Subgroups — C₂×#20288477 #28291981

Order 13568.

12378 conjugacy classes of subgroups.

The subgroup lattice has 760 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	2	yes	maximal, complemented
2	#20288477	C₂	1	32	yes	maximal, direct product factor
3	C₂×#16811278	C₂	1	2	yes	maximal, complemented
4	C₂×#16811276	C₂	1	2	yes	maximal, complemented
5	C₂×#16811269	C₂	1	4	yes	maximal, complemented
6	C₂×#16811266	C₂	1	4	yes	maximal, complemented
7	C₂×D₄×D₂₁₂	C₂	1	2	yes	maximal, complemented
8	C₂×#16811258	C₂	1	2	yes	maximal, complemented
9	C₂×#16811201	C₂	1	2	yes	maximal, complemented
10	C₂×#16811181	C₂	1	4	yes	maximal, complemented
11	C₂×#16811173	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#121×D₅₃	C₂	1	4	yes	maximal, complemented
13	C₂²×C₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#13133263	—	2	32	no	—
16	C₂×#13133263	C₂²	1	32	yes	complemented
17	C₂²×#11719949	C₂²	1	4	yes	complemented
18	C₂²×#11719945	C₂²	1	2	yes	complemented
19	C₂²×#11719945	C₂²	1	4	yes	complemented
20	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
21	C₂³×D₂₁₂	C₂²	1	4	yes	complemented
22	C₂²×D₄×D₅₃	C₂²	1	8	yes	complemented
23	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
24	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
25	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
26	#16811278	C₂²	1	32	yes	complemented
27	#16811276	C₂²	1	32	yes	complemented
28	#16811269	C₂²	1	64	yes	complemented
29	#16811266	C₂²	1	64	yes	complemented
30	D₄×D₂₁₂	C₂²	1	32	yes	complemented
31	#16811258	C₂²	1	32	yes	complemented
32	#16811201	C₂²	1	32	yes	complemented
33	#16811181	C₂²	1	64	yes	complemented
34	#16811173	C₂²	1	16	yes	complemented
35	C₂×#13133217	C₂²	1	1	yes	characteristic, complemented
36	C₂×#13133214	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13133205	C₂²	1	2	yes	complemented
38	C₂×#13133202	C₂²	1	8	yes	complemented
39	C₂×#13133199	C₂²	1	8	yes	complemented
40	C₂×#13133196	C₂²	1	4	yes	complemented
41	C₂×#13133193	C₂²	1	4	yes	complemented
42	C₂×#13133192	C₂²	1	4	yes	complemented
43	C₂×#13133191	C₂²	1	2	yes	complemented
44	C₂×#13133191	C₂²	1	4	yes	complemented
45	C₂×#13133191	C₂²	1	2	yes	complemented
46	C₂×#13133190	C₂²	1	8	yes	complemented
47	C₂×#13133189	C₂²	1	8	yes	complemented
48	C₂×#13133188	C₂²	1	4	yes	complemented
49	C₂×#13133188	C₂²	1	4	yes	complemented
50	#121×D₅₃	C₂²	1	64	yes	complemented
51	C₂×#13133187	C₂²	1	8	yes	complemented
52	C₂×#13133185	C₂²	1	8	yes	complemented
53	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
54	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
55	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
56	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
57	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
58	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
59	C₂×C₄×D₂₁₂	C₂²	1	16	yes	complemented
60	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄⋊C₄×D₅₃	C₂²	1	4	yes	complemented
62	C₂²×#11719921	C₂²	1	2	yes	complemented
63	C₂×C₂²⋊C₄×D₅₃	C₂²	1	8	yes	complemented
64	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
65	C₅₃×#532	C₂²	1	16	yes	complemented
66	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
69	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
70	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
71	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
72	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
73	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
74	C₂⁴×D₅₃	C₂³	1	8	yes	—
75	C₂⁴×D₅₃	C₂³	1	2	yes	—
76	#13133263	—	2	256	no	—
77	C₂×#11719949	—	2	32	no	—
78	C₂×#11719949	C₂³	1	32	yes	complemented
79	C₂×#11719945	—	2	16	no	—
80	C₂×#11719945	—	2	32	no	—
81	C₂×#11719945	C₂³	1	32	yes	complemented
82	C₂×#11719945	C₂³	1	16	yes	complemented
83	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
84	C₂²×D₂₁₂	—	2	32	no	—
85	C₂²×D₂₁₂	D₄	1	16	yes	complemented
86	C₂²×D₂₁₂	C₂³	1	2	yes	—
87	C₂²×D₂₁₂	C₂³	1	8	yes	—
88	C₂²×D₂₁₂	C₂³	1	2	yes	—
89	C₂²×D₂₁₂	C₂³	1	2	yes	—
90	C₂²×D₂₁₂	C₂³	1	2	yes	—
91	C₂²×D₂₁₂	C₂³	1	2	yes	—
92	C₂²×D₂₁₂	C₂³	1	8	yes	—
93	C₂²×D₂₁₂	C₂³	1	32	yes	complemented
94	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
95	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
96	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
97	C₂×D₄×D₅₃	—	2	64	no	—
98	C₂×D₄×D₅₃	—	2	32	no	—
99	C₂×D₄×D₅₃	—	4	16	no	—
100	C₂×D₄×D₅₃	C₂³	1	32	yes	complemented
101	C₂×D₄×D₅₃	C₂³	1	64	yes	complemented
102	C₂×D₄×D₅₃	C₂³	1	32	yes	complemented
103	C₂³×Dic₅₃	C₂³	1	2	yes	—
104	C₂²×C₄×D₅₃	—	4	8	no	—
105	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
106	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
107	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
108	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
109	C₂²×C₄×D₅₃	C₂³	1	16	yes	complemented
110	#13133217	C₂³	1	8	yes	complemented
111	#13133214	C₂³	1	8	yes	complemented
112	#13133205	C₂³	1	16	yes	complemented
113	#13133202	C₂³	1	64	yes	complemented
114	#13133199	C₂³	1	64	yes	complemented
115	#13133196	C₂³	1	32	yes	complemented
116	#13133193	C₂³	1	32	yes	complemented
117	#13133192	C₂³	1	32	yes	complemented
118	#13133191	C₂³	1	32	yes	complemented
119	#13133191	C₂³	1	16	yes	complemented
120	#13133191	C₂³	1	16	yes	complemented
121	#13133190	C₂³	1	64	yes	complemented
122	#13133189	C₂³	1	64	yes	complemented
123	#13133188	C₂³	1	32	yes	complemented
124	#13133188	C₂³	1	32	yes	complemented
125	#13133187	C₂³	1	64	yes	complemented
126	#13133185	C₂³	1	64	yes	complemented
127	C₄×D₂₁₂	C₂³	1	16	yes	complemented
128	C₄×D₂₁₂	C₂³	1	16	yes	complemented
129	C₄×D₂₁₂	C₂³	1	16	yes	complemented
130	C₄×D₂₁₂	C₂³	1	16	yes	complemented
131	C₄×D₂₁₂	C₂³	1	16	yes	complemented
132	C₄×D₂₁₂	C₂³	1	16	yes	complemented
133	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
134	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
135	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
136	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
137	C₂×C₄⋊Dic₅₃	C₂³	1	8	yes	complemented
138	C₂×#11719919	C₂³	1	8	yes	—
139	C₄⋊C₄×D₅₃	C₂³	1	32	yes	complemented
140	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	—
141	C₂×#11719921	C₂³	1	4	yes	—
142	C₂×#11719921	C₂³	1	8	yes	—
143	C₂×#11719921	C₂³	1	4	yes	—
144	C₂×#11719921	C₂³	1	4	yes	—
145	C₂×#11719921	C₂³	1	4	yes	—
146	C₂×#11719921	C₂³	1	16	yes	complemented
147	C₂²⋊C₄×D₅₃	C₂³	1	64	yes	complemented
148	C₂×#41×C₅₃	—	2	16	no	—
149	C₂×#41×C₅₃	C₂³	1	16	yes	complemented
150	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
151	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
152	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
153	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
154	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
155	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
157	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
160	#127×C₅₃	C₂³	1	8	yes	complemented
161	#124×C₅₃	C₂³	1	16	yes	complemented
162	#121×C₅₃	C₂³	1	16	yes	complemented
163	#121×C₅₃	C₂³	1	16	yes	complemented
164	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
165	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
166	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
169	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
170	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
175	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
176	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
177	C₂³×D₅₃	—	2	32	no	—
178	C₂³×D₅₃	—	4	4	no	—
179	C₂³×D₅₃	—	4	4	no	—
180	C₂³×D₅₃	—	4	16	no	—
181	C₂³×D₅₃	—	4	16	no	—
182	C₂³×D₅₃	C₂×D₄	1	16	yes	complemented
183	C₂³×D₅₃	C₂⁴	1	4	yes	—
184	C₂³×D₅₃	C₂⁴	1	4	yes	—
185	C₂³×D₅₃	C₂⁴	1	32	yes	—
186	C₂³×D₅₃	C₂⁴	1	8	yes	—
187	#41×C₅₃	—	2	64	no	—
188	C₂×Q₈×C₅₃	—	2	8	no	—
189	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
190	C₂×D₄×C₅₃	—	2	16	no	—
191	C₂×D₄×C₅₃	—	2	8	no	—
192	C₂×D₄×C₅₃	—	2	8	no	—
193	C₂×D₄×C₅₃	—	4	4	no	—
194	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
195	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
196	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
197	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
198	C₂²×C₄×C₅₃	—	2	16	no	—
199	C₂²×C₄×C₅₃	—	2	4	no	—
200	C₂²×C₄×C₅₃	—	4	2	no	—
201	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	complemented
202	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
208	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
213	C₂×C₂²⋊D₅₃	—	2	16	no	—
214	C₂×C₂²⋊D₅₃	—	2	32	no	—
215	C₂×C₂²⋊D₅₃	—	4	16	no	—
216	C₂×C₂²⋊D₅₃	C₂⁴	1	32	yes	—
217	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
218	C₂×C₂²⋊D₅₃	C₂⁴	1	32	yes	—
219	C₂²×Dic₅₃	—	4	4	no	—
220	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
221	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
222	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
223	#11719949	—	2	128	no	—
224	D₄×D₅₃	—	2	256	no	—
225	D₄×D₅₃	—	2	128	no	—
226	D₄×D₅₃	—	4	64	no	—
227	#11719945	—	2	64	no	—
228	#11719945	—	2	128	no	—
229	C₂×D₂₁₂	—	2	32	no	—
230	C₂×D₂₁₂	—	2	8	no	—
231	C₂×D₂₁₂	—	2	8	no	—
232	C₂×D₂₁₂	—	2	128	no	—
233	C₂×D₂₁₂	—	4	4	no	—
234	C₂×D₂₁₂	C₂×D₄	1	16	yes	complemented
235	C₂×D₂₁₂	C₂×D₄	1	16	yes	complemented
236	C₂×D₂₁₂	C₂×D₄	1	64	yes	complemented
237	C₂×D₂₁₂	C₂⁴	1	8	yes	—
238	C₂×D₂₁₂	C₂⁴	1	32	yes	—
239	C₂×D₂₁₂	C₂⁴	1	8	yes	—
240	C₂×D₂₁₂	C₂⁴	1	8	yes	—
241	C₂×D₂₁₂	C₂⁴	1	8	yes	—
242	C₂×D₂₁₂	C₂⁴	1	8	yes	—
243	C₂×C₄×D₅₃	—	2	32	no	—
244	C₂×C₄×D₅₃	—	2	16	no	—
245	C₂×C₄×D₅₃	—	2	16	no	—
246	C₂×C₄×D₅₃	—	4	32	no	—
247	C₂×C₄×D₅₃	—	4	8	no	—
248	C₂×C₄×D₅₃	C₂⁴	1	32	yes	—
249	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
250	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
251	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
252	C₂×Dic₁₀₆	—	2	8	no	—
253	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
254	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
255	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
256	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
257	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
258	C₄²×C₅₃	C₂⁴	1	4	yes	—
259	C₄²×C₅₃	C₂⁴	1	4	yes	—
260	C₄²×C₅₃	C₂⁴	1	4	yes	—
261	C₄²×C₅₃	C₂⁴	1	4	yes	—
262	C₂²⋊Dic₅₃	C₂⁴	1	32	yes	—
263	#11719921	C₂⁴	1	16	yes	—
264	#11719921	C₂⁴	1	32	yes	—
265	#11719921	C₂⁴	1	16	yes	—
266	#11719921	C₂⁴	1	16	yes	—
267	#11719921	C₂⁴	1	16	yes	—
268	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
269	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
270	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
271	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
272	#11719919	C₂⁴	1	32	yes	—
273	C₂³×C₅₃	—	2	2	no	—
274	C₂³×C₅₃	—	2	2	no	—
275	C₂³×C₅₃	—	2	8	no	—
276	C₂³×C₅₃	—	2	8	no	—
277	C₂³×C₅₃	—	2	8	no	—
278	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
279	C₂³×C₅₃	C₂⁵	1	8	yes	—
280	C₂³×C₅₃	C₂⁵	1	2	yes	—
281	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
282	C₂²×D₅₃	—	2	8	no	—
283	C₂²×D₅₃	—	2	8	no	—
284	C₂²×D₅₃	—	2	8	no	—
285	C₂²×D₅₃	—	2	8	no	—
286	C₂²×D₅₃	—	2	8	no	—
287	C₂²×D₅₃	—	2	64	no	—
288	C₂²×D₅₃	—	4	8	no	—
289	C₂²×D₅₃	—	4	32	no	—
290	C₂²×D₅₃	—	4	8	no	—
291	C₂²×D₅₃	—	4	32	no	—
292	C₂²×D₅₃	—	4	32	no	—
293	C₂²×D₅₃	—	8	64	no	—
294	C₂²×D₅₃	C₂²×D₄	1	16	yes	—
295	C₂²×D₅₃	C₂²×D₄	1	32	yes	complemented
296	C₂²×D₅₃	C₂⁵	1	8	yes	—
297	C₂²×D₅₃	C₂⁵	1	8	yes	—
298	Q₈×C₅₃	—	2	16	no	—
299	D₄×C₅₃	—	2	32	no	—
300	D₄×C₅₃	—	2	16	no	—
301	D₄×C₅₃	—	2	16	no	—
302	D₄×C₅₃	—	4	8	no	—
303	C₂×C₄×C₅₃	—	2	8	no	—
304	C₂×C₄×C₅₃	—	2	2	no	—
305	C₂×C₄×C₅₃	—	2	2	no	—
306	C₂×C₄×C₅₃	—	2	2	no	—
307	C₂×C₄×C₅₃	—	2	32	no	—
308	C₂×C₄×C₅₃	—	2	8	no	—
309	C₂×C₄×C₅₃	—	4	4	no	—
310	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
311	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
312	C₂×C₄×C₅₃	C₂²×D₄	1	16	yes	complemented
313	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	complemented
314	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
315	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
316	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
317	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
318	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
319	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
320	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
321	C₂²⋊D₅₃	—	2	32	no	—
322	C₂²⋊D₅₃	—	2	64	no	—
323	C₂²⋊D₅₃	—	4	32	no	—
324	C₂×Dic₅₃	—	2	8	no	—
325	C₂×Dic₅₃	—	2	8	no	—
326	C₂×Dic₅₃	—	4	8	no	—
327	C₂×Dic₅₃	C₂⁵	1	8	yes	—
328	C₂×Dic₅₃	C₂⁵	1	8	yes	—
329	D₂₁₂	—	2	64	no	—
330	D₂₁₂	—	2	16	no	—
331	D₂₁₂	—	2	16	no	—
332	D₂₁₂	—	4	8	no	—
333	D₂₁₂	C₂²×D₄	1	32	yes	complemented
334	D₂₁₂	C₂²×D₄	1	32	yes	complemented
335	C₄×D₅₃	—	2	64	no	—
336	C₄×D₅₃	—	2	32	no	—
337	C₄×D₅₃	—	2	32	no	—
338	C₄×D₅₃	—	4	16	no	—
339	Dic₁₀₆	—	2	16	no	—
340	C₂×#3496	—	53	1	no	maximal, Sylow
341	C₂²×C₅₃	—	2	2	no	—
342	C₂²×C₅₃	—	2	2	no	—
343	C₂²×C₅₃	—	2	8	no	—
344	C₂²×C₅₃	—	2	8	no	—
345	C₂²×C₅₃	—	2	8	no	—
346	C₂²×C₅₃	—	2	8	no	—
347	C₂²×C₅₃	—	4	16	no	—
348	C₂²×C₅₃	C₂³×D₄	1	4	yes	—
349	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
350	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
351	C₂²×C₅₃	#585	1	2	yes	—
352	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
353	C₂×D₅₃	—	2	8	no	—
354	C₂×D₅₃	—	2	8	no	—
355	C₂×D₅₃	—	2	32	no	—
356	C₂×D₅₃	—	2	8	no	—
357	C₂×D₅₃	—	2	8	no	—
358	C₂×D₅₃	—	2	8	no	—
359	C₂×D₅₃	—	4	32	no	—
360	C₂×D₅₃	—	4	16	no	—
361	C₂×D₅₃	—	8	64	no	—
362	C₂×D₅₃	C₂³×D₄	1	16	yes	—
363	C₄×C₅₃	—	2	8	no	—
364	C₄×C₅₃	—	2	2	no	—
365	C₄×C₅₃	—	2	2	no	—
366	C₄×C₅₃	—	2	2	no	—
367	C₄×C₅₃	C₂³×D₄	1	4	yes	—
368	C₄×C₅₃	C₂³×D₄	1	4	yes	—
369	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
370	Dic₅₃	—	2	8	no	—
371	Dic₅₃	—	2	8	no	—
372	C₂²×H(5,𝔽₂)	—	53	2	no	—
373	#3496	—	53	32	no	—
374	C₂×#547	—	53	2	no	—
375	C₂×#547	—	53	2	no	—
376	C₂×#546	—	53	4	no	—
377	C₂×#546	—	53	4	no	—
378	C₂×D₄²	—	53	2	no	—
379	C₂×D₄²	—	53	2	no	—
380	C₂×#537	—	53	2	no	—
381	C₂×#534	—	53	4	no	—
382	C₂×#532	—	53	1	no	—
383	C₂×#532	D₅₃	1	1	yes	characteristic, complemented
384	C₂²×#121	—	53	4	no	—
385	C₂²×C₄×D₄	—	53	1	no	—
386	C₂×C₅₃	—	2	4	no	—
387	C₂×C₅₃	—	4	8	no	—
388	C₂×C₅₃	#3496	1	4	yes	complemented
389	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
390	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
391	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
392	D₅₃	—	2	16	no	—
393	D₅₃	—	4	8	no	—
394	C₂×H(5,𝔽₂)	—	53	32	no	—
395	C₂×H(5,𝔽₂)	—	106	32	no	—
396	C₂²×#41	—	53	4	no	—
397	C₂²×#41	—	53	2	no	—
398	C₂²×#41	—	53	4	no	—
399	C₂²×#41	C₂×D₅₃	1	2	yes	complemented
400	C₂³×D₄	—	53	8	no	—
401	C₂³×D₄	—	53	4	no	—
402	C₂³×D₄	—	53	4	no	—
403	C₂³×D₄	—	53	1	no	—
404	C₂³×D₄	—	53	4	no	—
405	C₂⁴×C₄	—	53	2	no	—
406	#547	—	53	32	no	—
407	#547	—	53	32	no	—
408	#546	—	53	64	no	—
409	#546	—	53	64	no	—
410	D₄²	—	53	32	no	—
411	D₄²	—	53	32	no	—
412	#537	—	53	32	no	—
413	#534	—	53	64	no	—
414	#532	—	53	16	no	—
415	#532	C₂×D₅₃	1	16	yes	complemented
416	C₂×C₄⋊Q₈	—	53	1	no	—
417	C₂×C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
418	C₂×#127	—	53	1	no	—
419	C₂×#127	C₂×D₅₃	1	1	yes	characteristic, complemented
420	C₂×#124	—	53	2	no	—
421	C₂×#124	C₂×D₅₃	1	2	yes	complemented
422	C₂×#123	—	53	8	no	—
423	C₂×#123	—	53	8	no	—
424	C₂×C₂²⋊Q₈	—	53	4	no	—
425	C₂×C₂²⋊Q₈	—	53	4	no	—
426	C₂×#121	—	53	4	no	—
427	C₂×#121	—	53	8	no	—
428	C₂×#121	—	53	4	no	—
429	C₂×#121	—	53	2	no	—
430	C₂×#121	—	53	2	no	—
431	C₂×#121	—	53	4	no	—
432	C₂×#121	—	53	64	no	—
433	C₂×#121	—	53	4	no	—
434	C₂×#121	—	53	8	no	—
435	C₂×#121	C₂×D₅₃	1	2	yes	complemented
436	C₂×#121	C₂×D₅₃	1	2	yes	complemented
437	C₂×#120	—	53	8	no	—
438	C₂×#120	—	53	8	no	—
439	C₂×C₄×D₄	—	53	2	no	—
440	C₂×C₄×D₄	—	53	2	no	—
441	C₂×C₄×D₄	—	53	2	no	—
442	C₂×C₄×D₄	—	53	2	no	—
443	C₂×C₄×D₄	—	53	2	no	—
444	C₂×C₄×D₄	—	53	2	no	—
445	C₂×C₄×D₄	—	53	16	no	—
446	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
447	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
448	C₂²×C₄⋊C₄	—	53	1	no	—
449	C₂²×C₄⋊C₄	—	53	4	no	—
450	C₂²×C₂²⋊C₄	—	53	2	no	—
451	C₂²×C₂²⋊C₄	—	53	8	no	—
452	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
453	C₅₃	C₂×#3496	1	1	yes	characteristic, complemented, Sylow
454	C₂⁵	—	53	2	no	—
455	C₂⁵	—	53	8	no	—
456	H(5,𝔽₂)	—	106	256	no	—
457	C₂×#41	—	2	16	no	—
458	C₂×#41	—	53	32	no	—
459	C₂×#41	—	53	16	no	—
460	C₂×#41	—	53	32	no	—
461	C₂×#41	—	106	32	no	—
462	C₂×#41	—	106	32	no	—
463	C₂×#41	—	106	16	no	—
464	C₂×#41	C₂²×D₅₃	1	16	yes	complemented
465	C₂²×Q₈	—	53	2	no	—
466	C₂²×Q₈	C₂²×D₅₃	1	2	yes	—
467	C₂²×D₄	—	53	8	no	—
468	C₂²×D₄	—	53	4	no	—
469	C₂²×D₄	—	53	8	no	—
470	C₂²×D₄	—	53	64	no	—
471	C₂²×D₄	—	53	32	no	—
472	C₂²×D₄	—	53	32	no	—
473	C₂²×D₄	—	53	16	no	—
474	C₂²×D₄	—	53	2	no	—
475	C₂²×D₄	—	53	2	no	—
476	C₂²×D₄	—	53	8	no	—
477	C₂²×D₄	—	53	2	no	—
478	C₂²×D₄	—	53	8	no	—
479	C₂²×D₄	—	53	2	no	—
480	C₂²×D₄	—	53	32	no	—
481	C₂²×D₄	—	53	2	no	—
482	C₂²×D₄	—	106	32	no	—
483	C₂²×D₄	—	106	32	no	—
484	C₂²×D₄	—	106	64	no	—
485	C₂²×D₄	—	212	16	no	—
486	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
487	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
488	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
489	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
490	C₂³×C₄	—	53	2	no	—
491	C₂³×C₄	—	53	8	no	—
492	C₂³×C₄	—	53	4	no	—
493	C₂³×C₄	—	53	4	no	—
494	C₂³×C₄	—	53	4	no	—
495	C₂³×C₄	—	53	16	no	—
496	C₂³×C₄	—	212	8	no	—
497	C₂³×C₄	C₂²×D₅₃	1	4	yes	—
498	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
499	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
500	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
501	C₄⋊Q₈	—	53	8	no	—
502	C₄⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
503	#127	—	53	8	no	—
504	#127	C₂²×D₅₃	1	8	yes	complemented
505	#124	—	53	16	no	—
506	#124	C₂²×D₅₃	1	16	yes	complemented
507	#123	—	53	64	no	—
508	#123	—	53	64	no	—
509	C₂²⋊Q₈	—	53	32	no	—
510	C₂²⋊Q₈	—	53	32	no	—
511	#121	—	53	64	no	—
512	#121	—	53	32	no	—
513	#121	—	53	32	no	—
514	#121	—	53	16	no	—
515	#121	—	53	16	no	—
516	#121	—	53	32	no	—
517	#121	—	53	32	no	—
518	#121	—	53	64	no	—
519	#121	C₂²×D₅₃	1	16	yes	complemented
520	#121	C₂²×D₅₃	1	16	yes	complemented
521	#120	—	53	64	no	—
522	#120	—	53	64	no	—
523	C₄×D₄	—	53	16	no	—
524	C₄×D₄	—	53	16	no	—
525	C₄×D₄	—	53	16	no	—
526	C₄×D₄	—	53	16	no	—
527	C₄×D₄	—	53	16	no	—
528	C₄×D₄	—	53	16	no	—
529	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
530	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
531	C₂×C₄⋊C₄	—	53	2	no	—
532	C₂×C₄⋊C₄	—	53	2	no	—
533	C₂×C₄⋊C₄	—	53	2	no	—
534	C₂×C₄⋊C₄	—	53	8	no	—
535	C₂×C₄⋊C₄	—	53	8	no	—
536	C₂×C₄⋊C₄	—	53	2	no	—
537	C₂×C₄⋊C₄	—	53	32	no	—
538	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
540	C₂×C₂²⋊C₄	—	53	8	no	—
541	C₂×C₂²⋊C₄	—	53	4	no	—
542	C₂×C₂²⋊C₄	—	53	4	no	—
543	C₂×C₂²⋊C₄	—	53	4	no	—
544	C₂×C₂²⋊C₄	—	53	16	no	—
545	C₂×C₂²⋊C₄	—	53	8	no	—
546	C₂×C₂²⋊C₄	—	53	4	no	—
547	C₂×C₂²⋊C₄	—	53	64	no	—
548	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
550	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
551	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
552	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
553	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
554	C₂×C₄²	C₂²×D₅₃	1	8	yes	complemented
555	C₂⁴	—	53	4	no	—
556	C₂⁴	—	53	16	no	—
557	C₂⁴	—	53	8	no	—
558	C₂⁴	—	53	4	no	—
559	C₂⁴	—	53	32	no	—
560	C₂⁴	—	106	32	no	—
561	C₂⁴	—	212	16	no	—
562	C₂⁴	—	212	16	no	—
563	C₂⁴	—	212	4	no	—
564	C₂⁴	—	212	4	no	—
565	C₂⁴	C₂³×D₅₃	1	4	yes	—
566	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
567	#41	—	2	64	no	—
568	#41	—	106	128	no	—
569	#41	—	106	128	no	—
570	#41	—	106	64	no	—
571	C₂×Q₈	—	2	8	no	—
572	C₂×Q₈	—	53	8	no	—
573	C₂×Q₈	—	106	8	no	—
574	C₂×Q₈	C₂³×D₅₃	1	8	yes	—
575	C₂×D₄	—	2	16	no	—
576	C₂×D₄	—	2	8	no	—
577	C₂×D₄	—	2	8	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂×D₄	—	53	32	no	—
580	C₂×D₄	—	53	16	no	—
581	C₂×D₄	—	53	32	no	—
582	C₂×D₄	—	53	16	no	—
583	C₂×D₄	—	53	16	no	—
584	C₂×D₄	—	53	64	no	—
585	C₂×D₄	—	53	8	no	—
586	C₂×D₄	—	53	8	no	—
587	C₂×D₄	—	53	8	no	—
588	C₂×D₄	—	53	32	no	—
589	C₂×D₄	—	53	8	no	—
590	C₂×D₄	—	53	8	no	—
591	C₂×D₄	—	106	128	no	—
592	C₂×D₄	—	106	32	no	—
593	C₂×D₄	—	106	128	no	—
594	C₂×D₄	—	106	256	no	—
595	C₂×D₄	—	106	32	no	—
596	C₂×D₄	—	106	16	no	—
597	C₂×D₄	—	106	8	no	—
598	C₂×D₄	—	106	8	no	—
599	C₂×D₄	—	212	4	no	—
600	C₂×D₄	—	212	64	no	—
601	C₂×D₄	—	212	16	no	—
602	C₂×D₄	C₂³×D₅₃	1	8	yes	—
603	C₂×D₄	C₂³×D₅₃	1	16	yes	—
604	C₂×D₄	C₂³×D₅₃	1	8	yes	—
605	C₂×D₄	C₂³×D₅₃	1	8	yes	—
606	C₂²×C₄	—	2	16	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	—	53	4	no	—
610	C₂²×C₄	—	53	4	no	—
611	C₂²×C₄	—	53	8	no	—
612	C₂²×C₄	—	53	32	no	—
613	C₂²×C₄	—	53	16	no	—
614	C₂²×C₄	—	53	16	no	—
615	C₂²×C₄	—	53	16	no	—
616	C₂²×C₄	—	106	32	no	—
617	C₂²×C₄	—	106	16	no	—
618	C₂²×C₄	—	106	16	no	—
619	C₂²×C₄	—	212	32	no	—
620	C₂²×C₄	—	212	8	no	—
621	C₂²×C₄	—	212	4	no	—
622	C₂²×C₄	D₄×D₅₃	1	8	yes	complemented
623	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
624	C₂²×C₄	C₂³×D₅₃	1	16	yes	—
625	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
626	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
627	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
628	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
629	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
630	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
631	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
632	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
633	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
634	C₄⋊C₄	—	53	8	no	—
635	C₄⋊C₄	—	53	8	no	—
636	C₄⋊C₄	—	53	8	no	—
637	C₄⋊C₄	—	53	32	no	—
638	C₄⋊C₄	—	53	8	no	—
639	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
640	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
641	C₂²⋊C₄	—	53	32	no	—
642	C₂²⋊C₄	—	53	16	no	—
643	C₂²⋊C₄	—	53	16	no	—
644	C₂²⋊C₄	—	53	16	no	—
645	C₂²⋊C₄	—	53	32	no	—
646	C₂²⋊C₄	—	53	16	no	—
647	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
648	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
649	C₄²	C₂³×D₅₃	1	4	yes	—
650	C₄²	C₂³×D₅₃	1	4	yes	—
651	C₄²	C₂³×D₅₃	1	4	yes	—
652	C₄²	C₂³×D₅₃	1	4	yes	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	8	no	—
656	C₂³	—	2	8	no	—
657	C₂³	—	2	8	no	—
658	C₂³	—	53	16	no	—
659	C₂³	—	53	8	no	—
660	C₂³	—	53	32	no	—
661	C₂³	—	53	8	no	—
662	C₂³	—	106	64	no	—
663	C₂³	—	106	8	no	—
664	C₂³	—	106	8	no	—
665	C₂³	—	106	8	no	—
666	C₂³	—	106	8	no	—
667	C₂³	—	106	8	no	—
668	C₂³	—	424	64	no	—
669	C₂³	—	212	32	no	—
670	C₂³	—	212	32	no	—
671	C₂³	—	212	8	no	—
672	C₂³	—	212	32	no	—
673	C₂³	—	212	8	no	—
674	C₂³	C₂×D₄×D₅₃	1	4	yes	—
675	C₂³	C₂⁴×D₅₃	1	8	yes	—
676	C₂³	C₂⁴×D₅₃	1	2	yes	—
677	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
678	Q₈	—	2	16	no	—
679	Q₈	—	106	16	no	—
680	D₄	—	2	32	no	—
681	D₄	—	2	16	no	—
682	D₄	—	2	16	no	—
683	D₄	—	4	8	no	—
684	D₄	—	53	32	no	—
685	D₄	—	53	32	no	—
686	D₄	—	106	64	no	—
687	D₄	—	106	64	no	—
688	D₄	—	106	32	no	—
689	D₄	—	106	16	no	—
690	D₄	—	106	16	no	—
691	D₄	—	212	8	no	—
692	D₄	—	212	32	no	—
693	C₂×C₄	—	2	8	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	32	no	—
698	C₂×C₄	—	2	8	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	53	8	no	—
701	C₂×C₄	—	53	8	no	—
702	C₂×C₄	—	106	64	no	—
703	C₂×C₄	—	106	8	no	—
704	C₂×C₄	—	106	8	no	—
705	C₂×C₄	—	106	32	no	—
706	C₂×C₄	—	106	32	no	—
707	C₂×C₄	—	212	16	no	—
708	C₂×C₄	—	212	8	no	—
709	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
710	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
711	C₂×C₄	C₂×D₄×D₅₃	1	16	yes	complemented
712	C₂×C₄	#13133263	1	4	yes	complemented
713	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
714	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
715	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
716	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
717	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
718	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
719	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
720	C₂²	—	2	8	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	8	no	—
724	C₂²	—	2	8	no	—
725	C₂²	—	2	8	no	—
726	C₂²	—	4	16	no	—
727	C₂²	—	53	16	no	—
728	C₂²	—	106	32	no	—
729	C₂²	—	106	8	no	—
730	C₂²	—	106	8	no	—
731	C₂²	—	106	8	no	—
732	C₂²	—	106	8	no	—
733	C₂²	—	106	8	no	—
734	C₂²	—	424	64	no	—
735	C₂²	—	212	32	no	—
736	C₂²	—	212	16	no	—
737	C₂²	C₂²×D₄×D₅₃	1	4	yes	—
738	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
739	C₂²	C₂×#13133263	1	2	yes	—
740	C₂²	#16811459	1	2	yes	—
741	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
742	C₄	—	2	8	no	—
743	C₄	—	2	2	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	106	8	no	—
747	C₄	—	106	8	no	—
748	C₄	C₂²×D₄×D₅₃	1	4	yes	—
749	C₄	C₂²×D₄×D₅₃	1	4	yes	—
750	C₄	C₂×#13133263	1	4	yes	complemented
751	C₂	—	2	4	no	—
752	C₂	—	4	8	no	—
753	C₂	—	106	16	no	—
754	C₂	—	212	8	no	—
755	C₂	#20288477	1	4	yes	direct product factor
756	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
757	C₂	C₂²×#13133263	1	1	yes	characteristic
758	C₂	C₂×#16811459	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#532	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#532	D₅₃
hypocenter	C₅₃	C₂×#3496
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂²×#13133263	C₂	semidirect
2. #20288477	C₂	direct (N × H)
3. C₂×#16811278	C₂	semidirect
4. C₂×#16811276	C₂	semidirect
5. C₂×#16811269	C₂	semidirect
6. C₂×#16811266	C₂	semidirect
7. C₂×D₄×D₂₁₂	C₂	semidirect
8. C₂×#16811258	C₂	semidirect
9. C₂×#16811201	C₂	semidirect
10. C₂×#16811181	C₂	semidirect
11. C₂×#16811173	C₂	semidirect
12. C₂×#121×D₅₃	C₂	semidirect
13. C₂²×C₄×D₂₁₂	C₂	semidirect
14. C₂×C₅₃×#532	C₂	semidirect
16. C₂×#13133263	C₂²	semidirect
17. C₂²×#11719949	C₂²	semidirect
18. C₂²×#11719945	C₂²	semidirect
19. C₂²×#11719945	C₂²	semidirect
21. C₂³×D₂₁₂	C₂²	semidirect
22. C₂²×D₄×D₅₃	C₂²	semidirect
23. C₂²×D₄×D₅₃	C₂²	semidirect
24. C₂²×D₄×D₅₃	C₂²	semidirect
25. C₂³×C₄×D₅₃	C₂²	semidirect
26. #16811278	C₂²	semidirect
27. #16811276	C₂²	semidirect
28. #16811269	C₂²	semidirect
29. #16811266	C₂²	semidirect
30. D₄×D₂₁₂	C₂²	semidirect
31. #16811258	C₂²	semidirect
32. #16811201	C₂²	semidirect
33. #16811181	C₂²	semidirect
34. #16811173	C₂²	semidirect
35. C₂×#13133217	C₂²	semidirect
36. C₂×#13133214	C₂²	semidirect
37. C₂×#13133205	C₂²	semidirect
38. C₂×#13133202	C₂²	semidirect
39. C₂×#13133199	C₂²	semidirect
40. C₂×#13133196	C₂²	semidirect
41. C₂×#13133193	C₂²	semidirect
42. C₂×#13133192	C₂²	semidirect
43. C₂×#13133191	C₂²	semidirect
44. C₂×#13133191	C₂²	semidirect
45. C₂×#13133191	C₂²	semidirect
46. C₂×#13133190	C₂²	semidirect
47. C₂×#13133189	C₂²	semidirect
48. C₂×#13133188	C₂²	semidirect
49. C₂×#13133188	C₂²	semidirect
50. #121×D₅₃	C₂²	semidirect
51. C₂×#13133187	C₂²	semidirect
52. C₂×#13133185	C₂²	semidirect
53. C₂×C₄×D₂₁₂	C₂²	semidirect
54. C₂×C₄×D₂₁₂	C₂²	semidirect
55. C₂×C₄×D₂₁₂	C₂²	semidirect
56. C₂×C₄×D₂₁₂	C₂²	semidirect
57. C₂×C₄×D₂₁₂	C₂²	semidirect
58. C₂×C₄×D₂₁₂	C₂²	semidirect
59. C₂×C₄×D₂₁₂	C₂²	semidirect
60. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
61. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
62. C₂²×#11719921	C₂²	semidirect
63. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
64. C₂²×#41×C₅₃	C₂²	semidirect
65. C₅₃×#532	C₂²	semidirect
66. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
67. C₂×#127×C₅₃	C₂²	semidirect
68. C₂×#124×C₅₃	C₂²	semidirect
69. C₂×#121×C₅₃	C₂²	semidirect
70. C₂×#121×C₅₃	C₂²	semidirect
71. C₂×C₄×D₄×C₅₃	C₂²	semidirect
72. C₂×C₄×D₄×C₅₃	C₂²	semidirect
73. C₂²×C₄²×C₅₃	C₂²	semidirect
78. C₂×#11719949	C₂³	semidirect
81. C₂×#11719945	C₂³	semidirect
82. C₂×#11719945	C₂³	semidirect
85. C₂²×D₂₁₂	D₄	semidirect
93. C₂²×D₂₁₂	C₂³	semidirect
100. C₂×D₄×D₅₃	C₂³	semidirect
101. C₂×D₄×D₅₃	C₂³	semidirect
102. C₂×D₄×D₅₃	C₂³	semidirect
109. C₂²×C₄×D₅₃	C₂³	semidirect
110. #13133217	C₂³	semidirect
111. #13133214	C₂³	semidirect
112. #13133205	C₂³	semidirect
113. #13133202	C₂³	semidirect
114. #13133199	C₂³	semidirect
115. #13133196	C₂³	semidirect
116. #13133193	C₂³	semidirect
117. #13133192	C₂³	semidirect
118. #13133191	C₂³	semidirect
119. #13133191	C₂³	semidirect
120. #13133191	C₂³	semidirect
121. #13133190	C₂³	semidirect
122. #13133189	C₂³	semidirect
123. #13133188	C₂³	semidirect
124. #13133188	C₂³	semidirect
125. #13133187	C₂³	semidirect
126. #13133185	C₂³	semidirect
127. C₄×D₂₁₂	C₂³	semidirect
128. C₄×D₂₁₂	C₂³	semidirect
129. C₄×D₂₁₂	C₂³	semidirect
130. C₄×D₂₁₂	C₂³	semidirect
131. C₄×D₂₁₂	C₂³	semidirect
132. C₄×D₂₁₂	C₂³	semidirect
137. C₂×C₄⋊Dic₅₃	C₂³	semidirect
139. C₄⋊C₄×D₅₃	C₂³	semidirect
146. C₂×#11719921	C₂³	semidirect
147. C₂²⋊C₄×D₅₃	C₂³	semidirect
149. C₂×#41×C₅₃	C₂³	semidirect
159. C₄⋊Q₈×C₅₃	C₂³	semidirect
160. #127×C₅₃	C₂³	semidirect
161. #124×C₅₃	C₂³	semidirect
162. #121×C₅₃	C₂³	semidirect
163. #121×C₅₃	C₂³	semidirect
164. C₄×D₄×C₅₃	C₂³	semidirect
165. C₄×D₄×C₅₃	C₂³	semidirect
174. C₂×C₄²×C₅₃	C₂³	semidirect
182. C₂³×D₅₃	C₂×D₄	semidirect
201. C₂²×C₄×C₅₃	C₂×D₄	semidirect
234. C₂×D₂₁₂	C₂×D₄	semidirect
235. C₂×D₂₁₂	C₂×D₄	semidirect
236. C₂×D₂₁₂	C₂×D₄	semidirect
295. C₂²×D₅₃	C₂²×D₄	semidirect
312. C₂×C₄×C₅₃	C₂²×D₄	semidirect
313. C₂×C₄×C₅₃	H(5,𝔽₂)	semidirect
333. D₂₁₂	C₂²×D₄	semidirect
334. D₂₁₂	C₂²×D₄	semidirect
369. C₄×C₅₃	C₂×H(5,𝔽₂)	semidirect
383. C₂×#532	D₅₃	semidirect
388. C₂×C₅₃	#3496	semidirect
399. C₂²×#41	C₂×D₅₃	semidirect
415. #532	C₂×D₅₃	semidirect
417. C₂×C₄⋊Q₈	C₂×D₅₃	semidirect
419. C₂×#127	C₂×D₅₃	semidirect
421. C₂×#124	C₂×D₅₃	semidirect
435. C₂×#121	C₂×D₅₃	semidirect
436. C₂×#121	C₂×D₅₃	semidirect
446. C₂×C₄×D₄	C₂×D₅₃	semidirect
447. C₂×C₄×D₄	C₂×D₅₃	semidirect
452. C₂²×C₄²	C₂×D₅₃	semidirect
453. C₅₃	C₂×#3496	semidirect
464. C₂×#41	C₂²×D₅₃	semidirect
502. C₄⋊Q₈	C₂²×D₅₃	semidirect
504. #127	C₂²×D₅₃	semidirect
506. #124	C₂²×D₅₃	semidirect
519. #121	C₂²×D₅₃	semidirect
520. #121	C₂²×D₅₃	semidirect
529. C₄×D₄	C₂²×D₅₃	semidirect
530. C₄×D₄	C₂²×D₅₃	semidirect
554. C₂×C₄²	C₂²×D₅₃	semidirect
622. C₂²×C₄	D₄×D₅₃	semidirect
711. C₂×C₄	C₂×D₄×D₅₃	semidirect
712. C₂×C₄	#13133263	semidirect
750. C₄	C₂×#13133263	semidirect
755. C₂	#20288477	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
#20288477	2
C₂×#16811278	2
C₂×#16811276	2
C₂×#16811269	2
C₂×#16811266	2
C₂×D₄×D₂₁₂	2
C₂×#16811258	2
C₂×#16811201	2
C₂×#16811181	2
C₂×#16811173	2
C₂×#121×D₅₃	2
C₂²×C₄×D₂₁₂	2
C₂×C₅₃×#532	2
C₂×#3496	53

Subgroups — C2×#20288477 #28291981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20288477 #28291981