Subgroups — C₂×D₄²×D₅₃ #28290998

Order 13568.

20038 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×D₅₃	C₂	1	4	yes	maximal, complemented
2	C₂×D₄×D₂₁₂	C₂	1	2	yes	maximal, complemented
3	C₂×#16811258	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16811257	C₂	1	4	yes	maximal, complemented
5	C₂×D₄×C₂²⋊D₅₃	C₂	1	4	yes	maximal, complemented
6	C₂×#16811255	C₂	1	4	yes	maximal, complemented
7	D₄²×D₅₃	C₂	1	32	yes	maximal, direct product factor
8	C₂×#127×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#121×D₅₃	C₂	1	4	yes	maximal, complemented
10	C₂×#120×D₅₃	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
12	C₂×D₄²×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁵×D₅₃	C₂²	1	4	yes	complemented
14	C₂³×D₂₁₂	C₂²	1	4	yes	complemented
15	C₂³×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
16	C₂²×D₄×D₅₃	—	2	64	no	—
17	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
18	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
19	C₂²×D₄×D₅₃	C₂²	1	8	yes	complemented
20	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
21	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
22	C₂²×D₄×D₅₃	C₂²	1	64	yes	complemented
23	C₂²×D₄×D₅₃	C₂²	1	8	yes	complemented
24	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
25	C₂³×C₄×D₅₃	C₂²	1	4	yes	complemented
26	D₄×D₂₁₂	C₂²	1	32	yes	complemented
27	#16811258	C₂²	1	16	yes	complemented
28	#16811257	C₂²	1	64	yes	complemented
29	D₄×C₂²⋊D₅₃	C₂²	1	64	yes	complemented
30	#16811255	C₂²	1	64	yes	complemented
31	C₂×#13133214	C₂²	1	1	yes	characteristic, complemented
32	C₂×#13133213	C₂²	1	2	yes	complemented
33	C₂×#13133213	C₂²	1	4	yes	complemented
34	#127×D₅₃	C₂²	1	16	yes	complemented
35	C₂×#13133192	C₂²	1	4	yes	complemented
36	C₂×#13133191	C₂²	1	4	yes	complemented
37	C₂×#13133190	C₂²	1	8	yes	complemented
38	C₂×#13133189	C₂²	1	8	yes	complemented
39	C₂×#13133188	C₂²	1	4	yes	complemented
40	#121×D₅₃	C₂²	1	64	yes	complemented
41	C₂×#13133187	C₂²	1	8	yes	complemented
42	C₂×#13133187	C₂²	1	4	yes	complemented
43	C₂×#13133186	C₂²	1	4	yes	complemented
44	C₂×#13133185	C₂²	1	4	yes	complemented
45	C₂×#13133185	C₂²	1	8	yes	complemented
46	#120×D₅₃	C₂²	1	64	yes	complemented
47	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
48	C₂×D₄×Dic₅₃	C₂²	1	2	yes	complemented
49	C₂×#13133179	C₂²	1	2	yes	complemented
50	C₂×C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
51	C₂×#13133177	C₂²	1	4	yes	complemented
52	C₄×D₄×D₅₃	C₂²	1	32	yes	complemented
53	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
54	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
55	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
56	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂³×D₄×C₅₃	C₂²	1	4	yes	complemented
58	D₄²×C₅₃	C₂²	1	16	yes	complemented
59	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×#121×C₅₃	C₂²	1	4	yes	complemented
61	C₂×#120×C₅₃	C₂²	1	4	yes	complemented
62	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
63	C₂⁴×D₅₃	—	2	64	no	—
64	C₂⁴×D₅₃	—	4	16	no	—
65	C₂⁴×D₅₃	C₂³	1	4	yes	—
66	C₂⁴×D₅₃	C₂³	1	4	yes	—
67	C₂⁴×D₅₃	C₂³	1	32	yes	complemented
68	C₂⁴×D₅₃	C₂³	1	4	yes	complemented
69	C₂⁴×D₅₃	C₂³	1	8	yes	complemented
70	C₂²×D₂₁₂	—	2	32	no	—
71	C₂²×D₂₁₂	C₂³	1	2	yes	—
72	C₂²×D₂₁₂	C₂³	1	32	yes	complemented
73	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
74	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
75	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
76	C₂²×C₂²⋊D₅₃	—	2	64	no	—
77	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
78	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
79	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
80	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
81	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
82	C₂²×C₂²⋊D₅₃	C₂³	1	64	yes	complemented
83	C₂×D₄×D₅₃	—	2	64	no	—
84	C₂×D₄×D₅₃	—	2	32	no	—
85	C₂×D₄×D₅₃	—	2	64	no	—
86	C₂×D₄×D₅₃	—	2	512	no	—
87	C₂×D₄×D₅₃	—	2	32	no	—
88	C₂×D₄×D₅₃	—	2	32	no	—
89	C₂×D₄×D₅₃	—	4	8	no	—
90	C₂×D₄×D₅₃	D₄	1	32	yes	direct product factor
91	C₂×D₄×D₅₃	C₂³	1	16	yes	—
92	C₂×D₄×D₅₃	C₂³	1	64	yes	complemented
93	C₂×D₄×D₅₃	C₂³	1	32	yes	complemented
94	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
95	C₂×D₄×D₅₃	C₂³	1	32	yes	complemented
96	C₂×D₄×D₅₃	C₂³	1	64	yes	complemented
97	C₂×D₄×D₅₃	C₂³	1	32	yes	complemented
98	C₂³×Dic₅₃	C₂³	1	4	yes	complemented
99	C₂²×C₄×D₅₃	—	2	32	no	—
100	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
101	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
102	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
103	C₂²×C₄×D₅₃	C₂³	1	32	yes	complemented
104	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
105	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
106	#13133214	C₂³	1	8	yes	complemented
107	#13133213	C₂³	1	16	yes	complemented
108	#13133213	C₂³	1	32	yes	complemented
109	#13133192	C₂³	1	32	yes	complemented
110	#13133191	C₂³	1	32	yes	complemented
111	#13133190	C₂³	1	64	yes	complemented
112	#13133189	C₂³	1	64	yes	complemented
113	#13133188	C₂³	1	32	yes	complemented
114	#13133187	C₂³	1	64	yes	complemented
115	#13133187	C₂³	1	32	yes	complemented
116	#13133186	C₂³	1	32	yes	complemented
117	#13133185	C₂³	1	32	yes	complemented
118	#13133185	C₂³	1	64	yes	complemented
119	C₄×D₂₁₂	C₂³	1	16	yes	complemented
120	D₄×Dic₅₃	C₂³	1	16	yes	complemented
121	#13133179	C₂³	1	16	yes	complemented
122	C₄×C₂²⋊D₅₃	C₂³	1	32	yes	complemented
123	#13133177	C₂³	1	32	yes	complemented
124	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
125	C₂×#11719919	C₂³	1	4	yes	complemented
126	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
127	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
128	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
129	C₂×#11719921	C₂³	1	4	yes	complemented
130	C₂×#11719921	C₂³	1	4	yes	complemented
131	C₂×#11719921	C₂³	1	8	yes	complemented
132	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	complemented
133	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	complemented
134	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
135	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
136	C₄²×D₅₃	C₂³	1	8	yes	complemented
137	C₂⁵×C₅₃	C₂³	1	4	yes	complemented
138	C₂²×D₄×C₅₃	—	2	32	no	—
139	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
140	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
141	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
142	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
143	C₂²×D₄×C₅₃	C₂³	1	32	yes	complemented
144	C₂³×C₄×C₅₃	C₂³	1	4	yes	complemented
145	#127×C₅₃	C₂³	1	8	yes	complemented
146	#121×C₅₃	C₂³	1	32	yes	complemented
147	#120×C₅₃	C₂³	1	32	yes	complemented
148	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
149	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
150	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
151	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
152	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic, complemented
153	C₂⁴×C₅₃	—	2	32	no	—
154	C₂⁴×C₅₃	—	4	8	no	—
155	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
156	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
157	C₂⁴×C₅₃	C₂⁴	1	16	yes	complemented
158	C₂³×D₅₃	—	2	16	no	—
159	C₂³×D₅₃	—	2	16	no	—
160	C₂³×D₅₃	—	2	32	no	—
161	C₂³×D₅₃	—	2	32	no	—
162	C₂³×D₅₃	—	2	32	no	—
163	C₂³×D₅₃	—	2	256	no	—
164	C₂³×D₅₃	—	2	32	no	—
165	C₂³×D₅₃	—	2	16	no	—
166	C₂³×D₅₃	—	4	64	no	—
167	C₂³×D₅₃	—	4	8	no	—
168	C₂³×D₅₃	—	4	16	no	—
169	C₂³×D₅₃	—	4	256	no	—
170	C₂³×D₅₃	C₂×D₄	1	32	yes	complemented
171	C₂³×D₅₃	C₂⁴	1	16	yes	—
172	C₂³×D₅₃	C₂⁴	1	4	yes	—
173	C₂³×D₅₃	C₂⁴	1	16	yes	—
174	C₂³×D₅₃	C₂⁴	1	4	yes	—
175	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
176	C₂³×D₅₃	C₂⁴	1	16	yes	complemented
177	C₂³×D₅₃	C₂⁴	1	32	yes	complemented
178	C₂×D₄×C₅₃	—	2	32	no	—
179	C₂×D₄×C₅₃	—	2	128	no	—
180	C₂×D₄×C₅₃	—	2	16	no	—
181	C₂×D₄×C₅₃	—	4	4	no	—
182	C₂×D₄×C₅₃	C₂×D₄	1	16	yes	complemented
183	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
184	C₂×D₄×C₅₃	C₂⁴	1	32	yes	complemented
185	C₂×D₄×C₅₃	C₂⁴	1	16	yes	complemented
186	C₂×D₄×C₅₃	C₂⁴	1	8	yes	complemented
187	C₂²×C₄×C₅₃	—	2	16	no	—
188	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	complemented
192	C₂×C₂²⋊D₅₃	—	2	32	no	—
193	C₂×C₂²⋊D₅₃	—	2	32	no	—
194	C₂×C₂²⋊D₅₃	—	2	256	no	—
195	C₂×C₂²⋊D₅₃	—	2	32	no	—
196	C₂×C₂²⋊D₅₃	—	4	8	no	—
197	C₂×C₂²⋊D₅₃	C₂×D₄	1	32	yes	complemented
198	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
199	C₂×C₂²⋊D₅₃	C₂⁴	1	32	yes	complemented
200	C₂×C₂²⋊D₅₃	C₂⁴	1	32	yes	complemented
201	C₂×C₂²⋊D₅₃	C₂⁴	1	32	yes	complemented
202	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	complemented
203	C₂²×Dic₅₃	—	2	16	no	—
204	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
205	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
206	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
207	C₂²×Dic₅₃	C₂⁴	1	16	yes	complemented
208	D₄×D₅₃	—	2	256	no	—
209	D₄×D₅₃	—	2	128	no	—
210	D₄×D₅₃	—	2	256	no	—
211	D₄×D₅₃	—	2	128	no	—
212	D₄×D₅₃	—	2	128	no	—
213	D₄×D₅₃	—	4	32	no	—
214	D₄×D₅₃	C₂×D₄	1	128	yes	direct product factor
215	C₂×D₂₁₂	—	2	32	no	—
216	C₂×D₂₁₂	—	2	16	no	—
217	C₂×D₂₁₂	—	2	128	no	—
218	C₂×D₂₁₂	—	4	4	no	—
219	C₂×D₂₁₂	C₂×D₄	1	16	yes	complemented
220	C₂×D₂₁₂	C₂⁴	1	8	yes	—
221	C₂×D₂₁₂	C₂⁴	1	32	yes	complemented
222	C₂×D₂₁₂	C₂⁴	1	16	yes	complemented
223	C₂×D₂₁₂	C₂⁴	1	8	yes	complemented
224	C₂×C₄×D₅₃	—	2	16	no	—
225	C₂×C₄×D₅₃	—	2	4	no	—
226	C₂×C₄×D₅₃	—	2	16	no	—
227	C₂×C₄×D₅₃	—	2	16	no	—
228	C₂×C₄×D₅₃	—	2	128	no	—
229	C₂×C₄×D₅₃	C₂×D₄	1	16	yes	complemented
230	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
231	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
232	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
233	C₂×C₄×D₅₃	C₂⁴	1	16	yes	complemented
234	C₂×C₄×D₅₃	C₂⁴	1	16	yes	complemented
235	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
236	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
237	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
238	C₄²×C₅₃	C₂⁴	1	4	yes	complemented
239	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
240	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
241	#11719921	C₂⁴	1	16	yes	complemented
242	#11719921	C₂⁴	1	16	yes	complemented
243	#11719921	C₂⁴	1	32	yes	complemented
244	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
245	#11719919	C₂⁴	1	16	yes	complemented
246	C₄×Dic₅₃	C₂⁴	1	4	yes	complemented
247	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
248	C₂³×C₅₃	—	2	8	no	—
249	C₂³×C₅₃	—	2	8	no	—
250	C₂³×C₅₃	—	2	16	no	—
251	C₂³×C₅₃	—	2	64	no	—
252	C₂³×C₅₃	—	2	8	no	—
253	C₂³×C₅₃	—	4	16	no	—
254	C₂³×C₅₃	—	4	64	no	—
255	C₂³×C₅₃	C₂²×D₄	1	16	yes	complemented
256	C₂³×C₅₃	C₂⁵	1	8	yes	—
257	C₂³×C₅₃	C₂⁵	1	8	yes	—
258	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
259	C₂²×D₅₃	—	2	8	no	—
260	C₂²×D₅₃	—	2	8	no	—
261	C₂²×D₅₃	—	2	128	no	—
262	C₂²×D₅₃	—	2	32	no	—
263	C₂²×D₅₃	—	2	32	no	—
264	C₂²×D₅₃	—	2	16	no	—
265	C₂²×D₅₃	—	2	64	no	—
266	C₂²×D₅₃	—	2	8	no	—
267	C₂²×D₅₃	—	2	64	no	—
268	C₂²×D₅₃	—	2	64	no	—
269	C₂²×D₅₃	—	2	64	no	—
270	C₂²×D₅₃	—	2	32	no	—
271	C₂²×D₅₃	—	4	16	no	—
272	C₂²×D₅₃	—	4	32	no	—
273	C₂²×D₅₃	—	4	64	no	—
274	C₂²×D₅₃	—	4	512	no	—
275	C₂²×D₅₃	—	4	128	no	—
276	C₂²×D₅₃	—	4	64	no	—
277	C₂²×D₅₃	C₂²×D₄	1	8	yes	—
278	C₂²×D₅₃	C₂²×D₄	1	64	yes	complemented
279	C₂²×D₅₃	C₂²×D₄	1	16	yes	complemented
280	C₂²×D₅₃	H(5,𝔽₂)	1	4	yes	—
281	C₂²×D₅₃	C₂⁵	1	8	yes	—
282	C₂²×D₅₃	C₂⁵	1	8	yes	—
283	C₂²×D₅₃	C₂⁵	1	2	yes	—
284	D₄×C₅₃	—	2	64	no	—
285	D₄×C₅₃	—	2	32	no	—
286	D₄×C₅₃	—	4	8	no	—
287	D₄×C₅₃	C₂²×D₄	1	32	yes	complemented
288	C₂×C₄×C₅₃	—	2	8	no	—
289	C₂×C₄×C₅₃	—	2	2	no	—
290	C₂×C₄×C₅₃	—	2	32	no	—
291	C₂×C₄×C₅₃	C₂²×D₄	1	8	yes	complemented
292	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
293	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
294	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
295	C₂²⋊D₅₃	—	2	64	no	—
296	C₂²⋊D₅₃	—	2	64	no	—
297	C₂²⋊D₅₃	—	2	64	no	—
298	C₂²⋊D₅₃	—	4	16	no	—
299	C₂²⋊D₅₃	C₂²×D₄	1	64	yes	complemented
300	C₂×Dic₅₃	—	2	8	no	—
301	C₂×Dic₅₃	—	2	2	no	—
302	C₂×Dic₅₃	—	2	32	no	—
303	C₂×Dic₅₃	C₂²×D₄	1	8	yes	complemented
304	C₂×Dic₅₃	C₂⁵	1	8	yes	—
305	C₂×Dic₅₃	C₂⁵	1	2	yes	—
306	C₂×Dic₅₃	C₂⁵	1	4	yes	—
307	D₂₁₂	—	2	64	no	—
308	D₂₁₂	—	2	32	no	—
309	D₂₁₂	—	4	8	no	—
310	D₂₁₂	C₂²×D₄	1	32	yes	complemented
311	C₄×D₅₃	—	2	32	no	—
312	C₄×D₅₃	—	2	8	no	—
313	C₄×D₅₃	—	2	32	no	—
314	C₄×D₅₃	—	2	32	no	—
315	C₄×D₅₃	C₂²×D₄	1	32	yes	complemented
316	C₂²×D₄²	—	53	1	no	maximal, Sylow
317	C₂²×C₅₃	—	2	8	no	—
318	C₂²×C₅₃	—	2	8	no	—
319	C₂²×C₅₃	—	2	32	no	—
320	C₂²×C₅₃	—	2	16	no	—
321	C₂²×C₅₃	—	2	8	no	—
322	C₂²×C₅₃	—	4	64	no	—
323	C₂²×C₅₃	—	4	16	no	—
324	C₂²×C₅₃	C₂³×D₄	1	4	yes	—
325	C₂²×C₅₃	C₂³×D₄	1	16	yes	complemented
326	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
327	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
328	C₂×D₅₃	—	2	8	no	—
329	C₂×D₅₃	—	2	8	no	—
330	C₂×D₅₃	—	2	32	no	—
331	C₂×D₅₃	—	2	128	no	—
332	C₂×D₅₃	—	2	16	no	—
333	C₂×D₅₃	—	2	8	no	—
334	C₂×D₅₃	—	4	64	no	—
335	C₂×D₅₃	—	4	128	no	—
336	C₂×D₅₃	—	4	16	no	—
337	C₂×D₅₃	—	4	64	no	—
338	C₂×D₅₃	D₄²	1	16	yes	direct product factor
339	C₂×D₅₃	C₂³×D₄	1	8	yes	—
340	C₂×D₅₃	C₂³×D₄	1	16	yes	complemented
341	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
342	C₄×C₅₃	—	2	8	no	—
343	C₄×C₅₃	—	2	2	no	—
344	C₄×C₅₃	C₂³×D₄	1	8	yes	complemented
345	Dic₅₃	—	2	8	no	—
346	Dic₅₃	—	2	2	no	—
347	Dic₅₃	C₂³×D₄	1	8	yes	complemented
348	C₂⁴×D₄	—	53	4	no	—
349	C₂×D₄²	—	53	4	no	—
350	C₂×D₄²	—	53	32	no	—
351	C₂×D₄²	—	53	1	no	—
352	C₂×D₄²	—	53	4	no	—
353	C₂×D₄²	—	53	4	no	—
354	C₂×D₄²	—	53	2	no	—
355	C₂×D₄²	D₅₃	1	1	yes	characteristic, direct product factor
356	C₂²×#127	—	53	1	no	—
357	C₂²×#121	—	53	4	no	—
358	C₂²×#120	—	53	4	no	—
359	C₂²×C₄×D₄	—	53	2	no	—
360	C₂×C₅₃	—	2	16	no	—
361	C₂×C₅₃	—	4	8	no	—
362	C₂×C₅₃	C₂×D₄²	1	4	yes	complemented
363	C₂×C₅₃	C₂⁴×D₄	1	2	yes	—
364	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
365	D₅₃	—	2	16	no	—
366	D₅₃	—	4	8	no	—
367	D₅₃	C₂×D₄²	1	8	yes	direct product factor
368	C₂⁶	—	53	4	no	—
369	C₂³×D₄	—	53	2	no	—
370	C₂³×D₄	—	53	8	no	—
371	C₂³×D₄	—	53	4	no	—
372	C₂³×D₄	—	53	8	no	—
373	C₂³×D₄	—	53	4	no	—
374	C₂³×D₄	—	53	8	no	—
375	C₂³×D₄	—	53	4	no	—
376	C₂³×D₄	—	53	64	no	—
377	C₂³×D₄	—	53	2	no	—
378	C₂³×D₄	—	53	4	no	—
379	C₂³×D₄	—	106	64	no	—
380	C₂³×D₄	C₂×D₅₃	1	4	yes	complemented
381	C₂⁴×C₄	—	53	4	no	—
382	D₄²	—	53	64	no	—
383	D₄²	—	53	16	no	—
384	D₄²	—	53	64	no	—
385	D₄²	—	53	64	no	—
386	D₄²	—	53	32	no	—
387	D₄²	C₂×D₅₃	1	16	yes	direct product factor
388	C₂×#127	—	53	2	no	—
389	C₂×#127	—	53	4	no	—
390	C₂×#127	—	53	16	no	—
391	C₂×#127	—	53	1	no	—
392	C₂×#127	C₂×D₅₃	1	1	yes	characteristic, complemented
393	C₂×#121	—	53	4	no	—
394	C₂×#121	—	53	8	no	—
395	C₂×#121	—	53	4	no	—
396	C₂×#121	—	53	64	no	—
397	C₂×#121	—	53	4	no	—
398	C₂×#121	—	53	8	no	—
399	C₂×#121	C₂×D₅₃	1	4	yes	complemented
400	C₂×#120	—	53	4	no	—
401	C₂×#120	—	53	8	no	—
402	C₂×#120	—	53	4	no	—
403	C₂×#120	—	53	64	no	—
404	C₂×#120	—	53	4	no	—
405	C₂×#120	—	53	8	no	—
406	C₂×#120	C₂×D₅₃	1	4	yes	complemented
407	C₂×C₄×D₄	—	53	2	no	—
408	C₂×C₄×D₄	—	53	4	no	—
409	C₂×C₄×D₄	—	53	32	no	—
410	C₂×C₄×D₄	—	53	2	no	—
411	C₂×C₄×D₄	—	53	4	no	—
412	C₂×C₄×D₄	—	53	2	no	—
413	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
414	C₂²×C₄⋊C₄	—	53	2	no	—
415	C₂²×C₂²⋊C₄	—	53	4	no	—
416	C₂²×C₂²⋊C₄	—	53	4	no	—
417	C₂²×C₄²	—	53	1	no	—
418	C₅₃	C₂²×D₄²	1	1	yes	characteristic, complemented, Sylow
419	C₂⁵	—	53	4	no	—
420	C₂⁵	—	53	4	no	—
421	C₂⁵	—	53	4	no	—
422	C₂⁵	—	53	8	no	—
423	C₂⁵	—	53	32	no	—
424	C₂⁵	—	106	64	no	—
425	C₂⁵	—	212	16	no	—
426	C₂⁵	C₂²×D₅₃	1	4	yes	complemented
427	C₂²×D₄	—	2	32	no	—
428	C₂²×D₄	—	53	4	no	—
429	C₂²×D₄	—	53	32	no	—
430	C₂²×D₄	—	53	16	no	—
431	C₂²×D₄	—	53	8	no	—
432	C₂²×D₄	—	53	8	no	—
433	C₂²×D₄	—	53	8	no	—
434	C₂²×D₄	—	53	64	no	—
435	C₂²×D₄	—	53	4	no	—
436	C₂²×D₄	—	53	32	no	—
437	C₂²×D₄	—	53	64	no	—
438	C₂²×D₄	—	53	32	no	—
439	C₂²×D₄	—	53	64	no	—
440	C₂²×D₄	—	53	32	no	—
441	C₂²×D₄	—	53	16	no	—
442	C₂²×D₄	—	53	2	no	—
443	C₂²×D₄	—	53	8	no	—
444	C₂²×D₄	—	53	4	no	—
445	C₂²×D₄	—	53	2	no	—
446	C₂²×D₄	—	53	32	no	—
447	C₂²×D₄	—	106	32	no	—
448	C₂²×D₄	—	106	32	no	—
449	C₂²×D₄	—	106	64	no	—
450	C₂²×D₄	—	106	512	no	—
451	C₂²×D₄	—	106	32	no	—
452	C₂²×D₄	—	106	64	no	—
453	C₂²×D₄	—	106	64	no	—
454	C₂²×D₄	—	106	32	no	—
455	C₂²×D₄	—	212	8	no	—
456	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
457	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
458	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
459	C₂²×D₄	C₂²×D₅₃	1	2	yes	complemented
460	C₂²×D₄	C₂²×D₅₃	1	32	yes	complemented
461	C₂³×C₄	—	53	2	no	—
462	C₂³×C₄	—	53	4	no	—
463	C₂³×C₄	—	53	1	no	—
464	C₂³×C₄	—	53	4	no	—
465	C₂³×C₄	—	53	4	no	—
466	C₂³×C₄	—	53	4	no	—
467	C₂³×C₄	—	53	32	no	—
468	C₂³×C₄	—	106	32	no	—
469	C₂³×C₄	C₂²×D₅₃	1	4	yes	complemented
470	#127	—	53	16	no	—
471	#127	—	53	32	no	—
472	#127	—	53	8	no	—
473	#127	C₂²×D₅₃	1	8	yes	complemented
474	#121	—	53	32	no	—
475	#121	—	53	64	no	—
476	#121	—	53	32	no	—
477	#121	—	53	32	no	—
478	#121	—	53	64	no	—
479	#121	C₂²×D₅₃	1	32	yes	complemented
480	#120	—	53	32	no	—
481	#120	—	53	64	no	—
482	#120	—	53	32	no	—
483	#120	—	53	32	no	—
484	#120	—	53	64	no	—
485	#120	C₂²×D₅₃	1	32	yes	complemented
486	C₄×D₄	—	53	16	no	—
487	C₄×D₄	—	53	32	no	—
488	C₄×D₄	—	53	16	no	—
489	C₄×D₄	—	53	32	no	—
490	C₄×D₄	—	53	16	no	—
491	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
492	C₂×C₄⋊C₄	—	53	4	no	—
493	C₂×C₄⋊C₄	—	53	2	no	—
494	C₂×C₄⋊C₄	—	53	16	no	—
495	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
496	C₂×C₂²⋊C₄	—	53	4	no	—
497	C₂×C₂²⋊C₄	—	53	4	no	—
498	C₂×C₂²⋊C₄	—	53	4	no	—
499	C₂×C₂²⋊C₄	—	53	4	no	—
500	C₂×C₂²⋊C₄	—	53	8	no	—
501	C₂×C₂²⋊C₄	—	53	32	no	—
502	C₂×C₂²⋊C₄	—	53	32	no	—
503	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
504	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
505	C₂×C₄²	—	53	1	no	—
506	C₂×C₄²	—	53	2	no	—
507	C₂×C₄²	—	53	8	no	—
508	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic, complemented
509	C₂⁴	—	2	32	no	—
510	C₂⁴	—	4	8	no	—
511	C₂⁴	—	53	1	no	—
512	C₂⁴	—	53	32	no	—
513	C₂⁴	—	53	16	no	—
514	C₂⁴	—	53	4	no	—
515	C₂⁴	—	53	16	no	—
516	C₂⁴	—	53	4	no	—
517	C₂⁴	—	53	16	no	—
518	C₂⁴	—	53	32	no	—
519	C₂⁴	—	106	16	no	—
520	C₂⁴	—	106	16	no	—
521	C₂⁴	—	106	32	no	—
522	C₂⁴	—	106	32	no	—
523	C₂⁴	—	106	32	no	—
524	C₂⁴	—	106	256	no	—
525	C₂⁴	—	106	16	no	—
526	C₂⁴	—	106	32	no	—
527	C₂⁴	—	212	16	no	—
528	C₂⁴	—	212	8	no	—
529	C₂⁴	—	212	64	no	—
530	C₂⁴	—	212	256	no	—
531	C₂⁴	C₂³×D₅₃	1	4	yes	—
532	C₂⁴	C₂³×D₅₃	1	4	yes	—
533	C₂⁴	C₂³×D₅₃	1	16	yes	complemented
534	C₂×D₄	—	2	32	no	—
535	C₂×D₄	—	2	128	no	—
536	C₂×D₄	—	2	16	no	—
537	C₂×D₄	—	4	4	no	—
538	C₂×D₄	—	53	32	no	—
539	C₂×D₄	—	53	16	no	—
540	C₂×D₄	—	53	128	no	—
541	C₂×D₄	—	53	32	no	—
542	C₂×D₄	—	53	32	no	—
543	C₂×D₄	—	53	32	no	—
544	C₂×D₄	—	53	16	no	—
545	C₂×D₄	—	53	16	no	—
546	C₂×D₄	—	53	8	no	—
547	C₂×D₄	—	53	32	no	—
548	C₂×D₄	—	53	16	no	—
549	C₂×D₄	—	53	8	no	—
550	C₂×D₄	—	106	128	no	—
551	C₂×D₄	—	106	32	no	—
552	C₂×D₄	—	106	128	no	—
553	C₂×D₄	—	106	32	no	—
554	C₂×D₄	—	106	256	no	—
555	C₂×D₄	—	106	128	no	—
556	C₂×D₄	—	106	256	no	—
557	C₂×D₄	—	106	256	no	—
558	C₂×D₄	—	106	32	no	—
559	C₂×D₄	—	106	32	no	—
560	C₂×D₄	—	106	128	no	—
561	C₂×D₄	—	106	16	no	—
562	C₂×D₄	—	212	4	no	—
563	C₂×D₄	—	212	32	no	—
564	C₂×D₄	—	212	8	no	—
565	C₂×D₄	D₄×D₅₃	1	16	yes	direct product factor
566	C₂×D₄	C₂³×D₅₃	1	8	yes	—
567	C₂×D₄	C₂³×D₅₃	1	32	yes	complemented
568	C₂×D₄	C₂³×D₅₃	1	16	yes	complemented
569	C₂×D₄	C₂³×D₅₃	1	8	yes	complemented
570	C₂²×C₄	—	2	16	no	—
571	C₂²×C₄	—	53	2	no	—
572	C₂²×C₄	—	53	16	no	—
573	C₂²×C₄	—	53	8	no	—
574	C₂²×C₄	—	53	16	no	—
575	C₂²×C₄	—	53	1	no	—
576	C₂²×C₄	—	53	4	no	—
577	C₂²×C₄	—	53	4	no	—
578	C₂²×C₄	—	53	16	no	—
579	C₂²×C₄	—	53	16	no	—
580	C₂²×C₄	—	53	16	no	—
581	C₂²×C₄	—	106	16	no	—
582	C₂²×C₄	—	106	128	no	—
583	C₂²×C₄	—	106	16	no	—
584	C₂²×C₄	—	106	4	no	—
585	C₂²×C₄	—	106	16	no	—
586	C₂²×C₄	—	106	16	no	—
587	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
588	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
589	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
590	C₂²×C₄	C₂³×D₅₃	1	16	yes	complemented
591	C₄⋊C₄	—	53	16	no	—
592	C₄⋊C₄	—	53	8	no	—
593	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
594	C₂²⋊C₄	—	53	16	no	—
595	C₂²⋊C₄	—	53	16	no	—
596	C₂²⋊C₄	—	53	16	no	—
597	C₂²⋊C₄	—	53	16	no	—
598	C₂²⋊C₄	—	53	32	no	—
599	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	complemented
600	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	complemented
601	C₄²	—	53	4	no	—
602	C₄²	—	53	8	no	—
603	C₄²	C₂³×D₅₃	1	4	yes	complemented
604	C₂³	—	2	8	no	—
605	C₂³	—	2	8	no	—
606	C₂³	—	2	16	no	—
607	C₂³	—	2	64	no	—
608	C₂³	—	2	8	no	—
609	C₂³	—	4	16	no	—
610	C₂³	—	4	64	no	—
611	C₂³	—	53	8	no	—
612	C₂³	—	53	4	no	—
613	C₂³	—	53	2	no	—
614	C₂³	—	53	16	no	—
615	C₂³	—	53	64	no	—
616	C₂³	—	53	8	no	—
617	C₂³	—	53	8	no	—
618	C₂³	—	106	32	no	—
619	C₂³	—	106	128	no	—
620	C₂³	—	106	32	no	—
621	C₂³	—	106	64	no	—
622	C₂³	—	106	64	no	—
623	C₂³	—	106	64	no	—
624	C₂³	—	106	32	no	—
625	C₂³	—	106	8	no	—
626	C₂³	—	106	8	no	—
627	C₂³	—	106	16	no	—
628	C₂³	—	106	64	no	—
629	C₂³	—	106	8	no	—
630	C₂³	—	212	32	no	—
631	C₂³	—	212	16	no	—
632	C₂³	—	212	128	no	—
633	C₂³	—	212	64	no	—
634	C₂³	—	212	512	no	—
635	C₂³	—	212	64	no	—
636	C₂³	C₂×D₄×D₅₃	1	16	yes	complemented
637	C₂³	C₂⁴×D₅₃	1	8	yes	—
638	C₂³	C₂⁴×D₅₃	1	8	yes	—
639	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
640	D₄	—	2	64	no	—
641	D₄	—	2	32	no	—
642	D₄	—	4	8	no	—
643	D₄	—	53	64	no	—
644	D₄	—	53	32	no	—
645	D₄	—	106	64	no	—
646	D₄	—	106	64	no	—
647	D₄	—	106	64	no	—
648	D₄	—	106	64	no	—
649	D₄	—	106	32	no	—
650	D₄	—	212	8	no	—
651	D₄	—	212	16	no	—
652	D₄	C₂×D₄×D₅₃	1	32	yes	direct product factor
653	C₂×C₄	—	2	8	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	32	no	—
656	C₂×C₄	—	53	8	no	—
657	C₂×C₄	—	53	4	no	—
658	C₂×C₄	—	53	32	no	—
659	C₂×C₄	—	53	2	no	—
660	C₂×C₄	—	53	8	no	—
661	C₂×C₄	—	106	32	no	—
662	C₂×C₄	—	106	32	no	—
663	C₂×C₄	—	106	8	no	—
664	C₂×C₄	—	106	32	no	—
665	C₂×C₄	—	106	8	no	—
666	C₂×C₄	—	106	2	no	—
667	C₂×C₄	—	106	32	no	—
668	C₂×C₄	C₂×D₄×D₅₃	1	8	yes	complemented
669	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
670	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
671	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
672	C₂²	—	2	32	no	—
673	C₂²	—	2	8	no	—
674	C₂²	—	2	8	no	—
675	C₂²	—	2	16	no	—
676	C₂²	—	2	8	no	—
677	C₂²	—	4	64	no	—
678	C₂²	—	4	16	no	—
679	C₂²	—	53	16	no	—
680	C₂²	—	53	8	no	—
681	C₂²	—	53	4	no	—
682	C₂²	—	53	16	no	—
683	C₂²	—	106	128	no	—
684	C₂²	—	106	32	no	—
685	C₂²	—	106	8	no	—
686	C₂²	—	106	8	no	—
687	C₂²	—	106	16	no	—
688	C₂²	—	106	8	no	—
689	C₂²	—	212	128	no	—
690	C₂²	—	212	64	no	—
691	C₂²	—	212	64	no	—
692	C₂²	—	212	16	no	—
693	C₂²	C₂²×D₄×D₅₃	1	4	yes	—
694	C₂²	C₂²×D₄×D₅₃	1	16	yes	complemented
695	C₂²	H(5,𝔽₂)×D₅₃	1	2	yes	—
696	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
697	C₄	—	2	8	no	—
698	C₄	—	2	2	no	—
699	C₄	—	53	8	no	—
700	C₄	—	106	8	no	—
701	C₄	—	106	2	no	—
702	C₄	C₂²×D₄×D₅₃	1	8	yes	complemented
703	C₂	—	2	16	no	—
704	C₂	—	4	8	no	—
705	C₂	—	53	8	no	—
706	C₂	—	106	16	no	—
707	C₂	—	212	8	no	—
708	C₂	D₄²×D₅₃	1	4	yes	direct product factor
709	C₂	C₂³×D₄×D₅₃	1	2	yes	—
710	C₂	C₂×H(5,𝔽₂)×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×D₄²×C₅₃	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×D₄²	D₅₃
hypocenter	C₅₃	C₂²×D₄²
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×D₄²

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄×D₅₃	C₂	semidirect
2. C₂×D₄×D₂₁₂	C₂	semidirect
3. C₂×#16811258	C₂	semidirect
4. C₂×#16811257	C₂	semidirect
5. C₂×D₄×C₂²⋊D₅₃	C₂	semidirect
6. C₂×#16811255	C₂	semidirect
7. D₄²×D₅₃	C₂	direct (N × H)
8. C₂×#127×D₅₃	C₂	semidirect
9. C₂×#121×D₅₃	C₂	semidirect
10. C₂×#120×D₅₃	C₂	semidirect
11. C₂×C₄×D₄×D₅₃	C₂	semidirect
12. C₂×D₄²×C₅₃	C₂	semidirect
13. C₂⁵×D₅₃	C₂²	semidirect
14. C₂³×D₂₁₂	C₂²	semidirect
15. C₂³×C₂²⋊D₅₃	C₂²	semidirect
18. C₂²×D₄×D₅₃	C₂²	semidirect
19. C₂²×D₄×D₅₃	C₂²	semidirect
20. C₂²×D₄×D₅₃	C₂²	semidirect
21. C₂²×D₄×D₅₃	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. D₄×D₂₁₂	C₂²	semidirect
27. #16811258	C₂²	semidirect
28. #16811257	C₂²	semidirect
29. D₄×C₂²⋊D₅₃	C₂²	semidirect
30. #16811255	C₂²	semidirect
31. C₂×#13133214	C₂²	semidirect
32. C₂×#13133213	C₂²	semidirect
33. C₂×#13133213	C₂²	semidirect
34. #127×D₅₃	C₂²	semidirect
35. C₂×#13133192	C₂²	semidirect
36. C₂×#13133191	C₂²	semidirect
37. C₂×#13133190	C₂²	semidirect
38. C₂×#13133189	C₂²	semidirect
39. C₂×#13133188	C₂²	semidirect
40. #121×D₅₃	C₂²	semidirect
41. C₂×#13133187	C₂²	semidirect
42. C₂×#13133187	C₂²	semidirect
43. C₂×#13133186	C₂²	semidirect
44. C₂×#13133185	C₂²	semidirect
45. C₂×#13133185	C₂²	semidirect
46. #120×D₅₃	C₂²	semidirect
47. C₂×C₄×D₂₁₂	C₂²	semidirect
48. C₂×D₄×Dic₅₃	C₂²	semidirect
49. C₂×#13133179	C₂²	semidirect
50. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
51. C₂×#13133177	C₂²	semidirect
52. C₄×D₄×D₅₃	C₂²	semidirect
53. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
54. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
55. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
56. C₂×C₄²×D₅₃	C₂²	semidirect
57. C₂³×D₄×C₅₃	C₂²	semidirect
58. D₄²×C₅₃	C₂²	semidirect
59. C₂×#127×C₅₃	C₂²	semidirect
60. C₂×#121×C₅₃	C₂²	semidirect
61. C₂×#120×C₅₃	C₂²	semidirect
62. C₂×C₄×D₄×C₅₃	C₂²	semidirect
67. C₂⁴×D₅₃	C₂³	semidirect
68. C₂⁴×D₅₃	C₂³	semidirect
69. C₂⁴×D₅₃	C₂³	semidirect
72. C₂²×D₂₁₂	C₂³	semidirect
73. C₂²×D₂₁₂	C₂³	semidirect
74. C₂²×D₂₁₂	C₂³	semidirect
75. C₂²×D₂₁₂	C₂³	semidirect
78. C₂²×C₂²⋊D₅₃	C₂³	semidirect
79. C₂²×C₂²⋊D₅₃	C₂³	semidirect
80. C₂²×C₂²⋊D₅₃	C₂³	semidirect
81. C₂²×C₂²⋊D₅₃	C₂³	semidirect
82. C₂²×C₂²⋊D₅₃	C₂³	semidirect
90. C₂×D₄×D₅₃	D₄	direct (N × H)
92. C₂×D₄×D₅₃	C₂³	semidirect
93. C₂×D₄×D₅₃	C₂³	semidirect
94. C₂×D₄×D₅₃	C₂³	semidirect
95. C₂×D₄×D₅₃	C₂³	semidirect
96. C₂×D₄×D₅₃	C₂³	semidirect
97. C₂×D₄×D₅₃	C₂³	semidirect
98. C₂³×Dic₅₃	C₂³	semidirect
103. C₂²×C₄×D₅₃	C₂³	semidirect
104. C₂²×C₄×D₅₃	C₂³	semidirect
105. C₂²×C₄×D₅₃	C₂³	semidirect
106. #13133214	C₂³	semidirect
107. #13133213	C₂³	semidirect
108. #13133213	C₂³	semidirect
109. #13133192	C₂³	semidirect
110. #13133191	C₂³	semidirect
111. #13133190	C₂³	semidirect
112. #13133189	C₂³	semidirect
113. #13133188	C₂³	semidirect
114. #13133187	C₂³	semidirect
115. #13133187	C₂³	semidirect
116. #13133186	C₂³	semidirect
117. #13133185	C₂³	semidirect
118. #13133185	C₂³	semidirect
119. C₄×D₂₁₂	C₂³	semidirect
120. D₄×Dic₅₃	C₂³	semidirect
121. #13133179	C₂³	semidirect
122. C₄×C₂²⋊D₅₃	C₂³	semidirect
123. #13133177	C₂³	semidirect
124. C₂×C₄⋊Dic₅₃	C₂³	semidirect
125. C₂×#11719919	C₂³	semidirect
126. C₄⋊C₄×D₅₃	C₂³	semidirect
127. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
128. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
129. C₂×#11719921	C₂³	semidirect
130. C₂×#11719921	C₂³	semidirect
131. C₂×#11719921	C₂³	semidirect
132. C₂²⋊C₄×D₅₃	C₂³	semidirect
133. C₂²⋊C₄×D₅₃	C₂³	semidirect
134. C₂×C₄×Dic₅₃	C₂³	semidirect
135. C₂×C₄×Dic₅₃	C₂³	semidirect
136. C₄²×D₅₃	C₂³	semidirect
137. C₂⁵×C₅₃	C₂³	semidirect
140. C₂²×D₄×C₅₃	C₂³	semidirect
141. C₂²×D₄×C₅₃	C₂³	semidirect
142. C₂²×D₄×C₅₃	C₂³	semidirect
143. C₂²×D₄×C₅₃	C₂³	semidirect
144. C₂³×C₄×C₅₃	C₂³	semidirect
145. #127×C₅₃	C₂³	semidirect
146. #121×C₅₃	C₂³	semidirect
147. #120×C₅₃	C₂³	semidirect
148. C₄×D₄×C₅₃	C₂³	semidirect
149. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
150. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
151. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
152. C₂×C₄²×C₅₃	C₂³	semidirect
157. C₂⁴×C₅₃	C₂⁴	semidirect
170. C₂³×D₅₃	C₂×D₄	semidirect
176. C₂³×D₅₃	C₂⁴	semidirect
177. C₂³×D₅₃	C₂⁴	semidirect
182. C₂×D₄×C₅₃	C₂×D₄	semidirect
184. C₂×D₄×C₅₃	C₂⁴	semidirect
185. C₂×D₄×C₅₃	C₂⁴	semidirect
186. C₂×D₄×C₅₃	C₂⁴	semidirect
191. C₂²×C₄×C₅₃	C₂⁴	semidirect
197. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
199. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
200. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
201. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
202. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
207. C₂²×Dic₅₃	C₂⁴	semidirect
214. D₄×D₅₃	C₂×D₄	direct (N × H)
219. C₂×D₂₁₂	C₂×D₄	semidirect
221. C₂×D₂₁₂	C₂⁴	semidirect
222. C₂×D₂₁₂	C₂⁴	semidirect
223. C₂×D₂₁₂	C₂⁴	semidirect
229. C₂×C₄×D₅₃	C₂×D₄	semidirect
233. C₂×C₄×D₅₃	C₂⁴	semidirect
234. C₂×C₄×D₅₃	C₂⁴	semidirect
235. C₄⋊C₄×C₅₃	C₂⁴	semidirect
236. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
237. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
238. C₄²×C₅₃	C₂⁴	semidirect
239. C₂²⋊Dic₅₃	C₂⁴	semidirect
240. C₂²⋊Dic₅₃	C₂⁴	semidirect
241. #11719921	C₂⁴	semidirect
242. #11719921	C₂⁴	semidirect
243. #11719921	C₂⁴	semidirect
244. C₄⋊Dic₅₃	C₂⁴	semidirect
245. #11719919	C₂⁴	semidirect
246. C₄×Dic₅₃	C₂⁴	semidirect
247. C₄×Dic₅₃	C₂⁴	semidirect
255. C₂³×C₅₃	C₂²×D₄	semidirect
278. C₂²×D₅₃	C₂²×D₄	semidirect
279. C₂²×D₅₃	C₂²×D₄	semidirect
287. D₄×C₅₃	C₂²×D₄	semidirect
291. C₂×C₄×C₅₃	C₂²×D₄	semidirect
299. C₂²⋊D₅₃	C₂²×D₄	semidirect
303. C₂×Dic₅₃	C₂²×D₄	semidirect
310. D₂₁₂	C₂²×D₄	semidirect
315. C₄×D₅₃	C₂²×D₄	semidirect
325. C₂²×C₅₃	C₂³×D₄	semidirect
338. C₂×D₅₃	D₄²	direct (N × H)
340. C₂×D₅₃	C₂³×D₄	semidirect
344. C₄×C₅₃	C₂³×D₄	semidirect
347. Dic₅₃	C₂³×D₄	semidirect
355. C₂×D₄²	D₅₃	direct (N × H)
362. C₂×C₅₃	C₂×D₄²	semidirect
367. D₅₃	C₂×D₄²	direct (N × H)
380. C₂³×D₄	C₂×D₅₃	semidirect
387. D₄²	C₂×D₅₃	direct (N × H)
392. C₂×#127	C₂×D₅₃	semidirect
399. C₂×#121	C₂×D₅₃	semidirect
406. C₂×#120	C₂×D₅₃	semidirect
413. C₂×C₄×D₄	C₂×D₅₃	semidirect
418. C₅₃	C₂²×D₄²	semidirect
426. C₂⁵	C₂²×D₅₃	semidirect
457. C₂²×D₄	C₂²×D₅₃	semidirect
458. C₂²×D₄	C₂²×D₅₃	semidirect
459. C₂²×D₄	C₂²×D₅₃	semidirect
460. C₂²×D₄	C₂²×D₅₃	semidirect
469. C₂³×C₄	C₂²×D₅₃	semidirect
473. #127	C₂²×D₅₃	semidirect
479. #121	C₂²×D₅₃	semidirect
485. #120	C₂²×D₅₃	semidirect
491. C₄×D₄	C₂²×D₅₃	semidirect
495. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
503. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
504. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
508. C₂×C₄²	C₂²×D₅₃	semidirect
533. C₂⁴	C₂³×D₅₃	semidirect
565. C₂×D₄	D₄×D₅₃	direct (N × H)
567. C₂×D₄	C₂³×D₅₃	semidirect
568. C₂×D₄	C₂³×D₅₃	semidirect
569. C₂×D₄	C₂³×D₅₃	semidirect
590. C₂²×C₄	C₂³×D₅₃	semidirect
593. C₄⋊C₄	C₂³×D₅₃	semidirect
599. C₂²⋊C₄	C₂³×D₅₃	semidirect
600. C₂²⋊C₄	C₂³×D₅₃	semidirect
603. C₄²	C₂³×D₅₃	semidirect
636. C₂³	C₂×D₄×D₅₃	semidirect
652. D₄	C₂×D₄×D₅₃	direct (N × H)
668. C₂×C₄	C₂×D₄×D₅₃	semidirect
694. C₂²	C₂²×D₄×D₅₃	semidirect
702. C₄	C₂²×D₄×D₅₃	semidirect
708. C₂	D₄²×D₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄×D₅₃	2
C₂×D₄×D₂₁₂	2
C₂×#16811258	2
C₂×#16811257	2
C₂×D₄×C₂²⋊D₅₃	2
C₂×#16811255	2
D₄²×D₅₃	2
C₂×#127×D₅₃	2
C₂×#121×D₅₃	2
C₂×#120×D₅₃	2
C₂×C₄×D₄×D₅₃	2
C₂×D₄²×C₅₃	2
C₂²×D₄²	53

Subgroups — C2×D42×D53 #28290998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄²×D₅₃ #28290998