Subgroups — C₂×C₅₃×#3350 #27268754

Order 13568.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#553	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3350	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
20	C₅₃×#556	—	2	4	no	—
21	C₅₃×#556	C₂²	1	8	yes	complemented
22	C₅₃×#553	—	2	4	no	—
23	C₅₃×#553	C₂²	1	8	yes	—
24	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#126×C₅₃	—	2	1	no	—
26	C₂×#126×C₅₃	—	2	1	no	—
27	C₂×#126×C₅₃	—	2	1	no	—
28	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#124×C₅₃	—	2	1	no	—
30	C₂×#123×C₅₃	—	2	1	no	—
31	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#121×C₅₃	—	2	1	no	—
34	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₅₃	—	2	1	no	—
37	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₅₃	—	2	1	no	—
39	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#501	C₂²	1	8	yes	complemented
46	C₅₃×#485	C₂²	1	8	yes	complemented
47	C₅₃×#483	C₂²	1	8	yes	complemented
48	C₅₃×#482	C₂²	1	8	yes	complemented
49	C₅₃×#482	C₂²	1	8	yes	complemented
50	C₅₃×#479	C₂²	1	8	yes	complemented
51	C₅₃×#476	C₂²	1	8	yes	complemented
52	C₅₃×#468	C₂²	1	8	yes	complemented
53	C₅₃×#465	C₂²	1	8	yes	complemented
54	C₅₃×#440	C₂²	1	8	yes	complemented
55	C₅₃×#435	C₂²	1	8	yes	complemented
56	C₅₃×#428	C₂²	1	8	yes	complemented
57	C₅₃×#427	C₂²	1	8	yes	complemented
58	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
61	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
62	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
63	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
66	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
67	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
68	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
69	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
70	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
71	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
72	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
73	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
75	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
76	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₅₃	—	2	1	no	—
78	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₅₃	—	2	1	no	—
80	C₂²×D₄×C₅₃	—	2	1	no	—
81	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₅₃	—	2	1	no	—
84	C₂³×C₄×C₅₃	—	2	1	no	—
85	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
87	C₂×SD₁₆×C₅₃	—	2	4	no	—
88	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
89	C₂×M₁₆×C₅₃	—	2	4	no	—
90	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
91	C₂²×C₈×C₅₃	—	2	4	no	—
92	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
94	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
97	C₄⋊Q₈×C₅₃	—	2	2	no	—
98	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
99	#126×C₅₃	—	2	8	no	—
100	#126×C₅₃	—	2	8	no	—
101	#126×C₅₃	—	2	8	no	—
102	#125×C₅₃	—	2	2	no	—
103	#125×C₅₃	C₂³	1	4	yes	—
104	#124×C₅₃	—	2	8	no	—
105	#123×C₅₃	—	2	8	no	—
106	C₂²⋊Q₈×C₅₃	—	2	2	no	—
107	C₂²⋊Q₈×C₅₃	—	2	2	no	—
108	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
109	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
110	#121×C₅₃	—	2	8	no	—
111	#121×C₅₃	—	2	2	no	—
112	#121×C₅₃	—	2	2	no	—
113	#121×C₅₃	C₂³	1	4	yes	—
114	#121×C₅₃	C₂³	1	4	yes	—
115	C₄×Q₈×C₅₃	—	2	8	no	—
116	C₄×Q₈×C₅₃	—	2	2	no	—
117	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
118	C₄×D₄×C₅₃	—	2	8	no	—
119	C₄×D₄×C₅₃	—	2	2	no	—
120	C₄×D₄×C₅₃	D₄	1	4	yes	—
121	C₄×D₄×C₅₃	C₂³	1	4	yes	—
122	C₄×D₄×C₅₃	C₂³	1	4	yes	—
123	#117×C₅₃	—	2	2	no	—
124	#117×C₅₃	—	2	2	no	—
125	#117×C₅₃	—	2	2	no	—
126	#117×C₅₃	C₂³	1	4	yes	—
127	#117×C₅₃	C₂³	1	4	yes	—
128	#117×C₅₃	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
130	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
131	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
132	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
133	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
134	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
135	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
136	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
137	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
155	C₂×C₄²×C₅₃	—	2	1	no	—
156	C₂×C₄²×C₅₃	—	2	1	no	—
157	C₂×C₄²×C₅₃	—	2	1	no	—
158	C₂×C₄²×C₅₃	—	2	1	no	—
159	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
160	#107×C₅₃	C₂³	1	4	yes	—
161	#107×C₅₃	C₂³	1	4	yes	—
162	#107×C₅₃	C₂³	1	4	yes	—
163	#107×C₅₃	C₂³	1	4	yes	—
164	#106×C₅₃	C₂³	1	4	yes	—
165	#106×C₅₃	C₂³	1	4	yes	—
166	#106×C₅₃	C₂³	1	4	yes	—
167	#106×C₅₃	C₂³	1	4	yes	—
168	#106×C₅₃	C₂³	1	4	yes	—
169	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
170	#103×C₅₃	C₂³	1	4	yes	—
171	#103×C₅₃	C₂³	1	4	yes	—
172	#103×C₅₃	C₂³	1	4	yes	—
173	#102×C₅₃	C₂³	1	4	yes	—
174	#102×C₅₃	C₂³	1	4	yes	—
175	#102×C₅₃	C₂³	1	4	yes	—
176	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
177	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
178	#97×C₅₃	C₂³	1	4	yes	—
179	C₂⁴×C₅₃	—	2	1	no	—
180	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
181	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
182	C₂×Q₈×C₅₃	—	2	1	no	—
183	C₂×Q₈×C₅₃	—	2	4	no	—
184	C₂×Q₈×C₅₃	—	2	2	no	—
185	C₂×Q₈×C₅₃	—	2	2	no	—
186	C₂×Q₈×C₅₃	—	4	4	no	—
187	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
188	C₂×D₄×C₅₃	—	2	4	no	—
189	C₂×D₄×C₅₃	—	2	4	no	—
190	C₂×D₄×C₅₃	—	2	1	no	—
191	C₂×D₄×C₅₃	—	2	2	no	—
192	C₂×D₄×C₅₃	—	2	2	no	—
193	C₂×D₄×C₅₃	—	4	2	no	—
194	C₂×D₄×C₅₃	—	4	4	no	—
195	C₂×D₄×C₅₃	—	8	2	no	—
196	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
197	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₅₃	—	2	2	no	—
199	C₂²×C₄×C₅₃	—	2	2	no	—
200	C₂²×C₄×C₅₃	—	2	2	no	—
201	C₂²×C₄×C₅₃	—	2	2	no	—
202	C₂²×C₄×C₅₃	—	2	1	no	—
203	C₂²×C₄×C₅₃	—	2	1	no	—
204	C₂²×C₄×C₅₃	—	2	1	no	—
205	C₂²×C₄×C₅₃	—	2	1	no	—
206	C₂²×C₄×C₅₃	—	2	1	no	—
207	C₂²×C₄×C₅₃	—	2	1	no	—
208	C₂²×C₄×C₅₃	—	2	1	no	—
209	C₂²×C₄×C₅₃	—	2	4	no	—
210	C₂²×C₄×C₅₃	—	2	4	no	—
211	C₂²×C₄×C₅₃	—	8	2	no	—
212	C₂²×C₄×C₅₃	—	8	2	no	—
213	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
215	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
222	SD₁₆×C₅₃	—	2	8	no	—
223	M₁₆×C₅₃	—	2	8	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	—	2	8	no	—
228	C₂×C₈×C₅₃	#41	1	4	yes	—
229	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
230	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
231	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
232	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
233	C₄⋊C₄×C₅₃	—	2	1	no	—
234	C₄⋊C₄×C₅₃	—	2	1	no	—
235	C₄⋊C₄×C₅₃	—	2	4	no	—
236	C₄⋊C₄×C₅₃	—	2	4	no	—
237	C₄⋊C₄×C₅₃	—	2	4	no	—
238	C₄⋊C₄×C₅₃	—	2	4	no	—
239	C₄⋊C₄×C₅₃	—	2	4	no	—
240	C₄⋊C₄×C₅₃	—	2	4	no	—
241	C₄⋊C₄×C₅₃	—	2	4	no	—
242	C₄⋊C₄×C₅₃	—	2	1	no	—
243	C₄⋊C₄×C₅₃	—	2	1	no	—
244	C₄⋊C₄×C₅₃	—	2	1	no	—
245	C₄⋊C₄×C₅₃	—	2	1	no	—
246	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
247	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
248	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
249	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
250	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
252	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
253	C₂²⋊C₄×C₅₃	—	2	4	no	—
254	C₂²⋊C₄×C₅₃	—	2	4	no	—
255	C₂²⋊C₄×C₅₃	—	2	4	no	—
256	C₂²⋊C₄×C₅₃	—	2	4	no	—
257	C₂²⋊C₄×C₅₃	—	2	4	no	—
258	C₂²⋊C₄×C₅₃	—	2	4	no	—
259	C₂²⋊C₄×C₅₃	—	2	4	no	—
260	C₂²⋊C₄×C₅₃	—	2	4	no	—
261	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
262	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
263	C₄²×C₅₃	—	2	4	no	—
264	C₄²×C₅₃	—	2	4	no	—
265	C₄²×C₅₃	—	2	4	no	—
266	C₄²×C₅₃	—	2	4	no	—
267	C₄²×C₅₃	C₂×D₄	1	2	yes	—
268	C₄²×C₅₃	C₂⁴	1	2	yes	—
269	C₂³×C₅₃	—	2	2	no	—
270	C₂³×C₅₃	—	2	2	no	—
271	C₂³×C₅₃	—	2	2	no	—
272	C₂³×C₅₃	—	2	2	no	—
273	C₂³×C₅₃	—	2	2	no	—
274	C₂³×C₅₃	—	2	2	no	—
275	C₂³×C₅₃	—	2	2	no	—
276	C₂³×C₅₃	—	4	2	no	—
277	C₂³×C₅₃	—	4	2	no	—
278	C₂³×C₅₃	—	4	2	no	—
279	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
280	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
281	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
282	Q₈×C₅₃	—	2	2	no	—
283	Q₈×C₅₃	—	2	2	no	—
284	Q₈×C₅₃	—	4	8	no	—
285	Q₈×C₅₃	—	4	2	no	—
286	D₄×C₅₃	—	2	2	no	—
287	D₄×C₅₃	—	2	2	no	—
288	D₄×C₅₃	—	4	4	no	—
289	D₄×C₅₃	—	4	8	no	—
290	D₄×C₅₃	—	4	2	no	—
291	D₄×C₅₃	—	8	4	no	—
292	C₂×C₄×C₅₃	—	2	2	no	—
293	C₂×C₄×C₅₃	—	2	2	no	—
294	C₂×C₄×C₅₃	—	2	2	no	—
295	C₂×C₄×C₅₃	—	2	2	no	—
296	C₂×C₄×C₅₃	—	2	4	no	—
297	C₂×C₄×C₅₃	—	2	4	no	—
298	C₂×C₄×C₅₃	—	2	2	no	—
299	C₂×C₄×C₅₃	—	2	2	no	—
300	C₂×C₄×C₅₃	—	2	2	no	—
301	C₂×C₄×C₅₃	—	2	2	no	—
302	C₂×C₄×C₅₃	—	2	2	no	—
303	C₂×C₄×C₅₃	—	2	2	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	2	no	—
308	C₂×C₄×C₅₃	—	2	2	no	—
309	C₂×C₄×C₅₃	—	4	2	no	—
310	C₂×C₄×C₅₃	—	4	2	no	—
311	C₂×C₄×C₅₃	—	4	2	no	—
312	C₂×C₄×C₅₃	—	4	2	no	—
313	C₂×C₄×C₅₃	—	4	2	no	—
314	C₂×C₄×C₅₃	—	4	2	no	—
315	C₂×C₄×C₅₃	—	4	2	no	—
316	C₂×C₄×C₅₃	—	8	4	no	—
317	C₂×C₄×C₅₃	—	8	4	no	—
318	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
324	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
325	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
326	C₈×C₅₃	—	2	2	no	—
327	C₈×C₅₃	—	2	2	no	—
328	C₈×C₅₃	—	2	2	no	—
329	C₈×C₅₃	C₂×#41	1	4	yes	—
330	C₂×#3350	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
331	C₂²×C₅₃	—	2	2	no	—
332	C₂²×C₅₃	—	2	2	no	—
333	C₂²×C₅₃	—	2	2	no	—
334	C₂²×C₅₃	—	2	2	no	—
335	C₂²×C₅₃	—	2	2	no	—
336	C₂²×C₅₃	—	2	2	no	—
337	C₂²×C₅₃	—	4	4	no	—
338	C₂²×C₅₃	—	4	4	no	—
339	C₂²×C₅₃	—	4	2	no	—
340	C₂²×C₅₃	—	4	2	no	—
341	C₂²×C₅₃	—	4	2	no	—
342	C₂²×C₅₃	—	8	4	no	—
343	C₂²×C₅₃	#547	1	2	yes	—
344	C₂²×C₅₃	#575	1	2	yes	—
345	C₂²×C₅₃	#577	1	2	yes	—
346	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
347	C₄×C₅₃	—	2	2	no	—
348	C₄×C₅₃	—	2	2	no	—
349	C₄×C₅₃	—	2	2	no	—
350	C₄×C₅₃	—	2	2	no	—
351	C₄×C₅₃	—	4	2	no	—
352	C₄×C₅₃	—	4	2	no	—
353	C₄×C₅₃	—	4	2	no	—
354	C₄×C₅₃	—	4	2	no	—
355	C₄×C₅₃	—	4	2	no	—
356	C₄×C₅₃	—	4	2	no	—
357	C₄×C₅₃	—	4	2	no	—
358	C₄×C₅₃	#547	1	2	yes	—
359	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
360	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
361	C₂×#556	C₂×C₅₃	1	1	yes	characteristic, complemented
362	C₂×#553	C₂×C₅₃	1	1	yes	characteristic
363	#3350	C₂×C₅₃	1	16	yes	direct product factor
364	C₂×#501	C₂×C₅₃	1	1	yes	characteristic, complemented
365	C₂×#485	C₂×C₅₃	1	1	yes	characteristic, complemented
366	C₂×#482	C₂×C₅₃	1	1	yes	characteristic, complemented
367	C₂×#482	C₂×C₅₃	1	1	yes	characteristic, complemented
368	C₂×#483	C₂×C₅₃	1	1	yes	characteristic, complemented
369	C₂×#479	C₂×C₅₃	1	1	yes	characteristic, complemented
370	C₂×#476	C₂×C₅₃	1	1	yes	characteristic, complemented
371	C₂×#468	C₂×C₅₃	1	1	yes	characteristic, complemented
372	C₂×#465	C₂×C₅₃	1	1	yes	characteristic, complemented
373	C₂×#440	C₂×C₅₃	1	1	yes	characteristic, complemented
374	C₂×#435	C₂×C₅₃	1	1	yes	characteristic, complemented
375	C₂×#428	C₂×C₅₃	1	1	yes	characteristic, complemented
376	C₂×#427	C₂×C₅₃	1	1	yes	characteristic, complemented
377	C₂×C₅₃	—	4	2	no	—
378	C₂×C₅₃	—	4	2	no	—
379	C₂×C₅₃	—	8	2	no	—
380	C₂×C₅₃	#3350	1	4	yes	direct product factor
381	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
382	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
383	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
384	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
385	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
386	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
387	#556	—	2	4	no	—
388	#556	C₂²×C₅₃	1	8	yes	complemented
389	#553	—	2	4	no	—
390	#553	C₂²×C₅₃	1	8	yes	—
391	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
392	C₂×#126	—	2	1	no	—
393	C₂×#126	—	2	1	no	—
394	C₂×#126	—	2	1	no	—
395	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
396	C₂×#124	—	2	1	no	—
397	C₂×#123	—	2	1	no	—
398	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
399	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
400	C₂×#121	—	2	1	no	—
401	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
402	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
403	C₂×C₄×Q₈	—	2	1	no	—
404	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
405	C₂×C₄×D₄	—	2	1	no	—
406	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
408	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
409	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
410	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
411	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
412	#501	C₂²×C₅₃	1	8	yes	complemented
413	#485	C₂²×C₅₃	1	8	yes	complemented
414	#483	C₂²×C₅₃	1	8	yes	complemented
415	#482	C₂²×C₅₃	1	8	yes	complemented
416	#482	C₂²×C₅₃	1	8	yes	complemented
417	#479	C₂²×C₅₃	1	8	yes	complemented
418	#476	C₂²×C₅₃	1	8	yes	complemented
419	#468	C₂²×C₅₃	1	8	yes	complemented
420	#465	C₂²×C₅₃	1	8	yes	complemented
421	#440	C₂²×C₅₃	1	8	yes	complemented
422	#435	C₂²×C₅₃	1	8	yes	complemented
423	#428	C₂²×C₅₃	1	8	yes	complemented
424	#427	C₂²×C₅₃	1	8	yes	complemented
425	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
426	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
427	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
428	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
429	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
430	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
431	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
432	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
433	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
434	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
435	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
436	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
437	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
438	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
439	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
440	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
441	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
442	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
443	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
444	C₅₃	C₂×#3350	1	1	yes	characteristic, direct product factor, Sylow
445	C₂²×Q₈	—	2	1	no	—
446	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
447	C₂²×D₄	—	2	1	no	—
448	C₂²×D₄	—	2	1	no	—
449	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
450	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
451	C₂³×C₄	—	2	1	no	—
452	C₂³×C₄	—	2	1	no	—
453	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
455	C₂×SD₁₆	—	2	4	no	—
456	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
457	C₂×M₁₆	—	2	4	no	—
458	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
459	C₂²×C₈	—	2	4	no	—
460	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
461	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
462	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
463	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
464	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
465	C₄⋊Q₈	—	2	2	no	—
466	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
467	#126	—	2	8	no	—
468	#126	—	2	8	no	—
469	#126	—	2	8	no	—
470	#125	—	2	2	no	—
471	#125	C₂³×C₅₃	1	4	yes	—
472	#124	—	2	8	no	—
473	#123	—	2	8	no	—
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
477	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
478	#121	—	2	8	no	—
479	#121	—	2	2	no	—
480	#121	—	2	2	no	—
481	#121	C₂³×C₅₃	1	4	yes	—
482	#121	C₂³×C₅₃	1	4	yes	—
483	C₄×Q₈	—	2	8	no	—
484	C₄×Q₈	—	2	2	no	—
485	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
486	C₄×D₄	—	2	8	no	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	D₄×C₅₃	1	4	yes	—
489	C₄×D₄	C₂³×C₅₃	1	4	yes	—
490	C₄×D₄	C₂³×C₅₃	1	4	yes	—
491	#117	—	2	2	no	—
492	#117	—	2	2	no	—
493	#117	—	2	2	no	—
494	#117	C₂³×C₅₃	1	4	yes	—
495	#117	C₂³×C₅₃	1	4	yes	—
496	#117	C₂³×C₅₃	1	4	yes	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	2	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
523	C₂×C₄²	—	2	1	no	—
524	C₂×C₄²	—	2	1	no	—
525	C₂×C₄²	—	2	1	no	—
526	C₂×C₄²	—	2	1	no	—
527	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
528	#107	C₂³×C₅₃	1	4	yes	—
529	#107	C₂³×C₅₃	1	4	yes	—
530	#107	C₂³×C₅₃	1	4	yes	—
531	#107	C₂³×C₅₃	1	4	yes	—
532	#106	C₂³×C₅₃	1	4	yes	—
533	#106	C₂³×C₅₃	1	4	yes	—
534	#106	C₂³×C₅₃	1	4	yes	—
535	#106	C₂³×C₅₃	1	4	yes	—
536	#106	C₂³×C₅₃	1	4	yes	—
537	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
538	#103	C₂³×C₅₃	1	4	yes	—
539	#103	C₂³×C₅₃	1	4	yes	—
540	#103	C₂³×C₅₃	1	4	yes	—
541	#102	C₂³×C₅₃	1	4	yes	—
542	#102	C₂³×C₅₃	1	4	yes	—
543	#102	C₂³×C₅₃	1	4	yes	—
544	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
545	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
546	#97	C₂³×C₅₃	1	4	yes	—
547	C₂⁴	—	2	1	no	—
548	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
549	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	4	no	—
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	4	4	no	—
555	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	4	2	no	—
562	C₂×D₄	—	4	4	no	—
563	C₂×D₄	—	8	2	no	—
564	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
565	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	8	2	no	—
580	C₂²×C₄	—	8	2	no	—
581	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
586	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
590	SD₁₆	—	2	8	no	—
591	M₁₆	—	2	8	no	—
592	C₂×C₈	—	2	2	no	—
593	C₂×C₈	—	2	2	no	—
594	C₂×C₈	—	2	2	no	—
595	C₂×C₈	—	2	8	no	—
596	C₂×C₈	#41×C₅₃	1	4	yes	—
597	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
598	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
599	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
600	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
615	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
616	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
617	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
618	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
619	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
620	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
630	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	C₂×D₄×C₅₃	1	2	yes	—
636	C₄²	C₂⁴×C₅₃	1	2	yes	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	2	no	—
646	C₂³	—	4	2	no	—
647	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
648	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
649	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
650	Q₈	—	2	2	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	4	8	no	—
653	Q₈	—	4	2	no	—
654	D₄	—	2	2	no	—
655	D₄	—	2	2	no	—
656	D₄	—	4	4	no	—
657	D₄	—	4	8	no	—
658	D₄	—	4	2	no	—
659	D₄	—	8	4	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	2	4	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	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	4	2	no	—
678	C₂×C₄	—	4	2	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	2	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	8	4	no	—
685	C₂×C₄	—	8	4	no	—
686	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
687	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
689	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
691	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
692	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
693	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
694	C₈	—	2	2	no	—
695	C₈	—	2	2	no	—
696	C₈	—	2	2	no	—
697	C₈	C₂×#41×C₅₃	1	4	yes	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	4	4	no	—
705	C₂²	—	4	4	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	8	4	no	—
710	C₂²	C₅₃×#547	1	2	yes	—
711	C₂²	C₅₃×#575	1	2	yes	—
712	C₂²	C₅₃×#577	1	2	yes	—
713	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	C₅₃×#547	1	2	yes	—
726	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
727	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
728	C₂	—	4	2	no	—
729	C₂	—	4	2	no	—
730	C₂	—	8	2	no	—
731	C₂	C₅₃×#3350	1	4	yes	direct product factor
732	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
733	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
734	C₂	C₂×C₅₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₂×C₅₃×#553	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#556	C₂	semidirect
3. C₅₃×#3350	C₂	direct (N × H)
4. C₂×C₅₃×#501	C₂	semidirect
5. C₂×C₅₃×#485	C₂	semidirect
6. C₂×C₅₃×#482	C₂	semidirect
7. C₂×C₅₃×#482	C₂	semidirect
8. C₂×C₅₃×#483	C₂	semidirect
9. C₂×C₅₃×#479	C₂	semidirect
10. C₂×C₅₃×#476	C₂	semidirect
11. C₂×C₅₃×#468	C₂	semidirect
12. C₂×C₅₃×#465	C₂	semidirect
13. C₂×C₅₃×#440	C₂	semidirect
14. C₂×C₅₃×#435	C₂	semidirect
15. C₂×C₅₃×#428	C₂	semidirect
16. C₂×C₅₃×#427	C₂	semidirect
21. C₅₃×#556	C₂²	semidirect
45. C₅₃×#501	C₂²	semidirect
46. C₅₃×#485	C₂²	semidirect
47. C₅₃×#483	C₂²	semidirect
48. C₅₃×#482	C₂²	semidirect
49. C₅₃×#482	C₂²	semidirect
50. C₅₃×#479	C₂²	semidirect
51. C₅₃×#476	C₂²	semidirect
52. C₅₃×#468	C₂²	semidirect
53. C₅₃×#465	C₂²	semidirect
54. C₅₃×#440	C₂²	semidirect
55. C₅₃×#435	C₂²	semidirect
56. C₅₃×#428	C₂²	semidirect
57. C₅₃×#427	C₂²	semidirect
330. C₂×#3350	C₅₃	direct (N × H)
361. C₂×#556	C₂×C₅₃	semidirect
363. #3350	C₂×C₅₃	direct (N × H)
364. C₂×#501	C₂×C₅₃	semidirect
365. C₂×#485	C₂×C₅₃	semidirect
366. C₂×#482	C₂×C₅₃	semidirect
367. C₂×#482	C₂×C₅₃	semidirect
368. C₂×#483	C₂×C₅₃	semidirect
369. C₂×#479	C₂×C₅₃	semidirect
370. C₂×#476	C₂×C₅₃	semidirect
371. C₂×#468	C₂×C₅₃	semidirect
372. C₂×#465	C₂×C₅₃	semidirect
373. C₂×#440	C₂×C₅₃	semidirect
374. C₂×#435	C₂×C₅₃	semidirect
375. C₂×#428	C₂×C₅₃	semidirect
376. C₂×#427	C₂×C₅₃	semidirect
380. C₂×C₅₃	#3350	direct (N × H)
388. #556	C₂²×C₅₃	semidirect
412. #501	C₂²×C₅₃	semidirect
413. #485	C₂²×C₅₃	semidirect
414. #483	C₂²×C₅₃	semidirect
415. #482	C₂²×C₅₃	semidirect
416. #482	C₂²×C₅₃	semidirect
417. #479	C₂²×C₅₃	semidirect
418. #476	C₂²×C₅₃	semidirect
419. #468	C₂²×C₅₃	semidirect
420. #465	C₂²×C₅₃	semidirect
421. #440	C₂²×C₅₃	semidirect
422. #435	C₂²×C₅₃	semidirect
423. #428	C₂²×C₅₃	semidirect
424. #427	C₂²×C₅₃	semidirect
444. C₅₃	C₂×#3350	direct (N × H)
731. C₂	C₅₃×#3350	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×C₅₃×#556	2
C₂×C₅₃×#553	2
C₅₃×#3350	2
C₂×C₅₃×#501	2
C₂×C₅₃×#485	2
C₂×C₅₃×#482	2
C₂×C₅₃×#483	2
C₂×C₅₃×#479	2
C₂×C₅₃×#476	2
C₂×C₅₃×#468	2
C₂×C₅₃×#465	2
C₂×C₅₃×#440	2
C₂×C₅₃×#435	2
C₂×C₅₃×#428	2
C₂×C₅₃×#427	2
C₂×#3350	53

Subgroups — C2×C53×#3350 #27268754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3350 #27268754