Subgroups — C₂×#16811181 #20288014

Order 6784.

1984 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
2	#16811181	C₂	1	16	yes	maximal, direct product factor
3	C₂×#13133202	C₂	1	2	yes	maximal, complemented
4	C₂×#13133199	C₂	1	2	yes	maximal, complemented
5	C₂×#13133191	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13133189	C₂	1	2	yes	maximal, complemented
7	C₂×#13133187	C₂	1	2	yes	maximal, complemented
8	C₂×#13133185	C₂	1	2	yes	maximal, complemented
9	C₂²×#11719921	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁴×D₅₃	C₂²	1	1	yes	characteristic
12	C₂⁴×D₅₃	C₂²	1	2	yes	complemented
13	C₂²×D₂₁₂	C₂²	1	2	yes	—
14	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	—
16	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
17	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
18	C₂×D₄×D₅₃	—	2	16	no	—
19	C₂×D₄×D₅₃	C₂²	1	16	yes	complemented
20	C₂³×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₄×D₅₃	C₂²	1	2	yes	complemented
22	#13133202	C₂²	1	16	yes	complemented
23	#13133199	C₂²	1	16	yes	complemented
24	#13133191	C₂²	1	8	yes	complemented
25	#13133189	C₂²	1	16	yes	complemented
26	#13133187	C₂²	1	16	yes	complemented
27	#13133185	C₂²	1	16	yes	complemented
28	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#11719919	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Dic₅₃	C₂²	1	2	yes	complemented
31	C₂×#11719921	C₂²	1	2	yes	complemented
32	C₂×#11719921	C₂²	1	2	yes	complemented
33	C₂×#11719921	C₂²	1	2	yes	complemented
34	C₂×#11719921	C₂²	1	2	yes	complemented
35	C₂×#11719921	C₂²	1	8	yes	complemented
36	C₂²×D₄×C₅₃	C₂²	1	2	yes	complemented
37	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	#121×C₅₃	C₂²	1	8	yes	complemented
40	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
42	C₂⁴×C₅₃	C₂³	1	2	yes	—
43	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
44	C₂³×D₅₃	—	2	8	no	—
45	C₂³×D₅₃	—	4	2	no	—
46	C₂³×D₅₃	—	4	2	no	—
47	C₂³×D₅₃	—	4	4	no	—
48	C₂³×D₅₃	—	4	4	no	—
49	C₂³×D₅₃	D₄	1	8	yes	complemented
50	C₂³×D₅₃	C₂³	1	2	yes	—
51	C₂³×D₅₃	C₂³	1	2	yes	—
52	C₂³×D₅₃	C₂³	1	4	yes	—
53	C₂³×D₅₃	C₂³	1	8	yes	complemented
54	C₂×D₄×C₅₃	—	2	8	no	—
55	C₂×D₄×C₅₃	—	4	2	no	—
56	C₂×D₄×C₅₃	C₂³	1	8	yes	complemented
57	C₂×D₄×C₅₃	C₂³	1	4	yes	complemented
58	C₂²×C₄×C₅₃	—	4	2	no	—
59	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
61	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₅₃	C₂³	1	4	yes	complemented
63	C₂×C₂²⋊D₅₃	—	2	8	no	—
64	C₂×C₂²⋊D₅₃	—	2	8	no	—
65	C₂×C₂²⋊D₅₃	—	4	4	no	—
66	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	—
67	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
68	C₂×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
69	C₂²×Dic₅₃	—	4	2	no	—
70	C₂²×Dic₅₃	C₂³	1	2	yes	—
71	C₂²×Dic₅₃	C₂³	1	2	yes	—
72	C₂²×Dic₅₃	C₂³	1	4	yes	complemented
73	D₄×D₅₃	—	2	64	no	—
74	C₂×D₂₁₂	—	2	8	no	—
75	C₂×D₂₁₂	—	4	2	no	—
76	C₂×D₂₁₂	C₂³	1	8	yes	—
77	C₂×D₂₁₂	C₂³	1	4	yes	complemented
78	C₂×C₄×D₅₃	—	2	8	no	—
79	C₂×C₄×D₅₃	C₂³	1	8	yes	complemented
80	C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
81	C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
82	C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
83	#11719921	C₂³	1	8	yes	complemented
84	#11719921	C₂³	1	8	yes	complemented
85	#11719921	C₂³	1	8	yes	complemented
86	#11719921	C₂³	1	8	yes	complemented
87	C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
88	#11719919	C₂³	1	8	yes	complemented
89	C₂³×C₅₃	—	2	2	no	—
90	C₂³×C₅₃	—	2	2	no	—
91	C₂³×C₅₃	—	2	4	no	—
92	C₂³×C₅₃	—	2	4	no	—
93	C₂³×C₅₃	—	2	4	no	—
94	C₂³×C₅₃	C₂×D₄	1	4	yes	—
95	C₂³×C₅₃	C₂⁴	1	4	yes	—
96	C₂³×C₅₃	C₂⁴	1	2	yes	—
97	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
98	C₂²×D₅₃	—	2	4	no	—
99	C₂²×D₅₃	—	2	4	no	—
100	C₂²×D₅₃	—	2	4	no	—
101	C₂²×D₅₃	—	2	4	no	—
102	C₂²×D₅₃	—	2	4	no	—
103	C₂²×D₅₃	—	2	16	no	—
104	C₂²×D₅₃	—	4	16	no	—
105	C₂²×D₅₃	—	4	4	no	—
106	C₂²×D₅₃	—	4	4	no	—
107	C₂²×D₅₃	—	4	8	no	—
108	C₂²×D₅₃	—	4	8	no	—
109	C₂²×D₅₃	—	4	32	no	—
110	C₂²×D₅₃	C₂×D₄	1	8	yes	—
111	C₂²×D₅₃	C₂×D₄	1	16	yes	complemented
112	C₂²×D₅₃	C₂⁴	1	4	yes	—
113	C₂²×D₅₃	C₂⁴	1	4	yes	—
114	D₄×C₅₃	—	2	16	no	—
115	D₄×C₅₃	—	4	4	no	—
116	C₂×C₄×C₅₃	—	2	4	no	—
117	C₂×C₄×C₅₃	—	2	2	no	—
118	C₂×C₄×C₅₃	—	2	2	no	—
119	C₂×C₄×C₅₃	—	4	4	no	—
120	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
121	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
122	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
123	C₂²⋊D₅₃	—	2	16	no	—
124	C₂²⋊D₅₃	—	2	16	no	—
125	C₂²⋊D₅₃	—	4	8	no	—
126	C₂×Dic₅₃	—	2	4	no	—
127	C₂×Dic₅₃	—	2	4	no	—
128	C₂×Dic₅₃	—	4	4	no	—
129	C₂×Dic₅₃	C₂⁴	1	4	yes	—
130	C₂×Dic₅₃	C₂⁴	1	4	yes	—
131	D₂₁₂	—	2	16	no	—
132	D₂₁₂	—	4	4	no	—
133	C₄×D₅₃	—	2	16	no	—
134	C₂²×C₅₃	—	2	8	no	—
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	—	2	4	no	—
140	C₂²×C₅₃	—	4	8	no	—
141	C₂²×C₅₃	C₂²×D₄	1	4	yes	—
142	C₂²×C₅₃	C₂²×D₄	1	2	yes	—
143	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
144	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
145	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
146	C₂×D₅₃	—	2	16	no	—
147	C₂×D₅₃	—	2	4	no	—
148	C₂×D₅₃	—	2	4	no	—
149	C₂×D₅₃	—	2	4	no	—
150	C₂×D₅₃	—	2	4	no	—
151	C₂×D₅₃	—	2	4	no	—
152	C₂×D₅₃	—	4	16	no	—
153	C₂×D₅₃	—	4	32	no	—
154	C₂×D₅₃	—	4	8	no	—
155	C₂×D₅₃	C₂²×D₄	1	8	yes	—
156	C₄×C₅₃	—	2	4	no	—
157	C₄×C₅₃	—	2	2	no	—
158	C₄×C₅₃	—	2	2	no	—
159	Dic₅₃	—	2	4	no	—
160	Dic₅₃	—	2	4	no	—
161	C₂×#534	—	53	1	no	maximal, Sylow
162	C₂×C₅₃	—	2	4	no	—
163	C₂×C₅₃	—	4	4	no	—
164	C₂×C₅₃	#534	1	4	yes	complemented
165	C₂×C₅₃	C₂³×D₄	1	1	yes	characteristic
166	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
167	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
168	D₅₃	—	2	8	no	—
169	D₅₃	—	4	4	no	—
170	C₂³×D₄	—	53	2	no	—
171	#534	—	53	16	no	—
172	C₂×#123	—	53	2	no	—
173	C₂×#123	—	53	2	no	—
174	C₂×#121	—	53	2	no	—
175	C₂×#121	—	53	1	no	—
176	C₂×#121	D₅₃	1	1	yes	characteristic, complemented
177	C₂×#120	—	53	2	no	—
178	C₂×#120	—	53	2	no	—
179	C₂²×C₂²⋊C₄	—	53	1	no	—
180	C₅₃	C₂×#534	1	1	yes	characteristic, complemented, Sylow
181	C₂⁵	—	53	1	no	—
182	C₂⁵	—	53	2	no	—
183	C₂²×D₄	—	53	2	no	—
184	C₂²×D₄	—	53	2	no	—
185	C₂²×D₄	—	53	2	no	—
186	C₂²×D₄	—	53	16	no	—
187	C₂²×D₄	—	53	2	no	—
188	C₂²×D₄	—	53	1	no	—
189	C₂²×D₄	—	106	16	no	—
190	C₂²×D₄	C₂×D₅₃	1	2	yes	complemented
191	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
192	C₂³×C₄	—	53	1	no	—
193	C₂³×C₄	—	53	2	no	—
194	C₂³×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
195	#123	—	53	16	no	—
196	#123	—	53	16	no	—
197	#121	—	53	16	no	—
198	#121	—	53	8	no	—
199	#121	C₂×D₅₃	1	8	yes	complemented
200	#120	—	53	16	no	—
201	#120	—	53	16	no	—
202	C₂×C₄⋊C₄	—	53	2	no	—
203	C₂×C₄⋊C₄	—	53	1	no	—
204	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
205	C₂×C₂²⋊C₄	—	53	2	no	—
206	C₂×C₂²⋊C₄	—	53	2	no	—
207	C₂×C₂²⋊C₄	—	53	2	no	—
208	C₂×C₂²⋊C₄	—	53	2	no	—
209	C₂×C₂²⋊C₄	—	53	2	no	—
210	C₂×C₂²⋊C₄	—	53	8	no	—
211	C₂×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
212	C₂⁴	—	53	2	no	—
213	C₂⁴	—	53	8	no	—
214	C₂⁴	—	53	4	no	—
215	C₂⁴	—	53	2	no	—
216	C₂⁴	—	53	8	no	—
217	C₂⁴	—	106	8	no	—
218	C₂⁴	—	212	2	no	—
219	C₂⁴	—	212	2	no	—
220	C₂⁴	—	212	4	no	—
221	C₂⁴	—	212	4	no	—
222	C₂⁴	C₂²×D₅₃	1	2	yes	—
223	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
224	C₂×D₄	—	2	8	no	—
225	C₂×D₄	—	4	2	no	—
226	C₂×D₄	—	53	8	no	—
227	C₂×D₄	—	53	8	no	—
228	C₂×D₄	—	53	8	no	—
229	C₂×D₄	—	53	8	no	—
230	C₂×D₄	—	53	4	no	—
231	C₂×D₄	—	106	8	no	—
232	C₂×D₄	—	106	64	no	—
233	C₂×D₄	—	106	8	no	—
234	C₂×D₄	—	106	8	no	—
235	C₂×D₄	—	212	2	no	—
236	C₂×D₄	—	212	4	no	—
237	C₂×D₄	C₂²×D₅₃	1	8	yes	complemented
238	C₂×D₄	C₂²×D₅₃	1	4	yes	complemented
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	53	2	no	—
241	C₂²×C₄	—	53	2	no	—
242	C₂²×C₄	—	53	4	no	—
243	C₂²×C₄	—	53	8	no	—
244	C₂²×C₄	—	106	8	no	—
245	C₂²×C₄	—	212	2	no	—
246	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
247	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
248	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
249	C₂²×C₄	C₂²×D₅₃	1	4	yes	complemented
250	C₄⋊C₄	—	53	8	no	—
251	C₄⋊C₄	—	53	4	no	—
252	C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
253	C₂²⋊C₄	—	53	8	no	—
254	C₂²⋊C₄	—	53	8	no	—
255	C₂²⋊C₄	—	53	8	no	—
256	C₂²⋊C₄	—	53	8	no	—
257	C₂²⋊C₄	—	53	8	no	—
258	C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
259	C₂³	—	2	2	no	—
260	C₂³	—	2	2	no	—
261	C₂³	—	2	4	no	—
262	C₂³	—	2	4	no	—
263	C₂³	—	2	4	no	—
264	C₂³	—	53	8	no	—
265	C₂³	—	53	4	no	—
266	C₂³	—	53	16	no	—
267	C₂³	—	53	4	no	—
268	C₂³	—	106	16	no	—
269	C₂³	—	106	4	no	—
270	C₂³	—	106	4	no	—
271	C₂³	—	106	4	no	—
272	C₂³	—	106	4	no	—
273	C₂³	—	106	4	no	—
274	C₂³	—	212	16	no	—
275	C₂³	—	212	4	no	—
276	C₂³	—	212	4	no	—
277	C₂³	—	212	8	no	—
278	C₂³	—	212	8	no	—
279	C₂³	—	212	32	no	—
280	C₂³	D₄×D₅₃	1	4	yes	—
281	C₂³	C₂³×D₅₃	1	4	yes	—
282	C₂³	C₂³×D₅₃	1	2	yes	—
283	C₂³	C₂³×D₅₃	1	1	yes	characteristic
284	D₄	—	2	16	no	—
285	D₄	—	4	4	no	—
286	D₄	—	106	16	no	—
287	D₄	—	106	16	no	—
288	D₄	—	106	16	no	—
289	D₄	—	212	4	no	—
290	D₄	—	212	8	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	—	53	4	no	—
296	C₂×C₄	—	53	4	no	—
297	C₂×C₄	—	106	16	no	—
298	C₂×C₄	—	106	4	no	—
299	C₂×C₄	—	106	4	no	—
300	C₂×C₄	—	212	4	no	—
301	C₂×C₄	C₂³×D₅₃	1	2	yes	—
302	C₂×C₄	C₂³×D₅₃	1	2	yes	—
303	C₂×C₄	C₂³×D₅₃	1	4	yes	—
304	C₂²	—	2	8	no	—
305	C₂²	—	2	2	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	2	4	no	—
308	C₂²	—	2	4	no	—
309	C₂²	—	2	4	no	—
310	C₂²	—	4	8	no	—
311	C₂²	—	53	8	no	—
312	C₂²	—	106	16	no	—
313	C₂²	—	106	4	no	—
314	C₂²	—	106	4	no	—
315	C₂²	—	106	4	no	—
316	C₂²	—	106	4	no	—
317	C₂²	—	106	4	no	—
318	C₂²	—	212	16	no	—
319	C₂²	—	212	32	no	—
320	C₂²	—	212	8	no	—
321	C₂²	C₂×D₄×D₅₃	1	4	yes	—
322	C₂²	C₂×D₄×D₅₃	1	2	yes	—
323	C₂²	#13133262	1	2	yes	—
324	C₂²	#13133263	1	2	yes	—
325	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
326	C₄	—	2	4	no	—
327	C₄	—	2	2	no	—
328	C₄	—	2	2	no	—
329	C₄	—	106	4	no	—
330	C₄	—	106	4	no	—
331	C₂	—	2	4	no	—
332	C₂	—	4	4	no	—
333	C₂	—	106	8	no	—
334	C₂	—	212	4	no	—
335	C₂	#16811181	1	4	yes	direct product factor
336	C₂	C₂²×D₄×D₅₃	1	1	yes	characteristic
337	C₂	C₂×#13133262	1	1	yes	characteristic
338	C₂	C₂×#13133263	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₅₃
commutator	C₂²×C₅₃	C₂⁵
Frattini	C₂²	C₂⁴×D₅₃
Fitting	C₂×#121×C₅₃	C₂
socle	C₂³×C₅₃	C₂⁴
hypercenter	C₂×#121	D₅₃
hypocenter	C₅₃	C₂×#534
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×D₅₃	C₂	semidirect
2. #16811181	C₂	direct (N × H)
3. C₂×#13133202	C₂	semidirect
4. C₂×#13133199	C₂	semidirect
5. C₂×#13133191	C₂	semidirect
6. C₂×#13133189	C₂	semidirect
7. C₂×#13133187	C₂	semidirect
8. C₂×#13133185	C₂	semidirect
9. C₂²×#11719921	C₂	semidirect
10. C₂×#121×C₅₃	C₂	semidirect
12. C₂⁴×D₅₃	C₂²	semidirect
14. C₂²×D₂₁₂	C₂²	semidirect
16. C₂²×C₂²⋊D₅₃	C₂²	semidirect
17. C₂²×C₂²⋊D₅₃	C₂²	semidirect
19. C₂×D₄×D₅₃	C₂²	semidirect
20. C₂³×Dic₅₃	C₂²	semidirect
21. C₂²×C₄×D₅₃	C₂²	semidirect
22. #13133202	C₂²	semidirect
23. #13133199	C₂²	semidirect
24. #13133191	C₂²	semidirect
25. #13133189	C₂²	semidirect
26. #13133187	C₂²	semidirect
27. #13133185	C₂²	semidirect
28. C₂×C₄⋊Dic₅₃	C₂²	semidirect
29. C₂×#11719919	C₂²	semidirect
30. C₂×C₂²⋊Dic₅₃	C₂²	semidirect
31. C₂×#11719921	C₂²	semidirect
32. C₂×#11719921	C₂²	semidirect
33. C₂×#11719921	C₂²	semidirect
34. C₂×#11719921	C₂²	semidirect
35. C₂×#11719921	C₂²	semidirect
36. C₂²×D₄×C₅₃	C₂²	semidirect
37. C₂²×D₄×C₅₃	C₂²	semidirect
38. C₂³×C₄×C₅₃	C₂²	semidirect
39. #121×C₅₃	C₂²	semidirect
40. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
41. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
49. C₂³×D₅₃	D₄	semidirect
53. C₂³×D₅₃	C₂³	semidirect
56. C₂×D₄×C₅₃	C₂³	semidirect
57. C₂×D₄×C₅₃	C₂³	semidirect
62. C₂²×C₄×C₅₃	C₂³	semidirect
67. C₂×C₂²⋊D₅₃	C₂³	semidirect
68. C₂×C₂²⋊D₅₃	C₂³	semidirect
72. C₂²×Dic₅₃	C₂³	semidirect
77. C₂×D₂₁₂	C₂³	semidirect
79. C₂×C₄×D₅₃	C₂³	semidirect
80. C₄⋊C₄×C₅₃	C₂³	semidirect
81. C₂²⋊C₄×C₅₃	C₂³	semidirect
82. C₂²⋊Dic₅₃	C₂³	semidirect
83. #11719921	C₂³	semidirect
84. #11719921	C₂³	semidirect
85. #11719921	C₂³	semidirect
86. #11719921	C₂³	semidirect
87. C₄⋊Dic₅₃	C₂³	semidirect
88. #11719919	C₂³	semidirect
111. C₂²×D₅₃	C₂×D₄	semidirect
164. C₂×C₅₃	#534	semidirect
176. C₂×#121	D₅₃	semidirect
180. C₅₃	C₂×#534	semidirect
190. C₂²×D₄	C₂×D₅₃	semidirect
191. C₂²×D₄	C₂×D₅₃	semidirect
194. C₂³×C₄	C₂×D₅₃	semidirect
199. #121	C₂×D₅₃	semidirect
204. C₂×C₄⋊C₄	C₂×D₅₃	semidirect
211. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect
237. C₂×D₄	C₂²×D₅₃	semidirect
238. C₂×D₄	C₂²×D₅₃	semidirect
249. C₂²×C₄	C₂²×D₅₃	semidirect
252. C₄⋊C₄	C₂²×D₅₃	semidirect
258. C₂²⋊C₄	C₂²×D₅₃	semidirect
335. C₂	#16811181	direct (N × H)

Subgroups — C2×#16811181 #20288014

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16811181 #20288014