Subgroups — C₂×#16811255 #20288151

Order 6784.

2536 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊D₅₃	C₂	1	2	yes	maximal, complemented
2	C₂²×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
3	#16811255	C₂	1	16	yes	maximal, direct product factor
4	C₂×#13133213	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13133190	C₂	1	2	yes	maximal, complemented
6	C₂×#13133189	C₂	1	2	yes	maximal, complemented
7	C₂×#13133187	C₂	1	2	yes	maximal, complemented
8	C₂×#13133185	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13133177	C₂	1	2	yes	maximal, complemented
10	C₂×#120×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁴×D₅₃	C₂²	1	1	yes	characteristic, complemented
12	C₂⁴×D₅₃	C₂²	1	2	yes	complemented
13	C₂²×D₂₁₂	C₂²	1	2	yes	complemented
14	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₂²⋊D₅₃	—	2	16	no	—
16	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	—
17	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
18	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
19	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
20	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₅₃	C₂²	1	16	yes	complemented
22	C₂×D₄×D₅₃	—	2	16	no	—
23	C₂×D₄×D₅₃	C₂²	1	16	yes	complemented
24	C₂³×Dic₅₃	C₂²	1	2	yes	complemented
25	C₂²×C₄×D₅₃	C₂²	1	2	yes	complemented
26	#13133213	C₂²	1	8	yes	complemented
27	#13133190	C₂²	1	16	yes	complemented
28	#13133189	C₂²	1	16	yes	complemented
29	#13133187	C₂²	1	16	yes	complemented
30	#13133185	C₂²	1	8	yes	complemented
31	#13133177	C₂²	1	16	yes	complemented
32	C₂×#11719919	C₂²	1	2	yes	complemented
33	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#11719921	C₂²	1	2	yes	complemented
35	C₂×#11719921	C₂²	1	2	yes	complemented
36	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂⁵×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×D₄×C₅₃	C₂²	1	2	yes	complemented
39	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	#120×C₅₃	C₂²	1	8	yes	complemented
41	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
42	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₂⁴×C₅₃	—	2	8	no	—
44	C₂⁴×C₅₃	—	4	2	no	—
45	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
46	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
47	C₂⁴×C₅₃	C₂³	1	2	yes	—
48	C₂⁴×C₅₃	C₂³	1	4	yes	complemented
49	C₂³×D₅₃	—	2	8	no	—
50	C₂³×D₅₃	—	2	8	no	—
51	C₂³×D₅₃	—	2	8	no	—
52	C₂³×D₅₃	—	4	2	no	—
53	C₂³×D₅₃	—	4	4	no	—
54	C₂³×D₅₃	C₂³	1	2	yes	—
55	C₂³×D₅₃	C₂³	1	2	yes	—
56	C₂³×D₅₃	C₂³	1	4	yes	complemented
57	C₂³×D₅₃	C₂³	1	8	yes	complemented
58	C₂×D₄×C₅₃	—	2	8	no	—
59	C₂×D₄×C₅₃	—	4	2	no	—
60	C₂×D₄×C₅₃	C₂³	1	8	yes	complemented
61	C₂×D₄×C₅₃	C₂³	1	4	yes	complemented
62	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
64	C₂×C₂²⋊D₅₃	—	2	8	no	—
65	C₂×C₂²⋊D₅₃	—	2	8	no	—
66	C₂×C₂²⋊D₅₃	—	2	64	no	—
67	C₂×C₂²⋊D₅₃	—	2	8	no	—
68	C₂×C₂²⋊D₅₃	—	2	8	no	—
69	C₂×C₂²⋊D₅₃	D₄	1	16	yes	complemented
70	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	—
71	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
72	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
73	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
74	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
75	C₂²×Dic₅₃	—	2	8	no	—
76	C₂²×Dic₅₃	C₂³	1	2	yes	—
77	C₂²×Dic₅₃	C₂³	1	2	yes	—
78	C₂²×Dic₅₃	C₂³	1	8	yes	complemented
79	D₄×D₅₃	—	2	64	no	—
80	C₂×D₂₁₂	—	2	8	no	—
81	C₂×D₂₁₂	—	4	2	no	—
82	C₂×D₂₁₂	C₂³	1	8	yes	complemented
83	C₂×D₂₁₂	C₂³	1	4	yes	complemented
84	C₂×C₄×D₅₃	—	2	8	no	—
85	C₂×C₄×D₅₃	C₂³	1	8	yes	complemented
86	C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
87	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
88	C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
89	#11719921	C₂³	1	8	yes	complemented
90	#11719921	C₂³	1	8	yes	complemented
91	#11719919	C₂³	1	8	yes	complemented
92	C₄×Dic₅₃	C₂³	1	4	yes	complemented
93	C₂³×C₅₃	—	2	4	no	—
94	C₂³×C₅₃	—	2	4	no	—
95	C₂³×C₅₃	—	2	4	no	—
96	C₂³×C₅₃	—	2	4	no	—
97	C₂³×C₅₃	—	2	16	no	—
98	C₂³×C₅₃	—	2	2	no	—
99	C₂³×C₅₃	—	2	2	no	—
100	C₂³×C₅₃	—	4	4	no	—
101	C₂³×C₅₃	—	4	16	no	—
102	C₂³×C₅₃	C₂×D₄	1	8	yes	complemented
103	C₂³×C₅₃	C₂⁴	1	2	yes	—
104	C₂³×C₅₃	C₂⁴	1	2	yes	—
105	C₂³×C₅₃	C₂⁴	1	4	yes	—
106	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
107	C₂²×D₅₃	—	2	4	no	—
108	C₂²×D₅₃	—	2	4	no	—
109	C₂²×D₅₃	—	2	4	no	—
110	C₂²×D₅₃	—	2	4	no	—
111	C₂²×D₅₃	—	2	16	no	—
112	C₂²×D₅₃	—	2	4	no	—
113	C₂²×D₅₃	—	2	16	no	—
114	C₂²×D₅₃	—	2	16	no	—
115	C₂²×D₅₃	—	4	4	no	—
116	C₂²×D₅₃	—	4	8	no	—
117	C₂²×D₅₃	—	4	16	no	—
118	C₂²×D₅₃	—	4	32	no	—
119	C₂²×D₅₃	C₂×D₄	1	8	yes	complemented
120	C₂²×D₅₃	C₂⁴	1	4	yes	—
121	C₂²×D₅₃	C₂⁴	1	4	yes	—
122	D₄×C₅₃	—	2	16	no	—
123	D₄×C₅₃	—	4	4	no	—
124	C₂×C₄×C₅₃	—	2	4	no	—
125	C₂×C₄×C₅₃	—	2	2	no	—
126	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
127	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
128	C₂²⋊D₅₃	—	2	16	no	—
129	C₂²⋊D₅₃	—	2	16	no	—
130	C₂²⋊D₅₃	—	2	16	no	—
131	C₂²⋊D₅₃	—	2	16	no	—
132	C₂²⋊D₅₃	C₂×D₄	1	32	yes	complemented
133	C₂×Dic₅₃	—	2	4	no	—
134	C₂×Dic₅₃	—	2	16	no	—
135	C₂×Dic₅₃	C₂×D₄	1	8	yes	complemented
136	C₂×Dic₅₃	C₂⁴	1	4	yes	—
137	C₂×Dic₅₃	C₂⁴	1	4	yes	—
138	D₂₁₂	—	2	16	no	—
139	D₂₁₂	—	4	4	no	—
140	C₄×D₅₃	—	2	16	no	—
141	C₂²×C₅₃	—	2	16	no	—
142	C₂²×C₅₃	—	2	4	no	—
143	C₂²×C₅₃	—	2	4	no	—
144	C₂²×C₅₃	—	2	4	no	—
145	C₂²×C₅₃	—	2	4	no	—
146	C₂²×C₅₃	—	2	2	no	—
147	C₂²×C₅₃	—	2	2	no	—
148	C₂²×C₅₃	—	4	16	no	—
149	C₂²×C₅₃	—	4	4	no	—
150	C₂²×C₅₃	—	4	4	no	—
151	C₂²×C₅₃	C₂²×D₄	1	4	yes	—
152	C₂²×C₅₃	C₂²×D₄	1	8	yes	complemented
153	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
154	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
155	C₂×D₅₃	—	2	16	no	—
156	C₂×D₅₃	—	2	4	no	—
157	C₂×D₅₃	—	2	4	no	—
158	C₂×D₅₃	—	2	4	no	—
159	C₂×D₅₃	—	2	4	no	—
160	C₂×D₅₃	—	2	4	no	—
161	C₂×D₅₃	—	4	16	no	—
162	C₂×D₅₃	—	4	32	no	—
163	C₂×D₅₃	—	4	8	no	—
164	C₂×D₅₃	C₂²×D₄	1	8	yes	complemented
165	C₄×C₅₃	—	2	4	no	—
166	C₄×C₅₃	—	2	2	no	—
167	Dic₅₃	—	2	4	no	—
168	Dic₅₃	C₂²×D₄	1	8	yes	complemented
169	C₂×D₄²	—	53	1	no	maximal, Sylow
170	C₂×C₅₃	—	2	8	no	—
171	C₂×C₅₃	—	4	2	no	—
172	C₂×C₅₃	—	4	2	no	—
173	C₂×C₅₃	D₄²	1	4	yes	complemented
174	C₂×C₅₃	C₂³×D₄	1	2	yes	—
175	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
176	D₅₃	—	2	8	no	—
177	D₅₃	—	4	4	no	—
178	C₂³×D₄	—	53	2	no	—
179	C₂³×D₄	—	53	2	no	—
180	D₄²	—	53	16	no	—
181	C₂×#127	—	53	1	no	—
182	C₂×#121	—	53	2	no	—
183	C₂×#121	—	53	2	no	—
184	C₂×#120	—	53	1	no	—
185	C₂×#120	—	53	2	no	—
186	C₂×#120	D₅₃	1	1	yes	characteristic, complemented
187	C₂×C₄×D₄	—	53	2	no	—
188	C₅₃	C₂×D₄²	1	1	yes	characteristic, complemented, Sylow
189	C₂⁵	—	53	1	no	—
190	C₂⁵	—	53	2	no	—
191	C₂⁵	C₂×D₅₃	1	1	yes	characteristic, complemented
192	C₂²×D₄	—	53	2	no	—
193	C₂²×D₄	—	53	2	no	—
194	C₂²×D₄	—	53	2	no	—
195	C₂²×D₄	—	53	2	no	—
196	C₂²×D₄	—	53	2	no	—
197	C₂²×D₄	—	53	16	no	—
198	C₂²×D₄	—	53	16	no	—
199	C₂²×D₄	—	53	2	no	—
200	C₂²×D₄	—	53	1	no	—
201	C₂²×D₄	—	106	16	no	—
202	C₂²×D₄	—	106	16	no	—
203	C₂²×D₄	C₂×D₅₃	1	2	yes	complemented
204	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
205	C₂³×C₄	—	53	2	no	—
206	C₂³×C₄	—	53	2	no	—
207	#127	—	53	8	no	—
208	#121	—	53	16	no	—
209	#121	—	53	16	no	—
210	#120	—	53	8	no	—
211	#120	—	53	16	no	—
212	#120	C₂×D₅₃	1	8	yes	complemented
213	C₄×D₄	—	53	16	no	—
214	C₂×C₄⋊C₄	—	53	2	no	—
215	C₂×C₂²⋊C₄	—	53	1	no	—
216	C₂×C₂²⋊C₄	—	53	2	no	—
217	C₂×C₂²⋊C₄	—	53	2	no	—
218	C₂×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
219	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
220	C₂×C₄²	—	53	1	no	—
221	C₂⁴	—	2	8	no	—
222	C₂⁴	—	4	2	no	—
223	C₂⁴	—	53	2	no	—
224	C₂⁴	—	53	2	no	—
225	C₂⁴	—	53	4	no	—
226	C₂⁴	—	53	8	no	—
227	C₂⁴	—	106	8	no	—
228	C₂⁴	—	106	8	no	—
229	C₂⁴	—	106	8	no	—
230	C₂⁴	—	212	4	no	—
231	C₂⁴	—	212	2	no	—
232	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
233	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
234	C₂⁴	C₂²×D₅₃	1	2	yes	—
235	C₂⁴	C₂²×D₅₃	1	4	yes	complemented
236	C₂×D₄	—	2	8	no	—
237	C₂×D₄	—	4	2	no	—
238	C₂×D₄	—	53	16	no	—
239	C₂×D₄	—	53	8	no	—
240	C₂×D₄	—	53	8	no	—
241	C₂×D₄	—	53	8	no	—
242	C₂×D₄	—	53	8	no	—
243	C₂×D₄	—	53	8	no	—
244	C₂×D₄	—	53	8	no	—
245	C₂×D₄	—	53	4	no	—
246	C₂×D₄	—	106	8	no	—
247	C₂×D₄	—	106	8	no	—
248	C₂×D₄	—	106	8	no	—
249	C₂×D₄	—	106	64	no	—
250	C₂×D₄	—	106	64	no	—
251	C₂×D₄	—	106	8	no	—
252	C₂×D₄	—	106	8	no	—
253	C₂×D₄	—	212	2	no	—
254	C₂×D₄	C₂²×D₅₃	1	8	yes	complemented
255	C₂×D₄	C₂²×D₅₃	1	4	yes	complemented
256	C₂²×C₄	—	53	2	no	—
257	C₂²×C₄	—	53	8	no	—
258	C₂²×C₄	—	53	2	no	—
259	C₂²×C₄	—	53	8	no	—
260	C₂²×C₄	—	106	8	no	—
261	C₂²×C₄	—	106	8	no	—
262	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
263	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
264	C₄⋊C₄	—	53	8	no	—
265	C₂²⋊C₄	—	53	4	no	—
266	C₂²⋊C₄	—	53	8	no	—
267	C₂²⋊C₄	—	53	8	no	—
268	C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
269	C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
270	C₄²	—	53	4	no	—
271	C₂³	—	2	4	no	—
272	C₂³	—	2	4	no	—
273	C₂³	—	2	4	no	—
274	C₂³	—	2	4	no	—
275	C₂³	—	2	16	no	—
276	C₂³	—	2	2	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	4	4	no	—
279	C₂³	—	4	16	no	—
280	C₂³	—	53	8	no	—
281	C₂³	—	53	4	no	—
282	C₂³	—	53	4	no	—
283	C₂³	—	106	16	no	—
284	C₂³	—	106	16	no	—
285	C₂³	—	106	4	no	—
286	C₂³	—	106	4	no	—
287	C₂³	—	106	4	no	—
288	C₂³	—	106	4	no	—
289	C₂³	—	106	16	no	—
290	C₂³	—	106	4	no	—
291	C₂³	—	212	8	no	—
292	C₂³	—	212	4	no	—
293	C₂³	—	212	32	no	—
294	C₂³	—	212	16	no	—
295	C₂³	D₄×D₅₃	1	8	yes	complemented
296	C₂³	C₂³×D₅₃	1	2	yes	—
297	C₂³	C₂³×D₅₃	1	2	yes	—
298	C₂³	C₂³×D₅₃	1	4	yes	—
299	C₂³	C₂³×D₅₃	1	1	yes	characteristic
300	D₄	—	2	16	no	—
301	D₄	—	4	4	no	—
302	D₄	—	53	32	no	—
303	D₄	—	106	16	no	—
304	D₄	—	106	16	no	—
305	D₄	—	106	16	no	—
306	D₄	—	106	16	no	—
307	D₄	—	106	16	no	—
308	D₄	—	212	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	53	8	no	—
312	C₂×C₄	—	53	4	no	—
313	C₂×C₄	—	53	4	no	—
314	C₂×C₄	—	106	16	no	—
315	C₂×C₄	—	106	16	no	—
316	C₂×C₄	—	106	4	no	—
317	C₂×C₄	C₂³×D₅₃	1	2	yes	—
318	C₂×C₄	C₂³×D₅₃	1	4	yes	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	4	no	—
321	C₂²	—	2	16	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	4	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	4	16	no	—
327	C₂²	—	4	4	no	—
328	C₂²	—	4	4	no	—
329	C₂²	—	53	8	no	—
330	C₂²	—	106	4	no	—
331	C₂²	—	106	4	no	—
332	C₂²	—	106	16	no	—
333	C₂²	—	106	4	no	—
334	C₂²	—	106	4	no	—
335	C₂²	—	106	4	no	—
336	C₂²	—	212	32	no	—
337	C₂²	—	212	16	no	—
338	C₂²	—	212	8	no	—
339	C₂²	C₂×D₄×D₅₃	1	4	yes	—
340	C₂²	C₂×D₄×D₅₃	1	8	yes	complemented
341	C₂²	#13133262	1	2	yes	—
342	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
343	C₄	—	2	4	no	—
344	C₄	—	2	2	no	—
345	C₄	—	53	8	no	—
346	C₄	—	106	4	no	—
347	C₂	—	2	8	no	—
348	C₂	—	4	2	no	—
349	C₂	—	4	2	no	—
350	C₂	—	106	8	no	—
351	C₂	—	212	4	no	—
352	C₂	#16811255	1	4	yes	direct product factor
353	C₂	C₂²×D₄×D₅₃	1	2	yes	—
354	C₂	C₂×#13133262	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₅₃
commutator	C₂²×C₅₃	C₂⁵
Frattini	C₂²	C₂⁴×D₅₃
Fitting	C₂×#120×C₅₃	C₂
socle	C₂³×C₅₃	C₂⁴
hypercenter	C₂×#120	D₅₃
hypocenter	C₅₃	C₂×D₄²
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#120

Complements

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

N	H ≅ G/N	type
1. C₂³×C₂²⋊D₅₃	C₂	semidirect
2. C₂²×D₄×D₅₃	C₂	semidirect
3. #16811255	C₂	direct (N × H)
4. C₂×#13133213	C₂	semidirect
5. C₂×#13133190	C₂	semidirect
6. C₂×#13133189	C₂	semidirect
7. C₂×#13133187	C₂	semidirect
8. C₂×#13133185	C₂	semidirect
9. C₂×#13133177	C₂	semidirect
10. C₂×#120×C₅₃	C₂	semidirect
11. C₂⁴×D₅₃	C₂²	semidirect
12. C₂⁴×D₅₃	C₂²	semidirect
13. C₂²×D₂₁₂	C₂²	semidirect
14. C₂²×D₂₁₂	C₂²	semidirect
17. C₂²×C₂²⋊D₅₃	C₂²	semidirect
18. C₂²×C₂²⋊D₅₃	C₂²	semidirect
19. C₂²×C₂²⋊D₅₃	C₂²	semidirect
20. C₂²×C₂²⋊D₅₃	C₂²	semidirect
21. C₂²×C₂²⋊D₅₃	C₂²	semidirect
23. C₂×D₄×D₅₃	C₂²	semidirect
24. C₂³×Dic₅₃	C₂²	semidirect
25. C₂²×C₄×D₅₃	C₂²	semidirect
26. #13133213	C₂²	semidirect
27. #13133190	C₂²	semidirect
28. #13133189	C₂²	semidirect
29. #13133187	C₂²	semidirect
30. #13133185	C₂²	semidirect
31. #13133177	C₂²	semidirect
32. C₂×#11719919	C₂²	semidirect
33. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
34. C₂×#11719921	C₂²	semidirect
35. C₂×#11719921	C₂²	semidirect
36. C₂×C₄×Dic₅₃	C₂²	semidirect
37. C₂⁵×C₅₃	C₂²	semidirect
38. C₂²×D₄×C₅₃	C₂²	semidirect
39. C₂²×D₄×C₅₃	C₂²	semidirect
40. #120×C₅₃	C₂²	semidirect
41. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
42. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
48. C₂⁴×C₅₃	C₂³	semidirect
56. C₂³×D₅₃	C₂³	semidirect
57. C₂³×D₅₃	C₂³	semidirect
60. C₂×D₄×C₅₃	C₂³	semidirect
61. C₂×D₄×C₅₃	C₂³	semidirect
69. C₂×C₂²⋊D₅₃	D₄	semidirect
71. C₂×C₂²⋊D₅₃	C₂³	semidirect
72. C₂×C₂²⋊D₅₃	C₂³	semidirect
73. C₂×C₂²⋊D₅₃	C₂³	semidirect
74. C₂×C₂²⋊D₅₃	C₂³	semidirect
78. C₂²×Dic₅₃	C₂³	semidirect
82. C₂×D₂₁₂	C₂³	semidirect
83. C₂×D₂₁₂	C₂³	semidirect
85. C₂×C₄×D₅₃	C₂³	semidirect
86. C₂²⋊C₄×C₅₃	C₂³	semidirect
87. C₂²⋊C₄×C₅₃	C₂³	semidirect
88. C₂²⋊Dic₅₃	C₂³	semidirect
89. #11719921	C₂³	semidirect
90. #11719921	C₂³	semidirect
91. #11719919	C₂³	semidirect
92. C₄×Dic₅₃	C₂³	semidirect
102. C₂³×C₅₃	C₂×D₄	semidirect
119. C₂²×D₅₃	C₂×D₄	semidirect
132. C₂²⋊D₅₃	C₂×D₄	semidirect
135. C₂×Dic₅₃	C₂×D₄	semidirect
152. C₂²×C₅₃	C₂²×D₄	semidirect
164. C₂×D₅₃	C₂²×D₄	semidirect
168. Dic₅₃	C₂²×D₄	semidirect
173. C₂×C₅₃	D₄²	semidirect
186. C₂×#120	D₅₃	semidirect
188. C₅₃	C₂×D₄²	semidirect
191. C₂⁵	C₂×D₅₃	semidirect
203. C₂²×D₄	C₂×D₅₃	semidirect
204. C₂²×D₄	C₂×D₅₃	semidirect
212. #120	C₂×D₅₃	semidirect
218. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect
219. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect
235. C₂⁴	C₂²×D₅₃	semidirect
254. C₂×D₄	C₂²×D₅₃	semidirect
255. C₂×D₄	C₂²×D₅₃	semidirect
268. C₂²⋊C₄	C₂²×D₅₃	semidirect
269. C₂²⋊C₄	C₂²×D₅₃	semidirect
295. C₂³	D₄×D₅₃	semidirect
340. C₂²	C₂×D₄×D₅₃	semidirect
352. C₂	#16811255	direct (N × H)

Subgroups — C2×#16811255 #20288151

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16811255 #20288151