Subgroups — C₂×C₅₃×#1773 #27227955

Order 13568.

1062 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#108×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#427	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₃×#405	C₂	1	2	yes	maximal
4	C₂²×#97×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₅₃×#1773	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅₃×#339	C₂	1	2	yes	maximal
7	C₂²×M₁₆×C₅₃	C₂²	1	2	yes	—
8	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
10	C₂×#117×C₅₃	C₂²	1	2	yes	—
11	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
12	C₂×#108×C₅₃	C₄	1	8	yes	complemented
13	C₂×#108×C₅₃	C₂²	1	4	yes	—
14	C₅₃×#427	C₄	1	4	yes	complemented
15	C₅₃×#427	C₂²	1	4	yes	—
16	C₂×#107×C₅₃	C₄	1	2	yes	complemented
17	C₂×#106×C₅₃	C₄	1	2	yes	complemented
18	C₅₃×#405	—	2	4	no	—
19	C₅₃×#405	C₂²	1	8	yes	—
20	C₂×#97×C₅₃	—	2	2	no	—
21	C₂×#97×C₅₃	C₄	1	8	yes	complemented
22	C₂×#97×C₅₃	C₂²	1	4	yes	—
23	C₂×C₄×C₈×C₅₃	—	2	2	no	—
24	C₅₃×#339	C₂²	1	8	yes	—
25	C₂³×C₄×C₅₃	—	2	1	no	—
26	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
27	C₂×M₁₆×C₅₃	—	2	2	no	—
28	C₂×M₁₆×C₅₃	—	2	4	no	—
29	C₂×M₁₆×C₅₃	C₂×C₄	1	8	yes	—
30	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
31	C₂²×C₈×C₅₃	—	2	2	no	—
32	C₂²×C₈×C₅₃	C₂×C₄	1	4	yes	—
33	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₅₃	C₂×C₄	1	4	yes	—
37	C₂²×C₈×C₅₃	C₂×C₄	1	4	yes	—
38	C₂²×C₈×C₅₃	D₄	1	2	yes	—
39	C₂²×C₈×C₅₃	D₄	1	2	yes	—
40	C₂²×C₈×C₅₃	Q₈	1	4	yes	—
41	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
43	#117×C₅₃	—	2	2	no	—
44	#117×C₅₃	—	2	2	no	—
45	#117×C₅₃	C₂×C₄	1	4	yes	—
46	#117×C₅₃	C₂³	1	4	yes	—
47	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	4	yes	—
48	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
49	C₂×C₄²×C₅₃	—	2	2	no	—
50	C₂×C₄²×C₅₃	—	2	2	no	—
51	C₂×C₄²×C₅₃	—	2	1	no	—
52	C₂×C₄²×C₅₃	C₂×C₄	1	4	yes	—
53	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
54	#108×C₅₃	C₂×C₄	1	16	yes	complemented
55	#107×C₅₃	C₂×C₄	1	8	yes	complemented
56	#106×C₅₃	C₂×C₄	1	8	yes	complemented
57	#97×C₅₃	—	2	8	no	—
58	#97×C₅₃	C₂×C₄	1	16	yes	complemented
59	C₄×C₈×C₅₃	—	2	8	no	—
60	C₂⁴×C₅₃	#41	1	1	yes	characteristic
61	C₂²×C₄×C₅₃	—	2	4	no	—
62	C₂²×C₄×C₅₃	—	2	4	no	—
63	C₂²×C₄×C₅₃	—	2	2	no	—
64	C₂²×C₄×C₅₃	—	4	4	no	—
65	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
66	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
67	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₅₃	C₂×Q₈	1	2	yes	—
72	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	#41	1	2	yes	—
74	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
75	M₁₆×C₅₃	—	2	8	no	—
76	M₁₆×C₅₃	—	2	4	no	—
77	M₁₆×C₅₃	C₂²×C₄	1	8	yes	—
78	C₂×C₈×C₅₃	—	2	8	no	—
79	C₂×C₈×C₅₃	—	2	4	no	—
80	C₂×C₈×C₅₃	C₄²	1	4	yes	—
81	C₂×C₈×C₅₃	C₄²	1	4	yes	—
82	C₂×C₈×C₅₃	C₄²	1	8	yes	—
83	C₂×C₈×C₅₃	C₄⋊C₄	1	8	yes	—
84	C₂×C₈×C₅₃	C₄⋊C₄	1	8	yes	—
85	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
86	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
87	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
88	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
89	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
90	C₂×C₈×C₅₃	C₂×D₄	1	4	yes	—
91	C₂×C₈×C₅₃	C₂×Q₈	1	4	yes	—
92	C₄⋊C₄×C₅₃	—	2	4	no	—
93	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
94	C₂²⋊C₄×C₅₃	—	2	4	no	—
95	C₂²⋊C₄×C₅₃	—	2	4	no	—
96	C₄²×C₅₃	—	2	4	no	—
97	C₄²×C₅₃	—	2	4	no	—
98	C₄²×C₅₃	—	2	4	no	—
99	C₄²×C₅₃	—	2	2	no	—
100	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
101	C₂³×C₅₃	—	2	4	no	—
102	C₂³×C₅₃	#117	1	2	yes	—
103	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
104	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
105	C₂³×C₅₃	C₄×Q₈	1	2	yes	—
106	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
107	C₂×C₄×C₅₃	—	2	4	no	—
108	C₂×C₄×C₅₃	—	2	8	no	—
109	C₂×C₄×C₅₃	—	4	4	no	—
110	C₂×C₄×C₅₃	—	4	8	no	—
111	C₂×C₄×C₅₃	—	4	8	no	—
112	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
113	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
114	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
115	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
116	C₂×C₄×C₅₃	#117	1	2	yes	—
117	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
118	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
119	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
120	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
121	C₂×C₄×C₅₃	C₄×Q₈	1	2	yes	—
122	C₂×C₄×C₅₃	C₄×Q₈	1	2	yes	—
123	C₂×C₄×C₅₃	C₄×Q₈	1	2	yes	—
124	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
125	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
126	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
127	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
128	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
129	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
130	C₈×C₅₃	—	2	8	no	—
131	C₈×C₅₃	C₂×C₄²	1	4	yes	—
132	C₈×C₅₃	C₂×C₄²	1	4	yes	—
133	C₈×C₅₃	C₂×C₄⋊C₄	1	8	yes	—
134	C₂×#1773	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂²×C₅₃	—	2	2	no	—
136	C₂²×C₅₃	—	2	2	no	—
137	C₂²×C₅₃	—	2	4	no	—
138	C₂²×C₅₃	—	2	4	no	—
139	C₂²×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
140	C₂²×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
141	C₂²×C₅₃	#444	1	4	yes	—
142	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
143	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
144	C₂²×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
145	C₄×C₅₃	—	4	4	no	—
146	C₄×C₅₃	—	4	8	no	—
147	C₄×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
148	C₄×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
149	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
150	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
151	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
152	C₄×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
153	C₂²×#108	C₂×C₅₃	1	1	yes	characteristic
154	C₂×#427	C₂×C₅₃	1	1	yes	characteristic
155	C₂×#405	C₂×C₅₃	1	2	yes	—
156	C₂²×#97	C₂×C₅₃	1	1	yes	characteristic
157	#1773	C₂×C₅₃	1	8	yes	direct product factor
158	C₂×#339	C₂×C₅₃	1	2	yes	—
159	C₂×C₅₃	—	2	1	no	—
160	C₂×C₅₃	—	2	1	no	—
161	C₂×C₅₃	—	2	2	no	—
162	C₂×C₅₃	#1773	1	4	yes	direct product factor
163	C₂×C₅₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₅₃	C₂×#444	1	2	yes	—
165	C₂²×M₁₆	C₂²×C₅₃	1	2	yes	—
166	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
167	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
168	C₂×#117	C₂²×C₅₃	1	2	yes	—
169	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
170	C₂×#108	C₄×C₅₃	1	8	yes	complemented
171	C₂×#108	C₂²×C₅₃	1	4	yes	—
172	#427	C₄×C₅₃	1	4	yes	complemented
173	#427	C₂²×C₅₃	1	4	yes	—
174	C₂×#107	C₄×C₅₃	1	2	yes	complemented
175	C₂×#106	C₄×C₅₃	1	2	yes	complemented
176	#405	—	2	4	no	—
177	#405	C₂²×C₅₃	1	8	yes	—
178	C₂×#97	—	2	2	no	—
179	C₂×#97	C₄×C₅₃	1	8	yes	complemented
180	C₂×#97	C₂²×C₅₃	1	4	yes	—
181	C₂×C₄×C₈	—	2	2	no	—
182	#339	C₂²×C₅₃	1	8	yes	—
183	C₅₃	C₂×#1773	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³×C₄	—	2	1	no	—
185	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
186	C₂×M₁₆	—	2	2	no	—
187	C₂×M₁₆	—	2	4	no	—
188	C₂×M₁₆	C₂×C₄×C₅₃	1	8	yes	—
189	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
190	C₂²×C₈	—	2	2	no	—
191	C₂²×C₈	C₂×C₄×C₅₃	1	4	yes	—
192	C₂²×C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
193	C₂²×C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
194	C₂²×C₈	C₂×C₄×C₅₃	1	2	yes	—
195	C₂²×C₈	C₂×C₄×C₅₃	1	4	yes	—
196	C₂²×C₈	C₂×C₄×C₅₃	1	4	yes	—
197	C₂²×C₈	D₄×C₅₃	1	2	yes	—
198	C₂²×C₈	D₄×C₅₃	1	2	yes	—
199	C₂²×C₈	Q₈×C₅₃	1	4	yes	—
200	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
201	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
202	#117	—	2	2	no	—
203	#117	—	2	2	no	—
204	#117	C₂×C₄×C₅₃	1	4	yes	—
205	#117	C₂³×C₅₃	1	4	yes	—
206	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	4	yes	—
207	C₂×C₂²⋊C₄	—	2	2	no	—
208	C₂×C₄²	—	2	2	no	—
209	C₂×C₄²	—	2	1	no	—
210	C₂×C₄²	—	2	2	no	—
211	C₂×C₄²	C₂×C₄×C₅₃	1	4	yes	—
212	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
213	#108	C₂×C₄×C₅₃	1	16	yes	complemented
214	#107	C₂×C₄×C₅₃	1	8	yes	complemented
215	#106	C₂×C₄×C₅₃	1	8	yes	complemented
216	#97	—	2	8	no	—
217	#97	C₂×C₄×C₅₃	1	16	yes	complemented
218	C₄×C₈	—	2	8	no	—
219	C₂⁴	#41×C₅₃	1	1	yes	characteristic
220	C₂²×C₄	—	2	4	no	—
221	C₂²×C₄	—	2	4	no	—
222	C₂²×C₄	—	2	2	no	—
223	C₂²×C₄	—	4	4	no	—
224	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
225	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
226	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
227	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
228	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
229	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
230	C₂²×C₄	C₂×Q₈×C₅₃	1	2	yes	—
231	C₂²×C₄	#41×C₅₃	1	1	yes	characteristic
232	C₂²×C₄	#41×C₅₃	1	2	yes	—
233	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
234	M₁₆	—	2	8	no	—
235	M₁₆	—	2	4	no	—
236	M₁₆	C₂²×C₄×C₅₃	1	8	yes	—
237	C₂×C₈	—	2	8	no	—
238	C₂×C₈	—	2	4	no	—
239	C₂×C₈	C₄²×C₅₃	1	4	yes	—
240	C₂×C₈	C₄²×C₅₃	1	4	yes	—
241	C₂×C₈	C₄²×C₅₃	1	8	yes	—
242	C₂×C₈	C₄⋊C₄×C₅₃	1	8	yes	—
243	C₂×C₈	C₄⋊C₄×C₅₃	1	8	yes	—
244	C₂×C₈	C₂²×C₄×C₅₃	1	4	yes	—
245	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
246	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
247	C₂×C₈	C₂²×C₄×C₅₃	1	4	yes	—
248	C₂×C₈	C₂²×C₄×C₅₃	1	4	yes	—
249	C₂×C₈	C₂×D₄×C₅₃	1	4	yes	—
250	C₂×C₈	C₂×Q₈×C₅₃	1	4	yes	—
251	C₄⋊C₄	—	2	4	no	—
252	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
253	C₂²⋊C₄	—	2	4	no	—
254	C₂²⋊C₄	—	2	4	no	—
255	C₄²	—	2	4	no	—
256	C₄²	—	2	4	no	—
257	C₄²	—	2	4	no	—
258	C₄²	—	2	2	no	—
259	C₄²	C₂²×C₄×C₅₃	1	4	yes	—
260	C₂³	—	2	4	no	—
261	C₂³	#117×C₅₃	1	2	yes	—
262	C₂³	C₄×D₄×C₅₃	1	1	yes	characteristic
263	C₂³	C₄×D₄×C₅₃	1	1	yes	characteristic
264	C₂³	C₄×Q₈×C₅₃	1	2	yes	—
265	C₂³	C₂×#41×C₅₃	1	1	yes	characteristic
266	C₂×C₄	—	2	4	no	—
267	C₂×C₄	—	2	8	no	—
268	C₂×C₄	—	4	4	no	—
269	C₂×C₄	—	4	8	no	—
270	C₂×C₄	—	4	8	no	—
271	C₂×C₄	C₂×C₄²×C₅₃	1	2	yes	—
272	C₂×C₄	C₂×C₄²×C₅₃	1	2	yes	—
273	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
274	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
275	C₂×C₄	#117×C₅₃	1	2	yes	—
276	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
277	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
278	C₂×C₄	C₄×D₄×C₅₃	1	1	yes	characteristic
279	C₂×C₄	C₄×D₄×C₅₃	1	1	yes	characteristic
280	C₂×C₄	C₄×Q₈×C₅₃	1	2	yes	—
281	C₂×C₄	C₄×Q₈×C₅₃	1	2	yes	—
282	C₂×C₄	C₄×Q₈×C₅₃	1	2	yes	—
283	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
284	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
285	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
286	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
287	C₂×C₄	C₂²×Q₈×C₅₃	1	1	yes	characteristic
288	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
289	C₈	—	2	8	no	—
290	C₈	C₂×C₄²×C₅₃	1	4	yes	—
291	C₈	C₂×C₄²×C₅₃	1	4	yes	—
292	C₈	C₂×C₄⋊C₄×C₅₃	1	8	yes	—
293	C₂²	—	2	2	no	—
294	C₂²	—	2	2	no	—
295	C₂²	—	2	4	no	—
296	C₂²	—	2	4	no	—
297	C₂²	C₄×C₄⋊C₄×C₅₃	1	2	yes	—
298	C₂²	C₄×C₄⋊C₄×C₅₃	1	2	yes	—
299	C₂²	C₅₃×#444	1	4	yes	—
300	C₂²	C₂×#117×C₅₃	1	1	yes	characteristic
301	C₂²	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
302	C₂²	C₂×C₄×Q₈×C₅₃	1	1	yes	characteristic
303	C₄	—	4	4	no	—
304	C₄	—	4	8	no	—
305	C₄	C₄×C₄⋊C₄×C₅₃	1	2	yes	—
306	C₄	C₄×C₄⋊C₄×C₅₃	1	2	yes	—
307	C₄	C₂²×C₄²×C₅₃	1	1	yes	characteristic
308	C₄	C₂²×C₄⋊C₄×C₅₃	1	1	yes	characteristic
309	C₄	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
310	C₄	C₂×C₄×Q₈×C₅₃	1	1	yes	characteristic
311	C₂	—	2	1	no	—
312	C₂	—	2	1	no	—
313	C₂	—	2	2	no	—
314	C₂	C₅₃×#1773	1	4	yes	direct product factor
315	C₂	C₂×C₄×C₄⋊C₄×C₅₃	1	1	yes	characteristic
316	C₂	C₂×C₅₃×#444	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂×D₄
commutator	C₄	C₂²×C₄²×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
socle	C₂³×C₅₃	C₄×D₄
prime radical	C₂⁴×C₅₃	#41
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ C₂³×C₈×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₅₃×#1773	C₂	direct (N × H)
12. C₂×#108×C₅₃	C₄	semidirect
14. C₅₃×#427	C₄	semidirect
16. C₂×#107×C₅₃	C₄	semidirect
17. C₂×#106×C₅₃	C₄	semidirect
21. C₂×#97×C₅₃	C₄	semidirect
54. #108×C₅₃	C₂×C₄	semidirect
55. #107×C₅₃	C₂×C₄	semidirect
56. #106×C₅₃	C₂×C₄	semidirect
58. #97×C₅₃	C₂×C₄	semidirect
134. C₂×#1773	C₅₃	direct (N × H)
157. #1773	C₂×C₅₃	direct (N × H)
162. C₂×C₅₃	#1773	direct (N × H)
170. C₂×#108	C₄×C₅₃	semidirect
172. #427	C₄×C₅₃	semidirect
174. C₂×#107	C₄×C₅₃	semidirect
175. C₂×#106	C₄×C₅₃	semidirect
179. C₂×#97	C₄×C₅₃	semidirect
183. C₅₃	C₂×#1773	direct (N × H)
213. #108	C₂×C₄×C₅₃	semidirect
214. #107	C₂×C₄×C₅₃	semidirect
215. #106	C₂×C₄×C₅₃	semidirect
217. #97	C₂×C₄×C₅₃	semidirect
314. C₂	C₅₃×#1773	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#108×C₅₃	2
C₂×C₅₃×#427	2
C₂×C₅₃×#405	2
C₂²×#97×C₅₃	2
C₅₃×#1773	2
C₂×C₅₃×#339	2
C₂×#1773	53

Subgroups — C2×C53×#1773 #27227955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#1773 #27227955