Subgroups — C₂×C₃×#64969 #14439739

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4015	C₂	1	2	yes	maximal
2	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3949	C₂	1	4	yes	maximal
4	C₃×#64969	C₂	1	8	yes	maximal, direct product factor
5	C₂×#64969	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×Dic₁₀	—	2	2	no	—
7	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄⋊Dic₅	—	2	2	no	—
10	C₂×C₃×C₄⋊Dic₅	C₂²	1	4	yes	—
11	C₃×#4015	—	2	4	no	—
12	C₃×#4015	C₂²	1	8	yes	—
13	C₃×C₄×C₅×C₈	C₂²	1	4	yes	—
14	C₃×#3949	C₂²	1	16	yes	—
15	C₂×C₃×#498	—	5	1	no	maximal, Hall
16	C₂×#4015	C₂×C₃	1	2	yes	—
17	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic
18	C₂×#3949	C₂×C₃	1	4	yes	—
19	#64969	C₂×C₃	1	8	yes	direct product factor
20	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
21	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
22	C₂²×C₃×Dic₅	—	2	4	no	—
23	C₂×C₃×Dic₁₀	—	2	8	no	—
24	C₂×C₃×Dic₁₀	—	4	8	no	—
25	C₂×C₃×C₅×C₈	Q₈	1	8	yes	complemented
26	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
27	C₃×C₄²×C₅	D₄	1	2	yes	—
28	C₃×C₄²×C₅	C₂³	1	2	yes	—
29	C₃×C₄⋊Dic₅	—	2	4	no	—
30	C₃×C₄⋊Dic₅	—	2	8	no	—
31	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
32	C₂×C₃×C₄⋊Q₈	—	5	2	no	—
33	C₃×#498	—	5	8	no	—
34	C₂×C₃×#106	—	5	4	no	—
35	C₂×C₃×C₄×C₈	D₅	1	1	yes	characteristic
36	C₂²×Dic₁₀	—	2	2	no	—
37	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
38	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
39	C₂×C₄⋊Dic₅	—	2	2	no	—
40	C₂×C₄⋊Dic₅	C₂²×C₃	1	4	yes	—
41	#4015	—	2	4	no	—
42	#4015	C₂²×C₃	1	8	yes	—
43	C₄×C₅×C₈	C₂²×C₃	1	4	yes	—
44	#3949	C₂²×C₃	1	16	yes	—
45	C₂×#498	—	5	1	no	Sylow
46	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
47	C₂×C₃×C₄×C₅	SD₁₆	1	8	yes	—
48	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
49	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
50	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
51	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
52	C₂×C₃×Dic₅	—	2	8	no	—
53	C₂×C₃×Dic₅	—	4	8	no	—
54	C₃×Dic₁₀	—	4	16	no	—
55	C₃×C₅×C₈	C₂×Q₈	1	8	yes	complemented
56	C₂²×C₃×Q₈	—	10	2	no	—
57	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
58	C₃×C₄⋊Q₈	—	5	8	no	—
59	C₃×C₄⋊Q₈	—	10	4	no	—
60	C₂×C₃×C₄⋊C₄	—	5	4	no	—
61	C₂×C₃×C₄⋊C₄	—	10	2	no	—
62	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
63	C₃×#106	—	5	16	no	—
64	C₃×C₄×C₈	C₂×D₅	1	4	yes	—
65	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
66	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
67	C₂²×Dic₅	—	2	4	no	—
68	C₂×Dic₁₀	—	2	8	no	—
69	C₂×Dic₁₀	—	4	8	no	—
70	C₂×C₅×C₈	C₃×Q₈	1	8	yes	complemented
71	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
72	C₄²×C₅	C₃×D₄	1	2	yes	—
73	C₄²×C₅	C₂³×C₃	1	2	yes	—
74	C₄⋊Dic₅	—	2	4	no	—
75	C₄⋊Dic₅	—	2	8	no	—
76	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
77	C₂×C₄⋊Q₈	—	5	2	no	—
78	#498	—	5	8	no	—
79	C₂×#106	—	5	4	no	—
80	C₂×C₄×C₈	C₃×D₅	1	1	yes	characteristic
81	C₂²×C₃×C₅	C₄⋊Q₈	1	2	yes	—
82	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	—
83	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
84	C₃×C₄×C₅	C₄⋊Q₈	1	2	yes	—
85	C₃×C₄×C₅	C₂×SD₁₆	1	8	yes	—
86	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
87	C₃×Dic₅	—	4	8	no	—
88	C₂×C₃×Q₈	—	10	8	no	—
89	C₂×C₃×Q₈	—	20	8	no	—
90	C₂²×C₃×C₄	—	10	4	no	—
91	C₂²×C₃×C₄	D₂₀	1	2	yes	—
92	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
93	C₂×C₃×C₈	Dic₁₀	1	8	yes	complemented
94	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
95	C₃×C₄⋊C₄	—	5	8	no	—
96	C₃×C₄⋊C₄	—	10	4	no	—
97	C₃×C₄⋊C₄	—	10	8	no	—
98	C₃×C₄²	D₂₀	1	2	yes	—
99	C₃×C₄²	C₂²×D₅	1	2	yes	—
100	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
101	C₂×C₄×C₅	C₃×SD₁₆	1	8	yes	—
102	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
103	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
104	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
105	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
106	C₂×Dic₅	—	2	8	no	—
107	C₂×Dic₅	—	4	8	no	—
108	Dic₁₀	—	4	16	no	—
109	C₅×C₈	C₂×C₃×Q₈	1	8	yes	complemented
110	C₂²×Q₈	—	10	2	no	—
111	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
112	C₄⋊Q₈	—	5	8	no	—
113	C₄⋊Q₈	—	10	4	no	—
114	C₂×C₄⋊C₄	—	5	4	no	—
115	C₂×C₄⋊C₄	—	10	2	no	—
116	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
117	#106	—	5	16	no	—
118	C₄×C₈	C₂×C₃×D₅	1	4	yes	—
119	C₂×C₃×C₅	#498	1	4	yes	complemented
120	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
121	C₂×C₃×C₅	C₂²×SD₁₆	1	2	yes	—
122	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
123	C₃×Q₈	—	20	16	no	—
124	C₂×C₃×C₄	—	10	8	no	—
125	C₂×C₃×C₄	—	20	8	no	—
126	C₂×C₃×C₄	#677	1	8	yes	—
127	C₂×C₃×C₄	C₂×Dic₁₀	1	4	yes	—
128	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
129	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
130	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
131	C₃×C₈	C₂×Dic₁₀	1	8	yes	complemented
132	C₂²×C₅	C₃×C₄⋊Q₈	1	2	yes	—
133	C₂²×C₅	C₂×C₃×SD₁₆	1	4	yes	—
134	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
135	C₄×C₅	C₃×C₄⋊Q₈	1	2	yes	—
136	C₄×C₅	C₂×C₃×SD₁₆	1	8	yes	—
137	C₄×C₅	C₂²×C₃×Q₈	1	2	yes	—
138	Dic₅	—	4	8	no	—
139	C₂×Q₈	—	10	8	no	—
140	C₂×Q₈	—	20	8	no	—
141	C₂²×C₄	—	10	4	no	—
142	C₂²×C₄	C₃×D₂₀	1	2	yes	—
143	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
144	C₂×C₈	C₃×Dic₁₀	1	8	yes	complemented
145	C₂×C₈	C₂²×C₃×D₅	1	4	yes	—
146	C₄⋊C₄	—	5	8	no	—
147	C₄⋊C₄	—	10	4	no	—
148	C₄⋊C₄	—	10	8	no	—
149	C₄²	C₃×D₂₀	1	2	yes	—
150	C₄²	C₂²×C₃×D₅	1	2	yes	—
151	C₃×C₅	C₂×#498	1	1	yes	characteristic, complemented, Hall
152	C₂²×C₃	#4015	1	2	yes	—
153	C₂²×C₃	C₂×#677	1	4	yes	—
154	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
155	C₃×C₄	—	20	8	no	—
156	C₃×C₄	#4015	1	2	yes	—
157	C₃×C₄	C₂×#677	1	8	yes	—
158	C₃×C₄	C₂²×Dic₁₀	1	2	yes	—
159	C₂×C₅	C₃×#498	1	4	yes	complemented
160	C₂×C₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
161	C₂×C₅	C₂²×C₃×SD₁₆	1	2	yes	—
162	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
163	Q₈	—	20	16	no	—
164	C₂×C₄	—	10	8	no	—
165	C₂×C₄	—	20	8	no	—
166	C₂×C₄	C₃×#677	1	8	yes	—
167	C₂×C₄	C₂×C₃×Dic₁₀	1	4	yes	—
168	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
169	C₂×C₄	C₂×C₃×D₂₀	1	4	yes	—
170	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
171	C₈	C₂×C₃×Dic₁₀	1	8	yes	complemented
172	C₂×C₃	#64969	1	4	yes	direct product factor
173	C₂×C₃	C₂×#4015	1	1	yes	characteristic
174	C₂×C₃	C₂²×#677	1	2	yes	—
175	C₅	C₂×C₃×#498	1	1	yes	characteristic, complemented, Sylow
176	C₂²	C₃×#4015	1	2	yes	—
177	C₂²	C₂×C₃×#677	1	4	yes	—
178	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
179	C₄	—	20	8	no	—
180	C₄	C₃×#4015	1	2	yes	—
181	C₄	C₂×C₃×#677	1	8	yes	—
182	C₄	C₂²×C₃×Dic₁₀	1	2	yes	—
183	C₃	C₂×#64969	1	1	yes	characteristic, direct product factor, Sylow
184	C₂	C₃×#64969	1	4	yes	direct product factor
185	C₂	C₂×C₃×#4015	1	1	yes	characteristic
186	C₂	C₂²×C₃×#677	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle, prime radical	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₃×C₄×C₈	D₅
hypocenter	C₅	C₂×C₃×#498
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. C₃×#64969	C₂	direct (N × H)
5. C₂×#64969	C₃	direct (N × H)
19. #64969	C₂×C₃	direct (N × H)
25. C₂×C₃×C₅×C₈	Q₈	semidirect
55. C₃×C₅×C₈	C₂×Q₈	semidirect
70. C₂×C₅×C₈	C₃×Q₈	semidirect
93. C₂×C₃×C₈	Dic₁₀	semidirect
109. C₅×C₈	C₂×C₃×Q₈	semidirect
119. C₂×C₃×C₅	#498	semidirect
131. C₃×C₈	C₂×Dic₁₀	semidirect
144. C₂×C₈	C₃×Dic₁₀	semidirect
151. C₃×C₅	C₂×#498	semidirect
159. C₂×C₅	C₃×#498	semidirect
171. C₈	C₂×C₃×Dic₁₀	semidirect
172. C₂×C₃	#64969	direct (N × H)
175. C₅	C₂×C₃×#498	semidirect
183. C₃	C₂×#64969	direct (N × H)
184. C₂	C₃×#64969	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#4015	2
C₂×C₃×C₄×C₅×C₈	2
C₂×C₃×#3949	2
C₃×#64969	2
C₂×#64969	3
C₂×C₃×#498	5

Subgroups — C2×C3×#64969 #14439739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64969 #14439739