Subgroups — C₃×D₃×C₄⋊AGL(1,𝔽₅) #13088643

Order 1440.

394 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×AGL(1,𝔽₅)	C₂	1	2	yes	maximal
2	C₃×C₄×D₃×D₅	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊ΓL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×Dic₃⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₄⋊AGL(1,𝔽₅)	—	3	1	no	maximal
7	D₃×C₄⋊AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×D₃×D₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
10	C₂×C₃²×AGL(1,𝔽₅)	C₂²	1	2	yes	—
11	C₃×D₃×AGL(1,𝔽₅)	—	2	4	no	—
12	C₃×C₄×D₁₅	C₄	1	1	yes	characteristic, complemented
13	C₃×C₄×C₅×D₃	C₄	1	1	yes	characteristic, complemented
14	C₃²×C₄×D₅	C₂²	1	1	yes	characteristic
15	C₃×#1200	C₄	1	1	yes	characteristic, complemented
16	C₃×D₃×Dic₅	C₄	1	1	yes	characteristic, complemented
17	C₃×D₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₃×D₃×C₄⋊C₄	—	5	1	no	maximal, Hall
19	C₂²×C₃×AGL(1,𝔽₅)	—	3	2	no	—
20	C₂×D₃×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	—
21	C₂×C₃×C₄×D₅	—	3	1	no	—
22	C₄×D₃×D₅	C₂×C₃	1	1	yes	characteristic
23	C₄⋊ΓL(1,𝔽₁₆)	C₂×C₃	1	1	yes	characteristic, complemented
24	C₃×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
25	C₃×C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
26	C₃×C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
27	C₃×C₄⋊AGL(1,𝔽₅)	D₃	1	1	yes	characteristic, direct product factor
28	C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
29	Dic₃⋊AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
30	C₂×C₃×D₁₅	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃×C₅×D₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₃²×D₅	C₂³	1	1	yes	characteristic
33	C₃×D₃×D₅	D₄	1	2	yes	—
34	C₃×D₃×D₅	Q₈	1	2	yes	—
35	C₃×ΓL(1,𝔽₁₆)	—	2	2	no	—
36	C₃²×AGL(1,𝔽₅)	—	2	2	no	—
37	C₃²×C₄×C₅	C₂×C₄	1	1	yes	characteristic, complemented
38	C₃×Dic₁₅	C₂×C₄	1	1	yes	characteristic, complemented
39	C₃×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic, complemented
40	C₃²×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
41	C₂×C₄⋊AGL(1,𝔽₅)	—	3	1	no	Hall
42	C₂×C₃×C₄×D₃	—	5	1	no	—
43	C₂×C₃×C₄×D₃	—	5	2	no	—
44	C₃²×C₄⋊C₄	—	5	1	no	—
45	C₃×C₄⋊Dic₃	—	5	1	no	—
46	C₃×Dic₃⋊C₄	—	5	2	no	—
47	C₂²×C₃×D₅	—	3	1	no	—
48	C₂×D₃×D₅	C₂²×C₃	1	1	yes	characteristic
49	C₂×ΓL(1,𝔽₁₆)	C₂²×C₃	1	2	yes	—
50	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
51	C₂×C₃×AGL(1,𝔽₅)	—	3	2	no	—
52	C₂×C₃×AGL(1,𝔽₅)	—	6	4	no	—
53	C₂×C₃×AGL(1,𝔽₅)	C₂×D₃	1	2	yes	—
54	C₂×C₃×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
55	D₃×AGL(1,𝔽₅)	—	2	4	no	—
56	C₂×C₃×C₄×C₅	—	3	1	no	—
57	C₄×D₁₅	C₃×C₄	1	1	yes	characteristic, complemented
58	C₄×C₅×D₃	C₃×C₄	1	1	yes	characteristic, complemented
59	C₂×C₃×Dic₅	—	3	1	no	—
60	C₃×C₄×D₅	—	2	1	no	—
61	C₃×C₄×D₅	—	3	1	no	—
62	C₃×C₄×D₅	—	3	1	no	—
63	C₃×C₄×D₅	—	3	1	no	—
64	C₃×C₄×D₅	C₂×D₃	1	1	yes	characteristic
65	C₃×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
66	#1200	C₃×C₄	1	1	yes	characteristic, complemented
67	D₃×Dic₅	C₃×C₄	1	1	yes	characteristic, complemented
68	D₅×Dic₃	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₃×C₄⋊C₄	—	15	1	no	—
70	D₃×C₄⋊C₄	—	5	1	no	—
71	C₂×C₃²×C₅	C₂²×C₄	1	1	yes	characteristic
72	C₃×D₁₅	C₄⋊C₄	1	2	yes	complemented
73	C₃×C₅×D₃	C₄⋊C₄	1	2	yes	complemented
74	C₃²×D₅	C₂×D₄	1	1	yes	characteristic
75	C₃²×D₅	C₂×Q₈	1	1	yes	characteristic
76	C₂²×AGL(1,𝔽₅)	—	3	2	no	—
77	C₂×C₄×D₅	—	3	1	no	—
78	C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
79	C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
80	C₄⋊AGL(1,𝔽₅)	C₃×D₃	1	1	yes	characteristic, direct product factor
81	C₂²×C₃×D₃	—	5	1	no	—
82	C₂×C₃²×C₄	—	5	1	no	—
83	C₂×C₃²×C₄	—	5	2	no	—
84	C₂×C₃×Dic₃	—	5	1	no	—
85	C₂×C₃×Dic₃	—	5	2	no	—
86	C₃×C₄×D₃	—	5	1	no	—
87	C₃×C₄×D₃	—	5	1	no	—
88	C₃×C₄×D₃	—	5	1	no	—
89	C₃×C₄×D₃	—	10	4	no	—
90	C₃×C₄×D₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
91	C₂²×C₃×C₅	—	3	1	no	—
92	C₂×D₁₅	C₂×C₃×C₄	1	1	yes	characteristic
93	C₂×C₅×D₃	C₂×C₃×C₄	1	1	yes	characteristic
94	C₂×C₃×D₅	—	2	1	no	—
95	C₂×C₃×D₅	—	3	1	no	—
96	C₂×C₃×D₅	—	3	2	no	—
97	C₂×C₃×D₅	—	3	2	no	—
98	C₂×C₃×D₅	C₂²×D₃	1	1	yes	characteristic
99	C₂×C₃×D₅	C₂³×C₃	1	1	yes	characteristic
100	D₃×D₅	C₃×D₄	1	2	yes	—
101	D₃×D₅	C₃×Q₈	1	2	yes	—
102	ΓL(1,𝔽₁₆)	—	2	2	no	—
103	C₃×AGL(1,𝔽₅)	—	2	2	no	—
104	C₃×AGL(1,𝔽₅)	—	2	2	no	—
105	C₃×AGL(1,𝔽₅)	—	4	2	no	—
106	C₃×AGL(1,𝔽₅)	—	6	2	no	—
107	C₃×C₄×C₅	—	2	1	no	—
108	C₃×C₄×C₅	—	3	1	no	—
109	C₃×C₄×C₅	C₄×D₃	1	1	yes	characteristic, complemented
110	C₃×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
111	Dic₁₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
112	C₃×Dic₅	—	2	1	no	—
113	C₃×Dic₅	—	3	1	no	—
114	C₃×Dic₅	C₄×D₃	1	1	yes	characteristic, complemented
115	C₃×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
116	C₅×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic, complemented
117	C₂²×C₃×C₄	—	15	1	no	—
118	C₂²×C₃×C₄	—	15	2	no	—
119	C₂×C₄×D₃	—	5	1	no	—
120	C₂×C₄×D₃	—	5	2	no	—
121	C₃×C₄⋊C₄	—	5	1	no	—
122	C₃×C₄⋊C₄	—	5	1	no	—
123	C₃×C₄⋊C₄	—	10	1	no	—
124	C₃×C₄⋊C₄	—	15	2	no	—
125	C₃×C₄⋊C₄	—	15	1	no	—
126	C₄⋊Dic₃	—	5	1	no	—
127	Dic₃⋊C₄	—	5	2	no	—
128	C₃²×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
129	C₂²×D₅	—	3	1	no	—
130	C₂×AGL(1,𝔽₅)	—	3	2	no	—
131	C₂×AGL(1,𝔽₅)	—	6	4	no	—
132	C₂×AGL(1,𝔽₅)	C₂×C₃×D₃	1	2	yes	—
133	C₂×C₄×C₅	—	3	1	no	—
134	C₂×Dic₅	—	3	1	no	—
135	C₄×D₅	—	3	1	no	—
136	C₄×D₅	—	3	1	no	—
137	C₄×D₅	—	3	1	no	—
138	C₄×D₅	C₂×C₃×D₃	1	1	yes	characteristic
139	C₂²×C₃²	—	5	1	no	—
140	C₂×C₃×D₃	—	5	1	no	—
141	C₂×C₃×D₃	—	5	2	no	—
142	C₂×C₃×D₃	—	5	2	no	—
143	C₂×C₃×D₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
144	C₃²×C₄	—	5	1	no	—
145	C₃²×C₄	—	10	2	no	—
146	C₃²×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
147	C₃×Dic₃	—	5	1	no	—
148	C₃×Dic₃	—	10	2	no	—
149	C₃×Dic₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
150	C₂×C₄⋊C₄	—	15	1	no	Sylow
151	C₂×C₃×C₅	—	2	1	no	—
152	C₂×C₃×C₅	—	3	2	no	—
153	C₂×C₃×C₅	C₂×C₄×D₃	1	1	yes	characteristic
154	C₂×C₃×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
155	D₁₅	C₃×C₄⋊C₄	1	2	yes	complemented
156	C₃×D₅	—	2	1	no	—
157	C₃×D₅	—	2	1	no	—
158	C₃×D₅	—	3	2	no	—
159	C₃×D₅	D₃×D₄	1	1	yes	characteristic
160	C₃×D₅	D₃×Q₈	1	1	yes	characteristic
161	C₃×D₅	C₂×C₃×D₄	1	1	yes	characteristic
162	C₃×D₅	C₂×C₃×Q₈	1	1	yes	characteristic
163	C₅×D₃	C₃×C₄⋊C₄	1	2	yes	complemented
164	C₂³×C₃	—	15	1	no	—
165	C₂²×D₃	—	5	1	no	—
166	C₂×C₃×C₄	—	3	1	no	—
167	C₂×C₃×C₄	—	5	1	no	—
168	C₂×C₃×C₄	—	5	1	no	—
169	C₂×C₃×C₄	—	5	2	no	—
170	C₂×C₃×C₄	—	5	2	no	—
171	C₂×C₃×C₄	—	10	1	no	—
172	C₂×C₃×C₄	—	10	2	no	—
173	C₂×C₃×C₄	—	15	1	no	—
174	C₂×C₃×C₄	—	15	1	no	—
175	C₂×C₃×C₄	—	15	1	no	—
176	C₂×C₃×C₄	—	15	1	no	—
177	C₂×C₃×C₄	—	15	2	no	—
178	C₂×C₃×C₄	—	30	4	no	—
179	C₂×Dic₃	—	5	1	no	—
180	C₂×Dic₃	—	5	2	no	—
181	C₄×D₃	—	5	1	no	—
182	C₄×D₃	—	5	1	no	—
183	C₄×D₃	—	5	1	no	—
184	C₄×D₃	—	10	4	no	—
185	C₄×D₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
186	C₂²×C₅	—	3	1	no	—
187	C₂×D₅	—	3	1	no	—
188	C₂×D₅	—	3	2	no	—
189	C₂×D₅	—	3	2	no	—
190	C₂×D₅	C₂²×C₃×D₃	1	1	yes	characteristic
191	AGL(1,𝔽₅)	—	2	2	no	—
192	AGL(1,𝔽₅)	—	6	2	no	—
193	C₄×C₅	—	3	1	no	—
194	C₄×C₅	C₃×C₄×D₃	1	1	yes	characteristic, complemented
195	Dic₅	—	3	1	no	—
196	Dic₅	C₃×C₄×D₃	1	1	yes	characteristic, complemented
197	C₂×C₃²	—	5	1	no	—
198	C₂×C₃²	—	5	1	no	—
199	C₂×C₃²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
200	C₃×D₃	—	5	2	no	—
201	C₃×D₃	C₄⋊AGL(1,𝔽₅)	1	2	yes	direct product factor
202	C₂²×C₄	—	15	1	no	—
203	C₂²×C₄	—	15	2	no	—
204	C₄⋊C₄	—	5	1	no	—
205	C₄⋊C₄	—	15	2	no	—
206	C₄⋊C₄	—	15	1	no	—
207	C₃×C₅	—	2	1	no	—
208	C₃×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic, complemented
209	C₃×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic, complemented
210	C₂²×C₃	—	3	1	no	—
211	C₂²×C₃	—	5	1	no	—
212	C₂²×C₃	—	5	1	no	—
213	C₂²×C₃	—	10	1	no	—
214	C₂²×C₃	—	15	2	no	—
215	C₂²×C₃	—	15	2	no	—
216	C₂²×C₃	—	15	1	no	—
217	C₂×D₃	—	5	1	no	—
218	C₂×D₃	—	5	2	no	—
219	C₂×D₃	—	5	2	no	—
220	C₂×D₃	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
221	C₃×C₄	—	2	1	no	—
222	C₃×C₄	—	3	1	no	—
223	C₃×C₄	—	5	1	no	—
224	C₃×C₄	—	5	1	no	—
225	C₃×C₄	—	10	1	no	—
226	C₃×C₄	—	10	2	no	—
227	C₃×C₄	—	10	2	no	—
228	C₃×C₄	—	15	1	no	—
229	C₃×C₄	—	20	2	no	—
230	C₃×C₄	—	30	2	no	—
231	C₃×C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
232	C₃×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
233	Dic₃	—	5	1	no	—
234	Dic₃	—	10	2	no	—
235	Dic₃	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
236	C₂×C₅	—	3	2	no	—
237	C₂×C₅	C₂×C₃×C₄×D₃	1	1	yes	characteristic
238	D₅	—	3	2	no	—
239	D₅	C₃×D₃×D₄	1	1	yes	characteristic
240	D₅	C₃×D₃×Q₈	1	1	yes	characteristic
241	C₃²	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
242	C₂³	—	15	1	no	—
243	C₂×C₄	—	3	1	no	—
244	C₂×C₄	—	5	1	no	—
245	C₂×C₄	—	5	2	no	—
246	C₂×C₄	—	15	1	no	—
247	C₂×C₄	—	15	1	no	—
248	C₂×C₄	—	15	1	no	—
249	C₂×C₄	—	15	1	no	—
250	C₂×C₄	—	15	2	no	—
251	C₂×C₄	—	30	4	no	—
252	C₂×C₃	—	2	1	no	—
253	C₂×C₃	—	3	2	no	—
254	C₂×C₃	—	5	1	no	—
255	C₂×C₃	—	5	1	no	—
256	C₂×C₃	—	5	1	no	—
257	C₂×C₃	—	5	1	no	—
258	C₂×C₃	—	10	1	no	—
259	C₂×C₃	—	10	1	no	—
260	C₂×C₃	—	15	2	no	—
261	C₂×C₃	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
262	C₂×C₃	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
263	D₃	—	5	2	no	—
264	D₃	C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	direct product factor
265	C₅	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
266	C₂²	—	3	1	no	—
267	C₂²	—	5	1	no	—
268	C₂²	—	15	2	no	—
269	C₂²	—	15	2	no	—
270	C₂²	—	15	1	no	—
271	C₄	—	3	1	no	—
272	C₄	—	5	1	no	—
273	C₄	—	10	2	no	—
274	C₄	—	15	1	no	—
275	C₄	—	30	2	no	—
276	C₄	C₃×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
277	C₃	—	2	1	no	—
278	C₃	D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
279	C₃	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
280	C₂	—	3	2	no	—
281	C₂	—	5	1	no	—
282	C₂	—	5	1	no	—
283	C₂	—	15	2	no	—
284	C₂	C₂×C₃×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₃×AGL(1,𝔽₅)
commutator	C₂×C₃×C₅	C₂²×C₃×C₄
Frattini	C₂	C₂×C₃×D₃×AGL(1,𝔽₅)
Fitting	C₃²×C₄×C₅	C₂×C₄
socle	C₂×C₃²×C₅	C₂²×C₄
prime radical	C₂×C₃×D₃×D₅	C₂²
cosocle	C₂×C₃×D₅	C₂³×C₃
hypercenter	C₃×C₄	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×C₃×C₄⋊C₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
3. C₃×C₄⋊ΓL(1,𝔽₁₆)	C₂	semidirect
4. C₃²×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
5. C₃×Dic₃⋊AGL(1,𝔽₅)	C₂	semidirect
7. D₃×C₄⋊AGL(1,𝔽₅)	C₃	direct (N × H)
12. C₃×C₄×D₁₅	C₄	semidirect
13. C₃×C₄×C₅×D₃	C₄	semidirect
15. C₃×#1200	C₄	semidirect
16. C₃×D₃×Dic₅	C₄	semidirect
23. C₄⋊ΓL(1,𝔽₁₆)	C₂×C₃	semidirect
27. C₃×C₄⋊AGL(1,𝔽₅)	D₃	direct (N × H)
28. C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₃	semidirect
29. Dic₃⋊AGL(1,𝔽₅)	C₂×C₃	semidirect
37. C₃²×C₄×C₅	C₂×C₄	semidirect
38. C₃×Dic₁₅	C₂×C₄	semidirect
39. C₃×C₅×Dic₃	C₂×C₄	semidirect
40. C₃²×Dic₅	C₂×C₄	semidirect
57. C₄×D₁₅	C₃×C₄	semidirect
58. C₄×C₅×D₃	C₃×C₄	semidirect
66. #1200	C₃×C₄	semidirect
67. D₃×Dic₅	C₃×C₄	semidirect
72. C₃×D₁₅	C₄⋊C₄	semidirect
73. C₃×C₅×D₃	C₄⋊C₄	semidirect
80. C₄⋊AGL(1,𝔽₅)	C₃×D₃	direct (N × H)
90. C₃×C₄×D₃	AGL(1,𝔽₅)	semidirect
109. C₃×C₄×C₅	C₄×D₃	semidirect
110. C₃×C₄×C₅	C₂×C₃×C₄	semidirect
111. Dic₁₅	C₂×C₃×C₄	semidirect
114. C₃×Dic₅	C₄×D₃	semidirect
115. C₃×Dic₅	C₂×C₃×C₄	semidirect
116. C₅×Dic₃	C₂×C₃×C₄	semidirect
128. C₃²×C₅	C₂×C₄⋊C₄	semidirect
146. C₃²×C₄	C₂×AGL(1,𝔽₅)	semidirect
149. C₃×Dic₃	C₂×AGL(1,𝔽₅)	semidirect
155. D₁₅	C₃×C₄⋊C₄	semidirect
163. C₅×D₃	C₃×C₄⋊C₄	semidirect
185. C₄×D₃	C₃×AGL(1,𝔽₅)	semidirect
194. C₄×C₅	C₃×C₄×D₃	semidirect
196. Dic₅	C₃×C₄×D₃	semidirect
201. C₃×D₃	C₄⋊AGL(1,𝔽₅)	direct (N × H)
208. C₃×C₅	D₃×C₄⋊C₄	semidirect
209. C₃×C₅	C₂×C₃×C₄⋊C₄	semidirect
231. C₃×C₄	D₃×AGL(1,𝔽₅)	semidirect
232. C₃×C₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
235. Dic₃	C₂×C₃×AGL(1,𝔽₅)	semidirect
241. C₃²	C₂×C₄⋊AGL(1,𝔽₅)	semidirect
264. D₃	C₃×C₄⋊AGL(1,𝔽₅)	direct (N × H)
265. C₅	C₃×D₃×C₄⋊C₄	semidirect
276. C₄	C₃×D₃×AGL(1,𝔽₅)	semidirect
278. C₃	D₃×C₄⋊AGL(1,𝔽₅)	direct (N × H)
279. C₃	C₂×C₃×C₄⋊AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×AGL(1,𝔽₅)	2
C₃×C₄×D₃×D₅	2
C₃×C₄⋊ΓL(1,𝔽₁₆)	2
C₃²×C₄⋊AGL(1,𝔽₅)	2
C₃×Dic₃⋊AGL(1,𝔽₅)	2
C₂×C₃×C₄⋊AGL(1,𝔽₅)	3
D₃×C₄⋊AGL(1,𝔽₅)	3
C₃×D₃×C₄⋊C₄	5

Subgroups — C3×D3×C4⋊AGL(1,𝔽5) #13088643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×C₄⋊AGL(1,𝔽₅) #13088643