Subgroups — C₂×C₅₃×#1629 #27225987

Order 13568.

1722 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₃×#476	C₂	1	2	yes	maximal, complemented
4	C₅₃×#1629	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅₃×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×D₄⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₅₃	—	2	2	no	—
8	C₂²×SD₁₆×C₅₃	—	2	2	no	—
9	D₄²×C₅₃	—	2	2	no	—
10	D₄²×C₅₃	—	2	4	no	—
11	D₄²×C₅₃	C₂²	1	4	yes	—
12	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
13	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
14	C₂×#121×C₅₃	—	2	2	no	—
15	C₂×#120×C₅₃	—	2	2	no	—
16	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
17	C₅₃×#492	—	2	2	no	—
18	C₅₃×#492	C₂²	1	4	yes	complemented
19	C₅₃×#476	—	2	4	no	—
20	C₅₃×#476	C₂²	1	8	yes	complemented
21	C₂×#106×C₅₃	—	2	2	no	—
22	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	complemented
23	C₂×#102×C₅₃	—	2	2	no	—
24	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₅₃×#331	C₂²	1	4	yes	complemented
26	C₅₃×D₄⋊C₈	C₂²	1	8	yes	complemented
27	C₂⁵×C₅₃	—	2	2	no	—
28	C₂²×Q₈×C₅₃	—	2	1	no	—
29	C₂²×D₄×C₅₃	—	2	4	no	—
30	C₂²×D₄×C₅₃	—	2	8	no	—
31	C₂²×D₄×C₅₃	—	2	8	no	—
32	C₂²×D₄×C₅₃	—	2	2	no	—
33	C₂²×D₄×C₅₃	—	4	8	no	—
34	C₂²×D₄×C₅₃	—	4	8	no	—
35	C₂²×D₄×C₅₃	D₄	1	2	yes	—
36	C₂²×D₄×C₅₃	D₄	1	2	yes	—
37	C₂³×C₄×C₅₃	—	2	2	no	—
38	C₂×SD₁₆×C₅₃	—	2	8	no	—
39	C₂×SD₁₆×C₅₃	—	4	8	no	—
40	C₂²×C₈×C₅₃	—	2	1	no	—
41	C₂²×C₈×C₅₃	—	2	2	no	—
42	C₄⋊Q₈×C₅₃	—	2	1	no	—
43	C₄⋊Q₈×C₅₃	—	2	2	no	—
44	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
45	#127×C₅₃	—	2	2	no	—
46	#127×C₅₃	D₄	1	2	yes	—
47	#127×C₅₃	C₂³	1	2	yes	—
48	#121×C₅₃	—	2	8	no	—
49	#121×C₅₃	—	2	8	no	—
50	#120×C₅₃	—	2	8	no	—
51	#120×C₅₃	—	2	8	no	—
52	C₄×D₄×C₅₃	—	2	2	no	—
53	C₄×D₄×C₅₃	—	2	2	no	—
54	C₄×D₄×C₅₃	D₄	1	4	yes	—
55	C₄×D₄×C₅₃	C₂³	1	4	yes	—
56	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₅₃	D₄	1	2	yes	—
58	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
60	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
61	#106×C₅₃	—	2	8	no	—
62	C₄⋊C₈×C₅₃	—	2	2	no	—
63	C₄⋊C₈×C₅₃	C₂³	1	4	yes	complemented
64	#102×C₅₃	—	2	8	no	—
65	C₄×C₈×C₅₃	—	2	1	no	—
66	C₄×C₈×C₅₃	C₂³	1	2	yes	complemented
67	C₂⁴×C₅₃	—	2	2	no	—
68	C₂⁴×C₅₃	—	2	8	no	—
69	C₂⁴×C₅₃	—	2	2	no	—
70	C₂⁴×C₅₃	—	4	16	no	—
71	C₂⁴×C₅₃	—	8	4	no	—
72	C₂×Q₈×C₅₃	—	2	2	no	—
73	C₂×Q₈×C₅₃	—	4	4	no	—
74	C₂×Q₈×C₅₃	—	4	1	no	—
75	C₂×D₄×C₅₃	—	2	16	no	—
76	C₂×D₄×C₅₃	—	2	2	no	—
77	C₂×D₄×C₅₃	—	2	4	no	—
78	C₂×D₄×C₅₃	—	2	2	no	—
79	C₂×D₄×C₅₃	—	2	4	no	—
80	C₂×D₄×C₅₃	—	2	4	no	—
81	C₂×D₄×C₅₃	—	4	4	no	—
82	C₂×D₄×C₅₃	—	4	16	no	—
83	C₂×D₄×C₅₃	—	4	32	no	—
84	C₂×D₄×C₅₃	—	4	16	no	—
85	C₂×D₄×C₅₃	—	4	16	no	—
86	C₂×D₄×C₅₃	—	4	4	no	—
87	C₂×D₄×C₅₃	—	4	4	no	—
88	C₂×D₄×C₅₃	SD₁₆	1	8	yes	complemented
89	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
90	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₅₃	—	2	2	no	—
92	C₂²×C₄×C₅₃	—	2	4	no	—
93	C₂²×C₄×C₅₃	—	2	4	no	—
94	C₂²×C₄×C₅₃	—	4	4	no	—
95	C₂²×C₄×C₅₃	—	4	4	no	—
96	C₂²×C₄×C₅₃	—	4	1	no	—
97	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
99	SD₁₆×C₅₃	—	4	16	no	—
100	C₂×C₈×C₅₃	—	2	4	no	—
101	C₂×C₈×C₅₃	—	2	2	no	—
102	C₂×C₈×C₅₃	—	2	4	no	—
103	C₂×C₈×C₅₃	—	4	4	no	—
104	C₄⋊C₄×C₅₃	—	2	2	no	—
105	C₄⋊C₄×C₅₃	—	2	4	no	—
106	C₄⋊C₄×C₅₃	—	4	2	no	—
107	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
108	C₂²⋊C₄×C₅₃	—	2	8	no	—
109	C₂²⋊C₄×C₅₃	—	2	4	no	—
110	C₂²⋊C₄×C₅₃	—	2	4	no	—
111	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₅₃	C₂×D₄	1	2	yes	—
113	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
114	C₂³×C₅₃	—	2	4	no	—
115	C₂³×C₅₃	—	2	8	no	—
116	C₂³×C₅₃	—	2	4	no	—
117	C₂³×C₅₃	—	4	32	no	—
118	C₂³×C₅₃	—	4	4	no	—
119	C₂³×C₅₃	—	4	4	no	—
120	C₂³×C₅₃	—	4	8	no	—
121	C₂³×C₅₃	—	4	4	no	—
122	C₂³×C₅₃	—	8	8	no	—
123	C₂³×C₅₃	—	8	32	no	—
124	C₂³×C₅₃	#120	1	1	yes	characteristic
125	Q₈×C₅₃	—	4	4	no	—
126	Q₈×C₅₃	—	8	2	no	—
127	D₄×C₅₃	—	2	4	no	—
128	D₄×C₅₃	—	2	8	no	—
129	D₄×C₅₃	—	4	4	no	—
130	D₄×C₅₃	—	4	32	no	—
131	D₄×C₅₃	—	4	4	no	—
132	D₄×C₅₃	—	4	4	no	—
133	D₄×C₅₃	—	4	8	no	—
134	D₄×C₅₃	—	8	2	no	—
135	D₄×C₅₃	C₂×SD₁₆	1	8	yes	complemented
136	C₂×C₄×C₅₃	—	2	2	no	—
137	C₂×C₄×C₅₃	—	2	4	no	—
138	C₂×C₄×C₅₃	—	4	4	no	—
139	C₂×C₄×C₅₃	—	4	4	no	—
140	C₂×C₄×C₅₃	—	4	4	no	—
141	C₂×C₄×C₅₃	—	4	8	no	—
142	C₂×C₄×C₅₃	—	4	2	no	—
143	C₂×C₄×C₅₃	—	8	2	no	—
144	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
145	C₂×C₄×C₅₃	#120	1	2	yes	—
146	C₂×C₄×C₅₃	C₂×SD₁₆	1	4	yes	—
147	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	4	yes	—
148	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
150	C₈×C₅₃	—	2	4	no	—
151	C₈×C₅₃	—	4	4	no	—
152	C₂×#1629	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂²×C₅₃	—	2	8	no	—
154	C₂²×C₅₃	—	4	16	no	—
155	C₂²×C₅₃	—	4	4	no	—
156	C₂²×C₅₃	—	4	4	no	—
157	C₂²×C₅₃	—	4	8	no	—
158	C₂²×C₅₃	—	4	4	no	—
159	C₂²×C₅₃	—	8	32	no	—
160	C₂²×C₅₃	—	8	8	no	—
161	C₂²×C₅₃	#450	1	4	yes	—
162	C₂²×C₅₃	#453	1	2	yes	—
163	C₂²×C₅₃	C₂×#120	1	1	yes	characteristic
164	C₄×C₅₃	—	2	1	no	—
165	C₄×C₅₃	—	2	1	no	—
166	C₄×C₅₃	—	4	4	no	—
167	C₄×C₅₃	—	8	2	no	—
168	C₄×C₅₃	#450	1	4	yes	—
169	C₄×C₅₃	C₂²×SD₁₆	1	2	yes	—
170	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
171	C₂×D₄²	C₂×C₅₃	1	1	yes	characteristic
172	C₂×#492	C₂×C₅₃	1	1	yes	characteristic, complemented
173	C₂×#476	C₂×C₅₃	1	2	yes	complemented
174	#1629	C₂×C₅₃	1	8	yes	direct product factor
175	C₂×#331	C₂×C₅₃	1	1	yes	characteristic, complemented
176	C₂×D₄⋊C₈	C₂×C₅₃	1	2	yes	complemented
177	C₂×C₅₃	—	4	8	no	—
178	C₂×C₅₃	—	8	4	no	—
179	C₂×C₅₃	#1629	1	4	yes	direct product factor
180	C₂×C₅₃	C₂×#450	1	2	yes	—
181	C₂×C₅₃	C₂×#453	1	1	yes	characteristic
182	C₂³×D₄	—	2	2	no	—
183	C₂²×SD₁₆	—	2	2	no	—
184	D₄²	—	2	2	no	—
185	D₄²	—	2	4	no	—
186	D₄²	C₂²×C₅₃	1	4	yes	—
187	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
188	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
189	C₂×#121	—	2	2	no	—
190	C₂×#120	—	2	2	no	—
191	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
192	#492	—	2	2	no	—
193	#492	C₂²×C₅₃	1	4	yes	complemented
194	#476	—	2	4	no	—
195	#476	C₂²×C₅₃	1	8	yes	complemented
196	C₂×#106	—	2	2	no	—
197	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	complemented
198	C₂×#102	—	2	2	no	—
199	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
200	#331	C₂²×C₅₃	1	4	yes	complemented
201	D₄⋊C₈	C₂²×C₅₃	1	8	yes	complemented
202	C₅₃	C₂×#1629	1	1	yes	characteristic, direct product factor, Sylow
203	C₂⁵	—	2	2	no	—
204	C₂²×Q₈	—	2	1	no	—
205	C₂²×D₄	—	2	4	no	—
206	C₂²×D₄	—	2	8	no	—
207	C₂²×D₄	—	2	8	no	—
208	C₂²×D₄	—	2	2	no	—
209	C₂²×D₄	—	4	8	no	—
210	C₂²×D₄	—	4	8	no	—
211	C₂²×D₄	D₄×C₅₃	1	2	yes	—
212	C₂²×D₄	D₄×C₅₃	1	2	yes	—
213	C₂³×C₄	—	2	2	no	—
214	C₂×SD₁₆	—	2	8	no	—
215	C₂×SD₁₆	—	4	8	no	—
216	C₂²×C₈	—	2	1	no	—
217	C₂²×C₈	—	2	2	no	—
218	C₄⋊Q₈	—	2	2	no	—
219	C₄⋊Q₈	—	2	1	no	—
220	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
221	#127	—	2	2	no	—
222	#127	D₄×C₅₃	1	2	yes	—
223	#127	C₂³×C₅₃	1	2	yes	—
224	#121	—	2	8	no	—
225	#121	—	2	8	no	—
226	#120	—	2	8	no	—
227	#120	—	2	8	no	—
228	C₄×D₄	—	2	2	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	D₄×C₅₃	1	4	yes	—
231	C₄×D₄	C₂³×C₅₃	1	4	yes	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	D₄×C₅₃	1	2	yes	—
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
237	#106	—	2	8	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	C₂³×C₅₃	1	4	yes	complemented
240	#102	—	2	8	no	—
241	C₄×C₈	—	2	1	no	—
242	C₄×C₈	C₂³×C₅₃	1	2	yes	complemented
243	C₂⁴	—	2	2	no	—
244	C₂⁴	—	2	8	no	—
245	C₂⁴	—	2	2	no	—
246	C₂⁴	—	4	16	no	—
247	C₂⁴	—	8	4	no	—
248	C₂×Q₈	—	2	2	no	—
249	C₂×Q₈	—	4	4	no	—
250	C₂×Q₈	—	4	1	no	—
251	C₂×D₄	—	2	16	no	—
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	4	4	no	—
258	C₂×D₄	—	4	16	no	—
259	C₂×D₄	—	4	32	no	—
260	C₂×D₄	—	4	16	no	—
261	C₂×D₄	—	4	16	no	—
262	C₂×D₄	—	4	4	no	—
263	C₂×D₄	—	4	4	no	—
264	C₂×D₄	SD₁₆×C₅₃	1	8	yes	complemented
265	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
266	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
275	SD₁₆	—	4	16	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	4	4	no	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	4	2	no	—
283	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
284	C₂²⋊C₄	—	2	8	no	—
285	C₂²⋊C₄	—	2	4	no	—
286	C₂²⋊C₄	—	2	4	no	—
287	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
288	C₄²	C₂×D₄×C₅₃	1	2	yes	—
289	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
290	C₂³	—	2	4	no	—
291	C₂³	—	2	8	no	—
292	C₂³	—	2	4	no	—
293	C₂³	—	4	32	no	—
294	C₂³	—	4	4	no	—
295	C₂³	—	4	4	no	—
296	C₂³	—	4	8	no	—
297	C₂³	—	4	4	no	—
298	C₂³	—	8	8	no	—
299	C₂³	—	8	32	no	—
300	C₂³	#120×C₅₃	1	1	yes	characteristic
301	Q₈	—	4	4	no	—
302	Q₈	—	8	2	no	—
303	D₄	—	2	4	no	—
304	D₄	—	2	8	no	—
305	D₄	—	4	4	no	—
306	D₄	—	4	32	no	—
307	D₄	—	4	4	no	—
308	D₄	—	4	4	no	—
309	D₄	—	4	8	no	—
310	D₄	—	8	2	no	—
311	D₄	C₂×SD₁₆×C₅₃	1	8	yes	complemented
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	8	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	8	2	no	—
320	C₂×C₄	#120×C₅₃	1	1	yes	characteristic
321	C₂×C₄	#120×C₅₃	1	2	yes	—
322	C₂×C₄	C₂×SD₁₆×C₅₃	1	4	yes	—
323	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	4	yes	—
324	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
325	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
326	C₈	—	2	4	no	—
327	C₈	—	4	4	no	—
328	C₂²	—	2	8	no	—
329	C₂²	—	4	4	no	—
330	C₂²	—	4	4	no	—
331	C₂²	—	4	16	no	—
332	C₂²	—	4	8	no	—
333	C₂²	—	4	4	no	—
334	C₂²	—	8	32	no	—
335	C₂²	—	8	8	no	—
336	C₂²	C₅₃×#450	1	4	yes	—
337	C₂²	C₅₃×#453	1	2	yes	—
338	C₂²	C₂×#120×C₅₃	1	1	yes	characteristic
339	C₄	—	2	1	no	—
340	C₄	—	2	1	no	—
341	C₄	—	4	4	no	—
342	C₄	—	8	2	no	—
343	C₄	C₅₃×#450	1	4	yes	—
344	C₄	C₂²×SD₁₆×C₅₃	1	2	yes	—
345	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
346	C₂	—	4	8	no	—
347	C₂	—	8	4	no	—
348	C₂	C₅₃×#1629	1	4	yes	direct product factor
349	C₂	C₂×C₅₃×#450	1	2	yes	—
350	C₂	C₂×C₅₃×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₃
prime radical	C₂×D₄²×C₅₃	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₃×#492	C₂	semidirect
3. C₂×C₅₃×#476	C₂	semidirect
4. C₅₃×#1629	C₂	direct (N × H)
5. C₂×C₅₃×#331	C₂	semidirect
6. C₂×C₅₃×D₄⋊C₈	C₂	semidirect
12. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
18. C₅₃×#492	C₂²	semidirect
20. C₅₃×#476	C₂²	semidirect
22. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
24. C₂×C₄×C₈×C₅₃	C₂²	semidirect
25. C₅₃×#331	C₂²	semidirect
26. C₅₃×D₄⋊C₈	C₂²	semidirect
44. C₄⋊Q₈×C₅₃	C₂³	semidirect
63. C₄⋊C₈×C₅₃	C₂³	semidirect
66. C₄×C₈×C₅₃	C₂³	semidirect
88. C₂×D₄×C₅₃	SD₁₆	semidirect
135. D₄×C₅₃	C₂×SD₁₆	semidirect
152. C₂×#1629	C₅₃	direct (N × H)
172. C₂×#492	C₂×C₅₃	semidirect
173. C₂×#476	C₂×C₅₃	semidirect
174. #1629	C₂×C₅₃	direct (N × H)
175. C₂×#331	C₂×C₅₃	semidirect
176. C₂×D₄⋊C₈	C₂×C₅₃	semidirect
179. C₂×C₅₃	#1629	direct (N × H)
187. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
193. #492	C₂²×C₅₃	semidirect
195. #476	C₂²×C₅₃	semidirect
197. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
199. C₂×C₄×C₈	C₂²×C₅₃	semidirect
200. #331	C₂²×C₅₃	semidirect
201. D₄⋊C₈	C₂²×C₅₃	semidirect
202. C₅₃	C₂×#1629	direct (N × H)
220. C₄⋊Q₈	C₂³×C₅₃	semidirect
239. C₄⋊C₈	C₂³×C₅₃	semidirect
242. C₄×C₈	C₂³×C₅₃	semidirect
264. C₂×D₄	SD₁₆×C₅₃	semidirect
311. D₄	C₂×SD₁₆×C₅₃	semidirect
348. C₂	C₅₃×#1629	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×D₄²×C₅₃	2
C₂×C₅₃×#492	2
C₂×C₅₃×#476	2
C₅₃×#1629	2
C₂×C₅₃×#331	2
C₂×C₅₃×D₄⋊C₈	2
C₂×#1629	53

Subgroups — C2×C53×#1629 #27225987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#1629 #27225987