Subgroups — C₂×#20288325 #28291178

Order 13568.

8722 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288325	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16811358	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16811330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16811319	C₂	1	2	yes	maximal, complemented
6	C₂×#16811317	C₂	1	2	yes	maximal, complemented
7	C₂×#16811297	C₂	1	4	yes	maximal, complemented
8	C₂×#16811269	C₂	1	2	yes	maximal, complemented
9	C₂×#16811261	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16811173	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16811160	C₂	1	2	yes	maximal, complemented
13	C₂×#16811157	C₂	1	2	yes	maximal, complemented
14	C₂×#16811132	C₂	1	4	yes	maximal, complemented
15	C₂×C₄×#11719945	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₄×D₂₁₂	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
18	C₂×C₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#11719945	C₂²	1	1	yes	characteristic
20	C₂²×#11719945	C₂²	1	2	yes	complemented
21	C₂³×D₂₁₂	C₂²	1	2	yes	—
22	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
23	C₂³×C₄×D₅₃	C₂²	1	4	yes	complemented
24	#16811358	C₂²	1	16	yes	complemented
25	#16811333	C₂²	1	16	yes	complemented
26	#16811330	C₂²	1	16	yes	complemented
27	#16811319	C₂²	1	32	yes	complemented
28	#16811317	C₂²	1	32	yes	complemented
29	#16811297	C₂²	1	64	yes	complemented
30	#16811269	C₂²	1	32	yes	complemented
31	#16811261	C₂²	1	32	yes	complemented
32	D₄×D₂₁₂	C₂²	1	16	yes	complemented
33	#16811173	C₂²	1	16	yes	complemented
34	C₂×#13133217	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13133214	C₂²	1	1	yes	characteristic
36	#16811160	C₂²	1	32	yes	complemented
37	#16811157	C₂²	1	32	yes	complemented
38	C₂×#13133212	C₂²	1	4	yes	complemented
39	C₂×#13133211	C₂²	1	4	yes	complemented
40	C₂×#13133209	C₂²	1	2	yes	complemented
41	C₂×#13133208	C₂²	1	2	yes	complemented
42	C₂×#13133206	C₂²	1	2	yes	complemented
43	C₂×#13133205	C₂²	1	2	yes	complemented
44	C₂×#13133205	C₂²	1	2	yes	complemented
45	#16811132	C₂²	1	64	yes	complemented
46	C₂×#13133202	C₂²	1	4	yes	complemented
47	C₂×#13133202	C₂²	1	4	yes	complemented
48	C₂×#13133200	C₂²	1	4	yes	complemented
49	C₂×#13133199	C₂²	1	4	yes	complemented
50	C₂×#13133196	C₂²	1	2	yes	complemented
51	C₂×#13133195	C₂²	1	4	yes	complemented
52	C₂×#13133194	C₂²	1	4	yes	complemented
53	C₂×#13133193	C₂²	1	2	yes	complemented
54	C₂×#13133192	C₂²	1	2	yes	—
55	C₂×#13133191	C₂²	1	2	yes	—
56	C₂×#13133191	C₂²	1	2	yes	complemented
57	C₂×#13133191	C₂²	1	2	yes	complemented
58	C₂×#13133190	C₂²	1	4	yes	complemented
59	C₂×#13133189	C₂²	1	4	yes	complemented
60	C₂×#13133187	C₂²	1	4	yes	—
61	C₂×#13133185	C₂²	1	4	yes	complemented
62	C₄×#11719945	C₂²	1	16	yes	complemented
63	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
66	C₂×C₄×D₂₁₂	C₂²	1	2	yes	—
67	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
68	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
69	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
70	C₂×C₄×D₂₁₂	C₂²	1	4	yes	complemented
71	C₂×C₄×D₂₁₂	C₂²	1	4	yes	complemented
72	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
73	C₂×C₄×D₂₁₂	C₂²	1	32	yes	complemented
74	C₂×D₄×Dic₅₃	C₂²	1	2	yes	—
75	C₂×#13133179	C₂²	1	2	yes	complemented
76	C₂×C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
77	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
78	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
79	C₂×#13133177	C₂²	1	4	yes	complemented
80	C₄×D₄×D₅₃	C₂²	1	32	yes	complemented
81	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
82	C₂×#13133174	C₂²	1	2	yes	complemented
83	C₂×#13133174	C₂²	1	4	yes	complemented
84	C₂²×C₄⋊Dic₅₃	C₂²	1	2	yes	complemented
85	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
86	C₂²×#11719921	C₂²	1	4	yes	complemented
87	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
88	C₂×C₄²×D₅₃	C₂²	1	2	yes	complemented
89	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
90	C₄×#41×C₅₃	C₂²	1	16	yes	complemented
91	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
93	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
94	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
95	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
96	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
97	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
98	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
99	C₂²×C₄²×C₅₃	C₂²	1	2	yes	complemented
100	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
101	C₂⁴×D₅₃	C₂³	1	4	yes	—
102	C₂×#11719945	—	2	8	no	—
103	C₂×#11719945	—	4	8	no	—
104	C₂×#11719945	C₂³	1	8	yes	—
105	C₂×#11719945	C₂³	1	16	yes	complemented
106	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
107	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
108	C₂²×D₂₁₂	—	2	16	no	—
109	C₂²×D₂₁₂	C₂³	1	16	yes	—
110	C₂²×D₂₁₂	C₂³	1	2	yes	—
111	C₂²×D₂₁₂	C₂³	1	4	yes	—
112	C₂²×D₂₁₂	C₂³	1	2	yes	—
113	C₂²×D₂₁₂	C₂³	1	2	yes	—
114	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
115	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
116	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
117	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
118	C₂×D₄×D₅₃	—	2	16	no	—
119	C₂×D₄×D₅₃	C₂³	1	16	yes	—
120	C₂³×Dic₅₃	C₂³	1	4	yes	—
121	C₂²×C₄×D₅₃	—	4	16	no	—
122	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
123	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
124	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
125	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
126	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
127	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
128	C₂²×C₄×D₅₃	C₂³	1	32	yes	complemented
129	#13133217	C₂³	1	8	yes	complemented
130	#13133214	C₂³	1	8	yes	—
131	#13133212	C₂³	1	32	yes	complemented
132	#13133211	C₂³	1	32	yes	complemented
133	#13133209	C₂³	1	16	yes	complemented
134	#13133208	C₂³	1	16	yes	complemented
135	#13133206	C₂³	1	16	yes	complemented
136	#13133205	C₂³	1	16	yes	complemented
137	#13133205	C₂³	1	16	yes	complemented
138	#13133202	C₂³	1	32	yes	complemented
139	#13133202	C₂³	1	32	yes	complemented
140	#13133200	C₂³	1	32	yes	complemented
141	#13133199	C₂³	1	32	yes	complemented
142	#13133196	C₂³	1	16	yes	complemented
143	#13133195	C₂³	1	32	yes	complemented
144	#13133194	C₂³	1	32	yes	complemented
145	#13133193	C₂³	1	16	yes	complemented
146	#13133192	C₂³	1	16	yes	—
147	#13133191	C₂³	1	16	yes	—
148	#13133191	C₂³	1	16	yes	complemented
149	#13133191	C₂³	1	16	yes	complemented
150	#13133190	C₂³	1	32	yes	complemented
151	#13133189	C₂³	1	32	yes	complemented
152	#13133187	C₂³	1	32	yes	—
153	#13133185	C₂³	1	32	yes	complemented
154	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
155	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
156	C₄×D₂₁₂	C₂³	1	16	yes	—
157	C₄×D₂₁₂	C₂³	1	8	yes	—
158	C₄×D₂₁₂	C₂³	1	8	yes	—
159	C₄×D₂₁₂	C₂³	1	32	yes	complemented
160	C₄×D₂₁₂	C₂³	1	16	yes	complemented
161	C₄×D₂₁₂	C₂³	1	16	yes	complemented
162	C₄×D₂₁₂	C₂³	1	32	yes	complemented
163	C₄×D₂₁₂	C₂³	1	16	yes	complemented
164	D₄×Dic₅₃	C₂³	1	16	yes	—
165	#13133179	C₂³	1	16	yes	complemented
166	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
167	C₄×C₂²⋊D₅₃	C₂³	1	32	yes	complemented
168	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
169	#13133177	C₂³	1	32	yes	complemented
170	#13133176	C₂³	1	8	yes	complemented
171	#13133174	C₂³	1	16	yes	complemented
172	#13133174	C₂³	1	32	yes	complemented
173	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
174	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
176	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	—
177	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊Dic₅₃	C₂³	1	16	yes	complemented
179	C₂×#11719919	C₂³	1	4	yes	—
180	C₂×#11719919	C₂³	1	2	yes	—
181	C₂×#11719919	C₂³	1	2	yes	—
182	C₂×#11719919	C₂³	1	4	yes	—
183	C₂×#11719919	C₂³	1	4	yes	—
184	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
185	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
186	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
187	C₂×#11719921	C₂³	1	4	yes	—
188	C₂×#11719921	C₂³	1	4	yes	—
189	C₂×#11719921	C₂³	1	2	yes	—
190	C₂×#11719921	C₂³	1	4	yes	—
191	C₂×#11719921	C₂³	1	4	yes	—
192	C₂×#11719921	C₂³	1	4	yes	—
193	C₂×#11719921	C₂³	1	2	yes	—
194	C₂×#11719921	C₂³	1	4	yes	—
195	C₂×#11719921	C₂³	1	4	yes	—
196	C₂×#11719921	C₂³	1	32	yes	complemented
197	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	complemented
198	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
199	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
200	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
201	C₄²×D₅₃	C₂³	1	16	yes	complemented
202	C₂×#41×C₅₃	—	2	8	no	—
203	C₂×#41×C₅₃	C₂³	1	8	yes	—
204	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
205	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
206	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
208	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
210	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
211	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
214	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
215	C₄×D₄×C₅₃	C₂³	1	8	yes	—
216	C₄×D₄×C₅₃	C₂³	1	8	yes	—
217	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
218	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
219	#117×C₅₃	C₂³	1	16	yes	complemented
220	#117×C₅₃	C₂³	1	8	yes	complemented
221	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
224	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
228	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
231	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
234	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
235	C₂×C₄²×C₅₃	C₂³	1	16	yes	complemented
236	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
237	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
239	C₂³×D₅₃	—	2	16	no	—
240	C₂³×D₅₃	—	2	16	no	—
241	C₂³×D₅₃	—	4	8	no	—
242	C₂³×D₅₃	C₂⁴	1	4	yes	—
243	C₂³×D₅₃	C₂⁴	1	16	yes	—
244	C₂³×D₅₃	C₂⁴	1	2	yes	—
245	#41×C₅₃	—	2	32	no	—
246	C₂×Q₈×C₅₃	—	2	4	no	—
247	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
248	C₂×D₄×C₅₃	—	2	8	no	—
249	C₂×D₄×C₅₃	#41	1	8	yes	complemented
250	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
251	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
252	C₂²×C₄×C₅₃	—	2	8	no	—
253	C₂²×C₄×C₅₃	—	2	4	no	—
254	C₂²×C₄×C₅₃	—	2	8	no	—
255	C₂²×C₄×C₅₃	—	2	4	no	—
256	C₂²×C₄×C₅₃	—	2	8	no	—
257	C₂²×C₄×C₅₃	—	2	4	no	—
258	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
265	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
267	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
268	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
273	C₂×C₂²⋊D₅₃	—	2	16	no	—
274	C₂×C₂²⋊D₅₃	—	2	8	no	—
275	C₂×C₂²⋊D₅₃	—	4	8	no	—
276	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
277	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
278	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
279	C₂²×Dic₅₃	—	4	8	no	—
280	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
281	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
282	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
283	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
284	C₂²×Dic₅₃	C₂⁴	1	16	yes	—
285	D₄×D₅₃	—	2	64	no	—
286	#11719945	—	2	32	no	—
287	#11719945	—	4	32	no	—
288	C₂×D₂₁₂	—	2	16	no	—
289	C₂×D₂₁₂	—	2	8	no	—
290	C₂×D₂₁₂	—	2	8	no	—
291	C₂×D₂₁₂	—	2	64	no	—
292	C₂×D₂₁₂	—	4	4	no	—
293	C₂×D₂₁₂	#41	1	8	yes	complemented
294	C₂×D₂₁₂	C₂⁴	1	8	yes	—
295	C₂×D₂₁₂	C₂⁴	1	16	yes	—
296	C₂×D₂₁₂	C₂⁴	1	8	yes	—
297	C₂×D₂₁₂	C₂⁴	1	8	yes	—
298	C₂×D₂₁₂	C₂⁴	1	4	yes	—
299	C₂×C₄×D₅₃	—	2	8	no	—
300	C₂×C₄×D₅₃	—	2	8	no	—
301	C₂×C₄×D₅₃	—	2	8	no	—
302	C₂×C₄×D₅₃	—	2	16	no	—
303	C₂×C₄×D₅₃	—	4	64	no	—
304	C₂×C₄×D₅₃	—	4	8	no	—
305	C₂×C₄×D₅₃	—	4	8	no	—
306	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
307	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
308	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
309	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
310	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
311	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
312	C₂×Dic₁₀₆	—	2	4	no	—
313	C₂×Dic₁₀₆	—	4	4	no	—
314	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
315	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
316	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
317	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
318	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
319	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
320	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
321	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
322	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
323	C₄²×C₅₃	C₂⁴	1	4	yes	—
324	C₄²×C₅₃	C₂⁴	1	4	yes	—
325	C₄²×C₅₃	C₂⁴	1	8	yes	—
326	C₄²×C₅₃	C₂⁴	1	4	yes	—
327	C₄²×C₅₃	C₂⁴	1	4	yes	—
328	C₄²×C₅₃	C₂⁴	1	8	yes	—
329	C₄²×C₅₃	C₂⁴	1	8	yes	—
330	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
331	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
332	#11719921	C₂⁴	1	16	yes	—
333	#11719921	C₂⁴	1	16	yes	—
334	#11719921	C₂⁴	1	8	yes	—
335	#11719921	C₂⁴	1	16	yes	—
336	#11719921	C₂⁴	1	16	yes	—
337	#11719921	C₂⁴	1	16	yes	—
338	#11719921	C₂⁴	1	8	yes	—
339	#11719921	C₂⁴	1	16	yes	—
340	#11719921	C₂⁴	1	16	yes	—
341	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
342	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
343	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
344	C₄⋊Dic₅₃	C₂⁴	1	16	yes	—
345	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
346	#11719919	C₂⁴	1	16	yes	—
347	#11719919	C₂⁴	1	8	yes	—
348	#11719919	C₂⁴	1	8	yes	—
349	#11719919	C₂⁴	1	16	yes	—
350	#11719919	C₂⁴	1	16	yes	—
351	C₄×Dic₅₃	C₂⁴	1	8	yes	—
352	C₄×Dic₅₃	C₂⁴	1	8	yes	—
353	C₄×Dic₅₃	C₂⁴	1	8	yes	—
354	C₂³×C₅₃	—	2	4	no	—
355	C₂³×C₅₃	—	2	4	no	—
356	C₂³×C₅₃	—	2	2	no	—
357	C₂³×C₅₃	—	2	2	no	—
358	C₂³×C₅₃	—	2	2	no	—
359	C₂³×C₅₃	C₂×#41	1	8	yes	—
360	C₂³×C₅₃	C₂⁵	1	2	yes	—
361	C₂³×C₅₃	C₂⁵	1	4	yes	—
362	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
363	C₂²×D₅₃	—	2	4	no	—
364	C₂²×D₅₃	—	2	4	no	—
365	C₂²×D₅₃	—	2	8	no	—
366	C₂²×D₅₃	—	2	8	no	—
367	C₂²×D₅₃	—	2	32	no	—
368	C₂²×D₅₃	—	2	8	no	—
369	C₂²×D₅₃	—	2	32	no	—
370	C₂²×D₅₃	—	4	16	no	—
371	C₂²×D₅₃	—	4	64	no	—
372	C₂²×D₅₃	C₂×#41	1	8	yes	—
373	C₂²×D₅₃	C₂⁵	1	8	yes	—
374	C₂²×D₅₃	C₂⁵	1	4	yes	—
375	Q₈×C₅₃	—	2	8	no	—
376	D₄×C₅₃	—	2	16	no	—
377	D₄×C₅₃	C₂×#41	1	16	yes	complemented
378	C₂×C₄×C₅₃	—	2	2	no	—
379	C₂×C₄×C₅₃	—	2	4	no	—
380	C₂×C₄×C₅₃	—	2	2	no	—
381	C₂×C₄×C₅₃	—	2	4	no	—
382	C₂×C₄×C₅₃	—	2	16	no	—
383	C₂×C₄×C₅₃	—	2	2	no	—
384	C₂×C₄×C₅₃	—	2	4	no	—
385	C₂×C₄×C₅₃	—	2	16	no	—
386	C₂×C₄×C₅₃	—	2	8	no	—
387	C₂×C₄×C₅₃	—	2	8	no	—
388	C₂×C₄×C₅₃	—	2	16	no	—
389	C₂×C₄×C₅₃	—	2	8	no	—
390	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
391	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
392	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
393	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
394	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
395	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
396	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
397	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
398	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
399	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
400	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
401	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
402	C₂²⋊D₅₃	—	2	32	no	—
403	C₂²⋊D₅₃	—	2	16	no	—
404	C₂²⋊D₅₃	—	4	16	no	—
405	C₂×Dic₅₃	—	2	4	no	—
406	C₂×Dic₅₃	—	2	4	no	—
407	C₂×Dic₅₃	—	2	8	no	—
408	C₂×Dic₅₃	—	2	4	no	—
409	C₂×Dic₅₃	—	4	16	no	—
410	C₂×Dic₅₃	C₂⁵	1	8	yes	—
411	C₂×Dic₅₃	C₂⁵	1	4	yes	—
412	C₂×Dic₅₃	C₂⁵	1	4	yes	—
413	C₂×Dic₅₃	C₂⁵	1	4	yes	—
414	D₂₁₂	—	2	32	no	—
415	D₂₁₂	—	2	16	no	—
416	D₂₁₂	—	2	16	no	—
417	D₂₁₂	—	4	8	no	—
418	D₂₁₂	C₂×#41	1	16	yes	complemented
419	C₄×D₅₃	—	2	16	no	—
420	C₄×D₅₃	—	2	16	no	—
421	C₄×D₅₃	—	2	16	no	—
422	C₄×D₅₃	—	2	32	no	—
423	C₄×D₅₃	—	4	16	no	—
424	C₄×D₅₃	—	4	16	no	—
425	Dic₁₀₆	—	2	8	no	—
426	Dic₁₀₆	—	4	8	no	—
427	C₂×#3481	—	53	1	no	maximal, Sylow
428	C₂²×C₅₃	—	2	4	no	—
429	C₂²×C₅₃	—	2	4	no	—
430	C₂²×C₅₃	—	2	16	no	—
431	C₂²×C₅₃	—	2	2	no	—
432	C₂²×C₅₃	—	2	2	no	—
433	C₂²×C₅₃	—	2	2	no	—
434	C₂²×C₅₃	—	4	4	no	—
435	C₂²×C₅₃	C₂²×#41	1	2	yes	—
436	C₂²×C₅₃	C₂²×#41	1	8	yes	—
437	C₂²×C₅₃	C₂²×#41	1	2	yes	—
438	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
439	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
440	C₂×D₅₃	—	2	4	no	—
441	C₂×D₅₃	—	2	4	no	—
442	C₂×D₅₃	—	2	16	no	—
443	C₂×D₅₃	—	2	8	no	—
444	C₂×D₅₃	—	2	8	no	—
445	C₂×D₅₃	—	2	8	no	—
446	C₂×D₅₃	—	4	64	no	—
447	C₂×D₅₃	—	4	16	no	—
448	C₂×D₅₃	C₂²×#41	1	8	yes	—
449	C₄×C₅₃	—	2	2	no	—
450	C₄×C₅₃	—	2	4	no	—
451	C₄×C₅₃	—	2	2	no	—
452	C₄×C₅₃	—	2	4	no	—
453	C₄×C₅₃	—	2	2	no	—
454	C₄×C₅₃	—	2	4	no	—
455	C₄×C₅₃	C₂²×#41	1	4	yes	—
456	C₄×C₅₃	C₂²×#41	1	4	yes	—
457	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
458	Dic₅₃	—	2	4	no	—
459	Dic₅₃	—	2	4	no	—
460	Dic₅₃	—	2	8	no	—
461	Dic₅₃	—	2	4	no	—
462	#3481	—	53	32	no	—
463	C₂×#559	—	53	1	no	—
464	C₂×#554	—	53	1	no	—
465	C₂×#554	—	53	1	no	—
466	C₂×#553	—	53	2	no	—
467	C₂×#553	—	53	2	no	—
468	C₂×#551	—	53	4	no	—
469	C₂×#546	—	53	2	no	—
470	C₂×#546	—	53	2	no	—
471	C₂×D₄²	—	53	1	no	—
472	C₂×#532	—	53	1	no	—
473	C₂×#529	—	53	2	no	—
474	C₂×#529	—	53	2	no	—
475	C₂×#525	—	53	4	no	—
476	C₂×C₄×#41	—	53	1	no	—
477	C₂×C₄×#41	D₅₃	1	1	yes	characteristic, complemented
478	C₂²×C₄×D₄	—	53	2	no	—
479	C₂²×C₄×D₄	—	53	2	no	—
480	C₂×C₅₃	—	2	8	no	—
481	C₂×C₅₃	—	4	2	no	—
482	C₂×C₅₃	#3481	1	4	yes	complemented
483	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
484	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
485	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
486	D₅₃	—	2	8	no	—
487	D₅₃	—	4	8	no	—
488	C₂²×#41	—	53	1	no	—
489	C₂²×#41	—	53	2	no	—
490	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic
491	C₂³×D₄	—	53	2	no	—
492	C₂³×D₄	—	53	2	no	—
493	C₂⁴×C₄	—	53	4	no	—
494	#559	—	53	16	no	—
495	#554	—	53	16	no	—
496	#554	—	53	16	no	—
497	#553	—	53	32	no	—
498	#553	—	53	32	no	—
499	#551	—	53	64	no	—
500	#546	—	53	32	no	—
501	#546	—	53	32	no	—
502	D₄²	—	53	16	no	—
503	#532	—	53	16	no	—
504	C₂×C₄⋊Q₈	—	53	1	no	—
505	C₂×#127	—	53	1	no	—
506	#529	—	53	32	no	—
507	#529	—	53	32	no	—
508	C₂×#126	—	53	4	no	—
509	C₂×#126	—	53	4	no	—
510	C₂×#125	—	53	2	no	—
511	C₂×#125	—	53	2	no	—
512	C₂×#124	—	53	2	no	—
513	C₂×#124	—	53	2	no	—
514	C₂×#124	—	53	2	no	—
515	#525	—	53	64	no	—
516	C₂×#123	—	53	4	no	—
517	C₂×#123	—	53	4	no	—
518	C₂×#123	—	53	4	no	—
519	C₂×#123	—	53	4	no	—
520	C₂×C₂²⋊Q₈	—	53	2	no	—
521	C₂×C₂²⋊Q₈	—	53	2	no	—
522	C₂×C₂²⋊Q₈	—	53	4	no	—
523	C₂×C₂²⋊Q₈	—	53	4	no	—
524	C₂×#121	—	53	4	no	—
525	C₂×#121	—	53	2	no	—
526	C₂×#121	—	53	2	no	—
527	C₂×#121	—	53	2	no	—
528	C₂×#121	—	53	2	no	—
529	C₂×#121	—	53	4	no	—
530	C₂×#120	—	53	4	no	—
531	C₂×#120	—	53	4	no	—
532	C₄×#41	—	53	16	no	—
533	C₄×#41	C₂×D₅₃	1	16	yes	complemented
534	C₂×C₄×Q₈	—	53	1	no	—
535	C₂×C₄×Q₈	—	53	1	no	—
536	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
537	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
538	C₂×C₄×D₄	—	53	2	no	—
539	C₂×C₄×D₄	—	53	4	no	—
540	C₂×C₄×D₄	—	53	2	no	—
541	C₂×C₄×D₄	—	53	2	no	—
542	C₂×C₄×D₄	—	53	32	no	—
543	C₂×C₄×D₄	—	53	2	no	—
544	C₂×C₄×D₄	—	53	4	no	—
545	C₂×C₄×D₄	—	53	1	no	—
546	C₂×C₄×D₄	—	53	2	no	—
547	C₂×C₄×D₄	—	53	1	no	—
548	C₂×C₄×D₄	—	53	4	no	—
549	C₂×C₄×D₄	—	53	2	no	—
550	C₂×C₄×D₄	—	53	2	no	—
551	C₂×C₄×D₄	—	53	4	no	—
552	C₂×C₄×D₄	—	53	2	no	—
553	C₂×C₄×D₄	—	53	32	no	—
554	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
555	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
556	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
557	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
558	C₂×#117	—	53	1	no	—
559	C₂×#117	—	53	2	no	—
560	C₂×#117	—	53	4	no	—
561	C₂×#117	C₂×D₅₃	1	2	yes	complemented
562	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
563	C₂²×C₄⋊C₄	—	53	2	no	—
564	C₂²×C₄⋊C₄	—	53	2	no	—
565	C₂²×C₂²⋊C₄	—	53	4	no	—
566	C₂²×C₂²⋊C₄	—	53	4	no	—
567	C₂²×C₄²	—	53	2	no	—
568	C₂²×C₄²	C₂×D₅₃	1	2	yes	complemented
569	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
570	C₅₃	C₂×#3481	1	1	yes	characteristic, complemented, Sylow
571	C₂⁵	—	53	4	no	—
572	C₂×#41	—	2	8	no	—
573	C₂×#41	—	53	8	no	—
574	C₂×#41	—	53	16	no	—
575	C₂×#41	—	106	8	no	—
576	C₂×#41	—	212	8	no	—
577	C₂×#41	C₂²×D₅₃	1	8	yes	—
578	C₂²×Q₈	—	53	1	no	—
579	C₂²×Q₈	—	53	2	no	—
580	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
581	C₂²×D₄	—	53	2	no	—
582	C₂²×D₄	—	53	4	no	—
583	C₂²×D₄	—	53	4	no	—
584	C₂²×D₄	—	53	16	no	—
585	C₂²×D₄	—	53	1	no	—
586	C₂²×D₄	—	53	4	no	—
587	C₂²×D₄	—	53	2	no	—
588	C₂²×D₄	—	53	2	no	—
589	C₂²×D₄	—	53	16	no	—
590	C₂²×D₄	—	53	2	no	—
591	C₂²×D₄	—	106	16	no	—
592	C₂²×D₄	—	106	16	no	—
593	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
594	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
595	C₂³×C₄	—	53	4	no	—
596	C₂³×C₄	—	53	2	no	—
597	C₂³×C₄	—	53	2	no	—
598	C₂³×C₄	—	53	4	no	—
599	C₂³×C₄	—	53	2	no	—
600	C₂³×C₄	—	53	4	no	—
601	C₂³×C₄	—	53	4	no	—
602	C₂³×C₄	—	53	32	no	—
603	C₂³×C₄	—	212	16	no	—
604	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
605	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
606	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
607	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
608	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
609	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
610	C₄⋊Q₈	—	53	8	no	—
611	#127	—	53	8	no	—
612	#126	—	53	32	no	—
613	#126	—	53	32	no	—
614	#125	—	53	16	no	—
615	#125	—	53	16	no	—
616	#124	—	53	16	no	—
617	#124	—	53	16	no	—
618	#124	—	53	16	no	—
619	#123	—	53	32	no	—
620	#123	—	53	32	no	—
621	#123	—	53	32	no	—
622	#123	—	53	32	no	—
623	C₂²⋊Q₈	—	53	16	no	—
624	C₂²⋊Q₈	—	53	16	no	—
625	C₂²⋊Q₈	—	53	32	no	—
626	C₂²⋊Q₈	—	53	32	no	—
627	#121	—	53	32	no	—
628	#121	—	53	16	no	—
629	#121	—	53	16	no	—
630	#121	—	53	16	no	—
631	#121	—	53	16	no	—
632	#121	—	53	32	no	—
633	#120	—	53	32	no	—
634	#120	—	53	32	no	—
635	C₄×Q₈	—	53	8	no	—
636	C₄×Q₈	—	53	8	no	—
637	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
638	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
639	C₄×D₄	—	53	16	no	—
640	C₄×D₄	—	53	32	no	—
641	C₄×D₄	—	53	16	no	—
642	C₄×D₄	—	53	16	no	—
643	C₄×D₄	—	53	16	no	—
644	C₄×D₄	—	53	32	no	—
645	C₄×D₄	—	53	8	no	—
646	C₄×D₄	—	53	32	no	—
647	C₄×D₄	—	53	16	no	—
648	C₄×D₄	—	53	16	no	—
649	C₄×D₄	—	53	16	no	—
650	C₄×D₄	—	53	32	no	—
651	C₄×D₄	—	53	16	no	—
652	C₄×D₄	—	53	8	no	—
653	C₄×D₄	C₂²×D₅₃	1	8	yes	—
654	C₄×D₄	C₂²×D₅₃	1	8	yes	—
655	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
656	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
657	#117	—	53	8	no	—
658	#117	—	53	16	no	—
659	#117	—	53	32	no	—
660	#117	C₂²×D₅₃	1	16	yes	complemented
661	#117	C₂²×D₅₃	1	8	yes	complemented
662	C₂×C₄⋊C₄	—	53	1	no	—
663	C₂×C₄⋊C₄	—	53	2	no	—
664	C₂×C₄⋊C₄	—	53	2	no	—
665	C₂×C₄⋊C₄	—	53	4	no	—
666	C₂×C₄⋊C₄	—	53	4	no	—
667	C₂×C₄⋊C₄	—	53	16	no	—
668	C₂×C₄⋊C₄	—	53	1	no	—
669	C₂×C₄⋊C₄	—	53	2	no	—
670	C₂×C₄⋊C₄	—	53	2	no	—
671	C₂×C₄⋊C₄	—	53	4	no	—
672	C₂×C₄⋊C₄	—	53	4	no	—
673	C₂×C₄⋊C₄	—	53	16	no	—
674	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
677	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
678	C₂×C₂²⋊C₄	—	53	4	no	—
679	C₂×C₂²⋊C₄	—	53	2	no	—
680	C₂×C₂²⋊C₄	—	53	2	no	—
681	C₂×C₂²⋊C₄	—	53	4	no	—
682	C₂×C₂²⋊C₄	—	53	4	no	—
683	C₂×C₂²⋊C₄	—	53	4	no	—
684	C₂×C₂²⋊C₄	—	53	4	no	—
685	C₂×C₂²⋊C₄	—	53	4	no	—
686	C₂×C₂²⋊C₄	—	53	32	no	—
687	C₂×C₂²⋊C₄	—	53	2	no	—
688	C₂×C₂²⋊C₄	—	53	4	no	—
689	C₂×C₂²⋊C₄	—	53	4	no	—
690	C₂×C₂²⋊C₄	—	53	32	no	—
691	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
694	C₂×C₄²	—	53	2	no	—
695	C₂×C₄²	—	53	2	no	—
696	C₂×C₄²	—	53	2	no	—
697	C₂×C₄²	—	53	16	no	—
698	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
699	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
700	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
701	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
702	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
703	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
704	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
705	C₂×C₄²	C₂²×D₅₃	1	16	yes	complemented
706	C₂×C₄²	C₂²×D₅₃	1	8	yes	complemented
707	C₂⁴	—	53	2	no	—
708	C₂⁴	—	53	4	no	—
709	C₂⁴	—	53	16	no	—
710	C₂⁴	—	106	16	no	—
711	C₂⁴	—	106	16	no	—
712	C₂⁴	—	212	8	no	—
713	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
714	C₂⁴	C₂³×D₅₃	1	2	yes	—
715	#41	—	2	32	no	—
716	#41	—	106	32	no	—
717	#41	—	212	32	no	—
718	C₂×Q₈	—	2	4	no	—
719	C₂×Q₈	—	53	4	no	—
720	C₂×Q₈	—	53	8	no	—
721	C₂×Q₈	—	106	4	no	—
722	C₂×Q₈	—	212	4	no	—
723	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
724	C₂×D₄	—	2	8	no	—
725	C₂×D₄	—	53	8	no	—
726	C₂×D₄	—	53	16	no	—
727	C₂×D₄	—	53	16	no	—
728	C₂×D₄	—	53	8	no	—
729	C₂×D₄	—	53	4	no	—
730	C₂×D₄	—	53	16	no	—
731	C₂×D₄	—	53	8	no	—
732	C₂×D₄	—	53	8	no	—
733	C₂×D₄	—	53	8	no	—
734	C₂×D₄	—	106	64	no	—
735	C₂×D₄	—	106	16	no	—
736	C₂×D₄	—	106	8	no	—
737	C₂×D₄	—	106	16	no	—
738	C₂×D₄	—	106	64	no	—
739	C₂×D₄	—	106	8	no	—
740	C₂×D₄	—	106	8	no	—
741	C₂×D₄	—	212	4	no	—
742	C₂×D₄	—	212	8	no	—
743	C₂×D₄	#11719945	1	8	yes	complemented
744	C₂×D₄	C₂³×D₅₃	1	8	yes	—
745	C₂×D₄	C₂³×D₅₃	1	4	yes	—
746	C₂²×C₄	—	2	8	no	—
747	C₂²×C₄	—	2	8	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	8	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	53	2	no	—
753	C₂²×C₄	—	53	2	no	—
754	C₂²×C₄	—	53	2	no	—
755	C₂²×C₄	—	53	4	no	—
756	C₂²×C₄	—	53	16	no	—
757	C₂²×C₄	—	53	8	no	—
758	C₂²×C₄	—	53	8	no	—
759	C₂²×C₄	—	53	8	no	—
760	C₂²×C₄	—	53	16	no	—
761	C₂²×C₄	—	53	16	no	—
762	C₂²×C₄	—	53	16	no	—
763	C₂²×C₄	—	106	8	no	—
764	C₂²×C₄	—	106	8	no	—
765	C₂²×C₄	—	106	8	no	—
766	C₂²×C₄	—	106	16	no	—
767	C₂²×C₄	—	212	64	no	—
768	C₂²×C₄	—	212	8	no	—
769	C₂²×C₄	—	212	8	no	—
770	C₂²×C₄	—	212	8	no	—
771	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
772	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
773	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
774	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
775	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
776	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
777	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
778	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
779	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
780	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
781	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
782	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
783	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
784	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
785	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
786	C₄⋊C₄	—	53	4	no	—
787	C₄⋊C₄	—	53	8	no	—
788	C₄⋊C₄	—	53	8	no	—
789	C₄⋊C₄	—	53	16	no	—
790	C₄⋊C₄	—	53	16	no	—
791	C₄⋊C₄	—	53	4	no	—
792	C₄⋊C₄	—	53	8	no	—
793	C₄⋊C₄	—	53	8	no	—
794	C₄⋊C₄	—	53	16	no	—
795	C₄⋊C₄	—	53	16	no	—
796	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
797	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
798	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
799	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
800	C₂²⋊C₄	—	53	16	no	—
801	C₂²⋊C₄	—	53	8	no	—
802	C₂²⋊C₄	—	53	8	no	—
803	C₂²⋊C₄	—	53	16	no	—
804	C₂²⋊C₄	—	53	16	no	—
805	C₂²⋊C₄	—	53	16	no	—
806	C₂²⋊C₄	—	53	16	no	—
807	C₂²⋊C₄	—	53	16	no	—
808	C₂²⋊C₄	—	53	8	no	—
809	C₂²⋊C₄	—	53	16	no	—
810	C₂²⋊C₄	—	53	16	no	—
811	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
812	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
813	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
814	C₄²	—	53	8	no	—
815	C₄²	—	53	8	no	—
816	C₄²	—	53	8	no	—
817	C₄²	C₂³×D₅₃	1	4	yes	—
818	C₄²	C₂³×D₅₃	1	4	yes	—
819	C₄²	C₂³×D₅₃	1	4	yes	—
820	C₄²	C₂³×D₅₃	1	8	yes	—
821	C₄²	C₂³×D₅₃	1	8	yes	—
822	C₄²	C₂³×D₅₃	1	8	yes	—
823	C₄²	C₂³×D₅₃	1	4	yes	—
824	C₂³	—	2	4	no	—
825	C₂³	—	2	4	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	53	8	no	—
830	C₂³	—	53	4	no	—
831	C₂³	—	53	8	no	—
832	C₂³	—	106	32	no	—
833	C₂³	—	106	4	no	—
834	C₂³	—	106	4	no	—
835	C₂³	—	106	8	no	—
836	C₂³	—	106	32	no	—
837	C₂³	—	106	8	no	—
838	C₂³	—	106	8	no	—
839	C₂³	—	212	16	no	—
840	C₂³	—	212	64	no	—
841	C₂³	C₂×#11719945	1	8	yes	—
842	C₂³	C₂⁴×D₅₃	1	2	yes	—
843	C₂³	C₂⁴×D₅₃	1	4	yes	—
844	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
845	Q₈	—	2	8	no	—
846	Q₈	—	106	8	no	—
847	Q₈	—	212	8	no	—
848	D₄	—	2	16	no	—
849	D₄	—	53	16	no	—
850	D₄	—	106	32	no	—
851	D₄	—	106	16	no	—
852	D₄	—	106	32	no	—
853	D₄	—	106	16	no	—
854	D₄	—	106	16	no	—
855	D₄	—	212	8	no	—
856	D₄	—	212	16	no	—
857	D₄	C₂×#11719945	1	16	yes	complemented
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	4	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	4	no	—
862	C₂×C₄	—	2	16	no	—
863	C₂×C₄	—	2	4	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	16	no	—
866	C₂×C₄	—	2	8	no	—
867	C₂×C₄	—	2	8	no	—
868	C₂×C₄	—	2	16	no	—
869	C₂×C₄	—	2	8	no	—
870	C₂×C₄	—	53	4	no	—
871	C₂×C₄	—	53	4	no	—
872	C₂×C₄	—	53	4	no	—
873	C₂×C₄	—	53	8	no	—
874	C₂×C₄	—	106	16	no	—
875	C₂×C₄	—	106	4	no	—
876	C₂×C₄	—	106	4	no	—
877	C₂×C₄	—	106	4	no	—
878	C₂×C₄	—	106	8	no	—
879	C₂×C₄	—	106	16	no	—
880	C₂×C₄	—	106	16	no	—
881	C₂×C₄	—	106	32	no	—
882	C₂×C₄	—	212	16	no	—
883	C₂×C₄	—	212	16	no	—
884	C₂×C₄	—	212	16	no	—
885	C₂×C₄	#41×D₅₃	1	4	yes	—
886	C₂×C₄	C₂×#11719945	1	4	yes	—
887	C₂×C₄	#13133263	1	4	yes	—
888	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
889	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
890	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
891	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
892	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
893	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
894	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
895	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
896	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
897	C₂²	—	2	16	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	4	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	4	4	no	—
904	C₂²	—	53	8	no	—
905	C₂²	—	106	16	no	—
906	C₂²	—	106	4	no	—
907	C₂²	—	106	4	no	—
908	C₂²	—	106	8	no	—
909	C₂²	—	106	8	no	—
910	C₂²	—	106	8	no	—
911	C₂²	—	212	64	no	—
912	C₂²	—	212	16	no	—
913	C₂²	C₂×#41×D₅₃	1	2	yes	—
914	C₂²	C₂²×#11719945	1	8	yes	—
915	C₂²	C₂²×#11719945	1	2	yes	—
916	C₂²	C₂×#13133263	1	2	yes	—
917	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
918	C₄	—	2	2	no	—
919	C₄	—	2	4	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	4	no	—
922	C₄	—	2	4	no	—
923	C₄	—	2	2	no	—
924	C₄	—	106	4	no	—
925	C₄	—	106	4	no	—
926	C₄	—	106	4	no	—
927	C₄	—	106	8	no	—
928	C₄	C₂×#41×D₅₃	1	4	yes	—
929	C₄	C₂²×#11719945	1	4	yes	—
930	C₄	C₂×#13133263	1	4	yes	—
931	C₂	—	2	8	no	—
932	C₂	—	4	2	no	—
933	C₂	—	106	8	no	—
934	C₂	—	212	8	no	—
935	C₂	#20288325	1	4	yes	direct product factor
936	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
937	C₂	C₂³×#11719945	1	1	yes	characteristic
938	C₂	C₂²×#13133263	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₄×#41×C₅₃	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×C₄×#41	D₅₃
hypocenter	C₅₃	C₂×#3481
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. #20288325	C₂	direct (N × H)
2. C₂×#16811358	C₂	semidirect
3. C₂×#16811333	C₂	semidirect
4. C₂×#16811330	C₂	semidirect
5. C₂×#16811319	C₂	semidirect
6. C₂×#16811317	C₂	semidirect
7. C₂×#16811297	C₂	semidirect
8. C₂×#16811269	C₂	semidirect
9. C₂×#16811261	C₂	semidirect
10. C₂×D₄×D₂₁₂	C₂	semidirect
11. C₂×#16811173	C₂	semidirect
12. C₂×#16811160	C₂	semidirect
13. C₂×#16811157	C₂	semidirect
14. C₂×#16811132	C₂	semidirect
15. C₂×C₄×#11719945	C₂	semidirect
16. C₂²×C₄×D₂₁₂	C₂	semidirect
17. C₂×C₄×D₄×D₅₃	C₂	semidirect
18. C₂×C₄×#41×C₅₃	C₂	semidirect
20. C₂²×#11719945	C₂²	semidirect
23. C₂³×C₄×D₅₃	C₂²	semidirect
24. #16811358	C₂²	semidirect
25. #16811333	C₂²	semidirect
26. #16811330	C₂²	semidirect
27. #16811319	C₂²	semidirect
28. #16811317	C₂²	semidirect
29. #16811297	C₂²	semidirect
30. #16811269	C₂²	semidirect
31. #16811261	C₂²	semidirect
32. D₄×D₂₁₂	C₂²	semidirect
33. #16811173	C₂²	semidirect
34. C₂×#13133217	C₂²	semidirect
36. #16811160	C₂²	semidirect
37. #16811157	C₂²	semidirect
38. C₂×#13133212	C₂²	semidirect
39. C₂×#13133211	C₂²	semidirect
40. C₂×#13133209	C₂²	semidirect
41. C₂×#13133208	C₂²	semidirect
42. C₂×#13133206	C₂²	semidirect
43. C₂×#13133205	C₂²	semidirect
44. C₂×#13133205	C₂²	semidirect
45. #16811132	C₂²	semidirect
46. C₂×#13133202	C₂²	semidirect
47. C₂×#13133202	C₂²	semidirect
48. C₂×#13133200	C₂²	semidirect
49. C₂×#13133199	C₂²	semidirect
50. C₂×#13133196	C₂²	semidirect
51. C₂×#13133195	C₂²	semidirect
52. C₂×#13133194	C₂²	semidirect
53. C₂×#13133193	C₂²	semidirect
56. C₂×#13133191	C₂²	semidirect
57. C₂×#13133191	C₂²	semidirect
58. C₂×#13133190	C₂²	semidirect
59. C₂×#13133189	C₂²	semidirect
61. C₂×#13133185	C₂²	semidirect
62. C₄×#11719945	C₂²	semidirect
63. C₂×C₄×Dic₁₀₆	C₂²	semidirect
64. C₂×C₄×Dic₁₀₆	C₂²	semidirect
68. C₂×C₄×D₂₁₂	C₂²	semidirect
69. C₂×C₄×D₂₁₂	C₂²	semidirect
70. C₂×C₄×D₂₁₂	C₂²	semidirect
71. C₂×C₄×D₂₁₂	C₂²	semidirect
72. C₂×C₄×D₂₁₂	C₂²	semidirect
73. C₂×C₄×D₂₁₂	C₂²	semidirect
75. C₂×#13133179	C₂²	semidirect
76. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
77. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
78. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
79. C₂×#13133177	C₂²	semidirect
80. C₄×D₄×D₅₃	C₂²	semidirect
81. C₂×#13133176	C₂²	semidirect
82. C₂×#13133174	C₂²	semidirect
83. C₂×#13133174	C₂²	semidirect
84. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
85. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
86. C₂²×#11719921	C₂²	semidirect
87. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
88. C₂×C₄²×D₅₃	C₂²	semidirect
90. C₄×#41×C₅₃	C₂²	semidirect
91. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
92. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
95. C₂×C₄×D₄×C₅₃	C₂²	semidirect
96. C₂×C₄×D₄×C₅₃	C₂²	semidirect
97. C₂×#117×C₅₃	C₂²	semidirect
98. C₂×#117×C₅₃	C₂²	semidirect
99. C₂²×C₄²×C₅₃	C₂²	semidirect
100. C₂²×C₄²×C₅₃	C₂²	semidirect
105. C₂×#11719945	C₂³	semidirect
128. C₂²×C₄×D₅₃	C₂³	semidirect
129. #13133217	C₂³	semidirect
131. #13133212	C₂³	semidirect
132. #13133211	C₂³	semidirect
133. #13133209	C₂³	semidirect
134. #13133208	C₂³	semidirect
135. #13133206	C₂³	semidirect
136. #13133205	C₂³	semidirect
137. #13133205	C₂³	semidirect
138. #13133202	C₂³	semidirect
139. #13133202	C₂³	semidirect
140. #13133200	C₂³	semidirect
141. #13133199	C₂³	semidirect
142. #13133196	C₂³	semidirect
143. #13133195	C₂³	semidirect
144. #13133194	C₂³	semidirect
145. #13133193	C₂³	semidirect
148. #13133191	C₂³	semidirect
149. #13133191	C₂³	semidirect
150. #13133190	C₂³	semidirect
151. #13133189	C₂³	semidirect
153. #13133185	C₂³	semidirect
154. C₄×Dic₁₀₆	C₂³	semidirect
155. C₄×Dic₁₀₆	C₂³	semidirect
159. C₄×D₂₁₂	C₂³	semidirect
160. C₄×D₂₁₂	C₂³	semidirect
161. C₄×D₂₁₂	C₂³	semidirect
162. C₄×D₂₁₂	C₂³	semidirect
163. C₄×D₂₁₂	C₂³	semidirect
165. #13133179	C₂³	semidirect
166. C₄×C₂²⋊D₅₃	C₂³	semidirect
167. C₄×C₂²⋊D₅₃	C₂³	semidirect
168. C₄×C₂²⋊D₅₃	C₂³	semidirect
169. #13133177	C₂³	semidirect
170. #13133176	C₂³	semidirect
171. #13133174	C₂³	semidirect
172. #13133174	C₂³	semidirect
178. C₂×C₄⋊Dic₅₃	C₂³	semidirect
184. C₄⋊C₄×D₅₃	C₂³	semidirect
196. C₂×#11719921	C₂³	semidirect
197. C₂²⋊C₄×D₅₃	C₂³	semidirect
201. C₄²×D₅₃	C₂³	semidirect
213. C₄×Q₈×C₅₃	C₂³	semidirect
214. C₄×Q₈×C₅₃	C₂³	semidirect
217. C₄×D₄×C₅₃	C₂³	semidirect
218. C₄×D₄×C₅₃	C₂³	semidirect
219. #117×C₅₃	C₂³	semidirect
220. #117×C₅₃	C₂³	semidirect
235. C₂×C₄²×C₅₃	C₂³	semidirect
236. C₂×C₄²×C₅₃	C₂³	semidirect
249. C₂×D₄×C₅₃	#41	semidirect
293. C₂×D₂₁₂	#41	semidirect
377. D₄×C₅₃	C₂×#41	semidirect
418. D₂₁₂	C₂×#41	semidirect
477. C₂×C₄×#41	D₅₃	semidirect
482. C₂×C₅₃	#3481	semidirect
533. C₄×#41	C₂×D₅₃	semidirect
536. C₂×C₄×Q₈	C₂×D₅₃	semidirect
537. C₂×C₄×Q₈	C₂×D₅₃	semidirect
556. C₂×C₄×D₄	C₂×D₅₃	semidirect
557. C₂×C₄×D₄	C₂×D₅₃	semidirect
561. C₂×#117	C₂×D₅₃	semidirect
562. C₂×#117	C₂×D₅₃	semidirect
568. C₂²×C₄²	C₂×D₅₃	semidirect
569. C₂²×C₄²	C₂×D₅₃	semidirect
570. C₅₃	C₂×#3481	semidirect
637. C₄×Q₈	C₂²×D₅₃	semidirect
638. C₄×Q₈	C₂²×D₅₃	semidirect
655. C₄×D₄	C₂²×D₅₃	semidirect
656. C₄×D₄	C₂²×D₅₃	semidirect
660. #117	C₂²×D₅₃	semidirect
661. #117	C₂²×D₅₃	semidirect
705. C₂×C₄²	C₂²×D₅₃	semidirect
706. C₂×C₄²	C₂²×D₅₃	semidirect
743. C₂×D₄	#11719945	semidirect
857. D₄	C₂×#11719945	semidirect
935. C₂	#20288325	direct (N × H)

Maximal subgroups

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

subgroup	index
#20288325	2
C₂×#16811358	2
C₂×#16811333	2
C₂×#16811330	2
C₂×#16811319	2
C₂×#16811317	2
C₂×#16811297	2
C₂×#16811269	2
C₂×#16811261	2
C₂×D₄×D₂₁₂	2
C₂×#16811173	2
C₂×#16811160	2
C₂×#16811157	2
C₂×#16811132	2
C₂×C₄×#11719945	2
C₂²×C₄×D₂₁₂	2
C₂×C₄×D₄×D₅₃	2
C₂×C₄×#41×C₅₃	2
C₂×#3481	53

Subgroups — C2×#20288325 #28291178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20288325 #28291178