Subgroups — C₄×#106×D₅₃ #27382129

Order 13568.

1358 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#106×D₅₃	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄×D₅₃	C₂	1	2	yes	maximal
4	#106×Dic₅₃	C₂	1	2	yes	maximal, complemented
5	C₄×#13133148	C₂	1	2	yes	maximal, complemented
6	C₄×#13133149	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274603	C₂	1	2	yes	maximal, complemented
8	#340×D₅₃	C₂	1	2	yes	maximal
9	C₄×#106×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
11	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×D₅₃	C₂²	1	4	yes	—
13	C₂×C₄²×D₅₃	—	2	2	no	—
14	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
15	C₂×#13133149	C₂²	1	2	yes	—
16	C₂×#13133148	C₂²	1	4	yes	—
17	#106×D₅₃	C₄	1	16	yes	direct product factor
18	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
19	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
21	C₄×C₈×D₅₃	C₄	1	8	yes	complemented
22	C₄⋊C₄×Dic₅₃	C₂²	1	4	yes	—
23	C₄×#11719919	—	2	2	no	—
24	C₄×C₄⋊Dic₅₃	C₂²	1	2	yes	—
25	#16810474	—	2	2	no	—
26	#95×D₅₃	—	2	2	no	—
27	#16810386	C₂²	1	2	yes	—
28	#16810385	C₂²	1	4	yes	—
29	C₂×#106×C₅₃	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
32	C₅₃×#340	C₂²	1	2	yes	—
33	C₂²×C₄×D₅₃	—	2	4	no	—
34	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
37	C₂²×#88322	C₂³	1	1	yes	characteristic
38	C₂²×#88322	C₂³	1	1	yes	characteristic
39	C₂×C₈×D₅₃	—	2	4	no	—
40	C₂×C₈×D₅₃	C₂×C₄	1	4	yes	—
41	C₂×C₈×D₅₃	C₂×C₄	1	4	yes	—
42	C₂×C₈×D₅₃	C₂×C₄	1	8	yes	—
43	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	—
44	C₂×#11719919	—	2	4	no	—
45	C₄⋊C₄×D₅₃	—	2	8	no	—
46	C₄⋊C₄×D₅₃	C₂×C₄	1	16	yes	—
47	C₂×C₄×Dic₅₃	—	2	2	no	—
48	C₂×C₄×Dic₅₃	—	2	4	no	—
49	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
51	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
52	C₄²×D₅₃	—	4	8	no	—
53	C₄²×D₅₃	C₂×C₄	1	4	yes	—
54	C₄²×D₅₃	Q₈	1	4	yes	—
55	#13133149	C₂×C₄	1	8	yes	complemented
56	#13133148	C₂×C₄	1	16	yes	complemented
57	C₄×#88322	C₂×C₄	1	4	yes	complemented
58	C₈×Dic₅₃	C₂×C₄	1	4	yes	complemented
59	C₈×Dic₅₃	C₂×C₄	1	4	yes	complemented
60	#13133124	—	2	2	no	—
61	#13133124	—	2	4	no	—
62	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
65	C₂×C₄²×C₅₃	—	2	2	no	—
66	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
67	#106×C₅₃	C₂×C₄	1	8	yes	complemented
68	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	complemented
69	#95×C₅₃	—	2	2	no	—
70	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₅₃	—	2	4	no	—
72	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
75	C₂²×Dic₅₃	—	2	4	no	—
76	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×D₅₃	—	2	4	no	—
80	C₂×C₄×D₅₃	—	2	16	no	—
81	C₂×C₄×D₅₃	—	4	8	no	—
82	C₂×C₄×D₅₃	—	4	8	no	—
83	C₂×C₄×D₅₃	C₄⋊C₄	1	4	yes	—
84	C₂×C₄×D₅₃	C₄⋊C₄	1	4	yes	—
85	C₂×C₄×D₅₃	SD₁₆	1	8	yes	—
86	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
87	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
88	C₂×C₄×D₅₃	C₂×Q₈	1	2	yes	—
89	C₂×C₄×D₅₃	#41	1	4	yes	—
90	C₂×C₈×C₅₃	—	2	2	no	—
91	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
92	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
93	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
94	C₄⋊C₄×C₅₃	—	2	4	no	—
95	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
96	C₄²×C₅₃	—	4	4	no	—
97	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
98	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
99	C₄⋊Dic₅₃	—	2	4	no	—
100	C₄⋊Dic₅₃	C₂²×C₄	1	8	yes	—
101	#11719919	—	2	16	no	—
102	C₄×Dic₅₃	—	4	4	no	—
103	C₄×Dic₅₃	—	4	8	no	—
104	C₄×Dic₅₃	C₄⋊C₄	1	4	yes	—
105	C₄×Dic₅₃	C₄⋊C₄	1	4	yes	—
106	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
107	C₄×Dic₅₃	C₂×Q₈	1	2	yes	—
108	C₂×#88322	—	2	2	no	—
109	C₂×#88322	C₂²×C₄	1	2	yes	—
110	C₂×#88322	C₂²×C₄	1	2	yes	—
111	C₂×#88322	C₂²×C₄	1	4	yes	—
112	C₈×D₅₃	—	2	8	no	—
113	C₈×D₅₃	C₄²	1	16	yes	complemented
114	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
115	C₂²×D₅₃	C₂×C₄⋊C₄	1	2	yes	—
116	C₂²×D₅₃	C₄×D₄	1	4	yes	—
117	C₂²×D₅₃	C₂×SD₁₆	1	4	yes	—
118	C₂²×D₅₃	#135	1	4	yes	—
119	C₂×C₄×C₅₃	—	2	2	no	—
120	C₂×C₄×C₅₃	—	2	8	no	—
121	C₂×C₄×C₅₃	—	4	4	no	—
122	C₂×C₄×C₅₃	—	4	4	no	—
123	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
124	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
125	C₂×C₄×C₅₃	C₂×SD₁₆	1	4	yes	—
126	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
127	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
128	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
129	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
130	C₂×Dic₅₃	—	2	2	no	—
131	C₂×Dic₅₃	—	2	8	no	—
132	C₂×Dic₅₃	—	4	4	no	—
133	C₂×Dic₅₃	—	4	4	no	—
134	C₂×Dic₅₃	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×Dic₅₃	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×Dic₅₃	C₂×C₄⋊C₄	1	2	yes	—
137	C₂×Dic₅₃	C₄×D₄	1	4	yes	—
138	C₂×Dic₅₃	C₂×SD₁₆	1	4	yes	—
139	C₄×D₅₃	—	2	8	no	—
140	C₄×D₅₃	—	4	32	no	—
141	C₄×D₅₃	#106	1	16	yes	direct product factor
142	C₄×D₅₃	C₂×C₄²	1	4	yes	—
143	C₄×D₅₃	#117	1	4	yes	—
144	C₄×D₅₃	C₄×Q₈	1	8	yes	—
145	C₈×C₅₃	—	2	2	no	—
146	C₈×C₅₃	C₂×C₄²	1	4	yes	complemented
147	#88322	—	2	2	no	—
148	#88322	C₂×C₄²	1	4	yes	complemented
149	C₂×C₄×#106	—	53	1	no	maximal, Sylow
150	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
151	C₂²×C₅₃	C₂×C₄×D₄	1	2	yes	—
152	C₂²×C₅₃	C₂²×SD₁₆	1	2	yes	—
153	C₂²×C₅₃	C₂×#135	1	2	yes	—
154	C₂×D₅₃	C₄×C₄⋊C₄	1	4	yes	—
155	C₂×D₅₃	C₂×#106	1	4	yes	—
156	C₂×D₅₃	#427	1	4	yes	—
157	C₂×D₅₃	C₄×SD₁₆	1	16	yes	—
158	C₄×C₅₃	—	2	2	no	—
159	C₄×C₅₃	—	4	8	no	—
160	C₄×C₅₃	C₂×#106	1	4	yes	complemented
161	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
162	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
163	C₄×C₅₃	C₂×C₄×Q₈	1	2	yes	—
164	Dic₅₃	—	2	2	no	—
165	Dic₅₃	—	4	8	no	—
166	Dic₅₃	C₄×C₄⋊C₄	1	4	yes	—
167	Dic₅₃	C₂×#106	1	4	yes	complemented
168	C₂²×#106	—	53	2	no	—
169	C₂²×C₄×C₈	—	53	1	no	—
170	C₂×C₄×C₄⋊C₄	—	53	2	no	—
171	C₄×#106	—	53	2	no	—
172	C₄×#106	—	53	1	no	—
173	C₄×#106	—	53	2	no	—
174	C₄×#106	—	53	2	no	—
175	C₄×#106	D₅₃	1	1	yes	characteristic, direct product factor
176	C₂×#340	—	53	2	no	—
177	C₂×C₅₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₅₃	C₂²×#106	1	1	yes	characteristic
179	C₂×C₅₃	C₂×#427	1	1	yes	characteristic
180	C₂×C₅₃	C₂×C₄×SD₁₆	1	4	yes	—
181	D₅₃	C₄×#106	1	8	yes	direct product factor
182	C₂³×C₈	—	53	1	no	—
183	C₂³×C₈	—	53	1	no	—
184	C₂²×C₄⋊C₄	—	53	4	no	—
185	C₂²×C₄²	—	53	1	no	—
186	C₂²×C₄²	—	106	2	no	—
187	C₂×#106	—	53	2	no	—
188	C₂×#106	—	53	4	no	—
189	C₂×#106	—	53	16	no	—
190	C₂×#106	C₂×D₅₃	1	2	yes	—
191	C₂×C₄×C₈	—	53	1	no	—
192	C₂×C₄×C₈	—	53	1	no	—
193	C₂×C₄×C₈	—	53	1	no	—
194	C₂×C₄×C₈	—	53	8	no	—
195	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
196	C₄×C₄⋊C₄	—	53	4	no	—
197	C₄×C₄⋊C₄	—	53	2	no	—
198	C₄×C₄⋊C₄	—	106	2	no	—
199	C₄×C₄⋊C₄	—	106	2	no	—
200	C₄×C₄⋊C₄	C₂×D₅₃	1	2	yes	—
201	C₂×#95	—	106	2	no	—
202	#340	—	53	2	no	—
203	#340	—	53	4	no	—
204	#340	C₂×D₅₃	1	2	yes	—
205	C₅₃	C₂×C₄×#106	1	1	yes	characteristic, complemented, Sylow
206	C₂³×C₄	—	53	1	no	—
207	C₂³×C₄	—	53	1	no	—
208	C₂³×C₄	—	53	1	no	—
209	C₂³×C₄	—	106	4	no	—
210	C₂²×C₈	—	53	1	no	—
211	C₂²×C₈	—	53	4	no	—
212	C₂²×C₈	—	53	8	no	—
213	C₂²×C₈	—	53	1	no	—
214	C₂²×C₈	—	53	4	no	—
215	C₂²×C₈	—	106	4	no	—
216	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
217	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
218	C₂×C₄⋊C₄	—	53	4	no	—
219	C₂×C₄⋊C₄	—	53	16	no	—
220	C₂×C₄⋊C₄	—	106	8	no	—
221	C₂×C₄⋊C₄	—	106	4	no	—
222	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	—
223	C₂×C₄²	—	2	2	no	—
224	C₂×C₄²	—	53	1	no	—
225	C₂×C₄²	—	53	1	no	—
226	C₂×C₄²	—	53	1	no	—
227	C₂×C₄²	—	53	4	no	—
228	C₂×C₄²	—	53	4	no	—
229	C₂×C₄²	—	106	4	no	—
230	C₂×C₄²	—	106	2	no	—
231	C₂×C₄²	—	212	8	no	—
232	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
233	#106	—	53	8	no	—
234	#106	—	53	16	no	—
235	#106	C₄×D₅₃	1	8	yes	direct product factor
236	C₄×C₈	—	53	4	no	—
237	C₄×C₈	—	53	4	no	—
238	C₄×C₈	—	53	4	no	—
239	C₄×C₈	C₄×D₅₃	1	4	yes	complemented
240	#95	—	2	2	no	—
241	#95	—	106	4	no	—
242	#95	—	106	2	no	—
243	C₂⁴	—	53	1	no	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	53	1	no	—
246	C₂²×C₄	—	53	1	no	—
247	C₂²×C₄	—	53	4	no	—
248	C₂²×C₄	—	53	8	no	—
249	C₂²×C₄	—	53	2	no	—
250	C₂²×C₄	—	53	4	no	—
251	C₂²×C₄	—	53	2	no	—
252	C₂²×C₄	—	53	4	no	—
253	C₂²×C₄	—	53	1	no	—
254	C₂²×C₄	—	53	4	no	—
255	C₂²×C₄	—	106	4	no	—
256	C₂²×C₄	—	106	16	no	—
257	C₂²×C₄	—	106	4	no	—
258	C₂²×C₄	—	212	8	no	—
259	C₂²×C₄	—	212	8	no	—
260	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
261	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
262	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	53	2	no	—
265	C₂×C₈	—	53	4	no	—
266	C₂×C₈	—	53	16	no	—
267	C₂×C₈	—	53	2	no	—
268	C₂×C₈	—	106	8	no	—
269	C₂×C₈	—	106	2	no	—
270	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
271	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
272	C₂×C₈	C₂×C₄×D₅₃	1	4	yes	—
273	C₄⋊C₄	—	2	4	no	—
274	C₄⋊C₄	—	53	8	no	—
275	C₄⋊C₄	—	106	16	no	—
276	C₄⋊C₄	—	106	4	no	—
277	C₄⋊C₄	C₂×C₄×D₅₃	1	8	yes	—
278	C₄²	—	4	4	no	—
279	C₄²	—	53	4	no	—
280	C₄²	—	53	4	no	—
281	C₄²	—	53	2	no	—
282	C₄²	—	53	2	no	—
283	C₄²	—	212	8	no	—
284	C₄²	—	212	4	no	—
285	C₄²	C₂×C₄×D₅₃	1	2	yes	—
286	C₄²	Q₈×D₅₃	1	2	yes	—
287	C₂³	—	53	2	no	—
288	C₂³	—	53	4	no	—
289	C₂³	—	53	4	no	—
290	C₂³	—	53	4	no	—
291	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	8	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	53	2	no	—
297	C₂×C₄	—	53	2	no	—
298	C₂×C₄	—	53	4	no	—
299	C₂×C₄	—	53	4	no	—
300	C₂×C₄	—	53	4	no	—
301	C₂×C₄	—	53	4	no	—
302	C₂×C₄	—	53	8	no	—
303	C₂×C₄	—	53	16	no	—
304	C₂×C₄	—	53	2	no	—
305	C₂×C₄	—	106	8	no	—
306	C₂×C₄	—	106	2	no	—
307	C₂×C₄	—	106	8	no	—
308	C₂×C₄	—	212	32	no	—
309	C₂×C₄	—	212	4	no	—
310	C₂×C₄	—	212	4	no	—
311	C₂×C₄	C₄⋊C₄×D₅₃	1	2	yes	—
312	C₂×C₄	C₄⋊C₄×D₅₃	1	2	yes	—
313	C₂×C₄	SD₁₆×D₅₃	1	4	yes	—
314	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
315	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
316	C₂×C₄	C₂×Q₈×D₅₃	1	1	yes	characteristic
317	C₂×C₄	#41×D₅₃	1	2	yes	—
318	C₈	—	2	2	no	—
319	C₈	—	53	4	no	—
320	C₈	—	106	2	no	—
321	C₈	C₄²×D₅₃	1	4	yes	complemented
322	C₂²	—	53	4	no	—
323	C₂²	—	53	16	no	—
324	C₂²	—	53	4	no	—
325	C₂²	—	53	4	no	—
326	C₂²	C₂×C₄⋊C₄×D₅₃	1	1	yes	characteristic
327	C₂²	C₄×D₄×D₅₃	1	2	yes	—
328	C₂²	C₂×SD₁₆×D₅₃	1	2	yes	—
329	C₂²	#135×D₅₃	1	2	yes	—
330	C₄	—	2	2	no	—
331	C₄	—	4	8	no	—
332	C₄	—	53	4	no	—
333	C₄	—	53	4	no	—
334	C₄	—	106	2	no	—
335	C₄	—	212	8	no	—
336	C₄	#106×D₅₃	1	4	yes	direct product factor
337	C₄	C₂×C₄²×D₅₃	1	1	yes	characteristic
338	C₄	#117×D₅₃	1	1	yes	characteristic
339	C₄	C₄×Q₈×D₅₃	1	2	yes	—
340	C₂	—	53	8	no	—
341	C₂	C₄×C₄⋊C₄×D₅₃	1	1	yes	characteristic
342	C₂	C₂×#106×D₅₃	1	1	yes	characteristic
343	C₂	#427×D₅₃	1	1	yes	characteristic
344	C₂	C₄×SD₁₆×D₅₃	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₃
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₄×#106×C₅₃	C₂
socle	C₂³×C₅₃	C₂²×D₄
prime radical	C₂³×D₅₃	C₂×D₄
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	C₄×#106	D₅₃
hypocenter	C₅₃	C₂×C₄×#106
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×#106

Complements

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

N	H ≅ G/N	type
4. #106×Dic₅₃	C₂	semidirect
5. C₄×#13133148	C₂	semidirect
6. C₄×#13133149	C₂	semidirect
7. #20274603	C₂	semidirect
9. C₄×#106×C₅₃	C₂	semidirect
17. #106×D₅₃	C₄	direct (N × H)
21. C₄×C₈×D₅₃	C₄	semidirect
55. #13133149	C₂×C₄	semidirect
56. #13133148	C₂×C₄	semidirect
57. C₄×#88322	C₂×C₄	semidirect
58. C₈×Dic₅₃	C₂×C₄	semidirect
59. C₈×Dic₅₃	C₂×C₄	semidirect
67. #106×C₅₃	C₂×C₄	semidirect
68. C₄×C₈×C₅₃	C₂×C₄	semidirect
113. C₈×D₅₃	C₄²	semidirect
141. C₄×D₅₃	#106	direct (N × H)
146. C₈×C₅₃	C₂×C₄²	semidirect
148. #88322	C₂×C₄²	semidirect
160. C₄×C₅₃	C₂×#106	semidirect
167. Dic₅₃	C₂×#106	semidirect
175. C₄×#106	D₅₃	direct (N × H)
181. D₅₃	C₄×#106	direct (N × H)
205. C₅₃	C₂×C₄×#106	semidirect
235. #106	C₄×D₅₃	direct (N × H)
239. C₄×C₈	C₄×D₅₃	semidirect
321. C₈	C₄²×D₅₃	semidirect
336. C₄	#106×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
C₂×#106×D₅₃	2
C₂×C₄×C₈×D₅₃	2
C₄×C₄⋊C₄×D₅₃	2
#106×Dic₅₃	2
C₄×#13133148	2
C₄×#13133149	2
#20274603	2
#340×D₅₃	2
C₄×#106×C₅₃	2
C₂×C₄×#106	53

Subgroups — C4×#106×D53 #27382129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#106×D₅₃ #27382129