q₈	—	106	24	no	—
875	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
876	C₂×Q₈	C₂³×D₅₃	1	3	yes	—
877	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
878	C₂×Q₈	C₂³×D₅₃	1	12	yes	complemented
879	C₂×D₄	—	2	3	no	—
880	C₂×D₄	—	2	3	no	—
881	C₂×D₄	—	2	24	no	—
882	C₂×D₄	—	2	3	no	—
883	C₂×D₄	—	2	6	no	—
884	C₂×D₄	—	53	6	no	—
885	C₂×D₄	—	53	24	no	—
886	C₂×D₄	—	53	24	no	—
887	C₂×D₄	—	53	12	no	—
888	C₂×D₄	—	53	12	no	—
889	C₂×D₄	—	53	3	no	—
890	C₂×D₄	—	53	3	no	—
891	C₂×D₄	—	53	3	no	—
892	C₂×D₄	—	53	12	no	—
893	C₂×D₄	—	53	12	no	—
894	C₂×D₄	—	106	24	no	—
895	C₂×D₄	—	106	24	no	—
896	C₂×D₄	—	106	3	no	—
897	C₂×D₄	—	106	3	no	—
898	C₂×D₄	—	106	6	no	—
899	C₂×D₄	—	106	24	no	—
900	C₂×D₄	—	106	6	no	—
901	C₂×D₄	—	106	24	no	—
902	C₂×D₄	—	106	24	no	—
903	C₂×D₄	—	106	12	no	—
904	C₂×D₄	—	106	6	no	—
905	C₂×D₄	—	106	3	no	—
906	C₂×D₄	—	106	6	no	—
907	C₂×D₄	—	106	3	no	—
908	C₂×D₄	—	106	24	no	—
909	C₂×D₄	—	106	48	no	—
910	C₂×D₄	—	106	24	no	—
911	C₂×D₄	—	106	48	no	—
912	C₂×D₄	—	106	24	no	—
913	C₂×D₄	—	106	24	no	—
914	C₂×D₄	—	106	48	no	—
915	C₂×D₄	—	106	3	no	—
916	C₂×D₄	—	106	1	no	—
917	C₂×D₄	—	106	3	no	—
918	C₂×D₄	—	106	3	no	—
919	C₂×D₄	—	106	24	no	—
920	C₂×D₄	—	106	24	no	—
921	C₂×D₄	—	106	3	no	—
922	C₂×D₄	—	106	3	no	—
923	C₂×D₄	—	106	6	no	—
924	C₂×D₄	—	106	6	no	—
925	C₂×D₄	D₄×D₅₃	1	3	yes	—
926	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
927	C₂×D₄	C₂³×D₅₃	1	3	yes	—
928	C₂×D₄	C₂³×D₅₃	1	12	yes	—
929	C₂²×C₄	—	2	3	no	—
930	C₂²×C₄	—	2	3	no	—
931	C₂²×C₄	—	2	3	no	—
932	C₂²×C₄	—	53	3	no	—
933	C₂²×C₄	—	53	3	no	—
934	C₂²×C₄	—	53	3	no	—
935	C₂²×C₄	—	53	12	no	—
936	C₂²×C₄	—	53	3	no	—
937	C₂²×C₄	—	53	1	no	—
938	C₂²×C₄	—	53	12	no	—
939	C₂²×C₄	—	106	3	no	—
940	C₂²×C₄	—	106	3	no	—
941	C₂²×C₄	—	106	24	no	—
942	C₂²×C₄	—	106	6	no	—
943	C₂²×C₄	—	106	24	no	—
944	C₂²×C₄	—	106	24	no	—
945	C₂²×C₄	—	106	1	no	—
946	C₂²×C₄	—	106	3	no	—
947	C₂²×C₄	—	106	1	no	—
948	C₂²×C₄	—	106	3	no	—
949	C₂²×C₄	—	106	3	no	—
950	C₂²×C₄	—	106	3	no	—
951	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
952	Q₁₆	—	53	4	no	—
953	Q₁₆	—	53	12	no	—
954	Q₁₆	—	53	4	no	—
955	Q₁₆	C₂³×D₅₃	1	12	yes	complemented
956	SD₁₆	—	53	12	no	—
957	SD₁₆	—	53	24	no	—
958	SD₁₆	—	53	12	no	—
959	SD₁₆	—	53	12	no	—
960	SD₁₆	—	53	4	no	—
961	SD₁₆	—	53	12	no	—
962	SD₁₆	—	53	12	no	—
963	SD₁₆	C₂³×D₅₃	1	24	yes	complemented
964	SD₁₆	C₂³×D₅₃	1	12	yes	complemented
965	SD₁₆	C₂³×D₅₃	1	4	yes	complemented
966	D₈	—	53	12	no	—
967	D₈	—	53	24	no	—
968	D₈	—	53	12	no	—
969	D₈	—	53	24	no	—
970	D₈	—	53	12	no	—
971	D₈	C₂³×D₅₃	1	12	yes	complemented
972	M₁₆	—	53	12	no	—
973	M₁₆	—	53	12	no	—
974	M₁₆	—	53	4	no	—
975	M₁₆	—	53	12	no	—
976	M₁₆	—	53	12	no	—
977	M₁₆	C₂³×D₅₃	1	12	yes	complemented
978	C₂×C₈	—	53	1	no	—
979	C₂×C₈	—	53	3	no	—
980	C₂×C₈	—	53	12	no	—
981	C₂×C₈	—	53	24	no	—
982	C₂×C₈	C₂³×D₅₃	1	3	yes	—
983	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
984	C₂×C₈	C₂³×D₅₃	1	12	yes	complemented
985	C₂³	—	2	1	no	—
986	C₂³	—	2	3	no	—
987	C₂³	—	2	12	no	—
988	C₂³	—	8	6	no	—
989	C₂³	—	53	1	no	—
990	C₂³	—	53	3	no	—
991	C₂³	—	53	12	no	—
992	C₂³	—	106	12	no	—
993	C₂³	—	106	24	no	—
994	C₂³	—	106	12	no	—
995	C₂³	—	106	12	no	—
996	C₂³	—	106	12	no	—
997	C₂³	—	106	3	no	—
998	C₂³	—	106	3	no	—
999	C₂³	—	424	6	no	—
1000	C₂³	—	424	6	no	—
1001	C₂³	—	424	6	no	—
1002	C₂³	—	424	12	no	—
1003	C₂³	—	424	48	no	—
1004	C₂³	—	212	6	no	—
1005	C₂³	—	212	12	no	—
1006	C₂³	C₂×D₄×D₅₃	1	3	yes	—
1007	Q₈	—	2	3	no	—
1008	Q₈	—	2	12	no	—
1009	Q₈	—	2	1	no	—
1010	Q₈	—	53	12	no	—
1011	Q₈	—	53	2	no	—
1012	Q₈	—	53	2	no	—
1013	Q₈	—	106	12	no	—
1014	Q₈	—	106	4	no	—
1015	Q₈	—	106	1	no	—
1016	Q₈	—	106	1	no	—
1017	Q₈	C₂×D₄×D₅₃	1	4	yes	—
1018	Q₈	C₂⁴×D₅₃	1	6	yes	—
1019	Q₈	C₂⁴×D₅₃	1	2	yes	—
1020	D₄	—	2	12	no	—
1021	D₄	—	2	12	no	—
1022	D₄	—	2	12	no	—
1023	D₄	—	2	3	no	—
1024	D₄	—	2	1	no	—
1025	D₄	—	53	24	no	—
1026	D₄	—	53	12	no	—
1027	D₄	—	53	6	no	—
1028	D₄	—	53	6	no	—
1029	D₄	—	106	12	no	—
1030	D₄	—	106	12	no	—
1031	D₄	—	106	24	no	—
1032	D₄	—	106	12	no	—
1033	D₄	—	106	24	no	—
1034	D₄	—	106	12	no	—
1035	D₄	—	106	12	no	—
1036	D₄	—	106	4	no	—
1037	D₄	—	106	12	no	—
1038	D₄	—	106	12	no	—
1039	D₄	—	106	12	no	—
1040	D₄	—	106	3	no	—
1041	D₄	—	106	12	no	—
1042	D₄	—	106	3	no	—
1043	D₄	C₂×D₄×D₅₃	1	12	yes	—
1044	D₄	C₂⁴×D₅₃	1	2	yes	—
1045	D₄	C₂⁴×D₅₃	1	6	yes	—
1046	C₂×C₄	—	2	12	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	3	no	—
1049	C₂×C₄	—	2	12	no	—
1050	C₂×C₄	—	2	12	no	—
1051	C₂×C₄	—	53	12	no	—
1052	C₂×C₄	—	53	1	no	—
1053	C₂×C₄	—	53	3	no	—
1054	C₂×C₄	—	53	2	no	—
1055	C₂×C₄	—	53	12	no	—
1056	C₂×C₄	—	53	12	no	—
1057	C₂×C₄	—	53	6	no	—
1058	C₂×C₄	—	53	6	no	—
1059	C₂×C₄	—	53	2	no	—
1060	C₂×C₄	—	106	12	no	—
1061	C₂×C₄	—	106	12	no	—
1062	C₂×C₄	—	106	24	no	—
1063	C₂×C₄	—	106	4	no	—
1064	C₂×C₄	—	106	12	no	—
1065	C₂×C₄	—	106	4	no	—
1066	C₂×C₄	—	106	12	no	—
1067	C₂×C₄	—	106	1	no	—
1068	C₂×C₄	—	106	1	no	—
1069	C₂×C₄	—	106	12	no	—
1070	C₂×C₄	—	106	12	no	—
1071	C₂×C₄	C₂×D₄×D₅₃	1	6	yes	—
1072	C₂×C₄	C₂×D₄×D₅₃	1	3	yes	—
1073	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1074	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1075	C₈	—	53	6	no	—
1076	C₈	—	53	2	no	—
1077	C₈	C₂⁴×D₅₃	1	6	yes	—
1078	C₈	C₂⁴×D₅₃	1	2	yes	—
1079	C₂²	—	2	6	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	6	no	—
1082	C₂²	—	4	6	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	8	12	no	—
1085	C₂²	—	53	2	no	—
1086	C₂²	—	53	6	no	—
1087	C₂²	—	106	6	no	—
1088	C₂²	—	106	2	no	—
1089	C₂²	—	106	6	no	—
1090	C₂²	—	106	6	no	—
1091	C₂²	—	424	12	no	—
1092	C₂²	—	424	12	no	—
1093	C₂²	—	424	24	no	—
1094	C₂²	—	424	12	no	—
1095	C₂²	—	212	12	no	—
1096	C₂²	—	212	24	no	—
1097	C₂²	—	212	6	no	—
1098	C₂²	—	212	6	no	—
1099	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
1100	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1101	C₄	—	2	2	no	—
1102	C₄	—	2	6	no	—
1103	C₄	—	53	2	no	—
1104	C₄	—	53	6	no	—
1105	C₄	—	106	2	no	—
1106	C₄	—	106	2	no	—
1107	C₄	C₂²×D₄×D₅₃	1	6	yes	—
1108	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
1109	C₄	C₂⁵×D₅₃	1	1	yes	characteristic
1110	C₂	—	2	6	no	—
1111	C₂	—	4	6	no	—
1112	C₂	—	4	2	no	—
1113	C₂	—	106	6	no	—
1114	C₂	—	106	2	no	—
1115	C₂	—	212	6	no	—
1116	C₂	—	212	6	no	—
1117	C₂	#20289493	1	2	yes	direct product factor
1118	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×#577	C₂
socle	C₂²×C₅₃	C₂³×D₄
hypercenter	C₂×#577	D₅₃
hypocenter	C₅₃	C₂×#3585
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×#41 ◁ C₂×#577

Complements

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

N	H ≅ G/N	type
1. C₂×#16811460	C₂	semidirect
2. C₂×H(5,𝔽₂)×D₅₃	C₂	semidirect
3. #20289493	C₂	direct (N × H)
4. C₂×#16811432	C₂	semidirect
5. C₂×#16811431	C₂	semidirect
6. C₂×#16811429	C₂	semidirect
7. C₂×#16811428	C₂	semidirect
8. C₂×#16811427	C₂	semidirect
9. C₂×#16811426	C₂	semidirect
10. C₂×#16811425	C₂	semidirect
11. C₂×#16811422	C₂	semidirect
12. C₂×#16811420	C₂	semidirect
13. C₂²×#13133244	C₂	semidirect
14. C₂×AGL(1,ℤ/8)×D₅₃	C₂	semidirect
15. C₂×#16811388	C₂	semidirect
16. C₂×C₅₃×#577	C₂	semidirect
18. #16811460	C₂²	semidirect
20. C₂×#13133265	C₂²	semidirect
23. C₂×#13133263	C₂²	semidirect
24. C₂×#13133263	C₂²	semidirect
25. C₂×#13133263	C₂²	semidirect
26. C₂×#13133263	C₂²	semidirect
28. C₂×#13133262	C₂²	semidirect
30. H(5,𝔽₂)×D₅₃	C₂²	semidirect
32. C₂²×#11719949	C₂²	semidirect
36. C₂×#41×D₅₃	C₂²	semidirect
37. C₂×#41×D₅₃	C₂²	semidirect
39. C₂²×D₄×D₅₃	C₂²	semidirect
40. #16811432	C₂²	semidirect
41. #16811431	C₂²	semidirect
42. #16811429	C₂²	semidirect
43. #16811428	C₂²	semidirect
44. #16811427	C₂²	semidirect
45. #16811426	C₂²	semidirect
46. #16811425	C₂²	semidirect
47. #16811422	C₂²	semidirect
48. #16811420	C₂²	semidirect
49. C₂×#13133249	C₂²	semidirect
50. C₂×#13133249	C₂²	semidirect
51. C₂×#13133248	C₂²	semidirect
52. C₂×#13133246	C₂²	semidirect
53. C₂×#13133246	C₂²	semidirect
54. C₂×#13133245	C₂²	semidirect
55. C₂×#13133245	C₂²	semidirect
56. C₂×#13133244	C₂²	semidirect
57. C₂×#13133244	C₂²	semidirect
58. C₂×#13133244	C₂²	semidirect
59. C₂×#13133244	C₂²	semidirect
60. C₂×#13133244	C₂²	semidirect
61. C₂×#13133244	C₂²	semidirect
62. C₂×#13133243	C₂²	semidirect
63. C₂×#13133242	C₂²	semidirect
64. C₂×#13133242	C₂²	semidirect
65. C₂×#13133241	C₂²	semidirect
66. C₂×#13133241	C₂²	semidirect
67. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
68. C₂×#13133240	C₂²	semidirect
69. C₂×#13133239	C₂²	semidirect
70. C₂×#13133238	C₂²	semidirect
71. C₂×#13133237	C₂²	semidirect
72. C₂×#13133237	C₂²	semidirect
73. C₂²×#11719924	C₂²	semidirect
74. C₂×SD₁₆×D₅₃	C₂²	semidirect
75. C₂²×D₄₂₄	C₂²	semidirect
76. C₂²×#11719922	C₂²	semidirect
77. C₂×D₈×D₅₃	C₂²	semidirect
78. #16811388	C₂²	semidirect
79. C₂×#13133225	C₂²	semidirect
80. C₂×#13133224	C₂²	semidirect
81. C₂×#13133223	C₂²	semidirect
82. C₂²×#11719912	C₂²	semidirect
83. C₂×M₁₆×D₅₃	C₂²	semidirect
84. C₂×2₋¹⁺⁴×C₅₃	C₂²	semidirect
85. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
86. C₅₃×#577	C₂²	semidirect
87. C₂×#137×C₅₃	C₂²	semidirect
88. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
89. C₂×#135×C₅₃	C₂²	semidirect
90. C₂²×SD₁₆×C₅₃	C₂²	semidirect
91. C₂×#131×C₅₃	C₂²	semidirect
95. #13133265	C₂³	semidirect
102. #13133263	C₂³	semidirect
103. #13133263	C₂³	semidirect
104. #13133263	C₂³	semidirect
105. #13133263	C₂³	semidirect
108. #13133262	C₂³	semidirect
119. C₂×#11719949	C₂³	semidirect
120. C₂×#11719949	C₂³	semidirect
128. C₂×#11719945	C₂³	semidirect
141. #41×D₅₃	C₂³	semidirect
142. #41×D₅₃	C₂³	semidirect
146. C₂×Q₈×D₅₃	C₂³	semidirect
151. C₂²×D₂₁₂	C₂³	semidirect
168. C₂×D₄×D₅₃	C₂³	semidirect
169. C₂×D₄×D₅₃	C₂³	semidirect
174. #13133249	C₂³	semidirect
175. #13133249	C₂³	semidirect
176. #13133248	C₂³	semidirect
177. #13133246	C₂³	semidirect
178. #13133246	C₂³	semidirect
179. #13133245	C₂³	semidirect
180. #13133245	C₂³	semidirect
181. #13133244	C₂³	semidirect
182. #13133244	C₂³	semidirect
183. #13133244	C₂³	semidirect
184. #13133244	C₂³	semidirect
185. #13133244	C₂³	semidirect
186. #13133243	C₂³	semidirect
187. #13133242	C₂³	semidirect
188. #13133242	C₂³	semidirect
189. #13133241	C₂³	semidirect
190. #13133241	C₂³	semidirect
191. #13133240	C₂³	semidirect
192. #13133239	C₂³	semidirect
193. #13133238	C₂³	semidirect
194. #13133237	C₂³	semidirect
195. #13133237	C₂³	semidirect
196. C₂×Dic₂₁₂	C₂³	semidirect
197. C₂×#11719925	C₂³	semidirect
198. C₂×#11719925	C₂³	semidirect
199. C₂×#11719913	C₂³	semidirect
200. C₂×#11719913	C₂³	semidirect
201. C₂×#11719923	C₂³	semidirect
202. C₂×#11719923	C₂³	semidirect
203. C₂×#11719924	C₂³	semidirect
204. C₂×#11719924	C₂³	semidirect
205. C₂×#11719924	C₂³	semidirect
206. C₂×#11719924	C₂³	semidirect
207. SD₁₆×D₅₃	C₂³	semidirect
208. C₂×D₄₂₄	C₂³	semidirect
209. C₂×D₄₂₄	C₂³	semidirect
210. C₂×D₄₂₄	C₂³	semidirect
211. C₂×#11719922	C₂³	semidirect
212. C₂×#11719922	C₂³	semidirect
213. C₂×#11719922	C₂³	semidirect
214. C₂×#11719922	C₂³	semidirect
215. D₈×D₅₃	C₂³	semidirect
216. #13133225	C₂³	semidirect
217. #13133224	C₂³	semidirect
218. #13133223	C₂³	semidirect
219. C₂×#11719917	C₂³	semidirect
222. C₂×#11719912	C₂³	semidirect
223. C₂×#11719912	C₂³	semidirect
224. C₂×#11719912	C₂³	semidirect
225. M₁₆×D₅₃	C₂³	semidirect
226. C₂²×#88322	C₂³	semidirect
227. C₂×C₈×D₅₃	C₂³	semidirect
229. 2₋¹⁺⁴×C₅₃	C₂³	semidirect
231. H(5,𝔽₂)×C₅₃	C₂³	semidirect
236. C₂×#41×C₅₃	C₂³	semidirect
238. C₂²×Q₈×C₅₃	C₂³	semidirect
241. #137×C₅₃	C₂³	semidirect
242. AGL(1,ℤ/8)×C₅₃	C₂³	semidirect
243. #135×C₅₃	C₂³	semidirect
244. C₂×Q₁₆×C₅₃	C₂³	semidirect
245. C₂×SD₁₆×C₅₃	C₂³	semidirect
246. C₂×SD₁₆×C₅₃	C₂³	semidirect
247. C₂×SD₁₆×C₅₃	C₂³	semidirect
248. C₂×SD₁₆×C₅₃	C₂³	semidirect
249. C₂×D₈×C₅₃	C₂³	semidirect
250. #131×C₅₃	C₂³	semidirect
251. C₂×M₁₆×C₅₃	C₂³	semidirect
252. C₂²×C₈×C₅₃	C₂³	semidirect
269. #41×C₅₃	C₂⁴	semidirect
276. C₂×Q₈×C₅₃	C₂⁴	semidirect
314. #11719949	C₂⁴	semidirect
320. Q₈×D₅₃	C₂⁴	semidirect
344. D₄×D₅₃	C₂⁴	semidirect
355. #11719945	C₂⁴	semidirect
370. C₂×D₂₁₂	C₂⁴	semidirect
392. Q₁₆×C₅₃	C₂⁴	semidirect
393. SD₁₆×C₅₃	C₂⁴	semidirect
394. SD₁₆×C₅₃	C₂⁴	semidirect
395. SD₁₆×C₅₃	C₂⁴	semidirect
396. D₈×C₅₃	C₂⁴	semidirect
397. M₁₆×C₅₃	C₂⁴	semidirect
400. C₂×C₈×C₅₃	C₂⁴	semidirect
401. #11719925	C₂⁴	semidirect
402. #11719925	C₂⁴	semidirect
403. #11719924	C₂⁴	semidirect
404. #11719924	C₂⁴	semidirect
405. #11719924	C₂⁴	semidirect
406. #11719923	C₂⁴	semidirect
407. #11719923	C₂⁴	semidirect
408. #11719922	C₂⁴	semidirect
409. #11719922	C₂⁴	semidirect
410. #11719922	C₂⁴	semidirect
411. #11719917	C₂⁴	semidirect
414. C₂×#88322	C₂⁴	semidirect
415. Dic₂₁₂	C₂⁴	semidirect
416. D₄₂₄	C₂⁴	semidirect
417. D₄₂₄	C₂⁴	semidirect
418. #11719913	C₂⁴	semidirect
419. #11719913	C₂⁴	semidirect
422. #11719912	C₂⁴	semidirect
423. #11719912	C₂⁴	semidirect
424. C₈×D₅₃	C₂⁴	semidirect
557. C₂×#577	D₅₃	semidirect
570. C₂×C₅₃	#3585	semidirect
580. C₂×2₋¹⁺⁴	C₂×D₅₃	semidirect
591. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
604. #577	C₂×D₅₃	semidirect
616. C₂×#137	C₂×D₅₃	semidirect
631. C₂×AGL(1,ℤ/8)	C₂×D₅₃	semidirect
637. C₂×#135	C₂×D₅₃	semidirect
640. C₂²×SD₁₆	C₂×D₅₃	semidirect
648. C₂×#131	C₂×D₅₃	semidirect
651. C₅₃	C₂×#3585	semidirect
657. 2₋¹⁺⁴	C₂²×D₅₃	semidirect
672. H(5,𝔽₂)	C₂²×D₅₃	semidirect
711. C₂×#41	C₂²×D₅₃	semidirect
717. C₂²×Q₈	C₂²×D₅₃	semidirect
752. #137	C₂²×D₅₃	semidirect
765. AGL(1,ℤ/8)	C₂²×D₅₃	semidirect
771. #135	C₂²×D₅₃	semidirect
775. C₂×Q₁₆	C₂²×D₅₃	semidirect
785. C₂×SD₁₆	C₂²×D₅₃	semidirect
786. C₂×SD₁₆	C₂²×D₅₃	semidirect
787. C₂×SD₁₆	C₂²×D₅₃	semidirect
788. C₂×SD₁₆	C₂²×D₅₃	semidirect
797. C₂×D₈	C₂²×D₅₃	semidirect
801. #131	C₂²×D₅₃	semidirect
809. C₂×M₁₆	C₂²×D₅₃	semidirect
812. C₂²×C₈	C₂²×D₅₃	semidirect
860. #41	C₂³×D₅₃	semidirect
878. C₂×Q₈	C₂³×D₅₃	semidirect
955. Q₁₆	C₂³×D₅₃	semidirect
963. SD₁₆	C₂³×D₅₃	semidirect
964. SD₁₆	C₂³×D₅₃	semidirect
965. SD₁₆	C₂³×D₅₃	semidirect
971. D₈	C₂³×D₅₃	semidirect
977. M₁₆	C₂³×D₅₃	semidirect
984. C₂×C₈	C₂³×D₅₃	semidirect
1117. C₂	#20289493	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×#16811460	2
C₂×H(5,𝔽₂)×D₅₃	2
#20289493	2
C₂×#16811432	2
C₂×#16811431	2
C₂×#16811429	2
C₂×#16811428	2
C₂×#16811427	2
C₂×#16811426	2
C₂×#16811425	2
C₂×#16811422	2
C₂×#16811420	2
C₂²×#13133244	2
C₂×AGL(1,ℤ/8)×D₅₃	2
C₂×#16811388	2
C₂×C₅₃×#577	2
C₂×#3585	53

Subgroups — C2×#20289493 #28297931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20289493 #28297931