Subgroups — Dic₃×#3990 #14312624

Order 1920.

392 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91219	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#3990	C₂	1	1	yes	maximal, characteristic
3	C₈×D₅×Dic₃	C₂	1	1	yes	maximal, characteristic
4	#11746543	C₂	1	2	yes	maximal, complemented
5	Dic₃×#674	C₂	1	2	yes	maximal, complemented
6	C₄×#3990	—	3	1	no	maximal, Hall
7	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
8	C₄×D₅×Dic₃	C₄	1	1	yes	characteristic
9	C₂×D₅×C₃⋊C₈	C₄	1	1	yes	characteristic
10	C₂×C₃⋊#674	C₂²	1	2	yes	—
11	#91219	C₄	1	4	yes	complemented
12	C₂×C₃×#674	C₂²	1	2	yes	—
13	C₃×#3990	C₄	1	4	yes	complemented
14	C₈×Dic₁₅	C₄	1	1	yes	characteristic
15	C₅×C₈×Dic₃	C₄	1	1	yes	characteristic
16	#90951	C₂²	1	1	yes	characteristic
17	Dic₃×#168	C₂²	1	1	yes	characteristic
18	Dic₃×M₃₂	—	5	1	no	maximal, Hall
19	C₂×#3990	—	3	1	no	—
20	C₂×#3990	D₃	1	1	yes	characteristic
21	C₄×C₈×D₅	—	3	1	no	—
22	#64886	—	3	2	no	—
23	C₄×#674	—	3	2	no	—
24	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
25	C₂×D₅×Dic₃	C₈	1	2	yes	—
26	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
28	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
29	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃×#168	C₂³	1	1	yes	characteristic
32	C₃×C₈×D₅	C₂×C₄	1	2	yes	—
33	C₃×C₈×D₅	C₂×C₄	1	2	yes	—
34	Dic₃×Dic₅	C₈	1	2	yes	—
35	D₅×C₃⋊C₈	C₈	1	4	yes	—
36	C₃⋊#674	C₂×C₄	1	4	yes	complemented
37	C₃×#674	C₂×C₄	1	4	yes	complemented
38	C₂×C₃×M₃₂	—	5	1	no	—
39	C₂×C₈×Dic₃	—	5	1	no	—
40	C₂×#812	—	5	1	no	—
41	#4502	—	5	2	no	—
42	Dic₃×C₁₆	—	5	2	no	—
43	C₂×C₈×D₅	—	3	1	no	—
44	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
45	C₄²×D₅	—	3	1	no	—
46	C₂×#674	—	3	2	no	—
47	C₂×#674	C₂×D₃	1	2	yes	—
48	#3990	—	3	4	no	—
49	#3990	Dic₃	1	4	yes	direct product factor
50	C₄×C₅×C₈	—	3	1	no	—
51	C₈×Dic₅	—	3	1	no	—
52	C₈×Dic₅	—	3	1	no	—
53	C₄×#168	—	3	1	no	—
54	C₄×M₃₂	—	15	1	no	Sylow
55	C₂²×C₃×D₅	C₂×C₈	1	1	yes	characteristic
56	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
57	C₂×Dic₁₅	C₂×C₈	1	2	yes	—
58	C₂×C₅×Dic₃	C₂×C₈	1	2	yes	—
59	C₂×C₃×Dic₅	C₂×C₈	1	1	yes	characteristic
60	C₃×C₄×D₅	C₄²	1	2	yes	—
61	C₃×C₄×D₅	C₂×C₈	1	2	yes	—
62	D₅×Dic₃	—	2	4	no	—
63	C₃×C₅×C₈	C₄²	1	2	yes	—
64	C₃⋊#168	C₂×C₈	1	2	yes	—
65	C₃×#168	C₂²×C₄	1	1	yes	characteristic
66	C₃×#168	C₂²×C₄	1	1	yes	characteristic
67	C₅×C₃⋊C₈	C₂×C₈	1	2	yes	—
68	C₂²×C₃×C₈	—	5	1	no	—
69	C₂×C₄×Dic₃	—	5	1	no	—
70	C₂²×C₃⋊C₈	—	5	1	no	—
71	C₃×M₃₂	—	5	4	no	—
72	C₂×C₃×C₁₆	—	5	2	no	—
73	C₈×Dic₃	—	5	1	no	—
74	C₈×Dic₃	—	5	1	no	—
75	C₈×Dic₃	—	5	1	no	—
76	C₈×Dic₃	AGL(1,𝔽₅)	1	1	yes	characteristic
77	#812	—	5	4	no	—
78	C₂×C₃⋊C₁₆	—	5	2	no	—
79	C₂×C₄×D₅	—	3	2	no	—
80	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
81	C₂×C₅×C₈	—	3	1	no	—
82	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
83	C₄²×C₅	—	3	1	no	—
84	C₄×Dic₅	—	3	1	no	—
85	C₄×Dic₅	—	3	2	no	—
86	C₂×#168	—	3	1	no	—
87	C₂×#168	C₂²×D₃	1	1	yes	characteristic
88	C₈×D₅	—	3	4	no	—
89	C₈×D₅	C₄×D₃	1	2	yes	—
90	C₈×D₅	C₂×Dic₃	1	2	yes	—
91	#674	—	3	4	no	—
92	#674	C₂×Dic₃	1	4	yes	complemented
93	C₂×M₃₂	—	5	1	no	—
94	C₂×M₃₂	—	15	1	no	—
95	C₂×C₄×C₈	—	15	1	no	—
96	#346	—	15	2	no	—
97	C₄×C₁₆	—	15	2	no	—
98	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
99	C₂×C₃×D₅	—	2	2	no	—
100	C₂×C₃×D₅	C₄×C₈	1	2	yes	—
101	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
102	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
103	Dic₁₅	—	2	2	no	—
104	C₃×Dic₅	C₄×C₈	1	2	yes	—
105	C₅×Dic₃	M₃₂	1	4	yes	complemented
106	C₂²×C₃×C₄	—	5	1	no	—
107	C₂²×Dic₃	—	5	2	no	—
108	C₂×C₃×C₈	—	5	1	no	—
109	C₂×C₃×C₈	—	5	2	no	—
110	C₂×C₃×C₈	—	5	2	no	—
111	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
112	C₄×Dic₃	—	5	1	no	—
113	C₄×Dic₃	—	5	2	no	—
114	C₄×Dic₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
115	C₂×C₃⋊C₈	—	5	1	no	—
116	C₂×C₃⋊C₈	—	5	4	no	—
117	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
118	C₃×C₁₆	—	5	4	no	—
119	C₃⋊C₁₆	—	5	4	no	—
120	C₂²×D₅	D₃×C₈	1	1	yes	characteristic
121	C₂×C₄×C₅	—	3	2	no	—
122	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
123	C₂×Dic₅	—	3	2	no	—
124	C₂×Dic₅	D₃×C₈	1	1	yes	characteristic
125	C₄×D₅	—	6	4	no	—
126	C₄×D₅	D₃×C₈	1	2	yes	—
127	C₄×D₅	C₄×Dic₃	1	2	yes	—
128	C₅×C₈	—	3	2	no	—
129	C₅×C₈	C₄×Dic₃	1	2	yes	—
130	#168	—	3	2	no	—
131	#168	C₂×C₄×D₃	1	1	yes	characteristic
132	#168	C₂²×Dic₃	1	1	yes	characteristic
133	C₂²×C₈	—	5	1	no	—
134	C₂²×C₈	—	15	1	no	—
135	C₂×C₄²	—	15	1	no	—
136	M₃₂	—	5	4	no	—
137	M₃₂	—	15	4	no	—
138	C₂×C₁₆	—	5	2	no	—
139	C₂×C₁₆	—	15	2	no	—
140	C₄×C₈	—	3	1	no	—
141	C₄×C₈	—	15	1	no	—
142	C₄×C₈	—	15	1	no	—
143	C₄×C₈	—	15	1	no	—
144	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
145	C₂×C₃×C₅	C₂×M₃₂	1	2	yes	—
146	C₃×D₅	—	2	2	no	—
147	C₂³×C₃	—	5	1	no	—
148	C₂×C₃×C₄	—	5	1	no	—
149	C₂×C₃×C₄	—	5	2	no	—
150	C₂×C₃×C₄	—	5	2	no	—
151	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
152	C₂×Dic₃	—	5	2	no	—
153	C₂×Dic₃	—	10	4	no	—
154	C₂×Dic₃	D₅⋊C₈	1	2	yes	—
155	C₃×C₈	—	5	1	no	—
156	C₃×C₈	—	5	1	no	—
157	C₃×C₈	C₄×AGL(1,𝔽₅)	1	2	yes	—
158	C₃⋊C₈	—	5	2	no	—
159	C₃⋊C₈	D₅⋊C₈	1	2	yes	—
160	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
161	C₂×D₅	—	2	2	no	—
162	C₂×D₅	C₈×Dic₃	1	2	yes	—
163	C₄×C₅	—	3	4	no	—
164	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
165	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
166	Dic₅	—	6	2	no	—
167	Dic₅	C₈×Dic₃	1	2	yes	—
168	C₂²×C₄	—	5	1	no	—
169	C₂²×C₄	—	15	2	no	—
170	C₂×C₈	—	3	1	no	—
171	C₂×C₈	—	5	1	no	—
172	C₂×C₈	—	5	2	no	—
173	C₂×C₈	—	5	2	no	—
174	C₂×C₈	—	15	4	no	—
175	C₂×C₈	—	15	1	no	—
176	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
177	C₄²	—	3	1	no	—
178	C₄²	—	15	2	no	—
179	C₄²	—	15	1	no	—
180	C₁₆	—	5	4	no	—
181	C₁₆	—	15	4	no	—
182	C₃×C₅	C₄×M₃₂	1	1	yes	characteristic, complemented, Hall
183	C₂²×C₃	—	5	2	no	—
184	C₂²×C₃	—	10	2	no	—
185	C₂²×C₃	C₂×D₅⋊C₈	1	1	yes	characteristic
186	C₃×C₄	—	5	2	no	—
187	C₃×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
188	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
189	Dic₃	—	10	2	no	—
190	Dic₃	#3990	1	4	yes	direct product factor
191	C₂×C₅	D₃×M₃₂	1	2	yes	—
192	C₂×C₅	C₂×C₈×Dic₃	1	1	yes	characteristic
193	D₅	—	2	2	no	—
194	C₂³	—	5	1	no	—
195	C₂×C₄	—	3	2	no	—
196	C₂×C₄	—	5	1	no	—
197	C₂×C₄	—	5	2	no	—
198	C₂×C₄	—	5	2	no	—
199	C₂×C₄	—	15	2	no	—
200	C₂×C₄	—	30	4	no	—
201	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
202	C₈	—	3	2	no	—
203	C₈	—	5	1	no	—
204	C₈	—	5	1	no	—
205	C₈	—	15	2	no	—
206	C₈	Dic₃×AGL(1,𝔽₅)	1	2	yes	—
207	C₂×C₃	—	10	2	no	—
208	C₂×C₃	C₄×D₅⋊C₈	1	1	yes	characteristic
209	C₂×C₃	C₂×#3990	1	2	yes	—
210	C₅	Dic₃×M₃₂	1	1	yes	characteristic, complemented, Sylow
211	C₂²	—	5	2	no	—
212	C₂²	—	10	2	no	—
213	C₂²	D₃×D₅⋊C₈	1	1	yes	characteristic
214	C₄	—	3	4	no	—
215	C₄	—	5	2	no	—
216	C₄	—	30	2	no	—
217	C₄	D₃×D₅⋊C₈	1	1	yes	characteristic
218	C₄	C₂×Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
219	C₃	C₄×#3990	1	1	yes	characteristic, complemented, Sylow
220	C₂	—	10	2	no	—
221	C₂	D₃×#3990	1	2	yes	—
222	C₂	Dic₃×D₅⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
commutator	C₂×C₃×C₅	C₂×C₄×C₈
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
socle	C₂²×C₃×C₅	C₂²×C₈
prime radical	C₂²×C₃×D₅	C₂×C₈
cosocle	C₂×C₃×#168	C₂³
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₄×M₃₂
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
4. #11746543	C₂	semidirect
5. Dic₃×#674	C₂	semidirect
11. #91219	C₄	semidirect
13. C₃×#3990	C₄	semidirect
36. C₃⋊#674	C₂×C₄	semidirect
37. C₃×#674	C₂×C₄	semidirect
49. #3990	Dic₃	direct (N × H)
92. #674	C₂×Dic₃	semidirect
105. C₅×Dic₃	M₃₂	semidirect
182. C₃×C₅	C₄×M₃₂	semidirect
190. Dic₃	#3990	direct (N × H)
210. C₅	Dic₃×M₃₂	semidirect
219. C₃	C₄×#3990	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91219	2
C₂×C₃×#3990	2
C₈×D₅×Dic₃	2
#11746543	2
Dic₃×#674	2
C₄×#3990	3
Dic₃×M₃₂	5

Subgroups — Dic3×#3990 #14312624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×#3990 #14312624