Subgroups — C₄×#107×D₅₃ #27382134

Order 13568.

1358 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#107×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	#107×Dic₅₃	C₂	1	2	yes	maximal, complemented
5	C₄×#13133150	C₂	1	2	yes	maximal, complemented
6	C₄×#13133151	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274607	C₂	1	2	yes	maximal, complemented
8	#340×D₅₃	C₂	1	2	yes	maximal
9	C₄×#107×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×#13133151	C₂²	1	2	yes	—
16	C₂×#13133150	C₂²	1	4	yes	—
17	#107×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×#107×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	#13133151	C₂×C₄	1	8	yes	complemented
56	#13133150	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	#107×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	D₈	1	4	yes	—
86	C₂×C₄×D₅₃	Q₁₆	1	4	yes	—
87	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
88	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
89	C₂×C₄×D₅₃	C₂×Q₈	1	2	yes	—
90	C₂×C₄×D₅₃	#41	1	4	yes	—
91	C₂×C₈×C₅₃	—	2	2	no	—
92	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
93	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
94	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
95	C₄⋊C₄×C₅₃	—	2	4	no	—
96	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
97	C₄²×C₅₃	—	4	4	no	—
98	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
99	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
100	C₄⋊Dic₅₃	—	2	4	no	—
101	C₄⋊Dic₅₃	C₂²×C₄	1	8	yes	—
102	#11719919	—	2	16	no	—
103	C₄×Dic₅₃	—	4	4	no	—
104	C₄×Dic₅₃	—	4	8	no	—
105	C₄×Dic₅₃	C₄⋊C₄	1	4	yes	—
106	C₄×Dic₅₃	C₄⋊C₄	1	4	yes	—
107	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
108	C₄×Dic₅₃	C₂×Q₈	1	2	yes	—
109	C₂×#88322	—	2	2	no	—
110	C₂×#88322	C₂²×C₄	1	2	yes	—
111	C₂×#88322	C₂²×C₄	1	2	yes	—
112	C₂×#88322	C₂²×C₄	1	4	yes	—
113	C₈×D₅₃	—	2	8	no	—
114	C₈×D₅₃	C₄²	1	16	yes	complemented
115	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
116	C₂²×D₅₃	C₂×C₄⋊C₄	1	2	yes	—
117	C₂²×D₅₃	C₄×D₄	1	4	yes	—
118	C₂²×D₅₃	C₂×D₈	1	2	yes	—
119	C₂²×D₅₃	C₂×Q₁₆	1	2	yes	—
120	C₂²×D₅₃	#135	1	4	yes	—
121	C₂×C₄×C₅₃	—	2	2	no	—
122	C₂×C₄×C₅₃	—	2	8	no	—
123	C₂×C₄×C₅₃	—	4	4	no	—
124	C₂×C₄×C₅₃	—	4	4	no	—
125	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
126	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₅₃	C₂×D₈	1	2	yes	—
128	C₂×C₄×C₅₃	C₂×Q₁₆	1	2	yes	—
129	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
131	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
132	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
133	C₂×Dic₅₃	—	2	2	no	—
134	C₂×Dic₅₃	—	2	8	no	—
135	C₂×Dic₅₃	—	4	4	no	—
136	C₂×Dic₅₃	—	4	4	no	—
137	C₂×Dic₅₃	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×Dic₅₃	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×Dic₅₃	C₂×C₄⋊C₄	1	2	yes	—
140	C₂×Dic₅₃	C₄×D₄	1	4	yes	—
141	C₂×Dic₅₃	C₂×D₈	1	2	yes	—
142	C₂×Dic₅₃	C₂×Q₁₆	1	2	yes	—
143	C₄×D₅₃	—	2	8	no	—
144	C₄×D₅₃	—	4	32	no	—
145	C₄×D₅₃	#107	1	16	yes	direct product factor
146	C₄×D₅₃	C₂×C₄²	1	4	yes	—
147	C₄×D₅₃	#117	1	4	yes	—
148	C₄×D₅₃	C₄×Q₈	1	8	yes	—
149	C₈×C₅₃	—	2	2	no	—
150	C₈×C₅₃	C₂×C₄²	1	4	yes	complemented
151	#88322	—	2	2	no	—
152	#88322	C₂×C₄²	1	4	yes	complemented
153	C₂×C₄×#107	—	53	1	no	maximal, Sylow
154	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
155	C₂²×C₅₃	C₂×C₄×D₄	1	2	yes	—
156	C₂²×C₅₃	C₂²×D₈	1	1	yes	characteristic
157	C₂²×C₅₃	C₂²×Q₁₆	1	1	yes	characteristic
158	C₂²×C₅₃	C₂×#135	1	2	yes	—
159	C₂×D₅₃	C₄×C₄⋊C₄	1	4	yes	—
160	C₂×D₅₃	C₂×#107	1	4	yes	—
161	C₂×D₅₃	#427	1	4	yes	—
162	C₂×D₅₃	C₄×D₈	1	8	yes	—
163	C₂×D₅₃	C₄×Q₁₆	1	8	yes	—
164	C₄×C₅₃	—	2	2	no	—
165	C₄×C₅₃	—	4	8	no	—
166	C₄×C₅₃	C₂×#107	1	4	yes	complemented
167	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
168	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
169	C₄×C₅₃	C₂×C₄×Q₈	1	2	yes	—
170	Dic₅₃	—	2	2	no	—
171	Dic₅₃	—	4	8	no	—
172	Dic₅₃	C₄×C₄⋊C₄	1	4	yes	—
173	Dic₅₃	C₂×#107	1	4	yes	complemented
174	C₂²×#107	—	53	2	no	—
175	C₂²×C₄×C₈	—	53	1	no	—
176	C₂×C₄×C₄⋊C₄	—	53	2	no	—
177	C₄×#107	—	53	2	no	—
178	C₄×#107	—	53	1	no	—
179	C₄×#107	—	53	2	no	—
180	C₄×#107	—	53	2	no	—
181	C₄×#107	D₅₃	1	1	yes	characteristic, direct product factor
182	C₂×#340	—	53	2	no	—
183	C₂×C₅₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₅₃	C₂²×#107	1	1	yes	characteristic
185	C₂×C₅₃	C₂×#427	1	1	yes	characteristic
186	C₂×C₅₃	C₂×C₄×D₈	1	2	yes	—
187	C₂×C₅₃	C₂×C₄×Q₁₆	1	2	yes	—
188	D₅₃	C₄×#107	1	8	yes	direct product factor
189	C₂³×C₈	—	53	1	no	—
190	C₂³×C₈	—	53	1	no	—
191	C₂²×C₄⋊C₄	—	53	4	no	—
192	C₂²×C₄²	—	53	1	no	—
193	C₂²×C₄²	—	106	2	no	—
194	C₂×#107	—	53	2	no	—
195	C₂×#107	—	53	4	no	—
196	C₂×#107	—	53	16	no	—
197	C₂×#107	C₂×D₅₃	1	2	yes	—
198	C₂×C₄×C₈	—	53	1	no	—
199	C₂×C₄×C₈	—	53	1	no	—
200	C₂×C₄×C₈	—	53	1	no	—
201	C₂×C₄×C₈	—	53	8	no	—
202	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
203	C₄×C₄⋊C₄	—	53	4	no	—
204	C₄×C₄⋊C₄	—	53	2	no	—
205	C₄×C₄⋊C₄	—	106	2	no	—
206	C₄×C₄⋊C₄	—	106	2	no	—
207	C₄×C₄⋊C₄	C₂×D₅₃	1	2	yes	—
208	C₂×#95	—	106	2	no	—
209	#340	—	53	2	no	—
210	#340	—	53	4	no	—
211	#340	C₂×D₅₃	1	2	yes	—
212	C₅₃	C₂×C₄×#107	1	1	yes	characteristic, complemented, Sylow
213	C₂³×C₄	—	53	1	no	—
214	C₂³×C₄	—	53	1	no	—
215	C₂³×C₄	—	53	1	no	—
216	C₂³×C₄	—	106	4	no	—
217	C₂²×C₈	—	53	1	no	—
218	C₂²×C₈	—	53	4	no	—
219	C₂²×C₈	—	53	8	no	—
220	C₂²×C₈	—	53	1	no	—
221	C₂²×C₈	—	53	4	no	—
222	C₂²×C₈	—	106	4	no	—
223	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
224	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
225	C₂×C₄⋊C₄	—	53	4	no	—
226	C₂×C₄⋊C₄	—	53	16	no	—
227	C₂×C₄⋊C₄	—	106	8	no	—
228	C₂×C₄⋊C₄	—	106	4	no	—
229	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	—	53	1	no	—
232	C₂×C₄²	—	53	1	no	—
233	C₂×C₄²	—	53	1	no	—
234	C₂×C₄²	—	53	4	no	—
235	C₂×C₄²	—	53	4	no	—
236	C₂×C₄²	—	106	4	no	—
237	C₂×C₄²	—	106	2	no	—
238	C₂×C₄²	—	212	8	no	—
239	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
240	#107	—	53	8	no	—
241	#107	—	53	16	no	—
242	#107	C₄×D₅₃	1	8	yes	direct product factor
243	C₄×C₈	—	53	4	no	—
244	C₄×C₈	—	53	4	no	—
245	C₄×C₈	—	53	4	no	—
246	C₄×C₈	C₄×D₅₃	1	4	yes	complemented
247	#95	—	2	2	no	—
248	#95	—	106	4	no	—
249	#95	—	106	2	no	—
250	C₂⁴	—	53	1	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	53	1	no	—
253	C₂²×C₄	—	53	1	no	—
254	C₂²×C₄	—	53	4	no	—
255	C₂²×C₄	—	53	4	no	—
256	C₂²×C₄	—	53	4	no	—
257	C₂²×C₄	—	53	2	no	—
258	C₂²×C₄	—	53	4	no	—
259	C₂²×C₄	—	53	2	no	—
260	C₂²×C₄	—	53	4	no	—
261	C₂²×C₄	—	53	1	no	—
262	C₂²×C₄	—	53	4	no	—
263	C₂²×C₄	—	106	4	no	—
264	C₂²×C₄	—	106	16	no	—
265	C₂²×C₄	—	106	4	no	—
266	C₂²×C₄	—	212	8	no	—
267	C₂²×C₄	—	212	8	no	—
268	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
269	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
270	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	53	2	no	—
273	C₂×C₈	—	53	4	no	—
274	C₂×C₈	—	53	16	no	—
275	C₂×C₈	—	53	2	no	—
276	C₂×C₈	—	106	8	no	—
277	C₂×C₈	—	106	2	no	—
278	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
279	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
280	C₂×C₈	C₂×C₄×D₅₃	1	4	yes	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	53	8	no	—
283	C₄⋊C₄	—	106	16	no	—
284	C₄⋊C₄	—	106	4	no	—
285	C₄⋊C₄	C₂×C₄×D₅₃	1	8	yes	—
286	C₄²	—	4	4	no	—
287	C₄²	—	53	4	no	—
288	C₄²	—	53	4	no	—
289	C₄²	—	53	2	no	—
290	C₄²	—	53	2	no	—
291	C₄²	—	212	8	no	—
292	C₄²	—	212	4	no	—
293	C₄²	C₂×C₄×D₅₃	1	2	yes	—
294	C₄²	Q₈×D₅₃	1	2	yes	—
295	C₂³	—	53	2	no	—
296	C₂³	—	53	4	no	—
297	C₂³	—	53	2	no	—
298	C₂³	—	53	2	no	—
299	C₂³	—	53	4	no	—
300	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	4	4	no	—
305	C₂×C₄	—	53	2	no	—
306	C₂×C₄	—	53	2	no	—
307	C₂×C₄	—	53	4	no	—
308	C₂×C₄	—	53	2	no	—
309	C₂×C₄	—	53	2	no	—
310	C₂×C₄	—	53	4	no	—
311	C₂×C₄	—	53	4	no	—
312	C₂×C₄	—	53	8	no	—
313	C₂×C₄	—	53	16	no	—
314	C₂×C₄	—	53	2	no	—
315	C₂×C₄	—	106	8	no	—
316	C₂×C₄	—	106	2	no	—
317	C₂×C₄	—	106	8	no	—
318	C₂×C₄	—	212	32	no	—
319	C₂×C₄	—	212	4	no	—
320	C₂×C₄	—	212	4	no	—
321	C₂×C₄	C₄⋊C₄×D₅₃	1	2	yes	—
322	C₂×C₄	C₄⋊C₄×D₅₃	1	2	yes	—
323	C₂×C₄	D₈×D₅₃	1	2	yes	—
324	C₂×C₄	Q₁₆×D₅₃	1	2	yes	—
325	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
326	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
327	C₂×C₄	C₂×Q₈×D₅₃	1	1	yes	characteristic
328	C₂×C₄	#41×D₅₃	1	2	yes	—
329	C₈	—	2	2	no	—
330	C₈	—	53	4	no	—
331	C₈	—	106	2	no	—
332	C₈	C₄²×D₅₃	1	4	yes	complemented
333	C₂²	—	53	4	no	—
334	C₂²	—	53	8	no	—
335	C₂²	—	53	8	no	—
336	C₂²	—	53	4	no	—
337	C₂²	—	53	4	no	—
338	C₂²	C₂×C₄⋊C₄×D₅₃	1	1	yes	characteristic
339	C₂²	C₄×D₄×D₅₃	1	2	yes	—
340	C₂²	C₂×D₈×D₅₃	1	1	yes	characteristic
341	C₂²	C₂×Q₁₆×D₅₃	1	1	yes	characteristic
342	C₂²	#135×D₅₃	1	2	yes	—
343	C₄	—	2	2	no	—
344	C₄	—	4	8	no	—
345	C₄	—	53	4	no	—
346	C₄	—	53	4	no	—
347	C₄	—	106	2	no	—
348	C₄	—	212	8	no	—
349	C₄	#107×D₅₃	1	4	yes	direct product factor
350	C₄	C₂×C₄²×D₅₃	1	1	yes	characteristic
351	C₄	#117×D₅₃	1	1	yes	characteristic
352	C₄	C₄×Q₈×D₅₃	1	2	yes	—
353	C₂	—	53	8	no	—
354	C₂	C₄×C₄⋊C₄×D₅₃	1	1	yes	characteristic
355	C₂	C₂×#107×D₅₃	1	1	yes	characteristic
356	C₂	#427×D₅₃	1	1	yes	characteristic
357	C₂	C₄×D₈×D₅₃	1	2	yes	—
358	C₂	C₄×Q₁₆×D₅₃	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₃
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₄×#107×C₅₃	C₂
socle	C₂³×C₅₃	C₂²×D₄
prime radical	C₂³×D₅₃	C₂×D₄
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	C₄×#107	D₅₃
hypocenter	C₅₃	C₂×C₄×#107
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
4. #107×Dic₅₃	C₂	semidirect
5. C₄×#13133150	C₂	semidirect
6. C₄×#13133151	C₂	semidirect
7. #20274607	C₂	semidirect
9. C₄×#107×C₅₃	C₂	semidirect
17. #107×D₅₃	C₄	direct (N × H)
21. C₄×C₈×D₅₃	C₄	semidirect
55. #13133151	C₂×C₄	semidirect
56. #13133150	C₂×C₄	semidirect
57. C₄×#88322	C₂×C₄	semidirect
58. C₈×Dic₅₃	C₂×C₄	semidirect
59. C₈×Dic₅₃	C₂×C₄	semidirect
67. #107×C₅₃	C₂×C₄	semidirect
68. C₄×C₈×C₅₃	C₂×C₄	semidirect
114. C₈×D₅₃	C₄²	semidirect
145. C₄×D₅₃	#107	direct (N × H)
150. C₈×C₅₃	C₂×C₄²	semidirect
152. #88322	C₂×C₄²	semidirect
166. C₄×C₅₃	C₂×#107	semidirect
173. Dic₅₃	C₂×#107	semidirect
181. C₄×#107	D₅₃	direct (N × H)
188. D₅₃	C₄×#107	direct (N × H)
212. C₅₃	C₂×C₄×#107	semidirect
242. #107	C₄×D₅₃	direct (N × H)
246. C₄×C₈	C₄×D₅₃	semidirect
332. C₈	C₄²×D₅₃	semidirect
349. C₄	#107×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×#107×D₅₃	2
C₂×C₄×C₈×D₅₃	2
C₄×C₄⋊C₄×D₅₃	2
#107×Dic₅₃	2
C₄×#13133150	2
C₄×#13133151	2
#20274607	2
#340×D₅₃	2
C₄×#107×C₅₃	2
C₂×C₄×#107	53

Subgroups — C4×#107×D53 #27382134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#107×D₅₃ #27382134