Subgroups — C₃×#10617389 #14329836

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×(C₂×AGL(1,𝔽₅))⋊Q₈	C₂	1	4	yes	maximal
3	C₃×#65712	C₂	1	4	yes	maximal
4	C₃×C₄⋊C₄×AGL(1,𝔽₅)	C₂	1	4	yes	maximal
5	C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal
6	#10617389	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
8	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
9	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
10	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
11	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	4	yes	—
12	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	4	yes	—
13	C₃×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
14	C₃×#4090	C₄	1	2	yes	complemented
15	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
16	C₃×#4034	C₄	1	4	yes	complemented
17	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
18	C₃×#4015	C₄	1	1	yes	characteristic, complemented
19	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	4	yes	—
20	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	8	yes	—
21	C₃×#2369	—	5	1	no	maximal, Hall
22	D₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
23	(C₂×AGL(1,𝔽₅))⋊Q₈	C₂×C₃	1	4	yes	—
24	#65712	C₂×C₃	1	4	yes	—
25	C₄⋊C₄×AGL(1,𝔽₅)	C₂×C₃	1	4	yes	—
26	C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	2	yes	—
27	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	4	yes	—
28	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	4	yes	—
29	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
30	C₃×Q₈×D₅	—	4	2	no	—
31	C₃×Q₈×D₅	—	4	2	no	—
32	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
33	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
34	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
35	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
36	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	—
37	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
38	C₃×C₄⋊AGL(1,𝔽₅)	—	4	4	no	—
39	C₃×C₄⋊AGL(1,𝔽₅)	Q₈	1	8	yes	complemented
40	C₃×C₄×AGL(1,𝔽₅)	—	2	8	no	—
41	C₃×C₄×AGL(1,𝔽₅)	—	4	4	no	—
42	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
43	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
44	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
45	C₃×#683	C₂×C₄	1	8	yes	—
46	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
47	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
49	C₃×#391	—	5	4	no	—
50	C₃×#389	—	5	4	no	—
51	C₃×C₄×C₄⋊C₄	—	5	2	no	—
52	C₃×C₄×C₄⋊C₄	—	5	4	no	—
53	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
54	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
55	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
56	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
57	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
58	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
59	C₅×C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic, complemented
60	#4090	C₃×C₄	1	2	yes	complemented
61	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
62	#4034	C₃×C₄	1	4	yes	complemented
63	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
64	#4015	C₃×C₄	1	1	yes	characteristic, complemented
65	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	4	yes	—
66	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	8	yes	—
67	#2369	—	5	1	no	Sylow
68	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
69	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
70	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
71	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
72	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
73	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
74	C₂×C₃×AGL(1,𝔽₅)	C₂×Q₈	1	8	yes	—
75	C₃×C₅×Q₈	—	4	2	no	—
76	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
78	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
79	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
81	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
82	C₃×C₄×D₅	—	2	4	no	—
83	C₃×C₄×D₅	—	2	4	no	—
84	C₃×C₄×D₅	—	2	1	no	—
85	C₃×C₄×D₅	—	2	1	no	—
86	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
87	C₃×C₄×D₅	#41	1	4	yes	—
88	C₃×Dic₁₀	—	4	4	no	—
89	C₃×Dic₁₀	—	4	2	no	—
90	C₂²×C₃×Q₈	—	5	2	no	—
91	C₃×C₄⋊Q₈	—	5	2	no	—
92	C₃×C₄⋊Q₈	—	5	4	no	—
93	C₃×C₄⋊Q₈	—	5	1	no	—
94	C₃×C₄⋊Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
95	C₂×C₃×C₄⋊C₄	—	5	2	no	—
96	C₂×C₃×C₄⋊C₄	—	5	4	no	—
97	C₂×C₃×C₄⋊C₄	—	5	2	no	—
98	C₂×C₃×C₄⋊C₄	—	5	4	no	—
99	C₂×C₃×C₄²	—	5	1	no	—
100	C₂×C₃×C₄²	—	5	4	no	—
101	C₂×C₃×C₄²	—	5	4	no	—
102	C₃×#95	—	5	8	no	—
103	C₃×#95	—	5	4	no	—
104	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
105	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
106	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
107	Q₈×D₅	—	4	2	no	—
108	Q₈×D₅	—	4	2	no	—
109	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
110	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
111	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
112	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
113	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	—
114	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
115	C₄⋊AGL(1,𝔽₅)	—	4	4	no	—
116	C₄⋊AGL(1,𝔽₅)	C₃×Q₈	1	8	yes	complemented
117	C₄×AGL(1,𝔽₅)	—	2	8	no	—
118	C₄×AGL(1,𝔽₅)	—	4	4	no	—
119	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
120	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
121	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
122	#683	C₂×C₃×C₄	1	8	yes	—
123	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
124	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
125	C₂×C₄⋊Q₈	—	5	1	no	—
126	#391	—	5	4	no	—
127	#389	—	5	4	no	—
128	C₄×C₄⋊C₄	—	5	2	no	—
129	C₄×C₄⋊C₄	—	5	4	no	—
130	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₃×D₅	C₂²×Q₈	1	2	yes	—
132	C₂×C₃×D₅	C₂×#41	1	2	yes	—
133	C₂×C₃×D₅	H(5,𝔽₂)	1	1	yes	characteristic
134	C₂×C₃×D₅	H(5,𝔽₂)	1	1	yes	characteristic
135	C₃×AGL(1,𝔽₅)	—	2	8	no	—
136	C₃×AGL(1,𝔽₅)	—	4	4	no	—
137	C₃×C₄×C₅	—	2	1	no	—
138	C₃×C₄×C₅	—	2	4	no	—
139	C₃×C₄×C₅	C₄×Q₈	1	4	yes	—
140	C₃×Dic₅	—	2	1	no	—
141	C₃×Dic₅	—	2	4	no	—
142	C₃×Dic₅	C₄×Q₈	1	4	yes	—
143	C₂×C₃×Q₈	—	5	4	no	—
144	C₂×C₃×Q₈	—	5	2	no	—
145	C₂×C₃×Q₈	—	20	2	no	—
146	C₂×C₃×Q₈	—	20	2	no	—
147	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
148	C₂²×C₃×C₄	—	5	2	no	—
149	C₂²×C₃×C₄	—	5	4	no	—
150	C₂²×C₃×C₄	—	5	1	no	—
151	C₂²×C₃×C₄	—	5	4	no	—
152	C₂²×C₃×C₄	—	5	4	no	—
153	C₃×C₄⋊C₄	—	5	8	no	—
154	C₃×C₄⋊C₄	—	5	8	no	—
155	C₃×C₄⋊C₄	—	5	4	no	—
156	C₃×C₄⋊C₄	—	10	4	no	—
157	C₃×C₄⋊C₄	—	20	4	no	—
158	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	4	yes	—
159	C₃×C₄²	—	5	1	no	—
160	C₃×C₄²	—	5	2	no	—
161	C₃×C₄²	—	10	8	no	—
162	C₃×C₄²	—	20	4	no	—
163	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
164	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
165	C₂×AGL(1,𝔽₅)	—	2	4	no	—
166	C₂×AGL(1,𝔽₅)	—	2	4	no	—
167	C₂×AGL(1,𝔽₅)	—	2	4	no	—
168	C₂×AGL(1,𝔽₅)	—	2	4	no	—
169	C₂×AGL(1,𝔽₅)	—	2	4	no	—
170	C₂×AGL(1,𝔽₅)	C₂×C₃×Q₈	1	8	yes	—
171	C₅×Q₈	—	4	2	no	—
172	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
173	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
174	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
175	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
176	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
177	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
178	C₄×D₅	—	2	4	no	—
179	C₄×D₅	—	2	4	no	—
180	C₄×D₅	—	2	1	no	—
181	C₄×D₅	—	2	1	no	—
182	C₄×D₅	C₂×C₃×Q₈	1	4	yes	—
183	C₄×D₅	C₃×#41	1	4	yes	—
184	Dic₁₀	—	4	4	no	—
185	Dic₁₀	—	4	2	no	—
186	C₂²×Q₈	—	5	2	no	—
187	C₄⋊Q₈	—	5	2	no	—
188	C₄⋊Q₈	—	5	4	no	—
189	C₄⋊Q₈	—	5	1	no	—
190	C₄⋊Q₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
191	C₂×C₄⋊C₄	—	5	2	no	—
192	C₂×C₄⋊C₄	—	5	4	no	—
193	C₂×C₄⋊C₄	—	5	2	no	—
194	C₂×C₄⋊C₄	—	5	4	no	—
195	C₂×C₄²	—	5	1	no	—
196	C₂×C₄²	—	5	4	no	—
197	C₂×C₄²	—	5	4	no	—
198	#95	—	5	8	no	—
199	#95	—	5	4	no	—
200	C₂×C₃×C₅	C₂×C₄×Q₈	1	2	yes	—
201	C₂×C₃×C₅	#518	1	1	yes	characteristic
202	C₃×D₅	#554	1	2	yes	—
203	C₃×D₅	#555	1	1	yes	characteristic
204	C₃×D₅	Q₈²	1	1	yes	characteristic
205	C₂³×C₃	—	5	1	no	—
206	C₃×Q₈	—	4	2	no	—
207	C₃×Q₈	—	20	2	no	—
208	C₃×Q₈	—	20	4	no	—
209	C₂×C₃×C₄	—	5	2	no	—
210	C₂×C₃×C₄	—	5	4	no	—
211	C₂×C₃×C₄	—	5	4	no	—
212	C₂×C₃×C₄	—	5	8	no	—
213	C₂×C₃×C₄	—	5	1	no	—
214	C₂×C₃×C₄	—	5	4	no	—
215	C₂×C₃×C₄	—	10	4	no	—
216	C₂×C₃×C₄	—	10	4	no	—
217	C₂×C₃×C₄	—	10	1	no	—
218	C₂×C₃×C₄	—	10	1	no	—
219	C₂×C₃×C₄	—	10	4	no	—
220	C₂×C₃×C₄	—	10	4	no	—
221	C₂×C₃×C₄	—	10	4	no	—
222	C₂×C₃×C₄	—	10	4	no	—
223	C₂×C₃×C₄	—	10	4	no	—
224	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	4	yes	—
226	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
227	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
228	C₂×D₅	C₂²×C₃×Q₈	1	2	yes	—
229	C₂×D₅	C₂×C₃×#41	1	2	yes	—
230	C₂×D₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×D₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
232	AGL(1,𝔽₅)	—	2	8	no	—
233	AGL(1,𝔽₅)	—	4	4	no	—
234	C₄×C₅	—	2	1	no	—
235	C₄×C₅	—	2	4	no	—
236	C₄×C₅	C₃×C₄×Q₈	1	4	yes	—
237	Dic₅	—	2	1	no	—
238	Dic₅	—	2	4	no	—
239	Dic₅	C₃×C₄×Q₈	1	4	yes	—
240	C₂×Q₈	—	5	4	no	—
241	C₂×Q₈	—	5	2	no	—
242	C₂×Q₈	—	20	2	no	—
243	C₂×Q₈	—	20	2	no	—
244	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
245	C₂²×C₄	—	5	2	no	—
246	C₂²×C₄	—	5	4	no	—
247	C₂²×C₄	—	5	1	no	—
248	C₂²×C₄	—	5	4	no	—
249	C₂²×C₄	—	5	4	no	—
250	C₄⋊C₄	—	5	8	no	—
251	C₄⋊C₄	—	5	8	no	—
252	C₄⋊C₄	—	5	4	no	—
253	C₄⋊C₄	—	10	4	no	—
254	C₄⋊C₄	—	20	4	no	—
255	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	—
256	C₄²	—	5	1	no	—
257	C₄²	—	5	2	no	—
258	C₄²	—	10	8	no	—
259	C₄²	—	20	4	no	—
260	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
261	C₃×C₅	#2369	1	1	yes	characteristic, complemented, Hall
262	C₂²×C₃	—	5	1	no	—
263	C₂²×C₃	—	5	1	no	—
264	C₂²×C₃	—	5	2	no	—
265	C₂²×C₃	—	5	2	no	—
266	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
267	C₃×C₄	—	2	1	no	—
268	C₃×C₄	—	2	4	no	—
269	C₃×C₄	—	5	4	no	—
270	C₃×C₄	—	10	8	no	—
271	C₃×C₄	—	10	4	no	—
272	C₃×C₄	—	10	1	no	—
273	C₃×C₄	—	20	4	no	—
274	C₃×C₄	Q₈×AGL(1,𝔽₅)	1	4	yes	—
275	C₂×C₅	C₂×C₃×C₄×Q₈	1	2	yes	—
276	C₂×C₅	C₃×#518	1	1	yes	characteristic
277	D₅	C₃×#554	1	2	yes	—
278	D₅	C₃×#555	1	1	yes	characteristic
279	D₅	C₃×Q₈²	1	1	yes	characteristic
280	C₂³	—	5	1	no	—
281	Q₈	—	4	2	no	—
282	Q₈	—	20	2	no	—
283	Q₈	—	20	4	no	—
284	C₂×C₄	—	5	2	no	—
285	C₂×C₄	—	5	4	no	—
286	C₂×C₄	—	5	4	no	—
287	C₂×C₄	—	5	8	no	—
288	C₂×C₄	—	5	1	no	—
289	C₂×C₄	—	5	4	no	—
290	C₂×C₄	—	10	4	no	—
291	C₂×C₄	—	10	4	no	—
292	C₂×C₄	—	10	1	no	—
293	C₂×C₄	—	10	1	no	—
294	C₂×C₄	—	10	4	no	—
295	C₂×C₄	—	10	4	no	—
296	C₂×C₄	—	10	4	no	—
297	C₂×C₄	—	10	4	no	—
298	C₂×C₄	—	10	4	no	—
299	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
300	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	—
301	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
302	C₂×C₃	—	5	2	no	—
303	C₂×C₃	—	5	1	no	—
304	C₂×C₃	—	5	1	no	—
305	C₂×C₃	#66258	1	1	yes	characteristic
306	C₂×C₃	C₂×Q₈×AGL(1,𝔽₅)	1	2	yes	—
307	C₅	C₃×#2369	1	1	yes	characteristic, complemented, Sylow
308	C₂²	—	5	1	no	—
309	C₂²	—	5	1	no	—
310	C₂²	—	5	2	no	—
311	C₂²	—	5	2	no	—
312	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
313	C₄	—	2	1	no	—
314	C₄	—	2	4	no	—
315	C₄	—	5	4	no	—
316	C₄	—	10	8	no	—
317	C₄	—	10	1	no	—
318	C₄	—	10	4	no	—
319	C₄	—	20	4	no	—
320	C₄	C₃×Q₈×AGL(1,𝔽₅)	1	4	yes	—
321	C₃	#10617389	1	1	yes	characteristic, direct product factor, Sylow
322	C₂	—	5	2	no	—
323	C₂	—	5	1	no	—
324	C₂	—	5	1	no	—
325	C₂	C₃×#66258	1	1	yes	characteristic
326	C₂	C₂×C₃×Q₈×AGL(1,𝔽₅)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×C₄⋊Q₈	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×D₅	C₂⁴
cosocle	C₂²×D₅	C₂⁴×C₃
hypercenter	C₃×C₄⋊Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2369
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
6. #10617389	C₃	direct (N × H)
13. C₃×C₅×C₄⋊Q₈	C₄	semidirect
14. C₃×#4090	C₄	semidirect
16. C₃×#4034	C₄	semidirect
18. C₃×#4015	C₄	semidirect
39. C₃×C₄⋊AGL(1,𝔽₅)	Q₈	semidirect
59. C₅×C₄⋊Q₈	C₃×C₄	semidirect
60. #4090	C₃×C₄	semidirect
62. #4034	C₃×C₄	semidirect
64. #4015	C₃×C₄	semidirect
94. C₃×C₄⋊Q₈	AGL(1,𝔽₅)	semidirect
116. C₄⋊AGL(1,𝔽₅)	C₃×Q₈	semidirect
190. C₄⋊Q₈	C₃×AGL(1,𝔽₅)	semidirect
261. C₃×C₅	#2369	semidirect
307. C₅	C₃×#2369	semidirect
321. C₃	#10617389	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₅×C₄⋊Q₈	2
C₃×(C₂×AGL(1,𝔽₅))⋊Q₈	2
C₃×#65712	2
C₃×C₄⋊C₄×AGL(1,𝔽₅)	2
C₃×C₄×C₄⋊AGL(1,𝔽₅)	2
#10617389	3
C₃×#2369	5

Subgroups — C3×#10617389 #14329836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617389 #14329836