Subgroups — C₃×#10603775 #14295156

Order 1920.

768 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×C₃×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4003	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×#170	C₂	1	2	yes	maximal, complemented
4	C₃×#64955	C₂	1	1	yes	maximal, characteristic
5	C₃×#64918	C₂	1	2	yes	maximal, complemented
6	#10603775	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×#170	C₂²	1	2	yes	—
9	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
10	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
11	C₂×C₃×D₅⋊C₈	—	2	4	no	—
12	C₂×C₃×D₅⋊C₈	C₄	1	4	yes	complemented
13	C₂×C₃×#685	C₄	1	2	yes	—
14	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
15	C₃×#4003	C₄	1	4	yes	complemented
16	C₃×C₄×#170	—	2	4	no	—
17	C₃×C₅×#95	C₄	1	1	yes	characteristic
18	C₃×#3963	C₄	1	1	yes	characteristic
19	C₃×C₈×C₂²⋊C₄	—	5	1	no	maximal, Hall
20	C₂²×D₅⋊C₈	C₂×C₃	1	1	yes	characteristic
21	C₂×#4003	C₂×C₃	1	1	yes	characteristic
22	C₂×C₄×#170	C₂×C₃	1	2	yes	complemented
23	#64955	C₂×C₃	1	1	yes	characteristic
24	#64918	C₂×C₃	1	2	yes	complemented
25	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
28	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
29	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
30	C₂×C₃×C₄×D₅	—	2	2	no	—
31	C₂×C₃×C₄×D₅	—	2	2	no	—
32	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
33	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
34	C₂×C₃×#170	—	2	2	no	—
35	C₂×C₃×#170	—	2	2	no	—
36	C₂×C₃×#170	—	2	2	no	—
37	C₂×C₃×#170	C₂×C₄	1	2	yes	—
38	C₂×C₃×#170	C₂×C₄	1	4	yes	—
39	C₂×C₃×#170	C₂×C₄	1	2	yes	—
40	C₂×C₃×#170	D₄	1	4	yes	—
41	C₃×D₅⋊C₈	—	2	8	no	—
42	C₃×#685	C₈	1	8	yes	complemented
43	C₃×C₄×Dic₅	—	2	2	no	—
44	C₃×C₄×Dic₅	—	2	2	no	—
45	C₂³×C₃×C₈	—	5	1	no	—
46	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
47	C₂×C₃×C₄×C₈	—	5	2	no	—
48	C₃×C₄×C₂²⋊C₄	—	5	1	no	—
49	C₃×#336	—	5	2	no	—
50	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
51	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
52	C₂²×#170	C₂²×C₃	1	2	yes	—
53	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
54	C₂×D₅⋊C₈	—	2	4	no	—
55	C₂×D₅⋊C₈	C₃×C₄	1	4	yes	complemented
56	C₂×#685	C₃×C₄	1	2	yes	—
57	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
58	#4003	C₃×C₄	1	4	yes	complemented
59	C₄×#170	—	2	4	no	—
60	C₅×#95	C₃×C₄	1	1	yes	characteristic
61	#3963	C₃×C₄	1	1	yes	characteristic
62	C₈×C₂²⋊C₄	—	5	1	no	Sylow
63	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₃×D₅	—	2	2	no	—
65	C₂²×C₃×D₅	—	2	1	no	—
66	C₂²×C₃×D₅	—	2	1	no	—
67	C₂²×C₃×D₅	C₄²	1	2	yes	—
68	C₂²×C₃×D₅	C₂×C₈	1	4	yes	—
69	C₂×C₃×C₄×C₅	—	2	2	no	—
70	C₂×C₃×C₄×C₅	—	2	2	no	—
71	C₂×C₃×C₄×C₅	—	2	2	no	—
72	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
73	C₂×C₃×C₄×C₅	C₂×C₈	1	4	yes	complemented
74	C₂×C₃×Dic₅	—	2	2	no	—
75	C₂×C₃×Dic₅	—	2	2	no	—
76	C₂×C₃×Dic₅	C₂×C₈	1	4	yes	complemented
77	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
80	C₂×C₃×Dic₅	#41	1	2	yes	—
81	C₃×C₄×D₅	—	2	2	no	—
82	C₃×C₄×D₅	—	2	2	no	—
83	C₃×C₄×D₅	—	2	4	no	—
84	C₃×#170	—	2	2	no	—
85	C₃×#170	—	2	4	no	—
86	C₃×#170	C₂²⋊C₄	1	4	yes	complemented
87	C₂³×C₃×C₄	—	5	1	no	—
88	C₂²×C₃×C₈	—	5	1	no	—
89	C₂²×C₃×C₈	—	5	4	no	—
90	C₂²×C₃×C₈	—	5	1	no	—
91	C₂²×C₃×C₈	—	5	2	no	—
92	C₂²×C₃×C₈	—	10	4	no	—
93	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
94	C₂×C₃×C₄²	—	5	2	no	—
95	C₃×C₂²⋊C₈	—	5	4	no	—
96	C₃×C₄×C₈	—	10	4	no	—
97	C₃×#95	—	5	1	no	—
98	C₃×#95	AGL(1,𝔽₅)	1	1	yes	characteristic
99	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
102	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
103	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
104	C₂×C₄×D₅	—	2	2	no	—
105	C₂×C₄×D₅	—	2	2	no	—
106	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
107	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
108	C₂×#170	—	2	2	no	—
109	C₂×#170	—	2	2	no	—
110	C₂×#170	—	2	2	no	—
111	C₂×#170	C₂×C₃×C₄	1	2	yes	—
112	C₂×#170	C₂×C₃×C₄	1	4	yes	—
113	C₂×#170	C₂×C₃×C₄	1	2	yes	—
114	C₂×#170	C₃×D₄	1	4	yes	—
115	D₅⋊C₈	—	2	8	no	—
116	#685	C₃×C₈	1	8	yes	complemented
117	C₄×Dic₅	—	2	2	no	—
118	C₄×Dic₅	—	2	2	no	—
119	C₂³×C₈	—	5	1	no	—
120	C₂×C₂²⋊C₈	—	5	1	no	—
121	C₂×C₄×C₈	—	5	2	no	—
122	C₄×C₂²⋊C₄	—	5	1	no	—
123	#336	—	5	2	no	—
124	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
125	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
126	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
127	C₂²×C₃×C₅	#131	1	1	yes	characteristic
128	C₂²×C₃×C₅	#131	1	1	yes	characteristic
129	C₂×C₃×D₅	—	2	2	no	—
130	C₂×C₃×D₅	—	2	2	no	—
131	C₂×C₃×D₅	—	2	4	no	—
132	C₂×C₃×D₅	—	2	4	no	—
133	C₂×C₃×D₅	C₄×C₈	1	4	yes	complemented
134	C₃×C₄×C₅	—	2	2	no	—
135	C₃×C₄×C₅	—	2	4	no	—
136	C₃×Dic₅	—	2	4	no	—
137	C₃×Dic₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₃×Dic₅	#117	1	1	yes	characteristic
139	C₃×Dic₅	C₄×D₄	1	2	yes	—
140	C₂⁴×C₃	—	5	1	no	—
141	C₂²×C₃×C₄	—	5	1	no	—
142	C₂²×C₃×C₄	—	5	2	no	—
143	C₂²×C₃×C₄	—	5	2	no	—
144	C₂²×C₃×C₄	—	5	2	no	—
145	C₂²×C₃×C₄	—	10	2	no	—
146	C₂²×C₃×C₄	—	10	2	no	—
147	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
148	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
149	C₂×C₃×C₈	—	5	4	no	—
150	C₂×C₃×C₈	—	5	2	no	—
151	C₂×C₃×C₈	—	5	4	no	—
152	C₂×C₃×C₈	—	5	2	no	—
153	C₂×C₃×C₈	—	10	8	no	—
154	C₂×C₃×C₈	—	10	2	no	—
155	C₂×C₃×C₈	—	10	2	no	—
156	C₂×C₃×C₈	—	10	2	no	—
157	C₃×C₂²⋊C₄	—	5	8	no	—
158	C₃×C₄²	—	10	2	no	—
159	C₃×C₄²	—	10	2	no	—
160	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
161	C₂²×D₅	—	2	2	no	—
162	C₂²×D₅	—	2	1	no	—
163	C₂²×D₅	—	2	1	no	—
164	C₂²×D₅	C₃×C₄²	1	2	yes	—
165	C₂²×D₅	C₂×C₃×C₈	1	4	yes	—
166	C₂×C₄×C₅	—	2	2	no	—
167	C₂×C₄×C₅	—	2	2	no	—
168	C₂×C₄×C₅	—	2	2	no	—
169	C₂×C₄×C₅	C₃×C₄²	1	2	yes	—
170	C₂×C₄×C₅	C₂×C₃×C₈	1	4	yes	complemented
171	C₂×Dic₅	—	2	2	no	—
172	C₂×Dic₅	—	2	2	no	—
173	C₂×Dic₅	C₂×C₃×C₈	1	4	yes	complemented
174	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
175	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
176	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
177	C₂×Dic₅	C₃×#41	1	2	yes	—
178	C₄×D₅	—	2	2	no	—
179	C₄×D₅	—	2	2	no	—
180	C₄×D₅	—	2	4	no	—
181	#170	—	2	2	no	—
182	#170	—	2	4	no	—
183	#170	C₃×C₂²⋊C₄	1	4	yes	complemented
184	C₂³×C₄	—	5	1	no	—
185	C₂²×C₈	—	5	1	no	—
186	C₂²×C₈	—	5	4	no	—
187	C₂²×C₈	—	5	1	no	—
188	C₂²×C₈	—	5	2	no	—
189	C₂²×C₈	—	10	4	no	—
190	C₂×C₂²⋊C₄	—	5	2	no	—
191	C₂×C₄²	—	5	2	no	—
192	C₂²⋊C₈	—	5	4	no	—
193	C₄×C₈	—	10	4	no	—
194	#95	—	5	1	no	—
195	#95	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
196	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
198	C₂×C₃×C₅	#405	1	1	yes	characteristic
199	C₂×C₃×C₅	C₈×D₄	1	2	yes	—
200	C₂×C₃×C₅	C₈×D₄	1	2	yes	—
201	C₃×D₅	—	2	4	no	—
202	C₂³×C₃	—	5	4	no	—
203	C₂³×C₃	—	5	2	no	—
204	C₂³×C₃	—	10	1	no	—
205	C₂³×C₃	—	10	2	no	—
206	C₂³×C₃	—	10	1	no	—
207	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
208	C₂×C₃×C₄	—	2	2	no	—
209	C₂×C₃×C₄	—	2	2	no	—
210	C₂×C₃×C₄	—	2	2	no	—
211	C₂×C₃×C₄	—	5	1	no	—
212	C₂×C₃×C₄	—	5	1	no	—
213	C₂×C₃×C₄	—	5	2	no	—
214	C₂×C₃×C₄	—	5	2	no	—
215	C₂×C₃×C₄	—	5	4	no	—
216	C₂×C₃×C₄	—	10	2	no	—
217	C₂×C₃×C₄	—	10	2	no	—
218	C₂×C₃×C₄	—	10	4	no	—
219	C₂×C₃×C₄	—	10	2	no	—
220	C₂×C₃×C₄	—	10	2	no	—
221	C₂×C₃×C₄	D₅⋊C₈	1	4	yes	complemented
222	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	2	yes	—
223	C₃×C₈	—	5	4	no	—
224	C₃×C₈	—	10	4	no	—
225	C₃×C₈	—	10	2	no	—
226	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
227	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
228	C₂²×C₅	C₂²×C₃×C₈	1	2	yes	—
229	C₂²×C₅	C₃×#131	1	1	yes	characteristic
230	C₂²×C₅	C₃×#131	1	1	yes	characteristic
231	C₂×D₅	—	2	2	no	—
232	C₂×D₅	—	2	2	no	—
233	C₂×D₅	—	2	4	no	—
234	C₂×D₅	—	2	4	no	—
235	C₂×D₅	C₃×C₄×C₈	1	4	yes	complemented
236	C₄×C₅	—	2	2	no	—
237	C₄×C₅	—	2	4	no	—
238	Dic₅	—	2	4	no	—
239	Dic₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
240	Dic₅	C₃×#117	1	1	yes	characteristic
241	Dic₅	C₃×C₄×D₄	1	2	yes	—
242	C₂⁴	—	5	1	no	—
243	C₂²×C₄	—	5	1	no	—
244	C₂²×C₄	—	5	2	no	—
245	C₂²×C₄	—	5	2	no	—
246	C₂²×C₄	—	5	2	no	—
247	C₂²×C₄	—	10	2	no	—
248	C₂²×C₄	—	10	2	no	—
249	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
250	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
251	C₂×C₈	—	5	4	no	—
252	C₂×C₈	—	5	2	no	—
253	C₂×C₈	—	5	4	no	—
254	C₂×C₈	—	5	2	no	—
255	C₂×C₈	—	10	8	no	—
256	C₂×C₈	—	10	2	no	—
257	C₂×C₈	—	10	2	no	—
258	C₂×C₈	—	10	2	no	—
259	C₂²⋊C₄	—	5	8	no	—
260	C₄²	—	10	2	no	—
261	C₄²	—	10	2	no	—
262	C₃×C₅	C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
263	C₂²×C₃	—	5	4	no	—
264	C₂²×C₃	—	10	4	no	—
265	C₂²×C₃	—	10	2	no	—
266	C₂²×C₃	—	10	2	no	—
267	C₂²×C₃	—	10	4	no	—
268	C₂²×C₃	C₂×D₅⋊C₈	1	2	yes	—
269	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
270	C₂²×C₃	#4131	1	1	yes	characteristic
271	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	2	yes	—
272	C₂²×C₃	#4133	1	1	yes	characteristic
273	C₃×C₄	—	2	4	no	—
274	C₃×C₄	—	2	2	no	—
275	C₃×C₄	—	5	1	no	—
276	C₃×C₄	—	5	1	no	—
277	C₃×C₄	—	5	2	no	—
278	C₃×C₄	—	10	4	no	—
279	C₂×C₅	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₅	C₂×C₃×C₄×C₈	1	1	yes	characteristic
281	C₂×C₅	C₃×#405	1	1	yes	characteristic
282	C₂×C₅	C₃×C₈×D₄	1	2	yes	—
283	C₂×C₅	C₃×C₈×D₄	1	2	yes	—
284	D₅	—	2	4	no	—
285	C₂³	—	5	4	no	—
286	C₂³	—	5	2	no	—
287	C₂³	—	10	1	no	—
288	C₂³	—	10	2	no	—
289	C₂³	—	10	1	no	—
290	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	5	1	no	—
295	C₂×C₄	—	5	1	no	—
296	C₂×C₄	—	5	2	no	—
297	C₂×C₄	—	5	2	no	—
298	C₂×C₄	—	5	4	no	—
299	C₂×C₄	—	10	2	no	—
300	C₂×C₄	—	10	4	no	—
301	C₂×C₄	—	10	2	no	—
302	C₂×C₄	—	10	2	no	—
303	C₂×C₄	—	10	2	no	—
304	C₂×C₄	C₃×D₅⋊C₈	1	4	yes	complemented
305	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
306	C₈	—	5	4	no	—
307	C₈	—	10	2	no	—
308	C₈	—	10	4	no	—
309	C₂×C₃	—	10	4	no	—
310	C₂×C₃	C₄×D₅⋊C₈	1	1	yes	characteristic
311	C₂×C₃	#65692	1	2	yes	—
312	C₂×C₃	C₂²⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
313	C₂×C₃	#65701	1	1	yes	characteristic
314	C₂×C₃	#65702	1	2	yes	—
315	C₅	C₃×C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
316	C₂²	—	5	4	no	—
317	C₂²	—	10	4	no	—
318	C₂²	—	10	2	no	—
319	C₂²	—	10	2	no	—
320	C₂²	—	10	4	no	—
321	C₂²	C₂×C₃×D₅⋊C₈	1	2	yes	—
322	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
323	C₂²	C₃×#4131	1	1	yes	characteristic
324	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
325	C₂²	C₃×#4133	1	1	yes	characteristic
326	C₄	—	2	4	no	—
327	C₄	—	2	2	no	—
328	C₄	—	5	1	no	—
329	C₄	—	5	2	no	—
330	C₄	—	5	1	no	—
331	C₄	—	10	4	no	—
332	C₃	#10603775	1	1	yes	characteristic, direct product factor, Sylow
333	C₂	—	10	4	no	—
334	C₂	C₃×C₄×D₅⋊C₈	1	1	yes	characteristic
335	C₂	C₃×#65692	1	2	yes	—
336	C₂	C₃×C₂²⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
337	C₂	C₃×#65701	1	1	yes	characteristic
338	C₂	C₃×#65702	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂²×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂×C₃×C₄×C₈
Frattini	C₂³	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#95	C₄
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂²×Dic₅	C₂³×C₃
hypercenter	C₃×#95	AGL(1,𝔽₅)
hypocenter	C₅	C₃×C₈×C₂²⋊C₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#95

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₄×#170	C₂	semidirect
5. C₃×#64918	C₂	semidirect
6. #10603775	C₃	direct (N × H)
12. C₂×C₃×D₅⋊C₈	C₄	semidirect
15. C₃×#4003	C₄	semidirect
22. C₂×C₄×#170	C₂×C₃	semidirect
24. #64918	C₂×C₃	semidirect
42. C₃×#685	C₈	semidirect
55. C₂×D₅⋊C₈	C₃×C₄	semidirect
58. #4003	C₃×C₄	semidirect
73. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
76. C₂×C₃×Dic₅	C₂×C₈	semidirect
86. C₃×#170	C₂²⋊C₄	semidirect
116. #685	C₃×C₈	semidirect
133. C₂×C₃×D₅	C₄×C₈	semidirect
170. C₂×C₄×C₅	C₂×C₃×C₈	semidirect
173. C₂×Dic₅	C₂×C₃×C₈	semidirect
183. #170	C₃×C₂²⋊C₄	semidirect
221. C₂×C₃×C₄	D₅⋊C₈	semidirect
235. C₂×D₅	C₃×C₄×C₈	semidirect
262. C₃×C₅	C₈×C₂²⋊C₄	semidirect
304. C₂×C₄	C₃×D₅⋊C₈	semidirect
315. C₅	C₃×C₈×C₂²⋊C₄	semidirect
332. C₃	#10603775	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×C₃×D₅⋊C₈	2
C₂×C₃×#4003	2
C₂×C₃×C₄×#170	2
C₃×#64955	2
C₃×#64918	2
#10603775	3
C₃×C₈×C₂²⋊C₄	5

Subgroups — C3×#10603775 #14295156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10603775 #14295156