Subgroups — C₂×#20288348 #28291971

Order 13568.

14438 conjugacy classes of subgroups.

The subgroup lattice has 828 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	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288348	C₂	1	32	yes	maximal, direct product factor
4	C₂×#16811269	C₂	1	4	yes	maximal, complemented
5	C₂×#16811264	C₂	1	4	yes	maximal, complemented
6	C₂×D₄×D₂₁₂	C₂	1	4	yes	maximal, complemented
7	C₂×#16811257	C₂	1	4	yes	maximal, complemented
8	C₂×#16811192	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16811187	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811184	C₂	1	4	yes	maximal, complemented
11	C₂×#16811134	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#120×D₅₃	C₂	1	4	yes	maximal, complemented
13	C₂×#16811097	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁵×D₅₃	C₂²	1	2	yes	complemented
16	C₂×#13133263	—	2	16	no	—
17	C₂×#13133263	C₂²	1	16	yes	complemented
18	C₂²×#11719949	C₂²	1	2	yes	complemented
19	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
20	C₂²×#11719945	C₂²	1	2	yes	complemented
21	C₂³×D₂₁₂	—	2	16	no	—
22	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
23	C₂³×D₂₁₂	C₂²	1	2	yes	complemented
24	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
25	C₂³×D₂₁₂	C₂²	1	4	yes	complemented
26	C₂³×D₂₁₂	C₂²	1	4	yes	complemented
27	C₂³×D₂₁₂	C₂²	1	16	yes	complemented
28	C₂³×D₂₁₂	C₂²	1	2	yes	complemented
29	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
30	C₂²×D₄×D₅₃	C₂²	1	8	yes	complemented
31	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
32	#16811269	C₂²	1	64	yes	complemented
33	#16811264	C₂²	1	64	yes	complemented
34	D₄×D₂₁₂	C₂²	1	64	yes	complemented
35	#16811257	C₂²	1	64	yes	complemented
36	#16811192	C₂²	1	16	yes	complemented
37	#16811187	C₂²	1	16	yes	complemented
38	#16811184	C₂²	1	64	yes	complemented
39	C₂×#13133214	C₂²	1	2	yes	complemented
40	C₂×#13133213	C₂²	1	2	yes	complemented
41	C₂×#13133206	C₂²	1	2	yes	complemented
42	C₂×#13133205	C₂²	1	2	yes	complemented
43	#16811134	C₂²	1	16	yes	complemented
44	C₂×#13133202	C₂²	1	8	yes	complemented
45	C₂×#13133200	C₂²	1	2	yes	complemented
46	C₂×#13133196	C₂²	1	2	yes	complemented
47	C₂×#13133192	C₂²	1	8	yes	complemented
48	C₂×#13133192	C₂²	1	4	yes	complemented
49	C₂×#13133191	C₂²	1	2	yes	complemented
50	C₂×#13133191	C₂²	1	4	yes	complemented
51	C₂×#13133190	C₂²	1	8	yes	complemented
52	C₂×#13133187	C₂²	1	4	yes	complemented
53	C₂×#13133187	C₂²	1	8	yes	complemented
54	C₂×#13133187	C₂²	1	8	yes	complemented
55	C₂×#13133186	C₂²	1	2	yes	complemented
56	C₂×#13133185	C₂²	1	4	yes	complemented
57	C₂×#13133185	C₂²	1	8	yes	complemented
58	#120×D₅₃	C₂²	1	64	yes	complemented
59	#16811097	C₂²	1	16	yes	complemented
60	C₂×C₄×D₂₁₂	C₂²	1	4	yes	complemented
61	C₂×#13133179	C₂²	1	4	yes	complemented
62	C₂×C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
63	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
65	C₂×C₂²⋊C₄×D₅₃	C₂²	1	8	yes	complemented
66	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#525	C₂²	1	16	yes	complemented
69	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
70	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
71	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
72	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
73	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
74	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
75	C₂⁴×D₅₃	—	2	16	no	—
76	C₂⁴×D₅₃	—	4	16	no	—
77	C₂⁴×D₅₃	C₂³	1	8	yes	—
78	C₂⁴×D₅₃	C₂³	1	2	yes	—
79	C₂⁴×D₅₃	C₂³	1	2	yes	—
80	C₂⁴×D₅₃	C₂³	1	16	yes	complemented
81	C₂⁴×D₅₃	C₂³	1	4	yes	complemented
82	#13133263	—	2	128	no	—
83	C₂×#11719949	—	2	16	no	—
84	C₂×#11719949	C₂³	1	16	yes	complemented
85	C₂×#11719945	—	2	8	no	—
86	C₂×#11719945	—	2	16	no	—
87	C₂×#11719945	C₂³	1	16	yes	complemented
88	C₂×#11719945	C₂³	1	8	yes	complemented
89	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
90	C₂²×D₂₁₂	—	2	16	no	—
91	C₂²×D₂₁₂	—	2	8	no	—
92	C₂²×D₂₁₂	—	2	32	no	—
93	C₂²×D₂₁₂	—	2	32	no	—
94	C₂²×D₂₁₂	—	2	128	no	—
95	C₂²×D₂₁₂	—	2	16	no	—
96	C₂²×D₂₁₂	D₄	1	16	yes	complemented
97	C₂²×D₂₁₂	C₂³	1	8	yes	—
98	C₂²×D₂₁₂	C₂³	1	2	yes	—
99	C₂²×D₂₁₂	C₂³	1	2	yes	—
100	C₂²×D₂₁₂	C₂³	1	2	yes	—
101	C₂²×D₂₁₂	C₂³	1	2	yes	—
102	C₂²×D₂₁₂	C₂³	1	8	yes	—
103	C₂²×D₂₁₂	C₂³	1	32	yes	complemented
104	C₂²×D₂₁₂	C₂³	1	32	yes	complemented
105	C₂²×D₂₁₂	C₂³	1	16	yes	complemented
106	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
107	C₂²×D₂₁₂	C₂³	1	16	yes	complemented
108	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
109	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
110	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
111	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
112	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
113	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
114	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
115	C₂×D₄×D₅₃	—	2	32	no	—
116	C₂×D₄×D₅₃	—	2	16	no	—
117	C₂×D₄×D₅₃	—	4	32	no	—
118	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
119	C₂×D₄×D₅₃	C₂³	1	32	yes	complemented
120	C₂×D₄×D₅₃	C₂³	1	64	yes	complemented
121	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
122	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
123	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
124	#13133214	C₂³	1	16	yes	complemented
125	#13133213	C₂³	1	16	yes	complemented
126	#13133206	C₂³	1	16	yes	complemented
127	#13133205	C₂³	1	16	yes	complemented
128	#13133202	C₂³	1	64	yes	complemented
129	#13133200	C₂³	1	16	yes	complemented
130	#13133196	C₂³	1	16	yes	complemented
131	#13133192	C₂³	1	64	yes	complemented
132	#13133192	C₂³	1	32	yes	complemented
133	#13133191	C₂³	1	32	yes	complemented
134	#13133191	C₂³	1	16	yes	complemented
135	#13133190	C₂³	1	64	yes	complemented
136	#13133187	C₂³	1	64	yes	complemented
137	#13133187	C₂³	1	64	yes	complemented
138	#13133187	C₂³	1	32	yes	complemented
139	#13133186	C₂³	1	16	yes	complemented
140	#13133185	C₂³	1	64	yes	complemented
141	#13133185	C₂³	1	32	yes	complemented
142	C₄×D₂₁₂	C₂³	1	32	yes	complemented
143	#13133179	C₂³	1	32	yes	complemented
144	C₄×C₂²⋊D₅₃	C₂³	1	32	yes	complemented
145	#13133176	C₂³	1	8	yes	complemented
146	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
147	C₂×#11719919	C₂³	1	4	yes	complemented
148	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
150	C₂×#11719921	C₂³	1	8	yes	complemented
151	C₂×#11719921	C₂³	1	8	yes	complemented
152	C₂×#11719921	C₂³	1	8	yes	complemented
153	C₂×#11719921	C₂³	1	4	yes	complemented
154	C₂²⋊C₄×D₅₃	C₂³	1	64	yes	complemented
155	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	complemented
156	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
157	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
158	C₂×#41×C₅₃	—	2	8	no	—
159	C₂×#41×C₅₃	C₂³	1	8	yes	complemented
160	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
161	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
162	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
163	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
164	C₂³×C₄×C₅₃	—	2	8	no	—
165	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
166	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
167	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
168	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
169	C₂³×C₄×C₅₃	C₂³	1	8	yes	complemented
170	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
171	#123×C₅₃	C₂³	1	16	yes	complemented
172	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
173	#121×C₅₃	C₂³	1	16	yes	complemented
174	#120×C₅₃	C₂³	1	16	yes	complemented
175	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
176	#117×C₅₃	C₂³	1	8	yes	complemented
177	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
178	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
179	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
181	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
182	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
183	C₂⁴×C₅₃	—	2	4	no	—
184	C₂⁴×C₅₃	—	2	8	no	—
185	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
186	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
187	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
188	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
189	C₂³×D₅₃	—	2	8	no	—
190	C₂³×D₅₃	—	2	32	no	—
191	C₂³×D₅₃	—	2	32	no	—
192	C₂³×D₅₃	—	2	64	no	—
193	C₂³×D₅₃	—	2	16	no	—
194	C₂³×D₅₃	—	4	8	no	—
195	C₂³×D₅₃	—	4	16	no	—
196	C₂³×D₅₃	—	4	8	no	—
197	C₂³×D₅₃	—	4	64	no	—
198	C₂³×D₅₃	—	4	16	no	—
199	C₂³×D₅₃	—	4	128	no	—
200	C₂³×D₅₃	C₂×D₄	1	16	yes	complemented
201	C₂³×D₅₃	C₂⁴	1	4	yes	—
202	C₂³×D₅₃	C₂⁴	1	2	yes	—
203	C₂³×D₅₃	C₂⁴	1	32	yes	—
204	C₂³×D₅₃	C₂⁴	1	4	yes	—
205	C₂³×D₅₃	C₂⁴	1	8	yes	—
206	C₂³×D₅₃	C₂⁴	1	8	yes	—
207	C₂³×D₅₃	C₂⁴	1	16	yes	complemented
208	#41×C₅₃	—	2	32	no	—
209	C₂×Q₈×C₅₃	—	2	4	no	—
210	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	complemented
211	C₂×D₄×C₅₃	—	2	8	no	—
212	C₂×D₄×C₅₃	—	2	16	no	—
213	C₂×D₄×C₅₃	—	2	4	no	—
214	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
215	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
216	C₂×D₄×C₅₃	C₂⁴	1	4	yes	complemented
217	C₂²×C₄×C₅₃	—	2	4	no	—
218	C₂²×C₄×C₅₃	—	2	8	no	—
219	C₂²×C₄×C₅₃	—	2	8	no	—
220	C₂²×C₄×C₅₃	—	2	8	no	—
221	C₂²×C₄×C₅₃	—	2	32	no	—
222	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	complemented
223	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
227	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
228	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
229	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
232	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	complemented
233	C₂×C₂²⋊D₅₃	—	2	8	no	—
234	C₂×C₂²⋊D₅₃	—	2	16	no	—
235	C₂×C₂²⋊D₅₃	—	2	16	no	—
236	C₂×C₂²⋊D₅₃	—	4	16	no	—
237	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
238	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
239	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	complemented
240	C₂×C₂²⋊D₅₃	C₂⁴	1	32	yes	complemented
241	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
242	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
243	#11719949	—	2	64	no	—
244	D₄×D₅₃	—	2	128	no	—
245	D₄×D₅₃	—	2	64	no	—
246	D₄×D₅₃	—	4	128	no	—
247	#11719945	—	2	32	no	—
248	#11719945	—	2	64	no	—
249	C₂×D₂₁₂	—	2	16	no	—
250	C₂×D₂₁₂	—	2	32	no	—
251	C₂×D₂₁₂	—	2	64	no	—
252	C₂×D₂₁₂	—	2	8	no	—
253	C₂×D₂₁₂	—	2	8	no	—
254	C₂×D₂₁₂	—	2	4	no	—
255	C₂×D₂₁₂	—	2	32	no	—
256	C₂×D₂₁₂	—	2	128	no	—
257	C₂×D₂₁₂	—	2	128	no	—
258	C₂×D₂₁₂	—	2	64	no	—
259	C₂×D₂₁₂	—	4	16	no	—
260	C₂×D₂₁₂	C₂×D₄	1	16	yes	complemented
261	C₂×D₂₁₂	C₂×D₄	1	16	yes	complemented
262	C₂×D₂₁₂	C₂×D₄	1	64	yes	complemented
263	C₂×D₂₁₂	C₂⁴	1	32	yes	—
264	C₂×D₂₁₂	C₂⁴	1	8	yes	—
265	C₂×D₂₁₂	C₂⁴	1	8	yes	—
266	C₂×D₂₁₂	C₂⁴	1	8	yes	—
267	C₂×D₂₁₂	C₂⁴	1	8	yes	—
268	C₂×D₂₁₂	C₂⁴	1	16	yes	complemented
269	C₂×D₂₁₂	C₂⁴	1	4	yes	complemented
270	C₂×D₂₁₂	C₂⁴	1	32	yes	complemented
271	C₂×C₄×D₅₃	—	2	16	no	—
272	C₂×C₄×D₅₃	—	2	8	no	—
273	C₂×C₄×D₅₃	—	4	16	no	—
274	C₂×C₄×D₅₃	C₂⁴	1	16	yes	complemented
275	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
276	C₂×C₄×D₅₃	C₂⁴	1	32	yes	complemented
277	C₂×Dic₁₀₆	—	2	4	no	—
278	C₂×Dic₁₀₆	C₂⁴	1	4	yes	complemented
279	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
280	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
281	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
282	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
283	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
284	C₄²×C₅₃	C₂⁴	1	8	yes	complemented
285	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
286	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
287	#11719921	C₂⁴	1	32	yes	complemented
288	#11719921	C₂⁴	1	32	yes	complemented
289	#11719921	C₂⁴	1	32	yes	complemented
290	#11719921	C₂⁴	1	16	yes	complemented
291	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
292	#11719919	C₂⁴	1	16	yes	complemented
293	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
294	C₂³×C₅₃	—	2	32	no	—
295	C₂³×C₅₃	—	2	8	no	—
296	C₂³×C₅₃	—	2	4	no	—
297	C₂³×C₅₃	—	2	4	no	—
298	C₂³×C₅₃	—	2	4	no	—
299	C₂³×C₅₃	—	2	16	no	—
300	C₂³×C₅₃	—	2	4	no	—
301	C₂³×C₅₃	—	2	8	no	—
302	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
303	C₂³×C₅₃	H(5,𝔽₂)	1	8	yes	complemented
304	C₂³×C₅₃	C₂⁵	1	4	yes	—
305	C₂³×C₅₃	C₂⁵	1	2	yes	—
306	C₂³×C₅₃	C₂⁵	1	4	yes	—
307	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
308	C₂²×D₅₃	—	2	16	no	—
309	C₂²×D₅₃	—	2	4	no	—
310	C₂²×D₅₃	—	2	16	no	—
311	C₂²×D₅₃	—	2	8	no	—
312	C₂²×D₅₃	—	2	8	no	—
313	C₂²×D₅₃	—	2	16	no	—
314	C₂²×D₅₃	—	2	64	no	—
315	C₂²×D₅₃	—	2	64	no	—
316	C₂²×D₅₃	—	2	32	no	—
317	C₂²×D₅₃	—	4	32	no	—
318	C₂²×D₅₃	—	4	16	no	—
319	C₂²×D₅₃	—	4	32	no	—
320	C₂²×D₅₃	—	4	16	no	—
321	C₂²×D₅₃	—	4	32	no	—
322	C₂²×D₅₃	—	4	128	no	—
323	C₂²×D₅₃	—	4	256	no	—
324	C₂²×D₅₃	—	4	32	no	—
325	C₂²×D₅₃	—	8	32	no	—
326	C₂²×D₅₃	C₂²×D₄	1	16	yes	—
327	C₂²×D₅₃	C₂²×D₄	1	32	yes	complemented
328	C₂²×D₅₃	C₂⁵	1	4	yes	—
329	C₂²×D₅₃	C₂⁵	1	8	yes	—
330	C₂²×D₅₃	C₂⁵	1	8	yes	—
331	Q₈×C₅₃	—	2	8	no	—
332	D₄×C₅₃	—	2	16	no	—
333	D₄×C₅₃	—	2	32	no	—
334	D₄×C₅₃	—	2	8	no	—
335	C₂×C₄×C₅₃	—	2	4	no	—
336	C₂×C₄×C₅₃	—	2	8	no	—
337	C₂×C₄×C₅₃	—	2	4	no	—
338	C₂×C₄×C₅₃	—	2	8	no	—
339	C₂×C₄×C₅₃	—	2	16	no	—
340	C₂×C₄×C₅₃	—	2	16	no	—
341	C₂×C₄×C₅₃	—	2	16	no	—
342	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
343	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
344	C₂×C₄×C₅₃	C₂²×D₄	1	16	yes	complemented
345	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
346	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
347	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
348	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
349	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
350	C₂²⋊D₅₃	—	2	16	no	—
351	C₂²⋊D₅₃	—	2	32	no	—
352	C₂²⋊D₅₃	—	2	32	no	—
353	C₂²⋊D₅₃	—	4	32	no	—
354	C₂×Dic₅₃	—	2	4	no	—
355	C₂×Dic₅₃	—	2	8	no	—
356	C₂×Dic₅₃	C₂⁵	1	4	yes	—
357	C₂×Dic₅₃	C₂⁵	1	8	yes	—
358	D₂₁₂	—	2	64	no	—
359	D₂₁₂	—	2	32	no	—
360	D₂₁₂	—	2	16	no	—
361	D₂₁₂	—	2	16	no	—
362	D₂₁₂	—	2	8	no	—
363	D₂₁₂	—	4	32	no	—
364	D₂₁₂	C₂²×D₄	1	32	yes	complemented
365	D₂₁₂	C₂²×D₄	1	32	yes	complemented
366	C₄×D₅₃	—	2	32	no	—
367	C₄×D₅₃	—	2	16	no	—
368	C₄×D₅₃	—	4	32	no	—
369	Dic₁₀₆	—	2	8	no	—
370	C₂×#3484	—	53	1	no	maximal, Sylow
371	C₂²×C₅₃	—	2	32	no	—
372	C₂²×C₅₃	—	2	4	no	—
373	C₂²×C₅₃	—	2	4	no	—
374	C₂²×C₅₃	—	2	4	no	—
375	C₂²×C₅₃	—	2	8	no	—
376	C₂²×C₅₃	—	2	16	no	—
377	C₂²×C₅₃	—	2	4	no	—
378	C₂²×C₅₃	—	2	8	no	—
379	C₂²×C₅₃	—	4	8	no	—
380	C₂²×C₅₃	C₂³×D₄	1	4	yes	—
381	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
382	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
383	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	8	yes	complemented
384	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
385	C₂×D₅₃	—	2	16	no	—
386	C₂×D₅₃	—	2	32	no	—
387	C₂×D₅₃	—	2	4	no	—
388	C₂×D₅₃	—	2	8	no	—
389	C₂×D₅₃	—	2	8	no	—
390	C₂×D₅₃	—	2	16	no	—
391	C₂×D₅₃	—	4	32	no	—
392	C₂×D₅₃	—	4	128	no	—
393	C₂×D₅₃	—	4	32	no	—
394	C₂×D₅₃	—	4	16	no	—
395	C₂×D₅₃	—	4	8	no	—
396	C₂×D₅₃	—	8	32	no	—
397	C₂×D₅₃	C₂³×D₄	1	16	yes	—
398	C₄×C₅₃	—	2	4	no	—
399	C₄×C₅₃	—	2	4	no	—
400	C₄×C₅₃	—	2	8	no	—
401	C₄×C₅₃	C₂³×D₄	1	4	yes	—
402	C₄×C₅₃	C₂³×D₄	1	4	yes	—
403	Dic₅₃	—	2	4	no	—
404	Dic₅₃	—	2	8	no	—
405	C₂²×H(5,𝔽₂)	—	53	1	no	—
406	C₂⁴×D₄	—	53	1	no	—
407	#3484	—	53	32	no	—
408	C₂×#546	—	53	4	no	—
409	C₂×#546	—	53	4	no	—
410	C₂×D₄²	—	53	4	no	—
411	C₂×D₄²	—	53	4	no	—
412	C₂×#535	—	53	1	no	—
413	C₂×#535	—	53	1	no	—
414	C₂×#534	—	53	4	no	—
415	C₂×#525	—	53	1	no	—
416	C₂×#525	D₅₃	1	1	yes	characteristic, complemented
417	C₂²×#120	—	53	4	no	—
418	C₂×#518	—	53	1	no	—
419	C₂×C₅₃	—	2	4	no	—
420	C₂×C₅₃	—	2	8	no	—
421	C₂×C₅₃	—	4	4	no	—
422	C₂×C₅₃	#3484	1	4	yes	complemented
423	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
424	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	2	yes	—
425	D₅₃	—	2	16	no	—
426	D₅₃	—	4	8	no	—
427	D₅₃	—	4	4	no	—
428	C₂⁶	—	53	2	no	—
429	C₂×H(5,𝔽₂)	—	53	16	no	—
430	C₂×H(5,𝔽₂)	—	106	16	no	—
431	C₂²×#41	—	53	2	no	—
432	C₂²×#41	—	53	1	no	—
433	C₂²×#41	—	53	2	no	—
434	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
435	C₂³×D₄	—	53	4	no	—
436	C₂³×D₄	—	53	2	no	—
437	C₂³×D₄	—	53	8	no	—
438	C₂³×D₄	—	53	1	no	—
439	C₂³×D₄	—	53	2	no	—
440	C₂³×D₄	—	53	1	no	—
441	C₂³×D₄	—	53	4	no	—
442	C₂³×D₄	—	53	4	no	—
443	C₂³×D₄	—	53	16	no	—
444	C₂³×D₄	—	53	2	no	—
445	C₂³×D₄	—	106	16	no	—
446	C₂⁴×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
447	#546	—	53	64	no	—
448	#546	—	53	64	no	—
449	D₄²	—	53	64	no	—
450	D₄²	—	53	64	no	—
451	#535	—	53	16	no	—
452	#535	—	53	16	no	—
453	#534	—	53	64	no	—
454	C₂×#127	—	53	2	no	—
455	C₂×#127	—	53	2	no	—
456	C₂×#124	—	53	2	no	—
457	C₂×#124	—	53	2	no	—
458	#525	—	53	16	no	—
459	#525	C₂×D₅₃	1	16	yes	complemented
460	C₂×#123	—	53	2	no	—
461	C₂×#123	—	53	8	no	—
462	C₂×#123	C₂×D₅₃	1	2	yes	complemented
463	C₂×C₂²⋊Q₈	—	53	2	no	—
464	C₂×C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
465	C₂×#121	—	53	2	no	—
466	C₂×#121	—	53	4	no	—
467	C₂×#121	—	53	8	no	—
468	C₂×#121	—	53	4	no	—
469	C₂×#121	—	53	8	no	—
470	C₂×#121	C₂×D₅₃	1	2	yes	complemented
471	C₂×#120	—	53	2	no	—
472	C₂×#120	—	53	4	no	—
473	C₂×#120	—	53	8	no	—
474	C₂×#120	—	53	64	no	—
475	C₂×#120	—	53	4	no	—
476	C₂×#120	—	53	8	no	—
477	C₂×#120	—	53	8	no	—
478	C₂×#120	C₂×D₅₃	1	2	yes	complemented
479	#518	—	53	16	no	—
480	C₂×C₄×D₄	—	53	4	no	—
481	C₂×C₄×D₄	—	53	4	no	—
482	C₂×C₄×D₄	—	53	4	no	—
483	C₂×C₄×D₄	C₂×D₅₃	1	4	yes	complemented
484	C₂×#117	—	53	1	no	—
485	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
486	C₂²×C₂²⋊C₄	—	53	4	no	—
487	C₂²×C₂²⋊C₄	—	53	8	no	—
488	C₅₃	C₂×#3484	1	1	yes	characteristic, complemented, Sylow
489	C₂⁵	—	53	2	no	—
490	C₂⁵	—	53	8	no	—
491	C₂⁵	—	53	2	no	—
492	C₂⁵	—	53	16	no	—
493	C₂⁵	—	53	4	no	—
494	C₂⁵	—	106	16	no	—
495	C₂⁵	—	212	16	no	—
496	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
497	H(5,𝔽₂)	—	106	128	no	—
498	C₂×#41	—	2	8	no	—
499	C₂×#41	—	53	16	no	—
500	C₂×#41	—	53	8	no	—
501	C₂×#41	—	53	16	no	—
502	C₂×#41	—	106	16	no	—
503	C₂×#41	—	106	16	no	—
504	C₂×#41	—	106	8	no	—
505	C₂×#41	C₂²×D₅₃	1	8	yes	complemented
506	C₂²×Q₈	—	53	1	no	—
507	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
508	C₂²×D₄	—	53	4	no	—
509	C₂²×D₄	—	53	2	no	—
510	C₂²×D₄	—	53	4	no	—
511	C₂²×D₄	—	53	8	no	—
512	C₂²×D₄	—	53	32	no	—
513	C₂²×D₄	—	53	16	no	—
514	C₂²×D₄	—	53	64	no	—
515	C₂²×D₄	—	53	16	no	—
516	C₂²×D₄	—	53	2	no	—
517	C₂²×D₄	—	53	2	no	—
518	C₂²×D₄	—	53	8	no	—
519	C₂²×D₄	—	53	4	no	—
520	C₂²×D₄	—	53	8	no	—
521	C₂²×D₄	—	53	2	no	—
522	C₂²×D₄	—	53	2	no	—
523	C₂²×D₄	—	53	1	no	—
524	C₂²×D₄	—	53	16	no	—
525	C₂²×D₄	—	53	8	no	—
526	C₂²×D₄	—	53	32	no	—
527	C₂²×D₄	—	53	32	no	—
528	C₂²×D₄	—	53	8	no	—
529	C₂²×D₄	—	53	16	no	—
530	C₂²×D₄	—	106	32	no	—
531	C₂²×D₄	—	106	32	no	—
532	C₂²×D₄	—	106	128	no	—
533	C₂²×D₄	—	106	16	no	—
534	C₂²×D₄	—	106	16	no	—
535	C₂²×D₄	—	106	16	no	—
536	C₂²×D₄	—	106	32	no	—
537	C₂²×D₄	—	106	8	no	—
538	C₂²×D₄	—	212	32	no	—
539	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
540	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
541	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
542	C₂³×C₄	—	2	8	no	—
543	C₂³×C₄	—	53	4	no	—
544	C₂³×C₄	—	53	2	no	—
545	C₂³×C₄	—	53	8	no	—
546	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
547	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
548	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
549	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
550	C₂³×C₄	C₂²×D₅₃	1	8	yes	complemented
551	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
552	#127	—	53	16	no	—
553	#127	—	53	16	no	—
554	#124	—	53	16	no	—
555	#124	—	53	16	no	—
556	#123	—	53	16	no	—
557	#123	—	53	64	no	—
558	#123	C₂²×D₅₃	1	16	yes	complemented
559	C₂²⋊Q₈	—	53	16	no	—
560	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
561	#121	—	53	16	no	—
562	#121	—	53	32	no	—
563	#121	—	53	64	no	—
564	#121	—	53	32	no	—
565	#121	—	53	64	no	—
566	#121	C₂²×D₅₃	1	16	yes	complemented
567	#120	—	53	16	no	—
568	#120	—	53	32	no	—
569	#120	—	53	64	no	—
570	#120	—	53	32	no	—
571	#120	—	53	64	no	—
572	#120	—	53	64	no	—
573	#120	C₂²×D₅₃	1	16	yes	complemented
574	C₄×D₄	—	53	32	no	—
575	C₄×D₄	—	53	32	no	—
576	C₄×D₄	—	53	32	no	—
577	C₄×D₄	C₂²×D₅₃	1	32	yes	complemented
578	#117	—	53	8	no	—
579	#117	C₂²×D₅₃	1	8	yes	complemented
580	C₂×C₄⋊C₄	—	53	2	no	—
581	C₂×C₄⋊C₄	—	53	4	no	—
582	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
583	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
584	C₂×C₂²⋊C₄	—	53	2	no	—
585	C₂×C₂²⋊C₄	—	53	4	no	—
586	C₂×C₂²⋊C₄	—	53	8	no	—
587	C₂×C₂²⋊C₄	—	53	8	no	—
588	C₂×C₂²⋊C₄	—	53	8	no	—
589	C₂×C₂²⋊C₄	—	53	4	no	—
590	C₂×C₂²⋊C₄	—	53	32	no	—
591	C₂×C₂²⋊C₄	—	53	64	no	—
592	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
595	C₂×C₄²	—	53	2	no	—
596	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
597	C₂⁴	—	2	4	no	—
598	C₂⁴	—	2	8	no	—
599	C₂⁴	—	53	4	no	—
600	C₂⁴	—	53	16	no	—
601	C₂⁴	—	53	8	no	—
602	C₂⁴	—	53	4	no	—
603	C₂⁴	—	53	2	no	—
604	C₂⁴	—	53	32	no	—
605	C₂⁴	—	53	8	no	—
606	C₂⁴	—	53	16	no	—
607	C₂⁴	—	106	16	no	—
608	C₂⁴	—	106	32	no	—
609	C₂⁴	—	106	64	no	—
610	C₂⁴	—	106	8	no	—
611	C₂⁴	—	106	32	no	—
612	C₂⁴	—	212	16	no	—
613	C₂⁴	—	212	8	no	—
614	C₂⁴	—	212	16	no	—
615	C₂⁴	—	212	8	no	—
616	C₂⁴	—	212	64	no	—
617	C₂⁴	—	212	128	no	—
618	C₂⁴	C₂³×D₅₃	1	4	yes	—
619	C₂⁴	C₂³×D₅₃	1	2	yes	—
620	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
621	C₂⁴	C₂³×D₅₃	1	2	yes	—
622	#41	—	2	32	no	—
623	#41	—	106	64	no	—
624	#41	—	106	64	no	—
625	#41	—	106	32	no	—
626	C₂×Q₈	—	2	4	no	—
627	C₂×Q₈	—	53	4	no	—
628	C₂×Q₈	—	106	4	no	—
629	C₂×Q₈	C₂³×D₅₃	1	4	yes	complemented
630	C₂×D₄	—	2	8	no	—
631	C₂×D₄	—	2	16	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	53	16	no	—
634	C₂×D₄	—	53	8	no	—
635	C₂×D₄	—	53	16	no	—
636	C₂×D₄	—	53	32	no	—
637	C₂×D₄	—	53	16	no	—
638	C₂×D₄	—	53	16	no	—
639	C₂×D₄	—	53	64	no	—
640	C₂×D₄	—	53	8	no	—
641	C₂×D₄	—	53	8	no	—
642	C₂×D₄	—	53	32	no	—
643	C₂×D₄	—	53	8	no	—
644	C₂×D₄	—	53	8	no	—
645	C₂×D₄	—	53	16	no	—
646	C₂×D₄	—	53	4	no	—
647	C₂×D₄	—	53	32	no	—
648	C₂×D₄	—	106	128	no	—
649	C₂×D₄	—	106	128	no	—
650	C₂×D₄	—	106	64	no	—
651	C₂×D₄	—	106	32	no	—
652	C₂×D₄	—	106	64	no	—
653	C₂×D₄	—	106	16	no	—
654	C₂×D₄	—	106	64	no	—
655	C₂×D₄	—	106	128	no	—
656	C₂×D₄	—	106	16	no	—
657	C₂×D₄	—	106	8	no	—
658	C₂×D₄	—	106	16	no	—
659	C₂×D₄	—	106	8	no	—
660	C₂×D₄	—	106	8	no	—
661	C₂×D₄	—	106	4	no	—
662	C₂×D₄	—	106	32	no	—
663	C₂×D₄	—	212	16	no	—
664	C₂×D₄	—	212	16	no	—
665	C₂×D₄	—	212	128	no	—
666	C₂×D₄	C₂³×D₅₃	1	16	yes	—
667	C₂×D₄	C₂³×D₅₃	1	8	yes	—
668	C₂×D₄	C₂³×D₅₃	1	4	yes	complemented
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	8	no	—
671	C₂²×C₄	—	2	8	no	—
672	C₂²×C₄	—	2	8	no	—
673	C₂²×C₄	—	2	32	no	—
674	C₂²×C₄	—	53	4	no	—
675	C₂²×C₄	—	53	2	no	—
676	C₂²×C₄	—	53	16	no	—
677	C₂²×C₄	—	53	8	no	—
678	C₂²×C₄	—	53	32	no	—
679	C₂²×C₄	—	106	16	no	—
680	C₂²×C₄	—	106	8	no	—
681	C₂²×C₄	—	212	16	no	—
682	C₂²×C₄	D₄×D₅₃	1	8	yes	complemented
683	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
684	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
685	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
686	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
687	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
688	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
689	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
690	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
691	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
692	C₂²×C₄	C₂³×D₅₃	1	8	yes	complemented
693	C₄⋊C₄	—	53	8	no	—
694	C₄⋊C₄	—	53	16	no	—
695	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
696	C₄⋊C₄	C₂³×D₅₃	1	16	yes	complemented
697	C₂²⋊C₄	—	53	8	no	—
698	C₂²⋊C₄	—	53	16	no	—
699	C₂²⋊C₄	—	53	32	no	—
700	C₂²⋊C₄	—	53	32	no	—
701	C₂²⋊C₄	—	53	32	no	—
702	C₂²⋊C₄	—	53	16	no	—
703	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
704	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
705	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	complemented
706	C₄²	—	53	8	no	—
707	C₄²	C₂³×D₅₃	1	8	yes	complemented
708	C₂³	—	2	32	no	—
709	C₂³	—	2	8	no	—
710	C₂³	—	2	4	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	2	4	no	—
713	C₂³	—	2	16	no	—
714	C₂³	—	2	4	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	53	16	no	—
717	C₂³	—	53	8	no	—
718	C₂³	—	53	32	no	—
719	C₂³	—	53	8	no	—
720	C₂³	—	53	4	no	—
721	C₂³	—	106	32	no	—
722	C₂³	—	106	64	no	—
723	C₂³	—	106	16	no	—
724	C₂³	—	106	4	no	—
725	C₂³	—	106	16	no	—
726	C₂³	—	106	8	no	—
727	C₂³	—	106	8	no	—
728	C₂³	—	106	16	no	—
729	C₂³	—	106	64	no	—
730	C₂³	—	424	32	no	—
731	C₂³	—	212	32	no	—
732	C₂³	—	212	32	no	—
733	C₂³	—	212	16	no	—
734	C₂³	—	212	32	no	—
735	C₂³	—	212	16	no	—
736	C₂³	—	212	128	no	—
737	C₂³	—	212	256	no	—
738	C₂³	—	212	32	no	—
739	C₂³	C₂×D₄×D₅₃	1	4	yes	—
740	C₂³	#13133263	1	8	yes	complemented
741	C₂³	C₂⁴×D₅₃	1	4	yes	—
742	C₂³	C₂⁴×D₅₃	1	2	yes	—
743	C₂³	C₂⁴×D₅₃	1	4	yes	—
744	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
745	Q₈	—	2	8	no	—
746	Q₈	—	106	8	no	—
747	D₄	—	2	16	no	—
748	D₄	—	2	32	no	—
749	D₄	—	2	8	no	—
750	D₄	—	53	32	no	—
751	D₄	—	53	32	no	—
752	D₄	—	106	64	no	—
753	D₄	—	106	32	no	—
754	D₄	—	106	32	no	—
755	D₄	—	106	16	no	—
756	D₄	—	106	32	no	—
757	D₄	—	106	16	no	—
758	D₄	—	106	16	no	—
759	D₄	—	106	8	no	—
760	D₄	—	212	32	no	—
761	D₄	—	212	32	no	—
762	C₂×C₄	—	2	8	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	8	no	—
766	C₂×C₄	—	2	16	no	—
767	C₂×C₄	—	2	16	no	—
768	C₂×C₄	—	2	16	no	—
769	C₂×C₄	—	53	8	no	—
770	C₂×C₄	—	53	4	no	—
771	C₂×C₄	—	106	32	no	—
772	C₂×C₄	—	106	4	no	—
773	C₂×C₄	—	106	8	no	—
774	C₂×C₄	—	106	16	no	—
775	C₂×C₄	—	212	32	no	—
776	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
777	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
778	C₂×C₄	C₂×D₄×D₅₃	1	16	yes	complemented
779	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
780	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
781	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
782	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
783	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
784	C₂²	—	2	32	no	—
785	C₂²	—	2	8	no	—
786	C₂²	—	2	16	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	2	4	no	—
789	C₂²	—	2	4	no	—
790	C₂²	—	2	4	no	—
791	C₂²	—	2	8	no	—
792	C₂²	—	4	8	no	—
793	C₂²	—	53	16	no	—
794	C₂²	—	106	32	no	—
795	C₂²	—	106	16	no	—
796	C₂²	—	106	4	no	—
797	C₂²	—	106	8	no	—
798	C₂²	—	106	8	no	—
799	C₂²	—	106	16	no	—
800	C₂²	—	424	32	no	—
801	C₂²	—	212	32	no	—
802	C₂²	—	212	128	no	—
803	C₂²	—	212	32	no	—
804	C₂²	—	212	8	no	—
805	C₂²	—	212	16	no	—
806	C₂²	C₂²×D₄×D₅₃	1	4	yes	—
807	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
808	C₂²	C₂×#13133263	1	4	yes	—
809	C₂²	C₂×#13133263	1	8	yes	complemented
810	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
811	C₄	—	2	4	no	—
812	C₄	—	2	4	no	—
813	C₄	—	2	8	no	—
814	C₄	—	106	4	no	—
815	C₄	—	106	8	no	—
816	C₄	C₂²×D₄×D₅₃	1	4	yes	—
817	C₄	C₂²×D₄×D₅₃	1	4	yes	—
818	C₂	—	2	4	no	—
819	C₂	—	2	8	no	—
820	C₂	—	4	4	no	—
821	C₂	—	106	16	no	—
822	C₂	—	212	4	no	—
823	C₂	—	212	8	no	—
824	C₂	#20288348	1	4	yes	direct product factor
825	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
826	C₂	C₂²×#13133263	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#525	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#525	D₅₃
hypocenter	C₅₃	C₂×#3484
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. C₂²×#13133263	C₂	semidirect
2. C₂⁴×D₂₁₂	C₂	semidirect
3. #20288348	C₂	direct (N × H)
4. C₂×#16811269	C₂	semidirect
5. C₂×#16811264	C₂	semidirect
6. C₂×D₄×D₂₁₂	C₂	semidirect
7. C₂×#16811257	C₂	semidirect
8. C₂×#16811192	C₂	semidirect
9. C₂×#16811187	C₂	semidirect
10. C₂×#16811184	C₂	semidirect
11. C₂×#16811134	C₂	semidirect
12. C₂×#120×D₅₃	C₂	semidirect
13. C₂×#16811097	C₂	semidirect
14. C₂×C₅₃×#525	C₂	semidirect
15. C₂⁵×D₅₃	C₂²	semidirect
17. C₂×#13133263	C₂²	semidirect
18. C₂²×#11719949	C₂²	semidirect
19. C₂²×#11719945	C₂²	semidirect
20. C₂²×#11719945	C₂²	semidirect
23. C₂³×D₂₁₂	C₂²	semidirect
24. C₂³×D₂₁₂	C₂²	semidirect
25. C₂³×D₂₁₂	C₂²	semidirect
26. C₂³×D₂₁₂	C₂²	semidirect
27. C₂³×D₂₁₂	C₂²	semidirect
28. C₂³×D₂₁₂	C₂²	semidirect
29. C₂²×D₄×D₅₃	C₂²	semidirect
30. C₂²×D₄×D₅₃	C₂²	semidirect
31. C₂²×D₄×D₅₃	C₂²	semidirect
32. #16811269	C₂²	semidirect
33. #16811264	C₂²	semidirect
34. D₄×D₂₁₂	C₂²	semidirect
35. #16811257	C₂²	semidirect
36. #16811192	C₂²	semidirect
37. #16811187	C₂²	semidirect
38. #16811184	C₂²	semidirect
39. C₂×#13133214	C₂²	semidirect
40. C₂×#13133213	C₂²	semidirect
41. C₂×#13133206	C₂²	semidirect
42. C₂×#13133205	C₂²	semidirect
43. #16811134	C₂²	semidirect
44. C₂×#13133202	C₂²	semidirect
45. C₂×#13133200	C₂²	semidirect
46. C₂×#13133196	C₂²	semidirect
47. C₂×#13133192	C₂²	semidirect
48. C₂×#13133192	C₂²	semidirect
49. C₂×#13133191	C₂²	semidirect
50. C₂×#13133191	C₂²	semidirect
51. C₂×#13133190	C₂²	semidirect
52. C₂×#13133187	C₂²	semidirect
53. C₂×#13133187	C₂²	semidirect
54. C₂×#13133187	C₂²	semidirect
55. C₂×#13133186	C₂²	semidirect
56. C₂×#13133185	C₂²	semidirect
57. C₂×#13133185	C₂²	semidirect
58. #120×D₅₃	C₂²	semidirect
59. #16811097	C₂²	semidirect
60. C₂×C₄×D₂₁₂	C₂²	semidirect
61. C₂×#13133179	C₂²	semidirect
62. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
63. C₂×#13133176	C₂²	semidirect
64. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
65. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
66. C₂²×#41×C₅₃	C₂²	semidirect
67. C₂⁴×C₄×C₅₃	C₂²	semidirect
68. C₅₃×#525	C₂²	semidirect
69. C₂×#123×C₅₃	C₂²	semidirect
70. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
71. C₂×#121×C₅₃	C₂²	semidirect
72. C₂×#120×C₅₃	C₂²	semidirect
73. C₂×C₄×D₄×C₅₃	C₂²	semidirect
74. C₂×#117×C₅₃	C₂²	semidirect
80. C₂⁴×D₅₃	C₂³	semidirect
81. C₂⁴×D₅₃	C₂³	semidirect
84. C₂×#11719949	C₂³	semidirect
87. C₂×#11719945	C₂³	semidirect
88. C₂×#11719945	C₂³	semidirect
89. C₂²×Dic₁₀₆	C₂³	semidirect
96. C₂²×D₂₁₂	D₄	semidirect
103. C₂²×D₂₁₂	C₂³	semidirect
104. C₂²×D₂₁₂	C₂³	semidirect
105. C₂²×D₂₁₂	C₂³	semidirect
106. C₂²×D₂₁₂	C₂³	semidirect
107. C₂²×D₂₁₂	C₂³	semidirect
108. C₂²×D₂₁₂	C₂³	semidirect
109. C₂²×D₂₁₂	C₂³	semidirect
110. C₂²×D₂₁₂	C₂³	semidirect
113. C₂²×C₂²⋊D₅₃	C₂³	semidirect
114. C₂²×C₂²⋊D₅₃	C₂³	semidirect
118. C₂×D₄×D₅₃	C₂³	semidirect
119. C₂×D₄×D₅₃	C₂³	semidirect
120. C₂×D₄×D₅₃	C₂³	semidirect
121. C₂²×C₄×D₅₃	C₂³	semidirect
122. C₂²×C₄×D₅₃	C₂³	semidirect
123. C₂²×C₄×D₅₃	C₂³	semidirect
124. #13133214	C₂³	semidirect
125. #13133213	C₂³	semidirect
126. #13133206	C₂³	semidirect
127. #13133205	C₂³	semidirect
128. #13133202	C₂³	semidirect
129. #13133200	C₂³	semidirect
130. #13133196	C₂³	semidirect
131. #13133192	C₂³	semidirect
132. #13133192	C₂³	semidirect
133. #13133191	C₂³	semidirect
134. #13133191	C₂³	semidirect
135. #13133190	C₂³	semidirect
136. #13133187	C₂³	semidirect
137. #13133187	C₂³	semidirect
138. #13133187	C₂³	semidirect
139. #13133186	C₂³	semidirect
140. #13133185	C₂³	semidirect
141. #13133185	C₂³	semidirect
142. C₄×D₂₁₂	C₂³	semidirect
143. #13133179	C₂³	semidirect
144. C₄×C₂²⋊D₅₃	C₂³	semidirect
145. #13133176	C₂³	semidirect
146. C₂×C₄⋊Dic₅₃	C₂³	semidirect
147. C₂×#11719919	C₂³	semidirect
150. C₂×#11719921	C₂³	semidirect
151. C₂×#11719921	C₂³	semidirect
152. C₂×#11719921	C₂³	semidirect
153. C₂×#11719921	C₂³	semidirect
154. C₂²⋊C₄×D₅₃	C₂³	semidirect
155. C₂²⋊C₄×D₅₃	C₂³	semidirect
156. C₂×C₄×Dic₅₃	C₂³	semidirect
159. C₂×#41×C₅₃	C₂³	semidirect
160. C₂²×Q₈×C₅₃	C₂³	semidirect
163. C₂²×D₄×C₅₃	C₂³	semidirect
169. C₂³×C₄×C₅₃	C₂³	semidirect
170. C₂³×C₄×C₅₃	C₂³	semidirect
171. #123×C₅₃	C₂³	semidirect
172. C₂²⋊Q₈×C₅₃	C₂³	semidirect
173. #121×C₅₃	C₂³	semidirect
174. #120×C₅₃	C₂³	semidirect
175. C₄×D₄×C₅₃	C₂³	semidirect
176. #117×C₅₃	C₂³	semidirect
177. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
178. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
181. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
182. C₂×C₄²×C₅₃	C₂³	semidirect
200. C₂³×D₅₃	C₂×D₄	semidirect
207. C₂³×D₅₃	C₂⁴	semidirect
210. C₂×Q₈×C₅₃	C₂⁴	semidirect
216. C₂×D₄×C₅₃	C₂⁴	semidirect
222. C₂²×C₄×C₅₃	C₂×D₄	semidirect
232. C₂²×C₄×C₅₃	C₂⁴	semidirect
239. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
240. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
260. C₂×D₂₁₂	C₂×D₄	semidirect
261. C₂×D₂₁₂	C₂×D₄	semidirect
262. C₂×D₂₁₂	C₂×D₄	semidirect
268. C₂×D₂₁₂	C₂⁴	semidirect
269. C₂×D₂₁₂	C₂⁴	semidirect
270. C₂×D₂₁₂	C₂⁴	semidirect
274. C₂×C₄×D₅₃	C₂⁴	semidirect
275. C₂×C₄×D₅₃	C₂⁴	semidirect
276. C₂×C₄×D₅₃	C₂⁴	semidirect
278. C₂×Dic₁₀₆	C₂⁴	semidirect
279. C₄⋊C₄×C₅₃	C₂⁴	semidirect
280. C₄⋊C₄×C₅₃	C₂⁴	semidirect
283. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
284. C₄²×C₅₃	C₂⁴	semidirect
287. #11719921	C₂⁴	semidirect
288. #11719921	C₂⁴	semidirect
289. #11719921	C₂⁴	semidirect
290. #11719921	C₂⁴	semidirect
291. C₄⋊Dic₅₃	C₂⁴	semidirect
292. #11719919	C₂⁴	semidirect
293. C₄×Dic₅₃	C₂⁴	semidirect
303. C₂³×C₅₃	H(5,𝔽₂)	semidirect
327. C₂²×D₅₃	C₂²×D₄	semidirect
344. C₂×C₄×C₅₃	C₂²×D₄	semidirect
364. D₂₁₂	C₂²×D₄	semidirect
365. D₂₁₂	C₂²×D₄	semidirect
383. C₂²×C₅₃	C₂×H(5,𝔽₂)	semidirect
416. C₂×#525	D₅₃	semidirect
422. C₂×C₅₃	#3484	semidirect
434. C₂²×#41	C₂×D₅₃	semidirect
446. C₂⁴×C₄	C₂×D₅₃	semidirect
459. #525	C₂×D₅₃	semidirect
462. C₂×#123	C₂×D₅₃	semidirect
464. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
470. C₂×#121	C₂×D₅₃	semidirect
478. C₂×#120	C₂×D₅₃	semidirect
483. C₂×C₄×D₄	C₂×D₅₃	semidirect
485. C₂×#117	C₂×D₅₃	semidirect
488. C₅₃	C₂×#3484	semidirect
505. C₂×#41	C₂²×D₅₃	semidirect
507. C₂²×Q₈	C₂²×D₅₃	semidirect
541. C₂²×D₄	C₂²×D₅₃	semidirect
550. C₂³×C₄	C₂²×D₅₃	semidirect
551. C₂³×C₄	C₂²×D₅₃	semidirect
558. #123	C₂²×D₅₃	semidirect
560. C₂²⋊Q₈	C₂²×D₅₃	semidirect
566. #121	C₂²×D₅₃	semidirect
573. #120	C₂²×D₅₃	semidirect
577. C₄×D₄	C₂²×D₅₃	semidirect
579. #117	C₂²×D₅₃	semidirect
582. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
583. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
594. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
596. C₂×C₄²	C₂²×D₅₃	semidirect
629. C₂×Q₈	C₂³×D₅₃	semidirect
668. C₂×D₄	C₂³×D₅₃	semidirect
682. C₂²×C₄	D₄×D₅₃	semidirect
692. C₂²×C₄	C₂³×D₅₃	semidirect
695. C₄⋊C₄	C₂³×D₅₃	semidirect
696. C₄⋊C₄	C₂³×D₅₃	semidirect
705. C₂²⋊C₄	C₂³×D₅₃	semidirect
707. C₄²	C₂³×D₅₃	semidirect
740. C₂³	#13133263	semidirect
778. C₂×C₄	C₂×D₄×D₅₃	semidirect
809. C₂²	C₂×#13133263	semidirect
824. C₂	#20288348	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
C₂⁴×D₂₁₂	2
#20288348	2
C₂×#16811269	2
C₂×#16811264	2
C₂×D₄×D₂₁₂	2
C₂×#16811257	2
C₂×#16811192	2
C₂×#16811187	2
C₂×#16811184	2
C₂×#16811134	2
C₂×#120×D₅₃	2
C₂×#16811097	2
C₂×C₅₃×#525	2
C₂×#3484	53

Subgroups — C2×#20288348 #28291971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20288348 #28291971