Subgroups — C₂×C₄×#13133262 #28290693

Order 13568.

12378 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133262	C₂	1	1	yes	maximal, characteristic
2	C₄×#13133262	C₂	1	32	yes	maximal, direct product factor
3	C₂×#16811104	C₂	1	2	yes	maximal, complemented
4	C₂×#16811102	C₂	1	4	yes	maximal, complemented
5	C₂×#16811098	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16811096	C₂	1	4	yes	maximal, complemented
7	C₂×#16811095	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×#11719945	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×#11719947	C₂	1	4	yes	maximal, complemented
10	C₂²×C₄×C₂²⋊D₅₃	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×D₄×D₅₃	C₂	1	4	yes	maximal, complemented
12	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13133262	C₄	1	32	yes	direct product factor
14	C₂×#13133262	C₂²	1	16	yes	—
15	C₂²×#11719945	C₂²	1	2	yes	—
16	C₂²×#11719947	C₂²	1	4	yes	—
17	C₂³×C₂²⋊D₅₃	C₂²	1	4	yes	—
18	C₂²×D₄×D₅₃	C₂²	1	4	yes	—
19	C₂³×C₄×D₅₃	C₂²	1	4	yes	complemented
20	#16811104	C₂²	1	32	yes	complemented
21	#16811102	C₂²	1	64	yes	complemented
22	#16811098	C₂²	1	16	yes	complemented
23	#16811096	C₂²	1	64	yes	complemented
24	#16811095	C₂²	1	64	yes	complemented
25	C₄×#11719945	C₂²	1	32	yes	complemented
26	C₄×#11719947	C₂²	1	64	yes	complemented
27	C₂×C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
28	C₂×C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
29	C₂×#13133182	C₂²	1	4	yes	complemented
30	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
31	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
32	C₂×D₄×Dic₅₃	C₂²	1	4	yes	complemented
33	C₂×D₄×Dic₅₃	C₂²	1	4	yes	complemented
34	C₂×#13133179	C₂²	1	4	yes	complemented
35	C₂×C₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
36	C₂×C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
37	C₂×C₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
38	C₂×C₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
39	C₂×C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
40	C₂×C₄×C₂²⋊D₅₃	C₂²	1	64	yes	complemented
41	C₂×#13133177	C₂²	1	8	yes	complemented
42	C₂×#13133177	C₂²	1	8	yes	complemented
43	C₄×D₄×D₅₃	C₂²	1	64	yes	complemented
44	C₂×#13133176	C₂²	1	2	yes	complemented
45	C₂×#13133175	C₂²	1	4	yes	complemented
46	C₂×#13133174	C₂²	1	4	yes	complemented
47	C₂×#13133173	C₂²	1	8	yes	complemented
48	C₂²×#11719919	C₂²	1	4	yes	complemented
49	C₂×C₄⋊C₄×D₅₃	C₂²	1	4	yes	complemented
50	C₂²×C₂²⋊Dic₅₃	C₂²	1	4	yes	complemented
51	C₂²×#11719921	C₂²	1	4	yes	complemented
52	C₂×C₂²⋊C₄×D₅₃	C₂²	1	8	yes	complemented
53	C₂²×C₄×Dic₅₃	C₂²	1	4	yes	complemented
54	C₂×C₄²×D₅₃	C₂²	1	4	yes	complemented
55	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
56	C₂⁴×C₄×C₅₃	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
58	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
59	C₂×C₄×D₄×C₅₃	C₂²	1	16	yes	complemented
60	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
62	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₂⁴×D₅₃	C₂³	1	4	yes	—
64	#13133262	C₂×C₄	1	256	yes	direct product factor
65	C₂×#11719945	C₂×C₄	1	32	yes	complemented
66	C₂×#11719945	C₂³	1	16	yes	—
67	C₂×#11719947	C₂×C₄	1	64	yes	complemented
68	C₂×#11719947	C₂³	1	32	yes	—
69	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
70	C₂²×D₂₁₂	C₂³	1	2	yes	—
71	C₂²×C₂²⋊D₅₃	C₂×C₄	1	64	yes	complemented
72	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
73	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
74	C₂²×C₂²⋊D₅₃	C₂³	1	32	yes	—
75	C₂×D₄×D₅₃	C₂×C₄	1	64	yes	complemented
76	C₂×D₄×D₅₃	C₂³	1	32	yes	—
77	C₂³×Dic₅₃	C₂³	1	4	yes	—
78	C₂³×Dic₅₃	C₂³	1	4	yes	—
79	C₂³×Dic₅₃	C₂³	1	4	yes	—
80	C₂²×C₄×D₅₃	—	4	16	no	—
81	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
82	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
83	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
84	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
85	C₂²×C₄×D₅₃	C₂³	1	32	yes	complemented
86	C₄×Dic₁₀₆	C₂³	1	16	yes	complemented
87	C₄×Dic₁₀₆	C₂³	1	16	yes	complemented
88	#13133182	C₂³	1	32	yes	complemented
89	C₄×D₂₁₂	C₂³	1	16	yes	complemented
90	C₄×D₂₁₂	C₂³	1	16	yes	complemented
91	D₄×Dic₅₃	C₂³	1	32	yes	complemented
92	D₄×Dic₅₃	C₂³	1	32	yes	complemented
93	#13133179	C₂³	1	32	yes	complemented
94	C₄×C₂²⋊D₅₃	C₂³	1	64	yes	complemented
95	C₄×C₂²⋊D₅₃	C₂³	1	32	yes	complemented
96	C₄×C₂²⋊D₅₃	C₂³	1	64	yes	complemented
97	C₄×C₂²⋊D₅₃	C₂³	1	64	yes	complemented
98	C₄×C₂²⋊D₅₃	C₂³	1	32	yes	complemented
99	#13133177	C₂³	1	64	yes	complemented
100	#13133177	C₂³	1	64	yes	complemented
101	#13133176	C₂³	1	16	yes	complemented
102	#13133175	C₂³	1	32	yes	complemented
103	#13133174	C₂³	1	32	yes	complemented
104	#13133173	C₂³	1	64	yes	complemented
105	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
106	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
107	C₂×#11719919	C₂³	1	8	yes	—
108	C₂×#11719919	C₂³	1	4	yes	—
109	C₂×#11719919	C₂³	1	4	yes	—
110	C₂×#11719919	C₂³	1	32	yes	complemented
111	C₄⋊C₄×D₅₃	C₂³	1	32	yes	complemented
112	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	—
113	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
114	C₂×C₂²⋊Dic₅₃	C₂³	1	32	yes	complemented
115	C₂×#11719921	C₂³	1	4	yes	—
116	C₂×#11719921	C₂³	1	8	yes	—
117	C₂×#11719921	C₂³	1	4	yes	—
118	C₂×#11719921	C₂³	1	32	yes	complemented
119	C₂²⋊C₄×D₅₃	C₂³	1	64	yes	complemented
120	C₂×C₄×Dic₅₃	C₂³	1	4	yes	—
121	C₂×C₄×Dic₅₃	C₂³	1	4	yes	—
122	C₂×C₄×Dic₅₃	C₂³	1	4	yes	—
123	C₂×C₄×Dic₅₃	C₂³	1	8	yes	—
124	C₂×C₄×Dic₅₃	C₂³	1	32	yes	complemented
125	C₄²×D₅₃	C₂³	1	32	yes	complemented
126	C₂⁵×C₅₃	C₂³	1	2	yes	—
127	C₂²×D₄×C₅₃	C₂×C₄	1	16	yes	complemented
128	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
129	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
130	C₂³×C₄×C₅₃	—	4	8	no	—
131	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
133	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
136	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₅₃	C₂³	1	16	yes	complemented
138	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
139	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
140	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
142	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
143	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	complemented
144	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
145	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
147	C₂⁴×C₅₃	—	4	4	no	—
148	C₂⁴×C₅₃	—	4	4	no	—
149	C₂⁴×C₅₃	C₂²×C₄	1	16	yes	complemented
150	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
151	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
152	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
153	C₂³×D₅₃	—	4	8	no	—
154	C₂³×D₅₃	—	4	8	no	—
155	C₂³×D₅₃	C₂²×C₄	1	32	yes	complemented
156	C₂³×D₅₃	C₂⁴	1	4	yes	—
157	C₂³×D₅₃	C₂⁴	1	16	yes	—
158	C₂×D₄×C₅₃	C₂²×C₄	1	32	yes	complemented
159	C₂×D₄×C₅₃	C₂²×C₄	1	64	yes	complemented
160	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
161	C₂²×C₄×C₅₃	—	2	4	no	—
162	C₂²×C₄×C₅₃	—	2	16	no	—
163	C₂²×C₄×C₅₃	—	4	32	no	—
164	C₂²×C₄×C₅₃	—	4	4	no	—
165	C₂²×C₄×C₅₃	—	4	8	no	—
166	C₂²×C₄×C₅₃	—	4	2	no	—
167	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	complemented
168	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
173	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
175	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
176	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
179	C₂×C₂²⋊D₅₃	C₂²×C₄	1	64	yes	complemented
180	C₂×C₂²⋊D₅₃	C₂²×C₄	1	32	yes	complemented
181	C₂×C₂²⋊D₅₃	C₂²×C₄	1	256	yes	complemented
182	C₂×C₂²⋊D₅₃	C₂⁴	1	32	yes	—
183	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
184	C₂²×Dic₅₃	—	4	8	no	—
185	C₂²×Dic₅₃	—	4	8	no	—
186	C₂²×Dic₅₃	C₂²×C₄	1	32	yes	complemented
187	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
188	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
189	C₂²×Dic₅₃	C₂⁴	1	16	yes	—
190	C₂²×Dic₅₃	C₂⁴	1	16	yes	—
191	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
192	C₂²×Dic₅₃	C₂⁴	1	16	yes	—
193	#11719947	C₂²×C₄	1	256	yes	complemented
194	D₄×D₅₃	C₂²×C₄	1	256	yes	complemented
195	#11719945	C₂²×C₄	1	128	yes	complemented
196	C₂×D₂₁₂	C₂²×C₄	1	16	yes	complemented
197	C₂×D₂₁₂	C₂⁴	1	8	yes	—
198	C₂×C₄×D₅₃	—	2	16	no	—
199	C₂×C₄×D₅₃	—	4	64	no	—
200	C₂×C₄×D₅₃	—	4	16	no	—
201	C₂×C₄×D₅₃	—	4	8	no	—
202	C₂×C₄×D₅₃	C₂²×C₄	1	32	yes	complemented
203	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
204	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
205	C₂×C₄×D₅₃	C₂⁴	1	32	yes	—
206	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
207	C₂×Dic₁₀₆	C₂²×C₄	1	16	yes	complemented
208	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
209	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
210	C₂²⋊C₄×C₅₃	C₂⁴	1	32	yes	—
211	C₄²×C₅₃	C₂⁴	1	8	yes	—
212	C₄²×C₅₃	C₂⁴	1	8	yes	—
213	C₂²⋊Dic₅₃	C₂⁴	1	32	yes	—
214	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
215	#11719921	C₂⁴	1	16	yes	—
216	#11719921	C₂⁴	1	32	yes	—
217	#11719921	C₂⁴	1	16	yes	—
218	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
219	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
220	#11719919	C₂⁴	1	32	yes	—
221	#11719919	C₂⁴	1	16	yes	—
222	#11719919	C₂⁴	1	16	yes	—
223	C₄×Dic₅₃	C₂⁴	1	16	yes	—
224	C₄×Dic₅₃	C₂⁴	1	16	yes	—
225	C₄×Dic₅₃	C₂⁴	1	16	yes	—
226	C₄×Dic₅₃	C₂⁴	1	32	yes	—
227	C₂³×C₅₃	—	2	8	no	—
228	C₂³×C₅₃	—	2	2	no	—
229	C₂³×C₅₃	—	2	8	no	—
230	C₂³×C₅₃	—	2	2	no	—
231	C₂³×C₅₃	—	4	8	no	—
232	C₂³×C₅₃	—	4	32	no	—
233	C₂³×C₅₃	—	4	8	no	—
234	C₂³×C₅₃	C₂³×C₄	1	16	yes	—
235	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
236	C₂³×C₅₃	C₂³×C₄	1	32	yes	complemented
237	C₂³×C₅₃	C₂⁵	1	8	yes	—
238	C₂³×C₅₃	C₂⁵	1	2	yes	—
239	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
240	C₂²×D₅₃	—	2	8	no	—
241	C₂²×D₅₃	—	2	8	no	—
242	C₂²×D₅₃	—	4	16	no	—
243	C₂²×D₅₃	—	4	64	no	—
244	C₂²×D₅₃	—	4	16	no	—
245	C₂²×D₅₃	C₂³×C₄	1	16	yes	—
246	C₂²×D₅₃	C₂³×C₄	1	64	yes	complemented
247	C₂²×D₅₃	C₂⁵	1	8	yes	—
248	D₄×C₅₃	C₂³×C₄	1	64	yes	complemented
249	C₂×C₄×C₅₃	—	2	8	no	—
250	C₂×C₄×C₅₃	—	2	2	no	—
251	C₂×C₄×C₅₃	—	2	4	no	—
252	C₂×C₄×C₅₃	—	2	32	no	—
253	C₂×C₄×C₅₃	—	2	8	no	—
254	C₂×C₄×C₅₃	—	4	8	no	—
255	C₂×C₄×C₅₃	—	4	16	no	—
256	C₂×C₄×C₅₃	—	4	4	no	—
257	C₂×C₄×C₅₃	C₂³×C₄	1	8	yes	—
258	C₂×C₄×C₅₃	C₂³×C₄	1	16	yes	complemented
259	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	complemented
260	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
261	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
262	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
263	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
264	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
265	C₂²⋊D₅₃	C₂³×C₄	1	64	yes	complemented
266	C₂²⋊D₅₃	C₂³×C₄	1	128	yes	complemented
267	C₂×Dic₅₃	—	2	8	no	—
268	C₂×Dic₅₃	—	2	8	no	—
269	C₂×Dic₅₃	—	4	16	no	—
270	C₂×Dic₅₃	—	4	16	no	—
271	C₂×Dic₅₃	C₂³×C₄	1	16	yes	—
272	C₂×Dic₅₃	C₂³×C₄	1	64	yes	complemented
273	C₂×Dic₅₃	C₂⁵	1	8	yes	—
274	C₂×Dic₅₃	C₂⁵	1	8	yes	—
275	C₂×Dic₅₃	C₂⁵	1	8	yes	—
276	D₂₁₂	C₂³×C₄	1	32	yes	complemented
277	C₄×D₅₃	—	2	32	no	—
278	C₄×D₅₃	—	4	32	no	—
279	C₄×D₅₃	—	4	16	no	—
280	C₄×D₅₃	C₂³×C₄	1	64	yes	complemented
281	Dic₁₀₆	C₂³×C₄	1	32	yes	complemented
282	C₂×C₄×H(5,𝔽₂)	—	53	1	no	maximal, Sylow
283	C₂²×C₅₃	—	2	8	no	—
284	C₂²×C₅₃	—	2	2	no	—
285	C₂²×C₅₃	—	2	8	no	—
286	C₂²×C₅₃	—	2	2	no	—
287	C₂²×C₅₃	—	2	32	no	—
288	C₂²×C₅₃	—	2	8	no	—
289	C₂²×C₅₃	—	4	32	no	—
290	C₂²×C₅₃	C₂⁴×C₄	1	16	yes	—
291	C₂²×C₅₃	C₂⁴×C₄	1	4	yes	—
292	C₂²×C₅₃	C₂⁴×C₄	1	2	yes	—
293	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
294	C₂²×C₅₃	#585	1	2	yes	—
295	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
296	C₂×D₅₃	—	2	8	no	—
297	C₂×D₅₃	—	2	8	no	—
298	C₂×D₅₃	—	2	32	no	—
299	C₂×D₅₃	—	4	64	no	—
300	C₂×D₅₃	C₂⁴×C₄	1	16	yes	—
301	C₄×C₅₃	—	2	8	no	—
302	C₄×C₅₃	—	2	2	no	—
303	C₄×C₅₃	—	2	4	no	—
304	C₄×C₅₃	C₂⁴×C₄	1	8	yes	—
305	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
306	Dic₅₃	—	2	8	no	—
307	Dic₅₃	—	2	8	no	—
308	Dic₅₃	C₂⁴×C₄	1	16	yes	—
309	C₂²×H(5,𝔽₂)	—	53	1	no	—
310	C₄×H(5,𝔽₂)	—	53	32	no	—
311	C₂×#520	—	53	4	no	—
312	C₂×#520	—	53	2	no	—
313	C₂×#518	—	53	1	no	—
314	C₂×#518	—	53	4	no	—
315	C₂×#518	—	53	4	no	—
316	C₂×C₄×#41	—	53	2	no	—
317	C₂×C₄×#41	—	53	4	no	—
318	C₂²×C₄×D₄	—	53	4	no	—
319	C₂²×C₄×D₄	—	53	4	no	—
320	C₂²×C₄×D₄	D₅₃	1	1	yes	characteristic, complemented
321	C₂×C₅₃	—	2	16	no	—
322	C₂×C₅₃	—	2	4	no	—
323	C₂×C₅₃	C₄×H(5,𝔽₂)	1	4	yes	complemented
324	C₂×C₅₃	C₂⁵×C₄	1	1	yes	characteristic
325	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
327	D₅₃	—	2	16	no	—
328	C₂×H(5,𝔽₂)	—	53	32	no	—
329	C₂×H(5,𝔽₂)	—	53	16	no	—
330	C₂²×#41	—	53	4	no	—
331	C₂²×#41	—	53	2	no	—
332	C₂³×D₄	—	53	4	no	—
333	C₂³×D₄	—	53	4	no	—
334	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic
335	C₂⁴×C₄	—	53	4	no	—
336	C₂⁴×C₄	C₂×D₅₃	1	2	yes	complemented
337	#520	—	53	64	no	—
338	#520	—	53	32	no	—
339	#518	—	53	16	no	—
340	#518	—	53	64	no	—
341	#518	—	53	64	no	—
342	C₄×#41	—	53	64	no	—
343	C₄×#41	—	53	32	no	—
344	C₂×C₄×Q₈	—	53	4	no	—
345	C₂×C₄×Q₈	—	53	2	no	—
346	C₂×C₄×Q₈	—	53	2	no	—
347	C₂×C₄×D₄	—	53	4	no	—
348	C₂×C₄×D₄	—	53	4	no	—
349	C₂×C₄×D₄	—	53	4	no	—
350	C₂×C₄×D₄	—	53	8	no	—
351	C₂×C₄×D₄	—	53	8	no	—
352	C₂×C₄×D₄	—	53	8	no	—
353	C₂×C₄×D₄	—	53	4	no	—
354	C₂×C₄×D₄	—	53	64	no	—
355	C₂×C₄×D₄	—	53	64	no	—
356	C₂×C₄×D₄	—	53	4	no	—
357	C₂×C₄×D₄	—	53	8	no	—
358	C₂×C₄×D₄	—	53	8	no	—
359	C₂×C₄×D₄	—	53	2	no	—
360	C₂×C₄×D₄	—	53	2	no	—
361	C₂×C₄×D₄	C₂×D₅₃	1	4	yes	complemented
362	C₂×C₄×D₄	C₂×D₅₃	1	4	yes	complemented
363	C₂×C₄×D₄	C₂×D₅₃	1	16	yes	complemented
364	C₂×#117	—	53	2	no	—
365	C₂×#117	—	53	4	no	—
366	C₂×#117	—	53	8	no	—
367	C₂×#117	—	53	4	no	—
368	C₂²×C₄⋊C₄	—	53	4	no	—
369	C₂²×C₄⋊C₄	—	53	4	no	—
370	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
371	C₂²×C₂²⋊C₄	—	53	4	no	—
372	C₂²×C₂²⋊C₄	—	53	4	no	—
373	C₂²×C₂²⋊C₄	—	53	8	no	—
374	C₂²×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
375	C₂²×C₄²	—	53	4	no	—
376	C₂²×C₄²	—	53	4	no	—
377	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
378	C₅₃	C₂×C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
379	C₂⁵	—	53	4	no	—
380	C₂⁵	C₂²×D₅₃	1	2	yes	—
381	H(5,𝔽₂)	—	53	256	no	—
382	C₂×#41	—	53	64	no	—
383	C₂×#41	—	53	32	no	—
384	C₂×#41	—	53	32	no	—
385	C₂×#41	—	53	16	no	—
386	C₂²×Q₈	—	53	2	no	—
387	C₂²×D₄	—	53	64	no	—
388	C₂²×D₄	—	53	4	no	—
389	C₂²×D₄	—	53	8	no	—
390	C₂²×D₄	—	53	32	no	—
391	C₂²×D₄	—	53	64	no	—
392	C₂²×D₄	—	53	32	no	—
393	C₂²×D₄	—	53	2	no	—
394	C₂²×D₄	C₄×D₅₃	1	16	yes	complemented
395	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
396	C₂²×D₄	C₂²×D₅₃	1	8	yes	—
397	C₂³×C₄	—	4	8	no	—
398	C₂³×C₄	—	53	4	no	—
399	C₂³×C₄	—	53	4	no	—
400	C₂³×C₄	—	53	4	no	—
401	C₂³×C₄	—	53	4	no	—
402	C₂³×C₄	—	53	4	no	—
403	C₂³×C₄	—	53	4	no	—
404	C₂³×C₄	—	53	8	no	—
405	C₂³×C₄	—	53	32	no	—
406	C₂³×C₄	—	212	16	no	—
407	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
408	C₂³×C₄	C₂²×D₅₃	1	4	yes	—
409	C₂³×C₄	C₂²×D₅₃	1	4	yes	—
410	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
411	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
412	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
413	C₂³×C₄	C₂²×D₅₃	1	16	yes	complemented
414	C₄×Q₈	—	53	32	no	—
415	C₄×Q₈	—	53	16	no	—
416	C₄×Q₈	—	53	16	no	—
417	C₄×D₄	—	53	32	no	—
418	C₄×D₄	—	53	32	no	—
419	C₄×D₄	—	53	64	no	—
420	C₄×D₄	—	53	32	no	—
421	C₄×D₄	—	53	64	no	—
422	C₄×D₄	—	53	64	no	—
423	C₄×D₄	—	53	32	no	—
424	C₄×D₄	—	53	32	no	—
425	C₄×D₄	—	53	64	no	—
426	C₄×D₄	—	53	64	no	—
427	C₄×D₄	—	53	16	no	—
428	C₄×D₄	—	53	16	no	—
429	C₄×D₄	C₂²×D₅₃	1	32	yes	complemented
430	C₄×D₄	C₂²×D₅₃	1	32	yes	complemented
431	#117	—	53	16	no	—
432	#117	—	53	32	no	—
433	#117	—	53	64	no	—
434	#117	—	53	32	no	—
435	C₂×C₄⋊C₄	—	53	8	no	—
436	C₂×C₄⋊C₄	—	53	4	no	—
437	C₂×C₄⋊C₄	—	53	2	no	—
438	C₂×C₄⋊C₄	—	53	32	no	—
439	C₂×C₄⋊C₄	—	53	4	no	—
440	C₂×C₄⋊C₄	—	53	2	no	—
441	C₂×C₄⋊C₄	—	53	32	no	—
442	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	—
443	C₂×C₄⋊C₄	C₂²×D₅₃	1	8	yes	complemented
444	C₂×C₂²⋊C₄	—	53	4	no	—
445	C₂×C₂²⋊C₄	—	53	8	no	—
446	C₂×C₂²⋊C₄	—	53	32	no	—
447	C₂×C₂²⋊C₄	—	53	8	no	—
448	C₂×C₂²⋊C₄	—	53	4	no	—
449	C₂×C₂²⋊C₄	—	53	4	no	—
450	C₂×C₂²⋊C₄	—	53	32	no	—
451	C₂×C₂²⋊C₄	—	53	64	no	—
452	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	—
453	C₂×C₂²⋊C₄	C₂²×D₅₃	1	16	yes	complemented
454	C₂×C₄²	—	53	8	no	—
455	C₂×C₄²	—	53	4	no	—
456	C₂×C₄²	—	53	4	no	—
457	C₂×C₄²	—	53	32	no	—
458	C₂×C₄²	—	53	4	no	—
459	C₂×C₄²	—	53	32	no	—
460	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
461	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
462	C₂×C₄²	C₂²×D₅₃	1	8	yes	complemented
463	C₂⁴	—	4	4	no	—
464	C₂⁴	—	4	4	no	—
465	C₂⁴	—	53	4	no	—
466	C₂⁴	—	53	32	no	—
467	C₂⁴	—	53	16	no	—
468	C₂⁴	—	212	8	no	—
469	C₂⁴	—	212	8	no	—
470	C₂⁴	C₂×C₄×D₅₃	1	16	yes	complemented
471	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
472	C₂⁴	C₂³×D₅₃	1	4	yes	—
473	C₂⁴	C₂³×D₅₃	1	8	yes	—
474	#41	—	53	256	no	—
475	#41	—	53	128	no	—
476	C₂×Q₈	—	53	16	no	—
477	C₂×Q₈	—	53	8	no	—
478	C₂×D₄	—	53	64	no	—
479	C₂×D₄	—	53	32	no	—
480	C₂×D₄	—	53	256	no	—
481	C₂×D₄	—	53	16	no	—
482	C₂×D₄	—	53	32	no	—
483	C₂×D₄	—	53	256	no	—
484	C₂×D₄	—	53	16	no	—
485	C₂×D₄	—	53	8	no	—
486	C₂×D₄	C₂×C₄×D₅₃	1	32	yes	complemented
487	C₂×D₄	C₂×C₄×D₅₃	1	64	yes	complemented
488	C₂×D₄	C₂³×D₅₃	1	16	yes	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	16	no	—
491	C₂²×C₄	—	4	32	no	—
492	C₂²×C₄	—	4	8	no	—
493	C₂²×C₄	—	4	4	no	—
494	C₂²×C₄	—	4	2	no	—
495	C₂²×C₄	—	53	32	no	—
496	C₂²×C₄	—	53	4	no	—
497	C₂²×C₄	—	53	16	no	—
498	C₂²×C₄	—	53	32	no	—
499	C₂²×C₄	—	53	16	no	—
500	C₂²×C₄	—	53	4	no	—
501	C₂²×C₄	—	53	4	no	—
502	C₂²×C₄	—	53	16	no	—
503	C₂²×C₄	—	53	16	no	—
504	C₂²×C₄	—	53	16	no	—
505	C₂²×C₄	—	53	16	no	—
506	C₂²×C₄	—	53	32	no	—
507	C₂²×C₄	—	106	16	no	—
508	C₂²×C₄	—	212	64	no	—
509	C₂²×C₄	—	212	8	no	—
510	C₂²×C₄	—	212	16	no	—
511	C₂²×C₄	—	212	8	no	—
512	C₂²×C₄	—	212	8	no	—
513	C₂²×C₄	C₂×C₄×D₅₃	1	8	yes	complemented
514	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
515	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
516	C₂²×C₄	C₂³×D₅₃	1	16	yes	—
517	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
518	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
519	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
520	C₂²×C₄	C₂³×D₅₃	1	16	yes	—
521	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
522	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
523	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
524	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
525	C₄⋊C₄	—	53	32	no	—
526	C₄⋊C₄	—	53	16	no	—
527	C₄⋊C₄	—	53	8	no	—
528	C₄⋊C₄	—	53	16	no	—
529	C₄⋊C₄	—	53	8	no	—
530	C₄⋊C₄	C₂³×D₅₃	1	16	yes	—
531	C₂²⋊C₄	—	53	16	no	—
532	C₂²⋊C₄	—	53	32	no	—
533	C₂²⋊C₄	—	53	32	no	—
534	C₂²⋊C₄	—	53	16	no	—
535	C₂²⋊C₄	—	53	16	no	—
536	C₂²⋊C₄	C₂³×D₅₃	1	32	yes	—
537	C₄²	—	53	16	no	—
538	C₄²	—	53	32	no	—
539	C₄²	—	53	16	no	—
540	C₄²	—	53	16	no	—
541	C₄²	C₂³×D₅₃	1	8	yes	—
542	C₄²	C₂³×D₅₃	1	8	yes	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	8	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	8	no	—
547	C₂³	—	4	8	no	—
548	C₂³	—	4	32	no	—
549	C₂³	—	4	8	no	—
550	C₂³	—	53	16	no	—
551	C₂³	—	53	8	no	—
552	C₂³	—	53	64	no	—
553	C₂³	—	106	8	no	—
554	C₂³	—	106	8	no	—
555	C₂³	—	212	16	no	—
556	C₂³	—	212	64	no	—
557	C₂³	—	212	16	no	—
558	C₂³	C₂²×C₄×D₅₃	1	16	yes	—
559	C₂³	C₂²×C₄×D₅₃	1	4	yes	—
560	C₂³	C₂²×C₄×D₅₃	1	32	yes	complemented
561	C₂³	C₂⁴×D₅₃	1	2	yes	—
562	C₂³	C₂⁴×D₅₃	1	8	yes	—
563	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
564	Q₈	—	53	32	no	—
565	D₄	—	53	128	no	—
566	D₄	—	53	64	no	—
567	D₄	—	53	32	no	—
568	D₄	C₂²×C₄×D₅₃	1	64	yes	complemented
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	32	no	—
574	C₂×C₄	—	4	16	no	—
575	C₂×C₄	—	4	8	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	53	16	no	—
578	C₂×C₄	—	53	64	no	—
579	C₂×C₄	—	53	8	no	—
580	C₂×C₄	—	53	64	no	—
581	C₂×C₄	—	53	8	no	—
582	C₂×C₄	—	53	8	no	—
583	C₂×C₄	—	106	8	no	—
584	C₂×C₄	—	106	8	no	—
585	C₂×C₄	—	106	32	no	—
586	C₂×C₄	—	212	16	no	—
587	C₂×C₄	—	212	32	no	—
588	C₂×C₄	—	212	16	no	—
589	C₂×C₄	—	212	16	no	—
590	C₂×C₄	C₂²×C₄×D₅₃	1	8	yes	—
591	C₂×C₄	C₂²×C₄×D₅₃	1	16	yes	complemented
592	C₂×C₄	#13133262	1	4	yes	direct product factor
593	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
594	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
595	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
596	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
597	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
598	C₂²	—	2	8	no	—
599	C₂²	—	2	32	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	8	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	8	no	—
604	C₂²	—	4	32	no	—
605	C₂²	—	53	16	no	—
606	C₂²	—	106	32	no	—
607	C₂²	—	106	8	no	—
608	C₂²	—	106	8	no	—
609	C₂²	—	212	64	no	—
610	C₂²	C₂³×C₄×D₅₃	1	16	yes	—
611	C₂²	C₂³×C₄×D₅₃	1	4	yes	—
612	C₂²	C₂³×C₄×D₅₃	1	2	yes	—
613	C₂²	C₂×#13133262	1	2	yes	—
614	C₂²	#16811459	1	2	yes	—
615	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	2	8	no	—
618	C₄	—	2	4	no	—
619	C₄	—	53	16	no	—
620	C₄	—	106	8	no	—
621	C₄	—	106	8	no	—
622	C₄	C₂³×C₄×D₅₃	1	8	yes	—
623	C₄	C₂×#13133262	1	4	yes	direct product factor
624	C₂	—	2	4	no	—
625	C₂	—	2	16	no	—
626	C₂	—	106	16	no	—
627	C₂	C₄×#13133262	1	4	yes	direct product factor
628	C₂	C₂⁴×C₄×D₅₃	1	1	yes	characteristic
629	C₂	C₂²×#13133262	1	1	yes	characteristic
630	C₂	C₂×#16811459	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₅₃
commutator	C₂×C₅₃	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂²×C₄×D₄×C₅₃	C₂
socle	C₂³×C₅₃	C₂⁵
prime radical	C₂²×#13133262	C₂
cosocle	C₂²×C₅₃	C₂⁶
hypercenter	C₂²×C₄×D₄	D₅₃
hypocenter	C₅₃	C₂×C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₄×#13133262	C₂	direct (N × H)
3. C₂×#16811104	C₂	semidirect
4. C₂×#16811102	C₂	semidirect
5. C₂×#16811098	C₂	semidirect
6. C₂×#16811096	C₂	semidirect
7. C₂×#16811095	C₂	semidirect
8. C₂×C₄×#11719945	C₂	semidirect
9. C₂×C₄×#11719947	C₂	semidirect
10. C₂²×C₄×C₂²⋊D₅₃	C₂	semidirect
11. C₂×C₄×D₄×D₅₃	C₂	semidirect
12. C₂²×C₄×D₄×C₅₃	C₂	semidirect
13. C₂×#13133262	C₄	direct (N × H)
19. C₂³×C₄×D₅₃	C₂²	semidirect
20. #16811104	C₂²	semidirect
21. #16811102	C₂²	semidirect
22. #16811098	C₂²	semidirect
23. #16811096	C₂²	semidirect
24. #16811095	C₂²	semidirect
25. C₄×#11719945	C₂²	semidirect
26. C₄×#11719947	C₂²	semidirect
27. C₂×C₄×Dic₁₀₆	C₂²	semidirect
28. C₂×C₄×Dic₁₀₆	C₂²	semidirect
29. C₂×#13133182	C₂²	semidirect
30. C₂×C₄×D₂₁₂	C₂²	semidirect
31. C₂×C₄×D₂₁₂	C₂²	semidirect
32. C₂×D₄×Dic₅₃	C₂²	semidirect
33. C₂×D₄×Dic₅₃	C₂²	semidirect
34. C₂×#13133179	C₂²	semidirect
35. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
36. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
37. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
38. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
39. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
40. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
41. C₂×#13133177	C₂²	semidirect
42. C₂×#13133177	C₂²	semidirect
43. C₄×D₄×D₅₃	C₂²	semidirect
44. C₂×#13133176	C₂²	semidirect
45. C₂×#13133175	C₂²	semidirect
46. C₂×#13133174	C₂²	semidirect
47. C₂×#13133173	C₂²	semidirect
48. C₂²×#11719919	C₂²	semidirect
49. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
50. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
51. C₂²×#11719921	C₂²	semidirect
52. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
53. C₂²×C₄×Dic₅₃	C₂²	semidirect
54. C₂×C₄²×D₅₃	C₂²	semidirect
56. C₂⁴×C₄×C₅₃	C₂²	semidirect
57. C₂×C₄×D₄×C₅₃	C₂²	semidirect
58. C₂×C₄×D₄×C₅₃	C₂²	semidirect
59. C₂×C₄×D₄×C₅₃	C₂²	semidirect
60. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
61. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
62. C₂²×C₄²×C₅₃	C₂²	semidirect
64. #13133262	C₂×C₄	direct (N × H)
65. C₂×#11719945	C₂×C₄	semidirect
67. C₂×#11719947	C₂×C₄	semidirect
71. C₂²×C₂²⋊D₅₃	C₂×C₄	semidirect
75. C₂×D₄×D₅₃	C₂×C₄	semidirect
85. C₂²×C₄×D₅₃	C₂³	semidirect
86. C₄×Dic₁₀₆	C₂³	semidirect
87. C₄×Dic₁₀₆	C₂³	semidirect
88. #13133182	C₂³	semidirect
89. C₄×D₂₁₂	C₂³	semidirect
90. C₄×D₂₁₂	C₂³	semidirect
91. D₄×Dic₅₃	C₂³	semidirect
92. D₄×Dic₅₃	C₂³	semidirect
93. #13133179	C₂³	semidirect
94. C₄×C₂²⋊D₅₃	C₂³	semidirect
95. C₄×C₂²⋊D₅₃	C₂³	semidirect
96. C₄×C₂²⋊D₅₃	C₂³	semidirect
97. C₄×C₂²⋊D₅₃	C₂³	semidirect
98. C₄×C₂²⋊D₅₃	C₂³	semidirect
99. #13133177	C₂³	semidirect
100. #13133177	C₂³	semidirect
101. #13133176	C₂³	semidirect
102. #13133175	C₂³	semidirect
103. #13133174	C₂³	semidirect
104. #13133173	C₂³	semidirect
110. C₂×#11719919	C₂³	semidirect
111. C₄⋊C₄×D₅₃	C₂³	semidirect
114. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
118. C₂×#11719921	C₂³	semidirect
119. C₂²⋊C₄×D₅₃	C₂³	semidirect
124. C₂×C₄×Dic₅₃	C₂³	semidirect
125. C₄²×D₅₃	C₂³	semidirect
127. C₂²×D₄×C₅₃	C₂×C₄	semidirect
137. C₂³×C₄×C₅₃	C₂³	semidirect
138. C₄×D₄×C₅₃	C₂³	semidirect
139. C₄×D₄×C₅₃	C₂³	semidirect
141. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
143. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
146. C₂×C₄²×C₅₃	C₂³	semidirect
149. C₂⁴×C₅₃	C₂²×C₄	semidirect
155. C₂³×D₅₃	C₂²×C₄	semidirect
158. C₂×D₄×C₅₃	C₂²×C₄	semidirect
159. C₂×D₄×C₅₃	C₂²×C₄	semidirect
167. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
179. C₂×C₂²⋊D₅₃	C₂²×C₄	semidirect
180. C₂×C₂²⋊D₅₃	C₂²×C₄	semidirect
181. C₂×C₂²⋊D₅₃	C₂²×C₄	semidirect
186. C₂²×Dic₅₃	C₂²×C₄	semidirect
193. #11719947	C₂²×C₄	semidirect
194. D₄×D₅₃	C₂²×C₄	semidirect
195. #11719945	C₂²×C₄	semidirect
196. C₂×D₂₁₂	C₂²×C₄	semidirect
202. C₂×C₄×D₅₃	C₂²×C₄	semidirect
207. C₂×Dic₁₀₆	C₂²×C₄	semidirect
236. C₂³×C₅₃	C₂³×C₄	semidirect
246. C₂²×D₅₃	C₂³×C₄	semidirect
248. D₄×C₅₃	C₂³×C₄	semidirect
258. C₂×C₄×C₅₃	C₂³×C₄	semidirect
259. C₂×C₄×C₅₃	H(5,𝔽₂)	semidirect
265. C₂²⋊D₅₃	C₂³×C₄	semidirect
266. C₂²⋊D₅₃	C₂³×C₄	semidirect
272. C₂×Dic₅₃	C₂³×C₄	semidirect
276. D₂₁₂	C₂³×C₄	semidirect
280. C₄×D₅₃	C₂³×C₄	semidirect
281. Dic₁₀₆	C₂³×C₄	semidirect
305. C₄×C₅₃	C₂×H(5,𝔽₂)	semidirect
320. C₂²×C₄×D₄	D₅₃	semidirect
323. C₂×C₅₃	C₄×H(5,𝔽₂)	semidirect
336. C₂⁴×C₄	C₂×D₅₃	semidirect
361. C₂×C₄×D₄	C₂×D₅₃	semidirect
362. C₂×C₄×D₄	C₂×D₅₃	semidirect
363. C₂×C₄×D₄	C₂×D₅₃	semidirect
370. C₂²×C₄⋊C₄	C₂×D₅₃	semidirect
374. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
377. C₂²×C₄²	C₂×D₅₃	semidirect
378. C₅₃	C₂×C₄×H(5,𝔽₂)	semidirect
394. C₂²×D₄	C₄×D₅₃	semidirect
413. C₂³×C₄	C₂²×D₅₃	semidirect
429. C₄×D₄	C₂²×D₅₃	semidirect
430. C₄×D₄	C₂²×D₅₃	semidirect
443. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
453. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
462. C₂×C₄²	C₂²×D₅₃	semidirect
470. C₂⁴	C₂×C₄×D₅₃	semidirect
486. C₂×D₄	C₂×C₄×D₅₃	semidirect
487. C₂×D₄	C₂×C₄×D₅₃	semidirect
513. C₂²×C₄	C₂×C₄×D₅₃	semidirect
560. C₂³	C₂²×C₄×D₅₃	semidirect
568. D₄	C₂²×C₄×D₅₃	semidirect
591. C₂×C₄	C₂²×C₄×D₅₃	semidirect
592. C₂×C₄	#13133262	direct (N × H)
623. C₄	C₂×#13133262	direct (N × H)
627. C₂	C₄×#13133262	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×#13133262	2
C₄×#13133262	2
C₂×#16811104	2
C₂×#16811102	2
C₂×#16811098	2
C₂×#16811096	2
C₂×#16811095	2
C₂×C₄×#11719945	2
C₂×C₄×#11719947	2
C₂²×C₄×C₂²⋊D₅₃	2
C₂×C₄×D₄×D₅₃	2
C₂²×C₄×D₄×C₅₃	2
C₂×C₄×H(5,𝔽₂)	53

Subgroups — C2×C4×#13133262 #28290693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#13133262 #28290693