Subgroups — C₃×C₄×C₈×Dic₅ #14294183

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈×Dic₅	C₂	1	4	yes	maximal
3	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₄×#168	C₂	1	1	yes	maximal, characteristic
5	C₄×C₈×Dic₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
7	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×Dic₅	C₄	1	4	yes	—
9	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
10	C₂²×C₃×#168	C₂²	1	2	yes	—
11	C₃×C₄×C₅×C₈	C₄	1	4	yes	complemented
12	C₃×C₈×Dic₅	C₄	1	16	yes	direct product factor
13	C₃×C₄×#168	C₄	1	4	yes	complemented
14	C₃×C₄²×C₈	—	5	1	no	maximal, Hall
15	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic
16	C₂×C₈×Dic₅	C₂×C₃	1	4	yes	—
17	C₄²×Dic₅	C₂×C₃	1	1	yes	characteristic
18	C₂×C₄×#168	C₂×C₃	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
20	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
21	C₂²×C₃×Dic₅	C₂×C₄	1	4	yes	—
22	C₂×C₃×C₅×C₈	C₂×C₄	1	8	yes	—
23	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
24	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
25	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
26	C₃×C₄×Dic₅	C₈	1	16	yes	direct product factor
27	C₃×C₄×Dic₅	C₂×C₄	1	8	yes	—
28	C₂×C₃×#168	C₂×C₄	1	4	yes	—
29	C₂×C₃×#168	C₂×C₄	1	8	yes	—
30	C₂×C₃×C₄×C₈	—	5	4	no	—
31	C₂×C₃×C₄×C₈	—	5	1	no	—
32	C₂×C₃×C₄×C₈	D₅	1	1	yes	characteristic
33	C₃×C₄³	—	5	1	no	—
34	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
35	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
36	C₂×C₄×Dic₅	C₃×C₄	1	4	yes	—
37	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
38	C₂²×#168	C₂²×C₃	1	2	yes	—
39	C₄×C₅×C₈	C₃×C₄	1	4	yes	complemented
40	C₈×Dic₅	C₃×C₄	1	16	yes	direct product factor
41	C₄×#168	C₃×C₄	1	4	yes	complemented
42	C₄²×C₈	—	5	1	no	Sylow
43	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×C₅	C₄²	1	4	yes	—
45	C₂×C₃×C₄×C₅	C₂×C₈	1	8	yes	—
46	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
48	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₃×Dic₅	C₄²	1	8	yes	—
50	C₂×C₃×Dic₅	C₂×C₈	1	16	yes	—
51	C₃×C₅×C₈	C₄²	1	8	yes	complemented
52	C₃×#168	C₄²	1	8	yes	complemented
53	C₂²×C₃×C₈	—	5	2	no	—
54	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
55	C₂×C₃×C₄²	—	5	4	no	—
56	C₂×C₃×C₄²	—	5	2	no	—
57	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
58	C₃×C₄×C₈	—	5	16	no	—
59	C₃×C₄×C₈	—	5	4	no	—
60	C₃×C₄×C₈	Dic₅	1	4	yes	direct product factor
61	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
62	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
63	C₂²×Dic₅	C₂×C₃×C₄	1	4	yes	—
64	C₂×C₅×C₈	C₂×C₃×C₄	1	8	yes	—
65	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
66	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
67	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
68	C₄×Dic₅	C₃×C₈	1	16	yes	direct product factor
69	C₄×Dic₅	C₂×C₃×C₄	1	8	yes	—
70	C₂×#168	C₂×C₃×C₄	1	4	yes	—
71	C₂×#168	C₂×C₃×C₄	1	8	yes	—
72	C₂×C₄×C₈	—	5	4	no	—
73	C₂×C₄×C₈	—	5	1	no	—
74	C₂×C₄×C₈	C₃×D₅	1	1	yes	characteristic
75	C₄³	—	5	1	no	—
76	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
77	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
78	C₂²×C₃×C₅	C₂²×C₈	1	4	yes	—
79	C₃×C₄×C₅	C₄×C₈	1	8	yes	complemented
80	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
81	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
82	C₃×Dic₅	C₄×C₈	1	16	yes	direct product factor
83	C₂²×C₃×C₄	—	5	4	no	—
84	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
85	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
86	C₂×C₃×C₈	—	5	4	no	—
87	C₂×C₃×C₈	—	5	8	no	—
88	C₂×C₃×C₈	C₄×D₅	1	8	yes	—
89	C₂×C₃×C₈	C₂×Dic₅	1	4	yes	—
90	C₃×C₄²	—	5	16	no	—
91	C₃×C₄²	—	5	8	no	—
92	C₃×C₄²	C₄×D₅	1	2	yes	—
93	C₃×C₄²	C₂×Dic₅	1	2	yes	—
94	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
95	C₂×C₄×C₅	C₃×C₄²	1	4	yes	—
96	C₂×C₄×C₅	C₂×C₃×C₈	1	8	yes	—
97	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
98	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
99	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
100	C₂×Dic₅	C₃×C₄²	1	8	yes	—
101	C₂×Dic₅	C₂×C₃×C₈	1	16	yes	—
102	C₅×C₈	C₃×C₄²	1	8	yes	complemented
103	#168	C₃×C₄²	1	8	yes	complemented
104	C₂²×C₈	—	5	2	no	—
105	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
106	C₂×C₄²	—	5	4	no	—
107	C₂×C₄²	—	5	2	no	—
108	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
109	C₄×C₈	—	5	16	no	—
110	C₄×C₈	—	5	4	no	—
111	C₄×C₈	C₃×Dic₅	1	4	yes	direct product factor
112	C₂×C₃×C₅	C₄³	1	1	yes	characteristic
113	C₂×C₃×C₅	C₂×C₄×C₈	1	2	yes	—
114	C₂×C₃×C₅	C₂×C₄×C₈	1	4	yes	—
115	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
116	C₂×C₃×C₄	—	5	8	no	—
117	C₂×C₃×C₄	—	5	16	no	—
118	C₂×C₃×C₄	C₈×D₅	1	8	yes	—
119	C₂×C₃×C₄	C₄×Dic₅	1	4	yes	—
120	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
121	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
122	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
123	C₃×C₈	—	5	8	no	—
124	C₃×C₈	C₄×Dic₅	1	8	yes	direct product factor
125	C₂²×C₅	C₂×C₃×C₄²	1	2	yes	—
126	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
127	C₂²×C₅	C₂²×C₃×C₈	1	4	yes	—
128	C₄×C₅	C₃×C₄×C₈	1	8	yes	complemented
129	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
130	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
131	Dic₅	C₃×C₄×C₈	1	16	yes	direct product factor
132	C₂²×C₄	—	5	4	no	—
133	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
134	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
135	C₂×C₈	—	5	4	no	—
136	C₂×C₈	—	5	8	no	—
137	C₂×C₈	C₃×C₄×D₅	1	8	yes	—
138	C₂×C₈	C₂×C₃×Dic₅	1	4	yes	—
139	C₄²	—	5	16	no	—
140	C₄²	—	5	8	no	—
141	C₄²	C₃×C₄×D₅	1	2	yes	—
142	C₄²	C₂×C₃×Dic₅	1	2	yes	—
143	C₃×C₅	C₄²×C₈	1	1	yes	characteristic, complemented, Hall
144	C₂²×C₃	C₄²×D₅	1	2	yes	—
145	C₂²×C₃	C₂×C₈×D₅	1	4	yes	—
146	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
147	C₃×C₄	—	5	16	no	—
148	C₃×C₄	C₈×Dic₅	1	8	yes	direct product factor
149	C₃×C₄	C₄²×D₅	1	2	yes	—
150	C₃×C₄	C₂×C₄×Dic₅	1	2	yes	—
151	C₂×C₅	C₃×C₄³	1	1	yes	characteristic
152	C₂×C₅	C₂×C₃×C₄×C₈	1	2	yes	—
153	C₂×C₅	C₂×C₃×C₄×C₈	1	4	yes	—
154	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
155	C₂×C₄	—	5	8	no	—
156	C₂×C₄	—	5	16	no	—
157	C₂×C₄	C₃×C₈×D₅	1	8	yes	—
158	C₂×C₄	C₃×C₄×Dic₅	1	4	yes	—
159	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
160	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
161	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
162	C₈	—	5	8	no	—
163	C₈	C₃×C₄×Dic₅	1	8	yes	direct product factor
164	C₂×C₃	C₄×C₈×D₅	1	4	yes	—
165	C₂×C₃	C₄²×Dic₅	1	1	yes	characteristic
166	C₂×C₃	C₂×C₈×Dic₅	1	2	yes	—
167	C₅	C₃×C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
168	C₂²	C₃×C₄²×D₅	1	2	yes	—
169	C₂²	C₂×C₃×C₈×D₅	1	4	yes	—
170	C₂²	C₂×C₃×C₄×Dic₅	1	1	yes	characteristic
171	C₄	—	5	16	no	—
172	C₄	C₃×C₈×Dic₅	1	8	yes	direct product factor
173	C₄	C₃×C₄²×D₅	1	2	yes	—
174	C₄	C₂×C₃×C₄×Dic₅	1	2	yes	—
175	C₃	C₄×C₈×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
176	C₂	C₃×C₄×C₈×D₅	1	4	yes	—
177	C₂	C₃×C₄²×Dic₅	1	1	yes	characteristic
178	C₂	C₂×C₃×C₈×Dic₅	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄×C₈	D₅
commutator, hypocenter	C₅	C₃×C₄²×C₈
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
5. C₄×C₈×Dic₅	C₃	direct (N × H)
11. C₃×C₄×C₅×C₈	C₄	semidirect
12. C₃×C₈×Dic₅	C₄	direct (N × H)
13. C₃×C₄×#168	C₄	semidirect
26. C₃×C₄×Dic₅	C₈	direct (N × H)
39. C₄×C₅×C₈	C₃×C₄	semidirect
40. C₈×Dic₅	C₃×C₄	direct (N × H)
41. C₄×#168	C₃×C₄	semidirect
51. C₃×C₅×C₈	C₄²	semidirect
52. C₃×#168	C₄²	semidirect
60. C₃×C₄×C₈	Dic₅	direct (N × H)
68. C₄×Dic₅	C₃×C₈	direct (N × H)
79. C₃×C₄×C₅	C₄×C₈	semidirect
82. C₃×Dic₅	C₄×C₈	direct (N × H)
102. C₅×C₈	C₃×C₄²	semidirect
103. #168	C₃×C₄²	semidirect
111. C₄×C₈	C₃×Dic₅	direct (N × H)
124. C₃×C₈	C₄×Dic₅	direct (N × H)
128. C₄×C₅	C₃×C₄×C₈	semidirect
131. Dic₅	C₃×C₄×C₈	direct (N × H)
143. C₃×C₅	C₄²×C₈	semidirect
148. C₃×C₄	C₈×Dic₅	direct (N × H)
163. C₈	C₃×C₄×Dic₅	direct (N × H)
167. C₅	C₃×C₄²×C₈	semidirect
172. C₄	C₃×C₈×Dic₅	direct (N × H)
175. C₃	C₄×C₈×Dic₅	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×C₄×C₅×C₈	2
C₂×C₃×C₈×Dic₅	2
C₃×C₄²×Dic₅	2
C₂×C₃×C₄×#168	2
C₄×C₈×Dic₅	3
C₃×C₄²×C₈	5

Subgroups — C3×C4×C8×Dic5 #14294183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₈×Dic₅ #14294183