Subgroups — C₂×#20283371 #28247844

Order 13568.

2254 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#117×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#20283371	C₂	1	16	yes	maximal, direct product factor
3	C₂×#16810684	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16810681	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16810681	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16810679	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16810678	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16810675	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16810674	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16810648	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16810648	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16810585	C₂	1	1	yes	maximal, characteristic
13	C₂×C₂²⋊C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
14	C₂×#16810580	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16810577	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
18	C₂²×#11719912	C₂²	1	1	yes	characteristic
19	C₂²×#11719912	C₂²	1	1	yes	characteristic
20	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
21	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
22	C₂×#13133176	C₂²	1	1	yes	characteristic
23	C₂×#13133175	C₄	1	1	yes	characteristic
24	C₂×#13133175	C₄	1	1	yes	characteristic
25	C₂×#13133174	C₂²	1	1	yes	characteristic
26	C₂×#13133174	C₂²	1	1	yes	characteristic
27	C₂×#13133173	C₄	1	1	yes	characteristic
28	C₂×#13133173	C₄	1	1	yes	characteristic
29	#117×D₅₃	C₄	1	8	yes	—
30	#117×D₅₃	C₂²	1	8	yes	—
31	C₂×C₄⋊C₄×D₅₃	C₄	1	1	yes	characteristic
32	C₂×C₄⋊C₄×D₅₃	C₄	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×D₅₃	C₄	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×D₅₃	C₄	1	1	yes	characteristic
35	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
37	#16810684	C₂²	1	8	yes	complemented
38	#16810681	C₂²	1	8	yes	complemented
39	#16810681	C₂²	1	8	yes	complemented
40	#16810679	C₂²	1	8	yes	complemented
41	#16810678	C₂²	1	8	yes	complemented
42	#16810675	C₂²	1	8	yes	complemented
43	#16810674	C₂²	1	8	yes	complemented
44	#16810648	C₂²	1	8	yes	complemented
45	#16810648	C₂²	1	8	yes	complemented
46	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic, complemented
48	C₂×#13133146	C₂²	1	1	yes	characteristic, complemented
49	C₂×#13133146	C₂²	1	1	yes	characteristic, complemented
50	C₂×#13133146	C₂²	1	1	yes	characteristic, complemented
51	C₂×#13133146	C₂²	1	1	yes	characteristic, complemented
52	#16810585	C₂²	1	8	yes	—
53	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
55	C₂×#13133129	C₂²	1	1	yes	characteristic
56	C₂×#13133129	C₂²	1	1	yes	characteristic
57	C₂×#13133129	C₂²	1	1	yes	characteristic
58	C₂×#13133129	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×D₅₃	C₂²	1	8	yes	—
60	#16810580	C₂²	1	8	yes	complemented
61	#16810577	C₂²	1	8	yes	complemented
62	C₂×#13133128	C₂²	1	1	yes	characteristic, complemented
63	C₂×#13133127	C₂²	1	1	yes	characteristic, complemented
64	C₂×#13133127	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×#88322	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
69	C₅₃×#433	C₂²	1	8	yes	complemented
70	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
73	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
74	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
76	C₂⁴×D₅₃	C₂×C₄	1	1	yes	characteristic
77	C₂³×Dic₅₃	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₄×D₅₃	—	2	4	no	—
79	C₂²×C₄×D₅₃	—	2	4	no	—
80	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₄×D₅₃	C₂×C₄	1	4	yes	—
84	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
89	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
90	C₂×#11719912	—	2	4	no	—
91	C₂×#11719912	—	2	4	no	—
92	C₂×#11719912	C₂³	1	4	yes	—
93	C₂×#11719912	C₂³	1	4	yes	—
94	C₂²×#88322	C₂³	1	1	yes	characteristic
95	C₂²×#88322	C₂³	1	1	yes	characteristic
96	C₂²×#88322	C₂³	1	1	yes	characteristic
97	C₂²×#88322	C₂³	1	1	yes	characteristic
98	C₂×C₈×D₅₃	—	2	4	no	—
99	C₂×C₈×D₅₃	—	2	4	no	—
100	C₂×C₈×D₅₃	C₂³	1	4	yes	—
101	C₂×C₈×D₅₃	C₂³	1	4	yes	—
102	#13133176	C₂×C₄	1	4	yes	—
103	#13133176	C₂³	1	4	yes	—
104	#13133175	C₂×C₄	1	8	yes	—
105	#13133175	C₂×C₄	1	8	yes	—
106	#13133174	C₂×C₄	1	4	yes	—
107	#13133174	C₂×C₄	1	4	yes	—
108	#13133174	C₂³	1	4	yes	—
109	#13133174	C₂³	1	4	yes	—
110	#13133173	C₂×C₄	1	8	yes	—
111	#13133173	C₂×C₄	1	8	yes	—
112	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
114	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
115	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
116	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
117	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
118	C₄⋊C₄×D₅₃	C₂×C₄	1	8	yes	—
119	C₄⋊C₄×D₅₃	C₂×C₄	1	8	yes	—
120	C₂×C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
122	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
123	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
124	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
125	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
126	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	—
127	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	—
128	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
129	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
130	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
131	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
132	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
133	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
134	C₄²×D₅₃	C₂×C₄	1	4	yes	—
135	C₄²×D₅₃	C₂×C₄	1	4	yes	—
136	C₄²×D₅₃	C₂³	1	4	yes	—
137	C₄²×D₅₃	C₂³	1	4	yes	—
138	C₄⋊#88322	C₂³	1	4	yes	complemented
139	C₄⋊#88322	C₂³	1	4	yes	complemented
140	#13133146	C₂³	1	4	yes	complemented
141	#13133146	C₂³	1	4	yes	complemented
142	#13133146	C₂³	1	4	yes	complemented
143	#13133146	C₂³	1	4	yes	complemented
144	C₂²⋊#88322	C₂³	1	4	yes	—
145	C₂²⋊#88322	C₂³	1	4	yes	—
146	#13133129	C₂³	1	4	yes	—
147	#13133129	C₂³	1	4	yes	—
148	#13133129	C₂³	1	4	yes	—
149	#13133129	C₂³	1	4	yes	—
150	#13133128	C₂³	1	4	yes	complemented
151	#13133127	C₂³	1	4	yes	complemented
152	#13133127	C₂³	1	4	yes	complemented
153	C₄×#88322	C₂³	1	4	yes	complemented
154	C₈×Dic₅₃	C₂³	1	4	yes	complemented
155	C₈×Dic₅₃	C₂³	1	4	yes	complemented
156	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
161	#117×C₅₃	C₂×C₄	1	4	yes	—
162	#117×C₅₃	C₂³	1	4	yes	—
163	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
167	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
169	C₄⋊C₈×C₅₃	C₂³	1	4	yes	complemented
170	C₄⋊C₈×C₅₃	C₂³	1	4	yes	complemented
171	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
172	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
173	#97×C₅₃	C₂³	1	4	yes	complemented
174	C₄×C₈×C₅₃	C₂³	1	4	yes	complemented
175	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
176	C₂³×D₅₃	—	2	4	no	—
177	C₂³×D₅₃	—	2	4	no	—
178	C₂³×D₅₃	—	4	2	no	—
179	C₂³×D₅₃	C₂²×C₄	1	4	yes	—
180	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
181	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₅₃	—	2	2	no	—
183	C₂²×C₄×C₅₃	—	2	2	no	—
184	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
190	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
192	C₂²×Dic₅₃	—	2	4	no	—
193	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
194	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
195	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
196	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
197	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
198	C₂²×Dic₅₃	C₂²×C₄	1	4	yes	—
199	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₄×D₅₃	—	2	4	no	—
201	C₂×C₄×D₅₃	—	2	4	no	—
202	C₂×C₄×D₅₃	—	2	4	no	—
203	C₂×C₄×D₅₃	—	2	2	no	—
204	C₂×C₄×D₅₃	—	2	2	no	—
205	C₂×C₄×D₅₃	—	2	4	no	—
206	C₂×C₄×D₅₃	—	2	16	no	—
207	C₂×C₄×D₅₃	—	2	8	no	—
208	C₂×C₄×D₅₃	—	2	8	no	—
209	C₂×C₄×D₅₃	—	4	2	no	—
210	C₂×C₄×D₅₃	—	4	2	no	—
211	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
212	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
213	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
214	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
215	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
216	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
217	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
218	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
219	C₂×C₄×D₅₃	#41	1	4	yes	—
220	C₂×C₄×D₅₃	#41	1	4	yes	—
221	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
222	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
223	C₂×C₈×C₅₃	—	2	2	no	—
224	C₂×C₈×C₅₃	—	2	2	no	—
225	C₂×C₈×C₅₃	—	2	2	no	—
226	C₂×C₈×C₅₃	—	2	2	no	—
227	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
228	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
229	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
230	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
231	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
232	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
233	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
234	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
235	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
236	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
237	C₄²×C₅₃	C₂⁴	1	2	yes	—
238	C₄²×C₅₃	C₂⁴	1	2	yes	—
239	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
240	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
241	#11719921	C₂²×C₄	1	4	yes	—
242	#11719921	C₂²×C₄	1	4	yes	—
243	#11719921	C₂²×C₄	1	4	yes	—
244	#11719921	C₂²×C₄	1	4	yes	—
245	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
246	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
247	#11719919	C₂²×C₄	1	4	yes	—
248	#11719919	C₂²×C₄	1	4	yes	—
249	#11719919	C₂²×C₄	1	4	yes	—
250	#11719919	C₂²×C₄	1	4	yes	—
251	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
252	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
253	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
254	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
255	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
256	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
257	C₄×Dic₅₃	C₂⁴	1	2	yes	—
258	C₄×Dic₅₃	C₂⁴	1	2	yes	—
259	C₂×#88322	—	2	2	no	—
260	C₂×#88322	—	2	2	no	—
261	C₂×#88322	—	2	2	no	—
262	C₂×#88322	—	2	2	no	—
263	C₂×#88322	C₂⁴	1	2	yes	—
264	C₂×#88322	C₂⁴	1	2	yes	—
265	C₂×#88322	C₂⁴	1	2	yes	—
266	C₂×#88322	C₂⁴	1	2	yes	—
267	#11719912	—	2	8	no	—
268	#11719912	—	2	8	no	—
269	C₈×D₅₃	—	2	8	no	—
270	C₈×D₅₃	—	2	8	no	—
271	C₂³×C₅₃	—	2	2	no	—
272	C₂³×C₅₃	—	2	2	no	—
273	C₂³×C₅₃	—	2	2	no	—
274	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
275	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
276	C₂²×D₅₃	—	2	2	no	—
277	C₂²×D₅₃	—	2	2	no	—
278	C₂²×D₅₃	—	2	2	no	—
279	C₂²×D₅₃	—	2	2	no	—
280	C₂²×D₅₃	—	2	8	no	—
281	C₂²×D₅₃	—	2	8	no	—
282	C₂²×D₅₃	—	4	4	no	—
283	C₂²×D₅₃	—	4	16	no	—
284	C₂²×D₅₃	#117	1	4	yes	—
285	C₂²×D₅₃	#131	1	4	yes	—
286	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
287	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
288	C₂×C₄×C₅₃	—	2	2	no	—
289	C₂×C₄×C₅₃	—	2	2	no	—
290	C₂×C₄×C₅₃	—	2	2	no	—
291	C₂×C₄×C₅₃	—	2	2	no	—
292	C₂×C₄×C₅₃	—	2	2	no	—
293	C₂×C₄×C₅₃	—	2	4	no	—
294	C₂×C₄×C₅₃	—	2	2	no	—
295	C₂×C₄×C₅₃	—	2	2	no	—
296	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
297	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
298	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
299	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
300	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
301	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
302	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
303	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
304	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
305	C₂×Dic₅₃	—	2	2	no	—
306	C₂×Dic₅₃	—	2	2	no	—
307	C₂×Dic₅₃	—	2	2	no	—
308	C₂×Dic₅₃	—	2	2	no	—
309	C₂×Dic₅₃	—	2	2	no	—
310	C₂×Dic₅₃	—	2	8	no	—
311	C₂×Dic₅₃	#117	1	4	yes	—
312	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
313	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
314	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
315	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
316	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
317	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
318	C₄×D₅₃	—	2	8	no	—
319	C₄×D₅₃	—	2	8	no	—
320	C₄×D₅₃	—	2	8	no	—
321	C₄×D₅₃	—	2	4	no	—
322	C₄×D₅₃	—	2	2	no	—
323	C₄×D₅₃	—	2	2	no	—
324	C₄×D₅₃	—	2	8	no	—
325	C₄×D₅₃	—	4	4	no	—
326	C₄×D₅₃	—	4	4	no	—
327	C₄×D₅₃	#117	1	8	yes	—
328	C₄×D₅₃	C₂×#41	1	4	yes	—
329	C₄×D₅₃	C₂×#41	1	4	yes	—
330	C₈×C₅₃	—	2	2	no	—
331	C₈×C₅₃	—	2	2	no	—
332	C₈×C₅₃	—	2	2	no	—
333	C₈×C₅₃	—	2	2	no	—
334	#88322	—	2	2	no	—
335	#88322	—	2	2	no	—
336	#88322	—	2	2	no	—
337	#88322	—	2	2	no	—
338	C₂×#2924	—	53	1	no	maximal, Sylow
339	C₂²×C₅₃	—	2	2	no	—
340	C₂²×C₅₃	—	2	2	no	—
341	C₂²×C₅₃	—	2	2	no	—
342	C₂²×C₅₃	—	4	4	no	—
343	C₂²×C₅₃	C₂×#117	1	2	yes	—
344	C₂²×C₅₃	C₂×#131	1	2	yes	—
345	C₂²×C₅₃	#568	1	2	yes	—
346	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
347	C₂×D₅₃	—	2	2	no	—
348	C₂×D₅₃	—	2	8	no	—
349	C₂×D₅₃	—	2	8	no	—
350	C₂×D₅₃	—	2	2	no	—
351	C₂×D₅₃	—	2	2	no	—
352	C₂×D₅₃	—	2	2	no	—
353	C₂×D₅₃	—	4	16	no	—
354	C₂×D₅₃	C₂×#117	1	4	yes	—
355	C₂×D₅₃	C₂×#131	1	4	yes	—
356	C₄×C₅₃	—	2	2	no	—
357	C₄×C₅₃	—	2	2	no	—
358	C₄×C₅₃	—	2	2	no	—
359	C₄×C₅₃	—	2	2	no	—
360	C₄×C₅₃	—	2	2	no	—
361	C₄×C₅₃	C₂×#117	1	2	yes	—
362	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
363	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
364	Dic₅₃	—	2	2	no	—
365	Dic₅₃	—	2	2	no	—
366	Dic₅₃	—	2	2	no	—
367	Dic₅₃	—	2	2	no	—
368	Dic₅₃	—	2	2	no	—
369	Dic₅₃	C₂×#117	1	4	yes	—
370	C₂²×#117	—	53	1	no	—
371	#2924	—	53	16	no	—
372	C₂×#433	—	53	1	no	—
373	C₂×#433	—	53	1	no	—
374	C₂×#433	—	53	1	no	—
375	C₂×#433	D₅₃	1	1	yes	characteristic, complemented
376	C₂×#432	—	53	1	no	—
377	C₂×#432	—	53	1	no	—
378	C₂×#431	—	53	1	no	—
379	C₂×#431	—	53	1	no	—
380	C₂×#424	—	53	1	no	—
381	C₂×#424	—	53	1	no	—
382	C₂×#407	—	53	1	no	—
383	C₂²×C₂²⋊C₈	—	53	1	no	—
384	C₂×#405	—	53	1	no	—
385	C₂×#405	—	53	1	no	—
386	C₂×C₅₃	—	4	2	no	—
387	C₂×C₅₃	#2924	1	4	yes	complemented
388	C₂×C₅₃	C₂²×#117	1	1	yes	characteristic
389	C₂×C₅₃	C₂²×#131	1	1	yes	characteristic
390	C₂×C₅₃	C₂×#568	1	1	yes	characteristic
391	D₅₃	—	2	4	no	—
392	D₅₃	—	2	4	no	—
393	C₂⁴×C₄	—	53	1	no	—
394	C₂²×M₁₆	—	53	1	no	—
395	C₂²×M₁₆	—	53	1	no	—
396	C₂³×C₈	—	53	1	no	—
397	C₂³×C₈	—	53	1	no	—
398	C₂×#117	—	53	1	no	—
399	C₂×#117	—	53	8	no	—
400	C₂×#117	—	53	8	no	—
401	C₂×#117	—	53	1	no	—
402	C₂×#117	—	53	1	no	—
403	C₂×#117	—	53	1	no	—
404	C₂×#117	—	53	1	no	—
405	C₂×#117	—	53	1	no	—
406	C₂×#117	—	53	1	no	—
407	C₂×#117	C₂×D₅₃	1	1	yes	characteristic
408	C₂²×C₄⋊C₄	—	53	1	no	—
409	C₂²×C₄⋊C₄	—	53	1	no	—
410	C₂²×C₂²⋊C₄	—	53	1	no	—
411	C₂²×C₂²⋊C₄	—	53	1	no	—
412	C₂²×C₄²	—	53	1	no	—
413	C₂²×C₄²	—	53	1	no	—
414	#433	—	53	8	no	—
415	#433	—	53	8	no	—
416	#433	—	53	8	no	—
417	#433	C₂×D₅₃	1	8	yes	complemented
418	#432	—	53	8	no	—
419	#432	—	53	8	no	—
420	#431	—	53	8	no	—
421	#431	—	53	8	no	—
422	#424	—	53	8	no	—
423	#424	—	53	8	no	—
424	C₂×C₄⋊C₈	—	53	1	no	—
425	C₂×C₄⋊C₈	—	53	1	no	—
426	C₂×C₄⋊C₈	—	53	1	no	—
427	C₂×C₄⋊C₈	—	53	1	no	—
428	C₂×C₄⋊C₈	—	53	1	no	—
429	C₂×C₄⋊C₈	—	53	1	no	—
430	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
431	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
432	#407	—	53	8	no	—
433	C₂×C₂²⋊C₈	—	53	1	no	—
434	C₂×C₂²⋊C₈	—	53	1	no	—
435	C₂×C₂²⋊C₈	—	53	1	no	—
436	C₂×C₂²⋊C₈	—	53	1	no	—
437	C₂×C₂²⋊C₈	—	53	1	no	—
438	C₂×C₂²⋊C₈	—	53	1	no	—
439	C₂×C₂²⋊C₈	—	53	8	no	—
440	C₂×C₂²⋊C₈	C₂×D₅₃	1	1	yes	characteristic
441	C₂×C₂²⋊C₈	C₂×D₅₃	1	1	yes	characteristic
442	#405	—	53	8	no	—
443	#405	—	53	8	no	—
444	C₂×#97	—	53	1	no	—
445	C₂×#97	—	53	1	no	—
446	C₂×#97	—	53	1	no	—
447	C₂×#97	C₂×D₅₃	1	1	yes	characteristic, complemented
448	C₂×C₄×C₈	—	53	1	no	—
449	C₂×C₄×C₈	—	53	1	no	—
450	C₂×C₄×C₈	—	53	1	no	—
451	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
452	C₅₃	C₂×#2924	1	1	yes	characteristic, complemented, Sylow
453	C₂⁵	—	53	1	no	—
454	C₂³×C₄	—	53	1	no	—
455	C₂³×C₄	—	53	1	no	—
456	C₂³×C₄	—	53	1	no	—
457	C₂³×C₄	—	53	1	no	—
458	C₂³×C₄	—	53	1	no	—
459	C₂³×C₄	—	53	4	no	—
460	C₂³×C₄	—	53	1	no	—
461	C₂³×C₄	—	53	4	no	—
462	C₂³×C₄	—	53	1	no	—
463	C₂³×C₄	—	53	1	no	—
464	C₂³×C₄	—	53	1	no	—
465	C₂³×C₄	—	106	4	no	—
466	C₂³×C₄	—	106	4	no	—
467	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
468	C₂×M₁₆	—	53	4	no	—
469	C₂×M₁₆	—	53	4	no	—
470	C₂×M₁₆	—	106	4	no	—
471	C₂×M₁₆	—	106	4	no	—
472	C₂²×C₈	—	53	1	no	—
473	C₂²×C₈	—	53	1	no	—
474	C₂²×C₈	—	53	1	no	—
475	C₂²×C₈	—	53	1	no	—
476	C₂²×C₈	—	53	4	no	—
477	C₂²×C₈	—	53	4	no	—
478	C₂²×C₈	—	106	4	no	—
479	C₂²×C₈	—	106	4	no	—
480	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
481	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
482	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
483	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
484	#117	—	53	4	no	—
485	#117	—	53	4	no	—
486	#117	—	53	8	no	—
487	#117	—	53	8	no	—
488	#117	—	53	8	no	—
489	#117	—	53	8	no	—
490	#117	—	53	4	no	—
491	#117	—	53	4	no	—
492	#117	—	53	4	no	—
493	#117	—	53	4	no	—
494	#117	C₄×D₅₃	1	4	yes	—
495	#117	C₂²×D₅₃	1	4	yes	—
496	C₂×C₄⋊C₄	—	53	1	no	—
497	C₂×C₄⋊C₄	—	53	1	no	—
498	C₂×C₄⋊C₄	—	53	1	no	—
499	C₂×C₄⋊C₄	—	53	1	no	—
500	C₂×C₄⋊C₄	—	53	1	no	—
501	C₂×C₄⋊C₄	—	53	1	no	—
502	C₂×C₄⋊C₄	—	53	8	no	—
503	C₂×C₄⋊C₄	—	53	8	no	—
504	C₂×C₄⋊C₄	C₄×D₅₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₄×D₅₃	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	—	53	1	no	—
507	C₂×C₂²⋊C₄	—	53	1	no	—
508	C₂×C₂²⋊C₄	—	53	1	no	—
509	C₂×C₂²⋊C₄	—	53	1	no	—
510	C₂×C₂²⋊C₄	—	53	1	no	—
511	C₂×C₂²⋊C₄	—	53	1	no	—
512	C₂×C₂²⋊C₄	—	53	8	no	—
513	C₂×C₂²⋊C₄	—	53	8	no	—
514	C₂×C₂²⋊C₄	C₄×D₅₃	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	C₄×D₅₃	1	1	yes	characteristic
516	C₂×C₄²	—	53	1	no	—
517	C₂×C₄²	—	53	1	no	—
518	C₂×C₄²	—	53	1	no	—
519	C₂×C₄²	—	53	1	no	—
520	C₂×C₄²	—	53	1	no	—
521	C₂×C₄²	—	53	1	no	—
522	C₂×C₄²	—	53	4	no	—
523	C₂×C₄²	—	53	4	no	—
524	C₂×C₄²	—	53	4	no	—
525	C₂×C₄²	—	53	4	no	—
526	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
527	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
528	C₄⋊C₈	—	53	4	no	—
529	C₄⋊C₈	—	53	4	no	—
530	C₄⋊C₈	—	53	4	no	—
531	C₄⋊C₈	—	53	4	no	—
532	C₄⋊C₈	—	53	4	no	—
533	C₄⋊C₈	—	53	4	no	—
534	C₄⋊C₈	C₂²×D₅₃	1	4	yes	complemented
535	C₄⋊C₈	C₂²×D₅₃	1	4	yes	complemented
536	C₂²⋊C₈	—	53	4	no	—
537	C₂²⋊C₈	—	53	4	no	—
538	C₂²⋊C₈	—	53	4	no	—
539	C₂²⋊C₈	—	53	4	no	—
540	C₂²⋊C₈	—	53	4	no	—
541	C₂²⋊C₈	—	53	4	no	—
542	C₂²⋊C₈	C₂²×D₅₃	1	4	yes	—
543	C₂²⋊C₈	C₂²×D₅₃	1	4	yes	—
544	#97	—	53	4	no	—
545	#97	—	53	4	no	—
546	#97	—	53	4	no	—
547	#97	C₂²×D₅₃	1	4	yes	complemented
548	C₄×C₈	—	53	4	no	—
549	C₄×C₈	—	53	4	no	—
550	C₄×C₈	—	53	4	no	—
551	C₄×C₈	C₂²×D₅₃	1	4	yes	complemented
552	C₂⁴	—	53	1	no	—
553	C₂⁴	—	53	1	no	—
554	C₂⁴	—	53	4	no	—
555	C₂⁴	—	106	4	no	—
556	C₂⁴	—	106	4	no	—
557	C₂⁴	—	212	2	no	—
558	C₂⁴	C₂×C₄×D₅₃	1	1	yes	characteristic
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	53	1	no	—
562	C₂²×C₄	—	53	2	no	—
563	C₂²×C₄	—	53	4	no	—
564	C₂²×C₄	—	53	4	no	—
565	C₂²×C₄	—	53	2	no	—
566	C₂²×C₄	—	53	1	no	—
567	C₂²×C₄	—	53	1	no	—
568	C₂²×C₄	—	53	1	no	—
569	C₂²×C₄	—	53	1	no	—
570	C₂²×C₄	—	53	1	no	—
571	C₂²×C₄	—	53	4	no	—
572	C₂²×C₄	—	53	2	no	—
573	C₂²×C₄	—	53	4	no	—
574	C₂²×C₄	—	53	4	no	—
575	C₂²×C₄	—	53	4	no	—
576	C₂²×C₄	—	53	4	no	—
577	C₂²×C₄	—	53	2	no	—
578	C₂²×C₄	—	53	4	no	—
579	C₂²×C₄	—	53	4	no	—
580	C₂²×C₄	—	106	4	no	—
581	C₂²×C₄	—	106	16	no	—
582	C₂²×C₄	—	106	8	no	—
583	C₂²×C₄	—	106	8	no	—
584	C₂²×C₄	—	106	4	no	—
585	C₂²×C₄	—	106	4	no	—
586	C₂²×C₄	—	106	4	no	—
587	C₂²×C₄	—	106	4	no	—
588	C₂²×C₄	—	106	2	no	—
589	C₂²×C₄	—	106	2	no	—
590	C₂²×C₄	—	212	2	no	—
591	C₂²×C₄	—	212	2	no	—
592	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
593	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
594	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
597	C₂²×C₄	C₂×C₄×D₅₃	1	2	yes	—
598	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
599	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
600	M₁₆	—	106	8	no	—
601	M₁₆	—	106	8	no	—
602	C₂×C₈	—	2	2	no	—
603	C₂×C₈	—	2	2	no	—
604	C₂×C₈	—	2	2	no	—
605	C₂×C₈	—	2	2	no	—
606	C₂×C₈	—	53	2	no	—
607	C₂×C₈	—	53	2	no	—
608	C₂×C₈	—	53	2	no	—
609	C₂×C₈	—	53	2	no	—
610	C₂×C₈	—	106	8	no	—
611	C₂×C₈	—	106	8	no	—
612	C₂×C₈	—	106	2	no	—
613	C₂×C₈	—	106	2	no	—
614	C₂×C₈	—	106	2	no	—
615	C₂×C₈	—	106	2	no	—
616	C₂×C₈	C₂³×D₅₃	1	2	yes	—
617	C₂×C₈	C₂³×D₅₃	1	2	yes	—
618	C₂×C₈	C₂³×D₅₃	1	2	yes	—
619	C₂×C₈	C₂³×D₅₃	1	2	yes	—
620	C₄⋊C₄	—	53	4	no	—
621	C₄⋊C₄	—	53	4	no	—
622	C₄⋊C₄	—	53	4	no	—
623	C₄⋊C₄	—	53	4	no	—
624	C₄⋊C₄	—	53	4	no	—
625	C₄⋊C₄	—	53	4	no	—
626	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
627	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
628	C₂²⋊C₄	—	53	4	no	—
629	C₂²⋊C₄	—	53	4	no	—
630	C₂²⋊C₄	—	53	4	no	—
631	C₂²⋊C₄	—	53	4	no	—
632	C₂²⋊C₄	—	53	4	no	—
633	C₂²⋊C₄	—	53	4	no	—
634	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
635	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
636	C₄²	—	53	4	no	—
637	C₄²	—	53	4	no	—
638	C₄²	—	53	4	no	—
639	C₄²	—	53	4	no	—
640	C₄²	—	53	2	no	—
641	C₄²	—	53	2	no	—
642	C₄²	—	53	2	no	—
643	C₄²	—	53	2	no	—
644	C₄²	C₂×C₄×D₅₃	1	2	yes	—
645	C₄²	C₂×C₄×D₅₃	1	2	yes	—
646	C₄²	C₂³×D₅₃	1	2	yes	—
647	C₄²	C₂³×D₅₃	1	2	yes	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	53	4	no	—
652	C₂³	—	53	4	no	—
653	C₂³	—	53	2	no	—
654	C₂³	—	53	2	no	—
655	C₂³	—	106	8	no	—
656	C₂³	—	106	8	no	—
657	C₂³	—	106	2	no	—
658	C₂³	—	106	2	no	—
659	C₂³	—	106	2	no	—
660	C₂³	—	106	2	no	—
661	C₂³	—	212	4	no	—
662	C₂³	—	212	16	no	—
663	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
664	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	53	4	no	—
674	C₂×C₄	—	53	2	no	—
675	C₂×C₄	—	53	8	no	—
676	C₂×C₄	—	53	4	no	—
677	C₂×C₄	—	53	4	no	—
678	C₂×C₄	—	53	2	no	—
679	C₂×C₄	—	53	2	no	—
680	C₂×C₄	—	53	2	no	—
681	C₂×C₄	—	53	2	no	—
682	C₂×C₄	—	53	2	no	—
683	C₂×C₄	—	106	8	no	—
684	C₂×C₄	—	106	8	no	—
685	C₂×C₄	—	106	8	no	—
686	C₂×C₄	—	106	8	no	—
687	C₂×C₄	—	106	8	no	—
688	C₂×C₄	—	106	2	no	—
689	C₂×C₄	—	106	2	no	—
690	C₂×C₄	—	106	2	no	—
691	C₂×C₄	—	106	2	no	—
692	C₂×C₄	—	106	2	no	—
693	C₂×C₄	—	106	4	no	—
694	C₂×C₄	—	106	2	no	—
695	C₂×C₄	—	106	2	no	—
696	C₂×C₄	—	212	4	no	—
697	C₂×C₄	—	212	4	no	—
698	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
699	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
700	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
701	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
702	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
703	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
704	C₂×C₄	#41×D₅₃	1	2	yes	—
705	C₂×C₄	#41×D₅₃	1	2	yes	—
706	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
707	C₈	—	2	2	no	—
708	C₈	—	2	2	no	—
709	C₈	—	2	2	no	—
710	C₈	—	2	2	no	—
711	C₈	—	106	2	no	—
712	C₈	—	106	2	no	—
713	C₈	—	106	2	no	—
714	C₈	—	106	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	4	4	no	—
719	C₂²	—	53	4	no	—
720	C₂²	—	53	4	no	—
721	C₂²	—	106	2	no	—
722	C₂²	—	106	2	no	—
723	C₂²	—	106	2	no	—
724	C₂²	—	106	2	no	—
725	C₂²	—	106	8	no	—
726	C₂²	—	106	8	no	—
727	C₂²	—	212	16	no	—
728	C₂²	#117×D₅₃	1	2	yes	—
729	C₂²	#131×D₅₃	1	2	yes	—
730	C₂²	#16811388	1	2	yes	—
731	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	2	no	—
737	C₄	—	53	4	no	—
738	C₄	—	106	2	no	—
739	C₄	—	106	2	no	—
740	C₄	—	106	2	no	—
741	C₄	—	106	2	no	—
742	C₄	—	106	2	no	—
743	C₄	#117×D₅₃	1	2	yes	—
744	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
745	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
746	C₂	—	4	2	no	—
747	C₂	—	106	4	no	—
748	C₂	—	106	4	no	—
749	C₂	#20283371	1	4	yes	direct product factor
750	C₂	C₂×#117×D₅₃	1	1	yes	characteristic
751	C₂	C₂×#131×D₅₃	1	1	yes	characteristic
752	C₂	C₂×#16811388	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₂×C₅₃×#433	C₂
socle	C₂³×C₅₃	C₂³×C₄
prime radical	C₂⁴×D₅₃	C₂×C₄
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	C₂×#433	D₅₃
hypocenter	C₅₃	C₂×#2924
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#433

Complements

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

N	H ≅ G/N	type
2. #20283371	C₂	direct (N × H)
3. C₂×#16810684	C₂	semidirect
4. C₂×#16810681	C₂	semidirect
5. C₂×#16810681	C₂	semidirect
6. C₂×#16810679	C₂	semidirect
7. C₂×#16810678	C₂	semidirect
8. C₂×#16810675	C₂	semidirect
9. C₂×#16810674	C₂	semidirect
10. C₂×#16810648	C₂	semidirect
11. C₂×#16810648	C₂	semidirect
14. C₂×#16810580	C₂	semidirect
15. C₂×#16810577	C₂	semidirect
16. C₂×C₅₃×#433	C₂	semidirect
37. #16810684	C₂²	semidirect
38. #16810681	C₂²	semidirect
39. #16810681	C₂²	semidirect
40. #16810679	C₂²	semidirect
41. #16810678	C₂²	semidirect
42. #16810675	C₂²	semidirect
43. #16810674	C₂²	semidirect
44. #16810648	C₂²	semidirect
45. #16810648	C₂²	semidirect
46. C₂×C₄⋊#88322	C₂²	semidirect
47. C₂×C₄⋊#88322	C₂²	semidirect
48. C₂×#13133146	C₂²	semidirect
49. C₂×#13133146	C₂²	semidirect
50. C₂×#13133146	C₂²	semidirect
51. C₂×#13133146	C₂²	semidirect
60. #16810580	C₂²	semidirect
61. #16810577	C₂²	semidirect
62. C₂×#13133128	C₂²	semidirect
63. C₂×#13133127	C₂²	semidirect
64. C₂×#13133127	C₂²	semidirect
65. C₂×C₄×#88322	C₂²	semidirect
66. C₂×C₈×Dic₅₃	C₂²	semidirect
67. C₂×C₈×Dic₅₃	C₂²	semidirect
69. C₅₃×#433	C₂²	semidirect
70. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
71. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
74. C₂×#97×C₅₃	C₂²	semidirect
75. C₂×C₄×C₈×C₅₃	C₂²	semidirect
138. C₄⋊#88322	C₂³	semidirect
139. C₄⋊#88322	C₂³	semidirect
140. #13133146	C₂³	semidirect
141. #13133146	C₂³	semidirect
142. #13133146	C₂³	semidirect
143. #13133146	C₂³	semidirect
150. #13133128	C₂³	semidirect
151. #13133127	C₂³	semidirect
152. #13133127	C₂³	semidirect
153. C₄×#88322	C₂³	semidirect
154. C₈×Dic₅₃	C₂³	semidirect
155. C₈×Dic₅₃	C₂³	semidirect
169. C₄⋊C₈×C₅₃	C₂³	semidirect
170. C₄⋊C₈×C₅₃	C₂³	semidirect
173. #97×C₅₃	C₂³	semidirect
174. C₄×C₈×C₅₃	C₂³	semidirect
375. C₂×#433	D₅₃	semidirect
387. C₂×C₅₃	#2924	semidirect
417. #433	C₂×D₅₃	semidirect
430. C₂×C₄⋊C₈	C₂×D₅₃	semidirect
431. C₂×C₄⋊C₈	C₂×D₅₃	semidirect
447. C₂×#97	C₂×D₅₃	semidirect
451. C₂×C₄×C₈	C₂×D₅₃	semidirect
452. C₅₃	C₂×#2924	semidirect
534. C₄⋊C₈	C₂²×D₅₃	semidirect
535. C₄⋊C₈	C₂²×D₅₃	semidirect
547. #97	C₂²×D₅₃	semidirect
551. C₄×C₈	C₂²×D₅₃	semidirect
749. C₂	#20283371	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#117×D₅₃	2
#20283371	2
C₂×#16810684	2
C₂×#16810681	2
C₂×#16810679	2
C₂×#16810678	2
C₂×#16810675	2
C₂×#16810674	2
C₂×#16810648	2
C₂×#16810585	2
C₂×C₂²⋊C₈×D₅₃	2
C₂×#16810580	2
C₂×#16810577	2
C₂×C₅₃×#433	2
C₂×#2924	53

Subgroups — C2×#20283371 #28247844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20283371 #28247844